text:
@testset "1.1.3.2 (c x)^m (a+b x^n)^p" begin
    (a, b, c, d, e, m, n, p, q, x, ) = @variables a b c d e m n p q x

    #= ::Package:: =#

    #= ::Title::Closed:: =#
    #=Integrands*of*the*form*(c*x)^m*(b*x^n)^p=#

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(c*x)^m*(b*x^1)^p=#

    @test_int [(c*x)^m*(b*x)^p, x, 2, ((b*x)^(1 + p)*(c*x)^m)/(b*(1 + m + p))]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(c*x)^m*(b*x^2)^p=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(b*x^2)^(p/2)=#

    #= ::Subsubsection::Closed:: =#
    #=p>0=#

    @test_int [sqrt(b*x^2)*x^3, x, 2, (1/5)*x^4*sqrt(b*x^2)]
    @test_int [sqrt(b*x^2)*x^2, x, 2, (1/4)*x^3*sqrt(b*x^2)]
    @test_int [sqrt(b*x^2)*x^1, x, 2, (1/3)*x^2*sqrt(b*x^2)]
    @test_int [sqrt(b*x^2)*x^0, x, 2, (1/2)*x*sqrt(b*x^2)]
    @test_int [sqrt(b*x^2)/x^1, x, 2, sqrt(b*x^2)]
    @test_int [sqrt(b*x^2)/x^2, x, 2, (sqrt(b*x^2)*log(x))/x]
    @test_int [sqrt(b*x^2)/x^3, x, 2, -(sqrt(b*x^2)/x^2)]
    @test_int [sqrt(b*x^2)/x^4, x, 2, -(sqrt(b*x^2)/(2*x^3))]
    @test_int [sqrt(b*x^2)/x^5, x, 2, -(sqrt(b*x^2)/(3*x^4))]

    @test_int [sqrt(x^2)*x^2, x, 2, (1/4)*x^3*sqrt(x^2)]

    @test_int [(b*x^2)^(3/2)*x^2, x, 2, (1/6)*b*x^5*sqrt(b*x^2)]
    @test_int [(b*x^2)^(3/2)*x^1, x, 2, (1/5)*b*x^4*sqrt(b*x^2)]
    @test_int [(b*x^2)^(3/2)*x^0, x, 2, (1/4)*b*x^3*sqrt(b*x^2)]
    @test_int [(b*x^2)^(3/2)/x^1, x, 2, (1/3)*b*x^2*sqrt(b*x^2)]
    @test_int [(b*x^2)^(3/2)/x^2, x, 2, (1/2)*b*x*sqrt(b*x^2)]
    @test_int [(b*x^2)^(3/2)/x^3, x, 2, b*sqrt(b*x^2)]
    @test_int [(b*x^2)^(3/2)/x^4, x, 2, (b*sqrt(b*x^2)*log(x))/x]
    @test_int [(b*x^2)^(3/2)/x^5, x, 2, -((b*sqrt(b*x^2))/x^2)]
    @test_int [(b*x^2)^(3/2)/x^6, x, 2, -((b*sqrt(b*x^2))/(2*x^3))]
    @test_int [(b*x^2)^(3/2)/x^7, x, 2, -((b*sqrt(b*x^2))/(3*x^4))]

    @test_int [(x^2)^(3/2)*x^2, x, 2, (1/6)*x^5*sqrt(x^2)]

    @test_int [(b*x^2)^(5/2)*x^1, x, 2, (1/7)*b^2*x^6*sqrt(b*x^2)]
    @test_int [(b*x^2)^(5/2)*x^0, x, 2, (1/6)*b^2*x^5*sqrt(b*x^2)]
    @test_int [(b*x^2)^(5/2)/x^1, x, 2, (1/5)*b^2*x^4*sqrt(b*x^2)]
    @test_int [(b*x^2)^(5/2)/x^2, x, 2, (1/4)*b^2*x^3*sqrt(b*x^2)]
    @test_int [(b*x^2)^(5/2)/x^3, x, 2, (1/3)*b^2*x^2*sqrt(b*x^2)]
    @test_int [(b*x^2)^(5/2)/x^4, x, 2, (1/2)*b^2*x*sqrt(b*x^2)]
    @test_int [(b*x^2)^(5/2)/x^5, x, 2, b^2*sqrt(b*x^2)]
    @test_int [(b*x^2)^(5/2)/x^6, x, 2, (b^2*sqrt(b*x^2)*log(x))/x]
    @test_int [(b*x^2)^(5/2)/x^7, x, 2, -((b^2*sqrt(b*x^2))/x^2)]
    @test_int [(b*x^2)^(5/2)/x^8, x, 2, -((b^2*sqrt(b*x^2))/(2*x^3))]
    @test_int [(b*x^2)^(5/2)/x^9, x, 2, -((b^2*sqrt(b*x^2))/(3*x^4))]

    @test_int [(x^2)^(5/2)*x^2, x, 2, (1/8)*x^7*sqrt(x^2)]

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [1/sqrt(b*x^2)*x^3, x, 2, x^4/(3*sqrt(b*x^2))]
    @test_int [1/sqrt(b*x^2)*x^1, x, 2, x^2/sqrt(b*x^2)]
    @test_int [1/sqrt(b*x^2)/x^1, x, 2, -(1/sqrt(b*x^2))]
    @test_int [1/sqrt(b*x^2)/x^3, x, 2, -(1/(3*x^2*sqrt(b*x^2)))]

    @test_int [1/sqrt(b*x^2)*x^2, x, 2, x^3/(2*sqrt(b*x^2))]
    @test_int [1/sqrt(b*x^2)*x^0, x, 2, (x*log(x))/sqrt(b*x^2)]
    @test_int [1/sqrt(b*x^2)/x^2, x, 2, -(1/(2*x*sqrt(b*x^2)))]

    @test_int [1/(b*x^2)^(3/2)*x^5, x, 2, x^4/(3*b*sqrt(b*x^2))]
    @test_int [1/(b*x^2)^(3/2)*x^3, x, 2, x^2/(b*sqrt(b*x^2))]
    @test_int [1/(b*x^2)^(3/2)*x^1, x, 2, -(1/(b*sqrt(b*x^2)))]
    @test_int [1/(b*x^2)^(3/2)/x^1, x, 2, -(1/(3*b*x^2*sqrt(b*x^2)))]
    @test_int [1/(b*x^2)^(3/2)/x^3, x, 2, -(1/(5*b*x^4*sqrt(b*x^2)))]

    @test_int [1/(b*x^2)^(3/2)*x^6, x, 2, x^5/(4*b*sqrt(b*x^2))]
    @test_int [1/(b*x^2)^(3/2)*x^4, x, 2, x^3/(2*b*sqrt(b*x^2))]
    @test_int [1/(b*x^2)^(3/2)*x^2, x, 2, (x*log(x))/(b*sqrt(b*x^2))]
    @test_int [1/(b*x^2)^(3/2)*x^0, x, 2, -(1/(2*b*x*sqrt(b*x^2)))]
    @test_int [1/(b*x^2)^(3/2)/x^2, x, 2, -(1/(4*b*x^3*sqrt(b*x^2)))]

    @test_int [1/(b*x^2)^(5/2)*x^7, x, 2, x^4/(3*b^2*sqrt(b*x^2))]
    @test_int [1/(b*x^2)^(5/2)*x^5, x, 2, x^2/(b^2*sqrt(b*x^2))]
    @test_int [1/(b*x^2)^(5/2)*x^3, x, 2, -(1/(b^2*sqrt(b*x^2)))]
    @test_int [1/(b*x^2)^(5/2)*x^1, x, 2, -(1/(3*b^2*x^2*sqrt(b*x^2)))]
    @test_int [1/(b*x^2)^(5/2)/x^1, x, 2, -(1/(5*b^2*x^4*sqrt(b*x^2)))]

    @test_int [1/(b*x^2)^(5/2)*x^6, x, 2, x^3/(2*b^2*sqrt(b*x^2))]
    @test_int [1/(b*x^2)^(5/2)*x^4, x, 2, (x*log(x))/(b^2*sqrt(b*x^2))]
    @test_int [1/(b*x^2)^(5/2)*x^2, x, 2, -(1/(2*b^2*x*sqrt(b*x^2)))]
    @test_int [1/(b*x^2)^(5/2)*x^0, x, 2, -(1/(4*b^2*x^3*sqrt(b*x^2)))]
    @test_int [1/(b*x^2)^(5/2)/x^2, x, 2, -(1/(6*b^2*x^5*sqrt(b*x^2)))]

    #= ::Subsection:: =#
    #=Integrands*of*the*form*(c*x)^(m/2)*(b*x^2)^(p/2)=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(c*x)^m*(b*x^2)^(p/2)*with*m*symbolic=#

    @test_int [(c*x)^m*(b*x^2)^(3/2), x, 3, (b*(c*x)^(4 + m)*sqrt(b*x^2))/(c^4*(4 + m)*x)]
    @test_int [(c*x)^m*(b*x^2)^(1/2), x, 3, ((c*x)^(2 + m)*sqrt(b*x^2))/(c^2*(2 + m)*x)]
    @test_int [(c*x)^m/(b*x^2)^(1/2), x, 3, (x*(c*x)^m)/(m*sqrt(b*x^2))]
    @test_int [(c*x)^m/(b*x^2)^(3/2), x, 3, -((c^2*x*(c*x)^(-2 + m))/(b*(2 - m)*sqrt(b*x^2)))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(c*x)^m*(b*x^2)^p*with*p*symbolic=#

    @test_int [x^m*(b*x^2)^p, x, 2, (x^(1 + m)*(b*x^2)^p)/(1 + m + 2*p)]
    @test_int [(c*x)^m*(b*x^2)^p, x, 3, (x*(c*x)^m*(b*x^2)^p)/(1 + m + 2*p)]

    @test_int [(x^2)^p/x^(2*p + 1), x, 2, ((x^2)^p*log(x))/x^(2*p)]

    @test_int [(b*x^2)^p*x^3, x, 2, (x^4*(b*x^2)^p)/(2*(2 + p))]
    @test_int [(b*x^2)^p*x^2, x, 2, (x^3*(b*x^2)^p)/(3 + 2*p)]
    @test_int [(b*x^2)^p*x^1, x, 2, (x^2*(b*x^2)^p)/(2*(1 + p))]
    @test_int [(b*x^2)^p*x^0, x, 2, (x*(b*x^2)^p)/(1 + 2*p)]
    @test_int [(b*x^2)^p/x^1, x, 2, (b*x^2)^p/(2*p)]
    @test_int [(b*x^2)^p/x^2, x, 2, -((b*x^2)^p/((1 - 2*p)*x))]
    @test_int [(b*x^2)^p/x^3, x, 2, -((b*x^2)^p/(2*(1 - p)*x^2))]
    @test_int [(b*x^2)^p/x^4, x, 2, -((b*x^2)^p/((3 - 2*p)*x^3))]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(c*x)^m*(b*x^n)^p=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(b*x^n)^(p/2)=#

    #= ::Subsubsection::Closed:: =#
    #=p>0=#

    @test_int [sqrt(b*x^3), x, 2, (2/5)*x*sqrt(b*x^3)]
    @test_int [sqrt(b*x^2), x, 2, (1/2)*x*sqrt(b*x^2)]
    @test_int [sqrt(b*x^1), x, 1, (2*(b*x)^(3/2))/(3*b)]
    @test_int [sqrt(b/x^1), x, 2, 2*sqrt(b/x)*x]
    @test_int [sqrt(b/x^2), x, 2, sqrt(b/x^2)*x*log(x)]
    @test_int [sqrt(b/x^3), x, 2, -2*sqrt(b/x^3)*x]

    @test_int [(b*x^3)^(3/2), x, 2, (2/11)*b*x^4*sqrt(b*x^3)]
    @test_int [(b*x^2)^(3/2), x, 2, (1/4)*b*x^3*sqrt(b*x^2)]
    @test_int [(b*x^1)^(3/2), x, 1, (2*(b*x)^(5/2))/(5*b)]
    @test_int [(b/x^1)^(3/2), x, 2, -2*b*sqrt(b/x)]
    @test_int [(b/x^2)^(3/2), x, 2, -((b*sqrt(b/x^2))/(2*x))]
    @test_int [(b/x^3)^(3/2), x, 2, -((2*b*sqrt(b/x^3))/(7*x^2))]

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [1/sqrt(b*x^3), x, 2, -((2*x)/sqrt(b*x^3))]
    @test_int [1/sqrt(b*x^2), x, 2, (x*log(x))/sqrt(b*x^2)]
    @test_int [1/sqrt(b*x^1), x, 1, (2*sqrt(b*x))/b]
    @test_int [1/sqrt(b/x^1), x, 2, (2*x)/(3*sqrt(b/x))]
    @test_int [1/sqrt(b/x^2), x, 2, x/(2*sqrt(b/x^2))]
    @test_int [1/sqrt(b/x^3), x, 2, (2*x)/(5*sqrt(b/x^3))]

    @test_int [1/(b*x^3)^(3/2), x, 2, -(2/(7*b*x^2*sqrt(b*x^3)))]
    @test_int [1/(b*x^2)^(3/2), x, 2, -(1/(2*b*x*sqrt(b*x^2)))]
    @test_int [1/(b*x^1)^(3/2), x, 1, -(2/(b*sqrt(b*x)))]
    @test_int [1/(b/x^1)^(3/2), x, 2, (2*x^2)/(5*b*sqrt(b/x))]
    @test_int [1/(b/x^2)^(3/2), x, 2, x^3/(4*b*sqrt(b/x^2))]
    @test_int [1/(b/x^3)^(3/2), x, 2, (2*x^4)/(11*b*sqrt(b/x^3))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(b*x^n)^(p/3)=#

    #= ::Subsubsection::Closed:: =#
    #=p>0=#

    @test_int [(b*x^n)^(1/3), x, 2, (3*x*(b*x^n)^(1/3))/(3 + n)]

    @test_int [(b*x^3)^(1/3), x, 2, (1/2)*x*(b*x^3)^(1/3)]
    @test_int [(b*x^2)^(1/3), x, 2, (3/5)*x*(b*x^2)^(1/3)]
    @test_int [(b*x^1)^(1/3), x, 1, (3*(b*x)^(4/3))/(4*b)]
    @test_int [(b/x^1)^(1/3), x, 2, (3/2)*(b/x)^(1/3)*x]
    @test_int [(b/x^2)^(1/3), x, 2, 3*(b/x^2)^(1/3)*x]
    @test_int [(b/x^3)^(1/3), x, 2, (b/x^3)^(1/3)*x*log(x)]
    @test_int [(b/x^4)^(1/3), x, 2, -3*(b/x^4)^(1/3)*x]

    @test_int [(b*x^n)^(2/3), x, 2, (3*x*(b*x^n)^(2/3))/(3 + 2*n)]

    @test_int [(b*x^2)^(2/3), x, 2, (3/7)*x*(b*x^2)^(2/3)]
    @test_int [(b*x^1)^(2/3), x, 1, (3*(b*x)^(5/3))/(5*b)]
    @test_int [(b/x^1)^(2/3), x, 2, 3*(b/x)^(2/3)*x]
    @test_int [(b/x^2)^(2/3), x, 2, -3*(b/x^2)^(2/3)*x]
    @test_int [(b/x^3)^(2/3), x, 2, (-(b/x^3)^(2/3))*x]
    @test_int [(b/x^4)^(2/3), x, 2, (-(3/5))*(b/x^4)^(2/3)*x]

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [1/(b*x^n)^(1/3), x, 2, (3*x)/((3 - n)*(b*x^n)^(1/3))]

    @test_int [1/(b*x^4)^(1/3), x, 2, -((3*x)/(b*x^4)^(1/3))]
    @test_int [1/(b*x^3)^(1/3), x, 2, (x*log(x))/(b*x^3)^(1/3)]
    @test_int [1/(b*x^2)^(1/3), x, 2, (3*x)/(b*x^2)^(1/3)]
    @test_int [1/(b*x^1)^(1/3), x, 1, (3*(b*x)^(2/3))/(2*b)]
    @test_int [1/(b/x^1)^(1/3), x, 2, (3*x)/(4*(b/x)^(1/3))]
    @test_int [1/(b/x^2)^(1/3), x, 2, (3*x)/(5*(b/x^2)^(1/3))]
    @test_int [1/(b/x^3)^(1/3), x, 2, x/(2*(b/x^3)^(1/3))]

    @test_int [1/(b*x^n)^(2/3), x, 2, (3*x)/((3 - 2*n)*(b*x^n)^(2/3))]

    @test_int [1/(b*x^3)^(2/3), x, 2, -(x/(b*x^3)^(2/3))]
    @test_int [1/(b*x^2)^(2/3), x, 2, -((3*x)/(b*x^2)^(2/3))]
    @test_int [1/(b*x^1)^(2/3), x, 1, (3*(b*x)^(1/3))/b]
    @test_int [1/(b/x^1)^(2/3), x, 2, (3*x)/(5*(b/x)^(2/3))]
    @test_int [1/(b/x^2)^(2/3), x, 2, (3*x)/(7*(b/x^2)^(2/3))]
    @test_int [1/(b/x^3)^(2/3), x, 2, x/(3*(b/x^3)^(2/3))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(b*x^n)^(p/2)=#

    #= ::Subsubsection::Closed:: =#
    #=p>0=#

    @test_int [x^2*sqrt(b*x^n), x, 2, (2*x^3*sqrt(b*x^n))/(6 + n)]
    @test_int [x^1*sqrt(b*x^n), x, 2, (2*x^2*sqrt(b*x^n))/(4 + n)]
    @test_int [x^0*sqrt(b*x^n), x, 2, (2*x*sqrt(b*x^n))/(2 + n)]
    @test_int [sqrt(b*x^n)/x^1, x, 2, (2*sqrt(b*x^n))/n]
    @test_int [sqrt(b*x^n)/x^2, x, 2, -((2*sqrt(b*x^n))/((2 - n)*x))]
    @test_int [sqrt(b*x^n)/x^3, x, 2, -((2*sqrt(b*x^n))/((4 - n)*x^2))]

    @test_int [(b*x^n)^(3/2)*x^1, x, 2, (2*b*x^(2 + n)*sqrt(b*x^n))/(4 + 3*n)]
    @test_int [(b*x^n)^(3/2)*x^0, x, 2, (2*b*x^(1 + n)*sqrt(b*x^n))/(2 + 3*n)]
    @test_int [(b*x^n)^(3/2)/x^1, x, 2, (2*b*x^n*sqrt(b*x^n))/(3*n)]
    @test_int [(b*x^n)^(3/2)/x^2, x, 2, -((2*b*x^(-1 + n)*sqrt(b*x^n))/(2 - 3*n))]
    @test_int [(b*x^n)^(3/2)/x^3, x, 2, -((2*b*x^(-2 + n)*sqrt(b*x^n))/(4 - 3*n))]
    @test_int [(b*x^n)^(3/2)/x^4, x, 2, -((2*b*x^(-3 + n)*sqrt(b*x^n))/(3*(2 - n)))]

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [x^2/sqrt(b*x^n), x, 2, (2*x^3)/((6 - n)*sqrt(b*x^n))]
    @test_int [x^1/sqrt(b*x^n), x, 2, (2*x^2)/((4 - n)*sqrt(b*x^n))]
    @test_int [x^0/sqrt(b*x^n), x, 2, (2*x)/((2 - n)*sqrt(b*x^n))]
    @test_int [1/(x^1*sqrt(b*x^n)), x, 2, -(2/(n*sqrt(b*x^n)))]
    @test_int [1/(x^2*sqrt(b*x^n)), x, 2, -(2/((2 + n)*x*sqrt(b*x^n)))]
    @test_int [1/(x^3*sqrt(b*x^n)), x, 2, -(2/((4 + n)*x^2*sqrt(b*x^n)))]

    @test_int [1/(b*x^n)^(3/2)*x^2, x, 2, (2*x^(3 - n))/(3*b*(2 - n)*sqrt(b*x^n))]
    @test_int [1/(b*x^n)^(3/2)*x^1, x, 2, (2*x^(2 - n))/(b*(4 - 3*n)*sqrt(b*x^n))]
    @test_int [1/(b*x^n)^(3/2)*x^0, x, 2, (2*x^(1 - n))/(b*(2 - 3*n)*sqrt(b*x^n))]
    @test_int [1/(b*x^n)^(3/2)/x^1, x, 2, -(2/(x^n*(3*b*n*sqrt(b*x^n))))]
    @test_int [1/(b*x^n)^(3/2)/x^2, x, 2, -((2*x^(-1 - n))/(b*(2 + 3*n)*sqrt(b*x^n)))]
    @test_int [1/(b*x^n)^(3/2)/x^3, x, 2, -((2*x^(-2 - n))/(b*(4 + 3*n)*sqrt(b*x^n)))]
    @test_int [1/(b*x^n)^(3/2)/x^4, x, 2, -((2*x^(-3 - n))/(3*b*(2 + n)*sqrt(b*x^n)))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(c*x)^m*(b*x^n)^(p/2)*with*m*symbolic=#

    @test_int [x^m/(a*x^n)^(3/2), x, 2, (2*x^(1 + m - n))/(a*(2 + 2*m - 3*n)*sqrt(a*x^n))]
    @test_int [(c*x)^m/(a*x^n)^(3/2), x, 3, (2*x^(1 - n)*(c*x)^m)/(a*(2 + 2*m - 3*n)*sqrt(a*x^n))]

    @test_int [x^m*(b*x^n)^(3/2), x, 2, (2*b*x^(1 + m + n)*sqrt(b*x^n))/(2 + 2*m + 3*n)]
    @test_int [x^m*(b*x^n)^(1/2), x, 2, (2*x^(1 + m)*sqrt(b*x^n))/(2 + 2*m + n)]
    @test_int [x^m/(b*x^n)^(1/2), x, 2, (2*x^(1 + m))/((2 + 2*m - n)*sqrt(b*x^n))]
    @test_int [x^m/(b*x^n)^(3/2), x, 2, (2*x^(1 + m - n))/(b*(2 + 2*m - 3*n)*sqrt(b*x^n))]

    @test_int [(c*x)^m*(b*x^n)^(5/2), x, 3, (2*(c*x)^(1 + m)*(b*x^n)^(5/2))/(c*(2 + 2*m + 5*n)), (2*b^2*x^(1 + 2*n)*(c*x)^m*sqrt(b*x^n))/(2 + 2*m + 5*n)]
    @test_int [(c*x)^m*(b*x^n)^(3/2), x, 3, (2*b*x^(1 + n)*(c*x)^m*sqrt(b*x^n))/(2 + 2*m + 3*n)]
    @test_int [(c*x)^m*(b*x^n)^(1/2), x, 3, (2*(c*x)^(1 + m)*sqrt(b*x^n))/(c*(2 + 2*m + n)), (2*x*(c*x)^m*sqrt(b*x^n))/(2 + 2*m + n)]
    @test_int [(c*x)^m/(b*x^n)^(1/2), x, 3, (2*x*(c*x)^m)/((2 + 2*m - n)*sqrt(b*x^n))]
    @test_int [(c*x)^m/(b*x^n)^(3/2), x, 3, (2*x^(1 - n)*(c*x)^m)/(b*(2 + 2*m - 3*n)*sqrt(b*x^n))]
    @test_int [(c*x)^m/(b*x^n)^(5/2), x, 3, (2*x^(1 - 2*n)*(c*x)^m)/(b^2*(2 + 2*m - 5*n)*sqrt(b*x^n))]

    @test_int [(b*x^n)^(3/2)/x^(3*n/2+1), x, 2, (b*sqrt(b*x^n)*log(x))/x^(n/2)]
    @test_int [(b*x^n)^(1/2)/x^(n/2+1), x, 2, (sqrt(b*x^n)*log(x))/x^(n/2)]
    @test_int [x^(n/2-1)/(b*x^n)^(1/2), x, 2, (x^(n/2)*log(x))/sqrt(b*x^n)]
    @test_int [x^(3*n/2-1)/(b*x^n)^(3/2), x, 2, (x^(n/2)*log(x))/(b*sqrt(b*x^n))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(c*x)^m*(b*x^n)^p*with*p*symbolic=#

    @test_int [x^m*(b*x^n)^p, x, 2, (x^(1 + m)*(b*x^n)^p)/(1 + m + n*p)]
    @test_int [(c*x)^m*(b*x^n)^p, x, 3, ((c*x)^(m + 1)*(b*x^n)^p)/(c*(1 + m + n*p)), (x*(c*x)^m*(b*x^n)^p)/(1 + m + n*p)]

    @test_int [(b*x^n)^p*x^2, x, 2, (x^3*(b*x^n)^p)/(3 + n*p)]
    @test_int [(b*x^n)^p*x^1, x, 2, (x^2*(b*x^n)^p)/(2 + n*p)]
    @test_int [(b*x^n)^p*x^0, x, 2, (x*(b*x^n)^p)/(1 + n*p)]
    @test_int [(b*x^n)^p/x^1, x, 2, (b*x^n)^p/(n*p)]
    @test_int [(b*x^n)^p/x^2, x, 2, -((b*x^n)^p/((1 - n*p)*x))]
    @test_int [(b*x^n)^p/x^3, x, 2, -((b*x^n)^p/((2 - n*p)*x^2))]

    @test_int [x^m/(a*x^n)^(1/n), x, 2, x^(1 + m)/((a*x^n)^(1/n)*m)]
    @test_int [(c*x)^m/(a*x^n)^(1/n), x, 3, (x*(c*x)^m)/((a*x^n)^n^(-1)*m)]

    @test_int [x^2/(a*x^n)^(1/n), x, 2, ((1/2)*x^3)/(a*x^n)^(1/n)]
    @test_int [x^1/(a*x^n)^(1/n), x, 2, x^2/(a*x^n)^(1/n)]
    @test_int [x^0/(a*x^n)^(1/n), x, 2, (x*log(x))/(a*x^n)^(1/n)]
    @test_int [1/(x^1*(a*x^n)^(1/n)), x, 2, -(a*x^n)^(-n^(-1))]
    @test_int [1/(x^2*(a*x^n)^(1/n)), x, 2, -(1/((a*x^n)^(1/n)*(2*x)))]

    @test_int [x^m/(a*x^n)^((1 + m)/n), x, 2, (x^(1 + m)*log(x))/(a*x^n)^((1 + m)/n)]
    @test_int [(a*x^n)^p/x^(n*p+1), x, 2, ((a*x^n)^p*log(x))/x^(n*p)]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(c*x)^m*(a*(b*x^n)^p)^q=#

    @test_int [x^m*(a*(b*x^n)^p)^q, x, 2, (x^(1 + m)*(a*(b*x^n)^p)^q)/(1 + m + n*p*q)]

    @test_int [x^2*(a*(b*x^n)^p)^q, x, 2, (x^3*(a*(b*x^n)^p)^q)/(3 + n*p*q)]
    @test_int [x^1*(a*(b*x^n)^p)^q, x, 2, (x^2*(a*(b*x^n)^p)^q)/(2 + n*p*q)]
    @test_int [x^0*(a*(b*x^n)^p)^q, x, 2, (x*(a*(b*x^n)^p)^q)/(1 + n*p*q)]
    @test_int [(a*(b*x^n)^p)^q/x^1, x, 2, (a*(b*x^n)^p)^q/(n*p*q)]
    @test_int [(a*(b*x^n)^p)^q/x^2, x, 2, -((a*(b*x^n)^p)^q/((1 - n*p*q)*x))]
    @test_int [(a*(b*x^n)^p)^q/x^3, x, 2, -((a*(b*x^n)^p)^q/((2 - n*p*q)*x^2))]

    @test_int [x^2/(a*(b*x^m)^n)^(1/(m*n)), x, 2, ((1/2)*x^3)/(a*(b*x^m)^n)^(1/(m*n))]
    @test_int [x^1/(a*(b*x^m)^n)^(1/(m*n)), x, 2, x^2/(a*(b*x^m)^n)^(1/(m*n))]
    @test_int [x^0/(a*(b*x^m)^n)^(1/(m*n)), x, 2, (x*log(x))/(a*(b*x^m)^n)^(1/(m*n))]
    @test_int [1/(x^1*(a*(b*x^m)^n)^(1/(m*n))), x, 2, -(a*(b*x^m)^n)^(-(1/(m*n)))]
    @test_int [1/(x^2*(a*(b*x^m)^n)^(1/(m*n))), x, 2, -(1/((a*(b*x^m)^n)^(1/(m*n))*(2*x)))]

    @test_int [x^(2-n*p*q)*(a*(b*x^n)^p)^q, x, 2, (1/3)*x^(3 - n*p*q)*(a*(b*x^n)^p)^q]
    @test_int [x^(1-n*p*q)*(a*(b*x^n)^p)^q, x, 2, (1/2)*x^(2 - n*p*q)*(a*(b*x^n)^p)^q]
    @test_int [x^(0-n*p*q)*(a*(b*x^n)^p)^q, x, 2, x^(1 - n*p*q)*(a*(b*x^n)^p)^q]
    @test_int [x^(-1-n*p*q)*(a*(b*x^n)^p)^q, x, 2, ((a*(b*x^n)^p)^q*log(x))/x^(n*p*q)]
    @test_int [x^(-2-n*p*q)*(a*(b*x^n)^p)^q, x, 2, (-x^(-1 - n*p*q))*(a*(b*x^n)^p)^q]

    #= ::Title::Closed:: =#
    #=Integrands*of*the*form*(c*x)^m*(a+b*x^n)^p*when*n>2*is*an*integer=#

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(c*x)^m*(a+b*x^3)^p=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b*x^3)^p=#

    #= ::Subsubsection::Closed:: =#
    #=p>0=#

    @test_int [x^3*(a + b*x^3), x, 2, (a*x^4)/4 + (b*x^7)/7]
    @test_int [x^2*(a + b*x^3), x, 2, (a*x^3)/3 + (b*x^6)/6]
    @test_int [x*(a + b*x^3), x, 2, (a*x^2)/2 + (b*x^5)/5]
    @test_int [(a + b*x^3), x, 1, a*x + (b*x^4)/4]
    @test_int [(a + b*x^3)/x, x, 2, (b*x^3)/3 + a*log(x)]
    @test_int [(a + b*x^3)/x^2, x, 2, -(a/x) + (b*x^2)/2]
    @test_int [(a + b*x^3)/x^3, x, 2, -(a/(2*x^2)) + b*x]
    @test_int [(a + b*x^3)/x^4, x, 2, -(a/(3*x^3)) + b*log(x)]
    @test_int [(a + b*x^3)/x^5, x, 2, -(a/(4*x^4)) - b/x]
    @test_int [(a + b*x^3)/x^6, x, 2, -(a/(5*x^5)) - b/(2*x^2)]
    @test_int [(a + b*x^3)/x^7, x, 2, -(a/(6*x^6)) - b/(3*x^3)]
    @test_int [(a + b*x^3)/x^8, x, 2, -(a/(7*x^7)) - b/(4*x^4)]

    @test_int [x^4*(a + b*x^3)^2, x, 2, (a^2*x^5)/5 + (1/4)*a*b*x^8 + (b^2*x^11)/11]
    @test_int [x^3*(a + b*x^3)^2, x, 2, (a^2*x^4)/4 + (2/7)*a*b*x^7 + (b^2*x^10)/10]
    @test_int [x^2*(a + b*x^3)^2, x, 1, (a + b*x^3)^3/(9*b)]
    @test_int [x*(a + b*x^3)^2, x, 2, (a^2*x^2)/2 + (2/5)*a*b*x^5 + (b^2*x^8)/8]
    @test_int [(a + b*x^3)^2, x, 2, a^2*x + (1/2)*a*b*x^4 + (b^2*x^7)/7]
    @test_int [(a + b*x^3)^2/x, x, 3, (2/3)*a*b*x^3 + (b^2*x^6)/6 + a^2*log(x)]
    @test_int [(a + b*x^3)^2/x^2, x, 2, -(a^2/x) + a*b*x^2 + (b^2*x^5)/5]
    @test_int [(a + b*x^3)^2/x^3, x, 2, -(a^2/(2*x^2)) + 2*a*b*x + (b^2*x^4)/4]
    @test_int [(a + b*x^3)^2/x^4, x, 3, -(a^2/(3*x^3)) + (b^2*x^3)/3 + 2*a*b*log(x)]
    @test_int [(a + b*x^3)^2/x^5, x, 2, -(a^2/(4*x^4)) - (2*a*b)/x + (b^2*x^2)/2]
    @test_int [(a + b*x^3)^2/x^6, x, 2, -(a^2/(5*x^5)) - (a*b)/x^2 + b^2*x]
    @test_int [(a + b*x^3)^2/x^7, x, 3, -(a^2/(6*x^6)) - (2*a*b)/(3*x^3) + b^2*log(x)]
    @test_int [(a + b*x^3)^2/x^8, x, 2, -(a^2/(7*x^7)) - (a*b)/(2*x^4) - b^2/x]
    @test_int [(a + b*x^3)^2/x^9, x, 2, -(a^2/(8*x^8)) - (2*a*b)/(5*x^5) - b^2/(2*x^2)]
    @test_int [(a + b*x^3)^2/x^10, x, 1, -((a + b*x^3)^3/(9*a*x^9))]
    @test_int [(a + b*x^3)^2/x^11, x, 2, -(a^2/(10*x^10)) - (2*a*b)/(7*x^7) - b^2/(4*x^4)]
    @test_int [(a + b*x^3)^2/x^12, x, 2, -(a^2/(11*x^11)) - (a*b)/(4*x^8) - b^2/(5*x^5)]
    @test_int [(a + b*x^3)^2/x^13, x, 3, -(a^2/(12*x^12)) - (2*a*b)/(9*x^9) - b^2/(6*x^6)]

    @test_int [x^14*(a + b*x^3)^3, x, 3, (a^3*x^15)/15 + (1/6)*a^2*b*x^18 + (1/7)*a*b^2*x^21 + (b^3*x^24)/24]
    @test_int [x^11*(a + b*x^3)^3, x, 3, (a^3*x^12)/12 + (1/5)*a^2*b*x^15 + (1/6)*a*b^2*x^18 + (b^3*x^21)/21]
    @test_int [x^8*(a + b*x^3)^3, x, 3, (a^3*x^9)/9 + (1/4)*a^2*b*x^12 + (1/5)*a*b^2*x^15 + (b^3*x^18)/18]
    @test_int [x^5*(a + b*x^3)^3, x, 3, -((a*(a + b*x^3)^4)/(12*b^2)) + (a + b*x^3)^5/(15*b^2)]
    @test_int [x^2*(a + b*x^3)^3, x, 1, (a + b*x^3)^4/(12*b)]
    @test_int [(a + b*x^3)^3/x, x, 3, a^2*b*x^3 + (1/2)*a*b^2*x^6 + (b^3*x^9)/9 + a^3*log(x)]
    @test_int [(a + b*x^3)^3/x^4, x, 3, -(a^3/(3*x^3)) + a*b^2*x^3 + (b^3*x^6)/6 + 3*a^2*b*log(x)]
    @test_int [(a + b*x^3)^3/x^7, x, 3, -(a^3/(6*x^6)) - (a^2*b)/x^3 + (b^3*x^3)/3 + 3*a*b^2*log(x)]
    @test_int [(a + b*x^3)^3/x^10, x, 3, -(a^3/(9*x^9)) - (a^2*b)/(2*x^6) - (a*b^2)/x^3 + b^3*log(x)]
    @test_int [(a + b*x^3)^3/x^13, x, 1, -((a + b*x^3)^4/(12*a*x^12))]
    @test_int [(a + b*x^3)^3/x^16, x, 3, -((a + b*x^3)^4/(15*a*x^15)) + (b*(a + b*x^3)^4)/(60*a^2*x^12)]
    @test_int [(a + b*x^3)^3/x^19, x, 3, -(a^3/(18*x^18)) - (a^2*b)/(5*x^15) - (a*b^2)/(4*x^12) - b^3/(9*x^9)]
    @test_int [(a + b*x^3)^3/x^22, x, 3, -(a^3/(21*x^21)) - (a^2*b)/(6*x^18) - (a*b^2)/(5*x^15) - b^3/(12*x^12)]

    @test_int [x^4*(a + b*x^3)^3, x, 2, (a^3*x^5)/5 + (3/8)*a^2*b*x^8 + (3/11)*a*b^2*x^11 + (b^3*x^14)/14]
    @test_int [x^3*(a + b*x^3)^3, x, 2, (a^3*x^4)/4 + (3/7)*a^2*b*x^7 + (3/10)*a*b^2*x^10 + (b^3*x^13)/13]
    @test_int [x*(a + b*x^3)^3, x, 2, (a^3*x^2)/2 + (3/5)*a^2*b*x^5 + (3/8)*a*b^2*x^8 + (b^3*x^11)/11]
    @test_int [(a + b*x^3)^3, x, 2, a^3*x + (3/4)*a^2*b*x^4 + (3/7)*a*b^2*x^7 + (b^3*x^10)/10]
    @test_int [(a + b*x^3)^3/x^2, x, 2, -(a^3/x) + (3/2)*a^2*b*x^2 + (3/5)*a*b^2*x^5 + (b^3*x^8)/8]
    @test_int [(a + b*x^3)^3/x^3, x, 2, -(a^3/(2*x^2)) + 3*a^2*b*x + (3/4)*a*b^2*x^4 + (b^3*x^7)/7]
    @test_int [(a + b*x^3)^3/x^5, x, 2, -(a^3/(4*x^4)) - (3*a^2*b)/x + (3/2)*a*b^2*x^2 + (b^3*x^5)/5]
    @test_int [(a + b*x^3)^3/x^6, x, 2, -(a^3/(5*x^5)) - (3*a^2*b)/(2*x^2) + 3*a*b^2*x + (b^3*x^4)/4]
    @test_int [(a + b*x^3)^3/x^8, x, 2, -(a^3/(7*x^7)) - (3*a^2*b)/(4*x^4) - (3*a*b^2)/x + (b^3*x^2)/2]

    @test_int [x^17*(a + b*x^3)^5, x, 3, (a^5*x^18)/18 + (5*a^4*b*x^21)/21 + (5*a^3*b^2*x^24)/12 + (10*a^2*b^3*x^27)/27 + (a*b^4*x^30)/6 + (b^5*x^33)/33]
    @test_int [x^14*(a + b*x^3)^5, x, 3, (a^5*x^15)/15 + (5/18)*a^4*b*x^18 + (10/21)*a^3*b^2*x^21 + (5/12)*a^2*b^3*x^24 + (5/27)*a*b^4*x^27 + (b^5*x^30)/30]
    @test_int [x^11*(a + b*x^3)^5, x, 3, -((a^3*(a + b*x^3)^6)/(18*b^4)) + (a^2*(a + b*x^3)^7)/(7*b^4) - (a*(a + b*x^3)^8)/(8*b^4) + (a + b*x^3)^9/(27*b^4)]
    @test_int [x^8*(a + b*x^3)^5, x, 3, (a^2*(a + b*x^3)^6)/(18*b^3) - (2*a*(a + b*x^3)^7)/(21*b^3) + (a + b*x^3)^8/(24*b^3)]
    @test_int [x^5*(a + b*x^3)^5, x, 3, -((a*(a + b*x^3)^6)/(18*b^2)) + (a + b*x^3)^7/(21*b^2)]
    @test_int [x^2*(a + b*x^3)^5, x, 1, (a + b*x^3)^6/(18*b)]
    @test_int [(a + b*x^3)^5/x^1, x, 3, (5*a^4*b*x^3)/3 + (5*a^3*b^2*x^6)/3 + (10*a^2*b^3*x^9)/9 + (5*a*b^4*x^12)/12 + (b^5*x^15)/15 + a^5*log(x)]
    @test_int [(a + b*x^3)^5/x^4, x, 3, -a^5/(3*x^3) + (10*a^3*b^2*x^3)/3 + (5*a^2*b^3*x^6)/3 + (5*a*b^4*x^9)/9 + (b^5*x^12)/12 + 5*a^4*b*log(x)]
    @test_int [(a + b*x^3)^5/x^7, x, 3, -a^5/(6*x^6) - (5*a^4*b)/(3*x^3) + (10*a^2*b^3*x^3)/3 + (5*a*b^4*x^6)/6 + (b^5*x^9)/9 + 10*a^3*b^2*log(x)]
    @test_int [(a + b*x^3)^5/x^10, x, 3, -a^5/(9*x^9) - (5*a^4*b)/(6*x^6) - (10*a^3*b^2)/(3*x^3) + (5*a*b^4*x^3)/3 + (b^5*x^6)/6 + 10*a^2*b^3*log(x)]
    @test_int [(a + b*x^3)^5/x^13, x, 3, -a^5/(12*x^12) - (5*a^4*b)/(9*x^9) - (5*a^3*b^2)/(3*x^6) - (10*a^2*b^3)/(3*x^3) + (b^5*x^3)/3 + 5*a*b^4*log(x)]
    @test_int [(a + b*x^3)^5/x^16, x, 3, -a^5/(15*x^15) - (5*a^4*b)/(12*x^12) - (10*a^3*b^2)/(9*x^9) - (5*a^2*b^3)/(3*x^6) - (5*a*b^4)/(3*x^3) + b^5*log(x)]
    @test_int [(a + b*x^3)^5/x^19, x, 1, -(a + b*x^3)^6/(18*a*x^18)]
    @test_int [(a + b*x^3)^5/x^22, x, 3, -(a + b*x^3)^6/(21*a*x^21) + (b*(a + b*x^3)^6)/(126*a^2*x^18)]
    @test_int [(a + b*x^3)^5/x^25, x, 4, -((a + b*x^3)^6/(24*a*x^24)) + (b*(a + b*x^3)^6)/(84*a^2*x^21) - (b^2*(a + b*x^3)^6)/(504*a^3*x^18)]
    @test_int [(a + b*x^3)^5/x^28, x, 3, -a^5/(27*x^27) - (5*a^4*b)/(24*x^24) - (10*a^3*b^2)/(21*x^21) - (5*a^2*b^3)/(9*x^18) - (a*b^4)/(3*x^15) - b^5/(12*x^12)]
    @test_int [(a + b*x^3)^5/x^31, x, 3, -a^5/(30*x^30) - (5*a^4*b)/(27*x^27) - (5*a^3*b^2)/(12*x^24) - (10*a^2*b^3)/(21*x^21) - (5*a*b^4)/(18*x^18) - b^5/(15*x^15)]

    @test_int [x^4*(a + b*x^3)^5, x, 2, (a^5*x^5)/5 + (5*a^4*b*x^8)/8 + (10*a^3*b^2*x^11)/11 + (5*a^2*b^3*x^14)/7 + (5*a*b^4*x^17)/17 + (b^5*x^20)/20]
    @test_int [x^3*(a + b*x^3)^5, x, 2, (a^5*x^4)/4 + (5*a^4*b*x^7)/7 + a^3*b^2*x^10 + (10*a^2*b^3*x^13)/13 + (5*a*b^4*x^16)/16 + (b^5*x^19)/19]
    @test_int [x^1*(a + b*x^3)^5, x, 2, (a^5*x^2)/2 + a^4*b*x^5 + (5*a^3*b^2*x^8)/4 + (10*a^2*b^3*x^11)/11 + (5*a*b^4*x^14)/14 + (b^5*x^17)/17]
    @test_int [x^0*(a + b*x^3)^5, x, 2, a^5*x + (5*a^4*b*x^4)/4 + (10*a^3*b^2*x^7)/7 + a^2*b^3*x^10 + (5*a*b^4*x^13)/13 + (b^5*x^16)/16]
    @test_int [(a + b*x^3)^5/x^2, x, 2, -(a^5/x) + (5*a^4*b*x^2)/2 + 2*a^3*b^2*x^5 + (5*a^2*b^3*x^8)/4 + (5*a*b^4*x^11)/11 + (b^5*x^14)/14]
    @test_int [(a + b*x^3)^5/x^3, x, 2, -a^5/(2*x^2) + 5*a^4*b*x + (5*a^3*b^2*x^4)/2 + (10*a^2*b^3*x^7)/7 + (a*b^4*x^10)/2 + (b^5*x^13)/13]
    @test_int [(a + b*x^3)^5/x^5, x, 2, -a^5/(4*x^4) - (5*a^4*b)/x + 5*a^3*b^2*x^2 + 2*a^2*b^3*x^5 + (5*a*b^4*x^8)/8 + (b^5*x^11)/11]
    @test_int [(a + b*x^3)^5/x^6, x, 2, -a^5/(5*x^5) - (5*a^4*b)/(2*x^2) + 10*a^3*b^2*x + (5*a^2*b^3*x^4)/2 + (5*a*b^4*x^7)/7 + (b^5*x^10)/10]
    @test_int [(a + b*x^3)^5/x^8, x, 2, -a^5/(7*x^7) - (5*a^4*b)/(4*x^4) - (10*a^3*b^2)/x + 5*a^2*b^3*x^2 + a*b^4*x^5 + (b^5*x^8)/8]
    @test_int [(a + b*x^3)^5/x^9, x, 2, -a^5/(8*x^8) - (a^4*b)/x^5 - (5*a^3*b^2)/x^2 + 10*a^2*b^3*x + (5*a*b^4*x^4)/4 + (b^5*x^7)/7]

    @test_int [x^20*(a + b*x^3)^8, x, 3, (a^6*(a + b*x^3)^9)/(27*b^7) - (a^5*(a + b*x^3)^10)/(5*b^7) + (5*a^4*(a + b*x^3)^11)/(11*b^7) - (5*a^3*(a + b*x^3)^12)/(9*b^7) + (5*a^2*(a + b*x^3)^13)/(13*b^7) - (a*(a + b*x^3)^14)/(7*b^7) + (a + b*x^3)^15/(45*b^7)]
    @test_int [x^17*(a + b*x^3)^8, x, 3, -((a^5*(a + b*x^3)^9)/(27*b^6)) + (a^4*(a + b*x^3)^10)/(6*b^6) - (10*a^3*(a + b*x^3)^11)/(33*b^6) + (5*a^2*(a + b*x^3)^12)/(18*b^6) - (5*a*(a + b*x^3)^13)/(39*b^6) + (a + b*x^3)^14/(42*b^6)]
    @test_int [x^14*(a + b*x^3)^8, x, 3, (a^4*(a + b*x^3)^9)/(27*b^5) - (2*a^3*(a + b*x^3)^10)/(15*b^5) + (2*a^2*(a + b*x^3)^11)/(11*b^5) - (a*(a + b*x^3)^12)/(9*b^5) + (a + b*x^3)^13/(39*b^5)]
    @test_int [x^11*(a + b*x^3)^8, x, 3, -((a^3*(a + b*x^3)^9)/(27*b^4)) + (a^2*(a + b*x^3)^10)/(10*b^4) - (a*(a + b*x^3)^11)/(11*b^4) + (a + b*x^3)^12/(36*b^4)]
    @test_int [x^8*(a + b*x^3)^8, x, 3, (a^2*(a + b*x^3)^9)/(27*b^3) - (a*(a + b*x^3)^10)/(15*b^3) + (a + b*x^3)^11/(33*b^3)]
    @test_int [x^5*(a + b*x^3)^8, x, 3, -((a*(a + b*x^3)^9)/(27*b^2)) + (a + b*x^3)^10/(30*b^2)]
    @test_int [x^2*(a + b*x^3)^8, x, 1, (a + b*x^3)^9/(27*b)]
    @test_int [(a + b*x^3)^8/x^1, x, 3, (8*a^7*b*x^3)/3 + (14*a^6*b^2*x^6)/3 + (56*a^5*b^3*x^9)/9 + (35*a^4*b^4*x^12)/6 + (56*a^3*b^5*x^15)/15 + (14*a^2*b^6*x^18)/9 + (8*a*b^7*x^21)/21 + (b^8*x^24)/24 + a^8*log(x)]
    @test_int [(a + b*x^3)^8/x^4, x, 3, -a^8/(3*x^3) + (28*a^6*b^2*x^3)/3 + (28*a^5*b^3*x^6)/3 + (70*a^4*b^4*x^9)/9 + (14*a^3*b^5*x^12)/3 + (28*a^2*b^6*x^15)/15 + (4*a*b^7*x^18)/9 + (b^8*x^21)/21 + 8*a^7*b*log(x)]
    @test_int [(a + b*x^3)^8/x^7, x, 3, -a^8/(6*x^6) - (8*a^7*b)/(3*x^3) + (56*a^5*b^3*x^3)/3 + (35*a^4*b^4*x^6)/3 + (56*a^3*b^5*x^9)/9 + (7*a^2*b^6*x^12)/3 + (8*a*b^7*x^15)/15 + (b^8*x^18)/18 + 28*a^6*b^2*log(x)]
    @test_int [(a + b*x^3)^8/x^10, x, 3, -a^8/(9*x^9) - (4*a^7*b)/(3*x^6) - (28*a^6*b^2)/(3*x^3) + (70*a^4*b^4*x^3)/3 + (28*a^3*b^5*x^6)/3 + (28*a^2*b^6*x^9)/9 + (2*a*b^7*x^12)/3 + (b^8*x^15)/15 + 56*a^5*b^3*log(x)]
    @test_int [(a + b*x^3)^8/x^13, x, 3, -a^8/(12*x^12) - (8*a^7*b)/(9*x^9) - (14*a^6*b^2)/(3*x^6) - (56*a^5*b^3)/(3*x^3) + (56*a^3*b^5*x^3)/3 + (14*a^2*b^6*x^6)/3 + (8*a*b^7*x^9)/9 + (b^8*x^12)/12 + 70*a^4*b^4*log(x)]
    @test_int [(a + b*x^3)^8/x^16, x, 3, -a^8/(15*x^15) - (2*a^7*b)/(3*x^12) - (28*a^6*b^2)/(9*x^9) - (28*a^5*b^3)/(3*x^6) - (70*a^4*b^4)/(3*x^3) + (28*a^2*b^6*x^3)/3 + (4*a*b^7*x^6)/3 + (b^8*x^9)/9 + 56*a^3*b^5*log(x)]
    @test_int [(a + b*x^3)^8/x^19, x, 3, -a^8/(18*x^18) - (8*a^7*b)/(15*x^15) - (7*a^6*b^2)/(3*x^12) - (56*a^5*b^3)/(9*x^9) - (35*a^4*b^4)/(3*x^6) - (56*a^3*b^5)/(3*x^3) + (8*a*b^7*x^3)/3 + (b^8*x^6)/6 + 28*a^2*b^6*log(x)]
    @test_int [(a + b*x^3)^8/x^22, x, 3, -a^8/(21*x^21) - (4*a^7*b)/(9*x^18) - (28*a^6*b^2)/(15*x^15) - (14*a^5*b^3)/(3*x^12) - (70*a^4*b^4)/(9*x^9) - (28*a^3*b^5)/(3*x^6) - (28*a^2*b^6)/(3*x^3) + (b^8*x^3)/3 + 8*a*b^7*log(x)]
    @test_int [(a + b*x^3)^8/x^25, x, 3, -a^8/(24*x^24) - (8*a^7*b)/(21*x^21) - (14*a^6*b^2)/(9*x^18) - (56*a^5*b^3)/(15*x^15) - (35*a^4*b^4)/(6*x^12) - (56*a^3*b^5)/(9*x^9) - (14*a^2*b^6)/(3*x^6) - (8*a*b^7)/(3*x^3) + b^8*log(x)]
    @test_int [(a + b*x^3)^8/x^28, x, 1, -(a + b*x^3)^9/(27*a*x^27)]
    @test_int [(a + b*x^3)^8/x^31, x, 3, -(a + b*x^3)^9/(30*a*x^30) + (b*(a + b*x^3)^9)/(270*a^2*x^27)]
    @test_int [(a + b*x^3)^8/x^34, x, 4, -(a + b*x^3)^9/(33*a*x^33) + (b*(a + b*x^3)^9)/(165*a^2*x^30) - (b^2*(a + b*x^3)^9)/(1485*a^3*x^27)]
    @test_int [(a + b*x^3)^8/x^37, x, 5, -((a + b*x^3)^9/(36*a*x^36)) + (b*(a + b*x^3)^9)/(132*a^2*x^33) - (b^2*(a + b*x^3)^9)/(660*a^3*x^30) + (b^3*(a + b*x^3)^9)/(5940*a^4*x^27)]
    @test_int [(a + b*x^3)^8/x^40, x, 6, -((a + b*x^3)^9/(39*a*x^39)) + (b*(a + b*x^3)^9)/(117*a^2*x^36) - (b^2*(a + b*x^3)^9)/(429*a^3*x^33) + (b^3*(a + b*x^3)^9)/(2145*a^4*x^30) - (b^4*(a + b*x^3)^9)/(19305*a^5*x^27)]
    @test_int [(a + b*x^3)^8/x^43, x, 3, -a^8/(42*x^42) - (8*a^7*b)/(39*x^39) - (7*a^6*b^2)/(9*x^36) - (56*a^5*b^3)/(33*x^33) - (7*a^4*b^4)/(3*x^30) - (56*a^3*b^5)/(27*x^27) - (7*a^2*b^6)/(6*x^24) - (8*a*b^7)/(21*x^21) - b^8/(18*x^18)]
    @test_int [(a + b*x^3)^8/x^46, x, 3, -a^8/(45*x^45) - (4*a^7*b)/(21*x^42) - (28*a^6*b^2)/(39*x^39) - (14*a^5*b^3)/(9*x^36) - (70*a^4*b^4)/(33*x^33) - (28*a^3*b^5)/(15*x^30) - (28*a^2*b^6)/(27*x^27) - (a*b^7)/(3*x^24) - b^8/(21*x^21)]

    @test_int [x^4*(a + b*x^3)^8, x, 2, (a^8*x^5)/5 + a^7*b*x^8 + (28*a^6*b^2*x^11)/11 + 4*a^5*b^3*x^14 + (70*a^4*b^4*x^17)/17 + (14*a^3*b^5*x^20)/5 + (28*a^2*b^6*x^23)/23 + (4*a*b^7*x^26)/13 + (b^8*x^29)/29]
    @test_int [x^3*(a + b*x^3)^8, x, 2, (a^8*x^4)/4 + (8*a^7*b*x^7)/7 + (14*a^6*b^2*x^10)/5 + (56*a^5*b^3*x^13)/13 + (35*a^4*b^4*x^16)/8 + (56*a^3*b^5*x^19)/19 + (14*a^2*b^6*x^22)/11 + (8*a*b^7*x^25)/25 + (b^8*x^28)/28]
    @test_int [x^1*(a + b*x^3)^8, x, 2, (a^8*x^2)/2 + (8*a^7*b*x^5)/5 + (7*a^6*b^2*x^8)/2 + (56*a^5*b^3*x^11)/11 + 5*a^4*b^4*x^14 + (56*a^3*b^5*x^17)/17 + (7*a^2*b^6*x^20)/5 + (8*a*b^7*x^23)/23 + (b^8*x^26)/26]
    @test_int [x^0*(a + b*x^3)^8, x, 2, a^8*x + 2*a^7*b*x^4 + 4*a^6*b^2*x^7 + (28*a^5*b^3*x^10)/5 + (70*a^4*b^4*x^13)/13 + (7*a^3*b^5*x^16)/2 + (28*a^2*b^6*x^19)/19 + (4*a*b^7*x^22)/11 + (b^8*x^25)/25]
    @test_int [(a + b*x^3)^8/x^2, x, 2, -(a^8/x) + 4*a^7*b*x^2 + (28*a^6*b^2*x^5)/5 + 7*a^5*b^3*x^8 + (70*a^4*b^4*x^11)/11 + 4*a^3*b^5*x^14 + (28*a^2*b^6*x^17)/17 + (2*a*b^7*x^20)/5 + (b^8*x^23)/23]
    @test_int [(a + b*x^3)^8/x^3, x, 2, -a^8/(2*x^2) + 8*a^7*b*x + 7*a^6*b^2*x^4 + 8*a^5*b^3*x^7 + 7*a^4*b^4*x^10 + (56*a^3*b^5*x^13)/13 + (7*a^2*b^6*x^16)/4 + (8*a*b^7*x^19)/19 + (b^8*x^22)/22]
    @test_int [(a + b*x^3)^8/x^5, x, 2, -a^8/(4*x^4) - (8*a^7*b)/x + 14*a^6*b^2*x^2 + (56*a^5*b^3*x^5)/5 + (35*a^4*b^4*x^8)/4 + (56*a^3*b^5*x^11)/11 + 2*a^2*b^6*x^14 + (8*a*b^7*x^17)/17 + (b^8*x^20)/20]
    @test_int [(a + b*x^3)^8/x^6, x, 2, -a^8/(5*x^5) - (4*a^7*b)/x^2 + 28*a^6*b^2*x + 14*a^5*b^3*x^4 + 10*a^4*b^4*x^7 + (28*a^3*b^5*x^10)/5 + (28*a^2*b^6*x^13)/13 + (a*b^7*x^16)/2 + (b^8*x^19)/19]
    @test_int [(a + b*x^3)^8/x^8, x, 2, -a^8/(7*x^7) - (2*a^7*b)/x^4 - (28*a^6*b^2)/x + 28*a^5*b^3*x^2 + 14*a^4*b^4*x^5 + 7*a^3*b^5*x^8 + (28*a^2*b^6*x^11)/11 + (4*a*b^7*x^14)/7 + (b^8*x^17)/17]
    @test_int [(a + b*x^3)^8/x^9, x, 2, -a^8/(8*x^8) - (8*a^7*b)/(5*x^5) - (14*a^6*b^2)/x^2 + 56*a^5*b^3*x + (35*a^4*b^4*x^4)/2 + 8*a^3*b^5*x^7 + (14*a^2*b^6*x^10)/5 + (8*a*b^7*x^13)/13 + (b^8*x^16)/16]

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [x^8/(a + b*x^3), x, 3, -((a*x^3)/(3*b^2)) + x^6/(6*b) + (a^2*log(a + b*x^3))/(3*b^3)]
    @test_int [x^5/(a + b*x^3), x, 3, x^3/(3*b) - (a*log(a + b*x^3))/(3*b^2)]
    @test_int [x^2/(a + b*x^3), x, 1, log(a + b*x^3)/(3*b)]
    @test_int [1/(x^1*(a + b*x^3)), x, 4, log(x)/a - log(a + b*x^3)/(3*a)]
    @test_int [1/(x^4*(a + b*x^3)), x, 3, -(1/(3*a*x^3)) - (b*log(x))/a^2 + (b*log(a + b*x^3))/(3*a^2)]

    @test_int [x^4/(a + b*x^3), x, 7, x^2/(2*b) + (a^(2/3)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(sqrt(3)*b^(5/3)) + (a^(2/3)*log(a^(1/3) + b^(1/3)*x))/(3*b^(5/3)) - (a^(2/3)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(6*b^(5/3))]
    @test_int [x^3/(a + b*x^3), x, 7, x/b + (a^(1/3)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(sqrt(3)*b^(4/3)) - (a^(1/3)*log(a^(1/3) + b^(1/3)*x))/(3*b^(4/3)) + (a^(1/3)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(6*b^(4/3))]
    @test_int [x^1/(a + b*x^3), x, 6, -(atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3)))/(sqrt(3)*a^(1/3)*b^(2/3))) - log(a^(1/3) + b^(1/3)*x)/(3*a^(1/3)*b^(2/3)) + log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(6*a^(1/3)*b^(2/3))]
    @test_int [x^0/(a + b*x^3), x, 6, -(atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3)))/(sqrt(3)*a^(2/3)*b^(1/3))) + log(a^(1/3) + b^(1/3)*x)/(3*a^(2/3)*b^(1/3)) - log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(6*a^(2/3)*b^(1/3))]
    @test_int [1/(x^2*(a + b*x^3)), x, 7, -(1/(a*x)) + (b^(1/3)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(sqrt(3)*a^(4/3)) + (b^(1/3)*log(a^(1/3) + b^(1/3)*x))/(3*a^(4/3)) - (b^(1/3)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(6*a^(4/3))]
    @test_int [1/(x^3*(a + b*x^3)), x, 7, -(1/(2*a*x^2)) + (b^(2/3)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(sqrt(3)*a^(5/3)) - (b^(2/3)*log(a^(1/3) + b^(1/3)*x))/(3*a^(5/3)) + (b^(2/3)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(6*a^(5/3))]

    @test_int [x^8/(a + b*x^3)^2, x, 3, x^3/(3*b^2) - a^2/(3*b^3*(a + b*x^3)) - (2*a*log(a + b*x^3))/(3*b^3)]
    @test_int [x^5/(a + b*x^3)^2, x, 3, a/(3*b^2*(a + b*x^3)) + log(a + b*x^3)/(3*b^2)]
    @test_int [x^2/(a + b*x^3)^2, x, 1, -(1/(3*b*(a + b*x^3)))]
    @test_int [1/(x^1*(a + b*x^3)^2), x, 3, 1/(3*a*(a + b*x^3)) + log(x)/a^2 - log(a + b*x^3)/(3*a^2)]
    @test_int [1/(x^4*(a + b*x^3)^2), x, 3, -(1/(3*a^2*x^3)) - b/(3*a^2*(a + b*x^3)) - (2*b*log(x))/a^3 + (2*b*log(a + b*x^3))/(3*a^3)]

    @test_int [x^4/(a + b*x^3)^2, x, 7, -(x^2/(3*b*(a + b*x^3))) - (2*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(3*sqrt(3)*a^(1/3)*b^(5/3)) - (2*log(a^(1/3) + b^(1/3)*x))/(9*a^(1/3)*b^(5/3)) + log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(9*a^(1/3)*b^(5/3))]
    @test_int [x^3/(a + b*x^3)^2, x, 7, -(x/(3*b*(a + b*x^3))) - atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3)))/(3*sqrt(3)*a^(2/3)*b^(4/3)) + log(a^(1/3) + b^(1/3)*x)/(9*a^(2/3)*b^(4/3)) - log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(18*a^(2/3)*b^(4/3))]
    @test_int [x^1/(a + b*x^3)^2, x, 7, x^2/(3*a*(a + b*x^3)) - atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3)))/(3*sqrt(3)*a^(4/3)*b^(2/3)) - log(a^(1/3) + b^(1/3)*x)/(9*a^(4/3)*b^(2/3)) + log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(18*a^(4/3)*b^(2/3))]
    @test_int [x^0/(a + b*x^3)^2, x, 7, x/(3*a*(a + b*x^3)) - (2*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(3*sqrt(3)*a^(5/3)*b^(1/3)) + (2*log(a^(1/3) + b^(1/3)*x))/(9*a^(5/3)*b^(1/3)) - log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(9*a^(5/3)*b^(1/3))]
    @test_int [1/(x^2*(a + b*x^3)^2), x, 8, -(4/(3*a^2*x)) + 1/(3*a*x*(a + b*x^3)) + (4*b^(1/3)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(3*sqrt(3)*a^(7/3)) + (4*b^(1/3)*log(a^(1/3) + b^(1/3)*x))/(9*a^(7/3)) - (2*b^(1/3)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(9*a^(7/3))]
    @test_int [1/(x^3*(a + b*x^3)^2), x, 8, -(5/(6*a^2*x^2)) + 1/(3*a*x^2*(a + b*x^3)) + (5*b^(2/3)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(3*sqrt(3)*a^(8/3)) - (5*b^(2/3)*log(a^(1/3) + b^(1/3)*x))/(9*a^(8/3)) + (5*b^(2/3)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(18*a^(8/3))]

    @test_int [x^11/(a + b*x^3)^3, x, 3, x^3/(3*b^3) + a^3/(6*b^4*(a + b*x^3)^2) - a^2/(b^4*(a + b*x^3)) - (a*log(a + b*x^3))/b^4]
    @test_int [x^8/(a + b*x^3)^3, x, 3, -(a^2/(6*b^3*(a + b*x^3)^2)) + (2*a)/(3*b^3*(a + b*x^3)) + log(a + b*x^3)/(3*b^3)]
    @test_int [x^5/(a + b*x^3)^3, x, 1, x^6/(6*a*(a + b*x^3)^2)]
    @test_int [x^2/(a + b*x^3)^3, x, 1, -(1/(6*b*(a + b*x^3)^2))]
    @test_int [1/(x^1*(a + b*x^3)^3), x, 3, 1/(6*a*(a + b*x^3)^2) + 1/(3*a^2*(a + b*x^3)) + log(x)/a^3 - log(a + b*x^3)/(3*a^3)]
    @test_int [1/(x^4*(a + b*x^3)^3), x, 3, -(1/(3*a^3*x^3)) - b/(6*a^2*(a + b*x^3)^2) - (2*b)/(3*a^3*(a + b*x^3)) - (3*b*log(x))/a^4 + (b*log(a + b*x^3))/a^4]

    @test_int [x^7/(a + b*x^3)^3, x, 8, -(x^5/(6*b*(a + b*x^3)^2)) - (5*x^2)/(18*b^2*(a + b*x^3)) - (5*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(9*sqrt(3)*a^(1/3)*b^(8/3)) - (5*log(a^(1/3) + b^(1/3)*x))/(27*a^(1/3)*b^(8/3)) + (5*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(54*a^(1/3)*b^(8/3))]
    @test_int [x^6/(a + b*x^3)^3, x, 8, -(x^4/(6*b*(a + b*x^3)^2)) - (2*x)/(9*b^2*(a + b*x^3)) - (2*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(9*sqrt(3)*a^(2/3)*b^(7/3)) + (2*log(a^(1/3) + b^(1/3)*x))/(27*a^(2/3)*b^(7/3)) - log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(27*a^(2/3)*b^(7/3))]
    @test_int [x^4/(a + b*x^3)^3, x, 8, -(x^2/(6*b*(a + b*x^3)^2)) + x^2/(9*a*b*(a + b*x^3)) - atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3)))/(9*sqrt(3)*a^(4/3)*b^(5/3)) - log(a^(1/3) + b^(1/3)*x)/(27*a^(4/3)*b^(5/3)) + log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(54*a^(4/3)*b^(5/3))]
    @test_int [x^3/(a + b*x^3)^3, x, 8, -(x/(6*b*(a + b*x^3)^2)) + x/(18*a*b*(a + b*x^3)) - atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3)))/(9*sqrt(3)*a^(5/3)*b^(4/3)) + log(a^(1/3) + b^(1/3)*x)/(27*a^(5/3)*b^(4/3)) - log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(54*a^(5/3)*b^(4/3))]
    @test_int [x/(a + b*x^3)^3, x, 8, x^2/(6*a*(a + b*x^3)^2) + (2*x^2)/(9*a^2*(a + b*x^3)) - (2*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(9*sqrt(3)*a^(7/3)*b^(2/3)) - (2*log(a^(1/3) + b^(1/3)*x))/(27*a^(7/3)*b^(2/3)) + log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(27*a^(7/3)*b^(2/3))]
    @test_int [1/(a + b*x^3)^3, x, 8, x/(6*a*(a + b*x^3)^2) + (5*x)/(18*a^2*(a + b*x^3)) - (5*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(9*sqrt(3)*a^(8/3)*b^(1/3)) + (5*log(a^(1/3) + b^(1/3)*x))/(27*a^(8/3)*b^(1/3)) - (5*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(54*a^(8/3)*b^(1/3))]

    @test_int [x^8/(a - b*x^3), x, 3, -((a*x^3)/(3*b^2)) - x^6/(6*b) - (a^2*log(a - b*x^3))/(3*b^3)]
    @test_int [x^5/(a - b*x^3), x, 3, -(x^3/(3*b)) - (a*log(a - b*x^3))/(3*b^2)]
    @test_int [x^2/(a - b*x^3), x, 1, -(log(a - b*x^3)/(3*b))]
    @test_int [1/(x^1*(a - b*x^3)), x, 4, log(x)/a - log(a - b*x^3)/(3*a)]
    @test_int [1/(x^4*(a - b*x^3)), x, 3, -(1/(3*a*x^3)) + (b*log(x))/a^2 - (b*log(a - b*x^3))/(3*a^2)]

    @test_int [x^4/(a - b*x^3), x, 7, -(x^2/(2*b)) - (a^(2/3)*atan((a^(1/3) + 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(sqrt(3)*b^(5/3)) - (a^(2/3)*log(a^(1/3) - b^(1/3)*x))/(3*b^(5/3)) + (a^(2/3)*log(a^(2/3) + a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(6*b^(5/3))]
    @test_int [x^3/(a - b*x^3), x, 7, -(x/b) + (a^(1/3)*atan((a^(1/3) + 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(sqrt(3)*b^(4/3)) - (a^(1/3)*log(a^(1/3) - b^(1/3)*x))/(3*b^(4/3)) + (a^(1/3)*log(a^(2/3) + a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(6*b^(4/3))]
    @test_int [x^1/(a - b*x^3), x, 6, -(atan((a^(1/3) + 2*b^(1/3)*x)/(sqrt(3)*a^(1/3)))/(sqrt(3)*a^(1/3)*b^(2/3))) - log(a^(1/3) - b^(1/3)*x)/(3*a^(1/3)*b^(2/3)) + log(a^(2/3) + a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(6*a^(1/3)*b^(2/3))]
    @test_int [x^0/(a - b*x^3), x, 6, atan((a^(1/3) + 2*b^(1/3)*x)/(sqrt(3)*a^(1/3)))/(sqrt(3)*a^(2/3)*b^(1/3)) - log(a^(1/3) - b^(1/3)*x)/(3*a^(2/3)*b^(1/3)) + log(a^(2/3) + a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(6*a^(2/3)*b^(1/3))]
    @test_int [1/(x^2*(a - b*x^3)), x, 7, -(1/(a*x)) - (b^(1/3)*atan((a^(1/3) + 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(sqrt(3)*a^(4/3)) - (b^(1/3)*log(a^(1/3) - b^(1/3)*x))/(3*a^(4/3)) + (b^(1/3)*log(a^(2/3) + a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(6*a^(4/3))]
    @test_int [1/(x^3*(a - b*x^3)), x, 7, -(1/(2*a*x^2)) + (b^(2/3)*atan((a^(1/3) + 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(sqrt(3)*a^(5/3)) - (b^(2/3)*log(a^(1/3) - b^(1/3)*x))/(3*a^(5/3)) + (b^(2/3)*log(a^(2/3) + a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(6*a^(5/3))]

    @test_int [1/(1 + a + b*x^3), x, 6, -(atan((1 - (2*b^(1/3)*x)/(1 + a)^(1/3))/sqrt(3))/(sqrt(3)*(1 + a)^(2/3)*b^(1/3))) + log((1 + a)^(1/3) + b^(1/3)*x)/(3*(1 + a)^(2/3)*b^(1/3)) - log((1 + a)^(2/3) - (1 + a)^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(6*(1 + a)^(2/3)*b^(1/3))]
    @test_int [1/(1 + a - b*x^3), x, 6, atan((1 + (2*b^(1/3)*x)/(1 + a)^(1/3))/sqrt(3))/(sqrt(3)*(1 + a)^(2/3)*b^(1/3)) - log((1 + a)^(1/3) - b^(1/3)*x)/(3*(1 + a)^(2/3)*b^(1/3)) + log((1 + a)^(2/3) + (1 + a)^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(6*(1 + a)^(2/3)*b^(1/3))]
    @test_int [1/(-1 + a + b*x^3), x, 6, -(atan((1 + (2*b^(1/3)*x)/(1 - a)^(1/3))/sqrt(3))/(sqrt(3)*(1 - a)^(2/3)*b^(1/3))) + log((1 - a)^(1/3) - b^(1/3)*x)/(3*(1 - a)^(2/3)*b^(1/3)) - log((1 - a)^(2/3) + (1 - a)^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(6*(1 - a)^(2/3)*b^(1/3))]
    @test_int [1/(-1 + a - b*x^3), x, 6, atan((1 - (2*b^(1/3)*x)/(1 - a)^(1/3))/sqrt(3))/(sqrt(3)*(1 - a)^(2/3)*b^(1/3)) - log((1 - a)^(1/3) + b^(1/3)*x)/(3*(1 - a)^(2/3)*b^(1/3)) + log((1 - a)^(2/3) - (1 - a)^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(6*(1 - a)^(2/3)*b^(1/3))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^(m/2)*(a+b*x^3)^p=#

    #= ::Subsubsection:: =#
    #=p>0=#

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [sqrt(x)/(1 + x^3), x, 3, (2*atan(x^(3/2)))/3]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b*x^3)^(p/2)=#

    #= ::Subsubsection::Closed:: =#
    #=p>0=#

    @test_int [x^11*sqrt(a + b*x^3), x, 3, (-2*a^3*(a + b*x^3)^(3/2))/(9*b^4) + (2*a^2*(a + b*x^3)^(5/2))/(5*b^4) - (2*a*(a + b*x^3)^(7/2))/(7*b^4) + (2*(a + b*x^3)^(9/2))/(27*b^4)]
    @test_int [x^8*sqrt(a + b*x^3), x, 3, (2*a^2*(a + b*x^3)^(3/2))/(9*b^3) - (4*a*(a + b*x^3)^(5/2))/(15*b^3) + (2*(a + b*x^3)^(7/2))/(21*b^3)]
    @test_int [x^5*sqrt(a + b*x^3), x, 3, (-2*a*(a + b*x^3)^(3/2))/(9*b^2) + (2*(a + b*x^3)^(5/2))/(15*b^2)]
    @test_int [x^2*sqrt(a + b*x^3), x, 1, (2*(a + b*x^3)^(3/2))/(9*b)]
    @test_int [sqrt(a + b*x^3)/x^1, x, 4, (2*sqrt(a + b*x^3))/3 - (2*sqrt(a)*atanh(sqrt(a + b*x^3)/sqrt(a)))/3]
    @test_int [sqrt(a + b*x^3)/x^4, x, 4, -sqrt(a + b*x^3)/(3*x^3) - (b*atanh(sqrt(a + b*x^3)/sqrt(a)))/(3*sqrt(a))]
    @test_int [sqrt(a + b*x^3)/x^7, x, 5, -sqrt(a + b*x^3)/(6*x^6) - (b*sqrt(a + b*x^3))/(12*a*x^3) + (b^2*atanh(sqrt(a + b*x^3)/sqrt(a)))/(12*a^(3/2))]
    @test_int [sqrt(a + b*x^3)/x^10, x, 6, -sqrt(a + b*x^3)/(9*x^9) - (b*sqrt(a + b*x^3))/(36*a*x^6) + (b^2*sqrt(a + b*x^3))/(24*a^2*x^3) - (b^3*atanh(sqrt(a + b*x^3)/sqrt(a)))/(24*a^(5/2))]

    @test_int [x^6*sqrt(a + b*x^3), x, 4, (-48*a^2*x*sqrt(a + b*x^3))/(935*b^2) + (6*a*x^4*sqrt(a + b*x^3))/(187*b) + (2*x^7*sqrt(a + b*x^3))/17 + (32*3^(3/4)*sqrt(2+sqrt(3))*a^3*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(935*b^(7/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [x^3*sqrt(a + b*x^3), x, 3, (6*a*x*sqrt(a + b*x^3))/(55*b) + (2*x^4*sqrt(a + b*x^3))/11 - (4*3^(3/4)*sqrt(2+sqrt(3))*a^2*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(55*b^(4/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [x^0*sqrt(a + b*x^3), x, 2, (2*x*sqrt(a + b*x^3))/5 + (2*3^(3/4)*sqrt(2+sqrt(3))*a*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(5*b^(1/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [sqrt(a + b*x^3)/x^3, x, 2, -sqrt(a + b*x^3)/(2*x^2) + (3^(3/4)*sqrt(2+sqrt(3))*b^(2/3)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(2*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [sqrt(a + b*x^3)/x^6, x, 3, -sqrt(a + b*x^3)/(5*x^5) - (3*b*sqrt(a + b*x^3))/(20*a*x^2) - (3^(3/4)*sqrt(2+sqrt(3))*b^(5/3)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(20*a*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [sqrt(a + b*x^3)/x^9, x, 4, -sqrt(a + b*x^3)/(8*x^8) - (3*b*sqrt(a + b*x^3))/(80*a*x^5) + (21*b^2*sqrt(a + b*x^3))/(320*a^2*x^2) + (7*3^(3/4)*sqrt(2+sqrt(3))*b^(8/3)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(320*a^2*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]

    @test_int [x^7*sqrt(a + b*x^3), x, 6, (-60*a^2*x^2*sqrt(a + b*x^3))/(1729*b^2) + (6*a*x^5*sqrt(a + b*x^3))/(247*b) + (2*x^8*sqrt(a + b*x^3))/19 + (240*a^3*sqrt(a + b*x^3))/(1729*b^(8/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) - (120*3^(1/4)*sqrt(2 - sqrt(3))*a^(10/3)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(1729*b^(8/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) + (80*sqrt(2)*3^(3/4)*a^(10/3)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(1729*b^(8/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [x^4*sqrt(a + b*x^3), x, 5, (6*a*x^2*sqrt(a + b*x^3))/(91*b) + (2*x^5*sqrt(a + b*x^3))/13 - (24*a^2*sqrt(a + b*x^3))/(91*b^(5/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) + (12*3^(1/4)*sqrt(2 - sqrt(3))*a^(7/3)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(91*b^(5/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) - (8*sqrt(2)*3^(3/4)*a^(7/3)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(91*b^(5/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [x^1*sqrt(a + b*x^3), x, 4, (2*x^2*sqrt(a + b*x^3))/7 + (6*a*sqrt(a + b*x^3))/(7*b^(2/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) - (3*3^(1/4)*sqrt(2 - sqrt(3))*a^(4/3)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(7*b^(2/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) + (2*sqrt(2)*3^(3/4)*a^(4/3)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(7*b^(2/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [sqrt(a + b*x^3)/x^2, x, 4, -(sqrt(a + b*x^3)/x) + (3*b^(1/3)*sqrt(a + b*x^3))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x) - (3*3^(1/4)*sqrt(2 - sqrt(3))*a^(1/3)*b^(1/3)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(2*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) + (sqrt(2)*3^(3/4)*a^(1/3)*b^(1/3)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [sqrt(a + b*x^3)/x^5, x, 5, -sqrt(a + b*x^3)/(4*x^4) - (3*b*sqrt(a + b*x^3))/(8*a*x) + (3*b^(4/3)*sqrt(a + b*x^3))/(8*a*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) - (3*3^(1/4)*sqrt(2 - sqrt(3))*b^(4/3)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(16*a^(2/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) + (3^(3/4)*b^(4/3)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(4*sqrt(2)*a^(2/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]

    @test_int [x^11*(a + b*x^3)^(3/2), x, 3, (-2*a^3*(a + b*x^3)^(5/2))/(15*b^4) + (2*a^2*(a + b*x^3)^(7/2))/(7*b^4) - (2*a*(a + b*x^3)^(9/2))/(9*b^4) + (2*(a + b*x^3)^(11/2))/(33*b^4)]
    @test_int [x^8*(a + b*x^3)^(3/2), x, 3, (2*a^2*(a + b*x^3)^(5/2))/(15*b^3) - (4*a*(a + b*x^3)^(7/2))/(21*b^3) + (2*(a + b*x^3)^(9/2))/(27*b^3)]
    @test_int [x^5*(a + b*x^3)^(3/2), x, 3, (-2*a*(a + b*x^3)^(5/2))/(15*b^2) + (2*(a + b*x^3)^(7/2))/(21*b^2)]
    @test_int [x^2*(a + b*x^3)^(3/2), x, 1, (2*(a + b*x^3)^(5/2))/(15*b)]
    @test_int [(a + b*x^3)^(3/2)/x^1, x, 5, (2*a*sqrt(a + b*x^3))/3 + (2*(a + b*x^3)^(3/2))/9 - (2*a^(3/2)*atanh(sqrt(a + b*x^3)/sqrt(a)))/3]
    @test_int [(a + b*x^3)^(3/2)/x^4, x, 5, b*sqrt(a + b*x^3) - (a + b*x^3)^(3/2)/(3*x^3) - sqrt(a)*b*atanh(sqrt(a + b*x^3)/sqrt(a))]
    @test_int [(a + b*x^3)^(3/2)/x^7, x, 5, -(b*sqrt(a + b*x^3))/(4*x^3) - (a + b*x^3)^(3/2)/(6*x^6) - (b^2*atanh(sqrt(a + b*x^3)/sqrt(a)))/(4*sqrt(a))]

    @test_int [x^6*(a + b*x^3)^(3/2), x, 5, (-432*a^3*x*sqrt(a + b*x^3))/(21505*b^2) + (54*a^2*x^4*sqrt(a + b*x^3))/(4301*b) + (18*a*x^7*sqrt(a + b*x^3))/391 + (2*x^7*(a + b*x^3)^(3/2))/23 + (288*3^(3/4)*sqrt(2+sqrt(3))*a^4*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(21505*b^(7/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [x^3*(a + b*x^3)^(3/2), x, 4, (54*a^2*x*sqrt(a + b*x^3))/(935*b) + (18*a*x^4*sqrt(a + b*x^3))/187 + (2*x^4*(a + b*x^3)^(3/2))/17 - (36*3^(3/4)*sqrt(2+sqrt(3))*a^3*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(935*b^(4/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [x^0*(a + b*x^3)^(3/2), x, 3, (18*a*x*sqrt(a + b*x^3))/55 + (2*x*(a + b*x^3)^(3/2))/11 + (18*3^(3/4)*sqrt(2+sqrt(3))*a^2*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(55*b^(1/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(a + b*x^3)^(3/2)/x^3, x, 3, (9*b*x*sqrt(a + b*x^3))/10 - (a + b*x^3)^(3/2)/(2*x^2) + (9*3^(3/4)*sqrt(2+sqrt(3))*a*b^(2/3)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(10*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(a + b*x^3)^(3/2)/x^6, x, 3, (-9*b*sqrt(a + b*x^3))/(20*x^2) - (a + b*x^3)^(3/2)/(5*x^5) + (9*3^(3/4)*sqrt(2+sqrt(3))*b^(5/3)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(20*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]

    @test_int [x^7*(a + b*x^3)^(3/2), x, 7, (-108*a^3*x^2*sqrt(a + b*x^3))/(8645*b^2) + (54*a^2*x^5*sqrt(a + b*x^3))/(6175*b) + (18*a*x^8*sqrt(a + b*x^3))/475 + (432*a^4*sqrt(a + b*x^3))/(8645*b^(8/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) + (2*x^8*(a + b*x^3)^(3/2))/25 - (216*3^(1/4)*sqrt(2 - sqrt(3))*a^(13/3)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(8645*b^(8/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) + (144*sqrt(2)*3^(3/4)*a^(13/3)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(8645*b^(8/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [x^4*(a + b*x^3)^(3/2), x, 6, (54*a^2*x^2*sqrt(a + b*x^3))/(1729*b) + (18*a*x^5*sqrt(a + b*x^3))/247 - (216*a^3*sqrt(a + b*x^3))/(1729*b^(5/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) + (2*x^5*(a + b*x^3)^(3/2))/19 + (108*3^(1/4)*sqrt(2 - sqrt(3))*a^(10/3)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(1729*b^(5/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) - (72*sqrt(2)*3^(3/4)*a^(10/3)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(1729*b^(5/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [x^1*(a + b*x^3)^(3/2), x, 5, (18*a*x^2*sqrt(a + b*x^3))/91 + (54*a^2*sqrt(a + b*x^3))/(91*b^(2/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) + (2*x^2*(a + b*x^3)^(3/2))/13 - (27*3^(1/4)*sqrt(2 - sqrt(3))*a^(7/3)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(91*b^(2/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) + (18*sqrt(2)*3^(3/4)*a^(7/3)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(91*b^(2/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(a + b*x^3)^(3/2)/x^2, x, 5, (9*b*x^2*sqrt(a + b*x^3))/7 + (27*a*b^(1/3)*sqrt(a + b*x^3))/(7*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) - (a + b*x^3)^(3/2)/x - (27*3^(1/4)*sqrt(2 - sqrt(3))*a^(4/3)*b^(1/3)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(14*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) + (9*sqrt(2)*3^(3/4)*a^(4/3)*b^(1/3)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(7*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(a + b*x^3)^(3/2)/x^5, x, 5, (-9*b*sqrt(a + b*x^3))/(8*x) + (27*b^(4/3)*sqrt(a + b*x^3))/(8*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) - (a + b*x^3)^(3/2)/(4*x^4) - (27*3^(1/4)*sqrt(2 - sqrt(3))*a^(1/3)*b^(4/3)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(16*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) + (9*3^(3/4)*a^(1/3)*b^(4/3)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(4*sqrt(2)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [x^11/sqrt(a + b*x^3), x, 3, (-2*a^3*sqrt(a + b*x^3))/(3*b^4) + (2*a^2*(a + b*x^3)^(3/2))/(3*b^4) - (2*a*(a + b*x^3)^(5/2))/(5*b^4) + (2*(a + b*x^3)^(7/2))/(21*b^4)]
    @test_int [x^8/sqrt(a + b*x^3), x, 3, (2*a^2*sqrt(a + b*x^3))/(3*b^3) - (4*a*(a + b*x^3)^(3/2))/(9*b^3) + (2*(a + b*x^3)^(5/2))/(15*b^3)]
    @test_int [x^5/sqrt(a + b*x^3), x, 3, (-2*a*sqrt(a + b*x^3))/(3*b^2) + (2*(a + b*x^3)^(3/2))/(9*b^2)]
    @test_int [x^2/sqrt(a + b*x^3), x, 1, (2*sqrt(a + b*x^3))/(3*b)]
    @test_int [1/(x^1*sqrt(a + b*x^3)), x, 3, (-2*atanh(sqrt(a + b*x^3)/sqrt(a)))/(3*sqrt(a))]
    @test_int [1/(x^4*sqrt(a + b*x^3)), x, 4, -sqrt(a + b*x^3)/(3*a*x^3) + (b*atanh(sqrt(a + b*x^3)/sqrt(a)))/(3*a^(3/2))]
    @test_int [1/(x^7*sqrt(a + b*x^3)), x, 5, -sqrt(a + b*x^3)/(6*a*x^6) + (b*sqrt(a + b*x^3))/(4*a^2*x^3) - (b^2*atanh(sqrt(a + b*x^3)/sqrt(a)))/(4*a^(5/2))]

    @test_int [x^6/sqrt(a + b*x^3), x, 3, (-16*a*x*sqrt(a + b*x^3))/(55*b^2) + (2*x^4*sqrt(a + b*x^3))/(11*b) + (32*sqrt(2+sqrt(3))/3^(1/4)*a^2*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(55*b^(7/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [x^3/sqrt(a + b*x^3), x, 2, (2*x*sqrt(a + b*x^3))/(5*b) - (4*sqrt(2+sqrt(3))/3^(1/4)*a*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(5*b^(4/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [x^0/sqrt(a + b*x^3), x, 1, (2*sqrt(2 + sqrt(3))*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(3^(1/4)*b^(1/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [1/(x^3*sqrt(a + b*x^3)), x, 2, -sqrt(a + b*x^3)/(2*a*x^2) - (sqrt(2+sqrt(3))/3^(1/4)*b^(2/3)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(2*a*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [1/(x^6*sqrt(a + b*x^3)), x, 3, -sqrt(a + b*x^3)/(5*a*x^5) + (7*b*sqrt(a + b*x^3))/(20*a^2*x^2) + (7*sqrt(2+sqrt(3))/3^(1/4)*b^(5/3)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(20*a^2*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]

    @test_int [x^7/sqrt(a + b*x^3), x, 5, (-20*a*x^2*sqrt(a + b*x^3))/(91*b^2) + (2*x^5*sqrt(a + b*x^3))/(13*b) + (80*a^2*sqrt(a + b*x^3))/(91*b^(8/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) - (40*3^(1/4)*sqrt(2 - sqrt(3))*a^(7/3)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(91*b^(8/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) + (80*sqrt(2)*a^(7/3)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(91*3^(1/4)*b^(8/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [x^4/sqrt(a + b*x^3), x, 4, (2*x^2*sqrt(a + b*x^3))/(7*b) - (8*a*sqrt(a + b*x^3))/(7*b^(5/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) + (4*3^(1/4)*sqrt(2 - sqrt(3))*a^(4/3)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(7*b^(5/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) - (8*sqrt(2)*a^(4/3)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(7*3^(1/4)*b^(5/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [x^1/sqrt(a + b*x^3), x, 3, (2*sqrt(a + b*x^3))/(b^(2/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) - (3^(1/4)*sqrt(2 - sqrt(3))*a^(1/3)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(b^(2/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) + (2*sqrt(2)*a^(1/3)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(3^(1/4)*b^(2/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [1/(x^2*sqrt(a + b*x^3)), x, 4, -(sqrt(a + b*x^3)/(a*x)) + (b^(1/3)*sqrt(a + b*x^3))/(a*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) - (3^(1/4)*sqrt(2 - sqrt(3))*b^(1/3)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(2*a^(2/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) + (sqrt(2)*b^(1/3)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(3^(1/4)*a^(2/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [1/(x^5*sqrt(a + b*x^3)), x, 5, -sqrt(a + b*x^3)/(4*a*x^4) + (5*b*sqrt(a + b*x^3))/(8*a^2*x) - (5*b^(4/3)*sqrt(a + b*x^3))/(8*a^2*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) + (5*3^(1/4)*sqrt(2 - sqrt(3))*b^(4/3)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(16*a^(5/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) - (5*b^(4/3)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(4*sqrt(2)*3^(1/4)*a^(5/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]

    @test_int [x^11/(a + b*x^3)^(3/2), x, 3, (2*a^3)/(3*b^4*sqrt(a + b*x^3)) + (2*a^2*sqrt(a + b*x^3))/b^4 - (2*a*(a + b*x^3)^(3/2))/(3*b^4) + (2*(a + b*x^3)^(5/2))/(15*b^4)]
    @test_int [x^8/(a + b*x^3)^(3/2), x, 3, (-2*a^2)/(3*b^3*sqrt(a + b*x^3)) - (4*a*sqrt(a + b*x^3))/(3*b^3) + (2*(a + b*x^3)^(3/2))/(9*b^3)]
    @test_int [x^5/(a + b*x^3)^(3/2), x, 3, (2*a)/(3*b^2*sqrt(a + b*x^3)) + (2*sqrt(a + b*x^3))/(3*b^2)]
    @test_int [x^2/(a + b*x^3)^(3/2), x, 1, -2/(3*b*sqrt(a + b*x^3))]
    @test_int [1/(x^1*(a + b*x^3)^(3/2)), x, 4, 2/(3*a*sqrt(a + b*x^3)) - (2*atanh(sqrt(a + b*x^3)/sqrt(a)))/(3*a^(3/2))]
    @test_int [1/(x^4*(a + b*x^3)^(3/2)), x, 5, -(b/(a^2*sqrt(a + b*x^3))) - 1/(3*a*x^3*sqrt(a + b*x^3)) + (b*atanh(sqrt(a + b*x^3)/sqrt(a)))/a^(5/2)]
    @test_int [1/(x^7*(a + b*x^3)^(3/2)), x, 6, (5*b^2)/(4*a^3*sqrt(a + b*x^3)) - 1/(6*a*x^6*sqrt(a + b*x^3)) + (5*b)/(12*a^2*x^3*sqrt(a + b*x^3)) - (5*b^2*atanh(sqrt(a + b*x^3)/sqrt(a)))/(4*a^(7/2))]

    @test_int [x^6/(a + b*x^3)^(3/2), x, 3, (-2*x^4)/(3*b*sqrt(a + b*x^3)) + (16*x*sqrt(a + b*x^3))/(15*b^2) - (32*sqrt(2+sqrt(3))/3^(1/4)*a*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(15*b^(7/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [x^3/(a + b*x^3)^(3/2), x, 2, (-2*x)/(3*b*sqrt(a + b*x^3)) + (4*sqrt(2+sqrt(3))/3^(1/4)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(3*b^(4/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [x^0/(a + b*x^3)^(3/2), x, 2, (2*x)/(3*a*sqrt(a + b*x^3)) + (2*sqrt(2 + sqrt(3))*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(3*3^(1/4)*a*b^(1/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [1/(x^3*(a + b*x^3)^(3/2)), x, 3, 2/(3*a*x^2*sqrt(a + b*x^3)) - (7*sqrt(a + b*x^3))/(6*a^2*x^2) - (7*sqrt(2+sqrt(3))/3^(1/4)*b^(2/3)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(6*a^2*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [1/(x^6*(a + b*x^3)^(3/2)), x, 4, 2/(3*a*x^5*sqrt(a + b*x^3)) - (13*sqrt(a + b*x^3))/(15*a^2*x^5) + (91*b*sqrt(a + b*x^3))/(60*a^3*x^2) + (91*sqrt(2+sqrt(3))/3^(1/4)*b^(5/3)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(60*a^3*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]

    @test_int [x^7/(a + b*x^3)^(3/2), x, 5, (-2*x^5)/(3*b*sqrt(a + b*x^3)) + (20*x^2*sqrt(a + b*x^3))/(21*b^2) - (80*a*sqrt(a + b*x^3))/(21*b^(8/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) + (40*3^(1/4)*sqrt(2 - sqrt(3))*a^(4/3)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(21*b^(8/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) - (80*sqrt(2)*a^(4/3)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(21*3^(1/4)*b^(8/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [x^4/(a + b*x^3)^(3/2), x, 4, (-2*x^2)/(3*b*sqrt(a + b*x^3)) + (8*sqrt(a + b*x^3))/(3*b^(5/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) - (4*3^(1/4)*sqrt(2 - sqrt(3))*a^(1/3)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(3*b^(5/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) + (8*sqrt(2)*a^(1/3)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(3*3^(1/4)*b^(5/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [x^1/(a + b*x^3)^(3/2), x, 4, (2*x^2)/(3*a*sqrt(a + b*x^3)) - (2*sqrt(a + b*x^3))/(3*a*b^(2/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) + (3^(1/4)*sqrt(2 - sqrt(3))*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(3*a^(2/3)*b^(2/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) - (2*sqrt(2)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(3*3^(1/4)*a^(2/3)*b^(2/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [1/(x^2*(a + b*x^3)^(3/2)), x, 5, 2/(3*a*x*sqrt(a + b*x^3)) - (5*sqrt(a + b*x^3))/(3*a^2*x) + (5*b^(1/3)*sqrt(a + b*x^3))/(3*a^2*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) - (5*3^(1/4)*sqrt(2 - sqrt(3))*b^(1/3)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(6*a^(5/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) + (5*sqrt(2)*b^(1/3)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(3*3^(1/4)*a^(5/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [1/(x^5*(a + b*x^3)^(3/2)), x, 6, 2/(3*a*x^4*sqrt(a + b*x^3)) - (11*sqrt(a + b*x^3))/(12*a^2*x^4) + (55*b*sqrt(a + b*x^3))/(24*a^3*x) - (55*b^(4/3)*sqrt(a + b*x^3))/(24*a^3*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) + (55*3^(1/4)*sqrt(2 - sqrt(3))*b^(4/3)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(48*a^(8/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) - (55*b^(4/3)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(12*sqrt(2)*3^(1/4)*a^(8/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]

    @test_int [x^11/sqrt(1 + x^3), x, 3, (-(2/3))*sqrt(1 + x^3) + (2/3)*(1 + x^3)^(3/2) - (2/5)*(1 + x^3)^(5/2) + (2/21)*(1 + x^3)^(7/2)]
    @test_int [x^8/sqrt(1 + x^3), x, 3, (2*sqrt(1 + x^3))/3 - (4/9)*(1 + x^3)^(3/2) + (2/15)*(1 + x^3)^(5/2)]
    @test_int [x^5/sqrt(1 + x^3), x, 3, (-(2/3))*sqrt(1 + x^3) + (2/9)*(1 + x^3)^(3/2)]
    @test_int [x^2/sqrt(1 + x^3), x, 1, (2*sqrt(1 + x^3))/3]
    @test_int [1/(x^1*sqrt(1 + x^3)), x, 3, (-(2/3))*atanh(sqrt(1 + x^3))]
    @test_int [1/(x^4*sqrt(1 + x^3)), x, 4, -(sqrt(1 + x^3)/(3*x^3)) + (1/3)*atanh(sqrt(1 + x^3))]
    @test_int [1/(x^7*sqrt(1 + x^3)), x, 5, -(sqrt(1 + x^3)/(6*x^6)) + sqrt(1 + x^3)/(4*x^3) - (1/4)*atanh(sqrt(1 + x^3))]
    @test_int [1/(x^10*sqrt(1 + x^3)), x, 6, -(sqrt(1 + x^3)/(9*x^9)) + (5*sqrt(1 + x^3))/(36*x^6) - (5*sqrt(1 + x^3))/(24*x^3) + (5/24)*atanh(sqrt(1 + x^3))]

    @test_int [x^6/sqrt(1 + x^3), x, 3, (-(16/55))*x*sqrt(1 + x^3) + (2/11)*x^4*sqrt(1 + x^3) + (32*sqrt(2+sqrt(3))/3^(1/4)*(1 + x)*sqrt((1 - x + x^2)/(1 + sqrt(3) + x)^2)*Elliptic.F(asin((1 - sqrt(3) + x)/(1 + sqrt(3) + x)), -7 - 4*sqrt(3)))/(55*sqrt((1 + x)/(1 + sqrt(3) + x)^2)*sqrt(1 + x^3))]
    @test_int [x^3/sqrt(1 + x^3), x, 2, (2/5)*x*sqrt(1 + x^3) - (4*sqrt(2+sqrt(3))/3^(1/4)*(1 + x)*sqrt((1 - x + x^2)/(1 + sqrt(3) + x)^2)*Elliptic.F(asin((1 - sqrt(3) + x)/(1 + sqrt(3) + x)), -7 - 4*sqrt(3)))/(5*sqrt((1 + x)/(1 + sqrt(3) + x)^2)*sqrt(1 + x^3))]
    @test_int [x^0/sqrt(1 + x^3), x, 1, (2*sqrt(2+sqrt(3))/3^(1/4)*(1 + x)*sqrt((1 - x + x^2)/(1 + sqrt(3) + x)^2)*Elliptic.F(asin((1 - sqrt(3) + x)/(1 + sqrt(3) + x)), -7 - 4*sqrt(3)))/(sqrt((1 + x)/(1 + sqrt(3) + x)^2)*sqrt(1 + x^3))]
    @test_int [1/(x^3*sqrt(1 + x^3)), x, 2, -(sqrt(1 + x^3)/(2*x^2)) - (sqrt(2+sqrt(3))/3^(1/4)*(1 + x)*sqrt((1 - x + x^2)/(1 + sqrt(3) + x)^2)*Elliptic.F(asin((1 - sqrt(3) + x)/(1 + sqrt(3) + x)), -7 - 4*sqrt(3)))/(2*sqrt((1 + x)/(1 + sqrt(3) + x)^2)*sqrt(1 + x^3))]
    @test_int [1/(x^6*sqrt(1 + x^3)), x, 3, -(sqrt(1 + x^3)/(5*x^5)) + (7*sqrt(1 + x^3))/(20*x^2) + (7*sqrt(2+sqrt(3))/3^(1/4)*(1 + x)*sqrt((1 - x + x^2)/(1 + sqrt(3) + x)^2)*Elliptic.F(asin((1 - sqrt(3) + x)/(1 + sqrt(3) + x)), -7 - 4*sqrt(3)))/(20*sqrt((1 + x)/(1 + sqrt(3) + x)^2)*sqrt(1 + x^3))]

    @test_int [x^7/sqrt(1 + x^3), x, 5, (-(20/91))*x^2*sqrt(1 + x^3) + (2/13)*x^5*sqrt(1 + x^3) + (80*sqrt(1 + x^3))/(91*(1 + sqrt(3) + x)) - (40*3^(1/4)*sqrt(2 - sqrt(3))*(1 + x)*sqrt((1 - x + x^2)/(1 + sqrt(3) + x)^2)*Elliptic.E(asin((1 - sqrt(3) + x)/(1 + sqrt(3) + x)), -7 - 4*sqrt(3)))/(91*sqrt((1 + x)/(1 + sqrt(3) + x)^2)*sqrt(1 + x^3)) + (80*sqrt(2)*(1 + x)*sqrt((1 - x + x^2)/(1 + sqrt(3) + x)^2)*Elliptic.F(asin((1 - sqrt(3) + x)/(1 + sqrt(3) + x)), -7 - 4*sqrt(3)))/(91*3^(1/4)*sqrt((1 + x)/(1 + sqrt(3) + x)^2)*sqrt(1 + x^3))]
    @test_int [x^4/sqrt(1 + x^3), x, 4, (2/7)*x^2*sqrt(1 + x^3) - (8*sqrt(1 + x^3))/(7*(1 + sqrt(3) + x)) + (4*3^(1/4)*sqrt(2 - sqrt(3))*(1 + x)*sqrt((1 - x + x^2)/(1 + sqrt(3) + x)^2)*Elliptic.E(asin((1 - sqrt(3) + x)/(1 + sqrt(3) + x)), -7 - 4*sqrt(3)))/(7*sqrt((1 + x)/(1 + sqrt(3) + x)^2)*sqrt(1 + x^3)) - (8*sqrt(2)*(1 + x)*sqrt((1 - x + x^2)/(1 + sqrt(3) + x)^2)*Elliptic.F(asin((1 - sqrt(3) + x)/(1 + sqrt(3) + x)), -7 - 4*sqrt(3)))/(7*3^(1/4)*sqrt((1 + x)/(1 + sqrt(3) + x)^2)*sqrt(1 + x^3))]
    @test_int [x^1/sqrt(1 + x^3), x, 3, (2*sqrt(1 + x^3))/(1 + sqrt(3) + x) - (3^(1/4)*sqrt(2 - sqrt(3))*(1 + x)*sqrt((1 - x + x^2)/(1 + sqrt(3) + x)^2)*Elliptic.E(asin((1 - sqrt(3) + x)/(1 + sqrt(3) + x)), -7 - 4*sqrt(3)))/(sqrt((1 + x)/(1 + sqrt(3) + x)^2)*sqrt(1 + x^3)) + (2*sqrt(2)*(1 + x)*sqrt((1 - x + x^2)/(1 + sqrt(3) + x)^2)*Elliptic.F(asin((1 - sqrt(3) + x)/(1 + sqrt(3) + x)), -7 - 4*sqrt(3)))/(3^(1/4)*sqrt((1 + x)/(1 + sqrt(3) + x)^2)*sqrt(1 + x^3))]
    @test_int [1/(x^2*sqrt(1 + x^3)), x, 4, -(sqrt(1 + x^3)/x) + sqrt(1 + x^3)/(1 + sqrt(3) + x) - (3^(1/4)*sqrt(2 - sqrt(3))*(1 + x)*sqrt((1 - x + x^2)/(1 + sqrt(3) + x)^2)*Elliptic.E(asin((1 - sqrt(3) + x)/(1 + sqrt(3) + x)), -7 - 4*sqrt(3)))/(2*sqrt((1 + x)/(1 + sqrt(3) + x)^2)*sqrt(1 + x^3)) + (sqrt(2)*(1 + x)*sqrt((1 - x + x^2)/(1 + sqrt(3) + x)^2)*Elliptic.F(asin((1 - sqrt(3) + x)/(1 + sqrt(3) + x)), -7 - 4*sqrt(3)))/(3^(1/4)*sqrt((1 + x)/(1 + sqrt(3) + x)^2)*sqrt(1 + x^3))]
    @test_int [1/(x^5*sqrt(1 + x^3)), x, 5, -(sqrt(1 + x^3)/(4*x^4)) + (5*sqrt(1 + x^3))/(8*x) - (5*sqrt(1 + x^3))/(8*(1 + sqrt(3) + x)) + (5*3^(1/4)*sqrt(2 - sqrt(3))*(1 + x)*sqrt((1 - x + x^2)/(1 + sqrt(3) + x)^2)*Elliptic.E(asin((1 - sqrt(3) + x)/(1 + sqrt(3) + x)), -7 - 4*sqrt(3)))/(16*sqrt((1 + x)/(1 + sqrt(3) + x)^2)*sqrt(1 + x^3)) - (5*(1 + x)*sqrt((1 - x + x^2)/(1 + sqrt(3) + x)^2)*Elliptic.F(asin((1 - sqrt(3) + x)/(1 + sqrt(3) + x)), -7 - 4*sqrt(3)))/(4*sqrt(2)*3^(1/4)*sqrt((1 + x)/(1 + sqrt(3) + x)^2)*sqrt(1 + x^3))]

    @test_int [x^11/sqrt(1 - x^3), x, 3, (-(2/3))*sqrt(1 - x^3) + (2/3)*(1 - x^3)^(3/2) - (2/5)*(1 - x^3)^(5/2) + (2/21)*(1 - x^3)^(7/2)]
    @test_int [x^8/sqrt(1 - x^3), x, 3, (-(2/3))*sqrt(1 - x^3) + (4/9)*(1 - x^3)^(3/2) - (2/15)*(1 - x^3)^(5/2)]
    @test_int [x^5/sqrt(1 - x^3), x, 3, (-(2/3))*sqrt(1 - x^3) + (2/9)*(1 - x^3)^(3/2)]
    @test_int [x^2/sqrt(1 - x^3), x, 1, (-(2/3))*sqrt(1 - x^3)]
    @test_int [1/(x^1*sqrt(1 - x^3)), x, 3, (-(2/3))*atanh(sqrt(1 - x^3))]
    @test_int [1/(x^4*sqrt(1 - x^3)), x, 4, -(sqrt(1 - x^3)/(3*x^3)) - (1/3)*atanh(sqrt(1 - x^3))]
    @test_int [1/(x^7*sqrt(1 - x^3)), x, 5, -(sqrt(1 - x^3)/(6*x^6)) - sqrt(1 - x^3)/(4*x^3) - (1/4)*atanh(sqrt(1 - x^3))]
    @test_int [1/(x^10*sqrt(1 - x^3)), x, 6, -(sqrt(1 - x^3)/(9*x^9)) - (5*sqrt(1 - x^3))/(36*x^6) - (5*sqrt(1 - x^3))/(24*x^3) - (5/24)*atanh(sqrt(1 - x^3))]

    @test_int [x^6/sqrt(1 - x^3), x, 3, (-(16/55))*x*sqrt(1 - x^3) - (2/11)*x^4*sqrt(1 - x^3) - (32*sqrt(2+sqrt(3))/3^(1/4)*(1 - x)*sqrt((1 + x + x^2)/(1 + sqrt(3) - x)^2)*Elliptic.F(asin((1 - sqrt(3) - x)/(1 + sqrt(3) - x)), -7 - 4*sqrt(3)))/(55*sqrt((1 - x)/(1 + sqrt(3) - x)^2)*sqrt(1 - x^3))]
    @test_int [x^3/sqrt(1 - x^3), x, 2, (-(2/5))*x*sqrt(1 - x^3) - (4*sqrt(2+sqrt(3))/3^(1/4)*(1 - x)*sqrt((1 + x + x^2)/(1 + sqrt(3) - x)^2)*Elliptic.F(asin((1 - sqrt(3) - x)/(1 + sqrt(3) - x)), -7 - 4*sqrt(3)))/(5*sqrt((1 - x)/(1 + sqrt(3) - x)^2)*sqrt(1 - x^3))]
    @test_int [x^0/sqrt(1 - x^3), x, 1, -((2*sqrt(2+sqrt(3))/3^(1/4)*(1 - x)*sqrt((1 + x + x^2)/(1 + sqrt(3) - x)^2)*Elliptic.F(asin((1 - sqrt(3) - x)/(1 + sqrt(3) - x)), -7 - 4*sqrt(3)))/(sqrt((1 - x)/(1 + sqrt(3) - x)^2)*sqrt(1 - x^3)))]
    @test_int [1/(x^3*sqrt(1 - x^3)), x, 2, -(sqrt(1 - x^3)/(2*x^2)) - (sqrt(2+sqrt(3))/3^(1/4)*(1 - x)*sqrt((1 + x + x^2)/(1 + sqrt(3) - x)^2)*Elliptic.F(asin((1 - sqrt(3) - x)/(1 + sqrt(3) - x)), -7 - 4*sqrt(3)))/(2*sqrt((1 - x)/(1 + sqrt(3) - x)^2)*sqrt(1 - x^3))]
    @test_int [1/(x^6*sqrt(1 - x^3)), x, 3, -(sqrt(1 - x^3)/(5*x^5)) - (7*sqrt(1 - x^3))/(20*x^2) - (7*sqrt(2+sqrt(3))/3^(1/4)*(1 - x)*sqrt((1 + x + x^2)/(1 + sqrt(3) - x)^2)*Elliptic.F(asin((1 - sqrt(3) - x)/(1 + sqrt(3) - x)), -7 - 4*sqrt(3)))/(20*sqrt((1 - x)/(1 + sqrt(3) - x)^2)*sqrt(1 - x^3))]

    @test_int [x^7/sqrt(1 - x^3), x, 5, (80*sqrt(1 - x^3))/(91*(1 + sqrt(3) - x)) - (20/91)*x^2*sqrt(1 - x^3) - (2/13)*x^5*sqrt(1 - x^3) - (40*3^(1/4)*sqrt(2 - sqrt(3))*(1 - x)*sqrt((1 + x + x^2)/(1 + sqrt(3) - x)^2)*Elliptic.E(asin((1 - sqrt(3) - x)/(1 + sqrt(3) - x)), -7 - 4*sqrt(3)))/(91*sqrt((1 - x)/(1 + sqrt(3) - x)^2)*sqrt(1 - x^3)) + (80*sqrt(2)*(1 - x)*sqrt((1 + x + x^2)/(1 + sqrt(3) - x)^2)*Elliptic.F(asin((1 - sqrt(3) - x)/(1 + sqrt(3) - x)), -7 - 4*sqrt(3)))/(91*3^(1/4)*sqrt((1 - x)/(1 + sqrt(3) - x)^2)*sqrt(1 - x^3))]
    @test_int [x^4/sqrt(1 - x^3), x, 4, (8*sqrt(1 - x^3))/(7*(1 + sqrt(3) - x)) - (2/7)*x^2*sqrt(1 - x^3) - (4*3^(1/4)*sqrt(2 - sqrt(3))*(1 - x)*sqrt((1 + x + x^2)/(1 + sqrt(3) - x)^2)*Elliptic.E(asin((1 - sqrt(3) - x)/(1 + sqrt(3) - x)), -7 - 4*sqrt(3)))/(7*sqrt((1 - x)/(1 + sqrt(3) - x)^2)*sqrt(1 - x^3)) + (8*sqrt(2)*(1 - x)*sqrt((1 + x + x^2)/(1 + sqrt(3) - x)^2)*Elliptic.F(asin((1 - sqrt(3) - x)/(1 + sqrt(3) - x)), -7 - 4*sqrt(3)))/(7*3^(1/4)*sqrt((1 - x)/(1 + sqrt(3) - x)^2)*sqrt(1 - x^3))]
    @test_int [x^1/sqrt(1 - x^3), x, 3, (2*sqrt(1 - x^3))/(1 + sqrt(3) - x) - (3^(1/4)*sqrt(2 - sqrt(3))*(1 - x)*sqrt((1 + x + x^2)/(1 + sqrt(3) - x)^2)*Elliptic.E(asin((1 - sqrt(3) - x)/(1 + sqrt(3) - x)), -7 - 4*sqrt(3)))/(sqrt((1 - x)/(1 + sqrt(3) - x)^2)*sqrt(1 - x^3)) + (2*sqrt(2)*(1 - x)*sqrt((1 + x + x^2)/(1 + sqrt(3) - x)^2)*Elliptic.F(asin((1 - sqrt(3) - x)/(1 + sqrt(3) - x)), -7 - 4*sqrt(3)))/(3^(1/4)*sqrt((1 - x)/(1 + sqrt(3) - x)^2)*sqrt(1 - x^3))]
    @test_int [1/(x^2*sqrt(1 - x^3)), x, 4, -(sqrt(1 - x^3)/(1 + sqrt(3) - x)) - sqrt(1 - x^3)/x + (3^(1/4)*sqrt(2 - sqrt(3))*(1 - x)*sqrt((1 + x + x^2)/(1 + sqrt(3) - x)^2)*Elliptic.E(asin((1 - sqrt(3) - x)/(1 + sqrt(3) - x)), -7 - 4*sqrt(3)))/(2*sqrt((1 - x)/(1 + sqrt(3) - x)^2)*sqrt(1 - x^3)) - (sqrt(2)*(1 - x)*sqrt((1 + x + x^2)/(1 + sqrt(3) - x)^2)*Elliptic.F(asin((1 - sqrt(3) - x)/(1 + sqrt(3) - x)), -7 - 4*sqrt(3)))/(3^(1/4)*sqrt((1 - x)/(1 + sqrt(3) - x)^2)*sqrt(1 - x^3))]
    @test_int [1/(x^5*sqrt(1 - x^3)), x, 5, -((5*sqrt(1 - x^3))/(8*(1 + sqrt(3) - x))) - sqrt(1 - x^3)/(4*x^4) - (5*sqrt(1 - x^3))/(8*x) + (5*3^(1/4)*sqrt(2 - sqrt(3))*(1 - x)*sqrt((1 + x + x^2)/(1 + sqrt(3) - x)^2)*Elliptic.E(asin((1 - sqrt(3) - x)/(1 + sqrt(3) - x)), -7 - 4*sqrt(3)))/(16*sqrt((1 - x)/(1 + sqrt(3) - x)^2)*sqrt(1 - x^3)) - (5*(1 - x)*sqrt((1 + x + x^2)/(1 + sqrt(3) - x)^2)*Elliptic.F(asin((1 - sqrt(3) - x)/(1 + sqrt(3) - x)), -7 - 4*sqrt(3)))/(4*sqrt(2)*3^(1/4)*sqrt((1 - x)/(1 + sqrt(3) - x)^2)*sqrt(1 - x^3))]

    @test_int [x^11/sqrt(-1 + x^3), x, 3, (2/3)*sqrt(-1 + x^3) + (2/3)*(-1 + x^3)^(3/2) + (2/5)*(-1 + x^3)^(5/2) + (2/21)*(-1 + x^3)^(7/2)]
    @test_int [x^8/sqrt(-1 + x^3), x, 3, (2/3)*sqrt(-1 + x^3) + (4/9)*(-1 + x^3)^(3/2) + (2/15)*(-1 + x^3)^(5/2)]
    @test_int [x^5/sqrt(-1 + x^3), x, 3, (2/3)*sqrt(-1 + x^3) + (2/9)*(-1 + x^3)^(3/2)]
    @test_int [x^2/sqrt(-1 + x^3), x, 1, (2/3)*sqrt(-1 + x^3)]
    @test_int [1/(x^1*sqrt(-1 + x^3)), x, 3, (2/3)*atan(sqrt(-1 + x^3))]
    @test_int [1/(x^4*sqrt(-1 + x^3)), x, 4, sqrt(-1 + x^3)/(3*x^3) + (1/3)*atan(sqrt(-1 + x^3))]
    @test_int [1/(x^7*sqrt(-1 + x^3)), x, 5, sqrt(-1 + x^3)/(6*x^6) + sqrt(-1 + x^3)/(4*x^3) + (1/4)*atan(sqrt(-1 + x^3))]
    @test_int [1/(x^10*sqrt(-1 + x^3)), x, 6, sqrt(-1 + x^3)/(9*x^9) + (5*sqrt(-1 + x^3))/(36*x^6) + (5*sqrt(-1 + x^3))/(24*x^3) + (5/24)*atan(sqrt(-1 + x^3))]

    @test_int [x^6/sqrt(-1 + x^3), x, 3, (16/55)*x*sqrt(-1 + x^3) + (2/11)*x^4*sqrt(-1 + x^3) - (32*sqrt(2 - sqrt(3))*(1 - x)*sqrt((1 + x + x^2)/(1 - sqrt(3) - x)^2)*Elliptic.F(asin((1 + sqrt(3) - x)/(1 - sqrt(3) - x)), -7 + 4*sqrt(3)))/(55*3^(1/4)*sqrt(-((1 - x)/(1 - sqrt(3) - x)^2))*sqrt(-1 + x^3))]
    @test_int [x^3/sqrt(-1 + x^3), x, 2, (2/5)*x*sqrt(-1 + x^3) - (4*sqrt(2 - sqrt(3))*(1 - x)*sqrt((1 + x + x^2)/(1 - sqrt(3) - x)^2)*Elliptic.F(asin((1 + sqrt(3) - x)/(1 - sqrt(3) - x)), -7 + 4*sqrt(3)))/(5*3^(1/4)*sqrt(-((1 - x)/(1 - sqrt(3) - x)^2))*sqrt(-1 + x^3))]
    @test_int [x^0/sqrt(-1 + x^3), x, 1, -((2*sqrt(2 - sqrt(3))*(1 - x)*sqrt((1 + x + x^2)/(1 - sqrt(3) - x)^2)*Elliptic.F(asin((1 + sqrt(3) - x)/(1 - sqrt(3) - x)), -7 + 4*sqrt(3)))/(3^(1/4)*sqrt(-((1 - x)/(1 - sqrt(3) - x)^2))*sqrt(-1 + x^3)))]
    @test_int [1/(x^3*sqrt(-1 + x^3)), x, 2, sqrt(-1 + x^3)/(2*x^2) - (sqrt(2 - sqrt(3))*(1 - x)*sqrt((1 + x + x^2)/(1 - sqrt(3) - x)^2)*Elliptic.F(asin((1 + sqrt(3) - x)/(1 - sqrt(3) - x)), -7 + 4*sqrt(3)))/(2*3^(1/4)*sqrt(-((1 - x)/(1 - sqrt(3) - x)^2))*sqrt(-1 + x^3))]
    @test_int [1/(x^6*sqrt(-1 + x^3)), x, 3, sqrt(-1 + x^3)/(5*x^5) + (7*sqrt(-1 + x^3))/(20*x^2) - (7*sqrt(2 - sqrt(3))*(1 - x)*sqrt((1 + x + x^2)/(1 - sqrt(3) - x)^2)*Elliptic.F(asin((1 + sqrt(3) - x)/(1 - sqrt(3) - x)), -7 + 4*sqrt(3)))/(20*3^(1/4)*sqrt(-((1 - x)/(1 - sqrt(3) - x)^2))*sqrt(-1 + x^3))]

    @test_int [x^7/sqrt(-1 + x^3), x, 5, -((80*sqrt(-1 + x^3))/(91*(1 - sqrt(3) - x))) + (20/91)*x^2*sqrt(-1 + x^3) + (2/13)*x^5*sqrt(-1 + x^3) + (40*3^(1/4)*sqrt(2 + sqrt(3))*(1 - x)*sqrt((1 + x + x^2)/(1 - sqrt(3) - x)^2)*Elliptic.E(asin((1 + sqrt(3) - x)/(1 - sqrt(3) - x)), -7 + 4*sqrt(3)))/(91*sqrt(-((1 - x)/(1 - sqrt(3) - x)^2))*sqrt(-1 + x^3)) - (80*sqrt(2)*(1 - x)*sqrt((1 + x + x^2)/(1 - sqrt(3) - x)^2)*Elliptic.F(asin((1 + sqrt(3) - x)/(1 - sqrt(3) - x)), -7 + 4*sqrt(3)))/(91*3^(1/4)*sqrt(-((1 - x)/(1 - sqrt(3) - x)^2))*sqrt(-1 + x^3))]
    @test_int [x^4/sqrt(-1 + x^3), x, 4, -((8*sqrt(-1 + x^3))/(7*(1 - sqrt(3) - x))) + (2/7)*x^2*sqrt(-1 + x^3) + (4*3^(1/4)*sqrt(2 + sqrt(3))*(1 - x)*sqrt((1 + x + x^2)/(1 - sqrt(3) - x)^2)*Elliptic.E(asin((1 + sqrt(3) - x)/(1 - sqrt(3) - x)), -7 + 4*sqrt(3)))/(7*sqrt(-((1 - x)/(1 - sqrt(3) - x)^2))*sqrt(-1 + x^3)) - (8*sqrt(2)*(1 - x)*sqrt((1 + x + x^2)/(1 - sqrt(3) - x)^2)*Elliptic.F(asin((1 + sqrt(3) - x)/(1 - sqrt(3) - x)), -7 + 4*sqrt(3)))/(7*3^(1/4)*sqrt(-((1 - x)/(1 - sqrt(3) - x)^2))*sqrt(-1 + x^3))]
    @test_int [x^1/sqrt(-1 + x^3), x, 3, -((2*sqrt(-1 + x^3))/(1 - sqrt(3) - x)) + (3^(1/4)*sqrt(2 + sqrt(3))*(1 - x)*sqrt((1 + x + x^2)/(1 - sqrt(3) - x)^2)*Elliptic.E(asin((1 + sqrt(3) - x)/(1 - sqrt(3) - x)), -7 + 4*sqrt(3)))/(sqrt(-((1 - x)/(1 - sqrt(3) - x)^2))*sqrt(-1 + x^3)) - (2*sqrt(2)*(1 - x)*sqrt((1 + x + x^2)/(1 - sqrt(3) - x)^2)*Elliptic.F(asin((1 + sqrt(3) - x)/(1 - sqrt(3) - x)), -7 + 4*sqrt(3)))/(3^(1/4)*sqrt(-((1 - x)/(1 - sqrt(3) - x)^2))*sqrt(-1 + x^3))]
    @test_int [1/(x^2*sqrt(-1 + x^3)), x, 4, sqrt(-1 + x^3)/(1 - sqrt(3) - x) + sqrt(-1 + x^3)/x - (3^(1/4)*sqrt(2 + sqrt(3))*(1 - x)*sqrt((1 + x + x^2)/(1 - sqrt(3) - x)^2)*Elliptic.E(asin((1 + sqrt(3) - x)/(1 - sqrt(3) - x)), -7 + 4*sqrt(3)))/(2*sqrt(-((1 - x)/(1 - sqrt(3) - x)^2))*sqrt(-1 + x^3)) + (sqrt(2)*(1 - x)*sqrt((1 + x + x^2)/(1 - sqrt(3) - x)^2)*Elliptic.F(asin((1 + sqrt(3) - x)/(1 - sqrt(3) - x)), -7 + 4*sqrt(3)))/(3^(1/4)*sqrt(-((1 - x)/(1 - sqrt(3) - x)^2))*sqrt(-1 + x^3))]
    @test_int [1/(x^5*sqrt(-1 + x^3)), x, 5, (5*sqrt(-1 + x^3))/(8*(1 - sqrt(3) - x)) + sqrt(-1 + x^3)/(4*x^4) + (5*sqrt(-1 + x^3))/(8*x) - (5*3^(1/4)*sqrt(2 + sqrt(3))*(1 - x)*sqrt((1 + x + x^2)/(1 - sqrt(3) - x)^2)*Elliptic.E(asin((1 + sqrt(3) - x)/(1 - sqrt(3) - x)), -7 + 4*sqrt(3)))/(16*sqrt(-((1 - x)/(1 - sqrt(3) - x)^2))*sqrt(-1 + x^3)) + (5*(1 - x)*sqrt((1 + x + x^2)/(1 - sqrt(3) - x)^2)*Elliptic.F(asin((1 + sqrt(3) - x)/(1 - sqrt(3) - x)), -7 + 4*sqrt(3)))/(4*sqrt(2)*3^(1/4)*sqrt(-((1 - x)/(1 - sqrt(3) - x)^2))*sqrt(-1 + x^3))]

    @test_int [x^11/sqrt(-1 - x^3), x, 3, (2/3)*sqrt(-1 - x^3) + (2/3)*(-1 - x^3)^(3/2) + (2/5)*(-1 - x^3)^(5/2) + (2/21)*(-1 - x^3)^(7/2)]
    @test_int [x^8/sqrt(-1 - x^3), x, 3, (-(2/3))*sqrt(-1 - x^3) - (4/9)*(-1 - x^3)^(3/2) - (2/15)*(-1 - x^3)^(5/2)]
    @test_int [x^5/sqrt(-1 - x^3), x, 3, (2/3)*sqrt(-1 - x^3) + (2/9)*(-1 - x^3)^(3/2)]
    @test_int [x^2/sqrt(-1 - x^3), x, 1, (-(2/3))*sqrt(-1 - x^3)]
    @test_int [1/(x^1*sqrt(-1 - x^3)), x, 3, (2/3)*atan(sqrt(-1 - x^3))]
    @test_int [1/(x^4*sqrt(-1 - x^3)), x, 4, sqrt(-1 - x^3)/(3*x^3) - (1/3)*atan(sqrt(-1 - x^3))]
    @test_int [1/(x^7*sqrt(-1 - x^3)), x, 5, sqrt(-1 - x^3)/(6*x^6) - sqrt(-1 - x^3)/(4*x^3) + (1/4)*atan(sqrt(-1 - x^3))]
    @test_int [1/(x^10*sqrt(-1 - x^3)), x, 6, sqrt(-1 - x^3)/(9*x^9) - (5*sqrt(-1 - x^3))/(36*x^6) + (5*sqrt(-1 - x^3))/(24*x^3) - (5/24)*atan(sqrt(-1 - x^3))]

    @test_int [x^6/sqrt(-1 - x^3), x, 3, (16/55)*x*sqrt(-1 - x^3) - (2/11)*x^4*sqrt(-1 - x^3) + (32*sqrt(2 - sqrt(3))*(1 + x)*sqrt((1 - x + x^2)/(1 - sqrt(3) + x)^2)*Elliptic.F(asin((1 + sqrt(3) + x)/(1 - sqrt(3) + x)), -7 + 4*sqrt(3)))/(55*3^(1/4)*sqrt(-((1 + x)/(1 - sqrt(3) + x)^2))*sqrt(-1 - x^3))]
    @test_int [x^3/sqrt(-1 - x^3), x, 2, (-(2/5))*x*sqrt(-1 - x^3) - (4*sqrt(2 - sqrt(3))*(1 + x)*sqrt((1 - x + x^2)/(1 - sqrt(3) + x)^2)*Elliptic.F(asin((1 + sqrt(3) + x)/(1 - sqrt(3) + x)), -7 + 4*sqrt(3)))/(5*3^(1/4)*sqrt(-((1 + x)/(1 - sqrt(3) + x)^2))*sqrt(-1 - x^3))]
    @test_int [x^0/sqrt(-1 - x^3), x, 1, (2*sqrt(2 - sqrt(3))*(1 + x)*sqrt((1 - x + x^2)/(1 - sqrt(3) + x)^2)*Elliptic.F(asin((1 + sqrt(3) + x)/(1 - sqrt(3) + x)), -7 + 4*sqrt(3)))/(3^(1/4)*sqrt(-((1 + x)/(1 - sqrt(3) + x)^2))*sqrt(-1 - x^3))]
    @test_int [1/(x^3*sqrt(-1 - x^3)), x, 2, sqrt(-1 - x^3)/(2*x^2) - (sqrt(2 - sqrt(3))*(1 + x)*sqrt((1 - x + x^2)/(1 - sqrt(3) + x)^2)*Elliptic.F(asin((1 + sqrt(3) + x)/(1 - sqrt(3) + x)), -7 + 4*sqrt(3)))/(2*3^(1/4)*sqrt(-((1 + x)/(1 - sqrt(3) + x)^2))*sqrt(-1 - x^3))]
    @test_int [1/(x^6*sqrt(-1 - x^3)), x, 3, sqrt(-1 - x^3)/(5*x^5) - (7*sqrt(-1 - x^3))/(20*x^2) + (7*sqrt(2 - sqrt(3))*(1 + x)*sqrt((1 - x + x^2)/(1 - sqrt(3) + x)^2)*Elliptic.F(asin((1 + sqrt(3) + x)/(1 - sqrt(3) + x)), -7 + 4*sqrt(3)))/(20*3^(1/4)*sqrt(-((1 + x)/(1 - sqrt(3) + x)^2))*sqrt(-1 - x^3))]

    @test_int [x^7/sqrt(-1 - x^3), x, 5, (20/91)*x^2*sqrt(-1 - x^3) - (2/13)*x^5*sqrt(-1 - x^3) - (80*sqrt(-1 - x^3))/(91*(1 - sqrt(3) + x)) + (40*3^(1/4)*sqrt(2 + sqrt(3))*(1 + x)*sqrt((1 - x + x^2)/(1 - sqrt(3) + x)^2)*Elliptic.E(asin((1 + sqrt(3) + x)/(1 - sqrt(3) + x)), -7 + 4*sqrt(3)))/(91*sqrt(-((1 + x)/(1 - sqrt(3) + x)^2))*sqrt(-1 - x^3)) - (80*sqrt(2)*(1 + x)*sqrt((1 - x + x^2)/(1 - sqrt(3) + x)^2)*Elliptic.F(asin((1 + sqrt(3) + x)/(1 - sqrt(3) + x)), -7 + 4*sqrt(3)))/(91*3^(1/4)*sqrt(-((1 + x)/(1 - sqrt(3) + x)^2))*sqrt(-1 - x^3))]
    @test_int [x^4/sqrt(-1 - x^3), x, 4, (-(2/7))*x^2*sqrt(-1 - x^3) + (8*sqrt(-1 - x^3))/(7*(1 - sqrt(3) + x)) - (4*3^(1/4)*sqrt(2 + sqrt(3))*(1 + x)*sqrt((1 - x + x^2)/(1 - sqrt(3) + x)^2)*Elliptic.E(asin((1 + sqrt(3) + x)/(1 - sqrt(3) + x)), -7 + 4*sqrt(3)))/(7*sqrt(-((1 + x)/(1 - sqrt(3) + x)^2))*sqrt(-1 - x^3)) + (8*sqrt(2)*(1 + x)*sqrt((1 - x + x^2)/(1 - sqrt(3) + x)^2)*Elliptic.F(asin((1 + sqrt(3) + x)/(1 - sqrt(3) + x)), -7 + 4*sqrt(3)))/(7*3^(1/4)*sqrt(-((1 + x)/(1 - sqrt(3) + x)^2))*sqrt(-1 - x^3))]
    @test_int [x^1/sqrt(-1 - x^3), x, 3, -((2*sqrt(-1 - x^3))/(1 - sqrt(3) + x)) + (3^(1/4)*sqrt(2 + sqrt(3))*(1 + x)*sqrt((1 - x + x^2)/(1 - sqrt(3) + x)^2)*Elliptic.E(asin((1 + sqrt(3) + x)/(1 - sqrt(3) + x)), -7 + 4*sqrt(3)))/(sqrt(-((1 + x)/(1 - sqrt(3) + x)^2))*sqrt(-1 - x^3)) - (2*sqrt(2)*(1 + x)*sqrt((1 - x + x^2)/(1 - sqrt(3) + x)^2)*Elliptic.F(asin((1 + sqrt(3) + x)/(1 - sqrt(3) + x)), -7 + 4*sqrt(3)))/(3^(1/4)*sqrt(-((1 + x)/(1 - sqrt(3) + x)^2))*sqrt(-1 - x^3))]
    @test_int [1/(x^2*sqrt(-1 - x^3)), x, 4, sqrt(-1 - x^3)/x - sqrt(-1 - x^3)/(1 - sqrt(3) + x) + (3^(1/4)*sqrt(2 + sqrt(3))*(1 + x)*sqrt((1 - x + x^2)/(1 - sqrt(3) + x)^2)*Elliptic.E(asin((1 + sqrt(3) + x)/(1 - sqrt(3) + x)), -7 + 4*sqrt(3)))/(2*sqrt(-((1 + x)/(1 - sqrt(3) + x)^2))*sqrt(-1 - x^3)) - (sqrt(2)*(1 + x)*sqrt((1 - x + x^2)/(1 - sqrt(3) + x)^2)*Elliptic.F(asin((1 + sqrt(3) + x)/(1 - sqrt(3) + x)), -7 + 4*sqrt(3)))/(3^(1/4)*sqrt(-((1 + x)/(1 - sqrt(3) + x)^2))*sqrt(-1 - x^3))]
    @test_int [1/(x^5*sqrt(-1 - x^3)), x, 5, sqrt(-1 - x^3)/(4*x^4) - (5*sqrt(-1 - x^3))/(8*x) + (5*sqrt(-1 - x^3))/(8*(1 - sqrt(3) + x)) - (5*3^(1/4)*sqrt(2 + sqrt(3))*(1 + x)*sqrt((1 - x + x^2)/(1 - sqrt(3) + x)^2)*Elliptic.E(asin((1 + sqrt(3) + x)/(1 - sqrt(3) + x)), -7 + 4*sqrt(3)))/(16*sqrt(-((1 + x)/(1 - sqrt(3) + x)^2))*sqrt(-1 - x^3)) + (5*(1 + x)*sqrt((1 - x + x^2)/(1 - sqrt(3) + x)^2)*Elliptic.F(asin((1 + sqrt(3) + x)/(1 - sqrt(3) + x)), -7 + 4*sqrt(3)))/(4*sqrt(2)*3^(1/4)*sqrt(-((1 + x)/(1 - sqrt(3) + x)^2))*sqrt(-1 - x^3))]

    #= ::Subsection:: =#
    #=Integrands*of*the*form*x^(m/2)*(a+b*x^3)^(p/2)=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b*x^3)^(p/3)=#

    #= ::Subsubsection::Closed:: =#
    #=p>0=#

    @test_int [x^11*(a + b*x^3)^(1/3), x, 3, -((a^3*(a + b*x^3)^(4/3))/(4*b^4)) + (3*a^2*(a + b*x^3)^(7/3))/(7*b^4) - (3*a*(a + b*x^3)^(10/3))/(10*b^4) + (a + b*x^3)^(13/3)/(13*b^4)]
    @test_int [x^8*(a + b*x^3)^(1/3), x, 3, (a^2*(a + b*x^3)^(4/3))/(4*b^3) - (2*a*(a + b*x^3)^(7/3))/(7*b^3) + (a + b*x^3)^(10/3)/(10*b^3)]
    @test_int [x^5*(a + b*x^3)^(1/3), x, 3, -((a*(a + b*x^3)^(4/3))/(4*b^2)) + (a + b*x^3)^(7/3)/(7*b^2)]
    @test_int [x^2*(a + b*x^3)^(1/3), x, 1, (a + b*x^3)^(4/3)/(4*b)]
    @test_int [(a + b*x^3)^(1/3)/x^1, x, 6, (a + b*x^3)^(1/3) - (a^(1/3)*atan((a^(1/3) + 2*(a + b*x^3)^(1/3))/(sqrt(3)*a^(1/3))))/sqrt(3) - (1/2)*a^(1/3)*log(x) + (1/2)*a^(1/3)*log(a^(1/3) - (a + b*x^3)^(1/3))]
    @test_int [(a + b*x^3)^(1/3)/x^4, x, 6, -((a + b*x^3)^(1/3)/(3*x^3)) - (b*atan((a^(1/3) + 2*(a + b*x^3)^(1/3))/(sqrt(3)*a^(1/3))))/(3*sqrt(3)*a^(2/3)) - (b*log(x))/(6*a^(2/3)) + (b*log(a^(1/3) - (a + b*x^3)^(1/3)))/(6*a^(2/3))]

    @test_int [x^4*(a + b*x^3)^(1/3), x, 3, (a*x^2*(a + b*x^3)^(1/3))/(18*b) + (1/6)*x^5*(a + b*x^3)^(1/3) + (a^2*atan((1 + (2*b^(1/3)*x)/(a + b*x^3)^(1/3))/sqrt(3)))/(9*sqrt(3)*b^(5/3)) + (a^2*log(b^(1/3)*x - (a + b*x^3)^(1/3)))/(18*b^(5/3))]
    @test_int [x^1*(a + b*x^3)^(1/3), x, 2, (1/3)*x^2*(a + b*x^3)^(1/3) - (a*atan((1 + (2*b^(1/3)*x)/(a + b*x^3)^(1/3))/sqrt(3)))/(3*sqrt(3)*b^(2/3)) - (a*log(b^(1/3)*x - (a + b*x^3)^(1/3)))/(6*b^(2/3))]
    @test_int [(a + b*x^3)^(1/3)/x^2, x, 2, -((a + b*x^3)^(1/3)/x) - (b^(1/3)*atan((1 + (2*b^(1/3)*x)/(a + b*x^3)^(1/3))/sqrt(3)))/sqrt(3) - (1/2)*b^(1/3)*log(b^(1/3)*x - (a + b*x^3)^(1/3))]
    @test_int [(a + b*x^3)^(1/3)/x^5, x, 1, -((a + b*x^3)^(4/3)/(4*a*x^4))]
    @test_int [(a + b*x^3)^(1/3)/x^8, x, 2, -((a + b*x^3)^(4/3)/(7*a*x^7)) + (3*b*(a + b*x^3)^(4/3))/(28*a^2*x^4)]
    @test_int [(a + b*x^3)^(1/3)/x^11, x, 3, -((a + b*x^3)^(4/3)/(10*a*x^10)) + (3*b*(a + b*x^3)^(4/3))/(35*a^2*x^7) - (9*b^2*(a + b*x^3)^(4/3))/(140*a^3*x^4)]
    @test_int [(a + b*x^3)^(1/3)/x^14, x, 4, -((a + b*x^3)^(4/3)/(13*a*x^13)) + (9*b*(a + b*x^3)^(4/3))/(130*a^2*x^10) - (27*b^2*(a + b*x^3)^(4/3))/(455*a^3*x^7) + (81*b^3*(a + b*x^3)^(4/3))/(1820*a^4*x^4)]

    @test_int [x^3*(a + b*x^3)^(1/3), x, 2, (x^4*(a + b*x^3)^(4/3)*HypergeometricFunctions._₂F₁(1, 8/3, 7/3, -((b*x^3)/a)))/(4*a), (x^4*(a + b*x^3)^(1/3)*HypergeometricFunctions._₂F₁(-(1/3), 4/3, 7/3, -((b*x^3)/a)))/(4*(1 + (b*x^3)/a)^(1/3))]
    @test_int [x^0*(a + b*x^3)^(1/3), x, 2, (x*(a + b*x^3)^(4/3)*HypergeometricFunctions._₂F₁(1, 5/3, 4/3, -((b*x^3)/a)))/a, (x*(a + b*x^3)^(1/3)*HypergeometricFunctions._₂F₁(-(1/3), 1/3, 4/3, -((b*x^3)/a)))/(1 + (b*x^3)/a)^(1/3)]
    @test_int [(a + b*x^3)^(1/3)/x^3, x, 2, -(((a + b*x^3)^(4/3)*HypergeometricFunctions._₂F₁(2/3, 1, 1/3, -((b*x^3)/a)))/(2*a*x^2)), -(((a + b*x^3)^(1/3)*HypergeometricFunctions._₂F₁(-(2/3), -(1/3), 1/3, -((b*x^3)/a)))/(2*x^2*(1 + (b*x^3)/a)^(1/3)))]
    @test_int [(a + b*x^3)^(1/3)/x^6, x, 2, -(((a + b*x^3)^(4/3)*HypergeometricFunctions._₂F₁(-(1/3), 1, -(2/3), -((b*x^3)/a)))/(5*a*x^5)), -(((a + b*x^3)^(1/3)*HypergeometricFunctions._₂F₁(-(5/3), -(1/3), -(2/3), -((b*x^3)/a)))/(5*x^5*(1 + (b*x^3)/a)^(1/3)))]

