text:
@testset "7.3.4 u (a+b arctanh(c x))^p" begin
    (a, b, c, d, e, f, g, m, p, x, ) = @variables a b c d e f g m p x

    #= ::Package:: =#

    #= ::Title::Closed:: =#
    #=Integrands*of*the*form*(f*x)^m*(d+e*x)^q*(a+b*atanh(c*x))^p=#

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*x^m*(d+e*x)^q*(a+b*atanh(c*x))^p*when*c^2*d^2-e^2=0=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(d+e*x)^q*(a+b*atanh(c*x))^1*when*c^2*d^2 - e^2=0=#

    #= ::Subsubsection::Closed:: =#
    #=q>0=#

    @test_int [x^3*(d + c*d*x)*(a + b*atanh(c*x)), x, 7, (b*d*x)/(4*c^3) + (b*d*x^2)/(10*c^2) + (b*d*x^3)/(12*c) + (b*d*x^4)/20 + (d*x^4*(a + b*atanh(c*x)))/4 + (c*d*x^5*(a + b*atanh(c*x)))/5 + (9*b*d*log(1 - c*x))/(40*c^4) - (b*d*log(1 + c*x))/(40*c^4)]
    @test_int [x^2*(d + c*d*x)*(a + b*atanh(c*x)), x, 7, (b*d*x)/(4*c^2) + (b*d*x^2)/(6*c) + (b*d*x^3)/12 + (d*x^3*(a + b*atanh(c*x)))/3 + (c*d*x^4*(a + b*atanh(c*x)))/4 + (7*b*d*log(1 - c*x))/(24*c^3) + (b*d*log(1 + c*x))/(24*c^3)]
    @test_int [x^1*(d + c*d*x)*(a + b*atanh(c*x)), x, 7, (b*d*x)/(2*c) + (b*d*x^2)/6 + (d*x^2*(a + b*atanh(c*x)))/2 + (c*d*x^3*(a + b*atanh(c*x)))/3 + (5*b*d*log(1 - c*x))/(12*c^2) - (b*d*log(1 + c*x))/(12*c^2)]
    @test_int [x^0*(d + c*d*x)*(a + b*atanh(c*x)), x, 4, (b*d*x)/2 + (d*(1 + c*x)^2*(a + b*atanh(c*x)))/(2*c) + (b*d*log(1 - c*x))/c]
    @test_int [((d + c*d*x)*(a + b*atanh(c*x)))/x^1, x, 6, a*c*d*x + b*c*d*x*atanh(c*x) + a*d*log(x) + (1/2)*b*d*log(1 - c^2*x^2) - (1/2)*b*d*PolyLog(2, (-c)*x) + (1/2)*b*d*PolyLog(2, c*x)]
    @test_int [((d + c*d*x)*(a + b*atanh(c*x)))/x^2, x, 8, -((d*(a + b*atanh(c*x)))/x) + a*c*d*log(x) + b*c*d*log(x) - (1/2)*b*c*d*log(1 - c^2*x^2) - (1/2)*b*c*d*PolyLog(2, (-c)*x) + (1/2)*b*c*d*PolyLog(2, c*x)]
    @test_int [((d + c*d*x)*(a + b*atanh(c*x)))/x^3, x, 4, -(b*c*d)/(2*x) - (d*(1 + c*x)^2*(a + b*atanh(c*x)))/(2*x^2) + b*c^2*d*log(x) - b*c^2*d*log(1 - c*x)]
    @test_int [((d + c*d*x)*(a + b*atanh(c*x)))/x^4, x, 4, -(b*c*d)/(6*x^2) - (b*c^2*d)/(2*x) - (d*(a + b*atanh(c*x)))/(3*x^3) - (c*d*(a + b*atanh(c*x)))/(2*x^2) + (b*c^3*d*log(x))/3 - (5*b*c^3*d*log(1 - c*x))/12 + (b*c^3*d*log(1 + c*x))/12]
    @test_int [((d + c*d*x)*(a + b*atanh(c*x)))/x^5, x, 4, -((b*c*d)/(12*x^3)) - (b*c^2*d)/(6*x^2) - (b*c^3*d)/(4*x) - (d*(a + b*atanh(c*x)))/(4*x^4) - (c*d*(a + b*atanh(c*x)))/(3*x^3) + (1/3)*b*c^4*d*log(x) - (7/24)*b*c^4*d*log(1 - c*x) - (1/24)*b*c^4*d*log(1 + c*x)]

    @test_int [x^3*(d + c*d*x)^2*(a + b*atanh(c*x)), x, 7, (5*b*d^2*x)/(12*c^3) + (b*d^2*x^2)/(5*c^2) + (5*b*d^2*x^3)/(36*c) + (b*d^2*x^4)/10 + (b*c*d^2*x^5)/30 + (d^2*x^4*(a + b*atanh(c*x)))/4 + (2*c*d^2*x^5*(a + b*atanh(c*x)))/5 + (c^2*d^2*x^6*(a + b*atanh(c*x)))/6 + (49*b*d^2*log(1 - c*x))/(120*c^4) - (b*d^2*log(1 + c*x))/(120*c^4)]
    @test_int [x^2*(d + c*d*x)^2*(a + b*atanh(c*x)), x, 7, (b*d^2*x)/(2*c^2) + (4*b*d^2*x^2)/(15*c) + (b*d^2*x^3)/6 + (b*c*d^2*x^4)/20 + (d^2*x^3*(a + b*atanh(c*x)))/3 + (c*d^2*x^4*(a + b*atanh(c*x)))/2 + (c^2*d^2*x^5*(a + b*atanh(c*x)))/5 + (31*b*d^2*log(1 - c*x))/(60*c^3) + (b*d^2*log(1 + c*x))/(60*c^3)]
    @test_int [x^1*(d + c*d*x)^2*(a + b*atanh(c*x)), x, 7, (3*b*d^2*x)/(4*c) + (b*d^2*x^2)/3 + (b*c*d^2*x^3)/12 + (d^2*x^2*(a + b*atanh(c*x)))/2 + (2*c*d^2*x^3*(a + b*atanh(c*x)))/3 + (c^2*d^2*x^4*(a + b*atanh(c*x)))/4 + (17*b*d^2*log(1 - c*x))/(24*c^2) - (b*d^2*log(1 + c*x))/(24*c^2)]
    @test_int [x^0*(d + c*d*x)^2*(a + b*atanh(c*x)), x, 4, (2/3)*b*d^2*x + (b*d^2*(1 + c*x)^2)/(6*c) + (d^2*(1 + c*x)^3*(a + b*atanh(c*x)))/(3*c) + (4*b*d^2*log(1 - c*x))/(3*c)]
    @test_int [((d + c*d*x)^2*(a + b*atanh(c*x)))/x^1, x, 9, 2*a*c*d^2*x + (1/2)*b*c*d^2*x - (1/2)*b*d^2*atanh(c*x) + 2*b*c*d^2*x*atanh(c*x) + (1/2)*c^2*d^2*x^2*(a + b*atanh(c*x)) + a*d^2*log(x) + b*d^2*log(1 - c^2*x^2) - (1/2)*b*d^2*PolyLog(2, (-c)*x) + (1/2)*b*d^2*PolyLog(2, c*x)]
    @test_int [((d + c*d*x)^2*(a + b*atanh(c*x)))/x^2, x, 11, (d^2*(-1 + c^2*x^2)*(a + b*atanh(c*x)))/x + (2*a + b)*c*d^2*log(x) - b*c*d^2*PolyLog(2, (-c)*x) + b*c*d^2*PolyLog(2, c*x), a*c^2*d^2*x + b*c^2*d^2*x*atanh(c*x) - (d^2*(a + b*atanh(c*x)))/x + 2*a*c*d^2*log(x) + b*c*d^2*log(x) - b*c*d^2*PolyLog(2, (-c)*x) + b*c*d^2*PolyLog(2, c*x)]
    @test_int [((d + c*d*x)^2*(a + b*atanh(c*x)))/x^3, x, 11, -((b*c*d^2)/(2*x)) + (1/2)*b*c^2*d^2*atanh(c*x) - (d^2*(a + b*atanh(c*x)))/(2*x^2) - (2*c*d^2*(a + b*atanh(c*x)))/x + a*c^2*d^2*log(x) + 2*b*c^2*d^2*log(x) - b*c^2*d^2*log(1 - c^2*x^2) - (1/2)*b*c^2*d^2*PolyLog(2, (-c)*x) + (1/2)*b*c^2*d^2*PolyLog(2, c*x)]
    @test_int [((d + c*d*x)^2*(a + b*atanh(c*x)))/x^4, x, 4, -(b*c*d^2)/(6*x^2) - (b*c^2*d^2)/x - (d^2*(1 + c*x)^3*(a + b*atanh(c*x)))/(3*x^3) + (4*b*c^3*d^2*log(x))/3 - (4*b*c^3*d^2*log(1 - c*x))/3]
    @test_int [((d + c*d*x)^2*(a + b*atanh(c*x)))/x^5, x, 4, -((b*c*d^2)/(12*x^3)) - (b*c^2*d^2)/(3*x^2) - (3*b*c^3*d^2)/(4*x) - (d^2*(a + b*atanh(c*x)))/(4*x^4) - (2*c*d^2*(a + b*atanh(c*x)))/(3*x^3) - (c^2*d^2*(a + b*atanh(c*x)))/(2*x^2) + (2/3)*b*c^4*d^2*log(x) - (17/24)*b*c^4*d^2*log(1 - c*x) + (1/24)*b*c^4*d^2*log(1 + c*x)]
    @test_int [((d + c*d*x)^2*(a + b*atanh(c*x)))/x^6, x, 4, -((b*c*d^2)/(20*x^4)) - (b*c^2*d^2)/(6*x^3) - (4*b*c^3*d^2)/(15*x^2) - (b*c^4*d^2)/(2*x) - (d^2*(a + b*atanh(c*x)))/(5*x^5) - (c*d^2*(a + b*atanh(c*x)))/(2*x^4) - (c^2*d^2*(a + b*atanh(c*x)))/(3*x^3) + (8/15)*b*c^5*d^2*log(x) - (31/60)*b*c^5*d^2*log(1 - c*x) - (1/60)*b*c^5*d^2*log(1 + c*x)]

    @test_int [x^3*(d + c*d*x)^3*(a + b*atanh(c*x)), x, 7, (3*b*d^3*x)/(4*c^3) + (13*b*d^3*x^2)/(35*c^2) + (b*d^3*x^3)/(4*c) + (13*b*d^3*x^4)/70 + (b*c*d^3*x^5)/10 + (b*c^2*d^3*x^6)/42 + (d^3*x^4*(a + b*atanh(c*x)))/4 + (3*c*d^3*x^5*(a + b*atanh(c*x)))/5 + (c^2*d^3*x^6*(a + b*atanh(c*x)))/2 + (c^3*d^3*x^7*(a + b*atanh(c*x)))/7 + (209*b*d^3*log(1 - c*x))/(280*c^4) - (b*d^3*log(1 + c*x))/(280*c^4)]
    @test_int [x^2*(d + c*d*x)^3*(a + b*atanh(c*x)), x, 7, (11*b*d^3*x)/(12*c^2) + (7*b*d^3*x^2)/(15*c) + (11*b*d^3*x^3)/36 + (3*b*c*d^3*x^4)/20 + (b*c^2*d^3*x^5)/30 + (d^3*x^3*(a + b*atanh(c*x)))/3 + (3*c*d^3*x^4*(a + b*atanh(c*x)))/4 + (3*c^2*d^3*x^5*(a + b*atanh(c*x)))/5 + (c^3*d^3*x^6*(a + b*atanh(c*x)))/6 + (37*b*d^3*log(1 - c*x))/(40*c^3) + (b*d^3*log(1 + c*x))/(120*c^3)]
    @test_int [x^1*(d + c*d*x)^3*(a + b*atanh(c*x)), x, 4, (3*b*d^3*x)/(5*c) + (3*b*d^3*(1 + c*x)^2)/(20*c^2) + (b*d^3*(1 + c*x)^3)/(20*c^2) + (b*d^3*(1 + c*x)^4)/(20*c^2) - (d^3*(1 + c*x)^4*(a + b*atanh(c*x)))/(4*c^2) + (d^3*(1 + c*x)^5*(a + b*atanh(c*x)))/(5*c^2) + (6*b*d^3*log(1 - c*x))/(5*c^2)]
    @test_int [x^0*(d + c*d*x)^3*(a + b*atanh(c*x)), x, 4, b*d^3*x + (b*d^3*(1 + c*x)^2)/(4*c) + (b*d^3*(1 + c*x)^3)/(12*c) + (d^3*(1 + c*x)^4*(a + b*atanh(c*x)))/(4*c) + (2*b*d^3*log(1 - c*x))/c]
    @test_int [((d + c*d*x)^3*(a + b*atanh(c*x)))/x^1, x, 13, 3*a*c*d^3*x + (3/2)*b*c*d^3*x + (1/6)*b*c^2*d^3*x^2 - (3/2)*b*d^3*atanh(c*x) + 3*b*c*d^3*x*atanh(c*x) + (3/2)*c^2*d^3*x^2*(a + b*atanh(c*x)) + (1/3)*c^3*d^3*x^3*(a + b*atanh(c*x)) + a*d^3*log(x) + (5/3)*b*d^3*log(1 - c^2*x^2) - (1/2)*b*d^3*PolyLog(2, (-c)*x) + (1/2)*b*d^3*PolyLog(2, c*x)]
    @test_int [((d + c*d*x)^3*(a + b*atanh(c*x)))/x^2, x, 14, 3*a*c^2*d^3*x + (1/2)*b*c^2*d^3*x - (1/2)*b*c*d^3*atanh(c*x) + 3*b*c^2*d^3*x*atanh(c*x) - (d^3*(a + b*atanh(c*x)))/x + (1/2)*c^3*d^3*x^2*(a + b*atanh(c*x)) + 3*a*c*d^3*log(x) + b*c*d^3*log(x) + b*c*d^3*log(1 - c^2*x^2) - (3/2)*b*c*d^3*PolyLog(2, (-c)*x) + (3/2)*b*c*d^3*PolyLog(2, c*x)]
    @test_int [((d + c*d*x)^3*(a + b*atanh(c*x)))/x^3, x, 14, -((b*c*d^3)/(2*x)) + a*c^3*d^3*x + (1/2)*b*c^2*d^3*atanh(c*x) + b*c^3*d^3*x*atanh(c*x) - (d^3*(a + b*atanh(c*x)))/(2*x^2) - (3*c*d^3*(a + b*atanh(c*x)))/x + 3*a*c^2*d^3*log(x) + 3*b*c^2*d^3*log(x) - b*c^2*d^3*log(1 - c^2*x^2) - (3/2)*b*c^2*d^3*PolyLog(2, (-c)*x) + (3/2)*b*c^2*d^3*PolyLog(2, c*x)]
    @test_int [((d + c*d*x)^3*(a + b*atanh(c*x)))/x^4, x, 15, -((b*c*d^3)/(6*x^2)) - (3*b*c^2*d^3)/(2*x) + (3/2)*b*c^3*d^3*atanh(c*x) - (d^3*(a + b*atanh(c*x)))/(3*x^3) - (3*c*d^3*(a + b*atanh(c*x)))/(2*x^2) - (3*c^2*d^3*(a + b*atanh(c*x)))/x + a*c^3*d^3*log(x) + (10/3)*b*c^3*d^3*log(x) - (5/3)*b*c^3*d^3*log(1 - c^2*x^2) - (1/2)*b*c^3*d^3*PolyLog(2, (-c)*x) + (1/2)*b*c^3*d^3*PolyLog(2, c*x)]
    @test_int [((d + c*d*x)^3*(a + b*atanh(c*x)))/x^5, x, 4, -((b*c*d^3)/(12*x^3)) - (b*c^2*d^3)/(2*x^2) - (7*b*c^3*d^3)/(4*x) - (d^3*(1 + c*x)^4*(a + b*atanh(c*x)))/(4*x^4) + 2*b*c^4*d^3*log(x) - 2*b*c^4*d^3*log(1 - c*x)]
    @test_int [((d + c*d*x)^3*(a + b*atanh(c*x)))/x^6, x, 4, -((b*c*d^3)/(20*x^4)) - (b*c^2*d^3)/(4*x^3) - (3*b*c^3*d^3)/(5*x^2) - (5*b*c^4*d^3)/(4*x) - (d^3*(1 + c*x)^4*(a + b*atanh(c*x)))/(5*x^5) + (c*d^3*(1 + c*x)^4*(a + b*atanh(c*x)))/(20*x^4) + (6/5)*b*c^5*d^3*log(x) - (6/5)*b*c^5*d^3*log(1 - c*x)]
    @test_int [((d + c*d*x)^3*(a + b*atanh(c*x)))/x^7, x, 4, -((b*c*d^3)/(30*x^5)) - (3*b*c^2*d^3)/(20*x^4) - (11*b*c^3*d^3)/(36*x^3) - (7*b*c^4*d^3)/(15*x^2) - (11*b*c^5*d^3)/(12*x) - (d^3*(a + b*atanh(c*x)))/(6*x^6) - (3*c*d^3*(a + b*atanh(c*x)))/(5*x^5) - (3*c^2*d^3*(a + b*atanh(c*x)))/(4*x^4) - (c^3*d^3*(a + b*atanh(c*x)))/(3*x^3) + (14/15)*b*c^6*d^3*log(x) - (37/40)*b*c^6*d^3*log(1 - c*x) - (1/120)*b*c^6*d^3*log(1 + c*x)]

    @test_int [x^3*(d + c*d*x)^4*(a + b*atanh(c*x)), x, 7, (11*b*d^4*x)/(8*c^3) + (24*b*d^4*x^2)/(35*c^2) + (11*b*d^4*x^3)/(24*c) + (12/35)*b*d^4*x^4 + (9/40)*b*c*d^4*x^5 + (2/21)*b*c^2*d^4*x^6 + (1/56)*b*c^3*d^4*x^7 + (1/4)*d^4*x^4*(a + b*atanh(c*x)) + (4/5)*c*d^4*x^5*(a + b*atanh(c*x)) + c^2*d^4*x^6*(a + b*atanh(c*x)) + (4/7)*c^3*d^4*x^7*(a + b*atanh(c*x)) + (1/8)*c^4*d^4*x^8*(a + b*atanh(c*x)) + (769*b*d^4*log(1 - c*x))/(560*c^4) - (b*d^4*log(1 + c*x))/(560*c^4)]
    @test_int [x^2*(d + c*d*x)^4*(a + b*atanh(c*x)), x, 4, (5*b*d^4*x)/(3*c^2) + (88*b*d^4*x^2)/(105*c) + (5/9)*b*d^4*x^3 + (47/140)*b*c*d^4*x^4 + (2/15)*b*c^2*d^4*x^5 + (1/42)*b*c^3*d^4*x^6 + (d^4*(1 + c*x)^5*(a + b*atanh(c*x)))/(5*c^3) - (d^4*(1 + c*x)^6*(a + b*atanh(c*x)))/(3*c^3) + (d^4*(1 + c*x)^7*(a + b*atanh(c*x)))/(7*c^3) + (176*b*d^4*log(1 - c*x))/(105*c^3)]
    @test_int [x^1*(d + c*d*x)^4*(a + b*atanh(c*x)), x, 4, (16*b*d^4*x)/(15*c) + (4*b*d^4*(1 + c*x)^2)/(15*c^2) + (4*b*d^4*(1 + c*x)^3)/(45*c^2) + (b*d^4*(1 + c*x)^4)/(30*c^2) + (b*d^4*(1 + c*x)^5)/(30*c^2) - (d^4*(1 + c*x)^5*(a + b*atanh(c*x)))/(5*c^2) + (d^4*(1 + c*x)^6*(a + b*atanh(c*x)))/(6*c^2) + (32*b*d^4*log(1 - c*x))/(15*c^2)]
    @test_int [x^0*(d + c*d*x)^4*(a + b*atanh(c*x)), x, 4, (8/5)*b*d^4*x + (2*b*d^4*(1 + c*x)^2)/(5*c) + (2*b*d^4*(1 + c*x)^3)/(15*c) + (b*d^4*(1 + c*x)^4)/(20*c) + (d^4*(1 + c*x)^5*(a + b*atanh(c*x)))/(5*c) + (16*b*d^4*log(1 - c*x))/(5*c)]
    @test_int [((d + c*d*x)^4*(a + b*atanh(c*x)))/x^1, x, 17, 4*a*c*d^4*x + (13/4)*b*c*d^4*x + (2/3)*b*c^2*d^4*x^2 + (1/12)*b*c^3*d^4*x^3 - (13/4)*b*d^4*atanh(c*x) + 4*b*c*d^4*x*atanh(c*x) + 3*c^2*d^4*x^2*(a + b*atanh(c*x)) + (4/3)*c^3*d^4*x^3*(a + b*atanh(c*x)) + (1/4)*c^4*d^4*x^4*(a + b*atanh(c*x)) + a*d^4*log(x) + (8/3)*b*d^4*log(1 - c^2*x^2) - (1/2)*b*d^4*PolyLog(2, (-c)*x) + (1/2)*b*d^4*PolyLog(2, c*x)]
    @test_int [((d + c*d*x)^4*(a + b*atanh(c*x)))/x^2, x, 18, 6*a*c^2*d^4*x + 2*b*c^2*d^4*x + (1/6)*b*c^3*d^4*x^2 - 2*b*c*d^4*atanh(c*x) + 6*b*c^2*d^4*x*atanh(c*x) - (d^4*(a + b*atanh(c*x)))/x + 2*c^3*d^4*x^2*(a + b*atanh(c*x)) + (1/3)*c^4*d^4*x^3*(a + b*atanh(c*x)) + 4*a*c*d^4*log(x) + b*c*d^4*log(x) + (8/3)*b*c*d^4*log(1 - c^2*x^2) - 2*b*c*d^4*PolyLog(2, (-c)*x) + 2*b*c*d^4*PolyLog(2, c*x)]
    @test_int [((d + c*d*x)^4*(a + b*atanh(c*x)))/x^3, x, 17, -((b*c*d^4)/(2*x)) + 4*a*c^3*d^4*x + (1/2)*b*c^3*d^4*x + 4*b*c^3*d^4*x*atanh(c*x) - (d^4*(a + b*atanh(c*x)))/(2*x^2) - (4*c*d^4*(a + b*atanh(c*x)))/x + (1/2)*c^4*d^4*x^2*(a + b*atanh(c*x)) + 6*a*c^2*d^4*log(x) + 4*b*c^2*d^4*log(x) - 3*b*c^2*d^4*PolyLog(2, (-c)*x) + 3*b*c^2*d^4*PolyLog(2, c*x)]
    @test_int [((d + c*d*x)^4*(a + b*atanh(c*x)))/x^4, x, 18, -((b*c*d^4)/(6*x^2)) - (2*b*c^2*d^4)/x + a*c^4*d^4*x + 2*b*c^3*d^4*atanh(c*x) + b*c^4*d^4*x*atanh(c*x) - (d^4*(a + b*atanh(c*x)))/(3*x^3) - (2*c*d^4*(a + b*atanh(c*x)))/x^2 - (6*c^2*d^4*(a + b*atanh(c*x)))/x + 4*a*c^3*d^4*log(x) + (19/3)*b*c^3*d^4*log(x) - (8/3)*b*c^3*d^4*log(1 - c^2*x^2) - 2*b*c^3*d^4*PolyLog(2, (-c)*x) + 2*b*c^3*d^4*PolyLog(2, c*x)]
    @test_int [((d + c*d*x)^4*(a + b*atanh(c*x)))/x^5, x, 19, -((b*c*d^4)/(12*x^3)) - (2*b*c^2*d^4)/(3*x^2) - (13*b*c^3*d^4)/(4*x) + (13/4)*b*c^4*d^4*atanh(c*x) - (d^4*(a + b*atanh(c*x)))/(4*x^4) - (4*c*d^4*(a + b*atanh(c*x)))/(3*x^3) - (3*c^2*d^4*(a + b*atanh(c*x)))/x^2 - (4*c^3*d^4*(a + b*atanh(c*x)))/x + a*c^4*d^4*log(x) + (16/3)*b*c^4*d^4*log(x) - (8/3)*b*c^4*d^4*log(1 - c^2*x^2) - (1/2)*b*c^4*d^4*PolyLog(2, (-c)*x) + (1/2)*b*c^4*d^4*PolyLog(2, c*x)]
    @test_int [((d + c*d*x)^4*(a + b*atanh(c*x)))/x^6, x, 4, -((b*c*d^4)/(20*x^4)) - (b*c^2*d^4)/(3*x^3) - (11*b*c^3*d^4)/(10*x^2) - (3*b*c^4*d^4)/x - (d^4*(1 + c*x)^5*(a + b*atanh(c*x)))/(5*x^5) + (16/5)*b*c^5*d^4*log(x) - (16/5)*b*c^5*d^4*log(1 - c*x)]
    @test_int [((d + c*d*x)^4*(a + b*atanh(c*x)))/x^7, x, 4, -((b*c*d^4)/(30*x^5)) - (b*c^2*d^4)/(5*x^4) - (5*b*c^3*d^4)/(9*x^3) - (16*b*c^4*d^4)/(15*x^2) - (13*b*c^5*d^4)/(6*x) - (d^4*(1 + c*x)^5*(a + b*atanh(c*x)))/(6*x^6) + (c*d^4*(1 + c*x)^5*(a + b*atanh(c*x)))/(30*x^5) + (32/15)*b*c^6*d^4*log(x) - (32/15)*b*c^6*d^4*log(1 - c*x)]
    @test_int [((d + c*d*x)^4*(a + b*atanh(c*x)))/x^8, x, 4, -((b*c*d^4)/(42*x^6)) - (2*b*c^2*d^4)/(15*x^5) - (47*b*c^3*d^4)/(140*x^4) - (5*b*c^4*d^4)/(9*x^3) - (88*b*c^5*d^4)/(105*x^2) - (5*b*c^6*d^4)/(3*x) - (d^4*(a + b*atanh(c*x)))/(7*x^7) - (2*c*d^4*(a + b*atanh(c*x)))/(3*x^6) - (6*c^2*d^4*(a + b*atanh(c*x)))/(5*x^5) - (c^3*d^4*(a + b*atanh(c*x)))/x^4 - (c^4*d^4*(a + b*atanh(c*x)))/(3*x^3) + (176/105)*b*c^7*d^4*log(x) - (117/70)*b*c^7*d^4*log(1 - c*x) - (1/210)*b*c^7*d^4*log(1 + c*x)]

    #= ::Subsubsection::Closed:: =#
    #=q<0=#

    @test_int [(x^3*(a + b*atanh(c*x)))/(d + c*d*x), x, 16, (a*x)/(c^3*d) - (b*x)/(2*c^3*d) + (b*x^2)/(6*c^2*d) + (b*atanh(c*x))/(2*c^4*d) + (b*x*atanh(c*x))/(c^3*d) - (x^2*(a + b*atanh(c*x)))/(2*c^2*d) + (x^3*(a + b*atanh(c*x)))/(3*c*d) + ((a + b*atanh(c*x))*log(2/(1 + c*x)))/(c^4*d) + (2*b*log(1 - c^2*x^2))/(3*c^4*d) - (b*PolyLog(2, 1 - 2/(1 + c*x)))/(2*c^4*d)]
    @test_int [(x^2*(a + b*atanh(c*x)))/(d + c*d*x), x, 11, -((a*x)/(c^2*d)) + (b*x)/(2*c^2*d) - (b*atanh(c*x))/(2*c^3*d) - (b*x*atanh(c*x))/(c^2*d) + (x^2*(a + b*atanh(c*x)))/(2*c*d) - ((a + b*atanh(c*x))*log(2/(1 + c*x)))/(c^3*d) - (b*log(1 - c^2*x^2))/(2*c^3*d) + (b*PolyLog(2, 1 - 2/(1 + c*x)))/(2*c^3*d)]
    @test_int [(x^1*(a + b*atanh(c*x)))/(d + c*d*x), x, 7, (a*x)/(c*d) + (b*x*atanh(c*x))/(c*d) + ((a + b*atanh(c*x))*log(2/(1 + c*x)))/(c^2*d) + (b*log(1 - c^2*x^2))/(2*c^2*d) - (b*PolyLog(2, 1 - 2/(1 + c*x)))/(2*c^2*d)]
    @test_int [x^0*(a + b*atanh(c*x))/(d + c*d*x), x, 3, -(((a + b*atanh(c*x))*log(2/(1 + c*x)))/(c*d)) + (b*PolyLog(2, 1 - 2/(1 + c*x)))/(2*c*d)]
    @test_int [(a + b*atanh(c*x))/(x^1*(d + c*d*x)), x, 2, ((a + b*atanh(c*x))*log(2 - 2/(1 + c*x)))/d - (b*PolyLog(2, -1 + 2/(1 + c*x)))/(2*d)]
    @test_int [(a + b*atanh(c*x))/(x^2*(d + c*d*x)), x, 8, -((a + b*atanh(c*x))/(d*x)) + (b*c*log(x))/d - (b*c*log(1 - c^2*x^2))/(2*d) - (c*(a + b*atanh(c*x))*log(2 - 2/(1 + c*x)))/d + (b*c*PolyLog(2, -1 + 2/(1 + c*x)))/(2*d)]
    @test_int [(a + b*atanh(c*x))/(x^3*(d + c*d*x)), x, 12, -(b*c)/(2*d*x) + (b*c^2*atanh(c*x))/(2*d) - (a + b*atanh(c*x))/(2*d*x^2) + (c*(a + b*atanh(c*x)))/(d*x) - (b*c^2*log(x))/d + (b*c^2*log(1 - c^2*x^2))/(2*d) + (c^2*(a + b*atanh(c*x))*log(2 - 2/(1 + c*x)))/d - (b*c^2*PolyLog(2, -1 + 2/(1 + c*x)))/(2*d)]
    @test_int [(a + b*atanh(c*x))/(x^4*(d + c*d*x)), x, 17, -(b*c)/(6*d*x^2) + (b*c^2)/(2*d*x) - (b*c^3*atanh(c*x))/(2*d) - (a + b*atanh(c*x))/(3*d*x^3) + (c*(a + b*atanh(c*x)))/(2*d*x^2) - (c^2*(a + b*atanh(c*x)))/(d*x) + (4*b*c^3*log(x))/(3*d) - (2*b*c^3*log(1 - c^2*x^2))/(3*d) - (c^3*(a + b*atanh(c*x))*log(2 - 2/(1 + c*x)))/d + (b*c^3*PolyLog(2, -1 + 2/(1 + c*x)))/(2*d)]

    @test_int [(x^3*(a + b*atanh(c*x)))/(d + c*d*x)^2, x, 16, -((2*a*x)/(c^3*d^2)) + (b*x)/(2*c^3*d^2) + b/(2*c^4*d^2*(1 + c*x)) - (b*atanh(c*x))/(c^4*d^2) - (2*b*x*atanh(c*x))/(c^3*d^2) + (x^2*(a + b*atanh(c*x)))/(2*c^2*d^2) + (a + b*atanh(c*x))/(c^4*d^2*(1 + c*x)) - (3*(a + b*atanh(c*x))*log(2/(1 + c*x)))/(c^4*d^2) - (b*log(1 - c^2*x^2))/(c^4*d^2) + (3*b*PolyLog(2, 1 - 2/(1 + c*x)))/(2*c^4*d^2)]
    @test_int [(x^2*(a + b*atanh(c*x)))/(d + c*d*x)^2, x, 13, (a*x)/(c^2*d^2) - b/(2*c^3*d^2*(1 + c*x)) + (b*atanh(c*x))/(2*c^3*d^2) + (b*x*atanh(c*x))/(c^2*d^2) - (a + b*atanh(c*x))/(c^3*d^2*(1 + c*x)) + (2*(a + b*atanh(c*x))*log(2/(1 + c*x)))/(c^3*d^2) + (b*log(1 - c^2*x^2))/(2*c^3*d^2) - (b*PolyLog(2, 1 - 2/(1 + c*x)))/(c^3*d^2)]
    @test_int [(x^1*(a + b*atanh(c*x)))/(d + c*d*x)^2, x, 10, b/(2*c^2*d^2*(1 + c*x)) - (b*atanh(c*x))/(2*c^2*d^2) + (a + b*atanh(c*x))/(c^2*d^2*(1 + c*x)) - ((a + b*atanh(c*x))*log(2/(1 + c*x)))/(c^2*d^2) + (b*PolyLog(2, 1 - 2/(1 + c*x)))/(2*c^2*d^2)]
    @test_int [x^0*(a + b*atanh(c*x))/(d + c*d*x)^2, x, 5, -b/(2*c*d^2*(1 + c*x)) + (b*atanh(c*x))/(2*c*d^2) - (a + b*atanh(c*x))/(c*d^2*(1 + c*x))]
    @test_int [(a + b*atanh(c*x))/(x^1*(d + c*d*x)^2), x, 11, b/(2*d^2*(1 + c*x)) - (b*atanh(c*x))/(2*d^2) + (a + b*atanh(c*x))/(d^2*(1 + c*x)) + (a*log(x))/d^2 + ((a + b*atanh(c*x))*log(2/(1 + c*x)))/d^2 - (b*PolyLog(2, (-c)*x))/(2*d^2) + (b*PolyLog(2, c*x))/(2*d^2) - (b*PolyLog(2, 1 - 2/(1 + c*x)))/(2*d^2)]
    @test_int [(a + b*atanh(c*x))/(x^2*(d + c*d*x)^2), x, 16, -((b*c)/(2*d^2*(1 + c*x))) + (b*c*atanh(c*x))/(2*d^2) - (a + b*atanh(c*x))/(d^2*x) - (c*(a + b*atanh(c*x)))/(d^2*(1 + c*x)) - (2*a*c*log(x))/d^2 + (b*c*log(x))/d^2 - (2*c*(a + b*atanh(c*x))*log(2/(1 + c*x)))/d^2 - (b*c*log(1 - c^2*x^2))/(2*d^2) + (b*c*PolyLog(2, (-c)*x))/d^2 - (b*c*PolyLog(2, c*x))/d^2 + (b*c*PolyLog(2, 1 - 2/(1 + c*x)))/d^2]
    @test_int [(a + b*atanh(c*x))/(x^3*(d + c*d*x)^2), x, 19, -((b*c)/(2*d^2*x)) + (b*c^2)/(2*d^2*(1 + c*x)) - (a + b*atanh(c*x))/(2*d^2*x^2) + (2*c*(a + b*atanh(c*x)))/(d^2*x) + (c^2*(a + b*atanh(c*x)))/(d^2*(1 + c*x)) + (3*a*c^2*log(x))/d^2 - (2*b*c^2*log(x))/d^2 + (3*c^2*(a + b*atanh(c*x))*log(2/(1 + c*x)))/d^2 + (b*c^2*log(1 - c^2*x^2))/d^2 - (3*b*c^2*PolyLog(2, (-c)*x))/(2*d^2) + (3*b*c^2*PolyLog(2, c*x))/(2*d^2) - (3*b*c^2*PolyLog(2, 1 - 2/(1 + c*x)))/(2*d^2)]

    @test_int [(x^4*(a + b*atanh(c*x)))/(d + c*d*x)^3, x, 21, -((3*a*x)/(c^4*d^3)) + (b*x)/(2*c^4*d^3) - b/(8*c^5*d^3*(1 + c*x)^2) + (15*b)/(8*c^5*d^3*(1 + c*x)) - (19*b*atanh(c*x))/(8*c^5*d^3) - (3*b*x*atanh(c*x))/(c^4*d^3) + (x^2*(a + b*atanh(c*x)))/(2*c^3*d^3) - (a + b*atanh(c*x))/(2*c^5*d^3*(1 + c*x)^2) + (4*(a + b*atanh(c*x)))/(c^5*d^3*(1 + c*x)) - (6*(a + b*atanh(c*x))*log(2/(1 + c*x)))/(c^5*d^3) - (3*b*log(1 - c^2*x^2))/(2*c^5*d^3) + (3*b*PolyLog(2, 1 - 2/(1 + c*x)))/(c^5*d^3)]
    @test_int [(x^3*(a + b*atanh(c*x)))/(d + c*d*x)^3, x, 18, (a*x)/(c^3*d^3) + b/(8*c^4*d^3*(1 + c*x)^2) - (11*b)/(8*c^4*d^3*(1 + c*x)) + (11*b*atanh(c*x))/(8*c^4*d^3) + (b*x*atanh(c*x))/(c^3*d^3) + (a + b*atanh(c*x))/(2*c^4*d^3*(1 + c*x)^2) - (3*(a + b*atanh(c*x)))/(c^4*d^3*(1 + c*x)) + (3*(a + b*atanh(c*x))*log(2/(1 + c*x)))/(c^4*d^3) + (b*log(1 - c^2*x^2))/(2*c^4*d^3) - (3*b*PolyLog(2, 1 - 2/(1 + c*x)))/(2*c^4*d^3)]
    @test_int [(x^2*(a + b*atanh(c*x)))/(d + c*d*x)^3, x, 15, -(b/(8*c^3*d^3*(1 + c*x)^2)) + (7*b)/(8*c^3*d^3*(1 + c*x)) - (7*b*atanh(c*x))/(8*c^3*d^3) - (a + b*atanh(c*x))/(2*c^3*d^3*(1 + c*x)^2) + (2*(a + b*atanh(c*x)))/(c^3*d^3*(1 + c*x)) - ((a + b*atanh(c*x))*log(2/(1 + c*x)))/(c^3*d^3) + (b*PolyLog(2, 1 - 2/(1 + c*x)))/(2*c^3*d^3)]
    @test_int [(x^1*(a + b*atanh(c*x)))/(d + c*d*x)^3, x, 5, b/(8*c^2*d^3*(1 + c*x)^2) - (3*b)/(8*c^2*d^3*(1 + c*x)) - (b*atanh(c*x))/(8*c^2*d^3) + (x^2*(a + b*atanh(c*x)))/(2*d^3*(1 + c*x)^2)]
    @test_int [x^0*(a + b*atanh(c*x))/(d + c*d*x)^3, x, 5, -b/(8*c*d^3*(1 + c*x)^2) - b/(8*c*d^3*(1 + c*x)) + (b*atanh(c*x))/(8*c*d^3) - (a + b*atanh(c*x))/(2*c*d^3*(1 + c*x)^2)]
    @test_int [(a + b*atanh(c*x))/(x^1*(d + c*d*x)^3), x, 16, b/(8*d^3*(1 + c*x)^2) + (5*b)/(8*d^3*(1 + c*x)) - (5*b*atanh(c*x))/(8*d^3) + (a + b*atanh(c*x))/(2*d^3*(1 + c*x)^2) + (a + b*atanh(c*x))/(d^3*(1 + c*x)) + (a*log(x))/d^3 + ((a + b*atanh(c*x))*log(2/(1 + c*x)))/d^3 - (b*PolyLog(2, (-c)*x))/(2*d^3) + (b*PolyLog(2, c*x))/(2*d^3) - (b*PolyLog(2, 1 - 2/(1 + c*x)))/(2*d^3)]
    @test_int [(a + b*atanh(c*x))/(x^2*(d + c*d*x)^3), x, 21, -((b*c)/(8*d^3*(1 + c*x)^2)) - (9*b*c)/(8*d^3*(1 + c*x)) + (9*b*c*atanh(c*x))/(8*d^3) - (a + b*atanh(c*x))/(d^3*x) - (c*(a + b*atanh(c*x)))/(2*d^3*(1 + c*x)^2) - (2*c*(a + b*atanh(c*x)))/(d^3*(1 + c*x)) - (3*a*c*log(x))/d^3 + (b*c*log(x))/d^3 - (3*c*(a + b*atanh(c*x))*log(2/(1 + c*x)))/d^3 - (b*c*log(1 - c^2*x^2))/(2*d^3) + (3*b*c*PolyLog(2, (-c)*x))/(2*d^3) - (3*b*c*PolyLog(2, c*x))/(2*d^3) + (3*b*c*PolyLog(2, 1 - 2/(1 + c*x)))/(2*d^3)]
    @test_int [(a + b*atanh(c*x))/(x^3*(d + c*d*x)^3), x, 24, -((b*c)/(2*d^3*x)) + (b*c^2)/(8*d^3*(1 + c*x)^2) + (13*b*c^2)/(8*d^3*(1 + c*x)) - (9*b*c^2*atanh(c*x))/(8*d^3) - (a + b*atanh(c*x))/(2*d^3*x^2) + (3*c*(a + b*atanh(c*x)))/(d^3*x) + (c^2*(a + b*atanh(c*x)))/(2*d^3*(1 + c*x)^2) + (3*c^2*(a + b*atanh(c*x)))/(d^3*(1 + c*x)) + (6*a*c^2*log(x))/d^3 - (3*b*c^2*log(x))/d^3 + (6*c^2*(a + b*atanh(c*x))*log(2/(1 + c*x)))/d^3 + (3*b*c^2*log(1 - c^2*x^2))/(2*d^3) - (3*b*c^2*PolyLog(2, (-c)*x))/d^3 + (3*b*c^2*PolyLog(2, c*x))/d^3 - (3*b*c^2*PolyLog(2, 1 - 2/(1 + c*x)))/d^3]

    @test_int [(a + b*atanh(c*x))/(1 + c*x)^4, x, 5, -(b/(18*c*(1 + c*x)^3)) - b/(24*c*(1 + c*x)^2) - b/(24*c*(1 + c*x)) + (b*atanh(c*x))/(24*c) - (a + b*atanh(c*x))/(3*c*(1 + c*x)^3)]

    @test_int [atanh(a*x)/(c*x + a*c*x^2), x, 3, (atanh(a*x)*log(2 - 2/(1 + a*x)))/c - PolyLog(2, -1 + 2/(1 + a*x))/(2*c)]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(d+e*x)^q*(a+b*atanh(c*x))^2*when*c^2*d^2 - e^2=0=#

