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

@test integrate(1, x) == :(x)
@test integrate(5, x) == :(5x)
@test integrate(-2, x) == :(-2x)
@test integrate(-3//2, x) == :(-3//2*x)
@test integrate(pi, x) == :(pi*x)
@test integrate(a, x) == :(a*x)
@test integrate(3a, x) == :(3*a*x)
@test integrate(pi*(16+-1*exp(2))^-1//2, x) == :(pi*x*(16+-1*exp(2))^-1//2)
@test integrate(x^100, x) == :(1//101*x^101)
@test integrate(x^3, x) == :(1//4*x^4)
@test integrate(x^2, x) == :(1//3*x^3)
@test integrate(x, x) == :((1/2)*x^2)
@test integrate(1, x) == :(x)
@test integrate(x^-1, x) == :(log(x))
@test integrate(x^-2, x) == :(-1*x^-1)
@test integrate(x^-3, x) == :(-1//2*x^-2)
@test integrate(x^-4, x) == :(-1//3*x^-3)
@test integrate(x^-100, x) == :(-1//99*x^-99)
@test integrate(x^5//2, x) == :(2//7*x^7//2)
@test integrate(x^3//2, x) == :(2//5*x^5//2)
@test integrate(x^(1/2), x) == :(2//3*x^3//2)
@test integrate(x^-1//2, x) == :(2*x^(1/2))
@test integrate(x^-3//2, x) == :(-2*x^-1//2)
@test integrate(x^-5//2, x) == :(-2//3*x^-3//2)
@test integrate(x^5//3, x) == :(3//8*x^8//3)
@test integrate(x^4//3, x) == :(3//7*x^7//3)
@test integrate(x^2//3, x) == :(3//5*x^5//3)
@test integrate(x^1//3, x) == :(3//4*x^4//3)
@test integrate(x^-1//3, x) == :(3//2*x^2//3)
@test integrate(x^-2//3, x) == :(3*x^1//3)
@test integrate(x^-4//3, x) == :(-3*x^-1//3)
@test integrate(x^-5//3, x) == :(-3//2*x^-2//3)
@test integrate(x^n, x) == :(x^(1+n)*(1+n)^-1)
@test integrate((b*x)^n, x) == :(b^-1*(b*x)^(1+n)*(1+n)^-1)
@test integrate(((-1a)^(1/2)+e*(c+d*x))^-1, x) == :(d^-1*e^-1*log((-1a)^(1/2)+c*e+d*e*x))
@test integrate((c+d*(a+b*x))^5//2, x) == :(2//7*b^-1*d^-1*(c+d*(a+b*x))^7//2)
@test integrate((c+d*(a+b*x))^3//2, x) == :(2//5*b^-1*d^-1*(c+d*(a+b*x))^5//2)
@test integrate((c+d*(a+b*x))^(1/2), x) == :(2//3*b^-1*d^-1*(c+d*(a+b*x))^3//2)
@test integrate((c+d*(a+b*x))^-1//2, x) == :(2*b^-1*d^-1*(c+d*(a+b*x))^(1/2))
@test integrate((c+d*(a+b*x))^-3//2, x) == :(-2*b^-1*d^-1*(c+d*(a+b*x))^-1//2)
@test integrate((c+d*(a+b*x))^-5//2, x) == :(-2//3*b^-1*d^-1*(c+d*(a+b*x))^-3//2)
@test integrate(x^3*(a+b*x), x) == :(1//4*a*x^4+1//5*b*x^5)
@test integrate(x^2*(a+b*x), x) == :(1//3*a*x^3+1//4*b*x^4)
@test integrate(x*(a+b*x), x) == :((1/2)*a*x^2+1//3*b*x^3)
@test integrate(a+b*x, x) == :(a*x+(1/2)*b*x^2)
@test integrate(x^-1*(a+b*x), x) == :(a*log(x)+b*x)
@test integrate(x^-2*(a+b*x), x) == :(b*log(x)+-1*a*x^-1)
@test integrate(x^-3*(a+b*x), x) == :(-1//2*a^-1*x^-2*(a+b*x)^2)
@test integrate(x^-4*(a+b*x), x) == :(-1//2*b*x^-2+-1//3*a*x^-3)
@test integrate(x^-5*(a+b*x), x) == :(-1//3*b*x^-3+-1//4*a*x^-4)
@test integrate(x^3*(a+b*x)^2, x) == :(1//4*a^2*x^4+1//6*b^2*x^6+2//5*a*b*x^5)
@test integrate(x^2*(a+b*x)^2, x) == :(1//3*a^2*x^3+1//5*b^2*x^5+(1/2)*a*b*x^4)
@test integrate(x*(a+b*x)^2, x) == :((1/2)*a^2*x^2+1//4*b^2*x^4+2//3*a*b*x^3)
@test integrate((a+b*x)^2, x) == :(1//3*b^-1*(a+b*x)^3)
@test integrate(x^-1*(a+b*x)^2, x) == :(a^2*log(x)+(1/2)*b^2*x^2+2*a*b*x)
@test integrate(x^-2*(a+b*x)^2, x) == :(x*b^2+-1*a^2*x^-1+2*a*b*log(x))
@test integrate(x^-3*(a+b*x)^2, x) == :(b^2*log(x)+-1//2*a^2*x^-2+-2*a*b*x^-1)
@test integrate(x^-4*(a+b*x)^2, x) == :(-1//3*a^-1*x^-3*(a+b*x)^3)
@test integrate(x^-5*(a+b*x)^2, x) == :(-1//2*b^2*x^-2+-1//4*a^2*x^-4+-2//3*a*b*x^-3)
@test integrate(x^-6*(a+b*x)^2, x) == :(-1//3*b^2*x^-3+-1//5*a^2*x^-5+-1//2*a*b*x^-4)
@test integrate(x^-7*(a+b*x)^2, x) == :(-1//4*b^2*x^-4+-1//6*a^2*x^-6+-2//5*a*b*x^-5)
@test integrate(x^-8*(a+b*x)^2, x) == :(-1//5*b^2*x^-5+-1//7*a^2*x^-7+-1//3*a*b*x^-6)
@test integrate(x^4*(a+b*x)^3, x) == :(1//5*a^3*x^5+1//8*b^3*x^8+(1/2)*b*a^2*x^6+3//7*a*b^2*x^7)
@test integrate(x^3*(a+b*x)^3, x) == :(1//4*a^3*x^4+1//7*b^3*x^7+(1/2)*a*b^2*x^6+3//5*b*a^2*x^5)
@test integrate(x^2*(a+b*x)^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*(a+b*x)^3, x) == :(1//5*b^-2*(a+b*x)^5+-1//4*a*b^-2*(a+b*x)^4)
@test integrate((a+b*x)^3, x) == :(1//4*b^-1*(a+b*x)^4)
@test integrate(x^-1*(a+b*x)^3, x) == :(a^3*log(x)+1//3*b^3*x^3+3*b*x*a^2+3//2*a*b^2*x^2)
@test integrate(x^-2*(a+b*x)^3, x) == :((1/2)*b^3*x^2+-1*a^3*x^-1+3*a*x*b^2+3*b*a^2*log(x))
@test integrate(x^-3*(a+b*x)^3, x) == :(x*b^3+-1//2*a^3*x^-2+-3*b*a^2*x^-1+3*a*b^2*log(x))
@test integrate(x^-4*(a+b*x)^3, x) == :(b^3*log(x)+-1//3*a^3*x^-3+-3*a*b^2*x^-1+-3//2*b*a^2*x^-2)
@test integrate(x^-5*(a+b*x)^3, x) == :(-1//4*a^-1*x^-4*(a+b*x)^4)
@test integrate(x^-6*(a+b*x)^3, x) == :(-1//5*a^-1*x^-5*(a+b*x)^4+1//20*b*a^-2*x^-4*(a+b*x)^4)
@test integrate(x^-7*(a+b*x)^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^-8*(a+b*x)^3, x) == :(-1//4*b^3*x^-4+-1//7*a^3*x^-7+-3//5*a*b^2*x^-5+-1//2*b*a^2*x^-6)
@test integrate(x^6*(a+b*x)^5, x) == :(1//7*a^5*x^7+1//12*b^5*x^12+a^2*b^3*x^10+5//8*b*a^4*x^8+5//11*a*b^4*x^11+10//9*a^3*b^2*x^9)
@test integrate(x^5*(a+b*x)^5, x) == :(1//6*a^5*x^6+1//11*b^5*x^11+(1/2)*a*b^4*x^10+5//4*a^3*b^2*x^8+5//7*b*a^4*x^7+10//9*a^2*b^3*x^9)
@test integrate(x^4*(a+b*x)^5, x) == :(1//5*a^5*x^5+1//10*b^5*x^10+5//4*a^2*b^3*x^8+5//6*b*a^4*x^6+5//9*a*b^4*x^9+10//7*a^3*b^2*x^7)
@test integrate(x^3*(a+b*x)^5, x) == :(1//9*b^-4*(a+b*x)^9+-3//8*a*b^-4*(a+b*x)^8+-1//6*a^3*b^-4*(a+b*x)^6+3//7*a^2*b^-4*(a+b*x)^7)
@test integrate(x^2*(a+b*x)^5, x) == :(1//8*b^-3*(a+b*x)^8+-2//7*a*b^-3*(a+b*x)^7+1//6*a^2*b^-3*(a+b*x)^6)
@test integrate(x*(a+b*x)^5, x) == :(1//7*b^-2*(a+b*x)^7+-1//6*a*b^-2*(a+b*x)^6)
@test integrate((a+b*x)^5, x) == :(1//6*b^-1*(a+b*x)^6)
@test integrate(x^-1*(a+b*x)^5, x) == :(a^5*log(x)+1//5*b^5*x^5+5*b*x*a^4+5*a^3*b^2*x^2+5//4*a*b^4*x^4+10//3*a^2*b^3*x^3)
@test integrate(x^-2*(a+b*x)^5, x) == :(-1*a^5*x^-1+1//4*b^5*x^4+5*b*a^4*log(x)+5*a^2*b^3*x^2+10*x*a^3*b^2+5//3*a*b^4*x^3)
@test integrate(x^-3*(a+b*x)^5, x) == :(-1//2*a^5*x^-2+1//3*b^5*x^3+-5*b*a^4*x^-1+10*x*a^2*b^3+10*a^3*b^2*log(x)+5//2*a*b^4*x^2)
@test integrate(x^-4*(a+b*x)^5, x) == :((1/2)*b^5*x^2+-1//3*a^5*x^-3+-10*a^3*b^2*x^-1+5*a*x*b^4+10*a^2*b^3*log(x)+-5//2*b*a^4*x^-2)
@test integrate(x^-5*(a+b*x)^5, x) == :(x*b^5+-1//4*a^5*x^-4+-10*a^2*b^3*x^-1+-5*a^3*b^2*x^-2+5*a*b^4*log(x)+-5//3*b*a^4*x^-3)
@test integrate(x^-6*(a+b*x)^5, x) == :(b^5*log(x)+-1//5*a^5*x^-5+-5*a*b^4*x^-1+-5*a^2*b^3*x^-2+-10//3*a^3*b^2*x^-3+-5//4*b*a^4*x^-4)
@test integrate(x^-7*(a+b*x)^5, x) == :(-1//6*a^-1*x^-6*(a+b*x)^6)
@test integrate(x^-8*(a+b*x)^5, x) == :(-1//7*a^-1*x^-7*(a+b*x)^6+1//42*b*a^-2*x^-6*(a+b*x)^6)
@test integrate(x^-9*(a+b*x)^5, x) == :(-1//8*a^-1*x^-8*(a+b*x)^6+-1//168*a^-3*b^2*x^-6*(a+b*x)^6+1//28*b*a^-2*x^-7*(a+b*x)^6)
@test integrate(x^-10*(a+b*x)^5, x) == :(-1//4*b^5*x^-4+-1//9*a^5*x^-9+-1*a*b^4*x^-5+-10//7*a^3*b^2*x^-7+-5//3*a^2*b^3*x^-6+-5//8*b*a^4*x^-8)
@test integrate(x^-11*(a+b*x)^5, x) == :(-1//5*b^5*x^-5+-1//10*a^5*x^-10+-10//7*a^2*b^3*x^-7+-5//4*a^3*b^2*x^-8+-5//6*a*b^4*x^-6+-5//9*b*a^4*x^-9)
@test integrate(x^-12*(a+b*x)^5, x) == :(-1//6*b^5*x^-6+-1//11*a^5*x^-11+-10//9*a^3*b^2*x^-9+-5//4*a^2*b^3*x^-8+-5//7*a*b^4*x^-7+-1//2*b*a^4*x^-10)
@test integrate(x^-13*(a+b*x)^5, x) == :(-1//7*b^5*x^-7+-1//12*a^5*x^-12+-1*a^3*b^2*x^-10+-10//9*a^2*b^3*x^-9+-5//8*a*b^4*x^-8+-5//11*b*a^4*x^-11)
@test integrate(x^-14*(a+b*x)^5, x) == :(-1//8*b^5*x^-8+-1//13*a^5*x^-13+-1*a^2*b^3*x^-10+-10//11*a^3*b^2*x^-11+-5//9*a*b^4*x^-9+-5//12*b*a^4*x^-12)
@test integrate(x^8*(a+b*x)^7, x) == :(1//9*a^7*x^9+1//16*b^7*x^16+3//2*a^2*b^5*x^14+7//10*b*a^6*x^10+7//15*a*b^6*x^15+21//11*a^5*b^2*x^11+35//12*a^4*b^3*x^12+35//13*a^3*b^4*x^13)
@test integrate(x^7*(a+b*x)^7, x) == :(1//8*a^7*x^8+1//15*b^7*x^15+(1/2)*a*b^6*x^14+7//9*b*a^6*x^9+21//10*a^5*b^2*x^10+21//13*a^2*b^5*x^13+35//11*a^4*b^3*x^11+35//12*a^3*b^4*x^12)
@test integrate(x^6*(a+b*x)^7, x) == :(1//7*a^7*x^7+1//14*b^7*x^14+7//2*a^4*b^3*x^10+7//3*a^5*b^2*x^9+7//4*a^2*b^5*x^12+7//8*b*a^6*x^8+7//13*a*b^6*x^13+35//11*a^3*b^4*x^11)
@test integrate(x^5*(a+b*x)^7, x) == :(1//13*b^-6*(a+b*x)^13+-1*a^3*b^-6*(a+b*x)^10+-5//12*a*b^-6*(a+b*x)^12+-1//8*a^5*b^-6*(a+b*x)^8+5//9*a^4*b^-6*(a+b*x)^9+10//11*a^2*b^-6*(a+b*x)^11)
@test integrate(x^4*(a+b*x)^7, x) == :(1//12*b^-5*(a+b*x)^12+-4//9*a^3*b^-5*(a+b*x)^9+-4//11*a*b^-5*(a+b*x)^11+1//8*a^4*b^-5*(a+b*x)^8+3//5*a^2*b^-5*(a+b*x)^10)
@test integrate(x^3*(a+b*x)^7, x) == :(1//11*b^-4*(a+b*x)^11+-3//10*a*b^-4*(a+b*x)^10+-1//8*a^3*b^-4*(a+b*x)^8+1//3*a^2*b^-4*(a+b*x)^9)
@test integrate(x^2*(a+b*x)^7, x) == :(1//10*b^-3*(a+b*x)^10+-2//9*a*b^-3*(a+b*x)^9+1//8*a^2*b^-3*(a+b*x)^8)
@test integrate(x*(a+b*x)^7, x) == :(1//9*b^-2*(a+b*x)^9+-1//8*a*b^-2*(a+b*x)^8)
@test integrate((a+b*x)^7, x) == :(1//8*b^-1*(a+b*x)^8)
@test integrate(x^-1*(a+b*x)^7, x) == :(a^7*log(x)+1//7*b^7*x^7+7*b*x*a^6+7//6*a*b^6*x^6+21//2*a^5*b^2*x^2+21//5*a^2*b^5*x^5+35//3*a^4*b^3*x^3+35//4*a^3*b^4*x^4)
@test integrate(x^-2*(a+b*x)^7, x) == :(-1*a^7*x^-1+1//6*b^7*x^6+7*b*a^6*log(x)+21*x*a^5*b^2+7//5*a*b^6*x^5+21//4*a^2*b^5*x^4+35//2*a^4*b^3*x^2+35//3*a^3*b^4*x^3)
@test integrate(x^-3*(a+b*x)^7, x) == :(-1//2*a^7*x^-2+1//5*b^7*x^5+-7*b*a^6*x^-1+7*a^2*b^5*x^3+21*a^5*b^2*log(x)+35*x*a^4*b^3+7//4*a*b^6*x^4+35//2*a^3*b^4*x^2)
@test integrate(x^-4*(a+b*x)^7, x) == :(-1//3*a^7*x^-3+1//4*b^7*x^4+-21*a^5*b^2*x^-1+35*x*a^3*b^4+35*a^4*b^3*log(x)+-7//2*b*a^6*x^-2+7//3*a*b^6*x^3+21//2*a^2*b^5*x^2)
@test integrate(x^-5*(a+b*x)^7, x) == :(-1//4*a^7*x^-4+1//3*b^7*x^3+-35*a^4*b^3*x^-1+21*x*a^2*b^5+35*a^3*b^4*log(x)+-21//2*a^5*b^2*x^-2+-7//3*b*a^6*x^-3+7//2*a*b^6*x^2)
@test integrate(x^-6*(a+b*x)^7, x) == :((1/2)*b^7*x^2+-1//5*a^7*x^-5+-35*a^3*b^4*x^-1+-7*a^5*b^2*x^-3+7*a*x*b^6+21*a^2*b^5*log(x)+-35//2*a^4*b^3*x^-2+-7//4*b*a^6*x^-4)
@test integrate(x^-7*(a+b*x)^7, x) == :(x*b^7+-1//6*a^7*x^-6+-21*a^2*b^5*x^-1+7*a*b^6*log(x)+-35//2*a^3*b^4*x^-2+-35//3*a^4*b^3*x^-3+-21//4*a^5*b^2*x^-4+-7//5*b*a^6*x^-5)
@test integrate(x^-8*(a+b*x)^7, x) == :(b^7*log(x)+-1//7*a^7*x^-7+-7*a*b^6*x^-1+-35//3*a^3*b^4*x^-3+-35//4*a^4*b^3*x^-4+-21//2*a^2*b^5*x^-2+-21//5*a^5*b^2*x^-5+-7//6*b*a^6*x^-6)
@test integrate(x^-9*(a+b*x)^7, x) == :(-1//8*a^-1*x^-8*(a+b*x)^8)
@test integrate(x^-10*(a+b*x)^7, x) == :(-1//9*a^-1*x^-9*(a+b*x)^8+1//72*b*a^-2*x^-8*(a+b*x)^8)
@test integrate(x^-11*(a+b*x)^7, x) == :(-1//10*a^-1*x^-10*(a+b*x)^8+-1//360*a^-3*b^2*x^-8*(a+b*x)^8+1//45*b*a^-2*x^-9*(a+b*x)^8)
@test integrate(x^-12*(a+b*x)^7, x) == :(-1//11*a^-1*x^-11*(a+b*x)^8+-1//165*a^-3*b^2*x^-9*(a+b*x)^8+1//1320*a^-4*b^3*x^-8*(a+b*x)^8+3//110*b*a^-2*x^-10*(a+b*x)^8)
@test integrate(x^-13*(a+b*x)^7, x) == :(-1//12*a^-1*x^-12*(a+b*x)^8+-1//110*a^-3*b^2*x^-10*(a+b*x)^8+-1//3960*a^-5*b^4*x^-8*(a+b*x)^8+1//33*b*a^-2*x^-11*(a+b*x)^8+1//495*a^-4*b^3*x^-9*(a+b*x)^8)
@test integrate(x^-14*(a+b*x)^7, x) == :(-1//6*b^7*x^-6+-1//13*a^7*x^-13+-1*a*b^6*x^-7+-35//9*a^3*b^4*x^-9+-21//8*a^2*b^5*x^-8+-21//11*a^5*b^2*x^-11+-7//2*a^4*b^3*x^-10+-7//12*b*a^6*x^-12)
@test integrate(x^-15*(a+b*x)^7, x) == :(-1//7*b^7*x^-7+-1//14*a^7*x^-14+-35//11*a^4*b^3*x^-11+-7//2*a^3*b^4*x^-10+-7//3*a^2*b^5*x^-9+-7//4*a^5*b^2*x^-12+-7//8*a*b^6*x^-8+-7//13*b*a^6*x^-13)
@test integrate(x^-16*(a+b*x)^7, x) == :(-1//8*b^7*x^-8+-1//15*a^7*x^-15+-35//11*a^3*b^4*x^-11+-35//12*a^4*b^3*x^-12+-21//10*a^2*b^5*x^-10+-21//13*a^5*b^2*x^-13+-7//9*a*b^6*x^-9+-1//2*b*a^6*x^-14)
@test integrate(x^11*(a+b*x)^10, x) == :(1//12*a^10*x^12+1//22*b^10*x^22+8*a^7*b^3*x^15+9//4*a^2*b^8*x^20+10//13*b*a^9*x^13+10//21*a*b^9*x^21+35//3*a^4*b^6*x^18+45//14*a^8*b^2*x^14+105//8*a^6*b^4*x^16+120//19*a^3*b^7*x^19+252//17*a^5*b^5*x^17)
@test integrate(x^10*(a+b*x)^10, x) == :(1//11*a^10*x^11+1//21*b^10*x^21+(1/2)*a*b^9*x^20+14*a^6*b^4*x^15+5//6*b*a^9*x^12+20//3*a^3*b^7*x^18+45//13*a^8*b^2*x^13+45//19*a^2*b^8*x^19+60//7*a^7*b^3*x^14+63//4*a^5*b^5*x^16+210//17*a^4*b^6*x^17)
@test integrate(x^9*(a+b*x)^10, x) == :(1//10*a^10*x^10+1//20*b^10*x^20+15*a^6*b^4*x^14+5//2*a^2*b^8*x^18+10//11*b*a^9*x^11+10//19*a*b^9*x^19+15//4*a^8*b^2*x^12+84//5*a^5*b^5*x^15+105//8*a^4*b^6*x^16+120//13*a^7*b^3*x^13+120//17*a^3*b^7*x^17)
@test integrate(x^8*(a+b*x)^10, x) == :(1//19*b^-9*(a+b*x)^19+-4*a^5*b^-9*(a+b*x)^14+-7//2*a^3*b^-9*(a+b*x)^16+-4//9*a*b^-9*(a+b*x)^18+-2//3*a^7*b^-9*(a+b*x)^12+1//11*a^8*b^-9*(a+b*x)^11+14//3*a^4*b^-9*(a+b*x)^15+28//13*a^6*b^-9*(a+b*x)^13+28//17*a^2*b^-9*(a+b*x)^17)
@test integrate(x^7*(a+b*x)^10, x) == :(1//18*b^-8*(a+b*x)^18+-21//13*a^5*b^-8*(a+b*x)^13+-7//3*a^3*b^-8*(a+b*x)^15+-7//17*a*b^-8*(a+b*x)^17+-1//11*a^7*b^-8*(a+b*x)^11+5//2*a^4*b^-8*(a+b*x)^14+7//12*a^6*b^-8*(a+b*x)^12+21//16*a^2*b^-8*(a+b*x)^16)
@test integrate(x^6*(a+b*x)^10, x) == :(1//17*b^-7*(a+b*x)^17+a^2*b^-7*(a+b*x)^15+-10//7*a^3*b^-7*(a+b*x)^14+-3//8*a*b^-7*(a+b*x)^16+-1//2*a^5*b^-7*(a+b*x)^12+1//11*a^6*b^-7*(a+b*x)^11+15//13*a^4*b^-7*(a+b*x)^13)
@test integrate(x^5*(a+b*x)^10, x) == :(1//16*b^-6*(a+b*x)^16+-10//13*a^3*b^-6*(a+b*x)^13+-1//3*a*b^-6*(a+b*x)^15+-1//11*a^5*b^-6*(a+b*x)^11+5//7*a^2*b^-6*(a+b*x)^14+5//12*a^4*b^-6*(a+b*x)^12)
@test integrate(x^4*(a+b*x)^10, x) == :(1//15*b^-5*(a+b*x)^15+-2//7*a*b^-5*(a+b*x)^14+-1//3*a^3*b^-5*(a+b*x)^12+1//11*a^4*b^-5*(a+b*x)^11+6//13*a^2*b^-5*(a+b*x)^13)
@test integrate(x^3*(a+b*x)^10, x) == :(1//14*b^-4*(a+b*x)^14+-3//13*a*b^-4*(a+b*x)^13+-1//11*a^3*b^-4*(a+b*x)^11+1//4*a^2*b^-4*(a+b*x)^12)
@test integrate(x^2*(a+b*x)^10, x) == :(1//13*b^-3*(a+b*x)^13+-1//6*a*b^-3*(a+b*x)^12+1//11*a^2*b^-3*(a+b*x)^11)
@test integrate(x*(a+b*x)^10, x) == :(1//12*b^-2*(a+b*x)^12+-1//11*a*b^-2*(a+b*x)^11)
@test integrate((a+b*x)^10, x) == :(1//11*b^-1*(a+b*x)^11)
@test integrate(x^-1*(a+b*x)^10, x) == :(a^10*log(x)+1//10*b^10*x^10+10*b*x*a^9+35*a^4*b^6*x^6+40*a^7*b^3*x^3+10//9*a*b^9*x^9+45//2*a^8*b^2*x^2+45//8*a^2*b^8*x^8+105//2*a^6*b^4*x^4+120//7*a^3*b^7*x^7+252//5*a^5*b^5*x^5)
@test integrate(x^-2*(a+b*x)^10, x) == :(-1*a^10*x^-1+1//9*b^10*x^9+10*b*a^9*log(x)+20*a^3*b^7*x^6+42*a^4*b^6*x^5+45*x*a^8*b^2+60*a^7*b^3*x^2+63*a^5*b^5*x^4+70*a^6*b^4*x^3+5//4*a*b^9*x^8+45//7*a^2*b^8*x^7)
@test integrate(x^-3*(a+b*x)^10, x) == :(-1//2*a^10*x^-2+1//8*b^10*x^8+-10*b*a^9*x^-1+24*a^3*b^7*x^5+45*a^8*b^2*log(x)+84*a^5*b^5*x^3+105*a^6*b^4*x^2+120*x*a^7*b^3+10//7*a*b^9*x^7+15//2*a^2*b^8*x^6+105//2*a^4*b^6*x^4)
@test integrate(x^-4*(a+b*x)^10, x) == :(-1//3*a^10*x^-3+1//7*b^10*x^7+-45*a^8*b^2*x^-1+-5*b*a^9*x^-2+9*a^2*b^8*x^5+30*a^3*b^7*x^4+70*a^4*b^6*x^3+120*a^7*b^3*log(x)+126*a^5*b^5*x^2+210*x*a^6*b^4+5//3*a*b^9*x^6)
@test integrate(x^-5*(a+b*x)^10, x) == :(-1//4*a^10*x^-4+1//6*b^10*x^6+-120*a^7*b^3*x^-1+2*a*b^9*x^5+40*a^3*b^7*x^3+105*a^4*b^6*x^2+210*a^6*b^4*log(x)+252*x*a^5*b^5+-45//2*a^8*b^2*x^-2+-10//3*b*a^9*x^-3+45//4*a^2*b^8*x^4)
@test integrate(x^-6*(a+b*x)^10, x) == :(-1//5*a^10*x^-5+1//5*b^10*x^5+-210*a^6*b^4*x^-1+-60*a^7*b^3*x^-2+-15*a^8*b^2*x^-3+15*a^2*b^8*x^3+60*a^3*b^7*x^2+210*x*a^4*b^6+252*a^5*b^5*log(x)+-5//2*b*a^9*x^-4+5//2*a*b^9*x^4)
@test integrate(x^-7*(a+b*x)^10, x) == :(-1//6*a^10*x^-6+1//4*b^10*x^4+-252*a^5*b^5*x^-1+-105*a^6*b^4*x^-2+-40*a^7*b^3*x^-3+-2*b*a^9*x^-5+120*x*a^3*b^7+210*a^4*b^6*log(x)+-45//4*a^8*b^2*x^-4+10//3*a*b^9*x^3+45//2*a^2*b^8*x^2)
@test integrate(x^-8*(a+b*x)^10, x) == :(-1//7*a^10*x^-7+1//3*b^10*x^3+-210*a^4*b^6*x^-1+-126*a^5*b^5*x^-2+-70*a^6*b^4*x^-3+-30*a^7*b^3*x^-4+-9*a^8*b^2*x^-5+5*a*b^9*x^2+45*x*a^2*b^8+120*a^3*b^7*log(x)+-5//3*b*a^9*x^-6)
@test integrate(x^-9*(a+b*x)^10, x) == :((1/2)*b^10*x^2+-1//8*a^10*x^-8+-120*a^3*b^7*x^-1+-105*a^4*b^6*x^-2+-84*a^5*b^5*x^-3+-24*a^7*b^3*x^-5+10*a*x*b^9+45*a^2*b^8*log(x)+-105//2*a^6*b^4*x^-4+-15//2*a^8*b^2*x^-6+-10//7*b*a^9*x^-7)
@test integrate(x^-10*(a+b*x)^10, x) == :(x*b^10+-1//9*a^10*x^-9+-70*a^4*b^6*x^-3+-63*a^5*b^5*x^-4+-60*a^3*b^7*x^-2+-45*a^2*b^8*x^-1+-42*a^6*b^4*x^-5+-20*a^7*b^3*x^-6+10*a*b^9*log(x)+-45//7*a^8*b^2*x^-7+-5//4*b*a^9*x^-8)
@test integrate(x^-11*(a+b*x)^10, x) == :(b^10*log(x)+-1//10*a^10*x^-10+-40*a^3*b^7*x^-3+-35*a^6*b^4*x^-6+-10*a*b^9*x^-1+-252//5*a^5*b^5*x^-5+-120//7*a^7*b^3*x^-7+-105//2*a^4*b^6*x^-4+-45//2*a^2*b^8*x^-2+-45//8*a^8*b^2*x^-8+-10//9*b*a^9*x^-9)
@test integrate(x^-12*(a+b*x)^10, x) == :(-1//11*a^-1*x^-11*(a+b*x)^11)
@test integrate(x^-13*(a+b*x)^10, x) == :(-1//12*a^-1*x^-12*(a+b*x)^11+1//132*b*a^-2*x^-11*(a+b*x)^11)
@test integrate(x^-14*(a+b*x)^10, x) == :(-1//13*a^-1*x^-13*(a+b*x)^11+-1//858*a^-3*b^2*x^-11*(a+b*x)^11+1//78*b*a^-2*x^-12*(a+b*x)^11)
@test integrate(x^-15*(a+b*x)^10, x) == :(-1//14*a^-1*x^-14*(a+b*x)^11+-1//364*a^-3*b^2*x^-12*(a+b*x)^11+1//4004*a^-4*b^3*x^-11*(a+b*x)^11+3//182*b*a^-2*x^-13*(a+b*x)^11)
@test integrate(x^-16*(a+b*x)^10, x) == :(-1//15*a^-1*x^-15*(a+b*x)^11+-2//455*a^-3*b^2*x^-13*(a+b*x)^11+-1//15015*a^-5*b^4*x^-11*(a+b*x)^11+1//1365*a^-4*b^3*x^-12*(a+b*x)^11+2//105*b*a^-2*x^-14*(a+b*x)^11)
@test integrate(x^-17*(a+b*x)^10, x) == :(-1//16*a^-1*x^-16*(a+b*x)^11+-1//168*a^-3*b^2*x^-14*(a+b*x)^11+-1//4368*a^-5*b^4*x^-12*(a+b*x)^11+1//48*b*a^-2*x^-15*(a+b*x)^11+1//728*a^-4*b^3*x^-13*(a+b*x)^11+1//48048*a^-6*b^5*x^-11*(a+b*x)^11)
@test integrate(x^-18*(a+b*x)^10, x) == :(-1//17*a^-1*x^-17*(a+b*x)^11+-3//6188*a^-5*b^4*x^-13*(a+b*x)^11+-1//136*a^-3*b^2*x^-15*(a+b*x)^11+-1//136136*a^-7*b^6*x^-11*(a+b*x)^11+1//476*a^-4*b^3*x^-14*(a+b*x)^11+1//12376*a^-6*b^5*x^-12*(a+b*x)^11+3//136*b*a^-2*x^-16*(a+b*x)^11)
@test integrate(x^-19*(a+b*x)^10, x) == :(-1//8*b^10*x^-8+-1//18*a^10*x^-18+-15*a^6*b^4*x^-14+-8*a^7*b^3*x^-15+-252//13*a^5*b^5*x^-13+-120//11*a^3*b^7*x^-11+-45//16*a^8*b^2*x^-16+-35//2*a^4*b^6*x^-12+-10//9*a*b^9*x^-9+-10//17*b*a^9*x^-17+-9//2*a^2*b^8*x^-10)
@test integrate(x^-20*(a+b*x)^10, x) == :(-1//9*b^10*x^-9+-1//19*a^10*x^-19+-1*a*b^9*x^-10+-18*a^5*b^5*x^-14+-14*a^6*b^4*x^-15+-10*a^3*b^7*x^-12+-210//13*a^4*b^6*x^-13+-45//11*a^2*b^8*x^-11+-45//17*a^8*b^2*x^-17+-15//2*a^7*b^3*x^-16+-5//9*b*a^9*x^-18)
@test integrate(x^-32*(a+b*x)^20, x) == :(-1//31*a^-1*x^-31*(a+b*x)^21+-3//899*a^-3*b^2*x^-29*(a+b*x)^21+-2//8091*a^-5*b^4*x^-27*(a+b*x)^21+-2//175305*a^-7*b^6*x^-25*(a+b*x)^21+-1//4032015*a^-9*b^8*x^-23*(a+b*x)^21+-1//931395465*a^-11*b^10*x^-21*(a+b*x)^21+1//93*b*a^-2*x^-30*(a+b*x)^21+1//525915*a^-8*b^7*x^-24*(a+b*x)^21+1//44352165*a^-10*b^9*x^-22*(a+b*x)^21+2//35061*a^-6*b^5*x^-26*(a+b*x)^21+6//6293*a^-4*b^3*x^-28*(a+b*x)^21)
@test integrate(x^-33*(a+b*x)^20, x) == :(-1//32*a^-1*x^-32*(a+b*x)^21+-33//100688*a^-5*b^4*x^-28*(a+b*x)^21+-11//2976*a^-3*b^2*x^-30*(a+b*x)^21+-11//560976*a^-7*b^6*x^-26*(a+b*x)^21+-11//16829280*a^-9*b^8*x^-24*(a+b*x)^21+-1//129024480*a^-11*b^10*x^-22*(a+b*x)^21+1//2709514080*a^-12*b^11*x^-21*(a+b*x)^21+11//992*b*a^-2*x^-31*(a+b*x)^21+11//129456*a^-6*b^5*x^-27*(a+b*x)^21+11//2804880*a^-8*b^7*x^-25*(a+b*x)^21+11//129024480*a^-10*b^9*x^-23*(a+b*x)^21+33//28768*a^-4*b^3*x^-29*(a+b*x)^21)
@test integrate(x^-34*(a+b*x)^20, x) == :(-1//33*a^-1*x^-33*(a+b*x)^21+-3//7192*a^-5*b^4*x^-29*(a+b*x)^21+-1//248*a^-3*b^2*x^-31*(a+b*x)^21+-1//32364*a^-7*b^6*x^-27*(a+b*x)^21+-1//701220*a^-9*b^8*x^-25*(a+b*x)^21+-1//32256120*a^-11*b^10*x^-23*(a+b*x)^21+-1//7451163720*a^-13*b^12*x^-21*(a+b*x)^21+1//88*b*a^-2*x^-32*(a+b*x)^21+1//744*a^-4*b^3*x^-30*(a+b*x)^21+1//140244*a^-8*b^7*x^-26*(a+b*x)^21+1//4207320*a^-10*b^9*x^-24*(a+b*x)^21+1//354817320*a^-12*b^11*x^-22*(a+b*x)^21+3//25172*a^-6*b^5*x^-28*(a+b*x)^21)
@test integrate(x^-35*(a+b*x)^20, x) == :(-1//14*b^20*x^-14+-1//34*a^20*x^-34+-4845*a^12*b^8*x^-26+-1938*a^6*b^14*x^-20+-816*a^5*b^15*x^-19+-167960//23*a^9*b^11*x^-23+-62985//11*a^8*b^12*x^-22+-46189//6*a^10*b^10*x^-24+-33592//5*a^11*b^9*x^-25+-25840//7*a^7*b^13*x^-21+-25840//9*a^13*b^7*x^-27+-15504//29*a^15*b^5*x^-29+-9690//7*a^14*b^6*x^-28+-1615//6*a^4*b^16*x^-18+-1140//17*a^3*b^17*x^-17+-1140//31*a^17*b^3*x^-31+-323//2*a^16*b^4*x^-30+-95//8*a^2*b^18*x^-16+-95//16*a^18*b^2*x^-32+-20//33*b*a^19*x^-33+-4//3*a*b^19*x^-15)
@test integrate(x^-36*(a+b*x)^20, x) == :(-1//15*b^20*x^-15+-1//35*a^20*x^-35+-6460*a^11*b^9*x^-26+-255*a^4*b^16*x^-19+-184756//25*a^10*b^10*x^-25+-125970//23*a^8*b^12*x^-23+-41990//9*a^12*b^8*x^-27+-38760//11*a^7*b^13*x^-22+-38760//29*a^14*b^6*x^-29+-20995//3*a^9*b^11*x^-24+-19380//7*a^13*b^7*x^-28+-12920//7*a^6*b^14*x^-21+-4845//31*a^16*b^4*x^-31+-3876//5*a^5*b^15*x^-20+-2584//5*a^15*b^5*x^-30+-285//8*a^17*b^3*x^-32+-190//3*a^3*b^17*x^-18+-190//17*a^2*b^18*x^-17+-190//33*a^18*b^2*x^-33+-10//17*b*a^19*x^-34+-5//4*a*b^19*x^-16)
@test integrate(x^-37*(a+b*x)^20, x) == :(-1//16*b^20*x^-16+-1//36*a^20*x^-36+-7106*a^10*b^10*x^-26+-1292*a^14*b^6*x^-30+-60*a^3*b^17*x^-19+-167960//27*a^11*b^9*x^-27+-77520//23*a^7*b^13*x^-23+-77520//29*a^13*b^7*x^-29+-62985//14*a^12*b^8*x^-28+-33592//5*a^9*b^11*x^-25+-20995//4*a^8*b^12*x^-24+-19380//11*a^6*b^14*x^-22+-15504//31*a^15*b^5*x^-31+-5168//7*a^5*b^15*x^-21+-4845//32*a^16*b^4*x^-32+-969//4*a^4*b^16*x^-20+-380//11*a^17*b^3*x^-33+-95//9*a^2*b^18*x^-18+-95//17*a^18*b^2*x^-34+-20//17*a*b^19*x^-17+-4//7*b*a^19*x^-35)
@test integrate(c*(a+b*x), x) == :((1/2)*c*b^-1*(a+b*x)^2)
@test integrate(e^-1*(a+b*x)*(c+d), x) == :((1/2)*b^-1*e^-1*(a+b*x)^2*(c+d))
@test integrate(x^5*(a+b*x)^-1, x) == :(1//5*b^-1*x^5+x*a^4*b^-5+-1*a^5*b^-6*log(a+b*x)+-1//2*a^3*b^-4*x^2+-1//4*a*b^-2*x^4+1//3*a^2*b^-3*x^3)
@test integrate(x^4*(a+b*x)^-1, x) == :(1//4*b^-1*x^4+a^4*b^-5*log(a+b*x)+(1/2)*a^2*b^-3*x^2+-1*x*a^3*b^-4+-1//3*a*b^-2*x^3)
@test integrate(x^3*(a+b*x)^-1, x) == :(1//3*b^-1*x^3+x*a^2*b^-3+-1*a^3*b^-4*log(a+b*x)+-1//2*a*b^-2*x^2)
@test integrate(x^2*(a+b*x)^-1, x) == :((1/2)*b^-1*x^2+a^2*b^-3*log(a+b*x)+-1*a*x*b^-2)
@test integrate(x*(a+b*x)^-1, x) == :(x*b^-1+-1*a*b^-2*log(a+b*x))
@test integrate((a+b*x)^-1, x) == :(b^-1*log(a+b*x))
@test integrate(x^-1*(a+b*x)^-1, x) == :(a^-1*log(x)+-1*a^-1*log(a+b*x))
@test integrate(x^-2*(a+b*x)^-1, x) == :(-1*a^-1*x^-1+b*a^-2*log(a+b*x)+-1*b*a^-2*log(x))
@test integrate(x^-3*(a+b*x)^-1, x) == :(-1//2*a^-1*x^-2+b*a^-2*x^-1+a^-3*b^2*log(x)+-1*a^-3*b^2*log(a+b*x))
@test integrate(x^-4*(a+b*x)^-1, x) == :(-1//3*a^-1*x^-3+a^-4*b^3*log(a+b*x)+(1/2)*b*a^-2*x^-2+-1*a^-4*b^3*log(x)+-1*a^-3*b^2*x^-1)
@test integrate(x^-5*(a+b*x)^-1, x) == :(-1//4*a^-1*x^-4+a^-5*b^4*log(x)+a^-4*b^3*x^-1+-1*a^-5*b^4*log(a+b*x)+-1//2*a^-3*b^2*x^-2+1//3*b*a^-2*x^-3)
@test integrate(x^6*(a+b*x)^-2, x) == :(1//5*b^-2*x^5+a^2*b^-4*x^3+-1*a^6*b^-7*(a+b*x)^-1+-6*a^5*b^-7*log(a+b*x)+-2*a^3*b^-5*x^2+5*x*a^4*b^-6+-1//2*a*b^-3*x^4)
@test integrate(x^5*(a+b*x)^-2, x) == :(1//4*b^-2*x^4+a^5*b^-6*(a+b*x)^-1+-4*x*a^3*b^-5+5*a^4*b^-6*log(a+b*x)+-2//3*a*b^-3*x^3+3//2*a^2*b^-4*x^2)
@test integrate(x^4*(a+b*x)^-2, x) == :(1//3*b^-2*x^3+-1*a*b^-3*x^2+-1*a^4*b^-5*(a+b*x)^-1+-4*a^3*b^-5*log(a+b*x)+3*x*a^2*b^-4)
@test integrate(x^3*(a+b*x)^-2, x) == :((1/2)*b^-2*x^2+a^3*b^-4*(a+b*x)^-1+-2*a*x*b^-3+3*a^2*b^-4*log(a+b*x))
@test integrate(x^2*(a+b*x)^-2, x) == :(x*b^-2+-1*a^2*b^-3*(a+b*x)^-1+-2*a*b^-3*log(a+b*x))
@test integrate(x*(a+b*x)^-2, x) == :(b^-2*log(a+b*x)+a*b^-2*(a+b*x)^-1)
@test integrate((a+b*x)^-2, x) == :(-1*b^-1*(a+b*x)^-1)
@test integrate(x^-1*(a+b*x)^-2, x) == :(a^-1*(a+b*x)^-1+a^-2*log(x)+-1*a^-2*log(a+b*x))
@test integrate(x^-2*(a+b*x)^-2, x) == :(-1*a^-2*x^-1+-1*b*a^-2*(a+b*x)^-1+-2*b*a^-3*log(x)+2*b*a^-3*log(a+b*x))
@test integrate(x^-3*(a+b*x)^-2, x) == :(-1//2*a^-2*x^-2+a^-3*b^2*(a+b*x)^-1+-3*a^-4*b^2*log(a+b*x)+2*b*a^-3*x^-1+3*a^-4*b^2*log(x))
@test integrate(x^-4*(a+b*x)^-2, x) == :(-1//3*a^-2*x^-3+b*a^-3*x^-2+-1*a^-4*b^3*(a+b*x)^-1+-4*a^-5*b^3*log(x)+-3*a^-4*b^2*x^-1+4*a^-5*b^3*log(a+b*x))
@test integrate(x^-5*(a+b*x)^-2, x) == :(-1//4*a^-2*x^-4+a^-5*b^4*(a+b*x)^-1+-5*a^-6*b^4*log(a+b*x)+4*a^-5*b^3*x^-1+5*a^-6*b^4*log(x)+-3//2*a^-4*b^2*x^-2+2//3*b*a^-3*x^-3)
@test integrate(x^7*(a+b*x)^-3, x) == :(1//5*b^-3*x^5+(1/2)*a^7*b^-8*(a+b*x)^-2+-21*a^5*b^-8*log(a+b*x)+-7*a^6*b^-8*(a+b*x)^-1+-5*a^3*b^-6*x^2+2*a^2*b^-5*x^3+15*x*a^4*b^-7+-3//4*a*b^-4*x^4)
@test integrate(x^6*(a+b*x)^-3, x) == :(1//4*b^-3*x^4+-1*a*b^-4*x^3+-10*x*a^3*b^-6+3*a^2*b^-5*x^2+6*a^5*b^-7*(a+b*x)^-1+15*a^4*b^-7*log(a+b*x)+-1//2*a^6*b^-7*(a+b*x)^-2)
@test integrate(x^5*(a+b*x)^-3, x) == :(1//3*b^-3*x^3+(1/2)*a^5*b^-6*(a+b*x)^-2+-10*a^3*b^-6*log(a+b*x)+-5*a^4*b^-6*(a+b*x)^-1+6*x*a^2*b^-5+-3//2*a*b^-4*x^2)
@test integrate(x^4*(a+b*x)^-3, x) == :((1/2)*b^-3*x^2+-3*a*x*b^-4+4*a^3*b^-5*(a+b*x)^-1+6*a^2*b^-5*log(a+b*x)+-1//2*a^4*b^-5*(a+b*x)^-2)
@test integrate(x^3*(a+b*x)^-3, x) == :(x*b^-3+(1/2)*a^3*b^-4*(a+b*x)^-2+-3*a*b^-4*log(a+b*x)+-3*a^2*b^-4*(a+b*x)^-1)
@test integrate(x^2*(a+b*x)^-3, x) == :(b^-3*log(a+b*x)+2*a*b^-3*(a+b*x)^-1+-1//2*a^2*b^-3*(a+b*x)^-2)
@test integrate(x*(a+b*x)^-3, x) == :((1/2)*a^-1*x^2*(a+b*x)^-2)
@test integrate((a+b*x)^-3, x) == :(-1//2*b^-1*(a+b*x)^-2)
@test integrate(x^-1*(a+b*x)^-3, x) == :(a^-3*log(x)+a^-2*(a+b*x)^-1+(1/2)*a^-1*(a+b*x)^-2+-1*a^-3*log(a+b*x))
@test integrate(x^-2*(a+b*x)^-3, x) == :(-1*a^-3*x^-1+-3*b*a^-4*log(x)+-2*b*a^-3*(a+b*x)^-1+3*b*a^-4*log(a+b*x)+-1//2*b*a^-2*(a+b*x)^-2)
@test integrate(x^-3*(a+b*x)^-3, x) == :(-1//2*a^-3*x^-2+(1/2)*a^-3*b^2*(a+b*x)^-2+-6*a^-5*b^2*log(a+b*x)+3*b*a^-4*x^-1+3*a^-4*b^2*(a+b*x)^-1+6*a^-5*b^2*log(x))
@test integrate(x^-4*(a+b*x)^-3, x) == :(-1//3*a^-3*x^-3+-10*a^-6*b^3*log(x)+-6*a^-5*b^2*x^-1+-4*a^-5*b^3*(a+b*x)^-1+10*a^-6*b^3*log(a+b*x)+-1//2*a^-4*b^3*(a+b*x)^-2+3//2*b*a^-4*x^-2)
@test integrate(x^-5*(a+b*x)^-3, x) == :(-1//4*a^-3*x^-4+b*a^-4*x^-3+(1/2)*a^-5*b^4*(a+b*x)^-2+-15*a^-7*b^4*log(a+b*x)+-3*a^-5*b^2*x^-2+5*a^-6*b^4*(a+b*x)^-1+10*a^-6*b^3*x^-1+15*a^-7*b^4*log(x))
@test integrate(x^8*(a+b*x)^-4, x) == :(1//5*b^-4*x^5+-1*a*b^-5*x^4+-56*a^5*b^-9*log(a+b*x)+-28*a^6*b^-9*(a+b*x)^-1+-10*a^3*b^-7*x^2+4*a^7*b^-9*(a+b*x)^-2+35*x*a^4*b^-8+-1//3*a^8*b^-9*(a+b*x)^-3+10//3*a^2*b^-6*x^3)
@test integrate(x^7*(a+b*x)^-4, x) == :(1//4*b^-4*x^4+-20*x*a^3*b^-7+5*a^2*b^-6*x^2+21*a^5*b^-8*(a+b*x)^-1+35*a^4*b^-8*log(a+b*x)+-7//2*a^6*b^-8*(a+b*x)^-2+-4//3*a*b^-5*x^3+1//3*a^7*b^-8*(a+b*x)^-3)
@test integrate(x^6*(a+b*x)^-4, x) == :(1//3*b^-4*x^3+-20*a^3*b^-7*log(a+b*x)+-15*a^4*b^-7*(a+b*x)^-1+-2*a*b^-5*x^2+3*a^5*b^-7*(a+b*x)^-2+10*x*a^2*b^-6+-1//3*a^6*b^-7*(a+b*x)^-3)
@test integrate(x^5*(a+b*x)^-4, x) == :((1/2)*b^-4*x^2+-4*a*x*b^-5+10*a^2*b^-6*log(a+b*x)+10*a^3*b^-6*(a+b*x)^-1+-5//2*a^4*b^-6*(a+b*x)^-2+1//3*a^5*b^-6*(a+b*x)^-3)
@test integrate(x^4*(a+b*x)^-4, x) == :(x*b^-4+-6*a^2*b^-5*(a+b*x)^-1+-4*a*b^-5*log(a+b*x)+2*a^3*b^-5*(a+b*x)^-2+-1//3*a^4*b^-5*(a+b*x)^-3)
@test integrate(x^3*(a+b*x)^-4, x) == :(b^-4*log(a+b*x)+3*a*b^-4*(a+b*x)^-1+-3//2*a^2*b^-4*(a+b*x)^-2+1//3*a^3*b^-4*(a+b*x)^-3)
@test integrate(x^2*(a+b*x)^-4, x) == :(1//3*a^-1*x^3*(a+b*x)^-3)
@test integrate(x*(a+b*x)^-4, x) == :(-1//2*b^-2*(a+b*x)^-2+1//3*a*b^-2*(a+b*x)^-3)
@test integrate((a+b*x)^-4, x) == :(-1//3*b^-1*(a+b*x)^-3)
@test integrate(x^-1*(a+b*x)^-4, x) == :(a^-4*log(x)+a^-3*(a+b*x)^-1+(1/2)*a^-2*(a+b*x)^-2+-1*a^-4*log(a+b*x)+1//3*a^-1*(a+b*x)^-3)
@test integrate(x^-2*(a+b*x)^-4, x) == :(-1*a^-4*x^-1+-1*b*a^-3*(a+b*x)^-2+-4*b*a^-5*log(x)+-3*b*a^-4*(a+b*x)^-1+4*b*a^-5*log(a+b*x)+-1//3*b*a^-2*(a+b*x)^-3)
@test integrate(x^-3*(a+b*x)^-4, x) == :(-1//2*a^-4*x^-2+-10*a^-6*b^2*log(a+b*x)+4*b*a^-5*x^-1+6*a^-5*b^2*(a+b*x)^-1+10*a^-6*b^2*log(x)+1//3*a^-3*b^2*(a+b*x)^-3+3//2*a^-4*b^2*(a+b*x)^-2)
@test integrate(x^-4*(a+b*x)^-4, x) == :(-1//3*a^-4*x^-3+-20*a^-7*b^3*log(x)+-10*a^-6*b^2*x^-1+-10*a^-6*b^3*(a+b*x)^-1+-2*a^-5*b^3*(a+b*x)^-2+2*b*a^-5*x^-2+20*a^-7*b^3*log(a+b*x)+-1//3*a^-4*b^3*(a+b*x)^-3)
@test integrate(x^-5*(a+b*x)^-4, x) == :(-1//4*a^-4*x^-4+-35*a^-8*b^4*log(a+b*x)+-5*a^-6*b^2*x^-2+15*a^-7*b^4*(a+b*x)^-1+20*a^-7*b^3*x^-1+35*a^-8*b^4*log(x)+1//3*a^-5*b^4*(a+b*x)^-3+4//3*b*a^-5*x^-3+5//2*a^-6*b^4*(a+b*x)^-2)
@test integrate(x^10*(a+b*x)^-7, x) == :(1//4*b^-7*x^4+-105*a^6*b^-11*(a+b*x)^-2+-84*x*a^3*b^-10+2*a^9*b^-11*(a+b*x)^-5+14*a^2*b^-9*x^2+40*a^7*b^-11*(a+b*x)^-3+210*a^4*b^-11*log(a+b*x)+252*a^5*b^-11*(a+b*x)^-1+-45//4*a^8*b^-11*(a+b*x)^-4+-7//3*a*b^-8*x^3+-1//6*a^10*b^-11*(a+b*x)^-6)
@test integrate(x^9*(a+b*x)^-7, x) == :(1//3*b^-7*x^3+-126*a^4*b^-10*(a+b*x)^-1+-84*a^3*b^-10*log(a+b*x)+-28*a^6*b^-10*(a+b*x)^-3+9*a^7*b^-10*(a+b*x)^-4+28*x*a^2*b^-9+63*a^5*b^-10*(a+b*x)^-2+-9//5*a^8*b^-10*(a+b*x)^-5+-7//2*a*b^-8*x^2+1//6*a^9*b^-10*(a+b*x)^-6)
@test integrate(x^8*(a+b*x)^-7, x) == :((1/2)*b^-7*x^2+-35*a^4*b^-9*(a+b*x)^-2+-7*a*x*b^-8+-7*a^6*b^-9*(a+b*x)^-4+28*a^2*b^-9*log(a+b*x)+56*a^3*b^-9*(a+b*x)^-1+-1//6*a^8*b^-9*(a+b*x)^-6+8//5*a^7*b^-9*(a+b*x)^-5+56//3*a^5*b^-9*(a+b*x)^-3)
@test integrate(x^7*(a+b*x)^-7, x) == :(x*b^-7+-21*a^2*b^-8*(a+b*x)^-1+-7*a*b^-8*log(a+b*x)+-35//3*a^4*b^-8*(a+b*x)^-3+-7//5*a^6*b^-8*(a+b*x)^-5+1//6*a^7*b^-8*(a+b*x)^-6+21//4*a^5*b^-8*(a+b*x)^-4+35//2*a^3*b^-8*(a+b*x)^-2)
@test integrate(x^6*(a+b*x)^-7, x) == :(b^-7*log(a+b*x)+6*a*b^-7*(a+b*x)^-1+-15//2*a^2*b^-7*(a+b*x)^-2+-15//4*a^4*b^-7*(a+b*x)^-4+-1//6*a^6*b^-7*(a+b*x)^-6+6//5*a^5*b^-7*(a+b*x)^-5+20//3*a^3*b^-7*(a+b*x)^-3)
@test integrate(x^5*(a+b*x)^-7, x) == :(1//6*a^-1*x^6*(a+b*x)^-6)
@test integrate(x^4*(a+b*x)^-7, x) == :(1//6*a^-1*x^5*(a+b*x)^-6+1//30*a^-2*x^5*(a+b*x)^-5)
@test integrate(x^2*(a+b*x)^-7, x) == :(-1//4*b^-3*(a+b*x)^-4+-1//6*a^2*b^-3*(a+b*x)^-6+2//5*a*b^-3*(a+b*x)^-5)
@test integrate(x*(a+b*x)^-7, x) == :(-1//5*b^-2*(a+b*x)^-5+1//6*a*b^-2*(a+b*x)^-6)
@test integrate((a+b*x)^-7, x) == :(-1//6*b^-1*(a+b*x)^-6)
@test integrate(x^-1*(a+b*x)^-7, x) == :(a^-7*log(x)+a^-6*(a+b*x)^-1+(1/2)*a^-5*(a+b*x)^-2+-1*a^-7*log(a+b*x)+1//3*a^-4*(a+b*x)^-3+1//4*a^-3*(a+b*x)^-4+1//5*a^-2*(a+b*x)^-5+1//6*a^-1*(a+b*x)^-6)
@test integrate(x^-2*(a+b*x)^-7, x) == :(-1*a^-7*x^-1+-7*b*a^-8*log(x)+-6*b*a^-7*(a+b*x)^-1+7*b*a^-8*log(a+b*x)+-5//2*b*a^-6*(a+b*x)^-2+-4//3*b*a^-5*(a+b*x)^-3+-3//4*b*a^-4*(a+b*x)^-4+-2//5*b*a^-3*(a+b*x)^-5+-1//6*b*a^-2*(a+b*x)^-6)
@test integrate(x^-3*(a+b*x)^-7, x) == :(-1//2*a^-7*x^-2+-28*a^-9*b^2*log(a+b*x)+7*b*a^-8*x^-1+21*a^-8*b^2*(a+b*x)^-1+28*a^-9*b^2*log(x)+1//6*a^-3*b^2*(a+b*x)^-6+3//2*a^-5*b^2*(a+b*x)^-4+3//5*a^-4*b^2*(a+b*x)^-5+10//3*a^-6*b^2*(a+b*x)^-3+15//2*a^-7*b^2*(a+b*x)^-2)
@test integrate(x^-4*(a+b*x)^-7, x) == :(-1//3*a^-7*x^-3+-84*a^-10*b^3*log(x)+-56*a^-9*b^3*(a+b*x)^-1+-28*a^-9*b^2*x^-1+84*a^-10*b^3*log(a+b*x)+-35//2*a^-8*b^3*(a+b*x)^-2+-20//3*a^-7*b^3*(a+b*x)^-3+-5//2*a^-6*b^3*(a+b*x)^-4+-4//5*a^-5*b^3*(a+b*x)^-5+-1//6*a^-4*b^3*(a+b*x)^-6+7//2*b*a^-8*x^-2)
@test integrate(x^12*(a+b*x)^-10, x) == :(1//3*b^-10*x^3+-495*a^4*b^-13*(a+b*x)^-1+-308*a^6*b^-13*(a+b*x)^-3+-220*a^3*b^-13*log(a+b*x)+-99*a^8*b^-13*(a+b*x)^-5+-5*a*b^-11*x^2+55*x*a^2*b^-12+198*a^7*b^-13*(a+b*x)^-4+396*a^5*b^-13*(a+b*x)^-2+-66//7*a^10*b^-13*(a+b*x)^-7+-1//9*a^12*b^-13*(a+b*x)^-9+3//2*a^11*b^-13*(a+b*x)^-8+110//3*a^9*b^-13*(a+b*x)^-6)
@test integrate(x^11*(a+b*x)^-10, x) == :((1/2)*b^-10*x^2+-165*a^4*b^-12*(a+b*x)^-2+-10*a*x*b^-11+55*a^2*b^-12*log(a+b*x)+66*a^7*b^-12*(a+b*x)^-5+154*a^5*b^-12*(a+b*x)^-3+165*a^3*b^-12*(a+b*x)^-1+-231//2*a^6*b^-12*(a+b*x)^-4+-55//2*a^8*b^-12*(a+b*x)^-6+-11//8*a^10*b^-12*(a+b*x)^-8+1//9*a^11*b^-12*(a+b*x)^-9+55//7*a^9*b^-12*(a+b*x)^-7)
@test integrate(x^10*(a+b*x)^-10, x) == :(x*b^-10+-70*a^4*b^-11*(a+b*x)^-3+-45*a^2*b^-11*(a+b*x)^-1+-42*a^6*b^-11*(a+b*x)^-5+-10*a*b^-11*log(a+b*x)+20*a^7*b^-11*(a+b*x)^-6+60*a^3*b^-11*(a+b*x)^-2+63*a^5*b^-11*(a+b*x)^-4+-45//7*a^8*b^-11*(a+b*x)^-7+-1//9*a^10*b^-11*(a+b*x)^-9+5//4*a^9*b^-11*(a+b*x)^-8)
@test integrate(x^9*(a+b*x)^-10, x) == :(b^-10*log(a+b*x)+-18*a^2*b^-10*(a+b*x)^-2+-14*a^6*b^-10*(a+b*x)^-6+9*a*b^-10*(a+b*x)^-1+28*a^3*b^-10*(a+b*x)^-3+-63//2*a^4*b^-10*(a+b*x)^-4+-9//8*a^8*b^-10*(a+b*x)^-8+1//9*a^9*b^-10*(a+b*x)^-9+36//7*a^7*b^-10*(a+b*x)^-7+126//5*a^5*b^-10*(a+b*x)^-5)
@test integrate(x^8*(a+b*x)^-10, x) == :(1//9*a^-1*x^9*(a+b*x)^-9)
@test integrate(x^7*(a+b*x)^-10, x) == :(1//9*a^-1*x^8*(a+b*x)^-9+1//72*a^-2*x^8*(a+b*x)^-8)
@test integrate(x^6*(a+b*x)^-10, x) == :(1//9*a^-1*x^7*(a+b*x)^-9+1//36*a^-2*x^7*(a+b*x)^-8+1//252*a^-3*x^7*(a+b*x)^-7)
@test integrate(x^5*(a+b*x)^-10, x) == :(1//9*a^-1*x^6*(a+b*x)^-9+1//24*a^-2*x^6*(a+b*x)^-8+1//84*a^-3*x^6*(a+b*x)^-7+1//504*a^-4*x^6*(a+b*x)^-6)
@test integrate(x^4*(a+b*x)^-10, x) == :(-1//5*b^-5*(a+b*x)^-5+(1/2)*a^3*b^-5*(a+b*x)^-8+-6//7*a^2*b^-5*(a+b*x)^-7+-1//9*a^4*b^-5*(a+b*x)^-9+2//3*a*b^-5*(a+b*x)^-6)
@test integrate(x^3*(a+b*x)^-10, x) == :(-1//6*b^-4*(a+b*x)^-6+-3//8*a^2*b^-4*(a+b*x)^-8+1//9*a^3*b^-4*(a+b*x)^-9+3//7*a*b^-4*(a+b*x)^-7)
@test integrate(x^2*(a+b*x)^-10, x) == :(-1//7*b^-3*(a+b*x)^-7+-1//9*a^2*b^-3*(a+b*x)^-9+1//4*a*b^-3*(a+b*x)^-8)
@test integrate(x*(a+b*x)^-10, x) == :(-1//8*b^-2*(a+b*x)^-8+1//9*a*b^-2*(a+b*x)^-9)
@test integrate((a+b*x)^-10, x) == :(-1//9*b^-1*(a+b*x)^-9)
@test integrate(x^-1*(a+b*x)^-10, x) == :(a^-10*log(x)+a^-9*(a+b*x)^-1+(1/2)*a^-8*(a+b*x)^-2+-1*a^-10*log(a+b*x)+1//3*a^-7*(a+b*x)^-3+1//4*a^-6*(a+b*x)^-4+1//5*a^-5*(a+b*x)^-5+1//6*a^-4*(a+b*x)^-6+1//7*a^-3*(a+b*x)^-7+1//8*a^-2*(a+b*x)^-8+1//9*a^-1*(a+b*x)^-9)
@test integrate(x^-2*(a+b*x)^-10, x) == :(-1*a^-10*x^-1+-1*b*a^-6*(a+b*x)^-5+-10*b*a^-11*log(x)+-9*b*a^-10*(a+b*x)^-1+-4*b*a^-9*(a+b*x)^-2+10*b*a^-11*log(a+b*x)+-7//3*b*a^-8*(a+b*x)^-3+-3//2*b*a^-7*(a+b*x)^-4+-3//7*b*a^-4*(a+b*x)^-7+-2//3*b*a^-5*(a+b*x)^-6+-1//4*b*a^-3*(a+b*x)^-8+-1//9*b*a^-2*(a+b*x)^-9)
@test integrate(x^-3*(a+b*x)^-10, x) == :(-1//2*a^-10*x^-2+-55*a^-12*b^2*log(a+b*x)+3*a^-7*b^2*(a+b*x)^-5+10*b*a^-11*x^-1+18*a^-10*b^2*(a+b*x)^-2+45*a^-11*b^2*(a+b*x)^-1+55*a^-12*b^2*log(x)+1//9*a^-3*b^2*(a+b*x)^-9+3//8*a^-4*b^2*(a+b*x)^-8+5//3*a^-6*b^2*(a+b*x)^-6+6//7*a^-5*b^2*(a+b*x)^-7+21//4*a^-8*b^2*(a+b*x)^-4+28//3*a^-9*b^2*(a+b*x)^-3)
@test integrate(x^-4*(a+b*x)^-10, x) == :(-1//3*a^-10*x^-3+-220*a^-13*b^3*log(x)+-165*a^-12*b^3*(a+b*x)^-1+-60*a^-11*b^3*(a+b*x)^-2+-55*a^-12*b^2*x^-1+-28*a^-10*b^3*(a+b*x)^-3+-14*a^-9*b^3*(a+b*x)^-4+-7*a^-8*b^3*(a+b*x)^-5+5*b*a^-11*x^-2+220*a^-13*b^3*log(a+b*x)+-10//3*a^-7*b^3*(a+b*x)^-6+-10//7*a^-6*b^3*(a+b*x)^-7+-1//2*a^-5*b^3*(a+b*x)^-8+-1//9*a^-4*b^3*(a+b*x)^-9)
@test integrate(x^-10*(a+b*x)^12, x) == :(-1//9*a^12*x^-9+1//3*b^12*x^3+-495*a^4*b^8*x^-1+-396*a^5*b^7*x^-2+-308*a^6*b^6*x^-3+-198*a^7*b^5*x^-4+-99*a^8*b^4*x^-5+6*a*b^11*x^2+66*x*a^2*b^10+220*a^3*b^9*log(x)+-110//3*a^9*b^3*x^-6+-66//7*a^10*b^2*x^-7+-3//2*b*a^11*x^-8)
@test integrate(x^-10*(a+b*x)^11, x) == :((1/2)*b^11*x^2+-1//9*a^11*x^-9+-165*a^3*b^8*x^-1+-165*a^4*b^7*x^-2+-154*a^5*b^6*x^-3+-66*a^7*b^4*x^-5+11*a*x*b^10+55*a^2*b^9*log(x)+-231//2*a^6*b^5*x^-4+-55//2*a^8*b^3*x^-6+-55//7*a^9*b^2*x^-7+-11//8*b*a^10*x^-8)
@test integrate(x^-10*(a+b*x)^10, x) == :(x*b^10+-1//9*a^10*x^-9+-70*a^4*b^6*x^-3+-63*a^5*b^5*x^-4+-60*a^3*b^7*x^-2+-45*a^2*b^8*x^-1+-42*a^6*b^4*x^-5+-20*a^7*b^3*x^-6+10*a*b^9*log(x)+-45//7*a^8*b^2*x^-7+-5//4*b*a^9*x^-8)
@test integrate(x^-10*(a+b*x)^9, x) == :(b^9*log(x)+-1//9*a^9*x^-9+-28*a^3*b^6*x^-3+-18*a^2*b^7*x^-2+-14*a^6*b^3*x^-6+-9*a*b^8*x^-1+-126//5*a^5*b^4*x^-5+-63//2*a^4*b^5*x^-4+-36//7*a^7*b^2*x^-7+-9//8*b*a^8*x^-8)
@test integrate(x^-10*(a+b*x)^8, x) == :(-1//9*a^-1*x^-9*(a+b*x)^9)
@test integrate(x^-10*(a+b*x)^7, x) == :(-1//9*a^-1*x^-9*(a+b*x)^8+1//72*b*a^-2*x^-8*(a+b*x)^8)
@test integrate(x^-10*(a+b*x)^6, x) == :(-1//9*a^-1*x^-9*(a+b*x)^7+-1//252*a^-3*b^2*x^-7*(a+b*x)^7+1//36*b*a^-2*x^-8*(a+b*x)^7)
@test integrate(x^-10*(a+b*x)^5, x) == :(-1//4*b^5*x^-4+-1//9*a^5*x^-9+-1*a*b^4*x^-5+-10//7*a^3*b^2*x^-7+-5//3*a^2*b^3*x^-6+-5//8*b*a^4*x^-8)
@test integrate(x^-10*(a+b*x)^4, x) == :(-1//5*b^4*x^-5+-1//9*a^4*x^-9+-6//7*a^2*b^2*x^-7+-2//3*a*b^3*x^-6+-1//2*b*a^3*x^-8)
@test integrate(x^-10*(a+b*x)^3, x) == :(-1//6*b^3*x^-6+-1//9*a^3*x^-9+-3//7*a*b^2*x^-7+-3//8*b*a^2*x^-8)
@test integrate(x^-10*(a+b*x)^2, x) == :(-1//7*b^2*x^-7+-1//9*a^2*x^-9+-1//4*a*b*x^-8)
@test integrate(x^-10*(a+b*x), x) == :(-1//8*b*x^-8+-1//9*a*x^-9)
@test integrate(x^-10, x) == :(-1//9*x^-9)
@test integrate(x^-10*(a+b*x)^-1, x) == :(-1//9*a^-1*x^-9+a^-10*b^9*log(a+b*x)+(1/2)*a^-8*b^7*x^-2+-1*a^-10*b^9*log(x)+-1*a^-9*b^8*x^-1+-1//3*a^-7*b^6*x^-3+-1//5*a^-5*b^4*x^-5+-1//7*a^-3*b^2*x^-7+1//4*a^-6*b^5*x^-4+1//6*a^-4*b^3*x^-6+1//8*b*a^-2*x^-8)
@test integrate(x^-10*(a+b*x)^-2, x) == :(-1//9*a^-2*x^-9+-1*a^-10*b^9*(a+b*x)^-1+-1*a^-6*b^4*x^-5+-10*a^-11*b^9*log(x)+-9*a^-10*b^8*x^-1+4*a^-9*b^7*x^-2+10*a^-11*b^9*log(a+b*x)+-7//3*a^-8*b^6*x^-3+-3//7*a^-4*b^2*x^-7+1//4*b*a^-3*x^-8+2//3*a^-5*b^3*x^-6+3//2*a^-7*b^5*x^-4)
@test integrate(x^-10*(a+b*x)^-3, x) == :(-1//9*a^-3*x^-9+-55*a^-12*b^9*log(x)+-45*a^-11*b^8*x^-1+-10*a^-11*b^9*(a+b*x)^-1+-3*a^-7*b^4*x^-5+18*a^-10*b^7*x^-2+55*a^-12*b^9*log(a+b*x)+-28//3*a^-9*b^6*x^-3+-6//7*a^-5*b^2*x^-7+-1//2*a^-10*b^9*(a+b*x)^-2+3//8*b*a^-4*x^-8+5//3*a^-6*b^3*x^-6+21//4*a^-8*b^5*x^-4)
@test integrate(x^-1*(2+3x)^-1, x) == :((1/2)*log(x)+-1//2*log(2+3x))
@test integrate(x^-1*(4+6x)^-1, x) == :(-1//4*log(2+3x)+1//4*log(x))
@test integrate(x^-2*(4+6x)^-1, x) == :(-3//8*log(x)+-1//4*x^-1+3//8*log(2+3x))
@test integrate(x^-3*(4+6x)^-1, x) == :(-9//16*log(2+3x)+-1//8*x^-2+3//8*x^-1+9//16*log(x))
@test integrate(x^-4*(4+6x)^-1, x) == :(-27//32*log(x)+-9//16*x^-1+-1//12*x^-3+3//16*x^-2+27//32*log(2+3x))
@test integrate(x^-5*(4+6x)^-1, x) == :(-81//64*log(2+3x)+-9//32*x^-2+-1//16*x^-4+1//8*x^-3+27//32*x^-1+81//64*log(x))
@test integrate(x^-1*(4+6x)^-2, x) == :((16+24x)^-1+-1//16*log(2+3x)+1//16*log(x))
@test integrate(x^-2*(4+6x)^-2, x) == :(-3*(32+48x)^-1+-3//16*log(x)+-1//16*x^-1+3//16*log(2+3x))
@test integrate(x^-3*(4+6x)^-2, x) == :(9*(64+96x)^-1+-27//64*log(2+3x)+-1//32*x^-2+3//16*x^-1+27//64*log(x))
@test integrate(x^-4*(4+6x)^-2, x) == :(-27*(128+192x)^-1+-27//32*log(x)+-27//64*x^-1+-1//48*x^-3+3//32*x^-2+27//32*log(2+3x))
@test integrate(x^-5*(4+6x)^-2, x) == :(81*(256+384x)^-1+-405//256*log(2+3x)+-27//128*x^-2+-1//64*x^-4+1//16*x^-3+27//32*x^-1+405//256*log(x))
@test integrate(x^-1*(4+6x)^-3, x) == :((64+96x)^-1+-1//64*log(2+3x)+1//32*(2+3x)^-2+1//64*log(x))
@test integrate(x^-2*(4+6x)^-3, x) == :(-3*(64+96x)^-1+-9//128*log(x)+-3//64*(2+3x)^-2+-1//64*x^-1+9//128*log(2+3x))
@test integrate(x^-3*(4+6x)^-3, x) == :(27*(256+384x)^-1+-27//128*log(2+3x)+-1//128*x^-2+9//128*x^-1+9//128*(2+3x)^-2+27//128*log(x))
@test integrate(x^-4*(4+6x)^-3, x) == :(-27*(128+192x)^-1+-135//256*log(x)+-27//128*x^-1+-27//256*(2+3x)^-2+-1//192*x^-3+9//256*x^-2+135//256*log(2+3x))
@test integrate(x^-5*(4+6x)^-3, x) == :(405*(1024+1536x)^-1+-1215//1024*log(2+3x)+-27//256*x^-2+-1//256*x^-4+3//128*x^-3+81//512*(2+3x)^-2+135//256*x^-1+1215//1024*log(x))
@test integrate((2+2x)^-1, x) == :((1/2)*log(1+x))
@test integrate((4+-6x)^-1, x) == :(-1//6*log(2+-3x))
@test integrate((a+x*a^(1/2))^-1, x) == :(a^-1//2*log(x+a^(1/2)))
@test integrate((a+x*(-1a)^(1/2))^-1, x) == :((-1a)^-1//2*log(a+x*(-1a)^(1/2)))
@test integrate((a^2+x*(-1a)^(1/2))^-1, x) == :((-1a)^-1//2*log(a^2+x*(-1a)^(1/2)))