    @test_int [x^11*(a + b*x^3)^(2/3), x, 3, -((a^3*(a + b*x^3)^(5/3))/(5*b^4)) + (3*a^2*(a + b*x^3)^(8/3))/(8*b^4) - (3*a*(a + b*x^3)^(11/3))/(11*b^4) + (a + b*x^3)^(14/3)/(14*b^4)]
    @test_int [x^8*(a + b*x^3)^(2/3), x, 3, (a^2*(a + b*x^3)^(5/3))/(5*b^3) - (a*(a + b*x^3)^(8/3))/(4*b^3) + (a + b*x^3)^(11/3)/(11*b^3)]
    @test_int [x^5*(a + b*x^3)^(2/3), x, 3, -((a*(a + b*x^3)^(5/3))/(5*b^2)) + (a + b*x^3)^(8/3)/(8*b^2)]
    @test_int [x^2*(a + b*x^3)^(2/3), x, 1, (a + b*x^3)^(5/3)/(5*b)]
    @test_int [(a + b*x^3)^(2/3)/x^1, x, 6, (1/2)*(a + b*x^3)^(2/3) + (a^(2/3)*atan((a^(1/3) + 2*(a + b*x^3)^(1/3))/(sqrt(3)*a^(1/3))))/sqrt(3) - (1/2)*a^(2/3)*log(x) + (1/2)*a^(2/3)*log(a^(1/3) - (a + b*x^3)^(1/3))]
    @test_int [(a + b*x^3)^(2/3)/x^4, x, 6, -((a + b*x^3)^(2/3)/(3*x^3)) + (2*b*atan((a^(1/3) + 2*(a + b*x^3)^(1/3))/(sqrt(3)*a^(1/3))))/(3*sqrt(3)*a^(1/3)) - (b*log(x))/(3*a^(1/3)) + (b*log(a^(1/3) - (a + b*x^3)^(1/3)))/(3*a^(1/3))]

    @test_int [x^4*(a + b*x^3)^(2/3), x, 2, (x^5*(a + b*x^3)^(5/3)*HypergeometricFunctions._₂F₁(1, 10/3, 8/3, -((b*x^3)/a)))/(5*a), (x^5*(a + b*x^3)^(2/3)*HypergeometricFunctions._₂F₁(-(2/3), 5/3, 8/3, -((b*x^3)/a)))/(5*(1 + (b*x^3)/a)^(2/3))]
    @test_int [x^1*(a + b*x^3)^(2/3), x, 2, (x^2*(a + b*x^3)^(5/3)*HypergeometricFunctions._₂F₁(1, 7/3, 5/3, -((b*x^3)/a)))/(2*a), (x^2*(a + b*x^3)^(2/3)*HypergeometricFunctions._₂F₁(-(2/3), 2/3, 5/3, -((b*x^3)/a)))/(2*(1 + (b*x^3)/a)^(2/3))]
    @test_int [(a + b*x^3)^(2/3)/x^2, x, 2, -(((a + b*x^3)^(5/3)*HypergeometricFunctions._₂F₁(1, 4/3, 2/3, -((b*x^3)/a)))/(a*x)), -(((a + b*x^3)^(2/3)*HypergeometricFunctions._₂F₁(-(2/3), -(1/3), 2/3, -((b*x^3)/a)))/(x*(1 + (b*x^3)/a)^(2/3)))]
    @test_int [(a + b*x^3)^(2/3)/x^5, x, 2, -(((a + b*x^3)^(5/3)*HypergeometricFunctions._₂F₁(1/3, 1, -(1/3), -((b*x^3)/a)))/(4*a*x^4)), -(((a + b*x^3)^(2/3)*HypergeometricFunctions._₂F₁(-(4/3), -(2/3), -(1/3), -((b*x^3)/a)))/(4*x^4*(1 + (b*x^3)/a)^(2/3)))]

    @test_int [x^3*(a + b*x^3)^(2/3), x, 3, (a*x*(a + b*x^3)^(2/3))/(9*b) + (1/6)*x^4*(a + b*x^3)^(2/3) - (a^2*atan((1 + (2*b^(1/3)*x)/(a + b*x^3)^(1/3))/sqrt(3)))/(9*sqrt(3)*b^(4/3)) + (a^2*log((-b^(1/3))*x + (a + b*x^3)^(1/3)))/(18*b^(4/3))]
    @test_int [x^0*(a + b*x^3)^(2/3), x, 2, (1/3)*x*(a + b*x^3)^(2/3) + (2*a*atan((1 + (2*b^(1/3)*x)/(a + b*x^3)^(1/3))/sqrt(3)))/(3*sqrt(3)*b^(1/3)) - (a*log((-b^(1/3))*x + (a + b*x^3)^(1/3)))/(3*b^(1/3))]
    @test_int [(a + b*x^3)^(2/3)/x^3, x, 2, -((a + b*x^3)^(2/3)/(2*x^2)) + (b^(2/3)*atan((1 + (2*b^(1/3)*x)/(a + b*x^3)^(1/3))/sqrt(3)))/sqrt(3) - (1/2)*b^(2/3)*log((-b^(1/3))*x + (a + b*x^3)^(1/3))]
    @test_int [(a + b*x^3)^(2/3)/x^6, x, 1, -((a + b*x^3)^(5/3)/(5*a*x^5))]
    @test_int [(a + b*x^3)^(2/3)/x^9, x, 2, -((a + b*x^3)^(5/3)/(8*a*x^8)) + (3*b*(a + b*x^3)^(5/3))/(40*a^2*x^5)]
    @test_int [(a + b*x^3)^(2/3)/x^12, x, 3, -((a + b*x^3)^(5/3)/(11*a*x^11)) + (3*b*(a + b*x^3)^(5/3))/(44*a^2*x^8) - (9*b^2*(a + b*x^3)^(5/3))/(220*a^3*x^5)]

    @test_int [x^8*(1 - x^3)^(6/5), x, 3, (-(5/33))*(1 - x^3)^(11/5) + (5/24)*(1 - x^3)^(16/5) - (5/63)*(1 - x^3)^(21/5)]

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [x^11/(a + b*x^3)^(1/3), x, 3, -((a^3*(a + b*x^3)^(2/3))/(2*b^4)) + (3*a^2*(a + b*x^3)^(5/3))/(5*b^4) - (3*a*(a + b*x^3)^(8/3))/(8*b^4) + (a + b*x^3)^(11/3)/(11*b^4)]
    @test_int [x^8/(a + b*x^3)^(1/3), x, 3, (a^2*(a + b*x^3)^(2/3))/(2*b^3) - (2*a*(a + b*x^3)^(5/3))/(5*b^3) + (a + b*x^3)^(8/3)/(8*b^3)]
    @test_int [x^5/(a + b*x^3)^(1/3), x, 3, -((a*(a + b*x^3)^(2/3))/(2*b^2)) + (a + b*x^3)^(5/3)/(5*b^2)]
    @test_int [x^2/(a + b*x^3)^(1/3), x, 1, (a + b*x^3)^(2/3)/(2*b)]
    @test_int [1/(x^1*(a + b*x^3)^(1/3)), x, 5, atan((a^(1/3) + 2*(a + b*x^3)^(1/3))/(sqrt(3)*a^(1/3)))/(sqrt(3)*a^(1/3)) - log(x)/(2*a^(1/3)) + log(a^(1/3) - (a + b*x^3)^(1/3))/(2*a^(1/3))]
    @test_int [1/(x^4*(a + b*x^3)^(1/3)), x, 6, -((a + b*x^3)^(2/3)/(3*a*x^3)) - (b*atan((a^(1/3) + 2*(a + b*x^3)^(1/3))/(sqrt(3)*a^(1/3))))/(3*sqrt(3)*a^(4/3)) + (b*log(x))/(6*a^(4/3)) - (b*log(a^(1/3) - (a + b*x^3)^(1/3)))/(6*a^(4/3))]

    @test_int [x^7/(a + b*x^3)^(1/3), x, 2, (x^8*(a + b*x^3)^(2/3)*HypergeometricFunctions._₂F₁(1, 10/3, 11/3, -((b*x^3)/a)))/(8*a), (x^8*(1 + (b*x^3)/a)^(1/3)*HypergeometricFunctions._₂F₁(1/3, 8/3, 11/3, -((b*x^3)/a)))/(8*(a + b*x^3)^(1/3))]
    @test_int [x^4/(a + b*x^3)^(1/3), x, 2, (x^5*(a + b*x^3)^(2/3)*HypergeometricFunctions._₂F₁(1, 7/3, 8/3, -((b*x^3)/a)))/(5*a), (x^5*(1 + (b*x^3)/a)^(1/3)*HypergeometricFunctions._₂F₁(1/3, 5/3, 8/3, -((b*x^3)/a)))/(5*(a + b*x^3)^(1/3))]
    @test_int [x^1/(a + b*x^3)^(1/3), x, 2, (x^2*(a + b*x^3)^(2/3)*HypergeometricFunctions._₂F₁(1, 4/3, 5/3, -((b*x^3)/a)))/(2*a), (x^2*(1 + (b*x^3)/a)^(1/3)*HypergeometricFunctions._₂F₁(1/3, 2/3, 5/3, -((b*x^3)/a)))/(2*(a + b*x^3)^(1/3))]
    @test_int [1/(x^2*(a + b*x^3)^(1/3)), x, 2, -(((a + b*x^3)^(2/3)*HypergeometricFunctions._₂F₁(1/3, 1, 2/3, -((b*x^3)/a)))/(a*x)), -(((1 + (b*x^3)/a)^(1/3)*HypergeometricFunctions._₂F₁(-(1/3), 1/3, 2/3, -((b*x^3)/a)))/(x*(a + b*x^3)^(1/3)))]
    @test_int [1/(x^5*(a + b*x^3)^(1/3)), x, 2, -(((a + b*x^3)^(2/3)*HypergeometricFunctions._₂F₁(-(2/3), 1, -(1/3), -((b*x^3)/a)))/(4*a*x^4)), -(((1 + (b*x^3)/a)^(1/3)*HypergeometricFunctions._₂F₁(-(4/3), 1/3, -(1/3), -((b*x^3)/a)))/(4*x^4*(a + b*x^3)^(1/3)))]

    @test_int [x^3/(a + b*x^3)^(1/3), x, 2, (x*(a + b*x^3)^(2/3))/(3*b) - (a*atan((1 + (2*b^(1/3)*x)/(a + b*x^3)^(1/3))/sqrt(3)))/(3*sqrt(3)*b^(4/3)) + (a*log((-b^(1/3))*x + (a + b*x^3)^(1/3)))/(6*b^(4/3))]
    @test_int [x^0/(a + b*x^3)^(1/3), x, 1, atan((1 + (2*b^(1/3)*x)/(a + b*x^3)^(1/3))/sqrt(3))/(sqrt(3)*b^(1/3)) - log((-b^(1/3))*x + (a + b*x^3)^(1/3))/(2*b^(1/3))]
    @test_int [1/(x^3*(a + b*x^3)^(1/3)), x, 1, -((a + b*x^3)^(2/3)/(2*a*x^2))]
    @test_int [1/(x^6*(a + b*x^3)^(1/3)), x, 2, -((a + b*x^3)^(2/3)/(5*a*x^5)) + (3*b*(a + b*x^3)^(2/3))/(10*a^2*x^2)]
    @test_int [1/(x^9*(a + b*x^3)^(1/3)), x, 3, -((a + b*x^3)^(2/3)/(8*a*x^8)) + (3*b*(a + b*x^3)^(2/3))/(20*a^2*x^5) - (9*b^2*(a + b*x^3)^(2/3))/(40*a^3*x^2)]
    @test_int [1/(x^12*(a + b*x^3)^(1/3)), x, 4, -((a + b*x^3)^(2/3)/(11*a*x^11)) + (9*b*(a + b*x^3)^(2/3))/(88*a^2*x^8) - (27*b^2*(a + b*x^3)^(2/3))/(220*a^3*x^5) + (81*b^3*(a + b*x^3)^(2/3))/(440*a^4*x^2)]

    @test_int [x^11/(a + b*x^3)^(2/3), x, 3, -((a^3*(a + b*x^3)^(1/3))/b^4) + (3*a^2*(a + b*x^3)^(4/3))/(4*b^4) - (3*a*(a + b*x^3)^(7/3))/(7*b^4) + (a + b*x^3)^(10/3)/(10*b^4)]
    @test_int [x^8/(a + b*x^3)^(2/3), x, 3, (a^2*(a + b*x^3)^(1/3))/b^3 - (a*(a + b*x^3)^(4/3))/(2*b^3) + (a + b*x^3)^(7/3)/(7*b^3)]
    @test_int [x^5/(a + b*x^3)^(2/3), x, 3, -((a*(a + b*x^3)^(1/3))/b^2) + (a + b*x^3)^(4/3)/(4*b^2)]
    @test_int [x^2/(a + b*x^3)^(2/3), x, 1, (a + b*x^3)^(1/3)/b]
    @test_int [1/(x^1*(a + b*x^3)^(2/3)), x, 5, -(atan((a^(1/3) + 2*(a + b*x^3)^(1/3))/(sqrt(3)*a^(1/3)))/(sqrt(3)*a^(2/3))) - log(x)/(2*a^(2/3)) + log(a^(1/3) - (a + b*x^3)^(1/3))/(2*a^(2/3))]
    @test_int [1/(x^4*(a + b*x^3)^(2/3)), x, 6, -((a + b*x^3)^(1/3)/(3*a*x^3)) + (2*b*atan((a^(1/3) + 2*(a + b*x^3)^(1/3))/(sqrt(3)*a^(1/3))))/(3*sqrt(3)*a^(5/3)) + (b*log(x))/(3*a^(5/3)) - (b*log(a^(1/3) - (a + b*x^3)^(1/3)))/(3*a^(5/3))]

    @test_int [x^7/(a + b*x^3)^(2/3), x, 3, -((5*a*x^2*(a + b*x^3)^(1/3))/(18*b^2)) + (x^5*(a + b*x^3)^(1/3))/(6*b) - (5*a^2*atan((1 + (2*b^(1/3)*x)/(a + b*x^3)^(1/3))/sqrt(3)))/(9*sqrt(3)*b^(8/3)) - (5*a^2*log(b^(1/3)*x - (a + b*x^3)^(1/3)))/(18*b^(8/3))]
    @test_int [x^4/(a + b*x^3)^(2/3), x, 2, (x^2*(a + b*x^3)^(1/3))/(3*b) + (2*a*atan((1 + (2*b^(1/3)*x)/(a + b*x^3)^(1/3))/sqrt(3)))/(3*sqrt(3)*b^(5/3)) + (a*log(b^(1/3)*x - (a + b*x^3)^(1/3)))/(3*b^(5/3))]
    @test_int [x^1/(a + b*x^3)^(2/3), x, 1, -(atan((1 + (2*b^(1/3)*x)/(a + b*x^3)^(1/3))/sqrt(3))/(sqrt(3)*b^(2/3))) - log(b^(1/3)*x - (a + b*x^3)^(1/3))/(2*b^(2/3))]
    @test_int [1/(x^2*(a + b*x^3)^(2/3)), x, 1, -((a + b*x^3)^(1/3)/(a*x))]
    @test_int [1/(x^5*(a + b*x^3)^(2/3)), x, 2, -((a + b*x^3)^(1/3)/(4*a*x^4)) + (3*b*(a + b*x^3)^(1/3))/(4*a^2*x)]
    @test_int [1/(x^8*(a + b*x^3)^(2/3)), x, 3, -((a + b*x^3)^(1/3)/(7*a*x^7)) + (3*b*(a + b*x^3)^(1/3))/(14*a^2*x^4) - (9*b^2*(a + b*x^3)^(1/3))/(14*a^3*x)]
    @test_int [1/(x^11*(a + b*x^3)^(2/3)), x, 4, -((a + b*x^3)^(1/3)/(10*a*x^10)) + (9*b*(a + b*x^3)^(1/3))/(70*a^2*x^7) - (27*b^2*(a + b*x^3)^(1/3))/(140*a^3*x^4) + (81*b^3*(a + b*x^3)^(1/3))/(140*a^4*x)]

    @test_int [x^6/(a + b*x^3)^(2/3), x, 2, (x^7*(a + b*x^3)^(1/3)*HypergeometricFunctions._₂F₁(1, 8/3, 10/3, -((b*x^3)/a)))/(7*a), (x^7*(1 + (b*x^3)/a)^(2/3)*HypergeometricFunctions._₂F₁(2/3, 7/3, 10/3, -((b*x^3)/a)))/(7*(a + b*x^3)^(2/3))]
    @test_int [x^3/(a + b*x^3)^(2/3), x, 2, (x^4*(a + b*x^3)^(1/3)*HypergeometricFunctions._₂F₁(1, 5/3, 7/3, -((b*x^3)/a)))/(4*a), (x^4*(1 + (b*x^3)/a)^(2/3)*HypergeometricFunctions._₂F₁(2/3, 4/3, 7/3, -((b*x^3)/a)))/(4*(a + b*x^3)^(2/3))]
    @test_int [x^0/(a + b*x^3)^(2/3), x, 2, (x*(a + b*x^3)^(1/3)*HypergeometricFunctions._₂F₁(2/3, 1, 4/3, -((b*x^3)/a)))/a, (x*(1 + (b*x^3)/a)^(2/3)*HypergeometricFunctions._₂F₁(1/3, 2/3, 4/3, -((b*x^3)/a)))/(a + b*x^3)^(2/3)]
    @test_int [1/(x^3*(a + b*x^3)^(2/3)), x, 2, -(((a + b*x^3)^(1/3)*HypergeometricFunctions._₂F₁(-(1/3), 1, 1/3, -((b*x^3)/a)))/(2*a*x^2)), -(((1 + (b*x^3)/a)^(2/3)*HypergeometricFunctions._₂F₁(-(2/3), 2/3, 1/3, -((b*x^3)/a)))/(2*x^2*(a + b*x^3)^(2/3)))]
    @test_int [1/(x^6*(a + b*x^3)^(2/3)), x, 2, -(((a + b*x^3)^(1/3)*HypergeometricFunctions._₂F₁(-(4/3), 1, -(2/3), -((b*x^3)/a)))/(5*a*x^5)), -(((1 + (b*x^3)/a)^(2/3)*HypergeometricFunctions._₂F₁(-(5/3), 2/3, -(2/3), -((b*x^3)/a)))/(5*x^5*(a + b*x^3)^(2/3)))]

    @test_int [x^0/(a - b*x^3)^(1/3), x, 1, -(atan((1 - (2*b^(1/3)*x)/(a - b*x^3)^(1/3))/sqrt(3))/(sqrt(3)*b^(1/3))) + log(b^(1/3)*x + (a - b*x^3)^(1/3))/(2*b^(1/3))]

    @test_int [x^0/(2 + x^3)^(1/3), x, 1, atan((1 + (2*x)/(2 + x^3)^(1/3))/sqrt(3))/sqrt(3) - (1/2)*log(-x + (2 + x^3)^(1/3))]

    @test_int [x^1/(1 - x^3)^(2/3), x, 1, -(atan((1 - (2*x)/(1 - x^3)^(1/3))/sqrt(3))/sqrt(3)) - (1/2)*log(-x - (1 - x^3)^(1/3))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b*x^3)^(p/4)=#

    @test_int [x^2/(2 + x^3)^(1/4), x, 1, (4*(2 + x^3)^(3/4))/9]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(c*x)^m*(a+b*x^3)^p*with*m*symbolic=#

    @test_int [x^m*(a + b*x^3)^8, x, 2, (a^8*x^(1 + m))/(1 + m) + (8*a^7*b*x^(4 + m))/(4 + m) + (28*a^6*b^2*x^(7 + m))/(7 + m) + (56*a^5*b^3*x^(10 + m))/(10 + m) + (70*a^4*b^4*x^(13 + m))/(13 + m) + (56*a^3*b^5*x^(16 + m))/(16 + m) + (28*a^2*b^6*x^(19 + m))/(19 + m) + (8*a*b^7*x^(22 + m))/(22 + m) + (b^8*x^(25 + m))/(25 + m)]
    @test_int [x^m*(a + b*x^3)^5, x, 2, (a^5*x^(1 + m))/(1 + m) + (5*a^4*b*x^(4 + m))/(4 + m) + (10*a^3*b^2*x^(7 + m))/(7 + m) + (10*a^2*b^3*x^(10 + m))/(10 + m) + (5*a*b^4*x^(13 + m))/(13 + m) + (b^5*x^(16 + m))/(16 + m)]
    @test_int [x^m*(a + b*x^3)^3, x, 2, (a^3*x^(1 + m))/(1 + m) + (3*a^2*b*x^(4 + m))/(4 + m) + (3*a*b^2*x^(7 + m))/(7 + m) + (b^3*x^(10 + m))/(10 + m)]
    @test_int [x^m*(a + b*x^3)^2, x, 2, (a^2*x^(1 + m))/(1 + m) + (2*a*b*x^(4 + m))/(4 + m) + (b^2*x^(7 + m))/(7 + m)]
    @test_int [x^m*(a + b*x^3), x, 2, (a*x^(1 + m))/(1 + m) + (b*x^(4 + m))/(4 + m)]
    @test_int [x^m/(a + b*x^3), x, 1, (x^(1 + m)*HypergeometricFunctions._₂F₁(1, (1 + m)/3, (4 + m)/3, -((b*x^3)/a)))/(a*(1 + m))]
    @test_int [x^m/(a + b*x^3)^2, x, 1, (x^(1 + m)*HypergeometricFunctions._₂F₁(2, (1 + m)/3, (4 + m)/3, -((b*x^3)/a)))/(a^2*(1 + m))]
    @test_int [x^m/(a + b*x^3)^3, x, 1, (x^(1 + m)*HypergeometricFunctions._₂F₁(3, (1 + m)/3, (4 + m)/3, -((b*x^3)/a)))/(a^3*(1 + m))]

    @test_int [x^m*(a + b*x^3)^(3/2), x, 2, (a*x^(1 + m)*sqrt(a + b*x^3)*HypergeometricFunctions._₂F₁(-(3/2), (1 + m)/3, (4 + m)/3, -((b*x^3)/a)))/((1 + m)*sqrt(1 + (b*x^3)/a))]
    @test_int [x^m*sqrt(a + b*x^3), x, 2, (x^(1 + m)*sqrt(a + b*x^3)*HypergeometricFunctions._₂F₁(-(1/2), (1 + m)/3, (4 + m)/3, -((b*x^3)/a)))/((1 + m)*sqrt(1 + (b*x^3)/a))]
    @test_int [x^m/sqrt(a + b*x^3), x, 2, (x^(1 + m)*sqrt(a + b*x^3)*HypergeometricFunctions._₂F₁(1, (1/6)*(5 + 2*m), (4 + m)/3, -((b*x^3)/a)))/(a*(1 + m)), (x^(1 + m)*sqrt(1 + (b*x^3)/a)*HypergeometricFunctions._₂F₁(1/2, (1 + m)/3, (4 + m)/3, -((b*x^3)/a)))/((1 + m)*sqrt(a + b*x^3))]
    @test_int [x^m/(a + b*x^3)^(3/2), x, 2, (x^(1 + m)*sqrt(1 + (b*x^3)/a)*HypergeometricFunctions._₂F₁(3/2, (1 + m)/3, (4 + m)/3, -((b*x^3)/a)))/(a*(1 + m)*sqrt(a + b*x^3))]

    @test_int [(c*x)^m*(a + b*x^3)^(4/3), x, 2, (a*(c*x)^(1 + m)*(a + b*x^3)^(1/3)*HypergeometricFunctions._₂F₁(-(4/3), (1 + m)/3, (4 + m)/3, -((b*x^3)/a)))/(c*(1 + m)*(1 + (b*x^3)/a)^(1/3))]
    @test_int [(c*x)^m*(a + b*x^3)^(2/3), x, 2, ((c*x)^(1 + m)*(a + b*c^3*x^3)^(5/3)*HypergeometricFunctions._₂F₁(1, (6 + m)/3, (4 + m)/3, -((b*c^3*x^3)/a)))/(a*c*(1 + m)), ((c*x)^(1 + m)*(a + b*x^3)^(2/3)*HypergeometricFunctions._₂F₁(-(2/3), (1 + m)/3, (4 + m)/3, -((b*x^3)/a)))/(c*(1 + m)*(1 + (b*x^3)/a)^(2/3))]
    @test_int [(c*x)^m*(a + b*x^3)^(1/3), x, 2, ((c*x)^(1 + m)*(a + b*c^3*x^3)^(4/3)*HypergeometricFunctions._₂F₁(1, (5 + m)/3, (4 + m)/3, -((b*c^3*x^3)/a)))/(a*c*(1 + m)), ((c*x)^(1 + m)*(a + b*x^3)^(1/3)*HypergeometricFunctions._₂F₁(-(1/3), (1 + m)/3, (4 + m)/3, -((b*x^3)/a)))/(c*(1 + m)*(1 + (b*x^3)/a)^(1/3))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(c*x)^m*(a+b*x^3)^p*with*p*symbolic=#

    @test_int [(c*x)^m*(a + b*x^3)^p, x, 2, ((c*x)^(1 + m)*(a + b*x^3)^p*HypergeometricFunctions._₂F₁((1 + m)/3, -p, (4 + m)/3, -((b*x^3)/a)))/((1 + (b*x^3)/a)^p*(c*(1 + m)))]

    @test_int [x^2*(a + b*x^3)^p, x, 1, (a + b*x^3)^(1 + p)/(3*b*(1 + p))]
    @test_int [x^5*(a + b*x^3)^p, x, 3, -((a*(a + b*x^3)^(1 + p))/(3*b^2*(1 + p))) + (a + b*x^3)^(2 + p)/(3*b^2*(2 + p))]
    @test_int [x^8*(a + b*x^3)^p, x, 3, (a^2*(a + b*x^3)^(1 + p))/(3*b^3*(1 + p)) - (2*a*(a + b*x^3)^(2 + p))/(3*b^3*(2 + p)) + (a + b*x^3)^(3 + p)/(3*b^3*(3 + p))]
    @test_int [x^11*(a + b*x^3)^p, x, 3, -((a^3*(a + b*x^3)^(1 + p))/(3*b^4*(1 + p))) + (a^2*(a + b*x^3)^(2 + p))/(b^4*(2 + p)) - (a*(a + b*x^3)^(3 + p))/(b^4*(3 + p)) + (a + b*x^3)^(4 + p)/(3*b^4*(4 + p))]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(c*x)^m*(a+b*x^4)^p=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b*x^4)^p=#

    #= ::Subsubsection::Closed:: =#
    #=p>0=#

    @test_int [x^m*(a + b*x^4), x, 2, (a*x^(1 + m))/(1 + m) + (b*x^(5 + m))/(5 + m)]

    @test_int [x^5*(a + b*x^4), x, 2, (a*x^6)/6 + (b*x^10)/10]
    @test_int [x^4*(a + b*x^4), x, 2, (a*x^5)/5 + (b*x^9)/9]
    @test_int [x^3*(a + b*x^4), x, 2, (a*x^4)/4 + (b*x^8)/8]
    @test_int [x^2*(a + b*x^4), x, 2, (a*x^3)/3 + (b*x^7)/7]
    @test_int [x^1*(a + b*x^4), x, 2, (a*x^2)/2 + (b*x^6)/6]
    @test_int [x^0*(a + b*x^4), x, 1, a*x + (b*x^5)/5]
    @test_int [(a + b*x^4)/x^1, x, 2, (b*x^4)/4 + a*log(x)]
    @test_int [(a + b*x^4)/x^2, x, 2, -(a/x) + (b*x^3)/3]
    @test_int [(a + b*x^4)/x^3, x, 2, -(a/(2*x^2)) + (b*x^2)/2]
    @test_int [(a + b*x^4)/x^4, x, 2, -(a/(3*x^3)) + b*x]
    @test_int [(a + b*x^4)/x^5, x, 2, -(a/(4*x^4)) + b*log(x)]
    @test_int [(a + b*x^4)/x^6, x, 2, -(a/(5*x^5)) - b/x]
    @test_int [(a + b*x^4)/x^7, x, 2, -(a/(6*x^6)) - b/(2*x^2)]
    @test_int [(a + b*x^4)/x^8, x, 2, -(a/(7*x^7)) - b/(3*x^3)]
    @test_int [(a + b*x^4)/x^9, x, 2, -(a/(8*x^8)) - b/(4*x^4)]
    @test_int [(a + b*x^4)/x^10, x, 2, -(a/(9*x^9)) - b/(5*x^5)]

    @test_int [x^m*(a + b*x^4)^2, x, 2, (a^2*x^(1 + m))/(1 + m) + (2*a*b*x^(5 + m))/(5 + m) + (b^2*x^(9 + m))/(9 + m)]

    @test_int [x^5*(a + b*x^4)^2, x, 2, (a^2*x^6)/6 + (1/5)*a*b*x^10 + (b^2*x^14)/14]
    @test_int [x^4*(a + b*x^4)^2, x, 2, (a^2*x^5)/5 + (2/9)*a*b*x^9 + (b^2*x^13)/13]
    @test_int [x^3*(a + b*x^4)^2, x, 1, (a + b*x^4)^3/(12*b)]
    @test_int [x^2*(a + b*x^4)^2, x, 2, (a^2*x^3)/3 + (2/7)*a*b*x^7 + (b^2*x^11)/11]
    @test_int [x^1*(a + b*x^4)^2, x, 2, (a^2*x^2)/2 + (1/3)*a*b*x^6 + (b^2*x^10)/10]
    @test_int [x^0*(a + b*x^4)^2, x, 2, a^2*x + (2/5)*a*b*x^5 + (b^2*x^9)/9]
    @test_int [(a + b*x^4)^2/x^1, x, 3, (1/2)*a*b*x^4 + (b^2*x^8)/8 + a^2*log(x)]
    @test_int [(a + b*x^4)^2/x^2, x, 2, -(a^2/x) + (2/3)*a*b*x^3 + (b^2*x^7)/7]
    @test_int [(a + b*x^4)^2/x^3, x, 2, -(a^2/(2*x^2)) + a*b*x^2 + (b^2*x^6)/6]
    @test_int [(a + b*x^4)^2/x^4, x, 2, -(a^2/(3*x^3)) + 2*a*b*x + (b^2*x^5)/5]
    @test_int [(a + b*x^4)^2/x^5, x, 3, -(a^2/(4*x^4)) + (b^2*x^4)/4 + 2*a*b*log(x)]

    @test_int [x^m*(a + b*x^4)^3, x, 2, (a^3*x^(1 + m))/(1 + m) + (3*a^2*b*x^(5 + m))/(5 + m) + (3*a*b^2*x^(9 + m))/(9 + m) + (b^3*x^(13 + m))/(13 + m)]

    @test_int [x^5*(a + b*x^4)^3, x, 2, (a^3*x^6)/6 + (3/10)*a^2*b*x^10 + (3/14)*a*b^2*x^14 + (b^3*x^18)/18]
    @test_int [x^4*(a + b*x^4)^3, x, 2, (a^3*x^5)/5 + (1/3)*a^2*b*x^9 + (3/13)*a*b^2*x^13 + (b^3*x^17)/17]
    @test_int [x^3*(a + b*x^4)^3, x, 1, (a + b*x^4)^4/(16*b)]
    @test_int [x^2*(a + b*x^4)^3, x, 2, (a^3*x^3)/3 + (3/7)*a^2*b*x^7 + (3/11)*a*b^2*x^11 + (b^3*x^15)/15]
    @test_int [x^1*(a + b*x^4)^3, x, 2, (a^3*x^2)/2 + (1/2)*a^2*b*x^6 + (3/10)*a*b^2*x^10 + (b^3*x^14)/14]
    @test_int [x^0*(a + b*x^4)^3, x, 2, a^3*x + (3/5)*a^2*b*x^5 + (1/3)*a*b^2*x^9 + (b^3*x^13)/13]
    @test_int [(a + b*x^4)^3/x^1, x, 3, (3/4)*a^2*b*x^4 + (3/8)*a*b^2*x^8 + (b^3*x^12)/12 + a^3*log(x)]
    @test_int [(a + b*x^4)^3/x^2, x, 2, -(a^3/x) + a^2*b*x^3 + (3/7)*a*b^2*x^7 + (b^3*x^11)/11]
    @test_int [(a + b*x^4)^3/x^3, x, 2, -(a^3/(2*x^2)) + (3/2)*a^2*b*x^2 + (1/2)*a*b^2*x^6 + (b^3*x^10)/10]
    @test_int [(a + b*x^4)^3/x^4, x, 2, -(a^3/(3*x^3)) + 3*a^2*b*x + (3/5)*a*b^2*x^5 + (b^3*x^9)/9]
    @test_int [(a + b*x^4)^3/x^5, x, 3, -(a^3/(4*x^4)) + (3/4)*a*b^2*x^4 + (b^3*x^8)/8 + 3*a^2*b*log(x)]

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [x^9/(a + c*x^4), x, 4, -((a*x^2)/(2*c^2)) + x^6/(6*c) + (a^(3/2)*atan((sqrt(c)*x^2)/sqrt(a)))/(2*c^(5/2))]
    @test_int [x^7/(a + c*x^4), x, 3, x^4/(4*c) - (a*log(a + c*x^4))/(4*c^2)]
    @test_int [x^5/(a + c*x^4), x, 3, x^2/(2*c) - (sqrt(a)*atan((sqrt(c)*x^2)/sqrt(a)))/(2*c^(3/2))]
    @test_int [x^3/(a + c*x^4), x, 1, log(a + c*x^4)/(4*c)]
    @test_int [x^1/(a + c*x^4), x, 2, atan((sqrt(c)*x^2)/sqrt(a))/(2*sqrt(a)*sqrt(c))]
    @test_int [1/(x^1*(a + c*x^4)), x, 4, log(x)/a - log(a + c*x^4)/(4*a)]
    @test_int [1/(x^3*(a + c*x^4)), x, 3, -1/(2*a*x^2) - (sqrt(c)*atan((sqrt(c)*x^2)/sqrt(a)))/(2*a^(3/2))]
    @test_int [1/(x^5*(a + c*x^4)), x, 3, -1/(4*a*x^4) - (c*log(x))/a^2 + (c*log(a + c*x^4))/(4*a^2)]
    @test_int [1/(x^7*(a + c*x^4)), x, 4, -(1/(6*a*x^6)) + c/(2*a^2*x^2) + (c^(3/2)*atan((sqrt(c)*x^2)/sqrt(a)))/(2*a^(5/2))]

    @test_int [x^4/(a + c*x^4), x, 10, x/c + (a^(1/4)*atan(1 - (sqrt(2)*c^(1/4)*x)/a^(1/4)))/(2*sqrt(2)*c^(5/4)) - (a^(1/4)*atan(1 + (sqrt(2)*c^(1/4)*x)/a^(1/4)))/(2*sqrt(2)*c^(5/4)) + (a^(1/4)*log(sqrt(a) - sqrt(2)*a^(1/4)*c^(1/4)*x + sqrt(c)*x^2))/(4*sqrt(2)*c^(5/4)) - (a^(1/4)*log(sqrt(a) + sqrt(2)*a^(1/4)*c^(1/4)*x + sqrt(c)*x^2))/(4*sqrt(2)*c^(5/4))]
    @test_int [x^2/(a + c*x^4), x, 9, -(atan(1 - (sqrt(2)*c^(1/4)*x)/a^(1/4))/(2*sqrt(2)*a^(1/4)*c^(3/4))) + atan(1 + (sqrt(2)*c^(1/4)*x)/a^(1/4))/(2*sqrt(2)*a^(1/4)*c^(3/4)) + log(sqrt(a) - sqrt(2)*a^(1/4)*c^(1/4)*x + sqrt(c)*x^2)/(4*sqrt(2)*a^(1/4)*c^(3/4)) - log(sqrt(a) + sqrt(2)*a^(1/4)*c^(1/4)*x + sqrt(c)*x^2)/(4*sqrt(2)*a^(1/4)*c^(3/4))]
    @test_int [x^0/(a + c*x^4), x, 9, -(atan(1 - (sqrt(2)*c^(1/4)*x)/a^(1/4))/(2*sqrt(2)*a^(3/4)*c^(1/4))) + atan(1 + (sqrt(2)*c^(1/4)*x)/a^(1/4))/(2*sqrt(2)*a^(3/4)*c^(1/4)) - log(sqrt(a) - sqrt(2)*a^(1/4)*c^(1/4)*x + sqrt(c)*x^2)/(4*sqrt(2)*a^(3/4)*c^(1/4)) + log(sqrt(a) + sqrt(2)*a^(1/4)*c^(1/4)*x + sqrt(c)*x^2)/(4*sqrt(2)*a^(3/4)*c^(1/4))]
    @test_int [1/(x^2*(a + c*x^4)), x, 10, -(1/(a*x)) + (c^(1/4)*atan(1 - (sqrt(2)*c^(1/4)*x)/a^(1/4)))/(2*sqrt(2)*a^(5/4)) - (c^(1/4)*atan(1 + (sqrt(2)*c^(1/4)*x)/a^(1/4)))/(2*sqrt(2)*a^(5/4)) - (c^(1/4)*log(sqrt(a) - sqrt(2)*a^(1/4)*c^(1/4)*x + sqrt(c)*x^2))/(4*sqrt(2)*a^(5/4)) + (c^(1/4)*log(sqrt(a) + sqrt(2)*a^(1/4)*c^(1/4)*x + sqrt(c)*x^2))/(4*sqrt(2)*a^(5/4))]
    @test_int [1/(x^4*(a + c*x^4)), x, 10, -(1/(3*a*x^3)) + (c^(3/4)*atan(1 - (sqrt(2)*c^(1/4)*x)/a^(1/4)))/(2*sqrt(2)*a^(7/4)) - (c^(3/4)*atan(1 + (sqrt(2)*c^(1/4)*x)/a^(1/4)))/(2*sqrt(2)*a^(7/4)) + (c^(3/4)*log(sqrt(a) - sqrt(2)*a^(1/4)*c^(1/4)*x + sqrt(c)*x^2))/(4*sqrt(2)*a^(7/4)) - (c^(3/4)*log(sqrt(a) + sqrt(2)*a^(1/4)*c^(1/4)*x + sqrt(c)*x^2))/(4*sqrt(2)*a^(7/4))]

    @test_int [x^11/(a + c*x^4)^2, x, 3, x^4/(4*c^2) - a^2/(4*c^3*(a + c*x^4)) - (a*log(a + c*x^4))/(2*c^3)]
    @test_int [x^9/(a + c*x^4)^2, x, 4, (3*x^2)/(4*c^2) - x^6/(4*c*(a + c*x^4)) - (3*sqrt(a)*atan((sqrt(c)*x^2)/sqrt(a)))/(4*c^(5/2))]
    @test_int [x^7/(a + c*x^4)^2, x, 3, a/(4*c^2*(a + c*x^4)) + log(a + c*x^4)/(4*c^2)]
    @test_int [x^5/(a + c*x^4)^2, x, 3, -x^2/(4*c*(a + c*x^4)) + atan((sqrt(c)*x^2)/sqrt(a))/(4*sqrt(a)*c^(3/2))]
    @test_int [x^3/(a + c*x^4)^2, x, 1, -1/(4*c*(a + c*x^4))]
    @test_int [x^1/(a + c*x^4)^2, x, 3, x^2/(4*a*(a + c*x^4)) + atan((sqrt(c)*x^2)/sqrt(a))/(4*a^(3/2)*sqrt(c))]
    @test_int [1/(x^1*(a + c*x^4)^2), x, 3, 1/(4*a*(a + c*x^4)) + log(x)/a^2 - log(a + c*x^4)/(4*a^2)]
    @test_int [1/(x^3*(a + c*x^4)^2), x, 4, -3/(4*a^2*x^2) + 1/(4*a*x^2*(a + c*x^4)) - (3*sqrt(c)*atan((sqrt(c)*x^2)/sqrt(a)))/(4*a^(5/2))]

    @test_int [x^6/(a + c*x^4)^2, x, 10, -(x^3/(4*c*(a + c*x^4))) - (3*atan(1 - (sqrt(2)*c^(1/4)*x)/a^(1/4)))/(8*sqrt(2)*a^(1/4)*c^(7/4)) + (3*atan(1 + (sqrt(2)*c^(1/4)*x)/a^(1/4)))/(8*sqrt(2)*a^(1/4)*c^(7/4)) + (3*log(sqrt(a) - sqrt(2)*a^(1/4)*c^(1/4)*x + sqrt(c)*x^2))/(16*sqrt(2)*a^(1/4)*c^(7/4)) - (3*log(sqrt(a) + sqrt(2)*a^(1/4)*c^(1/4)*x + sqrt(c)*x^2))/(16*sqrt(2)*a^(1/4)*c^(7/4))]
    @test_int [x^4/(a + c*x^4)^2, x, 10, -(x/(4*c*(a + c*x^4))) - atan(1 - (sqrt(2)*c^(1/4)*x)/a^(1/4))/(8*sqrt(2)*a^(3/4)*c^(5/4)) + atan(1 + (sqrt(2)*c^(1/4)*x)/a^(1/4))/(8*sqrt(2)*a^(3/4)*c^(5/4)) - log(sqrt(a) - sqrt(2)*a^(1/4)*c^(1/4)*x + sqrt(c)*x^2)/(16*sqrt(2)*a^(3/4)*c^(5/4)) + log(sqrt(a) + sqrt(2)*a^(1/4)*c^(1/4)*x + sqrt(c)*x^2)/(16*sqrt(2)*a^(3/4)*c^(5/4))]
    @test_int [x^2/(a + c*x^4)^2, x, 10, x^3/(4*a*(a + c*x^4)) - atan(1 - (sqrt(2)*c^(1/4)*x)/a^(1/4))/(8*sqrt(2)*a^(5/4)*c^(3/4)) + atan(1 + (sqrt(2)*c^(1/4)*x)/a^(1/4))/(8*sqrt(2)*a^(5/4)*c^(3/4)) + log(sqrt(a) - sqrt(2)*a^(1/4)*c^(1/4)*x + sqrt(c)*x^2)/(16*sqrt(2)*a^(5/4)*c^(3/4)) - log(sqrt(a) + sqrt(2)*a^(1/4)*c^(1/4)*x + sqrt(c)*x^2)/(16*sqrt(2)*a^(5/4)*c^(3/4))]
    @test_int [x^0/(a + c*x^4)^2, x, 10, x/(4*a*(a + c*x^4)) - (3*atan(1 - (sqrt(2)*c^(1/4)*x)/a^(1/4)))/(8*sqrt(2)*a^(7/4)*c^(1/4)) + (3*atan(1 + (sqrt(2)*c^(1/4)*x)/a^(1/4)))/(8*sqrt(2)*a^(7/4)*c^(1/4)) - (3*log(sqrt(a) - sqrt(2)*a^(1/4)*c^(1/4)*x + sqrt(c)*x^2))/(16*sqrt(2)*a^(7/4)*c^(1/4)) + (3*log(sqrt(a) + sqrt(2)*a^(1/4)*c^(1/4)*x + sqrt(c)*x^2))/(16*sqrt(2)*a^(7/4)*c^(1/4))]
    @test_int [1/(x^2*(a + c*x^4)^2), x, 11, -(5/(4*a^2*x)) + 1/(4*a*x*(a + c*x^4)) + (5*c^(1/4)*atan(1 - (sqrt(2)*c^(1/4)*x)/a^(1/4)))/(8*sqrt(2)*a^(9/4)) - (5*c^(1/4)*atan(1 + (sqrt(2)*c^(1/4)*x)/a^(1/4)))/(8*sqrt(2)*a^(9/4)) - (5*c^(1/4)*log(sqrt(a) - sqrt(2)*a^(1/4)*c^(1/4)*x + sqrt(c)*x^2))/(16*sqrt(2)*a^(9/4)) + (5*c^(1/4)*log(sqrt(a) + sqrt(2)*a^(1/4)*c^(1/4)*x + sqrt(c)*x^2))/(16*sqrt(2)*a^(9/4))]
    @test_int [1/(x^4*(a + c*x^4)^2), x, 11, -(7/(12*a^2*x^3)) + 1/(4*a*x^3*(a + c*x^4)) + (7*c^(3/4)*atan(1 - (sqrt(2)*c^(1/4)*x)/a^(1/4)))/(8*sqrt(2)*a^(11/4)) - (7*c^(3/4)*atan(1 + (sqrt(2)*c^(1/4)*x)/a^(1/4)))/(8*sqrt(2)*a^(11/4)) + (7*c^(3/4)*log(sqrt(a) - sqrt(2)*a^(1/4)*c^(1/4)*x + sqrt(c)*x^2))/(16*sqrt(2)*a^(11/4)) - (7*c^(3/4)*log(sqrt(a) + sqrt(2)*a^(1/4)*c^(1/4)*x + sqrt(c)*x^2))/(16*sqrt(2)*a^(11/4))]

    @test_int [x^11/(a + c*x^4)^3, x, 3, -(a^2/(8*c^3*(a + c*x^4)^2)) + a/(2*c^3*(a + c*x^4)) + log(a + c*x^4)/(4*c^3)]
    @test_int [x^9/(a + c*x^4)^3, x, 4, -x^6/(8*c*(a + c*x^4)^2) - (3*x^2)/(16*c^2*(a + c*x^4)) + (3*atan((sqrt(c)*x^2)/sqrt(a)))/(16*sqrt(a)*c^(5/2))]
    @test_int [x^7/(a + c*x^4)^3, x, 1, x^8/(8*a*(a + c*x^4)^2)]
    @test_int [x^5/(a + c*x^4)^3, x, 4, -x^2/(8*c*(a + c*x^4)^2) + x^2/(16*a*c*(a + c*x^4)) + atan((sqrt(c)*x^2)/sqrt(a))/(16*a^(3/2)*c^(3/2))]
    @test_int [x^3/(a + c*x^4)^3, x, 1, -1/(8*c*(a + c*x^4)^2)]
    @test_int [x^1/(a + c*x^4)^3, x, 4, x^2/(8*a*(a + c*x^4)^2) + (3*x^2)/(16*a^2*(a + c*x^4)) + (3*atan((sqrt(c)*x^2)/sqrt(a)))/(16*a^(5/2)*sqrt(c))]
    @test_int [1/(x^1*(a + c*x^4)^3), x, 3, 1/(8*a*(a + c*x^4)^2) + 1/(4*a^2*(a + c*x^4)) + log(x)/a^3 - log(a + c*x^4)/(4*a^3)]
    @test_int [1/(x^3*(a + c*x^4)^3), x, 5, -15/(16*a^3*x^2) + 1/(8*a*x^2*(a + c*x^4)^2) + 5/(16*a^2*x^2*(a + c*x^4)) - (15*sqrt(c)*atan((sqrt(c)*x^2)/sqrt(a)))/(16*a^(7/2))]

    @test_int [x^10/(a + c*x^4)^3, x, 11, -(x^7/(8*c*(a + c*x^4)^2)) - (7*x^3)/(32*c^2*(a + c*x^4)) - (21*atan(1 - (sqrt(2)*c^(1/4)*x)/a^(1/4)))/(64*sqrt(2)*a^(1/4)*c^(11/4)) + (21*atan(1 + (sqrt(2)*c^(1/4)*x)/a^(1/4)))/(64*sqrt(2)*a^(1/4)*c^(11/4)) + (21*log(sqrt(a) - sqrt(2)*a^(1/4)*c^(1/4)*x + sqrt(c)*x^2))/(128*sqrt(2)*a^(1/4)*c^(11/4)) - (21*log(sqrt(a) + sqrt(2)*a^(1/4)*c^(1/4)*x + sqrt(c)*x^2))/(128*sqrt(2)*a^(1/4)*c^(11/4))]
    @test_int [x^8/(a + c*x^4)^3, x, 11, -(x^5/(8*c*(a + c*x^4)^2)) - (5*x)/(32*c^2*(a + c*x^4)) - (5*atan(1 - (sqrt(2)*c^(1/4)*x)/a^(1/4)))/(64*sqrt(2)*a^(3/4)*c^(9/4)) + (5*atan(1 + (sqrt(2)*c^(1/4)*x)/a^(1/4)))/(64*sqrt(2)*a^(3/4)*c^(9/4)) - (5*log(sqrt(a) - sqrt(2)*a^(1/4)*c^(1/4)*x + sqrt(c)*x^2))/(128*sqrt(2)*a^(3/4)*c^(9/4)) + (5*log(sqrt(a) + sqrt(2)*a^(1/4)*c^(1/4)*x + sqrt(c)*x^2))/(128*sqrt(2)*a^(3/4)*c^(9/4))]
    @test_int [x^6/(a + c*x^4)^3, x, 11, -(x^3/(8*c*(a + c*x^4)^2)) + (3*x^3)/(32*a*c*(a + c*x^4)) - (3*atan(1 - (sqrt(2)*c^(1/4)*x)/a^(1/4)))/(64*sqrt(2)*a^(5/4)*c^(7/4)) + (3*atan(1 + (sqrt(2)*c^(1/4)*x)/a^(1/4)))/(64*sqrt(2)*a^(5/4)*c^(7/4)) + (3*log(sqrt(a) - sqrt(2)*a^(1/4)*c^(1/4)*x + sqrt(c)*x^2))/(128*sqrt(2)*a^(5/4)*c^(7/4)) - (3*log(sqrt(a) + sqrt(2)*a^(1/4)*c^(1/4)*x + sqrt(c)*x^2))/(128*sqrt(2)*a^(5/4)*c^(7/4))]
    @test_int [x^4/(a + c*x^4)^3, x, 11, -(x/(8*c*(a + c*x^4)^2)) + x/(32*a*c*(a + c*x^4)) - (3*atan(1 - (sqrt(2)*c^(1/4)*x)/a^(1/4)))/(64*sqrt(2)*a^(7/4)*c^(5/4)) + (3*atan(1 + (sqrt(2)*c^(1/4)*x)/a^(1/4)))/(64*sqrt(2)*a^(7/4)*c^(5/4)) - (3*log(sqrt(a) - sqrt(2)*a^(1/4)*c^(1/4)*x + sqrt(c)*x^2))/(128*sqrt(2)*a^(7/4)*c^(5/4)) + (3*log(sqrt(a) + sqrt(2)*a^(1/4)*c^(1/4)*x + sqrt(c)*x^2))/(128*sqrt(2)*a^(7/4)*c^(5/4))]
    @test_int [x^2/(a + c*x^4)^3, x, 11, x^3/(8*a*(a + c*x^4)^2) + (5*x^3)/(32*a^2*(a + c*x^4)) - (5*atan(1 - (sqrt(2)*c^(1/4)*x)/a^(1/4)))/(64*sqrt(2)*a^(9/4)*c^(3/4)) + (5*atan(1 + (sqrt(2)*c^(1/4)*x)/a^(1/4)))/(64*sqrt(2)*a^(9/4)*c^(3/4)) + (5*log(sqrt(a) - sqrt(2)*a^(1/4)*c^(1/4)*x + sqrt(c)*x^2))/(128*sqrt(2)*a^(9/4)*c^(3/4)) - (5*log(sqrt(a) + sqrt(2)*a^(1/4)*c^(1/4)*x + sqrt(c)*x^2))/(128*sqrt(2)*a^(9/4)*c^(3/4))]
    @test_int [x^0/(a + c*x^4)^3, x, 11, x/(8*a*(a + c*x^4)^2) + (7*x)/(32*a^2*(a + c*x^4)) - (21*atan(1 - (sqrt(2)*c^(1/4)*x)/a^(1/4)))/(64*sqrt(2)*a^(11/4)*c^(1/4)) + (21*atan(1 + (sqrt(2)*c^(1/4)*x)/a^(1/4)))/(64*sqrt(2)*a^(11/4)*c^(1/4)) - (21*log(sqrt(a) - sqrt(2)*a^(1/4)*c^(1/4)*x + sqrt(c)*x^2))/(128*sqrt(2)*a^(11/4)*c^(1/4)) + (21*log(sqrt(a) + sqrt(2)*a^(1/4)*c^(1/4)*x + sqrt(c)*x^2))/(128*sqrt(2)*a^(11/4)*c^(1/4))]
    @test_int [1/(x^2*(a + c*x^4)^3), x, 12, -(45/(32*a^3*x)) + 1/(8*a*x*(a + c*x^4)^2) + 9/(32*a^2*x*(a + c*x^4)) + (45*c^(1/4)*atan(1 - (sqrt(2)*c^(1/4)*x)/a^(1/4)))/(64*sqrt(2)*a^(13/4)) - (45*c^(1/4)*atan(1 + (sqrt(2)*c^(1/4)*x)/a^(1/4)))/(64*sqrt(2)*a^(13/4)) - (45*c^(1/4)*log(sqrt(a) - sqrt(2)*a^(1/4)*c^(1/4)*x + sqrt(c)*x^2))/(128*sqrt(2)*a^(13/4)) + (45*c^(1/4)*log(sqrt(a) + sqrt(2)*a^(1/4)*c^(1/4)*x + sqrt(c)*x^2))/(128*sqrt(2)*a^(13/4))]

    @test_int [x^9/(2 + 3*x^4), x, 4, -(x^2/9) + x^6/18 + (1/9)*sqrt(2/3)*atan(sqrt(3/2)*x^2)]
    @test_int [x^7/(2 + 3*x^4), x, 3, x^4/12 - (1/18)*log(2 + 3*x^4)]
    @test_int [x^5/(2 + 3*x^4), x, 3, x^2/6 - atan(sqrt(3/2)*x^2)/(3*sqrt(6))]
    @test_int [x^3/(2 + 3*x^4), x, 1, (1/12)*log(2 + 3*x^4)]
    @test_int [x^1/(2 + 3*x^4), x, 2, atan(sqrt(3/2)*x^2)/(2*sqrt(6))]
    @test_int [1/(x^1*(2 + 3*x^4)), x, 4, log(x)/2 - (1/8)*log(2 + 3*x^4)]
    @test_int [1/(x^3*(2 + 3*x^4)), x, 3, -(1/(4*x^2)) - (1/4)*sqrt(3/2)*atan(sqrt(3/2)*x^2)]

    @test_int [x^6/(2 + 3*x^4), x, 10, x^3/9 + atan(1 - 6^(1/4)*x)/(3*6^(3/4)) - atan(1 + 6^(1/4)*x)/(3*6^(3/4)) - log(sqrt(6) - 6^(3/4)*x + 3*x^2)/(6*6^(3/4)) + log(sqrt(6) + 6^(3/4)*x + 3*x^2)/(6*6^(3/4))]
    @test_int [x^4/(2 + 3*x^4), x, 10, x/3 + atan(1 - 6^(1/4)*x)/(6*6^(1/4)) - atan(1 + 6^(1/4)*x)/(6*6^(1/4)) + log(sqrt(6) - 6^(3/4)*x + 3*x^2)/(12*6^(1/4)) - log(sqrt(6) + 6^(3/4)*x + 3*x^2)/(12*6^(1/4))]
    @test_int [x^2/(2 + 3*x^4), x, 9, -(atan(1 - 6^(1/4)*x)/(2*6^(3/4))) + atan(1 + 6^(1/4)*x)/(2*6^(3/4)) + log(sqrt(6) - 6^(3/4)*x + 3*x^2)/(4*6^(3/4)) - log(sqrt(6) + 6^(3/4)*x + 3*x^2)/(4*6^(3/4))]
    @test_int [x^0/(2 + 3*x^4), x, 9, -(atan(1 - 6^(1/4)*x)/(4*6^(1/4))) + atan(1 + 6^(1/4)*x)/(4*6^(1/4)) - log(sqrt(6) - 6^(3/4)*x + 3*x^2)/(8*6^(1/4)) + log(sqrt(6) + 6^(3/4)*x + 3*x^2)/(8*6^(1/4))]
    @test_int [1/(x^2*(2 + 3*x^4)), x, 10, -(1/(2*x)) + (3^(1/4)*atan(1 - 6^(1/4)*x))/(4*2^(3/4)) - (3^(1/4)*atan(1 + 6^(1/4)*x))/(4*2^(3/4)) - (3^(1/4)*log(sqrt(6) - 6^(3/4)*x + 3*x^2))/(8*2^(3/4)) + (3^(1/4)*log(sqrt(6) + 6^(3/4)*x + 3*x^2))/(8*2^(3/4))]

    @test_int [x^3/(2 + 3*x^4)^2, x, 1, -(1/(12*(2 + 3*x^4)))]
    @test_int [x^1/(2 + 3*x^4)^2, x, 3, x^2/(8*(2 + 3*x^4)) + atan(sqrt(3/2)*x^2)/(8*sqrt(6))]
    @test_int [1/(x^1*(2 + 3*x^4)^2), x, 3, 1/(8*(2 + 3*x^4)) + log(x)/4 - (1/16)*log(2 + 3*x^4)]
    @test_int [1/(x^3*(2 + 3*x^4)^2), x, 4, -(3/(16*x^2)) + 1/(8*x^2*(2 + 3*x^4)) - (3/16)*sqrt(3/2)*atan(sqrt(3/2)*x^2)]

    @test_int [x^4/(2 + 3*x^4)^2, x, 10, -(x/(12*(2 + 3*x^4))) - atan(1 - 6^(1/4)*x)/(48*6^(1/4)) + atan(1 + 6^(1/4)*x)/(48*6^(1/4)) - log(sqrt(6) - 6^(3/4)*x + 3*x^2)/(96*6^(1/4)) + log(sqrt(6) + 6^(3/4)*x + 3*x^2)/(96*6^(1/4))]
    @test_int [x^2/(2 + 3*x^4)^2, x, 10, x^3/(8*(2 + 3*x^4)) - atan(1 - 6^(1/4)*x)/(16*6^(3/4)) + atan(1 + 6^(1/4)*x)/(16*6^(3/4)) + log(sqrt(6) - 6^(3/4)*x + 3*x^2)/(32*6^(3/4)) - log(sqrt(6) + 6^(3/4)*x + 3*x^2)/(32*6^(3/4))]
    @test_int [x^0/(2 + 3*x^4)^2, x, 10, x/(8*(2 + 3*x^4)) - (3^(3/4)*atan(1 - 6^(1/4)*x))/(32*2^(1/4)) + (3^(3/4)*atan(1 + 6^(1/4)*x))/(32*2^(1/4)) - (3^(3/4)*log(sqrt(6) - 6^(3/4)*x + 3*x^2))/(64*2^(1/4)) + (3^(3/4)*log(sqrt(6) + 6^(3/4)*x + 3*x^2))/(64*2^(1/4))]
    @test_int [1/(x^2*(2 + 3*x^4)^2), x, 11, -(5/(16*x)) + 1/(8*x*(2 + 3*x^4)) + (5*3^(1/4)*atan(1 - 6^(1/4)*x))/(32*2^(3/4)) - (5*3^(1/4)*atan(1 + 6^(1/4)*x))/(32*2^(3/4)) - (5*3^(1/4)*log(sqrt(6) - 6^(3/4)*x + 3*x^2))/(64*2^(3/4)) + (5*3^(1/4)*log(sqrt(6) + 6^(3/4)*x + 3*x^2))/(64*2^(3/4))]

    @test_int [x^2/(3 + x^4), x, 9, -(atan(1 - (sqrt(2)*x)/3^(1/4))/(2*sqrt(2)*3^(1/4))) + atan(1 + (sqrt(2)*x)/3^(1/4))/(2*sqrt(2)*3^(1/4)) + log(sqrt(3) - sqrt(2)*3^(1/4)*x + x^2)/(4*sqrt(2)*3^(1/4)) - log(sqrt(3) + sqrt(2)*3^(1/4)*x + x^2)/(4*sqrt(2)*3^(1/4))]

    @test_int [1/(1 + a + (-1 + a)*x^4), x, 3, atan(((1 - a)^(1/4)*x)/(1 + a)^(1/4))/(2*sqrt(1 + a)*(1 - a^2)^(1/4)) + atanh(((1 - a)^(1/4)*x)/(1 + a)^(1/4))/(2*sqrt(1 + a)*(1 - a^2)^(1/4))]

    #= Following*pairs*of*integrands*are*equal. =#
    @test_int [1/(2*a + 2*b + x^4), x, 3, -(atan(x/(2^(1/4)*(-a - b)^(1/4)))/(2*2^(3/4)*(-a - b)^(3/4))) - atanh(x/(2^(1/4)*(-a - b)^(1/4)))/(2*2^(3/4)*(-a - b)^(3/4))]
    @test_int [1/(2*(a + b) + x^4), x, 3, -(atan(x/(2^(1/4)*(-a - b)^(1/4)))/(2*2^(3/4)*(-a - b)^(3/4))) - atanh(x/(2^(1/4)*(-a - b)^(1/4)))/(2*2^(3/4)*(-a - b)^(3/4))]

    @test_int [x/(2*a + 2*b + x^4), x, 2, atan(x^2/(sqrt(2)*sqrt(a + b)))/(2*sqrt(2)*sqrt(a + b))]
    @test_int [x/(2*(a + b) + x^4), x, 2, atan(x^2/(sqrt(2)*sqrt(a + b)))/(2*sqrt(2)*sqrt(a + b))]

    @test_int [x^2/(2*a + 2*b + x^4), x, 3, atan(x/(2^(1/4)*(-a - b)^(1/4)))/(2*2^(1/4)*(-a - b)^(1/4)) - atanh(x/(2^(1/4)*(-a - b)^(1/4)))/(2*2^(1/4)*(-a - b)^(1/4))]
    @test_int [x^2/(2*(a + b) + x^4), x, 3, atan(x/(2^(1/4)*(-a - b)^(1/4)))/(2*2^(1/4)*(-a - b)^(1/4)) - atanh(x/(2^(1/4)*(-a - b)^(1/4)))/(2*2^(1/4)*(-a - b)^(1/4))]

    @test_int [x^3/(2*a + 2*b + x^4), x, 1, (1/4)*log(2*(a + b) + x^4)]
    @test_int [x^3/(2*(a + b) + x^4), x, 1, (1/4)*log(2*(a + b) + x^4)]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^(m/2)*(a+b*x^4)^p=#

    #= ::Subsubsection::Closed:: =#
    #=p>0=#

    @test_int [x^(5/2)*(a + c*x^4), x, 2, (2*a*x^(7/2))/7 + (2*c*x^(15/2))/15]
    @test_int [x^(3/2)*(a + c*x^4), x, 2, (2*a*x^(5/2))/5 + (2*c*x^(13/2))/13]
    @test_int [sqrt(x)*(a + c*x^4), x, 2, (2*a*x^(3/2))/3 + (2*c*x^(11/2))/11]
    @test_int [(a + c*x^4)/sqrt(x), x, 2, 2*a*sqrt(x) + (2*c*x^(9/2))/9]
    @test_int [(a + c*x^4)/x^(3/2), x, 2, (-2*a)/sqrt(x) + (2*c*x^(7/2))/7]
    @test_int [(a + c*x^4)/x^(5/2), x, 2, (-2*a)/(3*x^(3/2)) + (2*c*x^(5/2))/5]
    @test_int [(a + c*x^4)/x^(7/2), x, 2, (-2*a)/(5*x^(5/2)) + (2*c*x^(3/2))/3]

    @test_int [x^(5/2)*(a + c*x^4)^2, x, 2, (2*a^2*x^(7/2))/7 + (4*a*c*x^(15/2))/15 + (2*c^2*x^(23/2))/23]
    @test_int [x^(3/2)*(a + c*x^4)^2, x, 2, (2*a^2*x^(5/2))/5 + (4*a*c*x^(13/2))/13 + (2*c^2*x^(21/2))/21]
    @test_int [sqrt(x)*(a + c*x^4)^2, x, 2, (2*a^2*x^(3/2))/3 + (4*a*c*x^(11/2))/11 + (2*c^2*x^(19/2))/19]
    @test_int [(a + c*x^4)^2/sqrt(x), x, 2, 2*a^2*sqrt(x) + (4*a*c*x^(9/2))/9 + (2*c^2*x^(17/2))/17]
    @test_int [(a + c*x^4)^2/x^(3/2), x, 2, (-2*a^2)/sqrt(x) + (4*a*c*x^(7/2))/7 + (2*c^2*x^(15/2))/15]
    @test_int [(a + c*x^4)^2/x^(5/2), x, 2, (-2*a^2)/(3*x^(3/2)) + (4*a*c*x^(5/2))/5 + (2*c^2*x^(13/2))/13]
    @test_int [(a + c*x^4)^2/x^(7/2), x, 2, (-2*a^2)/(5*x^(5/2)) + (4*a*c*x^(3/2))/3 + (2*c^2*x^(11/2))/11]

    @test_int [x^(5/2)*(a + c*x^4)^3, x, 2, (2*a^3*x^(7/2))/7 + (2*a^2*c*x^(15/2))/5 + (6*a*c^2*x^(23/2))/23 + (2*c^3*x^(31/2))/31]
    @test_int [x^(3/2)*(a + c*x^4)^3, x, 2, (2*a^3*x^(5/2))/5 + (6*a^2*c*x^(13/2))/13 + (2*a*c^2*x^(21/2))/7 + (2*c^3*x^(29/2))/29]
    @test_int [sqrt(x)*(a + c*x^4)^3, x, 2, (2*a^3*x^(3/2))/3 + (6*a^2*c*x^(11/2))/11 + (6*a*c^2*x^(19/2))/19 + (2*c^3*x^(27/2))/27]
    @test_int [(a + c*x^4)^3/sqrt(x), x, 2, 2*a^3*sqrt(x) + (2*a^2*c*x^(9/2))/3 + (6*a*c^2*x^(17/2))/17 + (2*c^3*x^(25/2))/25]
    @test_int [(a + c*x^4)^3/x^(3/2), x, 2, (-2*a^3)/sqrt(x) + (6*a^2*c*x^(7/2))/7 + (2*a*c^2*x^(15/2))/5 + (2*c^3*x^(23/2))/23]
    @test_int [(a + c*x^4)^3/x^(5/2), x, 2, (-2*a^3)/(3*x^(3/2)) + (6*a^2*c*x^(5/2))/5 + (6*a*c^2*x^(13/2))/13 + (2*c^3*x^(21/2))/21]
    @test_int [(a + c*x^4)^3/x^(7/2), x, 2, (-2*a^3)/(5*x^(5/2)) + 2*a^2*c*x^(3/2) + (6*a*c^2*x^(11/2))/11 + (2*c^3*x^(19/2))/19]

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [x^(9/2)/(a + c*x^4), x, 15, (2*x^(3/2))/(3*c) + ((-a)^(3/8)*atan(1 - (sqrt(2)*c^(1/8)*sqrt(x))/(-a)^(1/8)))/(2*sqrt(2)*c^(11/8)) - ((-a)^(3/8)*atan(1 + (sqrt(2)*c^(1/8)*sqrt(x))/(-a)^(1/8)))/(2*sqrt(2)*c^(11/8)) + ((-a)^(3/8)*atan((c^(1/8)*sqrt(x))/(-a)^(1/8)))/(2*c^(11/8)) - ((-a)^(3/8)*atanh((c^(1/8)*sqrt(x))/(-a)^(1/8)))/(2*c^(11/8)) - ((-a)^(3/8)*log((-a)^(1/4) - sqrt(2)*(-a)^(1/8)*c^(1/8)*sqrt(x) + c^(1/4)*x))/(4*sqrt(2)*c^(11/8)) + ((-a)^(3/8)*log((-a)^(1/4) + sqrt(2)*(-a)^(1/8)*c^(1/8)*sqrt(x) + c^(1/4)*x))/(4*sqrt(2)*c^(11/8))]
    @test_int [x^(7/2)/(a + c*x^4), x, 15, (2*sqrt(x))/c + ((-a)^(1/8)*atan(1 - (sqrt(2)*c^(1/8)*sqrt(x))/(-a)^(1/8)))/(2*sqrt(2)*c^(9/8)) - ((-a)^(1/8)*atan(1 + (sqrt(2)*c^(1/8)*sqrt(x))/(-a)^(1/8)))/(2*sqrt(2)*c^(9/8)) - ((-a)^(1/8)*atan((c^(1/8)*sqrt(x))/(-a)^(1/8)))/(2*c^(9/8)) - ((-a)^(1/8)*atanh((c^(1/8)*sqrt(x))/(-a)^(1/8)))/(2*c^(9/8)) + ((-a)^(1/8)*log((-a)^(1/4) - sqrt(2)*(-a)^(1/8)*c^(1/8)*sqrt(x) + c^(1/4)*x))/(4*sqrt(2)*c^(9/8)) - ((-a)^(1/8)*log((-a)^(1/4) + sqrt(2)*(-a)^(1/8)*c^(1/8)*sqrt(x) + c^(1/4)*x))/(4*sqrt(2)*c^(9/8))]
    @test_int [x^(5/2)/(a + c*x^4), x, 14, -(atan(1 - (sqrt(2)*c^(1/8)*sqrt(x))/(-a)^(1/8))/(2*sqrt(2)*(-a)^(1/8)*c^(7/8))) + atan(1 + (sqrt(2)*c^(1/8)*sqrt(x))/(-a)^(1/8))/(2*sqrt(2)*(-a)^(1/8)*c^(7/8)) + atan((c^(1/8)*sqrt(x))/(-a)^(1/8))/(2*(-a)^(1/8)*c^(7/8)) - atanh((c^(1/8)*sqrt(x))/(-a)^(1/8))/(2*(-a)^(1/8)*c^(7/8)) + log((-a)^(1/4) - sqrt(2)*(-a)^(1/8)*c^(1/8)*sqrt(x) + c^(1/4)*x)/(4*sqrt(2)*(-a)^(1/8)*c^(7/8)) - log((-a)^(1/4) + sqrt(2)*(-a)^(1/8)*c^(1/8)*sqrt(x) + c^(1/4)*x)/(4*sqrt(2)*(-a)^(1/8)*c^(7/8))]
    @test_int [x^(3/2)/(a + c*x^4), x, 14, -(atan(1 - (sqrt(2)*c^(1/8)*sqrt(x))/(-a)^(1/8))/(2*sqrt(2)*(-a)^(3/8)*c^(5/8))) + atan(1 + (sqrt(2)*c^(1/8)*sqrt(x))/(-a)^(1/8))/(2*sqrt(2)*(-a)^(3/8)*c^(5/8)) - atan((c^(1/8)*sqrt(x))/(-a)^(1/8))/(2*(-a)^(3/8)*c^(5/8)) - atanh((c^(1/8)*sqrt(x))/(-a)^(1/8))/(2*(-a)^(3/8)*c^(5/8)) - log((-a)^(1/4) - sqrt(2)*(-a)^(1/8)*c^(1/8)*sqrt(x) + c^(1/4)*x)/(4*sqrt(2)*(-a)^(3/8)*c^(5/8)) + log((-a)^(1/4) + sqrt(2)*(-a)^(1/8)*c^(1/8)*sqrt(x) + c^(1/4)*x)/(4*sqrt(2)*(-a)^(3/8)*c^(5/8))]
    @test_int [sqrt(x)/(a + c*x^4), x, 14, atan(1 - (sqrt(2)*c^(1/8)*sqrt(x))/(-a)^(1/8))/(2*sqrt(2)*(-a)^(5/8)*c^(3/8)) - atan(1 + (sqrt(2)*c^(1/8)*sqrt(x))/(-a)^(1/8))/(2*sqrt(2)*(-a)^(5/8)*c^(3/8)) + atan((c^(1/8)*sqrt(x))/(-a)^(1/8))/(2*(-a)^(5/8)*c^(3/8)) - atanh((c^(1/8)*sqrt(x))/(-a)^(1/8))/(2*(-a)^(5/8)*c^(3/8)) - log((-a)^(1/4) - sqrt(2)*(-a)^(1/8)*c^(1/8)*sqrt(x) + c^(1/4)*x)/(4*sqrt(2)*(-a)^(5/8)*c^(3/8)) + log((-a)^(1/4) + sqrt(2)*(-a)^(1/8)*c^(1/8)*sqrt(x) + c^(1/4)*x)/(4*sqrt(2)*(-a)^(5/8)*c^(3/8))]
    @test_int [1/(sqrt(x)*(a + c*x^4)), x, 14, atan(1 - (sqrt(2)*c^(1/8)*sqrt(x))/(-a)^(1/8))/(2*sqrt(2)*(-a)^(7/8)*c^(1/8)) - atan(1 + (sqrt(2)*c^(1/8)*sqrt(x))/(-a)^(1/8))/(2*sqrt(2)*(-a)^(7/8)*c^(1/8)) - atan((c^(1/8)*sqrt(x))/(-a)^(1/8))/(2*(-a)^(7/8)*c^(1/8)) - atanh((c^(1/8)*sqrt(x))/(-a)^(1/8))/(2*(-a)^(7/8)*c^(1/8)) + log((-a)^(1/4) - sqrt(2)*(-a)^(1/8)*c^(1/8)*sqrt(x) + c^(1/4)*x)/(4*sqrt(2)*(-a)^(7/8)*c^(1/8)) - log((-a)^(1/4) + sqrt(2)*(-a)^(1/8)*c^(1/8)*sqrt(x) + c^(1/4)*x)/(4*sqrt(2)*(-a)^(7/8)*c^(1/8))]
    @test_int [1/(x^(3/2)*(a + c*x^4)), x, 15, -(2/(a*sqrt(x))) - (c^(1/8)*atan(1 - (sqrt(2)*c^(1/8)*sqrt(x))/(-a)^(1/8)))/(2*sqrt(2)*(-a)^(9/8)) + (c^(1/8)*atan(1 + (sqrt(2)*c^(1/8)*sqrt(x))/(-a)^(1/8)))/(2*sqrt(2)*(-a)^(9/8)) + (c^(1/8)*atan((c^(1/8)*sqrt(x))/(-a)^(1/8)))/(2*(-a)^(9/8)) - (c^(1/8)*atanh((c^(1/8)*sqrt(x))/(-a)^(1/8)))/(2*(-a)^(9/8)) + (c^(1/8)*log((-a)^(1/4) - sqrt(2)*(-a)^(1/8)*c^(1/8)*sqrt(x) + c^(1/4)*x))/(4*sqrt(2)*(-a)^(9/8)) - (c^(1/8)*log((-a)^(1/4) + sqrt(2)*(-a)^(1/8)*c^(1/8)*sqrt(x) + c^(1/4)*x))/(4*sqrt(2)*(-a)^(9/8))]
    @test_int [1/(x^(5/2)*(a + c*x^4)), x, 15, -(2/(3*a*x^(3/2))) - (c^(3/8)*atan(1 - (sqrt(2)*c^(1/8)*sqrt(x))/(-a)^(1/8)))/(2*sqrt(2)*(-a)^(11/8)) + (c^(3/8)*atan(1 + (sqrt(2)*c^(1/8)*sqrt(x))/(-a)^(1/8)))/(2*sqrt(2)*(-a)^(11/8)) - (c^(3/8)*atan((c^(1/8)*sqrt(x))/(-a)^(1/8)))/(2*(-a)^(11/8)) - (c^(3/8)*atanh((c^(1/8)*sqrt(x))/(-a)^(1/8)))/(2*(-a)^(11/8)) - (c^(3/8)*log((-a)^(1/4) - sqrt(2)*(-a)^(1/8)*c^(1/8)*sqrt(x) + c^(1/4)*x))/(4*sqrt(2)*(-a)^(11/8)) + (c^(3/8)*log((-a)^(1/4) + sqrt(2)*(-a)^(1/8)*c^(1/8)*sqrt(x) + c^(1/4)*x))/(4*sqrt(2)*(-a)^(11/8))]

    @test_int [x^(13/2)/(a + c*x^4)^2, x, 15, -(x^(7/2)/(4*c*(a + c*x^4))) - (7*atan(1 - (sqrt(2)*c^(1/8)*sqrt(x))/(-a)^(1/8)))/(16*sqrt(2)*(-a)^(1/8)*c^(15/8)) + (7*atan(1 + (sqrt(2)*c^(1/8)*sqrt(x))/(-a)^(1/8)))/(16*sqrt(2)*(-a)^(1/8)*c^(15/8)) + (7*atan((c^(1/8)*sqrt(x))/(-a)^(1/8)))/(16*(-a)^(1/8)*c^(15/8)) - (7*atanh((c^(1/8)*sqrt(x))/(-a)^(1/8)))/(16*(-a)^(1/8)*c^(15/8)) + (7*log((-a)^(1/4) - sqrt(2)*(-a)^(1/8)*c^(1/8)*sqrt(x) + c^(1/4)*x))/(32*sqrt(2)*(-a)^(1/8)*c^(15/8)) - (7*log((-a)^(1/4) + sqrt(2)*(-a)^(1/8)*c^(1/8)*sqrt(x) + c^(1/4)*x))/(32*sqrt(2)*(-a)^(1/8)*c^(15/8))]
    @test_int [x^(11/2)/(a + c*x^4)^2, x, 15, -(x^(5/2)/(4*c*(a + c*x^4))) - (5*atan(1 - (sqrt(2)*c^(1/8)*sqrt(x))/(-a)^(1/8)))/(16*sqrt(2)*(-a)^(3/8)*c^(13/8)) + (5*atan(1 + (sqrt(2)*c^(1/8)*sqrt(x))/(-a)^(1/8)))/(16*sqrt(2)*(-a)^(3/8)*c^(13/8)) - (5*atan((c^(1/8)*sqrt(x))/(-a)^(1/8)))/(16*(-a)^(3/8)*c^(13/8)) - (5*atanh((c^(1/8)*sqrt(x))/(-a)^(1/8)))/(16*(-a)^(3/8)*c^(13/8)) - (5*log((-a)^(1/4) - sqrt(2)*(-a)^(1/8)*c^(1/8)*sqrt(x) + c^(1/4)*x))/(32*sqrt(2)*(-a)^(3/8)*c^(13/8)) + (5*log((-a)^(1/4) + sqrt(2)*(-a)^(1/8)*c^(1/8)*sqrt(x) + c^(1/4)*x))/(32*sqrt(2)*(-a)^(3/8)*c^(13/8))]
    @test_int [x^(9/2)/(a + c*x^4)^2, x, 15, -(x^(3/2)/(4*c*(a + c*x^4))) + (3*atan(1 - (sqrt(2)*c^(1/8)*sqrt(x))/(-a)^(1/8)))/(16*sqrt(2)*(-a)^(5/8)*c^(11/8)) - (3*atan(1 + (sqrt(2)*c^(1/8)*sqrt(x))/(-a)^(1/8)))/(16*sqrt(2)*(-a)^(5/8)*c^(11/8)) + (3*atan((c^(1/8)*sqrt(x))/(-a)^(1/8)))/(16*(-a)^(5/8)*c^(11/8)) - (3*atanh((c^(1/8)*sqrt(x))/(-a)^(1/8)))/(16*(-a)^(5/8)*c^(11/8)) - (3*log((-a)^(1/4) - sqrt(2)*(-a)^(1/8)*c^(1/8)*sqrt(x) + c^(1/4)*x))/(32*sqrt(2)*(-a)^(5/8)*c^(11/8)) + (3*log((-a)^(1/4) + sqrt(2)*(-a)^(1/8)*c^(1/8)*sqrt(x) + c^(1/4)*x))/(32*sqrt(2)*(-a)^(5/8)*c^(11/8))]
    @test_int [x^(7/2)/(a + c*x^4)^2, x, 15, -(sqrt(x)/(4*c*(a + c*x^4))) + atan(1 - (sqrt(2)*c^(1/8)*sqrt(x))/(-a)^(1/8))/(16*sqrt(2)*(-a)^(7/8)*c^(9/8)) - atan(1 + (sqrt(2)*c^(1/8)*sqrt(x))/(-a)^(1/8))/(16*sqrt(2)*(-a)^(7/8)*c^(9/8)) - atan((c^(1/8)*sqrt(x))/(-a)^(1/8))/(16*(-a)^(7/8)*c^(9/8)) - atanh((c^(1/8)*sqrt(x))/(-a)^(1/8))/(16*(-a)^(7/8)*c^(9/8)) + log((-a)^(1/4) - sqrt(2)*(-a)^(1/8)*c^(1/8)*sqrt(x) + c^(1/4)*x)/(32*sqrt(2)*(-a)^(7/8)*c^(9/8)) - log((-a)^(1/4) + sqrt(2)*(-a)^(1/8)*c^(1/8)*sqrt(x) + c^(1/4)*x)/(32*sqrt(2)*(-a)^(7/8)*c^(9/8))]
    @test_int [x^(5/2)/(a + c*x^4)^2, x, 15, x^(7/2)/(4*a*(a + c*x^4)) + atan(1 - (sqrt(2)*c^(1/8)*sqrt(x))/(-a)^(1/8))/(16*sqrt(2)*(-a)^(9/8)*c^(7/8)) - atan(1 + (sqrt(2)*c^(1/8)*sqrt(x))/(-a)^(1/8))/(16*sqrt(2)*(-a)^(9/8)*c^(7/8)) - atan((c^(1/8)*sqrt(x))/(-a)^(1/8))/(16*(-a)^(9/8)*c^(7/8)) + atanh((c^(1/8)*sqrt(x))/(-a)^(1/8))/(16*(-a)^(9/8)*c^(7/8)) - log((-a)^(1/4) - sqrt(2)*(-a)^(1/8)*c^(1/8)*sqrt(x) + c^(1/4)*x)/(32*sqrt(2)*(-a)^(9/8)*c^(7/8)) + log((-a)^(1/4) + sqrt(2)*(-a)^(1/8)*c^(1/8)*sqrt(x) + c^(1/4)*x)/(32*sqrt(2)*(-a)^(9/8)*c^(7/8))]
    @test_int [x^(3/2)/(a + c*x^4)^2, x, 15, x^(5/2)/(4*a*(a + c*x^4)) + (3*atan(1 - (sqrt(2)*c^(1/8)*sqrt(x))/(-a)^(1/8)))/(16*sqrt(2)*(-a)^(11/8)*c^(5/8)) - (3*atan(1 + (sqrt(2)*c^(1/8)*sqrt(x))/(-a)^(1/8)))/(16*sqrt(2)*(-a)^(11/8)*c^(5/8)) + (3*atan((c^(1/8)*sqrt(x))/(-a)^(1/8)))/(16*(-a)^(11/8)*c^(5/8)) + (3*atanh((c^(1/8)*sqrt(x))/(-a)^(1/8)))/(16*(-a)^(11/8)*c^(5/8)) + (3*log((-a)^(1/4) - sqrt(2)*(-a)^(1/8)*c^(1/8)*sqrt(x) + c^(1/4)*x))/(32*sqrt(2)*(-a)^(11/8)*c^(5/8)) - (3*log((-a)^(1/4) + sqrt(2)*(-a)^(1/8)*c^(1/8)*sqrt(x) + c^(1/4)*x))/(32*sqrt(2)*(-a)^(11/8)*c^(5/8))]
    @test_int [sqrt(x)/(a + c*x^4)^2, x, 15, x^(3/2)/(4*a*(a + c*x^4)) - (5*atan(1 - (sqrt(2)*c^(1/8)*sqrt(x))/(-a)^(1/8)))/(16*sqrt(2)*(-a)^(13/8)*c^(3/8)) + (5*atan(1 + (sqrt(2)*c^(1/8)*sqrt(x))/(-a)^(1/8)))/(16*sqrt(2)*(-a)^(13/8)*c^(3/8)) - (5*atan((c^(1/8)*sqrt(x))/(-a)^(1/8)))/(16*(-a)^(13/8)*c^(3/8)) + (5*atanh((c^(1/8)*sqrt(x))/(-a)^(1/8)))/(16*(-a)^(13/8)*c^(3/8)) + (5*log((-a)^(1/4) - sqrt(2)*(-a)^(1/8)*c^(1/8)*sqrt(x) + c^(1/4)*x))/(32*sqrt(2)*(-a)^(13/8)*c^(3/8)) - (5*log((-a)^(1/4) + sqrt(2)*(-a)^(1/8)*c^(1/8)*sqrt(x) + c^(1/4)*x))/(32*sqrt(2)*(-a)^(13/8)*c^(3/8))]
    @test_int [1/(sqrt(x)*(a + c*x^4)^2), x, 15, sqrt(x)/(4*a*(a + c*x^4)) - (7*atan(1 - (sqrt(2)*c^(1/8)*sqrt(x))/(-a)^(1/8)))/(16*sqrt(2)*(-a)^(15/8)*c^(1/8)) + (7*atan(1 + (sqrt(2)*c^(1/8)*sqrt(x))/(-a)^(1/8)))/(16*sqrt(2)*(-a)^(15/8)*c^(1/8)) + (7*atan((c^(1/8)*sqrt(x))/(-a)^(1/8)))/(16*(-a)^(15/8)*c^(1/8)) + (7*atanh((c^(1/8)*sqrt(x))/(-a)^(1/8)))/(16*(-a)^(15/8)*c^(1/8)) - (7*log((-a)^(1/4) - sqrt(2)*(-a)^(1/8)*c^(1/8)*sqrt(x) + c^(1/4)*x))/(32*sqrt(2)*(-a)^(15/8)*c^(1/8)) + (7*log((-a)^(1/4) + sqrt(2)*(-a)^(1/8)*c^(1/8)*sqrt(x) + c^(1/4)*x))/(32*sqrt(2)*(-a)^(15/8)*c^(1/8))]
    @test_int [1/(x^(3/2)*(a + c*x^4)^2), x, 16, -(9/(4*a^2*sqrt(x))) + 1/(4*a*sqrt(x)*(a + c*x^4)) + (9*c^(1/8)*atan(1 - (sqrt(2)*c^(1/8)*sqrt(x))/(-a)^(1/8)))/(16*sqrt(2)*(-a)^(17/8)) - (9*c^(1/8)*atan(1 + (sqrt(2)*c^(1/8)*sqrt(x))/(-a)^(1/8)))/(16*sqrt(2)*(-a)^(17/8)) - (9*c^(1/8)*atan((c^(1/8)*sqrt(x))/(-a)^(1/8)))/(16*(-a)^(17/8)) + (9*c^(1/8)*atanh((c^(1/8)*sqrt(x))/(-a)^(1/8)))/(16*(-a)^(17/8)) - (9*c^(1/8)*log((-a)^(1/4) - sqrt(2)*(-a)^(1/8)*c^(1/8)*sqrt(x) + c^(1/4)*x))/(32*sqrt(2)*(-a)^(17/8)) + (9*c^(1/8)*log((-a)^(1/4) + sqrt(2)*(-a)^(1/8)*c^(1/8)*sqrt(x) + c^(1/4)*x))/(32*sqrt(2)*(-a)^(17/8))]

    @test_int [x^(15/2)/(a + c*x^4)^3, x, 16, -(x^(9/2)/(8*c*(a + c*x^4)^2)) - (9*sqrt(x))/(64*c^2*(a + c*x^4)) + (9*atan(1 - (sqrt(2)*c^(1/8)*sqrt(x))/(-a)^(1/8)))/(256*sqrt(2)*(-a)^(7/8)*c^(17/8)) - (9*atan(1 + (sqrt(2)*c^(1/8)*sqrt(x))/(-a)^(1/8)))/(256*sqrt(2)*(-a)^(7/8)*c^(17/8)) - (9*atan((c^(1/8)*sqrt(x))/(-a)^(1/8)))/(256*(-a)^(7/8)*c^(17/8)) - (9*atanh((c^(1/8)*sqrt(x))/(-a)^(1/8)))/(256*(-a)^(7/8)*c^(17/8)) + (9*log((-a)^(1/4) - sqrt(2)*(-a)^(1/8)*c^(1/8)*sqrt(x) + c^(1/4)*x))/(512*sqrt(2)*(-a)^(7/8)*c^(17/8)) - (9*log((-a)^(1/4) + sqrt(2)*(-a)^(1/8)*c^(1/8)*sqrt(x) + c^(1/4)*x))/(512*sqrt(2)*(-a)^(7/8)*c^(17/8))]
    @test_int [x^(13/2)/(a + c*x^4)^3, x, 16, -(x^(7/2)/(8*c*(a + c*x^4)^2)) + (7*x^(7/2))/(64*a*c*(a + c*x^4)) + (7*atan(1 - (sqrt(2)*c^(1/8)*sqrt(x))/(-a)^(1/8)))/(256*sqrt(2)*(-a)^(9/8)*c^(15/8)) - (7*atan(1 + (sqrt(2)*c^(1/8)*sqrt(x))/(-a)^(1/8)))/(256*sqrt(2)*(-a)^(9/8)*c^(15/8)) - (7*atan((c^(1/8)*sqrt(x))/(-a)^(1/8)))/(256*(-a)^(9/8)*c^(15/8)) + (7*atanh((c^(1/8)*sqrt(x))/(-a)^(1/8)))/(256*(-a)^(9/8)*c^(15/8)) - (7*log((-a)^(1/4) - sqrt(2)*(-a)^(1/8)*c^(1/8)*sqrt(x) + c^(1/4)*x))/(512*sqrt(2)*(-a)^(9/8)*c^(15/8)) + (7*log((-a)^(1/4) + sqrt(2)*(-a)^(1/8)*c^(1/8)*sqrt(x) + c^(1/4)*x))/(512*sqrt(2)*(-a)^(9/8)*c^(15/8))]
    @test_int [x^(11/2)/(a + c*x^4)^3, x, 16, -(x^(5/2)/(8*c*(a + c*x^4)^2)) + (5*x^(5/2))/(64*a*c*(a + c*x^4)) + (15*atan(1 - (sqrt(2)*c^(1/8)*sqrt(x))/(-a)^(1/8)))/(256*sqrt(2)*(-a)^(11/8)*c^(13/8)) - (15*atan(1 + (sqrt(2)*c^(1/8)*sqrt(x))/(-a)^(1/8)))/(256*sqrt(2)*(-a)^(11/8)*c^(13/8)) + (15*atan((c^(1/8)*sqrt(x))/(-a)^(1/8)))/(256*(-a)^(11/8)*c^(13/8)) + (15*atanh((c^(1/8)*sqrt(x))/(-a)^(1/8)))/(256*(-a)^(11/8)*c^(13/8)) + (15*log((-a)^(1/4) - sqrt(2)*(-a)^(1/8)*c^(1/8)*sqrt(x) + c^(1/4)*x))/(512*sqrt(2)*(-a)^(11/8)*c^(13/8)) - (15*log((-a)^(1/4) + sqrt(2)*(-a)^(1/8)*c^(1/8)*sqrt(x) + c^(1/4)*x))/(512*sqrt(2)*(-a)^(11/8)*c^(13/8))]
    @test_int [x^(9/2)/(a + c*x^4)^3, x, 16, -(x^(3/2)/(8*c*(a + c*x^4)^2)) + (3*x^(3/2))/(64*a*c*(a + c*x^4)) - (15*atan(1 - (sqrt(2)*c^(1/8)*sqrt(x))/(-a)^(1/8)))/(256*sqrt(2)*(-a)^(13/8)*c^(11/8)) + (15*atan(1 + (sqrt(2)*c^(1/8)*sqrt(x))/(-a)^(1/8)))/(256*sqrt(2)*(-a)^(13/8)*c^(11/8)) - (15*atan((c^(1/8)*sqrt(x))/(-a)^(1/8)))/(256*(-a)^(13/8)*c^(11/8)) + (15*atanh((c^(1/8)*sqrt(x))/(-a)^(1/8)))/(256*(-a)^(13/8)*c^(11/8)) + (15*log((-a)^(1/4) - sqrt(2)*(-a)^(1/8)*c^(1/8)*sqrt(x) + c^(1/4)*x))/(512*sqrt(2)*(-a)^(13/8)*c^(11/8)) - (15*log((-a)^(1/4) + sqrt(2)*(-a)^(1/8)*c^(1/8)*sqrt(x) + c^(1/4)*x))/(512*sqrt(2)*(-a)^(13/8)*c^(11/8))]
    @test_int [x^(7/2)/(a + c*x^4)^3, x, 16, -(sqrt(x)/(8*c*(a + c*x^4)^2)) + sqrt(x)/(64*a*c*(a + c*x^4)) - (7*atan(1 - (sqrt(2)*c^(1/8)*sqrt(x))/(-a)^(1/8)))/(256*sqrt(2)*(-a)^(15/8)*c^(9/8)) + (7*atan(1 + (sqrt(2)*c^(1/8)*sqrt(x))/(-a)^(1/8)))/(256*sqrt(2)*(-a)^(15/8)*c^(9/8)) + (7*atan((c^(1/8)*sqrt(x))/(-a)^(1/8)))/(256*(-a)^(15/8)*c^(9/8)) + (7*atanh((c^(1/8)*sqrt(x))/(-a)^(1/8)))/(256*(-a)^(15/8)*c^(9/8)) - (7*log((-a)^(1/4) - sqrt(2)*(-a)^(1/8)*c^(1/8)*sqrt(x) + c^(1/4)*x))/(512*sqrt(2)*(-a)^(15/8)*c^(9/8)) + (7*log((-a)^(1/4) + sqrt(2)*(-a)^(1/8)*c^(1/8)*sqrt(x) + c^(1/4)*x))/(512*sqrt(2)*(-a)^(15/8)*c^(9/8))]
    @test_int [x^(5/2)/(a + c*x^4)^3, x, 16, x^(7/2)/(8*a*(a + c*x^4)^2) + (9*x^(7/2))/(64*a^2*(a + c*x^4)) - (9*atan(1 - (sqrt(2)*c^(1/8)*sqrt(x))/(-a)^(1/8)))/(256*sqrt(2)*(-a)^(17/8)*c^(7/8)) + (9*atan(1 + (sqrt(2)*c^(1/8)*sqrt(x))/(-a)^(1/8)))/(256*sqrt(2)*(-a)^(17/8)*c^(7/8)) + (9*atan((c^(1/8)*sqrt(x))/(-a)^(1/8)))/(256*(-a)^(17/8)*c^(7/8)) - (9*atanh((c^(1/8)*sqrt(x))/(-a)^(1/8)))/(256*(-a)^(17/8)*c^(7/8)) + (9*log((-a)^(1/4) - sqrt(2)*(-a)^(1/8)*c^(1/8)*sqrt(x) + c^(1/4)*x))/(512*sqrt(2)*(-a)^(17/8)*c^(7/8)) - (9*log((-a)^(1/4) + sqrt(2)*(-a)^(1/8)*c^(1/8)*sqrt(x) + c^(1/4)*x))/(512*sqrt(2)*(-a)^(17/8)*c^(7/8))]
    @test_int [x^(3/2)/(a + c*x^4)^3, x, 16, x^(5/2)/(8*a*(a + c*x^4)^2) + (11*x^(5/2))/(64*a^2*(a + c*x^4)) - (33*atan(1 - (sqrt(2)*c^(1/8)*sqrt(x))/(-a)^(1/8)))/(256*sqrt(2)*(-a)^(19/8)*c^(5/8)) + (33*atan(1 + (sqrt(2)*c^(1/8)*sqrt(x))/(-a)^(1/8)))/(256*sqrt(2)*(-a)^(19/8)*c^(5/8)) - (33*atan((c^(1/8)*sqrt(x))/(-a)^(1/8)))/(256*(-a)^(19/8)*c^(5/8)) - (33*atanh((c^(1/8)*sqrt(x))/(-a)^(1/8)))/(256*(-a)^(19/8)*c^(5/8)) - (33*log((-a)^(1/4) - sqrt(2)*(-a)^(1/8)*c^(1/8)*sqrt(x) + c^(1/4)*x))/(512*sqrt(2)*(-a)^(19/8)*c^(5/8)) + (33*log((-a)^(1/4) + sqrt(2)*(-a)^(1/8)*c^(1/8)*sqrt(x) + c^(1/4)*x))/(512*sqrt(2)*(-a)^(19/8)*c^(5/8))]
    @test_int [sqrt(x)/(a + c*x^4)^3, x, 16, x^(3/2)/(8*a*(a + c*x^4)^2) + (13*x^(3/2))/(64*a^2*(a + c*x^4)) + (65*atan(1 - (sqrt(2)*c^(1/8)*sqrt(x))/(-a)^(1/8)))/(256*sqrt(2)*(-a)^(21/8)*c^(3/8)) - (65*atan(1 + (sqrt(2)*c^(1/8)*sqrt(x))/(-a)^(1/8)))/(256*sqrt(2)*(-a)^(21/8)*c^(3/8)) + (65*atan((c^(1/8)*sqrt(x))/(-a)^(1/8)))/(256*(-a)^(21/8)*c^(3/8)) - (65*atanh((c^(1/8)*sqrt(x))/(-a)^(1/8)))/(256*(-a)^(21/8)*c^(3/8)) - (65*log((-a)^(1/4) - sqrt(2)*(-a)^(1/8)*c^(1/8)*sqrt(x) + c^(1/4)*x))/(512*sqrt(2)*(-a)^(21/8)*c^(3/8)) + (65*log((-a)^(1/4) + sqrt(2)*(-a)^(1/8)*c^(1/8)*sqrt(x) + c^(1/4)*x))/(512*sqrt(2)*(-a)^(21/8)*c^(3/8))]
    @test_int [1/(sqrt(x)*(a + c*x^4)^3), x, 16, sqrt(x)/(8*a*(a + c*x^4)^2) + (15*sqrt(x))/(64*a^2*(a + c*x^4)) + (105*atan(1 - (sqrt(2)*c^(1/8)*sqrt(x))/(-a)^(1/8)))/(256*sqrt(2)*(-a)^(23/8)*c^(1/8)) - (105*atan(1 + (sqrt(2)*c^(1/8)*sqrt(x))/(-a)^(1/8)))/(256*sqrt(2)*(-a)^(23/8)*c^(1/8)) - (105*atan((c^(1/8)*sqrt(x))/(-a)^(1/8)))/(256*(-a)^(23/8)*c^(1/8)) - (105*atanh((c^(1/8)*sqrt(x))/(-a)^(1/8)))/(256*(-a)^(23/8)*c^(1/8)) + (105*log((-a)^(1/4) - sqrt(2)*(-a)^(1/8)*c^(1/8)*sqrt(x) + c^(1/4)*x))/(512*sqrt(2)*(-a)^(23/8)*c^(1/8)) - (105*log((-a)^(1/4) + sqrt(2)*(-a)^(1/8)*c^(1/8)*sqrt(x) + c^(1/4)*x))/(512*sqrt(2)*(-a)^(23/8)*c^(1/8))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b*x^4)^(p/2)=#

    #= ::Subsubsection::Closed:: =#
    #=p>0=#

    @test_int [x^11*sqrt(a + c*x^4), x, 3, (a^2*(a + c*x^4)^(3/2))/(6*c^3) - (a*(a + c*x^4)^(5/2))/(5*c^3) + (a + c*x^4)^(7/2)/(14*c^3)]
    @test_int [x^7*sqrt(a + c*x^4), x, 3, -(a*(a + c*x^4)^(3/2))/(6*c^2) + (a + c*x^4)^(5/2)/(10*c^2)]
    @test_int [x^3*sqrt(a + c*x^4), x, 1, (a + c*x^4)^(3/2)/(6*c)]
    @test_int [sqrt(a + c*x^4)/x^1, x, 4, sqrt(a + c*x^4)/2 - (sqrt(a)*atanh(sqrt(a + c*x^4)/sqrt(a)))/2]
    @test_int [sqrt(a + c*x^4)/x^5, x, 4, -sqrt(a + c*x^4)/(4*x^4) - (c*atanh(sqrt(a + c*x^4)/sqrt(a)))/(4*sqrt(a))]
    @test_int [sqrt(a + c*x^4)/x^9, x, 5, -sqrt(a + c*x^4)/(8*x^8) - (c*sqrt(a + c*x^4))/(16*a*x^4) + (c^2*atanh(sqrt(a + c*x^4)/sqrt(a)))/(16*a^(3/2))]

    @test_int [x^5*sqrt(a + c*x^4), x, 5, (a*x^2*sqrt(a + c*x^4))/(16*c) + (x^6*sqrt(a + c*x^4))/8 - (a^2*atanh((sqrt(c)*x^2)/sqrt(a + c*x^4)))/(16*c^(3/2))]
    @test_int [x^1*sqrt(a + c*x^4), x, 4, (x^2*sqrt(a + c*x^4))/4 + (a*atanh((sqrt(c)*x^2)/sqrt(a + c*x^4)))/(4*sqrt(c))]
    @test_int [sqrt(a + c*x^4)/x^3, x, 4, -sqrt(a + c*x^4)/(2*x^2) + (sqrt(c)*atanh((sqrt(c)*x^2)/sqrt(a + c*x^4)))/2]
    @test_int [sqrt(a + c*x^4)/x^7, x, 1, -(a + c*x^4)^(3/2)/(6*a*x^6)]
    @test_int [sqrt(a + c*x^4)/x^11, x, 2, -(a + c*x^4)^(3/2)/(10*a*x^10) + (c*(a + c*x^4)^(3/2))/(15*a^2*x^6)]
    @test_int [sqrt(a + c*x^4)/x^15, x, 3, -((a + c*x^4)^(3/2)/(14*a*x^14)) + (2*c*(a + c*x^4)^(3/2))/(35*a^2*x^10) - (4*c^2*(a + c*x^4)^(3/2))/(105*a^3*x^6)]

    @test_int [x^4*sqrt(a + c*x^4), x, 3, (2*a*x*sqrt(a + c*x^4))/(21*c) + (1/7)*x^5*sqrt(a + c*x^4) - (a^(7/4)*(sqrt(a) + sqrt(c)*x^2)*sqrt((a + c*x^4)/(sqrt(a) + sqrt(c)*x^2)^2)*Elliptic.F(2*atan((c^(1/4)*x)/a^(1/4)), 1/2))/(21*c^(5/4)*sqrt(a + c*x^4))]
    @test_int [x^0*sqrt(a + c*x^4), x, 2, (1/3)*x*sqrt(a + c*x^4) + (a^(3/4)*(sqrt(a) + sqrt(c)*x^2)*sqrt((a + c*x^4)/(sqrt(a) + sqrt(c)*x^2)^2)*Elliptic.F(2*atan((c^(1/4)*x)/a^(1/4)), 1/2))/(3*c^(1/4)*sqrt(a + c*x^4))]
    @test_int [sqrt(a + c*x^4)/x^4, x, 2, -(sqrt(a + c*x^4)/(3*x^3)) + (c^(3/4)*(sqrt(a) + sqrt(c)*x^2)*sqrt((a + c*x^4)/(sqrt(a) + sqrt(c)*x^2)^2)*Elliptic.F(2*atan((c^(1/4)*x)/a^(1/4)), 1/2))/(3*a^(1/4)*sqrt(a + c*x^4))]
    @test_int [sqrt(a + c*x^4)/x^8, x, 3, -(sqrt(a + c*x^4)/(7*x^7)) - (2*c*sqrt(a + c*x^4))/(21*a*x^3) - (c^(7/4)*(sqrt(a) + sqrt(c)*x^2)*sqrt((a + c*x^4)/(sqrt(a) + sqrt(c)*x^2)^2)*Elliptic.F(2*atan((c^(1/4)*x)/a^(1/4)), 1/2))/(21*a^(5/4)*sqrt(a + c*x^4))]

    @test_int [x^2*sqrt(a + c*x^4), x, 4, (1/5)*x^3*sqrt(a + c*x^4) + (2*a*x*sqrt(a + c*x^4))/(5*sqrt(c)*(sqrt(a) + sqrt(c)*x^2)) - (2*a^(5/4)*(sqrt(a) + sqrt(c)*x^2)*sqrt((a + c*x^4)/(sqrt(a) + sqrt(c)*x^2)^2)*Elliptic.E(2*atan((c^(1/4)*x)/a^(1/4)), 1/2))/(5*c^(3/4)*sqrt(a + c*x^4)) + (a^(5/4)*(sqrt(a) + sqrt(c)*x^2)*sqrt((a + c*x^4)/(sqrt(a) + sqrt(c)*x^2)^2)*Elliptic.F(2*atan((c^(1/4)*x)/a^(1/4)), 1/2))/(5*c^(3/4)*sqrt(a + c*x^4))]
    @test_int [sqrt(a + c*x^4)/x^2, x, 4, -(sqrt(a + c*x^4)/x) + (2*sqrt(c)*x*sqrt(a + c*x^4))/(sqrt(a) + sqrt(c)*x^2) - (2*a^(1/4)*c^(1/4)*(sqrt(a) + sqrt(c)*x^2)*sqrt((a + c*x^4)/(sqrt(a) + sqrt(c)*x^2)^2)*Elliptic.E(2*atan((c^(1/4)*x)/a^(1/4)), 1/2))/sqrt(a + c*x^4) + (a^(1/4)*c^(1/4)*(sqrt(a) + sqrt(c)*x^2)*sqrt((a + c*x^4)/(sqrt(a) + sqrt(c)*x^2)^2)*Elliptic.F(2*atan((c^(1/4)*x)/a^(1/4)), 1/2))/sqrt(a + c*x^4)]
    @test_int [sqrt(a + c*x^4)/x^6, x, 5, -(sqrt(a + c*x^4)/(5*x^5)) - (2*c*sqrt(a + c*x^4))/(5*a*x) + (2*c^(3/2)*x*sqrt(a + c*x^4))/(5*a*(sqrt(a) + sqrt(c)*x^2)) - (2*c^(5/4)*(sqrt(a) + sqrt(c)*x^2)*sqrt((a + c*x^4)/(sqrt(a) + sqrt(c)*x^2)^2)*Elliptic.E(2*atan((c^(1/4)*x)/a^(1/4)), 1/2))/(5*a^(3/4)*sqrt(a + c*x^4)) + (c^(5/4)*(sqrt(a) + sqrt(c)*x^2)*sqrt((a + c*x^4)/(sqrt(a) + sqrt(c)*x^2)^2)*Elliptic.F(2*atan((c^(1/4)*x)/a^(1/4)), 1/2))/(5*a^(3/4)*sqrt(a + c*x^4))]

    @test_int [x^11*(a + c*x^4)^(3/2), x, 3, (a^2*(a + c*x^4)^(5/2))/(10*c^3) - (a*(a + c*x^4)^(7/2))/(7*c^3) + (a + c*x^4)^(9/2)/(18*c^3)]
    @test_int [x^7*(a + c*x^4)^(3/2), x, 3, -(a*(a + c*x^4)^(5/2))/(10*c^2) + (a + c*x^4)^(7/2)/(14*c^2)]
    @test_int [x^3*(a + c*x^4)^(3/2), x, 1, (a + c*x^4)^(5/2)/(10*c)]
    @test_int [(a + c*x^4)^(3/2)/x^1, x, 5, (a*sqrt(a + c*x^4))/2 + (a + c*x^4)^(3/2)/6 - (a^(3/2)*atanh(sqrt(a + c*x^4)/sqrt(a)))/2]
    @test_int [(a + c*x^4)^(3/2)/x^5, x, 5, (3*c*sqrt(a + c*x^4))/4 - (a + c*x^4)^(3/2)/(4*x^4) - (3*sqrt(a)*c*atanh(sqrt(a + c*x^4)/sqrt(a)))/4]
    @test_int [(a + c*x^4)^(3/2)/x^9, x, 5, (-3*c*sqrt(a + c*x^4))/(16*x^4) - (a + c*x^4)^(3/2)/(8*x^8) - (3*c^2*atanh(sqrt(a + c*x^4)/sqrt(a)))/(16*sqrt(a))]

    @test_int [x^5*(a + c*x^4)^(3/2), x, 6, (a^2*x^2*sqrt(a + c*x^4))/(32*c) + (a*x^6*sqrt(a + c*x^4))/16 + (x^6*(a + c*x^4)^(3/2))/12 - (a^3*atanh((sqrt(c)*x^2)/sqrt(a + c*x^4)))/(32*c^(3/2))]
    @test_int [x^1*(a + c*x^4)^(3/2), x, 5, (3*a*x^2*sqrt(a + c*x^4))/16 + (x^2*(a + c*x^4)^(3/2))/8 + (3*a^2*atanh((sqrt(c)*x^2)/sqrt(a + c*x^4)))/(16*sqrt(c))]
    @test_int [(a + c*x^4)^(3/2)/x^3, x, 5, (3*c*x^2*sqrt(a + c*x^4))/4 - (a + c*x^4)^(3/2)/(2*x^2) + (3*a*sqrt(c)*atanh((sqrt(c)*x^2)/sqrt(a + c*x^4)))/4]
    @test_int [(a + c*x^4)^(3/2)/x^7, x, 5, -(c*sqrt(a + c*x^4))/(2*x^2) - (a + c*x^4)^(3/2)/(6*x^6) + (c^(3/2)*atanh((sqrt(c)*x^2)/sqrt(a + c*x^4)))/2]
    @test_int [(a + c*x^4)^(3/2)/x^11, x, 1, -(a + c*x^4)^(5/2)/(10*a*x^10)]
    @test_int [(a + c*x^4)^(3/2)/x^15, x, 2, -(a + c*x^4)^(5/2)/(14*a*x^14) + (c*(a + c*x^4)^(5/2))/(35*a^2*x^10)]
    @test_int [(a + c*x^4)^(3/2)/x^19, x, 3, -((a + c*x^4)^(5/2)/(18*a*x^18)) + (2*c*(a + c*x^4)^(5/2))/(63*a^2*x^14) - (4*c^2*(a + c*x^4)^(5/2))/(315*a^3*x^10)]

    @test_int [x^4*(a + c*x^4)^(3/2), x, 4, (4*a^2*x*sqrt(a + c*x^4))/(77*c) + (6/77)*a*x^5*sqrt(a + c*x^4) + (1/11)*x^5*(a + c*x^4)^(3/2) - (2*a^(11/4)*(sqrt(a) + sqrt(c)*x^2)*sqrt((a + c*x^4)/(sqrt(a) + sqrt(c)*x^2)^2)*Elliptic.F(2*atan((c^(1/4)*x)/a^(1/4)), 1/2))/(77*c^(5/4)*sqrt(a + c*x^4))]
    @test_int [x^0*(a + c*x^4)^(3/2), x, 3, (2/7)*a*x*sqrt(a + c*x^4) + (1/7)*x*(a + c*x^4)^(3/2) + (2*a^(7/4)*(sqrt(a) + sqrt(c)*x^2)*sqrt((a + c*x^4)/(sqrt(a) + sqrt(c)*x^2)^2)*Elliptic.F(2*atan((c^(1/4)*x)/a^(1/4)), 1/2))/(7*c^(1/4)*sqrt(a + c*x^4))]
    @test_int [(a + c*x^4)^(3/2)/x^4, x, 3, (2/3)*c*x*sqrt(a + c*x^4) - (a + c*x^4)^(3/2)/(3*x^3) + (2*a^(3/4)*c^(3/4)*(sqrt(a) + sqrt(c)*x^2)*sqrt((a + c*x^4)/(sqrt(a) + sqrt(c)*x^2)^2)*Elliptic.F(2*atan((c^(1/4)*x)/a^(1/4)), 1/2))/(3*sqrt(a + c*x^4))]
    @test_int [(a + c*x^4)^(3/2)/x^8, x, 3, -((2*c*sqrt(a + c*x^4))/(7*x^3)) - (a + c*x^4)^(3/2)/(7*x^7) + (2*c^(7/4)*(sqrt(a) + sqrt(c)*x^2)*sqrt((a + c*x^4)/(sqrt(a) + sqrt(c)*x^2)^2)*Elliptic.F(2*atan((c^(1/4)*x)/a^(1/4)), 1/2))/(7*a^(1/4)*sqrt(a + c*x^4))]

    @test_int [x^2*(a + c*x^4)^(3/2), x, 5, (2/15)*a*x^3*sqrt(a + c*x^4) + (4*a^2*x*sqrt(a + c*x^4))/(15*sqrt(c)*(sqrt(a) + sqrt(c)*x^2)) + (1/9)*x^3*(a + c*x^4)^(3/2) - (4*a^(9/4)*(sqrt(a) + sqrt(c)*x^2)*sqrt((a + c*x^4)/(sqrt(a) + sqrt(c)*x^2)^2)*Elliptic.E(2*atan((c^(1/4)*x)/a^(1/4)), 1/2))/(15*c^(3/4)*sqrt(a + c*x^4)) + (2*a^(9/4)*(sqrt(a) + sqrt(c)*x^2)*sqrt((a + c*x^4)/(sqrt(a) + sqrt(c)*x^2)^2)*Elliptic.F(2*atan((c^(1/4)*x)/a^(1/4)), 1/2))/(15*c^(3/4)*sqrt(a + c*x^4))]
    @test_int [(a + c*x^4)^(3/2)/x^2, x, 5, (6/5)*c*x^3*sqrt(a + c*x^4) + (12*a*sqrt(c)*x*sqrt(a + c*x^4))/(5*(sqrt(a) + sqrt(c)*x^2)) - (a + c*x^4)^(3/2)/x - (12*a^(5/4)*c^(1/4)*(sqrt(a) + sqrt(c)*x^2)*sqrt((a + c*x^4)/(sqrt(a) + sqrt(c)*x^2)^2)*Elliptic.E(2*atan((c^(1/4)*x)/a^(1/4)), 1/2))/(5*sqrt(a + c*x^4)) + (6*a^(5/4)*c^(1/4)*(sqrt(a) + sqrt(c)*x^2)*sqrt((a + c*x^4)/(sqrt(a) + sqrt(c)*x^2)^2)*Elliptic.F(2*atan((c^(1/4)*x)/a^(1/4)), 1/2))/(5*sqrt(a + c*x^4))]
    @test_int [(a + c*x^4)^(3/2)/x^6, x, 5, -((6*c*sqrt(a + c*x^4))/(5*x)) + (12*c^(3/2)*x*sqrt(a + c*x^4))/(5*(sqrt(a) + sqrt(c)*x^2)) - (a + c*x^4)^(3/2)/(5*x^5) - (12*a^(1/4)*c^(5/4)*(sqrt(a) + sqrt(c)*x^2)*sqrt((a + c*x^4)/(sqrt(a) + sqrt(c)*x^2)^2)*Elliptic.E(2*atan((c^(1/4)*x)/a^(1/4)), 1/2))/(5*sqrt(a + c*x^4)) + (6*a^(1/4)*c^(5/4)*(sqrt(a) + sqrt(c)*x^2)*sqrt((a + c*x^4)/(sqrt(a) + sqrt(c)*x^2)^2)*Elliptic.F(2*atan((c^(1/4)*x)/a^(1/4)), 1/2))/(5*sqrt(a + c*x^4))]

    @test_int [(1 + x^4)^(3/2), x, 3, (2/7)*x*sqrt(1 + x^4) + (1/7)*x*(1 + x^4)^(3/2) + (2*(1 + x^2)*sqrt((1 + x^4)/(1 + x^2)^2)*Elliptic.F(2*atan(x), 1/2))/(7*sqrt(1 + x^4))]
    @test_int [(1 - x^4)^(3/2), x, 3, (2/7)*x*sqrt(1 - x^4) + (1/7)*x*(1 - x^4)^(3/2) + (4/7)*Elliptic.F(asin(x), -1)]

    @test_int [x^7*sqrt(5 + 3*x^4), x, 3, (-(5/54))*(5 + 3*x^4)^(3/2) + (1/90)*(5 + 3*x^4)^(5/2)]
    @test_int [x^3*sqrt(5 + x^4), x, 1, (1/6)*(5 + x^4)^(3/2)]
    @test_int [x*sqrt(3 + 2*x^4), x, 3, (1/4)*x^2*sqrt(3 + 2*x^4) + (3*asinh(sqrt(2/3)*x^2))/(4*sqrt(2))]
    @test_int [x*sqrt(-2 + x^4), x, 4, (1/4)*x^2*sqrt(-2 + x^4) - (1/2)*atanh(x^2/sqrt(-2 + x^4))]
    @test_int [(1 + x^4)^(1/2), x, 2, (1/3)*x*sqrt(1 + x^4) + ((1 + x^2)*sqrt((1 + x^4)/(1 + x^2)^2)*Elliptic.F(2*atan(x), 1/2))/(3*sqrt(1 + x^4))]
    @test_int [(1 - x^4)^(1/2), x, 2, (1/3)*x*sqrt(1 - x^4) + (2/3)*Elliptic.F(asin(x), -1)]

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [x^11/sqrt(a + b*x^4), x, 3, (a^2*sqrt(a + b*x^4))/(2*b^3) - (a*(a + b*x^4)^(3/2))/(3*b^3) + (a + b*x^4)^(5/2)/(10*b^3)]
    @test_int [x^7/sqrt(a + b*x^4), x, 3, -((a*sqrt(a + b*x^4))/(2*b^2)) + (a + b*x^4)^(3/2)/(6*b^2)]
    @test_int [x^3/sqrt(a + b*x^4), x, 1, sqrt(a + b*x^4)/(2*b)]
    @test_int [1/(x^1*sqrt(a + b*x^4)), x, 3, -atanh(sqrt(a + b*x^4)/sqrt(a))/(2*sqrt(a))]
    @test_int [1/(x^5*sqrt(a + b*x^4)), x, 4, -sqrt(a + b*x^4)/(4*a*x^4) + (b*atanh(sqrt(a + b*x^4)/sqrt(a)))/(4*a^(3/2))]

    @test_int [x^5/sqrt(a + b*x^4), x, 4, (x^2*sqrt(a + b*x^4))/(4*b) - (a*atanh((sqrt(b)*x^2)/sqrt(a + b*x^4)))/(4*b^(3/2))]
    @test_int [x^1/sqrt(a + b*x^4), x, 3, atanh((sqrt(b)*x^2)/sqrt(a + b*x^4))/(2*sqrt(b))]
    @test_int [1/(x^3*sqrt(a + b*x^4)), x, 1, -sqrt(a + b*x^4)/(2*a*x^2)]
    @test_int [1/(x^7*sqrt(a + b*x^4)), x, 2, -sqrt(a + b*x^4)/(6*a*x^6) + (b*sqrt(a + b*x^4))/(3*a^2*x^2)]
    @test_int [1/(x^11*sqrt(a + b*x^4)), x, 3, -(sqrt(a + b*x^4)/(10*a*x^10)) + (2*b*sqrt(a + b*x^4))/(15*a^2*x^6) - (4*b^2*sqrt(a + b*x^4))/(15*a^3*x^2)]

    @test_int [x^8/sqrt(a + b*x^4), x, 3, -((5*a*x*sqrt(a + b*x^4))/(21*b^2)) + (x^5*sqrt(a + b*x^4))/(7*b) + (5*a^(7/4)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(42*b^(9/4)*sqrt(a + b*x^4))]
    @test_int [x^4/sqrt(a + b*x^4), x, 2, (x*sqrt(a + b*x^4))/(3*b) - (a^(3/4)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(6*b^(5/4)*sqrt(a + b*x^4))]
    @test_int [x^0/sqrt(a + b*x^4), x, 1, ((sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(2*a^(1/4)*b^(1/4)*sqrt(a + b*x^4))]
    @test_int [1/(x^4*sqrt(a + b*x^4)), x, 2, -(sqrt(a + b*x^4)/(3*a*x^3)) - (b^(3/4)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(6*a^(5/4)*sqrt(a + b*x^4))]
    @test_int [1/(x^8*sqrt(a + b*x^4)), x, 3, -(sqrt(a + b*x^4)/(7*a*x^7)) + (5*b*sqrt(a + b*x^4))/(21*a^2*x^3) + (5*b^(7/4)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(42*a^(9/4)*sqrt(a + b*x^4))]

    @test_int [x^10/sqrt(a + b*x^4), x, 5, -((7*a*x^3*sqrt(a + b*x^4))/(45*b^2)) + (x^7*sqrt(a + b*x^4))/(9*b) + (7*a^2*x*sqrt(a + b*x^4))/(15*b^(5/2)*(sqrt(a) + sqrt(b)*x^2)) - (7*a^(9/4)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.E(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(15*b^(11/4)*sqrt(a + b*x^4)) + (7*a^(9/4)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(30*b^(11/4)*sqrt(a + b*x^4))]
    @test_int [x^6/sqrt(a + b*x^4), x, 4, (x^3*sqrt(a + b*x^4))/(5*b) - (3*a*x*sqrt(a + b*x^4))/(5*b^(3/2)*(sqrt(a) + sqrt(b)*x^2)) + (3*a^(5/4)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.E(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(5*b^(7/4)*sqrt(a + b*x^4)) - (3*a^(5/4)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(10*b^(7/4)*sqrt(a + b*x^4))]
    @test_int [x^2/sqrt(a + b*x^4), x, 3, (x*sqrt(a + b*x^4))/(sqrt(b)*(sqrt(a) + sqrt(b)*x^2)) - (a^(1/4)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.E(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(b^(3/4)*sqrt(a + b*x^4)) + (a^(1/4)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(2*b^(3/4)*sqrt(a + b*x^4))]
    @test_int [1/(x^2*sqrt(a + b*x^4)), x, 4, -(sqrt(a + b*x^4)/(a*x)) + (sqrt(b)*x*sqrt(a + b*x^4))/(a*(sqrt(a) + sqrt(b)*x^2)) - (b^(1/4)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.E(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(a^(3/4)*sqrt(a + b*x^4)) + (b^(1/4)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(2*a^(3/4)*sqrt(a + b*x^4))]
    @test_int [1/(x^6*sqrt(a + b*x^4)), x, 5, -(sqrt(a + b*x^4)/(5*a*x^5)) + (3*b*sqrt(a + b*x^4))/(5*a^2*x) - (3*b^(3/2)*x*sqrt(a + b*x^4))/(5*a^2*(sqrt(a) + sqrt(b)*x^2)) + (3*b^(5/4)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.E(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(5*a^(7/4)*sqrt(a + b*x^4)) - (3*b^(5/4)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(10*a^(7/4)*sqrt(a + b*x^4))]

    @test_int [x^11/sqrt(a - b*x^4), x, 3, -((a^2*sqrt(a - b*x^4))/(2*b^3)) + (a*(a - b*x^4)^(3/2))/(3*b^3) - (a - b*x^4)^(5/2)/(10*b^3)]
    @test_int [x^7/sqrt(a - b*x^4), x, 3, -((a*sqrt(a - b*x^4))/(2*b^2)) + (a - b*x^4)^(3/2)/(6*b^2)]
    @test_int [x^3/sqrt(a - b*x^4), x, 1, -(sqrt(a - b*x^4)/(2*b))]
    @test_int [1/(x^1*sqrt(a - b*x^4)), x, 3, -atanh(sqrt(a - b*x^4)/sqrt(a))/(2*sqrt(a))]
    @test_int [1/(x^5*sqrt(a - b*x^4)), x, 4, -(sqrt(a - b*x^4)/(4*a*x^4)) - (b*atanh(sqrt(a - b*x^4)/sqrt(a)))/(4*a^(3/2))]

    @test_int [x^5/sqrt(a - b*x^4), x, 4, -((x^2*sqrt(a - b*x^4))/(4*b)) + (a*atan((sqrt(b)*x^2)/sqrt(a - b*x^4)))/(4*b^(3/2))]
    @test_int [x^1/sqrt(a - b*x^4), x, 3, atan((sqrt(b)*x^2)/sqrt(a - b*x^4))/(2*sqrt(b))]
    @test_int [1/(x^3*sqrt(a - b*x^4)), x, 1, -sqrt(a - b*x^4)/(2*a*x^2)]
    @test_int [1/(x^7*sqrt(a - b*x^4)), x, 2, -(sqrt(a - b*x^4)/(6*a*x^6)) - (b*sqrt(a - b*x^4))/(3*a^2*x^2)]
    @test_int [1/(x^11*sqrt(a - b*x^4)), x, 3, -(sqrt(a - b*x^4)/(10*a*x^10)) - (2*b*sqrt(a - b*x^4))/(15*a^2*x^6) - (4*b^2*sqrt(a - b*x^4))/(15*a^3*x^2)]

    @test_int [x^8/sqrt(a - b*x^4), x, 4, -((5*a*x*sqrt(a - b*x^4))/(21*b^2)) - (x^5*sqrt(a - b*x^4))/(7*b) + (5*a^(9/4)*sqrt(1 - (b*x^4)/a)*Elliptic.F(asin((b^(1/4)*x)/a^(1/4)), -1))/(21*b^(9/4)*sqrt(a - b*x^4))]
    @test_int [x^4/sqrt(a - b*x^4), x, 3, -((x*sqrt(a - b*x^4))/(3*b)) + (a^(5/4)*sqrt(1 - (b*x^4)/a)*Elliptic.F(asin((b^(1/4)*x)/a^(1/4)), -1))/(3*b^(5/4)*sqrt(a - b*x^4))]
    @test_int [x^0/sqrt(a - b*x^4), x, 2, (a^(1/4)*sqrt(1 - (b*x^4)/a)*Elliptic.F(asin((b^(1/4)*x)/a^(1/4)), -1))/(b^(1/4)*sqrt(a - b*x^4))]
    @test_int [1/(x^4*sqrt(a - b*x^4)), x, 3, -(sqrt(a - b*x^4)/(3*a*x^3)) + (b^(3/4)*sqrt(1 - (b*x^4)/a)*Elliptic.F(asin((b^(1/4)*x)/a^(1/4)), -1))/(3*a^(3/4)*sqrt(a - b*x^4))]
    @test_int [1/(x^8*sqrt(a - b*x^4)), x, 4, -(sqrt(a - b*x^4)/(7*a*x^7)) - (5*b*sqrt(a - b*x^4))/(21*a^2*x^3) + (5*b^(7/4)*sqrt(1 - (b*x^4)/a)*Elliptic.F(asin((b^(1/4)*x)/a^(1/4)), -1))/(21*a^(7/4)*sqrt(a - b*x^4))]

    @test_int [x^10/sqrt(a - b*x^4), x, 8, -((7*a*x^3*sqrt(a - b*x^4))/(45*b^2)) - (x^7*sqrt(a - b*x^4))/(9*b) + (7*a^(11/4)*sqrt(1 - (b*x^4)/a)*Elliptic.E(asin((b^(1/4)*x)/a^(1/4)), -1))/(15*b^(11/4)*sqrt(a - b*x^4)) - (7*a^(11/4)*sqrt(1 - (b*x^4)/a)*Elliptic.F(asin((b^(1/4)*x)/a^(1/4)), -1))/(15*b^(11/4)*sqrt(a - b*x^4))]
    @test_int [x^6/sqrt(a - b*x^4), x, 7, -((x^3*sqrt(a - b*x^4))/(5*b)) + (3*a^(7/4)*sqrt(1 - (b*x^4)/a)*Elliptic.E(asin((b^(1/4)*x)/a^(1/4)), -1))/(5*b^(7/4)*sqrt(a - b*x^4)) - (3*a^(7/4)*sqrt(1 - (b*x^4)/a)*Elliptic.F(asin((b^(1/4)*x)/a^(1/4)), -1))/(5*b^(7/4)*sqrt(a - b*x^4))]
    @test_int [x^2/sqrt(a - b*x^4), x, 6, (a^(3/4)*sqrt(1 - (b*x^4)/a)*Elliptic.E(asin((b^(1/4)*x)/a^(1/4)), -1))/(b^(3/4)*sqrt(a - b*x^4)) - (a^(3/4)*sqrt(1 - (b*x^4)/a)*Elliptic.F(asin((b^(1/4)*x)/a^(1/4)), -1))/(b^(3/4)*sqrt(a - b*x^4))]
    @test_int [1/(x^2*sqrt(a - b*x^4)), x, 7, -(sqrt(a - b*x^4)/(a*x)) - (b^(1/4)*sqrt(1 - (b*x^4)/a)*Elliptic.E(asin((b^(1/4)*x)/a^(1/4)), -1))/(a^(1/4)*sqrt(a - b*x^4)) + (b^(1/4)*sqrt(1 - (b*x^4)/a)*Elliptic.F(asin((b^(1/4)*x)/a^(1/4)), -1))/(a^(1/4)*sqrt(a - b*x^4))]
    @test_int [1/(x^6*sqrt(a - b*x^4)), x, 8, -(sqrt(a - b*x^4)/(5*a*x^5)) - (3*b*sqrt(a - b*x^4))/(5*a^2*x) - (3*b^(5/4)*sqrt(1 - (b*x^4)/a)*Elliptic.E(asin((b^(1/4)*x)/a^(1/4)), -1))/(5*a^(5/4)*sqrt(a - b*x^4)) + (3*b^(5/4)*sqrt(1 - (b*x^4)/a)*Elliptic.F(asin((b^(1/4)*x)/a^(1/4)), -1))/(5*a^(5/4)*sqrt(a - b*x^4))]

    @test_int [x^11/(a + b*x^4)^(3/2), x, 3, -(a^2/(2*b^3*sqrt(a + b*x^4))) - (a*sqrt(a + b*x^4))/b^3 + (a + b*x^4)^(3/2)/(6*b^3)]
    @test_int [x^7/(a + b*x^4)^(3/2), x, 3, a/(2*b^2*sqrt(a + b*x^4)) + sqrt(a + b*x^4)/(2*b^2)]
    @test_int [x^3/(a + b*x^4)^(3/2), x, 1, -1/(2*b*sqrt(a + b*x^4))]
    @test_int [1/(x^1*(a + b*x^4)^(3/2)), x, 4, 1/(2*a*sqrt(a + b*x^4)) - atanh(sqrt(a + b*x^4)/sqrt(a))/(2*a^(3/2))]
    @test_int [1/(x^5*(a + b*x^4)^(3/2)), x, 5, -((3*b)/(4*a^2*sqrt(a + b*x^4))) - 1/(4*a*x^4*sqrt(a + b*x^4)) + (3*b*atanh(sqrt(a + b*x^4)/sqrt(a)))/(4*a^(5/2))]

    @test_int [x^9/(a + b*x^4)^(3/2), x, 5, -x^6/(2*b*sqrt(a + b*x^4)) + (3*x^2*sqrt(a + b*x^4))/(4*b^2) - (3*a*atanh((sqrt(b)*x^2)/sqrt(a + b*x^4)))/(4*b^(5/2))]
    @test_int [x^5/(a + b*x^4)^(3/2), x, 4, -x^2/(2*b*sqrt(a + b*x^4)) + atanh((sqrt(b)*x^2)/sqrt(a + b*x^4))/(2*b^(3/2))]
    @test_int [x^1/(a + b*x^4)^(3/2), x, 1, x^2/(2*a*sqrt(a + b*x^4))]
    @test_int [1/(x^3*(a + b*x^4)^(3/2)), x, 2, -(1/(2*a*x^2*sqrt(a + b*x^4))) - (b*x^2)/(a^2*sqrt(a + b*x^4))]
    @test_int [1/(x^7*(a + b*x^4)^(3/2)), x, 3, -(1/(6*a*x^6*sqrt(a + b*x^4))) + (2*b)/(3*a^2*x^2*sqrt(a + b*x^4)) + (4*b^2*x^2)/(3*a^3*sqrt(a + b*x^4))]

    @test_int [x^12/(a + b*x^4)^(3/2), x, 4, -(x^9/(2*b*sqrt(a + b*x^4))) - (15*a*x*sqrt(a + b*x^4))/(14*b^3) + (9*x^5*sqrt(a + b*x^4))/(14*b^2) + (15*a^(7/4)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(28*b^(13/4)*sqrt(a + b*x^4))]
    @test_int [x^8/(a + b*x^4)^(3/2), x, 3, -(x^5/(2*b*sqrt(a + b*x^4))) + (5*x*sqrt(a + b*x^4))/(6*b^2) - (5*a^(3/4)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(12*b^(9/4)*sqrt(a + b*x^4))]
    @test_int [x^4/(a + b*x^4)^(3/2), x, 2, -(x/(2*b*sqrt(a + b*x^4))) + ((sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(4*a^(1/4)*b^(5/4)*sqrt(a + b*x^4))]
    @test_int [x^0/(a + b*x^4)^(3/2), x, 2, x/(2*a*sqrt(a + b*x^4)) + ((sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(4*a^(5/4)*b^(1/4)*sqrt(a + b*x^4))]
    @test_int [1/(x^4*(a + b*x^4)^(3/2)), x, 3, 1/(2*a*x^3*sqrt(a + b*x^4)) - (5*sqrt(a + b*x^4))/(6*a^2*x^3) - (5*b^(3/4)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(12*a^(9/4)*sqrt(a + b*x^4))]
    @test_int [1/(x^8*(a + b*x^4)^(3/2)), x, 4, 1/(2*a*x^7*sqrt(a + b*x^4)) - (9*sqrt(a + b*x^4))/(14*a^2*x^7) + (15*b*sqrt(a + b*x^4))/(14*a^3*x^3) + (15*b^(7/4)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(28*a^(13/4)*sqrt(a + b*x^4))]

    @test_int [x^14/(a + b*x^4)^(3/2), x, 6, -(x^11/(2*b*sqrt(a + b*x^4))) - (77*a*x^3*sqrt(a + b*x^4))/(90*b^3) + (11*x^7*sqrt(a + b*x^4))/(18*b^2) + (77*a^2*x*sqrt(a + b*x^4))/(30*b^(7/2)*(sqrt(a) + sqrt(b)*x^2)) - (77*a^(9/4)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.E(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(30*b^(15/4)*sqrt(a + b*x^4)) + (77*a^(9/4)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(60*b^(15/4)*sqrt(a + b*x^4))]
    @test_int [x^10/(a + b*x^4)^(3/2), x, 5, -(x^7/(2*b*sqrt(a + b*x^4))) + (7*x^3*sqrt(a + b*x^4))/(10*b^2) - (21*a*x*sqrt(a + b*x^4))/(10*b^(5/2)*(sqrt(a) + sqrt(b)*x^2)) + (21*a^(5/4)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.E(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(10*b^(11/4)*sqrt(a + b*x^4)) - (21*a^(5/4)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(20*b^(11/4)*sqrt(a + b*x^4))]
    @test_int [x^6/(a + b*x^4)^(3/2), x, 4, -(x^3/(2*b*sqrt(a + b*x^4))) + (3*x*sqrt(a + b*x^4))/(2*b^(3/2)*(sqrt(a) + sqrt(b)*x^2)) - (3*a^(1/4)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.E(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(2*b^(7/4)*sqrt(a + b*x^4)) + (3*a^(1/4)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(4*b^(7/4)*sqrt(a + b*x^4))]
    @test_int [x^2/(a + b*x^4)^(3/2), x, 4, x^3/(2*a*sqrt(a + b*x^4)) - (x*sqrt(a + b*x^4))/(2*a*sqrt(b)*(sqrt(a) + sqrt(b)*x^2)) + ((sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.E(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(2*a^(3/4)*b^(3/4)*sqrt(a + b*x^4)) - ((sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(4*a^(3/4)*b^(3/4)*sqrt(a + b*x^4))]
    @test_int [1/(x^2*(a + b*x^4)^(3/2)), x, 5, 1/(2*a*x*sqrt(a + b*x^4)) - (3*sqrt(a + b*x^4))/(2*a^2*x) + (3*sqrt(b)*x*sqrt(a + b*x^4))/(2*a^2*(sqrt(a) + sqrt(b)*x^2)) - (3*b^(1/4)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.E(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(2*a^(7/4)*sqrt(a + b*x^4)) + (3*b^(1/4)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(4*a^(7/4)*sqrt(a + b*x^4))]
    @test_int [1/(x^6*(a + b*x^4)^(3/2)), x, 6, 1/(2*a*x^5*sqrt(a + b*x^4)) - (7*sqrt(a + b*x^4))/(10*a^2*x^5) + (21*b*sqrt(a + b*x^4))/(10*a^3*x) - (21*b^(3/2)*x*sqrt(a + b*x^4))/(10*a^3*(sqrt(a) + sqrt(b)*x^2)) + (21*b^(5/4)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.E(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(10*a^(11/4)*sqrt(a + b*x^4)) - (21*b^(5/4)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(20*a^(11/4)*sqrt(a + b*x^4))]

    @test_int [1/(a + b*x^4)^(5/2), x, 3, x/(6*a*(a + b*x^4)^(3/2)) + (5*x)/(12*a^2*sqrt(a + b*x^4)) + (5*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(24*a^(9/4)*b^(1/4)*sqrt(a + b*x^4))]

    @test_int [x^11/sqrt(1 - x^4), x, 3, -sqrt(1 - x^4)/2 + (1 - x^4)^(3/2)/3 - (1 - x^4)^(5/2)/10]
    @test_int [x^7/sqrt(1 - x^4), x, 3, -sqrt(1 - x^4)/2 + (1 - x^4)^(3/2)/6]
    @test_int [x^3/sqrt(1 - x^4), x, 1, -sqrt(1 - x^4)/2]
    @test_int [1/(x^1*sqrt(1 - x^4)), x, 3, -atanh(sqrt(1 - x^4))/2]
    @test_int [1/(x^5*sqrt(1 - x^4)), x, 4, -sqrt(1 - x^4)/(4*x^4) - atanh(sqrt(1 - x^4))/4]

    @test_int [x^5/sqrt(1 - x^4), x, 3, -(x^2*sqrt(1 - x^4))/4 + asin(x^2)/4]
    @test_int [x^1/sqrt(1 - x^4), x, 2, asin(x^2)/2]
    @test_int [1/(x^3*sqrt(1 - x^4)), x, 1, -sqrt(1 - x^4)/(2*x^2)]
    @test_int [1/(x^7*sqrt(1 - x^4)), x, 2, -sqrt(1 - x^4)/(6*x^6) - sqrt(1 - x^4)/(3*x^2)]
    @test_int [1/(x^11*sqrt(1 - x^4)), x, 3, -sqrt(1 - x^4)/(10*x^10) - (2*sqrt(1 - x^4))/(15*x^6) - (4*sqrt(1 - x^4))/(15*x^2)]

    @test_int [x^8/sqrt(1 - x^4), x, 3, (-5*x*sqrt(1 - x^4))/21 - (x^5*sqrt(1 - x^4))/7 + (5*Elliptic.F(asin(x), -1))/21]
    @test_int [x^4/sqrt(1 - x^4), x, 2, -(x*sqrt(1 - x^4))/3 + Elliptic.F(asin(x), -1)/3]
    @test_int [x^0/sqrt(1 - x^4), x, 1, Elliptic.F(asin(x), -1)]
    @test_int [1/(x^4*sqrt(1 - x^4)), x, 2, -sqrt(1 - x^4)/(3*x^3) + Elliptic.F(asin(x), -1)/3]
    @test_int [1/(x^8*sqrt(1 - x^4)), x, 3, -sqrt(1 - x^4)/(7*x^7) - (5*sqrt(1 - x^4))/(21*x^3) + (5*Elliptic.F(asin(x), -1))/21]

    @test_int [x^10/sqrt(1 - x^4), x, 6, (-7*x^3*sqrt(1 - x^4))/45 - (x^7*sqrt(1 - x^4))/9 + (7*Elliptic.E(asin(x), -1))/15 - (7*Elliptic.F(asin(x), -1))/15]
    @test_int [x^6/sqrt(1 - x^4), x, 5, -(x^3*sqrt(1 - x^4))/5 + (3*Elliptic.E(asin(x), -1))/5 - (3*Elliptic.F(asin(x), -1))/5]
    @test_int [x^2/sqrt(1 - x^4), x, 4, Elliptic.E(asin(x), -1) - Elliptic.F(asin(x), -1)]
    @test_int [1/(x^2*sqrt(1 - x^4)), x, 5, -(sqrt(1 - x^4)/x) - Elliptic.E(asin(x), -1) + Elliptic.F(asin(x), -1)]
    @test_int [1/(x^6*sqrt(1 - x^4)), x, 6, -sqrt(1 - x^4)/(5*x^5) - (3*sqrt(1 - x^4))/(5*x) - (3*Elliptic.E(asin(x), -1))/5 + (3*Elliptic.F(asin(x), -1))/5]

    @test_int [x^11/(1 - x^4)^(3/2), x, 3, 1/(2*sqrt(1 - x^4)) + sqrt(1 - x^4) - (1 - x^4)^(3/2)/6]
    @test_int [x^7/(1 - x^4)^(3/2), x, 3, 1/(2*sqrt(1 - x^4)) + sqrt(1 - x^4)/2]
    @test_int [x^3/(1 - x^4)^(3/2), x, 1, 1/(2*sqrt(1 - x^4))]
    @test_int [1/(x^1*(1 - x^4)^(3/2)), x, 4, 1/(2*sqrt(1 - x^4)) - atanh(sqrt(1 - x^4))/2]
    @test_int [1/(x^5*(1 - x^4)^(3/2)), x, 5, 3/(4*sqrt(1 - x^4)) - 1/(4*x^4*sqrt(1 - x^4)) - (3/4)*atanh(sqrt(1 - x^4))]

