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

@test integrate((b*x)^p*(c*x)^m, x) == :(b^-1*(b*x)^(1+p)*(c*x)^m*(1+m+p)^-1)
@test integrate(x^3*(b*x^2)^(1/2), x) == :(1//5*x^4*(b*x^2)^(1/2))
@test integrate(x^2*(b*x^2)^(1/2), x) == :(1//4*x^3*(b*x^2)^(1/2))
@test integrate(x*(b*x^2)^(1/2), x) == :(1//3*x^2*(b*x^2)^(1/2))
@test integrate((b*x^2)^(1/2), x) == :((1/2)*x*(b*x^2)^(1/2))
@test integrate(x^-1*(b*x^2)^(1/2), x) == :((b*x^2)^(1/2))
@test integrate(x^-2*(b*x^2)^(1/2), x) == :(x^-1*(b*x^2)^(1/2)*log(x))
@test integrate(x^-3*(b*x^2)^(1/2), x) == :(-1*x^-2*(b*x^2)^(1/2))
@test integrate(x^-4*(b*x^2)^(1/2), x) == :(-1//2*x^-3*(b*x^2)^(1/2))
@test integrate(x^-5*(b*x^2)^(1/2), x) == :(-1//3*x^-4*(b*x^2)^(1/2))
@test integrate(x^2*(x^2)^(1/2), x) == :(1//4*x^3*(x^2)^(1/2))
@test integrate(x^2*(b*x^2)^3//2, x) == :(1//6*b*x^5*(b*x^2)^(1/2))
@test integrate(x*(b*x^2)^3//2, x) == :(1//5*b*x^4*(b*x^2)^(1/2))
@test integrate((b*x^2)^3//2, x) == :(1//4*b*x^3*(b*x^2)^(1/2))
@test integrate(x^-1*(b*x^2)^3//2, x) == :(1//3*b*x^2*(b*x^2)^(1/2))
@test integrate(x^-2*(b*x^2)^3//2, x) == :((1/2)*b*x*(b*x^2)^(1/2))
@test integrate(x^-3*(b*x^2)^3//2, x) == :(b*(b*x^2)^(1/2))
@test integrate(x^-4*(b*x^2)^3//2, x) == :(b*x^-1*(b*x^2)^(1/2)*log(x))
@test integrate(x^-5*(b*x^2)^3//2, x) == :(-1*b*x^-2*(b*x^2)^(1/2))
@test integrate(x^-6*(b*x^2)^3//2, x) == :(-1//2*b*x^-3*(b*x^2)^(1/2))
@test integrate(x^-7*(b*x^2)^3//2, x) == :(-1//3*b*x^-4*(b*x^2)^(1/2))
@test integrate(x^2*(x^2)^3//2, x) == :(1//6*x^5*(x^2)^(1/2))
@test integrate(x*(b*x^2)^5//2, x) == :(1//7*b^2*x^6*(b*x^2)^(1/2))
@test integrate((b*x^2)^5//2, x) == :(1//6*b^2*x^5*(b*x^2)^(1/2))
@test integrate(x^-1*(b*x^2)^5//2, x) == :(1//5*b^2*x^4*(b*x^2)^(1/2))
@test integrate(x^-2*(b*x^2)^5//2, x) == :(1//4*b^2*x^3*(b*x^2)^(1/2))
@test integrate(x^-3*(b*x^2)^5//2, x) == :(1//3*b^2*x^2*(b*x^2)^(1/2))
@test integrate(x^-4*(b*x^2)^5//2, x) == :((1/2)*x*b^2*(b*x^2)^(1/2))
@test integrate(x^-5*(b*x^2)^5//2, x) == :(b^2*(b*x^2)^(1/2))
@test integrate(x^-6*(b*x^2)^5//2, x) == :(b^2*x^-1*(b*x^2)^(1/2)*log(x))
@test integrate(x^-7*(b*x^2)^5//2, x) == :(-1*b^2*x^-2*(b*x^2)^(1/2))
@test integrate(x^-8*(b*x^2)^5//2, x) == :(-1//2*b^2*x^-3*(b*x^2)^(1/2))
@test integrate(x^-9*(b*x^2)^5//2, x) == :(-1//3*b^2*x^-4*(b*x^2)^(1/2))
@test integrate(x^2*(x^2)^5//2, x) == :(1//8*x^7*(x^2)^(1/2))
@test integrate(x^3*(b*x^2)^-1//2, x) == :(1//3*x^4*(b*x^2)^-1//2)
@test integrate(x*(b*x^2)^-1//2, x) == :(x^2*(b*x^2)^-1//2)
@test integrate(x^-1*(b*x^2)^-1//2, x) == :(-1*(b*x^2)^-1//2)
@test integrate(x^-3*(b*x^2)^-1//2, x) == :(-1//3*x^-2*(b*x^2)^-1//2)
@test integrate(x^2*(b*x^2)^-1//2, x) == :((1/2)*x^3*(b*x^2)^-1//2)
@test integrate((b*x^2)^-1//2, x) == :(x*(b*x^2)^-1//2*log(x))
@test integrate(x^-2*(b*x^2)^-1//2, x) == :(-1//2*x^-1*(b*x^2)^-1//2)
@test integrate(x^5*(b*x^2)^-3//2, x) == :(1//3*b^-1*x^4*(b*x^2)^-1//2)
@test integrate(x^3*(b*x^2)^-3//2, x) == :(b^-1*x^2*(b*x^2)^-1//2)
@test integrate(x*(b*x^2)^-3//2, x) == :(-1*b^-1*(b*x^2)^-1//2)
@test integrate(x^-1*(b*x^2)^-3//2, x) == :(-1//3*b^-1*x^-2*(b*x^2)^-1//2)
@test integrate(x^-3*(b*x^2)^-3//2, x) == :(-1//5*b^-1*x^-4*(b*x^2)^-1//2)
@test integrate(x^6*(b*x^2)^-3//2, x) == :(1//4*b^-1*x^5*(b*x^2)^-1//2)
@test integrate(x^4*(b*x^2)^-3//2, x) == :((1/2)*b^-1*x^3*(b*x^2)^-1//2)
@test integrate(x^2*(b*x^2)^-3//2, x) == :(x*b^-1*(b*x^2)^-1//2*log(x))
@test integrate((b*x^2)^-3//2, x) == :(-1//2*b^-1*x^-1*(b*x^2)^-1//2)
@test integrate(x^-2*(b*x^2)^-3//2, x) == :(-1//4*b^-1*x^-3*(b*x^2)^-1//2)
@test integrate(x^7*(b*x^2)^-5//2, x) == :(1//3*b^-2*x^4*(b*x^2)^-1//2)
@test integrate(x^5*(b*x^2)^-5//2, x) == :(b^-2*x^2*(b*x^2)^-1//2)
@test integrate(x^3*(b*x^2)^-5//2, x) == :(-1*b^-2*(b*x^2)^-1//2)
@test integrate(x*(b*x^2)^-5//2, x) == :(-1//3*b^-2*x^-2*(b*x^2)^-1//2)
@test integrate(x^-1*(b*x^2)^-5//2, x) == :(-1//5*b^-2*x^-4*(b*x^2)^-1//2)
@test integrate(x^6*(b*x^2)^-5//2, x) == :((1/2)*b^-2*x^3*(b*x^2)^-1//2)
@test integrate(x^4*(b*x^2)^-5//2, x) == :(x*b^-2*(b*x^2)^-1//2*log(x))
@test integrate(x^2*(b*x^2)^-5//2, x) == :(-1//2*b^-2*x^-1*(b*x^2)^-1//2)
@test integrate((b*x^2)^-5//2, x) == :(-1//4*b^-2*x^-3*(b*x^2)^-1//2)
@test integrate(x^-2*(b*x^2)^-5//2, x) == :(-1//6*b^-2*x^-5*(b*x^2)^-1//2)
@test integrate((b*x^2)^3//2*(c*x)^m, x) == :(b*c^-4*x^-1*(b*x^2)^(1/2)*(c*x)^(4+m)*(4+m)^-1)
@test integrate((b*x^2)^(1/2)*(c*x)^m, x) == :(c^-2*x^-1*(b*x^2)^(1/2)*(c*x)^(2+m)*(2+m)^-1)
@test integrate((b*x^2)^-1//2*(c*x)^m, x) == :(x*m^-1*(b*x^2)^-1//2*(c*x)^m)
@test integrate((b*x^2)^-3//2*(c*x)^m, x) == :(-1*x*b^-1*c^2*(b*x^2)^-1//2*(c*x)^(-2+m)*(2+-1m)^-1)
@test integrate(x^m*(b*x^2)^p, x) == :(x^(1+m)*(b*x^2)^p*(1+m+2p)^-1)
@test integrate((b*x^2)^p*(c*x)^m, x) == :(x*(b*x^2)^p*(c*x)^m*(1+m+2p)^-1)
@test integrate(x^(-1+-2p)*(x^2)^p, x) == :(x^(-2p)*(x^2)^p*log(x))
@test integrate(x^3*(b*x^2)^p, x) == :(x^4*(b*x^2)^p*(4+2p)^-1)
@test integrate(x^2*(b*x^2)^p, x) == :(x^3*(b*x^2)^p*(3+2p)^-1)
@test integrate(x*(b*x^2)^p, x) == :(x^2*(b*x^2)^p*(2+2p)^-1)
@test integrate((b*x^2)^p, x) == :(x*(b*x^2)^p*(1+2p)^-1)
@test integrate(x^-1*(b*x^2)^p, x) == :((1/2)*p^-1*(b*x^2)^p)
@test integrate(x^-2*(b*x^2)^p, x) == :(-1*x^-1*(b*x^2)^p*(1+-2p)^-1)
@test integrate(x^-3*(b*x^2)^p, x) == :(-1*x^-2*(b*x^2)^p*(2+-2p)^-1)
@test integrate(x^-4*(b*x^2)^p, x) == :(-1*x^-3*(b*x^2)^p*(3+-2p)^-1)
@test integrate((b*x^3)^(1/2), x) == :(2//5*x*(b*x^3)^(1/2))
@test integrate((b*x^2)^(1/2), x) == :((1/2)*x*(b*x^2)^(1/2))
@test integrate((b*x)^(1/2), x) == :(2//3*b^-1*(b*x)^3//2)
@test integrate((b*x^-1)^(1/2), x) == :(2*x*(b*x^-1)^(1/2))
@test integrate((b*x^-2)^(1/2), x) == :(x*(b*x^-2)^(1/2)*log(x))
@test integrate((b*x^-3)^(1/2), x) == :(-2*x*(b*x^-3)^(1/2))
@test integrate((b*x^3)^3//2, x) == :(2//11*b*x^4*(b*x^3)^(1/2))
@test integrate((b*x^2)^3//2, x) == :(1//4*b*x^3*(b*x^2)^(1/2))
@test integrate((b*x)^3//2, x) == :(2//5*b^-1*(b*x)^5//2)
@test integrate((b*x^-1)^3//2, x) == :(-2*b*(b*x^-1)^(1/2))
@test integrate((b*x^-2)^3//2, x) == :(-1//2*b*x^-1*(b*x^-2)^(1/2))
@test integrate((b*x^-3)^3//2, x) == :(-2//7*b*x^-2*(b*x^-3)^(1/2))
@test integrate((b*x^3)^-1//2, x) == :(-2*x*(b*x^3)^-1//2)
@test integrate((b*x^2)^-1//2, x) == :(x*(b*x^2)^-1//2*log(x))
@test integrate((b*x)^-1//2, x) == :(2*b^-1*(b*x)^(1/2))
@test integrate((b*x^-1)^-1//2, x) == :(2//3*x*(b*x^-1)^-1//2)
@test integrate((b*x^-2)^-1//2, x) == :((1/2)*x*(b*x^-2)^-1//2)
@test integrate((b*x^-3)^-1//2, x) == :(2//5*x*(b*x^-3)^-1//2)
@test integrate((b*x^3)^-3//2, x) == :(-2//7*b^-1*x^-2*(b*x^3)^-1//2)
@test integrate((b*x^2)^-3//2, x) == :(-1//2*b^-1*x^-1*(b*x^2)^-1//2)
@test integrate((b*x)^-3//2, x) == :(-2*b^-1*(b*x)^-1//2)
@test integrate((b*x^-1)^-3//2, x) == :(2//5*b^-1*x^2*(b*x^-1)^-1//2)
@test integrate((b*x^-2)^-3//2, x) == :(1//4*b^-1*x^3*(b*x^-2)^-1//2)
@test integrate((b*x^-3)^-3//2, x) == :(2//11*b^-1*x^4*(b*x^-3)^-1//2)
@test integrate((b*x^n)^1//3, x) == :(3*x*(b*x^n)^1//3*(3+n)^-1)
@test integrate((b*x^3)^1//3, x) == :((1/2)*x*(b*x^3)^1//3)
@test integrate((b*x^2)^1//3, x) == :(3//5*x*(b*x^2)^1//3)
@test integrate((b*x)^1//3, x) == :(3//4*b^-1*(b*x)^4//3)
@test integrate((b*x^-1)^1//3, x) == :(3//2*x*(b*x^-1)^1//3)
@test integrate((b*x^-2)^1//3, x) == :(3*x*(b*x^-2)^1//3)
@test integrate((b*x^-3)^1//3, x) == :(x*(b*x^-3)^1//3*log(x))
@test integrate((b*x^-4)^1//3, x) == :(-3*x*(b*x^-4)^1//3)
@test integrate((b*x^n)^2//3, x) == :(3*x*(b*x^n)^2//3*(3+2n)^-1)
@test integrate((b*x^2)^2//3, x) == :(3//7*x*(b*x^2)^2//3)
@test integrate((b*x)^2//3, x) == :(3//5*b^-1*(b*x)^5//3)
@test integrate((b*x^-1)^2//3, x) == :(3*x*(b*x^-1)^2//3)
@test integrate((b*x^-2)^2//3, x) == :(-3*x*(b*x^-2)^2//3)
@test integrate((b*x^-3)^2//3, x) == :(-1*x*(b*x^-3)^2//3)
@test integrate((b*x^-4)^2//3, x) == :(-3//5*x*(b*x^-4)^2//3)
@test integrate((b*x^n)^-1//3, x) == :(3*x*(b*x^n)^-1//3*(3+-1n)^-1)
@test integrate((b*x^4)^-1//3, x) == :(-3*x*(b*x^4)^-1//3)
@test integrate((b*x^3)^-1//3, x) == :(x*(b*x^3)^-1//3*log(x))
@test integrate((b*x^2)^-1//3, x) == :(3*x*(b*x^2)^-1//3)
@test integrate((b*x)^-1//3, x) == :(3//2*b^-1*(b*x)^2//3)
@test integrate((b*x^-1)^-1//3, x) == :(3//4*x*(b*x^-1)^-1//3)
@test integrate((b*x^-2)^-1//3, x) == :(3//5*x*(b*x^-2)^-1//3)
@test integrate((b*x^-3)^-1//3, x) == :((1/2)*x*(b*x^-3)^-1//3)
@test integrate((b*x^n)^-2//3, x) == :(3*x*(b*x^n)^-2//3*(3+-2n)^-1)
@test integrate((b*x^3)^-2//3, x) == :(-1*x*(b*x^3)^-2//3)
@test integrate((b*x^2)^-2//3, x) == :(-3*x*(b*x^2)^-2//3)
@test integrate((b*x)^-2//3, x) == :(3*b^-1*(b*x)^1//3)
@test integrate((b*x^-1)^-2//3, x) == :(3//5*x*(b*x^-1)^-2//3)
@test integrate((b*x^-2)^-2//3, x) == :(3//7*x*(b*x^-2)^-2//3)
@test integrate((b*x^-3)^-2//3, x) == :(1//3*x*(b*x^-3)^-2//3)
@test integrate(x^2*(b*x^n)^(1/2), x) == :(2*x^3*(b*x^n)^(1/2)*(6+n)^-1)
@test integrate(x*(b*x^n)^(1/2), x) == :(2*x^2*(b*x^n)^(1/2)*(4+n)^-1)
@test integrate((b*x^n)^(1/2), x) == :(2*x*(b*x^n)^(1/2)*(2+n)^-1)
@test integrate(x^-1*(b*x^n)^(1/2), x) == :(2*n^-1*(b*x^n)^(1/2))
@test integrate(x^-2*(b*x^n)^(1/2), x) == :(-2*x^-1*(b*x^n)^(1/2)*(2+-1n)^-1)
@test integrate(x^-3*(b*x^n)^(1/2), x) == :(-2*x^-2*(b*x^n)^(1/2)*(4+-1n)^-1)
@test integrate(x*(b*x^n)^3//2, x) == :(2*b*x^(2+n)*(b*x^n)^(1/2)*(4+3n)^-1)
@test integrate((b*x^n)^3//2, x) == :(2*b*x^(1+n)*(b*x^n)^(1/2)*(2+3n)^-1)
@test integrate(x^-1*(b*x^n)^3//2, x) == :(2//3*b*n^-1*x^n*(b*x^n)^(1/2))
@test integrate(x^-2*(b*x^n)^3//2, x) == :(-2*b*x^(-1+n)*(b*x^n)^(1/2)*(2+-3n)^-1)
@test integrate(x^-3*(b*x^n)^3//2, x) == :(-2*b*x^(-2+n)*(b*x^n)^(1/2)*(4+-3n)^-1)
@test integrate(x^-4*(b*x^n)^3//2, x) == :(-2*b*x^(-3+n)*(b*x^n)^(1/2)*(6+-3n)^-1)
@test integrate(x^2*(b*x^n)^-1//2, x) == :(2*x^3*(b*x^n)^-1//2*(6+-1n)^-1)
@test integrate(x*(b*x^n)^-1//2, x) == :(2*x^2*(b*x^n)^-1//2*(4+-1n)^-1)
@test integrate((b*x^n)^-1//2, x) == :(2*x*(b*x^n)^-1//2*(2+-1n)^-1)
@test integrate(x^-1*(b*x^n)^-1//2, x) == :(-2*n^-1*(b*x^n)^-1//2)
@test integrate(x^-2*(b*x^n)^-1//2, x) == :(-2*x^-1*(b*x^n)^-1//2*(2+n)^-1)
@test integrate(x^-3*(b*x^n)^-1//2, x) == :(-2*x^-2*(b*x^n)^-1//2*(4+n)^-1)
@test integrate(x^2*(b*x^n)^-3//2, x) == :(2//3*b^-1*x^(3+-1n)*(b*x^n)^-1//2*(2+-1n)^-1)
@test integrate(x*(b*x^n)^-3//2, x) == :(2*b^-1*x^(2+-1n)*(b*x^n)^-1//2*(4+-3n)^-1)
@test integrate((b*x^n)^-3//2, x) == :(2*b^-1*x^(1+-1n)*(b*x^n)^-1//2*(2+-3n)^-1)
@test integrate(x^-1*(b*x^n)^-3//2, x) == :(-2//3*b^-1*n^-1*x^(-1n)*(b*x^n)^-1//2)
@test integrate(x^-2*(b*x^n)^-3//2, x) == :(-2*b^-1*x^(-1+-1n)*(b*x^n)^-1//2*(2+3n)^-1)
@test integrate(x^-3*(b*x^n)^-3//2, x) == :(-2*b^-1*x^(-2+-1n)*(b*x^n)^-1//2*(4+3n)^-1)
@test integrate(x^-4*(b*x^n)^-3//2, x) == :(-2//3*b^-1*x^(-3+-1n)*(b*x^n)^-1//2*(2+n)^-1)
@test integrate(x^m*(a*x^n)^-3//2, x) == :(2*a^-1*x^(1+m+-1n)*(a*x^n)^-1//2*(2+-3n+2m)^-1)
@test integrate((a*x^n)^-3//2*(c*x)^m, x) == :(2*a^-1*x^(1+-1n)*(a*x^n)^-1//2*(c*x)^m*(2+-3n+2m)^-1)
@test integrate(x^m*(b*x^n)^3//2, x) == :(2*b*x^(1+m+n)*(b*x^n)^(1/2)*(2+2m+3n)^-1)
@test integrate(x^m*(b*x^n)^(1/2), x) == :(2*x^(1+m)*(b*x^n)^(1/2)*(2+n+2m)^-1)
@test integrate(x^m*(b*x^n)^-1//2, x) == :(2*x^(1+m)*(b*x^n)^-1//2*(2+-1n+2m)^-1)
@test integrate(x^m*(b*x^n)^-3//2, x) == :(2*b^-1*x^(1+m+-1n)*(b*x^n)^-1//2*(2+-3n+2m)^-1)
@test integrate((b*x^n)^3//2*(c*x)^m, x) == :(2*b*x^(1+n)*(b*x^n)^(1/2)*(c*x)^m*(2+2m+3n)^-1)
@test integrate((b*x^n)^-1//2*(c*x)^m, x) == :(2*x*(b*x^n)^-1//2*(c*x)^m*(2+-1n+2m)^-1)
@test integrate((b*x^n)^-3//2*(c*x)^m, x) == :(2*b^-1*x^(1+-1n)*(b*x^n)^-1//2*(c*x)^m*(2+-3n+2m)^-1)
@test integrate((b*x^n)^-5//2*(c*x)^m, x) == :(2*b^-2*x^(1+-2n)*(b*x^n)^-1//2*(c*x)^m*(2+-5n+2m)^-1)
@test integrate(x^(-1+-3//2*n)*(b*x^n)^3//2, x) == :(b*x^(-1//2*n)*(b*x^n)^(1/2)*log(x))
@test integrate(x^(-1+-1//2*n)*(b*x^n)^(1/2), x) == :(x^(-1//2*n)*(b*x^n)^(1/2)*log(x))
@test integrate(x^(-1+(1/2)*n)*(b*x^n)^-1//2, x) == :(x^((1/2)*n)*(b*x^n)^-1//2*log(x))
@test integrate(x^(-1+3//2*n)*(b*x^n)^-3//2, x) == :(b^-1*x^((1/2)*n)*(b*x^n)^-1//2*log(x))
@test integrate(x^m*(b*x^n)^p, x) == :(x^(1+m)*(b*x^n)^p*(1+m+n*p)^-1)
@test integrate(x^2*(b*x^n)^p, x) == :(x^3*(b*x^n)^p*(3+n*p)^-1)
@test integrate(x*(b*x^n)^p, x) == :(x^2*(b*x^n)^p*(2+n*p)^-1)
@test integrate((b*x^n)^p, x) == :(x*(b*x^n)^p*(1+n*p)^-1)
@test integrate(x^-1*(b*x^n)^p, x) == :(n^-1*p^-1*(b*x^n)^p)
@test integrate(x^-2*(b*x^n)^p, x) == :(-1*x^-1*(b*x^n)^p*(1+-1*n*p)^-1)
@test integrate(x^-3*(b*x^n)^p, x) == :(-1*x^-2*(b*x^n)^p*(2+-1*n*p)^-1)
@test integrate(x^m*(a*x^n)^(-1*n^-1), x) == :(m^-1*x^(1+m)*(a*x^n)^(-1*n^-1))
@test integrate((a*x^n)^(-1*n^-1)*(c*x)^m, x) == :(x*m^-1*(a*x^n)^(-1*n^-1)*(c*x)^m)
@test integrate(x^2*(a*x^n)^(-1*n^-1), x) == :((1/2)*x^3*(a*x^n)^(-1*n^-1))
@test integrate(x*(a*x^n)^(-1*n^-1), x) == :(x^2*(a*x^n)^(-1*n^-1))
@test integrate((a*x^n)^(-1*n^-1), x) == :(x*(a*x^n)^(-1*n^-1)*log(x))
@test integrate(x^-1*(a*x^n)^(-1*n^-1), x) == :(-1*(a*x^n)^(-1*n^-1))
@test integrate(x^-2*(a*x^n)^(-1*n^-1), x) == :(-1//2*x^-1*(a*x^n)^(-1*n^-1))
@test integrate(x^m*(a*x^n)^(-1*n^-1*(1+m)), x) == :(x^(1+m)*(a*x^n)^(-1*n^-1*(1+m))*log(x))
@test integrate(x^(-1+-1*n*p)*(a*x^n)^p, x) == :(x^(-1*n*p)*(a*x^n)^p*log(x))
@test integrate(x^m*(a*(b*x^n)^p)^q, x) == :(x^(1+m)*(a*(b*x^n)^p)^q*(1+m+n*p*q)^-1)
@test integrate(x^2*(a*(b*x^n)^p)^q, x) == :(x^3*(a*(b*x^n)^p)^q*(3+n*p*q)^-1)
@test integrate(x*(a*(b*x^n)^p)^q, x) == :(x^2*(a*(b*x^n)^p)^q*(2+n*p*q)^-1)
@test integrate((a*(b*x^n)^p)^q, x) == :(x*(a*(b*x^n)^p)^q*(1+n*p*q)^-1)
@test integrate(x^-1*(a*(b*x^n)^p)^q, x) == :(n^-1*p^-1*q^-1*(a*(b*x^n)^p)^q)
@test integrate(x^-2*(a*(b*x^n)^p)^q, x) == :(-1*x^-1*(a*(b*x^n)^p)^q*(1+-1*n*p*q)^-1)
@test integrate(x^-3*(a*(b*x^n)^p)^q, x) == :(-1*x^-2*(a*(b*x^n)^p)^q*(2+-1*n*p*q)^-1)
@test integrate(x^2*(a*(b*x^m)^n)^(-1*m^-1*n^-1), x) == :((1/2)*x^3*(a*(b*x^m)^n)^(-1*m^-1*n^-1))
@test integrate(x*(a*(b*x^m)^n)^(-1*m^-1*n^-1), x) == :(x^2*(a*(b*x^m)^n)^(-1*m^-1*n^-1))
@test integrate((a*(b*x^m)^n)^(-1*m^-1*n^-1), x) == :(x*(a*(b*x^m)^n)^(-1*m^-1*n^-1)*log(x))
@test integrate(x^-1*(a*(b*x^m)^n)^(-1*m^-1*n^-1), x) == :(-1*(a*(b*x^m)^n)^(-1*m^-1*n^-1))
@test integrate(x^-2*(a*(b*x^m)^n)^(-1*m^-1*n^-1), x) == :(-1//2*x^-1*(a*(b*x^m)^n)^(-1*m^-1*n^-1))
@test integrate(x^(2+-1*n*p*q)*(a*(b*x^n)^p)^q, x) == :(1//3*x^(3+-1*n*p*q)*(a*(b*x^n)^p)^q)
@test integrate(x^(1+-1*n*p*q)*(a*(b*x^n)^p)^q, x) == :((1/2)*x^(2+-1*n*p*q)*(a*(b*x^n)^p)^q)
@test integrate(x^(-1*n*p*q)*(a*(b*x^n)^p)^q, x) == :(x^(1+-1*n*p*q)*(a*(b*x^n)^p)^q)
@test integrate(x^(-1+-1*n*p*q)*(a*(b*x^n)^p)^q, x) == :(x^(-1*n*p*q)*(a*(b*x^n)^p)^q*log(x))
@test integrate(x^(-2+-1*n*p*q)*(a*(b*x^n)^p)^q, x) == :(-1*x^(-1+-1*n*p*q)*(a*(b*x^n)^p)^q)
@test integrate(x^3*(a+b*x^3), x) == :(1//4*a*x^4+1//7*b*x^7)
@test integrate(x^2*(a+b*x^3), x) == :(1//3*a*x^3+1//6*b*x^6)
@test integrate(x*(a+b*x^3), x) == :((1/2)*a*x^2+1//5*b*x^5)
@test integrate(a+b*x^3, x) == :(a*x+1//4*b*x^4)
@test integrate(x^-1*(a+b*x^3), x) == :(a*log(x)+1//3*b*x^3)
@test integrate(x^-2*(a+b*x^3), x) == :((1/2)*b*x^2+-1*a*x^-1)
@test integrate(x^-3*(a+b*x^3), x) == :(b*x+-1//2*a*x^-2)
@test integrate(x^-4*(a+b*x^3), x) == :(b*log(x)+-1//3*a*x^-3)
@test integrate(x^-5*(a+b*x^3), x) == :(-1*b*x^-1+-1//4*a*x^-4)
@test integrate(x^-6*(a+b*x^3), x) == :(-1//2*b*x^-2+-1//5*a*x^-5)
@test integrate(x^-7*(a+b*x^3), x) == :(-1//3*b*x^-3+-1//6*a*x^-6)
@test integrate(x^-8*(a+b*x^3), x) == :(-1//4*b*x^-4+-1//7*a*x^-7)
@test integrate(x^4*(a+b*x^3)^2, x) == :(1//5*a^2*x^5+1//11*b^2*x^11+1//4*a*b*x^8)
@test integrate(x^3*(a+b*x^3)^2, x) == :(1//4*a^2*x^4+1//10*b^2*x^10+2//7*a*b*x^7)
@test integrate(x^2*(a+b*x^3)^2, x) == :(1//9*b^-1*(a+b*x^3)^3)
@test integrate(x*(a+b*x^3)^2, x) == :((1/2)*a^2*x^2+1//8*b^2*x^8+2//5*a*b*x^5)
@test integrate((a+b*x^3)^2, x) == :(x*a^2+1//7*b^2*x^7+(1/2)*a*b*x^4)
@test integrate(x^-1*(a+b*x^3)^2, x) == :(a^2*log(x)+1//6*b^2*x^6+2//3*a*b*x^3)
@test integrate(x^-2*(a+b*x^3)^2, x) == :(-1*a^2*x^-1+1//5*b^2*x^5+a*b*x^2)
@test integrate(x^-3*(a+b*x^3)^2, x) == :(-1//2*a^2*x^-2+1//4*b^2*x^4+2*a*b*x)
@test integrate(x^-4*(a+b*x^3)^2, x) == :(-1//3*a^2*x^-3+1//3*b^2*x^3+2*a*b*log(x))
@test integrate(x^-5*(a+b*x^3)^2, x) == :((1/2)*b^2*x^2+-1//4*a^2*x^-4+-2*a*b*x^-1)
@test integrate(x^-6*(a+b*x^3)^2, x) == :(x*b^2+-1//5*a^2*x^-5+-1*a*b*x^-2)
@test integrate(x^-7*(a+b*x^3)^2, x) == :(b^2*log(x)+-1//6*a^2*x^-6+-2//3*a*b*x^-3)
@test integrate(x^-8*(a+b*x^3)^2, x) == :(-1*b^2*x^-1+-1//7*a^2*x^-7+-1//2*a*b*x^-4)
@test integrate(x^-9*(a+b*x^3)^2, x) == :(-1//2*b^2*x^-2+-1//8*a^2*x^-8+-2//5*a*b*x^-5)
@test integrate(x^-10*(a+b*x^3)^2, x) == :(-1//9*a^-1*x^-9*(a+b*x^3)^3)
@test integrate(x^-11*(a+b*x^3)^2, x) == :(-1//4*b^2*x^-4+-1//10*a^2*x^-10+-2//7*a*b*x^-7)
@test integrate(x^-12*(a+b*x^3)^2, x) == :(-1//5*b^2*x^-5+-1//11*a^2*x^-11+-1//4*a*b*x^-8)
@test integrate(x^-13*(a+b*x^3)^2, x) == :(-1//6*b^2*x^-6+-1//12*a^2*x^-12+-2//9*a*b*x^-9)
@test integrate(x^14*(a+b*x^3)^3, x) == :(1//15*a^3*x^15+1//24*b^3*x^24+1//6*b*a^2*x^18+1//7*a*b^2*x^21)
@test integrate(x^11*(a+b*x^3)^3, x) == :(1//12*a^3*x^12+1//21*b^3*x^21+1//5*b*a^2*x^15+1//6*a*b^2*x^18)
@test integrate(x^8*(a+b*x^3)^3, x) == :(1//9*a^3*x^9+1//18*b^3*x^18+1//4*b*a^2*x^12+1//5*a*b^2*x^15)
@test integrate(x^5*(a+b*x^3)^3, x) == :(1//15*b^-2*(a+b*x^3)^5+-1//12*a*b^-2*(a+b*x^3)^4)
@test integrate(x^2*(a+b*x^3)^3, x) == :(1//12*b^-1*(a+b*x^3)^4)
@test integrate(x^-1*(a+b*x^3)^3, x) == :(a^3*log(x)+1//9*b^3*x^9+b*a^2*x^3+(1/2)*a*b^2*x^6)
@test integrate(x^-4*(a+b*x^3)^3, x) == :(-1//3*a^3*x^-3+1//6*b^3*x^6+a*b^2*x^3+3*b*a^2*log(x))
@test integrate(x^-7*(a+b*x^3)^3, x) == :(-1//6*a^3*x^-6+1//3*b^3*x^3+-1*b*a^2*x^-3+3*a*b^2*log(x))
@test integrate(x^-10*(a+b*x^3)^3, x) == :(b^3*log(x)+-1//9*a^3*x^-9+-1*a*b^2*x^-3+-1//2*b*a^2*x^-6)
@test integrate(x^-13*(a+b*x^3)^3, x) == :(-1//12*a^-1*x^-12*(a+b*x^3)^4)
@test integrate(x^-16*(a+b*x^3)^3, x) == :(-1//15*a^-1*x^-15*(a+b*x^3)^4+1//60*b*a^-2*x^-12*(a+b*x^3)^4)
@test integrate(x^-19*(a+b*x^3)^3, x) == :(-1//9*b^3*x^-9+-1//18*a^3*x^-18+-1//4*a*b^2*x^-12+-1//5*b*a^2*x^-15)
@test integrate(x^-22*(a+b*x^3)^3, x) == :(-1//12*b^3*x^-12+-1//21*a^3*x^-21+-1//5*a*b^2*x^-15+-1//6*b*a^2*x^-18)
@test integrate(x^4*(a+b*x^3)^3, x) == :(1//5*a^3*x^5+1//14*b^3*x^14+3//8*b*a^2*x^8+3//11*a*b^2*x^11)
@test integrate(x^3*(a+b*x^3)^3, x) == :(1//4*a^3*x^4+1//13*b^3*x^13+3//7*b*a^2*x^7+3//10*a*b^2*x^10)
@test integrate(x*(a+b*x^3)^3, x) == :((1/2)*a^3*x^2+1//11*b^3*x^11+3//5*b*a^2*x^5+3//8*a*b^2*x^8)
@test integrate((a+b*x^3)^3, x) == :(x*a^3+1//10*b^3*x^10+3//4*b*a^2*x^4+3//7*a*b^2*x^7)
@test integrate(x^-2*(a+b*x^3)^3, x) == :(-1*a^3*x^-1+1//8*b^3*x^8+3//2*b*a^2*x^2+3//5*a*b^2*x^5)
@test integrate(x^-3*(a+b*x^3)^3, x) == :(-1//2*a^3*x^-2+1//7*b^3*x^7+3*b*x*a^2+3//4*a*b^2*x^4)
@test integrate(x^-5*(a+b*x^3)^3, x) == :(-1//4*a^3*x^-4+1//5*b^3*x^5+-3*b*a^2*x^-1+3//2*a*b^2*x^2)
@test integrate(x^-6*(a+b*x^3)^3, x) == :(-1//5*a^3*x^-5+1//4*b^3*x^4+3*a*x*b^2+-3//2*b*a^2*x^-2)
@test integrate(x^-8*(a+b*x^3)^3, x) == :((1/2)*b^3*x^2+-1//7*a^3*x^-7+-3*a*b^2*x^-1+-3//4*b*a^2*x^-4)
@test integrate(x^17*(a+b*x^3)^5, x) == :(1//18*a^5*x^18+1//33*b^5*x^33+1//6*a*b^4*x^30+5//12*a^3*b^2*x^24+5//21*b*a^4*x^21+10//27*a^2*b^3*x^27)
@test integrate(x^14*(a+b*x^3)^5, x) == :(1//15*a^5*x^15+1//30*b^5*x^30+5//12*a^2*b^3*x^24+5//18*b*a^4*x^18+5//27*a*b^4*x^27+10//21*a^3*b^2*x^21)
@test integrate(x^11*(a+b*x^3)^5, x) == :(1//27*b^-4*(a+b*x^3)^9+-1//8*a*b^-4*(a+b*x^3)^8+-1//18*a^3*b^-4*(a+b*x^3)^6+1//7*a^2*b^-4*(a+b*x^3)^7)
@test integrate(x^8*(a+b*x^3)^5, x) == :(1//24*b^-3*(a+b*x^3)^8+-2//21*a*b^-3*(a+b*x^3)^7+1//18*a^2*b^-3*(a+b*x^3)^6)
@test integrate(x^5*(a+b*x^3)^5, x) == :(1//21*b^-2*(a+b*x^3)^7+-1//18*a*b^-2*(a+b*x^3)^6)
@test integrate(x^2*(a+b*x^3)^5, x) == :(1//18*b^-1*(a+b*x^3)^6)
@test integrate(x^-1*(a+b*x^3)^5, x) == :(a^5*log(x)+1//15*b^5*x^15+5//3*b*a^4*x^3+5//3*a^3*b^2*x^6+5//12*a*b^4*x^12+10//9*a^2*b^3*x^9)
@test integrate(x^-4*(a+b*x^3)^5, x) == :(-1//3*a^5*x^-3+1//12*b^5*x^12+5*b*a^4*log(x)+5//3*a^2*b^3*x^6+5//9*a*b^4*x^9+10//3*a^3*b^2*x^3)
@test integrate(x^-7*(a+b*x^3)^5, x) == :(-1//6*a^5*x^-6+1//9*b^5*x^9+10*a^3*b^2*log(x)+-5//3*b*a^4*x^-3+5//6*a*b^4*x^6+10//3*a^2*b^3*x^3)
@test integrate(x^-10*(a+b*x^3)^5, x) == :(-1//9*a^5*x^-9+1//6*b^5*x^6+10*a^2*b^3*log(x)+-10//3*a^3*b^2*x^-3+-5//6*b*a^4*x^-6+5//3*a*b^4*x^3)
@test integrate(x^-13*(a+b*x^3)^5, x) == :(-1//12*a^5*x^-12+1//3*b^5*x^3+5*a*b^4*log(x)+-10//3*a^2*b^3*x^-3+-5//3*a^3*b^2*x^-6+-5//9*b*a^4*x^-9)
@test integrate(x^-16*(a+b*x^3)^5, x) == :(b^5*log(x)+-1//15*a^5*x^-15+-10//9*a^3*b^2*x^-9+-5//3*a*b^4*x^-3+-5//3*a^2*b^3*x^-6+-5//12*b*a^4*x^-12)
@test integrate(x^-19*(a+b*x^3)^5, x) == :(-1//18*a^-1*x^-18*(a+b*x^3)^6)
@test integrate(x^-22*(a+b*x^3)^5, x) == :(-1//21*a^-1*x^-21*(a+b*x^3)^6+1//126*b*a^-2*x^-18*(a+b*x^3)^6)
@test integrate(x^-25*(a+b*x^3)^5, x) == :(-1//24*a^-1*x^-24*(a+b*x^3)^6+-1//504*a^-3*b^2*x^-18*(a+b*x^3)^6+1//84*b*a^-2*x^-21*(a+b*x^3)^6)
@test integrate(x^-28*(a+b*x^3)^5, x) == :(-1//12*b^5*x^-12+-1//27*a^5*x^-27+-10//21*a^3*b^2*x^-21+-5//9*a^2*b^3*x^-18+-5//24*b*a^4*x^-24+-1//3*a*b^4*x^-15)
@test integrate(x^-31*(a+b*x^3)^5, x) == :(-1//15*b^5*x^-15+-1//30*a^5*x^-30+-10//21*a^2*b^3*x^-21+-5//12*a^3*b^2*x^-24+-5//18*a*b^4*x^-18+-5//27*b*a^4*x^-27)
@test integrate(x^4*(a+b*x^3)^5, x) == :(1//5*a^5*x^5+1//20*b^5*x^20+5//7*a^2*b^3*x^14+5//8*b*a^4*x^8+5//17*a*b^4*x^17+10//11*a^3*b^2*x^11)
@test integrate(x^3*(a+b*x^3)^5, x) == :(1//4*a^5*x^4+1//19*b^5*x^19+a^3*b^2*x^10+5//7*b*a^4*x^7+5//16*a*b^4*x^16+10//13*a^2*b^3*x^13)
@test integrate(x*(a+b*x^3)^5, x) == :((1/2)*a^5*x^2+1//17*b^5*x^17+b*a^4*x^5+5//4*a^3*b^2*x^8+5//14*a*b^4*x^14+10//11*a^2*b^3*x^11)
@test integrate((a+b*x^3)^5, x) == :(x*a^5+1//16*b^5*x^16+a^2*b^3*x^10+5//4*b*a^4*x^4+5//13*a*b^4*x^13+10//7*a^3*b^2*x^7)
@test integrate(x^-2*(a+b*x^3)^5, x) == :(-1*a^5*x^-1+1//14*b^5*x^14+2*a^3*b^2*x^5+5//2*b*a^4*x^2+5//4*a^2*b^3*x^8+5//11*a*b^4*x^11)
@test integrate(x^-3*(a+b*x^3)^5, x) == :(-1//2*a^5*x^-2+1//13*b^5*x^13+(1/2)*a*b^4*x^10+5*b*x*a^4+5//2*a^3*b^2*x^4+10//7*a^2*b^3*x^7)
@test integrate(x^-5*(a+b*x^3)^5, x) == :(-1//4*a^5*x^-4+1//11*b^5*x^11+-5*b*a^4*x^-1+2*a^2*b^3*x^5+5*a^3*b^2*x^2+5//8*a*b^4*x^8)
@test integrate(x^-6*(a+b*x^3)^5, x) == :(-1//5*a^5*x^-5+1//10*b^5*x^10+10*x*a^3*b^2+-5//2*b*a^4*x^-2+5//2*a^2*b^3*x^4+5//7*a*b^4*x^7)
@test integrate(x^-8*(a+b*x^3)^5, x) == :(-1//7*a^5*x^-7+1//8*b^5*x^8+a*b^4*x^5+-10*a^3*b^2*x^-1+5*a^2*b^3*x^2+-5//4*b*a^4*x^-4)
@test integrate(x^-9*(a+b*x^3)^5, x) == :(-1//8*a^5*x^-8+1//7*b^5*x^7+-1*b*a^4*x^-5+-5*a^3*b^2*x^-2+10*x*a^2*b^3+5//4*a*b^4*x^4)
@test integrate(x^20*(a+b*x^3)^8, x) == :(1//45*b^-7*(a+b*x^3)^15+-5//9*a^3*b^-7*(a+b*x^3)^12+-1//5*a^5*b^-7*(a+b*x^3)^10+-1//7*a*b^-7*(a+b*x^3)^14+1//27*a^6*b^-7*(a+b*x^3)^9+5//11*a^4*b^-7*(a+b*x^3)^11+5//13*a^2*b^-7*(a+b*x^3)^13)
@test integrate(x^17*(a+b*x^3)^8, x) == :(1//42*b^-6*(a+b*x^3)^14+-10//33*a^3*b^-6*(a+b*x^3)^11+-5//39*a*b^-6*(a+b*x^3)^13+-1//27*a^5*b^-6*(a+b*x^3)^9+1//6*a^4*b^-6*(a+b*x^3)^10+5//18*a^2*b^-6*(a+b*x^3)^12)
@test integrate(x^14*(a+b*x^3)^8, x) == :(1//39*b^-5*(a+b*x^3)^13+-2//15*a^3*b^-5*(a+b*x^3)^10+-1//9*a*b^-5*(a+b*x^3)^12+1//27*a^4*b^-5*(a+b*x^3)^9+2//11*a^2*b^-5*(a+b*x^3)^11)
@test integrate(x^11*(a+b*x^3)^8, x) == :(1//36*b^-4*(a+b*x^3)^12+-1//11*a*b^-4*(a+b*x^3)^11+-1//27*a^3*b^-4*(a+b*x^3)^9+1//10*a^2*b^-4*(a+b*x^3)^10)
@test integrate(x^8*(a+b*x^3)^8, x) == :(1//33*b^-3*(a+b*x^3)^11+-1//15*a*b^-3*(a+b*x^3)^10+1//27*a^2*b^-3*(a+b*x^3)^9)
@test integrate(x^5*(a+b*x^3)^8, x) == :(1//30*b^-2*(a+b*x^3)^10+-1//27*a*b^-2*(a+b*x^3)^9)
@test integrate(x^2*(a+b*x^3)^8, x) == :(1//27*b^-1*(a+b*x^3)^9)
@test integrate(x^-1*(a+b*x^3)^8, x) == :(a^8*log(x)+1//24*b^8*x^24+8//3*b*a^7*x^3+8//21*a*b^7*x^21+14//3*a^6*b^2*x^6+14//9*a^2*b^6*x^18+35//6*a^4*b^4*x^12+56//9*a^5*b^3*x^9+56//15*a^3*b^5*x^15)
@test integrate(x^-4*(a+b*x^3)^8, x) == :(-1//3*a^8*x^-3+1//21*b^8*x^21+8*b*a^7*log(x)+4//9*a*b^7*x^18+14//3*a^3*b^5*x^12+28//3*a^5*b^3*x^6+28//3*a^6*b^2*x^3+28//15*a^2*b^6*x^15+70//9*a^4*b^4*x^9)
@test integrate(x^-7*(a+b*x^3)^8, x) == :(-1//6*a^8*x^-6+1//18*b^8*x^18+28*a^6*b^2*log(x)+-8//3*b*a^7*x^-3+7//3*a^2*b^6*x^12+8//15*a*b^7*x^15+35//3*a^4*b^4*x^6+56//3*a^5*b^3*x^3+56//9*a^3*b^5*x^9)
@test integrate(x^-10*(a+b*x^3)^8, x) == :(-1//9*a^8*x^-9+1//15*b^8*x^15+56*a^5*b^3*log(x)+-28//3*a^6*b^2*x^-3+-4//3*b*a^7*x^-6+2//3*a*b^7*x^12+28//3*a^3*b^5*x^6+28//9*a^2*b^6*x^9+70//3*a^4*b^4*x^3)
@test integrate(x^-13*(a+b*x^3)^8, x) == :(-1//12*a^8*x^-12+1//12*b^8*x^12+70*a^4*b^4*log(x)+-56//3*a^5*b^3*x^-3+-14//3*a^6*b^2*x^-6+-8//9*b*a^7*x^-9+8//9*a*b^7*x^9+14//3*a^2*b^6*x^6+56//3*a^3*b^5*x^3)
@test integrate(x^-16*(a+b*x^3)^8, x) == :(-1//15*a^8*x^-15+1//9*b^8*x^9+56*a^3*b^5*log(x)+-70//3*a^4*b^4*x^-3+-28//3*a^5*b^3*x^-6+-28//9*a^6*b^2*x^-9+-2//3*b*a^7*x^-12+4//3*a*b^7*x^6+28//3*a^2*b^6*x^3)
@test integrate(x^-19*(a+b*x^3)^8, x) == :(-1//18*a^8*x^-18+1//6*b^8*x^6+28*a^2*b^6*log(x)+-56//3*a^3*b^5*x^-3+-56//9*a^5*b^3*x^-9+-35//3*a^4*b^4*x^-6+-8//15*b*a^7*x^-15+-7//3*a^6*b^2*x^-12+8//3*a*b^7*x^3)
@test integrate(x^-22*(a+b*x^3)^8, x) == :(-1//21*a^8*x^-21+1//3*b^8*x^3+8*a*b^7*log(x)+-70//9*a^4*b^4*x^-9+-28//3*a^2*b^6*x^-3+-28//3*a^3*b^5*x^-6+-28//15*a^6*b^2*x^-15+-14//3*a^5*b^3*x^-12+-4//9*b*a^7*x^-18)
@test integrate(x^-25*(a+b*x^3)^8, x) == :(b^8*log(x)+-1//24*a^8*x^-24+-56//9*a^3*b^5*x^-9+-56//15*a^5*b^3*x^-15+-35//6*a^4*b^4*x^-12+-14//3*a^2*b^6*x^-6+-14//9*a^6*b^2*x^-18+-8//3*a*b^7*x^-3+-8//21*b*a^7*x^-21)
@test integrate(x^-28*(a+b*x^3)^8, x) == :(-1//27*a^-1*x^-27*(a+b*x^3)^9)
@test integrate(x^-31*(a+b*x^3)^8, x) == :(-1//30*a^-1*x^-30*(a+b*x^3)^9+1//270*b*a^-2*x^-27*(a+b*x^3)^9)
@test integrate(x^-34*(a+b*x^3)^8, x) == :(-1//33*a^-1*x^-33*(a+b*x^3)^9+-1//1485*a^-3*b^2*x^-27*(a+b*x^3)^9+1//165*b*a^-2*x^-30*(a+b*x^3)^9)
@test integrate(x^-37*(a+b*x^3)^8, x) == :(-1//36*a^-1*x^-36*(a+b*x^3)^9+-1//660*a^-3*b^2*x^-30*(a+b*x^3)^9+1//132*b*a^-2*x^-33*(a+b*x^3)^9+1//5940*a^-4*b^3*x^-27*(a+b*x^3)^9)
@test integrate(x^-40*(a+b*x^3)^8, x) == :(-1//39*a^-1*x^-39*(a+b*x^3)^9+-1//429*a^-3*b^2*x^-33*(a+b*x^3)^9+-1//19305*a^-5*b^4*x^-27*(a+b*x^3)^9+1//117*b*a^-2*x^-36*(a+b*x^3)^9+1//2145*a^-4*b^3*x^-30*(a+b*x^3)^9)
@test integrate(x^-43*(a+b*x^3)^8, x) == :(-1//18*b^8*x^-18+-1//42*a^8*x^-42+-56//27*a^3*b^5*x^-27+-56//33*a^5*b^3*x^-33+-8//21*a*b^7*x^-21+-8//39*b*a^7*x^-39+-7//3*a^4*b^4*x^-30+-7//6*a^2*b^6*x^-24+-7//9*a^6*b^2*x^-36)
@test integrate(x^-46*(a+b*x^3)^8, x) == :(-1//21*b^8*x^-21+-1//45*a^8*x^-45+-70//33*a^4*b^4*x^-33+-28//15*a^3*b^5*x^-30+-28//27*a^2*b^6*x^-27+-28//39*a^6*b^2*x^-39+-14//9*a^5*b^3*x^-36+-4//21*b*a^7*x^-42+-1//3*a*b^7*x^-24)
@test integrate(x^4*(a+b*x^3)^8, x) == :(1//5*a^8*x^5+1//29*b^8*x^29+b*a^7*x^8+4*a^5*b^3*x^14+4//13*a*b^7*x^26+14//5*a^3*b^5*x^20+28//11*a^6*b^2*x^11+28//23*a^2*b^6*x^23+70//17*a^4*b^4*x^17)
@test integrate(x^3*(a+b*x^3)^8, x) == :(1//4*a^8*x^4+1//28*b^8*x^28+8//7*b*a^7*x^7+8//25*a*b^7*x^25+14//5*a^6*b^2*x^10+14//11*a^2*b^6*x^22+35//8*a^4*b^4*x^16+56//13*a^5*b^3*x^13+56//19*a^3*b^5*x^19)
@test integrate(x*(a+b*x^3)^8, x) == :((1/2)*a^8*x^2+1//26*b^8*x^26+5*a^4*b^4*x^14+7//2*a^6*b^2*x^8+7//5*a^2*b^6*x^20+8//5*b*a^7*x^5+8//23*a*b^7*x^23+56//11*a^5*b^3*x^11+56//17*a^3*b^5*x^17)
@test integrate((a+b*x^3)^8, x) == :(x*a^8+1//25*b^8*x^25+2*b*a^7*x^4+4*a^6*b^2*x^7+4//11*a*b^7*x^22+7//2*a^3*b^5*x^16+28//5*a^5*b^3*x^10+28//19*a^2*b^6*x^19+70//13*a^4*b^4*x^13)
@test integrate(x^-2*(a+b*x^3)^8, x) == :(-1*a^8*x^-1+1//23*b^8*x^23+4*b*a^7*x^2+4*a^3*b^5*x^14+7*a^5*b^3*x^8+2//5*a*b^7*x^20+28//5*a^6*b^2*x^5+28//17*a^2*b^6*x^17+70//11*a^4*b^4*x^11)
@test integrate(x^-3*(a+b*x^3)^8, x) == :(-1//2*a^8*x^-2+1//22*b^8*x^22+7*a^4*b^4*x^10+7*a^6*b^2*x^4+8*b*x*a^7+8*a^5*b^3*x^7+7//4*a^2*b^6*x^16+8//19*a*b^7*x^19+56//13*a^3*b^5*x^13)
@test integrate(x^-5*(a+b*x^3)^8, x) == :(-1//4*a^8*x^-4+1//20*b^8*x^20+-8*b*a^7*x^-1+2*a^2*b^6*x^14+14*a^6*b^2*x^2+8//17*a*b^7*x^17+35//4*a^4*b^4*x^8+56//5*a^5*b^3*x^5+56//11*a^3*b^5*x^11)
@test integrate(x^-6*(a+b*x^3)^8, x) == :(-1//5*a^8*x^-5+1//19*b^8*x^19+(1/2)*a*b^7*x^16+-4*b*a^7*x^-2+10*a^4*b^4*x^7+14*a^5*b^3*x^4+28*x*a^6*b^2+28//5*a^3*b^5*x^10+28//13*a^2*b^6*x^13)
@test integrate(x^-8*(a+b*x^3)^8, x) == :(-1//7*a^8*x^-7+1//17*b^8*x^17+-28*a^6*b^2*x^-1+-2*b*a^7*x^-4+7*a^3*b^5*x^8+14*a^4*b^4*x^5+28*a^5*b^3*x^2+4//7*a*b^7*x^14+28//11*a^2*b^6*x^11)
@test integrate(x^-9*(a+b*x^3)^8, x) == :(-1//8*a^8*x^-8+1//16*b^8*x^16+-14*a^6*b^2*x^-2+8*a^3*b^5*x^7+56*x*a^5*b^3+-8//5*b*a^7*x^-5+8//13*a*b^7*x^13+14//5*a^2*b^6*x^10+35//2*a^4*b^4*x^4)
@test integrate(x^8*(a+b*x^3)^-1, x) == :(1//6*b^-1*x^6+-1//3*a*b^-2*x^3+1//3*a^2*b^-3*log(a+b*x^3))
@test integrate(x^5*(a+b*x^3)^-1, x) == :(1//3*b^-1*x^3+-1//3*a*b^-2*log(a+b*x^3))
@test integrate(x^2*(a+b*x^3)^-1, x) == :(1//3*b^-1*log(a+b*x^3))
@test integrate(x^-1*(a+b*x^3)^-1, x) == :(a^-1*log(x)+-1//3*a^-1*log(a+b*x^3))
@test integrate(x^-4*(a+b*x^3)^-1, x) == :(-1//3*a^-1*x^-3+-1*b*a^-2*log(x)+1//3*b*a^-2*log(a+b*x^3))
@test integrate(x^4*(a+b*x^3)^-1, x) == :((1/2)*b^-1*x^2+-1//6*a^2//3*b^-5//3*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//3*a^2//3*b^-5//3*log(a^1//3+x*b^1//3)+1//3*3^(1/2)*a^2//3*b^-5//3*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^3*(a+b*x^3)^-1, x) == :(x*b^-1+-1//3*a^1//3*b^-4//3*log(a^1//3+x*b^1//3)+1//6*a^1//3*b^-4//3*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//3*3^(1/2)*a^1//3*b^-4//3*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x*(a+b*x^3)^-1, x) == :(-1//3*a^-1//3*b^-2//3*log(a^1//3+x*b^1//3)+1//6*a^-1//3*b^-2//3*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+-1//3*3^(1/2)*a^-1//3*b^-2//3*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate((a+b*x^3)^-1, x) == :(-1//6*a^-2//3*b^-1//3*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//3*a^-2//3*b^-1//3*log(a^1//3+x*b^1//3)+-1//3*3^(1/2)*a^-2//3*b^-1//3*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^-2*(a+b*x^3)^-1, x) == :(-1*a^-1*x^-1+-1//6*a^-4//3*b^1//3*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//3*a^-4//3*b^1//3*log(a^1//3+x*b^1//3)+1//3*3^(1/2)*a^-4//3*b^1//3*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^-3*(a+b*x^3)^-1, x) == :(-1//2*a^-1*x^-2+-1//3*a^-5//3*b^2//3*log(a^1//3+x*b^1//3)+1//6*a^-5//3*b^2//3*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//3*3^(1/2)*a^-5//3*b^2//3*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^8*(a+b*x^3)^-2, x) == :(1//3*b^-2*x^3+-2//3*a*b^-3*log(a+b*x^3)+-1//3*a^2*b^-3*(a+b*x^3)^-1)
@test integrate(x^5*(a+b*x^3)^-2, x) == :(1//3*b^-2*log(a+b*x^3)+1//3*a*b^-2*(a+b*x^3)^-1)
@test integrate(x^2*(a+b*x^3)^-2, x) == :(-1//3*b^-1*(a+b*x^3)^-1)
@test integrate(x^-1*(a+b*x^3)^-2, x) == :(a^-2*log(x)+-1//3*a^-2*log(a+b*x^3)+1//3*a^-1*(a+b*x^3)^-1)
@test integrate(x^-4*(a+b*x^3)^-2, x) == :(-1//3*a^-2*x^-3+-2*b*a^-3*log(x)+-1//3*b*a^-2*(a+b*x^3)^-1+2//3*b*a^-3*log(a+b*x^3))
@test integrate(x^4*(a+b*x^3)^-2, x) == :(-2//9*a^-1//3*b^-5//3*log(a^1//3+x*b^1//3)+-1//3*b^-1*x^2*(a+b*x^3)^-1+1//9*a^-1//3*b^-5//3*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+-2//9*3^(1/2)*a^-1//3*b^-5//3*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^3*(a+b*x^3)^-2, x) == :(-1//3*x*b^-1*(a+b*x^3)^-1+-1//18*a^-2//3*b^-4//3*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//9*a^-2//3*b^-4//3*log(a^1//3+x*b^1//3)+-1//9*3^(1/2)*a^-2//3*b^-4//3*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x*(a+b*x^3)^-2, x) == :(-1//9*a^-4//3*b^-2//3*log(a^1//3+x*b^1//3)+1//3*a^-1*x^2*(a+b*x^3)^-1+1//18*a^-4//3*b^-2//3*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+-1//9*3^(1/2)*a^-4//3*b^-2//3*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate((a+b*x^3)^-2, x) == :(-1//9*a^-5//3*b^-1//3*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//3*x*a^-1*(a+b*x^3)^-1+2//9*a^-5//3*b^-1//3*log(a^1//3+x*b^1//3)+-2//9*3^(1/2)*a^-5//3*b^-1//3*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^-2*(a+b*x^3)^-2, x) == :(-4//3*a^-2*x^-1+-2//9*a^-7//3*b^1//3*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//3*a^-1*x^-1*(a+b*x^3)^-1+4//9*a^-7//3*b^1//3*log(a^1//3+x*b^1//3)+4//9*3^(1/2)*a^-7//3*b^1//3*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^-3*(a+b*x^3)^-2, x) == :(-5//6*a^-2*x^-2+-5//9*a^-8//3*b^2//3*log(a^1//3+x*b^1//3)+1//3*a^-1*x^-2*(a+b*x^3)^-1+5//18*a^-8//3*b^2//3*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+5//9*3^(1/2)*a^-8//3*b^2//3*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^11*(a+b*x^3)^-3, x) == :(1//3*b^-3*x^3+-1*a*b^-4*log(a+b*x^3)+-1*a^2*b^-4*(a+b*x^3)^-1+1//6*a^3*b^-4*(a+b*x^3)^-2)
@test integrate(x^8*(a+b*x^3)^-3, x) == :(1//3*b^-3*log(a+b*x^3)+-1//6*a^2*b^-3*(a+b*x^3)^-2+2//3*a*b^-3*(a+b*x^3)^-1)
@test integrate(x^5*(a+b*x^3)^-3, x) == :(1//6*a^-1*x^6*(a+b*x^3)^-2)
@test integrate(x^2*(a+b*x^3)^-3, x) == :(-1//6*b^-1*(a+b*x^3)^-2)
@test integrate(x^-1*(a+b*x^3)^-3, x) == :(a^-3*log(x)+-1//3*a^-3*log(a+b*x^3)+1//3*a^-2*(a+b*x^3)^-1+1//6*a^-1*(a+b*x^3)^-2)
@test integrate(x^-4*(a+b*x^3)^-3, x) == :(-1//3*a^-3*x^-3+b*a^-4*log(a+b*x^3)+-3*b*a^-4*log(x)+-2//3*b*a^-3*(a+b*x^3)^-1+-1//6*b*a^-2*(a+b*x^3)^-2)
@test integrate(x^7*(a+b*x^3)^-3, x) == :(-5//18*b^-2*x^2*(a+b*x^3)^-1+-5//27*a^-1//3*b^-8//3*log(a^1//3+x*b^1//3)+-1//6*b^-1*x^5*(a+b*x^3)^-2+5//54*a^-1//3*b^-8//3*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+-5//27*3^(1/2)*a^-1//3*b^-8//3*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^6*(a+b*x^3)^-3, x) == :(-2//9*x*b^-2*(a+b*x^3)^-1+-1//6*b^-1*x^4*(a+b*x^3)^-2+-1//27*a^-2//3*b^-7//3*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+2//27*a^-2//3*b^-7//3*log(a^1//3+x*b^1//3)+-2//27*3^(1/2)*a^-2//3*b^-7//3*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^4*(a+b*x^3)^-3, x) == :(-1//6*b^-1*x^2*(a+b*x^3)^-2+-1//27*a^-4//3*b^-5//3*log(a^1//3+x*b^1//3)+1//54*a^-4//3*b^-5//3*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+-1//27*3^(1/2)*a^-4//3*b^-5//3*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3))+1//9*a^-1*b^-1*x^2*(a+b*x^3)^-1)
@test integrate(x^3*(a+b*x^3)^-3, x) == :(-1//6*x*b^-1*(a+b*x^3)^-2+-1//54*a^-5//3*b^-4//3*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//27*a^-5//3*b^-4//3*log(a^1//3+x*b^1//3)+-1//27*3^(1/2)*a^-5//3*b^-4//3*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3))+1//18*x*a^-1*b^-1*(a+b*x^3)^-1)
@test integrate(x*(a+b*x^3)^-3, x) == :(-2//27*a^-7//3*b^-2//3*log(a^1//3+x*b^1//3)+1//6*a^-1*x^2*(a+b*x^3)^-2+1//27*a^-7//3*b^-2//3*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+2//9*a^-2*x^2*(a+b*x^3)^-1+-2//27*3^(1/2)*a^-7//3*b^-2//3*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate((a+b*x^3)^-3, x) == :(-5//54*a^-8//3*b^-1//3*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//6*x*a^-1*(a+b*x^3)^-2+5//18*x*a^-2*(a+b*x^3)^-1+5//27*a^-8//3*b^-1//3*log(a^1//3+x*b^1//3)+-5//27*3^(1/2)*a^-8//3*b^-1//3*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^8*(a+-1*b*x^3)^-1, x) == :(-1//6*b^-1*x^6+-1//3*a*b^-2*x^3+-1//3*a^2*b^-3*log(a+-1*b*x^3))
@test integrate(x^5*(a+-1*b*x^3)^-1, x) == :(-1//3*b^-1*x^3+-1//3*a*b^-2*log(a+-1*b*x^3))
@test integrate(x^2*(a+-1*b*x^3)^-1, x) == :(-1//3*b^-1*log(a+-1*b*x^3))
@test integrate(x^-1*(a+-1*b*x^3)^-1, x) == :(a^-1*log(x)+-1//3*a^-1*log(a+-1*b*x^3))
@test integrate(x^-4*(a+-1*b*x^3)^-1, x) == :(-1//3*a^-1*x^-3+b*a^-2*log(x)+-1//3*b*a^-2*log(a+-1*b*x^3))
@test integrate(x^4*(a+-1*b*x^3)^-1, x) == :(-1//2*b^-1*x^2+-1//3*a^2//3*b^-5//3*log(a^1//3+-1*x*b^1//3)+1//6*a^2//3*b^-5//3*log(a^2//3+b^2//3*x^2+x*a^1//3*b^1//3)+-1//3*3^(1/2)*a^2//3*b^-5//3*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+2*x*b^1//3)))
@test integrate(x^3*(a+-1*b*x^3)^-1, x) == :(-1*x*b^-1+-1//3*a^1//3*b^-4//3*log(a^1//3+-1*x*b^1//3)+1//6*a^1//3*b^-4//3*log(a^2//3+b^2//3*x^2+x*a^1//3*b^1//3)+1//3*3^(1/2)*a^1//3*b^-4//3*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+2*x*b^1//3)))
@test integrate(x*(a+-1*b*x^3)^-1, x) == :(-1//3*a^-1//3*b^-2//3*log(a^1//3+-1*x*b^1//3)+1//6*a^-1//3*b^-2//3*log(a^2//3+b^2//3*x^2+x*a^1//3*b^1//3)+-1//3*3^(1/2)*a^-1//3*b^-2//3*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+2*x*b^1//3)))
@test integrate((a+-1*b*x^3)^-1, x) == :(-1//3*a^-2//3*b^-1//3*log(a^1//3+-1*x*b^1//3)+1//6*a^-2//3*b^-1//3*log(a^2//3+b^2//3*x^2+x*a^1//3*b^1//3)+1//3*3^(1/2)*a^-2//3*b^-1//3*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+2*x*b^1//3)))
@test integrate(x^-2*(a+-1*b*x^3)^-1, x) == :(-1*a^-1*x^-1+-1//3*a^-4//3*b^1//3*log(a^1//3+-1*x*b^1//3)+1//6*a^-4//3*b^1//3*log(a^2//3+b^2//3*x^2+x*a^1//3*b^1//3)+-1//3*3^(1/2)*a^-4//3*b^1//3*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+2*x*b^1//3)))
@test integrate(x^-3*(a+-1*b*x^3)^-1, x) == :(-1//2*a^-1*x^-2+-1//3*a^-5//3*b^2//3*log(a^1//3+-1*x*b^1//3)+1//6*a^-5//3*b^2//3*log(a^2//3+b^2//3*x^2+x*a^1//3*b^1//3)+1//3*3^(1/2)*a^-5//3*b^2//3*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+2*x*b^1//3)))
@test integrate((1+a+b*x^3)^-1, x) == :(-1//6*b^-1//3*(1+a)^-2//3*log((1+a)^2//3+b^2//3*x^2+-1*x*b^1//3*(1+a)^1//3)+1//3*b^-1//3*(1+a)^-2//3*log((1+a)^1//3+x*b^1//3)+-1//3*3^(1/2)*b^-1//3*(1+a)^-2//3*arctan(1//3*3^(1/2)*(1+-2*x*b^1//3*(1+a)^-1//3)))
@test integrate((1+a+-1*b*x^3)^-1, x) == :(-1//3*b^-1//3*(1+a)^-2//3*log((1+a)^1//3+-1*x*b^1//3)+1//6*b^-1//3*(1+a)^-2//3*log((1+a)^2//3+b^2//3*x^2+x*b^1//3*(1+a)^1//3)+1//3*3^(1/2)*b^-1//3*(1+a)^-2//3*arctan(1//3*3^(1/2)*(1+2*x*b^1//3*(1+a)^-1//3)))
@test integrate((-1+a+b*x^3)^-1, x) == :(-1//6*b^-1//3*(1+-1a)^-2//3*log((1+-1a)^2//3+b^2//3*x^2+x*b^1//3*(1+-1a)^1//3)+1//3*b^-1//3*(1+-1a)^-2//3*log((1+-1a)^1//3+-1*x*b^1//3)+-1//3*3^(1/2)*b^-1//3*(1+-1a)^-2//3*arctan(1//3*3^(1/2)*(1+2*x*b^1//3*(1+-1a)^-1//3)))
@test integrate((-1+a+-1*b*x^3)^-1, x) == :(-1//3*b^-1//3*(1+-1a)^-2//3*log((1+-1a)^1//3+x*b^1//3)+1//6*b^-1//3*(1+-1a)^-2//3*log((1+-1a)^2//3+b^2//3*x^2+-1*x*b^1//3*(1+-1a)^1//3)+1//3*3^(1/2)*b^-1//3*(1+-1a)^-2//3*arctan(1//3*3^(1/2)*(1+-2*x*b^1//3*(1+-1a)^-1//3)))
@test integrate(x^(1/2)*(1+x^3)^-1, x) == :(2//3*arctan(x^3//2))
@test integrate(x^11*(a+b*x^3)^(1/2), x) == :(2//27*b^-4*(a+b*x^3)^9//2+-2//7*a*b^-4*(a+b*x^3)^7//2+-2//9*a^3*b^-4*(a+b*x^3)^3//2+2//5*a^2*b^-4*(a+b*x^3)^5//2)
@test integrate(x^8*(a+b*x^3)^(1/2), x) == :(2//21*b^-3*(a+b*x^3)^7//2+-4//15*a*b^-3*(a+b*x^3)^5//2+2//9*a^2*b^-3*(a+b*x^3)^3//2)
@test integrate(x^5*(a+b*x^3)^(1/2), x) == :(2//15*b^-2*(a+b*x^3)^5//2+-2//9*a*b^-2*(a+b*x^3)^3//2)
@test integrate(x^2*(a+b*x^3)^(1/2), x) == :(2//9*b^-1*(a+b*x^3)^3//2)
@test integrate(x^-1*(a+b*x^3)^(1/2), x) == :(2//3*(a+b*x^3)^(1/2)+-2//3*a^(1/2)*arctanh(a^-1//2*(a+b*x^3)^(1/2)))
@test integrate(x^-4*(a+b*x^3)^(1/2), x) == :(-1//3*x^-3*(a+b*x^3)^(1/2)+-1//3*b*a^-1//2*arctanh(a^-1//2*(a+b*x^3)^(1/2)))
@test integrate(x^-7*(a+b*x^3)^(1/2), x) == :(-1//6*x^-6*(a+b*x^3)^(1/2)+1//12*a^-3//2*b^2*arctanh(a^-1//2*(a+b*x^3)^(1/2))+-1//12*b*a^-1*x^-3*(a+b*x^3)^(1/2))
@test integrate(x^-10*(a+b*x^3)^(1/2), x) == :(-1//9*x^-9*(a+b*x^3)^(1/2)+-1//24*a^-5//2*b^3*arctanh(a^-1//2*(a+b*x^3)^(1/2))+-1//36*b*a^-1*x^-6*(a+b*x^3)^(1/2)+1//24*a^-2*b^2*x^-3*(a+b*x^3)^(1/2))
@test integrate(x^6*(a+b*x^3)^(1/2), x) == :(2//17*x^7*(a+b*x^3)^(1/2)+-48//935*x*a^2*b^-2*(a+b*x^3)^(1/2)+6//187*a*b^-1*x^4*(a+b*x^3)^(1/2)+32//935*3^3//4*a^3*b^-7//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^3*(a+b*x^3)^(1/2), x) == :(2//11*x^4*(a+b*x^3)^(1/2)+6//55*a*x*b^-1*(a+b*x^3)^(1/2)+-4//55*3^3//4*a^2*b^-4//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate((a+b*x^3)^(1/2), x) == :(2//5*x*(a+b*x^3)^(1/2)+2//5*a*3^3//4*b^-1//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-3*(a+b*x^3)^(1/2), x) == :(-1//2*x^-2*(a+b*x^3)^(1/2)+(1/2)*3^3//4*b^2//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-6*(a+b*x^3)^(1/2), x) == :(-1//5*x^-5*(a+b*x^3)^(1/2)+-3//20*b*a^-1*x^-2*(a+b*x^3)^(1/2)+-1//20*3^3//4*a^-1*b^5//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-9*(a+b*x^3)^(1/2), x) == :(-1//8*x^-8*(a+b*x^3)^(1/2)+-3//80*b*a^-1*x^-5*(a+b*x^3)^(1/2)+21//320*a^-2*b^2*x^-2*(a+b*x^3)^(1/2)+7//320*3^3//4*a^-2*b^8//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^7*(a+b*x^3)^(1/2), x) == :(2//19*x^8*(a+b*x^3)^(1/2)+-60//1729*a^2*b^-2*x^2*(a+b*x^3)^(1/2)+6//247*a*b^-1*x^5*(a+b*x^3)^(1/2)+240//1729*a^3*b^-8//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1+-120//1729*3^1//4*a^10//3*b^-8//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+80//1729*2^(1/2)*3^3//4*a^10//3*b^-8//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^4*(a+b*x^3)^(1/2), x) == :(2//13*x^5*(a+b*x^3)^(1/2)+-24//91*a^2*b^-5//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1+6//91*a*b^-1*x^2*(a+b*x^3)^(1/2)+-8//91*2^(1/2)*3^3//4*a^7//3*b^-5//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+12//91*3^1//4*a^7//3*b^-5//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x*(a+b*x^3)^(1/2), x) == :(2//7*x^2*(a+b*x^3)^(1/2)+6//7*a*b^-2//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1+-3//7*3^1//4*a^4//3*b^-2//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+2//7*2^(1/2)*3^3//4*a^4//3*b^-2//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-2*(a+b*x^3)^(1/2), x) == :(-1*x^-1*(a+b*x^3)^(1/2)+3*b^1//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1+2^(1/2)*3^3//4*a^1//3*b^1//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+-3//2*3^1//4*a^1//3*b^1//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-5*(a+b*x^3)^(1/2), x) == :(-1//4*x^-4*(a+b*x^3)^(1/2)+-3//8*b*a^-1*x^-1*(a+b*x^3)^(1/2)+3//8*a^-1*b^4//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1+-3//16*3^1//4*a^-2//3*b^4//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+1//8*2^(1/2)*3^3//4*a^-2//3*b^4//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^11*(a+b*x^3)^3//2, x) == :(2//33*b^-4*(a+b*x^3)^11//2+-2//9*a*b^-4*(a+b*x^3)^9//2+-2//15*a^3*b^-4*(a+b*x^3)^5//2+2//7*a^2*b^-4*(a+b*x^3)^7//2)
@test integrate(x^8*(a+b*x^3)^3//2, x) == :(2//27*b^-3*(a+b*x^3)^9//2+-4//21*a*b^-3*(a+b*x^3)^7//2+2//15*a^2*b^-3*(a+b*x^3)^5//2)
@test integrate(x^5*(a+b*x^3)^3//2, x) == :(2//21*b^-2*(a+b*x^3)^7//2+-2//15*a*b^-2*(a+b*x^3)^5//2)
@test integrate(x^2*(a+b*x^3)^3//2, x) == :(2//15*b^-1*(a+b*x^3)^5//2)
@test integrate(x^-1*(a+b*x^3)^3//2, x) == :(2//9*(a+b*x^3)^3//2+-2//3*a^3//2*arctanh(a^-1//2*(a+b*x^3)^(1/2))+2//3*a*(a+b*x^3)^(1/2))
@test integrate(x^-4*(a+b*x^3)^3//2, x) == :(b*(a+b*x^3)^(1/2)+-1//3*x^-3*(a+b*x^3)^3//2+-1*b*a^(1/2)*arctanh(a^-1//2*(a+b*x^3)^(1/2)))
@test integrate(x^-7*(a+b*x^3)^3//2, x) == :(-1//6*x^-6*(a+b*x^3)^3//2+-1//4*b*x^-3*(a+b*x^3)^(1/2)+-1//4*a^-1//2*b^2*arctanh(a^-1//2*(a+b*x^3)^(1/2)))
@test integrate(x^6*(a+b*x^3)^3//2, x) == :(2//23*x^7*(a+b*x^3)^3//2+18//391*a*x^7*(a+b*x^3)^(1/2)+-432//21505*x*a^3*b^-2*(a+b*x^3)^(1/2)+54//4301*a^2*b^-1*x^4*(a+b*x^3)^(1/2)+288//21505*3^3//4*a^4*b^-7//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^3*(a+b*x^3)^3//2, x) == :(2//17*x^4*(a+b*x^3)^3//2+18//187*a*x^4*(a+b*x^3)^(1/2)+54//935*x*a^2*b^-1*(a+b*x^3)^(1/2)+-36//935*3^3//4*a^3*b^-4//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate((a+b*x^3)^3//2, x) == :(2//11*x*(a+b*x^3)^3//2+18//55*a*x*(a+b*x^3)^(1/2)+18//55*3^3//4*a^2*b^-1//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-3*(a+b*x^3)^3//2, x) == :(-1//2*x^-2*(a+b*x^3)^3//2+9//10*b*x*(a+b*x^3)^(1/2)+9//10*a*3^3//4*b^2//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-6*(a+b*x^3)^3//2, x) == :(-1//5*x^-5*(a+b*x^3)^3//2+-9//20*b*x^-2*(a+b*x^3)^(1/2)+9//20*3^3//4*b^5//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^7*(a+b*x^3)^3//2, x) == :(2//25*x^8*(a+b*x^3)^3//2+18//475*a*x^8*(a+b*x^3)^(1/2)+-108//8645*a^3*b^-2*x^2*(a+b*x^3)^(1/2)+54//6175*a^2*b^-1*x^5*(a+b*x^3)^(1/2)+432//8645*a^4*b^-8//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1+-216//8645*3^1//4*a^13//3*b^-8//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+144//8645*2^(1/2)*3^3//4*a^13//3*b^-8//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^4*(a+b*x^3)^3//2, x) == :(2//19*x^5*(a+b*x^3)^3//2+18//247*a*x^5*(a+b*x^3)^(1/2)+-216//1729*a^3*b^-5//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1+54//1729*a^2*b^-1*x^2*(a+b*x^3)^(1/2)+-72//1729*2^(1/2)*3^3//4*a^10//3*b^-5//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+108//1729*3^1//4*a^10//3*b^-5//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x*(a+b*x^3)^3//2, x) == :(2//13*x^2*(a+b*x^3)^3//2+18//91*a*x^2*(a+b*x^3)^(1/2)+54//91*a^2*b^-2//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1+-27//91*3^1//4*a^7//3*b^-2//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+18//91*2^(1/2)*3^3//4*a^7//3*b^-2//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-2*(a+b*x^3)^3//2, x) == :(-1*x^-1*(a+b*x^3)^3//2+9//7*b*x^2*(a+b*x^3)^(1/2)+27*a*b^1//3*(a+b*x^3)^(1/2)*(7*x*b^1//3+7*a^1//3*(1+3^(1/2)))^-1+-27//14*3^1//4*a^4//3*b^1//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+9//7*2^(1/2)*3^3//4*a^4//3*b^1//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-5*(a+b*x^3)^3//2, x) == :(-1//4*x^-4*(a+b*x^3)^3//2+27*b^4//3*(a+b*x^3)^(1/2)*(8*x*b^1//3+8*a^1//3*(1+3^(1/2)))^-1+-9//8*b*x^-1*(a+b*x^3)^(1/2)+-27//16*3^1//4*a^1//3*b^4//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+9//8*2^(1/2)*3^3//4*a^1//3*b^4//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^11*(a+b*x^3)^-1//2, x) == :(2//21*b^-4*(a+b*x^3)^7//2+-2//3*a^3*b^-4*(a+b*x^3)^(1/2)+-2//5*a*b^-4*(a+b*x^3)^5//2+2//3*a^2*b^-4*(a+b*x^3)^3//2)
@test integrate(x^8*(a+b*x^3)^-1//2, x) == :(2//15*b^-3*(a+b*x^3)^5//2+-4//9*a*b^-3*(a+b*x^3)^3//2+2//3*a^2*b^-3*(a+b*x^3)^(1/2))
@test integrate(x^5*(a+b*x^3)^-1//2, x) == :(2//9*b^-2*(a+b*x^3)^3//2+-2//3*a*b^-2*(a+b*x^3)^(1/2))
@test integrate(x^2*(a+b*x^3)^-1//2, x) == :(2//3*b^-1*(a+b*x^3)^(1/2))
@test integrate(x^-1*(a+b*x^3)^-1//2, x) == :(-2//3*a^-1//2*arctanh(a^-1//2*(a+b*x^3)^(1/2)))
@test integrate(x^-4*(a+b*x^3)^-1//2, x) == :(-1//3*a^-1*x^-3*(a+b*x^3)^(1/2)+1//3*b*a^-3//2*arctanh(a^-1//2*(a+b*x^3)^(1/2)))
@test integrate(x^-7*(a+b*x^3)^-1//2, x) == :(-1//4*a^-5//2*b^2*arctanh(a^-1//2*(a+b*x^3)^(1/2))+-1//6*a^-1*x^-6*(a+b*x^3)^(1/2)+1//4*b*a^-2*x^-3*(a+b*x^3)^(1/2))
@test integrate(x^6*(a+b*x^3)^-1//2, x) == :(2//11*b^-1*x^4*(a+b*x^3)^(1/2)+-16//55*a*x*b^-2*(a+b*x^3)^(1/2)+32//165*3^3//4*a^2*b^-7//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^3*(a+b*x^3)^-1//2, x) == :(2//5*x*b^-1*(a+b*x^3)^(1/2)+-4//15*a*3^3//4*b^-4//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate((a+b*x^3)^-1//2, x) == :(2//3*3^3//4*b^-1//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-3*(a+b*x^3)^-1//2, x) == :(-1//2*a^-1*x^-2*(a+b*x^3)^(1/2)+-1//6*3^3//4*a^-1*b^2//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-6*(a+b*x^3)^-1//2, x) == :(-1//5*a^-1*x^-5*(a+b*x^3)^(1/2)+7//20*b*a^-2*x^-2*(a+b*x^3)^(1/2)+7//60*3^3//4*a^-2*b^5//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^7*(a+b*x^3)^-1//2, x) == :(2//13*b^-1*x^5*(a+b*x^3)^(1/2)+-20//91*a*b^-2*x^2*(a+b*x^3)^(1/2)+80//91*a^2*b^-8//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1+-40//91*3^1//4*a^7//3*b^-8//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+80//273*2^(1/2)*3^3//4*a^7//3*b^-8//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^4*(a+b*x^3)^-1//2, x) == :(2//7*b^-1*x^2*(a+b*x^3)^(1/2)+-8//7*a*b^-5//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1+-8//21*2^(1/2)*3^3//4*a^4//3*b^-5//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+4//7*3^1//4*a^4//3*b^-5//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x*(a+b*x^3)^-1//2, x) == :(2*b^-2//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1+-1*3^1//4*a^1//3*b^-2//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+2//3*2^(1/2)*3^3//4*a^1//3*b^-2//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-2*(a+b*x^3)^-1//2, x) == :(-1*a^-1*x^-1*(a+b*x^3)^(1/2)+a^-1*b^1//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1+-1//2*3^1//4*a^-2//3*b^1//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+1//3*2^(1/2)*3^3//4*a^-2//3*b^1//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-5*(a+b*x^3)^-1//2, x) == :(-1//4*a^-1*x^-4*(a+b*x^3)^(1/2)+-5//8*a^-2*b^4//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1+5//8*b*a^-2*x^-1*(a+b*x^3)^(1/2)+-5//24*2^(1/2)*3^3//4*a^-5//3*b^4//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+5//16*3^1//4*a^-5//3*b^4//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^11*(a+b*x^3)^-3//2, x) == :(2//15*b^-4*(a+b*x^3)^5//2+2*a^2*b^-4*(a+b*x^3)^(1/2)+-2//3*a*b^-4*(a+b*x^3)^3//2+2//3*a^3*b^-4*(a+b*x^3)^-1//2)
@test integrate(x^8*(a+b*x^3)^-3//2, x) == :(2//9*b^-3*(a+b*x^3)^3//2+-4//3*a*b^-3*(a+b*x^3)^(1/2)+-2//3*a^2*b^-3*(a+b*x^3)^-1//2)
@test integrate(x^5*(a+b*x^3)^-3//2, x) == :(2//3*b^-2*(a+b*x^3)^(1/2)+2//3*a*b^-2*(a+b*x^3)^-1//2)
@test integrate(x^2*(a+b*x^3)^-3//2, x) == :(-2//3*b^-1*(a+b*x^3)^-1//2)
@test integrate(x^-1*(a+b*x^3)^-3//2, x) == :(-2//3*a^-3//2*arctanh(a^-1//2*(a+b*x^3)^(1/2))+2//3*a^-1*(a+b*x^3)^-1//2)
@test integrate(x^-4*(a+b*x^3)^-3//2, x) == :(b*a^-5//2*arctanh(a^-1//2*(a+b*x^3)^(1/2))+-1*b*a^-2*(a+b*x^3)^-1//2+-1//3*a^-1*x^-3*(a+b*x^3)^-1//2)
@test integrate(x^-7*(a+b*x^3)^-3//2, x) == :(-5//4*a^-7//2*b^2*arctanh(a^-1//2*(a+b*x^3)^(1/2))+-1//6*a^-1*x^-6*(a+b*x^3)^-1//2+5//4*a^-3*b^2*(a+b*x^3)^-1//2+5//12*b*a^-2*x^-3*(a+b*x^3)^-1//2)
@test integrate(x^6*(a+b*x^3)^-3//2, x) == :(-2//3*b^-1*x^4*(a+b*x^3)^-1//2+16//15*x*b^-2*(a+b*x^3)^(1/2)+-32//45*a*3^3//4*b^-7//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^3*(a+b*x^3)^-3//2, x) == :(-2//3*x*b^-1*(a+b*x^3)^-1//2+4//9*3^3//4*b^-4//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate((a+b*x^3)^-3//2, x) == :(2//3*x*a^-1*(a+b*x^3)^-1//2+2//9*3^3//4*a^-1*b^-1//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-3*(a+b*x^3)^-3//2, x) == :(-7//6*a^-2*x^-2*(a+b*x^3)^(1/2)+2//3*a^-1*x^-2*(a+b*x^3)^-1//2+-7//18*3^3//4*a^-2*b^2//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-6*(a+b*x^3)^-3//2, x) == :(-13//15*a^-2*x^-5*(a+b*x^3)^(1/2)+2//3*a^-1*x^-5*(a+b*x^3)^-1//2+91//60*b*a^-3*x^-2*(a+b*x^3)^(1/2)+91//180*3^3//4*a^-3*b^5//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^7*(a+b*x^3)^-3//2, x) == :(-2//3*b^-1*x^5*(a+b*x^3)^-1//2+20//21*b^-2*x^2*(a+b*x^3)^(1/2)+-80//21*a*b^-8//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1+-80//63*2^(1/2)*3^3//4*a^4//3*b^-8//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+40//21*3^1//4*a^4//3*b^-8//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^4*(a+b*x^3)^-3//2, x) == :(-2//3*b^-1*x^2*(a+b*x^3)^-1//2+8//3*b^-5//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1+-4//3*3^1//4*a^1//3*b^-5//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+8//9*2^(1/2)*3^3//4*a^1//3*b^-5//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x*(a+b*x^3)^-3//2, x) == :(2//3*a^-1*x^2*(a+b*x^3)^-1//2+-2//3*a^-1*b^-2//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1+-2//9*2^(1/2)*3^3//4*a^-2//3*b^-2//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+1//3*3^1//4*a^-2//3*b^-2//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-2*(a+b*x^3)^-3//2, x) == :(-5//3*a^-2*x^-1*(a+b*x^3)^(1/2)+2//3*a^-1*x^-1*(a+b*x^3)^-1//2+5//3*a^-2*b^1//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1+-5//6*3^1//4*a^-5//3*b^1//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+5//9*2^(1/2)*3^3//4*a^-5//3*b^1//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-5*(a+b*x^3)^-3//2, x) == :(-11//12*a^-2*x^-4*(a+b*x^3)^(1/2)+2//3*a^-1*x^-4*(a+b*x^3)^-1//2+-55//24*a^-3*b^4//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1+55//24*b*a^-3*x^-1*(a+b*x^3)^(1/2)+-55//72*2^(1/2)*3^3//4*a^-8//3*b^4//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+55//48*3^1//4*a^-8//3*b^4//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^11*(1+x^3)^-1//2, x) == :(-2//3*(1+x^3)^(1/2)+-2//5*(1+x^3)^5//2+2//3*(1+x^3)^3//2+2//21*(1+x^3)^7//2)
@test integrate(x^8*(1+x^3)^-1//2, x) == :(-4//9*(1+x^3)^3//2+2//3*(1+x^3)^(1/2)+2//15*(1+x^3)^5//2)
@test integrate(x^5*(1+x^3)^-1//2, x) == :(-2//3*(1+x^3)^(1/2)+2//9*(1+x^3)^3//2)
@test integrate(x^2*(1+x^3)^-1//2, x) == :(2//3*(1+x^3)^(1/2))
@test integrate(x^-1*(1+x^3)^-1//2, x) == :(-2//3*arctanh((1+x^3)^(1/2)))
@test integrate(x^-4*(1+x^3)^-1//2, x) == :(1//3*arctanh((1+x^3)^(1/2))+-1//3*x^-3*(1+x^3)^(1/2))
@test integrate(x^-7*(1+x^3)^-1//2, x) == :(-1//4*arctanh((1+x^3)^(1/2))+-1//6*x^-6*(1+x^3)^(1/2)+1//4*x^-3*(1+x^3)^(1/2))
@test integrate(x^-10*(1+x^3)^-1//2, x) == :(5//24*arctanh((1+x^3)^(1/2))+-5//24*x^-3*(1+x^3)^(1/2)+-1//9*x^-9*(1+x^3)^(1/2)+5//36*x^-6*(1+x^3)^(1/2))
@test integrate(x^6*(1+x^3)^-1//2, x) == :(-16//55*x*(1+x^3)^(1/2)+2//11*x^4*(1+x^3)^(1/2)+32//165*3^3//4*((1+x+3^(1/2))^-2*(1+x))^-1//2*((1+x+3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(1+x^3)^-1//2*(2+3^(1/2))^(1/2)*(1+x)*Elliptic.F(arcsin((1+x+3^(1/2))^-1*(1+x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate(x^3*(1+x^3)^-1//2, x) == :(2//5*x*(1+x^3)^(1/2)+-4//15*3^3//4*((1+x+3^(1/2))^-2*(1+x))^-1//2*((1+x+3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(1+x^3)^-1//2*(2+3^(1/2))^(1/2)*(1+x)*Elliptic.F(arcsin((1+x+3^(1/2))^-1*(1+x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate((1+x^3)^-1//2, x) == :(2//3*3^3//4*((1+x+3^(1/2))^-2*(1+x))^-1//2*((1+x+3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(1+x^3)^-1//2*(2+3^(1/2))^(1/2)*(1+x)*Elliptic.F(arcsin((1+x+3^(1/2))^-1*(1+x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate(x^-3*(1+x^3)^-1//2, x) == :(-1//2*x^-2*(1+x^3)^(1/2)+-1//6*3^3//4*((1+x+3^(1/2))^-2*(1+x))^-1//2*((1+x+3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(1+x^3)^-1//2*(2+3^(1/2))^(1/2)*(1+x)*Elliptic.F(arcsin((1+x+3^(1/2))^-1*(1+x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate(x^-6*(1+x^3)^-1//2, x) == :(-1//5*x^-5*(1+x^3)^(1/2)+7//20*x^-2*(1+x^3)^(1/2)+7//60*3^3//4*((1+x+3^(1/2))^-2*(1+x))^-1//2*((1+x+3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(1+x^3)^-1//2*(2+3^(1/2))^(1/2)*(1+x)*Elliptic.F(arcsin((1+x+3^(1/2))^-1*(1+x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate(x^7*(1+x^3)^-1//2, x) == :(80*(1+x^3)^(1/2)*(91+91x+91*3^(1/2))^-1+-20//91*x^2*(1+x^3)^(1/2)+2//13*x^5*(1+x^3)^(1/2)+-40//91*3^1//4*((1+x+3^(1/2))^-2*(1+x))^-1//2*((1+x+3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(1+x^3)^-1//2*(2+-1*3^(1/2))^(1/2)*(1+x)*Elliptic.E(arcsin((1+x+3^(1/2))^-1*(1+x+-1*3^(1/2))),-7+-4*3^(1/2))+80//273*2^(1/2)*3^3//4*((1+x+3^(1/2))^-2*(1+x))^-1//2*((1+x+3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(1+x^3)^-1//2*(1+x)*Elliptic.F(arcsin((1+x+3^(1/2))^-1*(1+x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate(x^4*(1+x^3)^-1//2, x) == :(-8*(1+x^3)^(1/2)*(7+7x+7*3^(1/2))^-1+2//7*x^2*(1+x^3)^(1/2)+-8//21*2^(1/2)*3^3//4*((1+x+3^(1/2))^-2*(1+x))^-1//2*((1+x+3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(1+x^3)^-1//2*(1+x)*Elliptic.F(arcsin((1+x+3^(1/2))^-1*(1+x+-1*3^(1/2))),-7+-4*3^(1/2))+4//7*3^1//4*((1+x+3^(1/2))^-2*(1+x))^-1//2*((1+x+3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(1+x^3)^-1//2*(2+-1*3^(1/2))^(1/2)*(1+x)*Elliptic.E(arcsin((1+x+3^(1/2))^-1*(1+x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate(x*(1+x^3)^-1//2, x) == :(2*(1+x^3)^(1/2)*(1+x+3^(1/2))^-1+-1*3^1//4*((1+x+3^(1/2))^-2*(1+x))^-1//2*((1+x+3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(1+x^3)^-1//2*(2+-1*3^(1/2))^(1/2)*(1+x)*Elliptic.E(arcsin((1+x+3^(1/2))^-1*(1+x+-1*3^(1/2))),-7+-4*3^(1/2))+2//3*2^(1/2)*3^3//4*((1+x+3^(1/2))^-2*(1+x))^-1//2*((1+x+3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(1+x^3)^-1//2*(1+x)*Elliptic.F(arcsin((1+x+3^(1/2))^-1*(1+x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate(x^-2*(1+x^3)^-1//2, x) == :((1+x^3)^(1/2)*(1+x+3^(1/2))^-1+-1*x^-1*(1+x^3)^(1/2)+-1//2*3^1//4*((1+x+3^(1/2))^-2*(1+x))^-1//2*((1+x+3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(1+x^3)^-1//2*(2+-1*3^(1/2))^(1/2)*(1+x)*Elliptic.E(arcsin((1+x+3^(1/2))^-1*(1+x+-1*3^(1/2))),-7+-4*3^(1/2))+1//3*2^(1/2)*3^3//4*((1+x+3^(1/2))^-2*(1+x))^-1//2*((1+x+3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(1+x^3)^-1//2*(1+x)*Elliptic.F(arcsin((1+x+3^(1/2))^-1*(1+x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate(x^-5*(1+x^3)^-1//2, x) == :(-5*(1+x^3)^(1/2)*(8+8x+8*3^(1/2))^-1+-1//4*x^-4*(1+x^3)^(1/2)+5//8*x^-1*(1+x^3)^(1/2)+-1//24*2^(1/2)*3^3//4*((1+x+3^(1/2))^-2*(1+x))^-1//2*((1+x+3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(1+x^3)^-1//2*(5+5x)*Elliptic.F(arcsin((1+x+3^(1/2))^-1*(1+x+-1*3^(1/2))),-7+-4*3^(1/2))+5//16*3^1//4*((1+x+3^(1/2))^-2*(1+x))^-1//2*((1+x+3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(1+x^3)^-1//2*(2+-1*3^(1/2))^(1/2)*(1+x)*Elliptic.E(arcsin((1+x+3^(1/2))^-1*(1+x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate(x^11*(1+-1*x^3)^-1//2, x) == :(-2//3*(1+-1*x^3)^(1/2)+-2//5*(1+-1*x^3)^5//2+2//3*(1+-1*x^3)^3//2+2//21*(1+-1*x^3)^7//2)
@test integrate(x^8*(1+-1*x^3)^-1//2, x) == :(-2//3*(1+-1*x^3)^(1/2)+-2//15*(1+-1*x^3)^5//2+4//9*(1+-1*x^3)^3//2)
@test integrate(x^5*(1+-1*x^3)^-1//2, x) == :(-2//3*(1+-1*x^3)^(1/2)+2//9*(1+-1*x^3)^3//2)
@test integrate(x^2*(1+-1*x^3)^-1//2, x) == :(-2//3*(1+-1*x^3)^(1/2))
@test integrate(x^-1*(1+-1*x^3)^-1//2, x) == :(-2//3*arctanh((1+-1*x^3)^(1/2)))
@test integrate(x^-4*(1+-1*x^3)^-1//2, x) == :(-1//3*arctanh((1+-1*x^3)^(1/2))+-1//3*x^-3*(1+-1*x^3)^(1/2))
@test integrate(x^-7*(1+-1*x^3)^-1//2, x) == :(-1//4*arctanh((1+-1*x^3)^(1/2))+-1//4*x^-3*(1+-1*x^3)^(1/2)+-1//6*x^-6*(1+-1*x^3)^(1/2))
@test integrate(x^-10*(1+-1*x^3)^-1//2, x) == :(-5//24*arctanh((1+-1*x^3)^(1/2))+-5//24*x^-3*(1+-1*x^3)^(1/2)+-5//36*x^-6*(1+-1*x^3)^(1/2)+-1//9*x^-9*(1+-1*x^3)^(1/2))
@test integrate(x^6*(1+-1*x^3)^-1//2, x) == :(-16//55*x*(1+-1*x^3)^(1/2)+-2//11*x^4*(1+-1*x^3)^(1/2)+-32//165*3^3//4*((1+3^(1/2)+-1x)^-2*(1+-1x))^-1//2*((1+3^(1/2)+-1x)^-2*(1+x+x^2))^(1/2)*(1+-1*x^3)^-1//2*(2+3^(1/2))^(1/2)*(1+-1x)*Elliptic.F(arcsin((1+3^(1/2)+-1x)^-1*(1+-1x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate(x^3*(1+-1*x^3)^-1//2, x) == :(-2//5*x*(1+-1*x^3)^(1/2)+-4//15*3^3//4*((1+3^(1/2)+-1x)^-2*(1+-1x))^-1//2*((1+3^(1/2)+-1x)^-2*(1+x+x^2))^(1/2)*(1+-1*x^3)^-1//2*(2+3^(1/2))^(1/2)*(1+-1x)*Elliptic.F(arcsin((1+3^(1/2)+-1x)^-1*(1+-1x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate((1+-1*x^3)^-1//2, x) == :(-2//3*3^3//4*((1+3^(1/2)+-1x)^-2*(1+-1x))^-1//2*((1+3^(1/2)+-1x)^-2*(1+x+x^2))^(1/2)*(1+-1*x^3)^-1//2*(2+3^(1/2))^(1/2)*(1+-1x)*Elliptic.F(arcsin((1+3^(1/2)+-1x)^-1*(1+-1x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate(x^-3*(1+-1*x^3)^-1//2, x) == :(-1//2*x^-2*(1+-1*x^3)^(1/2)+-1//6*3^3//4*((1+3^(1/2)+-1x)^-2*(1+-1x))^-1//2*((1+3^(1/2)+-1x)^-2*(1+x+x^2))^(1/2)*(1+-1*x^3)^-1//2*(2+3^(1/2))^(1/2)*(1+-1x)*Elliptic.F(arcsin((1+3^(1/2)+-1x)^-1*(1+-1x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate(x^-6*(1+-1*x^3)^-1//2, x) == :(-7//20*x^-2*(1+-1*x^3)^(1/2)+-1//5*x^-5*(1+-1*x^3)^(1/2)+-7//60*3^3//4*((1+3^(1/2)+-1x)^-2*(1+-1x))^-1//2*((1+3^(1/2)+-1x)^-2*(1+x+x^2))^(1/2)*(1+-1*x^3)^-1//2*(2+3^(1/2))^(1/2)*(1+-1x)*Elliptic.F(arcsin((1+3^(1/2)+-1x)^-1*(1+-1x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate(x^7*(1+-1*x^3)^-1//2, x) == :(80*(1+-1*x^3)^(1/2)*(91+-91x+91*3^(1/2))^-1+-20//91*x^2*(1+-1*x^3)^(1/2)+-2//13*x^5*(1+-1*x^3)^(1/2)+-40//91*3^1//4*((1+3^(1/2)+-1x)^-2*(1+-1x))^-1//2*((1+3^(1/2)+-1x)^-2*(1+x+x^2))^(1/2)*(1+-1*x^3)^-1//2*(2+-1*3^(1/2))^(1/2)*(1+-1x)*Elliptic.E(arcsin((1+3^(1/2)+-1x)^-1*(1+-1x+-1*3^(1/2))),-7+-4*3^(1/2))+80//273*2^(1/2)*3^3//4*((1+3^(1/2)+-1x)^-2*(1+-1x))^-1//2*((1+3^(1/2)+-1x)^-2*(1+x+x^2))^(1/2)*(1+-1*x^3)^-1//2*(1+-1x)*Elliptic.F(arcsin((1+3^(1/2)+-1x)^-1*(1+-1x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate(x^4*(1+-1*x^3)^-1//2, x) == :(8*(1+-1*x^3)^(1/2)*(7+-7x+7*3^(1/2))^-1+-2//7*x^2*(1+-1*x^3)^(1/2)+-4//7*3^1//4*((1+3^(1/2)+-1x)^-2*(1+-1x))^-1//2*((1+3^(1/2)+-1x)^-2*(1+x+x^2))^(1/2)*(1+-1*x^3)^-1//2*(2+-1*3^(1/2))^(1/2)*(1+-1x)*Elliptic.E(arcsin((1+3^(1/2)+-1x)^-1*(1+-1x+-1*3^(1/2))),-7+-4*3^(1/2))+8//21*2^(1/2)*3^3//4*((1+3^(1/2)+-1x)^-2*(1+-1x))^-1//2*((1+3^(1/2)+-1x)^-2*(1+x+x^2))^(1/2)*(1+-1*x^3)^-1//2*(1+-1x)*Elliptic.F(arcsin((1+3^(1/2)+-1x)^-1*(1+-1x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate(x*(1+-1*x^3)^-1//2, x) == :(2*(1+-1*x^3)^(1/2)*(1+3^(1/2)+-1x)^-1+-1*3^1//4*((1+3^(1/2)+-1x)^-2*(1+-1x))^-1//2*((1+3^(1/2)+-1x)^-2*(1+x+x^2))^(1/2)*(1+-1*x^3)^-1//2*(2+-1*3^(1/2))^(1/2)*(1+-1x)*Elliptic.E(arcsin((1+3^(1/2)+-1x)^-1*(1+-1x+-1*3^(1/2))),-7+-4*3^(1/2))+2//3*2^(1/2)*3^3//4*((1+3^(1/2)+-1x)^-2*(1+-1x))^-1//2*((1+3^(1/2)+-1x)^-2*(1+x+x^2))^(1/2)*(1+-1*x^3)^-1//2*(1+-1x)*Elliptic.F(arcsin((1+3^(1/2)+-1x)^-1*(1+-1x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate(x^-2*(1+-1*x^3)^-1//2, x) == :(-1*x^-1*(1+-1*x^3)^(1/2)+-1*(1+-1*x^3)^(1/2)*(1+3^(1/2)+-1x)^-1+(1/2)*3^1//4*((1+3^(1/2)+-1x)^-2*(1+-1x))^-1//2*((1+3^(1/2)+-1x)^-2*(1+x+x^2))^(1/2)*(1+-1*x^3)^-1//2*(2+-1*3^(1/2))^(1/2)*(1+-1x)*Elliptic.E(arcsin((1+3^(1/2)+-1x)^-1*(1+-1x+-1*3^(1/2))),-7+-4*3^(1/2))+-1//3*2^(1/2)*3^3//4*((1+3^(1/2)+-1x)^-2*(1+-1x))^-1//2*((1+3^(1/2)+-1x)^-2*(1+x+x^2))^(1/2)*(1+-1*x^3)^-1//2*(1+-1x)*Elliptic.F(arcsin((1+3^(1/2)+-1x)^-1*(1+-1x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate(x^-5*(1+-1*x^3)^-1//2, x) == :(-5*(1+-1*x^3)^(1/2)*(8+-8x+8*3^(1/2))^-1+-5//8*x^-1*(1+-1*x^3)^(1/2)+-1//4*x^-4*(1+-1*x^3)^(1/2)+-1//24*2^(1/2)*3^3//4*((1+3^(1/2)+-1x)^-2*(1+-1x))^-1//2*((1+3^(1/2)+-1x)^-2*(1+x+x^2))^(1/2)*(1+-1*x^3)^-1//2*(5+-5x)*Elliptic.F(arcsin((1+3^(1/2)+-1x)^-1*(1+-1x+-1*3^(1/2))),-7+-4*3^(1/2))+5//16*3^1//4*((1+3^(1/2)+-1x)^-2*(1+-1x))^-1//2*((1+3^(1/2)+-1x)^-2*(1+x+x^2))^(1/2)*(1+-1*x^3)^-1//2*(2+-1*3^(1/2))^(1/2)*(1+-1x)*Elliptic.E(arcsin((1+3^(1/2)+-1x)^-1*(1+-1x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate(x^11*(-1+x^3)^-1//2, x) == :(2//3*(-1+x^3)^(1/2)+2//3*(-1+x^3)^3//2+2//5*(-1+x^3)^5//2+2//21*(-1+x^3)^7//2)
@test integrate(x^8*(-1+x^3)^-1//2, x) == :(2//3*(-1+x^3)^(1/2)+2//15*(-1+x^3)^5//2+4//9*(-1+x^3)^3//2)
@test integrate(x^5*(-1+x^3)^-1//2, x) == :(2//3*(-1+x^3)^(1/2)+2//9*(-1+x^3)^3//2)
@test integrate(x^2*(-1+x^3)^-1//2, x) == :(2//3*(-1+x^3)^(1/2))
@test integrate(x^-1*(-1+x^3)^-1//2, x) == :(2//3*arctan((-1+x^3)^(1/2)))
@test integrate(x^-4*(-1+x^3)^-1//2, x) == :(1//3*arctan((-1+x^3)^(1/2))+1//3*x^-3*(-1+x^3)^(1/2))
@test integrate(x^-7*(-1+x^3)^-1//2, x) == :(1//4*arctan((-1+x^3)^(1/2))+1//4*x^-3*(-1+x^3)^(1/2)+1//6*x^-6*(-1+x^3)^(1/2))
@test integrate(x^-10*(-1+x^3)^-1//2, x) == :(5//24*arctan((-1+x^3)^(1/2))+1//9*x^-9*(-1+x^3)^(1/2)+5//24*x^-3*(-1+x^3)^(1/2)+5//36*x^-6*(-1+x^3)^(1/2))
@test integrate(x^6*(-1+x^3)^-1//2, x) == :(2//11*x^4*(-1+x^3)^(1/2)+16//55*x*(-1+x^3)^(1/2)+-32//165*3^3//4*((1+-1x+-1*3^(1/2))^-2*(1+x+x^2))^(1/2)*(-1*(1+-1x+-1*3^(1/2))^-2*(1+-1x))^-1//2*(-1+x^3)^-1//2*(2+-1*3^(1/2))^(1/2)*(1+-1x)*Elliptic.F(arcsin((1+-1x+-1*3^(1/2))^-1*(1+3^(1/2)+-1x)),-7+4*3^(1/2)))
@test integrate(x^3*(-1+x^3)^-1//2, x) == :(2//5*x*(-1+x^3)^(1/2)+-4//15*3^3//4*((1+-1x+-1*3^(1/2))^-2*(1+x+x^2))^(1/2)*(-1*(1+-1x+-1*3^(1/2))^-2*(1+-1x))^-1//2*(-1+x^3)^-1//2*(2+-1*3^(1/2))^(1/2)*(1+-1x)*Elliptic.F(arcsin((1+-1x+-1*3^(1/2))^-1*(1+3^(1/2)+-1x)),-7+4*3^(1/2)))
@test integrate((-1+x^3)^-1//2, x) == :(-2//3*3^3//4*((1+-1x+-1*3^(1/2))^-2*(1+x+x^2))^(1/2)*(-1*(1+-1x+-1*3^(1/2))^-2*(1+-1x))^-1//2*(-1+x^3)^-1//2*(2+-1*3^(1/2))^(1/2)*(1+-1x)*Elliptic.F(arcsin((1+-1x+-1*3^(1/2))^-1*(1+3^(1/2)+-1x)),-7+4*3^(1/2)))
@test integrate(x^-3*(-1+x^3)^-1//2, x) == :((1/2)*x^-2*(-1+x^3)^(1/2)+-1//6*3^3//4*((1+-1x+-1*3^(1/2))^-2*(1+x+x^2))^(1/2)*(-1*(1+-1x+-1*3^(1/2))^-2*(1+-1x))^-1//2*(-1+x^3)^-1//2*(2+-1*3^(1/2))^(1/2)*(1+-1x)*Elliptic.F(arcsin((1+-1x+-1*3^(1/2))^-1*(1+3^(1/2)+-1x)),-7+4*3^(1/2)))
@test integrate(x^-6*(-1+x^3)^-1//2, x) == :(1//5*x^-5*(-1+x^3)^(1/2)+7//20*x^-2*(-1+x^3)^(1/2)+-7//60*3^3//4*((1+-1x+-1*3^(1/2))^-2*(1+x+x^2))^(1/2)*(-1*(1+-1x+-1*3^(1/2))^-2*(1+-1x))^-1//2*(-1+x^3)^-1//2*(2+-1*3^(1/2))^(1/2)*(1+-1x)*Elliptic.F(arcsin((1+-1x+-1*3^(1/2))^-1*(1+3^(1/2)+-1x)),-7+4*3^(1/2)))
@test integrate(x^7*(-1+x^3)^-1//2, x) == :(-80*(-1+x^3)^(1/2)*(91+-91x+-91*3^(1/2))^-1+2//13*x^5*(-1+x^3)^(1/2)+20//91*x^2*(-1+x^3)^(1/2)+-80//273*2^(1/2)*3^3//4*((1+-1x+-1*3^(1/2))^-2*(1+x+x^2))^(1/2)*(-1*(1+-1x+-1*3^(1/2))^-2*(1+-1x))^-1//2*(-1+x^3)^-1//2*(1+-1x)*Elliptic.F(arcsin((1+-1x+-1*3^(1/2))^-1*(1+3^(1/2)+-1x)),-7+4*3^(1/2))+40//91*3^1//4*((1+-1x+-1*3^(1/2))^-2*(1+x+x^2))^(1/2)*(-1*(1+-1x+-1*3^(1/2))^-2*(1+-1x))^-1//2*(-1+x^3)^-1//2*(2+3^(1/2))^(1/2)*(1+-1x)*Elliptic.E(arcsin((1+-1x+-1*3^(1/2))^-1*(1+3^(1/2)+-1x)),-7+4*3^(1/2)))
@test integrate(x^4*(-1+x^3)^-1//2, x) == :(-8*(-1+x^3)^(1/2)*(7+-7x+-7*3^(1/2))^-1+2//7*x^2*(-1+x^3)^(1/2)+-8//21*2^(1/2)*3^3//4*((1+-1x+-1*3^(1/2))^-2*(1+x+x^2))^(1/2)*(-1*(1+-1x+-1*3^(1/2))^-2*(1+-1x))^-1//2*(-1+x^3)^-1//2*(1+-1x)*Elliptic.F(arcsin((1+-1x+-1*3^(1/2))^-1*(1+3^(1/2)+-1x)),-7+4*3^(1/2))+4//7*3^1//4*((1+-1x+-1*3^(1/2))^-2*(1+x+x^2))^(1/2)*(-1*(1+-1x+-1*3^(1/2))^-2*(1+-1x))^-1//2*(-1+x^3)^-1//2*(2+3^(1/2))^(1/2)*(1+-1x)*Elliptic.E(arcsin((1+-1x+-1*3^(1/2))^-1*(1+3^(1/2)+-1x)),-7+4*3^(1/2)))
@test integrate(x*(-1+x^3)^-1//2, x) == :(-2*(-1+x^3)^(1/2)*(1+-1x+-1*3^(1/2))^-1+3^1//4*((1+-1x+-1*3^(1/2))^-2*(1+x+x^2))^(1/2)*(-1*(1+-1x+-1*3^(1/2))^-2*(1+-1x))^-1//2*(-1+x^3)^-1//2*(2+3^(1/2))^(1/2)*(1+-1x)*Elliptic.E(arcsin((1+-1x+-1*3^(1/2))^-1*(1+3^(1/2)+-1x)),-7+4*3^(1/2))+-2//3*2^(1/2)*3^3//4*((1+-1x+-1*3^(1/2))^-2*(1+x+x^2))^(1/2)*(-1*(1+-1x+-1*3^(1/2))^-2*(1+-1x))^-1//2*(-1+x^3)^-1//2*(1+-1x)*Elliptic.F(arcsin((1+-1x+-1*3^(1/2))^-1*(1+3^(1/2)+-1x)),-7+4*3^(1/2)))
@test integrate(x^-2*(-1+x^3)^-1//2, x) == :(x^-1*(-1+x^3)^(1/2)+(-1+x^3)^(1/2)*(1+-1x+-1*3^(1/2))^-1+-1//2*3^1//4*((1+-1x+-1*3^(1/2))^-2*(1+x+x^2))^(1/2)*(-1*(1+-1x+-1*3^(1/2))^-2*(1+-1x))^-1//2*(-1+x^3)^-1//2*(2+3^(1/2))^(1/2)*(1+-1x)*Elliptic.E(arcsin((1+-1x+-1*3^(1/2))^-1*(1+3^(1/2)+-1x)),-7+4*3^(1/2))+1//3*2^(1/2)*3^3//4*((1+-1x+-1*3^(1/2))^-2*(1+x+x^2))^(1/2)*(-1*(1+-1x+-1*3^(1/2))^-2*(1+-1x))^-1//2*(-1+x^3)^-1//2*(1+-1x)*Elliptic.F(arcsin((1+-1x+-1*3^(1/2))^-1*(1+3^(1/2)+-1x)),-7+4*3^(1/2)))