@test integrate((a^3+x*(-1a)^(1/2))^-1, x) == :((-1a)^-1//2*log(a^3+x*(-1a)^(1/2)))
@test integrate((a^-1+x*(-1a)^(1/2))^-1, x) == :((-1a)^-1//2*log(1+-1*x*(-1a)^3//2))
@test integrate((a^-2+x*(-1a)^(1/2))^-1, x) == :((-1a)^-1//2*log(1+x*(-1a)^5//2))
@test integrate(x^-1*(1+b*x)^-1, x) == :(-1*log(1+b*x)+log(x))
@test integrate(x^-1*(-1+b*x)^-1, x) == :(-1*log(x)+log(1+-1*b*x))
@test integrate(x^-2*(1+b*x)^-1, x) == :(-1*x^-1+b*log(1+b*x)+-1*b*log(x))
@test integrate(x^-2*(-1+b*x)^-1, x) == :(x^-1+b*log(1+-1*b*x)+-1*b*log(x))
@test integrate(b*x^-1+x^-2*(1+b*x)^-1, x) == :(-1*x^-1+b*log(1+b*x))
@test integrate(x^3*(a+b*x)^(1/2), x) == :(2//9*b^-4*(a+b*x)^9//2+-6//7*a*b^-4*(a+b*x)^7//2+-2//3*a^3*b^-4*(a+b*x)^3//2+6//5*a^2*b^-4*(a+b*x)^5//2)
@test integrate(x^2*(a+b*x)^(1/2), x) == :(2//7*b^-3*(a+b*x)^7//2+-4//5*a*b^-3*(a+b*x)^5//2+2//3*a^2*b^-3*(a+b*x)^3//2)
@test integrate(x*(a+b*x)^(1/2), x) == :(2//5*b^-2*(a+b*x)^5//2+-2//3*a*b^-2*(a+b*x)^3//2)
@test integrate((a+b*x)^(1/2), x) == :(2//3*b^-1*(a+b*x)^3//2)
@test integrate(x^-1*(a+b*x)^(1/2), x) == :(2*(a+b*x)^(1/2)+-2*a^(1/2)*arctanh(a^-1//2*(a+b*x)^(1/2)))
@test integrate(x^-2*(a+b*x)^(1/2), x) == :(-1*x^-1*(a+b*x)^(1/2)+-1*b*a^-1//2*arctanh(a^-1//2*(a+b*x)^(1/2)))
@test integrate(x^-3*(a+b*x)^(1/2), x) == :(-1//2*x^-2*(a+b*x)^(1/2)+1//4*a^-3//2*b^2*arctanh(a^-1//2*(a+b*x)^(1/2))+-1//4*b*a^-1*x^-1*(a+b*x)^(1/2))
@test integrate(x^-4*(a+b*x)^(1/2), x) == :(-1//3*x^-3*(a+b*x)^(1/2)+-1//8*a^-5//2*b^3*arctanh(a^-1//2*(a+b*x)^(1/2))+-1//12*b*a^-1*x^-2*(a+b*x)^(1/2)+1//8*a^-2*b^2*x^-1*(a+b*x)^(1/2))
@test integrate(x^3*(a+b*x)^3//2, x) == :(2//11*b^-4*(a+b*x)^11//2+-2//3*a*b^-4*(a+b*x)^9//2+-2//5*a^3*b^-4*(a+b*x)^5//2+6//7*a^2*b^-4*(a+b*x)^7//2)
@test integrate(x^2*(a+b*x)^3//2, x) == :(2//9*b^-3*(a+b*x)^9//2+-4//7*a*b^-3*(a+b*x)^7//2+2//5*a^2*b^-3*(a+b*x)^5//2)
@test integrate(x*(a+b*x)^3//2, x) == :(2//7*b^-2*(a+b*x)^7//2+-2//5*a*b^-2*(a+b*x)^5//2)
@test integrate((a+b*x)^3//2, x) == :(2//5*b^-1*(a+b*x)^5//2)
@test integrate(x^-1*(a+b*x)^3//2, x) == :(2//3*(a+b*x)^3//2+-2*a^3//2*arctanh(a^-1//2*(a+b*x)^(1/2))+2*a*(a+b*x)^(1/2))
@test integrate(x^-2*(a+b*x)^3//2, x) == :(-1*x^-1*(a+b*x)^3//2+3*b*(a+b*x)^(1/2)+-3*b*a^(1/2)*arctanh(a^-1//2*(a+b*x)^(1/2)))
@test integrate(x^-3*(a+b*x)^3//2, x) == :(-1//2*x^-2*(a+b*x)^3//2+-3//4*b*x^-1*(a+b*x)^(1/2)+-3//4*a^-1//2*b^2*arctanh(a^-1//2*(a+b*x)^(1/2)))
@test integrate(x^-4*(a+b*x)^3//2, x) == :(-1//3*x^-3*(a+b*x)^3//2+-1//4*b*x^-2*(a+b*x)^(1/2)+1//8*a^-3//2*b^3*arctanh(a^-1//2*(a+b*x)^(1/2))+-1//8*a^-1*b^2*x^-1*(a+b*x)^(1/2))
@test integrate(x^3*(a+b*x)^5//2, x) == :(2//13*b^-4*(a+b*x)^13//2+-6//11*a*b^-4*(a+b*x)^11//2+-2//7*a^3*b^-4*(a+b*x)^7//2+2//3*a^2*b^-4*(a+b*x)^9//2)
@test integrate(x^2*(a+b*x)^5//2, x) == :(2//11*b^-3*(a+b*x)^11//2+-4//9*a*b^-3*(a+b*x)^9//2+2//7*a^2*b^-3*(a+b*x)^7//2)
@test integrate(x*(a+b*x)^5//2, x) == :(2//9*b^-2*(a+b*x)^9//2+-2//7*a*b^-2*(a+b*x)^7//2)
@test integrate((a+b*x)^5//2, x) == :(2//7*b^-1*(a+b*x)^7//2)
@test integrate(x^-1*(a+b*x)^5//2, x) == :(2//5*(a+b*x)^5//2+-2*a^5//2*arctanh(a^-1//2*(a+b*x)^(1/2))+2*a^2*(a+b*x)^(1/2)+2//3*a*(a+b*x)^3//2)
@test integrate(x^-2*(a+b*x)^5//2, x) == :(-1*x^-1*(a+b*x)^5//2+5//3*b*(a+b*x)^3//2+-5*b*a^3//2*arctanh(a^-1//2*(a+b*x)^(1/2))+5*a*b*(a+b*x)^(1/2))
@test integrate(x^-3*(a+b*x)^5//2, x) == :(-1//2*x^-2*(a+b*x)^5//2+15//4*b^2*(a+b*x)^(1/2)+-15//4*a^(1/2)*b^2*arctanh(a^-1//2*(a+b*x)^(1/2))+-5//4*b*x^-1*(a+b*x)^3//2)
@test integrate(x^-4*(a+b*x)^5//2, x) == :(-1//3*x^-3*(a+b*x)^5//2+-5//8*a^-1//2*b^3*arctanh(a^-1//2*(a+b*x)^(1/2))+-5//8*b^2*x^-1*(a+b*x)^(1/2)+-5//12*b*x^-2*(a+b*x)^3//2)
@test integrate(x^-5*(a+b*x)^5//2, x) == :(-1//4*x^-4*(a+b*x)^5//2+-5//24*b*x^-3*(a+b*x)^3//2+-5//32*b^2*x^-2*(a+b*x)^(1/2)+5//64*a^-3//2*b^4*arctanh(a^-1//2*(a+b*x)^(1/2))+-5//64*a^-1*b^3*x^-1*(a+b*x)^(1/2))
@test integrate(x^7*(a+b*x)^9//2, x) == :(2//25*b^-8*(a+b*x)^25//2+2*a^2*b^-8*(a+b*x)^21//2+-70//19*a^3*b^-8*(a+b*x)^19//2+-14//5*a^5*b^-8*(a+b*x)^15//2+-14//23*a*b^-8*(a+b*x)^23//2+-2//11*a^7*b^-8*(a+b*x)^11//2+14//13*a^6*b^-8*(a+b*x)^13//2+70//17*a^4*b^-8*(a+b*x)^17//2)
@test integrate(x^6*(a+b*x)^9//2, x) == :(2//23*b^-7*(a+b*x)^23//2+2*a^4*b^-7*(a+b*x)^15//2+-40//17*a^3*b^-7*(a+b*x)^17//2+-12//13*a^5*b^-7*(a+b*x)^13//2+-4//7*a*b^-7*(a+b*x)^21//2+2//11*a^6*b^-7*(a+b*x)^11//2+30//19*a^2*b^-7*(a+b*x)^19//2)
@test integrate(x^5*(a+b*x)^9//2, x) == :(2//21*b^-6*(a+b*x)^21//2+-10//19*a*b^-6*(a+b*x)^19//2+-4//3*a^3*b^-6*(a+b*x)^15//2+-2//11*a^5*b^-6*(a+b*x)^11//2+10//13*a^4*b^-6*(a+b*x)^13//2+20//17*a^2*b^-6*(a+b*x)^17//2)
@test integrate(x^4*(a+b*x)^9//2, x) == :(2//19*b^-5*(a+b*x)^19//2+-8//13*a^3*b^-5*(a+b*x)^13//2+-8//17*a*b^-5*(a+b*x)^17//2+2//11*a^4*b^-5*(a+b*x)^11//2+4//5*a^2*b^-5*(a+b*x)^15//2)
@test integrate(x^3*(a+b*x)^9//2, x) == :(2//17*b^-4*(a+b*x)^17//2+-2//5*a*b^-4*(a+b*x)^15//2+-2//11*a^3*b^-4*(a+b*x)^11//2+6//13*a^2*b^-4*(a+b*x)^13//2)
@test integrate(x^2*(a+b*x)^9//2, x) == :(2//15*b^-3*(a+b*x)^15//2+-4//13*a*b^-3*(a+b*x)^13//2+2//11*a^2*b^-3*(a+b*x)^11//2)
@test integrate(x*(a+b*x)^9//2, x) == :(2//13*b^-2*(a+b*x)^13//2+-2//11*a*b^-2*(a+b*x)^11//2)
@test integrate((a+b*x)^9//2, x) == :(2//11*b^-1*(a+b*x)^11//2)
@test integrate(x^-1*(a+b*x)^9//2, x) == :(2//9*(a+b*x)^9//2+-2*a^9//2*arctanh(a^-1//2*(a+b*x)^(1/2))+2*a^4*(a+b*x)^(1/2)+2//3*a^3*(a+b*x)^3//2+2//5*a^2*(a+b*x)^5//2+2//7*a*(a+b*x)^7//2)
@test integrate(x^-2*(a+b*x)^9//2, x) == :(-1*x^-1*(a+b*x)^9//2+9//7*b*(a+b*x)^7//2+-9*b*a^7//2*arctanh(a^-1//2*(a+b*x)^(1/2))+3*b*a^2*(a+b*x)^3//2+9*b*a^3*(a+b*x)^(1/2)+9//5*a*b*(a+b*x)^5//2)
@test integrate(x^-3*(a+b*x)^9//2, x) == :(-1//2*x^-2*(a+b*x)^9//2+63//20*b^2*(a+b*x)^5//2+-63//4*a^5//2*b^2*arctanh(a^-1//2*(a+b*x)^(1/2))+-9//4*b*x^-1*(a+b*x)^7//2+21//4*a*b^2*(a+b*x)^3//2+63//4*a^2*b^2*(a+b*x)^(1/2))
@test integrate(x^-4*(a+b*x)^9//2, x) == :(-1//3*x^-3*(a+b*x)^9//2+35//8*b^3*(a+b*x)^3//2+-105//8*a^3//2*b^3*arctanh(a^-1//2*(a+b*x)^(1/2))+-21//8*b^2*x^-1*(a+b*x)^5//2+-3//4*b*x^-2*(a+b*x)^7//2+105//8*a*b^3*(a+b*x)^(1/2))
@test integrate(x^-5*(a+b*x)^9//2, x) == :(-1//4*x^-4*(a+b*x)^9//2+315//64*b^4*(a+b*x)^(1/2)+-315//64*a^(1/2)*b^4*arctanh(a^-1//2*(a+b*x)^(1/2))+-105//64*b^3*x^-1*(a+b*x)^3//2+-21//32*b^2*x^-2*(a+b*x)^5//2+-3//8*b*x^-3*(a+b*x)^7//2)
@test integrate(x^-6*(a+b*x)^9//2, x) == :(-1//5*x^-5*(a+b*x)^9//2+-63//128*a^-1//2*b^5*arctanh(a^-1//2*(a+b*x)^(1/2))+-63//128*b^4*x^-1*(a+b*x)^(1/2)+-21//64*b^3*x^-2*(a+b*x)^3//2+-21//80*b^2*x^-3*(a+b*x)^5//2+-9//40*b*x^-4*(a+b*x)^7//2)
@test integrate(x^-7*(a+b*x)^9//2, x) == :(-1//6*x^-6*(a+b*x)^9//2+-21//160*b^2*x^-4*(a+b*x)^5//2+-21//256*b^4*x^-2*(a+b*x)^(1/2)+-7//64*b^3*x^-3*(a+b*x)^3//2+-3//20*b*x^-5*(a+b*x)^7//2+21//512*a^-3//2*b^6*arctanh(a^-1//2*(a+b*x)^(1/2))+-21//512*a^-1*b^5*x^-1*(a+b*x)^(1/2))
@test integrate(x^-8*(a+b*x)^9//2, x) == :(-1//7*x^-7*(a+b*x)^9//2+-9//1024*a^-5//2*b^7*arctanh(a^-1//2*(a+b*x)^(1/2))+-3//28*b*x^-6*(a+b*x)^7//2+-3//40*b^2*x^-5*(a+b*x)^5//2+-3//64*b^3*x^-4*(a+b*x)^3//2+-3//128*b^4*x^-3*(a+b*x)^(1/2)+-3//512*a^-1*b^5*x^-2*(a+b*x)^(1/2)+9//1024*a^-2*b^6*x^-1*(a+b*x)^(1/2))
@test integrate(x^-1*(-1a+b*x)^(1/2), x) == :(2*(-1a+b*x)^(1/2)+-2*a^(1/2)*arctan(a^-1//2*(-1a+b*x)^(1/2)))
@test integrate(x^-2*(-1a+b*x)^(1/2), x) == :(-1*x^-1*(-1a+b*x)^(1/2)+b*a^-1//2*arctan(a^-1//2*(-1a+b*x)^(1/2)))
@test integrate(x^-3*(-1a+b*x)^(1/2), x) == :(-1//2*x^-2*(-1a+b*x)^(1/2)+1//4*a^-3//2*b^2*arctan(a^-1//2*(-1a+b*x)^(1/2))+1//4*b*a^-1*x^-1*(-1a+b*x)^(1/2))
@test integrate(x^-1*(-1a+b*x)^3//2, x) == :(2//3*(-1a+b*x)^3//2+-2*a*(-1a+b*x)^(1/2)+2*a^3//2*arctan(a^-1//2*(-1a+b*x)^(1/2)))
@test integrate(x^-2*(-1a+b*x)^3//2, x) == :(-1*x^-1*(-1a+b*x)^3//2+3*b*(-1a+b*x)^(1/2)+-3*b*a^(1/2)*arctan(a^-1//2*(-1a+b*x)^(1/2)))
@test integrate(x^-3*(-1a+b*x)^3//2, x) == :(-1//2*x^-2*(-1a+b*x)^3//2+-3//4*b*x^-1*(-1a+b*x)^(1/2)+3//4*a^-1//2*b^2*arctan(a^-1//2*(-1a+b*x)^(1/2)))
@test integrate(x^-1*(-1a+b*x)^5//2, x) == :(2//5*(-1a+b*x)^5//2+-2*a^5//2*arctan(a^-1//2*(-1a+b*x)^(1/2))+2*a^2*(-1a+b*x)^(1/2)+-2//3*a*(-1a+b*x)^3//2)
@test integrate(x^-2*(-1a+b*x)^5//2, x) == :(-1*x^-1*(-1a+b*x)^5//2+5//3*b*(-1a+b*x)^3//2+-5*a*b*(-1a+b*x)^(1/2)+5*b*a^3//2*arctan(a^-1//2*(-1a+b*x)^(1/2)))
@test integrate(x^-3*(-1a+b*x)^5//2, x) == :(-1//2*x^-2*(-1a+b*x)^5//2+15//4*b^2*(-1a+b*x)^(1/2)+-15//4*a^(1/2)*b^2*arctan(a^-1//2*(-1a+b*x)^(1/2))+-5//4*b*x^-1*(-1a+b*x)^3//2)
@test integrate(x^4*(a+b*x)^-1//2, x) == :(2//9*b^-5*(a+b*x)^9//2+2*a^4*b^-5*(a+b*x)^(1/2)+-8//3*a^3*b^-5*(a+b*x)^3//2+-8//7*a*b^-5*(a+b*x)^7//2+12//5*a^2*b^-5*(a+b*x)^5//2)
@test integrate(x^3*(a+b*x)^-1//2, x) == :(2//7*b^-4*(a+b*x)^7//2+-2*a^3*b^-4*(a+b*x)^(1/2)+2*a^2*b^-4*(a+b*x)^3//2+-6//5*a*b^-4*(a+b*x)^5//2)
@test integrate(x^2*(a+b*x)^-1//2, x) == :(2//5*b^-3*(a+b*x)^5//2+2*a^2*b^-3*(a+b*x)^(1/2)+-4//3*a*b^-3*(a+b*x)^3//2)
@test integrate(x*(a+b*x)^-1//2, x) == :(2//3*b^-2*(a+b*x)^3//2+-2*a*b^-2*(a+b*x)^(1/2))
@test integrate((a+b*x)^-1//2, x) == :(2*b^-1*(a+b*x)^(1/2))
@test integrate(x^-1*(a+b*x)^-1//2, x) == :(-2*a^-1//2*arctanh(a^-1//2*(a+b*x)^(1/2)))
@test integrate(x^-2*(a+b*x)^-1//2, x) == :(b*a^-3//2*arctanh(a^-1//2*(a+b*x)^(1/2))+-1*a^-1*x^-1*(a+b*x)^(1/2))
@test integrate(x^-3*(a+b*x)^-1//2, x) == :(-3//4*a^-5//2*b^2*arctanh(a^-1//2*(a+b*x)^(1/2))+-1//2*a^-1*x^-2*(a+b*x)^(1/2)+3//4*b*a^-2*x^-1*(a+b*x)^(1/2))
@test integrate(x^-4*(a+b*x)^-1//2, x) == :(-1//3*a^-1*x^-3*(a+b*x)^(1/2)+5//8*a^-7//2*b^3*arctanh(a^-1//2*(a+b*x)^(1/2))+-5//8*a^-3*b^2*x^-1*(a+b*x)^(1/2)+5//12*b*a^-2*x^-2*(a+b*x)^(1/2))
@test integrate(x^4*(a+b*x)^-3//2, x) == :(2//7*b^-5*(a+b*x)^7//2+-8*a^3*b^-5*(a+b*x)^(1/2)+-2*a^4*b^-5*(a+b*x)^-1//2+4*a^2*b^-5*(a+b*x)^3//2+-8//5*a*b^-5*(a+b*x)^5//2)
@test integrate(x^3*(a+b*x)^-3//2, x) == :(2//5*b^-4*(a+b*x)^5//2+-2*a*b^-4*(a+b*x)^3//2+2*a^3*b^-4*(a+b*x)^-1//2+6*a^2*b^-4*(a+b*x)^(1/2))
@test integrate(x^2*(a+b*x)^-3//2, x) == :(2//3*b^-3*(a+b*x)^3//2+-4*a*b^-3*(a+b*x)^(1/2)+-2*a^2*b^-3*(a+b*x)^-1//2)
@test integrate(x*(a+b*x)^-3//2, x) == :(2*b^-2*(a+b*x)^(1/2)+2*a*b^-2*(a+b*x)^-1//2)
@test integrate((a+b*x)^-3//2, x) == :(-2*b^-1*(a+b*x)^-1//2)
@test integrate(x^-1*(a+b*x)^-3//2, x) == :(-2*a^-3//2*arctanh(a^-1//2*(a+b*x)^(1/2))+2*a^-1*(a+b*x)^-1//2)
@test integrate(x^-2*(a+b*x)^-3//2, x) == :(-1*a^-1*x^-1*(a+b*x)^-1//2+-3*b*a^-2*(a+b*x)^-1//2+3*b*a^-5//2*arctanh(a^-1//2*(a+b*x)^(1/2)))
@test integrate(x^-3*(a+b*x)^-3//2, x) == :(-15//4*a^-7//2*b^2*arctanh(a^-1//2*(a+b*x)^(1/2))+-1//2*a^-1*x^-2*(a+b*x)^-1//2+15//4*a^-3*b^2*(a+b*x)^-1//2+5//4*b*a^-2*x^-1*(a+b*x)^-1//2)
@test integrate(x^4*(a+b*x)^-5//2, x) == :(2//5*b^-5*(a+b*x)^5//2+8*a^3*b^-5*(a+b*x)^-1//2+12*a^2*b^-5*(a+b*x)^(1/2)+-8//3*a*b^-5*(a+b*x)^3//2+-2//3*a^4*b^-5*(a+b*x)^-3//2)
@test integrate(x^3*(a+b*x)^-5//2, x) == :(2//3*b^-4*(a+b*x)^3//2+-6*a*b^-4*(a+b*x)^(1/2)+-6*a^2*b^-4*(a+b*x)^-1//2+2//3*a^3*b^-4*(a+b*x)^-3//2)
@test integrate(x^2*(a+b*x)^-5//2, x) == :(2*b^-3*(a+b*x)^(1/2)+4*a*b^-3*(a+b*x)^-1//2+-2//3*a^2*b^-3*(a+b*x)^-3//2)
@test integrate(x*(a+b*x)^-5//2, x) == :(-2*b^-2*(a+b*x)^-1//2+2//3*a*b^-2*(a+b*x)^-3//2)
@test integrate((a+b*x)^-5//2, x) == :(-2//3*b^-1*(a+b*x)^-3//2)
@test integrate(x^-1*(a+b*x)^-5//2, x) == :(-2*a^-5//2*arctanh(a^-1//2*(a+b*x)^(1/2))+2*a^-2*(a+b*x)^-1//2+2//3*a^-1*(a+b*x)^-3//2)
@test integrate(x^-2*(a+b*x)^-5//2, x) == :(-1*a^-1*x^-1*(a+b*x)^-3//2+-5*b*a^-3*(a+b*x)^-1//2+5*b*a^-7//2*arctanh(a^-1//2*(a+b*x)^(1/2))+-5//3*b*a^-2*(a+b*x)^-3//2)
@test integrate(x^-3*(a+b*x)^-5//2, x) == :(-35//4*a^-9//2*b^2*arctanh(a^-1//2*(a+b*x)^(1/2))+-1//2*a^-1*x^-2*(a+b*x)^-3//2+35//4*a^-4*b^2*(a+b*x)^-1//2+35//12*a^-3*b^2*(a+b*x)^-3//2+7//4*b*a^-2*x^-1*(a+b*x)^-3//2)
@test integrate(x^-1*(-1a+b*x)^-1//2, x) == :(2*a^-1//2*arctan(a^-1//2*(-1a+b*x)^(1/2)))
@test integrate(x^-2*(-1a+b*x)^-1//2, x) == :(b*a^-3//2*arctan(a^-1//2*(-1a+b*x)^(1/2))+a^-1*x^-1*(-1a+b*x)^(1/2))
@test integrate(x^-3*(-1a+b*x)^-1//2, x) == :((1/2)*a^-1*x^-2*(-1a+b*x)^(1/2)+3//4*a^-5//2*b^2*arctan(a^-1//2*(-1a+b*x)^(1/2))+3//4*b*a^-2*x^-1*(-1a+b*x)^(1/2))
@test integrate(x^-1*(-1a+b*x)^-3//2, x) == :(-2*a^-1*(-1a+b*x)^-1//2+-2*a^-3//2*arctan(a^-1//2*(-1a+b*x)^(1/2)))
@test integrate(x^-2*(-1a+b*x)^-3//2, x) == :(a^-1*x^-1*(-1a+b*x)^-1//2+-3*b*a^-2*(-1a+b*x)^-1//2+-3*b*a^-5//2*arctan(a^-1//2*(-1a+b*x)^(1/2)))
@test integrate(x^-3*(-1a+b*x)^-3//2, x) == :((1/2)*a^-1*x^-2*(-1a+b*x)^-1//2+-15//4*a^-3*b^2*(-1a+b*x)^-1//2+-15//4*a^-7//2*b^2*arctan(a^-1//2*(-1a+b*x)^(1/2))+5//4*b*a^-2*x^-1*(-1a+b*x)^-1//2)
@test integrate(x^-1*(-1a+b*x)^-5//2, x) == :(2*a^-2*(-1a+b*x)^-1//2+2*a^-5//2*arctan(a^-1//2*(-1a+b*x)^(1/2))+-2//3*a^-1*(-1a+b*x)^-3//2)
@test integrate(x^-2*(-1a+b*x)^-5//2, x) == :(a^-1*x^-1*(-1a+b*x)^-3//2+5*b*a^-3*(-1a+b*x)^-1//2+5*b*a^-7//2*arctan(a^-1//2*(-1a+b*x)^(1/2))+-5//3*b*a^-2*(-1a+b*x)^-3//2)
@test integrate(x^-3*(-1a+b*x)^-5//2, x) == :((1/2)*a^-1*x^-2*(-1a+b*x)^-3//2+-35//12*a^-3*b^2*(-1a+b*x)^-3//2+35//4*a^-4*b^2*(-1a+b*x)^-1//2+35//4*a^-9//2*b^2*arctan(a^-1//2*(-1a+b*x)^(1/2))+7//4*b*a^-2*x^-1*(-1a+b*x)^-3//2)
@test integrate((1/2)*x^(-1+m)*(a+b*x)^-3//2*(2*a*m+b*x*(-1+2m)), x) == :(x^m*(a+b*x)^-1//2)
@test integrate(m*x^(-1+m)*(a+b*x)^-1//2+-1//2*b*x^m*(a+b*x)^-3//2, x) == :(x^m*(a+b*x)^-1//2)
@test integrate(x^-1*(a+b*x)^-1//2, x) == :(-2*a^-1//2*arctanh(a^-1//2*(a+b*x)^(1/2)))
@test integrate(x^3*(a+b*x)^1//3, x) == :(3//13*b^-4*(a+b*x)^13//3+-9//10*a*b^-4*(a+b*x)^10//3+-3//4*a^3*b^-4*(a+b*x)^4//3+9//7*a^2*b^-4*(a+b*x)^7//3)
@test integrate(x^2*(a+b*x)^1//3, x) == :(3//10*b^-3*(a+b*x)^10//3+-6//7*a*b^-3*(a+b*x)^7//3+3//4*a^2*b^-3*(a+b*x)^4//3)
@test integrate(x*(a+b*x)^1//3, x) == :(3//7*b^-2*(a+b*x)^7//3+-3//4*a*b^-2*(a+b*x)^4//3)
@test integrate((a+b*x)^1//3, x) == :(3//4*b^-1*(a+b*x)^4//3)
@test integrate(x^-1*(a+b*x)^1//3, x) == :(3*(a+b*x)^1//3+-1//2*a^1//3*log(x)+3//2*a^1//3*log(a^1//3+-1*(a+b*x)^1//3)+-1*3^(1/2)*a^1//3*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+2*(a+b*x)^1//3)))
@test integrate(x^-2*(a+b*x)^1//3, x) == :(-1*x^-1*(a+b*x)^1//3+(1/2)*b*a^-2//3*log(a^1//3+-1*(a+b*x)^1//3)+-1//6*b*a^-2//3*log(x)+-1//3*b*3^(1/2)*a^-2//3*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+2*(a+b*x)^1//3)))
@test integrate(x^-3*(a+b*x)^1//3, x) == :(-1//2*x^-2*(a+b*x)^1//3+-1//6*a^-5//3*b^2*log(a^1//3+-1*(a+b*x)^1//3)+1//18*a^-5//3*b^2*log(x)+-1//6*b*a^-1*x^-1*(a+b*x)^1//3+1//9*3^(1/2)*a^-5//3*b^2*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+2*(a+b*x)^1//3)))
@test integrate(x^3*(a+b*x)^2//3, x) == :(3//14*b^-4*(a+b*x)^14//3+-9//11*a*b^-4*(a+b*x)^11//3+-3//5*a^3*b^-4*(a+b*x)^5//3+9//8*a^2*b^-4*(a+b*x)^8//3)
@test integrate(x^2*(a+b*x)^2//3, x) == :(3//11*b^-3*(a+b*x)^11//3+-3//4*a*b^-3*(a+b*x)^8//3+3//5*a^2*b^-3*(a+b*x)^5//3)
@test integrate(x*(a+b*x)^2//3, x) == :(3//8*b^-2*(a+b*x)^8//3+-3//5*a*b^-2*(a+b*x)^5//3)
@test integrate((a+b*x)^2//3, x) == :(3//5*b^-1*(a+b*x)^5//3)
@test integrate(x^-1*(a+b*x)^2//3, x) == :(3//2*(a+b*x)^2//3+-1//2*a^2//3*log(x)+3//2*a^2//3*log(a^1//3+-1*(a+b*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)^1//3)))
@test integrate(x^-2*(a+b*x)^2//3, x) == :(-1*x^-1*(a+b*x)^2//3+b*a^-1//3*log(a^1//3+-1*(a+b*x)^1//3)+-1//3*b*a^-1//3*log(x)+2//3*b*3^(1/2)*a^-1//3*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+2*(a+b*x)^1//3)))
@test integrate(x^-3*(a+b*x)^2//3, x) == :(-1//2*x^-2*(a+b*x)^2//3+-1//6*a^-4//3*b^2*log(a^1//3+-1*(a+b*x)^1//3)+1//18*a^-4//3*b^2*log(x)+-1//3*b*a^-1*x^-1*(a+b*x)^2//3+-1//9*3^(1/2)*a^-4//3*b^2*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+2*(a+b*x)^1//3)))
@test integrate(x^3*(a+b*x)^4//3, x) == :(3//16*b^-4*(a+b*x)^16//3+-9//13*a*b^-4*(a+b*x)^13//3+-3//7*a^3*b^-4*(a+b*x)^7//3+9//10*a^2*b^-4*(a+b*x)^10//3)
@test integrate(x^2*(a+b*x)^4//3, x) == :(3//13*b^-3*(a+b*x)^13//3+-3//5*a*b^-3*(a+b*x)^10//3+3//7*a^2*b^-3*(a+b*x)^7//3)
@test integrate(x*(a+b*x)^4//3, x) == :(3//10*b^-2*(a+b*x)^10//3+-3//7*a*b^-2*(a+b*x)^7//3)
@test integrate((a+b*x)^4//3, x) == :(3//7*b^-1*(a+b*x)^7//3)
@test integrate(x^-1*(a+b*x)^4//3, x) == :(3//4*(a+b*x)^4//3+3*a*(a+b*x)^1//3+-1//2*a^4//3*log(x)+3//2*a^4//3*log(a^1//3+-1*(a+b*x)^1//3)+-1*3^(1/2)*a^4//3*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+2*(a+b*x)^1//3)))
@test integrate(x^-2*(a+b*x)^4//3, x) == :(-1*x^-1*(a+b*x)^4//3+4*b*(a+b*x)^1//3+2*b*a^1//3*log(a^1//3+-1*(a+b*x)^1//3)+-2//3*b*a^1//3*log(x)+-4//3*b*3^(1/2)*a^1//3*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+2*(a+b*x)^1//3)))
@test integrate(x^-3*(a+b*x)^4//3, x) == :(-1//2*x^-2*(a+b*x)^4//3+-2//3*b*x^-1*(a+b*x)^1//3+-1//9*a^-2//3*b^2*log(x)+1//3*a^-2//3*b^2*log(a^1//3+-1*(a+b*x)^1//3)+-2//9*3^(1/2)*a^-2//3*b^2*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+2*(a+b*x)^1//3)))
@test integrate(x^3*(a+b*x)^-1//3, x) == :(3//11*b^-4*(a+b*x)^11//3+-9//8*a*b^-4*(a+b*x)^8//3+-3//2*a^3*b^-4*(a+b*x)^2//3+9//5*a^2*b^-4*(a+b*x)^5//3)
@test integrate(x^2*(a+b*x)^-1//3, x) == :(3//8*b^-3*(a+b*x)^8//3+-6//5*a*b^-3*(a+b*x)^5//3+3//2*a^2*b^-3*(a+b*x)^2//3)
@test integrate(x*(a+b*x)^-1//3, x) == :(3//5*b^-2*(a+b*x)^5//3+-3//2*a*b^-2*(a+b*x)^2//3)
@test integrate((a+b*x)^-1//3, x) == :(3//2*b^-1*(a+b*x)^2//3)
@test integrate(x^-1*(a+b*x)^-1//3, x) == :(-1//2*a^-1//3*log(x)+3//2*a^-1//3*log(a^1//3+-1*(a+b*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)^1//3)))
@test integrate(x^-2*(a+b*x)^-1//3, x) == :(-1*a^-1*x^-1*(a+b*x)^2//3+-1//2*b*a^-4//3*log(a^1//3+-1*(a+b*x)^1//3)+1//6*b*a^-4//3*log(x)+-1//3*b*3^(1/2)*a^-4//3*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+2*(a+b*x)^1//3)))
@test integrate(x^-3*(a+b*x)^-1//3, x) == :(-1//2*a^-1*x^-2*(a+b*x)^2//3+-1//9*a^-7//3*b^2*log(x)+1//3*a^-7//3*b^2*log(a^1//3+-1*(a+b*x)^1//3)+2//3*b*a^-2*x^-1*(a+b*x)^2//3+2//9*3^(1/2)*a^-7//3*b^2*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+2*(a+b*x)^1//3)))
@test integrate(x^3*(-1a+b*x)^-1//3, x) == :(3//11*b^-4*(-1a+b*x)^11//3+3//2*a^3*b^-4*(-1a+b*x)^2//3+9//5*a^2*b^-4*(-1a+b*x)^5//3+9//8*a*b^-4*(-1a+b*x)^8//3)
@test integrate(x^2*(-1a+b*x)^-1//3, x) == :(3//8*b^-3*(-1a+b*x)^8//3+3//2*a^2*b^-3*(-1a+b*x)^2//3+6//5*a*b^-3*(-1a+b*x)^5//3)
@test integrate(x*(-1a+b*x)^-1//3, x) == :(3//5*b^-2*(-1a+b*x)^5//3+3//2*a*b^-2*(-1a+b*x)^2//3)
@test integrate((-1a+b*x)^-1//3, x) == :(3//2*b^-1*(-1a+b*x)^2//3)
@test integrate(x^-1*(-1a+b*x)^-1//3, x) == :((1/2)*a^-1//3*log(x)+-3//2*a^-1//3*log(a^1//3+(-1a+b*x)^1//3)+-1*3^(1/2)*a^-1//3*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*(-1a+b*x)^1//3)))
@test integrate(x^-2*(-1a+b*x)^-1//3, x) == :(a^-1*x^-1*(-1a+b*x)^2//3+-1//2*b*a^-4//3*log(a^1//3+(-1a+b*x)^1//3)+1//6*b*a^-4//3*log(x)+-1//3*b*3^(1/2)*a^-4//3*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*(-1a+b*x)^1//3)))
@test integrate(x^-3*(-1a+b*x)^-1//3, x) == :((1/2)*a^-1*x^-2*(-1a+b*x)^2//3+-1//3*a^-7//3*b^2*log(a^1//3+(-1a+b*x)^1//3)+1//9*a^-7//3*b^2*log(x)+-2//9*3^(1/2)*a^-7//3*b^2*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*(-1a+b*x)^1//3))+2//3*b*a^-2*x^-1*(-1a+b*x)^2//3)
@test integrate(x^3*(a+b*x)^-2//3, x) == :(3//10*b^-4*(a+b*x)^10//3+-3*a^3*b^-4*(a+b*x)^1//3+-9//7*a*b^-4*(a+b*x)^7//3+9//4*a^2*b^-4*(a+b*x)^4//3)
@test integrate(x^2*(a+b*x)^-2//3, x) == :(3//7*b^-3*(a+b*x)^7//3+3*a^2*b^-3*(a+b*x)^1//3+-3//2*a*b^-3*(a+b*x)^4//3)
@test integrate(x*(a+b*x)^-2//3, x) == :(3//4*b^-2*(a+b*x)^4//3+-3*a*b^-2*(a+b*x)^1//3)
@test integrate((a+b*x)^-2//3, x) == :(3*b^-1*(a+b*x)^1//3)
@test integrate(x^-1*(a+b*x)^-2//3, x) == :(-1//2*a^-2//3*log(x)+3//2*a^-2//3*log(a^1//3+-1*(a+b*x)^1//3)+-1*3^(1/2)*a^-2//3*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+2*(a+b*x)^1//3)))
@test integrate(x^-2*(a+b*x)^-2//3, x) == :(-1*b*a^-5//3*log(a^1//3+-1*(a+b*x)^1//3)+-1*a^-1*x^-1*(a+b*x)^1//3+1//3*b*a^-5//3*log(x)+2//3*b*3^(1/2)*a^-5//3*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+2*(a+b*x)^1//3)))
@test integrate(x^-3*(a+b*x)^-2//3, x) == :(-5//18*a^-8//3*b^2*log(x)+-1//2*a^-1*x^-2*(a+b*x)^1//3+5//6*a^-8//3*b^2*log(a^1//3+-1*(a+b*x)^1//3)+-5//9*3^(1/2)*a^-8//3*b^2*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+2*(a+b*x)^1//3))+5//6*b*a^-2*x^-1*(a+b*x)^1//3)
@test integrate(x^3*(a+b*x)^-4//3, x) == :(3//8*b^-4*(a+b*x)^8//3+3*a^3*b^-4*(a+b*x)^-1//3+-9//5*a*b^-4*(a+b*x)^5//3+9//2*a^2*b^-4*(a+b*x)^2//3)
@test integrate(x^2*(a+b*x)^-4//3, x) == :(3//5*b^-3*(a+b*x)^5//3+-3*a*b^-3*(a+b*x)^2//3+-3*a^2*b^-3*(a+b*x)^-1//3)
@test integrate(x*(a+b*x)^-4//3, x) == :(3//2*b^-2*(a+b*x)^2//3+3*a*b^-2*(a+b*x)^-1//3)
@test integrate((a+b*x)^-4//3, x) == :(-3*b^-1*(a+b*x)^-1//3)
@test integrate(x^-1*(a+b*x)^-4//3, x) == :(3*a^-1*(a+b*x)^-1//3+-1//2*a^-4//3*log(x)+3//2*a^-4//3*log(a^1//3+-1*(a+b*x)^1//3)+3^(1/2)*a^-4//3*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+2*(a+b*x)^1//3)))
@test integrate(x^-2*(a+b*x)^-4//3, x) == :(-1*a^-1*x^-1*(a+b*x)^-1//3+-4*b*a^-2*(a+b*x)^-1//3+-2*b*a^-7//3*log(a^1//3+-1*(a+b*x)^1//3)+2//3*b*a^-7//3*log(x)+-4//3*b*3^(1/2)*a^-7//3*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+2*(a+b*x)^1//3)))
@test integrate(x^-3*(a+b*x)^-4//3, x) == :(-7//9*a^-10//3*b^2*log(x)+-1//2*a^-1*x^-2*(a+b*x)^-1//3+7//3*a^-10//3*b^2*log(a^1//3+-1*(a+b*x)^1//3)+14//3*a^-3*b^2*(a+b*x)^-1//3+7//6*b*a^-2*x^-1*(a+b*x)^-1//3+14//9*3^(1/2)*a^-10//3*b^2*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+2*(a+b*x)^1//3)))
@test integrate(x^-1*(a^3+x*b^3)^-1//3, x) == :(-1//2*a^-1*log(x)+3//2*a^-1*log(a+-1*(a^3+x*b^3)^1//3)+3^(1/2)*a^-1*arctan(1//3*3^(1/2)*a^-1*(a+2*(a^3+x*b^3)^1//3)))
@test integrate(x^-1*(a^3+-1*x*b^3)^-1//3, x) == :(-1//2*a^-1*log(x)+3//2*a^-1*log(a+-1*(a^3+-1*x*b^3)^1//3)+3^(1/2)*a^-1*arctan(1//3*3^(1/2)*a^-1*(a+2*(a^3+-1*x*b^3)^1//3)))
@test integrate(x^-1*(-1*a^3+x*b^3)^-1//3, x) == :((1/2)*a^-1*log(x)+-3//2*a^-1*log(a+(-1*a^3+x*b^3)^1//3)+-1*3^(1/2)*a^-1*arctan(1//3*3^(1/2)*a^-1*(a+-2*(-1*a^3+x*b^3)^1//3)))
@test integrate(x^-1*(-1*a^3+-1*x*b^3)^-1//3, x) == :((1/2)*a^-1*log(x)+-3//2*a^-1*log(a+(-1*a^3+-1*x*b^3)^1//3)+-1*3^(1/2)*a^-1*arctan(1//3*3^(1/2)*a^-1*(a+-2*(-1*a^3+-1*x*b^3)^1//3)))
@test integrate(x^-1*(a^3+x*b^3)^-2//3, x) == :(-1//2*a^-2*log(x)+3//2*a^-2*log(a+-1*(a^3+x*b^3)^1//3)+-1*3^(1/2)*a^-2*arctan(1//3*3^(1/2)*a^-1*(a+2*(a^3+x*b^3)^1//3)))
@test integrate(x^-1*(a^3+-1*x*b^3)^-2//3, x) == :(-1//2*a^-2*log(x)+3//2*a^-2*log(a+-1*(a^3+-1*x*b^3)^1//3)+-1*3^(1/2)*a^-2*arctan(1//3*3^(1/2)*a^-1*(a+2*(a^3+-1*x*b^3)^1//3)))
@test integrate(x^-1*(-1*a^3+x*b^3)^-2//3, x) == :(-1//2*a^-2*log(x)+3//2*a^-2*log(a+(-1*a^3+x*b^3)^1//3)+-1*3^(1/2)*a^-2*arctan(1//3*3^(1/2)*a^-1*(a+-2*(-1*a^3+x*b^3)^1//3)))
@test integrate(x^-1*(-1*a^3+-1*x*b^3)^-2//3, x) == :(-1//2*a^-2*log(x)+3//2*a^-2*log(a+(-1*a^3+-1*x*b^3)^1//3)+-1*3^(1/2)*a^-2*arctan(1//3*3^(1/2)*a^-1*(a+-2*(-1*a^3+-1*x*b^3)^1//3)))
@test integrate(x^m*(a+b*x), x) == :(a*x^(1+m)*(1+m)^-1+b*x^(2+m)*(2+m)^-1)
@test integrate(x^5//2*(a+b*x), x) == :(2//7*a*x^7//2+2//9*b*x^9//2)
@test integrate(x^3//2*(a+b*x), x) == :(2//5*a*x^5//2+2//7*b*x^7//2)
@test integrate(x^(1/2)*(a+b*x), x) == :(2//3*a*x^3//2+2//5*b*x^5//2)
@test integrate(x^-1//2*(a+b*x), x) == :(2*a*x^(1/2)+2//3*b*x^3//2)
@test integrate(x^-3//2*(a+b*x), x) == :(-2*a*x^-1//2+2*b*x^(1/2))
@test integrate(x^-5//2*(a+b*x), x) == :(-2*b*x^-1//2+-2//3*a*x^-3//2)
@test integrate(x^m*(a+b*x)^2, x) == :(a^2*x^(1+m)*(1+m)^-1+b^2*x^(3+m)*(3+m)^-1+2*a*b*x^(2+m)*(2+m)^-1)
@test integrate(x^5//2*(a+b*x)^2, x) == :(2//7*a^2*x^7//2+2//11*b^2*x^11//2+4//9*a*b*x^9//2)
@test integrate(x^3//2*(a+b*x)^2, x) == :(2//5*a^2*x^5//2+2//9*b^2*x^9//2+4//7*a*b*x^7//2)
@test integrate(x^(1/2)*(a+b*x)^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^-1//2*(a+b*x)^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^-3//2*(a+b*x)^2, x) == :(-2*a^2*x^-1//2+2//3*b^2*x^3//2+4*a*b*x^(1/2))
@test integrate(x^-5//2*(a+b*x)^2, x) == :(2*b^2*x^(1/2)+-2//3*a^2*x^-3//2+-4*a*b*x^-1//2)
@test integrate(x^m*(a+b*x)^3, x) == :(a^3*x^(1+m)*(1+m)^-1+b^3*x^(4+m)*(4+m)^-1+3*a*b^2*x^(3+m)*(3+m)^-1+3*b*a^2*x^(2+m)*(2+m)^-1)
@test integrate(x^5//2*(a+b*x)^3, x) == :(2//7*a^3*x^7//2+2//13*b^3*x^13//2+2//3*b*a^2*x^9//2+6//11*a*b^2*x^11//2)
@test integrate(x^3//2*(a+b*x)^3, x) == :(2//5*a^3*x^5//2+2//11*b^3*x^11//2+2//3*a*b^2*x^9//2+6//7*b*a^2*x^7//2)
@test integrate(x^(1/2)*(a+b*x)^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^-1//2*(a+b*x)^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^-3//2*(a+b*x)^3, x) == :(-2*a^3*x^-1//2+2//5*b^3*x^5//2+2*a*b^2*x^3//2+6*b*a^2*x^(1/2))
@test integrate(x^-5//2*(a+b*x)^3, x) == :(-2//3*a^3*x^-3//2+2//3*b^3*x^3//2+-6*b*a^2*x^-1//2+6*a*b^2*x^(1/2))
@test integrate(x^5//2*(a+b*x)^-1, x) == :(2//5*b^-1*x^5//2+-2*a^5//2*b^-7//2*arctan(a^-1//2*b^(1/2)*x^(1/2))+2*a^2*b^-3*x^(1/2)+-2//3*a*b^-2*x^3//2)
@test integrate(x^3//2*(a+b*x)^-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^(1/2)*(a+b*x)^-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^-1//2*(a+b*x)^-1, x) == :(2*a^-1//2*b^-1//2*arctan(a^-1//2*b^(1/2)*x^(1/2)))
@test integrate(x^-3//2*(a+b*x)^-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^-5//2*(a+b*x)^-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^-7//2*(a+b*x)^-1, x) == :(-2//5*a^-1*x^-5//2+-2*a^-3*b^2*x^-1//2+-2*a^-7//2*b^5//2*arctan(a^-1//2*b^(1/2)*x^(1/2))+2//3*b*a^-2*x^-3//2)
@test integrate(x^5//2*(a+b*x)^-2, x) == :(5//3*b^-2*x^3//2+-1*b^-1*x^5//2*(a+b*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^3//2*(a+b*x)^-2, x) == :(3*b^-2*x^(1/2)+-1*b^-1*x^3//2*(a+b*x)^-1+-3*a^(1/2)*b^-5//2*arctan(a^-1//2*b^(1/2)*x^(1/2)))
@test integrate(x^(1/2)*(a+b*x)^-2, x) == :(a^-1//2*b^-3//2*arctan(a^-1//2*b^(1/2)*x^(1/2))+-1*b^-1*x^(1/2)*(a+b*x)^-1)
@test integrate(x^-1//2*(a+b*x)^-2, x) == :(a^-1*x^(1/2)*(a+b*x)^-1+a^-3//2*b^-1//2*arctan(a^-1//2*b^(1/2)*x^(1/2)))
@test integrate(x^-3//2*(a+b*x)^-2, x) == :(-3*a^-2*x^-1//2+a^-1*x^-1//2*(a+b*x)^-1+-3*a^-5//2*b^(1/2)*arctan(a^-1//2*b^(1/2)*x^(1/2)))
@test integrate(x^-5//2*(a+b*x)^-2, x) == :(-5//3*a^-2*x^-3//2+a^-1*x^-3//2*(a+b*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^7//2*(a+b*x)^-3, x) == :(35//12*b^-3*x^3//2+-35//4*a*b^-4*x^(1/2)+-7//4*b^-2*x^5//2*(a+b*x)^-1+-1//2*b^-1*x^7//2*(a+b*x)^-2+35//4*a^3//2*b^-9//2*arctan(a^-1//2*b^(1/2)*x^(1/2)))
@test integrate(x^5//2*(a+b*x)^-3, x) == :(15//4*b^-3*x^(1/2)+-15//4*a^(1/2)*b^-7//2*arctan(a^-1//2*b^(1/2)*x^(1/2))+-5//4*b^-2*x^3//2*(a+b*x)^-1+-1//2*b^-1*x^5//2*(a+b*x)^-2)
@test integrate(x^3//2*(a+b*x)^-3, x) == :(-3//4*b^-2*x^(1/2)*(a+b*x)^-1+-1//2*b^-1*x^3//2*(a+b*x)^-2+3//4*a^-1//2*b^-5//2*arctan(a^-1//2*b^(1/2)*x^(1/2)))
@test integrate(x^(1/2)*(a+b*x)^-3, x) == :(-1//2*b^-1*x^(1/2)*(a+b*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)*(a+b*x)^-1)
@test integrate(x^-1//2*(a+b*x)^-3, x) == :((1/2)*a^-1*x^(1/2)*(a+b*x)^-2+3//4*a^-2*x^(1/2)*(a+b*x)^-1+3//4*a^-5//2*b^-1//2*arctan(a^-1//2*b^(1/2)*x^(1/2)))
@test integrate(x^-3//2*(a+b*x)^-3, x) == :(-15//4*a^-3*x^-1//2+(1/2)*a^-1*x^-1//2*(a+b*x)^-2+-15//4*a^-7//2*b^(1/2)*arctan(a^-1//2*b^(1/2)*x^(1/2))+5//4*a^-2*x^-1//2*(a+b*x)^-1)
@test integrate(x^-5//2*(a+b*x)^-3, x) == :(-35//12*a^-3*x^-3//2+(1/2)*a^-1*x^-3//2*(a+b*x)^-2+7//4*a^-2*x^-3//2*(a+b*x)^-1+35//4*b*a^-4*x^-1//2+35//4*a^-9//2*b^3//2*arctan(a^-1//2*b^(1/2)*x^(1/2)))
@test integrate(x^5//2*(-1a+b*x)^-1, x) == :(2//5*b^-1*x^5//2+-2*a^5//2*b^-7//2*arctanh(a^-1//2*b^(1/2)*x^(1/2))+2*a^2*b^-3*x^(1/2)+2//3*a*b^-2*x^3//2)
@test integrate(x^3//2*(-1a+b*x)^-1, x) == :(2//3*b^-1*x^3//2+-2*a^3//2*b^-5//2*arctanh(a^-1//2*b^(1/2)*x^(1/2))+2*a*b^-2*x^(1/2))
@test integrate(x^(1/2)*(-1a+b*x)^-1, x) == :(2*b^-1*x^(1/2)+-2*a^(1/2)*b^-3//2*arctanh(a^-1//2*b^(1/2)*x^(1/2)))
@test integrate(x^-1//2*(-1a+b*x)^-1, x) == :(-2*a^-1//2*b^-1//2*arctanh(a^-1//2*b^(1/2)*x^(1/2)))
@test integrate(x^-3//2*(-1a+b*x)^-1, x) == :(2*a^-1*x^-1//2+-2*a^-3//2*b^(1/2)*arctanh(a^-1//2*b^(1/2)*x^(1/2)))
@test integrate(x^-5//2*(-1a+b*x)^-1, x) == :(2//3*a^-1*x^-3//2+-2*a^-5//2*b^3//2*arctanh(a^-1//2*b^(1/2)*x^(1/2))+2*b*a^-2*x^-1//2)
@test integrate(x^-7//2*(-1a+b*x)^-1, x) == :(2//5*a^-1*x^-5//2+-2*a^-7//2*b^5//2*arctanh(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^5//2*(-1a+b*x)^-2, x) == :(5//3*b^-2*x^3//2+b^-1*x^5//2*(a+-1*b*x)^-1+-5*a^3//2*b^-7//2*arctanh(a^-1//2*b^(1/2)*x^(1/2))+5*a*b^-3*x^(1/2))
@test integrate(x^3//2*(-1a+b*x)^-2, x) == :(3*b^-2*x^(1/2)+b^-1*x^3//2*(a+-1*b*x)^-1+-3*a^(1/2)*b^-5//2*arctanh(a^-1//2*b^(1/2)*x^(1/2)))
@test integrate(x^(1/2)*(-1a+b*x)^-2, x) == :(b^-1*x^(1/2)*(a+-1*b*x)^-1+-1*a^-1//2*b^-3//2*arctanh(a^-1//2*b^(1/2)*x^(1/2)))
@test integrate(x^-1//2*(-1a+b*x)^-2, x) == :(a^-1*x^(1/2)*(a+-1*b*x)^-1+a^-3//2*b^-1//2*arctanh(a^-1//2*b^(1/2)*x^(1/2)))
@test integrate(x^-3//2*(-1a+b*x)^-2, x) == :(-3*a^-2*x^-1//2+a^-1*x^-1//2*(a+-1*b*x)^-1+3*a^-5//2*b^(1/2)*arctanh(a^-1//2*b^(1/2)*x^(1/2)))
@test integrate(x^-5//2*(-1a+b*x)^-2, x) == :(-5//3*a^-2*x^-3//2+a^-1*x^-3//2*(a+-1*b*x)^-1+-5*b*a^-3*x^-1//2+5*a^-7//2*b^3//2*arctanh(a^-1//2*b^(1/2)*x^(1/2)))
@test integrate(x^7//2*(-1a+b*x)^-3, x) == :(35//12*b^-3*x^3//2+-35//4*a^3//2*b^-9//2*arctanh(a^-1//2*b^(1/2)*x^(1/2))+-1//2*b^-1*x^7//2*(a+-1*b*x)^-2+7//4*b^-2*x^5//2*(a+-1*b*x)^-1+35//4*a*b^-4*x^(1/2))
@test integrate(x^5//2*(-1a+b*x)^-3, x) == :(15//4*b^-3*x^(1/2)+-15//4*a^(1/2)*b^-7//2*arctanh(a^-1//2*b^(1/2)*x^(1/2))+-1//2*b^-1*x^5//2*(a+-1*b*x)^-2+5//4*b^-2*x^3//2*(a+-1*b*x)^-1)
@test integrate(x^3//2*(-1a+b*x)^-3, x) == :(-3//4*a^-1//2*b^-5//2*arctanh(a^-1//2*b^(1/2)*x^(1/2))+-1//2*b^-1*x^3//2*(a+-1*b*x)^-2+3//4*b^-2*x^(1/2)*(a+-1*b*x)^-1)
@test integrate(x^(1/2)*(-1a+b*x)^-3, x) == :(-1//2*b^-1*x^(1/2)*(a+-1*b*x)^-2+1//4*a^-3//2*b^-3//2*arctanh(a^-1//2*b^(1/2)*x^(1/2))+1//4*a^-1*b^-1*x^(1/2)*(a+-1*b*x)^-1)
@test integrate(x^-1//2*(-1a+b*x)^-3, x) == :(-3//4*a^-2*x^(1/2)*(a+-1*b*x)^-1+-3//4*a^-5//2*b^-1//2*arctanh(a^-1//2*b^(1/2)*x^(1/2))+-1//2*a^-1*x^(1/2)*(a+-1*b*x)^-2)
@test integrate(x^-3//2*(-1a+b*x)^-3, x) == :(15//4*a^-3*x^-1//2+-15//4*a^-7//2*b^(1/2)*arctanh(a^-1//2*b^(1/2)*x^(1/2))+-5//4*a^-2*x^-1//2*(a+-1*b*x)^-1+-1//2*a^-1*x^-1//2*(a+-1*b*x)^-2)
@test integrate(x^-5//2*(-1a+b*x)^-3, x) == :(35//12*a^-3*x^-3//2+-35//4*a^-9//2*b^3//2*arctanh(a^-1//2*b^(1/2)*x^(1/2))+-7//4*a^-2*x^-3//2*(a+-1*b*x)^-1+-1//2*a^-1*x^-3//2*(a+-1*b*x)^-2+35//4*b*a^-4*x^-1//2)
@test integrate(x^5//2*(a+b*x)^(1/2), x) == :(1//4*x^7//2*(a+b*x)^(1/2)+-5//64*a^4*b^-7//2*arctanh(b^(1/2)*x^(1/2)*(a+b*x)^-1//2)+-5//96*a^2*b^-2*x^3//2*(a+b*x)^(1/2)+1//24*a*b^-1*x^5//2*(a+b*x)^(1/2)+5//64*a^3*b^-3*x^(1/2)*(a+b*x)^(1/2))
@test integrate(x^3//2*(a+b*x)^(1/2), x) == :(1//3*x^5//2*(a+b*x)^(1/2)+1//8*a^3*b^-5//2*arctanh(b^(1/2)*x^(1/2)*(a+b*x)^-1//2)+-1//8*a^2*b^-2*x^(1/2)*(a+b*x)^(1/2)+1//12*a*b^-1*x^3//2*(a+b*x)^(1/2))
@test integrate(x^(1/2)*(a+b*x)^(1/2), x) == :((1/2)*x^3//2*(a+b*x)^(1/2)+-1//4*a^2*b^-3//2*arctanh(b^(1/2)*x^(1/2)*(a+b*x)^-1//2)+1//4*a*b^-1*x^(1/2)*(a+b*x)^(1/2))
@test integrate(x^-1//2*(a+b*x)^(1/2), x) == :(x^(1/2)*(a+b*x)^(1/2)+a*b^-1//2*arctanh(b^(1/2)*x^(1/2)*(a+b*x)^-1//2))
@test integrate(x^-3//2*(a+b*x)^(1/2), x) == :(-2*x^-1//2*(a+b*x)^(1/2)+2*b^(1/2)*arctanh(b^(1/2)*x^(1/2)*(a+b*x)^-1//2))
@test integrate(x^-5//2*(a+b*x)^(1/2), x) == :(-2//3*a^-1*x^-3//2*(a+b*x)^3//2)
@test integrate(x^-7//2*(a+b*x)^(1/2), x) == :(-2//5*a^-1*x^-5//2*(a+b*x)^3//2+4//15*b*a^-2*x^-3//2*(a+b*x)^3//2)
@test integrate(x^-9//2*(a+b*x)^(1/2), x) == :(-2//7*a^-1*x^-7//2*(a+b*x)^3//2+-16//105*a^-3*b^2*x^-3//2*(a+b*x)^3//2+8//35*b*a^-2*x^-5//2*(a+b*x)^3//2)
@test integrate(x^5//2*(a+-1*b*x)^(1/2), x) == :(1//4*x^7//2*(a+-1*b*x)^(1/2)+5//64*a^4*b^-7//2*arctan(b^(1/2)*x^(1/2)*(a+-1*b*x)^-1//2)+-5//64*a^3*b^-3*x^(1/2)*(a+-1*b*x)^(1/2)+-5//96*a^2*b^-2*x^3//2*(a+-1*b*x)^(1/2)+-1//24*a*b^-1*x^5//2*(a+-1*b*x)^(1/2))
@test integrate(x^3//2*(a+-1*b*x)^(1/2), x) == :(1//3*x^5//2*(a+-1*b*x)^(1/2)+1//8*a^3*b^-5//2*arctan(b^(1/2)*x^(1/2)*(a+-1*b*x)^-1//2)+-1//8*a^2*b^-2*x^(1/2)*(a+-1*b*x)^(1/2)+-1//12*a*b^-1*x^3//2*(a+-1*b*x)^(1/2))
@test integrate(x^(1/2)*(a+-1*b*x)^(1/2), x) == :((1/2)*x^3//2*(a+-1*b*x)^(1/2)+1//4*a^2*b^-3//2*arctan(b^(1/2)*x^(1/2)*(a+-1*b*x)^-1//2)+-1//4*a*b^-1*x^(1/2)*(a+-1*b*x)^(1/2))
@test integrate(x^-1//2*(a+-1*b*x)^(1/2), x) == :(x^(1/2)*(a+-1*b*x)^(1/2)+a*b^-1//2*arctan(b^(1/2)*x^(1/2)*(a+-1*b*x)^-1//2))
@test integrate(x^-3//2*(a+-1*b*x)^(1/2), x) == :(-2*b^(1/2)*arctan(b^(1/2)*x^(1/2)*(a+-1*b*x)^-1//2)+-2*x^-1//2*(a+-1*b*x)^(1/2))
@test integrate(x^-5//2*(a+-1*b*x)^(1/2), x) == :(-2//3*a^-1*x^-3//2*(a+-1*b*x)^3//2)
@test integrate(x^-7//2*(a+-1*b*x)^(1/2), x) == :(-2//5*a^-1*x^-5//2*(a+-1*b*x)^3//2+-4//15*b*a^-2*x^-3//2*(a+-1*b*x)^3//2)
@test integrate(x^-9//2*(a+-1*b*x)^(1/2), x) == :(-2//7*a^-1*x^-7//2*(a+-1*b*x)^3//2+-16//105*a^-3*b^2*x^-3//2*(a+-1*b*x)^3//2+-8//35*b*a^-2*x^-5//2*(a+-1*b*x)^3//2)
@test integrate(x^5//2*(2+b*x)^(1/2), x) == :(-5//4*b^-7//2*arcsinh((1/2)*2^(1/2)*b^(1/2)*x^(1/2))+1//4*x^7//2*(2+b*x)^(1/2)+-5//24*b^-2*x^3//2*(2+b*x)^(1/2)+1//12*b^-1*x^5//2*(2+b*x)^(1/2)+5//8*b^-3*x^(1/2)*(2+b*x)^(1/2))
@test integrate(x^3//2*(2+b*x)^(1/2), x) == :(b^-5//2*arcsinh((1/2)*2^(1/2)*b^(1/2)*x^(1/2))+1//3*x^5//2*(2+b*x)^(1/2)+-1//2*b^-2*x^(1/2)*(2+b*x)^(1/2)+1//6*b^-1*x^3//2*(2+b*x)^(1/2))
@test integrate(x^(1/2)*(2+b*x)^(1/2), x) == :((1/2)*x^3//2*(2+b*x)^(1/2)+-1*b^-3//2*arcsinh((1/2)*2^(1/2)*b^(1/2)*x^(1/2))+(1/2)*b^-1*x^(1/2)*(2+b*x)^(1/2))
@test integrate(x^-1//2*(2+b*x)^(1/2), x) == :(x^(1/2)*(2+b*x)^(1/2)+2*b^-1//2*arcsinh((1/2)*2^(1/2)*b^(1/2)*x^(1/2)))
@test integrate(x^-3//2*(2+b*x)^(1/2), x) == :(-2*x^-1//2*(2+b*x)^(1/2)+2*b^(1/2)*arcsinh((1/2)*2^(1/2)*b^(1/2)*x^(1/2)))
@test integrate(x^-5//2*(2+b*x)^(1/2), x) == :(-1//3*x^-3//2*(2+b*x)^3//2)
@test integrate(x^-7//2*(2+b*x)^(1/2), x) == :(-1//5*x^-5//2*(2+b*x)^3//2+1//15*b*x^-3//2*(2+b*x)^3//2)
@test integrate(x^-9//2*(2+b*x)^(1/2), x) == :(-1//7*x^-7//2*(2+b*x)^3//2+-2//105*b^2*x^-3//2*(2+b*x)^3//2+2//35*b*x^-5//2*(2+b*x)^3//2)
@test integrate(x^5//2*(2+-1*b*x)^(1/2), x) == :(1//4*x^7//2*(2+-1*b*x)^(1/2)+5//4*b^-7//2*arcsin((1/2)*2^(1/2)*b^(1/2)*x^(1/2))+-5//8*b^-3*x^(1/2)*(2+-1*b*x)^(1/2)+-5//24*b^-2*x^3//2*(2+-1*b*x)^(1/2)+-1//12*b^-1*x^5//2*(2+-1*b*x)^(1/2))
@test integrate(x^3//2*(2+-1*b*x)^(1/2), x) == :(b^-5//2*arcsin((1/2)*2^(1/2)*b^(1/2)*x^(1/2))+1//3*x^5//2*(2+-1*b*x)^(1/2)+-1//2*b^-2*x^(1/2)*(2+-1*b*x)^(1/2)+-1//6*b^-1*x^3//2*(2+-1*b*x)^(1/2))
@test integrate(x^(1/2)*(2+-1*b*x)^(1/2), x) == :(b^-3//2*arcsin((1/2)*2^(1/2)*b^(1/2)*x^(1/2))+(1/2)*x^3//2*(2+-1*b*x)^(1/2)+-1//2*b^-1*x^(1/2)*(2+-1*b*x)^(1/2))
@test integrate(x^-1//2*(2+-1*b*x)^(1/2), x) == :(x^(1/2)*(2+-1*b*x)^(1/2)+2*b^-1//2*arcsin((1/2)*2^(1/2)*b^(1/2)*x^(1/2)))
@test integrate(x^-3//2*(2+-1*b*x)^(1/2), x) == :(-2*b^(1/2)*arcsin((1/2)*2^(1/2)*b^(1/2)*x^(1/2))+-2*x^-1//2*(2+-1*b*x)^(1/2))
@test integrate(x^-5//2*(2+-1*b*x)^(1/2), x) == :(-1//3*x^-3//2*(2+-1*b*x)^3//2)
@test integrate(x^-7//2*(2+-1*b*x)^(1/2), x) == :(-1//5*x^-5//2*(2+-1*b*x)^3//2+-1//15*b*x^-3//2*(2+-1*b*x)^3//2)
@test integrate(x^-9//2*(2+-1*b*x)^(1/2), x) == :(-1//7*x^-7//2*(2+-1*b*x)^3//2+-2//35*b*x^-5//2*(2+-1*b*x)^3//2+-2//105*b^2*x^-3//2*(2+-1*b*x)^3//2)
@test integrate(x^5//2*(a+b*x)^3//2, x) == :(1//5*x^7//2*(a+b*x)^3//2+-3//128*a^5*b^-7//2*arctanh(b^(1/2)*x^(1/2)*(a+b*x)^-1//2)+3//40*a*x^7//2*(a+b*x)^(1/2)+-1//64*a^3*b^-2*x^3//2*(a+b*x)^(1/2)+1//80*a^2*b^-1*x^5//2*(a+b*x)^(1/2)+3//128*a^4*b^-3*x^(1/2)*(a+b*x)^(1/2))
@test integrate(x^3//2*(a+b*x)^3//2, x) == :(1//4*x^5//2*(a+b*x)^3//2+1//8*a*x^5//2*(a+b*x)^(1/2)+3//64*a^4*b^-5//2*arctanh(b^(1/2)*x^(1/2)*(a+b*x)^-1//2)+-3//64*a^3*b^-2*x^(1/2)*(a+b*x)^(1/2)+1//32*a^2*b^-1*x^3//2*(a+b*x)^(1/2))
@test integrate(x^(1/2)*(a+b*x)^3//2, x) == :(1//3*x^3//2*(a+b*x)^3//2+-1//8*a^3*b^-3//2*arctanh(b^(1/2)*x^(1/2)*(a+b*x)^-1//2)+1//4*a*x^3//2*(a+b*x)^(1/2)+1//8*a^2*b^-1*x^(1/2)*(a+b*x)^(1/2))
@test integrate(x^-1//2*(a+b*x)^3//2, x) == :((1/2)*x^(1/2)*(a+b*x)^3//2+3//4*a*x^(1/2)*(a+b*x)^(1/2)+3//4*a^2*b^-1//2*arctanh(b^(1/2)*x^(1/2)*(a+b*x)^-1//2))
@test integrate(x^-3//2*(a+b*x)^3//2, x) == :(-2*x^-1//2*(a+b*x)^3//2+3*a*b^(1/2)*arctanh(b^(1/2)*x^(1/2)*(a+b*x)^-1//2)+3*b*x^(1/2)*(a+b*x)^(1/2))
@test integrate(x^-5//2*(a+b*x)^3//2, x) == :(2*b^3//2*arctanh(b^(1/2)*x^(1/2)*(a+b*x)^-1//2)+-2//3*x^-3//2*(a+b*x)^3//2+-2*b*x^-1//2*(a+b*x)^(1/2))
@test integrate(x^5//2*(a+-1*b*x)^3//2, x) == :(1//5*x^7//2*(a+-1*b*x)^3//2+3//40*a*x^7//2*(a+-1*b*x)^(1/2)+3//128*a^5*b^-7//2*arctan(b^(1/2)*x^(1/2)*(a+-1*b*x)^-1//2)+-3//128*a^4*b^-3*x^(1/2)*(a+-1*b*x)^(1/2)+-1//64*a^3*b^-2*x^3//2*(a+-1*b*x)^(1/2)+-1//80*a^2*b^-1*x^5//2*(a+-1*b*x)^(1/2))
@test integrate(x^3//2*(a+-1*b*x)^3//2, x) == :(1//4*x^5//2*(a+-1*b*x)^3//2+1//8*a*x^5//2*(a+-1*b*x)^(1/2)+3//64*a^4*b^-5//2*arctan(b^(1/2)*x^(1/2)*(a+-1*b*x)^-1//2)+-3//64*a^3*b^-2*x^(1/2)*(a+-1*b*x)^(1/2)+-1//32*a^2*b^-1*x^3//2*(a+-1*b*x)^(1/2))
@test integrate(x^(1/2)*(a+-1*b*x)^3//2, x) == :(1//3*x^3//2*(a+-1*b*x)^3//2+1//4*a*x^3//2*(a+-1*b*x)^(1/2)+1//8*a^3*b^-3//2*arctan(b^(1/2)*x^(1/2)*(a+-1*b*x)^-1//2)+-1//8*a^2*b^-1*x^(1/2)*(a+-1*b*x)^(1/2))
@test integrate(x^-1//2*(a+-1*b*x)^3//2, x) == :((1/2)*x^(1/2)*(a+-1*b*x)^3//2+3//4*a*x^(1/2)*(a+-1*b*x)^(1/2)+3//4*a^2*b^-1//2*arctan(b^(1/2)*x^(1/2)*(a+-1*b*x)^-1//2))
@test integrate(x^-3//2*(a+-1*b*x)^3//2, x) == :(-2*x^-1//2*(a+-1*b*x)^3//2+-3*a*b^(1/2)*arctan(b^(1/2)*x^(1/2)*(a+-1*b*x)^-1//2)+-3*b*x^(1/2)*(a+-1*b*x)^(1/2))
@test integrate(x^-5//2*(a+-1*b*x)^3//2, x) == :(2*b^3//2*arctan(b^(1/2)*x^(1/2)*(a+-1*b*x)^-1//2)+-2//3*x^-3//2*(a+-1*b*x)^3//2+2*b*x^-1//2*(a+-1*b*x)^(1/2))
@test integrate(x^5//2*(2+b*x)^3//2, x) == :(-3//4*b^-7//2*arcsinh((1/2)*2^(1/2)*b^(1/2)*x^(1/2))+1//5*x^7//2*(2+b*x)^3//2+3//20*x^7//2*(2+b*x)^(1/2)+-1//8*b^-2*x^3//2*(2+b*x)^(1/2)+1//20*b^-1*x^5//2*(2+b*x)^(1/2)+3//8*b^-3*x^(1/2)*(2+b*x)^(1/2))
@test integrate(x^3//2*(2+b*x)^3//2, x) == :(1//4*x^5//2*(2+b*x)^(1/2)+1//4*x^5//2*(2+b*x)^3//2+3//4*b^-5//2*arcsinh((1/2)*2^(1/2)*b^(1/2)*x^(1/2))+-3//8*b^-2*x^(1/2)*(2+b*x)^(1/2)+1//8*b^-1*x^3//2*(2+b*x)^(1/2))
@test integrate(x^(1/2)*(2+b*x)^3//2, x) == :((1/2)*x^3//2*(2+b*x)^(1/2)+-1*b^-3//2*arcsinh((1/2)*2^(1/2)*b^(1/2)*x^(1/2))+1//3*x^3//2*(2+b*x)^3//2+(1/2)*b^-1*x^(1/2)*(2+b*x)^(1/2))
@test integrate(x^-1//2*(2+b*x)^3//2, x) == :((1/2)*x^(1/2)*(2+b*x)^3//2+3*b^-1//2*arcsinh((1/2)*2^(1/2)*b^(1/2)*x^(1/2))+3//2*x^(1/2)*(2+b*x)^(1/2))
@test integrate(x^-3//2*(2+b*x)^3//2, x) == :(-2*x^-1//2*(2+b*x)^3//2+6*b^(1/2)*arcsinh((1/2)*2^(1/2)*b^(1/2)*x^(1/2))+3*b*x^(1/2)*(2+b*x)^(1/2))