    @test_int [x^9/(1 - x^4)^(3/2), x, 4, x^6/(2*sqrt(1 - x^4)) + (3*x^2*sqrt(1 - x^4))/4 - (3*asin(x^2))/4]
    @test_int [x^5/(1 - x^4)^(3/2), x, 3, x^2/(2*sqrt(1 - x^4)) - asin(x^2)/2]
    @test_int [x^1/(1 - x^4)^(3/2), x, 1, x^2/(2*sqrt(1 - x^4))]
    @test_int [1/(x^3*(1 - x^4)^(3/2)), x, 2, -1/(2*x^2*sqrt(1 - x^4)) + x^2/sqrt(1 - x^4)]
    @test_int [1/(x^7*(1 - x^4)^(3/2)), x, 3, -1/(6*x^6*sqrt(1 - x^4)) - 2/(3*x^2*sqrt(1 - x^4)) + (4*x^2)/(3*sqrt(1 - x^4))]

    @test_int [x^12/(1 - x^4)^(3/2), x, 4, x^9/(2*sqrt(1 - x^4)) + (15*x*sqrt(1 - x^4))/14 + (9*x^5*sqrt(1 - x^4))/14 - (15*Elliptic.F(asin(x), -1))/14]
    @test_int [x^8/(1 - x^4)^(3/2), x, 3, x^5/(2*sqrt(1 - x^4)) + (5*x*sqrt(1 - x^4))/6 - (5*Elliptic.F(asin(x), -1))/6]
    @test_int [x^4/(1 - x^4)^(3/2), x, 2, x/(2*sqrt(1 - x^4)) - Elliptic.F(asin(x), -1)/2]
    @test_int [x^0/(1 - x^4)^(3/2), x, 2, x/(2*sqrt(1 - x^4)) + Elliptic.F(asin(x), -1)/2]
    @test_int [1/(x^4*(1 - x^4)^(3/2)), x, 3, 1/(2*x^3*sqrt(1 - x^4)) - (5*sqrt(1 - x^4))/(6*x^3) + (5*Elliptic.F(asin(x), -1))/6]
    @test_int [1/(x^8*(1 - x^4)^(3/2)), x, 4, 1/(2*x^7*sqrt(1 - x^4)) - (9*sqrt(1 - x^4))/(14*x^7) - (15*sqrt(1 - x^4))/(14*x^3) + (15*Elliptic.F(asin(x), -1))/14]

    @test_int [x^14/(1 - x^4)^(3/2), x, 7, x^11/(2*sqrt(1 - x^4)) + (77*x^3*sqrt(1 - x^4))/90 + (11*x^7*sqrt(1 - x^4))/18 - (77*Elliptic.E(asin(x), -1))/30 + (77*Elliptic.F(asin(x), -1))/30]
    @test_int [x^10/(1 - x^4)^(3/2), x, 6, x^7/(2*sqrt(1 - x^4)) + (7*x^3*sqrt(1 - x^4))/10 - (21*Elliptic.E(asin(x), -1))/10 + (21*Elliptic.F(asin(x), -1))/10]
    @test_int [x^6/(1 - x^4)^(3/2), x, 5, x^3/(2*sqrt(1 - x^4)) - (3*Elliptic.E(asin(x), -1))/2 + (3*Elliptic.F(asin(x), -1))/2]
    @test_int [x^2/(1 - x^4)^(3/2), x, 5, x^3/(2*sqrt(1 - x^4)) - Elliptic.E(asin(x), -1)/2 + Elliptic.F(asin(x), -1)/2]
    @test_int [1/(x^2*(1 - x^4)^(3/2)), x, 6, 1/(2*x*sqrt(1 - x^4)) - (3*sqrt(1 - x^4))/(2*x) - (3*Elliptic.E(asin(x), -1))/2 + (3*Elliptic.F(asin(x), -1))/2]
    @test_int [1/(x^6*(1 - x^4)^(3/2)), x, 7, 1/(2*x^5*sqrt(1 - x^4)) - (7*sqrt(1 - x^4))/(10*x^5) - (21*sqrt(1 - x^4))/(10*x) - (21*Elliptic.E(asin(x), -1))/10 + (21*Elliptic.F(asin(x), -1))/10]

    @test_int [1/(1 - x^4)^(5/2), x, 3, x/(6*(1 - x^4)^(3/2)) + (5*x)/(12*sqrt(1 - x^4)) + (5/12)*Elliptic.F(asin(x), -1)]

    @test_int [x^11/sqrt(1 + x^4), x, 3, sqrt(1 + x^4)/2 - (1 + x^4)^(3/2)/3 + (1 + x^4)^(5/2)/10]
    @test_int [x^7/sqrt(1 + x^4), x, 3, -sqrt(1 + x^4)/2 + (1 + x^4)^(3/2)/6]
    @test_int [x^3/sqrt(1 + x^4), x, 1, sqrt(1 + x^4)/2]
    @test_int [1/(x^1*sqrt(1 + x^4)), x, 3, -atanh(sqrt(1 + x^4))/2]
    @test_int [1/(x^5*sqrt(1 + x^4)), x, 4, -sqrt(1 + x^4)/(4*x^4) + atanh(sqrt(1 + x^4))/4]

    @test_int [x^5/sqrt(1 + x^4), x, 3, (x^2*sqrt(1 + x^4))/4 - asinh(x^2)/4]
    @test_int [x^1/sqrt(1 + x^4), x, 2, asinh(x^2)/2]
    @test_int [1/(x^3*sqrt(1 + x^4)), x, 1, -sqrt(1 + x^4)/(2*x^2)]
    @test_int [1/(x^7*sqrt(1 + x^4)), x, 2, -sqrt(1 + x^4)/(6*x^6) + sqrt(1 + x^4)/(3*x^2)]
    @test_int [1/(x^11*sqrt(1 + x^4)), x, 3, -sqrt(1 + x^4)/(10*x^10) + (2*sqrt(1 + x^4))/(15*x^6) - (4*sqrt(1 + x^4))/(15*x^2)]

    @test_int [x^8/sqrt(1 + x^4), x, 3, (-5*x*sqrt(1 + x^4))/21 + (x^5*sqrt(1 + x^4))/7 + (5*(1 + x^2)*sqrt((1 + x^4)/(1 + x^2)^2)*Elliptic.F(2*atan(x), 1/2))/(42*sqrt(1 + x^4))]
    @test_int [x^4/sqrt(1 + x^4), x, 2, (x*sqrt(1 + x^4))/3 - ((1 + x^2)*sqrt((1 + x^4)/(1 + x^2)^2)*Elliptic.F(2*atan(x), 1/2))/(6*sqrt(1 + x^4))]
    @test_int [x^0/sqrt(1 + x^4), x, 1, ((1 + x^2)*sqrt((1 + x^4)/(1 + x^2)^2)*Elliptic.F(2*atan(x), 1/2))/(2*sqrt(1 + x^4))]
    @test_int [1/(x^4*sqrt(1 + x^4)), x, 2, -sqrt(1 + x^4)/(3*x^3) - ((1 + x^2)*sqrt((1 + x^4)/(1 + x^2)^2)*Elliptic.F(2*atan(x), 1/2))/(6*sqrt(1 + x^4))]
    @test_int [1/(x^8*sqrt(1 + x^4)), x, 3, -sqrt(1 + x^4)/(7*x^7) + (5*sqrt(1 + x^4))/(21*x^3) + (5*(1 + x^2)*sqrt((1 + x^4)/(1 + x^2)^2)*Elliptic.F(2*atan(x), 1/2))/(42*sqrt(1 + x^4))]

    @test_int [x^10/sqrt(1 + x^4), x, 5, (-(7/45))*x^3*sqrt(1 + x^4) + (1/9)*x^7*sqrt(1 + x^4) + (7*x*sqrt(1 + x^4))/(15*(1 + x^2)) - (7*(1 + x^2)*sqrt((1 + x^4)/(1 + x^2)^2)*Elliptic.E(2*atan(x), 1/2))/(15*sqrt(1 + x^4)) + (7*(1 + x^2)*sqrt((1 + x^4)/(1 + x^2)^2)*Elliptic.F(2*atan(x), 1/2))/(30*sqrt(1 + x^4))]
    @test_int [x^6/sqrt(1 + x^4), x, 4, (1/5)*x^3*sqrt(1 + x^4) - (3*x*sqrt(1 + x^4))/(5*(1 + x^2)) + (3*(1 + x^2)*sqrt((1 + x^4)/(1 + x^2)^2)*Elliptic.E(2*atan(x), 1/2))/(5*sqrt(1 + x^4)) - (3*(1 + x^2)*sqrt((1 + x^4)/(1 + x^2)^2)*Elliptic.F(2*atan(x), 1/2))/(10*sqrt(1 + x^4))]
    @test_int [x^2/sqrt(1 + x^4), x, 3, (x*sqrt(1 + x^4))/(1 + x^2) - ((1 + x^2)*sqrt((1 + x^4)/(1 + x^2)^2)*Elliptic.E(2*atan(x), 1/2))/sqrt(1 + x^4) + ((1 + x^2)*sqrt((1 + x^4)/(1 + x^2)^2)*Elliptic.F(2*atan(x), 1/2))/(2*sqrt(1 + x^4))]
    @test_int [1/(x^2*sqrt(1 + x^4)), x, 4, -(sqrt(1 + x^4)/x) + (x*sqrt(1 + x^4))/(1 + x^2) - ((1 + x^2)*sqrt((1 + x^4)/(1 + x^2)^2)*Elliptic.E(2*atan(x), 1/2))/sqrt(1 + x^4) + ((1 + x^2)*sqrt((1 + x^4)/(1 + x^2)^2)*Elliptic.F(2*atan(x), 1/2))/(2*sqrt(1 + x^4))]
    @test_int [1/(x^6*sqrt(1 + x^4)), x, 5, -(sqrt(1 + x^4)/(5*x^5)) + (3*sqrt(1 + x^4))/(5*x) - (3*x*sqrt(1 + x^4))/(5*(1 + x^2)) + (3*(1 + x^2)*sqrt((1 + x^4)/(1 + x^2)^2)*Elliptic.E(2*atan(x), 1/2))/(5*sqrt(1 + x^4)) - (3*(1 + x^2)*sqrt((1 + x^4)/(1 + x^2)^2)*Elliptic.F(2*atan(x), 1/2))/(10*sqrt(1 + x^4))]

    @test_int [x^11/(1 + x^4)^(3/2), x, 3, -1/(2*sqrt(1 + x^4)) - sqrt(1 + x^4) + (1 + x^4)^(3/2)/6]
    @test_int [x^7/(1 + x^4)^(3/2), x, 3, 1/(2*sqrt(1 + x^4)) + sqrt(1 + x^4)/2]
    @test_int [x^3/(1 + x^4)^(3/2), x, 1, -1/(2*sqrt(1 + x^4))]
    @test_int [1/(x^1*(1 + x^4)^(3/2)), x, 4, 1/(2*sqrt(1 + x^4)) - atanh(sqrt(1 + x^4))/2]
    @test_int [1/(x^5*(1 + x^4)^(3/2)), x, 5, -(3/(4*sqrt(1 + x^4))) - 1/(4*x^4*sqrt(1 + x^4)) + (3/4)*atanh(sqrt(1 + x^4))]

    @test_int [x^9/(1 + x^4)^(3/2), x, 4, -x^6/(2*sqrt(1 + x^4)) + (3*x^2*sqrt(1 + x^4))/4 - (3*asinh(x^2))/4]
    @test_int [x^5/(1 + x^4)^(3/2), x, 3, -x^2/(2*sqrt(1 + x^4)) + asinh(x^2)/2]
    @test_int [x^1/(1 + x^4)^(3/2), x, 1, x^2/(2*sqrt(1 + x^4))]
    @test_int [1/(x^3*(1 + x^4)^(3/2)), x, 2, -1/(2*x^2*sqrt(1 + x^4)) - x^2/sqrt(1 + x^4)]
    @test_int [1/(x^7*(1 + x^4)^(3/2)), x, 3, -1/(6*x^6*sqrt(1 + x^4)) + 2/(3*x^2*sqrt(1 + x^4)) + (4*x^2)/(3*sqrt(1 + x^4))]

    @test_int [x^12/(1 + x^4)^(3/2), x, 4, -x^9/(2*sqrt(1 + x^4)) - (15*x*sqrt(1 + x^4))/14 + (9*x^5*sqrt(1 + x^4))/14 + (15*(1 + x^2)*sqrt((1 + x^4)/(1 + x^2)^2)*Elliptic.F(2*atan(x), 1/2))/(28*sqrt(1 + x^4))]
    @test_int [x^8/(1 + x^4)^(3/2), x, 3, -x^5/(2*sqrt(1 + x^4)) + (5*x*sqrt(1 + x^4))/6 - (5*(1 + x^2)*sqrt((1 + x^4)/(1 + x^2)^2)*Elliptic.F(2*atan(x), 1/2))/(12*sqrt(1 + x^4))]
    @test_int [x^4/(1 + x^4)^(3/2), x, 2, -x/(2*sqrt(1 + x^4)) + ((1 + x^2)*sqrt((1 + x^4)/(1 + x^2)^2)*Elliptic.F(2*atan(x), 1/2))/(4*sqrt(1 + x^4))]
    @test_int [x^0/(1 + x^4)^(3/2), x, 2, x/(2*sqrt(1 + x^4)) + ((1 + x^2)*sqrt((1 + x^4)/(1 + x^2)^2)*Elliptic.F(2*atan(x), 1/2))/(4*sqrt(1 + x^4))]
    @test_int [1/(x^4*(1 + x^4)^(3/2)), x, 3, 1/(2*x^3*sqrt(1 + x^4)) - (5*sqrt(1 + x^4))/(6*x^3) - (5*(1 + x^2)*sqrt((1 + x^4)/(1 + x^2)^2)*Elliptic.F(2*atan(x), 1/2))/(12*sqrt(1 + x^4))]
    @test_int [1/(x^8*(1 + x^4)^(3/2)), x, 4, 1/(2*x^7*sqrt(1 + x^4)) - (9*sqrt(1 + x^4))/(14*x^7) + (15*sqrt(1 + x^4))/(14*x^3) + (15*(1 + x^2)*sqrt((1 + x^4)/(1 + x^2)^2)*Elliptic.F(2*atan(x), 1/2))/(28*sqrt(1 + x^4))]

    @test_int [x^14/(1 + x^4)^(3/2), x, 6, -(x^11/(2*sqrt(1 + x^4))) - (77/90)*x^3*sqrt(1 + x^4) + (11/18)*x^7*sqrt(1 + x^4) + (77*x*sqrt(1 + x^4))/(30*(1 + x^2)) - (77*(1 + x^2)*sqrt((1 + x^4)/(1 + x^2)^2)*Elliptic.E(2*atan(x), 1/2))/(30*sqrt(1 + x^4)) + (77*(1 + x^2)*sqrt((1 + x^4)/(1 + x^2)^2)*Elliptic.F(2*atan(x), 1/2))/(60*sqrt(1 + x^4))]
    @test_int [x^10/(1 + x^4)^(3/2), x, 5, -(x^7/(2*sqrt(1 + x^4))) + (7/10)*x^3*sqrt(1 + x^4) - (21*x*sqrt(1 + x^4))/(10*(1 + x^2)) + (21*(1 + x^2)*sqrt((1 + x^4)/(1 + x^2)^2)*Elliptic.E(2*atan(x), 1/2))/(10*sqrt(1 + x^4)) - (21*(1 + x^2)*sqrt((1 + x^4)/(1 + x^2)^2)*Elliptic.F(2*atan(x), 1/2))/(20*sqrt(1 + x^4))]
    @test_int [x^6/(1 + x^4)^(3/2), x, 4, -(x^3/(2*sqrt(1 + x^4))) + (3*x*sqrt(1 + x^4))/(2*(1 + x^2)) - (3*(1 + x^2)*sqrt((1 + x^4)/(1 + x^2)^2)*Elliptic.E(2*atan(x), 1/2))/(2*sqrt(1 + x^4)) + (3*(1 + x^2)*sqrt((1 + x^4)/(1 + x^2)^2)*Elliptic.F(2*atan(x), 1/2))/(4*sqrt(1 + x^4))]
    @test_int [x^2/(1 + x^4)^(3/2), x, 4, x^3/(2*sqrt(1 + x^4)) - (x*sqrt(1 + x^4))/(2*(1 + x^2)) + ((1 + x^2)*sqrt((1 + x^4)/(1 + x^2)^2)*Elliptic.E(2*atan(x), 1/2))/(2*sqrt(1 + x^4)) - ((1 + x^2)*sqrt((1 + x^4)/(1 + x^2)^2)*Elliptic.F(2*atan(x), 1/2))/(4*sqrt(1 + x^4))]
    @test_int [1/(x^2*(1 + x^4)^(3/2)), x, 5, 1/(2*x*sqrt(1 + x^4)) - (3*sqrt(1 + x^4))/(2*x) + (3*x*sqrt(1 + x^4))/(2*(1 + x^2)) - (3*(1 + x^2)*sqrt((1 + x^4)/(1 + x^2)^2)*Elliptic.E(2*atan(x), 1/2))/(2*sqrt(1 + x^4)) + (3*(1 + x^2)*sqrt((1 + x^4)/(1 + x^2)^2)*Elliptic.F(2*atan(x), 1/2))/(4*sqrt(1 + x^4))]
    @test_int [1/(x^6*(1 + x^4)^(3/2)), x, 6, 1/(2*x^5*sqrt(1 + x^4)) - (7*sqrt(1 + x^4))/(10*x^5) + (21*sqrt(1 + x^4))/(10*x) - (21*x*sqrt(1 + x^4))/(10*(1 + x^2)) + (21*(1 + x^2)*sqrt((1 + x^4)/(1 + x^2)^2)*Elliptic.E(2*atan(x), 1/2))/(10*sqrt(1 + x^4)) - (21*(1 + x^2)*sqrt((1 + x^4)/(1 + x^2)^2)*Elliptic.F(2*atan(x), 1/2))/(20*sqrt(1 + x^4))]

    @test_int [1/(1 + x^4)^(5/2), x, 3, x/(6*(1 + x^4)^(3/2)) + (5*x)/(12*sqrt(1 + x^4)) + (5*(1 + x^2)*sqrt((1 + x^4)/(1 + x^2)^2)*Elliptic.F(2*atan(x), 1/2))/(24*sqrt(1 + x^4))]

    @test_int [x^7/sqrt(16 - x^4), x, 3, -8*sqrt(16 - x^4) + (1/6)*(16 - x^4)^(3/2)]
    @test_int [x^5/sqrt(16 - x^4), x, 3, (-(1/4))*x^2*sqrt(16 - x^4) + 4*asin(x^2/4)]
    @test_int [x^3/sqrt(16 - x^4), x, 1, (-(1/2))*sqrt(16 - x^4)]
    @test_int [x^1/sqrt(16 - x^4), x, 2, (1/2)*asin(x^2/4)]
    @test_int [1/(x^1*sqrt(16 - x^4)), x, 3, (-(1/8))*atanh(sqrt(16 - x^4)/4)]
    @test_int [1/(x^3*sqrt(16 - x^4)), x, 1, -(sqrt(16 - x^4)/(32*x^2))]
    @test_int [1/(x^5*sqrt(16 - x^4)), x, 4, -(sqrt(16 - x^4)/(64*x^4)) - (1/256)*atanh(sqrt(16 - x^4)/4)]
    @test_int [1/(x^7*sqrt(16 - x^4)), x, 2, -(sqrt(16 - x^4)/(96*x^6)) - sqrt(16 - x^4)/(768*x^2)]

    @test_int [x^6/sqrt(16 - x^4), x, 6, (-(1/5))*x^3*sqrt(16 - x^4) + (96/5)*Elliptic.E(asin(x/2), -1) - (96/5)*Elliptic.F(asin(x/2), -1)]
    @test_int [x^4/sqrt(16 - x^4), x, 2, (-(1/3))*x*sqrt(16 - x^4) + (8/3)*Elliptic.F(asin(x/2), -1)]
    @test_int [x^2/sqrt(16 - x^4), x, 5, 2*Elliptic.E(asin(x/2), -1) - 2*Elliptic.F(asin(x/2), -1)]
    @test_int [x^0/sqrt(16 - x^4), x, 1, (1/2)*Elliptic.F(asin(x/2), -1)]
    @test_int [1/(x^2*sqrt(16 - x^4)), x, 6, -(sqrt(16 - x^4)/(16*x)) - (1/8)*Elliptic.E(asin(x/2), -1) + (1/8)*Elliptic.F(asin(x/2), -1)]
    @test_int [1/(x^4*sqrt(16 - x^4)), x, 2, -(sqrt(16 - x^4)/(48*x^3)) + (1/96)*Elliptic.F(asin(x/2), -1)]

    @test_int [x/sqrt(-4 + x^4), x, 3, (1/2)*atanh(x^2/sqrt(-4 + x^4))]
    @test_int [x/sqrt(4 + x^4), x, 2, asinh(x^2/2)/2]

    @test_int [1/(x*sqrt(-1 + x^4)), x, 3, atan(sqrt(-1 + x^4))/2]

    @test_int [x^4/sqrt(-1 + x^4), x, 2, (1/3)*x*sqrt(-1 + x^4) + (sqrt(-1 + x^2)*sqrt(1 + x^2)*Elliptic.F(asin((sqrt(2)*x)/sqrt(-1 + x^2)), 1/2))/(3*sqrt(2)*sqrt(-1 + x^4))]
    @test_int [x^0/sqrt(-1 + x^4), x, 1, (sqrt(-1 + x^2)*sqrt(1 + x^2)*Elliptic.F(asin((sqrt(2)*x)/sqrt(-1 + x^2)), 1/2))/(sqrt(2)*sqrt(-1 + x^4))]
    @test_int [1/(x^4*sqrt(-1 + x^4)), x, 2, sqrt(-1 + x^4)/(3*x^3) + (sqrt(-1 + x^2)*sqrt(1 + x^2)*Elliptic.F(asin((sqrt(2)*x)/sqrt(-1 + x^2)), 1/2))/(3*sqrt(2)*sqrt(-1 + x^4))]

    @test_int [x^6/sqrt(-1 + x^4), x, 4, (3*x*(1 + x^2))/(5*sqrt(-1 + x^4)) + (1/5)*x^3*sqrt(-1 + x^4) - (3*sqrt(2)*sqrt(-1 + x^2)*sqrt(1 + x^2)*Elliptic.E(asin((sqrt(2)*x)/sqrt(-1 + x^2)), 1/2))/(5*sqrt(-1 + x^4)) + (3*sqrt(-1 + x^2)*sqrt(1 + x^2)*Elliptic.F(asin((sqrt(2)*x)/sqrt(-1 + x^2)), 1/2))/(5*sqrt(2)*sqrt(-1 + x^4))]
    @test_int [x^2/sqrt(-1 + x^4), x, 3, (x*(1 + x^2))/sqrt(-1 + x^4) - (sqrt(2)*sqrt(-1 + x^2)*sqrt(1 + x^2)*Elliptic.E(asin((sqrt(2)*x)/sqrt(-1 + x^2)), 1/2))/sqrt(-1 + x^4) + (sqrt(-1 + x^2)*sqrt(1 + x^2)*Elliptic.F(asin((sqrt(2)*x)/sqrt(-1 + x^2)), 1/2))/(sqrt(2)*sqrt(-1 + x^4))]
    @test_int [1/(x^2*sqrt(-1 + x^4)), x, 4, -((x*(1 + x^2))/sqrt(-1 + x^4)) + sqrt(-1 + x^4)/x + (sqrt(2)*sqrt(-1 + x^2)*sqrt(1 + x^2)*Elliptic.E(asin((sqrt(2)*x)/sqrt(-1 + x^2)), 1/2))/sqrt(-1 + x^4) - (sqrt(-1 + x^2)*sqrt(1 + x^2)*Elliptic.F(asin((sqrt(2)*x)/sqrt(-1 + x^2)), 1/2))/(sqrt(2)*sqrt(-1 + x^4))]

    @test_int [x^2/sqrt(3 - 2*x^4), x, 5, (3^(1/4)*Elliptic.E(asin((2/3)^(1/4)*x), -1))/2^(3/4) - (3^(1/4)*Elliptic.F(asin((2/3)^(1/4)*x), -1))/2^(3/4)]
    @test_int [x^2/sqrt(3 - b*x^4), x, 4, (3^(1/4)*Elliptic.E(asin((b^(1/4)*x)/3^(1/4)), -1))/b^(3/4) - (3^(1/4)*Elliptic.F(asin((b^(1/4)*x)/3^(1/4)), -1))/b^(3/4)]

    #= ::Subsection:: =#
    #=Integrands*of*the*form*x^(m/2)*(a+b*x^4)^(p/2)=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b*x^4)^(p/3)=#

    @test_int [x^7*(1 + x^4)^(1/3), x, 3, (-(3/16))*(1 + x^4)^(4/3) + (3/28)*(1 + x^4)^(7/3)]

    @test_int [x^3/(1 + x^4)^(4/3), x, 1, -3/(4*(1 + x^4)^(1/3))]
    @test_int [x^3/(1 + x^4)^(1/3), x, 1, (3*(1 + x^4)^(2/3))/8]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b*x^4)^(p/4)=#

    #= ::Subsubsection::Closed:: =#
    #=p>0=#

    @test_int [x^19*(a + b*x^4)^(1/4), x, 3, (a^4*(a + b*x^4)^(5/4))/(5*b^5) - (4*a^3*(a + b*x^4)^(9/4))/(9*b^5) + (6*a^2*(a + b*x^4)^(13/4))/(13*b^5) - (4*a*(a + b*x^4)^(17/4))/(17*b^5) + (a + b*x^4)^(21/4)/(21*b^5)]
    @test_int [x^15*(a + b*x^4)^(1/4), x, 3, -(a^3*(a + b*x^4)^(5/4))/(5*b^4) + (a^2*(a + b*x^4)^(9/4))/(3*b^4) - (3*a*(a + b*x^4)^(13/4))/(13*b^4) + (a + b*x^4)^(17/4)/(17*b^4)]
    @test_int [x^11*(a + b*x^4)^(1/4), x, 3, (a^2*(a + b*x^4)^(5/4))/(5*b^3) - (2*a*(a + b*x^4)^(9/4))/(9*b^3) + (a + b*x^4)^(13/4)/(13*b^3)]
    @test_int [x^7*(a + b*x^4)^(1/4), x, 3, -(a*(a + b*x^4)^(5/4))/(5*b^2) + (a + b*x^4)^(9/4)/(9*b^2)]
    @test_int [x^3*(a + b*x^4)^(1/4), x, 1, (a + b*x^4)^(5/4)/(5*b)]
    @test_int [(a + b*x^4)^(1/4)/x^1, x, 6, (a + b*x^4)^(1/4) - (a^(1/4)*atan((a + b*x^4)^(1/4)/a^(1/4)))/2 - (a^(1/4)*atanh((a + b*x^4)^(1/4)/a^(1/4)))/2]
    @test_int [(a + b*x^4)^(1/4)/x^5, x, 6, -(a + b*x^4)^(1/4)/(4*x^4) - (b*atan((a + b*x^4)^(1/4)/a^(1/4)))/(8*a^(3/4)) - (b*atanh((a + b*x^4)^(1/4)/a^(1/4)))/(8*a^(3/4))]
    @test_int [(a + b*x^4)^(1/4)/x^9, x, 7, -(a + b*x^4)^(1/4)/(8*x^8) - (b*(a + b*x^4)^(1/4))/(32*a*x^4) + (3*b^2*atan((a + b*x^4)^(1/4)/a^(1/4)))/(64*a^(7/4)) + (3*b^2*atanh((a + b*x^4)^(1/4)/a^(1/4)))/(64*a^(7/4))]

    @test_int [x^9*(a + b*x^4)^(1/4), x, 6, -((2*a^2*x^2*(a + b*x^4)^(1/4))/(77*b^2)) + (a*x^6*(a + b*x^4)^(1/4))/(77*b) + (1/11)*x^10*(a + b*x^4)^(1/4) + (4*a^(7/2)*(1 + (b*x^4)/a)^(3/4)*Elliptic.F((1/2)*atan((sqrt(b)*x^2)/sqrt(a)), 2))/(77*b^(5/2)*(a + b*x^4)^(3/4))]
    @test_int [x^5*(a + b*x^4)^(1/4), x, 5, (a*x^2*(a + b*x^4)^(1/4))/(21*b) + (1/7)*x^6*(a + b*x^4)^(1/4) - (2*a^(5/2)*(1 + (b*x^4)/a)^(3/4)*Elliptic.F((1/2)*atan((sqrt(b)*x^2)/sqrt(a)), 2))/(21*b^(3/2)*(a + b*x^4)^(3/4))]
    @test_int [x^1*(a + b*x^4)^(1/4), x, 4, (1/3)*x^2*(a + b*x^4)^(1/4) + (a^(3/2)*(1 + (b*x^4)/a)^(3/4)*Elliptic.F((1/2)*atan((sqrt(b)*x^2)/sqrt(a)), 2))/(3*sqrt(b)*(a + b*x^4)^(3/4))]
    @test_int [(a + b*x^4)^(1/4)/x^3, x, 4, -((a + b*x^4)^(1/4)/(2*x^2)) + (sqrt(a)*sqrt(b)*(1 + (b*x^4)/a)^(3/4)*Elliptic.F((1/2)*atan((sqrt(b)*x^2)/sqrt(a)), 2))/(2*(a + b*x^4)^(3/4))]
    @test_int [(a + b*x^4)^(1/4)/x^7, x, 5, -((a + b*x^4)^(1/4)/(6*x^6)) - (b*(a + b*x^4)^(1/4))/(12*a*x^2) - (b^(3/2)*(1 + (b*x^4)/a)^(3/4)*Elliptic.F((1/2)*atan((sqrt(b)*x^2)/sqrt(a)), 2))/(12*sqrt(a)*(a + b*x^4)^(3/4))]
    @test_int [(a + b*x^4)^(1/4)/x^11, x, 6, -((a + b*x^4)^(1/4)/(10*x^10)) - (b*(a + b*x^4)^(1/4))/(60*a*x^6) + (b^2*(a + b*x^4)^(1/4))/(24*a^2*x^2) + (b^(5/2)*(1 + (b*x^4)/a)^(3/4)*Elliptic.F((1/2)*atan((sqrt(b)*x^2)/sqrt(a)), 2))/(24*a^(3/2)*(a + b*x^4)^(3/4))]

    @test_int [x^6*(a + b*x^4)^(1/4), x, 6, (a*x^3*(a + b*x^4)^(1/4))/(32*b) + (x^7*(a + b*x^4)^(1/4))/8 + (3*a^2*atan((b^(1/4)*x)/(a + b*x^4)^(1/4)))/(64*b^(7/4)) - (3*a^2*atanh((b^(1/4)*x)/(a + b*x^4)^(1/4)))/(64*b^(7/4))]
    @test_int [x^2*(a + b*x^4)^(1/4), x, 5, (x^3*(a + b*x^4)^(1/4))/4 - (a*atan((b^(1/4)*x)/(a + b*x^4)^(1/4)))/(8*b^(3/4)) + (a*atanh((b^(1/4)*x)/(a + b*x^4)^(1/4)))/(8*b^(3/4))]
    @test_int [(a + b*x^4)^(1/4)/x^2, x, 5, -((a + b*x^4)^(1/4)/x) - (b^(1/4)*atan((b^(1/4)*x)/(a + b*x^4)^(1/4)))/2 + (b^(1/4)*atanh((b^(1/4)*x)/(a + b*x^4)^(1/4)))/2]
    @test_int [(a + b*x^4)^(1/4)/x^6, x, 1, -(a + b*x^4)^(5/4)/(5*a*x^5)]
    @test_int [(a + b*x^4)^(1/4)/x^10, x, 2, -(a + b*x^4)^(5/4)/(9*a*x^9) + (4*b*(a + b*x^4)^(5/4))/(45*a^2*x^5)]
    @test_int [(a + b*x^4)^(1/4)/x^14, x, 3, -(a + b*x^4)^(5/4)/(13*a*x^13) + (8*b*(a + b*x^4)^(5/4))/(117*a^2*x^9) - (32*b^2*(a + b*x^4)^(5/4))/(585*a^3*x^5)]
    @test_int [(a + b*x^4)^(1/4)/x^18, x, 4, -(a + b*x^4)^(5/4)/(17*a*x^17) + (12*b*(a + b*x^4)^(5/4))/(221*a^2*x^13) - (32*b^2*(a + b*x^4)^(5/4))/(663*a^3*x^9) + (128*b^3*(a + b*x^4)^(5/4))/(3315*a^4*x^5)]

    @test_int [x^12*(a + b*x^4)^(1/4), x, 8, (3*a^3*x*(a + b*x^4)^(1/4))/(112*b^3) - (3*a^2*x^5*(a + b*x^4)^(1/4))/(280*b^2) + (a*x^9*(a + b*x^4)^(1/4))/(140*b) + (1/14)*x^13*(a + b*x^4)^(1/4) + (3*a^(7/2)*(1 + a/(b*x^4))^(3/4)*x^3*Elliptic.F((1/2)*acot((sqrt(b)*x^2)/sqrt(a)), 2))/(112*b^(5/2)*(a + b*x^4)^(3/4))]
    @test_int [x^8*(a + b*x^4)^(1/4), x, 7, -((a^2*x*(a + b*x^4)^(1/4))/(24*b^2)) + (a*x^5*(a + b*x^4)^(1/4))/(60*b) + (1/10)*x^9*(a + b*x^4)^(1/4) - (a^(5/2)*(1 + a/(b*x^4))^(3/4)*x^3*Elliptic.F((1/2)*acot((sqrt(b)*x^2)/sqrt(a)), 2))/(24*b^(3/2)*(a + b*x^4)^(3/4))]
    @test_int [x^4*(a + b*x^4)^(1/4), x, 6, (a*x*(a + b*x^4)^(1/4))/(12*b) + (1/6)*x^5*(a + b*x^4)^(1/4) + (a^(3/2)*(1 + a/(b*x^4))^(3/4)*x^3*Elliptic.F((1/2)*acot((sqrt(b)*x^2)/sqrt(a)), 2))/(12*sqrt(b)*(a + b*x^4)^(3/4))]
    @test_int [x^0*(a + b*x^4)^(1/4), x, 5, (1/2)*x*(a + b*x^4)^(1/4) - (sqrt(a)*sqrt(b)*(1 + a/(b*x^4))^(3/4)*x^3*Elliptic.F((1/2)*acot((sqrt(b)*x^2)/sqrt(a)), 2))/(2*(a + b*x^4)^(3/4))]
    @test_int [(a + b*x^4)^(1/4)/x^4, x, 5, -((a + b*x^4)^(1/4)/(3*x^3)) - (b^(3/2)*(1 + a/(b*x^4))^(3/4)*x^3*Elliptic.F((1/2)*acot((sqrt(b)*x^2)/sqrt(a)), 2))/(3*sqrt(a)*(a + b*x^4)^(3/4))]
    @test_int [(a + b*x^4)^(1/4)/x^8, x, 6, -((a + b*x^4)^(1/4)/(7*x^7)) - (b*(a + b*x^4)^(1/4))/(21*a*x^3) + (2*b^(5/2)*(1 + a/(b*x^4))^(3/4)*x^3*Elliptic.F((1/2)*acot((sqrt(b)*x^2)/sqrt(a)), 2))/(21*a^(3/2)*(a + b*x^4)^(3/4))]
    @test_int [(a + b*x^4)^(1/4)/x^12, x, 7, -((a + b*x^4)^(1/4)/(11*x^11)) - (b*(a + b*x^4)^(1/4))/(77*a*x^7) + (2*b^2*(a + b*x^4)^(1/4))/(77*a^2*x^3) - (4*b^(7/2)*(1 + a/(b*x^4))^(3/4)*x^3*Elliptic.F((1/2)*acot((sqrt(b)*x^2)/sqrt(a)), 2))/(77*a^(5/2)*(a + b*x^4)^(3/4))]
    @test_int [(a + b*x^4)^(1/4)/x^16, x, 8, -((a + b*x^4)^(1/4)/(15*x^15)) - (b*(a + b*x^4)^(1/4))/(165*a*x^11) + (2*b^2*(a + b*x^4)^(1/4))/(231*a^2*x^7) - (4*b^3*(a + b*x^4)^(1/4))/(231*a^3*x^3) + (8*b^(9/2)*(1 + a/(b*x^4))^(3/4)*x^3*Elliptic.F((1/2)*acot((sqrt(b)*x^2)/sqrt(a)), 2))/(231*a^(7/2)*(a + b*x^4)^(3/4))]

    @test_int [x^19*(a + b*x^4)^(3/4), x, 3, (a^4*(a + b*x^4)^(7/4))/(7*b^5) - (4*a^3*(a + b*x^4)^(11/4))/(11*b^5) + (2*a^2*(a + b*x^4)^(15/4))/(5*b^5) - (4*a*(a + b*x^4)^(19/4))/(19*b^5) + (a + b*x^4)^(23/4)/(23*b^5)]
    @test_int [x^15*(a + b*x^4)^(3/4), x, 3, -(a^3*(a + b*x^4)^(7/4))/(7*b^4) + (3*a^2*(a + b*x^4)^(11/4))/(11*b^4) - (a*(a + b*x^4)^(15/4))/(5*b^4) + (a + b*x^4)^(19/4)/(19*b^4)]
    @test_int [x^11*(a + b*x^4)^(3/4), x, 3, (a^2*(a + b*x^4)^(7/4))/(7*b^3) - (2*a*(a + b*x^4)^(11/4))/(11*b^3) + (a + b*x^4)^(15/4)/(15*b^3)]
    @test_int [x^7*(a + b*x^4)^(3/4), x, 3, -(a*(a + b*x^4)^(7/4))/(7*b^2) + (a + b*x^4)^(11/4)/(11*b^2)]
    @test_int [x^3*(a + b*x^4)^(3/4), x, 1, (a + b*x^4)^(7/4)/(7*b)]
    @test_int [(a + b*x^4)^(3/4)/x^1, x, 6, (a + b*x^4)^(3/4)/3 + (a^(3/4)*atan((a + b*x^4)^(1/4)/a^(1/4)))/2 - (a^(3/4)*atanh((a + b*x^4)^(1/4)/a^(1/4)))/2]
    @test_int [(a + b*x^4)^(3/4)/x^5, x, 6, -(a + b*x^4)^(3/4)/(4*x^4) + (3*b*atan((a + b*x^4)^(1/4)/a^(1/4)))/(8*a^(1/4)) - (3*b*atanh((a + b*x^4)^(1/4)/a^(1/4)))/(8*a^(1/4))]
    @test_int [(a + b*x^4)^(3/4)/x^9, x, 7, -(a + b*x^4)^(3/4)/(8*x^8) - (3*b*(a + b*x^4)^(3/4))/(32*a*x^4) - (3*b^2*atan((a + b*x^4)^(1/4)/a^(1/4)))/(64*a^(5/4)) + (3*b^2*atanh((a + b*x^4)^(1/4)/a^(1/4)))/(64*a^(5/4))]

    @test_int [x^9*(a + b*x^4)^(3/4), x, 7, (4*a^3*x^2)/(65*b^2*(a + b*x^4)^(1/4)) - (2*a^2*x^2*(a + b*x^4)^(3/4))/(65*b^2) + (a*x^6*(a + b*x^4)^(3/4))/(39*b) + (1/13)*x^10*(a + b*x^4)^(3/4) - (4*a^(7/2)*(1 + (b*x^4)/a)^(1/4)*Elliptic.E((1/2)*atan((sqrt(b)*x^2)/sqrt(a)), 2))/(65*b^(5/2)*(a + b*x^4)^(1/4))]
    @test_int [x^5*(a + b*x^4)^(3/4), x, 6, -((2*a^2*x^2)/(15*b*(a + b*x^4)^(1/4))) + (a*x^2*(a + b*x^4)^(3/4))/(15*b) + (1/9)*x^6*(a + b*x^4)^(3/4) + (2*a^(5/2)*(1 + (b*x^4)/a)^(1/4)*Elliptic.E((1/2)*atan((sqrt(b)*x^2)/sqrt(a)), 2))/(15*b^(3/2)*(a + b*x^4)^(1/4))]
    @test_int [x^1*(a + b*x^4)^(3/4), x, 5, (3*a*x^2)/(5*(a + b*x^4)^(1/4)) + (1/5)*x^2*(a + b*x^4)^(3/4) - (3*a^(3/2)*(1 + (b*x^4)/a)^(1/4)*Elliptic.E((1/2)*atan((sqrt(b)*x^2)/sqrt(a)), 2))/(5*sqrt(b)*(a + b*x^4)^(1/4))]
    @test_int [(a + b*x^4)^(3/4)/x^3, x, 5, (3*b*x^2)/(2*(a + b*x^4)^(1/4)) - (a + b*x^4)^(3/4)/(2*x^2) - (3*sqrt(a)*sqrt(b)*(1 + (b*x^4)/a)^(1/4)*Elliptic.E((1/2)*atan((sqrt(b)*x^2)/sqrt(a)), 2))/(2*(a + b*x^4)^(1/4))]
    @test_int [(a + b*x^4)^(3/4)/x^7, x, 6, (b^2*x^2)/(4*a*(a + b*x^4)^(1/4)) - (a + b*x^4)^(3/4)/(6*x^6) - (b*(a + b*x^4)^(3/4))/(4*a*x^2) - (b^(3/2)*(1 + (b*x^4)/a)^(1/4)*Elliptic.E((1/2)*atan((sqrt(b)*x^2)/sqrt(a)), 2))/(4*sqrt(a)*(a + b*x^4)^(1/4))]
    @test_int [(a + b*x^4)^(3/4)/x^11, x, 7, -((3*b^3*x^2)/(40*a^2*(a + b*x^4)^(1/4))) - (a + b*x^4)^(3/4)/(10*x^10) - (b*(a + b*x^4)^(3/4))/(20*a*x^6) + (3*b^2*(a + b*x^4)^(3/4))/(40*a^2*x^2) + (3*b^(5/2)*(1 + (b*x^4)/a)^(1/4)*Elliptic.E((1/2)*atan((sqrt(b)*x^2)/sqrt(a)), 2))/(40*a^(3/2)*(a + b*x^4)^(1/4))]

    @test_int [x^12*(a + b*x^4)^(3/4), x, 8, (45*a^3*x*(a + b*x^4)^(3/4))/(2048*b^3) - (9*a^2*x^5*(a + b*x^4)^(3/4))/(512*b^2) + (a*x^9*(a + b*x^4)^(3/4))/(64*b) + (x^13*(a + b*x^4)^(3/4))/16 - (45*a^4*atan((b^(1/4)*x)/(a + b*x^4)^(1/4)))/(4096*b^(13/4)) - (45*a^4*atanh((b^(1/4)*x)/(a + b*x^4)^(1/4)))/(4096*b^(13/4))]
    @test_int [x^8*(a + b*x^4)^(3/4), x, 7, (-5*a^2*x*(a + b*x^4)^(3/4))/(128*b^2) + (a*x^5*(a + b*x^4)^(3/4))/(32*b) + (x^9*(a + b*x^4)^(3/4))/12 + (5*a^3*atan((b^(1/4)*x)/(a + b*x^4)^(1/4)))/(256*b^(9/4)) + (5*a^3*atanh((b^(1/4)*x)/(a + b*x^4)^(1/4)))/(256*b^(9/4))]
    @test_int [x^4*(a + b*x^4)^(3/4), x, 6, (3*a*x*(a + b*x^4)^(3/4))/(32*b) + (x^5*(a + b*x^4)^(3/4))/8 - (3*a^2*atan((b^(1/4)*x)/(a + b*x^4)^(1/4)))/(64*b^(5/4)) - (3*a^2*atanh((b^(1/4)*x)/(a + b*x^4)^(1/4)))/(64*b^(5/4))]
    @test_int [x^0*(a + b*x^4)^(3/4), x, 5, (x*(a + b*x^4)^(3/4))/4 + (3*a*atan((b^(1/4)*x)/(a + b*x^4)^(1/4)))/(8*b^(1/4)) + (3*a*atanh((b^(1/4)*x)/(a + b*x^4)^(1/4)))/(8*b^(1/4))]
    @test_int [(a + b*x^4)^(3/4)/x^4, x, 5, -(a + b*x^4)^(3/4)/(3*x^3) + (b^(3/4)*atan((b^(1/4)*x)/(a + b*x^4)^(1/4)))/2 + (b^(3/4)*atanh((b^(1/4)*x)/(a + b*x^4)^(1/4)))/2]
    @test_int [(a + b*x^4)^(3/4)/x^8, x, 1, -(a + b*x^4)^(7/4)/(7*a*x^7)]
    @test_int [(a + b*x^4)^(3/4)/x^12, x, 2, -(a + b*x^4)^(7/4)/(11*a*x^11) + (4*b*(a + b*x^4)^(7/4))/(77*a^2*x^7)]
    @test_int [(a + b*x^4)^(3/4)/x^16, x, 3, -(a + b*x^4)^(7/4)/(15*a*x^15) + (8*b*(a + b*x^4)^(7/4))/(165*a^2*x^11) - (32*b^2*(a + b*x^4)^(7/4))/(1155*a^3*x^7)]
    @test_int [(a + b*x^4)^(3/4)/x^20, x, 4, -(a + b*x^4)^(7/4)/(19*a*x^19) + (4*b*(a + b*x^4)^(7/4))/(95*a^2*x^15) - (32*b^2*(a + b*x^4)^(7/4))/(1045*a^3*x^11) + (128*b^3*(a + b*x^4)^(7/4))/(7315*a^4*x^7)]

    @test_int [x^10*(a + b*x^4)^(3/4), x, 8, (3*a^3*x^3)/(80*b^2*(a + b*x^4)^(1/4)) - (a^2*x^3*(a + b*x^4)^(3/4))/(40*b^2) + (3*a*x^7*(a + b*x^4)^(3/4))/(140*b) + (1/14)*x^11*(a + b*x^4)^(3/4) + (3*a^(7/2)*(1 + a/(b*x^4))^(1/4)*x*Elliptic.E((1/2)*acot((sqrt(b)*x^2)/sqrt(a)), 2))/(80*b^(5/2)*(a + b*x^4)^(1/4))]
    @test_int [x^6*(a + b*x^4)^(3/4), x, 7, -((3*a^2*x^3)/(40*b*(a + b*x^4)^(1/4))) + (a*x^3*(a + b*x^4)^(3/4))/(20*b) + (1/10)*x^7*(a + b*x^4)^(3/4) - (3*a^(5/2)*(1 + a/(b*x^4))^(1/4)*x*Elliptic.E((1/2)*acot((sqrt(b)*x^2)/sqrt(a)), 2))/(40*b^(3/2)*(a + b*x^4)^(1/4))]
    @test_int [x^2*(a + b*x^4)^(3/4), x, 6, (a*x^3)/(4*(a + b*x^4)^(1/4)) + (1/6)*x^3*(a + b*x^4)^(3/4) + (a^(3/2)*(1 + a/(b*x^4))^(1/4)*x*Elliptic.E((1/2)*acot((sqrt(b)*x^2)/sqrt(a)), 2))/(4*sqrt(b)*(a + b*x^4)^(1/4))]
    @test_int [(a + b*x^4)^(3/4)/x^2, x, 6, (3*b*x^3)/(2*(a + b*x^4)^(1/4)) - (a + b*x^4)^(3/4)/x + (3*sqrt(a)*sqrt(b)*(1 + a/(b*x^4))^(1/4)*x*Elliptic.E((1/2)*acot((sqrt(b)*x^2)/sqrt(a)), 2))/(2*(a + b*x^4)^(1/4))]
    @test_int [(a + b*x^4)^(3/4)/x^6, x, 6, -((3*b)/(5*x*(a + b*x^4)^(1/4))) - (a + b*x^4)^(3/4)/(5*x^5) + (3*b^(3/2)*(1 + a/(b*x^4))^(1/4)*x*Elliptic.E((1/2)*acot((sqrt(b)*x^2)/sqrt(a)), 2))/(5*sqrt(a)*(a + b*x^4)^(1/4))]
    @test_int [(a + b*x^4)^(3/4)/x^10, x, 7, (2*b^2)/(15*a*x*(a + b*x^4)^(1/4)) - (a + b*x^4)^(3/4)/(9*x^9) - (b*(a + b*x^4)^(3/4))/(15*a*x^5) - (2*b^(5/2)*(1 + a/(b*x^4))^(1/4)*x*Elliptic.E((1/2)*acot((sqrt(b)*x^2)/sqrt(a)), 2))/(15*a^(3/2)*(a + b*x^4)^(1/4))]
    @test_int [(a + b*x^4)^(3/4)/x^14, x, 8, -((4*b^3)/(65*a^2*x*(a + b*x^4)^(1/4))) - (a + b*x^4)^(3/4)/(13*x^13) - (b*(a + b*x^4)^(3/4))/(39*a*x^9) + (2*b^2*(a + b*x^4)^(3/4))/(65*a^2*x^5) + (4*b^(7/2)*(1 + a/(b*x^4))^(1/4)*x*Elliptic.E((1/2)*acot((sqrt(b)*x^2)/sqrt(a)), 2))/(65*a^(5/2)*(a + b*x^4)^(1/4))]

    @test_int [x^19*(a + b*x^4)^(5/4), x, 3, (a^4*(a + b*x^4)^(9/4))/(9*b^5) - (4*a^3*(a + b*x^4)^(13/4))/(13*b^5) + (6*a^2*(a + b*x^4)^(17/4))/(17*b^5) - (4*a*(a + b*x^4)^(21/4))/(21*b^5) + (a + b*x^4)^(25/4)/(25*b^5)]
    @test_int [x^15*(a + b*x^4)^(5/4), x, 3, -(a^3*(a + b*x^4)^(9/4))/(9*b^4) + (3*a^2*(a + b*x^4)^(13/4))/(13*b^4) - (3*a*(a + b*x^4)^(17/4))/(17*b^4) + (a + b*x^4)^(21/4)/(21*b^4)]
    @test_int [x^11*(a + b*x^4)^(5/4), x, 3, (a^2*(a + b*x^4)^(9/4))/(9*b^3) - (2*a*(a + b*x^4)^(13/4))/(13*b^3) + (a + b*x^4)^(17/4)/(17*b^3)]
    @test_int [x^7*(a + b*x^4)^(5/4), x, 3, -(a*(a + b*x^4)^(9/4))/(9*b^2) + (a + b*x^4)^(13/4)/(13*b^2)]
    @test_int [x^3*(a + b*x^4)^(5/4), x, 1, (a + b*x^4)^(9/4)/(9*b)]
    @test_int [(a + b*x^4)^(5/4)/x^1, x, 7, a*(a + b*x^4)^(1/4) + (a + b*x^4)^(5/4)/5 - (a^(5/4)*atan((a + b*x^4)^(1/4)/a^(1/4)))/2 - (a^(5/4)*atanh((a + b*x^4)^(1/4)/a^(1/4)))/2]
    @test_int [(a + b*x^4)^(5/4)/x^5, x, 7, (5*b*(a + b*x^4)^(1/4))/4 - (a + b*x^4)^(5/4)/(4*x^4) - (5*a^(1/4)*b*atan((a + b*x^4)^(1/4)/a^(1/4)))/8 - (5*a^(1/4)*b*atanh((a + b*x^4)^(1/4)/a^(1/4)))/8]
    @test_int [(a + b*x^4)^(5/4)/x^9, x, 7, (-5*b*(a + b*x^4)^(1/4))/(32*x^4) - (a + b*x^4)^(5/4)/(8*x^8) - (5*b^2*atan((a + b*x^4)^(1/4)/a^(1/4)))/(64*a^(3/4)) - (5*b^2*atanh((a + b*x^4)^(1/4)/a^(1/4)))/(64*a^(3/4))]

    @test_int [x^9*(a + b*x^4)^(5/4), x, 7, -((2*a^3*x^2*(a + b*x^4)^(1/4))/(231*b^2)) + (a^2*x^6*(a + b*x^4)^(1/4))/(231*b) + (1/33)*a*x^10*(a + b*x^4)^(1/4) + (1/15)*x^10*(a + b*x^4)^(5/4) + (4*a^(9/2)*(1 + (b*x^4)/a)^(3/4)*Elliptic.F((1/2)*atan((sqrt(b)*x^2)/sqrt(a)), 2))/(231*b^(5/2)*(a + b*x^4)^(3/4))]
    @test_int [x^5*(a + b*x^4)^(5/4), x, 6, (5*a^2*x^2*(a + b*x^4)^(1/4))/(231*b) + (5/77)*a*x^6*(a + b*x^4)^(1/4) + (1/11)*x^6*(a + b*x^4)^(5/4) - (10*a^(7/2)*(1 + (b*x^4)/a)^(3/4)*Elliptic.F((1/2)*atan((sqrt(b)*x^2)/sqrt(a)), 2))/(231*b^(3/2)*(a + b*x^4)^(3/4))]
    @test_int [x^1*(a + b*x^4)^(5/4), x, 5, (5/21)*a*x^2*(a + b*x^4)^(1/4) + (1/7)*x^2*(a + b*x^4)^(5/4) + (5*a^(5/2)*(1 + (b*x^4)/a)^(3/4)*Elliptic.F((1/2)*atan((sqrt(b)*x^2)/sqrt(a)), 2))/(21*sqrt(b)*(a + b*x^4)^(3/4))]
    @test_int [(a + b*x^4)^(5/4)/x^3, x, 5, (5/6)*b*x^2*(a + b*x^4)^(1/4) - (a + b*x^4)^(5/4)/(2*x^2) + (5*a^(3/2)*sqrt(b)*(1 + (b*x^4)/a)^(3/4)*Elliptic.F((1/2)*atan((sqrt(b)*x^2)/sqrt(a)), 2))/(6*(a + b*x^4)^(3/4))]
    @test_int [(a + b*x^4)^(5/4)/x^7, x, 5, -((5*b*(a + b*x^4)^(1/4))/(12*x^2)) - (a + b*x^4)^(5/4)/(6*x^6) + (5*sqrt(a)*b^(3/2)*(1 + (b*x^4)/a)^(3/4)*Elliptic.F((1/2)*atan((sqrt(b)*x^2)/sqrt(a)), 2))/(12*(a + b*x^4)^(3/4))]
    @test_int [(a + b*x^4)^(5/4)/x^11, x, 6, -((b*(a + b*x^4)^(1/4))/(12*x^6)) - (b^2*(a + b*x^4)^(1/4))/(24*a*x^2) - (a + b*x^4)^(5/4)/(10*x^10) - (b^(5/2)*(1 + (b*x^4)/a)^(3/4)*Elliptic.F((1/2)*atan((sqrt(b)*x^2)/sqrt(a)), 2))/(24*sqrt(a)*(a + b*x^4)^(3/4))]
    @test_int [(a + b*x^4)^(5/4)/x^15, x, 7, -((b*(a + b*x^4)^(1/4))/(28*x^10)) - (b^2*(a + b*x^4)^(1/4))/(168*a*x^6) + (5*b^3*(a + b*x^4)^(1/4))/(336*a^2*x^2) - (a + b*x^4)^(5/4)/(14*x^14) + (5*b^(7/2)*(1 + (b*x^4)/a)^(3/4)*Elliptic.F((1/2)*atan((sqrt(b)*x^2)/sqrt(a)), 2))/(336*a^(3/2)*(a + b*x^4)^(3/4))]

    @test_int [x^10*(a + b*x^4)^(5/4), x, 8, (-35*a^3*x^3*(a + b*x^4)^(1/4))/(6144*b^2) + (5*a^2*x^7*(a + b*x^4)^(1/4))/(1536*b) + (5*a*x^11*(a + b*x^4)^(1/4))/192 + (x^11*(a + b*x^4)^(5/4))/16 - (35*a^4*atan((b^(1/4)*x)/(a + b*x^4)^(1/4)))/(4096*b^(11/4)) + (35*a^4*atanh((b^(1/4)*x)/(a + b*x^4)^(1/4)))/(4096*b^(11/4))]
    @test_int [x^6*(a + b*x^4)^(5/4), x, 7, (5*a^2*x^3*(a + b*x^4)^(1/4))/(384*b) + (5*a*x^7*(a + b*x^4)^(1/4))/96 + (x^7*(a + b*x^4)^(5/4))/12 + (5*a^3*atan((b^(1/4)*x)/(a + b*x^4)^(1/4)))/(256*b^(7/4)) - (5*a^3*atanh((b^(1/4)*x)/(a + b*x^4)^(1/4)))/(256*b^(7/4))]
    @test_int [x^2*(a + b*x^4)^(5/4), x, 6, (5*a*x^3*(a + b*x^4)^(1/4))/32 + (x^3*(a + b*x^4)^(5/4))/8 - (5*a^2*atan((b^(1/4)*x)/(a + b*x^4)^(1/4)))/(64*b^(3/4)) + (5*a^2*atanh((b^(1/4)*x)/(a + b*x^4)^(1/4)))/(64*b^(3/4))]
    @test_int [(a + b*x^4)^(5/4)/x^2, x, 6, (5*b*x^3*(a + b*x^4)^(1/4))/4 - (a + b*x^4)^(5/4)/x - (5*a*b^(1/4)*atan((b^(1/4)*x)/(a + b*x^4)^(1/4)))/8 + (5*a*b^(1/4)*atanh((b^(1/4)*x)/(a + b*x^4)^(1/4)))/8]
    @test_int [(a + b*x^4)^(5/4)/x^6, x, 6, -((b*(a + b*x^4)^(1/4))/x) - (a + b*x^4)^(5/4)/(5*x^5) - (b^(5/4)*atan((b^(1/4)*x)/(a + b*x^4)^(1/4)))/2 + (b^(5/4)*atanh((b^(1/4)*x)/(a + b*x^4)^(1/4)))/2]
    @test_int [(a + b*x^4)^(5/4)/x^10, x, 1, -(a + b*x^4)^(9/4)/(9*a*x^9)]
    @test_int [(a + b*x^4)^(5/4)/x^14, x, 2, -(a + b*x^4)^(9/4)/(13*a*x^13) + (4*b*(a + b*x^4)^(9/4))/(117*a^2*x^9)]
    @test_int [(a + b*x^4)^(5/4)/x^18, x, 3, -(a + b*x^4)^(9/4)/(17*a*x^17) + (8*b*(a + b*x^4)^(9/4))/(221*a^2*x^13) - (32*b^2*(a + b*x^4)^(9/4))/(1989*a^3*x^9)]
    @test_int [(a + b*x^4)^(5/4)/x^22, x, 4, -(a + b*x^4)^(9/4)/(21*a*x^21) + (4*b*(a + b*x^4)^(9/4))/(119*a^2*x^17) - (32*b^2*(a + b*x^4)^(9/4))/(1547*a^3*x^13) + (128*b^3*(a + b*x^4)^(9/4))/(13923*a^4*x^9)]

    @test_int [x^12*(a + b*x^4)^(5/4), x, 9, (5*a^4*x*(a + b*x^4)^(1/4))/(672*b^3) - (a^3*x^5*(a + b*x^4)^(1/4))/(336*b^2) + (a^2*x^9*(a + b*x^4)^(1/4))/(504*b) + (5/252)*a*x^13*(a + b*x^4)^(1/4) + (1/18)*x^13*(a + b*x^4)^(5/4) + (5*a^(9/2)*(1 + a/(b*x^4))^(3/4)*x^3*Elliptic.F((1/2)*acot((sqrt(b)*x^2)/sqrt(a)), 2))/(672*b^(5/2)*(a + b*x^4)^(3/4))]
    @test_int [x^8*(a + b*x^4)^(5/4), x, 8, -((5*a^3*x*(a + b*x^4)^(1/4))/(336*b^2)) + (a^2*x^5*(a + b*x^4)^(1/4))/(168*b) + (1/28)*a*x^9*(a + b*x^4)^(1/4) + (1/14)*x^9*(a + b*x^4)^(5/4) - (5*a^(7/2)*(1 + a/(b*x^4))^(3/4)*x^3*Elliptic.F((1/2)*acot((sqrt(b)*x^2)/sqrt(a)), 2))/(336*b^(3/2)*(a + b*x^4)^(3/4))]
    @test_int [x^4*(a + b*x^4)^(5/4), x, 7, (a^2*x*(a + b*x^4)^(1/4))/(24*b) + (1/12)*a*x^5*(a + b*x^4)^(1/4) + (1/10)*x^5*(a + b*x^4)^(5/4) + (a^(5/2)*(1 + a/(b*x^4))^(3/4)*x^3*Elliptic.F((1/2)*acot((sqrt(b)*x^2)/sqrt(a)), 2))/(24*sqrt(b)*(a + b*x^4)^(3/4))]
    @test_int [x^0*(a + b*x^4)^(5/4), x, 6, (5/12)*a*x*(a + b*x^4)^(1/4) + (1/6)*x*(a + b*x^4)^(5/4) - (5*a^(3/2)*sqrt(b)*(1 + a/(b*x^4))^(3/4)*x^3*Elliptic.F((1/2)*acot((sqrt(b)*x^2)/sqrt(a)), 2))/(12*(a + b*x^4)^(3/4))]
    @test_int [(a + b*x^4)^(5/4)/x^4, x, 6, (5/6)*b*x*(a + b*x^4)^(1/4) - (a + b*x^4)^(5/4)/(3*x^3) - (5*sqrt(a)*b^(3/2)*(1 + a/(b*x^4))^(3/4)*x^3*Elliptic.F((1/2)*acot((sqrt(b)*x^2)/sqrt(a)), 2))/(6*(a + b*x^4)^(3/4))]
    @test_int [(a + b*x^4)^(5/4)/x^8, x, 6, -((5*b*(a + b*x^4)^(1/4))/(21*x^3)) - (a + b*x^4)^(5/4)/(7*x^7) - (5*b^(5/2)*(1 + a/(b*x^4))^(3/4)*x^3*Elliptic.F((1/2)*acot((sqrt(b)*x^2)/sqrt(a)), 2))/(21*sqrt(a)*(a + b*x^4)^(3/4))]
    @test_int [(a + b*x^4)^(5/4)/x^12, x, 7, -((5*b*(a + b*x^4)^(1/4))/(77*x^7)) - (5*b^2*(a + b*x^4)^(1/4))/(231*a*x^3) - (a + b*x^4)^(5/4)/(11*x^11) + (10*b^(7/2)*(1 + a/(b*x^4))^(3/4)*x^3*Elliptic.F((1/2)*acot((sqrt(b)*x^2)/sqrt(a)), 2))/(231*a^(3/2)*(a + b*x^4)^(3/4))]
    @test_int [(a + b*x^4)^(5/4)/x^16, x, 8, -((b*(a + b*x^4)^(1/4))/(33*x^11)) - (b^2*(a + b*x^4)^(1/4))/(231*a*x^7) + (2*b^3*(a + b*x^4)^(1/4))/(231*a^2*x^3) - (a + b*x^4)^(5/4)/(15*x^15) - (4*b^(9/2)*(1 + a/(b*x^4))^(3/4)*x^3*Elliptic.F((1/2)*acot((sqrt(b)*x^2)/sqrt(a)), 2))/(231*a^(5/2)*(a + b*x^4)^(3/4))]

    @test_int [(a + b*x^4)^(7/4), x, 6, (7/32)*a*x*(a + b*x^4)^(3/4) + (1/8)*x*(a + b*x^4)^(7/4) + (21*a^2*atan((b^(1/4)*x)/(a + b*x^4)^(1/4)))/(64*b^(1/4)) + (21*a^2*atanh((b^(1/4)*x)/(a + b*x^4)^(1/4)))/(64*b^(1/4))]

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [x^19/(a + b*x^4)^(1/4), x, 3, (a^4*(a + b*x^4)^(3/4))/(3*b^5) - (4*a^3*(a + b*x^4)^(7/4))/(7*b^5) + (6*a^2*(a + b*x^4)^(11/4))/(11*b^5) - (4*a*(a + b*x^4)^(15/4))/(15*b^5) + (a + b*x^4)^(19/4)/(19*b^5)]
    @test_int [x^15/(a + b*x^4)^(1/4), x, 3, -(a^3*(a + b*x^4)^(3/4))/(3*b^4) + (3*a^2*(a + b*x^4)^(7/4))/(7*b^4) - (3*a*(a + b*x^4)^(11/4))/(11*b^4) + (a + b*x^4)^(15/4)/(15*b^4)]
    @test_int [x^11/(a + b*x^4)^(1/4), x, 3, (a^2*(a + b*x^4)^(3/4))/(3*b^3) - (2*a*(a + b*x^4)^(7/4))/(7*b^3) + (a + b*x^4)^(11/4)/(11*b^3)]
    @test_int [x^7/(a + b*x^4)^(1/4), x, 3, -(a*(a + b*x^4)^(3/4))/(3*b^2) + (a + b*x^4)^(7/4)/(7*b^2)]
    @test_int [x^3/(a + b*x^4)^(1/4), x, 1, (a + b*x^4)^(3/4)/(3*b)]
    @test_int [1/(x^1*(a + b*x^4)^(1/4)), x, 5, atan((a + b*x^4)^(1/4)/a^(1/4))/(2*a^(1/4)) - atanh((a + b*x^4)^(1/4)/a^(1/4))/(2*a^(1/4))]
    @test_int [1/(x^5*(a + b*x^4)^(1/4)), x, 6, -(a + b*x^4)^(3/4)/(4*a*x^4) - (b*atan((a + b*x^4)^(1/4)/a^(1/4)))/(8*a^(5/4)) + (b*atanh((a + b*x^4)^(1/4)/a^(1/4)))/(8*a^(5/4))]
    @test_int [1/(x^9*(a + b*x^4)^(1/4)), x, 7, -(a + b*x^4)^(3/4)/(8*a*x^8) + (5*b*(a + b*x^4)^(3/4))/(32*a^2*x^4) + (5*b^2*atan((a + b*x^4)^(1/4)/a^(1/4)))/(64*a^(9/4)) - (5*b^2*atanh((a + b*x^4)^(1/4)/a^(1/4)))/(64*a^(9/4))]

    @test_int [x^13/(a + b*x^4)^(1/4), x, 7, -((8*a^3*x^2)/(39*b^3*(a + b*x^4)^(1/4))) + (4*a^2*x^2*(a + b*x^4)^(3/4))/(39*b^3) - (10*a*x^6*(a + b*x^4)^(3/4))/(117*b^2) + (x^10*(a + b*x^4)^(3/4))/(13*b) + (8*a^(7/2)*(1 + (b*x^4)/a)^(1/4)*Elliptic.E((1/2)*atan((sqrt(b)*x^2)/sqrt(a)), 2))/(39*b^(7/2)*(a + b*x^4)^(1/4))]
    @test_int [x^9/(a + b*x^4)^(1/4), x, 6, (4*a^2*x^2)/(15*b^2*(a + b*x^4)^(1/4)) - (2*a*x^2*(a + b*x^4)^(3/4))/(15*b^2) + (x^6*(a + b*x^4)^(3/4))/(9*b) - (4*a^(5/2)*(1 + (b*x^4)/a)^(1/4)*Elliptic.E((1/2)*atan((sqrt(b)*x^2)/sqrt(a)), 2))/(15*b^(5/2)*(a + b*x^4)^(1/4))]
    @test_int [x^5/(a + b*x^4)^(1/4), x, 5, -((2*a*x^2)/(5*b*(a + b*x^4)^(1/4))) + (x^2*(a + b*x^4)^(3/4))/(5*b) + (2*a^(3/2)*(1 + (b*x^4)/a)^(1/4)*Elliptic.E((1/2)*atan((sqrt(b)*x^2)/sqrt(a)), 2))/(5*b^(3/2)*(a + b*x^4)^(1/4))]
    @test_int [x^1/(a + b*x^4)^(1/4), x, 4, x^2/(a + b*x^4)^(1/4) - (sqrt(a)*(1 + (b*x^4)/a)^(1/4)*Elliptic.E((1/2)*atan((sqrt(b)*x^2)/sqrt(a)), 2))/(sqrt(b)*(a + b*x^4)^(1/4))]
    @test_int [1/(x^3*(a + b*x^4)^(1/4)), x, 5, (b*x^2)/(2*a*(a + b*x^4)^(1/4)) - (a + b*x^4)^(3/4)/(2*a*x^2) - (sqrt(b)*(1 + (b*x^4)/a)^(1/4)*Elliptic.E((1/2)*atan((sqrt(b)*x^2)/sqrt(a)), 2))/(2*sqrt(a)*(a + b*x^4)^(1/4))]
    @test_int [1/(x^7*(a + b*x^4)^(1/4)), x, 6, -((b^2*x^2)/(4*a^2*(a + b*x^4)^(1/4))) - (a + b*x^4)^(3/4)/(6*a*x^6) + (b*(a + b*x^4)^(3/4))/(4*a^2*x^2) + (b^(3/2)*(1 + (b*x^4)/a)^(1/4)*Elliptic.E((1/2)*atan((sqrt(b)*x^2)/sqrt(a)), 2))/(4*a^(3/2)*(a + b*x^4)^(1/4))]
    @test_int [1/(x^11*(a + b*x^4)^(1/4)), x, 7, (7*b^3*x^2)/(40*a^3*(a + b*x^4)^(1/4)) - (a + b*x^4)^(3/4)/(10*a*x^10) + (7*b*(a + b*x^4)^(3/4))/(60*a^2*x^6) - (7*b^2*(a + b*x^4)^(3/4))/(40*a^3*x^2) - (7*b^(5/2)*(1 + (b*x^4)/a)^(1/4)*Elliptic.E((1/2)*atan((sqrt(b)*x^2)/sqrt(a)), 2))/(40*a^(5/2)*(a + b*x^4)^(1/4))]

    @test_int [x^8/(a + b*x^4)^(1/4), x, 6, (-5*a*x*(a + b*x^4)^(3/4))/(32*b^2) + (x^5*(a + b*x^4)^(3/4))/(8*b) + (5*a^2*atan((b^(1/4)*x)/(a + b*x^4)^(1/4)))/(64*b^(9/4)) + (5*a^2*atanh((b^(1/4)*x)/(a + b*x^4)^(1/4)))/(64*b^(9/4))]
    @test_int [x^4/(a + b*x^4)^(1/4), x, 5, (x*(a + b*x^4)^(3/4))/(4*b) - (a*atan((b^(1/4)*x)/(a + b*x^4)^(1/4)))/(8*b^(5/4)) - (a*atanh((b^(1/4)*x)/(a + b*x^4)^(1/4)))/(8*b^(5/4))]
    @test_int [x^0/(a + b*x^4)^(1/4), x, 4, atan((b^(1/4)*x)/(a + b*x^4)^(1/4))/(2*b^(1/4)) + atanh((b^(1/4)*x)/(a + b*x^4)^(1/4))/(2*b^(1/4))]
    @test_int [1/(x^4*(a + b*x^4)^(1/4)), x, 1, -(a + b*x^4)^(3/4)/(3*a*x^3)]
    @test_int [1/(x^8*(a + b*x^4)^(1/4)), x, 2, -(a + b*x^4)^(3/4)/(7*a*x^7) + (4*b*(a + b*x^4)^(3/4))/(21*a^2*x^3)]
    @test_int [1/(x^12*(a + b*x^4)^(1/4)), x, 3, -(a + b*x^4)^(3/4)/(11*a*x^11) + (8*b*(a + b*x^4)^(3/4))/(77*a^2*x^7) - (32*b^2*(a + b*x^4)^(3/4))/(231*a^3*x^3)]
    @test_int [1/(x^16*(a + b*x^4)^(1/4)), x, 4, -(a + b*x^4)^(3/4)/(15*a*x^15) + (4*b*(a + b*x^4)^(3/4))/(55*a^2*x^11) - (32*b^2*(a + b*x^4)^(3/4))/(385*a^3*x^7) + (128*b^3*(a + b*x^4)^(3/4))/(1155*a^4*x^3)]
    @test_int [1/(x^20*(a + b*x^4)^(1/4)), x, 5, -(a + b*x^4)^(3/4)/(19*a*x^19) + (16*b*(a + b*x^4)^(3/4))/(285*a^2*x^15) - (64*b^2*(a + b*x^4)^(3/4))/(1045*a^3*x^11) + (512*b^3*(a + b*x^4)^(3/4))/(7315*a^4*x^7) - (2048*b^4*(a + b*x^4)^(3/4))/(21945*a^5*x^3)]

    @test_int [x^10/(a + b*x^4)^(1/4), x, 7, (7*a^2*x^3)/(40*b^2*(a + b*x^4)^(1/4)) - (7*a*x^3*(a + b*x^4)^(3/4))/(60*b^2) + (x^7*(a + b*x^4)^(3/4))/(10*b) + (7*a^(5/2)*(1 + a/(b*x^4))^(1/4)*x*Elliptic.E((1/2)*acot((sqrt(b)*x^2)/sqrt(a)), 2))/(40*b^(5/2)*(a + b*x^4)^(1/4))]
    @test_int [x^6/(a + b*x^4)^(1/4), x, 6, -((a*x^3)/(4*b*(a + b*x^4)^(1/4))) + (x^3*(a + b*x^4)^(3/4))/(6*b) - (a^(3/2)*(1 + a/(b*x^4))^(1/4)*x*Elliptic.E((1/2)*acot((sqrt(b)*x^2)/sqrt(a)), 2))/(4*b^(3/2)*(a + b*x^4)^(1/4))]
    @test_int [x^2/(a + b*x^4)^(1/4), x, 5, x^3/(2*(a + b*x^4)^(1/4)) + (sqrt(a)*(1 + a/(b*x^4))^(1/4)*x*Elliptic.E((1/2)*acot((sqrt(b)*x^2)/sqrt(a)), 2))/(2*sqrt(b)*(a + b*x^4)^(1/4))]
    @test_int [1/(x^2*(a + b*x^4)^(1/4)), x, 5, -(1/(x*(a + b*x^4)^(1/4))) + (sqrt(b)*(1 + a/(b*x^4))^(1/4)*x*Elliptic.E((1/2)*acot((sqrt(b)*x^2)/sqrt(a)), 2))/(sqrt(a)*(a + b*x^4)^(1/4))]
    @test_int [1/(x^6*(a + b*x^4)^(1/4)), x, 6, (2*b)/(5*a*x*(a + b*x^4)^(1/4)) - (a + b*x^4)^(3/4)/(5*a*x^5) - (2*b^(3/2)*(1 + a/(b*x^4))^(1/4)*x*Elliptic.E((1/2)*acot((sqrt(b)*x^2)/sqrt(a)), 2))/(5*a^(3/2)*(a + b*x^4)^(1/4))]
    @test_int [1/(x^10*(a + b*x^4)^(1/4)), x, 7, -((4*b^2)/(15*a^2*x*(a + b*x^4)^(1/4))) - (a + b*x^4)^(3/4)/(9*a*x^9) + (2*b*(a + b*x^4)^(3/4))/(15*a^2*x^5) + (4*b^(5/2)*(1 + a/(b*x^4))^(1/4)*x*Elliptic.E((1/2)*acot((sqrt(b)*x^2)/sqrt(a)), 2))/(15*a^(5/2)*(a + b*x^4)^(1/4))]
    @test_int [1/(x^14*(a + b*x^4)^(1/4)), x, 8, (8*b^3)/(39*a^3*x*(a + b*x^4)^(1/4)) - (a + b*x^4)^(3/4)/(13*a*x^13) + (10*b*(a + b*x^4)^(3/4))/(117*a^2*x^9) - (4*b^2*(a + b*x^4)^(3/4))/(39*a^3*x^5) - (8*b^(7/2)*(1 + a/(b*x^4))^(1/4)*x*Elliptic.E((1/2)*acot((sqrt(b)*x^2)/sqrt(a)), 2))/(39*a^(7/2)*(a + b*x^4)^(1/4))]

    @test_int [x^19/(a + b*x^4)^(3/4), x, 3, (a^4*(a + b*x^4)^(1/4))/b^5 - (4*a^3*(a + b*x^4)^(5/4))/(5*b^5) + (2*a^2*(a + b*x^4)^(9/4))/(3*b^5) - (4*a*(a + b*x^4)^(13/4))/(13*b^5) + (a + b*x^4)^(17/4)/(17*b^5)]
    @test_int [x^15/(a + b*x^4)^(3/4), x, 3, -((a^3*(a + b*x^4)^(1/4))/b^4) + (3*a^2*(a + b*x^4)^(5/4))/(5*b^4) - (a*(a + b*x^4)^(9/4))/(3*b^4) + (a + b*x^4)^(13/4)/(13*b^4)]
    @test_int [x^11/(a + b*x^4)^(3/4), x, 3, (a^2*(a + b*x^4)^(1/4))/b^3 - (2*a*(a + b*x^4)^(5/4))/(5*b^3) + (a + b*x^4)^(9/4)/(9*b^3)]
    @test_int [x^7/(a + b*x^4)^(3/4), x, 3, -((a*(a + b*x^4)^(1/4))/b^2) + (a + b*x^4)^(5/4)/(5*b^2)]
    @test_int [x^3/(a + b*x^4)^(3/4), x, 1, (a + b*x^4)^(1/4)/b]
    @test_int [1/(x^1*(a + b*x^4)^(3/4)), x, 5, -atan((a + b*x^4)^(1/4)/a^(1/4))/(2*a^(3/4)) - atanh((a + b*x^4)^(1/4)/a^(1/4))/(2*a^(3/4))]
    @test_int [1/(x^5*(a + b*x^4)^(3/4)), x, 6, -(a + b*x^4)^(1/4)/(4*a*x^4) + (3*b*atan((a + b*x^4)^(1/4)/a^(1/4)))/(8*a^(7/4)) + (3*b*atanh((a + b*x^4)^(1/4)/a^(1/4)))/(8*a^(7/4))]
    @test_int [1/(x^9*(a + b*x^4)^(3/4)), x, 7, -(a + b*x^4)^(1/4)/(8*a*x^8) + (7*b*(a + b*x^4)^(1/4))/(32*a^2*x^4) - (21*b^2*atan((a + b*x^4)^(1/4)/a^(1/4)))/(64*a^(11/4)) - (21*b^2*atanh((a + b*x^4)^(1/4)/a^(1/4)))/(64*a^(11/4))]

    @test_int [x^13/(a + b*x^4)^(3/4), x, 6, (20*a^2*x^2*(a + b*x^4)^(1/4))/(77*b^3) - (10*a*x^6*(a + b*x^4)^(1/4))/(77*b^2) + (x^10*(a + b*x^4)^(1/4))/(11*b) - (40*a^(7/2)*(1 + (b*x^4)/a)^(3/4)*Elliptic.F((1/2)*atan((sqrt(b)*x^2)/sqrt(a)), 2))/(77*b^(7/2)*(a + b*x^4)^(3/4))]
    @test_int [x^9/(a + b*x^4)^(3/4), x, 5, -((2*a*x^2*(a + b*x^4)^(1/4))/(7*b^2)) + (x^6*(a + b*x^4)^(1/4))/(7*b) + (4*a^(5/2)*(1 + (b*x^4)/a)^(3/4)*Elliptic.F((1/2)*atan((sqrt(b)*x^2)/sqrt(a)), 2))/(7*b^(5/2)*(a + b*x^4)^(3/4))]
    @test_int [x^5/(a + b*x^4)^(3/4), x, 4, (x^2*(a + b*x^4)^(1/4))/(3*b) - (2*a^(3/2)*(1 + (b*x^4)/a)^(3/4)*Elliptic.F((1/2)*atan((sqrt(b)*x^2)/sqrt(a)), 2))/(3*b^(3/2)*(a + b*x^4)^(3/4))]
    @test_int [x^1/(a + b*x^4)^(3/4), x, 3, (sqrt(a)*(1 + (b*x^4)/a)^(3/4)*Elliptic.F((1/2)*atan((sqrt(b)*x^2)/sqrt(a)), 2))/(sqrt(b)*(a + b*x^4)^(3/4))]
    @test_int [1/(x^3*(a + b*x^4)^(3/4)), x, 4, -((a + b*x^4)^(1/4)/(2*a*x^2)) - (sqrt(b)*(1 + (b*x^4)/a)^(3/4)*Elliptic.F((1/2)*atan((sqrt(b)*x^2)/sqrt(a)), 2))/(2*sqrt(a)*(a + b*x^4)^(3/4))]
    @test_int [1/(x^7*(a + b*x^4)^(3/4)), x, 5, -((a + b*x^4)^(1/4)/(6*a*x^6)) + (5*b*(a + b*x^4)^(1/4))/(12*a^2*x^2) + (5*b^(3/2)*(1 + (b*x^4)/a)^(3/4)*Elliptic.F((1/2)*atan((sqrt(b)*x^2)/sqrt(a)), 2))/(12*a^(3/2)*(a + b*x^4)^(3/4))]
    @test_int [1/(x^11*(a + b*x^4)^(3/4)), x, 6, -((a + b*x^4)^(1/4)/(10*a*x^10)) + (3*b*(a + b*x^4)^(1/4))/(20*a^2*x^6) - (3*b^2*(a + b*x^4)^(1/4))/(8*a^3*x^2) - (3*b^(5/2)*(1 + (b*x^4)/a)^(3/4)*Elliptic.F((1/2)*atan((sqrt(b)*x^2)/sqrt(a)), 2))/(8*a^(5/2)*(a + b*x^4)^(3/4))]

    @test_int [x^10/(a + b*x^4)^(3/4), x, 6, (-7*a*x^3*(a + b*x^4)^(1/4))/(32*b^2) + (x^7*(a + b*x^4)^(1/4))/(8*b) - (21*a^2*atan((b^(1/4)*x)/(a + b*x^4)^(1/4)))/(64*b^(11/4)) + (21*a^2*atanh((b^(1/4)*x)/(a + b*x^4)^(1/4)))/(64*b^(11/4))]
    @test_int [x^6/(a + b*x^4)^(3/4), x, 5, (x^3*(a + b*x^4)^(1/4))/(4*b) + (3*a*atan((b^(1/4)*x)/(a + b*x^4)^(1/4)))/(8*b^(7/4)) - (3*a*atanh((b^(1/4)*x)/(a + b*x^4)^(1/4)))/(8*b^(7/4))]
    @test_int [x^2/(a + b*x^4)^(3/4), x, 4, -atan((b^(1/4)*x)/(a + b*x^4)^(1/4))/(2*b^(3/4)) + atanh((b^(1/4)*x)/(a + b*x^4)^(1/4))/(2*b^(3/4))]
    @test_int [1/(x^2*(a + b*x^4)^(3/4)), x, 1, -((a + b*x^4)^(1/4)/(a*x))]
    @test_int [1/(x^6*(a + b*x^4)^(3/4)), x, 2, -(a + b*x^4)^(1/4)/(5*a*x^5) + (4*b*(a + b*x^4)^(1/4))/(5*a^2*x)]
    @test_int [1/(x^10*(a + b*x^4)^(3/4)), x, 3, -(a + b*x^4)^(1/4)/(9*a*x^9) + (8*b*(a + b*x^4)^(1/4))/(45*a^2*x^5) - (32*b^2*(a + b*x^4)^(1/4))/(45*a^3*x)]
    @test_int [1/(x^14*(a + b*x^4)^(3/4)), x, 4, -(a + b*x^4)^(1/4)/(13*a*x^13) + (4*b*(a + b*x^4)^(1/4))/(39*a^2*x^9) - (32*b^2*(a + b*x^4)^(1/4))/(195*a^3*x^5) + (128*b^3*(a + b*x^4)^(1/4))/(195*a^4*x)]

    @test_int [x^12/(a + b*x^4)^(3/4), x, 7, (3*a^2*x*(a + b*x^4)^(1/4))/(8*b^3) - (3*a*x^5*(a + b*x^4)^(1/4))/(20*b^2) + (x^9*(a + b*x^4)^(1/4))/(10*b) + (3*a^(5/2)*(1 + a/(b*x^4))^(3/4)*x^3*Elliptic.F((1/2)*acot((sqrt(b)*x^2)/sqrt(a)), 2))/(8*b^(5/2)*(a + b*x^4)^(3/4))]
    @test_int [x^8/(a + b*x^4)^(3/4), x, 6, -((5*a*x*(a + b*x^4)^(1/4))/(12*b^2)) + (x^5*(a + b*x^4)^(1/4))/(6*b) - (5*a^(3/2)*(1 + a/(b*x^4))^(3/4)*x^3*Elliptic.F((1/2)*acot((sqrt(b)*x^2)/sqrt(a)), 2))/(12*b^(3/2)*(a + b*x^4)^(3/4))]
    @test_int [x^4/(a + b*x^4)^(3/4), x, 5, (x*(a + b*x^4)^(1/4))/(2*b) + (sqrt(a)*(1 + a/(b*x^4))^(3/4)*x^3*Elliptic.F((1/2)*acot((sqrt(b)*x^2)/sqrt(a)), 2))/(2*sqrt(b)*(a + b*x^4)^(3/4))]
    @test_int [x^0/(a + b*x^4)^(3/4), x, 4, -((sqrt(b)*(1 + a/(b*x^4))^(3/4)*x^3*Elliptic.F((1/2)*acot((sqrt(b)*x^2)/sqrt(a)), 2))/(sqrt(a)*(a + b*x^4)^(3/4)))]
    @test_int [1/(x^4*(a + b*x^4)^(3/4)), x, 5, -((a + b*x^4)^(1/4)/(3*a*x^3)) + (2*b^(3/2)*(1 + a/(b*x^4))^(3/4)*x^3*Elliptic.F((1/2)*acot((sqrt(b)*x^2)/sqrt(a)), 2))/(3*a^(3/2)*(a + b*x^4)^(3/4))]
    @test_int [1/(x^8*(a + b*x^4)^(3/4)), x, 6, -((a + b*x^4)^(1/4)/(7*a*x^7)) + (2*b*(a + b*x^4)^(1/4))/(7*a^2*x^3) - (4*b^(5/2)*(1 + a/(b*x^4))^(3/4)*x^3*Elliptic.F((1/2)*acot((sqrt(b)*x^2)/sqrt(a)), 2))/(7*a^(5/2)*(a + b*x^4)^(3/4))]
    @test_int [1/(x^12*(a + b*x^4)^(3/4)), x, 7, -((a + b*x^4)^(1/4)/(11*a*x^11)) + (10*b*(a + b*x^4)^(1/4))/(77*a^2*x^7) - (20*b^2*(a + b*x^4)^(1/4))/(77*a^3*x^3) + (40*b^(7/2)*(1 + a/(b*x^4))^(3/4)*x^3*Elliptic.F((1/2)*acot((sqrt(b)*x^2)/sqrt(a)), 2))/(77*a^(7/2)*(a + b*x^4)^(3/4))]

    @test_int [x^19/(a + b*x^4)^(5/4), x, 3, -(a^4/(b^5*(a + b*x^4)^(1/4))) - (4*a^3*(a + b*x^4)^(3/4))/(3*b^5) + (6*a^2*(a + b*x^4)^(7/4))/(7*b^5) - (4*a*(a + b*x^4)^(11/4))/(11*b^5) + (a + b*x^4)^(15/4)/(15*b^5)]
    @test_int [x^15/(a + b*x^4)^(5/4), x, 3, a^3/(b^4*(a + b*x^4)^(1/4)) + (a^2*(a + b*x^4)^(3/4))/b^4 - (3*a*(a + b*x^4)^(7/4))/(7*b^4) + (a + b*x^4)^(11/4)/(11*b^4)]
    @test_int [x^11/(a + b*x^4)^(5/4), x, 3, -(a^2/(b^3*(a + b*x^4)^(1/4))) - (2*a*(a + b*x^4)^(3/4))/(3*b^3) + (a + b*x^4)^(7/4)/(7*b^3)]
    @test_int [x^7/(a + b*x^4)^(5/4), x, 3, a/(b^2*(a + b*x^4)^(1/4)) + (a + b*x^4)^(3/4)/(3*b^2)]
    @test_int [x^3/(a + b*x^4)^(5/4), x, 1, -(1/(b*(a + b*x^4)^(1/4)))]
    @test_int [1/(x^1*(a + b*x^4)^(5/4)), x, 6, 1/(a*(a + b*x^4)^(1/4)) + atan((a + b*x^4)^(1/4)/a^(1/4))/(2*a^(5/4)) - atanh((a + b*x^4)^(1/4)/a^(1/4))/(2*a^(5/4))]
    @test_int [1/(x^5*(a + b*x^4)^(5/4)), x, 7, -((5*b)/(4*a^2*(a + b*x^4)^(1/4))) - 1/(4*a*x^4*(a + b*x^4)^(1/4)) - (5*b*atan((a + b*x^4)^(1/4)/a^(1/4)))/(8*a^(9/4)) + (5*b*atanh((a + b*x^4)^(1/4)/a^(1/4)))/(8*a^(9/4))]
    @test_int [1/(x^9*(a + b*x^4)^(5/4)), x, 8, (45*b^2)/(32*a^3*(a + b*x^4)^(1/4)) - 1/(8*a*x^8*(a + b*x^4)^(1/4)) + (9*b)/(32*a^2*x^4*(a + b*x^4)^(1/4)) + (45*b^2*atan((a + b*x^4)^(1/4)/a^(1/4)))/(64*a^(13/4)) - (45*b^2*atanh((a + b*x^4)^(1/4)/a^(1/4)))/(64*a^(13/4))]

    @test_int [x^13/(a + b*x^4)^(5/4), x, 6, (4*a^2*x^2)/(3*b^3*(a + b*x^4)^(1/4)) - (2*a*x^6)/(9*b^2*(a + b*x^4)^(1/4)) + x^10/(9*b*(a + b*x^4)^(1/4)) - (8*a^(5/2)*(1 + (b*x^4)/a)^(1/4)*Elliptic.E((1/2)*atan((sqrt(b)*x^2)/sqrt(a)), 2))/(3*b^(7/2)*(a + b*x^4)^(1/4))]
    @test_int [x^9/(a + b*x^4)^(5/4), x, 5, -((6*a*x^2)/(5*b^2*(a + b*x^4)^(1/4))) + x^6/(5*b*(a + b*x^4)^(1/4)) + (12*a^(3/2)*(1 + (b*x^4)/a)^(1/4)*Elliptic.E((1/2)*atan((sqrt(b)*x^2)/sqrt(a)), 2))/(5*b^(5/2)*(a + b*x^4)^(1/4))]
    @test_int [x^5/(a + b*x^4)^(5/4), x, 4, x^2/(b*(a + b*x^4)^(1/4)) - (2*sqrt(a)*(1 + (b*x^4)/a)^(1/4)*Elliptic.E((1/2)*atan((sqrt(b)*x^2)/sqrt(a)), 2))/(b^(3/2)*(a + b*x^4)^(1/4))]
    @test_int [x^1/(a + b*x^4)^(5/4), x, 3, ((1 + (b*x^4)/a)^(1/4)*Elliptic.E((1/2)*atan((sqrt(b)*x^2)/sqrt(a)), 2))/(sqrt(a)*sqrt(b)*(a + b*x^4)^(1/4))]
    @test_int [1/(x^3*(a + b*x^4)^(5/4)), x, 4, -(1/(2*a*x^2*(a + b*x^4)^(1/4))) - (3*sqrt(b)*(1 + (b*x^4)/a)^(1/4)*Elliptic.E((1/2)*atan((sqrt(b)*x^2)/sqrt(a)), 2))/(2*a^(3/2)*(a + b*x^4)^(1/4))]
    @test_int [1/(x^7*(a + b*x^4)^(5/4)), x, 5, -(1/(6*a*x^6*(a + b*x^4)^(1/4))) + (7*b)/(12*a^2*x^2*(a + b*x^4)^(1/4)) + (7*b^(3/2)*(1 + (b*x^4)/a)^(1/4)*Elliptic.E((1/2)*atan((sqrt(b)*x^2)/sqrt(a)), 2))/(4*a^(5/2)*(a + b*x^4)^(1/4))]
    @test_int [1/(x^11*(a + b*x^4)^(5/4)), x, 6, -(1/(10*a*x^10*(a + b*x^4)^(1/4))) + (11*b)/(60*a^2*x^6*(a + b*x^4)^(1/4)) - (77*b^2)/(120*a^3*x^2*(a + b*x^4)^(1/4)) - (77*b^(5/2)*(1 + (b*x^4)/a)^(1/4)*Elliptic.E((1/2)*atan((sqrt(b)*x^2)/sqrt(a)), 2))/(40*a^(7/2)*(a + b*x^4)^(1/4))]

    @test_int [x^12/(a + b*x^4)^(5/4), x, 7, -(x^9/(b*(a + b*x^4)^(1/4))) - (45*a*x*(a + b*x^4)^(3/4))/(32*b^3) + (9*x^5*(a + b*x^4)^(3/4))/(8*b^2) + (45*a^2*atan((b^(1/4)*x)/(a + b*x^4)^(1/4)))/(64*b^(13/4)) + (45*a^2*atanh((b^(1/4)*x)/(a + b*x^4)^(1/4)))/(64*b^(13/4))]
    @test_int [x^8/(a + b*x^4)^(5/4), x, 6, -(x^5/(b*(a + b*x^4)^(1/4))) + (5*x*(a + b*x^4)^(3/4))/(4*b^2) - (5*a*atan((b^(1/4)*x)/(a + b*x^4)^(1/4)))/(8*b^(9/4)) - (5*a*atanh((b^(1/4)*x)/(a + b*x^4)^(1/4)))/(8*b^(9/4))]
    @test_int [x^4/(a + b*x^4)^(5/4), x, 5, -(x/(b*(a + b*x^4)^(1/4))) + atan((b^(1/4)*x)/(a + b*x^4)^(1/4))/(2*b^(5/4)) + atanh((b^(1/4)*x)/(a + b*x^4)^(1/4))/(2*b^(5/4))]
    @test_int [x^0/(a + b*x^4)^(5/4), x, 1, x/(a*(a + b*x^4)^(1/4))]
    @test_int [1/(x^4*(a + b*x^4)^(5/4)), x, 2, -1/(3*a*x^3*(a + b*x^4)^(1/4)) - (4*b*x)/(3*a^2*(a + b*x^4)^(1/4))]
    @test_int [1/(x^8*(a + b*x^4)^(5/4)), x, 3, -1/(7*a*x^7*(a + b*x^4)^(1/4)) + (8*b)/(21*a^2*x^3*(a + b*x^4)^(1/4)) + (32*b^2*x)/(21*a^3*(a + b*x^4)^(1/4))]
    @test_int [1/(x^12*(a + b*x^4)^(5/4)), x, 4, -1/(11*a*x^11*(a + b*x^4)^(1/4)) + (12*b)/(77*a^2*x^7*(a + b*x^4)^(1/4)) - (32*b^2)/(77*a^3*x^3*(a + b*x^4)^(1/4)) - (128*b^3*x)/(77*a^4*(a + b*x^4)^(1/4))]
    @test_int [1/(x^16*(a + b*x^4)^(5/4)), x, 5, -1/(15*a*x^15*(a + b*x^4)^(1/4)) + (16*b)/(165*a^2*x^11*(a + b*x^4)^(1/4)) - (64*b^2)/(385*a^3*x^7*(a + b*x^4)^(1/4)) + (512*b^3)/(1155*a^4*x^3*(a + b*x^4)^(1/4)) + (2048*b^4*x)/(1155*a^5*(a + b*x^4)^(1/4))]

    @test_int [x^14/(a + b*x^4)^(5/4), x, 7, (77*a^2*x^3)/(120*b^3*(a + b*x^4)^(1/4)) - (11*a*x^7)/(60*b^2*(a + b*x^4)^(1/4)) + x^11/(10*b*(a + b*x^4)^(1/4)) + (77*a^(5/2)*(1 + a/(b*x^4))^(1/4)*x*Elliptic.E((1/2)*acot((sqrt(b)*x^2)/sqrt(a)), 2))/(40*b^(7/2)*(a + b*x^4)^(1/4))]
    @test_int [x^10/(a + b*x^4)^(5/4), x, 6, -((7*a*x^3)/(12*b^2*(a + b*x^4)^(1/4))) + x^7/(6*b*(a + b*x^4)^(1/4)) - (7*a^(3/2)*(1 + a/(b*x^4))^(1/4)*x*Elliptic.E((1/2)*acot((sqrt(b)*x^2)/sqrt(a)), 2))/(4*b^(5/2)*(a + b*x^4)^(1/4))]
    @test_int [x^6/(a + b*x^4)^(5/4), x, 5, x^3/(2*b*(a + b*x^4)^(1/4)) + (3*sqrt(a)*(1 + a/(b*x^4))^(1/4)*x*Elliptic.E((1/2)*acot((sqrt(b)*x^2)/sqrt(a)), 2))/(2*b^(3/2)*(a + b*x^4)^(1/4))]
    @test_int [x^2/(a + b*x^4)^(5/4), x, 4, -(((1 + a/(b*x^4))^(1/4)*x*Elliptic.E((1/2)*acot((sqrt(b)*x^2)/sqrt(a)), 2))/(sqrt(a)*sqrt(b)*(a + b*x^4)^(1/4)))]
    @test_int [1/(x^2*(a + b*x^4)^(5/4)), x, 5, -(1/(a*x*(a + b*x^4)^(1/4))) + (2*sqrt(b)*(1 + a/(b*x^4))^(1/4)*x*Elliptic.E((1/2)*acot((sqrt(b)*x^2)/sqrt(a)), 2))/(a^(3/2)*(a + b*x^4)^(1/4))]
    @test_int [1/(x^6*(a + b*x^4)^(5/4)), x, 6, -(1/(5*a*x^5*(a + b*x^4)^(1/4))) + (6*b)/(5*a^2*x*(a + b*x^4)^(1/4)) - (12*b^(3/2)*(1 + a/(b*x^4))^(1/4)*x*Elliptic.E((1/2)*acot((sqrt(b)*x^2)/sqrt(a)), 2))/(5*a^(5/2)*(a + b*x^4)^(1/4))]
    @test_int [1/(x^10*(a + b*x^4)^(5/4)), x, 7, -(1/(9*a*x^9*(a + b*x^4)^(1/4))) + (2*b)/(9*a^2*x^5*(a + b*x^4)^(1/4)) - (4*b^2)/(3*a^3*x*(a + b*x^4)^(1/4)) + (8*b^(5/2)*(1 + a/(b*x^4))^(1/4)*x*Elliptic.E((1/2)*acot((sqrt(b)*x^2)/sqrt(a)), 2))/(3*a^(7/2)*(a + b*x^4)^(1/4))]
    @test_int [1/(x^14*(a + b*x^4)^(5/4)), x, 8, -(1/(13*a*x^13*(a + b*x^4)^(1/4))) + (14*b)/(117*a^2*x^9*(a + b*x^4)^(1/4)) - (28*b^2)/(117*a^3*x^5*(a + b*x^4)^(1/4)) + (56*b^3)/(39*a^4*x*(a + b*x^4)^(1/4)) - (112*b^(7/2)*(1 + a/(b*x^4))^(1/4)*x*Elliptic.E((1/2)*acot((sqrt(b)*x^2)/sqrt(a)), 2))/(39*a^(9/2)*(a + b*x^4)^(1/4))]

    @test_int [1/(a + b*x^4)^(7/4), x, 5, x/(3*a*(a + b*x^4)^(3/4)) - (2*sqrt(b)*(1 + a/(b*x^4))^(3/4)*x^3*Elliptic.F((1/2)*acot((sqrt(b)*x^2)/sqrt(a)), 2))/(3*a^(3/2)*(a + b*x^4)^(3/4))]

    @test_int [1/(a + b*x^4)^(9/4), x, 2, x/(5*a*(a + b*x^4)^(5/4)) + (4*x)/(5*a^2*(a + b*x^4)^(1/4))]

    @test_int [1/(a + b*x^4)^(11/4), x, 6, x/(7*a*(a + b*x^4)^(7/4)) + (2*x)/(7*a^2*(a + b*x^4)^(3/4)) - (4*sqrt(b)*(1 + a/(b*x^4))^(3/4)*x^3*Elliptic.F((1/2)*acot((sqrt(b)*x^2)/sqrt(a)), 2))/(7*a^(5/2)*(a + b*x^4)^(3/4))]

    @test_int [1/(a + b*x^4)^(13/4), x, 3, x/(9*a*(a + b*x^4)^(9/4)) + (8*x)/(45*a^2*(a + b*x^4)^(5/4)) + (32*x)/(45*a^3*(a + b*x^4)^(1/4))]
    @test_int [1/(a + b*x^4)^(17/4), x, 4, x/(13*a*(a + b*x^4)^(13/4)) + (4*x)/(39*a^2*(a + b*x^4)^(9/4)) + (32*x)/(195*a^3*(a + b*x^4)^(5/4)) + (128*x)/(195*a^4*(a + b*x^4)^(1/4))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(a-b*x^4)^(p/4)=#

    #= ::Subsubsection::Closed:: =#
    #=p>0=#

    @test_int [x^19*(a - b*x^4)^(1/4), x, 3, -((a^4*(a - b*x^4)^(5/4))/(5*b^5)) + (4*a^3*(a - b*x^4)^(9/4))/(9*b^5) - (6*a^2*(a - b*x^4)^(13/4))/(13*b^5) + (4*a*(a - b*x^4)^(17/4))/(17*b^5) - (a - b*x^4)^(21/4)/(21*b^5)]
    @test_int [x^15*(a - b*x^4)^(1/4), x, 3, -((a^3*(a - b*x^4)^(5/4))/(5*b^4)) + (a^2*(a - b*x^4)^(9/4))/(3*b^4) - (3*a*(a - b*x^4)^(13/4))/(13*b^4) + (a - b*x^4)^(17/4)/(17*b^4)]
    @test_int [x^11*(a - b*x^4)^(1/4), x, 3, -((a^2*(a - b*x^4)^(5/4))/(5*b^3)) + (2*a*(a - b*x^4)^(9/4))/(9*b^3) - (a - b*x^4)^(13/4)/(13*b^3)]
    @test_int [x^7*(a - b*x^4)^(1/4), x, 3, -((a*(a - b*x^4)^(5/4))/(5*b^2)) + (a - b*x^4)^(9/4)/(9*b^2)]
    @test_int [x^3*(a - b*x^4)^(1/4), x, 1, -((a - b*x^4)^(5/4)/(5*b))]
    @test_int [(a - b*x^4)^(1/4)/x^1, x, 6, (a - b*x^4)^(1/4) - (1/2)*a^(1/4)*atan((a - b*x^4)^(1/4)/a^(1/4)) - (1/2)*a^(1/4)*atanh((a - b*x^4)^(1/4)/a^(1/4))]
    @test_int [(a - b*x^4)^(1/4)/x^5, x, 6, -((a - b*x^4)^(1/4)/(4*x^4)) + (b*atan((a - b*x^4)^(1/4)/a^(1/4)))/(8*a^(3/4)) + (b*atanh((a - b*x^4)^(1/4)/a^(1/4)))/(8*a^(3/4))]
    @test_int [(a - b*x^4)^(1/4)/x^9, x, 7, -((a - b*x^4)^(1/4)/(8*x^8)) + (b*(a - b*x^4)^(1/4))/(32*a*x^4) + (3*b^2*atan((a - b*x^4)^(1/4)/a^(1/4)))/(64*a^(7/4)) + (3*b^2*atanh((a - b*x^4)^(1/4)/a^(1/4)))/(64*a^(7/4))]

    @test_int [x^9*(a - b*x^4)^(1/4), x, 6, -((2*a^2*x^2*(a - b*x^4)^(1/4))/(77*b^2)) - (a*x^6*(a - b*x^4)^(1/4))/(77*b) + (1/11)*x^10*(a - b*x^4)^(1/4) + (4*a^(7/2)*(1 - (b*x^4)/a)^(3/4)*Elliptic.F((1/2)*asin((sqrt(b)*x^2)/sqrt(a)), 2))/(77*b^(5/2)*(a - b*x^4)^(3/4))]
    @test_int [x^5*(a - b*x^4)^(1/4), x, 5, -((a*x^2*(a - b*x^4)^(1/4))/(21*b)) + (1/7)*x^6*(a - b*x^4)^(1/4) + (2*a^(5/2)*(1 - (b*x^4)/a)^(3/4)*Elliptic.F((1/2)*asin((sqrt(b)*x^2)/sqrt(a)), 2))/(21*b^(3/2)*(a - b*x^4)^(3/4))]
    @test_int [x^1*(a - b*x^4)^(1/4), x, 4, (1/3)*x^2*(a - b*x^4)^(1/4) + (a^(3/2)*(1 - (b*x^4)/a)^(3/4)*Elliptic.F((1/2)*asin((sqrt(b)*x^2)/sqrt(a)), 2))/(3*sqrt(b)*(a - b*x^4)^(3/4))]
    @test_int [(a - b*x^4)^(1/4)/x^3, x, 4, -((a - b*x^4)^(1/4)/(2*x^2)) - (sqrt(a)*sqrt(b)*(1 - (b*x^4)/a)^(3/4)*Elliptic.F((1/2)*asin((sqrt(b)*x^2)/sqrt(a)), 2))/(2*(a - b*x^4)^(3/4))]
    @test_int [(a - b*x^4)^(1/4)/x^7, x, 5, -((a - b*x^4)^(1/4)/(6*x^6)) + (b*(a - b*x^4)^(1/4))/(12*a*x^2) - (b^(3/2)*(1 - (b*x^4)/a)^(3/4)*Elliptic.F((1/2)*asin((sqrt(b)*x^2)/sqrt(a)), 2))/(12*sqrt(a)*(a - b*x^4)^(3/4))]
    @test_int [(a - b*x^4)^(1/4)/x^11, x, 6, -((a - b*x^4)^(1/4)/(10*x^10)) + (b*(a - b*x^4)^(1/4))/(60*a*x^6) + (b^2*(a - b*x^4)^(1/4))/(24*a^2*x^2) - (b^(5/2)*(1 - (b*x^4)/a)^(3/4)*Elliptic.F((1/2)*asin((sqrt(b)*x^2)/sqrt(a)), 2))/(24*a^(3/2)*(a - b*x^4)^(3/4))]

    @test_int [x^6*(a - b*x^4)^(1/4), x, 12, -((a*x^3*(a - b*x^4)^(1/4))/(32*b)) + (1/8)*x^7*(a - b*x^4)^(1/4) - (3*a^2*atan(1 - (sqrt(2)*b^(1/4)*x)/(a - b*x^4)^(1/4)))/(64*sqrt(2)*b^(7/4)) + (3*a^2*atan(1 + (sqrt(2)*b^(1/4)*x)/(a - b*x^4)^(1/4)))/(64*sqrt(2)*b^(7/4)) + (3*a^2*log(1 + (sqrt(b)*x^2)/sqrt(a - b*x^4) - (sqrt(2)*b^(1/4)*x)/(a - b*x^4)^(1/4)))/(128*sqrt(2)*b^(7/4)) - (3*a^2*log(1 + (sqrt(b)*x^2)/sqrt(a - b*x^4) + (sqrt(2)*b^(1/4)*x)/(a - b*x^4)^(1/4)))/(128*sqrt(2)*b^(7/4))]
    @test_int [x^2*(a - b*x^4)^(1/4), x, 11, (1/4)*x^3*(a - b*x^4)^(1/4) - (a*atan(1 - (sqrt(2)*b^(1/4)*x)/(a - b*x^4)^(1/4)))/(8*sqrt(2)*b^(3/4)) + (a*atan(1 + (sqrt(2)*b^(1/4)*x)/(a - b*x^4)^(1/4)))/(8*sqrt(2)*b^(3/4)) + (a*log(1 + (sqrt(b)*x^2)/sqrt(a - b*x^4) - (sqrt(2)*b^(1/4)*x)/(a - b*x^4)^(1/4)))/(16*sqrt(2)*b^(3/4)) - (a*log(1 + (sqrt(b)*x^2)/sqrt(a - b*x^4) + (sqrt(2)*b^(1/4)*x)/(a - b*x^4)^(1/4)))/(16*sqrt(2)*b^(3/4))]
    @test_int [(a - b*x^4)^(1/4)/x^2, x, 11, -((a - b*x^4)^(1/4)/x) + (b^(1/4)*atan(1 - (sqrt(2)*b^(1/4)*x)/(a - b*x^4)^(1/4)))/(2*sqrt(2)) - (b^(1/4)*atan(1 + (sqrt(2)*b^(1/4)*x)/(a - b*x^4)^(1/4)))/(2*sqrt(2)) - (b^(1/4)*log(1 + (sqrt(b)*x^2)/sqrt(a - b*x^4) - (sqrt(2)*b^(1/4)*x)/(a - b*x^4)^(1/4)))/(4*sqrt(2)) + (b^(1/4)*log(1 + (sqrt(b)*x^2)/sqrt(a - b*x^4) + (sqrt(2)*b^(1/4)*x)/(a - b*x^4)^(1/4)))/(4*sqrt(2))]
    @test_int [(a - b*x^4)^(1/4)/x^6, x, 1, -((a - b*x^4)^(5/4)/(5*a*x^5))]
    @test_int [(a - b*x^4)^(1/4)/x^10, x, 2, -((a - b*x^4)^(5/4)/(9*a*x^9)) - (4*b*(a - b*x^4)^(5/4))/(45*a^2*x^5)]
    @test_int [(a - b*x^4)^(1/4)/x^14, x, 3, -((a - b*x^4)^(5/4)/(13*a*x^13)) - (8*b*(a - b*x^4)^(5/4))/(117*a^2*x^9) - (32*b^2*(a - b*x^4)^(5/4))/(585*a^3*x^5)]
    @test_int [(a - b*x^4)^(1/4)/x^18, x, 4, -((a - b*x^4)^(5/4)/(17*a*x^17)) - (12*b*(a - b*x^4)^(5/4))/(221*a^2*x^13) - (32*b^2*(a - b*x^4)^(5/4))/(663*a^3*x^9) - (128*b^3*(a - b*x^4)^(5/4))/(3315*a^4*x^5)]

    @test_int [x^12*(a - b*x^4)^(1/4), x, 8, -((3*a^3*x*(a - b*x^4)^(1/4))/(112*b^3)) - (3*a^2*x^5*(a - b*x^4)^(1/4))/(280*b^2) - (a*x^9*(a - b*x^4)^(1/4))/(140*b) + (1/14)*x^13*(a - b*x^4)^(1/4) - (3*a^(7/2)*(1 - a/(b*x^4))^(3/4)*x^3*Elliptic.F((1/2)*acsc((sqrt(b)*x^2)/sqrt(a)), 2))/(112*b^(5/2)*(a - b*x^4)^(3/4))]
    @test_int [x^8*(a - b*x^4)^(1/4), x, 7, -((a^2*x*(a - b*x^4)^(1/4))/(24*b^2)) - (a*x^5*(a - b*x^4)^(1/4))/(60*b) + (1/10)*x^9*(a - b*x^4)^(1/4) - (a^(5/2)*(1 - a/(b*x^4))^(3/4)*x^3*Elliptic.F((1/2)*acsc((sqrt(b)*x^2)/sqrt(a)), 2))/(24*b^(3/2)*(a - b*x^4)^(3/4))]
    @test_int [x^4*(a - b*x^4)^(1/4), x, 6, -((a*x*(a - b*x^4)^(1/4))/(12*b)) + (1/6)*x^5*(a - b*x^4)^(1/4) - (a^(3/2)*(1 - a/(b*x^4))^(3/4)*x^3*Elliptic.F((1/2)*acsc((sqrt(b)*x^2)/sqrt(a)), 2))/(12*sqrt(b)*(a - b*x^4)^(3/4))]
    @test_int [x^0*(a - b*x^4)^(1/4), x, 5, (1/2)*x*(a - b*x^4)^(1/4) - (sqrt(a)*sqrt(b)*(1 - a/(b*x^4))^(3/4)*x^3*Elliptic.F((1/2)*acsc((sqrt(b)*x^2)/sqrt(a)), 2))/(2*(a - b*x^4)^(3/4))]
    @test_int [(a - b*x^4)^(1/4)/x^4, x, 5, -((a - b*x^4)^(1/4)/(3*x^3)) + (b^(3/2)*(1 - a/(b*x^4))^(3/4)*x^3*Elliptic.F((1/2)*acsc((sqrt(b)*x^2)/sqrt(a)), 2))/(3*sqrt(a)*(a - b*x^4)^(3/4))]
    @test_int [(a - b*x^4)^(1/4)/x^8, x, 6, -((a - b*x^4)^(1/4)/(7*x^7)) + (b*(a - b*x^4)^(1/4))/(21*a*x^3) + (2*b^(5/2)*(1 - a/(b*x^4))^(3/4)*x^3*Elliptic.F((1/2)*acsc((sqrt(b)*x^2)/sqrt(a)), 2))/(21*a^(3/2)*(a - b*x^4)^(3/4))]
    @test_int [(a - b*x^4)^(1/4)/x^12, x, 7, -((a - b*x^4)^(1/4)/(11*x^11)) + (b*(a - b*x^4)^(1/4))/(77*a*x^7) + (2*b^2*(a - b*x^4)^(1/4))/(77*a^2*x^3) + (4*b^(7/2)*(1 - a/(b*x^4))^(3/4)*x^3*Elliptic.F((1/2)*acsc((sqrt(b)*x^2)/sqrt(a)), 2))/(77*a^(5/2)*(a - b*x^4)^(3/4))]
    @test_int [(a - b*x^4)^(1/4)/x^16, x, 8, -((a - b*x^4)^(1/4)/(15*x^15)) + (b*(a - b*x^4)^(1/4))/(165*a*x^11) + (2*b^2*(a - b*x^4)^(1/4))/(231*a^2*x^7) + (4*b^3*(a - b*x^4)^(1/4))/(231*a^3*x^3) + (8*b^(9/2)*(1 - a/(b*x^4))^(3/4)*x^3*Elliptic.F((1/2)*acsc((sqrt(b)*x^2)/sqrt(a)), 2))/(231*a^(7/2)*(a - b*x^4)^(3/4))]

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [x^19/(a - b*x^4)^(1/4), x, 3, -((a^4*(a - b*x^4)^(3/4))/(3*b^5)) + (4*a^3*(a - b*x^4)^(7/4))/(7*b^5) - (6*a^2*(a - b*x^4)^(11/4))/(11*b^5) + (4*a*(a - b*x^4)^(15/4))/(15*b^5) - (a - b*x^4)^(19/4)/(19*b^5)]
    @test_int [x^15/(a - b*x^4)^(1/4), x, 3, -((a^3*(a - b*x^4)^(3/4))/(3*b^4)) + (3*a^2*(a - b*x^4)^(7/4))/(7*b^4) - (3*a*(a - b*x^4)^(11/4))/(11*b^4) + (a - b*x^4)^(15/4)/(15*b^4)]
    @test_int [x^11/(a - b*x^4)^(1/4), x, 3, -((a^2*(a - b*x^4)^(3/4))/(3*b^3)) + (2*a*(a - b*x^4)^(7/4))/(7*b^3) - (a - b*x^4)^(11/4)/(11*b^3)]
    @test_int [x^7/(a - b*x^4)^(1/4), x, 3, -((a*(a - b*x^4)^(3/4))/(3*b^2)) + (a - b*x^4)^(7/4)/(7*b^2)]
    @test_int [x^3/(a - b*x^4)^(1/4), x, 1, -((a - b*x^4)^(3/4)/(3*b))]
    @test_int [1/(x^1*(a - b*x^4)^(1/4)), x, 5, atan((a - b*x^4)^(1/4)/a^(1/4))/(2*a^(1/4)) - atanh((a - b*x^4)^(1/4)/a^(1/4))/(2*a^(1/4))]
    @test_int [1/(x^5*(a - b*x^4)^(1/4)), x, 6, -((a - b*x^4)^(3/4)/(4*a*x^4)) + (b*atan((a - b*x^4)^(1/4)/a^(1/4)))/(8*a^(5/4)) - (b*atanh((a - b*x^4)^(1/4)/a^(1/4)))/(8*a^(5/4))]
    @test_int [1/(x^9*(a - b*x^4)^(1/4)), x, 7, -((a - b*x^4)^(3/4)/(8*a*x^8)) - (5*b*(a - b*x^4)^(3/4))/(32*a^2*x^4) + (5*b^2*atan((a - b*x^4)^(1/4)/a^(1/4)))/(64*a^(9/4)) - (5*b^2*atanh((a - b*x^4)^(1/4)/a^(1/4)))/(64*a^(9/4))]

    @test_int [x^13/(a - b*x^4)^(1/4), x, 6, -((4*a^2*x^2*(a - b*x^4)^(3/4))/(39*b^3)) - (10*a*x^6*(a - b*x^4)^(3/4))/(117*b^2) - (x^10*(a - b*x^4)^(3/4))/(13*b) + (8*a^(7/2)*(1 - (b*x^4)/a)^(1/4)*Elliptic.E((1/2)*asin((sqrt(b)*x^2)/sqrt(a)), 2))/(39*b^(7/2)*(a - b*x^4)^(1/4))]
    @test_int [x^9/(a - b*x^4)^(1/4), x, 5, -((2*a*x^2*(a - b*x^4)^(3/4))/(15*b^2)) - (x^6*(a - b*x^4)^(3/4))/(9*b) + (4*a^(5/2)*(1 - (b*x^4)/a)^(1/4)*Elliptic.E((1/2)*asin((sqrt(b)*x^2)/sqrt(a)), 2))/(15*b^(5/2)*(a - b*x^4)^(1/4))]
    @test_int [x^5/(a - b*x^4)^(1/4), x, 4, -((x^2*(a - b*x^4)^(3/4))/(5*b)) + (2*a^(3/2)*(1 - (b*x^4)/a)^(1/4)*Elliptic.E((1/2)*asin((sqrt(b)*x^2)/sqrt(a)), 2))/(5*b^(3/2)*(a - b*x^4)^(1/4))]
    @test_int [x^1/(a - b*x^4)^(1/4), x, 3, (sqrt(a)*(1 - (b*x^4)/a)^(1/4)*Elliptic.E((1/2)*asin((sqrt(b)*x^2)/sqrt(a)), 2))/(sqrt(b)*(a - b*x^4)^(1/4))]
    @test_int [1/(x^3*(a - b*x^4)^(1/4)), x, 4, -((a - b*x^4)^(3/4)/(2*a*x^2)) - (sqrt(b)*(1 - (b*x^4)/a)^(1/4)*Elliptic.E((1/2)*asin((sqrt(b)*x^2)/sqrt(a)), 2))/(2*sqrt(a)*(a - b*x^4)^(1/4))]
    @test_int [1/(x^7*(a - b*x^4)^(1/4)), x, 5, -((a - b*x^4)^(3/4)/(6*a*x^6)) - (b*(a - b*x^4)^(3/4))/(4*a^2*x^2) - (b^(3/2)*(1 - (b*x^4)/a)^(1/4)*Elliptic.E((1/2)*asin((sqrt(b)*x^2)/sqrt(a)), 2))/(4*a^(3/2)*(a - b*x^4)^(1/4))]
    @test_int [1/(x^11*(a - b*x^4)^(1/4)), x, 6, -((a - b*x^4)^(3/4)/(10*a*x^10)) - (7*b*(a - b*x^4)^(3/4))/(60*a^2*x^6) - (7*b^2*(a - b*x^4)^(3/4))/(40*a^3*x^2) - (7*b^(5/2)*(1 - (b*x^4)/a)^(1/4)*Elliptic.E((1/2)*asin((sqrt(b)*x^2)/sqrt(a)), 2))/(40*a^(5/2)*(a - b*x^4)^(1/4))]

    @test_int [x^8/(a - b*x^4)^(1/4), x, 12, -((5*a*x*(a - b*x^4)^(3/4))/(32*b^2)) - (x^5*(a - b*x^4)^(3/4))/(8*b) - (5*a^2*atan(1 - (sqrt(2)*b^(1/4)*x)/(a - b*x^4)^(1/4)))/(64*sqrt(2)*b^(9/4)) + (5*a^2*atan(1 + (sqrt(2)*b^(1/4)*x)/(a - b*x^4)^(1/4)))/(64*sqrt(2)*b^(9/4)) - (5*a^2*log(1 + (sqrt(b)*x^2)/sqrt(a - b*x^4) - (sqrt(2)*b^(1/4)*x)/(a - b*x^4)^(1/4)))/(128*sqrt(2)*b^(9/4)) + (5*a^2*log(1 + (sqrt(b)*x^2)/sqrt(a - b*x^4) + (sqrt(2)*b^(1/4)*x)/(a - b*x^4)^(1/4)))/(128*sqrt(2)*b^(9/4))]
    @test_int [x^4/(a - b*x^4)^(1/4), x, 11, -((x*(a - b*x^4)^(3/4))/(4*b)) - (a*atan(1 - (sqrt(2)*b^(1/4)*x)/(a - b*x^4)^(1/4)))/(8*sqrt(2)*b^(5/4)) + (a*atan(1 + (sqrt(2)*b^(1/4)*x)/(a - b*x^4)^(1/4)))/(8*sqrt(2)*b^(5/4)) - (a*log(1 + (sqrt(b)*x^2)/sqrt(a - b*x^4) - (sqrt(2)*b^(1/4)*x)/(a - b*x^4)^(1/4)))/(16*sqrt(2)*b^(5/4)) + (a*log(1 + (sqrt(b)*x^2)/sqrt(a - b*x^4) + (sqrt(2)*b^(1/4)*x)/(a - b*x^4)^(1/4)))/(16*sqrt(2)*b^(5/4))]
    @test_int [x^0/(a - b*x^4)^(1/4), x, 10, -(atan(1 - (sqrt(2)*b^(1/4)*x)/(a - b*x^4)^(1/4))/(2*sqrt(2)*b^(1/4))) + atan(1 + (sqrt(2)*b^(1/4)*x)/(a - b*x^4)^(1/4))/(2*sqrt(2)*b^(1/4)) - log(1 + (sqrt(b)*x^2)/sqrt(a - b*x^4) - (sqrt(2)*b^(1/4)*x)/(a - b*x^4)^(1/4))/(4*sqrt(2)*b^(1/4)) + log(1 + (sqrt(b)*x^2)/sqrt(a - b*x^4) + (sqrt(2)*b^(1/4)*x)/(a - b*x^4)^(1/4))/(4*sqrt(2)*b^(1/4))]
    @test_int [1/(x^4*(a - b*x^4)^(1/4)), x, 1, -((a - b*x^4)^(3/4)/(3*a*x^3))]
    @test_int [1/(x^8*(a - b*x^4)^(1/4)), x, 2, -((a - b*x^4)^(3/4)/(7*a*x^7)) - (4*b*(a - b*x^4)^(3/4))/(21*a^2*x^3)]
    @test_int [1/(x^12*(a - b*x^4)^(1/4)), x, 3, -((a - b*x^4)^(3/4)/(11*a*x^11)) - (8*b*(a - b*x^4)^(3/4))/(77*a^2*x^7) - (32*b^2*(a - b*x^4)^(3/4))/(231*a^3*x^3)]
    @test_int [1/(x^16*(a - b*x^4)^(1/4)), x, 4, -((a - b*x^4)^(3/4)/(15*a*x^15)) - (4*b*(a - b*x^4)^(3/4))/(55*a^2*x^11) - (32*b^2*(a - b*x^4)^(3/4))/(385*a^3*x^7) - (128*b^3*(a - b*x^4)^(3/4))/(1155*a^4*x^3)]
    @test_int [1/(x^20*(a - b*x^4)^(1/4)), x, 5, -((a - b*x^4)^(3/4)/(19*a*x^19)) - (16*b*(a - b*x^4)^(3/4))/(285*a^2*x^15) - (64*b^2*(a - b*x^4)^(3/4))/(1045*a^3*x^11) - (512*b^3*(a - b*x^4)^(3/4))/(7315*a^4*x^7) - (2048*b^4*(a - b*x^4)^(3/4))/(21945*a^5*x^3)]

    @test_int [x^10/(a - b*x^4)^(1/4), x, 7, -((7*a^2*(a - b*x^4)^(3/4))/(40*b^3*x)) - (7*a*x^3*(a - b*x^4)^(3/4))/(60*b^2) - (x^7*(a - b*x^4)^(3/4))/(10*b) + (7*a^(5/2)*(1 - a/(b*x^4))^(1/4)*x*Elliptic.E((1/2)*acsc((sqrt(b)*x^2)/sqrt(a)), 2))/(40*b^(5/2)*(a - b*x^4)^(1/4))]
    @test_int [x^6/(a - b*x^4)^(1/4), x, 6, -((a*(a - b*x^4)^(3/4))/(4*b^2*x)) - (x^3*(a - b*x^4)^(3/4))/(6*b) + (a^(3/2)*(1 - a/(b*x^4))^(1/4)*x*Elliptic.E((1/2)*acsc((sqrt(b)*x^2)/sqrt(a)), 2))/(4*b^(3/2)*(a - b*x^4)^(1/4))]
    @test_int [x^2/(a - b*x^4)^(1/4), x, 5, -((a - b*x^4)^(3/4)/(2*b*x)) + (sqrt(a)*(1 - a/(b*x^4))^(1/4)*x*Elliptic.E((1/2)*acsc((sqrt(b)*x^2)/sqrt(a)), 2))/(2*sqrt(b)*(a - b*x^4)^(1/4))]
    @test_int [1/(x^2*(a - b*x^4)^(1/4)), x, 4, -((sqrt(b)*(1 - a/(b*x^4))^(1/4)*x*Elliptic.E((1/2)*acsc((sqrt(b)*x^2)/sqrt(a)), 2))/(sqrt(a)*(a - b*x^4)^(1/4)))]
    @test_int [1/(x^6*(a - b*x^4)^(1/4)), x, 5, -((a - b*x^4)^(3/4)/(5*a*x^5)) - (2*b^(3/2)*(1 - a/(b*x^4))^(1/4)*x*Elliptic.E((1/2)*acsc((sqrt(b)*x^2)/sqrt(a)), 2))/(5*a^(3/2)*(a - b*x^4)^(1/4))]
    @test_int [1/(x^10*(a - b*x^4)^(1/4)), x, 6, -((a - b*x^4)^(3/4)/(9*a*x^9)) - (2*b*(a - b*x^4)^(3/4))/(15*a^2*x^5) - (4*b^(5/2)*(1 - a/(b*x^4))^(1/4)*x*Elliptic.E((1/2)*acsc((sqrt(b)*x^2)/sqrt(a)), 2))/(15*a^(5/2)*(a - b*x^4)^(1/4))]
    @test_int [1/(x^14*(a - b*x^4)^(1/4)), x, 7, -((a - b*x^4)^(3/4)/(13*a*x^13)) - (10*b*(a - b*x^4)^(3/4))/(117*a^2*x^9) - (4*b^2*(a - b*x^4)^(3/4))/(39*a^3*x^5) - (8*b^(7/2)*(1 - a/(b*x^4))^(1/4)*x*Elliptic.E((1/2)*acsc((sqrt(b)*x^2)/sqrt(a)), 2))/(39*a^(7/2)*(a - b*x^4)^(1/4))]

    @test_int [x^19/(a - b*x^4)^(3/4), x, 3, -((a^4*(a - b*x^4)^(1/4))/b^5) + (4*a^3*(a - b*x^4)^(5/4))/(5*b^5) - (2*a^2*(a - b*x^4)^(9/4))/(3*b^5) + (4*a*(a - b*x^4)^(13/4))/(13*b^5) - (a - b*x^4)^(17/4)/(17*b^5)]
    @test_int [x^15/(a - b*x^4)^(3/4), x, 3, -((a^3*(a - b*x^4)^(1/4))/b^4) + (3*a^2*(a - b*x^4)^(5/4))/(5*b^4) - (a*(a - b*x^4)^(9/4))/(3*b^4) + (a - b*x^4)^(13/4)/(13*b^4)]
    @test_int [x^11/(a - b*x^4)^(3/4), x, 3, -((a^2*(a - b*x^4)^(1/4))/b^3) + (2*a*(a - b*x^4)^(5/4))/(5*b^3) - (a - b*x^4)^(9/4)/(9*b^3)]
    @test_int [x^7/(a - b*x^4)^(3/4), x, 3, -((a*(a - b*x^4)^(1/4))/b^2) + (a - b*x^4)^(5/4)/(5*b^2)]
    @test_int [x^3/(a - b*x^4)^(3/4), x, 1, -((a - b*x^4)^(1/4)/b)]
    @test_int [1/(x^1*(a - b*x^4)^(3/4)), x, 5, -(atan((a - b*x^4)^(1/4)/a^(1/4))/(2*a^(3/4))) - atanh((a - b*x^4)^(1/4)/a^(1/4))/(2*a^(3/4))]
    @test_int [1/(x^5*(a - b*x^4)^(3/4)), x, 6, -((a - b*x^4)^(1/4)/(4*a*x^4)) - (3*b*atan((a - b*x^4)^(1/4)/a^(1/4)))/(8*a^(7/4)) - (3*b*atanh((a - b*x^4)^(1/4)/a^(1/4)))/(8*a^(7/4))]
    @test_int [1/(x^9*(a - b*x^4)^(3/4)), x, 7, -((a - b*x^4)^(1/4)/(8*a*x^8)) - (7*b*(a - b*x^4)^(1/4))/(32*a^2*x^4) - (21*b^2*atan((a - b*x^4)^(1/4)/a^(1/4)))/(64*a^(11/4)) - (21*b^2*atanh((a - b*x^4)^(1/4)/a^(1/4)))/(64*a^(11/4))]

    @test_int [x^13/(a - b*x^4)^(3/4), x, 6, -((20*a^2*x^2*(a - b*x^4)^(1/4))/(77*b^3)) - (10*a*x^6*(a - b*x^4)^(1/4))/(77*b^2) - (x^10*(a - b*x^4)^(1/4))/(11*b) + (40*a^(7/2)*(1 - (b*x^4)/a)^(3/4)*Elliptic.F((1/2)*asin((sqrt(b)*x^2)/sqrt(a)), 2))/(77*b^(7/2)*(a - b*x^4)^(3/4))]
    @test_int [x^9/(a - b*x^4)^(3/4), x, 5, -((2*a*x^2*(a - b*x^4)^(1/4))/(7*b^2)) - (x^6*(a - b*x^4)^(1/4))/(7*b) + (4*a^(5/2)*(1 - (b*x^4)/a)^(3/4)*Elliptic.F((1/2)*asin((sqrt(b)*x^2)/sqrt(a)), 2))/(7*b^(5/2)*(a - b*x^4)^(3/4))]
    @test_int [x^5/(a - b*x^4)^(3/4), x, 4, -((x^2*(a - b*x^4)^(1/4))/(3*b)) + (2*a^(3/2)*(1 - (b*x^4)/a)^(3/4)*Elliptic.F((1/2)*asin((sqrt(b)*x^2)/sqrt(a)), 2))/(3*b^(3/2)*(a - b*x^4)^(3/4))]
    @test_int [x^1/(a - b*x^4)^(3/4), x, 3, (sqrt(a)*(1 - (b*x^4)/a)^(3/4)*Elliptic.F((1/2)*asin((sqrt(b)*x^2)/sqrt(a)), 2))/(sqrt(b)*(a - b*x^4)^(3/4))]
    @test_int [1/(x^3*(a - b*x^4)^(3/4)), x, 4, -((a - b*x^4)^(1/4)/(2*a*x^2)) + (sqrt(b)*(1 - (b*x^4)/a)^(3/4)*Elliptic.F((1/2)*asin((sqrt(b)*x^2)/sqrt(a)), 2))/(2*sqrt(a)*(a - b*x^4)^(3/4))]
    @test_int [1/(x^7*(a - b*x^4)^(3/4)), x, 5, -((a - b*x^4)^(1/4)/(6*a*x^6)) - (5*b*(a - b*x^4)^(1/4))/(12*a^2*x^2) + (5*b^(3/2)*(1 - (b*x^4)/a)^(3/4)*Elliptic.F((1/2)*asin((sqrt(b)*x^2)/sqrt(a)), 2))/(12*a^(3/2)*(a - b*x^4)^(3/4))]
    @test_int [1/(x^11*(a - b*x^4)^(3/4)), x, 6, -((a - b*x^4)^(1/4)/(10*a*x^10)) - (3*b*(a - b*x^4)^(1/4))/(20*a^2*x^6) - (3*b^2*(a - b*x^4)^(1/4))/(8*a^3*x^2) + (3*b^(5/2)*(1 - (b*x^4)/a)^(3/4)*Elliptic.F((1/2)*asin((sqrt(b)*x^2)/sqrt(a)), 2))/(8*a^(5/2)*(a - b*x^4)^(3/4))]

    @test_int [x^10/(a - b*x^4)^(3/4), x, 12, -((7*a*x^3*(a - b*x^4)^(1/4))/(32*b^2)) - (x^7*(a - b*x^4)^(1/4))/(8*b) - (21*a^2*atan(1 - (sqrt(2)*b^(1/4)*x)/(a - b*x^4)^(1/4)))/(64*sqrt(2)*b^(11/4)) + (21*a^2*atan(1 + (sqrt(2)*b^(1/4)*x)/(a - b*x^4)^(1/4)))/(64*sqrt(2)*b^(11/4)) + (21*a^2*log(1 + (sqrt(b)*x^2)/sqrt(a - b*x^4) - (sqrt(2)*b^(1/4)*x)/(a - b*x^4)^(1/4)))/(128*sqrt(2)*b^(11/4)) - (21*a^2*log(1 + (sqrt(b)*x^2)/sqrt(a - b*x^4) + (sqrt(2)*b^(1/4)*x)/(a - b*x^4)^(1/4)))/(128*sqrt(2)*b^(11/4))]
    @test_int [x^6/(a - b*x^4)^(3/4), x, 11, -((x^3*(a - b*x^4)^(1/4))/(4*b)) - (3*a*atan(1 - (sqrt(2)*b^(1/4)*x)/(a - b*x^4)^(1/4)))/(8*sqrt(2)*b^(7/4)) + (3*a*atan(1 + (sqrt(2)*b^(1/4)*x)/(a - b*x^4)^(1/4)))/(8*sqrt(2)*b^(7/4)) + (3*a*log(1 + (sqrt(b)*x^2)/sqrt(a - b*x^4) - (sqrt(2)*b^(1/4)*x)/(a - b*x^4)^(1/4)))/(16*sqrt(2)*b^(7/4)) - (3*a*log(1 + (sqrt(b)*x^2)/sqrt(a - b*x^4) + (sqrt(2)*b^(1/4)*x)/(a - b*x^4)^(1/4)))/(16*sqrt(2)*b^(7/4))]
    @test_int [x^2/(a - b*x^4)^(3/4), x, 10, -(atan(1 - (sqrt(2)*b^(1/4)*x)/(a - b*x^4)^(1/4))/(2*sqrt(2)*b^(3/4))) + atan(1 + (sqrt(2)*b^(1/4)*x)/(a - b*x^4)^(1/4))/(2*sqrt(2)*b^(3/4)) + log(1 + (sqrt(b)*x^2)/sqrt(a - b*x^4) - (sqrt(2)*b^(1/4)*x)/(a - b*x^4)^(1/4))/(4*sqrt(2)*b^(3/4)) - log(1 + (sqrt(b)*x^2)/sqrt(a - b*x^4) + (sqrt(2)*b^(1/4)*x)/(a - b*x^4)^(1/4))/(4*sqrt(2)*b^(3/4))]
    @test_int [1/(x^2*(a - b*x^4)^(3/4)), x, 1, -((a - b*x^4)^(1/4)/(a*x))]
    @test_int [1/(x^6*(a - b*x^4)^(3/4)), x, 2, -((a - b*x^4)^(1/4)/(5*a*x^5)) - (4*b*(a - b*x^4)^(1/4))/(5*a^2*x)]
    @test_int [1/(x^10*(a - b*x^4)^(3/4)), x, 3, -((a - b*x^4)^(1/4)/(9*a*x^9)) - (8*b*(a - b*x^4)^(1/4))/(45*a^2*x^5) - (32*b^2*(a - b*x^4)^(1/4))/(45*a^3*x)]
    @test_int [1/(x^14*(a - b*x^4)^(3/4)), x, 4, -((a - b*x^4)^(1/4)/(13*a*x^13)) - (4*b*(a - b*x^4)^(1/4))/(39*a^2*x^9) - (32*b^2*(a - b*x^4)^(1/4))/(195*a^3*x^5) - (128*b^3*(a - b*x^4)^(1/4))/(195*a^4*x)]

    @test_int [x^12/(a - b*x^4)^(3/4), x, 7, -((3*a^2*x*(a - b*x^4)^(1/4))/(8*b^3)) - (3*a*x^5*(a - b*x^4)^(1/4))/(20*b^2) - (x^9*(a - b*x^4)^(1/4))/(10*b) - (3*a^(5/2)*(1 - a/(b*x^4))^(3/4)*x^3*Elliptic.F((1/2)*acsc((sqrt(b)*x^2)/sqrt(a)), 2))/(8*b^(5/2)*(a - b*x^4)^(3/4))]
    @test_int [x^8/(a - b*x^4)^(3/4), x, 6, -((5*a*x*(a - b*x^4)^(1/4))/(12*b^2)) - (x^5*(a - b*x^4)^(1/4))/(6*b) - (5*a^(3/2)*(1 - a/(b*x^4))^(3/4)*x^3*Elliptic.F((1/2)*acsc((sqrt(b)*x^2)/sqrt(a)), 2))/(12*b^(3/2)*(a - b*x^4)^(3/4))]
    @test_int [x^4/(a - b*x^4)^(3/4), x, 5, -((x*(a - b*x^4)^(1/4))/(2*b)) - (sqrt(a)*(1 - a/(b*x^4))^(3/4)*x^3*Elliptic.F((1/2)*acsc((sqrt(b)*x^2)/sqrt(a)), 2))/(2*sqrt(b)*(a - b*x^4)^(3/4))]
    @test_int [x^0/(a - b*x^4)^(3/4), x, 4, -((sqrt(b)*(1 - a/(b*x^4))^(3/4)*x^3*Elliptic.F((1/2)*acsc((sqrt(b)*x^2)/sqrt(a)), 2))/(sqrt(a)*(a - b*x^4)^(3/4)))]
    @test_int [1/(x^4*(a - b*x^4)^(3/4)), x, 5, -((a - b*x^4)^(1/4)/(3*a*x^3)) - (2*b^(3/2)*(1 - a/(b*x^4))^(3/4)*x^3*Elliptic.F((1/2)*acsc((sqrt(b)*x^2)/sqrt(a)), 2))/(3*a^(3/2)*(a - b*x^4)^(3/4))]
    @test_int [1/(x^8*(a - b*x^4)^(3/4)), x, 6, -((a - b*x^4)^(1/4)/(7*a*x^7)) - (2*b*(a - b*x^4)^(1/4))/(7*a^2*x^3) - (4*b^(5/2)*(1 - a/(b*x^4))^(3/4)*x^3*Elliptic.F((1/2)*acsc((sqrt(b)*x^2)/sqrt(a)), 2))/(7*a^(5/2)*(a - b*x^4)^(3/4))]
    @test_int [1/(x^12*(a - b*x^4)^(3/4)), x, 7, -((a - b*x^4)^(1/4)/(11*a*x^11)) - (10*b*(a - b*x^4)^(1/4))/(77*a^2*x^7) - (20*b^2*(a - b*x^4)^(1/4))/(77*a^3*x^3) - (40*b^(7/2)*(1 - a/(b*x^4))^(3/4)*x^3*Elliptic.F((1/2)*acsc((sqrt(b)*x^2)/sqrt(a)), 2))/(77*a^(7/2)*(a - b*x^4)^(3/4))]

    @test_int [x^2/(a - b*x^4)^(5/4), x, 5, 1/(b*x*(a - b*x^4)^(1/4)) - ((1 - a/(b*x^4))^(1/4)*x*Elliptic.E((1/2)*acsc((sqrt(b)*x^2)/sqrt(a)), 2))/(sqrt(a)*sqrt(b)*(a - b*x^4)^(1/4))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b*x^4)^p*with*p*symbolic=#