    #= ::Subsubsection::Closed:: =#
    #=q>0=#

    @test_int [x^3*(d + c*d*x)*(a + b*atanh(c*x))^2, x, 27, (a*b*d*x)/(2*c^3) + (3*b^2*d*x)/(10*c^3) + (b^2*d*x^2)/(12*c^2) + (b^2*d*x^3)/(30*c) - (3*b^2*d*atanh(c*x))/(10*c^4) + (b^2*d*x*atanh(c*x))/(2*c^3) + (b*d*x^2*(a + b*atanh(c*x)))/(5*c^2) + (b*d*x^3*(a + b*atanh(c*x)))/(6*c) + (1/10)*b*d*x^4*(a + b*atanh(c*x)) - (d*(a + b*atanh(c*x))^2)/(20*c^4) + (1/4)*d*x^4*(a + b*atanh(c*x))^2 + (1/5)*c*d*x^5*(a + b*atanh(c*x))^2 - (2*b*d*(a + b*atanh(c*x))*log(2/(1 - c*x)))/(5*c^4) + (b^2*d*log(1 - c^2*x^2))/(3*c^4) - (b^2*d*PolyLog(2, 1 - 2/(1 - c*x)))/(5*c^4)]
    @test_int [x^2*(d + c*d*x)*(a + b*atanh(c*x))^2, x, 22, (a*b*d*x)/(2*c^2) + (b^2*d*x)/(3*c^2) + (b^2*d*x^2)/(12*c) - (b^2*d*atanh(c*x))/(3*c^3) + (b^2*d*x*atanh(c*x))/(2*c^2) + (b*d*x^2*(a + b*atanh(c*x)))/(3*c) + (1/6)*b*d*x^3*(a + b*atanh(c*x)) + (d*(a + b*atanh(c*x))^2)/(12*c^3) + (1/3)*d*x^3*(a + b*atanh(c*x))^2 + (1/4)*c*d*x^4*(a + b*atanh(c*x))^2 - (2*b*d*(a + b*atanh(c*x))*log(2/(1 - c*x)))/(3*c^3) + (b^2*d*log(1 - c^2*x^2))/(3*c^3) - (b^2*d*PolyLog(2, 1 - 2/(1 - c*x)))/(3*c^3)]
    @test_int [x^1*(d + c*d*x)*(a + b*atanh(c*x))^2, x, 17, (a*b*d*x)/c + (b^2*d*x)/(3*c) - (b^2*d*atanh(c*x))/(3*c^2) + (b^2*d*x*atanh(c*x))/c + (1/3)*b*d*x^2*(a + b*atanh(c*x)) - (d*(a + b*atanh(c*x))^2)/(6*c^2) + (1/2)*d*x^2*(a + b*atanh(c*x))^2 + (1/3)*c*d*x^3*(a + b*atanh(c*x))^2 - (2*b*d*(a + b*atanh(c*x))*log(2/(1 - c*x)))/(3*c^2) + (b^2*d*log(1 - c^2*x^2))/(2*c^2) - (b^2*d*PolyLog(2, 1 - 2/(1 - c*x)))/(3*c^2)]
    @test_int [x^0*(d + c*d*x)*(a + b*atanh(c*x))^2, x, 9, a*b*d*x + b^2*d*x*atanh(c*x) + (d*(1 + c*x)^2*(a + b*atanh(c*x))^2)/(2*c) - (2*b*d*(a + b*atanh(c*x))*log(2/(1 - c*x)))/c + (b^2*d*log(1 - c^2*x^2))/(2*c) - (b^2*d*PolyLog(2, 1 - 2/(1 - c*x)))/c]
    @test_int [((d + c*d*x)*(a + b*atanh(c*x))^2)/x^1, x, 13, d*(a + b*atanh(c*x))^2 + c*d*x*(a + b*atanh(c*x))^2 + 2*d*(a + b*atanh(c*x))^2*atanh(1 - 2/(1 - c*x)) - 2*b*d*(a + b*atanh(c*x))*log(2/(1 - c*x)) - b^2*d*PolyLog(2, 1 - 2/(1 - c*x)) - b*d*(a + b*atanh(c*x))*PolyLog(2, 1 - 2/(1 - c*x)) + b*d*(a + b*atanh(c*x))*PolyLog(2, -1 + 2/(1 - c*x)) + (1/2)*b^2*d*PolyLog(3, 1 - 2/(1 - c*x)) - (1/2)*b^2*d*PolyLog(3, -1 + 2/(1 - c*x))]
    @test_int [((d + c*d*x)*(a + b*atanh(c*x))^2)/x^2, x, 12, c*d*(a + b*atanh(c*x))^2 - (d*(a + b*atanh(c*x))^2)/x + 2*c*d*(a + b*atanh(c*x))^2*atanh(1 - 2/(1 - c*x)) + 2*b*c*d*(a + b*atanh(c*x))*log(2 - 2/(1 + c*x)) - b*c*d*(a + b*atanh(c*x))*PolyLog(2, 1 - 2/(1 - c*x)) + b*c*d*(a + b*atanh(c*x))*PolyLog(2, -1 + 2/(1 - c*x)) - b^2*c*d*PolyLog(2, -1 + 2/(1 + c*x)) + (1/2)*b^2*c*d*PolyLog(3, 1 - 2/(1 - c*x)) - (1/2)*b^2*c*d*PolyLog(3, -1 + 2/(1 - c*x))]
    @test_int [((d + c*d*x)*(a + b*atanh(c*x))^2)/x^3, x, 14, -((b*c*d*(a + b*atanh(c*x)))/x) + (3/2)*c^2*d*(a + b*atanh(c*x))^2 - (d*(a + b*atanh(c*x))^2)/(2*x^2) - (c*d*(a + b*atanh(c*x))^2)/x + b^2*c^2*d*log(x) - (1/2)*b^2*c^2*d*log(1 - c^2*x^2) + 2*b*c^2*d*(a + b*atanh(c*x))*log(2 - 2/(1 + c*x)) - b^2*c^2*d*PolyLog(2, -1 + 2/(1 + c*x))]
    @test_int [((d + c*d*x)*(a + b*atanh(c*x))^2)/x^4, x, 18, -((b^2*c^2*d)/(3*x)) + (1/3)*b^2*c^3*d*atanh(c*x) - (b*c*d*(a + b*atanh(c*x)))/(3*x^2) - (b*c^2*d*(a + b*atanh(c*x)))/x + (5/6)*c^3*d*(a + b*atanh(c*x))^2 - (d*(a + b*atanh(c*x))^2)/(3*x^3) - (c*d*(a + b*atanh(c*x))^2)/(2*x^2) + b^2*c^3*d*log(x) - (1/2)*b^2*c^3*d*log(1 - c^2*x^2) + (2/3)*b*c^3*d*(a + b*atanh(c*x))*log(2 - 2/(1 + c*x)) - (1/3)*b^2*c^3*d*PolyLog(2, -1 + 2/(1 + c*x))]

    @test_int [x^3*(d + c*d*x)^2*(a + b*atanh(c*x))^2, x, 43, (5*a*b*d^2*x)/(6*c^3) + (3*b^2*d^2*x)/(5*c^3) + (31*b^2*d^2*x^2)/(180*c^2) + (b^2*d^2*x^3)/(15*c) + (1/60)*b^2*d^2*x^4 - (3*b^2*d^2*atanh(c*x))/(5*c^4) + (5*b^2*d^2*x*atanh(c*x))/(6*c^3) + (2*b*d^2*x^2*(a + b*atanh(c*x)))/(5*c^2) + (5*b*d^2*x^3*(a + b*atanh(c*x)))/(18*c) + (1/5)*b*d^2*x^4*(a + b*atanh(c*x)) + (1/15)*b*c*d^2*x^5*(a + b*atanh(c*x)) - (d^2*(a + b*atanh(c*x))^2)/(60*c^4) + (1/4)*d^2*x^4*(a + b*atanh(c*x))^2 + (2/5)*c*d^2*x^5*(a + b*atanh(c*x))^2 + (1/6)*c^2*d^2*x^6*(a + b*atanh(c*x))^2 - (4*b*d^2*(a + b*atanh(c*x))*log(2/(1 - c*x)))/(5*c^4) + (53*b^2*d^2*log(1 - c^2*x^2))/(90*c^4) - (2*b^2*d^2*PolyLog(2, 1 - 2/(1 - c*x)))/(5*c^4)]
    @test_int [x^2*(d + c*d*x)^2*(a + b*atanh(c*x))^2, x, 36, (a*b*d^2*x)/c^2 + (19*b^2*d^2*x)/(30*c^2) + (b^2*d^2*x^2)/(6*c) + (1/30)*b^2*d^2*x^3 - (19*b^2*d^2*atanh(c*x))/(30*c^3) + (b^2*d^2*x*atanh(c*x))/c^2 + (8*b*d^2*x^2*(a + b*atanh(c*x)))/(15*c) + (1/3)*b*d^2*x^3*(a + b*atanh(c*x)) + (1/10)*b*c*d^2*x^4*(a + b*atanh(c*x)) + (d^2*(a + b*atanh(c*x))^2)/(30*c^3) + (1/3)*d^2*x^3*(a + b*atanh(c*x))^2 + (1/2)*c*d^2*x^4*(a + b*atanh(c*x))^2 + (1/5)*c^2*d^2*x^5*(a + b*atanh(c*x))^2 - (16*b*d^2*(a + b*atanh(c*x))*log(2/(1 - c*x)))/(15*c^3) + (2*b^2*d^2*log(1 - c^2*x^2))/(3*c^3) - (8*b^2*d^2*PolyLog(2, 1 - 2/(1 - c*x)))/(15*c^3)]
    @test_int [x^1*(d + c*d*x)^2*(a + b*atanh(c*x))^2, x, 28, (3*a*b*d^2*x)/(2*c) + (2*b^2*d^2*x)/(3*c) + (1/12)*b^2*d^2*x^2 - (2*b^2*d^2*atanh(c*x))/(3*c^2) + (3*b^2*d^2*x*atanh(c*x))/(2*c) + (2/3)*b*d^2*x^2*(a + b*atanh(c*x)) + (1/6)*b*c*d^2*x^3*(a + b*atanh(c*x)) - (d^2*(a + b*atanh(c*x))^2)/(12*c^2) + (1/2)*d^2*x^2*(a + b*atanh(c*x))^2 + (2/3)*c*d^2*x^3*(a + b*atanh(c*x))^2 + (1/4)*c^2*d^2*x^4*(a + b*atanh(c*x))^2 - (4*b*d^2*(a + b*atanh(c*x))*log(2/(1 - c*x)))/(3*c^2) + (5*b^2*d^2*log(1 - c^2*x^2))/(6*c^2) - (2*b^2*d^2*PolyLog(2, 1 - 2/(1 - c*x)))/(3*c^2)]
    @test_int [x^0*(d + c*d*x)^2*(a + b*atanh(c*x))^2, x, 12, 2*a*b*d^2*x + (1/3)*b^2*d^2*x - (b^2*d^2*atanh(c*x))/(3*c) + 2*b^2*d^2*x*atanh(c*x) + (1/3)*b*c*d^2*x^2*(a + b*atanh(c*x)) + (d^2*(1 + c*x)^3*(a + b*atanh(c*x))^2)/(3*c) - (8*b*d^2*(a + b*atanh(c*x))*log(2/(1 - c*x)))/(3*c) + (b^2*d^2*log(1 - c^2*x^2))/c - (4*b^2*d^2*PolyLog(2, 1 - 2/(1 - c*x)))/(3*c)]
    @test_int [(d + c*d*x)^2*(a + b*atanh(c*x))^2/x^1, x, 19, a*b*c*d^2*x + b^2*c*d^2*x*atanh(c*x) + (3/2)*d^2*(a + b*atanh(c*x))^2 + 2*c*d^2*x*(a + b*atanh(c*x))^2 + (1/2)*c^2*d^2*x^2*(a + b*atanh(c*x))^2 + 2*d^2*(a + b*atanh(c*x))^2*atanh(1 - 2/(1 - c*x)) - 4*b*d^2*(a + b*atanh(c*x))*log(2/(1 - c*x)) + (1/2)*b^2*d^2*log(1 - c^2*x^2) - 2*b^2*d^2*PolyLog(2, 1 - 2/(1 - c*x)) - b*d^2*(a + b*atanh(c*x))*PolyLog(2, 1 - 2/(1 - c*x)) + b*d^2*(a + b*atanh(c*x))*PolyLog(2, -1 + 2/(1 - c*x)) + (1/2)*b^2*d^2*PolyLog(3, 1 - 2/(1 - c*x)) - (1/2)*b^2*d^2*PolyLog(3, -1 + 2/(1 - c*x))]
    @test_int [(d + c*d*x)^2*(a + b*atanh(c*x))^2/x^2, x, 17, 2*c*d^2*(a + b*atanh(c*x))^2 - (d^2*(a + b*atanh(c*x))^2)/x + c^2*d^2*x*(a + b*atanh(c*x))^2 + 4*c*d^2*(a + b*atanh(c*x))^2*atanh(1 - 2/(1 - c*x)) - 2*b*c*d^2*(a + b*atanh(c*x))*log(2/(1 - c*x)) + 2*b*c*d^2*(a + b*atanh(c*x))*log(2 - 2/(1 + c*x)) - b^2*c*d^2*PolyLog(2, 1 - 2/(1 - c*x)) - 2*b*c*d^2*(a + b*atanh(c*x))*PolyLog(2, 1 - 2/(1 - c*x)) + 2*b*c*d^2*(a + b*atanh(c*x))*PolyLog(2, -1 + 2/(1 - c*x)) - b^2*c*d^2*PolyLog(2, -1 + 2/(1 + c*x)) + b^2*c*d^2*PolyLog(3, 1 - 2/(1 - c*x)) - b^2*c*d^2*PolyLog(3, -1 + 2/(1 - c*x))]
    @test_int [(d + c*d*x)^2*(a + b*atanh(c*x))^2/x^3, x, 20, -((b*c*d^2*(a + b*atanh(c*x)))/x) + (5/2)*c^2*d^2*(a + b*atanh(c*x))^2 - (d^2*(a + b*atanh(c*x))^2)/(2*x^2) - (2*c*d^2*(a + b*atanh(c*x))^2)/x + 2*c^2*d^2*(a + b*atanh(c*x))^2*atanh(1 - 2/(1 - c*x)) + b^2*c^2*d^2*log(x) - (1/2)*b^2*c^2*d^2*log(1 - c^2*x^2) + 4*b*c^2*d^2*(a + b*atanh(c*x))*log(2 - 2/(1 + c*x)) - b*c^2*d^2*(a + b*atanh(c*x))*PolyLog(2, 1 - 2/(1 - c*x)) + b*c^2*d^2*(a + b*atanh(c*x))*PolyLog(2, -1 + 2/(1 - c*x)) - 2*b^2*c^2*d^2*PolyLog(2, -1 + 2/(1 + c*x)) + (1/2)*b^2*c^2*d^2*PolyLog(3, 1 - 2/(1 - c*x)) - (1/2)*b^2*c^2*d^2*PolyLog(3, -1 + 2/(1 - c*x))]
    @test_int [(d + c*d*x)^2*(a + b*atanh(c*x))^2/x^4, x, 14, -((b^2*c^2*d^2)/(3*x)) + (1/3)*b^2*c^3*d^2*atanh(c*x) - (b*c*d^2*(a + b*atanh(c*x)))/(3*x^2) - (2*b*c^2*d^2*(a + b*atanh(c*x)))/x - (d^2*(1 + c*x)^3*(a + b*atanh(c*x))^2)/(3*x^3) + (8/3)*a*b*c^3*d^2*log(x) + 2*b^2*c^3*d^2*log(x) + (8/3)*b*c^3*d^2*(a + b*atanh(c*x))*log(2/(1 - c*x)) - b^2*c^3*d^2*log(1 - c^2*x^2) - (4/3)*b^2*c^3*d^2*PolyLog(2, (-c)*x) + (4/3)*b^2*c^3*d^2*PolyLog(2, c*x) + (4/3)*b^2*c^3*d^2*PolyLog(2, 1 - 2/(1 - c*x))]

    @test_int [x^3*(d + c*d*x)^3*(a + b*atanh(c*x))^2, x, 62, (3*a*b*d^3*x)/(2*c^3) + (122*b^2*d^3*x)/(105*c^3) + (7*b^2*d^3*x^2)/(20*c^2) + (44*b^2*d^3*x^3)/(315*c) + (1/20)*b^2*d^3*x^4 + (1/105)*b^2*c*d^3*x^5 - (122*b^2*d^3*atanh(c*x))/(105*c^4) + (3*b^2*d^3*x*atanh(c*x))/(2*c^3) + (26*b*d^3*x^2*(a + b*atanh(c*x)))/(35*c^2) + (b*d^3*x^3*(a + b*atanh(c*x)))/(2*c) + (13/35)*b*d^3*x^4*(a + b*atanh(c*x)) + (1/5)*b*c*d^3*x^5*(a + b*atanh(c*x)) + (1/21)*b*c^2*d^3*x^6*(a + b*atanh(c*x)) - (d^3*(a + b*atanh(c*x))^2)/(140*c^4) + (1/4)*d^3*x^4*(a + b*atanh(c*x))^2 + (3/5)*c*d^3*x^5*(a + b*atanh(c*x))^2 + (1/2)*c^2*d^3*x^6*(a + b*atanh(c*x))^2 + (1/7)*c^3*d^3*x^7*(a + b*atanh(c*x))^2 - (52*b*d^3*(a + b*atanh(c*x))*log(2/(1 - c*x)))/(35*c^4) + (11*b^2*d^3*log(1 - c^2*x^2))/(10*c^4) - (26*b^2*d^3*PolyLog(2, 1 - 2/(1 - c*x)))/(35*c^4)]
    @test_int [x^2*(d + c*d*x)^3*(a + b*atanh(c*x))^2, x, 52, (11*a*b*d^3*x)/(6*c^2) + (37*b^2*d^3*x)/(30*c^2) + (61*b^2*d^3*x^2)/(180*c) + (1/10)*b^2*d^3*x^3 + (1/60)*b^2*c*d^3*x^4 - (37*b^2*d^3*atanh(c*x))/(30*c^3) + (11*b^2*d^3*x*atanh(c*x))/(6*c^2) + (14*b*d^3*x^2*(a + b*atanh(c*x)))/(15*c) + (11/18)*b*d^3*x^3*(a + b*atanh(c*x)) + (3/10)*b*c*d^3*x^4*(a + b*atanh(c*x)) + (1/15)*b*c^2*d^3*x^5*(a + b*atanh(c*x)) + (d^3*(a + b*atanh(c*x))^2)/(60*c^3) + (1/3)*d^3*x^3*(a + b*atanh(c*x))^2 + (3/4)*c*d^3*x^4*(a + b*atanh(c*x))^2 + (3/5)*c^2*d^3*x^5*(a + b*atanh(c*x))^2 + (1/6)*c^3*d^3*x^6*(a + b*atanh(c*x))^2 - (28*b*d^3*(a + b*atanh(c*x))*log(2/(1 - c*x)))/(15*c^3) + (113*b^2*d^3*log(1 - c^2*x^2))/(90*c^3) - (14*b^2*d^3*PolyLog(2, 1 - 2/(1 - c*x)))/(15*c^3)]
    @test_int [x^1*(d + c*d*x)^3*(a + b*atanh(c*x))^2, x, 38, (5*a*b*d^3*x)/(2*c) + (13*b^2*d^3*x)/(10*c) + (1/4)*b^2*d^3*x^2 + (1/30)*b^2*c*d^3*x^3 - (13*b^2*d^3*atanh(c*x))/(10*c^2) + (5*b^2*d^3*x*atanh(c*x))/(2*c) + (6/5)*b*d^3*x^2*(a + b*atanh(c*x)) + (1/2)*b*c*d^3*x^3*(a + b*atanh(c*x)) + (1/10)*b*c^2*d^3*x^4*(a + b*atanh(c*x)) - (d^3*(1 + c*x)^4*(a + b*atanh(c*x))^2)/(4*c^2) + (d^3*(1 + c*x)^5*(a + b*atanh(c*x))^2)/(5*c^2) - (12*b*d^3*(a + b*atanh(c*x))*log(2/(1 - c*x)))/(5*c^2) + (3*b^2*d^3*log(1 - c^2*x^2))/(2*c^2) - (6*b^2*d^3*PolyLog(2, 1 - 2/(1 - c*x)))/(5*c^2)]
    @test_int [x^0*(d + c*d*x)^3*(a + b*atanh(c*x))^2, x, 16, (7/2)*a*b*d^3*x + b^2*d^3*x + (1/12)*b^2*c*d^3*x^2 - (b^2*d^3*atanh(c*x))/c + (7/2)*b^2*d^3*x*atanh(c*x) + b*c*d^3*x^2*(a + b*atanh(c*x)) + (1/6)*b*c^2*d^3*x^3*(a + b*atanh(c*x)) + (d^3*(1 + c*x)^4*(a + b*atanh(c*x))^2)/(4*c) - (4*b*d^3*(a + b*atanh(c*x))*log(2/(1 - c*x)))/c + (11*b^2*d^3*log(1 - c^2*x^2))/(6*c) - (2*b^2*d^3*PolyLog(2, 1 - 2/(1 - c*x)))/c]
    @test_int [(d + c*d*x)^3*(a + b*atanh(c*x))^2/x^1, x, 28, 3*a*b*c*d^3*x + (1/3)*b^2*c*d^3*x - (1/3)*b^2*d^3*atanh(c*x) + 3*b^2*c*d^3*x*atanh(c*x) + (1/3)*b*c^2*d^3*x^2*(a + b*atanh(c*x)) + (11/6)*d^3*(a + b*atanh(c*x))^2 + 3*c*d^3*x*(a + b*atanh(c*x))^2 + (3/2)*c^2*d^3*x^2*(a + b*atanh(c*x))^2 + (1/3)*c^3*d^3*x^3*(a + b*atanh(c*x))^2 + 2*d^3*(a + b*atanh(c*x))^2*atanh(1 - 2/(1 - c*x)) - (20/3)*b*d^3*(a + b*atanh(c*x))*log(2/(1 - c*x)) + (3/2)*b^2*d^3*log(1 - c^2*x^2) - (10/3)*b^2*d^3*PolyLog(2, 1 - 2/(1 - c*x)) - b*d^3*(a + b*atanh(c*x))*PolyLog(2, 1 - 2/(1 - c*x)) + b*d^3*(a + b*atanh(c*x))*PolyLog(2, -1 + 2/(1 - c*x)) + (1/2)*b^2*d^3*PolyLog(3, 1 - 2/(1 - c*x)) - (1/2)*b^2*d^3*PolyLog(3, -1 + 2/(1 - c*x))]
    @test_int [(d + c*d*x)^3*(a + b*atanh(c*x))^2/x^2, x, 23, a*b*c^2*d^3*x + b^2*c^2*d^3*x*atanh(c*x) + (7/2)*c*d^3*(a + b*atanh(c*x))^2 - (d^3*(a + b*atanh(c*x))^2)/x + 3*c^2*d^3*x*(a + b*atanh(c*x))^2 + (1/2)*c^3*d^3*x^2*(a + b*atanh(c*x))^2 + 6*c*d^3*(a + b*atanh(c*x))^2*atanh(1 - 2/(1 - c*x)) - 6*b*c*d^3*(a + b*atanh(c*x))*log(2/(1 - c*x)) + (1/2)*b^2*c*d^3*log(1 - c^2*x^2) + 2*b*c*d^3*(a + b*atanh(c*x))*log(2 - 2/(1 + c*x)) - 3*b^2*c*d^3*PolyLog(2, 1 - 2/(1 - c*x)) - 3*b*c*d^3*(a + b*atanh(c*x))*PolyLog(2, 1 - 2/(1 - c*x)) + 3*b*c*d^3*(a + b*atanh(c*x))*PolyLog(2, -1 + 2/(1 - c*x)) - b^2*c*d^3*PolyLog(2, -1 + 2/(1 + c*x)) + (3/2)*b^2*c*d^3*PolyLog(3, 1 - 2/(1 - c*x)) - (3/2)*b^2*c*d^3*PolyLog(3, -1 + 2/(1 - c*x))]
    @test_int [(d + c*d*x)^3*(a + b*atanh(c*x))^2/x^3, x, 25, -((b*c*d^3*(a + b*atanh(c*x)))/x) + (9/2)*c^2*d^3*(a + b*atanh(c*x))^2 - (d^3*(a + b*atanh(c*x))^2)/(2*x^2) - (3*c*d^3*(a + b*atanh(c*x))^2)/x + c^3*d^3*x*(a + b*atanh(c*x))^2 + 6*c^2*d^3*(a + b*atanh(c*x))^2*atanh(1 - 2/(1 - c*x)) + b^2*c^2*d^3*log(x) - 2*b*c^2*d^3*(a + b*atanh(c*x))*log(2/(1 - c*x)) - (1/2)*b^2*c^2*d^3*log(1 - c^2*x^2) + 6*b*c^2*d^3*(a + b*atanh(c*x))*log(2 - 2/(1 + c*x)) - b^2*c^2*d^3*PolyLog(2, 1 - 2/(1 - c*x)) - 3*b*c^2*d^3*(a + b*atanh(c*x))*PolyLog(2, 1 - 2/(1 - c*x)) + 3*b*c^2*d^3*(a + b*atanh(c*x))*PolyLog(2, -1 + 2/(1 - c*x)) - 3*b^2*c^2*d^3*PolyLog(2, -1 + 2/(1 + c*x)) + (3/2)*b^2*c^2*d^3*PolyLog(3, 1 - 2/(1 - c*x)) - (3/2)*b^2*c^2*d^3*PolyLog(3, -1 + 2/(1 - c*x))]
    @test_int [(d + c*d*x)^3*(a + b*atanh(c*x))^2/x^4, x, 28, -((b^2*c^2*d^3)/(3*x)) + (1/3)*b^2*c^3*d^3*atanh(c*x) - (b*c*d^3*(a + b*atanh(c*x)))/(3*x^2) - (3*b*c^2*d^3*(a + b*atanh(c*x)))/x + (29/6)*c^3*d^3*(a + b*atanh(c*x))^2 - (d^3*(a + b*atanh(c*x))^2)/(3*x^3) - (3*c*d^3*(a + b*atanh(c*x))^2)/(2*x^2) - (3*c^2*d^3*(a + b*atanh(c*x))^2)/x + 2*c^3*d^3*(a + b*atanh(c*x))^2*atanh(1 - 2/(1 - c*x)) + 3*b^2*c^3*d^3*log(x) - (3/2)*b^2*c^3*d^3*log(1 - c^2*x^2) + (20/3)*b*c^3*d^3*(a + b*atanh(c*x))*log(2 - 2/(1 + c*x)) - b*c^3*d^3*(a + b*atanh(c*x))*PolyLog(2, 1 - 2/(1 - c*x)) + b*c^3*d^3*(a + b*atanh(c*x))*PolyLog(2, -1 + 2/(1 - c*x)) - (10/3)*b^2*c^3*d^3*PolyLog(2, -1 + 2/(1 + c*x)) + (1/2)*b^2*c^3*d^3*PolyLog(3, 1 - 2/(1 - c*x)) - (1/2)*b^2*c^3*d^3*PolyLog(3, -1 + 2/(1 - c*x))]
    @test_int [(d + c*d*x)^3*(a + b*atanh(c*x))^2/x^5, x, 18, -((b^2*c^2*d^3)/(12*x^2)) - (b^2*c^3*d^3)/x + b^2*c^4*d^3*atanh(c*x) - (b*c*d^3*(a + b*atanh(c*x)))/(6*x^3) - (b*c^2*d^3*(a + b*atanh(c*x)))/x^2 - (7*b*c^3*d^3*(a + b*atanh(c*x)))/(2*x) - (d^3*(1 + c*x)^4*(a + b*atanh(c*x))^2)/(4*x^4) + 4*a*b*c^4*d^3*log(x) + (11/3)*b^2*c^4*d^3*log(x) + 4*b*c^4*d^3*(a + b*atanh(c*x))*log(2/(1 - c*x)) - (11/6)*b^2*c^4*d^3*log(1 - c^2*x^2) - 2*b^2*c^4*d^3*PolyLog(2, (-c)*x) + 2*b^2*c^4*d^3*PolyLog(2, c*x) + 2*b^2*c^4*d^3*PolyLog(2, 1 - 2/(1 - c*x))]
    @test_int [(d + c*d*x)^3*(a + b*atanh(c*x))^2/x^6, x, 22, -((b^2*c^2*d^3)/(30*x^3)) - (b^2*c^3*d^3)/(4*x^2) - (13*b^2*c^4*d^3)/(10*x) + (13/10)*b^2*c^5*d^3*atanh(c*x) - (b*c*d^3*(a + b*atanh(c*x)))/(10*x^4) - (b*c^2*d^3*(a + b*atanh(c*x)))/(2*x^3) - (6*b*c^3*d^3*(a + b*atanh(c*x)))/(5*x^2) - (5*b*c^4*d^3*(a + b*atanh(c*x)))/(2*x) - (d^3*(1 + c*x)^4*(a + b*atanh(c*x))^2)/(5*x^5) + (c*d^3*(1 + c*x)^4*(a + b*atanh(c*x))^2)/(20*x^4) + (12/5)*a*b*c^5*d^3*log(x) + 3*b^2*c^5*d^3*log(x) + (12/5)*b*c^5*d^3*(a + b*atanh(c*x))*log(2/(1 - c*x)) - (3/2)*b^2*c^5*d^3*log(1 - c^2*x^2) - (6/5)*b^2*c^5*d^3*PolyLog(2, (-c)*x) + (6/5)*b^2*c^5*d^3*PolyLog(2, c*x) + (6/5)*b^2*c^5*d^3*PolyLog(2, 1 - 2/(1 - c*x))]
    @test_int [(d + c*d*x)^3*(a + b*atanh(c*x))^2/x^7, x, 29, -((b^2*c^2*d^3)/(60*x^4)) - (b^2*c^3*d^3)/(10*x^3) - (61*b^2*c^4*d^3)/(180*x^2) - (37*b^2*c^5*d^3)/(30*x) + (37/30)*b^2*c^6*d^3*atanh(c*x) - (b*c*d^3*(a + b*atanh(c*x)))/(15*x^5) - (3*b*c^2*d^3*(a + b*atanh(c*x)))/(10*x^4) - (11*b*c^3*d^3*(a + b*atanh(c*x)))/(18*x^3) - (14*b*c^4*d^3*(a + b*atanh(c*x)))/(15*x^2) - (11*b*c^5*d^3*(a + b*atanh(c*x)))/(6*x) - (d^3*(a + b*atanh(c*x))^2)/(6*x^6) - (3*c*d^3*(a + b*atanh(c*x))^2)/(5*x^5) - (3*c^2*d^3*(a + b*atanh(c*x))^2)/(4*x^4) - (c^3*d^3*(a + b*atanh(c*x))^2)/(3*x^3) + (28/15)*a*b*c^6*d^3*log(x) + (113/45)*b^2*c^6*d^3*log(x) + (37/20)*b*c^6*d^3*(a + b*atanh(c*x))*log(2/(1 - c*x)) + (1/60)*b*c^6*d^3*(a + b*atanh(c*x))*log(2/(1 + c*x)) - (113/90)*b^2*c^6*d^3*log(1 - c^2*x^2) - (14/15)*b^2*c^6*d^3*PolyLog(2, (-c)*x) + (14/15)*b^2*c^6*d^3*PolyLog(2, c*x) + (37/40)*b^2*c^6*d^3*PolyLog(2, 1 - 2/(1 - c*x)) - (1/120)*b^2*c^6*d^3*PolyLog(2, 1 - 2/(1 + c*x))]

    #= ::Subsubsection::Closed:: =#
    #=q<0=#

    @test_int [x^3/(d + c*d*x)*(a + b*atanh(c*x))^2, x, 26, -((a*b*x)/(c^3*d)) + (b^2*x)/(3*c^3*d) - (b^2*atanh(c*x))/(3*c^4*d) - (b^2*x*atanh(c*x))/(c^3*d) + (b*x^2*(a + b*atanh(c*x)))/(3*c^2*d) + (11*(a + b*atanh(c*x))^2)/(6*c^4*d) + (x*(a + b*atanh(c*x))^2)/(c^3*d) - (x^2*(a + b*atanh(c*x))^2)/(2*c^2*d) + (x^3*(a + b*atanh(c*x))^2)/(3*c*d) - (8*b*(a + b*atanh(c*x))*log(2/(1 - c*x)))/(3*c^4*d) + ((a + b*atanh(c*x))^2*log(2/(1 + c*x)))/(c^4*d) - (b^2*log(1 - c^2*x^2))/(2*c^4*d) - (4*b^2*PolyLog(2, 1 - 2/(1 - c*x)))/(3*c^4*d) - (b*(a + b*atanh(c*x))*PolyLog(2, 1 - 2/(1 + c*x)))/(c^4*d) - (b^2*PolyLog(3, 1 - 2/(1 + c*x)))/(2*c^4*d)]
    @test_int [x^2/(d + c*d*x)*(a + b*atanh(c*x))^2, x, 16, (a*b*x)/(c^2*d) + (b^2*x*atanh(c*x))/(c^2*d) - (3*(a + b*atanh(c*x))^2)/(2*c^3*d) - (x*(a + b*atanh(c*x))^2)/(c^2*d) + (x^2*(a + b*atanh(c*x))^2)/(2*c*d) + (2*b*(a + b*atanh(c*x))*log(2/(1 - c*x)))/(c^3*d) - ((a + b*atanh(c*x))^2*log(2/(1 + c*x)))/(c^3*d) + (b^2*log(1 - c^2*x^2))/(2*c^3*d) + (b^2*PolyLog(2, 1 - 2/(1 - c*x)))/(c^3*d) + (b*(a + b*atanh(c*x))*PolyLog(2, 1 - 2/(1 + c*x)))/(c^3*d) + (b^2*PolyLog(3, 1 - 2/(1 + c*x)))/(2*c^3*d)]
    @test_int [x^1/(d + c*d*x)*(a + b*atanh(c*x))^2, x, 9, (a + b*atanh(c*x))^2/(c^2*d) + (x*(a + b*atanh(c*x))^2)/(c*d) - (2*b*(a + b*atanh(c*x))*log(2/(1 - c*x)))/(c^2*d) + ((a + b*atanh(c*x))^2*log(2/(1 + c*x)))/(c^2*d) - (b^2*PolyLog(2, 1 - 2/(1 - c*x)))/(c^2*d) - (b*(a + b*atanh(c*x))*PolyLog(2, 1 - 2/(1 + c*x)))/(c^2*d) - (b^2*PolyLog(3, 1 - 2/(1 + c*x)))/(2*c^2*d)]
    @test_int [x^0/(d + c*d*x)*(a + b*atanh(c*x))^2, x, 3, -(((a + b*atanh(c*x))^2*log(2/(1 + c*x)))/(c*d)) + (b*(a + b*atanh(c*x))*PolyLog(2, 1 - 2/(1 + c*x)))/(c*d) + (b^2*PolyLog(3, 1 - 2/(1 + c*x)))/(2*c*d)]
    @test_int [1/(d + c*d*x)*(a + b*atanh(c*x))^2/x^1, x, 3, ((a + b*atanh(c*x))^2*log(2 - 2/(1 + c*x)))/d - (b*(a + b*atanh(c*x))*PolyLog(2, -1 + 2/(1 + c*x)))/d - (b^2*PolyLog(3, -1 + 2/(1 + c*x)))/(2*d)]
    @test_int [1/(d + c*d*x)*(a + b*atanh(c*x))^2/x^2, x, 8, (c*(a + b*atanh(c*x))^2)/d - (a + b*atanh(c*x))^2/(d*x) + (2*b*c*(a + b*atanh(c*x))*log(2 - 2/(1 + c*x)))/d - (c*(a + b*atanh(c*x))^2*log(2 - 2/(1 + c*x)))/d - (b^2*c*PolyLog(2, -1 + 2/(1 + c*x)))/d + (b*c*(a + b*atanh(c*x))*PolyLog(2, -1 + 2/(1 + c*x)))/d + (b^2*c*PolyLog(3, -1 + 2/(1 + c*x)))/(2*d)]
    @test_int [1/(d + c*d*x)*(a + b*atanh(c*x))^2/x^3, x, 17, -((b*c*(a + b*atanh(c*x)))/(d*x)) - (c^2*(a + b*atanh(c*x))^2)/(2*d) - (a + b*atanh(c*x))^2/(2*d*x^2) + (c*(a + b*atanh(c*x))^2)/(d*x) + (b^2*c^2*log(x))/d - (b^2*c^2*log(1 - c^2*x^2))/(2*d) - (2*b*c^2*(a + b*atanh(c*x))*log(2 - 2/(1 + c*x)))/d + (c^2*(a + b*atanh(c*x))^2*log(2 - 2/(1 + c*x)))/d + (b^2*c^2*PolyLog(2, -1 + 2/(1 + c*x)))/d - (b*c^2*(a + b*atanh(c*x))*PolyLog(2, -1 + 2/(1 + c*x)))/d - (b^2*c^2*PolyLog(3, -1 + 2/(1 + c*x)))/(2*d)]
    @test_int [1/(d + c*d*x)*(a + b*atanh(c*x))^2/x^4, x, 26, -((b^2*c^2)/(3*d*x)) + (b^2*c^3*atanh(c*x))/(3*d) - (b*c*(a + b*atanh(c*x)))/(3*d*x^2) + (b*c^2*(a + b*atanh(c*x)))/(d*x) + (5*c^3*(a + b*atanh(c*x))^2)/(6*d) - (a + b*atanh(c*x))^2/(3*d*x^3) + (c*(a + b*atanh(c*x))^2)/(2*d*x^2) - (c^2*(a + b*atanh(c*x))^2)/(d*x) - (b^2*c^3*log(x))/d + (b^2*c^3*log(1 - c^2*x^2))/(2*d) + (8*b*c^3*(a + b*atanh(c*x))*log(2 - 2/(1 + c*x)))/(3*d) - (c^3*(a + b*atanh(c*x))^2*log(2 - 2/(1 + c*x)))/d - (4*b^2*c^3*PolyLog(2, -1 + 2/(1 + c*x)))/(3*d) + (b*c^3*(a + b*atanh(c*x))*PolyLog(2, -1 + 2/(1 + c*x)))/d + (b^2*c^3*PolyLog(3, -1 + 2/(1 + c*x)))/(2*d)]