@test integrate(x^-5//2*(2+b*x)^3//2, x) == :(2*b^3//2*arcsinh((1/2)*2^(1/2)*b^(1/2)*x^(1/2))+-2//3*x^-3//2*(2+b*x)^3//2+-2*b*x^-1//2*(2+b*x)^(1/2))
@test integrate(x^5//2*(2+-1*b*x)^3//2, x) == :(1//5*x^7//2*(2+-1*b*x)^3//2+3//4*b^-7//2*arcsin((1/2)*2^(1/2)*b^(1/2)*x^(1/2))+3//20*x^7//2*(2+-1*b*x)^(1/2)+-3//8*b^-3*x^(1/2)*(2+-1*b*x)^(1/2)+-1//8*b^-2*x^3//2*(2+-1*b*x)^(1/2)+-1//20*b^-1*x^5//2*(2+-1*b*x)^(1/2))
@test integrate(x^3//2*(2+-1*b*x)^3//2, x) == :(1//4*x^5//2*(2+-1*b*x)^(1/2)+1//4*x^5//2*(2+-1*b*x)^3//2+3//4*b^-5//2*arcsin((1/2)*2^(1/2)*b^(1/2)*x^(1/2))+-3//8*b^-2*x^(1/2)*(2+-1*b*x)^(1/2)+-1//8*b^-1*x^3//2*(2+-1*b*x)^(1/2))
@test integrate(x^(1/2)*(2+-1*b*x)^3//2, x) == :(b^-3//2*arcsin((1/2)*2^(1/2)*b^(1/2)*x^(1/2))+(1/2)*x^3//2*(2+-1*b*x)^(1/2)+1//3*x^3//2*(2+-1*b*x)^3//2+-1//2*b^-1*x^(1/2)*(2+-1*b*x)^(1/2))
@test integrate(x^-1//2*(2+-1*b*x)^3//2, x) == :((1/2)*x^(1/2)*(2+-1*b*x)^3//2+3*b^-1//2*arcsin((1/2)*2^(1/2)*b^(1/2)*x^(1/2))+3//2*x^(1/2)*(2+-1*b*x)^(1/2))
@test integrate(x^-3//2*(2+-1*b*x)^3//2, x) == :(-6*b^(1/2)*arcsin((1/2)*2^(1/2)*b^(1/2)*x^(1/2))+-2*x^-1//2*(2+-1*b*x)^3//2+-3*b*x^(1/2)*(2+-1*b*x)^(1/2))
@test integrate(x^-5//2*(2+-1*b*x)^3//2, x) == :(2*b^3//2*arcsin((1/2)*2^(1/2)*b^(1/2)*x^(1/2))+-2//3*x^-3//2*(2+-1*b*x)^3//2+2*b*x^-1//2*(2+-1*b*x)^(1/2))
@test integrate(x^5//2*(a+b*x)^5//2, x) == :(1//6*x^7//2*(a+b*x)^5//2+-5//512*a^6*b^-7//2*arctanh(b^(1/2)*x^(1/2)*(a+b*x)^-1//2)+1//12*a*x^7//2*(a+b*x)^3//2+1//32*a^2*x^7//2*(a+b*x)^(1/2)+-5//768*a^4*b^-2*x^3//2*(a+b*x)^(1/2)+1//192*a^3*b^-1*x^5//2*(a+b*x)^(1/2)+5//512*a^5*b^-3*x^(1/2)*(a+b*x)^(1/2))
@test integrate(x^3//2*(a+b*x)^5//2, x) == :(1//5*x^5//2*(a+b*x)^5//2+1//8*a*x^5//2*(a+b*x)^3//2+1//16*a^2*x^5//2*(a+b*x)^(1/2)+3//128*a^5*b^-5//2*arctanh(b^(1/2)*x^(1/2)*(a+b*x)^-1//2)+-3//128*a^4*b^-2*x^(1/2)*(a+b*x)^(1/2)+1//64*a^3*b^-1*x^3//2*(a+b*x)^(1/2))
@test integrate(x^(1/2)*(a+b*x)^5//2, x) == :(1//4*x^3//2*(a+b*x)^5//2+-5//64*a^4*b^-3//2*arctanh(b^(1/2)*x^(1/2)*(a+b*x)^-1//2)+5//24*a*x^3//2*(a+b*x)^3//2+5//32*a^2*x^3//2*(a+b*x)^(1/2)+5//64*a^3*b^-1*x^(1/2)*(a+b*x)^(1/2))
@test integrate(x^-1//2*(a+b*x)^5//2, x) == :(1//3*x^(1/2)*(a+b*x)^5//2+5//8*a^2*x^(1/2)*(a+b*x)^(1/2)+5//8*a^3*b^-1//2*arctanh(b^(1/2)*x^(1/2)*(a+b*x)^-1//2)+5//12*a*x^(1/2)*(a+b*x)^3//2)
@test integrate(x^-3//2*(a+b*x)^5//2, x) == :(-2*x^-1//2*(a+b*x)^5//2+5//2*b*x^(1/2)*(a+b*x)^3//2+15//4*a^2*b^(1/2)*arctanh(b^(1/2)*x^(1/2)*(a+b*x)^-1//2)+15//4*a*b*x^(1/2)*(a+b*x)^(1/2))
@test integrate(x^-5//2*(a+b*x)^5//2, x) == :(-2//3*x^-3//2*(a+b*x)^5//2+5*a*b^3//2*arctanh(b^(1/2)*x^(1/2)*(a+b*x)^-1//2)+5*b^2*x^(1/2)*(a+b*x)^(1/2)+-10//3*b*x^-1//2*(a+b*x)^3//2)
@test integrate(x^5//2*(a+-1*b*x)^5//2, x) == :(1//6*x^7//2*(a+-1*b*x)^5//2+1//12*a*x^7//2*(a+-1*b*x)^3//2+1//32*a^2*x^7//2*(a+-1*b*x)^(1/2)+5//512*a^6*b^-7//2*arctan(b^(1/2)*x^(1/2)*(a+-1*b*x)^-1//2)+-5//512*a^5*b^-3*x^(1/2)*(a+-1*b*x)^(1/2)+-5//768*a^4*b^-2*x^3//2*(a+-1*b*x)^(1/2)+-1//192*a^3*b^-1*x^5//2*(a+-1*b*x)^(1/2))
@test integrate(x^3//2*(a+-1*b*x)^5//2, x) == :(1//5*x^5//2*(a+-1*b*x)^5//2+1//8*a*x^5//2*(a+-1*b*x)^3//2+1//16*a^2*x^5//2*(a+-1*b*x)^(1/2)+3//128*a^5*b^-5//2*arctan(b^(1/2)*x^(1/2)*(a+-1*b*x)^-1//2)+-3//128*a^4*b^-2*x^(1/2)*(a+-1*b*x)^(1/2)+-1//64*a^3*b^-1*x^3//2*(a+-1*b*x)^(1/2))
@test integrate(x^(1/2)*(a+-1*b*x)^5//2, x) == :(1//4*x^3//2*(a+-1*b*x)^5//2+5//24*a*x^3//2*(a+-1*b*x)^3//2+5//32*a^2*x^3//2*(a+-1*b*x)^(1/2)+5//64*a^4*b^-3//2*arctan(b^(1/2)*x^(1/2)*(a+-1*b*x)^-1//2)+-5//64*a^3*b^-1*x^(1/2)*(a+-1*b*x)^(1/2))
@test integrate(x^-1//2*(a+-1*b*x)^5//2, x) == :(1//3*x^(1/2)*(a+-1*b*x)^5//2+5//8*a^2*x^(1/2)*(a+-1*b*x)^(1/2)+5//8*a^3*b^-1//2*arctan(b^(1/2)*x^(1/2)*(a+-1*b*x)^-1//2)+5//12*a*x^(1/2)*(a+-1*b*x)^3//2)
@test integrate(x^-3//2*(a+-1*b*x)^5//2, x) == :(-2*x^-1//2*(a+-1*b*x)^5//2+-15//4*a^2*b^(1/2)*arctan(b^(1/2)*x^(1/2)*(a+-1*b*x)^-1//2)+-5//2*b*x^(1/2)*(a+-1*b*x)^3//2+-15//4*a*b*x^(1/2)*(a+-1*b*x)^(1/2))
@test integrate(x^-5//2*(a+-1*b*x)^5//2, x) == :(-2//3*x^-3//2*(a+-1*b*x)^5//2+5*a*b^3//2*arctan(b^(1/2)*x^(1/2)*(a+-1*b*x)^-1//2)+5*b^2*x^(1/2)*(a+-1*b*x)^(1/2)+10//3*b*x^-1//2*(a+-1*b*x)^3//2)
@test integrate(x^5//2*(2+b*x)^5//2, x) == :(-5//8*b^-7//2*arcsinh((1/2)*2^(1/2)*b^(1/2)*x^(1/2))+1//6*x^7//2*(2+b*x)^3//2+1//6*x^7//2*(2+b*x)^5//2+1//8*x^7//2*(2+b*x)^(1/2)+-5//48*b^-2*x^3//2*(2+b*x)^(1/2)+1//24*b^-1*x^5//2*(2+b*x)^(1/2)+5//16*b^-3*x^(1/2)*(2+b*x)^(1/2))
@test integrate(x^3//2*(2+b*x)^5//2, x) == :(1//4*x^5//2*(2+b*x)^(1/2)+1//4*x^5//2*(2+b*x)^3//2+1//5*x^5//2*(2+b*x)^5//2+3//4*b^-5//2*arcsinh((1/2)*2^(1/2)*b^(1/2)*x^(1/2))+-3//8*b^-2*x^(1/2)*(2+b*x)^(1/2)+1//8*b^-1*x^3//2*(2+b*x)^(1/2))
@test integrate(x^(1/2)*(2+b*x)^5//2, x) == :(-5//4*b^-3//2*arcsinh((1/2)*2^(1/2)*b^(1/2)*x^(1/2))+1//4*x^3//2*(2+b*x)^5//2+5//8*x^3//2*(2+b*x)^(1/2)+5//12*x^3//2*(2+b*x)^3//2+5//8*b^-1*x^(1/2)*(2+b*x)^(1/2))
@test integrate(x^-1//2*(2+b*x)^5//2, x) == :(5*b^-1//2*arcsinh((1/2)*2^(1/2)*b^(1/2)*x^(1/2))+1//3*x^(1/2)*(2+b*x)^5//2+5//2*x^(1/2)*(2+b*x)^(1/2)+5//6*x^(1/2)*(2+b*x)^3//2)
@test integrate(x^-3//2*(2+b*x)^5//2, x) == :(-2*x^-1//2*(2+b*x)^5//2+15*b^(1/2)*arcsinh((1/2)*2^(1/2)*b^(1/2)*x^(1/2))+5//2*b*x^(1/2)*(2+b*x)^3//2+15//2*b*x^(1/2)*(2+b*x)^(1/2))
@test integrate(x^-5//2*(2+b*x)^5//2, x) == :(10*b^3//2*arcsinh((1/2)*2^(1/2)*b^(1/2)*x^(1/2))+-2//3*x^-3//2*(2+b*x)^5//2+5*b^2*x^(1/2)*(2+b*x)^(1/2)+-10//3*b*x^-1//2*(2+b*x)^3//2)
@test integrate(x^5//2*(2+-1*b*x)^5//2, x) == :(1//6*x^7//2*(2+-1*b*x)^3//2+1//6*x^7//2*(2+-1*b*x)^5//2+1//8*x^7//2*(2+-1*b*x)^(1/2)+5//8*b^-7//2*arcsin((1/2)*2^(1/2)*b^(1/2)*x^(1/2))+-5//16*b^-3*x^(1/2)*(2+-1*b*x)^(1/2)+-5//48*b^-2*x^3//2*(2+-1*b*x)^(1/2)+-1//24*b^-1*x^5//2*(2+-1*b*x)^(1/2))
@test integrate(x^3//2*(2+-1*b*x)^5//2, x) == :(1//4*x^5//2*(2+-1*b*x)^(1/2)+1//4*x^5//2*(2+-1*b*x)^3//2+1//5*x^5//2*(2+-1*b*x)^5//2+3//4*b^-5//2*arcsin((1/2)*2^(1/2)*b^(1/2)*x^(1/2))+-3//8*b^-2*x^(1/2)*(2+-1*b*x)^(1/2)+-1//8*b^-1*x^3//2*(2+-1*b*x)^(1/2))
@test integrate(x^(1/2)*(2+-1*b*x)^5//2, x) == :(1//4*x^3//2*(2+-1*b*x)^5//2+5//4*b^-3//2*arcsin((1/2)*2^(1/2)*b^(1/2)*x^(1/2))+5//8*x^3//2*(2+-1*b*x)^(1/2)+5//12*x^3//2*(2+-1*b*x)^3//2+-5//8*b^-1*x^(1/2)*(2+-1*b*x)^(1/2))
@test integrate(x^-1//2*(2+-1*b*x)^5//2, x) == :(5*b^-1//2*arcsin((1/2)*2^(1/2)*b^(1/2)*x^(1/2))+1//3*x^(1/2)*(2+-1*b*x)^5//2+5//2*x^(1/2)*(2+-1*b*x)^(1/2)+5//6*x^(1/2)*(2+-1*b*x)^3//2)
@test integrate(x^-3//2*(2+-1*b*x)^5//2, x) == :(-15*b^(1/2)*arcsin((1/2)*2^(1/2)*b^(1/2)*x^(1/2))+-2*x^-1//2*(2+-1*b*x)^5//2+-15//2*b*x^(1/2)*(2+-1*b*x)^(1/2)+-5//2*b*x^(1/2)*(2+-1*b*x)^3//2)
@test integrate(x^-5//2*(2+-1*b*x)^5//2, x) == :(10*b^3//2*arcsin((1/2)*2^(1/2)*b^(1/2)*x^(1/2))+-2//3*x^-3//2*(2+-1*b*x)^5//2+5*b^2*x^(1/2)*(2+-1*b*x)^(1/2)+10//3*b*x^-1//2*(2+-1*b*x)^3//2)
@test integrate(x^5//2*(a+b*x)^-1//2, x) == :(-5//8*a^3*b^-7//2*arctanh(b^(1/2)*x^(1/2)*(a+b*x)^-1//2)+1//3*b^-1*x^5//2*(a+b*x)^(1/2)+-5//12*a*b^-2*x^3//2*(a+b*x)^(1/2)+5//8*a^2*b^-3*x^(1/2)*(a+b*x)^(1/2))
@test integrate(x^3//2*(a+b*x)^-1//2, x) == :((1/2)*b^-1*x^3//2*(a+b*x)^(1/2)+3//4*a^2*b^-5//2*arctanh(b^(1/2)*x^(1/2)*(a+b*x)^-1//2)+-3//4*a*b^-2*x^(1/2)*(a+b*x)^(1/2))
@test integrate(x^(1/2)*(a+b*x)^-1//2, x) == :(b^-1*x^(1/2)*(a+b*x)^(1/2)+-1*a*b^-3//2*arctanh(b^(1/2)*x^(1/2)*(a+b*x)^-1//2))
@test integrate(x^-1//2*(a+b*x)^-1//2, x) == :(2*b^-1//2*arctanh(b^(1/2)*x^(1/2)*(a+b*x)^-1//2))
@test integrate(x^-3//2*(a+b*x)^-1//2, x) == :(-2*a^-1*x^-1//2*(a+b*x)^(1/2))
@test integrate(x^-5//2*(a+b*x)^-1//2, x) == :(-2//3*a^-1*x^-3//2*(a+b*x)^(1/2)+4//3*b*a^-2*x^-1//2*(a+b*x)^(1/2))
@test integrate(x^-7//2*(a+b*x)^-1//2, x) == :(-2//5*a^-1*x^-5//2*(a+b*x)^(1/2)+-16//15*a^-3*b^2*x^-1//2*(a+b*x)^(1/2)+8//15*b*a^-2*x^-3//2*(a+b*x)^(1/2))
@test integrate(x^-9//2*(a+b*x)^-1//2, x) == :(-2//7*a^-1*x^-7//2*(a+b*x)^(1/2)+-16//35*a^-3*b^2*x^-3//2*(a+b*x)^(1/2)+12//35*b*a^-2*x^-5//2*(a+b*x)^(1/2)+32//35*a^-4*b^3*x^-1//2*(a+b*x)^(1/2))
@test integrate(x^5//2*(a+b*x)^-3//2, x) == :(-2*b^-1*x^5//2*(a+b*x)^-1//2+5//2*b^-2*x^3//2*(a+b*x)^(1/2)+15//4*a^2*b^-7//2*arctanh(b^(1/2)*x^(1/2)*(a+b*x)^-1//2)+-15//4*a*b^-3*x^(1/2)*(a+b*x)^(1/2))
@test integrate(x^3//2*(a+b*x)^-3//2, x) == :(-3*a*b^-5//2*arctanh(b^(1/2)*x^(1/2)*(a+b*x)^-1//2)+-2*b^-1*x^3//2*(a+b*x)^-1//2+3*b^-2*x^(1/2)*(a+b*x)^(1/2))
@test integrate(x^(1/2)*(a+b*x)^-3//2, x) == :(2*b^-3//2*arctanh(b^(1/2)*x^(1/2)*(a+b*x)^-1//2)+-2*b^-1*x^(1/2)*(a+b*x)^-1//2)
@test integrate(x^-1//2*(a+b*x)^-3//2, x) == :(2*a^-1*x^(1/2)*(a+b*x)^-1//2)
@test integrate(x^-3//2*(a+b*x)^-3//2, x) == :(-4*a^-2*x^-1//2*(a+b*x)^(1/2)+2*a^-1*x^-1//2*(a+b*x)^-1//2)
@test integrate(x^-5//2*(a+b*x)^-3//2, x) == :(2*a^-1*x^-3//2*(a+b*x)^-1//2+-8//3*a^-2*x^-3//2*(a+b*x)^(1/2)+16//3*b*a^-3*x^-1//2*(a+b*x)^(1/2))
@test integrate(x^-7//2*(a+b*x)^-3//2, x) == :(2*a^-1*x^-5//2*(a+b*x)^-1//2+-12//5*a^-2*x^-5//2*(a+b*x)^(1/2)+-32//5*a^-4*b^2*x^-1//2*(a+b*x)^(1/2)+16//5*b*a^-3*x^-3//2*(a+b*x)^(1/2))
@test integrate(x^5//2*(a+b*x)^-5//2, x) == :(-5*a*b^-7//2*arctanh(b^(1/2)*x^(1/2)*(a+b*x)^-1//2)+5*b^-3*x^(1/2)*(a+b*x)^(1/2)+-10//3*b^-2*x^3//2*(a+b*x)^-1//2+-2//3*b^-1*x^5//2*(a+b*x)^-3//2)
@test integrate(x^3//2*(a+b*x)^-5//2, x) == :(2*b^-5//2*arctanh(b^(1/2)*x^(1/2)*(a+b*x)^-1//2)+-2*b^-2*x^(1/2)*(a+b*x)^-1//2+-2//3*b^-1*x^3//2*(a+b*x)^-3//2)
@test integrate(x^(1/2)*(a+b*x)^-5//2, x) == :(2//3*a^-1*x^3//2*(a+b*x)^-3//2)
@test integrate(x^-1//2*(a+b*x)^-5//2, x) == :(2//3*a^-1*x^(1/2)*(a+b*x)^-3//2+4//3*a^-2*x^(1/2)*(a+b*x)^-1//2)
@test integrate(x^-3//2*(a+b*x)^-5//2, x) == :(-16//3*a^-3*x^-1//2*(a+b*x)^(1/2)+2//3*a^-1*x^-1//2*(a+b*x)^-3//2+8//3*a^-2*x^-1//2*(a+b*x)^-1//2)
@test integrate(x^-5//2*(a+b*x)^-5//2, x) == :(4*a^-2*x^-3//2*(a+b*x)^-1//2+-16//3*a^-3*x^-3//2*(a+b*x)^(1/2)+2//3*a^-1*x^-3//2*(a+b*x)^-3//2+32//3*b*a^-4*x^-1//2*(a+b*x)^(1/2))
@test integrate(x^5//2*(a+-1*b*x)^-1//2, x) == :(-1//3*b^-1*x^5//2*(a+-1*b*x)^(1/2)+5//8*a^3*b^-7//2*arctan(b^(1/2)*x^(1/2)*(a+-1*b*x)^-1//2)+-5//8*a^2*b^-3*x^(1/2)*(a+-1*b*x)^(1/2)+-5//12*a*b^-2*x^3//2*(a+-1*b*x)^(1/2))
@test integrate(x^3//2*(a+-1*b*x)^-1//2, x) == :(-1//2*b^-1*x^3//2*(a+-1*b*x)^(1/2)+3//4*a^2*b^-5//2*arctan(b^(1/2)*x^(1/2)*(a+-1*b*x)^-1//2)+-3//4*a*b^-2*x^(1/2)*(a+-1*b*x)^(1/2))
@test integrate(x^(1/2)*(a+-1*b*x)^-1//2, x) == :(a*b^-3//2*arctan(b^(1/2)*x^(1/2)*(a+-1*b*x)^-1//2)+-1*b^-1*x^(1/2)*(a+-1*b*x)^(1/2))
@test integrate(x^-1//2*(a+-1*b*x)^-1//2, x) == :(2*b^-1//2*arctan(b^(1/2)*x^(1/2)*(a+-1*b*x)^-1//2))
@test integrate(x^-3//2*(a+-1*b*x)^-1//2, x) == :(-2*a^-1*x^-1//2*(a+-1*b*x)^(1/2))
@test integrate(x^-5//2*(a+-1*b*x)^-1//2, x) == :(-2//3*a^-1*x^-3//2*(a+-1*b*x)^(1/2)+-4//3*b*a^-2*x^-1//2*(a+-1*b*x)^(1/2))
@test integrate(x^5//2*(a+-1*b*x)^-3//2, x) == :(2*b^-1*x^5//2*(a+-1*b*x)^-1//2+-15//4*a^2*b^-7//2*arctan(b^(1/2)*x^(1/2)*(a+-1*b*x)^-1//2)+5//2*b^-2*x^3//2*(a+-1*b*x)^(1/2)+15//4*a*b^-3*x^(1/2)*(a+-1*b*x)^(1/2))
@test integrate(x^3//2*(a+-1*b*x)^-3//2, x) == :(-3*a*b^-5//2*arctan(b^(1/2)*x^(1/2)*(a+-1*b*x)^-1//2)+2*b^-1*x^3//2*(a+-1*b*x)^-1//2+3*b^-2*x^(1/2)*(a+-1*b*x)^(1/2))
@test integrate(x^(1/2)*(a+-1*b*x)^-3//2, x) == :(-2*b^-3//2*arctan(b^(1/2)*x^(1/2)*(a+-1*b*x)^-1//2)+2*b^-1*x^(1/2)*(a+-1*b*x)^-1//2)
@test integrate(x^-1//2*(a+-1*b*x)^-3//2, x) == :(2*a^-1*x^(1/2)*(a+-1*b*x)^-1//2)
@test integrate(x^-3//2*(a+-1*b*x)^-3//2, x) == :(-4*a^-2*x^-1//2*(a+-1*b*x)^(1/2)+2*a^-1*x^-1//2*(a+-1*b*x)^-1//2)
@test integrate(x^-5//2*(a+-1*b*x)^-3//2, x) == :(2*a^-1*x^-3//2*(a+-1*b*x)^-1//2+-8//3*a^-2*x^-3//2*(a+-1*b*x)^(1/2)+-16//3*b*a^-3*x^-1//2*(a+-1*b*x)^(1/2))
@test integrate(x^5//2*(a+-1*b*x)^-5//2, x) == :(-5*b^-3*x^(1/2)*(a+-1*b*x)^(1/2)+5*a*b^-7//2*arctan(b^(1/2)*x^(1/2)*(a+-1*b*x)^-1//2)+-10//3*b^-2*x^3//2*(a+-1*b*x)^-1//2+2//3*b^-1*x^5//2*(a+-1*b*x)^-3//2)
@test integrate(x^3//2*(a+-1*b*x)^-5//2, x) == :(2*b^-5//2*arctan(b^(1/2)*x^(1/2)*(a+-1*b*x)^-1//2)+-2*b^-2*x^(1/2)*(a+-1*b*x)^-1//2+2//3*b^-1*x^3//2*(a+-1*b*x)^-3//2)
@test integrate(x^(1/2)*(a+-1*b*x)^-5//2, x) == :(2//3*a^-1*x^3//2*(a+-1*b*x)^-3//2)
@test integrate(x^-1//2*(a+-1*b*x)^-5//2, x) == :(2//3*a^-1*x^(1/2)*(a+-1*b*x)^-3//2+4//3*a^-2*x^(1/2)*(a+-1*b*x)^-1//2)
@test integrate(x^-3//2*(a+-1*b*x)^-5//2, x) == :(-16//3*a^-3*x^-1//2*(a+-1*b*x)^(1/2)+2//3*a^-1*x^-1//2*(a+-1*b*x)^-3//2+8//3*a^-2*x^-1//2*(a+-1*b*x)^-1//2)
@test integrate(x^-5//2*(a+-1*b*x)^-5//2, x) == :(4*a^-2*x^-3//2*(a+-1*b*x)^-1//2+-16//3*a^-3*x^-3//2*(a+-1*b*x)^(1/2)+2//3*a^-1*x^-3//2*(a+-1*b*x)^-3//2+-32//3*b*a^-4*x^-1//2*(a+-1*b*x)^(1/2))
@test integrate(x^5//2*(2+b*x)^-1//2, x) == :(-5*b^-7//2*arcsinh((1/2)*2^(1/2)*b^(1/2)*x^(1/2))+-5//6*b^-2*x^3//2*(2+b*x)^(1/2)+1//3*b^-1*x^5//2*(2+b*x)^(1/2)+5//2*b^-3*x^(1/2)*(2+b*x)^(1/2))
@test integrate(x^3//2*(2+b*x)^-1//2, x) == :(3*b^-5//2*arcsinh((1/2)*2^(1/2)*b^(1/2)*x^(1/2))+(1/2)*b^-1*x^3//2*(2+b*x)^(1/2)+-3//2*b^-2*x^(1/2)*(2+b*x)^(1/2))
@test integrate(x^(1/2)*(2+b*x)^-1//2, x) == :(-2*b^-3//2*arcsinh((1/2)*2^(1/2)*b^(1/2)*x^(1/2))+b^-1*x^(1/2)*(2+b*x)^(1/2))
@test integrate(x^-1//2*(2+b*x)^-1//2, x) == :(2*b^-1//2*arcsinh((1/2)*2^(1/2)*b^(1/2)*x^(1/2)))
@test integrate(x^-3//2*(2+b*x)^-1//2, x) == :(-1*x^-1//2*(2+b*x)^(1/2))
@test integrate(x^-5//2*(2+b*x)^-1//2, x) == :(-1//3*x^-3//2*(2+b*x)^(1/2)+1//3*b*x^-1//2*(2+b*x)^(1/2))
@test integrate(x^-7//2*(2+b*x)^-1//2, x) == :(-1//5*x^-5//2*(2+b*x)^(1/2)+-2//15*b^2*x^-1//2*(2+b*x)^(1/2)+2//15*b*x^-3//2*(2+b*x)^(1/2))
@test integrate(x^-9//2*(2+b*x)^-1//2, x) == :(-1//7*x^-7//2*(2+b*x)^(1/2)+-2//35*b^2*x^-3//2*(2+b*x)^(1/2)+2//35*b^3*x^-1//2*(2+b*x)^(1/2)+3//35*b*x^-5//2*(2+b*x)^(1/2))
@test integrate(x^5//2*(2+b*x)^-3//2, x) == :(15*b^-7//2*arcsinh((1/2)*2^(1/2)*b^(1/2)*x^(1/2))+-2*b^-1*x^5//2*(2+b*x)^-1//2+-15//2*b^-3*x^(1/2)*(2+b*x)^(1/2)+5//2*b^-2*x^3//2*(2+b*x)^(1/2))
@test integrate(x^3//2*(2+b*x)^-3//2, x) == :(-6*b^-5//2*arcsinh((1/2)*2^(1/2)*b^(1/2)*x^(1/2))+-2*b^-1*x^3//2*(2+b*x)^-1//2+3*b^-2*x^(1/2)*(2+b*x)^(1/2))
@test integrate(x^(1/2)*(2+b*x)^-3//2, x) == :(2*b^-3//2*arcsinh((1/2)*2^(1/2)*b^(1/2)*x^(1/2))+-2*b^-1*x^(1/2)*(2+b*x)^-1//2)
@test integrate(x^-1//2*(2+b*x)^-3//2, x) == :(x^(1/2)*(2+b*x)^-1//2)
@test integrate(x^-3//2*(2+b*x)^-3//2, x) == :(x^-1//2*(2+b*x)^-1//2+-1*x^-1//2*(2+b*x)^(1/2))
@test integrate(x^-5//2*(2+b*x)^-3//2, x) == :(x^-3//2*(2+b*x)^-1//2+-2//3*x^-3//2*(2+b*x)^(1/2)+2//3*b*x^-1//2*(2+b*x)^(1/2))
@test integrate(x^-7//2*(2+b*x)^-3//2, x) == :(x^-5//2*(2+b*x)^-1//2+-3//5*x^-5//2*(2+b*x)^(1/2)+-2//5*b^2*x^-1//2*(2+b*x)^(1/2)+2//5*b*x^-3//2*(2+b*x)^(1/2))
@test integrate(x^5//2*(2+b*x)^-5//2, x) == :(-10*b^-7//2*arcsinh((1/2)*2^(1/2)*b^(1/2)*x^(1/2))+5*b^-3*x^(1/2)*(2+b*x)^(1/2)+-10//3*b^-2*x^3//2*(2+b*x)^-1//2+-2//3*b^-1*x^5//2*(2+b*x)^-3//2)
@test integrate(x^3//2*(2+b*x)^-5//2, x) == :(2*b^-5//2*arcsinh((1/2)*2^(1/2)*b^(1/2)*x^(1/2))+-2*b^-2*x^(1/2)*(2+b*x)^-1//2+-2//3*b^-1*x^3//2*(2+b*x)^-3//2)
@test integrate(x^(1/2)*(2+b*x)^-5//2, x) == :(1//3*x^3//2*(2+b*x)^-3//2)
@test integrate(x^-1//2*(2+b*x)^-5//2, x) == :(1//3*x^(1/2)*(2+b*x)^-3//2+1//3*x^(1/2)*(2+b*x)^-1//2)
@test integrate(x^-3//2*(2+b*x)^-5//2, x) == :(-2//3*x^-1//2*(2+b*x)^(1/2)+1//3*x^-1//2*(2+b*x)^-3//2+2//3*x^-1//2*(2+b*x)^-1//2)
@test integrate(x^-5//2*(2+b*x)^-5//2, x) == :(x^-3//2*(2+b*x)^-1//2+-2//3*x^-3//2*(2+b*x)^(1/2)+1//3*x^-3//2*(2+b*x)^-3//2+2//3*b*x^-1//2*(2+b*x)^(1/2))
@test integrate(x^5//2*(2+-1*b*x)^-1//2, x) == :(5*b^-7//2*arcsin((1/2)*2^(1/2)*b^(1/2)*x^(1/2))+-5//2*b^-3*x^(1/2)*(2+-1*b*x)^(1/2)+-5//6*b^-2*x^3//2*(2+-1*b*x)^(1/2)+-1//3*b^-1*x^5//2*(2+-1*b*x)^(1/2))
@test integrate(x^3//2*(2+-1*b*x)^-1//2, x) == :(3*b^-5//2*arcsin((1/2)*2^(1/2)*b^(1/2)*x^(1/2))+-3//2*b^-2*x^(1/2)*(2+-1*b*x)^(1/2)+-1//2*b^-1*x^3//2*(2+-1*b*x)^(1/2))
@test integrate(x^(1/2)*(2+-1*b*x)^-1//2, x) == :(2*b^-3//2*arcsin((1/2)*2^(1/2)*b^(1/2)*x^(1/2))+-1*b^-1*x^(1/2)*(2+-1*b*x)^(1/2))
@test integrate(x^-1//2*(2+-1*b*x)^-1//2, x) == :(2*b^-1//2*arcsin((1/2)*2^(1/2)*b^(1/2)*x^(1/2)))
@test integrate(x^-3//2*(2+-1*b*x)^-1//2, x) == :(-1*x^-1//2*(2+-1*b*x)^(1/2))
@test integrate(x^-5//2*(2+-1*b*x)^-1//2, x) == :(-1//3*x^-3//2*(2+-1*b*x)^(1/2)+-1//3*b*x^-1//2*(2+-1*b*x)^(1/2))
@test integrate(x^5//2*(2+-1*b*x)^-3//2, x) == :(-15*b^-7//2*arcsin((1/2)*2^(1/2)*b^(1/2)*x^(1/2))+2*b^-1*x^5//2*(2+-1*b*x)^-1//2+5//2*b^-2*x^3//2*(2+-1*b*x)^(1/2)+15//2*b^-3*x^(1/2)*(2+-1*b*x)^(1/2))
@test integrate(x^3//2*(2+-1*b*x)^-3//2, x) == :(-6*b^-5//2*arcsin((1/2)*2^(1/2)*b^(1/2)*x^(1/2))+2*b^-1*x^3//2*(2+-1*b*x)^-1//2+3*b^-2*x^(1/2)*(2+-1*b*x)^(1/2))
@test integrate(x^(1/2)*(2+-1*b*x)^-3//2, x) == :(-2*b^-3//2*arcsin((1/2)*2^(1/2)*b^(1/2)*x^(1/2))+2*b^-1*x^(1/2)*(2+-1*b*x)^-1//2)
@test integrate(x^-1//2*(2+-1*b*x)^-3//2, x) == :(x^(1/2)*(2+-1*b*x)^-1//2)
@test integrate(x^-3//2*(2+-1*b*x)^-3//2, x) == :(x^-1//2*(2+-1*b*x)^-1//2+-1*x^-1//2*(2+-1*b*x)^(1/2))
@test integrate(x^-5//2*(2+-1*b*x)^-3//2, x) == :(x^-3//2*(2+-1*b*x)^-1//2+-2//3*x^-3//2*(2+-1*b*x)^(1/2)+-2//3*b*x^-1//2*(2+-1*b*x)^(1/2))
@test integrate(x^5//2*(2+-1*b*x)^-5//2, x) == :(10*b^-7//2*arcsin((1/2)*2^(1/2)*b^(1/2)*x^(1/2))+-5*b^-3*x^(1/2)*(2+-1*b*x)^(1/2)+-10//3*b^-2*x^3//2*(2+-1*b*x)^-1//2+2//3*b^-1*x^5//2*(2+-1*b*x)^-3//2)
@test integrate(x^3//2*(2+-1*b*x)^-5//2, x) == :(2*b^-5//2*arcsin((1/2)*2^(1/2)*b^(1/2)*x^(1/2))+-2*b^-2*x^(1/2)*(2+-1*b*x)^-1//2+2//3*b^-1*x^3//2*(2+-1*b*x)^-3//2)
@test integrate(x^(1/2)*(2+-1*b*x)^-5//2, x) == :(1//3*x^3//2*(2+-1*b*x)^-3//2)
@test integrate(x^-1//2*(2+-1*b*x)^-5//2, x) == :(1//3*x^(1/2)*(2+-1*b*x)^-3//2+1//3*x^(1/2)*(2+-1*b*x)^-1//2)
@test integrate(x^-3//2*(2+-1*b*x)^-5//2, x) == :(-2//3*x^-1//2*(2+-1*b*x)^(1/2)+1//3*x^-1//2*(2+-1*b*x)^-3//2+2//3*x^-1//2*(2+-1*b*x)^-1//2)
@test integrate(x^-5//2*(2+-1*b*x)^-5//2, x) == :(x^-3//2*(2+-1*b*x)^-1//2+-2//3*x^-3//2*(2+-1*b*x)^(1/2)+1//3*x^-3//2*(2+-1*b*x)^-3//2+-2//3*b*x^-1//2*(2+-1*b*x)^(1/2))
@test integrate(x^(1/2)*(1+-1x)^-1//2, x) == :(-1//2*arcsin(1+-2x)+-1*x^(1/2)*(1+-1x)^(1/2))
@test integrate(x^-1//2*(1+-1x)^-1//2, x) == :(-1*arcsin(1+-2x))
@test integrate(x^-1//2*(1+-1*b*x)^-1//2, x) == :(2*b^-1//2*arcsin(b^(1/2)*x^(1/2)))
@test integrate(x^5//3*(a+b*x), x) == :(3//8*a*x^8//3+3//11*b*x^11//3)
@test integrate(x^4//3*(a+b*x), x) == :(3//7*a*x^7//3+3//10*b*x^10//3)
@test integrate(x^2//3*(a+b*x), x) == :(3//5*a*x^5//3+3//8*b*x^8//3)
@test integrate(x^1//3*(a+b*x), x) == :(3//4*a*x^4//3+3//7*b*x^7//3)
@test integrate(x^-1//3*(a+b*x), x) == :(3//2*a*x^2//3+3//5*b*x^5//3)
@test integrate(x^-2//3*(a+b*x), x) == :(3*a*x^1//3+3//4*b*x^4//3)
@test integrate(x^-4//3*(a+b*x), x) == :(-3*a*x^-1//3+3//2*b*x^2//3)
@test integrate(x^-5//3*(a+b*x), x) == :(3*b*x^1//3+-3//2*a*x^-2//3)
@test integrate(x^5//3*(a+b*x)^2, x) == :(3//8*a^2*x^8//3+3//14*b^2*x^14//3+6//11*a*b*x^11//3)
@test integrate(x^4//3*(a+b*x)^2, x) == :(3//7*a^2*x^7//3+3//13*b^2*x^13//3+3//5*a*b*x^10//3)
@test integrate(x^2//3*(a+b*x)^2, x) == :(3//5*a^2*x^5//3+3//11*b^2*x^11//3+3//4*a*b*x^8//3)
@test integrate(x^1//3*(a+b*x)^2, x) == :(3//4*a^2*x^4//3+3//10*b^2*x^10//3+6//7*a*b*x^7//3)
@test integrate(x^-1//3*(a+b*x)^2, x) == :(3//2*a^2*x^2//3+3//8*b^2*x^8//3+6//5*a*b*x^5//3)
@test integrate(x^-2//3*(a+b*x)^2, x) == :(3*a^2*x^1//3+3//7*b^2*x^7//3+3//2*a*b*x^4//3)
@test integrate(x^-4//3*(a+b*x)^2, x) == :(-3*a^2*x^-1//3+3//5*b^2*x^5//3+3*a*b*x^2//3)
@test integrate(x^-5//3*(a+b*x)^2, x) == :(-3//2*a^2*x^-2//3+3//4*b^2*x^4//3+6*a*b*x^1//3)
@test integrate(x^5//3*(a+b*x)^3, x) == :(3//8*a^3*x^8//3+3//17*b^3*x^17//3+9//11*b*a^2*x^11//3+9//14*a*b^2*x^14//3)
@test integrate(x^4//3*(a+b*x)^3, x) == :(3//7*a^3*x^7//3+3//16*b^3*x^16//3+9//10*b*a^2*x^10//3+9//13*a*b^2*x^13//3)
@test integrate(x^2//3*(a+b*x)^3, x) == :(3//5*a^3*x^5//3+3//14*b^3*x^14//3+9//8*b*a^2*x^8//3+9//11*a*b^2*x^11//3)
@test integrate(x^1//3*(a+b*x)^3, x) == :(3//4*a^3*x^4//3+3//13*b^3*x^13//3+9//7*b*a^2*x^7//3+9//10*a*b^2*x^10//3)
@test integrate(x^-1//3*(a+b*x)^3, x) == :(3//2*a^3*x^2//3+3//11*b^3*x^11//3+9//5*b*a^2*x^5//3+9//8*a*b^2*x^8//3)
@test integrate(x^-2//3*(a+b*x)^3, x) == :(3*a^3*x^1//3+3//10*b^3*x^10//3+9//4*b*a^2*x^4//3+9//7*a*b^2*x^7//3)
@test integrate(x^-4//3*(a+b*x)^3, x) == :(-3*a^3*x^-1//3+3//8*b^3*x^8//3+9//2*b*a^2*x^2//3+9//5*a*b^2*x^5//3)
@test integrate(x^-5//3*(a+b*x)^3, x) == :(-3//2*a^3*x^-2//3+3//7*b^3*x^7//3+9*b*a^2*x^1//3+9//4*a*b^2*x^4//3)
@test integrate(x^5//3*(a+b*x)^-1, x) == :(3//5*b^-1*x^5//3+(1/2)*a^5//3*b^-8//3*log(a+b*x)+-3//2*a*b^-2*x^2//3+-3//2*a^5//3*b^-8//3*log(a^1//3+b^1//3*x^1//3)+-1*3^(1/2)*a^5//3*b^-8//3*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*b^1//3*x^1//3)))
@test integrate(x^4//3*(a+b*x)^-1, x) == :(3//4*b^-1*x^4//3+-3*a*b^-2*x^1//3+-1//2*a^4//3*b^-7//3*log(a+b*x)+3//2*a^4//3*b^-7//3*log(a^1//3+b^1//3*x^1//3)+-1*3^(1/2)*a^4//3*b^-7//3*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*b^1//3*x^1//3)))
@test integrate(x^2//3*(a+b*x)^-1, x) == :(3//2*b^-1*x^2//3+-1//2*a^2//3*b^-5//3*log(a+b*x)+3//2*a^2//3*b^-5//3*log(a^1//3+b^1//3*x^1//3)+3^(1/2)*a^2//3*b^-5//3*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*b^1//3*x^1//3)))
@test integrate(x^1//3*(a+b*x)^-1, x) == :(3*b^-1*x^1//3+(1/2)*a^1//3*b^-4//3*log(a+b*x)+-3//2*a^1//3*b^-4//3*log(a^1//3+b^1//3*x^1//3)+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^1//3)))
@test integrate(x^-1//3*(a+b*x)^-1, x) == :((1/2)*a^-1//3*b^-2//3*log(a+b*x)+-3//2*a^-1//3*b^-2//3*log(a^1//3+b^1//3*x^1//3)+-1*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^1//3)))
@test integrate(x^-2//3*(a+b*x)^-1, x) == :(-1//2*a^-2//3*b^-1//3*log(a+b*x)+3//2*a^-2//3*b^-1//3*log(a^1//3+b^1//3*x^1//3)+-1*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^1//3)))
@test integrate(x^-4//3*(a+b*x)^-1, x) == :(-3*a^-1*x^-1//3+-1//2*a^-4//3*b^1//3*log(a+b*x)+3//2*a^-4//3*b^1//3*log(a^1//3+b^1//3*x^1//3)+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^1//3)))
@test integrate(x^-5//3*(a+b*x)^-1, x) == :(-3//2*a^-1*x^-2//3+(1/2)*a^-5//3*b^2//3*log(a+b*x)+-3//2*a^-5//3*b^2//3*log(a^1//3+b^1//3*x^1//3)+3^(1/2)*a^-5//3*b^2//3*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*b^1//3*x^1//3)))
@test integrate(x^5//3*(a+b*x)^-2, x) == :(5//2*b^-2*x^2//3+-1*b^-1*x^5//3*(a+b*x)^-1+-5//6*a^2//3*b^-8//3*log(a+b*x)+5//2*a^2//3*b^-8//3*log(a^1//3+b^1//3*x^1//3)+5//3*3^(1/2)*a^2//3*b^-8//3*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*b^1//3*x^1//3)))
@test integrate(x^4//3*(a+b*x)^-2, x) == :(4*b^-2*x^1//3+-1*b^-1*x^4//3*(a+b*x)^-1+-2*a^1//3*b^-7//3*log(a^1//3+b^1//3*x^1//3)+2//3*a^1//3*b^-7//3*log(a+b*x)+4//3*3^(1/2)*a^1//3*b^-7//3*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*b^1//3*x^1//3)))
@test integrate(x^2//3*(a+b*x)^-2, x) == :(-1*a^-1//3*b^-5//3*log(a^1//3+b^1//3*x^1//3)+-1*b^-1*x^2//3*(a+b*x)^-1+1//3*a^-1//3*b^-5//3*log(a+b*x)+-2//3*3^(1/2)*a^-1//3*b^-5//3*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*b^1//3*x^1//3)))
@test integrate(x^1//3*(a+b*x)^-2, x) == :((1/2)*a^-2//3*b^-4//3*log(a^1//3+b^1//3*x^1//3)+-1*b^-1*x^1//3*(a+b*x)^-1+-1//6*a^-2//3*b^-4//3*log(a+b*x)+-1//3*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^1//3)))
@test integrate(x^-1//3*(a+b*x)^-2, x) == :(a^-1*x^2//3*(a+b*x)^-1+-1//2*a^-4//3*b^-2//3*log(a^1//3+b^1//3*x^1//3)+1//6*a^-4//3*b^-2//3*log(a+b*x)+-1//3*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^1//3)))
@test integrate(x^-2//3*(a+b*x)^-2, x) == :(a^-1*x^1//3*(a+b*x)^-1+a^-5//3*b^-1//3*log(a^1//3+b^1//3*x^1//3)+-1//3*a^-5//3*b^-1//3*log(a+b*x)+-2//3*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^1//3)))
@test integrate(x^-4//3*(a+b*x)^-2, x) == :(-4*a^-2*x^-1//3+a^-1*x^-1//3*(a+b*x)^-1+2*a^-7//3*b^1//3*log(a^1//3+b^1//3*x^1//3)+-2//3*a^-7//3*b^1//3*log(a+b*x)+4//3*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^1//3)))
@test integrate(x^-5//3*(a+b*x)^-2, x) == :(-5//2*a^-2*x^-2//3+a^-1*x^-2//3*(a+b*x)^-1+-5//2*a^-8//3*b^2//3*log(a^1//3+b^1//3*x^1//3)+5//6*a^-8//3*b^2//3*log(a+b*x)+5//3*3^(1/2)*a^-8//3*b^2//3*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*b^1//3*x^1//3)))
@test integrate(x^5//3*(a+b*x)^-3, x) == :(-5//6*a^-1//3*b^-8//3*log(a^1//3+b^1//3*x^1//3)+-5//6*b^-2*x^2//3*(a+b*x)^-1+-1//2*b^-1*x^5//3*(a+b*x)^-2+5//18*a^-1//3*b^-8//3*log(a+b*x)+-5//9*3^(1/2)*a^-1//3*b^-8//3*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*b^1//3*x^1//3)))
@test integrate(x^4//3*(a+b*x)^-3, x) == :(-2//3*b^-2*x^1//3*(a+b*x)^-1+-1//2*b^-1*x^4//3*(a+b*x)^-2+-1//9*a^-2//3*b^-7//3*log(a+b*x)+1//3*a^-2//3*b^-7//3*log(a^1//3+b^1//3*x^1//3)+-2//9*3^(1/2)*a^-2//3*b^-7//3*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*b^1//3*x^1//3)))
@test integrate(x^2//3*(a+b*x)^-3, x) == :(-1//2*b^-1*x^2//3*(a+b*x)^-2+-1//6*a^-4//3*b^-5//3*log(a^1//3+b^1//3*x^1//3)+1//18*a^-4//3*b^-5//3*log(a+b*x)+-1//9*3^(1/2)*a^-4//3*b^-5//3*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*b^1//3*x^1//3))+1//3*a^-1*b^-1*x^2//3*(a+b*x)^-1)
@test integrate(x^1//3*(a+b*x)^-3, x) == :(-1//2*b^-1*x^1//3*(a+b*x)^-2+-1//18*a^-5//3*b^-4//3*log(a+b*x)+1//6*a^-5//3*b^-4//3*log(a^1//3+b^1//3*x^1//3)+-1//9*3^(1/2)*a^-5//3*b^-4//3*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*b^1//3*x^1//3))+1//6*a^-1*b^-1*x^1//3*(a+b*x)^-1)
@test integrate(x^-1//3*(a+b*x)^-3, x) == :((1/2)*a^-1*x^2//3*(a+b*x)^-2+-1//3*a^-7//3*b^-2//3*log(a^1//3+b^1//3*x^1//3)+1//9*a^-7//3*b^-2//3*log(a+b*x)+2//3*a^-2*x^2//3*(a+b*x)^-1+-2//9*3^(1/2)*a^-7//3*b^-2//3*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*b^1//3*x^1//3)))
@test integrate(x^-2//3*(a+b*x)^-3, x) == :((1/2)*a^-1*x^1//3*(a+b*x)^-2+-5//18*a^-8//3*b^-1//3*log(a+b*x)+5//6*a^-2*x^1//3*(a+b*x)^-1+5//6*a^-8//3*b^-1//3*log(a^1//3+b^1//3*x^1//3)+-5//9*3^(1/2)*a^-8//3*b^-1//3*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*b^1//3*x^1//3)))
@test integrate(x^-4//3*(a+b*x)^-3, x) == :(-14//3*a^-3*x^-1//3+(1/2)*a^-1*x^-1//3*(a+b*x)^-2+-7//9*a^-10//3*b^1//3*log(a+b*x)+7//3*a^-10//3*b^1//3*log(a^1//3+b^1//3*x^1//3)+7//6*a^-2*x^-1//3*(a+b*x)^-1+14//9*3^(1/2)*a^-10//3*b^1//3*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*b^1//3*x^1//3)))
@test integrate(x^-5//3*(a+b*x)^-3, x) == :(-10//3*a^-3*x^-2//3+(1/2)*a^-1*x^-2//3*(a+b*x)^-2+-10//3*a^-11//3*b^2//3*log(a^1//3+b^1//3*x^1//3)+4//3*a^-2*x^-2//3*(a+b*x)^-1+10//9*a^-11//3*b^2//3*log(a+b*x)+20//9*3^(1/2)*a^-11//3*b^2//3*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*b^1//3*x^1//3)))
@test integrate((1+x)^-1*(1+-1x)^1//4, x) == :(4*(1+-1x)^1//4+-2*2^1//4*arctan((1/2)*2^3//4*(1+-1x)^1//4)+-2*2^1//4*arctanh((1/2)*2^3//4*(1+-1x)^1//4))
@test integrate(x^m*(a+b*x)^10, x) == :(a^10*x^(1+m)*(1+m)^-1+b^10*x^(11+m)*(11+m)^-1+10*a*b^9*x^(10+m)*(10+m)^-1+10*b*a^9*x^(2+m)*(2+m)^-1+45*a^2*b^8*x^(9+m)*(9+m)^-1+45*a^8*b^2*x^(3+m)*(3+m)^-1+120*a^3*b^7*x^(8+m)*(8+m)^-1+120*a^7*b^3*x^(4+m)*(4+m)^-1+210*a^4*b^6*x^(7+m)*(7+m)^-1+210*a^6*b^4*x^(5+m)*(5+m)^-1+252*a^5*b^5*x^(6+m)*(6+m)^-1)
@test integrate(x^m*(a+b*x)^7, x) == :(a^7*x^(1+m)*(1+m)^-1+b^7*x^(8+m)*(8+m)^-1+7*a*b^6*x^(7+m)*(7+m)^-1+7*b*a^6*x^(2+m)*(2+m)^-1+21*a^2*b^5*x^(6+m)*(6+m)^-1+21*a^5*b^2*x^(3+m)*(3+m)^-1+35*a^3*b^4*x^(5+m)*(5+m)^-1+35*a^4*b^3*x^(4+m)*(4+m)^-1)
@test integrate(x^m*(a+b*x)^3, x) == :(a^3*x^(1+m)*(1+m)^-1+b^3*x^(4+m)*(4+m)^-1+3*a*b^2*x^(3+m)*(3+m)^-1+3*b*a^2*x^(2+m)*(2+m)^-1)
@test integrate(x^m*(a+b*x)^2, x) == :(a^2*x^(1+m)*(1+m)^-1+b^2*x^(3+m)*(3+m)^-1+2*a*b*x^(2+m)*(2+m)^-1)
@test integrate(x^m*(a+b*x), x) == :(a*x^(1+m)*(1+m)^-1+b*x^(2+m)*(2+m)^-1)
@test integrate(x^3*(a+b*x)^n, x) == :(b^-4*(4+n)^-1*(a+b*x)^(4+n)+-1*a^3*b^-4*(1+n)^-1*(a+b*x)^(1+n)+-3*a*b^-4*(3+n)^-1*(a+b*x)^(3+n)+3*a^2*b^-4*(2+n)^-1*(a+b*x)^(2+n))
@test integrate(x^2*(a+b*x)^n, x) == :(b^-3*(3+n)^-1*(a+b*x)^(3+n)+a^2*b^-3*(1+n)^-1*(a+b*x)^(1+n)+-2*a*b^-3*(2+n)^-1*(a+b*x)^(2+n))
@test integrate(x*(a+b*x)^n, x) == :(b^-2*(2+n)^-1*(a+b*x)^(2+n)+-1*a*b^-2*(1+n)^-1*(a+b*x)^(1+n))
@test integrate((a+b*x)^n, x) == :(b^-1*(1+n)^-1*(a+b*x)^(1+n))
@test integrate(x^(-3+n)*(a+b*x)^(-1n), x) == :(-1*a^-1*x^(-2+n)*(2+-1n)^-1*(a+b*x)^(1+-1n)+b*a^-2*x^(-1+n)*(1+-1n)^-1*(2+-1n)^-1*(a+b*x)^(1+-1n))
@test integrate(x^(-2+n)*(a+b*x)^(-1n), x) == :(-1*a^-1*x^(-1+n)*(1+-1n)^-1*(a+b*x)^(1+-1n))
@test integrate(x^(-1+n)*(a+b*x)^(-1+-1n), x) == :(a^-1*n^-1*x^n*(a+b*x)^(-1n))
@test integrate(x^(-3+-1n)*(a+b*x)^n, x) == :(-1*a^-1*x^(-2+-1n)*(2+n)^-1*(a+b*x)^(1+n)+b*a^-2*x^(-1+-1n)*(1+n)^-1*(2+n)^-1*(a+b*x)^(1+n))
@test integrate(x^3*(c*x^2)^(1/2)*(a+b*x), x) == :(1//5*a*x^4*(c*x^2)^(1/2)+1//6*b*x^5*(c*x^2)^(1/2))
@test integrate(x^2*(c*x^2)^(1/2)*(a+b*x), x) == :(1//4*a*x^3*(c*x^2)^(1/2)+1//5*b*x^4*(c*x^2)^(1/2))
@test integrate(x*(c*x^2)^(1/2)*(a+b*x), x) == :(1//3*a*x^2*(c*x^2)^(1/2)+1//4*b*x^3*(c*x^2)^(1/2))
@test integrate((c*x^2)^(1/2)*(a+b*x), x) == :((1/2)*a*x*(c*x^2)^(1/2)+1//3*b*x^2*(c*x^2)^(1/2))
@test integrate(x^-1*(c*x^2)^(1/2)*(a+b*x), x) == :(a*(c*x^2)^(1/2)+(1/2)*b*x*(c*x^2)^(1/2))
@test integrate(x^-2*(c*x^2)^(1/2)*(a+b*x), x) == :(b*(c*x^2)^(1/2)+a*x^-1*(c*x^2)^(1/2)*log(x))
@test integrate(x^-3*(c*x^2)^(1/2)*(a+b*x), x) == :(-1*a*x^-2*(c*x^2)^(1/2)+b*x^-1*(c*x^2)^(1/2)*log(x))
@test integrate(x^-4*(c*x^2)^(1/2)*(a+b*x), x) == :(-1//2*a^-1*x^-3*(c*x^2)^(1/2)*(a+b*x)^2)
@test integrate(x^3*(c*x^2)^3//2*(a+b*x), x) == :(1//7*a*c*x^6*(c*x^2)^(1/2)+1//8*b*c*x^7*(c*x^2)^(1/2))
@test integrate(x^2*(c*x^2)^3//2*(a+b*x), x) == :(1//6*a*c*x^5*(c*x^2)^(1/2)+1//7*b*c*x^6*(c*x^2)^(1/2))
@test integrate(x*(c*x^2)^3//2*(a+b*x), x) == :(1//5*a*c*x^4*(c*x^2)^(1/2)+1//6*b*c*x^5*(c*x^2)^(1/2))
@test integrate((c*x^2)^3//2*(a+b*x), x) == :(1//4*a*c*x^3*(c*x^2)^(1/2)+1//5*b*c*x^4*(c*x^2)^(1/2))
@test integrate(x^-1*(c*x^2)^3//2*(a+b*x), x) == :(1//3*a*c*x^2*(c*x^2)^(1/2)+1//4*b*c*x^3*(c*x^2)^(1/2))
@test integrate(x^-2*(c*x^2)^3//2*(a+b*x), x) == :((1/2)*a*c*x*(c*x^2)^(1/2)+1//3*b*c*x^2*(c*x^2)^(1/2))
@test integrate(x^-3*(c*x^2)^3//2*(a+b*x), x) == :(a*c*(c*x^2)^(1/2)+(1/2)*b*c*x*(c*x^2)^(1/2))
@test integrate(x^-4*(c*x^2)^3//2*(a+b*x), x) == :(b*c*(c*x^2)^(1/2)+a*c*x^-1*(c*x^2)^(1/2)*log(x))
@test integrate(x^3*(c*x^2)^5//2*(a+b*x), x) == :(1//9*a*c^2*x^8*(c*x^2)^(1/2)+1//10*b*c^2*x^9*(c*x^2)^(1/2))
@test integrate(x^2*(c*x^2)^5//2*(a+b*x), x) == :(1//8*a*c^2*x^7*(c*x^2)^(1/2)+1//9*b*c^2*x^8*(c*x^2)^(1/2))
@test integrate(x*(c*x^2)^5//2*(a+b*x), x) == :(1//7*a*c^2*x^6*(c*x^2)^(1/2)+1//8*b*c^2*x^7*(c*x^2)^(1/2))
@test integrate((c*x^2)^5//2*(a+b*x), x) == :(1//6*a*c^2*x^5*(c*x^2)^(1/2)+1//7*b*c^2*x^6*(c*x^2)^(1/2))
@test integrate(x^-1*(c*x^2)^5//2*(a+b*x), x) == :(1//5*a*c^2*x^4*(c*x^2)^(1/2)+1//6*b*c^2*x^5*(c*x^2)^(1/2))
@test integrate(x^-2*(c*x^2)^5//2*(a+b*x), x) == :(1//4*a*c^2*x^3*(c*x^2)^(1/2)+1//5*b*c^2*x^4*(c*x^2)^(1/2))
@test integrate(x^-3*(c*x^2)^5//2*(a+b*x), x) == :(1//3*a*c^2*x^2*(c*x^2)^(1/2)+1//4*b*c^2*x^3*(c*x^2)^(1/2))
@test integrate(x^-4*(c*x^2)^5//2*(a+b*x), x) == :((1/2)*a*x*c^2*(c*x^2)^(1/2)+1//3*b*c^2*x^2*(c*x^2)^(1/2))
@test integrate(x^3*(c*x^2)^-1//2*(a+b*x), x) == :(1//3*a*x^4*(c*x^2)^-1//2+1//4*b*x^5*(c*x^2)^-1//2)
@test integrate(x^2*(c*x^2)^-1//2*(a+b*x), x) == :((1/2)*a*x^3*(c*x^2)^-1//2+1//3*b*x^4*(c*x^2)^-1//2)
@test integrate(x*(c*x^2)^-1//2*(a+b*x), x) == :(a*x^2*(c*x^2)^-1//2+(1/2)*b*x^3*(c*x^2)^-1//2)
@test integrate((c*x^2)^-1//2*(a+b*x), x) == :(b*x^2*(c*x^2)^-1//2+a*x*(c*x^2)^-1//2*log(x))
@test integrate(x^-1*(c*x^2)^-1//2*(a+b*x), x) == :(-1*a*(c*x^2)^-1//2+b*x*(c*x^2)^-1//2*log(x))
@test integrate(x^-2*(c*x^2)^-1//2*(a+b*x), x) == :(-1//2*a^-1*x^-1*(c*x^2)^-1//2*(a+b*x)^2)
@test integrate(x^-3*(c*x^2)^-1//2*(a+b*x), x) == :(-1//2*b*x^-1*(c*x^2)^-1//2+-1//3*a*x^-2*(c*x^2)^-1//2)
@test integrate(x^-4*(c*x^2)^-1//2*(a+b*x), x) == :(-1//3*b*x^-2*(c*x^2)^-1//2+-1//4*a*x^-3*(c*x^2)^-1//2)
@test integrate(x^3*(c*x^2)^-3//2*(a+b*x), x) == :(a*c^-1*x^2*(c*x^2)^-1//2+(1/2)*b*c^-1*x^3*(c*x^2)^-1//2)
@test integrate(x^2*(c*x^2)^-3//2*(a+b*x), x) == :(b*c^-1*x^2*(c*x^2)^-1//2+a*x*c^-1*(c*x^2)^-1//2*log(x))
@test integrate(x*(c*x^2)^-3//2*(a+b*x), x) == :(-1*a*c^-1*(c*x^2)^-1//2+b*x*c^-1*(c*x^2)^-1//2*log(x))
@test integrate((c*x^2)^-3//2*(a+b*x), x) == :(-1//2*a^-1*c^-1*x^-1*(c*x^2)^-1//2*(a+b*x)^2)
@test integrate(x^-1*(c*x^2)^-3//2*(a+b*x), x) == :(-1//2*b*c^-1*x^-1*(c*x^2)^-1//2+-1//3*a*c^-1*x^-2*(c*x^2)^-1//2)
@test integrate(x^-2*(c*x^2)^-3//2*(a+b*x), x) == :(-1//3*b*c^-1*x^-2*(c*x^2)^-1//2+-1//4*a*c^-1*x^-3*(c*x^2)^-1//2)
@test integrate(x^-3*(c*x^2)^-3//2*(a+b*x), x) == :(-1//4*b*c^-1*x^-3*(c*x^2)^-1//2+-1//5*a*c^-1*x^-4*(c*x^2)^-1//2)
@test integrate(x^-4*(c*x^2)^-3//2*(a+b*x), x) == :(-1//5*b*c^-1*x^-4*(c*x^2)^-1//2+-1//6*a*c^-1*x^-5*(c*x^2)^-1//2)
@test integrate(x^3*(c*x^2)^-5//2*(a+b*x), x) == :(-1*a*c^-2*(c*x^2)^-1//2+b*x*c^-2*(c*x^2)^-1//2*log(x))
@test integrate(x^2*(c*x^2)^-5//2*(a+b*x), x) == :(-1//2*a^-1*c^-2*x^-1*(c*x^2)^-1//2*(a+b*x)^2)
@test integrate(x*(c*x^2)^-5//2*(a+b*x), x) == :(-1//2*b*c^-2*x^-1*(c*x^2)^-1//2+-1//3*a*c^-2*x^-2*(c*x^2)^-1//2)
@test integrate((c*x^2)^-5//2*(a+b*x), x) == :(-1//3*b*c^-2*x^-2*(c*x^2)^-1//2+-1//4*a*c^-2*x^-3*(c*x^2)^-1//2)
@test integrate(x^-1*(c*x^2)^-5//2*(a+b*x), x) == :(-1//4*b*c^-2*x^-3*(c*x^2)^-1//2+-1//5*a*c^-2*x^-4*(c*x^2)^-1//2)
@test integrate(x^-2*(c*x^2)^-5//2*(a+b*x), x) == :(-1//5*b*c^-2*x^-4*(c*x^2)^-1//2+-1//6*a*c^-2*x^-5*(c*x^2)^-1//2)
@test integrate(x^-3*(c*x^2)^-5//2*(a+b*x), x) == :(-1//6*b*c^-2*x^-5*(c*x^2)^-1//2+-1//7*a*c^-2*x^-6*(c*x^2)^-1//2)
@test integrate(x^-4*(c*x^2)^-5//2*(a+b*x), x) == :(-1//7*b*c^-2*x^-6*(c*x^2)^-1//2+-1//8*a*c^-2*x^-7*(c*x^2)^-1//2)
@test integrate(x^3*(c*x^2)^(1/2)*(a+b*x)^2, x) == :(1//5*a^2*x^4*(c*x^2)^(1/2)+1//7*b^2*x^6*(c*x^2)^(1/2)+1//3*a*b*x^5*(c*x^2)^(1/2))
@test integrate(x^2*(c*x^2)^(1/2)*(a+b*x)^2, x) == :(1//4*a^2*x^3*(c*x^2)^(1/2)+1//6*b^2*x^5*(c*x^2)^(1/2)+2//5*a*b*x^4*(c*x^2)^(1/2))
@test integrate(x*(c*x^2)^(1/2)*(a+b*x)^2, x) == :(1//3*a^2*x^2*(c*x^2)^(1/2)+1//5*b^2*x^4*(c*x^2)^(1/2)+(1/2)*a*b*x^3*(c*x^2)^(1/2))
@test integrate((c*x^2)^(1/2)*(a+b*x)^2, x) == :((1/2)*x*a^2*(c*x^2)^(1/2)+1//4*b^2*x^3*(c*x^2)^(1/2)+2//3*a*b*x^2*(c*x^2)^(1/2))
@test integrate(x^-1*(c*x^2)^(1/2)*(a+b*x)^2, x) == :(1//3*b^-1*x^-1*(c*x^2)^(1/2)*(a+b*x)^3)
@test integrate(x^-2*(c*x^2)^(1/2)*(a+b*x)^2, x) == :((1/2)*x*b^2*(c*x^2)^(1/2)+2*a*b*(c*x^2)^(1/2)+a^2*x^-1*(c*x^2)^(1/2)*log(x))
@test integrate(x^-3*(c*x^2)^(1/2)*(a+b*x)^2, x) == :(b^2*(c*x^2)^(1/2)+-1*a^2*x^-2*(c*x^2)^(1/2)+2*a*b*x^-1*(c*x^2)^(1/2)*log(x))
@test integrate(x^-4*(c*x^2)^(1/2)*(a+b*x)^2, x) == :(-1//2*a^2*x^-3*(c*x^2)^(1/2)+b^2*x^-1*(c*x^2)^(1/2)*log(x)+-2*a*b*x^-2*(c*x^2)^(1/2))
@test integrate(x^3*(c*x^2)^3//2*(a+b*x)^2, x) == :(1//7*c*a^2*x^6*(c*x^2)^(1/2)+1//9*c*b^2*x^8*(c*x^2)^(1/2)+1//4*a*b*c*x^7*(c*x^2)^(1/2))
@test integrate(x^2*(c*x^2)^3//2*(a+b*x)^2, x) == :(1//6*c*a^2*x^5*(c*x^2)^(1/2)+1//8*c*b^2*x^7*(c*x^2)^(1/2)+2//7*a*b*c*x^6*(c*x^2)^(1/2))
@test integrate(x*(c*x^2)^3//2*(a+b*x)^2, x) == :(1//5*c*a^2*x^4*(c*x^2)^(1/2)+1//7*c*b^2*x^6*(c*x^2)^(1/2)+1//3*a*b*c*x^5*(c*x^2)^(1/2))
@test integrate((c*x^2)^3//2*(a+b*x)^2, x) == :(1//4*c*a^2*x^3*(c*x^2)^(1/2)+1//6*c*b^2*x^5*(c*x^2)^(1/2)+2//5*a*b*c*x^4*(c*x^2)^(1/2))
@test integrate(x^-1*(c*x^2)^3//2*(a+b*x)^2, x) == :(1//3*c*a^2*x^2*(c*x^2)^(1/2)+1//5*c*b^2*x^4*(c*x^2)^(1/2)+(1/2)*a*b*c*x^3*(c*x^2)^(1/2))
@test integrate(x^-2*(c*x^2)^3//2*(a+b*x)^2, x) == :((1/2)*c*x*a^2*(c*x^2)^(1/2)+1//4*c*b^2*x^3*(c*x^2)^(1/2)+2//3*a*b*c*x^2*(c*x^2)^(1/2))
@test integrate(x^-3*(c*x^2)^3//2*(a+b*x)^2, x) == :(1//3*c*b^-1*x^-1*(c*x^2)^(1/2)*(a+b*x)^3)
@test integrate(x^-4*(c*x^2)^3//2*(a+b*x)^2, x) == :((1/2)*c*x*b^2*(c*x^2)^(1/2)+2*a*b*c*(c*x^2)^(1/2)+c*a^2*x^-1*(c*x^2)^(1/2)*log(x))
@test integrate(x*(c*x^2)^5//2*(a+b*x)^2, x) == :(1//7*a^2*c^2*x^6*(c*x^2)^(1/2)+1//9*b^2*c^2*x^8*(c*x^2)^(1/2)+1//4*a*b*c^2*x^7*(c*x^2)^(1/2))
@test integrate((c*x^2)^5//2*(a+b*x)^2, x) == :(1//6*a^2*c^2*x^5*(c*x^2)^(1/2)+1//8*b^2*c^2*x^7*(c*x^2)^(1/2)+2//7*a*b*c^2*x^6*(c*x^2)^(1/2))
@test integrate(x^-1*(c*x^2)^5//2*(a+b*x)^2, x) == :(1//5*a^2*c^2*x^4*(c*x^2)^(1/2)+1//7*b^2*c^2*x^6*(c*x^2)^(1/2)+1//3*a*b*c^2*x^5*(c*x^2)^(1/2))
@test integrate(x^-2*(c*x^2)^5//2*(a+b*x)^2, x) == :(1//4*a^2*c^2*x^3*(c*x^2)^(1/2)+1//6*b^2*c^2*x^5*(c*x^2)^(1/2)+2//5*a*b*c^2*x^4*(c*x^2)^(1/2))
@test integrate(x^-3*(c*x^2)^5//2*(a+b*x)^2, x) == :(1//3*a^2*c^2*x^2*(c*x^2)^(1/2)+1//5*b^2*c^2*x^4*(c*x^2)^(1/2)+(1/2)*a*b*c^2*x^3*(c*x^2)^(1/2))
@test integrate(x^-4*(c*x^2)^5//2*(a+b*x)^2, x) == :((1/2)*x*a^2*c^2*(c*x^2)^(1/2)+1//4*b^2*c^2*x^3*(c*x^2)^(1/2)+2//3*a*b*c^2*x^2*(c*x^2)^(1/2))
@test integrate(x^-5*(c*x^2)^5//2*(a+b*x)^2, x) == :(1//3*b^-1*c^2*x^-1*(c*x^2)^(1/2)*(a+b*x)^3)
@test integrate(x^-6*(c*x^2)^5//2*(a+b*x)^2, x) == :((1/2)*x*b^2*c^2*(c*x^2)^(1/2)+2*a*b*c^2*(c*x^2)^(1/2)+a^2*c^2*x^-1*(c*x^2)^(1/2)*log(x))
@test integrate(x^3*(c*x^2)^-1//2*(a+b*x)^2, x) == :(1//3*a^2*x^4*(c*x^2)^-1//2+1//5*b^2*x^6*(c*x^2)^-1//2+(1/2)*a*b*x^5*(c*x^2)^-1//2)
@test integrate(x^2*(c*x^2)^-1//2*(a+b*x)^2, x) == :((1/2)*a^2*x^3*(c*x^2)^-1//2+1//4*b^2*x^5*(c*x^2)^-1//2+2//3*a*b*x^4*(c*x^2)^-1//2)
@test integrate(x*(c*x^2)^-1//2*(a+b*x)^2, x) == :(1//3*x*b^-1*(c*x^2)^-1//2*(a+b*x)^3)
@test integrate((c*x^2)^-1//2*(a+b*x)^2, x) == :((1/2)*b^2*x^3*(c*x^2)^-1//2+x*a^2*(c*x^2)^-1//2*log(x)+2*a*b*x^2*(c*x^2)^-1//2)
@test integrate(x^-1*(c*x^2)^-1//2*(a+b*x)^2, x) == :(-1*a^2*(c*x^2)^-1//2+b^2*x^2*(c*x^2)^-1//2+2*a*b*x*(c*x^2)^-1//2*log(x))
@test integrate(x^-2*(c*x^2)^-1//2*(a+b*x)^2, x) == :(-2*a*b*(c*x^2)^-1//2+-1//2*a^2*x^-1*(c*x^2)^-1//2+x*b^2*(c*x^2)^-1//2*log(x))
@test integrate(x^-3*(c*x^2)^-1//2*(a+b*x)^2, x) == :(-1//3*a^-1*x^-2*(c*x^2)^-1//2*(a+b*x)^3)
@test integrate(x^-4*(c*x^2)^-1//2*(a+b*x)^2, x) == :(-1//2*b^2*x^-1*(c*x^2)^-1//2+-1//4*a^2*x^-3*(c*x^2)^-1//2+-2//3*a*b*x^-2*(c*x^2)^-1//2)
@test integrate(x^3*(c*x^2)^-3//2*(a+b*x)^2, x) == :(1//3*x*b^-1*c^-1*(c*x^2)^-1//2*(a+b*x)^3)
@test integrate(x^2*(c*x^2)^-3//2*(a+b*x)^2, x) == :((1/2)*b^2*c^-1*x^3*(c*x^2)^-1//2+x*a^2*c^-1*(c*x^2)^-1//2*log(x)+2*a*b*c^-1*x^2*(c*x^2)^-1//2)
@test integrate(x*(c*x^2)^-3//2*(a+b*x)^2, x) == :(-1*a^2*c^-1*(c*x^2)^-1//2+b^2*c^-1*x^2*(c*x^2)^-1//2+2*a*b*x*c^-1*(c*x^2)^-1//2*log(x))
@test integrate((c*x^2)^-3//2*(a+b*x)^2, x) == :(-2*a*b*c^-1*(c*x^2)^-1//2+-1//2*a^2*c^-1*x^-1*(c*x^2)^-1//2+x*b^2*c^-1*(c*x^2)^-1//2*log(x))
@test integrate(x^-1*(c*x^2)^-3//2*(a+b*x)^2, x) == :(-1//3*a^-1*c^-1*x^-2*(c*x^2)^-1//2*(a+b*x)^3)
