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

@test integrate(sin(a+b*x), x) == :(-1*b^-1*cos(a+b*x))
@test integrate(sin(a+b*x)^2, x) == :((1/2)*x+-1//2*b^-1*cos(a+b*x)*sin(a+b*x))
@test integrate(sin(a+b*x)^3, x) == :(-1*b^-1*cos(a+b*x)+1//3*b^-1*cos(a+b*x)^3)
@test integrate(sin(a+b*x)^4, x) == :(3//8*x+-3//8*b^-1*cos(a+b*x)*sin(a+b*x)+-1//4*b^-1*sin(a+b*x)^3*cos(a+b*x))
@test integrate(sin(a+b*x)^5, x) == :(-1*b^-1*cos(a+b*x)+-1//5*b^-1*cos(a+b*x)^5+2//3*b^-1*cos(a+b*x)^3)
@test integrate(sin(a+b*x)^6, x) == :(5//16*x+-5//16*b^-1*cos(a+b*x)*sin(a+b*x)+-5//24*b^-1*sin(a+b*x)^3*cos(a+b*x)+-1//6*b^-1*sin(a+b*x)^5*cos(a+b*x))
@test integrate(sin(a+b*x)^7, x) == :(b^-1*cos(a+b*x)^3+-1*b^-1*cos(a+b*x)+-3//5*b^-1*cos(a+b*x)^5+1//7*b^-1*cos(a+b*x)^7)
@test integrate(sin(a+b*x)^8, x) == :(35//128*x+-35//128*b^-1*cos(a+b*x)*sin(a+b*x)+-35//192*b^-1*sin(a+b*x)^3*cos(a+b*x)+-7//48*b^-1*sin(a+b*x)^5*cos(a+b*x)+-1//8*b^-1*sin(a+b*x)^7*cos(a+b*x))
@test integrate(sin(b*x)^7//2, x) == :(-10//21*b^-1*Elliptic.F(1//4*pi+-1//2*b*x,2)+-10//21*b^-1*sin(b*x)^(1/2)*cos(b*x)+-2//7*b^-1*sin(b*x)^5//2*cos(b*x))
@test integrate(sin(b*x)^5//2, x) == :(-6//5*b^-1*Elliptic.E(1//4*pi+-1//2*b*x,2)+-2//5*b^-1*sin(b*x)^3//2*cos(b*x))
@test integrate(sin(b*x)^3//2, x) == :(-2//3*b^-1*Elliptic.F(1//4*pi+-1//2*b*x,2)+-2//3*b^-1*sin(b*x)^(1/2)*cos(b*x))
@test integrate(sin(b*x)^(1/2), x) == :(-2*b^-1*Elliptic.E(1//4*pi+-1//2*b*x,2))
@test integrate(sin(b*x)^-1//2, x) == :(-2*b^-1*Elliptic.F(1//4*pi+-1//2*b*x,2))
@test integrate(sin(b*x)^-3//2, x) == :(2*b^-1*Elliptic.E(1//4*pi+-1//2*b*x,2)+-2*b^-1*sin(b*x)^-1//2*cos(b*x))
@test integrate(sin(b*x)^-5//2, x) == :(-2//3*b^-1*Elliptic.F(1//4*pi+-1//2*b*x,2)+-2//3*b^-1*sin(b*x)^-3//2*cos(b*x))
@test integrate(sin(b*x)^-7//2, x) == :(6//5*b^-1*Elliptic.E(1//4*pi+-1//2*b*x,2)+-6//5*b^-1*sin(b*x)^-1//2*cos(b*x)+-2//5*b^-1*sin(b*x)^-5//2*cos(b*x))
@test integrate(sin(a+b*x)^7//2, x) == :(10//21*b^-1*Elliptic.F((1/2)*a+-1//4*pi+(1/2)*b*x,2)+-10//21*b^-1*sin(a+b*x)^(1/2)*cos(a+b*x)+-2//7*b^-1*sin(a+b*x)^5//2*cos(a+b*x))
@test integrate(sin(a+b*x)^5//2, x) == :(6//5*b^-1*Elliptic.E((1/2)*a+-1//4*pi+(1/2)*b*x,2)+-2//5*b^-1*sin(a+b*x)^3//2*cos(a+b*x))
@test integrate(sin(a+b*x)^3//2, x) == :(2//3*b^-1*Elliptic.F((1/2)*a+-1//4*pi+(1/2)*b*x,2)+-2//3*b^-1*sin(a+b*x)^(1/2)*cos(a+b*x))
@test integrate(sin(a+b*x)^(1/2), x) == :(2*b^-1*Elliptic.E((1/2)*a+-1//4*pi+(1/2)*b*x,2))
@test integrate(sin(a+b*x)^-1//2, x) == :(2*b^-1*Elliptic.F((1/2)*a+-1//4*pi+(1/2)*b*x,2))
@test integrate(sin(a+b*x)^-3//2, x) == :(-2*b^-1*Elliptic.E((1/2)*a+-1//4*pi+(1/2)*b*x,2)+-2*b^-1*sin(a+b*x)^-1//2*cos(a+b*x))
@test integrate(sin(a+b*x)^-5//2, x) == :(2//3*b^-1*Elliptic.F((1/2)*a+-1//4*pi+(1/2)*b*x,2)+-2//3*b^-1*sin(a+b*x)^-3//2*cos(a+b*x))
@test integrate(sin(a+b*x)^-7//2, x) == :(-6//5*b^-1*Elliptic.E((1/2)*a+-1//4*pi+(1/2)*b*x,2)+-6//5*b^-1*sin(a+b*x)^-1//2*cos(a+b*x)+-2//5*b^-1*sin(a+b*x)^-5//2*cos(a+b*x))
@test integrate((c*sin(a+b*x))^7//2, x) == :(-10//21*b^-1*c^3*(c*sin(a+b*x))^(1/2)*cos(a+b*x)+-2//7*c*b^-1*(c*sin(a+b*x))^5//2*cos(a+b*x)+10//21*b^-1*c^4*(c*sin(a+b*x))^-1//2*sin(a+b*x)^(1/2)*Elliptic.F((1/2)*a+-1//4*pi+(1/2)*b*x,2))
@test integrate((c*sin(a+b*x))^5//2, x) == :(-2//5*c*b^-1*(c*sin(a+b*x))^3//2*cos(a+b*x)+6//5*b^-1*c^2*(c*sin(a+b*x))^(1/2)*sin(a+b*x)^-1//2*Elliptic.E((1/2)*a+-1//4*pi+(1/2)*b*x,2))
@test integrate((c*sin(a+b*x))^3//2, x) == :(-2//3*c*b^-1*(c*sin(a+b*x))^(1/2)*cos(a+b*x)+2//3*b^-1*c^2*(c*sin(a+b*x))^-1//2*sin(a+b*x)^(1/2)*Elliptic.F((1/2)*a+-1//4*pi+(1/2)*b*x,2))
@test integrate((c*sin(a+b*x))^(1/2), x) == :(2*b^-1*(c*sin(a+b*x))^(1/2)*sin(a+b*x)^-1//2*Elliptic.E((1/2)*a+-1//4*pi+(1/2)*b*x,2))
@test integrate((c*sin(a+b*x))^-1//2, x) == :(2*b^-1*(c*sin(a+b*x))^-1//2*sin(a+b*x)^(1/2)*Elliptic.F((1/2)*a+-1//4*pi+(1/2)*b*x,2))
@test integrate((c*sin(a+b*x))^-3//2, x) == :(-2*b^-1*c^-1*(c*sin(a+b*x))^-1//2*cos(a+b*x)+-2*b^-1*c^-2*(c*sin(a+b*x))^(1/2)*sin(a+b*x)^-1//2*Elliptic.E((1/2)*a+-1//4*pi+(1/2)*b*x,2))
@test integrate((c*sin(a+b*x))^-5//2, x) == :(-2//3*b^-1*c^-1*(c*sin(a+b*x))^-3//2*cos(a+b*x)+2//3*b^-1*c^-2*(c*sin(a+b*x))^-1//2*sin(a+b*x)^(1/2)*Elliptic.F((1/2)*a+-1//4*pi+(1/2)*b*x,2))
@test integrate((c*sin(a+b*x))^-7//2, x) == :(-6//5*b^-1*c^-3*(c*sin(a+b*x))^-1//2*cos(a+b*x)+-2//5*b^-1*c^-1*(c*sin(a+b*x))^-5//2*cos(a+b*x)+-6//5*b^-1*c^-4*(c*sin(a+b*x))^(1/2)*sin(a+b*x)^-1//2*Elliptic.E((1/2)*a+-1//4*pi+(1/2)*b*x,2))
@test integrate(cos(a+b*x)^3*sin(a+b*x), x) == :(-1//4*b^-1*cos(a+b*x)^4)
@test integrate(cos(a+b*x)^2*sin(a+b*x), x) == :(-1//3*b^-1*cos(a+b*x)^3)
@test integrate(cos(a+b*x)*sin(a+b*x), x) == :((1/2)*b^-1*sin(a+b*x)^2)
@test integrate(sec(a+b*x)*sin(a+b*x), x) == :(-1*b^-1*log(cos(a+b*x)))
@test integrate(sec(a+b*x)^2*sin(a+b*x), x) == :(b^-1*sec(a+b*x))
@test integrate(sec(a+b*x)^3*sin(a+b*x), x) == :((1/2)*b^-1*sec(a+b*x)^2)
@test integrate(sec(a+b*x)^4*sin(a+b*x), x) == :(1//3*b^-1*sec(a+b*x)^3)
@test integrate(cos(a+b*x)^7*sin(a+b*x)^2, x) == :(-3//5*b^-1*sin(a+b*x)^5+-1//9*b^-1*sin(a+b*x)^9+1//3*b^-1*sin(a+b*x)^3+3//7*b^-1*sin(a+b*x)^7)
@test integrate(cos(a+b*x)^5*sin(a+b*x)^2, x) == :(-2//5*b^-1*sin(a+b*x)^5+1//3*b^-1*sin(a+b*x)^3+1//7*b^-1*sin(a+b*x)^7)
@test integrate(cos(a+b*x)^3*sin(a+b*x)^2, x) == :(-1//5*b^-1*sin(a+b*x)^5+1//3*b^-1*sin(a+b*x)^3)
@test integrate(sin(a+b*x)^2*cos(a+b*x), x) == :(1//3*b^-1*sin(a+b*x)^3)
@test integrate(sec(a+b*x)^2*sin(a+b*x)^2, x) == :(-1x+b^-1*tan(a+b*x))
@test integrate(sec(a+b*x)^4*sin(a+b*x)^2, x) == :(1//3*b^-1*tan(a+b*x)^3)
@test integrate(sec(a+b*x)^6*sin(a+b*x)^2, x) == :(1//3*b^-1*tan(a+b*x)^3+1//5*b^-1*tan(a+b*x)^5)
@test integrate(sec(a+b*x)^8*sin(a+b*x)^2, x) == :(1//3*b^-1*tan(a+b*x)^3+1//7*b^-1*tan(a+b*x)^7+2//5*b^-1*tan(a+b*x)^5)
@test integrate(sec(a+b*x)^10*sin(a+b*x)^2, x) == :(1//3*b^-1*tan(a+b*x)^3+1//9*b^-1*tan(a+b*x)^9+3//5*b^-1*tan(a+b*x)^5+3//7*b^-1*tan(a+b*x)^7)
@test integrate(cos(a+b*x)^6*sin(a+b*x)^2, x) == :(5//128*x+-1//8*b^-1*cos(a+b*x)^7*sin(a+b*x)+1//48*b^-1*cos(a+b*x)^5*sin(a+b*x)+5//128*b^-1*cos(a+b*x)*sin(a+b*x)+5//192*b^-1*cos(a+b*x)^3*sin(a+b*x))
@test integrate(cos(a+b*x)^4*sin(a+b*x)^2, x) == :(1//16*x+-1//6*b^-1*cos(a+b*x)^5*sin(a+b*x)+1//16*b^-1*cos(a+b*x)*sin(a+b*x)+1//24*b^-1*cos(a+b*x)^3*sin(a+b*x))
@test integrate(cos(a+b*x)^2*sin(a+b*x)^2, x) == :(1//8*x+-1//4*b^-1*cos(a+b*x)^3*sin(a+b*x)+1//8*b^-1*cos(a+b*x)*sin(a+b*x))
@test integrate(sin(a+b*x)^2, x) == :((1/2)*x+-1//2*b^-1*cos(a+b*x)*sin(a+b*x))
@test integrate(sin(a+b*x)^2*sec(a+b*x), x) == :(b^-1*arctanh(sin(a+b*x))+-1*b^-1*sin(a+b*x))
@test integrate(sec(a+b*x)^3*sin(a+b*x)^2, x) == :(-1//2*b^-1*arctanh(sin(a+b*x))+(1/2)*b^-1*sec(a+b*x)*tan(a+b*x))
@test integrate(sec(a+b*x)^5*sin(a+b*x)^2, x) == :(-1//8*b^-1*arctanh(sin(a+b*x))+-1//8*b^-1*sec(a+b*x)*tan(a+b*x)+1//4*b^-1*sec(a+b*x)^3*tan(a+b*x))
@test integrate(sec(a+b*x)^7*sin(a+b*x)^2, x) == :(-1//16*b^-1*arctanh(sin(a+b*x))+-1//16*b^-1*sec(a+b*x)*tan(a+b*x)+-1//24*b^-1*sec(a+b*x)^3*tan(a+b*x)+1//6*b^-1*sec(a+b*x)^5*tan(a+b*x))
@test integrate(cos(a+b*x)^5*sin(a+b*x)^3, x) == :(-1//6*b^-1*cos(a+b*x)^6+1//8*b^-1*cos(a+b*x)^8)
@test integrate(cos(a+b*x)^4*sin(a+b*x)^3, x) == :(-1//5*b^-1*cos(a+b*x)^5+1//7*b^-1*cos(a+b*x)^7)
@test integrate(cos(a+b*x)^3*sin(a+b*x)^3, x) == :(-1//6*b^-1*sin(a+b*x)^6+1//4*b^-1*sin(a+b*x)^4)
@test integrate(cos(a+b*x)^2*sin(a+b*x)^3, x) == :(-1//3*b^-1*cos(a+b*x)^3+1//5*b^-1*cos(a+b*x)^5)
@test integrate(sin(a+b*x)^3*cos(a+b*x), x) == :(1//4*b^-1*sin(a+b*x)^4)
@test integrate(sin(a+b*x)^3*sec(a+b*x), x) == :((1/2)*b^-1*cos(a+b*x)^2+-1*b^-1*log(cos(a+b*x)))
@test integrate(sec(a+b*x)^2*sin(a+b*x)^3, x) == :(b^-1*cos(a+b*x)+b^-1*sec(a+b*x))
@test integrate(sec(a+b*x)^3*sin(a+b*x)^3, x) == :(b^-1*log(cos(a+b*x))+(1/2)*b^-1*tan(a+b*x)^2)
@test integrate(sec(a+b*x)^4*sin(a+b*x)^3, x) == :(-1*b^-1*sec(a+b*x)+1//3*b^-1*sec(a+b*x)^3)
@test integrate(sec(a+b*x)^5*sin(a+b*x)^3, x) == :(1//4*b^-1*tan(a+b*x)^4)
@test integrate(sec(a+b*x)^6*sin(a+b*x)^3, x) == :(-1//3*b^-1*sec(a+b*x)^3+1//5*b^-1*sec(a+b*x)^5)
@test integrate(sec(a+b*x)^7*sin(a+b*x)^3, x) == :(-1//4*b^-1*sec(a+b*x)^4+1//6*b^-1*sec(a+b*x)^6)
@test integrate(sec(a+b*x)^8*sin(a+b*x)^3, x) == :(-1//5*b^-1*sec(a+b*x)^5+1//7*b^-1*sec(a+b*x)^7)
@test integrate(sec(a+b*x)^9*sin(a+b*x)^3, x) == :(-1//6*b^-1*sec(a+b*x)^6+1//8*b^-1*sec(a+b*x)^8)
@test integrate(cos(a+b*x)^7*sin(a+b*x)^4, x) == :(-3//7*b^-1*sin(a+b*x)^7+-1//11*b^-1*sin(a+b*x)^11+1//3*b^-1*sin(a+b*x)^9+1//5*b^-1*sin(a+b*x)^5)
@test integrate(cos(a+b*x)^5*sin(a+b*x)^4, x) == :(-2//7*b^-1*sin(a+b*x)^7+1//5*b^-1*sin(a+b*x)^5+1//9*b^-1*sin(a+b*x)^9)
@test integrate(cos(a+b*x)^3*sin(a+b*x)^4, x) == :(-1//7*b^-1*sin(a+b*x)^7+1//5*b^-1*sin(a+b*x)^5)
@test integrate(sin(a+b*x)^4*cos(a+b*x), x) == :(1//5*b^-1*sin(a+b*x)^5)
@test integrate(sec(a+b*x)^2*sin(a+b*x)^4, x) == :(-3//2*x+3//2*b^-1*tan(a+b*x)+-1//2*b^-1*sin(a+b*x)^2*tan(a+b*x))
@test integrate(sec(a+b*x)^4*sin(a+b*x)^4, x) == :(x+-1*b^-1*tan(a+b*x)+1//3*b^-1*tan(a+b*x)^3)
@test integrate(sec(a+b*x)^6*sin(a+b*x)^4, x) == :(1//5*b^-1*tan(a+b*x)^5)
@test integrate(sec(a+b*x)^8*sin(a+b*x)^4, x) == :(1//5*b^-1*tan(a+b*x)^5+1//7*b^-1*tan(a+b*x)^7)
@test integrate(sec(a+b*x)^10*sin(a+b*x)^4, x) == :(1//5*b^-1*tan(a+b*x)^5+1//9*b^-1*tan(a+b*x)^9+2//7*b^-1*tan(a+b*x)^7)
@test integrate(cos(a+b*x)^6*sin(a+b*x)^4, x) == :(3//256*x+-3//80*b^-1*cos(a+b*x)^7*sin(a+b*x)+-1//10*b^-1*cos(a+b*x)^7*sin(a+b*x)^3+1//128*b^-1*cos(a+b*x)^3*sin(a+b*x)+1//160*b^-1*cos(a+b*x)^5*sin(a+b*x)+3//256*b^-1*cos(a+b*x)*sin(a+b*x))
@test integrate(cos(a+b*x)^4*sin(a+b*x)^4, x) == :(3//128*x+-1//8*b^-1*cos(a+b*x)^5*sin(a+b*x)^3+-1//16*b^-1*cos(a+b*x)^5*sin(a+b*x)+1//64*b^-1*cos(a+b*x)^3*sin(a+b*x)+3//128*b^-1*cos(a+b*x)*sin(a+b*x))
@test integrate(cos(a+b*x)^2*sin(a+b*x)^4, x) == :(1//16*x+-1//6*b^-1*cos(a+b*x)^3*sin(a+b*x)^3+-1//8*b^-1*cos(a+b*x)^3*sin(a+b*x)+1//16*b^-1*cos(a+b*x)*sin(a+b*x))
@test integrate(sin(a+b*x)^4, x) == :(3//8*x+-3//8*b^-1*cos(a+b*x)*sin(a+b*x)+-1//4*b^-1*sin(a+b*x)^3*cos(a+b*x))
@test integrate(sin(a+b*x)^4*sec(a+b*x), x) == :(b^-1*arctanh(sin(a+b*x))+-1*b^-1*sin(a+b*x)+-1//3*b^-1*sin(a+b*x)^3)
@test integrate(sec(a+b*x)^3*sin(a+b*x)^4, x) == :(-3//2*b^-1*arctanh(sin(a+b*x))+3//2*b^-1*sin(a+b*x)+(1/2)*b^-1*tan(a+b*x)^2*sin(a+b*x))
@test integrate(sec(a+b*x)^5*sin(a+b*x)^4, x) == :(3//8*b^-1*arctanh(sin(a+b*x))+-3//8*b^-1*sec(a+b*x)*tan(a+b*x)+1//4*b^-1*tan(a+b*x)^3*sec(a+b*x))
@test integrate(sec(a+b*x)^7*sin(a+b*x)^4, x) == :(1//16*b^-1*arctanh(sin(a+b*x))+-1//8*b^-1*sec(a+b*x)^3*tan(a+b*x)+1//6*b^-1*sec(a+b*x)^3*tan(a+b*x)^3+1//16*b^-1*sec(a+b*x)*tan(a+b*x))
@test integrate(sec(a+b*x)^9*sin(a+b*x)^4, x) == :(3//128*b^-1*arctanh(sin(a+b*x))+-1//16*b^-1*sec(a+b*x)^5*tan(a+b*x)+1//8*b^-1*sec(a+b*x)^5*tan(a+b*x)^3+1//64*b^-1*sec(a+b*x)^3*tan(a+b*x)+3//128*b^-1*sec(a+b*x)*tan(a+b*x))
@test integrate(cos(a+b*x)^7*sin(a+b*x)^5, x) == :(-1//8*b^-1*cos(a+b*x)^8+-1//12*b^-1*cos(a+b*x)^12+1//5*b^-1*cos(a+b*x)^10)
@test integrate(cos(a+b*x)^6*sin(a+b*x)^5, x) == :(-1//7*b^-1*cos(a+b*x)^7+-1//11*b^-1*cos(a+b*x)^11+2//9*b^-1*cos(a+b*x)^9)
@test integrate(cos(a+b*x)^5*sin(a+b*x)^5, x) == :(-1//4*b^-1*sin(a+b*x)^8+1//6*b^-1*sin(a+b*x)^6+1//10*b^-1*sin(a+b*x)^10)
@test integrate(cos(a+b*x)^4*sin(a+b*x)^5, x) == :(-1//5*b^-1*cos(a+b*x)^5+-1//9*b^-1*cos(a+b*x)^9+2//7*b^-1*cos(a+b*x)^7)
