text:
using Rubin
using Tests
using Elliptic
using HypergeometricFunctions
using Polylogarithms
using SpecialFunctions

@test integrate((b*tan(e+f*x)^2)^5//2, x) == :(-1//2*b^2*f^-1*(b*tan(e+f*x)^2)^(1/2)*tan(e+f*x)+1//4*b^2*f^-1*(b*tan(e+f*x)^2)^(1/2)*tan(e+f*x)^3+-1*b^2*f^-1*(b*tan(e+f*x)^2)^(1/2)*cot(e+f*x)*log(cos(e+f*x)))
@test integrate((b*tan(e+f*x)^2)^3//2, x) == :((1/2)*b*f^-1*(b*tan(e+f*x)^2)^(1/2)*tan(e+f*x)+b*f^-1*(b*tan(e+f*x)^2)^(1/2)*cot(e+f*x)*log(cos(e+f*x)))
@test integrate((b*tan(e+f*x)^2)^(1/2), x) == :(-1*f^-1*(b*tan(e+f*x)^2)^(1/2)*cot(e+f*x)*log(cos(e+f*x)))
@test integrate((b*tan(e+f*x)^2)^-1//2, x) == :(f^-1*(b*tan(e+f*x)^2)^-1//2*log(sin(e+f*x))*tan(e+f*x))
@test integrate((b*tan(e+f*x)^2)^-3//2, x) == :(-1//2*b^-1*f^-1*(b*tan(e+f*x)^2)^-1//2*cot(e+f*x)+-1*b^-1*f^-1*(b*tan(e+f*x)^2)^-1//2*log(sin(e+f*x))*tan(e+f*x))
@test integrate((b*tan(e+f*x)^2)^-5//2, x) == :((1/2)*b^-2*f^-1*(b*tan(e+f*x)^2)^-1//2*cot(e+f*x)+-1//4*b^-2*f^-1*(b*tan(e+f*x)^2)^-1//2*cot(e+f*x)^3+b^-2*f^-1*(b*tan(e+f*x)^2)^-1//2*log(sin(e+f*x))*tan(e+f*x))
@test integrate((b*tan(e+f*x)^3)^5//2, x) == :(-2*b^2*f^-1*(b*tan(e+f*x)^3)^(1/2)*cot(e+f*x)+-2//9*b^2*f^-1*(b*tan(e+f*x)^3)^(1/2)*tan(e+f*x)^3+2//5*b^2*f^-1*(b*tan(e+f*x)^3)^(1/2)*tan(e+f*x)+2//13*b^2*f^-1*(b*tan(e+f*x)^3)^(1/2)*tan(e+f*x)^5+(1/2)*2^(1/2)*b^2*f^-1*(b*tan(e+f*x)^3)^(1/2)*tan(e+f*x)^-3//2*arctan(1+2^(1/2)*tan(e+f*x)^(1/2))+-1//2*2^(1/2)*b^2*f^-1*(b*tan(e+f*x)^3)^(1/2)*tan(e+f*x)^-3//2*arctan(1+-1*2^(1/2)*tan(e+f*x)^(1/2))+-1//4*2^(1/2)*b^2*f^-1*(b*tan(e+f*x)^3)^(1/2)*tan(e+f*x)^-3//2*log(1+-1*2^(1/2)*tan(e+f*x)^(1/2)+tan(e+f*x))+1//4*2^(1/2)*b^2*f^-1*(b*tan(e+f*x)^3)^(1/2)*tan(e+f*x)^-3//2*log(1+2^(1/2)*tan(e+f*x)^(1/2)+tan(e+f*x)))
@test integrate((b*tan(e+f*x)^3)^3//2, x) == :(-2//3*b*f^-1*(b*tan(e+f*x)^3)^(1/2)+2//7*b*f^-1*(b*tan(e+f*x)^3)^(1/2)*tan(e+f*x)^2+(1/2)*b*2^(1/2)*f^-1*(b*tan(e+f*x)^3)^(1/2)*tan(e+f*x)^-3//2*arctan(1+2^(1/2)*tan(e+f*x)^(1/2))+-1//2*b*2^(1/2)*f^-1*(b*tan(e+f*x)^3)^(1/2)*tan(e+f*x)^-3//2*arctan(1+-1*2^(1/2)*tan(e+f*x)^(1/2))+-1//4*b*2^(1/2)*f^-1*(b*tan(e+f*x)^3)^(1/2)*tan(e+f*x)^-3//2*log(1+2^(1/2)*tan(e+f*x)^(1/2)+tan(e+f*x))+1//4*b*2^(1/2)*f^-1*(b*tan(e+f*x)^3)^(1/2)*tan(e+f*x)^-3//2*log(1+-1*2^(1/2)*tan(e+f*x)^(1/2)+tan(e+f*x)))
@test integrate((b*tan(e+f*x)^3)^(1/2), x) == :(2*f^-1*(b*tan(e+f*x)^3)^(1/2)*cot(e+f*x)+(1/2)*2^(1/2)*f^-1*(b*tan(e+f*x)^3)^(1/2)*tan(e+f*x)^-3//2*arctan(1+-1*2^(1/2)*tan(e+f*x)^(1/2))+-1//2*2^(1/2)*f^-1*(b*tan(e+f*x)^3)^(1/2)*tan(e+f*x)^-3//2*arctan(1+2^(1/2)*tan(e+f*x)^(1/2))+-1//4*2^(1/2)*f^-1*(b*tan(e+f*x)^3)^(1/2)*tan(e+f*x)^-3//2*log(1+2^(1/2)*tan(e+f*x)^(1/2)+tan(e+f*x))+1//4*2^(1/2)*f^-1*(b*tan(e+f*x)^3)^(1/2)*tan(e+f*x)^-3//2*log(1+-1*2^(1/2)*tan(e+f*x)^(1/2)+tan(e+f*x)))
@test integrate((b*tan(e+f*x)^3)^-1//2, x) == :(-2*f^-1*(b*tan(e+f*x)^3)^-1//2*tan(e+f*x)+(1/2)*2^(1/2)*f^-1*(b*tan(e+f*x)^3)^-1//2*tan(e+f*x)^3//2*arctan(1+-1*2^(1/2)*tan(e+f*x)^(1/2))+-1//2*2^(1/2)*f^-1*(b*tan(e+f*x)^3)^-1//2*tan(e+f*x)^3//2*arctan(1+2^(1/2)*tan(e+f*x)^(1/2))+-1//4*2^(1/2)*f^-1*(b*tan(e+f*x)^3)^-1//2*tan(e+f*x)^3//2*log(1+-1*2^(1/2)*tan(e+f*x)^(1/2)+tan(e+f*x))+1//4*2^(1/2)*f^-1*(b*tan(e+f*x)^3)^-1//2*tan(e+f*x)^3//2*log(1+2^(1/2)*tan(e+f*x)^(1/2)+tan(e+f*x)))
@test integrate((b*tan(e+f*x)^3)^-3//2, x) == :(2//3*b^-1*f^-1*(b*tan(e+f*x)^3)^-1//2+-2//7*b^-1*f^-1*(b*tan(e+f*x)^3)^-1//2*cot(e+f*x)^2+(1/2)*2^(1/2)*b^-1*f^-1*(b*tan(e+f*x)^3)^-1//2*tan(e+f*x)^3//2*arctan(1+2^(1/2)*tan(e+f*x)^(1/2))+-1//2*2^(1/2)*b^-1*f^-1*(b*tan(e+f*x)^3)^-1//2*tan(e+f*x)^3//2*arctan(1+-1*2^(1/2)*tan(e+f*x)^(1/2))+-1//4*2^(1/2)*b^-1*f^-1*(b*tan(e+f*x)^3)^-1//2*tan(e+f*x)^3//2*log(1+-1*2^(1/2)*tan(e+f*x)^(1/2)+tan(e+f*x))+1//4*2^(1/2)*b^-1*f^-1*(b*tan(e+f*x)^3)^-1//2*tan(e+f*x)^3//2*log(1+2^(1/2)*tan(e+f*x)^(1/2)+tan(e+f*x)))
@test integrate((b*tan(e+f*x)^3)^-5//2, x) == :(2*b^-2*f^-1*(b*tan(e+f*x)^3)^-1//2*tan(e+f*x)+-2//5*b^-2*f^-1*(b*tan(e+f*x)^3)^-1//2*cot(e+f*x)+-2//13*b^-2*f^-1*(b*tan(e+f*x)^3)^-1//2*cot(e+f*x)^5+2//9*b^-2*f^-1*(b*tan(e+f*x)^3)^-1//2*cot(e+f*x)^3+(1/2)*2^(1/2)*b^-2*f^-1*(b*tan(e+f*x)^3)^-1//2*tan(e+f*x)^3//2*arctan(1+2^(1/2)*tan(e+f*x)^(1/2))+-1//2*2^(1/2)*b^-2*f^-1*(b*tan(e+f*x)^3)^-1//2*tan(e+f*x)^3//2*arctan(1+-1*2^(1/2)*tan(e+f*x)^(1/2))+-1//4*2^(1/2)*b^-2*f^-1*(b*tan(e+f*x)^3)^-1//2*tan(e+f*x)^3//2*log(1+2^(1/2)*tan(e+f*x)^(1/2)+tan(e+f*x))+1//4*2^(1/2)*b^-2*f^-1*(b*tan(e+f*x)^3)^-1//2*tan(e+f*x)^3//2*log(1+-1*2^(1/2)*tan(e+f*x)^(1/2)+tan(e+f*x)))
@test integrate((b*tan(e+f*x)^4)^5//2, x) == :(b^2*f^-1*(b*tan(e+f*x)^4)^(1/2)*cot(e+f*x)+-1*x*b^2*(b*tan(e+f*x)^4)^(1/2)*cot(e+f*x)^2+-1//3*b^2*f^-1*(b*tan(e+f*x)^4)^(1/2)*tan(e+f*x)+-1//7*b^2*f^-1*(b*tan(e+f*x)^4)^(1/2)*tan(e+f*x)^5+1//5*b^2*f^-1*(b*tan(e+f*x)^4)^(1/2)*tan(e+f*x)^3+1//9*b^2*f^-1*(b*tan(e+f*x)^4)^(1/2)*tan(e+f*x)^7)
@test integrate((b*tan(e+f*x)^4)^3//2, x) == :(b*f^-1*(b*tan(e+f*x)^4)^(1/2)*cot(e+f*x)+-1*b*x*(b*tan(e+f*x)^4)^(1/2)*cot(e+f*x)^2+-1//3*b*f^-1*(b*tan(e+f*x)^4)^(1/2)*tan(e+f*x)+1//5*b*f^-1*(b*tan(e+f*x)^4)^(1/2)*tan(e+f*x)^3)
@test integrate((b*tan(e+f*x)^4)^(1/2), x) == :(f^-1*(b*tan(e+f*x)^4)^(1/2)*cot(e+f*x)+-1*x*(b*tan(e+f*x)^4)^(1/2)*cot(e+f*x)^2)
@test integrate((b*tan(e+f*x)^4)^-1//2, x) == :(-1*x*(b*tan(e+f*x)^4)^-1//2*tan(e+f*x)^2+-1*f^-1*(b*tan(e+f*x)^4)^-1//2*tan(e+f*x))
@test integrate((b*tan(e+f*x)^4)^-3//2, x) == :(-1*x*b^-1*(b*tan(e+f*x)^4)^-1//2*tan(e+f*x)^2+-1*b^-1*f^-1*(b*tan(e+f*x)^4)^-1//2*tan(e+f*x)+-1//5*b^-1*f^-1*(b*tan(e+f*x)^4)^-1//2*cot(e+f*x)^3+1//3*b^-1*f^-1*(b*tan(e+f*x)^4)^-1//2*cot(e+f*x))
@test integrate((b*tan(e+f*x)^4)^-5//2, x) == :(-1*x*b^-2*(b*tan(e+f*x)^4)^-1//2*tan(e+f*x)^2+-1*b^-2*f^-1*(b*tan(e+f*x)^4)^-1//2*tan(e+f*x)+-1//5*b^-2*f^-1*(b*tan(e+f*x)^4)^-1//2*cot(e+f*x)^3+-1//9*b^-2*f^-1*(b*tan(e+f*x)^4)^-1//2*cot(e+f*x)^7+1//3*b^-2*f^-1*(b*tan(e+f*x)^4)^-1//2*cot(e+f*x)+1//7*b^-2*f^-1*(b*tan(e+f*x)^4)^-1//2*cot(e+f*x)^5)
@test integrate((b*tan(e+f*x)^n)^(n^-1), x) == :(-1*f^-1*(b*tan(e+f*x)^n)^(n^-1)*cot(e+f*x)*log(cos(e+f*x)))
@test integrate(sin(e+f*x)^5*(a+b*tan(e+f*x)^2), x) == :(b*f^-1*sec(e+f*x)+-1*f^-1*(a+-3b)*cos(e+f*x)+-1//5*f^-1*cos(e+f*x)^5*(a+-1b)+1//3*f^-1*cos(e+f*x)^3*(-3b+2a))
@test integrate(sin(e+f*x)^3*(a+b*tan(e+f*x)^2), x) == :(b*f^-1*sec(e+f*x)+-1*f^-1*(a+-2b)*cos(e+f*x)+1//3*f^-1*cos(e+f*x)^3*(a+-1b))
@test integrate((a+b*tan(e+f*x)^2)*sin(e+f*x), x) == :(b*f^-1*sec(e+f*x)+-1*f^-1*(a+-1b)*cos(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)*csc(e+f*x), x) == :(b*f^-1*sec(e+f*x)+-1*a*f^-1*arctanh(cos(e+f*x)))
@test integrate(csc(e+f*x)^3*(a+b*tan(e+f*x)^2), x) == :(b*f^-1*sec(e+f*x)+-1//2*f^-1*(a+2b)*arctanh(cos(e+f*x))+-1//2*a*f^-1*cot(e+f*x)*csc(e+f*x))
@test integrate(csc(e+f*x)^5*(a+b*tan(e+f*x)^2), x) == :(b*f^-1*sec(e+f*x)+1//8*f^-1*(-12b+-3a)*arctanh(cos(e+f*x))+-1//4*a*f^-1*cot(e+f*x)^3*csc(e+f*x)+-1//8*f^-1*(4b+5a)*cot(e+f*x)*csc(e+f*x))
@test integrate(sin(e+f*x)^6*(a+b*tan(e+f*x)^2), x) == :(1//16*x*(-35b+5a)+b*f^-1*tan(e+f*x)+-1//6*f^-1*cos(e+f*x)^5*(a+-1b)*sin(e+f*x)+-1//16*f^-1*(-29b+11a)*cos(e+f*x)*sin(e+f*x)+1//24*f^-1*cos(e+f*x)^3*(-19b+13a)*sin(e+f*x))
@test integrate(sin(e+f*x)^4*(a+b*tan(e+f*x)^2), x) == :(1//8*x*(-15b+3a)+b*f^-1*tan(e+f*x)+-1//8*f^-1*(-9b+5a)*cos(e+f*x)*sin(e+f*x)+1//4*f^-1*cos(e+f*x)^3*(a+-1b)*sin(e+f*x))
@test integrate(sin(e+f*x)^2*(a+b*tan(e+f*x)^2), x) == :((1/2)*x*(a+-3b)+b*f^-1*tan(e+f*x)+-1//2*f^-1*(a+-1b)*cos(e+f*x)*sin(e+f*x))
@test integrate(a+b*tan(e+f*x)^2, x) == :(a*x+-1*b*x+b*f^-1*tan(e+f*x))
@test integrate(csc(e+f*x)^2*(a+b*tan(e+f*x)^2), x) == :(b*f^-1*tan(e+f*x)+-1*a*f^-1*cot(e+f*x))
@test integrate(csc(e+f*x)^4*(a+b*tan(e+f*x)^2), x) == :(b*f^-1*tan(e+f*x)+-1*f^-1*(a+b)*cot(e+f*x)+-1//3*a*f^-1*cot(e+f*x)^3)
@test integrate(csc(e+f*x)^6*(a+b*tan(e+f*x)^2), x) == :(b*f^-1*tan(e+f*x)+-1*f^-1*(a+2b)*cot(e+f*x)+-1//3*f^-1*cot(e+f*x)^3*(b+2a)+-1//5*a*f^-1*cot(e+f*x)^5)
@test integrate((a+b*tan(e+f*x)^2)^2*sin(e+f*x)^5, x) == :(-1*f^-1*(a^2+6*b^2+-6*a*b)*cos(e+f*x)+-1//5*f^-1*(a+-1b)^2*cos(e+f*x)^5+1//3*b^2*f^-1*sec(e+f*x)^3+b*f^-1*(-4b+2a)*sec(e+f*x)+1//3*f^-1*cos(e+f*x)^3*(a+-1b)*(-4b+2a))
@test integrate((a+b*tan(e+f*x)^2)^2*sin(e+f*x)^3, x) == :(1//3*b^2*f^-1*sec(e+f*x)^3+1//3*f^-1*(a+-1b)^2*cos(e+f*x)^3+b*f^-1*(-3b+2a)*sec(e+f*x)+-1*f^-1*(a+-1b)*(a+-3b)*cos(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^2*sin(e+f*x), x) == :(-1*f^-1*(a+-1b)^2*cos(e+f*x)+1//3*b^2*f^-1*sec(e+f*x)^3+b*f^-1*(-2b+2a)*sec(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^2*csc(e+f*x), x) == :(-1*a^2*f^-1*arctanh(cos(e+f*x))+1//3*b^2*f^-1*sec(e+f*x)^3+b*f^-1*(-1b+2a)*sec(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^2*csc(e+f*x)^3, x) == :(1//3*b^2*f^-1*sec(e+f*x)^3+(1/2)*a*f^-1*(a+4b)*sec(e+f*x)+-1//2*a*f^-1*(a+4b)*arctanh(cos(e+f*x))+-1//2*a^2*f^-1*csc(e+f*x)^2*sec(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^2*csc(e+f*x)^5, x) == :(-1//8*f^-1*(3*a^2+8*b^2+24*a*b)*arctanh(cos(e+f*x))+1//3*b^2*f^-1*sec(e+f*x)^3+1//4*f^-1*(a^2+4*b^2+8*a*b)*sec(e+f*x)+-1//4*a^2*f^-1*csc(e+f*x)^4*sec(e+f*x)+-1//8*a*f^-1*(a+8b)*cot(e+f*x)*csc(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^2*sin(e+f*x)^4, x) == :(1//8*x*(3*a^2+35*b^2+-30*a*b)+-1//4*f^-1*(a^2+13*b^2+-10*a*b)*tan(e+f*x)+1//3*b^2*f^-1*tan(e+f*x)^3+1//4*f^-1*(a+-1b)^2*sin(e+f*x)^4*tan(e+f*x)+-1//8*f^-1*(a+-1b)*(a+-9b)*cos(e+f*x)*sin(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^2*sin(e+f*x)^2, x) == :((1/2)*x*(a+-1b)*(a+-5b)+1//3*b^2*f^-1*tan(e+f*x)^3+(1/2)*f^-1*(a+-1b)^2*sin(e+f*x)^2*tan(e+f*x)+-1//2*f^-1*(a+-1b)*(a+-5b)*tan(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^2, x) == :(x*(a+-1b)^2+1//3*b^2*f^-1*tan(e+f*x)^3+b*f^-1*(-1b+2a)*tan(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^2*csc(e+f*x)^2, x) == :(-1*a^2*f^-1*cot(e+f*x)+1//3*b^2*f^-1*tan(e+f*x)^3+2*a*b*f^-1*tan(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^2*csc(e+f*x)^4, x) == :(-1//3*a^2*f^-1*cot(e+f*x)^3+1//3*b^2*f^-1*tan(e+f*x)^3+b*f^-1*(b+2a)*tan(e+f*x)+-1*a*f^-1*(a+2b)*cot(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^2*csc(e+f*x)^6, x) == :(-1*f^-1*(a^2+b^2+4*a*b)*cot(e+f*x)+-1//5*a^2*f^-1*cot(e+f*x)^5+1//3*b^2*f^-1*tan(e+f*x)^3+2*b*f^-1*(a+b)*tan(e+f*x)+-2//3*a*f^-1*cot(e+f*x)^3*(a+b))
@test integrate((a+b*tan(e+f*x)^2)^-1*sin(e+f*x)^5, x) == :(-1*f^-1*(-5b+5a)^-1*cos(e+f*x)^5+-1*a^2*f^-1*(a+-1b)^-3*cos(e+f*x)+1//3*f^-1*(a+-1b)^-2*cos(e+f*x)^3*(-1b+2a)+-1*a^2*b^(1/2)*f^-1*(a+-1b)^-7//2*arctan(b^(1/2)*(a+-1b)^-1//2*sec(e+f*x)))
@test integrate((a+b*tan(e+f*x)^2)^-1*sin(e+f*x)^3, x) == :(f^-1*(-3b+3a)^-1*cos(e+f*x)^3+-1*a*f^-1*(a+-1b)^-2*cos(e+f*x)+-1*a*b^(1/2)*f^-1*(a+-1b)^-5//2*arctan(b^(1/2)*(a+-1b)^-1//2*sec(e+f*x)))
@test integrate((a+b*tan(e+f*x)^2)^-1*sin(e+f*x), x) == :(-1*f^-1*(a+-1b)^-1*cos(e+f*x)+-1*b^(1/2)*f^-1*(a+-1b)^-3//2*arctan(b^(1/2)*(a+-1b)^-1//2*sec(e+f*x)))
@test integrate((a+b*tan(e+f*x)^2)^-1*csc(e+f*x), x) == :(-1*a^-1*f^-1*arctanh(cos(e+f*x))+-1*a^-1*b^(1/2)*f^-1*(a+-1b)^-1//2*arctan(b^(1/2)*(a+-1b)^-1//2*sec(e+f*x)))
@test integrate((a+b*tan(e+f*x)^2)^-1*csc(e+f*x)^3, x) == :(-1//2*a^-1*f^-1*cot(e+f*x)*csc(e+f*x)+-1//2*a^-2*f^-1*(a+-2b)*arctanh(cos(e+f*x))+-1*a^-2*b^(1/2)*f^-1*(a+-1b)^(1/2)*arctan(b^(1/2)*(a+-1b)^-1//2*sec(e+f*x)))
@test integrate((a+b*tan(e+f*x)^2)^-1*csc(e+f*x)^5, x) == :(-1//4*a^-1*f^-1*cot(e+f*x)^3*csc(e+f*x)+-1//8*a^-3*f^-1*(3*a^2+8*b^2+-12*a*b)*arctanh(cos(e+f*x))+-1*a^-3*b^(1/2)*f^-1*(a+-1b)^3//2*arctan(b^(1/2)*(a+-1b)^-1//2*sec(e+f*x))+-1//8*a^-2*f^-1*(-4b+5a)*cot(e+f*x)*csc(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^-1*sin(e+f*x)^6, x) == :(1//16*x*(a+-1b)^-4*(b^3+5*a^3+-5*a*b^2+15*b*a^2)+f^-1*(-6b+6a)^-1*cos(e+f*x)^3*sin(e+f*x)^3+-1*a^5//2*b^(1/2)*f^-1*(a+-1b)^-4*arctan(a^-1//2*b^(1/2)*tan(e+f*x))+-1//16*f^-1*(a+-1b)^-3*(b^2+11*a^2+-4*a*b)*cos(e+f*x)*sin(e+f*x)+1//8*f^-1*(a+-1b)^-2*cos(e+f*x)^3*(-1b+3a)*sin(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^-1*sin(e+f*x)^4, x) == :(1//8*x*(a+-1b)^-3*(-1*b^2+3*a^2+6*a*b)+f^-1*(-4b+4a)^-1*cos(e+f*x)^3*sin(e+f*x)+-1*a^3//2*b^(1/2)*f^-1*(a+-1b)^-3*arctan(a^-1//2*b^(1/2)*tan(e+f*x))+-1//8*f^-1*(a+-1b)^-2*(-1b+5a)*cos(e+f*x)*sin(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^-1*sin(e+f*x)^2, x) == :((1/2)*x*(a+-1b)^-2*(a+b)+-1*f^-1*(-2b+2a)^-1*cos(e+f*x)*sin(e+f*x)+-1*a^(1/2)*b^(1/2)*f^-1*(a+-1b)^-2*arctan(a^-1//2*b^(1/2)*tan(e+f*x)))