@test integrate(x^-5*(-1+x^3)^-1//2, x) == :(5*(-1+x^3)^(1/2)*(8+-8x+-8*3^(1/2))^-1+1//4*x^-4*(-1+x^3)^(1/2)+5//8*x^-1*(-1+x^3)^(1/2)+-5//16*3^1//4*((1+-1x+-1*3^(1/2))^-2*(1+x+x^2))^(1/2)*(-1*(1+-1x+-1*3^(1/2))^-2*(1+-1x))^-1//2*(-1+x^3)^-1//2*(2+3^(1/2))^(1/2)*(1+-1x)*Elliptic.E(arcsin((1+-1x+-1*3^(1/2))^-1*(1+3^(1/2)+-1x)),-7+4*3^(1/2))+1//24*2^(1/2)*3^3//4*((1+-1x+-1*3^(1/2))^-2*(1+x+x^2))^(1/2)*(-1*(1+-1x+-1*3^(1/2))^-2*(1+-1x))^-1//2*(-1+x^3)^-1//2*(5+-5x)*Elliptic.F(arcsin((1+-1x+-1*3^(1/2))^-1*(1+3^(1/2)+-1x)),-7+4*3^(1/2)))
@test integrate(x^11*(-1+-1*x^3)^-1//2, x) == :(2//3*(-1+-1*x^3)^(1/2)+2//3*(-1+-1*x^3)^3//2+2//5*(-1+-1*x^3)^5//2+2//21*(-1+-1*x^3)^7//2)
@test integrate(x^8*(-1+-1*x^3)^-1//2, x) == :(-4//9*(-1+-1*x^3)^3//2+-2//3*(-1+-1*x^3)^(1/2)+-2//15*(-1+-1*x^3)^5//2)
@test integrate(x^5*(-1+-1*x^3)^-1//2, x) == :(2//3*(-1+-1*x^3)^(1/2)+2//9*(-1+-1*x^3)^3//2)
@test integrate(x^2*(-1+-1*x^3)^-1//2, x) == :(-2//3*(-1+-1*x^3)^(1/2))
@test integrate(x^-1*(-1+-1*x^3)^-1//2, x) == :(2//3*arctan((-1+-1*x^3)^(1/2)))
@test integrate(x^-4*(-1+-1*x^3)^-1//2, x) == :(-1//3*arctan((-1+-1*x^3)^(1/2))+1//3*x^-3*(-1+-1*x^3)^(1/2))
@test integrate(x^-7*(-1+-1*x^3)^-1//2, x) == :(1//4*arctan((-1+-1*x^3)^(1/2))+-1//4*x^-3*(-1+-1*x^3)^(1/2)+1//6*x^-6*(-1+-1*x^3)^(1/2))
@test integrate(x^-10*(-1+-1*x^3)^-1//2, x) == :(-5//24*arctan((-1+-1*x^3)^(1/2))+-5//36*x^-6*(-1+-1*x^3)^(1/2)+1//9*x^-9*(-1+-1*x^3)^(1/2)+5//24*x^-3*(-1+-1*x^3)^(1/2))
@test integrate(x^6*(-1+-1*x^3)^-1//2, x) == :(-2//11*x^4*(-1+-1*x^3)^(1/2)+16//55*x*(-1+-1*x^3)^(1/2)+32//165*3^3//4*((1+x+-1*3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(-1*(1+x+-1*3^(1/2))^-2*(1+x))^-1//2*(-1+-1*x^3)^-1//2*(2+-1*3^(1/2))^(1/2)*(1+x)*Elliptic.F(arcsin((1+x+-1*3^(1/2))^-1*(1+x+3^(1/2))),-7+4*3^(1/2)))
@test integrate(x^3*(-1+-1*x^3)^-1//2, x) == :(-2//5*x*(-1+-1*x^3)^(1/2)+-4//15*3^3//4*((1+x+-1*3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(-1*(1+x+-1*3^(1/2))^-2*(1+x))^-1//2*(-1+-1*x^3)^-1//2*(2+-1*3^(1/2))^(1/2)*(1+x)*Elliptic.F(arcsin((1+x+-1*3^(1/2))^-1*(1+x+3^(1/2))),-7+4*3^(1/2)))
@test integrate((-1+-1*x^3)^-1//2, x) == :(2//3*3^3//4*((1+x+-1*3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(-1*(1+x+-1*3^(1/2))^-2*(1+x))^-1//2*(-1+-1*x^3)^-1//2*(2+-1*3^(1/2))^(1/2)*(1+x)*Elliptic.F(arcsin((1+x+-1*3^(1/2))^-1*(1+x+3^(1/2))),-7+4*3^(1/2)))
@test integrate(x^-3*(-1+-1*x^3)^-1//2, x) == :((1/2)*x^-2*(-1+-1*x^3)^(1/2)+-1//6*3^3//4*((1+x+-1*3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(-1*(1+x+-1*3^(1/2))^-2*(1+x))^-1//2*(-1+-1*x^3)^-1//2*(2+-1*3^(1/2))^(1/2)*(1+x)*Elliptic.F(arcsin((1+x+-1*3^(1/2))^-1*(1+x+3^(1/2))),-7+4*3^(1/2)))
@test integrate(x^-6*(-1+-1*x^3)^-1//2, x) == :(-7//20*x^-2*(-1+-1*x^3)^(1/2)+1//5*x^-5*(-1+-1*x^3)^(1/2)+7//60*3^3//4*((1+x+-1*3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(-1*(1+x+-1*3^(1/2))^-2*(1+x))^-1//2*(-1+-1*x^3)^-1//2*(2+-1*3^(1/2))^(1/2)*(1+x)*Elliptic.F(arcsin((1+x+-1*3^(1/2))^-1*(1+x+3^(1/2))),-7+4*3^(1/2)))
@test integrate(x^7*(-1+-1*x^3)^-1//2, x) == :(-80*(-1+-1*x^3)^(1/2)*(91+-91*3^(1/2)+91x)^-1+-2//13*x^5*(-1+-1*x^3)^(1/2)+20//91*x^2*(-1+-1*x^3)^(1/2)+-80//273*2^(1/2)*3^3//4*((1+x+-1*3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(-1*(1+x+-1*3^(1/2))^-2*(1+x))^-1//2*(-1+-1*x^3)^-1//2*(1+x)*Elliptic.F(arcsin((1+x+-1*3^(1/2))^-1*(1+x+3^(1/2))),-7+4*3^(1/2))+40//91*3^1//4*((1+x+-1*3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(-1*(1+x+-1*3^(1/2))^-2*(1+x))^-1//2*(-1+-1*x^3)^-1//2*(2+3^(1/2))^(1/2)*(1+x)*Elliptic.E(arcsin((1+x+-1*3^(1/2))^-1*(1+x+3^(1/2))),-7+4*3^(1/2)))
@test integrate(x^4*(-1+-1*x^3)^-1//2, x) == :(8*(-1+-1*x^3)^(1/2)*(7+-7*3^(1/2)+7x)^-1+-2//7*x^2*(-1+-1*x^3)^(1/2)+-4//7*3^1//4*((1+x+-1*3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(-1*(1+x+-1*3^(1/2))^-2*(1+x))^-1//2*(-1+-1*x^3)^-1//2*(2+3^(1/2))^(1/2)*(1+x)*Elliptic.E(arcsin((1+x+-1*3^(1/2))^-1*(1+x+3^(1/2))),-7+4*3^(1/2))+8//21*2^(1/2)*3^3//4*((1+x+-1*3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(-1*(1+x+-1*3^(1/2))^-2*(1+x))^-1//2*(-1+-1*x^3)^-1//2*(1+x)*Elliptic.F(arcsin((1+x+-1*3^(1/2))^-1*(1+x+3^(1/2))),-7+4*3^(1/2)))
@test integrate(x*(-1+-1*x^3)^-1//2, x) == :(-2*(-1+-1*x^3)^(1/2)*(1+x+-1*3^(1/2))^-1+3^1//4*((1+x+-1*3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(-1*(1+x+-1*3^(1/2))^-2*(1+x))^-1//2*(-1+-1*x^3)^-1//2*(2+3^(1/2))^(1/2)*(1+x)*Elliptic.E(arcsin((1+x+-1*3^(1/2))^-1*(1+x+3^(1/2))),-7+4*3^(1/2))+-2//3*2^(1/2)*3^3//4*((1+x+-1*3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(-1*(1+x+-1*3^(1/2))^-2*(1+x))^-1//2*(-1+-1*x^3)^-1//2*(1+x)*Elliptic.F(arcsin((1+x+-1*3^(1/2))^-1*(1+x+3^(1/2))),-7+4*3^(1/2)))
@test integrate(x^-2*(-1+-1*x^3)^-1//2, x) == :(x^-1*(-1+-1*x^3)^(1/2)+-1*(-1+-1*x^3)^(1/2)*(1+x+-1*3^(1/2))^-1+(1/2)*3^1//4*((1+x+-1*3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(-1*(1+x+-1*3^(1/2))^-2*(1+x))^-1//2*(-1+-1*x^3)^-1//2*(2+3^(1/2))^(1/2)*(1+x)*Elliptic.E(arcsin((1+x+-1*3^(1/2))^-1*(1+x+3^(1/2))),-7+4*3^(1/2))+-1//3*2^(1/2)*3^3//4*((1+x+-1*3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(-1*(1+x+-1*3^(1/2))^-2*(1+x))^-1//2*(-1+-1*x^3)^-1//2*(1+x)*Elliptic.F(arcsin((1+x+-1*3^(1/2))^-1*(1+x+3^(1/2))),-7+4*3^(1/2)))
@test integrate(x^-5*(-1+-1*x^3)^-1//2, x) == :(5*(-1+-1*x^3)^(1/2)*(8+-8*3^(1/2)+8x)^-1+-5//8*x^-1*(-1+-1*x^3)^(1/2)+1//4*x^-4*(-1+-1*x^3)^(1/2)+-5//16*3^1//4*((1+x+-1*3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(-1*(1+x+-1*3^(1/2))^-2*(1+x))^-1//2*(-1+-1*x^3)^-1//2*(2+3^(1/2))^(1/2)*(1+x)*Elliptic.E(arcsin((1+x+-1*3^(1/2))^-1*(1+x+3^(1/2))),-7+4*3^(1/2))+1//24*2^(1/2)*3^3//4*((1+x+-1*3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(-1*(1+x+-1*3^(1/2))^-2*(1+x))^-1//2*(-1+-1*x^3)^-1//2*(5+5x)*Elliptic.F(arcsin((1+x+-1*3^(1/2))^-1*(1+x+3^(1/2))),-7+4*3^(1/2)))
@test integrate(x^11*(a+b*x^3)^1//3, x) == :(1//13*b^-4*(a+b*x^3)^13//3+-3//10*a*b^-4*(a+b*x^3)^10//3+-1//4*a^3*b^-4*(a+b*x^3)^4//3+3//7*a^2*b^-4*(a+b*x^3)^7//3)
@test integrate(x^8*(a+b*x^3)^1//3, x) == :(1//10*b^-3*(a+b*x^3)^10//3+-2//7*a*b^-3*(a+b*x^3)^7//3+1//4*a^2*b^-3*(a+b*x^3)^4//3)
@test integrate(x^5*(a+b*x^3)^1//3, x) == :(1//7*b^-2*(a+b*x^3)^7//3+-1//4*a*b^-2*(a+b*x^3)^4//3)
@test integrate(x^2*(a+b*x^3)^1//3, x) == :(1//4*b^-1*(a+b*x^3)^4//3)
@test integrate(x^-1*(a+b*x^3)^1//3, x) == :((a+b*x^3)^1//3+(1/2)*a^1//3*log(a^1//3+-1*(a+b*x^3)^1//3)+-1//2*a^1//3*log(x)+-1//3*3^(1/2)*a^1//3*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+2*(a+b*x^3)^1//3)))
@test integrate(x^-4*(a+b*x^3)^1//3, x) == :(-1//3*x^-3*(a+b*x^3)^1//3+-1//6*b*a^-2//3*log(x)+1//6*b*a^-2//3*log(a^1//3+-1*(a+b*x^3)^1//3)+-1//9*b*3^(1/2)*a^-2//3*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+2*(a+b*x^3)^1//3)))
@test integrate(x^4*(a+b*x^3)^1//3, x) == :(1//6*x^5*(a+b*x^3)^1//3+-1//54*a^2*b^-5//3*log(1+x*b^1//3*(a+b*x^3)^-1//3+b^2//3*x^2*(a+b*x^3)^-2//3)+1//27*a^2*b^-5//3*log(1+-1*x*b^1//3*(a+b*x^3)^-1//3)+1//18*a*b^-1*x^2*(a+b*x^3)^1//3+1//27*3^(1/2)*a^2*b^-5//3*arctan(1//3*3^(1/2)*(1+2*x*b^1//3*(a+b*x^3)^-1//3)))
@test integrate(x*(a+b*x^3)^1//3, x) == :(1//3*x^2*(a+b*x^3)^1//3+-1//9*a*b^-2//3*log(1+-1*x*b^1//3*(a+b*x^3)^-1//3)+1//18*a*b^-2//3*log(1+x*b^1//3*(a+b*x^3)^-1//3+b^2//3*x^2*(a+b*x^3)^-2//3)+-1//9*a*3^(1/2)*b^-2//3*arctan(1//3*3^(1/2)*(1+2*x*b^1//3*(a+b*x^3)^-1//3)))
@test integrate(x^-2*(a+b*x^3)^1//3, x) == :(-1*x^-1*(a+b*x^3)^1//3+-1//3*b^1//3*log(1+-1*x*b^1//3*(a+b*x^3)^-1//3)+1//6*b^1//3*log(1+x*b^1//3*(a+b*x^3)^-1//3+b^2//3*x^2*(a+b*x^3)^-2//3)+-1//3*3^(1/2)*b^1//3*arctan(1//3*3^(1/2)*(1+2*x*b^1//3*(a+b*x^3)^-1//3)))
@test integrate(x^-5*(a+b*x^3)^1//3, x) == :(-1//4*a^-1*x^-4*(a+b*x^3)^4//3)
@test integrate(x^-8*(a+b*x^3)^1//3, x) == :(-1//7*a^-1*x^-7*(a+b*x^3)^4//3+3//28*b*a^-2*x^-4*(a+b*x^3)^4//3)
@test integrate(x^-11*(a+b*x^3)^1//3, x) == :(-1//10*a^-1*x^-10*(a+b*x^3)^4//3+-9//140*a^-3*b^2*x^-4*(a+b*x^3)^4//3+3//35*b*a^-2*x^-7*(a+b*x^3)^4//3)
@test integrate(x^11*(a+b*x^3)^2//3, x) == :(1//14*b^-4*(a+b*x^3)^14//3+-3//11*a*b^-4*(a+b*x^3)^11//3+-1//5*a^3*b^-4*(a+b*x^3)^5//3+3//8*a^2*b^-4*(a+b*x^3)^8//3)
@test integrate(x^8*(a+b*x^3)^2//3, x) == :(1//11*b^-3*(a+b*x^3)^11//3+-1//4*a*b^-3*(a+b*x^3)^8//3+1//5*a^2*b^-3*(a+b*x^3)^5//3)
@test integrate(x^5*(a+b*x^3)^2//3, x) == :(1//8*b^-2*(a+b*x^3)^8//3+-1//5*a*b^-2*(a+b*x^3)^5//3)
@test integrate(x^2*(a+b*x^3)^2//3, x) == :(1//5*b^-1*(a+b*x^3)^5//3)
@test integrate(x^-1*(a+b*x^3)^2//3, x) == :((1/2)*(a+b*x^3)^2//3+(1/2)*a^2//3*log(a^1//3+-1*(a+b*x^3)^1//3)+-1//2*a^2//3*log(x)+1//3*3^(1/2)*a^2//3*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+2*(a+b*x^3)^1//3)))
@test integrate(x^-4*(a+b*x^3)^2//3, x) == :(-1//3*x^-3*(a+b*x^3)^2//3+-1//3*b*a^-1//3*log(x)+1//3*b*a^-1//3*log(a^1//3+-1*(a+b*x^3)^1//3)+2//9*b*3^(1/2)*a^-1//3*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+2*(a+b*x^3)^1//3)))
@test integrate(x^3*(a+b*x^3)^2//3, x) == :(1//6*x^4*(a+b*x^3)^2//3+1//18*a^2*b^-4//3*log((a+b*x^3)^1//3+-1*x*b^1//3)+-1//27*3^(1/2)*a^2*b^-4//3*arctan(1//3*3^(1/2)*(1+2*x*b^1//3*(a+b*x^3)^-1//3))+1//9*a*x*b^-1*(a+b*x^3)^2//3)
@test integrate((a+b*x^3)^2//3, x) == :(1//3*x*(a+b*x^3)^2//3+-1//3*a*b^-1//3*log((a+b*x^3)^1//3+-1*x*b^1//3)+2//9*a*3^(1/2)*b^-1//3*arctan(1//3*3^(1/2)*(1+2*x*b^1//3*(a+b*x^3)^-1//3)))
@test integrate(x^-3*(a+b*x^3)^2//3, x) == :(-1//2*b^2//3*log((a+b*x^3)^1//3+-1*x*b^1//3)+-1//2*x^-2*(a+b*x^3)^2//3+1//3*3^(1/2)*b^2//3*arctan(1//3*3^(1/2)*(1+2*x*b^1//3*(a+b*x^3)^-1//3)))
@test integrate(x^-6*(a+b*x^3)^2//3, x) == :(-1//5*a^-1*x^-5*(a+b*x^3)^5//3)
@test integrate(x^-9*(a+b*x^3)^2//3, x) == :(-1//8*a^-1*x^-8*(a+b*x^3)^5//3+3//40*b*a^-2*x^-5*(a+b*x^3)^5//3)
@test integrate(x^-12*(a+b*x^3)^2//3, x) == :(-1//11*a^-1*x^-11*(a+b*x^3)^5//3+-9//220*a^-3*b^2*x^-5*(a+b*x^3)^5//3+3//44*b*a^-2*x^-8*(a+b*x^3)^5//3)
@test integrate(x^8*(1+-1*x^3)^6//5, x) == :(-5//33*(1+-1*x^3)^11//5+-5//63*(1+-1*x^3)^21//5+5//24*(1+-1*x^3)^16//5)
@test integrate(x^11*(a+b*x^3)^-1//3, x) == :(1//11*b^-4*(a+b*x^3)^11//3+-3//8*a*b^-4*(a+b*x^3)^8//3+-1//2*a^3*b^-4*(a+b*x^3)^2//3+3//5*a^2*b^-4*(a+b*x^3)^5//3)
@test integrate(x^8*(a+b*x^3)^-1//3, x) == :(1//8*b^-3*(a+b*x^3)^8//3+(1/2)*a^2*b^-3*(a+b*x^3)^2//3+-2//5*a*b^-3*(a+b*x^3)^5//3)
@test integrate(x^5*(a+b*x^3)^-1//3, x) == :(1//5*b^-2*(a+b*x^3)^5//3+-1//2*a*b^-2*(a+b*x^3)^2//3)
@test integrate(x^2*(a+b*x^3)^-1//3, x) == :((1/2)*b^-1*(a+b*x^3)^2//3)
@test integrate(x^-1*(a+b*x^3)^-1//3, x) == :((1/2)*a^-1//3*log(a^1//3+-1*(a+b*x^3)^1//3)+-1//2*a^-1//3*log(x)+1//3*3^(1/2)*a^-1//3*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+2*(a+b*x^3)^1//3)))
@test integrate(x^-4*(a+b*x^3)^-1//3, x) == :(-1//3*a^-1*x^-3*(a+b*x^3)^2//3+-1//6*b*a^-4//3*log(a^1//3+-1*(a+b*x^3)^1//3)+1//6*b*a^-4//3*log(x)+-1//9*b*3^(1/2)*a^-4//3*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+2*(a+b*x^3)^1//3)))
@test integrate(x^3*(a+b*x^3)^-1//3, x) == :(1//3*x*b^-1*(a+b*x^3)^2//3+1//6*a*b^-4//3*log((a+b*x^3)^1//3+-1*x*b^1//3)+-1//9*a*3^(1/2)*b^-4//3*arctan(1//3*3^(1/2)*(1+2*x*b^1//3*(a+b*x^3)^-1//3)))
@test integrate((a+b*x^3)^-1//3, x) == :(-1//2*b^-1//3*log((a+b*x^3)^1//3+-1*x*b^1//3)+1//3*3^(1/2)*b^-1//3*arctan(1//3*3^(1/2)*(1+2*x*b^1//3*(a+b*x^3)^-1//3)))
@test integrate(x^-3*(a+b*x^3)^-1//3, x) == :(-1//2*a^-1*x^-2*(a+b*x^3)^2//3)
@test integrate(x^-6*(a+b*x^3)^-1//3, x) == :(-1//5*a^-1*x^-5*(a+b*x^3)^2//3+3//10*b*a^-2*x^-2*(a+b*x^3)^2//3)
@test integrate(x^-9*(a+b*x^3)^-1//3, x) == :(-1//8*a^-1*x^-8*(a+b*x^3)^2//3+-9//40*a^-3*b^2*x^-2*(a+b*x^3)^2//3+3//20*b*a^-2*x^-5*(a+b*x^3)^2//3)
@test integrate(x^-12*(a+b*x^3)^-1//3, x) == :(-1//11*a^-1*x^-11*(a+b*x^3)^2//3+-27//220*a^-3*b^2*x^-5*(a+b*x^3)^2//3+9//88*b*a^-2*x^-8*(a+b*x^3)^2//3+81//440*a^-4*b^3*x^-2*(a+b*x^3)^2//3)
@test integrate(x^11*(a+b*x^3)^-2//3, x) == :(1//10*b^-4*(a+b*x^3)^10//3+-1*a^3*b^-4*(a+b*x^3)^1//3+-3//7*a*b^-4*(a+b*x^3)^7//3+3//4*a^2*b^-4*(a+b*x^3)^4//3)
@test integrate(x^8*(a+b*x^3)^-2//3, x) == :(1//7*b^-3*(a+b*x^3)^7//3+a^2*b^-3*(a+b*x^3)^1//3+-1//2*a*b^-3*(a+b*x^3)^4//3)
@test integrate(x^5*(a+b*x^3)^-2//3, x) == :(1//4*b^-2*(a+b*x^3)^4//3+-1*a*b^-2*(a+b*x^3)^1//3)
@test integrate(x^2*(a+b*x^3)^-2//3, x) == :(b^-1*(a+b*x^3)^1//3)
@test integrate(x^-1*(a+b*x^3)^-2//3, x) == :((1/2)*a^-2//3*log(a^1//3+-1*(a+b*x^3)^1//3)+-1//2*a^-2//3*log(x)+-1//3*3^(1/2)*a^-2//3*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+2*(a+b*x^3)^1//3)))
@test integrate(x^-4*(a+b*x^3)^-2//3, x) == :(-1//3*b*a^-5//3*log(a^1//3+-1*(a+b*x^3)^1//3)+-1//3*a^-1*x^-3*(a+b*x^3)^1//3+1//3*b*a^-5//3*log(x)+2//9*b*3^(1/2)*a^-5//3*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+2*(a+b*x^3)^1//3)))
@test integrate(x^4*(a+b*x^3)^-2//3, x) == :(-1//9*a*b^-5//3*log(1+x*b^1//3*(a+b*x^3)^-1//3+b^2//3*x^2*(a+b*x^3)^-2//3)+1//3*b^-1*x^2*(a+b*x^3)^1//3+2//9*a*b^-5//3*log(1+-1*x*b^1//3*(a+b*x^3)^-1//3)+2//9*a*3^(1/2)*b^-5//3*arctan(1//3*3^(1/2)*(1+2*x*b^1//3*(a+b*x^3)^-1//3)))
@test integrate(x^-2*(a+b*x^3)^-2//3, x) == :(-1*a^-1*x^-1*(a+b*x^3)^1//3)
@test integrate(x^-5*(a+b*x^3)^-2//3, x) == :(-1//4*a^-1*x^-4*(a+b*x^3)^1//3+3//4*b*a^-2*x^-1*(a+b*x^3)^1//3)
@test integrate(x^-8*(a+b*x^3)^-2//3, x) == :(-1//7*a^-1*x^-7*(a+b*x^3)^1//3+-9//14*a^-3*b^2*x^-1*(a+b*x^3)^1//3+3//14*b*a^-2*x^-4*(a+b*x^3)^1//3)
@test integrate(x^-11*(a+b*x^3)^-2//3, x) == :(-1//10*a^-1*x^-10*(a+b*x^3)^1//3+-27//140*a^-3*b^2*x^-4*(a+b*x^3)^1//3+9//70*b*a^-2*x^-7*(a+b*x^3)^1//3+81//140*a^-4*b^3*x^-1*(a+b*x^3)^1//3)
@test integrate((a+-1*b*x^3)^-1//3, x) == :((1/2)*b^-1//3*log((a+-1*b*x^3)^1//3+x*b^1//3)+-1//3*3^(1/2)*b^-1//3*arctan(1//3*3^(1/2)*(1+-2*x*b^1//3*(a+-1*b*x^3)^-1//3)))
@test integrate((2+x^3)^-1//3, x) == :(-1//2*log((2+x^3)^1//3+-1x)+1//3*3^(1/2)*arctan(1//3*3^(1/2)*(1+2*x*(2+x^3)^-1//3)))
@test integrate(x^2*(2+x^3)^-1//4, x) == :(4//9*(2+x^3)^3//4)
@test integrate(x^m*(a+b*x^3)^8, x) == :(a^8*x^(1+m)*(1+m)^-1+b^8*x^(25+m)*(25+m)^-1+8*a*b^7*x^(22+m)*(22+m)^-1+8*b*a^7*x^(4+m)*(4+m)^-1+28*a^2*b^6*x^(19+m)*(19+m)^-1+28*a^6*b^2*x^(7+m)*(7+m)^-1+56*a^3*b^5*x^(16+m)*(16+m)^-1+56*a^5*b^3*x^(10+m)*(10+m)^-1+70*a^4*b^4*x^(13+m)*(13+m)^-1)
@test integrate(x^m*(a+b*x^3)^5, x) == :(a^5*x^(1+m)*(1+m)^-1+b^5*x^(16+m)*(16+m)^-1+5*a*b^4*x^(13+m)*(13+m)^-1+5*b*a^4*x^(4+m)*(4+m)^-1+10*a^2*b^3*x^(10+m)*(10+m)^-1+10*a^3*b^2*x^(7+m)*(7+m)^-1)
@test integrate(x^m*(a+b*x^3)^3, x) == :(a^3*x^(1+m)*(1+m)^-1+b^3*x^(10+m)*(10+m)^-1+3*a*b^2*x^(7+m)*(7+m)^-1+3*b*a^2*x^(4+m)*(4+m)^-1)
@test integrate(x^m*(a+b*x^3)^2, x) == :(a^2*x^(1+m)*(1+m)^-1+b^2*x^(7+m)*(7+m)^-1+2*a*b*x^(4+m)*(4+m)^-1)
@test integrate(x^m*(a+b*x^3), x) == :(a*x^(1+m)*(1+m)^-1+b*x^(4+m)*(4+m)^-1)
@test integrate(x^2*(a+b*x^3)^p, x) == :(1//3*b^-1*(1+p)^-1*(a+b*x^3)^(1+p))
@test integrate(x^5*(a+b*x^3)^p, x) == :(1//3*b^-2*(2+p)^-1*(a+b*x^3)^(2+p)+-1//3*a*b^-2*(1+p)^-1*(a+b*x^3)^(1+p))
@test integrate(x^8*(a+b*x^3)^p, x) == :(1//3*b^-3*(3+p)^-1*(a+b*x^3)^(3+p)+-2//3*a*b^-3*(2+p)^-1*(a+b*x^3)^(2+p)+1//3*a^2*b^-3*(1+p)^-1*(a+b*x^3)^(1+p))
@test integrate(x^11*(a+b*x^3)^p, x) == :(1//3*b^-4*(4+p)^-1*(a+b*x^3)^(4+p)+a^2*b^-4*(2+p)^-1*(a+b*x^3)^(2+p)+-1*a*b^-4*(3+p)^-1*(a+b*x^3)^(3+p)+-1//3*a^3*b^-4*(1+p)^-1*(a+b*x^3)^(1+p))
@test integrate(x^m*(a+b*x^4), x) == :(a*x^(1+m)*(1+m)^-1+b*x^(5+m)*(5+m)^-1)
@test integrate(x^5*(a+b*x^4), x) == :(1//6*a*x^6+1//10*b*x^10)
@test integrate(x^4*(a+b*x^4), x) == :(1//5*a*x^5+1//9*b*x^9)
@test integrate(x^3*(a+b*x^4), x) == :(1//4*a*x^4+1//8*b*x^8)
@test integrate(x^2*(a+b*x^4), x) == :(1//3*a*x^3+1//7*b*x^7)
@test integrate(x*(a+b*x^4), x) == :((1/2)*a*x^2+1//6*b*x^6)
@test integrate(a+b*x^4, x) == :(a*x+1//5*b*x^5)
@test integrate(x^-1*(a+b*x^4), x) == :(a*log(x)+1//4*b*x^4)
@test integrate(x^-2*(a+b*x^4), x) == :(-1*a*x^-1+1//3*b*x^3)
@test integrate(x^-3*(a+b*x^4), x) == :((1/2)*b*x^2+-1//2*a*x^-2)
@test integrate(x^-4*(a+b*x^4), x) == :(b*x+-1//3*a*x^-3)
@test integrate(x^-5*(a+b*x^4), x) == :(b*log(x)+-1//4*a*x^-4)
@test integrate(x^-6*(a+b*x^4), x) == :(-1*b*x^-1+-1//5*a*x^-5)
@test integrate(x^-7*(a+b*x^4), x) == :(-1//2*b*x^-2+-1//6*a*x^-6)
@test integrate(x^-8*(a+b*x^4), x) == :(-1//3*b*x^-3+-1//7*a*x^-7)
@test integrate(x^-9*(a+b*x^4), x) == :(-1//4*b*x^-4+-1//8*a*x^-8)
@test integrate(x^-10*(a+b*x^4), x) == :(-1//5*b*x^-5+-1//9*a*x^-9)
@test integrate(x^m*(a+b*x^4)^2, x) == :(a^2*x^(1+m)*(1+m)^-1+b^2*x^(9+m)*(9+m)^-1+2*a*b*x^(5+m)*(5+m)^-1)
@test integrate(x^5*(a+b*x^4)^2, x) == :(1//6*a^2*x^6+1//14*b^2*x^14+1//5*a*b*x^10)
@test integrate(x^4*(a+b*x^4)^2, x) == :(1//5*a^2*x^5+1//13*b^2*x^13+2//9*a*b*x^9)
@test integrate(x^3*(a+b*x^4)^2, x) == :(1//12*b^-1*(a+b*x^4)^3)
@test integrate(x^2*(a+b*x^4)^2, x) == :(1//3*a^2*x^3+1//11*b^2*x^11+2//7*a*b*x^7)
@test integrate(x*(a+b*x^4)^2, x) == :((1/2)*a^2*x^2+1//10*b^2*x^10+1//3*a*b*x^6)
@test integrate((a+b*x^4)^2, x) == :(x*a^2+1//9*b^2*x^9+2//5*a*b*x^5)
@test integrate(x^-1*(a+b*x^4)^2, x) == :(a^2*log(x)+1//8*b^2*x^8+(1/2)*a*b*x^4)
@test integrate(x^-2*(a+b*x^4)^2, x) == :(-1*a^2*x^-1+1//7*b^2*x^7+2//3*a*b*x^3)
@test integrate(x^-3*(a+b*x^4)^2, x) == :(-1//2*a^2*x^-2+1//6*b^2*x^6+a*b*x^2)
@test integrate(x^-4*(a+b*x^4)^2, x) == :(-1//3*a^2*x^-3+1//5*b^2*x^5+2*a*b*x)
@test integrate(x^-5*(a+b*x^4)^2, x) == :(-1//4*a^2*x^-4+1//4*b^2*x^4+2*a*b*log(x))
@test integrate(x^m*(a+b*x^4)^3, x) == :(a^3*x^(1+m)*(1+m)^-1+b^3*x^(13+m)*(13+m)^-1+3*a*b^2*x^(9+m)*(9+m)^-1+3*b*a^2*x^(5+m)*(5+m)^-1)
@test integrate(x^5*(a+b*x^4)^3, x) == :(1//6*a^3*x^6+1//18*b^3*x^18+3//10*b*a^2*x^10+3//14*a*b^2*x^14)
@test integrate(x^4*(a+b*x^4)^3, x) == :(1//5*a^3*x^5+1//17*b^3*x^17+1//3*b*a^2*x^9+3//13*a*b^2*x^13)
@test integrate(x^3*(a+b*x^4)^3, x) == :(1//16*b^-1*(a+b*x^4)^4)
@test integrate(x^2*(a+b*x^4)^3, x) == :(1//3*a^3*x^3+1//15*b^3*x^15+3//7*b*a^2*x^7+3//11*a*b^2*x^11)
@test integrate(x*(a+b*x^4)^3, x) == :((1/2)*a^3*x^2+1//14*b^3*x^14+(1/2)*b*a^2*x^6+3//10*a*b^2*x^10)
@test integrate((a+b*x^4)^3, x) == :(x*a^3+1//13*b^3*x^13+1//3*a*b^2*x^9+3//5*b*a^2*x^5)
@test integrate(x^-1*(a+b*x^4)^3, x) == :(a^3*log(x)+1//12*b^3*x^12+3//4*b*a^2*x^4+3//8*a*b^2*x^8)
@test integrate(x^-2*(a+b*x^4)^3, x) == :(-1*a^3*x^-1+1//11*b^3*x^11+b*a^2*x^3+3//7*a*b^2*x^7)
@test integrate(x^-3*(a+b*x^4)^3, x) == :(-1//2*a^3*x^-2+1//10*b^3*x^10+(1/2)*a*b^2*x^6+3//2*b*a^2*x^2)
@test integrate(x^-4*(a+b*x^4)^3, x) == :(-1//3*a^3*x^-3+1//9*b^3*x^9+3*b*x*a^2+3//5*a*b^2*x^5)
@test integrate(x^-5*(a+b*x^4)^3, x) == :(-1//4*a^3*x^-4+1//8*b^3*x^8+3*b*a^2*log(x)+3//4*a*b^2*x^4)
@test integrate(x^9*(a+c*x^4)^-1, x) == :(1//6*c^-1*x^6+(1/2)*a^3//2*c^-5//2*arctan(a^-1//2*c^(1/2)*x^2)+-1//2*a*c^-2*x^2)
@test integrate(x^7*(a+c*x^4)^-1, x) == :(1//4*c^-1*x^4+-1//4*a*c^-2*log(a+c*x^4))
@test integrate(x^5*(a+c*x^4)^-1, x) == :((1/2)*c^-1*x^2+-1//2*a^(1/2)*c^-3//2*arctan(a^-1//2*c^(1/2)*x^2))
@test integrate(x^3*(a+c*x^4)^-1, x) == :(1//4*c^-1*log(a+c*x^4))
@test integrate(x*(a+c*x^4)^-1, x) == :((1/2)*a^-1//2*c^-1//2*arctan(a^-1//2*c^(1/2)*x^2))
@test integrate(x^-1*(a+c*x^4)^-1, x) == :(a^-1*log(x)+-1//4*a^-1*log(a+c*x^4))
@test integrate(x^-3*(a+c*x^4)^-1, x) == :(-1//2*a^-1*x^-2+-1//2*a^-3//2*c^(1/2)*arctan(a^-1//2*c^(1/2)*x^2))
@test integrate(x^-5*(a+c*x^4)^-1, x) == :(-1//4*a^-1*x^-4+-1*c*a^-2*log(x)+1//4*c*a^-2*log(a+c*x^4))
@test integrate(x^-7*(a+c*x^4)^-1, x) == :(-1//6*a^-1*x^-6+(1/2)*c*a^-2*x^-2+(1/2)*a^-5//2*c^3//2*arctan(a^-1//2*c^(1/2)*x^2))
@test integrate(x^4*(a+c*x^4)^-1, x) == :(x*c^-1+-1//4*2^(1/2)*a^1//4*c^-5//4*arctan(1+x*2^(1/2)*a^-1//4*c^1//4)+-1//8*2^(1/2)*a^1//4*c^-5//4*log(a^(1/2)+c^(1/2)*x^2+x*2^(1/2)*a^1//4*c^1//4)+1//4*2^(1/2)*a^1//4*c^-5//4*arctan(1+-1*x*2^(1/2)*a^-1//4*c^1//4)+1//8*2^(1/2)*a^1//4*c^-5//4*log(a^(1/2)+c^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*c^1//4))
@test integrate(x^2*(a+c*x^4)^-1, x) == :(-1//4*2^(1/2)*a^-1//4*c^-3//4*arctan(1+-1*x*2^(1/2)*a^-1//4*c^1//4)+-1//8*2^(1/2)*a^-1//4*c^-3//4*log(a^(1/2)+c^(1/2)*x^2+x*2^(1/2)*a^1//4*c^1//4)+1//4*2^(1/2)*a^-1//4*c^-3//4*arctan(1+x*2^(1/2)*a^-1//4*c^1//4)+1//8*2^(1/2)*a^-1//4*c^-3//4*log(a^(1/2)+c^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*c^1//4))
@test integrate((a+c*x^4)^-1, x) == :(-1//4*2^(1/2)*a^-3//4*c^-1//4*arctan(1+-1*x*2^(1/2)*a^-1//4*c^1//4)+-1//8*2^(1/2)*a^-3//4*c^-1//4*log(a^(1/2)+c^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*c^1//4)+1//4*2^(1/2)*a^-3//4*c^-1//4*arctan(1+x*2^(1/2)*a^-1//4*c^1//4)+1//8*2^(1/2)*a^-3//4*c^-1//4*log(a^(1/2)+c^(1/2)*x^2+x*2^(1/2)*a^1//4*c^1//4))
@test integrate(x^-2*(a+c*x^4)^-1, x) == :(-1*a^-1*x^-1+-1//4*2^(1/2)*a^-5//4*c^1//4*arctan(1+x*2^(1/2)*a^-1//4*c^1//4)+-1//8*2^(1/2)*a^-5//4*c^1//4*log(a^(1/2)+c^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*c^1//4)+1//4*2^(1/2)*a^-5//4*c^1//4*arctan(1+-1*x*2^(1/2)*a^-1//4*c^1//4)+1//8*2^(1/2)*a^-5//4*c^1//4*log(a^(1/2)+c^(1/2)*x^2+x*2^(1/2)*a^1//4*c^1//4))
@test integrate(x^-4*(a+c*x^4)^-1, x) == :(-1//3*a^-1*x^-3+-1//4*2^(1/2)*a^-7//4*c^3//4*arctan(1+x*2^(1/2)*a^-1//4*c^1//4)+-1//8*2^(1/2)*a^-7//4*c^3//4*log(a^(1/2)+c^(1/2)*x^2+x*2^(1/2)*a^1//4*c^1//4)+1//4*2^(1/2)*a^-7//4*c^3//4*arctan(1+-1*x*2^(1/2)*a^-1//4*c^1//4)+1//8*2^(1/2)*a^-7//4*c^3//4*log(a^(1/2)+c^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*c^1//4))
@test integrate(x^11*(a+c*x^4)^-2, x) == :(1//4*c^-2*x^4+-1//2*a*c^-3*log(a+c*x^4)+-1//4*a^2*c^-3*(a+c*x^4)^-1)
@test integrate(x^9*(a+c*x^4)^-2, x) == :(3//4*c^-2*x^2+-3//4*a^(1/2)*c^-5//2*arctan(a^-1//2*c^(1/2)*x^2)+-1//4*c^-1*x^6*(a+c*x^4)^-1)
@test integrate(x^7*(a+c*x^4)^-2, x) == :(1//4*c^-2*log(a+c*x^4)+1//4*a*c^-2*(a+c*x^4)^-1)
@test integrate(x^5*(a+c*x^4)^-2, x) == :(-1//4*c^-1*x^2*(a+c*x^4)^-1+1//4*a^-1//2*c^-3//2*arctan(a^-1//2*c^(1/2)*x^2))
@test integrate(x^3*(a+c*x^4)^-2, x) == :(-1//4*c^-1*(a+c*x^4)^-1)
@test integrate(x*(a+c*x^4)^-2, x) == :(1//4*a^-1*x^2*(a+c*x^4)^-1+1//4*a^-3//2*c^-1//2*arctan(a^-1//2*c^(1/2)*x^2))
@test integrate(x^-1*(a+c*x^4)^-2, x) == :(a^-2*log(x)+-1//4*a^-2*log(a+c*x^4)+1//4*a^-1*(a+c*x^4)^-1)
@test integrate(x^-3*(a+c*x^4)^-2, x) == :(-3//4*a^-2*x^-2+-3//4*a^-5//2*c^(1/2)*arctan(a^-1//2*c^(1/2)*x^2)+1//4*a^-1*x^-2*(a+c*x^4)^-1)
@test integrate(x^6*(a+c*x^4)^-2, x) == :(-1//4*c^-1*x^3*(a+c*x^4)^-1+-3//16*2^(1/2)*a^-1//4*c^-7//4*arctan(1+-1*x*2^(1/2)*a^-1//4*c^1//4)+-3//32*2^(1/2)*a^-1//4*c^-7//4*log(a^(1/2)+c^(1/2)*x^2+x*2^(1/2)*a^1//4*c^1//4)+3//16*2^(1/2)*a^-1//4*c^-7//4*arctan(1+x*2^(1/2)*a^-1//4*c^1//4)+3//32*2^(1/2)*a^-1//4*c^-7//4*log(a^(1/2)+c^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*c^1//4))
@test integrate(x^4*(a+c*x^4)^-2, x) == :(-1//4*x*c^-1*(a+c*x^4)^-1+-1//16*2^(1/2)*a^-3//4*c^-5//4*arctan(1+-1*x*2^(1/2)*a^-1//4*c^1//4)+-1//32*2^(1/2)*a^-3//4*c^-5//4*log(a^(1/2)+c^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*c^1//4)+1//16*2^(1/2)*a^-3//4*c^-5//4*arctan(1+x*2^(1/2)*a^-1//4*c^1//4)+1//32*2^(1/2)*a^-3//4*c^-5//4*log(a^(1/2)+c^(1/2)*x^2+x*2^(1/2)*a^1//4*c^1//4))
@test integrate(x^2*(a+c*x^4)^-2, x) == :(1//4*a^-1*x^3*(a+c*x^4)^-1+-1//16*2^(1/2)*a^-5//4*c^-3//4*arctan(1+-1*x*2^(1/2)*a^-1//4*c^1//4)+-1//32*2^(1/2)*a^-5//4*c^-3//4*log(a^(1/2)+c^(1/2)*x^2+x*2^(1/2)*a^1//4*c^1//4)+1//16*2^(1/2)*a^-5//4*c^-3//4*arctan(1+x*2^(1/2)*a^-1//4*c^1//4)+1//32*2^(1/2)*a^-5//4*c^-3//4*log(a^(1/2)+c^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*c^1//4))
@test integrate((a+c*x^4)^-2, x) == :(1//4*x*a^-1*(a+c*x^4)^-1+-3//16*2^(1/2)*a^-7//4*c^-1//4*arctan(1+-1*x*2^(1/2)*a^-1//4*c^1//4)+-3//32*2^(1/2)*a^-7//4*c^-1//4*log(a^(1/2)+c^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*c^1//4)+3//16*2^(1/2)*a^-7//4*c^-1//4*arctan(1+x*2^(1/2)*a^-1//4*c^1//4)+3//32*2^(1/2)*a^-7//4*c^-1//4*log(a^(1/2)+c^(1/2)*x^2+x*2^(1/2)*a^1//4*c^1//4))
@test integrate(x^-2*(a+c*x^4)^-2, x) == :(-5//4*a^-2*x^-1+1//4*a^-1*x^-1*(a+c*x^4)^-1+-5//16*2^(1/2)*a^-9//4*c^1//4*arctan(1+x*2^(1/2)*a^-1//4*c^1//4)+-5//32*2^(1/2)*a^-9//4*c^1//4*log(a^(1/2)+c^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*c^1//4)+5//16*2^(1/2)*a^-9//4*c^1//4*arctan(1+-1*x*2^(1/2)*a^-1//4*c^1//4)+5//32*2^(1/2)*a^-9//4*c^1//4*log(a^(1/2)+c^(1/2)*x^2+x*2^(1/2)*a^1//4*c^1//4))
@test integrate(x^-4*(a+c*x^4)^-2, x) == :(-7//12*a^-2*x^-3+1//4*a^-1*x^-3*(a+c*x^4)^-1+-7//16*2^(1/2)*a^-11//4*c^3//4*arctan(1+x*2^(1/2)*a^-1//4*c^1//4)+-7//32*2^(1/2)*a^-11//4*c^3//4*log(a^(1/2)+c^(1/2)*x^2+x*2^(1/2)*a^1//4*c^1//4)+7//16*2^(1/2)*a^-11//4*c^3//4*arctan(1+-1*x*2^(1/2)*a^-1//4*c^1//4)+7//32*2^(1/2)*a^-11//4*c^3//4*log(a^(1/2)+c^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*c^1//4))
@test integrate(x^11*(a+c*x^4)^-3, x) == :(1//4*c^-3*log(a+c*x^4)+(1/2)*a*c^-3*(a+c*x^4)^-1+-1//8*a^2*c^-3*(a+c*x^4)^-2)
@test integrate(x^9*(a+c*x^4)^-3, x) == :(-3//16*c^-2*x^2*(a+c*x^4)^-1+-1//8*c^-1*x^6*(a+c*x^4)^-2+3//16*a^-1//2*c^-5//2*arctan(a^-1//2*c^(1/2)*x^2))
@test integrate(x^7*(a+c*x^4)^-3, x) == :(1//8*a^-1*x^8*(a+c*x^4)^-2)
@test integrate(x^5*(a+c*x^4)^-3, x) == :(-1//8*c^-1*x^2*(a+c*x^4)^-2+1//16*a^-3//2*c^-3//2*arctan(a^-1//2*c^(1/2)*x^2)+1//16*a^-1*c^-1*x^2*(a+c*x^4)^-1)
@test integrate(x^3*(a+c*x^4)^-3, x) == :(-1//8*c^-1*(a+c*x^4)^-2)
@test integrate(x*(a+c*x^4)^-3, x) == :(1//8*a^-1*x^2*(a+c*x^4)^-2+3//16*a^-2*x^2*(a+c*x^4)^-1+3//16*a^-5//2*c^-1//2*arctan(a^-1//2*c^(1/2)*x^2))
@test integrate(x^-1*(a+c*x^4)^-3, x) == :(a^-3*log(x)+-1//4*a^-3*log(a+c*x^4)+1//4*a^-2*(a+c*x^4)^-1+1//8*a^-1*(a+c*x^4)^-2)
@test integrate(x^-3*(a+c*x^4)^-3, x) == :(-15//16*a^-3*x^-2+-15//16*a^-7//2*c^(1/2)*arctan(a^-1//2*c^(1/2)*x^2)+1//8*a^-1*x^-2*(a+c*x^4)^-2+5//16*a^-2*x^-2*(a+c*x^4)^-1)
@test integrate(x^10*(a+c*x^4)^-3, x) == :(-7//32*c^-2*x^3*(a+c*x^4)^-1+-1//8*c^-1*x^7*(a+c*x^4)^-2+-21//128*2^(1/2)*a^-1//4*c^-11//4*arctan(1+-1*x*2^(1/2)*a^-1//4*c^1//4)+-21//256*2^(1/2)*a^-1//4*c^-11//4*log(a^(1/2)+c^(1/2)*x^2+x*2^(1/2)*a^1//4*c^1//4)+21//128*2^(1/2)*a^-1//4*c^-11//4*arctan(1+x*2^(1/2)*a^-1//4*c^1//4)+21//256*2^(1/2)*a^-1//4*c^-11//4*log(a^(1/2)+c^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*c^1//4))
@test integrate(x^8*(a+c*x^4)^-3, x) == :(-5//32*x*c^-2*(a+c*x^4)^-1+-1//8*c^-1*x^5*(a+c*x^4)^-2+-5//128*2^(1/2)*a^-3//4*c^-9//4*arctan(1+-1*x*2^(1/2)*a^-1//4*c^1//4)+-5//256*2^(1/2)*a^-3//4*c^-9//4*log(a^(1/2)+c^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*c^1//4)+5//128*2^(1/2)*a^-3//4*c^-9//4*arctan(1+x*2^(1/2)*a^-1//4*c^1//4)+5//256*2^(1/2)*a^-3//4*c^-9//4*log(a^(1/2)+c^(1/2)*x^2+x*2^(1/2)*a^1//4*c^1//4))
@test integrate(x^6*(a+c*x^4)^-3, x) == :(-1//8*c^-1*x^3*(a+c*x^4)^-2+-3//128*2^(1/2)*a^-5//4*c^-7//4*arctan(1+-1*x*2^(1/2)*a^-1//4*c^1//4)+-3//256*2^(1/2)*a^-5//4*c^-7//4*log(a^(1/2)+c^(1/2)*x^2+x*2^(1/2)*a^1//4*c^1//4)+3//32*a^-1*c^-1*x^3*(a+c*x^4)^-1+3//128*2^(1/2)*a^-5//4*c^-7//4*arctan(1+x*2^(1/2)*a^-1//4*c^1//4)+3//256*2^(1/2)*a^-5//4*c^-7//4*log(a^(1/2)+c^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*c^1//4))
@test integrate(x^4*(a+c*x^4)^-3, x) == :(-1//8*x*c^-1*(a+c*x^4)^-2+-3//128*2^(1/2)*a^-7//4*c^-5//4*arctan(1+-1*x*2^(1/2)*a^-1//4*c^1//4)+-3//256*2^(1/2)*a^-7//4*c^-5//4*log(a^(1/2)+c^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*c^1//4)+1//32*x*a^-1*c^-1*(a+c*x^4)^-1+3//128*2^(1/2)*a^-7//4*c^-5//4*arctan(1+x*2^(1/2)*a^-1//4*c^1//4)+3//256*2^(1/2)*a^-7//4*c^-5//4*log(a^(1/2)+c^(1/2)*x^2+x*2^(1/2)*a^1//4*c^1//4))
@test integrate(x^2*(a+c*x^4)^-3, x) == :(1//8*a^-1*x^3*(a+c*x^4)^-2+5//32*a^-2*x^3*(a+c*x^4)^-1+-5//128*2^(1/2)*a^-9//4*c^-3//4*arctan(1+-1*x*2^(1/2)*a^-1//4*c^1//4)+-5//256*2^(1/2)*a^-9//4*c^-3//4*log(a^(1/2)+c^(1/2)*x^2+x*2^(1/2)*a^1//4*c^1//4)+5//128*2^(1/2)*a^-9//4*c^-3//4*arctan(1+x*2^(1/2)*a^-1//4*c^1//4)+5//256*2^(1/2)*a^-9//4*c^-3//4*log(a^(1/2)+c^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*c^1//4))
@test integrate((a+c*x^4)^-3, x) == :(1//8*x*a^-1*(a+c*x^4)^-2+7//32*x*a^-2*(a+c*x^4)^-1+-21//128*2^(1/2)*a^-11//4*c^-1//4*arctan(1+-1*x*2^(1/2)*a^-1//4*c^1//4)+-21//256*2^(1/2)*a^-11//4*c^-1//4*log(a^(1/2)+c^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*c^1//4)+21//128*2^(1/2)*a^-11//4*c^-1//4*arctan(1+x*2^(1/2)*a^-1//4*c^1//4)+21//256*2^(1/2)*a^-11//4*c^-1//4*log(a^(1/2)+c^(1/2)*x^2+x*2^(1/2)*a^1//4*c^1//4))
@test integrate(x^-2*(a+c*x^4)^-3, x) == :(-45//32*a^-3*x^-1+1//8*a^-1*x^-1*(a+c*x^4)^-2+9//32*a^-2*x^-1*(a+c*x^4)^-1+-45//128*2^(1/2)*a^-13//4*c^1//4*arctan(1+x*2^(1/2)*a^-1//4*c^1//4)+-45//256*2^(1/2)*a^-13//4*c^1//4*log(a^(1/2)+c^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*c^1//4)+45//128*2^(1/2)*a^-13//4*c^1//4*arctan(1+-1*x*2^(1/2)*a^-1//4*c^1//4)+45//256*2^(1/2)*a^-13//4*c^1//4*log(a^(1/2)+c^(1/2)*x^2+x*2^(1/2)*a^1//4*c^1//4))
@test integrate(x^9*(2+3*x^4)^-1, x) == :(-1//9*x^2+1//18*x^6+1//27*6^(1/2)*arctan((1/2)*6^(1/2)*x^2))
@test integrate(x^7*(2+3*x^4)^-1, x) == :(-1//18*log(2+3*x^4)+1//12*x^4)
@test integrate(x^5*(2+3*x^4)^-1, x) == :(1//6*x^2+-1//18*6^(1/2)*arctan((1/2)*6^(1/2)*x^2))
@test integrate(x^3*(2+3*x^4)^-1, x) == :(1//12*log(2+3*x^4))
@test integrate(x*(2+3*x^4)^-1, x) == :(1//12*6^(1/2)*arctan((1/2)*6^(1/2)*x^2))
@test integrate(x^-1*(2+3*x^4)^-1, x) == :((1/2)*log(x)+-1//8*log(2+3*x^4))
@test integrate(x^-3*(2+3*x^4)^-1, x) == :(-1//4*x^-2+-1//8*6^(1/2)*arctan((1/2)*6^(1/2)*x^2))
@test integrate(x^6*(2+3*x^4)^-1, x) == :(1//9*x^3+-1//18*6^1//4*arctan(1+x*6^1//4)+-1//36*6^1//4*log(6^(1/2)+3*x^2+-1*x*6^3//4)+1//18*6^1//4*arctan(1+-1*x*6^1//4)+1//36*6^1//4*log(6^(1/2)+3*x^2+x*6^3//4))
@test integrate(x^4*(2+3*x^4)^-1, x) == :(1//3*x+-1//36*6^3//4*arctan(1+x*6^1//4)+-1//72*6^3//4*log(6^(1/2)+3*x^2+x*6^3//4)+1//36*6^3//4*arctan(1+-1*x*6^1//4)+1//72*6^3//4*log(6^(1/2)+3*x^2+-1*x*6^3//4))
@test integrate(x^2*(2+3*x^4)^-1, x) == :(-1//12*6^1//4*arctan(1+-1*x*6^1//4)+-1//24*6^1//4*log(6^(1/2)+3*x^2+x*6^3//4)+1//12*6^1//4*arctan(1+x*6^1//4)+1//24*6^1//4*log(6^(1/2)+3*x^2+-1*x*6^3//4))
@test integrate((2+3*x^4)^-1, x) == :(-1//24*6^3//4*arctan(1+-1*x*6^1//4)+-1//48*6^3//4*log(6^(1/2)+3*x^2+-1*x*6^3//4)+1//24*6^3//4*arctan(1+x*6^1//4)+1//48*6^3//4*log(6^(1/2)+3*x^2+x*6^3//4))
@test integrate(x^-2*(2+3*x^4)^-1, x) == :(-1//2*x^-1+-1//8*6^1//4*arctan(1+x*6^1//4)+-1//16*6^1//4*log(6^(1/2)+3*x^2+-1*x*6^3//4)+1//8*6^1//4*arctan(1+-1*x*6^1//4)+1//16*6^1//4*log(6^(1/2)+3*x^2+x*6^3//4))
@test integrate(x^3*(2+3*x^4)^-2, x) == :(-1*(24+36*x^4)^-1)
@test integrate(x*(2+3*x^4)^-2, x) == :(x^2*(16+24*x^4)^-1+1//48*6^(1/2)*arctan((1/2)*6^(1/2)*x^2))
@test integrate(x^-1*(2+3*x^4)^-2, x) == :((16+24*x^4)^-1+-1//16*log(2+3*x^4)+1//4*log(x))
@test integrate(x^-3*(2+3*x^4)^-2, x) == :(-3//16*x^-2+-3//32*6^(1/2)*arctan((1/2)*6^(1/2)*x^2)+1//8*x^-2*(2+3*x^4)^-1)
@test integrate(x^4*(2+3*x^4)^-2, x) == :(-1*x*(24+36*x^4)^-1+-1//288*6^3//4*arctan(1+-1*x*6^1//4)+-1//576*6^3//4*log(6^(1/2)+3*x^2+-1*x*6^3//4)+1//288*6^3//4*arctan(1+x*6^1//4)+1//576*6^3//4*log(6^(1/2)+3*x^2+x*6^3//4))
@test integrate(x^2*(2+3*x^4)^-2, x) == :(x^3*(16+24*x^4)^-1+-1//96*6^1//4*arctan(1+-1*x*6^1//4)+-1//192*6^1//4*log(6^(1/2)+3*x^2+x*6^3//4)+1//96*6^1//4*arctan(1+x*6^1//4)+1//192*6^1//4*log(6^(1/2)+3*x^2+-1*x*6^3//4))
@test integrate((2+3*x^4)^-2, x) == :(x*(16+24*x^4)^-1+-1//64*6^3//4*arctan(1+-1*x*6^1//4)+-1//128*6^3//4*log(6^(1/2)+3*x^2+-1*x*6^3//4)+1//64*6^3//4*arctan(1+x*6^1//4)+1//128*6^3//4*log(6^(1/2)+3*x^2+x*6^3//4))
@test integrate(x^-2*(2+3*x^4)^-2, x) == :(-5//16*x^-1+-5//64*6^1//4*arctan(1+x*6^1//4)+-5//128*6^1//4*log(6^(1/2)+3*x^2+-1*x*6^3//4)+1//8*x^-1*(2+3*x^4)^-1+5//64*6^1//4*arctan(1+-1*x*6^1//4)+5//128*6^1//4*log(6^(1/2)+3*x^2+x*6^3//4))
@test integrate(x^2*(3+x^4)^-1, x) == :(-1//12*2^(1/2)*3^3//4*arctan(1+-1//3*x*2^(1/2)*3^3//4)+-1//24*2^(1/2)*3^3//4*log(3^(1/2)+x^2+x*2^(1/2)*3^1//4)+1//12*2^(1/2)*3^3//4*arctan(1+1//3*x*2^(1/2)*3^3//4)+1//24*2^(1/2)*3^3//4*log(3^(1/2)+x^2+-1*x*2^(1/2)*3^1//4))
@test integrate((1+a+x^4*(-1+a))^-1, x) == :((1/2)*(1+a)^-1//2*(1+-1*a^2)^-1//4*arctan(x*(1+a)^-1//4*(1+-1a)^1//4)+(1/2)*(1+a)^-1//2*(1+-1*a^2)^-1//4*arctanh(x*(1+a)^-1//4*(1+-1a)^1//4))
@test integrate((x^4+2a+2b)^-1, x) == :(-1//4*2^1//4*(-1a+-1b)^-3//4*arctan((1/2)*x*2^3//4*(-1a+-1b)^-1//4)+-1//4*2^1//4*(-1a+-1b)^-3//4*arctanh((1/2)*x*2^3//4*(-1a+-1b)^-1//4))
@test integrate((x^4+2a+2b)^-1, x) == :(-1//4*2^1//4*(-1a+-1b)^-3//4*arctan((1/2)*x*2^3//4*(-1a+-1b)^-1//4)+-1//4*2^1//4*(-1a+-1b)^-3//4*arctanh((1/2)*x*2^3//4*(-1a+-1b)^-1//4))
@test integrate(x*(x^4+2a+2b)^-1, x) == :(1//4*2^(1/2)*(a+b)^-1//2*arctan((1/2)*2^(1/2)*x^2*(a+b)^-1//2))
@test integrate(x*(x^4+2a+2b)^-1, x) == :(1//4*2^(1/2)*(a+b)^-1//2*arctan((1/2)*2^(1/2)*x^2*(a+b)^-1//2))
@test integrate(x^2*(x^4+2a+2b)^-1, x) == :(-1//4*2^3//4*(-1a+-1b)^-1//4*arctanh((1/2)*x*2^3//4*(-1a+-1b)^-1//4)+1//4*2^3//4*(-1a+-1b)^-1//4*arctan((1/2)*x*2^3//4*(-1a+-1b)^-1//4))
@test integrate(x^2*(x^4+2a+2b)^-1, x) == :(-1//4*2^3//4*(-1a+-1b)^-1//4*arctanh((1/2)*x*2^3//4*(-1a+-1b)^-1//4)+1//4*2^3//4*(-1a+-1b)^-1//4*arctan((1/2)*x*2^3//4*(-1a+-1b)^-1//4))
@test integrate(x^3*(x^4+2a+2b)^-1, x) == :(1//4*log(x^4+2a+2b))
@test integrate(x^3*(x^4+2a+2b)^-1, x) == :(1//4*log(x^4+2a+2b))
@test integrate(x^5//2*(a+c*x^4), x) == :(2//7*a*x^7//2+2//15*c*x^15//2)
@test integrate(x^3//2*(a+c*x^4), x) == :(2//5*a*x^5//2+2//13*c*x^13//2)
@test integrate(x^(1/2)*(a+c*x^4), x) == :(2//3*a*x^3//2+2//11*c*x^11//2)
@test integrate(x^-1//2*(a+c*x^4), x) == :(2*a*x^(1/2)+2//9*c*x^9//2)
@test integrate(x^-3//2*(a+c*x^4), x) == :(-2*a*x^-1//2+2//7*c*x^7//2)
@test integrate(x^-5//2*(a+c*x^4), x) == :(-2//3*a*x^-3//2+2//5*c*x^5//2)
@test integrate(x^-7//2*(a+c*x^4), x) == :(-2//5*a*x^-5//2+2//3*c*x^3//2)
@test integrate(x^5//2*(a+c*x^4)^2, x) == :(2//7*a^2*x^7//2+2//23*c^2*x^23//2+4//15*a*c*x^15//2)
@test integrate(x^3//2*(a+c*x^4)^2, x) == :(2//5*a^2*x^5//2+2//21*c^2*x^21//2+4//13*a*c*x^13//2)
@test integrate(x^(1/2)*(a+c*x^4)^2, x) == :(2//3*a^2*x^3//2+2//19*c^2*x^19//2+4//11*a*c*x^11//2)
@test integrate(x^-1//2*(a+c*x^4)^2, x) == :(2*a^2*x^(1/2)+2//17*c^2*x^17//2+4//9*a*c*x^9//2)
@test integrate(x^-3//2*(a+c*x^4)^2, x) == :(-2*a^2*x^-1//2+2//15*c^2*x^15//2+4//7*a*c*x^7//2)
@test integrate(x^-5//2*(a+c*x^4)^2, x) == :(-2//3*a^2*x^-3//2+2//13*c^2*x^13//2+4//5*a*c*x^5//2)
@test integrate(x^-7//2*(a+c*x^4)^2, x) == :(-2//5*a^2*x^-5//2+2//11*c^2*x^11//2+4//3*a*c*x^3//2)
@test integrate(x^5//2*(a+c*x^4)^3, x) == :(2//7*a^3*x^7//2+2//31*c^3*x^31//2+2//5*c*a^2*x^15//2+6//23*a*c^2*x^23//2)
@test integrate(x^3//2*(a+c*x^4)^3, x) == :(2//5*a^3*x^5//2+2//29*c^3*x^29//2+2//7*a*c^2*x^21//2+6//13*c*a^2*x^13//2)
@test integrate(x^(1/2)*(a+c*x^4)^3, x) == :(2//3*a^3*x^3//2+2//27*c^3*x^27//2+6//11*c*a^2*x^11//2+6//19*a*c^2*x^19//2)
@test integrate(x^-1//2*(a+c*x^4)^3, x) == :(2*a^3*x^(1/2)+2//25*c^3*x^25//2+2//3*c*a^2*x^9//2+6//17*a*c^2*x^17//2)
@test integrate(x^-3//2*(a+c*x^4)^3, x) == :(-2*a^3*x^-1//2+2//23*c^3*x^23//2+2//5*a*c^2*x^15//2+6//7*c*a^2*x^7//2)
@test integrate(x^-5//2*(a+c*x^4)^3, x) == :(-2//3*a^3*x^-3//2+2//21*c^3*x^21//2+6//5*c*a^2*x^5//2+6//13*a*c^2*x^13//2)
@test integrate(x^-7//2*(a+c*x^4)^3, x) == :(-2//5*a^3*x^-5//2+2//19*c^3*x^19//2+2*c*a^2*x^3//2+6//11*a*c^2*x^11//2)
@test integrate(x^9//2*(a+c*x^4)^-1, x) == :(2//3*c^-1*x^3//2+(1/2)*c^-11//8*(-1a)^3//8*arctan(c^1//8*x^(1/2)*(-1a)^-1//8)+-1//2*c^-11//8*(-1a)^3//8*arctanh(c^1//8*x^(1/2)*(-1a)^-1//8)+-1//4*2^(1/2)*c^-11//8*(-1a)^3//8*arctan(1+2^(1/2)*c^1//8*x^(1/2)*(-1a)^-1//8)+-1//8*2^(1/2)*c^-11//8*(-1a)^3//8*log((-1a)^1//4+x*c^1//4+-1*2^(1/2)*c^1//8*x^(1/2)*(-1a)^1//8)+1//4*2^(1/2)*c^-11//8*(-1a)^3//8*arctan(1+-1*2^(1/2)*c^1//8*x^(1/2)*(-1a)^-1//8)+1//8*2^(1/2)*c^-11//8*(-1a)^3//8*log((-1a)^1//4+x*c^1//4+2^(1/2)*c^1//8*x^(1/2)*(-1a)^1//8))
@test integrate(x^7//2*(a+c*x^4)^-1, x) == :(2*c^-1*x^(1/2)+-1//2*c^-9//8*(-1a)^1//8*arctan(c^1//8*x^(1/2)*(-1a)^-1//8)+-1//2*c^-9//8*(-1a)^1//8*arctanh(c^1//8*x^(1/2)*(-1a)^-1//8)+-1//4*2^(1/2)*c^-9//8*(-1a)^1//8*arctan(1+2^(1/2)*c^1//8*x^(1/2)*(-1a)^-1//8)+-1//8*2^(1/2)*c^-9//8*(-1a)^1//8*log((-1a)^1//4+x*c^1//4+2^(1/2)*c^1//8*x^(1/2)*(-1a)^1//8)+1//4*2^(1/2)*c^-9//8*(-1a)^1//8*arctan(1+-1*2^(1/2)*c^1//8*x^(1/2)*(-1a)^-1//8)+1//8*2^(1/2)*c^-9//8*(-1a)^1//8*log((-1a)^1//4+x*c^1//4+-1*2^(1/2)*c^1//8*x^(1/2)*(-1a)^1//8))
@test integrate(x^5//2*(a+c*x^4)^-1, x) == :((1/2)*c^-7//8*(-1a)^-1//8*arctan(c^1//8*x^(1/2)*(-1a)^-1//8)+-1//2*c^-7//8*(-1a)^-1//8*arctanh(c^1//8*x^(1/2)*(-1a)^-1//8)+-1//4*2^(1/2)*c^-7//8*(-1a)^-1//8*arctan(1+-1*2^(1/2)*c^1//8*x^(1/2)*(-1a)^-1//8)+-1//8*2^(1/2)*c^-7//8*(-1a)^-1//8*log((-1a)^1//4+x*c^1//4+2^(1/2)*c^1//8*x^(1/2)*(-1a)^1//8)+1//4*2^(1/2)*c^-7//8*(-1a)^-1//8*arctan(1+2^(1/2)*c^1//8*x^(1/2)*(-1a)^-1//8)+1//8*2^(1/2)*c^-7//8*(-1a)^-1//8*log((-1a)^1//4+x*c^1//4+-1*2^(1/2)*c^1//8*x^(1/2)*(-1a)^1//8))
@test integrate(x^3//2*(a+c*x^4)^-1, x) == :(-1//2*c^-5//8*(-1a)^-3//8*arctan(c^1//8*x^(1/2)*(-1a)^-1//8)+-1//2*c^-5//8*(-1a)^-3//8*arctanh(c^1//8*x^(1/2)*(-1a)^-1//8)+-1//4*2^(1/2)*c^-5//8*(-1a)^-3//8*arctan(1+-1*2^(1/2)*c^1//8*x^(1/2)*(-1a)^-1//8)+-1//8*2^(1/2)*c^-5//8*(-1a)^-3//8*log((-1a)^1//4+x*c^1//4+-1*2^(1/2)*c^1//8*x^(1/2)*(-1a)^1//8)+1//4*2^(1/2)*c^-5//8*(-1a)^-3//8*arctan(1+2^(1/2)*c^1//8*x^(1/2)*(-1a)^-1//8)+1//8*2^(1/2)*c^-5//8*(-1a)^-3//8*log((-1a)^1//4+x*c^1//4+2^(1/2)*c^1//8*x^(1/2)*(-1a)^1//8))
@test integrate(x^(1/2)*(a+c*x^4)^-1, x) == :((1/2)*c^-3//8*(-1a)^-5//8*arctan(c^1//8*x^(1/2)*(-1a)^-1//8)+-1//2*c^-3//8*(-1a)^-5//8*arctanh(c^1//8*x^(1/2)*(-1a)^-1//8)+-1//4*2^(1/2)*c^-3//8*(-1a)^-5//8*arctan(1+2^(1/2)*c^1//8*x^(1/2)*(-1a)^-1//8)+-1//8*2^(1/2)*c^-3//8*(-1a)^-5//8*log((-1a)^1//4+x*c^1//4+-1*2^(1/2)*c^1//8*x^(1/2)*(-1a)^1//8)+1//4*2^(1/2)*c^-3//8*(-1a)^-5//8*arctan(1+-1*2^(1/2)*c^1//8*x^(1/2)*(-1a)^-1//8)+1//8*2^(1/2)*c^-3//8*(-1a)^-5//8*log((-1a)^1//4+x*c^1//4+2^(1/2)*c^1//8*x^(1/2)*(-1a)^1//8))
@test integrate(x^-1//2*(a+c*x^4)^-1, x) == :(-1//2*c^-1//8*(-1a)^-7//8*arctan(c^1//8*x^(1/2)*(-1a)^-1//8)+-1//2*c^-1//8*(-1a)^-7//8*arctanh(c^1//8*x^(1/2)*(-1a)^-1//8)+-1//4*2^(1/2)*c^-1//8*(-1a)^-7//8*arctan(1+2^(1/2)*c^1//8*x^(1/2)*(-1a)^-1//8)+-1//8*2^(1/2)*c^-1//8*(-1a)^-7//8*log((-1a)^1//4+x*c^1//4+2^(1/2)*c^1//8*x^(1/2)*(-1a)^1//8)+1//4*2^(1/2)*c^-1//8*(-1a)^-7//8*arctan(1+-1*2^(1/2)*c^1//8*x^(1/2)*(-1a)^-1//8)+1//8*2^(1/2)*c^-1//8*(-1a)^-7//8*log((-1a)^1//4+x*c^1//4+-1*2^(1/2)*c^1//8*x^(1/2)*(-1a)^1//8))
@test integrate(x^-3//2*(a+c*x^4)^-1, x) == :(-2*a^-1*x^-1//2+(1/2)*c^1//8*(-1a)^-9//8*arctan(c^1//8*x^(1/2)*(-1a)^-1//8)+-1//2*c^1//8*(-1a)^-9//8*arctanh(c^1//8*x^(1/2)*(-1a)^-1//8)+-1//4*2^(1/2)*c^1//8*(-1a)^-9//8*arctan(1+-1*2^(1/2)*c^1//8*x^(1/2)*(-1a)^-1//8)+-1//8*2^(1/2)*c^1//8*(-1a)^-9//8*log((-1a)^1//4+x*c^1//4+2^(1/2)*c^1//8*x^(1/2)*(-1a)^1//8)+1//4*2^(1/2)*c^1//8*(-1a)^-9//8*arctan(1+2^(1/2)*c^1//8*x^(1/2)*(-1a)^-1//8)+1//8*2^(1/2)*c^1//8*(-1a)^-9//8*log((-1a)^1//4+x*c^1//4+-1*2^(1/2)*c^1//8*x^(1/2)*(-1a)^1//8))
@test integrate(x^-5//2*(a+c*x^4)^-1, x) == :(-2//3*a^-1*x^-3//2+-1//2*c^3//8*(-1a)^-11//8*arctan(c^1//8*x^(1/2)*(-1a)^-1//8)+-1//2*c^3//8*(-1a)^-11//8*arctanh(c^1//8*x^(1/2)*(-1a)^-1//8)+-1//4*2^(1/2)*c^3//8*(-1a)^-11//8*arctan(1+-1*2^(1/2)*c^1//8*x^(1/2)*(-1a)^-1//8)+-1//8*2^(1/2)*c^3//8*(-1a)^-11//8*log((-1a)^1//4+x*c^1//4+-1*2^(1/2)*c^1//8*x^(1/2)*(-1a)^1//8)+1//4*2^(1/2)*c^3//8*(-1a)^-11//8*arctan(1+2^(1/2)*c^1//8*x^(1/2)*(-1a)^-1//8)+1//8*2^(1/2)*c^3//8*(-1a)^-11//8*log((-1a)^1//4+x*c^1//4+2^(1/2)*c^1//8*x^(1/2)*(-1a)^1//8))
@test integrate(x^13//2*(a+c*x^4)^-2, x) == :(-7//16*c^-15//8*(-1a)^-1//8*arctanh(c^1//8*x^(1/2)*(-1a)^-1//8)+-1//4*c^-1*x^7//2*(a+c*x^4)^-1+7//16*c^-15//8*(-1a)^-1//8*arctan(c^1//8*x^(1/2)*(-1a)^-1//8)+-7//32*2^(1/2)*c^-15//8*(-1a)^-1//8*arctan(1+-1*2^(1/2)*c^1//8*x^(1/2)*(-1a)^-1//8)+-7//64*2^(1/2)*c^-15//8*(-1a)^-1//8*log((-1a)^1//4+x*c^1//4+2^(1/2)*c^1//8*x^(1/2)*(-1a)^1//8)+7//32*2^(1/2)*c^-15//8*(-1a)^-1//8*arctan(1+2^(1/2)*c^1//8*x^(1/2)*(-1a)^-1//8)+7//64*2^(1/2)*c^-15//8*(-1a)^-1//8*log((-1a)^1//4+x*c^1//4+-1*2^(1/2)*c^1//8*x^(1/2)*(-1a)^1//8))
@test integrate(x^11//2*(a+c*x^4)^-2, x) == :(-5//16*c^-13//8*(-1a)^-3//8*arctan(c^1//8*x^(1/2)*(-1a)^-1//8)+-5//16*c^-13//8*(-1a)^-3//8*arctanh(c^1//8*x^(1/2)*(-1a)^-1//8)+-1//4*c^-1*x^5//2*(a+c*x^4)^-1+-5//32*2^(1/2)*c^-13//8*(-1a)^-3//8*arctan(1+-1*2^(1/2)*c^1//8*x^(1/2)*(-1a)^-1//8)+-5//64*2^(1/2)*c^-13//8*(-1a)^-3//8*log((-1a)^1//4+x*c^1//4+-1*2^(1/2)*c^1//8*x^(1/2)*(-1a)^1//8)+5//32*2^(1/2)*c^-13//8*(-1a)^-3//8*arctan(1+2^(1/2)*c^1//8*x^(1/2)*(-1a)^-1//8)+5//64*2^(1/2)*c^-13//8*(-1a)^-3//8*log((-1a)^1//4+x*c^1//4+2^(1/2)*c^1//8*x^(1/2)*(-1a)^1//8))
@test integrate(x^9//2*(a+c*x^4)^-2, x) == :(-3//16*c^-11//8*(-1a)^-5//8*arctanh(c^1//8*x^(1/2)*(-1a)^-1//8)+-1//4*c^-1*x^3//2*(a+c*x^4)^-1+3//16*c^-11//8*(-1a)^-5//8*arctan(c^1//8*x^(1/2)*(-1a)^-1//8)+-3//32*2^(1/2)*c^-11//8*(-1a)^-5//8*arctan(1+2^(1/2)*c^1//8*x^(1/2)*(-1a)^-1//8)+-3//64*2^(1/2)*c^-11//8*(-1a)^-5//8*log((-1a)^1//4+x*c^1//4+-1*2^(1/2)*c^1//8*x^(1/2)*(-1a)^1//8)+3//32*2^(1/2)*c^-11//8*(-1a)^-5//8*arctan(1+-1*2^(1/2)*c^1//8*x^(1/2)*(-1a)^-1//8)+3//64*2^(1/2)*c^-11//8*(-1a)^-5//8*log((-1a)^1//4+x*c^1//4+2^(1/2)*c^1//8*x^(1/2)*(-1a)^1//8))
@test integrate(x^7//2*(a+c*x^4)^-2, x) == :(-1//4*c^-1*x^(1/2)*(a+c*x^4)^-1+-1//16*c^-9//8*(-1a)^-7//8*arctan(c^1//8*x^(1/2)*(-1a)^-1//8)+-1//16*c^-9//8*(-1a)^-7//8*arctanh(c^1//8*x^(1/2)*(-1a)^-1//8)+-1//32*2^(1/2)*c^-9//8*(-1a)^-7//8*arctan(1+2^(1/2)*c^1//8*x^(1/2)*(-1a)^-1//8)+-1//64*2^(1/2)*c^-9//8*(-1a)^-7//8*log((-1a)^1//4+x*c^1//4+2^(1/2)*c^1//8*x^(1/2)*(-1a)^1//8)+1//32*2^(1/2)*c^-9//8*(-1a)^-7//8*arctan(1+-1*2^(1/2)*c^1//8*x^(1/2)*(-1a)^-1//8)+1//64*2^(1/2)*c^-9//8*(-1a)^-7//8*log((-1a)^1//4+x*c^1//4+-1*2^(1/2)*c^1//8*x^(1/2)*(-1a)^1//8))
@test integrate(x^5//2*(a+c*x^4)^-2, x) == :(-1//16*c^-7//8*(-1a)^-9//8*arctan(c^1//8*x^(1/2)*(-1a)^-1//8)+1//4*a^-1*x^7//2*(a+c*x^4)^-1+1//16*c^-7//8*(-1a)^-9//8*arctanh(c^1//8*x^(1/2)*(-1a)^-1//8)+-1//32*2^(1/2)*c^-7//8*(-1a)^-9//8*arctan(1+2^(1/2)*c^1//8*x^(1/2)*(-1a)^-1//8)+-1//64*2^(1/2)*c^-7//8*(-1a)^-9//8*log((-1a)^1//4+x*c^1//4+-1*2^(1/2)*c^1//8*x^(1/2)*(-1a)^1//8)+1//32*2^(1/2)*c^-7//8*(-1a)^-9//8*arctan(1+-1*2^(1/2)*c^1//8*x^(1/2)*(-1a)^-1//8)+1//64*2^(1/2)*c^-7//8*(-1a)^-9//8*log((-1a)^1//4+x*c^1//4+2^(1/2)*c^1//8*x^(1/2)*(-1a)^1//8))
@test integrate(x^3//2*(a+c*x^4)^-2, x) == :(1//4*a^-1*x^5//2*(a+c*x^4)^-1+3//16*c^-5//8*(-1a)^-11//8*arctan(c^1//8*x^(1/2)*(-1a)^-1//8)+3//16*c^-5//8*(-1a)^-11//8*arctanh(c^1//8*x^(1/2)*(-1a)^-1//8)+-3//32*2^(1/2)*c^-5//8*(-1a)^-11//8*arctan(1+2^(1/2)*c^1//8*x^(1/2)*(-1a)^-1//8)+-3//64*2^(1/2)*c^-5//8*(-1a)^-11//8*log((-1a)^1//4+x*c^1//4+2^(1/2)*c^1//8*x^(1/2)*(-1a)^1//8)+3//32*2^(1/2)*c^-5//8*(-1a)^-11//8*arctan(1+-1*2^(1/2)*c^1//8*x^(1/2)*(-1a)^-1//8)+3//64*2^(1/2)*c^-5//8*(-1a)^-11//8*log((-1a)^1//4+x*c^1//4+-1*2^(1/2)*c^1//8*x^(1/2)*(-1a)^1//8))
@test integrate(x^(1/2)*(a+c*x^4)^-2, x) == :(-5//16*c^-3//8*(-1a)^-13//8*arctan(c^1//8*x^(1/2)*(-1a)^-1//8)+1//4*a^-1*x^3//2*(a+c*x^4)^-1+5//16*c^-3//8*(-1a)^-13//8*arctanh(c^1//8*x^(1/2)*(-1a)^-1//8)+-5//32*2^(1/2)*c^-3//8*(-1a)^-13//8*arctan(1+-1*2^(1/2)*c^1//8*x^(1/2)*(-1a)^-1//8)+-5//64*2^(1/2)*c^-3//8*(-1a)^-13//8*log((-1a)^1//4+x*c^1//4+2^(1/2)*c^1//8*x^(1/2)*(-1a)^1//8)+5//32*2^(1/2)*c^-3//8*(-1a)^-13//8*arctan(1+2^(1/2)*c^1//8*x^(1/2)*(-1a)^-1//8)+5//64*2^(1/2)*c^-3//8*(-1a)^-13//8*log((-1a)^1//4+x*c^1//4+-1*2^(1/2)*c^1//8*x^(1/2)*(-1a)^1//8))
@test integrate(x^-1//2*(a+c*x^4)^-2, x) == :(1//4*a^-1*x^(1/2)*(a+c*x^4)^-1+7//16*c^-1//8*(-1a)^-15//8*arctan(c^1//8*x^(1/2)*(-1a)^-1//8)+7//16*c^-1//8*(-1a)^-15//8*arctanh(c^1//8*x^(1/2)*(-1a)^-1//8)+-7//32*2^(1/2)*c^-1//8*(-1a)^-15//8*arctan(1+-1*2^(1/2)*c^1//8*x^(1/2)*(-1a)^-1//8)+-7//64*2^(1/2)*c^-1//8*(-1a)^-15//8*log((-1a)^1//4+x*c^1//4+-1*2^(1/2)*c^1//8*x^(1/2)*(-1a)^1//8)+7//32*2^(1/2)*c^-1//8*(-1a)^-15//8*arctan(1+2^(1/2)*c^1//8*x^(1/2)*(-1a)^-1//8)+7//64*2^(1/2)*c^-1//8*(-1a)^-15//8*log((-1a)^1//4+x*c^1//4+2^(1/2)*c^1//8*x^(1/2)*(-1a)^1//8))
@test integrate(x^-3//2*(a+c*x^4)^-2, x) == :(-9//4*a^-2*x^-1//2+-9//16*c^1//8*(-1a)^-17//8*arctan(c^1//8*x^(1/2)*(-1a)^-1//8)+1//4*a^-1*x^-1//2*(a+c*x^4)^-1+9//16*c^1//8*(-1a)^-17//8*arctanh(c^1//8*x^(1/2)*(-1a)^-1//8)+-9//32*2^(1/2)*c^1//8*(-1a)^-17//8*arctan(1+2^(1/2)*c^1//8*x^(1/2)*(-1a)^-1//8)+-9//64*2^(1/2)*c^1//8*(-1a)^-17//8*log((-1a)^1//4+x*c^1//4+-1*2^(1/2)*c^1//8*x^(1/2)*(-1a)^1//8)+9//32*2^(1/2)*c^1//8*(-1a)^-17//8*arctan(1+-1*2^(1/2)*c^1//8*x^(1/2)*(-1a)^-1//8)+9//64*2^(1/2)*c^1//8*(-1a)^-17//8*log((-1a)^1//4+x*c^1//4+2^(1/2)*c^1//8*x^(1/2)*(-1a)^1//8))
@test integrate(x^15//2*(a+c*x^4)^-3, x) == :(-9//64*c^-2*x^(1/2)*(a+c*x^4)^-1+-9//256*c^-17//8*(-1a)^-7//8*arctan(c^1//8*x^(1/2)*(-1a)^-1//8)+-9//256*c^-17//8*(-1a)^-7//8*arctanh(c^1//8*x^(1/2)*(-1a)^-1//8)+-1//8*c^-1*x^9//2*(a+c*x^4)^-2+-9//512*2^(1/2)*c^-17//8*(-1a)^-7//8*arctan(1+2^(1/2)*c^1//8*x^(1/2)*(-1a)^-1//8)+-9//1024*2^(1/2)*c^-17//8*(-1a)^-7//8*log((-1a)^1//4+x*c^1//4+2^(1/2)*c^1//8*x^(1/2)*(-1a)^1//8)+9//512*2^(1/2)*c^-17//8*(-1a)^-7//8*arctan(1+-1*2^(1/2)*c^1//8*x^(1/2)*(-1a)^-1//8)+9//1024*2^(1/2)*c^-17//8*(-1a)^-7//8*log((-1a)^1//4+x*c^1//4+-1*2^(1/2)*c^1//8*x^(1/2)*(-1a)^1//8))
@test integrate(x^13//2*(a+c*x^4)^-3, x) == :(-7//256*c^-15//8*(-1a)^-9//8*arctan(c^1//8*x^(1/2)*(-1a)^-1//8)+-1//8*c^-1*x^7//2*(a+c*x^4)^-2+7//256*c^-15//8*(-1a)^-9//8*arctanh(c^1//8*x^(1/2)*(-1a)^-1//8)+-7//512*2^(1/2)*c^-15//8*(-1a)^-9//8*arctan(1+2^(1/2)*c^1//8*x^(1/2)*(-1a)^-1//8)+-7//1024*2^(1/2)*c^-15//8*(-1a)^-9//8*log((-1a)^1//4+x*c^1//4+-1*2^(1/2)*c^1//8*x^(1/2)*(-1a)^1//8)+7//64*a^-1*c^-1*x^7//2*(a+c*x^4)^-1+7//512*2^(1/2)*c^-15//8*(-1a)^-9//8*arctan(1+-1*2^(1/2)*c^1//8*x^(1/2)*(-1a)^-1//8)+7//1024*2^(1/2)*c^-15//8*(-1a)^-9//8*log((-1a)^1//4+x*c^1//4+2^(1/2)*c^1//8*x^(1/2)*(-1a)^1//8))
@test integrate(x^11//2*(a+c*x^4)^-3, x) == :(-1//8*c^-1*x^5//2*(a+c*x^4)^-2+15//256*c^-13//8*(-1a)^-11//8*arctan(c^1//8*x^(1/2)*(-1a)^-1//8)+15//256*c^-13//8*(-1a)^-11//8*arctanh(c^1//8*x^(1/2)*(-1a)^-1//8)+-15//512*2^(1/2)*c^-13//8*(-1a)^-11//8*arctan(1+2^(1/2)*c^1//8*x^(1/2)*(-1a)^-1//8)+-15//1024*2^(1/2)*c^-13//8*(-1a)^-11//8*log((-1a)^1//4+x*c^1//4+2^(1/2)*c^1//8*x^(1/2)*(-1a)^1//8)+5//64*a^-1*c^-1*x^5//2*(a+c*x^4)^-1+15//512*2^(1/2)*c^-13//8*(-1a)^-11//8*arctan(1+-1*2^(1/2)*c^1//8*x^(1/2)*(-1a)^-1//8)+15//1024*2^(1/2)*c^-13//8*(-1a)^-11//8*log((-1a)^1//4+x*c^1//4+-1*2^(1/2)*c^1//8*x^(1/2)*(-1a)^1//8))
@test integrate(x^9//2*(a+c*x^4)^-3, x) == :(-15//256*c^-11//8*(-1a)^-13//8*arctan(c^1//8*x^(1/2)*(-1a)^-1//8)+-1//8*c^-1*x^3//2*(a+c*x^4)^-2+15//256*c^-11//8*(-1a)^-13//8*arctanh(c^1//8*x^(1/2)*(-1a)^-1//8)+-15//512*2^(1/2)*c^-11//8*(-1a)^-13//8*arctan(1+-1*2^(1/2)*c^1//8*x^(1/2)*(-1a)^-1//8)+-15//1024*2^(1/2)*c^-11//8*(-1a)^-13//8*log((-1a)^1//4+x*c^1//4+2^(1/2)*c^1//8*x^(1/2)*(-1a)^1//8)+3//64*a^-1*c^-1*x^3//2*(a+c*x^4)^-1+15//512*2^(1/2)*c^-11//8*(-1a)^-13//8*arctan(1+2^(1/2)*c^1//8*x^(1/2)*(-1a)^-1//8)+15//1024*2^(1/2)*c^-11//8*(-1a)^-13//8*log((-1a)^1//4+x*c^1//4+-1*2^(1/2)*c^1//8*x^(1/2)*(-1a)^1//8))
@test integrate(x^7//2*(a+c*x^4)^-3, x) == :(-1//8*c^-1*x^(1/2)*(a+c*x^4)^-2+7//256*c^-9//8*(-1a)^-15//8*arctan(c^1//8*x^(1/2)*(-1a)^-1//8)+7//256*c^-9//8*(-1a)^-15//8*arctanh(c^1//8*x^(1/2)*(-1a)^-1//8)+-7//512*2^(1/2)*c^-9//8*(-1a)^-15//8*arctan(1+-1*2^(1/2)*c^1//8*x^(1/2)*(-1a)^-1//8)+-7//1024*2^(1/2)*c^-9//8*(-1a)^-15//8*log((-1a)^1//4+x*c^1//4+-1*2^(1/2)*c^1//8*x^(1/2)*(-1a)^1//8)+1//64*a^-1*c^-1*x^(1/2)*(a+c*x^4)^-1+7//512*2^(1/2)*c^-9//8*(-1a)^-15//8*arctan(1+2^(1/2)*c^1//8*x^(1/2)*(-1a)^-1//8)+7//1024*2^(1/2)*c^-9//8*(-1a)^-15//8*log((-1a)^1//4+x*c^1//4+2^(1/2)*c^1//8*x^(1/2)*(-1a)^1//8))
@test integrate(x^5//2*(a+c*x^4)^-3, x) == :(-9//256*c^-7//8*(-1a)^-17//8*arctanh(c^1//8*x^(1/2)*(-1a)^-1//8)+1//8*a^-1*x^7//2*(a+c*x^4)^-2+9//64*a^-2*x^7//2*(a+c*x^4)^-1+9//256*c^-7//8*(-1a)^-17//8*arctan(c^1//8*x^(1/2)*(-1a)^-1//8)+-9//512*2^(1/2)*c^-7//8*(-1a)^-17//8*arctan(1+-1*2^(1/2)*c^1//8*x^(1/2)*(-1a)^-1//8)+-9//1024*2^(1/2)*c^-7//8*(-1a)^-17//8*log((-1a)^1//4+x*c^1//4+2^(1/2)*c^1//8*x^(1/2)*(-1a)^1//8)+9//512*2^(1/2)*c^-7//8*(-1a)^-17//8*arctan(1+2^(1/2)*c^1//8*x^(1/2)*(-1a)^-1//8)+9//1024*2^(1/2)*c^-7//8*(-1a)^-17//8*log((-1a)^1//4+x*c^1//4+-1*2^(1/2)*c^1//8*x^(1/2)*(-1a)^1//8))
@test integrate(x^3//2*(a+c*x^4)^-3, x) == :(-33//256*c^-5//8*(-1a)^-19//8*arctan(c^1//8*x^(1/2)*(-1a)^-1//8)+-33//256*c^-5//8*(-1a)^-19//8*arctanh(c^1//8*x^(1/2)*(-1a)^-1//8)+1//8*a^-1*x^5//2*(a+c*x^4)^-2+11//64*a^-2*x^5//2*(a+c*x^4)^-1+-33//512*2^(1/2)*c^-5//8*(-1a)^-19//8*arctan(1+-1*2^(1/2)*c^1//8*x^(1/2)*(-1a)^-1//8)+-33//1024*2^(1/2)*c^-5//8*(-1a)^-19//8*log((-1a)^1//4+x*c^1//4+-1*2^(1/2)*c^1//8*x^(1/2)*(-1a)^1//8)+33//512*2^(1/2)*c^-5//8*(-1a)^-19//8*arctan(1+2^(1/2)*c^1//8*x^(1/2)*(-1a)^-1//8)+33//1024*2^(1/2)*c^-5//8*(-1a)^-19//8*log((-1a)^1//4+x*c^1//4+2^(1/2)*c^1//8*x^(1/2)*(-1a)^1//8))
@test integrate(x^(1/2)*(a+c*x^4)^-3, x) == :(-65//256*c^-3//8*(-1a)^-21//8*arctanh(c^1//8*x^(1/2)*(-1a)^-1//8)+1//8*a^-1*x^3//2*(a+c*x^4)^-2+13//64*a^-2*x^3//2*(a+c*x^4)^-1+65//256*c^-3//8*(-1a)^-21//8*arctan(c^1//8*x^(1/2)*(-1a)^-1//8)+-65//512*2^(1/2)*c^-3//8*(-1a)^-21//8*arctan(1+2^(1/2)*c^1//8*x^(1/2)*(-1a)^-1//8)+-65//1024*2^(1/2)*c^-3//8*(-1a)^-21//8*log((-1a)^1//4+x*c^1//4+-1*2^(1/2)*c^1//8*x^(1/2)*(-1a)^1//8)+65//512*2^(1/2)*c^-3//8*(-1a)^-21//8*arctan(1+-1*2^(1/2)*c^1//8*x^(1/2)*(-1a)^-1//8)+65//1024*2^(1/2)*c^-3//8*(-1a)^-21//8*log((-1a)^1//4+x*c^1//4+2^(1/2)*c^1//8*x^(1/2)*(-1a)^1//8))
@test integrate(x^-1//2*(a+c*x^4)^-3, x) == :(-105//256*c^-1//8*(-1a)^-23//8*arctan(c^1//8*x^(1/2)*(-1a)^-1//8)+-105//256*c^-1//8*(-1a)^-23//8*arctanh(c^1//8*x^(1/2)*(-1a)^-1//8)+1//8*a^-1*x^(1/2)*(a+c*x^4)^-2+15//64*a^-2*x^(1/2)*(a+c*x^4)^-1+-105//512*2^(1/2)*c^-1//8*(-1a)^-23//8*arctan(1+2^(1/2)*c^1//8*x^(1/2)*(-1a)^-1//8)+-105//1024*2^(1/2)*c^-1//8*(-1a)^-23//8*log((-1a)^1//4+x*c^1//4+2^(1/2)*c^1//8*x^(1/2)*(-1a)^1//8)+105//512*2^(1/2)*c^-1//8*(-1a)^-23//8*arctan(1+-1*2^(1/2)*c^1//8*x^(1/2)*(-1a)^-1//8)+105//1024*2^(1/2)*c^-1//8*(-1a)^-23//8*log((-1a)^1//4+x*c^1//4+-1*2^(1/2)*c^1//8*x^(1/2)*(-1a)^1//8))
@test integrate(x^11*(a+c*x^4)^(1/2), x) == :(1//14*c^-3*(a+c*x^4)^7//2+-1//5*a*c^-3*(a+c*x^4)^5//2+1//6*a^2*c^-3*(a+c*x^4)^3//2)
@test integrate(x^7*(a+c*x^4)^(1/2), x) == :(1//10*c^-2*(a+c*x^4)^5//2+-1//6*a*c^-2*(a+c*x^4)^3//2)
@test integrate(x^3*(a+c*x^4)^(1/2), x) == :(1//6*c^-1*(a+c*x^4)^3//2)
@test integrate(x^-1*(a+c*x^4)^(1/2), x) == :((1/2)*(a+c*x^4)^(1/2)+-1//2*a^(1/2)*arctanh(a^-1//2*(a+c*x^4)^(1/2)))
@test integrate(x^-5*(a+c*x^4)^(1/2), x) == :(-1//4*x^-4*(a+c*x^4)^(1/2)+-1//4*c*a^-1//2*arctanh(a^-1//2*(a+c*x^4)^(1/2)))
@test integrate(x^-9*(a+c*x^4)^(1/2), x) == :(-1//8*x^-8*(a+c*x^4)^(1/2)+1//16*a^-3//2*c^2*arctanh(a^-1//2*(a+c*x^4)^(1/2))+-1//16*c*a^-1*x^-4*(a+c*x^4)^(1/2))
@test integrate(x^5*(a+c*x^4)^(1/2), x) == :(1//8*x^6*(a+c*x^4)^(1/2)+-1//16*a^2*c^-3//2*arctanh(c^(1/2)*x^2*(a+c*x^4)^-1//2)+1//16*a*c^-1*x^2*(a+c*x^4)^(1/2))
@test integrate(x*(a+c*x^4)^(1/2), x) == :(1//4*x^2*(a+c*x^4)^(1/2)+1//4*a*c^-1//2*arctanh(c^(1/2)*x^2*(a+c*x^4)^-1//2))
@test integrate(x^-3*(a+c*x^4)^(1/2), x) == :((1/2)*c^(1/2)*arctanh(c^(1/2)*x^2*(a+c*x^4)^-1//2)+-1//2*x^-2*(a+c*x^4)^(1/2))
@test integrate(x^-7*(a+c*x^4)^(1/2), x) == :(-1//6*a^-1*x^-6*(a+c*x^4)^3//2)
@test integrate(x^-11*(a+c*x^4)^(1/2), x) == :(-1//10*a^-1*x^-10*(a+c*x^4)^3//2+1//15*c*a^-2*x^-6*(a+c*x^4)^3//2)
@test integrate(x^-15*(a+c*x^4)^(1/2), x) == :(-1//14*a^-1*x^-14*(a+c*x^4)^3//2+-4//105*a^-3*c^2*x^-6*(a+c*x^4)^3//2+2//35*c*a^-2*x^-10*(a+c*x^4)^3//2)
@test integrate(x^4*(a+c*x^4)^(1/2), x) == :(1//7*x^5*(a+c*x^4)^(1/2)+2//21*a*x*c^-1*(a+c*x^4)^(1/2)+-1//21*a^7//4*c^-5//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+c*x^4))^(1/2)*(a+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*Elliptic.F(2*arctan(x*a^-1//4*c^1//4),1/2))
@test integrate((a+c*x^4)^(1/2), x) == :(1//3*x*(a+c*x^4)^(1/2)+1//3*a^3//4*c^-1//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+c*x^4))^(1/2)*(a+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*Elliptic.F(2*arctan(x*a^-1//4*c^1//4),1/2))
@test integrate(x^-4*(a+c*x^4)^(1/2), x) == :(-1//3*x^-3*(a+c*x^4)^(1/2)+1//3*a^-1//4*c^3//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+c*x^4))^(1/2)*(a+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*Elliptic.F(2*arctan(x*a^-1//4*c^1//4),1/2))
@test integrate(x^-8*(a+c*x^4)^(1/2), x) == :(-1//7*x^-7*(a+c*x^4)^(1/2)+-2//21*c*a^-1*x^-3*(a+c*x^4)^(1/2)+-1//21*a^-5//4*c^7//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+c*x^4))^(1/2)*(a+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*Elliptic.F(2*arctan(x*a^-1//4*c^1//4),1/2))
@test integrate(x^2*(a+c*x^4)^(1/2), x) == :(1//5*x^3*(a+c*x^4)^(1/2)+2//5*a*x*c^-1//2*(a+c*x^4)^(1/2)*(a^(1/2)+c^(1/2)*x^2)^-1+-2//5*a^5//4*c^-3//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+c*x^4))^(1/2)*(a+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*c^1//4),1/2)+1//5*a^5//4*c^-3//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+c*x^4))^(1/2)*(a+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*Elliptic.F(2*arctan(x*a^-1//4*c^1//4),1/2))
@test integrate(x^-2*(a+c*x^4)^(1/2), x) == :(-1*x^-1*(a+c*x^4)^(1/2)+2*x*c^(1/2)*(a+c*x^4)^(1/2)*(a^(1/2)+c^(1/2)*x^2)^-1+a^1//4*c^1//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+c*x^4))^(1/2)*(a+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*Elliptic.F(2*arctan(x*a^-1//4*c^1//4),1/2)+-2*a^1//4*c^1//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+c*x^4))^(1/2)*(a+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*c^1//4),1/2))
@test integrate(x^-6*(a+c*x^4)^(1/2), x) == :(-1//5*x^-5*(a+c*x^4)^(1/2)+-2//5*c*a^-1*x^-1*(a+c*x^4)^(1/2)+2//5*x*a^-1*c^3//2*(a+c*x^4)^(1/2)*(a^(1/2)+c^(1/2)*x^2)^-1+-2//5*a^-3//4*c^5//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+c*x^4))^(1/2)*(a+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*c^1//4),1/2)+1//5*a^-3//4*c^5//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+c*x^4))^(1/2)*(a+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*Elliptic.F(2*arctan(x*a^-1//4*c^1//4),1/2))
@test integrate(x^11*(a+c*x^4)^3//2, x) == :(1//18*c^-3*(a+c*x^4)^9//2+-1//7*a*c^-3*(a+c*x^4)^7//2+1//10*a^2*c^-3*(a+c*x^4)^5//2)
@test integrate(x^7*(a+c*x^4)^3//2, x) == :(1//14*c^-2*(a+c*x^4)^7//2+-1//10*a*c^-2*(a+c*x^4)^5//2)
@test integrate(x^3*(a+c*x^4)^3//2, x) == :(1//10*c^-1*(a+c*x^4)^5//2)
@test integrate(x^-1*(a+c*x^4)^3//2, x) == :(1//6*(a+c*x^4)^3//2+(1/2)*a*(a+c*x^4)^(1/2)+-1//2*a^3//2*arctanh(a^-1//2*(a+c*x^4)^(1/2)))
@test integrate(x^-5*(a+c*x^4)^3//2, x) == :(-1//4*x^-4*(a+c*x^4)^3//2+3//4*c*(a+c*x^4)^(1/2)+-3//4*c*a^(1/2)*arctanh(a^-1//2*(a+c*x^4)^(1/2)))
@test integrate(x^-9*(a+c*x^4)^3//2, x) == :(-1//8*x^-8*(a+c*x^4)^3//2+-3//16*c*x^-4*(a+c*x^4)^(1/2)+-3//16*a^-1//2*c^2*arctanh(a^-1//2*(a+c*x^4)^(1/2)))
@test integrate(x^5*(a+c*x^4)^3//2, x) == :(1//12*x^6*(a+c*x^4)^3//2+-1//32*a^3*c^-3//2*arctanh(c^(1/2)*x^2*(a+c*x^4)^-1//2)+1//16*a*x^6*(a+c*x^4)^(1/2)+1//32*a^2*c^-1*x^2*(a+c*x^4)^(1/2))
@test integrate(x*(a+c*x^4)^3//2, x) == :(1//8*x^2*(a+c*x^4)^3//2+3//16*a*x^2*(a+c*x^4)^(1/2)+3//16*a^2*c^-1//2*arctanh(c^(1/2)*x^2*(a+c*x^4)^-1//2))
@test integrate(x^-3*(a+c*x^4)^3//2, x) == :(-1//2*x^-2*(a+c*x^4)^3//2+3//4*a*c^(1/2)*arctanh(c^(1/2)*x^2*(a+c*x^4)^-1//2)+3//4*c*x^2*(a+c*x^4)^(1/2))
@test integrate(x^-7*(a+c*x^4)^3//2, x) == :((1/2)*c^3//2*arctanh(c^(1/2)*x^2*(a+c*x^4)^-1//2)+-1//6*x^-6*(a+c*x^4)^3//2+-1//2*c*x^-2*(a+c*x^4)^(1/2))
@test integrate(x^-11*(a+c*x^4)^3//2, x) == :(-1//10*a^-1*x^-10*(a+c*x^4)^5//2)
@test integrate(x^-15*(a+c*x^4)^3//2, x) == :(-1//14*a^-1*x^-14*(a+c*x^4)^5//2+1//35*c*a^-2*x^-10*(a+c*x^4)^5//2)
@test integrate(x^-19*(a+c*x^4)^3//2, x) == :(-1//18*a^-1*x^-18*(a+c*x^4)^5//2+-4//315*a^-3*c^2*x^-10*(a+c*x^4)^5//2+2//63*c*a^-2*x^-14*(a+c*x^4)^5//2)
@test integrate(x^4*(a+c*x^4)^3//2, x) == :(1//11*x^5*(a+c*x^4)^3//2+6//77*a*x^5*(a+c*x^4)^(1/2)+4//77*x*a^2*c^-1*(a+c*x^4)^(1/2)+-2//77*a^11//4*c^-5//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+c*x^4))^(1/2)*(a+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*Elliptic.F(2*arctan(x*a^-1//4*c^1//4),1/2))
@test integrate((a+c*x^4)^3//2, x) == :(1//7*x*(a+c*x^4)^3//2+2//7*a*x*(a+c*x^4)^(1/2)+2//7*a^7//4*c^-1//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+c*x^4))^(1/2)*(a+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*Elliptic.F(2*arctan(x*a^-1//4*c^1//4),1/2))
@test integrate(x^-4*(a+c*x^4)^3//2, x) == :(-1//3*x^-3*(a+c*x^4)^3//2+2//3*c*x*(a+c*x^4)^(1/2)+2//3*a^3//4*c^3//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+c*x^4))^(1/2)*(a+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*Elliptic.F(2*arctan(x*a^-1//4*c^1//4),1/2))
@test integrate(x^-8*(a+c*x^4)^3//2, x) == :(-1//7*x^-7*(a+c*x^4)^3//2+-2//7*c*x^-3*(a+c*x^4)^(1/2)+2//7*a^-1//4*c^7//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+c*x^4))^(1/2)*(a+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*Elliptic.F(2*arctan(x*a^-1//4*c^1//4),1/2))
@test integrate(x^2*(a+c*x^4)^3//2, x) == :(1//9*x^3*(a+c*x^4)^3//2+2//15*a*x^3*(a+c*x^4)^(1/2)+4//15*x*a^2*c^-1//2*(a+c*x^4)^(1/2)*(a^(1/2)+c^(1/2)*x^2)^-1+-4//15*a^9//4*c^-3//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+c*x^4))^(1/2)*(a+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*c^1//4),1/2)+2//15*a^9//4*c^-3//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+c*x^4))^(1/2)*(a+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*Elliptic.F(2*arctan(x*a^-1//4*c^1//4),1/2))
@test integrate(x^-2*(a+c*x^4)^3//2, x) == :(-1*x^-1*(a+c*x^4)^3//2+6//5*c*x^3*(a+c*x^4)^(1/2)+12*a*x*c^(1/2)*(a+c*x^4)^(1/2)*(5*a^(1/2)+5*c^(1/2)*x^2)^-1+-12//5*a^5//4*c^1//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+c*x^4))^(1/2)*(a+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*c^1//4),1/2)+6//5*a^5//4*c^1//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+c*x^4))^(1/2)*(a+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*Elliptic.F(2*arctan(x*a^-1//4*c^1//4),1/2))
@test integrate(x^-6*(a+c*x^4)^3//2, x) == :(-1//5*x^-5*(a+c*x^4)^3//2+-6//5*c*x^-1*(a+c*x^4)^(1/2)+12*x*c^3//2*(a+c*x^4)^(1/2)*(5*a^(1/2)+5*c^(1/2)*x^2)^-1+-12//5*a^1//4*c^5//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+c*x^4))^(1/2)*(a+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*c^1//4),1/2)+6//5*a^1//4*c^5//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+c*x^4))^(1/2)*(a+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*Elliptic.F(2*arctan(x*a^-1//4*c^1//4),1/2))
@test integrate((1+x^4)^3//2, x) == :(1//7*x*(1+x^4)^3//2+2//7*x*(1+x^4)^(1/2)+1//7*((1+x^2)^-2*(1+x^4))^(1/2)*(1+x^4)^-1//2*(2+2*x^2)*Elliptic.F(2*arctan(x),1/2))
@test integrate((1+-1*x^4)^3//2, x) == :(4//7*Elliptic.F(arcsin(x),-1)+1//7*x*(1+-1*x^4)^3//2+2//7*x*(1+-1*x^4)^(1/2))
@test integrate(x^7*(5+3*x^4)^(1/2), x) == :(-5//54*(5+3*x^4)^3//2+1//90*(5+3*x^4)^5//2)
@test integrate(x^3*(5+x^4)^(1/2), x) == :(1//6*(5+x^4)^3//2)
@test integrate(x*(3+2*x^4)^(1/2), x) == :(1//4*x^2*(3+2*x^4)^(1/2)+3//8*2^(1/2)*arcsinh(1//3*6^(1/2)*x^2))
@test integrate(x*(-2+x^4)^(1/2), x) == :(-1//2*arctanh(x^2*(-2+x^4)^-1//2)+1//4*x^2*(-2+x^4)^(1/2))
@test integrate((1+x^4)^(1/2), x) == :(1//3*x*(1+x^4)^(1/2)+1//3*((1+x^2)^-2*(1+x^4))^(1/2)*(1+x^4)^-1//2*(1+x^2)*Elliptic.F(2*arctan(x),1/2))
@test integrate((1+-1*x^4)^(1/2), x) == :(2//3*Elliptic.F(arcsin(x),-1)+1//3*x*(1+-1*x^4)^(1/2))
@test integrate(x^11*(a+b*x^4)^-1//2, x) == :(1//10*b^-3*(a+b*x^4)^5//2+(1/2)*a^2*b^-3*(a+b*x^4)^(1/2)+-1//3*a*b^-3*(a+b*x^4)^3//2)
@test integrate(x^7*(a+b*x^4)^-1//2, x) == :(1//6*b^-2*(a+b*x^4)^3//2+-1//2*a*b^-2*(a+b*x^4)^(1/2))
@test integrate(x^3*(a+b*x^4)^-1//2, x) == :((1/2)*b^-1*(a+b*x^4)^(1/2))
@test integrate(x^-1*(a+b*x^4)^-1//2, x) == :(-1//2*a^-1//2*arctanh(a^-1//2*(a+b*x^4)^(1/2)))
@test integrate(x^-5*(a+b*x^4)^-1//2, x) == :(-1//4*a^-1*x^-4*(a+b*x^4)^(1/2)+1//4*b*a^-3//2*arctanh(a^-1//2*(a+b*x^4)^(1/2)))
@test integrate(x^5*(a+b*x^4)^-1//2, x) == :(-1//4*a*b^-3//2*arctanh(b^(1/2)*x^2*(a+b*x^4)^-1//2)+1//4*b^-1*x^2*(a+b*x^4)^(1/2))
@test integrate(x*(a+b*x^4)^-1//2, x) == :((1/2)*b^-1//2*arctanh(b^(1/2)*x^2*(a+b*x^4)^-1//2))
@test integrate(x^-3*(a+b*x^4)^-1//2, x) == :(-1//2*a^-1*x^-2*(a+b*x^4)^(1/2))
@test integrate(x^-7*(a+b*x^4)^-1//2, x) == :(-1//6*a^-1*x^-6*(a+b*x^4)^(1/2)+1//3*b*a^-2*x^-2*(a+b*x^4)^(1/2))
@test integrate(x^-11*(a+b*x^4)^-1//2, x) == :(-1//10*a^-1*x^-10*(a+b*x^4)^(1/2)+-4//15*a^-3*b^2*x^-2*(a+b*x^4)^(1/2)+2//15*b*a^-2*x^-6*(a+b*x^4)^(1/2))
@test integrate(x^8*(a+b*x^4)^-1//2, x) == :(1//7*b^-1*x^5*(a+b*x^4)^(1/2)+-5//21*a*x*b^-2*(a+b*x^4)^(1/2)+5//42*a^7//4*b^-9//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate(x^4*(a+b*x^4)^-1//2, x) == :(1//3*x*b^-1*(a+b*x^4)^(1/2)+-1//6*a^3//4*b^-5//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate((a+b*x^4)^-1//2, x) == :((1/2)*a^-1//4*b^-1//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate(x^-4*(a+b*x^4)^-1//2, x) == :(-1//3*a^-1*x^-3*(a+b*x^4)^(1/2)+-1//6*a^-5//4*b^3//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate(x^-8*(a+b*x^4)^-1//2, x) == :(-1//7*a^-1*x^-7*(a+b*x^4)^(1/2)+5//21*b*a^-2*x^-3*(a+b*x^4)^(1/2)+5//42*a^-9//4*b^7//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate(x^10*(a+b*x^4)^-1//2, x) == :(1//9*b^-1*x^7*(a+b*x^4)^(1/2)+-7//45*a*b^-2*x^3*(a+b*x^4)^(1/2)+7//15*x*a^2*b^-5//2*(a+b*x^4)^(1/2)*(a^(1/2)+b^(1/2)*x^2)^-1+-7//15*a^9//4*b^-11//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*b^1//4),1/2)+7//30*a^9//4*b^-11//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate(x^6*(a+b*x^4)^-1//2, x) == :(1//5*b^-1*x^3*(a+b*x^4)^(1/2)+-3//5*a*x*b^-3//2*(a+b*x^4)^(1/2)*(a^(1/2)+b^(1/2)*x^2)^-1+-3//10*a^5//4*b^-7//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2)+3//5*a^5//4*b^-7//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate(x^2*(a+b*x^4)^-1//2, x) == :(x*b^-1//2*(a+b*x^4)^(1/2)*(a^(1/2)+b^(1/2)*x^2)^-1+(1/2)*a^1//4*b^-3//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2)+-1*a^1//4*b^-3//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate(x^-2*(a+b*x^4)^-1//2, x) == :(-1*a^-1*x^-1*(a+b*x^4)^(1/2)+x*a^-1*b^(1/2)*(a+b*x^4)^(1/2)*(a^(1/2)+b^(1/2)*x^2)^-1+(1/2)*a^-3//4*b^1//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2)+-1*a^-3//4*b^1//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate(x^-6*(a+b*x^4)^-1//2, x) == :(-1//5*a^-1*x^-5*(a+b*x^4)^(1/2)+3//5*b*a^-2*x^-1*(a+b*x^4)^(1/2)+-3//5*x*a^-2*b^3//2*(a+b*x^4)^(1/2)*(a^(1/2)+b^(1/2)*x^2)^-1+-3//10*a^-7//4*b^5//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2)+3//5*a^-7//4*b^5//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate(x^11*(a+-1*b*x^4)^-1//2, x) == :(-1//10*b^-3*(a+-1*b*x^4)^5//2+-1//2*a^2*b^-3*(a+-1*b*x^4)^(1/2)+1//3*a*b^-3*(a+-1*b*x^4)^3//2)
@test integrate(x^7*(a+-1*b*x^4)^-1//2, x) == :(1//6*b^-2*(a+-1*b*x^4)^3//2+-1//2*a*b^-2*(a+-1*b*x^4)^(1/2))
@test integrate(x^3*(a+-1*b*x^4)^-1//2, x) == :(-1//2*b^-1*(a+-1*b*x^4)^(1/2))
@test integrate(x^-1*(a+-1*b*x^4)^-1//2, x) == :(-1//2*a^-1//2*arctanh(a^-1//2*(a+-1*b*x^4)^(1/2)))
@test integrate(x^-5*(a+-1*b*x^4)^-1//2, x) == :(-1//4*b*a^-3//2*arctanh(a^-1//2*(a+-1*b*x^4)^(1/2))+-1//4*a^-1*x^-4*(a+-1*b*x^4)^(1/2))
@test integrate(x^5*(a+-1*b*x^4)^-1//2, x) == :(-1//4*b^-1*x^2*(a+-1*b*x^4)^(1/2)+1//4*a*b^-3//2*arctan(b^(1/2)*x^2*(a+-1*b*x^4)^-1//2))
@test integrate(x*(a+-1*b*x^4)^-1//2, x) == :((1/2)*b^-1//2*arctan(b^(1/2)*x^2*(a+-1*b*x^4)^-1//2))
@test integrate(x^-3*(a+-1*b*x^4)^-1//2, x) == :(-1//2*a^-1*x^-2*(a+-1*b*x^4)^(1/2))
@test integrate(x^-7*(a+-1*b*x^4)^-1//2, x) == :(-1//6*a^-1*x^-6*(a+-1*b*x^4)^(1/2)+-1//3*b*a^-2*x^-2*(a+-1*b*x^4)^(1/2))
@test integrate(x^-11*(a+-1*b*x^4)^-1//2, x) == :(-1//10*a^-1*x^-10*(a+-1*b*x^4)^(1/2)+-4//15*a^-3*b^2*x^-2*(a+-1*b*x^4)^(1/2)+-2//15*b*a^-2*x^-6*(a+-1*b*x^4)^(1/2))
@test integrate(x^8*(a+-1*b*x^4)^-1//2, x) == :(-1//7*b^-1*x^5*(a+-1*b*x^4)^(1/2)+-5//21*a*x*b^-2*(a+-1*b*x^4)^(1/2)+5//21*a^9//4*b^-9//4*(1+-1*b*a^-1*x^4)^(1/2)*(a+-1*b*x^4)^-1//2*Elliptic.F(arcsin(x*a^-1//4*b^1//4),-1))
@test integrate(x^4*(a+-1*b*x^4)^-1//2, x) == :(-1//3*x*b^-1*(a+-1*b*x^4)^(1/2)+1//3*a^5//4*b^-5//4*(1+-1*b*a^-1*x^4)^(1/2)*(a+-1*b*x^4)^-1//2*Elliptic.F(arcsin(x*a^-1//4*b^1//4),-1))
@test integrate((a+-1*b*x^4)^-1//2, x) == :(a^1//4*b^-1//4*(1+-1*b*a^-1*x^4)^(1/2)*(a+-1*b*x^4)^-1//2*Elliptic.F(arcsin(x*a^-1//4*b^1//4),-1))
@test integrate(x^-4*(a+-1*b*x^4)^-1//2, x) == :(-1//3*a^-1*x^-3*(a+-1*b*x^4)^(1/2)+1//3*a^-3//4*b^3//4*(1+-1*b*a^-1*x^4)^(1/2)*(a+-1*b*x^4)^-1//2*Elliptic.F(arcsin(x*a^-1//4*b^1//4),-1))
@test integrate(x^-8*(a+-1*b*x^4)^-1//2, x) == :(-1//7*a^-1*x^-7*(a+-1*b*x^4)^(1/2)+-5//21*b*a^-2*x^-3*(a+-1*b*x^4)^(1/2)+5//21*a^-7//4*b^7//4*(1+-1*b*a^-1*x^4)^(1/2)*(a+-1*b*x^4)^-1//2*Elliptic.F(arcsin(x*a^-1//4*b^1//4),-1))
@test integrate(x^10*(a+-1*b*x^4)^-1//2, x) == :(-1//9*b^-1*x^7*(a+-1*b*x^4)^(1/2)+-7//45*a*b^-2*x^3*(a+-1*b*x^4)^(1/2)+-7//15*a^11//4*b^-11//4*(1+-1*b*a^-1*x^4)^(1/2)*(a+-1*b*x^4)^-1//2*Elliptic.F(arcsin(x*a^-1//4*b^1//4),-1)+7//15*a^11//4*b^-11//4*(1+-1*b*a^-1*x^4)^(1/2)*(a+-1*b*x^4)^-1//2*Elliptic.E(arcsin(x*a^-1//4*b^1//4),-1))
@test integrate(x^6*(a+-1*b*x^4)^-1//2, x) == :(-1//5*b^-1*x^3*(a+-1*b*x^4)^(1/2)+-3//5*a^7//4*b^-7//4*(1+-1*b*a^-1*x^4)^(1/2)*(a+-1*b*x^4)^-1//2*Elliptic.F(arcsin(x*a^-1//4*b^1//4),-1)+3//5*a^7//4*b^-7//4*(1+-1*b*a^-1*x^4)^(1/2)*(a+-1*b*x^4)^-1//2*Elliptic.E(arcsin(x*a^-1//4*b^1//4),-1))
@test integrate(x^2*(a+-1*b*x^4)^-1//2, x) == :(a^3//4*b^-3//4*(1+-1*b*a^-1*x^4)^(1/2)*(a+-1*b*x^4)^-1//2*Elliptic.E(arcsin(x*a^-1//4*b^1//4),-1)+-1*a^3//4*b^-3//4*(1+-1*b*a^-1*x^4)^(1/2)*(a+-1*b*x^4)^-1//2*Elliptic.F(arcsin(x*a^-1//4*b^1//4),-1))
@test integrate(x^-2*(a+-1*b*x^4)^-1//2, x) == :(-1*a^-1*x^-1*(a+-1*b*x^4)^(1/2)+a^-1//4*b^1//4*(1+-1*b*a^-1*x^4)^(1/2)*(a+-1*b*x^4)^-1//2*Elliptic.F(arcsin(x*a^-1//4*b^1//4),-1)+-1*a^-1//4*b^1//4*(1+-1*b*a^-1*x^4)^(1/2)*(a+-1*b*x^4)^-1//2*Elliptic.E(arcsin(x*a^-1//4*b^1//4),-1))
@test integrate(x^-6*(a+-1*b*x^4)^-1//2, x) == :(-1//5*a^-1*x^-5*(a+-1*b*x^4)^(1/2)+-3//5*b*a^-2*x^-1*(a+-1*b*x^4)^(1/2)+-3//5*a^-5//4*b^5//4*(1+-1*b*a^-1*x^4)^(1/2)*(a+-1*b*x^4)^-1//2*Elliptic.E(arcsin(x*a^-1//4*b^1//4),-1)+3//5*a^-5//4*b^5//4*(1+-1*b*a^-1*x^4)^(1/2)*(a+-1*b*x^4)^-1//2*Elliptic.F(arcsin(x*a^-1//4*b^1//4),-1))
@test integrate(x^11*(a+b*x^4)^-3//2, x) == :(1//6*b^-3*(a+b*x^4)^3//2+-1*a*b^-3*(a+b*x^4)^(1/2)+-1//2*a^2*b^-3*(a+b*x^4)^-1//2)
@test integrate(x^7*(a+b*x^4)^-3//2, x) == :((1/2)*b^-2*(a+b*x^4)^(1/2)+(1/2)*a*b^-2*(a+b*x^4)^-1//2)
@test integrate(x^3*(a+b*x^4)^-3//2, x) == :(-1//2*b^-1*(a+b*x^4)^-1//2)
@test integrate(x^-1*(a+b*x^4)^-3//2, x) == :((1/2)*a^-1*(a+b*x^4)^-1//2+-1//2*a^-3//2*arctanh(a^-1//2*(a+b*x^4)^(1/2)))
@test integrate(x^-5*(a+b*x^4)^-3//2, x) == :(-3//4*b*a^-2*(a+b*x^4)^-1//2+-1//4*a^-1*x^-4*(a+b*x^4)^-1//2+3//4*b*a^-5//2*arctanh(a^-1//2*(a+b*x^4)^(1/2)))