@test integrate(cos(a+b*x)^3*sin(a+b*x)^5, x) == :(-1//8*b^-1*sin(a+b*x)^8+1//6*b^-1*sin(a+b*x)^6)
@test integrate(cos(a+b*x)^2*sin(a+b*x)^5, x) == :(-1//3*b^-1*cos(a+b*x)^3+-1//7*b^-1*cos(a+b*x)^7+2//5*b^-1*cos(a+b*x)^5)
@test integrate(sin(a+b*x)^5*cos(a+b*x), x) == :(1//6*b^-1*sin(a+b*x)^6)
@test integrate(sin(a+b*x)^5*sec(a+b*x), x) == :(b^-1*cos(a+b*x)^2+-1*b^-1*log(cos(a+b*x))+-1//4*b^-1*cos(a+b*x)^4)
@test integrate(sec(a+b*x)^2*sin(a+b*x)^5, x) == :(b^-1*sec(a+b*x)+2*b^-1*cos(a+b*x)+-1//3*b^-1*cos(a+b*x)^3)
@test integrate(sec(a+b*x)^3*sin(a+b*x)^5, x) == :((1/2)*b^-1*sec(a+b*x)^2+2*b^-1*log(cos(a+b*x))+-1//2*b^-1*cos(a+b*x)^2)
@test integrate(sec(a+b*x)^4*sin(a+b*x)^5, x) == :(-1*b^-1*cos(a+b*x)+-2*b^-1*sec(a+b*x)+1//3*b^-1*sec(a+b*x)^3)
@test integrate(sec(a+b*x)^5*sin(a+b*x)^5, x) == :(-1*b^-1*log(cos(a+b*x))+-1//2*b^-1*tan(a+b*x)^2+1//4*b^-1*tan(a+b*x)^4)
@test integrate(sec(a+b*x)^6*sin(a+b*x)^5, x) == :(b^-1*sec(a+b*x)+-2//3*b^-1*sec(a+b*x)^3+1//5*b^-1*sec(a+b*x)^5)
@test integrate(sec(a+b*x)^7*sin(a+b*x)^5, x) == :(1//6*b^-1*tan(a+b*x)^6)
@test integrate(sec(a+b*x)^8*sin(a+b*x)^5, x) == :(-2//5*b^-1*sec(a+b*x)^5+1//3*b^-1*sec(a+b*x)^3+1//7*b^-1*sec(a+b*x)^7)
@test integrate(sec(a+b*x)^9*sin(a+b*x)^5, x) == :(1//6*b^-1*tan(a+b*x)^6+1//8*b^-1*tan(a+b*x)^8)
@test integrate(sec(a+b*x)^10*sin(a+b*x)^5, x) == :(-2//7*b^-1*sec(a+b*x)^7+1//5*b^-1*sec(a+b*x)^5+1//9*b^-1*sec(a+b*x)^9)
@test integrate(sec(a+b*x)^11*sin(a+b*x)^5, x) == :(-1//4*b^-1*sec(a+b*x)^8+1//6*b^-1*sec(a+b*x)^6+1//10*b^-1*sec(a+b*x)^10)
@test integrate(sec(a+b*x)^12*sin(a+b*x)^5, x) == :(-2//9*b^-1*sec(a+b*x)^9+1//7*b^-1*sec(a+b*x)^7+1//11*b^-1*sec(a+b*x)^11)
@test integrate(sec(a+b*x)^13*sin(a+b*x)^5, x) == :(-1//5*b^-1*sec(a+b*x)^10+1//8*b^-1*sec(a+b*x)^8+1//12*b^-1*sec(a+b*x)^12)
@test integrate(sec(a+b*x)^3*sin(a+b*x)^6, x) == :(-5//2*b^-1*arctanh(sin(a+b*x))+5//2*b^-1*sin(a+b*x)+5//6*b^-1*sin(a+b*x)^3+(1/2)*b^-1*sin(a+b*x)^3*tan(a+b*x)^2)
@test integrate(sec(a+b*x)^6*sin(a+b*x)^7, x) == :(b^-1*cos(a+b*x)+-1*b^-1*sec(a+b*x)^3+3*b^-1*sec(a+b*x)+1//5*b^-1*sec(a+b*x)^5)
@test integrate(cos(a+b*x)^6*sin(a+b*x)^-1, x) == :(b^-1*cos(a+b*x)+-1*b^-1*arctanh(cos(a+b*x))+1//3*b^-1*cos(a+b*x)^3+1//5*b^-1*cos(a+b*x)^5)
@test integrate(cos(a+b*x)^5*sin(a+b*x)^-1, x) == :(b^-1*log(sin(a+b*x))+-1*b^-1*sin(a+b*x)^2+1//4*b^-1*sin(a+b*x)^4)
@test integrate(cos(a+b*x)^4*sin(a+b*x)^-1, x) == :(b^-1*cos(a+b*x)+-1*b^-1*arctanh(cos(a+b*x))+1//3*b^-1*cos(a+b*x)^3)
@test integrate(cos(a+b*x)^3*sin(a+b*x)^-1, x) == :(b^-1*log(sin(a+b*x))+-1//2*b^-1*sin(a+b*x)^2)
@test integrate(cos(a+b*x)^2*sin(a+b*x)^-1, x) == :(b^-1*cos(a+b*x)+-1*b^-1*arctanh(cos(a+b*x)))
@test integrate(sin(a+b*x)^-1*cos(a+b*x), x) == :(b^-1*log(sin(a+b*x)))
@test integrate(sin(a+b*x)^-1*sec(a+b*x), x) == :(b^-1*log(tan(a+b*x)))
@test integrate(sec(a+b*x)^2*sin(a+b*x)^-1, x) == :(b^-1*sec(a+b*x)+-1*b^-1*arctanh(cos(a+b*x)))
@test integrate(sec(a+b*x)^3*sin(a+b*x)^-1, x) == :(b^-1*log(tan(a+b*x))+(1/2)*b^-1*tan(a+b*x)^2)
@test integrate(sec(a+b*x)^4*sin(a+b*x)^-1, x) == :(b^-1*sec(a+b*x)+-1*b^-1*arctanh(cos(a+b*x))+1//3*b^-1*sec(a+b*x)^3)
@test integrate(sec(a+b*x)^5*sin(a+b*x)^-1, x) == :(b^-1*tan(a+b*x)^2+b^-1*log(tan(a+b*x))+1//4*b^-1*tan(a+b*x)^4)
@test integrate(sec(a+b*x)^6*sin(a+b*x)^-1, x) == :(b^-1*sec(a+b*x)+-1*b^-1*arctanh(cos(a+b*x))+1//3*b^-1*sec(a+b*x)^3+1//5*b^-1*sec(a+b*x)^5)
@test integrate(sec(a+b*x)^7*sin(a+b*x)^-1, x) == :(b^-1*log(tan(a+b*x))+1//6*b^-1*tan(a+b*x)^6+3//2*b^-1*tan(a+b*x)^2+3//4*b^-1*tan(a+b*x)^4)
@test integrate(cos(a+b*x)^7*sin(a+b*x)^-2, x) == :(b^-1*sin(a+b*x)^3+-1*b^-1*csc(a+b*x)+-3*b^-1*sin(a+b*x)+-1//5*b^-1*sin(a+b*x)^5)
@test integrate(cos(a+b*x)^6*sin(a+b*x)^-2, x) == :(-15//8*x+-15//8*b^-1*cot(a+b*x)+1//4*b^-1*cos(a+b*x)^4*cot(a+b*x)+5//8*b^-1*cos(a+b*x)^2*cot(a+b*x))
@test integrate(cos(a+b*x)^5*sin(a+b*x)^-2, x) == :(-1*b^-1*csc(a+b*x)+-2*b^-1*sin(a+b*x)+1//3*b^-1*sin(a+b*x)^3)
@test integrate(cos(a+b*x)^4*sin(a+b*x)^-2, x) == :(-3//2*x+-3//2*b^-1*cot(a+b*x)+(1/2)*b^-1*cos(a+b*x)^2*cot(a+b*x))
@test integrate(cos(a+b*x)^3*sin(a+b*x)^-2, x) == :(-1*b^-1*csc(a+b*x)+-1*b^-1*sin(a+b*x))
@test integrate(cos(a+b*x)^2*sin(a+b*x)^-2, x) == :(-1x+-1*b^-1*cot(a+b*x))
@test integrate(sin(a+b*x)^-2*cos(a+b*x), x) == :(-1*b^-1*csc(a+b*x))
@test integrate(sin(a+b*x)^-2*sec(a+b*x), x) == :(b^-1*arctanh(sin(a+b*x))+-1*b^-1*csc(a+b*x))
@test integrate(sec(a+b*x)^2*sin(a+b*x)^-2, x) == :(b^-1*tan(a+b*x)+-1*b^-1*cot(a+b*x))
@test integrate(sec(a+b*x)^3*sin(a+b*x)^-2, x) == :(-3//2*b^-1*csc(a+b*x)+3//2*b^-1*arctanh(sin(a+b*x))+(1/2)*b^-1*sec(a+b*x)^2*csc(a+b*x))
@test integrate(sec(a+b*x)^4*sin(a+b*x)^-2, x) == :(-1*b^-1*cot(a+b*x)+2*b^-1*tan(a+b*x)+1//3*b^-1*tan(a+b*x)^3)
@test integrate(sec(a+b*x)^5*sin(a+b*x)^-2, x) == :(-15//8*b^-1*csc(a+b*x)+15//8*b^-1*arctanh(sin(a+b*x))+1//4*b^-1*sec(a+b*x)^4*csc(a+b*x)+5//8*b^-1*sec(a+b*x)^2*csc(a+b*x))
@test integrate(cos(a+b*x)^7*sin(a+b*x)^-3, x) == :(-3*b^-1*log(sin(a+b*x))+-1//2*b^-1*csc(a+b*x)^2+-1//4*b^-1*sin(a+b*x)^4+3//2*b^-1*sin(a+b*x)^2)
@test integrate(cos(a+b*x)^6*sin(a+b*x)^-3, x) == :(-5//2*b^-1*cos(a+b*x)+-5//6*b^-1*cos(a+b*x)^3+5//2*b^-1*arctanh(cos(a+b*x))+-1//2*b^-1*cos(a+b*x)^3*cot(a+b*x)^2)
@test integrate(cos(a+b*x)^5*sin(a+b*x)^-3, x) == :((1/2)*b^-1*sin(a+b*x)^2+-2*b^-1*log(sin(a+b*x))+-1//2*b^-1*csc(a+b*x)^2)
@test integrate(cos(a+b*x)^4*sin(a+b*x)^-3, x) == :(-3//2*b^-1*cos(a+b*x)+3//2*b^-1*arctanh(cos(a+b*x))+-1//2*b^-1*cot(a+b*x)^2*cos(a+b*x))
@test integrate(cos(a+b*x)^3*sin(a+b*x)^-3, x) == :(-1*b^-1*log(sin(a+b*x))+-1//2*b^-1*cot(a+b*x)^2)
@test integrate(cos(a+b*x)^2*sin(a+b*x)^-3, x) == :((1/2)*b^-1*arctanh(cos(a+b*x))+-1//2*b^-1*cot(a+b*x)*csc(a+b*x))
@test integrate(sin(a+b*x)^-3*cos(a+b*x), x) == :(-1//2*b^-1*csc(a+b*x)^2)
@test integrate(sin(a+b*x)^-3*sec(a+b*x), x) == :(b^-1*log(tan(a+b*x))+-1//2*b^-1*cot(a+b*x)^2)
@test integrate(sec(a+b*x)^2*sin(a+b*x)^-3, x) == :(-3//2*b^-1*arctanh(cos(a+b*x))+3//2*b^-1*sec(a+b*x)+-1//2*b^-1*csc(a+b*x)^2*sec(a+b*x))
@test integrate(sec(a+b*x)^3*sin(a+b*x)^-3, x) == :((1/2)*b^-1*tan(a+b*x)^2+2*b^-1*log(tan(a+b*x))+-1//2*b^-1*cot(a+b*x)^2)
@test integrate(sec(a+b*x)^4*sin(a+b*x)^-3, x) == :(-5//2*b^-1*arctanh(cos(a+b*x))+5//2*b^-1*sec(a+b*x)+5//6*b^-1*sec(a+b*x)^3+-1//2*b^-1*csc(a+b*x)^2*sec(a+b*x)^3)
@test integrate(sec(a+b*x)^5*sin(a+b*x)^-3, x) == :(3*b^-1*log(tan(a+b*x))+-1//2*b^-1*cot(a+b*x)^2+1//4*b^-1*tan(a+b*x)^4+3//2*b^-1*tan(a+b*x)^2)
@test integrate(cos(a+b*x)^9*sin(a+b*x)^-4, x) == :(4*b^-1*csc(a+b*x)+6*b^-1*sin(a+b*x)+-4//3*b^-1*sin(a+b*x)^3+-1//3*b^-1*csc(a+b*x)^3+1//5*b^-1*sin(a+b*x)^5)
@test integrate(cos(a+b*x)^8*sin(a+b*x)^-4, x) == :(35//8*x+-35//24*b^-1*cot(a+b*x)^3+35//8*b^-1*cot(a+b*x)+1//4*b^-1*cos(a+b*x)^4*cot(a+b*x)^3+7//8*b^-1*cos(a+b*x)^2*cot(a+b*x)^3)
@test integrate(cos(a+b*x)^7*sin(a+b*x)^-4, x) == :(3*b^-1*csc(a+b*x)+3*b^-1*sin(a+b*x)+-1//3*b^-1*csc(a+b*x)^3+-1//3*b^-1*sin(a+b*x)^3)
@test integrate(cos(a+b*x)^6*sin(a+b*x)^-4, x) == :(5//2*x+-5//6*b^-1*cot(a+b*x)^3+5//2*b^-1*cot(a+b*x)+(1/2)*b^-1*cos(a+b*x)^2*cot(a+b*x)^3)
@test integrate(cos(a+b*x)^5*sin(a+b*x)^-4, x) == :(b^-1*sin(a+b*x)+2*b^-1*csc(a+b*x)+-1//3*b^-1*csc(a+b*x)^3)
@test integrate(cos(a+b*x)^4*sin(a+b*x)^-4, x) == :(x+b^-1*cot(a+b*x)+-1//3*b^-1*cot(a+b*x)^3)
@test integrate(cos(a+b*x)^3*sin(a+b*x)^-4, x) == :(b^-1*csc(a+b*x)+-1//3*b^-1*csc(a+b*x)^3)
@test integrate(cos(a+b*x)^2*sin(a+b*x)^-4, x) == :(-1//3*b^-1*cot(a+b*x)^3)
@test integrate(sin(a+b*x)^-4*cos(a+b*x), x) == :(-1//3*b^-1*csc(a+b*x)^3)
@test integrate(sin(a+b*x)^-4*sec(a+b*x), x) == :(b^-1*arctanh(sin(a+b*x))+-1*b^-1*csc(a+b*x)+-1//3*b^-1*csc(a+b*x)^3)
@test integrate(sec(a+b*x)^2*sin(a+b*x)^-4, x) == :(b^-1*tan(a+b*x)+-2*b^-1*cot(a+b*x)+-1//3*b^-1*cot(a+b*x)^3)
@test integrate(sec(a+b*x)^3*sin(a+b*x)^-4, x) == :(-5//2*b^-1*csc(a+b*x)+-5//6*b^-1*csc(a+b*x)^3+5//2*b^-1*arctanh(sin(a+b*x))+(1/2)*b^-1*csc(a+b*x)^3*sec(a+b*x)^2)
@test integrate(sec(a+b*x)^4*sin(a+b*x)^-4, x) == :(-3*b^-1*cot(a+b*x)+3*b^-1*tan(a+b*x)+-1//3*b^-1*cot(a+b*x)^3+1//3*b^-1*tan(a+b*x)^3)
@test integrate(sec(a+b*x)^5*sin(a+b*x)^-4, x) == :(-35//8*b^-1*csc(a+b*x)+-35//24*b^-1*csc(a+b*x)^3+35//8*b^-1*arctanh(sin(a+b*x))+1//4*b^-1*csc(a+b*x)^3*sec(a+b*x)^4+7//8*b^-1*csc(a+b*x)^3*sec(a+b*x)^2)
@test integrate(cos(a+b*x)^9*sin(a+b*x)^-5, x) == :(-2*b^-1*sin(a+b*x)^2+2*b^-1*csc(a+b*x)^2+6*b^-1*log(sin(a+b*x))+-1//4*b^-1*csc(a+b*x)^4+1//4*b^-1*sin(a+b*x)^4)
@test integrate(cos(a+b*x)^8*sin(a+b*x)^-5, x) == :(-35//8*b^-1*arctanh(cos(a+b*x))+35//8*b^-1*cos(a+b*x)+35//24*b^-1*cos(a+b*x)^3+-1//4*b^-1*cos(a+b*x)^3*cot(a+b*x)^4+7//8*b^-1*cos(a+b*x)^3*cot(a+b*x)^2)
@test integrate(cos(a+b*x)^7*sin(a+b*x)^-5, x) == :(3*b^-1*log(sin(a+b*x))+-1//2*b^-1*sin(a+b*x)^2+-1//4*b^-1*csc(a+b*x)^4+3//2*b^-1*csc(a+b*x)^2)
@test integrate(cos(a+b*x)^6*sin(a+b*x)^-5, x) == :(-15//8*b^-1*arctanh(cos(a+b*x))+15//8*b^-1*cos(a+b*x)+-1//4*b^-1*cot(a+b*x)^4*cos(a+b*x)+5//8*b^-1*cot(a+b*x)^2*cos(a+b*x))
@test integrate(cos(a+b*x)^5*sin(a+b*x)^-5, x) == :(b^-1*log(sin(a+b*x))+(1/2)*b^-1*cot(a+b*x)^2+-1//4*b^-1*cot(a+b*x)^4)
@test integrate(cos(a+b*x)^4*sin(a+b*x)^-5, x) == :(-3//8*b^-1*arctanh(cos(a+b*x))+-1//4*b^-1*cot(a+b*x)^3*csc(a+b*x)+3//8*b^-1*cot(a+b*x)*csc(a+b*x))
@test integrate(cos(a+b*x)^3*sin(a+b*x)^-5, x) == :(-1//4*b^-1*cot(a+b*x)^4)
@test integrate(cos(a+b*x)^2*sin(a+b*x)^-5, x) == :(1//8*b^-1*arctanh(cos(a+b*x))+-1//4*b^-1*csc(a+b*x)^3*cot(a+b*x)+1//8*b^-1*cot(a+b*x)*csc(a+b*x))
@test integrate(sin(a+b*x)^-5*cos(a+b*x), x) == :(-1//4*b^-1*csc(a+b*x)^4)
@test integrate(sin(a+b*x)^-5*sec(a+b*x), x) == :(b^-1*log(tan(a+b*x))+-1*b^-1*cot(a+b*x)^2+-1//4*b^-1*cot(a+b*x)^4)
@test integrate(sec(a+b*x)^2*sin(a+b*x)^-5, x) == :(-15//8*b^-1*arctanh(cos(a+b*x))+15//8*b^-1*sec(a+b*x)+-5//8*b^-1*csc(a+b*x)^2*sec(a+b*x)+-1//4*b^-1*csc(a+b*x)^4*sec(a+b*x))
@test integrate(sec(a+b*x)^3*sin(a+b*x)^-5, x) == :((1/2)*b^-1*tan(a+b*x)^2+3*b^-1*log(tan(a+b*x))+-3//2*b^-1*cot(a+b*x)^2+-1//4*b^-1*cot(a+b*x)^4)
@test integrate(sec(a+b*x)^4*sin(a+b*x)^-5, x) == :(-35//8*b^-1*arctanh(cos(a+b*x))+35//8*b^-1*sec(a+b*x)+35//24*b^-1*sec(a+b*x)^3+-7//8*b^-1*csc(a+b*x)^2*sec(a+b*x)^3+-1//4*b^-1*csc(a+b*x)^4*sec(a+b*x)^3)
@test integrate(sec(a+b*x)^5*sin(a+b*x)^-5, x) == :(-2*b^-1*cot(a+b*x)^2+2*b^-1*tan(a+b*x)^2+6*b^-1*log(tan(a+b*x))+-1//4*b^-1*cot(a+b*x)^4+1//4*b^-1*tan(a+b*x)^4)
@test integrate(cos(x)^2*sin(x)^-6, x) == :(-1//3*cot(x)^3+-1//5*cot(x)^5)
@test integrate(cos(x)^3*sin(x)^-7, x) == :(-1//6*csc(x)^6+1//4*csc(x)^4)
@test integrate((d*cos(a+b*x))^3//2*sin(a+b*x), x) == :(-2//5*b^-1*d^-1*(d*cos(a+b*x))^5//2)
@test integrate((d*cos(a+b*x))^(1/2)*sin(a+b*x), x) == :(-2//3*b^-1*d^-1*(d*cos(a+b*x))^3//2)
@test integrate((d*cos(a+b*x))^-1//2*sin(a+b*x), x) == :(-2*b^-1*d^-1*(d*cos(a+b*x))^(1/2))
@test integrate((d*cos(a+b*x))^-3//2*sin(a+b*x), x) == :(2*b^-1*d^-1*(d*cos(a+b*x))^-1//2)
@test integrate((d*cos(a+b*x))^-5//2*sin(a+b*x), x) == :(2//3*b^-1*d^-1*(d*cos(a+b*x))^-3//2)
@test integrate((d*cos(a+b*x))^-7//2*sin(a+b*x), x) == :(2//5*b^-1*d^-1*(d*cos(a+b*x))^-5//2)
@test integrate((d*cos(a+b*x))^-9//2*sin(a+b*x), x) == :(2//7*b^-1*d^-1*(d*cos(a+b*x))^-7//2)