@test integrate((a+b*tan(e+f*x)^2)^-1, x) == :(x*(a+-1b)^-1+-1*a^-1//2*b^(1/2)*f^-1*(a+-1b)^-1*arctan(a^-1//2*b^(1/2)*tan(e+f*x)))
@test integrate((a+b*tan(e+f*x)^2)^-1*csc(e+f*x)^2, x) == :(-1*a^-1*f^-1*cot(e+f*x)+-1*a^-3//2*b^(1/2)*f^-1*arctan(a^-1//2*b^(1/2)*tan(e+f*x)))
@test integrate((a+b*tan(e+f*x)^2)^-1*csc(e+f*x)^4, x) == :(-1//3*a^-1*f^-1*cot(e+f*x)^3+-1*a^-2*f^-1*(a+-1b)*cot(e+f*x)+-1*a^-5//2*b^(1/2)*f^-1*(a+-1b)*arctan(a^-1//2*b^(1/2)*tan(e+f*x)))
@test integrate((a+b*tan(e+f*x)^2)^-1*csc(e+f*x)^6, x) == :(-1//5*a^-1*f^-1*cot(e+f*x)^5+-1*a^-3*f^-1*(a+-1b)^2*cot(e+f*x)+-1//3*a^-2*f^-1*cot(e+f*x)^3*(-1b+2a)+-1*a^-7//2*b^(1/2)*f^-1*(a+-1b)^2*arctan(a^-1//2*b^(1/2)*tan(e+f*x)))
@test integrate((a+b*tan(e+f*x)^2)^-2*sin(e+f*x)^5, x) == :(-1*f^-1*(-5b+5a)^-1*(a+-1b+b*sec(e+f*x)^2)^-1*cos(e+f*x)^5+-1//5*f^-1*(a+-1b)^-4*(-1*b^2+5*a^2+10*a*b)*cos(e+f*x)+1//15*f^-1*(a+-1b)^-3*cos(e+f*x)^3*(-3b+10a)+-1//2*a*b^(1/2)*f^-1*(a+-1b)^-9//2*(3a+4b)*arctan(b^(1/2)*(a+-1b)^-1//2*sec(e+f*x))+-1//10*b*f^-1*(a+-1b)^-4*(a+-1b+b*sec(e+f*x)^2)^-1*(2*b^2+5*a^2)*sec(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^-2*sin(e+f*x)^3, x) == :(1//3*f^-1*(a+-1b)^-2*cos(e+f*x)^3+-1*f^-1*(a+-1b)^-3*(a+b)*cos(e+f*x)+-1//2*b^(1/2)*f^-1*(a+-1b)^-7//2*(2b+3a)*arctan(b^(1/2)*(a+-1b)^-1//2*sec(e+f*x))+-1//2*a*b*f^-1*(a+-1b)^-3*(a+-1b+b*sec(e+f*x)^2)^-1*sec(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^-2*sin(e+f*x), x) == :(-3//2*f^-1*(a+-1b)^-2*cos(e+f*x)+f^-1*(-2b+2a)^-1*(a+-1b+b*sec(e+f*x)^2)^-1*cos(e+f*x)+-3//2*b^(1/2)*f^-1*(a+-1b)^-5//2*arctan(b^(1/2)*(a+-1b)^-1//2*sec(e+f*x)))
@test integrate((a+b*tan(e+f*x)^2)^-2*csc(e+f*x), x) == :(-1*a^-2*f^-1*arctanh(cos(e+f*x))+-1//2*b*a^-1*f^-1*(a+-1b)^-1*(a+-1b+b*sec(e+f*x)^2)^-1*sec(e+f*x)+-1//2*a^-2*b^(1/2)*f^-1*(a+-1b)^-3//2*(-2b+3a)*arctan(b^(1/2)*(a+-1b)^-1//2*sec(e+f*x)))
@test integrate((a+b*tan(e+f*x)^2)^-2*csc(e+f*x)^3, x) == :(-1//2*a^-3*f^-1*(a+-4b)*arctanh(cos(e+f*x))+-1*b*a^-2*f^-1*(a+-1b+b*sec(e+f*x)^2)^-1*sec(e+f*x)+-1//2*a^-1*f^-1*(a+-1b+b*sec(e+f*x)^2)^-1*cot(e+f*x)*csc(e+f*x)+-1//2*a^-3*b^(1/2)*f^-1*(a+-1b)^-1//2*(-4b+3a)*arctan(b^(1/2)*(a+-1b)^-1//2*sec(e+f*x)))
@test integrate((a+b*tan(e+f*x)^2)^-2*csc(e+f*x)^5, x) == :(-1//8*a^-4*f^-1*(3*a^2+24*b^2+-24*a*b)*arctanh(cos(e+f*x))+-1//4*a^-1*f^-1*(a+-1b+b*sec(e+f*x)^2)^-1*cot(e+f*x)^3*csc(e+f*x)+(1/2)*a^-4*b^(1/2)*f^-1*(a+-1b)^(1/2)*(-3a+6b)*arctan(b^(1/2)*(a+-1b)^-1//2*sec(e+f*x))+-1//8*b*a^-3*f^-1*(a+-1b+b*sec(e+f*x)^2)^-1*(-12b+9a)*sec(e+f*x)+-1//8*a^-2*f^-1*(a+-1b+b*sec(e+f*x)^2)^-1*(-6b+5a)*cot(e+f*x)*csc(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^-2*sin(e+f*x)^4, x) == :(1//8*x*(a+-1b)^-4*(3*a^2+3*b^2+18*a*b)+f^-1*(a+b*tan(e+f*x)^2)^-1*(-4b+4a)^-1*cos(e+f*x)^3*sin(e+f*x)+-3//2*a^(1/2)*b^(1/2)*f^-1*(a+-1b)^-4*(a+b)*arctan(a^-1//2*b^(1/2)*tan(e+f*x))+-3//8*b*f^-1*(a+-1b)^-3*(a+b*tan(e+f*x)^2)^-1*(b+3a)*tan(e+f*x)+-1//8*f^-1*(a+-1b)^-2*(a+b*tan(e+f*x)^2)^-1*(b+5a)*cos(e+f*x)*sin(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^-2*sin(e+f*x)^2, x) == :((1/2)*x*(a+-1b)^-3*(a+3b)+-1*b*f^-1*(a+-1b)^-2*(a+b*tan(e+f*x)^2)^-1*tan(e+f*x)+-1*f^-1*(a+b*tan(e+f*x)^2)^-1*(-2b+2a)^-1*cos(e+f*x)*sin(e+f*x)+-1//2*a^-1//2*b^(1/2)*f^-1*(a+-1b)^-3*(b+3a)*arctan(a^-1//2*b^(1/2)*tan(e+f*x)))
@test integrate((a+b*tan(e+f*x)^2)^-2, x) == :(x*(a+-1b)^-2+-1//2*b*a^-1*f^-1*(a+-1b)^-1*(a+b*tan(e+f*x)^2)^-1*tan(e+f*x)+-1//2*a^-3//2*b^(1/2)*f^-1*(a+-1b)^-2*(-1b+3a)*arctan(a^-1//2*b^(1/2)*tan(e+f*x)))
@test integrate((a+b*tan(e+f*x)^2)^-2*csc(e+f*x)^2, x) == :(-3//2*a^-2*f^-1*cot(e+f*x)+(1/2)*a^-1*f^-1*(a+b*tan(e+f*x)^2)^-1*cot(e+f*x)+-3//2*a^-5//2*b^(1/2)*f^-1*arctan(a^-1//2*b^(1/2)*tan(e+f*x)))
@test integrate((a+b*tan(e+f*x)^2)^-2*csc(e+f*x)^4, x) == :(-1//3*a^-2*f^-1*cot(e+f*x)^3+-1*a^-3*f^-1*(a+-2b)*cot(e+f*x)+-1//2*a^-7//2*b^(1/2)*f^-1*(-5b+3a)*arctan(a^-1//2*b^(1/2)*tan(e+f*x))+-1//2*b*a^-3*f^-1*(a+b*tan(e+f*x)^2)^-1*(a+-1b)*tan(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^-2*csc(e+f*x)^6, x) == :(-1//5*a^-1*f^-1*(a+b*tan(e+f*x)^2)^-1*cot(e+f*x)^5+-1//5*a^-4*f^-1*(5*a^2+14*b^2+-20*a*b)*cot(e+f*x)+-1//15*a^-3*f^-1*cot(e+f*x)^3*(-7b+10a)+-1//2*a^-9//2*b^(1/2)*f^-1*(a+-1b)*(-7b+3a)*arctan(a^-1//2*b^(1/2)*tan(e+f*x))+-1//10*b*a^-4*f^-1*(a+b*tan(e+f*x)^2)^-1*(5*a^2+7*b^2+-10*a*b)*tan(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^-3*sin(e+f*x)^5, x) == :(-1*f^-1*(-5b+5a)^-1*(a+-1b+b*sec(e+f*x)^2)^-2*cos(e+f*x)^5+-1//5*f^-1*(a+-1b)^-5*(2*b^2+5*a^2+20*a*b)*cos(e+f*x)+1//15*f^-1*(a+-1b)^-4*cos(e+f*x)^3*(-1b+10a)+-1//8*b^(1/2)*f^-1*(a+-1b)^-11//2*(8*b^2+15*a^2+40*a*b)*arctan(b^(1/2)*(a+-1b)^-1//2*sec(e+f*x))+-1//20*b*f^-1*(a+-1b)^-4*(a+-1b+b*sec(e+f*x)^2)^-2*(4*b^2+5*a^2)*sec(e+f*x)+-1//40*b*f^-1*(a+-1b)^-5*(a+-1b+b*sec(e+f*x)^2)^-1*(24*b^2+35*a^2+40*a*b)*sec(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^-3*sin(e+f*x)^3, x) == :(1//3*f^-1*(a+-1b)^-3*cos(e+f*x)^3+-1*f^-1*(a+-1b)^-4*(a+2b)*cos(e+f*x)+-5//8*b^(1/2)*f^-1*(a+-1b)^-9//2*(3a+4b)*arctan(b^(1/2)*(a+-1b)^-1//2*sec(e+f*x))+-1//4*a*b*f^-1*(a+-1b)^-3*(a+-1b+b*sec(e+f*x)^2)^-2*sec(e+f*x)+-1//8*b*f^-1*(a+-1b)^-4*(a+-1b+b*sec(e+f*x)^2)^-1*(4b+7a)*sec(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^-3*sin(e+f*x), x) == :(-15//8*f^-1*(a+-1b)^-3*cos(e+f*x)+f^-1*(-4b+4a)^-1*(a+-1b+b*sec(e+f*x)^2)^-2*cos(e+f*x)+-15//8*b^(1/2)*f^-1*(a+-1b)^-7//2*arctan(b^(1/2)*(a+-1b)^-1//2*sec(e+f*x))+5//8*f^-1*(a+-1b)^-2*(a+-1b+b*sec(e+f*x)^2)^-1*cos(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^-3*csc(e+f*x), x) == :(-1*a^-3*f^-1*arctanh(cos(e+f*x))+-1//4*b*a^-1*f^-1*(a+-1b)^-1*(a+-1b+b*sec(e+f*x)^2)^-2*sec(e+f*x)+-1//8*a^-3*b^(1/2)*f^-1*(a+-1b)^-5//2*(8*b^2+15*a^2+-20*a*b)*arctan(b^(1/2)*(a+-1b)^-1//2*sec(e+f*x))+-1//8*b*a^-2*f^-1*(a+-1b)^-2*(a+-1b+b*sec(e+f*x)^2)^-1*(-4b+7a)*sec(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^-3*csc(e+f*x)^3, x) == :(-1//2*a^-4*f^-1*(a+-6b)*arctanh(cos(e+f*x))+-3//4*b*a^-2*f^-1*(a+-1b+b*sec(e+f*x)^2)^-2*sec(e+f*x)+-1//2*a^-1*f^-1*(a+-1b+b*sec(e+f*x)^2)^-2*cot(e+f*x)*csc(e+f*x)+-1//8*a^-4*b^(1/2)*f^-1*(a+-1b)^-3//2*(15*a^2+24*b^2+-40*a*b)*arctan(b^(1/2)*(a+-1b)^-1//2*sec(e+f*x))+-1//8*b*a^-3*f^-1*(a+-1b)^-1*(a+-1b+b*sec(e+f*x)^2)^-1*(-12b+11a)*sec(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^-3*csc(e+f*x)^5, x) == :(-1//8*a^-5*f^-1*(3*a^2+48*b^2+-36*a*b)*arctanh(cos(e+f*x))+-1//4*a^-1*f^-1*(a+-1b+b*sec(e+f*x)^2)^-2*cot(e+f*x)^3*csc(e+f*x)+-3//8*a^-5*b^(1/2)*f^-1*(a+-1b)^-1//2*(5*a^2+16*b^2+-20*a*b)*arctan(b^(1/2)*(a+-1b)^-1//2*sec(e+f*x))+-1//2*b*a^-4*f^-1*(a+-1b+b*sec(e+f*x)^2)^-1*(-6b+3a)*sec(e+f*x)+-1//8*b*a^-3*f^-1*(a+-1b+b*sec(e+f*x)^2)^-2*(-12b+7a)*sec(e+f*x)+-1//8*a^-2*f^-1*(a+-1b+b*sec(e+f*x)^2)^-2*(-8b+5a)*cot(e+f*x)*csc(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^-3*sin(e+f*x)^4, x) == :(1//8*x*(a+-1b)^-5*(3*a^2+15*b^2+30*a*b)+f^-1*(a+b*tan(e+f*x)^2)^-2*(-4b+4a)^-1*cos(e+f*x)^3*sin(e+f*x)+-3//2*b*f^-1*(a+-1b)^-4*(a+b*tan(e+f*x)^2)^-1*(a+b)*tan(e+f*x)+-3//8*a^-1//2*b^(1/2)*f^-1*(a+-1b)^-5*(b^2+5*a^2+10*a*b)*arctan(a^-1//2*b^(1/2)*tan(e+f*x))+-1//8*b*f^-1*(a+-1b)^-3*(a+b*tan(e+f*x)^2)^-2*(5b+7a)*tan(e+f*x)+-1//8*f^-1*(a+-1b)^-2*(a+b*tan(e+f*x)^2)^-2*(3b+5a)*cos(e+f*x)*sin(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^-3*sin(e+f*x)^2, x) == :((1/2)*x*(a+-1b)^-4*(a+5b)+-1*f^-1*(a+b*tan(e+f*x)^2)^-2*(-2b+2a)^-1*cos(e+f*x)*sin(e+f*x)+-3//4*b*f^-1*(a+-1b)^-2*(a+b*tan(e+f*x)^2)^-2*tan(e+f*x)+-1//8*a^-3//2*b^(1/2)*f^-1*(a+-1b)^-4*(-1*b^2+15*a^2+10*a*b)*arctan(a^-1//2*b^(1/2)*tan(e+f*x))+-1//8*b*a^-1*f^-1*(a+-1b)^-3*(a+b*tan(e+f*x)^2)^-1*(b+11a)*tan(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^-3, x) == :(x*(a+-1b)^-3+-1//4*b*a^-1*f^-1*(a+-1b)^-1*(a+b*tan(e+f*x)^2)^-2*tan(e+f*x)+-1//8*a^-5//2*b^(1/2)*f^-1*(a+-1b)^-3*(3*b^2+15*a^2+-10*a*b)*arctan(a^-1//2*b^(1/2)*tan(e+f*x))+-1//8*b*a^-2*f^-1*(a+-1b)^-2*(a+b*tan(e+f*x)^2)^-1*(-3b+7a)*tan(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^-3*csc(e+f*x)^2, x) == :(-15//8*a^-3*f^-1*cot(e+f*x)+-15//8*a^-7//2*b^(1/2)*f^-1*arctan(a^-1//2*b^(1/2)*tan(e+f*x))+1//4*a^-1*f^-1*(a+b*tan(e+f*x)^2)^-2*cot(e+f*x)+5//8*a^-2*f^-1*(a+b*tan(e+f*x)^2)^-1*cot(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^-3*csc(e+f*x)^4, x) == :(-1//3*a^-3*f^-1*cot(e+f*x)^3+-1*a^-4*f^-1*(a+-3b)*cot(e+f*x)+1//8*a^-9//2*b^(1/2)*f^-1*(-15a+35b)*arctan(a^-1//2*b^(1/2)*tan(e+f*x))+-1//4*b*a^-3*f^-1*(a+b*tan(e+f*x)^2)^-2*(a+-1b)*tan(e+f*x)+-1//8*b*a^-4*f^-1*(a+b*tan(e+f*x)^2)^-1*(-11b+7a)*tan(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^-3*csc(e+f*x)^6, x) == :(-1//5*a^-1*f^-1*(a+b*tan(e+f*x)^2)^-2*cot(e+f*x)^5+-1//5*a^-5*f^-1*(5*a^2+27*b^2+-30*a*b)*cot(e+f*x)+-1//15*a^-4*f^-1*cot(e+f*x)^3*(-9b+10a)+-1//8*a^-11//2*b^(1/2)*f^-1*(15*a^2+63*b^2+-70*a*b)*arctan(a^-1//2*b^(1/2)*tan(e+f*x))+-1//20*b*a^-4*f^-1*(a+b*tan(e+f*x)^2)^-2*(5*a^2+9*b^2+-10*a*b)*tan(e+f*x)+-1//40*b*a^-5*f^-1*(a+b*tan(e+f*x)^2)^-1*(35*a^2+99*b^2+-110*a*b)*tan(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^(1/2)*sin(e+f*x)^5, x) == :(b^(1/2)*f^-1*arctanh(b^(1/2)*(a+-1b+b*sec(e+f*x)^2)^-1//2*sec(e+f*x))+-1*f^-1*(a+-1b+b*sec(e+f*x)^2)^(1/2)*cos(e+f*x)+-1*f^-1*(-5b+5a)^-1*(a+-1b+b*sec(e+f*x)^2)^3//2*cos(e+f*x)^5+1//15*f^-1*(a+-1b)^-2*(a+-1b+b*sec(e+f*x)^2)^3//2*cos(e+f*x)^3*(-8b+10a))
@test integrate((a+b*tan(e+f*x)^2)^(1/2)*sin(e+f*x)^3, x) == :(b^(1/2)*f^-1*arctanh(b^(1/2)*(a+-1b+b*sec(e+f*x)^2)^-1//2*sec(e+f*x))+-1*f^-1*(a+-1b+b*sec(e+f*x)^2)^(1/2)*cos(e+f*x)+f^-1*(-3b+3a)^-1*(a+-1b+b*sec(e+f*x)^2)^3//2*cos(e+f*x)^3)
@test integrate((a+b*tan(e+f*x)^2)^(1/2)*sin(e+f*x), x) == :(b^(1/2)*f^-1*arctanh(b^(1/2)*(a+-1b+b*sec(e+f*x)^2)^-1//2*sec(e+f*x))+-1*f^-1*(a+-1b+b*sec(e+f*x)^2)^(1/2)*cos(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^(1/2)*csc(e+f*x), x) == :(b^(1/2)*f^-1*arctanh(b^(1/2)*(a+-1b+b*sec(e+f*x)^2)^-1//2*sec(e+f*x))+-1*a^(1/2)*f^-1*arctanh(a^(1/2)*(a+-1b+b*sec(e+f*x)^2)^-1//2*sec(e+f*x)))
@test integrate((a+b*tan(e+f*x)^2)^(1/2)*csc(e+f*x)^3, x) == :(b^(1/2)*f^-1*arctanh(b^(1/2)*(a+-1b+b*sec(e+f*x)^2)^-1//2*sec(e+f*x))+-1//2*a^-1//2*f^-1*(a+b)*arctanh(a^(1/2)*(a+-1b+b*sec(e+f*x)^2)^-1//2*sec(e+f*x))+-1//2*f^-1*(a+-1b+b*sec(e+f*x)^2)^(1/2)*cot(e+f*x)*csc(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^(1/2)*csc(e+f*x)^5, x) == :(b^(1/2)*f^-1*arctanh(b^(1/2)*(a+-1b+b*sec(e+f*x)^2)^-1//2*sec(e+f*x))+-1//4*f^-1*(a+-1b+b*sec(e+f*x)^2)^(1/2)*csc(e+f*x)^3*cot(e+f*x)+-1//8*a^-3//2*f^-1*(-1*b^2+3*a^2+6*a*b)*arctanh(a^(1/2)*(a+-1b+b*sec(e+f*x)^2)^-1//2*sec(e+f*x))+-1//8*a^-1*f^-1*(a+-1b+b*sec(e+f*x)^2)^(1/2)*(b+3a)*cot(e+f*x)*csc(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^(1/2)*sin(e+f*x)^4, x) == :(b^(1/2)*f^-1*arctanh(b^(1/2)*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1//4*f^-1*(a+b*tan(e+f*x)^2)^(1/2)*sin(e+f*x)^3*cos(e+f*x)+1//8*f^-1*(a+-1b)^-3//2*(3*a^2+8*b^2+-12*a*b)*arctan((a+-1b)^(1/2)*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1*f^-1*(a+b*tan(e+f*x)^2)^(1/2)*(-8b+8a)^-1*(-4b+3a)*cos(e+f*x)*sin(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^(1/2)*sin(e+f*x)^2, x) == :(b^(1/2)*f^-1*arctanh(b^(1/2)*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+(1/2)*f^-1*(a+-1b)^-1//2*(a+-2b)*arctan((a+-1b)^(1/2)*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1//2*f^-1*(a+b*tan(e+f*x)^2)^(1/2)*cos(e+f*x)*sin(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^(1/2), x) == :(b^(1/2)*f^-1*arctanh(b^(1/2)*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+f^-1*(a+-1b)^(1/2)*arctan((a+-1b)^(1/2)*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x)))
@test integrate((a+b*tan(e+f*x)^2)^(1/2)*csc(e+f*x)^2, x) == :(b^(1/2)*f^-1*arctanh(b^(1/2)*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1*f^-1*(a+b*tan(e+f*x)^2)^(1/2)*cot(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^(1/2)*csc(e+f*x)^4, x) == :(b^(1/2)*f^-1*arctanh(b^(1/2)*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1*f^-1*(a+b*tan(e+f*x)^2)^(1/2)*cot(e+f*x)+-1//3*a^-1*f^-1*(a+b*tan(e+f*x)^2)^3//2*cot(e+f*x)^3)
@test integrate((a+b*tan(e+f*x)^2)^(1/2)*csc(e+f*x)^6, x) == :(b^(1/2)*f^-1*arctanh(b^(1/2)*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1*f^-1*(a+b*tan(e+f*x)^2)^(1/2)*cot(e+f*x)+-1//5*a^-1*f^-1*(a+b*tan(e+f*x)^2)^3//2*cot(e+f*x)^5+-1//15*a^-2*f^-1*(a+b*tan(e+f*x)^2)^3//2*cot(e+f*x)^3*(-2b+10a))