    @test_int [x^4/(d + c*d*x)^2*(a + b*atanh(c*x))^2, x, 33, -((2*a*b*x)/(c^4*d^2)) + (b^2*x)/(3*c^4*d^2) - b^2/(2*c^5*d^2*(1 + c*x)) + (b^2*atanh(c*x))/(6*c^5*d^2) - (2*b^2*x*atanh(c*x))/(c^4*d^2) + (b*x^2*(a + b*atanh(c*x)))/(3*c^3*d^2) - (b*(a + b*atanh(c*x)))/(c^5*d^2*(1 + c*x)) + (29*(a + b*atanh(c*x))^2)/(6*c^5*d^2) + (3*x*(a + b*atanh(c*x))^2)/(c^4*d^2) - (x^2*(a + b*atanh(c*x))^2)/(c^3*d^2) + (x^3*(a + b*atanh(c*x))^2)/(3*c^2*d^2) - (a + b*atanh(c*x))^2/(c^5*d^2*(1 + c*x)) - (20*b*(a + b*atanh(c*x))*log(2/(1 - c*x)))/(3*c^5*d^2) + (4*(a + b*atanh(c*x))^2*log(2/(1 + c*x)))/(c^5*d^2) - (b^2*log(1 - c^2*x^2))/(c^5*d^2) - (10*b^2*PolyLog(2, 1 - 2/(1 - c*x)))/(3*c^5*d^2) - (4*b*(a + b*atanh(c*x))*PolyLog(2, 1 - 2/(1 + c*x)))/(c^5*d^2) - (2*b^2*PolyLog(3, 1 - 2/(1 + c*x)))/(c^5*d^2)]
    @test_int [x^3/(d + c*d*x)^2*(a + b*atanh(c*x))^2, x, 24, (a*b*x)/(c^3*d^2) + b^2/(2*c^4*d^2*(1 + c*x)) - (b^2*atanh(c*x))/(2*c^4*d^2) + (b^2*x*atanh(c*x))/(c^3*d^2) + (b*(a + b*atanh(c*x)))/(c^4*d^2*(1 + c*x)) - (3*(a + b*atanh(c*x))^2)/(c^4*d^2) - (2*x*(a + b*atanh(c*x))^2)/(c^3*d^2) + (x^2*(a + b*atanh(c*x))^2)/(2*c^2*d^2) + (a + b*atanh(c*x))^2/(c^4*d^2*(1 + c*x)) + (4*b*(a + b*atanh(c*x))*log(2/(1 - c*x)))/(c^4*d^2) - (3*(a + b*atanh(c*x))^2*log(2/(1 + c*x)))/(c^4*d^2) + (b^2*log(1 - c^2*x^2))/(2*c^4*d^2) + (2*b^2*PolyLog(2, 1 - 2/(1 - c*x)))/(c^4*d^2) + (3*b*(a + b*atanh(c*x))*PolyLog(2, 1 - 2/(1 + c*x)))/(c^4*d^2) + (3*b^2*PolyLog(3, 1 - 2/(1 + c*x)))/(2*c^4*d^2)]
    @test_int [x^2/(d + c*d*x)^2*(a + b*atanh(c*x))^2, x, 18, -(b^2/(2*c^3*d^2*(1 + c*x))) + (b^2*atanh(c*x))/(2*c^3*d^2) - (b*(a + b*atanh(c*x)))/(c^3*d^2*(1 + c*x)) + (3*(a + b*atanh(c*x))^2)/(2*c^3*d^2) + (x*(a + b*atanh(c*x))^2)/(c^2*d^2) - (a + b*atanh(c*x))^2/(c^3*d^2*(1 + c*x)) - (2*b*(a + b*atanh(c*x))*log(2/(1 - c*x)))/(c^3*d^2) + (2*(a + b*atanh(c*x))^2*log(2/(1 + c*x)))/(c^3*d^2) - (b^2*PolyLog(2, 1 - 2/(1 - c*x)))/(c^3*d^2) - (2*b*(a + b*atanh(c*x))*PolyLog(2, 1 - 2/(1 + c*x)))/(c^3*d^2) - (b^2*PolyLog(3, 1 - 2/(1 + c*x)))/(c^3*d^2)]
    @test_int [x^1/(d + c*d*x)^2*(a + b*atanh(c*x))^2, x, 13, b^2/(2*c^2*d^2*(1 + c*x)) - (b^2*atanh(c*x))/(2*c^2*d^2) + (b*(a + b*atanh(c*x)))/(c^2*d^2*(1 + c*x)) - (a + b*atanh(c*x))^2/(2*c^2*d^2) + (a + b*atanh(c*x))^2/(c^2*d^2*(1 + c*x)) - ((a + b*atanh(c*x))^2*log(2/(1 + c*x)))/(c^2*d^2) + (b*(a + b*atanh(c*x))*PolyLog(2, 1 - 2/(1 + c*x)))/(c^2*d^2) + (b^2*PolyLog(3, 1 - 2/(1 + c*x)))/(2*c^2*d^2)]
    @test_int [x^0/(d + c*d*x)^2*(a + b*atanh(c*x))^2, x, 8, -(b^2/(2*c*d^2*(1 + c*x))) + (b^2*atanh(c*x))/(2*c*d^2) - (b*(a + b*atanh(c*x)))/(c*d^2*(1 + c*x)) + (a + b*atanh(c*x))^2/(2*c*d^2) - (a + b*atanh(c*x))^2/(c*d^2*(1 + c*x))]
    @test_int [1/(d + c*d*x)^2*(a + b*atanh(c*x))^2/x^1, x, 19, b^2/(2*d^2*(1 + c*x)) - (b^2*atanh(c*x))/(2*d^2) + (b*(a + b*atanh(c*x)))/(d^2*(1 + c*x)) - (a + b*atanh(c*x))^2/(2*d^2) + (a + b*atanh(c*x))^2/(d^2*(1 + c*x)) + (2*(a + b*atanh(c*x))^2*atanh(1 - 2/(1 - c*x)))/d^2 + ((a + b*atanh(c*x))^2*log(2/(1 + c*x)))/d^2 - (b*(a + b*atanh(c*x))*PolyLog(2, 1 - 2/(1 - c*x)))/d^2 + (b*(a + b*atanh(c*x))*PolyLog(2, -1 + 2/(1 - c*x)))/d^2 - (b*(a + b*atanh(c*x))*PolyLog(2, 1 - 2/(1 + c*x)))/d^2 + (b^2*PolyLog(3, 1 - 2/(1 - c*x)))/(2*d^2) - (b^2*PolyLog(3, -1 + 2/(1 - c*x)))/(2*d^2) - (b^2*PolyLog(3, 1 - 2/(1 + c*x)))/(2*d^2)]
    @test_int [1/(d + c*d*x)^2*(a + b*atanh(c*x))^2/x^2, x, 23, -((b^2*c)/(2*d^2*(1 + c*x))) + (b^2*c*atanh(c*x))/(2*d^2) - (b*c*(a + b*atanh(c*x)))/(d^2*(1 + c*x)) + (3*c*(a + b*atanh(c*x))^2)/(2*d^2) - (a + b*atanh(c*x))^2/(d^2*x) - (c*(a + b*atanh(c*x))^2)/(d^2*(1 + c*x)) - (4*c*(a + b*atanh(c*x))^2*atanh(1 - 2/(1 - c*x)))/d^2 - (2*c*(a + b*atanh(c*x))^2*log(2/(1 + c*x)))/d^2 + (2*b*c*(a + b*atanh(c*x))*log(2 - 2/(1 + c*x)))/d^2 + (2*b*c*(a + b*atanh(c*x))*PolyLog(2, 1 - 2/(1 - c*x)))/d^2 - (2*b*c*(a + b*atanh(c*x))*PolyLog(2, -1 + 2/(1 - c*x)))/d^2 + (2*b*c*(a + b*atanh(c*x))*PolyLog(2, 1 - 2/(1 + c*x)))/d^2 - (b^2*c*PolyLog(2, -1 + 2/(1 + c*x)))/d^2 - (b^2*c*PolyLog(3, 1 - 2/(1 - c*x)))/d^2 + (b^2*c*PolyLog(3, -1 + 2/(1 - c*x)))/d^2 + (b^2*c*PolyLog(3, 1 - 2/(1 + c*x)))/d^2]
    @test_int [1/(d + c*d*x)^2*(a + b*atanh(c*x))^2/x^3, x, 31, (b^2*c^2)/(2*d^2*(1 + c*x)) - (b^2*c^2*atanh(c*x))/(2*d^2) - (b*c*(a + b*atanh(c*x)))/(d^2*x) + (b*c^2*(a + b*atanh(c*x)))/(d^2*(1 + c*x)) - (2*c^2*(a + b*atanh(c*x))^2)/d^2 - (a + b*atanh(c*x))^2/(2*d^2*x^2) + (2*c*(a + b*atanh(c*x))^2)/(d^2*x) + (c^2*(a + b*atanh(c*x))^2)/(d^2*(1 + c*x)) + (6*c^2*(a + b*atanh(c*x))^2*atanh(1 - 2/(1 - c*x)))/d^2 + (b^2*c^2*log(x))/d^2 + (3*c^2*(a + b*atanh(c*x))^2*log(2/(1 + c*x)))/d^2 - (b^2*c^2*log(1 - c^2*x^2))/(2*d^2) - (4*b*c^2*(a + b*atanh(c*x))*log(2 - 2/(1 + c*x)))/d^2 - (3*b*c^2*(a + b*atanh(c*x))*PolyLog(2, 1 - 2/(1 - c*x)))/d^2 + (3*b*c^2*(a + b*atanh(c*x))*PolyLog(2, -1 + 2/(1 - c*x)))/d^2 - (3*b*c^2*(a + b*atanh(c*x))*PolyLog(2, 1 - 2/(1 + c*x)))/d^2 + (2*b^2*c^2*PolyLog(2, -1 + 2/(1 + c*x)))/d^2 + (3*b^2*c^2*PolyLog(3, 1 - 2/(1 - c*x)))/(2*d^2) - (3*b^2*c^2*PolyLog(3, -1 + 2/(1 - c*x)))/(2*d^2) - (3*b^2*c^2*PolyLog(3, 1 - 2/(1 + c*x)))/(2*d^2)]

    @test_int [x^4/(d + c*d*x)^3*(a + b*atanh(c*x))^2, x, 37, (a*b*x)/(c^4*d^3) - b^2/(16*c^5*d^3*(1 + c*x)^2) + (29*b^2)/(16*c^5*d^3*(1 + c*x)) - (29*b^2*atanh(c*x))/(16*c^5*d^3) + (b^2*x*atanh(c*x))/(c^4*d^3) - (b*(a + b*atanh(c*x)))/(4*c^5*d^3*(1 + c*x)^2) + (15*b*(a + b*atanh(c*x)))/(4*c^5*d^3*(1 + c*x)) - (43*(a + b*atanh(c*x))^2)/(8*c^5*d^3) - (3*x*(a + b*atanh(c*x))^2)/(c^4*d^3) + (x^2*(a + b*atanh(c*x))^2)/(2*c^3*d^3) - (a + b*atanh(c*x))^2/(2*c^5*d^3*(1 + c*x)^2) + (4*(a + b*atanh(c*x))^2)/(c^5*d^3*(1 + c*x)) + (6*b*(a + b*atanh(c*x))*log(2/(1 - c*x)))/(c^5*d^3) - (6*(a + b*atanh(c*x))^2*log(2/(1 + c*x)))/(c^5*d^3) + (b^2*log(1 - c^2*x^2))/(2*c^5*d^3) + (3*b^2*PolyLog(2, 1 - 2/(1 - c*x)))/(c^5*d^3) + (6*b*(a + b*atanh(c*x))*PolyLog(2, 1 - 2/(1 + c*x)))/(c^5*d^3) + (3*b^2*PolyLog(3, 1 - 2/(1 + c*x)))/(c^5*d^3)]
    @test_int [x^3/(d + c*d*x)^3*(a + b*atanh(c*x))^2, x, 31, b^2/(16*c^4*d^3*(1 + c*x)^2) - (21*b^2)/(16*c^4*d^3*(1 + c*x)) + (21*b^2*atanh(c*x))/(16*c^4*d^3) + (b*(a + b*atanh(c*x)))/(4*c^4*d^3*(1 + c*x)^2) - (11*b*(a + b*atanh(c*x)))/(4*c^4*d^3*(1 + c*x)) + (19*(a + b*atanh(c*x))^2)/(8*c^4*d^3) + (x*(a + b*atanh(c*x))^2)/(c^3*d^3) + (a + b*atanh(c*x))^2/(2*c^4*d^3*(1 + c*x)^2) - (3*(a + b*atanh(c*x))^2)/(c^4*d^3*(1 + c*x)) - (2*b*(a + b*atanh(c*x))*log(2/(1 - c*x)))/(c^4*d^3) + (3*(a + b*atanh(c*x))^2*log(2/(1 + c*x)))/(c^4*d^3) - (b^2*PolyLog(2, 1 - 2/(1 - c*x)))/(c^4*d^3) - (3*b*(a + b*atanh(c*x))*PolyLog(2, 1 - 2/(1 + c*x)))/(c^4*d^3) - (3*b^2*PolyLog(3, 1 - 2/(1 + c*x)))/(2*c^4*d^3)]
    @test_int [x^2/(d + c*d*x)^3*(a + b*atanh(c*x))^2, x, 26, -(b^2/(16*c^3*d^3*(1 + c*x)^2)) + (13*b^2)/(16*c^3*d^3*(1 + c*x)) - (13*b^2*atanh(c*x))/(16*c^3*d^3) - (b*(a + b*atanh(c*x)))/(4*c^3*d^3*(1 + c*x)^2) + (7*b*(a + b*atanh(c*x)))/(4*c^3*d^3*(1 + c*x)) - (7*(a + b*atanh(c*x))^2)/(8*c^3*d^3) - (a + b*atanh(c*x))^2/(2*c^3*d^3*(1 + c*x)^2) + (2*(a + b*atanh(c*x))^2)/(c^3*d^3*(1 + c*x)) - ((a + b*atanh(c*x))^2*log(2/(1 + c*x)))/(c^3*d^3) + (b*(a + b*atanh(c*x))*PolyLog(2, 1 - 2/(1 + c*x)))/(c^3*d^3) + (b^2*PolyLog(3, 1 - 2/(1 + c*x)))/(2*c^3*d^3)]
    @test_int [x^1/(d + c*d*x)^3*(a + b*atanh(c*x))^2, x, 13, b^2/(16*c^2*d^3*(1 + c*x)^2) - (5*b^2)/(16*c^2*d^3*(1 + c*x)) + (5*b^2*atanh(c*x))/(16*c^2*d^3) + (b*(a + b*atanh(c*x)))/(4*c^2*d^3*(1 + c*x)^2) - (3*b*(a + b*atanh(c*x)))/(4*c^2*d^3*(1 + c*x)) - (a + b*atanh(c*x))^2/(8*c^2*d^3) + (x^2*(a + b*atanh(c*x))^2)/(2*d^3*(1 + c*x)^2)]
    @test_int [x^0/(d + c*d*x)^3*(a + b*atanh(c*x))^2, x, 13, -(b^2/(16*c*d^3*(1 + c*x)^2)) - (3*b^2)/(16*c*d^3*(1 + c*x)) + (3*b^2*atanh(c*x))/(16*c*d^3) - (b*(a + b*atanh(c*x)))/(4*c*d^3*(1 + c*x)^2) - (b*(a + b*atanh(c*x)))/(4*c*d^3*(1 + c*x)) + (a + b*atanh(c*x))^2/(8*c*d^3) - (a + b*atanh(c*x))^2/(2*c*d^3*(1 + c*x)^2)]
    @test_int [1/(d + c*d*x)^3*(a + b*atanh(c*x))^2/x^1, x, 32, b^2/(16*d^3*(1 + c*x)^2) + (11*b^2)/(16*d^3*(1 + c*x)) - (11*b^2*atanh(c*x))/(16*d^3) + (b*(a + b*atanh(c*x)))/(4*d^3*(1 + c*x)^2) + (5*b*(a + b*atanh(c*x)))/(4*d^3*(1 + c*x)) - (5*(a + b*atanh(c*x))^2)/(8*d^3) + (a + b*atanh(c*x))^2/(2*d^3*(1 + c*x)^2) + (a + b*atanh(c*x))^2/(d^3*(1 + c*x)) + (2*(a + b*atanh(c*x))^2*atanh(1 - 2/(1 - c*x)))/d^3 + ((a + b*atanh(c*x))^2*log(2/(1 + c*x)))/d^3 - (b*(a + b*atanh(c*x))*PolyLog(2, 1 - 2/(1 - c*x)))/d^3 + (b*(a + b*atanh(c*x))*PolyLog(2, -1 + 2/(1 - c*x)))/d^3 - (b*(a + b*atanh(c*x))*PolyLog(2, 1 - 2/(1 + c*x)))/d^3 + (b^2*PolyLog(3, 1 - 2/(1 - c*x)))/(2*d^3) - (b^2*PolyLog(3, -1 + 2/(1 - c*x)))/(2*d^3) - (b^2*PolyLog(3, 1 - 2/(1 + c*x)))/(2*d^3)]
    @test_int [1/(d + c*d*x)^3*(a + b*atanh(c*x))^2/x^2, x, 36, -((b^2*c)/(16*d^3*(1 + c*x)^2)) - (19*b^2*c)/(16*d^3*(1 + c*x)) + (19*b^2*c*atanh(c*x))/(16*d^3) - (b*c*(a + b*atanh(c*x)))/(4*d^3*(1 + c*x)^2) - (9*b*c*(a + b*atanh(c*x)))/(4*d^3*(1 + c*x)) + (17*c*(a + b*atanh(c*x))^2)/(8*d^3) - (a + b*atanh(c*x))^2/(d^3*x) - (c*(a + b*atanh(c*x))^2)/(2*d^3*(1 + c*x)^2) - (2*c*(a + b*atanh(c*x))^2)/(d^3*(1 + c*x)) - (6*c*(a + b*atanh(c*x))^2*atanh(1 - 2/(1 - c*x)))/d^3 - (3*c*(a + b*atanh(c*x))^2*log(2/(1 + c*x)))/d^3 + (2*b*c*(a + b*atanh(c*x))*log(2 - 2/(1 + c*x)))/d^3 + (3*b*c*(a + b*atanh(c*x))*PolyLog(2, 1 - 2/(1 - c*x)))/d^3 - (3*b*c*(a + b*atanh(c*x))*PolyLog(2, -1 + 2/(1 - c*x)))/d^3 + (3*b*c*(a + b*atanh(c*x))*PolyLog(2, 1 - 2/(1 + c*x)))/d^3 - (b^2*c*PolyLog(2, -1 + 2/(1 + c*x)))/d^3 - (3*b^2*c*PolyLog(3, 1 - 2/(1 - c*x)))/(2*d^3) + (3*b^2*c*PolyLog(3, -1 + 2/(1 - c*x)))/(2*d^3) + (3*b^2*c*PolyLog(3, 1 - 2/(1 + c*x)))/(2*d^3)]

    @test_int [(a + b*atanh(c*x))^2/(1 + c*x)^4, x, 18, -(b^2/(54*c*(1 + c*x)^3)) - (5*b^2)/(144*c*(1 + c*x)^2) - (11*b^2)/(144*c*(1 + c*x)) + (11*b^2*atanh(c*x))/(144*c) - (b*(a + b*atanh(c*x)))/(9*c*(1 + c*x)^3) - (b*(a + b*atanh(c*x)))/(12*c*(1 + c*x)^2) - (b*(a + b*atanh(c*x)))/(12*c*(1 + c*x)) + (a + b*atanh(c*x))^2/(24*c) - (a + b*atanh(c*x))^2/(3*c*(1 + c*x)^3)]

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

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(d+e*x)^q*(a+b*atanh(c*x))^3*when*c^2*d^2 - e^2=0=#

    @test_int [(a + b*atanh(c*x))^3*(1 + c*x)^3, x, 26, 3*a*b^2*x + (b^3*x)/4 - (b^3*atanh(c*x))/(4*c) + 3*b^3*x*atanh(c*x) + (1/4)*b^2*c*x^2*(a + b*atanh(c*x)) + (4*b*(a + b*atanh(c*x))^2)/c + (21/4)*b*x*(a + b*atanh(c*x))^2 + (3/2)*b*c*x^2*(a + b*atanh(c*x))^2 + (1/4)*b*c^2*x^3*(a + b*atanh(c*x))^2 + ((1 + c*x)^4*(a + b*atanh(c*x))^3)/(4*c) - (11*b^2*(a + b*atanh(c*x))*log(2/(1 - c*x)))/c - (6*b*(a + b*atanh(c*x))^2*log(2/(1 - c*x)))/c + (3*b^3*log(1 - c^2*x^2))/(2*c) - (11*b^3*PolyLog(2, 1 - 2/(1 - c*x)))/(2*c) - (6*b^2*(a + b*atanh(c*x))*PolyLog(2, 1 - 2/(1 - c*x)))/c + (3*b^3*PolyLog(3, 1 - 2/(1 - c*x)))/c]
    @test_int [(a + b*atanh(c*x))^3*(1 + c*x)^2, x, 17, a*b^2*x + b^3*x*atanh(c*x) + (5*b*(a + b*atanh(c*x))^2)/(2*c) + 3*b*x*(a + b*atanh(c*x))^2 + (1/2)*b*c*x^2*(a + b*atanh(c*x))^2 + ((1 + c*x)^3*(a + b*atanh(c*x))^3)/(3*c) - (6*b^2*(a + b*atanh(c*x))*log(2/(1 - c*x)))/c - (4*b*(a + b*atanh(c*x))^2*log(2/(1 - c*x)))/c + (b^3*log(1 - c^2*x^2))/(2*c) - (3*b^3*PolyLog(2, 1 - 2/(1 - c*x)))/c - (4*b^2*(a + b*atanh(c*x))*PolyLog(2, 1 - 2/(1 - c*x)))/c + (2*b^3*PolyLog(3, 1 - 2/(1 - c*x)))/c]
    @test_int [(a + b*atanh(c*x))^3*(1 + c*x)^1, x, 11, (3*b*(a + b*atanh(c*x))^2)/(2*c) + (3/2)*b*x*(a + b*atanh(c*x))^2 + ((1 + c*x)^2*(a + b*atanh(c*x))^3)/(2*c) - (3*b^2*(a + b*atanh(c*x))*log(2/(1 - c*x)))/c - (3*b*(a + b*atanh(c*x))^2*log(2/(1 - c*x)))/c - (3*b^3*PolyLog(2, 1 - 2/(1 - c*x)))/(2*c) - (3*b^2*(a + b*atanh(c*x))*PolyLog(2, 1 - 2/(1 - c*x)))/c + (3*b^3*PolyLog(3, 1 - 2/(1 - c*x)))/(2*c)]
    @test_int [(a + b*atanh(c*x))^3/(1 + c*x)^1, x, 4, -(((a + b*atanh(c*x))^3*log(2/(1 + c*x)))/c) + (3*b*(a + b*atanh(c*x))^2*PolyLog(2, 1 - 2/(1 + c*x)))/(2*c) + (3*b^2*(a + b*atanh(c*x))*PolyLog(3, 1 - 2/(1 + c*x)))/(2*c) + (3*b^3*PolyLog(4, 1 - 2/(1 + c*x)))/(4*c)]
    @test_int [(a + b*atanh(c*x))^3/(1 + c*x)^2, x, 11, -((3*b^3)/(4*c*(1 + c*x))) + (3*b^3*atanh(c*x))/(4*c) - (3*b^2*(a + b*atanh(c*x)))/(2*c*(1 + c*x)) + (3*b*(a + b*atanh(c*x))^2)/(4*c) - (3*b*(a + b*atanh(c*x))^2)/(2*c*(1 + c*x)) + (a + b*atanh(c*x))^3/(2*c) - (a + b*atanh(c*x))^3/(c*(1 + c*x))]
    @test_int [(a + b*atanh(c*x))^3/(1 + c*x)^3, x, 24, -((3*b^3)/(64*c*(1 + c*x)^2)) - (21*b^3)/(64*c*(1 + c*x)) + (21*b^3*atanh(c*x))/(64*c) - (3*b^2*(a + b*atanh(c*x)))/(16*c*(1 + c*x)^2) - (9*b^2*(a + b*atanh(c*x)))/(16*c*(1 + c*x)) + (9*b*(a + b*atanh(c*x))^2)/(32*c) - (3*b*(a + b*atanh(c*x))^2)/(8*c*(1 + c*x)^2) - (3*b*(a + b*atanh(c*x))^2)/(8*c*(1 + c*x)) + (a + b*atanh(c*x))^3/(8*c) - (a + b*atanh(c*x))^3/(2*c*(1 + c*x)^2)]
    @test_int [(a + b*atanh(c*x))^3/(1 + c*x)^4, x, 42, -(b^3/(108*c*(1 + c*x)^3)) - (19*b^3)/(576*c*(1 + c*x)^2) - (85*b^3)/(576*c*(1 + c*x)) + (85*b^3*atanh(c*x))/(576*c) - (b^2*(a + b*atanh(c*x)))/(18*c*(1 + c*x)^3) - (5*b^2*(a + b*atanh(c*x)))/(48*c*(1 + c*x)^2) - (11*b^2*(a + b*atanh(c*x)))/(48*c*(1 + c*x)) + (11*b*(a + b*atanh(c*x))^2)/(96*c) - (b*(a + b*atanh(c*x))^2)/(6*c*(1 + c*x)^3) - (b*(a + b*atanh(c*x))^2)/(8*c*(1 + c*x)^2) - (b*(a + b*atanh(c*x))^2)/(8*c*(1 + c*x)) + (a + b*atanh(c*x))^3/(24*c) - (a + b*atanh(c*x))^3/(3*c*(1 + c*x)^3)]

    @test_int [(x^2*atanh(a*x)^3)/(c + a*c*x), x, 19, (3*atanh(a*x)^2)/(2*a^3*c) + (3*x*atanh(a*x)^2)/(2*a^2*c) - (3*atanh(a*x)^3)/(2*a^3*c) - (x*atanh(a*x)^3)/(a^2*c) + (x^2*atanh(a*x)^3)/(2*a*c) - (3*atanh(a*x)*log(2/(1 - a*x)))/(a^3*c) + (3*atanh(a*x)^2*log(2/(1 - a*x)))/(a^3*c) - (atanh(a*x)^3*log(2/(1 + a*x)))/(a^3*c) - (3*PolyLog(2, 1 - 2/(1 - a*x)))/(2*a^3*c) + (3*atanh(a*x)*PolyLog(2, 1 - 2/(1 - a*x)))/(a^3*c) + (3*atanh(a*x)^2*PolyLog(2, 1 - 2/(1 + a*x)))/(2*a^3*c) - (3*PolyLog(3, 1 - 2/(1 - a*x)))/(2*a^3*c) + (3*atanh(a*x)*PolyLog(3, 1 - 2/(1 + a*x)))/(2*a^3*c) + (3*PolyLog(4, 1 - 2/(1 + a*x)))/(4*a^3*c)]
    @test_int [(x*atanh(a*x)^3)/(c + a*c*x), x, 10, atanh(a*x)^3/(a^2*c) + (x*atanh(a*x)^3)/(a*c) - (3*atanh(a*x)^2*log(2/(1 - a*x)))/(a^2*c) + (atanh(a*x)^3*log(2/(1 + a*x)))/(a^2*c) - (3*atanh(a*x)*PolyLog(2, 1 - 2/(1 - a*x)))/(a^2*c) - (3*atanh(a*x)^2*PolyLog(2, 1 - 2/(1 + a*x)))/(2*a^2*c) + (3*PolyLog(3, 1 - 2/(1 - a*x)))/(2*a^2*c) - (3*atanh(a*x)*PolyLog(3, 1 - 2/(1 + a*x)))/(2*a^2*c) - (3*PolyLog(4, 1 - 2/(1 + a*x)))/(4*a^2*c)]
    @test_int [atanh(a*x)^3/(c + a*c*x), x, 4, -((atanh(a*x)^3*log(2/(1 + a*x)))/(a*c)) + (3*atanh(a*x)^2*PolyLog(2, 1 - 2/(1 + a*x)))/(2*a*c) + (3*atanh(a*x)*PolyLog(3, 1 - 2/(1 + a*x)))/(2*a*c) + (3*PolyLog(4, 1 - 2/(1 + a*x)))/(4*a*c)]
    @test_int [atanh(a*x)^3/(x*(c + a*c*x)), x, 4, (atanh(a*x)^3*log(2 - 2/(1 + a*x)))/c - (3*atanh(a*x)^2*PolyLog(2, -1 + 2/(1 + a*x)))/(2*c) - (3*atanh(a*x)*PolyLog(3, -1 + 2/(1 + a*x)))/(2*c) - (3*PolyLog(4, -1 + 2/(1 + a*x)))/(4*c)]
    @test_int [atanh(a*x)^3/(c*x + a*c*x^2), x, 5, (atanh(a*x)^3*log(2 - 2/(1 + a*x)))/c - (3*atanh(a*x)^2*PolyLog(2, -1 + 2/(1 + a*x)))/(2*c) - (3*atanh(a*x)*PolyLog(3, -1 + 2/(1 + a*x)))/(2*c) - (3*PolyLog(4, -1 + 2/(1 + a*x)))/(4*c)]
    @test_int [atanh(a*x)^3/(x^2*(c + a*c*x)), x, 10, (a*atanh(a*x)^3)/c - atanh(a*x)^3/(c*x) + (3*a*atanh(a*x)^2*log(2 - 2/(1 + a*x)))/c - (a*atanh(a*x)^3*log(2 - 2/(1 + a*x)))/c - (3*a*atanh(a*x)*PolyLog(2, -1 + 2/(1 + a*x)))/c + (3*a*atanh(a*x)^2*PolyLog(2, -1 + 2/(1 + a*x)))/(2*c) - (3*a*PolyLog(3, -1 + 2/(1 + a*x)))/(2*c) + (3*a*atanh(a*x)*PolyLog(3, -1 + 2/(1 + a*x)))/(2*c) + (3*a*PolyLog(4, -1 + 2/(1 + a*x)))/(4*c)]
    @test_int [atanh(a*x)^3/(x^3*(c + a*c*x)), x, 18, (3*a^2*atanh(a*x)^2)/(2*c) - (3*a*atanh(a*x)^2)/(2*c*x) - (a^2*atanh(a*x)^3)/(2*c) - atanh(a*x)^3/(2*c*x^2) + (a*atanh(a*x)^3)/(c*x) + (3*a^2*atanh(a*x)*log(2 - 2/(1 + a*x)))/c - (3*a^2*atanh(a*x)^2*log(2 - 2/(1 + a*x)))/c + (a^2*atanh(a*x)^3*log(2 - 2/(1 + a*x)))/c - (3*a^2*PolyLog(2, -1 + 2/(1 + a*x)))/(2*c) + (3*a^2*atanh(a*x)*PolyLog(2, -1 + 2/(1 + a*x)))/c - (3*a^2*atanh(a*x)^2*PolyLog(2, -1 + 2/(1 + a*x)))/(2*c) + (3*a^2*PolyLog(3, -1 + 2/(1 + a*x)))/(2*c) - (3*a^2*atanh(a*x)*PolyLog(3, -1 + 2/(1 + a*x)))/(2*c) - (3*a^2*PolyLog(4, -1 + 2/(1 + a*x)))/(4*c)]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(d+e*x)^q*(a+b*atanh(c*x))^4*when*c^2*d^2 - e^2=0=#

    @test_int [(x^2*atanh(a*x)^4)/(c - a*c*x), x, 21, (-2*atanh(a*x)^3)/(a^3*c) - (2*x*atanh(a*x)^3)/(a^2*c) - atanh(a*x)^4/(2*a^3*c) - (x*atanh(a*x)^4)/(a^2*c) - (x^2*atanh(a*x)^4)/(2*a*c) + (6*atanh(a*x)^2*log(2/(1 - a*x)))/(a^3*c) + (4*atanh(a*x)^3*log(2/(1 - a*x)))/(a^3*c) + (atanh(a*x)^4*log(2/(1 - a*x)))/(a^3*c) + (6*atanh(a*x)*PolyLog(2, 1 - 2/(1 - a*x)))/(a^3*c) + (6*atanh(a*x)^2*PolyLog(2, 1 - 2/(1 - a*x)))/(a^3*c) + (2*atanh(a*x)^3*PolyLog(2, 1 - 2/(1 - a*x)))/(a^3*c) - (3*PolyLog(3, 1 - 2/(1 - a*x)))/(a^3*c) - (6*atanh(a*x)*PolyLog(3, 1 - 2/(1 - a*x)))/(a^3*c) - (3*atanh(a*x)^2*PolyLog(3, 1 - 2/(1 - a*x)))/(a^3*c) + (3*PolyLog(4, 1 - 2/(1 - a*x)))/(a^3*c) + (3*atanh(a*x)*PolyLog(4, 1 - 2/(1 - a*x)))/(a^3*c) - (3*PolyLog(5, 1 - 2/(1 - a*x)))/(2*a^3*c)]
    @test_int [(x*atanh(a*x)^4)/(c - a*c*x), x, 12, -(atanh(a*x)^4/(a^2*c)) - (x*atanh(a*x)^4)/(a*c) + (4*atanh(a*x)^3*log(2/(1 - a*x)))/(a^2*c) + (atanh(a*x)^4*log(2/(1 - a*x)))/(a^2*c) + (6*atanh(a*x)^2*PolyLog(2, 1 - 2/(1 - a*x)))/(a^2*c) + (2*atanh(a*x)^3*PolyLog(2, 1 - 2/(1 - a*x)))/(a^2*c) - (6*atanh(a*x)*PolyLog(3, 1 - 2/(1 - a*x)))/(a^2*c) - (3*atanh(a*x)^2*PolyLog(3, 1 - 2/(1 - a*x)))/(a^2*c) + (3*PolyLog(4, 1 - 2/(1 - a*x)))/(a^2*c) + (3*atanh(a*x)*PolyLog(4, 1 - 2/(1 - a*x)))/(a^2*c) - (3*PolyLog(5, 1 - 2/(1 - a*x)))/(2*a^2*c)]
    @test_int [atanh(a*x)^4/(c - a*c*x), x, 5, (atanh(a*x)^4*log(2/(1 - a*x)))/(a*c) + (2*atanh(a*x)^3*PolyLog(2, 1 - 2/(1 - a*x)))/(a*c) - (3*atanh(a*x)^2*PolyLog(3, 1 - 2/(1 - a*x)))/(a*c) + (3*atanh(a*x)*PolyLog(4, 1 - 2/(1 - a*x)))/(a*c) - (3*PolyLog(5, 1 - 2/(1 - a*x)))/(2*a*c)]
    @test_int [atanh(a*x)^4/(x*(c - a*c*x)), x, 5, (atanh(a*x)^4*log(2 - 2/(1 - a*x)))/c + (2*atanh(a*x)^3*PolyLog(2, -1 + 2/(1 - a*x)))/c - (3*atanh(a*x)^2*PolyLog(3, -1 + 2/(1 - a*x)))/c + (3*atanh(a*x)*PolyLog(4, -1 + 2/(1 - a*x)))/c - (3*PolyLog(5, -1 + 2/(1 - a*x)))/(2*c)]
    @test_int [atanh(a*x)^4/(c*x - a*c*x^2), x, 6, (atanh(a*x)^4*log(2 - 2/(1 - a*x)))/c + (2*atanh(a*x)^3*PolyLog(2, -1 + 2/(1 - a*x)))/c - (3*atanh(a*x)^2*PolyLog(3, -1 + 2/(1 - a*x)))/c + (3*atanh(a*x)*PolyLog(4, -1 + 2/(1 - a*x)))/c - (3*PolyLog(5, -1 + 2/(1 - a*x)))/(2*c)]
    @test_int [atanh(a*x)^4/(x^2*(c - a*c*x)), x, 12, (a*atanh(a*x)^4)/c - atanh(a*x)^4/(c*x) + (a*atanh(a*x)^4*log(2 - 2/(1 - a*x)))/c + (4*a*atanh(a*x)^3*log(2 - 2/(1 + a*x)))/c + (2*a*atanh(a*x)^3*PolyLog(2, -1 + 2/(1 - a*x)))/c - (6*a*atanh(a*x)^2*PolyLog(2, -1 + 2/(1 + a*x)))/c - (3*a*atanh(a*x)^2*PolyLog(3, -1 + 2/(1 - a*x)))/c - (6*a*atanh(a*x)*PolyLog(3, -1 + 2/(1 + a*x)))/c + (3*a*atanh(a*x)*PolyLog(4, -1 + 2/(1 - a*x)))/c - (3*a*PolyLog(4, -1 + 2/(1 + a*x)))/c - (3*a*PolyLog(5, -1 + 2/(1 - a*x)))/(2*c)]
    @test_int [atanh(a*x)^4/(x^3*(c - a*c*x)), x, 21, (2*a^2*atanh(a*x)^3)/c - (2*a*atanh(a*x)^3)/(c*x) + (3*a^2*atanh(a*x)^4)/(2*c) - atanh(a*x)^4/(2*c*x^2) - (a*atanh(a*x)^4)/(c*x) + (a^2*atanh(a*x)^4*log(2 - 2/(1 - a*x)))/c + (6*a^2*atanh(a*x)^2*log(2 - 2/(1 + a*x)))/c + (4*a^2*atanh(a*x)^3*log(2 - 2/(1 + a*x)))/c + (2*a^2*atanh(a*x)^3*PolyLog(2, -1 + 2/(1 - a*x)))/c - (6*a^2*atanh(a*x)*PolyLog(2, -1 + 2/(1 + a*x)))/c - (6*a^2*atanh(a*x)^2*PolyLog(2, -1 + 2/(1 + a*x)))/c - (3*a^2*atanh(a*x)^2*PolyLog(3, -1 + 2/(1 - a*x)))/c - (3*a^2*PolyLog(3, -1 + 2/(1 + a*x)))/c - (6*a^2*atanh(a*x)*PolyLog(3, -1 + 2/(1 + a*x)))/c + (3*a^2*atanh(a*x)*PolyLog(4, -1 + 2/(1 - a*x)))/c - (3*a^2*PolyLog(4, -1 + 2/(1 + a*x)))/c - (3*a^2*PolyLog(5, -1 + 2/(1 - a*x)))/(2*c)]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(d+e*x)^q*(a+b*atanh(c*x))^-1*when*c^2*d^2 - e^2=0=#

    @test_int [x/(atanh(a*x)*(c + a*c*x)), x, 0, Unintegrable(x/((c + a*c*x)*atanh(a*x)), x)]
    @test_int [1/(atanh(a*x)*(c + a*c*x)), x, 0, Unintegrable(1/((c + a*c*x)*atanh(a*x)), x)]
    @test_int [1/(x*atanh(a*x)*(c + a*c*x)), x, 0, Unintegrable(1/(x*(c + a*c*x)*atanh(a*x)), x)]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(d+e*x)^q*(a+b*atanh(c*x))^-2*when*c^2*d^2 - e^2=0=#

    @test_int [x/(atanh(a*x)^2*(c + a*c*x)), x, 0, Unintegrable(x/((c + a*c*x)*atanh(a*x)^2), x)]
    @test_int [1/(atanh(a*x)^2*(c + a*c*x)), x, 0, Unintegrable(1/((c + a*c*x)*atanh(a*x)^2), x)]
    @test_int [1/(x*atanh(a*x)^2*(c + a*c*x)), x, 0, Unintegrable(1/(x*(c + a*c*x)*atanh(a*x)^2), x)]

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

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

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

    @test_int [x^3*(a + b*atanh(c*x))/(d + e*x), x, 16, (a*d^2*x)/e^3 - (b*d*x)/(2*c*e^2) + (b*x^2)/(6*c*e) + (b*d*atanh(c*x))/(2*c^2*e^2) + (b*d^2*x*atanh(c*x))/e^3 - (d*x^2*(a + b*atanh(c*x)))/(2*e^2) + (x^3*(a + b*atanh(c*x)))/(3*e) + (d^3*(a + b*atanh(c*x))*log(2/(1 + c*x)))/e^4 - (d^3*(a + b*atanh(c*x))*log((2*c*(d + e*x))/((c*d + e)*(1 + c*x))))/e^4 + (b*d^2*log(1 - c^2*x^2))/(2*c*e^3) + (b*log(1 - c^2*x^2))/(6*c^3*e) - (b*d^3*PolyLog(2, 1 - 2/(1 + c*x)))/(2*e^4) + (b*d^3*PolyLog(2, 1 - (2*c*(d + e*x))/((c*d + e)*(1 + c*x))))/(2*e^4)]
    @test_int [x^2*(a + b*atanh(c*x))/(d + e*x), x, 12, -((a*d*x)/e^2) + (b*x)/(2*c*e) - (b*atanh(c*x))/(2*c^2*e) - (b*d*x*atanh(c*x))/e^2 + (x^2*(a + b*atanh(c*x)))/(2*e) - (d^2*(a + b*atanh(c*x))*log(2/(1 + c*x)))/e^3 + (d^2*(a + b*atanh(c*x))*log((2*c*(d + e*x))/((c*d + e)*(1 + c*x))))/e^3 - (b*d*log(1 - c^2*x^2))/(2*c*e^2) + (b*d^2*PolyLog(2, 1 - 2/(1 + c*x)))/(2*e^3) - (b*d^2*PolyLog(2, 1 - (2*c*(d + e*x))/((c*d + e)*(1 + c*x))))/(2*e^3)]
    @test_int [x^1*(a + b*atanh(c*x))/(d + e*x), x, 9, (a*x)/e + (b*x*atanh(c*x))/e + (d*(a + b*atanh(c*x))*log(2/(1 + c*x)))/e^2 - (d*(a + b*atanh(c*x))*log((2*c*(d + e*x))/((c*d + e)*(1 + c*x))))/e^2 + (b*log(1 - c^2*x^2))/(2*c*e) - (b*d*PolyLog(2, 1 - 2/(1 + c*x)))/(2*e^2) + (b*d*PolyLog(2, 1 - (2*c*(d + e*x))/((c*d + e)*(1 + c*x))))/(2*e^2)]
    @test_int [x^0*(a + b*atanh(c*x))/(d + e*x), x, 4, -(((a + b*atanh(c*x))*log(2/(1 + c*x)))/e) + ((a + b*atanh(c*x))*log((2*c*(d + e*x))/((c*d + e)*(1 + c*x))))/e + (b*PolyLog(2, 1 - 2/(1 + c*x)))/(2*e) - (b*PolyLog(2, 1 - (2*c*(d + e*x))/((c*d + e)*(1 + c*x))))/(2*e)]
    @test_int [(a + b*atanh(c*x))/(x^1*(d + e*x)), x, 7, (a*log(x))/d + ((a + b*atanh(c*x))*log(2/(1 + c*x)))/d - ((a + b*atanh(c*x))*log((2*c*(d + e*x))/((c*d + e)*(1 + c*x))))/d - (b*PolyLog(2, (-c)*x))/(2*d) + (b*PolyLog(2, c*x))/(2*d) - (b*PolyLog(2, 1 - 2/(1 + c*x)))/(2*d) + (b*PolyLog(2, 1 - (2*c*(d + e*x))/((c*d + e)*(1 + c*x))))/(2*d)]
    @test_int [(a + b*atanh(c*x))/(x^2*(d + e*x)), x, 12, -((a + b*atanh(c*x))/(d*x)) + (b*c*log(x))/d - (a*e*log(x))/d^2 - (e*(a + b*atanh(c*x))*log(2/(1 + c*x)))/d^2 + (e*(a + b*atanh(c*x))*log((2*c*(d + e*x))/((c*d + e)*(1 + c*x))))/d^2 - (b*c*log(1 - c^2*x^2))/(2*d) + (b*e*PolyLog(2, (-c)*x))/(2*d^2) - (b*e*PolyLog(2, c*x))/(2*d^2) + (b*e*PolyLog(2, 1 - 2/(1 + c*x)))/(2*d^2) - (b*e*PolyLog(2, 1 - (2*c*(d + e*x))/((c*d + e)*(1 + c*x))))/(2*d^2)]
    @test_int [(a + b*atanh(c*x))/(x^3*(d + e*x)), x, 15, -((b*c)/(2*d*x)) + (b*c^2*atanh(c*x))/(2*d) - (a + b*atanh(c*x))/(2*d*x^2) + (e*(a + b*atanh(c*x)))/(d^2*x) - (b*c*e*log(x))/d^2 + (a*e^2*log(x))/d^3 + (e^2*(a + b*atanh(c*x))*log(2/(1 + c*x)))/d^3 - (e^2*(a + b*atanh(c*x))*log((2*c*(d + e*x))/((c*d + e)*(1 + c*x))))/d^3 + (b*c*e*log(1 - c^2*x^2))/(2*d^2) - (b*e^2*PolyLog(2, (-c)*x))/(2*d^3) + (b*e^2*PolyLog(2, c*x))/(2*d^3) - (b*e^2*PolyLog(2, 1 - 2/(1 + c*x)))/(2*d^3) + (b*e^2*PolyLog(2, 1 - (2*c*(d + e*x))/((c*d + e)*(1 + c*x))))/(2*d^3)]