@test integrate(x^9*(a+b*x^4)^-3//2, x) == :(-3//4*a*b^-5//2*arctanh(b^(1/2)*x^2*(a+b*x^4)^-1//2)+-1//2*b^-1*x^6*(a+b*x^4)^-1//2+3//4*b^-2*x^2*(a+b*x^4)^(1/2))
@test integrate(x^5*(a+b*x^4)^-3//2, x) == :((1/2)*b^-3//2*arctanh(b^(1/2)*x^2*(a+b*x^4)^-1//2)+-1//2*b^-1*x^2*(a+b*x^4)^-1//2)
@test integrate(x*(a+b*x^4)^-3//2, x) == :((1/2)*a^-1*x^2*(a+b*x^4)^-1//2)
@test integrate(x^-3*(a+b*x^4)^-3//2, x) == :(-1//2*a^-1*x^-2*(a+b*x^4)^-1//2+-1*b*a^-2*x^2*(a+b*x^4)^-1//2)
@test integrate(x^-7*(a+b*x^4)^-3//2, x) == :(-1//6*a^-1*x^-6*(a+b*x^4)^-1//2+2//3*b*a^-2*x^-2*(a+b*x^4)^-1//2+4//3*a^-3*b^2*x^2*(a+b*x^4)^-1//2)
@test integrate(x^12*(a+b*x^4)^-3//2, x) == :(-1//2*b^-1*x^9*(a+b*x^4)^-1//2+9//14*b^-2*x^5*(a+b*x^4)^(1/2)+-15//14*a*x*b^-3*(a+b*x^4)^(1/2)+15//28*a^7//4*b^-13//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate(x^8*(a+b*x^4)^-3//2, x) == :(-1//2*b^-1*x^5*(a+b*x^4)^-1//2+5//6*x*b^-2*(a+b*x^4)^(1/2)+-5//12*a^3//4*b^-9//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate(x^4*(a+b*x^4)^-3//2, x) == :(-1//2*x*b^-1*(a+b*x^4)^-1//2+1//4*a^-1//4*b^-5//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate((a+b*x^4)^-3//2, x) == :((1/2)*x*a^-1*(a+b*x^4)^-1//2+1//4*a^-5//4*b^-1//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate(x^-4*(a+b*x^4)^-3//2, x) == :((1/2)*a^-1*x^-3*(a+b*x^4)^-1//2+-5//6*a^-2*x^-3*(a+b*x^4)^(1/2)+-5//12*a^-9//4*b^3//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate(x^-8*(a+b*x^4)^-3//2, x) == :((1/2)*a^-1*x^-7*(a+b*x^4)^-1//2+-9//14*a^-2*x^-7*(a+b*x^4)^(1/2)+15//14*b*a^-3*x^-3*(a+b*x^4)^(1/2)+15//28*a^-13//4*b^7//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate(x^14*(a+b*x^4)^-3//2, x) == :(-1//2*b^-1*x^11*(a+b*x^4)^-1//2+11//18*b^-2*x^7*(a+b*x^4)^(1/2)+-77//90*a*b^-3*x^3*(a+b*x^4)^(1/2)+77//30*x*a^2*b^-7//2*(a+b*x^4)^(1/2)*(a^(1/2)+b^(1/2)*x^2)^-1+-77//30*a^9//4*b^-15//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*b^1//4),1/2)+77//60*a^9//4*b^-15//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate(x^10*(a+b*x^4)^-3//2, x) == :(-1//2*b^-1*x^7*(a+b*x^4)^-1//2+7//10*b^-2*x^3*(a+b*x^4)^(1/2)+-21//10*a*x*b^-5//2*(a+b*x^4)^(1/2)*(a^(1/2)+b^(1/2)*x^2)^-1+-21//20*a^5//4*b^-11//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2)+21//10*a^5//4*b^-11//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate(x^6*(a+b*x^4)^-3//2, x) == :(-1//2*b^-1*x^3*(a+b*x^4)^-1//2+3//2*x*b^-3//2*(a+b*x^4)^(1/2)*(a^(1/2)+b^(1/2)*x^2)^-1+-3//2*a^1//4*b^-7//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*b^1//4),1/2)+3//4*a^1//4*b^-7//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate(x^2*(a+b*x^4)^-3//2, x) == :((1/2)*a^-1*x^3*(a+b*x^4)^-1//2+-1//2*x*a^-1*b^-1//2*(a+b*x^4)^(1/2)*(a^(1/2)+b^(1/2)*x^2)^-1+(1/2)*a^-3//4*b^-3//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*b^1//4),1/2)+-1//4*a^-3//4*b^-3//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate(x^-2*(a+b*x^4)^-3//2, x) == :((1/2)*a^-1*x^-1*(a+b*x^4)^-1//2+-3//2*a^-2*x^-1*(a+b*x^4)^(1/2)+3//2*x*a^-2*b^(1/2)*(a+b*x^4)^(1/2)*(a^(1/2)+b^(1/2)*x^2)^-1+-3//2*a^-7//4*b^1//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*b^1//4),1/2)+3//4*a^-7//4*b^1//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate(x^-6*(a+b*x^4)^-3//2, x) == :((1/2)*a^-1*x^-5*(a+b*x^4)^-1//2+-7//10*a^-2*x^-5*(a+b*x^4)^(1/2)+21//10*b*a^-3*x^-1*(a+b*x^4)^(1/2)+-21//10*x*a^-3*b^3//2*(a+b*x^4)^(1/2)*(a^(1/2)+b^(1/2)*x^2)^-1+-21//20*a^-11//4*b^5//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2)+21//10*a^-11//4*b^5//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate((a+b*x^4)^-5//2, x) == :(1//6*x*a^-1*(a+b*x^4)^-3//2+5//12*x*a^-2*(a+b*x^4)^-1//2+1//24*a^-9//4*b^-1//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(5*a^(1/2)+5*b^(1/2)*x^2)*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate(x^11*(1+-1*x^4)^-1//2, x) == :(-1//2*(1+-1*x^4)^(1/2)+-1//10*(1+-1*x^4)^5//2+1//3*(1+-1*x^4)^3//2)
@test integrate(x^7*(1+-1*x^4)^-1//2, x) == :(-1//2*(1+-1*x^4)^(1/2)+1//6*(1+-1*x^4)^3//2)
@test integrate(x^3*(1+-1*x^4)^-1//2, x) == :(-1//2*(1+-1*x^4)^(1/2))
@test integrate(x^-1*(1+-1*x^4)^-1//2, x) == :(-1//2*arctanh((1+-1*x^4)^(1/2)))
@test integrate(x^-5*(1+-1*x^4)^-1//2, x) == :(-1//4*arctanh((1+-1*x^4)^(1/2))+-1//4*x^-4*(1+-1*x^4)^(1/2))
@test integrate(x^5*(1+-1*x^4)^-1//2, x) == :(1//4*arcsin(x^2)+-1//4*x^2*(1+-1*x^4)^(1/2))
@test integrate(x*(1+-1*x^4)^-1//2, x) == :((1/2)*arcsin(x^2))
@test integrate(x^-3*(1+-1*x^4)^-1//2, x) == :(-1//2*x^-2*(1+-1*x^4)^(1/2))
@test integrate(x^-7*(1+-1*x^4)^-1//2, x) == :(-1//3*x^-2*(1+-1*x^4)^(1/2)+-1//6*x^-6*(1+-1*x^4)^(1/2))
@test integrate(x^-11*(1+-1*x^4)^-1//2, x) == :(-4//15*x^-2*(1+-1*x^4)^(1/2)+-2//15*x^-6*(1+-1*x^4)^(1/2)+-1//10*x^-10*(1+-1*x^4)^(1/2))
@test integrate(x^8*(1+-1*x^4)^-1//2, x) == :(5//21*Elliptic.F(arcsin(x),-1)+-5//21*x*(1+-1*x^4)^(1/2)+-1//7*x^5*(1+-1*x^4)^(1/2))
@test integrate(x^4*(1+-1*x^4)^-1//2, x) == :(1//3*Elliptic.F(arcsin(x),-1)+-1//3*x*(1+-1*x^4)^(1/2))
@test integrate((1+-1*x^4)^-1//2, x) == :(Elliptic.F(arcsin(x),-1))
@test integrate(x^-4*(1+-1*x^4)^-1//2, x) == :(1//3*Elliptic.F(arcsin(x),-1)+-1//3*x^-3*(1+-1*x^4)^(1/2))
@test integrate(x^-8*(1+-1*x^4)^-1//2, x) == :(5//21*Elliptic.F(arcsin(x),-1)+-5//21*x^-3*(1+-1*x^4)^(1/2)+-1//7*x^-7*(1+-1*x^4)^(1/2))
@test integrate(x^10*(1+-1*x^4)^-1//2, x) == :(-7//15*Elliptic.F(arcsin(x),-1)+7//15*Elliptic.E(arcsin(x),-1)+-7//45*x^3*(1+-1*x^4)^(1/2)+-1//9*x^7*(1+-1*x^4)^(1/2))
@test integrate(x^6*(1+-1*x^4)^-1//2, x) == :(-3//5*Elliptic.F(arcsin(x),-1)+3//5*Elliptic.E(arcsin(x),-1)+-1//5*x^3*(1+-1*x^4)^(1/2))
@test integrate(x^2*(1+-1*x^4)^-1//2, x) == :(-1*Elliptic.F(arcsin(x),-1)+Elliptic.E(arcsin(x),-1))
@test integrate(x^-2*(1+-1*x^4)^-1//2, x) == :(-1*Elliptic.E(arcsin(x),-1)+-1*x^-1*(1+-1*x^4)^(1/2)+Elliptic.F(arcsin(x),-1))
@test integrate(x^-6*(1+-1*x^4)^-1//2, x) == :(-3//5*Elliptic.E(arcsin(x),-1)+3//5*Elliptic.F(arcsin(x),-1)+-3//5*x^-1*(1+-1*x^4)^(1/2)+-1//5*x^-5*(1+-1*x^4)^(1/2))
@test integrate(x^11*(1+-1*x^4)^-3//2, x) == :((1+-1*x^4)^(1/2)+(1/2)*(1+-1*x^4)^-1//2+-1//6*(1+-1*x^4)^3//2)
@test integrate(x^7*(1+-1*x^4)^-3//2, x) == :((1/2)*(1+-1*x^4)^(1/2)+(1/2)*(1+-1*x^4)^-1//2)
@test integrate(x^3*(1+-1*x^4)^-3//2, x) == :((1/2)*(1+-1*x^4)^-1//2)
@test integrate(x^-1*(1+-1*x^4)^-3//2, x) == :((1/2)*(1+-1*x^4)^-1//2+-1//2*arctanh((1+-1*x^4)^(1/2)))
@test integrate(x^-5*(1+-1*x^4)^-3//2, x) == :(-3//4*arctanh((1+-1*x^4)^(1/2))+3//4*(1+-1*x^4)^-1//2+-1//4*x^-4*(1+-1*x^4)^-1//2)
@test integrate(x^9*(1+-1*x^4)^-3//2, x) == :(-3//4*arcsin(x^2)+(1/2)*x^6*(1+-1*x^4)^-1//2+3//4*x^2*(1+-1*x^4)^(1/2))
@test integrate(x^5*(1+-1*x^4)^-3//2, x) == :(-1//2*arcsin(x^2)+(1/2)*x^2*(1+-1*x^4)^-1//2)
@test integrate(x*(1+-1*x^4)^-3//2, x) == :((1/2)*x^2*(1+-1*x^4)^-1//2)
@test integrate(x^-3*(1+-1*x^4)^-3//2, x) == :(x^2*(1+-1*x^4)^-1//2+-1//2*x^-2*(1+-1*x^4)^-1//2)
@test integrate(x^-7*(1+-1*x^4)^-3//2, x) == :(-2//3*x^-2*(1+-1*x^4)^-1//2+-1//6*x^-6*(1+-1*x^4)^-1//2+4//3*x^2*(1+-1*x^4)^-1//2)
@test integrate(x^12*(1+-1*x^4)^-3//2, x) == :(-15//14*Elliptic.F(arcsin(x),-1)+(1/2)*x^9*(1+-1*x^4)^-1//2+9//14*x^5*(1+-1*x^4)^(1/2)+15//14*x*(1+-1*x^4)^(1/2))
@test integrate(x^8*(1+-1*x^4)^-3//2, x) == :(-5//6*Elliptic.F(arcsin(x),-1)+(1/2)*x^5*(1+-1*x^4)^-1//2+5//6*x*(1+-1*x^4)^(1/2))
@test integrate(x^4*(1+-1*x^4)^-3//2, x) == :(-1//2*Elliptic.F(arcsin(x),-1)+(1/2)*x*(1+-1*x^4)^-1//2)
@test integrate((1+-1*x^4)^-3//2, x) == :((1/2)*Elliptic.F(arcsin(x),-1)+(1/2)*x*(1+-1*x^4)^-1//2)
@test integrate(x^-4*(1+-1*x^4)^-3//2, x) == :(5//6*Elliptic.F(arcsin(x),-1)+(1/2)*x^-3*(1+-1*x^4)^-1//2+-5//6*x^-3*(1+-1*x^4)^(1/2))
@test integrate(x^-8*(1+-1*x^4)^-3//2, x) == :(15//14*Elliptic.F(arcsin(x),-1)+(1/2)*x^-7*(1+-1*x^4)^-1//2+-15//14*x^-3*(1+-1*x^4)^(1/2)+-9//14*x^-7*(1+-1*x^4)^(1/2))
@test integrate(x^14*(1+-1*x^4)^-3//2, x) == :(-77//30*Elliptic.E(arcsin(x),-1)+77//30*Elliptic.F(arcsin(x),-1)+(1/2)*x^11*(1+-1*x^4)^-1//2+11//18*x^7*(1+-1*x^4)^(1/2)+77//90*x^3*(1+-1*x^4)^(1/2))
@test integrate(x^10*(1+-1*x^4)^-3//2, x) == :(-21//10*Elliptic.E(arcsin(x),-1)+21//10*Elliptic.F(arcsin(x),-1)+(1/2)*x^7*(1+-1*x^4)^-1//2+7//10*x^3*(1+-1*x^4)^(1/2))
@test integrate(x^6*(1+-1*x^4)^-3//2, x) == :(-3//2*Elliptic.E(arcsin(x),-1)+3//2*Elliptic.F(arcsin(x),-1)+(1/2)*x^3*(1+-1*x^4)^-1//2)
@test integrate(x^2*(1+-1*x^4)^-3//2, x) == :((1/2)*Elliptic.F(arcsin(x),-1)+-1//2*Elliptic.E(arcsin(x),-1)+(1/2)*x^3*(1+-1*x^4)^-1//2)
@test integrate(x^-2*(1+-1*x^4)^-3//2, x) == :(-3//2*Elliptic.E(arcsin(x),-1)+3//2*Elliptic.F(arcsin(x),-1)+(1/2)*x^-1*(1+-1*x^4)^-1//2+-3//2*x^-1*(1+-1*x^4)^(1/2))
@test integrate(x^-6*(1+-1*x^4)^-3//2, x) == :(-21//10*Elliptic.E(arcsin(x),-1)+21//10*Elliptic.F(arcsin(x),-1)+(1/2)*x^-5*(1+-1*x^4)^-1//2+-21//10*x^-1*(1+-1*x^4)^(1/2)+-7//10*x^-5*(1+-1*x^4)^(1/2))
@test integrate((1+-1*x^4)^-5//2, x) == :(5//12*Elliptic.F(arcsin(x),-1)+1//6*x*(1+-1*x^4)^-3//2+5//12*x*(1+-1*x^4)^-1//2)
@test integrate(x^11*(1+x^4)^-1//2, x) == :((1/2)*(1+x^4)^(1/2)+-1//3*(1+x^4)^3//2+1//10*(1+x^4)^5//2)
@test integrate(x^7*(1+x^4)^-1//2, x) == :(-1//2*(1+x^4)^(1/2)+1//6*(1+x^4)^3//2)
@test integrate(x^3*(1+x^4)^-1//2, x) == :((1/2)*(1+x^4)^(1/2))
@test integrate(x^-1*(1+x^4)^-1//2, x) == :(-1//2*arctanh((1+x^4)^(1/2)))
@test integrate(x^-5*(1+x^4)^-1//2, x) == :(1//4*arctanh((1+x^4)^(1/2))+-1//4*x^-4*(1+x^4)^(1/2))
@test integrate(x^5*(1+x^4)^-1//2, x) == :(-1//4*arcsinh(x^2)+1//4*x^2*(1+x^4)^(1/2))
@test integrate(x*(1+x^4)^-1//2, x) == :((1/2)*arcsinh(x^2))
@test integrate(x^-3*(1+x^4)^-1//2, x) == :(-1//2*x^-2*(1+x^4)^(1/2))
@test integrate(x^-7*(1+x^4)^-1//2, x) == :(-1//6*x^-6*(1+x^4)^(1/2)+1//3*x^-2*(1+x^4)^(1/2))
@test integrate(x^-11*(1+x^4)^-1//2, x) == :(-4//15*x^-2*(1+x^4)^(1/2)+-1//10*x^-10*(1+x^4)^(1/2)+2//15*x^-6*(1+x^4)^(1/2))
@test integrate(x^8*(1+x^4)^-1//2, x) == :(-5//21*x*(1+x^4)^(1/2)+1//7*x^5*(1+x^4)^(1/2)+1//42*((1+x^2)^-2*(1+x^4))^(1/2)*(1+x^4)^-1//2*(5+5*x^2)*Elliptic.F(2*arctan(x),1/2))
@test integrate(x^4*(1+x^4)^-1//2, x) == :(1//3*x*(1+x^4)^(1/2)+-1//6*((1+x^2)^-2*(1+x^4))^(1/2)*(1+x^4)^-1//2*(1+x^2)*Elliptic.F(2*arctan(x),1/2))
@test integrate((1+x^4)^-1//2, x) == :((1/2)*((1+x^2)^-2*(1+x^4))^(1/2)*(1+x^4)^-1//2*(1+x^2)*Elliptic.F(2*arctan(x),1/2))
@test integrate(x^-4*(1+x^4)^-1//2, x) == :(-1//3*x^-3*(1+x^4)^(1/2)+-1//6*((1+x^2)^-2*(1+x^4))^(1/2)*(1+x^4)^-1//2*(1+x^2)*Elliptic.F(2*arctan(x),1/2))
@test integrate(x^-8*(1+x^4)^-1//2, x) == :(-1//7*x^-7*(1+x^4)^(1/2)+5//21*x^-3*(1+x^4)^(1/2)+1//42*((1+x^2)^-2*(1+x^4))^(1/2)*(1+x^4)^-1//2*(5+5*x^2)*Elliptic.F(2*arctan(x),1/2))
@test integrate(x^10*(1+x^4)^-1//2, x) == :(-7//45*x^3*(1+x^4)^(1/2)+1//9*x^7*(1+x^4)^(1/2)+7*x*(1+x^4)^(1/2)*(15+15*x^2)^-1+-1//15*((1+x^2)^-2*(1+x^4))^(1/2)*(1+x^4)^-1//2*(7+7*x^2)*Elliptic.E(2*arctan(x),1/2)+1//30*((1+x^2)^-2*(1+x^4))^(1/2)*(1+x^4)^-1//2*(7+7*x^2)*Elliptic.F(2*arctan(x),1/2))
@test integrate(x^6*(1+x^4)^-1//2, x) == :(1//5*x^3*(1+x^4)^(1/2)+-3*x*(1+x^4)^(1/2)*(5+5*x^2)^-1+-1//10*((1+x^2)^-2*(1+x^4))^(1/2)*(1+x^4)^-1//2*(3+3*x^2)*Elliptic.F(2*arctan(x),1/2)+1//5*((1+x^2)^-2*(1+x^4))^(1/2)*(1+x^4)^-1//2*(3+3*x^2)*Elliptic.E(2*arctan(x),1/2))
@test integrate(x^2*(1+x^4)^-1//2, x) == :(x*(1+x^2)^-1*(1+x^4)^(1/2)+(1/2)*((1+x^2)^-2*(1+x^4))^(1/2)*(1+x^4)^-1//2*(1+x^2)*Elliptic.F(2*arctan(x),1/2)+-1*((1+x^2)^-2*(1+x^4))^(1/2)*(1+x^4)^-1//2*(1+x^2)*Elliptic.E(2*arctan(x),1/2))
@test integrate(x^-2*(1+x^4)^-1//2, x) == :(-1*x^-1*(1+x^4)^(1/2)+x*(1+x^2)^-1*(1+x^4)^(1/2)+(1/2)*((1+x^2)^-2*(1+x^4))^(1/2)*(1+x^4)^-1//2*(1+x^2)*Elliptic.F(2*arctan(x),1/2)+-1*((1+x^2)^-2*(1+x^4))^(1/2)*(1+x^4)^-1//2*(1+x^2)*Elliptic.E(2*arctan(x),1/2))
@test integrate(x^-6*(1+x^4)^-1//2, x) == :(-1//5*x^-5*(1+x^4)^(1/2)+3//5*x^-1*(1+x^4)^(1/2)+-3*x*(1+x^4)^(1/2)*(5+5*x^2)^-1+-1//10*((1+x^2)^-2*(1+x^4))^(1/2)*(1+x^4)^-1//2*(3+3*x^2)*Elliptic.F(2*arctan(x),1/2)+1//5*((1+x^2)^-2*(1+x^4))^(1/2)*(1+x^4)^-1//2*(3+3*x^2)*Elliptic.E(2*arctan(x),1/2))
@test integrate(x^11*(1+x^4)^-3//2, x) == :(-1*(1+x^4)^(1/2)+-1//2*(1+x^4)^-1//2+1//6*(1+x^4)^3//2)
@test integrate(x^7*(1+x^4)^-3//2, x) == :((1/2)*(1+x^4)^(1/2)+(1/2)*(1+x^4)^-1//2)
@test integrate(x^3*(1+x^4)^-3//2, x) == :(-1//2*(1+x^4)^-1//2)
@test integrate(x^-1*(1+x^4)^-3//2, x) == :((1/2)*(1+x^4)^-1//2+-1//2*arctanh((1+x^4)^(1/2)))
@test integrate(x^-5*(1+x^4)^-3//2, x) == :(-3//4*(1+x^4)^-1//2+3//4*arctanh((1+x^4)^(1/2))+-1//4*x^-4*(1+x^4)^-1//2)
@test integrate(x^9*(1+x^4)^-3//2, x) == :(-3//4*arcsinh(x^2)+-1//2*x^6*(1+x^4)^-1//2+3//4*x^2*(1+x^4)^(1/2))
@test integrate(x^5*(1+x^4)^-3//2, x) == :((1/2)*arcsinh(x^2)+-1//2*x^2*(1+x^4)^-1//2)
@test integrate(x*(1+x^4)^-3//2, x) == :((1/2)*x^2*(1+x^4)^-1//2)
@test integrate(x^-3*(1+x^4)^-3//2, x) == :(-1*x^2*(1+x^4)^-1//2+-1//2*x^-2*(1+x^4)^-1//2)
@test integrate(x^-7*(1+x^4)^-3//2, x) == :(-1//6*x^-6*(1+x^4)^-1//2+2//3*x^-2*(1+x^4)^-1//2+4//3*x^2*(1+x^4)^-1//2)
@test integrate(x^12*(1+x^4)^-3//2, x) == :(-15//14*x*(1+x^4)^(1/2)+-1//2*x^9*(1+x^4)^-1//2+9//14*x^5*(1+x^4)^(1/2)+1//28*((1+x^2)^-2*(1+x^4))^(1/2)*(1+x^4)^-1//2*(15+15*x^2)*Elliptic.F(2*arctan(x),1/2))
@test integrate(x^8*(1+x^4)^-3//2, x) == :(-1//2*x^5*(1+x^4)^-1//2+5//6*x*(1+x^4)^(1/2)+-1//12*((1+x^2)^-2*(1+x^4))^(1/2)*(1+x^4)^-1//2*(5+5*x^2)*Elliptic.F(2*arctan(x),1/2))
@test integrate(x^4*(1+x^4)^-3//2, x) == :(-1//2*x*(1+x^4)^-1//2+1//4*((1+x^2)^-2*(1+x^4))^(1/2)*(1+x^4)^-1//2*(1+x^2)*Elliptic.F(2*arctan(x),1/2))
@test integrate((1+x^4)^-3//2, x) == :((1/2)*x*(1+x^4)^-1//2+1//4*((1+x^2)^-2*(1+x^4))^(1/2)*(1+x^4)^-1//2*(1+x^2)*Elliptic.F(2*arctan(x),1/2))
@test integrate(x^-4*(1+x^4)^-3//2, x) == :((1/2)*x^-3*(1+x^4)^-1//2+-5//6*x^-3*(1+x^4)^(1/2)+-1//12*((1+x^2)^-2*(1+x^4))^(1/2)*(1+x^4)^-1//2*(5+5*x^2)*Elliptic.F(2*arctan(x),1/2))
@test integrate(x^-8*(1+x^4)^-3//2, x) == :((1/2)*x^-7*(1+x^4)^-1//2+-9//14*x^-7*(1+x^4)^(1/2)+15//14*x^-3*(1+x^4)^(1/2)+1//28*((1+x^2)^-2*(1+x^4))^(1/2)*(1+x^4)^-1//2*(15+15*x^2)*Elliptic.F(2*arctan(x),1/2))
@test integrate(x^14*(1+x^4)^-3//2, x) == :(-77//90*x^3*(1+x^4)^(1/2)+-1//2*x^11*(1+x^4)^-1//2+11//18*x^7*(1+x^4)^(1/2)+77*x*(1+x^4)^(1/2)*(30+30*x^2)^-1+-1//30*((1+x^2)^-2*(1+x^4))^(1/2)*(1+x^4)^-1//2*(77+77*x^2)*Elliptic.E(2*arctan(x),1/2)+1//60*((1+x^2)^-2*(1+x^4))^(1/2)*(1+x^4)^-1//2*(77+77*x^2)*Elliptic.F(2*arctan(x),1/2))
@test integrate(x^10*(1+x^4)^-3//2, x) == :(-1//2*x^7*(1+x^4)^-1//2+7//10*x^3*(1+x^4)^(1/2)+-21*x*(1+x^4)^(1/2)*(10+10*x^2)^-1+-1//20*((1+x^2)^-2*(1+x^4))^(1/2)*(1+x^4)^-1//2*(21+21*x^2)*Elliptic.F(2*arctan(x),1/2)+1//10*((1+x^2)^-2*(1+x^4))^(1/2)*(1+x^4)^-1//2*(21+21*x^2)*Elliptic.E(2*arctan(x),1/2))
@test integrate(x^6*(1+x^4)^-3//2, x) == :(-1//2*x^3*(1+x^4)^-1//2+3*x*(1+x^4)^(1/2)*(2+2*x^2)^-1+-1//2*((1+x^2)^-2*(1+x^4))^(1/2)*(1+x^4)^-1//2*(3+3*x^2)*Elliptic.E(2*arctan(x),1/2)+1//4*((1+x^2)^-2*(1+x^4))^(1/2)*(1+x^4)^-1//2*(3+3*x^2)*Elliptic.F(2*arctan(x),1/2))
@test integrate(x^2*(1+x^4)^-3//2, x) == :((1/2)*x^3*(1+x^4)^-1//2+-1*x*(1+x^4)^(1/2)*(2+2*x^2)^-1+(1/2)*((1+x^2)^-2*(1+x^4))^(1/2)*(1+x^4)^-1//2*(1+x^2)*Elliptic.E(2*arctan(x),1/2)+-1//4*((1+x^2)^-2*(1+x^4))^(1/2)*(1+x^4)^-1//2*(1+x^2)*Elliptic.F(2*arctan(x),1/2))
@test integrate(x^-2*(1+x^4)^-3//2, x) == :((1/2)*x^-1*(1+x^4)^-1//2+-3//2*x^-1*(1+x^4)^(1/2)+3*x*(1+x^4)^(1/2)*(2+2*x^2)^-1+-1//2*((1+x^2)^-2*(1+x^4))^(1/2)*(1+x^4)^-1//2*(3+3*x^2)*Elliptic.E(2*arctan(x),1/2)+1//4*((1+x^2)^-2*(1+x^4))^(1/2)*(1+x^4)^-1//2*(3+3*x^2)*Elliptic.F(2*arctan(x),1/2))
@test integrate(x^-6*(1+x^4)^-3//2, x) == :((1/2)*x^-5*(1+x^4)^-1//2+-7//10*x^-5*(1+x^4)^(1/2)+21//10*x^-1*(1+x^4)^(1/2)+-21*x*(1+x^4)^(1/2)*(10+10*x^2)^-1+-1//20*((1+x^2)^-2*(1+x^4))^(1/2)*(1+x^4)^-1//2*(21+21*x^2)*Elliptic.F(2*arctan(x),1/2)+1//10*((1+x^2)^-2*(1+x^4))^(1/2)*(1+x^4)^-1//2*(21+21*x^2)*Elliptic.E(2*arctan(x),1/2))
@test integrate((1+x^4)^-5//2, x) == :(1//6*x*(1+x^4)^-3//2+5//12*x*(1+x^4)^-1//2+1//24*((1+x^2)^-2*(1+x^4))^(1/2)*(1+x^4)^-1//2*(5+5*x^2)*Elliptic.F(2*arctan(x),1/2))
@test integrate(x^7*(16+-1*x^4)^-1//2, x) == :(-8*(16+-1*x^4)^(1/2)+1//6*(16+-1*x^4)^3//2)
@test integrate(x^5*(16+-1*x^4)^-1//2, x) == :(4*arcsin(1//4*x^2)+-1//4*x^2*(16+-1*x^4)^(1/2))
@test integrate(x^3*(16+-1*x^4)^-1//2, x) == :(-1//2*(16+-1*x^4)^(1/2))
@test integrate(x*(16+-1*x^4)^-1//2, x) == :((1/2)*arcsin(1//4*x^2))
@test integrate(x^-1*(16+-1*x^4)^-1//2, x) == :(-1//8*arctanh(1//4*(16+-1*x^4)^(1/2)))
@test integrate(x^-3*(16+-1*x^4)^-1//2, x) == :(-1//32*x^-2*(16+-1*x^4)^(1/2))
@test integrate(x^-5*(16+-1*x^4)^-1//2, x) == :(-1//256*arctanh(1//4*(16+-1*x^4)^(1/2))+-1//64*x^-4*(16+-1*x^4)^(1/2))
@test integrate(x^-7*(16+-1*x^4)^-1//2, x) == :(-1//96*x^-6*(16+-1*x^4)^(1/2)+-1//768*x^-2*(16+-1*x^4)^(1/2))
@test integrate(x^6*(16+-1*x^4)^-1//2, x) == :(-96//5*Elliptic.F(arcsin((1/2)*x),-1)+96//5*Elliptic.E(arcsin((1/2)*x),-1)+-1//5*x^3*(16+-1*x^4)^(1/2))
@test integrate(x^4*(16+-1*x^4)^-1//2, x) == :(8//3*Elliptic.F(arcsin((1/2)*x),-1)+-1//3*x*(16+-1*x^4)^(1/2))
@test integrate(x^2*(16+-1*x^4)^-1//2, x) == :(-2*Elliptic.F(arcsin((1/2)*x),-1)+2*Elliptic.E(arcsin((1/2)*x),-1))
@test integrate((16+-1*x^4)^-1//2, x) == :((1/2)*Elliptic.F(arcsin((1/2)*x),-1))
@test integrate(x^-2*(16+-1*x^4)^-1//2, x) == :(-1//8*Elliptic.E(arcsin((1/2)*x),-1)+1//8*Elliptic.F(arcsin((1/2)*x),-1)+-1//16*x^-1*(16+-1*x^4)^(1/2))
@test integrate(x^-4*(16+-1*x^4)^-1//2, x) == :(1//96*Elliptic.F(arcsin((1/2)*x),-1)+-1//48*x^-3*(16+-1*x^4)^(1/2))
@test integrate(x*(-4+x^4)^-1//2, x) == :((1/2)*arctanh(x^2*(-4+x^4)^-1//2))
@test integrate(x*(4+x^4)^-1//2, x) == :((1/2)*arcsinh((1/2)*x^2))
@test integrate(x^-1*(-1+x^4)^-1//2, x) == :((1/2)*arctan((-1+x^4)^(1/2)))
@test integrate(x^4*(-1+x^4)^-1//2, x) == :(1//3*x*(-1+x^4)^(1/2)+1//6*2^(1/2)*(1+x^2)^(1/2)*(-1+x^2)^(1/2)*(-1+x^4)^-1//2*Elliptic.F(arcsin(x*2^(1/2)*(-1+x^2)^-1//2),1/2))
@test integrate((-1+x^4)^-1//2, x) == :((1/2)*2^(1/2)*(1+x^2)^(1/2)*(-1+x^2)^(1/2)*(-1+x^4)^-1//2*Elliptic.F(arcsin(x*2^(1/2)*(-1+x^2)^-1//2),1/2))
@test integrate(x^-4*(-1+x^4)^-1//2, x) == :(1//3*x^-3*(-1+x^4)^(1/2)+1//6*2^(1/2)*(1+x^2)^(1/2)*(-1+x^2)^(1/2)*(-1+x^4)^-1//2*Elliptic.F(arcsin(x*2^(1/2)*(-1+x^2)^-1//2),1/2))
@test integrate(x^6*(-1+x^4)^-1//2, x) == :(1//5*x^3*(-1+x^4)^(1/2)+3//5*x*(-1+x^4)^-1//2*(1+x^2)+-3//5*2^(1/2)*(1+x^2)^(1/2)*(-1+x^2)^(1/2)*(-1+x^4)^-1//2*Elliptic.E(arcsin(x*2^(1/2)*(-1+x^2)^-1//2),1/2)+3//10*2^(1/2)*(1+x^2)^(1/2)*(-1+x^2)^(1/2)*(-1+x^4)^-1//2*Elliptic.F(arcsin(x*2^(1/2)*(-1+x^2)^-1//2),1/2))
@test integrate(x^2*(-1+x^4)^-1//2, x) == :(x*(-1+x^4)^-1//2*(1+x^2)+(1/2)*2^(1/2)*(1+x^2)^(1/2)*(-1+x^2)^(1/2)*(-1+x^4)^-1//2*Elliptic.F(arcsin(x*2^(1/2)*(-1+x^2)^-1//2),1/2)+-1*2^(1/2)*(1+x^2)^(1/2)*(-1+x^2)^(1/2)*(-1+x^4)^-1//2*Elliptic.E(arcsin(x*2^(1/2)*(-1+x^2)^-1//2),1/2))
@test integrate(x^-2*(-1+x^4)^-1//2, x) == :(x^-1*(-1+x^4)^(1/2)+-1*x*(-1+x^4)^-1//2*(1+x^2)+2^(1/2)*(1+x^2)^(1/2)*(-1+x^2)^(1/2)*(-1+x^4)^-1//2*Elliptic.E(arcsin(x*2^(1/2)*(-1+x^2)^-1//2),1/2)+-1//2*2^(1/2)*(1+x^2)^(1/2)*(-1+x^2)^(1/2)*(-1+x^4)^-1//2*Elliptic.F(arcsin(x*2^(1/2)*(-1+x^2)^-1//2),1/2))
@test integrate(x^2*(3+-2*x^4)^-1//2, x) == :((1/2)*6^1//4*Elliptic.E(arcsin(1//3*x*2^1//4*3^3//4),-1)+-1//2*6^1//4*Elliptic.F(arcsin(1//3*x*2^1//4*3^3//4),-1))
@test integrate(x^2*(3+-1*b*x^4)^-1//2, x) == :(3^1//4*b^-3//4*Elliptic.E(arcsin(1//3*x*3^3//4*b^1//4),-1)+-1*3^1//4*b^-3//4*Elliptic.F(arcsin(1//3*x*3^3//4*b^1//4),-1))
@test integrate(x^7*(1+x^4)^1//3, x) == :(-3//16*(1+x^4)^4//3+3//28*(1+x^4)^7//3)
@test integrate(x^3*(1+x^4)^-4//3, x) == :(-3//4*(1+x^4)^-1//3)
@test integrate(x^3*(1+x^4)^-1//3, x) == :(3//8*(1+x^4)^2//3)
@test integrate(x^19*(a+b*x^4)^1//4, x) == :(1//21*b^-5*(a+b*x^4)^21//4+-4//9*a^3*b^-5*(a+b*x^4)^9//4+-4//17*a*b^-5*(a+b*x^4)^17//4+1//5*a^4*b^-5*(a+b*x^4)^5//4+6//13*a^2*b^-5*(a+b*x^4)^13//4)
@test integrate(x^15*(a+b*x^4)^1//4, x) == :(1//17*b^-4*(a+b*x^4)^17//4+-3//13*a*b^-4*(a+b*x^4)^13//4+-1//5*a^3*b^-4*(a+b*x^4)^5//4+1//3*a^2*b^-4*(a+b*x^4)^9//4)
@test integrate(x^11*(a+b*x^4)^1//4, x) == :(1//13*b^-3*(a+b*x^4)^13//4+-2//9*a*b^-3*(a+b*x^4)^9//4+1//5*a^2*b^-3*(a+b*x^4)^5//4)
@test integrate(x^7*(a+b*x^4)^1//4, x) == :(1//9*b^-2*(a+b*x^4)^9//4+-1//5*a*b^-2*(a+b*x^4)^5//4)
@test integrate(x^3*(a+b*x^4)^1//4, x) == :(1//5*b^-1*(a+b*x^4)^5//4)
@test integrate(x^-1*(a+b*x^4)^1//4, x) == :((a+b*x^4)^1//4+-1//2*a^1//4*arctan(a^-1//4*(a+b*x^4)^1//4)+-1//2*a^1//4*arctanh(a^-1//4*(a+b*x^4)^1//4))
@test integrate(x^-5*(a+b*x^4)^1//4, x) == :(-1//4*x^-4*(a+b*x^4)^1//4+-1//8*b*a^-3//4*arctan(a^-1//4*(a+b*x^4)^1//4)+-1//8*b*a^-3//4*arctanh(a^-1//4*(a+b*x^4)^1//4))
@test integrate(x^-9*(a+b*x^4)^1//4, x) == :(-1//8*x^-8*(a+b*x^4)^1//4+3//64*a^-7//4*b^2*arctan(a^-1//4*(a+b*x^4)^1//4)+3//64*a^-7//4*b^2*arctanh(a^-1//4*(a+b*x^4)^1//4)+-1//32*b*a^-1*x^-4*(a+b*x^4)^1//4)
@test integrate(x^9*(a+b*x^4)^1//4, x) == :(1//11*x^10*(a+b*x^4)^1//4+-2//77*a^2*b^-2*x^2*(a+b*x^4)^1//4+1//77*a*b^-1*x^6*(a+b*x^4)^1//4+4//77*a^7//2*b^-5//2*(1+b*a^-1*x^4)^3//4*(a+b*x^4)^-3//4*Elliptic.F((1/2)*arctan(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^5*(a+b*x^4)^1//4, x) == :(1//7*x^6*(a+b*x^4)^1//4+1//21*a*b^-1*x^2*(a+b*x^4)^1//4+-2//21*a^5//2*b^-3//2*(1+b*a^-1*x^4)^3//4*(a+b*x^4)^-3//4*Elliptic.F((1/2)*arctan(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x*(a+b*x^4)^1//4, x) == :(1//3*x^2*(a+b*x^4)^1//4+1//3*a^3//2*b^-1//2*(1+b*a^-1*x^4)^3//4*(a+b*x^4)^-3//4*Elliptic.F((1/2)*arctan(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^-3*(a+b*x^4)^1//4, x) == :(-1//2*x^-2*(a+b*x^4)^1//4+(1/2)*a^(1/2)*b^(1/2)*(1+b*a^-1*x^4)^3//4*(a+b*x^4)^-3//4*Elliptic.F((1/2)*arctan(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^-7*(a+b*x^4)^1//4, x) == :(-1//6*x^-6*(a+b*x^4)^1//4+-1//12*b*a^-1*x^-2*(a+b*x^4)^1//4+-1//12*a^-1//2*b^3//2*(1+b*a^-1*x^4)^3//4*(a+b*x^4)^-3//4*Elliptic.F((1/2)*arctan(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^-11*(a+b*x^4)^1//4, x) == :(-1//10*x^-10*(a+b*x^4)^1//4+-1//60*b*a^-1*x^-6*(a+b*x^4)^1//4+1//24*a^-2*b^2*x^-2*(a+b*x^4)^1//4+1//24*a^-3//2*b^5//2*(1+b*a^-1*x^4)^3//4*(a+b*x^4)^-3//4*Elliptic.F((1/2)*arctan(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^6*(a+b*x^4)^1//4, x) == :(1//8*x^7*(a+b*x^4)^1//4+-3//64*a^2*b^-7//4*arctanh(x*b^1//4*(a+b*x^4)^-1//4)+3//64*a^2*b^-7//4*arctan(x*b^1//4*(a+b*x^4)^-1//4)+1//32*a*b^-1*x^3*(a+b*x^4)^1//4)
@test integrate(x^2*(a+b*x^4)^1//4, x) == :(1//4*x^3*(a+b*x^4)^1//4+-1//8*a*b^-3//4*arctan(x*b^1//4*(a+b*x^4)^-1//4)+1//8*a*b^-3//4*arctanh(x*b^1//4*(a+b*x^4)^-1//4))
@test integrate(x^-2*(a+b*x^4)^1//4, x) == :((1/2)*b^1//4*arctanh(x*b^1//4*(a+b*x^4)^-1//4)+-1*x^-1*(a+b*x^4)^1//4+-1//2*b^1//4*arctan(x*b^1//4*(a+b*x^4)^-1//4))
@test integrate(x^-6*(a+b*x^4)^1//4, x) == :(-1//5*a^-1*x^-5*(a+b*x^4)^5//4)
@test integrate(x^-10*(a+b*x^4)^1//4, x) == :(-1//9*a^-1*x^-9*(a+b*x^4)^5//4+4//45*b*a^-2*x^-5*(a+b*x^4)^5//4)
@test integrate(x^-14*(a+b*x^4)^1//4, x) == :(-1//13*a^-1*x^-13*(a+b*x^4)^5//4+-32//585*a^-3*b^2*x^-5*(a+b*x^4)^5//4+8//117*b*a^-2*x^-9*(a+b*x^4)^5//4)
@test integrate(x^-18*(a+b*x^4)^1//4, x) == :(-1//17*a^-1*x^-17*(a+b*x^4)^5//4+-32//663*a^-3*b^2*x^-9*(a+b*x^4)^5//4+12//221*b*a^-2*x^-13*(a+b*x^4)^5//4+128//3315*a^-4*b^3*x^-5*(a+b*x^4)^5//4)
@test integrate(x^12*(a+b*x^4)^1//4, x) == :(1//14*x^13*(a+b*x^4)^1//4+-3//280*a^2*b^-2*x^5*(a+b*x^4)^1//4+1//140*a*b^-1*x^9*(a+b*x^4)^1//4+3//112*x*a^3*b^-3*(a+b*x^4)^1//4+3//112*a^7//2*b^-5//2*x^3*(1+a*b^-1*x^-4)^3//4*(a+b*x^4)^-3//4*Elliptic.F((1/2)*arccot(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^8*(a+b*x^4)^1//4, x) == :(1//10*x^9*(a+b*x^4)^1//4+-1//24*x*a^2*b^-2*(a+b*x^4)^1//4+1//60*a*b^-1*x^5*(a+b*x^4)^1//4+-1//24*a^5//2*b^-3//2*x^3*(1+a*b^-1*x^-4)^3//4*(a+b*x^4)^-3//4*Elliptic.F((1/2)*arccot(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^4*(a+b*x^4)^1//4, x) == :(1//6*x^5*(a+b*x^4)^1//4+1//12*a*x*b^-1*(a+b*x^4)^1//4+1//12*a^3//2*b^-1//2*x^3*(1+a*b^-1*x^-4)^3//4*(a+b*x^4)^-3//4*Elliptic.F((1/2)*arccot(a^-1//2*b^(1/2)*x^2),2))
@test integrate((a+b*x^4)^1//4, x) == :((1/2)*x*(a+b*x^4)^1//4+-1//2*a^(1/2)*b^(1/2)*x^3*(1+a*b^-1*x^-4)^3//4*(a+b*x^4)^-3//4*Elliptic.F((1/2)*arccot(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^-4*(a+b*x^4)^1//4, x) == :(-1//3*x^-3*(a+b*x^4)^1//4+-1//3*a^-1//2*b^3//2*x^3*(1+a*b^-1*x^-4)^3//4*(a+b*x^4)^-3//4*Elliptic.F((1/2)*arccot(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^-8*(a+b*x^4)^1//4, x) == :(-1//7*x^-7*(a+b*x^4)^1//4+-1//21*b*a^-1*x^-3*(a+b*x^4)^1//4+2//21*a^-3//2*b^5//2*x^3*(1+a*b^-1*x^-4)^3//4*(a+b*x^4)^-3//4*Elliptic.F((1/2)*arccot(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^-12*(a+b*x^4)^1//4, x) == :(-1//11*x^-11*(a+b*x^4)^1//4+-1//77*b*a^-1*x^-7*(a+b*x^4)^1//4+2//77*a^-2*b^2*x^-3*(a+b*x^4)^1//4+-4//77*a^-5//2*b^7//2*x^3*(1+a*b^-1*x^-4)^3//4*(a+b*x^4)^-3//4*Elliptic.F((1/2)*arccot(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^-16*(a+b*x^4)^1//4, x) == :(-1//15*x^-15*(a+b*x^4)^1//4+-4//231*a^-3*b^3*x^-3*(a+b*x^4)^1//4+-1//165*b*a^-1*x^-11*(a+b*x^4)^1//4+2//231*a^-2*b^2*x^-7*(a+b*x^4)^1//4+8//231*a^-7//2*b^9//2*x^3*(1+a*b^-1*x^-4)^3//4*(a+b*x^4)^-3//4*Elliptic.F((1/2)*arccot(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^19*(a+b*x^4)^3//4, x) == :(1//23*b^-5*(a+b*x^4)^23//4+-4//11*a^3*b^-5*(a+b*x^4)^11//4+-4//19*a*b^-5*(a+b*x^4)^19//4+1//7*a^4*b^-5*(a+b*x^4)^7//4+2//5*a^2*b^-5*(a+b*x^4)^15//4)
@test integrate(x^15*(a+b*x^4)^3//4, x) == :(1//19*b^-4*(a+b*x^4)^19//4+-1//5*a*b^-4*(a+b*x^4)^15//4+-1//7*a^3*b^-4*(a+b*x^4)^7//4+3//11*a^2*b^-4*(a+b*x^4)^11//4)
@test integrate(x^11*(a+b*x^4)^3//4, x) == :(1//15*b^-3*(a+b*x^4)^15//4+-2//11*a*b^-3*(a+b*x^4)^11//4+1//7*a^2*b^-3*(a+b*x^4)^7//4)
@test integrate(x^7*(a+b*x^4)^3//4, x) == :(1//11*b^-2*(a+b*x^4)^11//4+-1//7*a*b^-2*(a+b*x^4)^7//4)
@test integrate(x^3*(a+b*x^4)^3//4, x) == :(1//7*b^-1*(a+b*x^4)^7//4)
@test integrate(x^-1*(a+b*x^4)^3//4, x) == :(1//3*(a+b*x^4)^3//4+(1/2)*a^3//4*arctan(a^-1//4*(a+b*x^4)^1//4)+-1//2*a^3//4*arctanh(a^-1//4*(a+b*x^4)^1//4))
@test integrate(x^-5*(a+b*x^4)^3//4, x) == :(-1//4*x^-4*(a+b*x^4)^3//4+-3//8*b*a^-1//4*arctanh(a^-1//4*(a+b*x^4)^1//4)+3//8*b*a^-1//4*arctan(a^-1//4*(a+b*x^4)^1//4))
@test integrate(x^-9*(a+b*x^4)^3//4, x) == :(-1//8*x^-8*(a+b*x^4)^3//4+-3//64*a^-5//4*b^2*arctan(a^-1//4*(a+b*x^4)^1//4)+3//64*a^-5//4*b^2*arctanh(a^-1//4*(a+b*x^4)^1//4)+-3//32*b*a^-1*x^-4*(a+b*x^4)^3//4)
@test integrate(x^9*(a+b*x^4)^3//4, x) == :(1//13*x^10*(a+b*x^4)^3//4+-2//65*a^2*b^-2*x^2*(a+b*x^4)^3//4+1//39*a*b^-1*x^6*(a+b*x^4)^3//4+4//65*a^3*b^-2*x^2*(a+b*x^4)^-1//4+-4//65*a^7//2*b^-5//2*(1+b*a^-1*x^4)^1//4*(a+b*x^4)^-1//4*Elliptic.E((1/2)*arctan(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^5*(a+b*x^4)^3//4, x) == :(1//9*x^6*(a+b*x^4)^3//4+-2//15*a^2*b^-1*x^2*(a+b*x^4)^-1//4+1//15*a*b^-1*x^2*(a+b*x^4)^3//4+2//15*a^5//2*b^-3//2*(1+b*a^-1*x^4)^1//4*(a+b*x^4)^-1//4*Elliptic.E((1/2)*arctan(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x*(a+b*x^4)^3//4, x) == :(1//5*x^2*(a+b*x^4)^3//4+3//5*a*x^2*(a+b*x^4)^-1//4+-3//5*a^3//2*b^-1//2*(1+b*a^-1*x^4)^1//4*(a+b*x^4)^-1//4*Elliptic.E((1/2)*arctan(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^-3*(a+b*x^4)^3//4, x) == :(-1//2*x^-2*(a+b*x^4)^3//4+3//2*b*x^2*(a+b*x^4)^-1//4+-3//2*a^(1/2)*b^(1/2)*(1+b*a^-1*x^4)^1//4*(a+b*x^4)^-1//4*Elliptic.E((1/2)*arctan(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^-7*(a+b*x^4)^3//4, x) == :(-1//6*x^-6*(a+b*x^4)^3//4+-1//4*b*a^-1*x^-2*(a+b*x^4)^3//4+1//4*a^-1*b^2*x^2*(a+b*x^4)^-1//4+-1//4*a^-1//2*b^3//2*(1+b*a^-1*x^4)^1//4*(a+b*x^4)^-1//4*Elliptic.E((1/2)*arctan(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^-11*(a+b*x^4)^3//4, x) == :(-1//10*x^-10*(a+b*x^4)^3//4+-3//40*a^-2*b^3*x^2*(a+b*x^4)^-1//4+-1//20*b*a^-1*x^-6*(a+b*x^4)^3//4+3//40*a^-2*b^2*x^-2*(a+b*x^4)^3//4+3//40*a^-3//2*b^5//2*(1+b*a^-1*x^4)^1//4*(a+b*x^4)^-1//4*Elliptic.E((1/2)*arctan(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^12*(a+b*x^4)^3//4, x) == :(1//16*x^13*(a+b*x^4)^3//4+-45//4096*a^4*b^-13//4*arctan(x*b^1//4*(a+b*x^4)^-1//4)+-45//4096*a^4*b^-13//4*arctanh(x*b^1//4*(a+b*x^4)^-1//4)+-9//512*a^2*b^-2*x^5*(a+b*x^4)^3//4+1//64*a*b^-1*x^9*(a+b*x^4)^3//4+45//2048*x*a^3*b^-3*(a+b*x^4)^3//4)
@test integrate(x^8*(a+b*x^4)^3//4, x) == :(1//12*x^9*(a+b*x^4)^3//4+5//256*a^3*b^-9//4*arctan(x*b^1//4*(a+b*x^4)^-1//4)+5//256*a^3*b^-9//4*arctanh(x*b^1//4*(a+b*x^4)^-1//4)+-5//128*x*a^2*b^-2*(a+b*x^4)^3//4+1//32*a*b^-1*x^5*(a+b*x^4)^3//4)
@test integrate(x^4*(a+b*x^4)^3//4, x) == :(1//8*x^5*(a+b*x^4)^3//4+-3//64*a^2*b^-5//4*arctan(x*b^1//4*(a+b*x^4)^-1//4)+-3//64*a^2*b^-5//4*arctanh(x*b^1//4*(a+b*x^4)^-1//4)+3//32*a*x*b^-1*(a+b*x^4)^3//4)
@test integrate((a+b*x^4)^3//4, x) == :(1//4*x*(a+b*x^4)^3//4+3//8*a*b^-1//4*arctan(x*b^1//4*(a+b*x^4)^-1//4)+3//8*a*b^-1//4*arctanh(x*b^1//4*(a+b*x^4)^-1//4))
@test integrate(x^-4*(a+b*x^4)^3//4, x) == :((1/2)*b^3//4*arctan(x*b^1//4*(a+b*x^4)^-1//4)+(1/2)*b^3//4*arctanh(x*b^1//4*(a+b*x^4)^-1//4)+-1//3*x^-3*(a+b*x^4)^3//4)
@test integrate(x^-8*(a+b*x^4)^3//4, x) == :(-1//7*a^-1*x^-7*(a+b*x^4)^7//4)
@test integrate(x^-12*(a+b*x^4)^3//4, x) == :(-1//11*a^-1*x^-11*(a+b*x^4)^7//4+4//77*b*a^-2*x^-7*(a+b*x^4)^7//4)
@test integrate(x^-16*(a+b*x^4)^3//4, x) == :(-1//15*a^-1*x^-15*(a+b*x^4)^7//4+-32//1155*a^-3*b^2*x^-7*(a+b*x^4)^7//4+8//165*b*a^-2*x^-11*(a+b*x^4)^7//4)
@test integrate(x^-20*(a+b*x^4)^3//4, x) == :(-1//19*a^-1*x^-19*(a+b*x^4)^7//4+-32//1045*a^-3*b^2*x^-11*(a+b*x^4)^7//4+4//95*b*a^-2*x^-15*(a+b*x^4)^7//4+128//7315*a^-4*b^3*x^-7*(a+b*x^4)^7//4)
@test integrate(x^10*(a+b*x^4)^3//4, x) == :(1//14*x^11*(a+b*x^4)^3//4+-1//40*a^2*b^-2*x^3*(a+b*x^4)^3//4+3//80*a^3*b^-2*x^3*(a+b*x^4)^-1//4+3//140*a*b^-1*x^7*(a+b*x^4)^3//4+3//80*x*a^7//2*b^-5//2*(1+a*b^-1*x^-4)^1//4*(a+b*x^4)^-1//4*Elliptic.E((1/2)*arccot(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^6*(a+b*x^4)^3//4, x) == :(1//10*x^7*(a+b*x^4)^3//4+-3//40*a^2*b^-1*x^3*(a+b*x^4)^-1//4+1//20*a*b^-1*x^3*(a+b*x^4)^3//4+-3//40*x*a^5//2*b^-3//2*(1+a*b^-1*x^-4)^1//4*(a+b*x^4)^-1//4*Elliptic.E((1/2)*arccot(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^2*(a+b*x^4)^3//4, x) == :(1//6*x^3*(a+b*x^4)^3//4+1//4*a*x^3*(a+b*x^4)^-1//4+1//4*x*a^3//2*b^-1//2*(1+a*b^-1*x^-4)^1//4*(a+b*x^4)^-1//4*Elliptic.E((1/2)*arccot(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^-2*(a+b*x^4)^3//4, x) == :(-1*x^-1*(a+b*x^4)^3//4+3//2*b*x^3*(a+b*x^4)^-1//4+3//2*x*a^(1/2)*b^(1/2)*(1+a*b^-1*x^-4)^1//4*(a+b*x^4)^-1//4*Elliptic.E((1/2)*arccot(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^-6*(a+b*x^4)^3//4, x) == :(-1//5*x^-5*(a+b*x^4)^3//4+-3//5*b*x^-1*(a+b*x^4)^-1//4+3//5*x*a^-1//2*b^3//2*(1+a*b^-1*x^-4)^1//4*(a+b*x^4)^-1//4*Elliptic.E((1/2)*arccot(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^-10*(a+b*x^4)^3//4, x) == :(-1//9*x^-9*(a+b*x^4)^3//4+-1//15*b*a^-1*x^-5*(a+b*x^4)^3//4+2//15*a^-1*b^2*x^-1*(a+b*x^4)^-1//4+-2//15*x*a^-3//2*b^5//2*(1+a*b^-1*x^-4)^1//4*(a+b*x^4)^-1//4*Elliptic.E((1/2)*arccot(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^-14*(a+b*x^4)^3//4, x) == :(-1//13*x^-13*(a+b*x^4)^3//4+-4//65*a^-2*b^3*x^-1*(a+b*x^4)^-1//4+-1//39*b*a^-1*x^-9*(a+b*x^4)^3//4+2//65*a^-2*b^2*x^-5*(a+b*x^4)^3//4+4//65*x*a^-5//2*b^7//2*(1+a*b^-1*x^-4)^1//4*(a+b*x^4)^-1//4*Elliptic.E((1/2)*arccot(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^19*(a+b*x^4)^5//4, x) == :(1//25*b^-5*(a+b*x^4)^25//4+-4//13*a^3*b^-5*(a+b*x^4)^13//4+-4//21*a*b^-5*(a+b*x^4)^21//4+1//9*a^4*b^-5*(a+b*x^4)^9//4+6//17*a^2*b^-5*(a+b*x^4)^17//4)
@test integrate(x^15*(a+b*x^4)^5//4, x) == :(1//21*b^-4*(a+b*x^4)^21//4+-3//17*a*b^-4*(a+b*x^4)^17//4+-1//9*a^3*b^-4*(a+b*x^4)^9//4+3//13*a^2*b^-4*(a+b*x^4)^13//4)
@test integrate(x^11*(a+b*x^4)^5//4, x) == :(1//17*b^-3*(a+b*x^4)^17//4+-2//13*a*b^-3*(a+b*x^4)^13//4+1//9*a^2*b^-3*(a+b*x^4)^9//4)
@test integrate(x^7*(a+b*x^4)^5//4, x) == :(1//13*b^-2*(a+b*x^4)^13//4+-1//9*a*b^-2*(a+b*x^4)^9//4)
@test integrate(x^3*(a+b*x^4)^5//4, x) == :(1//9*b^-1*(a+b*x^4)^9//4)
@test integrate(x^-1*(a+b*x^4)^5//4, x) == :(1//5*(a+b*x^4)^5//4+a*(a+b*x^4)^1//4+-1//2*a^5//4*arctan(a^-1//4*(a+b*x^4)^1//4)+-1//2*a^5//4*arctanh(a^-1//4*(a+b*x^4)^1//4))
@test integrate(x^-5*(a+b*x^4)^5//4, x) == :(-1//4*x^-4*(a+b*x^4)^5//4+5//4*b*(a+b*x^4)^1//4+-5//8*b*a^1//4*arctan(a^-1//4*(a+b*x^4)^1//4)+-5//8*b*a^1//4*arctanh(a^-1//4*(a+b*x^4)^1//4))
@test integrate(x^-9*(a+b*x^4)^5//4, x) == :(-1//8*x^-8*(a+b*x^4)^5//4+-5//32*b*x^-4*(a+b*x^4)^1//4+-5//64*a^-3//4*b^2*arctan(a^-1//4*(a+b*x^4)^1//4)+-5//64*a^-3//4*b^2*arctanh(a^-1//4*(a+b*x^4)^1//4))
@test integrate(x^9*(a+b*x^4)^5//4, x) == :(1//15*x^10*(a+b*x^4)^5//4+1//33*a*x^10*(a+b*x^4)^1//4+-2//231*a^3*b^-2*x^2*(a+b*x^4)^1//4+1//231*a^2*b^-1*x^6*(a+b*x^4)^1//4+4//231*a^9//2*b^-5//2*(1+b*a^-1*x^4)^3//4*(a+b*x^4)^-3//4*Elliptic.F((1/2)*arctan(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^5*(a+b*x^4)^5//4, x) == :(1//11*x^6*(a+b*x^4)^5//4+5//77*a*x^6*(a+b*x^4)^1//4+5//231*a^2*b^-1*x^2*(a+b*x^4)^1//4+-10//231*a^7//2*b^-3//2*(1+b*a^-1*x^4)^3//4*(a+b*x^4)^-3//4*Elliptic.F((1/2)*arctan(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x*(a+b*x^4)^5//4, x) == :(1//7*x^2*(a+b*x^4)^5//4+5//21*a*x^2*(a+b*x^4)^1//4+5//21*a^5//2*b^-1//2*(1+b*a^-1*x^4)^3//4*(a+b*x^4)^-3//4*Elliptic.F((1/2)*arctan(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^-3*(a+b*x^4)^5//4, x) == :(-1//2*x^-2*(a+b*x^4)^5//4+5//6*b*x^2*(a+b*x^4)^1//4+5//6*a^3//2*b^(1/2)*(1+b*a^-1*x^4)^3//4*(a+b*x^4)^-3//4*Elliptic.F((1/2)*arctan(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^-7*(a+b*x^4)^5//4, x) == :(-1//6*x^-6*(a+b*x^4)^5//4+-5//12*b*x^-2*(a+b*x^4)^1//4+5//12*a^(1/2)*b^3//2*(1+b*a^-1*x^4)^3//4*(a+b*x^4)^-3//4*Elliptic.F((1/2)*arctan(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^-11*(a+b*x^4)^5//4, x) == :(-1//10*x^-10*(a+b*x^4)^5//4+-1//12*b*x^-6*(a+b*x^4)^1//4+-1//24*a^-1*b^2*x^-2*(a+b*x^4)^1//4+-1//24*a^-1//2*b^5//2*(1+b*a^-1*x^4)^3//4*(a+b*x^4)^-3//4*Elliptic.F((1/2)*arctan(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^-15*(a+b*x^4)^5//4, x) == :(-1//14*x^-14*(a+b*x^4)^5//4+-1//28*b*x^-10*(a+b*x^4)^1//4+-1//168*a^-1*b^2*x^-6*(a+b*x^4)^1//4+5//336*a^-2*b^3*x^-2*(a+b*x^4)^1//4+5//336*a^-3//2*b^7//2*(1+b*a^-1*x^4)^3//4*(a+b*x^4)^-3//4*Elliptic.F((1/2)*arctan(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^10*(a+b*x^4)^5//4, x) == :(1//16*x^11*(a+b*x^4)^5//4+-35//4096*a^4*b^-11//4*arctan(x*b^1//4*(a+b*x^4)^-1//4)+5//192*a*x^11*(a+b*x^4)^1//4+35//4096*a^4*b^-11//4*arctanh(x*b^1//4*(a+b*x^4)^-1//4)+-35//6144*a^3*b^-2*x^3*(a+b*x^4)^1//4+5//1536*a^2*b^-1*x^7*(a+b*x^4)^1//4)
@test integrate(x^6*(a+b*x^4)^5//4, x) == :(1//12*x^7*(a+b*x^4)^5//4+-5//256*a^3*b^-7//4*arctanh(x*b^1//4*(a+b*x^4)^-1//4)+5//96*a*x^7*(a+b*x^4)^1//4+5//256*a^3*b^-7//4*arctan(x*b^1//4*(a+b*x^4)^-1//4)+5//384*a^2*b^-1*x^3*(a+b*x^4)^1//4)
@test integrate(x^2*(a+b*x^4)^5//4, x) == :(1//8*x^3*(a+b*x^4)^5//4+-5//64*a^2*b^-3//4*arctan(x*b^1//4*(a+b*x^4)^-1//4)+5//32*a*x^3*(a+b*x^4)^1//4+5//64*a^2*b^-3//4*arctanh(x*b^1//4*(a+b*x^4)^-1//4))
@test integrate(x^-2*(a+b*x^4)^5//4, x) == :(-1*x^-1*(a+b*x^4)^5//4+-5//8*a*b^1//4*arctan(x*b^1//4*(a+b*x^4)^-1//4)+5//4*b*x^3*(a+b*x^4)^1//4+5//8*a*b^1//4*arctanh(x*b^1//4*(a+b*x^4)^-1//4))
@test integrate(x^-6*(a+b*x^4)^5//4, x) == :((1/2)*b^5//4*arctanh(x*b^1//4*(a+b*x^4)^-1//4)+-1//2*b^5//4*arctan(x*b^1//4*(a+b*x^4)^-1//4)+-1//5*x^-5*(a+b*x^4)^5//4+-1*b*x^-1*(a+b*x^4)^1//4)
@test integrate(x^-10*(a+b*x^4)^5//4, x) == :(-1//9*a^-1*x^-9*(a+b*x^4)^9//4)
@test integrate(x^-14*(a+b*x^4)^5//4, x) == :(-1//13*a^-1*x^-13*(a+b*x^4)^9//4+4//117*b*a^-2*x^-9*(a+b*x^4)^9//4)
@test integrate(x^-18*(a+b*x^4)^5//4, x) == :(-1//17*a^-1*x^-17*(a+b*x^4)^9//4+-32//1989*a^-3*b^2*x^-9*(a+b*x^4)^9//4+8//221*b*a^-2*x^-13*(a+b*x^4)^9//4)
@test integrate(x^-22*(a+b*x^4)^5//4, x) == :(-1//21*a^-1*x^-21*(a+b*x^4)^9//4+-32//1547*a^-3*b^2*x^-13*(a+b*x^4)^9//4+4//119*b*a^-2*x^-17*(a+b*x^4)^9//4+128//13923*a^-4*b^3*x^-9*(a+b*x^4)^9//4)
@test integrate(x^12*(a+b*x^4)^5//4, x) == :(1//18*x^13*(a+b*x^4)^5//4+5//252*a*x^13*(a+b*x^4)^1//4+-1//336*a^3*b^-2*x^5*(a+b*x^4)^1//4+1//504*a^2*b^-1*x^9*(a+b*x^4)^1//4+5//672*x*a^4*b^-3*(a+b*x^4)^1//4+5//672*a^9//2*b^-5//2*x^3*(1+a*b^-1*x^-4)^3//4*(a+b*x^4)^-3//4*Elliptic.F((1/2)*arccot(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^8*(a+b*x^4)^5//4, x) == :(1//14*x^9*(a+b*x^4)^5//4+1//28*a*x^9*(a+b*x^4)^1//4+-5//336*x*a^3*b^-2*(a+b*x^4)^1//4+1//168*a^2*b^-1*x^5*(a+b*x^4)^1//4+-5//336*a^7//2*b^-3//2*x^3*(1+a*b^-1*x^-4)^3//4*(a+b*x^4)^-3//4*Elliptic.F((1/2)*arccot(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^4*(a+b*x^4)^5//4, x) == :(1//10*x^5*(a+b*x^4)^5//4+1//12*a*x^5*(a+b*x^4)^1//4+1//24*x*a^2*b^-1*(a+b*x^4)^1//4+1//24*a^5//2*b^-1//2*x^3*(1+a*b^-1*x^-4)^3//4*(a+b*x^4)^-3//4*Elliptic.F((1/2)*arccot(a^-1//2*b^(1/2)*x^2),2))
@test integrate((a+b*x^4)^5//4, x) == :(1//6*x*(a+b*x^4)^5//4+5//12*a*x*(a+b*x^4)^1//4+-5//12*a^3//2*b^(1/2)*x^3*(1+a*b^-1*x^-4)^3//4*(a+b*x^4)^-3//4*Elliptic.F((1/2)*arccot(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^-4*(a+b*x^4)^5//4, x) == :(-1//3*x^-3*(a+b*x^4)^5//4+5//6*b*x*(a+b*x^4)^1//4+-5//6*a^(1/2)*b^3//2*x^3*(1+a*b^-1*x^-4)^3//4*(a+b*x^4)^-3//4*Elliptic.F((1/2)*arccot(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^-8*(a+b*x^4)^5//4, x) == :(-1//7*x^-7*(a+b*x^4)^5//4+-5//21*b*x^-3*(a+b*x^4)^1//4+-5//21*a^-1//2*b^5//2*x^3*(1+a*b^-1*x^-4)^3//4*(a+b*x^4)^-3//4*Elliptic.F((1/2)*arccot(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^-12*(a+b*x^4)^5//4, x) == :(-1//11*x^-11*(a+b*x^4)^5//4+-5//77*b*x^-7*(a+b*x^4)^1//4+-5//231*a^-1*b^2*x^-3*(a+b*x^4)^1//4+10//231*a^-3//2*b^7//2*x^3*(1+a*b^-1*x^-4)^3//4*(a+b*x^4)^-3//4*Elliptic.F((1/2)*arccot(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^-16*(a+b*x^4)^5//4, x) == :(-1//15*x^-15*(a+b*x^4)^5//4+-1//33*b*x^-11*(a+b*x^4)^1//4+-1//231*a^-1*b^2*x^-7*(a+b*x^4)^1//4+2//231*a^-2*b^3*x^-3*(a+b*x^4)^1//4+-4//231*a^-5//2*b^9//2*x^3*(1+a*b^-1*x^-4)^3//4*(a+b*x^4)^-3//4*Elliptic.F((1/2)*arccot(a^-1//2*b^(1/2)*x^2),2))
@test integrate((a+b*x^4)^7//4, x) == :(1//8*x*(a+b*x^4)^7//4+7//32*a*x*(a+b*x^4)^3//4+21//64*a^2*b^-1//4*arctan(x*b^1//4*(a+b*x^4)^-1//4)+21//64*a^2*b^-1//4*arctanh(x*b^1//4*(a+b*x^4)^-1//4))
@test integrate(x^19*(a+b*x^4)^-1//4, x) == :(1//19*b^-5*(a+b*x^4)^19//4+-4//7*a^3*b^-5*(a+b*x^4)^7//4+-4//15*a*b^-5*(a+b*x^4)^15//4+1//3*a^4*b^-5*(a+b*x^4)^3//4+6//11*a^2*b^-5*(a+b*x^4)^11//4)
@test integrate(x^15*(a+b*x^4)^-1//4, x) == :(1//15*b^-4*(a+b*x^4)^15//4+-3//11*a*b^-4*(a+b*x^4)^11//4+-1//3*a^3*b^-4*(a+b*x^4)^3//4+3//7*a^2*b^-4*(a+b*x^4)^7//4)
@test integrate(x^11*(a+b*x^4)^-1//4, x) == :(1//11*b^-3*(a+b*x^4)^11//4+-2//7*a*b^-3*(a+b*x^4)^7//4+1//3*a^2*b^-3*(a+b*x^4)^3//4)
@test integrate(x^7*(a+b*x^4)^-1//4, x) == :(1//7*b^-2*(a+b*x^4)^7//4+-1//3*a*b^-2*(a+b*x^4)^3//4)
@test integrate(x^3*(a+b*x^4)^-1//4, x) == :(1//3*b^-1*(a+b*x^4)^3//4)
@test integrate(x^-1*(a+b*x^4)^-1//4, x) == :((1/2)*a^-1//4*arctan(a^-1//4*(a+b*x^4)^1//4)+-1//2*a^-1//4*arctanh(a^-1//4*(a+b*x^4)^1//4))
@test integrate(x^-5*(a+b*x^4)^-1//4, x) == :(-1//4*a^-1*x^-4*(a+b*x^4)^3//4+-1//8*b*a^-5//4*arctan(a^-1//4*(a+b*x^4)^1//4)+1//8*b*a^-5//4*arctanh(a^-1//4*(a+b*x^4)^1//4))
@test integrate(x^-9*(a+b*x^4)^-1//4, x) == :(-5//64*a^-9//4*b^2*arctanh(a^-1//4*(a+b*x^4)^1//4)+-1//8*a^-1*x^-8*(a+b*x^4)^3//4+5//64*a^-9//4*b^2*arctan(a^-1//4*(a+b*x^4)^1//4)+5//32*b*a^-2*x^-4*(a+b*x^4)^3//4)
@test integrate(x^13*(a+b*x^4)^-1//4, x) == :(1//13*b^-1*x^10*(a+b*x^4)^3//4+-10//117*a*b^-2*x^6*(a+b*x^4)^3//4+-8//39*a^3*b^-3*x^2*(a+b*x^4)^-1//4+4//39*a^2*b^-3*x^2*(a+b*x^4)^3//4+8//39*a^7//2*b^-7//2*(1+b*a^-1*x^4)^1//4*(a+b*x^4)^-1//4*Elliptic.E((1/2)*arctan(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^9*(a+b*x^4)^-1//4, x) == :(1//9*b^-1*x^6*(a+b*x^4)^3//4+-2//15*a*b^-2*x^2*(a+b*x^4)^3//4+4//15*a^2*b^-2*x^2*(a+b*x^4)^-1//4+-4//15*a^5//2*b^-5//2*(1+b*a^-1*x^4)^1//4*(a+b*x^4)^-1//4*Elliptic.E((1/2)*arctan(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^5*(a+b*x^4)^-1//4, x) == :(1//5*b^-1*x^2*(a+b*x^4)^3//4+-2//5*a*b^-1*x^2*(a+b*x^4)^-1//4+2//5*a^3//2*b^-3//2*(1+b*a^-1*x^4)^1//4*(a+b*x^4)^-1//4*Elliptic.E((1/2)*arctan(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x*(a+b*x^4)^-1//4, x) == :(x^2*(a+b*x^4)^-1//4+-1*a^(1/2)*b^-1//2*(1+b*a^-1*x^4)^1//4*(a+b*x^4)^-1//4*Elliptic.E((1/2)*arctan(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^-3*(a+b*x^4)^-1//4, x) == :(-1//2*a^-1*x^-2*(a+b*x^4)^3//4+(1/2)*b*a^-1*x^2*(a+b*x^4)^-1//4+-1//2*a^-1//2*b^(1/2)*(1+b*a^-1*x^4)^1//4*(a+b*x^4)^-1//4*Elliptic.E((1/2)*arctan(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^-7*(a+b*x^4)^-1//4, x) == :(-1//6*a^-1*x^-6*(a+b*x^4)^3//4+-1//4*a^-2*b^2*x^2*(a+b*x^4)^-1//4+1//4*b*a^-2*x^-2*(a+b*x^4)^3//4+1//4*a^-3//2*b^3//2*(1+b*a^-1*x^4)^1//4*(a+b*x^4)^-1//4*Elliptic.E((1/2)*arctan(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^-11*(a+b*x^4)^-1//4, x) == :(-1//10*a^-1*x^-10*(a+b*x^4)^3//4+-7//40*a^-3*b^2*x^-2*(a+b*x^4)^3//4+7//40*a^-3*b^3*x^2*(a+b*x^4)^-1//4+7//60*b*a^-2*x^-6*(a+b*x^4)^3//4+-7//40*a^-5//2*b^5//2*(1+b*a^-1*x^4)^1//4*(a+b*x^4)^-1//4*Elliptic.E((1/2)*arctan(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^8*(a+b*x^4)^-1//4, x) == :(1//8*b^-1*x^5*(a+b*x^4)^3//4+5//64*a^2*b^-9//4*arctan(x*b^1//4*(a+b*x^4)^-1//4)+5//64*a^2*b^-9//4*arctanh(x*b^1//4*(a+b*x^4)^-1//4)+-5//32*a*x*b^-2*(a+b*x^4)^3//4)
@test integrate(x^4*(a+b*x^4)^-1//4, x) == :(-1//8*a*b^-5//4*arctan(x*b^1//4*(a+b*x^4)^-1//4)+-1//8*a*b^-5//4*arctanh(x*b^1//4*(a+b*x^4)^-1//4)+1//4*x*b^-1*(a+b*x^4)^3//4)
@test integrate((a+b*x^4)^-1//4, x) == :((1/2)*b^-1//4*arctan(x*b^1//4*(a+b*x^4)^-1//4)+(1/2)*b^-1//4*arctanh(x*b^1//4*(a+b*x^4)^-1//4))
@test integrate(x^-4*(a+b*x^4)^-1//4, x) == :(-1//3*a^-1*x^-3*(a+b*x^4)^3//4)
@test integrate(x^-8*(a+b*x^4)^-1//4, x) == :(-1//7*a^-1*x^-7*(a+b*x^4)^3//4+4//21*b*a^-2*x^-3*(a+b*x^4)^3//4)
@test integrate(x^-12*(a+b*x^4)^-1//4, x) == :(-1//11*a^-1*x^-11*(a+b*x^4)^3//4+-32//231*a^-3*b^2*x^-3*(a+b*x^4)^3//4+8//77*b*a^-2*x^-7*(a+b*x^4)^3//4)
@test integrate(x^-16*(a+b*x^4)^-1//4, x) == :(-1//15*a^-1*x^-15*(a+b*x^4)^3//4+-32//385*a^-3*b^2*x^-7*(a+b*x^4)^3//4+4//55*b*a^-2*x^-11*(a+b*x^4)^3//4+128//1155*a^-4*b^3*x^-3*(a+b*x^4)^3//4)
@test integrate(x^-20*(a+b*x^4)^-1//4, x) == :(-1//19*a^-1*x^-19*(a+b*x^4)^3//4+-2048//21945*a^-5*b^4*x^-3*(a+b*x^4)^3//4+-64//1045*a^-3*b^2*x^-11*(a+b*x^4)^3//4+16//285*b*a^-2*x^-15*(a+b*x^4)^3//4+512//7315*a^-4*b^3*x^-7*(a+b*x^4)^3//4)
@test integrate(x^10*(a+b*x^4)^-1//4, x) == :(1//10*b^-1*x^7*(a+b*x^4)^3//4+-7//60*a*b^-2*x^3*(a+b*x^4)^3//4+7//40*a^2*b^-2*x^3*(a+b*x^4)^-1//4+7//40*x*a^5//2*b^-5//2*(1+a*b^-1*x^-4)^1//4*(a+b*x^4)^-1//4*Elliptic.E((1/2)*arccot(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^6*(a+b*x^4)^-1//4, x) == :(1//6*b^-1*x^3*(a+b*x^4)^3//4+-1//4*a*b^-1*x^3*(a+b*x^4)^-1//4+-1//4*x*a^3//2*b^-3//2*(1+a*b^-1*x^-4)^1//4*(a+b*x^4)^-1//4*Elliptic.E((1/2)*arccot(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^2*(a+b*x^4)^-1//4, x) == :((1/2)*x^3*(a+b*x^4)^-1//4+(1/2)*x*a^(1/2)*b^-1//2*(1+a*b^-1*x^-4)^1//4*(a+b*x^4)^-1//4*Elliptic.E((1/2)*arccot(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^-2*(a+b*x^4)^-1//4, x) == :(-1*x^-1*(a+b*x^4)^-1//4+x*a^-1//2*b^(1/2)*(1+a*b^-1*x^-4)^1//4*(a+b*x^4)^-1//4*Elliptic.E((1/2)*arccot(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^-6*(a+b*x^4)^-1//4, x) == :(-1//5*a^-1*x^-5*(a+b*x^4)^3//4+2//5*b*a^-1*x^-1*(a+b*x^4)^-1//4+-2//5*x*a^-3//2*b^3//2*(1+a*b^-1*x^-4)^1//4*(a+b*x^4)^-1//4*Elliptic.E((1/2)*arccot(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^-10*(a+b*x^4)^-1//4, x) == :(-1//9*a^-1*x^-9*(a+b*x^4)^3//4+-4//15*a^-2*b^2*x^-1*(a+b*x^4)^-1//4+2//15*b*a^-2*x^-5*(a+b*x^4)^3//4+4//15*x*a^-5//2*b^5//2*(1+a*b^-1*x^-4)^1//4*(a+b*x^4)^-1//4*Elliptic.E((1/2)*arccot(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^-14*(a+b*x^4)^-1//4, x) == :(-1//13*a^-1*x^-13*(a+b*x^4)^3//4+-4//39*a^-3*b^2*x^-5*(a+b*x^4)^3//4+8//39*a^-3*b^3*x^-1*(a+b*x^4)^-1//4+10//117*b*a^-2*x^-9*(a+b*x^4)^3//4+-8//39*x*a^-7//2*b^7//2*(1+a*b^-1*x^-4)^1//4*(a+b*x^4)^-1//4*Elliptic.E((1/2)*arccot(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^19*(a+b*x^4)^-3//4, x) == :(1//17*b^-5*(a+b*x^4)^17//4+a^4*b^-5*(a+b*x^4)^1//4+-4//5*a^3*b^-5*(a+b*x^4)^5//4+-4//13*a*b^-5*(a+b*x^4)^13//4+2//3*a^2*b^-5*(a+b*x^4)^9//4)
@test integrate(x^15*(a+b*x^4)^-3//4, x) == :(1//13*b^-4*(a+b*x^4)^13//4+-1*a^3*b^-4*(a+b*x^4)^1//4+-1//3*a*b^-4*(a+b*x^4)^9//4+3//5*a^2*b^-4*(a+b*x^4)^5//4)
@test integrate(x^11*(a+b*x^4)^-3//4, x) == :(1//9*b^-3*(a+b*x^4)^9//4+a^2*b^-3*(a+b*x^4)^1//4+-2//5*a*b^-3*(a+b*x^4)^5//4)
@test integrate(x^7*(a+b*x^4)^-3//4, x) == :(1//5*b^-2*(a+b*x^4)^5//4+-1*a*b^-2*(a+b*x^4)^1//4)
@test integrate(x^3*(a+b*x^4)^-3//4, x) == :(b^-1*(a+b*x^4)^1//4)
@test integrate(x^-1*(a+b*x^4)^-3//4, x) == :(-1//2*a^-3//4*arctan(a^-1//4*(a+b*x^4)^1//4)+-1//2*a^-3//4*arctanh(a^-1//4*(a+b*x^4)^1//4))
@test integrate(x^-5*(a+b*x^4)^-3//4, x) == :(-1//4*a^-1*x^-4*(a+b*x^4)^1//4+3//8*b*a^-7//4*arctan(a^-1//4*(a+b*x^4)^1//4)+3//8*b*a^-7//4*arctanh(a^-1//4*(a+b*x^4)^1//4))
@test integrate(x^-9*(a+b*x^4)^-3//4, x) == :(-21//64*a^-11//4*b^2*arctan(a^-1//4*(a+b*x^4)^1//4)+-21//64*a^-11//4*b^2*arctanh(a^-1//4*(a+b*x^4)^1//4)+-1//8*a^-1*x^-8*(a+b*x^4)^1//4+7//32*b*a^-2*x^-4*(a+b*x^4)^1//4)
@test integrate(x^13*(a+b*x^4)^-3//4, x) == :(1//11*b^-1*x^10*(a+b*x^4)^1//4+-10//77*a*b^-2*x^6*(a+b*x^4)^1//4+20//77*a^2*b^-3*x^2*(a+b*x^4)^1//4+-40//77*a^7//2*b^-7//2*(1+b*a^-1*x^4)^3//4*(a+b*x^4)^-3//4*Elliptic.F((1/2)*arctan(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^9*(a+b*x^4)^-3//4, x) == :(1//7*b^-1*x^6*(a+b*x^4)^1//4+-2//7*a*b^-2*x^2*(a+b*x^4)^1//4+4//7*a^5//2*b^-5//2*(1+b*a^-1*x^4)^3//4*(a+b*x^4)^-3//4*Elliptic.F((1/2)*arctan(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^5*(a+b*x^4)^-3//4, x) == :(1//3*b^-1*x^2*(a+b*x^4)^1//4+-2//3*a^3//2*b^-3//2*(1+b*a^-1*x^4)^3//4*(a+b*x^4)^-3//4*Elliptic.F((1/2)*arctan(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x*(a+b*x^4)^-3//4, x) == :(a^(1/2)*b^-1//2*(1+b*a^-1*x^4)^3//4*(a+b*x^4)^-3//4*Elliptic.F((1/2)*arctan(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^-3*(a+b*x^4)^-3//4, x) == :(-1//2*a^-1*x^-2*(a+b*x^4)^1//4+-1//2*a^-1//2*b^(1/2)*(1+b*a^-1*x^4)^3//4*(a+b*x^4)^-3//4*Elliptic.F((1/2)*arctan(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^-7*(a+b*x^4)^-3//4, x) == :(-1//6*a^-1*x^-6*(a+b*x^4)^1//4+5//12*b*a^-2*x^-2*(a+b*x^4)^1//4+5//12*a^-3//2*b^3//2*(1+b*a^-1*x^4)^3//4*(a+b*x^4)^-3//4*Elliptic.F((1/2)*arctan(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^-11*(a+b*x^4)^-3//4, x) == :(-1//10*a^-1*x^-10*(a+b*x^4)^1//4+-3//8*a^-3*b^2*x^-2*(a+b*x^4)^1//4+3//20*b*a^-2*x^-6*(a+b*x^4)^1//4+-3//8*a^-5//2*b^5//2*(1+b*a^-1*x^4)^3//4*(a+b*x^4)^-3//4*Elliptic.F((1/2)*arctan(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^10*(a+b*x^4)^-3//4, x) == :(-21//64*a^2*b^-11//4*arctan(x*b^1//4*(a+b*x^4)^-1//4)+1//8*b^-1*x^7*(a+b*x^4)^1//4+21//64*a^2*b^-11//4*arctanh(x*b^1//4*(a+b*x^4)^-1//4)+-7//32*a*b^-2*x^3*(a+b*x^4)^1//4)
@test integrate(x^6*(a+b*x^4)^-3//4, x) == :(-3//8*a*b^-7//4*arctanh(x*b^1//4*(a+b*x^4)^-1//4)+1//4*b^-1*x^3*(a+b*x^4)^1//4+3//8*a*b^-7//4*arctan(x*b^1//4*(a+b*x^4)^-1//4))
@test integrate(x^2*(a+b*x^4)^-3//4, x) == :((1/2)*b^-3//4*arctanh(x*b^1//4*(a+b*x^4)^-1//4)+-1//2*b^-3//4*arctan(x*b^1//4*(a+b*x^4)^-1//4))
@test integrate(x^-2*(a+b*x^4)^-3//4, x) == :(-1*a^-1*x^-1*(a+b*x^4)^1//4)
@test integrate(x^-6*(a+b*x^4)^-3//4, x) == :(-1//5*a^-1*x^-5*(a+b*x^4)^1//4+4//5*b*a^-2*x^-1*(a+b*x^4)^1//4)
@test integrate(x^-10*(a+b*x^4)^-3//4, x) == :(-1//9*a^-1*x^-9*(a+b*x^4)^1//4+-32//45*a^-3*b^2*x^-1*(a+b*x^4)^1//4+8//45*b*a^-2*x^-5*(a+b*x^4)^1//4)
@test integrate(x^-14*(a+b*x^4)^-3//4, x) == :(-1//13*a^-1*x^-13*(a+b*x^4)^1//4+-32//195*a^-3*b^2*x^-5*(a+b*x^4)^1//4+4//39*b*a^-2*x^-9*(a+b*x^4)^1//4+128//195*a^-4*b^3*x^-1*(a+b*x^4)^1//4)
@test integrate(x^12*(a+b*x^4)^-3//4, x) == :(1//10*b^-1*x^9*(a+b*x^4)^1//4+-3//20*a*b^-2*x^5*(a+b*x^4)^1//4+3//8*x*a^2*b^-3*(a+b*x^4)^1//4+3//8*a^5//2*b^-5//2*x^3*(1+a*b^-1*x^-4)^3//4*(a+b*x^4)^-3//4*Elliptic.F((1/2)*arccot(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^8*(a+b*x^4)^-3//4, x) == :(1//6*b^-1*x^5*(a+b*x^4)^1//4+-5//12*a*x*b^-2*(a+b*x^4)^1//4+-5//12*a^3//2*b^-3//2*x^3*(1+a*b^-1*x^-4)^3//4*(a+b*x^4)^-3//4*Elliptic.F((1/2)*arccot(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^4*(a+b*x^4)^-3//4, x) == :((1/2)*x*b^-1*(a+b*x^4)^1//4+(1/2)*a^(1/2)*b^-1//2*x^3*(1+a*b^-1*x^-4)^3//4*(a+b*x^4)^-3//4*Elliptic.F((1/2)*arccot(a^-1//2*b^(1/2)*x^2),2))
@test integrate((a+b*x^4)^-3//4, x) == :(-1*a^-1//2*b^(1/2)*x^3*(1+a*b^-1*x^-4)^3//4*(a+b*x^4)^-3//4*Elliptic.F((1/2)*arccot(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^-4*(a+b*x^4)^-3//4, x) == :(-1//3*a^-1*x^-3*(a+b*x^4)^1//4+2//3*a^-3//2*b^3//2*x^3*(1+a*b^-1*x^-4)^3//4*(a+b*x^4)^-3//4*Elliptic.F((1/2)*arccot(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^-8*(a+b*x^4)^-3//4, x) == :(-1//7*a^-1*x^-7*(a+b*x^4)^1//4+2//7*b*a^-2*x^-3*(a+b*x^4)^1//4+-4//7*a^-5//2*b^5//2*x^3*(1+a*b^-1*x^-4)^3//4*(a+b*x^4)^-3//4*Elliptic.F((1/2)*arccot(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^-12*(a+b*x^4)^-3//4, x) == :(-1//11*a^-1*x^-11*(a+b*x^4)^1//4+-20//77*a^-3*b^2*x^-3*(a+b*x^4)^1//4+10//77*b*a^-2*x^-7*(a+b*x^4)^1//4+40//77*a^-7//2*b^7//2*x^3*(1+a*b^-1*x^-4)^3//4*(a+b*x^4)^-3//4*Elliptic.F((1/2)*arccot(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^19*(a+b*x^4)^-5//4, x) == :(1//15*b^-5*(a+b*x^4)^15//4+-1*a^4*b^-5*(a+b*x^4)^-1//4+-4//3*a^3*b^-5*(a+b*x^4)^3//4+-4//11*a*b^-5*(a+b*x^4)^11//4+6//7*a^2*b^-5*(a+b*x^4)^7//4)
@test integrate(x^15*(a+b*x^4)^-5//4, x) == :(1//11*b^-4*(a+b*x^4)^11//4+a^2*b^-4*(a+b*x^4)^3//4+a^3*b^-4*(a+b*x^4)^-1//4+-3//7*a*b^-4*(a+b*x^4)^7//4)
@test integrate(x^11*(a+b*x^4)^-5//4, x) == :(1//7*b^-3*(a+b*x^4)^7//4+-1*a^2*b^-3*(a+b*x^4)^-1//4+-2//3*a*b^-3*(a+b*x^4)^3//4)
@test integrate(x^7*(a+b*x^4)^-5//4, x) == :(1//3*b^-2*(a+b*x^4)^3//4+a*b^-2*(a+b*x^4)^-1//4)
@test integrate(x^3*(a+b*x^4)^-5//4, x) == :(-1*b^-1*(a+b*x^4)^-1//4)
@test integrate(x^-1*(a+b*x^4)^-5//4, x) == :(a^-1*(a+b*x^4)^-1//4+(1/2)*a^-5//4*arctan(a^-1//4*(a+b*x^4)^1//4)+-1//2*a^-5//4*arctanh(a^-1//4*(a+b*x^4)^1//4))
@test integrate(x^-5*(a+b*x^4)^-5//4, x) == :(-5//4*b*a^-2*(a+b*x^4)^-1//4+-5//8*b*a^-9//4*arctan(a^-1//4*(a+b*x^4)^1//4)+-1//4*a^-1*x^-4*(a+b*x^4)^-1//4+5//8*b*a^-9//4*arctanh(a^-1//4*(a+b*x^4)^1//4))
@test integrate(x^-9*(a+b*x^4)^-5//4, x) == :(-45//64*a^-13//4*b^2*arctanh(a^-1//4*(a+b*x^4)^1//4)+-1//8*a^-1*x^-8*(a+b*x^4)^-1//4+45//32*a^-3*b^2*(a+b*x^4)^-1//4+45//64*a^-13//4*b^2*arctan(a^-1//4*(a+b*x^4)^1//4)+9//32*b*a^-2*x^-4*(a+b*x^4)^-1//4)
@test integrate(x^13*(a+b*x^4)^-5//4, x) == :(1//9*b^-1*x^10*(a+b*x^4)^-1//4+-2//9*a*b^-2*x^6*(a+b*x^4)^-1//4+4//3*a^2*b^-3*x^2*(a+b*x^4)^-1//4+-8//3*a^5//2*b^-7//2*(1+b*a^-1*x^4)^1//4*(a+b*x^4)^-1//4*Elliptic.E((1/2)*arctan(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^9*(a+b*x^4)^-5//4, x) == :(1//5*b^-1*x^6*(a+b*x^4)^-1//4+-6//5*a*b^-2*x^2*(a+b*x^4)^-1//4+12//5*a^3//2*b^-5//2*(1+b*a^-1*x^4)^1//4*(a+b*x^4)^-1//4*Elliptic.E((1/2)*arctan(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^5*(a+b*x^4)^-5//4, x) == :(b^-1*x^2*(a+b*x^4)^-1//4+-2*a^(1/2)*b^-3//2*(1+b*a^-1*x^4)^1//4*(a+b*x^4)^-1//4*Elliptic.E((1/2)*arctan(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x*(a+b*x^4)^-5//4, x) == :(a^-1//2*b^-1//2*(1+b*a^-1*x^4)^1//4*(a+b*x^4)^-1//4*Elliptic.E((1/2)*arctan(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^-3*(a+b*x^4)^-5//4, x) == :(-1//2*a^-1*x^-2*(a+b*x^4)^-1//4+-3//2*a^-3//2*b^(1/2)*(1+b*a^-1*x^4)^1//4*(a+b*x^4)^-1//4*Elliptic.E((1/2)*arctan(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^-7*(a+b*x^4)^-5//4, x) == :(-1//6*a^-1*x^-6*(a+b*x^4)^-1//4+7//12*b*a^-2*x^-2*(a+b*x^4)^-1//4+7//4*a^-5//2*b^3//2*(1+b*a^-1*x^4)^1//4*(a+b*x^4)^-1//4*Elliptic.E((1/2)*arctan(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^-11*(a+b*x^4)^-5//4, x) == :(-1//10*a^-1*x^-10*(a+b*x^4)^-1//4+-77//120*a^-3*b^2*x^-2*(a+b*x^4)^-1//4+11//60*b*a^-2*x^-6*(a+b*x^4)^-1//4+-77//40*a^-7//2*b^5//2*(1+b*a^-1*x^4)^1//4*(a+b*x^4)^-1//4*Elliptic.E((1/2)*arctan(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^12*(a+b*x^4)^-5//4, x) == :(-1*b^-1*x^9*(a+b*x^4)^-1//4+9//8*b^-2*x^5*(a+b*x^4)^3//4+45//64*a^2*b^-13//4*arctan(x*b^1//4*(a+b*x^4)^-1//4)+45//64*a^2*b^-13//4*arctanh(x*b^1//4*(a+b*x^4)^-1//4)+-45//32*a*x*b^-3*(a+b*x^4)^3//4)
@test integrate(x^8*(a+b*x^4)^-5//4, x) == :(-1*b^-1*x^5*(a+b*x^4)^-1//4+-5//8*a*b^-9//4*arctan(x*b^1//4*(a+b*x^4)^-1//4)+-5//8*a*b^-9//4*arctanh(x*b^1//4*(a+b*x^4)^-1//4)+5//4*x*b^-2*(a+b*x^4)^3//4)
@test integrate(x^4*(a+b*x^4)^-5//4, x) == :((1/2)*b^-5//4*arctan(x*b^1//4*(a+b*x^4)^-1//4)+(1/2)*b^-5//4*arctanh(x*b^1//4*(a+b*x^4)^-1//4)+-1*x*b^-1*(a+b*x^4)^-1//4)
@test integrate((a+b*x^4)^-5//4, x) == :(x*a^-1*(a+b*x^4)^-1//4)
@test integrate(x^-4*(a+b*x^4)^-5//4, x) == :(-1//3*a^-1*x^-3*(a+b*x^4)^-1//4+-4//3*b*x*a^-2*(a+b*x^4)^-1//4)
@test integrate(x^-8*(a+b*x^4)^-5//4, x) == :(-1//7*a^-1*x^-7*(a+b*x^4)^-1//4+8//21*b*a^-2*x^-3*(a+b*x^4)^-1//4+32//21*x*a^-3*b^2*(a+b*x^4)^-1//4)
@test integrate(x^-12*(a+b*x^4)^-5//4, x) == :(-1//11*a^-1*x^-11*(a+b*x^4)^-1//4+-128//77*x*a^-4*b^3*(a+b*x^4)^-1//4+-32//77*a^-3*b^2*x^-3*(a+b*x^4)^-1//4+12//77*b*a^-2*x^-7*(a+b*x^4)^-1//4)
@test integrate(x^-16*(a+b*x^4)^-5//4, x) == :(-1//15*a^-1*x^-15*(a+b*x^4)^-1//4+-64//385*a^-3*b^2*x^-7*(a+b*x^4)^-1//4+16//165*b*a^-2*x^-11*(a+b*x^4)^-1//4+512//1155*a^-4*b^3*x^-3*(a+b*x^4)^-1//4+2048//1155*x*a^-5*b^4*(a+b*x^4)^-1//4)
@test integrate(x^14*(a+b*x^4)^-5//4, x) == :(1//10*b^-1*x^11*(a+b*x^4)^-1//4+-11//60*a*b^-2*x^7*(a+b*x^4)^-1//4+77//120*a^2*b^-3*x^3*(a+b*x^4)^-1//4+77//40*x*a^5//2*b^-7//2*(1+a*b^-1*x^-4)^1//4*(a+b*x^4)^-1//4*Elliptic.E((1/2)*arccot(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^10*(a+b*x^4)^-5//4, x) == :(1//6*b^-1*x^7*(a+b*x^4)^-1//4+-7//12*a*b^-2*x^3*(a+b*x^4)^-1//4+-7//4*x*a^3//2*b^-5//2*(1+a*b^-1*x^-4)^1//4*(a+b*x^4)^-1//4*Elliptic.E((1/2)*arccot(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^6*(a+b*x^4)^-5//4, x) == :((1/2)*b^-1*x^3*(a+b*x^4)^-1//4+3//2*x*a^(1/2)*b^-3//2*(1+a*b^-1*x^-4)^1//4*(a+b*x^4)^-1//4*Elliptic.E((1/2)*arccot(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^2*(a+b*x^4)^-5//4, x) == :(-1*x*a^-1//2*b^-1//2*(1+a*b^-1*x^-4)^1//4*(a+b*x^4)^-1//4*Elliptic.E((1/2)*arccot(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^-2*(a+b*x^4)^-5//4, x) == :(-1*a^-1*x^-1*(a+b*x^4)^-1//4+2*x*a^-3//2*b^(1/2)*(1+a*b^-1*x^-4)^1//4*(a+b*x^4)^-1//4*Elliptic.E((1/2)*arccot(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^-6*(a+b*x^4)^-5//4, x) == :(-1//5*a^-1*x^-5*(a+b*x^4)^-1//4+6//5*b*a^-2*x^-1*(a+b*x^4)^-1//4+-12//5*x*a^-5//2*b^3//2*(1+a*b^-1*x^-4)^1//4*(a+b*x^4)^-1//4*Elliptic.E((1/2)*arccot(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^-10*(a+b*x^4)^-5//4, x) == :(-1//9*a^-1*x^-9*(a+b*x^4)^-1//4+-4//3*a^-3*b^2*x^-1*(a+b*x^4)^-1//4+2//9*b*a^-2*x^-5*(a+b*x^4)^-1//4+8//3*x*a^-7//2*b^5//2*(1+a*b^-1*x^-4)^1//4*(a+b*x^4)^-1//4*Elliptic.E((1/2)*arccot(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^-14*(a+b*x^4)^-5//4, x) == :(-1//13*a^-1*x^-13*(a+b*x^4)^-1//4+-28//117*a^-3*b^2*x^-5*(a+b*x^4)^-1//4+14//117*b*a^-2*x^-9*(a+b*x^4)^-1//4+56//39*a^-4*b^3*x^-1*(a+b*x^4)^-1//4+-112//39*x*a^-9//2*b^7//2*(1+a*b^-1*x^-4)^1//4*(a+b*x^4)^-1//4*Elliptic.E((1/2)*arccot(a^-1//2*b^(1/2)*x^2),2))
@test integrate((a+b*x^4)^-7//4, x) == :(1//3*x*a^-1*(a+b*x^4)^-3//4+-2//3*a^-3//2*b^(1/2)*x^3*(1+a*b^-1*x^-4)^3//4*(a+b*x^4)^-3//4*Elliptic.F((1/2)*arccot(a^-1//2*b^(1/2)*x^2),2))
@test integrate((a+b*x^4)^-9//4, x) == :(1//5*x*a^-1*(a+b*x^4)^-5//4+4//5*x*a^-2*(a+b*x^4)^-1//4)
@test integrate((a+b*x^4)^-11//4, x) == :(1//7*x*a^-1*(a+b*x^4)^-7//4+2//7*x*a^-2*(a+b*x^4)^-3//4+-4//7*a^-5//2*b^(1/2)*x^3*(1+a*b^-1*x^-4)^3//4*(a+b*x^4)^-3//4*Elliptic.F((1/2)*arccot(a^-1//2*b^(1/2)*x^2),2))
@test integrate((a+b*x^4)^-13//4, x) == :(1//9*x*a^-1*(a+b*x^4)^-9//4+8//45*x*a^-2*(a+b*x^4)^-5//4+32//45*x*a^-3*(a+b*x^4)^-1//4)
@test integrate((a+b*x^4)^-17//4, x) == :(1//13*x*a^-1*(a+b*x^4)^-13//4+4//39*x*a^-2*(a+b*x^4)^-9//4+32//195*x*a^-3*(a+b*x^4)^-5//4+128//195*x*a^-4*(a+b*x^4)^-1//4)
@test integrate(x^19*(a+-1*b*x^4)^1//4, x) == :(-1//21*b^-5*(a+-1*b*x^4)^21//4+-6//13*a^2*b^-5*(a+-1*b*x^4)^13//4+-1//5*a^4*b^-5*(a+-1*b*x^4)^5//4+4//9*a^3*b^-5*(a+-1*b*x^4)^9//4+4//17*a*b^-5*(a+-1*b*x^4)^17//4)
@test integrate(x^15*(a+-1*b*x^4)^1//4, x) == :(1//17*b^-4*(a+-1*b*x^4)^17//4+-3//13*a*b^-4*(a+-1*b*x^4)^13//4+-1//5*a^3*b^-4*(a+-1*b*x^4)^5//4+1//3*a^2*b^-4*(a+-1*b*x^4)^9//4)
@test integrate(x^11*(a+-1*b*x^4)^1//4, x) == :(-1//13*b^-3*(a+-1*b*x^4)^13//4+-1//5*a^2*b^-3*(a+-1*b*x^4)^5//4+2//9*a*b^-3*(a+-1*b*x^4)^9//4)
@test integrate(x^7*(a+-1*b*x^4)^1//4, x) == :(1//9*b^-2*(a+-1*b*x^4)^9//4+-1//5*a*b^-2*(a+-1*b*x^4)^5//4)
@test integrate(x^3*(a+-1*b*x^4)^1//4, x) == :(-1//5*b^-1*(a+-1*b*x^4)^5//4)
@test integrate(x^-1*(a+-1*b*x^4)^1//4, x) == :((a+-1*b*x^4)^1//4+-1//2*a^1//4*arctan(a^-1//4*(a+-1*b*x^4)^1//4)+-1//2*a^1//4*arctanh(a^-1//4*(a+-1*b*x^4)^1//4))
@test integrate(x^-5*(a+-1*b*x^4)^1//4, x) == :(-1//4*x^-4*(a+-1*b*x^4)^1//4+1//8*b*a^-3//4*arctan(a^-1//4*(a+-1*b*x^4)^1//4)+1//8*b*a^-3//4*arctanh(a^-1//4*(a+-1*b*x^4)^1//4))
@test integrate(x^-9*(a+-1*b*x^4)^1//4, x) == :(-1//8*x^-8*(a+-1*b*x^4)^1//4+3//64*a^-7//4*b^2*arctan(a^-1//4*(a+-1*b*x^4)^1//4)+3//64*a^-7//4*b^2*arctanh(a^-1//4*(a+-1*b*x^4)^1//4)+1//32*b*a^-1*x^-4*(a+-1*b*x^4)^1//4)
@test integrate(x^9*(a+-1*b*x^4)^1//4, x) == :(1//11*x^10*(a+-1*b*x^4)^1//4+-2//77*a^2*b^-2*x^2*(a+-1*b*x^4)^1//4+-1//77*a*b^-1*x^6*(a+-1*b*x^4)^1//4+4//77*a^7//2*b^-5//2*(1+-1*b*a^-1*x^4)^3//4*(a+-1*b*x^4)^-3//4*Elliptic.F((1/2)*arcsin(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^5*(a+-1*b*x^4)^1//4, x) == :(1//7*x^6*(a+-1*b*x^4)^1//4+-1//21*a*b^-1*x^2*(a+-1*b*x^4)^1//4+2//21*a^5//2*b^-3//2*(1+-1*b*a^-1*x^4)^3//4*(a+-1*b*x^4)^-3//4*Elliptic.F((1/2)*arcsin(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x*(a+-1*b*x^4)^1//4, x) == :(1//3*x^2*(a+-1*b*x^4)^1//4+1//3*a^3//2*b^-1//2*(1+-1*b*a^-1*x^4)^3//4*(a+-1*b*x^4)^-3//4*Elliptic.F((1/2)*arcsin(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^-3*(a+-1*b*x^4)^1//4, x) == :(-1//2*x^-2*(a+-1*b*x^4)^1//4+-1//2*a^(1/2)*b^(1/2)*(1+-1*b*a^-1*x^4)^3//4*(a+-1*b*x^4)^-3//4*Elliptic.F((1/2)*arcsin(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^-7*(a+-1*b*x^4)^1//4, x) == :(-1//6*x^-6*(a+-1*b*x^4)^1//4+1//12*b*a^-1*x^-2*(a+-1*b*x^4)^1//4+-1//12*a^-1//2*b^3//2*(1+-1*b*a^-1*x^4)^3//4*(a+-1*b*x^4)^-3//4*Elliptic.F((1/2)*arcsin(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^-11*(a+-1*b*x^4)^1//4, x) == :(-1//10*x^-10*(a+-1*b*x^4)^1//4+1//24*a^-2*b^2*x^-2*(a+-1*b*x^4)^1//4+1//60*b*a^-1*x^-6*(a+-1*b*x^4)^1//4+-1//24*a^-3//2*b^5//2*(1+-1*b*a^-1*x^4)^3//4*(a+-1*b*x^4)^-3//4*Elliptic.F((1/2)*arcsin(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^6*(a+-1*b*x^4)^1//4, x) == :(1//8*x^7*(a+-1*b*x^4)^1//4+-3//128*2^(1/2)*a^2*b^-7//4*arctan(1+-1*x*2^(1/2)*b^1//4*(a+-1*b*x^4)^-1//4)+-3//256*2^(1/2)*a^2*b^-7//4*log(1+b^(1/2)*x^2*(a+-1*b*x^4)^-1//2+x*2^(1/2)*b^1//4*(a+-1*b*x^4)^-1//4)+-1//32*a*b^-1*x^3*(a+-1*b*x^4)^1//4+3//128*2^(1/2)*a^2*b^-7//4*arctan(1+x*2^(1/2)*b^1//4*(a+-1*b*x^4)^-1//4)+3//256*2^(1/2)*a^2*b^-7//4*log(1+b^(1/2)*x^2*(a+-1*b*x^4)^-1//2+-1*x*2^(1/2)*b^1//4*(a+-1*b*x^4)^-1//4))
@test integrate(x^2*(a+-1*b*x^4)^1//4, x) == :(1//4*x^3*(a+-1*b*x^4)^1//4+-1//16*a*2^(1/2)*b^-3//4*arctan(1+-1*x*2^(1/2)*b^1//4*(a+-1*b*x^4)^-1//4)+-1//32*a*2^(1/2)*b^-3//4*log(1+b^(1/2)*x^2*(a+-1*b*x^4)^-1//2+x*2^(1/2)*b^1//4*(a+-1*b*x^4)^-1//4)+1//16*a*2^(1/2)*b^-3//4*arctan(1+x*2^(1/2)*b^1//4*(a+-1*b*x^4)^-1//4)+1//32*a*2^(1/2)*b^-3//4*log(1+b^(1/2)*x^2*(a+-1*b*x^4)^-1//2+-1*x*2^(1/2)*b^1//4*(a+-1*b*x^4)^-1//4))
@test integrate(x^-2*(a+-1*b*x^4)^1//4, x) == :(-1*x^-1*(a+-1*b*x^4)^1//4+-1//4*2^(1/2)*b^1//4*arctan(1+x*2^(1/2)*b^1//4*(a+-1*b*x^4)^-1//4)+-1//8*2^(1/2)*b^1//4*log(1+b^(1/2)*x^2*(a+-1*b*x^4)^-1//2+-1*x*2^(1/2)*b^1//4*(a+-1*b*x^4)^-1//4)+1//4*2^(1/2)*b^1//4*arctan(1+-1*x*2^(1/2)*b^1//4*(a+-1*b*x^4)^-1//4)+1//8*2^(1/2)*b^1//4*log(1+b^(1/2)*x^2*(a+-1*b*x^4)^-1//2+x*2^(1/2)*b^1//4*(a+-1*b*x^4)^-1//4))
@test integrate(x^-6*(a+-1*b*x^4)^1//4, x) == :(-1//5*a^-1*x^-5*(a+-1*b*x^4)^5//4)
@test integrate(x^-10*(a+-1*b*x^4)^1//4, x) == :(-1//9*a^-1*x^-9*(a+-1*b*x^4)^5//4+-4//45*b*a^-2*x^-5*(a+-1*b*x^4)^5//4)
@test integrate(x^-14*(a+-1*b*x^4)^1//4, x) == :(-1//13*a^-1*x^-13*(a+-1*b*x^4)^5//4+-32//585*a^-3*b^2*x^-5*(a+-1*b*x^4)^5//4+-8//117*b*a^-2*x^-9*(a+-1*b*x^4)^5//4)
@test integrate(x^-18*(a+-1*b*x^4)^1//4, x) == :(-1//17*a^-1*x^-17*(a+-1*b*x^4)^5//4+-128//3315*a^-4*b^3*x^-5*(a+-1*b*x^4)^5//4+-32//663*a^-3*b^2*x^-9*(a+-1*b*x^4)^5//4+-12//221*b*a^-2*x^-13*(a+-1*b*x^4)^5//4)
@test integrate(x^12*(a+-1*b*x^4)^1//4, x) == :(1//14*x^13*(a+-1*b*x^4)^1//4+-3//112*x*a^3*b^-3*(a+-1*b*x^4)^1//4+-3//280*a^2*b^-2*x^5*(a+-1*b*x^4)^1//4+-1//140*a*b^-1*x^9*(a+-1*b*x^4)^1//4+-3//112*a^7//2*b^-5//2*x^3*(1+-1*a*b^-1*x^-4)^3//4*(a+-1*b*x^4)^-3//4*Elliptic.F((1/2)*arccsc(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^8*(a+-1*b*x^4)^1//4, x) == :(1//10*x^9*(a+-1*b*x^4)^1//4+-1//24*x*a^2*b^-2*(a+-1*b*x^4)^1//4+-1//60*a*b^-1*x^5*(a+-1*b*x^4)^1//4+-1//24*a^5//2*b^-3//2*x^3*(1+-1*a*b^-1*x^-4)^3//4*(a+-1*b*x^4)^-3//4*Elliptic.F((1/2)*arccsc(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^4*(a+-1*b*x^4)^1//4, x) == :(1//6*x^5*(a+-1*b*x^4)^1//4+-1//12*a*x*b^-1*(a+-1*b*x^4)^1//4+-1//12*a^3//2*b^-1//2*x^3*(1+-1*a*b^-1*x^-4)^3//4*(a+-1*b*x^4)^-3//4*Elliptic.F((1/2)*arccsc(a^-1//2*b^(1/2)*x^2),2))
@test integrate((a+-1*b*x^4)^1//4, x) == :((1/2)*x*(a+-1*b*x^4)^1//4+-1//2*a^(1/2)*b^(1/2)*x^3*(1+-1*a*b^-1*x^-4)^3//4*(a+-1*b*x^4)^-3//4*Elliptic.F((1/2)*arccsc(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^-4*(a+-1*b*x^4)^1//4, x) == :(-1//3*x^-3*(a+-1*b*x^4)^1//4+1//3*a^-1//2*b^3//2*x^3*(1+-1*a*b^-1*x^-4)^3//4*(a+-1*b*x^4)^-3//4*Elliptic.F((1/2)*arccsc(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^-8*(a+-1*b*x^4)^1//4, x) == :(-1//7*x^-7*(a+-1*b*x^4)^1//4+1//21*b*a^-1*x^-3*(a+-1*b*x^4)^1//4+2//21*a^-3//2*b^5//2*x^3*(1+-1*a*b^-1*x^-4)^3//4*(a+-1*b*x^4)^-3//4*Elliptic.F((1/2)*arccsc(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^-12*(a+-1*b*x^4)^1//4, x) == :(-1//11*x^-11*(a+-1*b*x^4)^1//4+1//77*b*a^-1*x^-7*(a+-1*b*x^4)^1//4+2//77*a^-2*b^2*x^-3*(a+-1*b*x^4)^1//4+4//77*a^-5//2*b^7//2*x^3*(1+-1*a*b^-1*x^-4)^3//4*(a+-1*b*x^4)^-3//4*Elliptic.F((1/2)*arccsc(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^-16*(a+-1*b*x^4)^1//4, x) == :(-1//15*x^-15*(a+-1*b*x^4)^1//4+1//165*b*a^-1*x^-11*(a+-1*b*x^4)^1//4+2//231*a^-2*b^2*x^-7*(a+-1*b*x^4)^1//4+4//231*a^-3*b^3*x^-3*(a+-1*b*x^4)^1//4+8//231*a^-7//2*b^9//2*x^3*(1+-1*a*b^-1*x^-4)^3//4*(a+-1*b*x^4)^-3//4*Elliptic.F((1/2)*arccsc(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^19*(a+-1*b*x^4)^-1//4, x) == :(-1//19*b^-5*(a+-1*b*x^4)^19//4+-6//11*a^2*b^-5*(a+-1*b*x^4)^11//4+-1//3*a^4*b^-5*(a+-1*b*x^4)^3//4+4//7*a^3*b^-5*(a+-1*b*x^4)^7//4+4//15*a*b^-5*(a+-1*b*x^4)^15//4)
@test integrate(x^15*(a+-1*b*x^4)^-1//4, x) == :(1//15*b^-4*(a+-1*b*x^4)^15//4+-3//11*a*b^-4*(a+-1*b*x^4)^11//4+-1//3*a^3*b^-4*(a+-1*b*x^4)^3//4+3//7*a^2*b^-4*(a+-1*b*x^4)^7//4)
@test integrate(x^11*(a+-1*b*x^4)^-1//4, x) == :(-1//11*b^-3*(a+-1*b*x^4)^11//4+-1//3*a^2*b^-3*(a+-1*b*x^4)^3//4+2//7*a*b^-3*(a+-1*b*x^4)^7//4)
@test integrate(x^7*(a+-1*b*x^4)^-1//4, x) == :(1//7*b^-2*(a+-1*b*x^4)^7//4+-1//3*a*b^-2*(a+-1*b*x^4)^3//4)
@test integrate(x^3*(a+-1*b*x^4)^-1//4, x) == :(-1//3*b^-1*(a+-1*b*x^4)^3//4)
@test integrate(x^-1*(a+-1*b*x^4)^-1//4, x) == :((1/2)*a^-1//4*arctan(a^-1//4*(a+-1*b*x^4)^1//4)+-1//2*a^-1//4*arctanh(a^-1//4*(a+-1*b*x^4)^1//4))
@test integrate(x^-5*(a+-1*b*x^4)^-1//4, x) == :(-1//4*a^-1*x^-4*(a+-1*b*x^4)^3//4+-1//8*b*a^-5//4*arctanh(a^-1//4*(a+-1*b*x^4)^1//4)+1//8*b*a^-5//4*arctan(a^-1//4*(a+-1*b*x^4)^1//4))
@test integrate(x^-9*(a+-1*b*x^4)^-1//4, x) == :(-5//64*a^-9//4*b^2*arctanh(a^-1//4*(a+-1*b*x^4)^1//4)+-1//8*a^-1*x^-8*(a+-1*b*x^4)^3//4+5//64*a^-9//4*b^2*arctan(a^-1//4*(a+-1*b*x^4)^1//4)+-5//32*b*a^-2*x^-4*(a+-1*b*x^4)^3//4)
@test integrate(x^13*(a+-1*b*x^4)^-1//4, x) == :(-1//13*b^-1*x^10*(a+-1*b*x^4)^3//4+-10//117*a*b^-2*x^6*(a+-1*b*x^4)^3//4+-4//39*a^2*b^-3*x^2*(a+-1*b*x^4)^3//4+8//39*a^7//2*b^-7//2*(1+-1*b*a^-1*x^4)^1//4*(a+-1*b*x^4)^-1//4*Elliptic.E((1/2)*arcsin(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^9*(a+-1*b*x^4)^-1//4, x) == :(-1//9*b^-1*x^6*(a+-1*b*x^4)^3//4+-2//15*a*b^-2*x^2*(a+-1*b*x^4)^3//4+4//15*a^5//2*b^-5//2*(1+-1*b*a^-1*x^4)^1//4*(a+-1*b*x^4)^-1//4*Elliptic.E((1/2)*arcsin(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^5*(a+-1*b*x^4)^-1//4, x) == :(-1//5*b^-1*x^2*(a+-1*b*x^4)^3//4+2//5*a^3//2*b^-3//2*(1+-1*b*a^-1*x^4)^1//4*(a+-1*b*x^4)^-1//4*Elliptic.E((1/2)*arcsin(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x*(a+-1*b*x^4)^-1//4, x) == :(a^(1/2)*b^-1//2*(1+-1*b*a^-1*x^4)^1//4*(a+-1*b*x^4)^-1//4*Elliptic.E((1/2)*arcsin(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^-3*(a+-1*b*x^4)^-1//4, x) == :(-1//2*a^-1*x^-2*(a+-1*b*x^4)^3//4+-1//2*a^-1//2*b^(1/2)*(1+-1*b*a^-1*x^4)^1//4*(a+-1*b*x^4)^-1//4*Elliptic.E((1/2)*arcsin(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^-7*(a+-1*b*x^4)^-1//4, x) == :(-1//6*a^-1*x^-6*(a+-1*b*x^4)^3//4+-1//4*b*a^-2*x^-2*(a+-1*b*x^4)^3//4+-1//4*a^-3//2*b^3//2*(1+-1*b*a^-1*x^4)^1//4*(a+-1*b*x^4)^-1//4*Elliptic.E((1/2)*arcsin(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^-11*(a+-1*b*x^4)^-1//4, x) == :(-1//10*a^-1*x^-10*(a+-1*b*x^4)^3//4+-7//40*a^-3*b^2*x^-2*(a+-1*b*x^4)^3//4+-7//60*b*a^-2*x^-6*(a+-1*b*x^4)^3//4+-7//40*a^-5//2*b^5//2*(1+-1*b*a^-1*x^4)^1//4*(a+-1*b*x^4)^-1//4*Elliptic.E((1/2)*arcsin(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^8*(a+-1*b*x^4)^-1//4, x) == :(-1//8*b^-1*x^5*(a+-1*b*x^4)^3//4+-5//32*a*x*b^-2*(a+-1*b*x^4)^3//4+-5//128*2^(1/2)*a^2*b^-9//4*arctan(1+-1*x*2^(1/2)*b^1//4*(a+-1*b*x^4)^-1//4)+-5//256*2^(1/2)*a^2*b^-9//4*log(1+b^(1/2)*x^2*(a+-1*b*x^4)^-1//2+-1*x*2^(1/2)*b^1//4*(a+-1*b*x^4)^-1//4)+5//128*2^(1/2)*a^2*b^-9//4*arctan(1+x*2^(1/2)*b^1//4*(a+-1*b*x^4)^-1//4)+5//256*2^(1/2)*a^2*b^-9//4*log(1+b^(1/2)*x^2*(a+-1*b*x^4)^-1//2+x*2^(1/2)*b^1//4*(a+-1*b*x^4)^-1//4))