    @test_int [x^7*(a + b*x^4)^p, x, 3, -((a*(a + b*x^4)^(1 + p))/(4*b^2*(1 + p))) + (a + b*x^4)^(2 + p)/(4*b^2*(2 + p))]
    @test_int [x^3*(a + b*x^4)^p, x, 1, (a + b*x^4)^(1 + p)/(4*b*(1 + p))]
    @test_int [(a + b*x^4)^p/x^1, x, 2, -(((a + b*x^4)^(1 + p)*HypergeometricFunctions._₂F₁(1, 1 + p, 2 + p, 1 + (b*x^4)/a))/(4*a*(1 + p)))]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(c*x)^m*(a+b*x^5)^p=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b*x^5)^p=#

    #= ::Subsubsection:: =#
    #=p>0=#

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [x^24/(a + b*x^5), x, 3, -((a^3*x^5)/(5*b^4)) + (a^2*x^10)/(10*b^3) - (a*x^15)/(15*b^2) + x^20/(20*b) + (a^4*log(a + b*x^5))/(5*b^5)]
    @test_int [x^19/(a + b*x^5), x, 3, (a^2*x^5)/(5*b^3) - (a*x^10)/(10*b^2) + x^15/(15*b) - (a^3*log(a + b*x^5))/(5*b^4)]
    @test_int [x^14/(a + b*x^5), x, 3, -((a*x^5)/(5*b^2)) + x^10/(10*b) + (a^2*log(a + b*x^5))/(5*b^3)]
    @test_int [x^9/(a + b*x^5), x, 3, x^5/(5*b) - (a*log(a + b*x^5))/(5*b^2)]
    @test_int [x^4/(a + b*x^5), x, 1, log(a + b*x^5)/(5*b)]
    @test_int [1/(x^1*(a + b*x^5)), x, 4, log(x)/a - log(a + b*x^5)/(5*a)]
    @test_int [1/(x^6*(a + b*x^5)), x, 3, -(1/(5*a*x^5)) - (b*log(x))/a^2 + (b*log(a + b*x^5))/(5*a^2)]
    @test_int [1/(x^11*(a + b*x^5)), x, 3, -(1/(10*a*x^10)) + b/(5*a^2*x^5) + (b^2*log(x))/a^3 - (b^2*log(a + b*x^5))/(5*a^3)]
    @test_int [1/(x^16*(a + b*x^5)), x, 3, -(1/(15*a*x^15)) + b/(10*a^2*x^10) - b^2/(5*a^3*x^5) - (b^3*log(x))/a^4 + (b^3*log(a + b*x^5))/(5*a^4)]

    @test_int [1/(a + b*x^5), x, 6, -((sqrt((1/2)*(5 + sqrt(5)))*atan(((1 - sqrt(5))*a^(1/5) - 4*b^(1/5)*x)/(sqrt(2*(5 + sqrt(5)))*a^(1/5))))/(5*a^(4/5)*b^(1/5))) - (sqrt((1/2)*(5 - sqrt(5)))*atan(((1 + sqrt(5))*a^(1/5) - 4*b^(1/5)*x)/(sqrt(2*(5 - sqrt(5)))*a^(1/5))))/(5*a^(4/5)*b^(1/5)) + log(a^(1/5) + b^(1/5)*x)/(5*a^(4/5)*b^(1/5)) - ((1 - sqrt(5))*log(2*a^(2/5) - (1 - sqrt(5))*a^(1/5)*b^(1/5)*x + 2*b^(2/5)*x^2))/(20*a^(4/5)*b^(1/5)) - ((1 + sqrt(5))*log(2*a^(2/5) - (1 + sqrt(5))*a^(1/5)*b^(1/5)*x + 2*b^(2/5)*x^2))/(20*a^(4/5)*b^(1/5)), (sqrt((1/2)*(5 + sqrt(5)))*atan(sqrt((1/5)*(5 - 2*sqrt(5))) + (2*sqrt(2/(5 + sqrt(5)))*b^(1/5)*x)/a^(1/5)))/(5*a^(4/5)*b^(1/5)) - (sqrt((1/2)*(5 - sqrt(5)))*atan(sqrt((1/5)*(5 + 2*sqrt(5))) - (sqrt((2/5)*(5 + sqrt(5)))*b^(1/5)*x)/a^(1/5)))/(5*a^(4/5)*b^(1/5)) + log(a^(1/5) + b^(1/5)*x)/(5*a^(4/5)*b^(1/5)) - ((1 - sqrt(5))*log(a^(2/5) - (1/2)*(1 - sqrt(5))*a^(1/5)*b^(1/5)*x + b^(2/5)*x^2))/(20*a^(4/5)*b^(1/5)) - ((1 + sqrt(5))*log(a^(2/5) - (1/2)*(1 + sqrt(5))*a^(1/5)*b^(1/5)*x + b^(2/5)*x^2))/(20*a^(4/5)*b^(1/5))]

    @test_int [x^24/(a + b*x^5)^2, x, 3, (3*a^2*x^5)/(5*b^4) - (a*x^10)/(5*b^3) + x^15/(15*b^2) - a^4/(5*b^5*(a + b*x^5)) - (4*a^3*log(a + b*x^5))/(5*b^5)]
    @test_int [x^19/(a + b*x^5)^2, x, 3, -((2*a*x^5)/(5*b^3)) + x^10/(10*b^2) + a^3/(5*b^4*(a + b*x^5)) + (3*a^2*log(a + b*x^5))/(5*b^4)]
    @test_int [x^14/(a + b*x^5)^2, x, 3, x^5/(5*b^2) - a^2/(5*b^3*(a + b*x^5)) - (2*a*log(a + b*x^5))/(5*b^3)]
    @test_int [x^9/(a + b*x^5)^2, x, 3, a/(5*b^2*(a + b*x^5)) + log(a + b*x^5)/(5*b^2)]
    @test_int [x^4/(a + b*x^5)^2, x, 1, -(1/(5*b*(a + b*x^5)))]
    @test_int [1/(x^1*(a + b*x^5)^2), x, 3, 1/(5*a*(a + b*x^5)) + log(x)/a^2 - log(a + b*x^5)/(5*a^2)]
    @test_int [1/(x^6*(a + b*x^5)^2), x, 3, -(1/(5*a^2*x^5)) - b/(5*a^2*(a + b*x^5)) - (2*b*log(x))/a^3 + (2*b*log(a + b*x^5))/(5*a^3)]
    @test_int [1/(x^11*(a + b*x^5)^2), x, 3, -(1/(10*a^2*x^10)) + (2*b)/(5*a^3*x^5) + b^2/(5*a^3*(a + b*x^5)) + (3*b^2*log(x))/a^4 - (3*b^2*log(a + b*x^5))/(5*a^4)]

    @test_int [x^14/(2*b + b*x^5), x, 3, -((2*x^5)/(5*b)) + x^10/(10*b) + (4*log(2 + x^5))/(5*b)]
    @test_int [x^9/(2*b + b*x^5), x, 3, x^5/(5*b) - (2*log(2 + x^5))/(5*b)]
    @test_int [x^4/(2*b + b*x^5), x, 1, log(2 + x^5)/(5*b)]
    @test_int [1/(x^1*(2*b + b*x^5)), x, 4, log(x)/(2*b) - log(2 + x^5)/(10*b)]
    @test_int [1/(x^6*(2*b + b*x^5)), x, 3, -(1/(10*b*x^5)) - log(x)/(4*b) + log(2 + x^5)/(20*b)]

    @test_int [x^14/(3 + b*x^5), x, 3, -((3*x^5)/(5*b^2)) + x^10/(10*b) + (9*log(3 + b*x^5))/(5*b^3)]
    @test_int [x^9/(3 + b*x^5), x, 3, x^5/(5*b) - (3*log(3 + b*x^5))/(5*b^2)]
    @test_int [x^4/(3 + b*x^5), x, 1, log(3 + b*x^5)/(5*b)]
    @test_int [1/(x^1*(3 + b*x^5)), x, 4, log(x)/3 - (1/15)*log(3 + b*x^5)]
    @test_int [1/(x^6*(3 + b*x^5)), x, 3, -(1/(15*x^5)) - (1/9)*b*log(x) + (1/45)*b*log(3 + b*x^5)]

    @test_int [x^14/(1 + x^5), x, 3, -(x^5/5) + x^10/10 + (1/5)*log(1 + x^5)]
    @test_int [x^9/(1 + x^5), x, 3, x^5/5 - (1/5)*log(1 + x^5)]
    @test_int [x^4/(1 + x^5), x, 1, (1/5)*log(1 + x^5)]
    @test_int [1/(x^1*(1 + x^5)), x, 4, log(x) - (1/5)*log(1 + x^5)]
    @test_int [1/(x^6*(1 + x^5)), x, 3, -(1/(5*x^5)) - log(x) + (1/5)*log(1 + x^5)]

    @test_int [x^5/(1 + x^5), x, 7, x - (1/5)*sqrt((1/2)*(5 + sqrt(5)))*atan(sqrt((1/5)*(5 - 2*sqrt(5))) + 2*sqrt(2/(5 + sqrt(5)))*x) + (1/5)*sqrt((1/2)*(5 - sqrt(5)))*atan(sqrt((1/5)*(5 + 2*sqrt(5))) - sqrt((2/5)*(5 + sqrt(5)))*x) - (1/5)*log(1 + x) + (1/20)*(1 - sqrt(5))*log(1 - (1/2)*(1 - sqrt(5))*x + x^2) + (1/20)*(1 + sqrt(5))*log(1 - (1/2)*(1 + sqrt(5))*x + x^2)]
    @test_int [x^3/(1 + x^5), x, 6, (1/5)*sqrt((1/2)*(5 + sqrt(5)))*atan(sqrt((1/5)*(5 - 2*sqrt(5))) + 2*sqrt(2/(5 + sqrt(5)))*x) - (1/5)*sqrt((1/2)*(5 - sqrt(5)))*atan(sqrt((1/5)*(5 + 2*sqrt(5))) - sqrt((2/5)*(5 + sqrt(5)))*x) - (1/5)*log(1 + x) + (1/20)*(1 - sqrt(5))*log(1 - (1/2)*(1 - sqrt(5))*x + x^2) + (1/20)*(1 + sqrt(5))*log(1 - (1/2)*(1 + sqrt(5))*x + x^2)]
    @test_int [x^2/(1 + x^5), x, 6, (-(1/5))*sqrt((1/2)*(5 - sqrt(5)))*atan(sqrt((1/5)*(5 - 2*sqrt(5))) + 2*sqrt(2/(5 + sqrt(5)))*x) - (1/5)*sqrt((1/2)*(5 + sqrt(5)))*atan(sqrt((1/5)*(5 + 2*sqrt(5))) - sqrt((2/5)*(5 + sqrt(5)))*x) + (1/5)*log(1 + x) - (1/20)*(1 + sqrt(5))*log(1 - (1/2)*(1 - sqrt(5))*x + x^2) - (1/20)*(1 - sqrt(5))*log(1 - (1/2)*(1 + sqrt(5))*x + x^2)]
    @test_int [x^1/(1 + x^5), x, 6, (-(1/5))*sqrt((1/2)*(5 - sqrt(5)))*atan(sqrt((1/5)*(5 - 2*sqrt(5))) + 2*sqrt(2/(5 + sqrt(5)))*x) - (1/5)*sqrt((1/2)*(5 + sqrt(5)))*atan(sqrt((1/5)*(5 + 2*sqrt(5))) - sqrt((2/5)*(5 + sqrt(5)))*x) - (1/5)*log(1 + x) + (1/20)*(1 + sqrt(5))*log(1 - (1/2)*(1 - sqrt(5))*x + x^2) + (1/20)*(1 - sqrt(5))*log(1 - (1/2)*(1 + sqrt(5))*x + x^2)]
    @test_int [x^0/(1 + x^5), x, 6, (-(1/5))*sqrt((1/2)*(5 + sqrt(5)))*atan((1 - sqrt(5) - 4*x)/sqrt(2*(5 + sqrt(5)))) - (1/5)*sqrt((1/2)*(5 - sqrt(5)))*atan((1/2)*sqrt((1/10)*(5 + sqrt(5)))*(1 + sqrt(5) - 4*x)) + (1/5)*log(1 + x) - (1/20)*(1 - sqrt(5))*log(1 - (1/2)*(1 - sqrt(5))*x + x^2) - (1/20)*(1 + sqrt(5))*log(1 - (1/2)*(1 + sqrt(5))*x + x^2), (1/5)*sqrt((1/2)*(5 + sqrt(5)))*atan(sqrt((1/5)*(5 - 2*sqrt(5))) + 2*sqrt(2/(5 + sqrt(5)))*x) - (1/5)*sqrt((1/2)*(5 - sqrt(5)))*atan(sqrt((1/5)*(5 + 2*sqrt(5))) - sqrt((2/5)*(5 + sqrt(5)))*x) + (1/5)*log(1 + x) - (1/20)*(1 - sqrt(5))*log(1 - (1/2)*(1 - sqrt(5))*x + x^2) - (1/20)*(1 + sqrt(5))*log(1 - (1/2)*(1 + sqrt(5))*x + x^2)]
    @test_int [1/(x^2*(1 + x^5)), x, 7, -(1/x) - (1/5)*sqrt((1/2)*(5 + sqrt(5)))*atan(sqrt((1/5)*(5 - 2*sqrt(5))) + 2*sqrt(2/(5 + sqrt(5)))*x) + (1/5)*sqrt((1/2)*(5 - sqrt(5)))*atan(sqrt((1/5)*(5 + 2*sqrt(5))) - sqrt((2/5)*(5 + sqrt(5)))*x) + (1/5)*log(1 + x) - (1/20)*(1 - sqrt(5))*log(1 - (1/2)*(1 - sqrt(5))*x + x^2) - (1/20)*(1 + sqrt(5))*log(1 - (1/2)*(1 + sqrt(5))*x + x^2)]
    @test_int [1/(x^3*(1 + x^5)), x, 7, -(1/(2*x^2)) + (1/5)*sqrt((1/2)*(5 - sqrt(5)))*atan(sqrt((1/5)*(5 - 2*sqrt(5))) + 2*sqrt(2/(5 + sqrt(5)))*x) + (1/5)*sqrt((1/2)*(5 + sqrt(5)))*atan(sqrt((1/5)*(5 + 2*sqrt(5))) - sqrt((2/5)*(5 + sqrt(5)))*x) - (1/5)*log(1 + x) + (1/20)*(1 + sqrt(5))*log(1 - (1/2)*(1 - sqrt(5))*x + x^2) + (1/20)*(1 - sqrt(5))*log(1 - (1/2)*(1 + sqrt(5))*x + x^2)]
    @test_int [1/(x^4*(1 + x^5)), x, 7, -(1/(3*x^3)) + (1/5)*sqrt((1/2)*(5 - sqrt(5)))*atan(sqrt((1/5)*(5 - 2*sqrt(5))) + 2*sqrt(2/(5 + sqrt(5)))*x) + (1/5)*sqrt((1/2)*(5 + sqrt(5)))*atan(sqrt((1/5)*(5 + 2*sqrt(5))) - sqrt((2/5)*(5 + sqrt(5)))*x) + (1/5)*log(1 + x) - (1/20)*(1 + sqrt(5))*log(1 - (1/2)*(1 - sqrt(5))*x + x^2) - (1/20)*(1 - sqrt(5))*log(1 - (1/2)*(1 + sqrt(5))*x + x^2)]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^(m/2)*(a+b*x^5)^p=#

    #= ::Subsubsection:: =#
    #=p>0=#

    #= ::Subsubsection:: =#
    #=p<0=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b*x^5)^(p/2)=#

    #= ::Subsubsection:: =#
    #=p>0=#

    #= ::Subsubsection:: =#
    #=p<0=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^(m/2)*(a+b*x^5)^(p/2)=#

    #= ::Subsubsection:: =#
    #=p>0=#

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    #= Integrands*of*the*form*x^(n/2)/sqrt(a+b*x^5)*where*n*mod*10 = 0 =#
    @test_int [x^(23/2)/sqrt(a + b*x^5), x, 6, -((3*a*x^(5/2)*sqrt(a + b*x^5))/(20*b^2)) + (x^(15/2)*sqrt(a + b*x^5))/(10*b) + (3*a^2*atanh((sqrt(b)*x^(5/2))/sqrt(a + b*x^5)))/(20*b^(5/2))]
    @test_int [x^(13/2)/sqrt(a + b*x^5), x, 5, (x^(5/2)*sqrt(a + b*x^5))/(5*b) - (a*atanh((sqrt(b)*x^(5/2))/sqrt(a + b*x^5)))/(5*b^(3/2))]
    @test_int [x^(3/2)/sqrt(a + b*x^5), x, 4, (2*atanh((sqrt(b)*x^(5/2))/sqrt(a + b*x^5)))/(5*sqrt(b))]
    @test_int [x^(-7/2)/sqrt(a + b*x^5), x, 1, -((2*sqrt(a + b*x^5))/(5*a*x^(5/2)))]
    @test_int [x^(-17/2)/sqrt(a + b*x^5), x, 2, -((2*sqrt(a + b*x^5))/(15*a*x^(15/2))) + (4*b*sqrt(a + b*x^5))/(15*a^2*x^(5/2))]

    #= Integrands*of*the*form*x^(n/2)/sqrt(1+x^5)*where*n*mod*10 = 0 =#
    @test_int [x^(23/2)/sqrt(1 + x^5), x, 5, (-(3/20))*x^(5/2)*sqrt(1 + x^5) + (1/10)*x^(15/2)*sqrt(1 + x^5) + (3/20)*asinh(x^(5/2))]
    @test_int [x^(13/2)/sqrt(1 + x^5), x, 4, (1/5)*x^(5/2)*sqrt(1 + x^5) - (1/5)*asinh(x^(5/2))]
    @test_int [x^(3/2)/sqrt(1 + x^5), x, 3, (2/5)*asinh(x^(5/2))]
    @test_int [x^(-7/2)/sqrt(1 + x^5), x, 1, -((2*sqrt(1 + x^5))/(5*x^(5/2)))]
    @test_int [x^(-17/2)/sqrt(1 + x^5), x, 2, -((2*sqrt(1 + x^5))/(15*x^(15/2))) + (4*sqrt(1 + x^5))/(15*x^(5/2))]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(c*x)^m*(a+b*x^6)^p=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b*x^6)^p=#

    #= ::Subsubsection:: =#
    #=p>0=#

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [x^8/(a + b*x^6), x, 3, x^3/(3*b) - (sqrt(a)*atan((sqrt(b)*x^3)/sqrt(a)))/(3*b^(3/2))]
    @test_int [x^7/(a + b*x^6), x, 8, x^2/(2*b) + (a^(1/3)*atan((a^(1/3) - 2*b^(1/3)*x^2)/(sqrt(3)*a^(1/3))))/(2*sqrt(3)*b^(4/3)) - (a^(1/3)*log(a^(1/3) + b^(1/3)*x^2))/(6*b^(4/3)) + (a^(1/3)*log(a^(2/3) - a^(1/3)*b^(1/3)*x^2 + b^(2/3)*x^4))/(12*b^(4/3))]
    @test_int [x^6/(a + b*x^6), x, 11, x/b - (a^(1/6)*atan((b^(1/6)*x)/a^(1/6)))/(3*b^(7/6)) + (a^(1/6)*atan((sqrt(3)*a^(1/6) - 2*b^(1/6)*x)/a^(1/6)))/(6*b^(7/6)) - (a^(1/6)*atan((sqrt(3)*a^(1/6) + 2*b^(1/6)*x)/a^(1/6)))/(6*b^(7/6)) + (a^(1/6)*log(a^(1/3) - sqrt(3)*a^(1/6)*b^(1/6)*x + b^(1/3)*x^2))/(4*sqrt(3)*b^(7/6)) - (a^(1/6)*log(a^(1/3) + sqrt(3)*a^(1/6)*b^(1/6)*x + b^(1/3)*x^2))/(4*sqrt(3)*b^(7/6))]
    @test_int [x^5/(a + b*x^6), x, 1, log(a + b*x^6)/(6*b)]
    @test_int [x^4/(a + b*x^6), x, 10, atan((b^(1/6)*x)/a^(1/6))/(3*a^(1/6)*b^(5/6)) - atan((sqrt(3)*a^(1/6) - 2*b^(1/6)*x)/a^(1/6))/(6*a^(1/6)*b^(5/6)) + atan((sqrt(3)*a^(1/6) + 2*b^(1/6)*x)/a^(1/6))/(6*a^(1/6)*b^(5/6)) + log(a^(1/3) - sqrt(3)*a^(1/6)*b^(1/6)*x + b^(1/3)*x^2)/(4*sqrt(3)*a^(1/6)*b^(5/6)) - log(a^(1/3) + sqrt(3)*a^(1/6)*b^(1/6)*x + b^(1/3)*x^2)/(4*sqrt(3)*a^(1/6)*b^(5/6))]
    @test_int [x^3/(a + b*x^6), x, 7, -(atan((a^(1/3) - 2*b^(1/3)*x^2)/(sqrt(3)*a^(1/3)))/(2*sqrt(3)*a^(1/3)*b^(2/3))) - log(a^(1/3) + b^(1/3)*x^2)/(6*a^(1/3)*b^(2/3)) + log(a^(2/3) - a^(1/3)*b^(1/3)*x^2 + b^(2/3)*x^4)/(12*a^(1/3)*b^(2/3))]
    @test_int [x^2/(a + b*x^6), x, 2, atan((sqrt(b)*x^3)/sqrt(a))/(3*sqrt(a)*sqrt(b))]
    @test_int [x^1/(a + b*x^6), x, 7, -(atan((a^(1/3) - 2*b^(1/3)*x^2)/(sqrt(3)*a^(1/3)))/(2*sqrt(3)*a^(2/3)*b^(1/3))) + log(a^(1/3) + b^(1/3)*x^2)/(6*a^(2/3)*b^(1/3)) - log(a^(2/3) - a^(1/3)*b^(1/3)*x^2 + b^(2/3)*x^4)/(12*a^(2/3)*b^(1/3))]
    @test_int [x^0/(a + b*x^6), x, 10, atan((b^(1/6)*x)/a^(1/6))/(3*a^(5/6)*b^(1/6)) - atan((sqrt(3)*a^(1/6) - 2*b^(1/6)*x)/a^(1/6))/(6*a^(5/6)*b^(1/6)) + atan((sqrt(3)*a^(1/6) + 2*b^(1/6)*x)/a^(1/6))/(6*a^(5/6)*b^(1/6)) - log(a^(1/3) - sqrt(3)*a^(1/6)*b^(1/6)*x + b^(1/3)*x^2)/(4*sqrt(3)*a^(5/6)*b^(1/6)) + log(a^(1/3) + sqrt(3)*a^(1/6)*b^(1/6)*x + b^(1/3)*x^2)/(4*sqrt(3)*a^(5/6)*b^(1/6))]
    @test_int [1/(x^1*(a + b*x^6)), x, 4, log(x)/a - log(a + b*x^6)/(6*a)]
    @test_int [1/(x^2*(a + b*x^6)), x, 11, -(1/(a*x)) - (b^(1/6)*atan((b^(1/6)*x)/a^(1/6)))/(3*a^(7/6)) + (b^(1/6)*atan((sqrt(3)*a^(1/6) - 2*b^(1/6)*x)/a^(1/6)))/(6*a^(7/6)) - (b^(1/6)*atan((sqrt(3)*a^(1/6) + 2*b^(1/6)*x)/a^(1/6)))/(6*a^(7/6)) - (b^(1/6)*log(a^(1/3) - sqrt(3)*a^(1/6)*b^(1/6)*x + b^(1/3)*x^2))/(4*sqrt(3)*a^(7/6)) + (b^(1/6)*log(a^(1/3) + sqrt(3)*a^(1/6)*b^(1/6)*x + b^(1/3)*x^2))/(4*sqrt(3)*a^(7/6))]
    @test_int [1/(x^3*(a + b*x^6)), x, 8, -(1/(2*a*x^2)) + (b^(1/3)*atan((a^(1/3) - 2*b^(1/3)*x^2)/(sqrt(3)*a^(1/3))))/(2*sqrt(3)*a^(4/3)) + (b^(1/3)*log(a^(1/3) + b^(1/3)*x^2))/(6*a^(4/3)) - (b^(1/3)*log(a^(2/3) - a^(1/3)*b^(1/3)*x^2 + b^(2/3)*x^4))/(12*a^(4/3))]
    @test_int [1/(x^4*(a + b*x^6)), x, 3, -(1/(3*a*x^3)) - (sqrt(b)*atan((sqrt(b)*x^3)/sqrt(a)))/(3*a^(3/2))]

    @test_int [x^8/(a + b*x^6)^2, x, 3, -x^3/(6*b*(a + b*x^6)) + atan((sqrt(b)*x^3)/sqrt(a))/(6*sqrt(a)*b^(3/2))]
    @test_int [x^7/(a + b*x^6)^2, x, 8, -(x^2/(6*b*(a + b*x^6))) - atan((a^(1/3) - 2*b^(1/3)*x^2)/(sqrt(3)*a^(1/3)))/(6*sqrt(3)*a^(2/3)*b^(4/3)) + log(a^(1/3) + b^(1/3)*x^2)/(18*a^(2/3)*b^(4/3)) - log(a^(2/3) - a^(1/3)*b^(1/3)*x^2 + b^(2/3)*x^4)/(36*a^(2/3)*b^(4/3))]
    @test_int [x^6/(a + b*x^6)^2, x, 11, -(x/(6*b*(a + b*x^6))) + atan((b^(1/6)*x)/a^(1/6))/(18*a^(5/6)*b^(7/6)) - atan((sqrt(3)*a^(1/6) - 2*b^(1/6)*x)/a^(1/6))/(36*a^(5/6)*b^(7/6)) + atan((sqrt(3)*a^(1/6) + 2*b^(1/6)*x)/a^(1/6))/(36*a^(5/6)*b^(7/6)) - log(a^(1/3) - sqrt(3)*a^(1/6)*b^(1/6)*x + b^(1/3)*x^2)/(24*sqrt(3)*a^(5/6)*b^(7/6)) + log(a^(1/3) + sqrt(3)*a^(1/6)*b^(1/6)*x + b^(1/3)*x^2)/(24*sqrt(3)*a^(5/6)*b^(7/6))]
    @test_int [x^5/(a + b*x^6)^2, x, 1, -(1/(6*b*(a + b*x^6)))]
    @test_int [x^4/(a + b*x^6)^2, x, 11, x^5/(6*a*(a + b*x^6)) + atan((b^(1/6)*x)/a^(1/6))/(18*a^(7/6)*b^(5/6)) - atan((sqrt(3)*a^(1/6) - 2*b^(1/6)*x)/a^(1/6))/(36*a^(7/6)*b^(5/6)) + atan((sqrt(3)*a^(1/6) + 2*b^(1/6)*x)/a^(1/6))/(36*a^(7/6)*b^(5/6)) + log(a^(1/3) - sqrt(3)*a^(1/6)*b^(1/6)*x + b^(1/3)*x^2)/(24*sqrt(3)*a^(7/6)*b^(5/6)) - log(a^(1/3) + sqrt(3)*a^(1/6)*b^(1/6)*x + b^(1/3)*x^2)/(24*sqrt(3)*a^(7/6)*b^(5/6))]
    @test_int [x^3/(a + b*x^6)^2, x, 8, x^4/(6*a*(a + b*x^6)) - atan((a^(1/3) - 2*b^(1/3)*x^2)/(sqrt(3)*a^(1/3)))/(6*sqrt(3)*a^(4/3)*b^(2/3)) - log(a^(1/3) + b^(1/3)*x^2)/(18*a^(4/3)*b^(2/3)) + log(a^(2/3) - a^(1/3)*b^(1/3)*x^2 + b^(2/3)*x^4)/(36*a^(4/3)*b^(2/3))]
    @test_int [x^2/(a + b*x^6)^2, x, 3, x^3/(6*a*(a + b*x^6)) + atan((sqrt(b)*x^3)/sqrt(a))/(6*a^(3/2)*sqrt(b))]
    @test_int [x^1/(a + b*x^6)^2, x, 8, x^2/(6*a*(a + b*x^6)) - atan((a^(1/3) - 2*b^(1/3)*x^2)/(sqrt(3)*a^(1/3)))/(3*sqrt(3)*a^(5/3)*b^(1/3)) + log(a^(1/3) + b^(1/3)*x^2)/(9*a^(5/3)*b^(1/3)) - log(a^(2/3) - a^(1/3)*b^(1/3)*x^2 + b^(2/3)*x^4)/(18*a^(5/3)*b^(1/3))]
    @test_int [x^0/(a + b*x^6)^2, x, 11, x/(6*a*(a + b*x^6)) + (5*atan((b^(1/6)*x)/a^(1/6)))/(18*a^(11/6)*b^(1/6)) - (5*atan((sqrt(3)*a^(1/6) - 2*b^(1/6)*x)/a^(1/6)))/(36*a^(11/6)*b^(1/6)) + (5*atan((sqrt(3)*a^(1/6) + 2*b^(1/6)*x)/a^(1/6)))/(36*a^(11/6)*b^(1/6)) - (5*log(a^(1/3) - sqrt(3)*a^(1/6)*b^(1/6)*x + b^(1/3)*x^2))/(24*sqrt(3)*a^(11/6)*b^(1/6)) + (5*log(a^(1/3) + sqrt(3)*a^(1/6)*b^(1/6)*x + b^(1/3)*x^2))/(24*sqrt(3)*a^(11/6)*b^(1/6))]
    @test_int [1/(x^1*(a + b*x^6)^2), x, 3, 1/(6*a*(a + b*x^6)) + log(x)/a^2 - log(a + b*x^6)/(6*a^2)]
    @test_int [1/(x^2*(a + b*x^6)^2), x, 12, -(7/(6*a^2*x)) + 1/(6*a*x*(a + b*x^6)) - (7*b^(1/6)*atan((b^(1/6)*x)/a^(1/6)))/(18*a^(13/6)) + (7*b^(1/6)*atan((sqrt(3)*a^(1/6) - 2*b^(1/6)*x)/a^(1/6)))/(36*a^(13/6)) - (7*b^(1/6)*atan((sqrt(3)*a^(1/6) + 2*b^(1/6)*x)/a^(1/6)))/(36*a^(13/6)) - (7*b^(1/6)*log(a^(1/3) - sqrt(3)*a^(1/6)*b^(1/6)*x + b^(1/3)*x^2))/(24*sqrt(3)*a^(13/6)) + (7*b^(1/6)*log(a^(1/3) + sqrt(3)*a^(1/6)*b^(1/6)*x + b^(1/3)*x^2))/(24*sqrt(3)*a^(13/6))]
    @test_int [1/(x^3*(a + b*x^6)^2), x, 9, -(2/(3*a^2*x^2)) + 1/(6*a*x^2*(a + b*x^6)) + (2*b^(1/3)*atan((a^(1/3) - 2*b^(1/3)*x^2)/(sqrt(3)*a^(1/3))))/(3*sqrt(3)*a^(7/3)) + (2*b^(1/3)*log(a^(1/3) + b^(1/3)*x^2))/(9*a^(7/3)) - (b^(1/3)*log(a^(2/3) - a^(1/3)*b^(1/3)*x^2 + b^(2/3)*x^4))/(9*a^(7/3))]
    @test_int [1/(x^4*(a + b*x^6)^2), x, 4, -(1/(2*a^2*x^3)) + 1/(6*a*x^3*(a + b*x^6)) - (sqrt(b)*atan((sqrt(b)*x^3)/sqrt(a)))/(2*a^(5/2))]

    @test_int [x^8/(1 - x^6), x, 3, -(x^3/3) + atanh(x^3)/3]
    @test_int [x^7/(1 - x^6), x, 8, -(x^2/2) + atan((1 + 2*x^2)/sqrt(3))/(2*sqrt(3)) - (1/6)*log(1 - x^2) + (1/12)*log(1 + x^2 + x^4)]
    @test_int [x^6/(1 - x^6), x, 11, -x + atan((sqrt(3)*x)/(1 - x^2))/(2*sqrt(3)) + atanh(x)/3 + (1/6)*atanh(x/(1 + x^2)), -x - atan((1 - 2*x)/sqrt(3))/(2*sqrt(3)) + atan((1 + 2*x)/sqrt(3))/(2*sqrt(3)) + atanh(x)/3 - (1/12)*log(1 - x + x^2) + (1/12)*log(1 + x + x^2)]
    @test_int [x^5/(1 - x^6), x, 1, (-(1/6))*log(1 - x^6)]
    @test_int [x^4/(1 - x^6), x, 10, -(atan((sqrt(3)*x)/(1 - x^2))/(2*sqrt(3))) + atanh(x)/3 + (1/6)*atanh(x/(1 + x^2)), atan((1 - 2*x)/sqrt(3))/(2*sqrt(3)) - atan((1 + 2*x)/sqrt(3))/(2*sqrt(3)) + atanh(x)/3 - (1/12)*log(1 - x + x^2) + (1/12)*log(1 + x + x^2)]
    @test_int [x^3/(1 - x^6), x, 7, -(atan((1 + 2*x^2)/sqrt(3))/(2*sqrt(3))) - (1/6)*log(1 - x^2) + (1/12)*log(1 + x^2 + x^4)]
    @test_int [x^2/(1 - x^6), x, 2, atanh(x^3)/3]
    @test_int [x^1/(1 - x^6), x, 7, atan((1 + 2*x^2)/sqrt(3))/(2*sqrt(3)) - (1/6)*log(1 - x^2) + (1/12)*log(1 + x^2 + x^4)]
    @test_int [1/(1 - x^6), x, 10, atan((sqrt(3)*x)/(1 - x^2))/(2*sqrt(3)) + atanh(x)/3 + (1/6)*atanh(x/(1 + x^2)), -(atan((1 - 2*x)/sqrt(3))/(2*sqrt(3))) + atan((1 + 2*x)/sqrt(3))/(2*sqrt(3)) + atanh(x)/3 - (1/12)*log(1 - x + x^2) + (1/12)*log(1 + x + x^2)]
    @test_int [1/(x^1*(1 - x^6)), x, 4, log(x) - (1/6)*log(1 - x^6)]
    @test_int [1/(x^2*(1 - x^6)), x, 11, -(1/x) - atan((sqrt(3)*x)/(1 - x^2))/(2*sqrt(3)) + atanh(x)/3 + (1/6)*atanh(x/(1 + x^2)), -(1/x) + atan((1 - 2*x)/sqrt(3))/(2*sqrt(3)) - atan((1 + 2*x)/sqrt(3))/(2*sqrt(3)) + atanh(x)/3 - (1/12)*log(1 - x + x^2) + (1/12)*log(1 + x + x^2)]
    @test_int [1/(x^3*(1 - x^6)), x, 8, -(1/(2*x^2)) - atan((1 + 2*x^2)/sqrt(3))/(2*sqrt(3)) - (1/6)*log(1 - x^2) + (1/12)*log(1 + x^2 + x^4)]
    @test_int [1/(x^4*(1 - x^6)), x, 3, -(1/(3*x^3)) + atanh(x^3)/3]
    @test_int [1/(x^5*(1 - x^6)), x, 8, -(1/(4*x^4)) + atan((1 + 2*x^2)/sqrt(3))/(2*sqrt(3)) - (1/6)*log(1 - x^2) + (1/12)*log(1 + x^2 + x^4)]
    @test_int [1/(x^6*(1 - x^6)), x, 11, -(1/(5*x^5)) - atan((1 - 2*x)/sqrt(3))/(2*sqrt(3)) + atan((1 + 2*x)/sqrt(3))/(2*sqrt(3)) + atanh(x)/3 - (1/12)*log(1 - x + x^2) + (1/12)*log(1 + x + x^2)]
    @test_int [1/(x^7*(1 - x^6)), x, 3, -(1/(6*x^6)) + log(x) - (1/6)*log(1 - x^6)]
    @test_int [1/(x^8*(1 - x^6)), x, 12, -(1/(7*x^7)) - 1/x + atan((1 - 2*x)/sqrt(3))/(2*sqrt(3)) - atan((1 + 2*x)/sqrt(3))/(2*sqrt(3)) + atanh(x)/3 - (1/12)*log(1 - x + x^2) + (1/12)*log(1 + x + x^2)]

    @test_int [x^8/(1 + x^6), x, 3, x^3/3 - atan(x^3)/3]
    @test_int [x^7/(1 + x^6), x, 8, x^2/2 + atan((1 - 2*x^2)/sqrt(3))/(2*sqrt(3)) - (1/6)*log(1 + x^2) + (1/12)*log(1 - x^2 + x^4)]
    @test_int [x^6/(1 + x^6), x, 11, x + (1/6)*atan(sqrt(3) - 2*x) - atan(x)/3 - (1/6)*atan(sqrt(3) + 2*x) + log(1 - sqrt(3)*x + x^2)/(4*sqrt(3)) - log(1 + sqrt(3)*x + x^2)/(4*sqrt(3))]
    @test_int [x^5/(1 + x^6), x, 1, (1/6)*log(1 + x^6)]
    @test_int [x^4/(1 + x^6), x, 10, (-(1/6))*atan(sqrt(3) - 2*x) + atan(x)/3 + (1/6)*atan(sqrt(3) + 2*x) + log(1 - sqrt(3)*x + x^2)/(4*sqrt(3)) - log(1 + sqrt(3)*x + x^2)/(4*sqrt(3))]
    @test_int [x^3/(1 + x^6), x, 7, -(atan((1 - 2*x^2)/sqrt(3))/(2*sqrt(3))) - (1/6)*log(1 + x^2) + (1/12)*log(1 - x^2 + x^4)]
    @test_int [x^2/(1 + x^6), x, 2, atan(x^3)/3]
    @test_int [x^1/(1 + x^6), x, 7, -(atan((1 - 2*x^2)/sqrt(3))/(2*sqrt(3))) + (1/6)*log(1 + x^2) - (1/12)*log(1 - x^2 + x^4)]
    @test_int [1/(1 + x^6), x, 10, (-(1/6))*atan(sqrt(3) - 2*x) + atan(x)/3 + (1/6)*atan(sqrt(3) + 2*x) - log(1 - sqrt(3)*x + x^2)/(4*sqrt(3)) + log(1 + sqrt(3)*x + x^2)/(4*sqrt(3))]
    @test_int [1/(x^1*(1 + x^6)), x, 4, log(x) - (1/6)*log(1 + x^6)]
    @test_int [1/(x^2*(1 + x^6)), x, 11, -(1/x) + (1/6)*atan(sqrt(3) - 2*x) - atan(x)/3 - (1/6)*atan(sqrt(3) + 2*x) - log(1 - sqrt(3)*x + x^2)/(4*sqrt(3)) + log(1 + sqrt(3)*x + x^2)/(4*sqrt(3))]
    @test_int [1/(x^3*(1 + x^6)), x, 8, -(1/(2*x^2)) + atan((1 - 2*x^2)/sqrt(3))/(2*sqrt(3)) + (1/6)*log(1 + x^2) - (1/12)*log(1 - x^2 + x^4)]
    @test_int [1/(x^4*(1 + x^6)), x, 3, -(1/(3*x^3)) - atan(x^3)/3]
    @test_int [1/(x^5*(1 + x^6)), x, 8, -(1/(4*x^4)) + atan((1 - 2*x^2)/sqrt(3))/(2*sqrt(3)) - (1/6)*log(1 + x^2) + (1/12)*log(1 - x^2 + x^4)]
    @test_int [1/(x^6*(1 + x^6)), x, 11, -(1/(5*x^5)) + (1/6)*atan(sqrt(3) - 2*x) - atan(x)/3 - (1/6)*atan(sqrt(3) + 2*x) + log(1 - sqrt(3)*x + x^2)/(4*sqrt(3)) - log(1 + sqrt(3)*x + x^2)/(4*sqrt(3))]
    @test_int [1/(x^7*(1 + x^6)), x, 3, -(1/(6*x^6)) - log(x) + (1/6)*log(1 + x^6)]
    @test_int [1/(x^8*(1 + x^6)), x, 12, -(1/(7*x^7)) + 1/x - (1/6)*atan(sqrt(3) - 2*x) + atan(x)/3 + (1/6)*atan(sqrt(3) + 2*x) + log(1 - sqrt(3)*x + x^2)/(4*sqrt(3)) - log(1 + sqrt(3)*x + x^2)/(4*sqrt(3))]

    @test_int [1/(2 - 3*x^6), x, 10, If(13<9, -(atan(1/sqrt(3) - (2^(5/6)*x)/3^(1/3))/(2*2^(5/6)*3^(2/3))) + atan(1/sqrt(3) + (2^(5/6)*x)/3^(1/3))/(2*2^(5/6)*3^(2/3)) + atanh((3/2)^(1/6)*x)/(3*2^(5/6)*3^(1/6)) - log(2^(1/3) - 6^(1/6)*x + 3^(1/3)*x^2)/(12*2^(5/6)*3^(1/6)) + log(2^(1/3) + 6^(1/6)*x + 3^(1/3)*x^2)/(12*2^(5/6)*3^(1/6)), -(atan((6^(1/6) - 2*3^(1/3)*x)/(2^(1/6)*3^(2/3)))/(2*2^(5/6)*3^(2/3))) + atan((6^(1/6) + 2*3^(1/3)*x)/(2^(1/6)*3^(2/3)))/(2*2^(5/6)*3^(2/3)) + atanh((3/2)^(1/6)*x)/(3*2^(5/6)*3^(1/6)) - log(2^(1/3) - 6^(1/6)*x + 3^(1/3)*x^2)/(12*2^(5/6)*3^(1/6)) + log(2^(1/3) + 6^(1/6)*x + 3^(1/3)*x^2)/(12*2^(5/6)*3^(1/6)))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^(m/3)*(a+b*x^6)^p=#

    #= ::Subsubsection:: =#
    #=p>0=#

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [x^(1/3)/(1 - x^6), x, 8, -(atan((1 + 2*x^(2/3))/sqrt(3))/(2*sqrt(3))) + (1/3)*atan((x^(2/3) - cos((2*pi)/9))*csc((2*pi)/9))*cos(pi/18) - (1/6)*log(1 - x^(2/3)) + (1/12)*log(1 + x^(2/3) + x^(4/3)) - (1/6)*cos((2*pi)/9)*log(1 + x^(4/3) + 2*x^(2/3)*cos(pi/9)) + (1/6)*cos(pi/9)*log(1 + x^(4/3) - 2*x^(2/3)*sin(pi/18)) - (1/6)*log(1 + x^(4/3) - 2*x^(2/3)*cos((2*pi)/9))*sin(pi/18) + (1/3)*atan(sec(pi/18)*(x^(2/3) - sin(pi/18)))*sin(pi/9) - (1/3)*atan((x^(2/3) + cos(pi/9))*csc(pi/9))*sin((2*pi)/9)]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b*x^6)^(p/2)=#

    #= ::Subsubsection::Closed:: =#
    #=p>0=#

    @test_int [x^8*sqrt(-1 + 4*x^6), x, 5, (-(1/96))*x^3*sqrt(-1 + 4*x^6) + (1/12)*x^9*sqrt(-1 + 4*x^6) - (1/192)*atanh((2*x^3)/sqrt(-1 + 4*x^6))]
    @test_int [x^5*sqrt(a^6 - x^6), x, 1, -(a^6 - x^6)^(3/2)/9]
    @test_int [x^2*sqrt(-2 + x^6), x, 4, (1/6)*x^3*sqrt(-2 + x^6) - (1/3)*atanh(x^3/sqrt(-2 + x^6))]

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [x^23/sqrt(2 + x^6), x, 3, (-(8/3))*sqrt(2 + x^6) + (4/3)*(2 + x^6)^(3/2) - (2/5)*(2 + x^6)^(5/2) + (1/21)*(2 + x^6)^(7/2)]
    @test_int [x^17/sqrt(2 + x^6), x, 3, (4*sqrt(2 + x^6))/3 - (4/9)*(2 + x^6)^(3/2) + (1/15)*(2 + x^6)^(5/2)]
    @test_int [x^11/sqrt(2 + x^6), x, 3, (-(2/3))*sqrt(2 + x^6) + (1/9)*(2 + x^6)^(3/2)]
    @test_int [x^5/sqrt(2 + x^6), x, 1, sqrt(2 + x^6)/3]
    @test_int [1/(x^1*sqrt(2 + x^6)), x, 3, -(atanh(sqrt(2 + x^6)/sqrt(2))/(3*sqrt(2)))]
    @test_int [1/(x^7*sqrt(2 + x^6)), x, 4, -(sqrt(2 + x^6)/(12*x^6)) + atanh(sqrt(2 + x^6)/sqrt(2))/(12*sqrt(2))]
    @test_int [1/(x^13*sqrt(2 + x^6)), x, 5, -(sqrt(2 + x^6)/(24*x^12)) + sqrt(2 + x^6)/(32*x^6) - atanh(sqrt(2 + x^6)/sqrt(2))/(32*sqrt(2))]

    @test_int [x^14/sqrt(2 + x^6), x, 4, (-(1/4))*x^3*sqrt(2 + x^6) + (1/12)*x^9*sqrt(2 + x^6) + (1/2)*asinh(x^3/sqrt(2))]
    @test_int [x^8/sqrt(2 + x^6), x, 3, (1/6)*x^3*sqrt(2 + x^6) - (1/3)*asinh(x^3/sqrt(2))]
    @test_int [x^2/sqrt(2 + x^6), x, 2, (1/3)*asinh(x^3/sqrt(2))]
    @test_int [1/(x^4*sqrt(2 + x^6)), x, 1, -(sqrt(2 + x^6)/(6*x^3))]
    @test_int [1/(x^10*sqrt(2 + x^6)), x, 2, -(sqrt(2 + x^6)/(18*x^9)) + sqrt(2 + x^6)/(18*x^3)]
    @test_int [1/(x^16*sqrt(2 + x^6)), x, 3, -(sqrt(2 + x^6)/(30*x^15)) + sqrt(2 + x^6)/(45*x^9) - sqrt(2 + x^6)/(45*x^3)]

    @test_int [x^7/sqrt(2 + x^6), x, 3, (1/5)*x^2*sqrt(2 + x^6) - (2*2^(5/6)*sqrt(2 + sqrt(3))*(2^(1/3) + x^2)*sqrt((2^(2/3) - 2^(1/3)*x^2 + x^4)/(2^(1/3)*(1 + sqrt(3)) + x^2)^2)*Elliptic.F(asin((2^(1/3)*(1 - sqrt(3)) + x^2)/(2^(1/3)*(1 + sqrt(3)) + x^2)), -7 - 4*sqrt(3)))/(5*3^(1/4)*sqrt((2^(1/3) + x^2)/(2^(1/3)*(1 + sqrt(3)) + x^2)^2)*sqrt(2 + x^6))]
    @test_int [x^1/sqrt(2 + x^6), x, 2, (sqrt(2 + sqrt(3))*(2^(1/3) + x^2)*sqrt((2^(2/3) - 2^(1/3)*x^2 + x^4)/(2^(1/3)*(1 + sqrt(3)) + x^2)^2)*Elliptic.F(asin((2^(1/3)*(1 - sqrt(3)) + x^2)/(2^(1/3)*(1 + sqrt(3)) + x^2)), -7 - 4*sqrt(3)))/(2^(1/6)*3^(1/4)*sqrt((2^(1/3) + x^2)/(2^(1/3)*(1 + sqrt(3)) + x^2)^2)*sqrt(2 + x^6))]
    @test_int [1/(x^5*sqrt(2 + x^6)), x, 3, -(sqrt(2 + x^6)/(8*x^4)) - (sqrt(2 + sqrt(3))*(2^(1/3) + x^2)*sqrt((2^(2/3) - 2^(1/3)*x^2 + x^4)/(2^(1/3)*(1 + sqrt(3)) + x^2)^2)*Elliptic.F(asin((2^(1/3)*(1 - sqrt(3)) + x^2)/(2^(1/3)*(1 + sqrt(3)) + x^2)), -7 - 4*sqrt(3)))/(8*2^(1/6)*3^(1/4)*sqrt((2^(1/3) + x^2)/(2^(1/3)*(1 + sqrt(3)) + x^2)^2)*sqrt(2 + x^6))]

    @test_int [x^6/sqrt(2 + x^6), x, 2, (1/4)*x*sqrt(2 + x^6) - (x*(2^(1/3) + x^2)*sqrt((2^(2/3) - 2^(1/3)*x^2 + x^4)/(2^(1/3) + (1 + sqrt(3))*x^2)^2)*Elliptic.F(acos((2^(1/3) + (1 - sqrt(3))*x^2)/(2^(1/3) + (1 + sqrt(3))*x^2)), (1/4)*(2 + sqrt(3))))/(4*2^(1/3)*3^(1/4)*sqrt((x^2*(2^(1/3) + x^2))/(2^(1/3) + (1 + sqrt(3))*x^2)^2)*sqrt(2 + x^6))]
    @test_int [x^0/sqrt(2 + x^6), x, 1, (x*(2^(1/3) + x^2)*sqrt((2^(2/3) - 2^(1/3)*x^2 + x^4)/(2^(1/3) + (1 + sqrt(3))*x^2)^2)*Elliptic.F(acos((2^(1/3) + (1 - sqrt(3))*x^2)/(2^(1/3) + (1 + sqrt(3))*x^2)), (1/4)*(2 + sqrt(3))))/(2*2^(1/3)*3^(1/4)*sqrt((x^2*(2^(1/3) + x^2))/(2^(1/3) + (1 + sqrt(3))*x^2)^2)*sqrt(2 + x^6))]
    @test_int [1/(x^6*sqrt(2 + x^6)), x, 2, -(sqrt(2 + x^6)/(10*x^5)) - (x*(2^(1/3) + x^2)*sqrt((2^(2/3) - 2^(1/3)*x^2 + x^4)/(2^(1/3) + (1 + sqrt(3))*x^2)^2)*Elliptic.F(acos((2^(1/3) + (1 - sqrt(3))*x^2)/(2^(1/3) + (1 + sqrt(3))*x^2)), (1/4)*(2 + sqrt(3))))/(10*2^(1/3)*3^(1/4)*sqrt((x^2*(2^(1/3) + x^2))/(2^(1/3) + (1 + sqrt(3))*x^2)^2)*sqrt(2 + x^6))]

    @test_int [x^9/sqrt(2 + x^6), x, 5, (1/7)*x^4*sqrt(2 + x^6) - (8*sqrt(2 + x^6))/(7*(2^(1/3)*(1 + sqrt(3)) + x^2)) + (4*2^(1/6)*3^(1/4)*sqrt(2 - sqrt(3))*(2^(1/3) + x^2)*sqrt((2^(2/3) - 2^(1/3)*x^2 + x^4)/(2^(1/3)*(1 + sqrt(3)) + x^2)^2)*Elliptic.E(asin((2^(1/3)*(1 - sqrt(3)) + x^2)/(2^(1/3)*(1 + sqrt(3)) + x^2)), -7 - 4*sqrt(3)))/(7*sqrt((2^(1/3) + x^2)/(2^(1/3)*(1 + sqrt(3)) + x^2)^2)*sqrt(2 + x^6)) - (8*2^(2/3)*(2^(1/3) + x^2)*sqrt((2^(2/3) - 2^(1/3)*x^2 + x^4)/(2^(1/3)*(1 + sqrt(3)) + x^2)^2)*Elliptic.F(asin((2^(1/3)*(1 - sqrt(3)) + x^2)/(2^(1/3)*(1 + sqrt(3)) + x^2)), -7 - 4*sqrt(3)))/(7*3^(1/4)*sqrt((2^(1/3) + x^2)/(2^(1/3)*(1 + sqrt(3)) + x^2)^2)*sqrt(2 + x^6))]
    @test_int [x^3/sqrt(2 + x^6), x, 4, sqrt(2 + x^6)/(2^(1/3)*(1 + sqrt(3)) + x^2) - (3^(1/4)*sqrt(2 - sqrt(3))*(2^(1/3) + x^2)*sqrt((2^(2/3) - 2^(1/3)*x^2 + x^4)/(2^(1/3)*(1 + sqrt(3)) + x^2)^2)*Elliptic.E(asin((2^(1/3)*(1 - sqrt(3)) + x^2)/(2^(1/3)*(1 + sqrt(3)) + x^2)), -7 - 4*sqrt(3)))/(2^(5/6)*sqrt((2^(1/3) + x^2)/(2^(1/3)*(1 + sqrt(3)) + x^2)^2)*sqrt(2 + x^6)) + (2^(2/3)*(2^(1/3) + x^2)*sqrt((2^(2/3) - 2^(1/3)*x^2 + x^4)/(2^(1/3)*(1 + sqrt(3)) + x^2)^2)*Elliptic.F(asin((2^(1/3)*(1 - sqrt(3)) + x^2)/(2^(1/3)*(1 + sqrt(3)) + x^2)), -7 - 4*sqrt(3)))/(3^(1/4)*sqrt((2^(1/3) + x^2)/(2^(1/3)*(1 + sqrt(3)) + x^2)^2)*sqrt(2 + x^6))]
    @test_int [1/(x^3*sqrt(2 + x^6)), x, 5, -(sqrt(2 + x^6)/(4*x^2)) + sqrt(2 + x^6)/(4*(2^(1/3)*(1 + sqrt(3)) + x^2)) - (3^(1/4)*sqrt(2 - sqrt(3))*(2^(1/3) + x^2)*sqrt((2^(2/3) - 2^(1/3)*x^2 + x^4)/(2^(1/3)*(1 + sqrt(3)) + x^2)^2)*Elliptic.E(asin((2^(1/3)*(1 - sqrt(3)) + x^2)/(2^(1/3)*(1 + sqrt(3)) + x^2)), -7 - 4*sqrt(3)))/(4*2^(5/6)*sqrt((2^(1/3) + x^2)/(2^(1/3)*(1 + sqrt(3)) + x^2)^2)*sqrt(2 + x^6)) + ((2^(1/3) + x^2)*sqrt((2^(2/3) - 2^(1/3)*x^2 + x^4)/(2^(1/3)*(1 + sqrt(3)) + x^2)^2)*Elliptic.F(asin((2^(1/3)*(1 - sqrt(3)) + x^2)/(2^(1/3)*(1 + sqrt(3)) + x^2)), -7 - 4*sqrt(3)))/(2*2^(1/3)*3^(1/4)*sqrt((2^(1/3) + x^2)/(2^(1/3)*(1 + sqrt(3)) + x^2)^2)*sqrt(2 + x^6))]

    @test_int [x^10/sqrt(2 + x^6), x, 4, (1/8)*x^5*sqrt(2 + x^6) - (5*(1 + sqrt(3))*x*sqrt(2 + x^6))/(8*(2^(1/3) + (1 + sqrt(3))*x^2)) + (5*3^(1/4)*x*(2^(1/3) + x^2)*sqrt((2^(2/3) - 2^(1/3)*x^2 + x^4)/(2^(1/3) + (1 + sqrt(3))*x^2)^2)*Elliptic.E(acos((2^(1/3) + (1 - sqrt(3))*x^2)/(2^(1/3) + (1 + sqrt(3))*x^2)), (1/4)*(2 + sqrt(3))))/(4*2^(2/3)*sqrt((x^2*(2^(1/3) + x^2))/(2^(1/3) + (1 + sqrt(3))*x^2)^2)*sqrt(2 + x^6)) + (5*(1 - sqrt(3))*x*(2^(1/3) + x^2)*sqrt((2^(2/3) - 2^(1/3)*x^2 + x^4)/(2^(1/3) + (1 + sqrt(3))*x^2)^2)*Elliptic.F(acos((2^(1/3) + (1 - sqrt(3))*x^2)/(2^(1/3) + (1 + sqrt(3))*x^2)), (1/4)*(2 + sqrt(3))))/(8*2^(2/3)*3^(1/4)*sqrt((x^2*(2^(1/3) + x^2))/(2^(1/3) + (1 + sqrt(3))*x^2)^2)*sqrt(2 + x^6))]
    @test_int [x^4/sqrt(2 + x^6), x, 3, ((1 + sqrt(3))*x*sqrt(2 + x^6))/(2*(2^(1/3) + (1 + sqrt(3))*x^2)) - (3^(1/4)*x*(2^(1/3) + x^2)*sqrt((2^(2/3) - 2^(1/3)*x^2 + x^4)/(2^(1/3) + (1 + sqrt(3))*x^2)^2)*Elliptic.E(acos((2^(1/3) + (1 - sqrt(3))*x^2)/(2^(1/3) + (1 + sqrt(3))*x^2)), (1/4)*(2 + sqrt(3))))/(2^(2/3)*sqrt((x^2*(2^(1/3) + x^2))/(2^(1/3) + (1 + sqrt(3))*x^2)^2)*sqrt(2 + x^6)) - ((1 - sqrt(3))*x*(2^(1/3) + x^2)*sqrt((2^(2/3) - 2^(1/3)*x^2 + x^4)/(2^(1/3) + (1 + sqrt(3))*x^2)^2)*Elliptic.F(acos((2^(1/3) + (1 - sqrt(3))*x^2)/(2^(1/3) + (1 + sqrt(3))*x^2)), (1/4)*(2 + sqrt(3))))/(2*2^(2/3)*3^(1/4)*sqrt((x^2*(2^(1/3) + x^2))/(2^(1/3) + (1 + sqrt(3))*x^2)^2)*sqrt(2 + x^6))]
    @test_int [1/(x^2*sqrt(2 + x^6)), x, 4, -(sqrt(2 + x^6)/(2*x)) + ((1 + sqrt(3))*x*sqrt(2 + x^6))/(2*(2^(1/3) + (1 + sqrt(3))*x^2)) - (3^(1/4)*x*(2^(1/3) + x^2)*sqrt((2^(2/3) - 2^(1/3)*x^2 + x^4)/(2^(1/3) + (1 + sqrt(3))*x^2)^2)*Elliptic.E(acos((2^(1/3) + (1 - sqrt(3))*x^2)/(2^(1/3) + (1 + sqrt(3))*x^2)), (1/4)*(2 + sqrt(3))))/(2^(2/3)*sqrt((x^2*(2^(1/3) + x^2))/(2^(1/3) + (1 + sqrt(3))*x^2)^2)*sqrt(2 + x^6)) - ((1 - sqrt(3))*x*(2^(1/3) + x^2)*sqrt((2^(2/3) - 2^(1/3)*x^2 + x^4)/(2^(1/3) + (1 + sqrt(3))*x^2)^2)*Elliptic.F(acos((2^(1/3) + (1 - sqrt(3))*x^2)/(2^(1/3) + (1 + sqrt(3))*x^2)), (1/4)*(2 + sqrt(3))))/(2*2^(2/3)*3^(1/4)*sqrt((x^2*(2^(1/3) + x^2))/(2^(1/3) + (1 + sqrt(3))*x^2)^2)*sqrt(2 + x^6))]

    @test_int [x^23/(2 + x^6)^(3/2), x, 3, 8/(3*sqrt(2 + x^6)) + 4*sqrt(2 + x^6) - (2/3)*(2 + x^6)^(3/2) + (1/15)*(2 + x^6)^(5/2)]
    @test_int [x^17/(2 + x^6)^(3/2), x, 3, -(4/(3*sqrt(2 + x^6))) - (4*sqrt(2 + x^6))/3 + (1/9)*(2 + x^6)^(3/2)]
    @test_int [x^11/(2 + x^6)^(3/2), x, 3, 2/(3*sqrt(2 + x^6)) + sqrt(2 + x^6)/3]
    @test_int [x^5/(2 + x^6)^(3/2), x, 1, -(1/(3*sqrt(2 + x^6)))]
    @test_int [1/(x^1*(2 + x^6)^(3/2)), x, 4, 1/(6*sqrt(2 + x^6)) - atanh(sqrt(2 + x^6)/sqrt(2))/(6*sqrt(2))]
    @test_int [1/(x^7*(2 + x^6)^(3/2)), x, 5, -(1/(8*sqrt(2 + x^6))) - 1/(12*x^6*sqrt(2 + x^6)) + atanh(sqrt(2 + x^6)/sqrt(2))/(8*sqrt(2))]
    @test_int [1/(x^13*(2 + x^6)^(3/2)), x, 6, 5/(64*sqrt(2 + x^6)) - 1/(24*x^12*sqrt(2 + x^6)) + 5/(96*x^6*sqrt(2 + x^6)) - (5*atanh(sqrt(2 + x^6)/sqrt(2)))/(64*sqrt(2))]

    @test_int [x^14/(2 + x^6)^(3/2), x, 4, -(x^9/(3*sqrt(2 + x^6))) + (1/2)*x^3*sqrt(2 + x^6) - asinh(x^3/sqrt(2))]
    @test_int [x^8/(2 + x^6)^(3/2), x, 3, -(x^3/(3*sqrt(2 + x^6))) + (1/3)*asinh(x^3/sqrt(2))]
    @test_int [x^2/(2 + x^6)^(3/2), x, 1, x^3/(6*sqrt(2 + x^6))]
    @test_int [1/(x^4*(2 + x^6)^(3/2)), x, 2, -(1/(6*x^3*sqrt(2 + x^6))) - x^3/(6*sqrt(2 + x^6))]
    @test_int [1/(x^10*(2 + x^6)^(3/2)), x, 3, -(1/(18*x^9*sqrt(2 + x^6))) + 1/(9*x^3*sqrt(2 + x^6)) + x^3/(9*sqrt(2 + x^6))]

    @test_int [x^13/(2 + x^6)^(3/2), x, 4, -(x^8/(3*sqrt(2 + x^6))) + (8/15)*x^2*sqrt(2 + x^6) - (16*2^(5/6)*sqrt(2 + sqrt(3))*(2^(1/3) + x^2)*sqrt((2^(2/3) - 2^(1/3)*x^2 + x^4)/(2^(1/3)*(1 + sqrt(3)) + x^2)^2)*Elliptic.F(asin((2^(1/3)*(1 - sqrt(3)) + x^2)/(2^(1/3)*(1 + sqrt(3)) + x^2)), -7 - 4*sqrt(3)))/(15*3^(1/4)*sqrt((2^(1/3) + x^2)/(2^(1/3)*(1 + sqrt(3)) + x^2)^2)*sqrt(2 + x^6))]
    @test_int [x^7/(2 + x^6)^(3/2), x, 3, -(x^2/(3*sqrt(2 + x^6))) + (2^(5/6)*sqrt(2 + sqrt(3))*(2^(1/3) + x^2)*sqrt((2^(2/3) - 2^(1/3)*x^2 + x^4)/(2^(1/3)*(1 + sqrt(3)) + x^2)^2)*Elliptic.F(asin((2^(1/3)*(1 - sqrt(3)) + x^2)/(2^(1/3)*(1 + sqrt(3)) + x^2)), -7 - 4*sqrt(3)))/(3*3^(1/4)*sqrt((2^(1/3) + x^2)/(2^(1/3)*(1 + sqrt(3)) + x^2)^2)*sqrt(2 + x^6))]
    @test_int [x^1/(2 + x^6)^(3/2), x, 3, x^2/(6*sqrt(2 + x^6)) + (sqrt(2 + sqrt(3))*(2^(1/3) + x^2)*sqrt((2^(2/3) - 2^(1/3)*x^2 + x^4)/(2^(1/3)*(1 + sqrt(3)) + x^2)^2)*Elliptic.F(asin((2^(1/3)*(1 - sqrt(3)) + x^2)/(2^(1/3)*(1 + sqrt(3)) + x^2)), -7 - 4*sqrt(3)))/(6*2^(1/6)*3^(1/4)*sqrt((2^(1/3) + x^2)/(2^(1/3)*(1 + sqrt(3)) + x^2)^2)*sqrt(2 + x^6))]
    @test_int [1/(x^5*(2 + x^6)^(3/2)), x, 4, 1/(6*x^4*sqrt(2 + x^6)) - (7*sqrt(2 + x^6))/(48*x^4) - (7*sqrt(2 + sqrt(3))*(2^(1/3) + x^2)*sqrt((2^(2/3) - 2^(1/3)*x^2 + x^4)/(2^(1/3)*(1 + sqrt(3)) + x^2)^2)*Elliptic.F(asin((2^(1/3)*(1 - sqrt(3)) + x^2)/(2^(1/3)*(1 + sqrt(3)) + x^2)), -7 - 4*sqrt(3)))/(48*2^(1/6)*3^(1/4)*sqrt((2^(1/3) + x^2)/(2^(1/3)*(1 + sqrt(3)) + x^2)^2)*sqrt(2 + x^6))]

    @test_int [x^12/(2 + x^6)^(3/2), x, 3, -(x^7/(3*sqrt(2 + x^6))) + (7/12)*x*sqrt(2 + x^6) - (7*x*(2^(1/3) + x^2)*sqrt((2^(2/3) - 2^(1/3)*x^2 + x^4)/(2^(1/3) + (1 + sqrt(3))*x^2)^2)*Elliptic.F(acos((2^(1/3) + (1 - sqrt(3))*x^2)/(2^(1/3) + (1 + sqrt(3))*x^2)), (1/4)*(2 + sqrt(3))))/(12*2^(1/3)*3^(1/4)*sqrt((x^2*(2^(1/3) + x^2))/(2^(1/3) + (1 + sqrt(3))*x^2)^2)*sqrt(2 + x^6))]
    @test_int [x^6/(2 + x^6)^(3/2), x, 2, -(x/(3*sqrt(2 + x^6))) + (x*(2^(1/3) + x^2)*sqrt((2^(2/3) - 2^(1/3)*x^2 + x^4)/(2^(1/3) + (1 + sqrt(3))*x^2)^2)*Elliptic.F(acos((2^(1/3) + (1 - sqrt(3))*x^2)/(2^(1/3) + (1 + sqrt(3))*x^2)), (1/4)*(2 + sqrt(3))))/(6*2^(1/3)*3^(1/4)*sqrt((x^2*(2^(1/3) + x^2))/(2^(1/3) + (1 + sqrt(3))*x^2)^2)*sqrt(2 + x^6))]
    @test_int [x^0/(2 + x^6)^(3/2), x, 2, x/(6*sqrt(2 + x^6)) + (x*(2^(1/3) + x^2)*sqrt((2^(2/3) - 2^(1/3)*x^2 + x^4)/(2^(1/3) + (1 + sqrt(3))*x^2)^2)*Elliptic.F(acos((2^(1/3) + (1 - sqrt(3))*x^2)/(2^(1/3) + (1 + sqrt(3))*x^2)), (1/4)*(2 + sqrt(3))))/(6*2^(1/3)*3^(1/4)*sqrt((x^2*(2^(1/3) + x^2))/(2^(1/3) + (1 + sqrt(3))*x^2)^2)*sqrt(2 + x^6))]
    @test_int [1/(x^6*(2 + x^6)^(3/2)), x, 3, 1/(6*x^5*sqrt(2 + x^6)) - (2*sqrt(2 + x^6))/(15*x^5) - (2^(2/3)*x*(2^(1/3) + x^2)*sqrt((2^(2/3) - 2^(1/3)*x^2 + x^4)/(2^(1/3) + (1 + sqrt(3))*x^2)^2)*Elliptic.F(acos((2^(1/3) + (1 - sqrt(3))*x^2)/(2^(1/3) + (1 + sqrt(3))*x^2)), (1/4)*(2 + sqrt(3))))/(15*3^(1/4)*sqrt((x^2*(2^(1/3) + x^2))/(2^(1/3) + (1 + sqrt(3))*x^2)^2)*sqrt(2 + x^6))]

    @test_int [x^15/(2 + x^6)^(3/2), x, 6, -(x^10/(3*sqrt(2 + x^6))) + (10/21)*x^4*sqrt(2 + x^6) - (80*sqrt(2 + x^6))/(21*(2^(1/3)*(1 + sqrt(3)) + x^2)) + (40*2^(1/6)*sqrt(2 - sqrt(3))*(2^(1/3) + x^2)*sqrt((2^(2/3) - 2^(1/3)*x^2 + x^4)/(2^(1/3)*(1 + sqrt(3)) + x^2)^2)*Elliptic.E(asin((2^(1/3)*(1 - sqrt(3)) + x^2)/(2^(1/3)*(1 + sqrt(3)) + x^2)), -7 - 4*sqrt(3)))/(7*3^(3/4)*sqrt((2^(1/3) + x^2)/(2^(1/3)*(1 + sqrt(3)) + x^2)^2)*sqrt(2 + x^6)) - (80*2^(2/3)*(2^(1/3) + x^2)*sqrt((2^(2/3) - 2^(1/3)*x^2 + x^4)/(2^(1/3)*(1 + sqrt(3)) + x^2)^2)*Elliptic.F(asin((2^(1/3)*(1 - sqrt(3)) + x^2)/(2^(1/3)*(1 + sqrt(3)) + x^2)), -7 - 4*sqrt(3)))/(21*3^(1/4)*sqrt((2^(1/3) + x^2)/(2^(1/3)*(1 + sqrt(3)) + x^2)^2)*sqrt(2 + x^6))]
    @test_int [x^9/(2 + x^6)^(3/2), x, 5, -(x^4/(3*sqrt(2 + x^6))) + (4*sqrt(2 + x^6))/(3*(2^(1/3)*(1 + sqrt(3)) + x^2)) - (2*2^(1/6)*sqrt(2 - sqrt(3))*(2^(1/3) + x^2)*sqrt((2^(2/3) - 2^(1/3)*x^2 + x^4)/(2^(1/3)*(1 + sqrt(3)) + x^2)^2)*Elliptic.E(asin((2^(1/3)*(1 - sqrt(3)) + x^2)/(2^(1/3)*(1 + sqrt(3)) + x^2)), -7 - 4*sqrt(3)))/(3^(3/4)*sqrt((2^(1/3) + x^2)/(2^(1/3)*(1 + sqrt(3)) + x^2)^2)*sqrt(2 + x^6)) + (4*2^(2/3)*(2^(1/3) + x^2)*sqrt((2^(2/3) - 2^(1/3)*x^2 + x^4)/(2^(1/3)*(1 + sqrt(3)) + x^2)^2)*Elliptic.F(asin((2^(1/3)*(1 - sqrt(3)) + x^2)/(2^(1/3)*(1 + sqrt(3)) + x^2)), -7 - 4*sqrt(3)))/(3*3^(1/4)*sqrt((2^(1/3) + x^2)/(2^(1/3)*(1 + sqrt(3)) + x^2)^2)*sqrt(2 + x^6))]
    @test_int [x^3/(2 + x^6)^(3/2), x, 5, x^4/(6*sqrt(2 + x^6)) - sqrt(2 + x^6)/(6*(2^(1/3)*(1 + sqrt(3)) + x^2)) + (sqrt(2 - sqrt(3))*(2^(1/3) + x^2)*sqrt((2^(2/3) - 2^(1/3)*x^2 + x^4)/(2^(1/3)*(1 + sqrt(3)) + x^2)^2)*Elliptic.E(asin((2^(1/3)*(1 - sqrt(3)) + x^2)/(2^(1/3)*(1 + sqrt(3)) + x^2)), -7 - 4*sqrt(3)))/(2*2^(5/6)*3^(3/4)*sqrt((2^(1/3) + x^2)/(2^(1/3)*(1 + sqrt(3)) + x^2)^2)*sqrt(2 + x^6)) - ((2^(1/3) + x^2)*sqrt((2^(2/3) - 2^(1/3)*x^2 + x^4)/(2^(1/3)*(1 + sqrt(3)) + x^2)^2)*Elliptic.F(asin((2^(1/3)*(1 - sqrt(3)) + x^2)/(2^(1/3)*(1 + sqrt(3)) + x^2)), -7 - 4*sqrt(3)))/(3*2^(1/3)*3^(1/4)*sqrt((2^(1/3) + x^2)/(2^(1/3)*(1 + sqrt(3)) + x^2)^2)*sqrt(2 + x^6))]
    @test_int [1/(x^3*(2 + x^6)^(3/2)), x, 6, 1/(6*x^2*sqrt(2 + x^6)) - (5*sqrt(2 + x^6))/(24*x^2) + (5*sqrt(2 + x^6))/(24*(2^(1/3)*(1 + sqrt(3)) + x^2)) - (5*sqrt(2 - sqrt(3))*(2^(1/3) + x^2)*sqrt((2^(2/3) - 2^(1/3)*x^2 + x^4)/(2^(1/3)*(1 + sqrt(3)) + x^2)^2)*Elliptic.E(asin((2^(1/3)*(1 - sqrt(3)) + x^2)/(2^(1/3)*(1 + sqrt(3)) + x^2)), -7 - 4*sqrt(3)))/(8*2^(5/6)*3^(3/4)*sqrt((2^(1/3) + x^2)/(2^(1/3)*(1 + sqrt(3)) + x^2)^2)*sqrt(2 + x^6)) + (5*(2^(1/3) + x^2)*sqrt((2^(2/3) - 2^(1/3)*x^2 + x^4)/(2^(1/3)*(1 + sqrt(3)) + x^2)^2)*Elliptic.F(asin((2^(1/3)*(1 - sqrt(3)) + x^2)/(2^(1/3)*(1 + sqrt(3)) + x^2)), -7 - 4*sqrt(3)))/(12*2^(1/3)*3^(1/4)*sqrt((2^(1/3) + x^2)/(2^(1/3)*(1 + sqrt(3)) + x^2)^2)*sqrt(2 + x^6))]

    @test_int [x^10/(2 + x^6)^(3/2), x, 4, -(x^5/(3*sqrt(2 + x^6))) + (5*(1 + sqrt(3))*x*sqrt(2 + x^6))/(6*(2^(1/3) + (1 + sqrt(3))*x^2)) - (5*x*(2^(1/3) + x^2)*sqrt((2^(2/3) - 2^(1/3)*x^2 + x^4)/(2^(1/3) + (1 + sqrt(3))*x^2)^2)*Elliptic.E(acos((2^(1/3) + (1 - sqrt(3))*x^2)/(2^(1/3) + (1 + sqrt(3))*x^2)), (1/4)*(2 + sqrt(3))))/(2^(2/3)*3^(3/4)*sqrt((x^2*(2^(1/3) + x^2))/(2^(1/3) + (1 + sqrt(3))*x^2)^2)*sqrt(2 + x^6)) - (5*(1 - sqrt(3))*x*(2^(1/3) + x^2)*sqrt((2^(2/3) - 2^(1/3)*x^2 + x^4)/(2^(1/3) + (1 + sqrt(3))*x^2)^2)*Elliptic.F(acos((2^(1/3) + (1 - sqrt(3))*x^2)/(2^(1/3) + (1 + sqrt(3))*x^2)), (1/4)*(2 + sqrt(3))))/(6*2^(2/3)*3^(1/4)*sqrt((x^2*(2^(1/3) + x^2))/(2^(1/3) + (1 + sqrt(3))*x^2)^2)*sqrt(2 + x^6))]
    @test_int [x^4/(2 + x^6)^(3/2), x, 4, x^5/(6*sqrt(2 + x^6)) - ((1 + sqrt(3))*x*sqrt(2 + x^6))/(6*(2^(1/3) + (1 + sqrt(3))*x^2)) + (x*(2^(1/3) + x^2)*sqrt((2^(2/3) - 2^(1/3)*x^2 + x^4)/(2^(1/3) + (1 + sqrt(3))*x^2)^2)*Elliptic.E(acos((2^(1/3) + (1 - sqrt(3))*x^2)/(2^(1/3) + (1 + sqrt(3))*x^2)), (1/4)*(2 + sqrt(3))))/(2^(2/3)*3^(3/4)*sqrt((x^2*(2^(1/3) + x^2))/(2^(1/3) + (1 + sqrt(3))*x^2)^2)*sqrt(2 + x^6)) + ((1 - sqrt(3))*x*(2^(1/3) + x^2)*sqrt((2^(2/3) - 2^(1/3)*x^2 + x^4)/(2^(1/3) + (1 + sqrt(3))*x^2)^2)*Elliptic.F(acos((2^(1/3) + (1 - sqrt(3))*x^2)/(2^(1/3) + (1 + sqrt(3))*x^2)), (1/4)*(2 + sqrt(3))))/(6*2^(2/3)*3^(1/4)*sqrt((x^2*(2^(1/3) + x^2))/(2^(1/3) + (1 + sqrt(3))*x^2)^2)*sqrt(2 + x^6))]
    @test_int [1/(x^2*(2 + x^6)^(3/2)), x, 5, 1/(6*x*sqrt(2 + x^6)) - sqrt(2 + x^6)/(3*x) + ((1 + sqrt(3))*x*sqrt(2 + x^6))/(3*(2^(1/3) + (1 + sqrt(3))*x^2)) - (2^(1/3)*x*(2^(1/3) + x^2)*sqrt((2^(2/3) - 2^(1/3)*x^2 + x^4)/(2^(1/3) + (1 + sqrt(3))*x^2)^2)*Elliptic.E(acos((2^(1/3) + (1 - sqrt(3))*x^2)/(2^(1/3) + (1 + sqrt(3))*x^2)), (1/4)*(2 + sqrt(3))))/(3^(3/4)*sqrt((x^2*(2^(1/3) + x^2))/(2^(1/3) + (1 + sqrt(3))*x^2)^2)*sqrt(2 + x^6)) - ((1 - sqrt(3))*x*(2^(1/3) + x^2)*sqrt((2^(2/3) - 2^(1/3)*x^2 + x^4)/(2^(1/3) + (1 + sqrt(3))*x^2)^2)*Elliptic.F(acos((2^(1/3) + (1 - sqrt(3))*x^2)/(2^(1/3) + (1 + sqrt(3))*x^2)), (1/4)*(2 + sqrt(3))))/(3*2^(2/3)*3^(1/4)*sqrt((x^2*(2^(1/3) + x^2))/(2^(1/3) + (1 + sqrt(3))*x^2)^2)*sqrt(2 + x^6))]

    #= ::Subsection:: =#
    #=Integrands*of*the*form*x^(m/2)*(a+b*x^6)^(p/2)=#

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(c*x)^m*(a+b*x^7)^p=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b*x^7)^p=#

    #= ::Subsubsection::Closed:: =#
    #=p>0=#

    @test_int [(a + b*x^7)*x^m, x, 2, (a*x^(1 + m))/(1 + m) + (b*x^(8 + m))/(8 + m)]

    @test_int [(a + b*x^7)*x^8, x, 2, (a*x^9)/9 + (b*x^16)/16]
    @test_int [(a + b*x^7)/x^8, x, 2, -(a/(7*x^7)) + b*log(x)]

    @test_int [(a + b*x^7)^2*x^m, x, 2, (a^2*x^(1 + m))/(1 + m) + (2*a*b*x^(8 + m))/(8 + m) + (b^2*x^(15 + m))/(15 + m)]

    @test_int [(a + b*x^7)^2*x^8, x, 2, (a^2*x^9)/9 + (1/8)*a*b*x^16 + (b^2*x^23)/23]
    @test_int [(a + b*x^7)^2/x^8, x, 3, -(a^2/(7*x^7)) + (b^2*x^7)/7 + 2*a*b*log(x)]

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [x^m/(a + b*x^7), x, 1, (x^(1 + m)*HypergeometricFunctions._₂F₁(1, (1 + m)/7, (8 + m)/7, -((b*x^7)/a)))/(a*(1 + m))]

    @test_int [x^6/(a + b*x^7), x, 1, log(a + b*x^7)/(7*b)]
    @test_int [x^0/(a + b*x^7), x, 6, (2*atan((b^(1/7)*x*sec(pi/14))/a^(1/7) - tan(pi/14))*cos(pi/14))/(7*a^(6/7)*b^(1/7)) + (2*atan((b^(1/7)*x*sec((3*pi)/14))/a^(1/7) + tan((3*pi)/14))*cos((3*pi)/14))/(7*a^(6/7)*b^(1/7)) + log(a^(1/7) + b^(1/7)*x)/(7*a^(6/7)*b^(1/7)) - (cos(pi/7)*log(a^(2/7) + b^(2/7)*x^2 - 2*a^(1/7)*b^(1/7)*x*cos(pi/7)))/(7*a^(6/7)*b^(1/7)) - (log(a^(2/7) + b^(2/7)*x^2 - 2*a^(1/7)*b^(1/7)*x*sin(pi/14))*sin(pi/14))/(7*a^(6/7)*b^(1/7)) - (2*atan(cot(pi/7) - (b^(1/7)*x*csc(pi/7))/a^(1/7))*sin(pi/7))/(7*a^(6/7)*b^(1/7)) + (log(a^(2/7) + b^(2/7)*x^2 + 2*a^(1/7)*b^(1/7)*x*sin((3*pi)/14))*sin((3*pi)/14))/(7*a^(6/7)*b^(1/7))]
    @test_int [1/(x^1*(a + b*x^7)), x, 4, log(x)/a - log(a + b*x^7)/(7*a)]

    @test_int [x^m/(a - b*x^7), x, 1, (x^(1 + m)*HypergeometricFunctions._₂F₁(1, (1 + m)/7, (8 + m)/7, (b*x^7)/a))/(a*(1 + m))]

    @test_int [x^6/(a - b*x^7), x, 1, -(log(a - b*x^7)/(7*b))]
    @test_int [x^0/(a - b*x^7), x, 6, (2*atan((b^(1/7)*x*sec(pi/14))/a^(1/7) + tan(pi/14))*cos(pi/14))/(7*a^(6/7)*b^(1/7)) + (2*atan((b^(1/7)*x*sec((3*pi)/14))/a^(1/7) - tan((3*pi)/14))*cos((3*pi)/14))/(7*a^(6/7)*b^(1/7)) - log(a^(1/7) - b^(1/7)*x)/(7*a^(6/7)*b^(1/7)) + (cos(pi/7)*log(a^(2/7) + b^(2/7)*x^2 + 2*a^(1/7)*b^(1/7)*x*cos(pi/7)))/(7*a^(6/7)*b^(1/7)) + (log(a^(2/7) + b^(2/7)*x^2 + 2*a^(1/7)*b^(1/7)*x*sin(pi/14))*sin(pi/14))/(7*a^(6/7)*b^(1/7)) + (2*atan(cot(pi/7) + (b^(1/7)*x*csc(pi/7))/a^(1/7))*sin(pi/7))/(7*a^(6/7)*b^(1/7)) - (log(a^(2/7) + b^(2/7)*x^2 - 2*a^(1/7)*b^(1/7)*x*sin((3*pi)/14))*sin((3*pi)/14))/(7*a^(6/7)*b^(1/7))]
    @test_int [1/(x^1*(a - b*x^7)), x, 4, log(x)/a - log(a - b*x^7)/(7*a)]

    @test_int [1/(1 - x^7), x, 6, (2/7)*atan(sec(pi/14)*(x + sin(pi/14)))*cos(pi/14) + (2/7)*atan(sec((3*pi)/14)*(x - sin((3*pi)/14)))*cos((3*pi)/14) - (1/7)*log(1 - x) + (1/7)*cos(pi/7)*log(1 + x^2 + 2*x*cos(pi/7)) + (1/7)*log(1 + x^2 + 2*x*sin(pi/14))*sin(pi/14) + (2/7)*atan((x + cos(pi/7))*csc(pi/7))*sin(pi/7) - (1/7)*log(1 + x^2 - 2*x*sin((3*pi)/14))*sin((3*pi)/14)]
    @test_int [1/(1 + x^7), x, 6, (2/7)*atan(x*sec(pi/14) - tan(pi/14))*cos(pi/14) + (2/7)*atan(x*sec((3*pi)/14) + tan((3*pi)/14))*cos((3*pi)/14) + (1/7)*log(1 + x) - (1/7)*cos(pi/7)*log(1 + x^2 - 2*x*cos(pi/7)) - (1/7)*log(1 + x^2 - 2*x*sin(pi/14))*sin(pi/14) - (2/7)*atan(cot(pi/7) - x*csc(pi/7))*sin(pi/7) + (1/7)*log(1 + x^2 + 2*x*sin((3*pi)/14))*sin((3*pi)/14)]

    #= ::Subsection:: =#
    #=Integrands*of*the*form*x^(m/2)*(a+b*x^7)^p=#

    #= ::Subsection:: =#
    #=Integrands*of*the*form*x^m*(a+b*x^7)^(p/2)=#

    #= ::Subsection:: =#
    #=Integrands*of*the*form*x^(m/2)*(a+b*x^7)^(p/2)=#

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(c*x)^m*(a+b*x^8)^p=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b*x^8)^p=#

    #= ::Subsubsection:: =#
    #=p>0=#

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [x^9/(a + b*x^8), x, 11, x^2/(2*b) + (a^(1/4)*atan(1 - (sqrt(2)*b^(1/4)*x^2)/a^(1/4)))/(4*sqrt(2)*b^(5/4)) - (a^(1/4)*atan(1 + (sqrt(2)*b^(1/4)*x^2)/a^(1/4)))/(4*sqrt(2)*b^(5/4)) + (a^(1/4)*log(sqrt(a) - sqrt(2)*a^(1/4)*b^(1/4)*x^2 + sqrt(b)*x^4))/(8*sqrt(2)*b^(5/4)) - (a^(1/4)*log(sqrt(a) + sqrt(2)*a^(1/4)*b^(1/4)*x^2 + sqrt(b)*x^4))/(8*sqrt(2)*b^(5/4))]
    @test_int [x^7/(a + b*x^8), x, 1, log(a + b*x^8)/(8*b)]
    @test_int [x^5/(a + b*x^8), x, 10, -(atan(1 - (sqrt(2)*b^(1/4)*x^2)/a^(1/4))/(4*sqrt(2)*a^(1/4)*b^(3/4))) + atan(1 + (sqrt(2)*b^(1/4)*x^2)/a^(1/4))/(4*sqrt(2)*a^(1/4)*b^(3/4)) + log(sqrt(a) - sqrt(2)*a^(1/4)*b^(1/4)*x^2 + sqrt(b)*x^4)/(8*sqrt(2)*a^(1/4)*b^(3/4)) - log(sqrt(a) + sqrt(2)*a^(1/4)*b^(1/4)*x^2 + sqrt(b)*x^4)/(8*sqrt(2)*a^(1/4)*b^(3/4))]
    @test_int [x^3/(a + b*x^8), x, 2, atan((sqrt(b)*x^4)/sqrt(a))/(4*sqrt(a)*sqrt(b))]
    @test_int [x^1/(a + b*x^8), x, 10, -(atan(1 - (sqrt(2)*b^(1/4)*x^2)/a^(1/4))/(4*sqrt(2)*a^(3/4)*b^(1/4))) + atan(1 + (sqrt(2)*b^(1/4)*x^2)/a^(1/4))/(4*sqrt(2)*a^(3/4)*b^(1/4)) - log(sqrt(a) - sqrt(2)*a^(1/4)*b^(1/4)*x^2 + sqrt(b)*x^4)/(8*sqrt(2)*a^(3/4)*b^(1/4)) + log(sqrt(a) + sqrt(2)*a^(1/4)*b^(1/4)*x^2 + sqrt(b)*x^4)/(8*sqrt(2)*a^(3/4)*b^(1/4))]
    @test_int [1/(x^1*(a + b*x^8)), x, 4, log(x)/a - log(a + b*x^8)/(8*a)]
    @test_int [1/(x^3*(a + b*x^8)), x, 11, -(1/(2*a*x^2)) + (b^(1/4)*atan(1 - (sqrt(2)*b^(1/4)*x^2)/a^(1/4)))/(4*sqrt(2)*a^(5/4)) - (b^(1/4)*atan(1 + (sqrt(2)*b^(1/4)*x^2)/a^(1/4)))/(4*sqrt(2)*a^(5/4)) - (b^(1/4)*log(sqrt(a) - sqrt(2)*a^(1/4)*b^(1/4)*x^2 + sqrt(b)*x^4))/(8*sqrt(2)*a^(5/4)) + (b^(1/4)*log(sqrt(a) + sqrt(2)*a^(1/4)*b^(1/4)*x^2 + sqrt(b)*x^4))/(8*sqrt(2)*a^(5/4))]
    @test_int [1/(x^5*(a + b*x^8)), x, 3, -1/(4*a*x^4) - (sqrt(b)*atan((sqrt(b)*x^4)/sqrt(a)))/(4*a^(3/2))]
    @test_int [1/(x^7*(a + b*x^8)), x, 11, -(1/(6*a*x^6)) + (b^(3/4)*atan(1 - (sqrt(2)*b^(1/4)*x^2)/a^(1/4)))/(4*sqrt(2)*a^(7/4)) - (b^(3/4)*atan(1 + (sqrt(2)*b^(1/4)*x^2)/a^(1/4)))/(4*sqrt(2)*a^(7/4)) + (b^(3/4)*log(sqrt(a) - sqrt(2)*a^(1/4)*b^(1/4)*x^2 + sqrt(b)*x^4))/(8*sqrt(2)*a^(7/4)) - (b^(3/4)*log(sqrt(a) + sqrt(2)*a^(1/4)*b^(1/4)*x^2 + sqrt(b)*x^4))/(8*sqrt(2)*a^(7/4))]
    @test_int [1/(x^9*(a + b*x^8)), x, 3, -1/(8*a*x^8) - (b*log(x))/a^2 + (b*log(a + b*x^8))/(8*a^2)]

    @test_int [x^8/(a + b*x^8), x, 14, x/b - ((-a)^(1/8)*atan((b^(1/8)*x)/(-a)^(1/8)))/(4*b^(9/8)) + ((-a)^(1/8)*atan(1 - (sqrt(2)*b^(1/8)*x)/(-a)^(1/8)))/(4*sqrt(2)*b^(9/8)) - ((-a)^(1/8)*atan(1 + (sqrt(2)*b^(1/8)*x)/(-a)^(1/8)))/(4*sqrt(2)*b^(9/8)) - ((-a)^(1/8)*atanh((b^(1/8)*x)/(-a)^(1/8)))/(4*b^(9/8)) + ((-a)^(1/8)*log((-a)^(1/4) - sqrt(2)*(-a)^(1/8)*b^(1/8)*x + b^(1/4)*x^2))/(8*sqrt(2)*b^(9/8)) - ((-a)^(1/8)*log((-a)^(1/4) + sqrt(2)*(-a)^(1/8)*b^(1/8)*x + b^(1/4)*x^2))/(8*sqrt(2)*b^(9/8))]
    @test_int [x^6/(a + b*x^8), x, 13, atan((b^(1/8)*x)/(-a)^(1/8))/(4*(-a)^(1/8)*b^(7/8)) - atan(1 - (sqrt(2)*b^(1/8)*x)/(-a)^(1/8))/(4*sqrt(2)*(-a)^(1/8)*b^(7/8)) + atan(1 + (sqrt(2)*b^(1/8)*x)/(-a)^(1/8))/(4*sqrt(2)*(-a)^(1/8)*b^(7/8)) - atanh((b^(1/8)*x)/(-a)^(1/8))/(4*(-a)^(1/8)*b^(7/8)) + log((-a)^(1/4) - sqrt(2)*(-a)^(1/8)*b^(1/8)*x + b^(1/4)*x^2)/(8*sqrt(2)*(-a)^(1/8)*b^(7/8)) - log((-a)^(1/4) + sqrt(2)*(-a)^(1/8)*b^(1/8)*x + b^(1/4)*x^2)/(8*sqrt(2)*(-a)^(1/8)*b^(7/8))]
    @test_int [x^4/(a + b*x^8), x, 13, -(atan((b^(1/8)*x)/(-a)^(1/8))/(4*(-a)^(3/8)*b^(5/8))) - atan(1 - (sqrt(2)*b^(1/8)*x)/(-a)^(1/8))/(4*sqrt(2)*(-a)^(3/8)*b^(5/8)) + atan(1 + (sqrt(2)*b^(1/8)*x)/(-a)^(1/8))/(4*sqrt(2)*(-a)^(3/8)*b^(5/8)) - atanh((b^(1/8)*x)/(-a)^(1/8))/(4*(-a)^(3/8)*b^(5/8)) - log((-a)^(1/4) - sqrt(2)*(-a)^(1/8)*b^(1/8)*x + b^(1/4)*x^2)/(8*sqrt(2)*(-a)^(3/8)*b^(5/8)) + log((-a)^(1/4) + sqrt(2)*(-a)^(1/8)*b^(1/8)*x + b^(1/4)*x^2)/(8*sqrt(2)*(-a)^(3/8)*b^(5/8))]
    @test_int [x^2/(a + b*x^8), x, 13, atan((b^(1/8)*x)/(-a)^(1/8))/(4*(-a)^(5/8)*b^(3/8)) + atan(1 - (sqrt(2)*b^(1/8)*x)/(-a)^(1/8))/(4*sqrt(2)*(-a)^(5/8)*b^(3/8)) - atan(1 + (sqrt(2)*b^(1/8)*x)/(-a)^(1/8))/(4*sqrt(2)*(-a)^(5/8)*b^(3/8)) - atanh((b^(1/8)*x)/(-a)^(1/8))/(4*(-a)^(5/8)*b^(3/8)) - log((-a)^(1/4) - sqrt(2)*(-a)^(1/8)*b^(1/8)*x + b^(1/4)*x^2)/(8*sqrt(2)*(-a)^(5/8)*b^(3/8)) + log((-a)^(1/4) + sqrt(2)*(-a)^(1/8)*b^(1/8)*x + b^(1/4)*x^2)/(8*sqrt(2)*(-a)^(5/8)*b^(3/8))]
    @test_int [x^0/(a + b*x^8), x, 13, -(atan((b^(1/8)*x)/(-a)^(1/8))/(4*(-a)^(7/8)*b^(1/8))) + atan(1 - (sqrt(2)*b^(1/8)*x)/(-a)^(1/8))/(4*sqrt(2)*(-a)^(7/8)*b^(1/8)) - atan(1 + (sqrt(2)*b^(1/8)*x)/(-a)^(1/8))/(4*sqrt(2)*(-a)^(7/8)*b^(1/8)) - atanh((b^(1/8)*x)/(-a)^(1/8))/(4*(-a)^(7/8)*b^(1/8)) + log((-a)^(1/4) - sqrt(2)*(-a)^(1/8)*b^(1/8)*x + b^(1/4)*x^2)/(8*sqrt(2)*(-a)^(7/8)*b^(1/8)) - log((-a)^(1/4) + sqrt(2)*(-a)^(1/8)*b^(1/8)*x + b^(1/4)*x^2)/(8*sqrt(2)*(-a)^(7/8)*b^(1/8))]
    @test_int [1/(x^2*(a + b*x^8)), x, 14, -(1/(a*x)) + (b^(1/8)*atan((b^(1/8)*x)/(-a)^(1/8)))/(4*(-a)^(9/8)) - (b^(1/8)*atan(1 - (sqrt(2)*b^(1/8)*x)/(-a)^(1/8)))/(4*sqrt(2)*(-a)^(9/8)) + (b^(1/8)*atan(1 + (sqrt(2)*b^(1/8)*x)/(-a)^(1/8)))/(4*sqrt(2)*(-a)^(9/8)) - (b^(1/8)*atanh((b^(1/8)*x)/(-a)^(1/8)))/(4*(-a)^(9/8)) + (b^(1/8)*log((-a)^(1/4) - sqrt(2)*(-a)^(1/8)*b^(1/8)*x + b^(1/4)*x^2))/(8*sqrt(2)*(-a)^(9/8)) - (b^(1/8)*log((-a)^(1/4) + sqrt(2)*(-a)^(1/8)*b^(1/8)*x + b^(1/4)*x^2))/(8*sqrt(2)*(-a)^(9/8))]
    @test_int [1/(x^4*(a + b*x^8)), x, 14, -(1/(3*a*x^3)) - (b^(3/8)*atan((b^(1/8)*x)/(-a)^(1/8)))/(4*(-a)^(11/8)) - (b^(3/8)*atan(1 - (sqrt(2)*b^(1/8)*x)/(-a)^(1/8)))/(4*sqrt(2)*(-a)^(11/8)) + (b^(3/8)*atan(1 + (sqrt(2)*b^(1/8)*x)/(-a)^(1/8)))/(4*sqrt(2)*(-a)^(11/8)) - (b^(3/8)*atanh((b^(1/8)*x)/(-a)^(1/8)))/(4*(-a)^(11/8)) - (b^(3/8)*log((-a)^(1/4) - sqrt(2)*(-a)^(1/8)*b^(1/8)*x + b^(1/4)*x^2))/(8*sqrt(2)*(-a)^(11/8)) + (b^(3/8)*log((-a)^(1/4) + sqrt(2)*(-a)^(1/8)*b^(1/8)*x + b^(1/4)*x^2))/(8*sqrt(2)*(-a)^(11/8))]
    @test_int [1/(x^6*(a + b*x^8)), x, 14, -(1/(5*a*x^5)) + (b^(5/8)*atan((b^(1/8)*x)/(-a)^(1/8)))/(4*(-a)^(13/8)) + (b^(5/8)*atan(1 - (sqrt(2)*b^(1/8)*x)/(-a)^(1/8)))/(4*sqrt(2)*(-a)^(13/8)) - (b^(5/8)*atan(1 + (sqrt(2)*b^(1/8)*x)/(-a)^(1/8)))/(4*sqrt(2)*(-a)^(13/8)) - (b^(5/8)*atanh((b^(1/8)*x)/(-a)^(1/8)))/(4*(-a)^(13/8)) - (b^(5/8)*log((-a)^(1/4) - sqrt(2)*(-a)^(1/8)*b^(1/8)*x + b^(1/4)*x^2))/(8*sqrt(2)*(-a)^(13/8)) + (b^(5/8)*log((-a)^(1/4) + sqrt(2)*(-a)^(1/8)*b^(1/8)*x + b^(1/4)*x^2))/(8*sqrt(2)*(-a)^(13/8))]
    @test_int [1/(x^8*(a + b*x^8)), x, 14, -(1/(7*a*x^7)) - (b^(7/8)*atan((b^(1/8)*x)/(-a)^(1/8)))/(4*(-a)^(15/8)) + (b^(7/8)*atan(1 - (sqrt(2)*b^(1/8)*x)/(-a)^(1/8)))/(4*sqrt(2)*(-a)^(15/8)) - (b^(7/8)*atan(1 + (sqrt(2)*b^(1/8)*x)/(-a)^(1/8)))/(4*sqrt(2)*(-a)^(15/8)) - (b^(7/8)*atanh((b^(1/8)*x)/(-a)^(1/8)))/(4*(-a)^(15/8)) + (b^(7/8)*log((-a)^(1/4) - sqrt(2)*(-a)^(1/8)*b^(1/8)*x + b^(1/4)*x^2))/(8*sqrt(2)*(-a)^(15/8)) - (b^(7/8)*log((-a)^(1/4) + sqrt(2)*(-a)^(1/8)*b^(1/8)*x + b^(1/4)*x^2))/(8*sqrt(2)*(-a)^(15/8))]

    @test_int [1/(a - b*x^8), x, 13, atan((b^(1/8)*x)/a^(1/8))/(4*a^(7/8)*b^(1/8)) - atan(1 - (sqrt(2)*b^(1/8)*x)/a^(1/8))/(4*sqrt(2)*a^(7/8)*b^(1/8)) + atan(1 + (sqrt(2)*b^(1/8)*x)/a^(1/8))/(4*sqrt(2)*a^(7/8)*b^(1/8)) + atanh((b^(1/8)*x)/a^(1/8))/(4*a^(7/8)*b^(1/8)) - log(a^(1/4) - sqrt(2)*a^(1/8)*b^(1/8)*x + b^(1/4)*x^2)/(8*sqrt(2)*a^(7/8)*b^(1/8)) + log(a^(1/4) + sqrt(2)*a^(1/8)*b^(1/8)*x + b^(1/4)*x^2)/(8*sqrt(2)*a^(7/8)*b^(1/8))]

    @test_int [x^9/(1 - x^8), x, 5, -(x^2/2) + atan(x^2)/4 + atanh(x^2)/4]
    @test_int [x^7/(1 - x^8), x, 1, (-(1/8))*log(1 - x^8)]
    @test_int [x^5/(1 - x^8), x, 4, (-(1/4))*atan(x^2) + atanh(x^2)/4]
    @test_int [x^3/(1 - x^8), x, 2, atanh(x^4)/4]
    @test_int [x^1/(1 - x^8), x, 4, atan(x^2)/4 + atanh(x^2)/4]
    @test_int [1/(x^1*(1 - x^8)), x, 4, log(x) - (1/8)*log(1 - x^8)]
    @test_int [1/(x^3*(1 - x^8)), x, 5, -(1/(2*x^2)) - atan(x^2)/4 + atanh(x^2)/4]
    @test_int [1/(x^5*(1 - x^8)), x, 3, -(1/(4*x^4)) + atanh(x^4)/4]
    @test_int [1/(x^7*(1 - x^8)), x, 5, -(1/(6*x^6)) + atan(x^2)/4 + atanh(x^2)/4]
    @test_int [1/(x^9*(1 - x^8)), x, 3, -(1/(8*x^8)) + log(x) - (1/8)*log(1 - x^8)]

    @test_int [x^8/(1 - x^8), x, 14, -x + atan(x)/4 - atan(1 - sqrt(2)*x)/(4*sqrt(2)) + atan(1 + sqrt(2)*x)/(4*sqrt(2)) + atanh(x)/4 - log(1 - sqrt(2)*x + x^2)/(8*sqrt(2)) + log(1 + sqrt(2)*x + x^2)/(8*sqrt(2))]
    @test_int [x^6/(1 - x^8), x, 13, -(atan(x)/4) + atan(1 - sqrt(2)*x)/(4*sqrt(2)) - atan(1 + sqrt(2)*x)/(4*sqrt(2)) + atanh(x)/4 - log(1 - sqrt(2)*x + x^2)/(8*sqrt(2)) + log(1 + sqrt(2)*x + x^2)/(8*sqrt(2))]
    @test_int [x^4/(1 - x^8), x, 13, atan(x)/4 + atan(1 - sqrt(2)*x)/(4*sqrt(2)) - atan(1 + sqrt(2)*x)/(4*sqrt(2)) + atanh(x)/4 + log(1 - sqrt(2)*x + x^2)/(8*sqrt(2)) - log(1 + sqrt(2)*x + x^2)/(8*sqrt(2))]
    @test_int [x^2/(1 - x^8), x, 13, -(atan(x)/4) - atan(1 - sqrt(2)*x)/(4*sqrt(2)) + atan(1 + sqrt(2)*x)/(4*sqrt(2)) + atanh(x)/4 + log(1 - sqrt(2)*x + x^2)/(8*sqrt(2)) - log(1 + sqrt(2)*x + x^2)/(8*sqrt(2))]
    @test_int [x^0/(1 - x^8), x, 13, atan(x)/4 - atan(1 - sqrt(2)*x)/(4*sqrt(2)) + atan(1 + sqrt(2)*x)/(4*sqrt(2)) + atanh(x)/4 - log(1 - sqrt(2)*x + x^2)/(8*sqrt(2)) + log(1 + sqrt(2)*x + x^2)/(8*sqrt(2))]
    @test_int [1/(x^2*(1 - x^8)), x, 14, -(1/x) - atan(x)/4 + atan(1 - sqrt(2)*x)/(4*sqrt(2)) - atan(1 + sqrt(2)*x)/(4*sqrt(2)) + atanh(x)/4 - log(1 - sqrt(2)*x + x^2)/(8*sqrt(2)) + log(1 + sqrt(2)*x + x^2)/(8*sqrt(2))]
    @test_int [1/(x^4*(1 - x^8)), x, 14, -(1/(3*x^3)) + atan(x)/4 + atan(1 - sqrt(2)*x)/(4*sqrt(2)) - atan(1 + sqrt(2)*x)/(4*sqrt(2)) + atanh(x)/4 + log(1 - sqrt(2)*x + x^2)/(8*sqrt(2)) - log(1 + sqrt(2)*x + x^2)/(8*sqrt(2))]
    @test_int [1/(x^6*(1 - x^8)), x, 14, -(1/(5*x^5)) - atan(x)/4 - atan(1 - sqrt(2)*x)/(4*sqrt(2)) + atan(1 + sqrt(2)*x)/(4*sqrt(2)) + atanh(x)/4 + log(1 - sqrt(2)*x + x^2)/(8*sqrt(2)) - log(1 + sqrt(2)*x + x^2)/(8*sqrt(2))]
    @test_int [1/(x^8*(1 - x^8)), x, 14, -(1/(7*x^7)) + atan(x)/4 - atan(1 - sqrt(2)*x)/(4*sqrt(2)) + atan(1 + sqrt(2)*x)/(4*sqrt(2)) + atanh(x)/4 - log(1 - sqrt(2)*x + x^2)/(8*sqrt(2)) + log(1 + sqrt(2)*x + x^2)/(8*sqrt(2))]

    @test_int [x^9/(1 + x^8), x, 11, x^2/2 + atan(1 - sqrt(2)*x^2)/(4*sqrt(2)) - atan(1 + sqrt(2)*x^2)/(4*sqrt(2)) + log(1 - sqrt(2)*x^2 + x^4)/(8*sqrt(2)) - log(1 + sqrt(2)*x^2 + x^4)/(8*sqrt(2))]
    @test_int [x^7/(1 + x^8), x, 1, (1/8)*log(1 + x^8)]
    @test_int [x^5/(1 + x^8), x, 10, -(atan(1 - sqrt(2)*x^2)/(4*sqrt(2))) + atan(1 + sqrt(2)*x^2)/(4*sqrt(2)) + log(1 - sqrt(2)*x^2 + x^4)/(8*sqrt(2)) - log(1 + sqrt(2)*x^2 + x^4)/(8*sqrt(2))]
    @test_int [x^3/(1 + x^8), x, 2, atan(x^4)/4]
    @test_int [x^1/(1 + x^8), x, 10, -(atan(1 - sqrt(2)*x^2)/(4*sqrt(2))) + atan(1 + sqrt(2)*x^2)/(4*sqrt(2)) - log(1 - sqrt(2)*x^2 + x^4)/(8*sqrt(2)) + log(1 + sqrt(2)*x^2 + x^4)/(8*sqrt(2))]
    @test_int [1/(x^1*(1 + x^8)), x, 4, log(x) - (1/8)*log(1 + x^8)]
    @test_int [1/(x^3*(1 + x^8)), x, 11, -(1/(2*x^2)) + atan(1 - sqrt(2)*x^2)/(4*sqrt(2)) - atan(1 + sqrt(2)*x^2)/(4*sqrt(2)) - log(1 - sqrt(2)*x^2 + x^4)/(8*sqrt(2)) + log(1 + sqrt(2)*x^2 + x^4)/(8*sqrt(2))]
    @test_int [1/(x^5*(1 + x^8)), x, 3, -(1/(4*x^4)) - atan(x^4)/4]
    @test_int [1/(x^7*(1 + x^8)), x, 11, -(1/(6*x^6)) + atan(1 - sqrt(2)*x^2)/(4*sqrt(2)) - atan(1 + sqrt(2)*x^2)/(4*sqrt(2)) + log(1 - sqrt(2)*x^2 + x^4)/(8*sqrt(2)) - log(1 + sqrt(2)*x^2 + x^4)/(8*sqrt(2))]
    @test_int [1/(x^9*(1 + x^8)), x, 3, -(1/(8*x^8)) - log(x) + (1/8)*log(1 + x^8)]

    @test_int [x^8/(1 + x^8), x, 20, x + atan((sqrt(2 - sqrt(2)) - 2*x)/sqrt(2 + sqrt(2)))/(4*sqrt(2*(2 - sqrt(2)))) + atan((sqrt(2 + sqrt(2)) - 2*x)/sqrt(2 - sqrt(2)))/(4*sqrt(2*(2 + sqrt(2)))) - atan((sqrt(2 - sqrt(2)) + 2*x)/sqrt(2 + sqrt(2)))/(4*sqrt(2*(2 - sqrt(2)))) - atan((sqrt(2 + sqrt(2)) + 2*x)/sqrt(2 - sqrt(2)))/(4*sqrt(2*(2 + sqrt(2)))) + (1/16)*sqrt(2 - sqrt(2))*log(1 - sqrt(2 - sqrt(2))*x + x^2) - (1/16)*sqrt(2 - sqrt(2))*log(1 + sqrt(2 - sqrt(2))*x + x^2) + (1/16)*sqrt(2 + sqrt(2))*log(1 - sqrt(2 + sqrt(2))*x + x^2) - (1/16)*sqrt(2 + sqrt(2))*log(1 + sqrt(2 + sqrt(2))*x + x^2)]
    @test_int [x^6/(1 + x^8), x, 21, -(atan((sqrt(2 - sqrt(2)) - 2*x)/sqrt(2 + sqrt(2)))/(4*sqrt(2*(2 - sqrt(2))))) - atan((sqrt(2 + sqrt(2)) - 2*x)/sqrt(2 - sqrt(2)))/(4*sqrt(2*(2 + sqrt(2)))) + atan((sqrt(2 - sqrt(2)) + 2*x)/sqrt(2 + sqrt(2)))/(4*sqrt(2*(2 - sqrt(2)))) + atan((sqrt(2 + sqrt(2)) + 2*x)/sqrt(2 - sqrt(2)))/(4*sqrt(2*(2 + sqrt(2)))) + (1/16)*sqrt(2 - sqrt(2))*log(1 - sqrt(2 - sqrt(2))*x + x^2) - (1/16)*sqrt(2 - sqrt(2))*log(1 + sqrt(2 - sqrt(2))*x + x^2) + (1/16)*sqrt(2 + sqrt(2))*log(1 - sqrt(2 + sqrt(2))*x + x^2) - (1/16)*sqrt(2 + sqrt(2))*log(1 + sqrt(2 + sqrt(2))*x + x^2)]
    @test_int [x^4/(1 + x^8), x, 19, atan((sqrt(2 - sqrt(2)) - 2*x)/sqrt(2 + sqrt(2)))/(4*sqrt(2*(2 + sqrt(2)))) - atan((sqrt(2 + sqrt(2)) - 2*x)/sqrt(2 - sqrt(2)))/(4*sqrt(2*(2 - sqrt(2)))) - atan((sqrt(2 - sqrt(2)) + 2*x)/sqrt(2 + sqrt(2)))/(4*sqrt(2*(2 + sqrt(2)))) + atan((sqrt(2 + sqrt(2)) + 2*x)/sqrt(2 - sqrt(2)))/(4*sqrt(2*(2 - sqrt(2)))) - log(1 - sqrt(2 - sqrt(2))*x + x^2)/(8*sqrt(2*(2 - sqrt(2)))) + log(1 + sqrt(2 - sqrt(2))*x + x^2)/(8*sqrt(2*(2 - sqrt(2)))) + log(1 - sqrt(2 + sqrt(2))*x + x^2)/(8*sqrt(2*(2 + sqrt(2)))) - log(1 + sqrt(2 + sqrt(2))*x + x^2)/(8*sqrt(2*(2 + sqrt(2))))]
    @test_int [x^2/(1 + x^8), x, 19, (1/8)*sqrt(2 - sqrt(2))*atan((sqrt(2 - sqrt(2)) - 2*x)/sqrt(2 + sqrt(2))) - (1/8)*sqrt(2 + sqrt(2))*atan((sqrt(2 + sqrt(2)) - 2*x)/sqrt(2 - sqrt(2))) - (1/8)*sqrt(2 - sqrt(2))*atan((sqrt(2 - sqrt(2)) + 2*x)/sqrt(2 + sqrt(2))) + (1/8)*sqrt(2 + sqrt(2))*atan((sqrt(2 + sqrt(2)) + 2*x)/sqrt(2 - sqrt(2))) + log(1 - sqrt(2 - sqrt(2))*x + x^2)/(8*sqrt(2*(2 - sqrt(2)))) - log(1 + sqrt(2 - sqrt(2))*x + x^2)/(8*sqrt(2*(2 - sqrt(2)))) - log(1 - sqrt(2 + sqrt(2))*x + x^2)/(8*sqrt(2*(2 + sqrt(2)))) + log(1 + sqrt(2 + sqrt(2))*x + x^2)/(8*sqrt(2*(2 + sqrt(2))))]
    @test_int [x^0/(1 + x^8), x, 19, -(atan((sqrt(2 - sqrt(2)) - 2*x)/sqrt(2 + sqrt(2)))/(4*sqrt(2*(2 - sqrt(2))))) - atan((sqrt(2 + sqrt(2)) - 2*x)/sqrt(2 - sqrt(2)))/(4*sqrt(2*(2 + sqrt(2)))) + atan((sqrt(2 - sqrt(2)) + 2*x)/sqrt(2 + sqrt(2)))/(4*sqrt(2*(2 - sqrt(2)))) + atan((sqrt(2 + sqrt(2)) + 2*x)/sqrt(2 - sqrt(2)))/(4*sqrt(2*(2 + sqrt(2)))) - (1/16)*sqrt(2 - sqrt(2))*log(1 - sqrt(2 - sqrt(2))*x + x^2) + (1/16)*sqrt(2 - sqrt(2))*log(1 + sqrt(2 - sqrt(2))*x + x^2) - (1/16)*sqrt(2 + sqrt(2))*log(1 - sqrt(2 + sqrt(2))*x + x^2) + (1/16)*sqrt(2 + sqrt(2))*log(1 + sqrt(2 + sqrt(2))*x + x^2)]
    @test_int [1/(x^2*(1 + x^8)), x, 22, -(1/x) + atan((sqrt(2 - sqrt(2)) - 2*x)/sqrt(2 + sqrt(2)))/(4*sqrt(2*(2 - sqrt(2)))) + atan((sqrt(2 + sqrt(2)) - 2*x)/sqrt(2 - sqrt(2)))/(4*sqrt(2*(2 + sqrt(2)))) - atan((sqrt(2 - sqrt(2)) + 2*x)/sqrt(2 + sqrt(2)))/(4*sqrt(2*(2 - sqrt(2)))) - atan((sqrt(2 + sqrt(2)) + 2*x)/sqrt(2 - sqrt(2)))/(4*sqrt(2*(2 + sqrt(2)))) - (1/16)*sqrt(2 - sqrt(2))*log(1 - sqrt(2 - sqrt(2))*x + x^2) + (1/16)*sqrt(2 - sqrt(2))*log(1 + sqrt(2 - sqrt(2))*x + x^2) - (1/16)*sqrt(2 + sqrt(2))*log(1 - sqrt(2 + sqrt(2))*x + x^2) + (1/16)*sqrt(2 + sqrt(2))*log(1 + sqrt(2 + sqrt(2))*x + x^2)]
    @test_int [1/(x^4*(1 + x^8)), x, 20, -(1/(3*x^3)) - atan((sqrt(2 - sqrt(2)) - 2*x)/sqrt(2 + sqrt(2)))/(4*sqrt(2*(2 + sqrt(2)))) + atan((sqrt(2 + sqrt(2)) - 2*x)/sqrt(2 - sqrt(2)))/(4*sqrt(2*(2 - sqrt(2)))) + atan((sqrt(2 - sqrt(2)) + 2*x)/sqrt(2 + sqrt(2)))/(4*sqrt(2*(2 + sqrt(2)))) - atan((sqrt(2 + sqrt(2)) + 2*x)/sqrt(2 - sqrt(2)))/(4*sqrt(2*(2 - sqrt(2)))) + log(1 - sqrt(2 - sqrt(2))*x + x^2)/(8*sqrt(2*(2 - sqrt(2)))) - log(1 + sqrt(2 - sqrt(2))*x + x^2)/(8*sqrt(2*(2 - sqrt(2)))) - log(1 - sqrt(2 + sqrt(2))*x + x^2)/(8*sqrt(2*(2 + sqrt(2)))) + log(1 + sqrt(2 + sqrt(2))*x + x^2)/(8*sqrt(2*(2 + sqrt(2))))]
    @test_int [1/(x^6*(1 + x^8)), x, 20, -(1/(5*x^5)) - (1/8)*sqrt(2 - sqrt(2))*atan((sqrt(2 - sqrt(2)) - 2*x)/sqrt(2 + sqrt(2))) + (1/8)*sqrt(2 + sqrt(2))*atan((sqrt(2 + sqrt(2)) - 2*x)/sqrt(2 - sqrt(2))) + (1/8)*sqrt(2 - sqrt(2))*atan((sqrt(2 - sqrt(2)) + 2*x)/sqrt(2 + sqrt(2))) - (1/8)*sqrt(2 + sqrt(2))*atan((sqrt(2 + sqrt(2)) + 2*x)/sqrt(2 - sqrt(2))) - log(1 - sqrt(2 - sqrt(2))*x + x^2)/(8*sqrt(2*(2 - sqrt(2)))) + log(1 + sqrt(2 - sqrt(2))*x + x^2)/(8*sqrt(2*(2 - sqrt(2)))) + log(1 - sqrt(2 + sqrt(2))*x + x^2)/(8*sqrt(2*(2 + sqrt(2)))) - log(1 + sqrt(2 + sqrt(2))*x + x^2)/(8*sqrt(2*(2 + sqrt(2))))]
    @test_int [1/(x^8*(1 + x^8)), x, 20, -(1/(7*x^7)) + atan((sqrt(2 - sqrt(2)) - 2*x)/sqrt(2 + sqrt(2)))/(4*sqrt(2*(2 - sqrt(2)))) + atan((sqrt(2 + sqrt(2)) - 2*x)/sqrt(2 - sqrt(2)))/(4*sqrt(2*(2 + sqrt(2)))) - atan((sqrt(2 - sqrt(2)) + 2*x)/sqrt(2 + sqrt(2)))/(4*sqrt(2*(2 - sqrt(2)))) - atan((sqrt(2 + sqrt(2)) + 2*x)/sqrt(2 - sqrt(2)))/(4*sqrt(2*(2 + sqrt(2)))) + (1/16)*sqrt(2 - sqrt(2))*log(1 - sqrt(2 - sqrt(2))*x + x^2) - (1/16)*sqrt(2 - sqrt(2))*log(1 + sqrt(2 - sqrt(2))*x + x^2) + (1/16)*sqrt(2 + sqrt(2))*log(1 - sqrt(2 + sqrt(2))*x + x^2) - (1/16)*sqrt(2 + sqrt(2))*log(1 + sqrt(2 + sqrt(2))*x + x^2)]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^(m/2)*(a+b*x^8)^p=#

    #= ::Subsubsection:: =#
    #=p>0=#

    #= ::Subsubsection:: =#
    #=p<0=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b*x^8)^(p/2)=#

    #= ::Subsubsection::Closed:: =#
    #=p>0=#

    @test_int [x^3*sqrt(1 + x^8), x, 3, (1/8)*x^4*sqrt(1 + x^8) + asinh(x^4)/8]
    @test_int [x^1*sqrt(1 + x^8), x, 3, (1/6)*x^2*sqrt(1 + x^8) + ((1 + x^4)*sqrt((1 + x^8)/(1 + x^4)^2)*Elliptic.F(2*atan(x^2), 1/2))/(6*sqrt(1 + x^8))]
    @test_int [sqrt(1 + x^8)/x^1, x, 4, sqrt(1 + x^8)/4 - (1/4)*atanh(sqrt(1 + x^8))]
    @test_int [sqrt(1 + x^8)/x^3, x, 5, -(sqrt(1 + x^8)/(2*x^2)) + (x^2*sqrt(1 + x^8))/(1 + x^4) - ((1 + x^4)*sqrt((1 + x^8)/(1 + x^4)^2)*Elliptic.E(2*atan(x^2), 1/2))/sqrt(1 + x^8) + ((1 + x^4)*sqrt((1 + x^8)/(1 + x^4)^2)*Elliptic.F(2*atan(x^2), 1/2))/(2*sqrt(1 + x^8))]

    @test_int [x^3*sqrt(-2 + x^8), x, 4, (1/8)*x^4*sqrt(-2 + x^8) - (1/4)*atanh(x^4/sqrt(-2 + x^8))]

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [x^19/sqrt(1 + x^8), x, 4, (-(3/32))*x^4*sqrt(1 + x^8) + (1/16)*x^12*sqrt(1 + x^8) + (3*asinh(x^4))/32]
    @test_int [x^15/sqrt(1 + x^8), x, 3, (-(1/4))*sqrt(1 + x^8) + (1/12)*(1 + x^8)^(3/2)]
    @test_int [x^11/sqrt(1 + x^8), x, 3, (1/8)*x^4*sqrt(1 + x^8) - asinh(x^4)/8]
    @test_int [x^7/sqrt(1 + x^8), x, 1, sqrt(1 + x^8)/4]
    @test_int [x^3/sqrt(1 + x^8), x, 2, asinh(x^4)/4]
    @test_int [1/(x^1*sqrt(1 + x^8)), x, 3, -atanh(sqrt(1 + x^8))/4]
    @test_int [1/(x^5*sqrt(1 + x^8)), x, 1, -(sqrt(1 + x^8)/(4*x^4))]
    @test_int [1/(x^9*sqrt(1 + x^8)), x, 4, -(sqrt(1 + x^8)/(8*x^8)) + (1/8)*atanh(sqrt(1 + x^8))]
    @test_int [1/(x^13*sqrt(1 + x^8)), x, 2, -(sqrt(1 + x^8)/(12*x^12)) + sqrt(1 + x^8)/(6*x^4)]
    @test_int [1/(x^17*sqrt(1 + x^8)), x, 5, -(sqrt(1 + x^8)/(16*x^16)) + (3*sqrt(1 + x^8))/(32*x^8) - (3/32)*atanh(sqrt(1 + x^8))]

    @test_int [x^13/sqrt(1 + x^8), x, 5, (1/10)*x^6*sqrt(1 + x^8) - (3*x^2*sqrt(1 + x^8))/(10*(1 + x^4)) + (3*(1 + x^4)*sqrt((1 + x^8)/(1 + x^4)^2)*Elliptic.E(2*atan(x^2), 1/2))/(10*sqrt(1 + x^8)) - (3*(1 + x^4)*sqrt((1 + x^8)/(1 + x^4)^2)*Elliptic.F(2*atan(x^2), 1/2))/(20*sqrt(1 + x^8))]
    @test_int [x^9/sqrt(1 + x^8), x, 3, (1/6)*x^2*sqrt(1 + x^8) - ((1 + x^4)*sqrt((1 + x^8)/(1 + x^4)^2)*Elliptic.F(2*atan(x^2), 1/2))/(12*sqrt(1 + x^8))]
    @test_int [x^5/sqrt(1 + x^8), x, 4, (x^2*sqrt(1 + x^8))/(2*(1 + x^4)) - ((1 + x^4)*sqrt((1 + x^8)/(1 + x^4)^2)*Elliptic.E(2*atan(x^2), 1/2))/(2*sqrt(1 + x^8)) + ((1 + x^4)*sqrt((1 + x^8)/(1 + x^4)^2)*Elliptic.F(2*atan(x^2), 1/2))/(4*sqrt(1 + x^8))]
    @test_int [x^1/sqrt(1 + x^8), x, 2, ((1 + x^4)*sqrt((1 + x^8)/(1 + x^4)^2)*Elliptic.F(2*atan(x^2), 1/2))/(4*sqrt(1 + x^8))]
    @test_int [1/(x^3*sqrt(1 + x^8)), x, 5, -(sqrt(1 + x^8)/(2*x^2)) + (x^2*sqrt(1 + x^8))/(2*(1 + x^4)) - ((1 + x^4)*sqrt((1 + x^8)/(1 + x^4)^2)*Elliptic.E(2*atan(x^2), 1/2))/(2*sqrt(1 + x^8)) + ((1 + x^4)*sqrt((1 + x^8)/(1 + x^4)^2)*Elliptic.F(2*atan(x^2), 1/2))/(4*sqrt(1 + x^8))]
    @test_int [1/(x^7*sqrt(1 + x^8)), x, 3, -(sqrt(1 + x^8)/(6*x^6)) - ((1 + x^4)*sqrt((1 + x^8)/(1 + x^4)^2)*Elliptic.F(2*atan(x^2), 1/2))/(12*sqrt(1 + x^8))]

    @test_int [x^10/sqrt(1 + x^8), x, 4, (1/7)*x^3*sqrt(1 + x^8) + (3*x^3*sqrt((1 + x^2)^2/x^2)*sqrt(-((1 + x^8)/x^4))*Elliptic.F(asin((1/2)*sqrt(-((sqrt(2) - 2*x^2 + sqrt(2)*x^4)/x^2))), -2*(1 - sqrt(2))))/(14*sqrt(2 + sqrt(2))*(1 + x^2)*sqrt(1 + x^8)) + (3*x^3*sqrt(-((1 - x^2)^2/x^2))*sqrt(-((1 + x^8)/x^4))*Elliptic.F(asin((1/2)*sqrt((sqrt(2) + 2*x^2 + sqrt(2)*x^4)/x^2)), -2*(1 - sqrt(2))))/(14*sqrt(2 + sqrt(2))*(1 - x^2)*sqrt(1 + x^8))]
    @test_int [x^8/sqrt(1 + x^8), x, 4, (1/5)*x*sqrt(1 + x^8) - (x^3*sqrt((1 + x^2)^2/x^2)*sqrt(-((1 + x^8)/x^4))*Elliptic.F(asin((1/2)*sqrt(-((sqrt(2) - 2*x^2 + sqrt(2)*x^4)/x^2))), -2*(1 - sqrt(2))))/(10*sqrt(2 + sqrt(2))*(1 + x^2)*sqrt(1 + x^8)) + (x^3*sqrt(-((1 - x^2)^2/x^2))*sqrt(-((1 + x^8)/x^4))*Elliptic.F(asin((1/2)*sqrt((sqrt(2) + 2*x^2 + sqrt(2)*x^4)/x^2)), -2*(1 - sqrt(2))))/(10*sqrt(2 + sqrt(2))*(1 - x^2)*sqrt(1 + x^8))]
    @test_int [x^6/sqrt(1 + x^8), x, 1, (1/7)*x^7*HypergeometricFunctions._₂F₁(1/2, 7/8, 15/8, -x^8)]
    @test_int [x^4/sqrt(1 + x^8), x, 1, (1/5)*x^5*HypergeometricFunctions._₂F₁(1/2, 5/8, 13/8, -x^8)]
    @test_int [x^2/sqrt(1 + x^8), x, 3, -((x^3*sqrt((1 + x^2)^2/x^2)*sqrt(-((1 + x^8)/x^4))*Elliptic.F(asin((1/2)*sqrt(-((sqrt(2) - 2*x^2 + sqrt(2)*x^4)/x^2))), -2*(1 - sqrt(2))))/(2*sqrt(2 + sqrt(2))*(1 + x^2)*sqrt(1 + x^8))) - (x^3*sqrt(-((1 - x^2)^2/x^2))*sqrt(-((1 + x^8)/x^4))*Elliptic.F(asin((1/2)*sqrt((sqrt(2) + 2*x^2 + sqrt(2)*x^4)/x^2)), -2*(1 - sqrt(2))))/(2*sqrt(2 + sqrt(2))*(1 - x^2)*sqrt(1 + x^8))]
    @test_int [x^0/sqrt(1 + x^8), x, 3, (x^3*sqrt((1 + x^2)^2/x^2)*sqrt(-((1 + x^8)/x^4))*Elliptic.F(asin((1/2)*sqrt(-((sqrt(2) - 2*x^2 + sqrt(2)*x^4)/x^2))), -2*(1 - sqrt(2))))/(2*sqrt(2 + sqrt(2))*(1 + x^2)*sqrt(1 + x^8)) - (x^3*sqrt(-((1 - x^2)^2/x^2))*sqrt(-((1 + x^8)/x^4))*Elliptic.F(asin((1/2)*sqrt((sqrt(2) + 2*x^2 + sqrt(2)*x^4)/x^2)), -2*(1 - sqrt(2))))/(2*sqrt(2 + sqrt(2))*(1 - x^2)*sqrt(1 + x^8))]
    @test_int [1/(x^2*sqrt(1 + x^8)), x, 2, -(sqrt(1 + x^8)/x) + (3/7)*x^7*HypergeometricFunctions._₂F₁(1/2, 7/8, 15/8, -x^8)]
    @test_int [1/(x^4*sqrt(1 + x^8)), x, 2, -(sqrt(1 + x^8)/(3*x^3)) + (1/15)*x^5*HypergeometricFunctions._₂F₁(1/2, 5/8, 13/8, -x^8)]
    @test_int [1/(x^6*sqrt(1 + x^8)), x, 4, -(sqrt(1 + x^8)/(5*x^5)) + (x^3*sqrt((1 + x^2)^2/x^2)*sqrt(-((1 + x^8)/x^4))*Elliptic.F(asin((1/2)*sqrt(-((sqrt(2) - 2*x^2 + sqrt(2)*x^4)/x^2))), -2*(1 - sqrt(2))))/(10*sqrt(2 + sqrt(2))*(1 + x^2)*sqrt(1 + x^8)) + (x^3*sqrt(-((1 - x^2)^2/x^2))*sqrt(-((1 + x^8)/x^4))*Elliptic.F(asin((1/2)*sqrt((sqrt(2) + 2*x^2 + sqrt(2)*x^4)/x^2)), -2*(1 - sqrt(2))))/(10*sqrt(2 + sqrt(2))*(1 - x^2)*sqrt(1 + x^8))]
    @test_int [1/(x^8*sqrt(1 + x^8)), x, 4, -(sqrt(1 + x^8)/(7*x^7)) - (3*x^3*sqrt((1 + x^2)^2/x^2)*sqrt(-((1 + x^8)/x^4))*Elliptic.F(asin((1/2)*sqrt(-((sqrt(2) - 2*x^2 + sqrt(2)*x^4)/x^2))), -2*(1 - sqrt(2))))/(14*sqrt(2 + sqrt(2))*(1 + x^2)*sqrt(1 + x^8)) + (3*x^3*sqrt(-((1 - x^2)^2/x^2))*sqrt(-((1 + x^8)/x^4))*Elliptic.F(asin((1/2)*sqrt((sqrt(2) + 2*x^2 + sqrt(2)*x^4)/x^2)), -2*(1 - sqrt(2))))/(14*sqrt(2 + sqrt(2))*(1 - x^2)*sqrt(1 + x^8))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^(m/2)*(a+b*x^8)^(p/2)=#

    #= ::Subsubsection:: =#
    #=p>0=#

    #= ::Subsubsection:: =#
    #=p<0=#

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(c*x)^m*(a+b*x^10)^p=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b*x^10)^p=#

    #= ::Subsubsection:: =#
    #=p>0=#

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [1/(1 - x^10), x, 10, (1/20)*sqrt(10 - 2*sqrt(5))*atan((sqrt(10 - 2*sqrt(5))*x)/(2*(1 - x^2))) + (1/20)*sqrt(10 + 2*sqrt(5))*atan((sqrt(10 + 2*sqrt(5))*x)/(2*(1 - x^2))) + atanh(x)/5 + (1/20)*(1 - sqrt(5))*atanh(((1 - sqrt(5))*x)/(2*(1 + x^2))) + (1/20)*(1 + sqrt(5))*atanh(((1 + sqrt(5))*x)/(2*(1 + x^2))), (-(1/10))*sqrt((1/2)*(5 + sqrt(5)))*atan((1 - sqrt(5) - 4*x)/sqrt(2*(5 + sqrt(5)))) - (1/10)*sqrt((1/2)*(5 - sqrt(5)))*atan((1/2)*sqrt((1/10)*(5 + sqrt(5)))*(1 + sqrt(5) - 4*x)) + (1/10)*sqrt((1/2)*(5 + sqrt(5)))*atan((1 - sqrt(5) + 4*x)/sqrt(2*(5 + sqrt(5)))) + (1/10)*sqrt((1/2)*(5 - sqrt(5)))*atan((1/2)*sqrt((1/10)*(5 + sqrt(5)))*(1 + sqrt(5) + 4*x)) + atanh(x)/5 - (1/40)*(1 - sqrt(5))*log(1 - (1/2)*(1 - sqrt(5))*x + x^2) + (1/40)*(1 - sqrt(5))*log(1 + (1/2)*(1 - sqrt(5))*x + x^2) - (1/40)*(1 + sqrt(5))*log(1 - (1/2)*(1 + sqrt(5))*x + x^2) + (1/40)*(1 + sqrt(5))*log(1 + (1/2)*(1 + sqrt(5))*x + x^2)]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^(m/2)*(a+b*x^10)^p=#

    #= ::Subsubsection:: =#
    #=p>0=#

    #= ::Subsubsection:: =#
    #=p<0=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b*x^10)^(p/2)=#

    #= ::Subsubsection:: =#
    #=p>0=#

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [x^4/sqrt(1 - x^10), x, 2, asin(x^5)/5]
    @test_int [x^4/sqrt(-2 + x^10), x, 3, (1/5)*atanh(x^5/sqrt(-2 + x^10))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^(m/2)*(a+b*x^10)^(p/2)=#

    #= ::Subsubsection:: =#
    #=p>0=#

    #= ::Subsubsection:: =#
    #=p<0=#

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(c*x)^m*(a+b*x^12)^p=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b*x^12)^p=#

    #= ::Subsubsection:: =#
    #=p>0=#

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [x^5/(9 + x^12), x, 2, atan(x^6/3)/18]
    @test_int [x^5/(9 - x^12), x, 2, atanh(x^6/3)/18]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^(m/2)*(a+b*x^12)^p=#

    #= ::Subsubsection:: =#
    #=p>0=#

    #= ::Subsubsection:: =#
    #=p<0=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b*x^12)^(p/2)=#

    #= ::Subsubsection::Closed:: =#
    #=p>0=#

    @test_int [x^5*sqrt(9 + x^12), x, 3, (1/12)*x^6*sqrt(9 + x^12) + (3/4)*asinh(x^6/3)]

    #= ::Subsubsection:: =#
    #=p<0=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^(m/2)*(a+b*x^12)^(p/2)=#

    #= ::Subsubsection:: =#
    #=p>0=#

    #= ::Subsubsection:: =#
    #=p<0=#

    #= ::Title::Closed:: =#
    #=Integrands*of*the*form*(c*x)^m*(a+b*x^n)^p*when*n<0*is*an*integer=#

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(c*x)^m*(a+b/x)^p=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b/x)^p=#

    #= ::Subsubsection::Closed:: =#
    #=p>0=#

    @test_int [(a + b/x)*x^6, x, 2, (b*x^6)/6 + (a*x^7)/7]
    @test_int [(a + b/x)*x^5, x, 2, (b*x^5)/5 + (a*x^6)/6]
    @test_int [(a + b/x)*x^4, x, 2, (b*x^4)/4 + (a*x^5)/5]
    @test_int [(a + b/x)*x^3, x, 2, (b*x^3)/3 + (a*x^4)/4]
    @test_int [(a + b/x)*x^2, x, 2, (b*x^2)/2 + (a*x^3)/3]
    @test_int [(a + b/x)*x, x, 2, b*x + (a*x^2)/2]
    @test_int [a + b/x, x, 1, a*x + b*log(x)]
    @test_int [(a + b/x)/x, x, 2, -(b/x) + a*log(x)]
    @test_int [(a + b/x)/x^2, x, 2, -(b/(2*x^2)) - a/x]
    @test_int [(a + b/x)/x^3, x, 2, -b/(3*x^3) - a/(2*x^2)]
    @test_int [(a + b/x)/x^4, x, 2, -b/(4*x^4) - a/(3*x^3)]
    @test_int [(a + b/x)/x^5, x, 2, -b/(5*x^5) - a/(4*x^4)]
    @test_int [(a + b/x)/x^6, x, 2, -b/(6*x^6) - a/(5*x^5)]

    @test_int [(a + b/x)^2*x^5, x, 3, (b^2*x^4)/4 + (2*a*b*x^5)/5 + (a^2*x^6)/6]
    @test_int [(a + b/x)^2*x^4, x, 3, (b^2*x^3)/3 + (a*b*x^4)/2 + (a^2*x^5)/5]
    @test_int [(a + b/x)^2*x^3, x, 3, (b^2*x^2)/2 + (2/3)*a*b*x^3 + (a^2*x^4)/4]
    @test_int [(a + b/x)^2*x^2, x, 2, (b + a*x)^3/(3*a)]
    @test_int [(a + b/x)^2*x, x, 3, 2*a*b*x + (a^2*x^2)/2 + b^2*log(x)]
    @test_int [(a + b/x)^2, x, 3, -(b^2/x) + a^2*x + 2*a*b*log(x)]
    @test_int [(a + b/x)^2/x, x, 3, -b^2/(2*x^2) - (2*a*b)/x + a^2*log(x)]
    @test_int [(a + b/x)^2/x^2, x, 1, -(a + b/x)^3/(3*b)]
    @test_int [(a + b/x)^2/x^3, x, 3, -b^2/(4*x^4) - (2*a*b)/(3*x^3) - a^2/(2*x^2)]
    @test_int [(a + b/x)^2/x^4, x, 3, -b^2/(5*x^5) - (a*b)/(2*x^4) - a^2/(3*x^3)]
    @test_int [(a + b/x)^2/x^5, x, 3, -b^2/(6*x^6) - (2*a*b)/(5*x^5) - a^2/(4*x^4)]

    @test_int [(a + b/x)^3*x^6, x, 3, (b^3*x^4)/4 + (3*a*b^2*x^5)/5 + (a^2*b*x^6)/2 + (a^3*x^7)/7]
    @test_int [(a + b/x)^3*x^5, x, 3, (b^3*x^3)/3 + (3/4)*a*b^2*x^4 + (3/5)*a^2*b*x^5 + (a^3*x^6)/6]
    @test_int [(a + b/x)^3*x^4, x, 3, -(b*(b + a*x)^4)/(4*a^2) + (b + a*x)^5/(5*a^2)]
    @test_int [(a + b/x)^3*x^3, x, 2, (b + a*x)^4/(4*a)]
    @test_int [(a + b/x)^3*x^2, x, 3, 3*a*b^2*x + (3*a^2*b*x^2)/2 + (a^3*x^3)/3 + b^3*log(x)]
    @test_int [(a + b/x)^3*x, x, 3, -(b^3/x) + 3*a^2*b*x + (a^3*x^2)/2 + 3*a*b^2*log(x)]
    @test_int [(a + b/x)^3, x, 3, -b^3/(2*x^2) - (3*a*b^2)/x + a^3*x + 3*a^2*b*log(x)]
    @test_int [(a + b/x)^3/x, x, 3, -b^3/(3*x^3) - (3*a*b^2)/(2*x^2) - (3*a^2*b)/x + a^3*log(x)]
    @test_int [(a + b/x)^3/x^2, x, 1, -(a + b/x)^4/(4*b)]
    @test_int [(a + b/x)^3/x^3, x, 3, -((b + a*x)^4/(5*b*x^5)) + (a*(b + a*x)^4)/(20*b^2*x^4)]
    @test_int [(a + b/x)^3/x^4, x, 3, -b^3/(6*x^6) - (3*a*b^2)/(5*x^5) - (3*a^2*b)/(4*x^4) - a^3/(3*x^3)]
    @test_int [(a + b/x)^3/x^5, x, 3, -b^3/(7*x^7) - (a*b^2)/(2*x^6) - (3*a^2*b)/(5*x^5) - a^3/(4*x^4)]
    @test_int [(a + b/x)^3/x^6, x, 3, -b^3/(8*x^8) - (3*a*b^2)/(7*x^7) - (a^2*b)/(2*x^6) - a^3/(5*x^5)]