@test integrate((a+b*tan(e+f*x)^2)^3//2*sin(e+f*x)^5, x) == :((1/2)*b^(1/2)*f^-1*(-7b+3a)*arctanh(b^(1/2)*(a+-1b+b*sec(e+f*x)^2)^-1//2*sec(e+f*x))+-1*f^-1*(-5b+5a)^-1*(a+-1b+b*sec(e+f*x)^2)^5//2*cos(e+f*x)^5+2*f^-1*(-3b+3a)^-1*(a+-1b+b*sec(e+f*x)^2)^5//2*cos(e+f*x)^3+-1*f^-1*(-3b+3a)^-1*(a+-1b+b*sec(e+f*x)^2)^3//2*(-7b+3a)*cos(e+f*x)+b*f^-1*(-2b+2a)^-1*(a+-1b+b*sec(e+f*x)^2)^(1/2)*(-7b+3a)*sec(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^3//2*sin(e+f*x)^3, x) == :(f^-1*(-3b+3a)^-1*(a+-1b+b*sec(e+f*x)^2)^5//2*cos(e+f*x)^3+(1/2)*b^(1/2)*f^-1*(-5b+3a)*arctanh(b^(1/2)*(a+-1b+b*sec(e+f*x)^2)^-1//2*sec(e+f*x))+-1*f^-1*(-3b+3a)^-1*(a+-1b+b*sec(e+f*x)^2)^3//2*(-5b+3a)*cos(e+f*x)+b*f^-1*(-2b+2a)^-1*(a+-1b+b*sec(e+f*x)^2)^(1/2)*(-5b+3a)*sec(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^3//2*sin(e+f*x), x) == :(-1*f^-1*(a+-1b+b*sec(e+f*x)^2)^3//2*cos(e+f*x)+(1/2)*b^(1/2)*f^-1*(-3b+3a)*arctanh(b^(1/2)*(a+-1b+b*sec(e+f*x)^2)^-1//2*sec(e+f*x))+3//2*b*f^-1*(a+-1b+b*sec(e+f*x)^2)^(1/2)*sec(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^3//2*csc(e+f*x), x) == :(-1*a^3//2*f^-1*arctanh(a^(1/2)*(a+-1b+b*sec(e+f*x)^2)^-1//2*sec(e+f*x))+(1/2)*b*f^-1*(a+-1b+b*sec(e+f*x)^2)^(1/2)*sec(e+f*x)+(1/2)*b^(1/2)*f^-1*(-1b+3a)*arctanh(b^(1/2)*(a+-1b+b*sec(e+f*x)^2)^-1//2*sec(e+f*x)))
@test integrate((a+b*tan(e+f*x)^2)^3//2*csc(e+f*x)^3, x) == :(b*f^-1*(a+-1b+b*sec(e+f*x)^2)^(1/2)*sec(e+f*x)+(1/2)*b^(1/2)*f^-1*(b+3a)*arctanh(b^(1/2)*(a+-1b+b*sec(e+f*x)^2)^-1//2*sec(e+f*x))+-1//2*a^(1/2)*f^-1*(a+3b)*arctanh(a^(1/2)*(a+-1b+b*sec(e+f*x)^2)^-1//2*sec(e+f*x))+-1//2*f^-1*(a+-1b+b*sec(e+f*x)^2)^3//2*cot(e+f*x)*csc(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^3//2*csc(e+f*x)^5, x) == :(-1//4*f^-1*(a+-1b+b*sec(e+f*x)^2)^3//2*csc(e+f*x)^3*cot(e+f*x)+1//8*a^-1//2*f^-1*(-3*a^2+-3*b^2+-18*a*b)*arctanh(a^(1/2)*(a+-1b+b*sec(e+f*x)^2)^-1//2*sec(e+f*x))+1//8*f^-1*(a+-1b+b*sec(e+f*x)^2)^(1/2)*(3a+9b)*sec(e+f*x)+3//2*b^(1/2)*f^-1*(a+b)*arctanh(b^(1/2)*(a+-1b+b*sec(e+f*x)^2)^-1//2*sec(e+f*x))+-1//8*f^-1*(a+-1b+b*sec(e+f*x)^2)^(1/2)*csc(e+f*x)^2*(3a+3b)*sec(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^3//2*sin(e+f*x)^4, x) == :((1/2)*b^(1/2)*f^-1*(-6b+3a)*arctanh(b^(1/2)*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1//4*f^-1*(a+b*tan(e+f*x)^2)^3//2*sin(e+f*x)^3*cos(e+f*x)+-1//8*f^-1*(a+b*tan(e+f*x)^2)^(1/2)*(-12b+3a)*tan(e+f*x)+1//8*f^-1*(a+-1b)^-1//2*(3*a^2+24*b^2+-24*a*b)*arctan((a+-1b)^(1/2)*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+1//8*f^-1*(a+b*tan(e+f*x)^2)^(1/2)*sin(e+f*x)^2*(-6b+3a)*tan(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^3//2*sin(e+f*x)^2, x) == :(b*f^-1*(a+b*tan(e+f*x)^2)^(1/2)*tan(e+f*x)+(1/2)*b^(1/2)*f^-1*(-4b+3a)*arctanh(b^(1/2)*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+(1/2)*f^-1*(a+-1b)^(1/2)*(a+-4b)*arctan((a+-1b)^(1/2)*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1//2*f^-1*(a+b*tan(e+f*x)^2)^3//2*cos(e+f*x)*sin(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^3//2, x) == :(f^-1*(a+-1b)^3//2*arctan((a+-1b)^(1/2)*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+(1/2)*b*f^-1*(a+b*tan(e+f*x)^2)^(1/2)*tan(e+f*x)+(1/2)*b^(1/2)*f^-1*(-2b+3a)*arctanh(b^(1/2)*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x)))
@test integrate((a+b*tan(e+f*x)^2)^3//2*csc(e+f*x)^2, x) == :(-1*f^-1*(a+b*tan(e+f*x)^2)^3//2*cot(e+f*x)+3//2*a*b^(1/2)*f^-1*arctanh(b^(1/2)*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+3//2*b*f^-1*(a+b*tan(e+f*x)^2)^(1/2)*tan(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^3//2*csc(e+f*x)^4, x) == :((1/2)*b^(1/2)*f^-1*(2b+3a)*arctanh(b^(1/2)*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1//3*a^-1*f^-1*(a+b*tan(e+f*x)^2)^5//2*cot(e+f*x)^3+-1//3*a^-1*f^-1*(a+b*tan(e+f*x)^2)^3//2*(2b+3a)*cot(e+f*x)+(1/2)*b*a^-1*f^-1*(a+b*tan(e+f*x)^2)^(1/2)*(2b+3a)*tan(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^3//2*csc(e+f*x)^6, x) == :((1/2)*b^(1/2)*f^-1*(3a+4b)*arctanh(b^(1/2)*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-2//3*a^-1*f^-1*(a+b*tan(e+f*x)^2)^5//2*cot(e+f*x)^3+-1//5*a^-1*f^-1*(a+b*tan(e+f*x)^2)^5//2*cot(e+f*x)^5+-1//3*a^-1*f^-1*(a+b*tan(e+f*x)^2)^3//2*(3a+4b)*cot(e+f*x)+(1/2)*b*a^-1*f^-1*(a+b*tan(e+f*x)^2)^(1/2)*(3a+4b)*tan(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^-1//2*sin(e+f*x)^5, x) == :(-1*f^-1*(-5b+5a)^-1*(a+-1b+b*sec(e+f*x)^2)^(1/2)*cos(e+f*x)^5+-1//15*f^-1*(a+-1b)^-3*(a+-1b+b*sec(e+f*x)^2)^(1/2)*(3*b^2+15*a^2+-10*a*b)*cos(e+f*x)+1//15*f^-1*(a+-1b)^-2*(a+-1b+b*sec(e+f*x)^2)^(1/2)*cos(e+f*x)^3*(-6b+10a))
@test integrate((a+b*tan(e+f*x)^2)^-1//2*sin(e+f*x)^3, x) == :(f^-1*(-3b+3a)^-1*(a+-1b+b*sec(e+f*x)^2)^(1/2)*cos(e+f*x)^3+-1//3*f^-1*(a+-1b)^-2*(a+-1b+b*sec(e+f*x)^2)^(1/2)*(-1b+3a)*cos(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^-1//2*sin(e+f*x), x) == :(-1*f^-1*(a+-1b)^-1*(a+-1b+b*sec(e+f*x)^2)^(1/2)*cos(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^-1//2*csc(e+f*x), x) == :(-1*a^-1//2*f^-1*arctanh(a^(1/2)*(a+-1b+b*sec(e+f*x)^2)^-1//2*sec(e+f*x)))
@test integrate((a+b*tan(e+f*x)^2)^-1//2*csc(e+f*x)^3, x) == :(-1//2*a^-3//2*f^-1*(a+-1b)*arctanh(a^(1/2)*(a+-1b+b*sec(e+f*x)^2)^-1//2*sec(e+f*x))+-1//2*a^-1*f^-1*(a+-1b+b*sec(e+f*x)^2)^(1/2)*cot(e+f*x)*csc(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^-1//2*csc(e+f*x)^5, x) == :(-3//8*a^-5//2*f^-1*(a+-1b)^2*arctanh(a^(1/2)*(a+-1b+b*sec(e+f*x)^2)^-1//2*sec(e+f*x))+-1//4*a^-1*f^-1*(a+-1b+b*sec(e+f*x)^2)^(1/2)*cot(e+f*x)^3*csc(e+f*x)+-1//8*a^-2*f^-1*(a+-1b+b*sec(e+f*x)^2)^(1/2)*(-3b+5a)*cot(e+f*x)*csc(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^-1//2*sin(e+f*x)^4, x) == :(3//8*a^2*f^-1*(a+-1b)^-5//2*arctan((a+-1b)^(1/2)*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+f^-1*(a+b*tan(e+f*x)^2)^(1/2)*(-4b+4a)^-1*cos(e+f*x)^3*sin(e+f*x)+-1//8*f^-1*(a+-1b)^-2*(a+b*tan(e+f*x)^2)^(1/2)*(-2b+5a)*cos(e+f*x)*sin(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^-1//2*sin(e+f*x)^2, x) == :((1/2)*a*f^-1*(a+-1b)^-3//2*arctan((a+-1b)^(1/2)*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1*f^-1*(a+b*tan(e+f*x)^2)^(1/2)*(-2b+2a)^-1*cos(e+f*x)*sin(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^-1//2, x) == :(f^-1*(a+-1b)^-1//2*arctan((a+-1b)^(1/2)*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x)))
@test integrate((a+b*tan(e+f*x)^2)^-1//2*csc(e+f*x)^2, x) == :(-1*a^-1*f^-1*(a+b*tan(e+f*x)^2)^(1/2)*cot(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^-1//2*csc(e+f*x)^4, x) == :(-1//3*a^-1*f^-1*(a+b*tan(e+f*x)^2)^(1/2)*cot(e+f*x)^3+-1//3*a^-2*f^-1*(a+b*tan(e+f*x)^2)^(1/2)*(-2b+3a)*cot(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^-1//2*csc(e+f*x)^6, x) == :(-1//5*a^-1*f^-1*(a+b*tan(e+f*x)^2)^(1/2)*cot(e+f*x)^5+-1//15*a^-3*f^-1*(a+b*tan(e+f*x)^2)^(1/2)*(8*b^2+15*a^2+-20*a*b)*cot(e+f*x)+-1//15*a^-2*f^-1*(a+b*tan(e+f*x)^2)^(1/2)*cot(e+f*x)^3*(-4b+10a))
@test integrate((a+b*tan(e+f*x)^2)^-3//2*sin(e+f*x)^5, x) == :(-1*f^-1*(-5b+5a)^-1*(a+-1b+b*sec(e+f*x)^2)^-1//2*cos(e+f*x)^5+-1//15*f^-1*(a+-1b)^-3*(a+-1b+b*sec(e+f*x)^2)^-1//2*(-1*b^2+15*a^2+10*a*b)*cos(e+f*x)+1//15*f^-1*(a+-1b)^-2*(a+-1b+b*sec(e+f*x)^2)^-1//2*cos(e+f*x)^3*(-4b+10a)+-2//15*b*f^-1*(a+-1b)^-4*(a+-1b+b*sec(e+f*x)^2)^-1//2*(-1*b^2+15*a^2+10*a*b)*sec(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^-3//2*sin(e+f*x)^3, x) == :(f^-1*(-3b+3a)^-1*(a+-1b+b*sec(e+f*x)^2)^-1//2*cos(e+f*x)^3+-1//3*f^-1*(a+-1b)^-2*(a+-1b+b*sec(e+f*x)^2)^-1//2*(b+3a)*cos(e+f*x)+-2//3*b*f^-1*(a+-1b)^-3*(a+-1b+b*sec(e+f*x)^2)^-1//2*(b+3a)*sec(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^-3//2*sin(e+f*x), x) == :(-1*f^-1*(a+-1b)^-1*(a+-1b+b*sec(e+f*x)^2)^-1//2*cos(e+f*x)+-2*b*f^-1*(a+-1b)^-2*(a+-1b+b*sec(e+f*x)^2)^-1//2*sec(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^-3//2*csc(e+f*x), x) == :(-1*a^-3//2*f^-1*arctanh(a^(1/2)*(a+-1b+b*sec(e+f*x)^2)^-1//2*sec(e+f*x))+-1*b*a^-1*f^-1*(a+-1b)^-1*(a+-1b+b*sec(e+f*x)^2)^-1//2*sec(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^-3//2*csc(e+f*x)^3, x) == :(-1//2*a^-5//2*f^-1*(a+-3b)*arctanh(a^(1/2)*(a+-1b+b*sec(e+f*x)^2)^-1//2*sec(e+f*x))+-3//2*b*a^-2*f^-1*(a+-1b+b*sec(e+f*x)^2)^-1//2*sec(e+f*x)+-1//2*a^-1*f^-1*(a+-1b+b*sec(e+f*x)^2)^-1//2*cot(e+f*x)*csc(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^-3//2*csc(e+f*x)^5, x) == :(-1//4*a^-1*f^-1*(a+-1b+b*sec(e+f*x)^2)^-1//2*cot(e+f*x)^3*csc(e+f*x)+1//8*a^-7//2*f^-1*(a+-1b)*(-3a+15b)*arctanh(a^(1/2)*(a+-1b+b*sec(e+f*x)^2)^-1//2*sec(e+f*x))+-1//8*b*a^-3*f^-1*(a+-1b+b*sec(e+f*x)^2)^-1//2*(-15b+13a)*sec(e+f*x)+-1//8*a^-2*f^-1*(a+-1b+b*sec(e+f*x)^2)^-1//2*(-5b+5a)*cot(e+f*x)*csc(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^-3//2*sin(e+f*x)^4, x) == :(f^-1*(a+b*tan(e+f*x)^2)^-1//2*(-4b+4a)^-1*cos(e+f*x)^3*sin(e+f*x)+3//8*a*f^-1*(a+-1b)^-7//2*(a+4b)*arctan((a+-1b)^(1/2)*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-5//8*a*f^-1*(a+-1b)^-2*(a+b*tan(e+f*x)^2)^-1//2*cos(e+f*x)*sin(e+f*x)+-1//8*b*f^-1*(a+-1b)^-3*(a+b*tan(e+f*x)^2)^-1//2*(2b+13a)*tan(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^-3//2*sin(e+f*x)^2, x) == :((1/2)*f^-1*(a+-1b)^-5//2*(a+2b)*arctan((a+-1b)^(1/2)*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1*f^-1*(a+b*tan(e+f*x)^2)^-1//2*(-2b+2a)^-1*cos(e+f*x)*sin(e+f*x)+-3//2*b*f^-1*(a+-1b)^-2*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^-3//2, x) == :(f^-1*(a+-1b)^-3//2*arctan((a+-1b)^(1/2)*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1*b*a^-1*f^-1*(a+-1b)^-1*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^-3//2*csc(e+f*x)^2, x) == :(-1*a^-1*f^-1*(a+b*tan(e+f*x)^2)^-1//2*cot(e+f*x)+-2*b*a^-2*f^-1*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^-3//2*csc(e+f*x)^4, x) == :(-1//3*a^-1*f^-1*(a+b*tan(e+f*x)^2)^-1//2*cot(e+f*x)^3+-1//3*a^-2*f^-1*(a+b*tan(e+f*x)^2)^-1//2*(-4b+3a)*cot(e+f*x)+-1//3*b*a^-3*f^-1*(a+b*tan(e+f*x)^2)^-1//2*(-8b+6a)*tan(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^-3//2*csc(e+f*x)^6, x) == :(-1//5*a^-1*f^-1*(a+b*tan(e+f*x)^2)^-1//2*cot(e+f*x)^5+-1//15*a^-3*f^-1*(a+b*tan(e+f*x)^2)^-1//2*(15*a^2+24*b^2+-40*a*b)*cot(e+f*x)+-1//15*a^-2*f^-1*(a+b*tan(e+f*x)^2)^-1//2*cot(e+f*x)^3*(-6b+10a)+-2//15*b*a^-4*f^-1*(a+b*tan(e+f*x)^2)^-1//2*(15*a^2+24*b^2+-40*a*b)*tan(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^-5//2*sin(e+f*x)^5, x) == :(-1*f^-1*(-5b+5a)^-1*(a+-1b+b*sec(e+f*x)^2)^-3//2*cos(e+f*x)^5+-1//5*f^-1*(a+-1b)^-3*(a+-1b+b*sec(e+f*x)^2)^-3//2*(b^2+5*a^2+10*a*b)*cos(e+f*x)+1//15*f^-1*(a+-1b)^-2*(a+-1b+b*sec(e+f*x)^2)^-3//2*cos(e+f*x)^3*(-2b+10a)+-8//15*b*f^-1*(a+-1b)^-5*(a+-1b+b*sec(e+f*x)^2)^-1//2*(b^2+5*a^2+10*a*b)*sec(e+f*x)+-4//15*b*f^-1*(a+-1b)^-4*(a+-1b+b*sec(e+f*x)^2)^-3//2*(b^2+5*a^2+10*a*b)*sec(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^-5//2*sin(e+f*x)^3, x) == :(f^-1*(-3b+3a)^-1*(a+-1b+b*sec(e+f*x)^2)^-3//2*cos(e+f*x)^3+-1*f^-1*(a+-1b)^-2*(a+-1b+b*sec(e+f*x)^2)^-3//2*(a+b)*cos(e+f*x)+-8//3*b*f^-1*(a+-1b)^-4*(a+-1b+b*sec(e+f*x)^2)^-1//2*(a+b)*sec(e+f*x)+-4//3*b*f^-1*(a+-1b)^-3*(a+-1b+b*sec(e+f*x)^2)^-3//2*(a+b)*sec(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^-5//2*sin(e+f*x), x) == :(-1*f^-1*(a+-1b)^-1*(a+-1b+b*sec(e+f*x)^2)^-3//2*cos(e+f*x)+-8//3*b*f^-1*(a+-1b)^-3*(a+-1b+b*sec(e+f*x)^2)^-1//2*sec(e+f*x)+-4//3*b*f^-1*(a+-1b)^-2*(a+-1b+b*sec(e+f*x)^2)^-3//2*sec(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^-5//2*csc(e+f*x), x) == :(-1*a^-5//2*f^-1*arctanh(a^(1/2)*(a+-1b+b*sec(e+f*x)^2)^-1//2*sec(e+f*x))+-1//3*b*a^-1*f^-1*(a+-1b)^-1*(a+-1b+b*sec(e+f*x)^2)^-3//2*sec(e+f*x)+-1//3*b*a^-2*f^-1*(a+-1b)^-2*(a+-1b+b*sec(e+f*x)^2)^-1//2*(-3b+5a)*sec(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^-5//2*csc(e+f*x)^3, x) == :(-1//2*a^-7//2*f^-1*(a+-5b)*arctanh(a^(1/2)*(a+-1b+b*sec(e+f*x)^2)^-1//2*sec(e+f*x))+-5//6*b*a^-2*f^-1*(a+-1b+b*sec(e+f*x)^2)^-3//2*sec(e+f*x)+-1//2*a^-1*f^-1*(a+-1b+b*sec(e+f*x)^2)^-3//2*cot(e+f*x)*csc(e+f*x)+-1//6*b*a^-3*f^-1*(a+-1b)^-1*(a+-1b+b*sec(e+f*x)^2)^-1//2*(-15b+13a)*sec(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^-5//2*csc(e+f*x)^5, x) == :(-1//8*a^-9//2*f^-1*(3*a^2+35*b^2+-30*a*b)*arctanh(a^(1/2)*(a+-1b+b*sec(e+f*x)^2)^-1//2*sec(e+f*x))+-1//4*a^-1*f^-1*(a+-1b+b*sec(e+f*x)^2)^-3//2*cot(e+f*x)^3*csc(e+f*x)+-1//8*a^-2*f^-1*(a+-1b+b*sec(e+f*x)^2)^-3//2*(-7b+5a)*cot(e+f*x)*csc(e+f*x)+-1//24*b*a^-4*f^-1*(a+-1b+b*sec(e+f*x)^2)^-1//2*(-105b+55a)*sec(e+f*x)+-1//24*b*a^-3*f^-1*(a+-1b+b*sec(e+f*x)^2)^-3//2*(-35b+23a)*sec(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^-5//2*sin(e+f*x)^4, x) == :(1//8*f^-1*(a+-1b)^-9//2*(3*a^2+8*b^2+24*a*b)*arctan((a+-1b)^(1/2)*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+f^-1*(a+b*tan(e+f*x)^2)^-3//2*(-4b+4a)^-1*cos(e+f*x)^3*sin(e+f*x)+-5//24*b*f^-1*(a+-1b)^-4*(a+b*tan(e+f*x)^2)^-1//2*(10b+11a)*tan(e+f*x)+-1//8*f^-1*(a+-1b)^-2*(a+b*tan(e+f*x)^2)^-3//2*(2b+5a)*cos(e+f*x)*sin(e+f*x)+-1//24*b*f^-1*(a+-1b)^-3*(a+b*tan(e+f*x)^2)^-3//2*(12b+23a)*tan(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^-5//2*sin(e+f*x)^2, x) == :((1/2)*f^-1*(a+-1b)^-7//2*(a+4b)*arctan((a+-1b)^(1/2)*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1*f^-1*(a+b*tan(e+f*x)^2)^-3//2*(-2b+2a)^-1*cos(e+f*x)*sin(e+f*x)+-5//6*b*f^-1*(a+-1b)^-2*(a+b*tan(e+f*x)^2)^-3//2*tan(e+f*x)+-1//6*b*a^-1*f^-1*(a+-1b)^-3*(a+b*tan(e+f*x)^2)^-1//2*(2b+13a)*tan(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^-5//2, x) == :(f^-1*(a+-1b)^-5//2*arctan((a+-1b)^(1/2)*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1//3*b*a^-1*f^-1*(a+-1b)^-1*(a+b*tan(e+f*x)^2)^-3//2*tan(e+f*x)+-1//3*b*a^-2*f^-1*(a+-1b)^-2*(a+b*tan(e+f*x)^2)^-1//2*(-2b+5a)*tan(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^-5//2*csc(e+f*x)^2, x) == :(-1*a^-1*f^-1*(a+b*tan(e+f*x)^2)^-3//2*cot(e+f*x)+-8//3*b*a^-3*f^-1*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x)+-4//3*b*a^-2*f^-1*(a+b*tan(e+f*x)^2)^-3//2*tan(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^-5//2*csc(e+f*x)^4, x) == :(-1//3*a^-1*f^-1*(a+b*tan(e+f*x)^2)^-3//2*cot(e+f*x)^3+-1*a^-2*f^-1*(a+b*tan(e+f*x)^2)^-3//2*(a+-2b)*cot(e+f*x)+-1//3*b*a^-4*f^-1*(a+b*tan(e+f*x)^2)^-1//2*(-16b+8a)*tan(e+f*x)+-1//3*b*a^-3*f^-1*(a+b*tan(e+f*x)^2)^-3//2*(-8b+4a)*tan(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^-5//2*csc(e+f*x)^6, x) == :(-1//5*a^-1*f^-1*(a+b*tan(e+f*x)^2)^-3//2*cot(e+f*x)^5+-1//5*a^-3*f^-1*(a+b*tan(e+f*x)^2)^-3//2*(5*a^2+16*b^2+-20*a*b)*cot(e+f*x)+-1//15*a^-2*f^-1*(a+b*tan(e+f*x)^2)^-3//2*cot(e+f*x)^3*(-8b+10a)+-8//15*b*a^-5*f^-1*(a+b*tan(e+f*x)^2)^-1//2*(5*a^2+16*b^2+-20*a*b)*tan(e+f*x)+-4//15*b*a^-4*f^-1*(a+b*tan(e+f*x)^2)^-3//2*(5*a^2+16*b^2+-20*a*b)*tan(e+f*x))
@test integrate((b*(c*tan(e+f*x))^n)^p*csc(e+f*x)^2, x) == :(-1*f^-1*(b*(c*tan(e+f*x))^n)^p*(1+-1*n*p)^-1*cot(e+f*x))
@test integrate((b*(c*tan(e+f*x))^n)^p*csc(e+f*x)^4, x) == :(-1*f^-1*(b*(c*tan(e+f*x))^n)^p*(1+-1*n*p)^-1*cot(e+f*x)+-1*f^-1*(b*(c*tan(e+f*x))^n)^p*(3+-1*n*p)^-1*cot(e+f*x)^3)
@test integrate((b*(c*tan(e+f*x))^n)^p*csc(e+f*x)^6, x) == :(-1*f^-1*(b*(c*tan(e+f*x))^n)^p*(1+-1*n*p)^-1*cot(e+f*x)+-1*f^-1*(b*(c*tan(e+f*x))^n)^p*(5+-1*n*p)^-1*cot(e+f*x)^5+-2*f^-1*(b*(c*tan(e+f*x))^n)^p*(3+-1*n*p)^-1*cot(e+f*x)^3)
@test integrate((a+a*tan(c+d*x)^2)^4, x) == :(a^4*d^-1*tan(c+d*x)^3+a^4*d^-1*tan(c+d*x)+1//7*a^4*d^-1*tan(c+d*x)^7+3//5*a^4*d^-1*tan(c+d*x)^5)
@test integrate((a+a*tan(c+d*x)^2)^3, x) == :(a^3*d^-1*tan(c+d*x)+1//5*a^3*d^-1*tan(c+d*x)^5+2//3*a^3*d^-1*tan(c+d*x)^3)
@test integrate((a+a*tan(c+d*x)^2)^2, x) == :(a^2*d^-1*tan(c+d*x)+1//3*a^2*d^-1*tan(c+d*x)^3)
@test integrate((a+a*tan(c+d*x)^2)^-1, x) == :((1/2)*x*a^-1+(1/2)*a^-1*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*tan(c+d*x)^2)^-2, x) == :(3//8*x*a^-2+1//4*a^-2*d^-1*cos(c+d*x)^3*sin(c+d*x)+3//8*a^-2*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*tan(c+d*x)^2)^-3, x) == :(5//16*x*a^-3+1//6*a^-3*d^-1*cos(c+d*x)^5*sin(c+d*x)+5//16*a^-3*d^-1*cos(c+d*x)*sin(c+d*x)+5//24*a^-3*d^-1*cos(c+d*x)^3*sin(c+d*x))
@test integrate(tan(e+f*x)^5*(a+b*tan(e+f*x)^2), x) == :(-1*f^-1*(a+-1b)*log(cos(e+f*x))+-1//2*f^-1*tan(e+f*x)^2*(a+-1b)+1//4*f^-1*tan(e+f*x)^4*(a+-1b)+1//6*b*f^-1*tan(e+f*x)^6)
@test integrate(tan(e+f*x)^3*(a+b*tan(e+f*x)^2), x) == :(f^-1*(a+-1b)*log(cos(e+f*x))+(1/2)*f^-1*tan(e+f*x)^2*(a+-1b)+1//4*b*f^-1*tan(e+f*x)^4)
@test integrate((a+b*tan(e+f*x)^2)*tan(e+f*x), x) == :((1/2)*b*f^-1*tan(e+f*x)^2+-1*f^-1*(a+-1b)*log(cos(e+f*x)))
@test integrate((a+b*tan(e+f*x)^2)*cot(e+f*x), x) == :(a*f^-1*log(sin(e+f*x))+-1*b*f^-1*log(cos(e+f*x)))
@test integrate(cot(e+f*x)^3*(a+b*tan(e+f*x)^2), x) == :(-1*f^-1*(a+-1b)*log(sin(e+f*x))+-1//2*a*f^-1*cot(e+f*x)^2)
@test integrate(cot(e+f*x)^5*(a+b*tan(e+f*x)^2), x) == :(f^-1*(a+-1b)*log(sin(e+f*x))+(1/2)*f^-1*cot(e+f*x)^2*(a+-1b)+-1//4*a*f^-1*cot(e+f*x)^4)
@test integrate(tan(e+f*x)^6*(a+b*tan(e+f*x)^2), x) == :(-1*x*(a+-1b)+f^-1*(a+-1b)*tan(e+f*x)+-1//3*f^-1*tan(e+f*x)^3*(a+-1b)+1//5*f^-1*tan(e+f*x)^5*(a+-1b)+1//7*b*f^-1*tan(e+f*x)^7)
@test integrate(tan(e+f*x)^4*(a+b*tan(e+f*x)^2), x) == :(x*(a+-1b)+-1*f^-1*(a+-1b)*tan(e+f*x)+1//3*f^-1*tan(e+f*x)^3*(a+-1b)+1//5*b*f^-1*tan(e+f*x)^5)
@test integrate(tan(e+f*x)^2*(a+b*tan(e+f*x)^2), x) == :(-1*x*(a+-1b)+f^-1*(a+-1b)*tan(e+f*x)+1//3*b*f^-1*tan(e+f*x)^3)
@test integrate(a+b*tan(e+f*x)^2, x) == :(a*x+-1*b*x+b*f^-1*tan(e+f*x))
@test integrate(cot(e+f*x)^2*(a+b*tan(e+f*x)^2), x) == :(-1*x*(a+-1b)+-1*a*f^-1*cot(e+f*x))
@test integrate(cot(e+f*x)^4*(a+b*tan(e+f*x)^2), x) == :(x*(a+-1b)+f^-1*(a+-1b)*cot(e+f*x)+-1//3*a*f^-1*cot(e+f*x)^3)
@test integrate(cot(e+f*x)^6*(a+b*tan(e+f*x)^2), x) == :(-1*x*(a+-1b)+-1*f^-1*(a+-1b)*cot(e+f*x)+-1//5*a*f^-1*cot(e+f*x)^5+1//3*f^-1*cot(e+f*x)^3*(a+-1b))
@test integrate((a+b*tan(e+f*x)^2)^2*tan(e+f*x)^5, x) == :(-1*f^-1*(a+-1b)^2*log(cos(e+f*x))+-1//2*f^-1*(a+-1b)^2*tan(e+f*x)^2+1//4*f^-1*(a+-1b)^2*tan(e+f*x)^4+1//8*b^2*f^-1*tan(e+f*x)^8+1//6*b*f^-1*tan(e+f*x)^6*(-1b+2a))
@test integrate((a+b*tan(e+f*x)^2)^2*tan(e+f*x)^3, x) == :(f^-1*(a+-1b)^2*log(cos(e+f*x))+(1/2)*f^-1*(a+-1b)^2*tan(e+f*x)^2+1//6*b^2*f^-1*tan(e+f*x)^6+1//4*b*f^-1*tan(e+f*x)^4*(-1b+2a))
@test integrate((a+b*tan(e+f*x)^2)^2*tan(e+f*x), x) == :(1//4*f^-1*(a+b*tan(e+f*x)^2)^2+-1*f^-1*(a+-1b)^2*log(cos(e+f*x))+(1/2)*b*f^-1*tan(e+f*x)^2*(a+-1b))
@test integrate((a+b*tan(e+f*x)^2)^2*cot(e+f*x), x) == :(a^2*f^-1*log(tan(e+f*x))+f^-1*(a+-1b)^2*log(cos(e+f*x))+(1/2)*b^2*f^-1*tan(e+f*x)^2)
@test integrate((a+b*tan(e+f*x)^2)^2*cot(e+f*x)^3, x) == :(-1*f^-1*(a+-1b)^2*log(cos(e+f*x))+-1//2*a^2*f^-1*cot(e+f*x)^2+-1*a*f^-1*(a+-2b)*log(tan(e+f*x)))
@test integrate((a+b*tan(e+f*x)^2)^2*cot(e+f*x)^5, x) == :(f^-1*(a+-1b)^2*log(cos(e+f*x))+f^-1*(a+-1b)^2*log(tan(e+f*x))+-1//4*a^2*f^-1*cot(e+f*x)^4+(1/2)*a*f^-1*cot(e+f*x)^2*(a+-2b))
@test integrate((a+b*tan(e+f*x)^2)^2*tan(e+f*x)^6, x) == :(-1*x*(a+-1b)^2+f^-1*(a+-1b)^2*tan(e+f*x)+-1//3*f^-1*(a+-1b)^2*tan(e+f*x)^3+1//5*f^-1*(a+-1b)^2*tan(e+f*x)^5+1//9*b^2*f^-1*tan(e+f*x)^9+1//7*b*f^-1*tan(e+f*x)^7*(-1b+2a))
@test integrate((a+b*tan(e+f*x)^2)^2*tan(e+f*x)^4, x) == :(x*(a+-1b)^2+-1*f^-1*(a+-1b)^2*tan(e+f*x)+1//3*f^-1*(a+-1b)^2*tan(e+f*x)^3+1//7*b^2*f^-1*tan(e+f*x)^7+1//5*b*f^-1*tan(e+f*x)^5*(-1b+2a))
@test integrate((a+b*tan(e+f*x)^2)^2*tan(e+f*x)^2, x) == :(-1*x*(a+-1b)^2+f^-1*(a+-1b)^2*tan(e+f*x)+1//5*b^2*f^-1*tan(e+f*x)^5+1//3*b*f^-1*tan(e+f*x)^3*(-1b+2a))
@test integrate((a+b*tan(e+f*x)^2)^2, x) == :(x*(a+-1b)^2+1//3*b^2*f^-1*tan(e+f*x)^3+b*f^-1*(-1b+2a)*tan(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^2*cot(e+f*x)^2, x) == :(-1*x*(a+-1b)^2+b^2*f^-1*tan(e+f*x)+-1*a^2*f^-1*cot(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^2*cot(e+f*x)^4, x) == :(x*(a+-1b)^2+-1//3*a^2*f^-1*cot(e+f*x)^3+a*f^-1*(a+-2b)*cot(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^2*cot(e+f*x)^6, x) == :(-1*x*(a+-1b)^2+-1*f^-1*(a+-1b)^2*cot(e+f*x)+-1//5*a^2*f^-1*cot(e+f*x)^5+1//3*a*f^-1*cot(e+f*x)^3*(a+-2b))
@test integrate((a+b*tan(e+f*x)^2)^-1*tan(e+f*x)^5, x) == :((1/2)*b^-1*f^-1*tan(e+f*x)^2+-1*f^-1*(a+-1b)^-1*log(cos(e+f*x))+-1*a^2*b^-2*f^-1*(-2b+2a)^-1*log(a+b*tan(e+f*x)^2))
@test integrate((a+b*tan(e+f*x)^2)^-1*tan(e+f*x)^3, x) == :(f^-1*(a+-1b)^-1*log(cos(e+f*x))+a*b^-1*f^-1*(-2b+2a)^-1*log(a+b*tan(e+f*x)^2))
@test integrate((a+b*tan(e+f*x)^2)^-1*tan(e+f*x), x) == :(-1*f^-1*(-2b+2a)^-1*log(a*cos(e+f*x)^2+b*sin(e+f*x)^2))
@test integrate((a+b*tan(e+f*x)^2)^-1*cot(e+f*x), x) == :(a^-1*f^-1*log(tan(e+f*x))+f^-1*(a+-1b)^-1*log(cos(e+f*x))+(1/2)*b*a^-1*f^-1*(a+-1b)^-1*log(a+b*tan(e+f*x)^2))
@test integrate((a+b*tan(e+f*x)^2)^-1*cot(e+f*x)^3, x) == :(-1*f^-1*(a+-1b)^-1*log(cos(e+f*x))+-1//2*a^-1*f^-1*cot(e+f*x)^2+-1*a^-2*f^-1*(a+b)*log(tan(e+f*x))+-1//2*a^-2*b^2*f^-1*(a+-1b)^-1*log(a+b*tan(e+f*x)^2))
@test integrate((a+b*tan(e+f*x)^2)^-1*cot(e+f*x)^5, x) == :(f^-1*(a+-1b)^-1*log(cos(e+f*x))+-1//4*a^-1*f^-1*cot(e+f*x)^4+a^-3*f^-1*(a^2+b^2+a*b)*log(tan(e+f*x))+(1/2)*a^-2*f^-1*cot(e+f*x)^2*(a+b)+(1/2)*a^-3*b^3*f^-1*(a+-1b)^-1*log(a+b*tan(e+f*x)^2))
@test integrate((a+b*tan(e+f*x)^2)^-1*tan(e+f*x)^6, x) == :(-1*x*(a+-1b)^-1+1//3*b^-1*f^-1*tan(e+f*x)^3+-1*b^-2*f^-1*(a+b)*tan(e+f*x)+a^5//2*b^-5//2*f^-1*(a+-1b)^-1*arctan(a^-1//2*b^(1/2)*tan(e+f*x)))
@test integrate((a+b*tan(e+f*x)^2)^-1*tan(e+f*x)^4, x) == :(x*(a+-1b)^-1+b^-1*f^-1*tan(e+f*x)+-1*a^3//2*b^-3//2*f^-1*(a+-1b)^-1*arctan(a^-1//2*b^(1/2)*tan(e+f*x)))
@test integrate((a+b*tan(e+f*x)^2)^-1*tan(e+f*x)^2, x) == :(-1*x*(a+-1b)^-1+a^(1/2)*b^-1//2*f^-1*(a+-1b)^-1*arctan(a^-1//2*b^(1/2)*tan(e+f*x)))
@test integrate((a+b*tan(e+f*x)^2)^-1, x) == :(x*(a+-1b)^-1+-1*a^-1//2*b^(1/2)*f^-1*(a+-1b)^-1*arctan(a^-1//2*b^(1/2)*tan(e+f*x)))
@test integrate((a+b*tan(e+f*x)^2)^-1*cot(e+f*x)^2, x) == :(-1*x*(a+-1b)^-1+-1*a^-1*f^-1*cot(e+f*x)+a^-3//2*b^3//2*f^-1*(a+-1b)^-1*arctan(a^-1//2*b^(1/2)*tan(e+f*x)))
@test integrate((a+b*tan(e+f*x)^2)^-1*cot(e+f*x)^4, x) == :(x*(a+-1b)^-1+-1//3*a^-1*f^-1*cot(e+f*x)^3+a^-2*f^-1*(a+b)*cot(e+f*x)+-1*a^-5//2*b^5//2*f^-1*(a+-1b)^-1*arctan(a^-1//2*b^(1/2)*tan(e+f*x)))
@test integrate((a+b*tan(e+f*x)^2)^-1*cot(e+f*x)^6, x) == :(-1*x*(a+-1b)^-1+-1//5*a^-1*f^-1*cot(e+f*x)^5+-1*a^-3*f^-1*(a^2+b^2+a*b)*cot(e+f*x)+1//3*a^-2*f^-1*cot(e+f*x)^3*(a+b)+a^-7//2*b^7//2*f^-1*(a+-1b)^-1*arctan(a^-1//2*b^(1/2)*tan(e+f*x)))
@test integrate((a+b*tan(e+f*x)^2)^-2*tan(e+f*x)^5, x) == :(-1*f^-1*(a+-1b)^-2*log(cos(e+f*x))+a^2*b^-2*f^-1*(a+b*tan(e+f*x)^2)^-1*(-2b+2a)^-1+(1/2)*a*b^-2*f^-1*(a+-1b)^-2*(a+-2b)*log(a+b*tan(e+f*x)^2))
@test integrate((a+b*tan(e+f*x)^2)^-2*tan(e+f*x)^3, x) == :((1/2)*f^-1*(a+-1b)^-2*log(a*cos(e+f*x)^2+b*sin(e+f*x)^2)+-1*a*b^-1*f^-1*(a+b*tan(e+f*x)^2)^-1*(-2b+2a)^-1)
@test integrate((a+b*tan(e+f*x)^2)^-2*tan(e+f*x), x) == :(f^-1*(a+b*tan(e+f*x)^2)^-1*(-2b+2a)^-1+-1//2*f^-1*(a+-1b)^-2*log(a*cos(e+f*x)^2+b*sin(e+f*x)^2))
@test integrate((a+b*tan(e+f*x)^2)^-2*cot(e+f*x), x) == :(a^-2*f^-1*log(tan(e+f*x))+f^-1*(a+-1b)^-2*log(cos(e+f*x))+-1//2*b*a^-1*f^-1*(a+-1b)^-1*(a+b*tan(e+f*x)^2)^-1+(1/2)*b*a^-2*f^-1*(a+-1b)^-2*(-1b+2a)*log(a+b*tan(e+f*x)^2))
@test integrate((a+b*tan(e+f*x)^2)^-2*cot(e+f*x)^3, x) == :(-1*f^-1*(a+-1b)^-2*log(cos(e+f*x))+-1//2*a^-2*f^-1*cot(e+f*x)^2+-1*a^-3*f^-1*(a+2b)*log(tan(e+f*x))+(1/2)*a^-2*b^2*f^-1*(a+-1b)^-1*(a+b*tan(e+f*x)^2)^-1+-1//2*a^-3*b^2*f^-1*(a+-1b)^-2*(-2b+3a)*log(a+b*tan(e+f*x)^2))
@test integrate((a+b*tan(e+f*x)^2)^-2*cot(e+f*x)^5, x) == :(f^-1*(a+-1b)^-2*log(cos(e+f*x))+-1//4*a^-2*f^-1*cot(e+f*x)^4+a^-4*f^-1*(a^2+3*b^2+2*a*b)*log(tan(e+f*x))+(1/2)*a^-3*f^-1*cot(e+f*x)^2*(a+2b)+-1//2*a^-3*b^3*f^-1*(a+-1b)^-1*(a+b*tan(e+f*x)^2)^-1+(1/2)*a^-4*b^3*f^-1*(a+-1b)^-2*(-3b+4a)*log(a+b*tan(e+f*x)^2))
@test integrate((a+b*tan(e+f*x)^2)^-2*tan(e+f*x)^6, x) == :(-1*x*(a+-1b)^-2+b^-2*f^-1*(-2b+2a)^-1*(-2b+3a)*tan(e+f*x)+-1*a*b^-1*f^-1*(a+b*tan(e+f*x)^2)^-1*(-2b+2a)^-1*tan(e+f*x)^3+-1//2*a^3//2*b^-5//2*f^-1*(a+-1b)^-2*(-5b+3a)*arctan(a^-1//2*b^(1/2)*tan(e+f*x)))
@test integrate((a+b*tan(e+f*x)^2)^-2*tan(e+f*x)^4, x) == :(x*(a+-1b)^-2+(1/2)*a^(1/2)*b^-3//2*f^-1*(a+-1b)^-2*(a+-3b)*arctan(a^-1//2*b^(1/2)*tan(e+f*x))+-1*a*b^-1*f^-1*(a+b*tan(e+f*x)^2)^-1*(-2b+2a)^-1*tan(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^-2*tan(e+f*x)^2, x) == :(-1*x*(a+-1b)^-2+f^-1*(a+b*tan(e+f*x)^2)^-1*(-2b+2a)^-1*tan(e+f*x)+(1/2)*a^-1//2*b^-1//2*f^-1*(a+-1b)^-2*(a+b)*arctan(a^-1//2*b^(1/2)*tan(e+f*x)))
@test integrate((a+b*tan(e+f*x)^2)^-2, x) == :(x*(a+-1b)^-2+-1//2*b*a^-1*f^-1*(a+-1b)^-1*(a+b*tan(e+f*x)^2)^-1*tan(e+f*x)+-1//2*a^-3//2*b^(1/2)*f^-1*(a+-1b)^-2*(-1b+3a)*arctan(a^-1//2*b^(1/2)*tan(e+f*x)))
@test integrate((a+b*tan(e+f*x)^2)^-2*cot(e+f*x)^2, x) == :(-1*x*(a+-1b)^-2+-1//2*a^-2*f^-1*(a+-1b)^-1*(-3b+2a)*cot(e+f*x)+(1/2)*a^-5//2*b^3//2*f^-1*(a+-1b)^-2*(-3b+5a)*arctan(a^-1//2*b^(1/2)*tan(e+f*x))+-1//2*b*a^-1*f^-1*(a+-1b)^-1*(a+b*tan(e+f*x)^2)^-1*cot(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^-2*cot(e+f*x)^4, x) == :(x*(a+-1b)^-2+(1/2)*a^-3*f^-1*(a+-1b)^-1*(-5*b^2+2*a^2+2*a*b)*cot(e+f*x)+-1//6*a^-2*f^-1*(a+-1b)^-1*cot(e+f*x)^3*(-5b+2a)+-1//2*b*a^-1*f^-1*(a+-1b)^-1*(a+b*tan(e+f*x)^2)^-1*cot(e+f*x)^3+-1//2*a^-7//2*b^5//2*f^-1*(a+-1b)^-2*(-5b+7a)*arctan(a^-1//2*b^(1/2)*tan(e+f*x)))