@test integrate(x^4*(a+-1*b*x^4)^-1//4, x) == :(-1//4*x*b^-1*(a+-1*b*x^4)^3//4+-1//16*a*2^(1/2)*b^-5//4*arctan(1+-1*x*2^(1/2)*b^1//4*(a+-1*b*x^4)^-1//4)+-1//32*a*2^(1/2)*b^-5//4*log(1+b^(1/2)*x^2*(a+-1*b*x^4)^-1//2+-1*x*2^(1/2)*b^1//4*(a+-1*b*x^4)^-1//4)+1//16*a*2^(1/2)*b^-5//4*arctan(1+x*2^(1/2)*b^1//4*(a+-1*b*x^4)^-1//4)+1//32*a*2^(1/2)*b^-5//4*log(1+b^(1/2)*x^2*(a+-1*b*x^4)^-1//2+x*2^(1/2)*b^1//4*(a+-1*b*x^4)^-1//4))
@test integrate((a+-1*b*x^4)^-1//4, x) == :(-1//4*2^(1/2)*b^-1//4*arctan(1+-1*x*2^(1/2)*b^1//4*(a+-1*b*x^4)^-1//4)+-1//8*2^(1/2)*b^-1//4*log(1+b^(1/2)*x^2*(a+-1*b*x^4)^-1//2+-1*x*2^(1/2)*b^1//4*(a+-1*b*x^4)^-1//4)+1//4*2^(1/2)*b^-1//4*arctan(1+x*2^(1/2)*b^1//4*(a+-1*b*x^4)^-1//4)+1//8*2^(1/2)*b^-1//4*log(1+b^(1/2)*x^2*(a+-1*b*x^4)^-1//2+x*2^(1/2)*b^1//4*(a+-1*b*x^4)^-1//4))
@test integrate(x^-4*(a+-1*b*x^4)^-1//4, x) == :(-1//3*a^-1*x^-3*(a+-1*b*x^4)^3//4)
@test integrate(x^-8*(a+-1*b*x^4)^-1//4, x) == :(-1//7*a^-1*x^-7*(a+-1*b*x^4)^3//4+-4//21*b*a^-2*x^-3*(a+-1*b*x^4)^3//4)
@test integrate(x^-12*(a+-1*b*x^4)^-1//4, x) == :(-1//11*a^-1*x^-11*(a+-1*b*x^4)^3//4+-32//231*a^-3*b^2*x^-3*(a+-1*b*x^4)^3//4+-8//77*b*a^-2*x^-7*(a+-1*b*x^4)^3//4)
@test integrate(x^-16*(a+-1*b*x^4)^-1//4, x) == :(-1//15*a^-1*x^-15*(a+-1*b*x^4)^3//4+-128//1155*a^-4*b^3*x^-3*(a+-1*b*x^4)^3//4+-32//385*a^-3*b^2*x^-7*(a+-1*b*x^4)^3//4+-4//55*b*a^-2*x^-11*(a+-1*b*x^4)^3//4)
@test integrate(x^-20*(a+-1*b*x^4)^-1//4, x) == :(-1//19*a^-1*x^-19*(a+-1*b*x^4)^3//4+-2048//21945*a^-5*b^4*x^-3*(a+-1*b*x^4)^3//4+-512//7315*a^-4*b^3*x^-7*(a+-1*b*x^4)^3//4+-64//1045*a^-3*b^2*x^-11*(a+-1*b*x^4)^3//4+-16//285*b*a^-2*x^-15*(a+-1*b*x^4)^3//4)
@test integrate(x^10*(a+-1*b*x^4)^-1//4, x) == :(-1//10*b^-1*x^7*(a+-1*b*x^4)^3//4+-7//40*a^2*b^-3*x^-1*(a+-1*b*x^4)^3//4+-7//60*a*b^-2*x^3*(a+-1*b*x^4)^3//4+7//40*x*a^5//2*b^-5//2*(1+-1*a*b^-1*x^-4)^1//4*(a+-1*b*x^4)^-1//4*Elliptic.E((1/2)*arccsc(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^6*(a+-1*b*x^4)^-1//4, x) == :(-1//6*b^-1*x^3*(a+-1*b*x^4)^3//4+-1//4*a*b^-2*x^-1*(a+-1*b*x^4)^3//4+1//4*x*a^3//2*b^-3//2*(1+-1*a*b^-1*x^-4)^1//4*(a+-1*b*x^4)^-1//4*Elliptic.E((1/2)*arccsc(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^2*(a+-1*b*x^4)^-1//4, x) == :(-1//2*b^-1*x^-1*(a+-1*b*x^4)^3//4+(1/2)*x*a^(1/2)*b^-1//2*(1+-1*a*b^-1*x^-4)^1//4*(a+-1*b*x^4)^-1//4*Elliptic.E((1/2)*arccsc(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^-2*(a+-1*b*x^4)^-1//4, x) == :(-1*x*a^-1//2*b^(1/2)*(1+-1*a*b^-1*x^-4)^1//4*(a+-1*b*x^4)^-1//4*Elliptic.E((1/2)*arccsc(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^-6*(a+-1*b*x^4)^-1//4, x) == :(-1//5*a^-1*x^-5*(a+-1*b*x^4)^3//4+-2//5*x*a^-3//2*b^3//2*(1+-1*a*b^-1*x^-4)^1//4*(a+-1*b*x^4)^-1//4*Elliptic.E((1/2)*arccsc(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^-10*(a+-1*b*x^4)^-1//4, x) == :(-1//9*a^-1*x^-9*(a+-1*b*x^4)^3//4+-2//15*b*a^-2*x^-5*(a+-1*b*x^4)^3//4+-4//15*x*a^-5//2*b^5//2*(1+-1*a*b^-1*x^-4)^1//4*(a+-1*b*x^4)^-1//4*Elliptic.E((1/2)*arccsc(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^-14*(a+-1*b*x^4)^-1//4, x) == :(-1//13*a^-1*x^-13*(a+-1*b*x^4)^3//4+-10//117*b*a^-2*x^-9*(a+-1*b*x^4)^3//4+-4//39*a^-3*b^2*x^-5*(a+-1*b*x^4)^3//4+-8//39*x*a^-7//2*b^7//2*(1+-1*a*b^-1*x^-4)^1//4*(a+-1*b*x^4)^-1//4*Elliptic.E((1/2)*arccsc(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^19*(a+-1*b*x^4)^-3//4, x) == :(-1//17*b^-5*(a+-1*b*x^4)^17//4+-1*a^4*b^-5*(a+-1*b*x^4)^1//4+-2//3*a^2*b^-5*(a+-1*b*x^4)^9//4+4//5*a^3*b^-5*(a+-1*b*x^4)^5//4+4//13*a*b^-5*(a+-1*b*x^4)^13//4)
@test integrate(x^15*(a+-1*b*x^4)^-3//4, x) == :(1//13*b^-4*(a+-1*b*x^4)^13//4+-1*a^3*b^-4*(a+-1*b*x^4)^1//4+-1//3*a*b^-4*(a+-1*b*x^4)^9//4+3//5*a^2*b^-4*(a+-1*b*x^4)^5//4)
@test integrate(x^11*(a+-1*b*x^4)^-3//4, x) == :(-1//9*b^-3*(a+-1*b*x^4)^9//4+-1*a^2*b^-3*(a+-1*b*x^4)^1//4+2//5*a*b^-3*(a+-1*b*x^4)^5//4)
@test integrate(x^7*(a+-1*b*x^4)^-3//4, x) == :(1//5*b^-2*(a+-1*b*x^4)^5//4+-1*a*b^-2*(a+-1*b*x^4)^1//4)
@test integrate(x^3*(a+-1*b*x^4)^-3//4, x) == :(-1*b^-1*(a+-1*b*x^4)^1//4)
@test integrate(x^-1*(a+-1*b*x^4)^-3//4, x) == :(-1//2*a^-3//4*arctan(a^-1//4*(a+-1*b*x^4)^1//4)+-1//2*a^-3//4*arctanh(a^-1//4*(a+-1*b*x^4)^1//4))
@test integrate(x^-5*(a+-1*b*x^4)^-3//4, x) == :(-3//8*b*a^-7//4*arctan(a^-1//4*(a+-1*b*x^4)^1//4)+-3//8*b*a^-7//4*arctanh(a^-1//4*(a+-1*b*x^4)^1//4)+-1//4*a^-1*x^-4*(a+-1*b*x^4)^1//4)
@test integrate(x^-9*(a+-1*b*x^4)^-3//4, x) == :(-21//64*a^-11//4*b^2*arctan(a^-1//4*(a+-1*b*x^4)^1//4)+-21//64*a^-11//4*b^2*arctanh(a^-1//4*(a+-1*b*x^4)^1//4)+-1//8*a^-1*x^-8*(a+-1*b*x^4)^1//4+-7//32*b*a^-2*x^-4*(a+-1*b*x^4)^1//4)
@test integrate(x^13*(a+-1*b*x^4)^-3//4, x) == :(-1//11*b^-1*x^10*(a+-1*b*x^4)^1//4+-20//77*a^2*b^-3*x^2*(a+-1*b*x^4)^1//4+-10//77*a*b^-2*x^6*(a+-1*b*x^4)^1//4+40//77*a^7//2*b^-7//2*(1+-1*b*a^-1*x^4)^3//4*(a+-1*b*x^4)^-3//4*Elliptic.F((1/2)*arcsin(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^9*(a+-1*b*x^4)^-3//4, x) == :(-1//7*b^-1*x^6*(a+-1*b*x^4)^1//4+-2//7*a*b^-2*x^2*(a+-1*b*x^4)^1//4+4//7*a^5//2*b^-5//2*(1+-1*b*a^-1*x^4)^3//4*(a+-1*b*x^4)^-3//4*Elliptic.F((1/2)*arcsin(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^5*(a+-1*b*x^4)^-3//4, x) == :(-1//3*b^-1*x^2*(a+-1*b*x^4)^1//4+2//3*a^3//2*b^-3//2*(1+-1*b*a^-1*x^4)^3//4*(a+-1*b*x^4)^-3//4*Elliptic.F((1/2)*arcsin(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x*(a+-1*b*x^4)^-3//4, x) == :(a^(1/2)*b^-1//2*(1+-1*b*a^-1*x^4)^3//4*(a+-1*b*x^4)^-3//4*Elliptic.F((1/2)*arcsin(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^-3*(a+-1*b*x^4)^-3//4, x) == :(-1//2*a^-1*x^-2*(a+-1*b*x^4)^1//4+(1/2)*a^-1//2*b^(1/2)*(1+-1*b*a^-1*x^4)^3//4*(a+-1*b*x^4)^-3//4*Elliptic.F((1/2)*arcsin(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^-7*(a+-1*b*x^4)^-3//4, x) == :(-1//6*a^-1*x^-6*(a+-1*b*x^4)^1//4+-5//12*b*a^-2*x^-2*(a+-1*b*x^4)^1//4+5//12*a^-3//2*b^3//2*(1+-1*b*a^-1*x^4)^3//4*(a+-1*b*x^4)^-3//4*Elliptic.F((1/2)*arcsin(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^-11*(a+-1*b*x^4)^-3//4, x) == :(-1//10*a^-1*x^-10*(a+-1*b*x^4)^1//4+-3//8*a^-3*b^2*x^-2*(a+-1*b*x^4)^1//4+-3//20*b*a^-2*x^-6*(a+-1*b*x^4)^1//4+3//8*a^-5//2*b^5//2*(1+-1*b*a^-1*x^4)^3//4*(a+-1*b*x^4)^-3//4*Elliptic.F((1/2)*arcsin(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^10*(a+-1*b*x^4)^-3//4, x) == :(-1//8*b^-1*x^7*(a+-1*b*x^4)^1//4+-21//128*2^(1/2)*a^2*b^-11//4*arctan(1+-1*x*2^(1/2)*b^1//4*(a+-1*b*x^4)^-1//4)+-21//256*2^(1/2)*a^2*b^-11//4*log(1+b^(1/2)*x^2*(a+-1*b*x^4)^-1//2+x*2^(1/2)*b^1//4*(a+-1*b*x^4)^-1//4)+-7//32*a*b^-2*x^3*(a+-1*b*x^4)^1//4+21//128*2^(1/2)*a^2*b^-11//4*arctan(1+x*2^(1/2)*b^1//4*(a+-1*b*x^4)^-1//4)+21//256*2^(1/2)*a^2*b^-11//4*log(1+b^(1/2)*x^2*(a+-1*b*x^4)^-1//2+-1*x*2^(1/2)*b^1//4*(a+-1*b*x^4)^-1//4))
@test integrate(x^6*(a+-1*b*x^4)^-3//4, x) == :(-1//4*b^-1*x^3*(a+-1*b*x^4)^1//4+-3//16*a*2^(1/2)*b^-7//4*arctan(1+-1*x*2^(1/2)*b^1//4*(a+-1*b*x^4)^-1//4)+-3//32*a*2^(1/2)*b^-7//4*log(1+b^(1/2)*x^2*(a+-1*b*x^4)^-1//2+x*2^(1/2)*b^1//4*(a+-1*b*x^4)^-1//4)+3//16*a*2^(1/2)*b^-7//4*arctan(1+x*2^(1/2)*b^1//4*(a+-1*b*x^4)^-1//4)+3//32*a*2^(1/2)*b^-7//4*log(1+b^(1/2)*x^2*(a+-1*b*x^4)^-1//2+-1*x*2^(1/2)*b^1//4*(a+-1*b*x^4)^-1//4))
@test integrate(x^2*(a+-1*b*x^4)^-3//4, x) == :(-1//4*2^(1/2)*b^-3//4*arctan(1+-1*x*2^(1/2)*b^1//4*(a+-1*b*x^4)^-1//4)+-1//8*2^(1/2)*b^-3//4*log(1+b^(1/2)*x^2*(a+-1*b*x^4)^-1//2+x*2^(1/2)*b^1//4*(a+-1*b*x^4)^-1//4)+1//4*2^(1/2)*b^-3//4*arctan(1+x*2^(1/2)*b^1//4*(a+-1*b*x^4)^-1//4)+1//8*2^(1/2)*b^-3//4*log(1+b^(1/2)*x^2*(a+-1*b*x^4)^-1//2+-1*x*2^(1/2)*b^1//4*(a+-1*b*x^4)^-1//4))
@test integrate(x^-2*(a+-1*b*x^4)^-3//4, x) == :(-1*a^-1*x^-1*(a+-1*b*x^4)^1//4)
@test integrate(x^-6*(a+-1*b*x^4)^-3//4, x) == :(-1//5*a^-1*x^-5*(a+-1*b*x^4)^1//4+-4//5*b*a^-2*x^-1*(a+-1*b*x^4)^1//4)
@test integrate(x^-10*(a+-1*b*x^4)^-3//4, x) == :(-1//9*a^-1*x^-9*(a+-1*b*x^4)^1//4+-32//45*a^-3*b^2*x^-1*(a+-1*b*x^4)^1//4+-8//45*b*a^-2*x^-5*(a+-1*b*x^4)^1//4)
@test integrate(x^-14*(a+-1*b*x^4)^-3//4, x) == :(-1//13*a^-1*x^-13*(a+-1*b*x^4)^1//4+-128//195*a^-4*b^3*x^-1*(a+-1*b*x^4)^1//4+-32//195*a^-3*b^2*x^-5*(a+-1*b*x^4)^1//4+-4//39*b*a^-2*x^-9*(a+-1*b*x^4)^1//4)
@test integrate(x^12*(a+-1*b*x^4)^-3//4, x) == :(-1//10*b^-1*x^9*(a+-1*b*x^4)^1//4+-3//8*x*a^2*b^-3*(a+-1*b*x^4)^1//4+-3//20*a*b^-2*x^5*(a+-1*b*x^4)^1//4+-3//8*a^5//2*b^-5//2*x^3*(1+-1*a*b^-1*x^-4)^3//4*(a+-1*b*x^4)^-3//4*Elliptic.F((1/2)*arccsc(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^8*(a+-1*b*x^4)^-3//4, x) == :(-1//6*b^-1*x^5*(a+-1*b*x^4)^1//4+-5//12*a*x*b^-2*(a+-1*b*x^4)^1//4+-5//12*a^3//2*b^-3//2*x^3*(1+-1*a*b^-1*x^-4)^3//4*(a+-1*b*x^4)^-3//4*Elliptic.F((1/2)*arccsc(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^4*(a+-1*b*x^4)^-3//4, x) == :(-1//2*x*b^-1*(a+-1*b*x^4)^1//4+-1//2*a^(1/2)*b^-1//2*x^3*(1+-1*a*b^-1*x^-4)^3//4*(a+-1*b*x^4)^-3//4*Elliptic.F((1/2)*arccsc(a^-1//2*b^(1/2)*x^2),2))
@test integrate((a+-1*b*x^4)^-3//4, x) == :(-1*a^-1//2*b^(1/2)*x^3*(1+-1*a*b^-1*x^-4)^3//4*(a+-1*b*x^4)^-3//4*Elliptic.F((1/2)*arccsc(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^-4*(a+-1*b*x^4)^-3//4, x) == :(-1//3*a^-1*x^-3*(a+-1*b*x^4)^1//4+-2//3*a^-3//2*b^3//2*x^3*(1+-1*a*b^-1*x^-4)^3//4*(a+-1*b*x^4)^-3//4*Elliptic.F((1/2)*arccsc(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^-8*(a+-1*b*x^4)^-3//4, x) == :(-1//7*a^-1*x^-7*(a+-1*b*x^4)^1//4+-2//7*b*a^-2*x^-3*(a+-1*b*x^4)^1//4+-4//7*a^-5//2*b^5//2*x^3*(1+-1*a*b^-1*x^-4)^3//4*(a+-1*b*x^4)^-3//4*Elliptic.F((1/2)*arccsc(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^-12*(a+-1*b*x^4)^-3//4, x) == :(-1//11*a^-1*x^-11*(a+-1*b*x^4)^1//4+-20//77*a^-3*b^2*x^-3*(a+-1*b*x^4)^1//4+-10//77*b*a^-2*x^-7*(a+-1*b*x^4)^1//4+-40//77*a^-7//2*b^7//2*x^3*(1+-1*a*b^-1*x^-4)^3//4*(a+-1*b*x^4)^-3//4*Elliptic.F((1/2)*arccsc(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^2*(a+-1*b*x^4)^-5//4, x) == :(b^-1*x^-1*(a+-1*b*x^4)^-1//4+-1*x*a^-1//2*b^-1//2*(1+-1*a*b^-1*x^-4)^1//4*(a+-1*b*x^4)^-1//4*Elliptic.E((1/2)*arccsc(a^-1//2*b^(1/2)*x^2),2))
@test integrate(x^7*(a+b*x^4)^p, x) == :(1//4*b^-2*(2+p)^-1*(a+b*x^4)^(2+p)+-1//4*a*b^-2*(1+p)^-1*(a+b*x^4)^(1+p))
@test integrate(x^3*(a+b*x^4)^p, x) == :(1//4*b^-1*(1+p)^-1*(a+b*x^4)^(1+p))
@test integrate(x^24*(a+b*x^5)^-1, x) == :(1//20*b^-1*x^20+-1//5*a^3*b^-4*x^5+-1//15*a*b^-2*x^15+1//5*a^4*b^-5*log(a+b*x^5)+1//10*a^2*b^-3*x^10)
@test integrate(x^19*(a+b*x^5)^-1, x) == :(1//15*b^-1*x^15+-1//5*a^3*b^-4*log(a+b*x^5)+-1//10*a*b^-2*x^10+1//5*a^2*b^-3*x^5)
@test integrate(x^14*(a+b*x^5)^-1, x) == :(1//10*b^-1*x^10+-1//5*a*b^-2*x^5+1//5*a^2*b^-3*log(a+b*x^5))
@test integrate(x^9*(a+b*x^5)^-1, x) == :(1//5*b^-1*x^5+-1//5*a*b^-2*log(a+b*x^5))
@test integrate(x^4*(a+b*x^5)^-1, x) == :(1//5*b^-1*log(a+b*x^5))
@test integrate(x^-1*(a+b*x^5)^-1, x) == :(a^-1*log(x)+-1//5*a^-1*log(a+b*x^5))
@test integrate(x^-6*(a+b*x^5)^-1, x) == :(-1//5*a^-1*x^-5+-1*b*a^-2*log(x)+1//5*b*a^-2*log(a+b*x^5))
@test integrate(x^-11*(a+b*x^5)^-1, x) == :(-1//10*a^-1*x^-10+a^-3*b^2*log(x)+-1//5*a^-3*b^2*log(a+b*x^5)+1//5*b*a^-2*x^-5)
@test integrate(x^-16*(a+b*x^5)^-1, x) == :(-1//15*a^-1*x^-15+-1*a^-4*b^3*log(x)+-1//5*a^-3*b^2*x^-5+1//5*a^-4*b^3*log(a+b*x^5)+1//10*b*a^-2*x^-10)
@test integrate(x^24*(a+b*x^5)^-2, x) == :(1//15*b^-2*x^15+-4//5*a^3*b^-5*log(a+b*x^5)+-1//5*a*b^-3*x^10+-1//5*a^4*b^-5*(a+b*x^5)^-1+3//5*a^2*b^-4*x^5)
@test integrate(x^19*(a+b*x^5)^-2, x) == :(1//10*b^-2*x^10+-2//5*a*b^-3*x^5+1//5*a^3*b^-4*(a+b*x^5)^-1+3//5*a^2*b^-4*log(a+b*x^5))
@test integrate(x^14*(a+b*x^5)^-2, x) == :(1//5*b^-2*x^5+-2//5*a*b^-3*log(a+b*x^5)+-1//5*a^2*b^-3*(a+b*x^5)^-1)
@test integrate(x^9*(a+b*x^5)^-2, x) == :(1//5*b^-2*log(a+b*x^5)+1//5*a*b^-2*(a+b*x^5)^-1)
@test integrate(x^4*(a+b*x^5)^-2, x) == :(-1//5*b^-1*(a+b*x^5)^-1)
@test integrate(x^-1*(a+b*x^5)^-2, x) == :(a^-2*log(x)+-1//5*a^-2*log(a+b*x^5)+1//5*a^-1*(a+b*x^5)^-1)
@test integrate(x^-6*(a+b*x^5)^-2, x) == :(-1//5*a^-2*x^-5+-2*b*a^-3*log(x)+-1//5*b*a^-2*(a+b*x^5)^-1+2//5*b*a^-3*log(a+b*x^5))
@test integrate(x^-11*(a+b*x^5)^-2, x) == :(-1//10*a^-2*x^-10+3*a^-4*b^2*log(x)+-3//5*a^-4*b^2*log(a+b*x^5)+1//5*a^-3*b^2*(a+b*x^5)^-1+2//5*b*a^-3*x^-5)
@test integrate(x^14*(2b+b*x^5)^-1, x) == :(-2//5*b^-1*x^5+1//10*b^-1*x^10+4//5*b^-1*log(2+x^5))
@test integrate(x^9*(2b+b*x^5)^-1, x) == :(-2//5*b^-1*log(2+x^5)+1//5*b^-1*x^5)
@test integrate(x^4*(2b+b*x^5)^-1, x) == :(1//5*b^-1*log(2+x^5))
@test integrate(x^-1*(2b+b*x^5)^-1, x) == :((1/2)*b^-1*log(x)+-1//10*b^-1*log(2+x^5))
@test integrate(x^-6*(2b+b*x^5)^-1, x) == :(-1//4*b^-1*log(x)+-1//10*b^-1*x^-5+1//20*b^-1*log(2+x^5))
@test integrate(x^14*(3+b*x^5)^-1, x) == :(-3//5*b^-2*x^5+1//10*b^-1*x^10+9//5*b^-3*log(3+b*x^5))
@test integrate(x^9*(3+b*x^5)^-1, x) == :(-3//5*b^-2*log(3+b*x^5)+1//5*b^-1*x^5)
@test integrate(x^4*(3+b*x^5)^-1, x) == :(1//5*b^-1*log(3+b*x^5))
@test integrate(x^-1*(3+b*x^5)^-1, x) == :(-1//15*log(3+b*x^5)+1//3*log(x))
@test integrate(x^-6*(3+b*x^5)^-1, x) == :(-1//15*x^-5+-1//9*b*log(x)+1//45*b*log(3+b*x^5))
@test integrate(x^14*(1+x^5)^-1, x) == :(-1//5*x^5+1//5*log(1+x^5)+1//10*x^10)
@test integrate(x^9*(1+x^5)^-1, x) == :(-1//5*log(1+x^5)+1//5*x^5)
@test integrate(x^4*(1+x^5)^-1, x) == :(1//5*log(1+x^5))
@test integrate(x^-1*(1+x^5)^-1, x) == :(-1//5*log(1+x^5)+log(x))
@test integrate(x^-6*(1+x^5)^-1, x) == :(-1*log(x)+-1//5*x^-5+1//5*log(1+x^5))
@test integrate(x^5*(1+x^5)^-1, x) == :(x+-1//5*log(1+x)+(1//20+-1//20*5^(1/2))*log(1+x^2+-1*x*(1/2+-1//2*5^(1/2)))+(1//20+1//20*5^(1/2))*log(1+x^2+-1*x*(1/2+(1/2)*5^(1/2)))+-1//5*(5//2+(1/2)*5^(1/2))^(1/2)*arctan((1+-2//5*5^(1/2))^(1/2)+2*x*2^(1/2)*(5+5^(1/2))^-1//2)+1//5*(5//2+-1//2*5^(1/2))^(1/2)*arctan((1+2//5*5^(1/2))^(1/2)+-1*x*(2+2//5*5^(1/2))^(1/2)))
@test integrate(x^3*(1+x^5)^-1, x) == :(-1//5*log(1+x)+(1//20+-1//20*5^(1/2))*log(1+x^2+-1*x*(1/2+-1//2*5^(1/2)))+(1//20+1//20*5^(1/2))*log(1+x^2+-1*x*(1/2+(1/2)*5^(1/2)))+-1//5*(5//2+-1//2*5^(1/2))^(1/2)*arctan((1+2//5*5^(1/2))^(1/2)+-1*x*(2+2//5*5^(1/2))^(1/2))+1//5*(5//2+(1/2)*5^(1/2))^(1/2)*arctan((1+-2//5*5^(1/2))^(1/2)+2*x*2^(1/2)*(5+5^(1/2))^-1//2))
@test integrate(x^2*(1+x^5)^-1, x) == :(1//5*log(1+x)+-1*(1//20+-1//20*5^(1/2))*log(1+x^2+-1*x*(1/2+(1/2)*5^(1/2)))+-1*(1//20+1//20*5^(1/2))*log(1+x^2+-1*x*(1/2+-1//2*5^(1/2)))+-1//5*(5//2+(1/2)*5^(1/2))^(1/2)*arctan((1+2//5*5^(1/2))^(1/2)+-1*x*(2+2//5*5^(1/2))^(1/2))+-1//5*(5//2+-1//2*5^(1/2))^(1/2)*arctan((1+-2//5*5^(1/2))^(1/2)+2*x*2^(1/2)*(5+5^(1/2))^-1//2))
@test integrate(x*(1+x^5)^-1, x) == :(-1//5*log(1+x)+(1//20+-1//20*5^(1/2))*log(1+x^2+-1*x*(1/2+(1/2)*5^(1/2)))+(1//20+1//20*5^(1/2))*log(1+x^2+-1*x*(1/2+-1//2*5^(1/2)))+-1//5*(5//2+(1/2)*5^(1/2))^(1/2)*arctan((1+2//5*5^(1/2))^(1/2)+-1*x*(2+2//5*5^(1/2))^(1/2))+-1//5*(5//2+-1//2*5^(1/2))^(1/2)*arctan((1+-2//5*5^(1/2))^(1/2)+2*x*2^(1/2)*(5+5^(1/2))^-1//2))
@test integrate(x^-2*(1+x^5)^-1, x) == :(-1*x^-1+1//5*log(1+x)+-1*(1//20+-1//20*5^(1/2))*log(1+x^2+-1*x*(1/2+-1//2*5^(1/2)))+-1*(1//20+1//20*5^(1/2))*log(1+x^2+-1*x*(1/2+(1/2)*5^(1/2)))+-1//5*(5//2+(1/2)*5^(1/2))^(1/2)*arctan((1+-2//5*5^(1/2))^(1/2)+2*x*2^(1/2)*(5+5^(1/2))^-1//2)+1//5*(5//2+-1//2*5^(1/2))^(1/2)*arctan((1+2//5*5^(1/2))^(1/2)+-1*x*(2+2//5*5^(1/2))^(1/2)))
@test integrate(x^-3*(1+x^5)^-1, x) == :(-1//2*x^-2+-1//5*log(1+x)+(1//20+-1//20*5^(1/2))*log(1+x^2+-1*x*(1/2+(1/2)*5^(1/2)))+(1//20+1//20*5^(1/2))*log(1+x^2+-1*x*(1/2+-1//2*5^(1/2)))+1//5*(5//2+(1/2)*5^(1/2))^(1/2)*arctan((1+2//5*5^(1/2))^(1/2)+-1*x*(2+2//5*5^(1/2))^(1/2))+1//5*(5//2+-1//2*5^(1/2))^(1/2)*arctan((1+-2//5*5^(1/2))^(1/2)+2*x*2^(1/2)*(5+5^(1/2))^-1//2))
@test integrate(x^-4*(1+x^5)^-1, x) == :(-1//3*x^-3+1//5*log(1+x)+-1*(1//20+-1//20*5^(1/2))*log(1+x^2+-1*x*(1/2+(1/2)*5^(1/2)))+-1*(1//20+1//20*5^(1/2))*log(1+x^2+-1*x*(1/2+-1//2*5^(1/2)))+1//5*(5//2+(1/2)*5^(1/2))^(1/2)*arctan((1+2//5*5^(1/2))^(1/2)+-1*x*(2+2//5*5^(1/2))^(1/2))+1//5*(5//2+-1//2*5^(1/2))^(1/2)*arctan((1+-2//5*5^(1/2))^(1/2)+2*x*2^(1/2)*(5+5^(1/2))^-1//2))
@test integrate(x^23//2*(a+b*x^5)^-1//2, x) == :(1//10*b^-1*x^15//2*(a+b*x^5)^(1/2)+3//20*a^2*b^-5//2*arctanh(b^(1/2)*x^5//2*(a+b*x^5)^-1//2)+-3//20*a*b^-2*x^5//2*(a+b*x^5)^(1/2))
@test integrate(x^13//2*(a+b*x^5)^-1//2, x) == :(-1//5*a*b^-3//2*arctanh(b^(1/2)*x^5//2*(a+b*x^5)^-1//2)+1//5*b^-1*x^5//2*(a+b*x^5)^(1/2))
@test integrate(x^3//2*(a+b*x^5)^-1//2, x) == :(2//5*b^-1//2*arctanh(b^(1/2)*x^5//2*(a+b*x^5)^-1//2))
@test integrate(x^-7//2*(a+b*x^5)^-1//2, x) == :(-2//5*a^-1*x^-5//2*(a+b*x^5)^(1/2))
@test integrate(x^-17//2*(a+b*x^5)^-1//2, x) == :(-2//15*a^-1*x^-15//2*(a+b*x^5)^(1/2)+4//15*b*a^-2*x^-5//2*(a+b*x^5)^(1/2))
@test integrate(x^23//2*(1+x^5)^-1//2, x) == :(3//20*arcsinh(x^5//2)+-3//20*x^5//2*(1+x^5)^(1/2)+1//10*x^15//2*(1+x^5)^(1/2))
@test integrate(x^13//2*(1+x^5)^-1//2, x) == :(-1//5*arcsinh(x^5//2)+1//5*x^5//2*(1+x^5)^(1/2))
@test integrate(x^3//2*(1+x^5)^-1//2, x) == :(2//5*arcsinh(x^5//2))
@test integrate(x^-7//2*(1+x^5)^-1//2, x) == :(-2//5*x^-5//2*(1+x^5)^(1/2))
@test integrate(x^-17//2*(1+x^5)^-1//2, x) == :(-2//15*x^-15//2*(1+x^5)^(1/2)+4//15*x^-5//2*(1+x^5)^(1/2))
@test integrate(x^8*(a+b*x^6)^-1, x) == :(1//3*b^-1*x^3+-1//3*a^(1/2)*b^-3//2*arctan(a^-1//2*b^(1/2)*x^3))
@test integrate(x^7*(a+b*x^6)^-1, x) == :((1/2)*b^-1*x^2+-1//6*a^1//3*b^-4//3*log(a^1//3+b^1//3*x^2)+1//12*a^1//3*b^-4//3*log(a^2//3+b^2//3*x^4+-1*a^1//3*b^1//3*x^2)+1//6*3^(1/2)*a^1//3*b^-4//3*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*b^1//3*x^2)))
@test integrate(x^6*(a+b*x^6)^-1, x) == :(x*b^-1+-1//3*a^1//6*b^-7//6*arctan(x*a^-1//6*b^1//6)+-1//6*a^1//6*b^-7//6*arctan(a^-1//6*(3^(1/2)*a^1//6+2*x*b^1//6))+1//6*a^1//6*b^-7//6*arctan(a^-1//6*(3^(1/2)*a^1//6+-2*x*b^1//6))+-1//12*3^(1/2)*a^1//6*b^-7//6*log(a^1//3+b^1//3*x^2+x*3^(1/2)*a^1//6*b^1//6)+1//12*3^(1/2)*a^1//6*b^-7//6*log(a^1//3+b^1//3*x^2+-1*x*3^(1/2)*a^1//6*b^1//6))
@test integrate(x^5*(a+b*x^6)^-1, x) == :(1//6*b^-1*log(a+b*x^6))
@test integrate(x^4*(a+b*x^6)^-1, x) == :(-1//6*a^-1//6*b^-5//6*arctan(a^-1//6*(3^(1/2)*a^1//6+-2*x*b^1//6))+1//3*a^-1//6*b^-5//6*arctan(x*a^-1//6*b^1//6)+1//6*a^-1//6*b^-5//6*arctan(a^-1//6*(3^(1/2)*a^1//6+2*x*b^1//6))+-1//12*3^(1/2)*a^-1//6*b^-5//6*log(a^1//3+b^1//3*x^2+x*3^(1/2)*a^1//6*b^1//6)+1//12*3^(1/2)*a^-1//6*b^-5//6*log(a^1//3+b^1//3*x^2+-1*x*3^(1/2)*a^1//6*b^1//6))
@test integrate(x^3*(a+b*x^6)^-1, x) == :(-1//6*a^-1//3*b^-2//3*log(a^1//3+b^1//3*x^2)+1//12*a^-1//3*b^-2//3*log(a^2//3+b^2//3*x^4+-1*a^1//3*b^1//3*x^2)+-1//6*3^(1/2)*a^-1//3*b^-2//3*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*b^1//3*x^2)))
@test integrate(x^2*(a+b*x^6)^-1, x) == :(1//3*a^-1//2*b^-1//2*arctan(a^-1//2*b^(1/2)*x^3))
@test integrate(x*(a+b*x^6)^-1, x) == :(-1//12*a^-2//3*b^-1//3*log(a^2//3+b^2//3*x^4+-1*a^1//3*b^1//3*x^2)+1//6*a^-2//3*b^-1//3*log(a^1//3+b^1//3*x^2)+-1//6*3^(1/2)*a^-2//3*b^-1//3*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*b^1//3*x^2)))
@test integrate((a+b*x^6)^-1, x) == :(-1//6*a^-5//6*b^-1//6*arctan(a^-1//6*(3^(1/2)*a^1//6+-2*x*b^1//6))+1//3*a^-5//6*b^-1//6*arctan(x*a^-1//6*b^1//6)+1//6*a^-5//6*b^-1//6*arctan(a^-1//6*(3^(1/2)*a^1//6+2*x*b^1//6))+-1//12*3^(1/2)*a^-5//6*b^-1//6*log(a^1//3+b^1//3*x^2+-1*x*3^(1/2)*a^1//6*b^1//6)+1//12*3^(1/2)*a^-5//6*b^-1//6*log(a^1//3+b^1//3*x^2+x*3^(1/2)*a^1//6*b^1//6))
@test integrate(x^-1*(a+b*x^6)^-1, x) == :(a^-1*log(x)+-1//6*a^-1*log(a+b*x^6))
@test integrate(x^-2*(a+b*x^6)^-1, x) == :(-1*a^-1*x^-1+-1//3*a^-7//6*b^1//6*arctan(x*a^-1//6*b^1//6)+-1//6*a^-7//6*b^1//6*arctan(a^-1//6*(3^(1/2)*a^1//6+2*x*b^1//6))+1//6*a^-7//6*b^1//6*arctan(a^-1//6*(3^(1/2)*a^1//6+-2*x*b^1//6))+-1//12*3^(1/2)*a^-7//6*b^1//6*log(a^1//3+b^1//3*x^2+-1*x*3^(1/2)*a^1//6*b^1//6)+1//12*3^(1/2)*a^-7//6*b^1//6*log(a^1//3+b^1//3*x^2+x*3^(1/2)*a^1//6*b^1//6))
@test integrate(x^-3*(a+b*x^6)^-1, x) == :(-1//2*a^-1*x^-2+-1//12*a^-4//3*b^1//3*log(a^2//3+b^2//3*x^4+-1*a^1//3*b^1//3*x^2)+1//6*a^-4//3*b^1//3*log(a^1//3+b^1//3*x^2)+1//6*3^(1/2)*a^-4//3*b^1//3*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*b^1//3*x^2)))
@test integrate(x^-4*(a+b*x^6)^-1, x) == :(-1//3*a^-1*x^-3+-1//3*a^-3//2*b^(1/2)*arctan(a^-1//2*b^(1/2)*x^3))
@test integrate(x^8*(a+b*x^6)^-2, x) == :(-1//6*b^-1*x^3*(a+b*x^6)^-1+1//6*a^-1//2*b^-3//2*arctan(a^-1//2*b^(1/2)*x^3))
@test integrate(x^7*(a+b*x^6)^-2, x) == :(-1//6*b^-1*x^2*(a+b*x^6)^-1+-1//36*a^-2//3*b^-4//3*log(a^2//3+b^2//3*x^4+-1*a^1//3*b^1//3*x^2)+1//18*a^-2//3*b^-4//3*log(a^1//3+b^1//3*x^2)+-1//18*3^(1/2)*a^-2//3*b^-4//3*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*b^1//3*x^2)))
@test integrate(x^6*(a+b*x^6)^-2, x) == :(-1//6*x*b^-1*(a+b*x^6)^-1+-1//36*a^-5//6*b^-7//6*arctan(a^-1//6*(3^(1/2)*a^1//6+-2*x*b^1//6))+1//18*a^-5//6*b^-7//6*arctan(x*a^-1//6*b^1//6)+1//36*a^-5//6*b^-7//6*arctan(a^-1//6*(3^(1/2)*a^1//6+2*x*b^1//6))+-1//72*3^(1/2)*a^-5//6*b^-7//6*log(a^1//3+b^1//3*x^2+-1*x*3^(1/2)*a^1//6*b^1//6)+1//72*3^(1/2)*a^-5//6*b^-7//6*log(a^1//3+b^1//3*x^2+x*3^(1/2)*a^1//6*b^1//6))
@test integrate(x^5*(a+b*x^6)^-2, x) == :(-1//6*b^-1*(a+b*x^6)^-1)
@test integrate(x^4*(a+b*x^6)^-2, x) == :(-1//36*a^-7//6*b^-5//6*arctan(a^-1//6*(3^(1/2)*a^1//6+-2*x*b^1//6))+1//6*a^-1*x^5*(a+b*x^6)^-1+1//18*a^-7//6*b^-5//6*arctan(x*a^-1//6*b^1//6)+1//36*a^-7//6*b^-5//6*arctan(a^-1//6*(3^(1/2)*a^1//6+2*x*b^1//6))+-1//72*3^(1/2)*a^-7//6*b^-5//6*log(a^1//3+b^1//3*x^2+x*3^(1/2)*a^1//6*b^1//6)+1//72*3^(1/2)*a^-7//6*b^-5//6*log(a^1//3+b^1//3*x^2+-1*x*3^(1/2)*a^1//6*b^1//6))
@test integrate(x^3*(a+b*x^6)^-2, x) == :(-1//18*a^-4//3*b^-2//3*log(a^1//3+b^1//3*x^2)+1//6*a^-1*x^4*(a+b*x^6)^-1+1//36*a^-4//3*b^-2//3*log(a^2//3+b^2//3*x^4+-1*a^1//3*b^1//3*x^2)+-1//18*3^(1/2)*a^-4//3*b^-2//3*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*b^1//3*x^2)))
@test integrate(x^2*(a+b*x^6)^-2, x) == :(1//6*a^-1*x^3*(a+b*x^6)^-1+1//6*a^-3//2*b^-1//2*arctan(a^-1//2*b^(1/2)*x^3))
@test integrate(x*(a+b*x^6)^-2, x) == :(-1//18*a^-5//3*b^-1//3*log(a^2//3+b^2//3*x^4+-1*a^1//3*b^1//3*x^2)+1//6*a^-1*x^2*(a+b*x^6)^-1+1//9*a^-5//3*b^-1//3*log(a^1//3+b^1//3*x^2)+-1//9*3^(1/2)*a^-5//3*b^-1//3*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*b^1//3*x^2)))
@test integrate((a+b*x^6)^-2, x) == :(-5//36*a^-11//6*b^-1//6*arctan(a^-1//6*(3^(1/2)*a^1//6+-2*x*b^1//6))+1//6*x*a^-1*(a+b*x^6)^-1+5//18*a^-11//6*b^-1//6*arctan(x*a^-1//6*b^1//6)+5//36*a^-11//6*b^-1//6*arctan(a^-1//6*(3^(1/2)*a^1//6+2*x*b^1//6))+-5//72*3^(1/2)*a^-11//6*b^-1//6*log(a^1//3+b^1//3*x^2+-1*x*3^(1/2)*a^1//6*b^1//6)+5//72*3^(1/2)*a^-11//6*b^-1//6*log(a^1//3+b^1//3*x^2+x*3^(1/2)*a^1//6*b^1//6))
@test integrate(x^-1*(a+b*x^6)^-2, x) == :(a^-2*log(x)+-1//6*a^-2*log(a+b*x^6)+1//6*a^-1*(a+b*x^6)^-1)
@test integrate(x^-2*(a+b*x^6)^-2, x) == :(-7//6*a^-2*x^-1+-7//18*a^-13//6*b^1//6*arctan(x*a^-1//6*b^1//6)+-7//36*a^-13//6*b^1//6*arctan(a^-1//6*(3^(1/2)*a^1//6+2*x*b^1//6))+1//6*a^-1*x^-1*(a+b*x^6)^-1+7//36*a^-13//6*b^1//6*arctan(a^-1//6*(3^(1/2)*a^1//6+-2*x*b^1//6))+-7//72*3^(1/2)*a^-13//6*b^1//6*log(a^1//3+b^1//3*x^2+-1*x*3^(1/2)*a^1//6*b^1//6)+7//72*3^(1/2)*a^-13//6*b^1//6*log(a^1//3+b^1//3*x^2+x*3^(1/2)*a^1//6*b^1//6))
@test integrate(x^-3*(a+b*x^6)^-2, x) == :(-2//3*a^-2*x^-2+-1//9*a^-7//3*b^1//3*log(a^2//3+b^2//3*x^4+-1*a^1//3*b^1//3*x^2)+1//6*a^-1*x^-2*(a+b*x^6)^-1+2//9*a^-7//3*b^1//3*log(a^1//3+b^1//3*x^2)+2//9*3^(1/2)*a^-7//3*b^1//3*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*b^1//3*x^2)))
@test integrate(x^-4*(a+b*x^6)^-2, x) == :(-1//2*a^-2*x^-3+-1//2*a^-5//2*b^(1/2)*arctan(a^-1//2*b^(1/2)*x^3)+1//6*a^-1*x^-3*(a+b*x^6)^-1)
@test integrate(x^8*(1+-1*x^6)^-1, x) == :(-1//3*x^3+1//3*arctanh(x^3))
@test integrate(x^7*(1+-1*x^6)^-1, x) == :(-1//2*x^2+-1//6*log(1+-1*x^2)+1//12*log(1+x^2+x^4)+1//6*3^(1/2)*arctan(1//3*3^(1/2)*(1+2*x^2)))
@test integrate(x^5*(1+-1*x^6)^-1, x) == :(-1//6*log(1+-1*x^6))
@test integrate(x^3*(1+-1*x^6)^-1, x) == :(-1//6*log(1+-1*x^2)+1//12*log(1+x^2+x^4)+-1//6*3^(1/2)*arctan(1//3*3^(1/2)*(1+2*x^2)))
@test integrate(x^2*(1+-1*x^6)^-1, x) == :(1//3*arctanh(x^3))
@test integrate(x*(1+-1*x^6)^-1, x) == :(-1//6*log(1+-1*x^2)+1//12*log(1+x^2+x^4)+1//6*3^(1/2)*arctan(1//3*3^(1/2)*(1+2*x^2)))
@test integrate(x^-1*(1+-1*x^6)^-1, x) == :(-1//6*log(1+-1*x^6)+log(x))
@test integrate(x^-3*(1+-1*x^6)^-1, x) == :(-1//2*x^-2+-1//6*log(1+-1*x^2)+1//12*log(1+x^2+x^4)+-1//6*3^(1/2)*arctan(1//3*3^(1/2)*(1+2*x^2)))
@test integrate(x^-4*(1+-1*x^6)^-1, x) == :(-1//3*x^-3+1//3*arctanh(x^3))
@test integrate(x^-5*(1+-1*x^6)^-1, x) == :(-1//4*x^-4+-1//6*log(1+-1*x^2)+1//12*log(1+x^2+x^4)+1//6*3^(1/2)*arctan(1//3*3^(1/2)*(1+2*x^2)))
@test integrate(x^-6*(1+-1*x^6)^-1, x) == :(-1//5*x^-5+-1//12*log(1+x^2+-1x)+1//3*arctanh(x)+1//12*log(1+x+x^2)+-1//6*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2x))+1//6*3^(1/2)*arctan(1//3*3^(1/2)*(1+2x)))
@test integrate(x^-7*(1+-1*x^6)^-1, x) == :(-1//6*x^-6+-1//6*log(1+-1*x^6)+log(x))
@test integrate(x^-8*(1+-1*x^6)^-1, x) == :(-1*x^-1+-1//7*x^-7+-1//12*log(1+x^2+-1x)+1//3*arctanh(x)+1//12*log(1+x+x^2)+-1//6*3^(1/2)*arctan(1//3*3^(1/2)*(1+2x))+1//6*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2x)))
@test integrate(x^8*(1+x^6)^-1, x) == :(-1//3*arctan(x^3)+1//3*x^3)
@test integrate(x^7*(1+x^6)^-1, x) == :((1/2)*x^2+-1//6*log(1+x^2)+1//12*log(1+x^4+-1*x^2)+1//6*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2*x^2)))
@test integrate(x^6*(1+x^6)^-1, x) == :(x+-1//3*arctan(x)+-1//6*arctan(3^(1/2)+2x)+1//6*arctan(3^(1/2)+-2x)+-1//12*3^(1/2)*log(1+x^2+x*3^(1/2))+1//12*3^(1/2)*log(1+x^2+-1*x*3^(1/2)))
@test integrate(x^5*(1+x^6)^-1, x) == :(1//6*log(1+x^6))
@test integrate(x^4*(1+x^6)^-1, x) == :(-1//6*arctan(3^(1/2)+-2x)+1//3*arctan(x)+1//6*arctan(3^(1/2)+2x)+-1//12*3^(1/2)*log(1+x^2+x*3^(1/2))+1//12*3^(1/2)*log(1+x^2+-1*x*3^(1/2)))
@test integrate(x^3*(1+x^6)^-1, x) == :(-1//6*log(1+x^2)+1//12*log(1+x^4+-1*x^2)+-1//6*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2*x^2)))
@test integrate(x^2*(1+x^6)^-1, x) == :(1//3*arctan(x^3))
@test integrate(x*(1+x^6)^-1, x) == :(-1//12*log(1+x^4+-1*x^2)+1//6*log(1+x^2)+-1//6*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2*x^2)))
@test integrate((1+x^6)^-1, x) == :(-1//6*arctan(3^(1/2)+-2x)+1//3*arctan(x)+1//6*arctan(3^(1/2)+2x)+-1//12*3^(1/2)*log(1+x^2+-1*x*3^(1/2))+1//12*3^(1/2)*log(1+x^2+x*3^(1/2)))
@test integrate(x^-1*(1+x^6)^-1, x) == :(-1//6*log(1+x^6)+log(x))
@test integrate(x^-2*(1+x^6)^-1, x) == :(-1*x^-1+-1//3*arctan(x)+-1//6*arctan(3^(1/2)+2x)+1//6*arctan(3^(1/2)+-2x)+-1//12*3^(1/2)*log(1+x^2+-1*x*3^(1/2))+1//12*3^(1/2)*log(1+x^2+x*3^(1/2)))
@test integrate(x^-3*(1+x^6)^-1, x) == :(-1//2*x^-2+-1//12*log(1+x^4+-1*x^2)+1//6*log(1+x^2)+1//6*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2*x^2)))
@test integrate(x^-4*(1+x^6)^-1, x) == :(-1//3*x^-3+-1//3*arctan(x^3))
@test integrate(x^-5*(1+x^6)^-1, x) == :(-1//4*x^-4+-1//6*log(1+x^2)+1//12*log(1+x^4+-1*x^2)+1//6*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2*x^2)))
@test integrate(x^-6*(1+x^6)^-1, x) == :(-1//3*arctan(x)+-1//5*x^-5+-1//6*arctan(3^(1/2)+2x)+1//6*arctan(3^(1/2)+-2x)+-1//12*3^(1/2)*log(1+x^2+x*3^(1/2))+1//12*3^(1/2)*log(1+x^2+-1*x*3^(1/2)))
@test integrate(x^-7*(1+x^6)^-1, x) == :(-1*log(x)+-1//6*x^-6+1//6*log(1+x^6))
@test integrate(x^-8*(1+x^6)^-1, x) == :(x^-1+-1//6*arctan(3^(1/2)+-2x)+-1//7*x^-7+1//3*arctan(x)+1//6*arctan(3^(1/2)+2x)+-1//12*3^(1/2)*log(1+x^2+x*3^(1/2))+1//12*3^(1/2)*log(1+x^2+-1*x*3^(1/2)))
@test integrate(x^1//3*(1+-1*x^6)^-1, x) == :(-1//6*log(1+-1*x^2//3)+1//12*log(1+x^2//3+x^4//3)+-1//3*arctan((x^2//3+cos(1//9*pi))*csc(1//9*pi))*sin(2//9*pi)+-1//6*3^(1/2)*arctan(1//3*3^(1/2)*(1+2*x^2//3))+-1//6*cos(2//9*pi)*log(1+x^4//3+2*x^2//3*cos(1//9*pi))+-1//6*log(1+x^4//3+-2*x^2//3*cos(2//9*pi))*sin(1//18*pi)+1//3*arctan((x^2//3+-1*cos(2//9*pi))*csc(2//9*pi))*cos(1//18*pi)+1//3*arctan((x^2//3+-1*sin(1//18*pi))*sec(1//18*pi))*sin(1//9*pi)+1//6*cos(1//9*pi)*log(1+x^4//3+-2*x^2//3*sin(1//18*pi)))
@test integrate(x^8*(-1+4*x^6)^(1/2), x) == :(-1//192*arctanh(2*x^3*(-1+4*x^6)^-1//2)+-1//96*x^3*(-1+4*x^6)^(1/2)+1//12*x^9*(-1+4*x^6)^(1/2))
@test integrate(x^5*(a^6+-1*x^6)^(1/2), x) == :(-1//9*(a^6+-1*x^6)^3//2)
@test integrate(x^2*(-2+x^6)^(1/2), x) == :(-1//3*arctanh(x^3*(-2+x^6)^-1//2)+1//6*x^3*(-2+x^6)^(1/2))
@test integrate(x^23*(2+x^6)^-1//2, x) == :(-8//3*(2+x^6)^(1/2)+-2//5*(2+x^6)^5//2+1//21*(2+x^6)^7//2+4//3*(2+x^6)^3//2)
@test integrate(x^17*(2+x^6)^-1//2, x) == :(-4//9*(2+x^6)^3//2+1//15*(2+x^6)^5//2+4//3*(2+x^6)^(1/2))
@test integrate(x^11*(2+x^6)^-1//2, x) == :(-2//3*(2+x^6)^(1/2)+1//9*(2+x^6)^3//2)
@test integrate(x^5*(2+x^6)^-1//2, x) == :(1//3*(2+x^6)^(1/2))
@test integrate(x^-1*(2+x^6)^-1//2, x) == :(-1//6*2^(1/2)*arctanh((1/2)*2^(1/2)*(2+x^6)^(1/2)))
@test integrate(x^-7*(2+x^6)^-1//2, x) == :(-1//12*x^-6*(2+x^6)^(1/2)+1//24*2^(1/2)*arctanh((1/2)*2^(1/2)*(2+x^6)^(1/2)))
@test integrate(x^-13*(2+x^6)^-1//2, x) == :(-1//24*x^-12*(2+x^6)^(1/2)+-1//64*2^(1/2)*arctanh((1/2)*2^(1/2)*(2+x^6)^(1/2))+1//32*x^-6*(2+x^6)^(1/2))
@test integrate(x^14*(2+x^6)^-1//2, x) == :((1/2)*arcsinh((1/2)*2^(1/2)*x^3)+-1//4*x^3*(2+x^6)^(1/2)+1//12*x^9*(2+x^6)^(1/2))
@test integrate(x^8*(2+x^6)^-1//2, x) == :(-1//3*arcsinh((1/2)*2^(1/2)*x^3)+1//6*x^3*(2+x^6)^(1/2))
@test integrate(x^2*(2+x^6)^-1//2, x) == :(1//3*arcsinh((1/2)*2^(1/2)*x^3))
@test integrate(x^-4*(2+x^6)^-1//2, x) == :(-1//6*x^-3*(2+x^6)^(1/2))
@test integrate(x^-10*(2+x^6)^-1//2, x) == :(-1//18*x^-9*(2+x^6)^(1/2)+1//18*x^-3*(2+x^6)^(1/2))
@test integrate(x^-16*(2+x^6)^-1//2, x) == :(-1//30*x^-15*(2+x^6)^(1/2)+-1//45*x^-3*(2+x^6)^(1/2)+1//45*x^-9*(2+x^6)^(1/2))
@test integrate(x^7*(2+x^6)^-1//2, x) == :(1//5*x^2*(2+x^6)^(1/2)+-2//15*2^5//6*3^3//4*((x^2+2^1//3*(1+3^(1/2)))^-2*(2^1//3+x^2))^-1//2*((x^2+2^1//3*(1+3^(1/2)))^-2*(2^2//3+x^4+-1*2^1//3*x^2))^(1/2)*(2+3^(1/2))^(1/2)*(2+x^6)^-1//2*(2^1//3+x^2)*Elliptic.F(arcsin((x^2+2^1//3*(1+3^(1/2)))^-1*(x^2+2^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x*(2+x^6)^-1//2, x) == :(1//6*2^5//6*3^3//4*((x^2+2^1//3*(1+3^(1/2)))^-2*(2^1//3+x^2))^-1//2*((x^2+2^1//3*(1+3^(1/2)))^-2*(2^2//3+x^4+-1*2^1//3*x^2))^(1/2)*(2+3^(1/2))^(1/2)*(2+x^6)^-1//2*(2^1//3+x^2)*Elliptic.F(arcsin((x^2+2^1//3*(1+3^(1/2)))^-1*(x^2+2^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-5*(2+x^6)^-1//2, x) == :(-1//8*x^-4*(2+x^6)^(1/2)+-1//48*2^5//6*3^3//4*((x^2+2^1//3*(1+3^(1/2)))^-2*(2^1//3+x^2))^-1//2*((x^2+2^1//3*(1+3^(1/2)))^-2*(2^2//3+x^4+-1*2^1//3*x^2))^(1/2)*(2+3^(1/2))^(1/2)*(2+x^6)^-1//2*(2^1//3+x^2)*Elliptic.F(arcsin((x^2+2^1//3*(1+3^(1/2)))^-1*(x^2+2^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^6*(2+x^6)^-1//2, x) == :(1//4*x*(2+x^6)^(1/2)+-1//24*x*2^2//3*3^3//4*((2^1//3+x^2*(1+3^(1/2)))^-2*(2^2//3+x^4+-1*2^1//3*x^2))^(1/2)*(x^2*(2^1//3+x^2*(1+3^(1/2)))^-2*(2^1//3+x^2))^-1//2*(2+x^6)^-1//2*(2^1//3+x^2)*Elliptic.F(arccos((2^1//3+x^2*(1+3^(1/2)))^-1*(2^1//3+x^2*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate((2+x^6)^-1//2, x) == :(1//12*x*2^2//3*3^3//4*((2^1//3+x^2*(1+3^(1/2)))^-2*(2^2//3+x^4+-1*2^1//3*x^2))^(1/2)*(x^2*(2^1//3+x^2*(1+3^(1/2)))^-2*(2^1//3+x^2))^-1//2*(2+x^6)^-1//2*(2^1//3+x^2)*Elliptic.F(arccos((2^1//3+x^2*(1+3^(1/2)))^-1*(2^1//3+x^2*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate(x^-6*(2+x^6)^-1//2, x) == :(-1//10*x^-5*(2+x^6)^(1/2)+-1//60*x*2^2//3*3^3//4*((2^1//3+x^2*(1+3^(1/2)))^-2*(2^2//3+x^4+-1*2^1//3*x^2))^(1/2)*(x^2*(2^1//3+x^2*(1+3^(1/2)))^-2*(2^1//3+x^2))^-1//2*(2+x^6)^-1//2*(2^1//3+x^2)*Elliptic.F(arccos((2^1//3+x^2*(1+3^(1/2)))^-1*(2^1//3+x^2*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate(x^9*(2+x^6)^-1//2, x) == :(-8*(2+x^6)^(1/2)*(7*x^2+7*2^1//3*(1+3^(1/2)))^-1+1//7*x^4*(2+x^6)^(1/2)+-8//21*2^2//3*3^3//4*((x^2+2^1//3*(1+3^(1/2)))^-2*(2^1//3+x^2))^-1//2*((x^2+2^1//3*(1+3^(1/2)))^-2*(2^2//3+x^4+-1*2^1//3*x^2))^(1/2)*(2+x^6)^-1//2*(2^1//3+x^2)*Elliptic.F(arcsin((x^2+2^1//3*(1+3^(1/2)))^-1*(x^2+2^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+4//7*2^1//6*3^1//4*((x^2+2^1//3*(1+3^(1/2)))^-2*(2^1//3+x^2))^-1//2*((x^2+2^1//3*(1+3^(1/2)))^-2*(2^2//3+x^4+-1*2^1//3*x^2))^(1/2)*(2+x^6)^-1//2*(2+-1*3^(1/2))^(1/2)*(2^1//3+x^2)*Elliptic.E(arcsin((x^2+2^1//3*(1+3^(1/2)))^-1*(x^2+2^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^3*(2+x^6)^-1//2, x) == :((2+x^6)^(1/2)*(x^2+2^1//3*(1+3^(1/2)))^-1+1//3*2^2//3*3^3//4*((x^2+2^1//3*(1+3^(1/2)))^-2*(2^1//3+x^2))^-1//2*((x^2+2^1//3*(1+3^(1/2)))^-2*(2^2//3+x^4+-1*2^1//3*x^2))^(1/2)*(2+x^6)^-1//2*(2^1//3+x^2)*Elliptic.F(arcsin((x^2+2^1//3*(1+3^(1/2)))^-1*(x^2+2^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+-1//2*2^1//6*3^1//4*((x^2+2^1//3*(1+3^(1/2)))^-2*(2^1//3+x^2))^-1//2*((x^2+2^1//3*(1+3^(1/2)))^-2*(2^2//3+x^4+-1*2^1//3*x^2))^(1/2)*(2+x^6)^-1//2*(2+-1*3^(1/2))^(1/2)*(2^1//3+x^2)*Elliptic.E(arcsin((x^2+2^1//3*(1+3^(1/2)))^-1*(x^2+2^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-3*(2+x^6)^-1//2, x) == :((2+x^6)^(1/2)*(4*x^2+4*2^1//3*(1+3^(1/2)))^-1+-1//4*x^-2*(2+x^6)^(1/2)+1//12*2^2//3*3^3//4*((x^2+2^1//3*(1+3^(1/2)))^-2*(2^1//3+x^2))^-1//2*((x^2+2^1//3*(1+3^(1/2)))^-2*(2^2//3+x^4+-1*2^1//3*x^2))^(1/2)*(2+x^6)^-1//2*(2^1//3+x^2)*Elliptic.F(arcsin((x^2+2^1//3*(1+3^(1/2)))^-1*(x^2+2^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+-1//8*2^1//6*3^1//4*((x^2+2^1//3*(1+3^(1/2)))^-2*(2^1//3+x^2))^-1//2*((x^2+2^1//3*(1+3^(1/2)))^-2*(2^2//3+x^4+-1*2^1//3*x^2))^(1/2)*(2+x^6)^-1//2*(2+-1*3^(1/2))^(1/2)*(2^1//3+x^2)*Elliptic.E(arcsin((x^2+2^1//3*(1+3^(1/2)))^-1*(x^2+2^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^10*(2+x^6)^-1//2, x) == :(1//8*x^5*(2+x^6)^(1/2)+-1*x*(2+x^6)^(1/2)*(8*2^1//3+8*x^2*(1+3^(1/2)))^-1*(5+5*3^(1/2))+5//8*x*2^1//3*3^1//4*((2^1//3+x^2*(1+3^(1/2)))^-2*(2^2//3+x^4+-1*2^1//3*x^2))^(1/2)*(x^2*(2^1//3+x^2*(1+3^(1/2)))^-2*(2^1//3+x^2))^-1//2*(2+x^6)^-1//2*(2^1//3+x^2)*Elliptic.E(arccos((2^1//3+x^2*(1+3^(1/2)))^-1*(2^1//3+x^2*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2))+1//48*x*2^1//3*3^3//4*((2^1//3+x^2*(1+3^(1/2)))^-2*(2^2//3+x^4+-1*2^1//3*x^2))^(1/2)*(x^2*(2^1//3+x^2*(1+3^(1/2)))^-2*(2^1//3+x^2))^-1//2*(2+x^6)^-1//2*(5+-5*3^(1/2))*(2^1//3+x^2)*Elliptic.F(arccos((2^1//3+x^2*(1+3^(1/2)))^-1*(2^1//3+x^2*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate(x^4*(2+x^6)^-1//2, x) == :(x*(2+x^6)^(1/2)*(2*2^1//3+2*x^2*(1+3^(1/2)))^-1*(1+3^(1/2))+-1//2*x*2^1//3*3^1//4*((2^1//3+x^2*(1+3^(1/2)))^-2*(2^2//3+x^4+-1*2^1//3*x^2))^(1/2)*(x^2*(2^1//3+x^2*(1+3^(1/2)))^-2*(2^1//3+x^2))^-1//2*(2+x^6)^-1//2*(2^1//3+x^2)*Elliptic.E(arccos((2^1//3+x^2*(1+3^(1/2)))^-1*(2^1//3+x^2*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2))+-1//12*x*2^1//3*3^3//4*((2^1//3+x^2*(1+3^(1/2)))^-2*(2^2//3+x^4+-1*2^1//3*x^2))^(1/2)*(x^2*(2^1//3+x^2*(1+3^(1/2)))^-2*(2^1//3+x^2))^-1//2*(2+x^6)^-1//2*(1+-1*3^(1/2))*(2^1//3+x^2)*Elliptic.F(arccos((2^1//3+x^2*(1+3^(1/2)))^-1*(2^1//3+x^2*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate(x^-2*(2+x^6)^-1//2, x) == :(-1//2*x^-1*(2+x^6)^(1/2)+x*(2+x^6)^(1/2)*(2*2^1//3+2*x^2*(1+3^(1/2)))^-1*(1+3^(1/2))+-1//2*x*2^1//3*3^1//4*((2^1//3+x^2*(1+3^(1/2)))^-2*(2^2//3+x^4+-1*2^1//3*x^2))^(1/2)*(x^2*(2^1//3+x^2*(1+3^(1/2)))^-2*(2^1//3+x^2))^-1//2*(2+x^6)^-1//2*(2^1//3+x^2)*Elliptic.E(arccos((2^1//3+x^2*(1+3^(1/2)))^-1*(2^1//3+x^2*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2))+-1//12*x*2^1//3*3^3//4*((2^1//3+x^2*(1+3^(1/2)))^-2*(2^2//3+x^4+-1*2^1//3*x^2))^(1/2)*(x^2*(2^1//3+x^2*(1+3^(1/2)))^-2*(2^1//3+x^2))^-1//2*(2+x^6)^-1//2*(1+-1*3^(1/2))*(2^1//3+x^2)*Elliptic.F(arccos((2^1//3+x^2*(1+3^(1/2)))^-1*(2^1//3+x^2*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate(x^23*(2+x^6)^-3//2, x) == :(4*(2+x^6)^(1/2)+-2//3*(2+x^6)^3//2+1//15*(2+x^6)^5//2+8//3*(2+x^6)^-1//2)
@test integrate(x^17*(2+x^6)^-3//2, x) == :(-4//3*(2+x^6)^(1/2)+-4//3*(2+x^6)^-1//2+1//9*(2+x^6)^3//2)
@test integrate(x^11*(2+x^6)^-3//2, x) == :(1//3*(2+x^6)^(1/2)+2//3*(2+x^6)^-1//2)
@test integrate(x^5*(2+x^6)^-3//2, x) == :(-1//3*(2+x^6)^-1//2)
@test integrate(x^-1*(2+x^6)^-3//2, x) == :(1//6*(2+x^6)^-1//2+-1//12*2^(1/2)*arctanh((1/2)*2^(1/2)*(2+x^6)^(1/2)))
@test integrate(x^-7*(2+x^6)^-3//2, x) == :(-1//8*(2+x^6)^-1//2+-1//12*x^-6*(2+x^6)^-1//2+1//16*2^(1/2)*arctanh((1/2)*2^(1/2)*(2+x^6)^(1/2)))
@test integrate(x^-13*(2+x^6)^-3//2, x) == :(5//64*(2+x^6)^-1//2+-5//128*2^(1/2)*arctanh((1/2)*2^(1/2)*(2+x^6)^(1/2))+-1//24*x^-12*(2+x^6)^-1//2+5//96*x^-6*(2+x^6)^-1//2)
@test integrate(x^14*(2+x^6)^-3//2, x) == :(-1*arcsinh((1/2)*2^(1/2)*x^3)+(1/2)*x^3*(2+x^6)^(1/2)+-1//3*x^9*(2+x^6)^-1//2)
@test integrate(x^8*(2+x^6)^-3//2, x) == :(1//3*arcsinh((1/2)*2^(1/2)*x^3)+-1//3*x^3*(2+x^6)^-1//2)
@test integrate(x^2*(2+x^6)^-3//2, x) == :(1//6*x^3*(2+x^6)^-1//2)
@test integrate(x^-4*(2+x^6)^-3//2, x) == :(-1//6*x^-3*(2+x^6)^-1//2+-1//6*x^3*(2+x^6)^-1//2)
@test integrate(x^-10*(2+x^6)^-3//2, x) == :(-1//18*x^-9*(2+x^6)^-1//2+1//9*x^-3*(2+x^6)^-1//2+1//9*x^3*(2+x^6)^-1//2)
@test integrate(x^13*(2+x^6)^-3//2, x) == :(-1//3*x^8*(2+x^6)^-1//2+8//15*x^2*(2+x^6)^(1/2)+-16//45*2^5//6*3^3//4*((x^2+2^1//3*(1+3^(1/2)))^-2*(2^1//3+x^2))^-1//2*((x^2+2^1//3*(1+3^(1/2)))^-2*(2^2//3+x^4+-1*2^1//3*x^2))^(1/2)*(2+3^(1/2))^(1/2)*(2+x^6)^-1//2*(2^1//3+x^2)*Elliptic.F(arcsin((x^2+2^1//3*(1+3^(1/2)))^-1*(x^2+2^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^7*(2+x^6)^-3//2, x) == :(-1//3*x^2*(2+x^6)^-1//2+1//9*2^5//6*3^3//4*((x^2+2^1//3*(1+3^(1/2)))^-2*(2^1//3+x^2))^-1//2*((x^2+2^1//3*(1+3^(1/2)))^-2*(2^2//3+x^4+-1*2^1//3*x^2))^(1/2)*(2+3^(1/2))^(1/2)*(2+x^6)^-1//2*(2^1//3+x^2)*Elliptic.F(arcsin((x^2+2^1//3*(1+3^(1/2)))^-1*(x^2+2^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x*(2+x^6)^-3//2, x) == :(1//6*x^2*(2+x^6)^-1//2+1//36*2^5//6*3^3//4*((x^2+2^1//3*(1+3^(1/2)))^-2*(2^1//3+x^2))^-1//2*((x^2+2^1//3*(1+3^(1/2)))^-2*(2^2//3+x^4+-1*2^1//3*x^2))^(1/2)*(2+3^(1/2))^(1/2)*(2+x^6)^-1//2*(2^1//3+x^2)*Elliptic.F(arcsin((x^2+2^1//3*(1+3^(1/2)))^-1*(x^2+2^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-5*(2+x^6)^-3//2, x) == :(-7//48*x^-4*(2+x^6)^(1/2)+1//6*x^-4*(2+x^6)^-1//2+-7//288*2^5//6*3^3//4*((x^2+2^1//3*(1+3^(1/2)))^-2*(2^1//3+x^2))^-1//2*((x^2+2^1//3*(1+3^(1/2)))^-2*(2^2//3+x^4+-1*2^1//3*x^2))^(1/2)*(2+3^(1/2))^(1/2)*(2+x^6)^-1//2*(2^1//3+x^2)*Elliptic.F(arcsin((x^2+2^1//3*(1+3^(1/2)))^-1*(x^2+2^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^12*(2+x^6)^-3//2, x) == :(-1//3*x^7*(2+x^6)^-1//2+7//12*x*(2+x^6)^(1/2)+-7//72*x*2^2//3*3^3//4*((2^1//3+x^2*(1+3^(1/2)))^-2*(2^2//3+x^4+-1*2^1//3*x^2))^(1/2)*(x^2*(2^1//3+x^2*(1+3^(1/2)))^-2*(2^1//3+x^2))^-1//2*(2+x^6)^-1//2*(2^1//3+x^2)*Elliptic.F(arccos((2^1//3+x^2*(1+3^(1/2)))^-1*(2^1//3+x^2*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate(x^6*(2+x^6)^-3//2, x) == :(-1//3*x*(2+x^6)^-1//2+1//36*x*2^2//3*3^3//4*((2^1//3+x^2*(1+3^(1/2)))^-2*(2^2//3+x^4+-1*2^1//3*x^2))^(1/2)*(x^2*(2^1//3+x^2*(1+3^(1/2)))^-2*(2^1//3+x^2))^-1//2*(2+x^6)^-1//2*(2^1//3+x^2)*Elliptic.F(arccos((2^1//3+x^2*(1+3^(1/2)))^-1*(2^1//3+x^2*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate((2+x^6)^-3//2, x) == :(1//6*x*(2+x^6)^-1//2+1//36*x*2^2//3*3^3//4*((2^1//3+x^2*(1+3^(1/2)))^-2*(2^2//3+x^4+-1*2^1//3*x^2))^(1/2)*(x^2*(2^1//3+x^2*(1+3^(1/2)))^-2*(2^1//3+x^2))^-1//2*(2+x^6)^-1//2*(2^1//3+x^2)*Elliptic.F(arccos((2^1//3+x^2*(1+3^(1/2)))^-1*(2^1//3+x^2*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate(x^-6*(2+x^6)^-3//2, x) == :(-2//15*x^-5*(2+x^6)^(1/2)+1//6*x^-5*(2+x^6)^-1//2+-1//45*x*2^2//3*3^3//4*((2^1//3+x^2*(1+3^(1/2)))^-2*(2^2//3+x^4+-1*2^1//3*x^2))^(1/2)*(x^2*(2^1//3+x^2*(1+3^(1/2)))^-2*(2^1//3+x^2))^-1//2*(2+x^6)^-1//2*(2^1//3+x^2)*Elliptic.F(arccos((2^1//3+x^2*(1+3^(1/2)))^-1*(2^1//3+x^2*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate(x^15*(2+x^6)^-3//2, x) == :(-80*(2+x^6)^(1/2)*(21*x^2+21*2^1//3*(1+3^(1/2)))^-1+-1//3*x^10*(2+x^6)^-1//2+10//21*x^4*(2+x^6)^(1/2)+-80//63*2^2//3*3^3//4*((x^2+2^1//3*(1+3^(1/2)))^-2*(2^1//3+x^2))^-1//2*((x^2+2^1//3*(1+3^(1/2)))^-2*(2^2//3+x^4+-1*2^1//3*x^2))^(1/2)*(2+x^6)^-1//2*(2^1//3+x^2)*Elliptic.F(arcsin((x^2+2^1//3*(1+3^(1/2)))^-1*(x^2+2^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+40//21*2^1//6*3^1//4*((x^2+2^1//3*(1+3^(1/2)))^-2*(2^1//3+x^2))^-1//2*((x^2+2^1//3*(1+3^(1/2)))^-2*(2^2//3+x^4+-1*2^1//3*x^2))^(1/2)*(2+x^6)^-1//2*(2+-1*3^(1/2))^(1/2)*(2^1//3+x^2)*Elliptic.E(arcsin((x^2+2^1//3*(1+3^(1/2)))^-1*(x^2+2^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^9*(2+x^6)^-3//2, x) == :(4*(2+x^6)^(1/2)*(3*x^2+3*2^1//3*(1+3^(1/2)))^-1+-1//3*x^4*(2+x^6)^-1//2+4//9*2^2//3*3^3//4*((x^2+2^1//3*(1+3^(1/2)))^-2*(2^1//3+x^2))^-1//2*((x^2+2^1//3*(1+3^(1/2)))^-2*(2^2//3+x^4+-1*2^1//3*x^2))^(1/2)*(2+x^6)^-1//2*(2^1//3+x^2)*Elliptic.F(arcsin((x^2+2^1//3*(1+3^(1/2)))^-1*(x^2+2^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+-2//3*2^1//6*3^1//4*((x^2+2^1//3*(1+3^(1/2)))^-2*(2^1//3+x^2))^-1//2*((x^2+2^1//3*(1+3^(1/2)))^-2*(2^2//3+x^4+-1*2^1//3*x^2))^(1/2)*(2+x^6)^-1//2*(2+-1*3^(1/2))^(1/2)*(2^1//3+x^2)*Elliptic.E(arcsin((x^2+2^1//3*(1+3^(1/2)))^-1*(x^2+2^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^3*(2+x^6)^-3//2, x) == :(-1*(2+x^6)^(1/2)*(6*x^2+6*2^1//3*(1+3^(1/2)))^-1+1//6*x^4*(2+x^6)^-1//2+-1//18*2^2//3*3^3//4*((x^2+2^1//3*(1+3^(1/2)))^-2*(2^1//3+x^2))^-1//2*((x^2+2^1//3*(1+3^(1/2)))^-2*(2^2//3+x^4+-1*2^1//3*x^2))^(1/2)*(2+x^6)^-1//2*(2^1//3+x^2)*Elliptic.F(arcsin((x^2+2^1//3*(1+3^(1/2)))^-1*(x^2+2^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+1//12*2^1//6*3^1//4*((x^2+2^1//3*(1+3^(1/2)))^-2*(2^1//3+x^2))^-1//2*((x^2+2^1//3*(1+3^(1/2)))^-2*(2^2//3+x^4+-1*2^1//3*x^2))^(1/2)*(2+x^6)^-1//2*(2+-1*3^(1/2))^(1/2)*(2^1//3+x^2)*Elliptic.E(arcsin((x^2+2^1//3*(1+3^(1/2)))^-1*(x^2+2^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-3*(2+x^6)^-3//2, x) == :(5*(2+x^6)^(1/2)*(24*x^2+24*2^1//3*(1+3^(1/2)))^-1+-5//24*x^-2*(2+x^6)^(1/2)+1//6*x^-2*(2+x^6)^-1//2+1//72*2^2//3*3^3//4*((x^2+2^1//3*(1+3^(1/2)))^-2*(2^1//3+x^2))^-1//2*((x^2+2^1//3*(1+3^(1/2)))^-2*(2^2//3+x^4+-1*2^1//3*x^2))^(1/2)*(2+x^6)^-1//2*(5*2^1//3+5*x^2)*Elliptic.F(arcsin((x^2+2^1//3*(1+3^(1/2)))^-1*(x^2+2^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+-5//48*2^1//6*3^1//4*((x^2+2^1//3*(1+3^(1/2)))^-2*(2^1//3+x^2))^-1//2*((x^2+2^1//3*(1+3^(1/2)))^-2*(2^2//3+x^4+-1*2^1//3*x^2))^(1/2)*(2+x^6)^-1//2*(2+-1*3^(1/2))^(1/2)*(2^1//3+x^2)*Elliptic.E(arcsin((x^2+2^1//3*(1+3^(1/2)))^-1*(x^2+2^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^10*(2+x^6)^-3//2, x) == :(-1//3*x^5*(2+x^6)^-1//2+x*(2+x^6)^(1/2)*(6*2^1//3+6*x^2*(1+3^(1/2)))^-1*(5+5*3^(1/2))+-5//6*x*2^1//3*3^1//4*((2^1//3+x^2*(1+3^(1/2)))^-2*(2^2//3+x^4+-1*2^1//3*x^2))^(1/2)*(x^2*(2^1//3+x^2*(1+3^(1/2)))^-2*(2^1//3+x^2))^-1//2*(2+x^6)^-1//2*(2^1//3+x^2)*Elliptic.E(arccos((2^1//3+x^2*(1+3^(1/2)))^-1*(2^1//3+x^2*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2))+-1//36*x*2^1//3*3^3//4*((2^1//3+x^2*(1+3^(1/2)))^-2*(2^2//3+x^4+-1*2^1//3*x^2))^(1/2)*(x^2*(2^1//3+x^2*(1+3^(1/2)))^-2*(2^1//3+x^2))^-1//2*(2+x^6)^-1//2*(5+-5*3^(1/2))*(2^1//3+x^2)*Elliptic.F(arccos((2^1//3+x^2*(1+3^(1/2)))^-1*(2^1//3+x^2*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate(x^4*(2+x^6)^-3//2, x) == :(1//6*x^5*(2+x^6)^-1//2+-1*x*(2+x^6)^(1/2)*(6*2^1//3+6*x^2*(1+3^(1/2)))^-1*(1+3^(1/2))+1//6*x*2^1//3*3^1//4*((2^1//3+x^2*(1+3^(1/2)))^-2*(2^2//3+x^4+-1*2^1//3*x^2))^(1/2)*(x^2*(2^1//3+x^2*(1+3^(1/2)))^-2*(2^1//3+x^2))^-1//2*(2+x^6)^-1//2*(2^1//3+x^2)*Elliptic.E(arccos((2^1//3+x^2*(1+3^(1/2)))^-1*(2^1//3+x^2*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2))+1//36*x*2^1//3*3^3//4*((2^1//3+x^2*(1+3^(1/2)))^-2*(2^2//3+x^4+-1*2^1//3*x^2))^(1/2)*(x^2*(2^1//3+x^2*(1+3^(1/2)))^-2*(2^1//3+x^2))^-1//2*(2+x^6)^-1//2*(1+-1*3^(1/2))*(2^1//3+x^2)*Elliptic.F(arccos((2^1//3+x^2*(1+3^(1/2)))^-1*(2^1//3+x^2*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate(x^-2*(2+x^6)^-3//2, x) == :(-1//3*x^-1*(2+x^6)^(1/2)+1//6*x^-1*(2+x^6)^-1//2+x*(2+x^6)^(1/2)*(3*2^1//3+3*x^2*(1+3^(1/2)))^-1*(1+3^(1/2))+-1//3*x*2^1//3*3^1//4*((2^1//3+x^2*(1+3^(1/2)))^-2*(2^2//3+x^4+-1*2^1//3*x^2))^(1/2)*(x^2*(2^1//3+x^2*(1+3^(1/2)))^-2*(2^1//3+x^2))^-1//2*(2+x^6)^-1//2*(2^1//3+x^2)*Elliptic.E(arccos((2^1//3+x^2*(1+3^(1/2)))^-1*(2^1//3+x^2*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2))+-1//18*x*2^1//3*3^3//4*((2^1//3+x^2*(1+3^(1/2)))^-2*(2^2//3+x^4+-1*2^1//3*x^2))^(1/2)*(x^2*(2^1//3+x^2*(1+3^(1/2)))^-2*(2^1//3+x^2))^-1//2*(2+x^6)^-1//2*(1+-1*3^(1/2))*(2^1//3+x^2)*Elliptic.F(arccos((2^1//3+x^2*(1+3^(1/2)))^-1*(2^1//3+x^2*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate(x^m*(a+b*x^7), x) == :(a*x^(1+m)*(1+m)^-1+b*x^(8+m)*(8+m)^-1)
@test integrate(x^8*(a+b*x^7), x) == :(1//9*a*x^9+1//16*b*x^16)
@test integrate(x^-8*(a+b*x^7), x) == :(b*log(x)+-1//7*a*x^-7)
@test integrate(x^m*(a+b*x^7)^2, x) == :(a^2*x^(1+m)*(1+m)^-1+b^2*x^(15+m)*(15+m)^-1+2*a*b*x^(8+m)*(8+m)^-1)
@test integrate(x^8*(a+b*x^7)^2, x) == :(1//9*a^2*x^9+1//23*b^2*x^23+1//8*a*b*x^16)
@test integrate(x^-8*(a+b*x^7)^2, x) == :(-1//7*a^2*x^-7+1//7*b^2*x^7+2*a*b*log(x))
@test integrate(x^6*(a+b*x^7)^-1, x) == :(1//7*b^-1*log(a+b*x^7))
@test integrate((a+b*x^7)^-1, x) == :(1//7*a^-6//7*b^-1//7*log(a^1//7+x*b^1//7)+-2//7*a^-6//7*b^-1//7*arctan(-1*x*a^-1//7*b^1//7*csc(1//7*pi)+cot(1//7*pi))*sin(1//7*pi)+-1//7*a^-6//7*b^-1//7*cos(1//7*pi)*log(a^2//7+b^2//7*x^2+-2*x*a^1//7*b^1//7*cos(1//7*pi))+-1//7*a^-6//7*b^-1//7*log(a^2//7+b^2//7*x^2+-2*x*a^1//7*b^1//7*sin(1//14*pi))*sin(1//14*pi)+1//7*a^-6//7*b^-1//7*log(a^2//7+b^2//7*x^2+2*x*a^1//7*b^1//7*sin(3//14*pi))*sin(3//14*pi)+2//7*a^-6//7*b^-1//7*arctan(-1*tan(1//14*pi)+x*a^-1//7*b^1//7*sec(1//14*pi))*cos(1//14*pi)+2//7*a^-6//7*b^-1//7*arctan(x*a^-1//7*b^1//7*sec(3//14*pi)+tan(3//14*pi))*cos(3//14*pi))
@test integrate(x^-1*(a+b*x^7)^-1, x) == :(a^-1*log(x)+-1//7*a^-1*log(a+b*x^7))
@test integrate(x^6*(a+-1*b*x^7)^-1, x) == :(-1//7*b^-1*log(a+-1*b*x^7))
@test integrate((a+-1*b*x^7)^-1, x) == :(-1//7*a^-6//7*b^-1//7*log(a^1//7+-1*x*b^1//7)+-1//7*a^-6//7*b^-1//7*log(a^2//7+b^2//7*x^2+-2*x*a^1//7*b^1//7*sin(3//14*pi))*sin(3//14*pi)+1//7*a^-6//7*b^-1//7*cos(1//7*pi)*log(a^2//7+b^2//7*x^2+2*x*a^1//7*b^1//7*cos(1//7*pi))+1//7*a^-6//7*b^-1//7*log(a^2//7+b^2//7*x^2+2*x*a^1//7*b^1//7*sin(1//14*pi))*sin(1//14*pi)+2//7*a^-6//7*b^-1//7*arctan(-1*tan(3//14*pi)+x*a^-1//7*b^1//7*sec(3//14*pi))*cos(3//14*pi)+2//7*a^-6//7*b^-1//7*arctan(x*a^-1//7*b^1//7*csc(1//7*pi)+cot(1//7*pi))*sin(1//7*pi)+2//7*a^-6//7*b^-1//7*arctan(x*a^-1//7*b^1//7*sec(1//14*pi)+tan(1//14*pi))*cos(1//14*pi))
@test integrate(x^-1*(a+-1*b*x^7)^-1, x) == :(a^-1*log(x)+-1//7*a^-1*log(a+-1*b*x^7))
@test integrate((1+-1*x^7)^-1, x) == :(-1//7*log(1+-1x)+-1//7*log(1+x^2+-2*x*sin(3//14*pi))*sin(3//14*pi)+1//7*cos(1//7*pi)*log(1+x^2+2*x*cos(1//7*pi))+1//7*log(1+x^2+2*x*sin(1//14*pi))*sin(1//14*pi)+2//7*arctan((x+-1*sin(3//14*pi))*sec(3//14*pi))*cos(3//14*pi)+2//7*arctan((x+cos(1//7*pi))*csc(1//7*pi))*sin(1//7*pi)+2//7*arctan((x+sin(1//14*pi))*sec(1//14*pi))*cos(1//14*pi))
@test integrate((1+x^7)^-1, x) == :(1//7*log(1+x)+-2//7*arctan(-1*x*csc(1//7*pi)+cot(1//7*pi))*sin(1//7*pi)+-1//7*cos(1//7*pi)*log(1+x^2+-2*x*cos(1//7*pi))+-1//7*log(1+x^2+-2*x*sin(1//14*pi))*sin(1//14*pi)+1//7*log(1+x^2+2*x*sin(3//14*pi))*sin(3//14*pi)+2//7*arctan(-1*tan(1//14*pi)+x*sec(1//14*pi))*cos(1//14*pi)+2//7*arctan(x*sec(3//14*pi)+tan(3//14*pi))*cos(3//14*pi))
@test integrate(x^9*(a+b*x^8)^-1, x) == :((1/2)*b^-1*x^2+-1//8*2^(1/2)*a^1//4*b^-5//4*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^2)+-1//16*2^(1/2)*a^1//4*b^-5//4*log(a^(1/2)+b^(1/2)*x^4+2^(1/2)*a^1//4*b^1//4*x^2)+1//8*2^(1/2)*a^1//4*b^-5//4*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^2)+1//16*2^(1/2)*a^1//4*b^-5//4*log(a^(1/2)+b^(1/2)*x^4+-1*2^(1/2)*a^1//4*b^1//4*x^2))
@test integrate(x^7*(a+b*x^8)^-1, x) == :(1//8*b^-1*log(a+b*x^8))
@test integrate(x^5*(a+b*x^8)^-1, x) == :(-1//8*2^(1/2)*a^-1//4*b^-3//4*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^2)+-1//16*2^(1/2)*a^-1//4*b^-3//4*log(a^(1/2)+b^(1/2)*x^4+2^(1/2)*a^1//4*b^1//4*x^2)+1//8*2^(1/2)*a^-1//4*b^-3//4*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^2)+1//16*2^(1/2)*a^-1//4*b^-3//4*log(a^(1/2)+b^(1/2)*x^4+-1*2^(1/2)*a^1//4*b^1//4*x^2))
@test integrate(x^3*(a+b*x^8)^-1, x) == :(1//4*a^-1//2*b^-1//2*arctan(a^-1//2*b^(1/2)*x^4))
@test integrate(x*(a+b*x^8)^-1, x) == :(-1//8*2^(1/2)*a^-3//4*b^-1//4*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^2)+-1//16*2^(1/2)*a^-3//4*b^-1//4*log(a^(1/2)+b^(1/2)*x^4+-1*2^(1/2)*a^1//4*b^1//4*x^2)+1//8*2^(1/2)*a^-3//4*b^-1//4*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^2)+1//16*2^(1/2)*a^-3//4*b^-1//4*log(a^(1/2)+b^(1/2)*x^4+2^(1/2)*a^1//4*b^1//4*x^2))
@test integrate(x^-1*(a+b*x^8)^-1, x) == :(a^-1*log(x)+-1//8*a^-1*log(a+b*x^8))
@test integrate(x^-3*(a+b*x^8)^-1, x) == :(-1//2*a^-1*x^-2+-1//8*2^(1/2)*a^-5//4*b^1//4*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^2)+-1//16*2^(1/2)*a^-5//4*b^1//4*log(a^(1/2)+b^(1/2)*x^4+-1*2^(1/2)*a^1//4*b^1//4*x^2)+1//8*2^(1/2)*a^-5//4*b^1//4*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^2)+1//16*2^(1/2)*a^-5//4*b^1//4*log(a^(1/2)+b^(1/2)*x^4+2^(1/2)*a^1//4*b^1//4*x^2))
@test integrate(x^-5*(a+b*x^8)^-1, x) == :(-1//4*a^-1*x^-4+-1//4*a^-3//2*b^(1/2)*arctan(a^-1//2*b^(1/2)*x^4))
@test integrate(x^-7*(a+b*x^8)^-1, x) == :(-1//6*a^-1*x^-6+-1//8*2^(1/2)*a^-7//4*b^3//4*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^2)+-1//16*2^(1/2)*a^-7//4*b^3//4*log(a^(1/2)+b^(1/2)*x^4+2^(1/2)*a^1//4*b^1//4*x^2)+1//8*2^(1/2)*a^-7//4*b^3//4*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^2)+1//16*2^(1/2)*a^-7//4*b^3//4*log(a^(1/2)+b^(1/2)*x^4+-1*2^(1/2)*a^1//4*b^1//4*x^2))
@test integrate(x^-9*(a+b*x^8)^-1, x) == :(-1//8*a^-1*x^-8+-1*b*a^-2*log(x)+1//8*b*a^-2*log(a+b*x^8))
@test integrate(x^8*(a+b*x^8)^-1, x) == :(x*b^-1+-1//4*b^-9//8*(-1a)^1//8*arctan(x*b^1//8*(-1a)^-1//8)+-1//4*b^-9//8*(-1a)^1//8*arctanh(x*b^1//8*(-1a)^-1//8)+-1//8*2^(1/2)*b^-9//8*(-1a)^1//8*arctan(1+x*2^(1/2)*b^1//8*(-1a)^-1//8)+-1//16*2^(1/2)*b^-9//8*(-1a)^1//8*log((-1a)^1//4+b^1//4*x^2+x*2^(1/2)*b^1//8*(-1a)^1//8)+1//8*2^(1/2)*b^-9//8*(-1a)^1//8*arctan(1+-1*x*2^(1/2)*b^1//8*(-1a)^-1//8)+1//16*2^(1/2)*b^-9//8*(-1a)^1//8*log((-1a)^1//4+b^1//4*x^2+-1*x*2^(1/2)*b^1//8*(-1a)^1//8))
@test integrate(x^6*(a+b*x^8)^-1, x) == :(-1//4*b^-7//8*(-1a)^-1//8*arctanh(x*b^1//8*(-1a)^-1//8)+1//4*b^-7//8*(-1a)^-1//8*arctan(x*b^1//8*(-1a)^-1//8)+-1//8*2^(1/2)*b^-7//8*(-1a)^-1//8*arctan(1+-1*x*2^(1/2)*b^1//8*(-1a)^-1//8)+-1//16*2^(1/2)*b^-7//8*(-1a)^-1//8*log((-1a)^1//4+b^1//4*x^2+x*2^(1/2)*b^1//8*(-1a)^1//8)+1//8*2^(1/2)*b^-7//8*(-1a)^-1//8*arctan(1+x*2^(1/2)*b^1//8*(-1a)^-1//8)+1//16*2^(1/2)*b^-7//8*(-1a)^-1//8*log((-1a)^1//4+b^1//4*x^2+-1*x*2^(1/2)*b^1//8*(-1a)^1//8))
@test integrate(x^4*(a+b*x^8)^-1, x) == :(-1//4*b^-5//8*(-1a)^-3//8*arctan(x*b^1//8*(-1a)^-1//8)+-1//4*b^-5//8*(-1a)^-3//8*arctanh(x*b^1//8*(-1a)^-1//8)+-1//8*2^(1/2)*b^-5//8*(-1a)^-3//8*arctan(1+-1*x*2^(1/2)*b^1//8*(-1a)^-1//8)+-1//16*2^(1/2)*b^-5//8*(-1a)^-3//8*log((-1a)^1//4+b^1//4*x^2+-1*x*2^(1/2)*b^1//8*(-1a)^1//8)+1//8*2^(1/2)*b^-5//8*(-1a)^-3//8*arctan(1+x*2^(1/2)*b^1//8*(-1a)^-1//8)+1//16*2^(1/2)*b^-5//8*(-1a)^-3//8*log((-1a)^1//4+b^1//4*x^2+x*2^(1/2)*b^1//8*(-1a)^1//8))
@test integrate(x^2*(a+b*x^8)^-1, x) == :(-1//4*b^-3//8*(-1a)^-5//8*arctanh(x*b^1//8*(-1a)^-1//8)+1//4*b^-3//8*(-1a)^-5//8*arctan(x*b^1//8*(-1a)^-1//8)+-1//8*2^(1/2)*b^-3//8*(-1a)^-5//8*arctan(1+x*2^(1/2)*b^1//8*(-1a)^-1//8)+-1//16*2^(1/2)*b^-3//8*(-1a)^-5//8*log((-1a)^1//4+b^1//4*x^2+-1*x*2^(1/2)*b^1//8*(-1a)^1//8)+1//8*2^(1/2)*b^-3//8*(-1a)^-5//8*arctan(1+-1*x*2^(1/2)*b^1//8*(-1a)^-1//8)+1//16*2^(1/2)*b^-3//8*(-1a)^-5//8*log((-1a)^1//4+b^1//4*x^2+x*2^(1/2)*b^1//8*(-1a)^1//8))
@test integrate((a+b*x^8)^-1, x) == :(-1//4*b^-1//8*(-1a)^-7//8*arctan(x*b^1//8*(-1a)^-1//8)+-1//4*b^-1//8*(-1a)^-7//8*arctanh(x*b^1//8*(-1a)^-1//8)+-1//8*2^(1/2)*b^-1//8*(-1a)^-7//8*arctan(1+x*2^(1/2)*b^1//8*(-1a)^-1//8)+-1//16*2^(1/2)*b^-1//8*(-1a)^-7//8*log((-1a)^1//4+b^1//4*x^2+x*2^(1/2)*b^1//8*(-1a)^1//8)+1//8*2^(1/2)*b^-1//8*(-1a)^-7//8*arctan(1+-1*x*2^(1/2)*b^1//8*(-1a)^-1//8)+1//16*2^(1/2)*b^-1//8*(-1a)^-7//8*log((-1a)^1//4+b^1//4*x^2+-1*x*2^(1/2)*b^1//8*(-1a)^1//8))
@test integrate(x^-2*(a+b*x^8)^-1, x) == :(-1*a^-1*x^-1+-1//4*b^1//8*(-1a)^-9//8*arctanh(x*b^1//8*(-1a)^-1//8)+1//4*b^1//8*(-1a)^-9//8*arctan(x*b^1//8*(-1a)^-1//8)+-1//8*2^(1/2)*b^1//8*(-1a)^-9//8*arctan(1+-1*x*2^(1/2)*b^1//8*(-1a)^-1//8)+-1//16*2^(1/2)*b^1//8*(-1a)^-9//8*log((-1a)^1//4+b^1//4*x^2+x*2^(1/2)*b^1//8*(-1a)^1//8)+1//8*2^(1/2)*b^1//8*(-1a)^-9//8*arctan(1+x*2^(1/2)*b^1//8*(-1a)^-1//8)+1//16*2^(1/2)*b^1//8*(-1a)^-9//8*log((-1a)^1//4+b^1//4*x^2+-1*x*2^(1/2)*b^1//8*(-1a)^1//8))
@test integrate(x^-4*(a+b*x^8)^-1, x) == :(-1//3*a^-1*x^-3+-1//4*b^3//8*(-1a)^-11//8*arctan(x*b^1//8*(-1a)^-1//8)+-1//4*b^3//8*(-1a)^-11//8*arctanh(x*b^1//8*(-1a)^-1//8)+-1//8*2^(1/2)*b^3//8*(-1a)^-11//8*arctan(1+-1*x*2^(1/2)*b^1//8*(-1a)^-1//8)+-1//16*2^(1/2)*b^3//8*(-1a)^-11//8*log((-1a)^1//4+b^1//4*x^2+-1*x*2^(1/2)*b^1//8*(-1a)^1//8)+1//8*2^(1/2)*b^3//8*(-1a)^-11//8*arctan(1+x*2^(1/2)*b^1//8*(-1a)^-1//8)+1//16*2^(1/2)*b^3//8*(-1a)^-11//8*log((-1a)^1//4+b^1//4*x^2+x*2^(1/2)*b^1//8*(-1a)^1//8))
@test integrate(x^-6*(a+b*x^8)^-1, x) == :(-1//5*a^-1*x^-5+-1//4*b^5//8*(-1a)^-13//8*arctanh(x*b^1//8*(-1a)^-1//8)+1//4*b^5//8*(-1a)^-13//8*arctan(x*b^1//8*(-1a)^-1//8)+-1//8*2^(1/2)*b^5//8*(-1a)^-13//8*arctan(1+x*2^(1/2)*b^1//8*(-1a)^-1//8)+-1//16*2^(1/2)*b^5//8*(-1a)^-13//8*log((-1a)^1//4+b^1//4*x^2+-1*x*2^(1/2)*b^1//8*(-1a)^1//8)+1//8*2^(1/2)*b^5//8*(-1a)^-13//8*arctan(1+-1*x*2^(1/2)*b^1//8*(-1a)^-1//8)+1//16*2^(1/2)*b^5//8*(-1a)^-13//8*log((-1a)^1//4+b^1//4*x^2+x*2^(1/2)*b^1//8*(-1a)^1//8))
@test integrate(x^-8*(a+b*x^8)^-1, x) == :(-1//7*a^-1*x^-7+-1//4*b^7//8*(-1a)^-15//8*arctan(x*b^1//8*(-1a)^-1//8)+-1//4*b^7//8*(-1a)^-15//8*arctanh(x*b^1//8*(-1a)^-1//8)+-1//8*2^(1/2)*b^7//8*(-1a)^-15//8*arctan(1+x*2^(1/2)*b^1//8*(-1a)^-1//8)+-1//16*2^(1/2)*b^7//8*(-1a)^-15//8*log((-1a)^1//4+b^1//4*x^2+x*2^(1/2)*b^1//8*(-1a)^1//8)+1//8*2^(1/2)*b^7//8*(-1a)^-15//8*arctan(1+-1*x*2^(1/2)*b^1//8*(-1a)^-1//8)+1//16*2^(1/2)*b^7//8*(-1a)^-15//8*log((-1a)^1//4+b^1//4*x^2+-1*x*2^(1/2)*b^1//8*(-1a)^1//8))
@test integrate((a+-1*b*x^8)^-1, x) == :(1//4*a^-7//8*b^-1//8*arctan(x*a^-1//8*b^1//8)+1//4*a^-7//8*b^-1//8*arctanh(x*a^-1//8*b^1//8)+-1//8*2^(1/2)*a^-7//8*b^-1//8*arctan(1+-1*x*2^(1/2)*a^-1//8*b^1//8)+-1//16*2^(1/2)*a^-7//8*b^-1//8*log(a^1//4+b^1//4*x^2+-1*x*2^(1/2)*a^1//8*b^1//8)+1//8*2^(1/2)*a^-7//8*b^-1//8*arctan(1+x*2^(1/2)*a^-1//8*b^1//8)+1//16*2^(1/2)*a^-7//8*b^-1//8*log(a^1//4+b^1//4*x^2+x*2^(1/2)*a^1//8*b^1//8))
@test integrate(x^9*(1+-1*x^8)^-1, x) == :(-1//2*x^2+1//4*arctan(x^2)+1//4*arctanh(x^2))
@test integrate(x^7*(1+-1*x^8)^-1, x) == :(-1//8*log(1+-1*x^8))
@test integrate(x^5*(1+-1*x^8)^-1, x) == :(-1//4*arctan(x^2)+1//4*arctanh(x^2))
@test integrate(x^3*(1+-1*x^8)^-1, x) == :(1//4*arctanh(x^4))
@test integrate(x*(1+-1*x^8)^-1, x) == :(1//4*arctan(x^2)+1//4*arctanh(x^2))
@test integrate(x^-1*(1+-1*x^8)^-1, x) == :(-1//8*log(1+-1*x^8)+log(x))
@test integrate(x^-3*(1+-1*x^8)^-1, x) == :(-1//2*x^-2+-1//4*arctan(x^2)+1//4*arctanh(x^2))
@test integrate(x^-5*(1+-1*x^8)^-1, x) == :(-1//4*x^-4+1//4*arctanh(x^4))
@test integrate(x^-7*(1+-1*x^8)^-1, x) == :(-1//6*x^-6+1//4*arctan(x^2)+1//4*arctanh(x^2))
@test integrate(x^-9*(1+-1*x^8)^-1, x) == :(-1//8*x^-8+-1//8*log(1+-1*x^8)+log(x))
@test integrate(x^8*(1+-1*x^8)^-1, x) == :(-1x+1//4*arctan(x)+1//4*arctanh(x)+-1//8*2^(1/2)*arctan(1+-1*x*2^(1/2))+-1//16*2^(1/2)*log(1+x^2+-1*x*2^(1/2))+1//8*2^(1/2)*arctan(1+x*2^(1/2))+1//16*2^(1/2)*log(1+x^2+x*2^(1/2)))
@test integrate(x^6*(1+-1*x^8)^-1, x) == :(-1//4*arctan(x)+1//4*arctanh(x)+-1//8*2^(1/2)*arctan(1+x*2^(1/2))+-1//16*2^(1/2)*log(1+x^2+-1*x*2^(1/2))+1//8*2^(1/2)*arctan(1+-1*x*2^(1/2))+1//16*2^(1/2)*log(1+x^2+x*2^(1/2)))
@test integrate(x^4*(1+-1*x^8)^-1, x) == :(1//4*arctan(x)+1//4*arctanh(x)+-1//8*2^(1/2)*arctan(1+x*2^(1/2))+-1//16*2^(1/2)*log(1+x^2+x*2^(1/2))+1//8*2^(1/2)*arctan(1+-1*x*2^(1/2))+1//16*2^(1/2)*log(1+x^2+-1*x*2^(1/2)))
@test integrate(x^2*(1+-1*x^8)^-1, x) == :(-1//4*arctan(x)+1//4*arctanh(x)+-1//8*2^(1/2)*arctan(1+-1*x*2^(1/2))+-1//16*2^(1/2)*log(1+x^2+x*2^(1/2))+1//8*2^(1/2)*arctan(1+x*2^(1/2))+1//16*2^(1/2)*log(1+x^2+-1*x*2^(1/2)))
@test integrate((1+-1*x^8)^-1, x) == :(1//4*arctan(x)+1//4*arctanh(x)+-1//8*2^(1/2)*arctan(1+-1*x*2^(1/2))+-1//16*2^(1/2)*log(1+x^2+-1*x*2^(1/2))+1//8*2^(1/2)*arctan(1+x*2^(1/2))+1//16*2^(1/2)*log(1+x^2+x*2^(1/2)))
@test integrate(x^-2*(1+-1*x^8)^-1, x) == :(-1*x^-1+-1//4*arctan(x)+1//4*arctanh(x)+-1//8*2^(1/2)*arctan(1+x*2^(1/2))+-1//16*2^(1/2)*log(1+x^2+-1*x*2^(1/2))+1//8*2^(1/2)*arctan(1+-1*x*2^(1/2))+1//16*2^(1/2)*log(1+x^2+x*2^(1/2)))
@test integrate(x^-4*(1+-1*x^8)^-1, x) == :(-1//3*x^-3+1//4*arctan(x)+1//4*arctanh(x)+-1//8*2^(1/2)*arctan(1+x*2^(1/2))+-1//16*2^(1/2)*log(1+x^2+x*2^(1/2))+1//8*2^(1/2)*arctan(1+-1*x*2^(1/2))+1//16*2^(1/2)*log(1+x^2+-1*x*2^(1/2)))
@test integrate(x^-6*(1+-1*x^8)^-1, x) == :(-1//4*arctan(x)+-1//5*x^-5+1//4*arctanh(x)+-1//8*2^(1/2)*arctan(1+-1*x*2^(1/2))+-1//16*2^(1/2)*log(1+x^2+x*2^(1/2))+1//8*2^(1/2)*arctan(1+x*2^(1/2))+1//16*2^(1/2)*log(1+x^2+-1*x*2^(1/2)))
@test integrate(x^-8*(1+-1*x^8)^-1, x) == :(-1//7*x^-7+1//4*arctan(x)+1//4*arctanh(x)+-1//8*2^(1/2)*arctan(1+-1*x*2^(1/2))+-1//16*2^(1/2)*log(1+x^2+-1*x*2^(1/2))+1//8*2^(1/2)*arctan(1+x*2^(1/2))+1//16*2^(1/2)*log(1+x^2+x*2^(1/2)))
@test integrate(x^9*(1+x^8)^-1, x) == :((1/2)*x^2+-1//8*2^(1/2)*arctan(1+2^(1/2)*x^2)+-1//16*2^(1/2)*log(1+x^4+2^(1/2)*x^2)+1//8*2^(1/2)*arctan(1+-1*2^(1/2)*x^2)+1//16*2^(1/2)*log(1+x^4+-1*2^(1/2)*x^2))
@test integrate(x^7*(1+x^8)^-1, x) == :(1//8*log(1+x^8))
@test integrate(x^5*(1+x^8)^-1, x) == :(-1//8*2^(1/2)*arctan(1+-1*2^(1/2)*x^2)+-1//16*2^(1/2)*log(1+x^4+2^(1/2)*x^2)+1//8*2^(1/2)*arctan(1+2^(1/2)*x^2)+1//16*2^(1/2)*log(1+x^4+-1*2^(1/2)*x^2))
@test integrate(x^3*(1+x^8)^-1, x) == :(1//4*arctan(x^4))
@test integrate(x*(1+x^8)^-1, x) == :(-1//8*2^(1/2)*arctan(1+-1*2^(1/2)*x^2)+-1//16*2^(1/2)*log(1+x^4+-1*2^(1/2)*x^2)+1//8*2^(1/2)*arctan(1+2^(1/2)*x^2)+1//16*2^(1/2)*log(1+x^4+2^(1/2)*x^2))
@test integrate(x^-1*(1+x^8)^-1, x) == :(-1//8*log(1+x^8)+log(x))
@test integrate(x^-3*(1+x^8)^-1, x) == :(-1//2*x^-2+-1//8*2^(1/2)*arctan(1+2^(1/2)*x^2)+-1//16*2^(1/2)*log(1+x^4+-1*2^(1/2)*x^2)+1//8*2^(1/2)*arctan(1+-1*2^(1/2)*x^2)+1//16*2^(1/2)*log(1+x^4+2^(1/2)*x^2))
@test integrate(x^-5*(1+x^8)^-1, x) == :(-1//4*x^-4+-1//4*arctan(x^4))
@test integrate(x^-7*(1+x^8)^-1, x) == :(-1//6*x^-6+-1//8*2^(1/2)*arctan(1+2^(1/2)*x^2)+-1//16*2^(1/2)*log(1+x^4+2^(1/2)*x^2)+1//8*2^(1/2)*arctan(1+-1*2^(1/2)*x^2)+1//16*2^(1/2)*log(1+x^4+-1*2^(1/2)*x^2))
@test integrate(x^-9*(1+x^8)^-1, x) == :(-1*log(x)+-1//8*x^-8+1//8*log(1+x^8))
@test integrate(x^8*(1+x^8)^-1, x) == :(x+-1//4*(4+-2*2^(1/2))^-1//2*arctan((2+2^(1/2))^-1//2*((2+-1*2^(1/2))^(1/2)+2x))+-1//4*(4+2*2^(1/2))^-1//2*arctan((2+-1*2^(1/2))^-1//2*((2+2^(1/2))^(1/2)+2x))+-1//16*(2+2^(1/2))^(1/2)*log(1+x^2+x*(2+2^(1/2))^(1/2))+-1//16*(2+-1*2^(1/2))^(1/2)*log(1+x^2+x*(2+-1*2^(1/2))^(1/2))+1//4*(4+-2*2^(1/2))^-1//2*arctan((2+2^(1/2))^-1//2*((2+-1*2^(1/2))^(1/2)+-2x))+1//4*(4+2*2^(1/2))^-1//2*arctan((2+-1*2^(1/2))^-1//2*((2+2^(1/2))^(1/2)+-2x))+1//16*(2+2^(1/2))^(1/2)*log(1+x^2+-1*x*(2+2^(1/2))^(1/2))+1//16*(2+-1*2^(1/2))^(1/2)*log(1+x^2+-1*x*(2+-1*2^(1/2))^(1/2)))
@test integrate(x^6*(1+x^8)^-1, x) == :(-1//4*(4+-2*2^(1/2))^-1//2*arctan((2+2^(1/2))^-1//2*((2+-1*2^(1/2))^(1/2)+-2x))+-1//4*(4+2*2^(1/2))^-1//2*arctan((2+-1*2^(1/2))^-1//2*((2+2^(1/2))^(1/2)+-2x))+-1//16*(2+2^(1/2))^(1/2)*log(1+x^2+x*(2+2^(1/2))^(1/2))+-1//16*(2+-1*2^(1/2))^(1/2)*log(1+x^2+x*(2+-1*2^(1/2))^(1/2))+1//4*(4+-2*2^(1/2))^-1//2*arctan((2+2^(1/2))^-1//2*((2+-1*2^(1/2))^(1/2)+2x))+1//4*(4+2*2^(1/2))^-1//2*arctan((2+-1*2^(1/2))^-1//2*((2+2^(1/2))^(1/2)+2x))+1//16*(2+2^(1/2))^(1/2)*log(1+x^2+-1*x*(2+2^(1/2))^(1/2))+1//16*(2+-1*2^(1/2))^(1/2)*log(1+x^2+-1*x*(2+-1*2^(1/2))^(1/2)))
@test integrate(x^4*(1+x^8)^-1, x) == :(-1//4*(4+-2*2^(1/2))^-1//2*arctan((2+-1*2^(1/2))^-1//2*((2+2^(1/2))^(1/2)+-2x))+-1//4*(4+2*2^(1/2))^-1//2*arctan((2+2^(1/2))^-1//2*((2+-1*2^(1/2))^(1/2)+2x))+-1//8*(4+-2*2^(1/2))^-1//2*log(1+x^2+-1*x*(2+-1*2^(1/2))^(1/2))+-1//8*(4+2*2^(1/2))^-1//2*log(1+x^2+x*(2+2^(1/2))^(1/2))+1//4*(4+-2*2^(1/2))^-1//2*arctan((2+-1*2^(1/2))^-1//2*((2+2^(1/2))^(1/2)+2x))+1//4*(4+2*2^(1/2))^-1//2*arctan((2+2^(1/2))^-1//2*((2+-1*2^(1/2))^(1/2)+-2x))+1//8*(4+-2*2^(1/2))^-1//2*log(1+x^2+x*(2+-1*2^(1/2))^(1/2))+1//8*(4+2*2^(1/2))^-1//2*log(1+x^2+-1*x*(2+2^(1/2))^(1/2)))
@test integrate(x^2*(1+x^8)^-1, x) == :(-1//8*(2+2^(1/2))^(1/2)*arctan((2+-1*2^(1/2))^-1//2*((2+2^(1/2))^(1/2)+-2x))+-1//8*(2+-1*2^(1/2))^(1/2)*arctan((2+2^(1/2))^-1//2*((2+-1*2^(1/2))^(1/2)+2x))+-1//8*(4+-2*2^(1/2))^-1//2*log(1+x^2+x*(2+-1*2^(1/2))^(1/2))+-1//8*(4+2*2^(1/2))^-1//2*log(1+x^2+-1*x*(2+2^(1/2))^(1/2))+1//8*(2+2^(1/2))^(1/2)*arctan((2+-1*2^(1/2))^-1//2*((2+2^(1/2))^(1/2)+2x))+1//8*(2+-1*2^(1/2))^(1/2)*arctan((2+2^(1/2))^-1//2*((2+-1*2^(1/2))^(1/2)+-2x))+1//8*(4+-2*2^(1/2))^-1//2*log(1+x^2+-1*x*(2+-1*2^(1/2))^(1/2))+1//8*(4+2*2^(1/2))^-1//2*log(1+x^2+x*(2+2^(1/2))^(1/2)))
@test integrate((1+x^8)^-1, x) == :(-1//4*(4+-2*2^(1/2))^-1//2*arctan((2+2^(1/2))^-1//2*((2+-1*2^(1/2))^(1/2)+-2x))+-1//4*(4+2*2^(1/2))^-1//2*arctan((2+-1*2^(1/2))^-1//2*((2+2^(1/2))^(1/2)+-2x))+-1//16*(2+2^(1/2))^(1/2)*log(1+x^2+-1*x*(2+2^(1/2))^(1/2))+-1//16*(2+-1*2^(1/2))^(1/2)*log(1+x^2+-1*x*(2+-1*2^(1/2))^(1/2))+1//4*(4+-2*2^(1/2))^-1//2*arctan((2+2^(1/2))^-1//2*((2+-1*2^(1/2))^(1/2)+2x))+1//4*(4+2*2^(1/2))^-1//2*arctan((2+-1*2^(1/2))^-1//2*((2+2^(1/2))^(1/2)+2x))+1//16*(2+2^(1/2))^(1/2)*log(1+x^2+x*(2+2^(1/2))^(1/2))+1//16*(2+-1*2^(1/2))^(1/2)*log(1+x^2+x*(2+-1*2^(1/2))^(1/2)))
@test integrate(x^-2*(1+x^8)^-1, x) == :(-1*x^-1+-1//4*(4+-2*2^(1/2))^-1//2*arctan((2+2^(1/2))^-1//2*((2+-1*2^(1/2))^(1/2)+2x))+-1//4*(4+2*2^(1/2))^-1//2*arctan((2+-1*2^(1/2))^-1//2*((2+2^(1/2))^(1/2)+2x))+-1//16*(2+2^(1/2))^(1/2)*log(1+x^2+-1*x*(2+2^(1/2))^(1/2))+-1//16*(2+-1*2^(1/2))^(1/2)*log(1+x^2+-1*x*(2+-1*2^(1/2))^(1/2))+1//4*(4+-2*2^(1/2))^-1//2*arctan((2+2^(1/2))^-1//2*((2+-1*2^(1/2))^(1/2)+-2x))+1//4*(4+2*2^(1/2))^-1//2*arctan((2+-1*2^(1/2))^-1//2*((2+2^(1/2))^(1/2)+-2x))+1//16*(2+2^(1/2))^(1/2)*log(1+x^2+x*(2+2^(1/2))^(1/2))+1//16*(2+-1*2^(1/2))^(1/2)*log(1+x^2+x*(2+-1*2^(1/2))^(1/2)))
@test integrate(x^-4*(1+x^8)^-1, x) == :(-1//3*x^-3+-1//4*(4+-2*2^(1/2))^-1//2*arctan((2+-1*2^(1/2))^-1//2*((2+2^(1/2))^(1/2)+2x))+-1//4*(4+2*2^(1/2))^-1//2*arctan((2+2^(1/2))^-1//2*((2+-1*2^(1/2))^(1/2)+-2x))+-1//8*(4+-2*2^(1/2))^-1//2*log(1+x^2+x*(2+-1*2^(1/2))^(1/2))+-1//8*(4+2*2^(1/2))^-1//2*log(1+x^2+-1*x*(2+2^(1/2))^(1/2))+1//4*(4+-2*2^(1/2))^-1//2*arctan((2+-1*2^(1/2))^-1//2*((2+2^(1/2))^(1/2)+-2x))+1//4*(4+2*2^(1/2))^-1//2*arctan((2+2^(1/2))^-1//2*((2+-1*2^(1/2))^(1/2)+2x))+1//8*(4+-2*2^(1/2))^-1//2*log(1+x^2+-1*x*(2+-1*2^(1/2))^(1/2))+1//8*(4+2*2^(1/2))^-1//2*log(1+x^2+x*(2+2^(1/2))^(1/2)))
@test integrate(x^-6*(1+x^8)^-1, x) == :(-1//5*x^-5+-1//8*(2+2^(1/2))^(1/2)*arctan((2+-1*2^(1/2))^-1//2*((2+2^(1/2))^(1/2)+2x))+-1//8*(2+-1*2^(1/2))^(1/2)*arctan((2+2^(1/2))^-1//2*((2+-1*2^(1/2))^(1/2)+-2x))+-1//8*(4+-2*2^(1/2))^-1//2*log(1+x^2+-1*x*(2+-1*2^(1/2))^(1/2))+-1//8*(4+2*2^(1/2))^-1//2*log(1+x^2+x*(2+2^(1/2))^(1/2))+1//8*(2+2^(1/2))^(1/2)*arctan((2+-1*2^(1/2))^-1//2*((2+2^(1/2))^(1/2)+-2x))+1//8*(2+-1*2^(1/2))^(1/2)*arctan((2+2^(1/2))^-1//2*((2+-1*2^(1/2))^(1/2)+2x))+1//8*(4+-2*2^(1/2))^-1//2*log(1+x^2+x*(2+-1*2^(1/2))^(1/2))+1//8*(4+2*2^(1/2))^-1//2*log(1+x^2+-1*x*(2+2^(1/2))^(1/2)))
@test integrate(x^-8*(1+x^8)^-1, x) == :(-1//7*x^-7+-1//4*(4+-2*2^(1/2))^-1//2*arctan((2+2^(1/2))^-1//2*((2+-1*2^(1/2))^(1/2)+2x))+-1//4*(4+2*2^(1/2))^-1//2*arctan((2+-1*2^(1/2))^-1//2*((2+2^(1/2))^(1/2)+2x))+-1//16*(2+2^(1/2))^(1/2)*log(1+x^2+x*(2+2^(1/2))^(1/2))+-1//16*(2+-1*2^(1/2))^(1/2)*log(1+x^2+x*(2+-1*2^(1/2))^(1/2))+1//4*(4+-2*2^(1/2))^-1//2*arctan((2+2^(1/2))^-1//2*((2+-1*2^(1/2))^(1/2)+-2x))+1//4*(4+2*2^(1/2))^-1//2*arctan((2+-1*2^(1/2))^-1//2*((2+2^(1/2))^(1/2)+-2x))+1//16*(2+2^(1/2))^(1/2)*log(1+x^2+-1*x*(2+2^(1/2))^(1/2))+1//16*(2+-1*2^(1/2))^(1/2)*log(1+x^2+-1*x*(2+-1*2^(1/2))^(1/2)))
@test integrate(x^3*(1+x^8)^(1/2), x) == :(1//8*arcsinh(x^4)+1//8*x^4*(1+x^8)^(1/2))
@test integrate(x*(1+x^8)^(1/2), x) == :(1//6*x^2*(1+x^8)^(1/2)+1//6*((1+x^4)^-2*(1+x^8))^(1/2)*(1+x^8)^-1//2*(1+x^4)*Elliptic.F(2*arctan(x^2),1/2))
@test integrate(x^-1*(1+x^8)^(1/2), x) == :(-1//4*arctanh((1+x^8)^(1/2))+1//4*(1+x^8)^(1/2))
@test integrate(x^-3*(1+x^8)^(1/2), x) == :(-1//2*x^-2*(1+x^8)^(1/2)+x^2*(1+x^4)^-1*(1+x^8)^(1/2)+(1/2)*((1+x^4)^-2*(1+x^8))^(1/2)*(1+x^8)^-1//2*(1+x^4)*Elliptic.F(2*arctan(x^2),1/2)+-1*((1+x^4)^-2*(1+x^8))^(1/2)*(1+x^8)^-1//2*(1+x^4)*Elliptic.E(2*arctan(x^2),1/2))
@test integrate(x^3*(-2+x^8)^(1/2), x) == :(-1//4*arctanh(x^4*(-2+x^8)^-1//2)+1//8*x^4*(-2+x^8)^(1/2))
@test integrate(x^19*(1+x^8)^-1//2, x) == :(3//32*arcsinh(x^4)+-3//32*x^4*(1+x^8)^(1/2)+1//16*x^12*(1+x^8)^(1/2))
@test integrate(x^15*(1+x^8)^-1//2, x) == :(-1//4*(1+x^8)^(1/2)+1//12*(1+x^8)^3//2)
@test integrate(x^11*(1+x^8)^-1//2, x) == :(-1//8*arcsinh(x^4)+1//8*x^4*(1+x^8)^(1/2))
@test integrate(x^7*(1+x^8)^-1//2, x) == :(1//4*(1+x^8)^(1/2))
@test integrate(x^3*(1+x^8)^-1//2, x) == :(1//4*arcsinh(x^4))
@test integrate(x^-1*(1+x^8)^-1//2, x) == :(-1//4*arctanh((1+x^8)^(1/2)))
@test integrate(x^-5*(1+x^8)^-1//2, x) == :(-1//4*x^-4*(1+x^8)^(1/2))
@test integrate(x^-9*(1+x^8)^-1//2, x) == :(1//8*arctanh((1+x^8)^(1/2))+-1//8*x^-8*(1+x^8)^(1/2))
@test integrate(x^-13*(1+x^8)^-1//2, x) == :(-1//12*x^-12*(1+x^8)^(1/2)+1//6*x^-4*(1+x^8)^(1/2))
@test integrate(x^-17*(1+x^8)^-1//2, x) == :(-3//32*arctanh((1+x^8)^(1/2))+-1//16*x^-16*(1+x^8)^(1/2)+3//32*x^-8*(1+x^8)^(1/2))
@test integrate(x^13*(1+x^8)^-1//2, x) == :(1//10*x^6*(1+x^8)^(1/2)+-3*x^2*(1+x^8)^(1/2)*(10+10*x^4)^-1+-1//20*((1+x^4)^-2*(1+x^8))^(1/2)*(1+x^8)^-1//2*(3+3*x^4)*Elliptic.F(2*arctan(x^2),1/2)+1//10*((1+x^4)^-2*(1+x^8))^(1/2)*(1+x^8)^-1//2*(3+3*x^4)*Elliptic.E(2*arctan(x^2),1/2))
@test integrate(x^9*(1+x^8)^-1//2, x) == :(1//6*x^2*(1+x^8)^(1/2)+-1//12*((1+x^4)^-2*(1+x^8))^(1/2)*(1+x^8)^-1//2*(1+x^4)*Elliptic.F(2*arctan(x^2),1/2))
@test integrate(x^5*(1+x^8)^-1//2, x) == :(x^2*(1+x^8)^(1/2)*(2+2*x^4)^-1+-1//2*((1+x^4)^-2*(1+x^8))^(1/2)*(1+x^8)^-1//2*(1+x^4)*Elliptic.E(2*arctan(x^2),1/2)+1//4*((1+x^4)^-2*(1+x^8))^(1/2)*(1+x^8)^-1//2*(1+x^4)*Elliptic.F(2*arctan(x^2),1/2))