@test integrate((d*cos(a+b*x))^9//2*sin(a+b*x)^2, x) == :(-2//13*b^-1*d^-1*(d*cos(a+b*x))^11//2*sin(a+b*x)+4//117*d*b^-1*(d*cos(a+b*x))^7//2*sin(a+b*x)+28//585*b^-1*d^3*(d*cos(a+b*x))^3//2*sin(a+b*x)+28//195*b^-1*d^4*(d*cos(a+b*x))^(1/2)*cos(a+b*x)^-1//2*Elliptic.E((1/2)*a+(1/2)*b*x,2))
@test integrate((d*cos(a+b*x))^7//2*sin(a+b*x)^2, x) == :(-2//11*b^-1*d^-1*(d*cos(a+b*x))^9//2*sin(a+b*x)+4//77*d*b^-1*(d*cos(a+b*x))^5//2*sin(a+b*x)+20//231*b^-1*d^3*(d*cos(a+b*x))^(1/2)*sin(a+b*x)+20//231*b^-1*d^4*(d*cos(a+b*x))^-1//2*cos(a+b*x)^(1/2)*Elliptic.F((1/2)*a+(1/2)*b*x,2))
@test integrate((d*cos(a+b*x))^5//2*sin(a+b*x)^2, x) == :(-2//9*b^-1*d^-1*(d*cos(a+b*x))^7//2*sin(a+b*x)+4//45*d*b^-1*(d*cos(a+b*x))^3//2*sin(a+b*x)+4//15*b^-1*d^2*(d*cos(a+b*x))^(1/2)*cos(a+b*x)^-1//2*Elliptic.E((1/2)*a+(1/2)*b*x,2))
@test integrate((d*cos(a+b*x))^3//2*sin(a+b*x)^2, x) == :(-2//7*b^-1*d^-1*(d*cos(a+b*x))^5//2*sin(a+b*x)+4//21*d*b^-1*(d*cos(a+b*x))^(1/2)*sin(a+b*x)+4//21*b^-1*d^2*(d*cos(a+b*x))^-1//2*cos(a+b*x)^(1/2)*Elliptic.F((1/2)*a+(1/2)*b*x,2))
@test integrate((d*cos(a+b*x))^(1/2)*sin(a+b*x)^2, x) == :(-2//5*b^-1*d^-1*(d*cos(a+b*x))^3//2*sin(a+b*x)+4//5*b^-1*(d*cos(a+b*x))^(1/2)*cos(a+b*x)^-1//2*Elliptic.E((1/2)*a+(1/2)*b*x,2))
@test integrate((d*cos(a+b*x))^-1//2*sin(a+b*x)^2, x) == :(-2//3*b^-1*d^-1*(d*cos(a+b*x))^(1/2)*sin(a+b*x)+4//3*b^-1*(d*cos(a+b*x))^-1//2*cos(a+b*x)^(1/2)*Elliptic.F((1/2)*a+(1/2)*b*x,2))
@test integrate((d*cos(a+b*x))^-3//2*sin(a+b*x)^2, x) == :(2*b^-1*d^-1*(d*cos(a+b*x))^-1//2*sin(a+b*x)+-4*b^-1*d^-2*(d*cos(a+b*x))^(1/2)*cos(a+b*x)^-1//2*Elliptic.E((1/2)*a+(1/2)*b*x,2))
@test integrate((d*cos(a+b*x))^-5//2*sin(a+b*x)^2, x) == :(2//3*b^-1*d^-1*(d*cos(a+b*x))^-3//2*sin(a+b*x)+-4//3*b^-1*d^-2*(d*cos(a+b*x))^-1//2*cos(a+b*x)^(1/2)*Elliptic.F((1/2)*a+(1/2)*b*x,2))
@test integrate((d*cos(a+b*x))^-7//2*sin(a+b*x)^2, x) == :(-4//5*b^-1*d^-3*(d*cos(a+b*x))^-1//2*sin(a+b*x)+2//5*b^-1*d^-1*(d*cos(a+b*x))^-5//2*sin(a+b*x)+4//5*b^-1*d^-4*(d*cos(a+b*x))^(1/2)*cos(a+b*x)^-1//2*Elliptic.E((1/2)*a+(1/2)*b*x,2))
@test integrate((d*cos(a+b*x))^-9//2*sin(a+b*x)^2, x) == :(-4//21*b^-1*d^-3*(d*cos(a+b*x))^-3//2*sin(a+b*x)+2//7*b^-1*d^-1*(d*cos(a+b*x))^-7//2*sin(a+b*x)+-4//21*b^-1*d^-4*(d*cos(a+b*x))^-1//2*cos(a+b*x)^(1/2)*Elliptic.F((1/2)*a+(1/2)*b*x,2))
@test integrate((d*cos(a+b*x))^(1/2)*sin(a+b*x)^3, x) == :(-2//3*b^-1*d^-1*(d*cos(a+b*x))^3//2+2//7*b^-1*d^-3*(d*cos(a+b*x))^7//2)
@test integrate((d*cos(a+b*x))^-1//2*sin(a+b*x)^3, x) == :(-2*b^-1*d^-1*(d*cos(a+b*x))^(1/2)+2//5*b^-1*d^-3*(d*cos(a+b*x))^5//2)
@test integrate((d*cos(a+b*x))^-3//2*sin(a+b*x)^3, x) == :(2*b^-1*d^-1*(d*cos(a+b*x))^-1//2+2//3*b^-1*d^-3*(d*cos(a+b*x))^3//2)
@test integrate((d*cos(a+b*x))^-5//2*sin(a+b*x)^3, x) == :(2*b^-1*d^-3*(d*cos(a+b*x))^(1/2)+2//3*b^-1*d^-1*(d*cos(a+b*x))^-3//2)
@test integrate((d*cos(a+b*x))^-7//2*sin(a+b*x)^3, x) == :(-2*b^-1*d^-3*(d*cos(a+b*x))^-1//2+2//5*b^-1*d^-1*(d*cos(a+b*x))^-5//2)
@test integrate((d*cos(a+b*x))^-9//2*sin(a+b*x)^3, x) == :(-2//3*b^-1*d^-3*(d*cos(a+b*x))^-3//2+2//7*b^-1*d^-1*(d*cos(a+b*x))^-7//2)
@test integrate((d*cos(a+b*x))^-11//2*sin(a+b*x)^3, x) == :(-2//5*b^-1*d^-3*(d*cos(a+b*x))^-5//2+2//9*b^-1*d^-1*(d*cos(a+b*x))^-9//2)
@test integrate((d*cos(a+b*x))^9//2*sin(a+b*x)^4, x) == :(-12//221*b^-1*d^-1*(d*cos(a+b*x))^11//2*sin(a+b*x)+-2//17*b^-1*d^-1*(d*cos(a+b*x))^11//2*sin(a+b*x)^3+8//663*d*b^-1*(d*cos(a+b*x))^7//2*sin(a+b*x)+56//3315*b^-1*d^3*(d*cos(a+b*x))^3//2*sin(a+b*x)+56//1105*b^-1*d^4*(d*cos(a+b*x))^(1/2)*cos(a+b*x)^-1//2*Elliptic.E((1/2)*a+(1/2)*b*x,2))
@test integrate((d*cos(a+b*x))^7//2*sin(a+b*x)^4, x) == :(-4//55*b^-1*d^-1*(d*cos(a+b*x))^9//2*sin(a+b*x)+-2//15*b^-1*d^-1*(d*cos(a+b*x))^9//2*sin(a+b*x)^3+8//231*b^-1*d^3*(d*cos(a+b*x))^(1/2)*sin(a+b*x)+8//385*d*b^-1*(d*cos(a+b*x))^5//2*sin(a+b*x)+8//231*b^-1*d^4*(d*cos(a+b*x))^-1//2*cos(a+b*x)^(1/2)*Elliptic.F((1/2)*a+(1/2)*b*x,2))
@test integrate((d*cos(a+b*x))^5//2*sin(a+b*x)^4, x) == :(-4//39*b^-1*d^-1*(d*cos(a+b*x))^7//2*sin(a+b*x)+-2//13*b^-1*d^-1*(d*cos(a+b*x))^7//2*sin(a+b*x)^3+8//195*d*b^-1*(d*cos(a+b*x))^3//2*sin(a+b*x)+8//65*b^-1*d^2*(d*cos(a+b*x))^(1/2)*cos(a+b*x)^-1//2*Elliptic.E((1/2)*a+(1/2)*b*x,2))
@test integrate((d*cos(a+b*x))^3//2*sin(a+b*x)^4, x) == :(-12//77*b^-1*d^-1*(d*cos(a+b*x))^5//2*sin(a+b*x)+-2//11*b^-1*d^-1*(d*cos(a+b*x))^5//2*sin(a+b*x)^3+8//77*d*b^-1*(d*cos(a+b*x))^(1/2)*sin(a+b*x)+8//77*b^-1*d^2*(d*cos(a+b*x))^-1//2*cos(a+b*x)^(1/2)*Elliptic.F((1/2)*a+(1/2)*b*x,2))
@test integrate((d*cos(a+b*x))^(1/2)*sin(a+b*x)^4, x) == :(-4//15*b^-1*d^-1*(d*cos(a+b*x))^3//2*sin(a+b*x)+-2//9*b^-1*d^-1*(d*cos(a+b*x))^3//2*sin(a+b*x)^3+8//15*b^-1*(d*cos(a+b*x))^(1/2)*cos(a+b*x)^-1//2*Elliptic.E((1/2)*a+(1/2)*b*x,2))
@test integrate((d*cos(a+b*x))^-1//2*sin(a+b*x)^4, x) == :(-4//7*b^-1*d^-1*(d*cos(a+b*x))^(1/2)*sin(a+b*x)+-2//7*b^-1*d^-1*(d*cos(a+b*x))^(1/2)*sin(a+b*x)^3+8//7*b^-1*(d*cos(a+b*x))^-1//2*cos(a+b*x)^(1/2)*Elliptic.F((1/2)*a+(1/2)*b*x,2))
@test integrate((d*cos(a+b*x))^-3//2*sin(a+b*x)^4, x) == :(2*b^-1*d^-1*(d*cos(a+b*x))^-1//2*sin(a+b*x)^3+12//5*b^-1*d^-3*(d*cos(a+b*x))^3//2*sin(a+b*x)+-24//5*b^-1*d^-2*(d*cos(a+b*x))^(1/2)*cos(a+b*x)^-1//2*Elliptic.E((1/2)*a+(1/2)*b*x,2))
@test integrate((d*cos(a+b*x))^-5//2*sin(a+b*x)^4, x) == :(2//3*b^-1*d^-1*(d*cos(a+b*x))^-3//2*sin(a+b*x)^3+4//3*b^-1*d^-3*(d*cos(a+b*x))^(1/2)*sin(a+b*x)+-8//3*b^-1*d^-2*(d*cos(a+b*x))^-1//2*cos(a+b*x)^(1/2)*Elliptic.F((1/2)*a+(1/2)*b*x,2))
@test integrate((d*cos(a+b*x))^-7//2*sin(a+b*x)^4, x) == :(-12//5*b^-1*d^-3*(d*cos(a+b*x))^-1//2*sin(a+b*x)+2//5*b^-1*d^-1*(d*cos(a+b*x))^-5//2*sin(a+b*x)^3+24//5*b^-1*d^-4*(d*cos(a+b*x))^(1/2)*cos(a+b*x)^-1//2*Elliptic.E((1/2)*a+(1/2)*b*x,2))
@test integrate((d*cos(a+b*x))^-9//2*sin(a+b*x)^4, x) == :(-4//7*b^-1*d^-3*(d*cos(a+b*x))^-3//2*sin(a+b*x)+2//7*b^-1*d^-1*(d*cos(a+b*x))^-7//2*sin(a+b*x)^3+8//7*b^-1*d^-4*(d*cos(a+b*x))^-1//2*cos(a+b*x)^(1/2)*Elliptic.F((1/2)*a+(1/2)*b*x,2))
@test integrate(cos(a+b*x)^3//2*sin(a+b*x)^5, x) == :(-2//5*b^-1*cos(a+b*x)^5//2+-2//13*b^-1*cos(a+b*x)^13//2+4//9*b^-1*cos(a+b*x)^9//2)
@test integrate((d*cos(a+b*x))^9//2*csc(a+b*x), x) == :(b^-1*d^9//2*arctan(d^-1//2*(d*cos(a+b*x))^(1/2))+-1*b^-1*d^9//2*arctanh(d^-1//2*(d*cos(a+b*x))^(1/2))+2//3*b^-1*d^3*(d*cos(a+b*x))^3//2+2//7*d*b^-1*(d*cos(a+b*x))^7//2)
@test integrate((d*cos(a+b*x))^7//2*csc(a+b*x), x) == :(-1*b^-1*d^7//2*arctan(d^-1//2*(d*cos(a+b*x))^(1/2))+-1*b^-1*d^7//2*arctanh(d^-1//2*(d*cos(a+b*x))^(1/2))+2*b^-1*d^3*(d*cos(a+b*x))^(1/2)+2//5*d*b^-1*(d*cos(a+b*x))^5//2)
@test integrate((d*cos(a+b*x))^5//2*csc(a+b*x), x) == :(b^-1*d^5//2*arctan(d^-1//2*(d*cos(a+b*x))^(1/2))+-1*b^-1*d^5//2*arctanh(d^-1//2*(d*cos(a+b*x))^(1/2))+2//3*d*b^-1*(d*cos(a+b*x))^3//2)
@test integrate((d*cos(a+b*x))^3//2*csc(a+b*x), x) == :(-1*b^-1*d^3//2*arctan(d^-1//2*(d*cos(a+b*x))^(1/2))+-1*b^-1*d^3//2*arctanh(d^-1//2*(d*cos(a+b*x))^(1/2))+2*d*b^-1*(d*cos(a+b*x))^(1/2))
@test integrate((d*cos(a+b*x))^(1/2)*csc(a+b*x), x) == :(b^-1*d^(1/2)*arctan(d^-1//2*(d*cos(a+b*x))^(1/2))+-1*b^-1*d^(1/2)*arctanh(d^-1//2*(d*cos(a+b*x))^(1/2)))
@test integrate((d*cos(a+b*x))^-1//2*csc(a+b*x), x) == :(-1*b^-1*d^-1//2*arctan(d^-1//2*(d*cos(a+b*x))^(1/2))+-1*b^-1*d^-1//2*arctanh(d^-1//2*(d*cos(a+b*x))^(1/2)))
@test integrate((d*cos(a+b*x))^-3//2*csc(a+b*x), x) == :(b^-1*d^-3//2*arctan(d^-1//2*(d*cos(a+b*x))^(1/2))+-1*b^-1*d^-3//2*arctanh(d^-1//2*(d*cos(a+b*x))^(1/2))+2*b^-1*d^-1*(d*cos(a+b*x))^-1//2)
@test integrate((d*cos(a+b*x))^-5//2*csc(a+b*x), x) == :(-1*b^-1*d^-5//2*arctan(d^-1//2*(d*cos(a+b*x))^(1/2))+-1*b^-1*d^-5//2*arctanh(d^-1//2*(d*cos(a+b*x))^(1/2))+2//3*b^-1*d^-1*(d*cos(a+b*x))^-3//2)
@test integrate((d*cos(a+b*x))^-7//2*csc(a+b*x), x) == :(b^-1*d^-7//2*arctan(d^-1//2*(d*cos(a+b*x))^(1/2))+-1*b^-1*d^-7//2*arctanh(d^-1//2*(d*cos(a+b*x))^(1/2))+2*b^-1*d^-3*(d*cos(a+b*x))^-1//2+2//5*b^-1*d^-1*(d*cos(a+b*x))^-5//2)
@test integrate((d*cos(a+b*x))^-9//2*csc(a+b*x), x) == :(-1*b^-1*d^-9//2*arctan(d^-1//2*(d*cos(a+b*x))^(1/2))+-1*b^-1*d^-9//2*arctanh(d^-1//2*(d*cos(a+b*x))^(1/2))+2//3*b^-1*d^-3*(d*cos(a+b*x))^-3//2+2//7*b^-1*d^-1*(d*cos(a+b*x))^-7//2)
@test integrate((d*cos(a+b*x))^11//2*csc(a+b*x)^2, x) == :(-1*d*b^-1*(d*cos(a+b*x))^9//2*csc(a+b*x)+-15//7*b^-1*d^5*(d*cos(a+b*x))^(1/2)*sin(a+b*x)+-9//7*b^-1*d^3*(d*cos(a+b*x))^5//2*sin(a+b*x)+-15//7*b^-1*d^6*(d*cos(a+b*x))^-1//2*cos(a+b*x)^(1/2)*Elliptic.F((1/2)*a+(1/2)*b*x,2))
@test integrate((d*cos(a+b*x))^9//2*csc(a+b*x)^2, x) == :(-1*d*b^-1*(d*cos(a+b*x))^7//2*csc(a+b*x)+-7//5*b^-1*d^3*(d*cos(a+b*x))^3//2*sin(a+b*x)+-21//5*b^-1*d^4*(d*cos(a+b*x))^(1/2)*cos(a+b*x)^-1//2*Elliptic.E((1/2)*a+(1/2)*b*x,2))
@test integrate((d*cos(a+b*x))^7//2*csc(a+b*x)^2, x) == :(-1*d*b^-1*(d*cos(a+b*x))^5//2*csc(a+b*x)+-5//3*b^-1*d^3*(d*cos(a+b*x))^(1/2)*sin(a+b*x)+-5//3*b^-1*d^4*(d*cos(a+b*x))^-1//2*cos(a+b*x)^(1/2)*Elliptic.F((1/2)*a+(1/2)*b*x,2))
@test integrate((d*cos(a+b*x))^5//2*csc(a+b*x)^2, x) == :(-1*d*b^-1*(d*cos(a+b*x))^3//2*csc(a+b*x)+-3*b^-1*d^2*(d*cos(a+b*x))^(1/2)*cos(a+b*x)^-1//2*Elliptic.E((1/2)*a+(1/2)*b*x,2))
@test integrate((d*cos(a+b*x))^3//2*csc(a+b*x)^2, x) == :(-1*d*b^-1*(d*cos(a+b*x))^(1/2)*csc(a+b*x)+-1*b^-1*d^2*(d*cos(a+b*x))^-1//2*cos(a+b*x)^(1/2)*Elliptic.F((1/2)*a+(1/2)*b*x,2))
@test integrate((d*cos(a+b*x))^(1/2)*csc(a+b*x)^2, x) == :(-1*b^-1*d^-1*(d*cos(a+b*x))^3//2*csc(a+b*x)+-1*b^-1*(d*cos(a+b*x))^(1/2)*cos(a+b*x)^-1//2*Elliptic.E((1/2)*a+(1/2)*b*x,2))
@test integrate((d*cos(a+b*x))^-1//2*csc(a+b*x)^2, x) == :(b^-1*(d*cos(a+b*x))^-1//2*cos(a+b*x)^(1/2)*Elliptic.F((1/2)*a+(1/2)*b*x,2)+-1*b^-1*d^-1*(d*cos(a+b*x))^(1/2)*csc(a+b*x))
@test integrate((d*cos(a+b*x))^-3//2*csc(a+b*x)^2, x) == :(-1*b^-1*d^-1*(d*cos(a+b*x))^-1//2*csc(a+b*x)+3*b^-1*d^-1*(d*cos(a+b*x))^-1//2*sin(a+b*x)+-3*b^-1*d^-2*(d*cos(a+b*x))^(1/2)*cos(a+b*x)^-1//2*Elliptic.E((1/2)*a+(1/2)*b*x,2))
@test integrate((d*cos(a+b*x))^-5//2*csc(a+b*x)^2, x) == :(-1*b^-1*d^-1*(d*cos(a+b*x))^-3//2*csc(a+b*x)+5//3*b^-1*d^-1*(d*cos(a+b*x))^-3//2*sin(a+b*x)+5//3*b^-1*d^-2*(d*cos(a+b*x))^-1//2*cos(a+b*x)^(1/2)*Elliptic.F((1/2)*a+(1/2)*b*x,2))
@test integrate((d*cos(a+b*x))^-7//2*csc(a+b*x)^2, x) == :(-1*b^-1*d^-1*(d*cos(a+b*x))^-5//2*csc(a+b*x)+7//5*b^-1*d^-1*(d*cos(a+b*x))^-5//2*sin(a+b*x)+21//5*b^-1*d^-3*(d*cos(a+b*x))^-1//2*sin(a+b*x)+-21//5*b^-1*d^-4*(d*cos(a+b*x))^(1/2)*cos(a+b*x)^-1//2*Elliptic.E((1/2)*a+(1/2)*b*x,2))
@test integrate((d*cos(a+b*x))^11//2*csc(a+b*x)^3, x) == :(-9//2*b^-1*d^5*(d*cos(a+b*x))^(1/2)+-9//10*b^-1*d^3*(d*cos(a+b*x))^5//2+9//4*b^-1*d^11//2*arctan(d^-1//2*(d*cos(a+b*x))^(1/2))+9//4*b^-1*d^11//2*arctanh(d^-1//2*(d*cos(a+b*x))^(1/2))+-1//2*d*b^-1*(d*cos(a+b*x))^9//2*csc(a+b*x)^2)
@test integrate((d*cos(a+b*x))^9//2*csc(a+b*x)^3, x) == :(-7//4*b^-1*d^9//2*arctan(d^-1//2*(d*cos(a+b*x))^(1/2))+-7//6*b^-1*d^3*(d*cos(a+b*x))^3//2+7//4*b^-1*d^9//2*arctanh(d^-1//2*(d*cos(a+b*x))^(1/2))+-1//2*d*b^-1*(d*cos(a+b*x))^7//2*csc(a+b*x)^2)
@test integrate((d*cos(a+b*x))^7//2*csc(a+b*x)^3, x) == :(-5//2*b^-1*d^3*(d*cos(a+b*x))^(1/2)+5//4*b^-1*d^7//2*arctan(d^-1//2*(d*cos(a+b*x))^(1/2))+5//4*b^-1*d^7//2*arctanh(d^-1//2*(d*cos(a+b*x))^(1/2))+-1//2*d*b^-1*(d*cos(a+b*x))^5//2*csc(a+b*x)^2)
@test integrate((d*cos(a+b*x))^5//2*csc(a+b*x)^3, x) == :(-3//4*b^-1*d^5//2*arctan(d^-1//2*(d*cos(a+b*x))^(1/2))+3//4*b^-1*d^5//2*arctanh(d^-1//2*(d*cos(a+b*x))^(1/2))+-1//2*d*b^-1*(d*cos(a+b*x))^3//2*csc(a+b*x)^2)