@test integrate((a+b*tan(e+f*x)^2)^-2*cot(e+f*x)^6, x) == :(-1*x*(a+-1b)^-2+-1//2*a^-4*f^-1*(a+-1b)^-1*(-7*b^3+2*a^3+2*a*b^2+2*b*a^2)*cot(e+f*x)+-1//10*a^-2*f^-1*(a+-1b)^-1*cot(e+f*x)^5*(-7b+2a)+1//6*a^-3*f^-1*(a+-1b)^-1*cot(e+f*x)^3*(-7*b^2+2*a^2+2*a*b)+(1/2)*a^-9//2*b^7//2*f^-1*(a+-1b)^-2*(-7b+9a)*arctan(a^-1//2*b^(1/2)*tan(e+f*x))+-1//2*b*a^-1*f^-1*(a+-1b)^-1*(a+b*tan(e+f*x)^2)^-1*cot(e+f*x)^5)
@test integrate((a+b*tan(e+f*x)^2)^-3*tan(e+f*x)^5, x) == :(-1//2*f^-1*(a+-1b)^-3*log(a*cos(e+f*x)^2+b*sin(e+f*x)^2)+a^2*b^-2*f^-1*(a+b*tan(e+f*x)^2)^-2*(-4b+4a)^-1+-1//2*a*b^-2*f^-1*(a+-1b)^-2*(a+b*tan(e+f*x)^2)^-1*(a+-2b))
@test integrate((a+b*tan(e+f*x)^2)^-3*tan(e+f*x)^3, x) == :((1/2)*f^-1*(a+-1b)^-3*log(a*cos(e+f*x)^2+b*sin(e+f*x)^2)+-1//2*f^-1*(a+-1b)^-2*(a+b*tan(e+f*x)^2)^-1+-1*a*b^-1*f^-1*(a+b*tan(e+f*x)^2)^-2*(-4b+4a)^-1)
@test integrate((a+b*tan(e+f*x)^2)^-3*tan(e+f*x), x) == :(f^-1*(a+b*tan(e+f*x)^2)^-2*(-4b+4a)^-1+(1/2)*f^-1*(a+-1b)^-2*(a+b*tan(e+f*x)^2)^-1+-1//2*f^-1*(a+-1b)^-3*log(a*cos(e+f*x)^2+b*sin(e+f*x)^2))
@test integrate((a+b*tan(e+f*x)^2)^-3*cot(e+f*x), x) == :(a^-3*f^-1*log(tan(e+f*x))+f^-1*(a+-1b)^-3*log(cos(e+f*x))+-1//4*b*a^-1*f^-1*(a+-1b)^-1*(a+b*tan(e+f*x)^2)^-2+(1/2)*b*a^-3*f^-1*(a+-1b)^-3*(b^2+3*a^2+-3*a*b)*log(a+b*tan(e+f*x)^2)+-1//2*b*a^-2*f^-1*(a+-1b)^-2*(a+b*tan(e+f*x)^2)^-1*(-1b+2a))
@test integrate((a+b*tan(e+f*x)^2)^-3*cot(e+f*x)^3, x) == :(-1*f^-1*(a+-1b)^-3*log(cos(e+f*x))+-1//2*a^-3*f^-1*cot(e+f*x)^2+-1*a^-4*f^-1*(a+3b)*log(tan(e+f*x))+1//4*a^-2*b^2*f^-1*(a+-1b)^-1*(a+b*tan(e+f*x)^2)^-2+(1/2)*a^-3*b^2*f^-1*(a+-1b)^-2*(a+b*tan(e+f*x)^2)^-1*(-2b+3a)+-1//2*a^-4*b^2*f^-1*(a+-1b)^-3*(3*b^2+6*a^2+-8*a*b)*log(a+b*tan(e+f*x)^2))
@test integrate((a+b*tan(e+f*x)^2)^-3*cot(e+f*x)^5, x) == :(f^-1*(a+-1b)^-3*log(cos(e+f*x))+-1//4*a^-3*f^-1*cot(e+f*x)^4+a^-5*f^-1*(a^2+6*b^2+3*a*b)*log(tan(e+f*x))+(1/2)*a^-4*f^-1*cot(e+f*x)^2*(a+3b)+-1//4*a^-3*b^3*f^-1*(a+-1b)^-1*(a+b*tan(e+f*x)^2)^-2+(1/2)*a^-5*b^3*f^-1*(a+-1b)^-3*(6*b^2+10*a^2+-15*a*b)*log(a+b*tan(e+f*x)^2)+-1//2*a^-4*b^3*f^-1*(a+-1b)^-2*(a+b*tan(e+f*x)^2)^-1*(-3b+4a))
@test integrate((a+b*tan(e+f*x)^2)^-3*tan(e+f*x)^6, x) == :(-1*x*(a+-1b)^-3+-1*a*b^-1*f^-1*(a+b*tan(e+f*x)^2)^-2*(-4b+4a)^-1*tan(e+f*x)^3+1//8*a^(1/2)*b^-5//2*f^-1*(a+-1b)^-3*(3*a^2+15*b^2+-10*a*b)*arctan(a^-1//2*b^(1/2)*tan(e+f*x))+-1//8*a*b^-2*f^-1*(a+-1b)^-2*(a+b*tan(e+f*x)^2)^-1*(-7b+3a)*tan(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^-3*tan(e+f*x)^4, x) == :(x*(a+-1b)^-3+-1*a*b^-1*f^-1*(a+b*tan(e+f*x)^2)^-2*(-4b+4a)^-1*tan(e+f*x)+1//8*a^-1//2*b^-3//2*f^-1*(a+-1b)^-3*(a^2+-3*b^2+-6*a*b)*arctan(a^-1//2*b^(1/2)*tan(e+f*x))+1//8*b^-1*f^-1*(a+-1b)^-2*(a+b*tan(e+f*x)^2)^-1*(a+-5b)*tan(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^-3*tan(e+f*x)^2, x) == :(-1*x*(a+-1b)^-3+f^-1*(a+b*tan(e+f*x)^2)^-2*(-4b+4a)^-1*tan(e+f*x)+1//8*a^-1*f^-1*(a+-1b)^-2*(a+b*tan(e+f*x)^2)^-1*(b+3a)*tan(e+f*x)+1//8*a^-3//2*b^-1//2*f^-1*(a+-1b)^-3*(-1*b^2+3*a^2+6*a*b)*arctan(a^-1//2*b^(1/2)*tan(e+f*x)))
@test integrate((a+b*tan(e+f*x)^2)^-3, x) == :(x*(a+-1b)^-3+-1//4*b*a^-1*f^-1*(a+-1b)^-1*(a+b*tan(e+f*x)^2)^-2*tan(e+f*x)+-1//8*a^-5//2*b^(1/2)*f^-1*(a+-1b)^-3*(3*b^2+15*a^2+-10*a*b)*arctan(a^-1//2*b^(1/2)*tan(e+f*x))+-1//8*b*a^-2*f^-1*(a+-1b)^-2*(a+b*tan(e+f*x)^2)^-1*(-3b+7a)*tan(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^-3*cot(e+f*x)^2, x) == :(-1*x*(a+-1b)^-3+-1//8*a^-3*f^-1*(a+-1b)^-2*(8*a^2+15*b^2+-27*a*b)*cot(e+f*x)+-1//4*b*a^-1*f^-1*(a+-1b)^-1*(a+b*tan(e+f*x)^2)^-2*cot(e+f*x)+1//8*a^-7//2*b^3//2*f^-1*(a+-1b)^-3*(15*b^2+35*a^2+-42*a*b)*arctan(a^-1//2*b^(1/2)*tan(e+f*x))+-1//8*b*a^-2*f^-1*(a+-1b)^-2*(a+b*tan(e+f*x)^2)^-1*(-5b+9a)*cot(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^-3*cot(e+f*x)^4, x) == :(x*(a+-1b)^-3+-1//24*a^-3*f^-1*(a+-1b)^-2*cot(e+f*x)^3*(8*a^2+35*b^2+-55*a*b)+1//8*a^-4*f^-1*(a+-1b)^-2*(8*a^3+35*b^3+-55*a*b^2+8*b*a^2)*cot(e+f*x)+-1//4*b*a^-1*f^-1*(a+-1b)^-1*(a+b*tan(e+f*x)^2)^-2*cot(e+f*x)^3+-1//8*a^-9//2*b^5//2*f^-1*(a+-1b)^-3*(35*b^2+63*a^2+-90*a*b)*arctan(a^-1//2*b^(1/2)*tan(e+f*x))+-1//8*b*a^-2*f^-1*(a+-1b)^-2*(a+b*tan(e+f*x)^2)^-1*cot(e+f*x)^3*(-7b+11a))
@test integrate((a+b*tan(e+f*x)^2)^-3*cot(e+f*x)^6, x) == :(-1*x*(a+-1b)^-3+-1//8*a^-5*f^-1*(a+-1b)^-2*(8*a^4+63*b^4+-91*a*b^3+8*b*a^3+8*a^2*b^2)*cot(e+f*x)+-1//40*a^-3*f^-1*(a+-1b)^-2*cot(e+f*x)^5*(8*a^2+63*b^2+-91*a*b)+1//24*a^-4*f^-1*(a+-1b)^-2*cot(e+f*x)^3*(8*a^3+63*b^3+-91*a*b^2+8*b*a^2)+-1//4*b*a^-1*f^-1*(a+-1b)^-1*(a+b*tan(e+f*x)^2)^-2*cot(e+f*x)^5+1//8*a^-11//2*b^7//2*f^-1*(a+-1b)^-3*(63*b^2+99*a^2+-154*a*b)*arctan(a^-1//2*b^(1/2)*tan(e+f*x))+-1//8*b*a^-2*f^-1*(a+-1b)^-2*(a+b*tan(e+f*x)^2)^-1*cot(e+f*x)^5*(-9b+13a))
@test integrate((a+b*tan(c+d*x)^2)^4, x) == :(x*(a+-1b)^4+1//7*b^4*d^-1*tan(c+d*x)^7+1//3*b^2*d^-1*tan(c+d*x)^3*(b^2+6*a^2+-4*a*b)+1//5*b^3*d^-1*tan(c+d*x)^5*(-1b+4a)+b*d^-1*(-1b+2a)*(b^2+2*a^2+-2*a*b)*tan(c+d*x))
@test integrate((a+b*tan(c+d*x)^2)^3, x) == :(x*(a+-1b)^3+1//5*b^3*d^-1*tan(c+d*x)^5+b*d^-1*(b^2+3*a^2+-3*a*b)*tan(c+d*x)+1//3*b^2*d^-1*tan(c+d*x)^3*(-1b+3a))
@test integrate((a+b*tan(c+d*x)^2)^2, x) == :(x*(a+-1b)^2+1//3*b^2*d^-1*tan(c+d*x)^3+b*d^-1*(-1b+2a)*tan(c+d*x))
@test integrate(a+b*tan(c+d*x)^2, x) == :(a*x+-1*b*x+b*d^-1*tan(c+d*x))
@test integrate((a+b*tan(c+d*x)^2)^-1, x) == :(x*(a+-1b)^-1+-1*a^-1//2*b^(1/2)*d^-1*(a+-1b)^-1*arctan(a^-1//2*b^(1/2)*tan(c+d*x)))
@test integrate((a+b*tan(c+d*x)^2)^-2, x) == :(x*(a+-1b)^-2+-1//2*b*a^-1*d^-1*(a+-1b)^-1*(a+b*tan(c+d*x)^2)^-1*tan(c+d*x)+-1//2*a^-3//2*b^(1/2)*d^-1*(a+-1b)^-2*(-1b+3a)*arctan(a^-1//2*b^(1/2)*tan(c+d*x)))
@test integrate((a+b*tan(c+d*x)^2)^-3, x) == :(x*(a+-1b)^-3+-1//4*b*a^-1*d^-1*(a+-1b)^-1*(a+b*tan(c+d*x)^2)^-2*tan(c+d*x)+-1//8*a^-5//2*b^(1/2)*d^-1*(a+-1b)^-3*(3*b^2+15*a^2+-10*a*b)*arctan(a^-1//2*b^(1/2)*tan(c+d*x))+-1//8*b*a^-2*d^-1*(a+-1b)^-2*(a+b*tan(c+d*x)^2)^-1*(-3b+7a)*tan(c+d*x))
@test integrate((a+a*tan(x)^2)^(1/2)*tan(x)^4, x) == :(-3//8*(a*sec(x)^2)^(1/2)*tan(x)+1//4*(a*sec(x)^2)^(1/2)*tan(x)^3+3//8*(a*sec(x)^2)^(1/2)*arctanh(sin(x))*cos(x))
@test integrate((a+a*tan(x)^2)^(1/2)*tan(x)^3, x) == :(-1*(a*sec(x)^2)^(1/2)+1//3*a^-1*(a*sec(x)^2)^3//2)
@test integrate((a+a*tan(x)^2)^(1/2)*tan(x)^2, x) == :((1/2)*(a*sec(x)^2)^(1/2)*tan(x)+-1//2*(a*sec(x)^2)^(1/2)*arctanh(sin(x))*cos(x))
@test integrate((a+a*tan(x)^2)^(1/2)*tan(x), x) == :((a*sec(x)^2)^(1/2))
@test integrate((a+a*tan(x)^2)^(1/2)*cot(x), x) == :(-1*a^(1/2)*arctanh(a^-1//2*(a*sec(x)^2)^(1/2)))
@test integrate((a+a*tan(x)^2)^(1/2)*cot(x)^2, x) == :(-1*(a*sec(x)^2)^(1/2)*cot(x))
@test integrate((a+a*tan(x)^2)^(1/2)*cot(x)^3, x) == :((1/2)*a^(1/2)*arctanh(a^-1//2*(a*sec(x)^2)^(1/2))+-1//2*(a*sec(x)^2)^(1/2)*cot(x)^2)
@test integrate((a+a*tan(x)^2)^(1/2)*cot(x)^4, x) == :((a*sec(x)^2)^(1/2)*cot(x)+-1//3*(a*sec(x)^2)^(1/2)*csc(x)^2*cot(x))
@test integrate((a+a*tan(c+d*x)^2)^(1/2), x) == :(a^(1/2)*d^-1*arctanh(a^(1/2)*(a*sec(c+d*x)^2)^-1//2*tan(c+d*x)))
@test integrate((a+a*tan(x)^2)^3//2*tan(x)^3, x) == :(-1//3*(a*sec(x)^2)^3//2+1//5*a^-1*(a*sec(x)^2)^5//2)
@test integrate((a+a*tan(x)^2)^3//2*tan(x)^2, x) == :(-1//8*a*(a*sec(x)^2)^(1/2)*tan(x)+-1//8*a*(a*sec(x)^2)^(1/2)*arctanh(sin(x))*cos(x)+1//4*a*(a*sec(x)^2)^(1/2)*sec(x)^2*tan(x))
@test integrate((a+a*tan(x)^2)^3//2*tan(x), x) == :(1//3*(a*sec(x)^2)^3//2)
@test integrate((a+a*tan(x)^2)^3//2*cot(x), x) == :(a*(a*sec(x)^2)^(1/2)+-1*a^3//2*arctanh(a^-1//2*(a*sec(x)^2)^(1/2)))
@test integrate((a+a*tan(x)^2)^3//2*cot(x)^2, x) == :(-1*a*(a*sec(x)^2)^(1/2)*cot(x)+a*(a*sec(x)^2)^(1/2)*arctanh(sin(x))*cos(x))
@test integrate((a+a*tan(c+d*x)^2)^3//2, x) == :((1/2)*a^3//2*d^-1*arctanh(a^(1/2)*(a*sec(c+d*x)^2)^-1//2*tan(c+d*x))+(1/2)*a*d^-1*(a*sec(c+d*x)^2)^(1/2)*tan(c+d*x))
@test integrate((a+a*tan(c+d*x)^2)^5//2, x) == :(3//8*a^5//2*d^-1*arctanh(a^(1/2)*(a*sec(c+d*x)^2)^-1//2*tan(c+d*x))+1//4*a*d^-1*(a*sec(c+d*x)^2)^3//2*tan(c+d*x)+3//8*a^2*d^-1*(a*sec(c+d*x)^2)^(1/2)*tan(c+d*x))
@test integrate((a+a*tan(x)^2)^-1//2*tan(x)^3, x) == :((a*sec(x)^2)^-1//2+a^-1*(a*sec(x)^2)^(1/2))
@test integrate((a+a*tan(x)^2)^-1//2*tan(x)^2, x) == :(-1*(a*sec(x)^2)^-1//2*tan(x)+(a*sec(x)^2)^-1//2*arctanh(sin(x))*sec(x))
@test integrate((a+a*tan(x)^2)^-1//2*tan(x), x) == :(-1*(a*sec(x)^2)^-1//2)
@test integrate((a+a*tan(x)^2)^-1//2*cot(x), x) == :((a*sec(x)^2)^-1//2+-1*a^-1//2*arctanh(a^-1//2*(a*sec(x)^2)^(1/2)))
@test integrate((a+a*tan(x)^2)^-1//2*cot(x)^2, x) == :(-1*(a*sec(x)^2)^-1//2*tan(x)+-1*(a*sec(x)^2)^-1//2*csc(x)*sec(x))
@test integrate((a+a*tan(x)^2)^-3//2*tan(x)^3, x) == :(1//3*(a*sec(x)^2)^-3//2+-1*a^-1*(a*sec(x)^2)^-1//2)
@test integrate((a+a*tan(x)^2)^-3//2*tan(x)^2, x) == :(1//3*a^-1*(a*sec(x)^2)^-1//2*sin(x)^2*tan(x))
@test integrate((a+a*tan(x)^2)^-3//2*tan(x), x) == :(-1//3*(a*sec(x)^2)^-3//2)
@test integrate((a+a*tan(x)^2)^-3//2*cot(x), x) == :(1//3*(a*sec(x)^2)^-3//2+a^-1*(a*sec(x)^2)^-1//2+-1*a^-3//2*arctanh(a^-1//2*(a*sec(x)^2)^(1/2)))
@test integrate((a+a*tan(x)^2)^-3//2*cot(x)^2, x) == :(-2*a^-1*(a*sec(x)^2)^-1//2*tan(x)+-1*a^-1*(a*sec(x)^2)^-1//2*csc(x)*sec(x)+1//3*a^-1*(a*sec(x)^2)^-1//2*sin(x)^2*tan(x))
@test integrate((a+a*tan(c+d*x)^2)^-1//2, x) == :(d^-1*(a*sec(c+d*x)^2)^-1//2*tan(c+d*x))
@test integrate((a+a*tan(c+d*x)^2)^-3//2, x) == :(1//3*d^-1*(a*sec(c+d*x)^2)^-3//2*tan(c+d*x)+2//3*a^-1*d^-1*(a*sec(c+d*x)^2)^-1//2*tan(c+d*x))
@test integrate((a+a*tan(c+d*x)^2)^-5//2, x) == :(1//5*d^-1*(a*sec(c+d*x)^2)^-5//2*tan(c+d*x)+4//15*a^-1*d^-1*(a*sec(c+d*x)^2)^-3//2*tan(c+d*x)+8//15*a^-2*d^-1*(a*sec(c+d*x)^2)^-1//2*tan(c+d*x))
@test integrate((a+a*tan(c+d*x)^2)^-7//2, x) == :(1//7*d^-1*(a*sec(c+d*x)^2)^-7//2*tan(c+d*x)+6//35*a^-1*d^-1*(a*sec(c+d*x)^2)^-5//2*tan(c+d*x)+8//35*a^-2*d^-1*(a*sec(c+d*x)^2)^-3//2*tan(c+d*x)+16//35*a^-3*d^-1*(a*sec(c+d*x)^2)^-1//2*tan(c+d*x))
@test integrate((1+tan(x)^2)^3//2, x) == :((1/2)*arcsinh(tan(x))+(1/2)*(sec(x)^2)^(1/2)*tan(x))
@test integrate((1+tan(x)^2)^(1/2), x) == :(arcsinh(tan(x)))
@test integrate((1+tan(x)^2)^-1//2, x) == :((sec(x)^2)^-1//2*tan(x))
@test integrate((-1+-1*tan(x)^2)^3//2, x) == :((1/2)*arctan((-1*sec(x)^2)^-1//2*tan(x))+-1//2*(-1*sec(x)^2)^(1/2)*tan(x))
@test integrate((-1+-1*tan(x)^2)^(1/2), x) == :(-1*arctan((-1*sec(x)^2)^-1//2*tan(x)))
@test integrate((-1+-1*tan(x)^2)^-1//2, x) == :((-1*sec(x)^2)^-1//2*tan(x))
@test integrate((a+b*tan(e+f*x)^2)^(1/2)*tan(e+f*x)^5, x) == :(f^-1*(a+b*tan(e+f*x)^2)^(1/2)+-1*f^-1*(a+-1b)^(1/2)*arctanh((a+-1b)^-1//2*(a+b*tan(e+f*x)^2)^(1/2))+1//5*b^-2*f^-1*(a+b*tan(e+f*x)^2)^5//2+-1//3*b^-2*f^-1*(a+b*tan(e+f*x)^2)^3//2*(a+b))
@test integrate((a+b*tan(e+f*x)^2)^(1/2)*tan(e+f*x)^3, x) == :(-1*f^-1*(a+b*tan(e+f*x)^2)^(1/2)+f^-1*(a+-1b)^(1/2)*arctanh((a+-1b)^-1//2*(a+b*tan(e+f*x)^2)^(1/2))+1//3*b^-1*f^-1*(a+b*tan(e+f*x)^2)^3//2)
@test integrate((a+b*tan(e+f*x)^2)^(1/2)*tan(e+f*x), x) == :(f^-1*(a+b*tan(e+f*x)^2)^(1/2)+-1*f^-1*(a+-1b)^(1/2)*arctanh((a+-1b)^-1//2*(a+b*tan(e+f*x)^2)^(1/2)))
@test integrate((a+b*tan(e+f*x)^2)^(1/2)*cot(e+f*x), x) == :(f^-1*(a+-1b)^(1/2)*arctanh((a+-1b)^-1//2*(a+b*tan(e+f*x)^2)^(1/2))+-1*a^(1/2)*f^-1*arctanh(a^-1//2*(a+b*tan(e+f*x)^2)^(1/2)))
@test integrate((a+b*tan(e+f*x)^2)^(1/2)*cot(e+f*x)^3, x) == :(-1*f^-1*(a+-1b)^(1/2)*arctanh((a+-1b)^-1//2*(a+b*tan(e+f*x)^2)^(1/2))+-1//2*f^-1*(a+b*tan(e+f*x)^2)^(1/2)*cot(e+f*x)^2+(1/2)*a^-1//2*f^-1*(-1b+2a)*arctanh(a^-1//2*(a+b*tan(e+f*x)^2)^(1/2)))
@test integrate((a+b*tan(e+f*x)^2)^(1/2)*cot(e+f*x)^5, x) == :(f^-1*(a+-1b)^(1/2)*arctanh((a+-1b)^-1//2*(a+b*tan(e+f*x)^2)^(1/2))+-1//4*f^-1*(a+b*tan(e+f*x)^2)^(1/2)*cot(e+f*x)^4+-1//8*a^-3//2*f^-1*(-1*b^2+8*a^2+-4*a*b)*arctanh(a^-1//2*(a+b*tan(e+f*x)^2)^(1/2))+1//8*a^-1*f^-1*(a+b*tan(e+f*x)^2)^(1/2)*cot(e+f*x)^2*(-1b+4a))