@test integrate(x*(1+x^8)^-1//2, x) == :(1//4*((1+x^4)^-2*(1+x^8))^(1/2)*(1+x^8)^-1//2*(1+x^4)*Elliptic.F(2*arctan(x^2),1/2))
@test integrate(x^-3*(1+x^8)^-1//2, x) == :(-1//2*x^-2*(1+x^8)^(1/2)+x^2*(1+x^8)^(1/2)*(2+2*x^4)^-1+-1//2*((1+x^4)^-2*(1+x^8))^(1/2)*(1+x^8)^-1//2*(1+x^4)*Elliptic.E(2*arctan(x^2),1/2)+1//4*((1+x^4)^-2*(1+x^8))^(1/2)*(1+x^8)^-1//2*(1+x^4)*Elliptic.F(2*arctan(x^2),1/2))
@test integrate(x^-7*(1+x^8)^-1//2, x) == :(-1//6*x^-6*(1+x^8)^(1/2)+-1//12*((1+x^4)^-2*(1+x^8))^(1/2)*(1+x^8)^-1//2*(1+x^4)*Elliptic.F(2*arctan(x^2),1/2))
@test integrate(x^10*(1+x^8)^-1//2, x) == :(1//7*x^3*(1+x^8)^(1/2)+3//14*x^3*(x^-2*(1+x^2)^2)^(1/2)*(-1*x^-4*(1+x^8))^(1/2)*(1+x^2)^-1*(1+x^8)^-1//2*(2+2^(1/2))^-1//2*Elliptic.F(arcsin((1/2)*(-1*x^-2*(2^(1/2)+-2*x^2+2^(1/2)*x^4))^(1/2)),-2+2*2^(1/2))+3//14*x^3*(-1*x^-4*(1+x^8))^(1/2)*(-1*x^-2*(1+-1*x^2)^2)^(1/2)*(1+x^8)^-1//2*(1+-1*x^2)^-1*(2+2^(1/2))^-1//2*Elliptic.F(arcsin((1/2)*(x^-2*(2^(1/2)+2*x^2+2^(1/2)*x^4))^(1/2)),-2+2*2^(1/2)))
@test integrate(x^8*(1+x^8)^-1//2, x) == :(1//5*x*(1+x^8)^(1/2)+-1//10*x^3*(x^-2*(1+x^2)^2)^(1/2)*(-1*x^-4*(1+x^8))^(1/2)*(1+x^2)^-1*(1+x^8)^-1//2*(2+2^(1/2))^-1//2*Elliptic.F(arcsin((1/2)*(-1*x^-2*(2^(1/2)+-2*x^2+2^(1/2)*x^4))^(1/2)),-2+2*2^(1/2))+1//10*x^3*(-1*x^-4*(1+x^8))^(1/2)*(-1*x^-2*(1+-1*x^2)^2)^(1/2)*(1+x^8)^-1//2*(1+-1*x^2)^-1*(2+2^(1/2))^-1//2*Elliptic.F(arcsin((1/2)*(x^-2*(2^(1/2)+2*x^2+2^(1/2)*x^4))^(1/2)),-2+2*2^(1/2)))
@test integrate(x^2*(1+x^8)^-1//2, x) == :(-1//2*x^3*(x^-2*(1+x^2)^2)^(1/2)*(-1*x^-4*(1+x^8))^(1/2)*(1+x^2)^-1*(1+x^8)^-1//2*(2+2^(1/2))^-1//2*Elliptic.F(arcsin((1/2)*(-1*x^-2*(2^(1/2)+-2*x^2+2^(1/2)*x^4))^(1/2)),-2+2*2^(1/2))+-1//2*x^3*(-1*x^-4*(1+x^8))^(1/2)*(-1*x^-2*(1+-1*x^2)^2)^(1/2)*(1+x^8)^-1//2*(1+-1*x^2)^-1*(2+2^(1/2))^-1//2*Elliptic.F(arcsin((1/2)*(x^-2*(2^(1/2)+2*x^2+2^(1/2)*x^4))^(1/2)),-2+2*2^(1/2)))
@test integrate((1+x^8)^-1//2, x) == :((1/2)*x^3*(x^-2*(1+x^2)^2)^(1/2)*(-1*x^-4*(1+x^8))^(1/2)*(1+x^2)^-1*(1+x^8)^-1//2*(2+2^(1/2))^-1//2*Elliptic.F(arcsin((1/2)*(-1*x^-2*(2^(1/2)+-2*x^2+2^(1/2)*x^4))^(1/2)),-2+2*2^(1/2))+-1//2*x^3*(-1*x^-4*(1+x^8))^(1/2)*(-1*x^-2*(1+-1*x^2)^2)^(1/2)*(1+x^8)^-1//2*(1+-1*x^2)^-1*(2+2^(1/2))^-1//2*Elliptic.F(arcsin((1/2)*(x^-2*(2^(1/2)+2*x^2+2^(1/2)*x^4))^(1/2)),-2+2*2^(1/2)))
@test integrate(x^-6*(1+x^8)^-1//2, x) == :(-1//5*x^-5*(1+x^8)^(1/2)+1//10*x^3*(x^-2*(1+x^2)^2)^(1/2)*(-1*x^-4*(1+x^8))^(1/2)*(1+x^2)^-1*(1+x^8)^-1//2*(2+2^(1/2))^-1//2*Elliptic.F(arcsin((1/2)*(-1*x^-2*(2^(1/2)+-2*x^2+2^(1/2)*x^4))^(1/2)),-2+2*2^(1/2))+1//10*x^3*(-1*x^-4*(1+x^8))^(1/2)*(-1*x^-2*(1+-1*x^2)^2)^(1/2)*(1+x^8)^-1//2*(1+-1*x^2)^-1*(2+2^(1/2))^-1//2*Elliptic.F(arcsin((1/2)*(x^-2*(2^(1/2)+2*x^2+2^(1/2)*x^4))^(1/2)),-2+2*2^(1/2)))
@test integrate(x^-8*(1+x^8)^-1//2, x) == :(-1//7*x^-7*(1+x^8)^(1/2)+-3//14*x^3*(x^-2*(1+x^2)^2)^(1/2)*(-1*x^-4*(1+x^8))^(1/2)*(1+x^2)^-1*(1+x^8)^-1//2*(2+2^(1/2))^-1//2*Elliptic.F(arcsin((1/2)*(-1*x^-2*(2^(1/2)+-2*x^2+2^(1/2)*x^4))^(1/2)),-2+2*2^(1/2))+3//14*x^3*(-1*x^-4*(1+x^8))^(1/2)*(-1*x^-2*(1+-1*x^2)^2)^(1/2)*(1+x^8)^-1//2*(1+-1*x^2)^-1*(2+2^(1/2))^-1//2*Elliptic.F(arcsin((1/2)*(x^-2*(2^(1/2)+2*x^2+2^(1/2)*x^4))^(1/2)),-2+2*2^(1/2)))
@test integrate(x^4*(1+-1*x^10)^-1//2, x) == :(1//5*arcsin(x^5))
@test integrate(x^4*(-2+x^10)^-1//2, x) == :(1//5*arctanh(x^5*(-2+x^10)^-1//2))
@test integrate(x^5*(9+x^12)^-1, x) == :(1//18*arctan(1//3*x^6))
@test integrate(x^5*(9+-1*x^12)^-1, x) == :(1//18*arctanh(1//3*x^6))
@test integrate(x^5*(9+x^12)^(1/2), x) == :(3//4*arcsinh(1//3*x^6)+1//12*x^6*(9+x^12)^(1/2))
@test integrate(x^6*(a+b*x^-1), x) == :(1//6*b*x^6+1//7*a*x^7)
@test integrate(x^5*(a+b*x^-1), x) == :(1//5*b*x^5+1//6*a*x^6)
@test integrate(x^4*(a+b*x^-1), x) == :(1//4*b*x^4+1//5*a*x^5)
@test integrate(x^3*(a+b*x^-1), x) == :(1//3*b*x^3+1//4*a*x^4)
@test integrate(x^2*(a+b*x^-1), x) == :((1/2)*b*x^2+1//3*a*x^3)
@test integrate(x*(a+b*x^-1), x) == :(b*x+(1/2)*a*x^2)
@test integrate(a+b*x^-1, x) == :(a*x+b*log(x))
@test integrate(x^-1*(a+b*x^-1), x) == :(a*log(x)+-1*b*x^-1)
@test integrate(x^-2*(a+b*x^-1), x) == :(-1*a*x^-1+-1//2*b*x^-2)
@test integrate(x^-3*(a+b*x^-1), x) == :(-1//2*a*x^-2+-1//3*b*x^-3)
@test integrate(x^-4*(a+b*x^-1), x) == :(-1//3*a*x^-3+-1//4*b*x^-4)
@test integrate(x^-5*(a+b*x^-1), x) == :(-1//4*a*x^-4+-1//5*b*x^-5)
@test integrate(x^-6*(a+b*x^-1), x) == :(-1//5*a*x^-5+-1//6*b*x^-6)
@test integrate(x^5*(a+b*x^-1)^2, x) == :(1//4*b^2*x^4+1//6*a^2*x^6+2//5*a*b*x^5)
@test integrate(x^4*(a+b*x^-1)^2, x) == :(1//3*b^2*x^3+1//5*a^2*x^5+(1/2)*a*b*x^4)
@test integrate(x^3*(a+b*x^-1)^2, x) == :((1/2)*b^2*x^2+1//4*a^2*x^4+2//3*a*b*x^3)
@test integrate(x^2*(a+b*x^-1)^2, x) == :(1//3*a^-1*(b+a*x)^3)
@test integrate(x*(a+b*x^-1)^2, x) == :(b^2*log(x)+(1/2)*a^2*x^2+2*a*b*x)
@test integrate((a+b*x^-1)^2, x) == :(x*a^2+-1*b^2*x^-1+2*a*b*log(x))
@test integrate(x^-1*(a+b*x^-1)^2, x) == :(a^2*log(x)+-1//2*b^2*x^-2+-2*a*b*x^-1)
@test integrate(x^-2*(a+b*x^-1)^2, x) == :(-1//3*b^-1*(a+b*x^-1)^3)
@test integrate(x^-3*(a+b*x^-1)^2, x) == :(-1//2*a^2*x^-2+-1//4*b^2*x^-4+-2//3*a*b*x^-3)
@test integrate(x^-4*(a+b*x^-1)^2, x) == :(-1//3*a^2*x^-3+-1//5*b^2*x^-5+-1//2*a*b*x^-4)
@test integrate(x^-5*(a+b*x^-1)^2, x) == :(-1//4*a^2*x^-4+-1//6*b^2*x^-6+-2//5*a*b*x^-5)
@test integrate(x^6*(a+b*x^-1)^3, x) == :(1//4*b^3*x^4+1//7*a^3*x^7+(1/2)*b*a^2*x^6+3//5*a*b^2*x^5)
@test integrate(x^5*(a+b*x^-1)^3, x) == :(1//3*b^3*x^3+1//6*a^3*x^6+3//4*a*b^2*x^4+3//5*b*a^2*x^5)
@test integrate(x^4*(a+b*x^-1)^3, x) == :(1//5*a^-2*(b+a*x)^5+-1//4*b*a^-2*(b+a*x)^4)
@test integrate(x^3*(a+b*x^-1)^3, x) == :(1//4*a^-1*(b+a*x)^4)
@test integrate(x^2*(a+b*x^-1)^3, x) == :(b^3*log(x)+1//3*a^3*x^3+3*a*x*b^2+3//2*b*a^2*x^2)
@test integrate(x*(a+b*x^-1)^3, x) == :((1/2)*a^3*x^2+-1*b^3*x^-1+3*a*b^2*log(x)+3*b*x*a^2)
@test integrate((a+b*x^-1)^3, x) == :(x*a^3+-1//2*b^3*x^-2+-3*a*b^2*x^-1+3*b*a^2*log(x))
@test integrate(x^-1*(a+b*x^-1)^3, x) == :(a^3*log(x)+-1//3*b^3*x^-3+-3*b*a^2*x^-1+-3//2*a*b^2*x^-2)
@test integrate(x^-2*(a+b*x^-1)^3, x) == :(-1//4*b^-1*(a+b*x^-1)^4)
@test integrate(x^-3*(a+b*x^-1)^3, x) == :(-1//5*b^-1*x^-5*(b+a*x)^4+1//20*a*b^-2*x^-4*(b+a*x)^4)
@test integrate(x^-4*(a+b*x^-1)^3, x) == :(-1//3*a^3*x^-3+-1//6*b^3*x^-6+-3//4*b*a^2*x^-4+-3//5*a*b^2*x^-5)
@test integrate(x^-5*(a+b*x^-1)^3, x) == :(-1//4*a^3*x^-4+-1//7*b^3*x^-7+-3//5*b*a^2*x^-5+-1//2*a*b^2*x^-6)
@test integrate(x^-6*(a+b*x^-1)^3, x) == :(-1//5*a^3*x^-5+-1//8*b^3*x^-8+-3//7*a*b^2*x^-7+-1//2*b*a^2*x^-6)
@test integrate(x^16*(a+b*x^-1)^8, x) == :(1//9*b^8*x^9+1//17*a^8*x^17+(1/2)*b*a^7*x^16+4*a^5*b^3*x^14+4//5*a*b^7*x^10+14//3*a^3*b^5*x^12+28//11*a^2*b^6*x^11+28//15*a^6*b^2*x^15+70//13*a^4*b^4*x^13)
@test integrate(x^15*(a+b*x^-1)^8, x) == :(1//8*b^8*x^8+1//16*a^8*x^16+2*a^6*b^2*x^14+8//9*a*b^7*x^9+8//15*b*a^7*x^15+14//5*a^2*b^6*x^10+35//6*a^4*b^4*x^12+56//11*a^3*b^5*x^11+56//13*a^5*b^3*x^13)
@test integrate(x^13*(a+b*x^-1)^8, x) == :(1//14*a^-6*(b+a*x)^14+(1/2)*a^-6*b^4*(b+a*x)^10+-10//11*a^-6*b^3*(b+a*x)^11+-5//13*b*a^-6*(b+a*x)^13+-1//9*a^-6*b^5*(b+a*x)^9+5//6*a^-6*b^2*(b+a*x)^12)
@test integrate(x^12*(a+b*x^-1)^8, x) == :(1//13*a^-5*(b+a*x)^13+-2//5*a^-5*b^3*(b+a*x)^10+-1//3*b*a^-5*(b+a*x)^12+1//9*a^-5*b^4*(b+a*x)^9+6//11*a^-5*b^2*(b+a*x)^11)
@test integrate(x^11*(a+b*x^-1)^8, x) == :(1//12*a^-4*(b+a*x)^12+-3//11*b*a^-4*(b+a*x)^11+-1//9*a^-4*b^3*(b+a*x)^9+3//10*a^-4*b^2*(b+a*x)^10)
@test integrate(x^10*(a+b*x^-1)^8, x) == :(1//11*a^-3*(b+a*x)^11+-1//5*b*a^-3*(b+a*x)^10+1//9*a^-3*b^2*(b+a*x)^9)
@test integrate(x^9*(a+b*x^-1)^8, x) == :(1//10*a^-2*(b+a*x)^10+-1//9*b*a^-2*(b+a*x)^9)
@test integrate(x^8*(a+b*x^-1)^8, x) == :(1//9*a^-1*(b+a*x)^9)
@test integrate(x^7*(a+b*x^-1)^8, x) == :(b^8*log(x)+1//8*a^8*x^8+8*a*x*b^7+14*a^2*b^6*x^2+8//7*b*a^7*x^7+14//3*a^6*b^2*x^6+35//2*a^4*b^4*x^4+56//3*a^3*b^5*x^3+56//5*a^5*b^3*x^5)
@test integrate(x^6*(a+b*x^-1)^8, x) == :(-1*b^8*x^-1+1//7*a^8*x^7+8*a*b^7*log(x)+14*a^5*b^3*x^4+28*x*a^2*b^6+28*a^3*b^5*x^2+4//3*b*a^7*x^6+28//5*a^6*b^2*x^5+70//3*a^4*b^4*x^3)
@test integrate(x^5*(a+b*x^-1)^8, x) == :(-1//2*b^8*x^-2+1//6*a^8*x^6+-8*a*b^7*x^-1+7*a^6*b^2*x^4+28*a^2*b^6*log(x)+35*a^4*b^4*x^2+56*x*a^3*b^5+8//5*b*a^7*x^5+56//3*a^5*b^3*x^3)
@test integrate(x^4*(a+b*x^-1)^8, x) == :(-1//3*b^8*x^-3+1//5*a^8*x^5+-28*a^2*b^6*x^-1+-4*a*b^7*x^-2+2*b*a^7*x^4+28*a^5*b^3*x^2+56*a^3*b^5*log(x)+70*x*a^4*b^4+28//3*a^6*b^2*x^3)
@test integrate(x^3*(a+b*x^-1)^8, x) == :(-1//4*b^8*x^-4+1//4*a^8*x^4+-56*a^3*b^5*x^-1+-14*a^2*b^6*x^-2+14*a^6*b^2*x^2+56*x*a^5*b^3+70*a^4*b^4*log(x)+-8//3*a*b^7*x^-3+8//3*b*a^7*x^3)
@test integrate(x^2*(a+b*x^-1)^8, x) == :(-1//5*b^8*x^-5+1//3*a^8*x^3+-70*a^4*b^4*x^-1+-28*a^3*b^5*x^-2+-2*a*b^7*x^-4+4*b*a^7*x^2+28*x*a^6*b^2+56*a^5*b^3*log(x)+-28//3*a^2*b^6*x^-3)
@test integrate(x*(a+b*x^-1)^8, x) == :((1/2)*a^8*x^2+-1//6*b^8*x^-6+-56*a^5*b^3*x^-1+-35*a^4*b^4*x^-2+-7*a^2*b^6*x^-4+8*b*x*a^7+28*a^6*b^2*log(x)+-56//3*a^3*b^5*x^-3+-8//5*a*b^7*x^-5)
@test integrate((a+b*x^-1)^8, x) == :(x*a^8+-1//7*b^8*x^-7+-28*a^5*b^3*x^-2+-28*a^6*b^2*x^-1+-14*a^3*b^5*x^-4+8*b*a^7*log(x)+-70//3*a^4*b^4*x^-3+-28//5*a^2*b^6*x^-5+-4//3*a*b^7*x^-6)
@test integrate(x^-1*(a+b*x^-1)^8, x) == :(a^8*log(x)+-1//8*b^8*x^-8+-14*a^6*b^2*x^-2+-8*b*a^7*x^-1+-56//3*a^5*b^3*x^-3+-56//5*a^3*b^5*x^-5+-35//2*a^4*b^4*x^-4+-14//3*a^2*b^6*x^-6+-8//7*a*b^7*x^-7)
@test integrate(x^-2*(a+b*x^-1)^8, x) == :(-1//9*b^-1*(a+b*x^-1)^9)
@test integrate(x^-3*(a+b*x^-1)^8, x) == :(-1//10*b^-1*x^-10*(b+a*x)^9+1//90*a*b^-2*x^-9*(b+a*x)^9)
@test integrate(x^-4*(a+b*x^-1)^8, x) == :(-1//11*b^-1*x^-11*(b+a*x)^9+-1//495*a^2*b^-3*x^-9*(b+a*x)^9+1//55*a*b^-2*x^-10*(b+a*x)^9)
@test integrate(x^-5*(a+b*x^-1)^8, x) == :(-1//12*b^-1*x^-12*(b+a*x)^9+-1//220*a^2*b^-3*x^-10*(b+a*x)^9+1//44*a*b^-2*x^-11*(b+a*x)^9+1//1980*a^3*b^-4*x^-9*(b+a*x)^9)
@test integrate(x^-6*(a+b*x^-1)^8, x) == :(-1//13*b^-1*x^-13*(b+a*x)^9+-1//143*a^2*b^-3*x^-11*(b+a*x)^9+-1//6435*a^4*b^-5*x^-9*(b+a*x)^9+1//39*a*b^-2*x^-12*(b+a*x)^9+1//715*a^3*b^-4*x^-10*(b+a*x)^9)
@test integrate(x^-7*(a+b*x^-1)^8, x) == :(-1//6*a^8*x^-6+-1//14*b^8*x^-14+-7*a^4*b^4*x^-10+-56//9*a^5*b^3*x^-9+-56//11*a^3*b^5*x^-11+-8//7*b*a^7*x^-7+-8//13*a*b^7*x^-13+-7//2*a^6*b^2*x^-8+-7//3*a^2*b^6*x^-12)
@test integrate(x^-8*(a+b*x^-1)^8, x) == :(-1//7*a^8*x^-7+-1//15*b^8*x^-15+-1*b*a^7*x^-8+-70//11*a^4*b^4*x^-11+-28//5*a^5*b^3*x^-10+-28//9*a^6*b^2*x^-9+-28//13*a^2*b^6*x^-13+-14//3*a^3*b^5*x^-12+-4//7*a*b^7*x^-14)
@test integrate(x^4*(a+b*x^-1)^-1, x) == :(1//5*a^-1*x^5+x*a^-5*b^4+-1*a^-6*b^5*log(b+a*x)+-1//2*a^-4*b^3*x^2+-1//4*b*a^-2*x^4+1//3*a^-3*b^2*x^3)
@test integrate(x^3*(a+b*x^-1)^-1, x) == :(1//4*a^-1*x^4+a^-5*b^4*log(b+a*x)+(1/2)*a^-3*b^2*x^2+-1*x*a^-4*b^3+-1//3*b*a^-2*x^3)
@test integrate(x^2*(a+b*x^-1)^-1, x) == :(1//3*a^-1*x^3+x*a^-3*b^2+-1*a^-4*b^3*log(b+a*x)+-1//2*b*a^-2*x^2)
@test integrate(x*(a+b*x^-1)^-1, x) == :((1/2)*a^-1*x^2+a^-3*b^2*log(b+a*x)+-1*b*x*a^-2)
@test integrate((a+b*x^-1)^-1, x) == :(x*a^-1+-1*b*a^-2*log(b+a*x))
@test integrate(x^-1*(a+b*x^-1)^-1, x) == :(a^-1*log(b+a*x))
@test integrate(x^-2*(a+b*x^-1)^-1, x) == :(-1*b^-1*log(a+b*x^-1))
@test integrate(x^-3*(a+b*x^-1)^-1, x) == :(-1*b^-1*x^-1+a*b^-2*log(b+a*x)+-1*a*b^-2*log(x))
@test integrate(x^-4*(a+b*x^-1)^-1, x) == :(-1//2*b^-1*x^-2+a*b^-2*x^-1+a^2*b^-3*log(x)+-1*a^2*b^-3*log(b+a*x))
@test integrate(x^-5*(a+b*x^-1)^-1, x) == :(-1//3*b^-1*x^-3+a^3*b^-4*log(b+a*x)+(1/2)*a*b^-2*x^-2+-1*a^2*b^-3*x^-1+-1*a^3*b^-4*log(x))
@test integrate(x^-6*(a+b*x^-1)^-1, x) == :(-1//4*b^-1*x^-4+a^3*b^-4*x^-1+a^4*b^-5*log(x)+-1*a^4*b^-5*log(b+a*x)+-1//2*a^2*b^-3*x^-2+1//3*a*b^-2*x^-3)
@test integrate(x^-7*(a+b*x^-1)^-1, x) == :(-1//5*b^-1*x^-5+a^5*b^-6*log(b+a*x)+(1/2)*a^3*b^-4*x^-2+-1*a^4*b^-5*x^-1+-1*a^5*b^-6*log(x)+-1//3*a^2*b^-3*x^-3+1//4*a*b^-2*x^-4)
@test integrate(x^5*(a+b*x^-1)^-2, x) == :(1//6*a^-2*x^6+a^-8*b^7*(b+a*x)^-1+-6*x*a^-7*b^5+7*a^-8*b^6*log(b+a*x)+-4//3*a^-5*b^3*x^3+-2//5*b*a^-3*x^5+3//4*a^-4*b^2*x^4+5//2*a^-6*b^4*x^2)
@test integrate(x^4*(a+b*x^-1)^-2, x) == :(1//5*a^-2*x^5+a^-4*b^2*x^3+-1*a^-7*b^6*(b+a*x)^-1+-6*a^-7*b^5*log(b+a*x)+-2*a^-5*b^3*x^2+5*x*a^-6*b^4+-1//2*b*a^-3*x^4)
@test integrate(x^3*(a+b*x^-1)^-2, x) == :(1//4*a^-2*x^4+a^-6*b^5*(b+a*x)^-1+-4*x*a^-5*b^3+5*a^-6*b^4*log(b+a*x)+-2//3*b*a^-3*x^3+3//2*a^-4*b^2*x^2)
@test integrate(x^2*(a+b*x^-1)^-2, x) == :(1//3*a^-2*x^3+-1*b*a^-3*x^2+-1*a^-5*b^4*(b+a*x)^-1+-4*a^-5*b^3*log(b+a*x)+3*x*a^-4*b^2)
@test integrate(x*(a+b*x^-1)^-2, x) == :((1/2)*a^-2*x^2+a^-4*b^3*(b+a*x)^-1+-2*b*x*a^-3+3*a^-4*b^2*log(b+a*x))
@test integrate((a+b*x^-1)^-2, x) == :(2*x*a^-2+-1*x*a^-1*(a+b*x^-1)^-1+-2*b*a^-3*log(b+a*x))
@test integrate(x^-1*(a+b*x^-1)^-2, x) == :(a^-2*log(b+a*x)+b*a^-2*(b+a*x)^-1)
@test integrate(x^-2*(a+b*x^-1)^-2, x) == :(b^-1*(a+b*x^-1)^-1)
@test integrate(x^-3*(a+b*x^-1)^-2, x) == :(b^-1*(b+a*x)^-1+b^-2*log(x)+-1*b^-2*log(b+a*x))
@test integrate(x^-4*(a+b*x^-1)^-2, x) == :(-1*b^-2*x^-1+-1*a*b^-2*(b+a*x)^-1+-2*a*b^-3*log(x)+2*a*b^-3*log(b+a*x))
@test integrate(x^-5*(a+b*x^-1)^-2, x) == :(-1//2*b^-2*x^-2+a^2*b^-3*(b+a*x)^-1+-3*a^2*b^-4*log(b+a*x)+2*a*b^-3*x^-1+3*a^2*b^-4*log(x))
@test integrate(x^-6*(a+b*x^-1)^-2, x) == :(-1//3*b^-2*x^-3+a*b^-3*x^-2+-1*a^3*b^-4*(b+a*x)^-1+-4*a^3*b^-5*log(x)+-3*a^2*b^-4*x^-1+4*a^3*b^-5*log(b+a*x))
@test integrate(x^-7*(a+b*x^-1)^-2, x) == :(-1//4*b^-2*x^-4+a^4*b^-5*(b+a*x)^-1+-5*a^4*b^-6*log(b+a*x)+4*a^3*b^-5*x^-1+5*a^4*b^-6*log(x)+-3//2*a^2*b^-4*x^-2+2//3*a*b^-3*x^-3)
@test integrate(x^-8*(a+b*x^-1)^-2, x) == :(-1//5*b^-2*x^-5+(1/2)*a*b^-3*x^-4+-1*a^2*b^-4*x^-3+-1*a^5*b^-6*(b+a*x)^-1+-6*a^5*b^-7*log(x)+-5*a^4*b^-6*x^-1+2*a^3*b^-5*x^-2+6*a^5*b^-7*log(b+a*x))
@test integrate(x^4*(a+b*x^-1)^-3, x) == :(1//5*a^-3*x^5+(1/2)*a^-8*b^7*(b+a*x)^-2+-21*a^-8*b^5*log(b+a*x)+-7*a^-8*b^6*(b+a*x)^-1+-5*a^-6*b^3*x^2+2*a^-5*b^2*x^3+15*x*a^-7*b^4+-3//4*b*a^-4*x^4)
@test integrate(x^3*(a+b*x^-1)^-3, x) == :(1//4*a^-3*x^4+-1*b*a^-4*x^3+-10*x*a^-6*b^3+3*a^-5*b^2*x^2+6*a^-7*b^5*(b+a*x)^-1+15*a^-7*b^4*log(b+a*x)+-1//2*a^-7*b^6*(b+a*x)^-2)
@test integrate(x^2*(a+b*x^-1)^-3, x) == :(1//3*a^-3*x^3+(1/2)*a^-6*b^5*(b+a*x)^-2+-10*a^-6*b^3*log(b+a*x)+-5*a^-6*b^4*(b+a*x)^-1+6*x*a^-5*b^2+-3//2*b*a^-4*x^2)
@test integrate(x*(a+b*x^-1)^-3, x) == :((1/2)*a^-3*x^2+-3*b*x*a^-4+4*a^-5*b^3*(b+a*x)^-1+6*a^-5*b^2*log(b+a*x)+-1//2*a^-5*b^4*(b+a*x)^-2)
@test integrate((a+b*x^-1)^-3, x) == :(3*x*a^-3+-3*b*a^-4*log(b+a*x)+-3//2*x*a^-2*(a+b*x^-1)^-1+-1//2*x*a^-1*(a+b*x^-1)^-2)
@test integrate(x^-1*(a+b*x^-1)^-3, x) == :(a^-3*log(b+a*x)+2*b*a^-3*(b+a*x)^-1+-1//2*a^-3*b^2*(b+a*x)^-2)
@test integrate(x^-2*(a+b*x^-1)^-3, x) == :((1/2)*b^-1*(a+b*x^-1)^-2)
@test integrate(x^-3*(a+b*x^-1)^-3, x) == :(-1//2*a^-1*(b+a*x)^-2)
@test integrate(x^-4*(a+b*x^-1)^-3, x) == :(b^-3*log(x)+b^-2*(b+a*x)^-1+(1/2)*b^-1*(b+a*x)^-2+-1*b^-3*log(b+a*x))
@test integrate(x^-5*(a+b*x^-1)^-3, x) == :(-1*b^-3*x^-1+-3*a*b^-4*log(x)+-2*a*b^-3*(b+a*x)^-1+3*a*b^-4*log(b+a*x)+-1//2*a*b^-2*(b+a*x)^-2)
@test integrate(x^-6*(a+b*x^-1)^-3, x) == :(-1//2*b^-3*x^-2+(1/2)*a^2*b^-3*(b+a*x)^-2+-6*a^2*b^-5*log(b+a*x)+3*a*b^-4*x^-1+3*a^2*b^-4*(b+a*x)^-1+6*a^2*b^-5*log(x))
@test integrate(x^-7*(a+b*x^-1)^-3, x) == :(-1//3*b^-3*x^-3+-10*a^3*b^-6*log(x)+-6*a^2*b^-5*x^-1+-4*a^3*b^-5*(b+a*x)^-1+10*a^3*b^-6*log(b+a*x)+-1//2*a^3*b^-4*(b+a*x)^-2+3//2*a*b^-4*x^-2)
@test integrate(x^-8*(a+b*x^-1)^-3, x) == :(-1//4*b^-3*x^-4+a*b^-4*x^-3+(1/2)*a^4*b^-5*(b+a*x)^-2+-15*a^4*b^-7*log(b+a*x)+-3*a^2*b^-5*x^-2+5*a^4*b^-6*(b+a*x)^-1+10*a^3*b^-6*x^-1+15*a^4*b^-7*log(x))
@test integrate(x^-9*(a+b*x^-1)^-3, x) == :(-1//5*b^-3*x^-5+-21*a^5*b^-8*log(x)+-15*a^4*b^-7*x^-1+-6*a^5*b^-7*(b+a*x)^-1+-2*a^2*b^-5*x^-3+5*a^3*b^-6*x^-2+21*a^5*b^-8*log(b+a*x)+-1//2*a^5*b^-6*(b+a*x)^-2+3//4*a*b^-4*x^-4)
@test integrate(x^5//2*(a+b*x^-1), x) == :(2//5*b*x^5//2+2//7*a*x^7//2)
@test integrate(x^3//2*(a+b*x^-1), x) == :(2//3*b*x^3//2+2//5*a*x^5//2)
@test integrate(x^(1/2)*(a+b*x^-1), x) == :(2*b*x^(1/2)+2//3*a*x^3//2)
@test integrate(x^-1//2*(a+b*x^-1), x) == :(-2*b*x^-1//2+2*a*x^(1/2))
@test integrate(x^-3//2*(a+b*x^-1), x) == :(-2*a*x^-1//2+-2//3*b*x^-3//2)
@test integrate(x^-5//2*(a+b*x^-1), x) == :(-2//3*a*x^-3//2+-2//5*b*x^-5//2)
@test integrate(x^5//2*(a+b*x^-1)^2, x) == :(2//3*b^2*x^3//2+2//7*a^2*x^7//2+4//5*a*b*x^5//2)
@test integrate(x^3//2*(a+b*x^-1)^2, x) == :(2*b^2*x^(1/2)+2//5*a^2*x^5//2+4//3*a*b*x^3//2)
@test integrate(x^(1/2)*(a+b*x^-1)^2, x) == :(-2*b^2*x^-1//2+2//3*a^2*x^3//2+4*a*b*x^(1/2))
@test integrate(x^-1//2*(a+b*x^-1)^2, x) == :(2*a^2*x^(1/2)+-2//3*b^2*x^-3//2+-4*a*b*x^-1//2)
@test integrate(x^-3//2*(a+b*x^-1)^2, x) == :(-2*a^2*x^-1//2+-2//5*b^2*x^-5//2+-4//3*a*b*x^-3//2)
@test integrate(x^-5//2*(a+b*x^-1)^2, x) == :(-2//3*a^2*x^-3//2+-2//7*b^2*x^-7//2+-4//5*a*b*x^-5//2)
@test integrate(x^5//2*(a+b*x^-1)^3, x) == :(2*b^3*x^(1/2)+2//7*a^3*x^7//2+2*a*b^2*x^3//2+6//5*b*a^2*x^5//2)
@test integrate(x^3//2*(a+b*x^-1)^3, x) == :(-2*b^3*x^-1//2+2//5*a^3*x^5//2+2*b*a^2*x^3//2+6*a*b^2*x^(1/2))
@test integrate(x^(1/2)*(a+b*x^-1)^3, x) == :(-2//3*b^3*x^-3//2+2//3*a^3*x^3//2+-6*a*b^2*x^-1//2+6*b*a^2*x^(1/2))
@test integrate(x^-1//2*(a+b*x^-1)^3, x) == :(2*a^3*x^(1/2)+-2//5*b^3*x^-5//2+-6*b*a^2*x^-1//2+-2*a*b^2*x^-3//2)
@test integrate(x^-3//2*(a+b*x^-1)^3, x) == :(-2*a^3*x^-1//2+-2//7*b^3*x^-7//2+-2*b*a^2*x^-3//2+-6//5*a*b^2*x^-5//2)
@test integrate(x^-5//2*(a+b*x^-1)^3, x) == :(-2//3*a^3*x^-3//2+-2//9*b^3*x^-9//2+-6//5*b*a^2*x^-5//2+-6//7*a*b^2*x^-7//2)
@test integrate(x^5//2*(a+b*x^-1)^-1, x) == :(2//7*a^-1*x^7//2+-2*a^-4*b^3*x^(1/2)+2*a^-9//2*b^7//2*arctan(a^(1/2)*b^-1//2*x^(1/2))+-2//5*b*a^-2*x^5//2+2//3*a^-3*b^2*x^3//2)
@test integrate(x^3//2*(a+b*x^-1)^-1, x) == :(2//5*a^-1*x^5//2+-2*a^-7//2*b^5//2*arctan(a^(1/2)*b^-1//2*x^(1/2))+2*a^-3*b^2*x^(1/2)+-2//3*b*a^-2*x^3//2)
@test integrate(x^(1/2)*(a+b*x^-1)^-1, x) == :(2//3*a^-1*x^3//2+-2*b*a^-2*x^(1/2)+2*a^-5//2*b^3//2*arctan(a^(1/2)*b^-1//2*x^(1/2)))
@test integrate(x^-1//2*(a+b*x^-1)^-1, x) == :(2*a^-1*x^(1/2)+-2*a^-3//2*b^(1/2)*arctan(a^(1/2)*b^-1//2*x^(1/2)))
@test integrate(x^-3//2*(a+b*x^-1)^-1, x) == :(2*a^-1//2*b^-1//2*arctan(a^(1/2)*b^-1//2*x^(1/2)))
@test integrate(x^-5//2*(a+b*x^-1)^-1, x) == :(-2*b^-1*x^-1//2+-2*a^(1/2)*b^-3//2*arctan(a^(1/2)*b^-1//2*x^(1/2)))
@test integrate(x^-7//2*(a+b*x^-1)^-1, x) == :(-2//3*b^-1*x^-3//2+2*a*b^-2*x^-1//2+2*a^3//2*b^-5//2*arctan(a^(1/2)*b^-1//2*x^(1/2)))
@test integrate(x^-9//2*(a+b*x^-1)^-1, x) == :(-2//5*b^-1*x^-5//2+-2*a^2*b^-3*x^-1//2+-2*a^5//2*b^-7//2*arctan(a^(1/2)*b^-1//2*x^(1/2))+2//3*a*b^-2*x^-3//2)
@test integrate(x^5//2*(a+b*x^-1)^-2, x) == :(9//7*a^-2*x^7//2+-1*a^-1*x^9//2*(b+a*x)^-1+-9*a^-5*b^3*x^(1/2)+3*a^-4*b^2*x^3//2+9*a^-11//2*b^7//2*arctan(a^(1/2)*b^-1//2*x^(1/2))+-9//5*b*a^-3*x^5//2)
@test integrate(x^3//2*(a+b*x^-1)^-2, x) == :(7//5*a^-2*x^5//2+-1*a^-1*x^7//2*(b+a*x)^-1+-7*a^-9//2*b^5//2*arctan(a^(1/2)*b^-1//2*x^(1/2))+7*a^-4*b^2*x^(1/2)+-7//3*b*a^-3*x^3//2)
@test integrate(x^(1/2)*(a+b*x^-1)^-2, x) == :(5//3*a^-2*x^3//2+-1*a^-1*x^5//2*(b+a*x)^-1+-5*b*a^-3*x^(1/2)+5*a^-7//2*b^3//2*arctan(a^(1/2)*b^-1//2*x^(1/2)))
@test integrate(x^-1//2*(a+b*x^-1)^-2, x) == :(3*a^-2*x^(1/2)+-1*a^-1*x^3//2*(b+a*x)^-1+-3*a^-5//2*b^(1/2)*arctan(a^(1/2)*b^-1//2*x^(1/2)))
@test integrate(x^-3//2*(a+b*x^-1)^-2, x) == :(a^-3//2*b^-1//2*arctan(a^(1/2)*b^-1//2*x^(1/2))+-1*a^-1*x^(1/2)*(b+a*x)^-1)
@test integrate(x^-5//2*(a+b*x^-1)^-2, x) == :(a^-1//2*b^-3//2*arctan(a^(1/2)*b^-1//2*x^(1/2))+b^-1*x^(1/2)*(b+a*x)^-1)
@test integrate(x^-7//2*(a+b*x^-1)^-2, x) == :(-3*b^-2*x^-1//2+b^-1*x^-1//2*(b+a*x)^-1+-3*a^(1/2)*b^-5//2*arctan(a^(1/2)*b^-1//2*x^(1/2)))
@test integrate(x^-9//2*(a+b*x^-1)^-2, x) == :(-5//3*b^-2*x^-3//2+b^-1*x^-3//2*(b+a*x)^-1+5*a*b^-3*x^-1//2+5*a^3//2*b^-7//2*arctan(a^(1/2)*b^-1//2*x^(1/2)))
@test integrate(x^-11//2*(a+b*x^-1)^-2, x) == :(-7//5*b^-2*x^-5//2+b^-1*x^-5//2*(b+a*x)^-1+-7*a^2*b^-4*x^-1//2+-7*a^5//2*b^-9//2*arctan(a^(1/2)*b^-1//2*x^(1/2))+7//3*a*b^-3*x^-3//2)
@test integrate(x^3//2*(a+b*x^-1)^-3, x) == :(63//20*a^-3*x^5//2+-63//4*a^-11//2*b^5//2*arctan(a^(1/2)*b^-1//2*x^(1/2))+-21//4*b*a^-4*x^3//2+-9//4*a^-2*x^7//2*(b+a*x)^-1+-1//2*a^-1*x^9//2*(b+a*x)^-2+63//4*a^-5*b^2*x^(1/2))
@test integrate(x^(1/2)*(a+b*x^-1)^-3, x) == :(35//12*a^-3*x^3//2+-35//4*b*a^-4*x^(1/2)+-7//4*a^-2*x^5//2*(b+a*x)^-1+-1//2*a^-1*x^7//2*(b+a*x)^-2+35//4*a^-9//2*b^3//2*arctan(a^(1/2)*b^-1//2*x^(1/2)))
@test integrate(x^-1//2*(a+b*x^-1)^-3, x) == :(15//4*a^-3*x^(1/2)+-15//4*a^-7//2*b^(1/2)*arctan(a^(1/2)*b^-1//2*x^(1/2))+-5//4*a^-2*x^3//2*(b+a*x)^-1+-1//2*a^-1*x^5//2*(b+a*x)^-2)
@test integrate(x^-3//2*(a+b*x^-1)^-3, x) == :(-3//4*a^-2*x^(1/2)*(b+a*x)^-1+-1//2*a^-1*x^3//2*(b+a*x)^-2+3//4*a^-5//2*b^-1//2*arctan(a^(1/2)*b^-1//2*x^(1/2)))
@test integrate(x^-5//2*(a+b*x^-1)^-3, x) == :(-1//2*a^-1*x^(1/2)*(b+a*x)^-2+1//4*a^-3//2*b^-3//2*arctan(a^(1/2)*b^-1//2*x^(1/2))+1//4*a^-1*b^-1*x^(1/2)*(b+a*x)^-1)
@test integrate(x^-7//2*(a+b*x^-1)^-3, x) == :((1/2)*b^-1*x^(1/2)*(b+a*x)^-2+3//4*a^-1//2*b^-5//2*arctan(a^(1/2)*b^-1//2*x^(1/2))+3//4*b^-2*x^(1/2)*(b+a*x)^-1)
@test integrate(x^-9//2*(a+b*x^-1)^-3, x) == :(-15//4*b^-3*x^-1//2+(1/2)*b^-1*x^-1//2*(b+a*x)^-2+-15//4*a^(1/2)*b^-7//2*arctan(a^(1/2)*b^-1//2*x^(1/2))+5//4*b^-2*x^-1//2*(b+a*x)^-1)
@test integrate(x^-11//2*(a+b*x^-1)^-3, x) == :(-35//12*b^-3*x^-3//2+(1/2)*b^-1*x^-3//2*(b+a*x)^-2+7//4*b^-2*x^-3//2*(b+a*x)^-1+35//4*a*b^-4*x^-1//2+35//4*a^3//2*b^-9//2*arctan(a^(1/2)*b^-1//2*x^(1/2)))
@test integrate(x^-13//2*(a+b*x^-1)^-3, x) == :(-63//20*b^-3*x^-5//2+(1/2)*b^-1*x^-5//2*(b+a*x)^-2+-63//4*a^2*b^-5*x^-1//2+-63//4*a^5//2*b^-11//2*arctan(a^(1/2)*b^-1//2*x^(1/2))+9//4*b^-2*x^-5//2*(b+a*x)^-1+21//4*a*b^-4*x^-3//2)
@test integrate(x^3*(a+b*x^-1)^(1/2), x) == :(1//4*x^4*(a+b*x^-1)^(1/2)+-5//64*a^-7//2*b^4*arctanh(a^-1//2*(a+b*x^-1)^(1/2))+-5//96*a^-2*b^2*x^2*(a+b*x^-1)^(1/2)+1//24*b*a^-1*x^3*(a+b*x^-1)^(1/2)+5//64*x*a^-3*b^3*(a+b*x^-1)^(1/2))
@test integrate(x^2*(a+b*x^-1)^(1/2), x) == :(1//3*x^3*(a+b*x^-1)^(1/2)+1//8*a^-5//2*b^3*arctanh(a^-1//2*(a+b*x^-1)^(1/2))+-1//8*x*a^-2*b^2*(a+b*x^-1)^(1/2)+1//12*b*a^-1*x^2*(a+b*x^-1)^(1/2))
@test integrate(x*(a+b*x^-1)^(1/2), x) == :((1/2)*x^2*(a+b*x^-1)^(1/2)+-1//4*a^-3//2*b^2*arctanh(a^-1//2*(a+b*x^-1)^(1/2))+1//4*b*x*a^-1*(a+b*x^-1)^(1/2))
@test integrate((a+b*x^-1)^(1/2), x) == :(x*(a+b*x^-1)^(1/2)+b*a^-1//2*arctanh(a^-1//2*(a+b*x^-1)^(1/2)))
@test integrate(x^-1*(a+b*x^-1)^(1/2), x) == :(-2*(a+b*x^-1)^(1/2)+2*a^(1/2)*arctanh(a^-1//2*(a+b*x^-1)^(1/2)))
@test integrate(x^-2*(a+b*x^-1)^(1/2), x) == :(-2//3*b^-1*(a+b*x^-1)^3//2)
@test integrate(x^-3*(a+b*x^-1)^(1/2), x) == :(-2//5*b^-2*(a+b*x^-1)^5//2+2//3*a*b^-2*(a+b*x^-1)^3//2)
@test integrate(x^-4*(a+b*x^-1)^(1/2), x) == :(-2//7*b^-3*(a+b*x^-1)^7//2+-2//3*a^2*b^-3*(a+b*x^-1)^3//2+4//5*a*b^-3*(a+b*x^-1)^5//2)
@test integrate(x^-5*(a+b*x^-1)^(1/2), x) == :(-2//9*b^-4*(a+b*x^-1)^9//2+-6//5*a^2*b^-4*(a+b*x^-1)^5//2+2//3*a^3*b^-4*(a+b*x^-1)^3//2+6//7*a*b^-4*(a+b*x^-1)^7//2)
@test integrate(x^-6*(a+b*x^-1)^(1/2), x) == :(-2//11*b^-5*(a+b*x^-1)^11//2+-12//7*a^2*b^-5*(a+b*x^-1)^7//2+-2//3*a^4*b^-5*(a+b*x^-1)^3//2+8//5*a^3*b^-5*(a+b*x^-1)^5//2+8//9*a*b^-5*(a+b*x^-1)^9//2)
@test integrate(x^3*(a+b*x^-1)^3//2, x) == :(1//4*x^4*(a+b*x^-1)^3//2+1//8*b*x^3*(a+b*x^-1)^(1/2)+3//64*a^-5//2*b^4*arctanh(a^-1//2*(a+b*x^-1)^(1/2))+-3//64*x*a^-2*b^3*(a+b*x^-1)^(1/2)+1//32*a^-1*b^2*x^2*(a+b*x^-1)^(1/2))
@test integrate(x^2*(a+b*x^-1)^3//2, x) == :(1//3*x^3*(a+b*x^-1)^3//2+-1//8*a^-3//2*b^3*arctanh(a^-1//2*(a+b*x^-1)^(1/2))+1//4*b*x^2*(a+b*x^-1)^(1/2)+1//8*x*a^-1*b^2*(a+b*x^-1)^(1/2))
@test integrate(x*(a+b*x^-1)^3//2, x) == :((1/2)*x^2*(a+b*x^-1)^3//2+3//4*b*x*(a+b*x^-1)^(1/2)+3//4*a^-1//2*b^2*arctanh(a^-1//2*(a+b*x^-1)^(1/2)))
@test integrate((a+b*x^-1)^3//2, x) == :(x*(a+b*x^-1)^3//2+-3*b*(a+b*x^-1)^(1/2)+3*b*a^(1/2)*arctanh(a^-1//2*(a+b*x^-1)^(1/2)))
@test integrate(x^-1*(a+b*x^-1)^3//2, x) == :(-2//3*(a+b*x^-1)^3//2+-2*a*(a+b*x^-1)^(1/2)+2*a^3//2*arctanh(a^-1//2*(a+b*x^-1)^(1/2)))
@test integrate(x^-2*(a+b*x^-1)^3//2, x) == :(-2//5*b^-1*(a+b*x^-1)^5//2)
@test integrate(x^-3*(a+b*x^-1)^3//2, x) == :(-2//7*b^-2*(a+b*x^-1)^7//2+2//5*a*b^-2*(a+b*x^-1)^5//2)
@test integrate(x^-4*(a+b*x^-1)^3//2, x) == :(-2//9*b^-3*(a+b*x^-1)^9//2+-2//5*a^2*b^-3*(a+b*x^-1)^5//2+4//7*a*b^-3*(a+b*x^-1)^7//2)
@test integrate(x^-5*(a+b*x^-1)^3//2, x) == :(-2//11*b^-4*(a+b*x^-1)^11//2+-6//7*a^2*b^-4*(a+b*x^-1)^7//2+2//3*a*b^-4*(a+b*x^-1)^9//2+2//5*a^3*b^-4*(a+b*x^-1)^5//2)
@test integrate(x^-6*(a+b*x^-1)^3//2, x) == :(-2//13*b^-5*(a+b*x^-1)^13//2+-4//3*a^2*b^-5*(a+b*x^-1)^9//2+-2//5*a^4*b^-5*(a+b*x^-1)^5//2+8//7*a^3*b^-5*(a+b*x^-1)^7//2+8//11*a*b^-5*(a+b*x^-1)^11//2)
@test integrate(x^-7*(a+b*x^-1)^3//2, x) == :(-2//15*b^-6*(a+b*x^-1)^15//2+-20//11*a^2*b^-6*(a+b*x^-1)^11//2+-10//7*a^4*b^-6*(a+b*x^-1)^7//2+2//5*a^5*b^-6*(a+b*x^-1)^5//2+10//13*a*b^-6*(a+b*x^-1)^13//2+20//9*a^3*b^-6*(a+b*x^-1)^9//2)
@test integrate(x^3*(a+b*x^-1)^5//2, x) == :(1//4*x^4*(a+b*x^-1)^5//2+-5//64*a^-3//2*b^4*arctanh(a^-1//2*(a+b*x^-1)^(1/2))+5//24*b*x^3*(a+b*x^-1)^3//2+5//32*b^2*x^2*(a+b*x^-1)^(1/2)+5//64*x*a^-1*b^3*(a+b*x^-1)^(1/2))
@test integrate(x^2*(a+b*x^-1)^5//2, x) == :(1//3*x^3*(a+b*x^-1)^5//2+5//8*x*b^2*(a+b*x^-1)^(1/2)+5//8*a^-1//2*b^3*arctanh(a^-1//2*(a+b*x^-1)^(1/2))+5//12*b*x^2*(a+b*x^-1)^3//2)
@test integrate(x*(a+b*x^-1)^5//2, x) == :((1/2)*x^2*(a+b*x^-1)^5//2+-15//4*b^2*(a+b*x^-1)^(1/2)+5//4*b*x*(a+b*x^-1)^3//2+15//4*a^(1/2)*b^2*arctanh(a^-1//2*(a+b*x^-1)^(1/2)))
@test integrate((a+b*x^-1)^5//2, x) == :(x*(a+b*x^-1)^5//2+-5//3*b*(a+b*x^-1)^3//2+-5*a*b*(a+b*x^-1)^(1/2)+5*b*a^3//2*arctanh(a^-1//2*(a+b*x^-1)^(1/2)))
@test integrate(x^-1*(a+b*x^-1)^5//2, x) == :(-2//5*(a+b*x^-1)^5//2+-2*a^2*(a+b*x^-1)^(1/2)+2*a^5//2*arctanh(a^-1//2*(a+b*x^-1)^(1/2))+-2//3*a*(a+b*x^-1)^3//2)
@test integrate(x^-2*(a+b*x^-1)^5//2, x) == :(-2//7*b^-1*(a+b*x^-1)^7//2)
@test integrate(x^-3*(a+b*x^-1)^5//2, x) == :(-2//9*b^-2*(a+b*x^-1)^9//2+2//7*a*b^-2*(a+b*x^-1)^7//2)
@test integrate(x^-4*(a+b*x^-1)^5//2, x) == :(-2//11*b^-3*(a+b*x^-1)^11//2+-2//7*a^2*b^-3*(a+b*x^-1)^7//2+4//9*a*b^-3*(a+b*x^-1)^9//2)
@test integrate(x^-5*(a+b*x^-1)^5//2, x) == :(-2//13*b^-4*(a+b*x^-1)^13//2+-2//3*a^2*b^-4*(a+b*x^-1)^9//2+2//7*a^3*b^-4*(a+b*x^-1)^7//2+6//11*a*b^-4*(a+b*x^-1)^11//2)
@test integrate(x^-6*(a+b*x^-1)^5//2, x) == :(-2//15*b^-5*(a+b*x^-1)^15//2+-12//11*a^2*b^-5*(a+b*x^-1)^11//2+-2//7*a^4*b^-5*(a+b*x^-1)^7//2+8//9*a^3*b^-5*(a+b*x^-1)^9//2+8//13*a*b^-5*(a+b*x^-1)^13//2)
@test integrate(x^3*(a+b*x^-1)^-1//2, x) == :(1//4*a^-1*x^4*(a+b*x^-1)^(1/2)+35//64*a^-9//2*b^4*arctanh(a^-1//2*(a+b*x^-1)^(1/2))+-35//64*x*a^-4*b^3*(a+b*x^-1)^(1/2)+-7//24*b*a^-2*x^3*(a+b*x^-1)^(1/2)+35//96*a^-3*b^2*x^2*(a+b*x^-1)^(1/2))
@test integrate(x^2*(a+b*x^-1)^-1//2, x) == :(-5//8*a^-7//2*b^3*arctanh(a^-1//2*(a+b*x^-1)^(1/2))+1//3*a^-1*x^3*(a+b*x^-1)^(1/2)+-5//12*b*a^-2*x^2*(a+b*x^-1)^(1/2)+5//8*x*a^-3*b^2*(a+b*x^-1)^(1/2))
@test integrate(x*(a+b*x^-1)^-1//2, x) == :((1/2)*a^-1*x^2*(a+b*x^-1)^(1/2)+3//4*a^-5//2*b^2*arctanh(a^-1//2*(a+b*x^-1)^(1/2))+-3//4*b*x*a^-2*(a+b*x^-1)^(1/2))
@test integrate((a+b*x^-1)^-1//2, x) == :(x*a^-1*(a+b*x^-1)^(1/2)+-1*b*a^-3//2*arctanh(a^-1//2*(a+b*x^-1)^(1/2)))
@test integrate(x^-1*(a+b*x^-1)^-1//2, x) == :(2*a^-1//2*arctanh(a^-1//2*(a+b*x^-1)^(1/2)))
@test integrate(x^-2*(a+b*x^-1)^-1//2, x) == :(-2*b^-1*(a+b*x^-1)^(1/2))
@test integrate(x^-3*(a+b*x^-1)^-1//2, x) == :(-2//3*b^-2*(a+b*x^-1)^3//2+2*a*b^-2*(a+b*x^-1)^(1/2))
@test integrate(x^-4*(a+b*x^-1)^-1//2, x) == :(-2//5*b^-3*(a+b*x^-1)^5//2+-2*a^2*b^-3*(a+b*x^-1)^(1/2)+4//3*a*b^-3*(a+b*x^-1)^3//2)
@test integrate(x^-5*(a+b*x^-1)^-1//2, x) == :(-2//7*b^-4*(a+b*x^-1)^7//2+-2*a^2*b^-4*(a+b*x^-1)^3//2+2*a^3*b^-4*(a+b*x^-1)^(1/2)+6//5*a*b^-4*(a+b*x^-1)^5//2)
@test integrate(x^-6*(a+b*x^-1)^-1//2, x) == :(-2//9*b^-5*(a+b*x^-1)^9//2+-2*a^4*b^-5*(a+b*x^-1)^(1/2)+-12//5*a^2*b^-5*(a+b*x^-1)^5//2+8//3*a^3*b^-5*(a+b*x^-1)^3//2+8//7*a*b^-5*(a+b*x^-1)^7//2)
@test integrate(x^2*(a+b*x^-1)^-3//2, x) == :(-35//8*a^-9//2*b^3*arctanh(a^-1//2*(a+b*x^-1)^(1/2))+1//3*a^-1*x^3*(a+b*x^-1)^-1//2+35//8*a^-4*b^3*(a+b*x^-1)^-1//2+-7//12*b*a^-2*x^2*(a+b*x^-1)^-1//2+35//24*x*a^-3*b^2*(a+b*x^-1)^-1//2)
@test integrate(x*(a+b*x^-1)^-3//2, x) == :((1/2)*a^-1*x^2*(a+b*x^-1)^-1//2+-15//4*a^-3*b^2*(a+b*x^-1)^-1//2+15//4*a^-7//2*b^2*arctanh(a^-1//2*(a+b*x^-1)^(1/2))+-5//4*b*x*a^-2*(a+b*x^-1)^-1//2)
@test integrate((a+b*x^-1)^-3//2, x) == :(x*a^-1*(a+b*x^-1)^-1//2+-3*b*a^-5//2*arctanh(a^-1//2*(a+b*x^-1)^(1/2))+3*b*a^-2*(a+b*x^-1)^-1//2)
@test integrate(x^-1*(a+b*x^-1)^-3//2, x) == :(-2*a^-1*(a+b*x^-1)^-1//2+2*a^-3//2*arctanh(a^-1//2*(a+b*x^-1)^(1/2)))
@test integrate(x^-2*(a+b*x^-1)^-3//2, x) == :(2*b^-1*(a+b*x^-1)^-1//2)
@test integrate(x^-3*(a+b*x^-1)^-3//2, x) == :(-2*b^-2*(a+b*x^-1)^(1/2)+-2*a*b^-2*(a+b*x^-1)^-1//2)
@test integrate(x^-4*(a+b*x^-1)^-3//2, x) == :(-2//3*b^-3*(a+b*x^-1)^3//2+2*a^2*b^-3*(a+b*x^-1)^-1//2+4*a*b^-3*(a+b*x^-1)^(1/2))
@test integrate(x^-5*(a+b*x^-1)^-3//2, x) == :(-2//5*b^-4*(a+b*x^-1)^5//2+-6*a^2*b^-4*(a+b*x^-1)^(1/2)+-2*a^3*b^-4*(a+b*x^-1)^-1//2+2*a*b^-4*(a+b*x^-1)^3//2)
@test integrate(x^-6*(a+b*x^-1)^-3//2, x) == :(-2//7*b^-5*(a+b*x^-1)^7//2+-4*a^2*b^-5*(a+b*x^-1)^3//2+2*a^4*b^-5*(a+b*x^-1)^-1//2+8*a^3*b^-5*(a+b*x^-1)^(1/2)+8//5*a*b^-5*(a+b*x^-1)^5//2)
@test integrate(x^-7*(a+b*x^-1)^-3//2, x) == :(-2//9*b^-6*(a+b*x^-1)^9//2+-10*a^4*b^-6*(a+b*x^-1)^(1/2)+-4*a^2*b^-6*(a+b*x^-1)^5//2+-2*a^5*b^-6*(a+b*x^-1)^-1//2+10//7*a*b^-6*(a+b*x^-1)^7//2+20//3*a^3*b^-6*(a+b*x^-1)^3//2)
@test integrate(x^2*(a+b*x^-1)^-5//2, x) == :(-105//8*a^-11//2*b^3*arctanh(a^-1//2*(a+b*x^-1)^(1/2))+1//3*a^-1*x^3*(a+b*x^-1)^-3//2+35//8*a^-4*b^3*(a+b*x^-1)^-3//2+105//8*a^-5*b^3*(a+b*x^-1)^-1//2+-3//4*b*a^-2*x^2*(a+b*x^-1)^-3//2+21//8*x*a^-3*b^2*(a+b*x^-1)^-3//2)
@test integrate(x*(a+b*x^-1)^-5//2, x) == :((1/2)*a^-1*x^2*(a+b*x^-1)^-3//2+-35//4*a^-4*b^2*(a+b*x^-1)^-1//2+-35//12*a^-3*b^2*(a+b*x^-1)^-3//2+35//4*a^-9//2*b^2*arctanh(a^-1//2*(a+b*x^-1)^(1/2))+-7//4*b*x*a^-2*(a+b*x^-1)^-3//2)
@test integrate((a+b*x^-1)^-5//2, x) == :(x*a^-1*(a+b*x^-1)^-3//2+-5*b*a^-7//2*arctanh(a^-1//2*(a+b*x^-1)^(1/2))+5*b*a^-3*(a+b*x^-1)^-1//2+5//3*b*a^-2*(a+b*x^-1)^-3//2)
@test integrate(x^-1*(a+b*x^-1)^-5//2, x) == :(-2*a^-2*(a+b*x^-1)^-1//2+2*a^-5//2*arctanh(a^-1//2*(a+b*x^-1)^(1/2))+-2//3*a^-1*(a+b*x^-1)^-3//2)
@test integrate(x^-2*(a+b*x^-1)^-5//2, x) == :(2//3*b^-1*(a+b*x^-1)^-3//2)
@test integrate(x^-3*(a+b*x^-1)^-5//2, x) == :(2*b^-2*(a+b*x^-1)^-1//2+-2//3*a*b^-2*(a+b*x^-1)^-3//2)
@test integrate(x^-4*(a+b*x^-1)^-5//2, x) == :(-2*b^-3*(a+b*x^-1)^(1/2)+-4*a*b^-3*(a+b*x^-1)^-1//2+2//3*a^2*b^-3*(a+b*x^-1)^-3//2)
@test integrate(x^-5*(a+b*x^-1)^-5//2, x) == :(-2//3*b^-4*(a+b*x^-1)^3//2+6*a*b^-4*(a+b*x^-1)^(1/2)+6*a^2*b^-4*(a+b*x^-1)^-1//2+-2//3*a^3*b^-4*(a+b*x^-1)^-3//2)
@test integrate(x^-6*(a+b*x^-1)^-5//2, x) == :(-2//5*b^-5*(a+b*x^-1)^5//2+-12*a^2*b^-5*(a+b*x^-1)^(1/2)+-8*a^3*b^-5*(a+b*x^-1)^-1//2+2//3*a^4*b^-5*(a+b*x^-1)^-3//2+8//3*a*b^-5*(a+b*x^-1)^3//2)
@test integrate(x^-7*(a+b*x^-1)^-5//2, x) == :(-2//7*b^-6*(a+b*x^-1)^7//2+2*a*b^-6*(a+b*x^-1)^5//2+10*a^4*b^-6*(a+b*x^-1)^-1//2+20*a^3*b^-6*(a+b*x^-1)^(1/2)+-20//3*a^2*b^-6*(a+b*x^-1)^3//2+-2//3*a^5*b^-6*(a+b*x^-1)^-3//2)
@test integrate(x^7//2*(a+b*x^-1)^(1/2), x) == :(2//9*a^-1*x^9//2*(a+b*x^-1)^3//2+-32//315*a^-4*b^3*x^3//2*(a+b*x^-1)^3//2+-4//21*b*a^-2*x^7//2*(a+b*x^-1)^3//2+16//105*a^-3*b^2*x^5//2*(a+b*x^-1)^3//2)
@test integrate(x^5//2*(a+b*x^-1)^(1/2), x) == :(2//7*a^-1*x^7//2*(a+b*x^-1)^3//2+-8//35*b*a^-2*x^5//2*(a+b*x^-1)^3//2+16//105*a^-3*b^2*x^3//2*(a+b*x^-1)^3//2)
@test integrate(x^3//2*(a+b*x^-1)^(1/2), x) == :(2//5*a^-1*x^5//2*(a+b*x^-1)^3//2+-4//15*b*a^-2*x^3//2*(a+b*x^-1)^3//2)
@test integrate(x^(1/2)*(a+b*x^-1)^(1/2), x) == :(2//3*a^-1*x^3//2*(a+b*x^-1)^3//2)
@test integrate(x^-1//2*(a+b*x^-1)^(1/2), x) == :(-2*b^(1/2)*arctanh(b^(1/2)*x^-1//2*(a+b*x^-1)^-1//2)+2*x^(1/2)*(a+b*x^-1)^(1/2))
@test integrate(x^-3//2*(a+b*x^-1)^(1/2), x) == :(-1*x^-1//2*(a+b*x^-1)^(1/2)+-1*a*b^-1//2*arctanh(b^(1/2)*x^-1//2*(a+b*x^-1)^-1//2))
@test integrate(x^-5//2*(a+b*x^-1)^(1/2), x) == :(-1//2*x^-3//2*(a+b*x^-1)^(1/2)+1//4*a^2*b^-3//2*arctanh(b^(1/2)*x^-1//2*(a+b*x^-1)^-1//2)+-1//4*a*b^-1*x^-1//2*(a+b*x^-1)^(1/2))
@test integrate(x^-7//2*(a+b*x^-1)^(1/2), x) == :(-1//3*x^-5//2*(a+b*x^-1)^(1/2)+-1//8*a^3*b^-5//2*arctanh(b^(1/2)*x^-1//2*(a+b*x^-1)^-1//2)+-1//12*a*b^-1*x^-3//2*(a+b*x^-1)^(1/2)+1//8*a^2*b^-2*x^-1//2*(a+b*x^-1)^(1/2))
@test integrate(x^9//2*(a+b*x^-1)^3//2, x) == :(2//11*a^-1*x^11//2*(a+b*x^-1)^5//2+-32//1155*a^-4*b^3*x^5//2*(a+b*x^-1)^5//2+-4//33*b*a^-2*x^9//2*(a+b*x^-1)^5//2+16//231*a^-3*b^2*x^7//2*(a+b*x^-1)^5//2)
@test integrate(x^7//2*(a+b*x^-1)^3//2, x) == :(2//9*a^-1*x^9//2*(a+b*x^-1)^5//2+-8//63*b*a^-2*x^7//2*(a+b*x^-1)^5//2+16//315*a^-3*b^2*x^5//2*(a+b*x^-1)^5//2)
@test integrate(x^5//2*(a+b*x^-1)^3//2, x) == :(2//7*a^-1*x^7//2*(a+b*x^-1)^5//2+-4//35*b*a^-2*x^5//2*(a+b*x^-1)^5//2)
@test integrate(x^3//2*(a+b*x^-1)^3//2, x) == :(2//5*a^-1*x^5//2*(a+b*x^-1)^5//2)
@test integrate(x^(1/2)*(a+b*x^-1)^3//2, x) == :(-2*b^3//2*arctanh(b^(1/2)*x^-1//2*(a+b*x^-1)^-1//2)+2//3*x^3//2*(a+b*x^-1)^3//2+2*b*x^(1/2)*(a+b*x^-1)^(1/2))
@test integrate(x^-1//2*(a+b*x^-1)^3//2, x) == :(2*x^(1/2)*(a+b*x^-1)^3//2+-3*a*b^(1/2)*arctanh(b^(1/2)*x^-1//2*(a+b*x^-1)^-1//2)+-3*b*x^-1//2*(a+b*x^-1)^(1/2))
@test integrate(x^-3//2*(a+b*x^-1)^3//2, x) == :(-1//2*x^-1//2*(a+b*x^-1)^3//2+-3//4*a*x^-1//2*(a+b*x^-1)^(1/2)+-3//4*a^2*b^-1//2*arctanh(b^(1/2)*x^-1//2*(a+b*x^-1)^-1//2))
@test integrate(x^-5//2*(a+b*x^-1)^3//2, x) == :(-1//3*x^-3//2*(a+b*x^-1)^3//2+-1//4*a*x^-3//2*(a+b*x^-1)^(1/2)+1//8*a^3*b^-3//2*arctanh(b^(1/2)*x^-1//2*(a+b*x^-1)^-1//2)+-1//8*a^2*b^-1*x^-1//2*(a+b*x^-1)^(1/2))
@test integrate(x^11//2*(a+b*x^-1)^5//2, x) == :(2//13*a^-1*x^13//2*(a+b*x^-1)^7//2+-32//3003*a^-4*b^3*x^7//2*(a+b*x^-1)^7//2+-12//143*b*a^-2*x^11//2*(a+b*x^-1)^7//2+16//429*a^-3*b^2*x^9//2*(a+b*x^-1)^7//2)
@test integrate(x^9//2*(a+b*x^-1)^5//2, x) == :(2//11*a^-1*x^11//2*(a+b*x^-1)^7//2+-8//99*b*a^-2*x^9//2*(a+b*x^-1)^7//2+16//693*a^-3*b^2*x^7//2*(a+b*x^-1)^7//2)
@test integrate(x^7//2*(a+b*x^-1)^5//2, x) == :(2//9*a^-1*x^9//2*(a+b*x^-1)^7//2+-4//63*b*a^-2*x^7//2*(a+b*x^-1)^7//2)
@test integrate(x^5//2*(a+b*x^-1)^5//2, x) == :(2//7*a^-1*x^7//2*(a+b*x^-1)^7//2)
@test integrate(x^3//2*(a+b*x^-1)^5//2, x) == :(-2*b^5//2*arctanh(b^(1/2)*x^-1//2*(a+b*x^-1)^-1//2)+2//5*x^5//2*(a+b*x^-1)^5//2+2*b^2*x^(1/2)*(a+b*x^-1)^(1/2)+2//3*b*x^3//2*(a+b*x^-1)^3//2)
@test integrate(x^(1/2)*(a+b*x^-1)^5//2, x) == :(2//3*x^3//2*(a+b*x^-1)^5//2+-5*a*b^3//2*arctanh(b^(1/2)*x^-1//2*(a+b*x^-1)^-1//2)+-5*b^2*x^-1//2*(a+b*x^-1)^(1/2)+10//3*b*x^(1/2)*(a+b*x^-1)^3//2)
@test integrate(x^-1//2*(a+b*x^-1)^5//2, x) == :(2*x^(1/2)*(a+b*x^-1)^5//2+-15//4*a^2*b^(1/2)*arctanh(b^(1/2)*x^-1//2*(a+b*x^-1)^-1//2)+-5//2*b*x^-1//2*(a+b*x^-1)^3//2+-15//4*a*b*x^-1//2*(a+b*x^-1)^(1/2))
@test integrate(x^-3//2*(a+b*x^-1)^5//2, x) == :(-1//3*x^-1//2*(a+b*x^-1)^5//2+-5//8*a^2*x^-1//2*(a+b*x^-1)^(1/2)+-5//8*a^3*b^-1//2*arctanh(b^(1/2)*x^-1//2*(a+b*x^-1)^-1//2)+-5//12*a*x^-1//2*(a+b*x^-1)^3//2)
@test integrate(x^-5//2*(a+b*x^-1)^5//2, x) == :(-1//4*x^-3//2*(a+b*x^-1)^5//2+-5//24*a*x^-3//2*(a+b*x^-1)^3//2+-5//32*a^2*x^-3//2*(a+b*x^-1)^(1/2)+5//64*a^4*b^-3//2*arctanh(b^(1/2)*x^-1//2*(a+b*x^-1)^-1//2)+-5//64*a^3*b^-1*x^-1//2*(a+b*x^-1)^(1/2))
@test integrate(x^7//2*(a+b*x^-1)^-1//2, x) == :(2//9*a^-1*x^9//2*(a+b*x^-1)^(1/2)+-128//315*a^-4*b^3*x^3//2*(a+b*x^-1)^(1/2)+-16//63*b*a^-2*x^7//2*(a+b*x^-1)^(1/2)+32//105*a^-3*b^2*x^5//2*(a+b*x^-1)^(1/2)+256//315*a^-5*b^4*x^(1/2)*(a+b*x^-1)^(1/2))
@test integrate(x^5//2*(a+b*x^-1)^-1//2, x) == :(2//7*a^-1*x^7//2*(a+b*x^-1)^(1/2)+-32//35*a^-4*b^3*x^(1/2)*(a+b*x^-1)^(1/2)+-12//35*b*a^-2*x^5//2*(a+b*x^-1)^(1/2)+16//35*a^-3*b^2*x^3//2*(a+b*x^-1)^(1/2))
@test integrate(x^3//2*(a+b*x^-1)^-1//2, x) == :(2//5*a^-1*x^5//2*(a+b*x^-1)^(1/2)+-8//15*b*a^-2*x^3//2*(a+b*x^-1)^(1/2)+16//15*a^-3*b^2*x^(1/2)*(a+b*x^-1)^(1/2))
@test integrate(x^(1/2)*(a+b*x^-1)^-1//2, x) == :(2//3*a^-1*x^3//2*(a+b*x^-1)^(1/2)+-4//3*b*a^-2*x^(1/2)*(a+b*x^-1)^(1/2))
@test integrate(x^-1//2*(a+b*x^-1)^-1//2, x) == :(2*a^-1*x^(1/2)*(a+b*x^-1)^(1/2))
@test integrate(x^-3//2*(a+b*x^-1)^-1//2, x) == :(-2*b^-1//2*arctanh(b^(1/2)*x^-1//2*(a+b*x^-1)^-1//2))
@test integrate(x^-5//2*(a+b*x^-1)^-1//2, x) == :(a*b^-3//2*arctanh(b^(1/2)*x^-1//2*(a+b*x^-1)^-1//2)+-1*b^-1*x^-1//2*(a+b*x^-1)^(1/2))
@test integrate(x^-7//2*(a+b*x^-1)^-1//2, x) == :(-3//4*a^2*b^-5//2*arctanh(b^(1/2)*x^-1//2*(a+b*x^-1)^-1//2)+-1//2*b^-1*x^-3//2*(a+b*x^-1)^(1/2)+3//4*a*b^-2*x^-1//2*(a+b*x^-1)^(1/2))
@test integrate(x^-9//2*(a+b*x^-1)^-1//2, x) == :(-1//3*b^-1*x^-5//2*(a+b*x^-1)^(1/2)+5//8*a^3*b^-7//2*arctanh(b^(1/2)*x^-1//2*(a+b*x^-1)^-1//2)+-5//8*a^2*b^-3*x^-1//2*(a+b*x^-1)^(1/2)+5//12*a*b^-2*x^-3//2*(a+b*x^-1)^(1/2))
@test integrate(x^5//2*(a+b*x^-1)^-3//2, x) == :(2//7*a^-1*x^7//2*(a+b*x^-1)^-1//2+-256//35*a^-5*b^4*x^-1//2*(a+b*x^-1)^-1//2+-128//35*a^-4*b^3*x^(1/2)*(a+b*x^-1)^-1//2+-16//35*b*a^-2*x^5//2*(a+b*x^-1)^-1//2+32//35*a^-3*b^2*x^3//2*(a+b*x^-1)^-1//2)
@test integrate(x^3//2*(a+b*x^-1)^-3//2, x) == :(2//5*a^-1*x^5//2*(a+b*x^-1)^-1//2+-4//5*b*a^-2*x^3//2*(a+b*x^-1)^-1//2+16//5*a^-3*b^2*x^(1/2)*(a+b*x^-1)^-1//2+32//5*a^-4*b^3*x^-1//2*(a+b*x^-1)^-1//2)
@test integrate(x^(1/2)*(a+b*x^-1)^-3//2, x) == :(2//3*a^-1*x^3//2*(a+b*x^-1)^-1//2+-16//3*a^-3*b^2*x^-1//2*(a+b*x^-1)^-1//2+-8//3*b*a^-2*x^(1/2)*(a+b*x^-1)^-1//2)
@test integrate(x^-1//2*(a+b*x^-1)^-3//2, x) == :(2*a^-1*x^(1/2)*(a+b*x^-1)^-1//2+4*b*a^-2*x^-1//2*(a+b*x^-1)^-1//2)
@test integrate(x^-3//2*(a+b*x^-1)^-3//2, x) == :(-2*a^-1*x^-1//2*(a+b*x^-1)^-1//2)
@test integrate(x^-5//2*(a+b*x^-1)^-3//2, x) == :(-2*b^-3//2*arctanh(b^(1/2)*x^-1//2*(a+b*x^-1)^-1//2)+2*b^-1*x^-1//2*(a+b*x^-1)^-1//2)
@test integrate(x^-7//2*(a+b*x^-1)^-3//2, x) == :(-3*b^-2*x^-1//2*(a+b*x^-1)^(1/2)+2*b^-1*x^-3//2*(a+b*x^-1)^-1//2+3*a*b^-5//2*arctanh(b^(1/2)*x^-1//2*(a+b*x^-1)^-1//2))
@test integrate(x^-9//2*(a+b*x^-1)^-3//2, x) == :(2*b^-1*x^-5//2*(a+b*x^-1)^-1//2+-15//4*a^2*b^-7//2*arctanh(b^(1/2)*x^-1//2*(a+b*x^-1)^-1//2)+-5//2*b^-2*x^-3//2*(a+b*x^-1)^(1/2)+15//4*a*b^-3*x^-1//2*(a+b*x^-1)^(1/2))
@test integrate(x^-11//2*(a+b*x^-1)^-3//2, x) == :(2*b^-1*x^-7//2*(a+b*x^-1)^-1//2+-7//3*b^-2*x^-5//2*(a+b*x^-1)^(1/2)+35//8*a^3*b^-9//2*arctanh(b^(1/2)*x^-1//2*(a+b*x^-1)^-1//2)+-35//8*a^2*b^-4*x^-1//2*(a+b*x^-1)^(1/2)+35//12*a*b^-3*x^-3//2*(a+b*x^-1)^(1/2))
@test integrate(x^5//2*(a+b*x^-1)^-5//2, x) == :(2//7*a^-1*x^7//2*(a+b*x^-1)^-3//2+-512//21*a^-6*b^5*x^-3//2*(a+b*x^-1)^-3//2+-256//7*a^-5*b^4*x^-1//2*(a+b*x^-1)^-3//2+-64//7*a^-4*b^3*x^(1/2)*(a+b*x^-1)^-3//2+-4//7*b*a^-2*x^5//2*(a+b*x^-1)^-3//2+32//21*a^-3*b^2*x^3//2*(a+b*x^-1)^-3//2)
@test integrate(x^3//2*(a+b*x^-1)^-5//2, x) == :(2//5*a^-1*x^5//2*(a+b*x^-1)^-3//2+-16//15*b*a^-2*x^3//2*(a+b*x^-1)^-3//2+32//5*a^-3*b^2*x^(1/2)*(a+b*x^-1)^-3//2+128//5*a^-4*b^3*x^-1//2*(a+b*x^-1)^-3//2+256//15*a^-5*b^4*x^-3//2*(a+b*x^-1)^-3//2)
@test integrate(x^(1/2)*(a+b*x^-1)^-5//2, x) == :(2//3*a^-1*x^3//2*(a+b*x^-1)^-3//2+-16*a^-3*b^2*x^-1//2*(a+b*x^-1)^-3//2+-4*b*a^-2*x^(1/2)*(a+b*x^-1)^-3//2+-32//3*a^-4*b^3*x^-3//2*(a+b*x^-1)^-3//2)
@test integrate(x^-1//2*(a+b*x^-1)^-5//2, x) == :(2*a^-1*x^(1/2)*(a+b*x^-1)^-3//2+8*b*a^-2*x^-1//2*(a+b*x^-1)^-3//2+16//3*a^-3*b^2*x^-3//2*(a+b*x^-1)^-3//2)
@test integrate(x^-3//2*(a+b*x^-1)^-5//2, x) == :(-2*a^-1*x^-1//2*(a+b*x^-1)^-3//2+-4//3*b*a^-2*x^-3//2*(a+b*x^-1)^-3//2)
@test integrate(x^-5//2*(a+b*x^-1)^-5//2, x) == :(-2//3*a^-1*x^-3//2*(a+b*x^-1)^-3//2)
@test integrate(x^-7//2*(a+b*x^-1)^-5//2, x) == :(-2*b^-5//2*arctanh(b^(1/2)*x^-1//2*(a+b*x^-1)^-1//2)+2*b^-2*x^-1//2*(a+b*x^-1)^-1//2+2//3*b^-1*x^-3//2*(a+b*x^-1)^-3//2)
@test integrate(x^-9//2*(a+b*x^-1)^-5//2, x) == :(-5*b^-3*x^-1//2*(a+b*x^-1)^(1/2)+5*a*b^-7//2*arctanh(b^(1/2)*x^-1//2*(a+b*x^-1)^-1//2)+2//3*b^-1*x^-5//2*(a+b*x^-1)^-3//2+10//3*b^-2*x^-3//2*(a+b*x^-1)^-1//2)
@test integrate(x^-11//2*(a+b*x^-1)^-5//2, x) == :(-35//4*a^2*b^-9//2*arctanh(b^(1/2)*x^-1//2*(a+b*x^-1)^-1//2)+-35//6*b^-3*x^-3//2*(a+b*x^-1)^(1/2)+2//3*b^-1*x^-7//2*(a+b*x^-1)^-3//2+14//3*b^-2*x^-5//2*(a+b*x^-1)^-1//2+35//4*a*b^-4*x^-1//2*(a+b*x^-1)^(1/2))
@test integrate(x^6*(a+b*x^-2), x) == :(1//5*b*x^5+1//7*a*x^7)
@test integrate(x^5*(a+b*x^-2), x) == :(1//4*b*x^4+1//6*a*x^6)
@test integrate(x^4*(a+b*x^-2), x) == :(1//3*b*x^3+1//5*a*x^5)
@test integrate(x^3*(a+b*x^-2), x) == :((1/2)*b*x^2+1//4*a*x^4)
@test integrate(x^2*(a+b*x^-2), x) == :(b*x+1//3*a*x^3)
@test integrate(x*(a+b*x^-2), x) == :(b*log(x)+(1/2)*a*x^2)
@test integrate(a+b*x^-2, x) == :(a*x+-1*b*x^-1)
@test integrate(x^-1*(a+b*x^-2), x) == :(a*log(x)+-1//2*b*x^-2)
@test integrate(x^-2*(a+b*x^-2), x) == :(-1*a*x^-1+-1//3*b*x^-3)
@test integrate(x^-3*(a+b*x^-2), x) == :(-1//2*a*x^-2+-1//4*b*x^-4)
@test integrate(x^-4*(a+b*x^-2), x) == :(-1//3*a*x^-3+-1//5*b*x^-5)
@test integrate(x^-5*(a+b*x^-2), x) == :(-1//4*a*x^-4+-1//6*b*x^-6)
@test integrate(x^-6*(a+b*x^-2), x) == :(-1//5*a*x^-5+-1//7*b*x^-7)
@test integrate(x^6*(a+b*x^-2)^2, x) == :(1//3*b^2*x^3+1//7*a^2*x^7+2//5*a*b*x^5)
@test integrate(x^5*(a+b*x^-2)^2, x) == :(1//6*a^-1*(b+a*x^2)^3)
@test integrate(x^4*(a+b*x^-2)^2, x) == :(x*b^2+1//5*a^2*x^5+2//3*a*b*x^3)
@test integrate(x^3*(a+b*x^-2)^2, x) == :(b^2*log(x)+1//4*a^2*x^4+a*b*x^2)
@test integrate(x^2*(a+b*x^-2)^2, x) == :(-1*b^2*x^-1+1//3*a^2*x^3+2*a*b*x)
@test integrate(x*(a+b*x^-2)^2, x) == :((1/2)*a^2*x^2+-1//2*b^2*x^-2+2*a*b*log(x))
@test integrate((a+b*x^-2)^2, x) == :(x*a^2+-1//3*b^2*x^-3+-2*a*b*x^-1)
@test integrate(x^-1*(a+b*x^-2)^2, x) == :(a^2*log(x)+-1//4*b^2*x^-4+-1*a*b*x^-2)
@test integrate(x^-2*(a+b*x^-2)^2, x) == :(-1*a^2*x^-1+-1//5*b^2*x^-5+-2//3*a*b*x^-3)
@test integrate(x^-3*(a+b*x^-2)^2, x) == :(-1//6*b^-1*(a+b*x^-2)^3)
@test integrate(x^-4*(a+b*x^-2)^2, x) == :(-1//3*a^2*x^-3+-1//7*b^2*x^-7+-2//5*a*b*x^-5)
@test integrate(x^-5*(a+b*x^-2)^2, x) == :(-1//4*a^2*x^-4+-1//8*b^2*x^-8+-1//3*a*b*x^-6)
@test integrate(x^-6*(a+b*x^-2)^2, x) == :(-1//5*a^2*x^-5+-1//9*b^2*x^-9+-2//7*a*b*x^-7)
@test integrate(x^6*(a+b*x^-2)^3, x) == :(x*b^3+1//7*a^3*x^7+a*b^2*x^3+3//5*b*a^2*x^5)
@test integrate(x^5*(a+b*x^-2)^3, x) == :(b^3*log(x)+1//6*a^3*x^6+3//2*a*b^2*x^2+3//4*b*a^2*x^4)
@test integrate(x^4*(a+b*x^-2)^3, x) == :(-1*b^3*x^-1+1//5*a^3*x^5+b*a^2*x^3+3*a*x*b^2)
@test integrate(x^3*(a+b*x^-2)^3, x) == :(-1//2*b^3*x^-2+1//4*a^3*x^4+3*a*b^2*log(x)+3//2*b*a^2*x^2)
@test integrate(x^2*(a+b*x^-2)^3, x) == :(-1//3*b^3*x^-3+1//3*a^3*x^3+-3*a*b^2*x^-1+3*b*x*a^2)
@test integrate(x*(a+b*x^-2)^3, x) == :((1/2)*a^3*x^2+-1//4*b^3*x^-4+3*b*a^2*log(x)+-3//2*a*b^2*x^-2)
@test integrate((a+b*x^-2)^3, x) == :(x*a^3+-1//5*b^3*x^-5+-1*a*b^2*x^-3+-3*b*a^2*x^-1)
@test integrate(x^-1*(a+b*x^-2)^3, x) == :(a^3*log(x)+-1//6*b^3*x^-6+-3//2*b*a^2*x^-2+-3//4*a*b^2*x^-4)
@test integrate(x^-2*(a+b*x^-2)^3, x) == :(-1*a^3*x^-1+-1//7*b^3*x^-7+-1*b*a^2*x^-3+-3//5*a*b^2*x^-5)
@test integrate(x^-3*(a+b*x^-2)^3, x) == :(-1//8*b^-1*(a+b*x^-2)^4)
@test integrate(x^-4*(a+b*x^-2)^3, x) == :(-1//3*a^3*x^-3+-1//9*b^3*x^-9+-3//5*b*a^2*x^-5+-3//7*a*b^2*x^-7)
@test integrate(x^-5*(a+b*x^-2)^3, x) == :(-1//10*b^-1*x^-10*(b+a*x^2)^4+1//40*a*b^-2*x^-8*(b+a*x^2)^4)
@test integrate(x^-6*(a+b*x^-2)^3, x) == :(-1//5*a^3*x^-5+-1//11*b^3*x^-11+-3//7*b*a^2*x^-7+-1//3*a*b^2*x^-9)
@test integrate(x^6*(a+b*x^-2)^-1, x) == :(1//7*a^-1*x^7+a^-9//2*b^7//2*arctan(x*a^(1/2)*b^-1//2)+-1*x*a^-4*b^3+-1//5*b*a^-2*x^5+1//3*a^-3*b^2*x^3)
@test integrate(x^5*(a+b*x^-2)^-1, x) == :(1//6*a^-1*x^6+(1/2)*a^-3*b^2*x^2+-1//2*a^-4*b^3*log(b+a*x^2)+-1//4*b*a^-2*x^4)
@test integrate(x^4*(a+b*x^-2)^-1, x) == :(1//5*a^-1*x^5+x*a^-3*b^2+-1*a^-7//2*b^5//2*arctan(x*a^(1/2)*b^-1//2)+-1//3*b*a^-2*x^3)
@test integrate(x^3*(a+b*x^-2)^-1, x) == :(1//4*a^-1*x^4+(1/2)*a^-3*b^2*log(b+a*x^2)+-1//2*b*a^-2*x^2)
@test integrate(x^2*(a+b*x^-2)^-1, x) == :(1//3*a^-1*x^3+a^-5//2*b^3//2*arctan(x*a^(1/2)*b^-1//2)+-1*b*x*a^-2)
@test integrate(x*(a+b*x^-2)^-1, x) == :((1/2)*a^-1*x^2+-1//2*b*a^-2*log(b+a*x^2))
@test integrate((a+b*x^-2)^-1, x) == :(x*a^-1+-1*a^-3//2*b^(1/2)*arctan(x*a^(1/2)*b^-1//2))
@test integrate(x^-1*(a+b*x^-2)^-1, x) == :((1/2)*a^-1*log(b+a*x^2))
@test integrate(x^-2*(a+b*x^-2)^-1, x) == :(a^-1//2*b^-1//2*arctan(x*a^(1/2)*b^-1//2))
@test integrate(x^-3*(a+b*x^-2)^-1, x) == :(-1//2*b^-1*log(a+b*x^-2))
@test integrate(x^-4*(a+b*x^-2)^-1, x) == :(-1*b^-1*x^-1+-1*a^(1/2)*b^-3//2*arctan(x*a^(1/2)*b^-1//2))
@test integrate(x^-5*(a+b*x^-2)^-1, x) == :(-1//2*b^-1*x^-2+(1/2)*a*b^-2*log(b+a*x^2)+-1*a*b^-2*log(x))
@test integrate(x^-6*(a+b*x^-2)^-1, x) == :(-1//3*b^-1*x^-3+a*b^-2*x^-1+a^3//2*b^-5//2*arctan(x*a^(1/2)*b^-1//2))
@test integrate(x^-7*(a+b*x^-2)^-1, x) == :(-1//4*b^-1*x^-4+a^2*b^-3*log(x)+(1/2)*a*b^-2*x^-2+-1//2*a^2*b^-3*log(b+a*x^2))
@test integrate(x^-8*(a+b*x^-2)^-1, x) == :(-1//5*b^-1*x^-5+-1*a^2*b^-3*x^-1+-1*a^5//2*b^-7//2*arctan(x*a^(1/2)*b^-1//2)+1//3*a*b^-2*x^-3)
@test integrate(x^6*(a+b*x^-2)^-2, x) == :(9//14*a^-2*x^7+-9//2*x*a^-5*b^3+-9//10*b*a^-3*x^5+-1//2*a^-1*x^9*(b+a*x^2)^-1+3//2*a^-4*b^2*x^3+9//2*a^-11//2*b^7//2*arctan(x*a^(1/2)*b^-1//2))
@test integrate(x^5*(a+b*x^-2)^-2, x) == :(1//6*a^-2*x^6+-2*a^-5*b^3*log(b+a*x^2)+-1//2*b*a^-3*x^4+-1//2*a^-5*b^4*(b+a*x^2)^-1+3//2*a^-4*b^2*x^2)
@test integrate(x^4*(a+b*x^-2)^-2, x) == :(7//10*a^-2*x^5+-7//2*a^-9//2*b^5//2*arctan(x*a^(1/2)*b^-1//2)+-7//6*b*a^-3*x^3+-1//2*a^-1*x^7*(b+a*x^2)^-1+7//2*x*a^-4*b^2)
@test integrate(x^3*(a+b*x^-2)^-2, x) == :(1//4*a^-2*x^4+(1/2)*a^-4*b^3*(b+a*x^2)^-1+-1*b*a^-3*x^2+3//2*a^-4*b^2*log(b+a*x^2))
@test integrate(x^2*(a+b*x^-2)^-2, x) == :(5//6*a^-2*x^3+-5//2*b*x*a^-3+-1//2*a^-1*x^5*(b+a*x^2)^-1+5//2*a^-7//2*b^3//2*arctan(x*a^(1/2)*b^-1//2))
@test integrate(x*(a+b*x^-2)^-2, x) == :((1/2)*a^-2*x^2+-1*b*a^-3*log(b+a*x^2)+-1//2*a^-3*b^2*(b+a*x^2)^-1)
@test integrate((a+b*x^-2)^-2, x) == :(3//2*x*a^-2+-3//2*a^-5//2*b^(1/2)*arctan(x*a^(1/2)*b^-1//2)+-1//2*a^-1*x^3*(b+a*x^2)^-1)
@test integrate(x^-1*(a+b*x^-2)^-2, x) == :((1/2)*a^-2*log(b+a*x^2)+(1/2)*b*a^-2*(b+a*x^2)^-1)
@test integrate(x^-2*(a+b*x^-2)^-2, x) == :((1/2)*a^-3//2*b^-1//2*arctan(x*a^(1/2)*b^-1//2)+-1//2*x*a^-1*(b+a*x^2)^-1)
@test integrate(x^-3*(a+b*x^-2)^-2, x) == :((1/2)*b^-1*(a+b*x^-2)^-1)
@test integrate(x^-4*(a+b*x^-2)^-2, x) == :((1/2)*x*b^-1*(b+a*x^2)^-1+(1/2)*a^-1//2*b^-3//2*arctan(x*a^(1/2)*b^-1//2))
@test integrate(x^-5*(a+b*x^-2)^-2, x) == :(b^-2*log(x)+(1/2)*b^-1*(b+a*x^2)^-1+-1//2*b^-2*log(b+a*x^2))
@test integrate(x^-6*(a+b*x^-2)^-2, x) == :(-3//2*b^-2*x^-1+(1/2)*b^-1*x^-1*(b+a*x^2)^-1+-3//2*a^(1/2)*b^-5//2*arctan(x*a^(1/2)*b^-1//2))
@test integrate(x^-7*(a+b*x^-2)^-2, x) == :(-1//2*b^-2*x^-2+a*b^-3*log(b+a*x^2)+-2*a*b^-3*log(x)+-1//2*a*b^-2*(b+a*x^2)^-1)
@test integrate(x^-8*(a+b*x^-2)^-2, x) == :(-5//6*b^-2*x^-3+(1/2)*b^-1*x^-3*(b+a*x^2)^-1+5//2*a*b^-3*x^-1+5//2*a^3//2*b^-7//2*arctan(x*a^(1/2)*b^-1//2))
@test integrate(x^-9*(a+b*x^-2)^-2, x) == :(-1//4*b^-2*x^-4+a*b^-3*x^-2+(1/2)*a^2*b^-3*(b+a*x^2)^-1+3*a^2*b^-4*log(x)+-3//2*a^2*b^-4*log(b+a*x^2))
@test integrate(x^5*(a+b*x^-2)^-3, x) == :(1//6*a^-3*x^6+-5*a^-6*b^3*log(b+a*x^2)+3*a^-5*b^2*x^2+-5//2*a^-6*b^4*(b+a*x^2)^-1+-3//4*b*a^-4*x^4+1//4*a^-6*b^5*(b+a*x^2)^-2)
@test integrate(x^4*(a+b*x^-2)^-3, x) == :(63//40*a^-3*x^5+-63//8*a^-11//2*b^5//2*arctan(x*a^(1/2)*b^-1//2)+-21//8*b*a^-4*x^3+-9//8*a^-2*x^7*(b+a*x^2)^-1+-1//4*a^-1*x^9*(b+a*x^2)^-2+63//8*x*a^-5*b^2)
@test integrate(x^3*(a+b*x^-2)^-3, x) == :(1//4*a^-3*x^4+2*a^-5*b^3*(b+a*x^2)^-1+3*a^-5*b^2*log(b+a*x^2)+-3//2*b*a^-4*x^2+-1//4*a^-5*b^4*(b+a*x^2)^-2)
@test integrate(x^2*(a+b*x^-2)^-3, x) == :(35//24*a^-3*x^3+-35//8*b*x*a^-4+-7//8*a^-2*x^5*(b+a*x^2)^-1+-1//4*a^-1*x^7*(b+a*x^2)^-2+35//8*a^-9//2*b^3//2*arctan(x*a^(1/2)*b^-1//2))
@test integrate(x*(a+b*x^-2)^-3, x) == :((1/2)*a^-3*x^2+-3//2*b*a^-4*log(b+a*x^2)+-3//2*a^-4*b^2*(b+a*x^2)^-1+1//4*a^-4*b^3*(b+a*x^2)^-2)
@test integrate((a+b*x^-2)^-3, x) == :(15//8*x*a^-3+-15//8*a^-7//2*b^(1/2)*arctan(x*a^(1/2)*b^-1//2)+-5//8*a^-2*x^3*(b+a*x^2)^-1+-1//4*a^-1*x^5*(b+a*x^2)^-2)
@test integrate(x^-1*(a+b*x^-2)^-3, x) == :((1/2)*a^-3*log(b+a*x^2)+b*a^-3*(b+a*x^2)^-1+-1//4*a^-3*b^2*(b+a*x^2)^-2)
@test integrate(x^-2*(a+b*x^-2)^-3, x) == :(-3//8*x*a^-2*(b+a*x^2)^-1+-1//4*a^-1*x^3*(b+a*x^2)^-2+3//8*a^-5//2*b^-1//2*arctan(x*a^(1/2)*b^-1//2))
@test integrate(x^-3*(a+b*x^-2)^-3, x) == :(1//4*b^-1*(a+b*x^-2)^-2)
@test integrate(x^-4*(a+b*x^-2)^-3, x) == :(-1//4*x*a^-1*(b+a*x^2)^-2+1//8*a^-3//2*b^-3//2*arctan(x*a^(1/2)*b^-1//2)+1//8*x*a^-1*b^-1*(b+a*x^2)^-1)
@test integrate(x^-5*(a+b*x^-2)^-3, x) == :(-1//4*a^-1*(b+a*x^2)^-2)
@test integrate(x^-6*(a+b*x^-2)^-3, x) == :(1//4*x*b^-1*(b+a*x^2)^-2+3//8*x*b^-2*(b+a*x^2)^-1+3//8*a^-1//2*b^-5//2*arctan(x*a^(1/2)*b^-1//2))
@test integrate(x^-7*(a+b*x^-2)^-3, x) == :(b^-3*log(x)+(1/2)*b^-2*(b+a*x^2)^-1+-1//2*b^-3*log(b+a*x^2)+1//4*b^-1*(b+a*x^2)^-2)
@test integrate(x^-8*(a+b*x^-2)^-3, x) == :(-15//8*b^-3*x^-1+-15//8*a^(1/2)*b^-7//2*arctan(x*a^(1/2)*b^-1//2)+1//4*b^-1*x^-1*(b+a*x^2)^-2+5//8*b^-2*x^-1*(b+a*x^2)^-1)
@test integrate(x^-9*(a+b*x^-2)^-3, x) == :(-1//2*b^-3*x^-2+-1*a*b^-3*(b+a*x^2)^-1+-3*a*b^-4*log(x)+-1//4*a*b^-2*(b+a*x^2)^-2+3//2*a*b^-4*log(b+a*x^2))
@test integrate(x^-10*(a+b*x^-2)^-3, x) == :(-35//24*b^-3*x^-3+1//4*b^-1*x^-3*(b+a*x^2)^-2+7//8*b^-2*x^-3*(b+a*x^2)^-1+35//8*a*b^-4*x^-1+35//8*a^3//2*b^-9//2*arctan(x*a^(1/2)*b^-1//2))
@test integrate(x^-11*(a+b*x^-2)^-3, x) == :(-1//4*b^-3*x^-4+-3*a^2*b^-5*log(b+a*x^2)+6*a^2*b^-5*log(x)+1//4*a^2*b^-3*(b+a*x^2)^-2+3//2*a*b^-4*x^-2+3//2*a^2*b^-4*(b+a*x^2)^-1)
@test integrate(x^3*(a+b*x^-2)^(1/2), x) == :(1//4*x^4*(a+b*x^-2)^(1/2)+-1//8*a^-3//2*b^2*arctanh(a^-1//2*(a+b*x^-2)^(1/2))+1//8*b*a^-1*x^2*(a+b*x^-2)^(1/2))
@test integrate(x^2*(a+b*x^-2)^(1/2), x) == :(1//3*a^-1*x^3*(a+b*x^-2)^3//2)
@test integrate(x*(a+b*x^-2)^(1/2), x) == :((1/2)*x^2*(a+b*x^-2)^(1/2)+(1/2)*b*a^-1//2*arctanh(a^-1//2*(a+b*x^-2)^(1/2)))
@test integrate((a+b*x^-2)^(1/2), x) == :(x*(a+b*x^-2)^(1/2)+-1*b^(1/2)*arctanh(b^(1/2)*x^-1*(a+b*x^-2)^-1//2))
@test integrate(x^-1*(a+b*x^-2)^(1/2), x) == :(-1*(a+b*x^-2)^(1/2)+a^(1/2)*arctanh(a^-1//2*(a+b*x^-2)^(1/2)))
@test integrate(x^-2*(a+b*x^-2)^(1/2), x) == :(-1//2*x^-1*(a+b*x^-2)^(1/2)+-1//2*a*b^-1//2*arctanh(b^(1/2)*x^-1*(a+b*x^-2)^-1//2))
@test integrate(x^-3*(a+b*x^-2)^(1/2), x) == :(-1//3*b^-1*(a+b*x^-2)^3//2)
@test integrate(x^-4*(a+b*x^-2)^(1/2), x) == :(-1//4*x^-3*(a+b*x^-2)^(1/2)+1//8*a^2*b^-3//2*arctanh(b^(1/2)*x^-1*(a+b*x^-2)^-1//2)+-1//8*a*b^-1*x^-1*(a+b*x^-2)^(1/2))
@test integrate(x^3*(a+b*x^-2)^3//2, x) == :(1//4*x^4*(a+b*x^-2)^3//2+3//8*b*x^2*(a+b*x^-2)^(1/2)+3//8*a^-1//2*b^2*arctanh(a^-1//2*(a+b*x^-2)^(1/2)))
@test integrate(x^2*(a+b*x^-2)^3//2, x) == :(-1*b^3//2*arctanh(b^(1/2)*x^-1*(a+b*x^-2)^-1//2)+1//3*x^3*(a+b*x^-2)^3//2+b*x*(a+b*x^-2)^(1/2))
@test integrate(x*(a+b*x^-2)^3//2, x) == :((1/2)*x^2*(a+b*x^-2)^3//2+-3//2*b*(a+b*x^-2)^(1/2)+3//2*b*a^(1/2)*arctanh(a^-1//2*(a+b*x^-2)^(1/2)))
@test integrate((a+b*x^-2)^3//2, x) == :(x*(a+b*x^-2)^3//2+-3//2*a*b^(1/2)*arctanh(b^(1/2)*x^-1*(a+b*x^-2)^-1//2)+-3//2*b*x^-1*(a+b*x^-2)^(1/2))
@test integrate(x^-1*(a+b*x^-2)^3//2, x) == :(-1//3*(a+b*x^-2)^3//2+a^3//2*arctanh(a^-1//2*(a+b*x^-2)^(1/2))+-1*a*(a+b*x^-2)^(1/2))
@test integrate(x^-2*(a+b*x^-2)^3//2, x) == :(-1//4*x^-1*(a+b*x^-2)^3//2+-3//8*a*x^-1*(a+b*x^-2)^(1/2)+-3//8*a^2*b^-1//2*arctanh(b^(1/2)*x^-1*(a+b*x^-2)^-1//2))
@test integrate(x^-3*(a+b*x^-2)^3//2, x) == :(-1//5*b^-1*(a+b*x^-2)^5//2)
@test integrate(x^-4*(a+b*x^-2)^3//2, x) == :(-1//6*x^-3*(a+b*x^-2)^3//2+-1//8*a*x^-3*(a+b*x^-2)^(1/2)+1//16*a^3*b^-3//2*arctanh(b^(1/2)*x^-1*(a+b*x^-2)^-1//2)+-1//16*a^2*b^-1*x^-1*(a+b*x^-2)^(1/2))
@test integrate(x^3*(a+b*x^-2)^5//2, x) == :(-15//8*b^2*(a+b*x^-2)^(1/2)+1//4*x^4*(a+b*x^-2)^5//2+5//8*b*x^2*(a+b*x^-2)^3//2+15//8*a^(1/2)*b^2*arctanh(a^-1//2*(a+b*x^-2)^(1/2)))
@test integrate(x^2*(a+b*x^-2)^5//2, x) == :(1//3*x^3*(a+b*x^-2)^5//2+-5//2*a*b^3//2*arctanh(b^(1/2)*x^-1*(a+b*x^-2)^-1//2)+-5//2*b^2*x^-1*(a+b*x^-2)^(1/2)+5//3*b*x*(a+b*x^-2)^3//2)
@test integrate(x*(a+b*x^-2)^5//2, x) == :((1/2)*x^2*(a+b*x^-2)^5//2+-5//6*b*(a+b*x^-2)^3//2+-5//2*a*b*(a+b*x^-2)^(1/2)+5//2*b*a^3//2*arctanh(a^-1//2*(a+b*x^-2)^(1/2)))
@test integrate((a+b*x^-2)^5//2, x) == :(x*(a+b*x^-2)^5//2+-15//8*a^2*b^(1/2)*arctanh(b^(1/2)*x^-1*(a+b*x^-2)^-1//2)+-5//4*b*x^-1*(a+b*x^-2)^3//2+-15//8*a*b*x^-1*(a+b*x^-2)^(1/2))
@test integrate(x^-1*(a+b*x^-2)^5//2, x) == :(-1//5*(a+b*x^-2)^5//2+a^5//2*arctanh(a^-1//2*(a+b*x^-2)^(1/2))+-1*a^2*(a+b*x^-2)^(1/2)+-1//3*a*(a+b*x^-2)^3//2)
@test integrate(x^-2*(a+b*x^-2)^5//2, x) == :(-1//6*x^-1*(a+b*x^-2)^5//2+-5//16*a^2*x^-1*(a+b*x^-2)^(1/2)+-5//16*a^3*b^-1//2*arctanh(b^(1/2)*x^-1*(a+b*x^-2)^-1//2)+-5//24*a*x^-1*(a+b*x^-2)^3//2)
@test integrate(x^-3*(a+b*x^-2)^5//2, x) == :(-1//7*b^-1*(a+b*x^-2)^7//2)
@test integrate(x^-4*(a+b*x^-2)^5//2, x) == :(-1//8*x^-3*(a+b*x^-2)^5//2+-5//48*a*x^-3*(a+b*x^-2)^3//2+-5//64*a^2*x^-3*(a+b*x^-2)^(1/2)+5//128*a^4*b^-3//2*arctanh(b^(1/2)*x^-1*(a+b*x^-2)^-1//2)+-5//128*a^3*b^-1*x^-1*(a+b*x^-2)^(1/2))
@test integrate(x^3*(a+b*x^-2)^-1//2, x) == :(1//4*a^-1*x^4*(a+b*x^-2)^(1/2)+3//8*a^-5//2*b^2*arctanh(a^-1//2*(a+b*x^-2)^(1/2))+-3//8*b*a^-2*x^2*(a+b*x^-2)^(1/2))
@test integrate(x*(a+b*x^-2)^-1//2, x) == :((1/2)*a^-1*x^2*(a+b*x^-2)^(1/2)+-1//2*b*a^-3//2*arctanh(a^-1//2*(a+b*x^-2)^(1/2)))
@test integrate(x^-1*(a+b*x^-2)^-1//2, x) == :(a^-1//2*arctanh(a^-1//2*(a+b*x^-2)^(1/2)))
@test integrate(x^-3*(a+b*x^-2)^-1//2, x) == :(-1*b^-1*(a+b*x^-2)^(1/2))
@test integrate(x^-5*(a+b*x^-2)^-1//2, x) == :(-1//3*b^-2*(a+b*x^-2)^3//2+a*b^-2*(a+b*x^-2)^(1/2))
@test integrate(x^-7*(a+b*x^-2)^-1//2, x) == :(-1//5*b^-3*(a+b*x^-2)^5//2+-1*a^2*b^-3*(a+b*x^-2)^(1/2)+2//3*a*b^-3*(a+b*x^-2)^3//2)
@test integrate(x^-9*(a+b*x^-2)^-1//2, x) == :(-1//7*b^-4*(a+b*x^-2)^7//2+a^3*b^-4*(a+b*x^-2)^(1/2)+-1*a^2*b^-4*(a+b*x^-2)^3//2+3//5*a*b^-4*(a+b*x^-2)^5//2)
@test integrate(x^4*(a+b*x^-2)^-1//2, x) == :(1//5*a^-1*x^5*(a+b*x^-2)^(1/2)+-4//15*b*a^-2*x^3*(a+b*x^-2)^(1/2)+8//15*x*a^-3*b^2*(a+b*x^-2)^(1/2))
@test integrate(x^2*(a+b*x^-2)^-1//2, x) == :(1//3*a^-1*x^3*(a+b*x^-2)^(1/2)+-2//3*b*x*a^-2*(a+b*x^-2)^(1/2))
@test integrate((a+b*x^-2)^-1//2, x) == :(x*a^-1*(a+b*x^-2)^(1/2))
@test integrate(x^-2*(a+b*x^-2)^-1//2, x) == :(-1*b^-1//2*arctanh(b^(1/2)*x^-1*(a+b*x^-2)^-1//2))
@test integrate(x^-4*(a+b*x^-2)^-1//2, x) == :((1/2)*a*b^-3//2*arctanh(b^(1/2)*x^-1*(a+b*x^-2)^-1//2)+-1//2*b^-1*x^-1*(a+b*x^-2)^(1/2))
@test integrate(x^-1*(-1a+b*x^-2)^-1//2, x) == :(-1*a^-1//2*arctan(a^-1//2*(-1a+b*x^-2)^(1/2)))
@test integrate(x^-2*(2+b*x^-2)^-1//2, x) == :(-1*b^-1//2*arccsch(x*2^(1/2)*b^-1//2))
@test integrate(x^-2*(2+-1*b*x^-2)^-1//2, x) == :(-1*b^-1//2*arccsc(x*2^(1/2)*b^-1//2))
@test integrate(x^3*(a+b*x^-2)^-3//2, x) == :(-15//8*a^-3*b^2*(a+b*x^-2)^-1//2+1//4*a^-1*x^4*(a+b*x^-2)^-1//2+15//8*a^-7//2*b^2*arctanh(a^-1//2*(a+b*x^-2)^(1/2))+-5//8*b*a^-2*x^2*(a+b*x^-2)^-1//2)
@test integrate(x*(a+b*x^-2)^-3//2, x) == :((1/2)*a^-1*x^2*(a+b*x^-2)^-1//2+-3//2*b*a^-5//2*arctanh(a^-1//2*(a+b*x^-2)^(1/2))+3//2*b*a^-2*(a+b*x^-2)^-1//2)
@test integrate(x^-1*(a+b*x^-2)^-3//2, x) == :(a^-3//2*arctanh(a^-1//2*(a+b*x^-2)^(1/2))+-1*a^-1*(a+b*x^-2)^-1//2)
@test integrate(x^-3*(a+b*x^-2)^-3//2, x) == :(b^-1*(a+b*x^-2)^-1//2)
@test integrate(x^-5*(a+b*x^-2)^-3//2, x) == :(-1*b^-2*(a+b*x^-2)^(1/2)+-1*a*b^-2*(a+b*x^-2)^-1//2)
@test integrate(x^-7*(a+b*x^-2)^-3//2, x) == :(-1//3*b^-3*(a+b*x^-2)^3//2+a^2*b^-3*(a+b*x^-2)^-1//2+2*a*b^-3*(a+b*x^-2)^(1/2))
@test integrate(x^-9*(a+b*x^-2)^-3//2, x) == :(-1//5*b^-4*(a+b*x^-2)^5//2+a*b^-4*(a+b*x^-2)^3//2+-1*a^3*b^-4*(a+b*x^-2)^-1//2+-3*a^2*b^-4*(a+b*x^-2)^(1/2))
@test integrate(x^4*(a+b*x^-2)^-3//2, x) == :(1//5*a^-1*x^5*(a+b*x^-2)^-1//2+-8//5*x*a^-3*b^2*(a+b*x^-2)^-1//2+-2//5*b*a^-2*x^3*(a+b*x^-2)^-1//2+16//5*x*a^-4*b^2*(a+b*x^-2)^(1/2))
@test integrate(x^2*(a+b*x^-2)^-3//2, x) == :(1//3*a^-1*x^3*(a+b*x^-2)^-1//2+-8//3*b*x*a^-3*(a+b*x^-2)^(1/2)+4//3*b*x*a^-2*(a+b*x^-2)^-1//2)
@test integrate((a+b*x^-2)^-3//2, x) == :(-1*x*a^-1*(a+b*x^-2)^-1//2+2*x*a^-2*(a+b*x^-2)^(1/2))
@test integrate(x^-2*(a+b*x^-2)^-3//2, x) == :(-1*a^-1*x^-1*(a+b*x^-2)^-1//2)
@test integrate(x^-4*(a+b*x^-2)^-3//2, x) == :(-1*b^-3//2*arctanh(b^(1/2)*x^-1*(a+b*x^-2)^-1//2)+b^-1*x^-1*(a+b*x^-2)^-1//2)
@test integrate(x^-6*(a+b*x^-2)^-3//2, x) == :(b^-1*x^-3*(a+b*x^-2)^-1//2+-3//2*b^-2*x^-1*(a+b*x^-2)^(1/2)+3//2*a*b^-5//2*arctanh(b^(1/2)*x^-1*(a+b*x^-2)^-1//2))
@test integrate(x^-8*(a+b*x^-2)^-3//2, x) == :(b^-1*x^-5*(a+b*x^-2)^-1//2+-15//8*a^2*b^-7//2*arctanh(b^(1/2)*x^-1*(a+b*x^-2)^-1//2)+-5//4*b^-2*x^-3*(a+b*x^-2)^(1/2)+15//8*a*b^-3*x^-1*(a+b*x^-2)^(1/2))
@test integrate(x^3*(a+b*x^-2)^-5//2, x) == :(-35//8*a^-4*b^2*(a+b*x^-2)^-1//2+-35//24*a^-3*b^2*(a+b*x^-2)^-3//2+1//4*a^-1*x^4*(a+b*x^-2)^-3//2+35//8*a^-9//2*b^2*arctanh(a^-1//2*(a+b*x^-2)^(1/2))+-7//8*b*a^-2*x^2*(a+b*x^-2)^-3//2)
@test integrate(x*(a+b*x^-2)^-5//2, x) == :((1/2)*a^-1*x^2*(a+b*x^-2)^-3//2+-5//2*b*a^-7//2*arctanh(a^-1//2*(a+b*x^-2)^(1/2))+5//2*b*a^-3*(a+b*x^-2)^-1//2+5//6*b*a^-2*(a+b*x^-2)^-3//2)
@test integrate(x^-1*(a+b*x^-2)^-5//2, x) == :(a^-5//2*arctanh(a^-1//2*(a+b*x^-2)^(1/2))+-1*a^-2*(a+b*x^-2)^-1//2+-1//3*a^-1*(a+b*x^-2)^-3//2)
@test integrate(x^-3*(a+b*x^-2)^-5//2, x) == :(1//3*b^-1*(a+b*x^-2)^-3//2)
@test integrate(x^-5*(a+b*x^-2)^-5//2, x) == :(b^-2*(a+b*x^-2)^-1//2+-1//3*a*b^-2*(a+b*x^-2)^-3//2)
@test integrate(x^-7*(a+b*x^-2)^-5//2, x) == :(-1*b^-3*(a+b*x^-2)^(1/2)+-2*a*b^-3*(a+b*x^-2)^-1//2+1//3*a^2*b^-3*(a+b*x^-2)^-3//2)
@test integrate(x^-9*(a+b*x^-2)^-5//2, x) == :(-1//3*b^-4*(a+b*x^-2)^3//2+3*a*b^-4*(a+b*x^-2)^(1/2)+3*a^2*b^-4*(a+b*x^-2)^-1//2+-1//3*a^3*b^-4*(a+b*x^-2)^-3//2)
@test integrate(x^2*(a+b*x^-2)^-5//2, x) == :(1//3*a^-1*x^3*(a+b*x^-2)^-3//2+-16//3*b*x*a^-4*(a+b*x^-2)^(1/2)+2//3*b*x*a^-2*(a+b*x^-2)^-3//2+8//3*b*x*a^-3*(a+b*x^-2)^-1//2)
@test integrate((a+b*x^-2)^-5//2, x) == :(-4//3*x*a^-2*(a+b*x^-2)^-1//2+-1//3*x*a^-1*(a+b*x^-2)^-3//2+8//3*x*a^-3*(a+b*x^-2)^(1/2))
@test integrate(x^-2*(a+b*x^-2)^-5//2, x) == :(-1*a^-1*x^-1*(a+b*x^-2)^-3//2+-2//3*b*a^-2*x^-3*(a+b*x^-2)^-3//2)
@test integrate(x^-4*(a+b*x^-2)^-5//2, x) == :(-1//3*a^-1*x^-3*(a+b*x^-2)^-3//2)
@test integrate(x^-6*(a+b*x^-2)^-5//2, x) == :(-1*b^-5//2*arctanh(b^(1/2)*x^-1*(a+b*x^-2)^-1//2)+b^-2*x^-1*(a+b*x^-2)^-1//2+1//3*b^-1*x^-3*(a+b*x^-2)^-3//2)
@test integrate(x^-8*(a+b*x^-2)^-5//2, x) == :(-5//2*b^-3*x^-1*(a+b*x^-2)^(1/2)+1//3*b^-1*x^-5*(a+b*x^-2)^-3//2+5//2*a*b^-7//2*arctanh(b^(1/2)*x^-1*(a+b*x^-2)^-1//2)+5//3*b^-2*x^-3*(a+b*x^-2)^-1//2)
@test integrate(x^-3*(1+x^-2)^1//3, x) == :(-3//8*(1+x^-2)^4//3)
@test integrate(x^-3*(1+x^-2)^5//3, x) == :(-3//16*(1+x^-2)^8//3)
@test integrate(x^5*(a+b*x^-3)^-1, x) == :(1//6*a^-1*x^6+-1//3*b*a^-2*x^3+1//3*a^-3*b^2*log(b+a*x^3))
@test integrate(x^4*(a+b*x^-3)^-1, x) == :(1//5*a^-1*x^5+-1//2*b*a^-2*x^2+-1//3*a^-8//3*b^5//3*log(b^1//3+x*a^1//3)+1//6*a^-8//3*b^5//3*log(b^2//3+a^2//3*x^2+-1*x*a^1//3*b^1//3)+-1//3*3^(1/2)*a^-8//3*b^5//3*arctan(1//3*3^(1/2)*b^-1//3*(b^1//3+-2*x*a^1//3)))
@test integrate(x^3*(a+b*x^-3)^-1, x) == :(1//4*a^-1*x^4+-1*b*x*a^-2+-1//6*a^-7//3*b^4//3*log(b^2//3+a^2//3*x^2+-1*x*a^1//3*b^1//3)+1//3*a^-7//3*b^4//3*log(b^1//3+x*a^1//3)+-1//3*3^(1/2)*a^-7//3*b^4//3*arctan(1//3*3^(1/2)*b^-1//3*(b^1//3+-2*x*a^1//3)))
@test integrate(x^2*(a+b*x^-3)^-1, x) == :(1//3*a^-1*x^3+-1//3*b*a^-2*log(b+a*x^3))
@test integrate(x*(a+b*x^-3)^-1, x) == :((1/2)*a^-1*x^2+-1//6*a^-5//3*b^2//3*log(b^2//3+a^2//3*x^2+-1*x*a^1//3*b^1//3)+1//3*a^-5//3*b^2//3*log(b^1//3+x*a^1//3)+1//3*3^(1/2)*a^-5//3*b^2//3*arctan(1//3*3^(1/2)*b^-1//3*(b^1//3+-2*x*a^1//3)))
@test integrate((a+b*x^-3)^-1, x) == :(x*a^-1+-1//3*a^-4//3*b^1//3*log(b^1//3+x*a^1//3)+1//6*a^-4//3*b^1//3*log(b^2//3+a^2//3*x^2+-1*x*a^1//3*b^1//3)+1//3*3^(1/2)*a^-4//3*b^1//3*arctan(1//3*3^(1/2)*b^-1//3*(b^1//3+-2*x*a^1//3)))
@test integrate(x^-1*(a+b*x^-3)^-1, x) == :(1//3*a^-1*log(b+a*x^3))
@test integrate(x^-2*(a+b*x^-3)^-1, x) == :(-1//3*a^-2//3*b^-1//3*log(b^1//3+x*a^1//3)+1//6*a^-2//3*b^-1//3*log(b^2//3+a^2//3*x^2+-1*x*a^1//3*b^1//3)+-1//3*3^(1/2)*a^-2//3*b^-1//3*arctan(1//3*3^(1/2)*b^-1//3*(b^1//3+-2*x*a^1//3)))
@test integrate(x^-3*(a+b*x^-3)^-1, x) == :(-1//6*a^-1//3*b^-2//3*log(b^2//3+a^2//3*x^2+-1*x*a^1//3*b^1//3)+1//3*a^-1//3*b^-2//3*log(b^1//3+x*a^1//3)+-1//3*3^(1/2)*a^-1//3*b^-2//3*arctan(1//3*3^(1/2)*b^-1//3*(b^1//3+-2*x*a^1//3)))
@test integrate(x^-4*(a+b*x^-3)^-1, x) == :(-1//3*b^-1*log(a+b*x^-3))
@test integrate(x^-5*(a+b*x^-3)^-1, x) == :(-1*b^-1*x^-1+-1//6*a^1//3*b^-4//3*log(b^2//3+a^2//3*x^2+-1*x*a^1//3*b^1//3)+1//3*a^1//3*b^-4//3*log(b^1//3+x*a^1//3)+1//3*3^(1/2)*a^1//3*b^-4//3*arctan(1//3*3^(1/2)*b^-1//3*(b^1//3+-2*x*a^1//3)))
@test integrate(x^-6*(a+b*x^-3)^-1, x) == :(-1//2*b^-1*x^-2+-1//3*a^2//3*b^-5//3*log(b^1//3+x*a^1//3)+1//6*a^2//3*b^-5//3*log(b^2//3+a^2//3*x^2+-1*x*a^1//3*b^1//3)+1//3*3^(1/2)*a^2//3*b^-5//3*arctan(1//3*3^(1/2)*b^-1//3*(b^1//3+-2*x*a^1//3)))
@test integrate(x^-7*(a+b*x^-3)^-1, x) == :(-1//3*b^-1*x^-3+-1*a*b^-2*log(x)+1//3*a*b^-2*log(b+a*x^3))
@test integrate(x^5*(a+b*x^-3)^-2, x) == :(1//6*a^-2*x^6+a^-4*b^2*log(b+a*x^3)+-2//3*b*a^-3*x^3+1//3*a^-4*b^3*(b+a*x^3)^-1)
@test integrate(x^4*(a+b*x^-3)^-2, x) == :(8//15*a^-2*x^5+-8//9*a^-11//3*b^5//3*log(b^1//3+x*a^1//3)+-4//3*b*a^-3*x^2+-1//3*a^-1*x^8*(b+a*x^3)^-1+4//9*a^-11//3*b^5//3*log(b^2//3+a^2//3*x^2+-1*x*a^1//3*b^1//3)+-8//9*3^(1/2)*a^-11//3*b^5//3*arctan(1//3*3^(1/2)*b^-1//3*(b^1//3+-2*x*a^1//3)))
@test integrate(x^3*(a+b*x^-3)^-2, x) == :(7//12*a^-2*x^4+-7//3*b*x*a^-3+-7//18*a^-10//3*b^4//3*log(b^2//3+a^2//3*x^2+-1*x*a^1//3*b^1//3)+-1//3*a^-1*x^7*(b+a*x^3)^-1+7//9*a^-10//3*b^4//3*log(b^1//3+x*a^1//3)+-7//9*3^(1/2)*a^-10//3*b^4//3*arctan(1//3*3^(1/2)*b^-1//3*(b^1//3+-2*x*a^1//3)))
@test integrate(x^2*(a+b*x^-3)^-2, x) == :(1//3*a^-2*x^3+-2//3*b*a^-3*log(b+a*x^3)+-1//3*a^-3*b^2*(b+a*x^3)^-1)
@test integrate(x*(a+b*x^-3)^-2, x) == :(5//6*a^-2*x^2+-5//18*a^-8//3*b^2//3*log(b^2//3+a^2//3*x^2+-1*x*a^1//3*b^1//3)+-1//3*a^-1*x^5*(b+a*x^3)^-1+5//9*a^-8//3*b^2//3*log(b^1//3+x*a^1//3)+5//9*3^(1/2)*a^-8//3*b^2//3*arctan(1//3*3^(1/2)*b^-1//3*(b^1//3+-2*x*a^1//3)))
@test integrate((a+b*x^-3)^-2, x) == :(4//3*x*a^-2+-4//9*a^-7//3*b^1//3*log(b^1//3+x*a^1//3)+-1//3*a^-1*x^4*(b+a*x^3)^-1+2//9*a^-7//3*b^1//3*log(b^2//3+a^2//3*x^2+-1*x*a^1//3*b^1//3)+4//9*3^(1/2)*a^-7//3*b^1//3*arctan(1//3*3^(1/2)*b^-1//3*(b^1//3+-2*x*a^1//3)))
@test integrate(x^-1*(a+b*x^-3)^-2, x) == :(1//3*a^-2*log(b+a*x^3)+1//3*b*a^-2*(b+a*x^3)^-1)
@test integrate(x^-2*(a+b*x^-3)^-2, x) == :(-2//9*a^-5//3*b^-1//3*log(b^1//3+x*a^1//3)+-1//3*a^-1*x^2*(b+a*x^3)^-1+1//9*a^-5//3*b^-1//3*log(b^2//3+a^2//3*x^2+-1*x*a^1//3*b^1//3)+-2//9*3^(1/2)*a^-5//3*b^-1//3*arctan(1//3*3^(1/2)*b^-1//3*(b^1//3+-2*x*a^1//3)))
@test integrate(x^-3*(a+b*x^-3)^-2, x) == :(-1//3*x*a^-1*(b+a*x^3)^-1+-1//18*a^-4//3*b^-2//3*log(b^2//3+a^2//3*x^2+-1*x*a^1//3*b^1//3)+1//9*a^-4//3*b^-2//3*log(b^1//3+x*a^1//3)+-1//9*3^(1/2)*a^-4//3*b^-2//3*arctan(1//3*3^(1/2)*b^-1//3*(b^1//3+-2*x*a^1//3)))
@test integrate(x^-4*(a+b*x^-3)^-2, x) == :(1//3*b^-1*(a+b*x^-3)^-1)
@test integrate(x^-5*(a+b*x^-3)^-2, x) == :(-1//9*a^-2//3*b^-4//3*log(b^1//3+x*a^1//3)+1//3*b^-1*x^2*(b+a*x^3)^-1+1//18*a^-2//3*b^-4//3*log(b^2//3+a^2//3*x^2+-1*x*a^1//3*b^1//3)+-1//9*3^(1/2)*a^-2//3*b^-4//3*arctan(1//3*3^(1/2)*b^-1//3*(b^1//3+-2*x*a^1//3)))
@test integrate(x^-6*(a+b*x^-3)^-2, x) == :(-1//9*a^-1//3*b^-5//3*log(b^2//3+a^2//3*x^2+-1*x*a^1//3*b^1//3)+1//3*x*b^-1*(b+a*x^3)^-1+2//9*a^-1//3*b^-5//3*log(b^1//3+x*a^1//3)+-2//9*3^(1/2)*a^-1//3*b^-5//3*arctan(1//3*3^(1/2)*b^-1//3*(b^1//3+-2*x*a^1//3)))
@test integrate(x^-7*(a+b*x^-3)^-2, x) == :(b^-2*log(x)+-1//3*b^-2*log(b+a*x^3)+1//3*b^-1*(b+a*x^3)^-1)
@test integrate(x^5*(a+b*x^-3)^(1/2), x) == :(1//6*x^6*(a+b*x^-3)^(1/2)+-1//12*a^-3//2*b^2*arctanh(a^-1//2*(a+b*x^-3)^(1/2))+1//12*b*a^-1*x^3*(a+b*x^-3)^(1/2))
@test integrate(x^2*(a+b*x^-3)^(1/2), x) == :(1//3*x^3*(a+b*x^-3)^(1/2)+1//3*b*a^-1//2*arctanh(a^-1//2*(a+b*x^-3)^(1/2)))
@test integrate(x^-1*(a+b*x^-3)^(1/2), x) == :(-2//3*(a+b*x^-3)^(1/2)+2//3*a^(1/2)*arctanh(a^-1//2*(a+b*x^-3)^(1/2)))
@test integrate(x^-4*(a+b*x^-3)^(1/2), x) == :(-2//9*b^-1*(a+b*x^-3)^3//2)
@test integrate(x^-7*(a+b*x^-3)^(1/2), x) == :(-2//15*b^-2*(a+b*x^-3)^5//2+2//9*a*b^-2*(a+b*x^-3)^3//2)
@test integrate(x^-10*(a+b*x^-3)^(1/2), x) == :(-2//21*b^-3*(a+b*x^-3)^7//2+-2//9*a^2*b^-3*(a+b*x^-3)^3//2+4//15*a*b^-3*(a+b*x^-3)^5//2)
@test integrate(x^-13*(a+b*x^-3)^(1/2), x) == :(-2//27*b^-4*(a+b*x^-3)^9//2+-2//5*a^2*b^-4*(a+b*x^-3)^5//2+2//7*a*b^-4*(a+b*x^-3)^7//2+2//9*a^3*b^-4*(a+b*x^-3)^3//2)
@test integrate(x^7*(a+b*x^-3)^(1/2), x) == :(1//8*x^8*(a+b*x^-3)^(1/2)+-21//320*a^-2*b^2*x^2*(a+b*x^-3)^(1/2)+3//80*b*a^-1*x^5*(a+b*x^-3)^(1/2)+-7//320*3^3//4*a^-2*b^8//3*((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^2//3+b^2//3*x^-2+-1*a^1//3*b^1//3*x^-1))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^1//3+b^1//3*x^-1))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^-3)^-1//2*(a^1//3+b^1//3*x^-1)*Elliptic.F(arcsin((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-1*(a^1//3*(1+-1*3^(1/2))+b^1//3*x^-1)),-7+-4*3^(1/2)))
@test integrate(x^4*(a+b*x^-3)^(1/2), x) == :(1//5*x^5*(a+b*x^-3)^(1/2)+3//20*b*a^-1*x^2*(a+b*x^-3)^(1/2)+1//20*3^3//4*a^-1*b^5//3*((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^2//3+b^2//3*x^-2+-1*a^1//3*b^1//3*x^-1))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^1//3+b^1//3*x^-1))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^-3)^-1//2*(a^1//3+b^1//3*x^-1)*Elliptic.F(arcsin((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-1*(a^1//3*(1+-1*3^(1/2))+b^1//3*x^-1)),-7+-4*3^(1/2)))
@test integrate(x*(a+b*x^-3)^(1/2), x) == :((1/2)*x^2*(a+b*x^-3)^(1/2)+-1//2*3^3//4*b^2//3*((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^2//3+b^2//3*x^-2+-1*a^1//3*b^1//3*x^-1))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^1//3+b^1//3*x^-1))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^-3)^-1//2*(a^1//3+b^1//3*x^-1)*Elliptic.F(arcsin((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-1*(a^1//3*(1+-1*3^(1/2))+b^1//3*x^-1)),-7+-4*3^(1/2)))