@test integrate((d*cos(a+b*x))^3//2*csc(a+b*x)^3, x) == :(1//4*b^-1*d^3//2*arctan(d^-1//2*(d*cos(a+b*x))^(1/2))+1//4*b^-1*d^3//2*arctanh(d^-1//2*(d*cos(a+b*x))^(1/2))+-1//2*d*b^-1*(d*cos(a+b*x))^(1/2)*csc(a+b*x)^2)
@test integrate((d*cos(a+b*x))^(1/2)*csc(a+b*x)^3, x) == :(-1//4*b^-1*d^(1/2)*arctanh(d^-1//2*(d*cos(a+b*x))^(1/2))+1//4*b^-1*d^(1/2)*arctan(d^-1//2*(d*cos(a+b*x))^(1/2))+-1//2*b^-1*d^-1*(d*cos(a+b*x))^3//2*csc(a+b*x)^2)
@test integrate((d*cos(a+b*x))^-1//2*csc(a+b*x)^3, x) == :(-3//4*b^-1*d^-1//2*arctan(d^-1//2*(d*cos(a+b*x))^(1/2))+-3//4*b^-1*d^-1//2*arctanh(d^-1//2*(d*cos(a+b*x))^(1/2))+-1//2*b^-1*d^-1*(d*cos(a+b*x))^(1/2)*csc(a+b*x)^2)
@test integrate((d*cos(a+b*x))^-3//2*csc(a+b*x)^3, x) == :(-5//4*b^-1*d^-3//2*arctanh(d^-1//2*(d*cos(a+b*x))^(1/2))+5//2*b^-1*d^-1*(d*cos(a+b*x))^-1//2+5//4*b^-1*d^-3//2*arctan(d^-1//2*(d*cos(a+b*x))^(1/2))+-1//2*b^-1*d^-1*(d*cos(a+b*x))^-1//2*csc(a+b*x)^2)
@test integrate((d*cos(a+b*x))^-5//2*csc(a+b*x)^3, x) == :(-7//4*b^-1*d^-5//2*arctan(d^-1//2*(d*cos(a+b*x))^(1/2))+-7//4*b^-1*d^-5//2*arctanh(d^-1//2*(d*cos(a+b*x))^(1/2))+7//6*b^-1*d^-1*(d*cos(a+b*x))^-3//2+-1//2*b^-1*d^-1*(d*cos(a+b*x))^-3//2*csc(a+b*x)^2)
@test integrate((d*cos(a+b*x))^-7//2*csc(a+b*x)^3, x) == :(-9//4*b^-1*d^-7//2*arctanh(d^-1//2*(d*cos(a+b*x))^(1/2))+9//2*b^-1*d^-3*(d*cos(a+b*x))^-1//2+9//4*b^-1*d^-7//2*arctan(d^-1//2*(d*cos(a+b*x))^(1/2))+9//10*b^-1*d^-1*(d*cos(a+b*x))^-5//2+-1//2*b^-1*d^-1*(d*cos(a+b*x))^-5//2*csc(a+b*x)^2)
@test integrate((d*cos(a+b*x))^1//5*sin(a+b*x), x) == :(-5//6*b^-1*d^-1*(d*cos(a+b*x))^6//5)
@test integrate(cos(x)^3*sin(x)^(1/2), x) == :(-2//7*sin(x)^7//2+2//3*sin(x)^3//2)
@test integrate(cos(x)^3*sin(x)^3//2, x) == :(-2//9*sin(x)^9//2+2//5*sin(x)^5//2)
@test integrate(cos(x)^3*sin(x)^5//2, x) == :(-2//11*sin(x)^11//2+2//7*sin(x)^7//2)
@test integrate(cos(x)^3*sin(x)^-1//2, x) == :(2*sin(x)^(1/2)+-2//5*sin(x)^5//2)
@test integrate((c*sin(a+b*x))^(1/2)*(d*cos(a+b*x))^9//2, x) == :(1//5*d*b^-1*c^-1*(c*sin(a+b*x))^3//2*(d*cos(a+b*x))^7//2+7//30*b^-1*c^-1*d^3*(c*sin(a+b*x))^3//2*(d*cos(a+b*x))^3//2+7//20*b^-1*d^4*(c*sin(a+b*x))^(1/2)*(d*cos(a+b*x))^(1/2)*sin(2a+2*b*x)^-1//2*Elliptic.E(a+-1//4*pi+b*x,2))
@test integrate((c*sin(a+b*x))^(1/2)*(d*cos(a+b*x))^5//2, x) == :(1//3*d*b^-1*c^-1*(c*sin(a+b*x))^3//2*(d*cos(a+b*x))^3//2+(1/2)*b^-1*d^2*(c*sin(a+b*x))^(1/2)*(d*cos(a+b*x))^(1/2)*sin(2a+2*b*x)^-1//2*Elliptic.E(a+-1//4*pi+b*x,2))
@test integrate((c*sin(a+b*x))^(1/2)*(d*cos(a+b*x))^(1/2), x) == :(b^-1*(c*sin(a+b*x))^(1/2)*(d*cos(a+b*x))^(1/2)*sin(2a+2*b*x)^-1//2*Elliptic.E(a+-1//4*pi+b*x,2))
@test integrate((c*sin(a+b*x))^(1/2)*(d*cos(a+b*x))^-3//2, x) == :(2*b^-1*c^-1*d^-1*(c*sin(a+b*x))^3//2*(d*cos(a+b*x))^-1//2+-2*b^-1*d^-2*(c*sin(a+b*x))^(1/2)*(d*cos(a+b*x))^(1/2)*sin(2a+2*b*x)^-1//2*Elliptic.E(a+-1//4*pi+b*x,2))
@test integrate((c*sin(a+b*x))^(1/2)*(d*cos(a+b*x))^-7//2, x) == :(2//5*b^-1*c^-1*d^-1*(c*sin(a+b*x))^3//2*(d*cos(a+b*x))^-5//2+4//5*b^-1*c^-1*d^-3*(c*sin(a+b*x))^3//2*(d*cos(a+b*x))^-1//2+-4//5*b^-1*d^-4*(c*sin(a+b*x))^(1/2)*(d*cos(a+b*x))^(1/2)*sin(2a+2*b*x)^-1//2*Elliptic.E(a+-1//4*pi+b*x,2))
@test integrate((c*sin(a+b*x))^(1/2)*(d*cos(a+b*x))^3//2, x) == :((1/2)*d*b^-1*c^-1*(c*sin(a+b*x))^3//2*(d*cos(a+b*x))^(1/2)+-1//8*2^(1/2)*b^-1*c^(1/2)*d^3//2*arctan(1+-1*2^(1/2)*c^-1//2*d^(1/2)*(c*sin(a+b*x))^(1/2)*(d*cos(a+b*x))^-1//2)+-1//16*2^(1/2)*b^-1*c^(1/2)*d^3//2*log(c^(1/2)+c^(1/2)*tan(a+b*x)+2^(1/2)*d^(1/2)*(c*sin(a+b*x))^(1/2)*(d*cos(a+b*x))^-1//2)+1//8*2^(1/2)*b^-1*c^(1/2)*d^3//2*arctan(1+2^(1/2)*c^-1//2*d^(1/2)*(c*sin(a+b*x))^(1/2)*(d*cos(a+b*x))^-1//2)+1//16*2^(1/2)*b^-1*c^(1/2)*d^3//2*log(c^(1/2)+c^(1/2)*tan(a+b*x)+-1*2^(1/2)*d^(1/2)*(c*sin(a+b*x))^(1/2)*(d*cos(a+b*x))^-1//2))
@test integrate((c*sin(a+b*x))^(1/2)*(d*cos(a+b*x))^-1//2, x) == :((1/2)*2^(1/2)*b^-1*c^(1/2)*d^-1//2*arctan(1+2^(1/2)*c^-1//2*d^(1/2)*(c*sin(a+b*x))^(1/2)*(d*cos(a+b*x))^-1//2)+-1//2*2^(1/2)*b^-1*c^(1/2)*d^-1//2*arctan(1+-1*2^(1/2)*c^-1//2*d^(1/2)*(c*sin(a+b*x))^(1/2)*(d*cos(a+b*x))^-1//2)+-1//4*2^(1/2)*b^-1*c^(1/2)*d^-1//2*log(c^(1/2)+c^(1/2)*tan(a+b*x)+2^(1/2)*d^(1/2)*(c*sin(a+b*x))^(1/2)*(d*cos(a+b*x))^-1//2)+1//4*2^(1/2)*b^-1*c^(1/2)*d^-1//2*log(c^(1/2)+c^(1/2)*tan(a+b*x)+-1*2^(1/2)*d^(1/2)*(c*sin(a+b*x))^(1/2)*(d*cos(a+b*x))^-1//2))
@test integrate((c*sin(a+b*x))^(1/2)*(d*cos(a+b*x))^-5//2, x) == :(2//3*b^-1*c^-1*d^-1*(c*sin(a+b*x))^3//2*(d*cos(a+b*x))^-3//2)
@test integrate((c*sin(a+b*x))^(1/2)*(d*cos(a+b*x))^-9//2, x) == :(2//7*b^-1*c^-1*d^-1*(c*sin(a+b*x))^3//2*(d*cos(a+b*x))^-7//2+8//21*b^-1*c^-1*d^-3*(c*sin(a+b*x))^3//2*(d*cos(a+b*x))^-3//2)
@test integrate((c*sin(a+b*x))^(1/2)*(d*cos(a+b*x))^-13//2, x) == :(2//11*b^-1*c^-1*d^-1*(c*sin(a+b*x))^3//2*(d*cos(a+b*x))^-11//2+16//77*b^-1*c^-1*d^-3*(c*sin(a+b*x))^3//2*(d*cos(a+b*x))^-7//2+64//231*b^-1*c^-1*d^-5*(c*sin(a+b*x))^3//2*(d*cos(a+b*x))^-3//2)
@test integrate((c*sin(a+b*x))^3//2*(d*cos(a+b*x))^3//2, x) == :(-1//3*c*b^-1*d^-1*(c*sin(a+b*x))^(1/2)*(d*cos(a+b*x))^5//2+1//6*c*d*b^-1*(c*sin(a+b*x))^(1/2)*(d*cos(a+b*x))^(1/2)+1//12*b^-1*c^2*d^2*(c*sin(a+b*x))^-1//2*(d*cos(a+b*x))^-1//2*sin(2a+2*b*x)^(1/2)*Elliptic.F(a+-1//4*pi+b*x,2))
@test integrate((c*sin(a+b*x))^3//2*(d*cos(a+b*x))^-1//2, x) == :(-1*c*b^-1*d^-1*(c*sin(a+b*x))^(1/2)*(d*cos(a+b*x))^(1/2)+(1/2)*b^-1*c^2*(c*sin(a+b*x))^-1//2*(d*cos(a+b*x))^-1//2*sin(2a+2*b*x)^(1/2)*Elliptic.F(a+-1//4*pi+b*x,2))
@test integrate((c*sin(a+b*x))^3//2*(d*cos(a+b*x))^-5//2, x) == :(2//3*c*b^-1*d^-1*(c*sin(a+b*x))^(1/2)*(d*cos(a+b*x))^-3//2+-1//3*b^-1*c^2*d^-2*(c*sin(a+b*x))^-1//2*(d*cos(a+b*x))^-1//2*sin(2a+2*b*x)^(1/2)*Elliptic.F(a+-1//4*pi+b*x,2))
@test integrate((c*sin(a+b*x))^3//2*(d*cos(a+b*x))^-9//2, x) == :(-2//21*c*b^-1*d^-3*(c*sin(a+b*x))^(1/2)*(d*cos(a+b*x))^-3//2+2//7*c*b^-1*d^-1*(c*sin(a+b*x))^(1/2)*(d*cos(a+b*x))^-7//2+-2//21*b^-1*c^2*d^-4*(c*sin(a+b*x))^-1//2*(d*cos(a+b*x))^-1//2*sin(2a+2*b*x)^(1/2)*Elliptic.F(a+-1//4*pi+b*x,2))
@test integrate((c*sin(a+b*x))^3//2*(d*cos(a+b*x))^(1/2), x) == :(-1//2*c*b^-1*d^-1*(c*sin(a+b*x))^(1/2)*(d*cos(a+b*x))^3//2+-1//8*2^(1/2)*b^-1*c^3//2*d^(1/2)*arctan(1+2^(1/2)*c^(1/2)*d^-1//2*(c*sin(a+b*x))^-1//2*(d*cos(a+b*x))^(1/2))+-1//16*2^(1/2)*b^-1*c^3//2*d^(1/2)*log(d^(1/2)+d^(1/2)*cot(a+b*x)+-1*2^(1/2)*c^(1/2)*(c*sin(a+b*x))^-1//2*(d*cos(a+b*x))^(1/2))+1//8*2^(1/2)*b^-1*c^3//2*d^(1/2)*arctan(1+-1*2^(1/2)*c^(1/2)*d^-1//2*(c*sin(a+b*x))^-1//2*(d*cos(a+b*x))^(1/2))+1//16*2^(1/2)*b^-1*c^3//2*d^(1/2)*log(d^(1/2)+d^(1/2)*cot(a+b*x)+2^(1/2)*c^(1/2)*(c*sin(a+b*x))^-1//2*(d*cos(a+b*x))^(1/2)))
@test integrate((c*sin(a+b*x))^3//2*(d*cos(a+b*x))^-3//2, x) == :((1/2)*2^(1/2)*b^-1*c^3//2*d^-3//2*arctan(1+2^(1/2)*c^(1/2)*d^-1//2*(c*sin(a+b*x))^-1//2*(d*cos(a+b*x))^(1/2))+2*c*b^-1*d^-1*(c*sin(a+b*x))^(1/2)*(d*cos(a+b*x))^-1//2+-1//2*2^(1/2)*b^-1*c^3//2*d^-3//2*arctan(1+-1*2^(1/2)*c^(1/2)*d^-1//2*(c*sin(a+b*x))^-1//2*(d*cos(a+b*x))^(1/2))+-1//4*2^(1/2)*b^-1*c^3//2*d^-3//2*log(d^(1/2)+d^(1/2)*cot(a+b*x)+2^(1/2)*c^(1/2)*(c*sin(a+b*x))^-1//2*(d*cos(a+b*x))^(1/2))+1//4*2^(1/2)*b^-1*c^3//2*d^-3//2*log(d^(1/2)+d^(1/2)*cot(a+b*x)+-1*2^(1/2)*c^(1/2)*(c*sin(a+b*x))^-1//2*(d*cos(a+b*x))^(1/2)))
@test integrate((c*sin(a+b*x))^3//2*(d*cos(a+b*x))^-7//2, x) == :(2//5*b^-1*c^-1*d^-1*(c*sin(a+b*x))^5//2*(d*cos(a+b*x))^-5//2)
@test integrate((c*sin(a+b*x))^3//2*(d*cos(a+b*x))^-11//2, x) == :(-8//45*c*b^-1*d^-5*(c*sin(a+b*x))^(1/2)*(d*cos(a+b*x))^-1//2+-2//45*c*b^-1*d^-3*(c*sin(a+b*x))^(1/2)*(d*cos(a+b*x))^-5//2+2//9*c*b^-1*d^-1*(c*sin(a+b*x))^(1/2)*(d*cos(a+b*x))^-9//2)
@test integrate((c*sin(a+b*x))^3//2*(d*cos(a+b*x))^-15//2, x) == :(-64//585*c*b^-1*d^-7*(c*sin(a+b*x))^(1/2)*(d*cos(a+b*x))^-1//2+-16//585*c*b^-1*d^-5*(c*sin(a+b*x))^(1/2)*(d*cos(a+b*x))^-5//2+-2//117*c*b^-1*d^-3*(c*sin(a+b*x))^(1/2)*(d*cos(a+b*x))^-9//2+2//13*c*b^-1*d^-1*(c*sin(a+b*x))^(1/2)*(d*cos(a+b*x))^-13//2)
@test integrate((c*sin(a+b*x))^5//2*(d*cos(a+b*x))^9//2, x) == :(-1//7*c*b^-1*d^-1*(c*sin(a+b*x))^3//2*(d*cos(a+b*x))^11//2+1//20*c*b^-1*d^3*(c*sin(a+b*x))^3//2*(d*cos(a+b*x))^3//2+3//70*c*d*b^-1*(c*sin(a+b*x))^3//2*(d*cos(a+b*x))^7//2+3//40*b^-1*c^2*d^4*(c*sin(a+b*x))^(1/2)*(d*cos(a+b*x))^(1/2)*sin(2a+2*b*x)^-1//2*Elliptic.E(a+-1//4*pi+b*x,2))
@test integrate((c*sin(a+b*x))^5//2*(d*cos(a+b*x))^5//2, x) == :(-1//5*c*b^-1*d^-1*(c*sin(a+b*x))^3//2*(d*cos(a+b*x))^7//2+1//10*c*d*b^-1*(c*sin(a+b*x))^3//2*(d*cos(a+b*x))^3//2+3//20*b^-1*c^2*d^2*(c*sin(a+b*x))^(1/2)*(d*cos(a+b*x))^(1/2)*sin(2a+2*b*x)^-1//2*Elliptic.E(a+-1//4*pi+b*x,2))
@test integrate((c*sin(a+b*x))^5//2*(d*cos(a+b*x))^(1/2), x) == :(-1//3*c*b^-1*d^-1*(c*sin(a+b*x))^3//2*(d*cos(a+b*x))^3//2+(1/2)*b^-1*c^2*(c*sin(a+b*x))^(1/2)*(d*cos(a+b*x))^(1/2)*sin(2a+2*b*x)^-1//2*Elliptic.E(a+-1//4*pi+b*x,2))
@test integrate((c*sin(a+b*x))^5//2*(d*cos(a+b*x))^-3//2, x) == :(2*c*b^-1*d^-1*(c*sin(a+b*x))^3//2*(d*cos(a+b*x))^-1//2+-3*b^-1*c^2*d^-2*(c*sin(a+b*x))^(1/2)*(d*cos(a+b*x))^(1/2)*sin(2a+2*b*x)^-1//2*Elliptic.E(a+-1//4*pi+b*x,2))
@test integrate((c*sin(a+b*x))^5//2*(d*cos(a+b*x))^-7//2, x) == :(-6//5*c*b^-1*d^-3*(c*sin(a+b*x))^3//2*(d*cos(a+b*x))^-1//2+2//5*c*b^-1*d^-1*(c*sin(a+b*x))^3//2*(d*cos(a+b*x))^-5//2+6//5*b^-1*c^2*d^-4*(c*sin(a+b*x))^(1/2)*(d*cos(a+b*x))^(1/2)*sin(2a+2*b*x)^-1//2*Elliptic.E(a+-1//4*pi+b*x,2))
@test integrate((c*sin(a+b*x))^5//2*(d*cos(a+b*x))^-11//2, x) == :(-4//15*c*b^-1*d^-5*(c*sin(a+b*x))^3//2*(d*cos(a+b*x))^-1//2+-2//15*c*b^-1*d^-3*(c*sin(a+b*x))^3//2*(d*cos(a+b*x))^-5//2+2//9*c*b^-1*d^-1*(c*sin(a+b*x))^3//2*(d*cos(a+b*x))^-9//2+4//15*b^-1*c^2*d^-6*(c*sin(a+b*x))^(1/2)*(d*cos(a+b*x))^(1/2)*sin(2a+2*b*x)^-1//2*Elliptic.E(a+-1//4*pi+b*x,2))
@test integrate((c*sin(a+b*x))^5//2*(d*cos(a+b*x))^-1//2, x) == :(-3//8*2^(1/2)*b^-1*c^5//2*d^-1//2*arctan(1+-1*2^(1/2)*c^-1//2*d^(1/2)*(c*sin(a+b*x))^(1/2)*(d*cos(a+b*x))^-1//2)+-3//16*2^(1/2)*b^-1*c^5//2*d^-1//2*log(c^(1/2)+c^(1/2)*tan(a+b*x)+2^(1/2)*d^(1/2)*(c*sin(a+b*x))^(1/2)*(d*cos(a+b*x))^-1//2)+-1//2*c*b^-1*d^-1*(c*sin(a+b*x))^3//2*(d*cos(a+b*x))^(1/2)+3//8*2^(1/2)*b^-1*c^5//2*d^-1//2*arctan(1+2^(1/2)*c^-1//2*d^(1/2)*(c*sin(a+b*x))^(1/2)*(d*cos(a+b*x))^-1//2)+3//16*2^(1/2)*b^-1*c^5//2*d^-1//2*log(c^(1/2)+c^(1/2)*tan(a+b*x)+-1*2^(1/2)*d^(1/2)*(c*sin(a+b*x))^(1/2)*(d*cos(a+b*x))^-1//2))
@test integrate((c*sin(a+b*x))^5//2*(d*cos(a+b*x))^-5//2, x) == :((1/2)*2^(1/2)*b^-1*c^5//2*d^-5//2*arctan(1+-1*2^(1/2)*c^-1//2*d^(1/2)*(c*sin(a+b*x))^(1/2)*(d*cos(a+b*x))^-1//2)+-1//2*2^(1/2)*b^-1*c^5//2*d^-5//2*arctan(1+2^(1/2)*c^-1//2*d^(1/2)*(c*sin(a+b*x))^(1/2)*(d*cos(a+b*x))^-1//2)+-1//4*2^(1/2)*b^-1*c^5//2*d^-5//2*log(c^(1/2)+c^(1/2)*tan(a+b*x)+-1*2^(1/2)*d^(1/2)*(c*sin(a+b*x))^(1/2)*(d*cos(a+b*x))^-1//2)+1//4*2^(1/2)*b^-1*c^5//2*d^-5//2*log(c^(1/2)+c^(1/2)*tan(a+b*x)+2^(1/2)*d^(1/2)*(c*sin(a+b*x))^(1/2)*(d*cos(a+b*x))^-1//2)+2//3*c*b^-1*d^-1*(c*sin(a+b*x))^3//2*(d*cos(a+b*x))^-3//2)
@test integrate((c*sin(a+b*x))^5//2*(d*cos(a+b*x))^-9//2, x) == :(2//7*b^-1*c^-1*d^-1*(c*sin(a+b*x))^7//2*(d*cos(a+b*x))^-7//2)
@test integrate((c*sin(a+b*x))^5//2*(d*cos(a+b*x))^-13//2, x) == :(-8//77*c*b^-1*d^-5*(c*sin(a+b*x))^3//2*(d*cos(a+b*x))^-3//2+-6//77*c*b^-1*d^-3*(c*sin(a+b*x))^3//2*(d*cos(a+b*x))^-7//2+2//11*c*b^-1*d^-1*(c*sin(a+b*x))^3//2*(d*cos(a+b*x))^-11//2)
@test integrate((c*sin(a+b*x))^5//2*(d*cos(a+b*x))^-17//2, x) == :(-64//1155*c*b^-1*d^-7*(c*sin(a+b*x))^3//2*(d*cos(a+b*x))^-3//2+-16//385*c*b^-1*d^-5*(c*sin(a+b*x))^3//2*(d*cos(a+b*x))^-7//2+-2//55*c*b^-1*d^-3*(c*sin(a+b*x))^3//2*(d*cos(a+b*x))^-11//2+2//15*c*b^-1*d^-1*(c*sin(a+b*x))^3//2*(d*cos(a+b*x))^-15//2)