@test integrate(x^-2*(c*x^2)^-3//2*(a+b*x)^2, x) == :(-1//2*b^2*c^-1*x^-1*(c*x^2)^-1//2+-1//4*a^2*c^-1*x^-3*(c*x^2)^-1//2+-2//3*a*b*c^-1*x^-2*(c*x^2)^-1//2)
@test integrate(x^-3*(c*x^2)^-3//2*(a+b*x)^2, x) == :(-1//3*b^2*c^-1*x^-2*(c*x^2)^-1//2+-1//5*a^2*c^-1*x^-4*(c*x^2)^-1//2+-1//2*a*b*c^-1*x^-3*(c*x^2)^-1//2)
@test integrate(x^-4*(c*x^2)^-3//2*(a+b*x)^2, x) == :(-1//4*b^2*c^-1*x^-3*(c*x^2)^-1//2+-1//6*a^2*c^-1*x^-5*(c*x^2)^-1//2+-2//5*a*b*c^-1*x^-4*(c*x^2)^-1//2)
@test integrate(x^3*(c*x^2)^-5//2*(a+b*x)^2, x) == :(-1*a^2*c^-2*(c*x^2)^-1//2+b^2*c^-2*x^2*(c*x^2)^-1//2+2*a*b*x*c^-2*(c*x^2)^-1//2*log(x))
@test integrate(x^2*(c*x^2)^-5//2*(a+b*x)^2, x) == :(-2*a*b*c^-2*(c*x^2)^-1//2+-1//2*a^2*c^-2*x^-1*(c*x^2)^-1//2+x*b^2*c^-2*(c*x^2)^-1//2*log(x))
@test integrate(x*(c*x^2)^-5//2*(a+b*x)^2, x) == :(-1//3*a^-1*c^-2*x^-2*(c*x^2)^-1//2*(a+b*x)^3)
@test integrate((c*x^2)^-5//2*(a+b*x)^2, x) == :(-1//2*b^2*c^-2*x^-1*(c*x^2)^-1//2+-1//4*a^2*c^-2*x^-3*(c*x^2)^-1//2+-2//3*a*b*c^-2*x^-2*(c*x^2)^-1//2)
@test integrate(x^-1*(c*x^2)^-5//2*(a+b*x)^2, x) == :(-1//3*b^2*c^-2*x^-2*(c*x^2)^-1//2+-1//5*a^2*c^-2*x^-4*(c*x^2)^-1//2+-1//2*a*b*c^-2*x^-3*(c*x^2)^-1//2)
@test integrate(x^-2*(c*x^2)^-5//2*(a+b*x)^2, x) == :(-1//4*b^2*c^-2*x^-3*(c*x^2)^-1//2+-1//6*a^2*c^-2*x^-5*(c*x^2)^-1//2+-2//5*a*b*c^-2*x^-4*(c*x^2)^-1//2)
@test integrate(x^-3*(c*x^2)^-5//2*(a+b*x)^2, x) == :(-1//5*b^2*c^-2*x^-4*(c*x^2)^-1//2+-1//7*a^2*c^-2*x^-6*(c*x^2)^-1//2+-1//3*a*b*c^-2*x^-5*(c*x^2)^-1//2)
@test integrate(x^-4*(c*x^2)^-5//2*(a+b*x)^2, x) == :(-1//6*b^2*c^-2*x^-5*(c*x^2)^-1//2+-1//8*a^2*c^-2*x^-7*(c*x^2)^-1//2+-2//7*a*b*c^-2*x^-6*(c*x^2)^-1//2)
@test integrate(x^3*(c*x^2)^(1/2)*(a+b*x)^-1, x) == :(-1*a^3*b^-4*(c*x^2)^(1/2)+1//4*b^-1*x^3*(c*x^2)^(1/2)+(1/2)*x*a^2*b^-3*(c*x^2)^(1/2)+-1//3*a*b^-2*x^2*(c*x^2)^(1/2)+a^4*b^-5*x^-1*(c*x^2)^(1/2)*log(a+b*x))
@test integrate(x^2*(c*x^2)^(1/2)*(a+b*x)^-1, x) == :(a^2*b^-3*(c*x^2)^(1/2)+1//3*b^-1*x^2*(c*x^2)^(1/2)+-1//2*a*x*b^-2*(c*x^2)^(1/2)+-1*a^3*b^-4*x^-1*(c*x^2)^(1/2)*log(a+b*x))
@test integrate(x*(c*x^2)^(1/2)*(a+b*x)^-1, x) == :((1/2)*x*b^-1*(c*x^2)^(1/2)+-1*a*b^-2*(c*x^2)^(1/2)+a^2*b^-3*x^-1*(c*x^2)^(1/2)*log(a+b*x))
@test integrate((c*x^2)^(1/2)*(a+b*x)^-1, x) == :(b^-1*(c*x^2)^(1/2)+-1*a*b^-2*x^-1*(c*x^2)^(1/2)*log(a+b*x))
@test integrate(x^-1*(c*x^2)^(1/2)*(a+b*x)^-1, x) == :(b^-1*x^-1*(c*x^2)^(1/2)*log(a+b*x))
@test integrate(x^-2*(c*x^2)^(1/2)*(a+b*x)^-1, x) == :(a^-1*x^-1*(c*x^2)^(1/2)*log(x)+-1*a^-1*x^-1*(c*x^2)^(1/2)*log(a+b*x))
@test integrate(x^-3*(c*x^2)^(1/2)*(a+b*x)^-1, x) == :(-1*a^-1*x^-2*(c*x^2)^(1/2)+b*a^-2*x^-1*(c*x^2)^(1/2)*log(a+b*x)+-1*b*a^-2*x^-1*(c*x^2)^(1/2)*log(x))
@test integrate(x^-4*(c*x^2)^(1/2)*(a+b*x)^-1, x) == :(-1//2*a^-1*x^-3*(c*x^2)^(1/2)+b*a^-2*x^-2*(c*x^2)^(1/2)+a^-3*b^2*x^-1*(c*x^2)^(1/2)*log(x)+-1*a^-3*b^2*x^-1*(c*x^2)^(1/2)*log(a+b*x))
@test integrate(x*(c*x^2)^3//2*(a+b*x)^-1, x) == :(-1*c*a^3*b^-4*(c*x^2)^(1/2)+1//4*c*b^-1*x^3*(c*x^2)^(1/2)+(1/2)*c*x*a^2*b^-3*(c*x^2)^(1/2)+-1//3*a*c*b^-2*x^2*(c*x^2)^(1/2)+c*a^4*b^-5*x^-1*(c*x^2)^(1/2)*log(a+b*x))
@test integrate((c*x^2)^3//2*(a+b*x)^-1, x) == :(c*a^2*b^-3*(c*x^2)^(1/2)+1//3*c*b^-1*x^2*(c*x^2)^(1/2)+-1//2*a*c*x*b^-2*(c*x^2)^(1/2)+-1*c*a^3*b^-4*x^-1*(c*x^2)^(1/2)*log(a+b*x))
@test integrate(x^-1*(c*x^2)^3//2*(a+b*x)^-1, x) == :((1/2)*c*x*b^-1*(c*x^2)^(1/2)+-1*a*c*b^-2*(c*x^2)^(1/2)+c*a^2*b^-3*x^-1*(c*x^2)^(1/2)*log(a+b*x))
@test integrate(x^-2*(c*x^2)^3//2*(a+b*x)^-1, x) == :(c*b^-1*(c*x^2)^(1/2)+-1*a*c*b^-2*x^-1*(c*x^2)^(1/2)*log(a+b*x))
@test integrate(x^-3*(c*x^2)^3//2*(a+b*x)^-1, x) == :(c*b^-1*x^-1*(c*x^2)^(1/2)*log(a+b*x))
@test integrate(x^-4*(c*x^2)^3//2*(a+b*x)^-1, x) == :(c*a^-1*x^-1*(c*x^2)^(1/2)*log(x)+-1*c*a^-1*x^-1*(c*x^2)^(1/2)*log(a+b*x))
@test integrate(x^-5*(c*x^2)^3//2*(a+b*x)^-1, x) == :(-1*c*a^-1*x^-2*(c*x^2)^(1/2)+b*c*a^-2*x^-1*(c*x^2)^(1/2)*log(a+b*x)+-1*b*c*a^-2*x^-1*(c*x^2)^(1/2)*log(x))
@test integrate(x^-6*(c*x^2)^3//2*(a+b*x)^-1, x) == :(-1//2*c*a^-1*x^-3*(c*x^2)^(1/2)+b*c*a^-2*x^-2*(c*x^2)^(1/2)+c*a^-3*b^2*x^-1*(c*x^2)^(1/2)*log(x)+-1*c*a^-3*b^2*x^-1*(c*x^2)^(1/2)*log(a+b*x))
@test integrate(x^-7*(c*x^2)^3//2*(a+b*x)^-1, x) == :(-1//3*c*a^-1*x^-4*(c*x^2)^(1/2)+(1/2)*b*c*a^-2*x^-3*(c*x^2)^(1/2)+-1*c*a^-3*b^2*x^-2*(c*x^2)^(1/2)+c*a^-4*b^3*x^-1*(c*x^2)^(1/2)*log(a+b*x)+-1*c*a^-4*b^3*x^-1*(c*x^2)^(1/2)*log(x))
@test integrate((c*x^2)^5//2*(a+b*x)^-1, x) == :(a^4*b^-5*c^2*(c*x^2)^(1/2)+1//5*b^-1*c^2*x^4*(c*x^2)^(1/2)+-1//2*x*a^3*b^-4*c^2*(c*x^2)^(1/2)+-1//4*a*b^-2*c^2*x^3*(c*x^2)^(1/2)+1//3*a^2*b^-3*c^2*x^2*(c*x^2)^(1/2)+-1*a^5*b^-6*c^2*x^-1*(c*x^2)^(1/2)*log(a+b*x))
@test integrate(x^-1*(c*x^2)^5//2*(a+b*x)^-1, x) == :(-1*a^3*b^-4*c^2*(c*x^2)^(1/2)+1//4*b^-1*c^2*x^3*(c*x^2)^(1/2)+(1/2)*x*a^2*b^-3*c^2*(c*x^2)^(1/2)+-1//3*a*b^-2*c^2*x^2*(c*x^2)^(1/2)+a^4*b^-5*c^2*x^-1*(c*x^2)^(1/2)*log(a+b*x))
@test integrate(x^-2*(c*x^2)^5//2*(a+b*x)^-1, x) == :(a^2*b^-3*c^2*(c*x^2)^(1/2)+1//3*b^-1*c^2*x^2*(c*x^2)^(1/2)+-1//2*a*x*b^-2*c^2*(c*x^2)^(1/2)+-1*a^3*b^-4*c^2*x^-1*(c*x^2)^(1/2)*log(a+b*x))
@test integrate(x^-3*(c*x^2)^5//2*(a+b*x)^-1, x) == :((1/2)*x*b^-1*c^2*(c*x^2)^(1/2)+-1*a*b^-2*c^2*(c*x^2)^(1/2)+a^2*b^-3*c^2*x^-1*(c*x^2)^(1/2)*log(a+b*x))
@test integrate(x^-4*(c*x^2)^5//2*(a+b*x)^-1, x) == :(b^-1*c^2*(c*x^2)^(1/2)+-1*a*b^-2*c^2*x^-1*(c*x^2)^(1/2)*log(a+b*x))
@test integrate(x^-5*(c*x^2)^5//2*(a+b*x)^-1, x) == :(b^-1*c^2*x^-1*(c*x^2)^(1/2)*log(a+b*x))
@test integrate(x^-6*(c*x^2)^5//2*(a+b*x)^-1, x) == :(a^-1*c^2*x^-1*(c*x^2)^(1/2)*log(x)+-1*a^-1*c^2*x^-1*(c*x^2)^(1/2)*log(a+b*x))
@test integrate(x^-7*(c*x^2)^5//2*(a+b*x)^-1, x) == :(-1*a^-1*c^2*x^-2*(c*x^2)^(1/2)+b*a^-2*c^2*x^-1*(c*x^2)^(1/2)*log(a+b*x)+-1*b*a^-2*c^2*x^-1*(c*x^2)^(1/2)*log(x))
@test integrate(x^4*(c*x^2)^-1//2*(a+b*x)^-1, x) == :(1//3*b^-1*x^4*(c*x^2)^-1//2+a^2*b^-3*x^2*(c*x^2)^-1//2+-1//2*a*b^-2*x^3*(c*x^2)^-1//2+-1*x*a^3*b^-4*(c*x^2)^-1//2*log(a+b*x))
@test integrate(x^3*(c*x^2)^-1//2*(a+b*x)^-1, x) == :((1/2)*b^-1*x^3*(c*x^2)^-1//2+-1*a*b^-2*x^2*(c*x^2)^-1//2+x*a^2*b^-3*(c*x^2)^-1//2*log(a+b*x))
@test integrate(x^2*(c*x^2)^-1//2*(a+b*x)^-1, x) == :(b^-1*x^2*(c*x^2)^-1//2+-1*a*x*b^-2*(c*x^2)^-1//2*log(a+b*x))
@test integrate(x*(c*x^2)^-1//2*(a+b*x)^-1, x) == :(x*b^-1*(c*x^2)^-1//2*log(a+b*x))
@test integrate((c*x^2)^-1//2*(a+b*x)^-1, x) == :(x*a^-1*(c*x^2)^-1//2*log(x)+-1*x*a^-1*(c*x^2)^-1//2*log(a+b*x))
@test integrate(x^-1*(c*x^2)^-1//2*(a+b*x)^-1, x) == :(-1*a^-1*(c*x^2)^-1//2+b*x*a^-2*(c*x^2)^-1//2*log(a+b*x)+-1*b*x*a^-2*(c*x^2)^-1//2*log(x))
@test integrate(x^-2*(c*x^2)^-1//2*(a+b*x)^-1, x) == :(b*a^-2*(c*x^2)^-1//2+-1//2*a^-1*x^-1*(c*x^2)^-1//2+x*a^-3*b^2*(c*x^2)^-1//2*log(x)+-1*x*a^-3*b^2*(c*x^2)^-1//2*log(a+b*x))
@test integrate(x^-3*(c*x^2)^-1//2*(a+b*x)^-1, x) == :(-1*a^-3*b^2*(c*x^2)^-1//2+-1//3*a^-1*x^-2*(c*x^2)^-1//2+(1/2)*b*a^-2*x^-1*(c*x^2)^-1//2+x*a^-4*b^3*(c*x^2)^-1//2*log(a+b*x)+-1*x*a^-4*b^3*(c*x^2)^-1//2*log(x))
@test integrate(x^6*(c*x^2)^-3//2*(a+b*x)^-1, x) == :(1//3*b^-1*c^-1*x^4*(c*x^2)^-1//2+a^2*b^-3*c^-1*x^2*(c*x^2)^-1//2+-1//2*a*b^-2*c^-1*x^3*(c*x^2)^-1//2+-1*x*a^3*b^-4*c^-1*(c*x^2)^-1//2*log(a+b*x))
@test integrate(x^5*(c*x^2)^-3//2*(a+b*x)^-1, x) == :((1/2)*b^-1*c^-1*x^3*(c*x^2)^-1//2+-1*a*b^-2*c^-1*x^2*(c*x^2)^-1//2+x*a^2*b^-3*c^-1*(c*x^2)^-1//2*log(a+b*x))
@test integrate(x^4*(c*x^2)^-3//2*(a+b*x)^-1, x) == :(b^-1*c^-1*x^2*(c*x^2)^-1//2+-1*a*x*b^-2*c^-1*(c*x^2)^-1//2*log(a+b*x))
@test integrate(x^3*(c*x^2)^-3//2*(a+b*x)^-1, x) == :(x*b^-1*c^-1*(c*x^2)^-1//2*log(a+b*x))
@test integrate(x^2*(c*x^2)^-3//2*(a+b*x)^-1, x) == :(x*a^-1*c^-1*(c*x^2)^-1//2*log(x)+-1*x*a^-1*c^-1*(c*x^2)^-1//2*log(a+b*x))
@test integrate(x*(c*x^2)^-3//2*(a+b*x)^-1, x) == :(-1*a^-1*c^-1*(c*x^2)^-1//2+b*x*a^-2*c^-1*(c*x^2)^-1//2*log(a+b*x)+-1*b*x*a^-2*c^-1*(c*x^2)^-1//2*log(x))
@test integrate((c*x^2)^-3//2*(a+b*x)^-1, x) == :(b*a^-2*c^-1*(c*x^2)^-1//2+-1//2*a^-1*c^-1*x^-1*(c*x^2)^-1//2+x*a^-3*b^2*c^-1*(c*x^2)^-1//2*log(x)+-1*x*a^-3*b^2*c^-1*(c*x^2)^-1//2*log(a+b*x))
@test integrate(x^-1*(c*x^2)^-3//2*(a+b*x)^-1, x) == :(-1*a^-3*b^2*c^-1*(c*x^2)^-1//2+-1//3*a^-1*c^-1*x^-2*(c*x^2)^-1//2+(1/2)*b*a^-2*c^-1*x^-1*(c*x^2)^-1//2+x*a^-4*b^3*c^-1*(c*x^2)^-1//2*log(a+b*x)+-1*x*a^-4*b^3*c^-1*(c*x^2)^-1//2*log(x))
@test integrate(x^3*(c*x^2)^(1/2)*(a+b*x)^-2, x) == :(3*a^2*b^-4*(c*x^2)^(1/2)+1//3*b^-2*x^2*(c*x^2)^(1/2)+-1*a*x*b^-3*(c*x^2)^(1/2)+-1*a^4*b^-5*x^-1*(c*x^2)^(1/2)*(a+b*x)^-1+-4*a^3*b^-5*x^-1*(c*x^2)^(1/2)*log(a+b*x))
@test integrate(x^2*(c*x^2)^(1/2)*(a+b*x)^-2, x) == :((1/2)*x*b^-2*(c*x^2)^(1/2)+-2*a*b^-3*(c*x^2)^(1/2)+a^3*b^-4*x^-1*(c*x^2)^(1/2)*(a+b*x)^-1+3*a^2*b^-4*x^-1*(c*x^2)^(1/2)*log(a+b*x))
@test integrate(x*(c*x^2)^(1/2)*(a+b*x)^-2, x) == :(b^-2*(c*x^2)^(1/2)+-1*a^2*b^-3*x^-1*(c*x^2)^(1/2)*(a+b*x)^-1+-2*a*b^-3*x^-1*(c*x^2)^(1/2)*log(a+b*x))
@test integrate((c*x^2)^(1/2)*(a+b*x)^-2, x) == :(b^-2*x^-1*(c*x^2)^(1/2)*log(a+b*x)+a*b^-2*x^-1*(c*x^2)^(1/2)*(a+b*x)^-1)
@test integrate(x^-1*(c*x^2)^(1/2)*(a+b*x)^-2, x) == :(-1*b^-1*x^-1*(c*x^2)^(1/2)*(a+b*x)^-1)
@test integrate(x^-2*(c*x^2)^(1/2)*(a+b*x)^-2, x) == :(a^-1*x^-1*(c*x^2)^(1/2)*(a+b*x)^-1+a^-2*x^-1*(c*x^2)^(1/2)*log(x)+-1*a^-2*x^-1*(c*x^2)^(1/2)*log(a+b*x))
@test integrate(x^-3*(c*x^2)^(1/2)*(a+b*x)^-2, x) == :(-1*a^-2*x^-2*(c*x^2)^(1/2)+-1*b*a^-2*x^-1*(c*x^2)^(1/2)*(a+b*x)^-1+-2*b*a^-3*x^-1*(c*x^2)^(1/2)*log(x)+2*b*a^-3*x^-1*(c*x^2)^(1/2)*log(a+b*x))
@test integrate(x^-4*(c*x^2)^(1/2)*(a+b*x)^-2, x) == :(-1//2*a^-2*x^-3*(c*x^2)^(1/2)+2*b*a^-3*x^-2*(c*x^2)^(1/2)+a^-3*b^2*x^-1*(c*x^2)^(1/2)*(a+b*x)^-1+-3*a^-4*b^2*x^-1*(c*x^2)^(1/2)*log(a+b*x)+3*a^-4*b^2*x^-1*(c*x^2)^(1/2)*log(x))
@test integrate(x*(c*x^2)^3//2*(a+b*x)^-2, x) == :(3*c*a^2*b^-4*(c*x^2)^(1/2)+1//3*c*b^-2*x^2*(c*x^2)^(1/2)+-1*a*c*x*b^-3*(c*x^2)^(1/2)+-1*c*a^4*b^-5*x^-1*(c*x^2)^(1/2)*(a+b*x)^-1+-4*c*a^3*b^-5*x^-1*(c*x^2)^(1/2)*log(a+b*x))
@test integrate((c*x^2)^3//2*(a+b*x)^-2, x) == :((1/2)*c*x*b^-2*(c*x^2)^(1/2)+-2*a*c*b^-3*(c*x^2)^(1/2)+c*a^3*b^-4*x^-1*(c*x^2)^(1/2)*(a+b*x)^-1+3*c*a^2*b^-4*x^-1*(c*x^2)^(1/2)*log(a+b*x))
@test integrate(x^-1*(c*x^2)^3//2*(a+b*x)^-2, x) == :(c*b^-2*(c*x^2)^(1/2)+-1*c*a^2*b^-3*x^-1*(c*x^2)^(1/2)*(a+b*x)^-1+-2*a*c*b^-3*x^-1*(c*x^2)^(1/2)*log(a+b*x))
@test integrate(x^-2*(c*x^2)^3//2*(a+b*x)^-2, x) == :(c*b^-2*x^-1*(c*x^2)^(1/2)*log(a+b*x)+a*c*b^-2*x^-1*(c*x^2)^(1/2)*(a+b*x)^-1)
@test integrate(x^-3*(c*x^2)^3//2*(a+b*x)^-2, x) == :(-1*c*b^-1*x^-1*(c*x^2)^(1/2)*(a+b*x)^-1)
@test integrate(x^-4*(c*x^2)^3//2*(a+b*x)^-2, x) == :(c*a^-1*x^-1*(c*x^2)^(1/2)*(a+b*x)^-1+c*a^-2*x^-1*(c*x^2)^(1/2)*log(x)+-1*c*a^-2*x^-1*(c*x^2)^(1/2)*log(a+b*x))
@test integrate(x^-5*(c*x^2)^3//2*(a+b*x)^-2, x) == :(-1*c*a^-2*x^-2*(c*x^2)^(1/2)+-1*b*c*a^-2*x^-1*(c*x^2)^(1/2)*(a+b*x)^-1+-2*b*c*a^-3*x^-1*(c*x^2)^(1/2)*log(x)+2*b*c*a^-3*x^-1*(c*x^2)^(1/2)*log(a+b*x))
@test integrate(x^-6*(c*x^2)^3//2*(a+b*x)^-2, x) == :(-1//2*c*a^-2*x^-3*(c*x^2)^(1/2)+2*b*c*a^-3*x^-2*(c*x^2)^(1/2)+c*a^-3*b^2*x^-1*(c*x^2)^(1/2)*(a+b*x)^-1+-3*c*a^-4*b^2*x^-1*(c*x^2)^(1/2)*log(a+b*x)+3*c*a^-4*b^2*x^-1*(c*x^2)^(1/2)*log(x))
@test integrate(x^5*(c*x^2)^-1//2*(a+b*x)^-2, x) == :(1//3*b^-2*x^4*(c*x^2)^-1//2+-1*a*b^-3*x^3*(c*x^2)^-1//2+3*a^2*b^-4*x^2*(c*x^2)^-1//2+-1*x*a^4*b^-5*(c*x^2)^-1//2*(a+b*x)^-1+-4*x*a^3*b^-5*(c*x^2)^-1//2*log(a+b*x))
@test integrate(x^4*(c*x^2)^-1//2*(a+b*x)^-2, x) == :((1/2)*b^-2*x^3*(c*x^2)^-1//2+-2*a*b^-3*x^2*(c*x^2)^-1//2+x*a^3*b^-4*(c*x^2)^-1//2*(a+b*x)^-1+3*x*a^2*b^-4*(c*x^2)^-1//2*log(a+b*x))
@test integrate(x^3*(c*x^2)^-1//2*(a+b*x)^-2, x) == :(b^-2*x^2*(c*x^2)^-1//2+-1*x*a^2*b^-3*(c*x^2)^-1//2*(a+b*x)^-1+-2*a*x*b^-3*(c*x^2)^-1//2*log(a+b*x))
@test integrate(x^2*(c*x^2)^-1//2*(a+b*x)^-2, x) == :(x*b^-2*(c*x^2)^-1//2*log(a+b*x)+a*x*b^-2*(c*x^2)^-1//2*(a+b*x)^-1)
@test integrate(x*(c*x^2)^-1//2*(a+b*x)^-2, x) == :(-1*x*b^-1*(c*x^2)^-1//2*(a+b*x)^-1)
@test integrate((c*x^2)^-1//2*(a+b*x)^-2, x) == :(x*a^-1*(c*x^2)^-1//2*(a+b*x)^-1+x*a^-2*(c*x^2)^-1//2*log(x)+-1*x*a^-2*(c*x^2)^-1//2*log(a+b*x))
@test integrate(x^-1*(c*x^2)^-1//2*(a+b*x)^-2, x) == :(-1*a^-2*(c*x^2)^-1//2+-1*b*x*a^-2*(c*x^2)^-1//2*(a+b*x)^-1+-2*b*x*a^-3*(c*x^2)^-1//2*log(x)+2*b*x*a^-3*(c*x^2)^-1//2*log(a+b*x))
@test integrate(x^-2*(c*x^2)^-1//2*(a+b*x)^-2, x) == :(2*b*a^-3*(c*x^2)^-1//2+-1//2*a^-2*x^-1*(c*x^2)^-1//2+x*a^-3*b^2*(c*x^2)^-1//2*(a+b*x)^-1+-3*x*a^-4*b^2*(c*x^2)^-1//2*log(a+b*x)+3*x*a^-4*b^2*(c*x^2)^-1//2*log(x))
@test integrate(x^5*(c*x^2)^-3//2*(a+b*x)^-2, x) == :(b^-2*c^-1*x^2*(c*x^2)^-1//2+-1*x*a^2*b^-3*c^-1*(c*x^2)^-1//2*(a+b*x)^-1+-2*a*x*b^-3*c^-1*(c*x^2)^-1//2*log(a+b*x))
@test integrate(x^4*(c*x^2)^-3//2*(a+b*x)^-2, x) == :(x*b^-2*c^-1*(c*x^2)^-1//2*log(a+b*x)+a*x*b^-2*c^-1*(c*x^2)^-1//2*(a+b*x)^-1)
@test integrate(x^3*(c*x^2)^-3//2*(a+b*x)^-2, x) == :(-1*x*b^-1*c^-1*(c*x^2)^-1//2*(a+b*x)^-1)
@test integrate(x^2*(c*x^2)^-3//2*(a+b*x)^-2, x) == :(x*a^-1*c^-1*(c*x^2)^-1//2*(a+b*x)^-1+x*a^-2*c^-1*(c*x^2)^-1//2*log(x)+-1*x*a^-2*c^-1*(c*x^2)^-1//2*log(a+b*x))
@test integrate(x*(c*x^2)^-3//2*(a+b*x)^-2, x) == :(-1*a^-2*c^-1*(c*x^2)^-1//2+-1*b*x*a^-2*c^-1*(c*x^2)^-1//2*(a+b*x)^-1+-2*b*x*a^-3*c^-1*(c*x^2)^-1//2*log(x)+2*b*x*a^-3*c^-1*(c*x^2)^-1//2*log(a+b*x))
@test integrate((c*x^2)^-3//2*(a+b*x)^-2, x) == :(2*b*a^-3*c^-1*(c*x^2)^-1//2+-1//2*a^-2*c^-1*x^-1*(c*x^2)^-1//2+x*a^-3*b^2*c^-1*(c*x^2)^-1//2*(a+b*x)^-1+-3*x*a^-4*b^2*c^-1*(c*x^2)^-1//2*log(a+b*x)+3*x*a^-4*b^2*c^-1*(c*x^2)^-1//2*log(x))
@test integrate(x^2*(c*x^2)^(1/2)*(a+b*x)^n, x) == :(b^-4*x^-1*(c*x^2)^(1/2)*(4+n)^-1*(a+b*x)^(4+n)+-1*a^3*b^-4*x^-1*(c*x^2)^(1/2)*(1+n)^-1*(a+b*x)^(1+n)+-3*a*b^-4*x^-1*(c*x^2)^(1/2)*(3+n)^-1*(a+b*x)^(3+n)+3*a^2*b^-4*x^-1*(c*x^2)^(1/2)*(2+n)^-1*(a+b*x)^(2+n))
@test integrate(x*(c*x^2)^(1/2)*(a+b*x)^n, x) == :(b^-3*x^-1*(c*x^2)^(1/2)*(3+n)^-1*(a+b*x)^(3+n)+a^2*b^-3*x^-1*(c*x^2)^(1/2)*(1+n)^-1*(a+b*x)^(1+n)+-2*a*b^-3*x^-1*(c*x^2)^(1/2)*(2+n)^-1*(a+b*x)^(2+n))
@test integrate((c*x^2)^(1/2)*(a+b*x)^n, x) == :(b^-2*x^-1*(c*x^2)^(1/2)*(2+n)^-1*(a+b*x)^(2+n)+-1*a*b^-2*x^-1*(c*x^2)^(1/2)*(1+n)^-1*(a+b*x)^(1+n))
@test integrate(x^-1*(c*x^2)^(1/2)*(a+b*x)^n, x) == :(b^-1*x^-1*(c*x^2)^(1/2)*(1+n)^-1*(a+b*x)^(1+n))
@test integrate(x*(c*x^2)^3//2*(a+b*x)^n, x) == :(c*b^-5*x^-1*(c*x^2)^(1/2)*(5+n)^-1*(a+b*x)^(5+n)+c*a^4*b^-5*x^-1*(c*x^2)^(1/2)*(1+n)^-1*(a+b*x)^(1+n)+-4*a*c*b^-5*x^-1*(c*x^2)^(1/2)*(4+n)^-1*(a+b*x)^(4+n)+-4*c*a^3*b^-5*x^-1*(c*x^2)^(1/2)*(2+n)^-1*(a+b*x)^(2+n)+6*c*a^2*b^-5*x^-1*(c*x^2)^(1/2)*(3+n)^-1*(a+b*x)^(3+n))
@test integrate((c*x^2)^3//2*(a+b*x)^n, x) == :(c*b^-4*x^-1*(c*x^2)^(1/2)*(4+n)^-1*(a+b*x)^(4+n)+-1*c*a^3*b^-4*x^-1*(c*x^2)^(1/2)*(1+n)^-1*(a+b*x)^(1+n)+-3*a*c*b^-4*x^-1*(c*x^2)^(1/2)*(3+n)^-1*(a+b*x)^(3+n)+3*c*a^2*b^-4*x^-1*(c*x^2)^(1/2)*(2+n)^-1*(a+b*x)^(2+n))
@test integrate(x^-1*(c*x^2)^3//2*(a+b*x)^n, x) == :(c*b^-3*x^-1*(c*x^2)^(1/2)*(3+n)^-1*(a+b*x)^(3+n)+c*a^2*b^-3*x^-1*(c*x^2)^(1/2)*(1+n)^-1*(a+b*x)^(1+n)+-2*a*c*b^-3*x^-1*(c*x^2)^(1/2)*(2+n)^-1*(a+b*x)^(2+n))
@test integrate(x^-2*(c*x^2)^3//2*(a+b*x)^n, x) == :(c*b^-2*x^-1*(c*x^2)^(1/2)*(2+n)^-1*(a+b*x)^(2+n)+-1*a*c*b^-2*x^-1*(c*x^2)^(1/2)*(1+n)^-1*(a+b*x)^(1+n))
@test integrate(x^-3*(c*x^2)^3//2*(a+b*x)^n, x) == :(c*b^-1*x^-1*(c*x^2)^(1/2)*(1+n)^-1*(a+b*x)^(1+n))
@test integrate((c*x^2)^5//2*(a+b*x)^n, x) == :(b^-6*c^2*x^-1*(c*x^2)^(1/2)*(6+n)^-1*(a+b*x)^(6+n)+-1*a^5*b^-6*c^2*x^-1*(c*x^2)^(1/2)*(1+n)^-1*(a+b*x)^(1+n)+-10*a^3*b^-6*c^2*x^-1*(c*x^2)^(1/2)*(3+n)^-1*(a+b*x)^(3+n)+-5*a*b^-6*c^2*x^-1*(c*x^2)^(1/2)*(5+n)^-1*(a+b*x)^(5+n)+5*a^4*b^-6*c^2*x^-1*(c*x^2)^(1/2)*(2+n)^-1*(a+b*x)^(2+n)+10*a^2*b^-6*c^2*x^-1*(c*x^2)^(1/2)*(4+n)^-1*(a+b*x)^(4+n))
@test integrate(x^-1*(c*x^2)^5//2*(a+b*x)^n, x) == :(b^-5*c^2*x^-1*(c*x^2)^(1/2)*(5+n)^-1*(a+b*x)^(5+n)+a^4*b^-5*c^2*x^-1*(c*x^2)^(1/2)*(1+n)^-1*(a+b*x)^(1+n)+-4*a*b^-5*c^2*x^-1*(c*x^2)^(1/2)*(4+n)^-1*(a+b*x)^(4+n)+-4*a^3*b^-5*c^2*x^-1*(c*x^2)^(1/2)*(2+n)^-1*(a+b*x)^(2+n)+6*a^2*b^-5*c^2*x^-1*(c*x^2)^(1/2)*(3+n)^-1*(a+b*x)^(3+n))
@test integrate(x^-2*(c*x^2)^5//2*(a+b*x)^n, x) == :(b^-4*c^2*x^-1*(c*x^2)^(1/2)*(4+n)^-1*(a+b*x)^(4+n)+-1*a^3*b^-4*c^2*x^-1*(c*x^2)^(1/2)*(1+n)^-1*(a+b*x)^(1+n)+-3*a*b^-4*c^2*x^-1*(c*x^2)^(1/2)*(3+n)^-1*(a+b*x)^(3+n)+3*a^2*b^-4*c^2*x^-1*(c*x^2)^(1/2)*(2+n)^-1*(a+b*x)^(2+n))
@test integrate(x^-3*(c*x^2)^5//2*(a+b*x)^n, x) == :(b^-3*c^2*x^-1*(c*x^2)^(1/2)*(3+n)^-1*(a+b*x)^(3+n)+a^2*b^-3*c^2*x^-1*(c*x^2)^(1/2)*(1+n)^-1*(a+b*x)^(1+n)+-2*a*b^-3*c^2*x^-1*(c*x^2)^(1/2)*(2+n)^-1*(a+b*x)^(2+n))
@test integrate(x^-4*(c*x^2)^5//2*(a+b*x)^n, x) == :(b^-2*c^2*x^-1*(c*x^2)^(1/2)*(2+n)^-1*(a+b*x)^(2+n)+-1*a*b^-2*c^2*x^-1*(c*x^2)^(1/2)*(1+n)^-1*(a+b*x)^(1+n))
@test integrate(x^-5*(c*x^2)^5//2*(a+b*x)^n, x) == :(b^-1*c^2*x^-1*(c*x^2)^(1/2)*(1+n)^-1*(a+b*x)^(1+n))
@test integrate(x^4*(c*x^2)^-1//2*(a+b*x)^n, x) == :(x*b^-4*(c*x^2)^-1//2*(4+n)^-1*(a+b*x)^(4+n)+-1*x*a^3*b^-4*(c*x^2)^-1//2*(1+n)^-1*(a+b*x)^(1+n)+-3*a*x*b^-4*(c*x^2)^-1//2*(3+n)^-1*(a+b*x)^(3+n)+3*x*a^2*b^-4*(c*x^2)^-1//2*(2+n)^-1*(a+b*x)^(2+n))
@test integrate(x^3*(c*x^2)^-1//2*(a+b*x)^n, x) == :(x*b^-3*(c*x^2)^-1//2*(3+n)^-1*(a+b*x)^(3+n)+x*a^2*b^-3*(c*x^2)^-1//2*(1+n)^-1*(a+b*x)^(1+n)+-2*a*x*b^-3*(c*x^2)^-1//2*(2+n)^-1*(a+b*x)^(2+n))
@test integrate(x^2*(c*x^2)^-1//2*(a+b*x)^n, x) == :(x*b^-2*(c*x^2)^-1//2*(2+n)^-1*(a+b*x)^(2+n)+-1*a*x*b^-2*(c*x^2)^-1//2*(1+n)^-1*(a+b*x)^(1+n))
@test integrate(x*(c*x^2)^-1//2*(a+b*x)^n, x) == :(x*b^-1*(c*x^2)^-1//2*(1+n)^-1*(a+b*x)^(1+n))
@test integrate(x^6*(c*x^2)^-3//2*(a+b*x)^n, x) == :(x*b^-4*c^-1*(c*x^2)^-1//2*(4+n)^-1*(a+b*x)^(4+n)+-1*x*a^3*b^-4*c^-1*(c*x^2)^-1//2*(1+n)^-1*(a+b*x)^(1+n)+-3*a*x*b^-4*c^-1*(c*x^2)^-1//2*(3+n)^-1*(a+b*x)^(3+n)+3*x*a^2*b^-4*c^-1*(c*x^2)^-1//2*(2+n)^-1*(a+b*x)^(2+n))
@test integrate(x^5*(c*x^2)^-3//2*(a+b*x)^n, x) == :(x*b^-3*c^-1*(c*x^2)^-1//2*(3+n)^-1*(a+b*x)^(3+n)+x*a^2*b^-3*c^-1*(c*x^2)^-1//2*(1+n)^-1*(a+b*x)^(1+n)+-2*a*x*b^-3*c^-1*(c*x^2)^-1//2*(2+n)^-1*(a+b*x)^(2+n))
@test integrate(x^4*(c*x^2)^-3//2*(a+b*x)^n, x) == :(x*b^-2*c^-1*(c*x^2)^-1//2*(2+n)^-1*(a+b*x)^(2+n)+-1*a*x*b^-2*c^-1*(c*x^2)^-1//2*(1+n)^-1*(a+b*x)^(1+n))
@test integrate(x^3*(c*x^2)^-3//2*(a+b*x)^n, x) == :(x*b^-1*c^-1*(c*x^2)^-1//2*(1+n)^-1*(a+b*x)^(1+n))
@test integrate(x^8*(c*x^2)^-5//2*(a+b*x)^n, x) == :(x*b^-4*c^-2*(c*x^2)^-1//2*(4+n)^-1*(a+b*x)^(4+n)+-1*x*a^3*b^-4*c^-2*(c*x^2)^-1//2*(1+n)^-1*(a+b*x)^(1+n)+-3*a*x*b^-4*c^-2*(c*x^2)^-1//2*(3+n)^-1*(a+b*x)^(3+n)+3*x*a^2*b^-4*c^-2*(c*x^2)^-1//2*(2+n)^-1*(a+b*x)^(2+n))
@test integrate(x^7*(c*x^2)^-5//2*(a+b*x)^n, x) == :(x*b^-3*c^-2*(c*x^2)^-1//2*(3+n)^-1*(a+b*x)^(3+n)+x*a^2*b^-3*c^-2*(c*x^2)^-1//2*(1+n)^-1*(a+b*x)^(1+n)+-2*a*x*b^-3*c^-2*(c*x^2)^-1//2*(2+n)^-1*(a+b*x)^(2+n))
@test integrate(x^6*(c*x^2)^-5//2*(a+b*x)^n, x) == :(x*b^-2*c^-2*(c*x^2)^-1//2*(2+n)^-1*(a+b*x)^(2+n)+-1*a*x*b^-2*c^-2*(c*x^2)^-1//2*(1+n)^-1*(a+b*x)^(1+n))
@test integrate(x^5*(c*x^2)^-5//2*(a+b*x)^n, x) == :(x*b^-1*c^-2*(c*x^2)^-1//2*(1+n)^-1*(a+b*x)^(1+n))
@test integrate((c*x^2)^5//2*(d*x)^m*(a+b*x), x) == :(a*c^2*d^-6*x^-1*(c*x^2)^(1/2)*(d*x)^(6+m)*(6+m)^-1+b*c^2*d^-7*x^-1*(c*x^2)^(1/2)*(d*x)^(7+m)*(7+m)^-1)
@test integrate((c*x^2)^3//2*(d*x)^m*(a+b*x), x) == :(a*c*d^-4*x^-1*(c*x^2)^(1/2)*(d*x)^(4+m)*(4+m)^-1+b*c*d^-5*x^-1*(c*x^2)^(1/2)*(d*x)^(5+m)*(5+m)^-1)
@test integrate((c*x^2)^(1/2)*(d*x)^m*(a+b*x), x) == :(a*d^-2*x^-1*(c*x^2)^(1/2)*(d*x)^(2+m)*(2+m)^-1+b*d^-3*x^-1*(c*x^2)^(1/2)*(d*x)^(3+m)*(3+m)^-1)
@test integrate((c*x^2)^-1//2*(d*x)^m*(a+b*x), x) == :(a*x*m^-1*(c*x^2)^-1//2*(d*x)^m+b*x*d^-1*(c*x^2)^-1//2*(d*x)^(1+m)*(1+m)^-1)
@test integrate((c*x^2)^-3//2*(d*x)^m*(a+b*x), x) == :(-1*a*x*c^-1*d^2*(c*x^2)^-1//2*(d*x)^(-2+m)*(2+-1m)^-1+-1*b*d*x*c^-1*(c*x^2)^-1//2*(d*x)^(-1+m)*(1+-1m)^-1)
@test integrate((c*x^2)^-5//2*(d*x)^m*(a+b*x), x) == :(-1*a*x*c^-2*d^4*(c*x^2)^-1//2*(d*x)^(-4+m)*(4+-1m)^-1+-1*b*x*c^-2*d^3*(c*x^2)^-1//2*(d*x)^(-3+m)*(3+-1m)^-1)
@test integrate((c*x^2)^5//2*(d*x)^m*(a+b*x)^2, x) == :(a^2*c^2*d^-6*x^-1*(c*x^2)^(1/2)*(d*x)^(6+m)*(6+m)^-1+b^2*c^2*d^-8*x^-1*(c*x^2)^(1/2)*(d*x)^(8+m)*(8+m)^-1+2*a*b*c^2*d^-7*x^-1*(c*x^2)^(1/2)*(d*x)^(7+m)*(7+m)^-1)
@test integrate((c*x^2)^3//2*(d*x)^m*(a+b*x)^2, x) == :(c*a^2*d^-4*x^-1*(c*x^2)^(1/2)*(d*x)^(4+m)*(4+m)^-1+c*b^2*d^-6*x^-1*(c*x^2)^(1/2)*(d*x)^(6+m)*(6+m)^-1+2*a*b*c*d^-5*x^-1*(c*x^2)^(1/2)*(d*x)^(5+m)*(5+m)^-1)
@test integrate((c*x^2)^(1/2)*(d*x)^m*(a+b*x)^2, x) == :(a^2*d^-2*x^-1*(c*x^2)^(1/2)*(d*x)^(2+m)*(2+m)^-1+b^2*d^-4*x^-1*(c*x^2)^(1/2)*(d*x)^(4+m)*(4+m)^-1+2*a*b*d^-3*x^-1*(c*x^2)^(1/2)*(d*x)^(3+m)*(3+m)^-1)
@test integrate((c*x^2)^-1//2*(d*x)^m*(a+b*x)^2, x) == :(x*a^2*m^-1*(c*x^2)^-1//2*(d*x)^m+x*b^2*d^-2*(c*x^2)^-1//2*(d*x)^(2+m)*(2+m)^-1+2*a*b*x*d^-1*(c*x^2)^-1//2*(d*x)^(1+m)*(1+m)^-1)
@test integrate((c*x^2)^-3//2*(d*x)^m*(a+b*x)^2, x) == :(x*b^2*c^-1*m^-1*(c*x^2)^-1//2*(d*x)^m+-1*x*a^2*c^-1*d^2*(c*x^2)^-1//2*(d*x)^(-2+m)*(2+-1m)^-1+-2*a*b*d*x*c^-1*(c*x^2)^-1//2*(d*x)^(-1+m)*(1+-1m)^-1)
@test integrate((c*x^2)^-5//2*(d*x)^m*(a+b*x)^2, x) == :(-1*x*a^2*c^-2*d^4*(c*x^2)^-1//2*(d*x)^(-4+m)*(4+-1m)^-1+-1*x*b^2*c^-2*d^2*(c*x^2)^-1//2*(d*x)^(-2+m)*(2+-1m)^-1+-2*a*b*x*c^-2*d^3*(c*x^2)^-1//2*(d*x)^(-3+m)*(3+-1m)^-1)
@test integrate(x^3*(c*x^2)^p*(a+b*x)^(-5+-2p), x) == :((1/2)*a^-1*x^4*(c*x^2)^p*(2+p)^-1*(a+b*x)^(-4+-2p))
@test integrate(x^2*(c*x^2)^p*(a+b*x)^(-4+-2p), x) == :(a^-1*x^3*(c*x^2)^p*(3+2p)^-1*(a+b*x)^(-3+-2p))
@test integrate(x*(c*x^2)^p*(a+b*x)^(-3+-2p), x) == :((1/2)*a^-1*x^2*(c*x^2)^p*(1+p)^-1*(a+b*x)^(-2+-2p))
@test integrate((c*x^2)^p*(a+b*x)^(-2+-2p), x) == :(x*a^-1*(c*x^2)^p*(1+2p)^-1*(a+b*x)^(-1+-2p))
@test integrate(x^-1*(c*x^2)^p*(a+b*x)^(-1+-2p), x) == :((1/2)*a^-1*p^-1*(c*x^2)^p*(a+b*x)^(-2p))
@test integrate(x^-2*(c*x^2)^p*(a+b*x)^(-2p), x) == :(-1*a^-1*x^-1*(c*x^2)^p*(1+-2p)^-1*(a+b*x)^(1+-2p))
@test integrate(x^-3*(c*x^2)^p*(a+b*x)^(1+-2p), x) == :(-1//2*a^-1*x^-2*(c*x^2)^p*(1+-1p)^-1*(a+b*x)^(2+-2p))
@test integrate(x^-4*(c*x^2)^p*(a+b*x)^(2+-2p), x) == :(-1*a^-1*x^-3*(c*x^2)^p*(3+-2p)^-1*(a+b*x)^(3+-2p))
@test integrate(x^m*(c*x^2)^p*(a+b*x)^(-2+-1m+-2p), x) == :(a^-1*x^(1+m)*(c*x^2)^p*(a+b*x)^(-1+-1m+-2p)*(1+m+2p)^-1)
@test integrate((c*x^2)^p*(d*x)^m*(a+b*x)^(-2+-1m+-2p), x) == :(x*a^-1*(c*x^2)^p*(d*x)^m*(a+b*x)^(-1+-1m+-2p)*(1+m+2p)^-1)
@test integrate((a+b*x)^5*(d*x+a*d*b^-1)^-3, x) == :(1//3*b^2*d^-3*(a+b*x)^3)
@test integrate((a+b*x)^4*(d*x+a*d*b^-1)^-3, x) == :((1/2)*b^4*d^-3*x^2+a*x*b^3*d^-3)
@test integrate((a+b*x)^3*(d*x+a*d*b^-1)^-3, x) == :(x*b^3*d^-3)
@test integrate((a+b*x)^2*(d*x+a*d*b^-1)^-3, x) == :(b^2*d^-3*log(a+b*x))
@test integrate((d*x+a*d*b^-1)^-3*(a+b*x), x) == :(-1*b^2*d^-3*(a+b*x)^-1)
@test integrate((a+b*x)^-1*(d*x+a*d*b^-1)^-3, x) == :(-1//3*b^2*d^-3*(a+b*x)^-3)
@test integrate((a+b*x)^-2*(d*x+a*d*b^-1)^-3, x) == :(-1//4*b^2*d^-3*(a+b*x)^-4)
@test integrate((a+b*x)^-3*(d*x+a*d*b^-1)^-3, x) == :(-1//5*b^2*d^-3*(a+b*x)^-5)
@test integrate((c+d*x)^-3*(b*x+b*c*d^-1)^5, x) == :(1//3*b^5*d^-6*(c+d*x)^3)
@test integrate((c+d*x)^-3*(b*x+b*c*d^-1)^4, x) == :((1/2)*b^4*d^-3*x^2+c*x*b^4*d^-4)
@test integrate((c+d*x)^-3*(b*x+b*c*d^-1)^3, x) == :(x*b^3*d^-3)
@test integrate((c+d*x)^-3*(b*x+b*c*d^-1)^2, x) == :(b^2*d^-3*log(c+d*x))
@test integrate((c+d*x)^-3*(b*x+b*c*d^-1), x) == :(-1*b*d^-2*(c+d*x)^-1)
@test integrate((c+d*x)^-3*(b*x+b*c*d^-1)^-1, x) == :(-1//3*b^-1*(c+d*x)^-3)
@test integrate((c+d*x)^-3*(b*x+b*c*d^-1)^-2, x) == :(-1//4*d*b^-2*(c+d*x)^-4)
@test integrate((c+d*x)^-3*(b*x+b*c*d^-1)^-3, x) == :(-1//5*b^-3*d^2*(c+d*x)^-5)
@test integrate((a+b*x)^5*(a*c+b*c*x)^n, x) == :(b^-1*c^-6*(6+n)^-1*(a*c+b*c*x)^(6+n))
@test integrate((a+b*x)^5*(a*c+b*c*x)^3, x) == :(1//9*b^-1*c^3*(a+b*x)^9)
@test integrate((a+b*x)^5*(a*c+b*c*x)^2, x) == :(1//8*b^-1*c^2*(a+b*x)^8)
@test integrate((a+b*x)^5*(a*c+b*c*x), x) == :(1//7*c*b^-1*(a+b*x)^7)
@test integrate((a+b*x)^5*(a*c+b*c*x)^-1, x) == :(1//5*b^-1*c^-1*(a+b*x)^5)
@test integrate((a+b*x)^5*(a*c+b*c*x)^-2, x) == :(1//4*b^-1*c^-2*(a+b*x)^4)
@test integrate((a+b*x)^5*(a*c+b*c*x)^-3, x) == :(1//3*b^-1*c^-3*(a+b*x)^3)
@test integrate((a+b*x)^5*(a*c+b*c*x)^-4, x) == :(a*x*c^-4+(1/2)*b*c^-4*x^2)
@test integrate((a+b*x)^5*(a*c+b*c*x)^-5, x) == :(x*c^-5)
@test integrate((a+b*x)^5*(a*c+b*c*x)^-6, x) == :(b^-1*c^-6*log(a+b*x))
@test integrate((a+b*x)^5*(a*c+b*c*x)^-7, x) == :(-1*b^-1*c^-7*(a+b*x)^-1)
@test integrate((a+b*x)^5*(a*c+b*c*x)^-8, x) == :(-1//2*b^-1*c^-8*(a+b*x)^-2)
@test integrate((-2+-3x)^-1//2*(2+3x)^-1//2, x) == :(1//3*(-2+-3x)^-1//2*(2+3x)^(1/2)*log(2+3x))
@test integrate((a*c+-1*b*c*x)^3*(a+b*x), x) == :(1//5*b^-1*c^3*(a+-1*b*x)^5+-1//2*a*b^-1*c^3*(a+-1*b*x)^4)
@test integrate((a*c+-1*b*c*x)^2*(a+b*x), x) == :(1//4*b^-1*c^2*(a+-1*b*x)^4+-2//3*a*b^-1*c^2*(a+-1*b*x)^3)
@test integrate((a+b*x)*(a*c+-1*b*c*x), x) == :(c*x*a^2+-1//3*c*b^2*x^3)
@test integrate(a+b*x, x) == :(a*x+(1/2)*b*x^2)
@test integrate((a*c+-1*b*c*x)^-1*(a+b*x), x) == :(-1*x*c^-1+-2*a*b^-1*c^-1*log(a+-1*b*x))
@test integrate((a*c+-1*b*c*x)^-2*(a+b*x), x) == :(b^-1*c^-2*log(a+-1*b*x)+2*a*b^-1*c^-2*(a+-1*b*x)^-1)
@test integrate((a*c+-1*b*c*x)^-3*(a+b*x), x) == :(x*c^-3*(a+-1*b*x)^-2)
@test integrate((a*c+-1*b*c*x)^-4*(a+b*x), x) == :(-1//2*b^-1*c^-4*(a+-1*b*x)^-2+2//3*a*b^-1*c^-4*(a+-1*b*x)^-3)
@test integrate((a*c+-1*b*c*x)^-5*(a+b*x), x) == :(-1//3*b^-1*c^-5*(a+-1*b*x)^-3+(1/2)*a*b^-1*c^-5*(a+-1*b*x)^-4)
@test integrate((a*c+-1*b*c*x)^-6*(a+b*x), x) == :(-1//4*b^-1*c^-6*(a+-1*b*x)^-4+2//5*a*b^-1*c^-6*(a+-1*b*x)^-5)
@test integrate((a+b*x)^2*(a*c+-1*b*c*x)^3, x) == :(-1//6*b^-1*c^3*(a+-1*b*x)^6+-1*a^2*b^-1*c^3*(a+-1*b*x)^4+4//5*a*b^-1*c^3*(a+-1*b*x)^5)
@test integrate((a+b*x)^2*(a*c+-1*b*c*x)^2, x) == :(x*a^4*c^2+1//5*b^4*c^2*x^5+-2//3*a^2*b^2*c^2*x^3)
@test integrate((a+b*x)^2*(a*c+-1*b*c*x), x) == :(-1//4*c*b^-1*(a+b*x)^4+2//3*a*c*b^-1*(a+b*x)^3)
@test integrate((a+b*x)^2, x) == :(1//3*b^-1*(a+b*x)^3)
@test integrate((a+b*x)^2*(a*c+-1*b*c*x)^-1, x) == :(-2*a*x*c^-1+-1//2*b^-1*c^-1*(a+b*x)^2+-4*a^2*b^-1*c^-1*log(a+-1*b*x))
@test integrate((a+b*x)^2*(a*c+-1*b*c*x)^-2, x) == :(x*c^-2+4*a*b^-1*c^-2*log(a+-1*b*x)+4*a^2*b^-1*c^-2*(a+-1*b*x)^-1)
@test integrate((a+b*x)^2*(a*c+-1*b*c*x)^-3, x) == :(-1*b^-1*c^-3*log(a+-1*b*x)+-4*a*b^-1*c^-3*(a+-1*b*x)^-1+2*a^2*b^-1*c^-3*(a+-1*b*x)^-2)
@test integrate((a+b*x)^2*(a*c+-1*b*c*x)^-4, x) == :(1//6*a^-1*b^-1*c^-4*(a+b*x)^3*(a+-1*b*x)^-3)
@test integrate((a+b*x)^2*(a*c+-1*b*c*x)^-5, x) == :((1/2)*b^-1*c^-5*(a+-1*b*x)^-2+a^2*b^-1*c^-5*(a+-1*b*x)^-4+-4//3*a*b^-1*c^-5*(a+-1*b*x)^-3)
@test integrate((a+b*x)^2*(a*c+-1*b*c*x)^-6, x) == :(1//3*b^-1*c^-6*(a+-1*b*x)^-3+-1*a*b^-1*c^-6*(a+-1*b*x)^-4+4//5*a^2*b^-1*c^-6*(a+-1*b*x)^-5)
@test integrate((a+b*x)^2*(a*c+-1*b*c*x)^-7, x) == :(1//4*b^-1*c^-7*(a+-1*b*x)^-4+-4//5*a*b^-1*c^-7*(a+-1*b*x)^-5+2//3*a^2*b^-1*c^-7*(a+-1*b*x)^-6)
@test integrate((a+b*x)^-1*(a*c+-1*b*c*x)^3, x) == :(-4*x*a^2*c^3+1//3*b^-1*c^3*(a+-1*b*x)^3+a*b^-1*c^3*(a+-1*b*x)^2+8*a^3*b^-1*c^3*log(a+b*x))
@test integrate((a+b*x)^-1*(a*c+-1*b*c*x)^2, x) == :((1/2)*b^-1*c^2*(a+-1*b*x)^2+-2*a*x*c^2+4*a^2*b^-1*c^2*log(a+b*x))
@test integrate((a+b*x)^-1*(a*c+-1*b*c*x), x) == :(-1*c*x+2*a*c*b^-1*log(a+b*x))
@test integrate((a+b*x)^-1, x) == :(b^-1*log(a+b*x))
@test integrate((a+b*x)^-1*(a*c+-1*b*c*x)^-1, x) == :(a^-1*b^-1*c^-1*arctanh(b*x*a^-1))
@test integrate((a+b*x)^-1*(a*c+-1*b*c*x)^-2, x) == :((1/2)*a^-1*b^-1*c^-2*(a+-1*b*x)^-1+(1/2)*a^-2*b^-1*c^-2*arctanh(b*x*a^-1))
@test integrate((a+b*x)^-1*(a*c+-1*b*c*x)^-3, x) == :(1//4*a^-1*b^-1*c^-3*(a+-1*b*x)^-2+1//4*a^-3*b^-1*c^-3*arctanh(b*x*a^-1)+1//4*a^-2*b^-1*c^-3*(a+-1*b*x)^-1)
@test integrate((a+b*x)^-2*(a*c+-1*b*c*x)^3, x) == :(5*a*x*c^3+-1//2*b*c^3*x^2+-12*a^2*b^-1*c^3*log(a+b*x)+-8*a^3*b^-1*c^3*(a+b*x)^-1)
@test integrate((a+b*x)^-2*(a*c+-1*b*c*x)^2, x) == :(x*c^2+-4*a*b^-1*c^2*log(a+b*x)+-4*a^2*b^-1*c^2*(a+b*x)^-1)
@test integrate((a+b*x)^-2*(a*c+-1*b*c*x), x) == :(-1*c*b^-1*log(a+b*x)+-2*a*c*b^-1*(a+b*x)^-1)
@test integrate((a+b*x)^-2, x) == :(-1*b^-1*(a+b*x)^-1)
@test integrate((a+b*x)^-2*(a*c+-1*b*c*x)^-1, x) == :((1/2)*a^-2*b^-1*c^-1*arctanh(b*x*a^-1)+-1//2*a^-1*b^-1*c^-1*(a+b*x)^-1)
@test integrate((a+b*x)^-2*(a*c+-1*b*c*x)^-2, x) == :((1/2)*x*a^-2*c^-2*(a^2+-1*b^2*x^2)^-1+(1/2)*a^-3*b^-1*c^-2*arctanh(b*x*a^-1))
@test integrate((a+b*x)^-2*(a*c+-1*b*c*x)^-3, x) == :(-1//8*a^-3*b^-1*c^-3*(a+b*x)^-1+1//4*a^-3*b^-1*c^-3*(a+-1*b*x)^-1+1//8*a^-2*b^-1*c^-3*(a+-1*b*x)^-2+3//8*a^-4*b^-1*c^-3*arctanh(b*x*a^-1))
@test integrate((1+x)^(1/2)*(1+-1x)^9//2, x) == :(21//16*arcsin(x)+1//6*(1+x)^3//2*(1+-1x)^9//2+3//10*(1+x)^3//2*(1+-1x)^7//2+7//8*(1+x)^3//2*(1+-1x)^3//2+21//40*(1+x)^3//2*(1+-1x)^5//2+21//16*x*(1+x)^(1/2)*(1+-1x)^(1/2))
@test integrate((1+x)^(1/2)*(1+-1x)^7//2, x) == :(7//8*arcsin(x)+1//5*(1+x)^3//2*(1+-1x)^7//2+7//12*(1+x)^3//2*(1+-1x)^3//2+7//20*(1+x)^3//2*(1+-1x)^5//2+7//8*x*(1+x)^(1/2)*(1+-1x)^(1/2))
@test integrate((1+x)^(1/2)*(1+-1x)^5//2, x) == :(5//8*arcsin(x)+1//4*(1+x)^3//2*(1+-1x)^5//2+5//12*(1+x)^3//2*(1+-1x)^3//2+5//8*x*(1+x)^(1/2)*(1+-1x)^(1/2))
@test integrate((1+x)^(1/2)*(1+-1x)^3//2, x) == :((1/2)*arcsin(x)+1//3*(1+x)^3//2*(1+-1x)^3//2+(1/2)*x*(1+x)^(1/2)*(1+-1x)^(1/2))
@test integrate((1+x)^(1/2)*(1+-1x)^(1/2), x) == :((1/2)*arcsin(x)+(1/2)*x*(1+x)^(1/2)*(1+-1x)^(1/2))
@test integrate((1+x)^(1/2)*(1+-1x)^-1//2, x) == :(-1*(1+x)^(1/2)*(1+-1x)^(1/2)+arcsin(x))
@test integrate((1+x)^(1/2)*(1+-1x)^-3//2, x) == :(-1*arcsin(x)+2*(1+x)^(1/2)*(1+-1x)^-1//2)
@test integrate((1+x)^(1/2)*(1+-1x)^-5//2, x) == :(1//3*(1+x)^3//2*(1+-1x)^-3//2)
@test integrate((1+x)^(1/2)*(1+-1x)^-7//2, x) == :(1//5*(1+x)^3//2*(1+-1x)^-5//2+1//15*(1+x)^3//2*(1+-1x)^-3//2)
@test integrate((1+x)^(1/2)*(1+-1x)^-9//2, x) == :(1//7*(1+x)^3//2*(1+-1x)^-7//2+2//35*(1+x)^3//2*(1+-1x)^-5//2+2//105*(1+x)^3//2*(1+-1x)^-3//2)
@test integrate((1+x)^(1/2)*(1+-1x)^-11//2, x) == :(1//9*(1+x)^3//2*(1+-1x)^-9//2+1//21*(1+x)^3//2*(1+-1x)^-7//2+2//105*(1+x)^3//2*(1+-1x)^-5//2+2//315*(1+x)^3//2*(1+-1x)^-3//2)
@test integrate((1+x)^(1/2)*(1+-1x)^-13//2, x) == :(1//11*(1+x)^3//2*(1+-1x)^-11//2+4//99*(1+x)^3//2*(1+-1x)^-9//2+4//231*(1+x)^3//2*(1+-1x)^-7//2+8//1155*(1+x)^3//2*(1+-1x)^-5//2+8//3465*(1+x)^3//2*(1+-1x)^-3//2)
@test integrate((1+x)^3//2*(1+-1x)^9//2, x) == :(9//16*arcsin(x)+1//7*(1+x)^5//2*(1+-1x)^9//2+3//10*(1+x)^5//2*(1+-1x)^5//2+3//14*(1+x)^5//2*(1+-1x)^7//2+3//8*x*(1+x)^3//2*(1+-1x)^3//2+9//16*x*(1+x)^(1/2)*(1+-1x)^(1/2))
@test integrate((1+x)^3//2*(1+-1x)^7//2, x) == :(7//16*arcsin(x)+1//6*(1+x)^5//2*(1+-1x)^7//2+7//30*(1+x)^5//2*(1+-1x)^5//2+7//16*x*(1+x)^(1/2)*(1+-1x)^(1/2)+7//24*x*(1+x)^3//2*(1+-1x)^3//2)
@test integrate((1+x)^3//2*(1+-1x)^5//2, x) == :(3//8*arcsin(x)+1//5*(1+x)^5//2*(1+-1x)^5//2+1//4*x*(1+x)^3//2*(1+-1x)^3//2+3//8*x*(1+x)^(1/2)*(1+-1x)^(1/2))
@test integrate((1+x)^3//2*(1+-1x)^3//2, x) == :(3//8*arcsin(x)+1//4*x*(1+x)^3//2*(1+-1x)^3//2+3//8*x*(1+x)^(1/2)*(1+-1x)^(1/2))
@test integrate((1+x)^3//2*(1+-1x)^(1/2), x) == :((1/2)*arcsin(x)+-1//3*(1+x)^3//2*(1+-1x)^3//2+(1/2)*x*(1+x)^(1/2)*(1+-1x)^(1/2))
@test integrate((1+x)^3//2*(1+-1x)^-1//2, x) == :(3//2*arcsin(x)+-3//2*(1+x)^(1/2)*(1+-1x)^(1/2)+-1//2*(1+x)^3//2*(1+-1x)^(1/2))
@test integrate((1+x)^3//2*(1+-1x)^-3//2, x) == :(-3*arcsin(x)+2*(1+x)^3//2*(1+-1x)^-1//2+3*(1+x)^(1/2)*(1+-1x)^(1/2))
@test integrate((1+x)^3//2*(1+-1x)^-5//2, x) == :(-2*(1+x)^(1/2)*(1+-1x)^-1//2+2//3*(1+x)^3//2*(1+-1x)^-3//2+arcsin(x))
@test integrate((1+x)^3//2*(1+-1x)^-7//2, x) == :(1//5*(1+x)^5//2*(1+-1x)^-5//2)
@test integrate((1+x)^3//2*(1+-1x)^-9//2, x) == :(1//7*(1+x)^5//2*(1+-1x)^-7//2+1//35*(1+x)^5//2*(1+-1x)^-5//2)
@test integrate((1+x)^3//2*(1+-1x)^-11//2, x) == :(1//9*(1+x)^5//2*(1+-1x)^-9//2+2//63*(1+x)^5//2*(1+-1x)^-7//2+2//315*(1+x)^5//2*(1+-1x)^-5//2)
@test integrate((1+x)^3//2*(1+-1x)^-13//2, x) == :(1//11*(1+x)^5//2*(1+-1x)^-11//2+1//33*(1+x)^5//2*(1+-1x)^-9//2+2//231*(1+x)^5//2*(1+-1x)^-7//2+2//1155*(1+x)^5//2*(1+-1x)^-5//2)
@test integrate((1+x)^3//2*(1+-1x)^-15//2, x) == :(1//13*(1+x)^5//2*(1+-1x)^-13//2+4//143*(1+x)^5//2*(1+-1x)^-11//2+4//429*(1+x)^5//2*(1+-1x)^-9//2+8//3003*(1+x)^5//2*(1+-1x)^-7//2+8//15015*(1+x)^5//2*(1+-1x)^-5//2)
@test integrate((1+x)^5//2*(1+-1x)^11//2, x) == :(55//128*arcsin(x)+1//9*(1+x)^7//2*(1+-1x)^11//2+11//56*(1+x)^7//2*(1+-1x)^7//2+11//72*(1+x)^7//2*(1+-1x)^9//2+11//48*x*(1+x)^5//2*(1+-1x)^5//2+55//128*x*(1+x)^(1/2)*(1+-1x)^(1/2)+55//192*x*(1+x)^3//2*(1+-1x)^3//2)
@test integrate((1+x)^5//2*(1+-1x)^9//2, x) == :(45//128*arcsin(x)+1//8*(1+x)^7//2*(1+-1x)^9//2+9//56*(1+x)^7//2*(1+-1x)^7//2+3//16*x*(1+x)^5//2*(1+-1x)^5//2+15//64*x*(1+x)^3//2*(1+-1x)^3//2+45//128*x*(1+x)^(1/2)*(1+-1x)^(1/2))
@test integrate((1+x)^5//2*(1+-1x)^7//2, x) == :(5//16*arcsin(x)+1//7*(1+x)^7//2*(1+-1x)^7//2+1//6*x*(1+x)^5//2*(1+-1x)^5//2+5//16*x*(1+x)^(1/2)*(1+-1x)^(1/2)+5//24*x*(1+x)^3//2*(1+-1x)^3//2)
@test integrate((1+x)^5//2*(1+-1x)^5//2, x) == :(5//16*arcsin(x)+1//6*x*(1+x)^5//2*(1+-1x)^5//2+5//16*x*(1+x)^(1/2)*(1+-1x)^(1/2)+5//24*x*(1+x)^3//2*(1+-1x)^3//2)
@test integrate((1+x)^5//2*(1+-1x)^3//2, x) == :(3//8*arcsin(x)+-1//5*(1+x)^5//2*(1+-1x)^5//2+1//4*x*(1+x)^3//2*(1+-1x)^3//2+3//8*x*(1+x)^(1/2)*(1+-1x)^(1/2))
@test integrate((1+x)^5//2*(1+-1x)^(1/2), x) == :(5//8*arcsin(x)+-5//12*(1+x)^3//2*(1+-1x)^3//2+-1//4*(1+x)^5//2*(1+-1x)^3//2+5//8*x*(1+x)^(1/2)*(1+-1x)^(1/2))
@test integrate((1+x)^5//2*(1+-1x)^-1//2, x) == :(5//2*arcsin(x)+-5//2*(1+x)^(1/2)*(1+-1x)^(1/2)+-5//6*(1+x)^3//2*(1+-1x)^(1/2)+-1//3*(1+x)^5//2*(1+-1x)^(1/2))
@test integrate((1+x)^5//2*(1+-1x)^-3//2, x) == :(-15//2*arcsin(x)+2*(1+x)^5//2*(1+-1x)^-1//2+5//2*(1+x)^3//2*(1+-1x)^(1/2)+15//2*(1+x)^(1/2)*(1+-1x)^(1/2))
@test integrate((1+x)^5//2*(1+-1x)^-5//2, x) == :(5*arcsin(x)+-5*(1+x)^(1/2)*(1+-1x)^(1/2)+-10//3*(1+x)^3//2*(1+-1x)^-1//2+2//3*(1+x)^5//2*(1+-1x)^-3//2)
@test integrate((1+x)^5//2*(1+-1x)^-7//2, x) == :(-1*arcsin(x)+2*(1+x)^(1/2)*(1+-1x)^-1//2+-2//3*(1+x)^3//2*(1+-1x)^-3//2+2//5*(1+x)^5//2*(1+-1x)^-5//2)
@test integrate((1+x)^5//2*(1+-1x)^-9//2, x) == :(1//7*(1+x)^7//2*(1+-1x)^-7//2)
@test integrate((1+x)^5//2*(1+-1x)^-11//2, x) == :(1//9*(1+x)^7//2*(1+-1x)^-9//2+1//63*(1+x)^7//2*(1+-1x)^-7//2)
@test integrate((1+x)^5//2*(1+-1x)^-13//2, x) == :(1//11*(1+x)^7//2*(1+-1x)^-11//2+2//99*(1+x)^7//2*(1+-1x)^-9//2+2//693*(1+x)^7//2*(1+-1x)^-7//2)
@test integrate((1+x)^5//2*(1+-1x)^-15//2, x) == :(1//13*(1+x)^7//2*(1+-1x)^-13//2+2//429*(1+x)^7//2*(1+-1x)^-9//2+2//3003*(1+x)^7//2*(1+-1x)^-7//2+3//143*(1+x)^7//2*(1+-1x)^-11//2)
@test integrate((1+x)^5//2*(1+-1x)^-17//2, x) == :(1//15*(1+x)^7//2*(1+-1x)^-15//2+4//195*(1+x)^7//2*(1+-1x)^-13//2+4//715*(1+x)^7//2*(1+-1x)^-11//2+8//6435*(1+x)^7//2*(1+-1x)^-9//2+8//45045*(1+x)^7//2*(1+-1x)^-7//2)
@test integrate((1+x)^5//2*(1+-1x)^-19//2, x) == :(1//17*(1+x)^7//2*(1+-1x)^-17//2+1//51*(1+x)^7//2*(1+-1x)^-15//2+4//663*(1+x)^7//2*(1+-1x)^-13//2+4//2431*(1+x)^7//2*(1+-1x)^-11//2+8//21879*(1+x)^7//2*(1+-1x)^-9//2+8//153153*(1+x)^7//2*(1+-1x)^-7//2)
@test integrate((1+a*x)^3//2*(1+-1*a*x)^-1//2, x) == :(3//2*a^-1*arcsin(a*x)+-3//2*a^-1*(1+a*x)^(1/2)*(1+-1*a*x)^(1/2)+-1//2*a^-1*(1+a*x)^3//2*(1+-1*a*x)^(1/2))
@test integrate((1+-1*a*x)^-1*(1+-1*a^2*x^2)^(1/2)*(1+a*x), x) == :(-3//2*a^-1*(1+-1*a^2*x^2)^(1/2)+3//2*a^-1*arcsin(a*x)+-1//2*a^-1*(1+-1*a*x)^-1*(1+-1*a^2*x^2)^3//2)
@test integrate((1+x)^-1//2*(1+-1x)^7//2, x) == :(35//8*arcsin(x)+1//4*(1+x)^(1/2)*(1+-1x)^7//2+7//12*(1+x)^(1/2)*(1+-1x)^5//2+35//8*(1+x)^(1/2)*(1+-1x)^(1/2)+35//24*(1+x)^(1/2)*(1+-1x)^3//2)
@test integrate((1+x)^-1//2*(1+-1x)^5//2, x) == :(5//2*arcsin(x)+1//3*(1+x)^(1/2)*(1+-1x)^5//2+5//2*(1+x)^(1/2)*(1+-1x)^(1/2)+5//6*(1+x)^(1/2)*(1+-1x)^3//2)
@test integrate((1+x)^-1//2*(1+-1x)^3//2, x) == :(3//2*arcsin(x)+(1/2)*(1+x)^(1/2)*(1+-1x)^3//2+3//2*(1+x)^(1/2)*(1+-1x)^(1/2))
@test integrate((1+x)^-1//2*(1+-1x)^(1/2), x) == :((1+x)^(1/2)*(1+-1x)^(1/2)+arcsin(x))
@test integrate((1+x)^-1//2*(1+-1x)^-1//2, x) == :(arcsin(x))
@test integrate((1+x)^-1//2*(1+-1x)^-3//2, x) == :((1+x)^(1/2)*(1+-1x)^-1//2)
@test integrate((1+x)^-1//2*(1+-1x)^-5//2, x) == :(1//3*(1+x)^(1/2)*(1+-1x)^-3//2+1//3*(1+x)^(1/2)*(1+-1x)^-1//2)
@test integrate((1+x)^-1//2*(1+-1x)^-7//2, x) == :(1//5*(1+x)^(1/2)*(1+-1x)^-5//2+2//15*(1+x)^(1/2)*(1+-1x)^-3//2+2//15*(1+x)^(1/2)*(1+-1x)^-1//2)
@test integrate((1+x)^-1//2*(1+-1x)^-9//2, x) == :(1//7*(1+x)^(1/2)*(1+-1x)^-7//2+2//35*(1+x)^(1/2)*(1+-1x)^-3//2+2//35*(1+x)^(1/2)*(1+-1x)^-1//2+3//35*(1+x)^(1/2)*(1+-1x)^-5//2)
@test integrate((1+x)^-1//2*(1+-1x)^-11//2, x) == :(1//9*(1+x)^(1/2)*(1+-1x)^-9//2+4//63*(1+x)^(1/2)*(1+-1x)^-7//2+4//105*(1+x)^(1/2)*(1+-1x)^-5//2+8//315*(1+x)^(1/2)*(1+-1x)^-3//2+8//315*(1+x)^(1/2)*(1+-1x)^-1//2)
@test integrate((1+x)^-3//2*(1+-1x)^7//2, x) == :(-35//2*arcsin(x)+-2*(1+x)^-1//2*(1+-1x)^7//2+-35//2*(1+x)^(1/2)*(1+-1x)^(1/2)+-35//6*(1+x)^(1/2)*(1+-1x)^3//2+-7//3*(1+x)^(1/2)*(1+-1x)^5//2)
@test integrate((1+x)^-3//2*(1+-1x)^5//2, x) == :(-15//2*arcsin(x)+-2*(1+x)^-1//2*(1+-1x)^5//2+-15//2*(1+x)^(1/2)*(1+-1x)^(1/2)+-5//2*(1+x)^(1/2)*(1+-1x)^3//2)
@test integrate((1+x)^-3//2*(1+-1x)^3//2, x) == :(-3*arcsin(x)+-3*(1+x)^(1/2)*(1+-1x)^(1/2)+-2*(1+x)^-1//2*(1+-1x)^3//2)
@test integrate((1+x)^-3//2*(1+-1x)^(1/2), x) == :(-1*arcsin(x)+-2*(1+x)^-1//2*(1+-1x)^(1/2))
@test integrate((1+x)^-3//2*(1+-1x)^-1//2, x) == :(-1*(1+x)^-1//2*(1+-1x)^(1/2))
@test integrate((1+x)^-3//2*(1+-1x)^-3//2, x) == :(x*(1+x)^-1//2*(1+-1x)^-1//2)
@test integrate((1+x)^-3//2*(1+-1x)^-5//2, x) == :(1//3*(1+x)^-1//2*(1+-1x)^-3//2+2//3*x*(1+x)^-1//2*(1+-1x)^-1//2)
@test integrate((1+x)^-3//2*(1+-1x)^-7//2, x) == :(1//5*(1+x)^-1//2*(1+-1x)^-5//2+1//5*(1+x)^-1//2*(1+-1x)^-3//2+2//5*x*(1+x)^-1//2*(1+-1x)^-1//2)
@test integrate((1+x)^-3//2*(1+-1x)^-9//2, x) == :(1//7*(1+x)^-1//2*(1+-1x)^-7//2+4//35*(1+x)^-1//2*(1+-1x)^-5//2+4//35*(1+x)^-1//2*(1+-1x)^-3//2+8//35*x*(1+x)^-1//2*(1+-1x)^-1//2)
@test integrate((1+x)^-3//2*(1+-1x)^-11//2, x) == :(1//9*(1+x)^-1//2*(1+-1x)^-9//2+4//63*(1+x)^-1//2*(1+-1x)^-5//2+4//63*(1+x)^-1//2*(1+-1x)^-3//2+5//63*(1+x)^-1//2*(1+-1x)^-7//2+8//63*x*(1+x)^-1//2*(1+-1x)^-1//2)
@test integrate((1+x)^-5//2*(1+-1x)^9//2, x) == :(105//2*arcsin(x)+6*(1+x)^-1//2*(1+-1x)^7//2+7*(1+x)^(1/2)*(1+-1x)^5//2+-2//3*(1+x)^-3//2*(1+-1x)^9//2+35//2*(1+x)^(1/2)*(1+-1x)^3//2+105//2*(1+x)^(1/2)*(1+-1x)^(1/2))
@test integrate((1+x)^-5//2*(1+-1x)^7//2, x) == :(35//2*arcsin(x)+-2//3*(1+x)^-3//2*(1+-1x)^7//2+14//3*(1+x)^-1//2*(1+-1x)^5//2+35//2*(1+x)^(1/2)*(1+-1x)^(1/2)+35//6*(1+x)^(1/2)*(1+-1x)^3//2)
@test integrate((1+x)^-5//2*(1+-1x)^5//2, x) == :(5*arcsin(x)+5*(1+x)^(1/2)*(1+-1x)^(1/2)+-2//3*(1+x)^-3//2*(1+-1x)^5//2+10//3*(1+x)^-1//2*(1+-1x)^3//2)