    @test_int [(a + b/x)^8*x^16, x, 3, (b^8*x^9)/9 + (4/5)*a*b^7*x^10 + (28/11)*a^2*b^6*x^11 + (14/3)*a^3*b^5*x^12 + (70/13)*a^4*b^4*x^13 + 4*a^5*b^3*x^14 + (28/15)*a^6*b^2*x^15 + (1/2)*a^7*b*x^16 + (a^8*x^17)/17]
    @test_int [(a + b/x)^8*x^15, x, 3, (b^8*x^8)/8 + (8/9)*a*b^7*x^9 + (14/5)*a^2*b^6*x^10 + (56/11)*a^3*b^5*x^11 + (35/6)*a^4*b^4*x^12 + (56/13)*a^5*b^3*x^13 + 2*a^6*b^2*x^14 + (8/15)*a^7*b*x^15 + (a^8*x^16)/16]
    @test_int [(a + b/x)^8*x^13, x, 3, -((b^5*(b + a*x)^9)/(9*a^6)) + (b^4*(b + a*x)^10)/(2*a^6) - (10*b^3*(b + a*x)^11)/(11*a^6) + (5*b^2*(b + a*x)^12)/(6*a^6) - (5*b*(b + a*x)^13)/(13*a^6) + (b + a*x)^14/(14*a^6)]
    @test_int [(a + b/x)^8*x^12, x, 3, (b^4*(b + a*x)^9)/(9*a^5) - (2*b^3*(b + a*x)^10)/(5*a^5) + (6*b^2*(b + a*x)^11)/(11*a^5) - (b*(b + a*x)^12)/(3*a^5) + (b + a*x)^13/(13*a^5)]
    @test_int [(a + b/x)^8*x^11, x, 3, -((b^3*(b + a*x)^9)/(9*a^4)) + (3*b^2*(b + a*x)^10)/(10*a^4) - (3*b*(b + a*x)^11)/(11*a^4) + (b + a*x)^12/(12*a^4)]
    @test_int [(a + b/x)^8*x^10, x, 3, (b^2*(b + a*x)^9)/(9*a^3) - (b*(b + a*x)^10)/(5*a^3) + (b + a*x)^11/(11*a^3)]
    @test_int [(a + b/x)^8*x^9, x, 3, -((b*(b + a*x)^9)/(9*a^2)) + (b + a*x)^10/(10*a^2)]
    @test_int [(a + b/x)^8*x^8, x, 2, (b + a*x)^9/(9*a)]
    @test_int [(a + b/x)^8*x^7, x, 3, 8*a*b^7*x + 14*a^2*b^6*x^2 + (56/3)*a^3*b^5*x^3 + (35/2)*a^4*b^4*x^4 + (56/5)*a^5*b^3*x^5 + (14/3)*a^6*b^2*x^6 + (8/7)*a^7*b*x^7 + (a^8*x^8)/8 + b^8*log(x)]
    @test_int [(a + b/x)^8*x^6, x, 3, -(b^8/x) + 28*a^2*b^6*x + 28*a^3*b^5*x^2 + (70/3)*a^4*b^4*x^3 + 14*a^5*b^3*x^4 + (28/5)*a^6*b^2*x^5 + (4/3)*a^7*b*x^6 + (a^8*x^7)/7 + 8*a*b^7*log(x)]
    @test_int [(a + b/x)^8*x^5, x, 3, -(b^8/(2*x^2)) - (8*a*b^7)/x + 56*a^3*b^5*x + 35*a^4*b^4*x^2 + (56/3)*a^5*b^3*x^3 + 7*a^6*b^2*x^4 + (8/5)*a^7*b*x^5 + (a^8*x^6)/6 + 28*a^2*b^6*log(x)]
    @test_int [(a + b/x)^8*x^4, x, 3, -(b^8/(3*x^3)) - (4*a*b^7)/x^2 - (28*a^2*b^6)/x + 70*a^4*b^4*x + 28*a^5*b^3*x^2 + (28/3)*a^6*b^2*x^3 + 2*a^7*b*x^4 + (a^8*x^5)/5 + 56*a^3*b^5*log(x)]
    @test_int [(a + b/x)^8*x^3, x, 3, -(b^8/(4*x^4)) - (8*a*b^7)/(3*x^3) - (14*a^2*b^6)/x^2 - (56*a^3*b^5)/x + 56*a^5*b^3*x + 14*a^6*b^2*x^2 + (8/3)*a^7*b*x^3 + (a^8*x^4)/4 + 70*a^4*b^4*log(x)]
    @test_int [(a + b/x)^8*x^2, x, 3, -(b^8/(5*x^5)) - (2*a*b^7)/x^4 - (28*a^2*b^6)/(3*x^3) - (28*a^3*b^5)/x^2 - (70*a^4*b^4)/x + 28*a^6*b^2*x + 4*a^7*b*x^2 + (a^8*x^3)/3 + 56*a^5*b^3*log(x)]
    @test_int [(a + b/x)^8*x^1, x, 3, -(b^8/(6*x^6)) - (8*a*b^7)/(5*x^5) - (7*a^2*b^6)/x^4 - (56*a^3*b^5)/(3*x^3) - (35*a^4*b^4)/x^2 - (56*a^5*b^3)/x + 8*a^7*b*x + (a^8*x^2)/2 + 28*a^6*b^2*log(x)]
    @test_int [(a + b/x)^8*x^0, x, 3, -(b^8/(7*x^7)) - (4*a*b^7)/(3*x^6) - (28*a^2*b^6)/(5*x^5) - (14*a^3*b^5)/x^4 - (70*a^4*b^4)/(3*x^3) - (28*a^5*b^3)/x^2 - (28*a^6*b^2)/x + a^8*x + 8*a^7*b*log(x)]
    @test_int [(a + b/x)^8/x^1, x, 3, -(b^8/(8*x^8)) - (8*a*b^7)/(7*x^7) - (14*a^2*b^6)/(3*x^6) - (56*a^3*b^5)/(5*x^5) - (35*a^4*b^4)/(2*x^4) - (56*a^5*b^3)/(3*x^3) - (14*a^6*b^2)/x^2 - (8*a^7*b)/x + a^8*log(x)]
    @test_int [(a + b/x)^8/x^2, x, 1, -((a + b/x)^9/(9*b))]
    @test_int [(a + b/x)^8/x^3, x, 3, -((b + a*x)^9/(10*b*x^10)) + (a*(b + a*x)^9)/(90*b^2*x^9)]
    @test_int [(a + b/x)^8/x^4, x, 4, -((b + a*x)^9/(11*b*x^11)) + (a*(b + a*x)^9)/(55*b^2*x^10) - (a^2*(b + a*x)^9)/(495*b^3*x^9)]
    @test_int [(a + b/x)^8/x^5, x, 5, -((b + a*x)^9/(12*b*x^12)) + (a*(b + a*x)^9)/(44*b^2*x^11) - (a^2*(b + a*x)^9)/(220*b^3*x^10) + (a^3*(b + a*x)^9)/(1980*b^4*x^9)]
    @test_int [(a + b/x)^8/x^6, x, 6, -((b + a*x)^9/(13*b*x^13)) + (a*(b + a*x)^9)/(39*b^2*x^12) - (a^2*(b + a*x)^9)/(143*b^3*x^11) + (a^3*(b + a*x)^9)/(715*b^4*x^10) - (a^4*(b + a*x)^9)/(6435*b^5*x^9)]
    @test_int [(a + b/x)^8/x^7, x, 3, -(b^8/(14*x^14)) - (8*a*b^7)/(13*x^13) - (7*a^2*b^6)/(3*x^12) - (56*a^3*b^5)/(11*x^11) - (7*a^4*b^4)/x^10 - (56*a^5*b^3)/(9*x^9) - (7*a^6*b^2)/(2*x^8) - (8*a^7*b)/(7*x^7) - a^8/(6*x^6)]
    @test_int [(a + b/x)^8/x^8, x, 3, -(b^8/(15*x^15)) - (4*a*b^7)/(7*x^14) - (28*a^2*b^6)/(13*x^13) - (14*a^3*b^5)/(3*x^12) - (70*a^4*b^4)/(11*x^11) - (28*a^5*b^3)/(5*x^10) - (28*a^6*b^2)/(9*x^9) - (a^7*b)/x^8 - a^8/(7*x^7)]

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [x^4/(a + b/x), x, 3, (b^4*x)/a^5 - (b^3*x^2)/(2*a^4) + (b^2*x^3)/(3*a^3) - (b*x^4)/(4*a^2) + x^5/(5*a) - (b^5*log(b + a*x))/a^6]
    @test_int [x^3/(a + b/x), x, 3, -((b^3*x)/a^4) + (b^2*x^2)/(2*a^3) - (b*x^3)/(3*a^2) + x^4/(4*a) + (b^4*log(b + a*x))/a^5]
    @test_int [x^2/(a + b/x), x, 3, (b^2*x)/a^3 - (b*x^2)/(2*a^2) + x^3/(3*a) - (b^3*log(b + a*x))/a^4]
    @test_int [x/(a + b/x), x, 3, -((b*x)/a^2) + x^2/(2*a) + (b^2*log(b + a*x))/a^3]
    @test_int [1/(a + b/x), x, 3, x/a - (b*log(b + a*x))/a^2]
    @test_int [1/((a + b/x)*x), x, 2, log(b + a*x)/a]
    @test_int [1/((a + b/x)*x^2), x, 1, -(log(a + b/x)/b)]
    @test_int [1/((a + b/x)*x^3), x, 3, -(1/(b*x)) - (a*log(x))/b^2 + (a*log(b + a*x))/b^2]
    @test_int [1/((a + b/x)*x^4), x, 3, -(1/(2*b*x^2)) + a/(b^2*x) + (a^2*log(x))/b^3 - (a^2*log(b + a*x))/b^3]
    @test_int [1/((a + b/x)*x^5), x, 3, -(1/(3*b*x^3)) + a/(2*b^2*x^2) - a^2/(b^3*x) - (a^3*log(x))/b^4 + (a^3*log(b + a*x))/b^4]
    @test_int [1/((a + b/x)*x^6), x, 3, -(1/(4*b*x^4)) + a/(3*b^2*x^3) - a^2/(2*b^3*x^2) + a^3/(b^4*x) + (a^4*log(x))/b^5 - (a^4*log(b + a*x))/b^5]
    @test_int [1/((a + b/x)*x^7), x, 3, -(1/(5*b*x^5)) + a/(4*b^2*x^4) - a^2/(3*b^3*x^3) + a^3/(2*b^4*x^2) - a^4/(b^5*x) - (a^5*log(x))/b^6 + (a^5*log(b + a*x))/b^6]

    @test_int [x^5/(a + b/x)^2, x, 3, (-6*b^5*x)/a^7 + (5*b^4*x^2)/(2*a^6) - (4*b^3*x^3)/(3*a^5) + (3*b^2*x^4)/(4*a^4) - (2*b*x^5)/(5*a^3) + x^6/(6*a^2) + b^7/(a^8*(b + a*x)) + (7*b^6*log(b + a*x))/a^8]
    @test_int [x^4/(a + b/x)^2, x, 3, (5*b^4*x)/a^6 - (2*b^3*x^2)/a^5 + (b^2*x^3)/a^4 - (b*x^4)/(2*a^3) + x^5/(5*a^2) - b^6/(a^7*(b + a*x)) - (6*b^5*log(b + a*x))/a^7]
    @test_int [x^3/(a + b/x)^2, x, 3, (-4*b^3*x)/a^5 + (3*b^2*x^2)/(2*a^4) - (2*b*x^3)/(3*a^3) + x^4/(4*a^2) + b^5/(a^6*(b + a*x)) + (5*b^4*log(b + a*x))/a^6]
    @test_int [x^2/(a + b/x)^2, x, 3, (3*b^2*x)/a^4 - (b*x^2)/a^3 + x^3/(3*a^2) - b^4/(a^5*(b + a*x)) - (4*b^3*log(b + a*x))/a^5]
    @test_int [x/(a + b/x)^2, x, 3, (-2*b*x)/a^3 + x^2/(2*a^2) + b^3/(a^4*(b + a*x)) + (3*b^2*log(b + a*x))/a^4]
    @test_int [1/(a + b/x)^2, x, 4, (2*x)/a^2 - x/(a*(a + b/x)) - (2*b*log(b + a*x))/a^3]
    @test_int [1/((a + b/x)^2*x), x, 3, b/(a^2*(b + a*x)) + log(b + a*x)/a^2]
    @test_int [1/((a + b/x)^2*x^2), x, 1, 1/(b*(a + b/x))]
    @test_int [1/((a + b/x)^2*x^3), x, 3, 1/(b*(b + a*x)) + log(x)/b^2 - log(b + a*x)/b^2]
    @test_int [1/((a + b/x)^2*x^4), x, 3, -(1/(b^2*x)) - a/(b^2*(b + a*x)) - (2*a*log(x))/b^3 + (2*a*log(b + a*x))/b^3]
    @test_int [1/((a + b/x)^2*x^5), x, 3, -(1/(2*b^2*x^2)) + (2*a)/(b^3*x) + a^2/(b^3*(b + a*x)) + (3*a^2*log(x))/b^4 - (3*a^2*log(b + a*x))/b^4]
    @test_int [1/((a + b/x)^2*x^6), x, 3, -(1/(3*b^2*x^3)) + a/(b^3*x^2) - (3*a^2)/(b^4*x) - a^3/(b^4*(b + a*x)) - (4*a^3*log(x))/b^5 + (4*a^3*log(b + a*x))/b^5]
    @test_int [1/((a + b/x)^2*x^7), x, 3, -(1/(4*b^2*x^4)) + (2*a)/(3*b^3*x^3) - (3*a^2)/(2*b^4*x^2) + (4*a^3)/(b^5*x) + a^4/(b^5*(b + a*x)) + (5*a^4*log(x))/b^6 - (5*a^4*log(b + a*x))/b^6]
    @test_int [1/((a + b/x)^2*x^8), x, 3, -(1/(5*b^2*x^5)) + a/(2*b^3*x^4) - a^2/(b^4*x^3) + (2*a^3)/(b^5*x^2) - (5*a^4)/(b^6*x) - a^5/(b^6*(b + a*x)) - (6*a^5*log(x))/b^7 + (6*a^5*log(b + a*x))/b^7]

    @test_int [x^4/(a + b/x)^3, x, 3, (15*b^4*x)/a^7 - (5*b^3*x^2)/a^6 + (2*b^2*x^3)/a^5 - (3*b*x^4)/(4*a^4) + x^5/(5*a^3) + b^7/(2*a^8*(b + a*x)^2) - (7*b^6)/(a^8*(b + a*x)) - (21*b^5*log(b + a*x))/a^8]
    @test_int [x^3/(a + b/x)^3, x, 3, (-10*b^3*x)/a^6 + (3*b^2*x^2)/a^5 - (b*x^3)/a^4 + x^4/(4*a^3) - b^6/(2*a^7*(b + a*x)^2) + (6*b^5)/(a^7*(b + a*x)) + (15*b^4*log(b + a*x))/a^7]
    @test_int [x^2/(a + b/x)^3, x, 3, (6*b^2*x)/a^5 - (3*b*x^2)/(2*a^4) + x^3/(3*a^3) + b^5/(2*a^6*(b + a*x)^2) - (5*b^4)/(a^6*(b + a*x)) - (10*b^3*log(b + a*x))/a^6]
    @test_int [x/(a + b/x)^3, x, 3, (-3*b*x)/a^4 + x^2/(2*a^3) - b^4/(2*a^5*(b + a*x)^2) + (4*b^3)/(a^5*(b + a*x)) + (6*b^2*log(b + a*x))/a^5]
    @test_int [1/(a + b/x)^3, x, 5, (3*x)/a^3 - x/(2*a*(a + b/x)^2) - (3*x)/(2*a^2*(a + b/x)) - (3*b*log(b + a*x))/a^4]
    @test_int [1/((a + b/x)^3*x), x, 3, -(b^2/(2*a^3*(b + a*x)^2)) + (2*b)/(a^3*(b + a*x)) + log(b + a*x)/a^3]
    @test_int [1/((a + b/x)^3*x^2), x, 1, 1/(2*b*(a + b/x)^2)]
    @test_int [1/((a + b/x)^3*x^3), x, 2, -(1/(2*a*(b + a*x)^2))]
    @test_int [1/((a + b/x)^3*x^4), x, 3, 1/(2*b*(b + a*x)^2) + 1/(b^2*(b + a*x)) + log(x)/b^3 - log(b + a*x)/b^3]
    @test_int [1/((a + b/x)^3*x^5), x, 3, -(1/(b^3*x)) - a/(2*b^2*(b + a*x)^2) - (2*a)/(b^3*(b + a*x)) - (3*a*log(x))/b^4 + (3*a*log(b + a*x))/b^4]
    @test_int [1/((a + b/x)^3*x^6), x, 3, -(1/(2*b^3*x^2)) + (3*a)/(b^4*x) + a^2/(2*b^3*(b + a*x)^2) + (3*a^2)/(b^4*(b + a*x)) + (6*a^2*log(x))/b^5 - (6*a^2*log(b + a*x))/b^5]
    @test_int [1/((a + b/x)^3*x^7), x, 3, -(1/(3*b^3*x^3)) + (3*a)/(2*b^4*x^2) - (6*a^2)/(b^5*x) - a^3/(2*b^4*(b + a*x)^2) - (4*a^3)/(b^5*(b + a*x)) - (10*a^3*log(x))/b^6 + (10*a^3*log(b + a*x))/b^6]
    @test_int [1/((a + b/x)^3*x^8), x, 3, -(1/(4*b^3*x^4)) + a/(b^4*x^3) - (3*a^2)/(b^5*x^2) + (10*a^3)/(b^6*x) + a^4/(2*b^5*(b + a*x)^2) + (5*a^4)/(b^6*(b + a*x)) + (15*a^4*log(x))/b^7 - (15*a^4*log(b + a*x))/b^7]
    @test_int [1/((a + b/x)^3*x^9), x, 3, -(1/(5*b^3*x^5)) + (3*a)/(4*b^4*x^4) - (2*a^2)/(b^5*x^3) + (5*a^3)/(b^6*x^2) - (15*a^4)/(b^7*x) - a^5/(2*b^6*(b + a*x)^2) - (6*a^5)/(b^7*(b + a*x)) - (21*a^5*log(x))/b^8 + (21*a^5*log(b + a*x))/b^8]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^(m/2)*(a+b/x)^p=#

    #= ::Subsubsection::Closed:: =#
    #=p>0=#

    @test_int [(a + b/x)*x^(5/2), x, 2, (2/5)*b*x^(5/2) + (2/7)*a*x^(7/2)]
    @test_int [(a + b/x)*x^(3/2), x, 2, (2/3)*b*x^(3/2) + (2/5)*a*x^(5/2)]
    @test_int [(a + b/x)*x^(1/2), x, 2, 2*b*sqrt(x) + (2/3)*a*x^(3/2)]
    @test_int [(a + b/x)/x^(1/2), x, 2, -((2*b)/sqrt(x)) + 2*a*sqrt(x)]
    @test_int [(a + b/x)/x^(3/2), x, 2, -((2*b)/(3*x^(3/2))) - (2*a)/sqrt(x)]
    @test_int [(a + b/x)/x^(5/2), x, 2, -((2*b)/(5*x^(5/2))) - (2*a)/(3*x^(3/2))]

    @test_int [(a + b/x)^2*x^(5/2), x, 3, (2/3)*b^2*x^(3/2) + (4/5)*a*b*x^(5/2) + (2/7)*a^2*x^(7/2)]
    @test_int [(a + b/x)^2*x^(3/2), x, 3, 2*b^2*sqrt(x) + (4/3)*a*b*x^(3/2) + (2/5)*a^2*x^(5/2)]
    @test_int [(a + b/x)^2*x^(1/2), x, 3, -((2*b^2)/sqrt(x)) + 4*a*b*sqrt(x) + (2/3)*a^2*x^(3/2)]
    @test_int [(a + b/x)^2/x^(1/2), x, 3, -((2*b^2)/(3*x^(3/2))) - (4*a*b)/sqrt(x) + 2*a^2*sqrt(x)]
    @test_int [(a + b/x)^2/x^(3/2), x, 3, -((2*b^2)/(5*x^(5/2))) - (4*a*b)/(3*x^(3/2)) - (2*a^2)/sqrt(x)]
    @test_int [(a + b/x)^2/x^(5/2), x, 3, -((2*b^2)/(7*x^(7/2))) - (4*a*b)/(5*x^(5/2)) - (2*a^2)/(3*x^(3/2))]

    @test_int [(a + b/x)^3*x^(5/2), x, 3, 2*b^3*sqrt(x) + 2*a*b^2*x^(3/2) + (6/5)*a^2*b*x^(5/2) + (2/7)*a^3*x^(7/2)]
    @test_int [(a + b/x)^3*x^(3/2), x, 3, -((2*b^3)/sqrt(x)) + 6*a*b^2*sqrt(x) + 2*a^2*b*x^(3/2) + (2/5)*a^3*x^(5/2)]
    @test_int [(a + b/x)^3*x^(1/2), x, 3, -((2*b^3)/(3*x^(3/2))) - (6*a*b^2)/sqrt(x) + 6*a^2*b*sqrt(x) + (2/3)*a^3*x^(3/2)]
    @test_int [(a + b/x)^3/x^(1/2), x, 3, -((2*b^3)/(5*x^(5/2))) - (2*a*b^2)/x^(3/2) - (6*a^2*b)/sqrt(x) + 2*a^3*sqrt(x)]
    @test_int [(a + b/x)^3/x^(3/2), x, 3, -((2*b^3)/(7*x^(7/2))) - (6*a*b^2)/(5*x^(5/2)) - (2*a^2*b)/x^(3/2) - (2*a^3)/sqrt(x)]
    @test_int [(a + b/x)^3/x^(5/2), x, 3, -((2*b^3)/(9*x^(9/2))) - (6*a*b^2)/(7*x^(7/2)) - (6*a^2*b)/(5*x^(5/2)) - (2*a^3)/(3*x^(3/2))]

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [1/(a + b/x)*x^(5/2), x, 7, -((2*b^3*sqrt(x))/a^4) + (2*b^2*x^(3/2))/(3*a^3) - (2*b*x^(5/2))/(5*a^2) + (2*x^(7/2))/(7*a) + (2*b^(7/2)*atan((sqrt(a)*sqrt(x))/sqrt(b)))/a^(9/2)]
    @test_int [1/(a + b/x)*x^(3/2), x, 6, (2*b^2*sqrt(x))/a^3 - (2*b*x^(3/2))/(3*a^2) + (2*x^(5/2))/(5*a) - (2*b^(5/2)*atan((sqrt(a)*sqrt(x))/sqrt(b)))/a^(7/2)]
    @test_int [1/(a + b/x)*x^(1/2), x, 5, -((2*b*sqrt(x))/a^2) + (2*x^(3/2))/(3*a) + (2*b^(3/2)*atan((sqrt(a)*sqrt(x))/sqrt(b)))/a^(5/2)]
    @test_int [1/(a + b/x)/x^(1/2), x, 4, (2*sqrt(x))/a - (2*sqrt(b)*atan((sqrt(a)*sqrt(x))/sqrt(b)))/a^(3/2)]
    @test_int [1/(a + b/x)/x^(3/2), x, 3, (2*atan((sqrt(a)*sqrt(x))/sqrt(b)))/(sqrt(a)*sqrt(b))]
    @test_int [1/(a + b/x)/x^(5/2), x, 4, -(2/(b*sqrt(x))) - (2*sqrt(a)*atan((sqrt(a)*sqrt(x))/sqrt(b)))/b^(3/2)]
    @test_int [1/(a + b/x)/x^(7/2), x, 5, -(2/(3*b*x^(3/2))) + (2*a)/(b^2*sqrt(x)) + (2*a^(3/2)*atan((sqrt(a)*sqrt(x))/sqrt(b)))/b^(5/2)]
    @test_int [1/(a + b/x)/x^(9/2), x, 6, -(2/(5*b*x^(5/2))) + (2*a)/(3*b^2*x^(3/2)) - (2*a^2)/(b^3*sqrt(x)) - (2*a^(5/2)*atan((sqrt(a)*sqrt(x))/sqrt(b)))/b^(7/2)]

    @test_int [1/(a + b/x)^2*x^(5/2), x, 8, -((9*b^3*sqrt(x))/a^5) + (3*b^2*x^(3/2))/a^4 - (9*b*x^(5/2))/(5*a^3) + (9*x^(7/2))/(7*a^2) - x^(9/2)/(a*(b + a*x)) + (9*b^(7/2)*atan((sqrt(a)*sqrt(x))/sqrt(b)))/a^(11/2)]
    @test_int [1/(a + b/x)^2*x^(3/2), x, 7, (7*b^2*sqrt(x))/a^4 - (7*b*x^(3/2))/(3*a^3) + (7*x^(5/2))/(5*a^2) - x^(7/2)/(a*(b + a*x)) - (7*b^(5/2)*atan((sqrt(a)*sqrt(x))/sqrt(b)))/a^(9/2)]
    @test_int [1/(a + b/x)^2*x^(1/2), x, 6, -((5*b*sqrt(x))/a^3) + (5*x^(3/2))/(3*a^2) - x^(5/2)/(a*(b + a*x)) + (5*b^(3/2)*atan((sqrt(a)*sqrt(x))/sqrt(b)))/a^(7/2)]
    @test_int [1/(a + b/x)^2/x^(1/2), x, 5, (3*sqrt(x))/a^2 - x^(3/2)/(a*(b + a*x)) - (3*sqrt(b)*atan((sqrt(a)*sqrt(x))/sqrt(b)))/a^(5/2)]
    @test_int [1/(a + b/x)^2/x^(3/2), x, 4, -(sqrt(x)/(a*(b + a*x))) + atan((sqrt(a)*sqrt(x))/sqrt(b))/(a^(3/2)*sqrt(b))]
    @test_int [1/(a + b/x)^2/x^(5/2), x, 4, sqrt(x)/(b*(b + a*x)) + atan((sqrt(a)*sqrt(x))/sqrt(b))/(sqrt(a)*b^(3/2))]
    @test_int [1/(a + b/x)^2/x^(7/2), x, 5, -(3/(b^2*sqrt(x))) + 1/(b*sqrt(x)*(b + a*x)) - (3*sqrt(a)*atan((sqrt(a)*sqrt(x))/sqrt(b)))/b^(5/2)]
    @test_int [1/(a + b/x)^2/x^(9/2), x, 6, -(5/(3*b^2*x^(3/2))) + (5*a)/(b^3*sqrt(x)) + 1/(b*x^(3/2)*(b + a*x)) + (5*a^(3/2)*atan((sqrt(a)*sqrt(x))/sqrt(b)))/b^(7/2)]
    @test_int [1/(a + b/x)^2/x^(11/2), x, 7, -(7/(5*b^2*x^(5/2))) + (7*a)/(3*b^3*x^(3/2)) - (7*a^2)/(b^4*sqrt(x)) + 1/(b*x^(5/2)*(b + a*x)) - (7*a^(5/2)*atan((sqrt(a)*sqrt(x))/sqrt(b)))/b^(9/2)]

    @test_int [1/(a + b/x)^3*x^(3/2), x, 8, (63*b^2*sqrt(x))/(4*a^5) - (21*b*x^(3/2))/(4*a^4) + (63*x^(5/2))/(20*a^3) - x^(9/2)/(2*a*(b + a*x)^2) - (9*x^(7/2))/(4*a^2*(b + a*x)) - (63*b^(5/2)*atan((sqrt(a)*sqrt(x))/sqrt(b)))/(4*a^(11/2))]
    @test_int [1/(a + b/x)^3*x^(1/2), x, 7, -((35*b*sqrt(x))/(4*a^4)) + (35*x^(3/2))/(12*a^3) - x^(7/2)/(2*a*(b + a*x)^2) - (7*x^(5/2))/(4*a^2*(b + a*x)) + (35*b^(3/2)*atan((sqrt(a)*sqrt(x))/sqrt(b)))/(4*a^(9/2))]
    @test_int [1/(a + b/x)^3/x^(1/2), x, 6, (15*sqrt(x))/(4*a^3) - x^(5/2)/(2*a*(b + a*x)^2) - (5*x^(3/2))/(4*a^2*(b + a*x)) - (15*sqrt(b)*atan((sqrt(a)*sqrt(x))/sqrt(b)))/(4*a^(7/2))]
    @test_int [1/(a + b/x)^3/x^(3/2), x, 5, -(x^(3/2)/(2*a*(b + a*x)^2)) - (3*sqrt(x))/(4*a^2*(b + a*x)) + (3*atan((sqrt(a)*sqrt(x))/sqrt(b)))/(4*a^(5/2)*sqrt(b))]
    @test_int [1/(a + b/x)^3/x^(5/2), x, 5, -(sqrt(x)/(2*a*(b + a*x)^2)) + sqrt(x)/(4*a*b*(b + a*x)) + atan((sqrt(a)*sqrt(x))/sqrt(b))/(4*a^(3/2)*b^(3/2))]
    @test_int [1/(a + b/x)^3/x^(7/2), x, 5, sqrt(x)/(2*b*(b + a*x)^2) + (3*sqrt(x))/(4*b^2*(b + a*x)) + (3*atan((sqrt(a)*sqrt(x))/sqrt(b)))/(4*sqrt(a)*b^(5/2))]
    @test_int [1/(a + b/x)^3/x^(9/2), x, 6, -(15/(4*b^3*sqrt(x))) + 1/(2*b*sqrt(x)*(b + a*x)^2) + 5/(4*b^2*sqrt(x)*(b + a*x)) - (15*sqrt(a)*atan((sqrt(a)*sqrt(x))/sqrt(b)))/(4*b^(7/2))]
    @test_int [1/(a + b/x)^3/x^(11/2), x, 7, -(35/(12*b^3*x^(3/2))) + (35*a)/(4*b^4*sqrt(x)) + 1/(2*b*x^(3/2)*(b + a*x)^2) + 7/(4*b^2*x^(3/2)*(b + a*x)) + (35*a^(3/2)*atan((sqrt(a)*sqrt(x))/sqrt(b)))/(4*b^(9/2))]
    @test_int [1/(a + b/x)^3/x^(13/2), x, 8, -(63/(20*b^3*x^(5/2))) + (21*a)/(4*b^4*x^(3/2)) - (63*a^2)/(4*b^5*sqrt(x)) + 1/(2*b*x^(5/2)*(b + a*x)^2) + 9/(4*b^2*x^(5/2)*(b + a*x)) - (63*a^(5/2)*atan((sqrt(a)*sqrt(x))/sqrt(b)))/(4*b^(11/2))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b/x)^(p/2)=#

    #= ::Subsubsection::Closed:: =#
    #=p>0=#

    @test_int [x^3*sqrt(a + b/x), x, 7, (5*b^3*sqrt(a + b/x)*x)/(64*a^3) - (5*b^2*sqrt(a + b/x)*x^2)/(96*a^2) + (b*sqrt(a + b/x)*x^3)/(24*a) + (1/4)*sqrt(a + b/x)*x^4 - (5*b^4*atanh(sqrt(a + b/x)/sqrt(a)))/(64*a^(7/2))]
    @test_int [x^2*sqrt(a + b/x), x, 6, -((b^2*sqrt(a + b/x)*x)/(8*a^2)) + (b*sqrt(a + b/x)*x^2)/(12*a) + (1/3)*sqrt(a + b/x)*x^3 + (b^3*atanh(sqrt(a + b/x)/sqrt(a)))/(8*a^(5/2))]
    @test_int [x^1*sqrt(a + b/x), x, 5, (b*sqrt(a + b/x)*x)/(4*a) + (1/2)*sqrt(a + b/x)*x^2 - (b^2*atanh(sqrt(a + b/x)/sqrt(a)))/(4*a^(3/2))]
    @test_int [x^0*sqrt(a + b/x), x, 4, sqrt(a + b/x)*x + (b*atanh(sqrt(a + b/x)/sqrt(a)))/sqrt(a)]
    @test_int [sqrt(a + b/x)/x^1, x, 4, -2*sqrt(a + b/x) + 2*sqrt(a)*atanh(sqrt(a + b/x)/sqrt(a))]
    @test_int [sqrt(a + b/x)/x^2, x, 1, -((2*(a + b/x)^(3/2))/(3*b))]
    @test_int [sqrt(a + b/x)/x^3, x, 3, (2*a*(a + b/x)^(3/2))/(3*b^2) - (2*(a + b/x)^(5/2))/(5*b^2)]
    @test_int [sqrt(a + b/x)/x^4, x, 3, -((2*a^2*(a + b/x)^(3/2))/(3*b^3)) + (4*a*(a + b/x)^(5/2))/(5*b^3) - (2*(a + b/x)^(7/2))/(7*b^3)]
    @test_int [sqrt(a + b/x)/x^5, x, 3, (2*a^3*(a + b/x)^(3/2))/(3*b^4) - (6*a^2*(a + b/x)^(5/2))/(5*b^4) + (6*a*(a + b/x)^(7/2))/(7*b^4) - (2*(a + b/x)^(9/2))/(9*b^4)]
    @test_int [sqrt(a + b/x)/x^6, x, 3, -((2*a^4*(a + b/x)^(3/2))/(3*b^5)) + (8*a^3*(a + b/x)^(5/2))/(5*b^5) - (12*a^2*(a + b/x)^(7/2))/(7*b^5) + (8*a*(a + b/x)^(9/2))/(9*b^5) - (2*(a + b/x)^(11/2))/(11*b^5)]

    @test_int [x^3*(a + b/x)^(3/2), x, 7, -((3*b^3*sqrt(a + b/x)*x)/(64*a^2)) + (b^2*sqrt(a + b/x)*x^2)/(32*a) + (1/8)*b*sqrt(a + b/x)*x^3 + (1/4)*(a + b/x)^(3/2)*x^4 + (3*b^4*atanh(sqrt(a + b/x)/sqrt(a)))/(64*a^(5/2))]
    @test_int [x^2*(a + b/x)^(3/2), x, 6, (b^2*sqrt(a + b/x)*x)/(8*a) + (1/4)*b*sqrt(a + b/x)*x^2 + (1/3)*(a + b/x)^(3/2)*x^3 - (b^3*atanh(sqrt(a + b/x)/sqrt(a)))/(8*a^(3/2))]
    @test_int [x^1*(a + b/x)^(3/2), x, 5, (3/4)*b*sqrt(a + b/x)*x + (1/2)*(a + b/x)^(3/2)*x^2 + (3*b^2*atanh(sqrt(a + b/x)/sqrt(a)))/(4*sqrt(a))]
    @test_int [x^0*(a + b/x)^(3/2), x, 5, -3*b*sqrt(a + b/x) + (a + b/x)^(3/2)*x + 3*sqrt(a)*b*atanh(sqrt(a + b/x)/sqrt(a))]
    @test_int [(a + b/x)^(3/2)/x^1, x, 5, -2*a*sqrt(a + b/x) - (2/3)*(a + b/x)^(3/2) + 2*a^(3/2)*atanh(sqrt(a + b/x)/sqrt(a))]
    @test_int [(a + b/x)^(3/2)/x^2, x, 1, -((2*(a + b/x)^(5/2))/(5*b))]
    @test_int [(a + b/x)^(3/2)/x^3, x, 3, (2*a*(a + b/x)^(5/2))/(5*b^2) - (2*(a + b/x)^(7/2))/(7*b^2)]
    @test_int [(a + b/x)^(3/2)/x^4, x, 3, -((2*a^2*(a + b/x)^(5/2))/(5*b^3)) + (4*a*(a + b/x)^(7/2))/(7*b^3) - (2*(a + b/x)^(9/2))/(9*b^3)]
    @test_int [(a + b/x)^(3/2)/x^5, x, 3, (2*a^3*(a + b/x)^(5/2))/(5*b^4) - (6*a^2*(a + b/x)^(7/2))/(7*b^4) + (2*a*(a + b/x)^(9/2))/(3*b^4) - (2*(a + b/x)^(11/2))/(11*b^4)]
    @test_int [(a + b/x)^(3/2)/x^6, x, 3, -((2*a^4*(a + b/x)^(5/2))/(5*b^5)) + (8*a^3*(a + b/x)^(7/2))/(7*b^5) - (4*a^2*(a + b/x)^(9/2))/(3*b^5) + (8*a*(a + b/x)^(11/2))/(11*b^5) - (2*(a + b/x)^(13/2))/(13*b^5)]
    @test_int [(a + b/x)^(3/2)/x^7, x, 3, (2*a^5*(a + b/x)^(5/2))/(5*b^6) - (10*a^4*(a + b/x)^(7/2))/(7*b^6) + (20*a^3*(a + b/x)^(9/2))/(9*b^6) - (20*a^2*(a + b/x)^(11/2))/(11*b^6) + (10*a*(a + b/x)^(13/2))/(13*b^6) - (2*(a + b/x)^(15/2))/(15*b^6)]

    @test_int [x^3*(a + b/x)^(5/2), x, 7, (5*b^3*sqrt(a + b/x)*x)/(64*a) + (5/32)*b^2*sqrt(a + b/x)*x^2 + (5/24)*b*(a + b/x)^(3/2)*x^3 + (1/4)*(a + b/x)^(5/2)*x^4 - (5*b^4*atanh(sqrt(a + b/x)/sqrt(a)))/(64*a^(3/2))]
    @test_int [x^2*(a + b/x)^(5/2), x, 6, (5/8)*b^2*sqrt(a + b/x)*x + (5/12)*b*(a + b/x)^(3/2)*x^2 + (1/3)*(a + b/x)^(5/2)*x^3 + (5*b^3*atanh(sqrt(a + b/x)/sqrt(a)))/(8*sqrt(a))]
    @test_int [x^1*(a + b/x)^(5/2), x, 6, (-(15/4))*b^2*sqrt(a + b/x) + (5/4)*b*(a + b/x)^(3/2)*x + (1/2)*(a + b/x)^(5/2)*x^2 + (15/4)*sqrt(a)*b^2*atanh(sqrt(a + b/x)/sqrt(a))]
    @test_int [x^0*(a + b/x)^(5/2), x, 6, -5*a*b*sqrt(a + b/x) - (5/3)*b*(a + b/x)^(3/2) + (a + b/x)^(5/2)*x + 5*a^(3/2)*b*atanh(sqrt(a + b/x)/sqrt(a))]
    @test_int [(a + b/x)^(5/2)/x^1, x, 6, -2*a^2*sqrt(a + b/x) - (2/3)*a*(a + b/x)^(3/2) - (2/5)*(a + b/x)^(5/2) + 2*a^(5/2)*atanh(sqrt(a + b/x)/sqrt(a))]
    @test_int [(a + b/x)^(5/2)/x^2, x, 1, -((2*(a + b/x)^(7/2))/(7*b))]
    @test_int [(a + b/x)^(5/2)/x^3, x, 3, (2*a*(a + b/x)^(7/2))/(7*b^2) - (2*(a + b/x)^(9/2))/(9*b^2)]
    @test_int [(a + b/x)^(5/2)/x^4, x, 3, -((2*a^2*(a + b/x)^(7/2))/(7*b^3)) + (4*a*(a + b/x)^(9/2))/(9*b^3) - (2*(a + b/x)^(11/2))/(11*b^3)]
    @test_int [(a + b/x)^(5/2)/x^5, x, 3, (2*a^3*(a + b/x)^(7/2))/(7*b^4) - (2*a^2*(a + b/x)^(9/2))/(3*b^4) + (6*a*(a + b/x)^(11/2))/(11*b^4) - (2*(a + b/x)^(13/2))/(13*b^4)]
    @test_int [(a + b/x)^(5/2)/x^6, x, 3, -((2*a^4*(a + b/x)^(7/2))/(7*b^5)) + (8*a^3*(a + b/x)^(9/2))/(9*b^5) - (12*a^2*(a + b/x)^(11/2))/(11*b^5) + (8*a*(a + b/x)^(13/2))/(13*b^5) - (2*(a + b/x)^(15/2))/(15*b^5)]

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [x^3/sqrt(a + b/x), x, 7, -((35*b^3*sqrt(a + b/x)*x)/(64*a^4)) + (35*b^2*sqrt(a + b/x)*x^2)/(96*a^3) - (7*b*sqrt(a + b/x)*x^3)/(24*a^2) + (sqrt(a + b/x)*x^4)/(4*a) + (35*b^4*atanh(sqrt(a + b/x)/sqrt(a)))/(64*a^(9/2))]
    @test_int [x^2/sqrt(a + b/x), x, 6, (5*b^2*sqrt(a + b/x)*x)/(8*a^3) - (5*b*sqrt(a + b/x)*x^2)/(12*a^2) + (sqrt(a + b/x)*x^3)/(3*a) - (5*b^3*atanh(sqrt(a + b/x)/sqrt(a)))/(8*a^(7/2))]
    @test_int [x^1/sqrt(a + b/x), x, 5, -((3*b*sqrt(a + b/x)*x)/(4*a^2)) + (sqrt(a + b/x)*x^2)/(2*a) + (3*b^2*atanh(sqrt(a + b/x)/sqrt(a)))/(4*a^(5/2))]
    @test_int [x^0/sqrt(a + b/x), x, 4, (sqrt(a + b/x)*x)/a - (b*atanh(sqrt(a + b/x)/sqrt(a)))/a^(3/2)]
    @test_int [1/(x^1*sqrt(a + b/x)), x, 3, (2*atanh(sqrt(a + b/x)/sqrt(a)))/sqrt(a)]
    @test_int [1/(x^2*sqrt(a + b/x)), x, 1, -((2*sqrt(a + b/x))/b)]
    @test_int [1/(x^3*sqrt(a + b/x)), x, 3, (2*a*sqrt(a + b/x))/b^2 - (2*(a + b/x)^(3/2))/(3*b^2)]
    @test_int [1/(x^4*sqrt(a + b/x)), x, 3, -((2*a^2*sqrt(a + b/x))/b^3) + (4*a*(a + b/x)^(3/2))/(3*b^3) - (2*(a + b/x)^(5/2))/(5*b^3)]
    @test_int [1/(x^5*sqrt(a + b/x)), x, 3, (2*a^3*sqrt(a + b/x))/b^4 - (2*a^2*(a + b/x)^(3/2))/b^4 + (6*a*(a + b/x)^(5/2))/(5*b^4) - (2*(a + b/x)^(7/2))/(7*b^4)]
    @test_int [1/(x^6*sqrt(a + b/x)), x, 3, -((2*a^4*sqrt(a + b/x))/b^5) + (8*a^3*(a + b/x)^(3/2))/(3*b^5) - (12*a^2*(a + b/x)^(5/2))/(5*b^5) + (8*a*(a + b/x)^(7/2))/(7*b^5) - (2*(a + b/x)^(9/2))/(9*b^5)]

    @test_int [x^2/(a + b/x)^(3/2), x, 7, (35*b^3)/(8*a^4*sqrt(a + b/x)) + (35*b^2*x)/(24*a^3*sqrt(a + b/x)) - (7*b*x^2)/(12*a^2*sqrt(a + b/x)) + x^3/(3*a*sqrt(a + b/x)) - (35*b^3*atanh(sqrt(a + b/x)/sqrt(a)))/(8*a^(9/2))]
    @test_int [x^1/(a + b/x)^(3/2), x, 6, -((15*b^2)/(4*a^3*sqrt(a + b/x))) - (5*b*x)/(4*a^2*sqrt(a + b/x)) + x^2/(2*a*sqrt(a + b/x)) + (15*b^2*atanh(sqrt(a + b/x)/sqrt(a)))/(4*a^(7/2))]
    @test_int [x^0/(a + b/x)^(3/2), x, 5, (3*b)/(a^2*sqrt(a + b/x)) + x/(a*sqrt(a + b/x)) - (3*b*atanh(sqrt(a + b/x)/sqrt(a)))/a^(5/2)]
    @test_int [1/(x^1*(a + b/x)^(3/2)), x, 4, -(2/(a*sqrt(a + b/x))) + (2*atanh(sqrt(a + b/x)/sqrt(a)))/a^(3/2)]
    @test_int [1/(x^2*(a + b/x)^(3/2)), x, 1, 2/(b*sqrt(a + b/x))]
    @test_int [1/(x^3*(a + b/x)^(3/2)), x, 3, -((2*a)/(b^2*sqrt(a + b/x))) - (2*sqrt(a + b/x))/b^2]
    @test_int [1/(x^4*(a + b/x)^(3/2)), x, 3, (2*a^2)/(b^3*sqrt(a + b/x)) + (4*a*sqrt(a + b/x))/b^3 - (2*(a + b/x)^(3/2))/(3*b^3)]
    @test_int [1/(x^5*(a + b/x)^(3/2)), x, 3, -((2*a^3)/(b^4*sqrt(a + b/x))) - (6*a^2*sqrt(a + b/x))/b^4 + (2*a*(a + b/x)^(3/2))/b^4 - (2*(a + b/x)^(5/2))/(5*b^4)]
    @test_int [1/(x^6*(a + b/x)^(3/2)), x, 3, (2*a^4)/(b^5*sqrt(a + b/x)) + (8*a^3*sqrt(a + b/x))/b^5 - (4*a^2*(a + b/x)^(3/2))/b^5 + (8*a*(a + b/x)^(5/2))/(5*b^5) - (2*(a + b/x)^(7/2))/(7*b^5)]
    @test_int [1/(x^7*(a + b/x)^(3/2)), x, 3, -((2*a^5)/(b^6*sqrt(a + b/x))) - (10*a^4*sqrt(a + b/x))/b^6 + (20*a^3*(a + b/x)^(3/2))/(3*b^6) - (4*a^2*(a + b/x)^(5/2))/b^6 + (10*a*(a + b/x)^(7/2))/(7*b^6) - (2*(a + b/x)^(9/2))/(9*b^6)]

    @test_int [x^2/(a + b/x)^(5/2), x, 8, (35*b^3)/(8*a^4*(a + b/x)^(3/2)) + (105*b^3)/(8*a^5*sqrt(a + b/x)) + (21*b^2*x)/(8*a^3*(a + b/x)^(3/2)) - (3*b*x^2)/(4*a^2*(a + b/x)^(3/2)) + x^3/(3*a*(a + b/x)^(3/2)) - (105*b^3*atanh(sqrt(a + b/x)/sqrt(a)))/(8*a^(11/2))]
    @test_int [x^1/(a + b/x)^(5/2), x, 7, -((35*b^2)/(12*a^3*(a + b/x)^(3/2))) - (35*b^2)/(4*a^4*sqrt(a + b/x)) - (7*b*x)/(4*a^2*(a + b/x)^(3/2)) + x^2/(2*a*(a + b/x)^(3/2)) + (35*b^2*atanh(sqrt(a + b/x)/sqrt(a)))/(4*a^(9/2))]
    @test_int [x^0/(a + b/x)^(5/2), x, 6, (5*b)/(3*a^2*(a + b/x)^(3/2)) + (5*b)/(a^3*sqrt(a + b/x)) + x/(a*(a + b/x)^(3/2)) - (5*b*atanh(sqrt(a + b/x)/sqrt(a)))/a^(7/2)]
    @test_int [1/(x^1*(a + b/x)^(5/2)), x, 5, -(2/(3*a*(a + b/x)^(3/2))) - 2/(a^2*sqrt(a + b/x)) + (2*atanh(sqrt(a + b/x)/sqrt(a)))/a^(5/2)]
    @test_int [1/(x^2*(a + b/x)^(5/2)), x, 1, 2/(3*b*(a + b/x)^(3/2))]
    @test_int [1/(x^3*(a + b/x)^(5/2)), x, 3, -((2*a)/(3*b^2*(a + b/x)^(3/2))) + 2/(b^2*sqrt(a + b/x))]
    @test_int [1/(x^4*(a + b/x)^(5/2)), x, 3, (2*a^2)/(3*b^3*(a + b/x)^(3/2)) - (4*a)/(b^3*sqrt(a + b/x)) - (2*sqrt(a + b/x))/b^3]
    @test_int [1/(x^5*(a + b/x)^(5/2)), x, 3, -((2*a^3)/(3*b^4*(a + b/x)^(3/2))) + (6*a^2)/(b^4*sqrt(a + b/x)) + (6*a*sqrt(a + b/x))/b^4 - (2*(a + b/x)^(3/2))/(3*b^4)]
    @test_int [1/(x^6*(a + b/x)^(5/2)), x, 3, (2*a^4)/(3*b^5*(a + b/x)^(3/2)) - (8*a^3)/(b^5*sqrt(a + b/x)) - (12*a^2*sqrt(a + b/x))/b^5 + (8*a*(a + b/x)^(3/2))/(3*b^5) - (2*(a + b/x)^(5/2))/(5*b^5)]
    @test_int [1/(x^7*(a + b/x)^(5/2)), x, 3, -((2*a^5)/(3*b^6*(a + b/x)^(3/2))) + (10*a^4)/(b^6*sqrt(a + b/x)) + (20*a^3*sqrt(a + b/x))/b^6 - (20*a^2*(a + b/x)^(3/2))/(3*b^6) + (2*a*(a + b/x)^(5/2))/b^6 - (2*(a + b/x)^(7/2))/(7*b^6)]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^(m/2)*(a+b/x)^(p/2)=#

    #= ::Subsubsection::Closed:: =#
    #=p>0=#

    @test_int [(a + b/x)^(1/2)*x^(7/2), x, 4, -((32*b^3*(a + b/x)^(3/2)*x^(3/2))/(315*a^4)) + (16*b^2*(a + b/x)^(3/2)*x^(5/2))/(105*a^3) - (4*b*(a + b/x)^(3/2)*x^(7/2))/(21*a^2) + (2*(a + b/x)^(3/2)*x^(9/2))/(9*a)]
    @test_int [(a + b/x)^(1/2)*x^(5/2), x, 3, (16*b^2*(a + b/x)^(3/2)*x^(3/2))/(105*a^3) - (8*b*(a + b/x)^(3/2)*x^(5/2))/(35*a^2) + (2*(a + b/x)^(3/2)*x^(7/2))/(7*a)]
    @test_int [(a + b/x)^(1/2)*x^(3/2), x, 2, -((4*b*(a + b/x)^(3/2)*x^(3/2))/(15*a^2)) + (2*(a + b/x)^(3/2)*x^(5/2))/(5*a)]
    @test_int [(a + b/x)^(1/2)*x^(1/2), x, 1, (2*(a + b/x)^(3/2)*x^(3/2))/(3*a)]
    @test_int [(a + b/x)^(1/2)/x^(1/2), x, 4, 2*sqrt(a + b/x)*sqrt(x) - 2*sqrt(b)*atanh(sqrt(b)/(sqrt(a + b/x)*sqrt(x)))]
    @test_int [(a + b/x)^(1/2)/x^(3/2), x, 4, -(sqrt(a + b/x)/sqrt(x)) - (a*atanh(sqrt(b)/(sqrt(a + b/x)*sqrt(x))))/sqrt(b)]
    @test_int [(a + b/x)^(1/2)/x^(5/2), x, 5, -(sqrt(a + b/x)/(2*x^(3/2))) - (a*sqrt(a + b/x))/(4*b*sqrt(x)) + (a^2*atanh(sqrt(b)/(sqrt(a + b/x)*sqrt(x))))/(4*b^(3/2))]
    @test_int [(a + b/x)^(1/2)/x^(7/2), x, 6, -(sqrt(a + b/x)/(3*x^(5/2))) - (a*sqrt(a + b/x))/(12*b*x^(3/2)) + (a^2*sqrt(a + b/x))/(8*b^2*sqrt(x)) - (a^3*atanh(sqrt(b)/(sqrt(a + b/x)*sqrt(x))))/(8*b^(5/2))]

    @test_int [(a + b/x)^(3/2)*x^(9/2), x, 4, -((32*b^3*(a + b/x)^(5/2)*x^(5/2))/(1155*a^4)) + (16*b^2*(a + b/x)^(5/2)*x^(7/2))/(231*a^3) - (4*b*(a + b/x)^(5/2)*x^(9/2))/(33*a^2) + (2*(a + b/x)^(5/2)*x^(11/2))/(11*a)]
    @test_int [(a + b/x)^(3/2)*x^(7/2), x, 3, (16*b^2*(a + b/x)^(5/2)*x^(5/2))/(315*a^3) - (8*b*(a + b/x)^(5/2)*x^(7/2))/(63*a^2) + (2*(a + b/x)^(5/2)*x^(9/2))/(9*a)]
    @test_int [(a + b/x)^(3/2)*x^(5/2), x, 2, -((4*b*(a + b/x)^(5/2)*x^(5/2))/(35*a^2)) + (2*(a + b/x)^(5/2)*x^(7/2))/(7*a)]
    @test_int [(a + b/x)^(3/2)*x^(3/2), x, 1, (2*(a + b/x)^(5/2)*x^(5/2))/(5*a)]
    @test_int [(a + b/x)^(3/2)*x^(1/2), x, 5, 2*b*sqrt(a + b/x)*sqrt(x) + (2/3)*(a + b/x)^(3/2)*x^(3/2) - 2*b^(3/2)*atanh(sqrt(b)/(sqrt(a + b/x)*sqrt(x)))]
    @test_int [(a + b/x)^(3/2)/x^(1/2), x, 5, -((3*b*sqrt(a + b/x))/sqrt(x)) + 2*(a + b/x)^(3/2)*sqrt(x) - 3*a*sqrt(b)*atanh(sqrt(b)/(sqrt(a + b/x)*sqrt(x)))]
    @test_int [(a + b/x)^(3/2)/x^(3/2), x, 5, -((3*a*sqrt(a + b/x))/(4*sqrt(x))) - (a + b/x)^(3/2)/(2*sqrt(x)) - (3*a^2*atanh(sqrt(b)/(sqrt(a + b/x)*sqrt(x))))/(4*sqrt(b))]
    @test_int [(a + b/x)^(3/2)/x^(5/2), x, 6, -((a*sqrt(a + b/x))/(4*x^(3/2))) - (a + b/x)^(3/2)/(3*x^(3/2)) - (a^2*sqrt(a + b/x))/(8*b*sqrt(x)) + (a^3*atanh(sqrt(b)/(sqrt(a + b/x)*sqrt(x))))/(8*b^(3/2))]

    @test_int [(a + b/x)^(5/2)*x^(11/2), x, 4, -((32*b^3*(a + b/x)^(7/2)*x^(7/2))/(3003*a^4)) + (16*b^2*(a + b/x)^(7/2)*x^(9/2))/(429*a^3) - (12*b*(a + b/x)^(7/2)*x^(11/2))/(143*a^2) + (2*(a + b/x)^(7/2)*x^(13/2))/(13*a)]
    @test_int [(a + b/x)^(5/2)*x^(9/2), x, 3, (16*b^2*(a + b/x)^(7/2)*x^(7/2))/(693*a^3) - (8*b*(a + b/x)^(7/2)*x^(9/2))/(99*a^2) + (2*(a + b/x)^(7/2)*x^(11/2))/(11*a)]
    @test_int [(a + b/x)^(5/2)*x^(7/2), x, 2, -((4*b*(a + b/x)^(7/2)*x^(7/2))/(63*a^2)) + (2*(a + b/x)^(7/2)*x^(9/2))/(9*a)]
    @test_int [(a + b/x)^(5/2)*x^(5/2), x, 1, (2*(a + b/x)^(7/2)*x^(7/2))/(7*a)]
    @test_int [(a + b/x)^(5/2)*x^(3/2), x, 6, 2*b^2*sqrt(a + b/x)*sqrt(x) + (2/3)*b*(a + b/x)^(3/2)*x^(3/2) + (2/5)*(a + b/x)^(5/2)*x^(5/2) - 2*b^(5/2)*atanh(sqrt(b)/(sqrt(a + b/x)*sqrt(x)))]
    @test_int [(a + b/x)^(5/2)*x^(1/2), x, 6, -((5*b^2*sqrt(a + b/x))/sqrt(x)) + (10/3)*b*(a + b/x)^(3/2)*sqrt(x) + (2/3)*(a + b/x)^(5/2)*x^(3/2) - 5*a*b^(3/2)*atanh(sqrt(b)/(sqrt(a + b/x)*sqrt(x)))]
    @test_int [(a + b/x)^(5/2)/x^(1/2), x, 6, -((15*a*b*sqrt(a + b/x))/(4*sqrt(x))) - (5*b*(a + b/x)^(3/2))/(2*sqrt(x)) + 2*(a + b/x)^(5/2)*sqrt(x) - (15/4)*a^2*sqrt(b)*atanh(sqrt(b)/(sqrt(a + b/x)*sqrt(x)))]
    @test_int [(a + b/x)^(5/2)/x^(3/2), x, 6, -((5*a^2*sqrt(a + b/x))/(8*sqrt(x))) - (5*a*(a + b/x)^(3/2))/(12*sqrt(x)) - (a + b/x)^(5/2)/(3*sqrt(x)) - (5*a^3*atanh(sqrt(b)/(sqrt(a + b/x)*sqrt(x))))/(8*sqrt(b))]
    @test_int [(a + b/x)^(5/2)/x^(5/2), x, 7, -((5*a^2*sqrt(a + b/x))/(32*x^(3/2))) - (5*a*(a + b/x)^(3/2))/(24*x^(3/2)) - (a + b/x)^(5/2)/(4*x^(3/2)) - (5*a^3*sqrt(a + b/x))/(64*b*sqrt(x)) + (5*a^4*atanh(sqrt(b)/(sqrt(a + b/x)*sqrt(x))))/(64*b^(3/2))]

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [1/(a + b/x)^(1/2)*x^(7/2), x, 5, (256*b^4*sqrt(a + b/x)*sqrt(x))/(315*a^5) - (128*b^3*sqrt(a + b/x)*x^(3/2))/(315*a^4) + (32*b^2*sqrt(a + b/x)*x^(5/2))/(105*a^3) - (16*b*sqrt(a + b/x)*x^(7/2))/(63*a^2) + (2*sqrt(a + b/x)*x^(9/2))/(9*a)]
    @test_int [1/(a + b/x)^(1/2)*x^(5/2), x, 4, -((32*b^3*sqrt(a + b/x)*sqrt(x))/(35*a^4)) + (16*b^2*sqrt(a + b/x)*x^(3/2))/(35*a^3) - (12*b*sqrt(a + b/x)*x^(5/2))/(35*a^2) + (2*sqrt(a + b/x)*x^(7/2))/(7*a)]
    @test_int [1/(a + b/x)^(1/2)*x^(3/2), x, 3, (16*b^2*sqrt(a + b/x)*sqrt(x))/(15*a^3) - (8*b*sqrt(a + b/x)*x^(3/2))/(15*a^2) + (2*sqrt(a + b/x)*x^(5/2))/(5*a)]
    @test_int [1/(a + b/x)^(1/2)*x^(1/2), x, 2, -((4*b*sqrt(a + b/x)*sqrt(x))/(3*a^2)) + (2*sqrt(a + b/x)*x^(3/2))/(3*a)]
    @test_int [1/(a + b/x)^(1/2)/x^(1/2), x, 1, (2*sqrt(a + b/x)*sqrt(x))/a]
    @test_int [1/(a + b/x)^(1/2)/x^(3/2), x, 3, -((2*atanh(sqrt(b)/(sqrt(a + b/x)*sqrt(x))))/sqrt(b))]
    @test_int [1/(a + b/x)^(1/2)/x^(5/2), x, 4, -(sqrt(a + b/x)/(b*sqrt(x))) + (a*atanh(sqrt(b)/(sqrt(a + b/x)*sqrt(x))))/b^(3/2)]
    @test_int [1/(a + b/x)^(1/2)/x^(7/2), x, 5, -(sqrt(a + b/x)/(2*b*x^(3/2))) + (3*a*sqrt(a + b/x))/(4*b^2*sqrt(x)) - (3*a^2*atanh(sqrt(b)/(sqrt(a + b/x)*sqrt(x))))/(4*b^(5/2))]
    @test_int [1/(a + b/x)^(1/2)/x^(9/2), x, 6, -(sqrt(a + b/x)/(3*b*x^(5/2))) + (5*a*sqrt(a + b/x))/(12*b^2*x^(3/2)) - (5*a^2*sqrt(a + b/x))/(8*b^3*sqrt(x)) + (5*a^3*atanh(sqrt(b)/(sqrt(a + b/x)*sqrt(x))))/(8*b^(7/2))]

    @test_int [1/(a + b/x)^(3/2)*x^(5/2), x, 5, -((256*b^4)/(35*a^5*sqrt(a + b/x)*sqrt(x))) - (128*b^3*sqrt(x))/(35*a^4*sqrt(a + b/x)) + (32*b^2*x^(3/2))/(35*a^3*sqrt(a + b/x)) - (16*b*x^(5/2))/(35*a^2*sqrt(a + b/x)) + (2*x^(7/2))/(7*a*sqrt(a + b/x))]
    @test_int [1/(a + b/x)^(3/2)*x^(3/2), x, 4, (32*b^3)/(5*a^4*sqrt(a + b/x)*sqrt(x)) + (16*b^2*sqrt(x))/(5*a^3*sqrt(a + b/x)) - (4*b*x^(3/2))/(5*a^2*sqrt(a + b/x)) + (2*x^(5/2))/(5*a*sqrt(a + b/x))]
    @test_int [1/(a + b/x)^(3/2)*x^(1/2), x, 3, -((16*b^2)/(3*a^3*sqrt(a + b/x)*sqrt(x))) - (8*b*sqrt(x))/(3*a^2*sqrt(a + b/x)) + (2*x^(3/2))/(3*a*sqrt(a + b/x))]
    @test_int [1/(a + b/x)^(3/2)/x^(1/2), x, 2, (4*b)/(a^2*sqrt(a + b/x)*sqrt(x)) + (2*sqrt(x))/(a*sqrt(a + b/x))]
    @test_int [1/(a + b/x)^(3/2)/x^(3/2), x, 1, -(2/(a*sqrt(a + b/x)*sqrt(x)))]
    @test_int [1/(a + b/x)^(3/2)/x^(5/2), x, 4, 2/(b*sqrt(a + b/x)*sqrt(x)) - (2*atanh(sqrt(b)/(sqrt(a + b/x)*sqrt(x))))/b^(3/2)]
    @test_int [1/(a + b/x)^(3/2)/x^(7/2), x, 5, 2/(b*sqrt(a + b/x)*x^(3/2)) - (3*sqrt(a + b/x))/(b^2*sqrt(x)) + (3*a*atanh(sqrt(b)/(sqrt(a + b/x)*sqrt(x))))/b^(5/2)]
    @test_int [1/(a + b/x)^(3/2)/x^(9/2), x, 6, 2/(b*sqrt(a + b/x)*x^(5/2)) - (5*sqrt(a + b/x))/(2*b^2*x^(3/2)) + (15*a*sqrt(a + b/x))/(4*b^3*sqrt(x)) - (15*a^2*atanh(sqrt(b)/(sqrt(a + b/x)*sqrt(x))))/(4*b^(7/2))]
    @test_int [1/(a + b/x)^(3/2)/x^(11/2), x, 7, 2/(b*sqrt(a + b/x)*x^(7/2)) - (7*sqrt(a + b/x))/(3*b^2*x^(5/2)) + (35*a*sqrt(a + b/x))/(12*b^3*x^(3/2)) - (35*a^2*sqrt(a + b/x))/(8*b^4*sqrt(x)) + (35*a^3*atanh(sqrt(b)/(sqrt(a + b/x)*sqrt(x))))/(8*b^(9/2))]

    @test_int [1/(a + b/x)^(5/2)*x^(5/2), x, 6, -((512*b^5)/(21*a^6*(a + b/x)^(3/2)*x^(3/2))) - (256*b^4)/(7*a^5*(a + b/x)^(3/2)*sqrt(x)) - (64*b^3*sqrt(x))/(7*a^4*(a + b/x)^(3/2)) + (32*b^2*x^(3/2))/(21*a^3*(a + b/x)^(3/2)) - (4*b*x^(5/2))/(7*a^2*(a + b/x)^(3/2)) + (2*x^(7/2))/(7*a*(a + b/x)^(3/2))]
    @test_int [1/(a + b/x)^(5/2)*x^(3/2), x, 5, (256*b^4)/(15*a^5*(a + b/x)^(3/2)*x^(3/2)) + (128*b^3)/(5*a^4*(a + b/x)^(3/2)*sqrt(x)) + (32*b^2*sqrt(x))/(5*a^3*(a + b/x)^(3/2)) - (16*b*x^(3/2))/(15*a^2*(a + b/x)^(3/2)) + (2*x^(5/2))/(5*a*(a + b/x)^(3/2))]
    @test_int [1/(a + b/x)^(5/2)*x^(1/2), x, 4, -((32*b^3)/(3*a^4*(a + b/x)^(3/2)*x^(3/2))) - (16*b^2)/(a^3*(a + b/x)^(3/2)*sqrt(x)) - (4*b*sqrt(x))/(a^2*(a + b/x)^(3/2)) + (2*x^(3/2))/(3*a*(a + b/x)^(3/2))]
    @test_int [1/(a + b/x)^(5/2)/x^(1/2), x, 3, (16*b^2)/(3*a^3*(a + b/x)^(3/2)*x^(3/2)) + (8*b)/(a^2*(a + b/x)^(3/2)*sqrt(x)) + (2*sqrt(x))/(a*(a + b/x)^(3/2))]
    @test_int [1/(a + b/x)^(5/2)/x^(3/2), x, 2, -((4*b)/(3*a^2*(a + b/x)^(3/2)*x^(3/2))) - 2/(a*(a + b/x)^(3/2)*sqrt(x))]
    @test_int [1/(a + b/x)^(5/2)/x^(5/2), x, 1, -(2/(3*a*(a + b/x)^(3/2)*x^(3/2)))]
    @test_int [1/(a + b/x)^(5/2)/x^(7/2), x, 5, 2/(3*b*(a + b/x)^(3/2)*x^(3/2)) + 2/(b^2*sqrt(a + b/x)*sqrt(x)) - (2*atanh(sqrt(b)/(sqrt(a + b/x)*sqrt(x))))/b^(5/2)]
    @test_int [1/(a + b/x)^(5/2)/x^(9/2), x, 6, 2/(3*b*(a + b/x)^(3/2)*x^(5/2)) + 10/(3*b^2*sqrt(a + b/x)*x^(3/2)) - (5*sqrt(a + b/x))/(b^3*sqrt(x)) + (5*a*atanh(sqrt(b)/(sqrt(a + b/x)*sqrt(x))))/b^(7/2)]
    @test_int [1/(a + b/x)^(5/2)/x^(11/2), x, 7, 2/(3*b*(a + b/x)^(3/2)*x^(7/2)) + 14/(3*b^2*sqrt(a + b/x)*x^(5/2)) - (35*sqrt(a + b/x))/(6*b^3*x^(3/2)) + (35*a*sqrt(a + b/x))/(4*b^4*sqrt(x)) - (35*a^2*atanh(sqrt(b)/(sqrt(a + b/x)*sqrt(x))))/(4*b^(9/2))]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(c*x)^m*(a+b/x^2)^p=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b/x^2)^p=#

    #= ::Subsubsection::Closed:: =#
    #=p>0=#

    @test_int [(a + b/x^2)*x^6, x, 2, (b*x^5)/5 + (a*x^7)/7]
    @test_int [(a + b/x^2)*x^5, x, 2, (b*x^4)/4 + (a*x^6)/6]
    @test_int [(a + b/x^2)*x^4, x, 2, (b*x^3)/3 + (a*x^5)/5]
    @test_int [(a + b/x^2)*x^3, x, 2, (b*x^2)/2 + (a*x^4)/4]
    @test_int [(a + b/x^2)*x^2, x, 2, b*x + (a*x^3)/3]
    @test_int [(a + b/x^2)*x, x, 2, (a*x^2)/2 + b*log(x)]
    @test_int [a + b/x^2, x, 1, -(b/x) + a*x]
    @test_int [(a + b/x^2)/x, x, 2, -b/(2*x^2) + a*log(x)]
    @test_int [(a + b/x^2)/x^2, x, 2, -b/(3*x^3) - a/x]
    @test_int [(a + b/x^2)/x^3, x, 2, -b/(4*x^4) - a/(2*x^2)]
    @test_int [(a + b/x^2)/x^4, x, 2, -b/(5*x^5) - a/(3*x^3)]
    @test_int [(a + b/x^2)/x^5, x, 2, -b/(6*x^6) - a/(4*x^4)]
    @test_int [(a + b/x^2)/x^6, x, 2, -b/(7*x^7) - a/(5*x^5)]

    @test_int [(a + b/x^2)^2*x^6, x, 3, (b^2*x^3)/3 + (2*a*b*x^5)/5 + (a^2*x^7)/7]
    @test_int [(a + b/x^2)^2*x^5, x, 2, (b + a*x^2)^3/(6*a)]
    @test_int [(a + b/x^2)^2*x^4, x, 3, b^2*x + (2*a*b*x^3)/3 + (a^2*x^5)/5]
    @test_int [(a + b/x^2)^2*x^3, x, 4, a*b*x^2 + (a^2*x^4)/4 + b^2*log(x)]
    @test_int [(a + b/x^2)^2*x^2, x, 3, -(b^2/x) + 2*a*b*x + (a^2*x^3)/3]
    @test_int [(a + b/x^2)^2*x^1, x, 4, -b^2/(2*x^2) + (a^2*x^2)/2 + 2*a*b*log(x)]
    @test_int [(a + b/x^2)^2*x^0, x, 3, -b^2/(3*x^3) - (2*a*b)/x + a^2*x]
    @test_int [(a + b/x^2)^2/x^1, x, 4, -b^2/(4*x^4) - (a*b)/x^2 + a^2*log(x)]
    @test_int [(a + b/x^2)^2/x^2, x, 3, -b^2/(5*x^5) - (2*a*b)/(3*x^3) - a^2/x]
    @test_int [(a + b/x^2)^2/x^3, x, 1, -(a + b/x^2)^3/(6*b)]
    @test_int [(a + b/x^2)^2/x^4, x, 3, -b^2/(7*x^7) - (2*a*b)/(5*x^5) - a^2/(3*x^3)]
    @test_int [(a + b/x^2)^2/x^5, x, 4, -b^2/(8*x^8) - (a*b)/(3*x^6) - a^2/(4*x^4)]
    @test_int [(a + b/x^2)^2/x^6, x, 3, -b^2/(9*x^9) - (2*a*b)/(7*x^7) - a^2/(5*x^5)]

    @test_int [(a + b/x^2)^3*x^6, x, 3, b^3*x + a*b^2*x^3 + (3*a^2*b*x^5)/5 + (a^3*x^7)/7]
    @test_int [(a + b/x^2)^3*x^5, x, 4, (3*a*b^2*x^2)/2 + (3*a^2*b*x^4)/4 + (a^3*x^6)/6 + b^3*log(x)]
    @test_int [(a + b/x^2)^3*x^4, x, 3, -(b^3/x) + 3*a*b^2*x + a^2*b*x^3 + (a^3*x^5)/5]
    @test_int [(a + b/x^2)^3*x^3, x, 4, -b^3/(2*x^2) + (3*a^2*b*x^2)/2 + (a^3*x^4)/4 + 3*a*b^2*log(x)]
    @test_int [(a + b/x^2)^3*x^2, x, 3, -b^3/(3*x^3) - (3*a*b^2)/x + 3*a^2*b*x + (a^3*x^3)/3]
    @test_int [(a + b/x^2)^3*x, x, 4, -b^3/(4*x^4) - (3*a*b^2)/(2*x^2) + (a^3*x^2)/2 + 3*a^2*b*log(x)]
    @test_int [(a + b/x^2)^3, x, 3, -b^3/(5*x^5) - (a*b^2)/x^3 - (3*a^2*b)/x + a^3*x]
    @test_int [(a + b/x^2)^3/x, x, 4, -b^3/(6*x^6) - (3*a*b^2)/(4*x^4) - (3*a^2*b)/(2*x^2) + a^3*log(x)]
    @test_int [(a + b/x^2)^3/x^2, x, 3, -b^3/(7*x^7) - (3*a*b^2)/(5*x^5) - (a^2*b)/x^3 - a^3/x]
    @test_int [(a + b/x^2)^3/x^3, x, 1, -(a + b/x^2)^4/(8*b)]
    @test_int [(a + b/x^2)^3/x^4, x, 3, -b^3/(9*x^9) - (3*a*b^2)/(7*x^7) - (3*a^2*b)/(5*x^5) - a^3/(3*x^3)]
    @test_int [(a + b/x^2)^3/x^5, x, 4, -((b + a*x^2)^4/(10*b*x^10)) + (a*(b + a*x^2)^4)/(40*b^2*x^8)]
    @test_int [(a + b/x^2)^3/x^6, x, 3, -b^3/(11*x^11) - (a*b^2)/(3*x^9) - (3*a^2*b)/(7*x^7) - a^3/(5*x^5)]

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [x^6/(a + b/x^2), x, 4, -((b^3*x)/a^4) + (b^2*x^3)/(3*a^3) - (b*x^5)/(5*a^2) + x^7/(7*a) + (b^(7/2)*atan((sqrt(a)*x)/sqrt(b)))/a^(9/2)]
    @test_int [x^5/(a + b/x^2), x, 4, (b^2*x^2)/(2*a^3) - (b*x^4)/(4*a^2) + x^6/(6*a) - (b^3*log(b + a*x^2))/(2*a^4)]
    @test_int [x^4/(a + b/x^2), x, 4, (b^2*x)/a^3 - (b*x^3)/(3*a^2) + x^5/(5*a) - (b^(5/2)*atan((sqrt(a)*x)/sqrt(b)))/a^(7/2)]
    @test_int [x^3/(a + b/x^2), x, 4, -(b*x^2)/(2*a^2) + x^4/(4*a) + (b^2*log(b + a*x^2))/(2*a^3)]
    @test_int [x^2/(a + b/x^2), x, 4, -((b*x)/a^2) + x^3/(3*a) + (b^(3/2)*atan((sqrt(a)*x)/sqrt(b)))/a^(5/2)]
    @test_int [x/(a + b/x^2), x, 4, x^2/(2*a) - (b*log(b + a*x^2))/(2*a^2)]
    @test_int [1/(a + b/x^2), x, 3, x/a - (sqrt(b)*atan((sqrt(a)*x)/sqrt(b)))/a^(3/2)]
    @test_int [1/((a + b/x^2)*x), x, 2, log(b + a*x^2)/(2*a)]
    @test_int [1/((a + b/x^2)*x^2), x, 2, atan((sqrt(a)*x)/sqrt(b))/(sqrt(a)*sqrt(b))]
    @test_int [1/((a + b/x^2)*x^3), x, 1, -log(a + b/x^2)/(2*b)]
    @test_int [1/((a + b/x^2)*x^4), x, 3, -(1/(b*x)) - (sqrt(a)*atan((sqrt(a)*x)/sqrt(b)))/b^(3/2)]
    @test_int [1/((a + b/x^2)*x^5), x, 4, -(1/(2*b*x^2)) - (a*log(x))/b^2 + (a*log(b + a*x^2))/(2*b^2)]
    @test_int [1/((a + b/x^2)*x^6), x, 4, -(1/(3*b*x^3)) + a/(b^2*x) + (a^(3/2)*atan((sqrt(a)*x)/sqrt(b)))/b^(5/2)]
    @test_int [1/((a + b/x^2)*x^7), x, 4, -(1/(4*b*x^4)) + a/(2*b^2*x^2) + (a^2*log(x))/b^3 - (a^2*log(b + a*x^2))/(2*b^3)]
    @test_int [1/((a + b/x^2)*x^8), x, 5, -(1/(5*b*x^5)) + a/(3*b^2*x^3) - a^2/(b^3*x) - (a^(5/2)*atan((sqrt(a)*x)/sqrt(b)))/b^(7/2)]

    @test_int [x^6/(a + b/x^2)^2, x, 5, (-9*b^3*x)/(2*a^5) + (3*b^2*x^3)/(2*a^4) - (9*b*x^5)/(10*a^3) + (9*x^7)/(14*a^2) - x^9/(2*a*(b + a*x^2)) + (9*b^(7/2)*atan((sqrt(a)*x)/sqrt(b)))/(2*a^(11/2))]
    @test_int [x^5/(a + b/x^2)^2, x, 4, (3*b^2*x^2)/(2*a^4) - (b*x^4)/(2*a^3) + x^6/(6*a^2) - b^4/(2*a^5*(b + a*x^2)) - (2*b^3*log(b + a*x^2))/a^5]
    @test_int [x^4/(a + b/x^2)^2, x, 5, (7*b^2*x)/(2*a^4) - (7*b*x^3)/(6*a^3) + (7*x^5)/(10*a^2) - x^7/(2*a*(b + a*x^2)) - (7*b^(5/2)*atan((sqrt(a)*x)/sqrt(b)))/(2*a^(9/2))]
    @test_int [x^3/(a + b/x^2)^2, x, 4, -((b*x^2)/a^3) + x^4/(4*a^2) + b^3/(2*a^4*(b + a*x^2)) + (3*b^2*log(b + a*x^2))/(2*a^4)]
    @test_int [x^2/(a + b/x^2)^2, x, 5, (-5*b*x)/(2*a^3) + (5*x^3)/(6*a^2) - x^5/(2*a*(b + a*x^2)) + (5*b^(3/2)*atan((sqrt(a)*x)/sqrt(b)))/(2*a^(7/2))]
    @test_int [x/(a + b/x^2)^2, x, 4, x^2/(2*a^2) - b^2/(2*a^3*(b + a*x^2)) - (b*log(b + a*x^2))/a^3]
    @test_int [(a + b/x^2)^(-2), x, 4, (3*x)/(2*a^2) - x^3/(2*a*(b + a*x^2)) - (3*sqrt(b)*atan((sqrt(a)*x)/sqrt(b)))/(2*a^(5/2))]
    @test_int [1/((a + b/x^2)^2*x), x, 4, b/(2*a^2*(b + a*x^2)) + log(b + a*x^2)/(2*a^2)]
    @test_int [1/((a + b/x^2)^2*x^2), x, 3, -(x/(2*a*(b + a*x^2))) + atan((sqrt(a)*x)/sqrt(b))/(2*a^(3/2)*sqrt(b))]
    @test_int [1/((a + b/x^2)^2*x^3), x, 1, 1/(2*b*(a + b/x^2))]
    @test_int [1/((a + b/x^2)^2*x^4), x, 3, x/(2*b*(b + a*x^2)) + atan((sqrt(a)*x)/sqrt(b))/(2*sqrt(a)*b^(3/2))]
    @test_int [1/((a + b/x^2)^2*x^5), x, 4, 1/(2*b*(b + a*x^2)) + log(x)/b^2 - log(b + a*x^2)/(2*b^2)]
    @test_int [1/((a + b/x^2)^2*x^6), x, 4, -(3/(2*b^2*x)) + 1/(2*b*x*(b + a*x^2)) - (3*sqrt(a)*atan((sqrt(a)*x)/sqrt(b)))/(2*b^(5/2))]
    @test_int [1/((a + b/x^2)^2*x^7), x, 4, -(1/(2*b^2*x^2)) - a/(2*b^2*(b + a*x^2)) - (2*a*log(x))/b^3 + (a*log(b + a*x^2))/b^3]
    @test_int [1/((a + b/x^2)^2*x^8), x, 5, -(5/(6*b^2*x^3)) + (5*a)/(2*b^3*x) + 1/(2*b*x^3*(b + a*x^2)) + (5*a^(3/2)*atan((sqrt(a)*x)/sqrt(b)))/(2*b^(7/2))]
    @test_int [1/((a + b/x^2)^2*x^9), x, 4, -(1/(4*b^2*x^4)) + a/(b^3*x^2) + a^2/(2*b^3*(b + a*x^2)) + (3*a^2*log(x))/b^4 - (3*a^2*log(b + a*x^2))/(2*b^4)]

    @test_int [x^5/(a + b/x^2)^3, x, 4, (3*b^2*x^2)/a^5 - (3*b*x^4)/(4*a^4) + x^6/(6*a^3) + b^5/(4*a^6*(b + a*x^2)^2) - (5*b^4)/(2*a^6*(b + a*x^2)) - (5*b^3*log(b + a*x^2))/a^6]
    @test_int [x^4/(a + b/x^2)^3, x, 6, (63*b^2*x)/(8*a^5) - (21*b*x^3)/(8*a^4) + (63*x^5)/(40*a^3) - x^9/(4*a*(b + a*x^2)^2) - (9*x^7)/(8*a^2*(b + a*x^2)) - (63*b^(5/2)*atan((sqrt(a)*x)/sqrt(b)))/(8*a^(11/2))]
    @test_int [x^3/(a + b/x^2)^3, x, 4, (-3*b*x^2)/(2*a^4) + x^4/(4*a^3) - b^4/(4*a^5*(b + a*x^2)^2) + (2*b^3)/(a^5*(b + a*x^2)) + (3*b^2*log(b + a*x^2))/a^5]
    @test_int [x^2/(a + b/x^2)^3, x, 6, (-35*b*x)/(8*a^4) + (35*x^3)/(24*a^3) - x^7/(4*a*(b + a*x^2)^2) - (7*x^5)/(8*a^2*(b + a*x^2)) + (35*b^(3/2)*atan((sqrt(a)*x)/sqrt(b)))/(8*a^(9/2))]
    @test_int [x/(a + b/x^2)^3, x, 4, x^2/(2*a^3) + b^3/(4*a^4*(b + a*x^2)^2) - (3*b^2)/(2*a^4*(b + a*x^2)) - (3*b*log(b + a*x^2))/(2*a^4)]
    @test_int [(a + b/x^2)^(-3), x, 5, (15*x)/(8*a^3) - x^5/(4*a*(b + a*x^2)^2) - (5*x^3)/(8*a^2*(b + a*x^2)) - (15*sqrt(b)*atan((sqrt(a)*x)/sqrt(b)))/(8*a^(7/2))]
    @test_int [1/((a + b/x^2)^3*x), x, 4, -(b^2/(4*a^3*(b + a*x^2)^2)) + b/(a^3*(b + a*x^2)) + log(b + a*x^2)/(2*a^3)]
    @test_int [1/((a + b/x^2)^3*x^2), x, 4, -(x^3/(4*a*(b + a*x^2)^2)) - (3*x)/(8*a^2*(b + a*x^2)) + (3*atan((sqrt(a)*x)/sqrt(b)))/(8*a^(5/2)*sqrt(b))]
    @test_int [1/((a + b/x^2)^3*x^3), x, 1, 1/(4*b*(a + b/x^2)^2)]
    @test_int [1/((a + b/x^2)^3*x^4), x, 4, -(x/(4*a*(b + a*x^2)^2)) + x/(8*a*b*(b + a*x^2)) + atan((sqrt(a)*x)/sqrt(b))/(8*a^(3/2)*b^(3/2))]
    @test_int [1/((a + b/x^2)^3*x^5), x, 2, -(1/(4*a*(b + a*x^2)^2))]
    @test_int [1/((a + b/x^2)^3*x^6), x, 4, x/(4*b*(b + a*x^2)^2) + (3*x)/(8*b^2*(b + a*x^2)) + (3*atan((sqrt(a)*x)/sqrt(b)))/(8*sqrt(a)*b^(5/2))]
    @test_int [1/((a + b/x^2)^3*x^7), x, 4, 1/(4*b*(b + a*x^2)^2) + 1/(2*b^2*(b + a*x^2)) + log(x)/b^3 - log(b + a*x^2)/(2*b^3)]
    @test_int [1/((a + b/x^2)^3*x^8), x, 5, -(15/(8*b^3*x)) + 1/(4*b*x*(b + a*x^2)^2) + 5/(8*b^2*x*(b + a*x^2)) - (15*sqrt(a)*atan((sqrt(a)*x)/sqrt(b)))/(8*b^(7/2))]
    @test_int [1/((a + b/x^2)^3*x^9), x, 4, -(1/(2*b^3*x^2)) - a/(4*b^2*(b + a*x^2)^2) - a/(b^3*(b + a*x^2)) - (3*a*log(x))/b^4 + (3*a*log(b + a*x^2))/(2*b^4)]
    @test_int [1/((a + b/x^2)^3*x^10), x, 6, -(35/(24*b^3*x^3)) + (35*a)/(8*b^4*x) + 1/(4*b*x^3*(b + a*x^2)^2) + 7/(8*b^2*x^3*(b + a*x^2)) + (35*a^(3/2)*atan((sqrt(a)*x)/sqrt(b)))/(8*b^(9/2))]
    @test_int [1/((a + b/x^2)^3*x^11), x, 4, -(1/(4*b^3*x^4)) + (3*a)/(2*b^4*x^2) + a^2/(4*b^3*(b + a*x^2)^2) + (3*a^2)/(2*b^4*(b + a*x^2)) + (6*a^2*log(x))/b^5 - (3*a^2*log(b + a*x^2))/b^5]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b/x^2)^(p/2)=#

    #= ::Subsubsection::Closed:: =#
    #=p>0=#

    @test_int [x^3*(a + b/x^2)^(1/2), x, 5, (b*sqrt(a + b/x^2)*x^2)/(8*a) + (1/4)*sqrt(a + b/x^2)*x^4 - (b^2*atanh(sqrt(a + b/x^2)/sqrt(a)))/(8*a^(3/2))]
    @test_int [x^2*(a + b/x^2)^(1/2), x, 1, ((a + b/x^2)^(3/2)*x^3)/(3*a)]
    @test_int [x^1*(a + b/x^2)^(1/2), x, 4, (1/2)*sqrt(a + b/x^2)*x^2 + (b*atanh(sqrt(a + b/x^2)/sqrt(a)))/(2*sqrt(a))]
    @test_int [x^0*(a + b/x^2)^(1/2), x, 4, sqrt(a + b/x^2)*x - sqrt(b)*atanh(sqrt(b)/(sqrt(a + b/x^2)*x))]
    @test_int [(a + b/x^2)^(1/2)/x^1, x, 4, -sqrt(a + b/x^2) + sqrt(a)*atanh(sqrt(a + b/x^2)/sqrt(a))]
    @test_int [(a + b/x^2)^(1/2)/x^2, x, 4, -(sqrt(a + b/x^2)/(2*x)) - (a*atanh(sqrt(b)/(sqrt(a + b/x^2)*x)))/(2*sqrt(b))]
    @test_int [(a + b/x^2)^(1/2)/x^3, x, 1, -((a + b/x^2)^(3/2)/(3*b))]
    @test_int [(a + b/x^2)^(1/2)/x^4, x, 5, -(sqrt(a + b/x^2)/(4*x^3)) - (a*sqrt(a + b/x^2))/(8*b*x) + (a^2*atanh(sqrt(b)/(sqrt(a + b/x^2)*x)))/(8*b^(3/2))]

    @test_int [x^3*(a + b/x^2)^(3/2), x, 5, (3/8)*b*sqrt(a + b/x^2)*x^2 + (1/4)*(a + b/x^2)^(3/2)*x^4 + (3*b^2*atanh(sqrt(a + b/x^2)/sqrt(a)))/(8*sqrt(a))]
    @test_int [x^2*(a + b/x^2)^(3/2), x, 5, b*sqrt(a + b/x^2)*x + (1/3)*(a + b/x^2)^(3/2)*x^3 - b^(3/2)*atanh(sqrt(b)/(sqrt(a + b/x^2)*x))]
    @test_int [x^1*(a + b/x^2)^(3/2), x, 5, (-(3/2))*b*sqrt(a + b/x^2) + (1/2)*(a + b/x^2)^(3/2)*x^2 + (3/2)*sqrt(a)*b*atanh(sqrt(a + b/x^2)/sqrt(a))]
    @test_int [x^0*(a + b/x^2)^(3/2), x, 5, -((3*b*sqrt(a + b/x^2))/(2*x)) + (a + b/x^2)^(3/2)*x - (3/2)*a*sqrt(b)*atanh(sqrt(b)/(sqrt(a + b/x^2)*x))]
    @test_int [(a + b/x^2)^(3/2)/x^1, x, 5, (-a)*sqrt(a + b/x^2) - (1/3)*(a + b/x^2)^(3/2) + a^(3/2)*atanh(sqrt(a + b/x^2)/sqrt(a))]
    @test_int [(a + b/x^2)^(3/2)/x^2, x, 5, -((3*a*sqrt(a + b/x^2))/(8*x)) - (a + b/x^2)^(3/2)/(4*x) - (3*a^2*atanh(sqrt(b)/(sqrt(a + b/x^2)*x)))/(8*sqrt(b))]
    @test_int [(a + b/x^2)^(3/2)/x^3, x, 1, -((a + b/x^2)^(5/2)/(5*b))]
    @test_int [(a + b/x^2)^(3/2)/x^4, x, 6, -((a*sqrt(a + b/x^2))/(8*x^3)) - (a + b/x^2)^(3/2)/(6*x^3) - (a^2*sqrt(a + b/x^2))/(16*b*x) + (a^3*atanh(sqrt(b)/(sqrt(a + b/x^2)*x)))/(16*b^(3/2))]

    @test_int [x^3*(a + b/x^2)^(5/2), x, 6, (-(15/8))*b^2*sqrt(a + b/x^2) + (5/8)*b*(a + b/x^2)^(3/2)*x^2 + (1/4)*(a + b/x^2)^(5/2)*x^4 + (15/8)*sqrt(a)*b^2*atanh(sqrt(a + b/x^2)/sqrt(a))]
    @test_int [x^2*(a + b/x^2)^(5/2), x, 6, -((5*b^2*sqrt(a + b/x^2))/(2*x)) + (5/3)*b*(a + b/x^2)^(3/2)*x + (1/3)*(a + b/x^2)^(5/2)*x^3 - (5/2)*a*b^(3/2)*atanh(sqrt(b)/(sqrt(a + b/x^2)*x))]
    @test_int [x^1*(a + b/x^2)^(5/2), x, 6, (-(5/2))*a*b*sqrt(a + b/x^2) - (5/6)*b*(a + b/x^2)^(3/2) + (1/2)*(a + b/x^2)^(5/2)*x^2 + (5/2)*a^(3/2)*b*atanh(sqrt(a + b/x^2)/sqrt(a))]
    @test_int [x^0*(a + b/x^2)^(5/2), x, 6, -((15*a*b*sqrt(a + b/x^2))/(8*x)) - (5*b*(a + b/x^2)^(3/2))/(4*x) + (a + b/x^2)^(5/2)*x - (15/8)*a^2*sqrt(b)*atanh(sqrt(b)/(sqrt(a + b/x^2)*x))]
    @test_int [(a + b/x^2)^(5/2)/x^1, x, 6, (-a^2)*sqrt(a + b/x^2) - (1/3)*a*(a + b/x^2)^(3/2) - (1/5)*(a + b/x^2)^(5/2) + a^(5/2)*atanh(sqrt(a + b/x^2)/sqrt(a))]
    @test_int [(a + b/x^2)^(5/2)/x^2, x, 6, -((5*a^2*sqrt(a + b/x^2))/(16*x)) - (5*a*(a + b/x^2)^(3/2))/(24*x) - (a + b/x^2)^(5/2)/(6*x) - (5*a^3*atanh(sqrt(b)/(sqrt(a + b/x^2)*x)))/(16*sqrt(b))]
    @test_int [(a + b/x^2)^(5/2)/x^3, x, 1, -((a + b/x^2)^(7/2)/(7*b))]
    @test_int [(a + b/x^2)^(5/2)/x^4, x, 7, -((5*a^2*sqrt(a + b/x^2))/(64*x^3)) - (5*a*(a + b/x^2)^(3/2))/(48*x^3) - (a + b/x^2)^(5/2)/(8*x^3) - (5*a^3*sqrt(a + b/x^2))/(128*b*x) + (5*a^4*atanh(sqrt(b)/(sqrt(a + b/x^2)*x)))/(128*b^(3/2))]

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [x^3/(a + b/x^2)^(1/2), x, 5, -((3*b*sqrt(a + b/x^2)*x^2)/(8*a^2)) + (sqrt(a + b/x^2)*x^4)/(4*a) + (3*b^2*atanh(sqrt(a + b/x^2)/sqrt(a)))/(8*a^(5/2))]
    @test_int [x^1/(a + b/x^2)^(1/2), x, 4, (sqrt(a + b/x^2)*x^2)/(2*a) - (b*atanh(sqrt(a + b/x^2)/sqrt(a)))/(2*a^(3/2))]
    @test_int [1/(x^1*(a + b/x^2)^(1/2)), x, 3, atanh(sqrt(a + b/x^2)/sqrt(a))/sqrt(a)]
    @test_int [1/(x^3*(a + b/x^2)^(1/2)), x, 1, -(sqrt(a + b/x^2)/b)]
    @test_int [1/(x^5*(a + b/x^2)^(1/2)), x, 3, (a*sqrt(a + b/x^2))/b^2 - (a + b/x^2)^(3/2)/(3*b^2)]
    @test_int [1/(x^7*(a + b/x^2)^(1/2)), x, 3, -((a^2*sqrt(a + b/x^2))/b^3) + (2*a*(a + b/x^2)^(3/2))/(3*b^3) - (a + b/x^2)^(5/2)/(5*b^3)]
    @test_int [1/(x^9*(a + b/x^2)^(1/2)), x, 3, (a^3*sqrt(a + b/x^2))/b^4 - (a^2*(a + b/x^2)^(3/2))/b^4 + (3*a*(a + b/x^2)^(5/2))/(5*b^4) - (a + b/x^2)^(7/2)/(7*b^4)]

    @test_int [x^4/(a + b/x^2)^(1/2), x, 3, (8*b^2*sqrt(a + b/x^2)*x)/(15*a^3) - (4*b*sqrt(a + b/x^2)*x^3)/(15*a^2) + (sqrt(a + b/x^2)*x^5)/(5*a)]
    @test_int [x^2/(a + b/x^2)^(1/2), x, 2, -((2*b*sqrt(a + b/x^2)*x)/(3*a^2)) + (sqrt(a + b/x^2)*x^3)/(3*a)]
    @test_int [x^0/(a + b/x^2)^(1/2), x, 1, (sqrt(a + b/x^2)*x)/a]
    @test_int [1/(x^2*(a + b/x^2)^(1/2)), x, 3, -(atanh(sqrt(b)/(sqrt(a + b/x^2)*x))/sqrt(b))]
    @test_int [1/(x^4*(a + b/x^2)^(1/2)), x, 4, -(sqrt(a + b/x^2)/(2*b*x)) + (a*atanh(sqrt(b)/(sqrt(a + b/x^2)*x)))/(2*b^(3/2))]

    @test_int [1/(x^1*sqrt(-a + b/x^2)), x, 3, -(atan(sqrt(-a + b/x^2)/sqrt(a))/sqrt(a))]
    @test_int [1/(x^2*sqrt(2 + b/x^2)), x, 2, -(acsch((sqrt(2)*x)/sqrt(b))/sqrt(b))]
    @test_int [1/(x^2*sqrt(2 - b/x^2)), x, 2, -(acsc((sqrt(2)*x)/sqrt(b))/sqrt(b))]

    @test_int [x^3/(a + b/x^2)^(3/2), x, 6, -((15*b^2)/(8*a^3*sqrt(a + b/x^2))) - (5*b*x^2)/(8*a^2*sqrt(a + b/x^2)) + x^4/(4*a*sqrt(a + b/x^2)) + (15*b^2*atanh(sqrt(a + b/x^2)/sqrt(a)))/(8*a^(7/2))]
    @test_int [x^1/(a + b/x^2)^(3/2), x, 5, (3*b)/(2*a^2*sqrt(a + b/x^2)) + x^2/(2*a*sqrt(a + b/x^2)) - (3*b*atanh(sqrt(a + b/x^2)/sqrt(a)))/(2*a^(5/2))]
    @test_int [1/(x^1*(a + b/x^2)^(3/2)), x, 4, -(1/(a*sqrt(a + b/x^2))) + atanh(sqrt(a + b/x^2)/sqrt(a))/a^(3/2)]
    @test_int [1/(x^3*(a + b/x^2)^(3/2)), x, 1, 1/(b*sqrt(a + b/x^2))]
    @test_int [1/(x^5*(a + b/x^2)^(3/2)), x, 3, -(a/(b^2*sqrt(a + b/x^2))) - sqrt(a + b/x^2)/b^2]
    @test_int [1/(x^7*(a + b/x^2)^(3/2)), x, 3, a^2/(b^3*sqrt(a + b/x^2)) + (2*a*sqrt(a + b/x^2))/b^3 - (a + b/x^2)^(3/2)/(3*b^3)]
    @test_int [1/(x^9*(a + b/x^2)^(3/2)), x, 3, -(a^3/(b^4*sqrt(a + b/x^2))) - (3*a^2*sqrt(a + b/x^2))/b^4 + (a*(a + b/x^2)^(3/2))/b^4 - (a + b/x^2)^(5/2)/(5*b^4)]

    @test_int [x^4/(a + b/x^2)^(3/2), x, 4, -((8*b^2*x)/(5*a^3*sqrt(a + b/x^2))) + (16*b^2*sqrt(a + b/x^2)*x)/(5*a^4) - (2*b*x^3)/(5*a^2*sqrt(a + b/x^2)) + x^5/(5*a*sqrt(a + b/x^2))]
    @test_int [x^2/(a + b/x^2)^(3/2), x, 3, (4*b*x)/(3*a^2*sqrt(a + b/x^2)) - (8*b*sqrt(a + b/x^2)*x)/(3*a^3) + x^3/(3*a*sqrt(a + b/x^2))]
    @test_int [x^0/(a + b/x^2)^(3/2), x, 2, -(x/(a*sqrt(a + b/x^2))) + (2*sqrt(a + b/x^2)*x)/a^2]
    @test_int [1/(x^2*(a + b/x^2)^(3/2)), x, 1, -(1/(a*sqrt(a + b/x^2)*x))]
    @test_int [1/(x^4*(a + b/x^2)^(3/2)), x, 4, 1/(b*sqrt(a + b/x^2)*x) - atanh(sqrt(b)/(sqrt(a + b/x^2)*x))/b^(3/2)]
    @test_int [1/(x^6*(a + b/x^2)^(3/2)), x, 5, 1/(b*sqrt(a + b/x^2)*x^3) - (3*sqrt(a + b/x^2))/(2*b^2*x) + (3*a*atanh(sqrt(b)/(sqrt(a + b/x^2)*x)))/(2*b^(5/2))]
    @test_int [1/(x^8*(a + b/x^2)^(3/2)), x, 6, 1/(b*sqrt(a + b/x^2)*x^5) - (5*sqrt(a + b/x^2))/(4*b^2*x^3) + (15*a*sqrt(a + b/x^2))/(8*b^3*x) - (15*a^2*atanh(sqrt(b)/(sqrt(a + b/x^2)*x)))/(8*b^(7/2))]

    @test_int [x^3/(a + b/x^2)^(5/2), x, 7, -((35*b^2)/(24*a^3*(a + b/x^2)^(3/2))) - (35*b^2)/(8*a^4*sqrt(a + b/x^2)) - (7*b*x^2)/(8*a^2*(a + b/x^2)^(3/2)) + x^4/(4*a*(a + b/x^2)^(3/2)) + (35*b^2*atanh(sqrt(a + b/x^2)/sqrt(a)))/(8*a^(9/2))]
    @test_int [x^1/(a + b/x^2)^(5/2), x, 6, (5*b)/(6*a^2*(a + b/x^2)^(3/2)) + (5*b)/(2*a^3*sqrt(a + b/x^2)) + x^2/(2*a*(a + b/x^2)^(3/2)) - (5*b*atanh(sqrt(a + b/x^2)/sqrt(a)))/(2*a^(7/2))]
    @test_int [1/(x^1*(a + b/x^2)^(5/2)), x, 5, -(1/(3*a*(a + b/x^2)^(3/2))) - 1/(a^2*sqrt(a + b/x^2)) + atanh(sqrt(a + b/x^2)/sqrt(a))/a^(5/2)]
    @test_int [1/(x^3*(a + b/x^2)^(5/2)), x, 1, 1/(3*b*(a + b/x^2)^(3/2))]
    @test_int [1/(x^5*(a + b/x^2)^(5/2)), x, 3, -(a/(3*b^2*(a + b/x^2)^(3/2))) + 1/(b^2*sqrt(a + b/x^2))]
    @test_int [1/(x^7*(a + b/x^2)^(5/2)), x, 3, a^2/(3*b^3*(a + b/x^2)^(3/2)) - (2*a)/(b^3*sqrt(a + b/x^2)) - sqrt(a + b/x^2)/b^3]
    @test_int [1/(x^9*(a + b/x^2)^(5/2)), x, 3, -(a^3/(3*b^4*(a + b/x^2)^(3/2))) + (3*a^2)/(b^4*sqrt(a + b/x^2)) + (3*a*sqrt(a + b/x^2))/b^4 - (a + b/x^2)^(3/2)/(3*b^4)]

    @test_int [x^2/(a + b/x^2)^(5/2), x, 4, (2*b*x)/(3*a^2*(a + b/x^2)^(3/2)) + (8*b*x)/(3*a^3*sqrt(a + b/x^2)) - (16*b*sqrt(a + b/x^2)*x)/(3*a^4) + x^3/(3*a*(a + b/x^2)^(3/2))]
    @test_int [x^0/(a + b/x^2)^(5/2), x, 3, -(x/(3*a*(a + b/x^2)^(3/2))) - (4*x)/(3*a^2*sqrt(a + b/x^2)) + (8*sqrt(a + b/x^2)*x)/(3*a^3)]
    @test_int [1/(x^2*(a + b/x^2)^(5/2)), x, 2, -((2*b)/(3*a^2*(a + b/x^2)^(3/2)*x^3)) - 1/(a*(a + b/x^2)^(3/2)*x)]
    @test_int [1/(x^4*(a + b/x^2)^(5/2)), x, 1, -(1/(3*a*(a + b/x^2)^(3/2)*x^3))]
    @test_int [1/(x^6*(a + b/x^2)^(5/2)), x, 5, 1/(3*b*(a + b/x^2)^(3/2)*x^3) + 1/(b^2*sqrt(a + b/x^2)*x) - atanh(sqrt(b)/(sqrt(a + b/x^2)*x))/b^(5/2)]
    @test_int [1/(x^8*(a + b/x^2)^(5/2)), x, 6, 1/(3*b*(a + b/x^2)^(3/2)*x^5) + 5/(3*b^2*sqrt(a + b/x^2)*x^3) - (5*sqrt(a + b/x^2))/(2*b^3*x) + (5*a*atanh(sqrt(b)/(sqrt(a + b/x^2)*x)))/(2*b^(7/2))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b/x^2)^(p/3)=#

    @test_int [(1 + 1/x^2)^(1/3)/x^3, x, 1, (-3*(1 + x^(-2))^(4/3))/8]
    @test_int [(1 + 1/x^2)^(5/3)/x^3, x, 1, (-3*(1 + x^(-2))^(8/3))/16]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(c*x)^m*(a+b/x^2)^p*with*m*symbolic=#

    @test_int [(c*x)^m*(1 + b/x^2)^(3/2), x, 2, ((c*x)^(1 + m)*HypergeometricFunctions._₂F₁(-(3/2), (1/2)*(-1 - m), (1 - m)/2, -(b/x^2)))/(c*(1 + m))]
    @test_int [(c*x)^m*(1 + b/x^2)^(1/2), x, 2, ((c*x)^(1 + m)*HypergeometricFunctions._₂F₁(-(1/2), (1/2)*(-1 - m), (1 - m)/2, -(b/x^2)))/(c*(1 + m))]
    @test_int [(c*x)^m/(1 + b/x^2)^(1/2), x, 2, ((c*x)^(1 + m)*HypergeometricFunctions._₂F₁(1/2, (1/2)*(-1 - m), (1 - m)/2, -(b/x^2)))/(c*(1 + m))]
    @test_int [(c*x)^m/(1 + b/x^2)^(3/2), x, 2, ((c*x)^(1 + m)*HypergeometricFunctions._₂F₁(3/2, (1/2)*(-1 - m), (1 - m)/2, -(b/x^2)))/(c*(1 + m))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(c*x)^m*(a+b/x^2)^p*with*p*symbolic=#

    @test_int [(c*x)^m*(1 + b/x^2)^p, x, 2, ((c*x)^(1 + m)*HypergeometricFunctions._₂F₁((1/2)*(-1 - m), -p, (1 - m)/2, -(b/x^2)))/(c*(1 + m))]
    @test_int [(c*x)^m*(a + b/x^2)^p, x, 3, ((a + b/x^2)^p*(c*x)^(1 + m)*HypergeometricFunctions._₂F₁((1/2)*(-1 - m), -p, (1 - m)/2, -(b/(a*x^2))))/((1 + b/(a*x^2))^p*(c*(1 + m)))]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(c*x)^m*(a+b/x^3)^p=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b/x^3)^p=#

    #= ::Subsubsection:: =#
    #=p>0=#

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [x^5/(a + b/x^3), x, 4, -((b*x^3)/(3*a^2)) + x^6/(6*a) + (b^2*log(b + a*x^3))/(3*a^3)]
    @test_int [x^4/(a + b/x^3), x, 9, -((b*x^2)/(2*a^2)) + x^5/(5*a) - (b^(5/3)*atan((b^(1/3) - 2*a^(1/3)*x)/(sqrt(3)*b^(1/3))))/(sqrt(3)*a^(8/3)) - (b^(5/3)*log(b^(1/3) + a^(1/3)*x))/(3*a^(8/3)) + (b^(5/3)*log(b^(2/3) - a^(1/3)*b^(1/3)*x + a^(2/3)*x^2))/(6*a^(8/3))]
    @test_int [x^3/(a + b/x^3), x, 9, -((b*x)/a^2) + x^4/(4*a) - (b^(4/3)*atan((b^(1/3) - 2*a^(1/3)*x)/(sqrt(3)*b^(1/3))))/(sqrt(3)*a^(7/3)) + (b^(4/3)*log(b^(1/3) + a^(1/3)*x))/(3*a^(7/3)) - (b^(4/3)*log(b^(2/3) - a^(1/3)*b^(1/3)*x + a^(2/3)*x^2))/(6*a^(7/3))]
    @test_int [x^2/(a + b/x^3), x, 4, x^3/(3*a) - (b*log(b + a*x^3))/(3*a^2)]
    @test_int [x^1/(a + b/x^3), x, 8, x^2/(2*a) + (b^(2/3)*atan((b^(1/3) - 2*a^(1/3)*x)/(sqrt(3)*b^(1/3))))/(sqrt(3)*a^(5/3)) + (b^(2/3)*log(b^(1/3) + a^(1/3)*x))/(3*a^(5/3)) - (b^(2/3)*log(b^(2/3) - a^(1/3)*b^(1/3)*x + a^(2/3)*x^2))/(6*a^(5/3))]
    @test_int [x^0/(a + b/x^3), x, 8, x/a + (b^(1/3)*atan((b^(1/3) - 2*a^(1/3)*x)/(sqrt(3)*b^(1/3))))/(sqrt(3)*a^(4/3)) - (b^(1/3)*log(b^(1/3) + a^(1/3)*x))/(3*a^(4/3)) + (b^(1/3)*log(b^(2/3) - a^(1/3)*b^(1/3)*x + a^(2/3)*x^2))/(6*a^(4/3))]
    @test_int [1/(x^1*(a + b/x^3)), x, 2, log(b + a*x^3)/(3*a)]
    @test_int [1/(x^2*(a + b/x^3)), x, 7, -(atan((b^(1/3) - 2*a^(1/3)*x)/(sqrt(3)*b^(1/3)))/(sqrt(3)*a^(2/3)*b^(1/3))) - log(b^(1/3) + a^(1/3)*x)/(3*a^(2/3)*b^(1/3)) + log(b^(2/3) - a^(1/3)*b^(1/3)*x + a^(2/3)*x^2)/(6*a^(2/3)*b^(1/3))]
    @test_int [1/(x^3*(a + b/x^3)), x, 7, -(atan((b^(1/3) - 2*a^(1/3)*x)/(sqrt(3)*b^(1/3)))/(sqrt(3)*a^(1/3)*b^(2/3))) + log(b^(1/3) + a^(1/3)*x)/(3*a^(1/3)*b^(2/3)) - log(b^(2/3) - a^(1/3)*b^(1/3)*x + a^(2/3)*x^2)/(6*a^(1/3)*b^(2/3))]
    @test_int [1/(x^4*(a + b/x^3)), x, 1, -(log(a + b/x^3)/(3*b))]
    @test_int [1/(x^5*(a + b/x^3)), x, 8, -(1/(b*x)) + (a^(1/3)*atan((b^(1/3) - 2*a^(1/3)*x)/(sqrt(3)*b^(1/3))))/(sqrt(3)*b^(4/3)) + (a^(1/3)*log(b^(1/3) + a^(1/3)*x))/(3*b^(4/3)) - (a^(1/3)*log(b^(2/3) - a^(1/3)*b^(1/3)*x + a^(2/3)*x^2))/(6*b^(4/3))]
    @test_int [1/(x^6*(a + b/x^3)), x, 8, -(1/(2*b*x^2)) + (a^(2/3)*atan((b^(1/3) - 2*a^(1/3)*x)/(sqrt(3)*b^(1/3))))/(sqrt(3)*b^(5/3)) - (a^(2/3)*log(b^(1/3) + a^(1/3)*x))/(3*b^(5/3)) + (a^(2/3)*log(b^(2/3) - a^(1/3)*b^(1/3)*x + a^(2/3)*x^2))/(6*b^(5/3))]
    @test_int [1/(x^7*(a + b/x^3)), x, 4, -(1/(3*b*x^3)) - (a*log(x))/b^2 + (a*log(b + a*x^3))/(3*b^2)]

    @test_int [x^5/(a + b/x^3)^2, x, 4, -((2*b*x^3)/(3*a^3)) + x^6/(6*a^2) + b^3/(3*a^4*(b + a*x^3)) + (b^2*log(b + a*x^3))/a^4]
    @test_int [x^4/(a + b/x^3)^2, x, 10, -((4*b*x^2)/(3*a^3)) + (8*x^5)/(15*a^2) - x^8/(3*a*(b + a*x^3)) - (8*b^(5/3)*atan((b^(1/3) - 2*a^(1/3)*x)/(sqrt(3)*b^(1/3))))/(3*sqrt(3)*a^(11/3)) - (8*b^(5/3)*log(b^(1/3) + a^(1/3)*x))/(9*a^(11/3)) + (4*b^(5/3)*log(b^(2/3) - a^(1/3)*b^(1/3)*x + a^(2/3)*x^2))/(9*a^(11/3))]
    @test_int [x^3/(a + b/x^3)^2, x, 10, -((7*b*x)/(3*a^3)) + (7*x^4)/(12*a^2) - x^7/(3*a*(b + a*x^3)) - (7*b^(4/3)*atan((b^(1/3) - 2*a^(1/3)*x)/(sqrt(3)*b^(1/3))))/(3*sqrt(3)*a^(10/3)) + (7*b^(4/3)*log(b^(1/3) + a^(1/3)*x))/(9*a^(10/3)) - (7*b^(4/3)*log(b^(2/3) - a^(1/3)*b^(1/3)*x + a^(2/3)*x^2))/(18*a^(10/3))]
    @test_int [x^2/(a + b/x^3)^2, x, 4, x^3/(3*a^2) - b^2/(3*a^3*(b + a*x^3)) - (2*b*log(b + a*x^3))/(3*a^3)]
    @test_int [x^1/(a + b/x^3)^2, x, 9, (5*x^2)/(6*a^2) - x^5/(3*a*(b + a*x^3)) + (5*b^(2/3)*atan((b^(1/3) - 2*a^(1/3)*x)/(sqrt(3)*b^(1/3))))/(3*sqrt(3)*a^(8/3)) + (5*b^(2/3)*log(b^(1/3) + a^(1/3)*x))/(9*a^(8/3)) - (5*b^(2/3)*log(b^(2/3) - a^(1/3)*b^(1/3)*x + a^(2/3)*x^2))/(18*a^(8/3))]
    @test_int [x^0/(a + b/x^3)^2, x, 9, (4*x)/(3*a^2) - x^4/(3*a*(b + a*x^3)) + (4*b^(1/3)*atan((b^(1/3) - 2*a^(1/3)*x)/(sqrt(3)*b^(1/3))))/(3*sqrt(3)*a^(7/3)) - (4*b^(1/3)*log(b^(1/3) + a^(1/3)*x))/(9*a^(7/3)) + (2*b^(1/3)*log(b^(2/3) - a^(1/3)*b^(1/3)*x + a^(2/3)*x^2))/(9*a^(7/3))]
    @test_int [1/(x^1*(a + b/x^3)^2), x, 4, b/(3*a^2*(b + a*x^3)) + log(b + a*x^3)/(3*a^2)]
    @test_int [1/(x^2*(a + b/x^3)^2), x, 8, -(x^2/(3*a*(b + a*x^3))) - (2*atan((b^(1/3) - 2*a^(1/3)*x)/(sqrt(3)*b^(1/3))))/(3*sqrt(3)*a^(5/3)*b^(1/3)) - (2*log(b^(1/3) + a^(1/3)*x))/(9*a^(5/3)*b^(1/3)) + log(b^(2/3) - a^(1/3)*b^(1/3)*x + a^(2/3)*x^2)/(9*a^(5/3)*b^(1/3))]
    @test_int [1/(x^3*(a + b/x^3)^2), x, 8, -(x/(3*a*(b + a*x^3))) - atan((b^(1/3) - 2*a^(1/3)*x)/(sqrt(3)*b^(1/3)))/(3*sqrt(3)*a^(4/3)*b^(2/3)) + log(b^(1/3) + a^(1/3)*x)/(9*a^(4/3)*b^(2/3)) - log(b^(2/3) - a^(1/3)*b^(1/3)*x + a^(2/3)*x^2)/(18*a^(4/3)*b^(2/3))]
    @test_int [1/(x^4*(a + b/x^3)^2), x, 1, 1/(3*b*(a + b/x^3))]
    @test_int [1/(x^5*(a + b/x^3)^2), x, 8, x^2/(3*b*(b + a*x^3)) - atan((b^(1/3) - 2*a^(1/3)*x)/(sqrt(3)*b^(1/3)))/(3*sqrt(3)*a^(2/3)*b^(4/3)) - log(b^(1/3) + a^(1/3)*x)/(9*a^(2/3)*b^(4/3)) + log(b^(2/3) - a^(1/3)*b^(1/3)*x + a^(2/3)*x^2)/(18*a^(2/3)*b^(4/3))]
    @test_int [1/(x^6*(a + b/x^3)^2), x, 8, x/(3*b*(b + a*x^3)) - (2*atan((b^(1/3) - 2*a^(1/3)*x)/(sqrt(3)*b^(1/3))))/(3*sqrt(3)*a^(1/3)*b^(5/3)) + (2*log(b^(1/3) + a^(1/3)*x))/(9*a^(1/3)*b^(5/3)) - log(b^(2/3) - a^(1/3)*b^(1/3)*x + a^(2/3)*x^2)/(9*a^(1/3)*b^(5/3))]
    @test_int [1/(x^7*(a + b/x^3)^2), x, 4, 1/(3*b*(b + a*x^3)) + log(x)/b^2 - log(b + a*x^3)/(3*b^2)]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b/x^3)^(p/2)=#

    #= ::Subsubsection::Closed:: =#
    #=p>0=#

    @test_int [sqrt(a + b/x^3)*x^5, x, 5, (b*sqrt(a + b/x^3)*x^3)/(12*a) + (sqrt(a + b/x^3)*x^6)/6 - (b^2*atanh(sqrt(a + b/x^3)/sqrt(a)))/(12*a^(3/2))]
    @test_int [sqrt(a + b/x^3)*x^2, x, 4, (sqrt(a + b/x^3)*x^3)/3 + (b*atanh(sqrt(a + b/x^3)/sqrt(a)))/(3*sqrt(a))]
    @test_int [sqrt(a + b/x^3)/x^1, x, 4, (-2*sqrt(a + b/x^3))/3 + (2*sqrt(a)*atanh(sqrt(a + b/x^3)/sqrt(a)))/3]
    @test_int [sqrt(a + b/x^3)/x^4, x, 1, (-2*(a + b/x^3)^(3/2))/(9*b)]
    @test_int [sqrt(a + b/x^3)/x^7, x, 3, (2*a*(a + b/x^3)^(3/2))/(9*b^2) - (2*(a + b/x^3)^(5/2))/(15*b^2)]
    @test_int [sqrt(a + b/x^3)/x^10, x, 3, (-2*a^2*(a + b/x^3)^(3/2))/(9*b^3) + (4*a*(a + b/x^3)^(5/2))/(15*b^3) - (2*(a + b/x^3)^(7/2))/(21*b^3)]
    @test_int [sqrt(a + b/x^3)/x^13, x, 3, (2*a^3*(a + b/x^3)^(3/2))/(9*b^4) - (2*a^2*(a + b/x^3)^(5/2))/(5*b^4) + (2*a*(a + b/x^3)^(7/2))/(7*b^4) - (2*(a + b/x^3)^(9/2))/(27*b^4)]

    @test_int [sqrt(a + b/x^3)*x^7, x, 5, -((21*b^2*sqrt(a + b/x^3)*x^2)/(320*a^2)) + (3*b*sqrt(a + b/x^3)*x^5)/(80*a) + (1/8)*sqrt(a + b/x^3)*x^8 - (7*3^(3/4)*sqrt(2 + sqrt(3))*b^(8/3)*(a^(1/3) + b^(1/3)/x)*sqrt((a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)), -7 - 4*sqrt(3)))/(320*a^2*sqrt(a + b/x^3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2))]
    @test_int [sqrt(a + b/x^3)*x^4, x, 4, (3*b*sqrt(a + b/x^3)*x^2)/(20*a) + (1/5)*sqrt(a + b/x^3)*x^5 + (3^(3/4)*sqrt(2 + sqrt(3))*b^(5/3)*(a^(1/3) + b^(1/3)/x)*sqrt((a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)), -7 - 4*sqrt(3)))/(20*a*sqrt(a + b/x^3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2))]
    @test_int [sqrt(a + b/x^3)*x^1, x, 3, (1/2)*sqrt(a + b/x^3)*x^2 - (3^(3/4)*sqrt(2 + sqrt(3))*b^(2/3)*(a^(1/3) + b^(1/3)/x)*sqrt((a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)), -7 - 4*sqrt(3)))/(2*sqrt(a + b/x^3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2))]
    @test_int [sqrt(a + b/x^3)/x^2, x, 3, -((2*sqrt(a + b/x^3))/(5*x)) - (2*3^(3/4)*sqrt(2 + sqrt(3))*a*(a^(1/3) + b^(1/3)/x)*sqrt((a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)), -7 - 4*sqrt(3)))/(5*b^(1/3)*sqrt(a + b/x^3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2))]
    @test_int [sqrt(a + b/x^3)/x^5, x, 4, -((2*sqrt(a + b/x^3))/(11*x^4)) - (6*a*sqrt(a + b/x^3))/(55*b*x) + (4*3^(3/4)*sqrt(2 + sqrt(3))*a^2*(a^(1/3) + b^(1/3)/x)*sqrt((a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)), -7 - 4*sqrt(3)))/(55*b^(4/3)*sqrt(a + b/x^3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2))]
    @test_int [sqrt(a + b/x^3)/x^8, x, 5, -((2*sqrt(a + b/x^3))/(17*x^7)) - (6*a*sqrt(a + b/x^3))/(187*b*x^4) + (48*a^2*sqrt(a + b/x^3))/(935*b^2*x) - (32*3^(3/4)*sqrt(2 + sqrt(3))*a^3*(a^(1/3) + b^(1/3)/x)*sqrt((a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)), -7 - 4*sqrt(3)))/(935*b^(7/3)*sqrt(a + b/x^3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2))]

    @test_int [sqrt(a + b/x^3)*x^6, x, 7, (15*b^(7/3)*sqrt(a + b/x^3))/(112*a^2*((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)) - (15*b^2*sqrt(a + b/x^3)*x)/(112*a^2) + (3*b*sqrt(a + b/x^3)*x^4)/(56*a) + (1/7)*sqrt(a + b/x^3)*x^7 - (15*3^(1/4)*sqrt(2 - sqrt(3))*b^(7/3)*(a^(1/3) + b^(1/3)/x)*sqrt((a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)), -7 - 4*sqrt(3)))/(224*a^(5/3)*sqrt(a + b/x^3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2)) + (5*3^(3/4)*b^(7/3)*(a^(1/3) + b^(1/3)/x)*sqrt((a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)), -7 - 4*sqrt(3)))/(56*sqrt(2)*a^(5/3)*sqrt(a + b/x^3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2))]
    @test_int [sqrt(a + b/x^3)*x^3, x, 6, -((3*b^(4/3)*sqrt(a + b/x^3))/(8*a*((1 + sqrt(3))*a^(1/3) + b^(1/3)/x))) + (3*b*sqrt(a + b/x^3)*x)/(8*a) + (1/4)*sqrt(a + b/x^3)*x^4 + (3*3^(1/4)*sqrt(2 - sqrt(3))*b^(4/3)*(a^(1/3) + b^(1/3)/x)*sqrt((a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)), -7 - 4*sqrt(3)))/(16*a^(2/3)*sqrt(a + b/x^3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2)) - (3^(3/4)*b^(4/3)*(a^(1/3) + b^(1/3)/x)*sqrt((a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)), -7 - 4*sqrt(3)))/(4*sqrt(2)*a^(2/3)*sqrt(a + b/x^3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2))]
    @test_int [sqrt(a + b/x^3)*x^0, x, 5, -((3*b^(1/3)*sqrt(a + b/x^3))/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)) + sqrt(a + b/x^3)*x + (3*3^(1/4)*sqrt(2 - sqrt(3))*a^(1/3)*b^(1/3)*(a^(1/3) + b^(1/3)/x)*sqrt((a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)), -7 - 4*sqrt(3)))/(2*sqrt(a + b/x^3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2)) - (sqrt(2)*3^(3/4)*a^(1/3)*b^(1/3)*(a^(1/3) + b^(1/3)/x)*sqrt((a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)), -7 - 4*sqrt(3)))/(sqrt(a + b/x^3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2))]
    @test_int [sqrt(a + b/x^3)/x^3, x, 5, -((6*a*sqrt(a + b/x^3))/(7*b^(2/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)/x))) - (2*sqrt(a + b/x^3))/(7*x^2) + (3*3^(1/4)*sqrt(2 - sqrt(3))*a^(4/3)*(a^(1/3) + b^(1/3)/x)*sqrt((a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)), -7 - 4*sqrt(3)))/(7*b^(2/3)*sqrt(a + b/x^3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2)) - (2*sqrt(2)*3^(3/4)*a^(4/3)*(a^(1/3) + b^(1/3)/x)*sqrt((a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)), -7 - 4*sqrt(3)))/(7*b^(2/3)*sqrt(a + b/x^3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2))]
    @test_int [sqrt(a + b/x^3)/x^6, x, 6, (24*a^2*sqrt(a + b/x^3))/(91*b^(5/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)) - (2*sqrt(a + b/x^3))/(13*x^5) - (6*a*sqrt(a + b/x^3))/(91*b*x^2) - (12*3^(1/4)*sqrt(2 - sqrt(3))*a^(7/3)*(a^(1/3) + b^(1/3)/x)*sqrt((a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)), -7 - 4*sqrt(3)))/(91*b^(5/3)*sqrt(a + b/x^3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2)) + (8*sqrt(2)*3^(3/4)*a^(7/3)*(a^(1/3) + b^(1/3)/x)*sqrt((a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)), -7 - 4*sqrt(3)))/(91*b^(5/3)*sqrt(a + b/x^3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2))]
    @test_int [sqrt(a + b/x^3)/x^9, x, 7, -((240*a^3*sqrt(a + b/x^3))/(1729*b^(8/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)/x))) - (2*sqrt(a + b/x^3))/(19*x^8) - (6*a*sqrt(a + b/x^3))/(247*b*x^5) + (60*a^2*sqrt(a + b/x^3))/(1729*b^2*x^2) + (120*3^(1/4)*sqrt(2 - sqrt(3))*a^(10/3)*(a^(1/3) + b^(1/3)/x)*sqrt((a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)), -7 - 4*sqrt(3)))/(1729*b^(8/3)*sqrt(a + b/x^3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2)) - (80*sqrt(2)*3^(3/4)*a^(10/3)*(a^(1/3) + b^(1/3)/x)*sqrt((a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)), -7 - 4*sqrt(3)))/(1729*b^(8/3)*sqrt(a + b/x^3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2))]

    @test_int [(a + b/x^3)^(3/2)*x^5, x, 5, (b*sqrt(a + b/x^3)*x^3)/4 + ((a + b/x^3)^(3/2)*x^6)/6 + (b^2*atanh(sqrt(a + b/x^3)/sqrt(a)))/(4*sqrt(a))]
    @test_int [(a + b/x^3)^(3/2)*x^2, x, 5, -(b*sqrt(a + b/x^3)) + ((a + b/x^3)^(3/2)*x^3)/3 + sqrt(a)*b*atanh(sqrt(a + b/x^3)/sqrt(a))]
    @test_int [(a + b/x^3)^(3/2)/x^1, x, 5, (-2*a*sqrt(a + b/x^3))/3 - (2*(a + b/x^3)^(3/2))/9 + (2*a^(3/2)*atanh(sqrt(a + b/x^3)/sqrt(a)))/3]
    @test_int [(a + b/x^3)^(3/2)/x^4, x, 1, (-2*(a + b/x^3)^(5/2))/(15*b)]
    @test_int [(a + b/x^3)^(3/2)/x^7, x, 3, (2*a*(a + b/x^3)^(5/2))/(15*b^2) - (2*(a + b/x^3)^(7/2))/(21*b^2)]
    @test_int [(a + b/x^3)^(3/2)/x^10, x, 3, (-2*a^2*(a + b/x^3)^(5/2))/(15*b^3) + (4*a*(a + b/x^3)^(7/2))/(21*b^3) - (2*(a + b/x^3)^(9/2))/(27*b^3)]
    @test_int [(a + b/x^3)^(3/2)/x^13, x, 3, (2*a^3*(a + b/x^3)^(5/2))/(15*b^4) - (2*a^2*(a + b/x^3)^(7/2))/(7*b^4) + (2*a*(a + b/x^3)^(9/2))/(9*b^4) - (2*(a + b/x^3)^(11/2))/(33*b^4)]

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [x^5/sqrt(a + b/x^3), x, 5, -((b*sqrt(a + b/x^3)*x^3)/(4*a^2)) + (sqrt(a + b/x^3)*x^6)/(6*a) + (b^2*atanh(sqrt(a + b/x^3)/sqrt(a)))/(4*a^(5/2))]
    @test_int [x^2/sqrt(a + b/x^3), x, 4, (sqrt(a + b/x^3)*x^3)/(3*a) - (b*atanh(sqrt(a + b/x^3)/sqrt(a)))/(3*a^(3/2))]
    @test_int [1/(x^1*sqrt(a + b/x^3)), x, 3, (2*atanh(sqrt(a + b/x^3)/sqrt(a)))/(3*sqrt(a))]
    @test_int [1/(x^4*sqrt(a + b/x^3)), x, 1, -((2*sqrt(a + b/x^3))/(3*b))]
    @test_int [1/(x^7*sqrt(a + b/x^3)), x, 3, (2*a*sqrt(a + b/x^3))/(3*b^2) - (2*(a + b/x^3)^(3/2))/(9*b^2)]
    @test_int [1/(x^10*sqrt(a + b/x^3)), x, 3, -((2*a^2*sqrt(a + b/x^3))/(3*b^3)) + (4*a*(a + b/x^3)^(3/2))/(9*b^3) - (2*(a + b/x^3)^(5/2))/(15*b^3)]
    @test_int [1/(x^13*sqrt(a + b/x^3)), x, 3, (2*a^3*sqrt(a + b/x^3))/(3*b^4) - (2*a^2*(a + b/x^3)^(3/2))/(3*b^4) + (2*a*(a + b/x^3)^(5/2))/(5*b^4) - (2*(a + b/x^3)^(7/2))/(21*b^4)]

    @test_int [x^7/sqrt(a + b/x^3), x, 5, (91*b^2*sqrt(a + b/x^3)*x^2)/(320*a^3) - (13*b*sqrt(a + b/x^3)*x^5)/(80*a^2) + (sqrt(a + b/x^3)*x^8)/(8*a) + (91*sqrt(2 + sqrt(3))*b^(8/3)*(a^(1/3) + b^(1/3)/x)*sqrt((a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)), -7 - 4*sqrt(3)))/(320*3^(1/4)*a^3*sqrt(a + b/x^3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2))]
    @test_int [x^4/sqrt(a + b/x^3), x, 4, -((7*b*sqrt(a + b/x^3)*x^2)/(20*a^2)) + (sqrt(a + b/x^3)*x^5)/(5*a) - (7*sqrt(2 + sqrt(3))*b^(5/3)*(a^(1/3) + b^(1/3)/x)*sqrt((a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)), -7 - 4*sqrt(3)))/(20*3^(1/4)*a^2*sqrt(a + b/x^3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2))]
    @test_int [x^1/sqrt(a + b/x^3), x, 3, (sqrt(a + b/x^3)*x^2)/(2*a) + (sqrt(2 + sqrt(3))*b^(2/3)*(a^(1/3) + b^(1/3)/x)*sqrt((a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)), -7 - 4*sqrt(3)))/(2*3^(1/4)*a*sqrt(a + b/x^3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2))]
    @test_int [1/(x^2*sqrt(a + b/x^3)), x, 2, -((2*sqrt(2 + sqrt(3))*(a^(1/3) + b^(1/3)/x)*sqrt((a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)), -7 - 4*sqrt(3)))/(3^(1/4)*b^(1/3)*sqrt(a + b/x^3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2)))]
    @test_int [1/(x^5*sqrt(a + b/x^3)), x, 3, -((2*sqrt(a + b/x^3))/(5*b*x)) + (4*sqrt(2 + sqrt(3))*a*(a^(1/3) + b^(1/3)/x)*sqrt((a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)), -7 - 4*sqrt(3)))/(5*3^(1/4)*b^(4/3)*sqrt(a + b/x^3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2))]
    @test_int [1/(x^8*sqrt(a + b/x^3)), x, 4, -((2*sqrt(a + b/x^3))/(11*b*x^4)) + (16*a*sqrt(a + b/x^3))/(55*b^2*x) - (32*sqrt(2 + sqrt(3))*a^2*(a^(1/3) + b^(1/3)/x)*sqrt((a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)), -7 - 4*sqrt(3)))/(55*3^(1/4)*b^(7/3)*sqrt(a + b/x^3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2))]

    @test_int [x^6/sqrt(a + b/x^3), x, 7, -((55*b^(7/3)*sqrt(a + b/x^3))/(112*a^3*((1 + sqrt(3))*a^(1/3) + b^(1/3)/x))) + (55*b^2*sqrt(a + b/x^3)*x)/(112*a^3) - (11*b*sqrt(a + b/x^3)*x^4)/(56*a^2) + (sqrt(a + b/x^3)*x^7)/(7*a) + (55*3^(1/4)*sqrt(2 - sqrt(3))*b^(7/3)*(a^(1/3) + b^(1/3)/x)*sqrt((a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)), -7 - 4*sqrt(3)))/(224*a^(8/3)*sqrt(a + b/x^3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2)) - (55*b^(7/3)*(a^(1/3) + b^(1/3)/x)*sqrt((a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)), -7 - 4*sqrt(3)))/(56*sqrt(2)*3^(1/4)*a^(8/3)*sqrt(a + b/x^3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2))]
    @test_int [x^3/sqrt(a + b/x^3), x, 6, (5*b^(4/3)*sqrt(a + b/x^3))/(8*a^2*((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)) - (5*b*sqrt(a + b/x^3)*x)/(8*a^2) + (sqrt(a + b/x^3)*x^4)/(4*a) - (5*3^(1/4)*sqrt(2 - sqrt(3))*b^(4/3)*(a^(1/3) + b^(1/3)/x)*sqrt((a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)), -7 - 4*sqrt(3)))/(16*a^(5/3)*sqrt(a + b/x^3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2)) + (5*b^(4/3)*(a^(1/3) + b^(1/3)/x)*sqrt((a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)), -7 - 4*sqrt(3)))/(4*sqrt(2)*3^(1/4)*a^(5/3)*sqrt(a + b/x^3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2))]
    @test_int [x^0/sqrt(a + b/x^3), x, 5, -((b^(1/3)*sqrt(a + b/x^3))/(a*((1 + sqrt(3))*a^(1/3) + b^(1/3)/x))) + (sqrt(a + b/x^3)*x)/a + (3^(1/4)*sqrt(2 - sqrt(3))*b^(1/3)*(a^(1/3) + b^(1/3)/x)*sqrt((a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)), -7 - 4*sqrt(3)))/(2*a^(2/3)*sqrt(a + b/x^3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2)) - (sqrt(2)*b^(1/3)*(a^(1/3) + b^(1/3)/x)*sqrt((a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)), -7 - 4*sqrt(3)))/(3^(1/4)*a^(2/3)*sqrt(a + b/x^3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2))]
    @test_int [1/(x^3*sqrt(a + b/x^3)), x, 4, -((2*sqrt(a + b/x^3))/(b^(2/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)/x))) + (3^(1/4)*sqrt(2 - sqrt(3))*a^(1/3)*(a^(1/3) + b^(1/3)/x)*sqrt((a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)), -7 - 4*sqrt(3)))/(b^(2/3)*sqrt(a + b/x^3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2)) - (2*sqrt(2)*a^(1/3)*(a^(1/3) + b^(1/3)/x)*sqrt((a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)), -7 - 4*sqrt(3)))/(3^(1/4)*b^(2/3)*sqrt(a + b/x^3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2))]
    @test_int [1/(x^6*sqrt(a + b/x^3)), x, 5, (8*a*sqrt(a + b/x^3))/(7*b^(5/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)) - (2*sqrt(a + b/x^3))/(7*b*x^2) - (4*3^(1/4)*sqrt(2 - sqrt(3))*a^(4/3)*(a^(1/3) + b^(1/3)/x)*sqrt((a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)), -7 - 4*sqrt(3)))/(7*b^(5/3)*sqrt(a + b/x^3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2)) + (8*sqrt(2)*a^(4/3)*(a^(1/3) + b^(1/3)/x)*sqrt((a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)), -7 - 4*sqrt(3)))/(7*3^(1/4)*b^(5/3)*sqrt(a + b/x^3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2))]
    @test_int [1/(x^9*sqrt(a + b/x^3)), x, 6, -((80*a^2*sqrt(a + b/x^3))/(91*b^(8/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)/x))) - (2*sqrt(a + b/x^3))/(13*b*x^5) + (20*a*sqrt(a + b/x^3))/(91*b^2*x^2) + (40*3^(1/4)*sqrt(2 - sqrt(3))*a^(7/3)*(a^(1/3) + b^(1/3)/x)*sqrt((a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)), -7 - 4*sqrt(3)))/(91*b^(8/3)*sqrt(a + b/x^3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2)) - (80*sqrt(2)*a^(7/3)*(a^(1/3) + b^(1/3)/x)*sqrt((a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)), -7 - 4*sqrt(3)))/(91*3^(1/4)*b^(8/3)*sqrt(a + b/x^3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2))]
    @test_int [1/(x^12*sqrt(a + b/x^3)), x, 7, (1280*a^3*sqrt(a + b/x^3))/(1729*b^(11/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)) - (2*sqrt(a + b/x^3))/(19*b*x^8) + (32*a*sqrt(a + b/x^3))/(247*b^2*x^5) - (320*a^2*sqrt(a + b/x^3))/(1729*b^3*x^2) - (640*3^(1/4)*sqrt(2 - sqrt(3))*a^(10/3)*(a^(1/3) + b^(1/3)/x)*sqrt((a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)), -7 - 4*sqrt(3)))/(1729*b^(11/3)*sqrt(a + b/x^3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2)) + (1280*sqrt(2)*a^(10/3)*(a^(1/3) + b^(1/3)/x)*sqrt((a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)), -7 - 4*sqrt(3)))/(1729*3^(1/4)*b^(11/3)*sqrt(a + b/x^3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2))]

    @test_int [x^5/(a + b/x^3)^(3/2), x, 6, -((5*b^2)/(4*a^3*sqrt(a + b/x^3))) - (5*b*x^3)/(12*a^2*sqrt(a + b/x^3)) + x^6/(6*a*sqrt(a + b/x^3)) + (5*b^2*atanh(sqrt(a + b/x^3)/sqrt(a)))/(4*a^(7/2))]
    @test_int [x^2/(a + b/x^3)^(3/2), x, 5, b/(a^2*sqrt(a + b/x^3)) + x^3/(3*a*sqrt(a + b/x^3)) - (b*atanh(sqrt(a + b/x^3)/sqrt(a)))/a^(5/2)]
    @test_int [1/(x^1*(a + b/x^3)^(3/2)), x, 4, -(2/(3*a*sqrt(a + b/x^3))) + (2*atanh(sqrt(a + b/x^3)/sqrt(a)))/(3*a^(3/2))]
    @test_int [1/(x^4*(a + b/x^3)^(3/2)), x, 1, 2/(3*b*sqrt(a + b/x^3))]
    @test_int [1/(x^7*(a + b/x^3)^(3/2)), x, 3, -((2*a)/(3*b^2*sqrt(a + b/x^3))) - (2*sqrt(a + b/x^3))/(3*b^2)]
    @test_int [1/(x^10*(a + b/x^3)^(3/2)), x, 3, (2*a^2)/(3*b^3*sqrt(a + b/x^3)) + (4*a*sqrt(a + b/x^3))/(3*b^3) - (2*(a + b/x^3)^(3/2))/(9*b^3)]
    @test_int [1/(x^13*(a + b/x^3)^(3/2)), x, 3, -((2*a^3)/(3*b^4*sqrt(a + b/x^3))) - (2*a^2*sqrt(a + b/x^3))/b^4 + (2*a*(a + b/x^3)^(3/2))/(3*b^4) - (2*(a + b/x^3)^(5/2))/(15*b^4)]

    @test_int [x^7/(a + b/x^3)^(3/2), x, 6, (1729*b^2*sqrt(a + b/x^3)*x^2)/(960*a^4) - (247*b*sqrt(a + b/x^3)*x^5)/(240*a^3) - (2*x^8)/(3*a*sqrt(a + b/x^3)) + (19*sqrt(a + b/x^3)*x^8)/(24*a^2) + (1729*sqrt(2 + sqrt(3))*b^(8/3)*(a^(1/3) + b^(1/3)/x)*sqrt((a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)), -7 - 4*sqrt(3)))/(960*3^(1/4)*a^4*sqrt(a + b/x^3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2))]
    @test_int [x^4/(a + b/x^3)^(3/2), x, 5, -((91*b*sqrt(a + b/x^3)*x^2)/(60*a^3)) - (2*x^5)/(3*a*sqrt(a + b/x^3)) + (13*sqrt(a + b/x^3)*x^5)/(15*a^2) - (91*sqrt(2 + sqrt(3))*b^(5/3)*(a^(1/3) + b^(1/3)/x)*sqrt((a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)), -7 - 4*sqrt(3)))/(60*3^(1/4)*a^3*sqrt(a + b/x^3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2))]
    @test_int [x^1/(a + b/x^3)^(3/2), x, 4, -((2*x^2)/(3*a*sqrt(a + b/x^3))) + (7*sqrt(a + b/x^3)*x^2)/(6*a^2) + (7*sqrt(2 + sqrt(3))*b^(2/3)*(a^(1/3) + b^(1/3)/x)*sqrt((a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)), -7 - 4*sqrt(3)))/(6*3^(1/4)*a^2*sqrt(a + b/x^3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2))]
    @test_int [1/(x^2*(a + b/x^3)^(3/2)), x, 3, -(2/(3*a*sqrt(a + b/x^3)*x)) - (2*sqrt(2 + sqrt(3))*(a^(1/3) + b^(1/3)/x)*sqrt((a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)), -7 - 4*sqrt(3)))/(3*3^(1/4)*a*b^(1/3)*sqrt(a + b/x^3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2))]
    @test_int [1/(x^5*(a + b/x^3)^(3/2)), x, 3, 2/(3*b*sqrt(a + b/x^3)*x) - (4*sqrt(2 + sqrt(3))*(a^(1/3) + b^(1/3)/x)*sqrt((a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)), -7 - 4*sqrt(3)))/(3*3^(1/4)*b^(4/3)*sqrt(a + b/x^3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2))]
    @test_int [1/(x^8*(a + b/x^3)^(3/2)), x, 4, 2/(3*b*sqrt(a + b/x^3)*x^4) - (16*sqrt(a + b/x^3))/(15*b^2*x) + (32*sqrt(2 + sqrt(3))*a*(a^(1/3) + b^(1/3)/x)*sqrt((a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)), -7 - 4*sqrt(3)))/(15*3^(1/4)*b^(7/3)*sqrt(a + b/x^3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2))]