@test integrate(cos(a+b*x)^-7//2*sin(a+b*x)^7//2, x) == :((1/2)*2^(1/2)*b^-1*arctan(1+-1*2^(1/2)*cos(a+b*x)^(1/2)*sin(a+b*x)^-1//2)+-2*b^-1*cos(a+b*x)^-1//2*sin(a+b*x)^(1/2)+-1//2*2^(1/2)*b^-1*arctan(1+2^(1/2)*cos(a+b*x)^(1/2)*sin(a+b*x)^-1//2)+-1//4*2^(1/2)*b^-1*log(1+-1*2^(1/2)*cos(a+b*x)^(1/2)*sin(a+b*x)^-1//2+cot(a+b*x))+1//4*2^(1/2)*b^-1*log(1+2^(1/2)*cos(a+b*x)^(1/2)*sin(a+b*x)^-1//2+cot(a+b*x))+2//5*b^-1*cos(a+b*x)^-5//2*sin(a+b*x)^5//2)
@test integrate(cos(x)^-7//2*sin(x)^3//2, x) == :(2//5*cos(x)^-5//2*sin(x)^5//2)
@test integrate(cos(x)^-1//2*sin(x)^(1/2), x) == :((1/2)*2^(1/2)*arctan(1+2^(1/2)*cos(x)^-1//2*sin(x)^(1/2))+-1//2*2^(1/2)*arctan(1+-1*2^(1/2)*cos(x)^-1//2*sin(x)^(1/2))+-1//4*2^(1/2)*log(1+2^(1/2)*cos(x)^-1//2*sin(x)^(1/2)+tan(x))+1//4*2^(1/2)*log(1+-1*2^(1/2)*cos(x)^-1//2*sin(x)^(1/2)+tan(x)))
@test integrate(cos(x)^-1//2*sin(x)^5//2, x) == :(-3//8*2^(1/2)*arctan(1+-1*2^(1/2)*cos(x)^-1//2*sin(x)^(1/2))+-3//16*2^(1/2)*log(1+2^(1/2)*cos(x)^-1//2*sin(x)^(1/2)+tan(x))+-1//2*cos(x)^(1/2)*sin(x)^3//2+3//8*2^(1/2)*arctan(1+2^(1/2)*cos(x)^-1//2*sin(x)^(1/2))+3//16*2^(1/2)*log(1+-1*2^(1/2)*cos(x)^-1//2*sin(x)^(1/2)+tan(x)))
@test integrate((c*sin(a+b*x))^-1//2*(d*cos(a+b*x))^7//2, x) == :(1//3*d*b^-1*c^-1*(c*sin(a+b*x))^(1/2)*(d*cos(a+b*x))^5//2+5//6*b^-1*c^-1*d^3*(c*sin(a+b*x))^(1/2)*(d*cos(a+b*x))^(1/2)+5//12*b^-1*d^4*(c*sin(a+b*x))^-1//2*(d*cos(a+b*x))^-1//2*sin(2a+2*b*x)^(1/2)*Elliptic.F(a+-1//4*pi+b*x,2))
@test integrate((c*sin(a+b*x))^-1//2*(d*cos(a+b*x))^3//2, x) == :(d*b^-1*c^-1*(c*sin(a+b*x))^(1/2)*(d*cos(a+b*x))^(1/2)+(1/2)*b^-1*d^2*(c*sin(a+b*x))^-1//2*(d*cos(a+b*x))^-1//2*sin(2a+2*b*x)^(1/2)*Elliptic.F(a+-1//4*pi+b*x,2))
@test integrate((c*sin(a+b*x))^-1//2*(d*cos(a+b*x))^-1//2, x) == :(b^-1*(c*sin(a+b*x))^-1//2*(d*cos(a+b*x))^-1//2*sin(2a+2*b*x)^(1/2)*Elliptic.F(a+-1//4*pi+b*x,2))
@test integrate((c*sin(a+b*x))^-1//2*(d*cos(a+b*x))^-5//2, x) == :(2//3*b^-1*c^-1*d^-1*(c*sin(a+b*x))^(1/2)*(d*cos(a+b*x))^-3//2+2//3*b^-1*d^-2*(c*sin(a+b*x))^-1//2*(d*cos(a+b*x))^-1//2*sin(2a+2*b*x)^(1/2)*Elliptic.F(a+-1//4*pi+b*x,2))
@test integrate((c*sin(a+b*x))^-1//2*(d*cos(a+b*x))^-9//2, x) == :(2//7*b^-1*c^-1*d^-1*(c*sin(a+b*x))^(1/2)*(d*cos(a+b*x))^-7//2+4//7*b^-1*c^-1*d^-3*(c*sin(a+b*x))^(1/2)*(d*cos(a+b*x))^-3//2+4//7*b^-1*d^-4*(c*sin(a+b*x))^-1//2*(d*cos(a+b*x))^-1//2*sin(2a+2*b*x)^(1/2)*Elliptic.F(a+-1//4*pi+b*x,2))
@test integrate((c*sin(a+b*x))^-1//2*(d*cos(a+b*x))^(1/2), x) == :((1/2)*2^(1/2)*b^-1*c^-1//2*d^(1/2)*arctan(1+-1*2^(1/2)*c^(1/2)*d^-1//2*(c*sin(a+b*x))^-1//2*(d*cos(a+b*x))^(1/2))+-1//2*2^(1/2)*b^-1*c^-1//2*d^(1/2)*arctan(1+2^(1/2)*c^(1/2)*d^-1//2*(c*sin(a+b*x))^-1//2*(d*cos(a+b*x))^(1/2))+-1//4*2^(1/2)*b^-1*c^-1//2*d^(1/2)*log(d^(1/2)+d^(1/2)*cot(a+b*x)+-1*2^(1/2)*c^(1/2)*(c*sin(a+b*x))^-1//2*(d*cos(a+b*x))^(1/2))+1//4*2^(1/2)*b^-1*c^-1//2*d^(1/2)*log(d^(1/2)+d^(1/2)*cot(a+b*x)+2^(1/2)*c^(1/2)*(c*sin(a+b*x))^-1//2*(d*cos(a+b*x))^(1/2)))
@test integrate((c*sin(a+b*x))^-1//2*(d*cos(a+b*x))^-3//2, x) == :(2*b^-1*c^-1*d^-1*(c*sin(a+b*x))^(1/2)*(d*cos(a+b*x))^-1//2)
@test integrate((c*sin(a+b*x))^-1//2*(d*cos(a+b*x))^-7//2, x) == :(2//5*b^-1*c^-1*d^-1*(c*sin(a+b*x))^(1/2)*(d*cos(a+b*x))^-5//2+8//5*b^-1*c^-1*d^-3*(c*sin(a+b*x))^(1/2)*(d*cos(a+b*x))^-1//2)
@test integrate((c*sin(a+b*x))^-1//2*(d*cos(a+b*x))^-11//2, x) == :(2//9*b^-1*c^-1*d^-1*(c*sin(a+b*x))^(1/2)*(d*cos(a+b*x))^-9//2+16//45*b^-1*c^-1*d^-3*(c*sin(a+b*x))^(1/2)*(d*cos(a+b*x))^-5//2+64//45*b^-1*c^-1*d^-5*(c*sin(a+b*x))^(1/2)*(d*cos(a+b*x))^-1//2)
@test integrate(cos(a+b*x)^(1/2)*sin(a+b*x)^-1//2, x) == :((1/2)*2^(1/2)*b^-1*arctan(1+-1*2^(1/2)*cos(a+b*x)^(1/2)*sin(a+b*x)^-1//2)+-1//2*2^(1/2)*b^-1*arctan(1+2^(1/2)*cos(a+b*x)^(1/2)*sin(a+b*x)^-1//2)+-1//4*2^(1/2)*b^-1*log(1+-1*2^(1/2)*cos(a+b*x)^(1/2)*sin(a+b*x)^-1//2+cot(a+b*x))+1//4*2^(1/2)*b^-1*log(1+2^(1/2)*cos(a+b*x)^(1/2)*sin(a+b*x)^-1//2+cot(a+b*x)))
@test integrate(cos(a+b*x)^3//2*sin(a+b*x)^-3//2, x) == :((1/2)*2^(1/2)*b^-1*arctan(1+-1*2^(1/2)*cos(a+b*x)^-1//2*sin(a+b*x)^(1/2))+-2*b^-1*cos(a+b*x)^(1/2)*sin(a+b*x)^-1//2+-1//2*2^(1/2)*b^-1*arctan(1+2^(1/2)*cos(a+b*x)^-1//2*sin(a+b*x)^(1/2))+-1//4*2^(1/2)*b^-1*log(1+-1*2^(1/2)*cos(a+b*x)^-1//2*sin(a+b*x)^(1/2)+tan(a+b*x))+1//4*2^(1/2)*b^-1*log(1+2^(1/2)*cos(a+b*x)^-1//2*sin(a+b*x)^(1/2)+tan(a+b*x)))
@test integrate(cos(a+b*x)^5//2*sin(a+b*x)^-5//2, x) == :((1/2)*2^(1/2)*b^-1*arctan(1+2^(1/2)*cos(a+b*x)^(1/2)*sin(a+b*x)^-1//2)+-2//3*b^-1*cos(a+b*x)^3//2*sin(a+b*x)^-3//2+-1//2*2^(1/2)*b^-1*arctan(1+-1*2^(1/2)*cos(a+b*x)^(1/2)*sin(a+b*x)^-1//2)+-1//4*2^(1/2)*b^-1*log(1+2^(1/2)*cos(a+b*x)^(1/2)*sin(a+b*x)^-1//2+cot(a+b*x))+1//4*2^(1/2)*b^-1*log(1+-1*2^(1/2)*cos(a+b*x)^(1/2)*sin(a+b*x)^-1//2+cot(a+b*x)))
@test integrate(cos(a+b*x)^7//2*sin(a+b*x)^-7//2, x) == :((1/2)*2^(1/2)*b^-1*arctan(1+2^(1/2)*cos(a+b*x)^-1//2*sin(a+b*x)^(1/2))+2*b^-1*cos(a+b*x)^(1/2)*sin(a+b*x)^-1//2+-2//5*b^-1*cos(a+b*x)^5//2*sin(a+b*x)^-5//2+-1//2*2^(1/2)*b^-1*arctan(1+-1*2^(1/2)*cos(a+b*x)^-1//2*sin(a+b*x)^(1/2))+-1//4*2^(1/2)*b^-1*log(1+2^(1/2)*cos(a+b*x)^-1//2*sin(a+b*x)^(1/2)+tan(a+b*x))+1//4*2^(1/2)*b^-1*log(1+-1*2^(1/2)*cos(a+b*x)^-1//2*sin(a+b*x)^(1/2)+tan(a+b*x)))
@test integrate(cos(a+b*x)^-1//3*sin(a+b*x)^1//3, x) == :(-1//2*b^-1*log(1+cos(a+b*x)^-2//3*sin(a+b*x)^2//3)+1//4*b^-1*log(1+cos(a+b*x)^-4//3*sin(a+b*x)^4//3+-1*cos(a+b*x)^-2//3*sin(a+b*x)^2//3)+-1//2*3^(1/2)*b^-1*arctan(1//3*3^(1/2)*(1+-2*cos(a+b*x)^-2//3*sin(a+b*x)^2//3)))
@test integrate(cos(a+b*x)^-2//3*sin(a+b*x)^2//3, x) == :(b^-1*arctan(cos(a+b*x)^-1//3*sin(a+b*x)^1//3)+(1/2)*b^-1*arctan(3^(1/2)+2*cos(a+b*x)^-1//3*sin(a+b*x)^1//3)+-1//2*b^-1*arctan(3^(1/2)+-2*cos(a+b*x)^-1//3*sin(a+b*x)^1//3)+-1//4*3^(1/2)*b^-1*log(1+cos(a+b*x)^-2//3*sin(a+b*x)^2//3+3^(1/2)*cos(a+b*x)^-1//3*sin(a+b*x)^1//3)+1//4*3^(1/2)*b^-1*log(1+cos(a+b*x)^-2//3*sin(a+b*x)^2//3+-1*3^(1/2)*cos(a+b*x)^-1//3*sin(a+b*x)^1//3))
@test integrate(cos(a+b*x)^-4//3*sin(a+b*x)^4//3, x) == :(b^-1*arctan(cos(a+b*x)^1//3*sin(a+b*x)^-1//3)+(1/2)*b^-1*arctan(3^(1/2)+2*cos(a+b*x)^1//3*sin(a+b*x)^-1//3)+-1//2*b^-1*arctan(3^(1/2)+-2*cos(a+b*x)^1//3*sin(a+b*x)^-1//3)+3*b^-1*cos(a+b*x)^-1//3*sin(a+b*x)^1//3+-1//4*3^(1/2)*b^-1*log(1+cos(a+b*x)^2//3*sin(a+b*x)^-2//3+3^(1/2)*cos(a+b*x)^1//3*sin(a+b*x)^-1//3)+1//4*3^(1/2)*b^-1*log(1+cos(a+b*x)^2//3*sin(a+b*x)^-2//3+-1*3^(1/2)*cos(a+b*x)^1//3*sin(a+b*x)^-1//3))
@test integrate(cos(a+b*x)^-5//3*sin(a+b*x)^5//3, x) == :(-1//2*b^-1*log(1+cos(a+b*x)^2//3*sin(a+b*x)^-2//3)+1//4*b^-1*log(1+cos(a+b*x)^4//3*sin(a+b*x)^-4//3+-1*cos(a+b*x)^2//3*sin(a+b*x)^-2//3)+-1//2*3^(1/2)*b^-1*arctan(1//3*3^(1/2)*(1+-2*cos(a+b*x)^2//3*sin(a+b*x)^-2//3))+3//2*b^-1*cos(a+b*x)^-2//3*sin(a+b*x)^2//3)
@test integrate(cos(a+b*x)^-7//3*sin(a+b*x)^7//3, x) == :((1/2)*b^-1*log(1+cos(a+b*x)^-2//3*sin(a+b*x)^2//3)+-1//4*b^-1*log(1+cos(a+b*x)^-4//3*sin(a+b*x)^4//3+-1*cos(a+b*x)^-2//3*sin(a+b*x)^2//3)+(1/2)*3^(1/2)*b^-1*arctan(1//3*3^(1/2)*(1+-2*cos(a+b*x)^-2//3*sin(a+b*x)^2//3))+3//4*b^-1*cos(a+b*x)^-4//3*sin(a+b*x)^4//3)
@test integrate(cos(a+b*x)^1//3*sin(a+b*x)^-1//3, x) == :((1/2)*b^-1*log(1+cos(a+b*x)^2//3*sin(a+b*x)^-2//3)+-1//4*b^-1*log(1+cos(a+b*x)^4//3*sin(a+b*x)^-4//3+-1*cos(a+b*x)^2//3*sin(a+b*x)^-2//3)+(1/2)*3^(1/2)*b^-1*arctan(1//3*3^(1/2)*(1+-2*cos(a+b*x)^2//3*sin(a+b*x)^-2//3)))
@test integrate(cos(a+b*x)^2//3*sin(a+b*x)^-2//3, x) == :((1/2)*b^-1*arctan(3^(1/2)+-2*cos(a+b*x)^1//3*sin(a+b*x)^-1//3)+-1*b^-1*arctan(cos(a+b*x)^1//3*sin(a+b*x)^-1//3)+-1//2*b^-1*arctan(3^(1/2)+2*cos(a+b*x)^1//3*sin(a+b*x)^-1//3)+-1//4*3^(1/2)*b^-1*log(1+cos(a+b*x)^2//3*sin(a+b*x)^-2//3+-1*3^(1/2)*cos(a+b*x)^1//3*sin(a+b*x)^-1//3)+1//4*3^(1/2)*b^-1*log(1+cos(a+b*x)^2//3*sin(a+b*x)^-2//3+3^(1/2)*cos(a+b*x)^1//3*sin(a+b*x)^-1//3))
@test integrate(cos(a+b*x)^4//3*sin(a+b*x)^-4//3, x) == :((1/2)*b^-1*arctan(3^(1/2)+-2*cos(a+b*x)^-1//3*sin(a+b*x)^1//3)+-1*b^-1*arctan(cos(a+b*x)^-1//3*sin(a+b*x)^1//3)+-1//2*b^-1*arctan(3^(1/2)+2*cos(a+b*x)^-1//3*sin(a+b*x)^1//3)+-3*b^-1*cos(a+b*x)^1//3*sin(a+b*x)^-1//3+-1//4*3^(1/2)*b^-1*log(1+cos(a+b*x)^-2//3*sin(a+b*x)^2//3+-1*3^(1/2)*cos(a+b*x)^-1//3*sin(a+b*x)^1//3)+1//4*3^(1/2)*b^-1*log(1+cos(a+b*x)^-2//3*sin(a+b*x)^2//3+3^(1/2)*cos(a+b*x)^-1//3*sin(a+b*x)^1//3))
@test integrate(cos(a+b*x)^5//3*sin(a+b*x)^-5//3, x) == :((1/2)*b^-1*log(1+cos(a+b*x)^-2//3*sin(a+b*x)^2//3)+-1//4*b^-1*log(1+cos(a+b*x)^-4//3*sin(a+b*x)^4//3+-1*cos(a+b*x)^-2//3*sin(a+b*x)^2//3)+(1/2)*3^(1/2)*b^-1*arctan(1//3*3^(1/2)*(1+-2*cos(a+b*x)^-2//3*sin(a+b*x)^2//3))+-3//2*b^-1*cos(a+b*x)^2//3*sin(a+b*x)^-2//3)
@test integrate(cos(a+b*x)^7//3*sin(a+b*x)^-7//3, x) == :(-1//2*b^-1*log(1+cos(a+b*x)^2//3*sin(a+b*x)^-2//3)+1//4*b^-1*log(1+cos(a+b*x)^4//3*sin(a+b*x)^-4//3+-1*cos(a+b*x)^2//3*sin(a+b*x)^-2//3)+-3//4*b^-1*cos(a+b*x)^4//3*sin(a+b*x)^-4//3+-1//2*3^(1/2)*b^-1*arctan(1//3*3^(1/2)*(1+-2*cos(a+b*x)^2//3*sin(a+b*x)^-2//3)))
@test integrate(cos(x)^2//3*sin(x)^-8//3, x) == :(-3//5*cos(x)^5//3*sin(x)^-5//3)
@test integrate(cos(x)^-8//3*sin(x)^2//3, x) == :(3//5*cos(x)^-5//3*sin(x)^5//3)
@test integrate((c*sin(a+b*x))^m*cos(a+b*x)^5, x) == :(b^-1*c^-1*(c*sin(a+b*x))^(1+m)*(1+m)^-1+b^-1*c^-5*(c*sin(a+b*x))^(5+m)*(5+m)^-1+-2*b^-1*c^-3*(c*sin(a+b*x))^(3+m)*(3+m)^-1)
@test integrate((c*sin(a+b*x))^m*cos(a+b*x)^3, x) == :(b^-1*c^-1*(c*sin(a+b*x))^(1+m)*(1+m)^-1+-1*b^-1*c^-3*(c*sin(a+b*x))^(3+m)*(3+m)^-1)
@test integrate((c*sin(a+b*x))^m*cos(a+b*x), x) == :(b^-1*c^-1*(c*sin(a+b*x))^(1+m)*(1+m)^-1)
@test integrate((d*cos(a+b*x))^n*sin(a+b*x)^5, x) == :(-1*b^-1*d^-1*(d*cos(a+b*x))^(1+n)*(1+n)^-1+-1*b^-1*d^-5*(d*cos(a+b*x))^(5+n)*(5+n)^-1+2*b^-1*d^-3*(d*cos(a+b*x))^(3+n)*(3+n)^-1)
@test integrate((d*cos(a+b*x))^n*sin(a+b*x)^3, x) == :(b^-1*d^-3*(d*cos(a+b*x))^(3+n)*(3+n)^-1+-1*b^-1*d^-1*(d*cos(a+b*x))^(1+n)*(1+n)^-1)
@test integrate((d*cos(a+b*x))^n*sin(a+b*x), x) == :(-1*b^-1*d^-1*(d*cos(a+b*x))^(1+n)*(1+n)^-1)
@test integrate((b*sec(e+f*x))^(1/2)*sin(e+f*x)^7, x) == :(-2*b*f^-1*(b*sec(e+f*x))^-1//2+-2//3*b^5*f^-1*(b*sec(e+f*x))^-9//2+2//13*b^7*f^-1*(b*sec(e+f*x))^-13//2+6//5*b^3*f^-1*(b*sec(e+f*x))^-5//2)
@test integrate((b*sec(e+f*x))^(1/2)*sin(e+f*x)^5, x) == :(-2*b*f^-1*(b*sec(e+f*x))^-1//2+-2//9*b^5*f^-1*(b*sec(e+f*x))^-9//2+4//5*b^3*f^-1*(b*sec(e+f*x))^-5//2)
@test integrate((b*sec(e+f*x))^(1/2)*sin(e+f*x)^3, x) == :(-2*b*f^-1*(b*sec(e+f*x))^-1//2+2//5*b^3*f^-1*(b*sec(e+f*x))^-5//2)
@test integrate((b*sec(e+f*x))^(1/2)*sin(e+f*x), x) == :(-2*b*f^-1*(b*sec(e+f*x))^-1//2)
@test integrate((b*sec(e+f*x))^(1/2)*csc(e+f*x), x) == :(b^(1/2)*f^-1*arctan(b^-1//2*(b*sec(e+f*x))^(1/2))+-1*b^(1/2)*f^-1*arctanh(b^-1//2*(b*sec(e+f*x))^(1/2)))
@test integrate((b*sec(e+f*x))^(1/2)*csc(e+f*x)^3, x) == :(-3//4*b^(1/2)*f^-1*arctanh(b^-1//2*(b*sec(e+f*x))^(1/2))+3//4*b^(1/2)*f^-1*arctan(b^-1//2*(b*sec(e+f*x))^(1/2))+-1//2*b^-1*f^-1*(b*sec(e+f*x))^3//2*cot(e+f*x)^2)
@test integrate((b*sec(e+f*x))^(1/2)*csc(e+f*x)^5, x) == :(-21//32*b^(1/2)*f^-1*arctanh(b^-1//2*(b*sec(e+f*x))^(1/2))+21//32*b^(1/2)*f^-1*arctan(b^-1//2*(b*sec(e+f*x))^(1/2))+-7//16*b^-1*f^-1*(b*sec(e+f*x))^3//2*cot(e+f*x)^2+-1//4*b^-3*f^-1*(b*sec(e+f*x))^7//2*cot(e+f*x)^4)