@test integrate((1+x)^-5//2*(1+-1x)^3//2, x) == :(2*(1+x)^-1//2*(1+-1x)^(1/2)+-2//3*(1+x)^-3//2*(1+-1x)^3//2+arcsin(x))
@test integrate((1+x)^-5//2*(1+-1x)^(1/2), x) == :(-1//3*(1+x)^-3//2*(1+-1x)^3//2)
@test integrate((1+x)^-5//2*(1+-1x)^-1//2, x) == :(-1//3*(1+x)^-3//2*(1+-1x)^(1/2)+-1//3*(1+x)^-1//2*(1+-1x)^(1/2))
@test integrate((1+x)^-5//2*(1+-1x)^-3//2, x) == :((1+x)^-3//2*(1+-1x)^-1//2+-2//3*(1+x)^-3//2*(1+-1x)^(1/2)+-2//3*(1+x)^-1//2*(1+-1x)^(1/2))
@test integrate((1+x)^-5//2*(1+-1x)^-5//2, x) == :(1//3*x*(1+x)^-3//2*(1+-1x)^-3//2+2//3*x*(1+x)^-1//2*(1+-1x)^-1//2)
@test integrate((1+x)^-5//2*(1+-1x)^-7//2, x) == :(1//5*(1+x)^-3//2*(1+-1x)^-5//2+4//15*x*(1+x)^-3//2*(1+-1x)^-3//2+8//15*x*(1+x)^-1//2*(1+-1x)^-1//2)
@test integrate((1+x)^-5//2*(1+-1x)^-9//2, x) == :(1//7*(1+x)^-3//2*(1+-1x)^-7//2+1//7*(1+x)^-3//2*(1+-1x)^-5//2+4//21*x*(1+x)^-3//2*(1+-1x)^-3//2+8//21*x*(1+x)^-1//2*(1+-1x)^-1//2)
@test integrate((1+x)^-5//2*(1+-1x)^-11//2, x) == :(1//9*(1+x)^-3//2*(1+-1x)^-9//2+2//21*(1+x)^-3//2*(1+-1x)^-7//2+2//21*(1+x)^-3//2*(1+-1x)^-5//2+8//63*x*(1+x)^-3//2*(1+-1x)^-3//2+16//63*x*(1+x)^-1//2*(1+-1x)^-1//2)
@test integrate((a+a*x)^5//2*(c+-1*c*x)^5//2, x) == :(1//6*x*(a+a*x)^5//2*(c+-1*c*x)^5//2+5//8*a^5//2*c^5//2*arctan(a^-1//2*c^(1/2)*(a+a*x)^(1/2)*(c+-1*c*x)^-1//2)+5//16*x*a^2*c^2*(a+a*x)^(1/2)*(c+-1*c*x)^(1/2)+5//24*a*c*x*(a+a*x)^3//2*(c+-1*c*x)^3//2)
@test integrate((a+a*x)^3//2*(c+-1*c*x)^3//2, x) == :(1//4*x*(a+a*x)^3//2*(c+-1*c*x)^3//2+3//4*a^3//2*c^3//2*arctan(a^-1//2*c^(1/2)*(a+a*x)^(1/2)*(c+-1*c*x)^-1//2)+3//8*a*c*x*(a+a*x)^(1/2)*(c+-1*c*x)^(1/2))
@test integrate((a+a*x)^(1/2)*(c+-1*c*x)^(1/2), x) == :(a^(1/2)*c^(1/2)*arctan(a^-1//2*c^(1/2)*(a+a*x)^(1/2)*(c+-1*c*x)^-1//2)+(1/2)*x*(a+a*x)^(1/2)*(c+-1*c*x)^(1/2))
@test integrate((a+a*x)^-1//2*(c+-1*c*x)^-1//2, x) == :(2*a^-1//2*c^-1//2*arctan(a^-1//2*c^(1/2)*(a+a*x)^(1/2)*(c+-1*c*x)^-1//2))
@test integrate((a+a*x)^-3//2*(c+-1*c*x)^-3//2, x) == :(x*a^-1*c^-1*(a+a*x)^-1//2*(c+-1*c*x)^-1//2)
@test integrate((a+a*x)^-5//2*(c+-1*c*x)^-5//2, x) == :(1//3*x*a^-1*c^-1*(a+a*x)^-3//2*(c+-1*c*x)^-3//2+2//3*x*a^-2*c^-2*(a+a*x)^-1//2*(c+-1*c*x)^-1//2)
@test integrate((a+a*x)^-7//2*(c+-1*c*x)^-7//2, x) == :(1//5*x*a^-1*c^-1*(a+a*x)^-5//2*(c+-1*c*x)^-5//2+4//15*x*a^-2*c^-2*(a+a*x)^-3//2*(c+-1*c*x)^-3//2+8//15*x*a^-3*c^-3*(a+a*x)^-1//2*(c+-1*c*x)^-1//2)
@test integrate((a+a*x)^-9//2*(c+-1*c*x)^-9//2, x) == :(1//7*x*a^-1*c^-1*(a+a*x)^-7//2*(c+-1*c*x)^-7//2+6//35*x*a^-2*c^-2*(a+a*x)^-5//2*(c+-1*c*x)^-5//2+8//35*x*a^-3*c^-3*(a+a*x)^-3//2*(c+-1*c*x)^-3//2+16//35*x*a^-4*c^-4*(a+a*x)^-1//2*(c+-1*c*x)^-1//2)
@test integrate((a+b*x)^5//2*(a*c+-1*b*c*x)^5//2, x) == :(1//6*x*(a+b*x)^5//2*(a*c+-1*b*c*x)^5//2+5//8*a^6*b^-1*c^5//2*arctan(c^(1/2)*(c*(a+-1*b*x))^-1//2*(a+b*x)^(1/2))+5//16*x*a^4*c^2*(a+b*x)^(1/2)*(a*c+-1*b*c*x)^(1/2)+5//24*c*x*a^2*(a+b*x)^3//2*(a*c+-1*b*c*x)^3//2)
@test integrate((a+b*x)^3//2*(a*c+-1*b*c*x)^3//2, x) == :(1//4*x*(a+b*x)^3//2*(a*c+-1*b*c*x)^3//2+3//4*a^4*b^-1*c^3//2*arctan(c^(1/2)*(c*(a+-1*b*x))^-1//2*(a+b*x)^(1/2))+3//8*c*x*a^2*(a+b*x)^(1/2)*(a*c+-1*b*c*x)^(1/2))
@test integrate((a+b*x)^(1/2)*(a*c+-1*b*c*x)^(1/2), x) == :((1/2)*x*(a+b*x)^(1/2)*(a*c+-1*b*c*x)^(1/2)+a^2*b^-1*c^(1/2)*arctan(c^(1/2)*(c*(a+-1*b*x))^-1//2*(a+b*x)^(1/2)))
@test integrate((a+b*x)^-1//2*(a*c+-1*b*c*x)^-1//2, x) == :(2*b^-1*c^-1//2*arctan(c^(1/2)*(c*(a+-1*b*x))^-1//2*(a+b*x)^(1/2)))
@test integrate((a+b*x)^-3//2*(a*c+-1*b*c*x)^-3//2, x) == :(x*a^-2*c^-1*(a+b*x)^-1//2*(a*c+-1*b*c*x)^-1//2)
@test integrate((a+b*x)^-5//2*(a*c+-1*b*c*x)^-5//2, x) == :(1//3*x*a^-2*c^-1*(a+b*x)^-3//2*(a*c+-1*b*c*x)^-3//2+2//3*x*a^-4*c^-2*(a+b*x)^-1//2*(a*c+-1*b*c*x)^-1//2)
@test integrate((a+b*x)^-7//2*(a*c+-1*b*c*x)^-7//2, x) == :(1//5*x*a^-2*c^-1*(a+b*x)^-5//2*(a*c+-1*b*c*x)^-5//2+4//15*x*a^-4*c^-2*(a+b*x)^-3//2*(a*c+-1*b*c*x)^-3//2+8//15*x*a^-6*c^-3*(a+b*x)^-1//2*(a*c+-1*b*c*x)^-1//2)
@test integrate((a+b*x)^-9//2*(a*c+-1*b*c*x)^-9//2, x) == :(1//7*x*a^-2*c^-1*(a+b*x)^-7//2*(a*c+-1*b*c*x)^-7//2+6//35*x*a^-4*c^-2*(a+b*x)^-5//2*(a*c+-1*b*c*x)^-5//2+8//35*x*a^-6*c^-3*(a+b*x)^-3//2*(a*c+-1*b*c*x)^-3//2+16//35*x*a^-8*c^-4*(a+b*x)^-1//2*(a*c+-1*b*c*x)^-1//2)
@test integrate((2+4x)^5//2*(3+-6x)^5//2, x) == :(45//8*6^(1/2)*arcsin(2x)+6*x*6^(1/2)*(1+-2x)^5//2*(1+2x)^5//2+15//2*x*6^(1/2)*(1+-2x)^3//2*(1+2x)^3//2+45//4*x*6^(1/2)*(1+-2x)^(1/2)*(1+2x)^(1/2))
@test integrate((2+4x)^3//2*(3+-6x)^3//2, x) == :(9//8*6^(1/2)*arcsin(2x)+3//2*x*6^(1/2)*(1+-2x)^3//2*(1+2x)^3//2+9//4*x*6^(1/2)*(1+-2x)^(1/2)*(1+2x)^(1/2))
@test integrate((2+4x)^(1/2)*(3+-6x)^(1/2), x) == :(1//4*6^(1/2)*arcsin(2x)+(1/2)*x*6^(1/2)*(1+-2x)^(1/2)*(1+2x)^(1/2))
@test integrate((2+4x)^-1//2*(3+-6x)^-1//2, x) == :(1//12*6^(1/2)*arcsin(2x))
@test integrate((2+4x)^-3//2*(3+-6x)^-3//2, x) == :(1//36*x*6^(1/2)*(1+-2x)^-1//2*(1+2x)^-1//2)
@test integrate((2+4x)^-5//2*(3+-6x)^-5//2, x) == :(1//324*x*6^(1/2)*(1+-2x)^-1//2*(1+2x)^-1//2+1//648*x*6^(1/2)*(1+-2x)^-3//2*(1+2x)^-3//2)
@test integrate((2+4x)^-7//2*(3+-6x)^-7//2, x) == :(1//2430*x*6^(1/2)*(1+-2x)^-1//2*(1+2x)^-1//2+1//4860*x*6^(1/2)*(1+-2x)^-3//2*(1+2x)^-3//2+1//6480*x*6^(1/2)*(1+-2x)^-5//2*(1+2x)^-5//2)
@test integrate((-2+x)^3//2*(3+-1x)^3//2, x) == :(-3//128*arcsin(5+-2x)+-1//4*(-2+x)^3//2*(3+-1x)^5//2+-1//8*(-2+x)^(1/2)*(3+-1x)^5//2+1//32*(-2+x)^(1/2)*(3+-1x)^3//2+3//64*(-2+x)^(1/2)*(3+-1x)^(1/2))
@test integrate((-2+x)^(1/2)*(3+-1x)^(1/2), x) == :(-1//8*arcsin(5+-2x)+-1//2*(-2+x)^(1/2)*(3+-1x)^3//2+1//4*(-2+x)^(1/2)*(3+-1x)^(1/2))
@test integrate((-2+x)^-1//2*(3+-1x)^-1//2, x) == :(-1*arcsin(5+-2x))
@test integrate((-2+x)^-3//2*(3+-1x)^-3//2, x) == :(-4*(-2+x)^-1//2*(3+-1x)^(1/2)+2*(-2+x)^-1//2*(3+-1x)^-1//2)
@test integrate((-2+x)^-5//2*(3+-1x)^-5//2, x) == :(4*(-2+x)^-3//2*(3+-1x)^-1//2+-32//3*(-2+x)^-1//2*(3+-1x)^(1/2)+-16//3*(-2+x)^-3//2*(3+-1x)^(1/2)+2//3*(-2+x)^-3//2*(3+-1x)^-3//2)
@test integrate((3+x)^-3//2*(3+-1x)^-3//2, x) == :(1//9*x*(3+x)^-1//2*(3+-1x)^-1//2)
@test integrate((3+b*x)^-3//2*(3+-1*b*x)^-3//2, x) == :(1//9*x*(3+b*x)^-1//2*(3+-1*b*x)^-1//2)
@test integrate((3+x)^-3//2*(6+-2x)^-3//2, x) == :(1//36*x*2^(1/2)*(3+x)^-1//2*(3+-1x)^-1//2)
@test integrate((3+b*x)^-3//2*(6+-2*b*x)^-3//2, x) == :(1//36*x*2^(1/2)*(3+b*x)^-1//2*(3+-1*b*x)^-1//2)
@test integrate((a+b*x)^-1//2*(-1*a*d+b*d*x)^-1//2, x) == :(2*b^-1*d^-1//2*arctanh(d^(1/2)*(a+b*x)^(1/2)*(-1*a*d+b*d*x)^-1//2))
@test integrate((a+im*a*x)^-1//4*(a+-1*im*a*x)^7//4, x) == :(-14//15*im*(a+im*a*x)^3//4*(a+-1*im*a*x)^3//4+-2//5*im*a^-1*(a+im*a*x)^3//4*(a+-1*im*a*x)^7//4+14//5*x*a^2*(a+im*a*x)^-1//4*(a+-1*im*a*x)^-1//4+-14//5*a^2*(1+x^2)^1//4*(a+im*a*x)^-1//4*(a+-1*im*a*x)^-1//4*Elliptic.E((1/2)*arctan(x),2))
@test integrate((a+im*a*x)^-1//4*(a+-1*im*a*x)^3//4, x) == :(2*a*x*(a+im*a*x)^-1//4*(a+-1*im*a*x)^-1//4+-2//3*im*a^-1*(a+im*a*x)^3//4*(a+-1*im*a*x)^3//4+-2*a*(1+x^2)^1//4*(a+im*a*x)^-1//4*(a+-1*im*a*x)^-1//4*Elliptic.E((1/2)*arctan(x),2))
@test integrate((a+im*a*x)^-1//4*(a+-1*im*a*x)^-1//4, x) == :(2*x*(a+im*a*x)^-1//4*(a+-1*im*a*x)^-1//4+-2*(1+x^2)^1//4*(a+im*a*x)^-1//4*(a+-1*im*a*x)^-1//4*Elliptic.E((1/2)*arctan(x),2))
@test integrate((a+im*a*x)^-1//4*(a+-1*im*a*x)^-5//4, x) == :(-2*im*a^-1*(a+im*a*x)^-1//4*(a+-1*im*a*x)^-1//4+2*a^-1*(1+x^2)^1//4*(a+im*a*x)^-1//4*(a+-1*im*a*x)^-1//4*Elliptic.E((1/2)*arctan(x),2))
@test integrate((a+im*a*x)^-1//4*(a+-1*im*a*x)^-9//4, x) == :(-4//5*im*a^-1*(a+im*a*x)^-1//4*(a+-1*im*a*x)^-5//4+2//5*a^-2*(1+x^2)^1//4*(a+im*a*x)^-1//4*(a+-1*im*a*x)^-1//4*Elliptic.E((1/2)*arctan(x),2))
@test integrate((a+im*a*x)^-1//4*(a+-1*im*a*x)^-13//4, x) == :(-4//15*im*a^-2*(a+im*a*x)^-1//4*(a+-1*im*a*x)^-5//4+-2//9*im*a^-2*(a+im*a*x)^3//4*(a+-1*im*a*x)^-9//4+2//15*a^-3*(1+x^2)^1//4*(a+im*a*x)^-1//4*(a+-1*im*a*x)^-1//4*Elliptic.E((1/2)*arctan(x),2))
@test integrate((a+im*a*x)^-1//4*(a+-1*im*a*x)^-17//4, x) == :(-10//117*im*a^-3*(a+im*a*x)^3//4*(a+-1*im*a*x)^-9//4+-4//39*im*a^-3*(a+im*a*x)^-1//4*(a+-1*im*a*x)^-5//4+-2//13*im*a^-2*(a+im*a*x)^3//4*(a+-1*im*a*x)^-13//4+2//39*a^-4*(1+x^2)^1//4*(a+im*a*x)^-1//4*(a+-1*im*a*x)^-1//4*Elliptic.E((1/2)*arctan(x),2))
@test integrate((a+im*a*x)^-1//4*(a+-1*im*a*x)^1//4, x) == :((1/2)*im*2^(1/2)*arctan(1+2^(1/2)*(a+im*a*x)^-1//4*(a+-1*im*a*x)^1//4)+-1//2*im*2^(1/2)*arctan(1+-1*2^(1/2)*(a+im*a*x)^-1//4*(a+-1*im*a*x)^1//4)+-1//4*im*2^(1/2)*log(1+(a+im*a*x)^-1//2*(a+-1*im*a*x)^(1/2)+-1*2^(1/2)*(a+im*a*x)^-1//4*(a+-1*im*a*x)^1//4)+1//4*im*2^(1/2)*log(1+(a+im*a*x)^-1//2*(a+-1*im*a*x)^(1/2)+2^(1/2)*(a+im*a*x)^-1//4*(a+-1*im*a*x)^1//4)+-1*im*a^-1*(a+im*a*x)^3//4*(a+-1*im*a*x)^1//4)
@test integrate((a+im*a*x)^-1//4*(a+-1*im*a*x)^-3//4, x) == :(im*2^(1/2)*a^-1*arctan(1+2^(1/2)*(a+im*a*x)^-1//4*(a+-1*im*a*x)^1//4)+(1/2)*im*2^(1/2)*a^-1*log(1+(a+im*a*x)^-1//2*(a+-1*im*a*x)^(1/2)+2^(1/2)*(a+im*a*x)^-1//4*(a+-1*im*a*x)^1//4)+-1*im*2^(1/2)*a^-1*arctan(1+-1*2^(1/2)*(a+im*a*x)^-1//4*(a+-1*im*a*x)^1//4)+-1//2*im*2^(1/2)*a^-1*log(1+(a+im*a*x)^-1//2*(a+-1*im*a*x)^(1/2)+-1*2^(1/2)*(a+im*a*x)^-1//4*(a+-1*im*a*x)^1//4))
@test integrate((a+im*a*x)^-1//4*(a+-1*im*a*x)^-7//4, x) == :(-2//3*im*a^-2*(a+im*a*x)^3//4*(a+-1*im*a*x)^-3//4)
@test integrate((a+im*a*x)^-1//4*(a+-1*im*a*x)^-11//4, x) == :(-4//21*im*a^-3*(a+im*a*x)^3//4*(a+-1*im*a*x)^-3//4+-2//7*im*a^-2*(a+im*a*x)^3//4*(a+-1*im*a*x)^-7//4)
@test integrate((a+im*a*x)^-1//4*(a+-1*im*a*x)^-15//4, x) == :(-16//231*im*a^-4*(a+im*a*x)^3//4*(a+-1*im*a*x)^-3//4+-8//77*im*a^-3*(a+im*a*x)^3//4*(a+-1*im*a*x)^-7//4+-2//11*im*a^-2*(a+im*a*x)^3//4*(a+-1*im*a*x)^-11//4)
@test integrate((a+im*a*x)^-1//4*(a+-1*im*a*x)^-19//4, x) == :(-32//1155*im*a^-5*(a+im*a*x)^3//4*(a+-1*im*a*x)^-3//4+-16//385*im*a^-4*(a+im*a*x)^3//4*(a+-1*im*a*x)^-7//4+-4//55*im*a^-3*(a+im*a*x)^3//4*(a+-1*im*a*x)^-11//4+-2//15*im*a^-2*(a+im*a*x)^3//4*(a+-1*im*a*x)^-15//4)
@test integrate((a+im*a*x)^-3//4*(a+-1*im*a*x)^3//4, x) == :(-3//2*im*2^(1/2)*arctan(1+-1*2^(1/2)*(a+im*a*x)^-1//4*(a+-1*im*a*x)^1//4)+-3//4*im*2^(1/2)*log(1+(a+im*a*x)^-1//2*(a+-1*im*a*x)^(1/2)+2^(1/2)*(a+im*a*x)^-1//4*(a+-1*im*a*x)^1//4)+3//2*im*2^(1/2)*arctan(1+2^(1/2)*(a+im*a*x)^-1//4*(a+-1*im*a*x)^1//4)+3//4*im*2^(1/2)*log(1+(a+im*a*x)^-1//2*(a+-1*im*a*x)^(1/2)+-1*2^(1/2)*(a+im*a*x)^-1//4*(a+-1*im*a*x)^1//4)+-1*im*a^-1*(a+im*a*x)^1//4*(a+-1*im*a*x)^3//4)
@test integrate((a+im*a*x)^-3//4*(a+-1*im*a*x)^-1//4, x) == :(im*2^(1/2)*a^-1*arctan(1+2^(1/2)*(a+im*a*x)^-1//4*(a+-1*im*a*x)^1//4)+(1/2)*im*2^(1/2)*a^-1*log(1+(a+im*a*x)^-1//2*(a+-1*im*a*x)^(1/2)+-1*2^(1/2)*(a+im*a*x)^-1//4*(a+-1*im*a*x)^1//4)+-1*im*2^(1/2)*a^-1*arctan(1+-1*2^(1/2)*(a+im*a*x)^-1//4*(a+-1*im*a*x)^1//4)+-1//2*im*2^(1/2)*a^-1*log(1+(a+im*a*x)^-1//2*(a+-1*im*a*x)^(1/2)+2^(1/2)*(a+im*a*x)^-1//4*(a+-1*im*a*x)^1//4))
@test integrate((a+im*a*x)^-3//4*(a+-1*im*a*x)^-5//4, x) == :(-2*im*a^-2*(a+im*a*x)^1//4*(a+-1*im*a*x)^-1//4)
@test integrate((a+im*a*x)^-3//4*(a+-1*im*a*x)^-9//4, x) == :(-4//5*im*a^-3*(a+im*a*x)^1//4*(a+-1*im*a*x)^-1//4+-2//5*im*a^-2*(a+im*a*x)^1//4*(a+-1*im*a*x)^-5//4)
@test integrate((a+im*a*x)^-3//4*(a+-1*im*a*x)^-13//4, x) == :(-16//45*im*a^-4*(a+im*a*x)^1//4*(a+-1*im*a*x)^-1//4+-8//45*im*a^-3*(a+im*a*x)^1//4*(a+-1*im*a*x)^-5//4+-2//9*im*a^-2*(a+im*a*x)^1//4*(a+-1*im*a*x)^-9//4)
@test integrate((a+im*a*x)^-3//4*(a+-1*im*a*x)^5//4, x) == :(-10//3*im*(a+im*a*x)^1//4*(a+-1*im*a*x)^1//4+-2//3*im*a^-1*(a+im*a*x)^1//4*(a+-1*im*a*x)^5//4+10//3*a^2*(1+x^2)^3//4*(a+im*a*x)^-3//4*(a+-1*im*a*x)^-3//4*Elliptic.F((1/2)*arctan(x),2))
@test integrate((a+im*a*x)^-3//4*(a+-1*im*a*x)^1//4, x) == :(-2*im*a^-1*(a+im*a*x)^1//4*(a+-1*im*a*x)^1//4+2*a*(1+x^2)^3//4*(a+im*a*x)^-3//4*(a+-1*im*a*x)^-3//4*Elliptic.F((1/2)*arctan(x),2))
@test integrate((a+im*a*x)^-3//4*(a+-1*im*a*x)^-3//4, x) == :(2*(1+x^2)^3//4*(a+im*a*x)^-3//4*(a+-1*im*a*x)^-3//4*Elliptic.F((1/2)*arctan(x),2))
@test integrate((a+im*a*x)^-3//4*(a+-1*im*a*x)^-7//4, x) == :(-2//3*im*a^-2*(a+im*a*x)^1//4*(a+-1*im*a*x)^-3//4+2//3*a^-1*(1+x^2)^3//4*(a+im*a*x)^-3//4*(a+-1*im*a*x)^-3//4*Elliptic.F((1/2)*arctan(x),2))
@test integrate((a+im*a*x)^-3//4*(a+-1*im*a*x)^-11//4, x) == :(-2//7*im*a^-3*(a+im*a*x)^1//4*(a+-1*im*a*x)^-3//4+-2//7*im*a^-2*(a+im*a*x)^1//4*(a+-1*im*a*x)^-7//4+2//7*a^-2*(1+x^2)^3//4*(a+im*a*x)^-3//4*(a+-1*im*a*x)^-3//4*Elliptic.F((1/2)*arctan(x),2))
@test integrate((a+im*a*x)^-7//4*(a+-1*im*a*x)^7//4, x) == :(-7//2*im*2^(1/2)*arctan(1+2^(1/2)*(a+im*a*x)^-1//4*(a+-1*im*a*x)^1//4)+-7//4*im*2^(1/2)*log(1+(a+im*a*x)^-1//2*(a+-1*im*a*x)^(1/2)+-1*2^(1/2)*(a+im*a*x)^-1//4*(a+-1*im*a*x)^1//4)+7//2*im*2^(1/2)*arctan(1+-1*2^(1/2)*(a+im*a*x)^-1//4*(a+-1*im*a*x)^1//4)+7//4*im*2^(1/2)*log(1+(a+im*a*x)^-1//2*(a+-1*im*a*x)^(1/2)+2^(1/2)*(a+im*a*x)^-1//4*(a+-1*im*a*x)^1//4)+4//3*im*a^-1*(a+im*a*x)^-3//4*(a+-1*im*a*x)^7//4+7//3*im*a^-1*(a+im*a*x)^1//4*(a+-1*im*a*x)^3//4)
@test integrate((a+im*a*x)^-7//4*(a+-1*im*a*x)^3//4, x) == :(im*2^(1/2)*a^-1*arctan(1+-1*2^(1/2)*(a+im*a*x)^-1//4*(a+-1*im*a*x)^1//4)+(1/2)*im*2^(1/2)*a^-1*log(1+(a+im*a*x)^-1//2*(a+-1*im*a*x)^(1/2)+2^(1/2)*(a+im*a*x)^-1//4*(a+-1*im*a*x)^1//4)+-1*im*2^(1/2)*a^-1*arctan(1+2^(1/2)*(a+im*a*x)^-1//4*(a+-1*im*a*x)^1//4)+-1//2*im*2^(1/2)*a^-1*log(1+(a+im*a*x)^-1//2*(a+-1*im*a*x)^(1/2)+-1*2^(1/2)*(a+im*a*x)^-1//4*(a+-1*im*a*x)^1//4)+4//3*im*a^-1*(a+im*a*x)^-3//4*(a+-1*im*a*x)^3//4)
@test integrate((a+im*a*x)^-7//4*(a+-1*im*a*x)^-1//4, x) == :(2//3*im*a^-2*(a+im*a*x)^-3//4*(a+-1*im*a*x)^3//4)
@test integrate((a+im*a*x)^-7//4*(a+-1*im*a*x)^-5//4, x) == :(-2*im*a^-2*(a+im*a*x)^-3//4*(a+-1*im*a*x)^-1//4+4//3*im*a^-3*(a+im*a*x)^-3//4*(a+-1*im*a*x)^3//4)
@test integrate((a+im*a*x)^-7//4*(a+-1*im*a*x)^-9//4, x) == :(-8//5*im*a^-3*(a+im*a*x)^-3//4*(a+-1*im*a*x)^-1//4+-2//5*im*a^-2*(a+im*a*x)^-3//4*(a+-1*im*a*x)^-5//4+16//15*im*a^-4*(a+im*a*x)^-3//4*(a+-1*im*a*x)^3//4)
@test integrate((a+im*a*x)^-7//4*(a+-1*im*a*x)^9//4, x) == :(10*im*(a+im*a*x)^1//4*(a+-1*im*a*x)^1//4+2*im*a^-1*(a+im*a*x)^1//4*(a+-1*im*a*x)^5//4+4//3*im*a^-1*(a+im*a*x)^-3//4*(a+-1*im*a*x)^9//4+-10*a^2*(1+x^2)^3//4*(a+im*a*x)^-3//4*(a+-1*im*a*x)^-3//4*Elliptic.F((1/2)*arctan(x),2))
@test integrate((a+im*a*x)^-7//4*(a+-1*im*a*x)^5//4, x) == :(4//3*im*a^-1*(a+im*a*x)^-3//4*(a+-1*im*a*x)^5//4+10//3*im*a^-1*(a+im*a*x)^1//4*(a+-1*im*a*x)^1//4+-10//3*a*(1+x^2)^3//4*(a+im*a*x)^-3//4*(a+-1*im*a*x)^-3//4*Elliptic.F((1/2)*arctan(x),2))
@test integrate((a+im*a*x)^-7//4*(a+-1*im*a*x)^1//4, x) == :(-2//3*(1+x^2)^3//4*(a+im*a*x)^-3//4*(a+-1*im*a*x)^-3//4*Elliptic.F((1/2)*arctan(x),2)+4//3*im*a^-1*(a+im*a*x)^-3//4*(a+-1*im*a*x)^1//4)
@test integrate((a+im*a*x)^-7//4*(a+-1*im*a*x)^-3//4, x) == :(2//3*im*a^-2*(a+im*a*x)^-3//4*(a+-1*im*a*x)^1//4+2//3*a^-1*(1+x^2)^3//4*(a+im*a*x)^-3//4*(a+-1*im*a*x)^-3//4*Elliptic.F((1/2)*arctan(x),2))
@test integrate((a+im*a*x)^-7//4*(a+-1*im*a*x)^-7//4, x) == :(2//3*x*a^-2*(a+im*a*x)^-3//4*(a+-1*im*a*x)^-3//4+2//3*a^-2*(1+x^2)^3//4*(a+im*a*x)^-3//4*(a+-1*im*a*x)^-3//4*Elliptic.F((1/2)*arctan(x),2))
@test integrate((a+im*a*x)^-7//4*(a+-1*im*a*x)^-11//4, x) == :(-2//7*im*a^-2*(a+im*a*x)^-3//4*(a+-1*im*a*x)^-7//4+10//21*x*a^-3*(a+im*a*x)^-3//4*(a+-1*im*a*x)^-3//4+10//21*a^-3*(1+x^2)^3//4*(a+im*a*x)^-3//4*(a+-1*im*a*x)^-3//4*Elliptic.F((1/2)*arctan(x),2))
@test integrate((a+im*a*x)^-7//4*(a+-1*im*a*x)^-15//4, x) == :(-2//11*im*a^-3*(a+im*a*x)^-3//4*(a+-1*im*a*x)^-7//4+-2//11*im*a^-2*(a+im*a*x)^-3//4*(a+-1*im*a*x)^-11//4+10//33*x*a^-4*(a+im*a*x)^-3//4*(a+-1*im*a*x)^-3//4+10//33*a^-4*(1+x^2)^3//4*(a+im*a*x)^-3//4*(a+-1*im*a*x)^-3//4*Elliptic.F((1/2)*arctan(x),2))
@test integrate((a+im*a*x)^-5//4*(a+-1*im*a*x)^7//4, x) == :(-14*a*x*(a+im*a*x)^-1//4*(a+-1*im*a*x)^-1//4+4*im*a^-1*(a+im*a*x)^-1//4*(a+-1*im*a*x)^7//4+14//3*im*a^-1*(a+im*a*x)^3//4*(a+-1*im*a*x)^3//4+14*a*(1+x^2)^1//4*(a+im*a*x)^-1//4*(a+-1*im*a*x)^-1//4*Elliptic.E((1/2)*arctan(x),2))
@test integrate((a+im*a*x)^-5//4*(a+-1*im*a*x)^3//4, x) == :(-6*x*(a+im*a*x)^-1//4*(a+-1*im*a*x)^-1//4+4*im*a^-1*(a+im*a*x)^-1//4*(a+-1*im*a*x)^3//4+6*(1+x^2)^1//4*(a+im*a*x)^-1//4*(a+-1*im*a*x)^-1//4*Elliptic.E((1/2)*arctan(x),2))
@test integrate((a+im*a*x)^-5//4*(a+-1*im*a*x)^-1//4, x) == :(2*im*a^-1*(a+im*a*x)^-1//4*(a+-1*im*a*x)^-1//4+2*a^-1*(1+x^2)^1//4*(a+im*a*x)^-1//4*(a+-1*im*a*x)^-1//4*Elliptic.E((1/2)*arctan(x),2))
@test integrate((a+im*a*x)^-5//4*(a+-1*im*a*x)^-5//4, x) == :(2*a^-2*(1+x^2)^1//4*(a+im*a*x)^-1//4*(a+-1*im*a*x)^-1//4*Elliptic.E((1/2)*arctan(x),2))
@test integrate((a+im*a*x)^-5//4*(a+-1*im*a*x)^-9//4, x) == :(-2//5*im*a^-2*(a+im*a*x)^-1//4*(a+-1*im*a*x)^-5//4+6//5*a^-3*(1+x^2)^1//4*(a+im*a*x)^-1//4*(a+-1*im*a*x)^-1//4*Elliptic.E((1/2)*arctan(x),2))
@test integrate((a+im*a*x)^-5//4*(a+-1*im*a*x)^-13//4, x) == :(-2//9*im*a^-3*(a+im*a*x)^-1//4*(a+-1*im*a*x)^-5//4+-2//9*im*a^-2*(a+im*a*x)^-1//4*(a+-1*im*a*x)^-9//4+2//3*a^-4*(1+x^2)^1//4*(a+im*a*x)^-1//4*(a+-1*im*a*x)^-1//4*Elliptic.E((1/2)*arctan(x),2))
@test integrate((a+im*a*x)^-5//4*(a+-1*im*a*x)^5//4, x) == :(-5//2*im*2^(1/2)*arctan(1+2^(1/2)*(a+im*a*x)^-1//4*(a+-1*im*a*x)^1//4)+-5//4*im*2^(1/2)*log(1+(a+im*a*x)^-1//2*(a+-1*im*a*x)^(1/2)+2^(1/2)*(a+im*a*x)^-1//4*(a+-1*im*a*x)^1//4)+5//2*im*2^(1/2)*arctan(1+-1*2^(1/2)*(a+im*a*x)^-1//4*(a+-1*im*a*x)^1//4)+5//4*im*2^(1/2)*log(1+(a+im*a*x)^-1//2*(a+-1*im*a*x)^(1/2)+-1*2^(1/2)*(a+im*a*x)^-1//4*(a+-1*im*a*x)^1//4)+4*im*a^-1*(a+im*a*x)^-1//4*(a+-1*im*a*x)^5//4+5*im*a^-1*(a+im*a*x)^3//4*(a+-1*im*a*x)^1//4)
@test integrate((a+im*a*x)^-5//4*(a+-1*im*a*x)^1//4, x) == :(im*2^(1/2)*a^-1*arctan(1+-1*2^(1/2)*(a+im*a*x)^-1//4*(a+-1*im*a*x)^1//4)+(1/2)*im*2^(1/2)*a^-1*log(1+(a+im*a*x)^-1//2*(a+-1*im*a*x)^(1/2)+-1*2^(1/2)*(a+im*a*x)^-1//4*(a+-1*im*a*x)^1//4)+-1*im*2^(1/2)*a^-1*arctan(1+2^(1/2)*(a+im*a*x)^-1//4*(a+-1*im*a*x)^1//4)+4*im*a^-1*(a+im*a*x)^-1//4*(a+-1*im*a*x)^1//4+-1//2*im*2^(1/2)*a^-1*log(1+(a+im*a*x)^-1//2*(a+-1*im*a*x)^(1/2)+2^(1/2)*(a+im*a*x)^-1//4*(a+-1*im*a*x)^1//4))
@test integrate((a+im*a*x)^-5//4*(a+-1*im*a*x)^-3//4, x) == :(2*im*a^-2*(a+im*a*x)^-1//4*(a+-1*im*a*x)^1//4)
@test integrate((a+im*a*x)^-5//4*(a+-1*im*a*x)^-7//4, x) == :(-2//3*im*a^-2*(a+im*a*x)^-1//4*(a+-1*im*a*x)^-3//4+4//3*im*a^-3*(a+im*a*x)^-1//4*(a+-1*im*a*x)^1//4)
@test integrate((a+im*a*x)^-5//4*(a+-1*im*a*x)^-11//4, x) == :(-8//21*im*a^-3*(a+im*a*x)^-1//4*(a+-1*im*a*x)^-3//4+-2//7*im*a^-2*(a+im*a*x)^-1//4*(a+-1*im*a*x)^-7//4+16//21*im*a^-4*(a+im*a*x)^-1//4*(a+-1*im*a*x)^1//4)
@test integrate((a+im*a*x)^-9//4*(a+-1*im*a*x)^7//4, x) == :(42//5*x*(a+im*a*x)^-1//4*(a+-1*im*a*x)^-1//4+-42//5*(1+x^2)^1//4*(a+im*a*x)^-1//4*(a+-1*im*a*x)^-1//4*Elliptic.E((1/2)*arctan(x),2)+-28//5*im*a^-1*(a+im*a*x)^-1//4*(a+-1*im*a*x)^3//4+4//5*im*a^-1*(a+im*a*x)^-5//4*(a+-1*im*a*x)^7//4)
@test integrate((a+im*a*x)^-9//4*(a+-1*im*a*x)^3//4, x) == :(-6//5*im*a^-1*(a+im*a*x)^-1//4*(a+-1*im*a*x)^-1//4+4//5*im*a^-1*(a+im*a*x)^-5//4*(a+-1*im*a*x)^3//4+-6//5*a^-1*(1+x^2)^1//4*(a+im*a*x)^-1//4*(a+-1*im*a*x)^-1//4*Elliptic.E((1/2)*arctan(x),2))
@test integrate((a+im*a*x)^-9//4*(a+-1*im*a*x)^-1//4, x) == :(4//5*im*a^-1*(a+im*a*x)^-5//4*(a+-1*im*a*x)^-1//4+2//5*a^-2*(1+x^2)^1//4*(a+im*a*x)^-1//4*(a+-1*im*a*x)^-1//4*Elliptic.E((1/2)*arctan(x),2))
@test integrate((a+im*a*x)^-9//4*(a+-1*im*a*x)^-5//4, x) == :(2//5*im*a^-2*(a+im*a*x)^-5//4*(a+-1*im*a*x)^-1//4+6//5*a^-3*(1+x^2)^1//4*(a+im*a*x)^-1//4*(a+-1*im*a*x)^-1//4*Elliptic.E((1/2)*arctan(x),2))
@test integrate((a+im*a*x)^-9//4*(a+-1*im*a*x)^-9//4, x) == :(2//5*x*a^-4*(1+x^2)^-1*(a+im*a*x)^-1//4*(a+-1*im*a*x)^-1//4+6//5*a^-4*(1+x^2)^1//4*(a+im*a*x)^-1//4*(a+-1*im*a*x)^-1//4*Elliptic.E((1/2)*arctan(x),2))
@test integrate((a+im*a*x)^-9//4*(a+-1*im*a*x)^-13//4, x) == :(-2//9*im*a^-2*(a+im*a*x)^-5//4*(a+-1*im*a*x)^-9//4+14//15*a^-5*(1+x^2)^1//4*(a+im*a*x)^-1//4*(a+-1*im*a*x)^-1//4*Elliptic.E((1/2)*arctan(x),2)+14//45*x*a^-5*(1+x^2)^-1*(a+im*a*x)^-1//4*(a+-1*im*a*x)^-1//4)
@test integrate((a+im*a*x)^-9//4*(a+-1*im*a*x)^-17//4, x) == :(-2//13*im*a^-3*(a+im*a*x)^-5//4*(a+-1*im*a*x)^-9//4+-2//13*im*a^-2*(a+im*a*x)^-5//4*(a+-1*im*a*x)^-13//4+14//65*x*a^-6*(1+x^2)^-1*(a+im*a*x)^-1//4*(a+-1*im*a*x)^-1//4+42//65*a^-6*(1+x^2)^1//4*(a+im*a*x)^-1//4*(a+-1*im*a*x)^-1//4*Elliptic.E((1/2)*arctan(x),2))
@test integrate((a+im*a*x)^-9//4*(a+-1*im*a*x)^5//4, x) == :(im*2^(1/2)*a^-1*arctan(1+2^(1/2)*(a+im*a*x)^-1//4*(a+-1*im*a*x)^1//4)+(1/2)*im*2^(1/2)*a^-1*log(1+(a+im*a*x)^-1//2*(a+-1*im*a*x)^(1/2)+2^(1/2)*(a+im*a*x)^-1//4*(a+-1*im*a*x)^1//4)+-1*im*2^(1/2)*a^-1*arctan(1+-1*2^(1/2)*(a+im*a*x)^-1//4*(a+-1*im*a*x)^1//4)+-4*im*a^-1*(a+im*a*x)^-1//4*(a+-1*im*a*x)^1//4+-1//2*im*2^(1/2)*a^-1*log(1+(a+im*a*x)^-1//2*(a+-1*im*a*x)^(1/2)+-1*2^(1/2)*(a+im*a*x)^-1//4*(a+-1*im*a*x)^1//4)+4//5*im*a^-1*(a+im*a*x)^-5//4*(a+-1*im*a*x)^5//4)
@test integrate((a+im*a*x)^-9//4*(a+-1*im*a*x)^1//4, x) == :(2//5*im*a^-2*(a+im*a*x)^-5//4*(a+-1*im*a*x)^5//4)
@test integrate((a+im*a*x)^-9//4*(a+-1*im*a*x)^-3//4, x) == :(2//5*im*a^-2*(a+im*a*x)^-5//4*(a+-1*im*a*x)^1//4+4//5*im*a^-3*(a+im*a*x)^-1//4*(a+-1*im*a*x)^1//4)
@test integrate((a+im*a*x)^-9//4*(a+-1*im*a*x)^-7//4, x) == :(-2//3*im*a^-2*(a+im*a*x)^-5//4*(a+-1*im*a*x)^-3//4+8//15*im*a^-3*(a+im*a*x)^-5//4*(a+-1*im*a*x)^1//4+16//15*im*a^-4*(a+im*a*x)^-1//4*(a+-1*im*a*x)^1//4)
@test integrate((a+im*a*x)^-9//4*(a+-1*im*a*x)^-11//4, x) == :(-4//7*im*a^-3*(a+im*a*x)^-5//4*(a+-1*im*a*x)^-3//4+-2//7*im*a^-2*(a+im*a*x)^-5//4*(a+-1*im*a*x)^-7//4+16//35*im*a^-4*(a+im*a*x)^-5//4*(a+-1*im*a*x)^1//4+32//35*im*a^-5*(a+im*a*x)^-1//4*(a+-1*im*a*x)^1//4)
@test integrate((a+b*x)^2*(a*c+-1*b*c*x)^n, x) == :(-1*b^-1*c^-3*(3+n)^-1*(a*c+-1*b*c*x)^(3+n)+-4*a^2*b^-1*c^-1*(1+n)^-1*(a*c+-1*b*c*x)^(1+n)+4*a*b^-1*c^-2*(2+n)^-1*(a*c+-1*b*c*x)^(2+n))
@test integrate((a*c+-1*b*c*x)^n*(a+b*x), x) == :(b^-1*c^-2*(2+n)^-1*(a*c+-1*b*c*x)^(2+n)+-2*a*b^-1*c^-1*(1+n)^-1*(a*c+-1*b*c*x)^(1+n))
@test integrate((a+b*x)^4*(c+d*x), x) == :(1//5*b^-2*(a+b*x)^5*(b*c+-1*a*d)+1//6*d*b^-2*(a+b*x)^6)
@test integrate((a+b*x)^3*(c+d*x), x) == :(1//4*b^-2*(a+b*x)^4*(b*c+-1*a*d)+1//5*d*b^-2*(a+b*x)^5)
@test integrate((a+b*x)^2*(c+d*x), x) == :(1//3*b^-2*(a+b*x)^3*(b*c+-1*a*d)+1//4*d*b^-2*(a+b*x)^4)
@test integrate((a+b*x)*(c+d*x), x) == :(x^2*((1/2)*a*d+(1/2)*b*c)+a*c*x+1//3*b*d*x^3)
@test integrate(c+d*x, x) == :(c*x+(1/2)*d*x^2)
@test integrate((a+b*x)^-1*(c+d*x), x) == :(d*x*b^-1+b^-2*(b*c+-1*a*d)*log(a+b*x))
@test integrate((a+b*x)^-2*(c+d*x), x) == :(d*b^-2*log(a+b*x)+-1*b^-2*(a+b*x)^-1*(b*c+-1*a*d))
@test integrate((a+b*x)^-3*(c+d*x), x) == :(-1*(a+b*x)^-2*(c+d*x)^2*(-2*a*d+2*b*c)^-1)
@test integrate((a+b*x)^-4*(c+d*x), x) == :(-1//2*d*b^-2*(a+b*x)^-2+-1//3*b^-2*(a+b*x)^-3*(b*c+-1*a*d))
@test integrate((a+b*x)^-5*(c+d*x), x) == :(-1//3*d*b^-2*(a+b*x)^-3+-1//4*b^-2*(a+b*x)^-4*(b*c+-1*a*d))
@test integrate((a+b*x)^4*(c+d*x)^2, x) == :(1//5*b^-3*(a+b*x)^5*(b*c+-1*a*d)^2+1//7*b^-3*d^2*(a+b*x)^7+1//3*d*b^-3*(a+b*x)^6*(b*c+-1*a*d))
@test integrate((a+b*x)^3*(c+d*x)^2, x) == :(1//4*b^-3*(a+b*x)^4*(b*c+-1*a*d)^2+1//6*b^-3*d^2*(a+b*x)^6+2//5*d*b^-3*(a+b*x)^5*(b*c+-1*a*d))
@test integrate((a+b*x)^2*(c+d*x)^2, x) == :(1//3*b^-3*(a+b*x)^3*(b*c+-1*a*d)^2+1//5*b^-3*d^2*(a+b*x)^5+(1/2)*d*b^-3*(a+b*x)^4*(b*c+-1*a*d))
@test integrate((c+d*x)^2*(a+b*x), x) == :(-1//3*d^-2*(c+d*x)^3*(b*c+-1*a*d)+1//4*b*d^-2*(c+d*x)^4)
@test integrate((c+d*x)^2, x) == :(1//3*d^-1*(c+d*x)^3)
@test integrate((a+b*x)^-1*(c+d*x)^2, x) == :((1/2)*b^-1*(c+d*x)^2+b^-3*(b*c+-1*a*d)^2*log(a+b*x)+d*x*b^-2*(b*c+-1*a*d))
@test integrate((a+b*x)^-2*(c+d*x)^2, x) == :(x*b^-2*d^2+-1*b^-3*(a+b*x)^-1*(b*c+-1*a*d)^2+2*d*b^-3*(b*c+-1*a*d)*log(a+b*x))
@test integrate((a+b*x)^-3*(c+d*x)^2, x) == :(b^-3*d^2*log(a+b*x)+-1//2*b^-3*(a+b*x)^-2*(b*c+-1*a*d)^2+-2*d*b^-3*(a+b*x)^-1*(b*c+-1*a*d))
@test integrate((a+b*x)^-4*(c+d*x)^2, x) == :(-1*(a+b*x)^-3*(c+d*x)^3*(-3*a*d+3*b*c)^-1)
@test integrate((a+b*x)^-5*(c+d*x)^2, x) == :(-1//2*b^-3*d^2*(a+b*x)^-2+-1//4*b^-3*(a+b*x)^-4*(b*c+-1*a*d)^2+-2//3*d*b^-3*(a+b*x)^-3*(b*c+-1*a*d))
@test integrate((a+b*x)^-6*(c+d*x)^2, x) == :(-1//3*b^-3*d^2*(a+b*x)^-3+-1//5*b^-3*(a+b*x)^-5*(b*c+-1*a*d)^2+-1//2*d*b^-3*(a+b*x)^-4*(b*c+-1*a*d))
@test integrate((a+b*x)^-7*(c+d*x)^2, x) == :(-1//4*b^-3*d^2*(a+b*x)^-4+-1//6*b^-3*(a+b*x)^-6*(b*c+-1*a*d)^2+-2//5*d*b^-3*(a+b*x)^-5*(b*c+-1*a*d))
@test integrate((a+b*x)^5*(c+d*x)^3, x) == :(1//6*b^-4*(a+b*x)^6*(b*c+-1*a*d)^3+1//9*b^-4*d^3*(a+b*x)^9+3//7*d*b^-4*(a+b*x)^7*(b*c+-1*a*d)^2+3//8*b^-4*d^2*(a+b*x)^8*(b*c+-1*a*d))
@test integrate((a+b*x)^4*(c+d*x)^3, x) == :(1//5*b^-4*(a+b*x)^5*(b*c+-1*a*d)^3+1//8*b^-4*d^3*(a+b*x)^8+(1/2)*d*b^-4*(a+b*x)^6*(b*c+-1*a*d)^2+3//7*b^-4*d^2*(a+b*x)^7*(b*c+-1*a*d))
@test integrate((a+b*x)^3*(c+d*x)^3, x) == :(1//4*b^-4*(a+b*x)^4*(b*c+-1*a*d)^3+1//7*b^-4*d^3*(a+b*x)^7+(1/2)*b^-4*d^2*(a+b*x)^6*(b*c+-1*a*d)+3//5*d*b^-4*(a+b*x)^5*(b*c+-1*a*d)^2)
@test integrate((a+b*x)^2*(c+d*x)^3, x) == :(1//4*d^-3*(c+d*x)^4*(b*c+-1*a*d)^2+1//6*b^2*d^-3*(c+d*x)^6+-2//5*b*d^-3*(c+d*x)^5*(b*c+-1*a*d))
@test integrate((c+d*x)^3*(a+b*x), x) == :(-1//4*d^-2*(c+d*x)^4*(b*c+-1*a*d)+1//5*b*d^-2*(c+d*x)^5)
@test integrate((c+d*x)^3, x) == :(1//4*d^-1*(c+d*x)^4)
@test integrate((a+b*x)^-1*(c+d*x)^3, x) == :(1//3*b^-1*(c+d*x)^3+b^-4*(b*c+-1*a*d)^3*log(a+b*x)+(1/2)*b^-2*(c+d*x)^2*(b*c+-1*a*d)+d*x*b^-3*(b*c+-1*a*d)^2)
@test integrate((a+b*x)^-2*(c+d*x)^3, x) == :((1/2)*b^-2*d^3*x^2+-1*b^-4*(a+b*x)^-1*(b*c+-1*a*d)^3+x*b^-3*d^2*(-2*a*d+3*b*c)+3*d*b^-4*(b*c+-1*a*d)^2*log(a+b*x))
@test integrate((a+b*x)^-3*(c+d*x)^3, x) == :(x*b^-3*d^3+-1//2*b^-4*(a+b*x)^-2*(b*c+-1*a*d)^3+-3*d*b^-4*(a+b*x)^-1*(b*c+-1*a*d)^2+3*b^-4*d^2*(b*c+-1*a*d)*log(a+b*x))
@test integrate((a+b*x)^-4*(c+d*x)^3, x) == :(b^-4*d^3*log(a+b*x)+-1//3*b^-4*(a+b*x)^-3*(b*c+-1*a*d)^3+-3*b^-4*d^2*(a+b*x)^-1*(b*c+-1*a*d)+-3//2*d*b^-4*(a+b*x)^-2*(b*c+-1*a*d)^2)
@test integrate((a+b*x)^-5*(c+d*x)^3, x) == :(-1*(a+b*x)^-4*(c+d*x)^4*(-4*a*d+4*b*c)^-1)
@test integrate((a+b*x)^-6*(c+d*x)^3, x) == :(-1*(a+b*x)^-5*(c+d*x)^4*(-5*a*d+5*b*c)^-1+1//20*d*(a+b*x)^-4*(c+d*x)^4*(b*c+-1*a*d)^-2)
@test integrate((a+b*x)^-7*(c+d*x)^3, x) == :(-1//3*b^-4*d^3*(a+b*x)^-3+-1//6*b^-4*(a+b*x)^-6*(b*c+-1*a*d)^3+-3//4*b^-4*d^2*(a+b*x)^-4*(b*c+-1*a*d)+-3//5*d*b^-4*(a+b*x)^-5*(b*c+-1*a*d)^2)
@test integrate((a+b*x)^-8*(c+d*x)^3, x) == :(-1//4*b^-4*d^3*(a+b*x)^-4+-1//7*b^-4*(a+b*x)^-7*(b*c+-1*a*d)^3+-3//5*b^-4*d^2*(a+b*x)^-5*(b*c+-1*a*d)+-1//2*d*b^-4*(a+b*x)^-6*(b*c+-1*a*d)^2)
@test integrate((a+b*x)^-9*(c+d*x)^3, x) == :(-1//5*b^-4*d^3*(a+b*x)^-5+-1//8*b^-4*(a+b*x)^-8*(b*c+-1*a*d)^3+-3//7*d*b^-4*(a+b*x)^-7*(b*c+-1*a*d)^2+-1//2*b^-4*d^2*(a+b*x)^-6*(b*c+-1*a*d))
@test integrate((a+b*x)^9*(c+d*x)^7, x) == :(1//10*b^-8*(a+b*x)^10*(b*c+-1*a*d)^7+1//17*b^-8*d^7*(a+b*x)^17+5//2*b^-8*d^4*(a+b*x)^14*(b*c+-1*a*d)^3+7//4*b^-8*d^2*(a+b*x)^12*(b*c+-1*a*d)^5+7//5*b^-8*d^5*(a+b*x)^15*(b*c+-1*a*d)^2+7//11*d*b^-8*(a+b*x)^11*(b*c+-1*a*d)^6+7//16*b^-8*d^6*(a+b*x)^16*(b*c+-1*a*d)+35//13*b^-8*d^3*(a+b*x)^13*(b*c+-1*a*d)^4)
@test integrate((a+b*x)^8*(c+d*x)^7, x) == :(1//9*b^-8*(a+b*x)^9*(b*c+-1*a*d)^7+1//16*b^-8*d^7*(a+b*x)^16+3//2*b^-8*d^5*(a+b*x)^14*(b*c+-1*a*d)^2+7//10*d*b^-8*(a+b*x)^10*(b*c+-1*a*d)^6+7//15*b^-8*d^6*(a+b*x)^15*(b*c+-1*a*d)+21//11*b^-8*d^2*(a+b*x)^11*(b*c+-1*a*d)^5+35//12*b^-8*d^3*(a+b*x)^12*(b*c+-1*a*d)^4+35//13*b^-8*d^4*(a+b*x)^13*(b*c+-1*a*d)^3)
@test integrate((a+b*x)^7*(c+d*x)^7, x) == :(1//8*b^-8*(a+b*x)^8*(b*c+-1*a*d)^7+1//15*b^-8*d^7*(a+b*x)^15+(1/2)*b^-8*d^6*(a+b*x)^14*(b*c+-1*a*d)+7//9*d*b^-8*(a+b*x)^9*(b*c+-1*a*d)^6+21//10*b^-8*d^2*(a+b*x)^10*(b*c+-1*a*d)^5+21//13*b^-8*d^5*(a+b*x)^13*(b*c+-1*a*d)^2+35//11*b^-8*d^3*(a+b*x)^11*(b*c+-1*a*d)^4+35//12*b^-8*d^4*(a+b*x)^12*(b*c+-1*a*d)^3)
@test integrate((a+b*x)^6*(c+d*x)^7, x) == :(1//8*d^-7*(c+d*x)^8*(b*c+-1*a*d)^6+1//14*b^6*d^-7*(c+d*x)^14+-20//11*b^3*d^-7*(c+d*x)^11*(b*c+-1*a*d)^3+-6//13*b^5*d^-7*(c+d*x)^13*(b*c+-1*a*d)+-2//3*b*d^-7*(c+d*x)^9*(b*c+-1*a*d)^5+3//2*b^2*d^-7*(c+d*x)^10*(b*c+-1*a*d)^4+5//4*b^4*d^-7*(c+d*x)^12*(b*c+-1*a*d)^2)
@test integrate((a+b*x)^5*(c+d*x)^7, x) == :(-1//8*d^-6*(c+d*x)^8*(b*c+-1*a*d)^5+1//13*b^5*d^-6*(c+d*x)^13+-1*b^2*d^-6*(c+d*x)^10*(b*c+-1*a*d)^3+-5//12*b^4*d^-6*(c+d*x)^12*(b*c+-1*a*d)+5//9*b*d^-6*(c+d*x)^9*(b*c+-1*a*d)^4+10//11*b^3*d^-6*(c+d*x)^11*(b*c+-1*a*d)^2)
@test integrate((a+b*x)^4*(c+d*x)^7, x) == :(1//8*d^-5*(c+d*x)^8*(b*c+-1*a*d)^4+1//12*b^4*d^-5*(c+d*x)^12+-4//9*b*d^-5*(c+d*x)^9*(b*c+-1*a*d)^3+-4//11*b^3*d^-5*(c+d*x)^11*(b*c+-1*a*d)+3//5*b^2*d^-5*(c+d*x)^10*(b*c+-1*a*d)^2)
@test integrate((a+b*x)^3*(c+d*x)^7, x) == :(-1//8*d^-4*(c+d*x)^8*(b*c+-1*a*d)^3+1//11*b^3*d^-4*(c+d*x)^11+-3//10*b^2*d^-4*(c+d*x)^10*(b*c+-1*a*d)+1//3*b*d^-4*(c+d*x)^9*(b*c+-1*a*d)^2)
@test integrate((a+b*x)^2*(c+d*x)^7, x) == :(1//8*d^-3*(c+d*x)^8*(b*c+-1*a*d)^2+1//10*b^2*d^-3*(c+d*x)^10+-2//9*b*d^-3*(c+d*x)^9*(b*c+-1*a*d))
@test integrate((c+d*x)^7*(a+b*x), x) == :(-1//8*d^-2*(c+d*x)^8*(b*c+-1*a*d)+1//9*b*d^-2*(c+d*x)^9)
@test integrate((c+d*x)^7, x) == :(1//8*d^-1*(c+d*x)^8)
@test integrate((a+b*x)^-1*(c+d*x)^7, x) == :(1//7*b^-1*(c+d*x)^7+b^-8*(b*c+-1*a*d)^7*log(a+b*x)+(1/2)*b^-6*(c+d*x)^2*(b*c+-1*a*d)^5+1//3*b^-5*(c+d*x)^3*(b*c+-1*a*d)^4+1//4*b^-4*(c+d*x)^4*(b*c+-1*a*d)^3+1//5*b^-3*(c+d*x)^5*(b*c+-1*a*d)^2+1//6*b^-2*(c+d*x)^6*(b*c+-1*a*d)+d*x*b^-7*(b*c+-1*a*d)^6)
@test integrate((a+b*x)^-2*(c+d*x)^7, x) == :(-1*b^-8*(a+b*x)^-1*(b*c+-1*a*d)^7+1//6*b^-8*d^7*(a+b*x)^6+7*d*b^-8*(b*c+-1*a*d)^6*log(a+b*x)+21*x*b^-7*d^2*(b*c+-1*a*d)^5+7//5*b^-8*d^6*(a+b*x)^5*(b*c+-1*a*d)+21//4*b^-8*d^5*(a+b*x)^4*(b*c+-1*a*d)^2+35//2*b^-8*d^3*(a+b*x)^2*(b*c+-1*a*d)^4+35//3*b^-8*d^4*(a+b*x)^3*(b*c+-1*a*d)^3)
@test integrate((a+b*x)^-3*(c+d*x)^7, x) == :(-1//2*b^-8*(a+b*x)^-2*(b*c+-1*a*d)^7+1//5*b^-8*d^7*(a+b*x)^5+-7*d*b^-8*(a+b*x)^-1*(b*c+-1*a*d)^6+7*b^-8*d^5*(a+b*x)^3*(b*c+-1*a*d)^2+21*b^-8*d^2*(b*c+-1*a*d)^5*log(a+b*x)+35*x*b^-7*d^3*(b*c+-1*a*d)^4+7//4*b^-8*d^6*(a+b*x)^4*(b*c+-1*a*d)+35//2*b^-8*d^4*(a+b*x)^2*(b*c+-1*a*d)^3)
@test integrate((a+b*x)^-4*(c+d*x)^7, x) == :(-1//3*b^-8*(a+b*x)^-3*(b*c+-1*a*d)^7+1//4*b^-8*d^7*(a+b*x)^4+-21*b^-8*d^2*(a+b*x)^-1*(b*c+-1*a*d)^5+35*x*b^-7*d^4*(b*c+-1*a*d)^3+35*b^-8*d^3*(b*c+-1*a*d)^4*log(a+b*x)+-7//2*d*b^-8*(a+b*x)^-2*(b*c+-1*a*d)^6+7//3*b^-8*d^6*(a+b*x)^3*(b*c+-1*a*d)+21//2*b^-8*d^5*(a+b*x)^2*(b*c+-1*a*d)^2)
@test integrate((a+b*x)^-5*(c+d*x)^7, x) == :(-1//4*b^-8*(a+b*x)^-4*(b*c+-1*a*d)^7+1//3*b^-8*d^7*(a+b*x)^3+-35*b^-8*d^3*(a+b*x)^-1*(b*c+-1*a*d)^4+21*x*b^-7*d^5*(b*c+-1*a*d)^2+35*b^-8*d^4*(b*c+-1*a*d)^3*log(a+b*x)+-21//2*b^-8*d^2*(a+b*x)^-2*(b*c+-1*a*d)^5+-7//3*d*b^-8*(a+b*x)^-3*(b*c+-1*a*d)^6+7//2*b^-8*d^6*(a+b*x)^2*(b*c+-1*a*d))
@test integrate((a+b*x)^-6*(c+d*x)^7, x) == :((1/2)*b^-6*d^7*x^2+-1//5*b^-8*(a+b*x)^-5*(b*c+-1*a*d)^7+x*b^-7*d^6*(-6*a*d+7*b*c)+-35*b^-8*d^4*(a+b*x)^-1*(b*c+-1*a*d)^3+-7*b^-8*d^2*(a+b*x)^-3*(b*c+-1*a*d)^5+21*b^-8*d^5*(b*c+-1*a*d)^2*log(a+b*x)+-35//2*b^-8*d^3*(a+b*x)^-2*(b*c+-1*a*d)^4+-7//4*d*b^-8*(a+b*x)^-4*(b*c+-1*a*d)^6)
@test integrate((a+b*x)^-7*(c+d*x)^7, x) == :(x*b^-7*d^7+-1//6*b^-8*(a+b*x)^-6*(b*c+-1*a*d)^7+-21*b^-8*d^5*(a+b*x)^-1*(b*c+-1*a*d)^2+7*b^-8*d^6*(b*c+-1*a*d)*log(a+b*x)+-35//2*b^-8*d^4*(a+b*x)^-2*(b*c+-1*a*d)^3+-35//3*b^-8*d^3*(a+b*x)^-3*(b*c+-1*a*d)^4+-21//4*b^-8*d^2*(a+b*x)^-4*(b*c+-1*a*d)^5+-7//5*d*b^-8*(a+b*x)^-5*(b*c+-1*a*d)^6)
@test integrate((a+b*x)^-8*(c+d*x)^7, x) == :(b^-8*d^7*log(a+b*x)+-1//7*b^-8*(a+b*x)^-7*(b*c+-1*a*d)^7+-7*b^-8*d^6*(a+b*x)^-1*(b*c+-1*a*d)+-35//3*b^-8*d^4*(a+b*x)^-3*(b*c+-1*a*d)^3+-35//4*b^-8*d^3*(a+b*x)^-4*(b*c+-1*a*d)^4+-21//2*b^-8*d^5*(a+b*x)^-2*(b*c+-1*a*d)^2+-21//5*b^-8*d^2*(a+b*x)^-5*(b*c+-1*a*d)^5+-7//6*d*b^-8*(a+b*x)^-6*(b*c+-1*a*d)^6)
@test integrate((a+b*x)^-9*(c+d*x)^7, x) == :(-1*(a+b*x)^-8*(c+d*x)^8*(-8*a*d+8*b*c)^-1)
@test integrate((a+b*x)^-10*(c+d*x)^7, x) == :(-1*(a+b*x)^-9*(c+d*x)^8*(-9*a*d+9*b*c)^-1+1//72*d*(a+b*x)^-8*(c+d*x)^8*(b*c+-1*a*d)^-2)
@test integrate((a+b*x)^-11*(c+d*x)^7, x) == :(-1*(a+b*x)^-10*(c+d*x)^8*(-10*a*d+10*b*c)^-1+-1//360*d^2*(a+b*x)^-8*(c+d*x)^8*(b*c+-1*a*d)^-3+1//45*d*(a+b*x)^-9*(c+d*x)^8*(b*c+-1*a*d)^-2)
@test integrate((a+b*x)^-12*(c+d*x)^7, x) == :(-1*(a+b*x)^-11*(c+d*x)^8*(-11*a*d+11*b*c)^-1+-1//165*d^2*(a+b*x)^-9*(c+d*x)^8*(b*c+-1*a*d)^-3+1//1320*d^3*(a+b*x)^-8*(c+d*x)^8*(b*c+-1*a*d)^-4+3//110*d*(a+b*x)^-10*(c+d*x)^8*(b*c+-1*a*d)^-2)
@test integrate((a+b*x)^-13*(c+d*x)^7, x) == :(-1*(a+b*x)^-12*(c+d*x)^8*(-12*a*d+12*b*c)^-1+-1//110*d^2*(a+b*x)^-10*(c+d*x)^8*(b*c+-1*a*d)^-3+-1//3960*d^4*(a+b*x)^-8*(c+d*x)^8*(b*c+-1*a*d)^-5+1//33*d*(a+b*x)^-11*(c+d*x)^8*(b*c+-1*a*d)^-2+1//495*d^3*(a+b*x)^-9*(c+d*x)^8*(b*c+-1*a*d)^-4)
@test integrate((a+b*x)^-14*(c+d*x)^7, x) == :(-1//6*b^-8*d^7*(a+b*x)^-6+-1//13*b^-8*(a+b*x)^-13*(b*c+-1*a*d)^7+-1*b^-8*d^6*(a+b*x)^-7*(b*c+-1*a*d)+-35//9*b^-8*d^4*(a+b*x)^-9*(b*c+-1*a*d)^3+-21//8*b^-8*d^5*(a+b*x)^-8*(b*c+-1*a*d)^2+-21//11*b^-8*d^2*(a+b*x)^-11*(b*c+-1*a*d)^5+-7//2*b^-8*d^3*(a+b*x)^-10*(b*c+-1*a*d)^4+-7//12*d*b^-8*(a+b*x)^-12*(b*c+-1*a*d)^6)
@test integrate((a+b*x)^-15*(c+d*x)^7, x) == :(-1//7*b^-8*d^7*(a+b*x)^-7+-1//14*b^-8*(a+b*x)^-14*(b*c+-1*a*d)^7+-35//11*b^-8*d^3*(a+b*x)^-11*(b*c+-1*a*d)^4+-7//2*b^-8*d^4*(a+b*x)^-10*(b*c+-1*a*d)^3+-7//3*b^-8*d^5*(a+b*x)^-9*(b*c+-1*a*d)^2+-7//4*b^-8*d^2*(a+b*x)^-12*(b*c+-1*a*d)^5+-7//8*b^-8*d^6*(a+b*x)^-8*(b*c+-1*a*d)+-7//13*d*b^-8*(a+b*x)^-13*(b*c+-1*a*d)^6)
@test integrate((a+b*x)^-16*(c+d*x)^7, x) == :(-1//8*b^-8*d^7*(a+b*x)^-8+-1//15*b^-8*(a+b*x)^-15*(b*c+-1*a*d)^7+-35//11*b^-8*d^4*(a+b*x)^-11*(b*c+-1*a*d)^3+-35//12*b^-8*d^3*(a+b*x)^-12*(b*c+-1*a*d)^4+-21//10*b^-8*d^5*(a+b*x)^-10*(b*c+-1*a*d)^2+-21//13*b^-8*d^2*(a+b*x)^-13*(b*c+-1*a*d)^5+-7//9*b^-8*d^6*(a+b*x)^-9*(b*c+-1*a*d)+-1//2*d*b^-8*(a+b*x)^-14*(b*c+-1*a*d)^6)
@test integrate((a+b*x)^12*(c+d*x)^10, x) == :(1//13*b^-11*(a+b*x)^13*(b*c+-1*a*d)^10+1//23*b^-11*d^10*(a+b*x)^23+3*b^-11*d^2*(a+b*x)^15*(b*c+-1*a*d)^8+6*b^-11*d^7*(a+b*x)^20*(b*c+-1*a*d)^3+14*b^-11*d^5*(a+b*x)^18*(b*c+-1*a*d)^5+5//7*d*b^-11*(a+b*x)^14*(b*c+-1*a*d)^9+5//11*b^-11*d^9*(a+b*x)^22*(b*c+-1*a*d)+15//2*b^-11*d^3*(a+b*x)^16*(b*c+-1*a*d)^7+15//7*b^-11*d^8*(a+b*x)^21*(b*c+-1*a*d)^2+210//17*b^-11*d^4*(a+b*x)^17*(b*c+-1*a*d)^6+210//19*b^-11*d^6*(a+b*x)^19*(b*c+-1*a*d)^4)
@test integrate((a+b*x)^11*(c+d*x)^10, x) == :(1//12*b^-11*(a+b*x)^12*(b*c+-1*a*d)^10+1//22*b^-11*d^10*(a+b*x)^22+8*b^-11*d^3*(a+b*x)^15*(b*c+-1*a*d)^7+9//4*b^-11*d^8*(a+b*x)^20*(b*c+-1*a*d)^2+10//13*d*b^-11*(a+b*x)^13*(b*c+-1*a*d)^9+10//21*b^-11*d^9*(a+b*x)^21*(b*c+-1*a*d)+35//3*b^-11*d^6*(a+b*x)^18*(b*c+-1*a*d)^4+45//14*b^-11*d^2*(a+b*x)^14*(b*c+-1*a*d)^8+105//8*b^-11*d^4*(a+b*x)^16*(b*c+-1*a*d)^6+120//19*b^-11*d^7*(a+b*x)^19*(b*c+-1*a*d)^3+252//17*b^-11*d^5*(a+b*x)^17*(b*c+-1*a*d)^5)
@test integrate((a+b*x)^10*(c+d*x)^10, x) == :(1//11*b^-11*(a+b*x)^11*(b*c+-1*a*d)^10+1//21*b^-11*d^10*(a+b*x)^21+(1/2)*b^-11*d^9*(a+b*x)^20*(b*c+-1*a*d)+14*b^-11*d^4*(a+b*x)^15*(b*c+-1*a*d)^6+5//6*d*b^-11*(a+b*x)^12*(b*c+-1*a*d)^9+20//3*b^-11*d^7*(a+b*x)^18*(b*c+-1*a*d)^3+45//13*b^-11*d^2*(a+b*x)^13*(b*c+-1*a*d)^8+45//19*b^-11*d^8*(a+b*x)^19*(b*c+-1*a*d)^2+60//7*b^-11*d^3*(a+b*x)^14*(b*c+-1*a*d)^7+63//4*b^-11*d^5*(a+b*x)^16*(b*c+-1*a*d)^5+210//17*b^-11*d^6*(a+b*x)^17*(b*c+-1*a*d)^4)
@test integrate((a+b*x)^9*(c+d*x)^10, x) == :(-1//11*d^-10*(c+d*x)^11*(b*c+-1*a*d)^9+1//20*b^9*d^-10*(c+d*x)^20+2*b^7*d^-10*(c+d*x)^18*(b*c+-1*a*d)^2+6*b^3*d^-10*(c+d*x)^14*(b*c+-1*a*d)^6+-84//17*b^6*d^-10*(c+d*x)^17*(b*c+-1*a*d)^3+-42//5*b^4*d^-10*(c+d*x)^15*(b*c+-1*a*d)^5+-36//13*b^2*d^-10*(c+d*x)^13*(b*c+-1*a*d)^7+-9//19*b^8*d^-10*(c+d*x)^19*(b*c+-1*a*d)+3//4*b*d^-10*(c+d*x)^12*(b*c+-1*a*d)^8+63//8*b^5*d^-10*(c+d*x)^16*(b*c+-1*a*d)^4)
@test integrate((a+b*x)^8*(c+d*x)^10, x) == :(1//11*d^-9*(c+d*x)^11*(b*c+-1*a*d)^8+1//19*b^8*d^-9*(c+d*x)^19+-4*b^3*d^-9*(c+d*x)^14*(b*c+-1*a*d)^5+-7//2*b^5*d^-9*(c+d*x)^16*(b*c+-1*a*d)^3+-4//9*b^7*d^-9*(c+d*x)^18*(b*c+-1*a*d)+-2//3*b*d^-9*(c+d*x)^12*(b*c+-1*a*d)^7+14//3*b^4*d^-9*(c+d*x)^15*(b*c+-1*a*d)^4+28//13*b^2*d^-9*(c+d*x)^13*(b*c+-1*a*d)^6+28//17*b^6*d^-9*(c+d*x)^17*(b*c+-1*a*d)^2)
@test integrate((a+b*x)^7*(c+d*x)^10, x) == :(-1//11*d^-8*(c+d*x)^11*(b*c+-1*a*d)^7+1//18*b^7*d^-8*(c+d*x)^18+-21//13*b^2*d^-8*(c+d*x)^13*(b*c+-1*a*d)^5+-7//3*b^4*d^-8*(c+d*x)^15*(b*c+-1*a*d)^3+-7//17*b^6*d^-8*(c+d*x)^17*(b*c+-1*a*d)+5//2*b^3*d^-8*(c+d*x)^14*(b*c+-1*a*d)^4+7//12*b*d^-8*(c+d*x)^12*(b*c+-1*a*d)^6+21//16*b^5*d^-8*(c+d*x)^16*(b*c+-1*a*d)^2)
@test integrate((a+b*x)^6*(c+d*x)^10, x) == :(1//11*d^-7*(c+d*x)^11*(b*c+-1*a*d)^6+1//17*b^6*d^-7*(c+d*x)^17+b^4*d^-7*(c+d*x)^15*(b*c+-1*a*d)^2+-10//7*b^3*d^-7*(c+d*x)^14*(b*c+-1*a*d)^3+-3//8*b^5*d^-7*(c+d*x)^16*(b*c+-1*a*d)+-1//2*b*d^-7*(c+d*x)^12*(b*c+-1*a*d)^5+15//13*b^2*d^-7*(c+d*x)^13*(b*c+-1*a*d)^4)
@test integrate((a+b*x)^5*(c+d*x)^10, x) == :(-1//11*d^-6*(c+d*x)^11*(b*c+-1*a*d)^5+1//16*b^5*d^-6*(c+d*x)^16+-10//13*b^2*d^-6*(c+d*x)^13*(b*c+-1*a*d)^3+-1//3*b^4*d^-6*(c+d*x)^15*(b*c+-1*a*d)+5//7*b^3*d^-6*(c+d*x)^14*(b*c+-1*a*d)^2+5//12*b*d^-6*(c+d*x)^12*(b*c+-1*a*d)^4)
@test integrate((a+b*x)^4*(c+d*x)^10, x) == :(1//11*d^-5*(c+d*x)^11*(b*c+-1*a*d)^4+1//15*b^4*d^-5*(c+d*x)^15+-2//7*b^3*d^-5*(c+d*x)^14*(b*c+-1*a*d)+-1//3*b*d^-5*(c+d*x)^12*(b*c+-1*a*d)^3+6//13*b^2*d^-5*(c+d*x)^13*(b*c+-1*a*d)^2)
@test integrate((a+b*x)^3*(c+d*x)^10, x) == :(-1//11*d^-4*(c+d*x)^11*(b*c+-1*a*d)^3+1//14*b^3*d^-4*(c+d*x)^14+-3//13*b^2*d^-4*(c+d*x)^13*(b*c+-1*a*d)+1//4*b*d^-4*(c+d*x)^12*(b*c+-1*a*d)^2)
@test integrate((a+b*x)^2*(c+d*x)^10, x) == :(1//11*d^-3*(c+d*x)^11*(b*c+-1*a*d)^2+1//13*b^2*d^-3*(c+d*x)^13+-1//6*b*d^-3*(c+d*x)^12*(b*c+-1*a*d))
@test integrate((c+d*x)^10*(a+b*x), x) == :(-1//11*d^-2*(c+d*x)^11*(b*c+-1*a*d)+1//12*b*d^-2*(c+d*x)^12)
@test integrate((c+d*x)^10, x) == :(1//11*d^-1*(c+d*x)^11)
@test integrate((a+b*x)^-1*(c+d*x)^10, x) == :(1//10*b^-1*(c+d*x)^10+b^-11*(b*c+-1*a*d)^10*log(a+b*x)+(1/2)*b^-9*(c+d*x)^2*(b*c+-1*a*d)^8+1//3*b^-8*(c+d*x)^3*(b*c+-1*a*d)^7+1//4*b^-7*(c+d*x)^4*(b*c+-1*a*d)^6+1//5*b^-6*(c+d*x)^5*(b*c+-1*a*d)^5+1//6*b^-5*(c+d*x)^6*(b*c+-1*a*d)^4+1//7*b^-4*(c+d*x)^7*(b*c+-1*a*d)^3+1//8*b^-3*(c+d*x)^8*(b*c+-1*a*d)^2+1//9*b^-2*(c+d*x)^9*(b*c+-1*a*d)+d*x*b^-10*(b*c+-1*a*d)^9)
@test integrate((a+b*x)^-2*(c+d*x)^10, x) == :(-1*b^-11*(a+b*x)^-1*(b*c+-1*a*d)^10+1//9*b^-11*d^10*(a+b*x)^9+10*d*b^-11*(b*c+-1*a*d)^9*log(a+b*x)+20*b^-11*d^7*(a+b*x)^6*(b*c+-1*a*d)^3+42*b^-11*d^6*(a+b*x)^5*(b*c+-1*a*d)^4+45*x*b^-10*d^2*(b*c+-1*a*d)^8+60*b^-11*d^3*(a+b*x)^2*(b*c+-1*a*d)^7+63*b^-11*d^5*(a+b*x)^4*(b*c+-1*a*d)^5+70*b^-11*d^4*(a+b*x)^3*(b*c+-1*a*d)^6+5//4*b^-11*d^9*(a+b*x)^8*(b*c+-1*a*d)+45//7*b^-11*d^8*(a+b*x)^7*(b*c+-1*a*d)^2)