    @test_int [x^2*(a + b*atanh(c*x))^2/(d + e*x), x, 14, (a*b*x)/(c*e) + (b^2*x*atanh(c*x))/(c*e) - (d*(a + b*atanh(c*x))^2)/(c*e^2) - (a + b*atanh(c*x))^2/(2*c^2*e) - (d*x*(a + b*atanh(c*x))^2)/e^2 + (x^2*(a + b*atanh(c*x))^2)/(2*e) + (2*b*d*(a + b*atanh(c*x))*log(2/(1 - c*x)))/(c*e^2) - (d^2*(a + b*atanh(c*x))^2*log(2/(1 + c*x)))/e^3 + (d^2*(a + b*atanh(c*x))^2*log((2*c*(d + e*x))/((c*d + e)*(1 + c*x))))/e^3 + (b^2*log(1 - c^2*x^2))/(2*c^2*e) + (b^2*d*PolyLog(2, 1 - 2/(1 - c*x)))/(c*e^2) + (b*d^2*(a + b*atanh(c*x))*PolyLog(2, 1 - 2/(1 + c*x)))/e^3 - (b*d^2*(a + b*atanh(c*x))*PolyLog(2, 1 - (2*c*(d + e*x))/((c*d + e)*(1 + c*x))))/e^3 + (b^2*d^2*PolyLog(3, 1 - 2/(1 + c*x)))/(2*e^3) - (b^2*d^2*PolyLog(3, 1 - (2*c*(d + e*x))/((c*d + e)*(1 + c*x))))/(2*e^3)]
    @test_int [x^1*(a + b*atanh(c*x))^2/(d + e*x), x, 8, (a + b*atanh(c*x))^2/(c*e) + (x*(a + b*atanh(c*x))^2)/e - (2*b*(a + b*atanh(c*x))*log(2/(1 - c*x)))/(c*e) + (d*(a + b*atanh(c*x))^2*log(2/(1 + c*x)))/e^2 - (d*(a + b*atanh(c*x))^2*log((2*c*(d + e*x))/((c*d + e)*(1 + c*x))))/e^2 - (b^2*PolyLog(2, 1 - 2/(1 - c*x)))/(c*e) - (b*d*(a + b*atanh(c*x))*PolyLog(2, 1 - 2/(1 + c*x)))/e^2 + (b*d*(a + b*atanh(c*x))*PolyLog(2, 1 - (2*c*(d + e*x))/((c*d + e)*(1 + c*x))))/e^2 - (b^2*d*PolyLog(3, 1 - 2/(1 + c*x)))/(2*e^2) + (b^2*d*PolyLog(3, 1 - (2*c*(d + e*x))/((c*d + e)*(1 + c*x))))/(2*e^2)]
    @test_int [x^0*(a + b*atanh(c*x))^2/(d + e*x), x, 1, -(((a + b*atanh(c*x))^2*log(2/(1 + c*x)))/e) + ((a + b*atanh(c*x))^2*log((2*c*(d + e*x))/((c*d + e)*(1 + c*x))))/e + (b*(a + b*atanh(c*x))*PolyLog(2, 1 - 2/(1 + c*x)))/e - (b*(a + b*atanh(c*x))*PolyLog(2, 1 - (2*c*(d + e*x))/((c*d + e)*(1 + c*x))))/e + (b^2*PolyLog(3, 1 - 2/(1 + c*x)))/(2*e) - (b^2*PolyLog(3, 1 - (2*c*(d + e*x))/((c*d + e)*(1 + c*x))))/(2*e)]
    @test_int [(a + b*atanh(c*x))^2/(x^1*(d + e*x)), x, 9, (2*(a + b*atanh(c*x))^2*atanh(1 - 2/(1 - c*x)))/d + ((a + b*atanh(c*x))^2*log(2/(1 + c*x)))/d - ((a + b*atanh(c*x))^2*log((2*c*(d + e*x))/((c*d + e)*(1 + c*x))))/d - (b*(a + b*atanh(c*x))*PolyLog(2, 1 - 2/(1 - c*x)))/d + (b*(a + b*atanh(c*x))*PolyLog(2, -1 + 2/(1 - c*x)))/d - (b*(a + b*atanh(c*x))*PolyLog(2, 1 - 2/(1 + c*x)))/d + (b*(a + b*atanh(c*x))*PolyLog(2, 1 - (2*c*(d + e*x))/((c*d + e)*(1 + c*x))))/d + (b^2*PolyLog(3, 1 - 2/(1 - c*x)))/(2*d) - (b^2*PolyLog(3, -1 + 2/(1 - c*x)))/(2*d) - (b^2*PolyLog(3, 1 - 2/(1 + c*x)))/(2*d) + (b^2*PolyLog(3, 1 - (2*c*(d + e*x))/((c*d + e)*(1 + c*x))))/(2*d)]
    @test_int [(a + b*atanh(c*x))^2/(x^2*(d + e*x)), x, 13, (c*(a + b*atanh(c*x))^2)/d - (a + b*atanh(c*x))^2/(d*x) - (2*e*(a + b*atanh(c*x))^2*atanh(1 - 2/(1 - c*x)))/d^2 - (e*(a + b*atanh(c*x))^2*log(2/(1 + c*x)))/d^2 + (e*(a + b*atanh(c*x))^2*log((2*c*(d + e*x))/((c*d + e)*(1 + c*x))))/d^2 + (2*b*c*(a + b*atanh(c*x))*log(2 - 2/(1 + c*x)))/d + (b*e*(a + b*atanh(c*x))*PolyLog(2, 1 - 2/(1 - c*x)))/d^2 - (b*e*(a + b*atanh(c*x))*PolyLog(2, -1 + 2/(1 - c*x)))/d^2 + (b*e*(a + b*atanh(c*x))*PolyLog(2, 1 - 2/(1 + c*x)))/d^2 - (b^2*c*PolyLog(2, -1 + 2/(1 + c*x)))/d - (b*e*(a + b*atanh(c*x))*PolyLog(2, 1 - (2*c*(d + e*x))/((c*d + e)*(1 + c*x))))/d^2 - (b^2*e*PolyLog(3, 1 - 2/(1 - c*x)))/(2*d^2) + (b^2*e*PolyLog(3, -1 + 2/(1 - c*x)))/(2*d^2) + (b^2*e*PolyLog(3, 1 - 2/(1 + c*x)))/(2*d^2) - (b^2*e*PolyLog(3, 1 - (2*c*(d + e*x))/((c*d + e)*(1 + c*x))))/(2*d^2)]

    @test_int [atanh(c*x)^2/(x*(d + e*x)), x, 9, (2*atanh(c*x)^2*atanh(1 - 2/(1 - c*x)))/d + (atanh(c*x)^2*log(2/(1 + c*x)))/d - (atanh(c*x)^2*log((2*c*(d + e*x))/((c*d + e)*(1 + c*x))))/d - (atanh(c*x)*PolyLog(2, 1 - 2/(1 - c*x)))/d + (atanh(c*x)*PolyLog(2, -1 + 2/(1 - c*x)))/d - (atanh(c*x)*PolyLog(2, 1 - 2/(1 + c*x)))/d + (atanh(c*x)*PolyLog(2, 1 - (2*c*(d + e*x))/((c*d + e)*(1 + c*x))))/d + PolyLog(3, 1 - 2/(1 - c*x))/(2*d) - PolyLog(3, -1 + 2/(1 - c*x))/(2*d) - PolyLog(3, 1 - 2/(1 + c*x))/(2*d) + PolyLog(3, 1 - (2*c*(d + e*x))/((c*d + e)*(1 + c*x)))/(2*d)]

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

    @test_int [1/((d + e*x)*(a + b*atan(c*x))), x, 0, Unintegrable(1/((d + e*x)*(a + b*atan(c*x))), x)]

    #= ::Title::Closed:: =#
    #=Integrands*of*the*form*(f*x)^m*(d+e*x^2)^q*(a+b*atanh(c*x))^p*with*c^2*d+e=0=#

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

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*atanh(c*x)^p*(1-c^2*x^2)=#

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

    @test_int [atanh(a*x)*(1 - a^2*x^2)*x^4, x, 9, x^2/(35*a^3) + x^4/(70*a) - (a*x^6)/42 + (1/5)*x^5*atanh(a*x) - (1/7)*a^2*x^7*atanh(a*x) + log(1 - a^2*x^2)/(35*a^5)]
    @test_int [atanh(a*x)*(1 - a^2*x^2)*x^3, x, 9, x/(12*a^3) + x^3/(36*a) - (a*x^5)/30 - atanh(a*x)/(12*a^4) + (1/4)*x^4*atanh(a*x) - (1/6)*a^2*x^6*atanh(a*x)]
    @test_int [atanh(a*x)*(1 - a^2*x^2)*x^2, x, 9, x^2/(15*a) - (a*x^4)/20 + (1/3)*x^3*atanh(a*x) - (1/5)*a^2*x^5*atanh(a*x) + log(1 - a^2*x^2)/(15*a^3)]
    @test_int [atanh(a*x)*(1 - a^2*x^2)*x^1, x, 2, x/(4*a) - (a*x^3)/12 - ((1 - a^2*x^2)^2*atanh(a*x))/(4*a^2)]
    @test_int [atanh(a*x)*(1 - a^2*x^2)*x^0, x, 3, (1 - a^2*x^2)/(6*a) + (2/3)*x*atanh(a*x) + (1/3)*x*(1 - a^2*x^2)*atanh(a*x) + log(1 - a^2*x^2)/(3*a)]
    @test_int [atanh(a*x)*(1 - a^2*x^2)/x^1, x, 5, -((a*x)/2) + (1/2)*atanh(a*x) - (1/2)*a^2*x^2*atanh(a*x) - (1/2)*PolyLog(2, (-a)*x) + (1/2)*PolyLog(2, a*x)]
    @test_int [atanh(a*x)*(1 - a^2*x^2)/x^2, x, 8, -(atanh(a*x)/x) - a^2*x*atanh(a*x) + a*log(x) - a*log(1 - a^2*x^2)]
    @test_int [atanh(a*x)*(1 - a^2*x^2)/x^3, x, 5, -(a/(2*x)) + (1/2)*a^2*atanh(a*x) - atanh(a*x)/(2*x^2) + (1/2)*a^2*PolyLog(2, (-a)*x) - (1/2)*a^2*PolyLog(2, a*x)]
    @test_int [atanh(a*x)*(1 - a^2*x^2)/x^4, x, 10, -(a/(6*x^2)) - atanh(a*x)/(3*x^3) + (a^2*atanh(a*x))/x - (2/3)*a^3*log(x) + (1/3)*a^3*log(1 - a^2*x^2)]
    @test_int [atanh(a*x)*(1 - a^2*x^2)/x^5, x, 3, -(a/(12*x^3)) + a^3/(4*x) - ((1 - a^2*x^2)^2*atanh(a*x))/(4*x^4)]
    @test_int [atanh(a*x)*(1 - a^2*x^2)/x^6, x, 9, -(a/(20*x^4)) + a^3/(15*x^2) - atanh(a*x)/(5*x^5) + (a^2*atanh(a*x))/(3*x^3) - (2/15)*a^5*log(x) + (1/15)*a^5*log(1 - a^2*x^2)]

    @test_int [atanh(a*x)^2*(1 - a^2*x^2)*x^4, x, 34, (4*x)/(105*a^4) - (2*x^3)/(315*a^2) - x^5/105 - (4*atanh(a*x))/(105*a^5) + (2*x^2*atanh(a*x))/(35*a^3) + (x^4*atanh(a*x))/(35*a) - (1/21)*a*x^6*atanh(a*x) + (2*atanh(a*x)^2)/(35*a^5) + (1/5)*x^5*atanh(a*x)^2 - (1/7)*a^2*x^7*atanh(a*x)^2 - (4*atanh(a*x)*log(2/(1 - a*x)))/(35*a^5) - (2*PolyLog(2, 1 - 2/(1 - a*x)))/(35*a^5)]
    @test_int [atanh(a*x)^2*(1 - a^2*x^2)*x^3, x, 26, -(x^2/(180*a^2)) - x^4/60 + (x*atanh(a*x))/(6*a^3) + (x^3*atanh(a*x))/(18*a) - (1/15)*a*x^5*atanh(a*x) - atanh(a*x)^2/(12*a^4) + (1/4)*x^4*atanh(a*x)^2 - (1/6)*a^2*x^6*atanh(a*x)^2 + (7*log(1 - a^2*x^2))/(90*a^4)]
    @test_int [atanh(a*x)^2*(1 - a^2*x^2)*x^2, x, 24, x/(30*a^2) - x^3/30 - atanh(a*x)/(30*a^3) + (2*x^2*atanh(a*x))/(15*a) - (1/10)*a*x^4*atanh(a*x) + (2*atanh(a*x)^2)/(15*a^3) + (1/3)*x^3*atanh(a*x)^2 - (1/5)*a^2*x^5*atanh(a*x)^2 - (4*atanh(a*x)*log(2/(1 - a*x)))/(15*a^3) - (2*PolyLog(2, 1 - 2/(1 - a*x)))/(15*a^3)]
    @test_int [atanh(a*x)^2*(1 - a^2*x^2)*x^1, x, 4, (1 - a^2*x^2)/(12*a^2) + (x*atanh(a*x))/(3*a) + (x*(1 - a^2*x^2)*atanh(a*x))/(6*a) - ((1 - a^2*x^2)^2*atanh(a*x)^2)/(4*a^2) + log(1 - a^2*x^2)/(6*a^2)]
    @test_int [atanh(a*x)^2*(1 - a^2*x^2)*x^0, x, 7, -(x/3) + ((1 - a^2*x^2)*atanh(a*x))/(3*a) + (2*atanh(a*x)^2)/(3*a) + (2/3)*x*atanh(a*x)^2 + (1/3)*x*(1 - a^2*x^2)*atanh(a*x)^2 - (4*atanh(a*x)*log(2/(1 - a*x)))/(3*a) - (2*PolyLog(2, 1 - 2/(1 - a*x)))/(3*a)]
    @test_int [atanh(a*x)^2*(1 - a^2*x^2)/x^1, x, 12, (-a)*x*atanh(a*x) + (1/2)*atanh(a*x)^2 - (1/2)*a^2*x^2*atanh(a*x)^2 + 2*atanh(a*x)^2*atanh(1 - 2/(1 - a*x)) - (1/2)*log(1 - a^2*x^2) - atanh(a*x)*PolyLog(2, 1 - 2/(1 - a*x)) + atanh(a*x)*PolyLog(2, -1 + 2/(1 - a*x)) + (1/2)*PolyLog(3, 1 - 2/(1 - a*x)) - (1/2)*PolyLog(3, -1 + 2/(1 - a*x))]
    @test_int [atanh(a*x)^2*(1 - a^2*x^2)/x^2, x, 10, -(atanh(a*x)^2/x) - a^2*x*atanh(a*x)^2 + 2*a*atanh(a*x)*log(2/(1 - a*x)) + 2*a*atanh(a*x)*log(2 - 2/(1 + a*x)) + a*PolyLog(2, 1 - 2/(1 - a*x)) - a*PolyLog(2, -1 + 2/(1 + a*x))]
    @test_int [atanh(a*x)^2*(1 - a^2*x^2)/x^3, x, 15, -((a*atanh(a*x))/x) + (1/2)*a^2*atanh(a*x)^2 - atanh(a*x)^2/(2*x^2) - 2*a^2*atanh(a*x)^2*atanh(1 - 2/(1 - a*x)) + a^2*log(x) - (1/2)*a^2*log(1 - a^2*x^2) + a^2*atanh(a*x)*PolyLog(2, 1 - 2/(1 - a*x)) - a^2*atanh(a*x)*PolyLog(2, -1 + 2/(1 - a*x)) - (1/2)*a^2*PolyLog(3, 1 - 2/(1 - a*x)) + (1/2)*a^2*PolyLog(3, -1 + 2/(1 - a*x))]
    @test_int [atanh(a*x)^2*(1 - a^2*x^2)/x^4, x, 13, -(a^2/(3*x)) + (1/3)*a^3*atanh(a*x) - (a*atanh(a*x))/(3*x^2) - (2/3)*a^3*atanh(a*x)^2 - atanh(a*x)^2/(3*x^3) + (a^2*atanh(a*x)^2)/x - (4/3)*a^3*atanh(a*x)*log(2 - 2/(1 + a*x)) + (2/3)*a^3*PolyLog(2, -1 + 2/(1 + a*x))]
    @test_int [atanh(a*x)^2*(1 - a^2*x^2)/x^5, x, 11, -(a^2/(12*x^2)) - (a*atanh(a*x))/(6*x^3) + (a^3*atanh(a*x))/(2*x) - ((1 - a^2*x^2)^2*atanh(a*x)^2)/(4*x^4) - (1/3)*a^4*log(x) + (1/6)*a^4*log(1 - a^2*x^2)]
    @test_int [atanh(a*x)^2*(1 - a^2*x^2)/x^6, x, 22, -(a^2/(30*x^3)) + a^4/(30*x) - (1/30)*a^5*atanh(a*x) - (a*atanh(a*x))/(10*x^4) + (2*a^3*atanh(a*x))/(15*x^2) - (2/15)*a^5*atanh(a*x)^2 - atanh(a*x)^2/(5*x^5) + (a^2*atanh(a*x)^2)/(3*x^3) - (4/15)*a^5*atanh(a*x)*log(2 - 2/(1 + a*x)) + (2/15)*a^5*PolyLog(2, -1 + 2/(1 + a*x))]

    @test_int [atanh(a*x)^3*(1 - a^2*x^2), x, 8, (-x)*atanh(a*x) + ((1 - a^2*x^2)*atanh(a*x)^2)/(2*a) + (2*atanh(a*x)^3)/(3*a) + (2/3)*x*atanh(a*x)^3 + (1/3)*x*(1 - a^2*x^2)*atanh(a*x)^3 - (2*atanh(a*x)^2*log(2/(1 - a*x)))/a - log(1 - a^2*x^2)/(2*a) - (2*atanh(a*x)*PolyLog(2, 1 - 2/(1 - a*x)))/a + PolyLog(3, 1 - 2/(1 - a*x))/a]

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

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

    @test_int [1/atanh(a*x)*(1 - a^2*x^2)*x^1, x, 0, Unintegrable((x*(1 - a^2*x^2))/atanh(a*x), x)]
    @test_int [1/atanh(a*x)*(1 - a^2*x^2)*x^0, x, 0, Unintegrable((1 - a^2*x^2)/atanh(a*x), x)]
    @test_int [1/atanh(a*x)*(1 - a^2*x^2)/x^1, x, 0, Unintegrable((1 - a^2*x^2)/(x*atanh(a*x)), x)]

    @test_int [1/atanh(a*x)^2*(1 - a^2*x^2)*x^1, x, 0, Unintegrable((x*(1 - a^2*x^2))/atanh(a*x)^2, x)]
    @test_int [1/atanh(a*x)^2*(1 - a^2*x^2)*x^0, x, 0, Unintegrable((1 - a^2*x^2)/atanh(a*x)^2, x)]
    @test_int [1/atanh(a*x)^2*(1 - a^2*x^2)/x^1, x, 0, Unintegrable((1 - a^2*x^2)/(x*atanh(a*x)^2), x)]

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

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*atanh(c*x)^p*(1-c^2*x^2)^2=#

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

    @test_int [atanh(a*x)*(1 - a^2*x^2)^2*x^4, x, 14, (4*x^2)/(315*a^3) + (2*x^4)/(315*a) - (11*a*x^6)/378 + (a^3*x^8)/72 + (1/5)*x^5*atanh(a*x) - (2/7)*a^2*x^7*atanh(a*x) + (1/9)*a^4*x^9*atanh(a*x) + (4*log(1 - a^2*x^2))/(315*a^5)]
    @test_int [atanh(a*x)*(1 - a^2*x^2)^2*x^3, x, 14, x/(24*a^3) + x^3/(72*a) - (a*x^5)/24 + (a^3*x^7)/56 - atanh(a*x)/(24*a^4) + (1/4)*x^4*atanh(a*x) - (1/3)*a^2*x^6*atanh(a*x) + (1/8)*a^4*x^8*atanh(a*x)]
    @test_int [atanh(a*x)*(1 - a^2*x^2)^2*x^2, x, 14, (4*x^2)/(105*a) - (9*a*x^4)/140 + (a^3*x^6)/42 + (1/3)*x^3*atanh(a*x) - (2/5)*a^2*x^5*atanh(a*x) + (1/7)*a^4*x^7*atanh(a*x) + (4*log(1 - a^2*x^2))/(105*a^3)]
    @test_int [atanh(a*x)*(1 - a^2*x^2)^2*x^1, x, 3, x/(6*a) - (a*x^3)/9 + (a^3*x^5)/30 - ((1 - a^2*x^2)^3*atanh(a*x))/(6*a^2)]
    @test_int [atanh(a*x)*(1 - a^2*x^2)^2*x^0, x, 4, (2*(1 - a^2*x^2))/(15*a) + (1 - a^2*x^2)^2/(20*a) + (8/15)*x*atanh(a*x) + (4/15)*x*(1 - a^2*x^2)*atanh(a*x) + (1/5)*x*(1 - a^2*x^2)^2*atanh(a*x) + (4*log(1 - a^2*x^2))/(15*a)]
    @test_int [atanh(a*x)*(1 - a^2*x^2)^2/x^1, x, 10, -((3*a*x)/4) + (a^3*x^3)/12 + (3/4)*atanh(a*x) - a^2*x^2*atanh(a*x) + (1/4)*a^4*x^4*atanh(a*x) - (1/2)*PolyLog(2, (-a)*x) + (1/2)*PolyLog(2, a*x)]
    @test_int [atanh(a*x)*(1 - a^2*x^2)^2/x^2, x, 13, (a^3*x^2)/6 - atanh(a*x)/x - 2*a^2*x*atanh(a*x) + (1/3)*a^4*x^3*atanh(a*x) + a*log(x) - (4/3)*a*log(1 - a^2*x^2)]
    @test_int [atanh(a*x)*(1 - a^2*x^2)^2/x^3, x, 9, -(a/(2*x)) + (a^3*x)/2 - atanh(a*x)/(2*x^2) + (1/2)*a^4*x^2*atanh(a*x) + a^2*PolyLog(2, (-a)*x) - a^2*PolyLog(2, a*x)]
    @test_int [atanh(a*x)*(1 - a^2*x^2)^2/x^4, x, 13, -(a/(6*x^2)) - atanh(a*x)/(3*x^3) + (2*a^2*atanh(a*x))/x + a^4*x*atanh(a*x) - (5/3)*a^3*log(x) + (4/3)*a^3*log(1 - a^2*x^2)]
    @test_int [atanh(a*x)*(1 - a^2*x^2)^2/x^5, x, 10, -(a/(12*x^3)) + (3*a^3)/(4*x) - (3/4)*a^4*atanh(a*x) - atanh(a*x)/(4*x^4) + (a^2*atanh(a*x))/x^2 - (1/2)*a^4*PolyLog(2, (-a)*x) + (1/2)*a^4*PolyLog(2, a*x)]
    @test_int [atanh(a*x)*(1 - a^2*x^2)^2/x^6, x, 15, -(a/(20*x^4)) + (7*a^3)/(30*x^2) - atanh(a*x)/(5*x^5) + (2*a^2*atanh(a*x))/(3*x^3) - (a^4*atanh(a*x))/x + (8/15)*a^5*log(x) - (4/15)*a^5*log(1 - a^2*x^2)]

    @test_int [atanh(a*x)^2*(1 - a^2*x^2)^2*x^4, x, 59, (29*x)/(3780*a^4) - (67*x^3)/(11340*a^2) - (23*x^5)/3780 + (a^2*x^7)/252 - (29*atanh(a*x))/(3780*a^5) + (8*x^2*atanh(a*x))/(315*a^3) + (4*x^4*atanh(a*x))/(315*a) - (11/189)*a*x^6*atanh(a*x) + (1/36)*a^3*x^8*atanh(a*x) + (8*atanh(a*x)^2)/(315*a^5) + (1/5)*x^5*atanh(a*x)^2 - (2/7)*a^2*x^7*atanh(a*x)^2 + (1/9)*a^4*x^9*atanh(a*x)^2 - (16*atanh(a*x)*log(2/(1 - a*x)))/(315*a^5) - (8*PolyLog(2, 1 - 2/(1 - a*x)))/(315*a^5)]
    @test_int [atanh(a*x)^2*(1 - a^2*x^2)^2*x^3, x, 47, -((5*x^2)/(504*a^2)) - x^4/84 + (a^2*x^6)/168 + (x*atanh(a*x))/(12*a^3) + (x^3*atanh(a*x))/(36*a) - (1/12)*a*x^5*atanh(a*x) + (1/28)*a^3*x^7*atanh(a*x) - atanh(a*x)^2/(24*a^4) + (1/4)*x^4*atanh(a*x)^2 - (1/3)*a^2*x^6*atanh(a*x)^2 + (1/8)*a^4*x^8*atanh(a*x)^2 + (2*log(1 - a^2*x^2))/(63*a^4)]
    @test_int [atanh(a*x)^2*(1 - a^2*x^2)^2*x^2, x, 44, -(x/(210*a^2)) - (17*x^3)/630 + (a^2*x^5)/105 + atanh(a*x)/(210*a^3) + (8*x^2*atanh(a*x))/(105*a) - (9/70)*a*x^4*atanh(a*x) + (1/21)*a^3*x^6*atanh(a*x) + (8*atanh(a*x)^2)/(105*a^3) + (1/3)*x^3*atanh(a*x)^2 - (2/5)*a^2*x^5*atanh(a*x)^2 + (1/7)*a^4*x^7*atanh(a*x)^2 - (16*atanh(a*x)*log(2/(1 - a*x)))/(105*a^3) - (8*PolyLog(2, 1 - 2/(1 - a*x)))/(105*a^3)]
    @test_int [atanh(a*x)^2*(1 - a^2*x^2)^2*x^1, x, 5, (2*(1 - a^2*x^2))/(45*a^2) + (1 - a^2*x^2)^2/(60*a^2) + (8*x*atanh(a*x))/(45*a) + (4*x*(1 - a^2*x^2)*atanh(a*x))/(45*a) + (x*(1 - a^2*x^2)^2*atanh(a*x))/(15*a) - ((1 - a^2*x^2)^3*atanh(a*x)^2)/(6*a^2) + (4*log(1 - a^2*x^2))/(45*a^2)]
    @test_int [atanh(a*x)^2*(1 - a^2*x^2)^2*x^0, x, 9, -((11*x)/30) + (a^2*x^3)/30 + (4*(1 - a^2*x^2)*atanh(a*x))/(15*a) + ((1 - a^2*x^2)^2*atanh(a*x))/(10*a) + (8*atanh(a*x)^2)/(15*a) + (8/15)*x*atanh(a*x)^2 + (4/15)*x*(1 - a^2*x^2)*atanh(a*x)^2 + (1/5)*x*(1 - a^2*x^2)^2*atanh(a*x)^2 - (16*atanh(a*x)*log(2/(1 - a*x)))/(15*a) - (8*PolyLog(2, 1 - 2/(1 - a*x)))/(15*a)]
    @test_int [atanh(a*x)^2*(1 - a^2*x^2)^2/x^1, x, 23, (a^2*x^2)/12 - (3/2)*a*x*atanh(a*x) + (1/6)*a^3*x^3*atanh(a*x) + (3/4)*atanh(a*x)^2 - a^2*x^2*atanh(a*x)^2 + (1/4)*a^4*x^4*atanh(a*x)^2 + 2*atanh(a*x)^2*atanh(1 - 2/(1 - a*x)) - (2/3)*log(1 - a^2*x^2) - atanh(a*x)*PolyLog(2, 1 - 2/(1 - a*x)) + atanh(a*x)*PolyLog(2, -1 + 2/(1 - a*x)) + (1/2)*PolyLog(3, 1 - 2/(1 - a*x)) - (1/2)*PolyLog(3, -1 + 2/(1 - a*x))]
    @test_int [atanh(a*x)^2*(1 - a^2*x^2)^2/x^2, x, 20, (a^2*x)/3 - (1/3)*a*atanh(a*x) + (1/3)*a^3*x^2*atanh(a*x) - (2/3)*a*atanh(a*x)^2 - atanh(a*x)^2/x - 2*a^2*x*atanh(a*x)^2 + (1/3)*a^4*x^3*atanh(a*x)^2 + (10/3)*a*atanh(a*x)*log(2/(1 - a*x)) + 2*a*atanh(a*x)*log(2 - 2/(1 + a*x)) + (5/3)*a*PolyLog(2, 1 - 2/(1 - a*x)) - a*PolyLog(2, -1 + 2/(1 + a*x))]
    @test_int [atanh(a*x)^2*(1 - a^2*x^2)^2/x^3, x, 21, -((a*atanh(a*x))/x) + a^3*x*atanh(a*x) - atanh(a*x)^2/(2*x^2) + (1/2)*a^4*x^2*atanh(a*x)^2 - 4*a^2*atanh(a*x)^2*atanh(1 - 2/(1 - a*x)) + a^2*log(x) + 2*a^2*atanh(a*x)*PolyLog(2, 1 - 2/(1 - a*x)) - 2*a^2*atanh(a*x)*PolyLog(2, -1 + 2/(1 - a*x)) - a^2*PolyLog(3, 1 - 2/(1 - a*x)) + a^2*PolyLog(3, -1 + 2/(1 - a*x))]
    @test_int [atanh(a*x)^2*(1 - a^2*x^2)^2/x^4, x, 19, -(a^2/(3*x)) + (1/3)*a^3*atanh(a*x) - (a*atanh(a*x))/(3*x^2) - (2/3)*a^3*atanh(a*x)^2 - atanh(a*x)^2/(3*x^3) + (2*a^2*atanh(a*x)^2)/x + a^4*x*atanh(a*x)^2 - 2*a^3*atanh(a*x)*log(2/(1 - a*x)) - (10/3)*a^3*atanh(a*x)*log(2 - 2/(1 + a*x)) - a^3*PolyLog(2, 1 - 2/(1 - a*x)) + (5/3)*a^3*PolyLog(2, -1 + 2/(1 + a*x))]
    @test_int [atanh(a*x)^2*(1 - a^2*x^2)^2/x^5, x, 29, -(a^2/(12*x^2)) - (a*atanh(a*x))/(6*x^3) + (3*a^3*atanh(a*x))/(2*x) - (3/4)*a^4*atanh(a*x)^2 - atanh(a*x)^2/(4*x^4) + (a^2*atanh(a*x)^2)/x^2 + 2*a^4*atanh(a*x)^2*atanh(1 - 2/(1 - a*x)) - (4/3)*a^4*log(x) + (2/3)*a^4*log(1 - a^2*x^2) - a^4*atanh(a*x)*PolyLog(2, 1 - 2/(1 - a*x)) + a^4*atanh(a*x)*PolyLog(2, -1 + 2/(1 - a*x)) + (1/2)*a^4*PolyLog(3, 1 - 2/(1 - a*x)) - (1/2)*a^4*PolyLog(3, -1 + 2/(1 - a*x))]
    @test_int [atanh(a*x)^2*(1 - a^2*x^2)^2/x^6, x, 27, -(a^2/(30*x^3)) + (11*a^4)/(30*x) - (11/30)*a^5*atanh(a*x) - (a*atanh(a*x))/(10*x^4) + (7*a^3*atanh(a*x))/(15*x^2) + (8/15)*a^5*atanh(a*x)^2 - atanh(a*x)^2/(5*x^5) + (2*a^2*atanh(a*x)^2)/(3*x^3) - (a^4*atanh(a*x)^2)/x + (16/15)*a^5*atanh(a*x)*log(2 - 2/(1 + a*x)) - (8/15)*a^5*PolyLog(2, -1 + 2/(1 + a*x))]
    @test_int [atanh(a*x)^2*(1 - a^2*x^2)^2/x^7, x, 16, -(a^2/(60*x^4)) + (7*a^4)/(90*x^2) - (a*atanh(a*x))/(15*x^5) + (2*a^3*atanh(a*x))/(9*x^3) - (a^5*atanh(a*x))/(3*x) - ((1 - a^2*x^2)^3*atanh(a*x)^2)/(6*x^6) + (8/45)*a^6*log(x) - (4/45)*a^6*log(1 - a^2*x^2)]
    @test_int [atanh(a*x)^2*(1 - a^2*x^2)^2/x^8, x, 42, -(a^2/(105*x^5)) + (17*a^4)/(630*x^3) + a^6/(210*x) - (1/210)*a^7*atanh(a*x) - (a*atanh(a*x))/(21*x^6) + (9*a^3*atanh(a*x))/(70*x^4) - (8*a^5*atanh(a*x))/(105*x^2) + (8/105)*a^7*atanh(a*x)^2 - atanh(a*x)^2/(7*x^7) + (2*a^2*atanh(a*x)^2)/(5*x^5) - (a^4*atanh(a*x)^2)/(3*x^3) + (16/105)*a^7*atanh(a*x)*log(2 - 2/(1 + a*x)) - (8/105)*a^7*PolyLog(2, -1 + 2/(1 + a*x))]
    @test_int [atanh(a*x)^2*(1 - a^2*x^2)^2/x^9, x, 56, -(a^2/(168*x^6)) + a^4/(84*x^4) + (5*a^6)/(504*x^2) - (a*atanh(a*x))/(28*x^7) + (a^3*atanh(a*x))/(12*x^5) - (a^5*atanh(a*x))/(36*x^3) - (a^7*atanh(a*x))/(12*x) + (1/24)*a^8*atanh(a*x)^2 - atanh(a*x)^2/(8*x^8) + (a^2*atanh(a*x)^2)/(3*x^6) - (a^4*atanh(a*x)^2)/(4*x^4) + (4/63)*a^8*log(x) - (2/63)*a^8*log(1 - a^2*x^2)]

    @test_int [atanh(a*x)^3*(1 - a^2*x^2)^2, x, 12, -((1 - a^2*x^2)/(20*a)) - x*atanh(a*x) - (1/10)*x*(1 - a^2*x^2)*atanh(a*x) + (2*(1 - a^2*x^2)*atanh(a*x)^2)/(5*a) + (3*(1 - a^2*x^2)^2*atanh(a*x)^2)/(20*a) + (8*atanh(a*x)^3)/(15*a) + (8/15)*x*atanh(a*x)^3 + (4/15)*x*(1 - a^2*x^2)*atanh(a*x)^3 + (1/5)*x*(1 - a^2*x^2)^2*atanh(a*x)^3 - (8*atanh(a*x)^2*log(2/(1 - a*x)))/(5*a) - log(1 - a^2*x^2)/(2*a) - (8*atanh(a*x)*PolyLog(2, 1 - 2/(1 - a*x)))/(5*a) + (4*PolyLog(3, 1 - 2/(1 - a*x)))/(5*a)]

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

    @test_int [1/atanh(a*x)*(1 - a^2*x^2)^2*x^1, x, 0, Unintegrable((x*(1 - a^2*x^2)^2)/atanh(a*x), x)]
    @test_int [1/atanh(a*x)*(1 - a^2*x^2)^2*x^0, x, 0, Unintegrable((1 - a^2*x^2)^2/atanh(a*x), x)]
    @test_int [1/atanh(a*x)*(1 - a^2*x^2)^2/x^1, x, 0, Unintegrable((1 - a^2*x^2)^2/(x*atanh(a*x)), x)]

    @test_int [1/atanh(a*x)^2*(1 - a^2*x^2)^2*x^1, x, 0, Unintegrable((x*(1 - a^2*x^2)^2)/atanh(a*x)^2, x)]
    @test_int [1/atanh(a*x)^2*(1 - a^2*x^2)^2*x^0, x, 0, Unintegrable((1 - a^2*x^2)^2/atanh(a*x)^2, x)]
    @test_int [1/atanh(a*x)^2*(1 - a^2*x^2)^2/x^1, x, 0, Unintegrable((1 - a^2*x^2)^2/(x*atanh(a*x)^2), x)]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*atanh(c*x)^p*(1-c^2*x^2)^3=#

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

    @test_int [atanh(a*x)*(1 - a^2*x^2)^3, x, 5, (4*(1 - a^2*x^2))/(35*a) + (3*(1 - a^2*x^2)^2)/(70*a) + (1 - a^2*x^2)^3/(42*a) + (16/35)*x*atanh(a*x) + (8/35)*x*(1 - a^2*x^2)*atanh(a*x) + (6/35)*x*(1 - a^2*x^2)^2*atanh(a*x) + (1/7)*x*(1 - a^2*x^2)^3*atanh(a*x) + (8*log(1 - a^2*x^2))/(35*a)]

    @test_int [atanh(a*x)^2*(1 - a^2*x^2)^3, x, 12, -((38*x)/105) + (19*a^2*x^3)/315 - (a^4*x^5)/105 + (8*(1 - a^2*x^2)*atanh(a*x))/(35*a) + (3*(1 - a^2*x^2)^2*atanh(a*x))/(35*a) + ((1 - a^2*x^2)^3*atanh(a*x))/(21*a) + (16*atanh(a*x)^2)/(35*a) + (16/35)*x*atanh(a*x)^2 + (8/35)*x*(1 - a^2*x^2)*atanh(a*x)^2 + (6/35)*x*(1 - a^2*x^2)^2*atanh(a*x)^2 + (1/7)*x*(1 - a^2*x^2)^3*atanh(a*x)^2 - (32*atanh(a*x)*log(2/(1 - a*x)))/(35*a) - (16*PolyLog(2, 1 - 2/(1 - a*x)))/(35*a)]

    @test_int [atanh(a*x)^3*(1 - a^2*x^2)^3, x, 17, -((13*(1 - a^2*x^2))/(210*a)) - (1 - a^2*x^2)^2/(140*a) - (14/15)*x*atanh(a*x) - (13/105)*x*(1 - a^2*x^2)*atanh(a*x) - (1/35)*x*(1 - a^2*x^2)^2*atanh(a*x) + (12*(1 - a^2*x^2)*atanh(a*x)^2)/(35*a) + (9*(1 - a^2*x^2)^2*atanh(a*x)^2)/(70*a) + ((1 - a^2*x^2)^3*atanh(a*x)^2)/(14*a) + (16*atanh(a*x)^3)/(35*a) + (16/35)*x*atanh(a*x)^3 + (8/35)*x*(1 - a^2*x^2)*atanh(a*x)^3 + (6/35)*x*(1 - a^2*x^2)^2*atanh(a*x)^3 + (1/7)*x*(1 - a^2*x^2)^3*atanh(a*x)^3 - (48*atanh(a*x)^2*log(2/(1 - a*x)))/(35*a) - (7*log(1 - a^2*x^2))/(15*a) - (48*atanh(a*x)*PolyLog(2, 1 - 2/(1 - a*x)))/(35*a) + (24*PolyLog(3, 1 - 2/(1 - a*x)))/(35*a)]

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

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*atanh(c*x)^p / (1-c^2*x^2)=#

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

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

    @test_int [x^3*atanh(a*x)^2/(1 - a^2*x^2), x, 10, -((x*atanh(a*x))/a^3) + atanh(a*x)^2/(2*a^4) - (x^2*atanh(a*x)^2)/(2*a^2) - atanh(a*x)^3/(3*a^4) + (atanh(a*x)^2*log(2/(1 - a*x)))/a^4 - log(1 - a^2*x^2)/(2*a^4) + (atanh(a*x)*PolyLog(2, 1 - 2/(1 - a*x)))/a^4 - PolyLog(3, 1 - 2/(1 - a*x))/(2*a^4)]
    @test_int [x^2*atanh(a*x)^2/(1 - a^2*x^2), x, 7, -(atanh(a*x)^2/a^3) - (x*atanh(a*x)^2)/a^2 + atanh(a*x)^3/(3*a^3) + (2*atanh(a*x)*log(2/(1 - a*x)))/a^3 + PolyLog(2, 1 - 2/(1 - a*x))/a^3]
    @test_int [x*atanh(a*x)^2/(1 - a^2*x^2), x, 4, -(atanh(a*x)^3/(3*a^2)) + (atanh(a*x)^2*log(2/(1 - a*x)))/a^2 + (atanh(a*x)*PolyLog(2, 1 - 2/(1 - a*x)))/a^2 - PolyLog(3, 1 - 2/(1 - a*x))/(2*a^2)]
    @test_int [atanh(a*x)^2/(1 - a^2*x^2), x, 1, atanh(a*x)^3/(3*a)]
    @test_int [atanh(a*x)^2/(x*(1 - a^2*x^2)), x, 4, (1/3)*atanh(a*x)^3 + atanh(a*x)^2*log(2 - 2/(1 + a*x)) - atanh(a*x)*PolyLog(2, -1 + 2/(1 + a*x)) - (1/2)*PolyLog(3, -1 + 2/(1 + a*x))]
    @test_int [atanh(a*x)^2/(x^2*(1 - a^2*x^2)), x, 6, a*atanh(a*x)^2 - atanh(a*x)^2/x + (1/3)*a*atanh(a*x)^3 + 2*a*atanh(a*x)*log(2 - 2/(1 + a*x)) - a*PolyLog(2, -1 + 2/(1 + a*x))]
    @test_int [atanh(a*x)^2/(x^3*(1 - a^2*x^2)), x, 13, -((a*atanh(a*x))/x) + (1/2)*a^2*atanh(a*x)^2 - atanh(a*x)^2/(2*x^2) + (1/3)*a^2*atanh(a*x)^3 + a^2*log(x) - (1/2)*a^2*log(1 - a^2*x^2) + a^2*atanh(a*x)^2*log(2 - 2/(1 + a*x)) - a^2*atanh(a*x)*PolyLog(2, -1 + 2/(1 + a*x)) - (1/2)*a^2*PolyLog(3, -1 + 2/(1 + a*x))]

    @test_int [x^3*atanh(a*x)^3/(1 - a^2*x^2), x, 14, -((3*atanh(a*x)^2)/(2*a^4)) - (3*x*atanh(a*x)^2)/(2*a^3) + atanh(a*x)^3/(2*a^4) - (x^2*atanh(a*x)^3)/(2*a^2) - atanh(a*x)^4/(4*a^4) + (3*atanh(a*x)*log(2/(1 - a*x)))/a^4 + (atanh(a*x)^3*log(2/(1 - a*x)))/a^4 + (3*PolyLog(2, 1 - 2/(1 - a*x)))/(2*a^4) + (3*atanh(a*x)^2*PolyLog(2, 1 - 2/(1 - a*x)))/(2*a^4) - (3*atanh(a*x)*PolyLog(3, 1 - 2/(1 - a*x)))/(2*a^4) + (3*PolyLog(4, 1 - 2/(1 - a*x)))/(4*a^4)]
    @test_int [x^2*atanh(a*x)^3/(1 - a^2*x^2), x, 7, -(atanh(a*x)^3/a^3) - (x*atanh(a*x)^3)/a^2 + atanh(a*x)^4/(4*a^3) + (3*atanh(a*x)^2*log(2/(1 - a*x)))/a^3 + (3*atanh(a*x)*PolyLog(2, 1 - 2/(1 - a*x)))/a^3 - (3*PolyLog(3, 1 - 2/(1 - a*x)))/(2*a^3)]
    @test_int [x*atanh(a*x)^3/(1 - a^2*x^2), x, 5, -(atanh(a*x)^4/(4*a^2)) + (atanh(a*x)^3*log(2/(1 - a*x)))/a^2 + (3*atanh(a*x)^2*PolyLog(2, 1 - 2/(1 - a*x)))/(2*a^2) - (3*atanh(a*x)*PolyLog(3, 1 - 2/(1 - a*x)))/(2*a^2) + (3*PolyLog(4, 1 - 2/(1 - a*x)))/(4*a^2)]
    @test_int [atanh(a*x)^3/(1 - a^2*x^2), x, 1, atanh(a*x)^4/(4*a)]
    @test_int [atanh(a*x)^3/(x*(1 - a^2*x^2)), x, 5, (1/4)*atanh(a*x)^4 + atanh(a*x)^3*log(2 - 2/(1 + a*x)) - (3/2)*atanh(a*x)^2*PolyLog(2, -1 + 2/(1 + a*x)) - (3/2)*atanh(a*x)*PolyLog(3, -1 + 2/(1 + a*x)) - (3/4)*PolyLog(4, -1 + 2/(1 + a*x))]
    @test_int [atanh(a*x)^3/(x^2*(1 - a^2*x^2)), x, 7, a*atanh(a*x)^3 - atanh(a*x)^3/x + (1/4)*a*atanh(a*x)^4 + 3*a*atanh(a*x)^2*log(2 - 2/(1 + a*x)) - 3*a*atanh(a*x)*PolyLog(2, -1 + 2/(1 + a*x)) - (3/2)*a*PolyLog(3, -1 + 2/(1 + a*x))]
    @test_int [atanh(a*x)^3/(x^3*(1 - a^2*x^2)), x, 13, (3/2)*a^2*atanh(a*x)^2 - (3*a*atanh(a*x)^2)/(2*x) + (1/2)*a^2*atanh(a*x)^3 - atanh(a*x)^3/(2*x^2) + (1/4)*a^2*atanh(a*x)^4 + 3*a^2*atanh(a*x)*log(2 - 2/(1 + a*x)) + a^2*atanh(a*x)^3*log(2 - 2/(1 + a*x)) - (3/2)*a^2*PolyLog(2, -1 + 2/(1 + a*x)) - (3/2)*a^2*atanh(a*x)^2*PolyLog(2, -1 + 2/(1 + a*x)) - (3/2)*a^2*atanh(a*x)*PolyLog(3, -1 + 2/(1 + a*x)) - (3/4)*a^2*PolyLog(4, -1 + 2/(1 + a*x))]