@test integrate((b*sec(e+f*x))^(1/2)*sin(e+f*x)^6, x) == :(-40//77*b*f^-1*(b*sec(e+f*x))^-1//2*sin(e+f*x)+-20//77*b*f^-1*(b*sec(e+f*x))^-1//2*sin(e+f*x)^3+-2//11*b*f^-1*(b*sec(e+f*x))^-1//2*sin(e+f*x)^5+80//77*f^-1*(b*sec(e+f*x))^(1/2)*cos(e+f*x)^(1/2)*Elliptic.F((1/2)*e+(1/2)*f*x,2))
@test integrate((b*sec(e+f*x))^(1/2)*sin(e+f*x)^4, x) == :(-4//7*b*f^-1*(b*sec(e+f*x))^-1//2*sin(e+f*x)+-2//7*b*f^-1*(b*sec(e+f*x))^-1//2*sin(e+f*x)^3+8//7*f^-1*(b*sec(e+f*x))^(1/2)*cos(e+f*x)^(1/2)*Elliptic.F((1/2)*e+(1/2)*f*x,2))
@test integrate((b*sec(e+f*x))^(1/2)*sin(e+f*x)^2, x) == :(-2//3*b*f^-1*(b*sec(e+f*x))^-1//2*sin(e+f*x)+4//3*f^-1*(b*sec(e+f*x))^(1/2)*cos(e+f*x)^(1/2)*Elliptic.F((1/2)*e+(1/2)*f*x,2))
@test integrate((b*sec(e+f*x))^(1/2), x) == :(2*f^-1*(b*sec(e+f*x))^(1/2)*cos(e+f*x)^(1/2)*Elliptic.F((1/2)*e+(1/2)*f*x,2))
@test integrate((b*sec(e+f*x))^(1/2)*csc(e+f*x)^2, x) == :(f^-1*(b*sec(e+f*x))^(1/2)*cos(e+f*x)^(1/2)*Elliptic.F((1/2)*e+(1/2)*f*x,2)+-1*b*f^-1*(b*sec(e+f*x))^-1//2*csc(e+f*x))
@test integrate((b*sec(e+f*x))^(1/2)*csc(e+f*x)^4, x) == :(-5//6*b*f^-1*(b*sec(e+f*x))^-1//2*csc(e+f*x)+-1//3*b*f^-1*(b*sec(e+f*x))^-1//2*csc(e+f*x)^3+5//6*f^-1*(b*sec(e+f*x))^(1/2)*cos(e+f*x)^(1/2)*Elliptic.F((1/2)*e+(1/2)*f*x,2))
@test integrate((b*sec(e+f*x))^(1/2)*csc(e+f*x)^6, x) == :(-3//4*b*f^-1*(b*sec(e+f*x))^-1//2*csc(e+f*x)+-3//10*b*f^-1*(b*sec(e+f*x))^-1//2*csc(e+f*x)^3+-1//5*b*f^-1*(b*sec(e+f*x))^-1//2*csc(e+f*x)^5+3//4*f^-1*(b*sec(e+f*x))^(1/2)*cos(e+f*x)^(1/2)*Elliptic.F((1/2)*e+(1/2)*f*x,2))
@test integrate((b*sec(e+f*x))^3//2*sin(e+f*x)^7, x) == :(2*b*f^-1*(b*sec(e+f*x))^(1/2)+2*b^3*f^-1*(b*sec(e+f*x))^-3//2+-6//7*b^5*f^-1*(b*sec(e+f*x))^-7//2+2//11*b^7*f^-1*(b*sec(e+f*x))^-11//2)
@test integrate((b*sec(e+f*x))^3//2*sin(e+f*x)^5, x) == :(2*b*f^-1*(b*sec(e+f*x))^(1/2)+-2//7*b^5*f^-1*(b*sec(e+f*x))^-7//2+4//3*b^3*f^-1*(b*sec(e+f*x))^-3//2)
@test integrate((b*sec(e+f*x))^3//2*sin(e+f*x)^3, x) == :(2*b*f^-1*(b*sec(e+f*x))^(1/2)+2//3*b^3*f^-1*(b*sec(e+f*x))^-3//2)
@test integrate((b*sec(e+f*x))^3//2*sin(e+f*x), x) == :(2*b*f^-1*(b*sec(e+f*x))^(1/2))
@test integrate((b*sec(e+f*x))^3//2*csc(e+f*x), x) == :(-1*b^3//2*f^-1*arctan(b^-1//2*(b*sec(e+f*x))^(1/2))+-1*b^3//2*f^-1*arctanh(b^-1//2*(b*sec(e+f*x))^(1/2))+2*b*f^-1*(b*sec(e+f*x))^(1/2))
@test integrate((b*sec(e+f*x))^3//2*csc(e+f*x)^3, x) == :(-5//4*b^3//2*f^-1*arctan(b^-1//2*(b*sec(e+f*x))^(1/2))+-5//4*b^3//2*f^-1*arctanh(b^-1//2*(b*sec(e+f*x))^(1/2))+5//2*b*f^-1*(b*sec(e+f*x))^(1/2)+-1//2*b^-1*f^-1*(b*sec(e+f*x))^5//2*cot(e+f*x)^2)
@test integrate((b*sec(e+f*x))^3//2*sin(e+f*x)^6, x) == :(2*b*f^-1*(b*sec(e+f*x))^(1/2)*sin(e+f*x)^5+8//3*b^3*f^-1*(b*sec(e+f*x))^-3//2*sin(e+f*x)+20//9*b^3*f^-1*(b*sec(e+f*x))^-3//2*sin(e+f*x)^3+-16//3*b^2*f^-1*(b*sec(e+f*x))^-1//2*cos(e+f*x)^-1//2*Elliptic.E((1/2)*e+(1/2)*f*x,2))
@test integrate((b*sec(e+f*x))^3//2*sin(e+f*x)^4, x) == :(2*b*f^-1*(b*sec(e+f*x))^(1/2)*sin(e+f*x)^3+12//5*b^3*f^-1*(b*sec(e+f*x))^-3//2*sin(e+f*x)+-24//5*b^2*f^-1*(b*sec(e+f*x))^-1//2*cos(e+f*x)^-1//2*Elliptic.E((1/2)*e+(1/2)*f*x,2))
@test integrate((b*sec(e+f*x))^3//2*sin(e+f*x)^2, x) == :(2*b*f^-1*(b*sec(e+f*x))^(1/2)*sin(e+f*x)+-4*b^2*f^-1*(b*sec(e+f*x))^-1//2*cos(e+f*x)^-1//2*Elliptic.E((1/2)*e+(1/2)*f*x,2))
@test integrate((b*sec(e+f*x))^3//2, x) == :(2*b*f^-1*(b*sec(e+f*x))^(1/2)*sin(e+f*x)+-2*b^2*f^-1*(b*sec(e+f*x))^-1//2*cos(e+f*x)^-1//2*Elliptic.E((1/2)*e+(1/2)*f*x,2))
@test integrate((b*sec(e+f*x))^3//2*csc(e+f*x)^2, x) == :(-1*b*f^-1*(b*sec(e+f*x))^(1/2)*csc(e+f*x)+3*b*f^-1*(b*sec(e+f*x))^(1/2)*sin(e+f*x)+-3*b^2*f^-1*(b*sec(e+f*x))^-1//2*cos(e+f*x)^-1//2*Elliptic.E((1/2)*e+(1/2)*f*x,2))
@test integrate((b*sec(e+f*x))^3//2*csc(e+f*x)^4, x) == :(-7//6*b*f^-1*(b*sec(e+f*x))^(1/2)*csc(e+f*x)+-1//3*b*f^-1*(b*sec(e+f*x))^(1/2)*csc(e+f*x)^3+7//2*b*f^-1*(b*sec(e+f*x))^(1/2)*sin(e+f*x)+-7//2*b^2*f^-1*(b*sec(e+f*x))^-1//2*cos(e+f*x)^-1//2*Elliptic.E((1/2)*e+(1/2)*f*x,2))
@test integrate((b*sec(e+f*x))^5//2*sin(e+f*x)^7, x) == :(6*b^3*f^-1*(b*sec(e+f*x))^-1//2+-6//5*b^5*f^-1*(b*sec(e+f*x))^-5//2+2//3*b*f^-1*(b*sec(e+f*x))^3//2+2//9*b^7*f^-1*(b*sec(e+f*x))^-9//2)
@test integrate((b*sec(e+f*x))^5//2*sin(e+f*x)^5, x) == :(4*b^3*f^-1*(b*sec(e+f*x))^-1//2+-2//5*b^5*f^-1*(b*sec(e+f*x))^-5//2+2//3*b*f^-1*(b*sec(e+f*x))^3//2)
@test integrate((b*sec(e+f*x))^5//2*sin(e+f*x)^3, x) == :(2*b^3*f^-1*(b*sec(e+f*x))^-1//2+2//3*b*f^-1*(b*sec(e+f*x))^3//2)
@test integrate((b*sec(e+f*x))^5//2*sin(e+f*x), x) == :(2//3*b*f^-1*(b*sec(e+f*x))^3//2)
@test integrate((b*sec(e+f*x))^5//2*csc(e+f*x), x) == :(b^5//2*f^-1*arctan(b^-1//2*(b*sec(e+f*x))^(1/2))+-1*b^5//2*f^-1*arctanh(b^-1//2*(b*sec(e+f*x))^(1/2))+2//3*b*f^-1*(b*sec(e+f*x))^3//2)
@test integrate((b*sec(e+f*x))^5//2*csc(e+f*x)^3, x) == :(-7//4*b^5//2*f^-1*arctanh(b^-1//2*(b*sec(e+f*x))^(1/2))+7//4*b^5//2*f^-1*arctan(b^-1//2*(b*sec(e+f*x))^(1/2))+7//6*b*f^-1*(b*sec(e+f*x))^3//2+-1//2*b^-1*f^-1*(b*sec(e+f*x))^7//2*cot(e+f*x)^2)
@test integrate((b*sec(e+f*x))^5//2*csc(e+f*x)^5, x) == :(-77//32*b^5//2*f^-1*arctanh(b^-1//2*(b*sec(e+f*x))^(1/2))+77//32*b^5//2*f^-1*arctan(b^-1//2*(b*sec(e+f*x))^(1/2))+77//48*b*f^-1*(b*sec(e+f*x))^3//2+-11//16*b^-1*f^-1*(b*sec(e+f*x))^7//2*cot(e+f*x)^2+-1//4*b^-3*f^-1*(b*sec(e+f*x))^11//2*cot(e+f*x)^4)
@test integrate((b*sec(e+f*x))^5//2*sin(e+f*x)^6, x) == :(2//3*b*f^-1*(b*sec(e+f*x))^3//2*sin(e+f*x)^5+20//21*b^3*f^-1*(b*sec(e+f*x))^-1//2*sin(e+f*x)^3+40//21*b^3*f^-1*(b*sec(e+f*x))^-1//2*sin(e+f*x)+-80//21*b^2*f^-1*(b*sec(e+f*x))^(1/2)*cos(e+f*x)^(1/2)*Elliptic.F((1/2)*e+(1/2)*f*x,2))
@test integrate((b*sec(e+f*x))^5//2*sin(e+f*x)^4, x) == :(2//3*b*f^-1*(b*sec(e+f*x))^3//2*sin(e+f*x)^3+4//3*b^3*f^-1*(b*sec(e+f*x))^-1//2*sin(e+f*x)+-8//3*b^2*f^-1*(b*sec(e+f*x))^(1/2)*cos(e+f*x)^(1/2)*Elliptic.F((1/2)*e+(1/2)*f*x,2))
@test integrate((b*sec(e+f*x))^5//2*sin(e+f*x)^2, x) == :(2//3*b*f^-1*(b*sec(e+f*x))^3//2*sin(e+f*x)+-4//3*b^2*f^-1*(b*sec(e+f*x))^(1/2)*cos(e+f*x)^(1/2)*Elliptic.F((1/2)*e+(1/2)*f*x,2))
@test integrate((b*sec(e+f*x))^5//2, x) == :(2//3*b*f^-1*(b*sec(e+f*x))^3//2*sin(e+f*x)+2//3*b^2*f^-1*(b*sec(e+f*x))^(1/2)*cos(e+f*x)^(1/2)*Elliptic.F((1/2)*e+(1/2)*f*x,2))
@test integrate((b*sec(e+f*x))^5//2*csc(e+f*x)^2, x) == :(-5//3*b^3*f^-1*(b*sec(e+f*x))^-1//2*csc(e+f*x)+2//3*b*f^-1*(b*sec(e+f*x))^3//2*csc(e+f*x)+5//3*b^2*f^-1*(b*sec(e+f*x))^(1/2)*cos(e+f*x)^(1/2)*Elliptic.F((1/2)*e+(1/2)*f*x,2))
@test integrate((b*sec(e+f*x))^5//2*csc(e+f*x)^4, x) == :(b*f^-1*(b*sec(e+f*x))^3//2*csc(e+f*x)+-5//2*b^3*f^-1*(b*sec(e+f*x))^-1//2*csc(e+f*x)+-1//3*b*f^-1*(b*sec(e+f*x))^3//2*csc(e+f*x)^3+5//2*b^2*f^-1*(b*sec(e+f*x))^(1/2)*cos(e+f*x)^(1/2)*Elliptic.F((1/2)*e+(1/2)*f*x,2))
@test integrate((b*sec(e+f*x))^-1//2*sin(e+f*x)^7, x) == :(-6//11*b^5*f^-1*(b*sec(e+f*x))^-11//2+-2//3*b*f^-1*(b*sec(e+f*x))^-3//2+2//15*b^7*f^-1*(b*sec(e+f*x))^-15//2+6//7*b^3*f^-1*(b*sec(e+f*x))^-7//2)
@test integrate((b*sec(e+f*x))^-1//2*sin(e+f*x)^5, x) == :(-2//3*b*f^-1*(b*sec(e+f*x))^-3//2+-2//11*b^5*f^-1*(b*sec(e+f*x))^-11//2+4//7*b^3*f^-1*(b*sec(e+f*x))^-7//2)
@test integrate((b*sec(e+f*x))^-1//2*sin(e+f*x)^3, x) == :(-2//3*b*f^-1*(b*sec(e+f*x))^-3//2+2//7*b^3*f^-1*(b*sec(e+f*x))^-7//2)
@test integrate((b*sec(e+f*x))^-1//2*sin(e+f*x), x) == :(-2//3*b*f^-1*(b*sec(e+f*x))^-3//2)
@test integrate((b*sec(e+f*x))^-1//2*csc(e+f*x), x) == :(-1*b^-1//2*f^-1*arctan(b^-1//2*(b*sec(e+f*x))^(1/2))+-1*b^-1//2*f^-1*arctanh(b^-1//2*(b*sec(e+f*x))^(1/2)))
@test integrate((b*sec(e+f*x))^-1//2*csc(e+f*x)^3, x) == :(-1//4*b^-1//2*f^-1*arctan(b^-1//2*(b*sec(e+f*x))^(1/2))+-1//4*b^-1//2*f^-1*arctanh(b^-1//2*(b*sec(e+f*x))^(1/2))+-1//2*b^-1*f^-1*(b*sec(e+f*x))^(1/2)*cot(e+f*x)^2)
@test integrate((b*sec(e+f*x))^-1//2*csc(e+f*x)^5, x) == :(-5//32*b^-1//2*f^-1*arctan(b^-1//2*(b*sec(e+f*x))^(1/2))+-5//32*b^-1//2*f^-1*arctanh(b^-1//2*(b*sec(e+f*x))^(1/2))+-5//16*b^-1*f^-1*(b*sec(e+f*x))^(1/2)*cot(e+f*x)^2+-1//4*b^-3*f^-1*(b*sec(e+f*x))^5//2*cot(e+f*x)^4)
@test integrate((b*sec(e+f*x))^-1//2*sin(e+f*x)^6, x) == :(-20//117*b*f^-1*(b*sec(e+f*x))^-3//2*sin(e+f*x)^3+-8//39*b*f^-1*(b*sec(e+f*x))^-3//2*sin(e+f*x)+-2//13*b*f^-1*(b*sec(e+f*x))^-3//2*sin(e+f*x)^5+16//39*f^-1*(b*sec(e+f*x))^-1//2*cos(e+f*x)^-1//2*Elliptic.E((1/2)*e+(1/2)*f*x,2))
@test integrate((b*sec(e+f*x))^-1//2*sin(e+f*x)^4, x) == :(-4//15*b*f^-1*(b*sec(e+f*x))^-3//2*sin(e+f*x)+-2//9*b*f^-1*(b*sec(e+f*x))^-3//2*sin(e+f*x)^3+8//15*f^-1*(b*sec(e+f*x))^-1//2*cos(e+f*x)^-1//2*Elliptic.E((1/2)*e+(1/2)*f*x,2))
@test integrate((b*sec(e+f*x))^-1//2*sin(e+f*x)^2, x) == :(-2//5*b*f^-1*(b*sec(e+f*x))^-3//2*sin(e+f*x)+4//5*f^-1*(b*sec(e+f*x))^-1//2*cos(e+f*x)^-1//2*Elliptic.E((1/2)*e+(1/2)*f*x,2))
@test integrate((b*sec(e+f*x))^-1//2, x) == :(2*f^-1*(b*sec(e+f*x))^-1//2*cos(e+f*x)^-1//2*Elliptic.E((1/2)*e+(1/2)*f*x,2))
@test integrate((b*sec(e+f*x))^-1//2*csc(e+f*x)^2, x) == :(-1*b*f^-1*(b*sec(e+f*x))^-3//2*csc(e+f*x)+-1*f^-1*(b*sec(e+f*x))^-1//2*cos(e+f*x)^-1//2*Elliptic.E((1/2)*e+(1/2)*f*x,2))
@test integrate((b*sec(e+f*x))^-1//2*csc(e+f*x)^4, x) == :(-1//2*b*f^-1*(b*sec(e+f*x))^-3//2*csc(e+f*x)+-1//2*f^-1*(b*sec(e+f*x))^-1//2*cos(e+f*x)^-1//2*Elliptic.E((1/2)*e+(1/2)*f*x,2)+-1//3*b*f^-1*(b*sec(e+f*x))^-3//2*csc(e+f*x)^3)
@test integrate((b*sec(e+f*x))^-1//2*csc(e+f*x)^6, x) == :(-7//20*b*f^-1*(b*sec(e+f*x))^-3//2*csc(e+f*x)+-7//20*f^-1*(b*sec(e+f*x))^-1//2*cos(e+f*x)^-1//2*Elliptic.E((1/2)*e+(1/2)*f*x,2)+-7//30*b*f^-1*(b*sec(e+f*x))^-3//2*csc(e+f*x)^3+-1//5*b*f^-1*(b*sec(e+f*x))^-3//2*csc(e+f*x)^5)
@test integrate((b*sec(e+f*x))^-3//2*sin(e+f*x)^7, x) == :(-6//13*b^5*f^-1*(b*sec(e+f*x))^-13//2+-2//5*b*f^-1*(b*sec(e+f*x))^-5//2+2//3*b^3*f^-1*(b*sec(e+f*x))^-9//2+2//17*b^7*f^-1*(b*sec(e+f*x))^-17//2)
@test integrate((b*sec(e+f*x))^-3//2*sin(e+f*x)^5, x) == :(-2//5*b*f^-1*(b*sec(e+f*x))^-5//2+-2//13*b^5*f^-1*(b*sec(e+f*x))^-13//2+4//9*b^3*f^-1*(b*sec(e+f*x))^-9//2)
@test integrate((b*sec(e+f*x))^-3//2*sin(e+f*x)^3, x) == :(-2//5*b*f^-1*(b*sec(e+f*x))^-5//2+2//9*b^3*f^-1*(b*sec(e+f*x))^-9//2)
@test integrate((b*sec(e+f*x))^-3//2*sin(e+f*x), x) == :(-2//5*b*f^-1*(b*sec(e+f*x))^-5//2)
@test integrate((b*sec(e+f*x))^-3//2*csc(e+f*x), x) == :(b^-3//2*f^-1*arctan(b^-1//2*(b*sec(e+f*x))^(1/2))+-1*b^-3//2*f^-1*arctanh(b^-1//2*(b*sec(e+f*x))^(1/2))+2*b^-1*f^-1*(b*sec(e+f*x))^-1//2)
@test integrate((b*sec(e+f*x))^-3//2*csc(e+f*x)^3, x) == :(-1//4*b^-3//2*f^-1*arctan(b^-1//2*(b*sec(e+f*x))^(1/2))+1//4*b^-3//2*f^-1*arctanh(b^-1//2*(b*sec(e+f*x))^(1/2))+-1//2*b^-3*f^-1*(b*sec(e+f*x))^3//2*cot(e+f*x)^2)
@test integrate((b*sec(e+f*x))^-3//2*csc(e+f*x)^5, x) == :(-3//32*b^-3//2*f^-1*arctan(b^-1//2*(b*sec(e+f*x))^(1/2))+3//32*b^-3//2*f^-1*arctanh(b^-1//2*(b*sec(e+f*x))^(1/2))+-3//16*b^-3*f^-1*(b*sec(e+f*x))^3//2*cot(e+f*x)^2+-1//4*b^-3*f^-1*(b*sec(e+f*x))^3//2*cot(e+f*x)^4)
@test integrate((b*sec(e+f*x))^-3//2*sin(e+f*x)^4, x) == :(-12//77*b*f^-1*(b*sec(e+f*x))^-5//2*sin(e+f*x)+-2//11*b*f^-1*(b*sec(e+f*x))^-5//2*sin(e+f*x)^3+8//77*b^-1*f^-1*(b*sec(e+f*x))^-1//2*sin(e+f*x)+8//77*b^-2*f^-1*(b*sec(e+f*x))^(1/2)*cos(e+f*x)^(1/2)*Elliptic.F((1/2)*e+(1/2)*f*x,2))
@test integrate((b*sec(e+f*x))^-3//2*sin(e+f*x)^2, x) == :(-2//7*b*f^-1*(b*sec(e+f*x))^-5//2*sin(e+f*x)+4//21*b^-1*f^-1*(b*sec(e+f*x))^-1//2*sin(e+f*x)+4//21*b^-2*f^-1*(b*sec(e+f*x))^(1/2)*cos(e+f*x)^(1/2)*Elliptic.F((1/2)*e+(1/2)*f*x,2))
@test integrate((b*sec(e+f*x))^-3//2, x) == :(2//3*b^-1*f^-1*(b*sec(e+f*x))^-1//2*sin(e+f*x)+2//3*b^-2*f^-1*(b*sec(e+f*x))^(1/2)*cos(e+f*x)^(1/2)*Elliptic.F((1/2)*e+(1/2)*f*x,2))