@test integrate((a+b*x)^-3*(c+d*x)^10, x) == :(-1//2*b^-11*(a+b*x)^-2*(b*c+-1*a*d)^10+1//8*b^-11*d^10*(a+b*x)^8+-10*d*b^-11*(a+b*x)^-1*(b*c+-1*a*d)^9+24*b^-11*d^7*(a+b*x)^5*(b*c+-1*a*d)^3+45*b^-11*d^2*(b*c+-1*a*d)^8*log(a+b*x)+84*b^-11*d^5*(a+b*x)^3*(b*c+-1*a*d)^5+105*b^-11*d^4*(a+b*x)^2*(b*c+-1*a*d)^6+120*x*b^-10*d^3*(b*c+-1*a*d)^7+10//7*b^-11*d^9*(a+b*x)^7*(b*c+-1*a*d)+15//2*b^-11*d^8*(a+b*x)^6*(b*c+-1*a*d)^2+105//2*b^-11*d^6*(a+b*x)^4*(b*c+-1*a*d)^4)
@test integrate((a+b*x)^-4*(c+d*x)^10, x) == :(-1//3*b^-11*(a+b*x)^-3*(b*c+-1*a*d)^10+1//7*b^-11*d^10*(a+b*x)^7+-45*b^-11*d^2*(a+b*x)^-1*(b*c+-1*a*d)^8+-5*d*b^-11*(a+b*x)^-2*(b*c+-1*a*d)^9+9*b^-11*d^8*(a+b*x)^5*(b*c+-1*a*d)^2+30*b^-11*d^7*(a+b*x)^4*(b*c+-1*a*d)^3+70*b^-11*d^6*(a+b*x)^3*(b*c+-1*a*d)^4+120*b^-11*d^3*(b*c+-1*a*d)^7*log(a+b*x)+126*b^-11*d^5*(a+b*x)^2*(b*c+-1*a*d)^5+210*x*b^-10*d^4*(b*c+-1*a*d)^6+5//3*b^-11*d^9*(a+b*x)^6*(b*c+-1*a*d))
@test integrate((a+b*x)^-5*(c+d*x)^10, x) == :(-1//4*b^-11*(a+b*x)^-4*(b*c+-1*a*d)^10+1//6*b^-11*d^10*(a+b*x)^6+-120*b^-11*d^3*(a+b*x)^-1*(b*c+-1*a*d)^7+2*b^-11*d^9*(a+b*x)^5*(b*c+-1*a*d)+40*b^-11*d^7*(a+b*x)^3*(b*c+-1*a*d)^3+105*b^-11*d^6*(a+b*x)^2*(b*c+-1*a*d)^4+210*b^-11*d^4*(b*c+-1*a*d)^6*log(a+b*x)+252*x*b^-10*d^5*(b*c+-1*a*d)^5+-45//2*b^-11*d^2*(a+b*x)^-2*(b*c+-1*a*d)^8+-10//3*d*b^-11*(a+b*x)^-3*(b*c+-1*a*d)^9+45//4*b^-11*d^8*(a+b*x)^4*(b*c+-1*a*d)^2)
@test integrate((a+b*x)^-6*(c+d*x)^10, x) == :(-1//5*b^-11*(a+b*x)^-5*(b*c+-1*a*d)^10+1//5*b^-11*d^10*(a+b*x)^5+-210*b^-11*d^4*(a+b*x)^-1*(b*c+-1*a*d)^6+-60*b^-11*d^3*(a+b*x)^-2*(b*c+-1*a*d)^7+-15*b^-11*d^2*(a+b*x)^-3*(b*c+-1*a*d)^8+15*b^-11*d^8*(a+b*x)^3*(b*c+-1*a*d)^2+60*b^-11*d^7*(a+b*x)^2*(b*c+-1*a*d)^3+210*x*b^-10*d^6*(b*c+-1*a*d)^4+252*b^-11*d^5*(b*c+-1*a*d)^5*log(a+b*x)+-5//2*d*b^-11*(a+b*x)^-4*(b*c+-1*a*d)^9+5//2*b^-11*d^9*(a+b*x)^4*(b*c+-1*a*d))
@test integrate((a+b*x)^-7*(c+d*x)^10, x) == :(-1//6*b^-11*(a+b*x)^-6*(b*c+-1*a*d)^10+1//4*b^-11*d^10*(a+b*x)^4+-252*b^-11*d^5*(a+b*x)^-1*(b*c+-1*a*d)^5+-105*b^-11*d^4*(a+b*x)^-2*(b*c+-1*a*d)^6+-40*b^-11*d^3*(a+b*x)^-3*(b*c+-1*a*d)^7+-2*d*b^-11*(a+b*x)^-5*(b*c+-1*a*d)^9+120*x*b^-10*d^7*(b*c+-1*a*d)^3+210*b^-11*d^6*(b*c+-1*a*d)^4*log(a+b*x)+-45//4*b^-11*d^2*(a+b*x)^-4*(b*c+-1*a*d)^8+10//3*b^-11*d^9*(a+b*x)^3*(b*c+-1*a*d)+45//2*b^-11*d^8*(a+b*x)^2*(b*c+-1*a*d)^2)
@test integrate((a+b*x)^-8*(c+d*x)^10, x) == :(-1//7*b^-11*(a+b*x)^-7*(b*c+-1*a*d)^10+1//3*b^-11*d^10*(a+b*x)^3+-210*b^-11*d^6*(a+b*x)^-1*(b*c+-1*a*d)^4+-126*b^-11*d^5*(a+b*x)^-2*(b*c+-1*a*d)^5+-70*b^-11*d^4*(a+b*x)^-3*(b*c+-1*a*d)^6+-30*b^-11*d^3*(a+b*x)^-4*(b*c+-1*a*d)^7+-9*b^-11*d^2*(a+b*x)^-5*(b*c+-1*a*d)^8+5*b^-11*d^9*(a+b*x)^2*(b*c+-1*a*d)+45*x*b^-10*d^8*(b*c+-1*a*d)^2+120*b^-11*d^7*(b*c+-1*a*d)^3*log(a+b*x)+-5//3*d*b^-11*(a+b*x)^-6*(b*c+-1*a*d)^9)
@test integrate((a+b*x)^-9*(c+d*x)^10, x) == :((1/2)*b^-9*d^10*x^2+-1//8*b^-11*(a+b*x)^-8*(b*c+-1*a*d)^10+x*b^-10*d^9*(-9*a*d+10*b*c)+-120*b^-11*d^7*(a+b*x)^-1*(b*c+-1*a*d)^3+-105*b^-11*d^6*(a+b*x)^-2*(b*c+-1*a*d)^4+-84*b^-11*d^5*(a+b*x)^-3*(b*c+-1*a*d)^5+-24*b^-11*d^3*(a+b*x)^-5*(b*c+-1*a*d)^7+45*b^-11*d^8*(b*c+-1*a*d)^2*log(a+b*x)+-105//2*b^-11*d^4*(a+b*x)^-4*(b*c+-1*a*d)^6+-15//2*b^-11*d^2*(a+b*x)^-6*(b*c+-1*a*d)^8+-10//7*d*b^-11*(a+b*x)^-7*(b*c+-1*a*d)^9)
@test integrate((a+b*x)^-10*(c+d*x)^10, x) == :(x*b^-10*d^10+-1//9*b^-11*(a+b*x)^-9*(b*c+-1*a*d)^10+-70*b^-11*d^6*(a+b*x)^-3*(b*c+-1*a*d)^4+-63*b^-11*d^5*(a+b*x)^-4*(b*c+-1*a*d)^5+-60*b^-11*d^7*(a+b*x)^-2*(b*c+-1*a*d)^3+-45*b^-11*d^8*(a+b*x)^-1*(b*c+-1*a*d)^2+-42*b^-11*d^4*(a+b*x)^-5*(b*c+-1*a*d)^6+-20*b^-11*d^3*(a+b*x)^-6*(b*c+-1*a*d)^7+10*b^-11*d^9*(b*c+-1*a*d)*log(a+b*x)+-45//7*b^-11*d^2*(a+b*x)^-7*(b*c+-1*a*d)^8+-5//4*d*b^-11*(a+b*x)^-8*(b*c+-1*a*d)^9)
@test integrate((a+b*x)^-11*(c+d*x)^10, x) == :(b^-11*d^10*log(a+b*x)+-1//10*b^-11*(a+b*x)^-10*(b*c+-1*a*d)^10+-40*b^-11*d^7*(a+b*x)^-3*(b*c+-1*a*d)^3+-35*b^-11*d^4*(a+b*x)^-6*(b*c+-1*a*d)^6+-10*b^-11*d^9*(a+b*x)^-1*(b*c+-1*a*d)+-252//5*b^-11*d^5*(a+b*x)^-5*(b*c+-1*a*d)^5+-120//7*b^-11*d^3*(a+b*x)^-7*(b*c+-1*a*d)^7+-105//2*b^-11*d^6*(a+b*x)^-4*(b*c+-1*a*d)^4+-45//2*b^-11*d^8*(a+b*x)^-2*(b*c+-1*a*d)^2+-45//8*b^-11*d^2*(a+b*x)^-8*(b*c+-1*a*d)^8+-10//9*d*b^-11*(a+b*x)^-9*(b*c+-1*a*d)^9)
@test integrate((a+b*x)^-12*(c+d*x)^10, x) == :(-1*(a+b*x)^-11*(c+d*x)^11*(-11*a*d+11*b*c)^-1)
@test integrate((a+b*x)^-13*(c+d*x)^10, x) == :(-1*(a+b*x)^-12*(c+d*x)^11*(-12*a*d+12*b*c)^-1+1//132*d*(a+b*x)^-11*(c+d*x)^11*(b*c+-1*a*d)^-2)
@test integrate((a+b*x)^-14*(c+d*x)^10, x) == :(-1*(a+b*x)^-13*(c+d*x)^11*(-13*a*d+13*b*c)^-1+-1//858*d^2*(a+b*x)^-11*(c+d*x)^11*(b*c+-1*a*d)^-3+1//78*d*(a+b*x)^-12*(c+d*x)^11*(b*c+-1*a*d)^-2)
@test integrate((a+b*x)^-15*(c+d*x)^10, x) == :(-1*(a+b*x)^-14*(c+d*x)^11*(-14*a*d+14*b*c)^-1+-1//364*d^2*(a+b*x)^-12*(c+d*x)^11*(b*c+-1*a*d)^-3+1//4004*d^3*(a+b*x)^-11*(c+d*x)^11*(b*c+-1*a*d)^-4+3//182*d*(a+b*x)^-13*(c+d*x)^11*(b*c+-1*a*d)^-2)
@test integrate((a+b*x)^-16*(c+d*x)^10, x) == :(-1*(a+b*x)^-15*(c+d*x)^11*(-15*a*d+15*b*c)^-1+-2//455*d^2*(a+b*x)^-13*(c+d*x)^11*(b*c+-1*a*d)^-3+-1//15015*d^4*(a+b*x)^-11*(c+d*x)^11*(b*c+-1*a*d)^-5+1//1365*d^3*(a+b*x)^-12*(c+d*x)^11*(b*c+-1*a*d)^-4+2//105*d*(a+b*x)^-14*(c+d*x)^11*(b*c+-1*a*d)^-2)
@test integrate((a+b*x)^-17*(c+d*x)^10, x) == :(-1*(a+b*x)^-16*(c+d*x)^11*(-16*a*d+16*b*c)^-1+-1//168*d^2*(a+b*x)^-14*(c+d*x)^11*(b*c+-1*a*d)^-3+-1//4368*d^4*(a+b*x)^-12*(c+d*x)^11*(b*c+-1*a*d)^-5+1//48*d*(a+b*x)^-15*(c+d*x)^11*(b*c+-1*a*d)^-2+1//728*d^3*(a+b*x)^-13*(c+d*x)^11*(b*c+-1*a*d)^-4+1//48048*d^5*(a+b*x)^-11*(c+d*x)^11*(b*c+-1*a*d)^-6)
@test integrate((a+b*x)^-18*(c+d*x)^10, x) == :(-1*(a+b*x)^-17*(c+d*x)^11*(-17*a*d+17*b*c)^-1+-3//6188*d^4*(a+b*x)^-13*(c+d*x)^11*(b*c+-1*a*d)^-5+-1//136*d^2*(a+b*x)^-15*(c+d*x)^11*(b*c+-1*a*d)^-3+-1//136136*d^6*(a+b*x)^-11*(c+d*x)^11*(b*c+-1*a*d)^-7+1//476*d^3*(a+b*x)^-14*(c+d*x)^11*(b*c+-1*a*d)^-4+1//12376*d^5*(a+b*x)^-12*(c+d*x)^11*(b*c+-1*a*d)^-6+3//136*d*(a+b*x)^-16*(c+d*x)^11*(b*c+-1*a*d)^-2)
@test integrate((a+b*x)^-19*(c+d*x)^10, x) == :(-1*(a+b*x)^-18*(c+d*x)^11*(-18*a*d+18*b*c)^-1+-7//816*d^2*(a+b*x)^-16*(c+d*x)^11*(b*c+-1*a*d)^-3+-1//1224*d^4*(a+b*x)^-14*(c+d*x)^11*(b*c+-1*a*d)^-5+-1//31824*d^6*(a+b*x)^-12*(c+d*x)^11*(b*c+-1*a*d)^-7+1//5304*d^5*(a+b*x)^-13*(c+d*x)^11*(b*c+-1*a*d)^-6+1//350064*d^7*(a+b*x)^-11*(c+d*x)^11*(b*c+-1*a*d)^-8+7//306*d*(a+b*x)^-17*(c+d*x)^11*(b*c+-1*a*d)^-2+7//2448*d^3*(a+b*x)^-15*(c+d*x)^11*(b*c+-1*a*d)^-4)
@test integrate((a+b*x)^-20*(c+d*x)^10, x) == :(-1//9*b^-11*d^10*(a+b*x)^-9+-1//19*b^-11*(a+b*x)^-19*(b*c+-1*a*d)^10+-1*b^-11*d^9*(a+b*x)^-10*(b*c+-1*a*d)+-18*b^-11*d^5*(a+b*x)^-14*(b*c+-1*a*d)^5+-14*b^-11*d^4*(a+b*x)^-15*(b*c+-1*a*d)^6+-10*b^-11*d^7*(a+b*x)^-12*(b*c+-1*a*d)^3+-210//13*b^-11*d^6*(a+b*x)^-13*(b*c+-1*a*d)^4+-45//11*b^-11*d^8*(a+b*x)^-11*(b*c+-1*a*d)^2+-45//17*b^-11*d^2*(a+b*x)^-17*(b*c+-1*a*d)^8+-15//2*b^-11*d^3*(a+b*x)^-16*(b*c+-1*a*d)^7+-5//9*d*b^-11*(a+b*x)^-18*(b*c+-1*a*d)^9)
@test integrate((a+b*x)^-21*(c+d*x)^10, x) == :(-1//10*b^-11*d^10*(a+b*x)^-10+-1//20*b^-11*(a+b*x)^-20*(b*c+-1*a*d)^10+-15*b^-11*d^6*(a+b*x)^-14*(b*c+-1*a*d)^4+-120//13*b^-11*d^7*(a+b*x)^-13*(b*c+-1*a*d)^3+-120//17*b^-11*d^3*(a+b*x)^-17*(b*c+-1*a*d)^7+-105//8*b^-11*d^4*(a+b*x)^-16*(b*c+-1*a*d)^6+-84//5*b^-11*d^5*(a+b*x)^-15*(b*c+-1*a*d)^5+-15//4*b^-11*d^8*(a+b*x)^-12*(b*c+-1*a*d)^2+-10//11*b^-11*d^9*(a+b*x)^-11*(b*c+-1*a*d)+-10//19*d*b^-11*(a+b*x)^-19*(b*c+-1*a*d)^9+-5//2*b^-11*d^2*(a+b*x)^-18*(b*c+-1*a*d)^8)
@test integrate((a+b*x)^-22*(c+d*x)^10, x) == :(-1//11*b^-11*d^10*(a+b*x)^-11+-1//21*b^-11*(a+b*x)^-21*(b*c+-1*a*d)^10+-14*b^-11*d^6*(a+b*x)^-15*(b*c+-1*a*d)^4+-210//17*b^-11*d^4*(a+b*x)^-17*(b*c+-1*a*d)^6+-63//4*b^-11*d^5*(a+b*x)^-16*(b*c+-1*a*d)^5+-60//7*b^-11*d^7*(a+b*x)^-14*(b*c+-1*a*d)^3+-45//13*b^-11*d^8*(a+b*x)^-13*(b*c+-1*a*d)^2+-45//19*b^-11*d^2*(a+b*x)^-19*(b*c+-1*a*d)^8+-20//3*b^-11*d^3*(a+b*x)^-18*(b*c+-1*a*d)^7+-5//6*b^-11*d^9*(a+b*x)^-12*(b*c+-1*a*d)+-1//2*d*b^-11*(a+b*x)^-20*(b*c+-1*a*d)^9)
@test integrate((a+b*x)^17*(c+d*x)^15, x) == :(1//18*b^-16*(a+b*x)^18*(b*c+-1*a*d)^15+1//33*b^-16*d^15*(a+b*x)^33+15//19*d*b^-16*(a+b*x)^19*(b*c+-1*a*d)^14+15//32*b^-16*d^14*(a+b*x)^32*(b*c+-1*a*d)+21//4*b^-16*d^2*(a+b*x)^20*(b*c+-1*a*d)^13+65//3*b^-16*d^3*(a+b*x)^21*(b*c+-1*a*d)^12+91//6*b^-16*d^12*(a+b*x)^30*(b*c+-1*a*d)^3+105//31*b^-16*d^13*(a+b*x)^31*(b*c+-1*a*d)^2+429//4*b^-16*d^10*(a+b*x)^28*(b*c+-1*a*d)^5+495//2*b^-16*d^8*(a+b*x)^26*(b*c+-1*a*d)^7+1287//5*b^-16*d^7*(a+b*x)^25*(b*c+-1*a*d)^8+1365//22*b^-16*d^4*(a+b*x)^22*(b*c+-1*a*d)^11+1365//29*b^-16*d^11*(a+b*x)^29*(b*c+-1*a*d)^4+3003//23*b^-16*d^5*(a+b*x)^23*(b*c+-1*a*d)^10+5005//24*b^-16*d^6*(a+b*x)^24*(b*c+-1*a*d)^9+5005//27*b^-16*d^9*(a+b*x)^27*(b*c+-1*a*d)^6)
@test integrate((a+b*x)^16*(c+d*x)^15, x) == :(1//17*b^-16*(a+b*x)^17*(b*c+-1*a*d)^15+1//32*b^-16*d^15*(a+b*x)^32+65*b^-16*d^4*(a+b*x)^21*(b*c+-1*a*d)^11+5//6*d*b^-16*(a+b*x)^18*(b*c+-1*a*d)^14+7//2*b^-16*d^13*(a+b*x)^30*(b*c+-1*a*d)^2+15//31*b^-16*d^14*(a+b*x)^31*(b*c+-1*a*d)+91//4*b^-16*d^3*(a+b*x)^20*(b*c+-1*a*d)^12+105//19*b^-16*d^2*(a+b*x)^19*(b*c+-1*a*d)^13+195//4*b^-16*d^11*(a+b*x)^28*(b*c+-1*a*d)^4+273//2*b^-16*d^5*(a+b*x)^22*(b*c+-1*a*d)^10+385//2*b^-16*d^9*(a+b*x)^26*(b*c+-1*a*d)^6+455//29*b^-16*d^12*(a+b*x)^29*(b*c+-1*a*d)^3+1001//9*b^-16*d^10*(a+b*x)^27*(b*c+-1*a*d)^5+1287//5*b^-16*d^8*(a+b*x)^25*(b*c+-1*a*d)^7+2145//8*b^-16*d^7*(a+b*x)^24*(b*c+-1*a*d)^8+5005//23*b^-16*d^6*(a+b*x)^23*(b*c+-1*a*d)^9)
@test integrate((a+b*x)^15*(c+d*x)^15, x) == :(1//16*b^-16*(a+b*x)^16*(b*c+-1*a*d)^15+1//31*b^-16*d^15*(a+b*x)^31+(1/2)*b^-16*d^14*(a+b*x)^30*(b*c+-1*a*d)+143*b^-16*d^5*(a+b*x)^21*(b*c+-1*a*d)^10+15//17*d*b^-16*(a+b*x)^17*(b*c+-1*a*d)^14+35//6*b^-16*d^2*(a+b*x)^18*(b*c+-1*a*d)^13+65//4*b^-16*d^12*(a+b*x)^28*(b*c+-1*a*d)^3+105//29*b^-16*d^13*(a+b*x)^29*(b*c+-1*a*d)^2+231//2*b^-16*d^10*(a+b*x)^26*(b*c+-1*a*d)^5+273//4*b^-16*d^4*(a+b*x)^20*(b*c+-1*a*d)^11+455//2*b^-16*d^6*(a+b*x)^22*(b*c+-1*a*d)^9+455//9*b^-16*d^11*(a+b*x)^27*(b*c+-1*a*d)^4+455//19*b^-16*d^3*(a+b*x)^19*(b*c+-1*a*d)^12+1001//5*b^-16*d^9*(a+b*x)^25*(b*c+-1*a*d)^6+2145//8*b^-16*d^8*(a+b*x)^24*(b*c+-1*a*d)^7+6435//23*b^-16*d^7*(a+b*x)^23*(b*c+-1*a*d)^8)
@test integrate((a+b*x)^14*(c+d*x)^15, x) == :(1//16*d^-15*(c+d*x)^16*(b*c+-1*a*d)^14+1//30*b^14*d^-15*(c+d*x)^30+-3432//23*b^7*d^-15*(c+d*x)^23*(b*c+-1*a*d)^7+-2002//25*b^9*d^-15*(c+d*x)^25*(b*c+-1*a*d)^5+-364//19*b^3*d^-15*(c+d*x)^19*(b*c+-1*a*d)^11+-364//27*b^11*d^-15*(c+d*x)^27*(b*c+-1*a*d)^3+-286//3*b^5*d^-15*(c+d*x)^21*(b*c+-1*a*d)^9+-14//17*b*d^-15*(c+d*x)^17*(b*c+-1*a*d)^13+-14//29*b^13*d^-15*(c+d*x)^29*(b*c+-1*a*d)+13//4*b^12*d^-15*(c+d*x)^28*(b*c+-1*a*d)^2+77//2*b^10*d^-15*(c+d*x)^26*(b*c+-1*a*d)^4+91//18*b^2*d^-15*(c+d*x)^18*(b*c+-1*a*d)^12+273//2*b^6*d^-15*(c+d*x)^22*(b*c+-1*a*d)^8+1001//8*b^8*d^-15*(c+d*x)^24*(b*c+-1*a*d)^6+1001//20*b^4*d^-15*(c+d*x)^20*(b*c+-1*a*d)^10)
@test integrate((a+b*x)^13*(c+d*x)^15, x) == :(-1//16*d^-14*(c+d*x)^16*(b*c+-1*a*d)^13+1//29*b^13*d^-14*(c+d*x)^29+-78*b^6*d^-14*(c+d*x)^22*(b*c+-1*a*d)^7+-11*b^10*d^-14*(c+d*x)^26*(b*c+-1*a*d)^3+-429//8*b^8*d^-14*(c+d*x)^24*(b*c+-1*a*d)^5+-143//4*b^4*d^-14*(c+d*x)^20*(b*c+-1*a*d)^9+-13//3*b^2*d^-14*(c+d*x)^18*(b*c+-1*a*d)^11+-13//28*b^12*d^-14*(c+d*x)^28*(b*c+-1*a*d)+13//17*b*d^-14*(c+d*x)^17*(b*c+-1*a*d)^12+26//9*b^11*d^-14*(c+d*x)^27*(b*c+-1*a*d)^2+143//5*b^9*d^-14*(c+d*x)^25*(b*c+-1*a*d)^4+286//19*b^3*d^-14*(c+d*x)^19*(b*c+-1*a*d)^10+429//7*b^5*d^-14*(c+d*x)^21*(b*c+-1*a*d)^8+1716//23*b^7*d^-14*(c+d*x)^23*(b*c+-1*a*d)^6)
@test integrate((a+b*x)^12*(c+d*x)^15, x) == :(1//16*d^-13*(c+d*x)^16*(b*c+-1*a*d)^12+1//28*b^12*d^-13*(c+d*x)^28+42*b^6*d^-13*(c+d*x)^22*(b*c+-1*a*d)^6+-792//23*b^7*d^-13*(c+d*x)^23*(b*c+-1*a*d)^5+-264//7*b^5*d^-13*(c+d*x)^21*(b*c+-1*a*d)^7+-220//19*b^3*d^-13*(c+d*x)^19*(b*c+-1*a*d)^9+-44//5*b^9*d^-13*(c+d*x)^25*(b*c+-1*a*d)^3+-12//17*b*d^-13*(c+d*x)^17*(b*c+-1*a*d)^11+-4//9*b^11*d^-13*(c+d*x)^27*(b*c+-1*a*d)+11//3*b^2*d^-13*(c+d*x)^18*(b*c+-1*a*d)^10+33//13*b^10*d^-13*(c+d*x)^26*(b*c+-1*a*d)^2+99//4*b^4*d^-13*(c+d*x)^20*(b*c+-1*a*d)^8+165//8*b^8*d^-13*(c+d*x)^24*(b*c+-1*a*d)^4)
@test integrate((a+b*x)^11*(c+d*x)^15, x) == :(-1//16*d^-12*(c+d*x)^16*(b*c+-1*a*d)^11+1//27*b^11*d^-12*(c+d*x)^27+-21*b^6*d^-12*(c+d*x)^22*(b*c+-1*a*d)^5+22*b^5*d^-12*(c+d*x)^21*(b*c+-1*a*d)^6+-55//8*b^8*d^-12*(c+d*x)^24*(b*c+-1*a*d)^3+-55//18*b^2*d^-12*(c+d*x)^18*(b*c+-1*a*d)^9+-33//2*b^4*d^-12*(c+d*x)^20*(b*c+-1*a*d)^7+-11//26*b^10*d^-12*(c+d*x)^26*(b*c+-1*a*d)+11//5*b^9*d^-12*(c+d*x)^25*(b*c+-1*a*d)^2+11//17*b*d^-12*(c+d*x)^17*(b*c+-1*a*d)^10+165//19*b^3*d^-12*(c+d*x)^19*(b*c+-1*a*d)^8+330//23*b^7*d^-12*(c+d*x)^23*(b*c+-1*a*d)^4)
@test integrate((a+b*x)^10*(c+d*x)^15, x) == :(1//16*d^-11*(c+d*x)^16*(b*c+-1*a*d)^10+1//26*b^10*d^-11*(c+d*x)^26+-12*b^5*d^-11*(c+d*x)^21*(b*c+-1*a*d)^5+-120//19*b^3*d^-11*(c+d*x)^19*(b*c+-1*a*d)^7+-120//23*b^7*d^-11*(c+d*x)^23*(b*c+-1*a*d)^3+-10//17*b*d^-11*(c+d*x)^17*(b*c+-1*a*d)^9+-2//5*b^9*d^-11*(c+d*x)^25*(b*c+-1*a*d)+5//2*b^2*d^-11*(c+d*x)^18*(b*c+-1*a*d)^8+15//8*b^8*d^-11*(c+d*x)^24*(b*c+-1*a*d)^2+21//2*b^4*d^-11*(c+d*x)^20*(b*c+-1*a*d)^6+105//11*b^6*d^-11*(c+d*x)^22*(b*c+-1*a*d)^4)
@test integrate((a+b*x)^9*(c+d*x)^15, x) == :(-1//16*d^-10*(c+d*x)^16*(b*c+-1*a*d)^9+1//25*b^9*d^-10*(c+d*x)^25+-2*b^2*d^-10*(c+d*x)^18*(b*c+-1*a*d)^7+6*b^5*d^-10*(c+d*x)^21*(b*c+-1*a*d)^4+-63//10*b^4*d^-10*(c+d*x)^20*(b*c+-1*a*d)^5+-42//11*b^6*d^-10*(c+d*x)^22*(b*c+-1*a*d)^3+-3//8*b^8*d^-10*(c+d*x)^24*(b*c+-1*a*d)+9//17*b*d^-10*(c+d*x)^17*(b*c+-1*a*d)^8+36//23*b^7*d^-10*(c+d*x)^23*(b*c+-1*a*d)^2+84//19*b^3*d^-10*(c+d*x)^19*(b*c+-1*a*d)^6)
@test integrate((a+b*x)^8*(c+d*x)^15, x) == :(1//16*d^-9*(c+d*x)^16*(b*c+-1*a*d)^8+1//24*b^8*d^-9*(c+d*x)^24+-56//19*b^3*d^-9*(c+d*x)^19*(b*c+-1*a*d)^5+-8//3*b^5*d^-9*(c+d*x)^21*(b*c+-1*a*d)^3+-8//17*b*d^-9*(c+d*x)^17*(b*c+-1*a*d)^7+-8//23*b^7*d^-9*(c+d*x)^23*(b*c+-1*a*d)+7//2*b^4*d^-9*(c+d*x)^20*(b*c+-1*a*d)^4+14//9*b^2*d^-9*(c+d*x)^18*(b*c+-1*a*d)^6+14//11*b^6*d^-9*(c+d*x)^22*(b*c+-1*a*d)^2)
@test integrate((a+b*x)^7*(c+d*x)^15, x) == :(-1//16*d^-8*(c+d*x)^16*(b*c+-1*a*d)^7+1//23*b^7*d^-8*(c+d*x)^23+b^5*d^-8*(c+d*x)^21*(b*c+-1*a*d)^2+-7//4*b^4*d^-8*(c+d*x)^20*(b*c+-1*a*d)^3+-7//6*b^2*d^-8*(c+d*x)^18*(b*c+-1*a*d)^5+-7//22*b^6*d^-8*(c+d*x)^22*(b*c+-1*a*d)+7//17*b*d^-8*(c+d*x)^17*(b*c+-1*a*d)^6+35//19*b^3*d^-8*(c+d*x)^19*(b*c+-1*a*d)^4)
@test integrate((a+b*x)^6*(c+d*x)^15, x) == :(1//16*d^-7*(c+d*x)^16*(b*c+-1*a*d)^6+1//22*b^6*d^-7*(c+d*x)^22+-20//19*b^3*d^-7*(c+d*x)^19*(b*c+-1*a*d)^3+-6//17*b*d^-7*(c+d*x)^17*(b*c+-1*a*d)^5+-2//7*b^5*d^-7*(c+d*x)^21*(b*c+-1*a*d)+3//4*b^4*d^-7*(c+d*x)^20*(b*c+-1*a*d)^2+5//6*b^2*d^-7*(c+d*x)^18*(b*c+-1*a*d)^4)
@test integrate((a+b*x)^5*(c+d*x)^15, x) == :(-1//16*d^-6*(c+d*x)^16*(b*c+-1*a*d)^5+1//21*b^5*d^-6*(c+d*x)^21+-5//9*b^2*d^-6*(c+d*x)^18*(b*c+-1*a*d)^3+-1//4*b^4*d^-6*(c+d*x)^20*(b*c+-1*a*d)+5//17*b*d^-6*(c+d*x)^17*(b*c+-1*a*d)^4+10//19*b^3*d^-6*(c+d*x)^19*(b*c+-1*a*d)^2)
@test integrate((a+b*x)^4*(c+d*x)^15, x) == :(1//16*d^-5*(c+d*x)^16*(b*c+-1*a*d)^4+1//20*b^4*d^-5*(c+d*x)^20+-4//17*b*d^-5*(c+d*x)^17*(b*c+-1*a*d)^3+-4//19*b^3*d^-5*(c+d*x)^19*(b*c+-1*a*d)+1//3*b^2*d^-5*(c+d*x)^18*(b*c+-1*a*d)^2)
@test integrate((a+b*x)^3*(c+d*x)^15, x) == :(-1//16*d^-4*(c+d*x)^16*(b*c+-1*a*d)^3+1//19*b^3*d^-4*(c+d*x)^19+-1//6*b^2*d^-4*(c+d*x)^18*(b*c+-1*a*d)+3//17*b*d^-4*(c+d*x)^17*(b*c+-1*a*d)^2)
@test integrate((a+b*x)^2*(c+d*x)^15, x) == :(1//16*d^-3*(c+d*x)^16*(b*c+-1*a*d)^2+1//18*b^2*d^-3*(c+d*x)^18+-2//17*b*d^-3*(c+d*x)^17*(b*c+-1*a*d))
@test integrate((c+d*x)^15*(a+b*x), x) == :(-1//16*d^-2*(c+d*x)^16*(b*c+-1*a*d)+1//17*b*d^-2*(c+d*x)^17)
@test integrate((c+d*x)^15, x) == :(1//16*d^-1*(c+d*x)^16)
@test integrate((a+b*x)^-1*(c+d*x)^15, x) == :(1//15*b^-1*(c+d*x)^15+b^-16*(b*c+-1*a*d)^15*log(a+b*x)+(1/2)*b^-14*(c+d*x)^2*(b*c+-1*a*d)^13+1//3*b^-13*(c+d*x)^3*(b*c+-1*a*d)^12+1//4*b^-12*(c+d*x)^4*(b*c+-1*a*d)^11+1//5*b^-11*(c+d*x)^5*(b*c+-1*a*d)^10+1//6*b^-10*(c+d*x)^6*(b*c+-1*a*d)^9+1//7*b^-9*(c+d*x)^7*(b*c+-1*a*d)^8+1//8*b^-8*(c+d*x)^8*(b*c+-1*a*d)^7+1//9*b^-7*(c+d*x)^9*(b*c+-1*a*d)^6+1//10*b^-6*(c+d*x)^10*(b*c+-1*a*d)^5+1//11*b^-5*(c+d*x)^11*(b*c+-1*a*d)^4+1//12*b^-4*(c+d*x)^12*(b*c+-1*a*d)^3+1//13*b^-3*(c+d*x)^13*(b*c+-1*a*d)^2+1//14*b^-2*(c+d*x)^14*(b*c+-1*a*d)+d*x*b^-15*(b*c+-1*a*d)^14)
@test integrate((a+b*x)^-2*(c+d*x)^15, x) == :(-1*b^-16*(a+b*x)^-1*(b*c+-1*a*d)^15+1//14*b^-16*d^15*(a+b*x)^14+15*d*b^-16*(b*c+-1*a*d)^14*log(a+b*x)+105*x*b^-15*d^2*(b*c+-1*a*d)^13+455*b^-16*d^4*(a+b*x)^3*(b*c+-1*a*d)^11+1001*b^-16*d^6*(a+b*x)^5*(b*c+-1*a*d)^9+15//13*b^-16*d^14*(a+b*x)^13*(b*c+-1*a*d)+35//4*b^-16*d^13*(a+b*x)^12*(b*c+-1*a*d)^2+273//2*b^-16*d^11*(a+b*x)^10*(b*c+-1*a*d)^4+455//2*b^-16*d^3*(a+b*x)^2*(b*c+-1*a*d)^12+455//11*b^-16*d^12*(a+b*x)^11*(b*c+-1*a*d)^3+1001//3*b^-16*d^10*(a+b*x)^9*(b*c+-1*a*d)^5+2145//2*b^-16*d^7*(a+b*x)^6*(b*c+-1*a*d)^8+3003//4*b^-16*d^5*(a+b*x)^4*(b*c+-1*a*d)^10+5005//8*b^-16*d^9*(a+b*x)^8*(b*c+-1*a*d)^6+6435//7*b^-16*d^8*(a+b*x)^7*(b*c+-1*a*d)^7)
@test integrate((a+b*x)^-3*(c+d*x)^15, x) == :(-1//2*b^-16*(a+b*x)^-2*(b*c+-1*a*d)^15+1//13*b^-16*d^15*(a+b*x)^13+-15*d*b^-16*(a+b*x)^-1*(b*c+-1*a*d)^14+105*b^-16*d^2*(b*c+-1*a*d)^13*log(a+b*x)+455*x*b^-15*d^3*(b*c+-1*a*d)^12+715*b^-16*d^9*(a+b*x)^7*(b*c+-1*a*d)^6+1001*b^-16*d^5*(a+b*x)^3*(b*c+-1*a*d)^10+1287*b^-16*d^7*(a+b*x)^5*(b*c+-1*a*d)^8+5//4*b^-16*d^14*(a+b*x)^12*(b*c+-1*a*d)+91//2*b^-16*d^12*(a+b*x)^10*(b*c+-1*a*d)^3+105//11*b^-16*d^13*(a+b*x)^11*(b*c+-1*a*d)^2+455//3*b^-16*d^11*(a+b*x)^9*(b*c+-1*a*d)^4+1365//2*b^-16*d^4*(a+b*x)^2*(b*c+-1*a*d)^11+2145//2*b^-16*d^8*(a+b*x)^6*(b*c+-1*a*d)^7+3003//8*b^-16*d^10*(a+b*x)^8*(b*c+-1*a*d)^5+5005//4*b^-16*d^6*(a+b*x)^4*(b*c+-1*a*d)^9)
@test integrate((a+b*x)^-4*(c+d*x)^15, x) == :(-1//3*b^-16*(a+b*x)^-3*(b*c+-1*a*d)^15+1//12*b^-16*d^15*(a+b*x)^12+-105*b^-16*d^2*(a+b*x)^-1*(b*c+-1*a*d)^13+429*b^-16*d^10*(a+b*x)^7*(b*c+-1*a*d)^5+455*b^-16*d^3*(b*c+-1*a*d)^12*log(a+b*x)+1287*b^-16*d^8*(a+b*x)^5*(b*c+-1*a*d)^7+1365*x*b^-15*d^4*(b*c+-1*a*d)^11+-15//2*d*b^-16*(a+b*x)^-2*(b*c+-1*a*d)^14+15//11*b^-16*d^14*(a+b*x)^11*(b*c+-1*a*d)+21//2*b^-16*d^13*(a+b*x)^10*(b*c+-1*a*d)^2+455//9*b^-16*d^12*(a+b*x)^9*(b*c+-1*a*d)^3+1365//8*b^-16*d^11*(a+b*x)^8*(b*c+-1*a*d)^4+3003//2*b^-16*d^5*(a+b*x)^2*(b*c+-1*a*d)^10+5005//3*b^-16*d^6*(a+b*x)^3*(b*c+-1*a*d)^9+5005//6*b^-16*d^9*(a+b*x)^6*(b*c+-1*a*d)^6+6435//4*b^-16*d^7*(a+b*x)^4*(b*c+-1*a*d)^8)
@test integrate((a+b*x)^-5*(c+d*x)^15, x) == :(-1//4*b^-16*(a+b*x)^-4*(b*c+-1*a*d)^15+1//11*b^-16*d^15*(a+b*x)^11+-455*b^-16*d^3*(a+b*x)^-1*(b*c+-1*a*d)^12+-5*d*b^-16*(a+b*x)^-3*(b*c+-1*a*d)^14+195*b^-16*d^11*(a+b*x)^7*(b*c+-1*a*d)^4+1001*b^-16*d^9*(a+b*x)^5*(b*c+-1*a*d)^6+1365*b^-16*d^4*(b*c+-1*a*d)^11*log(a+b*x)+2145*b^-16*d^7*(a+b*x)^3*(b*c+-1*a*d)^8+3003*x*b^-15*d^5*(b*c+-1*a*d)^10+-105//2*b^-16*d^2*(a+b*x)^-2*(b*c+-1*a*d)^13+3//2*b^-16*d^14*(a+b*x)^10*(b*c+-1*a*d)+35//3*b^-16*d^13*(a+b*x)^9*(b*c+-1*a*d)^2+455//8*b^-16*d^12*(a+b*x)^8*(b*c+-1*a*d)^3+1001//2*b^-16*d^10*(a+b*x)^6*(b*c+-1*a*d)^5+5005//2*b^-16*d^6*(a+b*x)^2*(b*c+-1*a*d)^9+6435//4*b^-16*d^8*(a+b*x)^4*(b*c+-1*a*d)^7)
@test integrate((a+b*x)^-6*(c+d*x)^15, x) == :(-1//5*b^-16*(a+b*x)^-5*(b*c+-1*a*d)^15+1//10*b^-16*d^15*(a+b*x)^10+-1365*b^-16*d^4*(a+b*x)^-1*(b*c+-1*a*d)^11+-35*b^-16*d^2*(a+b*x)^-3*(b*c+-1*a*d)^13+65*b^-16*d^12*(a+b*x)^7*(b*c+-1*a*d)^3+2145*b^-16*d^8*(a+b*x)^3*(b*c+-1*a*d)^7+3003*b^-16*d^5*(b*c+-1*a*d)^10*log(a+b*x)+5005*x*b^-15*d^6*(b*c+-1*a*d)^9+-455//2*b^-16*d^3*(a+b*x)^-2*(b*c+-1*a*d)^12+-15//4*d*b^-16*(a+b*x)^-4*(b*c+-1*a*d)^14+5//3*b^-16*d^14*(a+b*x)^9*(b*c+-1*a*d)+105//8*b^-16*d^13*(a+b*x)^8*(b*c+-1*a*d)^2+455//2*b^-16*d^11*(a+b*x)^6*(b*c+-1*a*d)^4+3003//5*b^-16*d^10*(a+b*x)^5*(b*c+-1*a*d)^5+5005//4*b^-16*d^9*(a+b*x)^4*(b*c+-1*a*d)^6+6435//2*b^-16*d^7*(a+b*x)^2*(b*c+-1*a*d)^8)
@test integrate((a+b*x)^-7*(c+d*x)^15, x) == :(-1//6*b^-16*(a+b*x)^-6*(b*c+-1*a*d)^15+1//9*b^-16*d^15*(a+b*x)^9+-3003*b^-16*d^5*(a+b*x)^-1*(b*c+-1*a*d)^10+-3*d*b^-16*(a+b*x)^-5*(b*c+-1*a*d)^14+15*b^-16*d^13*(a+b*x)^7*(b*c+-1*a*d)^2+273*b^-16*d^11*(a+b*x)^5*(b*c+-1*a*d)^4+5005*b^-16*d^6*(b*c+-1*a*d)^9*log(a+b*x)+6435*x*b^-15*d^7*(b*c+-1*a*d)^8+-1365//2*b^-16*d^4*(a+b*x)^-2*(b*c+-1*a*d)^11+-455//3*b^-16*d^3*(a+b*x)^-3*(b*c+-1*a*d)^12+-105//4*b^-16*d^2*(a+b*x)^-4*(b*c+-1*a*d)^13+15//8*b^-16*d^14*(a+b*x)^8*(b*c+-1*a*d)+455//6*b^-16*d^12*(a+b*x)^6*(b*c+-1*a*d)^3+3003//4*b^-16*d^10*(a+b*x)^4*(b*c+-1*a*d)^5+5005//3*b^-16*d^9*(a+b*x)^3*(b*c+-1*a*d)^6+6435//2*b^-16*d^8*(a+b*x)^2*(b*c+-1*a*d)^7)
@test integrate((a+b*x)^-8*(c+d*x)^15, x) == :(-1//7*b^-16*(a+b*x)^-7*(b*c+-1*a*d)^15+1//8*b^-16*d^15*(a+b*x)^8+-5005*b^-16*d^6*(a+b*x)^-1*(b*c+-1*a*d)^9+-455*b^-16*d^4*(a+b*x)^-3*(b*c+-1*a*d)^11+-21*b^-16*d^2*(a+b*x)^-5*(b*c+-1*a*d)^13+91*b^-16*d^12*(a+b*x)^5*(b*c+-1*a*d)^3+1001*b^-16*d^10*(a+b*x)^3*(b*c+-1*a*d)^5+6435*x*b^-15*d^8*(b*c+-1*a*d)^7+6435*b^-16*d^7*(b*c+-1*a*d)^8*log(a+b*x)+-3003//2*b^-16*d^5*(a+b*x)^-2*(b*c+-1*a*d)^10+-455//4*b^-16*d^3*(a+b*x)^-4*(b*c+-1*a*d)^12+-5//2*d*b^-16*(a+b*x)^-6*(b*c+-1*a*d)^14+15//7*b^-16*d^14*(a+b*x)^7*(b*c+-1*a*d)+35//2*b^-16*d^13*(a+b*x)^6*(b*c+-1*a*d)^2+1365//4*b^-16*d^11*(a+b*x)^4*(b*c+-1*a*d)^4+5005//2*b^-16*d^9*(a+b*x)^2*(b*c+-1*a*d)^6)
@test integrate((a+b*x)^-9*(c+d*x)^15, x) == :(-1//8*b^-16*(a+b*x)^-8*(b*c+-1*a*d)^15+1//7*b^-16*d^15*(a+b*x)^7+-6435*b^-16*d^7*(a+b*x)^-1*(b*c+-1*a*d)^8+-1001*b^-16*d^5*(a+b*x)^-3*(b*c+-1*a*d)^10+-91*b^-16*d^3*(a+b*x)^-5*(b*c+-1*a*d)^12+21*b^-16*d^13*(a+b*x)^5*(b*c+-1*a*d)^2+455*b^-16*d^11*(a+b*x)^3*(b*c+-1*a*d)^4+5005*x*b^-15*d^9*(b*c+-1*a*d)^6+6435*b^-16*d^8*(b*c+-1*a*d)^7*log(a+b*x)+-5005//2*b^-16*d^6*(a+b*x)^-2*(b*c+-1*a*d)^9+-1365//4*b^-16*d^4*(a+b*x)^-4*(b*c+-1*a*d)^11+-35//2*b^-16*d^2*(a+b*x)^-6*(b*c+-1*a*d)^13+-15//7*d*b^-16*(a+b*x)^-7*(b*c+-1*a*d)^14+5//2*b^-16*d^14*(a+b*x)^6*(b*c+-1*a*d)+455//4*b^-16*d^12*(a+b*x)^4*(b*c+-1*a*d)^3+3003//2*b^-16*d^10*(a+b*x)^2*(b*c+-1*a*d)^5)
@test integrate((a+b*x)^-10*(c+d*x)^15, x) == :(-1//9*b^-16*(a+b*x)^-9*(b*c+-1*a*d)^15+1//6*b^-16*d^15*(a+b*x)^6+-6435*b^-16*d^8*(a+b*x)^-1*(b*c+-1*a*d)^7+-273*b^-16*d^4*(a+b*x)^-5*(b*c+-1*a*d)^11+-15*b^-16*d^2*(a+b*x)^-7*(b*c+-1*a*d)^13+3*b^-16*d^14*(a+b*x)^5*(b*c+-1*a*d)+3003*x*b^-15*d^10*(b*c+-1*a*d)^5+5005*b^-16*d^9*(b*c+-1*a*d)^6*log(a+b*x)+-6435//2*b^-16*d^7*(a+b*x)^-2*(b*c+-1*a*d)^8+-5005//3*b^-16*d^6*(a+b*x)^-3*(b*c+-1*a*d)^9+-3003//4*b^-16*d^5*(a+b*x)^-4*(b*c+-1*a*d)^10+-455//6*b^-16*d^3*(a+b*x)^-6*(b*c+-1*a*d)^12+-15//8*d*b^-16*(a+b*x)^-8*(b*c+-1*a*d)^14+105//4*b^-16*d^13*(a+b*x)^4*(b*c+-1*a*d)^2+455//3*b^-16*d^12*(a+b*x)^3*(b*c+-1*a*d)^3+1365//2*b^-16*d^11*(a+b*x)^2*(b*c+-1*a*d)^4)
@test integrate((a+b*x)^-11*(c+d*x)^15, x) == :(-1//10*b^-16*(a+b*x)^-10*(b*c+-1*a*d)^15+1//5*b^-16*d^15*(a+b*x)^5+-5005*b^-16*d^9*(a+b*x)^-1*(b*c+-1*a*d)^6+-2145*b^-16*d^7*(a+b*x)^-3*(b*c+-1*a*d)^8+-65*b^-16*d^3*(a+b*x)^-7*(b*c+-1*a*d)^12+35*b^-16*d^13*(a+b*x)^3*(b*c+-1*a*d)^2+1365*x*b^-15*d^11*(b*c+-1*a*d)^4+3003*b^-16*d^10*(b*c+-1*a*d)^5*log(a+b*x)+-6435//2*b^-16*d^8*(a+b*x)^-2*(b*c+-1*a*d)^7+-5005//4*b^-16*d^6*(a+b*x)^-4*(b*c+-1*a*d)^9+-3003//5*b^-16*d^5*(a+b*x)^-5*(b*c+-1*a*d)^10+-455//2*b^-16*d^4*(a+b*x)^-6*(b*c+-1*a*d)^11+-105//8*b^-16*d^2*(a+b*x)^-8*(b*c+-1*a*d)^13+-5//3*d*b^-16*(a+b*x)^-9*(b*c+-1*a*d)^14+15//4*b^-16*d^14*(a+b*x)^4*(b*c+-1*a*d)+455//2*b^-16*d^12*(a+b*x)^2*(b*c+-1*a*d)^3)
@test integrate((a+b*x)^-12*(c+d*x)^15, x) == :(-1//11*b^-16*(a+b*x)^-11*(b*c+-1*a*d)^15+1//4*b^-16*d^15*(a+b*x)^4+-3003*b^-16*d^10*(a+b*x)^-1*(b*c+-1*a*d)^5+-2145*b^-16*d^8*(a+b*x)^-3*(b*c+-1*a*d)^7+-1001*b^-16*d^6*(a+b*x)^-5*(b*c+-1*a*d)^9+-195*b^-16*d^4*(a+b*x)^-7*(b*c+-1*a*d)^11+5*b^-16*d^14*(a+b*x)^3*(b*c+-1*a*d)+455*x*b^-15*d^12*(b*c+-1*a*d)^3+1365*b^-16*d^11*(b*c+-1*a*d)^4*log(a+b*x)+-6435//4*b^-16*d^7*(a+b*x)^-4*(b*c+-1*a*d)^8+-5005//2*b^-16*d^9*(a+b*x)^-2*(b*c+-1*a*d)^6+-1001//2*b^-16*d^5*(a+b*x)^-6*(b*c+-1*a*d)^10+-455//8*b^-16*d^3*(a+b*x)^-8*(b*c+-1*a*d)^12+-35//3*b^-16*d^2*(a+b*x)^-9*(b*c+-1*a*d)^13+-3//2*d*b^-16*(a+b*x)^-10*(b*c+-1*a*d)^14+105//2*b^-16*d^13*(a+b*x)^2*(b*c+-1*a*d)^2)
@test integrate((a+b*x)^-13*(c+d*x)^15, x) == :(-1//12*b^-16*(a+b*x)^-12*(b*c+-1*a*d)^15+1//3*b^-16*d^15*(a+b*x)^3+-1365*b^-16*d^11*(a+b*x)^-1*(b*c+-1*a*d)^4+-1287*b^-16*d^7*(a+b*x)^-5*(b*c+-1*a*d)^8+-429*b^-16*d^5*(a+b*x)^-7*(b*c+-1*a*d)^10+105*x*b^-15*d^13*(b*c+-1*a*d)^2+455*b^-16*d^12*(b*c+-1*a*d)^3*log(a+b*x)+-6435//4*b^-16*d^8*(a+b*x)^-4*(b*c+-1*a*d)^7+-5005//3*b^-16*d^9*(a+b*x)^-3*(b*c+-1*a*d)^6+-5005//6*b^-16*d^6*(a+b*x)^-6*(b*c+-1*a*d)^9+-3003//2*b^-16*d^10*(a+b*x)^-2*(b*c+-1*a*d)^5+-1365//8*b^-16*d^4*(a+b*x)^-8*(b*c+-1*a*d)^11+-455//9*b^-16*d^3*(a+b*x)^-9*(b*c+-1*a*d)^12+-21//2*b^-16*d^2*(a+b*x)^-10*(b*c+-1*a*d)^13+-15//11*d*b^-16*(a+b*x)^-11*(b*c+-1*a*d)^14+15//2*b^-16*d^14*(a+b*x)^2*(b*c+-1*a*d))
@test integrate((a+b*x)^-14*(c+d*x)^15, x) == :((1/2)*b^-14*d^15*x^2+-1//13*b^-16*(a+b*x)^-13*(b*c+-1*a*d)^15+x*b^-15*d^14*(-14*a*d+15*b*c)+-1287*b^-16*d^8*(a+b*x)^-5*(b*c+-1*a*d)^7+-1001*b^-16*d^10*(a+b*x)^-3*(b*c+-1*a*d)^5+-715*b^-16*d^6*(a+b*x)^-7*(b*c+-1*a*d)^9+-455*b^-16*d^12*(a+b*x)^-1*(b*c+-1*a*d)^3+105*b^-16*d^13*(b*c+-1*a*d)^2*log(a+b*x)+-5005//4*b^-16*d^9*(a+b*x)^-4*(b*c+-1*a*d)^6+-3003//8*b^-16*d^5*(a+b*x)^-8*(b*c+-1*a*d)^10+-2145//2*b^-16*d^7*(a+b*x)^-6*(b*c+-1*a*d)^8+-1365//2*b^-16*d^11*(a+b*x)^-2*(b*c+-1*a*d)^4+-455//3*b^-16*d^4*(a+b*x)^-9*(b*c+-1*a*d)^11+-105//11*b^-16*d^2*(a+b*x)^-11*(b*c+-1*a*d)^13+-91//2*b^-16*d^3*(a+b*x)^-10*(b*c+-1*a*d)^12+-5//4*d*b^-16*(a+b*x)^-12*(b*c+-1*a*d)^14)
@test integrate((a+b*x)^-15*(c+d*x)^15, x) == :(x*b^-15*d^15+-1//14*b^-16*(a+b*x)^-14*(b*c+-1*a*d)^15+-1001*b^-16*d^9*(a+b*x)^-5*(b*c+-1*a*d)^6+-455*b^-16*d^11*(a+b*x)^-3*(b*c+-1*a*d)^4+-105*b^-16*d^13*(a+b*x)^-1*(b*c+-1*a*d)^2+15*b^-16*d^14*(b*c+-1*a*d)*log(a+b*x)+-6435//7*b^-16*d^7*(a+b*x)^-7*(b*c+-1*a*d)^8+-5005//8*b^-16*d^6*(a+b*x)^-8*(b*c+-1*a*d)^9+-3003//4*b^-16*d^10*(a+b*x)^-4*(b*c+-1*a*d)^5+-2145//2*b^-16*d^8*(a+b*x)^-6*(b*c+-1*a*d)^7+-1001//3*b^-16*d^5*(a+b*x)^-9*(b*c+-1*a*d)^10+-455//2*b^-16*d^12*(a+b*x)^-2*(b*c+-1*a*d)^3+-455//11*b^-16*d^3*(a+b*x)^-11*(b*c+-1*a*d)^12+-273//2*b^-16*d^4*(a+b*x)^-10*(b*c+-1*a*d)^11+-35//4*b^-16*d^2*(a+b*x)^-12*(b*c+-1*a*d)^13+-15//13*d*b^-16*(a+b*x)^-13*(b*c+-1*a*d)^14)
@test integrate((a+b*x)^-16*(c+d*x)^15, x) == :(b^-16*d^15*log(a+b*x)+-1//15*b^-16*(a+b*x)^-15*(b*c+-1*a*d)^15+-15*b^-16*d^14*(a+b*x)^-1*(b*c+-1*a*d)+-6435//7*b^-16*d^8*(a+b*x)^-7*(b*c+-1*a*d)^7+-6435//8*b^-16*d^7*(a+b*x)^-8*(b*c+-1*a*d)^8+-5005//6*b^-16*d^9*(a+b*x)^-6*(b*c+-1*a*d)^6+-5005//9*b^-16*d^6*(a+b*x)^-9*(b*c+-1*a*d)^9+-3003//5*b^-16*d^10*(a+b*x)^-5*(b*c+-1*a*d)^5+-3003//10*b^-16*d^5*(a+b*x)^-10*(b*c+-1*a*d)^10+-1365//4*b^-16*d^11*(a+b*x)^-4*(b*c+-1*a*d)^4+-1365//11*b^-16*d^4*(a+b*x)^-11*(b*c+-1*a*d)^11+-455//3*b^-16*d^12*(a+b*x)^-3*(b*c+-1*a*d)^3+-455//12*b^-16*d^3*(a+b*x)^-12*(b*c+-1*a*d)^12+-105//2*b^-16*d^13*(a+b*x)^-2*(b*c+-1*a*d)^2+-105//13*b^-16*d^2*(a+b*x)^-13*(b*c+-1*a*d)^13+-15//14*d*b^-16*(a+b*x)^-14*(b*c+-1*a*d)^14)
@test integrate((a+b*x)^-17*(c+d*x)^15, x) == :(-1*(a+b*x)^-16*(c+d*x)^16*(-16*a*d+16*b*c)^-1)
@test integrate((a+b*x)^-18*(c+d*x)^15, x) == :(-1*(a+b*x)^-17*(c+d*x)^16*(-17*a*d+17*b*c)^-1+1//272*d*(a+b*x)^-16*(c+d*x)^16*(b*c+-1*a*d)^-2)
@test integrate((a+b*x)^-19*(c+d*x)^15, x) == :(-1*(a+b*x)^-18*(c+d*x)^16*(-18*a*d+18*b*c)^-1+-1//2448*d^2*(a+b*x)^-16*(c+d*x)^16*(b*c+-1*a*d)^-3+1//153*d*(a+b*x)^-17*(c+d*x)^16*(b*c+-1*a*d)^-2)
@test integrate((a+b*x)^-20*(c+d*x)^15, x) == :(-1*(a+b*x)^-19*(c+d*x)^16*(-19*a*d+19*b*c)^-1+-1//969*d^2*(a+b*x)^-17*(c+d*x)^16*(b*c+-1*a*d)^-3+1//114*d*(a+b*x)^-18*(c+d*x)^16*(b*c+-1*a*d)^-2+1//15504*d^3*(a+b*x)^-16*(c+d*x)^16*(b*c+-1*a*d)^-4)
@test integrate((a+b*x)^-21*(c+d*x)^15, x) == :(-1*(a+b*x)^-20*(c+d*x)^16*(-20*a*d+20*b*c)^-1+-1//570*d^2*(a+b*x)^-18*(c+d*x)^16*(b*c+-1*a*d)^-3+-1//77520*d^4*(a+b*x)^-16*(c+d*x)^16*(b*c+-1*a*d)^-5+1//95*d*(a+b*x)^-19*(c+d*x)^16*(b*c+-1*a*d)^-2+1//4845*d^3*(a+b*x)^-17*(c+d*x)^16*(b*c+-1*a*d)^-4)
@test integrate((a+b*x)^-22*(c+d*x)^15, x) == :(-1*(a+b*x)^-21*(c+d*x)^16*(-21*a*d+21*b*c)^-1+-1//399*d^2*(a+b*x)^-19*(c+d*x)^16*(b*c+-1*a*d)^-3+-1//20349*d^4*(a+b*x)^-17*(c+d*x)^16*(b*c+-1*a*d)^-5+1//84*d*(a+b*x)^-20*(c+d*x)^16*(b*c+-1*a*d)^-2+1//2394*d^3*(a+b*x)^-18*(c+d*x)^16*(b*c+-1*a*d)^-4+1//325584*d^5*(a+b*x)^-16*(c+d*x)^16*(b*c+-1*a*d)^-6)
@test integrate((a+b*x)^-23*(c+d*x)^15, x) == :(-1*(a+b*x)^-22*(c+d*x)^16*(-22*a*d+22*b*c)^-1+-1//308*d^2*(a+b*x)^-20*(c+d*x)^16*(b*c+-1*a*d)^-3+-1//8778*d^4*(a+b*x)^-18*(c+d*x)^16*(b*c+-1*a*d)^-5+-1//1193808*d^6*(a+b*x)^-16*(c+d*x)^16*(b*c+-1*a*d)^-7+1//77*d*(a+b*x)^-21*(c+d*x)^16*(b*c+-1*a*d)^-2+1//1463*d^3*(a+b*x)^-19*(c+d*x)^16*(b*c+-1*a*d)^-4+1//74613*d^5*(a+b*x)^-17*(c+d*x)^16*(b*c+-1*a*d)^-6)
@test integrate((a+b*x)^-24*(c+d*x)^15, x) == :(-1*(a+b*x)^-23*(c+d*x)^16*(-23*a*d+23*b*c)^-1+-1//253*d^2*(a+b*x)^-21*(c+d*x)^16*(b*c+-1*a*d)^-3+-1//4807*d^4*(a+b*x)^-19*(c+d*x)^16*(b*c+-1*a*d)^-5+-1//245157*d^6*(a+b*x)^-17*(c+d*x)^16*(b*c+-1*a*d)^-7+1//1012*d^3*(a+b*x)^-20*(c+d*x)^16*(b*c+-1*a*d)^-4+1//28842*d^5*(a+b*x)^-18*(c+d*x)^16*(b*c+-1*a*d)^-6+1//3922512*d^7*(a+b*x)^-16*(c+d*x)^16*(b*c+-1*a*d)^-8+7//506*d*(a+b*x)^-22*(c+d*x)^16*(b*c+-1*a*d)^-2)
@test integrate((a+b*x)^-25*(c+d*x)^15, x) == :(-1*(a+b*x)^-24*(c+d*x)^16*(-24*a*d+24*b*c)^-1+-7//1518*d^2*(a+b*x)^-22*(c+d*x)^16*(b*c+-1*a*d)^-3+-1//3036*d^4*(a+b*x)^-20*(c+d*x)^16*(b*c+-1*a*d)^-5+-1//86526*d^6*(a+b*x)^-18*(c+d*x)^16*(b*c+-1*a*d)^-7+-1//11767536*d^8*(a+b*x)^-16*(c+d*x)^16*(b*c+-1*a*d)^-9+1//69*d*(a+b*x)^-23*(c+d*x)^16*(b*c+-1*a*d)^-2+1//759*d^3*(a+b*x)^-21*(c+d*x)^16*(b*c+-1*a*d)^-4+1//14421*d^5*(a+b*x)^-19*(c+d*x)^16*(b*c+-1*a*d)^-6+1//735471*d^7*(a+b*x)^-17*(c+d*x)^16*(b*c+-1*a*d)^-8)
@test integrate((a+b*x)^-26*(c+d*x)^15, x) == :(-1*(a+b*x)^-25*(c+d*x)^16*(-25*a*d+25*b*c)^-1+-3//575*d^2*(a+b*x)^-23*(c+d*x)^16*(b*c+-1*a*d)^-3+-3//6325*d^4*(a+b*x)^-21*(c+d*x)^16*(b*c+-1*a*d)^-5+-3//120175*d^6*(a+b*x)^-19*(c+d*x)^16*(b*c+-1*a*d)^-7+-1//2042975*d^8*(a+b*x)^-17*(c+d*x)^16*(b*c+-1*a*d)^-9+1//240350*d^7*(a+b*x)^-18*(c+d*x)^16*(b*c+-1*a*d)^-8+1//32687600*d^9*(a+b*x)^-16*(c+d*x)^16*(b*c+-1*a*d)^-10+3//200*d*(a+b*x)^-24*(c+d*x)^16*(b*c+-1*a*d)^-2+3//25300*d^5*(a+b*x)^-20*(c+d*x)^16*(b*c+-1*a*d)^-6+21//12650*d^3*(a+b*x)^-22*(c+d*x)^16*(b*c+-1*a*d)^-4)
@test integrate((a+b*x)^-27*(c+d*x)^15, x) == :(-1*(a+b*x)^-26*(c+d*x)^16*(-26*a*d+26*b*c)^-1+-21//32890*d^4*(a+b*x)^-22*(c+d*x)^16*(b*c+-1*a*d)^-5+-3//520*d^2*(a+b*x)^-24*(c+d*x)^16*(b*c+-1*a*d)^-3+-3//65780*d^6*(a+b*x)^-20*(c+d*x)^16*(b*c+-1*a*d)^-7+-1//624910*d^8*(a+b*x)^-18*(c+d*x)^16*(b*c+-1*a*d)^-9+-1//84987760*d^10*(a+b*x)^-16*(c+d*x)^16*(b*c+-1*a*d)^-11+1//65*d*(a+b*x)^-25*(c+d*x)^16*(b*c+-1*a*d)^-2+1//5311735*d^9*(a+b*x)^-17*(c+d*x)^16*(b*c+-1*a*d)^-10+3//1495*d^3*(a+b*x)^-23*(c+d*x)^16*(b*c+-1*a*d)^-4+3//16445*d^5*(a+b*x)^-21*(c+d*x)^16*(b*c+-1*a*d)^-6+3//312455*d^7*(a+b*x)^-19*(c+d*x)^16*(b*c+-1*a*d)^-8)
@test integrate((a+b*x)^-28*(c+d*x)^15, x) == :(-1*(a+b*x)^-27*(c+d*x)^16*(-27*a*d+27*b*c)^-1+-11//1755*d^2*(a+b*x)^-25*(c+d*x)^16*(b*c+-1*a*d)^-3+-11//13455*d^4*(a+b*x)^-23*(c+d*x)^16*(b*c+-1*a*d)^-5+-1//13455*d^6*(a+b*x)^-21*(c+d*x)^16*(b*c+-1*a*d)^-7+-1//255645*d^8*(a+b*x)^-19*(c+d*x)^16*(b*c+-1*a*d)^-9+-1//13037895*d^10*(a+b*x)^-17*(c+d*x)^16*(b*c+-1*a*d)^-11+1//53820*d^7*(a+b*x)^-20*(c+d*x)^16*(b*c+-1*a*d)^-8+1//1533870*d^9*(a+b*x)^-18*(c+d*x)^16*(b*c+-1*a*d)^-10+1//208606320*d^11*(a+b*x)^-16*(c+d*x)^16*(b*c+-1*a*d)^-12+7//26910*d^5*(a+b*x)^-22*(c+d*x)^16*(b*c+-1*a*d)^-6+11//702*d*(a+b*x)^-26*(c+d*x)^16*(b*c+-1*a*d)^-2+11//4680*d^3*(a+b*x)^-24*(c+d*x)^16*(b*c+-1*a*d)^-4)
@test integrate((a+b*x)^-29*(c+d*x)^15, x) == :(-1//13*b^-16*d^15*(a+b*x)^-13+-1//28*b^-16*(a+b*x)^-28*(b*c+-1*a*d)^15+-7*b^-16*d^13*(a+b*x)^-15*(b*c+-1*a*d)^2+-5005//19*b^-16*d^9*(a+b*x)^-19*(b*c+-1*a*d)^6+-3003//23*b^-16*d^5*(a+b*x)^-23*(b*c+-1*a*d)^10+-2145//7*b^-16*d^7*(a+b*x)^-21*(b*c+-1*a*d)^8+-1365//17*b^-16*d^11*(a+b*x)^-17*(b*c+-1*a*d)^4+-1287//4*b^-16*d^8*(a+b*x)^-20*(b*c+-1*a*d)^7+-1001//6*b^-16*d^10*(a+b*x)^-18*(b*c+-1*a*d)^5+-455//2*b^-16*d^6*(a+b*x)^-22*(b*c+-1*a*d)^9+-455//8*b^-16*d^4*(a+b*x)^-24*(b*c+-1*a*d)^11+-455//16*b^-16*d^12*(a+b*x)^-16*(b*c+-1*a*d)^3+-105//26*b^-16*d^2*(a+b*x)^-26*(b*c+-1*a*d)^13+-91//5*b^-16*d^3*(a+b*x)^-25*(b*c+-1*a*d)^12+-15//14*b^-16*d^14*(a+b*x)^-14*(b*c+-1*a*d)+-5//9*d*b^-16*(a+b*x)^-27*(b*c+-1*a*d)^14)
@test integrate((a+b*x)^-30*(c+d*x)^15, x) == :(-1//14*b^-16*d^15*(a+b*x)^-14+-1//29*b^-16*(a+b*x)^-29*(b*c+-1*a*d)^15+-1*b^-16*d^14*(a+b*x)^-15*(b*c+-1*a*d)+-5005//23*b^-16*d^6*(a+b*x)^-23*(b*c+-1*a*d)^9+-3003//19*b^-16*d^10*(a+b*x)^-19*(b*c+-1*a*d)^5+-2145//7*b^-16*d^8*(a+b*x)^-21*(b*c+-1*a*d)^7+-1001//4*b^-16*d^9*(a+b*x)^-20*(b*c+-1*a*d)^6+-1001//8*b^-16*d^5*(a+b*x)^-24*(b*c+-1*a*d)^10+-585//2*b^-16*d^7*(a+b*x)^-22*(b*c+-1*a*d)^8+-455//6*b^-16*d^11*(a+b*x)^-18*(b*c+-1*a*d)^4+-455//17*b^-16*d^12*(a+b*x)^-17*(b*c+-1*a*d)^3+-273//5*b^-16*d^4*(a+b*x)^-25*(b*c+-1*a*d)^11+-105//16*b^-16*d^13*(a+b*x)^-16*(b*c+-1*a*d)^2+-35//2*b^-16*d^3*(a+b*x)^-26*(b*c+-1*a*d)^12+-35//9*b^-16*d^2*(a+b*x)^-27*(b*c+-1*a*d)^13+-15//28*d*b^-16*(a+b*x)^-28*(b*c+-1*a*d)^14)
@test integrate((a+b*x)^-31*(c+d*x)^15, x) == :(-1//15*b^-16*d^15*(a+b*x)^-15+-1//30*b^-16*(a+b*x)^-30*(b*c+-1*a*d)^15+-6435//23*b^-16*d^7*(a+b*x)^-23*(b*c+-1*a*d)^8+-5005//24*b^-16*d^6*(a+b*x)^-24*(b*c+-1*a*d)^9+-3003//20*b^-16*d^10*(a+b*x)^-20*(b*c+-1*a*d)^5+-3003//25*b^-16*d^5*(a+b*x)^-25*(b*c+-1*a*d)^10+-1365//19*b^-16*d^11*(a+b*x)^-19*(b*c+-1*a*d)^4+-715//3*b^-16*d^9*(a+b*x)^-21*(b*c+-1*a*d)^6+-585//2*b^-16*d^8*(a+b*x)^-22*(b*c+-1*a*d)^7+-455//18*b^-16*d^12*(a+b*x)^-18*(b*c+-1*a*d)^3+-455//27*b^-16*d^3*(a+b*x)^-27*(b*c+-1*a*d)^12+-105//2*b^-16*d^4*(a+b*x)^-26*(b*c+-1*a*d)^11+-105//17*b^-16*d^13*(a+b*x)^-17*(b*c+-1*a*d)^2+-15//4*b^-16*d^2*(a+b*x)^-28*(b*c+-1*a*d)^13+-15//16*b^-16*d^14*(a+b*x)^-16*(b*c+-1*a*d)+-15//29*d*b^-16*(a+b*x)^-29*(b*c+-1*a*d)^14)
@test integrate((a+b*x)^5*(c+d*x)^-1, x) == :(1//5*d^-1*(a+b*x)^5+-1*d^-6*(b*c+-1*a*d)^5*log(c+d*x)+-1//2*d^-4*(a+b*x)^2*(b*c+-1*a*d)^3+-1//4*d^-2*(a+b*x)^4*(b*c+-1*a*d)+1//3*d^-3*(a+b*x)^3*(b*c+-1*a*d)^2+b*x*d^-5*(b*c+-1*a*d)^4)
@test integrate((a+b*x)^4*(c+d*x)^-1, x) == :(1//4*d^-1*(a+b*x)^4+d^-5*(b*c+-1*a*d)^4*log(c+d*x)+(1/2)*d^-3*(a+b*x)^2*(b*c+-1*a*d)^2+-1//3*d^-2*(a+b*x)^3*(b*c+-1*a*d)+-1*b*x*d^-4*(b*c+-1*a*d)^3)
@test integrate((a+b*x)^3*(c+d*x)^-1, x) == :(1//3*d^-1*(a+b*x)^3+-1*d^-4*(b*c+-1*a*d)^3*log(c+d*x)+-1//2*d^-2*(a+b*x)^2*(b*c+-1*a*d)+b*x*d^-3*(b*c+-1*a*d)^2)
@test integrate((a+b*x)^2*(c+d*x)^-1, x) == :((1/2)*d^-1*(a+b*x)^2+d^-3*(b*c+-1*a*d)^2*log(c+d*x)+-1*b*x*d^-2*(b*c+-1*a*d))
@test integrate((c+d*x)^-1*(a+b*x), x) == :(b*x*d^-1+-1*d^-2*(b*c+-1*a*d)*log(c+d*x))
@test integrate((c+d*x)^-1, x) == :(d^-1*log(c+d*x))
@test integrate((a+b*x)^-1*(c+d*x)^-1, x) == :((b*c+-1*a*d)^-1*log(a+b*x)+-1*(b*c+-1*a*d)^-1*log(c+d*x))
@test integrate((a+b*x)^-2*(c+d*x)^-1, x) == :(-1*(a+b*x)^-1*(b*c+-1*a*d)^-1+d*(b*c+-1*a*d)^-2*log(c+d*x)+-1*d*(b*c+-1*a*d)^-2*log(a+b*x))
@test integrate((a+b*x)^-3*(c+d*x)^-1, x) == :(-1*(a+b*x)^-2*(-2*a*d+2*b*c)^-1+d*(a+b*x)^-1*(b*c+-1*a*d)^-2+d^2*(b*c+-1*a*d)^-3*log(a+b*x)+-1*d^2*(b*c+-1*a*d)^-3*log(c+d*x))
@test integrate((a+b*x)^5*(c+d*x)^-2, x) == :(d^-6*(c+d*x)^-1*(b*c+-1*a*d)^5+1//4*b^5*d^-6*(c+d*x)^4+-10*x*b^2*d^-5*(b*c+-1*a*d)^3+5*b*d^-6*(b*c+-1*a*d)^4*log(c+d*x)+5*b^3*d^-6*(c+d*x)^2*(b*c+-1*a*d)^2+-5//3*b^4*d^-6*(c+d*x)^3*(b*c+-1*a*d))
@test integrate((a+b*x)^4*(c+d*x)^-2, x) == :(-1*d^-5*(c+d*x)^-1*(b*c+-1*a*d)^4+1//3*b^4*d^-5*(c+d*x)^3+-4*b*d^-5*(b*c+-1*a*d)^3*log(c+d*x)+-2*b^3*d^-5*(c+d*x)^2*(b*c+-1*a*d)+6*x*b^2*d^-4*(b*c+-1*a*d)^2)
@test integrate((a+b*x)^3*(c+d*x)^-2, x) == :(d^-4*(c+d*x)^-1*(b*c+-1*a*d)^3+(1/2)*b^3*d^-2*x^2+-1*x*b^2*d^-3*(-3*a*d+2*b*c)+3*b*d^-4*(b*c+-1*a*d)^2*log(c+d*x))
@test integrate((a+b*x)^2*(c+d*x)^-2, x) == :(x*b^2*d^-2+-1*d^-3*(c+d*x)^-1*(b*c+-1*a*d)^2+-2*b*d^-3*(b*c+-1*a*d)*log(c+d*x))
@test integrate((c+d*x)^-2*(a+b*x), x) == :(b*d^-2*log(c+d*x)+d^-2*(c+d*x)^-1*(b*c+-1*a*d))
@test integrate((c+d*x)^-2, x) == :(-1*d^-1*(c+d*x)^-1)
@test integrate((a+b*x)^-1*(c+d*x)^-2, x) == :((c+d*x)^-1*(b*c+-1*a*d)^-1+b*(b*c+-1*a*d)^-2*log(a+b*x)+-1*b*(b*c+-1*a*d)^-2*log(c+d*x))
@test integrate((a+b*x)^-2*(c+d*x)^-2, x) == :(-1*b*(a+b*x)^-1*(b*c+-1*a*d)^-2+-1*d*(c+d*x)^-1*(b*c+-1*a*d)^-2+-2*b*d*(b*c+-1*a*d)^-3*log(a+b*x)+2*b*d*(b*c+-1*a*d)^-3*log(c+d*x))
@test integrate((a+b*x)^-3*(c+d*x)^-2, x) == :(d^2*(c+d*x)^-1*(b*c+-1*a*d)^-3+-1//2*b*(a+b*x)^-2*(b*c+-1*a*d)^-2+-3*b*d^2*(b*c+-1*a*d)^-4*log(c+d*x)+2*b*d*(a+b*x)^-1*(b*c+-1*a*d)^-3+3*b*d^2*(b*c+-1*a*d)^-4*log(a+b*x))
@test integrate((a+b*x)^6*(c+d*x)^-3, x) == :(-1//2*d^-7*(c+d*x)^-2*(b*c+-1*a*d)^6+1//4*b^6*d^-7*(c+d*x)^4+-20*x*b^3*d^-6*(b*c+-1*a*d)^3+-2*b^5*d^-7*(c+d*x)^3*(b*c+-1*a*d)+6*b*d^-7*(c+d*x)^-1*(b*c+-1*a*d)^5+15*b^2*d^-7*(b*c+-1*a*d)^4*log(c+d*x)+15//2*b^4*d^-7*(c+d*x)^2*(b*c+-1*a*d)^2)
@test integrate((a+b*x)^5*(c+d*x)^-3, x) == :((1/2)*d^-6*(c+d*x)^-2*(b*c+-1*a*d)^5+1//3*b^5*d^-6*(c+d*x)^3+-10*b^2*d^-6*(b*c+-1*a*d)^3*log(c+d*x)+-5*b*d^-6*(c+d*x)^-1*(b*c+-1*a*d)^4+10*x*b^3*d^-5*(b*c+-1*a*d)^2+-5//2*b^4*d^-6*(c+d*x)^2*(b*c+-1*a*d))
@test integrate((a+b*x)^4*(c+d*x)^-3, x) == :((1/2)*b^4*d^-3*x^2+-1//2*d^-5*(c+d*x)^-2*(b*c+-1*a*d)^4+-1*x*b^3*d^-4*(-4*a*d+3*b*c)+4*b*d^-5*(c+d*x)^-1*(b*c+-1*a*d)^3+6*b^2*d^-5*(b*c+-1*a*d)^2*log(c+d*x))
@test integrate((a+b*x)^3*(c+d*x)^-3, x) == :(x*b^3*d^-3+(1/2)*d^-4*(c+d*x)^-2*(b*c+-1*a*d)^3+-3*b*d^-4*(c+d*x)^-1*(b*c+-1*a*d)^2+-3*b^2*d^-4*(b*c+-1*a*d)*log(c+d*x))
@test integrate((a+b*x)^2*(c+d*x)^-3, x) == :(b^2*d^-3*log(c+d*x)+-1//2*d^-3*(c+d*x)^-2*(b*c+-1*a*d)^2+2*b*d^-3*(c+d*x)^-1*(b*c+-1*a*d))
@test integrate((c+d*x)^-3*(a+b*x), x) == :((a+b*x)^2*(c+d*x)^-2*(-2*a*d+2*b*c)^-1)
@test integrate((c+d*x)^-3, x) == :(-1//2*d^-1*(c+d*x)^-2)
@test integrate((a+b*x)^-1*(c+d*x)^-3, x) == :((c+d*x)^-2*(-2*a*d+2*b*c)^-1+b*(c+d*x)^-1*(b*c+-1*a*d)^-2+b^2*(b*c+-1*a*d)^-3*log(a+b*x)+-1*b^2*(b*c+-1*a*d)^-3*log(c+d*x))
@test integrate((a+b*x)^-2*(c+d*x)^-3, x) == :(-1*b^2*(a+b*x)^-1*(b*c+-1*a*d)^-3+-1//2*d*(c+d*x)^-2*(b*c+-1*a*d)^-2+-3*d*b^2*(b*c+-1*a*d)^-4*log(a+b*x)+-2*b*d*(c+d*x)^-1*(b*c+-1*a*d)^-3+3*d*b^2*(b*c+-1*a*d)^-4*log(c+d*x))
@test integrate((a+b*x)^-3*(c+d*x)^-3, x) == :((1/2)*d^2*(c+d*x)^-2*(b*c+-1*a*d)^-3+-1//2*b^2*(a+b*x)^-2*(b*c+-1*a*d)^-3+-6*b^2*d^2*(b*c+-1*a*d)^-5*log(c+d*x)+3*b*d^2*(c+d*x)^-1*(b*c+-1*a*d)^-4+3*d*b^2*(a+b*x)^-1*(b*c+-1*a*d)^-4+6*b^2*d^2*(b*c+-1*a*d)^-5*log(a+b*x))