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

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

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

    @test_int [x/((1 - a^2*x^2)*atanh(a*x)^2), x, 1, -(x/(a*atanh(a*x))) + Unintegrable(1/atanh(a*x), x)/a]
    @test_int [1/((1 - a^2*x^2)*atanh(a*x)^2), x, 1, -(1/(a*atanh(a*x)))]
    @test_int [1/(x*(1 - a^2*x^2)*atanh(a*x)^2), x, 1, -(1/(a*x*atanh(a*x))) - Unintegrable(1/(x^2*atanh(a*x)), x)/a]

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

    #= ::Subsubsection::Closed:: =#
    #=p*symbolic=#

    @test_int [atanh(a*x)^p/(1 - a^2*x^2), x, 1, atanh(a*x)^(1 + p)/(a*(1 + p))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*atanh(c*x)^p / (1-c^2*x^2)^2=#

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

    @test_int [x^3*atanh(a*x)/(1 - a^2*x^2)^2, x, 8, -(x/(4*a^3*(1 - a^2*x^2))) - atanh(a*x)/(4*a^4) + atanh(a*x)/(2*a^4*(1 - a^2*x^2)) + atanh(a*x)^2/(2*a^4) - (atanh(a*x)*log(2/(1 - a*x)))/a^4 - PolyLog(2, 1 - 2/(1 - a*x))/(2*a^4)]
    @test_int [x^2*atanh(a*x)/(1 - a^2*x^2)^2, x, 2, -(1/(4*a^3*(1 - a^2*x^2))) + (x*atanh(a*x))/(2*a^2*(1 - a^2*x^2)) - atanh(a*x)^2/(4*a^3)]
    @test_int [x*atanh(a*x)/(1 - a^2*x^2)^2, x, 3, -(x/(4*a*(1 - a^2*x^2))) - atanh(a*x)/(4*a^2) + atanh(a*x)/(2*a^2*(1 - a^2*x^2))]
    @test_int [atanh(a*x)/(1 - a^2*x^2)^2, x, 2, -(1/(4*a*(1 - a^2*x^2))) + (x*atanh(a*x))/(2*(1 - a^2*x^2)) + atanh(a*x)^2/(4*a)]
    @test_int [atanh(a*x)/(x*(1 - a^2*x^2)^2), x, 7, -((a*x)/(4*(1 - a^2*x^2))) - (1/4)*atanh(a*x) + atanh(a*x)/(2*(1 - a^2*x^2)) + (1/2)*atanh(a*x)^2 + atanh(a*x)*log(2 - 2/(1 + a*x)) - (1/2)*PolyLog(2, -1 + 2/(1 + a*x))]
    @test_int [atanh(a*x)/(x^2*(1 - a^2*x^2)^2), x, 10, -(a/(4*(1 - a^2*x^2))) - atanh(a*x)/x + (a^2*x*atanh(a*x))/(2*(1 - a^2*x^2)) + (3/4)*a*atanh(a*x)^2 + a*log(x) - (1/2)*a*log(1 - a^2*x^2)]
    @test_int [atanh(a*x)/(x^3*(1 - a^2*x^2)^2), x, 15, -(a/(2*x)) - (a^3*x)/(4*(1 - a^2*x^2)) + (1/4)*a^2*atanh(a*x) - atanh(a*x)/(2*x^2) + (a^2*atanh(a*x))/(2*(1 - a^2*x^2)) + a^2*atanh(a*x)^2 + 2*a^2*atanh(a*x)*log(2 - 2/(1 + a*x)) - a^2*PolyLog(2, -1 + 2/(1 + a*x))]

    @test_int [x^3*atanh(a*x)^2/(1 - a^2*x^2)^2, x, 8, 1/(4*a^4*(1 - a^2*x^2)) - (x*atanh(a*x))/(2*a^3*(1 - a^2*x^2)) - atanh(a*x)^2/(4*a^4) + atanh(a*x)^2/(2*a^4*(1 - a^2*x^2)) + atanh(a*x)^3/(3*a^4) - (atanh(a*x)^2*log(2/(1 - a*x)))/a^4 - (atanh(a*x)*PolyLog(2, 1 - 2/(1 - a*x)))/a^4 + PolyLog(3, 1 - 2/(1 - a*x))/(2*a^4)]
    @test_int [x^2*atanh(a*x)^2/(1 - a^2*x^2)^2, x, 4, x/(4*a^2*(1 - a^2*x^2)) + atanh(a*x)/(4*a^3) - atanh(a*x)/(2*a^3*(1 - a^2*x^2)) + (x*atanh(a*x)^2)/(2*a^2*(1 - a^2*x^2)) - atanh(a*x)^3/(6*a^3)]
    @test_int [x*atanh(a*x)^2/(1 - a^2*x^2)^2, x, 3, 1/(4*a^2*(1 - a^2*x^2)) - (x*atanh(a*x))/(2*a*(1 - a^2*x^2)) - atanh(a*x)^2/(4*a^2) + atanh(a*x)^2/(2*a^2*(1 - a^2*x^2))]
    @test_int [atanh(a*x)^2/(1 - a^2*x^2)^2, x, 4, x/(4*(1 - a^2*x^2)) + atanh(a*x)/(4*a) - atanh(a*x)/(2*a*(1 - a^2*x^2)) + (x*atanh(a*x)^2)/(2*(1 - a^2*x^2)) + atanh(a*x)^3/(6*a)]
    @test_int [atanh(a*x)^2/(x*(1 - a^2*x^2)^2), x, 8, 1/(4*(1 - a^2*x^2)) - (a*x*atanh(a*x))/(2*(1 - a^2*x^2)) - (1/4)*atanh(a*x)^2 + atanh(a*x)^2/(2*(1 - a^2*x^2)) + (1/3)*atanh(a*x)^3 + atanh(a*x)^2*log(2 - 2/(1 + a*x)) - atanh(a*x)*PolyLog(2, -1 + 2/(1 + a*x)) - (1/2)*PolyLog(3, -1 + 2/(1 + a*x))]
    @test_int [atanh(a*x)^2/(x^2*(1 - a^2*x^2)^2), x, 11, (a^2*x)/(4*(1 - a^2*x^2)) + (1/4)*a*atanh(a*x) - (a*atanh(a*x))/(2*(1 - a^2*x^2)) + a*atanh(a*x)^2 - atanh(a*x)^2/x + (a^2*x*atanh(a*x)^2)/(2*(1 - a^2*x^2)) + (1/2)*a*atanh(a*x)^3 + 2*a*atanh(a*x)*log(2 - 2/(1 + a*x)) - a*PolyLog(2, -1 + 2/(1 + a*x))]
    @test_int [atanh(a*x)^2/(x^3*(1 - a^2*x^2)^2), x, 22, a^2/(4*(1 - a^2*x^2)) - (a*atanh(a*x))/x - (a^3*x*atanh(a*x))/(2*(1 - a^2*x^2)) + (1/4)*a^2*atanh(a*x)^2 - atanh(a*x)^2/(2*x^2) + (a^2*atanh(a*x)^2)/(2*(1 - a^2*x^2)) + (2/3)*a^2*atanh(a*x)^3 + a^2*log(x) - (1/2)*a^2*log(1 - a^2*x^2) + 2*a^2*atanh(a*x)^2*log(2 - 2/(1 + a*x)) - 2*a^2*atanh(a*x)*PolyLog(2, -1 + 2/(1 + a*x)) - a^2*PolyLog(3, -1 + 2/(1 + a*x))]

    @test_int [x^3*atanh(a*x)^3/(1 - a^2*x^2)^2, x, 11, -((3*x)/(8*a^3*(1 - a^2*x^2))) - (3*atanh(a*x))/(8*a^4) + (3*atanh(a*x))/(4*a^4*(1 - a^2*x^2)) - (3*x*atanh(a*x)^2)/(4*a^3*(1 - a^2*x^2)) - atanh(a*x)^3/(4*a^4) + atanh(a*x)^3/(2*a^4*(1 - a^2*x^2)) + atanh(a*x)^4/(4*a^4) - (atanh(a*x)^3*log(2/(1 - a*x)))/a^4 - (3*atanh(a*x)^2*PolyLog(2, 1 - 2/(1 - a*x)))/(2*a^4) + (3*atanh(a*x)*PolyLog(3, 1 - 2/(1 - a*x)))/(2*a^4) - (3*PolyLog(4, 1 - 2/(1 - a*x)))/(4*a^4)]
    @test_int [x^2*atanh(a*x)^3/(1 - a^2*x^2)^2, x, 4, -(3/(8*a^3*(1 - a^2*x^2))) + (3*x*atanh(a*x))/(4*a^2*(1 - a^2*x^2)) + (3*atanh(a*x)^2)/(8*a^3) - (3*atanh(a*x)^2)/(4*a^3*(1 - a^2*x^2)) + (x*atanh(a*x)^3)/(2*a^2*(1 - a^2*x^2)) - atanh(a*x)^4/(8*a^3)]
    @test_int [x*atanh(a*x)^3/(1 - a^2*x^2)^2, x, 5, -((3*x)/(8*a*(1 - a^2*x^2))) - (3*atanh(a*x))/(8*a^2) + (3*atanh(a*x))/(4*a^2*(1 - a^2*x^2)) - (3*x*atanh(a*x)^2)/(4*a*(1 - a^2*x^2)) - atanh(a*x)^3/(4*a^2) + atanh(a*x)^3/(2*a^2*(1 - a^2*x^2))]
    @test_int [atanh(a*x)^3/(1 - a^2*x^2)^2, x, 4, -(3/(8*a*(1 - a^2*x^2))) + (3*x*atanh(a*x))/(4*(1 - a^2*x^2)) + (3*atanh(a*x)^2)/(8*a) - (3*atanh(a*x)^2)/(4*a*(1 - a^2*x^2)) + (x*atanh(a*x)^3)/(2*(1 - a^2*x^2)) + atanh(a*x)^4/(8*a)]
    @test_int [atanh(a*x)^3/(x*(1 - a^2*x^2)^2), x, 11, -((3*a*x)/(8*(1 - a^2*x^2))) - (3/8)*atanh(a*x) + (3*atanh(a*x))/(4*(1 - a^2*x^2)) - (3*a*x*atanh(a*x)^2)/(4*(1 - a^2*x^2)) - (1/4)*atanh(a*x)^3 + atanh(a*x)^3/(2*(1 - a^2*x^2)) + (1/4)*atanh(a*x)^4 + atanh(a*x)^3*log(2 - 2/(1 + a*x)) - (3/2)*atanh(a*x)^2*PolyLog(2, -1 + 2/(1 + a*x)) - (3/2)*atanh(a*x)*PolyLog(3, -1 + 2/(1 + a*x)) - (3/4)*PolyLog(4, -1 + 2/(1 + a*x))]
    @test_int [atanh(a*x)^3/(x^2*(1 - a^2*x^2)^2), x, 12, -((3*a)/(8*(1 - a^2*x^2))) + (3*a^2*x*atanh(a*x))/(4*(1 - a^2*x^2)) + (3/8)*a*atanh(a*x)^2 - (3*a*atanh(a*x)^2)/(4*(1 - a^2*x^2)) + a*atanh(a*x)^3 - atanh(a*x)^3/x + (a^2*x*atanh(a*x)^3)/(2*(1 - a^2*x^2)) + (3/8)*a*atanh(a*x)^4 + 3*a*atanh(a*x)^2*log(2 - 2/(1 + a*x)) - 3*a*atanh(a*x)*PolyLog(2, -1 + 2/(1 + a*x)) - (3/2)*a*PolyLog(3, -1 + 2/(1 + a*x))]
    @test_int [atanh(a*x)^3/(x^3*(1 - a^2*x^2)^2), x, 25, -((3*a^3*x)/(8*(1 - a^2*x^2))) - (3/8)*a^2*atanh(a*x) + (3*a^2*atanh(a*x))/(4*(1 - a^2*x^2)) + (3/2)*a^2*atanh(a*x)^2 - (3*a*atanh(a*x)^2)/(2*x) - (3*a^3*x*atanh(a*x)^2)/(4*(1 - a^2*x^2)) + (1/4)*a^2*atanh(a*x)^3 - atanh(a*x)^3/(2*x^2) + (a^2*atanh(a*x)^3)/(2*(1 - a^2*x^2)) + (1/2)*a^2*atanh(a*x)^4 + 3*a^2*atanh(a*x)*log(2 - 2/(1 + a*x)) + 2*a^2*atanh(a*x)^3*log(2 - 2/(1 + a*x)) - (3/2)*a^2*PolyLog(2, -1 + 2/(1 + a*x)) - 3*a^2*atanh(a*x)^2*PolyLog(2, -1 + 2/(1 + a*x)) - 3*a^2*atanh(a*x)*PolyLog(3, -1 + 2/(1 + a*x)) - (3/2)*a^2*PolyLog(4, -1 + 2/(1 + a*x))]

    @test_int [sqrt(atanh(a*x))/(1 - a^2*x^2)^2, x, 9, (x*sqrt(atanh(a*x)))/(2*(1 - a^2*x^2)) + atanh(a*x)^(3/2)/(3*a) + (sqrt(pi/2)*erf(sqrt(2)*sqrt(atanh(a*x))))/(16*a) - (sqrt(pi/2)*erfi(sqrt(2)*sqrt(atanh(a*x))))/(16*a)]

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

    @test_int [x^4/((1 - a^2*x^2)^2*atanh(a*x)), x, 0, CoshIntegral(2*atanh(a*x))/(2*a^5) - (3*log(atanh(a*x)))/(2*a^5) + Unintegrable(atanh(a*x)^(-1), x)/a^4, Unintegrable(x^4/((1 - a^2*x^2)^2*atanh(a*x)), x)]
    @test_int [x^3/((1 - a^2*x^2)^2*atanh(a*x)), x, 0, SinhIntegral(2*atanh(a*x))/(2*a^4) - Unintegrable(x/((1 - a^2*x^2)*atanh(a*x)), x)/a^2, Unintegrable(x^3/((1 - a^2*x^2)^2*atanh(a*x)), x)]
    @test_int [x^2/((1 - a^2*x^2)^2*atanh(a*x)), x, 4, CoshIntegral(2*atanh(a*x))/(2*a^3) - log(atanh(a*x))/(2*a^3)]
    @test_int [x/((1 - a^2*x^2)^2*atanh(a*x)), x, 4, SinhIntegral(2*atanh(a*x))/(2*a^2)]
    @test_int [1/((1 - a^2*x^2)^2*atanh(a*x)), x, 4, CoshIntegral(2*atanh(a*x))/(2*a) + log(atanh(a*x))/(2*a)]
    @test_int [1/(x*(1 - a^2*x^2)^2*atanh(a*x)), x, 0, SinhIntegral(2*atanh(a*x))/2 + Unintegrable(1/(x*(1 - a^2*x^2)*atanh(a*x)), x), Unintegrable(1/(x*(1 - a^2*x^2)^2*atanh(a*x)), x)]

    @test_int [x^3/((1 - a^2*x^2)^2*atanh(a*x)^2), x, 11, x/(a^3*atanh(a*x)) - x/(a^3*(1 - a^2*x^2)*atanh(a*x)) + CoshIntegral(2*atanh(a*x))/a^4 - Unintegrable(1/atanh(a*x), x)/a^3]
    @test_int [x^2/((1 - a^2*x^2)^2*atanh(a*x)^2), x, 5, -(x^2/(a*(1 - a^2*x^2)*atanh(a*x))) + SinhIntegral(2*atanh(a*x))/a^3]
    @test_int [x/((1 - a^2*x^2)^2*atanh(a*x)^2), x, 9, -(x/(a*(1 - a^2*x^2)*atanh(a*x))) + CoshIntegral(2*atanh(a*x))/a^2]
    @test_int [1/((1 - a^2*x^2)^2*atanh(a*x)^2), x, 5, -(1/(a*(1 - a^2*x^2)*atanh(a*x))) + SinhIntegral(2*atanh(a*x))/a]
    @test_int [1/(x*(1 - a^2*x^2)^2*atanh(a*x)^2), x, 11, -(1/(a*x*atanh(a*x))) - (a*x)/((1 - a^2*x^2)*atanh(a*x)) + CoshIntegral(2*atanh(a*x)) - Unintegrable(1/(x^2*atanh(a*x)), x)/a]

    @test_int [x^3/((1 - a^2*x^2)^2*atanh(a*x)^3), x, 7, x/(2*a^3*atanh(a*x)^2) - x/(2*a^3*(1 - a^2*x^2)*atanh(a*x)^2) - (1 + a^2*x^2)/(2*a^4*(1 - a^2*x^2)*atanh(a*x)) + SinhIntegral(2*atanh(a*x))/a^4 - Unintegrable(1/atanh(a*x)^2, x)/(2*a^3)]
    @test_int [x^2/((1 - a^2*x^2)^2*atanh(a*x)^3), x, 10, -(x^2/(2*a*(1 - a^2*x^2)*atanh(a*x)^2)) - x/(a^2*(1 - a^2*x^2)*atanh(a*x)) + CoshIntegral(2*atanh(a*x))/a^3]
    @test_int [x/((1 - a^2*x^2)^2*atanh(a*x)^3), x, 5, -(x/(2*a*(1 - a^2*x^2)*atanh(a*x)^2)) - (1 + a^2*x^2)/(2*a^2*(1 - a^2*x^2)*atanh(a*x)) + SinhIntegral(2*atanh(a*x))/a^2]
    @test_int [1/((1 - a^2*x^2)^2*atanh(a*x)^3), x, 10, -(1/(2*a*(1 - a^2*x^2)*atanh(a*x)^2)) - x/((1 - a^2*x^2)*atanh(a*x)) + CoshIntegral(2*atanh(a*x))/a]
    @test_int [1/(x*(1 - a^2*x^2)^2*atanh(a*x)^3), x, 7, -(1/(2*a*x*atanh(a*x)^2)) - (a*x)/(2*(1 - a^2*x^2)*atanh(a*x)^2) - (1 + a^2*x^2)/(2*(1 - a^2*x^2)*atanh(a*x)) - Unintegrable(1/(x^2*atanh(a*x)^2), x)/(2*a) + SinhIntegral(2*atanh(a*x))]

    @test_int [1/((1 - a^2*x^2)^2*atanh(a*x)^4), x, 6, -(1/(3*a*(1 - a^2*x^2)*atanh(a*x)^3)) - x/(3*(1 - a^2*x^2)*atanh(a*x)^2) - (1 + a^2*x^2)/(3*a*(1 - a^2*x^2)*atanh(a*x)) + (2*SinhIntegral(2*atanh(a*x)))/(3*a)]
    @test_int [1/((1 - a^2*x^2)^2*atanh(a*x)^5), x, 11, -(1/(4*a*(1 - a^2*x^2)*atanh(a*x)^4)) - x/(6*(1 - a^2*x^2)*atanh(a*x)^3) - (1 + a^2*x^2)/(12*a*(1 - a^2*x^2)*atanh(a*x)^2) - x/(3*(1 - a^2*x^2)*atanh(a*x)) + CoshIntegral(2*atanh(a*x))/(3*a)]
    @test_int [1/((1 - a^2*x^2)^2*atanh(a*x)^6), x, 7, -(1/(5*a*(1 - a^2*x^2)*atanh(a*x)^5)) - x/(10*(1 - a^2*x^2)*atanh(a*x)^4) - (1 + a^2*x^2)/(30*a*(1 - a^2*x^2)*atanh(a*x)^3) - x/(15*(1 - a^2*x^2)*atanh(a*x)^2) - (1 + a^2*x^2)/(15*a*(1 - a^2*x^2)*atanh(a*x)) + (2*SinhIntegral(2*atanh(a*x)))/(15*a)]
    @test_int [1/((1 - a^2*x^2)^2*atanh(a*x)^7), x, 12, -(1/(6*a*(1 - a^2*x^2)*atanh(a*x)^6)) - x/(15*(1 - a^2*x^2)*atanh(a*x)^5) - (1 + a^2*x^2)/(60*a*(1 - a^2*x^2)*atanh(a*x)^4) - x/(45*(1 - a^2*x^2)*atanh(a*x)^3) - (1 + a^2*x^2)/(90*a*(1 - a^2*x^2)*atanh(a*x)^2) - (2*x)/(45*(1 - a^2*x^2)*atanh(a*x)) + (2*CoshIntegral(2*atanh(a*x)))/(45*a)]
    @test_int [1/((1 - a^2*x^2)^2*atanh(a*x)^8), x, 8, -(1/(7*a*(1 - a^2*x^2)*atanh(a*x)^7)) - x/(21*(1 - a^2*x^2)*atanh(a*x)^6) - (1 + a^2*x^2)/(105*a*(1 - a^2*x^2)*atanh(a*x)^5) - x/(105*(1 - a^2*x^2)*atanh(a*x)^4) - (1 + a^2*x^2)/(315*a*(1 - a^2*x^2)*atanh(a*x)^3) - (2*x)/(315*(1 - a^2*x^2)*atanh(a*x)^2) - (2*(1 + a^2*x^2))/(315*a*(1 - a^2*x^2)*atanh(a*x)) + (4*SinhIntegral(2*atanh(a*x)))/(315*a)]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*atanh(c*x)^p / (1-c^2*x^2)^3=#

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

    @test_int [x^3*atanh(a*x)/(1 - a^2*x^2)^3, x, 4, -(x^3/(16*a*(1 - a^2*x^2)^2)) + (3*x)/(32*a^3*(1 - a^2*x^2)) - (3*atanh(a*x))/(32*a^4) + (x^4*atanh(a*x))/(4*(1 - a^2*x^2)^2)]
    @test_int [x^2*atanh(a*x)/(1 - a^2*x^2)^3, x, 3, -(1/(16*a^3*(1 - a^2*x^2)^2)) + 1/(16*a^3*(1 - a^2*x^2)) + (x*atanh(a*x))/(4*a^2*(1 - a^2*x^2)^2) - (x*atanh(a*x))/(8*a^2*(1 - a^2*x^2)) - atanh(a*x)^2/(16*a^3)]
    @test_int [x*atanh(a*x)/(1 - a^2*x^2)^3, x, 4, -(x/(16*a*(1 - a^2*x^2)^2)) - (3*x)/(32*a*(1 - a^2*x^2)) - (3*atanh(a*x))/(32*a^2) + atanh(a*x)/(4*a^2*(1 - a^2*x^2)^2)]
    @test_int [atanh(a*x)/(1 - a^2*x^2)^3, x, 3, -(1/(16*a*(1 - a^2*x^2)^2)) - 3/(16*a*(1 - a^2*x^2)) + (x*atanh(a*x))/(4*(1 - a^2*x^2)^2) + (3*x*atanh(a*x))/(8*(1 - a^2*x^2)) + (3*atanh(a*x)^2)/(16*a)]
    @test_int [atanh(a*x)/(x*(1 - a^2*x^2)^3), x, 12, -((a*x)/(16*(1 - a^2*x^2)^2)) - (11*a*x)/(32*(1 - a^2*x^2)) - (11/32)*atanh(a*x) + atanh(a*x)/(4*(1 - a^2*x^2)^2) + atanh(a*x)/(2*(1 - a^2*x^2)) + (1/2)*atanh(a*x)^2 + atanh(a*x)*log(2 - 2/(1 + a*x)) - (1/2)*PolyLog(2, -1 + 2/(1 + a*x))]
    @test_int [atanh(a*x)/(x^2*(1 - a^2*x^2)^3), x, 14, -(a/(16*(1 - a^2*x^2)^2)) - (7*a)/(16*(1 - a^2*x^2)) - atanh(a*x)/x + (a^2*x*atanh(a*x))/(4*(1 - a^2*x^2)^2) + (7*a^2*x*atanh(a*x))/(8*(1 - a^2*x^2)) + (15/16)*a*atanh(a*x)^2 + a*log(x) - (1/2)*a*log(1 - a^2*x^2)]

    @test_int [x^3*atanh(a*x)^2/(1 - a^2*x^2)^3, x, 4, x^4/(32*(1 - a^2*x^2)^2) - 3/(32*a^4*(1 - a^2*x^2)) - (x^3*atanh(a*x))/(8*a*(1 - a^2*x^2)^2) + (3*x*atanh(a*x))/(16*a^3*(1 - a^2*x^2)) - (3*atanh(a*x)^2)/(32*a^4) + (x^4*atanh(a*x)^2)/(4*(1 - a^2*x^2)^2)]
    @test_int [x^2*atanh(a*x)^2/(1 - a^2*x^2)^3, x, 13, x/(32*a^2*(1 - a^2*x^2)^2) - x/(64*a^2*(1 - a^2*x^2)) - atanh(a*x)/(64*a^3) - atanh(a*x)/(8*a^3*(1 - a^2*x^2)^2) + atanh(a*x)/(8*a^3*(1 - a^2*x^2)) + (x*atanh(a*x)^2)/(4*a^2*(1 - a^2*x^2)^2) - (x*atanh(a*x)^2)/(8*a^2*(1 - a^2*x^2)) - atanh(a*x)^3/(24*a^3)]
    @test_int [x*atanh(a*x)^2/(1 - a^2*x^2)^3, x, 4, 1/(32*a^2*(1 - a^2*x^2)^2) + 3/(32*a^2*(1 - a^2*x^2)) - (x*atanh(a*x))/(8*a*(1 - a^2*x^2)^2) - (3*x*atanh(a*x))/(16*a*(1 - a^2*x^2)) - (3*atanh(a*x)^2)/(32*a^2) + atanh(a*x)^2/(4*a^2*(1 - a^2*x^2)^2)]
    @test_int [atanh(a*x)^2/(1 - a^2*x^2)^3, x, 8, x/(32*(1 - a^2*x^2)^2) + (15*x)/(64*(1 - a^2*x^2)) + (15*atanh(a*x))/(64*a) - atanh(a*x)/(8*a*(1 - a^2*x^2)^2) - (3*atanh(a*x))/(8*a*(1 - a^2*x^2)) + (x*atanh(a*x)^2)/(4*(1 - a^2*x^2)^2) + (3*x*atanh(a*x)^2)/(8*(1 - a^2*x^2)) + atanh(a*x)^3/(8*a)]
    @test_int [atanh(a*x)^2/(x*(1 - a^2*x^2)^3), x, 13, 1/(32*(1 - a^2*x^2)^2) + 11/(32*(1 - a^2*x^2)) - (a*x*atanh(a*x))/(8*(1 - a^2*x^2)^2) - (11*a*x*atanh(a*x))/(16*(1 - a^2*x^2)) - (11/32)*atanh(a*x)^2 + atanh(a*x)^2/(4*(1 - a^2*x^2)^2) + atanh(a*x)^2/(2*(1 - a^2*x^2)) + (1/3)*atanh(a*x)^3 + atanh(a*x)^2*log(2 - 2/(1 + a*x)) - atanh(a*x)*PolyLog(2, -1 + 2/(1 + a*x)) - (1/2)*PolyLog(3, -1 + 2/(1 + a*x))]
    @test_int [atanh(a*x)^2/(x^2*(1 - a^2*x^2)^3), x, 20, (a^2*x)/(32*(1 - a^2*x^2)^2) + (31*a^2*x)/(64*(1 - a^2*x^2)) + (31/64)*a*atanh(a*x) - (a*atanh(a*x))/(8*(1 - a^2*x^2)^2) - (7*a*atanh(a*x))/(8*(1 - a^2*x^2)) + a*atanh(a*x)^2 - atanh(a*x)^2/x + (a^2*x*atanh(a*x)^2)/(4*(1 - a^2*x^2)^2) + (7*a^2*x*atanh(a*x)^2)/(8*(1 - a^2*x^2)) + (5/8)*a*atanh(a*x)^3 + 2*a*atanh(a*x)*log(2 - 2/(1 + a*x)) - a*PolyLog(2, -1 + 2/(1 + a*x))]

    @test_int [x^3*atanh(a*x)^3/(1 - a^2*x^2)^3, x, 9, -((3*x^3)/(128*a*(1 - a^2*x^2)^2)) + (45*x)/(256*a^3*(1 - a^2*x^2)) + (27*atanh(a*x))/(256*a^4) + (3*x^4*atanh(a*x))/(32*(1 - a^2*x^2)^2) - (9*atanh(a*x))/(32*a^4*(1 - a^2*x^2)) - (3*x^3*atanh(a*x)^2)/(16*a*(1 - a^2*x^2)^2) + (9*x*atanh(a*x)^2)/(32*a^3*(1 - a^2*x^2)) - (3*atanh(a*x)^3)/(32*a^4) + (x^4*atanh(a*x)^3)/(4*(1 - a^2*x^2)^2)]
    @test_int [x^2*atanh(a*x)^3/(1 - a^2*x^2)^3, x, 13, -(3/(128*a^3*(1 - a^2*x^2)^2)) + 3/(128*a^3*(1 - a^2*x^2)) + (3*x*atanh(a*x))/(32*a^2*(1 - a^2*x^2)^2) - (3*x*atanh(a*x))/(64*a^2*(1 - a^2*x^2)) - (3*atanh(a*x)^2)/(128*a^3) - (3*atanh(a*x)^2)/(16*a^3*(1 - a^2*x^2)^2) + (3*atanh(a*x)^2)/(16*a^3*(1 - a^2*x^2)) + (x*atanh(a*x)^3)/(4*a^2*(1 - a^2*x^2)^2) - (x*atanh(a*x)^3)/(8*a^2*(1 - a^2*x^2)) - atanh(a*x)^4/(32*a^3)]
    @test_int [x*atanh(a*x)^3/(1 - a^2*x^2)^3, x, 9, -((3*x)/(128*a*(1 - a^2*x^2)^2)) - (45*x)/(256*a*(1 - a^2*x^2)) - (45*atanh(a*x))/(256*a^2) + (3*atanh(a*x))/(32*a^2*(1 - a^2*x^2)^2) + (9*atanh(a*x))/(32*a^2*(1 - a^2*x^2)) - (3*x*atanh(a*x)^2)/(16*a*(1 - a^2*x^2)^2) - (9*x*atanh(a*x)^2)/(32*a*(1 - a^2*x^2)) - (3*atanh(a*x)^3)/(32*a^2) + atanh(a*x)^3/(4*a^2*(1 - a^2*x^2)^2)]
    @test_int [atanh(a*x)^3/(1 - a^2*x^2)^3, x, 8, -(3/(128*a*(1 - a^2*x^2)^2)) - 45/(128*a*(1 - a^2*x^2)) + (3*x*atanh(a*x))/(32*(1 - a^2*x^2)^2) + (45*x*atanh(a*x))/(64*(1 - a^2*x^2)) + (45*atanh(a*x)^2)/(128*a) - (3*atanh(a*x)^2)/(16*a*(1 - a^2*x^2)^2) - (9*atanh(a*x)^2)/(16*a*(1 - a^2*x^2)) + (x*atanh(a*x)^3)/(4*(1 - a^2*x^2)^2) + (3*x*atanh(a*x)^3)/(8*(1 - a^2*x^2)) + (3*atanh(a*x)^4)/(32*a)]
    @test_int [atanh(a*x)^3/(x*(1 - a^2*x^2)^3), x, 21, -((3*a*x)/(128*(1 - a^2*x^2)^2)) - (141*a*x)/(256*(1 - a^2*x^2)) - (141/256)*atanh(a*x) + (3*atanh(a*x))/(32*(1 - a^2*x^2)^2) + (33*atanh(a*x))/(32*(1 - a^2*x^2)) - (3*a*x*atanh(a*x)^2)/(16*(1 - a^2*x^2)^2) - (33*a*x*atanh(a*x)^2)/(32*(1 - a^2*x^2)) - (11/32)*atanh(a*x)^3 + atanh(a*x)^3/(4*(1 - a^2*x^2)^2) + atanh(a*x)^3/(2*(1 - a^2*x^2)) + (1/4)*atanh(a*x)^4 + atanh(a*x)^3*log(2 - 2/(1 + a*x)) - (3/2)*atanh(a*x)^2*PolyLog(2, -1 + 2/(1 + a*x)) - (3/2)*atanh(a*x)*PolyLog(3, -1 + 2/(1 + a*x)) - (3/4)*PolyLog(4, -1 + 2/(1 + a*x))]
    @test_int [atanh(a*x)^3/(x^2*(1 - a^2*x^2)^3), x, 21, -((3*a)/(128*(1 - a^2*x^2)^2)) - (93*a)/(128*(1 - a^2*x^2)) + (3*a^2*x*atanh(a*x))/(32*(1 - a^2*x^2)^2) + (93*a^2*x*atanh(a*x))/(64*(1 - a^2*x^2)) + (93/128)*a*atanh(a*x)^2 - (3*a*atanh(a*x)^2)/(16*(1 - a^2*x^2)^2) - (21*a*atanh(a*x)^2)/(16*(1 - a^2*x^2)) + a*atanh(a*x)^3 - atanh(a*x)^3/x + (a^2*x*atanh(a*x)^3)/(4*(1 - a^2*x^2)^2) + (7*a^2*x*atanh(a*x)^3)/(8*(1 - a^2*x^2)) + (15/32)*a*atanh(a*x)^4 + 3*a*atanh(a*x)^2*log(2 - 2/(1 + a*x)) - 3*a*atanh(a*x)*PolyLog(2, -1 + 2/(1 + a*x)) - (3/2)*a*PolyLog(3, -1 + 2/(1 + a*x))]

    @test_int [sqrt(atanh(a*x))/(1 - a^2*x^2)^3, x, 15, atanh(a*x)^(3/2)/(4*a) + (sqrt(pi)*erf(2*sqrt(atanh(a*x))))/(256*a) + (sqrt(pi/2)*erf(sqrt(2)*sqrt(atanh(a*x))))/(16*a) - (sqrt(pi)*erfi(2*sqrt(atanh(a*x))))/(256*a) - (sqrt(pi/2)*erfi(sqrt(2)*sqrt(atanh(a*x))))/(16*a) + (sqrt(atanh(a*x))*sinh(2*atanh(a*x)))/(4*a) + (sqrt(atanh(a*x))*sinh(4*atanh(a*x)))/(32*a)]

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

    @test_int [x^6/((1 - a^2*x^2)^3*atanh(a*x)), x, 0, Unintegrable(x^6/((1 - a^2*x^2)^3*atanh(a*x)), x)]
    @test_int [x^5/((1 - a^2*x^2)^3*atanh(a*x)), x, 0, Unintegrable(x^5/((1 - a^2*x^2)^3*atanh(a*x)), x)]
    @test_int [x^4/((1 - a^2*x^2)^3*atanh(a*x)), x, 5, -(CoshIntegral(2*atanh(a*x))/(2*a^5)) + CoshIntegral(4*atanh(a*x))/(8*a^5) + (3*log(atanh(a*x)))/(8*a^5)]
    @test_int [x^3/((1 - a^2*x^2)^3*atanh(a*x)), x, 5, -(SinhIntegral(2*atanh(a*x))/(4*a^4)) + SinhIntegral(4*atanh(a*x))/(8*a^4)]
    @test_int [x^2/((1 - a^2*x^2)^3*atanh(a*x)), x, 4, CoshIntegral(4*atanh(a*x))/(8*a^3) - log(atanh(a*x))/(8*a^3)]
    @test_int [x/((1 - a^2*x^2)^3*atanh(a*x)), x, 5, SinhIntegral(2*atanh(a*x))/(4*a^2) + SinhIntegral(4*atanh(a*x))/(8*a^2)]
    @test_int [1/((1 - a^2*x^2)^3*atanh(a*x)), x, 5, CoshIntegral(2*atanh(a*x))/(2*a) + CoshIntegral(4*atanh(a*x))/(8*a) + (3*log(atanh(a*x)))/(8*a)]
    @test_int [1/(x*(1 - a^2*x^2)^3*atanh(a*x)), x, 0, (3*SinhIntegral(2*atanh(a*x)))/4 + SinhIntegral(4*atanh(a*x))/8 - Unintegrable(1/(x*(-1 + a^2*x^2)*atanh(a*x)), x), Unintegrable(1/(x*(1 - a^2*x^2)^3*atanh(a*x)), x)]

    @test_int [x^5/((1 - a^2*x^2)^3*atanh(a*x)^2), x, 32, -(x/(a^5*atanh(a*x))) - x/(a^5*(1 - a^2*x^2)^2*atanh(a*x)) + (2*x)/(a^5*(1 - a^2*x^2)*atanh(a*x)) - (3*CoshIntegral(2*atanh(a*x)))/(2*a^6) + CoshIntegral(4*atanh(a*x))/(2*a^6) + Unintegrable(1/atanh(a*x), x)/a^5]
    @test_int [x^4/((1 - a^2*x^2)^3*atanh(a*x)^2), x, 6, -(x^4/(a*(1 - a^2*x^2)^2*atanh(a*x))) - SinhIntegral(2*atanh(a*x))/a^5 + SinhIntegral(4*atanh(a*x))/(2*a^5)]
    @test_int [x^3/((1 - a^2*x^2)^3*atanh(a*x)^2), x, 20, -(x^3/(a*(1 - a^2*x^2)^2*atanh(a*x))) - CoshIntegral(2*atanh(a*x))/(2*a^4) + CoshIntegral(4*atanh(a*x))/(2*a^4), -(x/(a^3*(1 - a^2*x^2)^2*atanh(a*x))) + x/(a^3*(1 - a^2*x^2)*atanh(a*x)) - CoshIntegral(2*atanh(a*x))/(2*a^4) + CoshIntegral(4*atanh(a*x))/(2*a^4)]
    @test_int [x^2/((1 - a^2*x^2)^3*atanh(a*x)^2), x, 12, -(x^2/(a*(1 - a^2*x^2)^2*atanh(a*x))) + SinhIntegral(4*atanh(a*x))/(2*a^3), -(1/(a^3*(1 - a^2*x^2)^2*atanh(a*x))) + 1/(a^3*(1 - a^2*x^2)*atanh(a*x)) + SinhIntegral(4*atanh(a*x))/(2*a^3)]
    @test_int [x/((1 - a^2*x^2)^3*atanh(a*x)^2), x, 10, -(x/(a*(1 - a^2*x^2)^2*atanh(a*x))) + CoshIntegral(2*atanh(a*x))/(2*a^2) + CoshIntegral(4*atanh(a*x))/(2*a^2)]
    @test_int [1/((1 - a^2*x^2)^3*atanh(a*x)^2), x, 6, -(1/(a*(1 - a^2*x^2)^2*atanh(a*x))) + SinhIntegral(2*atanh(a*x))/a + SinhIntegral(4*atanh(a*x))/(2*a)]
    @test_int [1/(x*(1 - a^2*x^2)^3*atanh(a*x)^2), x, 22, -(1/(a*x*atanh(a*x))) - (a*x)/((1 - a^2*x^2)^2*atanh(a*x)) - (a*x)/((1 - a^2*x^2)*atanh(a*x)) + (3/2)*CoshIntegral(2*atanh(a*x)) + (1/2)*CoshIntegral(4*atanh(a*x)) - Unintegrable(1/(x^2*atanh(a*x)), x)/a]