@test integrate((b*sec(e+f*x))^-3//2*csc(e+f*x)^2, x) == :(-1*b^-1*f^-1*(b*sec(e+f*x))^-1//2*csc(e+f*x)+-1*b^-2*f^-1*(b*sec(e+f*x))^(1/2)*cos(e+f*x)^(1/2)*Elliptic.F((1/2)*e+(1/2)*f*x,2))
@test integrate((b*sec(e+f*x))^-3//2*csc(e+f*x)^4, x) == :(-1//3*b^-1*f^-1*(b*sec(e+f*x))^-1//2*csc(e+f*x)^3+1//6*b^-1*f^-1*(b*sec(e+f*x))^-1//2*csc(e+f*x)+-1//6*b^-2*f^-1*(b*sec(e+f*x))^(1/2)*cos(e+f*x)^(1/2)*Elliptic.F((1/2)*e+(1/2)*f*x,2))
@test integrate((b*sec(e+f*x))^-3//2*csc(e+f*x)^6, x) == :(-1//5*b^-1*f^-1*(b*sec(e+f*x))^-1//2*csc(e+f*x)^5+1//12*b^-1*f^-1*(b*sec(e+f*x))^-1//2*csc(e+f*x)+1//30*b^-1*f^-1*(b*sec(e+f*x))^-1//2*csc(e+f*x)^3+-1//12*b^-2*f^-1*(b*sec(e+f*x))^(1/2)*cos(e+f*x)^(1/2)*Elliptic.F((1/2)*e+(1/2)*f*x,2))
@test integrate((b*sec(e+f*x))^-5//2*sin(e+f*x)^7, x) == :(-2//5*b^5*f^-1*(b*sec(e+f*x))^-15//2+-2//7*b*f^-1*(b*sec(e+f*x))^-7//2+2//19*b^7*f^-1*(b*sec(e+f*x))^-19//2+6//11*b^3*f^-1*(b*sec(e+f*x))^-11//2)
@test integrate((b*sec(e+f*x))^-5//2*sin(e+f*x)^5, x) == :(-2//7*b*f^-1*(b*sec(e+f*x))^-7//2+-2//15*b^5*f^-1*(b*sec(e+f*x))^-15//2+4//11*b^3*f^-1*(b*sec(e+f*x))^-11//2)
@test integrate((b*sec(e+f*x))^-5//2*sin(e+f*x)^3, x) == :(-2//7*b*f^-1*(b*sec(e+f*x))^-7//2+2//11*b^3*f^-1*(b*sec(e+f*x))^-11//2)
@test integrate((b*sec(e+f*x))^-5//2*sin(e+f*x), x) == :(-2//7*b*f^-1*(b*sec(e+f*x))^-7//2)
@test integrate((b*sec(e+f*x))^-5//2*csc(e+f*x), x) == :(-1*b^-5//2*f^-1*arctan(b^-1//2*(b*sec(e+f*x))^(1/2))+-1*b^-5//2*f^-1*arctanh(b^-1//2*(b*sec(e+f*x))^(1/2))+2//3*b^-1*f^-1*(b*sec(e+f*x))^-3//2)
@test integrate((b*sec(e+f*x))^-5//2*csc(e+f*x)^3, x) == :(3//4*b^-5//2*f^-1*arctan(b^-1//2*(b*sec(e+f*x))^(1/2))+3//4*b^-5//2*f^-1*arctanh(b^-1//2*(b*sec(e+f*x))^(1/2))+-1//2*b^-3*f^-1*(b*sec(e+f*x))^(1/2)*cot(e+f*x)^2)
@test integrate((b*sec(e+f*x))^-5//2*csc(e+f*x)^5, x) == :(3//32*b^-5//2*f^-1*arctan(b^-1//2*(b*sec(e+f*x))^(1/2))+3//32*b^-5//2*f^-1*arctanh(b^-1//2*(b*sec(e+f*x))^(1/2))+-1//4*b^-3*f^-1*(b*sec(e+f*x))^(1/2)*cot(e+f*x)^4+-1//16*b^-3*f^-1*(b*sec(e+f*x))^(1/2)*cot(e+f*x)^2)
@test integrate((b*sec(e+f*x))^-5//2*sin(e+f*x)^4, x) == :(-4//39*b*f^-1*(b*sec(e+f*x))^-7//2*sin(e+f*x)+-2//13*b*f^-1*(b*sec(e+f*x))^-7//2*sin(e+f*x)^3+8//195*b^-1*f^-1*(b*sec(e+f*x))^-3//2*sin(e+f*x)+8//65*b^-2*f^-1*(b*sec(e+f*x))^-1//2*cos(e+f*x)^-1//2*Elliptic.E((1/2)*e+(1/2)*f*x,2))
@test integrate((b*sec(e+f*x))^-5//2*sin(e+f*x)^2, x) == :(-2//9*b*f^-1*(b*sec(e+f*x))^-7//2*sin(e+f*x)+4//45*b^-1*f^-1*(b*sec(e+f*x))^-3//2*sin(e+f*x)+4//15*b^-2*f^-1*(b*sec(e+f*x))^-1//2*cos(e+f*x)^-1//2*Elliptic.E((1/2)*e+(1/2)*f*x,2))
@test integrate((b*sec(e+f*x))^-5//2, x) == :(2//5*b^-1*f^-1*(b*sec(e+f*x))^-3//2*sin(e+f*x)+6//5*b^-2*f^-1*(b*sec(e+f*x))^-1//2*cos(e+f*x)^-1//2*Elliptic.E((1/2)*e+(1/2)*f*x,2))
@test integrate((b*sec(e+f*x))^-5//2*csc(e+f*x)^2, x) == :(-1*b^-1*f^-1*(b*sec(e+f*x))^-3//2*csc(e+f*x)+-3*b^-2*f^-1*(b*sec(e+f*x))^-1//2*cos(e+f*x)^-1//2*Elliptic.E((1/2)*e+(1/2)*f*x,2))
@test integrate((b*sec(e+f*x))^-5//2*csc(e+f*x)^4, x) == :((1/2)*b^-1*f^-1*(b*sec(e+f*x))^-3//2*csc(e+f*x)+-1//3*b^-1*f^-1*(b*sec(e+f*x))^-3//2*csc(e+f*x)^3+(1/2)*b^-2*f^-1*(b*sec(e+f*x))^-1//2*cos(e+f*x)^-1//2*Elliptic.E((1/2)*e+(1/2)*f*x,2))
@test integrate((b*sec(e+f*x))^-5//2*csc(e+f*x)^6, x) == :(-1//5*b^-1*f^-1*(b*sec(e+f*x))^-3//2*csc(e+f*x)^5+1//10*b^-1*f^-1*(b*sec(e+f*x))^-3//2*csc(e+f*x)^3+3//20*b^-1*f^-1*(b*sec(e+f*x))^-3//2*csc(e+f*x)+3//20*b^-2*f^-1*(b*sec(e+f*x))^-1//2*cos(e+f*x)^-1//2*Elliptic.E((1/2)*e+(1/2)*f*x,2))
@test integrate((a*sin(e+f*x))^9//2*(b*sec(e+f*x))^(1/2), x) == :(-7//16*b*a^3*f^-1*(a*sin(e+f*x))^3//2*(b*sec(e+f*x))^-1//2+-1//4*a*b*f^-1*(a*sin(e+f*x))^7//2*(b*sec(e+f*x))^-1//2+-21//64*2^(1/2)*a^9//2*b^-1//2*f^-1*(b*cos(e+f*x))^(1/2)*(b*sec(e+f*x))^(1/2)*arctan(1+-1*2^(1/2)*a^-1//2*b^(1/2)*(a*sin(e+f*x))^(1/2)*(b*cos(e+f*x))^-1//2)+-21//128*2^(1/2)*a^9//2*b^-1//2*f^-1*(b*cos(e+f*x))^(1/2)*(b*sec(e+f*x))^(1/2)*log(a^(1/2)+a^(1/2)*tan(e+f*x)+2^(1/2)*b^(1/2)*(a*sin(e+f*x))^(1/2)*(b*cos(e+f*x))^-1//2)+21//64*2^(1/2)*a^9//2*b^-1//2*f^-1*(b*cos(e+f*x))^(1/2)*(b*sec(e+f*x))^(1/2)*arctan(1+2^(1/2)*a^-1//2*b^(1/2)*(a*sin(e+f*x))^(1/2)*(b*cos(e+f*x))^-1//2)+21//128*2^(1/2)*a^9//2*b^-1//2*f^-1*(b*cos(e+f*x))^(1/2)*(b*sec(e+f*x))^(1/2)*log(a^(1/2)+a^(1/2)*tan(e+f*x)+-1*2^(1/2)*b^(1/2)*(a*sin(e+f*x))^(1/2)*(b*cos(e+f*x))^-1//2))
@test integrate((a*sin(e+f*x))^5//2*(b*sec(e+f*x))^(1/2), x) == :(-1//2*a*b*f^-1*(a*sin(e+f*x))^3//2*(b*sec(e+f*x))^-1//2+-3//8*2^(1/2)*a^5//2*b^-1//2*f^-1*(b*cos(e+f*x))^(1/2)*(b*sec(e+f*x))^(1/2)*arctan(1+-1*2^(1/2)*a^-1//2*b^(1/2)*(a*sin(e+f*x))^(1/2)*(b*cos(e+f*x))^-1//2)+-3//16*2^(1/2)*a^5//2*b^-1//2*f^-1*(b*cos(e+f*x))^(1/2)*(b*sec(e+f*x))^(1/2)*log(a^(1/2)+a^(1/2)*tan(e+f*x)+2^(1/2)*b^(1/2)*(a*sin(e+f*x))^(1/2)*(b*cos(e+f*x))^-1//2)+3//8*2^(1/2)*a^5//2*b^-1//2*f^-1*(b*cos(e+f*x))^(1/2)*(b*sec(e+f*x))^(1/2)*arctan(1+2^(1/2)*a^-1//2*b^(1/2)*(a*sin(e+f*x))^(1/2)*(b*cos(e+f*x))^-1//2)+3//16*2^(1/2)*a^5//2*b^-1//2*f^-1*(b*cos(e+f*x))^(1/2)*(b*sec(e+f*x))^(1/2)*log(a^(1/2)+a^(1/2)*tan(e+f*x)+-1*2^(1/2)*b^(1/2)*(a*sin(e+f*x))^(1/2)*(b*cos(e+f*x))^-1//2))
@test integrate((a*sin(e+f*x))^(1/2)*(b*sec(e+f*x))^(1/2), x) == :((1/2)*2^(1/2)*a^(1/2)*b^-1//2*f^-1*(b*cos(e+f*x))^(1/2)*(b*sec(e+f*x))^(1/2)*arctan(1+2^(1/2)*a^-1//2*b^(1/2)*(a*sin(e+f*x))^(1/2)*(b*cos(e+f*x))^-1//2)+-1//2*2^(1/2)*a^(1/2)*b^-1//2*f^-1*(b*cos(e+f*x))^(1/2)*(b*sec(e+f*x))^(1/2)*arctan(1+-1*2^(1/2)*a^-1//2*b^(1/2)*(a*sin(e+f*x))^(1/2)*(b*cos(e+f*x))^-1//2)+-1//4*2^(1/2)*a^(1/2)*b^-1//2*f^-1*(b*cos(e+f*x))^(1/2)*(b*sec(e+f*x))^(1/2)*log(a^(1/2)+a^(1/2)*tan(e+f*x)+2^(1/2)*b^(1/2)*(a*sin(e+f*x))^(1/2)*(b*cos(e+f*x))^-1//2)+1//4*2^(1/2)*a^(1/2)*b^-1//2*f^-1*(b*cos(e+f*x))^(1/2)*(b*sec(e+f*x))^(1/2)*log(a^(1/2)+a^(1/2)*tan(e+f*x)+-1*2^(1/2)*b^(1/2)*(a*sin(e+f*x))^(1/2)*(b*cos(e+f*x))^-1//2))
@test integrate((a*sin(e+f*x))^-3//2*(b*sec(e+f*x))^(1/2), x) == :(-2*b*a^-1*f^-1*(a*sin(e+f*x))^-1//2*(b*sec(e+f*x))^-1//2)
@test integrate((a*sin(e+f*x))^-7//2*(b*sec(e+f*x))^(1/2), x) == :(-8//5*b*a^-3*f^-1*(a*sin(e+f*x))^-1//2*(b*sec(e+f*x))^-1//2+-2//5*b*a^-1*f^-1*(a*sin(e+f*x))^-5//2*(b*sec(e+f*x))^-1//2)
@test integrate((a*sin(e+f*x))^-11//2*(b*sec(e+f*x))^(1/2), x) == :(-64//45*b*a^-5*f^-1*(a*sin(e+f*x))^-1//2*(b*sec(e+f*x))^-1//2+-16//45*b*a^-3*f^-1*(a*sin(e+f*x))^-5//2*(b*sec(e+f*x))^-1//2+-2//9*b*a^-1*f^-1*(a*sin(e+f*x))^-9//2*(b*sec(e+f*x))^-1//2)
@test integrate((a*sin(e+f*x))^7//2*(b*sec(e+f*x))^(1/2), x) == :(-5//6*b*a^3*f^-1*(a*sin(e+f*x))^(1/2)*(b*sec(e+f*x))^-1//2+-1//3*a*b*f^-1*(a*sin(e+f*x))^5//2*(b*sec(e+f*x))^-1//2+5//12*a^4*f^-1*(a*sin(e+f*x))^-1//2*(b*sec(e+f*x))^(1/2)*sin(2*e+2*f*x)^(1/2)*Elliptic.F(e+-1//4*pi+f*x,2))
@test integrate((a*sin(e+f*x))^3//2*(b*sec(e+f*x))^(1/2), x) == :(-1*a*b*f^-1*(a*sin(e+f*x))^(1/2)*(b*sec(e+f*x))^-1//2+(1/2)*a^2*f^-1*(a*sin(e+f*x))^-1//2*(b*sec(e+f*x))^(1/2)*sin(2*e+2*f*x)^(1/2)*Elliptic.F(e+-1//4*pi+f*x,2))
@test integrate((a*sin(e+f*x))^-1//2*(b*sec(e+f*x))^(1/2), x) == :(f^-1*(a*sin(e+f*x))^-1//2*(b*sec(e+f*x))^(1/2)*sin(2*e+2*f*x)^(1/2)*Elliptic.F(e+-1//4*pi+f*x,2))
@test integrate((a*sin(e+f*x))^-5//2*(b*sec(e+f*x))^(1/2), x) == :(-2//3*b*a^-1*f^-1*(a*sin(e+f*x))^-3//2*(b*sec(e+f*x))^-1//2+2//3*a^-2*f^-1*(a*sin(e+f*x))^-1//2*(b*sec(e+f*x))^(1/2)*sin(2*e+2*f*x)^(1/2)*Elliptic.F(e+-1//4*pi+f*x,2))
@test integrate((a*sin(e+f*x))^-9//2*(b*sec(e+f*x))^(1/2), x) == :(-4//7*b*a^-3*f^-1*(a*sin(e+f*x))^-3//2*(b*sec(e+f*x))^-1//2+-2//7*b*a^-1*f^-1*(a*sin(e+f*x))^-7//2*(b*sec(e+f*x))^-1//2+4//7*a^-4*f^-1*(a*sin(e+f*x))^-1//2*(b*sec(e+f*x))^(1/2)*sin(2*e+2*f*x)^(1/2)*Elliptic.F(e+-1//4*pi+f*x,2))
@test integrate((b*sec(e+f*x))^-1//2*sin(e+f*x)^9//2, x) == :(-7//30*b*f^-1*(b*sec(e+f*x))^-3//2*sin(e+f*x)^3//2+-1//5*b*f^-1*(b*sec(e+f*x))^-3//2*sin(e+f*x)^7//2+7//20*f^-1*(b*sec(e+f*x))^-1//2*sin(e+f*x)^(1/2)*sin(2*e+2*f*x)^-1//2*Elliptic.E(e+-1//4*pi+f*x,2))
@test integrate((b*sec(e+f*x))^-1//2*sin(e+f*x)^5//2, x) == :(-1//3*b*f^-1*(b*sec(e+f*x))^-3//2*sin(e+f*x)^3//2+(1/2)*f^-1*(b*sec(e+f*x))^-1//2*sin(e+f*x)^(1/2)*sin(2*e+2*f*x)^-1//2*Elliptic.E(e+-1//4*pi+f*x,2))
@test integrate((b*sec(e+f*x))^-1//2*sin(e+f*x)^(1/2), x) == :(f^-1*(b*sec(e+f*x))^-1//2*sin(e+f*x)^(1/2)*sin(2*e+2*f*x)^-1//2*Elliptic.E(e+-1//4*pi+f*x,2))
@test integrate((b*sec(e+f*x))^-1//2*sin(e+f*x)^-3//2, x) == :(-2*b*f^-1*(b*sec(e+f*x))^-3//2*sin(e+f*x)^-1//2+-2*f^-1*(b*sec(e+f*x))^-1//2*sin(e+f*x)^(1/2)*sin(2*e+2*f*x)^-1//2*Elliptic.E(e+-1//4*pi+f*x,2))
@test integrate((b*sec(e+f*x))^-1//2*sin(e+f*x)^-7//2, x) == :(-4//5*b*f^-1*(b*sec(e+f*x))^-3//2*sin(e+f*x)^-1//2+-2//5*b*f^-1*(b*sec(e+f*x))^-3//2*sin(e+f*x)^-5//2+-4//5*f^-1*(b*sec(e+f*x))^-1//2*sin(e+f*x)^(1/2)*sin(2*e+2*f*x)^-1//2*Elliptic.E(e+-1//4*pi+f*x,2))
@test integrate((b*sec(e+f*x))^-1//2*sin(e+f*x)^3//2, x) == :(-1//2*b*f^-1*(b*sec(e+f*x))^-3//2*sin(e+f*x)^(1/2)+-1//8*2^(1/2)*b^(1/2)*f^-1*(b*cos(e+f*x))^-1//2*(b*sec(e+f*x))^-1//2*arctan(1+2^(1/2)*b^-1//2*(b*cos(e+f*x))^(1/2)*sin(e+f*x)^-1//2)+-1//16*2^(1/2)*b^(1/2)*f^-1*(b*cos(e+f*x))^-1//2*(b*sec(e+f*x))^-1//2*log(b^(1/2)+b^(1/2)*cot(e+f*x)+-1*2^(1/2)*(b*cos(e+f*x))^(1/2)*sin(e+f*x)^-1//2)+1//8*2^(1/2)*b^(1/2)*f^-1*(b*cos(e+f*x))^-1//2*(b*sec(e+f*x))^-1//2*arctan(1+-1*2^(1/2)*b^-1//2*(b*cos(e+f*x))^(1/2)*sin(e+f*x)^-1//2)+1//16*2^(1/2)*b^(1/2)*f^-1*(b*cos(e+f*x))^-1//2*(b*sec(e+f*x))^-1//2*log(b^(1/2)+b^(1/2)*cot(e+f*x)+2^(1/2)*(b*cos(e+f*x))^(1/2)*sin(e+f*x)^-1//2))
@test integrate((b*sec(e+f*x))^-1//2*sin(e+f*x)^-1//2, x) == :((1/2)*2^(1/2)*b^(1/2)*f^-1*(b*cos(e+f*x))^-1//2*(b*sec(e+f*x))^-1//2*arctan(1+-1*2^(1/2)*b^-1//2*(b*cos(e+f*x))^(1/2)*sin(e+f*x)^-1//2)+-1//2*2^(1/2)*b^(1/2)*f^-1*(b*cos(e+f*x))^-1//2*(b*sec(e+f*x))^-1//2*arctan(1+2^(1/2)*b^-1//2*(b*cos(e+f*x))^(1/2)*sin(e+f*x)^-1//2)+-1//4*2^(1/2)*b^(1/2)*f^-1*(b*cos(e+f*x))^-1//2*(b*sec(e+f*x))^-1//2*log(b^(1/2)+b^(1/2)*cot(e+f*x)+-1*2^(1/2)*(b*cos(e+f*x))^(1/2)*sin(e+f*x)^-1//2)+1//4*2^(1/2)*b^(1/2)*f^-1*(b*cos(e+f*x))^-1//2*(b*sec(e+f*x))^-1//2*log(b^(1/2)+b^(1/2)*cot(e+f*x)+2^(1/2)*(b*cos(e+f*x))^(1/2)*sin(e+f*x)^-1//2))
@test integrate((b*sec(e+f*x))^-1//2*sin(e+f*x)^-5//2, x) == :(-2//3*b*f^-1*(b*sec(e+f*x))^-3//2*sin(e+f*x)^-3//2)
@test integrate((b*sec(e+f*x))^-1//2*sin(e+f*x)^-9//2, x) == :(-8//21*b*f^-1*(b*sec(e+f*x))^-3//2*sin(e+f*x)^-3//2+-2//7*b*f^-1*(b*sec(e+f*x))^-3//2*sin(e+f*x)^-7//2)
@test integrate((b*sec(e+f*x))^-1//2*sin(e+f*x)^-13//2, x) == :(-64//231*b*f^-1*(b*sec(e+f*x))^-3//2*sin(e+f*x)^-3//2+-16//77*b*f^-1*(b*sec(e+f*x))^-3//2*sin(e+f*x)^-7//2+-2//11*b*f^-1*(b*sec(e+f*x))^-3//2*sin(e+f*x)^-11//2)
@test integrate((b*sec(e+f*x))^-1//2*sin(e+f*x)^-17//2, x) == :(-256//1155*b*f^-1*(b*sec(e+f*x))^-3//2*sin(e+f*x)^-3//2+-64//385*b*f^-1*(b*sec(e+f*x))^-3//2*sin(e+f*x)^-7//2+-8//55*b*f^-1*(b*sec(e+f*x))^-3//2*sin(e+f*x)^-11//2+-2//15*b*f^-1*(b*sec(e+f*x))^-3//2*sin(e+f*x)^-15//2)
@test integrate((a*sin(e+f*x))^9//2*(b*sec(e+f*x))^-3//2, x) == :(-7//192*a^3*b^-1*f^-1*(a*sin(e+f*x))^3//2*(b*sec(e+f*x))^-1//2+-1//48*a*b^-1*f^-1*(a*sin(e+f*x))^7//2*(b*sec(e+f*x))^-1//2+1//6*a^-1*b^-1*f^-1*(a*sin(e+f*x))^11//2*(b*sec(e+f*x))^-1//2+-7//256*2^(1/2)*a^9//2*b^-5//2*f^-1*(b*cos(e+f*x))^(1/2)*(b*sec(e+f*x))^(1/2)*arctan(1+-1*2^(1/2)*a^-1//2*b^(1/2)*(a*sin(e+f*x))^(1/2)*(b*cos(e+f*x))^-1//2)+-7//512*2^(1/2)*a^9//2*b^-5//2*f^-1*(b*cos(e+f*x))^(1/2)*(b*sec(e+f*x))^(1/2)*log(a^(1/2)+a^(1/2)*tan(e+f*x)+2^(1/2)*b^(1/2)*(a*sin(e+f*x))^(1/2)*(b*cos(e+f*x))^-1//2)+7//256*2^(1/2)*a^9//2*b^-5//2*f^-1*(b*cos(e+f*x))^(1/2)*(b*sec(e+f*x))^(1/2)*arctan(1+2^(1/2)*a^-1//2*b^(1/2)*(a*sin(e+f*x))^(1/2)*(b*cos(e+f*x))^-1//2)+7//512*2^(1/2)*a^9//2*b^-5//2*f^-1*(b*cos(e+f*x))^(1/2)*(b*sec(e+f*x))^(1/2)*log(a^(1/2)+a^(1/2)*tan(e+f*x)+-1*2^(1/2)*b^(1/2)*(a*sin(e+f*x))^(1/2)*(b*cos(e+f*x))^-1//2))