@test integrate(x^-2*(a+b*x^-3)^(1/2), x) == :(-2//5*x^-1*(a+b*x^-3)^(1/2)+-2//5*a*3^3//4*b^-1//3*((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^2//3+b^2//3*x^-2+-1*a^1//3*b^1//3*x^-1))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^1//3+b^1//3*x^-1))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^-3)^-1//2*(a^1//3+b^1//3*x^-1)*Elliptic.F(arcsin((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-1*(a^1//3*(1+-1*3^(1/2))+b^1//3*x^-1)),-7+-4*3^(1/2)))
@test integrate(x^-5*(a+b*x^-3)^(1/2), x) == :(-2//11*x^-4*(a+b*x^-3)^(1/2)+-6//55*a*b^-1*x^-1*(a+b*x^-3)^(1/2)+4//55*3^3//4*a^2*b^-4//3*((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^2//3+b^2//3*x^-2+-1*a^1//3*b^1//3*x^-1))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^1//3+b^1//3*x^-1))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^-3)^-1//2*(a^1//3+b^1//3*x^-1)*Elliptic.F(arcsin((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-1*(a^1//3*(1+-1*3^(1/2))+b^1//3*x^-1)),-7+-4*3^(1/2)))
@test integrate(x^-8*(a+b*x^-3)^(1/2), x) == :(-2//17*x^-7*(a+b*x^-3)^(1/2)+-6//187*a*b^-1*x^-4*(a+b*x^-3)^(1/2)+48//935*a^2*b^-2*x^-1*(a+b*x^-3)^(1/2)+-32//935*3^3//4*a^3*b^-7//3*((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^2//3+b^2//3*x^-2+-1*a^1//3*b^1//3*x^-1))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^1//3+b^1//3*x^-1))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^-3)^-1//2*(a^1//3+b^1//3*x^-1)*Elliptic.F(arcsin((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-1*(a^1//3*(1+-1*3^(1/2))+b^1//3*x^-1)),-7+-4*3^(1/2)))
@test integrate(x^6*(a+b*x^-3)^(1/2), x) == :(1//7*x^7*(a+b*x^-3)^(1/2)+-15//112*x*a^-2*b^2*(a+b*x^-3)^(1/2)+3//56*b*a^-1*x^4*(a+b*x^-3)^(1/2)+15//112*a^-2*b^7//3*(a+b*x^-3)^(1/2)*(a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-1+-15//224*3^1//4*a^-5//3*b^7//3*((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^2//3+b^2//3*x^-2+-1*a^1//3*b^1//3*x^-1))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^1//3+b^1//3*x^-1))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^-3)^-1//2*(a^1//3+b^1//3*x^-1)*Elliptic.E(arcsin((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-1*(a^1//3*(1+-1*3^(1/2))+b^1//3*x^-1)),-7+-4*3^(1/2))+5//112*2^(1/2)*3^3//4*a^-5//3*b^7//3*((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^2//3+b^2//3*x^-2+-1*a^1//3*b^1//3*x^-1))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^1//3+b^1//3*x^-1))^-1//2*(a+b*x^-3)^-1//2*(a^1//3+b^1//3*x^-1)*Elliptic.F(arcsin((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-1*(a^1//3*(1+-1*3^(1/2))+b^1//3*x^-1)),-7+-4*3^(1/2)))
@test integrate(x^3*(a+b*x^-3)^(1/2), x) == :(1//4*x^4*(a+b*x^-3)^(1/2)+-3//8*a^-1*b^4//3*(a+b*x^-3)^(1/2)*(a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-1+3//8*b*x*a^-1*(a+b*x^-3)^(1/2)+-1//8*2^(1/2)*3^3//4*a^-2//3*b^4//3*((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^2//3+b^2//3*x^-2+-1*a^1//3*b^1//3*x^-1))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^1//3+b^1//3*x^-1))^-1//2*(a+b*x^-3)^-1//2*(a^1//3+b^1//3*x^-1)*Elliptic.F(arcsin((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-1*(a^1//3*(1+-1*3^(1/2))+b^1//3*x^-1)),-7+-4*3^(1/2))+3//16*3^1//4*a^-2//3*b^4//3*((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^2//3+b^2//3*x^-2+-1*a^1//3*b^1//3*x^-1))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^1//3+b^1//3*x^-1))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^-3)^-1//2*(a^1//3+b^1//3*x^-1)*Elliptic.E(arcsin((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-1*(a^1//3*(1+-1*3^(1/2))+b^1//3*x^-1)),-7+-4*3^(1/2)))
@test integrate((a+b*x^-3)^(1/2), x) == :(x*(a+b*x^-3)^(1/2)+-3*b^1//3*(a+b*x^-3)^(1/2)*(a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-1+-1*2^(1/2)*3^3//4*a^1//3*b^1//3*((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^2//3+b^2//3*x^-2+-1*a^1//3*b^1//3*x^-1))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^1//3+b^1//3*x^-1))^-1//2*(a+b*x^-3)^-1//2*(a^1//3+b^1//3*x^-1)*Elliptic.F(arcsin((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-1*(a^1//3*(1+-1*3^(1/2))+b^1//3*x^-1)),-7+-4*3^(1/2))+3//2*3^1//4*a^1//3*b^1//3*((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^2//3+b^2//3*x^-2+-1*a^1//3*b^1//3*x^-1))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^1//3+b^1//3*x^-1))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^-3)^-1//2*(a^1//3+b^1//3*x^-1)*Elliptic.E(arcsin((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-1*(a^1//3*(1+-1*3^(1/2))+b^1//3*x^-1)),-7+-4*3^(1/2)))
@test integrate(x^-3*(a+b*x^-3)^(1/2), x) == :(-2//7*x^-2*(a+b*x^-3)^(1/2)+-6//7*a*b^-2//3*(a+b*x^-3)^(1/2)*(a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-1+-2//7*2^(1/2)*3^3//4*a^4//3*b^-2//3*((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^2//3+b^2//3*x^-2+-1*a^1//3*b^1//3*x^-1))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^1//3+b^1//3*x^-1))^-1//2*(a+b*x^-3)^-1//2*(a^1//3+b^1//3*x^-1)*Elliptic.F(arcsin((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-1*(a^1//3*(1+-1*3^(1/2))+b^1//3*x^-1)),-7+-4*3^(1/2))+3//7*3^1//4*a^4//3*b^-2//3*((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^2//3+b^2//3*x^-2+-1*a^1//3*b^1//3*x^-1))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^1//3+b^1//3*x^-1))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^-3)^-1//2*(a^1//3+b^1//3*x^-1)*Elliptic.E(arcsin((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-1*(a^1//3*(1+-1*3^(1/2))+b^1//3*x^-1)),-7+-4*3^(1/2)))
@test integrate(x^-6*(a+b*x^-3)^(1/2), x) == :(-2//13*x^-5*(a+b*x^-3)^(1/2)+-6//91*a*b^-1*x^-2*(a+b*x^-3)^(1/2)+24//91*a^2*b^-5//3*(a+b*x^-3)^(1/2)*(a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-1+-12//91*3^1//4*a^7//3*b^-5//3*((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^2//3+b^2//3*x^-2+-1*a^1//3*b^1//3*x^-1))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^1//3+b^1//3*x^-1))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^-3)^-1//2*(a^1//3+b^1//3*x^-1)*Elliptic.E(arcsin((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-1*(a^1//3*(1+-1*3^(1/2))+b^1//3*x^-1)),-7+-4*3^(1/2))+8//91*2^(1/2)*3^3//4*a^7//3*b^-5//3*((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^2//3+b^2//3*x^-2+-1*a^1//3*b^1//3*x^-1))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^1//3+b^1//3*x^-1))^-1//2*(a+b*x^-3)^-1//2*(a^1//3+b^1//3*x^-1)*Elliptic.F(arcsin((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-1*(a^1//3*(1+-1*3^(1/2))+b^1//3*x^-1)),-7+-4*3^(1/2)))
@test integrate(x^-9*(a+b*x^-3)^(1/2), x) == :(-2//19*x^-8*(a+b*x^-3)^(1/2)+-240//1729*a^3*b^-8//3*(a+b*x^-3)^(1/2)*(a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-1+-6//247*a*b^-1*x^-5*(a+b*x^-3)^(1/2)+60//1729*a^2*b^-2*x^-2*(a+b*x^-3)^(1/2)+-80//1729*2^(1/2)*3^3//4*a^10//3*b^-8//3*((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^2//3+b^2//3*x^-2+-1*a^1//3*b^1//3*x^-1))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^1//3+b^1//3*x^-1))^-1//2*(a+b*x^-3)^-1//2*(a^1//3+b^1//3*x^-1)*Elliptic.F(arcsin((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-1*(a^1//3*(1+-1*3^(1/2))+b^1//3*x^-1)),-7+-4*3^(1/2))+120//1729*3^1//4*a^10//3*b^-8//3*((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^2//3+b^2//3*x^-2+-1*a^1//3*b^1//3*x^-1))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^1//3+b^1//3*x^-1))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^-3)^-1//2*(a^1//3+b^1//3*x^-1)*Elliptic.E(arcsin((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-1*(a^1//3*(1+-1*3^(1/2))+b^1//3*x^-1)),-7+-4*3^(1/2)))
@test integrate(x^5*(a+b*x^-3)^3//2, x) == :(1//6*x^6*(a+b*x^-3)^3//2+1//4*b*x^3*(a+b*x^-3)^(1/2)+1//4*a^-1//2*b^2*arctanh(a^-1//2*(a+b*x^-3)^(1/2)))
@test integrate(x^2*(a+b*x^-3)^3//2, x) == :(-1*b*(a+b*x^-3)^(1/2)+1//3*x^3*(a+b*x^-3)^3//2+b*a^(1/2)*arctanh(a^-1//2*(a+b*x^-3)^(1/2)))
@test integrate(x^-1*(a+b*x^-3)^3//2, x) == :(-2//9*(a+b*x^-3)^3//2+-2//3*a*(a+b*x^-3)^(1/2)+2//3*a^3//2*arctanh(a^-1//2*(a+b*x^-3)^(1/2)))
@test integrate(x^-4*(a+b*x^-3)^3//2, x) == :(-2//15*b^-1*(a+b*x^-3)^5//2)
@test integrate(x^-7*(a+b*x^-3)^3//2, x) == :(-2//21*b^-2*(a+b*x^-3)^7//2+2//15*a*b^-2*(a+b*x^-3)^5//2)
@test integrate(x^-10*(a+b*x^-3)^3//2, x) == :(-2//27*b^-3*(a+b*x^-3)^9//2+-2//15*a^2*b^-3*(a+b*x^-3)^5//2+4//21*a*b^-3*(a+b*x^-3)^7//2)
@test integrate(x^-13*(a+b*x^-3)^3//2, x) == :(-2//33*b^-4*(a+b*x^-3)^11//2+-2//7*a^2*b^-4*(a+b*x^-3)^7//2+2//9*a*b^-4*(a+b*x^-3)^9//2+2//15*a^3*b^-4*(a+b*x^-3)^5//2)
@test integrate(x^5*(a+b*x^-3)^-1//2, x) == :(1//4*a^-5//2*b^2*arctanh(a^-1//2*(a+b*x^-3)^(1/2))+1//6*a^-1*x^6*(a+b*x^-3)^(1/2)+-1//4*b*a^-2*x^3*(a+b*x^-3)^(1/2))
@test integrate(x^2*(a+b*x^-3)^-1//2, x) == :(-1//3*b*a^-3//2*arctanh(a^-1//2*(a+b*x^-3)^(1/2))+1//3*a^-1*x^3*(a+b*x^-3)^(1/2))
@test integrate(x^-1*(a+b*x^-3)^-1//2, x) == :(2//3*a^-1//2*arctanh(a^-1//2*(a+b*x^-3)^(1/2)))
@test integrate(x^-4*(a+b*x^-3)^-1//2, x) == :(-2//3*b^-1*(a+b*x^-3)^(1/2))
@test integrate(x^-7*(a+b*x^-3)^-1//2, x) == :(-2//9*b^-2*(a+b*x^-3)^3//2+2//3*a*b^-2*(a+b*x^-3)^(1/2))
@test integrate(x^-10*(a+b*x^-3)^-1//2, x) == :(-2//15*b^-3*(a+b*x^-3)^5//2+-2//3*a^2*b^-3*(a+b*x^-3)^(1/2)+4//9*a*b^-3*(a+b*x^-3)^3//2)
@test integrate(x^-13*(a+b*x^-3)^-1//2, x) == :(-2//21*b^-4*(a+b*x^-3)^7//2+-2//3*a^2*b^-4*(a+b*x^-3)^3//2+2//3*a^3*b^-4*(a+b*x^-3)^(1/2)+2//5*a*b^-4*(a+b*x^-3)^5//2)
@test integrate(x^7*(a+b*x^-3)^-1//2, x) == :(1//8*a^-1*x^8*(a+b*x^-3)^(1/2)+-13//80*b*a^-2*x^5*(a+b*x^-3)^(1/2)+91//320*a^-3*b^2*x^2*(a+b*x^-3)^(1/2)+91//960*3^3//4*a^-3*b^8//3*((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^2//3+b^2//3*x^-2+-1*a^1//3*b^1//3*x^-1))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^1//3+b^1//3*x^-1))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^-3)^-1//2*(a^1//3+b^1//3*x^-1)*Elliptic.F(arcsin((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-1*(a^1//3*(1+-1*3^(1/2))+b^1//3*x^-1)),-7+-4*3^(1/2)))
@test integrate(x^4*(a+b*x^-3)^-1//2, x) == :(1//5*a^-1*x^5*(a+b*x^-3)^(1/2)+-7//20*b*a^-2*x^2*(a+b*x^-3)^(1/2)+-7//60*3^3//4*a^-2*b^5//3*((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^2//3+b^2//3*x^-2+-1*a^1//3*b^1//3*x^-1))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^1//3+b^1//3*x^-1))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^-3)^-1//2*(a^1//3+b^1//3*x^-1)*Elliptic.F(arcsin((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-1*(a^1//3*(1+-1*3^(1/2))+b^1//3*x^-1)),-7+-4*3^(1/2)))
@test integrate(x*(a+b*x^-3)^-1//2, x) == :((1/2)*a^-1*x^2*(a+b*x^-3)^(1/2)+1//6*3^3//4*a^-1*b^2//3*((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^2//3+b^2//3*x^-2+-1*a^1//3*b^1//3*x^-1))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^1//3+b^1//3*x^-1))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^-3)^-1//2*(a^1//3+b^1//3*x^-1)*Elliptic.F(arcsin((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-1*(a^1//3*(1+-1*3^(1/2))+b^1//3*x^-1)),-7+-4*3^(1/2)))
@test integrate(x^-2*(a+b*x^-3)^-1//2, x) == :(-2//3*3^3//4*b^-1//3*((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^2//3+b^2//3*x^-2+-1*a^1//3*b^1//3*x^-1))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^1//3+b^1//3*x^-1))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^-3)^-1//2*(a^1//3+b^1//3*x^-1)*Elliptic.F(arcsin((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-1*(a^1//3*(1+-1*3^(1/2))+b^1//3*x^-1)),-7+-4*3^(1/2)))
@test integrate(x^-5*(a+b*x^-3)^-1//2, x) == :(-2//5*b^-1*x^-1*(a+b*x^-3)^(1/2)+4//15*a*3^3//4*b^-4//3*((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^2//3+b^2//3*x^-2+-1*a^1//3*b^1//3*x^-1))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^1//3+b^1//3*x^-1))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^-3)^-1//2*(a^1//3+b^1//3*x^-1)*Elliptic.F(arcsin((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-1*(a^1//3*(1+-1*3^(1/2))+b^1//3*x^-1)),-7+-4*3^(1/2)))
@test integrate(x^-8*(a+b*x^-3)^-1//2, x) == :(-2//11*b^-1*x^-4*(a+b*x^-3)^(1/2)+16//55*a*b^-2*x^-1*(a+b*x^-3)^(1/2)+-32//165*3^3//4*a^2*b^-7//3*((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^2//3+b^2//3*x^-2+-1*a^1//3*b^1//3*x^-1))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^1//3+b^1//3*x^-1))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^-3)^-1//2*(a^1//3+b^1//3*x^-1)*Elliptic.F(arcsin((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-1*(a^1//3*(1+-1*3^(1/2))+b^1//3*x^-1)),-7+-4*3^(1/2)))
@test integrate(x^6*(a+b*x^-3)^-1//2, x) == :(1//7*a^-1*x^7*(a+b*x^-3)^(1/2)+-55//112*a^-3*b^7//3*(a+b*x^-3)^(1/2)*(a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-1+-11//56*b*a^-2*x^4*(a+b*x^-3)^(1/2)+55//112*x*a^-3*b^2*(a+b*x^-3)^(1/2)+-55//336*2^(1/2)*3^3//4*a^-8//3*b^7//3*((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^2//3+b^2//3*x^-2+-1*a^1//3*b^1//3*x^-1))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^1//3+b^1//3*x^-1))^-1//2*(a+b*x^-3)^-1//2*(a^1//3+b^1//3*x^-1)*Elliptic.F(arcsin((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-1*(a^1//3*(1+-1*3^(1/2))+b^1//3*x^-1)),-7+-4*3^(1/2))+55//224*3^1//4*a^-8//3*b^7//3*((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^2//3+b^2//3*x^-2+-1*a^1//3*b^1//3*x^-1))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^1//3+b^1//3*x^-1))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^-3)^-1//2*(a^1//3+b^1//3*x^-1)*Elliptic.E(arcsin((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-1*(a^1//3*(1+-1*3^(1/2))+b^1//3*x^-1)),-7+-4*3^(1/2)))
@test integrate(x^3*(a+b*x^-3)^-1//2, x) == :(1//4*a^-1*x^4*(a+b*x^-3)^(1/2)+-5//8*b*x*a^-2*(a+b*x^-3)^(1/2)+5//8*a^-2*b^4//3*(a+b*x^-3)^(1/2)*(a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-1+-5//16*3^1//4*a^-5//3*b^4//3*((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^2//3+b^2//3*x^-2+-1*a^1//3*b^1//3*x^-1))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^1//3+b^1//3*x^-1))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^-3)^-1//2*(a^1//3+b^1//3*x^-1)*Elliptic.E(arcsin((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-1*(a^1//3*(1+-1*3^(1/2))+b^1//3*x^-1)),-7+-4*3^(1/2))+5//24*2^(1/2)*3^3//4*a^-5//3*b^4//3*((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^2//3+b^2//3*x^-2+-1*a^1//3*b^1//3*x^-1))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^1//3+b^1//3*x^-1))^-1//2*(a+b*x^-3)^-1//2*(a^1//3+b^1//3*x^-1)*Elliptic.F(arcsin((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-1*(a^1//3*(1+-1*3^(1/2))+b^1//3*x^-1)),-7+-4*3^(1/2)))
@test integrate((a+b*x^-3)^-1//2, x) == :(x*a^-1*(a+b*x^-3)^(1/2)+-1*a^-1*b^1//3*(a+b*x^-3)^(1/2)*(a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-1+(1/2)*3^1//4*a^-2//3*b^1//3*((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^2//3+b^2//3*x^-2+-1*a^1//3*b^1//3*x^-1))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^1//3+b^1//3*x^-1))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^-3)^-1//2*(a^1//3+b^1//3*x^-1)*Elliptic.E(arcsin((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-1*(a^1//3*(1+-1*3^(1/2))+b^1//3*x^-1)),-7+-4*3^(1/2))+-1//3*2^(1/2)*3^3//4*a^-2//3*b^1//3*((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^2//3+b^2//3*x^-2+-1*a^1//3*b^1//3*x^-1))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^1//3+b^1//3*x^-1))^-1//2*(a+b*x^-3)^-1//2*(a^1//3+b^1//3*x^-1)*Elliptic.F(arcsin((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-1*(a^1//3*(1+-1*3^(1/2))+b^1//3*x^-1)),-7+-4*3^(1/2)))
@test integrate(x^-3*(a+b*x^-3)^-1//2, x) == :(-2*b^-2//3*(a+b*x^-3)^(1/2)*(a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-1+3^1//4*a^1//3*b^-2//3*((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^2//3+b^2//3*x^-2+-1*a^1//3*b^1//3*x^-1))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^1//3+b^1//3*x^-1))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^-3)^-1//2*(a^1//3+b^1//3*x^-1)*Elliptic.E(arcsin((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-1*(a^1//3*(1+-1*3^(1/2))+b^1//3*x^-1)),-7+-4*3^(1/2))+-2//3*2^(1/2)*3^3//4*a^1//3*b^-2//3*((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^2//3+b^2//3*x^-2+-1*a^1//3*b^1//3*x^-1))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^1//3+b^1//3*x^-1))^-1//2*(a+b*x^-3)^-1//2*(a^1//3+b^1//3*x^-1)*Elliptic.F(arcsin((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-1*(a^1//3*(1+-1*3^(1/2))+b^1//3*x^-1)),-7+-4*3^(1/2)))
@test integrate(x^-6*(a+b*x^-3)^-1//2, x) == :(-2//7*b^-1*x^-2*(a+b*x^-3)^(1/2)+8//7*a*b^-5//3*(a+b*x^-3)^(1/2)*(a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-1+-4//7*3^1//4*a^4//3*b^-5//3*((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^2//3+b^2//3*x^-2+-1*a^1//3*b^1//3*x^-1))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^1//3+b^1//3*x^-1))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^-3)^-1//2*(a^1//3+b^1//3*x^-1)*Elliptic.E(arcsin((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-1*(a^1//3*(1+-1*3^(1/2))+b^1//3*x^-1)),-7+-4*3^(1/2))+8//21*2^(1/2)*3^3//4*a^4//3*b^-5//3*((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^2//3+b^2//3*x^-2+-1*a^1//3*b^1//3*x^-1))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^1//3+b^1//3*x^-1))^-1//2*(a+b*x^-3)^-1//2*(a^1//3+b^1//3*x^-1)*Elliptic.F(arcsin((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-1*(a^1//3*(1+-1*3^(1/2))+b^1//3*x^-1)),-7+-4*3^(1/2)))
@test integrate(x^-9*(a+b*x^-3)^-1//2, x) == :(-2//13*b^-1*x^-5*(a+b*x^-3)^(1/2)+-80//91*a^2*b^-8//3*(a+b*x^-3)^(1/2)*(a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-1+20//91*a*b^-2*x^-2*(a+b*x^-3)^(1/2)+-80//273*2^(1/2)*3^3//4*a^7//3*b^-8//3*((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^2//3+b^2//3*x^-2+-1*a^1//3*b^1//3*x^-1))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^1//3+b^1//3*x^-1))^-1//2*(a+b*x^-3)^-1//2*(a^1//3+b^1//3*x^-1)*Elliptic.F(arcsin((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-1*(a^1//3*(1+-1*3^(1/2))+b^1//3*x^-1)),-7+-4*3^(1/2))+40//91*3^1//4*a^7//3*b^-8//3*((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^2//3+b^2//3*x^-2+-1*a^1//3*b^1//3*x^-1))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^1//3+b^1//3*x^-1))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^-3)^-1//2*(a^1//3+b^1//3*x^-1)*Elliptic.E(arcsin((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-1*(a^1//3*(1+-1*3^(1/2))+b^1//3*x^-1)),-7+-4*3^(1/2)))
@test integrate(x^-12*(a+b*x^-3)^-1//2, x) == :(-2//19*b^-1*x^-8*(a+b*x^-3)^(1/2)+-320//1729*a^2*b^-3*x^-2*(a+b*x^-3)^(1/2)+32//247*a*b^-2*x^-5*(a+b*x^-3)^(1/2)+1280//1729*a^3*b^-11//3*(a+b*x^-3)^(1/2)*(a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-1+-640//1729*3^1//4*a^10//3*b^-11//3*((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^2//3+b^2//3*x^-2+-1*a^1//3*b^1//3*x^-1))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^1//3+b^1//3*x^-1))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^-3)^-1//2*(a^1//3+b^1//3*x^-1)*Elliptic.E(arcsin((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-1*(a^1//3*(1+-1*3^(1/2))+b^1//3*x^-1)),-7+-4*3^(1/2))+1280//5187*2^(1/2)*3^3//4*a^10//3*b^-11//3*((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^2//3+b^2//3*x^-2+-1*a^1//3*b^1//3*x^-1))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^1//3+b^1//3*x^-1))^-1//2*(a+b*x^-3)^-1//2*(a^1//3+b^1//3*x^-1)*Elliptic.F(arcsin((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-1*(a^1//3*(1+-1*3^(1/2))+b^1//3*x^-1)),-7+-4*3^(1/2)))
@test integrate(x^5*(a+b*x^-3)^-3//2, x) == :(-5//4*a^-3*b^2*(a+b*x^-3)^-1//2+1//6*a^-1*x^6*(a+b*x^-3)^-1//2+5//4*a^-7//2*b^2*arctanh(a^-1//2*(a+b*x^-3)^(1/2))+-5//12*b*a^-2*x^3*(a+b*x^-3)^-1//2)
@test integrate(x^2*(a+b*x^-3)^-3//2, x) == :(b*a^-2*(a+b*x^-3)^-1//2+-1*b*a^-5//2*arctanh(a^-1//2*(a+b*x^-3)^(1/2))+1//3*a^-1*x^3*(a+b*x^-3)^-1//2)
@test integrate(x^-1*(a+b*x^-3)^-3//2, x) == :(-2//3*a^-1*(a+b*x^-3)^-1//2+2//3*a^-3//2*arctanh(a^-1//2*(a+b*x^-3)^(1/2)))
@test integrate(x^-4*(a+b*x^-3)^-3//2, x) == :(2//3*b^-1*(a+b*x^-3)^-1//2)
@test integrate(x^-7*(a+b*x^-3)^-3//2, x) == :(-2//3*b^-2*(a+b*x^-3)^(1/2)+-2//3*a*b^-2*(a+b*x^-3)^-1//2)
@test integrate(x^-10*(a+b*x^-3)^-3//2, x) == :(-2//9*b^-3*(a+b*x^-3)^3//2+2//3*a^2*b^-3*(a+b*x^-3)^-1//2+4//3*a*b^-3*(a+b*x^-3)^(1/2))
@test integrate(x^-13*(a+b*x^-3)^-3//2, x) == :(-2//15*b^-4*(a+b*x^-3)^5//2+-2*a^2*b^-4*(a+b*x^-3)^(1/2)+-2//3*a^3*b^-4*(a+b*x^-3)^-1//2+2//3*a*b^-4*(a+b*x^-3)^3//2)
@test integrate(x^7*(a+b*x^-3)^-3//2, x) == :(-2//3*a^-1*x^8*(a+b*x^-3)^-1//2+19//24*a^-2*x^8*(a+b*x^-3)^(1/2)+-247//240*b*a^-3*x^5*(a+b*x^-3)^(1/2)+1729//960*a^-4*b^2*x^2*(a+b*x^-3)^(1/2)+1729//2880*3^3//4*a^-4*b^8//3*((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^2//3+b^2//3*x^-2+-1*a^1//3*b^1//3*x^-1))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^1//3+b^1//3*x^-1))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^-3)^-1//2*(a^1//3+b^1//3*x^-1)*Elliptic.F(arcsin((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-1*(a^1//3*(1+-1*3^(1/2))+b^1//3*x^-1)),-7+-4*3^(1/2)))
@test integrate(x^4*(a+b*x^-3)^-3//2, x) == :(-2//3*a^-1*x^5*(a+b*x^-3)^-1//2+13//15*a^-2*x^5*(a+b*x^-3)^(1/2)+-91//60*b*a^-3*x^2*(a+b*x^-3)^(1/2)+-91//180*3^3//4*a^-3*b^5//3*((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^2//3+b^2//3*x^-2+-1*a^1//3*b^1//3*x^-1))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^1//3+b^1//3*x^-1))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^-3)^-1//2*(a^1//3+b^1//3*x^-1)*Elliptic.F(arcsin((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-1*(a^1//3*(1+-1*3^(1/2))+b^1//3*x^-1)),-7+-4*3^(1/2)))
@test integrate(x*(a+b*x^-3)^-3//2, x) == :(-2//3*a^-1*x^2*(a+b*x^-3)^-1//2+7//6*a^-2*x^2*(a+b*x^-3)^(1/2)+7//18*3^3//4*a^-2*b^2//3*((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^2//3+b^2//3*x^-2+-1*a^1//3*b^1//3*x^-1))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^1//3+b^1//3*x^-1))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^-3)^-1//2*(a^1//3+b^1//3*x^-1)*Elliptic.F(arcsin((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-1*(a^1//3*(1+-1*3^(1/2))+b^1//3*x^-1)),-7+-4*3^(1/2)))
@test integrate(x^-2*(a+b*x^-3)^-3//2, x) == :(-2//3*a^-1*x^-1*(a+b*x^-3)^-1//2+-2//9*3^3//4*a^-1*b^-1//3*((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^2//3+b^2//3*x^-2+-1*a^1//3*b^1//3*x^-1))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^1//3+b^1//3*x^-1))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^-3)^-1//2*(a^1//3+b^1//3*x^-1)*Elliptic.F(arcsin((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-1*(a^1//3*(1+-1*3^(1/2))+b^1//3*x^-1)),-7+-4*3^(1/2)))
@test integrate(x^-5*(a+b*x^-3)^-3//2, x) == :(2//3*b^-1*x^-1*(a+b*x^-3)^-1//2+-4//9*3^3//4*b^-4//3*((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^2//3+b^2//3*x^-2+-1*a^1//3*b^1//3*x^-1))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^1//3+b^1//3*x^-1))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^-3)^-1//2*(a^1//3+b^1//3*x^-1)*Elliptic.F(arcsin((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-1*(a^1//3*(1+-1*3^(1/2))+b^1//3*x^-1)),-7+-4*3^(1/2)))
@test integrate(x^-8*(a+b*x^-3)^-3//2, x) == :(-16//15*b^-2*x^-1*(a+b*x^-3)^(1/2)+2//3*b^-1*x^-4*(a+b*x^-3)^-1//2+32//45*a*3^3//4*b^-7//3*((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^2//3+b^2//3*x^-2+-1*a^1//3*b^1//3*x^-1))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^1//3+b^1//3*x^-1))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^-3)^-1//2*(a^1//3+b^1//3*x^-1)*Elliptic.F(arcsin((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-1*(a^1//3*(1+-1*3^(1/2))+b^1//3*x^-1)),-7+-4*3^(1/2)))
@test integrate(x^6*(a+b*x^-3)^-3//2, x) == :(-2//3*a^-1*x^7*(a+b*x^-3)^-1//2+17//21*a^-2*x^7*(a+b*x^-3)^(1/2)+-935//336*a^-4*b^7//3*(a+b*x^-3)^(1/2)*(a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-1+-187//168*b*a^-3*x^4*(a+b*x^-3)^(1/2)+935//336*x*a^-4*b^2*(a+b*x^-3)^(1/2)+-935//1008*2^(1/2)*3^3//4*a^-11//3*b^7//3*((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^2//3+b^2//3*x^-2+-1*a^1//3*b^1//3*x^-1))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^1//3+b^1//3*x^-1))^-1//2*(a+b*x^-3)^-1//2*(a^1//3+b^1//3*x^-1)*Elliptic.F(arcsin((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-1*(a^1//3*(1+-1*3^(1/2))+b^1//3*x^-1)),-7+-4*3^(1/2))+935//672*3^1//4*a^-11//3*b^7//3*((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^2//3+b^2//3*x^-2+-1*a^1//3*b^1//3*x^-1))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^1//3+b^1//3*x^-1))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^-3)^-1//2*(a^1//3+b^1//3*x^-1)*Elliptic.E(arcsin((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-1*(a^1//3*(1+-1*3^(1/2))+b^1//3*x^-1)),-7+-4*3^(1/2)))
@test integrate(x^3*(a+b*x^-3)^-3//2, x) == :(-2//3*a^-1*x^4*(a+b*x^-3)^-1//2+11//12*a^-2*x^4*(a+b*x^-3)^(1/2)+-55//24*b*x*a^-3*(a+b*x^-3)^(1/2)+55//24*a^-3*b^4//3*(a+b*x^-3)^(1/2)*(a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-1+-55//48*3^1//4*a^-8//3*b^4//3*((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^2//3+b^2//3*x^-2+-1*a^1//3*b^1//3*x^-1))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^1//3+b^1//3*x^-1))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^-3)^-1//2*(a^1//3+b^1//3*x^-1)*Elliptic.E(arcsin((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-1*(a^1//3*(1+-1*3^(1/2))+b^1//3*x^-1)),-7+-4*3^(1/2))+55//72*2^(1/2)*3^3//4*a^-8//3*b^4//3*((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^2//3+b^2//3*x^-2+-1*a^1//3*b^1//3*x^-1))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^1//3+b^1//3*x^-1))^-1//2*(a+b*x^-3)^-1//2*(a^1//3+b^1//3*x^-1)*Elliptic.F(arcsin((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-1*(a^1//3*(1+-1*3^(1/2))+b^1//3*x^-1)),-7+-4*3^(1/2)))
@test integrate((a+b*x^-3)^-3//2, x) == :(-2//3*x*a^-1*(a+b*x^-3)^-1//2+5//3*x*a^-2*(a+b*x^-3)^(1/2)+-5//3*a^-2*b^1//3*(a+b*x^-3)^(1/2)*(a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-1+-5//9*2^(1/2)*3^3//4*a^-5//3*b^1//3*((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^2//3+b^2//3*x^-2+-1*a^1//3*b^1//3*x^-1))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^1//3+b^1//3*x^-1))^-1//2*(a+b*x^-3)^-1//2*(a^1//3+b^1//3*x^-1)*Elliptic.F(arcsin((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-1*(a^1//3*(1+-1*3^(1/2))+b^1//3*x^-1)),-7+-4*3^(1/2))+5//6*3^1//4*a^-5//3*b^1//3*((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^2//3+b^2//3*x^-2+-1*a^1//3*b^1//3*x^-1))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^1//3+b^1//3*x^-1))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^-3)^-1//2*(a^1//3+b^1//3*x^-1)*Elliptic.E(arcsin((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-1*(a^1//3*(1+-1*3^(1/2))+b^1//3*x^-1)),-7+-4*3^(1/2)))
@test integrate(x^-3*(a+b*x^-3)^-3//2, x) == :(-2//3*a^-1*x^-2*(a+b*x^-3)^-1//2+2//3*a^-1*b^-2//3*(a+b*x^-3)^(1/2)*(a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-1+-1//3*3^1//4*a^-2//3*b^-2//3*((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^2//3+b^2//3*x^-2+-1*a^1//3*b^1//3*x^-1))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^1//3+b^1//3*x^-1))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^-3)^-1//2*(a^1//3+b^1//3*x^-1)*Elliptic.E(arcsin((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-1*(a^1//3*(1+-1*3^(1/2))+b^1//3*x^-1)),-7+-4*3^(1/2))+2//9*2^(1/2)*3^3//4*a^-2//3*b^-2//3*((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^2//3+b^2//3*x^-2+-1*a^1//3*b^1//3*x^-1))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^1//3+b^1//3*x^-1))^-1//2*(a+b*x^-3)^-1//2*(a^1//3+b^1//3*x^-1)*Elliptic.F(arcsin((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-1*(a^1//3*(1+-1*3^(1/2))+b^1//3*x^-1)),-7+-4*3^(1/2)))
@test integrate(x^-6*(a+b*x^-3)^-3//2, x) == :(-8//3*b^-5//3*(a+b*x^-3)^(1/2)*(a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-1+2//3*b^-1*x^-2*(a+b*x^-3)^-1//2+-8//9*2^(1/2)*3^3//4*a^1//3*b^-5//3*((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^2//3+b^2//3*x^-2+-1*a^1//3*b^1//3*x^-1))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^1//3+b^1//3*x^-1))^-1//2*(a+b*x^-3)^-1//2*(a^1//3+b^1//3*x^-1)*Elliptic.F(arcsin((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-1*(a^1//3*(1+-1*3^(1/2))+b^1//3*x^-1)),-7+-4*3^(1/2))+4//3*3^1//4*a^1//3*b^-5//3*((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^2//3+b^2//3*x^-2+-1*a^1//3*b^1//3*x^-1))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^1//3+b^1//3*x^-1))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^-3)^-1//2*(a^1//3+b^1//3*x^-1)*Elliptic.E(arcsin((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-1*(a^1//3*(1+-1*3^(1/2))+b^1//3*x^-1)),-7+-4*3^(1/2)))
@test integrate(x^-9*(a+b*x^-3)^-3//2, x) == :(-20//21*b^-2*x^-2*(a+b*x^-3)^(1/2)+2//3*b^-1*x^-5*(a+b*x^-3)^-1//2+80//21*a*b^-8//3*(a+b*x^-3)^(1/2)*(a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-1+-40//21*3^1//4*a^4//3*b^-8//3*((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^2//3+b^2//3*x^-2+-1*a^1//3*b^1//3*x^-1))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^1//3+b^1//3*x^-1))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^-3)^-1//2*(a^1//3+b^1//3*x^-1)*Elliptic.E(arcsin((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-1*(a^1//3*(1+-1*3^(1/2))+b^1//3*x^-1)),-7+-4*3^(1/2))+80//63*2^(1/2)*3^3//4*a^4//3*b^-8//3*((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^2//3+b^2//3*x^-2+-1*a^1//3*b^1//3*x^-1))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^1//3+b^1//3*x^-1))^-1//2*(a+b*x^-3)^-1//2*(a^1//3+b^1//3*x^-1)*Elliptic.F(arcsin((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-1*(a^1//3*(1+-1*3^(1/2))+b^1//3*x^-1)),-7+-4*3^(1/2)))
@test integrate(x^-12*(a+b*x^-3)^-3//2, x) == :(-32//39*b^-2*x^-5*(a+b*x^-3)^(1/2)+2//3*b^-1*x^-8*(a+b*x^-3)^-1//2+-1280//273*a^2*b^-11//3*(a+b*x^-3)^(1/2)*(a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-1+320//273*a*b^-3*x^-2*(a+b*x^-3)^(1/2)+-1280//819*2^(1/2)*3^3//4*a^7//3*b^-11//3*((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^2//3+b^2//3*x^-2+-1*a^1//3*b^1//3*x^-1))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^1//3+b^1//3*x^-1))^-1//2*(a+b*x^-3)^-1//2*(a^1//3+b^1//3*x^-1)*Elliptic.F(arcsin((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-1*(a^1//3*(1+-1*3^(1/2))+b^1//3*x^-1)),-7+-4*3^(1/2))+640//273*3^1//4*a^7//3*b^-11//3*((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^2//3+b^2//3*x^-2+-1*a^1//3*b^1//3*x^-1))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-2*(a^1//3+b^1//3*x^-1))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^-3)^-1//2*(a^1//3+b^1//3*x^-1)*Elliptic.E(arcsin((a^1//3*(1+3^(1/2))+b^1//3*x^-1)^-1*(a^1//3*(1+-1*3^(1/2))+b^1//3*x^-1)),-7+-4*3^(1/2)))
@test integrate((a+b*x^-4)^-1, x) == :(x*a^-1+-1//4*2^(1/2)*a^-5//4*b^1//4*arctan(1+x*2^(1/2)*a^1//4*b^-1//4)+-1//8*2^(1/2)*a^-5//4*b^1//4*log(b^(1/2)+a^(1/2)*x^2+x*2^(1/2)*a^1//4*b^1//4)+1//4*2^(1/2)*a^-5//4*b^1//4*arctan(1+-1*x*2^(1/2)*a^1//4*b^-1//4)+1//8*2^(1/2)*a^-5//4*b^1//4*log(b^(1/2)+a^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*b^1//4))
@test integrate(x^3*(a+b*x^-4)^(1/2), x) == :(1//4*x^4*(a+b*x^-4)^(1/2)+1//4*b*a^-1//2*arctanh(a^-1//2*(a+b*x^-4)^(1/2)))
@test integrate(x*(a+b*x^-4)^(1/2), x) == :((1/2)*x^2*(a+b*x^-4)^(1/2)+-1//2*b^(1/2)*arctanh(b^(1/2)*x^-2*(a+b*x^-4)^-1//2))
@test integrate(x^-1*(a+b*x^-4)^(1/2), x) == :(-1//2*(a+b*x^-4)^(1/2)+(1/2)*a^(1/2)*arctanh(a^-1//2*(a+b*x^-4)^(1/2)))
@test integrate(x^-3*(a+b*x^-4)^(1/2), x) == :(-1//4*x^-2*(a+b*x^-4)^(1/2)+-1//4*a*b^-1//2*arctanh(b^(1/2)*x^-2*(a+b*x^-4)^-1//2))
@test integrate(x^2*(a+b*x^-4)^(1/2), x) == :(1//3*x^3*(a+b*x^-4)^(1/2)+-1//3*a^-1//4*b^3//4*((a^(1/2)+b^(1/2)*x^-2)^-2*(a+b*x^-4))^(1/2)*(a+b*x^-4)^-1//2*(a^(1/2)+b^(1/2)*x^-2)*Elliptic.F(2*arccot(x*a^1//4*b^-1//4),1/2))
@test integrate((a+b*x^-4)^(1/2), x) == :(x*(a+b*x^-4)^(1/2)+-2*b^(1/2)*x^-1*(a+b*x^-4)^(1/2)*(a^(1/2)+b^(1/2)*x^-2)^-1+-1*a^1//4*b^1//4*((a^(1/2)+b^(1/2)*x^-2)^-2*(a+b*x^-4))^(1/2)*(a+b*x^-4)^-1//2*(a^(1/2)+b^(1/2)*x^-2)*Elliptic.F(2*arccot(x*a^1//4*b^-1//4),1/2)+2*a^1//4*b^1//4*((a^(1/2)+b^(1/2)*x^-2)^-2*(a+b*x^-4))^(1/2)*(a+b*x^-4)^-1//2*(a^(1/2)+b^(1/2)*x^-2)*Elliptic.E(2*arccot(x*a^1//4*b^-1//4),1/2))
@test integrate(x^-2*(a+b*x^-4)^(1/2), x) == :(-1//3*x^-1*(a+b*x^-4)^(1/2)+-1//3*a^3//4*b^-1//4*((a^(1/2)+b^(1/2)*x^-2)^-2*(a+b*x^-4))^(1/2)*(a+b*x^-4)^-1//2*(a^(1/2)+b^(1/2)*x^-2)*Elliptic.F(2*arccot(x*a^1//4*b^-1//4),1/2))
@test integrate(x^-4*(a+b*x^-4)^(1/2), x) == :(-1//5*x^-3*(a+b*x^-4)^(1/2)+-2//5*a*b^-1//2*x^-1*(a+b*x^-4)^(1/2)*(a^(1/2)+b^(1/2)*x^-2)^-1+-1//5*a^5//4*b^-3//4*((a^(1/2)+b^(1/2)*x^-2)^-2*(a+b*x^-4))^(1/2)*(a+b*x^-4)^-1//2*(a^(1/2)+b^(1/2)*x^-2)*Elliptic.F(2*arccot(x*a^1//4*b^-1//4),1/2)+2//5*a^5//4*b^-3//4*((a^(1/2)+b^(1/2)*x^-2)^-2*(a+b*x^-4))^(1/2)*(a+b*x^-4)^-1//2*(a^(1/2)+b^(1/2)*x^-2)*Elliptic.E(2*arccot(x*a^1//4*b^-1//4),1/2))
@test integrate(x^3*(a+b*x^-4)^3//2, x) == :(-3//4*b*(a+b*x^-4)^(1/2)+1//4*x^4*(a+b*x^-4)^3//2+3//4*b*a^(1/2)*arctanh(a^-1//2*(a+b*x^-4)^(1/2)))
@test integrate(x*(a+b*x^-4)^3//2, x) == :((1/2)*x^2*(a+b*x^-4)^3//2+-3//4*a*b^(1/2)*arctanh(b^(1/2)*x^-2*(a+b*x^-4)^-1//2)+-3//4*b*x^-2*(a+b*x^-4)^(1/2))
@test integrate(x^-1*(a+b*x^-4)^3//2, x) == :(-1//6*(a+b*x^-4)^3//2+(1/2)*a^3//2*arctanh(a^-1//2*(a+b*x^-4)^(1/2))+-1//2*a*(a+b*x^-4)^(1/2))
@test integrate(x^-3*(a+b*x^-4)^3//2, x) == :(-1//8*x^-2*(a+b*x^-4)^3//2+-3//16*a*x^-2*(a+b*x^-4)^(1/2)+-3//16*a^2*b^-1//2*arctanh(b^(1/2)*x^-2*(a+b*x^-4)^-1//2))
@test integrate(x^2*(a+b*x^-4)^3//2, x) == :(1//3*x^3*(a+b*x^-4)^3//2+-2//3*b*x^-1*(a+b*x^-4)^(1/2)+-2//3*a^3//4*b^3//4*((a^(1/2)+b^(1/2)*x^-2)^-2*(a+b*x^-4))^(1/2)*(a+b*x^-4)^-1//2*(a^(1/2)+b^(1/2)*x^-2)*Elliptic.F(2*arccot(x*a^1//4*b^-1//4),1/2))
@test integrate((a+b*x^-4)^3//2, x) == :(x*(a+b*x^-4)^3//2+-6//5*b*x^-3*(a+b*x^-4)^(1/2)+-12*a*b^(1/2)*x^-1*(a+b*x^-4)^(1/2)*(5*a^(1/2)+5*b^(1/2)*x^-2)^-1+-6//5*a^5//4*b^1//4*((a^(1/2)+b^(1/2)*x^-2)^-2*(a+b*x^-4))^(1/2)*(a+b*x^-4)^-1//2*(a^(1/2)+b^(1/2)*x^-2)*Elliptic.F(2*arccot(x*a^1//4*b^-1//4),1/2)+12//5*a^5//4*b^1//4*((a^(1/2)+b^(1/2)*x^-2)^-2*(a+b*x^-4))^(1/2)*(a+b*x^-4)^-1//2*(a^(1/2)+b^(1/2)*x^-2)*Elliptic.E(2*arccot(x*a^1//4*b^-1//4),1/2))
@test integrate(x^-2*(a+b*x^-4)^3//2, x) == :(-1//7*x^-1*(a+b*x^-4)^3//2+-2//7*a*x^-1*(a+b*x^-4)^(1/2)+-2//7*a^7//4*b^-1//4*((a^(1/2)+b^(1/2)*x^-2)^-2*(a+b*x^-4))^(1/2)*(a+b*x^-4)^-1//2*(a^(1/2)+b^(1/2)*x^-2)*Elliptic.F(2*arccot(x*a^1//4*b^-1//4),1/2))
@test integrate(x^-4*(a+b*x^-4)^3//2, x) == :(-1//9*x^-3*(a+b*x^-4)^3//2+-2//15*a*x^-3*(a+b*x^-4)^(1/2)+-4//15*a^2*b^-1//2*x^-1*(a+b*x^-4)^(1/2)*(a^(1/2)+b^(1/2)*x^-2)^-1+-2//15*a^9//4*b^-3//4*((a^(1/2)+b^(1/2)*x^-2)^-2*(a+b*x^-4))^(1/2)*(a+b*x^-4)^-1//2*(a^(1/2)+b^(1/2)*x^-2)*Elliptic.F(2*arccot(x*a^1//4*b^-1//4),1/2)+4//15*a^9//4*b^-3//4*((a^(1/2)+b^(1/2)*x^-2)^-2*(a+b*x^-4))^(1/2)*(a+b*x^-4)^-1//2*(a^(1/2)+b^(1/2)*x^-2)*Elliptic.E(2*arccot(x*a^1//4*b^-1//4),1/2))
@test integrate(x^3*(a+b*x^-4)^5//2, x) == :(-5//12*b*(a+b*x^-4)^3//2+1//4*x^4*(a+b*x^-4)^5//2+-5//4*a*b*(a+b*x^-4)^(1/2)+5//4*b*a^3//2*arctanh(a^-1//2*(a+b*x^-4)^(1/2)))
@test integrate(x*(a+b*x^-4)^5//2, x) == :((1/2)*x^2*(a+b*x^-4)^5//2+-15//16*a^2*b^(1/2)*arctanh(b^(1/2)*x^-2*(a+b*x^-4)^-1//2)+-5//8*b*x^-2*(a+b*x^-4)^3//2+-15//16*a*b*x^-2*(a+b*x^-4)^(1/2))
@test integrate(x^-1*(a+b*x^-4)^5//2, x) == :(-1//10*(a+b*x^-4)^5//2+(1/2)*a^5//2*arctanh(a^-1//2*(a+b*x^-4)^(1/2))+-1//2*a^2*(a+b*x^-4)^(1/2)+-1//6*a*(a+b*x^-4)^3//2)
@test integrate(x^-3*(a+b*x^-4)^5//2, x) == :(-1//12*x^-2*(a+b*x^-4)^5//2+-5//32*a^2*x^-2*(a+b*x^-4)^(1/2)+-5//32*a^3*b^-1//2*arctanh(b^(1/2)*x^-2*(a+b*x^-4)^-1//2)+-5//48*a*x^-2*(a+b*x^-4)^3//2)
@test integrate(x^2*(a+b*x^-4)^5//2, x) == :(1//3*x^3*(a+b*x^-4)^5//2+-10//21*b*x^-1*(a+b*x^-4)^3//2+-20//21*a*b*x^-1*(a+b*x^-4)^(1/2)+-20//21*a^7//4*b^3//4*((a^(1/2)+b^(1/2)*x^-2)^-2*(a+b*x^-4))^(1/2)*(a+b*x^-4)^-1//2*(a^(1/2)+b^(1/2)*x^-2)*Elliptic.F(2*arccot(x*a^1//4*b^-1//4),1/2))
@test integrate((a+b*x^-4)^5//2, x) == :(x*(a+b*x^-4)^5//2+-10//9*b*x^-3*(a+b*x^-4)^3//2+-4//3*a*b*x^-3*(a+b*x^-4)^(1/2)+-8*a^2*b^(1/2)*x^-1*(a+b*x^-4)^(1/2)*(3*a^(1/2)+3*b^(1/2)*x^-2)^-1+-4//3*a^9//4*b^1//4*((a^(1/2)+b^(1/2)*x^-2)^-2*(a+b*x^-4))^(1/2)*(a+b*x^-4)^-1//2*(a^(1/2)+b^(1/2)*x^-2)*Elliptic.F(2*arccot(x*a^1//4*b^-1//4),1/2)+8//3*a^9//4*b^1//4*((a^(1/2)+b^(1/2)*x^-2)^-2*(a+b*x^-4))^(1/2)*(a+b*x^-4)^-1//2*(a^(1/2)+b^(1/2)*x^-2)*Elliptic.E(2*arccot(x*a^1//4*b^-1//4),1/2))
@test integrate(x^-2*(a+b*x^-4)^5//2, x) == :(-1//11*x^-1*(a+b*x^-4)^5//2+-20//77*a^2*x^-1*(a+b*x^-4)^(1/2)+-10//77*a*x^-1*(a+b*x^-4)^3//2+-20//77*a^11//4*b^-1//4*((a^(1/2)+b^(1/2)*x^-2)^-2*(a+b*x^-4))^(1/2)*(a+b*x^-4)^-1//2*(a^(1/2)+b^(1/2)*x^-2)*Elliptic.F(2*arccot(x*a^1//4*b^-1//4),1/2))
@test integrate(x^-4*(a+b*x^-4)^5//2, x) == :(-1//13*x^-3*(a+b*x^-4)^5//2+-10//117*a*x^-3*(a+b*x^-4)^3//2+-4//39*a^2*x^-3*(a+b*x^-4)^(1/2)+-8//39*a^3*b^-1//2*x^-1*(a+b*x^-4)^(1/2)*(a^(1/2)+b^(1/2)*x^-2)^-1+-4//39*a^13//4*b^-3//4*((a^(1/2)+b^(1/2)*x^-2)^-2*(a+b*x^-4))^(1/2)*(a+b*x^-4)^-1//2*(a^(1/2)+b^(1/2)*x^-2)*Elliptic.F(2*arccot(x*a^1//4*b^-1//4),1/2)+8//39*a^13//4*b^-3//4*((a^(1/2)+b^(1/2)*x^-2)^-2*(a+b*x^-4))^(1/2)*(a+b*x^-4)^-1//2*(a^(1/2)+b^(1/2)*x^-2)*Elliptic.E(2*arccot(x*a^1//4*b^-1//4),1/2))
@test integrate(x^3*(a+b*x^-4)^-1//2, x) == :(-1//4*b*a^-3//2*arctanh(a^-1//2*(a+b*x^-4)^(1/2))+1//4*a^-1*x^4*(a+b*x^-4)^(1/2))
@test integrate(x*(a+b*x^-4)^-1//2, x) == :((1/2)*a^-1*x^2*(a+b*x^-4)^(1/2))
@test integrate(x^-1*(a+b*x^-4)^-1//2, x) == :((1/2)*a^-1//2*arctanh(a^-1//2*(a+b*x^-4)^(1/2)))
@test integrate(x^-3*(a+b*x^-4)^-1//2, x) == :(-1//2*b^-1//2*arctanh(b^(1/2)*x^-2*(a+b*x^-4)^-1//2))
@test integrate(x^2*(a+b*x^-4)^-1//2, x) == :(1//3*a^-1*x^3*(a+b*x^-4)^(1/2)+1//6*a^-5//4*b^3//4*((a^(1/2)+b^(1/2)*x^-2)^-2*(a+b*x^-4))^(1/2)*(a+b*x^-4)^-1//2*(a^(1/2)+b^(1/2)*x^-2)*Elliptic.F(2*arccot(x*a^1//4*b^-1//4),1/2))
@test integrate((a+b*x^-4)^-1//2, x) == :(x*a^-1*(a+b*x^-4)^(1/2)+-1*a^-1*b^(1/2)*x^-1*(a+b*x^-4)^(1/2)*(a^(1/2)+b^(1/2)*x^-2)^-1+a^-3//4*b^1//4*((a^(1/2)+b^(1/2)*x^-2)^-2*(a+b*x^-4))^(1/2)*(a+b*x^-4)^-1//2*(a^(1/2)+b^(1/2)*x^-2)*Elliptic.E(2*arccot(x*a^1//4*b^-1//4),1/2)+-1//2*a^-3//4*b^1//4*((a^(1/2)+b^(1/2)*x^-2)^-2*(a+b*x^-4))^(1/2)*(a+b*x^-4)^-1//2*(a^(1/2)+b^(1/2)*x^-2)*Elliptic.F(2*arccot(x*a^1//4*b^-1//4),1/2))
@test integrate(x^-2*(a+b*x^-4)^-1//2, x) == :(-1//2*a^-1//4*b^-1//4*((a^(1/2)+b^(1/2)*x^-2)^-2*(a+b*x^-4))^(1/2)*(a+b*x^-4)^-1//2*(a^(1/2)+b^(1/2)*x^-2)*Elliptic.F(2*arccot(x*a^1//4*b^-1//4),1/2))
@test integrate(x^-4*(a+b*x^-4)^-1//2, x) == :(-1*b^-1//2*x^-1*(a+b*x^-4)^(1/2)*(a^(1/2)+b^(1/2)*x^-2)^-1+a^1//4*b^-3//4*((a^(1/2)+b^(1/2)*x^-2)^-2*(a+b*x^-4))^(1/2)*(a+b*x^-4)^-1//2*(a^(1/2)+b^(1/2)*x^-2)*Elliptic.E(2*arccot(x*a^1//4*b^-1//4),1/2)+-1//2*a^1//4*b^-3//4*((a^(1/2)+b^(1/2)*x^-2)^-2*(a+b*x^-4))^(1/2)*(a+b*x^-4)^-1//2*(a^(1/2)+b^(1/2)*x^-2)*Elliptic.F(2*arccot(x*a^1//4*b^-1//4),1/2))
@test integrate(x^3*(a+b*x^-4)^-3//2, x) == :(-3//4*b*a^-5//2*arctanh(a^-1//2*(a+b*x^-4)^(1/2))+1//4*a^-1*x^4*(a+b*x^-4)^-1//2+3//4*b*a^-2*(a+b*x^-4)^-1//2)
@test integrate(x*(a+b*x^-4)^-3//2, x) == :(a^-2*x^2*(a+b*x^-4)^(1/2)+-1//2*a^-1*x^2*(a+b*x^-4)^-1//2)
@test integrate(x^-1*(a+b*x^-4)^-3//2, x) == :((1/2)*a^-3//2*arctanh(a^-1//2*(a+b*x^-4)^(1/2))+-1//2*a^-1*(a+b*x^-4)^-1//2)
@test integrate(x^-3*(a+b*x^-4)^-3//2, x) == :(-1//2*a^-1*x^-2*(a+b*x^-4)^-1//2)
@test integrate(x^2*(a+b*x^-4)^-3//2, x) == :(-1//2*a^-1*x^3*(a+b*x^-4)^-1//2+5//6*a^-2*x^3*(a+b*x^-4)^(1/2)+5//12*a^-9//4*b^3//4*((a^(1/2)+b^(1/2)*x^-2)^-2*(a+b*x^-4))^(1/2)*(a+b*x^-4)^-1//2*(a^(1/2)+b^(1/2)*x^-2)*Elliptic.F(2*arccot(x*a^1//4*b^-1//4),1/2))
@test integrate((a+b*x^-4)^-3//2, x) == :(-1//2*x*a^-1*(a+b*x^-4)^-1//2+3//2*x*a^-2*(a+b*x^-4)^(1/2)+-3//2*a^-2*b^(1/2)*x^-1*(a+b*x^-4)^(1/2)*(a^(1/2)+b^(1/2)*x^-2)^-1+-3//4*a^-7//4*b^1//4*((a^(1/2)+b^(1/2)*x^-2)^-2*(a+b*x^-4))^(1/2)*(a+b*x^-4)^-1//2*(a^(1/2)+b^(1/2)*x^-2)*Elliptic.F(2*arccot(x*a^1//4*b^-1//4),1/2)+3//2*a^-7//4*b^1//4*((a^(1/2)+b^(1/2)*x^-2)^-2*(a+b*x^-4))^(1/2)*(a+b*x^-4)^-1//2*(a^(1/2)+b^(1/2)*x^-2)*Elliptic.E(2*arccot(x*a^1//4*b^-1//4),1/2))
@test integrate(x^-2*(a+b*x^-4)^-3//2, x) == :(-1//2*a^-1*x^-1*(a+b*x^-4)^-1//2+-1//4*a^-5//4*b^-1//4*((a^(1/2)+b^(1/2)*x^-2)^-2*(a+b*x^-4))^(1/2)*(a+b*x^-4)^-1//2*(a^(1/2)+b^(1/2)*x^-2)*Elliptic.F(2*arccot(x*a^1//4*b^-1//4),1/2))
@test integrate(x^-4*(a+b*x^-4)^-3//2, x) == :(-1//2*a^-1*x^-3*(a+b*x^-4)^-1//2+(1/2)*a^-1*b^-1//2*x^-1*(a+b*x^-4)^(1/2)*(a^(1/2)+b^(1/2)*x^-2)^-1+-1//2*a^-3//4*b^-3//4*((a^(1/2)+b^(1/2)*x^-2)^-2*(a+b*x^-4))^(1/2)*(a+b*x^-4)^-1//2*(a^(1/2)+b^(1/2)*x^-2)*Elliptic.E(2*arccot(x*a^1//4*b^-1//4),1/2)+1//4*a^-3//4*b^-3//4*((a^(1/2)+b^(1/2)*x^-2)^-2*(a+b*x^-4))^(1/2)*(a+b*x^-4)^-1//2*(a^(1/2)+b^(1/2)*x^-2)*Elliptic.F(2*arccot(x*a^1//4*b^-1//4),1/2))
@test integrate(x^3*(a+b*x^-4)^-5//2, x) == :(-5//4*b*a^-7//2*arctanh(a^-1//2*(a+b*x^-4)^(1/2))+1//4*a^-1*x^4*(a+b*x^-4)^-3//2+5//4*b*a^-3*(a+b*x^-4)^-1//2+5//12*b*a^-2*(a+b*x^-4)^-3//2)
@test integrate(x*(a+b*x^-4)^-5//2, x) == :(-2//3*a^-2*x^2*(a+b*x^-4)^-1//2+-1//6*a^-1*x^2*(a+b*x^-4)^-3//2+4//3*a^-3*x^2*(a+b*x^-4)^(1/2))
@test integrate(x^-1*(a+b*x^-4)^-5//2, x) == :((1/2)*a^-5//2*arctanh(a^-1//2*(a+b*x^-4)^(1/2))+-1//2*a^-2*(a+b*x^-4)^-1//2+-1//6*a^-1*(a+b*x^-4)^-3//2)
@test integrate(x^-3*(a+b*x^-4)^-5//2, x) == :(-1//2*a^-1*x^-2*(a+b*x^-4)^-3//2+-1//3*b*a^-2*x^-6*(a+b*x^-4)^-3//2)
@test integrate(x^2*(a+b*x^-4)^-5//2, x) == :(-3//4*a^-2*x^3*(a+b*x^-4)^-1//2+-1//6*a^-1*x^3*(a+b*x^-4)^-3//2+5//4*a^-3*x^3*(a+b*x^-4)^(1/2)+5//8*a^-13//4*b^3//4*((a^(1/2)+b^(1/2)*x^-2)^-2*(a+b*x^-4))^(1/2)*(a+b*x^-4)^-1//2*(a^(1/2)+b^(1/2)*x^-2)*Elliptic.F(2*arccot(x*a^1//4*b^-1//4),1/2))
@test integrate((a+b*x^-4)^-5//2, x) == :(-7//12*x*a^-2*(a+b*x^-4)^-1//2+-1//6*x*a^-1*(a+b*x^-4)^-3//2+7//4*x*a^-3*(a+b*x^-4)^(1/2)+-7//4*a^-3*b^(1/2)*x^-1*(a+b*x^-4)^(1/2)*(a^(1/2)+b^(1/2)*x^-2)^-1+-7//8*a^-11//4*b^1//4*((a^(1/2)+b^(1/2)*x^-2)^-2*(a+b*x^-4))^(1/2)*(a+b*x^-4)^-1//2*(a^(1/2)+b^(1/2)*x^-2)*Elliptic.F(2*arccot(x*a^1//4*b^-1//4),1/2)+7//4*a^-11//4*b^1//4*((a^(1/2)+b^(1/2)*x^-2)^-2*(a+b*x^-4))^(1/2)*(a+b*x^-4)^-1//2*(a^(1/2)+b^(1/2)*x^-2)*Elliptic.E(2*arccot(x*a^1//4*b^-1//4),1/2))
@test integrate(x^-2*(a+b*x^-4)^-5//2, x) == :(-5//12*a^-2*x^-1*(a+b*x^-4)^-1//2+-1//6*a^-1*x^-1*(a+b*x^-4)^-3//2+-5//24*a^-9//4*b^-1//4*((a^(1/2)+b^(1/2)*x^-2)^-2*(a+b*x^-4))^(1/2)*(a+b*x^-4)^-1//2*(a^(1/2)+b^(1/2)*x^-2)*Elliptic.F(2*arccot(x*a^1//4*b^-1//4),1/2))
@test integrate(x^-4*(a+b*x^-4)^-5//2, x) == :(-1//4*a^-2*x^-3*(a+b*x^-4)^-1//2+-1//6*a^-1*x^-3*(a+b*x^-4)^-3//2+1//4*a^-2*b^-1//2*x^-1*(a+b*x^-4)^(1/2)*(a^(1/2)+b^(1/2)*x^-2)^-1+-1//4*a^-7//4*b^-3//4*((a^(1/2)+b^(1/2)*x^-2)^-2*(a+b*x^-4))^(1/2)*(a+b*x^-4)^-1//2*(a^(1/2)+b^(1/2)*x^-2)*Elliptic.E(2*arccot(x*a^1//4*b^-1//4),1/2)+1//8*a^-7//4*b^-3//4*((a^(1/2)+b^(1/2)*x^-2)^-2*(a+b*x^-4))^(1/2)*(a+b*x^-4)^-1//2*(a^(1/2)+b^(1/2)*x^-2)*Elliptic.F(2*arccot(x*a^1//4*b^-1//4),1/2))
@test integrate((a+b*x^-5)^-1, x) == :(x*a^-1+-1//5*a^-6//5*b^1//5*log(b^1//5+x*a^1//5)+-1//5*a^-6//5*b^1//5*(5//2+(1/2)*5^(1/2))^(1/2)*arctan((1+-2//5*5^(1/2))^(1/2)+2*x*2^(1/2)*a^1//5*b^-1//5*(5+5^(1/2))^-1//2)+1//5*a^-6//5*b^1//5*(5//2+-1//2*5^(1/2))^(1/2)*arctan((1+2//5*5^(1/2))^(1/2)+-1*x*a^1//5*b^-1//5*(2+2//5*5^(1/2))^(1/2))+1//20*a^-6//5*b^1//5*(1+5^(1/2))*log(b^2//5+a^2//5*x^2+-1*x*a^1//5*b^1//5*(1/2+(1/2)*5^(1/2)))+1//20*a^-6//5*b^1//5*(1+-1*5^(1/2))*log(b^2//5+a^2//5*x^2+-1*x*a^1//5*b^1//5*(1/2+-1//2*5^(1/2))))
@test integrate(x^-1*(a+b*x^-5)^-1//2, x) == :(2//5*a^-1//2*arctanh(a^-1//2*(a+b*x^-5)^(1/2)))
@test integrate(x^-1*(-1a+b*x^-5)^-1//2, x) == :(-2//5*a^-1//2*arctan(a^-1//2*(-1a+b*x^-5)^(1/2)))
@test integrate((a+b*x^-6)^-1, x) == :(x*a^-1+-1//3*a^-7//6*b^1//6*arctan(x*a^1//6*b^-1//6)+-1//6*a^-7//6*b^1//6*arctan(b^-1//6*(3^(1/2)*b^1//6+2*x*a^1//6))+1//6*a^-7//6*b^1//6*arctan(b^-1//6*(3^(1/2)*b^1//6+-2*x*a^1//6))+-1//12*3^(1/2)*a^-7//6*b^1//6*log(b^1//3+a^1//3*x^2+x*3^(1/2)*a^1//6*b^1//6)+1//12*3^(1/2)*a^-7//6*b^1//6*log(b^1//3+a^1//3*x^2+-1*x*3^(1/2)*a^1//6*b^1//6))
@test integrate((a+b*x^-8)^-1, x) == :(x*a^-1+1//4*b^1//8*(-1a)^-9//8*arctan(x*b^-1//8*(-1a)^1//8)+1//4*b^1//8*(-1a)^-9//8*arctanh(x*b^-1//8*(-1a)^1//8)+-1//8*2^(1/2)*b^1//8*(-1a)^-9//8*arctan(1+-1*x*2^(1/2)*b^-1//8*(-1a)^1//8)+-1//16*2^(1/2)*b^1//8*(-1a)^-9//8*log(b^1//4+x^2*(-1a)^1//4+-1*x*2^(1/2)*b^1//8*(-1a)^1//8)+1//8*2^(1/2)*b^1//8*(-1a)^-9//8*arctan(1+x*2^(1/2)*b^-1//8*(-1a)^1//8)+1//16*2^(1/2)*b^1//8*(-1a)^-9//8*log(b^1//4+x^2*(-1a)^1//4+x*2^(1/2)*b^1//8*(-1a)^1//8))
@test integrate(x^4*(a+b*x^(1/2)), x) == :(1//5*a*x^5+2//11*b*x^11//2)
@test integrate(x^3*(a+b*x^(1/2)), x) == :(1//4*a*x^4+2//9*b*x^9//2)
@test integrate(x^2*(a+b*x^(1/2)), x) == :(1//3*a*x^3+2//7*b*x^7//2)
@test integrate(x*(a+b*x^(1/2)), x) == :((1/2)*a*x^2+2//5*b*x^5//2)
@test integrate(a+b*x^(1/2), x) == :(a*x+2//3*b*x^3//2)
@test integrate(x^-1*(a+b*x^(1/2)), x) == :(a*log(x)+2*b*x^(1/2))
@test integrate(x^-2*(a+b*x^(1/2)), x) == :(-1*a*x^-1+-2*b*x^-1//2)
@test integrate(x^-3*(a+b*x^(1/2)), x) == :(-2//3*b*x^-3//2+-1//2*a*x^-2)
@test integrate(x^-4*(a+b*x^(1/2)), x) == :(-2//5*b*x^-5//2+-1//3*a*x^-3)
@test integrate(x^4*(a+b*x^(1/2))^2, x) == :(1//5*a^2*x^5+1//6*b^2*x^6+4//11*a*b*x^11//2)
@test integrate(x^3*(a+b*x^(1/2))^2, x) == :(1//4*a^2*x^4+1//5*b^2*x^5+4//9*a*b*x^9//2)
@test integrate(x^2*(a+b*x^(1/2))^2, x) == :(1//3*a^2*x^3+1//4*b^2*x^4+4//7*a*b*x^7//2)
@test integrate(x*(a+b*x^(1/2))^2, x) == :((1/2)*a^2*x^2+1//3*b^2*x^3+4//5*a*b*x^5//2)
@test integrate((a+b*x^(1/2))^2, x) == :(x*a^2+(1/2)*b^2*x^2+4//3*a*b*x^3//2)
@test integrate(x^-1*(a+b*x^(1/2))^2, x) == :(x*b^2+a^2*log(x)+4*a*b*x^(1/2))
@test integrate(x^-2*(a+b*x^(1/2))^2, x) == :(b^2*log(x)+-1*a^2*x^-1+-4*a*b*x^-1//2)
@test integrate(x^-3*(a+b*x^(1/2))^2, x) == :(-1*b^2*x^-1+-1//2*a^2*x^-2+-4//3*a*b*x^-3//2)
@test integrate(x^-4*(a+b*x^(1/2))^2, x) == :(-1//2*b^2*x^-2+-1//3*a^2*x^-3+-4//5*a*b*x^-5//2)
@test integrate(x^-5*(a+b*x^(1/2))^2, x) == :(-1//3*b^2*x^-3+-1//4*a^2*x^-4+-4//7*a*b*x^-7//2)
@test integrate(x^4*(a+b*x^(1/2))^3, x) == :(1//5*a^3*x^5+2//13*b^3*x^13//2+(1/2)*a*b^2*x^6+6//11*b*a^2*x^11//2)
@test integrate(x^3*(a+b*x^(1/2))^3, x) == :(1//4*a^3*x^4+2//11*b^3*x^11//2+2//3*b*a^2*x^9//2+3//5*a*b^2*x^5)
@test integrate(x^2*(a+b*x^(1/2))^3, x) == :(1//3*a^3*x^3+2//9*b^3*x^9//2+3//4*a*b^2*x^4+6//7*b*a^2*x^7//2)
@test integrate(x*(a+b*x^(1/2))^3, x) == :((1/2)*a^3*x^2+2//7*b^3*x^7//2+a*b^2*x^3+6//5*b*a^2*x^5//2)
@test integrate((a+b*x^(1/2))^3, x) == :(2//5*b^-2*(a+b*x^(1/2))^5+-1//2*a*b^-2*(a+b*x^(1/2))^4)
@test integrate(x^-1*(a+b*x^(1/2))^3, x) == :(a^3*log(x)+2//3*b^3*x^3//2+3*a*x*b^2+6*b*a^2*x^(1/2))
@test integrate(x^-2*(a+b*x^(1/2))^3, x) == :(-1*a^3*x^-1+2*b^3*x^(1/2)+-6*b*a^2*x^-1//2+3*a*b^2*log(x))
@test integrate(x^-3*(a+b*x^(1/2))^3, x) == :(-1//2*a^-1*x^-2*(a+b*x^(1/2))^4)
@test integrate(x^-4*(a+b*x^(1/2))^3, x) == :(-2//3*b^3*x^-3//2+-1//3*a^3*x^-3+-6//5*b*a^2*x^-5//2+-3//2*a*b^2*x^-2)
@test integrate(x^-5*(a+b*x^(1/2))^3, x) == :(-2//5*b^3*x^-5//2+-1//4*a^3*x^-4+-1*a*b^2*x^-3+-6//7*b*a^2*x^-7//2)
@test integrate(x^-6*(a+b*x^(1/2))^3, x) == :(-2//7*b^3*x^-7//2+-1//5*a^3*x^-5+-3//4*a*b^2*x^-4+-2//3*b*a^2*x^-9//2)
@test integrate(x^4*(a+b*x^(1/2))^5, x) == :(1//5*a^5*x^5+2//15*b^5*x^15//2+5//3*a^3*b^2*x^6+5//7*a*b^4*x^7+10//11*b*a^4*x^11//2+20//13*a^2*b^3*x^13//2)
@test integrate(x^3*(a+b*x^(1/2))^5, x) == :(1//4*a^5*x^4+2//13*b^5*x^13//2+2*a^3*b^2*x^5+5//6*a*b^4*x^6+10//9*b*a^4*x^9//2+20//11*a^2*b^3*x^11//2)
@test integrate(x^2*(a+b*x^(1/2))^5, x) == :(1//3*a^5*x^3+2//11*b^5*x^11//2+a*b^4*x^5+5//2*a^3*b^2*x^4+10//7*b*a^4*x^7//2+20//9*a^2*b^3*x^9//2)
@test integrate(x*(a+b*x^(1/2))^5, x) == :(2//9*b^-4*(a+b*x^(1/2))^9+-3//4*a*b^-4*(a+b*x^(1/2))^8+-1//3*a^3*b^-4*(a+b*x^(1/2))^6+6//7*a^2*b^-4*(a+b*x^(1/2))^7)
@test integrate((a+b*x^(1/2))^5, x) == :(2//7*b^-2*(a+b*x^(1/2))^7+-1//3*a*b^-2*(a+b*x^(1/2))^6)
@test integrate(x^-1*(a+b*x^(1/2))^5, x) == :(a^5*log(x)+2//5*b^5*x^5//2+10*b*a^4*x^(1/2)+10*x*a^3*b^2+5//2*a*b^4*x^2+20//3*a^2*b^3*x^3//2)
@test integrate(x^-2*(a+b*x^(1/2))^5, x) == :(-1*a^5*x^-1+2//3*b^5*x^3//2+-10*b*a^4*x^-1//2+5*a*x*b^4+10*a^3*b^2*log(x)+20*a^2*b^3*x^(1/2))
@test integrate(x^-3*(a+b*x^(1/2))^5, x) == :(2*b^5*x^(1/2)+-1//2*a^5*x^-2+-20*a^2*b^3*x^-1//2+-10*a^3*b^2*x^-1+5*a*b^4*log(x)+-10//3*b*a^4*x^-3//2)
@test integrate(x^-4*(a+b*x^(1/2))^5, x) == :(-1//3*a^-1*x^-3*(a+b*x^(1/2))^6)
@test integrate(x^-5*(a+b*x^(1/2))^5, x) == :(-1//4*a^-1*x^-4*(a+b*x^(1/2))^6+-1//84*a^-3*b^2*x^-3*(a+b*x^(1/2))^6+1//14*b*a^-2*x^-7//2*(a+b*x^(1/2))^6)
@test integrate(x^-6*(a+b*x^(1/2))^5, x) == :(-2//5*b^5*x^-5//2+-1//5*a^5*x^-5+-20//7*a^2*b^3*x^-7//2+-10//9*b*a^4*x^-9//2+-5//2*a^3*b^2*x^-4+-5//3*a*b^4*x^-3)
@test integrate(x^-7*(a+b*x^(1/2))^5, x) == :(-2//7*b^5*x^-7//2+-1//6*a^5*x^-6+-2*a^3*b^2*x^-5+-20//9*a^2*b^3*x^-9//2+-10//11*b*a^4*x^-11//2+-5//4*a*b^4*x^-4)
@test integrate(x^4*(a+b*x^(1/2))^10, x) == :(1//5*a^10*x^5+1//10*b^10*x^10+5*a^2*b^8*x^9+30*a^6*b^4*x^7+15//2*a^8*b^2*x^6+20//11*b*a^9*x^11//2+20//19*a*b^9*x^19//2+105//4*a^4*b^6*x^8+168//5*a^5*b^5*x^15//2+240//13*a^7*b^3*x^13//2+240//17*a^3*b^7*x^17//2)
@test integrate(x^3*(a+b*x^(1/2))^10, x) == :(1//9*b^-8*(a+b*x^(1/2))^18+5*a^4*b^-8*(a+b*x^(1/2))^14+-42//13*a^5*b^-8*(a+b*x^(1/2))^13+-14//3*a^3*b^-8*(a+b*x^(1/2))^15+-14//17*a*b^-8*(a+b*x^(1/2))^17+-2//11*a^7*b^-8*(a+b*x^(1/2))^11+7//6*a^6*b^-8*(a+b*x^(1/2))^12+21//8*a^2*b^-8*(a+b*x^(1/2))^16)
@test integrate(x^2*(a+b*x^(1/2))^10, x) == :(1//8*b^-6*(a+b*x^(1/2))^16+-20//13*a^3*b^-6*(a+b*x^(1/2))^13+-2//3*a*b^-6*(a+b*x^(1/2))^15+-2//11*a^5*b^-6*(a+b*x^(1/2))^11+5//6*a^4*b^-6*(a+b*x^(1/2))^12+10//7*a^2*b^-6*(a+b*x^(1/2))^14)
@test integrate(x*(a+b*x^(1/2))^10, x) == :(1//7*b^-4*(a+b*x^(1/2))^14+(1/2)*a^2*b^-4*(a+b*x^(1/2))^12+-6//13*a*b^-4*(a+b*x^(1/2))^13+-2//11*a^3*b^-4*(a+b*x^(1/2))^11)
@test integrate((a+b*x^(1/2))^10, x) == :(1//6*b^-2*(a+b*x^(1/2))^12+-2//11*a*b^-2*(a+b*x^(1/2))^11)
@test integrate(x^-1*(a+b*x^(1/2))^10, x) == :(a^10*log(x)+1//5*b^10*x^5+20*b*a^9*x^(1/2)+45*x*a^8*b^2+70*a^4*b^6*x^3+80*a^7*b^3*x^3//2+105*a^6*b^4*x^2+20//9*a*b^9*x^9//2+45//4*a^2*b^8*x^4+240//7*a^3*b^7*x^7//2+504//5*a^5*b^5*x^5//2)
@test integrate(x^-2*(a+b*x^(1/2))^10, x) == :(-1*a^10*x^-1+1//4*b^10*x^4+-20*b*a^9*x^-1//2+15*a^2*b^8*x^3+45*a^8*b^2*log(x)+48*a^3*b^7*x^5//2+105*a^4*b^6*x^2+168*a^5*b^5*x^3//2+210*x*a^6*b^4+240*a^7*b^3*x^(1/2)+20//7*a*b^9*x^7//2)
@test integrate(x^-3*(a+b*x^(1/2))^10, x) == :(-1//2*a^10*x^-2+1//3*b^10*x^3+-240*a^7*b^3*x^-1//2+-45*a^8*b^2*x^-1+4*a*b^9*x^5//2+80*a^3*b^7*x^3//2+210*x*a^4*b^6+210*a^6*b^4*log(x)+504*a^5*b^5*x^(1/2)+-20//3*b*a^9*x^-3//2+45//2*a^2*b^8*x^2)
@test integrate(x^-4*(a+b*x^(1/2))^10, x) == :((1/2)*b^10*x^2+-1//3*a^10*x^-3+-504*a^5*b^5*x^-1//2+-210*a^6*b^4*x^-1+-80*a^7*b^3*x^-3//2+-4*b*a^9*x^-5//2+45*x*a^2*b^8+210*a^4*b^6*log(x)+240*a^3*b^7*x^(1/2)+-45//2*a^8*b^2*x^-2+20//3*a*b^9*x^3//2)
@test integrate(x^-5*(a+b*x^(1/2))^10, x) == :(x*b^10+-1//4*a^10*x^-4+-240*a^3*b^7*x^-1//2+-210*a^4*b^6*x^-1+-168*a^5*b^5*x^-3//2+-105*a^6*b^4*x^-2+-48*a^7*b^3*x^-5//2+-15*a^8*b^2*x^-3+20*a*b^9*x^(1/2)+45*a^2*b^8*log(x)+-20//7*b*a^9*x^-7//2)
@test integrate(x^-6*(a+b*x^(1/2))^10, x) == :(b^10*log(x)+-1//5*a^10*x^-5+-105*a^4*b^6*x^-2+-80*a^3*b^7*x^-3//2+-70*a^6*b^4*x^-3+-45*a^2*b^8*x^-1+-20*a*b^9*x^-1//2+-504//5*a^5*b^5*x^-5//2+-240//7*a^7*b^3*x^-7//2+-45//4*a^8*b^2*x^-4+-20//9*b*a^9*x^-9//2)
@test integrate(x^-7*(a+b*x^(1/2))^10, x) == :(-1//6*a^-1*x^-6*(a+b*x^(1/2))^11+1//66*b*a^-2*x^-11//2*(a+b*x^(1/2))^11)
@test integrate(x^-8*(a+b*x^(1/2))^10, x) == :(-1//7*a^-1*x^-7*(a+b*x^(1/2))^11+-1//182*a^-3*b^2*x^-6*(a+b*x^(1/2))^11+1//2002*a^-4*b^3*x^-11//2*(a+b*x^(1/2))^11+3//91*b*a^-2*x^-13//2*(a+b*x^(1/2))^11)
@test integrate(x^-9*(a+b*x^(1/2))^10, x) == :(-1//8*a^-1*x^-8*(a+b*x^(1/2))^11+-1//84*a^-3*b^2*x^-7*(a+b*x^(1/2))^11+-1//2184*a^-5*b^4*x^-6*(a+b*x^(1/2))^11+1//24*b*a^-2*x^-15//2*(a+b*x^(1/2))^11+1//364*a^-4*b^3*x^-13//2*(a+b*x^(1/2))^11+1//24024*a^-6*b^5*x^-11//2*(a+b*x^(1/2))^11)
@test integrate(x^-10*(a+b*x^(1/2))^10, x) == :(-1//4*b^10*x^-4+-1//9*a^10*x^-9+-35*a^4*b^6*x^-6+-30*a^6*b^4*x^-7+-16*a^7*b^3*x^-15//2+-9*a^2*b^8*x^-5+-504//13*a^5*b^5*x^-13//2+-240//11*a^3*b^7*x^-11//2+-45//8*a^8*b^2*x^-8+-20//9*a*b^9*x^-9//2+-20//17*b*a^9*x^-17//2)
@test integrate(x^-11*(a+b*x^(1/2))^10, x) == :(-1//5*b^10*x^-5+-1//10*a^10*x^-10+-30*a^4*b^6*x^-7+-5*a^8*b^2*x^-9+-240//13*a^3*b^7*x^-13//2+-240//17*a^7*b^3*x^-17//2+-168//5*a^5*b^5*x^-15//2+-105//4*a^6*b^4*x^-8+-20//11*a*b^9*x^-11//2+-20//19*b*a^9*x^-19//2+-15//2*a^2*b^8*x^-6)
@test integrate(x^5*(a+b*x^(1/2))^15, x) == :(2//27*b^-12*(a+b*x^(1/2))^27+-42*a^5*b^-12*(a+b*x^(1/2))^22+-33*a^7*b^-12*(a+b*x^(1/2))^20+44*a^6*b^-12*(a+b*x^(1/2))^21+-55//4*a^3*b^-12*(a+b*x^(1/2))^24+-55//9*a^9*b^-12*(a+b*x^(1/2))^18+-11//13*a*b^-12*(a+b*x^(1/2))^26+-1//8*a^11*b^-12*(a+b*x^(1/2))^16+22//5*a^2*b^-12*(a+b*x^(1/2))^25+22//17*a^10*b^-12*(a+b*x^(1/2))^17+330//19*a^8*b^-12*(a+b*x^(1/2))^19+660//23*a^4*b^-12*(a+b*x^(1/2))^23)
@test integrate(x^4*(a+b*x^(1/2))^15, x) == :(2//25*b^-10*(a+b*x^(1/2))^25+-4*a^7*b^-10*(a+b*x^(1/2))^18+12*a^4*b^-10*(a+b*x^(1/2))^21+-84//11*a^3*b^-10*(a+b*x^(1/2))^22+-63//5*a^5*b^-10*(a+b*x^(1/2))^20+-3//4*a*b^-10*(a+b*x^(1/2))^24+-1//8*a^9*b^-10*(a+b*x^(1/2))^16+18//17*a^8*b^-10*(a+b*x^(1/2))^17+72//23*a^2*b^-10*(a+b*x^(1/2))^23+168//19*a^6*b^-10*(a+b*x^(1/2))^19)
@test integrate(x^3*(a+b*x^(1/2))^15, x) == :(2//23*b^-8*(a+b*x^(1/2))^23+2*a^2*b^-8*(a+b*x^(1/2))^21+-7//2*a^3*b^-8*(a+b*x^(1/2))^20+-7//3*a^5*b^-8*(a+b*x^(1/2))^18+-7//11*a*b^-8*(a+b*x^(1/2))^22+-1//8*a^7*b^-8*(a+b*x^(1/2))^16+14//17*a^6*b^-8*(a+b*x^(1/2))^17+70//19*a^4*b^-8*(a+b*x^(1/2))^19)
@test integrate(x^2*(a+b*x^(1/2))^15, x) == :(2//21*b^-6*(a+b*x^(1/2))^21+-10//9*a^3*b^-6*(a+b*x^(1/2))^18+-1//2*a*b^-6*(a+b*x^(1/2))^20+-1//8*a^5*b^-6*(a+b*x^(1/2))^16+10//17*a^4*b^-6*(a+b*x^(1/2))^17+20//19*a^2*b^-6*(a+b*x^(1/2))^19)
@test integrate(x*(a+b*x^(1/2))^15, x) == :(2//19*b^-4*(a+b*x^(1/2))^19+-1//3*a*b^-4*(a+b*x^(1/2))^18+-1//8*a^3*b^-4*(a+b*x^(1/2))^16+6//17*a^2*b^-4*(a+b*x^(1/2))^17)
@test integrate((a+b*x^(1/2))^15, x) == :(2//17*b^-2*(a+b*x^(1/2))^17+-1//8*a*b^-2*(a+b*x^(1/2))^16)
@test integrate(x^-1*(a+b*x^(1/2))^15, x) == :(a^15*log(x)+2//15*b^15*x^15//2+30*b*a^14*x^(1/2)+105*x*a^13*b^2+15//7*a*b^14*x^7+210//13*a^2*b^13*x^13//2+455//6*a^3*b^12*x^6+910//3*a^12*b^3*x^3//2+1365//2*a^11*b^4*x^2+2730//11*a^4*b^11*x^11//2+3003//5*a^5*b^10*x^5+5005//3*a^9*b^6*x^3+6006//5*a^10*b^5*x^5//2+6435//4*a^7*b^8*x^4+10010//9*a^6*b^9*x^9//2+12870//7*a^8*b^7*x^7//2)
@test integrate(x^-2*(a+b*x^(1/2))^15, x) == :(-1*a^15*x^-1+2//13*b^15*x^13//2+-30*b*a^14*x^-1//2+91*a^3*b^12*x^5+105*a^13*b^2*log(x)+910*a^12*b^3*x^(1/2)+1365*x*a^11*b^4+1430*a^6*b^9*x^7//2+2002*a^10*b^5*x^3//2+2145*a^7*b^8*x^3+2574*a^8*b^7*x^5//2+5//2*a*b^14*x^6+210//11*a^2*b^13*x^11//2+910//3*a^4*b^11*x^9//2+3003//4*a^5*b^10*x^4+5005//2*a^9*b^6*x^2)
@test integrate(x^-3*(a+b*x^(1/2))^15, x) == :(-1//2*a^15*x^-2+2//11*b^15*x^11//2+-910*a^12*b^3*x^-1//2+-105*a^13*b^2*x^-1+-10*b*a^14*x^-3//2+3*a*b^14*x^5+390*a^4*b^11*x^7//2+1001*a^5*b^10*x^3+1365*a^11*b^4*log(x)+2002*a^6*b^9*x^5//2+4290*a^8*b^7*x^3//2+5005*x*a^9*b^6+6006*a^10*b^5*x^(1/2)+70//3*a^2*b^13*x^9//2+455//4*a^3*b^12*x^4+6435//2*a^7*b^8*x^2)
@test integrate(x^-4*(a+b*x^(1/2))^15, x) == :(-1//3*a^15*x^-3+2//9*b^15*x^9//2+-6006*a^10*b^5*x^-1//2+-1365*a^11*b^4*x^-1+-6*b*a^14*x^-5//2+30*a^2*b^13*x^7//2+546*a^4*b^11*x^5//2+5005*a^9*b^6*log(x)+6435*x*a^7*b^8+12870*a^8*b^7*x^(1/2)+-910//3*a^12*b^3*x^-3//2+-105//2*a^13*b^2*x^-2+15//4*a*b^14*x^4+455//3*a^3*b^12*x^3+3003//2*a^5*b^10*x^2+10010//3*a^6*b^9*x^3//2)
@test integrate(x^-6*(a+b*x^(1/2))^15, x) == :(-1//5*a^15*x^-5+2//5*b^15*x^5//2+-10010*a^6*b^9*x^-1//2+-6435*a^7*b^8*x^-1+-4290*a^8*b^7*x^-3//2+-455*a^11*b^4*x^-3+-130*a^12*b^3*x^-7//2+70*a^2*b^13*x^3//2+455*x*a^3*b^12+2730*a^4*b^11*x^(1/2)+3003*a^5*b^10*log(x)+-6006//5*a^10*b^5*x^-5//2+-5005//2*a^9*b^6*x^-2+-105//4*a^13*b^2*x^-4+-10//3*b*a^14*x^-9//2+15//2*a*b^14*x^2)
@test integrate(x^-7*(a+b*x^(1/2))^15, x) == :(-1//6*a^15*x^-6+2//3*b^15*x^3//2+-3003*a^5*b^10*x^-1+-2730*a^4*b^11*x^-1//2+-2574*a^8*b^7*x^-5//2+-858*a^10*b^5*x^-7//2+-21*a^13*b^2*x^-5+15*a*x*b^14+210*a^2*b^13*x^(1/2)+455*a^3*b^12*log(x)+-10010//3*a^6*b^9*x^-3//2+-6435//2*a^7*b^8*x^-2+-5005//3*a^9*b^6*x^-3+-1365//4*a^11*b^4*x^-4+-910//9*a^12*b^3*x^-9//2+-30//11*b*a^14*x^-11//2)
@test integrate(x^-8*(a+b*x^(1/2))^15, x) == :(2*b^15*x^(1/2)+-1//7*a^15*x^-7+-2145*a^7*b^8*x^-3+-2002*a^6*b^9*x^-5//2+-910*a^4*b^11*x^-3//2+-455*a^3*b^12*x^-1+-273*a^11*b^4*x^-5+-210*a^2*b^13*x^-1//2+15*a*b^14*log(x)+-12870//7*a^8*b^7*x^-7//2+-5005//4*a^9*b^6*x^-4+-3003//2*a^5*b^10*x^-2+-2002//3*a^10*b^5*x^-9//2+-910//11*a^12*b^3*x^-11//2+-35//2*a^13*b^2*x^-6+-30//13*b*a^14*x^-13//2)
@test integrate(x^-9*(a+b*x^(1/2))^15, x) == :(-1//8*a^-1*x^-8*(a+b*x^(1/2))^16)
@test integrate(x^-10*(a+b*x^(1/2))^15, x) == :(-1//9*a^-1*x^-9*(a+b*x^(1/2))^16+-1//1224*a^-3*b^2*x^-8*(a+b*x^(1/2))^16+2//153*b*a^-2*x^-17//2*(a+b*x^(1/2))^16)
@test integrate(x^-11*(a+b*x^(1/2))^15, x) == :(-1//10*a^-1*x^-10*(a+b*x^(1/2))^16+-1//285*a^-3*b^2*x^-9*(a+b*x^(1/2))^16+-1//38760*a^-5*b^4*x^-8*(a+b*x^(1/2))^16+2//95*b*a^-2*x^-19//2*(a+b*x^(1/2))^16+2//4845*a^-4*b^3*x^-17//2*(a+b*x^(1/2))^16)
@test integrate(x^-12*(a+b*x^(1/2))^15, x) == :(-1//11*a^-1*x^-11*(a+b*x^(1/2))^16+-1//154*a^-3*b^2*x^-10*(a+b*x^(1/2))^16+-1//4389*a^-5*b^4*x^-9*(a+b*x^(1/2))^16+-1//596904*a^-7*b^6*x^-8*(a+b*x^(1/2))^16+2//77*b*a^-2*x^-21//2*(a+b*x^(1/2))^16+2//1463*a^-4*b^3*x^-19//2*(a+b*x^(1/2))^16+2//74613*a^-6*b^5*x^-17//2*(a+b*x^(1/2))^16)
@test integrate(x^-13*(a+b*x^(1/2))^15, x) == :(-1//12*a^-1*x^-12*(a+b*x^(1/2))^16+-7//759*a^-3*b^2*x^-11*(a+b*x^(1/2))^16+-1//1518*a^-5*b^4*x^-10*(a+b*x^(1/2))^16+-1//43263*a^-7*b^6*x^-9*(a+b*x^(1/2))^16+-1//5883768*a^-9*b^8*x^-8*(a+b*x^(1/2))^16+2//69*b*a^-2*x^-23//2*(a+b*x^(1/2))^16+2//759*a^-4*b^3*x^-21//2*(a+b*x^(1/2))^16+2//14421*a^-6*b^5*x^-19//2*(a+b*x^(1/2))^16+2//735471*a^-8*b^7*x^-17//2*(a+b*x^(1/2))^16)
@test integrate(x^-14*(a+b*x^(1/2))^15, x) == :(-1//13*a^-1*x^-13*(a+b*x^(1/2))^16+-21//16445*a^-5*b^4*x^-11*(a+b*x^(1/2))^16+-3//260*a^-3*b^2*x^-12*(a+b*x^(1/2))^16+-3//32890*a^-7*b^6*x^-10*(a+b*x^(1/2))^16+-1//312455*a^-9*b^8*x^-9*(a+b*x^(1/2))^16+-1//42493880*a^-11*b^10*x^-8*(a+b*x^(1/2))^16+2//65*b*a^-2*x^-25//2*(a+b*x^(1/2))^16+2//5311735*a^-10*b^9*x^-17//2*(a+b*x^(1/2))^16+6//1495*a^-4*b^3*x^-23//2*(a+b*x^(1/2))^16+6//16445*a^-6*b^5*x^-21//2*(a+b*x^(1/2))^16+6//312455*a^-8*b^7*x^-19//2*(a+b*x^(1/2))^16)
@test integrate(x^-15*(a+b*x^(1/2))^15, x) == :(-2//13*b^15*x^-13//2+-1//14*a^15*x^-14+-455*a^9*b^6*x^-11+-14*a^2*b^13*x^-15//2+-10010//19*a^6*b^9*x^-19//2+-6006//23*a^10*b^5*x^-23//2+-4290//7*a^8*b^7*x^-21//2+-2730//17*a^4*b^11*x^-17//2+-1287//2*a^7*b^8*x^-10+-1001//3*a^5*b^10*x^-9+-455//4*a^11*b^4*x^-12+-455//8*a^3*b^12*x^-8+-182//5*a^12*b^3*x^-25//2+-105//13*a^13*b^2*x^-13+-15//7*a*b^14*x^-7+-10//9*b*a^14*x^-27//2)
@test integrate(x^-16*(a+b*x^(1/2))^15, x) == :(-2//15*b^15*x^-15//2+-1//15*a^15*x^-15+-585*a^7*b^8*x^-11+-105*a^11*b^4*x^-13+-12870//23*a^8*b^7*x^-23//2+-6006//25*a^10*b^5*x^-25//2+-5005//12*a^9*b^6*x^-12+-3003//10*a^5*b^10*x^-10+-2730//19*a^4*b^11*x^-19//2+-1430//3*a^6*b^9*x^-21//2+-910//27*a^12*b^3*x^-27//2+-455//9*a^3*b^12*x^-9+-210//17*a^2*b^13*x^-17//2+-30//29*b*a^14*x^-29//2+-15//2*a^13*b^2*x^-14+-15//8*a*b^14*x^-8)
@test integrate(x^-17*(a+b*x^(1/2))^15, x) == :(-2//17*b^15*x^-17//2+-1//16*a^15*x^-16+-385*a^9*b^6*x^-13+-273*a^5*b^10*x^-11+-130*a^4*b^11*x^-21//2+-7*a^13*b^2*x^-15+-10010//23*a^6*b^9*x^-23//2+-2574//5*a^8*b^7*x^-25//2+-2145//4*a^7*b^8*x^-12+-2002//9*a^10*b^5*x^-27//2+-910//29*a^12*b^3*x^-29//2+-210//19*a^2*b^13*x^-19//2+-195//2*a^11*b^4*x^-14+-91//2*a^3*b^12*x^-10+-30//31*b*a^14*x^-31//2+-5//3*a*b^14*x^-9)
@test integrate(x^3*(a+b*x^(1/2))^-1, x) == :(2//7*b^-1*x^7//2+-1*x*a^5*b^-6+-2*a^7*b^-8*log(a+b*x^(1/2))+2*a^6*b^-7*x^(1/2)+-1//2*a^3*b^-4*x^2+-1//3*a*b^-2*x^3+2//3*a^4*b^-5*x^3//2+2//5*a^2*b^-3*x^5//2)
@test integrate(x^2*(a+b*x^(1/2))^-1, x) == :(2//5*b^-1*x^5//2+-1*x*a^3*b^-4+-2*a^5*b^-6*log(a+b*x^(1/2))+2*a^4*b^-5*x^(1/2)+-1//2*a*b^-2*x^2+2//3*a^2*b^-3*x^3//2)
@test integrate(x*(a+b*x^(1/2))^-1, x) == :(2//3*b^-1*x^3//2+-1*a*x*b^-2+-2*a^3*b^-4*log(a+b*x^(1/2))+2*a^2*b^-3*x^(1/2))
@test integrate((a+b*x^(1/2))^-1, x) == :(2*b^-1*x^(1/2)+-2*a*b^-2*log(a+b*x^(1/2)))
@test integrate(x^-1*(a+b*x^(1/2))^-1, x) == :(a^-1*log(x)+-2*a^-1*log(a+b*x^(1/2)))
@test integrate(x^-2*(a+b*x^(1/2))^-1, x) == :(-1*a^-1*x^-1+a^-3*b^2*log(x)+-2*a^-3*b^2*log(a+b*x^(1/2))+2*b*a^-2*x^-1//2)
@test integrate(x^-3*(a+b*x^(1/2))^-1, x) == :(-1//2*a^-1*x^-2+a^-5*b^4*log(x)+-1*a^-3*b^2*x^-1+-2*a^-5*b^4*log(a+b*x^(1/2))+2*a^-4*b^3*x^-1//2+2//3*b*a^-2*x^-3//2)
@test integrate(x^-4*(a+b*x^(1/2))^-1, x) == :(-1//3*a^-1*x^-3+a^-7*b^6*log(x)+-1*a^-5*b^4*x^-1+-2*a^-7*b^6*log(a+b*x^(1/2))+2*a^-6*b^5*x^-1//2+-1//2*a^-3*b^2*x^-2+2//3*a^-4*b^3*x^-3//2+2//5*b*a^-2*x^-5//2)
@test integrate(x^3*(a+b*x^(1/2))^-2, x) == :(1//3*b^-2*x^3+-12*a^5*b^-7*x^(1/2)+2*a^7*b^-8*(a+b*x^(1/2))^-1+5*x*a^4*b^-6+14*a^6*b^-8*log(a+b*x^(1/2))+-8//3*a^3*b^-5*x^3//2+-4//5*a*b^-3*x^5//2+3//2*a^2*b^-4*x^2)
@test integrate(x^2*(a+b*x^(1/2))^-2, x) == :((1/2)*b^-2*x^2+-8*a^3*b^-5*x^(1/2)+2*a^5*b^-6*(a+b*x^(1/2))^-1+3*x*a^2*b^-4+10*a^4*b^-6*log(a+b*x^(1/2))+-4//3*a*b^-3*x^3//2)
@test integrate(x*(a+b*x^(1/2))^-2, x) == :(x*b^-2+-4*a*b^-3*x^(1/2)+2*a^3*b^-4*(a+b*x^(1/2))^-1+6*a^2*b^-4*log(a+b*x^(1/2)))
@test integrate((a+b*x^(1/2))^-2, x) == :(2*b^-2*log(a+b*x^(1/2))+2*a*b^-2*(a+b*x^(1/2))^-1)
@test integrate(x^-1*(a+b*x^(1/2))^-2, x) == :(a^-2*log(x)+-2*a^-2*log(a+b*x^(1/2))+2*a^-1*(a+b*x^(1/2))^-1)
@test integrate(x^-2*(a+b*x^(1/2))^-2, x) == :(-1*a^-2*x^-1+-6*a^-4*b^2*log(a+b*x^(1/2))+2*a^-3*b^2*(a+b*x^(1/2))^-1+3*a^-4*b^2*log(x)+4*b*a^-3*x^-1//2)
@test integrate(x^-3*(a+b*x^(1/2))^-2, x) == :(-1//2*a^-2*x^-2+-10*a^-6*b^4*log(a+b*x^(1/2))+-3*a^-4*b^2*x^-1+2*a^-5*b^4*(a+b*x^(1/2))^-1+5*a^-6*b^4*log(x)+8*a^-5*b^3*x^-1//2+4//3*b*a^-3*x^-3//2)
@test integrate(x^-4*(a+b*x^(1/2))^-2, x) == :(-1//3*a^-2*x^-3+-14*a^-8*b^6*log(a+b*x^(1/2))+-5*a^-6*b^4*x^-1+2*a^-7*b^6*(a+b*x^(1/2))^-1+7*a^-8*b^6*log(x)+12*a^-7*b^5*x^-1//2+-3//2*a^-4*b^2*x^-2+4//5*b*a^-3*x^-5//2+8//3*a^-5*b^3*x^-3//2)
@test integrate(x^3*(a+b*x^(1/2))^-3, x) == :(2//5*b^-3*x^5//2+a^7*b^-8*(a+b*x^(1/2))^-2+-42*a^5*b^-8*log(a+b*x^(1/2))+-14*a^6*b^-8*(a+b*x^(1/2))^-1+-10*x*a^3*b^-6+4*a^2*b^-5*x^3//2+30*a^4*b^-7*x^(1/2)+-3//2*a*b^-4*x^2)
@test integrate(x^2*(a+b*x^(1/2))^-3, x) == :(2//3*b^-3*x^3//2+a^5*b^-6*(a+b*x^(1/2))^-2+-20*a^3*b^-6*log(a+b*x^(1/2))+-10*a^4*b^-6*(a+b*x^(1/2))^-1+-3*a*x*b^-4+12*a^2*b^-5*x^(1/2))
@test integrate(x*(a+b*x^(1/2))^-3, x) == :(2*b^-3*x^(1/2)+a^3*b^-4*(a+b*x^(1/2))^-2+-6*a*b^-4*log(a+b*x^(1/2))+-6*a^2*b^-4*(a+b*x^(1/2))^-1)
@test integrate((a+b*x^(1/2))^-3, x) == :(x*a^-1*(a+b*x^(1/2))^-2)
@test integrate(x^-1*(a+b*x^(1/2))^-3, x) == :(a^-1*(a+b*x^(1/2))^-2+a^-3*log(x)+-2*a^-3*log(a+b*x^(1/2))+2*a^-2*(a+b*x^(1/2))^-1)
@test integrate(x^-2*(a+b*x^(1/2))^-3, x) == :(-1*a^-3*x^-1+a^-3*b^2*(a+b*x^(1/2))^-2+-12*a^-5*b^2*log(a+b*x^(1/2))+6*b*a^-4*x^-1//2+6*a^-5*b^2*log(x)+6*a^-4*b^2*(a+b*x^(1/2))^-1)
@test integrate(x^-3*(a+b*x^(1/2))^-3, x) == :(-1//2*a^-3*x^-2+a^-5*b^4*(a+b*x^(1/2))^-2+-30*a^-7*b^4*log(a+b*x^(1/2))+-6*a^-5*b^2*x^-1+2*b*a^-4*x^-3//2+10*a^-6*b^4*(a+b*x^(1/2))^-1+15*a^-7*b^4*log(x)+20*a^-6*b^3*x^-1//2)
@test integrate(x^-4*(a+b*x^(1/2))^-3, x) == :(-1//3*a^-3*x^-3+a^-7*b^6*(a+b*x^(1/2))^-2+-56*a^-9*b^6*log(a+b*x^(1/2))+-15*a^-7*b^4*x^-1+-3*a^-5*b^2*x^-2+14*a^-8*b^6*(a+b*x^(1/2))^-1+28*a^-9*b^6*log(x)+42*a^-8*b^5*x^-1//2+6//5*b*a^-4*x^-5//2+20//3*a^-6*b^3*x^-3//2)
@test integrate(x^4*(a+b*x^(1/2))^-5, x) == :(2//5*b^-5*x^5//2+(1/2)*a^9*b^-10*(a+b*x^(1/2))^-4+-252*a^5*b^-10*log(a+b*x^(1/2))+-168*a^6*b^-10*(a+b*x^(1/2))^-1+-35*x*a^3*b^-8+-6*a^8*b^-10*(a+b*x^(1/2))^-3+10*a^2*b^-7*x^3//2+36*a^7*b^-10*(a+b*x^(1/2))^-2+140*a^4*b^-9*x^(1/2)+-5//2*a*b^-6*x^2)
@test integrate(x^3*(a+b*x^(1/2))^-5, x) == :(2//3*b^-5*x^3//2+(1/2)*a^7*b^-8*(a+b*x^(1/2))^-4+-70*a^3*b^-8*log(a+b*x^(1/2))+-70*a^4*b^-8*(a+b*x^(1/2))^-1+-5*a*x*b^-6+21*a^5*b^-8*(a+b*x^(1/2))^-2+30*a^2*b^-7*x^(1/2)+-14//3*a^6*b^-8*(a+b*x^(1/2))^-3)
@test integrate(x^2*(a+b*x^(1/2))^-5, x) == :(2*b^-5*x^(1/2)+(1/2)*a^5*b^-6*(a+b*x^(1/2))^-4+-20*a^2*b^-6*(a+b*x^(1/2))^-1+-10*a*b^-6*log(a+b*x^(1/2))+10*a^3*b^-6*(a+b*x^(1/2))^-2+-10//3*a^4*b^-6*(a+b*x^(1/2))^-3)
@test integrate(x*(a+b*x^(1/2))^-5, x) == :((1/2)*a^-1*x^2*(a+b*x^(1/2))^-4)
@test integrate((a+b*x^(1/2))^-5, x) == :(-2//3*b^-2*(a+b*x^(1/2))^-3+(1/2)*a*b^-2*(a+b*x^(1/2))^-4)
@test integrate(x^-1*(a+b*x^(1/2))^-5, x) == :(a^-5*log(x)+a^-3*(a+b*x^(1/2))^-2+(1/2)*a^-1*(a+b*x^(1/2))^-4+-2*a^-5*log(a+b*x^(1/2))+2*a^-4*(a+b*x^(1/2))^-1+2//3*a^-2*(a+b*x^(1/2))^-3)
@test integrate(x^-2*(a+b*x^(1/2))^-5, x) == :(-1*a^-5*x^-1+(1/2)*a^-3*b^2*(a+b*x^(1/2))^-4+-30*a^-7*b^2*log(a+b*x^(1/2))+2*a^-4*b^2*(a+b*x^(1/2))^-3+6*a^-5*b^2*(a+b*x^(1/2))^-2+10*b*a^-6*x^-1//2+15*a^-7*b^2*log(x)+20*a^-6*b^2*(a+b*x^(1/2))^-1)
@test integrate(x^-3*(a+b*x^(1/2))^-5, x) == :(-1//2*a^-5*x^-2+(1/2)*a^-5*b^4*(a+b*x^(1/2))^-4+-140*a^-9*b^4*log(a+b*x^(1/2))+-15*a^-7*b^2*x^-1+15*a^-7*b^4*(a+b*x^(1/2))^-2+70*a^-9*b^4*log(x)+70*a^-8*b^3*x^-1//2+70*a^-8*b^4*(a+b*x^(1/2))^-1+10//3*b*a^-6*x^-3//2+10//3*a^-6*b^4*(a+b*x^(1/2))^-3)
@test integrate(x^5*(a+b*x^(1/2))^-8, x) == :((1/2)*b^-8*x^2+-462*a^6*b^-12*(a+b*x^(1/2))^-2+-240*a^3*b^-11*x^(1/2)+22*a^9*b^-12*(a+b*x^(1/2))^-5+36*x*a^2*b^-10+220*a^7*b^-12*(a+b*x^(1/2))^-3+660*a^4*b^-12*log(a+b*x^(1/2))+924*a^5*b^-12*(a+b*x^(1/2))^-1+-165//2*a^8*b^-12*(a+b*x^(1/2))^-4+-16//3*a*b^-9*x^3//2+-11//3*a^10*b^-12*(a+b*x^(1/2))^-6+2//7*a^11*b^-12*(a+b*x^(1/2))^-7)
@test integrate(x^4*(a+b*x^(1/2))^-8, x) == :(x*b^-8+-126*a^4*b^-10*(a+b*x^(1/2))^-2+-42*a^6*b^-10*(a+b*x^(1/2))^-4+-16*a*b^-9*x^(1/2)+-3*a^8*b^-10*(a+b*x^(1/2))^-6+72*a^2*b^-10*log(a+b*x^(1/2))+84*a^5*b^-10*(a+b*x^(1/2))^-3+168*a^3*b^-10*(a+b*x^(1/2))^-1+2//7*a^9*b^-10*(a+b*x^(1/2))^-7+72//5*a^7*b^-10*(a+b*x^(1/2))^-5)
@test integrate(x^3*(a+b*x^(1/2))^-8, x) == :(2*b^-8*log(a+b*x^(1/2))+-21*a^2*b^-8*(a+b*x^(1/2))^-2+14*a*b^-8*(a+b*x^(1/2))^-1+-35//2*a^4*b^-8*(a+b*x^(1/2))^-4+-7//3*a^6*b^-8*(a+b*x^(1/2))^-6+2//7*a^7*b^-8*(a+b*x^(1/2))^-7+42//5*a^5*b^-8*(a+b*x^(1/2))^-5+70//3*a^3*b^-8*(a+b*x^(1/2))^-3)
@test integrate(x^2*(a+b*x^(1/2))^-8, x) == :(1//21*a^-2*x^3*(a+b*x^(1/2))^-6+2//7*a^-1*x^3*(a+b*x^(1/2))^-7)