@test integrate((a+b*tan(e+f*x)^2)^(1/2)*tan(e+f*x)^6, x) == :(-1*f^-1*(a+-1b)^(1/2)*arctan((a+-1b)^(1/2)*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+1//6*f^-1*(a+b*tan(e+f*x)^2)^(1/2)*tan(e+f*x)^5+1//16*b^-5//2*f^-1*(a^3+-16*b^3+2*b*a^2+8*a*b^2)*arctanh(b^(1/2)*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+1//24*b^-1*f^-1*(a+b*tan(e+f*x)^2)^(1/2)*tan(e+f*x)^3*(a+-6b)+-1//16*b^-2*f^-1*(a+b*tan(e+f*x)^2)^(1/2)*(a+-2b)*(a+4b)*tan(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^(1/2)*tan(e+f*x)^4, x) == :(f^-1*(a+-1b)^(1/2)*arctan((a+-1b)^(1/2)*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+1//4*f^-1*(a+b*tan(e+f*x)^2)^(1/2)*tan(e+f*x)^3+-1//8*b^-3//2*f^-1*(a^2+-8*b^2+4*a*b)*arctanh(b^(1/2)*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+1//8*b^-1*f^-1*(a+b*tan(e+f*x)^2)^(1/2)*(a+-4b)*tan(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^(1/2)*tan(e+f*x)^2, x) == :((1/2)*f^-1*(a+b*tan(e+f*x)^2)^(1/2)*tan(e+f*x)+-1*f^-1*(a+-1b)^(1/2)*arctan((a+-1b)^(1/2)*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+(1/2)*b^-1//2*f^-1*(a+-2b)*arctanh(b^(1/2)*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x)))
@test integrate((a+b*tan(e+f*x)^2)^(1/2), x) == :(b^(1/2)*f^-1*arctanh(b^(1/2)*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+f^-1*(a+-1b)^(1/2)*arctan((a+-1b)^(1/2)*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x)))
@test integrate((a+b*tan(e+f*x)^2)^(1/2)*cot(e+f*x)^2, x) == :(-1*f^-1*(a+-1b)^(1/2)*arctan((a+-1b)^(1/2)*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1*f^-1*(a+b*tan(e+f*x)^2)^(1/2)*cot(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^(1/2)*cot(e+f*x)^4, x) == :(f^-1*(a+-1b)^(1/2)*arctan((a+-1b)^(1/2)*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1//3*f^-1*(a+b*tan(e+f*x)^2)^(1/2)*cot(e+f*x)^3+1//3*a^-1*f^-1*(a+b*tan(e+f*x)^2)^(1/2)*(-1b+3a)*cot(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^(1/2)*cot(e+f*x)^6, x) == :(-1*f^-1*(a+-1b)^(1/2)*arctan((a+-1b)^(1/2)*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1//5*f^-1*(a+b*tan(e+f*x)^2)^(1/2)*cot(e+f*x)^5+-1//15*a^-2*f^-1*(a+b*tan(e+f*x)^2)^(1/2)*(-2*b^2+15*a^2+-5*a*b)*cot(e+f*x)+1//15*a^-1*f^-1*(a+b*tan(e+f*x)^2)^(1/2)*cot(e+f*x)^3*(-1b+5a))
@test integrate((a+b*tan(e+f*x)^2)^3//2*tan(e+f*x)^5, x) == :(1//3*f^-1*(a+b*tan(e+f*x)^2)^3//2+f^-1*(a+b*tan(e+f*x)^2)^(1/2)*(a+-1b)+-1*f^-1*(a+-1b)^3//2*arctanh((a+-1b)^-1//2*(a+b*tan(e+f*x)^2)^(1/2))+1//7*b^-2*f^-1*(a+b*tan(e+f*x)^2)^7//2+-1//5*b^-2*f^-1*(a+b*tan(e+f*x)^2)^5//2*(a+b))
@test integrate((a+b*tan(e+f*x)^2)^3//2*tan(e+f*x)^3, x) == :(-1//3*f^-1*(a+b*tan(e+f*x)^2)^3//2+f^-1*(a+-1b)^3//2*arctanh((a+-1b)^-1//2*(a+b*tan(e+f*x)^2)^(1/2))+-1*f^-1*(a+b*tan(e+f*x)^2)^(1/2)*(a+-1b)+1//5*b^-1*f^-1*(a+b*tan(e+f*x)^2)^5//2)
@test integrate((a+b*tan(e+f*x)^2)^3//2*tan(e+f*x), x) == :(1//3*f^-1*(a+b*tan(e+f*x)^2)^3//2+f^-1*(a+b*tan(e+f*x)^2)^(1/2)*(a+-1b)+-1*f^-1*(a+-1b)^3//2*arctanh((a+-1b)^-1//2*(a+b*tan(e+f*x)^2)^(1/2)))
@test integrate((a+b*tan(e+f*x)^2)^3//2*cot(e+f*x), x) == :(b*f^-1*(a+b*tan(e+f*x)^2)^(1/2)+f^-1*(a+-1b)^3//2*arctanh((a+-1b)^-1//2*(a+b*tan(e+f*x)^2)^(1/2))+-1*a^3//2*f^-1*arctanh(a^-1//2*(a+b*tan(e+f*x)^2)^(1/2)))
@test integrate((a+b*tan(e+f*x)^2)^3//2*cot(e+f*x)^3, x) == :(-1*f^-1*(a+-1b)^3//2*arctanh((a+-1b)^-1//2*(a+b*tan(e+f*x)^2)^(1/2))+(1/2)*a^(1/2)*f^-1*(-3b+2a)*arctanh(a^-1//2*(a+b*tan(e+f*x)^2)^(1/2))+-1//2*a*f^-1*(a+b*tan(e+f*x)^2)^(1/2)*cot(e+f*x)^2)
@test integrate((a+b*tan(e+f*x)^2)^3//2*cot(e+f*x)^5, x) == :(f^-1*(a+-1b)^3//2*arctanh((a+-1b)^-1//2*(a+b*tan(e+f*x)^2)^(1/2))+-1//4*a*f^-1*(a+b*tan(e+f*x)^2)^(1/2)*cot(e+f*x)^4+-1//8*a^-1//2*f^-1*(3*b^2+8*a^2+-12*a*b)*arctanh(a^-1//2*(a+b*tan(e+f*x)^2)^(1/2))+1//8*f^-1*(a+b*tan(e+f*x)^2)^(1/2)*cot(e+f*x)^2*(-5b+4a))
@test integrate((a+b*tan(e+f*x)^2)^3//2*tan(e+f*x)^6, x) == :(-1*f^-1*(a+-1b)^3//2*arctan((a+-1b)^(1/2)*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+1//8*b*f^-1*(a+b*tan(e+f*x)^2)^(1/2)*tan(e+f*x)^7+1//48*f^-1*(a+b*tan(e+f*x)^2)^(1/2)*tan(e+f*x)^5*(-8b+9a)+1//128*b^-5//2*f^-1*(3*a^4+128*b^4+-192*a*b^3+8*b*a^3+48*a^2*b^2)*arctanh(b^(1/2)*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1//128*b^-2*f^-1*(a+b*tan(e+f*x)^2)^(1/2)*(3*a^3+64*b^3+-80*a*b^2+8*b*a^2)*tan(e+f*x)+1//192*b^-1*f^-1*(a+b*tan(e+f*x)^2)^(1/2)*tan(e+f*x)^3*(3*a^2+48*b^2+-56*a*b))
@test integrate((a+b*tan(e+f*x)^2)^3//2*tan(e+f*x)^4, x) == :(f^-1*(a+-1b)^3//2*arctan((a+-1b)^(1/2)*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1//16*b^-3//2*f^-1*(a^3+16*b^3+-24*a*b^2+6*b*a^2)*arctanh(b^(1/2)*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+1//6*b*f^-1*(a+b*tan(e+f*x)^2)^(1/2)*tan(e+f*x)^5+1//24*f^-1*(a+b*tan(e+f*x)^2)^(1/2)*tan(e+f*x)^3*(-6b+7a)+1//16*b^-1*f^-1*(a+b*tan(e+f*x)^2)^(1/2)*(a^2+8*b^2+-10*a*b)*tan(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^3//2*tan(e+f*x)^2, x) == :(-1*f^-1*(a+-1b)^3//2*arctan((a+-1b)^(1/2)*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+1//4*b*f^-1*(a+b*tan(e+f*x)^2)^(1/2)*tan(e+f*x)^3+1//8*b^-1//2*f^-1*(3*a^2+8*b^2+-12*a*b)*arctanh(b^(1/2)*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+1//8*f^-1*(a+b*tan(e+f*x)^2)^(1/2)*(-4b+5a)*tan(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^3//2, x) == :(f^-1*(a+-1b)^3//2*arctan((a+-1b)^(1/2)*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+(1/2)*b*f^-1*(a+b*tan(e+f*x)^2)^(1/2)*tan(e+f*x)+(1/2)*b^(1/2)*f^-1*(-2b+3a)*arctanh(b^(1/2)*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x)))
@test integrate((a+b*tan(e+f*x)^2)^3//2*cot(e+f*x)^2, x) == :(b^3//2*f^-1*arctanh(b^(1/2)*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1*f^-1*(a+-1b)^3//2*arctan((a+-1b)^(1/2)*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1*a*f^-1*(a+b*tan(e+f*x)^2)^(1/2)*cot(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^3//2*cot(e+f*x)^4, x) == :(f^-1*(a+-1b)^3//2*arctan((a+-1b)^(1/2)*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1//3*a*f^-1*(a+b*tan(e+f*x)^2)^(1/2)*cot(e+f*x)^3+1//3*f^-1*(a+b*tan(e+f*x)^2)^(1/2)*(-4b+3a)*cot(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^3//2*cot(e+f*x)^6, x) == :(-1*f^-1*(a+-1b)^3//2*arctan((a+-1b)^(1/2)*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1//5*a*f^-1*(a+b*tan(e+f*x)^2)^(1/2)*cot(e+f*x)^5+1//15*f^-1*(a+b*tan(e+f*x)^2)^(1/2)*cot(e+f*x)^3*(-6b+5a)+-1//15*a^-1*f^-1*(a+b*tan(e+f*x)^2)^(1/2)*(3*b^2+15*a^2+-20*a*b)*cot(e+f*x))
@test integrate((a+b*tan(c+d*x)^2)^5//2, x) == :(d^-1*(a+-1b)^5//2*arctan((a+-1b)^(1/2)*(a+b*tan(c+d*x)^2)^-1//2*tan(c+d*x))+1//4*b*d^-1*(a+b*tan(c+d*x)^2)^3//2*tan(c+d*x)+1//8*b^(1/2)*d^-1*(8*b^2+15*a^2+-20*a*b)*arctanh(b^(1/2)*(a+b*tan(c+d*x)^2)^-1//2*tan(c+d*x))+1//8*b*d^-1*(a+b*tan(c+d*x)^2)^(1/2)*(-4b+7a)*tan(c+d*x))
@test integrate((a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x)^5, x) == :(-1*f^-1*(a+-1b)^-1//2*arctanh((a+-1b)^-1//2*(a+b*tan(e+f*x)^2)^(1/2))+1//3*b^-2*f^-1*(a+b*tan(e+f*x)^2)^3//2+-1*b^-2*f^-1*(a+b*tan(e+f*x)^2)^(1/2)*(a+b))
@test integrate((a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x)^3, x) == :(b^-1*f^-1*(a+b*tan(e+f*x)^2)^(1/2)+f^-1*(a+-1b)^-1//2*arctanh((a+-1b)^-1//2*(a+b*tan(e+f*x)^2)^(1/2)))
@test integrate((a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x), x) == :(-1*f^-1*(a+-1b)^-1//2*arctanh((a+-1b)^-1//2*(a+b*tan(e+f*x)^2)^(1/2)))
@test integrate((a+b*tan(e+f*x)^2)^-1//2*cot(e+f*x), x) == :(f^-1*(a+-1b)^-1//2*arctanh((a+-1b)^-1//2*(a+b*tan(e+f*x)^2)^(1/2))+-1*a^-1//2*f^-1*arctanh(a^-1//2*(a+b*tan(e+f*x)^2)^(1/2)))
@test integrate((a+b*tan(e+f*x)^2)^-1//2*cot(e+f*x)^3, x) == :(-1*f^-1*(a+-1b)^-1//2*arctanh((a+-1b)^-1//2*(a+b*tan(e+f*x)^2)^(1/2))+(1/2)*a^-3//2*f^-1*(b+2a)*arctanh(a^-1//2*(a+b*tan(e+f*x)^2)^(1/2))+-1//2*a^-1*f^-1*(a+b*tan(e+f*x)^2)^(1/2)*cot(e+f*x)^2)
@test integrate((a+b*tan(e+f*x)^2)^-1//2*cot(e+f*x)^5, x) == :(f^-1*(a+-1b)^-1//2*arctanh((a+-1b)^-1//2*(a+b*tan(e+f*x)^2)^(1/2))+-1//4*a^-1*f^-1*(a+b*tan(e+f*x)^2)^(1/2)*cot(e+f*x)^4+-1//8*a^-5//2*f^-1*(3*b^2+8*a^2+4*a*b)*arctanh(a^-1//2*(a+b*tan(e+f*x)^2)^(1/2))+1//8*a^-2*f^-1*(a+b*tan(e+f*x)^2)^(1/2)*cot(e+f*x)^2*(3b+4a))
@test integrate((a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x)^6, x) == :(-1*f^-1*(a+-1b)^-1//2*arctan((a+-1b)^(1/2)*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+1//4*b^-1*f^-1*(a+b*tan(e+f*x)^2)^(1/2)*tan(e+f*x)^3+1//8*b^-5//2*f^-1*(3*a^2+8*b^2+4*a*b)*arctanh(b^(1/2)*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1//8*b^-2*f^-1*(a+b*tan(e+f*x)^2)^(1/2)*(3a+4b)*tan(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x)^4, x) == :(f^-1*(a+-1b)^-1//2*arctan((a+-1b)^(1/2)*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+(1/2)*b^-1*f^-1*(a+b*tan(e+f*x)^2)^(1/2)*tan(e+f*x)+-1//2*b^-3//2*f^-1*(a+2b)*arctanh(b^(1/2)*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x)))
@test integrate((a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x)^2, x) == :(b^-1//2*f^-1*arctanh(b^(1/2)*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1*f^-1*(a+-1b)^-1//2*arctan((a+-1b)^(1/2)*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x)))
@test integrate((a+b*tan(e+f*x)^2)^-1//2, x) == :(f^-1*(a+-1b)^-1//2*arctan((a+-1b)^(1/2)*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x)))
@test integrate((a+b*tan(e+f*x)^2)^-1//2*cot(e+f*x)^2, x) == :(-1*f^-1*(a+-1b)^-1//2*arctan((a+-1b)^(1/2)*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1*a^-1*f^-1*(a+b*tan(e+f*x)^2)^(1/2)*cot(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^-1//2*cot(e+f*x)^4, x) == :(f^-1*(a+-1b)^-1//2*arctan((a+-1b)^(1/2)*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1//3*a^-1*f^-1*(a+b*tan(e+f*x)^2)^(1/2)*cot(e+f*x)^3+1//3*a^-2*f^-1*(a+b*tan(e+f*x)^2)^(1/2)*(2b+3a)*cot(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^-1//2*cot(e+f*x)^6, x) == :(-1*f^-1*(a+-1b)^-1//2*arctan((a+-1b)^(1/2)*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1//5*a^-1*f^-1*(a+b*tan(e+f*x)^2)^(1/2)*cot(e+f*x)^5+-1//15*a^-3*f^-1*(a+b*tan(e+f*x)^2)^(1/2)*(8*b^2+15*a^2+10*a*b)*cot(e+f*x)+1//15*a^-2*f^-1*(a+b*tan(e+f*x)^2)^(1/2)*cot(e+f*x)^3*(4b+5a))
@test integrate((a+b*tan(e+f*x)^2)^-3//2*tan(e+f*x)^5, x) == :(b^-2*f^-1*(a+b*tan(e+f*x)^2)^(1/2)+-1*f^-1*(a+-1b)^-3//2*arctanh((a+-1b)^-1//2*(a+b*tan(e+f*x)^2)^(1/2))+a^2*b^-2*f^-1*(a+-1b)^-1*(a+b*tan(e+f*x)^2)^-1//2)
@test integrate((a+b*tan(e+f*x)^2)^-3//2*tan(e+f*x)^3, x) == :(f^-1*(a+-1b)^-3//2*arctanh((a+-1b)^-1//2*(a+b*tan(e+f*x)^2)^(1/2))+-1*a*b^-1*f^-1*(a+-1b)^-1*(a+b*tan(e+f*x)^2)^-1//2)
@test integrate((a+b*tan(e+f*x)^2)^-3//2*tan(e+f*x), x) == :(f^-1*(a+-1b)^-1*(a+b*tan(e+f*x)^2)^-1//2+-1*f^-1*(a+-1b)^-3//2*arctanh((a+-1b)^-1//2*(a+b*tan(e+f*x)^2)^(1/2)))
@test integrate((a+b*tan(e+f*x)^2)^-3//2*cot(e+f*x), x) == :(f^-1*(a+-1b)^-3//2*arctanh((a+-1b)^-1//2*(a+b*tan(e+f*x)^2)^(1/2))+-1*a^-3//2*f^-1*arctanh(a^-1//2*(a+b*tan(e+f*x)^2)^(1/2))+-1*b*a^-1*f^-1*(a+-1b)^-1*(a+b*tan(e+f*x)^2)^-1//2)
@test integrate((a+b*tan(e+f*x)^2)^-3//2*cot(e+f*x)^3, x) == :(-1*f^-1*(a+-1b)^-3//2*arctanh((a+-1b)^-1//2*(a+b*tan(e+f*x)^2)^(1/2))+(1/2)*a^-5//2*f^-1*(2a+3b)*arctanh(a^-1//2*(a+b*tan(e+f*x)^2)^(1/2))+-1//2*a^-1*f^-1*(a+b*tan(e+f*x)^2)^-1//2*cot(e+f*x)^2+-1//2*b*a^-2*f^-1*(a+-1b)^-1*(a+b*tan(e+f*x)^2)^-1//2*(a+-3b))
@test integrate((a+b*tan(e+f*x)^2)^-3//2*cot(e+f*x)^5, x) == :(f^-1*(a+-1b)^-3//2*arctanh((a+-1b)^-1//2*(a+b*tan(e+f*x)^2)^(1/2))+-1//4*a^-1*f^-1*(a+b*tan(e+f*x)^2)^-1//2*cot(e+f*x)^4+-1//8*a^-7//2*f^-1*(8*a^2+15*b^2+12*a*b)*arctanh(a^-1//2*(a+b*tan(e+f*x)^2)^(1/2))+1//8*a^-2*f^-1*(a+b*tan(e+f*x)^2)^-1//2*cot(e+f*x)^2*(4a+5b)+1//8*b*a^-3*f^-1*(a+-1b)^-1*(a+b*tan(e+f*x)^2)^-1//2*(-15*b^2+4*a^2+3*a*b))
@test integrate((a+b*tan(e+f*x)^2)^-3//2*tan(e+f*x)^6, x) == :(-1*f^-1*(a+-1b)^-3//2*arctan((a+-1b)^(1/2)*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1//2*b^-5//2*f^-1*(2b+3a)*arctanh(b^(1/2)*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+b^-2*f^-1*(a+b*tan(e+f*x)^2)^(1/2)*(-2b+2a)^-1*(-1b+3a)*tan(e+f*x)+-1*a*b^-1*f^-1*(a+-1b)^-1*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x)^3)