@test integrate((a*sin(e+f*x))^5//2*(b*sec(e+f*x))^-3//2, x) == :(-1//16*a*b^-1*f^-1*(a*sin(e+f*x))^3//2*(b*sec(e+f*x))^-1//2+1//4*a^-1*b^-1*f^-1*(a*sin(e+f*x))^7//2*(b*sec(e+f*x))^-1//2+-3//64*2^(1/2)*a^5//2*b^-5//2*f^-1*(b*cos(e+f*x))^(1/2)*(b*sec(e+f*x))^(1/2)*arctan(1+-1*2^(1/2)*a^-1//2*b^(1/2)*(a*sin(e+f*x))^(1/2)*(b*cos(e+f*x))^-1//2)+-3//128*2^(1/2)*a^5//2*b^-5//2*f^-1*(b*cos(e+f*x))^(1/2)*(b*sec(e+f*x))^(1/2)*log(a^(1/2)+a^(1/2)*tan(e+f*x)+2^(1/2)*b^(1/2)*(a*sin(e+f*x))^(1/2)*(b*cos(e+f*x))^-1//2)+3//64*2^(1/2)*a^5//2*b^-5//2*f^-1*(b*cos(e+f*x))^(1/2)*(b*sec(e+f*x))^(1/2)*arctan(1+2^(1/2)*a^-1//2*b^(1/2)*(a*sin(e+f*x))^(1/2)*(b*cos(e+f*x))^-1//2)+3//128*2^(1/2)*a^5//2*b^-5//2*f^-1*(b*cos(e+f*x))^(1/2)*(b*sec(e+f*x))^(1/2)*log(a^(1/2)+a^(1/2)*tan(e+f*x)+-1*2^(1/2)*b^(1/2)*(a*sin(e+f*x))^(1/2)*(b*cos(e+f*x))^-1//2))
@test integrate((a*sin(e+f*x))^(1/2)*(b*sec(e+f*x))^-3//2, x) == :((1/2)*a^-1*b^-1*f^-1*(a*sin(e+f*x))^3//2*(b*sec(e+f*x))^-1//2+-1//8*2^(1/2)*a^(1/2)*b^-5//2*f^-1*(b*cos(e+f*x))^(1/2)*(b*sec(e+f*x))^(1/2)*arctan(1+-1*2^(1/2)*a^-1//2*b^(1/2)*(a*sin(e+f*x))^(1/2)*(b*cos(e+f*x))^-1//2)+-1//16*2^(1/2)*a^(1/2)*b^-5//2*f^-1*(b*cos(e+f*x))^(1/2)*(b*sec(e+f*x))^(1/2)*log(a^(1/2)+a^(1/2)*tan(e+f*x)+2^(1/2)*b^(1/2)*(a*sin(e+f*x))^(1/2)*(b*cos(e+f*x))^-1//2)+1//8*2^(1/2)*a^(1/2)*b^-5//2*f^-1*(b*cos(e+f*x))^(1/2)*(b*sec(e+f*x))^(1/2)*arctan(1+2^(1/2)*a^-1//2*b^(1/2)*(a*sin(e+f*x))^(1/2)*(b*cos(e+f*x))^-1//2)+1//16*2^(1/2)*a^(1/2)*b^-5//2*f^-1*(b*cos(e+f*x))^(1/2)*(b*sec(e+f*x))^(1/2)*log(a^(1/2)+a^(1/2)*tan(e+f*x)+-1*2^(1/2)*b^(1/2)*(a*sin(e+f*x))^(1/2)*(b*cos(e+f*x))^-1//2))
@test integrate((a*sin(e+f*x))^-3//2*(b*sec(e+f*x))^-3//2, x) == :(-2*a^-1*b^-1*f^-1*(a*sin(e+f*x))^-1//2*(b*sec(e+f*x))^-1//2+(1/2)*2^(1/2)*a^-3//2*b^-5//2*f^-1*(b*cos(e+f*x))^(1/2)*(b*sec(e+f*x))^(1/2)*arctan(1+-1*2^(1/2)*a^-1//2*b^(1/2)*(a*sin(e+f*x))^(1/2)*(b*cos(e+f*x))^-1//2)+-1//2*2^(1/2)*a^-3//2*b^-5//2*f^-1*(b*cos(e+f*x))^(1/2)*(b*sec(e+f*x))^(1/2)*arctan(1+2^(1/2)*a^-1//2*b^(1/2)*(a*sin(e+f*x))^(1/2)*(b*cos(e+f*x))^-1//2)+-1//4*2^(1/2)*a^-3//2*b^-5//2*f^-1*(b*cos(e+f*x))^(1/2)*(b*sec(e+f*x))^(1/2)*log(a^(1/2)+a^(1/2)*tan(e+f*x)+-1*2^(1/2)*b^(1/2)*(a*sin(e+f*x))^(1/2)*(b*cos(e+f*x))^-1//2)+1//4*2^(1/2)*a^-3//2*b^-5//2*f^-1*(b*cos(e+f*x))^(1/2)*(b*sec(e+f*x))^(1/2)*log(a^(1/2)+a^(1/2)*tan(e+f*x)+2^(1/2)*b^(1/2)*(a*sin(e+f*x))^(1/2)*(b*cos(e+f*x))^-1//2))
@test integrate((a*sin(e+f*x))^-7//2*(b*sec(e+f*x))^-3//2, x) == :(-2//5*b*a^-1*f^-1*(a*sin(e+f*x))^-5//2*(b*sec(e+f*x))^-5//2)
@test integrate((a*sin(e+f*x))^7//2*(b*sec(e+f*x))^-3//2, x) == :(-1//12*a^3*b^-1*f^-1*(a*sin(e+f*x))^(1/2)*(b*sec(e+f*x))^-1//2+-1//30*a*b^-1*f^-1*(a*sin(e+f*x))^5//2*(b*sec(e+f*x))^-1//2+1//5*a^-1*b^-1*f^-1*(a*sin(e+f*x))^9//2*(b*sec(e+f*x))^-1//2+1//24*a^4*b^-2*f^-1*(a*sin(e+f*x))^-1//2*(b*sec(e+f*x))^(1/2)*sin(2*e+2*f*x)^(1/2)*Elliptic.F(e+-1//4*pi+f*x,2))
@test integrate((a*sin(e+f*x))^3//2*(b*sec(e+f*x))^-3//2, x) == :(-1//6*a*b^-1*f^-1*(a*sin(e+f*x))^(1/2)*(b*sec(e+f*x))^-1//2+1//3*a^-1*b^-1*f^-1*(a*sin(e+f*x))^5//2*(b*sec(e+f*x))^-1//2+1//12*a^2*b^-2*f^-1*(a*sin(e+f*x))^-1//2*(b*sec(e+f*x))^(1/2)*sin(2*e+2*f*x)^(1/2)*Elliptic.F(e+-1//4*pi+f*x,2))
@test integrate((a*sin(e+f*x))^-1//2*(b*sec(e+f*x))^-3//2, x) == :(a^-1*b^-1*f^-1*(a*sin(e+f*x))^(1/2)*(b*sec(e+f*x))^-1//2+(1/2)*b^-2*f^-1*(a*sin(e+f*x))^-1//2*(b*sec(e+f*x))^(1/2)*sin(2*e+2*f*x)^(1/2)*Elliptic.F(e+-1//4*pi+f*x,2))
@test integrate((a*sin(e+f*x))^-5//2*(b*sec(e+f*x))^-3//2, x) == :(-2//3*a^-1*b^-1*f^-1*(a*sin(e+f*x))^-3//2*(b*sec(e+f*x))^-1//2+-1//3*a^-2*b^-2*f^-1*(a*sin(e+f*x))^-1//2*(b*sec(e+f*x))^(1/2)*sin(2*e+2*f*x)^(1/2)*Elliptic.F(e+-1//4*pi+f*x,2))
@test integrate((a*sin(e+f*x))^-9//2*(b*sec(e+f*x))^-3//2, x) == :(-2//7*a^-1*b^-1*f^-1*(a*sin(e+f*x))^-7//2*(b*sec(e+f*x))^-1//2+2//21*a^-3*b^-1*f^-1*(a*sin(e+f*x))^-3//2*(b*sec(e+f*x))^-1//2+-2//21*a^-4*b^-2*f^-1*(a*sin(e+f*x))^-1//2*(b*sec(e+f*x))^(1/2)*sin(2*e+2*f*x)^(1/2)*Elliptic.F(e+-1//4*pi+f*x,2))
@test integrate((a*sin(e+f*x))^-13//2*(b*sec(e+f*x))^-3//2, x) == :(-2//11*a^-1*b^-1*f^-1*(a*sin(e+f*x))^-11//2*(b*sec(e+f*x))^-1//2+2//77*a^-3*b^-1*f^-1*(a*sin(e+f*x))^-7//2*(b*sec(e+f*x))^-1//2+4//77*a^-5*b^-1*f^-1*(a*sin(e+f*x))^-3//2*(b*sec(e+f*x))^-1//2+-4//77*a^-6*b^-2*f^-1*(a*sin(e+f*x))^-1//2*(b*sec(e+f*x))^(1/2)*sin(2*e+2*f*x)^(1/2)*Elliptic.F(e+-1//4*pi+f*x,2))
@test integrate((b*sec(e+f*x))^n*sin(e+f*x)^5, x) == :(-1*b*f^-1*(b*sec(e+f*x))^(-1+n)*(1+-1n)^-1+-1*b^5*f^-1*(b*sec(e+f*x))^(-5+n)*(5+-1n)^-1+2*b^3*f^-1*(b*sec(e+f*x))^(-3+n)*(3+-1n)^-1)
@test integrate((b*sec(e+f*x))^n*sin(e+f*x)^3, x) == :(b^3*f^-1*(b*sec(e+f*x))^(-3+n)*(3+-1n)^-1+-1*b*f^-1*(b*sec(e+f*x))^(-1+n)*(1+-1n)^-1)
@test integrate((b*sec(e+f*x))^n*sin(e+f*x), x) == :(-1*b*f^-1*(b*sec(e+f*x))^(-1+n)*(1+-1n)^-1)
@test integrate((d*csc(e+f*x))^(1/2)*sin(e+f*x)^4, x) == :(-10//21*d*f^-1*(d*csc(e+f*x))^-1//2*cos(e+f*x)+-2//7*d^3*f^-1*(d*csc(e+f*x))^-5//2*cos(e+f*x)+10//21*f^-1*(d*csc(e+f*x))^(1/2)*sin(e+f*x)^(1/2)*Elliptic.F((1/2)*e+-1//4*pi+(1/2)*f*x,2))
@test integrate((d*csc(e+f*x))^(1/2)*sin(e+f*x)^3, x) == :(-2//5*d^2*f^-1*(d*csc(e+f*x))^-3//2*cos(e+f*x)+6//5*d*f^-1*(d*csc(e+f*x))^-1//2*sin(e+f*x)^-1//2*Elliptic.E((1/2)*e+-1//4*pi+(1/2)*f*x,2))
@test integrate((d*csc(e+f*x))^(1/2)*sin(e+f*x)^2, x) == :(-2//3*d*f^-1*(d*csc(e+f*x))^-1//2*cos(e+f*x)+2//3*f^-1*(d*csc(e+f*x))^(1/2)*sin(e+f*x)^(1/2)*Elliptic.F((1/2)*e+-1//4*pi+(1/2)*f*x,2))
@test integrate((d*csc(e+f*x))^(1/2)*sin(e+f*x), x) == :(2*d*f^-1*(d*csc(e+f*x))^-1//2*sin(e+f*x)^-1//2*Elliptic.E((1/2)*e+-1//4*pi+(1/2)*f*x,2))
@test integrate((d*csc(e+f*x))^(1/2), x) == :(2*f^-1*(d*csc(e+f*x))^(1/2)*sin(e+f*x)^(1/2)*Elliptic.F((1/2)*e+-1//4*pi+(1/2)*f*x,2))
@test integrate((d*csc(e+f*x))^(1/2)*csc(e+f*x), x) == :(-2*f^-1*(d*csc(e+f*x))^(1/2)*cos(e+f*x)+-2*d*f^-1*(d*csc(e+f*x))^-1//2*sin(e+f*x)^-1//2*Elliptic.E((1/2)*e+-1//4*pi+(1/2)*f*x,2))
@test integrate((d*csc(e+f*x))^(1/2)*csc(e+f*x)^2, x) == :(-2//3*d^-1*f^-1*(d*csc(e+f*x))^3//2*cos(e+f*x)+2//3*f^-1*(d*csc(e+f*x))^(1/2)*sin(e+f*x)^(1/2)*Elliptic.F((1/2)*e+-1//4*pi+(1/2)*f*x,2))
@test integrate((d*csc(e+f*x))^(1/2)*csc(e+f*x)^3, x) == :(-6//5*f^-1*(d*csc(e+f*x))^(1/2)*cos(e+f*x)+-2//5*d^-2*f^-1*(d*csc(e+f*x))^5//2*cos(e+f*x)+-6//5*d*f^-1*(d*csc(e+f*x))^-1//2*sin(e+f*x)^-1//2*Elliptic.E((1/2)*e+-1//4*pi+(1/2)*f*x,2))
@test integrate((d*csc(e+f*x))^3//2*sin(e+f*x)^5, x) == :(-10//21*d^2*f^-1*(d*csc(e+f*x))^-1//2*cos(e+f*x)+-2//7*d^4*f^-1*(d*csc(e+f*x))^-5//2*cos(e+f*x)+10//21*d*f^-1*(d*csc(e+f*x))^(1/2)*sin(e+f*x)^(1/2)*Elliptic.F((1/2)*e+-1//4*pi+(1/2)*f*x,2))
@test integrate((d*csc(e+f*x))^3//2*sin(e+f*x)^4, x) == :(-2//5*d^3*f^-1*(d*csc(e+f*x))^-3//2*cos(e+f*x)+6//5*d^2*f^-1*(d*csc(e+f*x))^-1//2*sin(e+f*x)^-1//2*Elliptic.E((1/2)*e+-1//4*pi+(1/2)*f*x,2))
@test integrate((d*csc(e+f*x))^3//2*sin(e+f*x)^3, x) == :(-2//3*d^2*f^-1*(d*csc(e+f*x))^-1//2*cos(e+f*x)+2//3*d*f^-1*(d*csc(e+f*x))^(1/2)*sin(e+f*x)^(1/2)*Elliptic.F((1/2)*e+-1//4*pi+(1/2)*f*x,2))
@test integrate((d*csc(e+f*x))^3//2*sin(e+f*x)^2, x) == :(2*d^2*f^-1*(d*csc(e+f*x))^-1//2*sin(e+f*x)^-1//2*Elliptic.E((1/2)*e+-1//4*pi+(1/2)*f*x,2))
@test integrate((d*csc(e+f*x))^3//2*sin(e+f*x), x) == :(2*d*f^-1*(d*csc(e+f*x))^(1/2)*sin(e+f*x)^(1/2)*Elliptic.F((1/2)*e+-1//4*pi+(1/2)*f*x,2))
@test integrate((d*csc(e+f*x))^3//2, x) == :(-2*d*f^-1*(d*csc(e+f*x))^(1/2)*cos(e+f*x)+-2*d^2*f^-1*(d*csc(e+f*x))^-1//2*sin(e+f*x)^-1//2*Elliptic.E((1/2)*e+-1//4*pi+(1/2)*f*x,2))
@test integrate((d*csc(e+f*x))^3//2*csc(e+f*x), x) == :(-2//3*f^-1*(d*csc(e+f*x))^3//2*cos(e+f*x)+2//3*d*f^-1*(d*csc(e+f*x))^(1/2)*sin(e+f*x)^(1/2)*Elliptic.F((1/2)*e+-1//4*pi+(1/2)*f*x,2))
@test integrate((d*csc(e+f*x))^3//2*csc(e+f*x)^2, x) == :(-6//5*d*f^-1*(d*csc(e+f*x))^(1/2)*cos(e+f*x)+-2//5*d^-1*f^-1*(d*csc(e+f*x))^5//2*cos(e+f*x)+-6//5*d^2*f^-1*(d*csc(e+f*x))^-1//2*sin(e+f*x)^-1//2*Elliptic.E((1/2)*e+-1//4*pi+(1/2)*f*x,2))
@test integrate((d*csc(e+f*x))^-1//2*sin(e+f*x)^3, x) == :(-10//21*f^-1*(d*csc(e+f*x))^-1//2*cos(e+f*x)+-2//7*d^2*f^-1*(d*csc(e+f*x))^-5//2*cos(e+f*x)+10//21*d^-1*f^-1*(d*csc(e+f*x))^(1/2)*sin(e+f*x)^(1/2)*Elliptic.F((1/2)*e+-1//4*pi+(1/2)*f*x,2))
@test integrate((d*csc(e+f*x))^-1//2*sin(e+f*x)^2, x) == :(-2//5*d*f^-1*(d*csc(e+f*x))^-3//2*cos(e+f*x)+6//5*f^-1*(d*csc(e+f*x))^-1//2*sin(e+f*x)^-1//2*Elliptic.E((1/2)*e+-1//4*pi+(1/2)*f*x,2))
@test integrate((d*csc(e+f*x))^-1//2*sin(e+f*x), x) == :(-2//3*f^-1*(d*csc(e+f*x))^-1//2*cos(e+f*x)+2//3*d^-1*f^-1*(d*csc(e+f*x))^(1/2)*sin(e+f*x)^(1/2)*Elliptic.F((1/2)*e+-1//4*pi+(1/2)*f*x,2))
@test integrate((d*csc(e+f*x))^-1//2, x) == :(2*f^-1*(d*csc(e+f*x))^-1//2*sin(e+f*x)^-1//2*Elliptic.E((1/2)*e+-1//4*pi+(1/2)*f*x,2))
@test integrate((d*csc(e+f*x))^-1//2*csc(e+f*x), x) == :(2*d^-1*f^-1*(d*csc(e+f*x))^(1/2)*sin(e+f*x)^(1/2)*Elliptic.F((1/2)*e+-1//4*pi+(1/2)*f*x,2))
@test integrate((d*csc(e+f*x))^-1//2*csc(e+f*x)^2, x) == :(-2*d^-1*f^-1*(d*csc(e+f*x))^(1/2)*cos(e+f*x)+-2*f^-1*(d*csc(e+f*x))^-1//2*sin(e+f*x)^-1//2*Elliptic.E((1/2)*e+-1//4*pi+(1/2)*f*x,2))
@test integrate((d*csc(e+f*x))^-1//2*csc(e+f*x)^3, x) == :(-2//3*d^-2*f^-1*(d*csc(e+f*x))^3//2*cos(e+f*x)+2//3*d^-1*f^-1*(d*csc(e+f*x))^(1/2)*sin(e+f*x)^(1/2)*Elliptic.F((1/2)*e+-1//4*pi+(1/2)*f*x,2))
@test integrate((d*csc(e+f*x))^-3//2*sin(e+f*x)^2, x) == :(-10//21*d^-1*f^-1*(d*csc(e+f*x))^-1//2*cos(e+f*x)+-2//7*d*f^-1*(d*csc(e+f*x))^-5//2*cos(e+f*x)+10//21*d^-2*f^-1*(d*csc(e+f*x))^(1/2)*sin(e+f*x)^(1/2)*Elliptic.F((1/2)*e+-1//4*pi+(1/2)*f*x,2))
@test integrate((d*csc(e+f*x))^-3//2*sin(e+f*x), x) == :(-2//5*f^-1*(d*csc(e+f*x))^-3//2*cos(e+f*x)+6//5*d^-1*f^-1*(d*csc(e+f*x))^-1//2*sin(e+f*x)^-1//2*Elliptic.E((1/2)*e+-1//4*pi+(1/2)*f*x,2))
@test integrate((d*csc(e+f*x))^-3//2, x) == :(-2//3*d^-1*f^-1*(d*csc(e+f*x))^-1//2*cos(e+f*x)+2//3*d^-2*f^-1*(d*csc(e+f*x))^(1/2)*sin(e+f*x)^(1/2)*Elliptic.F((1/2)*e+-1//4*pi+(1/2)*f*x,2))
@test integrate((d*csc(e+f*x))^-3//2*csc(e+f*x), x) == :(2*d^-1*f^-1*(d*csc(e+f*x))^-1//2*sin(e+f*x)^-1//2*Elliptic.E((1/2)*e+-1//4*pi+(1/2)*f*x,2))
@test integrate((d*csc(e+f*x))^-3//2*csc(e+f*x)^2, x) == :(2*d^-2*f^-1*(d*csc(e+f*x))^(1/2)*sin(e+f*x)^(1/2)*Elliptic.F((1/2)*e+-1//4*pi+(1/2)*f*x,2))
@test integrate((d*csc(e+f*x))^-3//2*csc(e+f*x)^3, x) == :(-2*d^-2*f^-1*(d*csc(e+f*x))^(1/2)*cos(e+f*x)+-2*d^-1*f^-1*(d*csc(e+f*x))^-1//2*sin(e+f*x)^-1//2*Elliptic.E((1/2)*e+-1//4*pi+(1/2)*f*x,2))
@test integrate((d*csc(e+f*x))^-3//2*csc(e+f*x)^4, x) == :(-2//3*d^-3*f^-1*(d*csc(e+f*x))^3//2*cos(e+f*x)+2//3*d^-2*f^-1*(d*csc(e+f*x))^(1/2)*sin(e+f*x)^(1/2)*Elliptic.F((1/2)*e+-1//4*pi+(1/2)*f*x,2))
@test integrate((d*csc(e+f*x))^-3//2*csc(e+f*x)^5, x) == :(-6//5*d^-2*f^-1*(d*csc(e+f*x))^(1/2)*cos(e+f*x)+-2//5*d^-4*f^-1*(d*csc(e+f*x))^5//2*cos(e+f*x)+-6//5*d^-1*f^-1*(d*csc(e+f*x))^-1//2*sin(e+f*x)^-1//2*Elliptic.E((1/2)*e+-1//4*pi+(1/2)*f*x,2))

max_stars_repo_path: test/4 Trig functions/4.1 Sine/4.1.0 (a sin)^m (b trg)^n.jl