@test integrate(x*(a+b*x^(1/2))^-8, x) == :(-1//2*b^-4*(a+b*x^(1/2))^-4+-1*a^2*b^-4*(a+b*x^(1/2))^-6+2//7*a^3*b^-4*(a+b*x^(1/2))^-7+6//5*a*b^-4*(a+b*x^(1/2))^-5)
@test integrate((a+b*x^(1/2))^-8, x) == :(-1//3*b^-2*(a+b*x^(1/2))^-6+2//7*a*b^-2*(a+b*x^(1/2))^-7)
@test integrate(x^-1*(a+b*x^(1/2))^-8, x) == :(a^-8*log(x)+a^-6*(a+b*x^(1/2))^-2+(1/2)*a^-4*(a+b*x^(1/2))^-4+-2*a^-8*log(a+b*x^(1/2))+2*a^-7*(a+b*x^(1/2))^-1+1//3*a^-2*(a+b*x^(1/2))^-6+2//3*a^-5*(a+b*x^(1/2))^-3+2//5*a^-3*(a+b*x^(1/2))^-5+2//7*a^-1*(a+b*x^(1/2))^-7)
@test integrate(x^-2*(a+b*x^(1/2))^-8, x) == :(-1*a^-8*x^-1+a^-4*b^2*(a+b*x^(1/2))^-6+-72*a^-10*b^2*log(a+b*x^(1/2))+5*a^-6*b^2*(a+b*x^(1/2))^-4+10*a^-7*b^2*(a+b*x^(1/2))^-3+16*b*a^-9*x^-1//2+21*a^-8*b^2*(a+b*x^(1/2))^-2+36*a^-10*b^2*log(x)+56*a^-9*b^2*(a+b*x^(1/2))^-1+2//7*a^-3*b^2*(a+b*x^(1/2))^-7+12//5*a^-5*b^2*(a+b*x^(1/2))^-5)
@test integrate(x^-3*(a+b*x^(1/2))^-8, x) == :(-1//2*a^-8*x^-2+-660*a^-12*b^4*log(a+b*x^(1/2))+-36*a^-10*b^2*x^-1+6*a^-7*b^4*(a+b*x^(1/2))^-5+126*a^-10*b^4*(a+b*x^(1/2))^-2+240*a^-11*b^3*x^-1//2+330*a^-12*b^4*log(x)+420*a^-11*b^4*(a+b*x^(1/2))^-1+2//7*a^-5*b^4*(a+b*x^(1/2))^-7+5//3*a^-6*b^4*(a+b*x^(1/2))^-6+16//3*b*a^-9*x^-3//2+35//2*a^-8*b^4*(a+b*x^(1/2))^-4+140//3*a^-9*b^4*(a+b*x^(1/2))^-3)
@test integrate(x^-1*(2+b*x^(1/2))^-1, x) == :((1/2)*log(x)+-1*log(2+b*x^(1/2)))
@test integrate(x^2*(a+b*x^(1/2))^(1/2), x) == :(4//13*b^-6*(a+b*x^(1/2))^13//2+4*a^4*b^-6*(a+b*x^(1/2))^5//2+-40//7*a^3*b^-6*(a+b*x^(1/2))^7//2+-20//11*a*b^-6*(a+b*x^(1/2))^11//2+-4//3*a^5*b^-6*(a+b*x^(1/2))^3//2+40//9*a^2*b^-6*(a+b*x^(1/2))^9//2)
@test integrate(x*(a+b*x^(1/2))^(1/2), x) == :(4//9*b^-4*(a+b*x^(1/2))^9//2+-12//7*a*b^-4*(a+b*x^(1/2))^7//2+-4//3*a^3*b^-4*(a+b*x^(1/2))^3//2+12//5*a^2*b^-4*(a+b*x^(1/2))^5//2)
@test integrate((a+b*x^(1/2))^(1/2), x) == :(4//5*b^-2*(a+b*x^(1/2))^5//2+-4//3*a*b^-2*(a+b*x^(1/2))^3//2)
@test integrate(x^-1*(a+b*x^(1/2))^(1/2), x) == :(4*(a+b*x^(1/2))^(1/2)+-4*a^(1/2)*arctanh(a^-1//2*(a+b*x^(1/2))^(1/2)))
@test integrate(x^-2*(a+b*x^(1/2))^(1/2), x) == :(-1*x^-1*(a+b*x^(1/2))^(1/2)+(1/2)*a^-3//2*b^2*arctanh(a^-1//2*(a+b*x^(1/2))^(1/2))+-1//2*b*a^-1*x^-1//2*(a+b*x^(1/2))^(1/2))
@test integrate(x^-3*(a+b*x^(1/2))^(1/2), x) == :(-1//2*x^-2*(a+b*x^(1/2))^(1/2)+5//32*a^-7//2*b^4*arctanh(a^-1//2*(a+b*x^(1/2))^(1/2))+-5//32*a^-3*b^3*x^-1//2*(a+b*x^(1/2))^(1/2)+-1//12*b*a^-1*x^-3//2*(a+b*x^(1/2))^(1/2)+5//48*a^-2*b^2*x^-1*(a+b*x^(1/2))^(1/2))
@test integrate(x^2*(a+b*x^(1/2))^-1//2, x) == :(4//11*b^-6*(a+b*x^(1/2))^11//2+-8*a^3*b^-6*(a+b*x^(1/2))^5//2+-4*a^5*b^-6*(a+b*x^(1/2))^(1/2)+-20//9*a*b^-6*(a+b*x^(1/2))^9//2+20//3*a^4*b^-6*(a+b*x^(1/2))^3//2+40//7*a^2*b^-6*(a+b*x^(1/2))^7//2)
@test integrate(x*(a+b*x^(1/2))^-1//2, x) == :(4//7*b^-4*(a+b*x^(1/2))^7//2+-4*a^3*b^-4*(a+b*x^(1/2))^(1/2)+4*a^2*b^-4*(a+b*x^(1/2))^3//2+-12//5*a*b^-4*(a+b*x^(1/2))^5//2)
@test integrate((a+b*x^(1/2))^-1//2, x) == :(4//3*b^-2*(a+b*x^(1/2))^3//2+-4*a*b^-2*(a+b*x^(1/2))^(1/2))
@test integrate(x^-1*(a+b*x^(1/2))^-1//2, x) == :(-4*a^-1//2*arctanh(a^-1//2*(a+b*x^(1/2))^(1/2)))
@test integrate(x^-2*(a+b*x^(1/2))^-1//2, x) == :(-1*a^-1*x^-1*(a+b*x^(1/2))^(1/2)+-3//2*a^-5//2*b^2*arctanh(a^-1//2*(a+b*x^(1/2))^(1/2))+3//2*b*a^-2*x^-1//2*(a+b*x^(1/2))^(1/2))
@test integrate(x^-3*(a+b*x^(1/2))^-1//2, x) == :(-35//32*a^-9//2*b^4*arctanh(a^-1//2*(a+b*x^(1/2))^(1/2))+-1//2*a^-1*x^-2*(a+b*x^(1/2))^(1/2)+-35//48*a^-3*b^2*x^-1*(a+b*x^(1/2))^(1/2)+7//12*b*a^-2*x^-3//2*(a+b*x^(1/2))^(1/2)+35//32*a^-4*b^3*x^-1//2*(a+b*x^(1/2))^(1/2))
@test integrate(x^(1/2)*(a+b*x^(1/2))^n, x) == :(2*b^-3*(3+n)^-1*(a+b*x^(1/2))^(3+n)+-4*a*b^-3*(2+n)^-1*(a+b*x^(1/2))^(2+n)+2*a^2*b^-3*(1+n)^-1*(a+b*x^(1/2))^(1+n))
@test integrate(x^-1//2*(a+b*x^(1/2))^n, x) == :(2*b^-1*(1+n)^-1*(a+b*x^(1/2))^(1+n))
@test integrate(x^-1//2*(1+x^(1/2)), x) == :(x+2*x^(1/2))
@test integrate(x^-1//2*(1+x^(1/2))^2, x) == :(2//3*(1+x^(1/2))^3)
@test integrate(x^-1//2*(1+x^(1/2))^3, x) == :((1/2)*(1+x^(1/2))^4)
@test integrate(x^(1/2)*(1+x^(1/2))^-1, x) == :(x+-2*x^(1/2)+2*log(1+x^(1/2)))
@test integrate(x^-1//2*(1+x^(1/2))^-1, x) == :(2*log(1+x^(1/2)))
@test integrate(x^-1//2*(1+x^(1/2))^-2, x) == :(-2*(1+x^(1/2))^-1)
@test integrate(x^-1//2*(1+x^(1/2))^-3, x) == :(-1*(1+x^(1/2))^-2)
@test integrate(x^(1/2)*(1+x^(1/2))^(1/2), x) == :(-8//5*(1+x^(1/2))^5//2+4//3*(1+x^(1/2))^3//2+4//7*(1+x^(1/2))^7//2)
@test integrate(x^-1//2*(1+x^(1/2))^(1/2), x) == :(4//3*(1+x^(1/2))^3//2)
@test integrate(x^1//3*(1+x^(1/2))^-1, x) == :(-3*x^1//3+-3*log(1+x^1//6)+6//5*x^5//6+-2*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2*x^1//6))+log(1+x^(1/2)))
@test integrate(x^m*(a+b*x^(1/2))^4, x) == :(a^4*x^(1+m)*(1+m)^-1+b^4*x^(3+m)*(3+m)^-1+6*a^2*b^2*x^(2+m)*(2+m)^-1+8*a*b^3*x^(5//2+m)*(5+2m)^-1+8*b*a^3*x^(3//2+m)*(3+2m)^-1)
@test integrate(x^m*(a+b*x^(1/2))^3, x) == :(a^3*x^(1+m)*(1+m)^-1+2*b^3*x^(5//2+m)*(5+2m)^-1+3*a*b^2*x^(2+m)*(2+m)^-1+6*b*a^2*x^(3//2+m)*(3+2m)^-1)
@test integrate(x^m*(a+b*x^(1/2))^2, x) == :(a^2*x^(1+m)*(1+m)^-1+b^2*x^(2+m)*(2+m)^-1+4*a*b*x^(3//2+m)*(3+2m)^-1)
@test integrate(x^m*(a+b*x^(1/2)), x) == :(a*x^(1+m)*(1+m)^-1+2*b*x^(3//2+m)*(3+2m)^-1)
@test integrate(x^3*(a+b*x^(1/2))^p, x) == :(2*b^-8*(8+p)^-1*(a+b*x^(1/2))^(8+p)+-70*a^3*b^-8*(5+p)^-1*(a+b*x^(1/2))^(5+p)+-42*a^5*b^-8*(3+p)^-1*(a+b*x^(1/2))^(3+p)+-14*a*b^-8*(7+p)^-1*(a+b*x^(1/2))^(7+p)+-2*a^7*b^-8*(1+p)^-1*(a+b*x^(1/2))^(1+p)+14*a^6*b^-8*(2+p)^-1*(a+b*x^(1/2))^(2+p)+42*a^2*b^-8*(6+p)^-1*(a+b*x^(1/2))^(6+p)+70*a^4*b^-8*(4+p)^-1*(a+b*x^(1/2))^(4+p))
@test integrate(x^2*(a+b*x^(1/2))^p, x) == :(2*b^-6*(6+p)^-1*(a+b*x^(1/2))^(6+p)+-20*a^3*b^-6*(3+p)^-1*(a+b*x^(1/2))^(3+p)+-10*a*b^-6*(5+p)^-1*(a+b*x^(1/2))^(5+p)+-2*a^5*b^-6*(1+p)^-1*(a+b*x^(1/2))^(1+p)+10*a^4*b^-6*(2+p)^-1*(a+b*x^(1/2))^(2+p)+20*a^2*b^-6*(4+p)^-1*(a+b*x^(1/2))^(4+p))
@test integrate(x*(a+b*x^(1/2))^p, x) == :(2*b^-4*(4+p)^-1*(a+b*x^(1/2))^(4+p)+-6*a*b^-4*(3+p)^-1*(a+b*x^(1/2))^(3+p)+-2*a^3*b^-4*(1+p)^-1*(a+b*x^(1/2))^(1+p)+6*a^2*b^-4*(2+p)^-1*(a+b*x^(1/2))^(2+p))
@test integrate((a+b*x^(1/2))^p, x) == :(2*b^-2*(2+p)^-1*(a+b*x^(1/2))^(2+p)+-2*a*b^-2*(1+p)^-1*(a+b*x^(1/2))^(1+p))
@test integrate(x^3*(a+b*x^3//2)^-2//3, x) == :(-10//27*a^2*b^-8//3*log(1+-1*b^1//3*x^(1/2)*(a+b*x^3//2)^-1//3)+1//3*b^-1*x^5//2*(a+b*x^3//2)^1//3+5//27*a^2*b^-8//3*log(1+x*b^2//3*(a+b*x^3//2)^-2//3+b^1//3*x^(1/2)*(a+b*x^3//2)^-1//3)+-10//27*3^(1/2)*a^2*b^-8//3*arctan(1//3*3^(1/2)*(1+2*b^1//3*x^(1/2)*(a+b*x^3//2)^-1//3))+-5//9*a*x*b^-2*(a+b*x^3//2)^1//3)
@test integrate(x^2*(a+b*x^3//2)^-2//3, x) == :((1/2)*b^-2*(a+b*x^3//2)^4//3+-2*a*b^-2*(a+b*x^3//2)^1//3)
@test integrate((a+b*x^3//2)^-2//3, x) == :(-2//3*b^-2//3*log(1+-1*b^1//3*x^(1/2)*(a+b*x^3//2)^-1//3)+1//3*b^-2//3*log(1+x*b^2//3*(a+b*x^3//2)^-2//3+b^1//3*x^(1/2)*(a+b*x^3//2)^-1//3)+-2//3*3^(1/2)*b^-2//3*arctan(1//3*3^(1/2)*(1+2*b^1//3*x^(1/2)*(a+b*x^3//2)^-1//3)))
@test integrate(x^-1*(a+b*x^3//2)^-2//3, x) == :(a^-2//3*log(a^1//3+-1*(a+b*x^3//2)^1//3)+-1//2*a^-2//3*log(x)+-2//3*3^(1/2)*a^-2//3*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+2*(a+b*x^3//2)^1//3)))
@test integrate(x^-3*(a+b*x^3//2)^-2//3, x) == :(-1//2*a^-1*x^-2*(a+b*x^3//2)^1//3+3//2*b*a^-2*x^-1//2*(a+b*x^3//2)^1//3)
@test integrate(x^-4*(a+b*x^3//2)^-2//3, x) == :(-5//18*a^-8//3*b^2*log(x)+-1//3*a^-1*x^-3*(a+b*x^3//2)^1//3+5//9*a^-8//3*b^2*log(a^1//3+-1*(a+b*x^3//2)^1//3)+-10//27*3^(1/2)*a^-8//3*b^2*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+2*(a+b*x^3//2)^1//3))+5//9*b*a^-2*x^-3//2*(a+b*x^3//2)^1//3)
@test integrate(x^(1/2)*(1+x^3//2)^-1, x) == :(2//3*log(1+x^3//2))
@test integrate(x^4*(a+b*x^1//3), x) == :(1//5*a*x^5+3//16*b*x^16//3)
@test integrate(x^3*(a+b*x^1//3), x) == :(1//4*a*x^4+3//13*b*x^13//3)
@test integrate(x^2*(a+b*x^1//3), x) == :(1//3*a*x^3+3//10*b*x^10//3)
@test integrate(x*(a+b*x^1//3), x) == :((1/2)*a*x^2+3//7*b*x^7//3)
@test integrate(a+b*x^1//3, x) == :(a*x+3//4*b*x^4//3)
@test integrate(x^-1*(a+b*x^1//3), x) == :(a*log(x)+3*b*x^1//3)
@test integrate(x^-2*(a+b*x^1//3), x) == :(-1*a*x^-1+-3//2*b*x^-2//3)
@test integrate(x^-3*(a+b*x^1//3), x) == :(-3//5*b*x^-5//3+-1//2*a*x^-2)
@test integrate(x^-4*(a+b*x^1//3), x) == :(-3//8*b*x^-8//3+-1//3*a*x^-3)
@test integrate(x^4*(a+b*x^1//3)^2, x) == :(1//5*a^2*x^5+3//17*b^2*x^17//3+3//8*a*b*x^16//3)
@test integrate(x^3*(a+b*x^1//3)^2, x) == :(1//4*a^2*x^4+3//14*b^2*x^14//3+6//13*a*b*x^13//3)
@test integrate(x^2*(a+b*x^1//3)^2, x) == :(1//3*a^2*x^3+3//11*b^2*x^11//3+3//5*a*b*x^10//3)
@test integrate(x*(a+b*x^1//3)^2, x) == :((1/2)*a^2*x^2+3//8*b^2*x^8//3+6//7*a*b*x^7//3)
@test integrate((a+b*x^1//3)^2, x) == :(x*a^2+3//5*b^2*x^5//3+3//2*a*b*x^4//3)
@test integrate(x^-1*(a+b*x^1//3)^2, x) == :(a^2*log(x)+3//2*b^2*x^2//3+6*a*b*x^1//3)
@test integrate(x^-2*(a+b*x^1//3)^2, x) == :(-1*a^-1*x^-1*(a+b*x^1//3)^3)
@test integrate(x^-3*(a+b*x^1//3)^2, x) == :(-3//4*b^2*x^-4//3+-1//2*a^2*x^-2+-6//5*a*b*x^-5//3)
@test integrate(x^-4*(a+b*x^1//3)^2, x) == :(-3//7*b^2*x^-7//3+-1//3*a^2*x^-3+-3//4*a*b*x^-8//3)
@test integrate(x^4*(a+b*x^1//3)^3, x) == :(1//5*a^3*x^5+1//6*b^3*x^6+9//16*b*a^2*x^16//3+9//17*a*b^2*x^17//3)
@test integrate(x^3*(a+b*x^1//3)^3, x) == :(1//4*a^3*x^4+1//5*b^3*x^5+9//13*b*a^2*x^13//3+9//14*a*b^2*x^14//3)
@test integrate(x^2*(a+b*x^1//3)^3, x) == :(1//3*a^3*x^3+1//4*b^3*x^4+9//10*b*a^2*x^10//3+9//11*a*b^2*x^11//3)
@test integrate(x*(a+b*x^1//3)^3, x) == :((1/2)*a^3*x^2+1//3*b^3*x^3+9//7*b*a^2*x^7//3+9//8*a*b^2*x^8//3)
@test integrate((a+b*x^1//3)^3, x) == :(x*a^3+(1/2)*b^3*x^2+9//4*b*a^2*x^4//3+9//5*a*b^2*x^5//3)
@test integrate(x^-1*(a+b*x^1//3)^3, x) == :(x*b^3+a^3*log(x)+9*b*a^2*x^1//3+9//2*a*b^2*x^2//3)
@test integrate(x^-2*(a+b*x^1//3)^3, x) == :(b^3*log(x)+-1*a^3*x^-1+-9*a*b^2*x^-1//3+-9//2*b*a^2*x^-2//3)
@test integrate(x^-3*(a+b*x^1//3)^3, x) == :(-1*b^3*x^-1+-1//2*a^3*x^-2+-9//4*a*b^2*x^-4//3+-9//5*b*a^2*x^-5//3)
@test integrate(x^-4*(a+b*x^1//3)^3, x) == :(-1//2*b^3*x^-2+-1//3*a^3*x^-3+-9//7*a*b^2*x^-7//3+-9//8*b*a^2*x^-8//3)
@test integrate(x^4*(a+b*x^1//3)^5, x) == :(1//5*a^5*x^5+3//20*b^5*x^20//3+5//3*a^2*b^3*x^6+15//16*b*a^4*x^16//3+15//19*a*b^4*x^19//3+30//17*a^3*b^2*x^17//3)
@test integrate(x^3*(a+b*x^1//3)^5, x) == :(1//4*a^5*x^4+3//17*b^5*x^17//3+2*a^2*b^3*x^5+15//7*a^3*b^2*x^14//3+15//13*b*a^4*x^13//3+15//16*a*b^4*x^16//3)
@test integrate(x^2*(a+b*x^1//3)^5, x) == :(1//3*a^5*x^3+3//14*b^5*x^14//3+3//2*b*a^4*x^10//3+5//2*a^2*b^3*x^4+15//13*a*b^4*x^13//3+30//11*a^3*b^2*x^11//3)
@test integrate(x*(a+b*x^1//3)^5, x) == :((1/2)*a^5*x^2+3//11*b^5*x^11//3+3//2*a*b^4*x^10//3+10//3*a^2*b^3*x^3+15//4*a^3*b^2*x^8//3+15//7*b*a^4*x^7//3)
@test integrate((a+b*x^1//3)^5, x) == :(3//8*b^-3*(a+b*x^1//3)^8+(1/2)*a^2*b^-3*(a+b*x^1//3)^6+-6//7*a*b^-3*(a+b*x^1//3)^7)
@test integrate(x^-1*(a+b*x^1//3)^5, x) == :(a^5*log(x)+3//5*b^5*x^5//3+10*x*a^2*b^3+15*b*a^4*x^1//3+15*a^3*b^2*x^2//3+15//4*a*b^4*x^4//3)
@test integrate(x^-2*(a+b*x^1//3)^5, x) == :(-1*a^5*x^-1+3//2*b^5*x^2//3+-30*a^3*b^2*x^-1//3+10*a^2*b^3*log(x)+15*a*b^4*x^1//3+-15//2*b*a^4*x^-2//3)
@test integrate(x^-3*(a+b*x^1//3)^5, x) == :(-1//2*a^-1*x^-2*(a+b*x^1//3)^6)
@test integrate(x^-4*(a+b*x^1//3)^5, x) == :(-3//4*b^5*x^-4//3+-1//3*a^5*x^-3+-5*a^2*b^3*x^-2+-3*a*b^4*x^-5//3+-30//7*a^3*b^2*x^-7//3+-15//8*b*a^4*x^-8//3)
@test integrate(x^-5*(a+b*x^1//3)^5, x) == :(-3//7*b^5*x^-7//3+-1//4*a^5*x^-4+-3*a^3*b^2*x^-10//3+-15//8*a*b^4*x^-8//3+-15//11*b*a^4*x^-11//3+-10//3*a^2*b^3*x^-3)
@test integrate(x^-6*(a+b*x^1//3)^5, x) == :(-3//10*b^5*x^-10//3+-1//5*a^5*x^-5+-30//13*a^3*b^2*x^-13//3+-15//11*a*b^4*x^-11//3+-15//14*b*a^4*x^-14//3+-5//2*a^2*b^3*x^-4)
@test integrate(x^-7*(a+b*x^1//3)^5, x) == :(-3//13*b^5*x^-13//3+-1//6*a^5*x^-6+-2*a^2*b^3*x^-5+-15//8*a^3*b^2*x^-16//3+-15//14*a*b^4*x^-14//3+-15//17*b*a^4*x^-17//3)
@test integrate(x^4*(a+b*x^1//3)^10, x) == :(1//5*a^10*x^5+3//25*b^10*x^25//3+20*a^7*b^3*x^6+30*a^4*b^6*x^7+5//4*a*b^9*x^8+15//8*b*a^9*x^16//3+135//17*a^8*b^2*x^17//3+135//23*a^2*b^8*x^23//3+180//11*a^3*b^7*x^22//3+189//5*a^5*b^5*x^20//3+630//19*a^6*b^4*x^19//3)
@test integrate(x^3*(a+b*x^1//3)^10, x) == :(1//4*a^10*x^4+3//22*b^10*x^22//3+24*a^7*b^3*x^5+35*a^4*b^6*x^6+10//7*a*b^9*x^7+27//4*a^2*b^8*x^20//3+30//13*b*a^9*x^13//3+135//14*a^8*b^2*x^14//3+315//8*a^6*b^4*x^16//3+360//19*a^3*b^7*x^19//3+756//17*a^5*b^5*x^17//3)
@test integrate(x^2*(a+b*x^1//3)^10, x) == :(3//19*b^-9*(a+b*x^1//3)^19+-12*a^5*b^-9*(a+b*x^1//3)^14+-2*a^7*b^-9*(a+b*x^1//3)^12+14*a^4*b^-9*(a+b*x^1//3)^15+-21//2*a^3*b^-9*(a+b*x^1//3)^16+-4//3*a*b^-9*(a+b*x^1//3)^18+3//11*a^8*b^-9*(a+b*x^1//3)^11+84//13*a^6*b^-9*(a+b*x^1//3)^13+84//17*a^2*b^-9*(a+b*x^1//3)^17)
@test integrate(x*(a+b*x^1//3)^10, x) == :(3//16*b^-6*(a+b*x^1//3)^16+-1*a*b^-6*(a+b*x^1//3)^15+-30//13*a^3*b^-6*(a+b*x^1//3)^13+-3//11*a^5*b^-6*(a+b*x^1//3)^11+5//4*a^4*b^-6*(a+b*x^1//3)^12+15//7*a^2*b^-6*(a+b*x^1//3)^14)
@test integrate((a+b*x^1//3)^10, x) == :(3//13*b^-3*(a+b*x^1//3)^13+-1//2*a*b^-3*(a+b*x^1//3)^12+3//11*a^2*b^-3*(a+b*x^1//3)^11)
@test integrate(x^-1*(a+b*x^1//3)^10, x) == :(a^10*log(x)+3//10*b^10*x^10//3+30*b*a^9*x^1//3+105*a^4*b^6*x^2+120*x*a^7*b^3+10//3*a*b^9*x^3+135//2*a^8*b^2*x^2//3+135//8*a^2*b^8*x^8//3+315//2*a^6*b^4*x^4//3+360//7*a^3*b^7*x^7//3+756//5*a^5*b^5*x^5//3)
@test integrate(x^-2*(a+b*x^1//3)^10, x) == :(-1*a^10*x^-1+3//7*b^10*x^7//3+-135*a^8*b^2*x^-1//3+-15*b*a^9*x^-2//3+5*a*b^9*x^2+27*a^2*b^8*x^5//3+90*a^3*b^7*x^4//3+120*a^7*b^3*log(x)+210*x*a^4*b^6+378*a^5*b^5*x^2//3+630*a^6*b^4*x^1//3)
@test integrate(x^-3*(a+b*x^1//3)^10, x) == :(-1//2*a^10*x^-2+3//4*b^10*x^4//3+-756*a^5*b^5*x^-1//3+-315*a^6*b^4*x^-2//3+-120*a^7*b^3*x^-1+-6*b*a^9*x^-5//3+10*a*x*b^9+210*a^4*b^6*log(x)+360*a^3*b^7*x^1//3+-135//4*a^8*b^2*x^-4//3+135//2*a^2*b^8*x^2//3)
@test integrate(x^-4*(a+b*x^1//3)^10, x) == :(3*b^10*x^1//3+-1//3*a^10*x^-3+-210*a^4*b^6*x^-1+-189*a^5*b^5*x^-4//3+-180*a^3*b^7*x^-2//3+-135*a^2*b^8*x^-1//3+-126*a^6*b^4*x^-5//3+-60*a^7*b^3*x^-2+10*a*b^9*log(x)+-135//7*a^8*b^2*x^-7//3+-15//4*b*a^9*x^-8//3)
@test integrate(x^-5*(a+b*x^1//3)^10, x) == :(-1//4*a^-1*x^-4*(a+b*x^1//3)^11+1//44*b*a^-2*x^-11//3*(a+b*x^1//3)^11)
@test integrate(x^-6*(a+b*x^1//3)^10, x) == :(-1//5*a^-1*x^-5*(a+b*x^1//3)^11+-6//455*a^-3*b^2*x^-13//3*(a+b*x^1//3)^11+-1//5005*a^-5*b^4*x^-11//3*(a+b*x^1//3)^11+1//455*a^-4*b^3*x^-4*(a+b*x^1//3)^11+2//35*b*a^-2*x^-14//3*(a+b*x^1//3)^11)
@test integrate(x^-7*(a+b*x^1//3)^10, x) == :(-3//8*b^10*x^-8//3+-1//6*a^10*x^-6+-45*a^6*b^4*x^-14//3+-24*a^7*b^3*x^-5+-756//13*a^5*b^5*x^-13//3+-360//11*a^3*b^7*x^-11//3+-135//16*a^8*b^2*x^-16//3+-105//2*a^4*b^6*x^-4+-30//17*b*a^9*x^-17//3+-27//2*a^2*b^8*x^-10//3+-10//3*a*b^9*x^-3)
@test integrate(x^-8*(a+b*x^1//3)^10, x) == :(-3//11*b^10*x^-11//3+-1//7*a^10*x^-7+-42*a^4*b^6*x^-5+-20*a^7*b^3*x^-6+-630//17*a^6*b^4*x^-17//3+-189//4*a^5*b^5*x^-16//3+-180//7*a^3*b^7*x^-14//3+-135//13*a^2*b^8*x^-13//3+-135//19*a^8*b^2*x^-19//3+-5//2*a*b^9*x^-4+-3//2*b*a^9*x^-20//3)
@test integrate(x^-9*(a+b*x^1//3)^10, x) == :(-3//14*b^10*x^-14//3+-1//8*a^10*x^-8+-35*a^4*b^6*x^-6+-2*a*b^9*x^-5+-756//19*a^5*b^5*x^-19//3+-360//17*a^3*b^7*x^-17//3+-135//16*a^2*b^8*x^-16//3+-135//22*a^8*b^2*x^-22//3+-120//7*a^7*b^3*x^-7+-63//2*a^6*b^4*x^-20//3+-30//23*b*a^9*x^-23//3)
@test integrate(x^-10*(a+b*x^1//3)^10, x) == :(-3//17*b^10*x^-17//3+-1//9*a^10*x^-9+-30*a^4*b^6*x^-7+-18*a^3*b^7*x^-20//3+-15*a^7*b^3*x^-8+-630//23*a^6*b^4*x^-23//3+-378//11*a^5*b^5*x^-22//3+-135//19*a^2*b^8*x^-19//3+-27//5*a^8*b^2*x^-25//3+-15//13*b*a^9*x^-26//3+-5//3*a*b^9*x^-6)
@test integrate(x^5*(a+b*x^1//3)^15, x) == :(1//6*a^15*x^6+1//11*b^15*x^11+65*a^12*b^3*x^7+45//19*b*a^14*x^19//3+45//32*a*b^14*x^32//3+63//4*a^13*b^2*x^20//3+91//2*a^3*b^12*x^10+315//31*a^2*b^13*x^31//3+1287//4*a^5*b^10*x^28//3+1485//2*a^7*b^8*x^26//3+3861//5*a^8*b^7*x^25//3+4095//22*a^11*b^4*x^22//3+4095//29*a^4*b^11*x^29//3+5005//8*a^9*b^6*x^8+5005//9*a^6*b^9*x^9+9009//23*a^10*b^5*x^23//3)
@test integrate(x^4*(a+b*x^1//3)^15, x) == :(1//5*a^15*x^5+1//10*b^15*x^10+715*a^9*b^6*x^7+45//4*a^2*b^13*x^28//3+45//16*b*a^14*x^16//3+45//29*a*b^14*x^29//3+315//2*a^4*b^11*x^26//3+315//17*a^13*b^2*x^17//3+455//6*a^12*b^3*x^6+455//9*a^3*b^12*x^9+1755//2*a^8*b^7*x^22//3+4095//19*a^11*b^4*x^19//3+5005//8*a^6*b^9*x^8+9009//20*a^10*b^5*x^20//3+9009//25*a^5*b^10*x^25//3+19305//23*a^7*b^8*x^23//3)
@test integrate(x^3*(a+b*x^1//3)^15, x) == :(1//9*b^-12*(a+b*x^1//3)^27+-63*a^5*b^-12*(a+b*x^1//3)^22+66*a^6*b^-12*(a+b*x^1//3)^21+-165//8*a^3*b^-12*(a+b*x^1//3)^24+-99//2*a^7*b^-12*(a+b*x^1//3)^20+-55//6*a^9*b^-12*(a+b*x^1//3)^18+-33//26*a*b^-12*(a+b*x^1//3)^26+-3//16*a^11*b^-12*(a+b*x^1//3)^16+33//5*a^2*b^-12*(a+b*x^1//3)^25+33//17*a^10*b^-12*(a+b*x^1//3)^17+495//19*a^8*b^-12*(a+b*x^1//3)^19+990//23*a^4*b^-12*(a+b*x^1//3)^23)
@test integrate(x^2*(a+b*x^1//3)^15, x) == :(1//8*b^-9*(a+b*x^1//3)^24+-8*a^3*b^-9*(a+b*x^1//3)^21+-168//19*a^5*b^-9*(a+b*x^1//3)^19+-24//17*a^7*b^-9*(a+b*x^1//3)^17+-24//23*a*b^-9*(a+b*x^1//3)^23+3//16*a^8*b^-9*(a+b*x^1//3)^16+14//3*a^6*b^-9*(a+b*x^1//3)^18+21//2*a^4*b^-9*(a+b*x^1//3)^20+42//11*a^2*b^-9*(a+b*x^1//3)^22)
@test integrate(x*(a+b*x^1//3)^15, x) == :(1//7*b^-6*(a+b*x^1//3)^21+-5//3*a^3*b^-6*(a+b*x^1//3)^18+-3//4*a*b^-6*(a+b*x^1//3)^20+-3//16*a^5*b^-6*(a+b*x^1//3)^16+15//17*a^4*b^-6*(a+b*x^1//3)^17+30//19*a^2*b^-6*(a+b*x^1//3)^19)
@test integrate((a+b*x^1//3)^15, x) == :(1//6*b^-3*(a+b*x^1//3)^18+-6//17*a*b^-3*(a+b*x^1//3)^17+3//16*a^2*b^-3*(a+b*x^1//3)^16)
@test integrate(x^-1*(a+b*x^1//3)^15, x) == :(a^15*log(x)+1//5*b^15*x^5+45*b*a^14*x^1//3+455*x*a^12*b^3+45//14*a*b^14*x^14//3+315//2*a^13*b^2*x^2//3+315//13*a^2*b^13*x^13//3+455//4*a^3*b^12*x^4+4095//4*a^11*b^4*x^4//3+4095//11*a^4*b^11*x^11//3+5005//2*a^9*b^6*x^2+5005//3*a^6*b^9*x^3+9009//5*a^10*b^5*x^5//3+9009//10*a^5*b^10*x^10//3+19305//7*a^8*b^7*x^7//3+19305//8*a^7*b^8*x^8//3)
@test integrate(x^-2*(a+b*x^1//3)^15, x) == :(-1*a^15*x^-1+1//4*b^15*x^4+-315*a^13*b^2*x^-1//3+455*a^12*b^3*log(x)+1287*a^5*b^10*x^7//3+3861*a^7*b^8*x^5//3+4095*a^11*b^4*x^1//3+5005*x*a^9*b^6+-45//2*b*a^14*x^-2//3+45//11*a*b^14*x^11//3+63//2*a^2*b^13*x^10//3+455//3*a^3*b^12*x^3+4095//8*a^4*b^11*x^8//3+5005//2*a^6*b^9*x^2+9009//2*a^10*b^5*x^2//3+19305//4*a^8*b^7*x^4//3)
@test integrate(x^-3*(a+b*x^1//3)^15, x) == :(-1//2*a^15*x^-2+1//3*b^15*x^3+-9009*a^10*b^5*x^-1//3+-455*a^12*b^3*x^-1+-9*b*a^14*x^-5//3+45*a^2*b^13*x^7//3+819*a^4*b^11*x^5//3+5005*x*a^6*b^9+5005*a^9*b^6*log(x)+19305*a^8*b^7*x^1//3+-4095//2*a^11*b^4*x^-2//3+-315//4*a^13*b^2*x^-4//3+45//8*a*b^14*x^8//3+455//2*a^3*b^12*x^2+9009//4*a^5*b^10*x^4//3+19305//2*a^7*b^8*x^2//3)
@test integrate(x^-4*(a+b*x^1//3)^15, x) == :((1/2)*b^15*x^2+-1//3*a^15*x^-3+-19305*a^7*b^8*x^-1//3+-5005*a^9*b^6*x^-1+-819*a^11*b^4*x^-5//3+-45*a^13*b^2*x^-7//3+9*a*b^14*x^5//3+455*x*a^3*b^12+5005*a^6*b^9*log(x)+9009*a^5*b^10*x^1//3+-19305//2*a^8*b^7*x^-2//3+-9009//4*a^10*b^5*x^-4//3+-455//2*a^12*b^3*x^-2+-45//8*b*a^14*x^-8//3+315//4*a^2*b^13*x^4//3+4095//2*a^4*b^11*x^2//3)
@test integrate(x^-6*(a+b*x^1//3)^15, x) == :(b^15*log(x)+-1//5*a^15*x^-5+-455*a^3*b^12*x^-1+-45*a*b^14*x^-1//3+-19305//7*a^7*b^8*x^-7//3+-19305//8*a^8*b^7*x^-8//3+-9009//5*a^5*b^10*x^-5//3+-9009//10*a^10*b^5*x^-10//3+-5005//2*a^6*b^9*x^-2+-5005//3*a^9*b^6*x^-3+-4095//4*a^4*b^11*x^-4//3+-4095//11*a^11*b^4*x^-11//3+-455//4*a^12*b^3*x^-4+-315//2*a^2*b^13*x^-2//3+-315//13*a^13*b^2*x^-13//3+-45//14*b*a^14*x^-14//3)
@test integrate(x^-7*(a+b*x^1//3)^15, x) == :(-1//6*a^-1*x^-6*(a+b*x^1//3)^16+-1//816*a^-3*b^2*x^-16//3*(a+b*x^1//3)^16+1//51*b*a^-2*x^-17//3*(a+b*x^1//3)^16)
@test integrate(x^-8*(a+b*x^1//3)^15, x) == :(-1//7*a^-1*x^-7*(a+b*x^1//3)^16+-1//133*a^-3*b^2*x^-19//3*(a+b*x^1//3)^16+-1//6783*a^-5*b^4*x^-17//3*(a+b*x^1//3)^16+1//28*b*a^-2*x^-20//3*(a+b*x^1//3)^16+1//798*a^-4*b^3*x^-6*(a+b*x^1//3)^16+1//108528*a^-6*b^5*x^-16//3*(a+b*x^1//3)^16)
@test integrate(x^-9*(a+b*x^1//3)^15, x) == :(-1//8*a^-1*x^-8*(a+b*x^1//3)^16+-7//506*a^-3*b^2*x^-22//3*(a+b*x^1//3)^16+-1//1012*a^-5*b^4*x^-20//3*(a+b*x^1//3)^16+-1//28842*a^-7*b^6*x^-6*(a+b*x^1//3)^16+-1//3922512*a^-9*b^8*x^-16//3*(a+b*x^1//3)^16+1//23*b*a^-2*x^-23//3*(a+b*x^1//3)^16+1//253*a^-4*b^3*x^-7*(a+b*x^1//3)^16+1//4807*a^-6*b^5*x^-19//3*(a+b*x^1//3)^16+1//245157*a^-8*b^7*x^-17//3*(a+b*x^1//3)^16)
@test integrate(x^-10*(a+b*x^1//3)^15, x) == :(-1//4*b^15*x^-4+-1//9*a^15*x^-9+-715*a^9*b^6*x^-7+-91*a^3*b^12*x^-5+-19305//19*a^7*b^8*x^-19//3+-9009//17*a^5*b^10*x^-17//3+-5005//6*a^6*b^9*x^-6+-4095//16*a^4*b^11*x^-16//3+-4095//23*a^11*b^4*x^-23//3+-3861//4*a^8*b^7*x^-20//3+-819//2*a^10*b^5*x^-22//3+-455//8*a^12*b^3*x^-8+-63//5*a^13*b^2*x^-25//3+-45//2*a^2*b^13*x^-14//3+-45//13*a*b^14*x^-13//3+-45//26*b*a^14*x^-26//3)
@test integrate(x^-11*(a+b*x^1//3)^15, x) == :(-1//5*b^15*x^-5+-1//10*a^15*x^-10+-715*a^6*b^9*x^-7+-19305//23*a^8*b^7*x^-23//3+-9009//20*a^5*b^10*x^-20//3+-9009//25*a^10*b^5*x^-25//3+-5005//8*a^9*b^6*x^-8+-4095//19*a^4*b^11*x^-19//3+-1755//2*a^7*b^8*x^-22//3+-455//6*a^3*b^12*x^-6+-455//9*a^12*b^3*x^-9+-315//2*a^11*b^4*x^-26//3+-315//17*a^2*b^13*x^-17//3+-45//4*a^13*b^2*x^-28//3+-45//16*a*b^14*x^-16//3+-45//29*b*a^14*x^-29//3)
@test integrate(x^-12*(a+b*x^1//3)^15, x) == :(-1//6*b^15*x^-6+-1//11*a^15*x^-11+-65*a^3*b^12*x^-7+-9009//23*a^5*b^10*x^-23//3+-5005//8*a^6*b^9*x^-8+-5005//9*a^9*b^6*x^-9+-4095//22*a^4*b^11*x^-22//3+-4095//29*a^11*b^4*x^-29//3+-3861//5*a^7*b^8*x^-25//3+-1485//2*a^8*b^7*x^-26//3+-1287//4*a^10*b^5*x^-28//3+-315//31*a^13*b^2*x^-31//3+-91//2*a^12*b^3*x^-10+-63//4*a^2*b^13*x^-20//3+-45//19*a*b^14*x^-19//3+-45//32*b*a^14*x^-32//3)
@test integrate(x^3*(a+b*x^1//3)^-1, x) == :(3//11*b^-1*x^11//3+x*a^8*b^-9+-3*a^11*b^-12*log(a+b*x^1//3)+3*a^10*b^-11*x^1//3+-3//2*a^9*b^-10*x^2//3+-3//4*a^7*b^-8*x^4//3+-3//8*a^3*b^-4*x^8//3+-3//10*a*b^-2*x^10//3+-1//2*a^5*b^-6*x^2+1//3*a^2*b^-3*x^3+3//5*a^6*b^-7*x^5//3+3//7*a^4*b^-5*x^7//3)
@test integrate(x^2*(a+b*x^1//3)^-1, x) == :(3//8*b^-1*x^8//3+(1/2)*a^2*b^-3*x^2+-1*x*a^5*b^-6+-3*a^7*b^-8*x^1//3+3*a^8*b^-9*log(a+b*x^1//3)+-3//5*a^3*b^-4*x^5//3+-3//7*a*b^-2*x^7//3+3//2*a^6*b^-7*x^2//3+3//4*a^4*b^-5*x^4//3)
@test integrate(x*(a+b*x^1//3)^-1, x) == :(3//5*b^-1*x^5//3+x*a^2*b^-3+-3*a^5*b^-6*log(a+b*x^1//3)+3*a^4*b^-5*x^1//3+-3//2*a^3*b^-4*x^2//3+-3//4*a*b^-2*x^4//3)
@test integrate((a+b*x^1//3)^-1, x) == :(3//2*b^-1*x^2//3+-3*a*b^-2*x^1//3+3*a^2*b^-3*log(a+b*x^1//3))
@test integrate(x^-1*(a+b*x^1//3)^-1, x) == :(a^-1*log(x)+-3*a^-1*log(a+b*x^1//3))
@test integrate(x^-2*(a+b*x^1//3)^-1, x) == :(-1*a^-1*x^-1+-1*a^-4*b^3*log(x)+-3*a^-3*b^2*x^-1//3+3*a^-4*b^3*log(a+b*x^1//3)+3//2*b*a^-2*x^-2//3)
@test integrate(x^-3*(a+b*x^1//3)^-1, x) == :(-1//2*a^-1*x^-2+a^-7*b^6*log(x)+a^-4*b^3*x^-1+-3*a^-7*b^6*log(a+b*x^1//3)+3*a^-6*b^5*x^-1//3+-3//2*a^-5*b^4*x^-2//3+-3//4*a^-3*b^2*x^-4//3+3//5*b*a^-2*x^-5//3)
@test integrate(x^-4*(a+b*x^1//3)^-1, x) == :(-1//3*a^-1*x^-3+(1/2)*a^-4*b^3*x^-2+-1*a^-10*b^9*log(x)+-1*a^-7*b^6*x^-1+-3*a^-9*b^8*x^-1//3+3*a^-10*b^9*log(a+b*x^1//3)+-3//5*a^-5*b^4*x^-5//3+-3//7*a^-3*b^2*x^-7//3+3//2*a^-8*b^7*x^-2//3+3//4*a^-6*b^5*x^-4//3+3//8*b*a^-2*x^-8//3)
@test integrate(x^-1*(2+b*x^1//3)^-1, x) == :((1/2)*log(x)+-3//2*log(2+b*x^1//3))
@test integrate(x^3*(a+b*x^1//3)^-2, x) == :(3//10*b^-2*x^10//3+-30*a^9*b^-11*x^1//3+-8*x*a^7*b^-9+3*a^11*b^-12*(a+b*x^1//3)^-1+33*a^10*b^-12*log(a+b*x^1//3)+-18//5*a^5*b^-7*x^5//3+-12//7*a^3*b^-5*x^7//3+-2//3*a*b^-3*x^3+5//2*a^4*b^-6*x^2+9//8*a^2*b^-4*x^8//3+21//4*a^6*b^-8*x^4//3+27//2*a^8*b^-10*x^2//3)
@test integrate(x^2*(a+b*x^1//3)^-2, x) == :(3//7*b^-2*x^7//3+-1*a*b^-3*x^2+-24*a^7*b^-9*log(a+b*x^1//3)+-9*a^5*b^-7*x^2//3+-3*a^3*b^-5*x^4//3+-3*a^8*b^-9*(a+b*x^1//3)^-1+5*x*a^4*b^-6+21*a^6*b^-8*x^1//3+9//5*a^2*b^-4*x^5//3)
@test integrate(x*(a+b*x^1//3)^-2, x) == :(3//4*b^-2*x^4//3+-12*a^3*b^-5*x^1//3+-2*a*x*b^-3+3*a^5*b^-6*(a+b*x^1//3)^-1+15*a^4*b^-6*log(a+b*x^1//3)+9//2*a^2*b^-4*x^2//3)
@test integrate((a+b*x^1//3)^-2, x) == :(3*b^-2*x^1//3+-6*a*b^-3*log(a+b*x^1//3)+-3*a^2*b^-3*(a+b*x^1//3)^-1)
@test integrate(x^-1*(a+b*x^1//3)^-2, x) == :(a^-2*log(x)+-3*a^-2*log(a+b*x^1//3)+3*a^-1*(a+b*x^1//3)^-1)
@test integrate(x^-2*(a+b*x^1//3)^-2, x) == :(-1*a^-2*x^-1+-9*a^-4*b^2*x^-1//3+-4*a^-5*b^3*log(x)+-3*a^-4*b^3*(a+b*x^1//3)^-1+3*b*a^-3*x^-2//3+12*a^-5*b^3*log(a+b*x^1//3))
@test integrate(x^-3*(a+b*x^1//3)^-2, x) == :(-1//2*a^-2*x^-2+-21*a^-8*b^6*log(a+b*x^1//3)+3*a^-7*b^6*(a+b*x^1//3)^-1+4*a^-5*b^3*x^-1+7*a^-8*b^6*log(x)+18*a^-7*b^5*x^-1//3+-15//2*a^-6*b^4*x^-2//3+-9//4*a^-4*b^2*x^-4//3+6//5*b*a^-3*x^-5//3)
@test integrate(x^-4*(a+b*x^1//3)^-2, x) == :(-1//3*a^-2*x^-3+-27*a^-10*b^8*x^-1//3+-10*a^-11*b^9*log(x)+-7*a^-8*b^6*x^-1+-3*a^-10*b^9*(a+b*x^1//3)^-1+-3*a^-6*b^4*x^-5//3+2*a^-5*b^3*x^-2+12*a^-9*b^7*x^-2//3+30*a^-11*b^9*log(a+b*x^1//3)+-9//7*a^-4*b^2*x^-7//3+3//4*b*a^-3*x^-8//3+9//2*a^-7*b^5*x^-4//3)
@test integrate(x^3*(a+b*x^1//3)^-3, x) == :(1//3*b^-3*x^3+-165*a^9*b^-12*log(a+b*x^1//3)+-54*a^7*b^-10*x^2//3+-33*a^10*b^-12*(a+b*x^1//3)^-1+-5*a^3*b^-6*x^2+9*a^4*b^-7*x^5//3+28*x*a^6*b^-9+135*a^8*b^-11*x^1//3+-63//4*a^5*b^-8*x^4//3+-9//8*a*b^-4*x^8//3+3//2*a^11*b^-12*(a+b*x^1//3)^-2+18//7*a^2*b^-5*x^7//3)
@test integrate(x^2*(a+b*x^1//3)^-3, x) == :((1/2)*b^-3*x^2+-63*a^5*b^-8*x^1//3+-10*x*a^3*b^-6+24*a^7*b^-9*(a+b*x^1//3)^-1+84*a^6*b^-9*log(a+b*x^1//3)+-9//5*a*b^-4*x^5//3+-3//2*a^8*b^-9*(a+b*x^1//3)^-2+9//2*a^2*b^-5*x^4//3+45//2*a^4*b^-7*x^2//3)
@test integrate(x*(a+b*x^1//3)^-3, x) == :(x*b^-3+-30*a^3*b^-6*log(a+b*x^1//3)+-15*a^4*b^-6*(a+b*x^1//3)^-1+18*a^2*b^-5*x^1//3+-9//2*a*b^-4*x^2//3+3//2*a^5*b^-6*(a+b*x^1//3)^-2)
@test integrate((a+b*x^1//3)^-3, x) == :(3*b^-3*log(a+b*x^1//3)+6*a*b^-3*(a+b*x^1//3)^-1+-3//2*a^2*b^-3*(a+b*x^1//3)^-2)
@test integrate(x^-1*(a+b*x^1//3)^-3, x) == :(a^-3*log(x)+-3*a^-3*log(a+b*x^1//3)+3*a^-2*(a+b*x^1//3)^-1+3//2*a^-1*(a+b*x^1//3)^-2)
@test integrate(x^-2*(a+b*x^1//3)^-3, x) == :(-1*a^-3*x^-1+-18*a^-5*b^2*x^-1//3+-12*a^-5*b^3*(a+b*x^1//3)^-1+-10*a^-6*b^3*log(x)+30*a^-6*b^3*log(a+b*x^1//3)+-3//2*a^-4*b^3*(a+b*x^1//3)^-2+9//2*b*a^-4*x^-2//3)
@test integrate(x^-3*(a+b*x^1//3)^-3, x) == :(-1//2*a^-3*x^-2+-84*a^-9*b^6*log(a+b*x^1//3)+10*a^-6*b^3*x^-1+21*a^-8*b^6*(a+b*x^1//3)^-1+28*a^-9*b^6*log(x)+63*a^-8*b^5*x^-1//3+-45//2*a^-7*b^4*x^-2//3+-9//2*a^-5*b^2*x^-4//3+3//2*a^-7*b^6*(a+b*x^1//3)^-2+9//5*b*a^-4*x^-5//3)
@test integrate(x^-4*(a+b*x^1//3)^-3, x) == :(-1//3*a^-3*x^-3+-135*a^-11*b^8*x^-1//3+-55*a^-12*b^9*log(x)+-30*a^-11*b^9*(a+b*x^1//3)^-1+-28*a^-9*b^6*x^-1+-9*a^-7*b^4*x^-5//3+5*a^-6*b^3*x^-2+54*a^-10*b^7*x^-2//3+165*a^-12*b^9*log(a+b*x^1//3)+-18//7*a^-5*b^2*x^-7//3+-3//2*a^-10*b^9*(a+b*x^1//3)^-2+9//8*b*a^-4*x^-8//3+63//4*a^-8*b^5*x^-4//3)
@test integrate((1+x^1//3)^-1//2, x) == :(-4*(1+x^1//3)^3//2+6*(1+x^1//3)^(1/2)+6//5*(1+x^1//3)^5//2)
@test integrate(x^-3//2*(1+x^1//3)^-1, x) == :(-2*x^-1//2+6*x^-1//6+6*arctan(x^1//6))
@test integrate(x^2//3*(1+x^1//3)^-1, x) == :(-1x+-3*x^1//3+3*log(1+x^1//3)+3//2*x^2//3+3//4*x^4//3)
@test integrate((1+x^2//3)^-1, x) == :(-3*arctan(x^1//3)+3*x^1//3)
@test integrate(x^-1//3*(1+x^2//3)^-1, x) == :(3//2*log(1+x^2//3))
@test integrate(x^-2//3*(1+x^2//3)^-1, x) == :(3*arctan(x^1//3))
@test integrate(x^-1//3*(-1+x^2//3)^(1/2), x) == :((-1+x^2//3)^3//2)
@test integrate(x^-1//3*(1+x^2//3)^3//2, x) == :(3//5*(1+x^2//3)^5//2)
@test integrate(x^(1/2)*(1+x^2//3)^-1, x) == :(-6*x^1//6+6//5*x^5//6+-3//2*2^(1/2)*arctan(1+-1*2^(1/2)*x^1//6)+-3//4*2^(1/2)*log(1+x^1//3+-1*2^(1/2)*x^1//6)+3//2*2^(1/2)*arctan(1+2^(1/2)*x^1//6)+3//4*2^(1/2)*log(1+x^1//3+2^(1/2)*x^1//6))
@test integrate((3+-1*x^-1//2)^(1/2), x) == :(x*(3+-1*x^-1//2)^(1/2)+-1//6*x^(1/2)*(3+-1*x^-1//2)^(1/2)+-1//18*3^(1/2)*arctanh(1//3*3^(1/2)*(3+-1*x^-1//2)^(1/2)))
@test integrate((1+x^-1//2)^-1//2, x) == :(3//2*arctanh((1+x^-1//2)^(1/2))+x*(1+x^-1//2)^(1/2)+-3//2*x^(1/2)*(1+x^-1//2)^(1/2))
@test integrate((a+b*x^-3//2)^2//3, x) == :(x*(a+b*x^-3//2)^2//3+b^2//3*log((a+b*x^-3//2)^1//3+-1*b^1//3*x^-1//2)+-2//3*3^(1/2)*b^2//3*arctan(1//3*3^(1/2)*(1+2*b^1//3*x^-1//2*(a+b*x^-3//2)^-1//3)))
@test integrate(x^4*(a+b*x^-1//3), x) == :(1//5*a*x^5+3//14*b*x^14//3)
@test integrate(x^3*(a+b*x^-1//3), x) == :(1//4*a*x^4+3//11*b*x^11//3)
@test integrate(x^2*(a+b*x^-1//3), x) == :(1//3*a*x^3+3//8*b*x^8//3)
@test integrate(x*(a+b*x^-1//3), x) == :((1/2)*a*x^2+3//5*b*x^5//3)
@test integrate(a+b*x^-1//3, x) == :(a*x+3//2*b*x^2//3)
@test integrate(x^-1*(a+b*x^-1//3), x) == :(a*log(x)+-3*b*x^-1//3)
@test integrate(x^-2*(a+b*x^-1//3), x) == :(-1*a*x^-1+-3//4*b*x^-4//3)
@test integrate(x^-3*(a+b*x^-1//3), x) == :(-3//7*b*x^-7//3+-1//2*a*x^-2)
@test integrate(x^-4*(a+b*x^-1//3), x) == :(-3//10*b*x^-10//3+-1//3*a*x^-3)
@test integrate(x^4*(a+b*x^-1//3)^2, x) == :(1//5*a^2*x^5+3//13*b^2*x^13//3+3//7*a*b*x^14//3)
@test integrate(x^3*(a+b*x^-1//3)^2, x) == :(1//4*a^2*x^4+3//10*b^2*x^10//3+6//11*a*b*x^11//3)
@test integrate(x^2*(a+b*x^-1//3)^2, x) == :(1//3*a^2*x^3+3//7*b^2*x^7//3+3//4*a*b*x^8//3)
@test integrate(x*(a+b*x^-1//3)^2, x) == :((1/2)*a^2*x^2+3//4*b^2*x^4//3+6//5*a*b*x^5//3)
@test integrate((a+b*x^-1//3)^2, x) == :(x*a^-1*(a+b*x^-1//3)^3)
@test integrate(x^-1*(a+b*x^-1//3)^2, x) == :(a^2*log(x)+-3//2*b^2*x^-2//3+-6*a*b*x^-1//3)
@test integrate(x^-2*(a+b*x^-1//3)^2, x) == :(-1*a^2*x^-1+-3//5*b^2*x^-5//3+-3//2*a*b*x^-4//3)
@test integrate(x^-3*(a+b*x^-1//3)^2, x) == :(-3//8*b^2*x^-8//3+-1//2*a^2*x^-2+-6//7*a*b*x^-7//3)
@test integrate(x^-4*(a+b*x^-1//3)^2, x) == :(-3//11*b^2*x^-11//3+-1//3*a^2*x^-3+-3//5*a*b*x^-10//3)
@test integrate(x^4*(a+b*x^-1//3)^3, x) == :(1//4*b^3*x^4+1//5*a^3*x^5+9//13*a*b^2*x^13//3+9//14*b*a^2*x^14//3)
@test integrate(x^3*(a+b*x^-1//3)^3, x) == :(1//3*b^3*x^3+1//4*a^3*x^4+9//10*a*b^2*x^10//3+9//11*b*a^2*x^11//3)
@test integrate(x^2*(a+b*x^-1//3)^3, x) == :((1/2)*b^3*x^2+1//3*a^3*x^3+9//7*a*b^2*x^7//3+9//8*b*a^2*x^8//3)
@test integrate(x*(a+b*x^-1//3)^3, x) == :(x*b^3+(1/2)*a^3*x^2+9//4*a*b^2*x^4//3+9//5*b*a^2*x^5//3)
@test integrate((a+b*x^-1//3)^3, x) == :(x*a^3+b^3*log(x)+9*a*b^2*x^1//3+9//2*b*a^2*x^2//3)
@test integrate(x^-1*(a+b*x^-1//3)^3, x) == :(a^3*log(x)+-1*b^3*x^-1+-9*b*a^2*x^-1//3+-9//2*a*b^2*x^-2//3)
@test integrate(x^-2*(a+b*x^-1//3)^3, x) == :(-1*a^3*x^-1+-1//2*b^3*x^-2+-9//4*b*a^2*x^-4//3+-9//5*a*b^2*x^-5//3)
@test integrate(x^-3*(a+b*x^-1//3)^3, x) == :(-1//2*a^3*x^-2+-1//3*b^3*x^-3+-9//7*b*a^2*x^-7//3+-9//8*a*b^2*x^-8//3)
@test integrate(x^-4*(a+b*x^-1//3)^3, x) == :(-1//3*a^3*x^-3+-1//4*b^3*x^-4+-9//10*b*a^2*x^-10//3+-9//11*a*b^2*x^-11//3)
@test integrate(x^2*(a+b*x^-1//3)^-1, x) == :(1//3*a^-1*x^3+x*a^-7*b^6+-3*a^-10*b^9*log(b+a*x^1//3)+3*a^-9*b^8*x^1//3+-3//2*a^-8*b^7*x^2//3+-3//4*a^-6*b^5*x^4//3+-3//8*b*a^-2*x^8//3+-1//2*a^-4*b^3*x^2+3//5*a^-5*b^4*x^5//3+3//7*a^-3*b^2*x^7//3)
@test integrate(x*(a+b*x^-1//3)^-1, x) == :((1/2)*a^-1*x^2+-1*x*a^-4*b^3+-3*a^-6*b^5*x^1//3+3*a^-7*b^6*log(b+a*x^1//3)+-3//5*b*a^-2*x^5//3+3//2*a^-5*b^4*x^2//3+3//4*a^-3*b^2*x^4//3)
@test integrate((a+b*x^-1//3)^-1, x) == :(x*a^-1+-1*a^-4*b^3*log(x)+-3*a^-4*b^3*log(a+b*x^-1//3)+3*a^-3*b^2*x^1//3+-3//2*b*a^-2*x^2//3)
@test integrate(x^-1*(a+b*x^-1//3)^-1, x) == :(3*a^-1*log(b+a*x^1//3))
@test integrate(x^-2*(a+b*x^-1//3)^-1, x) == :(-3//2*b^-1*x^-2//3+a^2*b^-3*log(x)+-3*a^2*b^-3*log(b+a*x^1//3)+3*a*b^-2*x^-1//3)
@test integrate(x^-3*(a+b*x^-1//3)^-1, x) == :(-3//5*b^-1*x^-5//3+-1*a^2*b^-3*x^-1+-1*a^5*b^-6*log(x)+-3*a^4*b^-5*x^-1//3+3*a^5*b^-6*log(b+a*x^1//3)+3//2*a^3*b^-4*x^-2//3+3//4*a*b^-2*x^-4//3)
@test integrate(x^-4*(a+b*x^-1//3)^-1, x) == :(-3//8*b^-1*x^-8//3+a^5*b^-6*x^-1+a^8*b^-9*log(x)+-3*a^8*b^-9*log(b+a*x^1//3)+3*a^7*b^-8*x^-1//3+-3//2*a^6*b^-7*x^-2//3+-3//4*a^4*b^-5*x^-4//3+-1//2*a^2*b^-3*x^-2+3//5*a^3*b^-4*x^-5//3+3//7*a*b^-2*x^-7//3)
@test integrate(x^-5*(a+b*x^-1//3)^-1, x) == :(-3//11*b^-1*x^-11//3+(1/2)*a^5*b^-6*x^-2+-1*a^8*b^-9*x^-1+-1*a^11*b^-12*log(x)+-3*a^10*b^-11*x^-1//3+3*a^11*b^-12*log(b+a*x^1//3)+-3//5*a^6*b^-7*x^-5//3+-3//7*a^4*b^-5*x^-7//3+-1//3*a^2*b^-3*x^-3+3//2*a^9*b^-10*x^-2//3+3//4*a^7*b^-8*x^-4//3+3//8*a^3*b^-4*x^-8//3+3//10*a*b^-2*x^-10//3)
@test integrate(x^2*(a+b*x^-1//3)^-2, x) == :(1//3*a^-2*x^3+-30*a^-11*b^9*log(b+a*x^1//3)+-12*a^-9*b^7*x^2//3+-3*a^-11*b^10*(b+a*x^1//3)^-1+-2*a^-5*b^3*x^2+3*a^-6*b^4*x^5//3+7*x*a^-8*b^6+27*a^-10*b^8*x^1//3+-9//2*a^-7*b^5*x^4//3+-3//4*b*a^-3*x^8//3+9//7*a^-4*b^2*x^7//3)
@test integrate(x*(a+b*x^-1//3)^-2, x) == :((1/2)*a^-2*x^2+-18*a^-7*b^5*x^1//3+-4*x*a^-5*b^3+3*a^-8*b^7*(b+a*x^1//3)^-1+21*a^-8*b^6*log(b+a*x^1//3)+-6//5*b*a^-3*x^5//3+9//4*a^-4*b^2*x^4//3+15//2*a^-6*b^4*x^2//3)
@test integrate((a+b*x^-1//3)^-2, x) == :(x*a^-2+-12*a^-5*b^3*log(a+b*x^-1//3)+-4*a^-5*b^3*log(x)+-3*b*a^-3*x^2//3+3*a^-4*b^3*(a+b*x^-1//3)^-1+9*a^-4*b^2*x^1//3)
@test integrate(x^-1*(a+b*x^-1//3)^-2, x) == :(3*a^-2*log(b+a*x^1//3)+3*b*a^-2*(b+a*x^1//3)^-1)
@test integrate(x^-2*(a+b*x^-1//3)^-2, x) == :(-3*b^-2*x^-1//3+-3*a*b^-2*(b+a*x^1//3)^-1+-2*a*b^-3*log(x)+6*a*b^-3*log(b+a*x^1//3))
@test integrate(x^-3*(a+b*x^-1//3)^-2, x) == :(-3//4*b^-2*x^-4//3+-15*a^4*b^-6*log(b+a*x^1//3)+2*a*b^-3*x^-1+3*a^4*b^-5*(b+a*x^1//3)^-1+5*a^4*b^-6*log(x)+12*a^3*b^-5*x^-1//3+-9//2*a^2*b^-4*x^-2//3)
@test integrate(x^-4*(a+b*x^-1//3)^-2, x) == :(-3//7*b^-2*x^-7//3+a*b^-3*x^-2+-21*a^6*b^-8*x^-1//3+-8*a^7*b^-9*log(x)+-5*a^4*b^-6*x^-1+-3*a^7*b^-8*(b+a*x^1//3)^-1+3*a^3*b^-5*x^-4//3+9*a^5*b^-7*x^-2//3+24*a^7*b^-9*log(b+a*x^1//3)+-9//5*a^2*b^-4*x^-5//3)
@test integrate(x^-5*(a+b*x^-1//3)^-2, x) == :(-3//10*b^-2*x^-10//3+-33*a^10*b^-12*log(b+a*x^1//3)+3*a^10*b^-11*(b+a*x^1//3)^-1+8*a^7*b^-9*x^-1+11*a^10*b^-12*log(x)+30*a^9*b^-11*x^-1//3+-27//2*a^8*b^-10*x^-2//3+-21//4*a^6*b^-8*x^-4//3+-9//8*a^2*b^-4*x^-8//3+-5//2*a^4*b^-6*x^-2+2//3*a*b^-3*x^-3+12//7*a^3*b^-5*x^-7//3+18//5*a^5*b^-7*x^-5//3)
@test integrate(x^2*(a+b*x^-1//3)^-3, x) == :(1//3*a^-3*x^3+-165*a^-12*b^9*log(b+a*x^1//3)+-54*a^-10*b^7*x^2//3+-33*a^-12*b^10*(b+a*x^1//3)^-1+-5*a^-6*b^3*x^2+9*a^-7*b^4*x^5//3+28*x*a^-9*b^6+135*a^-11*b^8*x^1//3+-63//4*a^-8*b^5*x^4//3+-9//8*b*a^-4*x^8//3+3//2*a^-12*b^11*(b+a*x^1//3)^-2+18//7*a^-5*b^2*x^7//3)
@test integrate(x*(a+b*x^-1//3)^-3, x) == :((1/2)*a^-3*x^2+-63*a^-8*b^5*x^1//3+-10*x*a^-6*b^3+24*a^-9*b^7*(b+a*x^1//3)^-1+84*a^-9*b^6*log(b+a*x^1//3)+-9//5*b*a^-4*x^5//3+-3//2*a^-9*b^8*(b+a*x^1//3)^-2+9//2*a^-5*b^2*x^4//3+45//2*a^-7*b^4*x^2//3)
@test integrate((a+b*x^-1//3)^-3, x) == :(x*a^-3+-30*a^-6*b^3*log(a+b*x^-1//3)+-10*a^-6*b^3*log(x)+12*a^-5*b^3*(a+b*x^-1//3)^-1+18*a^-5*b^2*x^1//3+-9//2*b*a^-4*x^2//3+3//2*a^-4*b^3*(a+b*x^-1//3)^-2)
@test integrate(x^-1*(a+b*x^-1//3)^-3, x) == :(3*a^-3*log(b+a*x^1//3)+6*b*a^-3*(b+a*x^1//3)^-1+-3//2*a^-3*b^2*(b+a*x^1//3)^-2)
@test integrate(x^-2*(a+b*x^-1//3)^-3, x) == :(b^-3*log(x)+-3*b^-3*log(b+a*x^1//3)+3*b^-2*(b+a*x^1//3)^-1+3//2*b^-1*(b+a*x^1//3)^-2)
@test integrate(x^-3*(a+b*x^-1//3)^-3, x) == :(-1*b^-3*x^-1+-18*a^2*b^-5*x^-1//3+-12*a^3*b^-5*(b+a*x^1//3)^-1+-10*a^3*b^-6*log(x)+30*a^3*b^-6*log(b+a*x^1//3)+-3//2*a^3*b^-4*(b+a*x^1//3)^-2+9//2*a*b^-4*x^-2//3)
@test integrate(x^-4*(a+b*x^-1//3)^-3, x) == :(-1//2*b^-3*x^-2+-84*a^6*b^-9*log(b+a*x^1//3)+10*a^3*b^-6*x^-1+21*a^6*b^-8*(b+a*x^1//3)^-1+28*a^6*b^-9*log(x)+63*a^5*b^-8*x^-1//3+-45//2*a^4*b^-7*x^-2//3+-9//2*a^2*b^-5*x^-4//3+3//2*a^6*b^-7*(b+a*x^1//3)^-2+9//5*a*b^-4*x^-5//3)
@test integrate(x^-5*(a+b*x^-1//3)^-3, x) == :(-1//3*b^-3*x^-3+-135*a^8*b^-11*x^-1//3+-55*a^9*b^-12*log(x)+-30*a^9*b^-11*(b+a*x^1//3)^-1+-28*a^6*b^-9*x^-1+-9*a^4*b^-7*x^-5//3+5*a^3*b^-6*x^-2+54*a^7*b^-10*x^-2//3+165*a^9*b^-12*log(b+a*x^1//3)+-18//7*a^2*b^-5*x^-7//3+-3//2*a^9*b^-10*(b+a*x^1//3)^-2+9//8*a*b^-4*x^-8//3+63//4*a^5*b^-8*x^-4//3)
@test integrate((1+b*x^-1//3)^-1, x) == :(x+-1*b^3*log(x)+-3*b^3*log(1+b*x^-1//3)+3*b^2*x^1//3+-3//2*b*x^2//3)
@test integrate(x^2//3*(1+x^5//3)^2//3, x) == :(9//25*(1+x^5//3)^5//3)
@test integrate(x^7//3*(a^10//3+-1*x^10//3)^19//7, x) == :(-21//260*(a^10//3+-1*x^10//3)^26//7)
@test integrate((1+x^1//5)^-1, x) == :(-5*x^1//5+5*log(1+x^1//5)+-5//3*x^3//5+5//2*x^2//5+5//4*x^4//5)
@test integrate(x^-1//5*(1+x^4//5)^-1//2, x) == :(5//2*(1+x^4//5)^(1/2))
@test integrate((a+b*x^-3//5)^2//3, x) == :(x*a^-1*(a+b*x^-3//5)^5//3)
@test integrate(x^3*(a+b*x^n), x) == :(1//4*a*x^4+b*x^(4+n)*(4+n)^-1)
@test integrate(x^2*(a+b*x^n), x) == :(1//3*a*x^3+b*x^(3+n)*(3+n)^-1)
@test integrate(x*(a+b*x^n), x) == :((1/2)*a*x^2+b*x^(2+n)*(2+n)^-1)
@test integrate(a+b*x^n, x) == :(a*x+b*x^(1+n)*(1+n)^-1)
@test integrate(x^-1*(a+b*x^n), x) == :(a*log(x)+b*n^-1*x^n)
@test integrate(x^-2*(a+b*x^n), x) == :(-1*a*x^-1+-1*b*x^(-1+n)*(1+-1n)^-1)
@test integrate(x^-3*(a+b*x^n), x) == :(-1//2*a*x^-2+-1*b*x^(-2+n)*(2+-1n)^-1)
@test integrate(x^3*(a+b*x^n)^2, x) == :(1//4*a^2*x^4+b^2*x^(4+2n)*(4+2n)^-1+2*a*b*x^(4+n)*(4+n)^-1)
@test integrate(x^2*(a+b*x^n)^2, x) == :(1//3*a^2*x^3+b^2*x^(3+2n)*(3+2n)^-1+2*a*b*x^(3+n)*(3+n)^-1)
@test integrate(x*(a+b*x^n)^2, x) == :((1/2)*a^2*x^2+b^2*x^(2+2n)*(2+2n)^-1+2*a*b*x^(2+n)*(2+n)^-1)
@test integrate((a+b*x^n)^2, x) == :(x*a^2+b^2*x^(1+2n)*(1+2n)^-1+2*a*b*x^(1+n)*(1+n)^-1)
@test integrate(x^-1*(a+b*x^n)^2, x) == :(a^2*log(x)+(1/2)*b^2*n^-1*x^(2n)+2*a*b*n^-1*x^n)
@test integrate(x^-2*(a+b*x^n)^2, x) == :(-1*a^2*x^-1+-1*b^2*x^(-1+2n)*(1+-2n)^-1+-2*a*b*x^(-1+n)*(1+-1n)^-1)
@test integrate(x^-3*(a+b*x^n)^2, x) == :(-1//2*a^2*x^-2+-1*b^2*x^(-2+2n)*(2+-2n)^-1+-2*a*b*x^(-2+n)*(2+-1n)^-1)
@test integrate(x^3*(a+b*x^n)^3, x) == :(1//4*a^3*x^4+b^3*x^(4+3n)*(4+3n)^-1+3*a*b^2*x^(4+2n)*(4+2n)^-1+3*b*a^2*x^(4+n)*(4+n)^-1)
@test integrate(x^2*(a+b*x^n)^3, x) == :(1//3*a^3*x^3+b^3*x^(3+3n)*(3+3n)^-1+3*a*b^2*x^(3+2n)*(3+2n)^-1+3*b*a^2*x^(3+n)*(3+n)^-1)
@test integrate(x*(a+b*x^n)^3, x) == :((1/2)*a^3*x^2+b^3*x^(2+3n)*(2+3n)^-1+3*a*b^2*x^(2+2n)*(2+2n)^-1+3*b*a^2*x^(2+n)*(2+n)^-1)
@test integrate((a+b*x^n)^3, x) == :(x*a^3+b^3*x^(1+3n)*(1+3n)^-1+3*a*b^2*x^(1+2n)*(1+2n)^-1+3*b*a^2*x^(1+n)*(1+n)^-1)
@test integrate(x^-1*(a+b*x^n)^3, x) == :(a^3*log(x)+1//3*b^3*n^-1*x^(3n)+3*b*a^2*n^-1*x^n+3//2*a*b^2*n^-1*x^(2n))
@test integrate(x^-2*(a+b*x^n)^3, x) == :(-1*a^3*x^-1+-1*b^3*x^(-1+3n)*(1+-3n)^-1+-3*a*b^2*x^(-1+2n)*(1+-2n)^-1+-3*b*a^2*x^(-1+n)*(1+-1n)^-1)
@test integrate(x^-3*(a+b*x^n)^3, x) == :(-1//2*a^3*x^-2+-1*b^3*x^(-2+3n)*(2+-3n)^-1+-3*a*b^2*x^(-2+2n)*(2+-2n)^-1+-3*b*a^2*x^(-2+n)*(2+-1n)^-1)
@test integrate(x^-1*(a+b*x^n)^-1, x) == :(a^-1*log(x)+-1*a^-1*n^-1*log(a+b*x^n))
@test integrate(x^-1*(a+b*x^n)^-2, x) == :(a^-2*log(x)+a^-1*n^-1*(a+b*x^n)^-1+-1*a^-2*n^-1*log(a+b*x^n))
@test integrate(x^-1*(a+b*x^n)^-3, x) == :(a^-3*log(x)+a^-2*n^-1*(a+b*x^n)^-1+(1/2)*a^-1*n^-1*(a+b*x^n)^-2+-1*a^-3*n^-1*log(a+b*x^n))
@test integrate(x^-1*(a+b*x^n)^(1/2), x) == :(2*n^-1*(a+b*x^n)^(1/2)+-2*a^(1/2)*n^-1*arctanh(a^-1//2*(a+b*x^n)^(1/2)))
@test integrate(x^-1*(a+b*x^n)^3//2, x) == :(2//3*n^-1*(a+b*x^n)^3//2+-2*a^3//2*n^-1*arctanh(a^-1//2*(a+b*x^n)^(1/2))+2*a*n^-1*(a+b*x^n)^(1/2))
@test integrate(x^-1*(a+b*x^n)^5//2, x) == :(2//5*n^-1*(a+b*x^n)^5//2+-2*a^5//2*n^-1*arctanh(a^-1//2*(a+b*x^n)^(1/2))+2*a^2*n^-1*(a+b*x^n)^(1/2)+2//3*a*n^-1*(a+b*x^n)^3//2)
@test integrate(x^-1*(a+b*x^n)^-1//2, x) == :(-2*a^-1//2*n^-1*arctanh(a^-1//2*(a+b*x^n)^(1/2)))
@test integrate(x^-1*(a+b*x^n)^-3//2, x) == :(-2*a^-3//2*n^-1*arctanh(a^-1//2*(a+b*x^n)^(1/2))+2*a^-1*n^-1*(a+b*x^n)^-1//2)
@test integrate(x^-1*(a+b*x^n)^-5//2, x) == :(-2*a^-5//2*n^-1*arctanh(a^-1//2*(a+b*x^n)^(1/2))+2*a^-2*n^-1*(a+b*x^n)^-1//2+2//3*a^-1*n^-1*(a+b*x^n)^-3//2)
@test integrate(x^-1*(a+b*x^n)^1//3, x) == :(3*n^-1*(a+b*x^n)^1//3+-1//2*a^1//3*log(x)+3//2*a^1//3*n^-1*log(a^1//3+-1*(a+b*x^n)^1//3)+-1*3^(1/2)*a^1//3*n^-1*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+2*(a+b*x^n)^1//3)))
@test integrate(x^(-1+4n)*(a+b*x^n), x) == :(1//4*a*n^-1*x^(4n)+1//5*b*n^-1*x^(5n))
@test integrate(x^(-1+3n)*(a+b*x^n), x) == :(1//3*a*n^-1*x^(3n)+1//4*b*n^-1*x^(4n))
@test integrate(x^(-1+2n)*(a+b*x^n), x) == :((1/2)*a*n^-1*x^(2n)+1//3*b*n^-1*x^(3n))
@test integrate(x^(-1+n)*(a+b*x^n), x) == :(a*n^-1*x^n+(1/2)*b*n^-1*x^(2n))
@test integrate(x^-1*(a+b*x^n), x) == :(a*log(x)+b*n^-1*x^n)
@test integrate(x^(-1+-1n)*(a+b*x^n), x) == :(b*log(x)+-1*a*n^-1*x^(-1n))
@test integrate(x^(-1+-2n)*(a+b*x^n), x) == :(-1*b*n^-1*x^(-1n)+-1//2*a*n^-1*x^(-2n))
@test integrate(x^(-1+-3n)*(a+b*x^n), x) == :(-1//2*b*n^-1*x^(-2n)+-1//3*a*n^-1*x^(-3n))
@test integrate(x^(-1+-4n)*(a+b*x^n), x) == :(-1//3*b*n^-1*x^(-3n)+-1//4*a*n^-1*x^(-4n))
@test integrate(x^(-1+-5n)*(a+b*x^n), x) == :(-1//4*b*n^-1*x^(-4n)+-1//5*a*n^-1*x^(-5n))
@test integrate(x^(-1+4n)*(a+b*x^n)^2, x) == :(1//4*a^2*n^-1*x^(4n)+1//6*b^2*n^-1*x^(6n)+2//5*a*b*n^-1*x^(5n))
@test integrate(x^(-1+3n)*(a+b*x^n)^2, x) == :(1//3*a^2*n^-1*x^(3n)+1//5*b^2*n^-1*x^(5n)+(1/2)*a*b*n^-1*x^(4n))
@test integrate(x^(-1+2n)*(a+b*x^n)^2, x) == :((1/2)*a^2*n^-1*x^(2n)+1//4*b^2*n^-1*x^(4n)+2//3*a*b*n^-1*x^(3n))
@test integrate(x^(-1+n)*(a+b*x^n)^2, x) == :(1//3*b^-1*n^-1*(a+b*x^n)^3)
@test integrate(x^-1*(a+b*x^n)^2, x) == :(a^2*log(x)+(1/2)*b^2*n^-1*x^(2n)+2*a*b*n^-1*x^n)
@test integrate(x^(-1+-1n)*(a+b*x^n)^2, x) == :(b^2*n^-1*x^n+-1*a^2*n^-1*x^(-1n)+2*a*b*log(x))
@test integrate(x^(-1+-2n)*(a+b*x^n)^2, x) == :(b^2*log(x)+-1//2*a^2*n^-1*x^(-2n)+-2*a*b*n^-1*x^(-1n))
@test integrate(x^(-1+-3n)*(a+b*x^n)^2, x) == :(-1//3*a^-1*n^-1*x^(-3n)*(a+b*x^n)^3)
@test integrate(x^(-1+-4n)*(a+b*x^n)^2, x) == :(-1//2*b^2*n^-1*x^(-2n)+-1//4*a^2*n^-1*x^(-4n)+-2//3*a*b*n^-1*x^(-3n))
@test integrate(x^(-1+-5n)*(a+b*x^n)^2, x) == :(-1//3*b^2*n^-1*x^(-3n)+-1//5*a^2*n^-1*x^(-5n)+-1//2*a*b*n^-1*x^(-4n))
@test integrate(x^(-1+-6n)*(a+b*x^n)^2, x) == :(-1//4*b^2*n^-1*x^(-4n)+-1//6*a^2*n^-1*x^(-6n)+-2//5*a*b*n^-1*x^(-5n))
@test integrate(x^(-1+4n)*(a+b*x^n)^3, x) == :(1//4*a^3*n^-1*x^(4n)+1//7*b^3*n^-1*x^(7n)+(1/2)*a*b^2*n^-1*x^(6n)+3//5*b*a^2*n^-1*x^(5n))
@test integrate(x^(-1+3n)*(a+b*x^n)^3, x) == :(1//3*a^3*n^-1*x^(3n)+1//6*b^3*n^-1*x^(6n)+3//4*b*a^2*n^-1*x^(4n)+3//5*a*b^2*n^-1*x^(5n))
@test integrate(x^(-1+2n)*(a+b*x^n)^3, x) == :(1//5*b^-2*n^-1*(a+b*x^n)^5+-1//4*a*b^-2*n^-1*(a+b*x^n)^4)
@test integrate(x^(-1+n)*(a+b*x^n)^3, x) == :(1//4*b^-1*n^-1*(a+b*x^n)^4)
@test integrate(x^-1*(a+b*x^n)^3, x) == :(a^3*log(x)+1//3*b^3*n^-1*x^(3n)+3*b*a^2*n^-1*x^n+3//2*a*b^2*n^-1*x^(2n))
@test integrate(x^(-1+-1n)*(a+b*x^n)^3, x) == :((1/2)*b^3*n^-1*x^(2n)+-1*a^3*n^-1*x^(-1n)+3*b*a^2*log(x)+3*a*b^2*n^-1*x^n)
@test integrate(x^(-1+-2n)*(a+b*x^n)^3, x) == :(b^3*n^-1*x^n+3*a*b^2*log(x)+-1//2*a^3*n^-1*x^(-2n)+-3*b*a^2*n^-1*x^(-1n))
@test integrate(x^(-1+-3n)*(a+b*x^n)^3, x) == :(b^3*log(x)+-1//3*a^3*n^-1*x^(-3n)+-3*a*b^2*n^-1*x^(-1n)+-3//2*b*a^2*n^-1*x^(-2n))
@test integrate(x^(-1+-4n)*(a+b*x^n)^3, x) == :(-1//4*a^-1*n^-1*x^(-4n)*(a+b*x^n)^4)
@test integrate(x^(-1+-5n)*(a+b*x^n)^3, x) == :(-1//5*a^-1*n^-1*x^(-5n)*(a+b*x^n)^4+1//20*b*a^-2*n^-1*x^(-4n)*(a+b*x^n)^4)
@test integrate(x^(-1+-6n)*(a+b*x^n)^3, x) == :(-1//3*b^3*n^-1*x^(-3n)+-1//6*a^3*n^-1*x^(-6n)+-3//4*a*b^2*n^-1*x^(-4n)+-3//5*b*a^2*n^-1*x^(-5n))
@test integrate(x^(-1+-7n)*(a+b*x^n)^3, x) == :(-1//4*b^3*n^-1*x^(-4n)+-1//7*a^3*n^-1*x^(-7n)+-3//5*a*b^2*n^-1*x^(-5n)+-1//2*b*a^2*n^-1*x^(-6n))
@test integrate(x^(-1+4n)*(a+b*x^n)^5, x) == :(1//9*b^-4*n^-1*(a+b*x^n)^9+-3//8*a*b^-4*n^-1*(a+b*x^n)^8+-1//6*a^3*b^-4*n^-1*(a+b*x^n)^6+3//7*a^2*b^-4*n^-1*(a+b*x^n)^7)
@test integrate(x^(-1+3n)*(a+b*x^n)^5, x) == :(1//8*b^-3*n^-1*(a+b*x^n)^8+-2//7*a*b^-3*n^-1*(a+b*x^n)^7+1//6*a^2*b^-3*n^-1*(a+b*x^n)^6)
@test integrate(x^(-1+2n)*(a+b*x^n)^5, x) == :(1//7*b^-2*n^-1*(a+b*x^n)^7+-1//6*a*b^-2*n^-1*(a+b*x^n)^6)
@test integrate(x^(-1+n)*(a+b*x^n)^5, x) == :(1//6*b^-1*n^-1*(a+b*x^n)^6)
@test integrate(x^-1*(a+b*x^n)^5, x) == :(a^5*log(x)+1//5*b^5*n^-1*x^(5n)+5*b*a^4*n^-1*x^n+5*a^3*b^2*n^-1*x^(2n)+5//4*a*b^4*n^-1*x^(4n)+10//3*a^2*b^3*n^-1*x^(3n))
@test integrate(x^(-1+-1n)*(a+b*x^n)^5, x) == :(-1*a^5*n^-1*x^(-1n)+5*b*a^4*log(x)+1//4*b^5*n^-1*x^(4n)+5*a^2*b^3*n^-1*x^(2n)+10*a^3*b^2*n^-1*x^n+5//3*a*b^4*n^-1*x^(3n))
@test integrate(x^(-1+-2n)*(a+b*x^n)^5, x) == :(10*a^3*b^2*log(x)+-1//2*a^5*n^-1*x^(-2n)+1//3*b^5*n^-1*x^(3n)+-5*b*a^4*n^-1*x^(-1n)+10*a^2*b^3*n^-1*x^n+5//2*a*b^4*n^-1*x^(2n))
@test integrate(x^(-1+-3n)*(a+b*x^n)^5, x) == :((1/2)*b^5*n^-1*x^(2n)+10*a^2*b^3*log(x)+-1//3*a^5*n^-1*x^(-3n)+-10*a^3*b^2*n^-1*x^(-1n)+5*a*b^4*n^-1*x^n+-5//2*b*a^4*n^-1*x^(-2n))
@test integrate(x^(-1+-4n)*(a+b*x^n)^5, x) == :(b^5*n^-1*x^n+5*a*b^4*log(x)+-1//4*a^5*n^-1*x^(-4n)+-10*a^2*b^3*n^-1*x^(-1n)+-5*a^3*b^2*n^-1*x^(-2n)+-5//3*b*a^4*n^-1*x^(-3n))
@test integrate(x^(-1+-5n)*(a+b*x^n)^5, x) == :(b^5*log(x)+-1//5*a^5*n^-1*x^(-5n)+-5*a*b^4*n^-1*x^(-1n)+-5*a^2*b^3*n^-1*x^(-2n)+-10//3*a^3*b^2*n^-1*x^(-3n)+-5//4*b*a^4*n^-1*x^(-4n))
@test integrate(x^(-1+-6n)*(a+b*x^n)^5, x) == :(-1//6*a^-1*n^-1*x^(-6n)*(a+b*x^n)^6)
@test integrate(x^(-1+-7n)*(a+b*x^n)^5, x) == :(-1//7*a^-1*n^-1*x^(-7n)*(a+b*x^n)^6+1//42*b*a^-2*n^-1*x^(-6n)*(a+b*x^n)^6)
@test integrate(x^(-1+-8n)*(a+b*x^n)^5, x) == :(-1//8*a^-1*n^-1*x^(-8n)*(a+b*x^n)^6+-1//168*a^-3*b^2*n^-1*x^(-6n)*(a+b*x^n)^6+1//28*b*a^-2*n^-1*x^(-7n)*(a+b*x^n)^6)
@test integrate(x^(-1+-9n)*(a+b*x^n)^5, x) == :(-1//4*b^5*n^-1*x^(-4n)+-1//9*a^5*n^-1*x^(-9n)+-1*a*b^4*n^-1*x^(-5n)+-10//7*a^3*b^2*n^-1*x^(-7n)+-5//3*a^2*b^3*n^-1*x^(-6n)+-5//8*b*a^4*n^-1*x^(-8n))
@test integrate(x^(-1+-10n)*(a+b*x^n)^5, x) == :(-1//5*b^5*n^-1*x^(-5n)+-1//10*a^5*n^-1*x^(-10n)+-10//7*a^2*b^3*n^-1*x^(-7n)+-5//4*a^3*b^2*n^-1*x^(-8n)+-5//6*a*b^4*n^-1*x^(-6n)+-5//9*b*a^4*n^-1*x^(-9n))
@test integrate(x^(-1+9n)*(a+b*x^n)^8, x) == :(1//9*a^8*n^-1*x^(9n)+1//17*b^8*n^-1*x^(17n)+(1/2)*a*b^7*n^-1*x^(16n)+4*a^3*b^5*n^-1*x^(14n)+4//5*b*a^7*n^-1*x^(10n)+14//3*a^5*b^3*n^-1*x^(12n)+28//11*a^6*b^2*n^-1*x^(11n)+28//15*a^2*b^6*n^-1*x^(15n)+70//13*a^4*b^4*n^-1*x^(13n))
@test integrate(x^(-1+8n)*(a+b*x^n)^8, x) == :(1//8*a^8*n^-1*x^(8n)+1//16*b^8*n^-1*x^(16n)+2*a^2*b^6*n^-1*x^(14n)+8//9*b*a^7*n^-1*x^(9n)+8//15*a*b^7*n^-1*x^(15n)+14//5*a^6*b^2*n^-1*x^(10n)+35//6*a^4*b^4*n^-1*x^(12n)+56//11*a^5*b^3*n^-1*x^(11n)+56//13*a^3*b^5*n^-1*x^(13n))
@test integrate(x^(-1+7n)*(a+b*x^n)^8, x) == :(1//15*b^-7*n^-1*(a+b*x^n)^15+-5//3*a^3*b^-7*n^-1*(a+b*x^n)^12+-3//5*a^5*b^-7*n^-1*(a+b*x^n)^10+-3//7*a*b^-7*n^-1*(a+b*x^n)^14+1//9*a^6*b^-7*n^-1*(a+b*x^n)^9+15//11*a^4*b^-7*n^-1*(a+b*x^n)^11+15//13*a^2*b^-7*n^-1*(a+b*x^n)^13)
@test integrate(x^(-1+6n)*(a+b*x^n)^8, x) == :(1//14*b^-6*n^-1*(a+b*x^n)^14+(1/2)*a^4*b^-6*n^-1*(a+b*x^n)^10+-10//11*a^3*b^-6*n^-1*(a+b*x^n)^11+-5//13*a*b^-6*n^-1*(a+b*x^n)^13+-1//9*a^5*b^-6*n^-1*(a+b*x^n)^9+5//6*a^2*b^-6*n^-1*(a+b*x^n)^12)
@test integrate(x^(-1+5n)*(a+b*x^n)^8, x) == :(1//13*b^-5*n^-1*(a+b*x^n)^13+-2//5*a^3*b^-5*n^-1*(a+b*x^n)^10+-1//3*a*b^-5*n^-1*(a+b*x^n)^12+1//9*a^4*b^-5*n^-1*(a+b*x^n)^9+6//11*a^2*b^-5*n^-1*(a+b*x^n)^11)
@test integrate(x^(-1+4n)*(a+b*x^n)^8, x) == :(1//12*b^-4*n^-1*(a+b*x^n)^12+-3//11*a*b^-4*n^-1*(a+b*x^n)^11+-1//9*a^3*b^-4*n^-1*(a+b*x^n)^9+3//10*a^2*b^-4*n^-1*(a+b*x^n)^10)
@test integrate(x^(-1+3n)*(a+b*x^n)^8, x) == :(1//11*b^-3*n^-1*(a+b*x^n)^11+-1//5*a*b^-3*n^-1*(a+b*x^n)^10+1//9*a^2*b^-3*n^-1*(a+b*x^n)^9)
@test integrate(x^(-1+2n)*(a+b*x^n)^8, x) == :(1//10*b^-2*n^-1*(a+b*x^n)^10+-1//9*a*b^-2*n^-1*(a+b*x^n)^9)
@test integrate(x^(-1+n)*(a+b*x^n)^8, x) == :(1//9*b^-1*n^-1*(a+b*x^n)^9)
@test integrate(x^-1*(a+b*x^n)^8, x) == :(a^8*log(x)+1//8*b^8*n^-1*x^(8n)+8*b*a^7*n^-1*x^n+14*a^6*b^2*n^-1*x^(2n)+8//7*a*b^7*n^-1*x^(7n)+14//3*a^2*b^6*n^-1*x^(6n)+35//2*a^4*b^4*n^-1*x^(4n)+56//3*a^5*b^3*n^-1*x^(3n)+56//5*a^3*b^5*n^-1*x^(5n))
@test integrate(x^(-1+-1n)*(a+b*x^n)^8, x) == :(-1*a^8*n^-1*x^(-1n)+8*b*a^7*log(x)+1//7*b^8*n^-1*x^(7n)+14*a^3*b^5*n^-1*x^(4n)+28*a^5*b^3*n^-1*x^(2n)+28*a^6*b^2*n^-1*x^n+4//3*a*b^7*n^-1*x^(6n)+28//5*a^2*b^6*n^-1*x^(5n)+70//3*a^4*b^4*n^-1*x^(3n))
@test integrate(x^(-1+-2n)*(a+b*x^n)^8, x) == :(28*a^6*b^2*log(x)+-1//2*a^8*n^-1*x^(-2n)+1//6*b^8*n^-1*x^(6n)+-8*b*a^7*n^-1*x^(-1n)+7*a^2*b^6*n^-1*x^(4n)+35*a^4*b^4*n^-1*x^(2n)+56*a^5*b^3*n^-1*x^n+8//5*a*b^7*n^-1*x^(5n)+56//3*a^3*b^5*n^-1*x^(3n))
@test integrate(x^(-1+-3n)*(a+b*x^n)^8, x) == :(56*a^5*b^3*log(x)+-1//3*a^8*n^-1*x^(-3n)+1//5*b^8*n^-1*x^(5n)+-28*a^6*b^2*n^-1*x^(-1n)+-4*b*a^7*n^-1*x^(-2n)+2*a*b^7*n^-1*x^(4n)+28*a^3*b^5*n^-1*x^(2n)+70*a^4*b^4*n^-1*x^n+28//3*a^2*b^6*n^-1*x^(3n))
@test integrate(x^(-1+-4n)*(a+b*x^n)^8, x) == :(70*a^4*b^4*log(x)+-1//4*a^8*n^-1*x^(-4n)+1//4*b^8*n^-1*x^(4n)+-56*a^5*b^3*n^-1*x^(-1n)+-14*a^6*b^2*n^-1*x^(-2n)+14*a^2*b^6*n^-1*x^(2n)+56*a^3*b^5*n^-1*x^n+-8//3*b*a^7*n^-1*x^(-3n)+8//3*a*b^7*n^-1*x^(3n))
@test integrate(x^(-1+-5n)*(a+b*x^n)^8, x) == :(56*a^3*b^5*log(x)+-1//5*a^8*n^-1*x^(-5n)+1//3*b^8*n^-1*x^(3n)+-70*a^4*b^4*n^-1*x^(-1n)+-28*a^5*b^3*n^-1*x^(-2n)+-2*b*a^7*n^-1*x^(-4n)+4*a*b^7*n^-1*x^(2n)+28*a^2*b^6*n^-1*x^n+-28//3*a^6*b^2*n^-1*x^(-3n))
@test integrate(x^(-1+-6n)*(a+b*x^n)^8, x) == :((1/2)*b^8*n^-1*x^(2n)+28*a^2*b^6*log(x)+-1//6*a^8*n^-1*x^(-6n)+-56*a^3*b^5*n^-1*x^(-1n)+-35*a^4*b^4*n^-1*x^(-2n)+-7*a^6*b^2*n^-1*x^(-4n)+8*a*b^7*n^-1*x^n+-56//3*a^5*b^3*n^-1*x^(-3n)+-8//5*b*a^7*n^-1*x^(-5n))
@test integrate(x^(-1+-7n)*(a+b*x^n)^8, x) == :(b^8*n^-1*x^n+8*a*b^7*log(x)+-1//7*a^8*n^-1*x^(-7n)+-28*a^2*b^6*n^-1*x^(-1n)+-28*a^3*b^5*n^-1*x^(-2n)+-14*a^5*b^3*n^-1*x^(-4n)+-70//3*a^4*b^4*n^-1*x^(-3n)+-28//5*a^6*b^2*n^-1*x^(-5n)+-4//3*b*a^7*n^-1*x^(-6n))
@test integrate(x^(-1+-8n)*(a+b*x^n)^8, x) == :(b^8*log(x)+-1//8*a^8*n^-1*x^(-8n)+-14*a^2*b^6*n^-1*x^(-2n)+-8*a*b^7*n^-1*x^(-1n)+-56//3*a^3*b^5*n^-1*x^(-3n)+-56//5*a^5*b^3*n^-1*x^(-5n)+-35//2*a^4*b^4*n^-1*x^(-4n)+-14//3*a^6*b^2*n^-1*x^(-6n)+-8//7*b*a^7*n^-1*x^(-7n))
@test integrate(x^(-1+-9n)*(a+b*x^n)^8, x) == :(-1//9*a^-1*n^-1*x^(-9n)*(a+b*x^n)^9)
@test integrate(x^(-1+-10n)*(a+b*x^n)^8, x) == :(-1//10*a^-1*n^-1*x^(-10n)*(a+b*x^n)^9+1//90*b*a^-2*n^-1*x^(-9n)*(a+b*x^n)^9)
@test integrate(x^(-1+-11n)*(a+b*x^n)^8, x) == :(-1//11*a^-1*n^-1*x^(-11n)*(a+b*x^n)^9+-1//495*a^-3*b^2*n^-1*x^(-9n)*(a+b*x^n)^9+1//55*b*a^-2*n^-1*x^(-10n)*(a+b*x^n)^9)
@test integrate(x^(-1+-12n)*(a+b*x^n)^8, x) == :(-1//12*a^-1*n^-1*x^(-12n)*(a+b*x^n)^9+-1//220*a^-3*b^2*n^-1*x^(-10n)*(a+b*x^n)^9+1//44*b*a^-2*n^-1*x^(-11n)*(a+b*x^n)^9+1//1980*a^-4*b^3*n^-1*x^(-9n)*(a+b*x^n)^9)
@test integrate(x^(-1+-13n)*(a+b*x^n)^8, x) == :(-1//13*a^-1*n^-1*x^(-13n)*(a+b*x^n)^9+-1//143*a^-3*b^2*n^-1*x^(-11n)*(a+b*x^n)^9+-1//6435*a^-5*b^4*n^-1*x^(-9n)*(a+b*x^n)^9+1//39*b*a^-2*n^-1*x^(-12n)*(a+b*x^n)^9+1//715*a^-4*b^3*n^-1*x^(-10n)*(a+b*x^n)^9)
@test integrate(x^(-1+-14n)*(a+b*x^n)^8, x) == :(-1//6*b^8*n^-1*x^(-6n)+-1//14*a^8*n^-1*x^(-14n)+-7*a^4*b^4*n^-1*x^(-10n)+-56//9*a^3*b^5*n^-1*x^(-9n)+-56//11*a^5*b^3*n^-1*x^(-11n)+-8//7*a*b^7*n^-1*x^(-7n)+-8//13*b*a^7*n^-1*x^(-13n)+-7//2*a^2*b^6*n^-1*x^(-8n)+-7//3*a^6*b^2*n^-1*x^(-12n))
@test integrate(x^(-1+-15n)*(a+b*x^n)^8, x) == :(-1//7*b^8*n^-1*x^(-7n)+-1//15*a^8*n^-1*x^(-15n)+-1*a*b^7*n^-1*x^(-8n)+-70//11*a^4*b^4*n^-1*x^(-11n)+-28//5*a^3*b^5*n^-1*x^(-10n)+-28//9*a^2*b^6*n^-1*x^(-9n)+-28//13*a^6*b^2*n^-1*x^(-13n)+-14//3*a^5*b^3*n^-1*x^(-12n)+-4//7*b*a^7*n^-1*x^(-14n))
@test integrate(x^(-1+n)*(a+b*x^n)^16, x) == :(1//17*b^-1*n^-1*(a+b*x^n)^17)
@test integrate(x^12*(a+b*x^13)^12, x) == :(1//169*b^-1*(a+b*x^13)^13)
@test integrate(x^24*(a+b*x^25)^12, x) == :(1//325*b^-1*(a+b*x^25)^13)
@test integrate(x^36*(a+b*x^37)^12, x) == :(1//481*b^-1*(a+b*x^37)^13)
@test integrate(x^(12m)*(a+b*x^(1+12m))^12, x) == :(1//13*b^-1*(1+12m)^-1*(a+b*x^(1+12m))^13)
@test integrate(x^(12m)*(a+b*x^(1+12m))^12, x) == :(1//13*b^-1*(1+12m)^-1*(a+b*x^(1+12m))^13)
@test integrate(x^(-1+5n)*(a+b*x^n)^-1, x) == :(1//4*b^-1*n^-1*x^(4n)+a^4*b^-5*n^-1*log(a+b*x^n)+(1/2)*a^2*b^-3*n^-1*x^(2n)+-1*a^3*b^-4*n^-1*x^n+-1//3*a*b^-2*n^-1*x^(3n))
@test integrate(x^(-1+4n)*(a+b*x^n)^-1, x) == :(1//3*b^-1*n^-1*x^(3n)+a^2*b^-3*n^-1*x^n+-1*a^3*b^-4*n^-1*log(a+b*x^n)+-1//2*a*b^-2*n^-1*x^(2n))
@test integrate(x^(-1+3n)*(a+b*x^n)^-1, x) == :((1/2)*b^-1*n^-1*x^(2n)+a^2*b^-3*n^-1*log(a+b*x^n)+-1*a*b^-2*n^-1*x^n)
@test integrate(x^(-1+2n)*(a+b*x^n)^-1, x) == :(b^-1*n^-1*x^n+-1*a*b^-2*n^-1*log(a+b*x^n))
@test integrate(x^(-1+n)*(a+b*x^n)^-1, x) == :(b^-1*n^-1*log(a+b*x^n))
@test integrate(x^-1*(a+b*x^n)^-1, x) == :(a^-1*log(x)+-1*a^-1*n^-1*log(a+b*x^n))
@test integrate(x^(-1+-1n)*(a+b*x^n)^-1, x) == :(-1*b*a^-2*log(x)+-1*a^-1*n^-1*x^(-1n)+b*a^-2*n^-1*log(a+b*x^n))
@test integrate(x^(-1+-2n)*(a+b*x^n)^-1, x) == :(a^-3*b^2*log(x)+-1//2*a^-1*n^-1*x^(-2n)+b*a^-2*n^-1*x^(-1n)+-1*a^-3*b^2*n^-1*log(a+b*x^n))
@test integrate(x^(-1+-3n)*(a+b*x^n)^-1, x) == :(-1*a^-4*b^3*log(x)+-1//3*a^-1*n^-1*x^(-3n)+a^-4*b^3*n^-1*log(a+b*x^n)+(1/2)*b*a^-2*n^-1*x^(-2n)+-1*a^-3*b^2*n^-1*x^(-1n))
@test integrate(x^(-1+5n)*(a+b*x^n)^-1, x) == :(1//4*b^-1*n^-1*x^(4n)+a^4*b^-5*n^-1*log(a+b*x^n)+(1/2)*a^2*b^-3*n^-1*x^(2n)+-1*a^3*b^-4*n^-1*x^n+-1//3*a*b^-2*n^-1*x^(3n))
@test integrate(x^(-1+4n)*(a+b*x^n)^-1, x) == :(1//3*b^-1*n^-1*x^(3n)+a^2*b^-3*n^-1*x^n+-1*a^3*b^-4*n^-1*log(a+b*x^n)+-1//2*a*b^-2*n^-1*x^(2n))
@test integrate(x^(-1+3n)*(a+b*x^n)^-1, x) == :((1/2)*b^-1*n^-1*x^(2n)+a^2*b^-3*n^-1*log(a+b*x^n)+-1*a*b^-2*n^-1*x^n)
@test integrate(x^(-1+2n)*(a+b*x^n)^-1, x) == :(b^-1*n^-1*x^n+-1*a*b^-2*n^-1*log(a+b*x^n))
@test integrate(x^(-1+n)*(a+b*x^n)^-1, x) == :(b^-1*n^-1*log(a+b*x^n))
@test integrate(x^-1*(a+b*x^n)^-1, x) == :(a^-1*log(x)+-1*a^-1*n^-1*log(a+b*x^n))
@test integrate(x^(-1+-1n)*(a+b*x^n)^-1, x) == :(-1*b*a^-2*log(x)+-1*a^-1*n^-1*x^(-1n)+b*a^-2*n^-1*log(a+b*x^n))
@test integrate(x^(-1+-2n)*(a+b*x^n)^-1, x) == :(a^-3*b^2*log(x)+-1//2*a^-1*n^-1*x^(-2n)+b*a^-2*n^-1*x^(-1n)+-1*a^-3*b^2*n^-1*log(a+b*x^n))
@test integrate(x^(-1+-3n)*(a+b*x^n)^-1, x) == :(-1*a^-4*b^3*log(x)+-1//3*a^-1*n^-1*x^(-3n)+a^-4*b^3*n^-1*log(a+b*x^n)+(1/2)*b*a^-2*n^-1*x^(-2n)+-1*a^-3*b^2*n^-1*x^(-1n))
@test integrate(x^(-1+5n)*(2+b*x^n)^-1, x) == :(-8*b^-4*n^-1*x^n+2*b^-3*n^-1*x^(2n)+16*b^-5*n^-1*log(2+b*x^n)+-2//3*b^-2*n^-1*x^(3n)+1//4*b^-1*n^-1*x^(4n))
@test integrate(x^(-1+4n)*(2+b*x^n)^-1, x) == :(-1*b^-2*n^-1*x^(2n)+-8*b^-4*n^-1*log(2+b*x^n)+4*b^-3*n^-1*x^n+1//3*b^-1*n^-1*x^(3n))
@test integrate(x^(-1+3n)*(2+b*x^n)^-1, x) == :((1/2)*b^-1*n^-1*x^(2n)+-2*b^-2*n^-1*x^n+4*b^-3*n^-1*log(2+b*x^n))
@test integrate(x^(-1+2n)*(2+b*x^n)^-1, x) == :(b^-1*n^-1*x^n+-2*b^-2*n^-1*log(2+b*x^n))
@test integrate(x^(-1+n)*(2+b*x^n)^-1, x) == :(b^-1*n^-1*log(2+b*x^n))
@test integrate(x^-1*(2+b*x^n)^-1, x) == :((1/2)*log(x)+-1//2*n^-1*log(2+b*x^n))
@test integrate(x^(-1+-1n)*(2+b*x^n)^-1, x) == :(-1//2*n^-1*x^(-1n)+-1//4*b*log(x)+1//4*b*n^-1*log(2+b*x^n))
@test integrate(x^(-1+-2n)*(2+b*x^n)^-1, x) == :(-1//4*n^-1*x^(-2n)+1//8*b^2*log(x)+-1//8*b^2*n^-1*log(2+b*x^n)+1//4*b*n^-1*x^(-1n))
@test integrate(x^(-1+-3n)*(2+b*x^n)^-1, x) == :(-1//6*n^-1*x^(-3n)+-1//16*b^3*log(x)+-1//8*b^2*n^-1*x^(-1n)+1//8*b*n^-1*x^(-2n)+1//16*b^3*n^-1*log(2+b*x^n))
@test integrate(x^(-1+4n)*(a+b*x^n)^-2, x) == :((1/2)*b^-2*n^-1*x^(2n)+a^3*b^-4*n^-1*(a+b*x^n)^-1+-2*a*b^-3*n^-1*x^n+3*a^2*b^-4*n^-1*log(a+b*x^n))
@test integrate(x^(-1+3n)*(a+b*x^n)^-2, x) == :(b^-2*n^-1*x^n+-1*a^2*b^-3*n^-1*(a+b*x^n)^-1+-2*a*b^-3*n^-1*log(a+b*x^n))
@test integrate(x^(-1+2n)*(a+b*x^n)^-2, x) == :(b^-2*n^-1*log(a+b*x^n)+a*b^-2*n^-1*(a+b*x^n)^-1)
@test integrate(x^(-1+n)*(a+b*x^n)^-2, x) == :(-1*b^-1*n^-1*(a+b*x^n)^-1)
@test integrate(x^-1*(a+b*x^n)^-2, x) == :(a^-2*log(x)+a^-1*n^-1*(a+b*x^n)^-1+-1*a^-2*n^-1*log(a+b*x^n))
@test integrate(x^(-1+-1n)*(a+b*x^n)^-2, x) == :(-1*a^-2*n^-1*x^(-1n)+-2*b*a^-3*log(x)+-1*b*a^-2*n^-1*(a+b*x^n)^-1+2*b*a^-3*n^-1*log(a+b*x^n))
@test integrate(x^(-1+-2n)*(a+b*x^n)^-2, x) == :(3*a^-4*b^2*log(x)+-1//2*a^-2*n^-1*x^(-2n)+a^-3*b^2*n^-1*(a+b*x^n)^-1+-3*a^-4*b^2*n^-1*log(a+b*x^n)+2*b*a^-3*n^-1*x^(-1n))
@test integrate(x^(-1+-3n)*(a+b*x^n)^-2, x) == :(-4*a^-5*b^3*log(x)+-1//3*a^-2*n^-1*x^(-3n)+b*a^-3*n^-1*x^(-2n)+-1*a^-4*b^3*n^-1*(a+b*x^n)^-1+-3*a^-4*b^2*n^-1*x^(-1n)+4*a^-5*b^3*n^-1*log(a+b*x^n))
@test integrate(x^(-1+4n)*(a+b*x^n)^-3, x) == :(b^-3*n^-1*x^n+(1/2)*a^3*b^-4*n^-1*(a+b*x^n)^-2+-3*a*b^-4*n^-1*log(a+b*x^n)+-3*a^2*b^-4*n^-1*(a+b*x^n)^-1)
@test integrate(x^(-1+3n)*(a+b*x^n)^-3, x) == :(b^-3*n^-1*log(a+b*x^n)+2*a*b^-3*n^-1*(a+b*x^n)^-1+-1//2*a^2*b^-3*n^-1*(a+b*x^n)^-2)
@test integrate(x^(-1+2n)*(a+b*x^n)^-3, x) == :((1/2)*a^-1*n^-1*x^(2n)*(a+b*x^n)^-2)
@test integrate(x^(-1+n)*(a+b*x^n)^-3, x) == :(-1//2*b^-1*n^-1*(a+b*x^n)^-2)
@test integrate(x^-1*(a+b*x^n)^-3, x) == :(a^-3*log(x)+a^-2*n^-1*(a+b*x^n)^-1+(1/2)*a^-1*n^-1*(a+b*x^n)^-2+-1*a^-3*n^-1*log(a+b*x^n))
@test integrate(x^(-1+-1n)*(a+b*x^n)^-3, x) == :(-1*a^-3*n^-1*x^(-1n)+-3*b*a^-4*log(x)+-2*b*a^-3*n^-1*(a+b*x^n)^-1+3*b*a^-4*n^-1*log(a+b*x^n)+-1//2*b*a^-2*n^-1*(a+b*x^n)^-2)
@test integrate(x^(-1+-2n)*(a+b*x^n)^-3, x) == :(6*a^-5*b^2*log(x)+-1//2*a^-3*n^-1*x^(-2n)+(1/2)*a^-3*b^2*n^-1*(a+b*x^n)^-2+-6*a^-5*b^2*n^-1*log(a+b*x^n)+3*b*a^-4*n^-1*x^(-1n)+3*a^-4*b^2*n^-1*(a+b*x^n)^-1)
@test integrate(x^(-1+-1//2*n)*(a+b*x^n)^-1, x) == :(-2*a^-1*n^-1*x^(-1//2*n)+2*a^-3//2*b^(1/2)*n^-1*arctan(a^(1/2)*b^-1//2*x^(-1//2*n)))
@test integrate(x^(-1+-2//3*n)*(a+b*x^n)^-1, x) == :(-3//2*a^-1*n^-1*x^(-2//3*n)+(1/2)*a^-5//3*b^2//3*n^-1*log(a^2//3+b^2//3*x^(2//3*n)+-1*a^1//3*b^1//3*x^(1//3*n))+-1*a^-5//3*b^2//3*n^-1*log(a^1//3+b^1//3*x^(1//3*n))+3^(1/2)*a^-5//3*b^2//3*n^-1*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*b^1//3*x^(1//3*n))))
@test integrate(x^(-1+-3//4*n)*(a+b*x^n)^-1, x) == :(-4//3*a^-1*n^-1*x^(-3//4*n)+2^(1/2)*a^-7//4*b^3//4*n^-1*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1//4*n))+(1/2)*2^(1/2)*a^-7//4*b^3//4*n^-1*log(a^(1/2)+b^(1/2)*x^((1/2)*n)+-1*2^(1/2)*a^1//4*b^1//4*x^(1//4*n))+-1*2^(1/2)*a^-7//4*b^3//4*n^-1*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1//4*n))+-1//2*2^(1/2)*a^-7//4*b^3//4*n^-1*log(a^(1/2)+b^(1/2)*x^((1/2)*n)+2^(1/2)*a^1//4*b^1//4*x^(1//4*n)))
@test integrate(x^(-1+-1n)*(a+b*x^n)^-1, x) == :(-1*b*a^-2*log(x)+-1*a^-1*n^-1*x^(-1n)+b*a^-2*n^-1*log(a+b*x^n))
@test integrate(x^(-1+-1//2*n)*(a+b*x^n)^-1, x) == :(-2*a^-1*n^-1*x^(-1//2*n)+2*a^-3//2*b^(1/2)*n^-1*arctan(a^(1/2)*b^-1//2*x^(-1//2*n)))
@test integrate(x^(-1+-1//3*n)*(a+b*x^n)^-1, x) == :(-3*a^-1*n^-1*x^(-1//3*n)+a^-4//3*b^1//3*n^-1*log(b^1//3+a^1//3*x^(-1//3*n))+-1//2*a^-4//3*b^1//3*n^-1*log(b^2//3+a^2//3*x^(-2//3*n)+-1*a^1//3*b^1//3*x^(-1//3*n))+-1*3^(1/2)*a^-4//3*b^1//3*n^-1*arctan(1//3*3^(1/2)*b^-1//3*(b^1//3+-2*a^1//3*x^(-1//3*n))))
@test integrate(x^(-1+-1//4*n)*(a+b*x^n)^-1, x) == :(-4*a^-1*n^-1*x^(-1//4*n)+2^(1/2)*a^-5//4*b^1//4*n^-1*arctan(1+2^(1/2)*a^1//4*b^-1//4*x^(-1//4*n))+(1/2)*2^(1/2)*a^-5//4*b^1//4*n^-1*log(b^(1/2)+a^(1/2)*x^(-1//2*n)+2^(1/2)*a^1//4*b^1//4*x^(-1//4*n))+-1*2^(1/2)*a^-5//4*b^1//4*n^-1*arctan(1+-1*2^(1/2)*a^1//4*b^-1//4*x^(-1//4*n))+-1//2*2^(1/2)*a^-5//4*b^1//4*n^-1*log(b^(1/2)+a^(1/2)*x^(-1//2*n)+-1*2^(1/2)*a^1//4*b^1//4*x^(-1//4*n)))
@test integrate(x^(-1+-3//2*n)*(a+b*x^n)^-1, x) == :(-2//3*a^-1*n^-1*x^(-3//2*n)+-2*a^-5//2*b^3//2*n^-1*arctan(a^(1/2)*b^-1//2*x^(-1//2*n))+2*b*a^-2*n^-1*x^(-1//2*n))
@test integrate(x^(-1+-5//4*n)*(a+b*x^n)^-1, x) == :(-4//5*a^-1*n^-1*x^(-5//4*n)+4*b*a^-2*n^-1*x^(-1//4*n)+2^(1/2)*a^-9//4*b^5//4*n^-1*arctan(1+-1*2^(1/2)*a^1//4*b^-1//4*x^(-1//4*n))+(1/2)*2^(1/2)*a^-9//4*b^5//4*n^-1*log(b^(1/2)+a^(1/2)*x^(-1//2*n)+-1*2^(1/2)*a^1//4*b^1//4*x^(-1//4*n))+-1*2^(1/2)*a^-9//4*b^5//4*n^-1*arctan(1+2^(1/2)*a^1//4*b^-1//4*x^(-1//4*n))+-1//2*2^(1/2)*a^-9//4*b^5//4*n^-1*log(b^(1/2)+a^(1/2)*x^(-1//2*n)+2^(1/2)*a^1//4*b^1//4*x^(-1//4*n)))
@test integrate(x^(-1+4n)*(a+b*x^n)^(1/2), x) == :(2//9*b^-4*n^-1*(a+b*x^n)^9//2+-6//7*a*b^-4*n^-1*(a+b*x^n)^7//2+-2//3*a^3*b^-4*n^-1*(a+b*x^n)^3//2+6//5*a^2*b^-4*n^-1*(a+b*x^n)^5//2)
@test integrate(x^(-1+3n)*(a+b*x^n)^(1/2), x) == :(2//7*b^-3*n^-1*(a+b*x^n)^7//2+-4//5*a*b^-3*n^-1*(a+b*x^n)^5//2+2//3*a^2*b^-3*n^-1*(a+b*x^n)^3//2)
@test integrate(x^(-1+2n)*(a+b*x^n)^(1/2), x) == :(2//5*b^-2*n^-1*(a+b*x^n)^5//2+-2//3*a*b^-2*n^-1*(a+b*x^n)^3//2)
@test integrate(x^(-1+n)*(a+b*x^n)^(1/2), x) == :(2//3*b^-1*n^-1*(a+b*x^n)^3//2)
@test integrate(x^-1*(a+b*x^n)^(1/2), x) == :(2*n^-1*(a+b*x^n)^(1/2)+-2*a^(1/2)*n^-1*arctanh(a^-1//2*(a+b*x^n)^(1/2)))
@test integrate(x^(-1+-1n)*(a+b*x^n)^(1/2), x) == :(-1*n^-1*x^(-1n)*(a+b*x^n)^(1/2)+-1*b*a^-1//2*n^-1*arctanh(a^-1//2*(a+b*x^n)^(1/2)))
@test integrate(x^(-1+-2n)*(a+b*x^n)^(1/2), x) == :(-1//2*n^-1*x^(-2n)*(a+b*x^n)^(1/2)+1//4*a^-3//2*b^2*n^-1*arctanh(a^-1//2*(a+b*x^n)^(1/2))+-1//4*b*a^-1*n^-1*x^(-1n)*(a+b*x^n)^(1/2))
@test integrate(x^(-1+-3n)*(a+b*x^n)^(1/2), x) == :(-1//3*n^-1*x^(-3n)*(a+b*x^n)^(1/2)+-1//8*a^-5//2*b^3*n^-1*arctanh(a^-1//2*(a+b*x^n)^(1/2))+-1//12*b*a^-1*n^-1*x^(-2n)*(a+b*x^n)^(1/2)+1//8*a^-2*b^2*n^-1*x^(-1n)*(a+b*x^n)^(1/2))
@test integrate(x^(-1+-4n)*(a+b*x^n)^(1/2), x) == :(-1//4*n^-1*x^(-4n)*(a+b*x^n)^(1/2)+5//64*a^-7//2*b^4*n^-1*arctanh(a^-1//2*(a+b*x^n)^(1/2))+-5//64*a^-3*b^3*n^-1*x^(-1n)*(a+b*x^n)^(1/2)+-1//24*b*a^-1*n^-1*x^(-3n)*(a+b*x^n)^(1/2)+5//96*a^-2*b^2*n^-1*x^(-2n)*(a+b*x^n)^(1/2))
@test integrate(x^(-1+4n)*(a+b*x^n)^-1//2, x) == :(2//7*b^-4*n^-1*(a+b*x^n)^7//2+-2*a^3*b^-4*n^-1*(a+b*x^n)^(1/2)+2*a^2*b^-4*n^-1*(a+b*x^n)^3//2+-6//5*a*b^-4*n^-1*(a+b*x^n)^5//2)
@test integrate(x^(-1+3n)*(a+b*x^n)^-1//2, x) == :(2//5*b^-3*n^-1*(a+b*x^n)^5//2+2*a^2*b^-3*n^-1*(a+b*x^n)^(1/2)+-4//3*a*b^-3*n^-1*(a+b*x^n)^3//2)
@test integrate(x^(-1+2n)*(a+b*x^n)^-1//2, x) == :(2//3*b^-2*n^-1*(a+b*x^n)^3//2+-2*a*b^-2*n^-1*(a+b*x^n)^(1/2))
@test integrate(x^(-1+n)*(a+b*x^n)^-1//2, x) == :(2*b^-1*n^-1*(a+b*x^n)^(1/2))
@test integrate(x^-1*(a+b*x^n)^-1//2, x) == :(-2*a^-1//2*n^-1*arctanh(a^-1//2*(a+b*x^n)^(1/2)))
@test integrate(x^(-1+-1n)*(a+b*x^n)^-1//2, x) == :(b*a^-3//2*n^-1*arctanh(a^-1//2*(a+b*x^n)^(1/2))+-1*a^-1*n^-1*x^(-1n)*(a+b*x^n)^(1/2))
@test integrate(x^(-1+-2n)*(a+b*x^n)^-1//2, x) == :(-3//4*a^-5//2*b^2*n^-1*arctanh(a^-1//2*(a+b*x^n)^(1/2))+-1//2*a^-1*n^-1*x^(-2n)*(a+b*x^n)^(1/2)+3//4*b*a^-2*n^-1*x^(-1n)*(a+b*x^n)^(1/2))
@test integrate(x^(-1+-3n)*(a+b*x^n)^-1//2, x) == :(-1//3*a^-1*n^-1*x^(-3n)*(a+b*x^n)^(1/2)+5//8*a^-7//2*b^3*n^-1*arctanh(a^-1//2*(a+b*x^n)^(1/2))+-5//8*a^-3*b^2*n^-1*x^(-1n)*(a+b*x^n)^(1/2)+5//12*b*a^-2*n^-1*x^(-2n)*(a+b*x^n)^(1/2))
@test integrate(x^(-1+-4n)*(a+b*x^n)^-1//2, x) == :(-35//64*a^-9//2*b^4*n^-1*arctanh(a^-1//2*(a+b*x^n)^(1/2))+-1//4*a^-1*n^-1*x^(-4n)*(a+b*x^n)^(1/2)+-35//96*a^-3*b^2*n^-1*x^(-2n)*(a+b*x^n)^(1/2)+7//24*b*a^-2*n^-1*x^(-3n)*(a+b*x^n)^(1/2)+35//64*a^-4*b^3*n^-1*x^(-1n)*(a+b*x^n)^(1/2))
@test integrate(x^m*(a+b*x^n)^3, x) == :(a^3*x^(1+m)*(1+m)^-1+b^3*x^(1+m+3n)*(1+m+3n)^-1+3*a*b^2*x^(1+m+2n)*(1+m+2n)^-1+3*b*a^2*x^(1+m+n)*(1+m+n)^-1)
@test integrate(x^m*(a+b*x^n)^2, x) == :(a^2*x^(1+m)*(1+m)^-1+b^2*x^(1+m+2n)*(1+m+2n)^-1+2*a*b*x^(1+m+n)*(1+m+n)^-1)
@test integrate(x^m*(a+b*x^n), x) == :(a*x^(1+m)*(1+m)^-1+b*x^(1+m+n)*(1+m+n)^-1)
@test integrate(x^(-1+7//2*n)*(a+b*x^n)^-1//2, x) == :(-5//8*a^3*b^-7//2*n^-1*arctanh(b^(1/2)*x^((1/2)*n)*(a+b*x^n)^-1//2)+1//3*b^-1*n^-1*x^(5//2*n)*(a+b*x^n)^(1/2)+-5//12*a*b^-2*n^-1*x^(3//2*n)*(a+b*x^n)^(1/2)+5//8*a^2*b^-3*n^-1*x^((1/2)*n)*(a+b*x^n)^(1/2))
@test integrate(x^(-1+5//2*n)*(a+b*x^n)^-1//2, x) == :((1/2)*b^-1*n^-1*x^(3//2*n)*(a+b*x^n)^(1/2)+3//4*a^2*b^-5//2*n^-1*arctanh(b^(1/2)*x^((1/2)*n)*(a+b*x^n)^-1//2)+-3//4*a*b^-2*n^-1*x^((1/2)*n)*(a+b*x^n)^(1/2))
@test integrate(x^(-1+3//2*n)*(a+b*x^n)^-1//2, x) == :(b^-1*n^-1*x^((1/2)*n)*(a+b*x^n)^(1/2)+-1*a*b^-3//2*n^-1*arctanh(b^(1/2)*x^((1/2)*n)*(a+b*x^n)^-1//2))
@test integrate(x^(-1+(1/2)*n)*(a+b*x^n)^-1//2, x) == :(2*b^-1//2*n^-1*arctanh(b^(1/2)*x^((1/2)*n)*(a+b*x^n)^-1//2))
@test integrate(x^(-1+-1//2*n)*(a+b*x^n)^-1//2, x) == :(-2*a^-1*n^-1*x^(-1//2*n)*(a+b*x^n)^(1/2))
@test integrate(x^(-1+-3//2*n)*(a+b*x^n)^-1//2, x) == :(-2//3*a^-1*n^-1*x^(-3//2*n)*(a+b*x^n)^(1/2)+4//3*b*a^-2*n^-1*x^(-1//2*n)*(a+b*x^n)^(1/2))
@test integrate(x^(-1+-5//2*n)*(a+b*x^n)^-1//2, x) == :(-2//5*a^-1*n^-1*x^(-5//2*n)*(a+b*x^n)^(1/2)+-16//15*a^-3*b^2*n^-1*x^(-1//2*n)*(a+b*x^n)^(1/2)+8//15*b*a^-2*n^-1*x^(-3//2*n)*(a+b*x^n)^(1/2))
@test integrate(x^(-1+-7//2*n)*(a+b*x^n)^-1//2, x) == :(-2//7*a^-1*n^-1*x^(-7//2*n)*(a+b*x^n)^(1/2)+-16//35*a^-3*b^2*n^-1*x^(-3//2*n)*(a+b*x^n)^(1/2)+12//35*b*a^-2*n^-1*x^(-5//2*n)*(a+b*x^n)^(1/2)+32//35*a^-4*b^3*n^-1*x^(-1//2*n)*(a+b*x^n)^(1/2))
@test integrate((1/2)*x^(-1+m)*(a+b*x^n)^-3//2*(2*a*m+b*x^n*(-1n+2m)), x) == :(x^m*(a+b*x^n)^-1//2)
@test integrate(x^m*(a+b*x^(3+3m))^-1//3, x) == :(-1//2*b^-1//3*(1+m)^-1*log(-1*(a+b*x^(3+3m))^1//3+b^1//3*x^(1+m))+1//3*3^(1/2)*b^-1//3*(1+m)^-1*arctan(1//3*3^(1/2)*(1+2*b^1//3*x^(1+m)*(a+b*x^(3+3m))^-1//3)))
@test integrate(x^(-1+1//3*n)*(a+b*x^n)^-1//3, x) == :(-3//2*b^-1//3*n^-1*log(-1*(a+b*x^n)^1//3+b^1//3*x^(1//3*n))+3^(1/2)*b^-1//3*n^-1*arctan(1//3*3^(1/2)*(1+2*b^1//3*x^(1//3*n)*(a+b*x^n)^-1//3)))
@test integrate(x^(-1+-2//3*n)*(a+b*x^n)^2//3, x) == :(-3//2*b^2//3*n^-1*log(-1*(a+b*x^n)^1//3+b^1//3*x^(1//3*n))+-3//2*n^-1*x^(-2//3*n)*(a+b*x^n)^2//3+3^(1/2)*b^2//3*n^-1*arctan(1//3*3^(1/2)*(1+2*b^1//3*x^(1//3*n)*(a+b*x^n)^-1//3)))
@test integrate((a+b*x^n)^(-2+-1*n^-1), x) == :(x*a^-1*(1+n)^-1*(a+b*x^n)^(-1+-1*n^-1)+n*x*a^-2*(1+n)^-1*(a+b*x^n)^(-1*n^-1))
@test integrate((a+b*x^n)^(-1+-1*n^-1), x) == :(x*a^-1*(a+b*x^n)^(-1*n^-1))
@test integrate(x^m*(b*x^n)^p, x) == :(x^(1+m)*(b*x^n)^p*(1+m+n*p)^-1)
@test integrate(x^2*(b*x^n)^p, x) == :(x^3*(b*x^n)^p*(3+n*p)^-1)
@test integrate(x*(b*x^n)^p, x) == :(x^2*(b*x^n)^p*(2+n*p)^-1)
@test integrate((b*x^n)^p, x) == :(x*(b*x^n)^p*(1+n*p)^-1)
@test integrate(x^-1*(b*x^n)^p, x) == :(n^-1*p^-1*(b*x^n)^p)
@test integrate(x^-2*(b*x^n)^p, x) == :(-1*x^-1*(b*x^n)^p*(1+-1*n*p)^-1)
@test integrate(x^-3*(b*x^n)^p, x) == :(-1*x^-2*(b*x^n)^p*(2+-1*n*p)^-1)
@test integrate(x^-4*(b*x^n)^p, x) == :(-1*x^-3*(b*x^n)^p*(3+-1*n*p)^-1)
@test integrate(x^(-1+n)*(a+b*x^n)^p, x) == :(b^-1*n^-1*(1+p)^-1*(a+b*x^n)^(1+p))
@test integrate(x^(-1+2n)*(a+b*x^n)^p, x) == :(b^-2*n^-1*(2+p)^-1*(a+b*x^n)^(2+p)+-1*a*b^-2*n^-1*(1+p)^-1*(a+b*x^n)^(1+p))
@test integrate(x^(-1+3n)*(a+b*x^n)^p, x) == :(b^-3*n^-1*(3+p)^-1*(a+b*x^n)^(3+p)+a^2*b^-3*n^-1*(1+p)^-1*(a+b*x^n)^(1+p)+-2*a*b^-3*n^-1*(2+p)^-1*(a+b*x^n)^(2+p))
@test integrate(x^(-1+4n)*(a+b*x^n)^p, x) == :(b^-4*n^-1*(4+p)^-1*(a+b*x^n)^(4+p)+-1*a^3*b^-4*n^-1*(1+p)^-1*(a+b*x^n)^(1+p)+-3*a*b^-4*n^-1*(3+p)^-1*(a+b*x^n)^(3+p)+3*a^2*b^-4*n^-1*(2+p)^-1*(a+b*x^n)^(2+p))
@test integrate(x^(-1+-1n+-1*n*p)*(a+b*x^n)^p, x) == :(-1*a^-1*n^-1*x^(-1*n*(1+p))*(1+p)^-1*(a+b*x^n)^(1+p))
@test integrate(x^(-1+-9n)*(a+b*x^n)^8, x) == :(-1//9*a^-1*n^-1*x^(-9n)*(a+b*x^n)^9)
@test integrate(x^(-4+-3p)*(a+b*x^3)^p, x) == :(-1//3*a^-1*x^(-3+-3p)*(1+p)^-1*(a+b*x^3)^(1+p))
@test integrate(x^-28*(a+b*x^3)^8, x) == :(-1//27*a^-1*x^-27*(a+b*x^3)^9)