    @test_int [x^6/(a + b/x^3)^(3/2), x, 8, -((935*b^(7/3)*sqrt(a + b/x^3))/(336*a^4*((1 + sqrt(3))*a^(1/3) + b^(1/3)/x))) + (935*b^2*sqrt(a + b/x^3)*x)/(336*a^4) - (187*b*sqrt(a + b/x^3)*x^4)/(168*a^3) - (2*x^7)/(3*a*sqrt(a + b/x^3)) + (17*sqrt(a + b/x^3)*x^7)/(21*a^2) + (935*3^(1/4)*sqrt(2 - sqrt(3))*b^(7/3)*(a^(1/3) + b^(1/3)/x)*sqrt((a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)), -7 - 4*sqrt(3)))/(672*a^(11/3)*sqrt(a + b/x^3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2)) - (935*b^(7/3)*(a^(1/3) + b^(1/3)/x)*sqrt((a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)), -7 - 4*sqrt(3)))/(168*sqrt(2)*3^(1/4)*a^(11/3)*sqrt(a + b/x^3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2))]
    @test_int [x^3/(a + b/x^3)^(3/2), x, 7, (55*b^(4/3)*sqrt(a + b/x^3))/(24*a^3*((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)) - (55*b*sqrt(a + b/x^3)*x)/(24*a^3) - (2*x^4)/(3*a*sqrt(a + b/x^3)) + (11*sqrt(a + b/x^3)*x^4)/(12*a^2) - (55*3^(1/4)*sqrt(2 - sqrt(3))*b^(4/3)*(a^(1/3) + b^(1/3)/x)*sqrt((a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)), -7 - 4*sqrt(3)))/(48*a^(8/3)*sqrt(a + b/x^3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2)) + (55*b^(4/3)*(a^(1/3) + b^(1/3)/x)*sqrt((a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)), -7 - 4*sqrt(3)))/(12*sqrt(2)*3^(1/4)*a^(8/3)*sqrt(a + b/x^3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2))]
    @test_int [x^0/(a + b/x^3)^(3/2), x, 6, -((5*b^(1/3)*sqrt(a + b/x^3))/(3*a^2*((1 + sqrt(3))*a^(1/3) + b^(1/3)/x))) - (2*x)/(3*a*sqrt(a + b/x^3)) + (5*sqrt(a + b/x^3)*x)/(3*a^2) + (5*3^(1/4)*sqrt(2 - sqrt(3))*b^(1/3)*(a^(1/3) + b^(1/3)/x)*sqrt((a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)), -7 - 4*sqrt(3)))/(6*a^(5/3)*sqrt(a + b/x^3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2)) - (5*sqrt(2)*b^(1/3)*(a^(1/3) + b^(1/3)/x)*sqrt((a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)), -7 - 4*sqrt(3)))/(3*3^(1/4)*a^(5/3)*sqrt(a + b/x^3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2))]
    @test_int [1/(x^3*(a + b/x^3)^(3/2)), x, 5, (2*sqrt(a + b/x^3))/(3*a*b^(2/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)) - 2/(3*a*sqrt(a + b/x^3)*x^2) - (3^(1/4)*sqrt(2 - sqrt(3))*(a^(1/3) + b^(1/3)/x)*sqrt((a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)), -7 - 4*sqrt(3)))/(3*a^(2/3)*b^(2/3)*sqrt(a + b/x^3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2)) + (2*sqrt(2)*(a^(1/3) + b^(1/3)/x)*sqrt((a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)), -7 - 4*sqrt(3)))/(3*3^(1/4)*a^(2/3)*b^(2/3)*sqrt(a + b/x^3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2))]
    @test_int [1/(x^6*(a + b/x^3)^(3/2)), x, 5, -((8*sqrt(a + b/x^3))/(3*b^(5/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)/x))) + 2/(3*b*sqrt(a + b/x^3)*x^2) + (4*3^(1/4)*sqrt(2 - sqrt(3))*a^(1/3)*(a^(1/3) + b^(1/3)/x)*sqrt((a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)), -7 - 4*sqrt(3)))/(3*b^(5/3)*sqrt(a + b/x^3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2)) - (8*sqrt(2)*a^(1/3)*(a^(1/3) + b^(1/3)/x)*sqrt((a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)), -7 - 4*sqrt(3)))/(3*3^(1/4)*b^(5/3)*sqrt(a + b/x^3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2))]
    @test_int [1/(x^9*(a + b/x^3)^(3/2)), x, 6, (80*a*sqrt(a + b/x^3))/(21*b^(8/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)) + 2/(3*b*sqrt(a + b/x^3)*x^5) - (20*sqrt(a + b/x^3))/(21*b^2*x^2) - (40*3^(1/4)*sqrt(2 - sqrt(3))*a^(4/3)*(a^(1/3) + b^(1/3)/x)*sqrt((a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)), -7 - 4*sqrt(3)))/(21*b^(8/3)*sqrt(a + b/x^3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2)) + (80*sqrt(2)*a^(4/3)*(a^(1/3) + b^(1/3)/x)*sqrt((a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)), -7 - 4*sqrt(3)))/(21*3^(1/4)*b^(8/3)*sqrt(a + b/x^3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2))]
    @test_int [1/(x^12*(a + b/x^3)^(3/2)), x, 7, -((1280*a^2*sqrt(a + b/x^3))/(273*b^(11/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)/x))) + 2/(3*b*sqrt(a + b/x^3)*x^8) - (32*sqrt(a + b/x^3))/(39*b^2*x^5) + (320*a*sqrt(a + b/x^3))/(273*b^3*x^2) + (640*3^(1/4)*sqrt(2 - sqrt(3))*a^(7/3)*(a^(1/3) + b^(1/3)/x)*sqrt((a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)), -7 - 4*sqrt(3)))/(273*b^(11/3)*sqrt(a + b/x^3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2)) - (1280*sqrt(2)*a^(7/3)*(a^(1/3) + b^(1/3)/x)*sqrt((a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)/x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)), -7 - 4*sqrt(3)))/(273*3^(1/4)*b^(11/3)*sqrt(a + b/x^3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)/x)^2))]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(c*x)^m*(a+b/x^4)^p=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b/x^4)^p=#

    #= ::Subsubsection:: =#
    #=p>0=#

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [1/(a + b/x^4), x, 11, x/a + (b^(1/4)*atan(1 - (sqrt(2)*a^(1/4)*x)/b^(1/4)))/(2*sqrt(2)*a^(5/4)) - (b^(1/4)*atan(1 + (sqrt(2)*a^(1/4)*x)/b^(1/4)))/(2*sqrt(2)*a^(5/4)) + (b^(1/4)*log(sqrt(b) - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a)*x^2))/(4*sqrt(2)*a^(5/4)) - (b^(1/4)*log(sqrt(b) + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(a)*x^2))/(4*sqrt(2)*a^(5/4))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b/x^4)^(p/2)=#

    #= ::Subsubsection::Closed:: =#
    #=p>0=#

    @test_int [sqrt(a + b/x^4)*x^3, x, 4, (sqrt(a + b/x^4)*x^4)/4 + (b*atanh(sqrt(a + b/x^4)/sqrt(a)))/(4*sqrt(a))]
    @test_int [sqrt(a + b/x^4)*x^1, x, 5, (sqrt(a + b/x^4)*x^2)/2 - (sqrt(b)*atanh(sqrt(b)/(sqrt(a + b/x^4)*x^2)))/2]
    @test_int [sqrt(a + b/x^4)/x^1, x, 4, -sqrt(a + b/x^4)/2 + (sqrt(a)*atanh(sqrt(a + b/x^4)/sqrt(a)))/2]
    @test_int [sqrt(a + b/x^4)/x^3, x, 5, -sqrt(a + b/x^4)/(4*x^2) - (a*atanh(sqrt(b)/(sqrt(a + b/x^4)*x^2)))/(4*sqrt(b))]

    @test_int [sqrt(a + b/x^4)*x^2, x, 3, (1/3)*sqrt(a + b/x^4)*x^3 - (b^(3/4)*sqrt((a + b/x^4)/(sqrt(a) + sqrt(b)/x^2)^2)*(sqrt(a) + sqrt(b)/x^2)*Elliptic.F(2*acot((a^(1/4)*x)/b^(1/4)), 1/2))/(3*a^(1/4)*sqrt(a + b/x^4))]
    @test_int [sqrt(a + b/x^4)*x^0, x, 5, -((2*sqrt(b)*sqrt(a + b/x^4))/((sqrt(a) + sqrt(b)/x^2)*x)) + sqrt(a + b/x^4)*x + (2*a^(1/4)*b^(1/4)*sqrt((a + b/x^4)/(sqrt(a) + sqrt(b)/x^2)^2)*(sqrt(a) + sqrt(b)/x^2)*Elliptic.E(2*acot((a^(1/4)*x)/b^(1/4)), 1/2))/sqrt(a + b/x^4) - (a^(1/4)*b^(1/4)*sqrt((a + b/x^4)/(sqrt(a) + sqrt(b)/x^2)^2)*(sqrt(a) + sqrt(b)/x^2)*Elliptic.F(2*acot((a^(1/4)*x)/b^(1/4)), 1/2))/sqrt(a + b/x^4)]
    @test_int [sqrt(a + b/x^4)/x^2, x, 3, -(sqrt(a + b/x^4)/(3*x)) - (a^(3/4)*sqrt((a + b/x^4)/(sqrt(a) + sqrt(b)/x^2)^2)*(sqrt(a) + sqrt(b)/x^2)*Elliptic.F(2*acot((a^(1/4)*x)/b^(1/4)), 1/2))/(3*b^(1/4)*sqrt(a + b/x^4))]
    @test_int [sqrt(a + b/x^4)/x^4, x, 5, -(sqrt(a + b/x^4)/(5*x^3)) - (2*a*sqrt(a + b/x^4))/(5*sqrt(b)*(sqrt(a) + sqrt(b)/x^2)*x) + (2*a^(5/4)*sqrt((a + b/x^4)/(sqrt(a) + sqrt(b)/x^2)^2)*(sqrt(a) + sqrt(b)/x^2)*Elliptic.E(2*acot((a^(1/4)*x)/b^(1/4)), 1/2))/(5*b^(3/4)*sqrt(a + b/x^4)) - (a^(5/4)*sqrt((a + b/x^4)/(sqrt(a) + sqrt(b)/x^2)^2)*(sqrt(a) + sqrt(b)/x^2)*Elliptic.F(2*acot((a^(1/4)*x)/b^(1/4)), 1/2))/(5*b^(3/4)*sqrt(a + b/x^4))]

    @test_int [(a + b/x^4)^(3/2)*x^3, x, 5, (-3*b*sqrt(a + b/x^4))/4 + ((a + b/x^4)^(3/2)*x^4)/4 + (3*sqrt(a)*b*atanh(sqrt(a + b/x^4)/sqrt(a)))/4]
    @test_int [(a + b/x^4)^(3/2)*x^1, x, 6, (-3*b*sqrt(a + b/x^4))/(4*x^2) + ((a + b/x^4)^(3/2)*x^2)/2 - (3*a*sqrt(b)*atanh(sqrt(b)/(sqrt(a + b/x^4)*x^2)))/4]
    @test_int [(a + b/x^4)^(3/2)/x^1, x, 5, -(a*sqrt(a + b/x^4))/2 - (a + b/x^4)^(3/2)/6 + (a^(3/2)*atanh(sqrt(a + b/x^4)/sqrt(a)))/2]
    @test_int [(a + b/x^4)^(3/2)/x^3, x, 6, (-3*a*sqrt(a + b/x^4))/(16*x^2) - (a + b/x^4)^(3/2)/(8*x^2) - (3*a^2*atanh(sqrt(b)/(sqrt(a + b/x^4)*x^2)))/(16*sqrt(b))]

    @test_int [(a + b/x^4)^(3/2)*x^2, x, 4, -((2*b*sqrt(a + b/x^4))/(3*x)) + (1/3)*(a + b/x^4)^(3/2)*x^3 - (2*a^(3/4)*b^(3/4)*sqrt((a + b/x^4)/(sqrt(a) + sqrt(b)/x^2)^2)*(sqrt(a) + sqrt(b)/x^2)*Elliptic.F(2*acot((a^(1/4)*x)/b^(1/4)), 1/2))/(3*sqrt(a + b/x^4))]
    @test_int [(a + b/x^4)^(3/2)*x^0, x, 6, -((6*b*sqrt(a + b/x^4))/(5*x^3)) - (12*a*sqrt(b)*sqrt(a + b/x^4))/(5*(sqrt(a) + sqrt(b)/x^2)*x) + (a + b/x^4)^(3/2)*x + (12*a^(5/4)*b^(1/4)*sqrt((a + b/x^4)/(sqrt(a) + sqrt(b)/x^2)^2)*(sqrt(a) + sqrt(b)/x^2)*Elliptic.E(2*acot((a^(1/4)*x)/b^(1/4)), 1/2))/(5*sqrt(a + b/x^4)) - (6*a^(5/4)*b^(1/4)*sqrt((a + b/x^4)/(sqrt(a) + sqrt(b)/x^2)^2)*(sqrt(a) + sqrt(b)/x^2)*Elliptic.F(2*acot((a^(1/4)*x)/b^(1/4)), 1/2))/(5*sqrt(a + b/x^4))]
    @test_int [(a + b/x^4)^(3/2)/x^2, x, 4, -((2*a*sqrt(a + b/x^4))/(7*x)) - (a + b/x^4)^(3/2)/(7*x) - (2*a^(7/4)*sqrt((a + b/x^4)/(sqrt(a) + sqrt(b)/x^2)^2)*(sqrt(a) + sqrt(b)/x^2)*Elliptic.F(2*acot((a^(1/4)*x)/b^(1/4)), 1/2))/(7*b^(1/4)*sqrt(a + b/x^4))]
    @test_int [(a + b/x^4)^(3/2)/x^4, x, 6, -((2*a*sqrt(a + b/x^4))/(15*x^3)) - (a + b/x^4)^(3/2)/(9*x^3) - (4*a^2*sqrt(a + b/x^4))/(15*sqrt(b)*(sqrt(a) + sqrt(b)/x^2)*x) + (4*a^(9/4)*sqrt((a + b/x^4)/(sqrt(a) + sqrt(b)/x^2)^2)*(sqrt(a) + sqrt(b)/x^2)*Elliptic.E(2*acot((a^(1/4)*x)/b^(1/4)), 1/2))/(15*b^(3/4)*sqrt(a + b/x^4)) - (2*a^(9/4)*sqrt((a + b/x^4)/(sqrt(a) + sqrt(b)/x^2)^2)*(sqrt(a) + sqrt(b)/x^2)*Elliptic.F(2*acot((a^(1/4)*x)/b^(1/4)), 1/2))/(15*b^(3/4)*sqrt(a + b/x^4))]

    @test_int [(a + b/x^4)^(5/2)*x^3, x, 6, (-5*a*b*sqrt(a + b/x^4))/4 - (5*b*(a + b/x^4)^(3/2))/12 + ((a + b/x^4)^(5/2)*x^4)/4 + (5*a^(3/2)*b*atanh(sqrt(a + b/x^4)/sqrt(a)))/4]
    @test_int [(a + b/x^4)^(5/2)*x^1, x, 7, (-15*a*b*sqrt(a + b/x^4))/(16*x^2) - (5*b*(a + b/x^4)^(3/2))/(8*x^2) + ((a + b/x^4)^(5/2)*x^2)/2 - (15*a^2*sqrt(b)*atanh(sqrt(b)/(sqrt(a + b/x^4)*x^2)))/16]
    @test_int [(a + b/x^4)^(5/2)/x^1, x, 6, -(a^2*sqrt(a + b/x^4))/2 - (a*(a + b/x^4)^(3/2))/6 - (a + b/x^4)^(5/2)/10 + (a^(5/2)*atanh(sqrt(a + b/x^4)/sqrt(a)))/2]
    @test_int [(a + b/x^4)^(5/2)/x^3, x, 7, (-5*a^2*sqrt(a + b/x^4))/(32*x^2) - (5*a*(a + b/x^4)^(3/2))/(48*x^2) - (a + b/x^4)^(5/2)/(12*x^2) - (5*a^3*atanh(sqrt(b)/(sqrt(a + b/x^4)*x^2)))/(32*sqrt(b))]

    @test_int [(a + b/x^4)^(5/2)*x^2, x, 5, -((20*a*b*sqrt(a + b/x^4))/(21*x)) - (10*b*(a + b/x^4)^(3/2))/(21*x) + (1/3)*(a + b/x^4)^(5/2)*x^3 - (20*a^(7/4)*b^(3/4)*sqrt((a + b/x^4)/(sqrt(a) + sqrt(b)/x^2)^2)*(sqrt(a) + sqrt(b)/x^2)*Elliptic.F(2*acot((a^(1/4)*x)/b^(1/4)), 1/2))/(21*sqrt(a + b/x^4))]
    @test_int [(a + b/x^4)^(5/2)*x^0, x, 7, -((4*a*b*sqrt(a + b/x^4))/(3*x^3)) - (10*b*(a + b/x^4)^(3/2))/(9*x^3) - (8*a^2*sqrt(b)*sqrt(a + b/x^4))/(3*(sqrt(a) + sqrt(b)/x^2)*x) + (a + b/x^4)^(5/2)*x + (8*a^(9/4)*b^(1/4)*sqrt((a + b/x^4)/(sqrt(a) + sqrt(b)/x^2)^2)*(sqrt(a) + sqrt(b)/x^2)*Elliptic.E(2*acot((a^(1/4)*x)/b^(1/4)), 1/2))/(3*sqrt(a + b/x^4)) - (4*a^(9/4)*b^(1/4)*sqrt((a + b/x^4)/(sqrt(a) + sqrt(b)/x^2)^2)*(sqrt(a) + sqrt(b)/x^2)*Elliptic.F(2*acot((a^(1/4)*x)/b^(1/4)), 1/2))/(3*sqrt(a + b/x^4))]
    @test_int [(a + b/x^4)^(5/2)/x^2, x, 5, -((20*a^2*sqrt(a + b/x^4))/(77*x)) - (10*a*(a + b/x^4)^(3/2))/(77*x) - (a + b/x^4)^(5/2)/(11*x) - (20*a^(11/4)*sqrt((a + b/x^4)/(sqrt(a) + sqrt(b)/x^2)^2)*(sqrt(a) + sqrt(b)/x^2)*Elliptic.F(2*acot((a^(1/4)*x)/b^(1/4)), 1/2))/(77*b^(1/4)*sqrt(a + b/x^4))]
    @test_int [(a + b/x^4)^(5/2)/x^4, x, 7, -((4*a^2*sqrt(a + b/x^4))/(39*x^3)) - (10*a*(a + b/x^4)^(3/2))/(117*x^3) - (a + b/x^4)^(5/2)/(13*x^3) - (8*a^3*sqrt(a + b/x^4))/(39*sqrt(b)*(sqrt(a) + sqrt(b)/x^2)*x) + (8*a^(13/4)*sqrt((a + b/x^4)/(sqrt(a) + sqrt(b)/x^2)^2)*(sqrt(a) + sqrt(b)/x^2)*Elliptic.E(2*acot((a^(1/4)*x)/b^(1/4)), 1/2))/(39*b^(3/4)*sqrt(a + b/x^4)) - (4*a^(13/4)*sqrt((a + b/x^4)/(sqrt(a) + sqrt(b)/x^2)^2)*(sqrt(a) + sqrt(b)/x^2)*Elliptic.F(2*acot((a^(1/4)*x)/b^(1/4)), 1/2))/(39*b^(3/4)*sqrt(a + b/x^4))]

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [x^3/sqrt(a + b/x^4), x, 4, (sqrt(a + b/x^4)*x^4)/(4*a) - (b*atanh(sqrt(a + b/x^4)/sqrt(a)))/(4*a^(3/2))]
    @test_int [x^1/sqrt(a + b/x^4), x, 1, (sqrt(a + b/x^4)*x^2)/(2*a)]
    @test_int [1/(sqrt(a + b/x^4)*x^1), x, 3, atanh(sqrt(a + b/x^4)/sqrt(a))/(2*sqrt(a))]
    @test_int [1/(sqrt(a + b/x^4)*x^3), x, 4, -atanh(sqrt(b)/(sqrt(a + b/x^4)*x^2))/(2*sqrt(b))]

    @test_int [x^2/sqrt(a + b/x^4), x, 3, (sqrt(a + b/x^4)*x^3)/(3*a) + (b^(3/4)*sqrt((a + b/x^4)/(sqrt(a) + sqrt(b)/x^2)^2)*(sqrt(a) + sqrt(b)/x^2)*Elliptic.F(2*acot((a^(1/4)*x)/b^(1/4)), 1/2))/(6*a^(5/4)*sqrt(a + b/x^4))]
    @test_int [x^0/sqrt(a + b/x^4), x, 5, -((sqrt(b)*sqrt(a + b/x^4))/(a*(sqrt(a) + sqrt(b)/x^2)*x)) + (sqrt(a + b/x^4)*x)/a + (b^(1/4)*sqrt((a + b/x^4)/(sqrt(a) + sqrt(b)/x^2)^2)*(sqrt(a) + sqrt(b)/x^2)*Elliptic.E(2*acot((a^(1/4)*x)/b^(1/4)), 1/2))/(a^(3/4)*sqrt(a + b/x^4)) - (b^(1/4)*sqrt((a + b/x^4)/(sqrt(a) + sqrt(b)/x^2)^2)*(sqrt(a) + sqrt(b)/x^2)*Elliptic.F(2*acot((a^(1/4)*x)/b^(1/4)), 1/2))/(2*a^(3/4)*sqrt(a + b/x^4))]
    @test_int [1/(sqrt(a + b/x^4)*x^2), x, 2, -((sqrt((a + b/x^4)/(sqrt(a) + sqrt(b)/x^2)^2)*(sqrt(a) + sqrt(b)/x^2)*Elliptic.F(2*acot((a^(1/4)*x)/b^(1/4)), 1/2))/(2*a^(1/4)*b^(1/4)*sqrt(a + b/x^4)))]
    @test_int [1/(sqrt(a + b/x^4)*x^4), x, 4, -(sqrt(a + b/x^4)/(sqrt(b)*(sqrt(a) + sqrt(b)/x^2)*x)) + (a^(1/4)*sqrt((a + b/x^4)/(sqrt(a) + sqrt(b)/x^2)^2)*(sqrt(a) + sqrt(b)/x^2)*Elliptic.E(2*acot((a^(1/4)*x)/b^(1/4)), 1/2))/(b^(3/4)*sqrt(a + b/x^4)) - (a^(1/4)*sqrt((a + b/x^4)/(sqrt(a) + sqrt(b)/x^2)^2)*(sqrt(a) + sqrt(b)/x^2)*Elliptic.F(2*acot((a^(1/4)*x)/b^(1/4)), 1/2))/(2*b^(3/4)*sqrt(a + b/x^4))]

    @test_int [x^3/(a + b/x^4)^(3/2), x, 5, (3*b)/(4*a^2*sqrt(a + b/x^4)) + x^4/(4*a*sqrt(a + b/x^4)) - (3*b*atanh(sqrt(a + b/x^4)/sqrt(a)))/(4*a^(5/2))]
    @test_int [x^1/(a + b/x^4)^(3/2), x, 2, -(x^2/(2*a*sqrt(a + b/x^4))) + (sqrt(a + b/x^4)*x^2)/a^2]
    @test_int [1/((a + b/x^4)^(3/2)*x^1), x, 4, -1/(2*a*sqrt(a + b/x^4)) + atanh(sqrt(a + b/x^4)/sqrt(a))/(2*a^(3/2))]
    @test_int [1/((a + b/x^4)^(3/2)*x^3), x, 1, -1/(2*a*sqrt(a + b/x^4)*x^2)]

    @test_int [x^2/(a + b/x^4)^(3/2), x, 4, -(x^3/(2*a*sqrt(a + b/x^4))) + (5*sqrt(a + b/x^4)*x^3)/(6*a^2) + (5*b^(3/4)*sqrt((a + b/x^4)/(sqrt(a) + sqrt(b)/x^2)^2)*(sqrt(a) + sqrt(b)/x^2)*Elliptic.F(2*acot((a^(1/4)*x)/b^(1/4)), 1/2))/(12*a^(9/4)*sqrt(a + b/x^4))]
    @test_int [x^0/(a + b/x^4)^(3/2), x, 6, -((3*sqrt(b)*sqrt(a + b/x^4))/(2*a^2*(sqrt(a) + sqrt(b)/x^2)*x)) - x/(2*a*sqrt(a + b/x^4)) + (3*sqrt(a + b/x^4)*x)/(2*a^2) + (3*b^(1/4)*sqrt((a + b/x^4)/(sqrt(a) + sqrt(b)/x^2)^2)*(sqrt(a) + sqrt(b)/x^2)*Elliptic.E(2*acot((a^(1/4)*x)/b^(1/4)), 1/2))/(2*a^(7/4)*sqrt(a + b/x^4)) - (3*b^(1/4)*sqrt((a + b/x^4)/(sqrt(a) + sqrt(b)/x^2)^2)*(sqrt(a) + sqrt(b)/x^2)*Elliptic.F(2*acot((a^(1/4)*x)/b^(1/4)), 1/2))/(4*a^(7/4)*sqrt(a + b/x^4))]
    @test_int [1/((a + b/x^4)^(3/2)*x^2), x, 3, -(1/(2*a*sqrt(a + b/x^4)*x)) - (sqrt((a + b/x^4)/(sqrt(a) + sqrt(b)/x^2)^2)*(sqrt(a) + sqrt(b)/x^2)*Elliptic.F(2*acot((a^(1/4)*x)/b^(1/4)), 1/2))/(4*a^(5/4)*b^(1/4)*sqrt(a + b/x^4))]
    @test_int [1/((a + b/x^4)^(3/2)*x^4), x, 5, -(1/(2*a*sqrt(a + b/x^4)*x^3)) + sqrt(a + b/x^4)/(2*a*sqrt(b)*(sqrt(a) + sqrt(b)/x^2)*x) - (sqrt((a + b/x^4)/(sqrt(a) + sqrt(b)/x^2)^2)*(sqrt(a) + sqrt(b)/x^2)*Elliptic.E(2*acot((a^(1/4)*x)/b^(1/4)), 1/2))/(2*a^(3/4)*b^(3/4)*sqrt(a + b/x^4)) + (sqrt((a + b/x^4)/(sqrt(a) + sqrt(b)/x^2)^2)*(sqrt(a) + sqrt(b)/x^2)*Elliptic.F(2*acot((a^(1/4)*x)/b^(1/4)), 1/2))/(4*a^(3/4)*b^(3/4)*sqrt(a + b/x^4))]

    @test_int [x^3/(a + b/x^4)^(5/2), x, 6, (5*b)/(12*a^2*(a + b/x^4)^(3/2)) + (5*b)/(4*a^3*sqrt(a + b/x^4)) + x^4/(4*a*(a + b/x^4)^(3/2)) - (5*b*atanh(sqrt(a + b/x^4)/sqrt(a)))/(4*a^(7/2))]
    @test_int [x^1/(a + b/x^4)^(5/2), x, 3, -(x^2/(6*a*(a + b/x^4)^(3/2))) - (2*x^2)/(3*a^2*sqrt(a + b/x^4)) + (4*sqrt(a + b/x^4)*x^2)/(3*a^3)]
    @test_int [1/((a + b/x^4)^(5/2)*x^1), x, 5, -1/(6*a*(a + b/x^4)^(3/2)) - 1/(2*a^2*sqrt(a + b/x^4)) + atanh(sqrt(a + b/x^4)/sqrt(a))/(2*a^(5/2))]
    @test_int [1/((a + b/x^4)^(5/2)*x^3), x, 2, -(b/(3*a^2*(a + b/x^4)^(3/2)*x^6)) - 1/(2*a*(a + b/x^4)^(3/2)*x^2)]

    @test_int [x^2/(a + b/x^4)^(5/2), x, 5, -(x^3/(6*a*(a + b/x^4)^(3/2))) - (3*x^3)/(4*a^2*sqrt(a + b/x^4)) + (5*sqrt(a + b/x^4)*x^3)/(4*a^3) + (5*b^(3/4)*sqrt((a + b/x^4)/(sqrt(a) + sqrt(b)/x^2)^2)*(sqrt(a) + sqrt(b)/x^2)*Elliptic.F(2*acot((a^(1/4)*x)/b^(1/4)), 1/2))/(8*a^(13/4)*sqrt(a + b/x^4))]
    @test_int [x^0/(a + b/x^4)^(5/2), x, 7, -((7*sqrt(b)*sqrt(a + b/x^4))/(4*a^3*(sqrt(a) + sqrt(b)/x^2)*x)) - x/(6*a*(a + b/x^4)^(3/2)) - (7*x)/(12*a^2*sqrt(a + b/x^4)) + (7*sqrt(a + b/x^4)*x)/(4*a^3) + (7*b^(1/4)*sqrt((a + b/x^4)/(sqrt(a) + sqrt(b)/x^2)^2)*(sqrt(a) + sqrt(b)/x^2)*Elliptic.E(2*acot((a^(1/4)*x)/b^(1/4)), 1/2))/(4*a^(11/4)*sqrt(a + b/x^4)) - (7*b^(1/4)*sqrt((a + b/x^4)/(sqrt(a) + sqrt(b)/x^2)^2)*(sqrt(a) + sqrt(b)/x^2)*Elliptic.F(2*acot((a^(1/4)*x)/b^(1/4)), 1/2))/(8*a^(11/4)*sqrt(a + b/x^4))]
    @test_int [1/((a + b/x^4)^(5/2)*x^2), x, 4, -(1/(6*a*(a + b/x^4)^(3/2)*x)) - 5/(12*a^2*sqrt(a + b/x^4)*x) - (5*sqrt((a + b/x^4)/(sqrt(a) + sqrt(b)/x^2)^2)*(sqrt(a) + sqrt(b)/x^2)*Elliptic.F(2*acot((a^(1/4)*x)/b^(1/4)), 1/2))/(24*a^(9/4)*b^(1/4)*sqrt(a + b/x^4))]
    @test_int [1/((a + b/x^4)^(5/2)*x^4), x, 6, -(1/(6*a*(a + b/x^4)^(3/2)*x^3)) - 1/(4*a^2*sqrt(a + b/x^4)*x^3) + sqrt(a + b/x^4)/(4*a^2*sqrt(b)*(sqrt(a) + sqrt(b)/x^2)*x) - (sqrt((a + b/x^4)/(sqrt(a) + sqrt(b)/x^2)^2)*(sqrt(a) + sqrt(b)/x^2)*Elliptic.E(2*acot((a^(1/4)*x)/b^(1/4)), 1/2))/(4*a^(7/4)*b^(3/4)*sqrt(a + b/x^4)) + (sqrt((a + b/x^4)/(sqrt(a) + sqrt(b)/x^2)^2)*(sqrt(a) + sqrt(b)/x^2)*Elliptic.F(2*acot((a^(1/4)*x)/b^(1/4)), 1/2))/(8*a^(7/4)*b^(3/4)*sqrt(a + b/x^4))]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(c*x)^m*(a+b/x^5)^p=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b/x^5)^p=#

    #= ::Subsubsection:: =#
    #=p>0=#

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [1/(a + b/x^5), x, 8, x/a - (sqrt((1/2)*(5 + sqrt(5)))*b^(1/5)*atan(sqrt((1/5)*(5 - 2*sqrt(5))) + (2*sqrt(2/(5 + sqrt(5)))*a^(1/5)*x)/b^(1/5)))/(5*a^(6/5)) + (sqrt((1/2)*(5 - sqrt(5)))*b^(1/5)*atan(sqrt((1/5)*(5 + 2*sqrt(5))) - (sqrt((2/5)*(5 + sqrt(5)))*a^(1/5)*x)/b^(1/5)))/(5*a^(6/5)) - (b^(1/5)*log(b^(1/5) + a^(1/5)*x))/(5*a^(6/5)) + ((1 - sqrt(5))*b^(1/5)*log(b^(2/5) - (1/2)*(1 - sqrt(5))*a^(1/5)*b^(1/5)*x + a^(2/5)*x^2))/(20*a^(6/5)) + ((1 + sqrt(5))*b^(1/5)*log(b^(2/5) - (1/2)*(1 + sqrt(5))*a^(1/5)*b^(1/5)*x + a^(2/5)*x^2))/(20*a^(6/5))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b/x^5)^(p/2)=#

    #= ::Subsubsection:: =#
    #=p>0=#

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [1/(sqrt(a + b/x^5)*x), x, 3, (2*atanh(sqrt(a + b/x^5)/sqrt(a)))/(5*sqrt(a))]
    @test_int [1/(sqrt(-a + b/x^5)*x), x, 3, (-2*atan(sqrt(-a + b/x^5)/sqrt(a)))/(5*sqrt(a))]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(c*x)^m*(a+b/x^6)^p=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b/x^6)^p=#

    #= ::Subsubsection:: =#
    #=p>0=#

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [1/(a + b/x^6), x, 12, x/a - (b^(1/6)*atan((a^(1/6)*x)/b^(1/6)))/(3*a^(7/6)) + (b^(1/6)*atan((sqrt(3)*b^(1/6) - 2*a^(1/6)*x)/b^(1/6)))/(6*a^(7/6)) - (b^(1/6)*atan((sqrt(3)*b^(1/6) + 2*a^(1/6)*x)/b^(1/6)))/(6*a^(7/6)) + (b^(1/6)*log(b^(1/3) - sqrt(3)*a^(1/6)*b^(1/6)*x + a^(1/3)*x^2))/(4*sqrt(3)*a^(7/6)) - (b^(1/6)*log(b^(1/3) + sqrt(3)*a^(1/6)*b^(1/6)*x + a^(1/3)*x^2))/(4*sqrt(3)*a^(7/6))]

    #= ::Subsection:: =#
    #=Integrands*of*the*form*x^m*(a+b/x^6)^(p/2)=#

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(c*x)^m*(a+b/x^8)^p=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b/x^8)^p=#

    #= ::Subsubsection:: =#
    #=p>0=#

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [1/(a + b/x^8), x, 15, x/a + (b^(1/8)*atan(((-a)^(1/8)*x)/b^(1/8)))/(4*(-a)^(9/8)) - (b^(1/8)*atan(1 - (sqrt(2)*(-a)^(1/8)*x)/b^(1/8)))/(4*sqrt(2)*(-a)^(9/8)) + (b^(1/8)*atan(1 + (sqrt(2)*(-a)^(1/8)*x)/b^(1/8)))/(4*sqrt(2)*(-a)^(9/8)) + (b^(1/8)*atanh(((-a)^(1/8)*x)/b^(1/8)))/(4*(-a)^(9/8)) - (b^(1/8)*log(b^(1/4) - sqrt(2)*(-a)^(1/8)*b^(1/8)*x + (-a)^(1/4)*x^2))/(8*sqrt(2)*(-a)^(9/8)) + (b^(1/8)*log(b^(1/4) + sqrt(2)*(-a)^(1/8)*b^(1/8)*x + (-a)^(1/4)*x^2))/(8*sqrt(2)*(-a)^(9/8))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b/x^8)^(p/2)=#

    #= ::Subsubsection:: =#
    #=p>0=#

    #= ::Subsubsection:: =#
    #=p<0=#

    #= ::Title::Closed:: =#
    #=Integrands*of*the*form*(c*x)^m*(a+b*x^n)^p*when*n>0*is*a*fraction=#

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(c*x)^m*(a+b*x^(1/2))^p=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b*sqrt(x))^p=#

    #= ::Subsubsection::Closed:: =#
    #=p>0=#

    @test_int [(a + b*sqrt(x))*x^4, x, 2, (a*x^5)/5 + (2*b*x^(11/2))/11]
    @test_int [(a + b*sqrt(x))*x^3, x, 2, (a*x^4)/4 + (2*b*x^(9/2))/9]
    @test_int [(a + b*sqrt(x))*x^2, x, 2, (a*x^3)/3 + (2*b*x^(7/2))/7]
    @test_int [(a + b*sqrt(x))*x^1, x, 2, (a*x^2)/2 + (2*b*x^(5/2))/5]
    @test_int [(a + b*sqrt(x))*x^0, x, 1, a*x + (2*b*x^(3/2))/3]

    @test_int [(a + b*sqrt(x))/x^1, x, 2, 2*b*sqrt(x) + a*log(x)]

    @test_int [(a + b*sqrt(x))/x^2, x, 2, -(a/x) - (2*b)/sqrt(x)]
    @test_int [(a + b*sqrt(x))/x^3, x, 2, -a/(2*x^2) - (2*b)/(3*x^(3/2))]
    @test_int [(a + b*sqrt(x))/x^4, x, 2, -a/(3*x^3) - (2*b)/(5*x^(5/2))]

    @test_int [(a + b*sqrt(x))^2*x^4, x, 3, (a^2*x^5)/5 + (4*a*b*x^(11/2))/11 + (b^2*x^6)/6]
    @test_int [(a + b*sqrt(x))^2*x^3, x, 3, (a^2*x^4)/4 + (4*a*b*x^(9/2))/9 + (b^2*x^5)/5]
    @test_int [(a + b*sqrt(x))^2*x^2, x, 3, (a^2*x^3)/3 + (4*a*b*x^(7/2))/7 + (b^2*x^4)/4]
    @test_int [(a + b*sqrt(x))^2*x^1, x, 3, (a^2*x^2)/2 + (4*a*b*x^(5/2))/5 + (b^2*x^3)/3]
    @test_int [(a + b*sqrt(x))^2*x^0, x, 3, a^2*x + (4*a*b*x^(3/2))/3 + (b^2*x^2)/2]

    @test_int [(a + b*sqrt(x))^2/x^1, x, 3, 4*a*b*sqrt(x) + b^2*x + a^2*log(x)]
    @test_int [(a + b*sqrt(x))^2/x^2, x, 3, -(a^2/x) - (4*a*b)/sqrt(x) + b^2*log(x)]

    @test_int [(a + b*sqrt(x))^2/x^3, x, 3, -a^2/(2*x^2) - (4*a*b)/(3*x^(3/2)) - b^2/x]
    @test_int [(a + b*sqrt(x))^2/x^4, x, 3, -a^2/(3*x^3) - (4*a*b)/(5*x^(5/2)) - b^2/(2*x^2)]
    @test_int [(a + b*sqrt(x))^2/x^5, x, 3, -a^2/(4*x^4) - (4*a*b)/(7*x^(7/2)) - b^2/(3*x^3)]

    @test_int [(a + b*sqrt(x))^3*x^4, x, 3, (a^3*x^5)/5 + (6*a^2*b*x^(11/2))/11 + (a*b^2*x^6)/2 + (2*b^3*x^(13/2))/13]
    @test_int [(a + b*sqrt(x))^3*x^3, x, 3, (a^3*x^4)/4 + (2*a^2*b*x^(9/2))/3 + (3*a*b^2*x^5)/5 + (2*b^3*x^(11/2))/11]
    @test_int [(a + b*sqrt(x))^3*x^2, x, 3, (a^3*x^3)/3 + (6*a^2*b*x^(7/2))/7 + (3*a*b^2*x^4)/4 + (2*b^3*x^(9/2))/9]
    @test_int [(a + b*sqrt(x))^3*x^1, x, 3, (a^3*x^2)/2 + (6*a^2*b*x^(5/2))/5 + a*b^2*x^3 + (2*b^3*x^(7/2))/7]
    @test_int [(a + b*sqrt(x))^3*x^0, x, 3, -(a*(a + b*sqrt(x))^4)/(2*b^2) + (2*(a + b*sqrt(x))^5)/(5*b^2)]

    @test_int [(a + b*sqrt(x))^3/x^1, x, 3, 6*a^2*b*sqrt(x) + 3*a*b^2*x + (2*b^3*x^(3/2))/3 + a^3*log(x)]
    @test_int [(a + b*sqrt(x))^3/x^2, x, 3, -(a^3/x) - (6*a^2*b)/sqrt(x) + 2*b^3*sqrt(x) + 3*a*b^2*log(x)]

    @test_int [(a + b*sqrt(x))^3/x^3, x, 1, -(a + b*sqrt(x))^4/(2*a*x^2)]
    @test_int [(a + b*sqrt(x))^3/x^4, x, 3, -a^3/(3*x^3) - (6*a^2*b)/(5*x^(5/2)) - (3*a*b^2)/(2*x^2) - (2*b^3)/(3*x^(3/2))]
    @test_int [(a + b*sqrt(x))^3/x^5, x, 3, -a^3/(4*x^4) - (6*a^2*b)/(7*x^(7/2)) - (a*b^2)/x^3 - (2*b^3)/(5*x^(5/2))]
    @test_int [(a + b*sqrt(x))^3/x^6, x, 3, -a^3/(5*x^5) - (2*a^2*b)/(3*x^(9/2)) - (3*a*b^2)/(4*x^4) - (2*b^3)/(7*x^(7/2))]

    @test_int [(a + b*sqrt(x))^5*x^4, x, 3, (a^5*x^5)/5 + (10*a^4*b*x^(11/2))/11 + (5*a^3*b^2*x^6)/3 + (20*a^2*b^3*x^(13/2))/13 + (5*a*b^4*x^7)/7 + (2*b^5*x^(15/2))/15]
    @test_int [(a + b*sqrt(x))^5*x^3, x, 3, (a^5*x^4)/4 + (10*a^4*b*x^(9/2))/9 + 2*a^3*b^2*x^5 + (20*a^2*b^3*x^(11/2))/11 + (5*a*b^4*x^6)/6 + (2*b^5*x^(13/2))/13]
    @test_int [(a + b*sqrt(x))^5*x^2, x, 3, (a^5*x^3)/3 + (10*a^4*b*x^(7/2))/7 + (5*a^3*b^2*x^4)/2 + (20*a^2*b^3*x^(9/2))/9 + a*b^4*x^5 + (2*b^5*x^(11/2))/11]
    @test_int [(a + b*sqrt(x))^5*x^1, x, 3, -((a^3*(a + b*sqrt(x))^6)/(3*b^4)) + (6*a^2*(a + b*sqrt(x))^7)/(7*b^4) - (3*a*(a + b*sqrt(x))^8)/(4*b^4) + (2*(a + b*sqrt(x))^9)/(9*b^4)]
    @test_int [(a + b*sqrt(x))^5*x^0, x, 3, -(a*(a + b*sqrt(x))^6)/(3*b^2) + (2*(a + b*sqrt(x))^7)/(7*b^2)]

    @test_int [(a + b*sqrt(x))^5/x^1, x, 3, 10*a^4*b*sqrt(x) + 10*a^3*b^2*x + (20*a^2*b^3*x^(3/2))/3 + (5*a*b^4*x^2)/2 + (2*b^5*x^(5/2))/5 + a^5*log(x)]
    @test_int [(a + b*sqrt(x))^5/x^2, x, 3, -(a^5/x) - (10*a^4*b)/sqrt(x) + 20*a^2*b^3*sqrt(x) + 5*a*b^4*x + (2*b^5*x^(3/2))/3 + 10*a^3*b^2*log(x)]
    @test_int [(a + b*sqrt(x))^5/x^3, x, 3, -a^5/(2*x^2) - (10*a^4*b)/(3*x^(3/2)) - (10*a^3*b^2)/x - (20*a^2*b^3)/sqrt(x) + 2*b^5*sqrt(x) + 5*a*b^4*log(x)]

    @test_int [(a + b*sqrt(x))^5/x^4, x, 1, -(a + b*sqrt(x))^6/(3*a*x^3)]
    @test_int [(a + b*sqrt(x))^5/x^5, x, 4, -((a + b*sqrt(x))^6/(4*a*x^4)) + (b*(a + b*sqrt(x))^6)/(14*a^2*x^(7/2)) - (b^2*(a + b*sqrt(x))^6)/(84*a^3*x^3)]

    @test_int [(a + b*sqrt(x))^5/x^6, x, 3, -a^5/(5*x^5) - (10*a^4*b)/(9*x^(9/2)) - (5*a^3*b^2)/(2*x^4) - (20*a^2*b^3)/(7*x^(7/2)) - (5*a*b^4)/(3*x^3) - (2*b^5)/(5*x^(5/2))]
    @test_int [(a + b*sqrt(x))^5/x^7, x, 3, -a^5/(6*x^6) - (10*a^4*b)/(11*x^(11/2)) - (2*a^3*b^2)/x^5 - (20*a^2*b^3)/(9*x^(9/2)) - (5*a*b^4)/(4*x^4) - (2*b^5)/(7*x^(7/2))]

    @test_int [(a + b*sqrt(x))^10*x^4, x, 3, (a^10*x^5)/5 + (20/11)*a^9*b*x^(11/2) + (15/2)*a^8*b^2*x^6 + (240/13)*a^7*b^3*x^(13/2) + 30*a^6*b^4*x^7 + (168/5)*a^5*b^5*x^(15/2) + (105/4)*a^4*b^6*x^8 + (240/17)*a^3*b^7*x^(17/2) + 5*a^2*b^8*x^9 + (20/19)*a*b^9*x^(19/2) + (b^10*x^10)/10]
    @test_int [(a + b*sqrt(x))^10*x^3, x, 3, -((2*a^7*(a + b*sqrt(x))^11)/(11*b^8)) + (7*a^6*(a + b*sqrt(x))^12)/(6*b^8) - (42*a^5*(a + b*sqrt(x))^13)/(13*b^8) + (5*a^4*(a + b*sqrt(x))^14)/b^8 - (14*a^3*(a + b*sqrt(x))^15)/(3*b^8) + (21*a^2*(a + b*sqrt(x))^16)/(8*b^8) - (14*a*(a + b*sqrt(x))^17)/(17*b^8) + (a + b*sqrt(x))^18/(9*b^8)]
    @test_int [(a + b*sqrt(x))^10*x^2, x, 3, (-2*a^5*(a + b*sqrt(x))^11)/(11*b^6) + (5*a^4*(a + b*sqrt(x))^12)/(6*b^6) - (20*a^3*(a + b*sqrt(x))^13)/(13*b^6) + (10*a^2*(a + b*sqrt(x))^14)/(7*b^6) - (2*a*(a + b*sqrt(x))^15)/(3*b^6) + (a + b*sqrt(x))^16/(8*b^6)]
    @test_int [(a + b*sqrt(x))^10*x^1, x, 3, (-2*a^3*(a + b*sqrt(x))^11)/(11*b^4) + (a^2*(a + b*sqrt(x))^12)/(2*b^4) - (6*a*(a + b*sqrt(x))^13)/(13*b^4) + (a + b*sqrt(x))^14/(7*b^4)]
    @test_int [(a + b*sqrt(x))^10*x^0, x, 3, (-2*a*(a + b*sqrt(x))^11)/(11*b^2) + (a + b*sqrt(x))^12/(6*b^2)]

    @test_int [(a + b*sqrt(x))^10/x^1, x, 3, 20*a^9*b*sqrt(x) + 45*a^8*b^2*x + 80*a^7*b^3*x^(3/2) + 105*a^6*b^4*x^2 + (504*a^5*b^5*x^(5/2))/5 + 70*a^4*b^6*x^3 + (240*a^3*b^7*x^(7/2))/7 + (45*a^2*b^8*x^4)/4 + (20*a*b^9*x^(9/2))/9 + (b^10*x^5)/5 + a^10*log(x)]
    @test_int [(a + b*sqrt(x))^10/x^2, x, 3, -(a^10/x) - (20*a^9*b)/sqrt(x) + 240*a^7*b^3*sqrt(x) + 210*a^6*b^4*x + 168*a^5*b^5*x^(3/2) + 105*a^4*b^6*x^2 + 48*a^3*b^7*x^(5/2) + 15*a^2*b^8*x^3 + (20*a*b^9*x^(7/2))/7 + (b^10*x^4)/4 + 45*a^8*b^2*log(x)]
    @test_int [(a + b*sqrt(x))^10/x^3, x, 3, -a^10/(2*x^2) - (20*a^9*b)/(3*x^(3/2)) - (45*a^8*b^2)/x - (240*a^7*b^3)/sqrt(x) + 504*a^5*b^5*sqrt(x) + 210*a^4*b^6*x + 80*a^3*b^7*x^(3/2) + (45*a^2*b^8*x^2)/2 + 4*a*b^9*x^(5/2) + (b^10*x^3)/3 + 210*a^6*b^4*log(x)]
    @test_int [(a + b*sqrt(x))^10/x^4, x, 3, -a^10/(3*x^3) - (4*a^9*b)/x^(5/2) - (45*a^8*b^2)/(2*x^2) - (80*a^7*b^3)/x^(3/2) - (210*a^6*b^4)/x - (504*a^5*b^5)/sqrt(x) + 240*a^3*b^7*sqrt(x) + 45*a^2*b^8*x + (20*a*b^9*x^(3/2))/3 + (b^10*x^2)/2 + 210*a^4*b^6*log(x)]
    @test_int [(a + b*sqrt(x))^10/x^5, x, 3, -a^10/(4*x^4) - (20*a^9*b)/(7*x^(7/2)) - (15*a^8*b^2)/x^3 - (48*a^7*b^3)/x^(5/2) - (105*a^6*b^4)/x^2 - (168*a^5*b^5)/x^(3/2) - (210*a^4*b^6)/x - (240*a^3*b^7)/sqrt(x) + 20*a*b^9*sqrt(x) + b^10*x + 45*a^2*b^8*log(x)]
    @test_int [(a + b*sqrt(x))^10/x^6, x, 3, -a^10/(5*x^5) - (20*a^9*b)/(9*x^(9/2)) - (45*a^8*b^2)/(4*x^4) - (240*a^7*b^3)/(7*x^(7/2)) - (70*a^6*b^4)/x^3 - (504*a^5*b^5)/(5*x^(5/2)) - (105*a^4*b^6)/x^2 - (80*a^3*b^7)/x^(3/2) - (45*a^2*b^8)/x - (20*a*b^9)/sqrt(x) + b^10*log(x)]

    @test_int [(a + b*sqrt(x))^10/x^7, x, 3, -(a + b*sqrt(x))^11/(6*a*x^6) + (b*(a + b*sqrt(x))^11)/(66*a^2*x^(11/2))]
    @test_int [(a + b*sqrt(x))^10/x^8, x, 5, -(a + b*sqrt(x))^11/(7*a*x^7) + (3*b*(a + b*sqrt(x))^11)/(91*a^2*x^(13/2)) - (b^2*(a + b*sqrt(x))^11)/(182*a^3*x^6) + (b^3*(a + b*sqrt(x))^11)/(2002*a^4*x^(11/2))]
    @test_int [(a + b*sqrt(x))^10/x^9, x, 7, -(a + b*sqrt(x))^11/(8*a*x^8) + (b*(a + b*sqrt(x))^11)/(24*a^2*x^(15/2)) - (b^2*(a + b*sqrt(x))^11)/(84*a^3*x^7) + (b^3*(a + b*sqrt(x))^11)/(364*a^4*x^(13/2)) - (b^4*(a + b*sqrt(x))^11)/(2184*a^5*x^6) + (b^5*(a + b*sqrt(x))^11)/(24024*a^6*x^(11/2))]

    @test_int [(a + b*sqrt(x))^10/x^10, x, 3, -a^10/(9*x^9) - (20*a^9*b)/(17*x^(17/2)) - (45*a^8*b^2)/(8*x^8) - (16*a^7*b^3)/x^(15/2) - (30*a^6*b^4)/x^7 - (504*a^5*b^5)/(13*x^(13/2)) - (35*a^4*b^6)/x^6 - (240*a^3*b^7)/(11*x^(11/2)) - (9*a^2*b^8)/x^5 - (20*a*b^9)/(9*x^(9/2)) - b^10/(4*x^4)]
    @test_int [(a + b*sqrt(x))^10/x^11, x, 3, -a^10/(10*x^10) - (20*a^9*b)/(19*x^(19/2)) - (5*a^8*b^2)/x^9 - (240*a^7*b^3)/(17*x^(17/2)) - (105*a^6*b^4)/(4*x^8) - (168*a^5*b^5)/(5*x^(15/2)) - (30*a^4*b^6)/x^7 - (240*a^3*b^7)/(13*x^(13/2)) - (15*a^2*b^8)/(2*x^6) - (20*a*b^9)/(11*x^(11/2)) - b^10/(5*x^5)]

    @test_int [(a + b*sqrt(x))^15*x^5, x, 3, -((a^11*(a + b*sqrt(x))^16)/(8*b^12)) + (22*a^10*(a + b*sqrt(x))^17)/(17*b^12) - (55*a^9*(a + b*sqrt(x))^18)/(9*b^12) + (330*a^8*(a + b*sqrt(x))^19)/(19*b^12) - (33*a^7*(a + b*sqrt(x))^20)/b^12 + (44*a^6*(a + b*sqrt(x))^21)/b^12 - (42*a^5*(a + b*sqrt(x))^22)/b^12 + (660*a^4*(a + b*sqrt(x))^23)/(23*b^12) - (55*a^3*(a + b*sqrt(x))^24)/(4*b^12) + (22*a^2*(a + b*sqrt(x))^25)/(5*b^12) - (11*a*(a + b*sqrt(x))^26)/(13*b^12) + (2*(a + b*sqrt(x))^27)/(27*b^12)]
    @test_int [(a + b*sqrt(x))^15*x^4, x, 3, -(a^9*(a + b*sqrt(x))^16)/(8*b^10) + (18*a^8*(a + b*sqrt(x))^17)/(17*b^10) - (4*a^7*(a + b*sqrt(x))^18)/b^10 + (168*a^6*(a + b*sqrt(x))^19)/(19*b^10) - (63*a^5*(a + b*sqrt(x))^20)/(5*b^10) + (12*a^4*(a + b*sqrt(x))^21)/b^10 - (84*a^3*(a + b*sqrt(x))^22)/(11*b^10) + (72*a^2*(a + b*sqrt(x))^23)/(23*b^10) - (3*a*(a + b*sqrt(x))^24)/(4*b^10) + (2*(a + b*sqrt(x))^25)/(25*b^10)]
    @test_int [(a + b*sqrt(x))^15*x^3, x, 3, -(a^7*(a + b*sqrt(x))^16)/(8*b^8) + (14*a^6*(a + b*sqrt(x))^17)/(17*b^8) - (7*a^5*(a + b*sqrt(x))^18)/(3*b^8) + (70*a^4*(a + b*sqrt(x))^19)/(19*b^8) - (7*a^3*(a + b*sqrt(x))^20)/(2*b^8) + (2*a^2*(a + b*sqrt(x))^21)/b^8 - (7*a*(a + b*sqrt(x))^22)/(11*b^8) + (2*(a + b*sqrt(x))^23)/(23*b^8)]
    @test_int [(a + b*sqrt(x))^15*x^2, x, 3, -(a^5*(a + b*sqrt(x))^16)/(8*b^6) + (10*a^4*(a + b*sqrt(x))^17)/(17*b^6) - (10*a^3*(a + b*sqrt(x))^18)/(9*b^6) + (20*a^2*(a + b*sqrt(x))^19)/(19*b^6) - (a*(a + b*sqrt(x))^20)/(2*b^6) + (2*(a + b*sqrt(x))^21)/(21*b^6)]
    @test_int [(a + b*sqrt(x))^15*x^1, x, 3, -(a^3*(a + b*sqrt(x))^16)/(8*b^4) + (6*a^2*(a + b*sqrt(x))^17)/(17*b^4) - (a*(a + b*sqrt(x))^18)/(3*b^4) + (2*(a + b*sqrt(x))^19)/(19*b^4)]
    @test_int [(a + b*sqrt(x))^15*x^0, x, 3, -(a*(a + b*sqrt(x))^16)/(8*b^2) + (2*(a + b*sqrt(x))^17)/(17*b^2)]

    @test_int [(a + b*sqrt(x))^15/x^1, x, 3, 30*a^14*b*sqrt(x) + 105*a^13*b^2*x + (910*a^12*b^3*x^(3/2))/3 + (1365*a^11*b^4*x^2)/2 + (6006*a^10*b^5*x^(5/2))/5 + (5005*a^9*b^6*x^3)/3 + (12870*a^8*b^7*x^(7/2))/7 + (6435*a^7*b^8*x^4)/4 + (10010*a^6*b^9*x^(9/2))/9 + (3003*a^5*b^10*x^5)/5 + (2730*a^4*b^11*x^(11/2))/11 + (455*a^3*b^12*x^6)/6 + (210*a^2*b^13*x^(13/2))/13 + (15*a*b^14*x^7)/7 + (2*b^15*x^(15/2))/15 + a^15*log(x)]
    @test_int [(a + b*sqrt(x))^15/x^2, x, 3, -(a^15/x) - (30*a^14*b)/sqrt(x) + 910*a^12*b^3*sqrt(x) + 1365*a^11*b^4*x + 2002*a^10*b^5*x^(3/2) + (5005*a^9*b^6*x^2)/2 + 2574*a^8*b^7*x^(5/2) + 2145*a^7*b^8*x^3 + 1430*a^6*b^9*x^(7/2) + (3003*a^5*b^10*x^4)/4 + (910*a^4*b^11*x^(9/2))/3 + 91*a^3*b^12*x^5 + (210*a^2*b^13*x^(11/2))/11 + (5*a*b^14*x^6)/2 + (2*b^15*x^(13/2))/13 + 105*a^13*b^2*log(x)]
    @test_int [(a + b*sqrt(x))^15/x^3, x, 3, -a^15/(2*x^2) - (10*a^14*b)/x^(3/2) - (105*a^13*b^2)/x - (910*a^12*b^3)/sqrt(x) + 6006*a^10*b^5*sqrt(x) + 5005*a^9*b^6*x + 4290*a^8*b^7*x^(3/2) + (6435*a^7*b^8*x^2)/2 + 2002*a^6*b^9*x^(5/2) + 1001*a^5*b^10*x^3 + 390*a^4*b^11*x^(7/2) + (455*a^3*b^12*x^4)/4 + (70*a^2*b^13*x^(9/2))/3 + 3*a*b^14*x^5 + (2*b^15*x^(11/2))/11 + 1365*a^11*b^4*log(x)]
    @test_int [(a + b*sqrt(x))^15/x^4, x, 3, -a^15/(3*x^3) - (6*a^14*b)/x^(5/2) - (105*a^13*b^2)/(2*x^2) - (910*a^12*b^3)/(3*x^(3/2)) - (1365*a^11*b^4)/x - (6006*a^10*b^5)/sqrt(x) + 12870*a^8*b^7*sqrt(x) + 6435*a^7*b^8*x + (10010*a^6*b^9*x^(3/2))/3 + (3003*a^5*b^10*x^2)/2 + 546*a^4*b^11*x^(5/2) + (455*a^3*b^12*x^3)/3 + 30*a^2*b^13*x^(7/2) + (15*a*b^14*x^4)/4 + (2*b^15*x^(9/2))/9 + 5005*a^9*b^6*log(x)]
    @test_int [(a + b*sqrt(x))^15/x^6, x, 3, -a^15/(5*x^5) - (10*a^14*b)/(3*x^(9/2)) - (105*a^13*b^2)/(4*x^4) - (130*a^12*b^3)/x^(7/2) - (455*a^11*b^4)/x^3 - (6006*a^10*b^5)/(5*x^(5/2)) - (5005*a^9*b^6)/(2*x^2) - (4290*a^8*b^7)/x^(3/2) - (6435*a^7*b^8)/x - (10010*a^6*b^9)/sqrt(x) + 2730*a^4*b^11*sqrt(x) + 455*a^3*b^12*x + 70*a^2*b^13*x^(3/2) + (15*a*b^14*x^2)/2 + (2*b^15*x^(5/2))/5 + 3003*a^5*b^10*log(x)]
    @test_int [(a + b*sqrt(x))^15/x^7, x, 3, -a^15/(6*x^6) - (30*a^14*b)/(11*x^(11/2)) - (21*a^13*b^2)/x^5 - (910*a^12*b^3)/(9*x^(9/2)) - (1365*a^11*b^4)/(4*x^4) - (858*a^10*b^5)/x^(7/2) - (5005*a^9*b^6)/(3*x^3) - (2574*a^8*b^7)/x^(5/2) - (6435*a^7*b^8)/(2*x^2) - (10010*a^6*b^9)/(3*x^(3/2)) - (3003*a^5*b^10)/x - (2730*a^4*b^11)/sqrt(x) + 210*a^2*b^13*sqrt(x) + 15*a*b^14*x + (2*b^15*x^(3/2))/3 + 455*a^3*b^12*log(x)]
    @test_int [(a + b*sqrt(x))^15/x^8, x, 3, -a^15/(7*x^7) - (30*a^14*b)/(13*x^(13/2)) - (35*a^13*b^2)/(2*x^6) - (910*a^12*b^3)/(11*x^(11/2)) - (273*a^11*b^4)/x^5 - (2002*a^10*b^5)/(3*x^(9/2)) - (5005*a^9*b^6)/(4*x^4) - (12870*a^8*b^7)/(7*x^(7/2)) - (2145*a^7*b^8)/x^3 - (2002*a^6*b^9)/x^(5/2) - (3003*a^5*b^10)/(2*x^2) - (910*a^4*b^11)/x^(3/2) - (455*a^3*b^12)/x - (210*a^2*b^13)/sqrt(x) + 2*b^15*sqrt(x) + 15*a*b^14*log(x)]

    @test_int [(a + b*sqrt(x))^15/x^9, x, 1, -(a + b*sqrt(x))^16/(8*a*x^8)]
    @test_int [(a + b*sqrt(x))^15/x^10, x, 4, -(a + b*sqrt(x))^16/(9*a*x^9) + (2*b*(a + b*sqrt(x))^16)/(153*a^2*x^(17/2)) - (b^2*(a + b*sqrt(x))^16)/(1224*a^3*x^8)]
    @test_int [(a + b*sqrt(x))^15/x^11, x, 6, -(a + b*sqrt(x))^16/(10*a*x^10) + (2*b*(a + b*sqrt(x))^16)/(95*a^2*x^(19/2)) - (b^2*(a + b*sqrt(x))^16)/(285*a^3*x^9) + (2*b^3*(a + b*sqrt(x))^16)/(4845*a^4*x^(17/2)) - (b^4*(a + b*sqrt(x))^16)/(38760*a^5*x^8)]
    @test_int [(a + b*sqrt(x))^15/x^12, x, 8, -(a + b*sqrt(x))^16/(11*a*x^11) + (2*b*(a + b*sqrt(x))^16)/(77*a^2*x^(21/2)) - (b^2*(a + b*sqrt(x))^16)/(154*a^3*x^10) + (2*b^3*(a + b*sqrt(x))^16)/(1463*a^4*x^(19/2)) - (b^4*(a + b*sqrt(x))^16)/(4389*a^5*x^9) + (2*b^5*(a + b*sqrt(x))^16)/(74613*a^6*x^(17/2)) - (b^6*(a + b*sqrt(x))^16)/(596904*a^7*x^8)]
    @test_int [(a + b*sqrt(x))^15/x^13, x, 10, -(a + b*sqrt(x))^16/(12*a*x^12) + (2*b*(a + b*sqrt(x))^16)/(69*a^2*x^(23/2)) - (7*b^2*(a + b*sqrt(x))^16)/(759*a^3*x^11) + (2*b^3*(a + b*sqrt(x))^16)/(759*a^4*x^(21/2)) - (b^4*(a + b*sqrt(x))^16)/(1518*a^5*x^10) + (2*b^5*(a + b*sqrt(x))^16)/(14421*a^6*x^(19/2)) - (b^6*(a + b*sqrt(x))^16)/(43263*a^7*x^9) + (2*b^7*(a + b*sqrt(x))^16)/(735471*a^8*x^(17/2)) - (b^8*(a + b*sqrt(x))^16)/(5883768*a^9*x^8)]
    @test_int [(a + b*sqrt(x))^15/x^14, x, 12, -((a + b*sqrt(x))^16/(13*a*x^13)) + (2*b*(a + b*sqrt(x))^16)/(65*a^2*x^(25/2)) - (3*b^2*(a + b*sqrt(x))^16)/(260*a^3*x^12) + (6*b^3*(a + b*sqrt(x))^16)/(1495*a^4*x^(23/2)) - (21*b^4*(a + b*sqrt(x))^16)/(16445*a^5*x^11) + (6*b^5*(a + b*sqrt(x))^16)/(16445*a^6*x^(21/2)) - (3*b^6*(a + b*sqrt(x))^16)/(32890*a^7*x^10) + (6*b^7*(a + b*sqrt(x))^16)/(312455*a^8*x^(19/2)) - (b^8*(a + b*sqrt(x))^16)/(312455*a^9*x^9) + (2*b^9*(a + b*sqrt(x))^16)/(5311735*a^10*x^(17/2)) - (b^10*(a + b*sqrt(x))^16)/(42493880*a^11*x^8)]

    @test_int [(a + b*sqrt(x))^15/x^15, x, 3, -a^15/(14*x^14) - (10*a^14*b)/(9*x^(27/2)) - (105*a^13*b^2)/(13*x^13) - (182*a^12*b^3)/(5*x^(25/2)) - (455*a^11*b^4)/(4*x^12) - (6006*a^10*b^5)/(23*x^(23/2)) - (455*a^9*b^6)/x^11 - (4290*a^8*b^7)/(7*x^(21/2)) - (1287*a^7*b^8)/(2*x^10) - (10010*a^6*b^9)/(19*x^(19/2)) - (1001*a^5*b^10)/(3*x^9) - (2730*a^4*b^11)/(17*x^(17/2)) - (455*a^3*b^12)/(8*x^8) - (14*a^2*b^13)/x^(15/2) - (15*a*b^14)/(7*x^7) - (2*b^15)/(13*x^(13/2))]
    @test_int [(a + b*sqrt(x))^15/x^16, x, 3, -a^15/(15*x^15) - (30*a^14*b)/(29*x^(29/2)) - (15*a^13*b^2)/(2*x^14) - (910*a^12*b^3)/(27*x^(27/2)) - (105*a^11*b^4)/x^13 - (6006*a^10*b^5)/(25*x^(25/2)) - (5005*a^9*b^6)/(12*x^12) - (12870*a^8*b^7)/(23*x^(23/2)) - (585*a^7*b^8)/x^11 - (1430*a^6*b^9)/(3*x^(21/2)) - (3003*a^5*b^10)/(10*x^10) - (2730*a^4*b^11)/(19*x^(19/2)) - (455*a^3*b^12)/(9*x^9) - (210*a^2*b^13)/(17*x^(17/2)) - (15*a*b^14)/(8*x^8) - (2*b^15)/(15*x^(15/2))]
    @test_int [(a + b*sqrt(x))^15/x^17, x, 3, -a^15/(16*x^16) - (30*a^14*b)/(31*x^(31/2)) - (7*a^13*b^2)/x^15 - (910*a^12*b^3)/(29*x^(29/2)) - (195*a^11*b^4)/(2*x^14) - (2002*a^10*b^5)/(9*x^(27/2)) - (385*a^9*b^6)/x^13 - (2574*a^8*b^7)/(5*x^(25/2)) - (2145*a^7*b^8)/(4*x^12) - (10010*a^6*b^9)/(23*x^(23/2)) - (273*a^5*b^10)/x^11 - (130*a^4*b^11)/x^(21/2) - (91*a^3*b^12)/(2*x^10) - (210*a^2*b^13)/(19*x^(19/2)) - (5*a*b^14)/(3*x^9) - (2*b^15)/(17*x^(17/2))]

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [x^3/(a + b*sqrt(x)), x, 3, (2*a^6*sqrt(x))/b^7 - (a^5*x)/b^6 + (2*a^4*x^(3/2))/(3*b^5) - (a^3*x^2)/(2*b^4) + (2*a^2*x^(5/2))/(5*b^3) - (a*x^3)/(3*b^2) + (2*x^(7/2))/(7*b) - (2*a^7*log(a + b*sqrt(x)))/b^8]
    @test_int [x^2/(a + b*sqrt(x)), x, 3, (2*a^4*sqrt(x))/b^5 - (a^3*x)/b^4 + (2*a^2*x^(3/2))/(3*b^3) - (a*x^2)/(2*b^2) + (2*x^(5/2))/(5*b) - (2*a^5*log(a + b*sqrt(x)))/b^6]
    @test_int [x^1/(a + b*sqrt(x)), x, 3, (2*a^2*sqrt(x))/b^3 - (a*x)/b^2 + (2*x^(3/2))/(3*b) - (2*a^3*log(a + b*sqrt(x)))/b^4]
    @test_int [x^0/(a + b*sqrt(x)), x, 3, (2*sqrt(x))/b - (2*a*log(a + b*sqrt(x)))/b^2]
    @test_int [1/(x^1*(a + b*sqrt(x))), x, 4, (-2*log(a + b*sqrt(x)))/a + log(x)/a]
    @test_int [1/(x^2*(a + b*sqrt(x))), x, 3, -(1/(a*x)) + (2*b)/(a^2*sqrt(x)) - (2*b^2*log(a + b*sqrt(x)))/a^3 + (b^2*log(x))/a^3]
    @test_int [1/(x^3*(a + b*sqrt(x))), x, 3, -1/(2*a*x^2) + (2*b)/(3*a^2*x^(3/2)) - b^2/(a^3*x) + (2*b^3)/(a^4*sqrt(x)) - (2*b^4*log(a + b*sqrt(x)))/a^5 + (b^4*log(x))/a^5]
    @test_int [1/(x^4*(a + b*sqrt(x))), x, 3, -1/(3*a*x^3) + (2*b)/(5*a^2*x^(5/2)) - b^2/(2*a^3*x^2) + (2*b^3)/(3*a^4*x^(3/2)) - b^4/(a^5*x) + (2*b^5)/(a^6*sqrt(x)) - (2*b^6*log(a + b*sqrt(x)))/a^7 + (b^6*log(x))/a^7]

    @test_int [x^3/(a + b*sqrt(x))^2, x, 3, (2*a^7)/(b^8*(a + b*sqrt(x))) - (12*a^5*sqrt(x))/b^7 + (5*a^4*x)/b^6 - (8*a^3*x^(3/2))/(3*b^5) + (3*a^2*x^2)/(2*b^4) - (4*a*x^(5/2))/(5*b^3) + x^3/(3*b^2) + (14*a^6*log(a + b*sqrt(x)))/b^8]
    @test_int [x^2/(a + b*sqrt(x))^2, x, 3, (2*a^5)/(b^6*(a + b*sqrt(x))) - (8*a^3*sqrt(x))/b^5 + (3*a^2*x)/b^4 - (4*a*x^(3/2))/(3*b^3) + x^2/(2*b^2) + (10*a^4*log(a + b*sqrt(x)))/b^6]
    @test_int [x^1/(a + b*sqrt(x))^2, x, 3, (2*a^3)/(b^4*(a + b*sqrt(x))) - (4*a*sqrt(x))/b^3 + x/b^2 + (6*a^2*log(a + b*sqrt(x)))/b^4]
    @test_int [x^0/(a + b*sqrt(x))^2, x, 3, (2*a)/(b^2*(a + b*sqrt(x))) + (2*log(a + b*sqrt(x)))/b^2]
    @test_int [1/(x^1*(a + b*sqrt(x))^2), x, 3, 2/(a*(a + b*sqrt(x))) - (2*log(a + b*sqrt(x)))/a^2 + log(x)/a^2]
    @test_int [1/(x^2*(a + b*sqrt(x))^2), x, 3, (2*b^2)/(a^3*(a + b*sqrt(x))) - 1/(a^2*x) + (4*b)/(a^3*sqrt(x)) - (6*b^2*log(a + b*sqrt(x)))/a^4 + (3*b^2*log(x))/a^4]
    @test_int [1/(x^3*(a + b*sqrt(x))^2), x, 3, (2*b^4)/(a^5*(a + b*sqrt(x))) - 1/(2*a^2*x^2) + (4*b)/(3*a^3*x^(3/2)) - (3*b^2)/(a^4*x) + (8*b^3)/(a^5*sqrt(x)) - (10*b^4*log(a + b*sqrt(x)))/a^6 + (5*b^4*log(x))/a^6]
    @test_int [1/(x^4*(a + b*sqrt(x))^2), x, 3, (2*b^6)/(a^7*(a + b*sqrt(x))) - 1/(3*a^2*x^3) + (4*b)/(5*a^3*x^(5/2)) - (3*b^2)/(2*a^4*x^2) + (8*b^3)/(3*a^5*x^(3/2)) - (5*b^4)/(a^6*x) + (12*b^5)/(a^7*sqrt(x)) - (14*b^6*log(a + b*sqrt(x)))/a^8 + (7*b^6*log(x))/a^8]

    @test_int [x^3/(a + b*sqrt(x))^3, x, 3, a^7/(b^8*(a + b*sqrt(x))^2) - (14*a^6)/(b^8*(a + b*sqrt(x))) + (30*a^4*sqrt(x))/b^7 - (10*a^3*x)/b^6 + (4*a^2*x^(3/2))/b^5 - (3*a*x^2)/(2*b^4) + (2*x^(5/2))/(5*b^3) - (42*a^5*log(a + b*sqrt(x)))/b^8]
    @test_int [x^2/(a + b*sqrt(x))^3, x, 3, a^5/(b^6*(a + b*sqrt(x))^2) - (10*a^4)/(b^6*(a + b*sqrt(x))) + (12*a^2*sqrt(x))/b^5 - (3*a*x)/b^4 + (2*x^(3/2))/(3*b^3) - (20*a^3*log(a + b*sqrt(x)))/b^6]
    @test_int [x^1/(a + b*sqrt(x))^3, x, 3, a^3/(b^4*(a + b*sqrt(x))^2) - (6*a^2)/(b^4*(a + b*sqrt(x))) + (2*sqrt(x))/b^3 - (6*a*log(a + b*sqrt(x)))/b^4]
    @test_int [x^0/(a + b*sqrt(x))^3, x, 2, x/(a*(a + b*sqrt(x))^2)]
    @test_int [1/(x^1*(a + b*sqrt(x))^3), x, 3, 1/(a*(a + b*sqrt(x))^2) + 2/(a^2*(a + b*sqrt(x))) - (2*log(a + b*sqrt(x)))/a^3 + log(x)/a^3]
    @test_int [1/(x^2*(a + b*sqrt(x))^3), x, 3, b^2/(a^3*(a + b*sqrt(x))^2) + (6*b^2)/(a^4*(a + b*sqrt(x))) - 1/(a^3*x) + (6*b)/(a^4*sqrt(x)) - (12*b^2*log(a + b*sqrt(x)))/a^5 + (6*b^2*log(x))/a^5]
    @test_int [1/(x^3*(a + b*sqrt(x))^3), x, 3, b^4/(a^5*(a + b*sqrt(x))^2) + (10*b^4)/(a^6*(a + b*sqrt(x))) - 1/(2*a^3*x^2) + (2*b)/(a^4*x^(3/2)) - (6*b^2)/(a^5*x) + (20*b^3)/(a^6*sqrt(x)) - (30*b^4*log(a + b*sqrt(x)))/a^7 + (15*b^4*log(x))/a^7]
    @test_int [1/(x^4*(a + b*sqrt(x))^3), x, 3, b^6/(a^7*(a + b*sqrt(x))^2) + (14*b^6)/(a^8*(a + b*sqrt(x))) - 1/(3*a^3*x^3) + (6*b)/(5*a^4*x^(5/2)) - (3*b^2)/(a^5*x^2) + (20*b^3)/(3*a^6*x^(3/2)) - (15*b^4)/(a^7*x) + (42*b^5)/(a^8*sqrt(x)) - (56*b^6*log(a + b*sqrt(x)))/a^9 + (28*b^6*log(x))/a^9]

    @test_int [x^4/(a + b*sqrt(x))^5, x, 3, a^9/(2*b^10*(a + b*sqrt(x))^4) - (6*a^8)/(b^10*(a + b*sqrt(x))^3) + (36*a^7)/(b^10*(a + b*sqrt(x))^2) - (168*a^6)/(b^10*(a + b*sqrt(x))) + (140*a^4*sqrt(x))/b^9 - (35*a^3*x)/b^8 + (10*a^2*x^(3/2))/b^7 - (5*a*x^2)/(2*b^6) + (2*x^(5/2))/(5*b^5) - (252*a^5*log(a + b*sqrt(x)))/b^10]
    @test_int [x^3/(a + b*sqrt(x))^5, x, 3, a^7/(2*b^8*(a + b*sqrt(x))^4) - (14*a^6)/(3*b^8*(a + b*sqrt(x))^3) + (21*a^5)/(b^8*(a + b*sqrt(x))^2) - (70*a^4)/(b^8*(a + b*sqrt(x))) + (30*a^2*sqrt(x))/b^7 - (5*a*x)/b^6 + (2*x^(3/2))/(3*b^5) - (70*a^3*log(a + b*sqrt(x)))/b^8]
    @test_int [x^2/(a + b*sqrt(x))^5, x, 3, a^5/(2*b^6*(a + b*sqrt(x))^4) - (10*a^4)/(3*b^6*(a + b*sqrt(x))^3) + (10*a^3)/(b^6*(a + b*sqrt(x))^2) - (20*a^2)/(b^6*(a + b*sqrt(x))) + (2*sqrt(x))/b^5 - (10*a*log(a + b*sqrt(x)))/b^6]
    @test_int [x^1/(a + b*sqrt(x))^5, x, 1, x^2/(2*a*(a + b*sqrt(x))^4)]
    @test_int [x^0/(a + b*sqrt(x))^5, x, 3, a/(2*b^2*(a + b*sqrt(x))^4) - 2/(3*b^2*(a + b*sqrt(x))^3)]
    @test_int [1/(x^1*(a + b*sqrt(x))^5), x, 3, 1/(2*a*(a + b*sqrt(x))^4) + 2/(3*a^2*(a + b*sqrt(x))^3) + 1/(a^3*(a + b*sqrt(x))^2) + 2/(a^4*(a + b*sqrt(x))) - (2*log(a + b*sqrt(x)))/a^5 + log(x)/a^5]
    @test_int [1/(x^2*(a + b*sqrt(x))^5), x, 3, b^2/(2*a^3*(a + b*sqrt(x))^4) + (2*b^2)/(a^4*(a + b*sqrt(x))^3) + (6*b^2)/(a^5*(a + b*sqrt(x))^2) + (20*b^2)/(a^6*(a + b*sqrt(x))) - 1/(a^5*x) + (10*b)/(a^6*sqrt(x)) - (30*b^2*log(a + b*sqrt(x)))/a^7 + (15*b^2*log(x))/a^7]
    @test_int [1/(x^3*(a + b*sqrt(x))^5), x, 3, b^4/(2*a^5*(a + b*sqrt(x))^4) + (10*b^4)/(3*a^6*(a + b*sqrt(x))^3) + (15*b^4)/(a^7*(a + b*sqrt(x))^2) + (70*b^4)/(a^8*(a + b*sqrt(x))) - 1/(2*a^5*x^2) + (10*b)/(3*a^6*x^(3/2)) - (15*b^2)/(a^7*x) + (70*b^3)/(a^8*sqrt(x)) - (140*b^4*log(a + b*sqrt(x)))/a^9 + (70*b^4*log(x))/a^9]

    @test_int [x^5/(a + b*sqrt(x))^8, x, 3, (2*a^11)/(7*b^12*(a + b*sqrt(x))^7) - (11*a^10)/(3*b^12*(a + b*sqrt(x))^6) + (22*a^9)/(b^12*(a + b*sqrt(x))^5) - (165*a^8)/(2*b^12*(a + b*sqrt(x))^4) + (220*a^7)/(b^12*(a + b*sqrt(x))^3) - (462*a^6)/(b^12*(a + b*sqrt(x))^2) + (924*a^5)/(b^12*(a + b*sqrt(x))) - (240*a^3*sqrt(x))/b^11 + (36*a^2*x)/b^10 - (16*a*x^(3/2))/(3*b^9) + x^2/(2*b^8) + (660*a^4*log(a + b*sqrt(x)))/b^12]
    @test_int [x^4/(a + b*sqrt(x))^8, x, 3, (2*a^9)/(7*b^10*(a + b*sqrt(x))^7) - (3*a^8)/(b^10*(a + b*sqrt(x))^6) + (72*a^7)/(5*b^10*(a + b*sqrt(x))^5) - (42*a^6)/(b^10*(a + b*sqrt(x))^4) + (84*a^5)/(b^10*(a + b*sqrt(x))^3) - (126*a^4)/(b^10*(a + b*sqrt(x))^2) + (168*a^3)/(b^10*(a + b*sqrt(x))) - (16*a*sqrt(x))/b^9 + x/b^8 + (72*a^2*log(a + b*sqrt(x)))/b^10]
    @test_int [x^3/(a + b*sqrt(x))^8, x, 3, (2*a^7)/(7*b^8*(a + b*sqrt(x))^7) - (7*a^6)/(3*b^8*(a + b*sqrt(x))^6) + (42*a^5)/(5*b^8*(a + b*sqrt(x))^5) - (35*a^4)/(2*b^8*(a + b*sqrt(x))^4) + (70*a^3)/(3*b^8*(a + b*sqrt(x))^3) - (21*a^2)/(b^8*(a + b*sqrt(x))^2) + (14*a)/(b^8*(a + b*sqrt(x))) + (2*log(a + b*sqrt(x)))/b^8]
    @test_int [x^2/(a + b*sqrt(x))^8, x, 3, (2*x^3)/(7*a*(a + b*sqrt(x))^7) + x^3/(21*a^2*(a + b*sqrt(x))^6)]
    @test_int [x^1/(a + b*sqrt(x))^8, x, 3, (2*a^3)/(7*b^4*(a + b*sqrt(x))^7) - a^2/(b^4*(a + b*sqrt(x))^6) + (6*a)/(5*b^4*(a + b*sqrt(x))^5) - 1/(2*b^4*(a + b*sqrt(x))^4)]
    @test_int [x^0/(a + b*sqrt(x))^8, x, 3, (2*a)/(7*b^2*(a + b*sqrt(x))^7) - 1/(3*b^2*(a + b*sqrt(x))^6)]
    @test_int [1/(x^1*(a + b*sqrt(x))^8), x, 3, 2/(7*a*(a + b*sqrt(x))^7) + 1/(3*a^2*(a + b*sqrt(x))^6) + 2/(5*a^3*(a + b*sqrt(x))^5) + 1/(2*a^4*(a + b*sqrt(x))^4) + 2/(3*a^5*(a + b*sqrt(x))^3) + 1/(a^6*(a + b*sqrt(x))^2) + 2/(a^7*(a + b*sqrt(x))) - (2*log(a + b*sqrt(x)))/a^8 + log(x)/a^8]
    @test_int [1/(x^2*(a + b*sqrt(x))^8), x, 3, (2*b^2)/(7*a^3*(a + b*sqrt(x))^7) + b^2/(a^4*(a + b*sqrt(x))^6) + (12*b^2)/(5*a^5*(a + b*sqrt(x))^5) + (5*b^2)/(a^6*(a + b*sqrt(x))^4) + (10*b^2)/(a^7*(a + b*sqrt(x))^3) + (21*b^2)/(a^8*(a + b*sqrt(x))^2) + (56*b^2)/(a^9*(a + b*sqrt(x))) - 1/(a^8*x) + (16*b)/(a^9*sqrt(x)) - (72*b^2*log(a + b*sqrt(x)))/a^10 + (36*b^2*log(x))/a^10]
    @test_int [1/(x^3*(a + b*sqrt(x))^8), x, 3, (2*b^4)/(7*a^5*(a + b*sqrt(x))^7) + (5*b^4)/(3*a^6*(a + b*sqrt(x))^6) + (6*b^4)/(a^7*(a + b*sqrt(x))^5) + (35*b^4)/(2*a^8*(a + b*sqrt(x))^4) + (140*b^4)/(3*a^9*(a + b*sqrt(x))^3) + (126*b^4)/(a^10*(a + b*sqrt(x))^2) + (420*b^4)/(a^11*(a + b*sqrt(x))) - 1/(2*a^8*x^2) + (16*b)/(3*a^9*x^(3/2)) - (36*b^2)/(a^10*x) + (240*b^3)/(a^11*sqrt(x)) - (660*b^4*log(a + b*sqrt(x)))/a^12 + (330*b^4*log(x))/a^12]

    @test_int [1/(x*(2 + b*sqrt(x))), x, 4, -log(2 + b*sqrt(x)) + log(x)/2]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b*sqrt(x))^(p/2)=#

    #= ::Subsubsection::Closed:: =#
    #=p>0=#

    @test_int [x^2*sqrt(a + b*sqrt(x)), x, 3, -((4*a^5*(a + b*sqrt(x))^(3/2))/(3*b^6)) + (4*a^4*(a + b*sqrt(x))^(5/2))/b^6 - (40*a^3*(a + b*sqrt(x))^(7/2))/(7*b^6) + (40*a^2*(a + b*sqrt(x))^(9/2))/(9*b^6) - (20*a*(a + b*sqrt(x))^(11/2))/(11*b^6) + (4*(a + b*sqrt(x))^(13/2))/(13*b^6)]
    @test_int [x^1*sqrt(a + b*sqrt(x)), x, 3, -((4*a^3*(a + b*sqrt(x))^(3/2))/(3*b^4)) + (12*a^2*(a + b*sqrt(x))^(5/2))/(5*b^4) - (12*a*(a + b*sqrt(x))^(7/2))/(7*b^4) + (4*(a + b*sqrt(x))^(9/2))/(9*b^4)]
    @test_int [x^0*sqrt(a + b*sqrt(x)), x, 3, -((4*a*(a + b*sqrt(x))^(3/2))/(3*b^2)) + (4*(a + b*sqrt(x))^(5/2))/(5*b^2)]
    @test_int [1/x^1*sqrt(a + b*sqrt(x)), x, 4, 4*sqrt(a + b*sqrt(x)) - 4*sqrt(a)*atanh(sqrt(a + b*sqrt(x))/sqrt(a))]
    @test_int [1/x^2*sqrt(a + b*sqrt(x)), x, 5, -(sqrt(a + b*sqrt(x))/x) - (b*sqrt(a + b*sqrt(x)))/(2*a*sqrt(x)) + (b^2*atanh(sqrt(a + b*sqrt(x))/sqrt(a)))/(2*a^(3/2))]
    @test_int [1/x^3*sqrt(a + b*sqrt(x)), x, 7, -(sqrt(a + b*sqrt(x))/(2*x^2)) - (b*sqrt(a + b*sqrt(x)))/(12*a*x^(3/2)) + (5*b^2*sqrt(a + b*sqrt(x)))/(48*a^2*x) - (5*b^3*sqrt(a + b*sqrt(x)))/(32*a^3*sqrt(x)) + (5*b^4*atanh(sqrt(a + b*sqrt(x))/sqrt(a)))/(32*a^(7/2))]

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [x^2/sqrt(a + b*sqrt(x)), x, 3, -((4*a^5*sqrt(a + b*sqrt(x)))/b^6) + (20*a^4*(a + b*sqrt(x))^(3/2))/(3*b^6) - (8*a^3*(a + b*sqrt(x))^(5/2))/b^6 + (40*a^2*(a + b*sqrt(x))^(7/2))/(7*b^6) - (20*a*(a + b*sqrt(x))^(9/2))/(9*b^6) + (4*(a + b*sqrt(x))^(11/2))/(11*b^6)]
    @test_int [x^1/sqrt(a + b*sqrt(x)), x, 3, -((4*a^3*sqrt(a + b*sqrt(x)))/b^4) + (4*a^2*(a + b*sqrt(x))^(3/2))/b^4 - (12*a*(a + b*sqrt(x))^(5/2))/(5*b^4) + (4*(a + b*sqrt(x))^(7/2))/(7*b^4)]
    @test_int [x^0/sqrt(a + b*sqrt(x)), x, 3, -((4*a*sqrt(a + b*sqrt(x)))/b^2) + (4*(a + b*sqrt(x))^(3/2))/(3*b^2)]
    @test_int [1/(x^1*sqrt(a + b*sqrt(x))), x, 3, -((4*atanh(sqrt(a + b*sqrt(x))/sqrt(a)))/sqrt(a))]
    @test_int [1/(x^2*sqrt(a + b*sqrt(x))), x, 5, -(sqrt(a + b*sqrt(x))/(a*x)) + (3*b*sqrt(a + b*sqrt(x)))/(2*a^2*sqrt(x)) - (3*b^2*atanh(sqrt(a + b*sqrt(x))/sqrt(a)))/(2*a^(5/2))]
    @test_int [1/(x^3*sqrt(a + b*sqrt(x))), x, 7, -(sqrt(a + b*sqrt(x))/(2*a*x^2)) + (7*b*sqrt(a + b*sqrt(x)))/(12*a^2*x^(3/2)) - (35*b^2*sqrt(a + b*sqrt(x)))/(48*a^3*x) + (35*b^3*sqrt(a + b*sqrt(x)))/(32*a^4*sqrt(x)) - (35*b^4*atanh(sqrt(a + b*sqrt(x))/sqrt(a)))/(32*a^(9/2))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^(m/2)*(a+b*sqrt(x))^p=#

    #= ::Subsubsection::Closed:: =#
    #=p>0=#

    @test_int [(a + b*sqrt(x))^n*sqrt(x), x, 3, (2*a^2*(a + b*sqrt(x))^(1 + n))/(b^3*(1 + n)) - (4*a*(a + b*sqrt(x))^(2 + n))/(b^3*(2 + n)) + (2*(a + b*sqrt(x))^(3 + n))/(b^3*(3 + n))]
    @test_int [(a + b*sqrt(x))^n/sqrt(x), x, 1, (2*(a + b*sqrt(x))^(1 + n))/(b*(1 + n))]

    @test_int [(1 + sqrt(x))/sqrt(x), x, 2, 2*sqrt(x) + x]
    @test_int [(1 + sqrt(x))^2/sqrt(x), x, 1, (2*(1 + sqrt(x))^3)/3]
    @test_int [(1 + sqrt(x))^3/sqrt(x), x, 1, (1 + sqrt(x))^4/2]

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [sqrt(x)/(1 + sqrt(x)), x, 3, -2*sqrt(x) + x + 2*log(1 + sqrt(x))]
    @test_int [1/((1 + sqrt(x))*sqrt(x)), x, 1, 2*log(1 + sqrt(x))]

    @test_int [1/((1 + sqrt(x))^2*sqrt(x)), x, 1, -2/(1 + sqrt(x))]

    @test_int [1/((1 + sqrt(x))^3*sqrt(x)), x, 1, -(1 + sqrt(x))^(-2)]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^(m/2)*(a+b*sqrt(x))^(p/2)=#

    #= ::Subsubsection::Closed:: =#
    #=p>0=#

    @test_int [sqrt(1 + sqrt(x))*sqrt(x), x, 3, (4/3)*(1 + sqrt(x))^(3/2) - (8/5)*(1 + sqrt(x))^(5/2) + (4/7)*(1 + sqrt(x))^(7/2)]
    @test_int [sqrt(1 + sqrt(x))/sqrt(x), x, 1, (4*(1 + sqrt(x))^(3/2))/3]

    #= ::Subsubsection:: =#
    #=p<0=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^(m/3)*(a+b*sqrt(x))^p=#

    #= ::Subsubsection:: =#
    #=p>0=#

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [x^(1/3)/(1 + sqrt(x)), x, 7, -3*x^(1/3) + (6*x^(5/6))/5 - 2*sqrt(3)*atan((1 - 2*x^(1/6))/sqrt(3)) - 3*log(1 + x^(1/6)) + log(1 + sqrt(x))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b*sqrt(x))^p*with*m*symbolic=#

    @test_int [x^m*(a + b*sqrt(x))^4, x, 2, (a^4*x^(1 + m))/(1 + m) + (8*a^3*b*x^(3/2 + m))/(3 + 2*m) + (6*a^2*b^2*x^(2 + m))/(2 + m) + (8*a*b^3*x^(5/2 + m))/(5 + 2*m) + (b^4*x^(3 + m))/(3 + m)]
    @test_int [x^m*(a + b*sqrt(x))^3, x, 2, (a^3*x^(1 + m))/(1 + m) + (6*a^2*b*x^(3/2 + m))/(3 + 2*m) + (3*a*b^2*x^(2 + m))/(2 + m) + (2*b^3*x^(5/2 + m))/(5 + 2*m)]
    @test_int [x^m*(a + b*sqrt(x))^2, x, 2, (a^2*x^(1 + m))/(1 + m) + (4*a*b*x^(3/2 + m))/(3 + 2*m) + (b^2*x^(2 + m))/(2 + m)]
    @test_int [x^m*(a + b*sqrt(x))^1, x, 2, (a*x^(1 + m))/(1 + m) + (2*b*x^(3/2 + m))/(3 + 2*m)]
    @test_int [x^m/(a + b*sqrt(x))^1, x, 2, (x^(1 + m)*HypergeometricFunctions._₂F₁(1, 2*(1 + m), 3 + 2*m, -((b*sqrt(x))/a)))/(a*(1 + m))]
    @test_int [x^m/(a + b*sqrt(x))^2, x, 2, (x^(1 + m)*HypergeometricFunctions._₂F₁(2, 2*(1 + m), 3 + 2*m, -((b*sqrt(x))/a)))/(a^2*(1 + m))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b*sqrt(x))^p*with*p*symbolic=#

    @test_int [x^m*(a + b*sqrt(x))^p, x, 3, -((2*(a + b*sqrt(x))^(1 + p)*x^(1 + m)*HypergeometricFunctions._₂F₁(1, 3 + 2*m + p, 2 + p, (a + b*sqrt(x))/a))/(a*(1 + p))), ((a + b*sqrt(x))^p*x^(1 + m)*HypergeometricFunctions._₂F₁(2*(1 + m), -p, 3 + 2*m, -((b*sqrt(x))/a)))/((1 + b*sqrt(x)/a)^p*(1 + m))]

    @test_int [x^3*(a + b*sqrt(x))^p, x, 3, -((2*a^7*(a + b*sqrt(x))^(1 + p))/(b^8*(1 + p))) + (14*a^6*(a + b*sqrt(x))^(2 + p))/(b^8*(2 + p)) - (42*a^5*(a + b*sqrt(x))^(3 + p))/(b^8*(3 + p)) + (70*a^4*(a + b*sqrt(x))^(4 + p))/(b^8*(4 + p)) - (70*a^3*(a + b*sqrt(x))^(5 + p))/(b^8*(5 + p)) + (42*a^2*(a + b*sqrt(x))^(6 + p))/(b^8*(6 + p)) - (14*a*(a + b*sqrt(x))^(7 + p))/(b^8*(7 + p)) + (2*(a + b*sqrt(x))^(8 + p))/(b^8*(8 + p))]
    @test_int [x^2*(a + b*sqrt(x))^p, x, 3, -((2*a^5*(a + b*sqrt(x))^(1 + p))/(b^6*(1 + p))) + (10*a^4*(a + b*sqrt(x))^(2 + p))/(b^6*(2 + p)) - (20*a^3*(a + b*sqrt(x))^(3 + p))/(b^6*(3 + p)) + (20*a^2*(a + b*sqrt(x))^(4 + p))/(b^6*(4 + p)) - (10*a*(a + b*sqrt(x))^(5 + p))/(b^6*(5 + p)) + (2*(a + b*sqrt(x))^(6 + p))/(b^6*(6 + p))]
    @test_int [x^1*(a + b*sqrt(x))^p, x, 3, -((2*a^3*(a + b*sqrt(x))^(1 + p))/(b^4*(1 + p))) + (6*a^2*(a + b*sqrt(x))^(2 + p))/(b^4*(2 + p)) - (6*a*(a + b*sqrt(x))^(3 + p))/(b^4*(3 + p)) + (2*(a + b*sqrt(x))^(4 + p))/(b^4*(4 + p))]
    @test_int [x^0*(a + b*sqrt(x))^p, x, 3, -((2*a*(a + b*sqrt(x))^(1 + p))/(b^2*(1 + p))) + (2*(a + b*sqrt(x))^(2 + p))/(b^2*(2 + p))]
    @test_int [(a + b*sqrt(x))^p/x^1, x, 2, -((2*(a + b*sqrt(x))^(1 + p)*HypergeometricFunctions._₂F₁(1, 1 + p, 2 + p, 1 + (b*sqrt(x))/a))/(a*(1 + p)))]
    @test_int [(a + b*sqrt(x))^p/x^2, x, 2, -((2*b^2*(a + b*sqrt(x))^(1 + p)*HypergeometricFunctions._₂F₁(3, 1 + p, 2 + p, 1 + (b*sqrt(x))/a))/(a^3*(1 + p)))]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(c*x)^m*(a+b*x^(3/2))^p=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^(m/2)*(a+b*x^(3/2))^p=#

    #= ::Subsubsection:: =#
    #=p>0=#

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [sqrt(x)/(1 + x^(3/2)), x, 1, (2*log(1 + x^(3/2)))/3]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b*x^(3/2))^(p/3)=#

    #= ::Subsubsection:: =#
    #=p>0=#

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [x^3/(a + b*x^(3/2))^(2/3), x, 4, -((5*a*x*(a + b*x^(3/2))^(1/3))/(9*b^2)) + (x^(5/2)*(a + b*x^(3/2))^(1/3))/(3*b) - (10*a^2*atan((1 + (2*b^(1/3)*sqrt(x))/(a + b*x^(3/2))^(1/3))/sqrt(3)))/(9*sqrt(3)*b^(8/3)) - (5*a^2*log(b^(1/3)*sqrt(x) - (a + b*x^(3/2))^(1/3)))/(9*b^(8/3))]
    @test_int [x^0/(a + b*x^(3/2))^(2/3), x, 2, -((2*atan((1 + (2*b^(1/3)*sqrt(x))/(a + b*x^(3/2))^(1/3))/sqrt(3)))/(sqrt(3)*b^(2/3))) - log(b^(1/3)*sqrt(x) - (a + b*x^(3/2))^(1/3))/b^(2/3)]
    @test_int [1/(x^3*(a + b*x^(3/2))^(2/3)), x, 2, -((a + b*x^(3/2))^(1/3)/(2*a*x^2)) + (3*b*(a + b*x^(3/2))^(1/3))/(2*a^2*sqrt(x))]
    @test_int [1/(x^6*(a + b*x^(3/2))^(2/3)), x, 4, -((a + b*x^(3/2))^(1/3)/(5*a*x^5)) + (9*b*(a + b*x^(3/2))^(1/3))/(35*a^2*x^(7/2)) - (27*b^2*(a + b*x^(3/2))^(1/3))/(70*a^3*x^2) + (81*b^3*(a + b*x^(3/2))^(1/3))/(70*a^4*sqrt(x))]
    @test_int [1/(x^9*(a + b*x^(3/2))^(2/3)), x, 6, -((a + b*x^(3/2))^(1/3)/(8*a*x^8)) + (15*b*(a + b*x^(3/2))^(1/3))/(104*a^2*x^(13/2)) - (9*b^2*(a + b*x^(3/2))^(1/3))/(52*a^3*x^5) + (81*b^3*(a + b*x^(3/2))^(1/3))/(364*a^4*x^(7/2)) - (243*b^4*(a + b*x^(3/2))^(1/3))/(728*a^5*x^2) + (729*b^5*(a + b*x^(3/2))^(1/3))/(728*a^6*sqrt(x))]

    @test_int [x^8/(a + b*x^(3/2))^(2/3), x, 3, -((2*a^5*(a + b*x^(3/2))^(1/3))/b^6) + (5*a^4*(a + b*x^(3/2))^(4/3))/(2*b^6) - (20*a^3*(a + b*x^(3/2))^(7/3))/(7*b^6) + (2*a^2*(a + b*x^(3/2))^(10/3))/b^6 - (10*a*(a + b*x^(3/2))^(13/3))/(13*b^6) + (a + b*x^(3/2))^(16/3)/(8*b^6)]
    @test_int [x^5/(a + b*x^(3/2))^(2/3), x, 3, -((2*a^3*(a + b*x^(3/2))^(1/3))/b^4) + (3*a^2*(a + b*x^(3/2))^(4/3))/(2*b^4) - (6*a*(a + b*x^(3/2))^(7/3))/(7*b^4) + (a + b*x^(3/2))^(10/3)/(5*b^4)]
    @test_int [x^2/(a + b*x^(3/2))^(2/3), x, 3, -((2*a*(a + b*x^(3/2))^(1/3))/b^2) + (a + b*x^(3/2))^(4/3)/(2*b^2)]
    @test_int [1/(x^1*(a + b*x^(3/2))^(2/3)), x, 5, -((2*atan((a^(1/3) + 2*(a + b*x^(3/2))^(1/3))/(sqrt(3)*a^(1/3))))/(sqrt(3)*a^(2/3))) - log(x)/(2*a^(2/3)) + log(a^(1/3) - (a + b*x^(3/2))^(1/3))/a^(2/3)]
    @test_int [1/(x^4*(a + b*x^(3/2))^(2/3)), x, 7, -((a + b*x^(3/2))^(1/3)/(3*a*x^3)) + (5*b*(a + b*x^(3/2))^(1/3))/(9*a^2*x^(3/2)) - (10*b^2*atan((a^(1/3) + 2*(a + b*x^(3/2))^(1/3))/(sqrt(3)*a^(1/3))))/(9*sqrt(3)*a^(8/3)) - (5*b^2*log(x))/(18*a^(8/3)) + (5*b^2*log(a^(1/3) - (a + b*x^(3/2))^(1/3)))/(9*a^(8/3))]

    @test_int [x^4/(a + b*x^(3/2))^(2/3), x, 3, (x^5*(a + b*x^(3/2))^(1/3)*HypergeometricFunctions._₂F₁(1, 11/3, 13/3, -((b*x^(3/2))/a)))/(5*a), (x^5*(1 + (b*x^(3/2))/a)^(2/3)*HypergeometricFunctions._₂F₁(2/3, 10/3, 13/3, -((b*x^(3/2))/a)))/(5*(a + b*x^(3/2))^(2/3))]
    @test_int [x^1/(a + b*x^(3/2))^(2/3), x, 3, (x^2*(a + b*x^(3/2))^(1/3)*HypergeometricFunctions._₂F₁(1, 5/3, 7/3, -((b*x^(3/2))/a)))/(2*a), (x^2*(1 + (b*x^(3/2))/a)^(2/3)*HypergeometricFunctions._₂F₁(2/3, 4/3, 7/3, -((b*x^(3/2))/a)))/(2*(a + b*x^(3/2))^(2/3))]
    @test_int [1/(x^2*(a + b*x^(3/2))^(2/3)), x, 3, -(((a + b*x^(3/2))^(1/3)*HypergeometricFunctions._₂F₁(-(1/3), 1, 1/3, -((b*x^(3/2))/a)))/(a*x)), -(((1 + (b*x^(3/2))/a)^(2/3)*HypergeometricFunctions._₂F₁(-(2/3), 2/3, 1/3, -((b*x^(3/2))/a)))/(x*(a + b*x^(3/2))^(2/3)))]
    @test_int [1/(x^5*(a + b*x^(3/2))^(2/3)), x, 3, -(((1 + (b*x^(3/2))/a)^(2/3)*HypergeometricFunctions._₂F₁(-(8/3), 2/3, -(5/3), -((b*x^(3/2))/a)))/(4*x^4*(a + b*x^(3/2))^(2/3)))]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(c*x)^m*(a+b*x^(1/3))^p=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b*x^(1/3))^p=#

    #= ::Subsubsection::Closed:: =#
    #=p>0=#

    @test_int [(a + b*x^(1/3))*x^4, x, 2, (a*x^5)/5 + (3*b*x^(16/3))/16]
    @test_int [(a + b*x^(1/3))*x^3, x, 2, (a*x^4)/4 + (3*b*x^(13/3))/13]
    @test_int [(a + b*x^(1/3))*x^2, x, 2, (a*x^3)/3 + (3*b*x^(10/3))/10]
    @test_int [(a + b*x^(1/3))*x, x, 2, (a*x^2)/2 + (3*b*x^(7/3))/7]
    @test_int [a + b*x^(1/3), x, 1, a*x + (3*b*x^(4/3))/4]
    @test_int [(a + b*x^(1/3))/x, x, 2, 3*b*x^(1/3) + a*log(x)]
    @test_int [(a + b*x^(1/3))/x^2, x, 2, -(a/x) - (3*b)/(2*x^(2/3))]
    @test_int [(a + b*x^(1/3))/x^3, x, 2, -a/(2*x^2) - (3*b)/(5*x^(5/3))]
    @test_int [(a + b*x^(1/3))/x^4, x, 2, -a/(3*x^3) - (3*b)/(8*x^(8/3))]

    @test_int [(a + b*x^(1/3))^2*x^4, x, 3, (a^2*x^5)/5 + (3*a*b*x^(16/3))/8 + (3*b^2*x^(17/3))/17]
    @test_int [(a + b*x^(1/3))^2*x^3, x, 3, (a^2*x^4)/4 + (6*a*b*x^(13/3))/13 + (3*b^2*x^(14/3))/14]
    @test_int [(a + b*x^(1/3))^2*x^2, x, 3, (a^2*x^3)/3 + (3*a*b*x^(10/3))/5 + (3*b^2*x^(11/3))/11]
    @test_int [(a + b*x^(1/3))^2*x, x, 3, (a^2*x^2)/2 + (6*a*b*x^(7/3))/7 + (3*b^2*x^(8/3))/8]
    @test_int [(a + b*x^(1/3))^2, x, 3, a^2*x + (3*a*b*x^(4/3))/2 + (3*b^2*x^(5/3))/5]
    @test_int [(a + b*x^(1/3))^2/x, x, 3, 6*a*b*x^(1/3) + (3*b^2*x^(2/3))/2 + a^2*log(x)]
    @test_int [(a + b*x^(1/3))^2/x^2, x, 1, -((a + b*x^(1/3))^3/(a*x))]
    @test_int [(a + b*x^(1/3))^2/x^3, x, 3, -a^2/(2*x^2) - (6*a*b)/(5*x^(5/3)) - (3*b^2)/(4*x^(4/3))]
    @test_int [(a + b*x^(1/3))^2/x^4, x, 3, -a^2/(3*x^3) - (3*a*b)/(4*x^(8/3)) - (3*b^2)/(7*x^(7/3))]

    @test_int [(a + b*x^(1/3))^3*x^4, x, 3, (a^3*x^5)/5 + (9*a^2*b*x^(16/3))/16 + (9*a*b^2*x^(17/3))/17 + (b^3*x^6)/6]
    @test_int [(a + b*x^(1/3))^3*x^3, x, 3, (a^3*x^4)/4 + (9*a^2*b*x^(13/3))/13 + (9*a*b^2*x^(14/3))/14 + (b^3*x^5)/5]
    @test_int [(a + b*x^(1/3))^3*x^2, x, 3, (a^3*x^3)/3 + (9*a^2*b*x^(10/3))/10 + (9*a*b^2*x^(11/3))/11 + (b^3*x^4)/4]
    @test_int [(a + b*x^(1/3))^3*x, x, 3, (a^3*x^2)/2 + (9*a^2*b*x^(7/3))/7 + (9*a*b^2*x^(8/3))/8 + (b^3*x^3)/3]
    @test_int [(a + b*x^(1/3))^3, x, 3, a^3*x + (9/4)*a^2*b*x^(4/3) + (9/5)*a*b^2*x^(5/3) + (b^3*x^2)/2]
    @test_int [(a + b*x^(1/3))^3/x, x, 3, 9*a^2*b*x^(1/3) + (9*a*b^2*x^(2/3))/2 + b^3*x + a^3*log(x)]
    @test_int [(a + b*x^(1/3))^3/x^2, x, 3, -(a^3/x) - (9*a^2*b)/(2*x^(2/3)) - (9*a*b^2)/x^(1/3) + b^3*log(x)]
    @test_int [(a + b*x^(1/3))^3/x^3, x, 3, -a^3/(2*x^2) - (9*a^2*b)/(5*x^(5/3)) - (9*a*b^2)/(4*x^(4/3)) - b^3/x]
    @test_int [(a + b*x^(1/3))^3/x^4, x, 3, -a^3/(3*x^3) - (9*a^2*b)/(8*x^(8/3)) - (9*a*b^2)/(7*x^(7/3)) - b^3/(2*x^2)]

    @test_int [(a + b*x^(1/3))^5*x^4, x, 3, (a^5*x^5)/5 + (15*a^4*b*x^(16/3))/16 + (30*a^3*b^2*x^(17/3))/17 + (5*a^2*b^3*x^6)/3 + (15*a*b^4*x^(19/3))/19 + (3*b^5*x^(20/3))/20]
    @test_int [(a + b*x^(1/3))^5*x^3, x, 3, (a^5*x^4)/4 + (15*a^4*b*x^(13/3))/13 + (15*a^3*b^2*x^(14/3))/7 + 2*a^2*b^3*x^5 + (15*a*b^4*x^(16/3))/16 + (3*b^5*x^(17/3))/17]
    @test_int [(a + b*x^(1/3))^5*x^2, x, 3, (a^5*x^3)/3 + (3*a^4*b*x^(10/3))/2 + (30*a^3*b^2*x^(11/3))/11 + (5*a^2*b^3*x^4)/2 + (15*a*b^4*x^(13/3))/13 + (3*b^5*x^(14/3))/14]
    @test_int [(a + b*x^(1/3))^5*x, x, 3, (a^5*x^2)/2 + (15*a^4*b*x^(7/3))/7 + (15*a^3*b^2*x^(8/3))/4 + (10*a^2*b^3*x^3)/3 + (3*a*b^4*x^(10/3))/2 + (3*b^5*x^(11/3))/11]
    @test_int [(a + b*x^(1/3))^5, x, 3, (a^2*(a + b*x^(1/3))^6)/(2*b^3) - (6*a*(a + b*x^(1/3))^7)/(7*b^3) + (3*(a + b*x^(1/3))^8)/(8*b^3)]
    @test_int [(a + b*x^(1/3))^5/x, x, 3, 15*a^4*b*x^(1/3) + 15*a^3*b^2*x^(2/3) + 10*a^2*b^3*x + (15*a*b^4*x^(4/3))/4 + (3*b^5*x^(5/3))/5 + a^5*log(x)]
    @test_int [(a + b*x^(1/3))^5/x^2, x, 3, -(a^5/x) - (15*a^4*b)/(2*x^(2/3)) - (30*a^3*b^2)/x^(1/3) + 15*a*b^4*x^(1/3) + (3*b^5*x^(2/3))/2 + 10*a^2*b^3*log(x)]
    @test_int [(a + b*x^(1/3))^5/x^3, x, 1, -(a + b*x^(1/3))^6/(2*a*x^2)]
    @test_int [(a + b*x^(1/3))^5/x^4, x, 3, -a^5/(3*x^3) - (15*a^4*b)/(8*x^(8/3)) - (30*a^3*b^2)/(7*x^(7/3)) - (5*a^2*b^3)/x^2 - (3*a*b^4)/x^(5/3) - (3*b^5)/(4*x^(4/3))]
    @test_int [(a + b*x^(1/3))^5/x^5, x, 3, -a^5/(4*x^4) - (15*a^4*b)/(11*x^(11/3)) - (3*a^3*b^2)/x^(10/3) - (10*a^2*b^3)/(3*x^3) - (15*a*b^4)/(8*x^(8/3)) - (3*b^5)/(7*x^(7/3))]
    @test_int [(a + b*x^(1/3))^5/x^6, x, 3, -a^5/(5*x^5) - (15*a^4*b)/(14*x^(14/3)) - (30*a^3*b^2)/(13*x^(13/3)) - (5*a^2*b^3)/(2*x^4) - (15*a*b^4)/(11*x^(11/3)) - (3*b^5)/(10*x^(10/3))]
    @test_int [(a + b*x^(1/3))^5/x^7, x, 3, -a^5/(6*x^6) - (15*a^4*b)/(17*x^(17/3)) - (15*a^3*b^2)/(8*x^(16/3)) - (2*a^2*b^3)/x^5 - (15*a*b^4)/(14*x^(14/3)) - (3*b^5)/(13*x^(13/3))]

    @test_int [(a + b*x^(1/3))^10*x^4, x, 3, (a^10*x^5)/5 + (15*a^9*b*x^(16/3))/8 + (135*a^8*b^2*x^(17/3))/17 + 20*a^7*b^3*x^6 + (630*a^6*b^4*x^(19/3))/19 + (189*a^5*b^5*x^(20/3))/5 + 30*a^4*b^6*x^7 + (180*a^3*b^7*x^(22/3))/11 + (135*a^2*b^8*x^(23/3))/23 + (5*a*b^9*x^8)/4 + (3*b^10*x^(25/3))/25]
    @test_int [(a + b*x^(1/3))^10*x^3, x, 3, (a^10*x^4)/4 + (30*a^9*b*x^(13/3))/13 + (135*a^8*b^2*x^(14/3))/14 + 24*a^7*b^3*x^5 + (315*a^6*b^4*x^(16/3))/8 + (756*a^5*b^5*x^(17/3))/17 + 35*a^4*b^6*x^6 + (360*a^3*b^7*x^(19/3))/19 + (27*a^2*b^8*x^(20/3))/4 + (10*a*b^9*x^7)/7 + (3*b^10*x^(22/3))/22]
    @test_int [(a + b*x^(1/3))^10*x^2, x, 3, (3*a^8*(a + b*x^(1/3))^11)/(11*b^9) - (2*a^7*(a + b*x^(1/3))^12)/b^9 + (84*a^6*(a + b*x^(1/3))^13)/(13*b^9) - (12*a^5*(a + b*x^(1/3))^14)/b^9 + (14*a^4*(a + b*x^(1/3))^15)/b^9 - (21*a^3*(a + b*x^(1/3))^16)/(2*b^9) + (84*a^2*(a + b*x^(1/3))^17)/(17*b^9) - (4*a*(a + b*x^(1/3))^18)/(3*b^9) + (3*(a + b*x^(1/3))^19)/(19*b^9)]
    @test_int [(a + b*x^(1/3))^10*x, x, 3, (-3*a^5*(a + b*x^(1/3))^11)/(11*b^6) + (5*a^4*(a + b*x^(1/3))^12)/(4*b^6) - (30*a^3*(a + b*x^(1/3))^13)/(13*b^6) + (15*a^2*(a + b*x^(1/3))^14)/(7*b^6) - (a*(a + b*x^(1/3))^15)/b^6 + (3*(a + b*x^(1/3))^16)/(16*b^6)]
    @test_int [(a + b*x^(1/3))^10, x, 3, (3*a^2*(a + b*x^(1/3))^11)/(11*b^3) - (a*(a + b*x^(1/3))^12)/(2*b^3) + (3*(a + b*x^(1/3))^13)/(13*b^3)]
    @test_int [(a + b*x^(1/3))^10/x, x, 3, 30*a^9*b*x^(1/3) + (135*a^8*b^2*x^(2/3))/2 + 120*a^7*b^3*x + (315*a^6*b^4*x^(4/3))/2 + (756*a^5*b^5*x^(5/3))/5 + 105*a^4*b^6*x^2 + (360*a^3*b^7*x^(7/3))/7 + (135*a^2*b^8*x^(8/3))/8 + (10*a*b^9*x^3)/3 + (3*b^10*x^(10/3))/10 + a^10*log(x)]
    @test_int [(a + b*x^(1/3))^10/x^2, x, 3, -(a^10/x) - (15*a^9*b)/x^(2/3) - (135*a^8*b^2)/x^(1/3) + 630*a^6*b^4*x^(1/3) + 378*a^5*b^5*x^(2/3) + 210*a^4*b^6*x + 90*a^3*b^7*x^(4/3) + 27*a^2*b^8*x^(5/3) + 5*a*b^9*x^2 + (3*b^10*x^(7/3))/7 + 120*a^7*b^3*log(x)]
    @test_int [(a + b*x^(1/3))^10/x^3, x, 3, -a^10/(2*x^2) - (6*a^9*b)/x^(5/3) - (135*a^8*b^2)/(4*x^(4/3)) - (120*a^7*b^3)/x - (315*a^6*b^4)/x^(2/3) - (756*a^5*b^5)/x^(1/3) + 360*a^3*b^7*x^(1/3) + (135*a^2*b^8*x^(2/3))/2 + 10*a*b^9*x + (3*b^10*x^(4/3))/4 + 210*a^4*b^6*log(x)]
    @test_int [(a + b*x^(1/3))^10/x^4, x, 3, -a^10/(3*x^3) - (15*a^9*b)/(4*x^(8/3)) - (135*a^8*b^2)/(7*x^(7/3)) - (60*a^7*b^3)/x^2 - (126*a^6*b^4)/x^(5/3) - (189*a^5*b^5)/x^(4/3) - (210*a^4*b^6)/x - (180*a^3*b^7)/x^(2/3) - (135*a^2*b^8)/x^(1/3) + 3*b^10*x^(1/3) + 10*a*b^9*log(x)]
    @test_int [(a + b*x^(1/3))^10/x^5, x, 3, -(a + b*x^(1/3))^11/(4*a*x^4) + (b*(a + b*x^(1/3))^11)/(44*a^2*x^(11/3))]
    @test_int [(a + b*x^(1/3))^10/x^6, x, 6, -(a + b*x^(1/3))^11/(5*a*x^5) + (2*b*(a + b*x^(1/3))^11)/(35*a^2*x^(14/3)) - (6*b^2*(a + b*x^(1/3))^11)/(455*a^3*x^(13/3)) + (b^3*(a + b*x^(1/3))^11)/(455*a^4*x^4) - (b^4*(a + b*x^(1/3))^11)/(5005*a^5*x^(11/3))]
    @test_int [(a + b*x^(1/3))^10/x^7, x, 3, -a^10/(6*x^6) - (30*a^9*b)/(17*x^(17/3)) - (135*a^8*b^2)/(16*x^(16/3)) - (24*a^7*b^3)/x^5 - (45*a^6*b^4)/x^(14/3) - (756*a^5*b^5)/(13*x^(13/3)) - (105*a^4*b^6)/(2*x^4) - (360*a^3*b^7)/(11*x^(11/3)) - (27*a^2*b^8)/(2*x^(10/3)) - (10*a*b^9)/(3*x^3) - (3*b^10)/(8*x^(8/3))]
    @test_int [(a + b*x^(1/3))^10/x^8, x, 3, -a^10/(7*x^7) - (3*a^9*b)/(2*x^(20/3)) - (135*a^8*b^2)/(19*x^(19/3)) - (20*a^7*b^3)/x^6 - (630*a^6*b^4)/(17*x^(17/3)) - (189*a^5*b^5)/(4*x^(16/3)) - (42*a^4*b^6)/x^5 - (180*a^3*b^7)/(7*x^(14/3)) - (135*a^2*b^8)/(13*x^(13/3)) - (5*a*b^9)/(2*x^4) - (3*b^10)/(11*x^(11/3))]
    @test_int [(a + b*x^(1/3))^10/x^9, x, 3, -a^10/(8*x^8) - (30*a^9*b)/(23*x^(23/3)) - (135*a^8*b^2)/(22*x^(22/3)) - (120*a^7*b^3)/(7*x^7) - (63*a^6*b^4)/(2*x^(20/3)) - (756*a^5*b^5)/(19*x^(19/3)) - (35*a^4*b^6)/x^6 - (360*a^3*b^7)/(17*x^(17/3)) - (135*a^2*b^8)/(16*x^(16/3)) - (2*a*b^9)/x^5 - (3*b^10)/(14*x^(14/3))]
    @test_int [(a + b*x^(1/3))^10/x^10, x, 3, -a^10/(9*x^9) - (15*a^9*b)/(13*x^(26/3)) - (27*a^8*b^2)/(5*x^(25/3)) - (15*a^7*b^3)/x^8 - (630*a^6*b^4)/(23*x^(23/3)) - (378*a^5*b^5)/(11*x^(22/3)) - (30*a^4*b^6)/x^7 - (18*a^3*b^7)/x^(20/3) - (135*a^2*b^8)/(19*x^(19/3)) - (5*a*b^9)/(3*x^6) - (3*b^10)/(17*x^(17/3))]

    @test_int [(a + b*x^(1/3))^15*x^5, x, 3, (a^15*x^6)/6 + (45/19)*a^14*b*x^(19/3) + (63/4)*a^13*b^2*x^(20/3) + 65*a^12*b^3*x^7 + (4095/22)*a^11*b^4*x^(22/3) + (9009/23)*a^10*b^5*x^(23/3) + (5005/8)*a^9*b^6*x^8 + (3861/5)*a^8*b^7*x^(25/3) + (1485/2)*a^7*b^8*x^(26/3) + (5005/9)*a^6*b^9*x^9 + (1287/4)*a^5*b^10*x^(28/3) + (4095/29)*a^4*b^11*x^(29/3) + (91/2)*a^3*b^12*x^10 + (315/31)*a^2*b^13*x^(31/3) + (45/32)*a*b^14*x^(32/3) + (b^15*x^11)/11]
    @test_int [(a + b*x^(1/3))^15*x^4, x, 3, (a^15*x^5)/5 + (45/16)*a^14*b*x^(16/3) + (315/17)*a^13*b^2*x^(17/3) + (455/6)*a^12*b^3*x^6 + (4095/19)*a^11*b^4*x^(19/3) + (9009/20)*a^10*b^5*x^(20/3) + 715*a^9*b^6*x^7 + (1755/2)*a^8*b^7*x^(22/3) + (19305/23)*a^7*b^8*x^(23/3) + (5005/8)*a^6*b^9*x^8 + (9009/25)*a^5*b^10*x^(25/3) + (315/2)*a^4*b^11*x^(26/3) + (455/9)*a^3*b^12*x^9 + (45/4)*a^2*b^13*x^(28/3) + (45/29)*a*b^14*x^(29/3) + (b^15*x^10)/10]
    @test_int [(a + b*x^(1/3))^15*x^3, x, 3, -((3*a^11*(a + b*x^(1/3))^16)/(16*b^12)) + (33*a^10*(a + b*x^(1/3))^17)/(17*b^12) - (55*a^9*(a + b*x^(1/3))^18)/(6*b^12) + (495*a^8*(a + b*x^(1/3))^19)/(19*b^12) - (99*a^7*(a + b*x^(1/3))^20)/(2*b^12) + (66*a^6*(a + b*x^(1/3))^21)/b^12 - (63*a^5*(a + b*x^(1/3))^22)/b^12 + (990*a^4*(a + b*x^(1/3))^23)/(23*b^12) - (165*a^3*(a + b*x^(1/3))^24)/(8*b^12) + (33*a^2*(a + b*x^(1/3))^25)/(5*b^12) - (33*a*(a + b*x^(1/3))^26)/(26*b^12) + (a + b*x^(1/3))^27/(9*b^12)]
    @test_int [(a + b*x^(1/3))^15*x^2, x, 3, (3*a^8*(a + b*x^(1/3))^16)/(16*b^9) - (24*a^7*(a + b*x^(1/3))^17)/(17*b^9) + (14*a^6*(a + b*x^(1/3))^18)/(3*b^9) - (168*a^5*(a + b*x^(1/3))^19)/(19*b^9) + (21*a^4*(a + b*x^(1/3))^20)/(2*b^9) - (8*a^3*(a + b*x^(1/3))^21)/b^9 + (42*a^2*(a + b*x^(1/3))^22)/(11*b^9) - (24*a*(a + b*x^(1/3))^23)/(23*b^9) + (a + b*x^(1/3))^24/(8*b^9)]
    @test_int [(a + b*x^(1/3))^15*x, x, 3, (-3*a^5*(a + b*x^(1/3))^16)/(16*b^6) + (15*a^4*(a + b*x^(1/3))^17)/(17*b^6) - (5*a^3*(a + b*x^(1/3))^18)/(3*b^6) + (30*a^2*(a + b*x^(1/3))^19)/(19*b^6) - (3*a*(a + b*x^(1/3))^20)/(4*b^6) + (a + b*x^(1/3))^21/(7*b^6)]
    @test_int [(a + b*x^(1/3))^15, x, 3, (3*a^2*(a + b*x^(1/3))^16)/(16*b^3) - (6*a*(a + b*x^(1/3))^17)/(17*b^3) + (a + b*x^(1/3))^18/(6*b^3)]
    @test_int [(a + b*x^(1/3))^15/x, x, 3, 45*a^14*b*x^(1/3) + (315*a^13*b^2*x^(2/3))/2 + 455*a^12*b^3*x + (4095*a^11*b^4*x^(4/3))/4 + (9009*a^10*b^5*x^(5/3))/5 + (5005*a^9*b^6*x^2)/2 + (19305*a^8*b^7*x^(7/3))/7 + (19305*a^7*b^8*x^(8/3))/8 + (5005*a^6*b^9*x^3)/3 + (9009*a^5*b^10*x^(10/3))/10 + (4095*a^4*b^11*x^(11/3))/11 + (455*a^3*b^12*x^4)/4 + (315*a^2*b^13*x^(13/3))/13 + (45*a*b^14*x^(14/3))/14 + (b^15*x^5)/5 + a^15*log(x)]
    @test_int [(a + b*x^(1/3))^15/x^2, x, 3, -(a^15/x) - (45*a^14*b)/(2*x^(2/3)) - (315*a^13*b^2)/x^(1/3) + 4095*a^11*b^4*x^(1/3) + (9009*a^10*b^5*x^(2/3))/2 + 5005*a^9*b^6*x + (19305*a^8*b^7*x^(4/3))/4 + 3861*a^7*b^8*x^(5/3) + (5005*a^6*b^9*x^2)/2 + 1287*a^5*b^10*x^(7/3) + (4095*a^4*b^11*x^(8/3))/8 + (455*a^3*b^12*x^3)/3 + (63*a^2*b^13*x^(10/3))/2 + (45*a*b^14*x^(11/3))/11 + (b^15*x^4)/4 + 455*a^12*b^3*log(x)]
    @test_int [(a + b*x^(1/3))^15/x^3, x, 3, -a^15/(2*x^2) - (9*a^14*b)/x^(5/3) - (315*a^13*b^2)/(4*x^(4/3)) - (455*a^12*b^3)/x - (4095*a^11*b^4)/(2*x^(2/3)) - (9009*a^10*b^5)/x^(1/3) + 19305*a^8*b^7*x^(1/3) + (19305*a^7*b^8*x^(2/3))/2 + 5005*a^6*b^9*x + (9009*a^5*b^10*x^(4/3))/4 + 819*a^4*b^11*x^(5/3) + (455*a^3*b^12*x^2)/2 + 45*a^2*b^13*x^(7/3) + (45*a*b^14*x^(8/3))/8 + (b^15*x^3)/3 + 5005*a^9*b^6*log(x)]
    @test_int [(a + b*x^(1/3))^15/x^4, x, 3, -a^15/(3*x^3) - (45*a^14*b)/(8*x^(8/3)) - (45*a^13*b^2)/x^(7/3) - (455*a^12*b^3)/(2*x^2) - (819*a^11*b^4)/x^(5/3) - (9009*a^10*b^5)/(4*x^(4/3)) - (5005*a^9*b^6)/x - (19305*a^8*b^7)/(2*x^(2/3)) - (19305*a^7*b^8)/x^(1/3) + 9009*a^5*b^10*x^(1/3) + (4095*a^4*b^11*x^(2/3))/2 + 455*a^3*b^12*x + (315*a^2*b^13*x^(4/3))/4 + 9*a*b^14*x^(5/3) + (b^15*x^2)/2 + 5005*a^6*b^9*log(x)]
    @test_int [(a + b*x^(1/3))^15/x^6, x, 3, -a^15/(5*x^5) - (45*a^14*b)/(14*x^(14/3)) - (315*a^13*b^2)/(13*x^(13/3)) - (455*a^12*b^3)/(4*x^4) - (4095*a^11*b^4)/(11*x^(11/3)) - (9009*a^10*b^5)/(10*x^(10/3)) - (5005*a^9*b^6)/(3*x^3) - (19305*a^8*b^7)/(8*x^(8/3)) - (19305*a^7*b^8)/(7*x^(7/3)) - (5005*a^6*b^9)/(2*x^2) - (9009*a^5*b^10)/(5*x^(5/3)) - (4095*a^4*b^11)/(4*x^(4/3)) - (455*a^3*b^12)/x - (315*a^2*b^13)/(2*x^(2/3)) - (45*a*b^14)/x^(1/3) + b^15*log(x)]
    @test_int [(a + b*x^(1/3))^15/x^7, x, 4, -(a + b*x^(1/3))^16/(6*a*x^6) + (b*(a + b*x^(1/3))^16)/(51*a^2*x^(17/3)) - (b^2*(a + b*x^(1/3))^16)/(816*a^3*x^(16/3))]
    @test_int [(a + b*x^(1/3))^15/x^8, x, 7, -(a + b*x^(1/3))^16/(7*a*x^7) + (b*(a + b*x^(1/3))^16)/(28*a^2*x^(20/3)) - (b^2*(a + b*x^(1/3))^16)/(133*a^3*x^(19/3)) + (b^3*(a + b*x^(1/3))^16)/(798*a^4*x^6) - (b^4*(a + b*x^(1/3))^16)/(6783*a^5*x^(17/3)) + (b^5*(a + b*x^(1/3))^16)/(108528*a^6*x^(16/3))]
    @test_int [(a + b*x^(1/3))^15/x^9, x, 10, -(a + b*x^(1/3))^16/(8*a*x^8) + (b*(a + b*x^(1/3))^16)/(23*a^2*x^(23/3)) - (7*b^2*(a + b*x^(1/3))^16)/(506*a^3*x^(22/3)) + (b^3*(a + b*x^(1/3))^16)/(253*a^4*x^7) - (b^4*(a + b*x^(1/3))^16)/(1012*a^5*x^(20/3)) + (b^5*(a + b*x^(1/3))^16)/(4807*a^6*x^(19/3)) - (b^6*(a + b*x^(1/3))^16)/(28842*a^7*x^6) + (b^7*(a + b*x^(1/3))^16)/(245157*a^8*x^(17/3)) - (b^8*(a + b*x^(1/3))^16)/(3922512*a^9*x^(16/3))]
    @test_int [(a + b*x^(1/3))^15/x^10, x, 3, -a^15/(9*x^9) - (45*a^14*b)/(26*x^(26/3)) - (63*a^13*b^2)/(5*x^(25/3)) - (455*a^12*b^3)/(8*x^8) - (4095*a^11*b^4)/(23*x^(23/3)) - (819*a^10*b^5)/(2*x^(22/3)) - (715*a^9*b^6)/x^7 - (3861*a^8*b^7)/(4*x^(20/3)) - (19305*a^7*b^8)/(19*x^(19/3)) - (5005*a^6*b^9)/(6*x^6) - (9009*a^5*b^10)/(17*x^(17/3)) - (4095*a^4*b^11)/(16*x^(16/3)) - (91*a^3*b^12)/x^5 - (45*a^2*b^13)/(2*x^(14/3)) - (45*a*b^14)/(13*x^(13/3)) - b^15/(4*x^4)]
    @test_int [(a + b*x^(1/3))^15/x^11, x, 3, -a^15/(10*x^10) - (45*a^14*b)/(29*x^(29/3)) - (45*a^13*b^2)/(4*x^(28/3)) - (455*a^12*b^3)/(9*x^9) - (315*a^11*b^4)/(2*x^(26/3)) - (9009*a^10*b^5)/(25*x^(25/3)) - (5005*a^9*b^6)/(8*x^8) - (19305*a^8*b^7)/(23*x^(23/3)) - (1755*a^7*b^8)/(2*x^(22/3)) - (715*a^6*b^9)/x^7 - (9009*a^5*b^10)/(20*x^(20/3)) - (4095*a^4*b^11)/(19*x^(19/3)) - (455*a^3*b^12)/(6*x^6) - (315*a^2*b^13)/(17*x^(17/3)) - (45*a*b^14)/(16*x^(16/3)) - b^15/(5*x^5)]
    @test_int [(a + b*x^(1/3))^15/x^12, x, 3, -a^15/(11*x^11) - (45*a^14*b)/(32*x^(32/3)) - (315*a^13*b^2)/(31*x^(31/3)) - (91*a^12*b^3)/(2*x^10) - (4095*a^11*b^4)/(29*x^(29/3)) - (1287*a^10*b^5)/(4*x^(28/3)) - (5005*a^9*b^6)/(9*x^9) - (1485*a^8*b^7)/(2*x^(26/3)) - (3861*a^7*b^8)/(5*x^(25/3)) - (5005*a^6*b^9)/(8*x^8) - (9009*a^5*b^10)/(23*x^(23/3)) - (4095*a^4*b^11)/(22*x^(22/3)) - (65*a^3*b^12)/x^7 - (63*a^2*b^13)/(4*x^(20/3)) - (45*a*b^14)/(19*x^(19/3)) - b^15/(6*x^6)]

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [x^3/(a + b*x^(1/3)), x, 3, (3*a^10*x^(1/3))/b^11 - (3*a^9*x^(2/3))/(2*b^10) + (a^8*x)/b^9 - (3*a^7*x^(4/3))/(4*b^8) + (3*a^6*x^(5/3))/(5*b^7) - (a^5*x^2)/(2*b^6) + (3*a^4*x^(7/3))/(7*b^5) - (3*a^3*x^(8/3))/(8*b^4) + (a^2*x^3)/(3*b^3) - (3*a*x^(10/3))/(10*b^2) + (3*x^(11/3))/(11*b) - (3*a^11*log(a + b*x^(1/3)))/b^12]
    @test_int [x^2/(a + b*x^(1/3)), x, 3, (-3*a^7*x^(1/3))/b^8 + (3*a^6*x^(2/3))/(2*b^7) - (a^5*x)/b^6 + (3*a^4*x^(4/3))/(4*b^5) - (3*a^3*x^(5/3))/(5*b^4) + (a^2*x^2)/(2*b^3) - (3*a*x^(7/3))/(7*b^2) + (3*x^(8/3))/(8*b) + (3*a^8*log(a + b*x^(1/3)))/b^9]
    @test_int [x/(a + b*x^(1/3)), x, 3, (3*a^4*x^(1/3))/b^5 - (3*a^3*x^(2/3))/(2*b^4) + (a^2*x)/b^3 - (3*a*x^(4/3))/(4*b^2) + (3*x^(5/3))/(5*b) - (3*a^5*log(a + b*x^(1/3)))/b^6]
    @test_int [1/(a + b*x^(1/3)), x, 3, (-3*a*x^(1/3))/b^2 + (3*x^(2/3))/(2*b) + (3*a^2*log(a + b*x^(1/3)))/b^3]
    @test_int [1/((a + b*x^(1/3))*x), x, 4, (-3*log(a + b*x^(1/3)))/a + log(x)/a]
    @test_int [1/((a + b*x^(1/3))*x^2), x, 3, -(1/(a*x)) + (3*b)/(2*a^2*x^(2/3)) - (3*b^2)/(a^3*x^(1/3)) + (3*b^3*log(a + b*x^(1/3)))/a^4 - (b^3*log(x))/a^4]
    @test_int [1/((a + b*x^(1/3))*x^3), x, 3, -1/(2*a*x^2) + (3*b)/(5*a^2*x^(5/3)) - (3*b^2)/(4*a^3*x^(4/3)) + b^3/(a^4*x) - (3*b^4)/(2*a^5*x^(2/3)) + (3*b^5)/(a^6*x^(1/3)) - (3*b^6*log(a + b*x^(1/3)))/a^7 + (b^6*log(x))/a^7]
    @test_int [1/((a + b*x^(1/3))*x^4), x, 3, -1/(3*a*x^3) + (3*b)/(8*a^2*x^(8/3)) - (3*b^2)/(7*a^3*x^(7/3)) + b^3/(2*a^4*x^2) - (3*b^4)/(5*a^5*x^(5/3)) + (3*b^5)/(4*a^6*x^(4/3)) - b^6/(a^7*x) + (3*b^7)/(2*a^8*x^(2/3)) - (3*b^8)/(a^9*x^(1/3)) + (3*b^9*log(a + b*x^(1/3)))/a^10 - (b^9*log(x))/a^10]

    @test_int [1/((2 + b*x^(1/3))*x), x, 4, (-(3/2))*log(2 + b*x^(1/3)) + log(x)/2]

    @test_int [x^3/(a + b*x^(1/3))^2, x, 3, (3*a^11)/(b^12*(a + b*x^(1/3))) - (30*a^9*x^(1/3))/b^11 + (27*a^8*x^(2/3))/(2*b^10) - (8*a^7*x)/b^9 + (21*a^6*x^(4/3))/(4*b^8) - (18*a^5*x^(5/3))/(5*b^7) + (5*a^4*x^2)/(2*b^6) - (12*a^3*x^(7/3))/(7*b^5) + (9*a^2*x^(8/3))/(8*b^4) - (2*a*x^3)/(3*b^3) + (3*x^(10/3))/(10*b^2) + (33*a^10*log(a + b*x^(1/3)))/b^12]
    @test_int [x^2/(a + b*x^(1/3))^2, x, 3, (-3*a^8)/(b^9*(a + b*x^(1/3))) + (21*a^6*x^(1/3))/b^8 - (9*a^5*x^(2/3))/b^7 + (5*a^4*x)/b^6 - (3*a^3*x^(4/3))/b^5 + (9*a^2*x^(5/3))/(5*b^4) - (a*x^2)/b^3 + (3*x^(7/3))/(7*b^2) - (24*a^7*log(a + b*x^(1/3)))/b^9]
    @test_int [x/(a + b*x^(1/3))^2, x, 3, (3*a^5)/(b^6*(a + b*x^(1/3))) - (12*a^3*x^(1/3))/b^5 + (9*a^2*x^(2/3))/(2*b^4) - (2*a*x)/b^3 + (3*x^(4/3))/(4*b^2) + (15*a^4*log(a + b*x^(1/3)))/b^6]
    @test_int [1/(a + b*x^(1/3))^2, x, 3, -((3*a^2)/(b^3*(a + b*x^(1/3)))) + (3*x^(1/3))/b^2 - (6*a*log(a + b*x^(1/3)))/b^3]
    @test_int [1/((a + b*x^(1/3))^2*x), x, 3, 3/(a*(a + b*x^(1/3))) - (3*log(a + b*x^(1/3)))/a^2 + log(x)/a^2]
    @test_int [1/((a + b*x^(1/3))^2*x^2), x, 3, -((3*b^3)/(a^4*(a + b*x^(1/3)))) - 1/(a^2*x) + (3*b)/(a^3*x^(2/3)) - (9*b^2)/(a^4*x^(1/3)) + (12*b^3*log(a + b*x^(1/3)))/a^5 - (4*b^3*log(x))/a^5]
    @test_int [1/((a + b*x^(1/3))^2*x^3), x, 3, (3*b^6)/(a^7*(a + b*x^(1/3))) - 1/(2*a^2*x^2) + (6*b)/(5*a^3*x^(5/3)) - (9*b^2)/(4*a^4*x^(4/3)) + (4*b^3)/(a^5*x) - (15*b^4)/(2*a^6*x^(2/3)) + (18*b^5)/(a^7*x^(1/3)) - (21*b^6*log(a + b*x^(1/3)))/a^8 + (7*b^6*log(x))/a^8]
    @test_int [1/((a + b*x^(1/3))^2*x^4), x, 3, -((3*b^9)/(a^10*(a + b*x^(1/3)))) - 1/(3*a^2*x^3) + (3*b)/(4*a^3*x^(8/3)) - (9*b^2)/(7*a^4*x^(7/3)) + (2*b^3)/(a^5*x^2) - (3*b^4)/(a^6*x^(5/3)) + (9*b^5)/(2*a^7*x^(4/3)) - (7*b^6)/(a^8*x) + (12*b^7)/(a^9*x^(2/3)) - (27*b^8)/(a^10*x^(1/3)) + (30*b^9*log(a + b*x^(1/3)))/a^11 - (10*b^9*log(x))/a^11]