@test integrate((a+b*tan(e+f*x)^2)^-3//2*tan(e+f*x)^4, x) == :(b^-3//2*f^-1*arctanh(b^(1/2)*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+f^-1*(a+-1b)^-3//2*arctan((a+-1b)^(1/2)*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1*a*b^-1*f^-1*(a+-1b)^-1*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^-3//2*tan(e+f*x)^2, x) == :(-1*f^-1*(a+-1b)^-3//2*arctan((a+-1b)^(1/2)*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+f^-1*(a+-1b)^-1*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^-3//2, x) == :(f^-1*(a+-1b)^-3//2*arctan((a+-1b)^(1/2)*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1*b*a^-1*f^-1*(a+-1b)^-1*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^-3//2*cot(e+f*x)^2, x) == :(-1*f^-1*(a+-1b)^-3//2*arctan((a+-1b)^(1/2)*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1*b*a^-1*f^-1*(a+-1b)^-1*(a+b*tan(e+f*x)^2)^-1//2*cot(e+f*x)+-1*a^-2*f^-1*(a+-1b)^-1*(a+b*tan(e+f*x)^2)^(1/2)*(a+-2b)*cot(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^-3//2*cot(e+f*x)^4, x) == :(f^-1*(a+-1b)^-3//2*arctan((a+-1b)^(1/2)*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1*b*a^-1*f^-1*(a+-1b)^-1*(a+b*tan(e+f*x)^2)^-1//2*cot(e+f*x)^3+-1//3*a^-2*f^-1*(a+-1b)^-1*(a+b*tan(e+f*x)^2)^(1/2)*cot(e+f*x)^3*(a+-4b)+1//3*a^-3*f^-1*(a+-1b)^-1*(a+b*tan(e+f*x)^2)^(1/2)*(a+2b)*(-4b+3a)*cot(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^-3//2*cot(e+f*x)^6, x) == :(-1*f^-1*(a+-1b)^-3//2*arctan((a+-1b)^(1/2)*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1*b*a^-1*f^-1*(a+-1b)^-1*(a+b*tan(e+f*x)^2)^-1//2*cot(e+f*x)^5+-1//5*a^-2*f^-1*(a+-1b)^-1*(a+b*tan(e+f*x)^2)^(1/2)*cot(e+f*x)^5*(a+-6b)+-1//15*a^-4*f^-1*(a+-1b)^-1*(a+b*tan(e+f*x)^2)^(1/2)*(-48*b^3+15*a^3+8*a*b^2+10*b*a^2)*cot(e+f*x)+1//15*a^-3*f^-1*(a+-1b)^-1*(a+b*tan(e+f*x)^2)^(1/2)*cot(e+f*x)^3*(-24*b^2+5*a^2+4*a*b))
@test integrate((a+b*tan(e+f*x)^2)^-5//2*tan(e+f*x)^5, x) == :(-1*f^-1*(a+-1b)^-5//2*arctanh((a+-1b)^-1//2*(a+b*tan(e+f*x)^2)^(1/2))+a^2*b^-2*f^-1*(a+b*tan(e+f*x)^2)^-3//2*(-3b+3a)^-1+-1*a*b^-2*f^-1*(a+-1b)^-2*(a+b*tan(e+f*x)^2)^-1//2*(a+-2b))
@test integrate((a+b*tan(e+f*x)^2)^-5//2*tan(e+f*x)^3, x) == :(f^-1*(a+-1b)^-5//2*arctanh((a+-1b)^-1//2*(a+b*tan(e+f*x)^2)^(1/2))+-1*f^-1*(a+-1b)^-2*(a+b*tan(e+f*x)^2)^-1//2+-1*a*b^-1*f^-1*(a+b*tan(e+f*x)^2)^-3//2*(-3b+3a)^-1)
@test integrate((a+b*tan(e+f*x)^2)^-5//2*tan(e+f*x), x) == :(f^-1*(a+-1b)^-2*(a+b*tan(e+f*x)^2)^-1//2+f^-1*(a+b*tan(e+f*x)^2)^-3//2*(-3b+3a)^-1+-1*f^-1*(a+-1b)^-5//2*arctanh((a+-1b)^-1//2*(a+b*tan(e+f*x)^2)^(1/2)))
@test integrate((a+b*tan(e+f*x)^2)^-5//2*cot(e+f*x), x) == :(f^-1*(a+-1b)^-5//2*arctanh((a+-1b)^-1//2*(a+b*tan(e+f*x)^2)^(1/2))+-1*a^-5//2*f^-1*arctanh(a^-1//2*(a+b*tan(e+f*x)^2)^(1/2))+-1//3*b*a^-1*f^-1*(a+-1b)^-1*(a+b*tan(e+f*x)^2)^-3//2+-1*b*a^-2*f^-1*(a+-1b)^-2*(a+b*tan(e+f*x)^2)^-1//2*(-1b+2a))
@test integrate((a+b*tan(e+f*x)^2)^-5//2*cot(e+f*x)^3, x) == :(-1*f^-1*(a+-1b)^-5//2*arctanh((a+-1b)^-1//2*(a+b*tan(e+f*x)^2)^(1/2))+(1/2)*a^-7//2*f^-1*(2a+5b)*arctanh(a^-1//2*(a+b*tan(e+f*x)^2)^(1/2))+-1//2*a^-1*f^-1*(a+b*tan(e+f*x)^2)^-3//2*cot(e+f*x)^2+-1//2*b*a^-3*f^-1*(a+-1b)^-2*(a+b*tan(e+f*x)^2)^-1//2*(a^2+5*b^2+-8*a*b)+-1//6*b*a^-2*f^-1*(a+-1b)^-1*(a+b*tan(e+f*x)^2)^-3//2*(-5b+3a))
@test integrate((a+b*tan(e+f*x)^2)^-5//2*cot(e+f*x)^5, x) == :(f^-1*(a+-1b)^-5//2*arctanh((a+-1b)^-1//2*(a+b*tan(e+f*x)^2)^(1/2))+-1//4*a^-1*f^-1*(a+b*tan(e+f*x)^2)^-3//2*cot(e+f*x)^4+-1//8*a^-9//2*f^-1*(8*a^2+35*b^2+20*a*b)*arctanh(a^-1//2*(a+b*tan(e+f*x)^2)^(1/2))+1//8*a^-2*f^-1*(a+b*tan(e+f*x)^2)^-3//2*cot(e+f*x)^2*(4a+7b)+1//8*b*a^-4*f^-1*(a+-1b)^-2*(a+b*tan(e+f*x)^2)^-1//2*(4*a^3+35*b^3+-50*a*b^2+3*b*a^2)+1//24*b*a^-3*f^-1*(a+-1b)^-1*(a+b*tan(e+f*x)^2)^-3//2*(-35*b^2+12*a^2+15*a*b))
@test integrate((a+b*tan(e+f*x)^2)^-5//2*tan(e+f*x)^6, x) == :(b^-5//2*f^-1*arctanh(b^(1/2)*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1*f^-1*(a+-1b)^-5//2*arctan((a+-1b)^(1/2)*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1*a*b^-1*f^-1*(a+b*tan(e+f*x)^2)^-3//2*(-3b+3a)^-1*tan(e+f*x)^3+-1*a*b^-2*f^-1*(a+-1b)^-2*(a+b*tan(e+f*x)^2)^-1//2*(a+-2b)*tan(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^-5//2*tan(e+f*x)^4, x) == :(f^-1*(a+-1b)^-5//2*arctan((a+-1b)^(1/2)*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1*a*b^-1*f^-1*(a+b*tan(e+f*x)^2)^-3//2*(-3b+3a)^-1*tan(e+f*x)+1//3*b^-1*f^-1*(a+-1b)^-2*(a+b*tan(e+f*x)^2)^-1//2*(a+-4b)*tan(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^-5//2*tan(e+f*x)^2, x) == :(-1*f^-1*(a+-1b)^-5//2*arctan((a+-1b)^(1/2)*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+f^-1*(a+b*tan(e+f*x)^2)^-3//2*(-3b+3a)^-1*tan(e+f*x)+1//3*a^-1*f^-1*(a+-1b)^-2*(a+b*tan(e+f*x)^2)^-1//2*(b+2a)*tan(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^-5//2, x) == :(f^-1*(a+-1b)^-5//2*arctan((a+-1b)^(1/2)*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1//3*b*a^-1*f^-1*(a+-1b)^-1*(a+b*tan(e+f*x)^2)^-3//2*tan(e+f*x)+-1//3*b*a^-2*f^-1*(a+-1b)^-2*(a+b*tan(e+f*x)^2)^-1//2*(-2b+5a)*tan(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^-5//2*cot(e+f*x)^2, x) == :(-1*f^-1*(a+-1b)^-5//2*arctan((a+-1b)^(1/2)*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1//3*b*a^-1*f^-1*(a+-1b)^-1*(a+b*tan(e+f*x)^2)^-3//2*cot(e+f*x)+-1//3*b*a^-2*f^-1*(a+-1b)^-2*(a+b*tan(e+f*x)^2)^-1//2*(-4b+7a)*cot(e+f*x)+-1//3*a^-3*f^-1*(a+-1b)^-2*(a+b*tan(e+f*x)^2)^(1/2)*(a+-4b)*(-2b+3a)*cot(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^-5//2*cot(e+f*x)^4, x) == :(f^-1*(a+-1b)^-5//2*arctan((a+-1b)^(1/2)*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1//3*b*a^-1*f^-1*(a+-1b)^-1*(a+b*tan(e+f*x)^2)^-3//2*cot(e+f*x)^3+-1//3*a^-3*f^-1*(a+-1b)^-2*(a+b*tan(e+f*x)^2)^(1/2)*cot(e+f*x)^3*(a^2+8*b^2+-12*a*b)+-1*b*a^-2*f^-1*(a+-1b)^-2*(a+b*tan(e+f*x)^2)^-1//2*cot(e+f*x)^3*(-2b+3a)+1//3*a^-4*f^-1*(a+-1b)^-2*(a+b*tan(e+f*x)^2)^(1/2)*(a+-2b)*(-8*b^2+3*a^2+8*a*b)*cot(e+f*x))
@test integrate((a+b*tan(e+f*x)^2)^-5//2*cot(e+f*x)^6, x) == :(-1*f^-1*(a+-1b)^-5//2*arctan((a+-1b)^(1/2)*(a+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1//3*b*a^-1*f^-1*(a+-1b)^-1*(a+b*tan(e+f*x)^2)^-3//2*cot(e+f*x)^5+-1//5*a^-3*f^-1*(a+-1b)^-2*(a+b*tan(e+f*x)^2)^(1/2)*cot(e+f*x)^5*(a^2+16*b^2+-22*a*b)+-1//15*a^-5*f^-1*(a+-1b)^-2*(a+b*tan(e+f*x)^2)^(1/2)*(15*a^4+128*b^4+-176*a*b^3+8*a^2*b^2+10*b*a^3)*cot(e+f*x)+1//15*a^-4*f^-1*(a+-1b)^-2*(a+b*tan(e+f*x)^2)^(1/2)*cot(e+f*x)^3*(5*a^3+64*b^3+-88*a*b^2+4*b*a^2)+-1//3*b*a^-2*f^-1*(a+-1b)^-2*(a+b*tan(e+f*x)^2)^-1//2*cot(e+f*x)^5*(-8b+11a))
@test integrate((a+b*tan(c+d*x)^3)^4, x) == :(x*(a^4+b^4+-6*a^2*b^2)+-1//9*b^4*d^-1*tan(c+d*x)^9+1//7*b^4*d^-1*tan(c+d*x)^7+1//11*b^4*d^-1*tan(c+d*x)^11+a*b^3*d^-1*tan(c+d*x)^4+b^2*d^-1*(-1*b^2+6*a^2)*tan(c+d*x)+(1/2)*a*b^3*d^-1*tan(c+d*x)^8+-2//3*a*b^3*d^-1*tan(c+d*x)^6+-1//3*b^2*d^-1*tan(c+d*x)^3*(-1*b^2+6*a^2)+1//5*b^2*d^-1*tan(c+d*x)^5*(-1*b^2+6*a^2)+2*a*b*d^-1*tan(c+d*x)^2*(a^2+-1*b^2)+4*a*b*d^-1*(a^2+-1*b^2)*log(cos(c+d*x)))
@test integrate((a+b*tan(c+d*x)^3)^3, x) == :(a*x*(a^2+-3*b^2)+-1//6*b^3*d^-1*tan(c+d*x)^6+1//4*b^3*d^-1*tan(c+d*x)^4+1//8*b^3*d^-1*tan(c+d*x)^8+b*d^-1*(-1*b^2+3*a^2)*log(cos(c+d*x))+(1/2)*b*d^-1*tan(c+d*x)^2*(-1*b^2+3*a^2)+-1*a*b^2*d^-1*tan(c+d*x)^3+3*a*b^2*d^-1*tan(c+d*x)+3//5*a*b^2*d^-1*tan(c+d*x)^5)
@test integrate((a+b*tan(c+d*x)^3)^2, x) == :(x*(a^2+-1*b^2)+b^2*d^-1*tan(c+d*x)+-1//3*b^2*d^-1*tan(c+d*x)^3+1//5*b^2*d^-1*tan(c+d*x)^5+a*b*d^-1*tan(c+d*x)^2+2*a*b*d^-1*log(cos(c+d*x)))
@test integrate(a+b*tan(c+d*x)^3, x) == :(a*x+b*d^-1*log(cos(c+d*x))+(1/2)*b*d^-1*tan(c+d*x)^2)
@test integrate((a+b*tan(c+d*x)^3)^-1, x) == :(a*x*(a^2+b^2)^-1+-1*b*d^-1*(3*a^2+3*b^2)^-1*log(a*cos(c+d*x)^3+b*sin(c+d*x)^3)+-1//6*a^-2//3*b^1//3*d^-1*(a^2+b^2)^-1*(a^4//3+b^4//3)*log(a^2//3+b^2//3*tan(c+d*x)^2+-1*a^1//3*b^1//3*tan(c+d*x))+1//3*a^-2//3*b^1//3*d^-1*(a^2+b^2)^-1*(a^4//3+b^4//3)*log(a^1//3+b^1//3*tan(c+d*x))+1//3*3^(1/2)*a^-2//3*b^1//3*d^-1*(a^2+b^2)^-1*(a^4//3+-1*b^4//3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*b^1//3*tan(c+d*x))))
@test integrate((a+b*tan(c+d*x)^3)^-2, x) == :(x*(a^2+b^2)^-2*(a^2+-1*b^2)+-2//3*a*b*d^-1*(a^2+b^2)^-2*log(a*cos(c+d*x)^3+b*sin(c+d*x)^3)+-1//6*a^-1//3*b^1//3*d^-1*(a^2+b^2)^-2*(a^2+-1*b^2+2*a^2//3*b^4//3)*log(a^2//3+b^2//3*tan(c+d*x)^2+-1*a^1//3*b^1//3*tan(c+d*x))+-1//18*a^-5//3*b^1//3*d^-1*(a^2+b^2)^-1*(a^4//3+2*b^4//3)*log(a^2//3+b^2//3*tan(c+d*x)^2+-1*a^1//3*b^1//3*tan(c+d*x))+1//3*b*a^-1*d^-1*(a+b*tan(c+d*x)^3)^-1*(a^2+b^2)^-1*(a+(b+-1*a*tan(c+d*x))*tan(c+d*x))+1//3*a^-1//3*b^1//3*d^-1*(a^2+b^2)^-2*(a^2+-1*b^2+2*a^2//3*b^4//3)*log(a^1//3+b^1//3*tan(c+d*x))+1//9*a^-5//3*b^1//3*d^-1*(a^2+b^2)^-1*(a^4//3+2*b^4//3)*log(a^1//3+b^1//3*tan(c+d*x))+1//3*3^(1/2)*a^-1//3*b^1//3*d^-1*(a^2+b^2)^-2*(a^2+-1*b^2+-2*a^2//3*b^4//3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*b^1//3*tan(c+d*x)))+1//9*3^(1/2)*a^-5//3*b^1//3*d^-1*(a^2+b^2)^-1*(a^4//3+-2*b^4//3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*b^1//3*tan(c+d*x))))
@test integrate((1+tan(x)^3)^-1, x) == :((1/2)*x+-1//2*log(cos(x))+-1//3*log(1+tan(x)^2+-1*tan(x))+1//6*log(1+tan(x)))
@test integrate((a+b*tan(c+d*x)^4)^4, x) == :(x*(a+b)^4+-1//13*b^4*d^-1*tan(c+d*x)^13+1//15*b^4*d^-1*tan(c+d*x)^15+-1//5*b^2*d^-1*tan(c+d*x)^5*(b^2+6*a^2+4*a*b)+-1//9*b^3*d^-1*tan(c+d*x)^9*(b+4a)+1//7*b^2*d^-1*tan(c+d*x)^7*(b^2+6*a^2+4*a*b)+1//11*b^3*d^-1*tan(c+d*x)^11*(b+4a)+-1*b*d^-1*(b+2a)*(b^2+2*a^2+2*a*b)*tan(c+d*x)+1//3*b*d^-1*tan(c+d*x)^3*(b+2a)*(b^2+2*a^2+2*a*b))
@test integrate((a+b*tan(c+d*x)^4)^3, x) == :(x*(a+b)^3+-1//9*b^3*d^-1*tan(c+d*x)^9+1//11*b^3*d^-1*tan(c+d*x)^11+-1*b*d^-1*(b^2+3*a^2+3*a*b)*tan(c+d*x)+-1//5*b^2*d^-1*tan(c+d*x)^5*(b+3a)+1//3*b*d^-1*tan(c+d*x)^3*(b^2+3*a^2+3*a*b)+1//7*b^2*d^-1*tan(c+d*x)^7*(b+3a))
@test integrate((a+b*tan(c+d*x)^4)^2, x) == :(x*(a+b)^2+-1//5*b^2*d^-1*tan(c+d*x)^5+1//7*b^2*d^-1*tan(c+d*x)^7+-1*b*d^-1*(b+2a)*tan(c+d*x)+1//3*b*d^-1*tan(c+d*x)^3*(b+2a))
@test integrate(a+b*tan(c+d*x)^4, x) == :(a*x+b*x+-1*b*d^-1*tan(c+d*x)+1//3*b*d^-1*tan(c+d*x)^3)
@test integrate((a+b*tan(c+d*x)^4)^-1, x) == :(x*(a+b)^-1+-1//4*2^(1/2)*a^-3//4*b^1//4*d^-1*(a+b)^-1*(a^(1/2)+-1*b^(1/2))*arctan(1+2^(1/2)*a^-1//4*b^1//4*tan(c+d*x))+-1//8*2^(1/2)*a^-3//4*b^1//4*d^-1*(a+b)^-1*(a^(1/2)+b^(1/2))*log(a^(1/2)+b^(1/2)*tan(c+d*x)^2+-1*2^(1/2)*a^1//4*b^1//4*tan(c+d*x))+1//4*2^(1/2)*a^-3//4*b^1//4*d^-1*(a+b)^-1*(a^(1/2)+-1*b^(1/2))*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*tan(c+d*x))+1//8*2^(1/2)*a^-3//4*b^1//4*d^-1*(a+b)^-1*(a^(1/2)+b^(1/2))*log(a^(1/2)+b^(1/2)*tan(c+d*x)^2+2^(1/2)*a^1//4*b^1//4*tan(c+d*x)))
@test integrate((a+b*tan(c+d*x)^4)^-2, x) == :(x*(a+b)^-2+-1//4*2^(1/2)*a^-3//4*b^1//4*d^-1*(a+b)^-2*(a^(1/2)+-1*b^(1/2))*arctan(1+2^(1/2)*a^-1//4*b^1//4*tan(c+d*x))+-1//8*2^(1/2)*a^-3//4*b^1//4*d^-1*(a+b)^-2*(a^(1/2)+b^(1/2))*log(a^(1/2)+b^(1/2)*tan(c+d*x)^2+-1*2^(1/2)*a^1//4*b^1//4*tan(c+d*x))+-1//16*2^(1/2)*a^-7//4*b^1//4*d^-1*(a+b)^-1*(a^(1/2)+-3*b^(1/2))*arctan(1+2^(1/2)*a^-1//4*b^1//4*tan(c+d*x))+-1//32*2^(1/2)*a^-7//4*b^1//4*d^-1*(a+b)^-1*(a^(1/2)+3*b^(1/2))*log(a^(1/2)+b^(1/2)*tan(c+d*x)^2+-1*2^(1/2)*a^1//4*b^1//4*tan(c+d*x))+1//4*b*a^-1*d^-1*(a+b)^-1*(a+b*tan(c+d*x)^4)^-1*(1+-1*tan(c+d*x)^2)*tan(c+d*x)+1//4*2^(1/2)*a^-3//4*b^1//4*d^-1*(a+b)^-2*(a^(1/2)+-1*b^(1/2))*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*tan(c+d*x))+1//8*2^(1/2)*a^-3//4*b^1//4*d^-1*(a+b)^-2*(a^(1/2)+b^(1/2))*log(a^(1/2)+b^(1/2)*tan(c+d*x)^2+2^(1/2)*a^1//4*b^1//4*tan(c+d*x))+1//16*2^(1/2)*a^-7//4*b^1//4*d^-1*(a+b)^-1*(a^(1/2)+-3*b^(1/2))*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*tan(c+d*x))+1//32*2^(1/2)*a^-7//4*b^1//4*d^-1*(a+b)^-1*(a^(1/2)+3*b^(1/2))*log(a^(1/2)+b^(1/2)*tan(c+d*x)^2+2^(1/2)*a^1//4*b^1//4*tan(c+d*x)))
@test integrate((a+b*tan(x)^4)^(1/2)*tan(x)^3, x) == :((1/2)*(a+b)^(1/2)*arctanh((a+b)^-1//2*(a+b*tan(x)^4)^-1//2*(a+-1*b*tan(x)^2))+-1*(a+b*tan(x)^4)^(1/2)*(1/2+-1//4*tan(x)^2)+1//4*b^-1//2*(a+2b)*arctanh(b^(1/2)*(a+b*tan(x)^4)^-1//2*tan(x)^2))
@test integrate((a+b*tan(x)^4)^(1/2)*tan(x), x) == :((1/2)*(a+b*tan(x)^4)^(1/2)+-1//2*b^(1/2)*arctanh(b^(1/2)*(a+b*tan(x)^4)^-1//2*tan(x)^2)+-1//2*(a+b)^(1/2)*arctanh((a+b)^-1//2*(a+b*tan(x)^4)^-1//2*(a+-1*b*tan(x)^2)))
@test integrate((a+b*tan(x)^4)^(1/2)*cot(x), x) == :((1/2)*b^(1/2)*arctanh(b^(1/2)*(a+b*tan(x)^4)^-1//2*tan(x)^2)+(1/2)*(a+b)^(1/2)*arctanh((a+b)^-1//2*(a+b*tan(x)^4)^-1//2*(a+-1*b*tan(x)^2))+-1//2*a^(1/2)*arctanh(a^-1//2*(a+b*tan(x)^4)^(1/2)))
@test integrate((a+b*tan(x)^4)^3//2*tan(x)^3, x) == :((1/2)*(a+b)^3//2*arctanh((a+b)^-1//2*(a+b*tan(x)^4)^-1//2*(a+-1*b*tan(x)^2))+-1*(a+b*tan(x)^4)^(1/2)*((1/2)*a+(1/2)*b+-1//16*tan(x)^2*(3a+4b))+-1*(a+b*tan(x)^4)^3//2*(1//6+-1//8*tan(x)^2)+1//16*b^-1//2*(3*a^2+8*b^2+12*a*b)*arctanh(b^(1/2)*(a+b*tan(x)^4)^-1//2*tan(x)^2))
@test integrate((a+b*tan(x)^4)^3//2*tan(x), x) == :(1//6*(a+b*tan(x)^4)^3//2+(a+b*tan(x)^4)^(1/2)*((1/2)*a+(1/2)*b+-1//4*b*tan(x)^2)+-1//2*(a+b)^3//2*arctanh((a+b)^-1//2*(a+b*tan(x)^4)^-1//2*(a+-1*b*tan(x)^2))+-1//4*b^(1/2)*(2b+3a)*arctanh(b^(1/2)*(a+b*tan(x)^4)^-1//2*tan(x)^2))
@test integrate((a+b*tan(x)^4)^3//2*cot(x), x) == :((1/2)*a*(a+b*tan(x)^4)^(1/2)+(1/2)*(a+b)^3//2*arctanh((a+b)^-1//2*(a+b*tan(x)^4)^-1//2*(a+-1*b*tan(x)^2))+-1*(a+b*tan(x)^4)^(1/2)*((1/2)*a+(1/2)*b+-1//4*b*tan(x)^2)+-1//2*a^3//2*arctanh(a^-1//2*(a+b*tan(x)^4)^(1/2))+1//4*b^(1/2)*(2b+3a)*arctanh(b^(1/2)*(a+b*tan(x)^4)^-1//2*tan(x)^2))