    @test_int [x^4/((1 - a^2*x^2)^3*atanh(a*x)^3), x, 21, -(x^4/(2*a*(1 - a^2*x^2)^2*atanh(a*x)^2)) - (2*x)/(a^4*(1 - a^2*x^2)^2*atanh(a*x)) + (2*x)/(a^4*(1 - a^2*x^2)*atanh(a*x)) - CoshIntegral(2*atanh(a*x))/a^5 + CoshIntegral(4*atanh(a*x))/a^5]
    @test_int [x^3/((1 - a^2*x^2)^3*atanh(a*x)^3), x, 25, -(x^3/(2*a*(1 - a^2*x^2)^2*atanh(a*x)^2)) - (3*x^2)/(2*a^2*(1 - a^2*x^2)^2*atanh(a*x)) - x^4/(2*(1 - a^2*x^2)^2*atanh(a*x)) - SinhIntegral(2*atanh(a*x))/(2*a^4) + SinhIntegral(4*atanh(a*x))/a^4, -(x/(2*a^3*(1 - a^2*x^2)^2*atanh(a*x)^2)) + x/(2*a^3*(1 - a^2*x^2)*atanh(a*x)^2) - 2/(a^4*(1 - a^2*x^2)^2*atanh(a*x)) + 3/(2*a^4*(1 - a^2*x^2)*atanh(a*x)) + (1 + a^2*x^2)/(2*a^4*(1 - a^2*x^2)*atanh(a*x)) - SinhIntegral(2*atanh(a*x))/(2*a^4) + SinhIntegral(4*atanh(a*x))/a^4]
    @test_int [x^2/((1 - a^2*x^2)^3*atanh(a*x)^3), x, 22, -(x^2/(2*a*(-1 + a^2*x^2)^2*atanh(a*x)^2)) - (2*x)/(a^2*(1 - a^2*x^2)^2*atanh(a*x)) + x/(a^2*(1 - a^2*x^2)*atanh(a*x)) + CoshIntegral(4*atanh(a*x))/a^3, -(1/(2*a^3*(1 - a^2*x^2)^2*atanh(a*x)^2)) + 1/(2*a^3*(1 - a^2*x^2)*atanh(a*x)^2) - (2*x)/(a^2*(1 - a^2*x^2)^2*atanh(a*x)) + x/(a^2*(1 - a^2*x^2)*atanh(a*x)) + CoshIntegral(4*atanh(a*x))/a^3]
    @test_int [x/((1 - a^2*x^2)^3*atanh(a*x)^3), x, 19, -(x/(2*a*(1 - a^2*x^2)^2*atanh(a*x)^2)) - 2/(a^2*(1 - a^2*x^2)^2*atanh(a*x)) + 3/(2*a^2*(1 - a^2*x^2)*atanh(a*x)) + SinhIntegral(2*atanh(a*x))/(2*a^2) + SinhIntegral(4*atanh(a*x))/a^2]
    @test_int [1/((1 - a^2*x^2)^3*atanh(a*x)^3), x, 11, -(1/(2*a*(1 - a^2*x^2)^2*atanh(a*x)^2)) - (2*x)/((1 - a^2*x^2)^2*atanh(a*x)) + CoshIntegral(2*atanh(a*x))/a + CoshIntegral(4*atanh(a*x))/a]
    @test_int [1/(x*(1 - a^2*x^2)^3*atanh(a*x)^3), x, 27, -(1/(2*a*x*atanh(a*x)^2)) - (a*x)/(2*(1 - a^2*x^2)^2*atanh(a*x)^2) - (a*x)/(2*(1 - a^2*x^2)*atanh(a*x)^2) - 2/((1 - a^2*x^2)^2*atanh(a*x)) + 3/(2*(1 - a^2*x^2)*atanh(a*x)) - (1 + a^2*x^2)/(2*(1 - a^2*x^2)*atanh(a*x)) - Unintegrable(1/(x^2*atanh(a*x)^2), x)/(2*a) + (3/2)*SinhIntegral(2*atanh(a*x)) + SinhIntegral(4*atanh(a*x))]

    @test_int [1/((1 - a^2*x^2)^3*atanh(a*x)^4), x, 20, -(1/(3*a*(1 - a^2*x^2)^2*atanh(a*x)^3)) - (2*x)/(3*(1 - a^2*x^2)^2*atanh(a*x)^2) - 8/(3*a*(1 - a^2*x^2)^2*atanh(a*x)) + 2/(a*(1 - a^2*x^2)*atanh(a*x)) + (2*SinhIntegral(2*atanh(a*x)))/(3*a) + (4*SinhIntegral(4*atanh(a*x)))/(3*a)]
    @test_int [1/((1 - a^2*x^2)^3*atanh(a*x)^5), x, 35, -(1/(4*a*(1 - a^2*x^2)^2*atanh(a*x)^4)) - x/(3*(1 - a^2*x^2)^2*atanh(a*x)^3) - 2/(3*a*(1 - a^2*x^2)^2*atanh(a*x)^2) + 1/(2*a*(1 - a^2*x^2)*atanh(a*x)^2) - (8*x)/(3*(1 - a^2*x^2)^2*atanh(a*x)) + x/((1 - a^2*x^2)*atanh(a*x)) + CoshIntegral(2*atanh(a*x))/(3*a) + (4*CoshIntegral(4*atanh(a*x)))/(3*a)]
    @test_int [1/((1 - a^2*x^2)^3*atanh(a*x)^6), x, 49, -(1/(5*a*(1 - a^2*x^2)^2*atanh(a*x)^5)) - x/(5*(1 - a^2*x^2)^2*atanh(a*x)^4) - 4/(15*a*(1 - a^2*x^2)^2*atanh(a*x)^3) + 1/(5*a*(1 - a^2*x^2)*atanh(a*x)^3) - (8*x)/(15*(1 - a^2*x^2)^2*atanh(a*x)^2) + x/(5*(1 - a^2*x^2)*atanh(a*x)^2) - 32/(15*a*(1 - a^2*x^2)^2*atanh(a*x)) + 8/(5*a*(1 - a^2*x^2)*atanh(a*x)) + (1 + a^2*x^2)/(5*a*(1 - a^2*x^2)*atanh(a*x)) + (2*SinhIntegral(2*atanh(a*x)))/(15*a) + (16*SinhIntegral(4*atanh(a*x)))/(15*a)]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*atanh(c*x)^p / (1-c^2*x^2)^4=#

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

    @test_int [atanh(a*x)/(1 - a^2*x^2)^4, x, 4, -(1/(36*a*(1 - a^2*x^2)^3)) - 5/(96*a*(1 - a^2*x^2)^2) - 5/(32*a*(1 - a^2*x^2)) + (x*atanh(a*x))/(6*(1 - a^2*x^2)^3) + (5*x*atanh(a*x))/(24*(1 - a^2*x^2)^2) + (5*x*atanh(a*x))/(16*(1 - a^2*x^2)) + (5*atanh(a*x)^2)/(32*a)]

    @test_int [atanh(a*x)^2/(1 - a^2*x^2)^4, x, 13, x/(108*(1 - a^2*x^2)^3) + (65*x)/(1728*(1 - a^2*x^2)^2) + (245*x)/(1152*(1 - a^2*x^2)) + (245*atanh(a*x))/(1152*a) - atanh(a*x)/(18*a*(1 - a^2*x^2)^3) - (5*atanh(a*x))/(48*a*(1 - a^2*x^2)^2) - (5*atanh(a*x))/(16*a*(1 - a^2*x^2)) + (x*atanh(a*x)^2)/(6*(1 - a^2*x^2)^3) + (5*x*atanh(a*x)^2)/(24*(1 - a^2*x^2)^2) + (5*x*atanh(a*x)^2)/(16*(1 - a^2*x^2)) + (5*atanh(a*x)^3)/(48*a)]

    @test_int [atanh(a*x)^3/(1 - a^2*x^2)^4, x, 13, -(1/(216*a*(1 - a^2*x^2)^3)) - 65/(2304*a*(1 - a^2*x^2)^2) - 245/(768*a*(1 - a^2*x^2)) + (x*atanh(a*x))/(36*(1 - a^2*x^2)^3) + (65*x*atanh(a*x))/(576*(1 - a^2*x^2)^2) + (245*x*atanh(a*x))/(384*(1 - a^2*x^2)) + (245*atanh(a*x)^2)/(768*a) - atanh(a*x)^2/(12*a*(1 - a^2*x^2)^3) - (5*atanh(a*x)^2)/(32*a*(1 - a^2*x^2)^2) - (15*atanh(a*x)^2)/(32*a*(1 - a^2*x^2)) + (x*atanh(a*x)^3)/(6*(1 - a^2*x^2)^3) + (5*x*atanh(a*x)^3)/(24*(1 - a^2*x^2)^2) + (5*x*atanh(a*x)^3)/(16*(1 - a^2*x^2)) + (5*atanh(a*x)^4)/(64*a)]

    @test_int [sqrt(atanh(a*x))/(1 - a^2*x^2)^4, x, 21, (5*atanh(a*x)^(3/2))/(24*a) + (3*sqrt(pi)*erf(2*sqrt(atanh(a*x))))/(512*a) + (15*sqrt(pi/2)*erf(sqrt(2)*sqrt(atanh(a*x))))/(256*a) + (sqrt(pi/6)*erf(sqrt(6)*sqrt(atanh(a*x))))/(768*a) - (3*sqrt(pi)*erfi(2*sqrt(atanh(a*x))))/(512*a) - (15*sqrt(pi/2)*erfi(sqrt(2)*sqrt(atanh(a*x))))/(256*a) - (sqrt(pi/6)*erfi(sqrt(6)*sqrt(atanh(a*x))))/(768*a) + (15*sqrt(atanh(a*x))*sinh(2*atanh(a*x)))/(64*a) + (3*sqrt(atanh(a*x))*sinh(4*atanh(a*x)))/(64*a) + (sqrt(atanh(a*x))*sinh(6*atanh(a*x)))/(192*a)]

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

    @test_int [x^8/((1 - a^2*x^2)^4*atanh(a*x)), x, 0, Unintegrable(x^8/((1 - a^2*x^2)^4*atanh(a*x)), x)]
    @test_int [x^7/((1 - a^2*x^2)^4*atanh(a*x)), x, 0, Unintegrable(x^7/((1 - a^2*x^2)^4*atanh(a*x)), x)]
    @test_int [x^6/((1 - a^2*x^2)^4*atanh(a*x)), x, 6, (15*CoshIntegral(2*atanh(a*x)))/(32*a^7) - (3*CoshIntegral(4*atanh(a*x)))/(16*a^7) + CoshIntegral(6*atanh(a*x))/(32*a^7) - (5*log(atanh(a*x)))/(16*a^7)]
    @test_int [x^5/((1 - a^2*x^2)^4*atanh(a*x)), x, 6, (5*SinhIntegral(2*atanh(a*x)))/(32*a^6) - SinhIntegral(4*atanh(a*x))/(8*a^6) + SinhIntegral(6*atanh(a*x))/(32*a^6)]
    @test_int [x^4/((1 - a^2*x^2)^4*atanh(a*x)), x, 6, -(CoshIntegral(2*atanh(a*x))/(32*a^5)) - CoshIntegral(4*atanh(a*x))/(16*a^5) + CoshIntegral(6*atanh(a*x))/(32*a^5) + log(atanh(a*x))/(16*a^5)]
    @test_int [x^3/((1 - a^2*x^2)^4*atanh(a*x)), x, 5, -((3*SinhIntegral(2*atanh(a*x)))/(32*a^4)) + SinhIntegral(6*atanh(a*x))/(32*a^4)]
    @test_int [x^2/((1 - a^2*x^2)^4*atanh(a*x)), x, 6, -(CoshIntegral(2*atanh(a*x))/(32*a^3)) + CoshIntegral(4*atanh(a*x))/(16*a^3) + CoshIntegral(6*atanh(a*x))/(32*a^3) - log(atanh(a*x))/(16*a^3)]
    @test_int [x^1/((1 - a^2*x^2)^4*atanh(a*x)), x, 6, (5*SinhIntegral(2*atanh(a*x)))/(32*a^2) + SinhIntegral(4*atanh(a*x))/(8*a^2) + SinhIntegral(6*atanh(a*x))/(32*a^2)]
    @test_int [x^0/((1 - a^2*x^2)^4*atanh(a*x)), x, 6, (15*CoshIntegral(2*atanh(a*x)))/(32*a) + (3*CoshIntegral(4*atanh(a*x)))/(16*a) + CoshIntegral(6*atanh(a*x))/(32*a) + (5*log(atanh(a*x)))/(16*a)]
    @test_int [1/(x^1*(1 - a^2*x^2)^4*atanh(a*x)), x, 0, Unintegrable(1/(x*(1 - a^2*x^2)^4*atanh(a*x)), x)]
    @test_int [1/(x^2*(1 - a^2*x^2)^4*atanh(a*x)), x, 0, Unintegrable(1/(x^2*(1 - a^2*x^2)^4*atanh(a*x)), x)]

    @test_int [x/((1 - a^2*x^2)^4*atanh(a*x)^2), x, 13, -(x/(a*(1 - a^2*x^2)^3*atanh(a*x))) + (5*CoshIntegral(2*atanh(a*x)))/(16*a^2) + CoshIntegral(4*atanh(a*x))/(2*a^2) + (3*CoshIntegral(6*atanh(a*x)))/(16*a^2)]
    @test_int [1/((1 - a^2*x^2)^4*atanh(a*x)^2), x, 7, -(1/(a*(1 - a^2*x^2)^3*atanh(a*x))) + (15*SinhIntegral(2*atanh(a*x)))/(16*a) + (3*SinhIntegral(4*atanh(a*x)))/(4*a) + (3*SinhIntegral(6*atanh(a*x)))/(16*a)]

    @test_int [x/((1 - a^2*x^2)^4*atanh(a*x)^3), x, 22, -(x/(2*a*(1 - a^2*x^2)^3*atanh(a*x)^2)) - 3/(a^2*(1 - a^2*x^2)^3*atanh(a*x)) + 5/(2*a^2*(1 - a^2*x^2)^2*atanh(a*x)) + (5*SinhIntegral(2*atanh(a*x)))/(16*a^2) + SinhIntegral(4*atanh(a*x))/a^2 + (9*SinhIntegral(6*atanh(a*x)))/(16*a^2)]
    @test_int [1/((1 - a^2*x^2)^4*atanh(a*x)^3), x, 14, -(1/(2*a*(1 - a^2*x^2)^3*atanh(a*x)^2)) - (3*x)/((1 - a^2*x^2)^3*atanh(a*x)) + (15*CoshIntegral(2*atanh(a*x)))/(16*a) + (3*CoshIntegral(4*atanh(a*x)))/(2*a) + (9*CoshIntegral(6*atanh(a*x)))/(16*a)]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*atanh(c*x)^p / (1-c^2*x^2)^(1/2)=#

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

    @test_int [x^5*atanh(a*x)/(1 - a^2*x^2)^(1/2), x, 9, -((5*x*sqrt(1 - a^2*x^2))/(24*a^5)) - (x^3*sqrt(1 - a^2*x^2))/(20*a^3) + (89*asin(a*x))/(120*a^6) - (8*sqrt(1 - a^2*x^2)*atanh(a*x))/(15*a^6) - (4*x^2*sqrt(1 - a^2*x^2)*atanh(a*x))/(15*a^4) - (x^4*sqrt(1 - a^2*x^2)*atanh(a*x))/(5*a^2)]
    @test_int [x^4*atanh(a*x)/(1 - a^2*x^2)^(1/2), x, 7, -((5*sqrt(1 - a^2*x^2))/(8*a^5)) + (1 - a^2*x^2)^(3/2)/(12*a^5) - (3*x*sqrt(1 - a^2*x^2)*atanh(a*x))/(8*a^4) - (x^3*sqrt(1 - a^2*x^2)*atanh(a*x))/(4*a^2) - (3*atan(sqrt(1 - a*x)/sqrt(1 + a*x))*atanh(a*x))/(4*a^5) - (3*im*PolyLog(2, -((im*sqrt(1 - a*x))/sqrt(1 + a*x))))/(8*a^5) + (3*im*PolyLog(2, (im*sqrt(1 - a*x))/sqrt(1 + a*x)))/(8*a^5)]
    @test_int [x^3*atanh(a*x)/(1 - a^2*x^2)^(1/2), x, 5, -((x*sqrt(1 - a^2*x^2))/(6*a^3)) + (5*asin(a*x))/(6*a^4) - (2*sqrt(1 - a^2*x^2)*atanh(a*x))/(3*a^4) - (x^2*sqrt(1 - a^2*x^2)*atanh(a*x))/(3*a^2)]
    @test_int [x^2*atanh(a*x)/(1 - a^2*x^2)^(1/2), x, 3, -(sqrt(1 - a^2*x^2)/(2*a^3)) - (x*sqrt(1 - a^2*x^2)*atanh(a*x))/(2*a^2) - (atan(sqrt(1 - a*x)/sqrt(1 + a*x))*atanh(a*x))/a^3 - (im*PolyLog(2, -((im*sqrt(1 - a*x))/sqrt(1 + a*x))))/(2*a^3) + (im*PolyLog(2, (im*sqrt(1 - a*x))/sqrt(1 + a*x)))/(2*a^3)]
    @test_int [x^1*atanh(a*x)/(1 - a^2*x^2)^(1/2), x, 2, asin(a*x)/a^2 - (sqrt(1 - a^2*x^2)*atanh(a*x))/a^2]
    @test_int [x^0*atanh(a*x)/(1 - a^2*x^2)^(1/2), x, 1, -((2*atan(sqrt(1 - a*x)/sqrt(1 + a*x))*atanh(a*x))/a) - (im*PolyLog(2, -((im*sqrt(1 - a*x))/sqrt(1 + a*x))))/a + (im*PolyLog(2, (im*sqrt(1 - a*x))/sqrt(1 + a*x)))/a]
    @test_int [atanh(a*x)/(x^1*(1 - a^2*x^2)^(1/2)), x, 1, -2*atanh(a*x)*atanh(sqrt(1 - a*x)/sqrt(1 + a*x)) + PolyLog(2, -(sqrt(1 - a*x)/sqrt(1 + a*x))) - PolyLog(2, sqrt(1 - a*x)/sqrt(1 + a*x))]
    @test_int [atanh(a*x)/(x^2*(1 - a^2*x^2)^(1/2)), x, 4, -((sqrt(1 - a^2*x^2)*atanh(a*x))/x) - a*atanh(sqrt(1 - a^2*x^2))]
    @test_int [atanh(a*x)/(x^3*(1 - a^2*x^2)^(1/2)), x, 3, -((a*sqrt(1 - a^2*x^2))/(2*x)) - (sqrt(1 - a^2*x^2)*atanh(a*x))/(2*x^2) - a^2*atanh(a*x)*atanh(sqrt(1 - a*x)/sqrt(1 + a*x)) + (1/2)*a^2*PolyLog(2, -(sqrt(1 - a*x)/sqrt(1 + a*x))) - (1/2)*a^2*PolyLog(2, sqrt(1 - a*x)/sqrt(1 + a*x))]

    @test_int [x^3*atanh(a*x)^2/(1 - a^2*x^2)^(1/2), x, 6, -(sqrt(1 - a^2*x^2)/(3*a^4)) - (x*sqrt(1 - a^2*x^2)*atanh(a*x))/(3*a^3) - (10*atan(sqrt(1 - a*x)/sqrt(1 + a*x))*atanh(a*x))/(3*a^4) - (2*sqrt(1 - a^2*x^2)*atanh(a*x)^2)/(3*a^4) - (x^2*sqrt(1 - a^2*x^2)*atanh(a*x)^2)/(3*a^2) - (5*im*PolyLog(2, -((im*sqrt(1 - a*x))/sqrt(1 + a*x))))/(3*a^4) + (5*im*PolyLog(2, (im*sqrt(1 - a*x))/sqrt(1 + a*x)))/(3*a^4)]
    @test_int [x^2*atanh(a*x)^2/(1 - a^2*x^2)^(1/2), x, 11, asin(a*x)/a^3 - (sqrt(1 - a^2*x^2)*atanh(a*x))/a^3 - (x*sqrt(1 - a^2*x^2)*atanh(a*x)^2)/(2*a^2) + (atan(ℯ^atanh(a*x))*atanh(a*x)^2)/a^3 - (im*atanh(a*x)*PolyLog(2, (-im)*ℯ^atanh(a*x)))/a^3 + (im*atanh(a*x)*PolyLog(2, im*ℯ^atanh(a*x)))/a^3 + (im*PolyLog(3, (-im)*ℯ^atanh(a*x)))/a^3 - (im*PolyLog(3, im*ℯ^atanh(a*x)))/a^3]
    @test_int [x^1*atanh(a*x)^2/(1 - a^2*x^2)^(1/2), x, 2, -((4*atan(sqrt(1 - a*x)/sqrt(1 + a*x))*atanh(a*x))/a^2) - (sqrt(1 - a^2*x^2)*atanh(a*x)^2)/a^2 - (2*im*PolyLog(2, -((im*sqrt(1 - a*x))/sqrt(1 + a*x))))/a^2 + (2*im*PolyLog(2, (im*sqrt(1 - a*x))/sqrt(1 + a*x)))/a^2]
    @test_int [x^0*atanh(a*x)^2/(1 - a^2*x^2)^(1/2), x, 8, (2*atan(ℯ^atanh(a*x))*atanh(a*x)^2)/a - (2*im*atanh(a*x)*PolyLog(2, (-im)*ℯ^atanh(a*x)))/a + (2*im*atanh(a*x)*PolyLog(2, im*ℯ^atanh(a*x)))/a + (2*im*PolyLog(3, (-im)*ℯ^atanh(a*x)))/a - (2*im*PolyLog(3, im*ℯ^atanh(a*x)))/a]
    @test_int [atanh(a*x)^2/(x^1*(1 - a^2*x^2)^(1/2)), x, 8, -2*atanh(ℯ^atanh(a*x))*atanh(a*x)^2 - 2*atanh(a*x)*PolyLog(2, -ℯ^atanh(a*x)) + 2*atanh(a*x)*PolyLog(2, ℯ^atanh(a*x)) + 2*PolyLog(3, -ℯ^atanh(a*x)) - 2*PolyLog(3, ℯ^atanh(a*x))]
    @test_int [atanh(a*x)^2/(x^2*(1 - a^2*x^2)^(1/2)), x, 2, -((sqrt(1 - a^2*x^2)*atanh(a*x)^2)/x) - 4*a*atanh(a*x)*atanh(sqrt(1 - a*x)/sqrt(1 + a*x)) + 2*a*PolyLog(2, -(sqrt(1 - a*x)/sqrt(1 + a*x))) - 2*a*PolyLog(2, sqrt(1 - a*x)/sqrt(1 + a*x))]
    @test_int [atanh(a*x)^2/(x^3*(1 - a^2*x^2)^(1/2)), x, 13, -((a*sqrt(1 - a^2*x^2)*atanh(a*x))/x) - (sqrt(1 - a^2*x^2)*atanh(a*x)^2)/(2*x^2) - a^2*atanh(ℯ^atanh(a*x))*atanh(a*x)^2 - a^2*atanh(sqrt(1 - a^2*x^2)) - a^2*atanh(a*x)*PolyLog(2, -ℯ^atanh(a*x)) + a^2*atanh(a*x)*PolyLog(2, ℯ^atanh(a*x)) + a^2*PolyLog(3, -ℯ^atanh(a*x)) - a^2*PolyLog(3, ℯ^atanh(a*x))]

    @test_int [x^3*atanh(a*x)^3/(1 - a^2*x^2)^(1/2), x, 21, asin(a*x)/a^4 - (sqrt(1 - a^2*x^2)*atanh(a*x))/a^4 - (x*sqrt(1 - a^2*x^2)*atanh(a*x)^2)/(2*a^3) + (5*atan(ℯ^atanh(a*x))*atanh(a*x)^2)/a^4 - (2*sqrt(1 - a^2*x^2)*atanh(a*x)^3)/(3*a^4) - (x^2*sqrt(1 - a^2*x^2)*atanh(a*x)^3)/(3*a^2) - (5*im*atanh(a*x)*PolyLog(2, (-im)*ℯ^atanh(a*x)))/a^4 + (5*im*atanh(a*x)*PolyLog(2, im*ℯ^atanh(a*x)))/a^4 + (5*im*PolyLog(3, (-im)*ℯ^atanh(a*x)))/a^4 - (5*im*PolyLog(3, im*ℯ^atanh(a*x)))/a^4]
    @test_int [x^2*atanh(a*x)^3/(1 - a^2*x^2)^(1/2), x, 13, -((6*atan(sqrt(1 - a*x)/sqrt(1 + a*x))*atanh(a*x))/a^3) - (3*sqrt(1 - a^2*x^2)*atanh(a*x)^2)/(2*a^3) - (x*sqrt(1 - a^2*x^2)*atanh(a*x)^3)/(2*a^2) + (atan(ℯ^atanh(a*x))*atanh(a*x)^3)/a^3 - (3*im*atanh(a*x)^2*PolyLog(2, (-im)*ℯ^atanh(a*x)))/(2*a^3) + (3*im*atanh(a*x)^2*PolyLog(2, im*ℯ^atanh(a*x)))/(2*a^3) - (3*im*PolyLog(2, -((im*sqrt(1 - a*x))/sqrt(1 + a*x))))/a^3 + (3*im*PolyLog(2, (im*sqrt(1 - a*x))/sqrt(1 + a*x)))/a^3 + (3*im*atanh(a*x)*PolyLog(3, (-im)*ℯ^atanh(a*x)))/a^3 - (3*im*atanh(a*x)*PolyLog(3, im*ℯ^atanh(a*x)))/a^3 - (3*im*PolyLog(4, (-im)*ℯ^atanh(a*x)))/a^3 + (3*im*PolyLog(4, im*ℯ^atanh(a*x)))/a^3]
    @test_int [x^1*atanh(a*x)^3/(1 - a^2*x^2)^(1/2), x, 9, (6*atan(ℯ^atanh(a*x))*atanh(a*x)^2)/a^2 - (sqrt(1 - a^2*x^2)*atanh(a*x)^3)/a^2 - (6*im*atanh(a*x)*PolyLog(2, (-im)*ℯ^atanh(a*x)))/a^2 + (6*im*atanh(a*x)*PolyLog(2, im*ℯ^atanh(a*x)))/a^2 + (6*im*PolyLog(3, (-im)*ℯ^atanh(a*x)))/a^2 - (6*im*PolyLog(3, im*ℯ^atanh(a*x)))/a^2]
    @test_int [x^0*atanh(a*x)^3/(1 - a^2*x^2)^(1/2), x, 10, (2*atan(ℯ^atanh(a*x))*atanh(a*x)^3)/a - (3*im*atanh(a*x)^2*PolyLog(2, (-im)*ℯ^atanh(a*x)))/a + (3*im*atanh(a*x)^2*PolyLog(2, im*ℯ^atanh(a*x)))/a + (6*im*atanh(a*x)*PolyLog(3, (-im)*ℯ^atanh(a*x)))/a - (6*im*atanh(a*x)*PolyLog(3, im*ℯ^atanh(a*x)))/a - (6*im*PolyLog(4, (-im)*ℯ^atanh(a*x)))/a + (6*im*PolyLog(4, im*ℯ^atanh(a*x)))/a]
    @test_int [atanh(a*x)^3/(x^1*(1 - a^2*x^2)^(1/2)), x, 10, -2*atanh(ℯ^atanh(a*x))*atanh(a*x)^3 - 3*atanh(a*x)^2*PolyLog(2, -ℯ^atanh(a*x)) + 3*atanh(a*x)^2*PolyLog(2, ℯ^atanh(a*x)) + 6*atanh(a*x)*PolyLog(3, -ℯ^atanh(a*x)) - 6*atanh(a*x)*PolyLog(3, ℯ^atanh(a*x)) - 6*PolyLog(4, -ℯ^atanh(a*x)) + 6*PolyLog(4, ℯ^atanh(a*x))]
    @test_int [atanh(a*x)^3/(x^2*(1 - a^2*x^2)^(1/2)), x, 9, -6*a*atanh(ℯ^atanh(a*x))*atanh(a*x)^2 - (sqrt(1 - a^2*x^2)*atanh(a*x)^3)/x - 6*a*atanh(a*x)*PolyLog(2, -ℯ^atanh(a*x)) + 6*a*atanh(a*x)*PolyLog(2, ℯ^atanh(a*x)) + 6*a*PolyLog(3, -ℯ^atanh(a*x)) - 6*a*PolyLog(3, ℯ^atanh(a*x))]
    @test_int [atanh(a*x)^3/(x^3*(1 - a^2*x^2)^(1/2)), x, 13, -((3*a*sqrt(1 - a^2*x^2)*atanh(a*x)^2)/(2*x)) - (sqrt(1 - a^2*x^2)*atanh(a*x)^3)/(2*x^2) - a^2*atanh(ℯ^atanh(a*x))*atanh(a*x)^3 - 6*a^2*atanh(a*x)*atanh(sqrt(1 - a*x)/sqrt(1 + a*x)) - (3/2)*a^2*atanh(a*x)^2*PolyLog(2, -ℯ^atanh(a*x)) + (3/2)*a^2*atanh(a*x)^2*PolyLog(2, ℯ^atanh(a*x)) + 3*a^2*PolyLog(2, -(sqrt(1 - a*x)/sqrt(1 + a*x))) - 3*a^2*PolyLog(2, sqrt(1 - a*x)/sqrt(1 + a*x)) + 3*a^2*atanh(a*x)*PolyLog(3, -ℯ^atanh(a*x)) - 3*a^2*atanh(a*x)*PolyLog(3, ℯ^atanh(a*x)) - 3*a^2*PolyLog(4, -ℯ^atanh(a*x)) + 3*a^2*PolyLog(4, ℯ^atanh(a*x))]

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

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*atanh(c*x)^p / (1-c^2*x^2)^(3/2)=#

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

    @test_int [atanh(a*x)/(1 - a^2*x^2)^(3/2)*x^m, x, 0, Unintegrable((x^m*atanh(a*x))/(1 - a^2*x^2)^(3/2), x)]

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

    @test_int [atanh(a*x)^2/(1 - a^2*x^2)^(3/2)*x^m, x, 0, Unintegrable((x^m*atanh(a*x)^2)/(1 - a^2*x^2)^(3/2), x)]

    @test_int [atanh(a*x)^2/(1 - a^2*x^2)^(3/2)*x^3, x, 5, 2/(a^4*sqrt(1 - a^2*x^2)) - (2*x*atanh(a*x))/(a^3*sqrt(1 - a^2*x^2)) + (4*atan(sqrt(1 - a*x)/sqrt(1 + a*x))*atanh(a*x))/a^4 + atanh(a*x)^2/(a^4*sqrt(1 - a^2*x^2)) + (sqrt(1 - a^2*x^2)*atanh(a*x)^2)/a^4 + (2*im*PolyLog(2, -((im*sqrt(1 - a*x))/sqrt(1 + a*x))))/a^4 - (2*im*PolyLog(2, (im*sqrt(1 - a*x))/sqrt(1 + a*x)))/a^4]
    @test_int [atanh(a*x)^2/(1 - a^2*x^2)^(3/2)*x^2, x, 11, (2*x)/(a^2*sqrt(1 - a^2*x^2)) - (2*atanh(a*x))/(a^3*sqrt(1 - a^2*x^2)) + (x*atanh(a*x)^2)/(a^2*sqrt(1 - a^2*x^2)) - (2*atan(ℯ^atanh(a*x))*atanh(a*x)^2)/a^3 + (2*im*atanh(a*x)*PolyLog(2, (-im)*ℯ^atanh(a*x)))/a^3 - (2*im*atanh(a*x)*PolyLog(2, im*ℯ^atanh(a*x)))/a^3 - (2*im*PolyLog(3, (-im)*ℯ^atanh(a*x)))/a^3 + (2*im*PolyLog(3, im*ℯ^atanh(a*x)))/a^3]
    @test_int [atanh(a*x)^2/(1 - a^2*x^2)^(3/2)*x^1, x, 2, 2/(a^2*sqrt(1 - a^2*x^2)) - (2*x*atanh(a*x))/(a*sqrt(1 - a^2*x^2)) + atanh(a*x)^2/(a^2*sqrt(1 - a^2*x^2))]
    @test_int [atanh(a*x)^2/(1 - a^2*x^2)^(3/2)*x^0, x, 2, (2*x)/sqrt(1 - a^2*x^2) - (2*atanh(a*x))/(a*sqrt(1 - a^2*x^2)) + (x*atanh(a*x)^2)/sqrt(1 - a^2*x^2)]
    @test_int [atanh(a*x)^2/(1 - a^2*x^2)^(3/2)/x^1, x, 11, 2/sqrt(1 - a^2*x^2) - (2*a*x*atanh(a*x))/sqrt(1 - a^2*x^2) + atanh(a*x)^2/sqrt(1 - a^2*x^2) - 2*atanh(ℯ^atanh(a*x))*atanh(a*x)^2 - 2*atanh(a*x)*PolyLog(2, -ℯ^atanh(a*x)) + 2*atanh(a*x)*PolyLog(2, ℯ^atanh(a*x)) + 2*PolyLog(3, -ℯ^atanh(a*x)) - 2*PolyLog(3, ℯ^atanh(a*x))]
    @test_int [atanh(a*x)^2/(1 - a^2*x^2)^(3/2)/x^2, x, 5, (2*a^2*x)/sqrt(1 - a^2*x^2) - (2*a*atanh(a*x))/sqrt(1 - a^2*x^2) + (a^2*x*atanh(a*x)^2)/sqrt(1 - a^2*x^2) - (sqrt(1 - a^2*x^2)*atanh(a*x)^2)/x - 4*a*atanh(a*x)*atanh(sqrt(1 - a*x)/sqrt(1 + a*x)) + 2*a*PolyLog(2, -(sqrt(1 - a*x)/sqrt(1 + a*x))) - 2*a*PolyLog(2, sqrt(1 - a*x)/sqrt(1 + a*x))]
    @test_int [atanh(a*x)^2/(1 - a^2*x^2)^(3/2)/x^3, x, 25, (2*a^2)/sqrt(1 - a^2*x^2) - (2*a^3*x*atanh(a*x))/sqrt(1 - a^2*x^2) - (a*sqrt(1 - a^2*x^2)*atanh(a*x))/x + (a^2*atanh(a*x)^2)/sqrt(1 - a^2*x^2) - (sqrt(1 - a^2*x^2)*atanh(a*x)^2)/(2*x^2) - 3*a^2*atanh(ℯ^atanh(a*x))*atanh(a*x)^2 - a^2*atanh(sqrt(1 - a^2*x^2)) - 3*a^2*atanh(a*x)*PolyLog(2, -ℯ^atanh(a*x)) + 3*a^2*atanh(a*x)*PolyLog(2, ℯ^atanh(a*x)) + 3*a^2*PolyLog(3, -ℯ^atanh(a*x)) - 3*a^2*PolyLog(3, ℯ^atanh(a*x))]

    @test_int [atanh(a*x)^3/(1 - a^2*x^2)^(3/2)*x^m, x, 0, Unintegrable((x^m*atanh(a*x)^3)/(1 - a^2*x^2)^(3/2), x)]

    @test_int [atanh(a*x)^3/(1 - a^2*x^2)^(3/2)*x^3, x, 13, -((6*x)/(a^3*sqrt(1 - a^2*x^2))) + (6*atanh(a*x))/(a^4*sqrt(1 - a^2*x^2)) - (3*x*atanh(a*x)^2)/(a^3*sqrt(1 - a^2*x^2)) - (6*atan(ℯ^atanh(a*x))*atanh(a*x)^2)/a^4 + atanh(a*x)^3/(a^4*sqrt(1 - a^2*x^2)) + (sqrt(1 - a^2*x^2)*atanh(a*x)^3)/a^4 + (6*im*atanh(a*x)*PolyLog(2, (-im)*ℯ^atanh(a*x)))/a^4 - (6*im*atanh(a*x)*PolyLog(2, im*ℯ^atanh(a*x)))/a^4 - (6*im*PolyLog(3, (-im)*ℯ^atanh(a*x)))/a^4 + (6*im*PolyLog(3, im*ℯ^atanh(a*x)))/a^4]
    @test_int [atanh(a*x)^3/(1 - a^2*x^2)^(3/2)*x^2, x, 13, -(6/(a^3*sqrt(1 - a^2*x^2))) + (6*x*atanh(a*x))/(a^2*sqrt(1 - a^2*x^2)) - (3*atanh(a*x)^2)/(a^3*sqrt(1 - a^2*x^2)) + (x*atanh(a*x)^3)/(a^2*sqrt(1 - a^2*x^2)) - (2*atan(ℯ^atanh(a*x))*atanh(a*x)^3)/a^3 + (3*im*atanh(a*x)^2*PolyLog(2, (-im)*ℯ^atanh(a*x)))/a^3 - (3*im*atanh(a*x)^2*PolyLog(2, im*ℯ^atanh(a*x)))/a^3 - (6*im*atanh(a*x)*PolyLog(3, (-im)*ℯ^atanh(a*x)))/a^3 + (6*im*atanh(a*x)*PolyLog(3, im*ℯ^atanh(a*x)))/a^3 + (6*im*PolyLog(4, (-im)*ℯ^atanh(a*x)))/a^3 - (6*im*PolyLog(4, im*ℯ^atanh(a*x)))/a^3]
    @test_int [atanh(a*x)^3/(1 - a^2*x^2)^(3/2)*x^1, x, 3, -((6*x)/(a*sqrt(1 - a^2*x^2))) + (6*atanh(a*x))/(a^2*sqrt(1 - a^2*x^2)) - (3*x*atanh(a*x)^2)/(a*sqrt(1 - a^2*x^2)) + atanh(a*x)^3/(a^2*sqrt(1 - a^2*x^2))]
    @test_int [atanh(a*x)^3/(1 - a^2*x^2)^(3/2)*x^0, x, 2, -(6/(a*sqrt(1 - a^2*x^2))) + (6*x*atanh(a*x))/sqrt(1 - a^2*x^2) - (3*atanh(a*x)^2)/(a*sqrt(1 - a^2*x^2)) + (x*atanh(a*x)^3)/sqrt(1 - a^2*x^2)]
    @test_int [atanh(a*x)^3/(1 - a^2*x^2)^(3/2)/x^1, x, 14, -((6*a*x)/sqrt(1 - a^2*x^2)) + (6*atanh(a*x))/sqrt(1 - a^2*x^2) - (3*a*x*atanh(a*x)^2)/sqrt(1 - a^2*x^2) + atanh(a*x)^3/sqrt(1 - a^2*x^2) - 2*atanh(ℯ^atanh(a*x))*atanh(a*x)^3 - 3*atanh(a*x)^2*PolyLog(2, -ℯ^atanh(a*x)) + 3*atanh(a*x)^2*PolyLog(2, ℯ^atanh(a*x)) + 6*atanh(a*x)*PolyLog(3, -ℯ^atanh(a*x)) - 6*atanh(a*x)*PolyLog(3, ℯ^atanh(a*x)) - 6*PolyLog(4, -ℯ^atanh(a*x)) + 6*PolyLog(4, ℯ^atanh(a*x))]
    @test_int [atanh(a*x)^3/(1 - a^2*x^2)^(3/2)/x^2, x, 12, -((6*a)/sqrt(1 - a^2*x^2)) + (6*a^2*x*atanh(a*x))/sqrt(1 - a^2*x^2) - (3*a*atanh(a*x)^2)/sqrt(1 - a^2*x^2) - 6*a*atanh(ℯ^atanh(a*x))*atanh(a*x)^2 + (a^2*x*atanh(a*x)^3)/sqrt(1 - a^2*x^2) - (sqrt(1 - a^2*x^2)*atanh(a*x)^3)/x - 6*a*atanh(a*x)*PolyLog(2, -ℯ^atanh(a*x)) + 6*a*atanh(a*x)*PolyLog(2, ℯ^atanh(a*x)) + 6*a*PolyLog(3, -ℯ^atanh(a*x)) - 6*a*PolyLog(3, ℯ^atanh(a*x))]
    @test_int [atanh(a*x)^3/(1 - a^2*x^2)^(3/2)/x^3, x, 28, -((6*a^3*x)/sqrt(1 - a^2*x^2)) + (6*a^2*atanh(a*x))/sqrt(1 - a^2*x^2) - (3*a^3*x*atanh(a*x)^2)/sqrt(1 - a^2*x^2) - (3*a*sqrt(1 - a^2*x^2)*atanh(a*x)^2)/(2*x) + (a^2*atanh(a*x)^3)/sqrt(1 - a^2*x^2) - (sqrt(1 - a^2*x^2)*atanh(a*x)^3)/(2*x^2) - 3*a^2*atanh(ℯ^atanh(a*x))*atanh(a*x)^3 - 6*a^2*atanh(a*x)*atanh(sqrt(1 - a*x)/sqrt(1 + a*x)) - (9/2)*a^2*atanh(a*x)^2*PolyLog(2, -ℯ^atanh(a*x)) + (9/2)*a^2*atanh(a*x)^2*PolyLog(2, ℯ^atanh(a*x)) + 3*a^2*PolyLog(2, -(sqrt(1 - a*x)/sqrt(1 + a*x))) - 3*a^2*PolyLog(2, sqrt(1 - a*x)/sqrt(1 + a*x)) + 9*a^2*atanh(a*x)*PolyLog(3, -ℯ^atanh(a*x)) - 9*a^2*atanh(a*x)*PolyLog(3, ℯ^atanh(a*x)) - 9*a^2*PolyLog(4, -ℯ^atanh(a*x)) + 9*a^2*PolyLog(4, ℯ^atanh(a*x))]

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

    @test_int [1/atanh(a*x)/(1 - a^2*x^2)^(3/2)*x^m, x, 0, Unintegrable(x^m/((1 - a^2*x^2)^(3/2)*atanh(a*x)), x)]

    @test_int [1/atanh(a*x)/(1 - a^2*x^2)^(3/2)*x^2, x, 0, Unintegrable(x^2/((1 - a^2*x^2)^(3/2)*atanh(a*x)), x)]
    @test_int [1/atanh(a*x)/(1 - a^2*x^2)^(3/2)*x^1, x, 2, SinhIntegral(atanh(a*x))/a^2]
    @test_int [1/atanh(a*x)/(1 - a^2*x^2)^(3/2)*x^0, x, 2, CoshIntegral(atanh(a*x))/a]
    @test_int [1/atanh(a*x)/(1 - a^2*x^2)^(3/2)/x^1, x, 0, Unintegrable(1/(x*(1 - a^2*x^2)^(3/2)*atanh(a*x)), x)]

    @test_int [1/atanh(a*x)^2/(1 - a^2*x^2)^(3/2)*x^m, x, 0, Unintegrable(x^m/((1 - a^2*x^2)^(3/2)*atanh(a*x)^2), x)]

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

    @test_int [1/atanh(a*x)^3/(1 - a^2*x^2)^(3/2)*x^m, x, 0, Unintegrable(x^m/((1 - a^2*x^2)^(3/2)*atanh(a*x)^3), x)]

    @test_int [1/atanh(a*x)^3/(1 - a^2*x^2)^(3/2)*x^2, x, 5, -(1/(2*a^3*sqrt(1 - a^2*x^2)*atanh(a*x)^2)) - x/(2*a^2*sqrt(1 - a^2*x^2)*atanh(a*x)) + CoshIntegral(atanh(a*x))/(2*a^3) - Unintegrable(1/(sqrt(1 - a^2*x^2)*atanh(a*x)^3), x)/a^2]
    @test_int [1/atanh(a*x)^3/(1 - a^2*x^2)^(3/2)*x^1, x, 4, -(x/(2*a*sqrt(1 - a^2*x^2)*atanh(a*x)^2)) - 1/(2*a^2*sqrt(1 - a^2*x^2)*atanh(a*x)) + SinhIntegral(atanh(a*x))/(2*a^2)]
    @test_int [1/atanh(a*x)^3/(1 - a^2*x^2)^(3/2)*x^0, x, 4, -(1/(2*a*sqrt(1 - a^2*x^2)*atanh(a*x)^2)) - x/(2*sqrt(1 - a^2*x^2)*atanh(a*x)) + CoshIntegral(atanh(a*x))/(2*a)]
    @test_int [1/atanh(a*x)^3/(1 - a^2*x^2)^(3/2)/x^1, x, 6, -((a*x)/(2*sqrt(1 - a^2*x^2)*atanh(a*x)^2)) - sqrt(1 - a^2*x^2)/(2*a*x*atanh(a*x)^2) - 1/(2*sqrt(1 - a^2*x^2)*atanh(a*x)) + (1/2)*SinhIntegral(atanh(a*x)) - Unintegrable(1/(x^2*sqrt(1 - a^2*x^2)*atanh(a*x)^2), x)/(2*a)]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*atanh(c*x)^p*(1-c^2*x^2)^(1/2)=#