    @test_int [x^3/(a + b*x^(1/3))^3, x, 3, (3*a^11)/(2*b^12*(a + b*x^(1/3))^2) - (33*a^10)/(b^12*(a + b*x^(1/3))) + (135*a^8*x^(1/3))/b^11 - (54*a^7*x^(2/3))/b^10 + (28*a^6*x)/b^9 - (63*a^5*x^(4/3))/(4*b^8) + (9*a^4*x^(5/3))/b^7 - (5*a^3*x^2)/b^6 + (18*a^2*x^(7/3))/(7*b^5) - (9*a*x^(8/3))/(8*b^4) + x^3/(3*b^3) - (165*a^9*log(a + b*x^(1/3)))/b^12]
    @test_int [x^2/(a + b*x^(1/3))^3, x, 3, (-3*a^8)/(2*b^9*(a + b*x^(1/3))^2) + (24*a^7)/(b^9*(a + b*x^(1/3))) - (63*a^5*x^(1/3))/b^8 + (45*a^4*x^(2/3))/(2*b^7) - (10*a^3*x)/b^6 + (9*a^2*x^(4/3))/(2*b^5) - (9*a*x^(5/3))/(5*b^4) + x^2/(2*b^3) + (84*a^6*log(a + b*x^(1/3)))/b^9]
    @test_int [x/(a + b*x^(1/3))^3, x, 3, (3*a^5)/(2*b^6*(a + b*x^(1/3))^2) - (15*a^4)/(b^6*(a + b*x^(1/3))) + (18*a^2*x^(1/3))/b^5 - (9*a*x^(2/3))/(2*b^4) + x/b^3 - (30*a^3*log(a + b*x^(1/3)))/b^6]
    @test_int [1/(a + b*x^(1/3))^3, x, 3, -((3*a^2)/(2*b^3*(a + b*x^(1/3))^2)) + (6*a)/(b^3*(a + b*x^(1/3))) + (3*log(a + b*x^(1/3)))/b^3]
    @test_int [1/((a + b*x^(1/3))^3*x), x, 3, 3/(2*a*(a + b*x^(1/3))^2) + 3/(a^2*(a + b*x^(1/3))) - (3*log(a + b*x^(1/3)))/a^3 + log(x)/a^3]
    @test_int [1/((a + b*x^(1/3))^3*x^2), x, 3, -((3*b^3)/(2*a^4*(a + b*x^(1/3))^2)) - (12*b^3)/(a^5*(a + b*x^(1/3))) - 1/(a^3*x) + (9*b)/(2*a^4*x^(2/3)) - (18*b^2)/(a^5*x^(1/3)) + (30*b^3*log(a + b*x^(1/3)))/a^6 - (10*b^3*log(x))/a^6]
    @test_int [1/((a + b*x^(1/3))^3*x^3), x, 3, (3*b^6)/(2*a^7*(a + b*x^(1/3))^2) + (21*b^6)/(a^8*(a + b*x^(1/3))) - 1/(2*a^3*x^2) + (9*b)/(5*a^4*x^(5/3)) - (9*b^2)/(2*a^5*x^(4/3)) + (10*b^3)/(a^6*x) - (45*b^4)/(2*a^7*x^(2/3)) + (63*b^5)/(a^8*x^(1/3)) - (84*b^6*log(a + b*x^(1/3)))/a^9 + (28*b^6*log(x))/a^9]
    @test_int [1/((a + b*x^(1/3))^3*x^4), x, 3, -((3*b^9)/(2*a^10*(a + b*x^(1/3))^2)) - (30*b^9)/(a^11*(a + b*x^(1/3))) - 1/(3*a^3*x^3) + (9*b)/(8*a^4*x^(8/3)) - (18*b^2)/(7*a^5*x^(7/3)) + (5*b^3)/(a^6*x^2) - (9*b^4)/(a^7*x^(5/3)) + (63*b^5)/(4*a^8*x^(4/3)) - (28*b^6)/(a^9*x) + (54*b^7)/(a^10*x^(2/3)) - (135*b^8)/(a^11*x^(1/3)) + (165*b^9*log(a + b*x^(1/3)))/a^12 - (55*b^9*log(x))/a^12]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b*x^(1/3))^(p/2)=#

    #= ::Subsubsection:: =#
    #=p>0=#

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [1/sqrt(1 + x^(1/3)), x, 3, 6*sqrt(1 + x^(1/3)) - 4*(1 + x^(1/3))^(3/2) + (6/5)*(1 + x^(1/3))^(5/2)]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^(m/2)*(a+b*x^(1/3))^p=#

    #= ::Subsubsection:: =#
    #=p>0=#

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [1/((1 + x^(1/3))*x^(3/2)), x, 5, -(2/sqrt(x)) + 6/x^(1/6) + 6*atan(x^(1/6))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^(m/3)*(a+b*x^(1/3))^p=#

    #= ::Subsubsection:: =#
    #=p>0=#

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [x^(2/3)/(1 + x^(1/3)), x, 3, -3*x^(1/3) + (3*x^(2/3))/2 - x + (3*x^(4/3))/4 + 3*log(1 + x^(1/3))]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(c*x)^m*(a+b*x^(2/3))^p=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b*x^(2/3))^p=#

    #= ::Subsubsection:: =#
    #=p>0=#

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [1/(1 + x^(2/3)), x, 3, 3*x^(1/3) - 3*atan(x^(1/3))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^(m/3)*(a+b*x^(2/3))^p=#

    #= ::Subsubsection:: =#
    #=p>0=#

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [1/((1 + x^(2/3))*x^(1/3)), x, 1, (3*log(1 + x^(2/3)))/2]
    @test_int [1/((1 + x^(2/3))*x^(2/3)), x, 2, 3*atan(x^(1/3))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^(m/3)*(a+b*x^(2/3))^(p/2)=#

    #= ::Subsubsection::Closed:: =#
    #=p>0=#

    @test_int [sqrt(-1 + x^(2/3))/x^(1/3), x, 1, (-1 + x^(2/3))^(3/2)]
    @test_int [(1 + x^(2/3))^(3/2)/x^(1/3), x, 1, (3*(1 + x^(2/3))^(5/2))/5]

    #= ::Subsubsection:: =#
    #=p<0=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^(m/2)*(a+b*x^(2/3))^p=#

    #= ::Subsubsection:: =#
    #=p>0=#

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [sqrt(x)/(1 + x^(2/3)), x, 13, -6*x^(1/6) + (6*x^(5/6))/5 - (3*atan(1 - sqrt(2)*x^(1/6)))/sqrt(2) + (3*atan(1 + sqrt(2)*x^(1/6)))/sqrt(2) - (3*log(1 - sqrt(2)*x^(1/6) + x^(1/3)))/(2*sqrt(2)) + (3*log(1 + sqrt(2)*x^(1/6) + x^(1/3)))/(2*sqrt(2))]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(c*x)^m*(a+b*x^(5/6))^p=#

    @test_int [x^(1/3)/(-1 + x^(5/6)), x, 8, 2*sqrt(x) + (3/5)*sqrt(10 - 2*sqrt(5))*atan((1 - sqrt(5) + 4*x^(1/6))/sqrt(10 + 2*sqrt(5))) - (3/5)*sqrt(10 + 2*sqrt(5))*atan((1 + sqrt(5) + 4*x^(1/6))/sqrt(10 - 2*sqrt(5))) + (6/5)*log(1 - x^(1/6)) - (3/10)*(1 + sqrt(5))*log(2 + (1 - sqrt(5))*x^(1/6) + 2*x^(1/3)) - (3/10)*(1 - sqrt(5))*log(2 + (1 + sqrt(5))*x^(1/6) + 2*x^(1/3)), 2*sqrt(x) + (3/5)*sqrt(2*(5 - sqrt(5)))*atan((1 - sqrt(5) + 4*x^(1/6))/sqrt(2*(5 + sqrt(5)))) - (3/5)*sqrt(2*(5 + sqrt(5)))*atan((1/2)*sqrt((1/10)*(5 + sqrt(5)))*(1 + sqrt(5) + 4*x^(1/6))) + (6/5)*log(1 - x^(1/6)) - (3/10)*(1 + sqrt(5))*log(2 + x^(1/6) - sqrt(5)*x^(1/6) + 2*x^(1/3)) - (3/10)*(1 - sqrt(5))*log(2 + x^(1/6) + sqrt(5)*x^(1/6) + 2*x^(1/3))]

    #= ::Title::Closed:: =#
    #=Integrands*of*the*form*(c*x)^m*(a+b*x^n)^p*when*n<0*is*a*fraction=#

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(c*x)^m*(a+b/x^(n/2))^p=#

    #= ::Subsection:: =#
    #=Integrands*of*the*form*x^m*(a+b/x^(n/2))^p=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b/x^(n/2))^(p/2)=#

    #= ::Subsubsection::Closed:: =#
    #=p>0=#

    @test_int [sqrt(3 - 1/sqrt(x)), x, 5, (-(1/6))*sqrt(3 - 1/sqrt(x))*sqrt(x) + sqrt(3 - 1/sqrt(x))*x - atanh(sqrt(3 - 1/sqrt(x))/sqrt(3))/(6*sqrt(3))]

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [1/sqrt(1 + 1/sqrt(x)), x, 5, (-(3/2))*sqrt(1 + 1/sqrt(x))*sqrt(x) + sqrt(1 + 1/sqrt(x))*x + (3/2)*atanh(sqrt(1 + 1/sqrt(x)))]

    #= ::Subsection:: =#
    #=Integrands*of*the*form*x^(m/2)*(a+b/x^(n/2))^p=#

    #= ::Subsection:: =#
    #=Integrands*of*the*form*x^(m/2)*(a+b/x^(n/2))^(p/2)=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b/x^(n/2))^(p/3)=#

    @test_int [(a + b/x^(3/2))^(2/3), x, 4, (a + b/x^(3/2))^(2/3)*x - (2*b^(2/3)*atan((1 + (2*b^(1/3))/((a + b/x^(3/2))^(1/3)*sqrt(x)))/sqrt(3)))/sqrt(3) + b^(2/3)*log((a + b/x^(3/2))^(1/3) - b^(1/3)/sqrt(x))]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(c*x)^m*(a+b/x^(n/3))^p=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b/x^(n/3))^p=#

    #= ::Subsubsection::Closed:: =#
    #=p>0=#

    @test_int [(a + b/x^(1/3))*x^4, x, 2, (3*b*x^(14/3))/14 + (a*x^5)/5]
    @test_int [(a + b/x^(1/3))*x^3, x, 2, (3*b*x^(11/3))/11 + (a*x^4)/4]
    @test_int [(a + b/x^(1/3))*x^2, x, 2, (3*b*x^(8/3))/8 + (a*x^3)/3]
    @test_int [(a + b/x^(1/3))*x^1, x, 2, (3*b*x^(5/3))/5 + (a*x^2)/2]
    @test_int [(a + b/x^(1/3))*x^0, x, 1, (3*b*x^(2/3))/2 + a*x]
    @test_int [(a + b/x^(1/3))/x^1, x, 2, (-3*b)/x^(1/3) + a*log(x)]
    @test_int [(a + b/x^(1/3))/x^2, x, 2, (-3*b)/(4*x^(4/3)) - a/x]
    @test_int [(a + b/x^(1/3))/x^3, x, 2, (-3*b)/(7*x^(7/3)) - a/(2*x^2)]
    @test_int [(a + b/x^(1/3))/x^4, x, 2, (-3*b)/(10*x^(10/3)) - a/(3*x^3)]

    @test_int [(a + b/x^(1/3))^2*x^4, x, 4, (3*b^2*x^(13/3))/13 + (3*a*b*x^(14/3))/7 + (a^2*x^5)/5]
    @test_int [(a + b/x^(1/3))^2*x^3, x, 4, (3*b^2*x^(10/3))/10 + (6*a*b*x^(11/3))/11 + (a^2*x^4)/4]
    @test_int [(a + b/x^(1/3))^2*x^2, x, 4, (3*b^2*x^(7/3))/7 + (3*a*b*x^(8/3))/4 + (a^2*x^3)/3]
    @test_int [(a + b/x^(1/3))^2*x^1, x, 4, (3*b^2*x^(4/3))/4 + (6*a*b*x^(5/3))/5 + (a^2*x^2)/2]
    @test_int [(a + b/x^(1/3))^2*x^0, x, 2, ((a + b/x^(1/3))^3*x)/a]
    @test_int [(a + b/x^(1/3))^2/x^1, x, 4, (-3*b^2)/(2*x^(2/3)) - (6*a*b)/x^(1/3) + a^2*log(x)]
    @test_int [(a + b/x^(1/3))^2/x^2, x, 4, (-3*b^2)/(5*x^(5/3)) - (3*a*b)/(2*x^(4/3)) - a^2/x]
    @test_int [(a + b/x^(1/3))^2/x^3, x, 4, (-3*b^2)/(8*x^(8/3)) - (6*a*b)/(7*x^(7/3)) - a^2/(2*x^2)]
    @test_int [(a + b/x^(1/3))^2/x^4, x, 4, (-3*b^2)/(11*x^(11/3)) - (3*a*b)/(5*x^(10/3)) - a^2/(3*x^3)]

    @test_int [(a + b/x^(1/3))^3*x^4, x, 4, (b^3*x^4)/4 + (9*a*b^2*x^(13/3))/13 + (9*a^2*b*x^(14/3))/14 + (a^3*x^5)/5]
    @test_int [(a + b/x^(1/3))^3*x^3, x, 4, (b^3*x^3)/3 + (9*a*b^2*x^(10/3))/10 + (9*a^2*b*x^(11/3))/11 + (a^3*x^4)/4]
    @test_int [(a + b/x^(1/3))^3*x^2, x, 4, (b^3*x^2)/2 + (9*a*b^2*x^(7/3))/7 + (9*a^2*b*x^(8/3))/8 + (a^3*x^3)/3]
    @test_int [(a + b/x^(1/3))^3*x^1, x, 4, b^3*x + (9/4)*a*b^2*x^(4/3) + (9/5)*a^2*b*x^(5/3) + (a^3*x^2)/2]
    @test_int [(a + b/x^(1/3))^3*x^0, x, 3, 9*a*b^2*x^(1/3) + (9*a^2*b*x^(2/3))/2 + a^3*x + b^3*log(x)]
    @test_int [(a + b/x^(1/3))^3/x^1, x, 4, -(b^3/x) - (9*a*b^2)/(2*x^(2/3)) - (9*a^2*b)/x^(1/3) + a^3*log(x)]
    @test_int [(a + b/x^(1/3))^3/x^2, x, 4, -b^3/(2*x^2) - (9*a*b^2)/(5*x^(5/3)) - (9*a^2*b)/(4*x^(4/3)) - a^3/x]
    @test_int [(a + b/x^(1/3))^3/x^3, x, 4, -b^3/(3*x^3) - (9*a*b^2)/(8*x^(8/3)) - (9*a^2*b)/(7*x^(7/3)) - a^3/(2*x^2)]
    @test_int [(a + b/x^(1/3))^3/x^4, x, 4, -b^3/(4*x^4) - (9*a*b^2)/(11*x^(11/3)) - (9*a^2*b)/(10*x^(10/3)) - a^3/(3*x^3)]

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [x^2/(a + b/x^(1/3)), x, 4, (3*b^8*x^(1/3))/a^9 - (3*b^7*x^(2/3))/(2*a^8) + (b^6*x)/a^7 - (3*b^5*x^(4/3))/(4*a^6) + (3*b^4*x^(5/3))/(5*a^5) - (b^3*x^2)/(2*a^4) + (3*b^2*x^(7/3))/(7*a^3) - (3*b*x^(8/3))/(8*a^2) + x^3/(3*a) - (3*b^9*log(b + a*x^(1/3)))/a^10]
    @test_int [x^1/(a + b/x^(1/3)), x, 4, -((3*b^5*x^(1/3))/a^6) + (3*b^4*x^(2/3))/(2*a^5) - (b^3*x)/a^4 + (3*b^2*x^(4/3))/(4*a^3) - (3*b*x^(5/3))/(5*a^2) + x^2/(2*a) + (3*b^6*log(b + a*x^(1/3)))/a^7]
    @test_int [x^0/(a + b/x^(1/3)), x, 3, (3*b^2*x^(1/3))/a^3 - (3*b*x^(2/3))/(2*a^2) + x/a - (3*b^3*log(a + b/x^(1/3)))/a^4 - (b^3*log(x))/a^4]
    @test_int [1/((a + b/x^(1/3))*x^1), x, 2, (3*log(b + a*x^(1/3)))/a]
    @test_int [1/((a + b/x^(1/3))*x^2), x, 4, -(3/(2*b*x^(2/3))) + (3*a)/(b^2*x^(1/3)) - (3*a^2*log(b + a*x^(1/3)))/b^3 + (a^2*log(x))/b^3]
    @test_int [1/((a + b/x^(1/3))*x^3), x, 4, -(3/(5*b*x^(5/3))) + (3*a)/(4*b^2*x^(4/3)) - a^2/(b^3*x) + (3*a^3)/(2*b^4*x^(2/3)) - (3*a^4)/(b^5*x^(1/3)) + (3*a^5*log(b + a*x^(1/3)))/b^6 - (a^5*log(x))/b^6]
    @test_int [1/((a + b/x^(1/3))*x^4), x, 4, -(3/(8*b*x^(8/3))) + (3*a)/(7*b^2*x^(7/3)) - a^2/(2*b^3*x^2) + (3*a^3)/(5*b^4*x^(5/3)) - (3*a^4)/(4*b^5*x^(4/3)) + a^5/(b^6*x) - (3*a^6)/(2*b^7*x^(2/3)) + (3*a^7)/(b^8*x^(1/3)) - (3*a^8*log(b + a*x^(1/3)))/b^9 + (a^8*log(x))/b^9]
    @test_int [1/((a + b/x^(1/3))*x^5), x, 4, -(3/(11*b*x^(11/3))) + (3*a)/(10*b^2*x^(10/3)) - a^2/(3*b^3*x^3) + (3*a^3)/(8*b^4*x^(8/3)) - (3*a^4)/(7*b^5*x^(7/3)) + a^5/(2*b^6*x^2) - (3*a^6)/(5*b^7*x^(5/3)) + (3*a^7)/(4*b^8*x^(4/3)) - a^8/(b^9*x) + (3*a^9)/(2*b^10*x^(2/3)) - (3*a^10)/(b^11*x^(1/3)) + (3*a^11*log(b + a*x^(1/3)))/b^12 - (a^11*log(x))/b^12]

    @test_int [x^2/(a + b/x^(1/3))^2, x, 4, -((3*b^10)/(a^11*(b + a*x^(1/3)))) + (27*b^8*x^(1/3))/a^10 - (12*b^7*x^(2/3))/a^9 + (7*b^6*x)/a^8 - (9*b^5*x^(4/3))/(2*a^7) + (3*b^4*x^(5/3))/a^6 - (2*b^3*x^2)/a^5 + (9*b^2*x^(7/3))/(7*a^4) - (3*b*x^(8/3))/(4*a^3) + x^3/(3*a^2) - (30*b^9*log(b + a*x^(1/3)))/a^11]
    @test_int [x^1/(a + b/x^(1/3))^2, x, 4, (3*b^7)/(a^8*(b + a*x^(1/3))) - (18*b^5*x^(1/3))/a^7 + (15*b^4*x^(2/3))/(2*a^6) - (4*b^3*x)/a^5 + (9*b^2*x^(4/3))/(4*a^4) - (6*b*x^(5/3))/(5*a^3) + x^2/(2*a^2) + (21*b^6*log(b + a*x^(1/3)))/a^8]
    @test_int [x^0/(a + b/x^(1/3))^2, x, 3, (3*b^3)/(a^4*(a + b/x^(1/3))) + (9*b^2*x^(1/3))/a^4 - (3*b*x^(2/3))/a^3 + x/a^2 - (12*b^3*log(a + b/x^(1/3)))/a^5 - (4*b^3*log(x))/a^5]
    @test_int [1/((a + b/x^(1/3))^2*x^1), x, 4, (3*b)/(a^2*(b + a*x^(1/3))) + (3*log(b + a*x^(1/3)))/a^2]
    @test_int [1/((a + b/x^(1/3))^2*x^2), x, 4, -((3*a)/(b^2*(b + a*x^(1/3)))) - 3/(b^2*x^(1/3)) + (6*a*log(b + a*x^(1/3)))/b^3 - (2*a*log(x))/b^3]
    @test_int [1/((a + b/x^(1/3))^2*x^3), x, 4, (3*a^4)/(b^5*(b + a*x^(1/3))) - 3/(4*b^2*x^(4/3)) + (2*a)/(b^3*x) - (9*a^2)/(2*b^4*x^(2/3)) + (12*a^3)/(b^5*x^(1/3)) - (15*a^4*log(b + a*x^(1/3)))/b^6 + (5*a^4*log(x))/b^6]
    @test_int [1/((a + b/x^(1/3))^2*x^4), x, 4, -((3*a^7)/(b^8*(b + a*x^(1/3)))) - 3/(7*b^2*x^(7/3)) + a/(b^3*x^2) - (9*a^2)/(5*b^4*x^(5/3)) + (3*a^3)/(b^5*x^(4/3)) - (5*a^4)/(b^6*x) + (9*a^5)/(b^7*x^(2/3)) - (21*a^6)/(b^8*x^(1/3)) + (24*a^7*log(b + a*x^(1/3)))/b^9 - (8*a^7*log(x))/b^9]
    @test_int [1/((a + b/x^(1/3))^2*x^5), x, 4, (3*a^10)/(b^11*(b + a*x^(1/3))) - 3/(10*b^2*x^(10/3)) + (2*a)/(3*b^3*x^3) - (9*a^2)/(8*b^4*x^(8/3)) + (12*a^3)/(7*b^5*x^(7/3)) - (5*a^4)/(2*b^6*x^2) + (18*a^5)/(5*b^7*x^(5/3)) - (21*a^6)/(4*b^8*x^(4/3)) + (8*a^7)/(b^9*x) - (27*a^8)/(2*b^10*x^(2/3)) + (30*a^9)/(b^11*x^(1/3)) - (33*a^10*log(b + a*x^(1/3)))/b^12 + (11*a^10*log(x))/b^12]

    @test_int [x^2/(a + b/x^(1/3))^3, x, 4, (3*b^11)/(2*a^12*(b + a*x^(1/3))^2) - (33*b^10)/(a^12*(b + a*x^(1/3))) + (135*b^8*x^(1/3))/a^11 - (54*b^7*x^(2/3))/a^10 + (28*b^6*x)/a^9 - (63*b^5*x^(4/3))/(4*a^8) + (9*b^4*x^(5/3))/a^7 - (5*b^3*x^2)/a^6 + (18*b^2*x^(7/3))/(7*a^5) - (9*b*x^(8/3))/(8*a^4) + x^3/(3*a^3) - (165*b^9*log(b + a*x^(1/3)))/a^12]
    @test_int [x^1/(a + b/x^(1/3))^3, x, 4, -((3*b^8)/(2*a^9*(b + a*x^(1/3))^2)) + (24*b^7)/(a^9*(b + a*x^(1/3))) - (63*b^5*x^(1/3))/a^8 + (45*b^4*x^(2/3))/(2*a^7) - (10*b^3*x)/a^6 + (9*b^2*x^(4/3))/(2*a^5) - (9*b*x^(5/3))/(5*a^4) + x^2/(2*a^3) + (84*b^6*log(b + a*x^(1/3)))/a^9]
    @test_int [x^0/(a + b/x^(1/3))^3, x, 3, (3*b^3)/(2*a^4*(a + b/x^(1/3))^2) + (12*b^3)/(a^5*(a + b/x^(1/3))) + (18*b^2*x^(1/3))/a^5 - (9*b*x^(2/3))/(2*a^4) + x/a^3 - (30*b^3*log(a + b/x^(1/3)))/a^6 - (10*b^3*log(x))/a^6]
    @test_int [1/((a + b/x^(1/3))^3*x^1), x, 4, -((3*b^2)/(2*a^3*(b + a*x^(1/3))^2)) + (6*b)/(a^3*(b + a*x^(1/3))) + (3*log(b + a*x^(1/3)))/a^3]
    @test_int [1/((a + b/x^(1/3))^3*x^2), x, 4, 3/(2*b*(b + a*x^(1/3))^2) + 3/(b^2*(b + a*x^(1/3))) - (3*log(b + a*x^(1/3)))/b^3 + log(x)/b^3]
    @test_int [1/((a + b/x^(1/3))^3*x^3), x, 4, -((3*a^3)/(2*b^4*(b + a*x^(1/3))^2)) - (12*a^3)/(b^5*(b + a*x^(1/3))) - 1/(b^3*x) + (9*a)/(2*b^4*x^(2/3)) - (18*a^2)/(b^5*x^(1/3)) + (30*a^3*log(b + a*x^(1/3)))/b^6 - (10*a^3*log(x))/b^6]
    @test_int [1/((a + b/x^(1/3))^3*x^4), x, 4, (3*a^6)/(2*b^7*(b + a*x^(1/3))^2) + (21*a^6)/(b^8*(b + a*x^(1/3))) - 1/(2*b^3*x^2) + (9*a)/(5*b^4*x^(5/3)) - (9*a^2)/(2*b^5*x^(4/3)) + (10*a^3)/(b^6*x) - (45*a^4)/(2*b^7*x^(2/3)) + (63*a^5)/(b^8*x^(1/3)) - (84*a^6*log(b + a*x^(1/3)))/b^9 + (28*a^6*log(x))/b^9]
    @test_int [1/((a + b/x^(1/3))^3*x^5), x, 4, -((3*a^9)/(2*b^10*(b + a*x^(1/3))^2)) - (30*a^9)/(b^11*(b + a*x^(1/3))) - 1/(3*b^3*x^3) + (9*a)/(8*b^4*x^(8/3)) - (18*a^2)/(7*b^5*x^(7/3)) + (5*a^3)/(b^6*x^2) - (9*a^4)/(b^7*x^(5/3)) + (63*a^5)/(4*b^8*x^(4/3)) - (28*a^6)/(b^9*x) + (54*a^7)/(b^10*x^(2/3)) - (135*a^8)/(b^11*x^(1/3)) + (165*a^9*log(b + a*x^(1/3)))/b^12 - (55*a^9*log(x))/b^12]

    @test_int [1/(1 + b/x^(1/3)), x, 3, 3*b^2*x^(1/3) - (3/2)*b*x^(2/3) + x - 3*b^3*log(1 + b/x^(1/3)) - b^3*log(x)]

    #= ::Subsection:: =#
    #=Integrands*of*the*form*x^m*(a+b/x^(n/3))^(p/2)=#

    #= ::Subsection:: =#
    #=Integrands*of*the*form*x^(m/2)*(a+b/x^(n/3))^p=#

    #= ::Subsection:: =#
    #=Integrands*of*the*form*x^(m/2)*(a+b/x^(n/3))^(p/2)=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^(m/3)*(a+b/x^(n/3))^(p/3)=#

    @test_int [x^(2/3)*(1 + x^(5/3))^(2/3), x, 1, (9*(1 + x^(5/3))^(5/3))/25]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^(m/3)*(a+b/x^(n/3))^(p/7)=#

    @test_int [x^(7/3)*(a^(10/3) - x^(10/3))^(19/7), x, 1, (-21*(a^(10/3) - x^(10/3))^(26/7))/260]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(c*x)^m*(a+b/x^(n/5))^p=#

    @test_int [1/(1 + x^(1/5)), x, 3, -5*x^(1/5) + (5*x^(2/5))/2 - (5*x^(3/5))/3 + (5*x^(4/5))/4 + 5*log(1 + x^(1/5))]
    @test_int [1/(sqrt(1 + x^(4/5))*x^(1/5)), x, 1, (5*sqrt(1 + x^(4/5)))/2]

    @test_int [(a + b/x^(3/5))^(2/3), x, 1, ((a + b/x^(3/5))^(5/3)*x)/a]

    #= ::Title::Closed:: =#
    #=Integrands*of*the*form*(c*x)^m*(a+b*x^n)^p*when*n*symbolic=#

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b*x^n)^p=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b*x^n)^p=#

    #= ::Subsubsection::Closed:: =#
    #=p>0=#

    @test_int [x^3*(a + b*x^n), x, 2, (a*x^4)/4 + (b*x^(4 + n))/(4 + n)]
    @test_int [x^2*(a + b*x^n), x, 2, (a*x^3)/3 + (b*x^(3 + n))/(3 + n)]
    @test_int [x^1*(a + b*x^n), x, 2, (a*x^2)/2 + (b*x^(2 + n))/(2 + n)]
    @test_int [x^0*(a + b*x^n), x, 1, a*x + (b*x^(1 + n))/(1 + n)]
    @test_int [(a + b*x^n)/x^1, x, 2, (b*x^n)/n + a*log(x)]
    @test_int [(a + b*x^n)/x^2, x, 2, -(a/x) - (b*x^(-1 + n))/(1 - n)]
    @test_int [(a + b*x^n)/x^3, x, 2, -(a/(2*x^2)) - (b*x^(-2 + n))/(2 - n)]

    @test_int [x^3*(a + b*x^n)^2, x, 2, (a^2*x^4)/4 + (b^2*x^(2*(2 + n)))/(2*(2 + n)) + (2*a*b*x^(4 + n))/(4 + n)]
    @test_int [x^2*(a + b*x^n)^2, x, 2, (a^2*x^3)/3 + (2*a*b*x^(3 + n))/(3 + n) + (b^2*x^(3 + 2*n))/(3 + 2*n)]
    @test_int [x^1*(a + b*x^n)^2, x, 2, (a^2*x^2)/2 + (b^2*x^(2*(1 + n)))/(2*(1 + n)) + (2*a*b*x^(2 + n))/(2 + n)]
    @test_int [x^0*(a + b*x^n)^2, x, 2, a^2*x + (2*a*b*x^(1 + n))/(1 + n) + (b^2*x^(1 + 2*n))/(1 + 2*n)]
    @test_int [(a + b*x^n)^2/x^1, x, 3, (2*a*b*x^n)/n + (b^2*x^(2*n))/(2*n) + a^2*log(x)]
    @test_int [(a + b*x^n)^2/x^2, x, 2, -(a^2/x) - (2*a*b*x^(-1 + n))/(1 - n) - (b^2*x^(-1 + 2*n))/(1 - 2*n)]
    @test_int [(a + b*x^n)^2/x^3, x, 2, -(a^2/(2*x^2)) - b^2/(x^(2*(1 - n))*(2*(1 - n))) - (2*a*b*x^(-2 + n))/(2 - n)]

    @test_int [x^3*(a + b*x^n)^3, x, 2, (a^3*x^4)/4 + (3*a*b^2*x^(2*(2 + n)))/(2*(2 + n)) + (3*a^2*b*x^(4 + n))/(4 + n) + (b^3*x^(4 + 3*n))/(4 + 3*n)]
    @test_int [x^2*(a + b*x^n)^3, x, 2, (a^3*x^3)/3 + (b^3*x^(3*(1 + n)))/(3*(1 + n)) + (3*a^2*b*x^(3 + n))/(3 + n) + (3*a*b^2*x^(3 + 2*n))/(3 + 2*n)]
    @test_int [x^1*(a + b*x^n)^3, x, 2, (a^3*x^2)/2 + (3*a*b^2*x^(2*(1 + n)))/(2*(1 + n)) + (3*a^2*b*x^(2 + n))/(2 + n) + (b^3*x^(2 + 3*n))/(2 + 3*n)]
    @test_int [x^0*(a + b*x^n)^3, x, 2, a^3*x + (3*a^2*b*x^(1 + n))/(1 + n) + (3*a*b^2*x^(1 + 2*n))/(1 + 2*n) + (b^3*x^(1 + 3*n))/(1 + 3*n)]
    @test_int [(a + b*x^n)^3/x^1, x, 3, (3*a^2*b*x^n)/n + (3*a*b^2*x^(2*n))/(2*n) + (b^3*x^(3*n))/(3*n) + a^3*log(x)]
    @test_int [(a + b*x^n)^3/x^2, x, 2, -(a^3/x) - (3*a^2*b*x^(-1 + n))/(1 - n) - (3*a*b^2*x^(-1 + 2*n))/(1 - 2*n) - (b^3*x^(-1 + 3*n))/(1 - 3*n)]
    @test_int [(a + b*x^n)^3/x^3, x, 2, -(a^3/(2*x^2)) - (3*a*b^2)/(x^(2*(1 - n))*(2*(1 - n))) - (3*a^2*b*x^(-2 + n))/(2 - n) - (b^3*x^(-2 + 3*n))/(2 - 3*n)]

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [x^1/(a + b*x^n), x, 1, (x^2*HypergeometricFunctions._₂F₁(1, 2/n, (2 + n)/n, -((b*x^n)/a)))/(2*a)]
    @test_int [x^0/(a + b*x^n), x, 1, (x*HypergeometricFunctions._₂F₁(1, 1/n, 1 + 1/n, -((b*x^n)/a)))/a]
    @test_int [1/(x^1*(a + b*x^n)), x, 4, log(x)/a - log(a + b*x^n)/(a*n)]
    @test_int [1/(x^2*(a + b*x^n)), x, 1, -(HypergeometricFunctions._₂F₁(1, -(1/n), -((1 - n)/n), -((b*x^n)/a))/(a*x))]
    @test_int [1/(x^3*(a + b*x^n)), x, 1, -(HypergeometricFunctions._₂F₁(1, -(2/n), -((2 - n)/n), -((b*x^n)/a))/(2*a*x^2))]

    @test_int [x^1/(a + b*x^n)^2, x, 1, (x^2*HypergeometricFunctions._₂F₁(2, 2/n, (2 + n)/n, -((b*x^n)/a)))/(2*a^2)]
    @test_int [x^0/(a + b*x^n)^2, x, 1, (x*HypergeometricFunctions._₂F₁(2, 1/n, 1 + 1/n, -((b*x^n)/a)))/a^2]
    @test_int [1/(x^1*(a + b*x^n)^2), x, 3, 1/(a*n*(a + b*x^n)) + log(x)/a^2 - log(a + b*x^n)/(a^2*n)]
    @test_int [1/(x^2*(a + b*x^n)^2), x, 1, -(HypergeometricFunctions._₂F₁(2, -(1/n), -((1 - n)/n), -((b*x^n)/a))/(a^2*x))]
    @test_int [1/(x^3*(a + b*x^n)^2), x, 1, -(HypergeometricFunctions._₂F₁(2, -(2/n), -((2 - n)/n), -((b*x^n)/a))/(2*a^2*x^2))]

    @test_int [x^1/(a + b*x^n)^3, x, 1, (x^2*HypergeometricFunctions._₂F₁(3, 2/n, (2 + n)/n, -((b*x^n)/a)))/(2*a^3)]
    @test_int [x^0/(a + b*x^n)^3, x, 1, (x*HypergeometricFunctions._₂F₁(3, 1/n, 1 + 1/n, -((b*x^n)/a)))/a^3]
    @test_int [1/(x^1*(a + b*x^n)^3), x, 3, 1/(2*a*n*(a + b*x^n)^2) + 1/(a^2*n*(a + b*x^n)) + log(x)/a^3 - log(a + b*x^n)/(a^3*n)]
    @test_int [1/(x^2*(a + b*x^n)^3), x, 1, -(HypergeometricFunctions._₂F₁(3, -(1/n), -((1 - n)/n), -((b*x^n)/a))/(a^3*x))]
    @test_int [1/(x^3*(a + b*x^n)^3), x, 1, -(HypergeometricFunctions._₂F₁(3, -(2/n), -((2 - n)/n), -((b*x^n)/a))/(2*a^3*x^2))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b*x^n)^(p/2)=#

    #= ::Subsubsection::Closed:: =#
    #=p>0=#

    @test_int [x^1*(a + b*x^n)^(1/2), x, 2, (x^2*(a + b*x^n)^(3/2)*HypergeometricFunctions._₂F₁(1, 3/2 + 2/n, (2 + n)/n, -((b*x^n)/a)))/(2*a), (x^2*sqrt(a + b*x^n)*HypergeometricFunctions._₂F₁(-(1/2), 2/n, (2 + n)/n, -((b*x^n)/a)))/(2*sqrt(1 + (b*x^n)/a))]
    @test_int [x^0*(a + b*x^n)^(1/2), x, 2, (x*(a + b*x^n)^(3/2)*HypergeometricFunctions._₂F₁(1, 3/2 + 1/n, 1 + 1/n, -((b*x^n)/a)))/a, (x*sqrt(a + b*x^n)*HypergeometricFunctions._₂F₁(-(1/2), 1/n, 1 + 1/n, -((b*x^n)/a)))/sqrt(1 + (b*x^n)/a)]
    @test_int [(a + b*x^n)^(1/2)/x^1, x, 4, (2*sqrt(a + b*x^n))/n - (2*sqrt(a)*atanh(sqrt(a + b*x^n)/sqrt(a)))/n]
    @test_int [(a + b*x^n)^(1/2)/x^2, x, 2, -(((a + b*x^n)^(3/2)*HypergeometricFunctions._₂F₁(1, 3/2 - 1/n, -((1 - n)/n), -((b*x^n)/a)))/(a*x)), -((sqrt(a + b*x^n)*HypergeometricFunctions._₂F₁(-(1/2), -(1/n), -((1 - n)/n), -((b*x^n)/a)))/(x*sqrt(1 + (b*x^n)/a)))]
    @test_int [(a + b*x^n)^(1/2)/x^3, x, 2, -(((a + b*x^n)^(3/2)*HypergeometricFunctions._₂F₁(1, 3/2 - 2/n, -((2 - n)/n), -((b*x^n)/a)))/(2*a*x^2)), -((sqrt(a + b*x^n)*HypergeometricFunctions._₂F₁(-(1/2), -(2/n), -((2 - n)/n), -((b*x^n)/a)))/(2*x^2*sqrt(1 + (b*x^n)/a)))]

    @test_int [x^1*(a + b*x^n)^(3/2), x, 2, (x^2*(a + b*x^n)^(5/2)*HypergeometricFunctions._₂F₁(1, 5/2 + 2/n, (2 + n)/n, -((b*x^n)/a)))/(2*a), (a*x^2*sqrt(a + b*x^n)*HypergeometricFunctions._₂F₁(-(3/2), 2/n, (2 + n)/n, -((b*x^n)/a)))/(2*sqrt(1 + (b*x^n)/a))]
    @test_int [x^0*(a + b*x^n)^(3/2), x, 2, (x*(a + b*x^n)^(5/2)*HypergeometricFunctions._₂F₁(1, 5/2 + 1/n, 1 + 1/n, -((b*x^n)/a)))/a, (a*x*sqrt(a + b*x^n)*HypergeometricFunctions._₂F₁(-(3/2), 1/n, 1 + 1/n, -((b*x^n)/a)))/sqrt(1 + (b*x^n)/a)]
    @test_int [(a + b*x^n)^(3/2)/x^1, x, 5, (2*a*sqrt(a + b*x^n))/n + (2*(a + b*x^n)^(3/2))/(3*n) - (2*a^(3/2)*atanh(sqrt(a + b*x^n)/sqrt(a)))/n]
    @test_int [(a + b*x^n)^(3/2)/x^2, x, 2, -(((a + b*x^n)^(5/2)*HypergeometricFunctions._₂F₁(1, 5/2 - 1/n, -((1 - n)/n), -((b*x^n)/a)))/(a*x)), -((a*sqrt(a + b*x^n)*HypergeometricFunctions._₂F₁(-(3/2), -(1/n), -((1 - n)/n), -((b*x^n)/a)))/(x*sqrt(1 + (b*x^n)/a)))]
    @test_int [(a + b*x^n)^(3/2)/x^3, x, 2, -(((a + b*x^n)^(5/2)*HypergeometricFunctions._₂F₁(1, 5/2 - 2/n, -((2 - n)/n), -((b*x^n)/a)))/(2*a*x^2)), -((a*sqrt(a + b*x^n)*HypergeometricFunctions._₂F₁(-(3/2), -(2/n), -((2 - n)/n), -((b*x^n)/a)))/(2*x^2*sqrt(1 + (b*x^n)/a)))]

    @test_int [x^1*(a + b*x^n)^(5/2), x, 2, (x^2*(a + b*x^n)^(7/2)*HypergeometricFunctions._₂F₁(1, 7/2 + 2/n, (2 + n)/n, -((b*x^n)/a)))/(2*a), (a^2*x^2*sqrt(a + b*x^n)*HypergeometricFunctions._₂F₁(-(5/2), 2/n, (2 + n)/n, -((b*x^n)/a)))/(2*sqrt(1 + (b*x^n)/a))]
    @test_int [x^0*(a + b*x^n)^(5/2), x, 2, (x*(a + b*x^n)^(7/2)*HypergeometricFunctions._₂F₁(1, 7/2 + 1/n, 1 + 1/n, -((b*x^n)/a)))/a, (a^2*x*sqrt(a + b*x^n)*HypergeometricFunctions._₂F₁(-(5/2), 1/n, 1 + 1/n, -((b*x^n)/a)))/sqrt(1 + (b*x^n)/a)]
    @test_int [(a + b*x^n)^(5/2)/x^1, x, 6, (2*a^2*sqrt(a + b*x^n))/n + (2*a*(a + b*x^n)^(3/2))/(3*n) + (2*(a + b*x^n)^(5/2))/(5*n) - (2*a^(5/2)*atanh(sqrt(a + b*x^n)/sqrt(a)))/n]
    @test_int [(a + b*x^n)^(5/2)/x^2, x, 2, -(((a + b*x^n)^(7/2)*HypergeometricFunctions._₂F₁(1, 7/2 - 1/n, -((1 - n)/n), -((b*x^n)/a)))/(a*x)), -((a^2*sqrt(a + b*x^n)*HypergeometricFunctions._₂F₁(-(5/2), -(1/n), -((1 - n)/n), -((b*x^n)/a)))/(x*sqrt(1 + (b*x^n)/a)))]
    @test_int [(a + b*x^n)^(5/2)/x^3, x, 2, -(((a + b*x^n)^(7/2)*HypergeometricFunctions._₂F₁(1, 7/2 - 2/n, -((2 - n)/n), -((b*x^n)/a)))/(2*a*x^2)), -((a^2*sqrt(a + b*x^n)*HypergeometricFunctions._₂F₁(-(5/2), -(2/n), -((2 - n)/n), -((b*x^n)/a)))/(2*x^2*sqrt(1 + (b*x^n)/a)))]

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [x^1/(a + b*x^n)^(1/2), x, 2, (x^2*sqrt(a + b*x^n)*HypergeometricFunctions._₂F₁(1, 1/2 + 2/n, (2 + n)/n, -((b*x^n)/a)))/(2*a), (x^2*sqrt(1 + (b*x^n)/a)*HypergeometricFunctions._₂F₁(1/2, 2/n, (2 + n)/n, -((b*x^n)/a)))/(2*sqrt(a + b*x^n))]
    @test_int [x^0/(a + b*x^n)^(1/2), x, 2, (x*sqrt(a + b*x^n)*HypergeometricFunctions._₂F₁(1, 1/2 + 1/n, 1 + 1/n, -((b*x^n)/a)))/a, (x*sqrt(1 + (b*x^n)/a)*HypergeometricFunctions._₂F₁(1/2, 1/n, 1 + 1/n, -((b*x^n)/a)))/sqrt(a + b*x^n)]
    @test_int [1/(x^1*(a + b*x^n)^(1/2)), x, 3, -((2*atanh(sqrt(a + b*x^n)/sqrt(a)))/(sqrt(a)*n))]
    @test_int [1/(x^2*(a + b*x^n)^(1/2)), x, 2, -((sqrt(a + b*x^n)*HypergeometricFunctions._₂F₁(1, 1/2 - 1/n, -((1 - n)/n), -((b*x^n)/a)))/(a*x)), -((sqrt(1 + (b*x^n)/a)*HypergeometricFunctions._₂F₁(1/2, -(1/n), -((1 - n)/n), -((b*x^n)/a)))/(x*sqrt(a + b*x^n)))]
    @test_int [1/(x^3*(a + b*x^n)^(1/2)), x, 2, -((sqrt(a + b*x^n)*HypergeometricFunctions._₂F₁(1, 1/2 - 2/n, -((2 - n)/n), -((b*x^n)/a)))/(2*a*x^2)), -((sqrt(1 + (b*x^n)/a)*HypergeometricFunctions._₂F₁(1/2, -(2/n), -((2 - n)/n), -((b*x^n)/a)))/(2*x^2*sqrt(a + b*x^n)))]

    @test_int [x^1/(a + b*x^n)^(3/2), x, 2, (x^2*HypergeometricFunctions._₂F₁(1, -(1/2) + 2/n, (2 + n)/n, -((b*x^n)/a)))/(2*a*sqrt(a + b*x^n)), (x^2*sqrt(1 + (b*x^n)/a)*HypergeometricFunctions._₂F₁(3/2, 2/n, (2 + n)/n, -((b*x^n)/a)))/(2*a*sqrt(a + b*x^n))]
    @test_int [x^0/(a + b*x^n)^(3/2), x, 2, (x*HypergeometricFunctions._₂F₁(1, -(1/2) + 1/n, 1 + 1/n, -((b*x^n)/a)))/(a*sqrt(a + b*x^n)), (x*sqrt(1 + (b*x^n)/a)*HypergeometricFunctions._₂F₁(3/2, 1/n, 1 + 1/n, -((b*x^n)/a)))/(a*sqrt(a + b*x^n))]
    @test_int [1/(x^1*(a + b*x^n)^(3/2)), x, 4, 2/(a*n*sqrt(a + b*x^n)) - (2*atanh(sqrt(a + b*x^n)/sqrt(a)))/(a^(3/2)*n)]
    @test_int [1/(x^2*(a + b*x^n)^(3/2)), x, 2, -(HypergeometricFunctions._₂F₁(1, -(1/2) - 1/n, -((1 - n)/n), -((b*x^n)/a))/(a*x*sqrt(a + b*x^n))), -((sqrt(1 + (b*x^n)/a)*HypergeometricFunctions._₂F₁(3/2, -(1/n), -((1 - n)/n), -((b*x^n)/a)))/(a*x*sqrt(a + b*x^n)))]
    @test_int [1/(x^3*(a + b*x^n)^(3/2)), x, 2, -(HypergeometricFunctions._₂F₁(1, -(1/2) - 2/n, -((2 - n)/n), -((b*x^n)/a))/(2*a*x^2*sqrt(a + b*x^n))), -((sqrt(1 + (b*x^n)/a)*HypergeometricFunctions._₂F₁(3/2, -(2/n), -((2 - n)/n), -((b*x^n)/a)))/(2*a*x^2*sqrt(a + b*x^n)))]

    @test_int [x^1/(a + b*x^n)^(5/2), x, 2, (x^2*HypergeometricFunctions._₂F₁(1, -(3/2) + 2/n, (2 + n)/n, -((b*x^n)/a)))/(2*a*(a + b*x^n)^(3/2)), (x^2*sqrt(1 + (b*x^n)/a)*HypergeometricFunctions._₂F₁(5/2, 2/n, (2 + n)/n, -((b*x^n)/a)))/(2*a^2*sqrt(a + b*x^n))]
    @test_int [x^0/(a + b*x^n)^(5/2), x, 2, (x*HypergeometricFunctions._₂F₁(1, -(3/2) + 1/n, 1 + 1/n, -((b*x^n)/a)))/(a*(a + b*x^n)^(3/2)), (x*sqrt(1 + (b*x^n)/a)*HypergeometricFunctions._₂F₁(5/2, 1/n, 1 + 1/n, -((b*x^n)/a)))/(a^2*sqrt(a + b*x^n))]
    @test_int [1/(x^1*(a + b*x^n)^(5/2)), x, 5, 2/(3*a*n*(a + b*x^n)^(3/2)) + 2/(a^2*n*sqrt(a + b*x^n)) - (2*atanh(sqrt(a + b*x^n)/sqrt(a)))/(a^(5/2)*n)]
    @test_int [1/(x^2*(a + b*x^n)^(5/2)), x, 2, -(HypergeometricFunctions._₂F₁(1, -(3/2) - 1/n, -((1 - n)/n), -((b*x^n)/a))/(a*x*(a + b*x^n)^(3/2))), -((sqrt(1 + (b*x^n)/a)*HypergeometricFunctions._₂F₁(5/2, -(1/n), -((1 - n)/n), -((b*x^n)/a)))/(a^2*x*sqrt(a + b*x^n)))]
    @test_int [1/(x^3*(a + b*x^n)^(5/2)), x, 2, -(HypergeometricFunctions._₂F₁(1, -(3/2) - 2/n, -((2 - n)/n), -((b*x^n)/a))/(2*a*x^2*(a + b*x^n)^(3/2))), -((sqrt(1 + (b*x^n)/a)*HypergeometricFunctions._₂F₁(5/2, -(2/n), -((2 - n)/n), -((b*x^n)/a)))/(2*a^2*x^2*sqrt(a + b*x^n)))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b*x^n)^(p/3)=#

    #= ::Subsubsection::Closed:: =#
    #=p>0=#

    @test_int [(a + b*x^n)^(1/3)/x, x, 6, (3*(a + b*x^n)^(1/3))/n - (sqrt(3)*a^(1/3)*atan((a^(1/3) + 2*(a + b*x^n)^(1/3))/(sqrt(3)*a^(1/3))))/n - (1/2)*a^(1/3)*log(x) + (3*a^(1/3)*log(a^(1/3) - (a + b*x^n)^(1/3)))/(2*n)]

    #= ::Subsubsection:: =#
    #=p<0=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^(k*n-1)*(a+b*x^n)^p=#

    #= ::Subsubsection::Closed:: =#
    #=p>0=#

    @test_int [x^(4*n - 1)*(a + b*x^n), x, 2, (a*x^(4*n))/(4*n) + (b*x^(5*n))/(5*n)]
    @test_int [x^(3*n - 1)*(a + b*x^n), x, 2, (a*x^(3*n))/(3*n) + (b*x^(4*n))/(4*n)]
    @test_int [x^(2*n - 1)*(a + b*x^n), x, 2, (a*x^(2*n))/(2*n) + (b*x^(3*n))/(3*n)]
    @test_int [x^(1*n - 1)*(a + b*x^n), x, 2, (a*x^n)/n + (b*x^(2*n))/(2*n)]
    @test_int [x^(0*n - 1)*(a + b*x^n), x, 2, (b*x^n)/n + a*log(x)]
    @test_int [x^(-1*n - 1)*(a + b*x^n), x, 2, -(a/(x^n*n)) + b*log(x)]
    @test_int [x^(-2*n - 1)*(a + b*x^n), x, 2, -(a/(x^(2*n)*(2*n))) - b/(x^n*n)]
    @test_int [x^(-3*n - 1)*(a + b*x^n), x, 2, -(a/(x^(3*n)*(3*n))) - b/(x^(2*n)*(2*n))]
    @test_int [x^(-4*n - 1)*(a + b*x^n), x, 2, -(a/(x^(4*n)*(4*n))) - b/(x^(3*n)*(3*n))]
    @test_int [x^(-5*n - 1)*(a + b*x^n), x, 2, -(a/(x^(5*n)*(5*n))) - b/(x^(4*n)*(4*n))]

    @test_int [x^(4*n - 1)*(a + b*x^n)^2, x, 3, (a^2*x^(4*n))/(4*n) + (2*a*b*x^(5*n))/(5*n) + (b^2*x^(6*n))/(6*n)]
    @test_int [x^(3*n - 1)*(a + b*x^n)^2, x, 3, (a^2*x^(3*n))/(3*n) + (a*b*x^(4*n))/(2*n) + (b^2*x^(5*n))/(5*n)]
    @test_int [x^(2*n - 1)*(a + b*x^n)^2, x, 3, (a^2*x^(2*n))/(2*n) + (2*a*b*x^(3*n))/(3*n) + (b^2*x^(4*n))/(4*n)]
    @test_int [x^(1*n - 1)*(a + b*x^n)^2, x, 1, (a + b*x^n)^3/(3*b*n)]
    @test_int [x^(0*n - 1)*(a + b*x^n)^2, x, 3, (2*a*b*x^n)/n + (b^2*x^(2*n))/(2*n) + a^2*log(x)]
    @test_int [x^(-1*n - 1)*(a + b*x^n)^2, x, 3, -(a^2/(x^n*n)) + (b^2*x^n)/n + 2*a*b*log(x)]
    @test_int [x^(-2*n - 1)*(a + b*x^n)^2, x, 3, -(a^2/(x^(2*n)*(2*n))) - (2*a*b)/(x^n*n) + b^2*log(x)]
    @test_int [x^(-3*n - 1)*(a + b*x^n)^2, x, 1, -((a + b*x^n)^3/(x^(3*n)*(3*a*n)))]
    @test_int [x^(-4*n - 1)*(a + b*x^n)^2, x, 3, -(a^2/(x^(4*n)*(4*n))) - (2*a*b)/(x^(3*n)*(3*n)) - b^2/(x^(2*n)*(2*n))]
    @test_int [x^(-5*n - 1)*(a + b*x^n)^2, x, 3, -(a^2/(x^(5*n)*(5*n))) - (a*b)/(x^(4*n)*(2*n)) - b^2/(x^(3*n)*(3*n))]
    @test_int [x^(-6*n - 1)*(a + b*x^n)^2, x, 3, -(a^2/(x^(6*n)*(6*n))) - (2*a*b)/(x^(5*n)*(5*n)) - b^2/(x^(4*n)*(4*n))]

    @test_int [x^(4*n - 1)*(a + b*x^n)^3, x, 3, (a^3*x^(4*n))/(4*n) + (3*a^2*b*x^(5*n))/(5*n) + (a*b^2*x^(6*n))/(2*n) + (b^3*x^(7*n))/(7*n)]
    @test_int [x^(3*n - 1)*(a + b*x^n)^3, x, 3, (a^3*x^(3*n))/(3*n) + (3*a^2*b*x^(4*n))/(4*n) + (3*a*b^2*x^(5*n))/(5*n) + (b^3*x^(6*n))/(6*n)]
    @test_int [x^(2*n - 1)*(a + b*x^n)^3, x, 3, -((a*(a + b*x^n)^4)/(4*b^2*n)) + (a + b*x^n)^5/(5*b^2*n)]
    @test_int [x^(1*n - 1)*(a + b*x^n)^3, x, 1, (a + b*x^n)^4/(4*b*n)]
    @test_int [x^(0*n - 1)*(a + b*x^n)^3, x, 3, (3*a^2*b*x^n)/n + (3*a*b^2*x^(2*n))/(2*n) + (b^3*x^(3*n))/(3*n) + a^3*log(x)]
    @test_int [x^(-1*n - 1)*(a + b*x^n)^3, x, 3, -(a^3/(x^n*n)) + (3*a*b^2*x^n)/n + (b^3*x^(2*n))/(2*n) + 3*a^2*b*log(x)]
    @test_int [x^(-2*n - 1)*(a + b*x^n)^3, x, 3, -(a^3/(x^(2*n)*(2*n))) - (3*a^2*b)/(x^n*n) + (b^3*x^n)/n + 3*a*b^2*log(x)]
    @test_int [x^(-3*n - 1)*(a + b*x^n)^3, x, 3, -(a^3/(x^(3*n)*(3*n))) - (3*a^2*b)/(x^(2*n)*(2*n)) - (3*a*b^2)/(x^n*n) + b^3*log(x)]
    @test_int [x^(-4*n - 1)*(a + b*x^n)^3, x, 1, -((a + b*x^n)^4/(x^(4*n)*(4*a*n)))]
    @test_int [x^(-5*n - 1)*(a + b*x^n)^3, x, 3, -((a + b*x^n)^4/(x^(5*n)*(5*a*n))) + (b*(a + b*x^n)^4)/(x^(4*n)*(20*a^2*n))]
    @test_int [x^(-6*n - 1)*(a + b*x^n)^3, x, 3, -(a^3/(x^(6*n)*(6*n))) - (3*a^2*b)/(x^(5*n)*(5*n)) - (3*a*b^2)/(x^(4*n)*(4*n)) - b^3/(x^(3*n)*(3*n))]
    @test_int [x^(-7*n - 1)*(a + b*x^n)^3, x, 3, -(a^3/(x^(7*n)*(7*n))) - (a^2*b)/(x^(6*n)*(2*n)) - (3*a*b^2)/(x^(5*n)*(5*n)) - b^3/(x^(4*n)*(4*n))]

    @test_int [x^(4*n - 1)*(a + b*x^n)^5, x, 3, -((a^3*(a + b*x^n)^6)/(6*b^4*n)) + (3*a^2*(a + b*x^n)^7)/(7*b^4*n) - (3*a*(a + b*x^n)^8)/(8*b^4*n) + (a + b*x^n)^9/(9*b^4*n)]
    @test_int [x^(3*n - 1)*(a + b*x^n)^5, x, 3, (a^2*(a + b*x^n)^6)/(6*b^3*n) - (2*a*(a + b*x^n)^7)/(7*b^3*n) + (a + b*x^n)^8/(8*b^3*n)]
    @test_int [x^(2*n - 1)*(a + b*x^n)^5, x, 3, -((a*(a + b*x^n)^6)/(6*b^2*n)) + (a + b*x^n)^7/(7*b^2*n)]
    @test_int [x^(1*n - 1)*(a + b*x^n)^5, x, 1, (a + b*x^n)^6/(6*b*n)]
    @test_int [x^(0*n - 1)*(a + b*x^n)^5, x, 3, (5*a^4*b*x^n)/n + (5*a^3*b^2*x^(2*n))/n + (10*a^2*b^3*x^(3*n))/(3*n) + (5*a*b^4*x^(4*n))/(4*n) + (b^5*x^(5*n))/(5*n) + a^5*log(x)]
    @test_int [x^(-1*n - 1)*(a + b*x^n)^5, x, 3, -(a^5/(x^n*n)) + (10*a^3*b^2*x^n)/n + (5*a^2*b^3*x^(2*n))/n + (5*a*b^4*x^(3*n))/(3*n) + (b^5*x^(4*n))/(4*n) + 5*a^4*b*log(x)]
    @test_int [x^(-2*n - 1)*(a + b*x^n)^5, x, 3, -(a^5/(x^(2*n)*(2*n))) - (5*a^4*b)/(x^n*n) + (10*a^2*b^3*x^n)/n + (5*a*b^4*x^(2*n))/(2*n) + (b^5*x^(3*n))/(3*n) + 10*a^3*b^2*log(x)]
    @test_int [x^(-3*n - 1)*(a + b*x^n)^5, x, 3, -(a^5/(x^(3*n)*(3*n))) - (5*a^4*b)/(x^(2*n)*(2*n)) - (10*a^3*b^2)/(x^n*n) + (5*a*b^4*x^n)/n + (b^5*x^(2*n))/(2*n) + 10*a^2*b^3*log(x)]
    @test_int [x^(-4*n - 1)*(a + b*x^n)^5, x, 3, -(a^5/(x^(4*n)*(4*n))) - (5*a^4*b)/(x^(3*n)*(3*n)) - (5*a^3*b^2)/(x^(2*n)*n) - (10*a^2*b^3)/(x^n*n) + (b^5*x^n)/n + 5*a*b^4*log(x)]
    @test_int [x^(-5*n - 1)*(a + b*x^n)^5, x, 3, -(a^5/(x^(5*n)*(5*n))) - (5*a^4*b)/(x^(4*n)*(4*n)) - (10*a^3*b^2)/(x^(3*n)*(3*n)) - (5*a^2*b^3)/(x^(2*n)*n) - (5*a*b^4)/(x^n*n) + b^5*log(x)]
    @test_int [x^(-6*n - 1)*(a + b*x^n)^5, x, 1, -((a + b*x^n)^6/(x^(6*n)*(6*a*n)))]
    @test_int [x^(-7*n - 1)*(a + b*x^n)^5, x, 3, -((a + b*x^n)^6/(x^(7*n)*(7*a*n))) + (b*(a + b*x^n)^6)/(x^(6*n)*(42*a^2*n))]
    @test_int [x^(-8*n - 1)*(a + b*x^n)^5, x, 4, -((a + b*x^n)^6/(x^(8*n)*(8*a*n))) + (b*(a + b*x^n)^6)/(x^(7*n)*(28*a^2*n)) - (b^2*(a + b*x^n)^6)/(x^(6*n)*(168*a^3*n))]
    @test_int [x^(-9*n - 1)*(a + b*x^n)^5, x, 3, -(a^5/(x^(9*n)*(9*n))) - (5*a^4*b)/(x^(8*n)*(8*n)) - (10*a^3*b^2)/(x^(7*n)*(7*n)) - (5*a^2*b^3)/(x^(6*n)*(3*n)) - (a*b^4)/(x^(5*n)*n) - b^5/(x^(4*n)*(4*n))]
    @test_int [x^(-10*n - 1)*(a + b*x^n)^5, x, 3, -(a^5/(x^(10*n)*(10*n))) - (5*a^4*b)/(x^(9*n)*(9*n)) - (5*a^3*b^2)/(x^(8*n)*(4*n)) - (10*a^2*b^3)/(x^(7*n)*(7*n)) - (5*a*b^4)/(x^(6*n)*(6*n)) - b^5/(x^(5*n)*(5*n))]

    @test_int [x^(9*n - 1)*(a + b*x^n)^8, x, 3, (a^8*x^(9*n))/(9*n) + (4*a^7*b*x^(10*n))/(5*n) + (28*a^6*b^2*x^(11*n))/(11*n) + (14*a^5*b^3*x^(12*n))/(3*n) + (70*a^4*b^4*x^(13*n))/(13*n) + (4*a^3*b^5*x^(14*n))/n + (28*a^2*b^6*x^(15*n))/(15*n) + (a*b^7*x^(16*n))/(2*n) + (b^8*x^(17*n))/(17*n)]
    @test_int [x^(8*n - 1)*(a + b*x^n)^8, x, 3, (a^8*x^(8*n))/(8*n) + (8*a^7*b*x^(9*n))/(9*n) + (14*a^6*b^2*x^(10*n))/(5*n) + (56*a^5*b^3*x^(11*n))/(11*n) + (35*a^4*b^4*x^(12*n))/(6*n) + (56*a^3*b^5*x^(13*n))/(13*n) + (2*a^2*b^6*x^(14*n))/n + (8*a*b^7*x^(15*n))/(15*n) + (b^8*x^(16*n))/(16*n)]
    @test_int [x^(7*n - 1)*(a + b*x^n)^8, x, 3, (a^6*(a + b*x^n)^9)/(9*b^7*n) - (3*a^5*(a + b*x^n)^10)/(5*b^7*n) + (15*a^4*(a + b*x^n)^11)/(11*b^7*n) - (5*a^3*(a + b*x^n)^12)/(3*b^7*n) + (15*a^2*(a + b*x^n)^13)/(13*b^7*n) - (3*a*(a + b*x^n)^14)/(7*b^7*n) + (a + b*x^n)^15/(15*b^7*n)]
    @test_int [x^(6*n - 1)*(a + b*x^n)^8, x, 3, -((a^5*(a + b*x^n)^9)/(9*b^6*n)) + (a^4*(a + b*x^n)^10)/(2*b^6*n) - (10*a^3*(a + b*x^n)^11)/(11*b^6*n) + (5*a^2*(a + b*x^n)^12)/(6*b^6*n) - (5*a*(a + b*x^n)^13)/(13*b^6*n) + (a + b*x^n)^14/(14*b^6*n)]
    @test_int [x^(5*n - 1)*(a + b*x^n)^8, x, 3, (a^4*(a + b*x^n)^9)/(9*b^5*n) - (2*a^3*(a + b*x^n)^10)/(5*b^5*n) + (6*a^2*(a + b*x^n)^11)/(11*b^5*n) - (a*(a + b*x^n)^12)/(3*b^5*n) + (a + b*x^n)^13/(13*b^5*n)]
    @test_int [x^(4*n - 1)*(a + b*x^n)^8, x, 3, -((a^3*(a + b*x^n)^9)/(9*b^4*n)) + (3*a^2*(a + b*x^n)^10)/(10*b^4*n) - (3*a*(a + b*x^n)^11)/(11*b^4*n) + (a + b*x^n)^12/(12*b^4*n)]
    @test_int [x^(3*n - 1)*(a + b*x^n)^8, x, 3, (a^2*(a + b*x^n)^9)/(9*b^3*n) - (a*(a + b*x^n)^10)/(5*b^3*n) + (a + b*x^n)^11/(11*b^3*n)]
    @test_int [x^(2*n - 1)*(a + b*x^n)^8, x, 3, -((a*(a + b*x^n)^9)/(9*b^2*n)) + (a + b*x^n)^10/(10*b^2*n)]
    @test_int [x^(1*n - 1)*(a + b*x^n)^8, x, 1, (a + b*x^n)^9/(9*b*n)]
    @test_int [x^(0*n - 1)*(a + b*x^n)^8, x, 3, (8*a^7*b*x^n)/n + (14*a^6*b^2*x^(2*n))/n + (56*a^5*b^3*x^(3*n))/(3*n) + (35*a^4*b^4*x^(4*n))/(2*n) + (56*a^3*b^5*x^(5*n))/(5*n) + (14*a^2*b^6*x^(6*n))/(3*n) + (8*a*b^7*x^(7*n))/(7*n) + (b^8*x^(8*n))/(8*n) + a^8*log(x)]
    @test_int [x^(-1*n - 1)*(a + b*x^n)^8, x, 3, -(a^8/(x^n*n)) + (28*a^6*b^2*x^n)/n + (28*a^5*b^3*x^(2*n))/n + (70*a^4*b^4*x^(3*n))/(3*n) + (14*a^3*b^5*x^(4*n))/n + (28*a^2*b^6*x^(5*n))/(5*n) + (4*a*b^7*x^(6*n))/(3*n) + (b^8*x^(7*n))/(7*n) + 8*a^7*b*log(x)]
    @test_int [x^(-2*n - 1)*(a + b*x^n)^8, x, 3, -(a^8/(x^(2*n)*(2*n))) - (8*a^7*b)/(x^n*n) + (56*a^5*b^3*x^n)/n + (35*a^4*b^4*x^(2*n))/n + (56*a^3*b^5*x^(3*n))/(3*n) + (7*a^2*b^6*x^(4*n))/n + (8*a*b^7*x^(5*n))/(5*n) + (b^8*x^(6*n))/(6*n) + 28*a^6*b^2*log(x)]
    @test_int [x^(-3*n - 1)*(a + b*x^n)^8, x, 3, -(a^8/(x^(3*n)*(3*n))) - (4*a^7*b)/(x^(2*n)*n) - (28*a^6*b^2)/(x^n*n) + (70*a^4*b^4*x^n)/n + (28*a^3*b^5*x^(2*n))/n + (28*a^2*b^6*x^(3*n))/(3*n) + (2*a*b^7*x^(4*n))/n + (b^8*x^(5*n))/(5*n) + 56*a^5*b^3*log(x)]
    @test_int [x^(-4*n - 1)*(a + b*x^n)^8, x, 3, -(a^8/(x^(4*n)*(4*n))) - (8*a^7*b)/(x^(3*n)*(3*n)) - (14*a^6*b^2)/(x^(2*n)*n) - (56*a^5*b^3)/(x^n*n) + (56*a^3*b^5*x^n)/n + (14*a^2*b^6*x^(2*n))/n + (8*a*b^7*x^(3*n))/(3*n) + (b^8*x^(4*n))/(4*n) + 70*a^4*b^4*log(x)]
    @test_int [x^(-5*n - 1)*(a + b*x^n)^8, x, 3, -(a^8/(x^(5*n)*(5*n))) - (2*a^7*b)/(x^(4*n)*n) - (28*a^6*b^2)/(x^(3*n)*(3*n)) - (28*a^5*b^3)/(x^(2*n)*n) - (70*a^4*b^4)/(x^n*n) + (28*a^2*b^6*x^n)/n + (4*a*b^7*x^(2*n))/n + (b^8*x^(3*n))/(3*n) + 56*a^3*b^5*log(x)]
    @test_int [x^(-6*n - 1)*(a + b*x^n)^8, x, 3, -(a^8/(x^(6*n)*(6*n))) - (8*a^7*b)/(x^(5*n)*(5*n)) - (7*a^6*b^2)/(x^(4*n)*n) - (56*a^5*b^3)/(x^(3*n)*(3*n)) - (35*a^4*b^4)/(x^(2*n)*n) - (56*a^3*b^5)/(x^n*n) + (8*a*b^7*x^n)/n + (b^8*x^(2*n))/(2*n) + 28*a^2*b^6*log(x)]
    @test_int [x^(-7*n - 1)*(a + b*x^n)^8, x, 3, -(a^8/(x^(7*n)*(7*n))) - (4*a^7*b)/(x^(6*n)*(3*n)) - (28*a^6*b^2)/(x^(5*n)*(5*n)) - (14*a^5*b^3)/(x^(4*n)*n) - (70*a^4*b^4)/(x^(3*n)*(3*n)) - (28*a^3*b^5)/(x^(2*n)*n) - (28*a^2*b^6)/(x^n*n) + (b^8*x^n)/n + 8*a*b^7*log(x)]
    @test_int [x^(-8*n - 1)*(a + b*x^n)^8, x, 3, -(a^8/(x^(8*n)*(8*n))) - (8*a^7*b)/(x^(7*n)*(7*n)) - (14*a^6*b^2)/(x^(6*n)*(3*n)) - (56*a^5*b^3)/(x^(5*n)*(5*n)) - (35*a^4*b^4)/(x^(4*n)*(2*n)) - (56*a^3*b^5)/(x^(3*n)*(3*n)) - (14*a^2*b^6)/(x^(2*n)*n) - (8*a*b^7)/(x^n*n) + b^8*log(x)]
    @test_int [x^(-9*n - 1)*(a + b*x^n)^8, x, 1, -((a + b*x^n)^9/(x^(9*n)*(9*a*n)))]
    @test_int [x^(-10*n - 1)*(a + b*x^n)^8, x, 3, -((a + b*x^n)^9/(x^(10*n)*(10*a*n))) + (b*(a + b*x^n)^9)/(x^(9*n)*(90*a^2*n))]
    @test_int [x^(-11*n - 1)*(a + b*x^n)^8, x, 4, -((a + b*x^n)^9/(x^(11*n)*(11*a*n))) + (b*(a + b*x^n)^9)/(x^(10*n)*(55*a^2*n)) - (b^2*(a + b*x^n)^9)/(x^(9*n)*(495*a^3*n))]
    @test_int [x^(-12*n - 1)*(a + b*x^n)^8, x, 5, -((a + b*x^n)^9/(x^(12*n)*(12*a*n))) + (b*(a + b*x^n)^9)/(x^(11*n)*(44*a^2*n)) - (b^2*(a + b*x^n)^9)/(x^(10*n)*(220*a^3*n)) + (b^3*(a + b*x^n)^9)/(x^(9*n)*(1980*a^4*n))]
    @test_int [x^(-13*n - 1)*(a + b*x^n)^8, x, 6, -((a + b*x^n)^9/(x^(13*n)*(13*a*n))) + (b*(a + b*x^n)^9)/(x^(12*n)*(39*a^2*n)) - (b^2*(a + b*x^n)^9)/(x^(11*n)*(143*a^3*n)) + (b^3*(a + b*x^n)^9)/(x^(10*n)*(715*a^4*n)) - (b^4*(a + b*x^n)^9)/(x^(9*n)*(6435*a^5*n))]
    @test_int [x^(-14*n - 1)*(a + b*x^n)^8, x, 3, -(a^8/(x^(14*n)*(14*n))) - (8*a^7*b)/(x^(13*n)*(13*n)) - (7*a^6*b^2)/(x^(12*n)*(3*n)) - (56*a^5*b^3)/(x^(11*n)*(11*n)) - (7*a^4*b^4)/(x^(10*n)*n) - (56*a^3*b^5)/(x^(9*n)*(9*n)) - (7*a^2*b^6)/(x^(8*n)*(2*n)) - (8*a*b^7)/(x^(7*n)*(7*n)) - b^8/(x^(6*n)*(6*n))]
    @test_int [x^(-15*n - 1)*(a + b*x^n)^8, x, 3, -(a^8/(x^(15*n)*(15*n))) - (4*a^7*b)/(x^(14*n)*(7*n)) - (28*a^6*b^2)/(x^(13*n)*(13*n)) - (14*a^5*b^3)/(x^(12*n)*(3*n)) - (70*a^4*b^4)/(x^(11*n)*(11*n)) - (28*a^3*b^5)/(x^(10*n)*(5*n)) - (28*a^2*b^6)/(x^(9*n)*(9*n)) - (a*b^7)/(x^(8*n)*n) - b^8/(x^(7*n)*(7*n))]

    @test_int [x^(n - 1)*(a + b*x^n)^16, x, 1, (a + b*x^n)^17/(17*b*n)]

    @test_int [x^12*(a + b*x^13)^12, x, 1, (a + b*x^13)^13/(169*b)]
    @test_int [x^24*(a + b*x^25)^12, x, 1, (a + b*x^25)^13/(325*b)]
    @test_int [x^36*(a + b*x^37)^12, x, 1, (a + b*x^37)^13/(481*b)]
    @test_int [x^(12*m)*(a + b*x^(12*m + 1))^12, x, 1, (a + b*x^(1 + 12*m))^13/(13*b*(1 + 12*m))]

    #= Need*to*detect*that*degree*of*nomomial*simplifies*to*12*m*so*integrand*is*not*be*expanded! =#
    @test_int [x^(12 + 12*(m - 1))*(a + b*x^(12*m + 1))^12, x, 1, (a + b*x^(1 + 12*m))^13/(13*b*(1 + 12*m))]

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [x^(5*n - 1)/(a + b*x^n), x, 3, -((a^3*x^n)/(b^4*n)) + (a^2*x^(2*n))/(2*b^3*n) - (a*x^(3*n))/(3*b^2*n) + x^(4*n)/(4*b*n) + (a^4*log(a + b*x^n))/(b^5*n)]
    @test_int [x^(4*n - 1)/(a + b*x^n), x, 3, (a^2*x^n)/(b^3*n) - (a*x^(2*n))/(2*b^2*n) + x^(3*n)/(3*b*n) - (a^3*log(a + b*x^n))/(b^4*n)]
    @test_int [x^(3*n - 1)/(a + b*x^n), x, 3, -((a*x^n)/(b^2*n)) + x^(2*n)/(2*b*n) + (a^2*log(a + b*x^n))/(b^3*n)]
    @test_int [x^(2*n - 1)/(a + b*x^n), x, 3, x^n/(b*n) - (a*log(a + b*x^n))/(b^2*n)]
    @test_int [x^(1*n - 1)/(a + b*x^n), x, 1, log(a + b*x^n)/(b*n)]
    @test_int [x^(0*n - 1)/(a + b*x^n), x, 4, log(x)/a - log(a + b*x^n)/(a*n)]
    @test_int [x^(-1*n - 1)/(a + b*x^n), x, 3, -(1/(x^n*(a*n))) - (b*log(x))/a^2 + (b*log(a + b*x^n))/(a^2*n)]
    @test_int [x^(-2*n - 1)/(a + b*x^n), x, 3, -(1/(x^(2*n)*(2*a*n))) + b/(x^n*(a^2*n)) + (b^2*log(x))/a^3 - (b^2*log(a + b*x^n))/(a^3*n)]
    @test_int [x^(-3*n - 1)/(a + b*x^n), x, 3, -(1/(x^(3*n)*(3*a*n))) + b/(x^(2*n)*(2*a^2*n)) - b^2/(x^n*(a^3*n)) - (b^3*log(x))/a^4 + (b^3*log(a + b*x^n))/(a^4*n)]

    #= Note: Requires*simplification*of*the*exponent*of*the*monomial. =#
    @test_int [x^(5*(n - 1) + 4)/(a + b*x^n), x, 3, -((a^3*x^n)/(b^4*n)) + (a^2*x^(2*n))/(2*b^3*n) - (a*x^(3*n))/(3*b^2*n) + x^(4*n)/(4*b*n) + (a^4*log(a + b*x^n))/(b^5*n)]
    @test_int [x^(4*(n - 1) + 3)/(a + b*x^n), x, 3, (a^2*x^n)/(b^3*n) - (a*x^(2*n))/(2*b^2*n) + x^(3*n)/(3*b*n) - (a^3*log(a + b*x^n))/(b^4*n)]
    @test_int [x^(3*(n - 1) + 2)/(a + b*x^n), x, 3, -((a*x^n)/(b^2*n)) + x^(2*n)/(2*b*n) + (a^2*log(a + b*x^n))/(b^3*n)]
    @test_int [x^(2*(n - 1) + 1)/(a + b*x^n), x, 3, x^n/(b*n) - (a*log(a + b*x^n))/(b^2*n)]
    @test_int [x^(1*(n - 1) + 0)/(a + b*x^n), x, 1, log(a + b*x^n)/(b*n)]
    @test_int [x^(0*(n - 1) - 1)/(a + b*x^n), x, 4, log(x)/a - log(a + b*x^n)/(a*n)]
    @test_int [x^(-1*(n - 1) - 2)/(a + b*x^n), x, 3, -(1/(x^n*(a*n))) - (b*log(x))/a^2 + (b*log(a + b*x^n))/(a^2*n)]
    @test_int [x^(-2*(n - 1) - 3)/(a + b*x^n), x, 3, -(1/(x^(2*n)*(2*a*n))) + b/(x^n*(a^2*n)) + (b^2*log(x))/a^3 - (b^2*log(a + b*x^n))/(a^3*n)]
    @test_int [x^(-3*(n - 1) - 4)/(a + b*x^n), x, 3, -(1/(x^(3*n)*(3*a*n))) + b/(x^(2*n)*(2*a^2*n)) - b^2/(x^n*(a^3*n)) - (b^3*log(x))/a^4 + (b^3*log(a + b*x^n))/(a^4*n)]

    @test_int [x^(5*n - 1)/(2 + b*x^n), x, 3, -((8*x^n)/(b^4*n)) + (2*x^(2*n))/(b^3*n) - (2*x^(3*n))/(3*b^2*n) + x^(4*n)/(4*b*n) + (16*log(2 + b*x^n))/(b^5*n)]
    @test_int [x^(4*n - 1)/(2 + b*x^n), x, 3, (4*x^n)/(b^3*n) - x^(2*n)/(b^2*n) + x^(3*n)/(3*b*n) - (8*log(2 + b*x^n))/(b^4*n)]
    @test_int [x^(3*n - 1)/(2 + b*x^n), x, 3, -((2*x^n)/(b^2*n)) + x^(2*n)/(2*b*n) + (4*log(2 + b*x^n))/(b^3*n)]
    @test_int [x^(2*n - 1)/(2 + b*x^n), x, 3, x^n/(b*n) - (2*log(2 + b*x^n))/(b^2*n)]
    @test_int [x^(1*n - 1)/(2 + b*x^n), x, 1, log(2 + b*x^n)/(b*n)]
    @test_int [x^(0*n - 1)/(2 + b*x^n), x, 4, log(x)/2 - log(2 + b*x^n)/(2*n)]
    @test_int [x^(-1*n - 1)/(2 + b*x^n), x, 3, -(1/(x^n*(2*n))) - (1/4)*b*log(x) + (b*log(2 + b*x^n))/(4*n)]
    @test_int [x^(-2*n - 1)/(2 + b*x^n), x, 3, -(1/(x^(2*n)*(4*n))) + b/(x^n*(4*n)) + (1/8)*b^2*log(x) - (b^2*log(2 + b*x^n))/(8*n)]
    @test_int [x^(-3*n - 1)/(2 + b*x^n), x, 3, -(1/(x^(3*n)*(6*n))) + b/(x^(2*n)*(8*n)) - b^2/(x^n*(8*n)) - (1/16)*b^3*log(x) + (b^3*log(2 + b*x^n))/(16*n)]

    @test_int [x^(4*n - 1)/(a + b*x^n)^2, x, 3, -((2*a*x^n)/(b^3*n)) + x^(2*n)/(2*b^2*n) + a^3/(b^4*n*(a + b*x^n)) + (3*a^2*log(a + b*x^n))/(b^4*n)]
    @test_int [x^(3*n - 1)/(a + b*x^n)^2, x, 3, x^n/(b^2*n) - a^2/(b^3*n*(a + b*x^n)) - (2*a*log(a + b*x^n))/(b^3*n)]
    @test_int [x^(2*n - 1)/(a + b*x^n)^2, x, 3, a/(b^2*n*(a + b*x^n)) + log(a + b*x^n)/(b^2*n)]
    @test_int [x^(1*n - 1)/(a + b*x^n)^2, x, 1, -(1/(b*n*(a + b*x^n)))]
    @test_int [x^(0*n - 1)/(a + b*x^n)^2, x, 3, 1/(a*n*(a + b*x^n)) + log(x)/a^2 - log(a + b*x^n)/(a^2*n)]
    @test_int [x^(-1*n - 1)/(a + b*x^n)^2, x, 3, -(1/(x^n*(a^2*n))) - b/(a^2*n*(a + b*x^n)) - (2*b*log(x))/a^3 + (2*b*log(a + b*x^n))/(a^3*n)]
    @test_int [x^(-2*n - 1)/(a + b*x^n)^2, x, 3, -(1/(x^(2*n)*(2*a^2*n))) + (2*b)/(x^n*(a^3*n)) + b^2/(a^3*n*(a + b*x^n)) + (3*b^2*log(x))/a^4 - (3*b^2*log(a + b*x^n))/(a^4*n)]
    @test_int [x^(-3*n - 1)/(a + b*x^n)^2, x, 3, -(1/(x^(3*n)*(3*a^2*n))) + b/(x^(2*n)*(a^3*n)) - (3*b^2)/(x^n*(a^4*n)) - b^3/(a^4*n*(a + b*x^n)) - (4*b^3*log(x))/a^5 + (4*b^3*log(a + b*x^n))/(a^5*n)]

    @test_int [x^(4*n - 1)/(a + b*x^n)^3, x, 3, x^n/(b^3*n) + a^3/(2*b^4*n*(a + b*x^n)^2) - (3*a^2)/(b^4*n*(a + b*x^n)) - (3*a*log(a + b*x^n))/(b^4*n)]
    @test_int [x^(3*n - 1)/(a + b*x^n)^3, x, 3, -(a^2/(2*b^3*n*(a + b*x^n)^2)) + (2*a)/(b^3*n*(a + b*x^n)) + log(a + b*x^n)/(b^3*n)]
    @test_int [x^(2*n - 1)/(a + b*x^n)^3, x, 1, x^(2*n)/(2*a*n*(a + b*x^n)^2)]
    @test_int [x^(1*n - 1)/(a + b*x^n)^3, x, 1, -(1/(2*b*n*(a + b*x^n)^2))]
    @test_int [x^(0*n - 1)/(a + b*x^n)^3, x, 3, 1/(2*a*n*(a + b*x^n)^2) + 1/(a^2*n*(a + b*x^n)) + log(x)/a^3 - log(a + b*x^n)/(a^3*n)]
    @test_int [x^(-1*n - 1)/(a + b*x^n)^3, x, 3, -(1/(x^n*(a^3*n))) - b/(2*a^2*n*(a + b*x^n)^2) - (2*b)/(a^3*n*(a + b*x^n)) - (3*b*log(x))/a^4 + (3*b*log(a + b*x^n))/(a^4*n)]
    @test_int [x^(-2*n - 1)/(a + b*x^n)^3, x, 3, -(1/(x^(2*n)*(2*a^3*n))) + (3*b)/(x^n*(a^4*n)) + b^2/(2*a^3*n*(a + b*x^n)^2) + (3*b^2)/(a^4*n*(a + b*x^n)) + (6*b^2*log(x))/a^5 - (6*b^2*log(a + b*x^n))/(a^5*n)]

    @test_int [x^(-1 - 1*n/2)/(a + b*x^n), x, 4, -(2/(x^(n/2)*(a*n))) + (2*sqrt(b)*atan(sqrt(a)/(x^(n/2)*sqrt(b))))/(a^(3/2)*n)]
    @test_int [x^(-1 - 2*n/3)/(a + b*x^n), x, 8, -(3/(x^((2*n)/3)*(2*a*n))) + (sqrt(3)*b^(2/3)*atan((a^(1/3) - 2*b^(1/3)*x^(n/3))/(sqrt(3)*a^(1/3))))/(a^(5/3)*n) - (b^(2/3)*log(a^(1/3) + b^(1/3)*x^(n/3)))/(a^(5/3)*n) + (b^(2/3)*log(a^(2/3) - a^(1/3)*b^(1/3)*x^(n/3) + b^(2/3)*x^((2*n)/3)))/(2*a^(5/3)*n)]
    @test_int [x^(-1 - 3*n/4)/(a + b*x^n), x, 11, -(4/(x^((3*n)/4)*(3*a*n))) + (sqrt(2)*b^(3/4)*atan(1 - (sqrt(2)*b^(1/4)*x^(n/4))/a^(1/4)))/(a^(7/4)*n) - (sqrt(2)*b^(3/4)*atan(1 + (sqrt(2)*b^(1/4)*x^(n/4))/a^(1/4)))/(a^(7/4)*n) + (b^(3/4)*log(sqrt(a) - sqrt(2)*a^(1/4)*b^(1/4)*x^(n/4) + sqrt(b)*x^(n/2)))/(sqrt(2)*a^(7/4)*n) - (b^(3/4)*log(sqrt(a) + sqrt(2)*a^(1/4)*b^(1/4)*x^(n/4) + sqrt(b)*x^(n/2)))/(sqrt(2)*a^(7/4)*n)]

    @test_int [x^(-1 - n/1)/(a + b*x^n), x, 3, -(1/(x^n*(a*n))) - (b*log(x))/a^2 + (b*log(a + b*x^n))/(a^2*n)]
    @test_int [x^(-1 - n/2)/(a + b*x^n), x, 4, -(2/(x^(n/2)*(a*n))) + (2*sqrt(b)*atan(sqrt(a)/(x^(n/2)*sqrt(b))))/(a^(3/2)*n)]
    @test_int [x^(-1 - n/3)/(a + b*x^n), x, 9, -(3/(x^(n/3)*(a*n))) - (sqrt(3)*b^(1/3)*atan((b^(1/3) - (2*a^(1/3))/x^(n/3))/(sqrt(3)*b^(1/3))))/(a^(4/3)*n) + (b^(1/3)*log(b^(1/3) + a^(1/3)/x^(n/3)))/(a^(4/3)*n) - (b^(1/3)*log(b^(2/3) + a^(2/3)/x^((2*n)/3) - (a^(1/3)*b^(1/3))/x^(n/3)))/(2*a^(4/3)*n)]
    @test_int [x^(-1 - n/4)/(a + b*x^n), x, 12, -(4/(x^(n/4)*(a*n))) - (sqrt(2)*b^(1/4)*atan(1 - (sqrt(2)*a^(1/4))/(x^(n/4)*b^(1/4))))/(a^(5/4)*n) + (sqrt(2)*b^(1/4)*atan(1 + (sqrt(2)*a^(1/4))/(x^(n/4)*b^(1/4))))/(a^(5/4)*n) - (b^(1/4)*log(sqrt(b) + sqrt(a)/x^(n/2) - (sqrt(2)*a^(1/4)*b^(1/4))/x^(n/4)))/(sqrt(2)*a^(5/4)*n) + (b^(1/4)*log(sqrt(b) + sqrt(a)/x^(n/2) + (sqrt(2)*a^(1/4)*b^(1/4))/x^(n/4)))/(sqrt(2)*a^(5/4)*n)]

    @test_int [x^(-1 - 3*n/2)/(a + b*x^n), x, 5, -(2/(x^((3*n)/2)*(3*a*n))) + (2*b)/(x^(n/2)*(a^2*n)) - (2*b^(3/2)*atan(sqrt(a)/(x^(n/2)*sqrt(b))))/(a^(5/2)*n)]
    @test_int [x^(-1 - 4*n/3)/(a + b*x^n), x, 10, If(13>=8, -(3/(x^((4*n)/3)*(4*a*n))) + (3*b)/(x^(n/3)*(a^2*n)) + (sqrt(3)*b^(4/3)*atan((b^(1/3) - (2*a^(1/3))/x^(n/3))/(sqrt(3)*b^(1/3))))/(a^(7/3)*n) - (b^(4/3)*log(b^(1/3) + a^(1/3)/x^(n/3)))/(a^(7/3)*n) + (b^(4/3)*log(b^(2/3) + a^(2/3)/x^((2*n)/3) - (a^(1/3)*b^(1/3))/x^(n/3)))/(2*a^(7/3)*n), -(3/(x^((4*n)/3)*(4*a*n))) + (3*b)/(x^(n/3)*(a^2*n)) + (sqrt(3)*b^(4/3)*atan((1 - (2*a^(1/3))/(x^(n/3)*b^(1/3)))/sqrt(3)))/(a^(7/3)*n) - (b^(4/3)*log(b^(1/3) + a^(1/3)/x^(n/3)))/(a^(7/3)*n) + (b^(4/3)*log(b^(2/3) + a^(2/3)/x^((2*n)/3) - (a^(1/3)*b^(1/3))/x^(n/3)))/(2*a^(7/3)*n))]
    @test_int [x^(-1 - 5*n/4)/(a + b*x^n), x, 13, -(4/(x^((5*n)/4)*(5*a*n))) + (4*b)/(x^(n/4)*(a^2*n)) + (sqrt(2)*b^(5/4)*atan(1 - (sqrt(2)*a^(1/4))/(x^(n/4)*b^(1/4))))/(a^(9/4)*n) - (sqrt(2)*b^(5/4)*atan(1 + (sqrt(2)*a^(1/4))/(x^(n/4)*b^(1/4))))/(a^(9/4)*n) + (b^(5/4)*log(sqrt(b) + sqrt(a)/x^(n/2) - (sqrt(2)*a^(1/4)*b^(1/4))/x^(n/4)))/(sqrt(2)*a^(9/4)*n) - (b^(5/4)*log(sqrt(b) + sqrt(a)/x^(n/2) + (sqrt(2)*a^(1/4)*b^(1/4))/x^(n/4)))/(sqrt(2)*a^(9/4)*n)]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^(k*n-1)*(a+b*x^n)^(p/2)=#

    #= ::Subsubsection::Closed:: =#
    #=p>0=#

    @test_int [x^(4*n - 1)*(a + b*x^n)^(1/2), x, 3, -((2*a^3*(a + b*x^n)^(3/2))/(3*b^4*n)) + (6*a^2*(a + b*x^n)^(5/2))/(5*b^4*n) - (6*a*(a + b*x^n)^(7/2))/(7*b^4*n) + (2*(a + b*x^n)^(9/2))/(9*b^4*n)]
    @test_int [x^(3*n - 1)*(a + b*x^n)^(1/2), x, 3, (2*a^2*(a + b*x^n)^(3/2))/(3*b^3*n) - (4*a*(a + b*x^n)^(5/2))/(5*b^3*n) + (2*(a + b*x^n)^(7/2))/(7*b^3*n)]
    @test_int [x^(2*n - 1)*(a + b*x^n)^(1/2), x, 3, -((2*a*(a + b*x^n)^(3/2))/(3*b^2*n)) + (2*(a + b*x^n)^(5/2))/(5*b^2*n)]
    @test_int [x^(1*n - 1)*(a + b*x^n)^(1/2), x, 1, (2*(a + b*x^n)^(3/2))/(3*b*n)]
    @test_int [x^(0*n - 1)*(a + b*x^n)^(1/2), x, 4, (2*sqrt(a + b*x^n))/n - (2*sqrt(a)*atanh(sqrt(a + b*x^n)/sqrt(a)))/n]
    @test_int [x^(-1*n - 1)*(a + b*x^n)^(1/2), x, 4, -(sqrt(a + b*x^n)/(x^n*n)) - (b*atanh(sqrt(a + b*x^n)/sqrt(a)))/(sqrt(a)*n)]
    @test_int [x^(-2*n - 1)*(a + b*x^n)^(1/2), x, 5, -(sqrt(a + b*x^n)/(x^(2*n)*(2*n))) - (b*sqrt(a + b*x^n))/(x^n*(4*a*n)) + (b^2*atanh(sqrt(a + b*x^n)/sqrt(a)))/(4*a^(3/2)*n)]
    @test_int [x^(-3*n - 1)*(a + b*x^n)^(1/2), x, 6, -(sqrt(a + b*x^n)/(x^(3*n)*(3*n))) - (b*sqrt(a + b*x^n))/(x^(2*n)*(12*a*n)) + (b^2*sqrt(a + b*x^n))/(x^n*(8*a^2*n)) - (b^3*atanh(sqrt(a + b*x^n)/sqrt(a)))/(8*a^(5/2)*n)]
    @test_int [x^(-4*n - 1)*(a + b*x^n)^(1/2), x, 7, -(sqrt(a + b*x^n)/(x^(4*n)*(4*n))) - (b*sqrt(a + b*x^n))/(x^(3*n)*(24*a*n)) + (5*b^2*sqrt(a + b*x^n))/(x^(2*n)*(96*a^2*n)) - (5*b^3*sqrt(a + b*x^n))/(x^n*(64*a^3*n)) + (5*b^4*atanh(sqrt(a + b*x^n)/sqrt(a)))/(64*a^(7/2)*n)]

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [x^(4*n - 1)/(a + b*x^n)^(1/2), x, 3, -((2*a^3*sqrt(a + b*x^n))/(b^4*n)) + (2*a^2*(a + b*x^n)^(3/2))/(b^4*n) - (6*a*(a + b*x^n)^(5/2))/(5*b^4*n) + (2*(a + b*x^n)^(7/2))/(7*b^4*n)]
    @test_int [x^(3*n - 1)/(a + b*x^n)^(1/2), x, 3, (2*a^2*sqrt(a + b*x^n))/(b^3*n) - (4*a*(a + b*x^n)^(3/2))/(3*b^3*n) + (2*(a + b*x^n)^(5/2))/(5*b^3*n)]
    @test_int [x^(2*n - 1)/(a + b*x^n)^(1/2), x, 3, -((2*a*sqrt(a + b*x^n))/(b^2*n)) + (2*(a + b*x^n)^(3/2))/(3*b^2*n)]
    @test_int [x^(1*n - 1)/(a + b*x^n)^(1/2), x, 1, (2*sqrt(a + b*x^n))/(b*n)]
    @test_int [x^(0*n - 1)/(a + b*x^n)^(1/2), x, 3, -((2*atanh(sqrt(a + b*x^n)/sqrt(a)))/(sqrt(a)*n))]
    @test_int [x^(-1*n - 1)/(a + b*x^n)^(1/2), x, 4, -(sqrt(a + b*x^n)/(x^n*(a*n))) + (b*atanh(sqrt(a + b*x^n)/sqrt(a)))/(a^(3/2)*n)]
    @test_int [x^(-2*n - 1)/(a + b*x^n)^(1/2), x, 5, -(sqrt(a + b*x^n)/(x^(2*n)*(2*a*n))) + (3*b*sqrt(a + b*x^n))/(x^n*(4*a^2*n)) - (3*b^2*atanh(sqrt(a + b*x^n)/sqrt(a)))/(4*a^(5/2)*n)]
    @test_int [x^(-3*n - 1)/(a + b*x^n)^(1/2), x, 6, -(sqrt(a + b*x^n)/(x^(3*n)*(3*a*n))) + (5*b*sqrt(a + b*x^n))/(x^(2*n)*(12*a^2*n)) - (5*b^2*sqrt(a + b*x^n))/(x^n*(8*a^3*n)) + (5*b^3*atanh(sqrt(a + b*x^n)/sqrt(a)))/(8*a^(7/2)*n)]
    @test_int [x^(-4*n - 1)/(a + b*x^n)^(1/2), x, 7, -(sqrt(a + b*x^n)/(x^(4*n)*(4*a*n))) + (7*b*sqrt(a + b*x^n))/(x^(3*n)*(24*a^2*n)) - (35*b^2*sqrt(a + b*x^n))/(x^(2*n)*(96*a^3*n)) + (35*b^3*sqrt(a + b*x^n))/(x^n*(64*a^4*n)) - (35*b^4*atanh(sqrt(a + b*x^n)/sqrt(a)))/(64*a^(9/2)*n)]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b*x^n)^p*with*m*symbolic=#

    @test_int [x^m*(a + b*x^n)^3, x, 2, (a^3*x^(1 + m))/(1 + m) + (3*a^2*b*x^(1 + m + n))/(1 + m + n) + (3*a*b^2*x^(1 + m + 2*n))/(1 + m + 2*n) + (b^3*x^(1 + m + 3*n))/(1 + m + 3*n)]
    @test_int [x^m*(a + b*x^n)^2, x, 2, (a^2*x^(1 + m))/(1 + m) + (2*a*b*x^(1 + m + n))/(1 + m + n) + (b^2*x^(1 + m + 2*n))/(1 + m + 2*n)]
    @test_int [x^m*(a + b*x^n)^1, x, 2, (a*x^(1 + m))/(1 + m) + (b*x^(1 + m + n))/(1 + m + n)]
    @test_int [x^m/(a + b*x^n)^1, x, 1, (x^(1 + m)*HypergeometricFunctions._₂F₁(1, (1 + m)/n, (1 + m + n)/n, -((b*x^n)/a)))/(a*(1 + m))]
    @test_int [x^m/(a + b*x^n)^2, x, 1, (x^(1 + m)*HypergeometricFunctions._₂F₁(2, (1 + m)/n, (1 + m + n)/n, -((b*x^n)/a)))/(a^2*(1 + m))]
    @test_int [x^m/(a + b*x^n)^3, x, 1, (x^(1 + m)*HypergeometricFunctions._₂F₁(3, (1 + m)/n, (1 + m + n)/n, -((b*x^n)/a)))/(a^3*(1 + m))]

    @test_int [x^m*(a + b*x^n)^(3/2), x, 2, (x^(1 + m)*(a + b*x^n)^(5/2)*HypergeometricFunctions._₂F₁(1, 5/2 + (1 + m)/n, (1 + m + n)/n, -((b*x^n)/a)))/(a*(1 + m)), (a*x^(1 + m)*sqrt(a + b*x^n)*HypergeometricFunctions._₂F₁(-(3/2), (1 + m)/n, (1 + m + n)/n, -((b*x^n)/a)))/((1 + m)*sqrt(1 + (b*x^n)/a))]
    @test_int [x^m*(a + b*x^n)^(1/2), x, 2, (x^(1 + m)*(a + b*x^n)^(3/2)*HypergeometricFunctions._₂F₁(1, 3/2 + (1 + m)/n, (1 + m + n)/n, -((b*x^n)/a)))/(a*(1 + m)), (x^(1 + m)*sqrt(a + b*x^n)*HypergeometricFunctions._₂F₁(-(1/2), (1 + m)/n, (1 + m + n)/n, -((b*x^n)/a)))/((1 + m)*sqrt(1 + (b*x^n)/a))]
    @test_int [x^m/(a + b*x^n)^(1/2), x, 2, (x^(1 + m)*sqrt(a + b*x^n)*HypergeometricFunctions._₂F₁(1, 1/2 + (1 + m)/n, (1 + m + n)/n, -((b*x^n)/a)))/(a*(1 + m)), (x^(1 + m)*sqrt(1 + (b*x^n)/a)*HypergeometricFunctions._₂F₁(1/2, (1 + m)/n, (1 + m + n)/n, -((b*x^n)/a)))/((1 + m)*sqrt(a + b*x^n))]
    @test_int [x^m/(a + b*x^n)^(3/2), x, 2, (x^(1 + m)*HypergeometricFunctions._₂F₁(1, -(1/2) + (1 + m)/n, (1 + m + n)/n, -((b*x^n)/a)))/(a*(1 + m)*sqrt(a + b*x^n)), (x^(1 + m)*sqrt(1 + (b*x^n)/a)*HypergeometricFunctions._₂F₁(3/2, (1 + m)/n, (1 + m + n)/n, -((b*x^n)/a)))/(a*(1 + m)*sqrt(a + b*x^n))]
    @test_int [x^m/(a + b*x^n)^(5/2), x, 2, (x^(1 + m)*HypergeometricFunctions._₂F₁(1, -(3/2) + (1 + m)/n, (1 + m + n)/n, -((b*x^n)/a)))/(a*(1 + m)*(a + b*x^n)^(3/2)), (x^(1 + m)*sqrt(1 + (b*x^n)/a)*HypergeometricFunctions._₂F₁(5/2, (1 + m)/n, (1 + m + n)/n, -((b*x^n)/a)))/(a^2*(1 + m)*sqrt(a + b*x^n))]

    @test_int [x^(3 + 2*n)/sqrt(a + b*x^n), x, 2, (x^(2*(2 + n))*sqrt(a + b*x^n)*HypergeometricFunctions._₂F₁(1, (1/2)*(5 + 8/n), 3 + 4/n, -((b*x^n)/a)))/(2*a*(2 + n)), (x^(2*(2 + n))*sqrt(1 + (b*x^n)/a)*HypergeometricFunctions._₂F₁(1/2, 2*(1 + 2/n), 3 + 4/n, -((b*x^n)/a)))/(2*(2 + n)*sqrt(a + b*x^n))]
    @test_int [x^(3 + n)/sqrt(a + b*x^n), x, 2, (x^(4 + n)*sqrt(a + b*x^n)*HypergeometricFunctions._₂F₁(1, (1/2)*(3 + 8/n), 2*(1 + 2/n), -((b*x^n)/a)))/(a*(4 + n)), (x^(4 + n)*sqrt(1 + (b*x^n)/a)*HypergeometricFunctions._₂F₁(1/2, (4 + n)/n, 2*(1 + 2/n), -((b*x^n)/a)))/((4 + n)*sqrt(a + b*x^n))]
    @test_int [x^(3 - n)/sqrt(a + b*x^n), x, 2, (x^(4 - n)*sqrt(a + b*x^n)*HypergeometricFunctions._₂F₁(1, (1/2)*(-1 + 8/n), 4/n, -((b*x^n)/a)))/(a*(4 - n)), (x^(4 - n)*sqrt(1 + (b*x^n)/a)*HypergeometricFunctions._₂F₁(1/2, -1 + 4/n, 4/n, -((b*x^n)/a)))/((4 - n)*sqrt(a + b*x^n))]
    @test_int [x^(3 - 2*n)/sqrt(a + b*x^n), x, 2, (x^(4 - 2*n)*sqrt(a + b*x^n)*HypergeometricFunctions._₂F₁(1, (1/2)*(-3 + 8/n), -1 + 4/n, -((b*x^n)/a)))/(2*a*(2 - n)), (x^(4 - 2*n)*sqrt(1 + (b*x^n)/a)*HypergeometricFunctions._₂F₁(1/2, -2*(1 - 2/n), -1 + 4/n, -((b*x^n)/a)))/(2*(2 - n)*sqrt(a + b*x^n))]

    @test_int [x^(m + 2*n)/sqrt(a + b*x^n), x, 2, (x^(1 + m + 2*n)*sqrt(a + b*x^n)*HypergeometricFunctions._₂F₁(1, (1/2)*(5 + (2*(1 + m))/n), (1 + m + 3*n)/n, -((b*x^n)/a)))/(a*(1 + m + 2*n)), (x^(1 + m + 2*n)*sqrt(1 + (b*x^n)/a)*HypergeometricFunctions._₂F₁(1/2, (1 + m + 2*n)/n, (1 + m + 3*n)/n, -((b*x^n)/a)))/((1 + m + 2*n)*sqrt(a + b*x^n))]
    @test_int [x^(m + n)/sqrt(a + b*x^n), x, 2, (x^(1 + m + n)*sqrt(a + b*x^n)*HypergeometricFunctions._₂F₁(1, 1/2 + (1 + m + n)/n, (1 + m + 2*n)/n, -((b*x^n)/a)))/(a*(1 + m + n)), (x^(1 + m + n)*sqrt(1 + (b*x^n)/a)*HypergeometricFunctions._₂F₁(1/2, (1 + m + n)/n, (1 + m + 2*n)/n, -((b*x^n)/a)))/((1 + m + n)*sqrt(a + b*x^n))]
    @test_int [x^(m - n)/sqrt(a + b*x^n), x, 2, (x^(1 + m - n)*sqrt(a + b*x^n)*HypergeometricFunctions._₂F₁(1, (1/2)*(-1 + (2*(1 + m))/n), (1 + m)/n, -((b*x^n)/a)))/(a*(1 + m - n)), (x^(1 + m - n)*sqrt(1 + (b*x^n)/a)*HypergeometricFunctions._₂F₁(1/2, (1 + m - n)/n, (1 + m)/n, -((b*x^n)/a)))/((1 + m - n)*sqrt(a + b*x^n))]
    @test_int [x^(m - 2*n)/sqrt(a + b*x^n), x, 2, (x^(1 + m - 2*n)*sqrt(a + b*x^n)*HypergeometricFunctions._₂F₁(1, (1/2)*(-3 + (2*(1 + m))/n), (1 + m - n)/n, -((b*x^n)/a)))/(a*(1 + m - 2*n)), (x^(1 + m - 2*n)*sqrt(1 + (b*x^n)/a)*HypergeometricFunctions._₂F₁(1/2, (1 + m - 2*n)/n, (1 + m - n)/n, -((b*x^n)/a)))/((1 + m - 2*n)*sqrt(a + b*x^n))]

    @test_int [-((b*n*x^(-1 + m + n))/(2*(a + b*x^n)^(3/2))) + (m*x^(-1 + m))/sqrt(a + b*x^n), x, -5, x^m/sqrt(a + b*x^n), -((b*x^(m + n))/(a*sqrt(a + b*x^n))) + (x^m*sqrt(a + b*x^n))/a]

    @test_int [x^(7*n/2 - 1)/sqrt(a + b*x^n), x, 5, (5*a^2*x^(n/2)*sqrt(a + b*x^n))/(8*b^3*n) - (5*a*x^((3*n)/2)*sqrt(a + b*x^n))/(12*b^2*n) + (x^((5*n)/2)*sqrt(a + b*x^n))/(3*b*n) - (5*a^3*atanh((sqrt(b)*x^(n/2))/sqrt(a + b*x^n)))/(8*b^(7/2)*n)]
    @test_int [x^(5*n/2 - 1)/sqrt(a + b*x^n), x, 4, -((3*a*x^(n/2)*sqrt(a + b*x^n))/(4*b^2*n)) + (x^((3*n)/2)*sqrt(a + b*x^n))/(2*b*n) + (3*a^2*atanh((sqrt(b)*x^(n/2))/sqrt(a + b*x^n)))/(4*b^(5/2)*n)]
    @test_int [x^(3*n/2 - 1)/sqrt(a + b*x^n), x, 3, (x^(n/2)*sqrt(a + b*x^n))/(b*n) - (a*atanh((sqrt(b)*x^(n/2))/sqrt(a + b*x^n)))/(b^(3/2)*n)]
    @test_int [x^(1*n/2 - 1)/sqrt(a + b*x^n), x, 3, (2*atanh((sqrt(b)*x^(n/2))/sqrt(a + b*x^n)))/(sqrt(b)*n)]
    @test_int [x^(-1*n/2 - 1)/sqrt(a + b*x^n), x, 1, -((2*sqrt(a + b*x^n))/(x^(n/2)*(a*n)))]
    @test_int [x^(-3*n/2 - 1)/sqrt(a + b*x^n), x, 2, -((2*sqrt(a + b*x^n))/(x^((3*n)/2)*(3*a*n))) + (4*b*sqrt(a + b*x^n))/(x^(n/2)*(3*a^2*n))]
    @test_int [x^(-5*n/2 - 1)/sqrt(a + b*x^n), x, 3, -((2*sqrt(a + b*x^n))/(x^((5*n)/2)*(5*a*n))) + (8*b*sqrt(a + b*x^n))/(x^((3*n)/2)*(15*a^2*n)) - (16*b^2*sqrt(a + b*x^n))/(x^(n/2)*(15*a^3*n))]
    @test_int [x^(-7*n/2 - 1)/sqrt(a + b*x^n), x, 4, -((2*sqrt(a + b*x^n))/(x^((7*n)/2)*(7*a*n))) + (12*b*sqrt(a + b*x^n))/(x^((5*n)/2)*(35*a^2*n)) - (16*b^2*sqrt(a + b*x^n))/(x^((3*n)/2)*(35*a^3*n)) + (32*b^3*sqrt(a + b*x^n))/(x^(n/2)*(35*a^4*n))]

    @test_int [x^m/sqrt(a + b*x^(m-2)), x, 2, (x^(1 + m)*sqrt(a + b*x^(-2 + m))*HypergeometricFunctions._₂F₁(1, -((3*m)/(2*(2 - m))), (1 - 2*m)/(2 - m), -((b*x^(-2 + m))/a)))/(a*(1 + m)), (x^(1 + m)*sqrt(1 + (b*x^(-2 + m))/a)*HypergeometricFunctions._₂F₁(1/2, -((1 + m)/(2 - m)), (1 - 2*m)/(2 - m), -((b*x^(-2 + m))/a)))/((1 + m)*sqrt(a + b*x^(-2 + m)))]
    @test_int [x^m/sqrt(a + b*x^(2-m)), x, 2, (x^(1 + m)*sqrt(a + b*x^(2 - m))*HypergeometricFunctions._₂F₁(1, (4 + m)/(2*(2 - m)), 3/(2 - m), -((b*x^(2 - m))/a)))/(a*(1 + m)), (x^(1 + m)*sqrt(1 + (b*x^(2 - m))/a)*HypergeometricFunctions._₂F₁(1/2, (1 + m)/(2 - m), 3/(2 - m), -((b*x^(2 - m))/a)))/((1 + m)*sqrt(a + b*x^(2 - m)))]

    @test_int [(6*a*x^2)/(b*(4 + m)*sqrt(a + b*x^(-2 + m))) + x^m/sqrt(a + b*x^(-2 + m)), x, -5, (2*x^3*sqrt(a + b*x^(-2 + m)))/(b*(4 + m)), (2*x^(1 + m)*(b + a*x^(2 - m)))/(b*(4 + m)*sqrt(a + b*x^(-2 + m)))]

    @test_int [(x^(-1 + m)*(2*a*m + b*(2*m - n)*x^n))/(2*(a + b*x^n)^(3/2)), x, 2, x^m/sqrt(a + b*x^n)]
    @test_int [-((b*n*x^(-1 + m + n))/(2*(a + b*x^n)^(3/2))) + (m*x^(-1 + m))/sqrt(a + b*x^n), x, -5, x^m/sqrt(a + b*x^n), -((b*x^(m + n))/(a*sqrt(a + b*x^n))) + (x^m*sqrt(a + b*x^n))/a]

    #= The*substitution*m->-1-2*n/3*transforms*the*first*integrand*into*the*second. =#
    @test_int [x^m/(a + b*x^(3*(1 + m)))^(1/3), x, 2, atan((1 + (2*b^(1/3)*x^(1 + m))/(a + b*x^(3*(1 + m)))^(1/3))/sqrt(3))/(sqrt(3)*b^(1/3)*(1 + m)) - log(b^(1/3)*x^(1 + m) - (a + b*x^(3*(1 + m)))^(1/3))/(2*b^(1/3)*(1 + m))]
    @test_int [x^m*(a + b/x^((3/2)*(1 + m)))^(2/3), x, 3, (x^(1 + m)*(a + b/x^((3/2)*(1 + m)))^(2/3))/(1 + m) - (2*b^(2/3)*atan((1 + (2*b^(1/3)*x^((1/2)*(-1 - m)))/(a + b/x^((3/2)*(1 + m)))^(1/3))/sqrt(3)))/(sqrt(3)*(1 + m)) + (b^(2/3)*log(b^(1/3)*x^((1/2)*(-1 - m)) - (a + b/x^((3/2)*(1 + m)))^(1/3)))/(1 + m), (x^(1 + m)*(a + b/x^((3/2)*(1 + m)))^(2/3))/(1 + m) - (2*b^(2/3)*atan((1 + (2*b^(1/3)*x^((1/2)*(-1 - m)))/(a + b/x^((3/2)*(1 + m)))^(1/3))/sqrt(3)))/(sqrt(3)*(1 + m)) + (b^(2/3)*log((-x^((1/2)*(-1 - m)))*(b^(1/3) - x^((1 + m)/2)*(a + b/x^((3/2)*(1 + m)))^(1/3))))/(1 + m)]

    @test_int [x^(-1 + n/3)/(a + b*x^n)^(1/3), x, 2, (sqrt(3)*atan((1 + (2*b^(1/3)*x^(n/3))/(a + b*x^n)^(1/3))/sqrt(3)))/(b^(1/3)*n) - (3*log(b^(1/3)*x^(n/3) - (a + b*x^n)^(1/3)))/(2*b^(1/3)*n)]
    @test_int [x^(-1 - (2*n)/3)*(a + b*x^n)^(2/3), x, 3, -((3*(a + b*x^n)^(2/3))/(x^((2*n)/3)*(2*n))) + (sqrt(3)*b^(2/3)*atan((1 + (2*b^(1/3)*x^(n/3))/(a + b*x^n)^(1/3))/sqrt(3)))/n - (3*b^(2/3)*log(b^(1/3)*x^(n/3) - (a + b*x^n)^(1/3)))/(2*n)]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b*x^n)^p*with*p*symbolic=#

    @test_int [x^m*(a + b*x^n)^p, x, 2, (x^(1 + m)*(a + b*x^n)^(1 + p)*HypergeometricFunctions._₂F₁(1, 1 + (1 + m)/n + p, (1 + m + n)/n, -((b*x^n)/a)))/(a*(1 + m)), (x^(1 + m)*(a + b*x^n)^p*HypergeometricFunctions._₂F₁((1 + m)/n, -p, (1 + m + n)/n, -((b*x^n)/a)))/((1 + (b*x^n)/a)^p*(1 + m))]

    @test_int [1/(a + b*x^n)^(1/n + 4), x, 4, If(13>=8, (x*(a + b*x^n)^(-3 - 1/n))/(a*(1 + 3*n)) + (3*n*x*(a + b*x^n)^(-2 - 1/n))/(a^2*(1 + 5*n + 6*n^2)) + (6*n^2*x*(a + b*x^n)^(-1 - 1/n))/(a^3*(1 + n)*(1 + 2*n)*(1 + 3*n)) + (6*n^3*x)/((a + b*x^n)^n^(-1)*(a^4*(1 + n)*(1 + 2*n)*(1 + 3*n))), (x*(a + b*x^n)^(-3 - 1/n))/(a*(1 + 3*n)) + (3*n*x*(a + b*x^n)^(-2 - 1/n))/(a^2*(1 + 5*n + 6*n^2)) + (6*n^2*x*(a + b*x^n)^(-1 - 1/n))/(a^3*(1 + 6*n + 11*n^2 + 6*n^3)) + (6*n^3*x)/((a + b*x^n)^n^(-1)*(a^4*(1 + 6*n + 11*n^2 + 6*n^3))))]
    @test_int [1/(a + b*x^n)^(1/n + 3), x, 3, If(13>=8, (x*(a + b*x^n)^(-2 - 1/n))/(a*(1 + 2*n)) + (2*n*x*(a + b*x^n)^(-1 - 1/n))/(a^2*(1 + n)*(1 + 2*n)) + (2*n^2*x)/((a + b*x^n)^n^(-1)*(a^3*(1 + n)*(1 + 2*n))), (x*(a + b*x^n)^(-2 - 1/n))/(a*(1 + 2*n)) + (2*n*x*(a + b*x^n)^(-1 - 1/n))/(a^2*(1 + 3*n + 2*n^2)) + (2*n^2*x)/((a + b*x^n)^n^(-1)*(a^3*(1 + 3*n + 2*n^2))))]
    @test_int [1/(a + b*x^n)^(1/n + 2), x, 2, (x*(a + b*x^n)^(-1 - 1/n))/(a*(1 + n)) + (n*x)/((a + b*x^n)^n^(-1)*(a^2*(1 + n)))]
    @test_int [1/(a + b*x^n)^(1/n + 1), x, 1, x/((a + b*x^n)^n^(-1)*a)]
    @test_int [1/(a + b*x^n)^(1/n + 0), x, 2, (x*(1 + (b*x^n)/a)^(1/n)*HypergeometricFunctions._₂F₁(1/n, 1/n, 1 + 1/n, -((b*x^n)/a)))/(a + b*x^n)^n^(-1)]
    @test_int [1/(a + b*x^n)^(1/n - 1), x, 2, (a*x*(1 + (b*x^n)/a)^(1/n)*HypergeometricFunctions._₂F₁(-1 + 1/n, 1/n, 1 + 1/n, -((b*x^n)/a)))/(a + b*x^n)^n^(-1)]
    @test_int [1/(a + b*x^n)^(1/n - 2), x, 2, (a^2*x*(1 + (b*x^n)/a)^(1/n)*HypergeometricFunctions._₂F₁(-2 + 1/n, 1/n, 1 + 1/n, -((b*x^n)/a)))/(a + b*x^n)^n^(-1)]

    @test_int [(b*x^n)^p*x^m, x, 2, (x^(1 + m)*(b*x^n)^p)/(1 + m + n*p)]

    @test_int [(b*x^n)^p*x^2, x, 2, (x^3*(b*x^n)^p)/(3 + n*p)]
    @test_int [(b*x^n)^p*x^1, x, 2, (x^2*(b*x^n)^p)/(2 + n*p)]
    @test_int [(b*x^n)^p*x^0, x, 2, (x*(b*x^n)^p)/(1 + n*p)]
    @test_int [(b*x^n)^p/x^1, x, 2, (b*x^n)^p/(n*p)]
    @test_int [(b*x^n)^p/x^2, x, 2, -((b*x^n)^p/((1 - n*p)*x))]
    @test_int [(b*x^n)^p/x^3, x, 2, -((b*x^n)^p/((2 - n*p)*x^2))]
    @test_int [(b*x^n)^p/x^4, x, 2, -((b*x^n)^p/((3 - n*p)*x^3))]

    @test_int [x^(n - 1)*(a + b*x^n)^p, x, 1, (a + b*x^n)^(1 + p)/(b*n*(1 + p))]
    @test_int [x^(2*n - 1)*(a + b*x^n)^p, x, 3, -((a*(a + b*x^n)^(1 + p))/(b^2*n*(1 + p))) + (a + b*x^n)^(2 + p)/(b^2*n*(2 + p))]
    @test_int [x^(3*n - 1)*(a + b*x^n)^p, x, 3, (a^2*(a + b*x^n)^(1 + p))/(b^3*n*(1 + p)) - (2*a*(a + b*x^n)^(2 + p))/(b^3*n*(2 + p)) + (a + b*x^n)^(3 + p)/(b^3*n*(3 + p))]
    @test_int [x^(4*n - 1)*(a + b*x^n)^p, x, 3, -((a^3*(a + b*x^n)^(1 + p))/(b^4*n*(1 + p))) + (3*a^2*(a + b*x^n)^(2 + p))/(b^4*n*(2 + p)) - (3*a*(a + b*x^n)^(3 + p))/(b^4*n*(3 + p)) + (a + b*x^n)^(4 + p)/(b^4*n*(4 + p))]

    #= Integrands*of*the*form*x^m*(a+b*x^n)^p*where*n*p+n+m+1=0 =#
    @test_int [(a + b*x^n)^p/x^(n*p + n + 1), x, 1, -((a + b*x^n)^(1 + p)/(x^(n*(1 + p))*(a*n*(1 + p))))]
    @test_int [(a + b*x^n)^8/x^(n*8 + n + 1), x, 1, -((a + b*x^n)^9/(x^(9*n)*(9*a*n)))]
    @test_int [(a + b*x^3)^p/x^(3*p + 3 + 1), x, 1, -((a + b*x^3)^(1 + p)/(x^(3*(1 + p))*(3*a*(1 + p))))]
    @test_int [(a + b*x^3)^8/x^(3*8 + 3 + 1), x, 1, -((a + b*x^3)^9/(27*a*x^27))]
    @test_int [(a + b*x^n)^(-1)/x^(n*(-1) + n + 1), x, 4, log(x)/a - log(a + b*x^n)/(a*n)]
    @test_int [(a + b*x^3)^(-1)/x^(3*(-1) + 3 + 1), x, 4, log(x)/a - log(a + b*x^3)/(3*a)]

    @test_int [1/(a + b*x^n)^((1 + 4*n)/n), x, 4, If(13>=8, (x*(a + b*x^n)^(-3 - 1/n))/(a*(1 + 3*n)) + (3*n*x*(a + b*x^n)^(-2 - 1/n))/(a^2*(1 + 5*n + 6*n^2)) + (6*n^3*x)/((a + b*x^n)^n^(-1)*(a^4*(1 + n)*(1 + 2*n)*(1 + 3*n))) + (6*n^2*x)/((a + b*x^n)^((1 + n)/n)*(a^3*(1 + n)*(1 + 2*n)*(1 + 3*n))), (x*(a + b*x^n)^(-3 - 1/n))/(a*(1 + 3*n)) + (3*n*x*(a + b*x^n)^(-2 - 1/n))/(a^2*(1 + 5*n + 6*n^2)) + (6*n^3*x)/((a + b*x^n)^n^(-1)*(a^4*(1 + 6*n + 11*n^2 + 6*n^3))) + (6*n^2*x)/((a + b*x^n)^((1 + n)/n)*(a^3*(1 + 6*n + 11*n^2 + 6*n^3))))]
    @test_int [1/(a + b*x^n)^((1 + 3*n)/n), x, 3, If(13>=8, (x*(a + b*x^n)^(-2 - 1/n))/(a*(1 + 2*n)) + (2*n^2*x)/((a + b*x^n)^n^(-1)*(a^3*(1 + n)*(1 + 2*n))) + (2*n*x)/((a + b*x^n)^((1 + n)/n)*(a^2*(1 + n)*(1 + 2*n))), (x*(a + b*x^n)^(-2 - 1/n))/(a*(1 + 2*n)) + (2*n^2*x)/((a + b*x^n)^n^(-1)*(a^3*(1 + 3*n + 2*n^2))) + (2*n*x)/((a + b*x^n)^((1 + n)/n)*(a^2*(1 + 3*n + 2*n^2))))]
    @test_int [1/(a + b*x^n)^((1 + 2*n)/n), x, 2, (n*x)/((a + b*x^n)^n^(-1)*(a^2*(1 + n))) + x/((a + b*x^n)^((1 + n)/n)*(a*(1 + n)))]
    @test_int [1/(a + b*x^n)^((1 + 1*n)/n), x, 1, x/((a + b*x^n)^n^(-1)*a)]
    @test_int [1/(a + b*x^n)^((1 + 0*n)/n), x, 2, (x*(1 + (b*x^n)/a)^(1/n)*HypergeometricFunctions._₂F₁(1/n, 1/n, 1 + 1/n, -((b*x^n)/a)))/(a + b*x^n)^n^(-1)]
    @test_int [1/(a + b*x^n)^((1 - 1*n)/n), x, 2, (x*(1 + (b*x^n)/a)^(-1 + 1/n)*HypergeometricFunctions._₂F₁(-1 + 1/n, 1/n, 1 + 1/n, -((b*x^n)/a)))/(a + b*x^n)^((1 - n)/n)]
    @test_int [1/(a + b*x^n)^((1 - 2*n)/n), x, 2, x*(a + b*x^n)^(2 - 1/n)*(1 + (b*x^n)/a)^(-2 + 1/n)*HypergeometricFunctions._₂F₁(-2 + 1/n, 1/n, 1 + 1/n, -((b*x^n)/a))]

    @test_int [1/(x*(a + b/x^n)), x, 2, log(b + a*x^n)/(a*n)]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b*x^(n*(m + 1)))^p=#

    @test_int [x^m/(a + b*x^(m + 1)), x, 1, log(a + b*x^(1 + m))/(b*(1 + m))]
    @test_int [x^m*(a + b*x^(m + 1))^n, x, 1, (a + b*x^(1 + m))^(1 + n)/(b*(1 + m)*(1 + n))]

    @test_int [x^m*(a + b*x^(2 + 2*m))^3, x, 2, (a^3*x^(1 + m))/(1 + m) + (a^2*b*x^(3*(1 + m)))/(1 + m) + (3*a*b^2*x^(5*(1 + m)))/(5*(1 + m)) + (b^3*x^(7*(1 + m)))/(7*(1 + m))]
    @test_int [x^m*(a + b*x^(2 + 2*m))^2, x, 2, (a^2*x^(1 + m))/(1 + m) + (2*a*b*x^(3*(1 + m)))/(3*(1 + m)) + (b^2*x^(5*(1 + m)))/(5*(1 + m))]
    @test_int [x^m*(a + b*x^(2 + 2*m)), x, 2, (a*x^(1 + m))/(1 + m) + (b*x^(3*(1 + m)))/(3*(1 + m))]
    @test_int [x^m/(a + b*x^(2 + 2*m)), x, 2, atan((sqrt(b)*x^(1 + m))/sqrt(a))/(sqrt(a)*sqrt(b)*(1 + m))]
    @test_int [x^m/(a + b*x^(2 + 2*m))^2, x, 3, x^(1 + m)/(2*a*(1 + m)*(a + b*x^(2*(1 + m)))) + atan((sqrt(b)*x^(1 + m))/sqrt(a))/(2*a^(3/2)*sqrt(b)*(1 + m))]
    @test_int [x^m/(a + b*x^(2 + 2*m))^3, x, 4, x^(1 + m)/(4*a*(1 + m)*(a + b*x^(2*(1 + m)))^2) + (3*x^(1 + m))/(8*a^2*(1 + m)*(a + b*x^(2*(1 + m)))) + (3*atan((sqrt(b)*x^(1 + m))/sqrt(a)))/(8*a^(5/2)*sqrt(b)*(1 + m))]

    @test_int [x^m*(a + b*x^(2 + 2*m))^(5/2), x, 6, (5*a^2*x^(1 + m)*sqrt(a + b*x^(2*(1 + m))))/(16*(1 + m)) + (5*a*x^(1 + m)*(a + b*x^(2*(1 + m)))^(3/2))/(24*(1 + m)) + (x^(1 + m)*(a + b*x^(2*(1 + m)))^(5/2))/(6*(1 + m)) + (5*a^3*atanh((sqrt(b)*x^(1 + m))/sqrt(a + b*x^(2*(1 + m)))))/(16*sqrt(b)*(1 + m))]
    @test_int [x^m*(a + b*x^(2 + 2*m))^(3/2), x, 5, (3*a*x^(1 + m)*sqrt(a + b*x^(2*(1 + m))))/(8*(1 + m)) + (x^(1 + m)*(a + b*x^(2*(1 + m)))^(3/2))/(4*(1 + m)) + (3*a^2*atanh((sqrt(b)*x^(1 + m))/sqrt(a + b*x^(2*(1 + m)))))/(8*sqrt(b)*(1 + m))]
    @test_int [x^m*(a + b*x^(2 + 2*m))^(1/2), x, 4, (x^(1 + m)*sqrt(a + b*x^(2*(1 + m))))/(2*(1 + m)) + (a*atanh((sqrt(b)*x^(1 + m))/sqrt(a + b*x^(2*(1 + m)))))/(2*sqrt(b)*(1 + m))]
    @test_int [x^m/(a + b*x^(2 + 2*m))^(1/2), x, 3, atanh((sqrt(b)*x^(1 + m))/sqrt(a + b*x^(2*(1 + m))))/(sqrt(b)*(1 + m))]
    @test_int [x^m/(a + b*x^(2 + 2*m))^(3/2), x, 1, x^(1 + m)/(a*(1 + m)*sqrt(a + b*x^(2*(1 + m))))]
    @test_int [x^m/(a + b*x^(2 + 2*m))^(5/2), x, 2, x^(1 + m)/(a*(1 + m)*(a + b*x^(2*(1 + m)))^(3/2)) + (2*b*x^(3*(1 + m)))/(3*a^2*(1 + m)*(a + b*x^(2*(1 + m)))^(3/2))]
    @test_int [x^m/(a + b*x^(2 + 2*m))^(7/2), x, 3, x^(1 + m)/(a*(1 + m)*(a + b*x^(2*(1 + m)))^(5/2)) + (4*b*x^(3*(1 + m)))/(3*a^2*(1 + m)*(a + b*x^(2*(1 + m)))^(5/2)) + (8*b^2*x^(5*(1 + m)))/(15*a^3*(1 + m)*(a + b*x^(2*(1 + m)))^(5/2))]

    @test_int [x^n*sqrt(1 + x^(1 + n)), x, 1, (2*(1 + x^(1 + n))^(3/2))/(3*(1 + n))]
    @test_int [x^n*sqrt(a^2 + x^(1 + n)), x, 1, (2*(a^2 + x^(1 + n))^(3/2))/(3*(1 + n))]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(c*x)^m*(a+b*x^n)^p=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(c*x)^m*(a+b*x^n)^p=#

    #= ::Subsubsection::Closed:: =#
    #=p>0=#

    @test_int [(c*x)^m*(a + b*x^n)^2, x, 6, (2*a*b*x^(1 + n)*(c*x)^m)/(1 + m + n) + (b^2*x^(1 + 2*n)*(c*x)^m)/(1 + m + 2*n) + (a^2*(c*x)^(1 + m))/(c*(1 + m))]

    @test_int [(c*x)^m*(a + b*x^3)^2, x, 2, (a^2*(c*x)^(1 + m))/(c*(1 + m)) + (2*a*b*(c*x)^(4 + m))/(c^4*(4 + m)) + (b^2*(c*x)^(7 + m))/(c^7*(7 + m))]
    @test_int [(c*x)^m*(a + b*x^2)^2, x, 2, (a^2*(c*x)^(1 + m))/(c*(1 + m)) + (2*a*b*(c*x)^(3 + m))/(c^3*(3 + m)) + (b^2*(c*x)^(5 + m))/(c^5*(5 + m))]
    @test_int [(c*x)^m*(a + b*x^1)^2, x, 2, (a^2*(c*x)^(1 + m))/(c*(1 + m)) + (2*a*b*(c*x)^(2 + m))/(c^2*(2 + m)) + (b^2*(c*x)^(3 + m))/(c^3*(3 + m))]
    @test_int [(c*x)^m*(a + b/x^1)^2, x, 2, -((b^2*c*(c*x)^(-1 + m))/(1 - m)) + (2*a*b*(c*x)^m)/m + (a^2*(c*x)^(1 + m))/(c*(1 + m))]
    @test_int [(c*x)^m*(a + b/x^2)^2, x, 2, -((b^2*c^3*(c*x)^(-3 + m))/(3 - m)) - (2*a*b*c*(c*x)^(-1 + m))/(1 - m) + (a^2*(c*x)^(1 + m))/(c*(1 + m))]
    @test_int [(c*x)^m*(a + b/x^3)^2, x, 2, -((b^2*c^5*(c*x)^(-5 + m))/(5 - m)) - (2*a*b*c^2*(c*x)^(-2 + m))/(2 - m) + (a^2*(c*x)^(1 + m))/(c*(1 + m))]

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [(c*x)^(-1 - 1*n/2)/(a + b*x^n), x, 5, -(2/((c*x)^(n/2)*(a*c*n))) + (2*sqrt(b)*x^(n/2)*atan(sqrt(a)/(x^(n/2)*sqrt(b))))/((c*x)^(n/2)*(a^(3/2)*c*n))]
    @test_int [(c*x)^(-1 - 2*n/3)/(a + b*x^n), x, 9, -(3/((c*x)^((2*n)/3)*(2*a*c*n))) + (sqrt(3)*b^(2/3)*x^((2*n)/3)*atan((a^(1/3) - 2*b^(1/3)*x^(n/3))/(sqrt(3)*a^(1/3))))/((c*x)^((2*n)/3)*(a^(5/3)*c*n)) - (b^(2/3)*x^((2*n)/3)*log(a^(1/3) + b^(1/3)*x^(n/3)))/((c*x)^((2*n)/3)*(a^(5/3)*c*n)) + (b^(2/3)*x^((2*n)/3)*log(a^(2/3) - a^(1/3)*b^(1/3)*x^(n/3) + b^(2/3)*x^((2*n)/3)))/((c*x)^((2*n)/3)*(2*a^(5/3)*c*n))]
    @test_int [(c*x)^(-1 - 3*n/4)/(a + b*x^n), x, 12, -(4/((c*x)^((3*n)/4)*(3*a*c*n))) + (sqrt(2)*b^(3/4)*x^((3*n)/4)*atan(1 - (sqrt(2)*b^(1/4)*x^(n/4))/a^(1/4)))/((c*x)^((3*n)/4)*(a^(7/4)*c*n)) - (sqrt(2)*b^(3/4)*x^((3*n)/4)*atan(1 + (sqrt(2)*b^(1/4)*x^(n/4))/a^(1/4)))/((c*x)^((3*n)/4)*(a^(7/4)*c*n)) + (b^(3/4)*x^((3*n)/4)*log(sqrt(a) - sqrt(2)*a^(1/4)*b^(1/4)*x^(n/4) + sqrt(b)*x^(n/2)))/((c*x)^((3*n)/4)*(sqrt(2)*a^(7/4)*c*n)) - (b^(3/4)*x^((3*n)/4)*log(sqrt(a) + sqrt(2)*a^(1/4)*b^(1/4)*x^(n/4) + sqrt(b)*x^(n/2)))/((c*x)^((3*n)/4)*(sqrt(2)*a^(7/4)*c*n))]

    @test_int [(c*x)^(-1 - n/1)/(a + b*x^n), x, 4, -(1/((c*x)^n*(a*c*n))) - (b*x^n*log(x))/((c*x)^n*(a^2*c)) + (b*x^n*log(a + b*x^n))/((c*x)^n*(a^2*c*n))]
    @test_int [(c*x)^(-1 - n/2)/(a + b*x^n), x, 5, -(2/((c*x)^(n/2)*(a*c*n))) + (2*sqrt(b)*x^(n/2)*atan(sqrt(a)/(x^(n/2)*sqrt(b))))/((c*x)^(n/2)*(a^(3/2)*c*n))]
    @test_int [(c*x)^(-1 - n/3)/(a + b*x^n), x, 10, -(3/((c*x)^(n/3)*(a*c*n))) - (sqrt(3)*b^(1/3)*x^(n/3)*atan((b^(1/3) - (2*a^(1/3))/x^(n/3))/(sqrt(3)*b^(1/3))))/((c*x)^(n/3)*(a^(4/3)*c*n)) + (b^(1/3)*x^(n/3)*log(b^(1/3) + a^(1/3)/x^(n/3)))/((c*x)^(n/3)*(a^(4/3)*c*n)) - (b^(1/3)*x^(n/3)*log(b^(2/3) + a^(2/3)/x^((2*n)/3) - (a^(1/3)*b^(1/3))/x^(n/3)))/((c*x)^(n/3)*(2*a^(4/3)*c*n))]
    @test_int [(c*x)^(-1 - n/4)/(a + b*x^n), x, 13, -(4/((c*x)^(n/4)*(a*c*n))) - (sqrt(2)*b^(1/4)*x^(n/4)*atan(1 - (sqrt(2)*a^(1/4))/(x^(n/4)*b^(1/4))))/((c*x)^(n/4)*(a^(5/4)*c*n)) + (sqrt(2)*b^(1/4)*x^(n/4)*atan(1 + (sqrt(2)*a^(1/4))/(x^(n/4)*b^(1/4))))/((c*x)^(n/4)*(a^(5/4)*c*n)) - (b^(1/4)*x^(n/4)*log(sqrt(b) + sqrt(a)/x^(n/2) - (sqrt(2)*a^(1/4)*b^(1/4))/x^(n/4)))/((c*x)^(n/4)*(sqrt(2)*a^(5/4)*c*n)) + (b^(1/4)*x^(n/4)*log(sqrt(b) + sqrt(a)/x^(n/2) + (sqrt(2)*a^(1/4)*b^(1/4))/x^(n/4)))/((c*x)^(n/4)*(sqrt(2)*a^(5/4)*c*n))]

    @test_int [(c*x)^(-1 - 3*n/2)/(a + b*x^n), x, 6, -(2/((c*x)^((3*n)/2)*(3*a*c*n))) + (2*b*x^n)/((c*x)^((3*n)/2)*(a^2*c*n)) - (2*b^(3/2)*x^((3*n)/2)*atan(sqrt(a)/(x^(n/2)*sqrt(b))))/((c*x)^((3*n)/2)*(a^(5/2)*c*n))]
    @test_int [(c*x)^(-1 - 4*n/3)/(a + b*x^n), x, 11, If(13>=8, -(3/((c*x)^((4*n)/3)*(4*a*c*n))) + (3*b*x^n)/((c*x)^((4*n)/3)*(a^2*c*n)) + (sqrt(3)*b^(4/3)*x^((4*n)/3)*atan((b^(1/3) - (2*a^(1/3))/x^(n/3))/(sqrt(3)*b^(1/3))))/((c*x)^((4*n)/3)*(a^(7/3)*c*n)) - (b^(4/3)*x^((4*n)/3)*log(b^(1/3) + a^(1/3)/x^(n/3)))/((c*x)^((4*n)/3)*(a^(7/3)*c*n)) + (b^(4/3)*x^((4*n)/3)*log(b^(2/3) + a^(2/3)/x^((2*n)/3) - (a^(1/3)*b^(1/3))/x^(n/3)))/((c*x)^((4*n)/3)*(2*a^(7/3)*c*n)), -(3/((c*x)^((4*n)/3)*(4*a*c*n))) + (3*b*x^n)/((c*x)^((4*n)/3)*(a^2*c*n)) + (sqrt(3)*b^(4/3)*x^((4*n)/3)*atan((1 - (2*a^(1/3))/(x^(n/3)*b^(1/3)))/sqrt(3)))/((c*x)^((4*n)/3)*(a^(7/3)*c*n)) - (b^(4/3)*x^((4*n)/3)*log(b^(1/3) + a^(1/3)/x^(n/3)))/((c*x)^((4*n)/3)*(a^(7/3)*c*n)) + (b^(4/3)*x^((4*n)/3)*log(b^(2/3) + a^(2/3)/x^((2*n)/3) - (a^(1/3)*b^(1/3))/x^(n/3)))/((c*x)^((4*n)/3)*(2*a^(7/3)*c*n)))]
    @test_int [(c*x)^(-1 - 5*n/4)/(a + b*x^n), x, 14, -(4/((c*x)^((5*n)/4)*(5*a*c*n))) + (4*b*x^n)/((c*x)^((5*n)/4)*(a^2*c*n)) + (sqrt(2)*b^(5/4)*x^((5*n)/4)*atan(1 - (sqrt(2)*a^(1/4))/(x^(n/4)*b^(1/4))))/((c*x)^((5*n)/4)*(a^(9/4)*c*n)) - (sqrt(2)*b^(5/4)*x^((5*n)/4)*atan(1 + (sqrt(2)*a^(1/4))/(x^(n/4)*b^(1/4))))/((c*x)^((5*n)/4)*(a^(9/4)*c*n)) + (b^(5/4)*x^((5*n)/4)*log(sqrt(b) + sqrt(a)/x^(n/2) - (sqrt(2)*a^(1/4)*b^(1/4))/x^(n/4)))/((c*x)^((5*n)/4)*(sqrt(2)*a^(9/4)*c*n)) - (b^(5/4)*x^((5*n)/4)*log(sqrt(b) + sqrt(a)/x^(n/2) + (sqrt(2)*a^(1/4)*b^(1/4))/x^(n/4)))/((c*x)^((5*n)/4)*(sqrt(2)*a^(9/4)*c*n))]