@test integrate((a+b*x)^9*(c+d*x)^-8, x) == :((1/2)*b^9*d^-8*x^2+1//7*d^-10*(c+d*x)^-7*(b*c+-1*a*d)^9+-1*x*b^8*d^-9*(-9*a*d+8*b*c)+-63*b^5*d^-10*(c+d*x)^-2*(b*c+-1*a*d)^4+-21*b^3*d^-10*(c+d*x)^-4*(b*c+-1*a*d)^6+36*b^7*d^-10*(b*c+-1*a*d)^2*log(c+d*x)+42*b^4*d^-10*(c+d*x)^-3*(b*c+-1*a*d)^5+84*b^6*d^-10*(c+d*x)^-1*(b*c+-1*a*d)^3+-3//2*b*d^-10*(c+d*x)^-6*(b*c+-1*a*d)^8+36//5*b^2*d^-10*(c+d*x)^-5*(b*c+-1*a*d)^7)
@test integrate((a+b*x)^8*(c+d*x)^-8, x) == :(x*b^8*d^-8+-1//7*d^-9*(c+d*x)^-7*(b*c+-1*a*d)^8+-28*b^6*d^-9*(c+d*x)^-1*(b*c+-1*a*d)^2+-8*b^7*d^-9*(b*c+-1*a*d)*log(c+d*x)+14*b^3*d^-9*(c+d*x)^-4*(b*c+-1*a*d)^5+28*b^5*d^-9*(c+d*x)^-2*(b*c+-1*a*d)^3+-70//3*b^4*d^-9*(c+d*x)^-3*(b*c+-1*a*d)^4+-28//5*b^2*d^-9*(c+d*x)^-5*(b*c+-1*a*d)^6+4//3*b*d^-9*(c+d*x)^-6*(b*c+-1*a*d)^7)
@test integrate((a+b*x)^7*(c+d*x)^-8, x) == :(b^7*d^-8*log(c+d*x)+1//7*d^-8*(c+d*x)^-7*(b*c+-1*a*d)^7+7*b^6*d^-8*(c+d*x)^-1*(b*c+-1*a*d)+-35//4*b^3*d^-8*(c+d*x)^-4*(b*c+-1*a*d)^4+-21//2*b^5*d^-8*(c+d*x)^-2*(b*c+-1*a*d)^2+-7//6*b*d^-8*(c+d*x)^-6*(b*c+-1*a*d)^6+21//5*b^2*d^-8*(c+d*x)^-5*(b*c+-1*a*d)^5+35//3*b^4*d^-8*(c+d*x)^-3*(b*c+-1*a*d)^3)
@test integrate((a+b*x)^6*(c+d*x)^-8, x) == :((a+b*x)^7*(c+d*x)^-7*(-7*a*d+7*b*c)^-1)
@test integrate((a+b*x)^5*(c+d*x)^-8, x) == :((a+b*x)^6*(c+d*x)^-7*(-7*a*d+7*b*c)^-1+1//42*b*(a+b*x)^6*(c+d*x)^-6*(b*c+-1*a*d)^-2)
@test integrate((a+b*x)^4*(c+d*x)^-8, x) == :((a+b*x)^5*(c+d*x)^-7*(-7*a*d+7*b*c)^-1+1//21*b*(a+b*x)^5*(c+d*x)^-6*(b*c+-1*a*d)^-2+1//105*b^2*(a+b*x)^5*(c+d*x)^-5*(b*c+-1*a*d)^-3)
@test integrate((a+b*x)^3*(c+d*x)^-8, x) == :(-1//4*b^3*d^-4*(c+d*x)^-4+1//7*d^-4*(c+d*x)^-7*(b*c+-1*a*d)^3+-1//2*b*d^-4*(c+d*x)^-6*(b*c+-1*a*d)^2+3//5*b^2*d^-4*(c+d*x)^-5*(b*c+-1*a*d))
@test integrate((a+b*x)^2*(c+d*x)^-8, x) == :(-1//5*b^2*d^-3*(c+d*x)^-5+-1//7*d^-3*(c+d*x)^-7*(b*c+-1*a*d)^2+1//3*b*d^-3*(c+d*x)^-6*(b*c+-1*a*d))
@test integrate((c+d*x)^-8*(a+b*x), x) == :(-1//6*b*d^-2*(c+d*x)^-6+1//7*d^-2*(c+d*x)^-7*(b*c+-1*a*d))
@test integrate((c+d*x)^-8, x) == :(-1//7*d^-1*(c+d*x)^-7)
@test integrate((a+b*x)^-1*(c+d*x)^-8, x) == :((c+d*x)^-7*(-7*a*d+7*b*c)^-1+b^6*(c+d*x)^-1*(b*c+-1*a*d)^-7+b^7*(b*c+-1*a*d)^-8*log(a+b*x)+(1/2)*b^5*(c+d*x)^-2*(b*c+-1*a*d)^-6+-1*b^7*(b*c+-1*a*d)^-8*log(c+d*x)+1//3*b^4*(c+d*x)^-3*(b*c+-1*a*d)^-5+1//4*b^3*(c+d*x)^-4*(b*c+-1*a*d)^-4+1//5*b^2*(c+d*x)^-5*(b*c+-1*a*d)^-3+1//6*b*(c+d*x)^-6*(b*c+-1*a*d)^-2)
@test integrate((a+b*x)^-2*(c+d*x)^-8, x) == :(-1*b^7*(a+b*x)^-1*(b*c+-1*a*d)^-8+-1//7*d*(c+d*x)^-7*(b*c+-1*a*d)^-2+-1*d*b^3*(c+d*x)^-4*(b*c+-1*a*d)^-5+-8*d*b^7*(b*c+-1*a*d)^-9*log(a+b*x)+-7*d*b^6*(c+d*x)^-1*(b*c+-1*a*d)^-8+-3*d*b^5*(c+d*x)^-2*(b*c+-1*a*d)^-7+8*d*b^7*(b*c+-1*a*d)^-9*log(c+d*x)+-5//3*d*b^4*(c+d*x)^-3*(b*c+-1*a*d)^-6+-3//5*d*b^2*(c+d*x)^-5*(b*c+-1*a*d)^-4+-1//3*b*d*(c+d*x)^-6*(b*c+-1*a*d)^-3)
@test integrate((a+b*x)^-3*(c+d*x)^-8, x) == :(-1//2*b^7*(a+b*x)^-2*(b*c+-1*a*d)^-8+1//7*d^2*(c+d*x)^-7*(b*c+-1*a*d)^-3+(1/2)*b*d^2*(c+d*x)^-6*(b*c+-1*a*d)^-4+-36*b^7*d^2*(b*c+-1*a*d)^-10*log(c+d*x)+5*b^4*d^2*(c+d*x)^-3*(b*c+-1*a*d)^-7+8*d*b^7*(a+b*x)^-1*(b*c+-1*a*d)^-9+28*b^6*d^2*(c+d*x)^-1*(b*c+-1*a*d)^-9+36*b^7*d^2*(b*c+-1*a*d)^-10*log(a+b*x)+5//2*b^3*d^2*(c+d*x)^-4*(b*c+-1*a*d)^-6+6//5*b^2*d^2*(c+d*x)^-5*(b*c+-1*a*d)^-5+21//2*b^5*d^2*(c+d*x)^-2*(b*c+-1*a*d)^-8)
@test integrate((a+b*x)^5*(c+d*x)^(1/2), x) == :(-2//3*d^-6*(c+d*x)^3//2*(b*c+-1*a*d)^5+2//13*b^5*d^-6*(c+d*x)^13//2+2*b*d^-6*(c+d*x)^5//2*(b*c+-1*a*d)^4+-20//7*b^2*d^-6*(c+d*x)^7//2*(b*c+-1*a*d)^3+-10//11*b^4*d^-6*(c+d*x)^11//2*(b*c+-1*a*d)+20//9*b^3*d^-6*(c+d*x)^9//2*(b*c+-1*a*d)^2)
@test integrate((a+b*x)^4*(c+d*x)^(1/2), x) == :(2//3*d^-5*(c+d*x)^3//2*(b*c+-1*a*d)^4+2//11*b^4*d^-5*(c+d*x)^11//2+-8//5*b*d^-5*(c+d*x)^5//2*(b*c+-1*a*d)^3+-8//9*b^3*d^-5*(c+d*x)^9//2*(b*c+-1*a*d)+12//7*b^2*d^-5*(c+d*x)^7//2*(b*c+-1*a*d)^2)
@test integrate((a+b*x)^3*(c+d*x)^(1/2), x) == :(-2//3*d^-4*(c+d*x)^3//2*(b*c+-1*a*d)^3+2//9*b^3*d^-4*(c+d*x)^9//2+-6//7*b^2*d^-4*(c+d*x)^7//2*(b*c+-1*a*d)+6//5*b*d^-4*(c+d*x)^5//2*(b*c+-1*a*d)^2)
@test integrate((a+b*x)^2*(c+d*x)^(1/2), x) == :(2//3*d^-3*(c+d*x)^3//2*(b*c+-1*a*d)^2+2//7*b^2*d^-3*(c+d*x)^7//2+-4//5*b*d^-3*(c+d*x)^5//2*(b*c+-1*a*d))
@test integrate((c+d*x)^(1/2)*(a+b*x), x) == :(-1//3*d^-2*(c+d*x)^3//2*(-2*a*d+2*b*c)+2//5*b*d^-2*(c+d*x)^5//2)
@test integrate((c+d*x)^(1/2), x) == :(2//3*d^-1*(c+d*x)^3//2)
@test integrate((a+b*x)^-1*(c+d*x)^(1/2), x) == :(2*b^-1*(c+d*x)^(1/2)+-2*b^-3//2*(b*c+-1*a*d)^(1/2)*arctanh(b^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate((a+b*x)^-2*(c+d*x)^(1/2), x) == :(-1*b^-1*(a+b*x)^-1*(c+d*x)^(1/2)+-1*d*b^-3//2*(b*c+-1*a*d)^-1//2*arctanh(b^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate((a+b*x)^-3*(c+d*x)^(1/2), x) == :(-1//2*b^-1*(a+b*x)^-2*(c+d*x)^(1/2)+1//4*b^-3//2*d^2*(b*c+-1*a*d)^-3//2*arctanh(b^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^-1//2)+-1//4*d*b^-1*(a+b*x)^-1*(c+d*x)^(1/2)*(b*c+-1*a*d)^-1)
@test integrate((a+b*x)^-4*(c+d*x)^(1/2), x) == :(-1//3*b^-1*(a+b*x)^-3*(c+d*x)^(1/2)+-1//8*b^-3//2*d^3*(b*c+-1*a*d)^-5//2*arctanh(b^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^-1//2)+-1//12*d*b^-1*(a+b*x)^-2*(c+d*x)^(1/2)*(b*c+-1*a*d)^-1+1//8*b^-1*d^2*(a+b*x)^-1*(c+d*x)^(1/2)*(b*c+-1*a*d)^-2)
@test integrate((a+b*x)^-5*(c+d*x)^(1/2), x) == :(-1//4*b^-1*(a+b*x)^-4*(c+d*x)^(1/2)+5//64*b^-3//2*d^4*(b*c+-1*a*d)^-7//2*arctanh(b^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^-1//2)+-5//64*b^-1*d^3*(a+b*x)^-1*(c+d*x)^(1/2)*(b*c+-1*a*d)^-3+-1//24*d*b^-1*(a+b*x)^-3*(c+d*x)^(1/2)*(b*c+-1*a*d)^-1+5//96*b^-1*d^2*(a+b*x)^-2*(c+d*x)^(1/2)*(b*c+-1*a*d)^-2)
@test integrate((a+b*x)^-6*(c+d*x)^(1/2), x) == :(-1//5*b^-1*(a+b*x)^-5*(c+d*x)^(1/2)+-7//128*b^-3//2*d^5*(b*c+-1*a*d)^-9//2*arctanh(b^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^-1//2)+-7//192*b^-1*d^3*(a+b*x)^-2*(c+d*x)^(1/2)*(b*c+-1*a*d)^-3+-1//40*d*b^-1*(a+b*x)^-4*(c+d*x)^(1/2)*(b*c+-1*a*d)^-1+7//128*b^-1*d^4*(a+b*x)^-1*(c+d*x)^(1/2)*(b*c+-1*a*d)^-4+7//240*b^-1*d^2*(a+b*x)^-3*(c+d*x)^(1/2)*(b*c+-1*a*d)^-2)
@test integrate((a+b*x)^5*(c+d*x)^3//2, x) == :(-2//5*d^-6*(c+d*x)^5//2*(b*c+-1*a*d)^5+2//15*b^5*d^-6*(c+d*x)^15//2+-20//9*b^2*d^-6*(c+d*x)^9//2*(b*c+-1*a*d)^3+-10//13*b^4*d^-6*(c+d*x)^13//2*(b*c+-1*a*d)+10//7*b*d^-6*(c+d*x)^7//2*(b*c+-1*a*d)^4+20//11*b^3*d^-6*(c+d*x)^11//2*(b*c+-1*a*d)^2)
@test integrate((a+b*x)^4*(c+d*x)^3//2, x) == :(2//5*d^-5*(c+d*x)^5//2*(b*c+-1*a*d)^4+2//13*b^4*d^-5*(c+d*x)^13//2+-8//7*b*d^-5*(c+d*x)^7//2*(b*c+-1*a*d)^3+-8//11*b^3*d^-5*(c+d*x)^11//2*(b*c+-1*a*d)+4//3*b^2*d^-5*(c+d*x)^9//2*(b*c+-1*a*d)^2)
@test integrate((a+b*x)^3*(c+d*x)^3//2, x) == :(-2//5*d^-4*(c+d*x)^5//2*(b*c+-1*a*d)^3+2//11*b^3*d^-4*(c+d*x)^11//2+-2//3*b^2*d^-4*(c+d*x)^9//2*(b*c+-1*a*d)+6//7*b*d^-4*(c+d*x)^7//2*(b*c+-1*a*d)^2)
@test integrate((a+b*x)^2*(c+d*x)^3//2, x) == :(2//5*d^-3*(c+d*x)^5//2*(b*c+-1*a*d)^2+2//9*b^2*d^-3*(c+d*x)^9//2+-4//7*b*d^-3*(c+d*x)^7//2*(b*c+-1*a*d))
@test integrate((c+d*x)^3//2*(a+b*x), x) == :(-1//5*d^-2*(c+d*x)^5//2*(-2*a*d+2*b*c)+2//7*b*d^-2*(c+d*x)^7//2)
@test integrate((c+d*x)^3//2, x) == :(2//5*d^-1*(c+d*x)^5//2)
@test integrate((a+b*x)^-1*(c+d*x)^3//2, x) == :(2//3*b^-1*(c+d*x)^3//2+b^-2*(c+d*x)^(1/2)*(-2*a*d+2*b*c)+-2*b^-5//2*(b*c+-1*a*d)^3//2*arctanh(b^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate((a+b*x)^-2*(c+d*x)^3//2, x) == :(-1*b^-1*(a+b*x)^-1*(c+d*x)^3//2+3*d*b^-2*(c+d*x)^(1/2)+-3*d*b^-5//2*(b*c+-1*a*d)^(1/2)*arctanh(b^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate((a+b*x)^-3*(c+d*x)^3//2, x) == :(-1//2*b^-1*(a+b*x)^-2*(c+d*x)^3//2+-3//4*d*b^-2*(a+b*x)^-1*(c+d*x)^(1/2)+-3//4*b^-5//2*d^2*(b*c+-1*a*d)^-1//2*arctanh(b^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate((a+b*x)^-4*(c+d*x)^3//2, x) == :(-1//3*b^-1*(a+b*x)^-3*(c+d*x)^3//2+-1//4*d*b^-2*(a+b*x)^-2*(c+d*x)^(1/2)+1//8*b^-5//2*d^3*(b*c+-1*a*d)^-3//2*arctanh(b^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^-1//2)+-1//8*b^-2*d^2*(a+b*x)^-1*(c+d*x)^(1/2)*(b*c+-1*a*d)^-1)
@test integrate((a+b*x)^-5*(c+d*x)^3//2, x) == :(-1//4*b^-1*(a+b*x)^-4*(c+d*x)^3//2+-3//64*b^-5//2*d^4*(b*c+-1*a*d)^-5//2*arctanh(b^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^-1//2)+-1//8*d*b^-2*(a+b*x)^-3*(c+d*x)^(1/2)+-1//32*b^-2*d^2*(a+b*x)^-2*(c+d*x)^(1/2)*(b*c+-1*a*d)^-1+3//64*b^-2*d^3*(a+b*x)^-1*(c+d*x)^(1/2)*(b*c+-1*a*d)^-2)
@test integrate((a+b*x)^-6*(c+d*x)^3//2, x) == :(-1//5*b^-1*(a+b*x)^-5*(c+d*x)^3//2+-3//40*d*b^-2*(a+b*x)^-4*(c+d*x)^(1/2)+3//128*b^-5//2*d^5*(b*c+-1*a*d)^-7//2*arctanh(b^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^-1//2)+-3//128*b^-2*d^4*(a+b*x)^-1*(c+d*x)^(1/2)*(b*c+-1*a*d)^-3+-1//80*b^-2*d^2*(a+b*x)^-3*(c+d*x)^(1/2)*(b*c+-1*a*d)^-1+1//64*b^-2*d^3*(a+b*x)^-2*(c+d*x)^(1/2)*(b*c+-1*a*d)^-2)
@test integrate((a+b*x)^5*(c+d*x)^5//2, x) == :(-2//7*d^-6*(c+d*x)^7//2*(b*c+-1*a*d)^5+2//17*b^5*d^-6*(c+d*x)^17//2+-20//11*b^2*d^-6*(c+d*x)^11//2*(b*c+-1*a*d)^3+-2//3*b^4*d^-6*(c+d*x)^15//2*(b*c+-1*a*d)+10//9*b*d^-6*(c+d*x)^9//2*(b*c+-1*a*d)^4+20//13*b^3*d^-6*(c+d*x)^13//2*(b*c+-1*a*d)^2)
@test integrate((a+b*x)^4*(c+d*x)^5//2, x) == :(2//7*d^-5*(c+d*x)^7//2*(b*c+-1*a*d)^4+2//15*b^4*d^-5*(c+d*x)^15//2+-8//9*b*d^-5*(c+d*x)^9//2*(b*c+-1*a*d)^3+-8//13*b^3*d^-5*(c+d*x)^13//2*(b*c+-1*a*d)+12//11*b^2*d^-5*(c+d*x)^11//2*(b*c+-1*a*d)^2)
@test integrate((a+b*x)^3*(c+d*x)^5//2, x) == :(-2//7*d^-4*(c+d*x)^7//2*(b*c+-1*a*d)^3+2//13*b^3*d^-4*(c+d*x)^13//2+-6//11*b^2*d^-4*(c+d*x)^11//2*(b*c+-1*a*d)+2//3*b*d^-4*(c+d*x)^9//2*(b*c+-1*a*d)^2)
@test integrate((a+b*x)^2*(c+d*x)^5//2, x) == :(2//7*d^-3*(c+d*x)^7//2*(b*c+-1*a*d)^2+2//11*b^2*d^-3*(c+d*x)^11//2+-4//9*b*d^-3*(c+d*x)^9//2*(b*c+-1*a*d))
@test integrate((c+d*x)^5//2*(a+b*x), x) == :(-1//7*d^-2*(c+d*x)^7//2*(-2*a*d+2*b*c)+2//9*b*d^-2*(c+d*x)^9//2)
@test integrate((c+d*x)^5//2, x) == :(2//7*d^-1*(c+d*x)^7//2)
@test integrate((a+b*x)^-1*(c+d*x)^5//2, x) == :(2//5*b^-1*(c+d*x)^5//2+-2*b^-7//2*(b*c+-1*a*d)^5//2*arctanh(b^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^-1//2)+2*b^-3*(c+d*x)^(1/2)*(b*c+-1*a*d)^2+1//3*b^-2*(c+d*x)^3//2*(-2*a*d+2*b*c))
@test integrate((a+b*x)^-2*(c+d*x)^5//2, x) == :(-1*b^-1*(a+b*x)^-1*(c+d*x)^5//2+5//3*d*b^-2*(c+d*x)^3//2+-5*d*b^-7//2*(b*c+-1*a*d)^3//2*arctanh(b^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^-1//2)+5*d*b^-3*(c+d*x)^(1/2)*(b*c+-1*a*d))
@test integrate((a+b*x)^-3*(c+d*x)^5//2, x) == :(-1//2*b^-1*(a+b*x)^-2*(c+d*x)^5//2+15//4*b^-3*d^2*(c+d*x)^(1/2)+-15//4*b^-7//2*d^2*(b*c+-1*a*d)^(1/2)*arctanh(b^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^-1//2)+-5//4*d*b^-2*(a+b*x)^-1*(c+d*x)^3//2)
@test integrate((a+b*x)^-4*(c+d*x)^5//2, x) == :(-1//3*b^-1*(a+b*x)^-3*(c+d*x)^5//2+-5//8*b^-3*d^2*(a+b*x)^-1*(c+d*x)^(1/2)+-5//8*b^-7//2*d^3*(b*c+-1*a*d)^-1//2*arctanh(b^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^-1//2)+-5//12*d*b^-2*(a+b*x)^-2*(c+d*x)^3//2)
@test integrate((a+b*x)^-5*(c+d*x)^5//2, x) == :(-1//4*b^-1*(a+b*x)^-4*(c+d*x)^5//2+-5//24*d*b^-2*(a+b*x)^-3*(c+d*x)^3//2+-5//32*b^-3*d^2*(a+b*x)^-2*(c+d*x)^(1/2)+5//64*b^-7//2*d^4*(b*c+-1*a*d)^-3//2*arctanh(b^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^-1//2)+-5//64*b^-3*d^3*(a+b*x)^-1*(c+d*x)^(1/2)*(b*c+-1*a*d)^-1)
@test integrate((a+b*x)^-6*(c+d*x)^5//2, x) == :(-1//5*b^-1*(a+b*x)^-5*(c+d*x)^5//2+-3//128*b^-7//2*d^5*(b*c+-1*a*d)^-5//2*arctanh(b^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^-1//2)+-1//8*d*b^-2*(a+b*x)^-4*(c+d*x)^3//2+-1//16*b^-3*d^2*(a+b*x)^-3*(c+d*x)^(1/2)+-1//64*b^-3*d^3*(a+b*x)^-2*(c+d*x)^(1/2)*(b*c+-1*a*d)^-1+3//128*b^-3*d^4*(a+b*x)^-1*(c+d*x)^(1/2)*(b*c+-1*a*d)^-2)
@test integrate((1+x)^-2*(-1+x)^(1/2), x) == :((1/2)*2^(1/2)*arctan((1/2)*2^(1/2)*(-1+x)^(1/2))+-1*(1+x)^-1*(-1+x)^(1/2))
@test integrate((1+x)^-3*(-1+x)^(1/2), x) == :((-1+x)^(1/2)*(8+8x)^-1+-1//2*(1+x)^-2*(-1+x)^(1/2)+1//16*2^(1/2)*arctan((1/2)*2^(1/2)*(-1+x)^(1/2)))
@test integrate((a+b*x)^5*(c+d*x)^-1//2, x) == :(-2*d^-6*(c+d*x)^(1/2)*(b*c+-1*a*d)^5+2//11*b^5*d^-6*(c+d*x)^11//2+-4*b^2*d^-6*(c+d*x)^5//2*(b*c+-1*a*d)^3+-10//9*b^4*d^-6*(c+d*x)^9//2*(b*c+-1*a*d)+10//3*b*d^-6*(c+d*x)^3//2*(b*c+-1*a*d)^4+20//7*b^3*d^-6*(c+d*x)^7//2*(b*c+-1*a*d)^2)
@test integrate((a+b*x)^4*(c+d*x)^-1//2, x) == :(2*d^-5*(c+d*x)^(1/2)*(b*c+-1*a*d)^4+2//9*b^4*d^-5*(c+d*x)^9//2+-8//3*b*d^-5*(c+d*x)^3//2*(b*c+-1*a*d)^3+-8//7*b^3*d^-5*(c+d*x)^7//2*(b*c+-1*a*d)+12//5*b^2*d^-5*(c+d*x)^5//2*(b*c+-1*a*d)^2)
@test integrate((a+b*x)^3*(c+d*x)^-1//2, x) == :(-2*d^-4*(c+d*x)^(1/2)*(b*c+-1*a*d)^3+2//7*b^3*d^-4*(c+d*x)^7//2+2*b*d^-4*(c+d*x)^3//2*(b*c+-1*a*d)^2+-6//5*b^2*d^-4*(c+d*x)^5//2*(b*c+-1*a*d))
@test integrate((a+b*x)^2*(c+d*x)^-1//2, x) == :(2*d^-3*(c+d*x)^(1/2)*(b*c+-1*a*d)^2+2//5*b^2*d^-3*(c+d*x)^5//2+-4//3*b*d^-3*(c+d*x)^3//2*(b*c+-1*a*d))
@test integrate((c+d*x)^-1//2*(a+b*x), x) == :(-1*d^-2*(c+d*x)^(1/2)*(-2*a*d+2*b*c)+2//3*b*d^-2*(c+d*x)^3//2)
@test integrate((c+d*x)^-1//2, x) == :(2*d^-1*(c+d*x)^(1/2))
@test integrate((a+b*x)^-1*(c+d*x)^-1//2, x) == :(-2*b^-1//2*(b*c+-1*a*d)^-1//2*arctanh(b^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate((a+b*x)^-2*(c+d*x)^-1//2, x) == :(-1*(a+b*x)^-1*(c+d*x)^(1/2)*(b*c+-1*a*d)^-1+d*b^-1//2*(b*c+-1*a*d)^-3//2*arctanh(b^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate((a+b*x)^-3*(c+d*x)^-1//2, x) == :(-1*(a+b*x)^-2*(c+d*x)^(1/2)*(-2*a*d+2*b*c)^-1+-3//4*b^-1//2*d^2*(b*c+-1*a*d)^-5//2*arctanh(b^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^-1//2)+3//4*d*(a+b*x)^-1*(c+d*x)^(1/2)*(b*c+-1*a*d)^-2)
@test integrate((a+b*x)^-4*(c+d*x)^-1//2, x) == :(-1*(a+b*x)^-3*(c+d*x)^(1/2)*(-3*a*d+3*b*c)^-1+-5//8*d^2*(a+b*x)^-1*(c+d*x)^(1/2)*(b*c+-1*a*d)^-3+5//8*b^-1//2*d^3*(b*c+-1*a*d)^-7//2*arctanh(b^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^-1//2)+5//12*d*(a+b*x)^-2*(c+d*x)^(1/2)*(b*c+-1*a*d)^-2)
@test integrate((a+b*x)^-5*(c+d*x)^-1//2, x) == :(-1*(a+b*x)^-4*(c+d*x)^(1/2)*(-4*a*d+4*b*c)^-1+-35//64*b^-1//2*d^4*(b*c+-1*a*d)^-9//2*arctanh(b^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^-1//2)+-35//96*d^2*(a+b*x)^-2*(c+d*x)^(1/2)*(b*c+-1*a*d)^-3+7//24*d*(a+b*x)^-3*(c+d*x)^(1/2)*(b*c+-1*a*d)^-2+35//64*d^3*(a+b*x)^-1*(c+d*x)^(1/2)*(b*c+-1*a*d)^-4)
@test integrate((a+b*x)^5*(c+d*x)^-3//2, x) == :(2*d^-6*(c+d*x)^-1//2*(b*c+-1*a*d)^5+2//9*b^5*d^-6*(c+d*x)^9//2+4*b^3*d^-6*(c+d*x)^5//2*(b*c+-1*a*d)^2+10*b*d^-6*(c+d*x)^(1/2)*(b*c+-1*a*d)^4+-20//3*b^2*d^-6*(c+d*x)^3//2*(b*c+-1*a*d)^3+-10//7*b^4*d^-6*(c+d*x)^7//2*(b*c+-1*a*d))
@test integrate((a+b*x)^4*(c+d*x)^-3//2, x) == :(-2*d^-5*(c+d*x)^-1//2*(b*c+-1*a*d)^4+2//7*b^4*d^-5*(c+d*x)^7//2+-8*b*d^-5*(c+d*x)^(1/2)*(b*c+-1*a*d)^3+4*b^2*d^-5*(c+d*x)^3//2*(b*c+-1*a*d)^2+-8//5*b^3*d^-5*(c+d*x)^5//2*(b*c+-1*a*d))
@test integrate((a+b*x)^3*(c+d*x)^-3//2, x) == :(2*d^-4*(c+d*x)^-1//2*(b*c+-1*a*d)^3+2//5*b^3*d^-4*(c+d*x)^5//2+-2*b^2*d^-4*(c+d*x)^3//2*(b*c+-1*a*d)+6*b*d^-4*(c+d*x)^(1/2)*(b*c+-1*a*d)^2)
@test integrate((a+b*x)^2*(c+d*x)^-3//2, x) == :(-2*d^-3*(c+d*x)^-1//2*(b*c+-1*a*d)^2+2//3*b^2*d^-3*(c+d*x)^3//2+-4*b*d^-3*(c+d*x)^(1/2)*(b*c+-1*a*d))
@test integrate((c+d*x)^-3//2*(a+b*x), x) == :(d^-2*(c+d*x)^-1//2*(-2*a*d+2*b*c)+2*b*d^-2*(c+d*x)^(1/2))
@test integrate((c+d*x)^-3//2, x) == :(-2*d^-1*(c+d*x)^-1//2)
@test integrate((a+b*x)^-1*(c+d*x)^-3//2, x) == :(2*(c+d*x)^-1//2*(b*c+-1*a*d)^-1+-2*b^(1/2)*(b*c+-1*a*d)^-3//2*arctanh(b^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate((a+b*x)^-2*(c+d*x)^-3//2, x) == :(-1*(a+b*x)^-1*(c+d*x)^-1//2*(b*c+-1*a*d)^-1+-3*d*(c+d*x)^-1//2*(b*c+-1*a*d)^-2+3*d*b^(1/2)*(b*c+-1*a*d)^-5//2*arctanh(b^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate((a+b*x)^-3*(c+d*x)^-3//2, x) == :(-1*(a+b*x)^-2*(c+d*x)^-1//2*(-2*a*d+2*b*c)^-1+15//4*d^2*(c+d*x)^-1//2*(b*c+-1*a*d)^-3+-15//4*b^(1/2)*d^2*(b*c+-1*a*d)^-7//2*arctanh(b^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^-1//2)+5//4*d*(a+b*x)^-1*(c+d*x)^-1//2*(b*c+-1*a*d)^-2)
@test integrate((a+b*x)^-4*(c+d*x)^-3//2, x) == :(-1*(a+b*x)^-3*(c+d*x)^-1//2*(-3*a*d+3*b*c)^-1+-35//8*d^3*(c+d*x)^-1//2*(b*c+-1*a*d)^-4+-35//24*d^2*(a+b*x)^-1*(c+d*x)^-1//2*(b*c+-1*a*d)^-3+7//12*d*(a+b*x)^-2*(c+d*x)^-1//2*(b*c+-1*a*d)^-2+35//8*b^(1/2)*d^3*(b*c+-1*a*d)^-9//2*arctanh(b^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate((a+b*x)^5*(c+d*x)^-5//2, x) == :(2//3*d^-6*(c+d*x)^-3//2*(b*c+-1*a*d)^5+2//7*b^5*d^-6*(c+d*x)^7//2+-20*b^2*d^-6*(c+d*x)^(1/2)*(b*c+-1*a*d)^3+-10*b*d^-6*(c+d*x)^-1//2*(b*c+-1*a*d)^4+-2*b^4*d^-6*(c+d*x)^5//2*(b*c+-1*a*d)+20//3*b^3*d^-6*(c+d*x)^3//2*(b*c+-1*a*d)^2)
@test integrate((a+b*x)^4*(c+d*x)^-5//2, x) == :(-2//3*d^-5*(c+d*x)^-3//2*(b*c+-1*a*d)^4+2//5*b^4*d^-5*(c+d*x)^5//2+8*b*d^-5*(c+d*x)^-1//2*(b*c+-1*a*d)^3+12*b^2*d^-5*(c+d*x)^(1/2)*(b*c+-1*a*d)^2+-8//3*b^3*d^-5*(c+d*x)^3//2*(b*c+-1*a*d))
@test integrate((a+b*x)^3*(c+d*x)^-5//2, x) == :(2//3*b^3*d^-4*(c+d*x)^3//2+2//3*d^-4*(c+d*x)^-3//2*(b*c+-1*a*d)^3+-6*b*d^-4*(c+d*x)^-1//2*(b*c+-1*a*d)^2+-6*b^2*d^-4*(c+d*x)^(1/2)*(b*c+-1*a*d))
@test integrate((a+b*x)^2*(c+d*x)^-5//2, x) == :(2*b^2*d^-3*(c+d*x)^(1/2)+-2//3*d^-3*(c+d*x)^-3//2*(b*c+-1*a*d)^2+4*b*d^-3*(c+d*x)^-1//2*(b*c+-1*a*d))
@test integrate((c+d*x)^-5//2*(a+b*x), x) == :(-2*b*d^-2*(c+d*x)^-1//2+1//3*d^-2*(c+d*x)^-3//2*(-2*a*d+2*b*c))
@test integrate((c+d*x)^-5//2, x) == :(-2//3*d^-1*(c+d*x)^-3//2)
@test integrate((a+b*x)^-1*(c+d*x)^-5//2, x) == :(2*(c+d*x)^-3//2*(-3*a*d+3*b*c)^-1+-2*b^3//2*(b*c+-1*a*d)^-5//2*arctanh(b^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^-1//2)+2*b*(c+d*x)^-1//2*(b*c+-1*a*d)^-2)
@test integrate((a+b*x)^-2*(c+d*x)^-5//2, x) == :(-1*(a+b*x)^-1*(c+d*x)^-3//2*(b*c+-1*a*d)^-1+-5//3*d*(c+d*x)^-3//2*(b*c+-1*a*d)^-2+-5*b*d*(c+d*x)^-1//2*(b*c+-1*a*d)^-3+5*d*b^3//2*(b*c+-1*a*d)^-7//2*arctanh(b^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate((a+b*x)^-3*(c+d*x)^-5//2, x) == :(-1*(a+b*x)^-2*(c+d*x)^-3//2*(-2*a*d+2*b*c)^-1+35//12*d^2*(c+d*x)^-3//2*(b*c+-1*a*d)^-3+-35//4*b^3//2*d^2*(b*c+-1*a*d)^-9//2*arctanh(b^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^-1//2)+7//4*d*(a+b*x)^-1*(c+d*x)^-3//2*(b*c+-1*a*d)^-2+35//4*b*d^2*(c+d*x)^-1//2*(b*c+-1*a*d)^-4)
@test integrate((a+b*x)^-4*(c+d*x)^-5//2, x) == :(-1*(a+b*x)^-3*(c+d*x)^-3//2*(-3*a*d+3*b*c)^-1+-35//8*d^3*(c+d*x)^-3//2*(b*c+-1*a*d)^-4+-105//8*b*d^3*(c+d*x)^-1//2*(b*c+-1*a*d)^-5+-21//8*d^2*(a+b*x)^-1*(c+d*x)^-3//2*(b*c+-1*a*d)^-3+3//4*d*(a+b*x)^-2*(c+d*x)^-3//2*(b*c+-1*a*d)^-2+105//8*b^3//2*d^3*(b*c+-1*a*d)^-11//2*arctanh(b^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate((a+b*x)^5*(a*c+b*c*x)^3//2, x) == :(2//15*b^-1*c^-6*(a*c+b*c*x)^15//2)
@test integrate((a+b*x)^5*(a*c+b*c*x)^(1/2), x) == :(2//13*b^-1*c^-6*(a*c+b*c*x)^13//2)
@test integrate((a+b*x)^5*(a*c+b*c*x)^-1//2, x) == :(2//11*b^-1*c^-6*(a*c+b*c*x)^11//2)
@test integrate((a+b*x)^5*(a*c+b*c*x)^-3//2, x) == :(2//9*b^-1*c^-6*(a*c+b*c*x)^9//2)
@test integrate((a+b*x)^5*(a*c+b*c*x)^-5//2, x) == :(2//7*b^-1*c^-6*(a*c+b*c*x)^7//2)
@test integrate((a+b*x)^5*(a*c+b*c*x)^-7//2, x) == :(2//5*b^-1*c^-6*(a*c+b*c*x)^5//2)
@test integrate((a+b*x)^5*(a*c+b*c*x)^-9//2, x) == :(2//3*b^-1*c^-6*(a*c+b*c*x)^3//2)
@test integrate((a+b*x)^5*(a*c+b*c*x)^-11//2, x) == :(2*b^-1*c^-6*(a*c+b*c*x)^(1/2))
@test integrate((a+b*x)^5*(a*c+b*c*x)^-13//2, x) == :(-2*b^-1*c^-6*(a*c+b*c*x)^-1//2)
@test integrate((-2+x)^-1*(2+x)^-1//2, x) == :(-1*arctanh((1/2)*(2+x)^(1/2)))
@test integrate((1+5x)^-1//2*(2+3x)^-1, x) == :(2//21*21^(1/2)*arctan(1//7*21^(1/2)*(1+5x)^(1/2)))
@test integrate((1+x)^-1*(1+-1x)^1//3, x) == :(3*(1+-1x)^1//3+-1//2*2^1//3*log(1+x)+3//2*2^1//3*log(2^1//3+-1*(1+-1x)^1//3)+-1*2^1//3*3^(1/2)*arctan(1//3*3^(1/2)*(1+2^2//3*(1+-1x)^1//3)))
@test integrate((3+-2x)^1//3*(7+x), x) == :(-51//16*(3+-2x)^4//3+3//28*(3+-2x)^7//3)
@test integrate((1+x)^2*(1+-1x)^1//3, x) == :(-3*(1+-1x)^4//3+-3//10*(1+-1x)^10//3+12//7*(1+-1x)^7//3)
@test integrate((a+b*x)^-1*(c+d*x)^-1//3, x) == :(-1//2*b^-2//3*(b*c+-1*a*d)^-1//3*log(a+b*x)+3//2*b^-2//3*(b*c+-1*a*d)^-1//3*log((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3)+3^(1/2)*b^-2//3*(b*c+-1*a*d)^-1//3*arctan(1//3*3^(1/2)*(1+2*b^1//3*(c+d*x)^1//3*(b*c+-1*a*d)^-1//3)))
@test integrate((a+b*x)^-1*(c+d*x)^-2//3, x) == :(-1//2*b^-1//3*(b*c+-1*a*d)^-2//3*log(a+b*x)+3//2*b^-1//3*(b*c+-1*a*d)^-2//3*log((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3)+-1*3^(1/2)*b^-1//3*(b*c+-1*a*d)^-2//3*arctan(1//3*3^(1/2)*(1+2*b^1//3*(c+d*x)^1//3*(b*c+-1*a*d)^-1//3)))
@test integrate((a+b*x)^7//2*(c+d*x)^(1/2), x) == :(1//5*b^-1*(a+b*x)^9//2*(c+d*x)^(1/2)+7//128*b^-3//2*d^-9//2*(b*c+-1*a*d)^5*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-7//128*b^-1*d^-4*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^4+-7//240*b^-1*d^-2*(a+b*x)^5//2*(c+d*x)^(1/2)*(b*c+-1*a*d)^2+1//40*b^-1*d^-1*(a+b*x)^7//2*(c+d*x)^(1/2)*(b*c+-1*a*d)+7//192*b^-1*d^-3*(a+b*x)^3//2*(c+d*x)^(1/2)*(b*c+-1*a*d)^3)
@test integrate((a+b*x)^5//2*(c+d*x)^(1/2), x) == :(1//4*b^-1*(a+b*x)^7//2*(c+d*x)^(1/2)+-5//64*b^-3//2*d^-7//2*(b*c+-1*a*d)^4*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-5//96*b^-1*d^-2*(a+b*x)^3//2*(c+d*x)^(1/2)*(b*c+-1*a*d)^2+1//24*b^-1*d^-1*(a+b*x)^5//2*(c+d*x)^(1/2)*(b*c+-1*a*d)+5//64*b^-1*d^-3*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^3)
@test integrate((a+b*x)^3//2*(c+d*x)^(1/2), x) == :(1//3*b^-1*(a+b*x)^5//2*(c+d*x)^(1/2)+1//8*b^-3//2*d^-5//2*(b*c+-1*a*d)^3*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//8*b^-1*d^-2*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^2+1//12*b^-1*d^-1*(a+b*x)^3//2*(c+d*x)^(1/2)*(b*c+-1*a*d))
@test integrate((a+b*x)^(1/2)*(c+d*x)^(1/2), x) == :((1/2)*b^-1*(a+b*x)^3//2*(c+d*x)^(1/2)+-1//4*b^-3//2*d^-3//2*(b*c+-1*a*d)^2*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+1//4*b^-1*d^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d))
@test integrate((a+b*x)^-1//2*(c+d*x)^(1/2), x) == :(b^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)+b^-3//2*d^-1//2*(b*c+-1*a*d)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2))
@test integrate((a+b*x)^-3//2*(c+d*x)^(1/2), x) == :(-2*b^-1*(a+b*x)^-1//2*(c+d*x)^(1/2)+2*b^-3//2*d^(1/2)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2))
@test integrate((a+b*x)^-5//2*(c+d*x)^(1/2), x) == :(-2*(a+b*x)^-3//2*(c+d*x)^3//2*(-3*a*d+3*b*c)^-1)
@test integrate((a+b*x)^-7//2*(c+d*x)^(1/2), x) == :(-2*(a+b*x)^-5//2*(c+d*x)^3//2*(-5*a*d+5*b*c)^-1+4//15*d*(a+b*x)^-3//2*(c+d*x)^3//2*(b*c+-1*a*d)^-2)
@test integrate((a+b*x)^-9//2*(c+d*x)^(1/2), x) == :(-2*(a+b*x)^-7//2*(c+d*x)^3//2*(-7*a*d+7*b*c)^-1+-16//105*d^2*(a+b*x)^-3//2*(c+d*x)^3//2*(b*c+-1*a*d)^-3+8//35*d*(a+b*x)^-5//2*(c+d*x)^3//2*(b*c+-1*a*d)^-2)
@test integrate((a+b*x)^-11//2*(c+d*x)^(1/2), x) == :(-2*(a+b*x)^-9//2*(c+d*x)^3//2*(-9*a*d+9*b*c)^-1+-16//105*d^2*(a+b*x)^-5//2*(c+d*x)^3//2*(b*c+-1*a*d)^-3+4//21*d*(a+b*x)^-7//2*(c+d*x)^3//2*(b*c+-1*a*d)^-2+32//315*d^3*(a+b*x)^-3//2*(c+d*x)^3//2*(b*c+-1*a*d)^-4)
@test integrate((a+b*x)^-13//2*(c+d*x)^(1/2), x) == :(-2*(a+b*x)^-11//2*(c+d*x)^3//2*(-11*a*d+11*b*c)^-1+-256//3465*d^4*(a+b*x)^-3//2*(c+d*x)^3//2*(b*c+-1*a*d)^-5+-32//231*d^2*(a+b*x)^-7//2*(c+d*x)^3//2*(b*c+-1*a*d)^-3+16//99*d*(a+b*x)^-9//2*(c+d*x)^3//2*(b*c+-1*a*d)^-2+128//1155*d^3*(a+b*x)^-5//2*(c+d*x)^3//2*(b*c+-1*a*d)^-4)
@test integrate((a+b*x)^5//2*(c+d*x)^3//2, x) == :(1//5*b^-1*(a+b*x)^7//2*(c+d*x)^3//2+-3//128*b^-5//2*d^-7//2*(b*c+-1*a*d)^5*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+1//40*b^-2*(a+b*x)^7//2*(c+d*x)^(1/2)*(-3*a*d+3*b*c)+-1//64*b^-2*d^-2*(a+b*x)^3//2*(c+d*x)^(1/2)*(b*c+-1*a*d)^3+1//80*b^-2*d^-1*(a+b*x)^5//2*(c+d*x)^(1/2)*(b*c+-1*a*d)^2+3//128*b^-2*d^-3*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^4)
@test integrate((a+b*x)^3//2*(c+d*x)^3//2, x) == :(1//4*b^-1*(a+b*x)^5//2*(c+d*x)^3//2+1//8*b^-2*(a+b*x)^5//2*(c+d*x)^(1/2)*(b*c+-1*a*d)+3//64*b^-5//2*d^-5//2*(b*c+-1*a*d)^4*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-3//64*b^-2*d^-2*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^3+1//32*b^-2*d^-1*(a+b*x)^3//2*(c+d*x)^(1/2)*(b*c+-1*a*d)^2)
@test integrate((a+b*x)^(1/2)*(c+d*x)^3//2, x) == :(1//3*b^-1*(a+b*x)^3//2*(c+d*x)^3//2+-1//8*b^-5//2*d^-3//2*(b*c+-1*a*d)^3*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+1//4*b^-2*(a+b*x)^3//2*(c+d*x)^(1/2)*(b*c+-1*a*d)+1//8*b^-2*d^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^2)
@test integrate((a+b*x)^-1//2*(c+d*x)^3//2, x) == :((1/2)*b^-1*(a+b*x)^(1/2)*(c+d*x)^3//2+1//4*b^-2*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(-3*a*d+3*b*c)+3//4*b^-5//2*d^-1//2*(b*c+-1*a*d)^2*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2))
@test integrate((a+b*x)^-3//2*(c+d*x)^3//2, x) == :(-2*b^-1*(a+b*x)^-1//2*(c+d*x)^3//2+3*d*b^-2*(a+b*x)^(1/2)*(c+d*x)^(1/2)+3*b^-5//2*d^(1/2)*(b*c+-1*a*d)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2))
@test integrate((a+b*x)^-5//2*(c+d*x)^3//2, x) == :(2*b^-5//2*d^3//2*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-2//3*b^-1*(a+b*x)^-3//2*(c+d*x)^3//2+-2*d*b^-2*(a+b*x)^-1//2*(c+d*x)^(1/2))
@test integrate((a+b*x)^-7//2*(c+d*x)^3//2, x) == :(-2*(a+b*x)^-5//2*(c+d*x)^5//2*(-5*a*d+5*b*c)^-1)
@test integrate((a+b*x)^-9//2*(c+d*x)^3//2, x) == :(-2*(a+b*x)^-7//2*(c+d*x)^5//2*(-7*a*d+7*b*c)^-1+4//35*d*(a+b*x)^-5//2*(c+d*x)^5//2*(b*c+-1*a*d)^-2)
@test integrate((a+b*x)^-11//2*(c+d*x)^3//2, x) == :(-2*(a+b*x)^-9//2*(c+d*x)^5//2*(-9*a*d+9*b*c)^-1+-16//315*d^2*(a+b*x)^-5//2*(c+d*x)^5//2*(b*c+-1*a*d)^-3+8//63*d*(a+b*x)^-7//2*(c+d*x)^5//2*(b*c+-1*a*d)^-2)
@test integrate((a+b*x)^-13//2*(c+d*x)^3//2, x) == :(-2*(a+b*x)^-11//2*(c+d*x)^5//2*(-11*a*d+11*b*c)^-1+-16//231*d^2*(a+b*x)^-7//2*(c+d*x)^5//2*(b*c+-1*a*d)^-3+4//33*d*(a+b*x)^-9//2*(c+d*x)^5//2*(b*c+-1*a*d)^-2+32//1155*d^3*(a+b*x)^-5//2*(c+d*x)^5//2*(b*c+-1*a*d)^-4)
@test integrate((a+b*x)^5//2*(c+d*x)^5//2, x) == :(1//6*b^-1*(a+b*x)^7//2*(c+d*x)^5//2+-5//512*b^-7//2*d^-7//2*(b*c+-1*a*d)^6*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+1//12*b^-2*(a+b*x)^7//2*(c+d*x)^3//2*(b*c+-1*a*d)+1//32*b^-3*(a+b*x)^7//2*(c+d*x)^(1/2)*(b*c+-1*a*d)^2+-5//768*b^-3*d^-2*(a+b*x)^3//2*(c+d*x)^(1/2)*(b*c+-1*a*d)^4+1//192*b^-3*d^-1*(a+b*x)^5//2*(c+d*x)^(1/2)*(b*c+-1*a*d)^3+5//512*b^-3*d^-3*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^5)
@test integrate((a+b*x)^3//2*(c+d*x)^5//2, x) == :(1//5*b^-1*(a+b*x)^5//2*(c+d*x)^5//2+1//8*b^-2*(a+b*x)^5//2*(c+d*x)^3//2*(b*c+-1*a*d)+1//16*b^-3*(a+b*x)^5//2*(c+d*x)^(1/2)*(b*c+-1*a*d)^2+3//128*b^-7//2*d^-5//2*(b*c+-1*a*d)^5*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-3//128*b^-3*d^-2*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^4+1//64*b^-3*d^-1*(a+b*x)^3//2*(c+d*x)^(1/2)*(b*c+-1*a*d)^3)
@test integrate((a+b*x)^(1/2)*(c+d*x)^5//2, x) == :(1//4*b^-1*(a+b*x)^3//2*(c+d*x)^5//2+-5//64*b^-7//2*d^-3//2*(b*c+-1*a*d)^4*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+1//24*b^-2*(a+b*x)^3//2*(c+d*x)^3//2*(-5*a*d+5*b*c)+5//32*b^-3*(a+b*x)^3//2*(c+d*x)^(1/2)*(b*c+-1*a*d)^2+5//64*b^-3*d^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^3)
@test integrate((a+b*x)^-1//2*(c+d*x)^5//2, x) == :(1//3*b^-1*(a+b*x)^(1/2)*(c+d*x)^5//2+1//12*b^-2*(a+b*x)^(1/2)*(c+d*x)^3//2*(-5*a*d+5*b*c)+5//8*b^-3*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^2+5//8*b^-7//2*d^-1//2*(b*c+-1*a*d)^3*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2))
@test integrate((a+b*x)^-3//2*(c+d*x)^5//2, x) == :(-2*b^-1*(a+b*x)^-1//2*(c+d*x)^5//2+5//2*d*b^-2*(a+b*x)^(1/2)*(c+d*x)^3//2+15//4*b^-7//2*d^(1/2)*(b*c+-1*a*d)^2*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+15//4*d*b^-3*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d))
@test integrate((a+b*x)^-5//2*(c+d*x)^5//2, x) == :(-2//3*b^-1*(a+b*x)^-3//2*(c+d*x)^5//2+5*b^-3*d^2*(a+b*x)^(1/2)*(c+d*x)^(1/2)+5*b^-7//2*d^3//2*(b*c+-1*a*d)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-10//3*d*b^-2*(a+b*x)^-1//2*(c+d*x)^3//2)
@test integrate((a+b*x)^-7//2*(c+d*x)^5//2, x) == :(2*b^-7//2*d^5//2*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-2//5*b^-1*(a+b*x)^-5//2*(c+d*x)^5//2+-2*b^-3*d^2*(a+b*x)^-1//2*(c+d*x)^(1/2)+-2//3*d*b^-2*(a+b*x)^-3//2*(c+d*x)^3//2)
@test integrate((a+b*x)^-9//2*(c+d*x)^5//2, x) == :(-2*(a+b*x)^-7//2*(c+d*x)^7//2*(-7*a*d+7*b*c)^-1)
@test integrate((a+b*x)^-11//2*(c+d*x)^5//2, x) == :(-2*(a+b*x)^-9//2*(c+d*x)^7//2*(-9*a*d+9*b*c)^-1+4//63*d*(a+b*x)^-7//2*(c+d*x)^7//2*(b*c+-1*a*d)^-2)
@test integrate((a+b*x)^-13//2*(c+d*x)^5//2, x) == :(-2*(a+b*x)^-11//2*(c+d*x)^7//2*(-11*a*d+11*b*c)^-1+-16//693*d^2*(a+b*x)^-7//2*(c+d*x)^7//2*(b*c+-1*a*d)^-3+8//99*d*(a+b*x)^-9//2*(c+d*x)^7//2*(b*c+-1*a*d)^-2)
@test integrate((a+b*x)^-15//2*(c+d*x)^5//2, x) == :(-2*(a+b*x)^-13//2*(c+d*x)^7//2*(-13*a*d+13*b*c)^-1+-16//429*d^2*(a+b*x)^-9//2*(c+d*x)^7//2*(b*c+-1*a*d)^-3+12//143*d*(a+b*x)^-11//2*(c+d*x)^7//2*(b*c+-1*a*d)^-2+32//3003*d^3*(a+b*x)^-7//2*(c+d*x)^7//2*(b*c+-1*a*d)^-4)
@test integrate((a+b*x)^7//2*(c+d*x)^-1//2, x) == :(1//4*d^-1*(a+b*x)^7//2*(c+d*x)^(1/2)+-35//64*d^-4*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^3+-1//24*d^-2*(a+b*x)^5//2*(c+d*x)^(1/2)*(-7*a*d+7*b*c)+35//64*b^-1//2*d^-9//2*(b*c+-1*a*d)^4*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+35//96*d^-3*(a+b*x)^3//2*(c+d*x)^(1/2)*(b*c+-1*a*d)^2)
@test integrate((a+b*x)^5//2*(c+d*x)^-1//2, x) == :(1//3*d^-1*(a+b*x)^5//2*(c+d*x)^(1/2)+-5//8*b^-1//2*d^-7//2*(b*c+-1*a*d)^3*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//12*d^-2*(a+b*x)^3//2*(c+d*x)^(1/2)*(-5*a*d+5*b*c)+5//8*d^-3*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^2)
@test integrate((a+b*x)^3//2*(c+d*x)^-1//2, x) == :((1/2)*d^-1*(a+b*x)^3//2*(c+d*x)^(1/2)+-1//4*d^-2*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(-3*a*d+3*b*c)+3//4*b^-1//2*d^-5//2*(b*c+-1*a*d)^2*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2))
@test integrate((a+b*x)^(1/2)*(c+d*x)^-1//2, x) == :(d^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)+-1*b^-1//2*d^-3//2*(b*c+-1*a*d)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2))
@test integrate((a+b*x)^-1//2*(c+d*x)^-1//2, x) == :(2*b^-1//2*d^-1//2*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2))
@test integrate((a+b*x)^-3//2*(c+d*x)^-1//2, x) == :(-2*(a+b*x)^-1//2*(c+d*x)^(1/2)*(b*c+-1*a*d)^-1)
@test integrate((a+b*x)^-5//2*(c+d*x)^-1//2, x) == :(-2*(a+b*x)^-3//2*(c+d*x)^(1/2)*(-3*a*d+3*b*c)^-1+4//3*d*(a+b*x)^-1//2*(c+d*x)^(1/2)*(b*c+-1*a*d)^-2)
@test integrate((a+b*x)^-7//2*(c+d*x)^-1//2, x) == :(-2*(a+b*x)^-5//2*(c+d*x)^(1/2)*(-5*a*d+5*b*c)^-1+-16//15*d^2*(a+b*x)^-1//2*(c+d*x)^(1/2)*(b*c+-1*a*d)^-3+8//15*d*(a+b*x)^-3//2*(c+d*x)^(1/2)*(b*c+-1*a*d)^-2)
@test integrate((a+b*x)^-9//2*(c+d*x)^-1//2, x) == :(-2*(a+b*x)^-7//2*(c+d*x)^(1/2)*(-7*a*d+7*b*c)^-1+-16//35*d^2*(a+b*x)^-3//2*(c+d*x)^(1/2)*(b*c+-1*a*d)^-3+12//35*d*(a+b*x)^-5//2*(c+d*x)^(1/2)*(b*c+-1*a*d)^-2+32//35*d^3*(a+b*x)^-1//2*(c+d*x)^(1/2)*(b*c+-1*a*d)^-4)
@test integrate((a+b*x)^-11//2*(c+d*x)^-1//2, x) == :(-2*(a+b*x)^-9//2*(c+d*x)^(1/2)*(-9*a*d+9*b*c)^-1+-256//315*d^4*(a+b*x)^-1//2*(c+d*x)^(1/2)*(b*c+-1*a*d)^-5+-32//105*d^2*(a+b*x)^-5//2*(c+d*x)^(1/2)*(b*c+-1*a*d)^-3+16//63*d*(a+b*x)^-7//2*(c+d*x)^(1/2)*(b*c+-1*a*d)^-2+128//315*d^3*(a+b*x)^-3//2*(c+d*x)^(1/2)*(b*c+-1*a*d)^-4)
@test integrate((a+b*x)^7//2*(c+d*x)^-3//2, x) == :(-2*d^-1*(a+b*x)^7//2*(c+d*x)^-1//2+-35//8*b^(1/2)*d^-9//2*(b*c+-1*a*d)^3*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+7//3*b*d^-2*(a+b*x)^5//2*(c+d*x)^(1/2)+-35//12*b*d^-3*(a+b*x)^3//2*(c+d*x)^(1/2)*(b*c+-1*a*d)+35//8*b*d^-4*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^2)
@test integrate((a+b*x)^5//2*(c+d*x)^-3//2, x) == :(-2*d^-1*(a+b*x)^5//2*(c+d*x)^-1//2+5//2*b*d^-2*(a+b*x)^3//2*(c+d*x)^(1/2)+15//4*b^(1/2)*d^-7//2*(b*c+-1*a*d)^2*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-15//4*b*d^-3*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d))
@test integrate((a+b*x)^3//2*(c+d*x)^-3//2, x) == :(-2*d^-1*(a+b*x)^3//2*(c+d*x)^-1//2+-3*b^(1/2)*d^-5//2*(b*c+-1*a*d)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+3*b*d^-2*(a+b*x)^(1/2)*(c+d*x)^(1/2))
@test integrate((a+b*x)^(1/2)*(c+d*x)^-3//2, x) == :(-2*d^-1*(a+b*x)^(1/2)*(c+d*x)^-1//2+2*b^(1/2)*d^-3//2*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2))
@test integrate((a+b*x)^-1//2*(c+d*x)^-3//2, x) == :(2*(a+b*x)^(1/2)*(c+d*x)^-1//2*(b*c+-1*a*d)^-1)
@test integrate((a+b*x)^-3//2*(c+d*x)^-3//2, x) == :(-2*(a+b*x)^-1//2*(c+d*x)^-1//2*(b*c+-1*a*d)^-1+-4*d*(a+b*x)^(1/2)*(c+d*x)^-1//2*(b*c+-1*a*d)^-2)
@test integrate((a+b*x)^-5//2*(c+d*x)^-3//2, x) == :(-2*(a+b*x)^-3//2*(c+d*x)^-1//2*(-3*a*d+3*b*c)^-1+8//3*d*(a+b*x)^-1//2*(c+d*x)^-1//2*(b*c+-1*a*d)^-2+16//3*d^2*(a+b*x)^(1/2)*(c+d*x)^-1//2*(b*c+-1*a*d)^-3)
@test integrate((a+b*x)^-7//2*(c+d*x)^-3//2, x) == :(-2*(a+b*x)^-5//2*(c+d*x)^-1//2*(-5*a*d+5*b*c)^-1+-32//5*d^3*(a+b*x)^(1/2)*(c+d*x)^-1//2*(b*c+-1*a*d)^-4+-16//5*d^2*(a+b*x)^-1//2*(c+d*x)^-1//2*(b*c+-1*a*d)^-3+4//5*d*(a+b*x)^-3//2*(c+d*x)^-1//2*(b*c+-1*a*d)^-2)
@test integrate((a+b*x)^-9//2*(c+d*x)^-3//2, x) == :(-2*(a+b*x)^-7//2*(c+d*x)^-1//2*(-7*a*d+7*b*c)^-1+-32//35*d^2*(a+b*x)^-3//2*(c+d*x)^-1//2*(b*c+-1*a*d)^-3+16//35*d*(a+b*x)^-5//2*(c+d*x)^-1//2*(b*c+-1*a*d)^-2+128//35*d^3*(a+b*x)^-1//2*(c+d*x)^-1//2*(b*c+-1*a*d)^-4+256//35*d^4*(a+b*x)^(1/2)*(c+d*x)^-1//2*(b*c+-1*a*d)^-5)
@test integrate((a+b*x)^-11//2*(c+d*x)^-3//2, x) == :(-2*(a+b*x)^-9//2*(c+d*x)^-1//2*(-9*a*d+9*b*c)^-1+-512//63*d^5*(a+b*x)^(1/2)*(c+d*x)^-1//2*(b*c+-1*a*d)^-6+-256//63*d^4*(a+b*x)^-1//2*(c+d*x)^-1//2*(b*c+-1*a*d)^-5+-32//63*d^2*(a+b*x)^-5//2*(c+d*x)^-1//2*(b*c+-1*a*d)^-3+20//63*d*(a+b*x)^-7//2*(c+d*x)^-1//2*(b*c+-1*a*d)^-2+64//63*d^3*(a+b*x)^-3//2*(c+d*x)^-1//2*(b*c+-1*a*d)^-4)
@test integrate((a+b*x)^9//2*(c+d*x)^-5//2, x) == :(-2//3*d^-1*(a+b*x)^9//2*(c+d*x)^-3//2+-6*b*d^-2*(a+b*x)^7//2*(c+d*x)^-1//2+7*b^2*d^-3*(a+b*x)^5//2*(c+d*x)^(1/2)+-105//8*b^3//2*d^-11//2*(b*c+-1*a*d)^3*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-35//4*b^2*d^-4*(a+b*x)^3//2*(c+d*x)^(1/2)*(b*c+-1*a*d)+105//8*b^2*d^-5*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^2)
@test integrate((a+b*x)^7//2*(c+d*x)^-5//2, x) == :(-2//3*d^-1*(a+b*x)^7//2*(c+d*x)^-3//2+-14//3*b*d^-2*(a+b*x)^5//2*(c+d*x)^-1//2+35//4*b^3//2*d^-9//2*(b*c+-1*a*d)^2*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+35//6*b^2*d^-3*(a+b*x)^3//2*(c+d*x)^(1/2)+-35//4*b^2*d^-4*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d))
@test integrate((a+b*x)^5//2*(c+d*x)^-5//2, x) == :(-2//3*d^-1*(a+b*x)^5//2*(c+d*x)^-3//2+-5*b^3//2*d^-7//2*(b*c+-1*a*d)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+5*b^2*d^-3*(a+b*x)^(1/2)*(c+d*x)^(1/2)+-10//3*b*d^-2*(a+b*x)^3//2*(c+d*x)^-1//2)
@test integrate((a+b*x)^3//2*(c+d*x)^-5//2, x) == :(2*b^3//2*d^-5//2*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-2//3*d^-1*(a+b*x)^3//2*(c+d*x)^-3//2+-2*b*d^-2*(a+b*x)^(1/2)*(c+d*x)^-1//2)
@test integrate((a+b*x)^(1/2)*(c+d*x)^-5//2, x) == :(2*(a+b*x)^3//2*(c+d*x)^-3//2*(-3*a*d+3*b*c)^-1)
@test integrate((a+b*x)^-1//2*(c+d*x)^-5//2, x) == :(2*(a+b*x)^(1/2)*(c+d*x)^-3//2*(-3*a*d+3*b*c)^-1+4//3*b*(a+b*x)^(1/2)*(c+d*x)^-1//2*(b*c+-1*a*d)^-2)
@test integrate((a+b*x)^-3//2*(c+d*x)^-5//2, x) == :(-2*(a+b*x)^-1//2*(c+d*x)^-3//2*(b*c+-1*a*d)^-1+-8//3*d*(a+b*x)^(1/2)*(c+d*x)^-3//2*(b*c+-1*a*d)^-2+-16//3*b*d*(a+b*x)^(1/2)*(c+d*x)^-1//2*(b*c+-1*a*d)^-3)
@test integrate((a+b*x)^-5//2*(c+d*x)^-5//2, x) == :(-2*(a+b*x)^-3//2*(c+d*x)^-3//2*(-3*a*d+3*b*c)^-1+4*d*(a+b*x)^-1//2*(c+d*x)^-3//2*(b*c+-1*a*d)^-2+16//3*d^2*(a+b*x)^(1/2)*(c+d*x)^-3//2*(b*c+-1*a*d)^-3+32//3*b*d^2*(a+b*x)^(1/2)*(c+d*x)^-1//2*(b*c+-1*a*d)^-4)
@test integrate((a+b*x)^-7//2*(c+d*x)^-5//2, x) == :(-2*(a+b*x)^-5//2*(c+d*x)^-3//2*(-5*a*d+5*b*c)^-1+-128//15*d^3*(a+b*x)^(1/2)*(c+d*x)^-3//2*(b*c+-1*a*d)^-4+-32//5*d^2*(a+b*x)^-1//2*(c+d*x)^-3//2*(b*c+-1*a*d)^-3+16//15*d*(a+b*x)^-3//2*(c+d*x)^-3//2*(b*c+-1*a*d)^-2+-256//15*b*d^3*(a+b*x)^(1/2)*(c+d*x)^-1//2*(b*c+-1*a*d)^-5)
@test integrate((a+b*x)^-9//2*(c+d*x)^-5//2, x) == :(-2*(a+b*x)^-7//2*(c+d*x)^-3//2*(-7*a*d+7*b*c)^-1+-32//21*d^2*(a+b*x)^-3//2*(c+d*x)^-3//2*(b*c+-1*a*d)^-3+4//7*d*(a+b*x)^-5//2*(c+d*x)^-3//2*(b*c+-1*a*d)^-2+64//7*d^3*(a+b*x)^-1//2*(c+d*x)^-3//2*(b*c+-1*a*d)^-4+256//21*d^4*(a+b*x)^(1/2)*(c+d*x)^-3//2*(b*c+-1*a*d)^-5+512//21*b*d^4*(a+b*x)^(1/2)*(c+d*x)^-1//2*(b*c+-1*a*d)^-6)
@test integrate((a+b*x)^-1//2*(4+a+b*x)^-1//2, x) == :(2*b^-1*arcsinh((1/2)*(a+b*x)^(1/2)))
@test integrate((2+b*x)^-1//2*(6+b*x)^-1//2, x) == :(2*b^-1*arcsinh((1/2)*(2+b*x)^(1/2)))
@test integrate((1+b*x)^-1//2*(5+b*x)^-1//2, x) == :(2*b^-1*arcsinh((1/2)*(1+b*x)^(1/2)))
@test integrate((b*x)^-1//2*(4+b*x)^-1//2, x) == :(2*b^-1*arcsinh((1/2)*(b*x)^(1/2)))
@test integrate((-1+b*x)^-1//2*(3+b*x)^-1//2, x) == :(2*b^-1*arcsinh((1/2)*(-1+b*x)^(1/2)))
@test integrate((-2+b*x)^-1//2*(2+b*x)^-1//2, x) == :(b^-1*arccosh((1/2)*b*x))
@test integrate((1+b*x)^-1//2*(-3+b*x)^-1//2, x) == :(2*b^-1*arcsinh((1/2)*(-3+b*x)^(1/2)))
@test integrate((2+b*x)^-1//2*(3+b*x)^-1//2, x) == :(2*b^-1*arcsinh((2+b*x)^(1/2)))
@test integrate((2+b*x)^-1, x) == :(b^-1*log(2+b*x))
@test integrate((1+b*x)^-1//2*(2+b*x)^-1//2, x) == :(2*b^-1*arcsinh((1+b*x)^(1/2)))
@test integrate((b*x)^-1//2*(2+b*x)^-1//2, x) == :(2*b^-1*arcsinh((1/2)*2^(1/2)*(b*x)^(1/2)))
@test integrate((-1+b*x)^-1//2*(2+b*x)^-1//2, x) == :(2*b^-1*arcsinh(1//3*3^(1/2)*(-1+b*x)^(1/2)))
@test integrate((-2+b*x)^-1//2*(2+b*x)^-1//2, x) == :(b^-1*arccosh((1/2)*b*x))
@test integrate((-3+b*x)^-1//2*(2+b*x)^-1//2, x) == :(2*b^-1*arcsinh(1//5*5^(1/2)*(-3+b*x)^(1/2)))
@test integrate((2+b*x)^-1//2*(3+-1*b*x)^-1//2, x) == :(-1*b^-1*arcsin(1//5+-2//5*b*x))
@test integrate((2+b*x)^-1//2*(2+-1*b*x)^-1//2, x) == :(b^-1*arcsin((1/2)*b*x))
@test integrate((1+-1*b*x)^-1//2*(2+b*x)^-1//2, x) == :(-1*b^-1*arcsin(-1//3+-2//3*b*x))
@test integrate((-1*b*x)^-1//2*(2+b*x)^-1//2, x) == :(b^-1*arcsin(1+b*x))
@test integrate((-1+-1*b*x)^-1//2*(2+b*x)^-1//2, x) == :(b^-1*arcsin(3+2*b*x))
@test integrate((-2+-1*b*x)^-1//2*(2+b*x)^-1//2, x) == :(b^-1*(-2+-1*b*x)^-1//2*(2+b*x)^(1/2)*log(2+b*x))
@test integrate((-3+-1*b*x)^-1//2*(2+b*x)^-1//2, x) == :(-2*b^-1*arctan((-3+-1*b*x)^(1/2)*(2+b*x)^-1//2))
@test integrate((2+-1*b*x)^-1//2*(3+-1*b*x)^-1//2, x) == :(-2*b^-1*arcsinh((2+-1*b*x)^(1/2)))
@test integrate((2+-1*b*x)^-1, x) == :(-1*b^-1*log(2+-1*b*x))
@test integrate((1+-1*b*x)^-1//2*(2+-1*b*x)^-1//2, x) == :(-2*b^-1*arcsinh((1+-1*b*x)^(1/2)))
@test integrate((-1*b*x)^-1//2*(2+-1*b*x)^-1//2, x) == :(-2*b^-1*arcsinh((1/2)*2^(1/2)*(-1*b*x)^(1/2)))
@test integrate((-1+-1*b*x)^-1//2*(2+-1*b*x)^-1//2, x) == :(-2*b^-1*arcsinh(1//3*3^(1/2)*(-1+-1*b*x)^(1/2)))