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

    @test_int [sqrt(1 - a^2*x^2)*atanh(a*x)*x^4, x, 11, sqrt(1 - a^2*x^2)/(16*a^5) - (7*(1 - a^2*x^2)^(3/2))/(72*a^5) + (1 - a^2*x^2)^(5/2)/(30*a^5) - (x*sqrt(1 - a^2*x^2)*atanh(a*x))/(16*a^4) - (x^3*sqrt(1 - a^2*x^2)*atanh(a*x))/(24*a^2) + (1/6)*x^5*sqrt(1 - a^2*x^2)*atanh(a*x) - (atan(sqrt(1 - a*x)/sqrt(1 + a*x))*atanh(a*x))/(8*a^5) - (im*PolyLog(2, -((im*sqrt(1 - a*x))/sqrt(1 + a*x))))/(16*a^5) + (im*PolyLog(2, (im*sqrt(1 - a*x))/sqrt(1 + a*x)))/(16*a^5)]
    @test_int [sqrt(1 - a^2*x^2)*atanh(a*x)*x^3, x, 9, (x*sqrt(1 - a^2*x^2))/(24*a^3) + (x^3*sqrt(1 - a^2*x^2))/(20*a) + (11*asin(a*x))/(120*a^4) - (2*sqrt(1 - a^2*x^2)*atanh(a*x))/(15*a^4) - (x^2*sqrt(1 - a^2*x^2)*atanh(a*x))/(15*a^2) + (1/5)*x^4*sqrt(1 - a^2*x^2)*atanh(a*x)]
    @test_int [sqrt(1 - a^2*x^2)*atanh(a*x)*x^2, x, 7, sqrt(1 - a^2*x^2)/(8*a^3) - (1 - a^2*x^2)^(3/2)/(12*a^3) - (x*sqrt(1 - a^2*x^2)*atanh(a*x))/(8*a^2) + (1/4)*x^3*sqrt(1 - a^2*x^2)*atanh(a*x) - (atan(sqrt(1 - a*x)/sqrt(1 + a*x))*atanh(a*x))/(4*a^3) - (im*PolyLog(2, -((im*sqrt(1 - a*x))/sqrt(1 + a*x))))/(8*a^3) + (im*PolyLog(2, (im*sqrt(1 - a*x))/sqrt(1 + a*x)))/(8*a^3)]
    @test_int [sqrt(1 - a^2*x^2)*atanh(a*x)*x^1, x, 3, (x*sqrt(1 - a^2*x^2))/(6*a) + asin(a*x)/(6*a^2) - ((1 - a^2*x^2)^(3/2)*atanh(a*x))/(3*a^2)]
    @test_int [sqrt(1 - a^2*x^2)*atanh(a*x)*x^0, x, 2, sqrt(1 - a^2*x^2)/(2*a) + (1/2)*x*sqrt(1 - a^2*x^2)*atanh(a*x) - (atan(sqrt(1 - a*x)/sqrt(1 + a*x))*atanh(a*x))/a - (im*PolyLog(2, -((im*sqrt(1 - a*x))/sqrt(1 + a*x))))/(2*a) + (im*PolyLog(2, (im*sqrt(1 - a*x))/sqrt(1 + a*x)))/(2*a)]
    @test_int [sqrt(1 - a^2*x^2)*atanh(a*x)/x^1, x, 3, -asin(a*x) + sqrt(1 - a^2*x^2)*atanh(a*x) - 2*atanh(a*x)*atanh(sqrt(1 - a*x)/sqrt(1 + a*x)) + PolyLog(2, -(sqrt(1 - a*x)/sqrt(1 + a*x))) - PolyLog(2, sqrt(1 - a*x)/sqrt(1 + a*x))]
    @test_int [sqrt(1 - a^2*x^2)*atanh(a*x)/x^2, x, 6, -((sqrt(1 - a^2*x^2)*atanh(a*x))/x) + 2*a*atan(sqrt(1 - a*x)/sqrt(1 + a*x))*atanh(a*x) - a*atanh(sqrt(1 - a^2*x^2)) + im*a*PolyLog(2, -((im*sqrt(1 - a*x))/sqrt(1 + a*x))) - im*a*PolyLog(2, (im*sqrt(1 - a*x))/sqrt(1 + a*x))]
    @test_int [sqrt(1 - a^2*x^2)*atanh(a*x)/x^3, x, 5, -((a*sqrt(1 - a^2*x^2))/(2*x)) - (sqrt(1 - a^2*x^2)*atanh(a*x))/(2*x^2) + a^2*atanh(a*x)*atanh(sqrt(1 - a*x)/sqrt(1 + a*x)) - (1/2)*a^2*PolyLog(2, -(sqrt(1 - a*x)/sqrt(1 + a*x))) + (1/2)*a^2*PolyLog(2, sqrt(1 - a*x)/sqrt(1 + a*x))]
    @test_int [sqrt(1 - a^2*x^2)*atanh(a*x)/x^4, x, 5, -((a*sqrt(1 - a^2*x^2))/(6*x^2)) - ((1 - a^2*x^2)^(3/2)*atanh(a*x))/(3*x^3) + (1/6)*a^3*atanh(sqrt(1 - a^2*x^2))]
    @test_int [sqrt(1 - a^2*x^2)*atanh(a*x)/x^5, x, 9, -((a*sqrt(1 - a^2*x^2))/(12*x^3)) - (a^3*sqrt(1 - a^2*x^2))/(24*x) - (sqrt(1 - a^2*x^2)*atanh(a*x))/(4*x^4) + (a^2*sqrt(1 - a^2*x^2)*atanh(a*x))/(8*x^2) + (1/4)*a^4*atanh(a*x)*atanh(sqrt(1 - a*x)/sqrt(1 + a*x)) - (1/8)*a^4*PolyLog(2, -(sqrt(1 - a*x)/sqrt(1 + a*x))) + (1/8)*a^4*PolyLog(2, sqrt(1 - a*x)/sqrt(1 + a*x))]
    @test_int [sqrt(1 - a^2*x^2)*atanh(a*x)/x^6, x, 21, -((a*sqrt(1 - a^2*x^2))/(20*x^4)) - (a^3*sqrt(1 - a^2*x^2))/(24*x^2) - (sqrt(1 - a^2*x^2)*atanh(a*x))/(5*x^5) + (a^2*sqrt(1 - a^2*x^2)*atanh(a*x))/(15*x^3) + (2*a^4*sqrt(1 - a^2*x^2)*atanh(a*x))/(15*x) + (11/120)*a^5*atanh(sqrt(1 - a^2*x^2))]
    @test_int [sqrt(1 - a^2*x^2)*atanh(a*x)/x^7, x, 14, -((a*sqrt(1 - a^2*x^2))/(30*x^5)) - (11*a^3*sqrt(1 - a^2*x^2))/(360*x^3) + (a^5*sqrt(1 - a^2*x^2))/(720*x) - (sqrt(1 - a^2*x^2)*atanh(a*x))/(6*x^6) + (a^2*sqrt(1 - a^2*x^2)*atanh(a*x))/(24*x^4) + (a^4*sqrt(1 - a^2*x^2)*atanh(a*x))/(16*x^2) + (1/8)*a^6*atanh(a*x)*atanh(sqrt(1 - a*x)/sqrt(1 + a*x)) - (1/16)*a^6*PolyLog(2, -(sqrt(1 - a*x)/sqrt(1 + a*x))) + (1/16)*a^6*PolyLog(2, sqrt(1 - a*x)/sqrt(1 + a*x))]

    @test_int [sqrt(1 - a^2*x^2)*atanh(a*x)^2*x^4, x, 45, (x*sqrt(1 - a^2*x^2))/(18*a^4) + (x^3*sqrt(1 - a^2*x^2))/(60*a^2) - (19*asin(a*x))/(360*a^5) - (sqrt(1 - a^2*x^2)*atanh(a*x))/(360*a^5) + (11*x^2*sqrt(1 - a^2*x^2)*atanh(a*x))/(180*a^3) + (x^4*sqrt(1 - a^2*x^2)*atanh(a*x))/(15*a) - (x*sqrt(1 - a^2*x^2)*atanh(a*x)^2)/(16*a^4) - (x^3*sqrt(1 - a^2*x^2)*atanh(a*x)^2)/(24*a^2) + (1/6)*x^5*sqrt(1 - a^2*x^2)*atanh(a*x)^2 + (atan(ℯ^atanh(a*x))*atanh(a*x)^2)/(8*a^5) - (im*atanh(a*x)*PolyLog(2, (-im)*ℯ^atanh(a*x)))/(8*a^5) + (im*atanh(a*x)*PolyLog(2, im*ℯ^atanh(a*x)))/(8*a^5) + (im*PolyLog(3, (-im)*ℯ^atanh(a*x)))/(8*a^5) - (im*PolyLog(3, im*ℯ^atanh(a*x)))/(8*a^5)]
    @test_int [sqrt(1 - a^2*x^2)*atanh(a*x)^2*x^3, x, 21, (11*sqrt(1 - a^2*x^2))/(60*a^4) - (1 - a^2*x^2)^(3/2)/(30*a^4) + (x*sqrt(1 - a^2*x^2)*atanh(a*x))/(12*a^3) + (x^3*sqrt(1 - a^2*x^2)*atanh(a*x))/(10*a) - (11*atan(sqrt(1 - a*x)/sqrt(1 + a*x))*atanh(a*x))/(30*a^4) - (2*sqrt(1 - a^2*x^2)*atanh(a*x)^2)/(15*a^4) - (x^2*sqrt(1 - a^2*x^2)*atanh(a*x)^2)/(15*a^2) + (1/5)*x^4*sqrt(1 - a^2*x^2)*atanh(a*x)^2 - (11*im*PolyLog(2, -((im*sqrt(1 - a*x))/sqrt(1 + a*x))))/(60*a^4) + (11*im*PolyLog(2, (im*sqrt(1 - a*x))/sqrt(1 + a*x)))/(60*a^4)]
    @test_int [sqrt(1 - a^2*x^2)*atanh(a*x)^2*x^2, x, 29, (x*sqrt(1 - a^2*x^2))/(12*a^2) - asin(a*x)/(6*a^3) + (sqrt(1 - a^2*x^2)*atanh(a*x))/(12*a^3) + (x^2*sqrt(1 - a^2*x^2)*atanh(a*x))/(6*a) - (x*sqrt(1 - a^2*x^2)*atanh(a*x)^2)/(8*a^2) + (1/4)*x^3*sqrt(1 - a^2*x^2)*atanh(a*x)^2 + (atan(ℯ^atanh(a*x))*atanh(a*x)^2)/(4*a^3) - (im*atanh(a*x)*PolyLog(2, (-im)*ℯ^atanh(a*x)))/(4*a^3) + (im*atanh(a*x)*PolyLog(2, im*ℯ^atanh(a*x)))/(4*a^3) + (im*PolyLog(3, (-im)*ℯ^atanh(a*x)))/(4*a^3) - (im*PolyLog(3, im*ℯ^atanh(a*x)))/(4*a^3)]
    @test_int [sqrt(1 - a^2*x^2)*atanh(a*x)^2*x^1, x, 3, sqrt(1 - a^2*x^2)/(3*a^2) + (x*sqrt(1 - a^2*x^2)*atanh(a*x))/(3*a) - (2*atan(sqrt(1 - a*x)/sqrt(1 + a*x))*atanh(a*x))/(3*a^2) - ((1 - a^2*x^2)^(3/2)*atanh(a*x)^2)/(3*a^2) - (im*PolyLog(2, -((im*sqrt(1 - a*x))/sqrt(1 + a*x))))/(3*a^2) + (im*PolyLog(2, (im*sqrt(1 - a*x))/sqrt(1 + a*x)))/(3*a^2)]
    @test_int [sqrt(1 - a^2*x^2)*atanh(a*x)^2*x^0, x, 10, -(asin(a*x)/a) + (sqrt(1 - a^2*x^2)*atanh(a*x))/a + (1/2)*x*sqrt(1 - a^2*x^2)*atanh(a*x)^2 + (atan(ℯ^atanh(a*x))*atanh(a*x)^2)/a - (im*atanh(a*x)*PolyLog(2, (-im)*ℯ^atanh(a*x)))/a + (im*atanh(a*x)*PolyLog(2, im*ℯ^atanh(a*x)))/a + (im*PolyLog(3, (-im)*ℯ^atanh(a*x)))/a - (im*PolyLog(3, im*ℯ^atanh(a*x)))/a]
    @test_int [sqrt(1 - a^2*x^2)*atanh(a*x)^2/x^1, x, 11, 4*atan(sqrt(1 - a*x)/sqrt(1 + a*x))*atanh(a*x) + sqrt(1 - a^2*x^2)*atanh(a*x)^2 - 2*atanh(ℯ^atanh(a*x))*atanh(a*x)^2 - 2*atanh(a*x)*PolyLog(2, -ℯ^atanh(a*x)) + 2*atanh(a*x)*PolyLog(2, ℯ^atanh(a*x)) + 2*im*PolyLog(2, -((im*sqrt(1 - a*x))/sqrt(1 + a*x))) - 2*im*PolyLog(2, (im*sqrt(1 - a*x))/sqrt(1 + a*x)) + 2*PolyLog(3, -ℯ^atanh(a*x)) - 2*PolyLog(3, ℯ^atanh(a*x))]
    @test_int [sqrt(1 - a^2*x^2)*atanh(a*x)^2/x^2, x, 11, -((sqrt(1 - a^2*x^2)*atanh(a*x)^2)/x) - 2*a*atan(ℯ^atanh(a*x))*atanh(a*x)^2 - 4*a*atanh(a*x)*atanh(sqrt(1 - a*x)/sqrt(1 + a*x)) + 2*im*a*atanh(a*x)*PolyLog(2, (-im)*ℯ^atanh(a*x)) - 2*im*a*atanh(a*x)*PolyLog(2, im*ℯ^atanh(a*x)) + 2*a*PolyLog(2, -(sqrt(1 - a*x)/sqrt(1 + a*x))) - 2*a*PolyLog(2, sqrt(1 - a*x)/sqrt(1 + a*x)) - 2*im*a*PolyLog(3, (-im)*ℯ^atanh(a*x)) + 2*im*a*PolyLog(3, im*ℯ^atanh(a*x))]
    @test_int [sqrt(1 - a^2*x^2)*atanh(a*x)^2/x^3, x, 22, -((a*sqrt(1 - a^2*x^2)*atanh(a*x))/x) - (sqrt(1 - a^2*x^2)*atanh(a*x)^2)/(2*x^2) + a^2*atanh(ℯ^atanh(a*x))*atanh(a*x)^2 - a^2*atanh(sqrt(1 - a^2*x^2)) + a^2*atanh(a*x)*PolyLog(2, -ℯ^atanh(a*x)) - a^2*atanh(a*x)*PolyLog(2, ℯ^atanh(a*x)) - a^2*PolyLog(3, -ℯ^atanh(a*x)) + a^2*PolyLog(3, ℯ^atanh(a*x))]
    @test_int [sqrt(1 - a^2*x^2)*atanh(a*x)^2/x^4, x, 6, -((a^2*sqrt(1 - a^2*x^2))/(3*x)) - (a*sqrt(1 - a^2*x^2)*atanh(a*x))/(3*x^2) - ((1 - a^2*x^2)^(3/2)*atanh(a*x)^2)/(3*x^3) + (2/3)*a^3*atanh(a*x)*atanh(sqrt(1 - a*x)/sqrt(1 + a*x)) - (1/3)*a^3*PolyLog(2, -(sqrt(1 - a*x)/sqrt(1 + a*x))) + (1/3)*a^3*PolyLog(2, sqrt(1 - a*x)/sqrt(1 + a*x))]

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

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*atanh(c*x)^p*(1-c^2*x^2)^(3/2)=#

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

    @test_int [(1 - a^2*x^2)^(3/2)*atanh(a*x)*x^4, x, 27, (3*sqrt(1 - a^2*x^2))/(128*a^5) + (1 - a^2*x^2)^(3/2)/(192*a^5) - (3*(1 - a^2*x^2)^(5/2))/(80*a^5) + (1 - a^2*x^2)^(7/2)/(56*a^5) - (3*x*sqrt(1 - a^2*x^2)*atanh(a*x))/(128*a^4) - (x^3*sqrt(1 - a^2*x^2)*atanh(a*x))/(64*a^2) + (3/16)*x^5*sqrt(1 - a^2*x^2)*atanh(a*x) - (1/8)*a^2*x^7*sqrt(1 - a^2*x^2)*atanh(a*x) - (3*atan(sqrt(1 - a*x)/sqrt(1 + a*x))*atanh(a*x))/(64*a^5) - (3*im*PolyLog(2, -((im*sqrt(1 - a*x))/sqrt(1 + a*x))))/(128*a^5) + (3*im*PolyLog(2, (im*sqrt(1 - a*x))/sqrt(1 + a*x)))/(128*a^5)]
    @test_int [(1 - a^2*x^2)^(3/2)*atanh(a*x)*x^3, x, 24, (3*x*sqrt(1 - a^2*x^2))/(112*a^3) + (23*x^3*sqrt(1 - a^2*x^2))/(840*a) - (1/42)*a*x^5*sqrt(1 - a^2*x^2) + (17*asin(a*x))/(560*a^4) - (2*sqrt(1 - a^2*x^2)*atanh(a*x))/(35*a^4) - (x^2*sqrt(1 - a^2*x^2)*atanh(a*x))/(35*a^2) + (8/35)*x^4*sqrt(1 - a^2*x^2)*atanh(a*x) - (1/7)*a^2*x^6*sqrt(1 - a^2*x^2)*atanh(a*x)]
    @test_int [(1 - a^2*x^2)^(3/2)*atanh(a*x)*x^2, x, 19, sqrt(1 - a^2*x^2)/(16*a^3) + (1 - a^2*x^2)^(3/2)/(72*a^3) - (1 - a^2*x^2)^(5/2)/(30*a^3) - (x*sqrt(1 - a^2*x^2)*atanh(a*x))/(16*a^2) + (7/24)*x^3*sqrt(1 - a^2*x^2)*atanh(a*x) - (1/6)*a^2*x^5*sqrt(1 - a^2*x^2)*atanh(a*x) - (atan(sqrt(1 - a*x)/sqrt(1 + a*x))*atanh(a*x))/(8*a^3) - (im*PolyLog(2, -((im*sqrt(1 - a*x))/sqrt(1 + a*x))))/(16*a^3) + (im*PolyLog(2, (im*sqrt(1 - a*x))/sqrt(1 + a*x)))/(16*a^3)]
    @test_int [(1 - a^2*x^2)^(3/2)*atanh(a*x)*x^1, x, 4, (3*x*sqrt(1 - a^2*x^2))/(40*a) + (x*(1 - a^2*x^2)^(3/2))/(20*a) + (3*asin(a*x))/(40*a^2) - ((1 - a^2*x^2)^(5/2)*atanh(a*x))/(5*a^2)]
    @test_int [(1 - a^2*x^2)^(3/2)*atanh(a*x)*x^0, x, 3, (3*sqrt(1 - a^2*x^2))/(8*a) + (1 - a^2*x^2)^(3/2)/(12*a) + (3/8)*x*sqrt(1 - a^2*x^2)*atanh(a*x) + (1/4)*x*(1 - a^2*x^2)^(3/2)*atanh(a*x) - (3*atan(sqrt(1 - a*x)/sqrt(1 + a*x))*atanh(a*x))/(4*a) - (3*im*PolyLog(2, -((im*sqrt(1 - a*x))/sqrt(1 + a*x))))/(8*a) + (3*im*PolyLog(2, (im*sqrt(1 - a*x))/sqrt(1 + a*x)))/(8*a)]
    @test_int [(1 - a^2*x^2)^(3/2)*atanh(a*x)/x^1, x, 7, (-(1/6))*a*x*sqrt(1 - a^2*x^2) - (7/6)*asin(a*x) + sqrt(1 - a^2*x^2)*atanh(a*x) + (1/3)*(1 - a^2*x^2)^(3/2)*atanh(a*x) - 2*atanh(a*x)*atanh(sqrt(1 - a*x)/sqrt(1 + a*x)) + PolyLog(2, -(sqrt(1 - a*x)/sqrt(1 + a*x))) - PolyLog(2, sqrt(1 - a*x)/sqrt(1 + a*x))]
    @test_int [(1 - a^2*x^2)^(3/2)*atanh(a*x)/x^2, x, 9, (-(1/2))*a*sqrt(1 - a^2*x^2) - (sqrt(1 - a^2*x^2)*atanh(a*x))/x - (1/2)*a^2*x*sqrt(1 - a^2*x^2)*atanh(a*x) + 3*a*atan(sqrt(1 - a*x)/sqrt(1 + a*x))*atanh(a*x) - a*atanh(sqrt(1 - a^2*x^2)) + (3/2)*im*a*PolyLog(2, -((im*sqrt(1 - a*x))/sqrt(1 + a*x))) - (3/2)*im*a*PolyLog(2, (im*sqrt(1 - a*x))/sqrt(1 + a*x))]
    @test_int [(1 - a^2*x^2)^(3/2)*atanh(a*x)/x^3, x, 9, -((a*sqrt(1 - a^2*x^2))/(2*x)) + a^2*asin(a*x) - a^2*sqrt(1 - a^2*x^2)*atanh(a*x) - (sqrt(1 - a^2*x^2)*atanh(a*x))/(2*x^2) + 3*a^2*atanh(a*x)*atanh(sqrt(1 - a*x)/sqrt(1 + a*x)) - (3/2)*a^2*PolyLog(2, -(sqrt(1 - a*x)/sqrt(1 + a*x))) + (3/2)*a^2*PolyLog(2, sqrt(1 - a*x)/sqrt(1 + a*x))]
    @test_int [(1 - a^2*x^2)^(3/2)*atanh(a*x)/x^4, x, 12, -((a*sqrt(1 - a^2*x^2))/(6*x^2)) + (a^2*sqrt(1 - a^2*x^2)*atanh(a*x))/x - ((1 - a^2*x^2)^(3/2)*atanh(a*x))/(3*x^3) - 2*a^3*atan(sqrt(1 - a*x)/sqrt(1 + a*x))*atanh(a*x) + (7/6)*a^3*atanh(sqrt(1 - a^2*x^2)) - im*a^3*PolyLog(2, -((im*sqrt(1 - a*x))/sqrt(1 + a*x))) + im*a^3*PolyLog(2, (im*sqrt(1 - a*x))/sqrt(1 + a*x))]
    @test_int [(1 - a^2*x^2)^(3/2)*atanh(a*x)/x^5, x, 15, -((a*sqrt(1 - a^2*x^2))/(12*x^3)) + (11*a^3*sqrt(1 - a^2*x^2))/(24*x) - (sqrt(1 - a^2*x^2)*atanh(a*x))/(4*x^4) + (5*a^2*sqrt(1 - a^2*x^2)*atanh(a*x))/(8*x^2) - (3/4)*a^4*atanh(a*x)*atanh(sqrt(1 - a*x)/sqrt(1 + a*x)) + (3/8)*a^4*PolyLog(2, -(sqrt(1 - a*x)/sqrt(1 + a*x))) - (3/8)*a^4*PolyLog(2, sqrt(1 - a*x)/sqrt(1 + a*x))]
    @test_int [(1 - a^2*x^2)^(3/2)*atanh(a*x)/x^6, x, 6, (3*a^3*sqrt(1 - a^2*x^2))/(40*x^2) - (a*(1 - a^2*x^2)^(3/2))/(20*x^4) - ((1 - a^2*x^2)^(5/2)*atanh(a*x))/(5*x^5) - (3/40)*a^5*atanh(sqrt(1 - a^2*x^2))]
    @test_int [(1 - a^2*x^2)^(3/2)*atanh(a*x)/x^7, x, 24, -((a*sqrt(1 - a^2*x^2))/(30*x^5)) + (19*a^3*sqrt(1 - a^2*x^2))/(360*x^3) + (31*a^5*sqrt(1 - a^2*x^2))/(720*x) - (sqrt(1 - a^2*x^2)*atanh(a*x))/(6*x^6) + (7*a^2*sqrt(1 - a^2*x^2)*atanh(a*x))/(24*x^4) - (a^4*sqrt(1 - a^2*x^2)*atanh(a*x))/(16*x^2) - (1/8)*a^6*atanh(a*x)*atanh(sqrt(1 - a*x)/sqrt(1 + a*x)) + (1/16)*a^6*PolyLog(2, -(sqrt(1 - a*x)/sqrt(1 + a*x))) - (1/16)*a^6*PolyLog(2, sqrt(1 - a*x)/sqrt(1 + a*x))]

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

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*atanh(c*x)^p*(1-c^2*x^2)^(p/2)=#

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

    @test_int [atanh(a*x)*(1 - a^2*x^2)^(5/2), x, 4, (5*sqrt(1 - a^2*x^2))/(16*a) + (5*(1 - a^2*x^2)^(3/2))/(72*a) + (1 - a^2*x^2)^(5/2)/(30*a) + (5/16)*x*sqrt(1 - a^2*x^2)*atanh(a*x) + (5/24)*x*(1 - a^2*x^2)^(3/2)*atanh(a*x) + (1/6)*x*(1 - a^2*x^2)^(5/2)*atanh(a*x) - (5*atan(sqrt(1 - a*x)/sqrt(1 + a*x))*atanh(a*x))/(8*a) - (5*im*PolyLog(2, -((im*sqrt(1 - a*x))/sqrt(1 + a*x))))/(16*a) + (5*im*PolyLog(2, (im*sqrt(1 - a*x))/sqrt(1 + a*x)))/(16*a)]
    @test_int [atanh(a*x)*(1 - a^2*x^2)^(3/2), x, 3, (3*sqrt(1 - a^2*x^2))/(8*a) + (1 - a^2*x^2)^(3/2)/(12*a) + (3/8)*x*sqrt(1 - a^2*x^2)*atanh(a*x) + (1/4)*x*(1 - a^2*x^2)^(3/2)*atanh(a*x) - (3*atan(sqrt(1 - a*x)/sqrt(1 + a*x))*atanh(a*x))/(4*a) - (3*im*PolyLog(2, -((im*sqrt(1 - a*x))/sqrt(1 + a*x))))/(8*a) + (3*im*PolyLog(2, (im*sqrt(1 - a*x))/sqrt(1 + a*x)))/(8*a)]
    @test_int [atanh(a*x)*(1 - a^2*x^2)^(1/2), x, 2, sqrt(1 - a^2*x^2)/(2*a) + (1/2)*x*sqrt(1 - a^2*x^2)*atanh(a*x) - (atan(sqrt(1 - a*x)/sqrt(1 + a*x))*atanh(a*x))/a - (im*PolyLog(2, -((im*sqrt(1 - a*x))/sqrt(1 + a*x))))/(2*a) + (im*PolyLog(2, (im*sqrt(1 - a*x))/sqrt(1 + a*x)))/(2*a)]
    @test_int [atanh(a*x)/(1 - a^2*x^2)^(5/2), x, 2, -(1/(9*a*(1 - a^2*x^2)^(3/2))) - 2/(3*a*sqrt(1 - a^2*x^2)) + (x*atanh(a*x))/(3*(1 - a^2*x^2)^(3/2)) + (2*x*atanh(a*x))/(3*sqrt(1 - a^2*x^2))]
    @test_int [atanh(a*x)/(1 - a^2*x^2)^(7/2), x, 3, -(1/(25*a*(1 - a^2*x^2)^(5/2))) - 4/(45*a*(1 - a^2*x^2)^(3/2)) - 8/(15*a*sqrt(1 - a^2*x^2)) + (x*atanh(a*x))/(5*(1 - a^2*x^2)^(5/2)) + (4*x*atanh(a*x))/(15*(1 - a^2*x^2)^(3/2)) + (8*x*atanh(a*x))/(15*sqrt(1 - a^2*x^2))]
    @test_int [atanh(a*x)/(1 - a^2*x^2)^(9/2), x, 4, -(1/(49*a*(1 - a^2*x^2)^(7/2))) - 6/(175*a*(1 - a^2*x^2)^(5/2)) - 8/(105*a*(1 - a^2*x^2)^(3/2)) - 16/(35*a*sqrt(1 - a^2*x^2)) + (x*atanh(a*x))/(7*(1 - a^2*x^2)^(7/2)) + (6*x*atanh(a*x))/(35*(1 - a^2*x^2)^(5/2)) + (8*x*atanh(a*x))/(35*(1 - a^2*x^2)^(3/2)) + (16*x*atanh(a*x))/(35*sqrt(1 - a^2*x^2))]

    @test_int [atanh(a*x)*(c - c*a^2*x^2)^(3/2), x, 4, (3*c*sqrt(c - a^2*c*x^2))/(8*a) + (c - a^2*c*x^2)^(3/2)/(12*a) + (3/8)*c*x*sqrt(c - a^2*c*x^2)*atanh(a*x) + (1/4)*x*(c - a^2*c*x^2)^(3/2)*atanh(a*x) - (3*c^2*sqrt(1 - a^2*x^2)*atan(sqrt(1 - a*x)/sqrt(1 + a*x))*atanh(a*x))/(4*a*sqrt(c - a^2*c*x^2)) - (3*im*c^2*sqrt(1 - a^2*x^2)*PolyLog(2, -((im*sqrt(1 - a*x))/sqrt(1 + a*x))))/(8*a*sqrt(c - a^2*c*x^2)) + (3*im*c^2*sqrt(1 - a^2*x^2)*PolyLog(2, (im*sqrt(1 - a*x))/sqrt(1 + a*x)))/(8*a*sqrt(c - a^2*c*x^2))]
    @test_int [atanh(a*x)*(c - c*a^2*x^2)^(1/2), x, 3, sqrt(c - a^2*c*x^2)/(2*a) + (1/2)*x*sqrt(c - a^2*c*x^2)*atanh(a*x) - (c*sqrt(1 - a^2*x^2)*atan(sqrt(1 - a*x)/sqrt(1 + a*x))*atanh(a*x))/(a*sqrt(c - a^2*c*x^2)) - (im*c*sqrt(1 - a^2*x^2)*PolyLog(2, -((im*sqrt(1 - a*x))/sqrt(1 + a*x))))/(2*a*sqrt(c - a^2*c*x^2)) + (im*c*sqrt(1 - a^2*x^2)*PolyLog(2, (im*sqrt(1 - a*x))/sqrt(1 + a*x)))/(2*a*sqrt(c - a^2*c*x^2))]
    @test_int [atanh(a*x)/(c - c*a^2*x^2)^(1/2), x, 2, -((2*sqrt(1 - a^2*x^2)*atan(sqrt(1 - a*x)/sqrt(1 + a*x))*atanh(a*x))/(a*sqrt(c - a^2*c*x^2))) - (im*sqrt(1 - a^2*x^2)*PolyLog(2, -((im*sqrt(1 - a*x))/sqrt(1 + a*x))))/(a*sqrt(c - a^2*c*x^2)) + (im*sqrt(1 - a^2*x^2)*PolyLog(2, (im*sqrt(1 - a*x))/sqrt(1 + a*x)))/(a*sqrt(c - a^2*c*x^2))]
    @test_int [atanh(a*x)/(c - c*a^2*x^2)^(3/2), x, 1, -(1/(a*c*sqrt(c - a^2*c*x^2))) + (x*atanh(a*x))/(c*sqrt(c - a^2*c*x^2))]
    @test_int [atanh(a*x)/(c - c*a^2*x^2)^(5/2), x, 2, -(1/(9*a*c*(c - a^2*c*x^2)^(3/2))) - 2/(3*a*c^2*sqrt(c - a^2*c*x^2)) + (x*atanh(a*x))/(3*c*(c - a^2*c*x^2)^(3/2)) + (2*x*atanh(a*x))/(3*c^2*sqrt(c - a^2*c*x^2))]
    @test_int [atanh(a*x)/(c - c*a^2*x^2)^(7/2), x, 3, -(1/(25*a*c*(c - a^2*c*x^2)^(5/2))) - 4/(45*a*c^2*(c - a^2*c*x^2)^(3/2)) - 8/(15*a*c^3*sqrt(c - a^2*c*x^2)) + (x*atanh(a*x))/(5*c*(c - a^2*c*x^2)^(5/2)) + (4*x*atanh(a*x))/(15*c^2*(c - a^2*c*x^2)^(3/2)) + (8*x*atanh(a*x))/(15*c^3*sqrt(c - a^2*c*x^2))]

    @test_int [atanh(a*x)^2*(1 - a^2*x^2)^(1/2), x, 10, -(asin(a*x)/a) + (sqrt(1 - a^2*x^2)*atanh(a*x))/a + (1/2)*x*sqrt(1 - a^2*x^2)*atanh(a*x)^2 + (atan(ℯ^atanh(a*x))*atanh(a*x)^2)/a - (im*atanh(a*x)*PolyLog(2, (-im)*ℯ^atanh(a*x)))/a + (im*atanh(a*x)*PolyLog(2, im*ℯ^atanh(a*x)))/a + (im*PolyLog(3, (-im)*ℯ^atanh(a*x)))/a - (im*PolyLog(3, im*ℯ^atanh(a*x)))/a]
    @test_int [atanh(a*x)^2/(1 - a^2*x^2)^(5/2), x, 5, (2*x)/(27*(1 - a^2*x^2)^(3/2)) + (40*x)/(27*sqrt(1 - a^2*x^2)) - (2*atanh(a*x))/(9*a*(1 - a^2*x^2)^(3/2)) - (4*atanh(a*x))/(3*a*sqrt(1 - a^2*x^2)) + (x*atanh(a*x)^2)/(3*(1 - a^2*x^2)^(3/2)) + (2*x*atanh(a*x)^2)/(3*sqrt(1 - a^2*x^2))]
    @test_int [atanh(a*x)^2/(1 - a^2*x^2)^(7/2), x, 9, (2*x)/(125*(1 - a^2*x^2)^(5/2)) + (272*x)/(3375*(1 - a^2*x^2)^(3/2)) + (4144*x)/(3375*sqrt(1 - a^2*x^2)) - (2*atanh(a*x))/(25*a*(1 - a^2*x^2)^(5/2)) - (8*atanh(a*x))/(45*a*(1 - a^2*x^2)^(3/2)) - (16*atanh(a*x))/(15*a*sqrt(1 - a^2*x^2)) + (x*atanh(a*x)^2)/(5*(1 - a^2*x^2)^(5/2)) + (4*x*atanh(a*x)^2)/(15*(1 - a^2*x^2)^(3/2)) + (8*x*atanh(a*x)^2)/(15*sqrt(1 - a^2*x^2))]
    @test_int [atanh(a*x)^2/(1 - a^2*x^2)^(9/2), x, 14, (2*x)/(343*(1 - a^2*x^2)^(7/2)) + (888*x)/(42875*(1 - a^2*x^2)^(5/2)) + (30256*x)/(385875*(1 - a^2*x^2)^(3/2)) + (413312*x)/(385875*sqrt(1 - a^2*x^2)) - (2*atanh(a*x))/(49*a*(1 - a^2*x^2)^(7/2)) - (12*atanh(a*x))/(175*a*(1 - a^2*x^2)^(5/2)) - (16*atanh(a*x))/(105*a*(1 - a^2*x^2)^(3/2)) - (32*atanh(a*x))/(35*a*sqrt(1 - a^2*x^2)) + (x*atanh(a*x)^2)/(7*(1 - a^2*x^2)^(7/2)) + (6*x*atanh(a*x)^2)/(35*(1 - a^2*x^2)^(5/2)) + (8*x*atanh(a*x)^2)/(35*(1 - a^2*x^2)^(3/2)) + (16*x*atanh(a*x)^2)/(35*sqrt(1 - a^2*x^2))]

    @test_int [atanh(a*x)^3*(1 - a^2*x^2)^(1/2), x, 12, (6*atan(sqrt(1 - a*x)/sqrt(1 + a*x))*atanh(a*x))/a + (3*sqrt(1 - a^2*x^2)*atanh(a*x)^2)/(2*a) + (1/2)*x*sqrt(1 - a^2*x^2)*atanh(a*x)^3 + (atan(ℯ^atanh(a*x))*atanh(a*x)^3)/a - (3*im*atanh(a*x)^2*PolyLog(2, (-im)*ℯ^atanh(a*x)))/(2*a) + (3*im*atanh(a*x)^2*PolyLog(2, im*ℯ^atanh(a*x)))/(2*a) + (3*im*PolyLog(2, -((im*sqrt(1 - a*x))/sqrt(1 + a*x))))/a - (3*im*PolyLog(2, (im*sqrt(1 - a*x))/sqrt(1 + a*x)))/a + (3*im*atanh(a*x)*PolyLog(3, (-im)*ℯ^atanh(a*x)))/a - (3*im*atanh(a*x)*PolyLog(3, im*ℯ^atanh(a*x)))/a - (3*im*PolyLog(4, (-im)*ℯ^atanh(a*x)))/a + (3*im*PolyLog(4, im*ℯ^atanh(a*x)))/a]
    @test_int [atanh(a*x)^3/(1 - a^2*x^2)^(5/2), x, 5, -(2/(27*a*(1 - a^2*x^2)^(3/2))) - 40/(9*a*sqrt(1 - a^2*x^2)) + (2*x*atanh(a*x))/(9*(1 - a^2*x^2)^(3/2)) + (40*x*atanh(a*x))/(9*sqrt(1 - a^2*x^2)) - atanh(a*x)^2/(3*a*(1 - a^2*x^2)^(3/2)) - (2*atanh(a*x)^2)/(a*sqrt(1 - a^2*x^2)) + (x*atanh(a*x)^3)/(3*(1 - a^2*x^2)^(3/2)) + (2*x*atanh(a*x)^3)/(3*sqrt(1 - a^2*x^2))]
    @test_int [atanh(a*x)^3/(1 - a^2*x^2)^(7/2), x, 9, -(6/(625*a*(1 - a^2*x^2)^(5/2))) - 272/(3375*a*(1 - a^2*x^2)^(3/2)) - 4144/(1125*a*sqrt(1 - a^2*x^2)) + (6*x*atanh(a*x))/(125*(1 - a^2*x^2)^(5/2)) + (272*x*atanh(a*x))/(1125*(1 - a^2*x^2)^(3/2)) + (4144*x*atanh(a*x))/(1125*sqrt(1 - a^2*x^2)) - (3*atanh(a*x)^2)/(25*a*(1 - a^2*x^2)^(5/2)) - (4*atanh(a*x)^2)/(15*a*(1 - a^2*x^2)^(3/2)) - (8*atanh(a*x)^2)/(5*a*sqrt(1 - a^2*x^2)) + (x*atanh(a*x)^3)/(5*(1 - a^2*x^2)^(5/2)) + (4*x*atanh(a*x)^3)/(15*(1 - a^2*x^2)^(3/2)) + (8*x*atanh(a*x)^3)/(15*sqrt(1 - a^2*x^2))]
    @test_int [atanh(a*x)^3/(1 - a^2*x^2)^(9/2), x, 14, -(6/(2401*a*(1 - a^2*x^2)^(7/2))) - 2664/(214375*a*(1 - a^2*x^2)^(5/2)) - 30256/(385875*a*(1 - a^2*x^2)^(3/2)) - 413312/(128625*a*sqrt(1 - a^2*x^2)) + (6*x*atanh(a*x))/(343*(1 - a^2*x^2)^(7/2)) + (2664*x*atanh(a*x))/(42875*(1 - a^2*x^2)^(5/2)) + (30256*x*atanh(a*x))/(128625*(1 - a^2*x^2)^(3/2)) + (413312*x*atanh(a*x))/(128625*sqrt(1 - a^2*x^2)) - (3*atanh(a*x)^2)/(49*a*(1 - a^2*x^2)^(7/2)) - (18*atanh(a*x)^2)/(175*a*(1 - a^2*x^2)^(5/2)) - (8*atanh(a*x)^2)/(35*a*(1 - a^2*x^2)^(3/2)) - (48*atanh(a*x)^2)/(35*a*sqrt(1 - a^2*x^2)) + (x*atanh(a*x)^3)/(7*(1 - a^2*x^2)^(7/2)) + (6*x*atanh(a*x)^3)/(35*(1 - a^2*x^2)^(5/2)) + (8*x*atanh(a*x)^3)/(35*(1 - a^2*x^2)^(3/2)) + (16*x*atanh(a*x)^3)/(35*sqrt(1 - a^2*x^2))]

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

    @test_int [(1 - a^2*x^2)^(1/2)/atanh(a*x), x, 0, Unintegrable(sqrt(1 - a^2*x^2)/atanh(a*x), x)]
    @test_int [1/(1 - a^2*x^2)^(1/2)/atanh(a*x), x, 0, Unintegrable(1/(sqrt(1 - a^2*x^2)*atanh(a*x)), x)]
    @test_int [1/(1 - a^2*x^2)^(3/2)/atanh(a*x), x, 2, CoshIntegral(atanh(a*x))/a]
    @test_int [1/(1 - a^2*x^2)^(5/2)/atanh(a*x), x, 5, (3*CoshIntegral(atanh(a*x)))/(4*a) + CoshIntegral(3*atanh(a*x))/(4*a)]
    @test_int [1/(1 - a^2*x^2)^(7/2)/atanh(a*x), x, 6, (5*CoshIntegral(atanh(a*x)))/(8*a) + (5*CoshIntegral(3*atanh(a*x)))/(16*a) + CoshIntegral(5*atanh(a*x))/(16*a)]
    @test_int [1/(1 - a^2*x^2)^(9/2)/atanh(a*x), x, 7, (35*CoshIntegral(atanh(a*x)))/(64*a) + (21*CoshIntegral(3*atanh(a*x)))/(64*a) + (7*CoshIntegral(5*atanh(a*x)))/(64*a) + CoshIntegral(7*atanh(a*x))/(64*a)]