    @test_int [(c*x)^(n + 4)/(a + b*x^n), x, 1, ((c*x)^(5 + n)*HypergeometricFunctions._₂F₁(1, (5 + n)/n, 2 + 5/n, -((b*x^n)/a)))/(a*c*(5 + n))]
    @test_int [(c*x)^(n + 3)/(a + b*x^n), x, 1, ((c*x)^(4 + n)*HypergeometricFunctions._₂F₁(1, (4 + n)/n, 2*(1 + 2/n), -((b*x^n)/a)))/(a*c*(4 + n))]
    @test_int [(c*x)^(n + 2)/(a + b*x^n), x, 1, ((c*x)^(3 + n)*HypergeometricFunctions._₂F₁(1, (3 + n)/n, 2 + 3/n, -((b*x^n)/a)))/(a*c*(3 + n))]
    @test_int [(c*x)^(n + 1)/(a + b*x^n), x, 1, ((c*x)^(2 + n)*HypergeometricFunctions._₂F₁(1, (2 + n)/n, 2*(1 + 1/n), -((b*x^n)/a)))/(a*c*(2 + n))]
    @test_int [(c*x)^(n + 0)/(a + b*x^n), x, 1, ((c*x)^(1 + n)*HypergeometricFunctions._₂F₁(1, 1 + 1/n, 2 + 1/n, -((b*x^n)/a)))/(a*c*(1 + n))]
    @test_int [(c*x)^(n - 1)/(a + b*x^n), x, 2, ((c*x)^n*log(a + b*x^n))/(x^n*(b*c*n))]
    @test_int [(c*x)^(n - 2)/(a + b*x^n), x, 1, -(((c*x)^(-1 + n)*HypergeometricFunctions._₂F₁(1, -((1 - n)/n), 2 - 1/n, -((b*x^n)/a)))/(a*c*(1 - n)))]
    @test_int [(c*x)^(n - 3)/(a + b*x^n), x, 1, -(((c*x)^(-2 + n)*HypergeometricFunctions._₂F₁(1, -((2 - n)/n), 2*(1 - 1/n), -((b*x^n)/a)))/(a*c*(2 - n)))]

    @test_int [(c*x)^(n - 1)/(a + b*x^n)^2, x, 1, (c*x)^n/(a*c*n*(a + b*x^n))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(c*x)^m*(a+b*x^n)^(p/2)=#

    #= ::Subsubsection:: =#
    #=p>0=#

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [(c*x)^(7*n/2 - 1)/sqrt(a + b*x^n), x, 6, (5*a^2*(c*x)^((7*n)/2)*sqrt(a + b*x^n))/(x^(3*n)*(8*b^3*c*n)) - (5*a*(c*x)^((7*n)/2)*sqrt(a + b*x^n))/(x^(2*n)*(12*b^2*c*n)) + ((c*x)^((7*n)/2)*sqrt(a + b*x^n))/(x^n*(3*b*c*n)) - (5*a^3*(c*x)^((7*n)/2)*atanh((sqrt(b)*x^(n/2))/sqrt(a + b*x^n)))/(x^((7*n)/2)*(8*b^(7/2)*c*n))]
    @test_int [(c*x)^(5*n/2 - 1)/sqrt(a + b*x^n), x, 5, -((3*a*(c*x)^((5*n)/2)*sqrt(a + b*x^n))/(x^(2*n)*(4*b^2*c*n))) + ((c*x)^((5*n)/2)*sqrt(a + b*x^n))/(x^n*(2*b*c*n)) + (3*a^2*(c*x)^((5*n)/2)*atanh((sqrt(b)*x^(n/2))/sqrt(a + b*x^n)))/(x^((5*n)/2)*(4*b^(5/2)*c*n))]
    @test_int [(c*x)^(3*n/2 - 1)/sqrt(a + b*x^n), x, 4, ((c*x)^((3*n)/2)*sqrt(a + b*x^n))/(x^n*(b*c*n)) - (a*(c*x)^((3*n)/2)*atanh((sqrt(b)*x^(n/2))/sqrt(a + b*x^n)))/(x^((3*n)/2)*(b^(3/2)*c*n))]
    @test_int [(c*x)^(1*n/2 - 1)/sqrt(a + b*x^n), x, 4, (2*(c*x)^(n/2)*atanh((sqrt(b)*x^(n/2))/sqrt(a + b*x^n)))/(x^(n/2)*(sqrt(b)*c*n))]
    @test_int [(c*x)^(-1*n/2 - 1)/sqrt(a + b*x^n), x, 1, -((2*sqrt(a + b*x^n))/((c*x)^(n/2)*(a*c*n)))]
    @test_int [(c*x)^(-3*n/2 - 1)/sqrt(a + b*x^n), x, 2, -((2*sqrt(a + b*x^n))/((c*x)^((3*n)/2)*(a*c*n))) + (4*(a + b*x^n)^(3/2))/((c*x)^((3*n)/2)*(3*a^2*c*n))]
    @test_int [(c*x)^(-5*n/2 - 1)/sqrt(a + b*x^n), x, 3, -((2*sqrt(a + b*x^n))/((c*x)^((5*n)/2)*(a*c*n))) + (8*(a + b*x^n)^(3/2))/((c*x)^((5*n)/2)*(3*a^2*c*n)) - (16*(a + b*x^n)^(5/2))/((c*x)^((5*n)/2)*(15*a^3*c*n))]
    @test_int [(c*x)^(-7*n/2 - 1)/sqrt(a + b*x^n), x, 4, -((2*sqrt(a + b*x^n))/((c*x)^((7*n)/2)*(a*c*n))) + (4*(a + b*x^n)^(3/2))/((c*x)^((7*n)/2)*(a^2*c*n)) - (16*(a + b*x^n)^(5/2))/((c*x)^((7*n)/2)*(5*a^3*c*n)) + (32*(a + b*x^n)^(7/2))/((c*x)^((7*n)/2)*(35*a^4*c*n))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(c*x)^m*(a+b*x^n)^p*with*p*symbolic=#

    @test_int [(c*x)^m*(a + b*x^n)^p, x, 2, ((c*x)^(1 + m)*(a + b*x^n)^(1 + p)*HypergeometricFunctions._₂F₁(1, 1 + (1 + m)/n + p, (1 + m + n)/n, -((b*x^n)/a)))/(a*c*(1 + m)), ((c*x)^(1 + m)*(a + b*x^n)^p*HypergeometricFunctions._₂F₁((1 + m)/n, -p, (1 + m + n)/n, -((b*x^n)/a)))/((1 + (b*x^n)/a)^p*(c*(1 + m)))]

    @test_int [(a + b*x^n)^p*(c*x)^(3*n), x, 2, ((c*x)^(1 + 3*n)*(a + b*x^n)^(1 + p)*HypergeometricFunctions._₂F₁(1, 4 + 1/n + p, 4 + 1/n, -((b*x^n)/a)))/(a*c*(1 + 3*n)), ((c*x)^(1 + 3*n)*(a + b*x^n)^p*HypergeometricFunctions._₂F₁(3 + 1/n, -p, 4 + 1/n, -((b*x^n)/a)))/((1 + (b*x^n)/a)^p*(c*(1 + 3*n)))]
    @test_int [(a + b*x^n)^p*(c*x)^(2*n), x, 2, ((c*x)^(1 + 2*n)*(a + b*x^n)^(1 + p)*HypergeometricFunctions._₂F₁(1, 3 + 1/n + p, 3 + 1/n, -((b*x^n)/a)))/(a*c*(1 + 2*n)), ((c*x)^(1 + 2*n)*(a + b*x^n)^p*HypergeometricFunctions._₂F₁(2 + 1/n, -p, 3 + 1/n, -((b*x^n)/a)))/((1 + (b*x^n)/a)^p*(c*(1 + 2*n)))]
    @test_int [(a + b*x^n)^p*(c*x)^(1*n), x, 2, ((c*x)^(1 + n)*(a + b*x^n)^(1 + p)*HypergeometricFunctions._₂F₁(1, 2 + 1/n + p, 2 + 1/n, -((b*x^n)/a)))/(a*c*(1 + n)), ((c*x)^(1 + n)*(a + b*x^n)^p*HypergeometricFunctions._₂F₁(1 + 1/n, -p, 2 + 1/n, -((b*x^n)/a)))/((1 + (b*x^n)/a)^p*(c*(1 + n)))]
    @test_int [(a + b*x^n)^p*(c*x)^(0*n), x, 2, (x*(a + b*x^n)^(1 + p)*HypergeometricFunctions._₂F₁(1, 1 + 1/n + p, 1 + 1/n, -((b*x^n)/a)))/a, (x*(a + b*x^n)^p*HypergeometricFunctions._₂F₁(1/n, -p, 1 + 1/n, -((b*x^n)/a)))/(1 + (b*x^n)/a)^p]
    @test_int [(a + b*x^n)^p/(c*x)^(1*n), x, 2, ((c*x)^(1 - n)*(a + b*x^n)^(1 + p)*HypergeometricFunctions._₂F₁(1, 1/n + p, 1/n, -((b*x^n)/a)))/(a*c*(1 - n)), ((c*x)^(1 - n)*(a + b*x^n)^p*HypergeometricFunctions._₂F₁(-1 + 1/n, -p, 1/n, -((b*x^n)/a)))/((1 + (b*x^n)/a)^p*(c*(1 - n)))]
    @test_int [(a + b*x^n)^p/(c*x)^(2*n), x, 2, ((c*x)^(1 - 2*n)*(a + b*x^n)^(1 + p)*HypergeometricFunctions._₂F₁(1, -1 + 1/n + p, -1 + 1/n, -((b*x^n)/a)))/(a*c*(1 - 2*n)), ((c*x)^(1 - 2*n)*(a + b*x^n)^p*HypergeometricFunctions._₂F₁(-2 + 1/n, -p, -1 + 1/n, -((b*x^n)/a)))/((1 + (b*x^n)/a)^p*(c*(1 - 2*n)))]
    @test_int [(a + b*x^n)^p/(c*x)^(3*n), x, 2, ((c*x)^(1 - 3*n)*(a + b*x^n)^(1 + p)*HypergeometricFunctions._₂F₁(1, -2 + 1/n + p, -2 + 1/n, -((b*x^n)/a)))/(a*c*(1 - 3*n)), ((c*x)^(1 - 3*n)*(a + b*x^n)^p*HypergeometricFunctions._₂F₁(-3 + 1/n, -p, -2 + 1/n, -((b*x^n)/a)))/((1 + (b*x^n)/a)^p*(c*(1 - 3*n)))]

    @test_int [(a + b*x^n)^p/(c*x)^(n*p + 0*n + 1), x, 2, -(((a + b*x^n)^p*HypergeometricFunctions._₂F₁(-p, -p, 1 - p, -((b*x^n)/a)))/((c*x)^(n*p)*(1 + (b*x^n)/a)^p*(c*n*p)))]
    @test_int [(a + b*x^n)^p/(c*x)^(n*p + 1*n + 1), x, 1, -((a + b*x^n)^(1 + p)/((c*x)^(n*(1 + p))*(a*c*n*(1 + p))))]
    @test_int [(a + b*x^n)^p/(c*x)^(n*p + 2*n + 1), x, 2, -((a + b*x^n)^(1 + p)/((c*x)^(n*(2 + p))*(a*c*n*(1 + p)))) + (a + b*x^n)^(2 + p)/((c*x)^(n*(2 + p))*(a^2*c*n*(1 + p)*(2 + p)))]
    @test_int [(a + b*x^n)^p/(c*x)^(n*p + 3*n + 1), x, 3, -((a + b*x^n)^(1 + p)/((c*x)^(n*(3 + p))*(a*c*n*(1 + p)))) + (2*(a + b*x^n)^(2 + p))/((c*x)^(n*(3 + p))*(a^2*c*n*(1 + p)*(2 + p))) - (2*(a + b*x^n)^(3 + p))/((c*x)^(n*(3 + p))*(a^3*c*n*(1 + p)*(2 + p)*(3 + p)))]
    @test_int [(a + b*x^n)^p/(c*x)^(n*p + 4*n + 1), x, 4, If(13>=8, -((a + b*x^n)^(1 + p)/((c*x)^(n*(4 + p))*(a*c*n*(1 + p)))) + (3*(a + b*x^n)^(2 + p))/((c*x)^(n*(4 + p))*(a^2*c*n*(1 + p)*(2 + p))) - (6*(a + b*x^n)^(3 + p))/((c*x)^(n*(4 + p))*(a^3*c*n*(1 + p)*(2 + p)*(3 + p))) + (6*(a + b*x^n)^(4 + p))/((c*x)^(n*(4 + p))*(a^4*c*n*(1 + p)*(2 + p)*(3 + p)*(4 + p))), -((a + b*x^n)^(1 + p)/((c*x)^(n*(4 + p))*(a*c*n*(1 + p)))) + (3*(a + b*x^n)^(2 + p))/((c*x)^(n*(4 + p))*(a^2*c*n*(1 + p)*(2 + p))) - (6*(a + b*x^n)^(3 + p))/((c*x)^(n*(4 + p))*(a^3*c*n*(1 + p)*(2 + p)*(3 + p))) + (6*(a + b*x^n)^(4 + p))/((c*x)^(n*(4 + p))*(a^4*c*n*(2 + 3*p + p^2)*(12 + 7*p + p^2))))]

    #= ::Title::Closed:: =#
    #=Integrands*of*the*form*(c+d*x)^m*(b*(c+d*x)^n)^p=#

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(c+d*x)^m*(b*(c+d*x)^2)^p=#

    @test_int [(c*(a + b*x)^2)^(5/2), x, 3, (c^2*(a + b*x)^5*sqrt(c*(a + b*x)^2))/(6*b)]
    @test_int [(c*(a + b*x)^2)^(3/2), x, 3, (c*(a + b*x)^3*sqrt(c*(a + b*x)^2))/(4*b)]
    @test_int [(c*(a + b*x)^2)^(1/2), x, 3, ((a + b*x)*sqrt(c*(a + b*x)^2))/(2*b)]
    @test_int [1/(c*(a + b*x)^2)^(1/2), x, 3, ((a + b*x)*log(a + b*x))/(b*sqrt(c*(a + b*x)^2))]
    @test_int [1/(c*(a + b*x)^2)^(3/2), x, 3, -(1/(2*b*c*(a + b*x)*sqrt(c*(a + b*x)^2)))]
    @test_int [1/(c*(a + b*x)^2)^(5/2), x, 3, -(1/(4*b*c^2*(a + b*x)^3*sqrt(c*(a + b*x)^2)))]

    @test_int [sqrt((3 + 5*x)^2), x, 3, (1/10)*(3 + 5*x)*sqrt((3 + 5*x)^2)]
    @test_int [sqrt((6 + 10*x)^2), x, 3, (1/5)*(3 + 5*x)*sqrt((3 + 5*x)^2)]

    @test_int [1/sqrt((3 + 5*x)^2), x, 3, (3 + 5*x)*(log(3 + 5*x)/(5*sqrt((3 + 5*x)^2)))]
    @test_int [1/sqrt((6 + 10*x)^2), x, 3, ((3 + 5*x)*log(3 + 5*x))/(10*sqrt((3 + 5*x)^2)), ((3 + 5*x)*log(6 + 10*x))/(10*sqrt((3 + 5*x)^2))]

    @test_int [1/sqrt(-(2 + 3*x)^2), x, 3, ((2 + 3*x)*log(2 + 3*x))/(3*sqrt(-(2 + 3*x)^2))]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(c+d*x)^m*(b*(c+d*x)^3)^p=#

    @test_int [(c*(a + b*x)^3)^(5/2), x, 3, (2*c^2*(a + b*x)^7*sqrt(c*(a + b*x)^3))/(17*b)]
    @test_int [(c*(a + b*x)^3)^(3/2), x, 3, (2*c*(a + b*x)^4*sqrt(c*(a + b*x)^3))/(11*b)]
    @test_int [(c*(a + b*x)^3)^(1/2), x, 3, (2*(a + b*x)*sqrt(c*(a + b*x)^3))/(5*b)]
    @test_int [1/(c*(a + b*x)^3)^(1/2), x, 3, -((2*(a + b*x))/(b*sqrt(c*(a + b*x)^3)))]
    @test_int [1/(c*(a + b*x)^3)^(3/2), x, 3, -(2/(7*b*c*(a + b*x)^2*sqrt(c*(a + b*x)^3)))]
    @test_int [1/(c*(a + b*x)^3)^(5/2), x, 3, -(2/(13*b*c^2*(a + b*x)^5*sqrt(c*(a + b*x)^3)))]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(c+d*x)^m*(b*(c+d*x)^(-1))^p=#

    @test_int [(c/(a + b*x))^(5/2), x, 3, -((2*c^2*sqrt(c/(a + b*x)))/(3*b*(a + b*x)))]
    @test_int [(c/(a + b*x))^(3/2), x, 3, -((2*c*sqrt(c/(a + b*x)))/b)]
    @test_int [(c/(a + b*x))^(1/2), x, 3, (2*sqrt(c/(a + b*x))*(a + b*x))/b]
    @test_int [1/(c/(a + b*x))^(1/2), x, 3, (2*(a + b*x))/(3*b*sqrt(c/(a + b*x)))]
    @test_int [1/(c/(a + b*x))^(3/2), x, 3, (2*(a + b*x)^2)/(5*b*c*sqrt(c/(a + b*x)))]
    @test_int [1/(c/(a + b*x))^(5/2), x, 3, (2*(a + b*x)^3)/(7*b*c^2*sqrt(c/(a + b*x)))]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(c+d*x)^m*(b*(c+d*x)^(-2))^p=#

    @test_int [(c/(a + b*x)^2)^(5/2), x, 3, -((c^2*sqrt(c/(a + b*x)^2))/(4*b*(a + b*x)^3))]
    @test_int [(c/(a + b*x)^2)^(3/2), x, 3, -((c*sqrt(c/(a + b*x)^2))/(2*b*(a + b*x)))]
    @test_int [(c/(a + b*x)^2)^(1/2), x, 3, (sqrt(c/(a + b*x)^2)*(a + b*x)*log(a + b*x))/b]
    @test_int [1/(c/(a + b*x)^2)^(1/2), x, 3, (a + b*x)/(2*b*sqrt(c/(a + b*x)^2))]
    @test_int [1/(c/(a + b*x)^2)^(3/2), x, 3, (a + b*x)^3/(4*b*c*sqrt(c/(a + b*x)^2))]
    @test_int [1/(c/(a + b*x)^2)^(5/2), x, 3, (a + b*x)^5/(6*b*c^2*sqrt(c/(a + b*x)^2))]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(c+d*x)^m*(b*(c+d*x)^(-3))^p=#

    @test_int [(c/(a + b*x)^3)^(5/2), x, 3, -((2*c^2*sqrt(c/(a + b*x)^3))/(13*b*(a + b*x)^5))]
    @test_int [(c/(a + b*x)^3)^(3/2), x, 3, -((2*c*sqrt(c/(a + b*x)^3))/(7*b*(a + b*x)^2))]
    @test_int [(c/(a + b*x)^3)^(1/2), x, 3, -((2*sqrt(c/(a + b*x)^3)*(a + b*x))/b)]
    @test_int [1/(c/(a + b*x)^3)^(1/2), x, 3, (2*(a + b*x))/(5*b*sqrt(c/(a + b*x)^3))]
    @test_int [1/(c/(a + b*x)^3)^(3/2), x, 3, (2*(a + b*x)^4)/(11*b*c*sqrt(c/(a + b*x)^3))]
    @test_int [1/(c/(a + b*x)^3)^(5/2), x, 3, (2*(a + b*x)^7)/(17*b*c^2*sqrt(c/(a + b*x)^3))]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(c+d*x)^m*(b*(c+d*x)^n)^p=#

    @test_int [(c*(a + b*x)^(3/2))^(2/3), x, 3, ((a + b*x)*(c*(a + b*x)^(3/2))^(2/3))/(2*b)]
    @test_int [(c*(a + b*x)^(2/3))^(3/2), x, 3, (c*sqrt(c*(a + b*x)^(2/3))*(a + b*x)^(5/3))/(2*b)]

    @test_int [1/(c/(a + b*x)^(3/2))^(2/3), x, 3, (a + b*x)/(2*b*(c/(a + b*x)^(3/2))^(2/3))]
    @test_int [1/(c/(a + b*x)^(2/3))^(3/2), x, 3, (a + b*x)^(5/3)/(2*b*c*sqrt(c/(a + b*x)^(2/3)))]

    #= ::Title::Closed:: =#
    #=Integrands*of*the*form*(c+d*x)^m*(a+b*(c+d*x)^n)^p=#

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(c+d*x)^m*(a+b*(c+d*x)^2)^p=#

    #= ::Subsubsection::Closed:: =#
    #=p>0=#

    @test_int [(c + d*x)^3*(a + b*(c + d*x)^2), x, 3, (a*(c + d*x)^4)/(4*d) + (b*(c + d*x)^6)/(6*d)]
    @test_int [(c + d*x)^3*(a + b*(c + d*x)^2)^2, x, 4, (a^2*(c + d*x)^4)/(4*d) + (a*b*(c + d*x)^6)/(3*d) + (b^2*(c + d*x)^8)/(8*d)]
    @test_int [(c + d*x)^3*(a + b*(c + d*x)^2)^3, x, 4, -((a*(a + b*(c + d*x)^2)^4)/(8*b^2*d)) + (a + b*(c + d*x)^2)^5/(10*b^2*d)]

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [(2 + x)/(1 + (2 + x)^2), x, 2, (1/2)*log(1 + (2 + x)^2)]
    @test_int [(2 + x)/(1 + (2 + x)^2)^2, x, 2, -(1/(2*(1 + (2 + x)^2)))]
    @test_int [(2 + x)/(1 + (2 + x)^2)^3, x, 2, -(1/(4*(1 + (2 + x)^2)^2))]

    #= ::Subsubsection::Closed:: =#
    #=p*symbolic=#

    @test_int [(c + d*x)^5*(a + b*(c + d*x)^2)^p, x, 4, (a^2*(a + b*(c + d*x)^2)^(1 + p))/(2*b^3*d*(1 + p)) - (a*(a + b*(c + d*x)^2)^(2 + p))/(b^3*d*(2 + p)) + (a + b*(c + d*x)^2)^(3 + p)/(2*b^3*d*(3 + p))]
    @test_int [(c + d*x)^4*(a + b*(c + d*x)^2)^p, x, 3, ((c + d*x)^5*(a + b*(c + d*x)^2)^(1 + p)*HypergeometricFunctions._₂F₁(1, 7/2 + p, 7/2, -((b*(c + d*x)^2)/a)))/(5*a*d), ((c + d*x)^5*(a + b*(c + d*x)^2)^p*HypergeometricFunctions._₂F₁(5/2, -p, 7/2, -((b*(c + d*x)^2)/a)))/((1 + (b*(c + d*x)^2)/a)^p*(5*d))]
    @test_int [(c + d*x)^3*(a + b*(c + d*x)^2)^p, x, 4, -((a*(a + b*(c + d*x)^2)^(1 + p))/(2*b^2*d*(1 + p))) + (a + b*(c + d*x)^2)^(2 + p)/(2*b^2*d*(2 + p))]
    @test_int [(c + d*x)^2*(a + b*(c + d*x)^2)^p, x, 3, ((c + d*x)^3*(a + b*(c + d*x)^2)^(1 + p)*HypergeometricFunctions._₂F₁(1, 5/2 + p, 5/2, -((b*(c + d*x)^2)/a)))/(3*a*d), ((c + d*x)^3*(a + b*(c + d*x)^2)^p*HypergeometricFunctions._₂F₁(3/2, -p, 5/2, -((b*(c + d*x)^2)/a)))/((1 + (b*(c + d*x)^2)/a)^p*(3*d))]
    @test_int [(c + d*x)^1*(a + b*(c + d*x)^2)^p, x, 2, (a + b*(c + d*x)^2)^(1 + p)/(2*b*d*(1 + p))]
    @test_int [(a + b*(c + d*x)^2)^p/(c + d*x)^1, x, 3, -(((a + b*(c + d*x)^2)^(1 + p)*HypergeometricFunctions._₂F₁(1, 1 + p, 2 + p, 1 + (b*(c + d*x)^2)/a))/(2*a*d*(1 + p)))]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(c+d*x)^m*(a+b*(c+d*x)^3)^p=#

    #= ::Subsubsection::Closed:: =#
    #=p>0=#

    @test_int [(c + d*x)^3*(a + b*(c + d*x)^3), x, 3, (a*(c + d*x)^4)/(4*d) + (b*(c + d*x)^7)/(7*d)]
    @test_int [(c + d*x)^3*(a + b*(c + d*x)^3)^2, x, 3, (a^2*(c + d*x)^4)/(4*d) + (2*a*b*(c + d*x)^7)/(7*d) + (b^2*(c + d*x)^10)/(10*d)]
    @test_int [(c + d*x)^3*(a + b*(c + d*x)^3)^3, x, 3, (1/4)*a^3*((c + d*x)^4/d) + (3/(7*d))*a^2*b*(c + d*x)^7 + (3/(10*d))*a*b^2*(c + d*x)^10 + (1/(13*d))*b^3*(c + d*x)^13]

    @test_int [(c*e + d*e*x)^3*(a + b*(c + d*x)^3), x, 3, (a*e^3*(c + d*x)^4)/(4*d) + (b*e^3*(c + d*x)^7)/(7*d)]
    @test_int [(c*e + d*e*x)^3*(a + b*(c + d*x)^3)^2, x, 3, (a^2*e^3*(c + d*x)^4)/(4*d) + (2*a*b*e^3*(c + d*x)^7)/(7*d) + (b^2*e^3*(c + d*x)^10)/(10*d)]
    @test_int [(c*e + d*e*x)^3*(a + b*(c + d*x)^3)^3, x, 3, (a^3*e^3*(c + d*x)^4)/(4*d) + (3*a^2*b*e^3*(c + d*x)^7)/(7*d) + (3*a*b^2*e^3*(c + d*x)^10)/(10*d) + (b^3*e^3*(c + d*x)^13)/(13*d)]

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [(c + d*x)^4/(a + b*(c + d*x)^3), x, 8, (c + d*x)^2/(2*b*d) + (a^(2/3)*atan((a^(1/3) - 2*b^(1/3)*(c + d*x))/(sqrt(3)*a^(1/3))))/(sqrt(3)*b^(5/3)*d) + (a^(2/3)*log(a^(1/3) + b^(1/3)*(c + d*x)))/(3*b^(5/3)*d) - (a^(2/3)*log(a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2))/(6*b^(5/3)*d)]
    @test_int [(c + d*x)^3/(a + b*(c + d*x)^3), x, 8, x/b + (a^(1/3)*atan((a^(1/3) - 2*b^(1/3)*(c + d*x))/(sqrt(3)*a^(1/3))))/(sqrt(3)*b^(4/3)*d) - (a^(1/3)*log(a^(1/3) + b^(1/3)*(c + d*x)))/(3*b^(4/3)*d) + (a^(1/3)*log(a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2))/(6*b^(4/3)*d)]
    @test_int [(c + d*x)^2/(a + b*(c + d*x)^3), x, 2, log(a + b*(c + d*x)^3)/(3*b*d)]
    @test_int [(c + d*x)^1/(a + b*(c + d*x)^3), x, 7, -(atan((a^(1/3) - 2*b^(1/3)*(c + d*x))/(sqrt(3)*a^(1/3)))/(sqrt(3)*a^(1/3)*b^(2/3)*d)) - log(a^(1/3) + b^(1/3)*(c + d*x))/(3*a^(1/3)*b^(2/3)*d) + log(a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2)/(6*a^(1/3)*b^(2/3)*d)]
    @test_int [(c + d*x)^0/(a + b*(c + d*x)^3), x, 7, -(atan((a^(1/3) - 2*b^(1/3)*(c + d*x))/(sqrt(3)*a^(1/3)))/(sqrt(3)*a^(2/3)*b^(1/3)*d)) + log(a^(1/3) + b^(1/3)*(c + d*x))/(3*a^(2/3)*b^(1/3)*d) - log(a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2)/(6*a^(2/3)*b^(1/3)*d)]
    @test_int [1/((c + d*x)^1*(a + b*(c + d*x)^3)), x, 5, log(c + d*x)/(a*d) - log(a + b*(c + d*x)^3)/(3*a*d)]
    @test_int [1/((c + d*x)^2*(a + b*(c + d*x)^3)), x, 8, -(1/(a*d*(c + d*x))) + (b^(1/3)*atan((a^(1/3) - 2*b^(1/3)*(c + d*x))/(sqrt(3)*a^(1/3))))/(sqrt(3)*a^(4/3)*d) + (b^(1/3)*log(a^(1/3) + b^(1/3)*(c + d*x)))/(3*a^(4/3)*d) - (b^(1/3)*log(a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2))/(6*a^(4/3)*d)]
    @test_int [1/((c + d*x)^3*(a + b*(c + d*x)^3)), x, 8, -(1/(2*a*d*(c + d*x)^2)) + (b^(2/3)*atan((a^(1/3) - 2*b^(1/3)*(c + d*x))/(sqrt(3)*a^(1/3))))/(sqrt(3)*a^(5/3)*d) - (b^(2/3)*log(a^(1/3) + b^(1/3)*(c + d*x)))/(3*a^(5/3)*d) + (b^(2/3)*log(a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2))/(6*a^(5/3)*d)]
    @test_int [1/((c + d*x)^4*(a + b*(c + d*x)^3)), x, 4, -(1/(3*a*d*(c + d*x)^3)) - (b*log(c + d*x))/(a^2*d) + (b*log(a + b*(c + d*x)^3))/(3*a^2*d)]

    @test_int [(c + d*x)^4/(a + b*(c + d*x)^3)^2, x, 8, -((c + d*x)^2/(3*b*d*(a + b*(c + d*x)^3))) - (2*atan((a^(1/3) - 2*b^(1/3)*(c + d*x))/(sqrt(3)*a^(1/3))))/(3*sqrt(3)*a^(1/3)*b^(5/3)*d) - (2*log(a^(1/3) + b^(1/3)*(c + d*x)))/(9*a^(1/3)*b^(5/3)*d) + log(a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2)/(9*a^(1/3)*b^(5/3)*d)]
    @test_int [(c + d*x)^3/(a + b*(c + d*x)^3)^2, x, 8, -((c + d*x)/(3*b*d*(a + b*(c + d*x)^3))) - atan((a^(1/3) - 2*b^(1/3)*(c + d*x))/(sqrt(3)*a^(1/3)))/(3*sqrt(3)*a^(2/3)*b^(4/3)*d) + log(a^(1/3) + b^(1/3)*(c + d*x))/(9*a^(2/3)*b^(4/3)*d) - log(a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2)/(18*a^(2/3)*b^(4/3)*d)]
    @test_int [(c + d*x)^2/(a + b*(c + d*x)^3)^2, x, 2, -(1/(3*b*d*(a + b*(c + d*x)^3)))]
    @test_int [(c + d*x)^1/(a + b*(c + d*x)^3)^2, x, 8, (c + d*x)^2/(3*a*d*(a + b*(c + d*x)^3)) - atan((a^(1/3) - 2*b^(1/3)*(c + d*x))/(sqrt(3)*a^(1/3)))/(3*sqrt(3)*a^(4/3)*b^(2/3)*d) - log(a^(1/3) + b^(1/3)*(c + d*x))/(9*a^(4/3)*b^(2/3)*d) + log(a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2)/(18*a^(4/3)*b^(2/3)*d)]
    @test_int [(c + d*x)^0/(a + b*(c + d*x)^3)^2, x, 8, (c + d*x)/(3*a*d*(a + b*(c + d*x)^3)) - (2*atan((a^(1/3) - 2*b^(1/3)*(c + d*x))/(sqrt(3)*a^(1/3))))/(3*sqrt(3)*a^(5/3)*b^(1/3)*d) + (2*log(a^(1/3) + b^(1/3)*(c + d*x)))/(9*a^(5/3)*b^(1/3)*d) - log(a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2)/(9*a^(5/3)*b^(1/3)*d)]
    @test_int [1/((c + d*x)^1*(a + b*(c + d*x)^3)^2), x, 4, 1/(3*a*d*(a + b*(c + d*x)^3)) + log(c + d*x)/(a^2*d) - log(a + b*(c + d*x)^3)/(3*a^2*d)]
    @test_int [1/((c + d*x)^2*(a + b*(c + d*x)^3)^2), x, 9, -(4/(3*a^2*d*(c + d*x))) + 1/(3*a*d*(c + d*x)*(a + b*(c + d*x)^3)) + (4*b^(1/3)*atan((a^(1/3) - 2*b^(1/3)*(c + d*x))/(sqrt(3)*a^(1/3))))/(3*sqrt(3)*a^(7/3)*d) + (4*b^(1/3)*log(a^(1/3) + b^(1/3)*(c + d*x)))/(9*a^(7/3)*d) - (2*b^(1/3)*log(a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2))/(9*a^(7/3)*d)]
    @test_int [1/((c + d*x)^3*(a + b*(c + d*x)^3)^2), x, 9, -(5/(6*a^2*d*(c + d*x)^2)) + 1/(3*a*d*(c + d*x)^2*(a + b*(c + d*x)^3)) + (5*b^(2/3)*atan((a^(1/3) - 2*b^(1/3)*(c + d*x))/(sqrt(3)*a^(1/3))))/(3*sqrt(3)*a^(8/3)*d) - (5*b^(2/3)*log(a^(1/3) + b^(1/3)*(c + d*x)))/(9*a^(8/3)*d) + (5*b^(2/3)*log(a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2))/(18*a^(8/3)*d)]
    @test_int [1/((c + d*x)^4*(a + b*(c + d*x)^3)^2), x, 4, -(1/(3*a^2*d*(c + d*x)^3)) - b/(3*a^2*d*(a + b*(c + d*x)^3)) - (2*b*log(c + d*x))/(a^3*d) + (2*b*log(a + b*(c + d*x)^3))/(3*a^3*d)]

    @test_int [(c + d*x)^4/(a + b*(c + d*x)^3)^3, x, 9, -((c + d*x)^2/(6*b*d*(a + b*(c + d*x)^3)^2)) + (c + d*x)^2/(9*a*b*d*(a + b*(c + d*x)^3)) - atan((a^(1/3) - 2*b^(1/3)*(c + d*x))/(sqrt(3)*a^(1/3)))/(9*sqrt(3)*a^(4/3)*b^(5/3)*d) - log(a^(1/3) + b^(1/3)*(c + d*x))/(27*a^(4/3)*b^(5/3)*d) + log(a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2)/(54*a^(4/3)*b^(5/3)*d)]
    @test_int [(c + d*x)^3/(a + b*(c + d*x)^3)^3, x, 9, -((c + d*x)/(6*b*d*(a + b*(c + d*x)^3)^2)) + (c + d*x)/(18*a*b*d*(a + b*(c + d*x)^3)) - atan((a^(1/3) - 2*b^(1/3)*(c + d*x))/(sqrt(3)*a^(1/3)))/(9*sqrt(3)*a^(5/3)*b^(4/3)*d) + log(a^(1/3) + b^(1/3)*(c + d*x))/(27*a^(5/3)*b^(4/3)*d) - log(a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2)/(54*a^(5/3)*b^(4/3)*d)]
    @test_int [(c + d*x)^2/(a + b*(c + d*x)^3)^3, x, 2, -(1/(6*b*d*(a + b*(c + d*x)^3)^2))]
    @test_int [(c + d*x)^1/(a + b*(c + d*x)^3)^3, x, 9, (c + d*x)^2/(6*a*d*(a + b*(c + d*x)^3)^2) + (2*(c + d*x)^2)/(9*a^2*d*(a + b*(c + d*x)^3)) - (2*atan((a^(1/3) - 2*b^(1/3)*(c + d*x))/(sqrt(3)*a^(1/3))))/(9*sqrt(3)*a^(7/3)*b^(2/3)*d) - (2*log(a^(1/3) + b^(1/3)*(c + d*x)))/(27*a^(7/3)*b^(2/3)*d) + log(a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2)/(27*a^(7/3)*b^(2/3)*d)]
    @test_int [(c + d*x)^0/(a + b*(c + d*x)^3)^3, x, 9, (c + d*x)/(6*a*d*(a + b*(c + d*x)^3)^2) + (5*(c + d*x))/(18*a^2*d*(a + b*(c + d*x)^3)) - (5*atan((a^(1/3) - 2*b^(1/3)*(c + d*x))/(sqrt(3)*a^(1/3))))/(9*sqrt(3)*a^(8/3)*b^(1/3)*d) + (5*log(a^(1/3) + b^(1/3)*(c + d*x)))/(27*a^(8/3)*b^(1/3)*d) - (5*log(a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2))/(54*a^(8/3)*b^(1/3)*d)]
    @test_int [1/((c + d*x)^1*(a + b*(c + d*x)^3)^3), x, 4, 1/(6*a*d*(a + b*(c + d*x)^3)^2) + 1/(3*a^2*d*(a + b*(c + d*x)^3)) + log(c + d*x)/(a^3*d) - log(a + b*(c + d*x)^3)/(3*a^3*d)]
    @test_int [1/((c + d*x)^2*(a + b*(c + d*x)^3)^3), x, 10, -(14/(9*a^3*d*(c + d*x))) + 1/(6*a*d*(c + d*x)*(a + b*(c + d*x)^3)^2) + 7/(18*a^2*d*(c + d*x)*(a + b*(c + d*x)^3)) + (14*b^(1/3)*atan((a^(1/3) - 2*b^(1/3)*(c + d*x))/(sqrt(3)*a^(1/3))))/(9*sqrt(3)*a^(10/3)*d) + (14*b^(1/3)*log(a^(1/3) + b^(1/3)*(c + d*x)))/(27*a^(10/3)*d) - (7*b^(1/3)*log(a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2))/(27*a^(10/3)*d)]
    @test_int [1/((c + d*x)^3*(a + b*(c + d*x)^3)^3), x, 10, -(10/(9*a^3*d*(c + d*x)^2)) + 1/(6*a*d*(c + d*x)^2*(a + b*(c + d*x)^3)^2) + 4/(9*a^2*d*(c + d*x)^2*(a + b*(c + d*x)^3)) + (20*b^(2/3)*atan((a^(1/3) - 2*b^(1/3)*(c + d*x))/(sqrt(3)*a^(1/3))))/(9*sqrt(3)*a^(11/3)*d) - (20*b^(2/3)*log(a^(1/3) + b^(1/3)*(c + d*x)))/(27*a^(11/3)*d) + (10*b^(2/3)*log(a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2))/(27*a^(11/3)*d)]
    @test_int [1/((c + d*x)^4*(a + b*(c + d*x)^3)^3), x, 4, -(1/(3*a^3*d*(c + d*x)^3)) - b/(6*a^2*d*(a + b*(c + d*x)^3)^2) - (2*b)/(3*a^3*d*(a + b*(c + d*x)^3)) - (3*b*log(c + d*x))/(a^4*d) + (b*log(a + b*(c + d*x)^3))/(a^4*d)]

    @test_int [(c*e + d*e*x)^4/(a + b*(c + d*x)^3), x, 8, (e^4*(c + d*x)^2)/(2*b*d) + (a^(2/3)*e^4*atan((a^(1/3) - 2*b^(1/3)*(c + d*x))/(sqrt(3)*a^(1/3))))/(sqrt(3)*b^(5/3)*d) + (a^(2/3)*e^4*log(a^(1/3) + b^(1/3)*(c + d*x)))/(3*b^(5/3)*d) - (a^(2/3)*e^4*log(a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2))/(6*b^(5/3)*d)]
    @test_int [(c*e + d*e*x)^3/(a + b*(c + d*x)^3), x, 8, (e^3*x)/b + (a^(1/3)*e^3*atan((a^(1/3) - 2*b^(1/3)*(c + d*x))/(sqrt(3)*a^(1/3))))/(sqrt(3)*b^(4/3)*d) - (a^(1/3)*e^3*log(a^(1/3) + b^(1/3)*(c + d*x)))/(3*b^(4/3)*d) + (a^(1/3)*e^3*log(a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2))/(6*b^(4/3)*d)]
    @test_int [(c*e + d*e*x)^2/(a + b*(c + d*x)^3), x, 2, (e^2*log(a + b*(c + d*x)^3))/(3*b*d)]
    @test_int [(c*e + d*e*x)^1/(a + b*(c + d*x)^3), x, 7, -((e*atan((a^(1/3) - 2*b^(1/3)*(c + d*x))/(sqrt(3)*a^(1/3))))/(sqrt(3)*a^(1/3)*b^(2/3)*d)) - (e*log(a^(1/3) + b^(1/3)*(c + d*x)))/(3*a^(1/3)*b^(2/3)*d) + (e*log(a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2))/(6*a^(1/3)*b^(2/3)*d)]
    @test_int [1/((c*e + d*e*x)^1*(a + b*(c + d*x)^3)), x, 5, log(c + d*x)/(a*d*e) - log(a + b*(c + d*x)^3)/(3*a*d*e)]
    @test_int [1/((c*e + d*e*x)^2*(a + b*(c + d*x)^3)), x, 8, -(1/(a*d*e^2*(c + d*x))) + (b^(1/3)*atan((a^(1/3) - 2*b^(1/3)*(c + d*x))/(sqrt(3)*a^(1/3))))/(sqrt(3)*a^(4/3)*d*e^2) + (b^(1/3)*log(a^(1/3) + b^(1/3)*(c + d*x)))/(3*a^(4/3)*d*e^2) - (b^(1/3)*log(a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2))/(6*a^(4/3)*d*e^2)]
    @test_int [1/((c*e + d*e*x)^3*(a + b*(c + d*x)^3)), x, 8, -1/(2*a*d*e^3*(c + d*x)^2) + (b^(2/3)*atan((a^(1/3) - 2*b^(1/3)*(c + d*x))/(sqrt(3)*a^(1/3))))/(sqrt(3)*a^(5/3)*d*e^3) - (b^(2/3)*log(a^(1/3) + b^(1/3)*(c + d*x)))/(3*a^(5/3)*d*e^3) + (b^(2/3)*log(a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2))/(6*a^(5/3)*d*e^3)]
    @test_int [1/((c*e + d*e*x)^4*(a + b*(c + d*x)^3)), x, 4, -1/(3*a*d*e^4*(c + d*x)^3) - (b*log(c + d*x))/(a^2*d*e^4) + (b*log(a + b*(c + d*x)^3))/(3*a^2*d*e^4)]

    @test_int [(c*e + d*e*x)^4/(a + b*(c + d*x)^3)^2, x, 8, -(e^4*(c + d*x)^2)/(3*b*d*(a + b*(c + d*x)^3)) - (2*e^4*atan((a^(1/3) - 2*b^(1/3)*(c + d*x))/(sqrt(3)*a^(1/3))))/(3*sqrt(3)*a^(1/3)*b^(5/3)*d) - (2*e^4*log(a^(1/3) + b^(1/3)*(c + d*x)))/(9*a^(1/3)*b^(5/3)*d) + (e^4*log(a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2))/(9*a^(1/3)*b^(5/3)*d)]
    @test_int [(c*e + d*e*x)^3/(a + b*(c + d*x)^3)^2, x, 8, -(e^3*(c + d*x))/(3*b*d*(a + b*(c + d*x)^3)) - (e^3*atan((a^(1/3) - 2*b^(1/3)*(c + d*x))/(sqrt(3)*a^(1/3))))/(3*sqrt(3)*a^(2/3)*b^(4/3)*d) + (e^3*log(a^(1/3) + b^(1/3)*(c + d*x)))/(9*a^(2/3)*b^(4/3)*d) - (e^3*log(a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2))/(18*a^(2/3)*b^(4/3)*d)]
    @test_int [(c*e + d*e*x)^2/(a + b*(c + d*x)^3)^2, x, 2, -e^2/(3*b*d*(a + b*(c + d*x)^3))]
    @test_int [(c*e + d*e*x)^1/(a + b*(c + d*x)^3)^2, x, 8, (e*(c + d*x)^2)/(3*a*d*(a + b*(c + d*x)^3)) - (e*atan((a^(1/3) - 2*b^(1/3)*(c + d*x))/(sqrt(3)*a^(1/3))))/(3*sqrt(3)*a^(4/3)*b^(2/3)*d) - (e*log(a^(1/3) + b^(1/3)*(c + d*x)))/(9*a^(4/3)*b^(2/3)*d) + (e*log(a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2))/(18*a^(4/3)*b^(2/3)*d)]
    @test_int [1/((c*e + d*e*x)^1*(a + b*(c + d*x)^3)^2), x, 4, 1/(3*a*d*e*(a + b*(c + d*x)^3)) + log(c + d*x)/(a^2*d*e) - log(a + b*(c + d*x)^3)/(3*a^2*d*e)]
    @test_int [1/((c*e + d*e*x)^2*(a + b*(c + d*x)^3)^2), x, 9, -4/(3*a^2*d*e^2*(c + d*x)) + 1/(3*a*d*e^2*(c + d*x)*(a + b*(c + d*x)^3)) + (4*b^(1/3)*atan((a^(1/3) - 2*b^(1/3)*(c + d*x))/(sqrt(3)*a^(1/3))))/(3*sqrt(3)*a^(7/3)*d*e^2) + (4*b^(1/3)*log(a^(1/3) + b^(1/3)*(c + d*x)))/(9*a^(7/3)*d*e^2) - (2*b^(1/3)*log(a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2))/(9*a^(7/3)*d*e^2)]
    @test_int [1/((c*e + d*e*x)^3*(a + b*(c + d*x)^3)^2), x, 9, -5/(6*a^2*d*e^3*(c + d*x)^2) + 1/(3*a*d*e^3*(c + d*x)^2*(a + b*(c + d*x)^3)) + (5*b^(2/3)*atan((a^(1/3) - 2*b^(1/3)*(c + d*x))/(sqrt(3)*a^(1/3))))/(3*sqrt(3)*a^(8/3)*d*e^3) - (5*b^(2/3)*log(a^(1/3) + b^(1/3)*(c + d*x)))/(9*a^(8/3)*d*e^3) + (5*b^(2/3)*log(a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2))/(18*a^(8/3)*d*e^3)]
    @test_int [1/((c*e + d*e*x)^4*(a + b*(c + d*x)^3)^2), x, 4, -(1/(3*a^2*d*e^4*(c + d*x)^3)) - b/(3*a^2*d*e^4*(a + b*(c + d*x)^3)) - (2*b*log(c + d*x))/(a^3*d*e^4) + (2*b*log(a + b*(c + d*x)^3))/(3*a^3*d*e^4)]

    @test_int [(c*e + d*e*x)^4/(a + b*(c + d*x)^3)^3, x, 9, -(e^4*(c + d*x)^2)/(6*b*d*(a + b*(c + d*x)^3)^2) + (e^4*(c + d*x)^2)/(9*a*b*d*(a + b*(c + d*x)^3)) - (e^4*atan((a^(1/3) - 2*b^(1/3)*(c + d*x))/(sqrt(3)*a^(1/3))))/(9*sqrt(3)*a^(4/3)*b^(5/3)*d) - (e^4*log(a^(1/3) + b^(1/3)*(c + d*x)))/(27*a^(4/3)*b^(5/3)*d) + (e^4*log(a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2))/(54*a^(4/3)*b^(5/3)*d)]
    @test_int [(c*e + d*e*x)^3/(a + b*(c + d*x)^3)^3, x, 9, -(e^3*(c + d*x))/(6*b*d*(a + b*(c + d*x)^3)^2) + (e^3*(c + d*x))/(18*a*b*d*(a + b*(c + d*x)^3)) - (e^3*atan((a^(1/3) - 2*b^(1/3)*(c + d*x))/(sqrt(3)*a^(1/3))))/(9*sqrt(3)*a^(5/3)*b^(4/3)*d) + (e^3*log(a^(1/3) + b^(1/3)*(c + d*x)))/(27*a^(5/3)*b^(4/3)*d) - (e^3*log(a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2))/(54*a^(5/3)*b^(4/3)*d)]
    @test_int [(c*e + d*e*x)^2/(a + b*(c + d*x)^3)^3, x, 2, -e^2/(6*b*d*(a + b*(c + d*x)^3)^2)]
    @test_int [(c*e + d*e*x)^1/(a + b*(c + d*x)^3)^3, x, 9, (e*(c + d*x)^2)/(6*a*d*(a + b*(c + d*x)^3)^2) + (2*e*(c + d*x)^2)/(9*a^2*d*(a + b*(c + d*x)^3)) - (2*e*atan((a^(1/3) - 2*b^(1/3)*(c + d*x))/(sqrt(3)*a^(1/3))))/(9*sqrt(3)*a^(7/3)*b^(2/3)*d) - (2*e*log(a^(1/3) + b^(1/3)*(c + d*x)))/(27*a^(7/3)*b^(2/3)*d) + (e*log(a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2))/(27*a^(7/3)*b^(2/3)*d)]
    @test_int [1/((c*e + d*e*x)^1*(a + b*(c + d*x)^3)^3), x, 4, 1/(6*a*d*e*(a + b*(c + d*x)^3)^2) + 1/(3*a^2*d*e*(a + b*(c + d*x)^3)) + log(c + d*x)/(a^3*d*e) - log(a + b*(c + d*x)^3)/(3*a^3*d*e)]
    @test_int [1/((c*e + d*e*x)^2*(a + b*(c + d*x)^3)^3), x, 10, -14/(9*a^3*d*e^2*(c + d*x)) + 1/(6*a*d*e^2*(c + d*x)*(a + b*(c + d*x)^3)^2) + 7/(18*a^2*d*e^2*(c + d*x)*(a + b*(c + d*x)^3)) + (14*b^(1/3)*atan((a^(1/3) - 2*b^(1/3)*(c + d*x))/(sqrt(3)*a^(1/3))))/(9*sqrt(3)*a^(10/3)*d*e^2) + (14*b^(1/3)*log(a^(1/3) + b^(1/3)*(c + d*x)))/(27*a^(10/3)*d*e^2) - (7*b^(1/3)*log(a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2))/(27*a^(10/3)*d*e^2)]
    @test_int [1/((c*e + d*e*x)^3*(a + b*(c + d*x)^3)^3), x, 10, -10/(9*a^3*d*e^3*(c + d*x)^2) + 1/(6*a*d*e^3*(c + d*x)^2*(a + b*(c + d*x)^3)^2) + 4/(9*a^2*d*e^3*(c + d*x)^2*(a + b*(c + d*x)^3)) + (20*b^(2/3)*atan((a^(1/3) - 2*b^(1/3)*(c + d*x))/(sqrt(3)*a^(1/3))))/(9*sqrt(3)*a^(11/3)*d*e^3) - (20*b^(2/3)*log(a^(1/3) + b^(1/3)*(c + d*x)))/(27*a^(11/3)*d*e^3) + (10*b^(2/3)*log(a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2))/(27*a^(11/3)*d*e^3)]
    @test_int [1/((c*e + d*e*x)^4*(a + b*(c + d*x)^3)^3), x, 4, -(1/(3*a^3*d*e^4*(c + d*x)^3)) - b/(6*a^2*d*e^4*(a + b*(c + d*x)^3)^2) - (2*b)/(3*a^3*d*e^4*(a + b*(c + d*x)^3)) - (3*b*log(c + d*x))/(a^4*d*e^4) + (b*log(a + b*(c + d*x)^3))/(a^4*d*e^4)]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(c+d*x)^m*(a+b*(c+d*x)^4)^p=#

    #= ::Subsubsection::Closed:: =#
    #=p>0=#

    @test_int [(c + d*x)^3*(a + b*(c + d*x)^4)^p, x, 2, (a + b*(c + d*x)^4)^(1 + p)/(4*b*d*(1 + p))]

    @test_int [(c + d*x)^3*(a + b*(c + d*x)^4)^1, x, 3, (a + b*(c + d*x)^4)^2/(8*b*d), (a*(c + d*x)^4)/(4*d) + (b*(c + d*x)^8)/(8*d)]
    @test_int [(c + d*x)^3*(a + b*(c + d*x)^4)^2, x, 2, (a + b*(c + d*x)^4)^3/(12*b*d)]
    @test_int [(c + d*x)^3*(a + b*(c + d*x)^4)^3, x, 2, (a + b*(c + d*x)^4)^4/(16*b*d)]

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [(c + d*x)^3/(a + b*(c + d*x)^4), x, 2, log(a + b*(c + d*x)^4)/(4*b*d)]
    @test_int [(c + d*x)^3/(a + b*(c + d*x)^4)^2, x, 2, -(1/(4*b*d*(a + b*(c + d*x)^4)))]
    @test_int [(c + d*x)^3/(a + b*(c + d*x)^4)^3, x, 2, -(1/(8*b*d*(a + b*(c + d*x)^4)^2))]

    @test_int [1/sqrt(a + b*(c + d*x)^4), x, 2, ((sqrt(a) + sqrt(b)*(c + d*x)^2)*sqrt((a + b*(c + d*x)^4)/(sqrt(a) + sqrt(b)*(c + d*x)^2)^2)*Elliptic.F(2*atan((b^(1/4)*(c + d*x))/a^(1/4)), 1/2))/(2*a^(1/4)*b^(1/4)*d*sqrt(a + b*(c + d*x)^4))]

    @test_int [x/sqrt(a + b*(c + d*x)^4), x, 7, atanh((sqrt(b)*(c + d*x)^2)/sqrt(a + b*(c + d*x)^4))/(2*sqrt(b)*d^2) - (c*(sqrt(a) + sqrt(b)*(c + d*x)^2)*sqrt((a + b*(c + d*x)^4)/(sqrt(a) + sqrt(b)*(c + d*x)^2)^2)*Elliptic.F(2*atan((b^(1/4)*(c + d*x))/a^(1/4)), 1/2))/(2*a^(1/4)*b^(1/4)*d^2*sqrt(a + b*(c + d*x)^4))]

    #= ::Title::Closed:: =#
    #=Integrands*of*the*form*(d*x)^m*(a+b*(c*x^q)^n)^p=#

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(d*x)^m*(a+b*(c*x^1)^n)^p=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(d*x)^m*(a+b*(c*x)^(n/2))^p*with*m*symbolic=#

    #= ::Subsubsection::Closed:: =#
    #=p>0=#

    @test_int [(d*x)^m*sqrt(a + b*(c*x)^(3/2)), x, 5, (x*(d*x)^m*sqrt(a + b*(c*x)^(3/2))*HypergeometricFunctions._₂F₁(-(1/2), (2*(1 + m))/3, (1/3)*(5 + 2*m), -((b*(c*x)^(3/2))/a)))/((1 + m)*sqrt(1 + (b*(c*x)^(3/2))/a))]
    @test_int [(d*x)^m*sqrt(a + b*(c*x)^(1/2)), x, 5, -((4*a*(d*x)^m*(a + b*sqrt(c*x))^(3/2)*HypergeometricFunctions._₂F₁(3/2, -1 - 2*m, 5/2, 1 + (b*sqrt(c*x))/a))/((-((b*sqrt(c*x))/a))^(2*m)*(3*b^2*c)))]
    @test_int [(d*x)^m*sqrt(a + b/(c*x)^(1/2)), x, 6, (4*b^2*(d*x)^m*(-(b/(a*sqrt(c*x))))^(2*m)*(a + b/sqrt(c*x))^(3/2)*HypergeometricFunctions._₂F₁(3/2, 3 + 2*m, 5/2, 1 + b/(a*sqrt(c*x))))/(3*a^3*c)]
    @test_int [(d*x)^m*sqrt(a + b/(c*x)^(3/2)), x, 6, (x*(d*x)^m*sqrt(a + b/(c*x)^(3/2))*HypergeometricFunctions._₂F₁(-(1/2), (-(2/3))*(1 + m), (1/3)*(1 - 2*m), -(b/(a*(c*x)^(3/2)))))/((1 + m)*sqrt(1 + b/(a*(c*x)^(3/2))))]

    #= ::Subsubsection:: =#
    #=p<0=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(d*x)^m*(a+b*(c*x)^n)^p*with*n*and*p*symbolic=#

    @test_int [(d*x)^m*(a + b*(c*x)^n)^p, x, 3, ((d*x)^(1 + m)*(a + b*(c*x)^n)^p*HypergeometricFunctions._₂F₁((1 + m)/n, -p, (1 + m + n)/n, -((b*(c*x)^n)/a)))/((1 + (b*(c*x)^n)/a)^p*(d*(1 + m)))]

    @test_int [x^2*(a + b*(c*x)^n)^p, x, 4, ((1/3)*x^3*(a + b*(c*x)^n)^p*HypergeometricFunctions._₂F₁(3/n, -p, (3 + n)/n, -((b*(c*x)^n)/a)))/(1 + (b*(c*x)^n)/a)^p]
    @test_int [x^1*(a + b*(c*x)^n)^p, x, 4, ((1/2)*x^2*(a + b*(c*x)^n)^p*HypergeometricFunctions._₂F₁(2/n, -p, (2 + n)/n, -((b*(c*x)^n)/a)))/(1 + (b*(c*x)^n)/a)^p]
    @test_int [x^0*(a + b*(c*x)^n)^p, x, 3, (x*(a + b*(c*x)^n)^p*HypergeometricFunctions._₂F₁(1/n, -p, 1 + 1/n, -((b*(c*x)^n)/a)))/(1 + (b*(c*x)^n)/a)^p]
    @test_int [(a + b*(c*x)^n)^p/x^1, x, 4, -(((a + b*(c*x)^n)^(1 + p)*HypergeometricFunctions._₂F₁(1, 1 + p, 2 + p, 1 + (b*(c*x)^n)/a))/(a*n*(1 + p)))]
    @test_int [(a + b*(c*x)^n)^p/x^2, x, 4, -(((a + b*(c*x)^n)^p*HypergeometricFunctions._₂F₁(-(1/n), -p, -((1 - n)/n), -((b*(c*x)^n)/a)))/((1 + (b*(c*x)^n)/a)^p*x))]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(d*x)^m*(a+b*(c*x^2)^n)^p=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b*(c*x^2)^(n/2))^(-1)=#

    @test_int [1/(1 + (x^2)^(3/2)), x, 7, -((x*atan((1 - 2*sqrt(x^2))/sqrt(3)))/(sqrt(3)*sqrt(x^2))) - (x*log(1 + x^2 - sqrt(x^2)))/(6*sqrt(x^2)) + (x*log(1 + sqrt(x^2)))/(3*sqrt(x^2))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b*(c*x^2)^(n/2))^(1/2)=#

    #= ::Subsubsection::Closed:: =#
    #=n>0=#

    @test_int [x^5*sqrt(a + b*sqrt(c*x^2)), x, 3, -((2*a^5*(a + b*sqrt(c*x^2))^(3/2))/(3*b^6*c^3)) + (2*a^4*(a + b*sqrt(c*x^2))^(5/2))/(b^6*c^3) - (20*a^3*(a + b*sqrt(c*x^2))^(7/2))/(7*b^6*c^3) + (20*a^2*(a + b*sqrt(c*x^2))^(9/2))/(9*b^6*c^3) - (10*a*(a + b*sqrt(c*x^2))^(11/2))/(11*b^6*c^3) + (2*(a + b*sqrt(c*x^2))^(13/2))/(13*b^6*c^3)]
    @test_int [x^3*sqrt(a + b*sqrt(c*x^2)), x, 3, -((2*a^3*(a + b*sqrt(c*x^2))^(3/2))/(3*b^4*c^2)) + (6*a^2*(a + b*sqrt(c*x^2))^(5/2))/(5*b^4*c^2) - (6*a*(a + b*sqrt(c*x^2))^(7/2))/(7*b^4*c^2) + (2*(a + b*sqrt(c*x^2))^(9/2))/(9*b^4*c^2)]
    @test_int [x^1*sqrt(a + b*sqrt(c*x^2)), x, 3, -((2*a*(a + b*sqrt(c*x^2))^(3/2))/(3*b^2*c)) + (2*(a + b*sqrt(c*x^2))^(5/2))/(5*b^2*c)]
    @test_int [sqrt(a + b*sqrt(c*x^2))/x^1, x, 4, 2*sqrt(a + b*sqrt(c*x^2)) - 2*sqrt(a)*atanh(sqrt(a + b*sqrt(c*x^2))/sqrt(a))]
    @test_int [sqrt(a + b*sqrt(c*x^2))/x^3, x, 5, -(sqrt(a + b*sqrt(c*x^2))/(2*x^2)) - (b*c*sqrt(a + b*sqrt(c*x^2)))/(4*a*sqrt(c*x^2)) + (b^2*c*atanh(sqrt(a + b*sqrt(c*x^2))/sqrt(a)))/(4*a^(3/2))]
    @test_int [sqrt(a + b*sqrt(c*x^2))/x^5, x, 7, -(sqrt(a + b*sqrt(c*x^2))/(4*x^4)) + (5*b^2*c*sqrt(a + b*sqrt(c*x^2)))/(96*a^2*x^2) - (b*c^2*sqrt(a + b*sqrt(c*x^2)))/(24*a*(c*x^2)^(3/2)) - (5*b^3*c^2*sqrt(a + b*sqrt(c*x^2)))/(64*a^3*sqrt(c*x^2)) + (5*b^4*c^2*atanh(sqrt(a + b*sqrt(c*x^2))/sqrt(a)))/(64*a^(7/2))]

    @test_int [x^4*sqrt(a + b*sqrt(c*x^2)), x, 3, (2*a^4*x^5*(a + b*sqrt(c*x^2))^(3/2))/(3*b^5*(c*x^2)^(5/2)) - (8*a^3*x^5*(a + b*sqrt(c*x^2))^(5/2))/(5*b^5*(c*x^2)^(5/2)) + (12*a^2*x^5*(a + b*sqrt(c*x^2))^(7/2))/(7*b^5*(c*x^2)^(5/2)) - (8*a*x^5*(a + b*sqrt(c*x^2))^(9/2))/(9*b^5*(c*x^2)^(5/2)) + (2*x^5*(a + b*sqrt(c*x^2))^(11/2))/(11*b^5*(c*x^2)^(5/2))]
    @test_int [x^2*sqrt(a + b*sqrt(c*x^2)), x, 3, (2*a^2*x^3*(a + b*sqrt(c*x^2))^(3/2))/(3*b^3*(c*x^2)^(3/2)) - (4*a*x^3*(a + b*sqrt(c*x^2))^(5/2))/(5*b^3*(c*x^2)^(3/2)) + (2*x^3*(a + b*sqrt(c*x^2))^(7/2))/(7*b^3*(c*x^2)^(3/2))]
    @test_int [x^0*sqrt(a + b*sqrt(c*x^2)), x, 2, (2*x*(a + b*sqrt(c*x^2))^(3/2))/(3*b*sqrt(c*x^2))]
    @test_int [sqrt(a + b*sqrt(c*x^2))/x^2, x, 4, -(sqrt(a + b*sqrt(c*x^2))/x) - (b*sqrt(c*x^2)*atanh(sqrt(a + b*sqrt(c*x^2))/sqrt(a)))/(sqrt(a)*x)]
    @test_int [sqrt(a + b*sqrt(c*x^2))/x^4, x, 6, -(sqrt(a + b*sqrt(c*x^2))/(3*x^3)) + (b^2*c*sqrt(a + b*sqrt(c*x^2)))/(8*a^2*x) - (b*(c*x^2)^(3/2)*sqrt(a + b*sqrt(c*x^2)))/(12*a*c*x^5) - (b^3*(c*x^2)^(3/2)*atanh(sqrt(a + b*sqrt(c*x^2))/sqrt(a)))/(8*a^(5/2)*x^3)]
    @test_int [sqrt(a + b*sqrt(c*x^2))/x^6, x, 8, -(sqrt(a + b*sqrt(c*x^2))/(5*x^5)) + (7*b^2*c*sqrt(a + b*sqrt(c*x^2)))/(240*a^2*x^3) + (7*b^4*c^2*sqrt(a + b*sqrt(c*x^2)))/(128*a^4*x) - (b*(c*x^2)^(5/2)*sqrt(a + b*sqrt(c*x^2)))/(40*a*c^2*x^9) - (7*b^3*(c*x^2)^(5/2)*sqrt(a + b*sqrt(c*x^2)))/(192*a^3*c*x^7) - (7*b^5*(c*x^2)^(5/2)*atanh(sqrt(a + b*sqrt(c*x^2))/sqrt(a)))/(128*a^(9/2)*x^5)]

    @test_int [x^8*sqrt(a + b*(c*x^2)^(3/2)), x, 4, (2*a^2*x^9*(a + b*(c*x^2)^(3/2))^(3/2))/(9*b^3*(c*x^2)^(9/2)) - (4*a*x^9*(a + b*(c*x^2)^(3/2))^(5/2))/(15*b^3*(c*x^2)^(9/2)) + (2*x^9*(a + b*(c*x^2)^(3/2))^(7/2))/(21*b^3*(c*x^2)^(9/2))]
    @test_int [x^5*sqrt(a + b*(c*x^2)^(3/2)), x, 4, -((2*a*(a + b*(c*x^2)^(3/2))^(3/2))/(9*b^2*c^3)) + (2*(a + b*(c*x^2)^(3/2))^(5/2))/(15*b^2*c^3)]
    @test_int [x^2*sqrt(a + b*(c*x^2)^(3/2)), x, 2, (2*x^3*(a + b*(c*x^2)^(3/2))^(3/2))/(9*b*(c*x^2)^(3/2))]
    @test_int [sqrt(a + b*(c*x^2)^(3/2))/x^1, x, 5, (2/3)*sqrt(a + b*(c*x^2)^(3/2)) - (2/3)*sqrt(a)*atanh(sqrt(a + b*(c*x^2)^(3/2))/sqrt(a))]
    @test_int [sqrt(a + b*(c*x^2)^(3/2))/x^4, x, 5, -(sqrt(a + b*(c*x^2)^(3/2))/(3*x^3)) - (b*(c*x^2)^(3/2)*atanh(sqrt(a + b*(c*x^2)^(3/2))/sqrt(a)))/(3*sqrt(a)*x^3)]

    @test_int [x^3*sqrt(a + b*(c*x^2)^(3/2)), x, 4, (2/11)*x^4*sqrt(a + b*(c*x^2)^(3/2)) + (6*a*sqrt(c*x^2)*sqrt(a + b*(c*x^2)^(3/2)))/(55*b*c^2) - (4*3^(3/4)*sqrt(2 + sqrt(3))*a^2*(a^(1/3) + b^(1/3)*sqrt(c*x^2))*sqrt((a^(2/3) + b^(2/3)*c*x^2 - a^(1/3)*b^(1/3)*sqrt(c*x^2))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*sqrt(c*x^2))^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*sqrt(c*x^2))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*sqrt(c*x^2))), -7 - 4*sqrt(3)))/(55*b^(4/3)*c^2*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*sqrt(c*x^2)))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*sqrt(c*x^2))^2)*sqrt(a + b*(c*x^2)^(3/2)))]
    @test_int [x^0*sqrt(a + b*(c*x^2)^(3/2)), x, 3, (2/5)*x*sqrt(a + b*(c*x^2)^(3/2)) + (2*3^(3/4)*sqrt(2 + sqrt(3))*a*x*(a^(1/3) + b^(1/3)*sqrt(c*x^2))*sqrt((a^(2/3) + b^(2/3)*c*x^2 - a^(1/3)*b^(1/3)*sqrt(c*x^2))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*sqrt(c*x^2))^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*sqrt(c*x^2))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*sqrt(c*x^2))), -7 - 4*sqrt(3)))/(5*b^(1/3)*sqrt(c*x^2)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*sqrt(c*x^2)))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*sqrt(c*x^2))^2)*sqrt(a + b*(c*x^2)^(3/2)))]
    @test_int [sqrt(a + b*(c*x^2)^(3/2))/x^3, x, 3, -(sqrt(a + b*(c*x^2)^(3/2))/(2*x^2)) + (3^(3/4)*sqrt(2 + sqrt(3))*b^(2/3)*c*(a^(1/3) + b^(1/3)*sqrt(c*x^2))*sqrt((a^(2/3) + b^(2/3)*c*x^2 - a^(1/3)*b^(1/3)*sqrt(c*x^2))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*sqrt(c*x^2))^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*sqrt(c*x^2))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*sqrt(c*x^2))), -7 - 4*sqrt(3)))/(2*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*sqrt(c*x^2)))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*sqrt(c*x^2))^2)*sqrt(a + b*(c*x^2)^(3/2)))]
    @test_int [sqrt(a + b*(c*x^2)^(3/2))/x^6, x, 4, -(sqrt(a + b*(c*x^2)^(3/2))/(5*x^5)) - (3*b*(c*x^2)^(5/2)*sqrt(a + b*(c*x^2)^(3/2)))/(20*a*c*x^7) - (3^(3/4)*sqrt(2 + sqrt(3))*b^(5/3)*(c*x^2)^(5/2)*(a^(1/3) + b^(1/3)*sqrt(c*x^2))*sqrt((a^(2/3) + b^(2/3)*c*x^2 - a^(1/3)*b^(1/3)*sqrt(c*x^2))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*sqrt(c*x^2))^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*sqrt(c*x^2))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*sqrt(c*x^2))), -7 - 4*sqrt(3)))/(20*a*x^5*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*sqrt(c*x^2)))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*sqrt(c*x^2))^2)*sqrt(a + b*(c*x^2)^(3/2)))]

    @test_int [x^4*sqrt(a + b*(c*x^2)^(3/2)), x, 6, (2/13)*x^5*sqrt(a + b*(c*x^2)^(3/2)) + (6*a*c*x^7*sqrt(a + b*(c*x^2)^(3/2)))/(91*b*(c*x^2)^(5/2)) - (24*a^2*x^5*sqrt(a + b*(c*x^2)^(3/2)))/(91*b^(5/3)*(c*x^2)^(5/2)*((1 + sqrt(3))*a^(1/3) + b^(1/3)*sqrt(c*x^2))) + (12*3^(1/4)*sqrt(2 - sqrt(3))*a^(7/3)*x^5*(a^(1/3) + b^(1/3)*sqrt(c*x^2))*sqrt((a^(2/3) + b^(2/3)*c*x^2 - a^(1/3)*b^(1/3)*sqrt(c*x^2))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*sqrt(c*x^2))^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*sqrt(c*x^2))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*sqrt(c*x^2))), -7 - 4*sqrt(3)))/(91*b^(5/3)*(c*x^2)^(5/2)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*sqrt(c*x^2)))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*sqrt(c*x^2))^2)*sqrt(a + b*(c*x^2)^(3/2))) - (8*sqrt(2)*3^(3/4)*a^(7/3)*x^5*(a^(1/3) + b^(1/3)*sqrt(c*x^2))*sqrt((a^(2/3) + b^(2/3)*c*x^2 - a^(1/3)*b^(1/3)*sqrt(c*x^2))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*sqrt(c*x^2))^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*sqrt(c*x^2))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*sqrt(c*x^2))), -7 - 4*sqrt(3)))/(91*b^(5/3)*(c*x^2)^(5/2)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*sqrt(c*x^2)))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*sqrt(c*x^2))^2)*sqrt(a + b*(c*x^2)^(3/2)))]
    @test_int [x^1*sqrt(a + b*(c*x^2)^(3/2)), x, 5, (2/7)*x^2*sqrt(a + b*(c*x^2)^(3/2)) + (6*a*sqrt(a + b*(c*x^2)^(3/2)))/(7*b^(2/3)*c*((1 + sqrt(3))*a^(1/3) + b^(1/3)*sqrt(c*x^2))) - (3*3^(1/4)*sqrt(2 - sqrt(3))*a^(4/3)*(a^(1/3) + b^(1/3)*sqrt(c*x^2))*sqrt((a^(2/3) + b^(2/3)*c*x^2 - a^(1/3)*b^(1/3)*sqrt(c*x^2))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*sqrt(c*x^2))^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*sqrt(c*x^2))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*sqrt(c*x^2))), -7 - 4*sqrt(3)))/(7*b^(2/3)*c*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*sqrt(c*x^2)))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*sqrt(c*x^2))^2)*sqrt(a + b*(c*x^2)^(3/2))) + (2*sqrt(2)*3^(3/4)*a^(4/3)*(a^(1/3) + b^(1/3)*sqrt(c*x^2))*sqrt((a^(2/3) + b^(2/3)*c*x^2 - a^(1/3)*b^(1/3)*sqrt(c*x^2))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*sqrt(c*x^2))^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*sqrt(c*x^2))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*sqrt(c*x^2))), -7 - 4*sqrt(3)))/(7*b^(2/3)*c*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*sqrt(c*x^2)))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*sqrt(c*x^2))^2)*sqrt(a + b*(c*x^2)^(3/2)))]
    @test_int [sqrt(a + b*(c*x^2)^(3/2))/x^2, x, 5, -(sqrt(a + b*(c*x^2)^(3/2))/x) + (3*b^(1/3)*sqrt(c*x^2)*sqrt(a + b*(c*x^2)^(3/2)))/(x*((1 + sqrt(3))*a^(1/3) + b^(1/3)*sqrt(c*x^2))) - (3*3^(1/4)*sqrt(2 - sqrt(3))*a^(1/3)*b^(1/3)*sqrt(c*x^2)*(a^(1/3) + b^(1/3)*sqrt(c*x^2))*sqrt((a^(2/3) + b^(2/3)*c*x^2 - a^(1/3)*b^(1/3)*sqrt(c*x^2))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*sqrt(c*x^2))^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*sqrt(c*x^2))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*sqrt(c*x^2))), -7 - 4*sqrt(3)))/(2*x*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*sqrt(c*x^2)))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*sqrt(c*x^2))^2)*sqrt(a + b*(c*x^2)^(3/2))) + (sqrt(2)*3^(3/4)*a^(1/3)*b^(1/3)*sqrt(c*x^2)*(a^(1/3) + b^(1/3)*sqrt(c*x^2))*sqrt((a^(2/3) + b^(2/3)*c*x^2 - a^(1/3)*b^(1/3)*sqrt(c*x^2))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*sqrt(c*x^2))^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*sqrt(c*x^2))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*sqrt(c*x^2))), -7 - 4*sqrt(3)))/(x*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*sqrt(c*x^2)))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*sqrt(c*x^2))^2)*sqrt(a + b*(c*x^2)^(3/2)))]
    @test_int [sqrt(a + b*(c*x^2)^(3/2))/x^5, x, 6, -(sqrt(a + b*(c*x^2)^(3/2))/(4*x^4)) - (3*b*c^2*sqrt(a + b*(c*x^2)^(3/2)))/(8*a*sqrt(c*x^2)) + (3*b^(4/3)*c^2*sqrt(a + b*(c*x^2)^(3/2)))/(8*a*((1 + sqrt(3))*a^(1/3) + b^(1/3)*sqrt(c*x^2))) - (3*3^(1/4)*sqrt(2 - sqrt(3))*b^(4/3)*c^2*(a^(1/3) + b^(1/3)*sqrt(c*x^2))*sqrt((a^(2/3) + b^(2/3)*c*x^2 - a^(1/3)*b^(1/3)*sqrt(c*x^2))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*sqrt(c*x^2))^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*sqrt(c*x^2))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*sqrt(c*x^2))), -7 - 4*sqrt(3)))/(16*a^(2/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*sqrt(c*x^2)))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*sqrt(c*x^2))^2)*sqrt(a + b*(c*x^2)^(3/2))) + (3^(3/4)*b^(4/3)*c^2*(a^(1/3) + b^(1/3)*sqrt(c*x^2))*sqrt((a^(2/3) + b^(2/3)*c*x^2 - a^(1/3)*b^(1/3)*sqrt(c*x^2))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*sqrt(c*x^2))^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*sqrt(c*x^2))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*sqrt(c*x^2))), -7 - 4*sqrt(3)))/(4*sqrt(2)*a^(2/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*sqrt(c*x^2)))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*sqrt(c*x^2))^2)*sqrt(a + b*(c*x^2)^(3/2)))]

    #= ::Subsubsection:: =#
    #=n<0=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(d*x)^m*(a+b*(c*x^2)^(n/2))^p*with*m*symbolic=#

    #= ::Subsubsection::Closed:: =#
    #=p>0=#

    @test_int [(d*x)^m*sqrt(a + b*(c*x^2)^(3/2)), x, 3, ((d*x)^(1 + m)*sqrt(a + b*(c*x^2)^(3/2))*HypergeometricFunctions._₂F₁(-(1/2), (1 + m)/3, (4 + m)/3, -((b*(c*x^2)^(3/2))/a)))/(d*(1 + m)*sqrt(1 + (b*(c*x^2)^(3/2))/a))]
    @test_int [(d*x)^m*sqrt(a + b*(c*x^2)^(1/2)), x, 3, (2*(d*x)^(1 + m)*(a + b*sqrt(c*x^2))^(3/2)*HypergeometricFunctions._₂F₁(3/2, -m, 5/2, 1 + (b*sqrt(c*x^2))/a))/((-((b*sqrt(c*x^2))/a))^m*(3*b*d*sqrt(c*x^2)))]
    @test_int [(d*x)^m*sqrt(a + b/(c*x^2)^(1/2)), x, 4, -((2*b*(d*x)^(1 + m)*(-(b/(a*sqrt(c*x^2))))^m*(a + b/sqrt(c*x^2))^(3/2)*HypergeometricFunctions._₂F₁(3/2, 2 + m, 5/2, 1 + b/(a*sqrt(c*x^2))))/(3*a^2*d*sqrt(c*x^2)))]
    @test_int [(d*x)^m*sqrt(a + b/(c*x^2)^(3/2)), x, 4, ((d*x)^(1 + m)*sqrt(a + b/(c*x^2)^(3/2))*HypergeometricFunctions._₂F₁(-(1/2), (1/3)*(-1 - m), (2 - m)/3, -(b/(a*(c*x^2)^(3/2)))))/(d*(1 + m)*sqrt(1 + b/(a*(c*x^2)^(3/2))))]

    #= ::Subsubsection:: =#
    #=p<0=#

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(d*x)^m*(a+b*(c*x^3)^n)^p=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b*(c*x^3)^(n/2))^(-1)=#

    @test_int [1/(1 + (x^3)^(2/3)), x, 2, (x*atan((x^3)^(1/3)))/(x^3)^(1/3)]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b*(c*x^3)^(n/2))^(1/2)=#

    #= ::Subsubsection::Closed:: =#
    #=n>0=#

    @test_int [x^5*sqrt(a + b*sqrt(c*x^3)), x, 4, -((4*a^3*(a + b*sqrt(c*x^3))^(3/2))/(9*b^4*c^2)) + (4*a^2*(a + b*sqrt(c*x^3))^(5/2))/(5*b^4*c^2) - (4*a*(a + b*sqrt(c*x^3))^(7/2))/(7*b^4*c^2) + (4*(a + b*sqrt(c*x^3))^(9/2))/(27*b^4*c^2)]
    @test_int [x^2*sqrt(a + b*sqrt(c*x^3)), x, 4, -((4*a*(a + b*sqrt(c*x^3))^(3/2))/(9*b^2*c)) + (4*(a + b*sqrt(c*x^3))^(5/2))/(15*b^2*c)]
    @test_int [sqrt(a + b*sqrt(c*x^3))/x^1, x, 5, (4/3)*sqrt(a + b*sqrt(c*x^3)) - (4/3)*sqrt(a)*atanh(sqrt(a + b*sqrt(c*x^3))/sqrt(a))]
    @test_int [sqrt(a + b*sqrt(c*x^3))/x^4, x, 6, -(sqrt(a + b*sqrt(c*x^3))/(3*x^3)) - (b*c*sqrt(a + b*sqrt(c*x^3)))/(6*a*sqrt(c*x^3)) + (b^2*c*atanh(sqrt(a + b*sqrt(c*x^3))/sqrt(a)))/(6*a^(3/2))]

    @test_int [x^1*sqrt(a + b*sqrt(c*x^3)), x, 5, (4/11)*x^2*sqrt(a + b*sqrt(c*x^3)) + (12*a*x^2*sqrt(a + b*sqrt(c*x^3)))/(55*b*sqrt(c*x^3)) - (8*3^(3/4)*sqrt(2 + sqrt(3))*a^2*(a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/sqrt(c*x^3))*sqrt((a^(2/3) + b^(2/3)*c^(1/3)*x - (a^(1/3)*b^(1/3)*c^(2/3)*x^2)/sqrt(c*x^3))/((1 + sqrt(3))*a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/sqrt(c*x^3))^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/sqrt(c*x^3))/((1 + sqrt(3))*a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/sqrt(c*x^3))), -7 - 4*sqrt(3)))/(55*b^(4/3)*c^(2/3)*sqrt((a^(1/3)*(a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/sqrt(c*x^3)))/((1 + sqrt(3))*a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/sqrt(c*x^3))^2)*sqrt(a + b*sqrt(c*x^3)))]
    @test_int [sqrt(a + b*sqrt(c*x^3))/x^2, x, 4, -(sqrt(a + b*sqrt(c*x^3))/x) + (3^(3/4)*sqrt(2 + sqrt(3))*b^(2/3)*c^(1/3)*(a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/sqrt(c*x^3))*sqrt((a^(2/3) + b^(2/3)*c^(1/3)*x - (a^(1/3)*b^(1/3)*c^(2/3)*x^2)/sqrt(c*x^3))/((1 + sqrt(3))*a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/sqrt(c*x^3))^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/sqrt(c*x^3))/((1 + sqrt(3))*a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/sqrt(c*x^3))), -7 - 4*sqrt(3)))/(sqrt((a^(1/3)*(a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/sqrt(c*x^3)))/((1 + sqrt(3))*a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/sqrt(c*x^3))^2)*sqrt(a + b*sqrt(c*x^3)))]
    @test_int [sqrt(a + b*sqrt(c*x^3))/x^5, x, 6, -(sqrt(a + b*sqrt(c*x^3))/(4*x^4)) + (21*b^2*c*sqrt(a + b*sqrt(c*x^3)))/(160*a^2*x) - (3*b*c^3*x^5*sqrt(a + b*sqrt(c*x^3)))/(40*a*(c*x^3)^(5/2)) + (7*3^(3/4)*sqrt(2 + sqrt(3))*b^(8/3)*c^(4/3)*(a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/sqrt(c*x^3))*sqrt((a^(2/3) + b^(2/3)*c^(1/3)*x - (a^(1/3)*b^(1/3)*c^(2/3)*x^2)/sqrt(c*x^3))/((1 + sqrt(3))*a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/sqrt(c*x^3))^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/sqrt(c*x^3))/((1 + sqrt(3))*a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/sqrt(c*x^3))), -7 - 4*sqrt(3)))/(160*a^2*sqrt((a^(1/3)*(a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/sqrt(c*x^3)))/((1 + sqrt(3))*a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/sqrt(c*x^3))^2)*sqrt(a + b*sqrt(c*x^3)))]

    @test_int [x^3*sqrt(a + b*sqrt(c*x^3)), x, 8, -((120*a^2*x*sqrt(a + b*sqrt(c*x^3)))/(1729*b^2*c)) + (4/19)*x^4*sqrt(a + b*sqrt(c*x^3)) + (12*a*x*sqrt(c*x^3)*sqrt(a + b*sqrt(c*x^3)))/(247*b*c) + (480*a^3*sqrt(a + b*sqrt(c*x^3)))/(1729*b^(8/3)*c^(4/3)*((1 + sqrt(3))*a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/sqrt(c*x^3))) - (240*3^(1/4)*sqrt(2 - sqrt(3))*a^(10/3)*(a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/sqrt(c*x^3))*sqrt((a^(2/3) + b^(2/3)*c^(1/3)*x - (a^(1/3)*b^(1/3)*c^(2/3)*x^2)/sqrt(c*x^3))/((1 + sqrt(3))*a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/sqrt(c*x^3))^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/sqrt(c*x^3))/((1 + sqrt(3))*a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/sqrt(c*x^3))), -7 - 4*sqrt(3)))/(1729*b^(8/3)*c^(4/3)*sqrt((a^(1/3)*(a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/sqrt(c*x^3)))/((1 + sqrt(3))*a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/sqrt(c*x^3))^2)*sqrt(a + b*sqrt(c*x^3))) + (160*sqrt(2)*3^(3/4)*a^(10/3)*(a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/sqrt(c*x^3))*sqrt((a^(2/3) + b^(2/3)*c^(1/3)*x - (a^(1/3)*b^(1/3)*c^(2/3)*x^2)/sqrt(c*x^3))/((1 + sqrt(3))*a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/sqrt(c*x^3))^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/sqrt(c*x^3))/((1 + sqrt(3))*a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/sqrt(c*x^3))), -7 - 4*sqrt(3)))/(1729*b^(8/3)*c^(4/3)*sqrt((a^(1/3)*(a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/sqrt(c*x^3)))/((1 + sqrt(3))*a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/sqrt(c*x^3))^2)*sqrt(a + b*sqrt(c*x^3)))]
    @test_int [x^0*sqrt(a + b*sqrt(c*x^3)), x, 6, (4/7)*x*sqrt(a + b*sqrt(c*x^3)) + (12*a*sqrt(a + b*sqrt(c*x^3)))/(7*b^(2/3)*c^(1/3)*((1 + sqrt(3))*a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/sqrt(c*x^3))) - (6*3^(1/4)*sqrt(2 - sqrt(3))*a^(4/3)*(a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/sqrt(c*x^3))*sqrt((a^(2/3) + b^(2/3)*c^(1/3)*x - (a^(1/3)*b^(1/3)*c^(2/3)*x^2)/sqrt(c*x^3))/((1 + sqrt(3))*a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/sqrt(c*x^3))^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/sqrt(c*x^3))/((1 + sqrt(3))*a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/sqrt(c*x^3))), -7 - 4*sqrt(3)))/(7*b^(2/3)*c^(1/3)*sqrt((a^(1/3)*(a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/sqrt(c*x^3)))/((1 + sqrt(3))*a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/sqrt(c*x^3))^2)*sqrt(a + b*sqrt(c*x^3))) + (4*sqrt(2)*3^(3/4)*a^(4/3)*(a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/sqrt(c*x^3))*sqrt((a^(2/3) + b^(2/3)*c^(1/3)*x - (a^(1/3)*b^(1/3)*c^(2/3)*x^2)/sqrt(c*x^3))/((1 + sqrt(3))*a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/sqrt(c*x^3))^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/sqrt(c*x^3))/((1 + sqrt(3))*a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/sqrt(c*x^3))), -7 - 4*sqrt(3)))/(7*b^(2/3)*c^(1/3)*sqrt((a^(1/3)*(a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/sqrt(c*x^3)))/((1 + sqrt(3))*a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/sqrt(c*x^3))^2)*sqrt(a + b*sqrt(c*x^3)))]
    @test_int [sqrt(a + b*sqrt(c*x^3))/x^3, x, 7, -(sqrt(a + b*sqrt(c*x^3))/(2*x^2)) - (3*b*c*x*sqrt(a + b*sqrt(c*x^3)))/(4*a*sqrt(c*x^3)) + (3*b^(4/3)*c^(2/3)*sqrt(a + b*sqrt(c*x^3)))/(4*a*((1 + sqrt(3))*a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/sqrt(c*x^3))) - (3*3^(1/4)*sqrt(2 - sqrt(3))*b^(4/3)*c^(2/3)*(a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/sqrt(c*x^3))*sqrt((a^(2/3) + b^(2/3)*c^(1/3)*x - (a^(1/3)*b^(1/3)*c^(2/3)*x^2)/sqrt(c*x^3))/((1 + sqrt(3))*a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/sqrt(c*x^3))^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/sqrt(c*x^3))/((1 + sqrt(3))*a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/sqrt(c*x^3))), -7 - 4*sqrt(3)))/(8*a^(2/3)*sqrt((a^(1/3)*(a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/sqrt(c*x^3)))/((1 + sqrt(3))*a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/sqrt(c*x^3))^2)*sqrt(a + b*sqrt(c*x^3))) + (3^(3/4)*b^(4/3)*c^(2/3)*(a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/sqrt(c*x^3))*sqrt((a^(2/3) + b^(2/3)*c^(1/3)*x - (a^(1/3)*b^(1/3)*c^(2/3)*x^2)/sqrt(c*x^3))/((1 + sqrt(3))*a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/sqrt(c*x^3))^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/sqrt(c*x^3))/((1 + sqrt(3))*a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/sqrt(c*x^3))), -7 - 4*sqrt(3)))/(2*sqrt(2)*a^(2/3)*sqrt((a^(1/3)*(a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/sqrt(c*x^3)))/((1 + sqrt(3))*a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/sqrt(c*x^3))^2)*sqrt(a + b*sqrt(c*x^3)))]

    @test_int [x^17*sqrt(a + b*(c*x^3)^(3/2)), x, 4, -((4*a^3*(a + b*(c*x^3)^(3/2))^(3/2))/(27*b^4*c^6)) + (4*a^2*(a + b*(c*x^3)^(3/2))^(5/2))/(15*b^4*c^6) - (4*a*(a + b*(c*x^3)^(3/2))^(7/2))/(21*b^4*c^6) + (4*(a + b*(c*x^3)^(3/2))^(9/2))/(81*b^4*c^6)]
    @test_int [x^8*sqrt(a + b*(c*x^3)^(3/2)), x, 4, -((4*a*(a + b*(c*x^3)^(3/2))^(3/2))/(27*b^2*c^3)) + (4*(a + b*(c*x^3)^(3/2))^(5/2))/(45*b^2*c^3)]
    @test_int [sqrt(a + b*(c*x^3)^(3/2))/x^1, x, 5, (4/9)*sqrt(a + b*(c*x^3)^(3/2)) - (4/9)*sqrt(a)*atanh(sqrt(a + b*(c*x^3)^(3/2))/sqrt(a))]
    @test_int [sqrt(a + b*(c*x^3)^(3/2))/x^10, x, 6, -(sqrt(a + b*(c*x^3)^(3/2))/(9*x^9)) - (b*c^3*sqrt(a + b*(c*x^3)^(3/2)))/(18*a*(c*x^3)^(3/2)) + (b^2*c^3*atanh(sqrt(a + b*(c*x^3)^(3/2))/sqrt(a)))/(18*a^(3/2)), -(sqrt(a + b*(c*x^3)^(3/2))/(9*x^9)) - (b*c^6*x^9*sqrt(a + b*(c*x^3)^(3/2)))/(18*a*(c*x^3)^(9/2)) + (b^2*c^3*atanh(sqrt(a + b*(c*x^3)^(3/2))/sqrt(a)))/(18*a^(3/2))]

    @test_int [x^2*sqrt(a + b*(c*x^3)^(3/2)), x, 7, (4/21)*x^3*sqrt(a + b*(c*x^3)^(3/2)) + (4*a*sqrt(a + b*(c*x^3)^(3/2)))/(7*b^(2/3)*c*((1 + sqrt(3))*a^(1/3) + b^(1/3)*sqrt(c*x^3))) - (2*3^(1/4)*sqrt(2 - sqrt(3))*a^(4/3)*(a^(1/3) + b^(1/3)*sqrt(c*x^3))*sqrt((a^(2/3) + b^(2/3)*c*x^3 - a^(1/3)*b^(1/3)*sqrt(c*x^3))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*sqrt(c*x^3))^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*sqrt(c*x^3))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*sqrt(c*x^3))), -7 - 4*sqrt(3)))/(7*b^(2/3)*c*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*sqrt(c*x^3)))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*sqrt(c*x^3))^2)*sqrt(a + b*(c*x^3)^(3/2))) + (4*sqrt(2)*a^(4/3)*(a^(1/3) + b^(1/3)*sqrt(c*x^3))*sqrt((a^(2/3) + b^(2/3)*c*x^3 - a^(1/3)*b^(1/3)*sqrt(c*x^3))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*sqrt(c*x^3))^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*sqrt(c*x^3))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*sqrt(c*x^3))), -7 - 4*sqrt(3)))/(7*3^(1/4)*b^(2/3)*c*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*sqrt(c*x^3)))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*sqrt(c*x^3))^2)*sqrt(a + b*(c*x^3)^(3/2)))]

    @test_int [x^9*sqrt(a + b*(c*x^3)^(3/2)), x, 7, -((792*a^2*x*sqrt(a + b*(c*x^3)^(3/2)))/(19747*b^2*c^3)) + (4/49)*x^10*sqrt(a + b*(c*x^3)^(3/2)) + (36*a*x*(c*x^3)^(3/2)*sqrt(a + b*(c*x^3)^(3/2)))/(1519*b*c^3) + (792*a^3*x*sqrt(1 + (b*(c*x^3)^(3/2))/a)*HypergeometricFunctions._₂F₁(2/9, 1/2, 11/9, -((b*(c*x^3)^(3/2))/a)))/(19747*b^2*c^3*sqrt(a + b*(c*x^3)^(3/2)))]
    @test_int [x^0*sqrt(a + b*(c*x^3)^(3/2)), x, 5, (4/13)*x*sqrt(a + b*(c*x^3)^(3/2)) + (9*a*x*sqrt(1 + (b*(c*x^3)^(3/2))/a)*HypergeometricFunctions._₂F₁(2/9, 1/2, 11/9, -((b*(c*x^3)^(3/2))/a)))/(13*sqrt(a + b*(c*x^3)^(3/2)))]
    @test_int [sqrt(a + b*(c*x^3)^(3/2))/x^9, x, 6, -(sqrt(a + b*(c*x^3)^(3/2))/(8*x^8)) - (9*b*c^3*x*sqrt(a + b*(c*x^3)^(3/2)))/(112*a*(c*x^3)^(3/2)) - (45*b^2*c^3*x*sqrt(1 + (b*(c*x^3)^(3/2))/a)*HypergeometricFunctions._₂F₁(2/9, 1/2, 11/9, -((b*(c*x^3)^(3/2))/a)))/(448*a*sqrt(a + b*(c*x^3)^(3/2))), -(sqrt(a + b*(c*x^3)^(3/2))/(8*x^8)) - (9*b*c^5*x^7*sqrt(a + b*(c*x^3)^(3/2)))/(112*a*(c*x^3)^(7/2)) - (45*b^2*c^3*x*sqrt(1 + (b*(c*x^3)^(3/2))/a)*HypergeometricFunctions._₂F₁(2/9, 1/2, 11/9, -((b*(c*x^3)^(3/2))/a)))/(448*a*sqrt(a + b*(c*x^3)^(3/2)))]

    #= ::Subsubsection:: =#
    #=n<0=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(d*x)^m*(a+b*(c*x^3)^(n/2))^p*with*m*symbolic=#

    #= ::Subsubsection::Closed:: =#
    #=p>0=#

    @test_int [(d*x)^m*sqrt(a + b*(c*x^3)^(3/2)), x, 5, (x*(d*x)^m*sqrt(a + b*(c*x^3)^(3/2))*HypergeometricFunctions._₂F₁(-(1/2), (2*(1 + m))/9, 1 + (2*(1 + m))/9, -((b*(c*x^3)^(3/2))/a)))/((1 + m)*sqrt(1 + (b*(c*x^3)^(3/2))/a))]
    @test_int [(d*x)^m*sqrt(a + b*(c*x^3)^(1/2)), x, 5, (x*(d*x)^m*sqrt(a + b*sqrt(c*x^3))*HypergeometricFunctions._₂F₁(-(1/2), (2*(1 + m))/3, (1/3)*(5 + 2*m), -((b*sqrt(c*x^3))/a)))/((1 + m)*sqrt(1 + (b*sqrt(c*x^3))/a))]
    @test_int [(d*x)^m*sqrt(a + b/(c*x^3)^(1/2)), x, 6, (x*(d*x)^m*sqrt(a + b/sqrt(c*x^3))*HypergeometricFunctions._₂F₁(-(1/2), (-(2/3))*(1 + m), (1/3)*(1 - 2*m), -(b/(a*sqrt(c*x^3)))))/((1 + m)*sqrt(1 + b/(a*sqrt(c*x^3))))]
    @test_int [(d*x)^m*sqrt(a + b/(c*x^3)^(3/2)), x, 6, (x*(d*x)^m*sqrt(a + (b*c^3*x^9)/(c*x^3)^(9/2))*HypergeometricFunctions._₂F₁(-(1/2), (-(2/9))*(1 + m), (1/9)*(7 - 2*m), -((b*c^3*x^9)/(a*(c*x^3)^(9/2)))))/((1 + m)*sqrt(1 + (b*c^3*x^9)/(a*(c*x^3)^(9/2))))]

    #= ::Subsubsection:: =#
    #=p<0=#

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(d*x)^m*(a+b*(c*x^-1)^n)^p=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b*(c /x)^(n/2))^(1/2)=#

    #= ::Subsubsection::Closed:: =#
    #=n>0=#

    @test_int [x^1*sqrt(a + b*sqrt(c/x)), x, 8, (b*c^2*sqrt(a + b*sqrt(c/x)))/(12*a*(c/x)^(3/2)) + (5*b^3*c^2*sqrt(a + b*sqrt(c/x)))/(32*a^3*sqrt(c/x)) - (5*b^2*c*sqrt(a + b*sqrt(c/x))*x)/(48*a^2) + (1/2)*sqrt(a + b*sqrt(c/x))*x^2 - (5*b^4*c^2*atanh(sqrt(a + b*sqrt(c/x))/sqrt(a)))/(32*a^(7/2)), (5*b^3*c^2*sqrt(a + b*sqrt(c/x)))/(32*a^3*sqrt(c/x)) - (5*b^2*c*sqrt(a + b*sqrt(c/x))*x)/(48*a^2) + (1/2)*sqrt(a + b*sqrt(c/x))*x^2 + (b*sqrt(a + b*sqrt(c/x))*(c/x)^(3/2)*x^3)/(12*a*c) - (5*b^4*c^2*atanh(sqrt(a + b*sqrt(c/x))/sqrt(a)))/(32*a^(7/2))]
    @test_int [x^0*sqrt(a + b*sqrt(c/x)), x, 6, (b*c*sqrt(a + b*sqrt(c/x)))/(2*a*sqrt(c/x)) + sqrt(a + b*sqrt(c/x))*x - (b^2*c*atanh(sqrt(a + b*sqrt(c/x))/sqrt(a)))/(2*a^(3/2))]
    @test_int [sqrt(a + b*sqrt(c/x))/x^1, x, 5, -4*sqrt(a + b*sqrt(c/x)) + 4*sqrt(a)*atanh(sqrt(a + b*sqrt(c/x))/sqrt(a))]
    @test_int [sqrt(a + b*sqrt(c/x))/x^2, x, 4, (4*a*(a + b*sqrt(c/x))^(3/2))/(3*b^2*c) - (4*(a + b*sqrt(c/x))^(5/2))/(5*b^2*c)]
    @test_int [sqrt(a + b*sqrt(c/x))/x^3, x, 4, (4*a^3*(a + b*sqrt(c/x))^(3/2))/(3*b^4*c^2) - (12*a^2*(a + b*sqrt(c/x))^(5/2))/(5*b^4*c^2) + (12*a*(a + b*sqrt(c/x))^(7/2))/(7*b^4*c^2) - (4*(a + b*sqrt(c/x))^(9/2))/(9*b^4*c^2)]
    @test_int [sqrt(a + b*sqrt(c/x))/x^4, x, 4, (4*a^5*(a + b*sqrt(c/x))^(3/2))/(3*b^6*c^3) - (4*a^4*(a + b*sqrt(c/x))^(5/2))/(b^6*c^3) + (40*a^3*(a + b*sqrt(c/x))^(7/2))/(7*b^6*c^3) - (40*a^2*(a + b*sqrt(c/x))^(9/2))/(9*b^6*c^3) + (20*a*(a + b*sqrt(c/x))^(11/2))/(11*b^6*c^3) - (4*(a + b*sqrt(c/x))^(13/2))/(13*b^6*c^3)]

    #= ::Subsubsection:: =#
    #=n<0=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b*(c /x)^(n/2))^(-1/2)=#

    #= ::Subsubsection::Closed:: =#
    #=n>0=#

    @test_int [x^1/sqrt(a + b*sqrt(c/x)), x, 8, -((7*b*c^2*sqrt(a + b*sqrt(c/x)))/(12*a^2*(c/x)^(3/2))) - (35*b^3*c^2*sqrt(a + b*sqrt(c/x)))/(32*a^4*sqrt(c/x)) + (35*b^2*c*sqrt(a + b*sqrt(c/x))*x)/(48*a^3) + (sqrt(a + b*sqrt(c/x))*x^2)/(2*a) + (35*b^4*c^2*atanh(sqrt(a + b*sqrt(c/x))/sqrt(a)))/(32*a^(9/2)), -((35*b^3*c^2*sqrt(a + b*sqrt(c/x)))/(32*a^4*sqrt(c/x))) + (35*b^2*c*sqrt(a + b*sqrt(c/x))*x)/(48*a^3) + (sqrt(a + b*sqrt(c/x))*x^2)/(2*a) - (7*b*sqrt(a + b*sqrt(c/x))*(c/x)^(3/2)*x^3)/(12*a^2*c) + (35*b^4*c^2*atanh(sqrt(a + b*sqrt(c/x))/sqrt(a)))/(32*a^(9/2))]
    @test_int [x^0/sqrt(a + b*sqrt(c/x)), x, 6, -((3*b*c*sqrt(a + b*sqrt(c/x)))/(2*a^2*sqrt(c/x))) + (sqrt(a + b*sqrt(c/x))*x)/a + (3*b^2*c*atanh(sqrt(a + b*sqrt(c/x))/sqrt(a)))/(2*a^(5/2))]
    @test_int [1/(x^1*sqrt(a + b*sqrt(c/x))), x, 4, (4*atanh(sqrt(a + b*sqrt(c/x))/sqrt(a)))/sqrt(a)]
    @test_int [1/(x^2*sqrt(a + b*sqrt(c/x))), x, 4, (4*a*sqrt(a + b*sqrt(c/x)))/(b^2*c) - (4*(a + b*sqrt(c/x))^(3/2))/(3*b^2*c)]
    @test_int [1/(x^3*sqrt(a + b*sqrt(c/x))), x, 4, (4*a^3*sqrt(a + b*sqrt(c/x)))/(b^4*c^2) - (4*a^2*(a + b*sqrt(c/x))^(3/2))/(b^4*c^2) + (12*a*(a + b*sqrt(c/x))^(5/2))/(5*b^4*c^2) - (4*(a + b*sqrt(c/x))^(7/2))/(7*b^4*c^2)]
    @test_int [1/(x^4*sqrt(a + b*sqrt(c/x))), x, 4, (4*a^5*sqrt(a + b*sqrt(c/x)))/(b^6*c^3) - (20*a^4*(a + b*sqrt(c/x))^(3/2))/(3*b^6*c^3) + (8*a^3*(a + b*sqrt(c/x))^(5/2))/(b^6*c^3) - (40*a^2*(a + b*sqrt(c/x))^(7/2))/(7*b^6*c^3) + (20*a*(a + b*sqrt(c/x))^(9/2))/(9*b^6*c^3) - (4*(a + b*sqrt(c/x))^(11/2))/(11*b^6*c^3)]

    @test_int [1/sqrt(1 + sqrt(1/x)), x, 6, -((3*sqrt(1 + sqrt(1/x)))/(2*sqrt(1/x))) + sqrt(1 + sqrt(1/x))*x + (3/2)*atanh(sqrt(1 + sqrt(1/x)))]

    #= ::Subsubsection:: =#
    #=n<0=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(d*x)^m*(a+b*(c*x^-1)^(n/2))^(p/2)*with*m*symbolic=#

    #= ::Subsubsection::Closed:: =#
    #=p>0=#

    @test_int [(d*x)^m*sqrt(a + b*(c/x)^(3/2)), x, 6, (sqrt(a + (b*c^3)/((c/x)^(3/2)*x^3))*x*(d*x)^m*HypergeometricFunctions._₂F₁(-(1/2), (-(2/3))*(1 + m), (1/3)*(1 - 2*m), -((b*c^3)/(a*(c/x)^(3/2)*x^3))))/((1 + m)*sqrt(1 + (b*c^3)/(a*(c/x)^(3/2)*x^3)))]
    @test_int [(d*x)^m*sqrt(a + b*(c/x)^(1/2)), x, 6, (4*(a + b*sqrt(c/x))^(3/2)*x^(1 + m)*HypergeometricFunctions._₂F₁(1, (1/2)*(-1 - 4*m), 5/2, (a + b*sqrt(c/x))/a))/(3*a), (4*b^2*c*(a + b*sqrt(c/x))^(3/2)*(-((b*sqrt(c/x))/a))^(2*m)*(d*x)^m*HypergeometricFunctions._₂F₁(3/2, 3 + 2*m, 5/2, 1 + (b*sqrt(c/x))/a))/(3*a^3)]
    @test_int [(d*x)^m*sqrt(a + b/(c/x)^(1/2)), x, 5, -((4*a*c*(a + b/sqrt(c/x))^(3/2)*(d*x)^m*HypergeometricFunctions._₂F₁(3/2, -1 - 2*m, 5/2, 1 + b/(a*sqrt(c/x))))/((-(b/(a*sqrt(c/x))))^(2*m)*(3*b^2)))]
    @test_int [(d*x)^m*sqrt(a + b/(c/x)^(3/2)), x, 5, (x*(d*x)^m*sqrt(a + (b*(c/x)^(3/2)*x^3)/c^3)*HypergeometricFunctions._₂F₁(-(1/2), (2*(1 + m))/3, (1/3)*(5 + 2*m), -((b*(c/x)^(3/2)*x^3)/(a*c^3))))/((1 + m)*sqrt(1 + (b*(c/x)^(3/2)*x^3)/(a*c^3)))]

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [(d*x)^m/sqrt(a + b*(c/x)^(3/2)), x, 6, (sqrt(1 + (b*c^3)/(a*(c/x)^(3/2)*x^3))*x*(d*x)^m*HypergeometricFunctions._₂F₁(1/2, (-(2/3))*(1 + m), (1/3)*(1 - 2*m), -((b*c^3)/(a*(c/x)^(3/2)*x^3))))/((1 + m)*sqrt(a + (b*c^3)/((c/x)^(3/2)*x^3)))]
    @test_int [(d*x)^m/sqrt(a + b*(c/x)^(1/2)), x, 6, (4*sqrt(a + b*sqrt(c/x))*x^(1 + m)*HypergeometricFunctions._₂F₁(1, (1/2)*(-3 - 4*m), 3/2, (a + b*sqrt(c/x))/a))/a, (4*b^2*c*sqrt(a + b*sqrt(c/x))*(-((b*sqrt(c/x))/a))^(2*m)*(d*x)^m*HypergeometricFunctions._₂F₁(1/2, 3 + 2*m, 3/2, 1 + (b*sqrt(c/x))/a))/a^3]
    @test_int [(d*x)^m/sqrt(a + b/(c/x)^(1/2)), x, 5, -((4*a*c*sqrt(a + b/sqrt(c/x))*(d*x)^m*HypergeometricFunctions._₂F₁(1/2, -1 - 2*m, 3/2, 1 + b/(a*sqrt(c/x))))/((-(b/(a*sqrt(c/x))))^(2*m)*b^2))]
    @test_int [(d*x)^m/sqrt(a + b/(c/x)^(3/2)), x, 5, (x*(d*x)^m*sqrt(1 + (b*(c/x)^(3/2)*x^3)/(a*c^3))*HypergeometricFunctions._₂F₁(1/2, (2*(1 + m))/3, (1/3)*(5 + 2*m), -((b*(c/x)^(3/2)*x^3)/(a*c^3))))/((1 + m)*sqrt(a + (b*(c/x)^(3/2)*x^3)/c^3))]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(d*x)^m*(a+b*(c*x^q)^n)^p=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b*(c*x^n)^(1/n))^p=#

    #= ::Subsubsection::Closed:: =#
    #=p>0=#

    @test_int [(a + b*(c*x^n)^(1/n)), x, 3, a*x + (1/2)*b*x*(c*x^n)^(1/n)]

    @test_int [(a + b*(c*x^n)^(1/n))^2, x, 2, (x*(a + b*(c*x^n)^(1/n))^3)/((c*x^n)^n^(-1)*(3*b))]

    @test_int [(a + b*(c*x^n)^(1/n))^3, x, 2, (x*(a + b*(c*x^n)^(1/n))^4)/((c*x^n)^n^(-1)*(4*b))]

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [x^3/(a + b*(c*x^n)^(1/n)), x, 3, (a^2*x^4)/((c*x^n)^(3/n)*b^3) - (a*x^4)/((c*x^n)^(2/n)*(2*b^2)) + x^4/((c*x^n)^n^(-1)*(3*b)) - (a^3*x^4*log(a + b*(c*x^n)^(1/n)))/((c*x^n)^(4/n)*b^4)]
    @test_int [x^2/(a + b*(c*x^n)^(1/n)), x, 3, -((a*x^3)/((c*x^n)^(2/n)*b^2)) + x^3/((c*x^n)^n^(-1)*(2*b)) + (a^2*x^3*log(a + b*(c*x^n)^(1/n)))/((c*x^n)^(3/n)*b^3)]
    @test_int [x^1/(a + b*(c*x^n)^(1/n)), x, 3, x^2/((c*x^n)^n^(-1)*b) - (a*x^2*log(a + b*(c*x^n)^(1/n)))/((c*x^n)^(2/n)*b^2)]
    @test_int [x^0/(a + b*(c*x^n)^(1/n)), x, 2, (x*log(a + b*(c*x^n)^(1/n)))/((c*x^n)^n^(-1)*b)]
    @test_int [1/(x^1*(a + b*(c*x^n)^(1/n))), x, 4, log(x)/a - log(a + b*(c*x^n)^(1/n))/a]
    @test_int [1/(x^2*(a + b*(c*x^n)^(1/n))), x, 3, -(1/(a*x)) - (b*(c*x^n)^(1/n)*log(x))/(a^2*x) + (b*(c*x^n)^(1/n)*log(a + b*(c*x^n)^(1/n)))/(a^2*x)]
    @test_int [1/(x^3*(a + b*(c*x^n)^(1/n))), x, 3, -(1/(2*a*x^2)) + (b*(c*x^n)^(1/n))/(a^2*x^2) + (b^2*(c*x^n)^(2/n)*log(x))/(a^3*x^2) - (b^2*(c*x^n)^(2/n)*log(a + b*(c*x^n)^(1/n)))/(a^3*x^2)]

    @test_int [x^3/(a + b*(c*x^n)^(1/n))^2, x, 3, -((2*a*x^4)/((c*x^n)^(3/n)*b^3)) + x^4/((c*x^n)^(2/n)*(2*b^2)) + (a^3*x^4)/((c*x^n)^(4/n)*(b^4*(a + b*(c*x^n)^(1/n)))) + (3*a^2*x^4*log(a + b*(c*x^n)^(1/n)))/((c*x^n)^(4/n)*b^4)]
    @test_int [x^2/(a + b*(c*x^n)^(1/n))^2, x, 3, x^3/((c*x^n)^(2/n)*b^2) - (a^2*x^3)/((c*x^n)^(3/n)*(b^3*(a + b*(c*x^n)^(1/n)))) - (2*a*x^3*log(a + b*(c*x^n)^(1/n)))/((c*x^n)^(3/n)*b^3)]
    @test_int [x^1/(a + b*(c*x^n)^(1/n))^2, x, 3, (a*x^2)/((c*x^n)^(2/n)*(b^2*(a + b*(c*x^n)^(1/n)))) + (x^2*log(a + b*(c*x^n)^(1/n)))/((c*x^n)^(2/n)*b^2)]
    @test_int [x^0/(a + b*(c*x^n)^(1/n))^2, x, 2, x/(a^2 + a*b*(c*x^n)^(1/n)), -(x/((c*x^n)^n^(-1)*(b*(a + b*(c*x^n)^(1/n)))))]
    @test_int [1/(x^1*(a + b*(c*x^n)^(1/n))^2), x, 3, 1/(a*(a + b*(c*x^n)^(1/n))) + log(x)/a^2 - log(a + b*(c*x^n)^(1/n))/a^2]
    @test_int [1/(x^2*(a + b*(c*x^n)^(1/n))^2), x, 3, -(1/(a^2*x)) - (b*(c*x^n)^(1/n))/(a^2*x*(a + b*(c*x^n)^(1/n))) - (2*b*(c*x^n)^(1/n)*log(x))/(a^3*x) + (2*b*(c*x^n)^(1/n)*log(a + b*(c*x^n)^(1/n)))/(a^3*x)]
    @test_int [1/(x^3*(a + b*(c*x^n)^(1/n))^2), x, 3, -(1/(2*a^2*x^2)) + (2*b*(c*x^n)^(1/n))/(a^3*x^2) + (b^2*(c*x^n)^(2/n))/(a^3*x^2*(a + b*(c*x^n)^(1/n))) + (3*b^2*(c*x^n)^(2/n)*log(x))/(a^4*x^2) - (3*b^2*(c*x^n)^(2/n)*log(a + b*(c*x^n)^(1/n)))/(a^4*x^2)]

    @test_int [1/(a + b*(c*x^n)^(1/n))^3, x, 2, -(x/((c*x^n)^n^(-1)*(2*b*(a + b*(c*x^n)^(1/n))^2)))]

    @test_int [x/(1 + (x^n)^(1/n))^2, x, 3, x^2/((x^n)^(2/n)*(1 + (x^n)^(1/n))) + (x^2*log(1 + (x^n)^(1/n)))/(x^n)^(2/n)]

    #= ::Subsubsection::Closed:: =#
    #=p*symbolic=#

    @test_int [x^3*(a + b*(c*x^n)^(1/n))^p, x, 3, -((a^3*x^4*(a + b*(c*x^n)^(1/n))^(1 + p))/((c*x^n)^(4/n)*(b^4*(1 + p)))) + (3*a^2*x^4*(a + b*(c*x^n)^(1/n))^(2 + p))/((c*x^n)^(4/n)*(b^4*(2 + p))) - (3*a*x^4*(a + b*(c*x^n)^(1/n))^(3 + p))/((c*x^n)^(4/n)*(b^4*(3 + p))) + (x^4*(a + b*(c*x^n)^(1/n))^(4 + p))/((c*x^n)^(4/n)*(b^4*(4 + p)))]
    @test_int [x^2*(a + b*(c*x^n)^(1/n))^p, x, 3, (a^2*x^3*(a + b*(c*x^n)^(1/n))^(1 + p))/((c*x^n)^(3/n)*(b^3*(1 + p))) - (2*a*x^3*(a + b*(c*x^n)^(1/n))^(2 + p))/((c*x^n)^(3/n)*(b^3*(2 + p))) + (x^3*(a + b*(c*x^n)^(1/n))^(3 + p))/((c*x^n)^(3/n)*(b^3*(3 + p)))]
    @test_int [x^1*(a + b*(c*x^n)^(1/n))^p, x, 3, -((a*x^2*(a + b*(c*x^n)^(1/n))^(1 + p))/((c*x^n)^(2/n)*(b^2*(1 + p)))) + (x^2*(a + b*(c*x^n)^(1/n))^(2 + p))/((c*x^n)^(2/n)*(b^2*(2 + p)))]
    @test_int [x^0*(a + b*(c*x^n)^(1/n))^p, x, 2, (x*(a + b*(c*x^n)^(1/n))^(1 + p))/((c*x^n)^n^(-1)*(b*(1 + p)))]
    @test_int [(a + b*(c*x^n)^(1/n))^p/x^1, x, 2, -(((a + b*(c*x^n)^(1/n))^(1 + p)*HypergeometricFunctions._₂F₁(1, 1 + p, 2 + p, 1 + (b*(c*x^n)^(1/n))/a))/(a*(1 + p)))]
    @test_int [(a + b*(c*x^n)^(1/n))^p/x^2, x, 2, (b*(c*x^n)^(1/n)*(a + b*(c*x^n)^(1/n))^(1 + p)*HypergeometricFunctions._₂F₁(2, 1 + p, 2 + p, 1 + (b*(c*x^n)^(1/n))/a))/(a^2*(1 + p)*x)]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b*(c*x^n)^(2/n))^p=#

    @test_int [(a + b*(c*x^n)^(2/n))^3, x, 3, a^3*x + a^2*b*x*(c*x^n)^(2/n) + (3/5)*a*b^2*x*(c*x^n)^(4/n) + (1/7)*b^3*x*(c*x^n)^(6/n)]
    @test_int [(a + b*(c*x^n)^(2/n))^2, x, 3, a^2*x + (2/3)*a*b*x*(c*x^n)^(2/n) + (1/5)*b^2*x*(c*x^n)^(4/n)]
    @test_int [(a + b*(c*x^n)^(2/n)), x, 3, a*x + (1/3)*b*x*(c*x^n)^(2/n)]
    @test_int [1/(a + b*(c*x^n)^(2/n)), x, 2, (x*atan((sqrt(b)*(c*x^n)^(1/n))/sqrt(a)))/((c*x^n)^n^(-1)*(sqrt(a)*sqrt(b)))]
    @test_int [1/(a + b*(c*x^n)^(2/n))^2, x, 3, x/(2*a*(a + b*(c*x^n)^(2/n))) + (x*atan((sqrt(b)*(c*x^n)^(1/n))/sqrt(a)))/((c*x^n)^n^(-1)*(2*a^(3/2)*sqrt(b)))]
    @test_int [1/(a + b*(c*x^n)^(2/n))^3, x, 4, x/(4*a*(a + b*(c*x^n)^(2/n))^2) + (3*x)/(8*a^2*(a + b*(c*x^n)^(2/n))) + (3*x*atan((sqrt(b)*(c*x^n)^(1/n))/sqrt(a)))/((c*x^n)^n^(-1)*(8*a^(5/2)*sqrt(b)))]

    @test_int [1/(1 + 4*sqrt(x^4)), x, 2, (x*atan(2*(x^4)^(1/4)))/(2*(x^4)^(1/4))]
    @test_int [1/(1 - 4*sqrt(x^4)), x, 2, (x*atanh(2*(x^4)^(1/4)))/(2*(x^4)^(1/4))]

    @test_int [1/(1 + 4*(x^6)^(1/3)), x, 2, (x*atan(2*(x^6)^(1/6)))/(2*(x^6)^(1/6))]
    @test_int [1/(1 - 4*(x^6)^(1/3)), x, 2, (x*atanh(2*(x^6)^(1/6)))/(2*(x^6)^(1/6))]

    @test_int [1/(1 + 4*(x^(2*n))^(1/n)), x, 2, ((1/2)*x*atan(2*(x^(2*n))^(1/(2*n))))/(x^(2*n))^(1/(2*n))]
    @test_int [1/(1 - 4*(x^(2*n))^(1/n)), x, 2, ((1/2)*x*atanh(2*(x^(2*n))^(1/(2*n))))/(x^(2*n))^(1/(2*n))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b*(c*x^n)^(3/n))^p=#

    @test_int [(a + b*(c*x^n)^(3/n))^3, x, 3, a^3*x + (3/4)*a^2*b*x*(c*x^n)^(3/n) + (3/7)*a*b^2*x*(c*x^n)^(6/n) + (1/10)*b^3*x*(c*x^n)^(9/n)]
    @test_int [(a + b*(c*x^n)^(3/n))^2, x, 3, a^2*x + (1/2)*a*b*x*(c*x^n)^(3/n) + (1/7)*b^2*x*(c*x^n)^(6/n)]
    @test_int [(a + b*(c*x^n)^(3/n)), x, 3, a*x + (1/4)*b*x*(c*x^n)^(3/n)]
    @test_int [1/(a + b*(c*x^n)^(3/n)), x, 7, -((x*atan((a^(1/3) - 2*b^(1/3)*(c*x^n)^(1/n))/(sqrt(3)*a^(1/3))))/((c*x^n)^(1/n)*(sqrt(3)*a^(2/3)*b^(1/3)))) + (x*log(a^(1/3) + b^(1/3)*(c*x^n)^(1/n)))/((c*x^n)^(1/n)*(3*a^(2/3)*b^(1/3))) - (x*log(a^(2/3) - a^(1/3)*b^(1/3)*(c*x^n)^(1/n) + b^(2/3)*(c*x^n)^(2/n)))/((c*x^n)^(1/n)*(6*a^(2/3)*b^(1/3)))]
    @test_int [1/(a + b*(c*x^n)^(3/n))^2, x, 8, x/(3*a*(a + b*(c*x^n)^(3/n))) - (2*x*atan((a^(1/3) - 2*b^(1/3)*(c*x^n)^(1/n))/(sqrt(3)*a^(1/3))))/((c*x^n)^n^(-1)*(3*sqrt(3)*a^(5/3)*b^(1/3))) + (2*x*log(a^(1/3) + b^(1/3)*(c*x^n)^(1/n)))/((c*x^n)^n^(-1)*(9*a^(5/3)*b^(1/3))) - (x*log(a^(2/3) - a^(1/3)*b^(1/3)*(c*x^n)^(1/n) + b^(2/3)*(c*x^n)^(2/n)))/((c*x^n)^n^(-1)*(9*a^(5/3)*b^(1/3)))]
    @test_int [1/(a + b*(c*x^n)^(3/n))^3, x, 9, x/(6*a*(a + b*(c*x^n)^(3/n))^2) + (5*x)/(18*a^2*(a + b*(c*x^n)^(3/n))) - (5*x*atan((a^(1/3) - 2*b^(1/3)*(c*x^n)^(1/n))/(sqrt(3)*a^(1/3))))/((c*x^n)^n^(-1)*(9*sqrt(3)*a^(8/3)*b^(1/3))) + (5*x*log(a^(1/3) + b^(1/3)*(c*x^n)^(1/n)))/((c*x^n)^n^(-1)*(27*a^(8/3)*b^(1/3))) - (5*x*log(a^(2/3) - a^(1/3)*b^(1/3)*(c*x^n)^(1/n) + b^(2/3)*(c*x^n)^(2/n)))/((c*x^n)^n^(-1)*(54*a^(8/3)*b^(1/3)))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(d*x)^m*(a+b*(c*x^q)^n)^p*with*n, p*and*q*symbolic=#

    @test_int [(d*x)^m*(a + b*(c*x^q)^n)^p, x, 3, ((d*x)^(1 + m)*(a + b*(c*x^q)^n)^p*HypergeometricFunctions._₂F₁(-p, (1 + m)/(n*q), 1 + (1 + m)/(n*q), -((b*(c*x^q)^n)/a)))/((1 + (b*(c*x^q)^n)/a)^p*(d*(1 + m)))]

    @test_int [x^2*(a + b*(c*x^q)^n)^p, x, 3, ((1/3)*x^3*(a + b*(c*x^q)^n)^p*HypergeometricFunctions._₂F₁(-p, 3/(n*q), 1 + 3/(n*q), -((b*(c*x^q)^n)/a)))/(1 + (b*(c*x^q)^n)/a)^p]
    @test_int [x^1*(a + b*(c*x^q)^n)^p, x, 3, ((1/2)*x^2*(a + b*(c*x^q)^n)^p*HypergeometricFunctions._₂F₁(-p, 2/(n*q), 1 + 2/(n*q), -((b*(c*x^q)^n)/a)))/(1 + (b*(c*x^q)^n)/a)^p]
    @test_int [x^0*(a + b*(c*x^q)^n)^p, x, 3, (x*(a + b*(c*x^q)^n)^p*HypergeometricFunctions._₂F₁(-p, 1/(n*q), 1 + 1/(n*q), -((b*(c*x^q)^n)/a)))/(1 + (b*(c*x^q)^n)/a)^p]
    @test_int [(a + b*(c*x^q)^n)^p/x^1, x, 3, -(((a + b*(c*x^q)^n)^(1 + p)*HypergeometricFunctions._₂F₁(1, 1 + p, 2 + p, 1 + (b*(c*x^q)^n)/a))/(a*n*(1 + p)*q))]
    @test_int [(a + b*(c*x^q)^n)^p/x^2, x, 3, -(((a + b*(c*x^q)^n)^p*HypergeometricFunctions._₂F₁(-p, -(1/(n*q)), 1 - 1/(n*q), -((b*(c*x^q)^n)/a)))/((1 + (b*(c*x^q)^n)/a)^p*x))]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b*(d/x)^n+c*(d/x)^(2n))^p=#

    @test_int [x^m*sqrt(a + b*sqrt(d/x) + c/x), x, 4, (sqrt(a + b*sqrt(d/x) + c/x)*x^(1 + m)*AppellF1(-2*(1 + m), -(1/2), -(1/2), -1 - 2*m, -((2*c*sqrt(d/x))/(sqrt(d)*(b*sqrt(d) - sqrt(-4*a*c + b^2*d)))), -((2*c*sqrt(d/x))/(sqrt(d)*(b*sqrt(d) + sqrt(-4*a*c + b^2*d))))))/((1 + m)*sqrt(1 + (2*c*sqrt(d/x))/(sqrt(d)*(b*sqrt(d) - sqrt(-4*a*c + b^2*d))))*sqrt(1 + (2*c*sqrt(d/x))/(sqrt(d)*(b*sqrt(d) + sqrt(-4*a*c + b^2*d)))))]

    @test_int [x^2*sqrt(a + b*sqrt(d/x) + c/x), x, 9, -((3*b*d^3*(a + b*sqrt(d/x) + c/x)^(3/2))/(10*a^2*(d/x)^(5/2))) + (7*b*d^2*(28*a*c - 15*b^2*d)*(a + b*sqrt(d/x) + c/x)^(3/2))/(480*a^4*(d/x)^(3/2)) + ((16*a^2*c^2 - 56*a*b^2*c*d + 21*b^4*d^2)*(2*a + b*sqrt(d/x))*sqrt(a + b*sqrt(d/x) + c/x)*x)/(256*a^5) - ((20*a*c - 21*b^2*d)*(a + b*sqrt(d/x) + c/x)^(3/2)*x^2)/(80*a^3) + ((a + b*sqrt(d/x) + c/x)^(3/2)*x^3)/(3*a) + ((4*a*c - b^2*d)*(16*a^2*c^2 - 56*a*b^2*c*d + 21*b^4*d^2)*atanh((2*a + b*sqrt(d/x))/(2*sqrt(a)*sqrt(a + b*sqrt(d/x) + c/x))))/(512*a^(11/2))]
    @test_int [x^1*sqrt(a + b*sqrt(d/x) + c/x), x, 7, -((5*b*d^2*(a + b*sqrt(d/x) + c/x)^(3/2))/(12*a^2*(d/x)^(3/2))) - ((4*a*c - 5*b^2*d)*(2*a + b*sqrt(d/x))*sqrt(a + b*sqrt(d/x) + c/x)*x)/(32*a^3) + ((a + b*sqrt(d/x) + c/x)^(3/2)*x^2)/(2*a) - ((4*a*c - 5*b^2*d)*(4*a*c - b^2*d)*atanh((2*a + b*sqrt(d/x))/(2*sqrt(a)*sqrt(a + b*sqrt(d/x) + c/x))))/(64*a^(7/2))]
    @test_int [x^0*sqrt(a + b*sqrt(d/x) + c/x), x, 5, ((2*a + b*sqrt(d/x))*sqrt(a + b*sqrt(d/x) + c/x)*x)/(2*a) + ((4*a*c - b^2*d)*atanh((2*a + b*sqrt(d/x))/(2*sqrt(a)*sqrt(a + b*sqrt(d/x) + c/x))))/(4*a^(3/2))]
    @test_int [sqrt(a + b*sqrt(d/x) + c/x)/x^1, x, 8, -2*sqrt(a + b*sqrt(d/x) + c/x) + 2*sqrt(a)*atanh((2*a + b*sqrt(d/x))/(2*sqrt(a)*sqrt(a + b*sqrt(d/x) + c/x))) - (b*sqrt(d)*atanh((b*d + 2*c*sqrt(d/x))/(2*sqrt(c)*sqrt(d)*sqrt(a + b*sqrt(d/x) + c/x))))/sqrt(c)]
    @test_int [sqrt(a + b*sqrt(d/x) + c/x)/x^2, x, 6, (b*(b*d + 2*c*sqrt(d/x))*sqrt(a + b*sqrt(d/x) + c/x))/(4*c^2) - (2*(a + b*sqrt(d/x) + c/x)^(3/2))/(3*c) + (b*sqrt(d)*(4*a*c - b^2*d)*atanh((b*d + 2*c*sqrt(d/x))/(2*sqrt(c)*sqrt(d)*sqrt(a + b*sqrt(d/x) + c/x))))/(8*c^(5/2))]
    @test_int [sqrt(a + b*sqrt(d/x) + c/x)/x^3, x, 7, -((b*(12*a*c - 7*b^2*d)*(b*d + 2*c*sqrt(d/x))*sqrt(a + b*sqrt(d/x) + c/x))/(64*c^4)) + ((32*a*c - 35*b^2*d + 42*b*c*sqrt(d/x))*(a + b*sqrt(d/x) + c/x)^(3/2))/(120*c^3) - (2*(a + b*sqrt(d/x) + c/x)^(3/2))/(5*c*x) - (b*sqrt(d)*(12*a*c - 7*b^2*d)*(4*a*c - b^2*d)*atanh((b*d + 2*c*sqrt(d/x))/(2*sqrt(c)*sqrt(d)*sqrt(a + b*sqrt(d/x) + c/x))))/(128*c^(9/2))]
    @test_int [sqrt(a + b*sqrt(d/x) + c/x)/x^4, x, 9, (b*(80*a^2*c^2 - 120*a*b^2*c*d + 33*b^4*d^2)*(b*d + 2*c*sqrt(d/x))*sqrt(a + b*sqrt(d/x) + c/x))/(512*c^6) - ((1024*a^2*c^2 - 3276*a*b^2*c*d + 1155*b^4*d^2 + 18*b*c*(148*a*c - 77*b^2*d)*sqrt(d/x))*(a + b*sqrt(d/x) + c/x)^(3/2))/(6720*c^5) + (11*b*(a + b*sqrt(d/x) + c/x)^(3/2)*(d/x)^(3/2))/(42*c^2*d) - (2*(a + b*sqrt(d/x) + c/x)^(3/2))/(7*c*x^2) + ((32*a*c - 33*b^2*d)*(a + b*sqrt(d/x) + c/x)^(3/2))/(140*c^3*x) + (b*sqrt(d)*(4*a*c - b^2*d)*(80*a^2*c^2 - 120*a*b^2*c*d + 33*b^4*d^2)*atanh((b*d + 2*c*sqrt(d/x))/(2*sqrt(c)*sqrt(d)*sqrt(a + b*sqrt(d/x) + c/x))))/(1024*c^(13/2))]

    @test_int [x^m/sqrt(a + b*sqrt(d/x) + c/x), x, 4, (sqrt(1 + (2*c*sqrt(d/x))/(sqrt(d)*(b*sqrt(d) - sqrt(-4*a*c + b^2*d))))*sqrt(1 + (2*c*sqrt(d/x))/(sqrt(d)*(b*sqrt(d) + sqrt(-4*a*c + b^2*d))))*x^(1 + m)*AppellF1(-2*(1 + m), 1/2, 1/2, -1 - 2*m, -((2*c*sqrt(d/x))/(sqrt(d)*(b*sqrt(d) - sqrt(-4*a*c + b^2*d)))), -((2*c*sqrt(d/x))/(sqrt(d)*(b*sqrt(d) + sqrt(-4*a*c + b^2*d))))))/((1 + m)*sqrt(a + b*sqrt(d/x) + c/x))]

    @test_int [x^2/sqrt(a + b*sqrt(d/x) + c/x), x, 10, -((11*b*d^3*sqrt(a + b*sqrt(d/x) + c/x))/(30*a^2*(d/x)^(5/2))) + (b*d^2*(156*a*c - 77*b^2*d)*sqrt(a + b*sqrt(d/x) + c/x))/(160*a^4*(d/x)^(3/2)) - (7*b*d*(528*a^2*c^2 - 680*a*b^2*c*d + 165*b^4*d^2)*sqrt(a + b*sqrt(d/x) + c/x))/(1280*a^6*sqrt(d/x)) + ((400*a^2*c^2 - 1176*a*b^2*c*d + 385*b^4*d^2)*sqrt(a + b*sqrt(d/x) + c/x)*x)/(640*a^5) - ((100*a*c - 99*b^2*d)*sqrt(a + b*sqrt(d/x) + c/x)*x^2)/(240*a^3) + (sqrt(a + b*sqrt(d/x) + c/x)*x^3)/(3*a) - ((320*a^3*c^3 - 1680*a^2*b^2*c^2*d + 1260*a*b^4*c*d^2 - 231*b^6*d^3)*atanh((2*a + b*sqrt(d/x))/(2*sqrt(a)*sqrt(a + b*sqrt(d/x) + c/x))))/(512*a^(13/2))]
    @test_int [x^1/sqrt(a + b*sqrt(d/x) + c/x), x, 8, -((7*b*d^2*sqrt(a + b*sqrt(d/x) + c/x))/(12*a^2*(d/x)^(3/2))) + (5*b*d*(44*a*c - 21*b^2*d)*sqrt(a + b*sqrt(d/x) + c/x))/(96*a^4*sqrt(d/x)) - ((36*a*c - 35*b^2*d)*sqrt(a + b*sqrt(d/x) + c/x)*x)/(48*a^3) + (sqrt(a + b*sqrt(d/x) + c/x)*x^2)/(2*a) + ((48*a^2*c^2 - 120*a*b^2*c*d + 35*b^4*d^2)*atanh((2*a + b*sqrt(d/x))/(2*sqrt(a)*sqrt(a + b*sqrt(d/x) + c/x))))/(64*a^(9/2))]
    @test_int [x^0/sqrt(a + b*sqrt(d/x) + c/x), x, 6, -((3*b*d*sqrt(a + b*sqrt(d/x) + c/x))/(2*a^2*sqrt(d/x))) + (sqrt(a + b*sqrt(d/x) + c/x)*x)/a - ((4*a*c - 3*b^2*d)*atanh((2*a + b*sqrt(d/x))/(2*sqrt(a)*sqrt(a + b*sqrt(d/x) + c/x))))/(4*a^(5/2))]
    @test_int [1/(x^1*sqrt(a + b*sqrt(d/x) + c/x)), x, 4, (2*atanh((2*a + b*sqrt(d/x))/(2*sqrt(a)*sqrt(a + b*sqrt(d/x) + c/x))))/sqrt(a)]
    @test_int [1/(x^2*sqrt(a + b*sqrt(d/x) + c/x)), x, 5, -((2*sqrt(a + b*sqrt(d/x) + c/x))/c) + (b*sqrt(d)*atanh((b*d + 2*c*sqrt(d/x))/(2*sqrt(c)*sqrt(d)*sqrt(a + b*sqrt(d/x) + c/x))))/c^(3/2)]
    @test_int [1/(x^3*sqrt(a + b*sqrt(d/x) + c/x)), x, 6, ((16*a*c - 15*b^2*d + 10*b*c*sqrt(d/x))*sqrt(a + b*sqrt(d/x) + c/x))/(12*c^3) - (2*sqrt(a + b*sqrt(d/x) + c/x))/(3*c*x) - (b*sqrt(d)*(12*a*c - 5*b^2*d)*atanh((b*d + 2*c*sqrt(d/x))/(2*sqrt(c)*sqrt(d)*sqrt(a + b*sqrt(d/x) + c/x))))/(8*c^(7/2))]
    @test_int [1/(x^4*sqrt(a + b*sqrt(d/x) + c/x)), x, 8, -(((1024*a^2*c^2 - 2940*a*b^2*c*d + 945*b^4*d^2 + 14*b*c*(92*a*c - 45*b^2*d)*sqrt(d/x))*sqrt(a + b*sqrt(d/x) + c/x))/(960*c^5)) + (9*b*sqrt(a + b*sqrt(d/x) + c/x)*(d/x)^(3/2))/(20*c^2*d) - (2*sqrt(a + b*sqrt(d/x) + c/x))/(5*c*x^2) + ((64*a*c - 63*b^2*d)*sqrt(a + b*sqrt(d/x) + c/x))/(120*c^3*x) + (b*sqrt(d)*(240*a^2*c^2 - 280*a*b^2*c*d + 63*b^4*d^2)*atanh((b*d + 2*c*sqrt(d/x))/(2*sqrt(c)*sqrt(d)*sqrt(a + b*sqrt(d/x) + c/x))))/(128*c^(11/2))]

    @test_int [sqrt(sqrt(1/x) + 1/x), x, 2, (4*(sqrt(1/x) + 1/x)^(3/2))/(3*(1/x)^(3/2))]
    @test_int [sqrt(2 + sqrt(1/x) + 1/x), x, 5, (1/4)*(4 + sqrt(1/x))*sqrt(2 + sqrt(1/x) + 1/x)*x + (7*atanh((4 + sqrt(1/x))/(2*sqrt(2)*sqrt(2 + sqrt(1/x) + 1/x))))/(8*sqrt(2))]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(c*x^n)^(1/n)*(a+b*(c*x^n)^(m/n))^p=#

    @test_int [(c*x^n)^(1/n)*(a + b*(c*x^n)^(1/n))^p, x, 4, -((a*x*(a + b*(c*x^n)^(1/n))^(1 + p))/((c*x^n)^n^(-1)*(b^2*(1 + p)))) + (x*(a + b*(c*x^n)^(1/n))^(2 + p))/((c*x^n)^n^(-1)*(b^2*(2 + p)))]

    @test_int [(c*x^n)^(1/n)*(a + b*(c*x^n)^(1/n))^3, x, 4, -((a*x*(a + b*(c*x^n)^(1/n))^4)/((c*x^n)^n^(-1)*(4*b^2))) + (x*(a + b*(c*x^n)^(1/n))^5)/((c*x^n)^n^(-1)*(5*b^2))]
    @test_int [(c*x^n)^(1/n)*(a + b*(c*x^n)^(1/n))^2, x, 4, (1/2)*a^2*x*(c*x^n)^(1/n) + (2/3)*a*b*x*(c*x^n)^(2/n) + (1/4)*b^2*x*(c*x^n)^(3/n)]
    @test_int [(c*x^n)^(1/n)*(a + b*(c*x^n)^(1/n))^1, x, 5, (1/2)*a*x*(c*x^n)^(1/n) + (1/3)*b*x*(c*x^n)^(2/n)]
    @test_int [(c*x^n)^(1/n)/(a + b*(c*x^n)^(1/n))^1, x, 4, x/b - (a*x*log(a + b*(c*x^n)^(1/n)))/((c*x^n)^n^(-1)*b^2)]
    @test_int [(c*x^n)^(1/n)/(a + b*(c*x^n)^(1/n))^2, x, 4, (a*x)/((c*x^n)^n^(-1)*(b^2*(a + b*(c*x^n)^(1/n)))) + (x*log(a + b*(c*x^n)^(1/n)))/((c*x^n)^n^(-1)*b^2)]
    @test_int [(c*x^n)^(1/n)/(a + b*(c*x^n)^(1/n))^3, x, 3, (x*(c*x^n)^(1/n))/(2*a*(a + b*(c*x^n)^(1/n))^2)]
    @test_int [(c*x^n)^(1/n)/(a + b*(c*x^n)^(1/n))^4, x, 4, (a*x)/((c*x^n)^n^(-1)*(3*b^2*(a + b*(c*x^n)^(1/n))^3)) - x/((c*x^n)^n^(-1)*(2*b^2*(a + b*(c*x^n)^(1/n))^2))]
    @test_int [(c*x^n)^(1/n)/(a + b*(c*x^n)^(1/n))^5, x, 4, (a*x)/((c*x^n)^n^(-1)*(4*b^2*(a + b*(c*x^n)^(1/n))^4)) - x/((c*x^n)^n^(-1)*(3*b^2*(a + b*(c*x^n)^(1/n))^3))]
    end

ext: jl

max_stars_repo_path: test/1 Algebraic functions/1.1 Binomial products/1.1.3 General/1.1.3.2 (c x)^m (a+b x^n)^p.jl