@test integrate(x^-1*(a+b*x^n)^-1, x) == :(a^-1*log(x)+-1*a^-1*n^-1*log(a+b*x^n))
@test integrate(x^-1*(a+b*x^3)^-1, x) == :(a^-1*log(x)+-1//3*a^-1*log(a+b*x^3))
@test integrate((a+b*x^n)^(-1*n^-1*(1+2n)), x) == :(x*a^-1*(1+n)^-1*(a+b*x^n)^(-1*n^-1*(1+n))+n*x*a^-2*(1+n)^-1*(a+b*x^n)^(-1*n^-1))
@test integrate((a+b*x^n)^(-1*n^-1*(1+n)), x) == :(x*a^-1*(a+b*x^n)^(-1*n^-1))
@test integrate(x^-1*(a+b*x^(-1n))^-1, x) == :(a^-1*n^-1*log(b+a*x^n))
@test integrate(x^m*(a+b*x^(1+m))^-1, x) == :(b^-1*(1+m)^-1*log(a+b*x^(1+m)))
@test integrate(x^m*(a+b*x^(1+m))^n, x) == :(b^-1*(1+m)^-1*(1+n)^-1*(a+b*x^(1+m))^(1+n))
@test integrate(x^m*(a+b*x^(2+2m))^3, x) == :(a^3*x^(1+m)*(1+m)^-1+b^3*x^(7+7m)*(7+7m)^-1+b*a^2*x^(3+3m)*(1+m)^-1+3*a*b^2*x^(5+5m)*(5+5m)^-1)
@test integrate(x^m*(a+b*x^(2+2m))^2, x) == :(a^2*x^(1+m)*(1+m)^-1+b^2*x^(5+5m)*(5+5m)^-1+2*a*b*x^(3+3m)*(3+3m)^-1)
@test integrate(x^m*(a+b*x^(2+2m)), x) == :(a*x^(1+m)*(1+m)^-1+b*x^(3+3m)*(3+3m)^-1)
@test integrate(x^m*(a+b*x^(2+2m))^-1, x) == :(a^-1//2*b^-1//2*(1+m)^-1*arctan(a^-1//2*b^(1/2)*x^(1+m)))
@test integrate(x^m*(a+b*x^(2+2m))^-2, x) == :((1/2)*a^-1*x^(1+m)*(1+m)^-1*(a+b*x^(2+2m))^-1+(1/2)*a^-3//2*b^-1//2*(1+m)^-1*arctan(a^-1//2*b^(1/2)*x^(1+m)))
@test integrate(x^m*(a+b*x^(2+2m))^-3, x) == :(1//4*a^-1*x^(1+m)*(1+m)^-1*(a+b*x^(2+2m))^-2+3//8*a^-2*x^(1+m)*(1+m)^-1*(a+b*x^(2+2m))^-1+3//8*a^-5//2*b^-1//2*(1+m)^-1*arctan(a^-1//2*b^(1/2)*x^(1+m)))
@test integrate(x^m*(a+b*x^(2+2m))^5//2, x) == :(x^(1+m)*(6+6m)^-1*(a+b*x^(2+2m))^5//2+5*a*x^(1+m)*(24+24m)^-1*(a+b*x^(2+2m))^3//2+5*a^2*x^(1+m)*(16+16m)^-1*(a+b*x^(2+2m))^(1/2)+5//16*a^3*b^-1//2*(1+m)^-1*arctanh(b^(1/2)*x^(1+m)*(a+b*x^(2+2m))^-1//2))
@test integrate(x^m*(a+b*x^(2+2m))^3//2, x) == :(x^(1+m)*(4+4m)^-1*(a+b*x^(2+2m))^3//2+3*a*x^(1+m)*(8+8m)^-1*(a+b*x^(2+2m))^(1/2)+3//8*a^2*b^-1//2*(1+m)^-1*arctanh(b^(1/2)*x^(1+m)*(a+b*x^(2+2m))^-1//2))
@test integrate(x^m*(a+b*x^(2+2m))^(1/2), x) == :(x^(1+m)*(2+2m)^-1*(a+b*x^(2+2m))^(1/2)+(1/2)*a*b^-1//2*(1+m)^-1*arctanh(b^(1/2)*x^(1+m)*(a+b*x^(2+2m))^-1//2))
@test integrate(x^m*(a+b*x^(2+2m))^-1//2, x) == :(b^-1//2*(1+m)^-1*arctanh(b^(1/2)*x^(1+m)*(a+b*x^(2+2m))^-1//2))
@test integrate(x^m*(a+b*x^(2+2m))^-3//2, x) == :(a^-1*x^(1+m)*(1+m)^-1*(a+b*x^(2+2m))^-1//2)
@test integrate(x^m*(a+b*x^(2+2m))^-5//2, x) == :(a^-1*x^(1+m)*(1+m)^-1*(a+b*x^(2+2m))^-3//2+2//3*b*a^-2*x^(3+3m)*(1+m)^-1*(a+b*x^(2+2m))^-3//2)
@test integrate(x^m*(a+b*x^(2+2m))^-7//2, x) == :(a^-1*x^(1+m)*(1+m)^-1*(a+b*x^(2+2m))^-5//2+4//3*b*a^-2*x^(3+3m)*(1+m)^-1*(a+b*x^(2+2m))^-5//2+8//15*a^-3*b^2*x^(5+5m)*(1+m)^-1*(a+b*x^(2+2m))^-5//2)
@test integrate(x^n*(1+x^(1+n))^(1/2), x) == :(2*(1+x^(1+n))^3//2*(3+3n)^-1)
@test integrate(x^n*(a^2+x^(1+n))^(1/2), x) == :(2*(3+3n)^-1*(a^2+x^(1+n))^3//2)
@test integrate((c*x)^m*(a+b*x^n)^2, x) == :(a^2*c^-1*(c*x)^(1+m)*(1+m)^-1+b^2*x^(1+2n)*(c*x)^m*(1+m+2n)^-1+2*a*b*x^(1+n)*(c*x)^m*(1+m+n)^-1)
@test integrate((c*x)^m*(a+b*x^3)^2, x) == :(a^2*c^-1*(c*x)^(1+m)*(1+m)^-1+b^2*c^-7*(c*x)^(7+m)*(7+m)^-1+2*a*b*c^-4*(c*x)^(4+m)*(4+m)^-1)
@test integrate((c*x)^m*(a+b*x^2)^2, x) == :(a^2*c^-1*(c*x)^(1+m)*(1+m)^-1+b^2*c^-5*(c*x)^(5+m)*(5+m)^-1+2*a*b*c^-3*(c*x)^(3+m)*(3+m)^-1)
@test integrate((c*x)^m*(a+b*x)^2, x) == :(a^2*c^-1*(c*x)^(1+m)*(1+m)^-1+b^2*c^-3*(c*x)^(3+m)*(3+m)^-1+2*a*b*c^-2*(c*x)^(2+m)*(2+m)^-1)
@test integrate((c*x)^m*(a+b*x^-1)^2, x) == :(a^2*c^-1*(c*x)^(1+m)*(1+m)^-1+-1*c*b^2*(c*x)^(-1+m)*(1+-1m)^-1+2*a*b*m^-1*(c*x)^m)
@test integrate((c*x)^m*(a+b*x^-2)^2, x) == :(a^2*c^-1*(c*x)^(1+m)*(1+m)^-1+-1*b^2*c^3*(c*x)^(-3+m)*(3+-1m)^-1+-2*a*b*c*(c*x)^(-1+m)*(1+-1m)^-1)
@test integrate((c*x)^m*(a+b*x^-3)^2, x) == :(a^2*c^-1*(c*x)^(1+m)*(1+m)^-1+-1*b^2*c^5*(c*x)^(-5+m)*(5+-1m)^-1+-2*a*b*c^2*(c*x)^(-2+m)*(2+-1m)^-1)
@test integrate((c*x)^(-1+-1//2*n)*(a+b*x^n)^-1, x) == :(-2*a^-1*c^-1*n^-1*(c*x)^(-1//2*n)+2*a^-3//2*b^(1/2)*c^-1*n^-1*x^((1/2)*n)*(c*x)^(-1//2*n)*arctan(a^(1/2)*b^-1//2*x^(-1//2*n)))
@test integrate((c*x)^(-1+-2//3*n)*(a+b*x^n)^-1, x) == :(-3//2*a^-1*c^-1*n^-1*(c*x)^(-2//3*n)+(1/2)*a^-5//3*b^2//3*c^-1*n^-1*x^(2//3*n)*(c*x)^(-2//3*n)*log(a^2//3+b^2//3*x^(2//3*n)+-1*a^1//3*b^1//3*x^(1//3*n))+-1*a^-5//3*b^2//3*c^-1*n^-1*x^(2//3*n)*(c*x)^(-2//3*n)*log(a^1//3+b^1//3*x^(1//3*n))+3^(1/2)*a^-5//3*b^2//3*c^-1*n^-1*x^(2//3*n)*(c*x)^(-2//3*n)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*b^1//3*x^(1//3*n))))
@test integrate((c*x)^(-1+-3//4*n)*(a+b*x^n)^-1, x) == :(-4//3*a^-1*c^-1*n^-1*(c*x)^(-3//4*n)+2^(1/2)*a^-7//4*b^3//4*c^-1*n^-1*x^(3//4*n)*(c*x)^(-3//4*n)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1//4*n))+(1/2)*2^(1/2)*a^-7//4*b^3//4*c^-1*n^-1*x^(3//4*n)*(c*x)^(-3//4*n)*log(a^(1/2)+b^(1/2)*x^((1/2)*n)+-1*2^(1/2)*a^1//4*b^1//4*x^(1//4*n))+-1*2^(1/2)*a^-7//4*b^3//4*c^-1*n^-1*x^(3//4*n)*(c*x)^(-3//4*n)*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1//4*n))+-1//2*2^(1/2)*a^-7//4*b^3//4*c^-1*n^-1*x^(3//4*n)*(c*x)^(-3//4*n)*log(a^(1/2)+b^(1/2)*x^((1/2)*n)+2^(1/2)*a^1//4*b^1//4*x^(1//4*n)))
@test integrate((c*x)^(-1+-1n)*(a+b*x^n)^-1, x) == :(-1*a^-1*c^-1*n^-1*(c*x)^(-1n)+-1*b*a^-2*c^-1*x^n*(c*x)^(-1n)*log(x)+b*a^-2*c^-1*n^-1*x^n*(c*x)^(-1n)*log(a+b*x^n))
@test integrate((c*x)^(-1+-1//2*n)*(a+b*x^n)^-1, x) == :(-2*a^-1*c^-1*n^-1*(c*x)^(-1//2*n)+2*a^-3//2*b^(1/2)*c^-1*n^-1*x^((1/2)*n)*(c*x)^(-1//2*n)*arctan(a^(1/2)*b^-1//2*x^(-1//2*n)))
@test integrate((c*x)^(-1+-1//3*n)*(a+b*x^n)^-1, x) == :(-3*a^-1*c^-1*n^-1*(c*x)^(-1//3*n)+a^-4//3*b^1//3*c^-1*n^-1*x^(1//3*n)*(c*x)^(-1//3*n)*log(b^1//3+a^1//3*x^(-1//3*n))+-1//2*a^-4//3*b^1//3*c^-1*n^-1*x^(1//3*n)*(c*x)^(-1//3*n)*log(b^2//3+a^2//3*x^(-2//3*n)+-1*a^1//3*b^1//3*x^(-1//3*n))+-1*3^(1/2)*a^-4//3*b^1//3*c^-1*n^-1*x^(1//3*n)*(c*x)^(-1//3*n)*arctan(1//3*3^(1/2)*b^-1//3*(b^1//3+-2*a^1//3*x^(-1//3*n))))
@test integrate((c*x)^(-1+-1//4*n)*(a+b*x^n)^-1, x) == :(-4*a^-1*c^-1*n^-1*(c*x)^(-1//4*n)+2^(1/2)*a^-5//4*b^1//4*c^-1*n^-1*x^(1//4*n)*(c*x)^(-1//4*n)*arctan(1+2^(1/2)*a^1//4*b^-1//4*x^(-1//4*n))+(1/2)*2^(1/2)*a^-5//4*b^1//4*c^-1*n^-1*x^(1//4*n)*(c*x)^(-1//4*n)*log(b^(1/2)+a^(1/2)*x^(-1//2*n)+2^(1/2)*a^1//4*b^1//4*x^(-1//4*n))+-1*2^(1/2)*a^-5//4*b^1//4*c^-1*n^-1*x^(1//4*n)*(c*x)^(-1//4*n)*arctan(1+-1*2^(1/2)*a^1//4*b^-1//4*x^(-1//4*n))+-1//2*2^(1/2)*a^-5//4*b^1//4*c^-1*n^-1*x^(1//4*n)*(c*x)^(-1//4*n)*log(b^(1/2)+a^(1/2)*x^(-1//2*n)+-1*2^(1/2)*a^1//4*b^1//4*x^(-1//4*n)))
@test integrate((c*x)^(-1+-3//2*n)*(a+b*x^n)^-1, x) == :(-2//3*a^-1*c^-1*n^-1*(c*x)^(-3//2*n)+2*b*a^-2*c^-1*n^-1*x^n*(c*x)^(-3//2*n)+-2*a^-5//2*b^3//2*c^-1*n^-1*x^(3//2*n)*(c*x)^(-3//2*n)*arctan(a^(1/2)*b^-1//2*x^(-1//2*n)))
@test integrate((c*x)^(-1+-5//4*n)*(a+b*x^n)^-1, x) == :(-4//5*a^-1*c^-1*n^-1*(c*x)^(-5//4*n)+4*b*a^-2*c^-1*n^-1*x^n*(c*x)^(-5//4*n)+2^(1/2)*a^-9//4*b^5//4*c^-1*n^-1*x^(5//4*n)*(c*x)^(-5//4*n)*arctan(1+-1*2^(1/2)*a^1//4*b^-1//4*x^(-1//4*n))+(1/2)*2^(1/2)*a^-9//4*b^5//4*c^-1*n^-1*x^(5//4*n)*(c*x)^(-5//4*n)*log(b^(1/2)+a^(1/2)*x^(-1//2*n)+-1*2^(1/2)*a^1//4*b^1//4*x^(-1//4*n))+-1*2^(1/2)*a^-9//4*b^5//4*c^-1*n^-1*x^(5//4*n)*(c*x)^(-5//4*n)*arctan(1+2^(1/2)*a^1//4*b^-1//4*x^(-1//4*n))+-1//2*2^(1/2)*a^-9//4*b^5//4*c^-1*n^-1*x^(5//4*n)*(c*x)^(-5//4*n)*log(b^(1/2)+a^(1/2)*x^(-1//2*n)+2^(1/2)*a^1//4*b^1//4*x^(-1//4*n)))
@test integrate((c*x)^(-1+n)*(a+b*x^n)^-1, x) == :(b^-1*c^-1*n^-1*x^(-1n)*(c*x)^n*log(a+b*x^n))
@test integrate((c*x)^(-1+n)*(a+b*x^n)^-2, x) == :(a^-1*c^-1*n^-1*(c*x)^n*(a+b*x^n)^-1)
@test integrate((c*x)^(-1+7//2*n)*(a+b*x^n)^-1//2, x) == :(1//3*b^-1*c^-1*n^-1*x^(-1n)*(c*x)^(7//2*n)*(a+b*x^n)^(1/2)+-5//8*a^3*b^-7//2*c^-1*n^-1*x^(-7//2*n)*(c*x)^(7//2*n)*arctanh(b^(1/2)*x^((1/2)*n)*(a+b*x^n)^-1//2)+-5//12*a*b^-2*c^-1*n^-1*x^(-2n)*(c*x)^(7//2*n)*(a+b*x^n)^(1/2)+5//8*a^2*b^-3*c^-1*n^-1*x^(-3n)*(c*x)^(7//2*n)*(a+b*x^n)^(1/2))
@test integrate((c*x)^(-1+5//2*n)*(a+b*x^n)^-1//2, x) == :((1/2)*b^-1*c^-1*n^-1*x^(-1n)*(c*x)^(5//2*n)*(a+b*x^n)^(1/2)+-3//4*a*b^-2*c^-1*n^-1*x^(-2n)*(c*x)^(5//2*n)*(a+b*x^n)^(1/2)+3//4*a^2*b^-5//2*c^-1*n^-1*x^(-5//2*n)*(c*x)^(5//2*n)*arctanh(b^(1/2)*x^((1/2)*n)*(a+b*x^n)^-1//2))
@test integrate((c*x)^(-1+3//2*n)*(a+b*x^n)^-1//2, x) == :(b^-1*c^-1*n^-1*x^(-1n)*(c*x)^(3//2*n)*(a+b*x^n)^(1/2)+-1*a*b^-3//2*c^-1*n^-1*x^(-3//2*n)*(c*x)^(3//2*n)*arctanh(b^(1/2)*x^((1/2)*n)*(a+b*x^n)^-1//2))
@test integrate((c*x)^(-1+(1/2)*n)*(a+b*x^n)^-1//2, x) == :(2*b^-1//2*c^-1*n^-1*x^(-1//2*n)*(c*x)^((1/2)*n)*arctanh(b^(1/2)*x^((1/2)*n)*(a+b*x^n)^-1//2))
@test integrate((c*x)^(-1+-1//2*n)*(a+b*x^n)^-1//2, x) == :(-2*a^-1*c^-1*n^-1*(c*x)^(-1//2*n)*(a+b*x^n)^(1/2))
@test integrate((c*x)^(-1+-3//2*n)*(a+b*x^n)^-1//2, x) == :(-2*a^-1*c^-1*n^-1*(c*x)^(-3//2*n)*(a+b*x^n)^(1/2)+4//3*a^-2*c^-1*n^-1*(c*x)^(-3//2*n)*(a+b*x^n)^3//2)
@test integrate((c*x)^(-1+-5//2*n)*(a+b*x^n)^-1//2, x) == :(-2*a^-1*c^-1*n^-1*(c*x)^(-5//2*n)*(a+b*x^n)^(1/2)+-16//15*a^-3*c^-1*n^-1*(c*x)^(-5//2*n)*(a+b*x^n)^5//2+8//3*a^-2*c^-1*n^-1*(c*x)^(-5//2*n)*(a+b*x^n)^3//2)
@test integrate((c*x)^(-1+-7//2*n)*(a+b*x^n)^-1//2, x) == :(-2*a^-1*c^-1*n^-1*(c*x)^(-7//2*n)*(a+b*x^n)^(1/2)+4*a^-2*c^-1*n^-1*(c*x)^(-7//2*n)*(a+b*x^n)^3//2+-16//5*a^-3*c^-1*n^-1*(c*x)^(-7//2*n)*(a+b*x^n)^5//2+32//35*a^-4*c^-1*n^-1*(c*x)^(-7//2*n)*(a+b*x^n)^7//2)
@test integrate((c*x)^(-1+-1n+-1*n*p)*(a+b*x^n)^p, x) == :(-1*a^-1*c^-1*n^-1*(c*x)^(-1*n*(1+p))*(1+p)^-1*(a+b*x^n)^(1+p))
@test integrate((c*x)^(-1+-2n+-1*n*p)*(a+b*x^n)^p, x) == :(-1*a^-1*c^-1*n^-1*(c*x)^(-1*n*(2+p))*(1+p)^-1*(a+b*x^n)^(1+p)+a^-2*c^-1*n^-1*(c*x)^(-1*n*(2+p))*(1+p)^-1*(2+p)^-1*(a+b*x^n)^(2+p))
@test integrate((c*x)^(-1+-3n+-1*n*p)*(a+b*x^n)^p, x) == :(-1*a^-1*c^-1*n^-1*(c*x)^(-1*n*(3+p))*(1+p)^-1*(a+b*x^n)^(1+p)+2*a^-2*c^-1*n^-1*(c*x)^(-1*n*(3+p))*(1+p)^-1*(2+p)^-1*(a+b*x^n)^(2+p)+-2*a^-3*c^-1*n^-1*(c*x)^(-1*n*(3+p))*(1+p)^-1*(2+p)^-1*(3+p)^-1*(a+b*x^n)^(3+p))
@test integrate((c*(a+b*x)^2)^5//2, x) == :(1//6*b^-1*c^2*(c*(a+b*x)^2)^(1/2)*(a+b*x)^5)
@test integrate((c*(a+b*x)^2)^3//2, x) == :(1//4*c*b^-1*(c*(a+b*x)^2)^(1/2)*(a+b*x)^3)
@test integrate((c*(a+b*x)^2)^(1/2), x) == :((1/2)*b^-1*(c*(a+b*x)^2)^(1/2)*(a+b*x))
@test integrate((c*(a+b*x)^2)^-1//2, x) == :(b^-1*(c*(a+b*x)^2)^-1//2*(a+b*x)*log(a+b*x))
@test integrate((c*(a+b*x)^2)^-3//2, x) == :(-1//2*b^-1*c^-1*(c*(a+b*x)^2)^-1//2*(a+b*x)^-1)
@test integrate((c*(a+b*x)^2)^-5//2, x) == :(-1//4*b^-1*c^-2*(c*(a+b*x)^2)^-1//2*(a+b*x)^-3)
@test integrate(((3+5x)^2)^(1/2), x) == :(((3+5x)^2)^(1/2)*(3//10+(1/2)*x))
@test integrate(((6+10x)^2)^(1/2), x) == :(((3+5x)^2)^(1/2)*(3//5+x))
@test integrate(((3+5x)^2)^-1//2, x) == :(1//5*((3+5x)^2)^-1//2*(3+5x)*log(3+5x))
@test integrate((-1*(2+3x)^2)^-1//2, x) == :(1//3*(-1*(2+3x)^2)^-1//2*(2+3x)*log(2+3x))
@test integrate((c*(a+b*x)^3)^5//2, x) == :(2//17*b^-1*c^2*(c*(a+b*x)^3)^(1/2)*(a+b*x)^7)
@test integrate((c*(a+b*x)^3)^3//2, x) == :(2//11*c*b^-1*(c*(a+b*x)^3)^(1/2)*(a+b*x)^4)
@test integrate((c*(a+b*x)^3)^(1/2), x) == :(1//5*b^-1*(c*(a+b*x)^3)^(1/2)*(2a+2*b*x))
@test integrate((c*(a+b*x)^3)^-1//2, x) == :(-1*b^-1*(c*(a+b*x)^3)^-1//2*(2a+2*b*x))
@test integrate((c*(a+b*x)^3)^-3//2, x) == :(-2//7*b^-1*c^-1*(c*(a+b*x)^3)^-1//2*(a+b*x)^-2)
@test integrate((c*(a+b*x)^3)^-5//2, x) == :(-2//13*b^-1*c^-2*(c*(a+b*x)^3)^-1//2*(a+b*x)^-5)
@test integrate((c*(a+b*x)^-1)^5//2, x) == :(-2//3*b^-1*c^2*(c*(a+b*x)^-1)^(1/2)*(a+b*x)^-1)
@test integrate((c*(a+b*x)^-1)^3//2, x) == :(-2*c*b^-1*(c*(a+b*x)^-1)^(1/2))
@test integrate((c*(a+b*x)^-1)^(1/2), x) == :(2*b^-1*(c*(a+b*x)^-1)^(1/2)*(a+b*x))
@test integrate((c*(a+b*x)^-1)^-1//2, x) == :(1//3*b^-1*(c*(a+b*x)^-1)^-1//2*(2a+2*b*x))
@test integrate((c*(a+b*x)^-1)^-3//2, x) == :(2//5*b^-1*c^-1*(c*(a+b*x)^-1)^-1//2*(a+b*x)^2)
@test integrate((c*(a+b*x)^-1)^-5//2, x) == :(2//7*b^-1*c^-2*(c*(a+b*x)^-1)^-1//2*(a+b*x)^3)
@test integrate((c*(a+b*x)^-2)^5//2, x) == :(-1//4*b^-1*c^2*(c*(a+b*x)^-2)^(1/2)*(a+b*x)^-3)
@test integrate((c*(a+b*x)^-2)^3//2, x) == :(-1//2*c*b^-1*(c*(a+b*x)^-2)^(1/2)*(a+b*x)^-1)
@test integrate((c*(a+b*x)^-2)^(1/2), x) == :(b^-1*(c*(a+b*x)^-2)^(1/2)*(a+b*x)*log(a+b*x))
@test integrate((c*(a+b*x)^-2)^-1//2, x) == :((1/2)*b^-1*(c*(a+b*x)^-2)^-1//2*(a+b*x))
@test integrate((c*(a+b*x)^-2)^-3//2, x) == :(1//4*b^-1*c^-1*(c*(a+b*x)^-2)^-1//2*(a+b*x)^3)
@test integrate((c*(a+b*x)^-2)^-5//2, x) == :(1//6*b^-1*c^-2*(c*(a+b*x)^-2)^-1//2*(a+b*x)^5)
@test integrate((c*(a+b*x)^-3)^5//2, x) == :(-2//13*b^-1*c^2*(c*(a+b*x)^-3)^(1/2)*(a+b*x)^-5)
@test integrate((c*(a+b*x)^-3)^3//2, x) == :(-2//7*c*b^-1*(c*(a+b*x)^-3)^(1/2)*(a+b*x)^-2)
@test integrate((c*(a+b*x)^-3)^(1/2), x) == :(-2*b^-1*(c*(a+b*x)^-3)^(1/2)*(a+b*x))
@test integrate((c*(a+b*x)^-3)^-1//2, x) == :(1//5*b^-1*(c*(a+b*x)^-3)^-1//2*(2a+2*b*x))
@test integrate((c*(a+b*x)^-3)^-3//2, x) == :(2//11*b^-1*c^-1*(c*(a+b*x)^-3)^-1//2*(a+b*x)^4)
@test integrate((c*(a+b*x)^-3)^-5//2, x) == :(2//17*b^-1*c^-2*(c*(a+b*x)^-3)^-1//2*(a+b*x)^7)
@test integrate((c*(a+b*x)^3//2)^2//3, x) == :((1/2)*b^-1*(c*(a+b*x)^3//2)^2//3*(a+b*x))
@test integrate((c*(a+b*x)^2//3)^3//2, x) == :((1/2)*c*b^-1*(c*(a+b*x)^2//3)^(1/2)*(a+b*x)^5//3)
@test integrate((c*(a+b*x)^-3//2)^-2//3, x) == :((1/2)*b^-1*(c*(a+b*x)^-3//2)^-2//3*(a+b*x))
@test integrate((c*(a+b*x)^-2//3)^-3//2, x) == :((1/2)*b^-1*c^-1*(c*(a+b*x)^-2//3)^-1//2*(a+b*x)^5//3)
@test integrate((c+d*x)^3*(a+b*(c+d*x)^2), x) == :(1//4*a*d^-1*(c+d*x)^4+1//6*b*d^-1*(c+d*x)^6)
@test integrate((a+b*(c+d*x)^2)^2*(c+d*x)^3, x) == :(1//4*a^2*d^-1*(c+d*x)^4+1//8*b^2*d^-1*(c+d*x)^8+1//3*a*b*d^-1*(c+d*x)^6)
@test integrate((a+b*(c+d*x)^2)^3*(c+d*x)^3, x) == :(1//10*b^-2*d^-1*(a+b*(c+d*x)^2)^5+-1//8*a*b^-2*d^-1*(a+b*(c+d*x)^2)^4)
@test integrate((1+(2+x)^2)^-1*(2+x), x) == :((1/2)*log(1+(2+x)^2))
@test integrate((1+(2+x)^2)^-2*(2+x), x) == :(-1*(2+2*(2+x)^2)^-1)
@test integrate((1+(2+x)^2)^-3*(2+x), x) == :(-1//4*(1+(2+x)^2)^-2)
@test integrate((a+b*(c+d*x)^2)^p*(c+d*x)^5, x) == :((1/2)*b^-3*d^-1*(3+p)^-1*(a+b*(c+d*x)^2)^(3+p)+(1/2)*a^2*b^-3*d^-1*(1+p)^-1*(a+b*(c+d*x)^2)^(1+p)+-1*a*b^-3*d^-1*(2+p)^-1*(a+b*(c+d*x)^2)^(2+p))
@test integrate((a+b*(c+d*x)^2)^p*(c+d*x)^3, x) == :((1/2)*b^-2*d^-1*(2+p)^-1*(a+b*(c+d*x)^2)^(2+p)+-1//2*a*b^-2*d^-1*(1+p)^-1*(a+b*(c+d*x)^2)^(1+p))
@test integrate((a+b*(c+d*x)^2)^p*(c+d*x), x) == :((1/2)*b^-1*d^-1*(1+p)^-1*(a+b*(c+d*x)^2)^(1+p))
@test integrate((c+d*x)^3*(a+b*(c+d*x)^3), x) == :(1//4*a*d^-1*(c+d*x)^4+1//7*b*d^-1*(c+d*x)^7)
@test integrate((a+b*(c+d*x)^3)^2*(c+d*x)^3, x) == :(1//4*a^2*d^-1*(c+d*x)^4+1//10*b^2*d^-1*(c+d*x)^10+2//7*a*b*d^-1*(c+d*x)^7)
@test integrate((a+b*(c+d*x)^3)^3*(c+d*x)^3, x) == :(1//4*a^3*d^-1*(c+d*x)^4+1//13*b^3*d^-1*(c+d*x)^13+3//7*b*a^2*d^-1*(c+d*x)^7+3//10*a*b^2*d^-1*(c+d*x)^10)
@test integrate((c*e+d*e*x)^3*(a+b*(c+d*x)^3), x) == :(1//4*a*d^-1*e^3*(c+d*x)^4+1//7*b*d^-1*e^3*(c+d*x)^7)
@test integrate((a+b*(c+d*x)^3)^2*(c*e+d*e*x)^3, x) == :(1//4*a^2*d^-1*e^3*(c+d*x)^4+1//10*b^2*d^-1*e^3*(c+d*x)^10+2//7*a*b*d^-1*e^3*(c+d*x)^7)
@test integrate((a+b*(c+d*x)^3)^3*(c*e+d*e*x)^3, x) == :(1//4*a^3*d^-1*e^3*(c+d*x)^4+1//13*b^3*d^-1*e^3*(c+d*x)^13+3//7*b*a^2*d^-1*e^3*(c+d*x)^7+3//10*a*b^2*d^-1*e^3*(c+d*x)^10)
@test integrate((a+b*(c+d*x)^3)^-1*(c+d*x)^4, x) == :((1/2)*b^-1*d^-1*(c+d*x)^2+-1//6*a^2//3*b^-5//3*d^-1*log(a^2//3+b^2//3*(c+d*x)^2+-1*a^1//3*b^1//3*(c+d*x))+1//3*a^2//3*b^-5//3*d^-1*log(a^1//3+b^1//3*(c+d*x))+1//3*3^(1/2)*a^2//3*b^-5//3*d^-1*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*b^1//3*(c+d*x))))
@test integrate((a+b*(c+d*x)^3)^-1*(c+d*x)^3, x) == :(x*b^-1+-1//3*a^1//3*b^-4//3*d^-1*log(a^1//3+b^1//3*(c+d*x))+1//6*a^1//3*b^-4//3*d^-1*log(a^2//3+b^2//3*(c+d*x)^2+-1*a^1//3*b^1//3*(c+d*x))+1//3*3^(1/2)*a^1//3*b^-4//3*d^-1*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*b^1//3*(c+d*x))))
@test integrate((a+b*(c+d*x)^3)^-1*(c+d*x)^2, x) == :(1//3*b^-1*d^-1*log(a+b*(c+d*x)^3))
@test integrate((a+b*(c+d*x)^3)^-1*(c+d*x), x) == :(-1//3*a^-1//3*b^-2//3*d^-1*log(a^1//3+b^1//3*(c+d*x))+1//6*a^-1//3*b^-2//3*d^-1*log(a^2//3+b^2//3*(c+d*x)^2+-1*a^1//3*b^1//3*(c+d*x))+-1//3*3^(1/2)*a^-1//3*b^-2//3*d^-1*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*b^1//3*(c+d*x))))
@test integrate((a+b*(c+d*x)^3)^-1, x) == :(-1//6*a^-2//3*b^-1//3*d^-1*log(a^2//3+b^2//3*(c+d*x)^2+-1*a^1//3*b^1//3*(c+d*x))+1//3*a^-2//3*b^-1//3*d^-1*log(a^1//3+b^1//3*(c+d*x))+-1//3*3^(1/2)*a^-2//3*b^-1//3*d^-1*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*b^1//3*(c+d*x))))
@test integrate((a+b*(c+d*x)^3)^-1*(c+d*x)^-1, x) == :(a^-1*d^-1*log(c+d*x)+-1//3*a^-1*d^-1*log(a+b*(c+d*x)^3))
@test integrate((a+b*(c+d*x)^3)^-1*(c+d*x)^-2, x) == :(-1*a^-1*d^-1*(c+d*x)^-1+-1//6*a^-4//3*b^1//3*d^-1*log(a^2//3+b^2//3*(c+d*x)^2+-1*a^1//3*b^1//3*(c+d*x))+1//3*a^-4//3*b^1//3*d^-1*log(a^1//3+b^1//3*(c+d*x))+1//3*3^(1/2)*a^-4//3*b^1//3*d^-1*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*b^1//3*(c+d*x))))
@test integrate((a+b*(c+d*x)^3)^-1*(c+d*x)^-3, x) == :(-1//2*a^-1*d^-1*(c+d*x)^-2+-1//3*a^-5//3*b^2//3*d^-1*log(a^1//3+b^1//3*(c+d*x))+1//6*a^-5//3*b^2//3*d^-1*log(a^2//3+b^2//3*(c+d*x)^2+-1*a^1//3*b^1//3*(c+d*x))+1//3*3^(1/2)*a^-5//3*b^2//3*d^-1*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*b^1//3*(c+d*x))))
@test integrate((a+b*(c+d*x)^3)^-1*(c+d*x)^-4, x) == :(-1//3*a^-1*d^-1*(c+d*x)^-3+-1*b*a^-2*d^-1*log(c+d*x)+1//3*b*a^-2*d^-1*log(a+b*(c+d*x)^3))
@test integrate((a+b*(c+d*x)^3)^-2*(c+d*x)^4, x) == :(-2//9*a^-1//3*b^-5//3*d^-1*log(a^1//3+b^1//3*(c+d*x))+-1//3*b^-1*d^-1*(a+b*(c+d*x)^3)^-1*(c+d*x)^2+1//9*a^-1//3*b^-5//3*d^-1*log(a^2//3+b^2//3*(c+d*x)^2+-1*a^1//3*b^1//3*(c+d*x))+-2//9*3^(1/2)*a^-1//3*b^-5//3*d^-1*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*b^1//3*(c+d*x))))
@test integrate((a+b*(c+d*x)^3)^-2*(c+d*x)^3, x) == :(-1//3*b^-1*d^-1*(a+b*(c+d*x)^3)^-1*(c+d*x)+-1//18*a^-2//3*b^-4//3*d^-1*log(a^2//3+b^2//3*(c+d*x)^2+-1*a^1//3*b^1//3*(c+d*x))+1//9*a^-2//3*b^-4//3*d^-1*log(a^1//3+b^1//3*(c+d*x))+-1//9*3^(1/2)*a^-2//3*b^-4//3*d^-1*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*b^1//3*(c+d*x))))
@test integrate((a+b*(c+d*x)^3)^-2*(c+d*x)^2, x) == :(-1//3*b^-1*d^-1*(a+b*(c+d*x)^3)^-1)
@test integrate((a+b*(c+d*x)^3)^-2*(c+d*x), x) == :(-1//9*a^-4//3*b^-2//3*d^-1*log(a^1//3+b^1//3*(c+d*x))+1//3*a^-1*d^-1*(a+b*(c+d*x)^3)^-1*(c+d*x)^2+1//18*a^-4//3*b^-2//3*d^-1*log(a^2//3+b^2//3*(c+d*x)^2+-1*a^1//3*b^1//3*(c+d*x))+-1//9*3^(1/2)*a^-4//3*b^-2//3*d^-1*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*b^1//3*(c+d*x))))
@test integrate((a+b*(c+d*x)^3)^-2, x) == :(-1//9*a^-5//3*b^-1//3*d^-1*log(a^2//3+b^2//3*(c+d*x)^2+-1*a^1//3*b^1//3*(c+d*x))+1//3*a^-1*d^-1*(a+b*(c+d*x)^3)^-1*(c+d*x)+2//9*a^-5//3*b^-1//3*d^-1*log(a^1//3+b^1//3*(c+d*x))+-2//9*3^(1/2)*a^-5//3*b^-1//3*d^-1*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*b^1//3*(c+d*x))))
@test integrate((a+b*(c+d*x)^3)^-2*(c+d*x)^-1, x) == :(a^-2*d^-1*log(c+d*x)+-1//3*a^-2*d^-1*log(a+b*(c+d*x)^3)+1//3*a^-1*d^-1*(a+b*(c+d*x)^3)^-1)
@test integrate((a+b*(c+d*x)^3)^-2*(c+d*x)^-2, x) == :(-4//3*a^-2*d^-1*(c+d*x)^-1+-2//9*a^-7//3*b^1//3*d^-1*log(a^2//3+b^2//3*(c+d*x)^2+-1*a^1//3*b^1//3*(c+d*x))+1//3*a^-1*d^-1*(a+b*(c+d*x)^3)^-1*(c+d*x)^-1+4//9*a^-7//3*b^1//3*d^-1*log(a^1//3+b^1//3*(c+d*x))+4//9*3^(1/2)*a^-7//3*b^1//3*d^-1*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*b^1//3*(c+d*x))))
@test integrate((a+b*(c+d*x)^3)^-2*(c+d*x)^-3, x) == :(-5//6*a^-2*d^-1*(c+d*x)^-2+-5//9*a^-8//3*b^2//3*d^-1*log(a^1//3+b^1//3*(c+d*x))+1//3*a^-1*d^-1*(a+b*(c+d*x)^3)^-1*(c+d*x)^-2+5//18*a^-8//3*b^2//3*d^-1*log(a^2//3+b^2//3*(c+d*x)^2+-1*a^1//3*b^1//3*(c+d*x))+5//9*3^(1/2)*a^-8//3*b^2//3*d^-1*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*b^1//3*(c+d*x))))
@test integrate((a+b*(c+d*x)^3)^-2*(c+d*x)^-4, x) == :(-1//3*a^-2*d^-1*(c+d*x)^-3+-2*b*a^-3*d^-1*log(c+d*x)+-1//3*b*a^-2*d^-1*(a+b*(c+d*x)^3)^-1+2//3*b*a^-3*d^-1*log(a+b*(c+d*x)^3))
@test integrate((a+b*(c+d*x)^3)^-3*(c+d*x)^4, x) == :(-1//6*b^-1*d^-1*(a+b*(c+d*x)^3)^-2*(c+d*x)^2+-1//27*a^-4//3*b^-5//3*d^-1*log(a^1//3+b^1//3*(c+d*x))+1//54*a^-4//3*b^-5//3*d^-1*log(a^2//3+b^2//3*(c+d*x)^2+-1*a^1//3*b^1//3*(c+d*x))+-1//27*3^(1/2)*a^-4//3*b^-5//3*d^-1*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*b^1//3*(c+d*x)))+1//9*a^-1*b^-1*d^-1*(a+b*(c+d*x)^3)^-1*(c+d*x)^2)
@test integrate((a+b*(c+d*x)^3)^-3*(c+d*x)^3, x) == :(-1//6*b^-1*d^-1*(a+b*(c+d*x)^3)^-2*(c+d*x)+-1//54*a^-5//3*b^-4//3*d^-1*log(a^2//3+b^2//3*(c+d*x)^2+-1*a^1//3*b^1//3*(c+d*x))+1//27*a^-5//3*b^-4//3*d^-1*log(a^1//3+b^1//3*(c+d*x))+-1//27*3^(1/2)*a^-5//3*b^-4//3*d^-1*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*b^1//3*(c+d*x)))+1//18*a^-1*b^-1*d^-1*(a+b*(c+d*x)^3)^-1*(c+d*x))
@test integrate((a+b*(c+d*x)^3)^-3*(c+d*x)^2, x) == :(-1//6*b^-1*d^-1*(a+b*(c+d*x)^3)^-2)
@test integrate((a+b*(c+d*x)^3)^-3*(c+d*x), x) == :(-2//27*a^-7//3*b^-2//3*d^-1*log(a^1//3+b^1//3*(c+d*x))+1//6*a^-1*d^-1*(a+b*(c+d*x)^3)^-2*(c+d*x)^2+1//27*a^-7//3*b^-2//3*d^-1*log(a^2//3+b^2//3*(c+d*x)^2+-1*a^1//3*b^1//3*(c+d*x))+2//9*a^-2*d^-1*(a+b*(c+d*x)^3)^-1*(c+d*x)^2+-2//27*3^(1/2)*a^-7//3*b^-2//3*d^-1*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*b^1//3*(c+d*x))))
@test integrate((a+b*(c+d*x)^3)^-3, x) == :(-5//54*a^-8//3*b^-1//3*d^-1*log(a^2//3+b^2//3*(c+d*x)^2+-1*a^1//3*b^1//3*(c+d*x))+1//6*a^-1*d^-1*(a+b*(c+d*x)^3)^-2*(c+d*x)+1//18*a^-2*d^-1*(a+b*(c+d*x)^3)^-1*(5c+5*d*x)+5//27*a^-8//3*b^-1//3*d^-1*log(a^1//3+b^1//3*(c+d*x))+-5//27*3^(1/2)*a^-8//3*b^-1//3*d^-1*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*b^1//3*(c+d*x))))
@test integrate((a+b*(c+d*x)^3)^-3*(c+d*x)^-1, x) == :(a^-3*d^-1*log(c+d*x)+-1//3*a^-3*d^-1*log(a+b*(c+d*x)^3)+1//3*a^-2*d^-1*(a+b*(c+d*x)^3)^-1+1//6*a^-1*d^-1*(a+b*(c+d*x)^3)^-2)
@test integrate((a+b*(c+d*x)^3)^-3*(c+d*x)^-2, x) == :(-14//9*a^-3*d^-1*(c+d*x)^-1+-7//27*a^-10//3*b^1//3*d^-1*log(a^2//3+b^2//3*(c+d*x)^2+-1*a^1//3*b^1//3*(c+d*x))+1//6*a^-1*d^-1*(a+b*(c+d*x)^3)^-2*(c+d*x)^-1+7//18*a^-2*d^-1*(a+b*(c+d*x)^3)^-1*(c+d*x)^-1+14//27*a^-10//3*b^1//3*d^-1*log(a^1//3+b^1//3*(c+d*x))+14//27*3^(1/2)*a^-10//3*b^1//3*d^-1*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*b^1//3*(c+d*x))))
@test integrate((a+b*(c+d*x)^3)^-3*(c+d*x)^-3, x) == :(-10//9*a^-3*d^-1*(c+d*x)^-2+-20//27*a^-11//3*b^2//3*d^-1*log(a^1//3+b^1//3*(c+d*x))+1//6*a^-1*d^-1*(a+b*(c+d*x)^3)^-2*(c+d*x)^-2+4//9*a^-2*d^-1*(a+b*(c+d*x)^3)^-1*(c+d*x)^-2+10//27*a^-11//3*b^2//3*d^-1*log(a^2//3+b^2//3*(c+d*x)^2+-1*a^1//3*b^1//3*(c+d*x))+20//27*3^(1/2)*a^-11//3*b^2//3*d^-1*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*b^1//3*(c+d*x))))
@test integrate((a+b*(c+d*x)^3)^-3*(c+d*x)^-4, x) == :(-1//3*a^-3*d^-1*(c+d*x)^-3+b*a^-4*d^-1*log(a+b*(c+d*x)^3)+-3*b*a^-4*d^-1*log(c+d*x)+-2//3*b*a^-3*d^-1*(a+b*(c+d*x)^3)^-1+-1//6*b*a^-2*d^-1*(a+b*(c+d*x)^3)^-2)
@test integrate((a+b*(c+d*x)^3)^-1*(c*e+d*e*x)^4, x) == :((1/2)*b^-1*d^-1*e^4*(c+d*x)^2+-1//6*a^2//3*b^-5//3*d^-1*e^4*log(a^2//3+b^2//3*(c+d*x)^2+-1*a^1//3*b^1//3*(c+d*x))+1//3*a^2//3*b^-5//3*d^-1*e^4*log(a^1//3+b^1//3*(c+d*x))+1//3*3^(1/2)*a^2//3*b^-5//3*d^-1*e^4*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*b^1//3*(c+d*x))))
@test integrate((a+b*(c+d*x)^3)^-1*(c*e+d*e*x)^3, x) == :(x*b^-1*e^3+-1//3*a^1//3*b^-4//3*d^-1*e^3*log(a^1//3+b^1//3*(c+d*x))+1//6*a^1//3*b^-4//3*d^-1*e^3*log(a^2//3+b^2//3*(c+d*x)^2+-1*a^1//3*b^1//3*(c+d*x))+1//3*3^(1/2)*a^1//3*b^-4//3*d^-1*e^3*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*b^1//3*(c+d*x))))
@test integrate((a+b*(c+d*x)^3)^-1*(c*e+d*e*x)^2, x) == :(1//3*b^-1*d^-1*e^2*log(a+b*(c+d*x)^3))
@test integrate((a+b*(c+d*x)^3)^-1*(c*e+d*e*x), x) == :(-1//3*e*a^-1//3*b^-2//3*d^-1*log(a^1//3+b^1//3*(c+d*x))+1//6*e*a^-1//3*b^-2//3*d^-1*log(a^2//3+b^2//3*(c+d*x)^2+-1*a^1//3*b^1//3*(c+d*x))+-1//3*e*3^(1/2)*a^-1//3*b^-2//3*d^-1*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*b^1//3*(c+d*x))))
@test integrate((a+b*(c+d*x)^3)^-1*(c*e+d*e*x)^-1, x) == :(a^-1*d^-1*e^-1*log(c+d*x)+-1//3*a^-1*d^-1*e^-1*log(a+b*(c+d*x)^3))
@test integrate((a+b*(c+d*x)^3)^-1*(c*e+d*e*x)^-2, x) == :(-1*a^-1*d^-1*e^-2*(c+d*x)^-1+-1//6*a^-4//3*b^1//3*d^-1*e^-2*log(a^2//3+b^2//3*(c+d*x)^2+-1*a^1//3*b^1//3*(c+d*x))+1//3*a^-4//3*b^1//3*d^-1*e^-2*log(a^1//3+b^1//3*(c+d*x))+1//3*3^(1/2)*a^-4//3*b^1//3*d^-1*e^-2*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*b^1//3*(c+d*x))))
@test integrate((a+b*(c+d*x)^3)^-1*(c*e+d*e*x)^-3, x) == :(-1//2*a^-1*d^-1*e^-3*(c+d*x)^-2+-1//3*a^-5//3*b^2//3*d^-1*e^-3*log(a^1//3+b^1//3*(c+d*x))+1//6*a^-5//3*b^2//3*d^-1*e^-3*log(a^2//3+b^2//3*(c+d*x)^2+-1*a^1//3*b^1//3*(c+d*x))+1//3*3^(1/2)*a^-5//3*b^2//3*d^-1*e^-3*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*b^1//3*(c+d*x))))
@test integrate((a+b*(c+d*x)^3)^-1*(c*e+d*e*x)^-4, x) == :(-1//3*a^-1*d^-1*e^-4*(c+d*x)^-3+-1*b*a^-2*d^-1*e^-4*log(c+d*x)+1//3*b*a^-2*d^-1*e^-4*log(a+b*(c+d*x)^3))
@test integrate((a+b*(c+d*x)^3)^-2*(c*e+d*e*x)^4, x) == :(-2//9*a^-1//3*b^-5//3*d^-1*e^4*log(a^1//3+b^1//3*(c+d*x))+-1//3*b^-1*d^-1*e^4*(a+b*(c+d*x)^3)^-1*(c+d*x)^2+1//9*a^-1//3*b^-5//3*d^-1*e^4*log(a^2//3+b^2//3*(c+d*x)^2+-1*a^1//3*b^1//3*(c+d*x))+-2//9*3^(1/2)*a^-1//3*b^-5//3*d^-1*e^4*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*b^1//3*(c+d*x))))
@test integrate((a+b*(c+d*x)^3)^-2*(c*e+d*e*x)^3, x) == :(-1//3*b^-1*d^-1*e^3*(a+b*(c+d*x)^3)^-1*(c+d*x)+-1//18*a^-2//3*b^-4//3*d^-1*e^3*log(a^2//3+b^2//3*(c+d*x)^2+-1*a^1//3*b^1//3*(c+d*x))+1//9*a^-2//3*b^-4//3*d^-1*e^3*log(a^1//3+b^1//3*(c+d*x))+-1//9*3^(1/2)*a^-2//3*b^-4//3*d^-1*e^3*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*b^1//3*(c+d*x))))
@test integrate((a+b*(c+d*x)^3)^-2*(c*e+d*e*x)^2, x) == :(-1//3*b^-1*d^-1*e^2*(a+b*(c+d*x)^3)^-1)
@test integrate((a+b*(c+d*x)^3)^-2*(c*e+d*e*x), x) == :(-1//9*e*a^-4//3*b^-2//3*d^-1*log(a^1//3+b^1//3*(c+d*x))+1//3*e*a^-1*d^-1*(a+b*(c+d*x)^3)^-1*(c+d*x)^2+1//18*e*a^-4//3*b^-2//3*d^-1*log(a^2//3+b^2//3*(c+d*x)^2+-1*a^1//3*b^1//3*(c+d*x))+-1//9*e*3^(1/2)*a^-4//3*b^-2//3*d^-1*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*b^1//3*(c+d*x))))
@test integrate((a+b*(c+d*x)^3)^-2*(c*e+d*e*x)^-1, x) == :(a^-2*d^-1*e^-1*log(c+d*x)+-1//3*a^-2*d^-1*e^-1*log(a+b*(c+d*x)^3)+1//3*a^-1*d^-1*e^-1*(a+b*(c+d*x)^3)^-1)
@test integrate((a+b*(c+d*x)^3)^-2*(c*e+d*e*x)^-2, x) == :(-4//3*a^-2*d^-1*e^-2*(c+d*x)^-1+-2//9*a^-7//3*b^1//3*d^-1*e^-2*log(a^2//3+b^2//3*(c+d*x)^2+-1*a^1//3*b^1//3*(c+d*x))+1//3*a^-1*d^-1*e^-2*(a+b*(c+d*x)^3)^-1*(c+d*x)^-1+4//9*a^-7//3*b^1//3*d^-1*e^-2*log(a^1//3+b^1//3*(c+d*x))+4//9*3^(1/2)*a^-7//3*b^1//3*d^-1*e^-2*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*b^1//3*(c+d*x))))
@test integrate((a+b*(c+d*x)^3)^-2*(c*e+d*e*x)^-3, x) == :(-5//6*a^-2*d^-1*e^-3*(c+d*x)^-2+-5//9*a^-8//3*b^2//3*d^-1*e^-3*log(a^1//3+b^1//3*(c+d*x))+1//3*a^-1*d^-1*e^-3*(a+b*(c+d*x)^3)^-1*(c+d*x)^-2+5//18*a^-8//3*b^2//3*d^-1*e^-3*log(a^2//3+b^2//3*(c+d*x)^2+-1*a^1//3*b^1//3*(c+d*x))+5//9*3^(1/2)*a^-8//3*b^2//3*d^-1*e^-3*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*b^1//3*(c+d*x))))
@test integrate((a+b*(c+d*x)^3)^-2*(c*e+d*e*x)^-4, x) == :(-1//3*a^-2*d^-1*e^-4*(c+d*x)^-3+-2*b*a^-3*d^-1*e^-4*log(c+d*x)+-1//3*b*a^-2*d^-1*e^-4*(a+b*(c+d*x)^3)^-1+2//3*b*a^-3*d^-1*e^-4*log(a+b*(c+d*x)^3))
@test integrate((a+b*(c+d*x)^3)^-3*(c*e+d*e*x)^4, x) == :(-1//6*b^-1*d^-1*e^4*(a+b*(c+d*x)^3)^-2*(c+d*x)^2+-1//27*a^-4//3*b^-5//3*d^-1*e^4*log(a^1//3+b^1//3*(c+d*x))+1//54*a^-4//3*b^-5//3*d^-1*e^4*log(a^2//3+b^2//3*(c+d*x)^2+-1*a^1//3*b^1//3*(c+d*x))+-1//27*3^(1/2)*a^-4//3*b^-5//3*d^-1*e^4*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*b^1//3*(c+d*x)))+1//9*a^-1*b^-1*d^-1*e^4*(a+b*(c+d*x)^3)^-1*(c+d*x)^2)
@test integrate((a+b*(c+d*x)^3)^-3*(c*e+d*e*x)^3, x) == :(-1//6*b^-1*d^-1*e^3*(a+b*(c+d*x)^3)^-2*(c+d*x)+-1//54*a^-5//3*b^-4//3*d^-1*e^3*log(a^2//3+b^2//3*(c+d*x)^2+-1*a^1//3*b^1//3*(c+d*x))+1//27*a^-5//3*b^-4//3*d^-1*e^3*log(a^1//3+b^1//3*(c+d*x))+-1//27*3^(1/2)*a^-5//3*b^-4//3*d^-1*e^3*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*b^1//3*(c+d*x)))+1//18*a^-1*b^-1*d^-1*e^3*(a+b*(c+d*x)^3)^-1*(c+d*x))
@test integrate((a+b*(c+d*x)^3)^-3*(c*e+d*e*x)^2, x) == :(-1//6*b^-1*d^-1*e^2*(a+b*(c+d*x)^3)^-2)
@test integrate((a+b*(c+d*x)^3)^-3*(c*e+d*e*x), x) == :(-2//27*e*a^-7//3*b^-2//3*d^-1*log(a^1//3+b^1//3*(c+d*x))+1//6*e*a^-1*d^-1*(a+b*(c+d*x)^3)^-2*(c+d*x)^2+1//27*e*a^-7//3*b^-2//3*d^-1*log(a^2//3+b^2//3*(c+d*x)^2+-1*a^1//3*b^1//3*(c+d*x))+2//9*e*a^-2*d^-1*(a+b*(c+d*x)^3)^-1*(c+d*x)^2+-2//27*e*3^(1/2)*a^-7//3*b^-2//3*d^-1*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*b^1//3*(c+d*x))))
@test integrate((a+b*(c+d*x)^3)^-3*(c*e+d*e*x)^-1, x) == :(a^-3*d^-1*e^-1*log(c+d*x)+-1//3*a^-3*d^-1*e^-1*log(a+b*(c+d*x)^3)+1//3*a^-2*d^-1*e^-1*(a+b*(c+d*x)^3)^-1+1//6*a^-1*d^-1*e^-1*(a+b*(c+d*x)^3)^-2)
@test integrate((a+b*(c+d*x)^3)^-3*(c*e+d*e*x)^-2, x) == :(-14//9*a^-3*d^-1*e^-2*(c+d*x)^-1+-7//27*a^-10//3*b^1//3*d^-1*e^-2*log(a^2//3+b^2//3*(c+d*x)^2+-1*a^1//3*b^1//3*(c+d*x))+1//6*a^-1*d^-1*e^-2*(a+b*(c+d*x)^3)^-2*(c+d*x)^-1+7//18*a^-2*d^-1*e^-2*(a+b*(c+d*x)^3)^-1*(c+d*x)^-1+14//27*a^-10//3*b^1//3*d^-1*e^-2*log(a^1//3+b^1//3*(c+d*x))+14//27*3^(1/2)*a^-10//3*b^1//3*d^-1*e^-2*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*b^1//3*(c+d*x))))
@test integrate((a+b*(c+d*x)^3)^-3*(c*e+d*e*x)^-3, x) == :(-10//9*a^-3*d^-1*e^-3*(c+d*x)^-2+-20//27*a^-11//3*b^2//3*d^-1*e^-3*log(a^1//3+b^1//3*(c+d*x))+1//6*a^-1*d^-1*e^-3*(a+b*(c+d*x)^3)^-2*(c+d*x)^-2+4//9*a^-2*d^-1*e^-3*(a+b*(c+d*x)^3)^-1*(c+d*x)^-2+10//27*a^-11//3*b^2//3*d^-1*e^-3*log(a^2//3+b^2//3*(c+d*x)^2+-1*a^1//3*b^1//3*(c+d*x))+20//27*3^(1/2)*a^-11//3*b^2//3*d^-1*e^-3*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*b^1//3*(c+d*x))))
@test integrate((a+b*(c+d*x)^3)^-3*(c*e+d*e*x)^-4, x) == :(-1//3*a^-3*d^-1*e^-4*(c+d*x)^-3+b*a^-4*d^-1*e^-4*log(a+b*(c+d*x)^3)+-3*b*a^-4*d^-1*e^-4*log(c+d*x)+-2//3*b*a^-3*d^-1*e^-4*(a+b*(c+d*x)^3)^-1+-1//6*b*a^-2*d^-1*e^-4*(a+b*(c+d*x)^3)^-2)
@test integrate((a+b*(c+d*x)^4)^p*(c+d*x)^3, x) == :(1//4*b^-1*d^-1*(1+p)^-1*(a+b*(c+d*x)^4)^(1+p))
@test integrate((a+b*(c+d*x)^4)^2*(c+d*x)^3, x) == :(1//12*b^-1*d^-1*(a+b*(c+d*x)^4)^3)
@test integrate((a+b*(c+d*x)^4)^3*(c+d*x)^3, x) == :(1//16*b^-1*d^-1*(a+b*(c+d*x)^4)^4)
@test integrate((a+b*(c+d*x)^4)^-1*(c+d*x)^3, x) == :(1//4*b^-1*d^-1*log(a+b*(c+d*x)^4))
@test integrate((a+b*(c+d*x)^4)^-2*(c+d*x)^3, x) == :(-1//4*b^-1*d^-1*(a+b*(c+d*x)^4)^-1)
@test integrate((a+b*(c+d*x)^4)^-3*(c+d*x)^3, x) == :(-1//8*b^-1*d^-1*(a+b*(c+d*x)^4)^-2)
@test integrate((a+b*(c+d*x)^4)^-1//2, x) == :((1/2)*a^-1//4*b^-1//4*d^-1*((a^(1/2)+b^(1/2)*(c+d*x)^2)^-2*(a+b*(c+d*x)^4))^(1/2)*(a+b*(c+d*x)^4)^-1//2*(a^(1/2)+b^(1/2)*(c+d*x)^2)*Elliptic.F(2*arctan(a^-1//4*b^1//4*(c+d*x)),1/2))
@test integrate(x*(a+b*(c+d*x)^4)^-1//2, x) == :((1/2)*b^-1//2*d^-2*arctanh(b^(1/2)*(a+b*(c+d*x)^4)^-1//2*(c+d*x)^2)+-1//2*c*a^-1//4*b^-1//4*d^-2*((a^(1/2)+b^(1/2)*(c+d*x)^2)^-2*(a+b*(c+d*x)^4))^(1/2)*(a+b*(c+d*x)^4)^-1//2*(a^(1/2)+b^(1/2)*(c+d*x)^2)*Elliptic.F(2*arctan(a^-1//4*b^1//4*(c+d*x)),1/2))
@test integrate((1+(x^2)^3//2)^-1, x) == :(-1//6*x*(x^2)^-1//2*log(1+x^2+-1*(x^2)^(1/2))+1//3*x*(x^2)^-1//2*log(1+(x^2)^(1/2))+-1//3*x*3^(1/2)*(x^2)^-1//2*arctan(1//3*3^(1/2)*(1+-2*(x^2)^(1/2))))
@test integrate(x^5*(a+b*(c*x^2)^(1/2))^(1/2), x) == :(2//13*b^-6*c^-3*(a+b*(c*x^2)^(1/2))^13//2+2*a^4*b^-6*c^-3*(a+b*(c*x^2)^(1/2))^5//2+-20//7*a^3*b^-6*c^-3*(a+b*(c*x^2)^(1/2))^7//2+-10//11*a*b^-6*c^-3*(a+b*(c*x^2)^(1/2))^11//2+-2//3*a^5*b^-6*c^-3*(a+b*(c*x^2)^(1/2))^3//2+20//9*a^2*b^-6*c^-3*(a+b*(c*x^2)^(1/2))^9//2)
@test integrate(x^3*(a+b*(c*x^2)^(1/2))^(1/2), x) == :(2//9*b^-4*c^-2*(a+b*(c*x^2)^(1/2))^9//2+-6//7*a*b^-4*c^-2*(a+b*(c*x^2)^(1/2))^7//2+-2//3*a^3*b^-4*c^-2*(a+b*(c*x^2)^(1/2))^3//2+6//5*a^2*b^-4*c^-2*(a+b*(c*x^2)^(1/2))^5//2)
@test integrate(x*(a+b*(c*x^2)^(1/2))^(1/2), x) == :(2//5*b^-2*c^-1*(a+b*(c*x^2)^(1/2))^5//2+-2//3*a*b^-2*c^-1*(a+b*(c*x^2)^(1/2))^3//2)
@test integrate(x^-1*(a+b*(c*x^2)^(1/2))^(1/2), x) == :(2*(a+b*(c*x^2)^(1/2))^(1/2)+-2*a^(1/2)*arctanh(a^-1//2*(a+b*(c*x^2)^(1/2))^(1/2)))
@test integrate(x^-3*(a+b*(c*x^2)^(1/2))^(1/2), x) == :(-1//2*x^-2*(a+b*(c*x^2)^(1/2))^(1/2)+1//4*c*a^-3//2*b^2*arctanh(a^-1//2*(a+b*(c*x^2)^(1/2))^(1/2))+-1//4*b*c*a^-1*(c*x^2)^-1//2*(a+b*(c*x^2)^(1/2))^(1/2))
@test integrate(x^-5*(a+b*(c*x^2)^(1/2))^(1/2), x) == :(-1//4*x^-4*(a+b*(c*x^2)^(1/2))^(1/2)+5//64*a^-7//2*b^4*c^2*arctanh(a^-1//2*(a+b*(c*x^2)^(1/2))^(1/2))+-5//64*a^-3*b^3*c^2*(c*x^2)^-1//2*(a+b*(c*x^2)^(1/2))^(1/2)+-1//24*b*a^-1*c^2*(c*x^2)^-3//2*(a+b*(c*x^2)^(1/2))^(1/2)+5//96*c*a^-2*b^2*x^-2*(a+b*(c*x^2)^(1/2))^(1/2))
@test integrate(x^4*(a+b*(c*x^2)^(1/2))^(1/2), x) == :(2//11*b^-5*x^5*(c*x^2)^-5//2*(a+b*(c*x^2)^(1/2))^11//2+-8//5*a^3*b^-5*x^5*(c*x^2)^-5//2*(a+b*(c*x^2)^(1/2))^5//2+-8//9*a*b^-5*x^5*(c*x^2)^-5//2*(a+b*(c*x^2)^(1/2))^9//2+2//3*a^4*b^-5*x^5*(c*x^2)^-5//2*(a+b*(c*x^2)^(1/2))^3//2+12//7*a^2*b^-5*x^5*(c*x^2)^-5//2*(a+b*(c*x^2)^(1/2))^7//2)
@test integrate(x^2*(a+b*(c*x^2)^(1/2))^(1/2), x) == :(2//7*b^-3*x^3*(c*x^2)^-3//2*(a+b*(c*x^2)^(1/2))^7//2+-4//5*a*b^-3*x^3*(c*x^2)^-3//2*(a+b*(c*x^2)^(1/2))^5//2+2//3*a^2*b^-3*x^3*(c*x^2)^-3//2*(a+b*(c*x^2)^(1/2))^3//2)
@test integrate((a+b*(c*x^2)^(1/2))^(1/2), x) == :(2//3*x*b^-1*(c*x^2)^-1//2*(a+b*(c*x^2)^(1/2))^3//2)
@test integrate(x^-2*(a+b*(c*x^2)^(1/2))^(1/2), x) == :(-1*x^-1*(a+b*(c*x^2)^(1/2))^(1/2)+-1*b*a^-1//2*x^-1*(c*x^2)^(1/2)*arctanh(a^-1//2*(a+b*(c*x^2)^(1/2))^(1/2)))
@test integrate(x^-4*(a+b*(c*x^2)^(1/2))^(1/2), x) == :(-1//3*x^-3*(a+b*(c*x^2)^(1/2))^(1/2)+-1//8*a^-5//2*b^3*x^-3*(c*x^2)^3//2*arctanh(a^-1//2*(a+b*(c*x^2)^(1/2))^(1/2))+1//8*c*a^-2*b^2*x^-1*(a+b*(c*x^2)^(1/2))^(1/2)+-1//12*b*a^-1*c^-1*x^-5*(c*x^2)^3//2*(a+b*(c*x^2)^(1/2))^(1/2))
@test integrate(x^-6*(a+b*(c*x^2)^(1/2))^(1/2), x) == :(-1//5*x^-5*(a+b*(c*x^2)^(1/2))^(1/2)+-7//128*a^-9//2*b^5*x^-5*(c*x^2)^5//2*arctanh(a^-1//2*(a+b*(c*x^2)^(1/2))^(1/2))+7//128*a^-4*b^4*c^2*x^-1*(a+b*(c*x^2)^(1/2))^(1/2)+7//240*c*a^-2*b^2*x^-3*(a+b*(c*x^2)^(1/2))^(1/2)+-7//192*a^-3*b^3*c^-1*x^-7*(c*x^2)^5//2*(a+b*(c*x^2)^(1/2))^(1/2)+-1//40*b*a^-1*c^-2*x^-9*(c*x^2)^5//2*(a+b*(c*x^2)^(1/2))^(1/2))
@test integrate(x^8*(a+b*(c*x^2)^3//2)^(1/2), x) == :(2//21*b^-3*x^9*(c*x^2)^-9//2*(a+b*(c*x^2)^3//2)^7//2+-4//15*a*b^-3*x^9*(c*x^2)^-9//2*(a+b*(c*x^2)^3//2)^5//2+2//9*a^2*b^-3*x^9*(c*x^2)^-9//2*(a+b*(c*x^2)^3//2)^3//2)
@test integrate(x^5*(a+b*(c*x^2)^3//2)^(1/2), x) == :(2//15*b^-2*c^-3*(a+b*(c*x^2)^3//2)^5//2+-2//9*a*b^-2*c^-3*(a+b*(c*x^2)^3//2)^3//2)
@test integrate(x^2*(a+b*(c*x^2)^3//2)^(1/2), x) == :(2//9*b^-1*x^3*(c*x^2)^-3//2*(a+b*(c*x^2)^3//2)^3//2)
@test integrate(x^-1*(a+b*(c*x^2)^3//2)^(1/2), x) == :(2//3*(a+b*(c*x^2)^3//2)^(1/2)+-2//3*a^(1/2)*arctanh(a^-1//2*(a+b*(c*x^2)^3//2)^(1/2)))
@test integrate(x^-4*(a+b*(c*x^2)^3//2)^(1/2), x) == :(-1//3*x^-3*(a+b*(c*x^2)^3//2)^(1/2)+-1//3*b*a^-1//2*x^-3*(c*x^2)^3//2*arctanh(a^-1//2*(a+b*(c*x^2)^3//2)^(1/2)))
@test integrate(x^3*(a+b*(c*x^2)^3//2)^(1/2), x) == :(2//11*x^4*(a+b*(c*x^2)^3//2)^(1/2)+6//55*a*b^-1*c^-2*(c*x^2)^(1/2)*(a+b*(c*x^2)^3//2)^(1/2)+-4//55*3^3//4*a^2*b^-4//3*c^-2*((a^1//3*(1+3^(1/2))+b^1//3*(c*x^2)^(1/2))^-2*(a^2//3+c*b^2//3*x^2+-1*a^1//3*b^1//3*(c*x^2)^(1/2)))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+b^1//3*(c*x^2)^(1/2))^-2*(a^1//3+b^1//3*(c*x^2)^(1/2)))^-1//2*(2+3^(1/2))^(1/2)*(a+b*(c*x^2)^3//2)^-1//2*(a^1//3+b^1//3*(c*x^2)^(1/2))*Elliptic.F(arcsin((a^1//3*(1+3^(1/2))+b^1//3*(c*x^2)^(1/2))^-1*(a^1//3*(1+-1*3^(1/2))+b^1//3*(c*x^2)^(1/2))),-7+-4*3^(1/2)))
@test integrate((a+b*(c*x^2)^3//2)^(1/2), x) == :(2//5*x*(a+b*(c*x^2)^3//2)^(1/2)+2//5*a*x*3^3//4*b^-1//3*(c*x^2)^-1//2*((a^1//3*(1+3^(1/2))+b^1//3*(c*x^2)^(1/2))^-2*(a^2//3+c*b^2//3*x^2+-1*a^1//3*b^1//3*(c*x^2)^(1/2)))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+b^1//3*(c*x^2)^(1/2))^-2*(a^1//3+b^1//3*(c*x^2)^(1/2)))^-1//2*(2+3^(1/2))^(1/2)*(a+b*(c*x^2)^3//2)^-1//2*(a^1//3+b^1//3*(c*x^2)^(1/2))*Elliptic.F(arcsin((a^1//3*(1+3^(1/2))+b^1//3*(c*x^2)^(1/2))^-1*(a^1//3*(1+-1*3^(1/2))+b^1//3*(c*x^2)^(1/2))),-7+-4*3^(1/2)))
@test integrate(x^-3*(a+b*(c*x^2)^3//2)^(1/2), x) == :(-1//2*x^-2*(a+b*(c*x^2)^3//2)^(1/2)+(1/2)*c*3^3//4*b^2//3*((a^1//3*(1+3^(1/2))+b^1//3*(c*x^2)^(1/2))^-2*(a^2//3+c*b^2//3*x^2+-1*a^1//3*b^1//3*(c*x^2)^(1/2)))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+b^1//3*(c*x^2)^(1/2))^-2*(a^1//3+b^1//3*(c*x^2)^(1/2)))^-1//2*(2+3^(1/2))^(1/2)*(a+b*(c*x^2)^3//2)^-1//2*(a^1//3+b^1//3*(c*x^2)^(1/2))*Elliptic.F(arcsin((a^1//3*(1+3^(1/2))+b^1//3*(c*x^2)^(1/2))^-1*(a^1//3*(1+-1*3^(1/2))+b^1//3*(c*x^2)^(1/2))),-7+-4*3^(1/2)))
@test integrate(x^-6*(a+b*(c*x^2)^3//2)^(1/2), x) == :(-1//5*x^-5*(a+b*(c*x^2)^3//2)^(1/2)+-3//20*b*a^-1*c^-1*x^-7*(c*x^2)^5//2*(a+b*(c*x^2)^3//2)^(1/2)+-1//20*3^3//4*a^-1*b^5//3*x^-5*(c*x^2)^5//2*((a^1//3*(1+3^(1/2))+b^1//3*(c*x^2)^(1/2))^-2*(a^2//3+c*b^2//3*x^2+-1*a^1//3*b^1//3*(c*x^2)^(1/2)))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+b^1//3*(c*x^2)^(1/2))^-2*(a^1//3+b^1//3*(c*x^2)^(1/2)))^-1//2*(2+3^(1/2))^(1/2)*(a+b*(c*x^2)^3//2)^-1//2*(a^1//3+b^1//3*(c*x^2)^(1/2))*Elliptic.F(arcsin((a^1//3*(1+3^(1/2))+b^1//3*(c*x^2)^(1/2))^-1*(a^1//3*(1+-1*3^(1/2))+b^1//3*(c*x^2)^(1/2))),-7+-4*3^(1/2)))
@test integrate(x^4*(a+b*(c*x^2)^3//2)^(1/2), x) == :(2//13*x^5*(a+b*(c*x^2)^3//2)^(1/2)+-24//91*a^2*b^-5//3*x^5*(c*x^2)^-5//2*(a+b*(c*x^2)^3//2)^(1/2)*(a^1//3*(1+3^(1/2))+b^1//3*(c*x^2)^(1/2))^-1+6//91*a*c*b^-1*x^7*(c*x^2)^-5//2*(a+b*(c*x^2)^3//2)^(1/2)+-8//91*2^(1/2)*3^3//4*a^7//3*b^-5//3*x^5*(c*x^2)^-5//2*((a^1//3*(1+3^(1/2))+b^1//3*(c*x^2)^(1/2))^-2*(a^2//3+c*b^2//3*x^2+-1*a^1//3*b^1//3*(c*x^2)^(1/2)))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+b^1//3*(c*x^2)^(1/2))^-2*(a^1//3+b^1//3*(c*x^2)^(1/2)))^-1//2*(a+b*(c*x^2)^3//2)^-1//2*(a^1//3+b^1//3*(c*x^2)^(1/2))*Elliptic.F(arcsin((a^1//3*(1+3^(1/2))+b^1//3*(c*x^2)^(1/2))^-1*(a^1//3*(1+-1*3^(1/2))+b^1//3*(c*x^2)^(1/2))),-7+-4*3^(1/2))+12//91*3^1//4*a^7//3*b^-5//3*x^5*(c*x^2)^-5//2*((a^1//3*(1+3^(1/2))+b^1//3*(c*x^2)^(1/2))^-2*(a^2//3+c*b^2//3*x^2+-1*a^1//3*b^1//3*(c*x^2)^(1/2)))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+b^1//3*(c*x^2)^(1/2))^-2*(a^1//3+b^1//3*(c*x^2)^(1/2)))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*(c*x^2)^3//2)^-1//2*(a^1//3+b^1//3*(c*x^2)^(1/2))*Elliptic.E(arcsin((a^1//3*(1+3^(1/2))+b^1//3*(c*x^2)^(1/2))^-1*(a^1//3*(1+-1*3^(1/2))+b^1//3*(c*x^2)^(1/2))),-7+-4*3^(1/2)))
@test integrate(x*(a+b*(c*x^2)^3//2)^(1/2), x) == :(2//7*x^2*(a+b*(c*x^2)^3//2)^(1/2)+6//7*a*b^-2//3*c^-1*(a+b*(c*x^2)^3//2)^(1/2)*(a^1//3*(1+3^(1/2))+b^1//3*(c*x^2)^(1/2))^-1+-3//7*3^1//4*a^4//3*b^-2//3*c^-1*((a^1//3*(1+3^(1/2))+b^1//3*(c*x^2)^(1/2))^-2*(a^2//3+c*b^2//3*x^2+-1*a^1//3*b^1//3*(c*x^2)^(1/2)))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+b^1//3*(c*x^2)^(1/2))^-2*(a^1//3+b^1//3*(c*x^2)^(1/2)))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*(c*x^2)^3//2)^-1//2*(a^1//3+b^1//3*(c*x^2)^(1/2))*Elliptic.E(arcsin((a^1//3*(1+3^(1/2))+b^1//3*(c*x^2)^(1/2))^-1*(a^1//3*(1+-1*3^(1/2))+b^1//3*(c*x^2)^(1/2))),-7+-4*3^(1/2))+2//7*2^(1/2)*3^3//4*a^4//3*b^-2//3*c^-1*((a^1//3*(1+3^(1/2))+b^1//3*(c*x^2)^(1/2))^-2*(a^2//3+c*b^2//3*x^2+-1*a^1//3*b^1//3*(c*x^2)^(1/2)))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+b^1//3*(c*x^2)^(1/2))^-2*(a^1//3+b^1//3*(c*x^2)^(1/2)))^-1//2*(a+b*(c*x^2)^3//2)^-1//2*(a^1//3+b^1//3*(c*x^2)^(1/2))*Elliptic.F(arcsin((a^1//3*(1+3^(1/2))+b^1//3*(c*x^2)^(1/2))^-1*(a^1//3*(1+-1*3^(1/2))+b^1//3*(c*x^2)^(1/2))),-7+-4*3^(1/2)))
@test integrate(x^-2*(a+b*(c*x^2)^3//2)^(1/2), x) == :(-1*x^-1*(a+b*(c*x^2)^3//2)^(1/2)+3*b^1//3*x^-1*(c*x^2)^(1/2)*(a+b*(c*x^2)^3//2)^(1/2)*(a^1//3*(1+3^(1/2))+b^1//3*(c*x^2)^(1/2))^-1+2^(1/2)*3^3//4*a^1//3*b^1//3*x^-1*(c*x^2)^(1/2)*((a^1//3*(1+3^(1/2))+b^1//3*(c*x^2)^(1/2))^-2*(a^2//3+c*b^2//3*x^2+-1*a^1//3*b^1//3*(c*x^2)^(1/2)))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+b^1//3*(c*x^2)^(1/2))^-2*(a^1//3+b^1//3*(c*x^2)^(1/2)))^-1//2*(a+b*(c*x^2)^3//2)^-1//2*(a^1//3+b^1//3*(c*x^2)^(1/2))*Elliptic.F(arcsin((a^1//3*(1+3^(1/2))+b^1//3*(c*x^2)^(1/2))^-1*(a^1//3*(1+-1*3^(1/2))+b^1//3*(c*x^2)^(1/2))),-7+-4*3^(1/2))+-3//2*3^1//4*a^1//3*b^1//3*x^-1*(c*x^2)^(1/2)*((a^1//3*(1+3^(1/2))+b^1//3*(c*x^2)^(1/2))^-2*(a^2//3+c*b^2//3*x^2+-1*a^1//3*b^1//3*(c*x^2)^(1/2)))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+b^1//3*(c*x^2)^(1/2))^-2*(a^1//3+b^1//3*(c*x^2)^(1/2)))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*(c*x^2)^3//2)^-1//2*(a^1//3+b^1//3*(c*x^2)^(1/2))*Elliptic.E(arcsin((a^1//3*(1+3^(1/2))+b^1//3*(c*x^2)^(1/2))^-1*(a^1//3*(1+-1*3^(1/2))+b^1//3*(c*x^2)^(1/2))),-7+-4*3^(1/2)))
@test integrate(x^-5*(a+b*(c*x^2)^3//2)^(1/2), x) == :(-1//4*x^-4*(a+b*(c*x^2)^3//2)^(1/2)+-3//8*b*a^-1*c^2*(c*x^2)^-1//2*(a+b*(c*x^2)^3//2)^(1/2)+3//8*a^-1*b^4//3*c^2*(a+b*(c*x^2)^3//2)^(1/2)*(a^1//3*(1+3^(1/2))+b^1//3*(c*x^2)^(1/2))^-1+-3//16*3^1//4*a^-2//3*b^4//3*c^2*((a^1//3*(1+3^(1/2))+b^1//3*(c*x^2)^(1/2))^-2*(a^2//3+c*b^2//3*x^2+-1*a^1//3*b^1//3*(c*x^2)^(1/2)))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+b^1//3*(c*x^2)^(1/2))^-2*(a^1//3+b^1//3*(c*x^2)^(1/2)))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*(c*x^2)^3//2)^-1//2*(a^1//3+b^1//3*(c*x^2)^(1/2))*Elliptic.E(arcsin((a^1//3*(1+3^(1/2))+b^1//3*(c*x^2)^(1/2))^-1*(a^1//3*(1+-1*3^(1/2))+b^1//3*(c*x^2)^(1/2))),-7+-4*3^(1/2))+1//8*2^(1/2)*3^3//4*a^-2//3*b^4//3*c^2*((a^1//3*(1+3^(1/2))+b^1//3*(c*x^2)^(1/2))^-2*(a^2//3+c*b^2//3*x^2+-1*a^1//3*b^1//3*(c*x^2)^(1/2)))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+b^1//3*(c*x^2)^(1/2))^-2*(a^1//3+b^1//3*(c*x^2)^(1/2)))^-1//2*(a+b*(c*x^2)^3//2)^-1//2*(a^1//3+b^1//3*(c*x^2)^(1/2))*Elliptic.F(arcsin((a^1//3*(1+3^(1/2))+b^1//3*(c*x^2)^(1/2))^-1*(a^1//3*(1+-1*3^(1/2))+b^1//3*(c*x^2)^(1/2))),-7+-4*3^(1/2)))
@test integrate((1+(x^3)^2//3)^-1, x) == :(x*(x^3)^-1//3*arctan((x^3)^1//3))
@test integrate(x^5*(a+b*(c*x^3)^(1/2))^(1/2), x) == :(4//27*b^-4*c^-2*(a+b*(c*x^3)^(1/2))^9//2+-4//7*a*b^-4*c^-2*(a+b*(c*x^3)^(1/2))^7//2+-4//9*a^3*b^-4*c^-2*(a+b*(c*x^3)^(1/2))^3//2+4//5*a^2*b^-4*c^-2*(a+b*(c*x^3)^(1/2))^5//2)
@test integrate(x^2*(a+b*(c*x^3)^(1/2))^(1/2), x) == :(4//15*b^-2*c^-1*(a+b*(c*x^3)^(1/2))^5//2+-4//9*a*b^-2*c^-1*(a+b*(c*x^3)^(1/2))^3//2)
@test integrate(x^-1*(a+b*(c*x^3)^(1/2))^(1/2), x) == :(4//3*(a+b*(c*x^3)^(1/2))^(1/2)+-4//3*a^(1/2)*arctanh(a^-1//2*(a+b*(c*x^3)^(1/2))^(1/2)))
@test integrate(x^-4*(a+b*(c*x^3)^(1/2))^(1/2), x) == :(-1//3*x^-3*(a+b*(c*x^3)^(1/2))^(1/2)+1//6*c*a^-3//2*b^2*arctanh(a^-1//2*(a+b*(c*x^3)^(1/2))^(1/2))+-1//6*b*c*a^-1*(c*x^3)^-1//2*(a+b*(c*x^3)^(1/2))^(1/2))
@test integrate(x*(a+b*(c*x^3)^(1/2))^(1/2), x) == :(4//11*x^2*(a+b*(c*x^3)^(1/2))^(1/2)+12//55*a*b^-1*x^2*(c*x^3)^-1//2*(a+b*(c*x^3)^(1/2))^(1/2)+-8//55*3^3//4*a^2*b^-4//3*c^-2//3*((a^1//3*(1+3^(1/2))+b^1//3*c^2//3*x^2*(c*x^3)^-1//2)^-2*(a^2//3+x*b^2//3*c^1//3+-1*a^1//3*b^1//3*c^2//3*x^2*(c*x^3)^-1//2))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+b^1//3*c^2//3*x^2*(c*x^3)^-1//2)^-2*(a^1//3+b^1//3*c^2//3*x^2*(c*x^3)^-1//2))^-1//2*(2+3^(1/2))^(1/2)*(a+b*(c*x^3)^(1/2))^-1//2*(a^1//3+b^1//3*c^2//3*x^2*(c*x^3)^-1//2)*Elliptic.F(arcsin((a^1//3*(1+3^(1/2))+b^1//3*c^2//3*x^2*(c*x^3)^-1//2)^-1*(a^1//3*(1+-1*3^(1/2))+b^1//3*c^2//3*x^2*(c*x^3)^-1//2)),-7+-4*3^(1/2)))
@test integrate(x^-2*(a+b*(c*x^3)^(1/2))^(1/2), x) == :(-1*x^-1*(a+b*(c*x^3)^(1/2))^(1/2)+3^3//4*b^2//3*c^1//3*((a^1//3*(1+3^(1/2))+b^1//3*c^2//3*x^2*(c*x^3)^-1//2)^-2*(a^2//3+x*b^2//3*c^1//3+-1*a^1//3*b^1//3*c^2//3*x^2*(c*x^3)^-1//2))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+b^1//3*c^2//3*x^2*(c*x^3)^-1//2)^-2*(a^1//3+b^1//3*c^2//3*x^2*(c*x^3)^-1//2))^-1//2*(2+3^(1/2))^(1/2)*(a+b*(c*x^3)^(1/2))^-1//2*(a^1//3+b^1//3*c^2//3*x^2*(c*x^3)^-1//2)*Elliptic.F(arcsin((a^1//3*(1+3^(1/2))+b^1//3*c^2//3*x^2*(c*x^3)^-1//2)^-1*(a^1//3*(1+-1*3^(1/2))+b^1//3*c^2//3*x^2*(c*x^3)^-1//2)),-7+-4*3^(1/2)))
@test integrate(x^-5*(a+b*(c*x^3)^(1/2))^(1/2), x) == :(-1//4*x^-4*(a+b*(c*x^3)^(1/2))^(1/2)+21//160*c*a^-2*b^2*x^-1*(a+b*(c*x^3)^(1/2))^(1/2)+-3//40*b*a^-1*c^3*x^5*(c*x^3)^-5//2*(a+b*(c*x^3)^(1/2))^(1/2)+7//160*3^3//4*a^-2*b^8//3*c^4//3*((a^1//3*(1+3^(1/2))+b^1//3*c^2//3*x^2*(c*x^3)^-1//2)^-2*(a^2//3+x*b^2//3*c^1//3+-1*a^1//3*b^1//3*c^2//3*x^2*(c*x^3)^-1//2))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+b^1//3*c^2//3*x^2*(c*x^3)^-1//2)^-2*(a^1//3+b^1//3*c^2//3*x^2*(c*x^3)^-1//2))^-1//2*(2+3^(1/2))^(1/2)*(a+b*(c*x^3)^(1/2))^-1//2*(a^1//3+b^1//3*c^2//3*x^2*(c*x^3)^-1//2)*Elliptic.F(arcsin((a^1//3*(1+3^(1/2))+b^1//3*c^2//3*x^2*(c*x^3)^-1//2)^-1*(a^1//3*(1+-1*3^(1/2))+b^1//3*c^2//3*x^2*(c*x^3)^-1//2)),-7+-4*3^(1/2)))
@test integrate(x^3*(a+b*(c*x^3)^(1/2))^(1/2), x) == :(4//19*x^4*(a+b*(c*x^3)^(1/2))^(1/2)+-120//1729*x*a^2*b^-2*c^-1*(a+b*(c*x^3)^(1/2))^(1/2)+480//1729*a^3*b^-8//3*c^-4//3*(a+b*(c*x^3)^(1/2))^(1/2)*(a^1//3*(1+3^(1/2))+b^1//3*c^2//3*x^2*(c*x^3)^-1//2)^-1+12//247*a*x*b^-1*c^-1*(c*x^3)^(1/2)*(a+b*(c*x^3)^(1/2))^(1/2)+-240//1729*3^1//4*a^10//3*b^-8//3*c^-4//3*((a^1//3*(1+3^(1/2))+b^1//3*c^2//3*x^2*(c*x^3)^-1//2)^-2*(a^2//3+x*b^2//3*c^1//3+-1*a^1//3*b^1//3*c^2//3*x^2*(c*x^3)^-1//2))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+b^1//3*c^2//3*x^2*(c*x^3)^-1//2)^-2*(a^1//3+b^1//3*c^2//3*x^2*(c*x^3)^-1//2))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*(c*x^3)^(1/2))^-1//2*(a^1//3+b^1//3*c^2//3*x^2*(c*x^3)^-1//2)*Elliptic.E(arcsin((a^1//3*(1+3^(1/2))+b^1//3*c^2//3*x^2*(c*x^3)^-1//2)^-1*(a^1//3*(1+-1*3^(1/2))+b^1//3*c^2//3*x^2*(c*x^3)^-1//2)),-7+-4*3^(1/2))+160//1729*2^(1/2)*3^3//4*a^10//3*b^-8//3*c^-4//3*((a^1//3*(1+3^(1/2))+b^1//3*c^2//3*x^2*(c*x^3)^-1//2)^-2*(a^2//3+x*b^2//3*c^1//3+-1*a^1//3*b^1//3*c^2//3*x^2*(c*x^3)^-1//2))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+b^1//3*c^2//3*x^2*(c*x^3)^-1//2)^-2*(a^1//3+b^1//3*c^2//3*x^2*(c*x^3)^-1//2))^-1//2*(a+b*(c*x^3)^(1/2))^-1//2*(a^1//3+b^1//3*c^2//3*x^2*(c*x^3)^-1//2)*Elliptic.F(arcsin((a^1//3*(1+3^(1/2))+b^1//3*c^2//3*x^2*(c*x^3)^-1//2)^-1*(a^1//3*(1+-1*3^(1/2))+b^1//3*c^2//3*x^2*(c*x^3)^-1//2)),-7+-4*3^(1/2)))
@test integrate((a+b*(c*x^3)^(1/2))^(1/2), x) == :(4//7*x*(a+b*(c*x^3)^(1/2))^(1/2)+12//7*a*b^-2//3*c^-1//3*(a+b*(c*x^3)^(1/2))^(1/2)*(a^1//3*(1+3^(1/2))+b^1//3*c^2//3*x^2*(c*x^3)^-1//2)^-1+-6//7*3^1//4*a^4//3*b^-2//3*c^-1//3*((a^1//3*(1+3^(1/2))+b^1//3*c^2//3*x^2*(c*x^3)^-1//2)^-2*(a^2//3+x*b^2//3*c^1//3+-1*a^1//3*b^1//3*c^2//3*x^2*(c*x^3)^-1//2))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+b^1//3*c^2//3*x^2*(c*x^3)^-1//2)^-2*(a^1//3+b^1//3*c^2//3*x^2*(c*x^3)^-1//2))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*(c*x^3)^(1/2))^-1//2*(a^1//3+b^1//3*c^2//3*x^2*(c*x^3)^-1//2)*Elliptic.E(arcsin((a^1//3*(1+3^(1/2))+b^1//3*c^2//3*x^2*(c*x^3)^-1//2)^-1*(a^1//3*(1+-1*3^(1/2))+b^1//3*c^2//3*x^2*(c*x^3)^-1//2)),-7+-4*3^(1/2))+4//7*2^(1/2)*3^3//4*a^4//3*b^-2//3*c^-1//3*((a^1//3*(1+3^(1/2))+b^1//3*c^2//3*x^2*(c*x^3)^-1//2)^-2*(a^2//3+x*b^2//3*c^1//3+-1*a^1//3*b^1//3*c^2//3*x^2*(c*x^3)^-1//2))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+b^1//3*c^2//3*x^2*(c*x^3)^-1//2)^-2*(a^1//3+b^1//3*c^2//3*x^2*(c*x^3)^-1//2))^-1//2*(a+b*(c*x^3)^(1/2))^-1//2*(a^1//3+b^1//3*c^2//3*x^2*(c*x^3)^-1//2)*Elliptic.F(arcsin((a^1//3*(1+3^(1/2))+b^1//3*c^2//3*x^2*(c*x^3)^-1//2)^-1*(a^1//3*(1+-1*3^(1/2))+b^1//3*c^2//3*x^2*(c*x^3)^-1//2)),-7+-4*3^(1/2)))
@test integrate(x^-3*(a+b*(c*x^3)^(1/2))^(1/2), x) == :(-1//2*x^-2*(a+b*(c*x^3)^(1/2))^(1/2)+3//4*a^-1*b^4//3*c^2//3*(a+b*(c*x^3)^(1/2))^(1/2)*(a^1//3*(1+3^(1/2))+b^1//3*c^2//3*x^2*(c*x^3)^-1//2)^-1+-3//4*b*c*x*a^-1*(c*x^3)^-1//2*(a+b*(c*x^3)^(1/2))^(1/2)+-3//8*3^1//4*a^-2//3*b^4//3*c^2//3*((a^1//3*(1+3^(1/2))+b^1//3*c^2//3*x^2*(c*x^3)^-1//2)^-2*(a^2//3+x*b^2//3*c^1//3+-1*a^1//3*b^1//3*c^2//3*x^2*(c*x^3)^-1//2))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+b^1//3*c^2//3*x^2*(c*x^3)^-1//2)^-2*(a^1//3+b^1//3*c^2//3*x^2*(c*x^3)^-1//2))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*(c*x^3)^(1/2))^-1//2*(a^1//3+b^1//3*c^2//3*x^2*(c*x^3)^-1//2)*Elliptic.E(arcsin((a^1//3*(1+3^(1/2))+b^1//3*c^2//3*x^2*(c*x^3)^-1//2)^-1*(a^1//3*(1+-1*3^(1/2))+b^1//3*c^2//3*x^2*(c*x^3)^-1//2)),-7+-4*3^(1/2))+1//4*2^(1/2)*3^3//4*a^-2//3*b^4//3*c^2//3*((a^1//3*(1+3^(1/2))+b^1//3*c^2//3*x^2*(c*x^3)^-1//2)^-2*(a^2//3+x*b^2//3*c^1//3+-1*a^1//3*b^1//3*c^2//3*x^2*(c*x^3)^-1//2))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+b^1//3*c^2//3*x^2*(c*x^3)^-1//2)^-2*(a^1//3+b^1//3*c^2//3*x^2*(c*x^3)^-1//2))^-1//2*(a+b*(c*x^3)^(1/2))^-1//2*(a^1//3+b^1//3*c^2//3*x^2*(c*x^3)^-1//2)*Elliptic.F(arcsin((a^1//3*(1+3^(1/2))+b^1//3*c^2//3*x^2*(c*x^3)^-1//2)^-1*(a^1//3*(1+-1*3^(1/2))+b^1//3*c^2//3*x^2*(c*x^3)^-1//2)),-7+-4*3^(1/2)))
@test integrate(x^17*(a+b*(c*x^3)^3//2)^(1/2), x) == :(4//81*b^-4*c^-6*(a+b*(c*x^3)^3//2)^9//2+-4//21*a*b^-4*c^-6*(a+b*(c*x^3)^3//2)^7//2+-4//27*a^3*b^-4*c^-6*(a+b*(c*x^3)^3//2)^3//2+4//15*a^2*b^-4*c^-6*(a+b*(c*x^3)^3//2)^5//2)
@test integrate(x^8*(a+b*(c*x^3)^3//2)^(1/2), x) == :(4//45*b^-2*c^-3*(a+b*(c*x^3)^3//2)^5//2+-4//27*a*b^-2*c^-3*(a+b*(c*x^3)^3//2)^3//2)
@test integrate(x^-1*(a+b*(c*x^3)^3//2)^(1/2), x) == :(4//9*(a+b*(c*x^3)^3//2)^(1/2)+-4//9*a^(1/2)*arctanh(a^-1//2*(a+b*(c*x^3)^3//2)^(1/2)))
@test integrate(x^2*(a+b*(c*x^3)^3//2)^(1/2), x) == :(4//21*x^3*(a+b*(c*x^3)^3//2)^(1/2)+4//7*a*b^-2//3*c^-1*(a+b*(c*x^3)^3//2)^(1/2)*(a^1//3*(1+3^(1/2))+b^1//3*(c*x^3)^(1/2))^-1+-2//7*3^1//4*a^4//3*b^-2//3*c^-1*((a^1//3*(1+3^(1/2))+b^1//3*(c*x^3)^(1/2))^-2*(a^2//3+c*b^2//3*x^3+-1*a^1//3*b^1//3*(c*x^3)^(1/2)))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+b^1//3*(c*x^3)^(1/2))^-2*(a^1//3+b^1//3*(c*x^3)^(1/2)))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*(c*x^3)^3//2)^-1//2*(a^1//3+b^1//3*(c*x^3)^(1/2))*Elliptic.E(arcsin((a^1//3*(1+3^(1/2))+b^1//3*(c*x^3)^(1/2))^-1*(a^1//3*(1+-1*3^(1/2))+b^1//3*(c*x^3)^(1/2))),-7+-4*3^(1/2))+4//21*2^(1/2)*3^3//4*a^4//3*b^-2//3*c^-1*((a^1//3*(1+3^(1/2))+b^1//3*(c*x^3)^(1/2))^-2*(a^2//3+c*b^2//3*x^3+-1*a^1//3*b^1//3*(c*x^3)^(1/2)))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+b^1//3*(c*x^3)^(1/2))^-2*(a^1//3+b^1//3*(c*x^3)^(1/2)))^-1//2*(a+b*(c*x^3)^3//2)^-1//2*(a^1//3+b^1//3*(c*x^3)^(1/2))*Elliptic.F(arcsin((a^1//3*(1+3^(1/2))+b^1//3*(c*x^3)^(1/2))^-1*(a^1//3*(1+-1*3^(1/2))+b^1//3*(c*x^3)^(1/2))),-7+-4*3^(1/2)))
@test integrate((a+b*(c*x^-1)^(1/2))^(1/2), x) == :(x*(a+b*(c*x^-1)^(1/2))^(1/2)+-1//2*c*a^-3//2*b^2*arctanh(a^-1//2*(a+b*(c*x^-1)^(1/2))^(1/2))+(1/2)*b*c*a^-1*(c*x^-1)^-1//2*(a+b*(c*x^-1)^(1/2))^(1/2))
@test integrate(x^-1*(a+b*(c*x^-1)^(1/2))^(1/2), x) == :(-4*(a+b*(c*x^-1)^(1/2))^(1/2)+4*a^(1/2)*arctanh(a^-1//2*(a+b*(c*x^-1)^(1/2))^(1/2)))
@test integrate(x^-2*(a+b*(c*x^-1)^(1/2))^(1/2), x) == :(-4//5*b^-2*c^-1*(a+b*(c*x^-1)^(1/2))^5//2+4//3*a*b^-2*c^-1*(a+b*(c*x^-1)^(1/2))^3//2)
@test integrate(x^-3*(a+b*(c*x^-1)^(1/2))^(1/2), x) == :(-4//9*b^-4*c^-2*(a+b*(c*x^-1)^(1/2))^9//2+-12//5*a^2*b^-4*c^-2*(a+b*(c*x^-1)^(1/2))^5//2+4//3*a^3*b^-4*c^-2*(a+b*(c*x^-1)^(1/2))^3//2+12//7*a*b^-4*c^-2*(a+b*(c*x^-1)^(1/2))^7//2)
@test integrate(x^-4*(a+b*(c*x^-1)^(1/2))^(1/2), x) == :(-4//13*b^-6*c^-3*(a+b*(c*x^-1)^(1/2))^13//2+-4*a^4*b^-6*c^-3*(a+b*(c*x^-1)^(1/2))^5//2+-40//9*a^2*b^-6*c^-3*(a+b*(c*x^-1)^(1/2))^9//2+4//3*a^5*b^-6*c^-3*(a+b*(c*x^-1)^(1/2))^3//2+20//11*a*b^-6*c^-3*(a+b*(c*x^-1)^(1/2))^11//2+40//7*a^3*b^-6*c^-3*(a+b*(c*x^-1)^(1/2))^7//2)
@test integrate((a+b*(c*x^-1)^(1/2))^-1//2, x) == :(x*a^-1*(a+b*(c*x^-1)^(1/2))^(1/2)+3//2*c*a^-5//2*b^2*arctanh(a^-1//2*(a+b*(c*x^-1)^(1/2))^(1/2))+-3//2*b*c*a^-2*(c*x^-1)^-1//2*(a+b*(c*x^-1)^(1/2))^(1/2))
@test integrate(x^-1*(a+b*(c*x^-1)^(1/2))^-1//2, x) == :(4*a^-1//2*arctanh(a^-1//2*(a+b*(c*x^-1)^(1/2))^(1/2)))
@test integrate(x^-2*(a+b*(c*x^-1)^(1/2))^-1//2, x) == :(-4//3*b^-2*c^-1*(a+b*(c*x^-1)^(1/2))^3//2+4*a*b^-2*c^-1*(a+b*(c*x^-1)^(1/2))^(1/2))
@test integrate(x^-3*(a+b*(c*x^-1)^(1/2))^-1//2, x) == :(-4//7*b^-4*c^-2*(a+b*(c*x^-1)^(1/2))^7//2+-4*a^2*b^-4*c^-2*(a+b*(c*x^-1)^(1/2))^3//2+4*a^3*b^-4*c^-2*(a+b*(c*x^-1)^(1/2))^(1/2)+12//5*a*b^-4*c^-2*(a+b*(c*x^-1)^(1/2))^5//2)
@test integrate(x^-4*(a+b*(c*x^-1)^(1/2))^-1//2, x) == :(-4//11*b^-6*c^-3*(a+b*(c*x^-1)^(1/2))^11//2+4*a^5*b^-6*c^-3*(a+b*(c*x^-1)^(1/2))^(1/2)+8*a^3*b^-6*c^-3*(a+b*(c*x^-1)^(1/2))^5//2+-40//7*a^2*b^-6*c^-3*(a+b*(c*x^-1)^(1/2))^7//2+-20//3*a^4*b^-6*c^-3*(a+b*(c*x^-1)^(1/2))^3//2+20//9*a*b^-6*c^-3*(a+b*(c*x^-1)^(1/2))^9//2)
@test integrate((1+(x^-1)^(1/2))^-1//2, x) == :(3//2*arctanh((1+(x^-1)^(1/2))^(1/2))+x*(1+(x^-1)^(1/2))^(1/2)+-3//2*(x^-1)^-1//2*(1+(x^-1)^(1/2))^(1/2))
@test integrate(a+b*(c*x^n)^(n^-1), x) == :(a*x+(1/2)*b*x*(c*x^n)^(n^-1))
@test integrate((a+b*(c*x^n)^(n^-1))^2, x) == :(1//3*x*b^-1*(c*x^n)^(-1*n^-1)*(a+b*(c*x^n)^(n^-1))^3)
@test integrate((a+b*(c*x^n)^(n^-1))^3, x) == :(1//4*x*b^-1*(c*x^n)^(-1*n^-1)*(a+b*(c*x^n)^(n^-1))^4)
@test integrate(x^3*(a+b*(c*x^n)^(n^-1))^-1, x) == :(1//3*b^-1*x^4*(c*x^n)^(-1*n^-1)+a^2*b^-3*x^4*(c*x^n)^(-3*n^-1)+-1//2*a*b^-2*x^4*(c*x^n)^(-2*n^-1)+-1*a^3*b^-4*x^4*(c*x^n)^(-4*n^-1)*log(a+b*(c*x^n)^(n^-1)))
@test integrate(x^2*(a+b*(c*x^n)^(n^-1))^-1, x) == :((1/2)*b^-1*x^3*(c*x^n)^(-1*n^-1)+-1*a*b^-2*x^3*(c*x^n)^(-2*n^-1)+a^2*b^-3*x^3*(c*x^n)^(-3*n^-1)*log(a+b*(c*x^n)^(n^-1)))
@test integrate(x*(a+b*(c*x^n)^(n^-1))^-1, x) == :(b^-1*x^2*(c*x^n)^(-1*n^-1)+-1*a*b^-2*x^2*(c*x^n)^(-2*n^-1)*log(a+b*(c*x^n)^(n^-1)))
@test integrate((a+b*(c*x^n)^(n^-1))^-1, x) == :(x*b^-1*(c*x^n)^(-1*n^-1)*log(a+b*(c*x^n)^(n^-1)))
@test integrate(x^-1*(a+b*(c*x^n)^(n^-1))^-1, x) == :(a^-1*log(x)+-1*a^-1*log(a+b*(c*x^n)^(n^-1)))
@test integrate(x^-2*(a+b*(c*x^n)^(n^-1))^-1, x) == :(-1*a^-1*x^-1+b*a^-2*x^-1*(c*x^n)^(n^-1)*log(a+b*(c*x^n)^(n^-1))+-1*b*a^-2*x^-1*(c*x^n)^(n^-1)*log(x))
@test integrate(x^-3*(a+b*(c*x^n)^(n^-1))^-1, x) == :(-1//2*a^-1*x^-2+b*a^-2*x^-2*(c*x^n)^(n^-1)+a^-3*b^2*x^-2*(c*x^n)^(2*n^-1)*log(x)+-1*a^-3*b^2*x^-2*(c*x^n)^(2*n^-1)*log(a+b*(c*x^n)^(n^-1)))
@test integrate(x^3*(a+b*(c*x^n)^(n^-1))^-2, x) == :((1/2)*b^-2*x^4*(c*x^n)^(-2*n^-1)+-2*a*b^-3*x^4*(c*x^n)^(-3*n^-1)+a^3*b^-4*x^4*(c*x^n)^(-4*n^-1)*(a+b*(c*x^n)^(n^-1))^-1+3*a^2*b^-4*x^4*(c*x^n)^(-4*n^-1)*log(a+b*(c*x^n)^(n^-1)))
@test integrate(x^2*(a+b*(c*x^n)^(n^-1))^-2, x) == :(b^-2*x^3*(c*x^n)^(-2*n^-1)+-1*a^2*b^-3*x^3*(c*x^n)^(-3*n^-1)*(a+b*(c*x^n)^(n^-1))^-1+-2*a*b^-3*x^3*(c*x^n)^(-3*n^-1)*log(a+b*(c*x^n)^(n^-1)))
@test integrate(x*(a+b*(c*x^n)^(n^-1))^-2, x) == :(b^-2*x^2*(c*x^n)^(-2*n^-1)*log(a+b*(c*x^n)^(n^-1))+a*b^-2*x^2*(c*x^n)^(-2*n^-1)*(a+b*(c*x^n)^(n^-1))^-1)
@test integrate(x^-1*(a+b*(c*x^n)^(n^-1))^-2, x) == :(a^-1*(a+b*(c*x^n)^(n^-1))^-1+a^-2*log(x)+-1*a^-2*log(a+b*(c*x^n)^(n^-1)))
@test integrate(x^-2*(a+b*(c*x^n)^(n^-1))^-2, x) == :(-1*a^-2*x^-1+-1*b*a^-2*x^-1*(c*x^n)^(n^-1)*(a+b*(c*x^n)^(n^-1))^-1+-2*b*a^-3*x^-1*(c*x^n)^(n^-1)*log(x)+2*b*a^-3*x^-1*(c*x^n)^(n^-1)*log(a+b*(c*x^n)^(n^-1)))
@test integrate(x^-3*(a+b*(c*x^n)^(n^-1))^-2, x) == :(-1//2*a^-2*x^-2+2*b*a^-3*x^-2*(c*x^n)^(n^-1)+a^-3*b^2*x^-2*(c*x^n)^(2*n^-1)*(a+b*(c*x^n)^(n^-1))^-1+-3*a^-4*b^2*x^-2*(c*x^n)^(2*n^-1)*log(a+b*(c*x^n)^(n^-1))+3*a^-4*b^2*x^-2*(c*x^n)^(2*n^-1)*log(x))
@test integrate((a+b*(c*x^n)^(n^-1))^-3, x) == :(-1//2*x*b^-1*(c*x^n)^(-1*n^-1)*(a+b*(c*x^n)^(n^-1))^-2)
@test integrate(x*(1+(x^n)^(n^-1))^-2, x) == :(x^2*(x^n)^(-2*n^-1)*(1+(x^n)^(n^-1))^-1+x^2*(x^n)^(-2*n^-1)*log(1+(x^n)^(n^-1)))
@test integrate(x^3*(a+b*(c*x^n)^(n^-1))^p, x) == :(b^-4*x^4*(c*x^n)^(-4*n^-1)*(4+p)^-1*(a+b*(c*x^n)^(n^-1))^(4+p)+-1*a^3*b^-4*x^4*(c*x^n)^(-4*n^-1)*(1+p)^-1*(a+b*(c*x^n)^(n^-1))^(1+p)+-3*a*b^-4*x^4*(c*x^n)^(-4*n^-1)*(3+p)^-1*(a+b*(c*x^n)^(n^-1))^(3+p)+3*a^2*b^-4*x^4*(c*x^n)^(-4*n^-1)*(2+p)^-1*(a+b*(c*x^n)^(n^-1))^(2+p))
@test integrate(x^2*(a+b*(c*x^n)^(n^-1))^p, x) == :(b^-3*x^3*(c*x^n)^(-3*n^-1)*(3+p)^-1*(a+b*(c*x^n)^(n^-1))^(3+p)+a^2*b^-3*x^3*(c*x^n)^(-3*n^-1)*(1+p)^-1*(a+b*(c*x^n)^(n^-1))^(1+p)+-2*a*b^-3*x^3*(c*x^n)^(-3*n^-1)*(2+p)^-1*(a+b*(c*x^n)^(n^-1))^(2+p))
@test integrate(x*(a+b*(c*x^n)^(n^-1))^p, x) == :(b^-2*x^2*(c*x^n)^(-2*n^-1)*(2+p)^-1*(a+b*(c*x^n)^(n^-1))^(2+p)+-1*a*b^-2*x^2*(c*x^n)^(-2*n^-1)*(1+p)^-1*(a+b*(c*x^n)^(n^-1))^(1+p))
@test integrate((a+b*(c*x^n)^(n^-1))^p, x) == :(x*b^-1*(c*x^n)^(-1*n^-1)*(1+p)^-1*(a+b*(c*x^n)^(n^-1))^(1+p))
@test integrate((a+b*(c*x^n)^(2*n^-1))^3, x) == :(x*a^3+1//7*x*b^3*(c*x^n)^(6*n^-1)+b*x*a^2*(c*x^n)^(2*n^-1)+3//5*a*x*b^2*(c*x^n)^(4*n^-1))
@test integrate((a+b*(c*x^n)^(2*n^-1))^2, x) == :(x*a^2+1//5*x*b^2*(c*x^n)^(4*n^-1)+2//3*a*b*x*(c*x^n)^(2*n^-1))
@test integrate(a+b*(c*x^n)^(2*n^-1), x) == :(a*x+1//3*b*x*(c*x^n)^(2*n^-1))
@test integrate((a+b*(c*x^n)^(2*n^-1))^-1, x) == :(x*a^-1//2*b^-1//2*(c*x^n)^(-1*n^-1)*arctan(a^-1//2*b^(1/2)*(c*x^n)^(n^-1)))
@test integrate((a+b*(c*x^n)^(2*n^-1))^-2, x) == :((1/2)*x*a^-1*(a+b*(c*x^n)^(2*n^-1))^-1+(1/2)*x*a^-3//2*b^-1//2*(c*x^n)^(-1*n^-1)*arctan(a^-1//2*b^(1/2)*(c*x^n)^(n^-1)))
@test integrate((a+b*(c*x^n)^(2*n^-1))^-3, x) == :(1//4*x*a^-1*(a+b*(c*x^n)^(2*n^-1))^-2+3//8*x*a^-2*(a+b*(c*x^n)^(2*n^-1))^-1+3//8*x*a^-5//2*b^-1//2*(c*x^n)^(-1*n^-1)*arctan(a^-1//2*b^(1/2)*(c*x^n)^(n^-1)))
@test integrate((1+4*(x^4)^(1/2))^-1, x) == :((1/2)*x*(x^4)^-1//4*arctan(2*(x^4)^1//4))
@test integrate((1+-4*(x^4)^(1/2))^-1, x) == :((1/2)*x*(x^4)^-1//4*arctanh(2*(x^4)^1//4))
@test integrate((1+4*(x^6)^1//3)^-1, x) == :((1/2)*x*(x^6)^-1//6*arctan(2*(x^6)^1//6))
@test integrate((1+-4*(x^6)^1//3)^-1, x) == :((1/2)*x*(x^6)^-1//6*arctanh(2*(x^6)^1//6))
@test integrate((1+4*(x^(2n))^(n^-1))^-1, x) == :((1/2)*x*(x^(2n))^(-1//2*n^-1)*arctan(2*(x^(2n))^((1/2)*n^-1)))
@test integrate((1+-4*(x^(2n))^(n^-1))^-1, x) == :((1/2)*x*(x^(2n))^(-1//2*n^-1)*arctanh(2*(x^(2n))^((1/2)*n^-1)))
@test integrate((a+b*(c*x^n)^(3*n^-1))^3, x) == :(x*a^3+1//10*x*b^3*(c*x^n)^(9*n^-1)+3//4*b*x*a^2*(c*x^n)^(3*n^-1)+3//7*a*x*b^2*(c*x^n)^(6*n^-1))
@test integrate((a+b*(c*x^n)^(3*n^-1))^2, x) == :(x*a^2+1//7*x*b^2*(c*x^n)^(6*n^-1)+(1/2)*a*b*x*(c*x^n)^(3*n^-1))
@test integrate(a+b*(c*x^n)^(3*n^-1), x) == :(a*x+1//4*b*x*(c*x^n)^(3*n^-1))
@test integrate((a+b*(c*x^n)^(3*n^-1))^-1, x) == :(-1//6*x*a^-2//3*b^-1//3*(c*x^n)^(-1*n^-1)*log(a^2//3+b^2//3*(c*x^n)^(2*n^-1)+-1*a^1//3*b^1//3*(c*x^n)^(n^-1))+1//3*x*a^-2//3*b^-1//3*(c*x^n)^(-1*n^-1)*log(a^1//3+b^1//3*(c*x^n)^(n^-1))+-1//3*x*3^(1/2)*a^-2//3*b^-1//3*(c*x^n)^(-1*n^-1)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*b^1//3*(c*x^n)^(n^-1))))
@test integrate((a+b*(c*x^n)^(3*n^-1))^-2, x) == :(1//3*x*a^-1*(a+b*(c*x^n)^(3*n^-1))^-1+-1//9*x*a^-5//3*b^-1//3*(c*x^n)^(-1*n^-1)*log(a^2//3+b^2//3*(c*x^n)^(2*n^-1)+-1*a^1//3*b^1//3*(c*x^n)^(n^-1))+2//9*x*a^-5//3*b^-1//3*(c*x^n)^(-1*n^-1)*log(a^1//3+b^1//3*(c*x^n)^(n^-1))+-2//9*x*3^(1/2)*a^-5//3*b^-1//3*(c*x^n)^(-1*n^-1)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*b^1//3*(c*x^n)^(n^-1))))
@test integrate((a+b*(c*x^n)^(3*n^-1))^-3, x) == :(1//6*x*a^-1*(a+b*(c*x^n)^(3*n^-1))^-2+5//18*x*a^-2*(a+b*(c*x^n)^(3*n^-1))^-1+-5//54*x*a^-8//3*b^-1//3*(c*x^n)^(-1*n^-1)*log(a^2//3+b^2//3*(c*x^n)^(2*n^-1)+-1*a^1//3*b^1//3*(c*x^n)^(n^-1))+5//27*x*a^-8//3*b^-1//3*(c*x^n)^(-1*n^-1)*log(a^1//3+b^1//3*(c*x^n)^(n^-1))+-5//27*x*3^(1/2)*a^-8//3*b^-1//3*(c*x^n)^(-1*n^-1)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*b^1//3*(c*x^n)^(n^-1))))
@test integrate(x^2*(a+b*(d*x^-1)^(1/2)+c*x^-1)^(1/2), x) == :(1//3*a^-1*x^3*(a+b*(d*x^-1)^(1/2)+c*x^-1)^3//2+-1//80*a^-3*x^2*(a+b*(d*x^-1)^(1/2)+c*x^-1)^3//2*(-21*d*b^2+20*a*c)+1//512*a^-11//2*(-1*d*b^2+4*a*c)*(16*a^2*c^2+21*b^4*d^2+-56*a*c*d*b^2)*arctanh((1/2)*a^-1//2*(a+b*(d*x^-1)^(1/2)+c*x^-1)^-1//2*(2a+b*(d*x^-1)^(1/2)))+-3//10*b*a^-2*d^3*(d*x^-1)^-5//2*(a+b*(d*x^-1)^(1/2)+c*x^-1)^3//2+1//256*x*a^-5*(a+b*(d*x^-1)^(1/2)+c*x^-1)^(1/2)*(2a+b*(d*x^-1)^(1/2))*(16*a^2*c^2+21*b^4*d^2+-56*a*c*d*b^2)+7//480*b*a^-4*d^2*(d*x^-1)^-3//2*(a+b*(d*x^-1)^(1/2)+c*x^-1)^3//2*(-15*d*b^2+28*a*c))
@test integrate(x*(a+b*(d*x^-1)^(1/2)+c*x^-1)^(1/2), x) == :((1/2)*a^-1*x^2*(a+b*(d*x^-1)^(1/2)+c*x^-1)^3//2+-1//64*a^-7//2*(-1*d*b^2+4*a*c)*(-5*d*b^2+4*a*c)*arctanh((1/2)*a^-1//2*(a+b*(d*x^-1)^(1/2)+c*x^-1)^-1//2*(2a+b*(d*x^-1)^(1/2)))+-5//12*b*a^-2*d^2*(d*x^-1)^-3//2*(a+b*(d*x^-1)^(1/2)+c*x^-1)^3//2+-1//32*x*a^-3*(a+b*(d*x^-1)^(1/2)+c*x^-1)^(1/2)*(2a+b*(d*x^-1)^(1/2))*(-5*d*b^2+4*a*c))
@test integrate((a+b*(d*x^-1)^(1/2)+c*x^-1)^(1/2), x) == :(1//4*a^-3//2*(-1*d*b^2+4*a*c)*arctanh((1/2)*a^-1//2*(a+b*(d*x^-1)^(1/2)+c*x^-1)^-1//2*(2a+b*(d*x^-1)^(1/2)))+(1/2)*x*a^-1*(a+b*(d*x^-1)^(1/2)+c*x^-1)^(1/2)*(2a+b*(d*x^-1)^(1/2)))
@test integrate(x^-1*(a+b*(d*x^-1)^(1/2)+c*x^-1)^(1/2), x) == :(-2*(a+b*(d*x^-1)^(1/2)+c*x^-1)^(1/2)+2*a^(1/2)*arctanh((1/2)*a^-1//2*(a+b*(d*x^-1)^(1/2)+c*x^-1)^-1//2*(2a+b*(d*x^-1)^(1/2)))+-1*b*c^-1//2*d^(1/2)*arctanh((1/2)*c^-1//2*d^-1//2*(a+b*(d*x^-1)^(1/2)+c*x^-1)^-1//2*(b*d+2*c*(d*x^-1)^(1/2))))
@test integrate(x^-2*(a+b*(d*x^-1)^(1/2)+c*x^-1)^(1/2), x) == :(-2//3*c^-1*(a+b*(d*x^-1)^(1/2)+c*x^-1)^3//2+1//4*b*c^-2*(a+b*(d*x^-1)^(1/2)+c*x^-1)^(1/2)*(b*d+2*c*(d*x^-1)^(1/2))+1//8*b*c^-5//2*d^(1/2)*(-1*d*b^2+4*a*c)*arctanh((1/2)*c^-1//2*d^-1//2*(a+b*(d*x^-1)^(1/2)+c*x^-1)^-1//2*(b*d+2*c*(d*x^-1)^(1/2))))
@test integrate(x^-3*(a+b*(d*x^-1)^(1/2)+c*x^-1)^(1/2), x) == :(-2//5*c^-1*x^-1*(a+b*(d*x^-1)^(1/2)+c*x^-1)^3//2+1//120*c^-3*(a+b*(d*x^-1)^(1/2)+c*x^-1)^3//2*(-35*d*b^2+32*a*c+42*b*c*(d*x^-1)^(1/2))+-1//64*b*c^-4*(a+b*(d*x^-1)^(1/2)+c*x^-1)^(1/2)*(b*d+2*c*(d*x^-1)^(1/2))*(-7*d*b^2+12*a*c)+-1//128*b*c^-9//2*d^(1/2)*(-1*d*b^2+4*a*c)*(-7*d*b^2+12*a*c)*arctanh((1/2)*c^-1//2*d^-1//2*(a+b*(d*x^-1)^(1/2)+c*x^-1)^-1//2*(b*d+2*c*(d*x^-1)^(1/2))))
@test integrate(x^-4*(a+b*(d*x^-1)^(1/2)+c*x^-1)^(1/2), x) == :(-2//7*c^-1*x^-2*(a+b*(d*x^-1)^(1/2)+c*x^-1)^3//2+-1//6720*c^-5*(a+b*(d*x^-1)^(1/2)+c*x^-1)^3//2*(1024*a^2*c^2+1155*b^4*d^2+-3276*a*c*d*b^2+18*b*c*(d*x^-1)^(1/2)*(-77*d*b^2+148*a*c))+1//140*c^-3*x^-1*(a+b*(d*x^-1)^(1/2)+c*x^-1)^3//2*(-33*d*b^2+32*a*c)+1//512*b*c^-6*(a+b*(d*x^-1)^(1/2)+c*x^-1)^(1/2)*(b*d+2*c*(d*x^-1)^(1/2))*(33*b^4*d^2+80*a^2*c^2+-120*a*c*d*b^2)+11//42*b*c^-2*d^-1*(d*x^-1)^3//2*(a+b*(d*x^-1)^(1/2)+c*x^-1)^3//2+1//1024*b*c^-13//2*d^(1/2)*(-1*d*b^2+4*a*c)*(33*b^4*d^2+80*a^2*c^2+-120*a*c*d*b^2)*arctanh((1/2)*c^-1//2*d^-1//2*(a+b*(d*x^-1)^(1/2)+c*x^-1)^-1//2*(b*d+2*c*(d*x^-1)^(1/2))))
@test integrate(x^2*(a+b*(d*x^-1)^(1/2)+c*x^-1)^-1//2, x) == :(-1//512*a^-13//2*(-231*b^6*d^3+320*a^3*c^3+-1680*d*a^2*b^2*c^2+1260*a*c*b^4*d^2)*arctanh((1/2)*a^-1//2*(a+b*(d*x^-1)^(1/2)+c*x^-1)^-1//2*(2a+b*(d*x^-1)^(1/2)))+1//3*a^-1*x^3*(a+b*(d*x^-1)^(1/2)+c*x^-1)^(1/2)+-1//240*a^-3*x^2*(a+b*(d*x^-1)^(1/2)+c*x^-1)^(1/2)*(-99*d*b^2+100*a*c)+1//640*x*a^-5*(a+b*(d*x^-1)^(1/2)+c*x^-1)^(1/2)*(385*b^4*d^2+400*a^2*c^2+-1176*a*c*d*b^2)+-11//30*b*a^-2*d^3*(d*x^-1)^-5//2*(a+b*(d*x^-1)^(1/2)+c*x^-1)^(1/2)+-7//1280*b*d*a^-6*(d*x^-1)^-1//2*(a+b*(d*x^-1)^(1/2)+c*x^-1)^(1/2)*(165*b^4*d^2+528*a^2*c^2+-680*a*c*d*b^2)+1//160*b*a^-4*d^2*(d*x^-1)^-3//2*(a+b*(d*x^-1)^(1/2)+c*x^-1)^(1/2)*(-77*d*b^2+156*a*c))
@test integrate(x*(a+b*(d*x^-1)^(1/2)+c*x^-1)^-1//2, x) == :((1/2)*a^-1*x^2*(a+b*(d*x^-1)^(1/2)+c*x^-1)^(1/2)+1//64*a^-9//2*(35*b^4*d^2+48*a^2*c^2+-120*a*c*d*b^2)*arctanh((1/2)*a^-1//2*(a+b*(d*x^-1)^(1/2)+c*x^-1)^-1//2*(2a+b*(d*x^-1)^(1/2)))+-1//48*x*a^-3*(a+b*(d*x^-1)^(1/2)+c*x^-1)^(1/2)*(-35*d*b^2+36*a*c)+-7//12*b*a^-2*d^2*(d*x^-1)^-3//2*(a+b*(d*x^-1)^(1/2)+c*x^-1)^(1/2)+5//96*b*d*a^-4*(d*x^-1)^-1//2*(a+b*(d*x^-1)^(1/2)+c*x^-1)^(1/2)*(-21*d*b^2+44*a*c))
@test integrate((a+b*(d*x^-1)^(1/2)+c*x^-1)^-1//2, x) == :(x*a^-1*(a+b*(d*x^-1)^(1/2)+c*x^-1)^(1/2)+-1//4*a^-5//2*(-3*d*b^2+4*a*c)*arctanh((1/2)*a^-1//2*(a+b*(d*x^-1)^(1/2)+c*x^-1)^-1//2*(2a+b*(d*x^-1)^(1/2)))+-3//2*b*d*a^-2*(d*x^-1)^-1//2*(a+b*(d*x^-1)^(1/2)+c*x^-1)^(1/2))
@test integrate(x^-1*(a+b*(d*x^-1)^(1/2)+c*x^-1)^-1//2, x) == :(2*a^-1//2*arctanh((1/2)*a^-1//2*(a+b*(d*x^-1)^(1/2)+c*x^-1)^-1//2*(2a+b*(d*x^-1)^(1/2))))
@test integrate(x^-2*(a+b*(d*x^-1)^(1/2)+c*x^-1)^-1//2, x) == :(-2*c^-1*(a+b*(d*x^-1)^(1/2)+c*x^-1)^(1/2)+b*c^-3//2*d^(1/2)*arctanh((1/2)*c^-1//2*d^-1//2*(a+b*(d*x^-1)^(1/2)+c*x^-1)^-1//2*(b*d+2*c*(d*x^-1)^(1/2))))
@test integrate(x^-3*(a+b*(d*x^-1)^(1/2)+c*x^-1)^-1//2, x) == :(-2//3*c^-1*x^-1*(a+b*(d*x^-1)^(1/2)+c*x^-1)^(1/2)+1//12*c^-3*(a+b*(d*x^-1)^(1/2)+c*x^-1)^(1/2)*(-15*d*b^2+16*a*c+10*b*c*(d*x^-1)^(1/2))+-1//8*b*c^-7//2*d^(1/2)*(-5*d*b^2+12*a*c)*arctanh((1/2)*c^-1//2*d^-1//2*(a+b*(d*x^-1)^(1/2)+c*x^-1)^-1//2*(b*d+2*c*(d*x^-1)^(1/2))))
@test integrate(x^-4*(a+b*(d*x^-1)^(1/2)+c*x^-1)^-1//2, x) == :(-2//5*c^-1*x^-2*(a+b*(d*x^-1)^(1/2)+c*x^-1)^(1/2)+-1//960*c^-5*(a+b*(d*x^-1)^(1/2)+c*x^-1)^(1/2)*(945*b^4*d^2+1024*a^2*c^2+-2940*a*c*d*b^2+14*b*c*(d*x^-1)^(1/2)*(-45*d*b^2+92*a*c))+1//120*c^-3*x^-1*(a+b*(d*x^-1)^(1/2)+c*x^-1)^(1/2)*(-63*d*b^2+64*a*c)+1//128*b*c^-11//2*d^(1/2)*(63*b^4*d^2+240*a^2*c^2+-280*a*c*d*b^2)*arctanh((1/2)*c^-1//2*d^-1//2*(a+b*(d*x^-1)^(1/2)+c*x^-1)^-1//2*(b*d+2*c*(d*x^-1)^(1/2)))+9//20*b*c^-2*d^-1*(d*x^-1)^3//2*(a+b*(d*x^-1)^(1/2)+c*x^-1)^(1/2))
@test integrate((x^-1+(x^-1)^(1/2))^(1/2), x) == :(4//3*(x^-1)^-3//2*(x^-1+(x^-1)^(1/2))^3//2)
@test integrate((2+x^-1+(x^-1)^(1/2))^(1/2), x) == :(7//16*2^(1/2)*arctanh(1//4*2^(1/2)*(2+x^-1+(x^-1)^(1/2))^-1//2*(4+(x^-1)^(1/2)))+x*(2+x^-1+(x^-1)^(1/2))^(1/2)*(1+1//4*(x^-1)^(1/2)))
@test integrate((c*x^n)^(n^-1)*(a+b*(c*x^n)^(n^-1))^p, x) == :(x*b^-2*(c*x^n)^(-1*n^-1)*(2+p)^-1*(a+b*(c*x^n)^(n^-1))^(2+p)+-1*a*x*b^-2*(c*x^n)^(-1*n^-1)*(1+p)^-1*(a+b*(c*x^n)^(n^-1))^(1+p))
@test integrate((c*x^n)^(n^-1)*(a+b*(c*x^n)^(n^-1))^3, x) == :(1//5*x*b^-2*(c*x^n)^(-1*n^-1)*(a+b*(c*x^n)^(n^-1))^5+-1//4*a*x*b^-2*(c*x^n)^(-1*n^-1)*(a+b*(c*x^n)^(n^-1))^4)
@test integrate((c*x^n)^(n^-1)*(a+b*(c*x^n)^(n^-1))^2, x) == :((1/2)*x*a^2*(c*x^n)^(n^-1)+1//4*x*b^2*(c*x^n)^(3*n^-1)+2//3*a*b*x*(c*x^n)^(2*n^-1))
@test integrate((c*x^n)^(n^-1)*(a+b*(c*x^n)^(n^-1)), x) == :((1/2)*a*x*(c*x^n)^(n^-1)+1//3*b*x*(c*x^n)^(2*n^-1))
@test integrate((c*x^n)^(n^-1)*(a+b*(c*x^n)^(n^-1))^-1, x) == :(x*b^-1+-1*a*x*b^-2*(c*x^n)^(-1*n^-1)*log(a+b*(c*x^n)^(n^-1)))
@test integrate((c*x^n)^(n^-1)*(a+b*(c*x^n)^(n^-1))^-2, x) == :(x*b^-2*(c*x^n)^(-1*n^-1)*log(a+b*(c*x^n)^(n^-1))+a*x*b^-2*(c*x^n)^(-1*n^-1)*(a+b*(c*x^n)^(n^-1))^-1)
@test integrate((c*x^n)^(n^-1)*(a+b*(c*x^n)^(n^-1))^-3, x) == :((1/2)*x*a^-1*(c*x^n)^(n^-1)*(a+b*(c*x^n)^(n^-1))^-2)
@test integrate((c*x^n)^(n^-1)*(a+b*(c*x^n)^(n^-1))^-4, x) == :(-1//2*x*b^-2*(c*x^n)^(-1*n^-1)*(a+b*(c*x^n)^(n^-1))^-2+1//3*a*x*b^-2*(c*x^n)^(-1*n^-1)*(a+b*(c*x^n)^(n^-1))^-3)
@test integrate((c*x^n)^(n^-1)*(a+b*(c*x^n)^(n^-1))^-5, x) == :(-1//3*x*b^-2*(c*x^n)^(-1*n^-1)*(a+b*(c*x^n)^(n^-1))^-3+1//4*a*x*b^-2*(c*x^n)^(-1*n^-1)*(a+b*(c*x^n)^(n^-1))^-4)

max_stars_repo_path: test/1 Algebraic functions/1.1 Binomial products/1.1.3 General/1.1.3.2 (c x)^m (a+b x^n)^p.jl