@test integrate((a+b*tan(x)^4)^-1//2*tan(x)^3, x) == :((1/2)*b^-1//2*arctanh(b^(1/2)*(a+b*tan(x)^4)^-1//2*tan(x)^2)+(1/2)*(a+b)^-1//2*arctanh((a+b)^-1//2*(a+b*tan(x)^4)^-1//2*(a+-1*b*tan(x)^2)))
@test integrate((a+b*tan(x)^4)^-1//2*tan(x), x) == :(-1//2*(a+b)^-1//2*arctanh((a+b)^-1//2*(a+b*tan(x)^4)^-1//2*(a+-1*b*tan(x)^2)))
@test integrate((a+b*tan(x)^4)^-1//2*cot(x), x) == :((1/2)*(a+b)^-1//2*arctanh((a+b)^-1//2*(a+b*tan(x)^4)^-1//2*(a+-1*b*tan(x)^2))+-1//2*a^-1//2*arctanh(a^-1//2*(a+b*tan(x)^4)^(1/2)))
@test integrate((a+b*tan(x)^4)^-3//2*tan(x)^3, x) == :((1/2)*(a+b)^-3//2*arctanh((a+b)^-1//2*(a+b*tan(x)^4)^-1//2*(a+-1*b*tan(x)^2))+-1*(a+b*tan(x)^4)^-1//2*(2a+2b)^-1*(1+-1*tan(x)^2))
@test integrate((a+b*tan(x)^4)^-3//2*tan(x), x) == :(-1//2*(a+b)^-3//2*arctanh((a+b)^-1//2*(a+b*tan(x)^4)^-1//2*(a+-1*b*tan(x)^2))+(1/2)*a^-1*(a+b)^-1*(a+b*tan(x)^4)^-1//2*(a+b*tan(x)^2))
@test integrate((a+b*tan(x)^4)^-3//2*cot(x), x) == :((1/2)*a^-1*(a+b*tan(x)^4)^-1//2+(1/2)*(a+b)^-3//2*arctanh((a+b)^-1//2*(a+b*tan(x)^4)^-1//2*(a+-1*b*tan(x)^2))+-1//2*a^-3//2*arctanh(a^-1//2*(a+b*tan(x)^4)^(1/2))+-1//2*a^-1*(a+b)^-1*(a+b*tan(x)^4)^-1//2*(a+b*tan(x)^2))
@test integrate((a+b*tan(x)^4)^-5//2*tan(x)^3, x) == :((1/2)*(a+b)^-5//2*arctanh((a+b)^-1//2*(a+b*tan(x)^4)^-1//2*(a+-1*b*tan(x)^2))+-1*(a+b*tan(x)^4)^-3//2*(6a+6b)^-1*(1+-1*tan(x)^2)+-1//6*a^-1*(a+b)^-2*(a+b*tan(x)^4)^-1//2*(3a+tan(x)^2*(b+-2a)))
@test integrate((a+b*tan(x)^4)^-5//2*tan(x), x) == :(-1//2*(a+b)^-5//2*arctanh((a+b)^-1//2*(a+b*tan(x)^4)^-1//2*(a+-1*b*tan(x)^2))+1//6*a^-1*(a+b)^-1*(a+b*tan(x)^4)^-3//2*(a+b*tan(x)^2)+1//6*a^-2*(a+b)^-2*(a+b*tan(x)^4)^-1//2*(3*a^2+b*tan(x)^2*(2b+5a)))
@test integrate((a+b*tan(x)^4)^-5//2*cot(x), x) == :((1/2)*a^-2*(a+b*tan(x)^4)^-1//2+(1/2)*(a+b)^-5//2*arctanh((a+b)^-1//2*(a+b*tan(x)^4)^-1//2*(a+-1*b*tan(x)^2))+-1//2*a^-5//2*arctanh(a^-1//2*(a+b*tan(x)^4)^(1/2))+1//6*a^-1*(a+b*tan(x)^4)^-3//2+-1//6*a^-1*(a+b)^-1*(a+b*tan(x)^4)^-3//2*(a+b*tan(x)^2)+-1//6*a^-2*(a+b)^-2*(a+b*tan(x)^4)^-1//2*(3*a^2+b*tan(x)^2*(2b+5a)))
@test integrate(sec(c+d*x)^3*(a+b*tan(c+d*x)^2), x) == :(1//8*d^-1*(-1b+4a)*arctanh(sin(c+d*x))+1//4*b*d^-1*sec(c+d*x)^3*tan(c+d*x)+1//8*d^-1*(-1b+4a)*sec(c+d*x)*tan(c+d*x))
@test integrate((a+b*tan(c+d*x)^2)*sec(c+d*x), x) == :((1/2)*d^-1*(-1b+2a)*arctanh(sin(c+d*x))+(1/2)*b*d^-1*sec(c+d*x)*tan(c+d*x))
@test integrate((a+b*tan(c+d*x)^2)*cos(c+d*x), x) == :(b*d^-1*arctanh(sin(c+d*x))+d^-1*(a+-1b)*sin(c+d*x))
@test integrate(cos(c+d*x)^3*(a+b*tan(c+d*x)^2), x) == :(a*d^-1*sin(c+d*x)+-1//3*d^-1*sin(c+d*x)^3*(a+-1b))
@test integrate(cos(c+d*x)^5*(a+b*tan(c+d*x)^2), x) == :(a*d^-1*sin(c+d*x)+-1//3*d^-1*sin(c+d*x)^3*(-1b+2a)+1//5*d^-1*sin(c+d*x)^5*(a+-1b))
@test integrate(cos(c+d*x)^7*(a+b*tan(c+d*x)^2), x) == :(a*d^-1*sin(c+d*x)+-1//3*d^-1*sin(c+d*x)^3*(-1b+3a)+-1//7*d^-1*sin(c+d*x)^7*(a+-1b)+1//5*d^-1*sin(c+d*x)^5*(-2b+3a))
@test integrate(sec(c+d*x)^6*(a+b*tan(c+d*x)^2), x) == :(a*d^-1*tan(c+d*x)+1//3*d^-1*tan(c+d*x)^3*(b+2a)+1//5*d^-1*tan(c+d*x)^5*(a+2b)+1//7*b*d^-1*tan(c+d*x)^7)
@test integrate(sec(c+d*x)^4*(a+b*tan(c+d*x)^2), x) == :(a*d^-1*tan(c+d*x)+1//3*d^-1*tan(c+d*x)^3*(a+b)+1//5*b*d^-1*tan(c+d*x)^5)
@test integrate(sec(c+d*x)^2*(a+b*tan(c+d*x)^2), x) == :(a*d^-1*tan(c+d*x)+1//3*b*d^-1*tan(c+d*x)^3)
@test integrate(cos(c+d*x)^2*(a+b*tan(c+d*x)^2), x) == :(x*((1/2)*a+(1/2)*b)+(1/2)*d^-1*(a+-1b)*cos(c+d*x)*sin(c+d*x))
@test integrate(cos(c+d*x)^4*(a+b*tan(c+d*x)^2), x) == :(x*(1//8*b+3//8*a)+1//4*d^-1*cos(c+d*x)^3*(a+-1b)*sin(c+d*x)+1//8*d^-1*(b+3a)*cos(c+d*x)*sin(c+d*x))
@test integrate(cos(c+d*x)^6*(a+b*tan(c+d*x)^2), x) == :(x*(1//16*b+5//16*a)+1//6*d^-1*cos(c+d*x)^5*(a+-1b)*sin(c+d*x)+1//16*d^-1*(b+5a)*cos(c+d*x)*sin(c+d*x)+1//24*d^-1*cos(c+d*x)^3*(b+5a)*sin(c+d*x))
@test integrate((a+b*tan(c+d*x)^2)^2*sec(c+d*x)^3, x) == :(1//16*d^-1*(b^2+8*a^2+-4*a*b)*arctanh(sin(c+d*x))+1//16*d^-1*(b^2+8*a^2+-4*a*b)*sec(c+d*x)*tan(c+d*x)+1//6*b*d^-1*sec(c+d*x)^5*(a+-1*sin(c+d*x)^2*(a+-1b))*tan(c+d*x)+1//24*b*d^-1*sec(c+d*x)^3*(-3b+8a)*tan(c+d*x))
@test integrate((a+b*tan(c+d*x)^2)^2*sec(c+d*x), x) == :(1//8*d^-1*(3*b^2+8*a^2+-8*a*b)*arctanh(sin(c+d*x))+1//4*b*d^-1*sec(c+d*x)^3*(a+-1*sin(c+d*x)^2*(a+-1b))*tan(c+d*x)+1//8*b*d^-1*(-3b+6a)*sec(c+d*x)*tan(c+d*x))
@test integrate((a+b*tan(c+d*x)^2)^2*cos(c+d*x), x) == :(d^-1*(a+-1b)^2*sin(c+d*x)+(1/2)*b*d^-1*(-3b+4a)*arctanh(sin(c+d*x))+(1/2)*b^2*d^-1*sec(c+d*x)*tan(c+d*x))
@test integrate((a+b*tan(c+d*x)^2)^2*cos(c+d*x)^3, x) == :(b^2*d^-1*arctanh(sin(c+d*x))+d^-1*(a^2+-1*b^2)*sin(c+d*x)+-1//3*d^-1*(a+-1b)^2*sin(c+d*x)^3)
@test integrate((a+b*tan(c+d*x)^2)^2*cos(c+d*x)^5, x) == :(a^2*d^-1*sin(c+d*x)+1//5*d^-1*(a+-1b)^2*sin(c+d*x)^5+-2//3*a*d^-1*sin(c+d*x)^3*(a+-1b))
@test integrate((a+b*tan(c+d*x)^2)^2*cos(c+d*x)^7, x) == :(a^2*d^-1*sin(c+d*x)+-1//7*d^-1*(a+-1b)^2*sin(c+d*x)^7+-1//3*a*d^-1*sin(c+d*x)^3*(-2b+3a)+1//5*d^-1*sin(c+d*x)^5*(a+-1b)*(-1b+3a))
@test integrate((a+b*tan(c+d*x)^2)^2*cos(c+d*x)^9, x) == :(a^2*d^-1*sin(c+d*x)+1//5*d^-1*sin(c+d*x)^5*(b^2+6*a^2+-6*a*b)+1//9*d^-1*(a+-1b)^2*sin(c+d*x)^9+-2//3*a*d^-1*sin(c+d*x)^3*(-1b+2a)+-1//7*d^-1*sin(c+d*x)^7*(-1b+2a)*(-2b+2a))
@test integrate((a+b*tan(c+d*x)^2)^2*sec(c+d*x)^6, x) == :(a^2*d^-1*tan(c+d*x)+1//5*d^-1*tan(c+d*x)^5*(a^2+b^2+4*a*b)+1//9*b^2*d^-1*tan(c+d*x)^9+2//3*a*d^-1*tan(c+d*x)^3*(a+b)+2//7*b*d^-1*tan(c+d*x)^7*(a+b))
@test integrate((a+b*tan(c+d*x)^2)^2*sec(c+d*x)^4, x) == :(a^2*d^-1*tan(c+d*x)+1//7*b^2*d^-1*tan(c+d*x)^7+1//3*a*d^-1*tan(c+d*x)^3*(a+2b)+1//5*b*d^-1*tan(c+d*x)^5*(b+2a))
@test integrate((a+b*tan(c+d*x)^2)^2*sec(c+d*x)^2, x) == :(a^2*d^-1*tan(c+d*x)+1//5*b^2*d^-1*tan(c+d*x)^5+2//3*a*b*d^-1*tan(c+d*x)^3)
@test integrate((a+b*tan(c+d*x)^2)^2*cos(c+d*x)^2, x) == :(x*(a+3b)*((1/2)*a+-1//2*b)+b^2*d^-1*tan(c+d*x)+(1/2)*d^-1*(a+-1b)^2*cos(c+d*x)*sin(c+d*x))
@test integrate((a+b*tan(c+d*x)^2)^2*cos(c+d*x)^4, x) == :(x*(3//8*a^2+3//8*b^2+1//4*a*b)+1//8*d^-1*(-3*b^2+3*a^2)*cos(c+d*x)*sin(c+d*x)+1//4*d^-1*cos(c+d*x)^3*(a+-1b)*(a+b*tan(c+d*x)^2)*sin(c+d*x))
@test integrate((a+b*tan(c+d*x)^2)^2*cos(c+d*x)^6, x) == :(x*(1//16*b^2+5//16*a^2+1//8*a*b)+1//16*d^-1*(b^2+5*a^2+2*a*b)*cos(c+d*x)*sin(c+d*x)+1//6*d^-1*cos(c+d*x)^5*(a+-1b)*(a+b*tan(c+d*x)^2)*sin(c+d*x)+1//24*d^-1*cos(c+d*x)^3*(a+-1b)*(3b+5a)*sin(c+d*x))
@test integrate((a+b*tan(c+d*x)^2)^-1*sec(c+d*x)^5, x) == :((1/2)*b^-1*d^-1*sec(c+d*x)*tan(c+d*x)+-1//2*b^-2*d^-1*(-3b+2a)*arctanh(sin(c+d*x))+a^-1//2*b^-2*d^-1*(a+-1b)^3//2*arctanh(a^-1//2*(a+-1b)^(1/2)*sin(c+d*x)))
@test integrate((a+b*tan(c+d*x)^2)^-1*sec(c+d*x)^3, x) == :(b^-1*d^-1*arctanh(sin(c+d*x))+-1*a^-1//2*b^-1*d^-1*(a+-1b)^(1/2)*arctanh(a^-1//2*(a+-1b)^(1/2)*sin(c+d*x)))
@test integrate((a+b*tan(c+d*x)^2)^-1*sec(c+d*x), x) == :(a^-1//2*d^-1*(a+-1b)^-1//2*arctanh(a^-1//2*(a+-1b)^(1/2)*sin(c+d*x)))
@test integrate((a+b*tan(c+d*x)^2)^-1*cos(c+d*x), x) == :(d^-1*(a+-1b)^-1*sin(c+d*x)+-1*b*a^-1//2*d^-1*(a+-1b)^-3//2*arctanh(a^-1//2*(a+-1b)^(1/2)*sin(c+d*x)))
@test integrate((a+b*tan(c+d*x)^2)^-1*cos(c+d*x)^3, x) == :(-1*d^-1*(-3b+3a)^-1*sin(c+d*x)^3+d^-1*(a+-1b)^-2*(a+-2b)*sin(c+d*x)+a^-1//2*b^2*d^-1*(a+-1b)^-5//2*arctanh(a^-1//2*(a+-1b)^(1/2)*sin(c+d*x)))
@test integrate((a+b*tan(c+d*x)^2)^-1*cos(c+d*x)^5, x) == :(d^-1*(-5b+5a)^-1*sin(c+d*x)^5+d^-1*(a+-1b)^-3*(a^2+3*b^2+-3*a*b)*sin(c+d*x)+-1//3*d^-1*(a+-1b)^-2*sin(c+d*x)^3*(-3b+2a)+-1*a^-1//2*b^3*d^-1*(a+-1b)^-7//2*arctanh(a^-1//2*(a+-1b)^(1/2)*sin(c+d*x)))
@test integrate((a+b*tan(c+d*x)^2)^-1*sec(c+d*x)^8, x) == :(1//5*b^-1*d^-1*tan(c+d*x)^5+b^-3*d^-1*(a^2+3*b^2+-3*a*b)*tan(c+d*x)+-1//3*b^-2*d^-1*tan(c+d*x)^3*(a+-3b)+-1*a^-1//2*b^-7//2*d^-1*(a+-1b)^3*arctan(a^-1//2*b^(1/2)*tan(c+d*x)))
@test integrate((a+b*tan(c+d*x)^2)^-1*sec(c+d*x)^6, x) == :(1//3*b^-1*d^-1*tan(c+d*x)^3+-1*b^-2*d^-1*(a+-2b)*tan(c+d*x)+a^-1//2*b^-5//2*d^-1*(a+-1b)^2*arctan(a^-1//2*b^(1/2)*tan(c+d*x)))
@test integrate((a+b*tan(c+d*x)^2)^-1*sec(c+d*x)^4, x) == :(b^-1*d^-1*tan(c+d*x)+-1*a^-1//2*b^-3//2*d^-1*(a+-1b)*arctan(a^-1//2*b^(1/2)*tan(c+d*x)))
@test integrate((a+b*tan(c+d*x)^2)^-1*sec(c+d*x)^2, x) == :(a^-1//2*b^-1//2*d^-1*arctan(a^-1//2*b^(1/2)*tan(c+d*x)))
@test integrate((a+b*tan(c+d*x)^2)^-1*cos(c+d*x)^2, x) == :((1/2)*x*(a+-1b)^-2*(a+-3b)+d^-1*(-2b+2a)^-1*cos(c+d*x)*sin(c+d*x)+a^-1//2*b^3//2*d^-1*(a+-1b)^-2*arctan(a^-1//2*b^(1/2)*tan(c+d*x)))
@test integrate((a+b*tan(c+d*x)^2)^-1*cos(c+d*x)^4, x) == :(1//8*x*(a+-1b)^-3*(3*a^2+15*b^2+-10*a*b)+d^-1*(-4b+4a)^-1*cos(c+d*x)^3*sin(c+d*x)+-1*a^-1//2*b^5//2*d^-1*(a+-1b)^-3*arctan(a^-1//2*b^(1/2)*tan(c+d*x))+1//8*d^-1*(a+-1b)^-2*(-7b+3a)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+b*tan(c+d*x)^2)^-2*sec(c+d*x)^7, x) == :(-1//2*b^-3*d^-1*(-5b+4a)*arctanh(sin(c+d*x))+(1/2)*b^-1*d^-1*(a+-1*sin(c+d*x)^2*(a+-1b))^-1*sec(c+d*x)*tan(c+d*x)+(1/2)*a^-3//2*b^-3*d^-1*(a+-1b)^3//2*(b+4a)*arctanh(a^-1//2*(a+-1b)^(1/2)*sin(c+d*x))+(1/2)*a^-1*b^-2*d^-1*(a+-1*sin(c+d*x)^2*(a+-1b))^-1*(a+-1b)*(-1b+2a)*sin(c+d*x))
@test integrate((a+b*tan(c+d*x)^2)^-2*sec(c+d*x)^5, x) == :(b^-2*d^-1*arctanh(sin(c+d*x))+-1//2*a^-1*b^-1*d^-1*(a+-1*sin(c+d*x)^2*(a+-1b))^-1*(a+-1b)*sin(c+d*x)+-1//2*a^-3//2*b^-2*d^-1*(a+-1b)^(1/2)*(b+2a)*arctanh(a^-1//2*(a+-1b)^(1/2)*sin(c+d*x)))
@test integrate((a+b*tan(c+d*x)^2)^-2*sec(c+d*x)^3, x) == :((1/2)*a^-1*d^-1*(a+-1*sin(c+d*x)^2*(a+-1b))^-1*sin(c+d*x)+(1/2)*a^-3//2*d^-1*(a+-1b)^-1//2*arctanh(a^-1//2*(a+-1b)^(1/2)*sin(c+d*x)))
@test integrate((a+b*tan(c+d*x)^2)^-2*sec(c+d*x), x) == :((1/2)*a^-3//2*d^-1*(a+-1b)^-3//2*(-1b+2a)*arctanh(a^-1//2*(a+-1b)^(1/2)*sin(c+d*x))+-1//2*b*a^-1*d^-1*(a+-1b)^-1*(a+-1*sin(c+d*x)^2*(a+-1b))^-1*sin(c+d*x))
@test integrate((a+b*tan(c+d*x)^2)^-2*cos(c+d*x), x) == :(d^-1*(a+-1b)^-2*sin(c+d*x)+(1/2)*a^-1*b^2*d^-1*(a+-1b)^-2*(a+-1*sin(c+d*x)^2*(a+-1b))^-1*sin(c+d*x)+-1//2*b*a^-3//2*d^-1*(a+-1b)^-5//2*(-1b+4a)*arctanh(a^-1//2*(a+-1b)^(1/2)*sin(c+d*x)))
@test integrate((a+b*tan(c+d*x)^2)^-2*cos(c+d*x)^3, x) == :(-1//3*d^-1*(a+-1b)^-2*sin(c+d*x)^3+d^-1*(a+-1b)^-3*(a+-3b)*sin(c+d*x)+(1/2)*a^-3//2*b^2*d^-1*(a+-1b)^-7//2*(-1b+6a)*arctanh(a^-1//2*(a+-1b)^(1/2)*sin(c+d*x))+-1//2*a^-1*b^3*d^-1*(a+-1b)^-3*(a+-1*sin(c+d*x)^2*(a+-1b))^-1*sin(c+d*x))
@test integrate((a+b*tan(c+d*x)^2)^-2*sec(c+d*x)^8, x) == :(1//3*b^-2*d^-1*tan(c+d*x)^3+-1*b^-3*d^-1*(-3b+2a)*tan(c+d*x)+(1/2)*a^-3//2*b^-7//2*d^-1*(a+-1b)^2*(b+5a)*arctan(a^-1//2*b^(1/2)*tan(c+d*x))+-1//2*a^-1*b^-3*d^-1*(a+-1b)^3*(a+b*tan(c+d*x)^2)^-1*tan(c+d*x))
@test integrate((a+b*tan(c+d*x)^2)^-2*sec(c+d*x)^6, x) == :(b^-2*d^-1*tan(c+d*x)+-1//2*a^-3//2*b^-5//2*d^-1*(-1*b^2+3*a^2+-2*a*b)*arctan(a^-1//2*b^(1/2)*tan(c+d*x))+(1/2)*a^-1*b^-2*d^-1*(a+-1b)^2*(a+b*tan(c+d*x)^2)^-1*tan(c+d*x))
@test integrate((a+b*tan(c+d*x)^2)^-2*sec(c+d*x)^4, x) == :((1/2)*a^-3//2*b^-3//2*d^-1*(a+b)*arctan(a^-1//2*b^(1/2)*tan(c+d*x))+-1//2*a^-1*b^-1*d^-1*(a+b*tan(c+d*x)^2)^-1*(a+-1b)*tan(c+d*x))
@test integrate((a+b*tan(c+d*x)^2)^-2*sec(c+d*x)^2, x) == :((1/2)*a^-1*d^-1*(a+b*tan(c+d*x)^2)^-1*tan(c+d*x)+(1/2)*a^-3//2*b^-1//2*d^-1*arctan(a^-1//2*b^(1/2)*tan(c+d*x)))
@test integrate((a+b*tan(c+d*x)^2)^-2*cos(c+d*x)^2, x) == :((1/2)*x*(a+-1b)^-3*(a+-5b)+d^-1*(a+b*tan(c+d*x)^2)^-1*(-2b+2a)^-1*cos(c+d*x)*sin(c+d*x)+(1/2)*a^-3//2*b^3//2*d^-1*(a+-1b)^-3*(-1b+5a)*arctan(a^-1//2*b^(1/2)*tan(c+d*x))+(1/2)*b*a^-1*d^-1*(a+-1b)^-2*(a+b*tan(c+d*x)^2)^-1*(a+b)*tan(c+d*x))
@test integrate((a+b*tan(c+d*x)^2)^-2*cos(c+d*x)^4, x) == :(1//8*x*(a+-1b)^-4*(3*a^2+35*b^2+-14*a*b)+d^-1*(a+b*tan(c+d*x)^2)^-1*(-4b+4a)^-1*cos(c+d*x)^3*sin(c+d*x)+-1//2*a^-3//2*b^5//2*d^-1*(a+-1b)^-4*(-1b+7a)*arctan(a^-1//2*b^(1/2)*tan(c+d*x))+1//8*d^-1*(a+-1b)^-2*(a+b*tan(c+d*x)^2)^-1*(-9b+3a)*cos(c+d*x)*sin(c+d*x)+1//8*b*a^-1*d^-1*(a+-1b)^-3*(a+b*tan(c+d*x)^2)^-1*(a+-4b)*(b+3a)*tan(c+d*x))
@test integrate((b*(c*tan(e+f*x))^n)^p*sec(e+f*x)^6, x) == :(f^-1*(b*(c*tan(e+f*x))^n)^p*(1+n*p)^-1*tan(e+f*x)+f^-1*(b*(c*tan(e+f*x))^n)^p*(5+n*p)^-1*tan(e+f*x)^5+2*f^-1*(b*(c*tan(e+f*x))^n)^p*(3+n*p)^-1*tan(e+f*x)^3)
@test integrate((b*(c*tan(e+f*x))^n)^p*sec(e+f*x)^4, x) == :(f^-1*(b*(c*tan(e+f*x))^n)^p*(1+n*p)^-1*tan(e+f*x)+f^-1*(b*(c*tan(e+f*x))^n)^p*(3+n*p)^-1*tan(e+f*x)^3)
@test integrate((b*(c*tan(e+f*x))^n)^p*sec(e+f*x)^2, x) == :(f^-1*(b*(c*tan(e+f*x))^n)^p*(1+n*p)^-1*tan(e+f*x))

max_stars_repo_path: test/4 Trig functions/4.3 Tangent/4.3.7 (d trig)^m (a+b (c tan)^n)^p.jl