    @test_int [(1 - a^2*x^2)^(1/2)/atanh(a*x)^2, x, 0, Unintegrable(sqrt(1 - a^2*x^2)/atanh(a*x)^2, x)]
    @test_int [1/(1 - a^2*x^2)^(1/2)/atanh(a*x)^2, x, 0, Unintegrable(1/(sqrt(1 - a^2*x^2)*atanh(a*x)^2), x)]
    @test_int [1/(1 - a^2*x^2)^(3/2)/atanh(a*x)^2, x, 3, -(1/(a*sqrt(1 - a^2*x^2)*atanh(a*x))) + SinhIntegral(atanh(a*x))/a]
    @test_int [1/(1 - a^2*x^2)^(5/2)/atanh(a*x)^2, x, 6, -(1/(a*(1 - a^2*x^2)^(3/2)*atanh(a*x))) + (3*SinhIntegral(atanh(a*x)))/(4*a) + (3*SinhIntegral(3*atanh(a*x)))/(4*a)]
    @test_int [1/(1 - a^2*x^2)^(7/2)/atanh(a*x)^2, x, 7, -(1/(a*(1 - a^2*x^2)^(5/2)*atanh(a*x))) + (5*SinhIntegral(atanh(a*x)))/(8*a) + (15*SinhIntegral(3*atanh(a*x)))/(16*a) + (5*SinhIntegral(5*atanh(a*x)))/(16*a)]
    @test_int [1/(1 - a^2*x^2)^(9/2)/atanh(a*x)^2, x, 8, -(1/(a*(1 - a^2*x^2)^(7/2)*atanh(a*x))) + (35*SinhIntegral(atanh(a*x)))/(64*a) + (63*SinhIntegral(3*atanh(a*x)))/(64*a) + (35*SinhIntegral(5*atanh(a*x)))/(64*a) + (7*SinhIntegral(7*atanh(a*x)))/(64*a)]

    @test_int [(1 - a^2*x^2)^(1/2)/atanh(a*x)^3, x, 0, Unintegrable(sqrt(1 - a^2*x^2)/atanh(a*x)^3, x)]
    @test_int [1/(1 - a^2*x^2)^(1/2)/atanh(a*x)^3, x, 0, Unintegrable(1/(sqrt(1 - a^2*x^2)*atanh(a*x)^3), x)]
    @test_int [1/(1 - a^2*x^2)^(3/2)/atanh(a*x)^3, x, 4, -(1/(2*a*sqrt(1 - a^2*x^2)*atanh(a*x)^2)) - x/(2*sqrt(1 - a^2*x^2)*atanh(a*x)) + CoshIntegral(atanh(a*x))/(2*a)]
    @test_int [1/(1 - a^2*x^2)^(5/2)/atanh(a*x)^3, x, 12, -(1/(2*a*(1 - a^2*x^2)^(3/2)*atanh(a*x)^2)) - (3*x)/(2*(1 - a^2*x^2)^(3/2)*atanh(a*x)) + (3*CoshIntegral(atanh(a*x)))/(8*a) + (9*CoshIntegral(3*atanh(a*x)))/(8*a)]
    @test_int [1/(1 - a^2*x^2)^(7/2)/atanh(a*x)^3, x, 14, -(1/(2*a*(1 - a^2*x^2)^(5/2)*atanh(a*x)^2)) - (5*x)/(2*(1 - a^2*x^2)^(5/2)*atanh(a*x)) + (5*CoshIntegral(atanh(a*x)))/(16*a) + (45*CoshIntegral(3*atanh(a*x)))/(32*a) + (25*CoshIntegral(5*atanh(a*x)))/(32*a)]
    @test_int [1/(1 - a^2*x^2)^(9/2)/atanh(a*x)^3, x, 16, -(1/(2*a*(1 - a^2*x^2)^(7/2)*atanh(a*x)^2)) - (7*x)/(2*(1 - a^2*x^2)^(7/2)*atanh(a*x)) + (35*CoshIntegral(atanh(a*x)))/(128*a) + (189*CoshIntegral(3*atanh(a*x)))/(128*a) + (175*CoshIntegral(5*atanh(a*x)))/(128*a) + (49*CoshIntegral(7*atanh(a*x)))/(128*a)]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(f+g*x)^m*(d+e*x^2)^q*(a+b*atanh(c*x))^p*with*c^2*d+e=0=#

    @test_int [(d + e*x)*(a + b*atanh(c*x))^2/(1 - c^2*x^2), x, 7, (d*(a + b*atanh(c*x))^3)/(3*b*c) - (e*(a + b*atanh(c*x))^3)/(3*b*c^2) + (e*(a + b*atanh(c*x))^2*log(2/(1 - c*x)))/c^2 + (b*e*(a + b*atanh(c*x))*PolyLog(2, 1 - 2/(1 - c*x)))/c^2 - (b^2*e*PolyLog(3, 1 - 2/(1 - c*x)))/(2*c^2)]

    #= ::Title::Closed:: =#
    #=Integrands*of*the*form*(f*x)^m*(d+e*x^2)^q*(a+b*atanh(c*x))^p=#

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

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(d+e*x^2)^q*(a+b*atanh(c*x))^p=#

    @test_int [atanh(a*x)*(c + d*x^2)^4, x, 4, (d*(420*a^6*c^3 + 378*a^4*c^2*d + 180*a^2*c*d^2 + 35*d^3)*x^2)/(630*a^7) + (d^2*(378*a^4*c^2 + 180*a^2*c*d + 35*d^2)*x^4)/(1260*a^5) + (d^3*(36*a^2*c + 7*d)*x^6)/(378*a^3) + (d^4*x^8)/(72*a) + c^4*x*atanh(a*x) + (4/3)*c^3*d*x^3*atanh(a*x) + (6/5)*c^2*d^2*x^5*atanh(a*x) + (4/7)*c*d^3*x^7*atanh(a*x) + (1/9)*d^4*x^9*atanh(a*x) + ((315*a^8*c^4 + 420*a^6*c^3*d + 378*a^4*c^2*d^2 + 180*a^2*c*d^3 + 35*d^4)*log(1 - a^2*x^2))/(630*a^9)]
    @test_int [atanh(a*x)*(c + d*x^2)^3, x, 4, (d*(35*a^4*c^2 + 21*a^2*c*d + 5*d^2)*x^2)/(70*a^5) + (d^2*(21*a^2*c + 5*d)*x^4)/(140*a^3) + (d^3*x^6)/(42*a) + c^3*x*atanh(a*x) + c^2*d*x^3*atanh(a*x) + (3/5)*c*d^2*x^5*atanh(a*x) + (1/7)*d^3*x^7*atanh(a*x) + ((35*a^6*c^3 + 35*a^4*c^2*d + 21*a^2*c*d^2 + 5*d^3)*log(1 - a^2*x^2))/(70*a^7)]
    @test_int [atanh(a*x)*(c + d*x^2)^2, x, 5, (d*(10*a^2*c + 3*d)*x^2)/(30*a^3) + (d^2*x^4)/(20*a) + c^2*x*atanh(a*x) + (2/3)*c*d*x^3*atanh(a*x) + (1/5)*d^2*x^5*atanh(a*x) + ((15*a^4*c^2 + 10*a^2*c*d + 3*d^2)*log(1 - a^2*x^2))/(30*a^5)]
    @test_int [atanh(a*x)*(c + d*x^2)^1, x, 5, (d*x^2)/(6*a) + c*x*atanh(a*x) + (1/3)*d*x^3*atanh(a*x) + ((3*a^2*c + d)*log(1 - a^2*x^2))/(6*a^3)]
    @test_int [atanh(a*x)/(c + d*x^2)^1, x, 17, -((log(1 - a*x)*log((a*(sqrt(-c) - sqrt(d)*x))/(a*sqrt(-c) - sqrt(d))))/(4*sqrt(-c)*sqrt(d))) + (log(1 + a*x)*log((a*(sqrt(-c) - sqrt(d)*x))/(a*sqrt(-c) + sqrt(d))))/(4*sqrt(-c)*sqrt(d)) - (log(1 + a*x)*log((a*(sqrt(-c) + sqrt(d)*x))/(a*sqrt(-c) - sqrt(d))))/(4*sqrt(-c)*sqrt(d)) + (log(1 - a*x)*log((a*(sqrt(-c) + sqrt(d)*x))/(a*sqrt(-c) + sqrt(d))))/(4*sqrt(-c)*sqrt(d)) - PolyLog(2, -((sqrt(d)*(1 - a*x))/(a*sqrt(-c) - sqrt(d))))/(4*sqrt(-c)*sqrt(d)) + PolyLog(2, (sqrt(d)*(1 - a*x))/(a*sqrt(-c) + sqrt(d)))/(4*sqrt(-c)*sqrt(d)) - PolyLog(2, -((sqrt(d)*(1 + a*x))/(a*sqrt(-c) - sqrt(d))))/(4*sqrt(-c)*sqrt(d)) + PolyLog(2, (sqrt(d)*(1 + a*x))/(a*sqrt(-c) + sqrt(d)))/(4*sqrt(-c)*sqrt(d))]
    @test_int [atanh(a*x)/(c + d*x^2)^2, x, If(13<11, 24, 25), (x*atanh(a*x))/(2*c*(c + d*x^2)) + (atan((sqrt(d)*x)/sqrt(c))*atanh(a*x))/(2*c^(3/2)*sqrt(d)) + (im*log((sqrt(d)*(1 - a*x))/(im*a*sqrt(c) + sqrt(d)))*log(1 - (im*sqrt(d)*x)/sqrt(c)))/(8*c^(3/2)*sqrt(d)) - (im*log(-((sqrt(d)*(1 + a*x))/(im*a*sqrt(c) - sqrt(d))))*log(1 - (im*sqrt(d)*x)/sqrt(c)))/(8*c^(3/2)*sqrt(d)) - (im*log(-((sqrt(d)*(1 - a*x))/(im*a*sqrt(c) - sqrt(d))))*log(1 + (im*sqrt(d)*x)/sqrt(c)))/(8*c^(3/2)*sqrt(d)) + (im*log((sqrt(d)*(1 + a*x))/(im*a*sqrt(c) + sqrt(d)))*log(1 + (im*sqrt(d)*x)/sqrt(c)))/(8*c^(3/2)*sqrt(d)) + (a*log(1 - a^2*x^2))/(4*c*(a^2*c + d)) - (a*log(c + d*x^2))/(4*c*(a^2*c + d)) + (im*PolyLog(2, (a*(sqrt(c) - im*sqrt(d)*x))/(a*sqrt(c) - im*sqrt(d))))/(8*c^(3/2)*sqrt(d)) - (im*PolyLog(2, (a*(sqrt(c) - im*sqrt(d)*x))/(a*sqrt(c) + im*sqrt(d))))/(8*c^(3/2)*sqrt(d)) + (im*PolyLog(2, (a*(sqrt(c) + im*sqrt(d)*x))/(a*sqrt(c) - im*sqrt(d))))/(8*c^(3/2)*sqrt(d)) - (im*PolyLog(2, (a*(sqrt(c) + im*sqrt(d)*x))/(a*sqrt(c) + im*sqrt(d))))/(8*c^(3/2)*sqrt(d))]
    @test_int [atanh(a*x)/(c + d*x^2)^3, x, 23, a/(8*c*(a^2*c + d)*(c + d*x^2)) + (x*atanh(a*x))/(4*c*(c + d*x^2)^2) + (3*x*atanh(a*x))/(8*c^2*(c + d*x^2)) + (3*atan((sqrt(d)*x)/sqrt(c))*atanh(a*x))/(8*c^(5/2)*sqrt(d)) + (3*im*log((sqrt(d)*(1 - a*x))/(im*a*sqrt(c) + sqrt(d)))*log(1 - (im*sqrt(d)*x)/sqrt(c)))/(32*c^(5/2)*sqrt(d)) - (3*im*log(-((sqrt(d)*(1 + a*x))/(im*a*sqrt(c) - sqrt(d))))*log(1 - (im*sqrt(d)*x)/sqrt(c)))/(32*c^(5/2)*sqrt(d)) - (3*im*log(-((sqrt(d)*(1 - a*x))/(im*a*sqrt(c) - sqrt(d))))*log(1 + (im*sqrt(d)*x)/sqrt(c)))/(32*c^(5/2)*sqrt(d)) + (3*im*log((sqrt(d)*(1 + a*x))/(im*a*sqrt(c) + sqrt(d)))*log(1 + (im*sqrt(d)*x)/sqrt(c)))/(32*c^(5/2)*sqrt(d)) + (a*(5*a^2*c + 3*d)*log(1 - a^2*x^2))/(16*c^2*(a^2*c + d)^2) - (a*(5*a^2*c + 3*d)*log(c + d*x^2))/(16*c^2*(a^2*c + d)^2) + (3*im*PolyLog(2, (a*(sqrt(c) - im*sqrt(d)*x))/(a*sqrt(c) - im*sqrt(d))))/(32*c^(5/2)*sqrt(d)) - (3*im*PolyLog(2, (a*(sqrt(c) - im*sqrt(d)*x))/(a*sqrt(c) + im*sqrt(d))))/(32*c^(5/2)*sqrt(d)) + (3*im*PolyLog(2, (a*(sqrt(c) + im*sqrt(d)*x))/(a*sqrt(c) - im*sqrt(d))))/(32*c^(5/2)*sqrt(d)) - (3*im*PolyLog(2, (a*(sqrt(c) + im*sqrt(d)*x))/(a*sqrt(c) + im*sqrt(d))))/(32*c^(5/2)*sqrt(d))]

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

    @test_int [atanh(b*x)/(1 - x^2), x, 17, (1/4)*log(-((b*(1 - x))/(1 - b)))*log(1 - b*x) - (1/4)*log((b*(1 + x))/(1 + b))*log(1 - b*x) - (1/4)*log((b*(1 - x))/(1 + b))*log(1 + b*x) + (1/4)*log(-((b*(1 + x))/(1 - b)))*log(1 + b*x) + (1/4)*PolyLog(2, (1 - b*x)/(1 - b)) - (1/4)*PolyLog(2, (1 - b*x)/(1 + b)) + (1/4)*PolyLog(2, (1 + b*x)/(1 - b)) - (1/4)*PolyLog(2, (1 + b*x)/(1 + b))]
    @test_int [atanh(a+b*x)/(1 - x^2), x, 17, (1/4)*log(-((b*(1 - x))/(1 - a - b)))*log(1 - a - b*x) - (1/4)*log((b*(1 + x))/(1 - a + b))*log(1 - a - b*x) - (1/4)*log((b*(1 - x))/(1 + a + b))*log(1 + a + b*x) + (1/4)*log(-((b*(1 + x))/(1 + a - b)))*log(1 + a + b*x) + (1/4)*PolyLog(2, (1 - a - b*x)/(1 - a - b)) - (1/4)*PolyLog(2, (1 - a - b*x)/(1 - a + b)) + (1/4)*PolyLog(2, (1 + a + b*x)/(1 + a - b)) - (1/4)*PolyLog(2, (1 + a + b*x)/(1 + a + b))]

    @test_int [atanh(x)/(a + b*x), x, 4, -((atanh(x)*log(2/(1 + x)))/b) + (atanh(x)*log((2*(a + b*x))/((a + b)*(1 + x))))/b + PolyLog(2, 1 - 2/(1 + x))/(2*b) - PolyLog(2, 1 - (2*(a + b*x))/((a + b)*(1 + x)))/(2*b)]
    @test_int [atanh(x)/(a + b*x^2), x, 17, -((log(1 - x)*log((sqrt(-a) - sqrt(b)*x)/(sqrt(-a) - sqrt(b))))/(4*sqrt(-a)*sqrt(b))) + (log(1 + x)*log((sqrt(-a) - sqrt(b)*x)/(sqrt(-a) + sqrt(b))))/(4*sqrt(-a)*sqrt(b)) - (log(1 + x)*log((sqrt(-a) + sqrt(b)*x)/(sqrt(-a) - sqrt(b))))/(4*sqrt(-a)*sqrt(b)) + (log(1 - x)*log((sqrt(-a) + sqrt(b)*x)/(sqrt(-a) + sqrt(b))))/(4*sqrt(-a)*sqrt(b)) - PolyLog(2, -((sqrt(b)*(1 - x))/(sqrt(-a) - sqrt(b))))/(4*sqrt(-a)*sqrt(b)) + PolyLog(2, (sqrt(b)*(1 - x))/(sqrt(-a) + sqrt(b)))/(4*sqrt(-a)*sqrt(b)) - PolyLog(2, -((sqrt(b)*(1 + x))/(sqrt(-a) - sqrt(b))))/(4*sqrt(-a)*sqrt(b)) + PolyLog(2, (sqrt(b)*(1 + x))/(sqrt(-a) + sqrt(b)))/(4*sqrt(-a)*sqrt(b))]
    @test_int [atanh(x)/(a + b*x + c*x^2), x, 10, (atanh(x)*log((2*(b - sqrt(b^2 - 4*a*c) + 2*c*x))/((b + 2*c - sqrt(b^2 - 4*a*c))*(1 + x))))/sqrt(b^2 - 4*a*c) - (atanh(x)*log((2*(b + sqrt(b^2 - 4*a*c) + 2*c*x))/((b + 2*c + sqrt(b^2 - 4*a*c))*(1 + x))))/sqrt(b^2 - 4*a*c) - PolyLog(2, 1 - (2*(b - sqrt(b^2 - 4*a*c) + 2*c*x))/((b + 2*c - sqrt(b^2 - 4*a*c))*(1 + x)))/(2*sqrt(b^2 - 4*a*c)) + PolyLog(2, 1 - (2*(b + sqrt(b^2 - 4*a*c) + 2*c*x))/((b + 2*c + sqrt(b^2 - 4*a*c))*(1 + x)))/(2*sqrt(b^2 - 4*a*c))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(d+e*x^2)^(q/2)*(a+b*atanh(c*x))^p=#

    @test_int [atanh(a*x)*(c + d*x^2)^(1/2), x, 0, Unintegrable(sqrt(c + d*x^2)*atanh(a*x), x)]
    @test_int [atanh(a*x)/(c + d*x^2)^(1/2), x, 0, Unintegrable(atanh(a*x)/sqrt(c + d*x^2), x)]
    @test_int [atanh(a*x)/(c + d*x^2)^(3/2), x, 5, (x*atanh(a*x))/(c*sqrt(c + d*x^2)) - atanh((a*sqrt(c + d*x^2))/sqrt(a^2*c + d))/(c*sqrt(a^2*c + d))]
    @test_int [atanh(a*x)/(c + d*x^2)^(5/2), x, 7, a/(3*c*(a^2*c + d)*sqrt(c + d*x^2)) + (x*atanh(a*x))/(3*c*(c + d*x^2)^(3/2)) + (2*x*atanh(a*x))/(3*c^2*sqrt(c + d*x^2)) - ((3*a^2*c + 2*d)*atanh((a*sqrt(c + d*x^2))/sqrt(a^2*c + d)))/(3*c^2*(a^2*c + d)^(3/2))]
    @test_int [atanh(a*x)/(c + d*x^2)^(7/2), x, 8, a/(15*c*(a^2*c + d)*(c + d*x^2)^(3/2)) + (a*(7*a^2*c + 4*d))/(15*c^2*(a^2*c + d)^2*sqrt(c + d*x^2)) + (x*atanh(a*x))/(5*c*(c + d*x^2)^(5/2)) + (4*x*atanh(a*x))/(15*c^2*(c + d*x^2)^(3/2)) + (8*x*atanh(a*x))/(15*c^3*sqrt(c + d*x^2)) - ((15*a^4*c^2 + 20*a^2*c*d + 8*d^2)*atanh((a*sqrt(c + d*x^2))/sqrt(a^2*c + d)))/(15*c^3*(a^2*c + d)^(5/2))]
    @test_int [atanh(a*x)/(c + d*x^2)^(9/2), x, 8, a/(35*c*(a^2*c + d)*(c + d*x^2)^(5/2)) + (a*(11*a^2*c + 6*d))/(105*c^2*(a^2*c + d)^2*(c + d*x^2)^(3/2)) + (a*(19*a^4*c^2 + 22*a^2*c*d + 8*d^2))/(35*c^3*(a^2*c + d)^3*sqrt(c + d*x^2)) + (x*atanh(a*x))/(7*c*(c + d*x^2)^(7/2)) + (6*x*atanh(a*x))/(35*c^2*(c + d*x^2)^(5/2)) + (8*x*atanh(a*x))/(35*c^3*(c + d*x^2)^(3/2)) + (16*x*atanh(a*x))/(35*c^4*sqrt(c + d*x^2)) - ((35*a^6*c^3 + 70*a^4*c^2*d + 56*a^2*c*d^2 + 16*d^3)*atanh((a*sqrt(c + d*x^2))/sqrt(a^2*c + d)))/(35*c^4*(a^2*c + d)^(7/2))]

    @test_int [atanh(x)*(a - a*x^2)^(1/2), x, 3, (1/2)*sqrt(a - a*x^2) + (1/2)*x*sqrt(a - a*x^2)*atanh(x) - (a*sqrt(1 - x^2)*atan(sqrt(1 - x)/sqrt(1 + x))*atanh(x))/sqrt(a - a*x^2) - (im*a*sqrt(1 - x^2)*PolyLog(2, -((im*sqrt(1 - x))/sqrt(1 + x))))/(2*sqrt(a - a*x^2)) + (im*a*sqrt(1 - x^2)*PolyLog(2, (im*sqrt(1 - x))/sqrt(1 + x)))/(2*sqrt(a - a*x^2))]
    @test_int [atanh(x)/(a - a*x^2)^(1/2), x, 2, -((2*sqrt(1 - x^2)*atan(sqrt(1 - x)/sqrt(1 + x))*atanh(x))/sqrt(a - a*x^2)) - (im*sqrt(1 - x^2)*PolyLog(2, -((im*sqrt(1 - x))/sqrt(1 + x))))/sqrt(a - a*x^2) + (im*sqrt(1 - x^2)*PolyLog(2, (im*sqrt(1 - x))/sqrt(1 + x)))/sqrt(a - a*x^2)]
    @test_int [atanh(x)/(a - a*x^2)^(3/2), x, 1, -(1/(a*sqrt(a - a*x^2))) + (x*atanh(x))/(a*sqrt(a - a*x^2))]
    @test_int [atanh(x)/(a - a*x^2)^(5/2), x, 2, -(1/(9*a*(a - a*x^2)^(3/2))) - 2/(3*a^2*sqrt(a - a*x^2)) + (x*atanh(x))/(3*a*(a - a*x^2)^(3/2)) + (2*x*atanh(x))/(3*a^2*sqrt(a - a*x^2))]
    @test_int [atanh(x)/(a - a*x^2)^(7/2), x, 3, -(1/(25*a*(a - a*x^2)^(5/2))) - 4/(45*a^2*(a - a*x^2)^(3/2)) - 8/(15*a^3*sqrt(a - a*x^2)) + (x*atanh(x))/(5*a*(a - a*x^2)^(5/2)) + (4*x*atanh(x))/(15*a^2*(a - a*x^2)^(3/2)) + (8*x*atanh(x))/(15*a^3*sqrt(a - a*x^2))]

    #= ::Title::Closed:: =#
    #=Integrands*of*the*form*(h*x)^m*(d+e*log(f+g*x^2))*(a+b*atanh(c*x))^p=#

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*x^m*(d+e*log(f+g*x^2))*(a+b*atanh(c*x))=#

    @test_int [x^4*(a + b*atanh(c*x))*(d + e*log(1 - c^2*x^2)), x, 26, -((2*a*e*x)/(5*c^4)) - (77*b*e*x^2)/(300*c^3) - (2*a*e*x^3)/(15*c^2) - (9*b*e*x^4)/(200*c) - (2/25)*a*e*x^5 - (2*b*e*x*atanh(c*x))/(5*c^4) - (2*b*e*x^3*atanh(c*x))/(15*c^2) - (2/25)*b*e*x^5*atanh(c*x) + (b*e*atanh(c*x)^2)/(5*c^5) - ((4*a + 3*b)*e*log(1 - c*x))/(20*c^5) + ((4*a - 3*b)*e*log(1 + c*x))/(20*c^5) - (23*b*e*log(1 - c^2*x^2))/(75*c^5) - (b*e*log(1 - c^2*x^2)^2)/(20*c^5) + (b*x^2*(d + e*log(1 - c^2*x^2)))/(10*c^3) + (b*x^4*(d + e*log(1 - c^2*x^2)))/(20*c) + (1/5)*x^5*(a + b*atanh(c*x))*(d + e*log(1 - c^2*x^2)) + (b*log(1 - c^2*x^2)*(d + e*log(1 - c^2*x^2)))/(10*c^5)]
    @test_int [x^3*(a + b*atanh(c*x))*(d + e*log(1 - c^2*x^2)), x, 14, (b*(2*d - 3*e)*x)/(8*c^3) - (2*b*e*x)/(3*c^3) + (b*(2*d - e)*x^3)/(24*c) - (b*e*x^3)/(18*c) - (b*(2*d - 3*e)*atanh(c*x))/(8*c^4) + (2*b*e*atanh(c*x))/(3*c^4) - (e*x^2*(a + b*atanh(c*x)))/(4*c^2) - (1/8)*e*x^4*(a + b*atanh(c*x)) + (b*e*x*log(1 - c^2*x^2))/(4*c^3) + (b*e*x^3*log(1 - c^2*x^2))/(12*c) - (e*(a + b*atanh(c*x))*log(1 - c^2*x^2))/(4*c^4) + (1/4)*x^4*(a + b*atanh(c*x))*(d + e*log(1 - c^2*x^2))]
    @test_int [x^2*(a + b*atanh(c*x))*(d + e*log(1 - c^2*x^2)), x, 21, -((2*a*e*x)/(3*c^2)) - (5*b*e*x^2)/(18*c) - (2/9)*a*e*x^3 - (2*b*e*x*atanh(c*x))/(3*c^2) - (2/9)*b*e*x^3*atanh(c*x) + (b*e*atanh(c*x)^2)/(3*c^3) - ((2*a + b)*e*log(1 - c*x))/(6*c^3) + ((2*a - b)*e*log(1 + c*x))/(6*c^3) - (4*b*e*log(1 - c^2*x^2))/(9*c^3) - (b*e*log(1 - c^2*x^2)^2)/(12*c^3) + (b*x^2*(d + e*log(1 - c^2*x^2)))/(6*c) + (1/3)*x^3*(a + b*atanh(c*x))*(d + e*log(1 - c^2*x^2)) + (b*log(1 - c^2*x^2)*(d + e*log(1 - c^2*x^2)))/(6*c^3)]
    @test_int [x^1*(a + b*atanh(c*x))*(d + e*log(1 - c^2*x^2)), x, 7, (b*(d - e)*x)/(2*c) - (b*e*x)/c - (b*(d - e)*atanh(c*x))/(2*c^2) + (b*e*atanh(c*x))/c^2 + (1/2)*d*x^2*(a + b*atanh(c*x)) - (1/2)*e*x^2*(a + b*atanh(c*x)) + (b*e*x*log(1 - c^2*x^2))/(2*c) - (e*(1 - c^2*x^2)*(a + b*atanh(c*x))*log(1 - c^2*x^2))/(2*c^2)]
    @test_int [x^0*(a + b*atanh(c*x))*(d + e*log(1 - c^2*x^2)), x, 9, -2*a*e*x - 2*b*e*x*atanh(c*x) + (e*(a + b*atanh(c*x))^2)/(b*c) - (b*e*log(1 - c^2*x^2))/c + x*(a + b*atanh(c*x))*(d + e*log(1 - c^2*x^2)) + (b*(d + e*log(1 - c^2*x^2))^2)/(4*c*e)]
    @test_int [(a + b*atanh(c*x))*(d + e*log(1 - c^2*x^2))/x^1, x, 14, a*d*log(x) - (1/2)*b*e*log(c*x)*log(1 - c*x)^2 + (1/2)*b*e*log((-c)*x)*log(1 + c*x)^2 - (1/2)*b*d*PolyLog(2, (-c)*x) + (1/2)*b*e*(log(1 - c*x) + log(1 + c*x) - log(1 - c^2*x^2))*PolyLog(2, (-c)*x) + (1/2)*b*d*PolyLog(2, c*x) - (1/2)*b*e*(log(1 - c*x) + log(1 + c*x) - log(1 - c^2*x^2))*PolyLog(2, c*x) - (1/2)*a*e*PolyLog(2, c^2*x^2) - b*e*log(1 - c*x)*PolyLog(2, 1 - c*x) + b*e*log(1 + c*x)*PolyLog(2, 1 + c*x) + b*e*PolyLog(3, 1 - c*x) - b*e*PolyLog(3, 1 + c*x)]
    @test_int [(a + b*atanh(c*x))*(d + e*log(1 - c^2*x^2))/x^2, x, 6, -((c*e*(a + b*atanh(c*x))^2)/b) - ((a + b*atanh(c*x))*(d + e*log(1 - c^2*x^2)))/x + (1/2)*b*c*(d + e*log(1 - c^2*x^2))*log(1 - 1/(1 - c^2*x^2)) - (1/2)*b*c*e*PolyLog(2, 1/(1 - c^2*x^2))]
    @test_int [(a + b*atanh(c*x))*(d + e*log(1 - c^2*x^2))/x^3, x, 5, (-a)*c^2*e*log(x) + (1/2)*(a + b)*c^2*e*log(1 - c*x) + (1/2)*(a - b)*c^2*e*log(1 + c*x) - (b*c*(d + e*log(1 - c^2*x^2)))/(2*x) + (1/2)*b*c^2*atanh(c*x)*(d + e*log(1 - c^2*x^2)) - ((a + b*atanh(c*x))*(d + e*log(1 - c^2*x^2)))/(2*x^2) + (1/2)*b*c^2*e*PolyLog(2, (-c)*x) - (1/2)*b*c^2*e*PolyLog(2, c*x)]
    @test_int [(a + b*atanh(c*x))*(d + e*log(1 - c^2*x^2))/x^4, x, 15, (2*c^2*e*(a + b*atanh(c*x)))/(3*x) - (c^3*e*(a + b*atanh(c*x))^2)/(3*b) - b*c^3*e*log(x) + (1/3)*b*c^3*e*log(1 - c^2*x^2) - (b*c*(1 - c^2*x^2)*(d + e*log(1 - c^2*x^2)))/(6*x^2) - ((a + b*atanh(c*x))*(d + e*log(1 - c^2*x^2)))/(3*x^3) + (1/6)*b*c^3*(d + e*log(1 - c^2*x^2))*log(1 - 1/(1 - c^2*x^2)) - (1/6)*b*c^3*e*PolyLog(2, 1/(1 - c^2*x^2))]
    @test_int [(a + b*atanh(c*x))*(d + e*log(1 - c^2*x^2))/x^5, x, 10, (a*c^2*e)/(4*x^2) + (5*b*c^3*e)/(12*x) - (1/4)*b*c^4*e*atanh(c*x) + (b*c^2*e*atanh(c*x))/(4*x^2) - (1/2)*a*c^4*e*log(x) + (1/12)*(3*a + 4*b)*c^4*e*log(1 - c*x) + (1/12)*(3*a - 4*b)*c^4*e*log(1 + c*x) - (b*c*(d + e*log(1 - c^2*x^2)))/(12*x^3) - (b*c^3*(d + e*log(1 - c^2*x^2)))/(4*x) + (1/4)*b*c^4*atanh(c*x)*(d + e*log(1 - c^2*x^2)) - ((a + b*atanh(c*x))*(d + e*log(1 - c^2*x^2)))/(4*x^4) + (1/4)*b*c^4*e*PolyLog(2, (-c)*x) - (1/4)*b*c^4*e*PolyLog(2, c*x)]
    @test_int [(a + b*atanh(c*x))*(d + e*log(1 - c^2*x^2))/x^6, x, 24, (7*b*c^3*e)/(60*x^2) + (2*c^2*e*(a + b*atanh(c*x)))/(15*x^3) + (2*c^4*e*(a + b*atanh(c*x)))/(5*x) - (c^5*e*(a + b*atanh(c*x))^2)/(5*b) - (5/6)*b*c^5*e*log(x) + (19/60)*b*c^5*e*log(1 - c^2*x^2) - (b*c*(d + e*log(1 - c^2*x^2)))/(20*x^4) - (b*c^3*(1 - c^2*x^2)*(d + e*log(1 - c^2*x^2)))/(10*x^2) - ((a + b*atanh(c*x))*(d + e*log(1 - c^2*x^2)))/(5*x^5) + (1/10)*b*c^5*(d + e*log(1 - c^2*x^2))*log(1 - 1/(1 - c^2*x^2)) - (1/10)*b*c^5*e*PolyLog(2, 1/(1 - c^2*x^2))]

    @test_int [x^1*(a + b*atanh(c*x))*(d + e*log(f + g*x^2)), x, If(13<11, 21, 22), (b*(d - e)*x)/(2*c) - (b*e*x)/c + (b*e*sqrt(f)*atan((sqrt(g)*x)/sqrt(f)))/(c*sqrt(g)) - (b*(d - e)*atanh(c*x))/(2*c^2) + (1/2)*d*x^2*(a + b*atanh(c*x)) - (1/2)*e*x^2*(a + b*atanh(c*x)) - (b*e*(c^2*f + g)*atanh(c*x)*log(2/(1 + c*x)))/(c^2*g) + (b*e*(c^2*f + g)*atanh(c*x)*log((2*c*(sqrt(-f) - sqrt(g)*x))/((c*sqrt(-f) - sqrt(g))*(1 + c*x))))/(2*c^2*g) + (b*e*(c^2*f + g)*atanh(c*x)*log((2*c*(sqrt(-f) + sqrt(g)*x))/((c*sqrt(-f) + sqrt(g))*(1 + c*x))))/(2*c^2*g) + (b*e*x*log(f + g*x^2))/(2*c) - (b*e*(c^2*f + g)*atanh(c*x)*log(f + g*x^2))/(2*c^2*g) + (e*(f + g*x^2)*(a + b*atanh(c*x))*log(f + g*x^2))/(2*g) + (b*e*(c^2*f + g)*PolyLog(2, 1 - 2/(1 + c*x)))/(2*c^2*g) - (b*e*(c^2*f + g)*PolyLog(2, 1 - (2*c*(sqrt(-f) - sqrt(g)*x))/((c*sqrt(-f) - sqrt(g))*(1 + c*x))))/(4*c^2*g) - (b*e*(c^2*f + g)*PolyLog(2, 1 - (2*c*(sqrt(-f) + sqrt(g)*x))/((c*sqrt(-f) + sqrt(g))*(1 + c*x))))/(4*c^2*g)]
    @test_int [x^0*(a + b*atanh(c*x))*(d + e*log(f + g*x^2)), x, 28, -2*a*e*x + (2*a*e*sqrt(f)*atan((sqrt(g)*x)/sqrt(f)))/sqrt(g) - 2*b*e*x*atanh(c*x) + (b*e*sqrt(-f)*log(1 - c*x)*log((c*(sqrt(-f) - sqrt(g)*x))/(c*sqrt(-f) - sqrt(g))))/(2*sqrt(g)) - (b*e*sqrt(-f)*log(1 + c*x)*log((c*(sqrt(-f) - sqrt(g)*x))/(c*sqrt(-f) + sqrt(g))))/(2*sqrt(g)) + (b*e*sqrt(-f)*log(1 + c*x)*log((c*(sqrt(-f) + sqrt(g)*x))/(c*sqrt(-f) - sqrt(g))))/(2*sqrt(g)) - (b*e*sqrt(-f)*log(1 - c*x)*log((c*(sqrt(-f) + sqrt(g)*x))/(c*sqrt(-f) + sqrt(g))))/(2*sqrt(g)) - (b*e*log(1 - c^2*x^2))/c + x*(a + b*atanh(c*x))*(d + e*log(f + g*x^2)) + (b*log((g*(1 - c^2*x^2))/(c^2*f + g))*(d + e*log(f + g*x^2)))/(2*c) + (b*e*sqrt(-f)*PolyLog(2, -((sqrt(g)*(1 - c*x))/(c*sqrt(-f) - sqrt(g)))))/(2*sqrt(g)) - (b*e*sqrt(-f)*PolyLog(2, (sqrt(g)*(1 - c*x))/(c*sqrt(-f) + sqrt(g))))/(2*sqrt(g)) + (b*e*sqrt(-f)*PolyLog(2, -((sqrt(g)*(1 + c*x))/(c*sqrt(-f) - sqrt(g)))))/(2*sqrt(g)) - (b*e*sqrt(-f)*PolyLog(2, (sqrt(g)*(1 + c*x))/(c*sqrt(-f) + sqrt(g))))/(2*sqrt(g)) + (b*e*PolyLog(2, (c^2*(f + g*x^2))/(c^2*f + g)))/(2*c)]
    @test_int [(a + b*atanh(c*x))*(d + e*log(f + g*x^2))/x^1, x, 6, b*e*CannotIntegrate((atanh(c*x)*log(f + g*x^2))/x, x) + a*d*log(x) + (1/2)*a*e*log(-((g*x^2)/f))*log(f + g*x^2) - (1/2)*b*d*PolyLog(2, (-c)*x) + (1/2)*b*d*PolyLog(2, c*x) + (1/2)*a*e*PolyLog(2, 1 + (g*x^2)/f)]
    @test_int [(a + b*atanh(c*x))*(d + e*log(f + g*x^2))/x^2, x, 28, (2*a*e*sqrt(g)*atan((sqrt(g)*x)/sqrt(f)))/sqrt(f) - (b*e*sqrt(g)*log(1 - c*x)*log((c*(sqrt(-f) - sqrt(g)*x))/(c*sqrt(-f) - sqrt(g))))/(2*sqrt(-f)) + (b*e*sqrt(g)*log(1 + c*x)*log((c*(sqrt(-f) - sqrt(g)*x))/(c*sqrt(-f) + sqrt(g))))/(2*sqrt(-f)) - (b*e*sqrt(g)*log(1 + c*x)*log((c*(sqrt(-f) + sqrt(g)*x))/(c*sqrt(-f) - sqrt(g))))/(2*sqrt(-f)) + (b*e*sqrt(g)*log(1 - c*x)*log((c*(sqrt(-f) + sqrt(g)*x))/(c*sqrt(-f) + sqrt(g))))/(2*sqrt(-f)) - ((a + b*atanh(c*x))*(d + e*log(f + g*x^2)))/x + (1/2)*b*c*log(-((g*x^2)/f))*(d + e*log(f + g*x^2)) - (1/2)*b*c*log((g*(1 - c^2*x^2))/(c^2*f + g))*(d + e*log(f + g*x^2)) - (b*e*sqrt(g)*PolyLog(2, -((sqrt(g)*(1 - c*x))/(c*sqrt(-f) - sqrt(g)))))/(2*sqrt(-f)) + (b*e*sqrt(g)*PolyLog(2, (sqrt(g)*(1 - c*x))/(c*sqrt(-f) + sqrt(g))))/(2*sqrt(-f)) - (b*e*sqrt(g)*PolyLog(2, -((sqrt(g)*(1 + c*x))/(c*sqrt(-f) - sqrt(g)))))/(2*sqrt(-f)) + (b*e*sqrt(g)*PolyLog(2, (sqrt(g)*(1 + c*x))/(c*sqrt(-f) + sqrt(g))))/(2*sqrt(-f)) - (1/2)*b*c*e*PolyLog(2, (c^2*(f + g*x^2))/(c^2*f + g)) + (1/2)*b*c*e*PolyLog(2, 1 + (g*x^2)/f)]
    @test_int [(a + b*atanh(c*x))*(d + e*log(f + g*x^2))/x^3, x, 20, (b*c*e*sqrt(g)*atan((sqrt(g)*x)/sqrt(f)))/sqrt(f) + (a*e*g*log(x))/f + (b*e*(c^2*f + g)*atanh(c*x)*log(2/(1 + c*x)))/f - (b*e*(c^2*f + g)*atanh(c*x)*log((2*c*(sqrt(-f) - sqrt(g)*x))/((c*sqrt(-f) - sqrt(g))*(1 + c*x))))/(2*f) - (b*e*(c^2*f + g)*atanh(c*x)*log((2*c*(sqrt(-f) + sqrt(g)*x))/((c*sqrt(-f) + sqrt(g))*(1 + c*x))))/(2*f) - (a*e*g*log(f + g*x^2))/(2*f) - (b*c*(d + e*log(f + g*x^2)))/(2*x) + (1/2)*b*c^2*atanh(c*x)*(d + e*log(f + g*x^2)) - ((a + b*atanh(c*x))*(d + e*log(f + g*x^2)))/(2*x^2) - (b*e*g*PolyLog(2, (-c)*x))/(2*f) + (b*e*g*PolyLog(2, c*x))/(2*f) - (b*e*(c^2*f + g)*PolyLog(2, 1 - 2/(1 + c*x)))/(2*f) + (b*e*(c^2*f + g)*PolyLog(2, 1 - (2*c*(sqrt(-f) - sqrt(g)*x))/((c*sqrt(-f) - sqrt(g))*(1 + c*x))))/(4*f) + (b*e*(c^2*f + g)*PolyLog(2, 1 - (2*c*(sqrt(-f) + sqrt(g)*x))/((c*sqrt(-f) + sqrt(g))*(1 + c*x))))/(4*f)]

    #= ::Title::Closed:: =#
    #=Integrands*of*the*form*u*(a+b*atanh(c*x))^p=#

    @test_int [atanh(c*x)*(a + b*atanh(c*x))/(1 + c*x)^2, x, 16, -((a + b)/(2*c*(1 + c*x))) + ((a + b)*atanh(c*x))/(2*c) - ((a + b)*atanh(c*x))/(c*(1 + c*x)) - (b*(1 - c*x)*atanh(c*x)^2)/(2*c*(1 + c*x)), -(a/(2*c*(1 + c*x))) - b/(2*c*(1 + c*x)) + (a*atanh(c*x))/(2*c) + (b*atanh(c*x))/(2*c) - (a*atanh(c*x))/(c*(1 + c*x)) - (b*atanh(c*x))/(c*(1 + c*x)) + (b*atanh(c*x)^2)/(2*c) - (b*atanh(c*x)^2)/(c*(1 + c*x))]
    end

max_stars_repo_path: test/7 Inverse hyperbolic functions/7.3 Inverse hyperbolic tangent/7.3.4 u (a+b arctanh(c x))^p.jl