@test integrate((-2+-1*b*x)^-1//2*(2+-1*b*x)^-1//2, x) == :(-1*b^-1*arccosh(-1//2*b*x))
@test integrate((-3+-1*b*x)^-1//2*(2+-1*b*x)^-1//2, x) == :(-2*b^-1*arcsinh(1//5*5^(1/2)*(-3+-1*b*x)^(1/2)))
@test integrate((-4+b*x)^-1//2*(4+b*x)^-1//2, x) == :(b^-1*arccosh(1//4*b*x))
@test integrate((c+d*x)^-1//2*(b*x+d^-1*(-1b+b*c))^-1//2, x) == :(2*b^-1//2*d^-1//2*arcsinh(b^-1//2*d^(1/2)*(b*x+-1*b*d^-1*(1+-1c))^(1/2)))
@test integrate(x^-1//2*(-3+2x)^-1//2, x) == :(2^(1/2)*arcsinh(1//3*3^(1/2)*(-3+2x)^(1/2)))
@test integrate((-3+2x)^-1//2*(2+3x)^-1//2, x) == :(1//3*6^(1/2)*arcsinh(1//13*39^(1/2)*(-3+2x)^(1/2)))
@test integrate((c+-1*d*x)^-1//2*(b*x+d^-1*(b+-1*b*c))^-1//2, x) == :(2*b^-1//2*d^-1//2*arcsin(b^-1//2*d^(1/2)*(b*x+b*d^-1*(1+-1c))^(1/2)))
@test integrate(x^-1//2*(4+-1x)^-1//2, x) == :(-1*arcsin(1+-1//2*x))
@test integrate(x^-1//2*(3+-2x)^-1//2, x) == :(2^(1/2)*arcsin(1//3*6^(1/2)*x^(1/2)))
@test integrate((3+-2x)^-1//2*(3+5x)^-1//2, x) == :(1//5*10^(1/2)*arcsin(1//21*42^(1/2)*(3+5x)^(1/2)))
@test integrate((a+-1*b*x)^-1//2*(c+d*x)^-1//2, x) == :(-2*b^-1//2*d^-1//2*arctan(b^-1//2*d^(1/2)*(a+-1*b*x)^(1/2)*(c+d*x)^-1//2))
@test integrate((a+b*x)^3//2*(c+d*x)^1//3, x) == :(6//17*b^-1*(a+b*x)^5//2*(c+d*x)^1//3+-108//935*b^-1*d^-2*(a+b*x)^(1/2)*(c+d*x)^1//3*(b*c+-1*a*d)^2+1//187*b^-1*d^-1*(a+b*x)^3//2*(c+d*x)^1//3*(-12*a*d+12*b*c)+-108//935*3^3//4*b^-4//3*d^-3*(((b*c+-1*a*d)^1//3*(1+-1*3^(1/2))+-1*b^1//3*(c+d*x)^1//3)^-2*((b*c+-1*a*d)^2//3+b^2//3*(c+d*x)^2//3+b^1//3*(c+d*x)^1//3*(b*c+-1*a*d)^1//3))^(1/2)*(-1*(b*c+-1*a*d)^1//3*((b*c+-1*a*d)^1//3*(1+-1*3^(1/2))+-1*b^1//3*(c+d*x)^1//3)^-2*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3)*Elliptic.F(arcsin(((b*c+-1*a*d)^1//3*(1+-1*3^(1/2))+-1*b^1//3*(c+d*x)^1//3)^-1*((b*c+-1*a*d)^1//3*(1+3^(1/2))+-1*b^1//3*(c+d*x)^1//3)),-7+4*3^(1/2)))
@test integrate((a+b*x)^(1/2)*(c+d*x)^1//3, x) == :(6//11*b^-1*(a+b*x)^3//2*(c+d*x)^1//3+1//55*b^-1*d^-1*(a+b*x)^(1/2)*(c+d*x)^1//3*(-12*a*d+12*b*c)+12//55*3^3//4*b^-4//3*d^-2*(((b*c+-1*a*d)^1//3*(1+-1*3^(1/2))+-1*b^1//3*(c+d*x)^1//3)^-2*((b*c+-1*a*d)^2//3+b^2//3*(c+d*x)^2//3+b^1//3*(c+d*x)^1//3*(b*c+-1*a*d)^1//3))^(1/2)*(-1*(b*c+-1*a*d)^1//3*((b*c+-1*a*d)^1//3*(1+-1*3^(1/2))+-1*b^1//3*(c+d*x)^1//3)^-2*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^2*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3)*Elliptic.F(arcsin(((b*c+-1*a*d)^1//3*(1+-1*3^(1/2))+-1*b^1//3*(c+d*x)^1//3)^-1*((b*c+-1*a*d)^1//3*(1+3^(1/2))+-1*b^1//3*(c+d*x)^1//3)),-7+4*3^(1/2)))
@test integrate((a+b*x)^-1//2*(c+d*x)^1//3, x) == :(6//5*b^-1*(a+b*x)^(1/2)*(c+d*x)^1//3+-4//5*3^3//4*b^-4//3*d^-1*(((b*c+-1*a*d)^1//3*(1+-1*3^(1/2))+-1*b^1//3*(c+d*x)^1//3)^-2*((b*c+-1*a*d)^2//3+b^2//3*(c+d*x)^2//3+b^1//3*(c+d*x)^1//3*(b*c+-1*a*d)^1//3))^(1/2)*(-1*(b*c+-1*a*d)^1//3*((b*c+-1*a*d)^1//3*(1+-1*3^(1/2))+-1*b^1//3*(c+d*x)^1//3)^-2*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x)^-1//2*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3)*(b*c+-1*a*d)*Elliptic.F(arcsin(((b*c+-1*a*d)^1//3*(1+-1*3^(1/2))+-1*b^1//3*(c+d*x)^1//3)^-1*((b*c+-1*a*d)^1//3*(1+3^(1/2))+-1*b^1//3*(c+d*x)^1//3)),-7+4*3^(1/2)))
@test integrate((a+b*x)^-3//2*(c+d*x)^1//3, x) == :(-2*b^-1*(a+b*x)^-1//2*(c+d*x)^1//3+-4//3*3^3//4*b^-4//3*(((b*c+-1*a*d)^1//3*(1+-1*3^(1/2))+-1*b^1//3*(c+d*x)^1//3)^-2*((b*c+-1*a*d)^2//3+b^2//3*(c+d*x)^2//3+b^1//3*(c+d*x)^1//3*(b*c+-1*a*d)^1//3))^(1/2)*(-1*(b*c+-1*a*d)^1//3*((b*c+-1*a*d)^1//3*(1+-1*3^(1/2))+-1*b^1//3*(c+d*x)^1//3)^-2*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x)^-1//2*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3)*Elliptic.F(arcsin(((b*c+-1*a*d)^1//3*(1+-1*3^(1/2))+-1*b^1//3*(c+d*x)^1//3)^-1*((b*c+-1*a*d)^1//3*(1+3^(1/2))+-1*b^1//3*(c+d*x)^1//3)),-7+4*3^(1/2)))
@test integrate((a+b*x)^-5//2*(c+d*x)^1//3, x) == :(-2//3*b^-1*(a+b*x)^-3//2*(c+d*x)^1//3+-4//9*d*b^-1*(a+b*x)^-1//2*(c+d*x)^1//3*(b*c+-1*a*d)^-1+4//27*d*3^3//4*b^-4//3*(((b*c+-1*a*d)^1//3*(1+-1*3^(1/2))+-1*b^1//3*(c+d*x)^1//3)^-2*((b*c+-1*a*d)^2//3+b^2//3*(c+d*x)^2//3+b^1//3*(c+d*x)^1//3*(b*c+-1*a*d)^1//3))^(1/2)*(-1*(b*c+-1*a*d)^1//3*((b*c+-1*a*d)^1//3*(1+-1*3^(1/2))+-1*b^1//3*(c+d*x)^1//3)^-2*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^-1*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3)*Elliptic.F(arcsin(((b*c+-1*a*d)^1//3*(1+-1*3^(1/2))+-1*b^1//3*(c+d*x)^1//3)^-1*((b*c+-1*a*d)^1//3*(1+3^(1/2))+-1*b^1//3*(c+d*x)^1//3)),-7+4*3^(1/2)))
@test integrate((a+b*x)^-7//2*(c+d*x)^1//3, x) == :(-2//5*b^-1*(a+b*x)^-5//2*(c+d*x)^1//3+-4//45*d*b^-1*(a+b*x)^-3//2*(c+d*x)^1//3*(b*c+-1*a*d)^-1+28//135*b^-1*d^2*(a+b*x)^-1//2*(c+d*x)^1//3*(b*c+-1*a*d)^-2+-28//405*3^3//4*b^-4//3*d^2*(((b*c+-1*a*d)^1//3*(1+-1*3^(1/2))+-1*b^1//3*(c+d*x)^1//3)^-2*((b*c+-1*a*d)^2//3+b^2//3*(c+d*x)^2//3+b^1//3*(c+d*x)^1//3*(b*c+-1*a*d)^1//3))^(1/2)*(-1*(b*c+-1*a*d)^1//3*((b*c+-1*a*d)^1//3*(1+-1*3^(1/2))+-1*b^1//3*(c+d*x)^1//3)^-2*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^-2*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3)*Elliptic.F(arcsin(((b*c+-1*a*d)^1//3*(1+-1*3^(1/2))+-1*b^1//3*(c+d*x)^1//3)^-1*((b*c+-1*a*d)^1//3*(1+3^(1/2))+-1*b^1//3*(c+d*x)^1//3)),-7+4*3^(1/2)))
@test integrate((a+b*x)^3//2*(c+d*x)^-1//3, x) == :(6//13*d^-1*(a+b*x)^3//2*(c+d*x)^2//3+-1//91*d^-2*(a+b*x)^(1/2)*(c+d*x)^2//3*(-54*a*d+54*b*c)+-162//91*b^-2//3*d^-2*(a+b*x)^(1/2)*(b*c+-1*a*d)^2*((b*c+-1*a*d)^1//3*(1+-1*3^(1/2))+-1*b^1//3*(c+d*x)^1//3)^-1+-54//91*2^(1/2)*3^3//4*b^-2//3*d^-3*(((b*c+-1*a*d)^1//3*(1+-1*3^(1/2))+-1*b^1//3*(c+d*x)^1//3)^-2*((b*c+-1*a*d)^2//3+b^2//3*(c+d*x)^2//3+b^1//3*(c+d*x)^1//3*(b*c+-1*a*d)^1//3))^(1/2)*(-1*(b*c+-1*a*d)^1//3*((b*c+-1*a*d)^1//3*(1+-1*3^(1/2))+-1*b^1//3*(c+d*x)^1//3)^-2*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3))^-1//2*(a+b*x)^-1//2*(b*c+-1*a*d)^7//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3)*Elliptic.F(arcsin(((b*c+-1*a*d)^1//3*(1+-1*3^(1/2))+-1*b^1//3*(c+d*x)^1//3)^-1*((b*c+-1*a*d)^1//3*(1+3^(1/2))+-1*b^1//3*(c+d*x)^1//3)),-7+4*3^(1/2))+81//91*3^1//4*b^-2//3*d^-3*(((b*c+-1*a*d)^1//3*(1+-1*3^(1/2))+-1*b^1//3*(c+d*x)^1//3)^-2*((b*c+-1*a*d)^2//3+b^2//3*(c+d*x)^2//3+b^1//3*(c+d*x)^1//3*(b*c+-1*a*d)^1//3))^(1/2)*(-1*(b*c+-1*a*d)^1//3*((b*c+-1*a*d)^1//3*(1+-1*3^(1/2))+-1*b^1//3*(c+d*x)^1//3)^-2*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^7//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3)*Elliptic.E(arcsin(((b*c+-1*a*d)^1//3*(1+-1*3^(1/2))+-1*b^1//3*(c+d*x)^1//3)^-1*((b*c+-1*a*d)^1//3*(1+3^(1/2))+-1*b^1//3*(c+d*x)^1//3)),-7+4*3^(1/2)))
@test integrate((a+b*x)^(1/2)*(c+d*x)^-1//3, x) == :(6//7*d^-1*(a+b*x)^(1/2)*(c+d*x)^2//3+1//7*b^-2//3*d^-1*(a+b*x)^(1/2)*((b*c+-1*a*d)^1//3*(1+-1*3^(1/2))+-1*b^1//3*(c+d*x)^1//3)^-1*(-18*a*d+18*b*c)+-9//7*3^1//4*b^-2//3*d^-2*(((b*c+-1*a*d)^1//3*(1+-1*3^(1/2))+-1*b^1//3*(c+d*x)^1//3)^-2*((b*c+-1*a*d)^2//3+b^2//3*(c+d*x)^2//3+b^1//3*(c+d*x)^1//3*(b*c+-1*a*d)^1//3))^(1/2)*(-1*(b*c+-1*a*d)^1//3*((b*c+-1*a*d)^1//3*(1+-1*3^(1/2))+-1*b^1//3*(c+d*x)^1//3)^-2*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^4//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3)*Elliptic.E(arcsin(((b*c+-1*a*d)^1//3*(1+-1*3^(1/2))+-1*b^1//3*(c+d*x)^1//3)^-1*((b*c+-1*a*d)^1//3*(1+3^(1/2))+-1*b^1//3*(c+d*x)^1//3)),-7+4*3^(1/2))+6//7*2^(1/2)*3^3//4*b^-2//3*d^-2*(((b*c+-1*a*d)^1//3*(1+-1*3^(1/2))+-1*b^1//3*(c+d*x)^1//3)^-2*((b*c+-1*a*d)^2//3+b^2//3*(c+d*x)^2//3+b^1//3*(c+d*x)^1//3*(b*c+-1*a*d)^1//3))^(1/2)*(-1*(b*c+-1*a*d)^1//3*((b*c+-1*a*d)^1//3*(1+-1*3^(1/2))+-1*b^1//3*(c+d*x)^1//3)^-2*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3))^-1//2*(a+b*x)^-1//2*(b*c+-1*a*d)^4//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3)*Elliptic.F(arcsin(((b*c+-1*a*d)^1//3*(1+-1*3^(1/2))+-1*b^1//3*(c+d*x)^1//3)^-1*((b*c+-1*a*d)^1//3*(1+3^(1/2))+-1*b^1//3*(c+d*x)^1//3)),-7+4*3^(1/2)))
@test integrate((a+b*x)^-1//2*(c+d*x)^-1//3, x) == :(-6*b^-2//3*(a+b*x)^(1/2)*((b*c+-1*a*d)^1//3*(1+-1*3^(1/2))+-1*b^1//3*(c+d*x)^1//3)^-1+-2*2^(1/2)*3^3//4*b^-2//3*d^-1*(((b*c+-1*a*d)^1//3*(1+-1*3^(1/2))+-1*b^1//3*(c+d*x)^1//3)^-2*((b*c+-1*a*d)^2//3+b^2//3*(c+d*x)^2//3+b^1//3*(c+d*x)^1//3*(b*c+-1*a*d)^1//3))^(1/2)*(-1*(b*c+-1*a*d)^1//3*((b*c+-1*a*d)^1//3*(1+-1*3^(1/2))+-1*b^1//3*(c+d*x)^1//3)^-2*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3))^-1//2*(a+b*x)^-1//2*(b*c+-1*a*d)^1//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3)*Elliptic.F(arcsin(((b*c+-1*a*d)^1//3*(1+-1*3^(1/2))+-1*b^1//3*(c+d*x)^1//3)^-1*((b*c+-1*a*d)^1//3*(1+3^(1/2))+-1*b^1//3*(c+d*x)^1//3)),-7+4*3^(1/2))+3*3^1//4*b^-2//3*d^-1*(((b*c+-1*a*d)^1//3*(1+-1*3^(1/2))+-1*b^1//3*(c+d*x)^1//3)^-2*((b*c+-1*a*d)^2//3+b^2//3*(c+d*x)^2//3+b^1//3*(c+d*x)^1//3*(b*c+-1*a*d)^1//3))^(1/2)*(-1*(b*c+-1*a*d)^1//3*((b*c+-1*a*d)^1//3*(1+-1*3^(1/2))+-1*b^1//3*(c+d*x)^1//3)^-2*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^1//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3)*Elliptic.E(arcsin(((b*c+-1*a*d)^1//3*(1+-1*3^(1/2))+-1*b^1//3*(c+d*x)^1//3)^-1*((b*c+-1*a*d)^1//3*(1+3^(1/2))+-1*b^1//3*(c+d*x)^1//3)),-7+4*3^(1/2)))
@test integrate((a+b*x)^-3//2*(c+d*x)^-1//3, x) == :(-2*(a+b*x)^-1//2*(c+d*x)^2//3*(b*c+-1*a*d)^-1+-2*d*b^-2//3*(a+b*x)^(1/2)*(b*c+-1*a*d)^-1*((b*c+-1*a*d)^1//3*(1+-1*3^(1/2))+-1*b^1//3*(c+d*x)^1//3)^-1+3^1//4*b^-2//3*(((b*c+-1*a*d)^1//3*(1+-1*3^(1/2))+-1*b^1//3*(c+d*x)^1//3)^-2*((b*c+-1*a*d)^2//3+b^2//3*(c+d*x)^2//3+b^1//3*(c+d*x)^1//3*(b*c+-1*a*d)^1//3))^(1/2)*(-1*(b*c+-1*a*d)^1//3*((b*c+-1*a*d)^1//3*(1+-1*3^(1/2))+-1*b^1//3*(c+d*x)^1//3)^-2*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^-2//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3)*Elliptic.E(arcsin(((b*c+-1*a*d)^1//3*(1+-1*3^(1/2))+-1*b^1//3*(c+d*x)^1//3)^-1*((b*c+-1*a*d)^1//3*(1+3^(1/2))+-1*b^1//3*(c+d*x)^1//3)),-7+4*3^(1/2))+-2//3*2^(1/2)*3^3//4*b^-2//3*(((b*c+-1*a*d)^1//3*(1+-1*3^(1/2))+-1*b^1//3*(c+d*x)^1//3)^-2*((b*c+-1*a*d)^2//3+b^2//3*(c+d*x)^2//3+b^1//3*(c+d*x)^1//3*(b*c+-1*a*d)^1//3))^(1/2)*(-1*(b*c+-1*a*d)^1//3*((b*c+-1*a*d)^1//3*(1+-1*3^(1/2))+-1*b^1//3*(c+d*x)^1//3)^-2*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3))^-1//2*(a+b*x)^-1//2*(b*c+-1*a*d)^-2//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3)*Elliptic.F(arcsin(((b*c+-1*a*d)^1//3*(1+-1*3^(1/2))+-1*b^1//3*(c+d*x)^1//3)^-1*((b*c+-1*a*d)^1//3*(1+3^(1/2))+-1*b^1//3*(c+d*x)^1//3)),-7+4*3^(1/2)))
@test integrate((a+b*x)^-5//2*(c+d*x)^-1//3, x) == :(-2*(a+b*x)^-3//2*(c+d*x)^2//3*(-3*a*d+3*b*c)^-1+10//9*d*(a+b*x)^-1//2*(c+d*x)^2//3*(b*c+-1*a*d)^-2+10//9*b^-2//3*d^2*(a+b*x)^(1/2)*(b*c+-1*a*d)^-2*((b*c+-1*a*d)^1//3*(1+-1*3^(1/2))+-1*b^1//3*(c+d*x)^1//3)^-1+-5//9*d*3^1//4*b^-2//3*(((b*c+-1*a*d)^1//3*(1+-1*3^(1/2))+-1*b^1//3*(c+d*x)^1//3)^-2*((b*c+-1*a*d)^2//3+b^2//3*(c+d*x)^2//3+b^1//3*(c+d*x)^1//3*(b*c+-1*a*d)^1//3))^(1/2)*(-1*(b*c+-1*a*d)^1//3*((b*c+-1*a*d)^1//3*(1+-1*3^(1/2))+-1*b^1//3*(c+d*x)^1//3)^-2*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^-5//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3)*Elliptic.E(arcsin(((b*c+-1*a*d)^1//3*(1+-1*3^(1/2))+-1*b^1//3*(c+d*x)^1//3)^-1*((b*c+-1*a*d)^1//3*(1+3^(1/2))+-1*b^1//3*(c+d*x)^1//3)),-7+4*3^(1/2))+10//27*d*2^(1/2)*3^3//4*b^-2//3*(((b*c+-1*a*d)^1//3*(1+-1*3^(1/2))+-1*b^1//3*(c+d*x)^1//3)^-2*((b*c+-1*a*d)^2//3+b^2//3*(c+d*x)^2//3+b^1//3*(c+d*x)^1//3*(b*c+-1*a*d)^1//3))^(1/2)*(-1*(b*c+-1*a*d)^1//3*((b*c+-1*a*d)^1//3*(1+-1*3^(1/2))+-1*b^1//3*(c+d*x)^1//3)^-2*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3))^-1//2*(a+b*x)^-1//2*(b*c+-1*a*d)^-5//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3)*Elliptic.F(arcsin(((b*c+-1*a*d)^1//3*(1+-1*3^(1/2))+-1*b^1//3*(c+d*x)^1//3)^-1*((b*c+-1*a*d)^1//3*(1+3^(1/2))+-1*b^1//3*(c+d*x)^1//3)),-7+4*3^(1/2)))
@test integrate((a+b*x)^3//2*(c+d*x)^-2//3, x) == :(6//11*d^-1*(a+b*x)^3//2*(c+d*x)^1//3+-1//55*d^-2*(a+b*x)^(1/2)*(c+d*x)^1//3*(-54*a*d+54*b*c)+-54//55*3^3//4*b^-1//3*d^-3*(((b*c+-1*a*d)^1//3*(1+-1*3^(1/2))+-1*b^1//3*(c+d*x)^1//3)^-2*((b*c+-1*a*d)^2//3+b^2//3*(c+d*x)^2//3+b^1//3*(c+d*x)^1//3*(b*c+-1*a*d)^1//3))^(1/2)*(-1*(b*c+-1*a*d)^1//3*((b*c+-1*a*d)^1//3*(1+-1*3^(1/2))+-1*b^1//3*(c+d*x)^1//3)^-2*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^2*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3)*Elliptic.F(arcsin(((b*c+-1*a*d)^1//3*(1+-1*3^(1/2))+-1*b^1//3*(c+d*x)^1//3)^-1*((b*c+-1*a*d)^1//3*(1+3^(1/2))+-1*b^1//3*(c+d*x)^1//3)),-7+4*3^(1/2)))
@test integrate((a+b*x)^(1/2)*(c+d*x)^-2//3, x) == :(6//5*d^-1*(a+b*x)^(1/2)*(c+d*x)^1//3+6//5*3^3//4*b^-1//3*d^-2*(((b*c+-1*a*d)^1//3*(1+-1*3^(1/2))+-1*b^1//3*(c+d*x)^1//3)^-2*((b*c+-1*a*d)^2//3+b^2//3*(c+d*x)^2//3+b^1//3*(c+d*x)^1//3*(b*c+-1*a*d)^1//3))^(1/2)*(-1*(b*c+-1*a*d)^1//3*((b*c+-1*a*d)^1//3*(1+-1*3^(1/2))+-1*b^1//3*(c+d*x)^1//3)^-2*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x)^-1//2*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3)*(b*c+-1*a*d)*Elliptic.F(arcsin(((b*c+-1*a*d)^1//3*(1+-1*3^(1/2))+-1*b^1//3*(c+d*x)^1//3)^-1*((b*c+-1*a*d)^1//3*(1+3^(1/2))+-1*b^1//3*(c+d*x)^1//3)),-7+4*3^(1/2)))
@test integrate((a+b*x)^-1//2*(c+d*x)^-2//3, x) == :(-2*3^3//4*b^-1//3*d^-1*(((b*c+-1*a*d)^1//3*(1+-1*3^(1/2))+-1*b^1//3*(c+d*x)^1//3)^-2*((b*c+-1*a*d)^2//3+b^2//3*(c+d*x)^2//3+b^1//3*(c+d*x)^1//3*(b*c+-1*a*d)^1//3))^(1/2)*(-1*(b*c+-1*a*d)^1//3*((b*c+-1*a*d)^1//3*(1+-1*3^(1/2))+-1*b^1//3*(c+d*x)^1//3)^-2*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x)^-1//2*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3)*Elliptic.F(arcsin(((b*c+-1*a*d)^1//3*(1+-1*3^(1/2))+-1*b^1//3*(c+d*x)^1//3)^-1*((b*c+-1*a*d)^1//3*(1+3^(1/2))+-1*b^1//3*(c+d*x)^1//3)),-7+4*3^(1/2)))
@test integrate((a+b*x)^-3//2*(c+d*x)^-2//3, x) == :(-2*(a+b*x)^-1//2*(c+d*x)^1//3*(b*c+-1*a*d)^-1+2//3*3^3//4*b^-1//3*(((b*c+-1*a*d)^1//3*(1+-1*3^(1/2))+-1*b^1//3*(c+d*x)^1//3)^-2*((b*c+-1*a*d)^2//3+b^2//3*(c+d*x)^2//3+b^1//3*(c+d*x)^1//3*(b*c+-1*a*d)^1//3))^(1/2)*(-1*(b*c+-1*a*d)^1//3*((b*c+-1*a*d)^1//3*(1+-1*3^(1/2))+-1*b^1//3*(c+d*x)^1//3)^-2*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^-1*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3)*Elliptic.F(arcsin(((b*c+-1*a*d)^1//3*(1+-1*3^(1/2))+-1*b^1//3*(c+d*x)^1//3)^-1*((b*c+-1*a*d)^1//3*(1+3^(1/2))+-1*b^1//3*(c+d*x)^1//3)),-7+4*3^(1/2)))
@test integrate((a+b*x)^-5//2*(c+d*x)^-2//3, x) == :(-2*(a+b*x)^-3//2*(c+d*x)^1//3*(-3*a*d+3*b*c)^-1+14//9*d*(a+b*x)^-1//2*(c+d*x)^1//3*(b*c+-1*a*d)^-2+-14//27*d*3^3//4*b^-1//3*(((b*c+-1*a*d)^1//3*(1+-1*3^(1/2))+-1*b^1//3*(c+d*x)^1//3)^-2*((b*c+-1*a*d)^2//3+b^2//3*(c+d*x)^2//3+b^1//3*(c+d*x)^1//3*(b*c+-1*a*d)^1//3))^(1/2)*(-1*(b*c+-1*a*d)^1//3*((b*c+-1*a*d)^1//3*(1+-1*3^(1/2))+-1*b^1//3*(c+d*x)^1//3)^-2*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^-2*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3)*Elliptic.F(arcsin(((b*c+-1*a*d)^1//3*(1+-1*3^(1/2))+-1*b^1//3*(c+d*x)^1//3)^-1*((b*c+-1*a*d)^1//3*(1+3^(1/2))+-1*b^1//3*(c+d*x)^1//3)),-7+4*3^(1/2)))
@test integrate((a+b*x)^2//3*(c+d*x)^1//3, x) == :((1/2)*b^-1*(a+b*x)^5//3*(c+d*x)^1//3+1//6*b^-4//3*d^-5//3*(b*c+-1*a*d)^2*log(-1+b^-1//3*d^1//3*(a+b*x)^1//3*(c+d*x)^-1//3)+1//18*b^-4//3*d^-5//3*(b*c+-1*a*d)^2*log(c+d*x)+1//6*b^-1*d^-1*(a+b*x)^2//3*(c+d*x)^1//3*(b*c+-1*a*d)+1//9*3^(1/2)*b^-4//3*d^-5//3*(b*c+-1*a*d)^2*arctan(1//3*3^(1/2)+2//3*3^(1/2)*b^-1//3*d^1//3*(a+b*x)^1//3*(c+d*x)^-1//3))
@test integrate((a+b*x)^-1//3*(c+d*x)^1//3, x) == :(b^-1*(a+b*x)^2//3*(c+d*x)^1//3+-1//2*b^-4//3*d^-2//3*(b*c+-1*a*d)*log(-1+b^-1//3*d^1//3*(a+b*x)^1//3*(c+d*x)^-1//3)+-1//6*b^-4//3*d^-2//3*(b*c+-1*a*d)*log(c+d*x)+-1//3*3^(1/2)*b^-4//3*d^-2//3*(b*c+-1*a*d)*arctan(1//3*3^(1/2)+2//3*3^(1/2)*b^-1//3*d^1//3*(a+b*x)^1//3*(c+d*x)^-1//3))
@test integrate((a+b*x)^-4//3*(c+d*x)^1//3, x) == :(-3*b^-1*(a+b*x)^-1//3*(c+d*x)^1//3+-3//2*b^-4//3*d^1//3*log(-1+b^-1//3*d^1//3*(a+b*x)^1//3*(c+d*x)^-1//3)+-1//2*b^-4//3*d^1//3*log(c+d*x)+-1*3^(1/2)*b^-4//3*d^1//3*arctan(1//3*3^(1/2)+2//3*3^(1/2)*b^-1//3*d^1//3*(a+b*x)^1//3*(c+d*x)^-1//3))
@test integrate((a+b*x)^-7//3*(c+d*x)^1//3, x) == :(-3*(a+b*x)^-4//3*(c+d*x)^4//3*(-4*a*d+4*b*c)^-1)
@test integrate((a+b*x)^-10//3*(c+d*x)^1//3, x) == :(-3*(a+b*x)^-7//3*(c+d*x)^4//3*(-7*a*d+7*b*c)^-1+9//28*d*(a+b*x)^-4//3*(c+d*x)^4//3*(b*c+-1*a*d)^-2)
@test integrate((a+b*x)^-13//3*(c+d*x)^1//3, x) == :(-3*(a+b*x)^-10//3*(c+d*x)^4//3*(-10*a*d+10*b*c)^-1+-27//140*d^2*(a+b*x)^-4//3*(c+d*x)^4//3*(b*c+-1*a*d)^-3+9//35*d*(a+b*x)^-7//3*(c+d*x)^4//3*(b*c+-1*a*d)^-2)
@test integrate((a+b*x)^-16//3*(c+d*x)^1//3, x) == :(-3*(a+b*x)^-13//3*(c+d*x)^4//3*(-13*a*d+13*b*c)^-1+-81//455*d^2*(a+b*x)^-7//3*(c+d*x)^4//3*(b*c+-1*a*d)^-3+27//130*d*(a+b*x)^-10//3*(c+d*x)^4//3*(b*c+-1*a*d)^-2+243//1820*d^3*(a+b*x)^-4//3*(c+d*x)^4//3*(b*c+-1*a*d)^-4)
@test integrate((a+b*x)^4//3*(c+d*x)^1//3, x) == :(3//8*b^-1*(a+b*x)^7//3*(c+d*x)^1//3+-3//20*b^-1*d^-2*(a+b*x)^1//3*(c+d*x)^1//3*(b*c+-1*a*d)^2+1//40*b^-1*d^-1*(a+b*x)^4//3*(c+d*x)^1//3*(-3*a*d+3*b*c)+1//20*2^1//3*3^3//4*b^-4//3*d^-7//3*((a*d+b*(c+2*d*x))^2)^-1//2*((a*d+b*c+2*b*d*x)^2)^(1/2)*(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-2*((b*c+-1*a*d)^4//3+2*2^1//3*b^2//3*d^2//3*((a+b*x)*(c+d*x))^2//3+-1*2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3*(b*c+-1*a*d)^2//3))^(1/2)*((a+b*x)*(c+d*x))^2//3*((b*c+-1*a*d)^2//3*((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-2*((b*c+-1*a*d)^2//3+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x)^-2//3*(c+d*x)^-2//3*(b*c+-1*a*d)^3*(a*d+b*c+2*b*d*x)^-1*((b*c+-1*a*d)^2//3+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)*Elliptic.F(arcsin(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-1*((b*c+-1*a*d)^2//3*(1+-1*3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)),-7+-4*3^(1/2)))
@test integrate((a+b*x)^1//3*(c+d*x)^1//3, x) == :(3//5*b^-1*(a+b*x)^4//3*(c+d*x)^1//3+1//10*b^-1*d^-1*(a+b*x)^1//3*(c+d*x)^1//3*(-3*a*d+3*b*c)+-1//10*2^1//3*3^3//4*b^-4//3*d^-4//3*((a*d+b*(c+2*d*x))^2)^-1//2*((a*d+b*c+2*b*d*x)^2)^(1/2)*(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-2*((b*c+-1*a*d)^4//3+2*2^1//3*b^2//3*d^2//3*((a+b*x)*(c+d*x))^2//3+-1*2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3*(b*c+-1*a*d)^2//3))^(1/2)*((a+b*x)*(c+d*x))^2//3*((b*c+-1*a*d)^2//3*((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-2*((b*c+-1*a*d)^2//3+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x)^-2//3*(c+d*x)^-2//3*(b*c+-1*a*d)^2*(a*d+b*c+2*b*d*x)^-1*((b*c+-1*a*d)^2//3+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)*Elliptic.F(arcsin(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-1*((b*c+-1*a*d)^2//3*(1+-1*3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)),-7+-4*3^(1/2)))
@test integrate((a+b*x)^-2//3*(c+d*x)^1//3, x) == :(3//2*b^-1*(a+b*x)^1//3*(c+d*x)^1//3+(1/2)*2^1//3*3^3//4*b^-4//3*d^-1//3*((a*d+b*(c+2*d*x))^2)^-1//2*((a*d+b*c+2*b*d*x)^2)^(1/2)*(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-2*((b*c+-1*a*d)^4//3+2*2^1//3*b^2//3*d^2//3*((a+b*x)*(c+d*x))^2//3+-1*2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3*(b*c+-1*a*d)^2//3))^(1/2)*((a+b*x)*(c+d*x))^2//3*((b*c+-1*a*d)^2//3*((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-2*((b*c+-1*a*d)^2//3+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x)^-2//3*(c+d*x)^-2//3*(a*d+b*c+2*b*d*x)^-1*((b*c+-1*a*d)^2//3+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)*(b*c+-1*a*d)*Elliptic.F(arcsin(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-1*((b*c+-1*a*d)^2//3*(1+-1*3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)),-7+-4*3^(1/2)))
@test integrate((a+b*x)^-5//3*(c+d*x)^1//3, x) == :(-3//2*b^-1*(a+b*x)^-2//3*(c+d*x)^1//3+(1/2)*2^1//3*3^3//4*b^-4//3*d^2//3*((a*d+b*(c+2*d*x))^2)^-1//2*((a*d+b*c+2*b*d*x)^2)^(1/2)*(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-2*((b*c+-1*a*d)^4//3+2*2^1//3*b^2//3*d^2//3*((a+b*x)*(c+d*x))^2//3+-1*2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3*(b*c+-1*a*d)^2//3))^(1/2)*((a+b*x)*(c+d*x))^2//3*((b*c+-1*a*d)^2//3*((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-2*((b*c+-1*a*d)^2//3+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x)^-2//3*(c+d*x)^-2//3*(a*d+b*c+2*b*d*x)^-1*((b*c+-1*a*d)^2//3+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)*Elliptic.F(arcsin(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-1*((b*c+-1*a*d)^2//3*(1+-1*3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)),-7+-4*3^(1/2)))
@test integrate((a+b*x)^-8//3*(c+d*x)^1//3, x) == :(-3//5*b^-1*(a+b*x)^-5//3*(c+d*x)^1//3+-3//10*d*b^-1*(a+b*x)^-2//3*(c+d*x)^1//3*(b*c+-1*a*d)^-1+-1//10*2^1//3*3^3//4*b^-4//3*d^5//3*((a*d+b*(c+2*d*x))^2)^-1//2*((a*d+b*c+2*b*d*x)^2)^(1/2)*(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-2*((b*c+-1*a*d)^4//3+2*2^1//3*b^2//3*d^2//3*((a+b*x)*(c+d*x))^2//3+-1*2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3*(b*c+-1*a*d)^2//3))^(1/2)*((a+b*x)*(c+d*x))^2//3*((b*c+-1*a*d)^2//3*((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-2*((b*c+-1*a*d)^2//3+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x)^-2//3*(c+d*x)^-2//3*(b*c+-1*a*d)^-1*(a*d+b*c+2*b*d*x)^-1*((b*c+-1*a*d)^2//3+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)*Elliptic.F(arcsin(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-1*((b*c+-1*a*d)^2//3*(1+-1*3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)),-7+-4*3^(1/2)))
@test integrate((a+b*x)^4//3*(c+d*x)^-1//3, x) == :((1/2)*d^-1*(a+b*x)^4//3*(c+d*x)^2//3+-1//3*b^-2//3*d^-7//3*(b*c+-1*a*d)^2*log(-1+b^1//3*d^-1//3*(a+b*x)^-1//3*(c+d*x)^1//3)+-1//9*b^-2//3*d^-7//3*(b*c+-1*a*d)^2*log(a+b*x)+1//3*d^-2*(a+b*x)^1//3*(c+d*x)^2//3*(-2*b*c+2*a*d)+-2//9*3^(1/2)*b^-2//3*d^-7//3*(b*c+-1*a*d)^2*arctan(1//3*3^(1/2)+2//3*3^(1/2)*b^1//3*d^-1//3*(a+b*x)^-1//3*(c+d*x)^1//3))
@test integrate((a+b*x)^1//3*(c+d*x)^-1//3, x) == :(d^-1*(a+b*x)^1//3*(c+d*x)^2//3+(1/2)*b^-2//3*d^-4//3*(b*c+-1*a*d)*log(-1+b^1//3*d^-1//3*(a+b*x)^-1//3*(c+d*x)^1//3)+1//6*b^-2//3*d^-4//3*(b*c+-1*a*d)*log(a+b*x)+1//3*3^(1/2)*b^-2//3*d^-4//3*(b*c+-1*a*d)*arctan(1//3*3^(1/2)+2//3*3^(1/2)*b^1//3*d^-1//3*(a+b*x)^-1//3*(c+d*x)^1//3))
@test integrate((a+b*x)^-2//3*(c+d*x)^-1//3, x) == :(-3//2*b^-2//3*d^-1//3*log(-1+b^1//3*d^-1//3*(a+b*x)^-1//3*(c+d*x)^1//3)+-1//2*b^-2//3*d^-1//3*log(a+b*x)+-1*3^(1/2)*b^-2//3*d^-1//3*arctan(1//3*3^(1/2)+2//3*3^(1/2)*b^1//3*d^-1//3*(a+b*x)^-1//3*(c+d*x)^1//3))
@test integrate((a+b*x)^-5//3*(c+d*x)^-1//3, x) == :(-3*(a+b*x)^-2//3*(c+d*x)^2//3*(-2*a*d+2*b*c)^-1)
@test integrate((a+b*x)^-8//3*(c+d*x)^-1//3, x) == :(-3*(a+b*x)^-5//3*(c+d*x)^2//3*(-5*a*d+5*b*c)^-1+9//10*d*(a+b*x)^-2//3*(c+d*x)^2//3*(b*c+-1*a*d)^-2)
@test integrate((a+b*x)^-11//3*(c+d*x)^-1//3, x) == :(-3*(a+b*x)^-8//3*(c+d*x)^2//3*(-8*a*d+8*b*c)^-1+-27//40*d^2*(a+b*x)^-2//3*(c+d*x)^2//3*(b*c+-1*a*d)^-3+9//20*d*(a+b*x)^-5//3*(c+d*x)^2//3*(b*c+-1*a*d)^-2)
@test integrate((a+b*x)^-14//3*(c+d*x)^-1//3, x) == :(-3*(a+b*x)^-11//3*(c+d*x)^2//3*(-11*a*d+11*b*c)^-1+-81//220*d^2*(a+b*x)^-5//3*(c+d*x)^2//3*(b*c+-1*a*d)^-3+27//88*d*(a+b*x)^-8//3*(c+d*x)^2//3*(b*c+-1*a*d)^-2+243//440*d^3*(a+b*x)^-2//3*(c+d*x)^2//3*(b*c+-1*a*d)^-4)
@test integrate((a+b*x)^8//3*(c+d*x)^-1//3, x) == :(3//10*d^-1*(a+b*x)^8//3*(c+d*x)^2//3+-1//35*d^-2*(a+b*x)^5//3*(c+d*x)^2//3*(-12*a*d+12*b*c)+3//7*d^-3*(a+b*x)^2//3*(c+d*x)^2//3*(b*c+-1*a*d)^2+-3//7*2^2//3*b^-2//3*d^-11//3*((a*d+b*(c+2*d*x))^2)^(1/2)*((a*d+b*c+2*b*d*x)^2)^(1/2)*((a+b*x)*(c+d*x))^1//3*(a+b*x)^-1//3*(c+d*x)^-1//3*(b*c+-1*a*d)^3*((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-1*(a*d+b*c+2*b*d*x)^-1+-2//7*2^1//6*3^3//4*b^-2//3*d^-11//3*((a*d+b*(c+2*d*x))^2)^-1//2*((a*d+b*c+2*b*d*x)^2)^(1/2)*(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-2*((b*c+-1*a*d)^4//3+2*2^1//3*b^2//3*d^2//3*((a+b*x)*(c+d*x))^2//3+-1*2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3*(b*c+-1*a*d)^2//3))^(1/2)*((a+b*x)*(c+d*x))^1//3*((b*c+-1*a*d)^2//3*((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-2*((b*c+-1*a*d)^2//3+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3))^-1//2*(a+b*x)^-1//3*(c+d*x)^-1//3*(b*c+-1*a*d)^11//3*(a*d+b*c+2*b*d*x)^-1*((b*c+-1*a*d)^2//3+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)*Elliptic.F(arcsin(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-1*((b*c+-1*a*d)^2//3*(1+-1*3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)),-7+-4*3^(1/2))+3//14*2^2//3*3^1//4*b^-2//3*d^-11//3*((a*d+b*(c+2*d*x))^2)^-1//2*((a*d+b*c+2*b*d*x)^2)^(1/2)*(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-2*((b*c+-1*a*d)^4//3+2*2^1//3*b^2//3*d^2//3*((a+b*x)*(c+d*x))^2//3+-1*2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3*(b*c+-1*a*d)^2//3))^(1/2)*((a+b*x)*(c+d*x))^1//3*((b*c+-1*a*d)^2//3*((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-2*((b*c+-1*a*d)^2//3+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x)^-1//3*(c+d*x)^-1//3*(b*c+-1*a*d)^11//3*(a*d+b*c+2*b*d*x)^-1*((b*c+-1*a*d)^2//3+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)*Elliptic.E(arcsin(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-1*((b*c+-1*a*d)^2//3*(1+-1*3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)),-7+-4*3^(1/2)))
@test integrate((a+b*x)^5//3*(c+d*x)^-1//3, x) == :(3//7*d^-1*(a+b*x)^5//3*(c+d*x)^2//3+-1//28*d^-2*(a+b*x)^2//3*(c+d*x)^2//3*(-15*a*d+15*b*c)+15//28*2^2//3*b^-2//3*d^-8//3*((a*d+b*(c+2*d*x))^2)^(1/2)*((a*d+b*c+2*b*d*x)^2)^(1/2)*((a+b*x)*(c+d*x))^1//3*(a+b*x)^-1//3*(c+d*x)^-1//3*(b*c+-1*a*d)^2*((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-1*(a*d+b*c+2*b*d*x)^-1+5//14*2^1//6*3^3//4*b^-2//3*d^-8//3*((a*d+b*(c+2*d*x))^2)^-1//2*((a*d+b*c+2*b*d*x)^2)^(1/2)*(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-2*((b*c+-1*a*d)^4//3+2*2^1//3*b^2//3*d^2//3*((a+b*x)*(c+d*x))^2//3+-1*2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3*(b*c+-1*a*d)^2//3))^(1/2)*((a+b*x)*(c+d*x))^1//3*((b*c+-1*a*d)^2//3*((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-2*((b*c+-1*a*d)^2//3+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3))^-1//2*(a+b*x)^-1//3*(c+d*x)^-1//3*(b*c+-1*a*d)^8//3*(a*d+b*c+2*b*d*x)^-1*((b*c+-1*a*d)^2//3+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)*Elliptic.F(arcsin(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-1*((b*c+-1*a*d)^2//3*(1+-1*3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)),-7+-4*3^(1/2))+-15//56*2^2//3*3^1//4*b^-2//3*d^-8//3*((a*d+b*(c+2*d*x))^2)^-1//2*((a*d+b*c+2*b*d*x)^2)^(1/2)*(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-2*((b*c+-1*a*d)^4//3+2*2^1//3*b^2//3*d^2//3*((a+b*x)*(c+d*x))^2//3+-1*2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3*(b*c+-1*a*d)^2//3))^(1/2)*((a+b*x)*(c+d*x))^1//3*((b*c+-1*a*d)^2//3*((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-2*((b*c+-1*a*d)^2//3+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x)^-1//3*(c+d*x)^-1//3*(b*c+-1*a*d)^8//3*(a*d+b*c+2*b*d*x)^-1*((b*c+-1*a*d)^2//3+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)*Elliptic.E(arcsin(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-1*((b*c+-1*a*d)^2//3*(1+-1*3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)),-7+-4*3^(1/2)))
@test integrate((a+b*x)^2//3*(c+d*x)^-1//3, x) == :(3//4*d^-1*(a+b*x)^2//3*(c+d*x)^2//3+-1//4*2^2//3*b^-2//3*d^-5//3*((a*d+b*(c+2*d*x))^2)^(1/2)*((a*d+b*c+2*b*d*x)^2)^(1/2)*((a+b*x)*(c+d*x))^1//3*(a+b*x)^-1//3*(c+d*x)^-1//3*((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-1*(a*d+b*c+2*b*d*x)^-1*(-3*a*d+3*b*c)+-1//2*2^1//6*3^3//4*b^-2//3*d^-5//3*((a*d+b*(c+2*d*x))^2)^-1//2*((a*d+b*c+2*b*d*x)^2)^(1/2)*(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-2*((b*c+-1*a*d)^4//3+2*2^1//3*b^2//3*d^2//3*((a+b*x)*(c+d*x))^2//3+-1*2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3*(b*c+-1*a*d)^2//3))^(1/2)*((a+b*x)*(c+d*x))^1//3*((b*c+-1*a*d)^2//3*((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-2*((b*c+-1*a*d)^2//3+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3))^-1//2*(a+b*x)^-1//3*(c+d*x)^-1//3*(b*c+-1*a*d)^5//3*(a*d+b*c+2*b*d*x)^-1*((b*c+-1*a*d)^2//3+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)*Elliptic.F(arcsin(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-1*((b*c+-1*a*d)^2//3*(1+-1*3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)),-7+-4*3^(1/2))+3//8*2^2//3*3^1//4*b^-2//3*d^-5//3*((a*d+b*(c+2*d*x))^2)^-1//2*((a*d+b*c+2*b*d*x)^2)^(1/2)*(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-2*((b*c+-1*a*d)^4//3+2*2^1//3*b^2//3*d^2//3*((a+b*x)*(c+d*x))^2//3+-1*2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3*(b*c+-1*a*d)^2//3))^(1/2)*((a+b*x)*(c+d*x))^1//3*((b*c+-1*a*d)^2//3*((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-2*((b*c+-1*a*d)^2//3+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x)^-1//3*(c+d*x)^-1//3*(b*c+-1*a*d)^5//3*(a*d+b*c+2*b*d*x)^-1*((b*c+-1*a*d)^2//3+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)*Elliptic.E(arcsin(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-1*((b*c+-1*a*d)^2//3*(1+-1*3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)),-7+-4*3^(1/2)))
@test integrate((a+b*x)^-1//3*(c+d*x)^-1//3, x) == :(3//2*2^2//3*b^-2//3*d^-2//3*((a*d+b*(c+2*d*x))^2)^(1/2)*((a*d+b*c+2*b*d*x)^2)^(1/2)*((a+b*x)*(c+d*x))^1//3*(a+b*x)^-1//3*(c+d*x)^-1//3*((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-1*(a*d+b*c+2*b*d*x)^-1+2^1//6*3^3//4*b^-2//3*d^-2//3*((a*d+b*(c+2*d*x))^2)^-1//2*((a*d+b*c+2*b*d*x)^2)^(1/2)*(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-2*((b*c+-1*a*d)^4//3+2*2^1//3*b^2//3*d^2//3*((a+b*x)*(c+d*x))^2//3+-1*2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3*(b*c+-1*a*d)^2//3))^(1/2)*((a+b*x)*(c+d*x))^1//3*((b*c+-1*a*d)^2//3*((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-2*((b*c+-1*a*d)^2//3+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3))^-1//2*(a+b*x)^-1//3*(c+d*x)^-1//3*(b*c+-1*a*d)^2//3*(a*d+b*c+2*b*d*x)^-1*((b*c+-1*a*d)^2//3+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)*Elliptic.F(arcsin(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-1*((b*c+-1*a*d)^2//3*(1+-1*3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)),-7+-4*3^(1/2))+-3//4*2^2//3*3^1//4*b^-2//3*d^-2//3*((a*d+b*(c+2*d*x))^2)^-1//2*((a*d+b*c+2*b*d*x)^2)^(1/2)*(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-2*((b*c+-1*a*d)^4//3+2*2^1//3*b^2//3*d^2//3*((a+b*x)*(c+d*x))^2//3+-1*2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3*(b*c+-1*a*d)^2//3))^(1/2)*((a+b*x)*(c+d*x))^1//3*((b*c+-1*a*d)^2//3*((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-2*((b*c+-1*a*d)^2//3+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x)^-1//3*(c+d*x)^-1//3*(b*c+-1*a*d)^2//3*(a*d+b*c+2*b*d*x)^-1*((b*c+-1*a*d)^2//3+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)*Elliptic.E(arcsin(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-1*((b*c+-1*a*d)^2//3*(1+-1*3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)),-7+-4*3^(1/2)))
@test integrate((a+b*x)^-4//3*(c+d*x)^-1//3, x) == :(-3*(a+b*x)^-1//3*(c+d*x)^2//3*(b*c+-1*a*d)^-1+3//2*2^2//3*b^-2//3*d^1//3*((a*d+b*(c+2*d*x))^2)^(1/2)*((a*d+b*c+2*b*d*x)^2)^(1/2)*((a+b*x)*(c+d*x))^1//3*(a+b*x)^-1//3*(c+d*x)^-1//3*(b*c+-1*a*d)^-1*((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-1*(a*d+b*c+2*b*d*x)^-1+2^1//6*3^3//4*b^-2//3*d^1//3*((a*d+b*(c+2*d*x))^2)^-1//2*((a*d+b*c+2*b*d*x)^2)^(1/2)*(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-2*((b*c+-1*a*d)^4//3+2*2^1//3*b^2//3*d^2//3*((a+b*x)*(c+d*x))^2//3+-1*2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3*(b*c+-1*a*d)^2//3))^(1/2)*((a+b*x)*(c+d*x))^1//3*((b*c+-1*a*d)^2//3*((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-2*((b*c+-1*a*d)^2//3+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3))^-1//2*(a+b*x)^-1//3*(c+d*x)^-1//3*(b*c+-1*a*d)^-1//3*(a*d+b*c+2*b*d*x)^-1*((b*c+-1*a*d)^2//3+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)*Elliptic.F(arcsin(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-1*((b*c+-1*a*d)^2//3*(1+-1*3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)),-7+-4*3^(1/2))+-3//4*2^2//3*3^1//4*b^-2//3*d^1//3*((a*d+b*(c+2*d*x))^2)^-1//2*((a*d+b*c+2*b*d*x)^2)^(1/2)*(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-2*((b*c+-1*a*d)^4//3+2*2^1//3*b^2//3*d^2//3*((a+b*x)*(c+d*x))^2//3+-1*2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3*(b*c+-1*a*d)^2//3))^(1/2)*((a+b*x)*(c+d*x))^1//3*((b*c+-1*a*d)^2//3*((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-2*((b*c+-1*a*d)^2//3+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x)^-1//3*(c+d*x)^-1//3*(b*c+-1*a*d)^-1//3*(a*d+b*c+2*b*d*x)^-1*((b*c+-1*a*d)^2//3+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)*Elliptic.E(arcsin(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-1*((b*c+-1*a*d)^2//3*(1+-1*3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)),-7+-4*3^(1/2)))
@test integrate((a+b*x)^-7//3*(c+d*x)^-1//3, x) == :(-3*(a+b*x)^-4//3*(c+d*x)^2//3*(-4*a*d+4*b*c)^-1+3//2*d*(a+b*x)^-1//3*(c+d*x)^2//3*(b*c+-1*a*d)^-2+-3//4*2^2//3*b^-2//3*d^4//3*((a*d+b*(c+2*d*x))^2)^(1/2)*((a*d+b*c+2*b*d*x)^2)^(1/2)*((a+b*x)*(c+d*x))^1//3*(a+b*x)^-1//3*(c+d*x)^-1//3*(b*c+-1*a*d)^-2*((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-1*(a*d+b*c+2*b*d*x)^-1+-1//2*2^1//6*3^3//4*b^-2//3*d^4//3*((a*d+b*(c+2*d*x))^2)^-1//2*((a*d+b*c+2*b*d*x)^2)^(1/2)*(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-2*((b*c+-1*a*d)^4//3+2*2^1//3*b^2//3*d^2//3*((a+b*x)*(c+d*x))^2//3+-1*2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3*(b*c+-1*a*d)^2//3))^(1/2)*((a+b*x)*(c+d*x))^1//3*((b*c+-1*a*d)^2//3*((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-2*((b*c+-1*a*d)^2//3+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3))^-1//2*(a+b*x)^-1//3*(c+d*x)^-1//3*(b*c+-1*a*d)^-4//3*(a*d+b*c+2*b*d*x)^-1*((b*c+-1*a*d)^2//3+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)*Elliptic.F(arcsin(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-1*((b*c+-1*a*d)^2//3*(1+-1*3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)),-7+-4*3^(1/2))+3//8*2^2//3*3^1//4*b^-2//3*d^4//3*((a*d+b*(c+2*d*x))^2)^-1//2*((a*d+b*c+2*b*d*x)^2)^(1/2)*(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-2*((b*c+-1*a*d)^4//3+2*2^1//3*b^2//3*d^2//3*((a+b*x)*(c+d*x))^2//3+-1*2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3*(b*c+-1*a*d)^2//3))^(1/2)*((a+b*x)*(c+d*x))^1//3*((b*c+-1*a*d)^2//3*((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-2*((b*c+-1*a*d)^2//3+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x)^-1//3*(c+d*x)^-1//3*(b*c+-1*a*d)^-4//3*(a*d+b*c+2*b*d*x)^-1*((b*c+-1*a*d)^2//3+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)*Elliptic.E(arcsin(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-1*((b*c+-1*a*d)^2//3*(1+-1*3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)),-7+-4*3^(1/2)))
@test integrate((a+b*x)^-10//3*(c+d*x)^-1//3, x) == :(-3*(a+b*x)^-7//3*(c+d*x)^2//3*(-7*a*d+7*b*c)^-1+-15//14*d^2*(a+b*x)^-1//3*(c+d*x)^2//3*(b*c+-1*a*d)^-3+15//28*d*(a+b*x)^-4//3*(c+d*x)^2//3*(b*c+-1*a*d)^-2+15//28*2^2//3*b^-2//3*d^7//3*((a*d+b*(c+2*d*x))^2)^(1/2)*((a*d+b*c+2*b*d*x)^2)^(1/2)*((a+b*x)*(c+d*x))^1//3*(a+b*x)^-1//3*(c+d*x)^-1//3*(b*c+-1*a*d)^-3*((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-1*(a*d+b*c+2*b*d*x)^-1+5//14*2^1//6*3^3//4*b^-2//3*d^7//3*((a*d+b*(c+2*d*x))^2)^-1//2*((a*d+b*c+2*b*d*x)^2)^(1/2)*(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-2*((b*c+-1*a*d)^4//3+2*2^1//3*b^2//3*d^2//3*((a+b*x)*(c+d*x))^2//3+-1*2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3*(b*c+-1*a*d)^2//3))^(1/2)*((a+b*x)*(c+d*x))^1//3*((b*c+-1*a*d)^2//3*((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-2*((b*c+-1*a*d)^2//3+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3))^-1//2*(a+b*x)^-1//3*(c+d*x)^-1//3*(b*c+-1*a*d)^-7//3*(a*d+b*c+2*b*d*x)^-1*((b*c+-1*a*d)^2//3+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)*Elliptic.F(arcsin(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-1*((b*c+-1*a*d)^2//3*(1+-1*3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)),-7+-4*3^(1/2))+-15//56*2^2//3*3^1//4*b^-2//3*d^7//3*((a*d+b*(c+2*d*x))^2)^-1//2*((a*d+b*c+2*b*d*x)^2)^(1/2)*(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-2*((b*c+-1*a*d)^4//3+2*2^1//3*b^2//3*d^2//3*((a+b*x)*(c+d*x))^2//3+-1*2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3*(b*c+-1*a*d)^2//3))^(1/2)*((a+b*x)*(c+d*x))^1//3*((b*c+-1*a*d)^2//3*((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-2*((b*c+-1*a*d)^2//3+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x)^-1//3*(c+d*x)^-1//3*(b*c+-1*a*d)^-7//3*(a*d+b*c+2*b*d*x)^-1*((b*c+-1*a*d)^2//3+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)*Elliptic.E(arcsin(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-1*((b*c+-1*a*d)^2//3*(1+-1*3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)),-7+-4*3^(1/2)))
@test integrate((a+b*x)^5//3*(c+d*x)^-2//3, x) == :((1/2)*d^-1*(a+b*x)^5//3*(c+d*x)^1//3+-5//6*b^-1//3*d^-8//3*(b*c+-1*a*d)^2*log(-1+b^-1//3*d^1//3*(a+b*x)^1//3*(c+d*x)^-1//3)+-5//18*b^-1//3*d^-8//3*(b*c+-1*a*d)^2*log(c+d*x)+1//6*d^-2*(a+b*x)^2//3*(c+d*x)^1//3*(-5*b*c+5*a*d)+-5//9*3^(1/2)*b^-1//3*d^-8//3*(b*c+-1*a*d)^2*arctan(1//3*3^(1/2)+2//3*3^(1/2)*b^-1//3*d^1//3*(a+b*x)^1//3*(c+d*x)^-1//3))
@test integrate((a+b*x)^2//3*(c+d*x)^-2//3, x) == :(d^-1*(a+b*x)^2//3*(c+d*x)^1//3+b^-1//3*d^-5//3*(b*c+-1*a*d)*log(-1+b^-1//3*d^1//3*(a+b*x)^1//3*(c+d*x)^-1//3)+1//3*b^-1//3*d^-5//3*(b*c+-1*a*d)*log(c+d*x)+1//3*3^(1/2)*b^-1//3*d^-5//3*(-2*a*d+2*b*c)*arctan(1//3*3^(1/2)+2//3*3^(1/2)*b^-1//3*d^1//3*(a+b*x)^1//3*(c+d*x)^-1//3))
@test integrate((a+b*x)^-1//3*(c+d*x)^-2//3, x) == :(-3//2*b^-1//3*d^-2//3*log(-1+b^-1//3*d^1//3*(a+b*x)^1//3*(c+d*x)^-1//3)+-1//2*b^-1//3*d^-2//3*log(c+d*x)+-1*3^(1/2)*b^-1//3*d^-2//3*arctan(1//3*3^(1/2)+2//3*3^(1/2)*b^-1//3*d^1//3*(a+b*x)^1//3*(c+d*x)^-1//3))
@test integrate((a+b*x)^-4//3*(c+d*x)^-2//3, x) == :(-3*(a+b*x)^-1//3*(c+d*x)^1//3*(b*c+-1*a*d)^-1)
@test integrate((a+b*x)^-7//3*(c+d*x)^-2//3, x) == :(-3*(a+b*x)^-4//3*(c+d*x)^1//3*(-4*a*d+4*b*c)^-1+9//4*d*(a+b*x)^-1//3*(c+d*x)^1//3*(b*c+-1*a*d)^-2)
@test integrate((a+b*x)^-10//3*(c+d*x)^-2//3, x) == :(-3*(a+b*x)^-7//3*(c+d*x)^1//3*(-7*a*d+7*b*c)^-1+-27//14*d^2*(a+b*x)^-1//3*(c+d*x)^1//3*(b*c+-1*a*d)^-3+9//14*d*(a+b*x)^-4//3*(c+d*x)^1//3*(b*c+-1*a*d)^-2)
@test integrate((a+b*x)^-13//3*(c+d*x)^-2//3, x) == :(-3*(a+b*x)^-10//3*(c+d*x)^1//3*(-10*a*d+10*b*c)^-1+-81//140*d^2*(a+b*x)^-4//3*(c+d*x)^1//3*(b*c+-1*a*d)^-3+27//70*d*(a+b*x)^-7//3*(c+d*x)^1//3*(b*c+-1*a*d)^-2+243//140*d^3*(a+b*x)^-1//3*(c+d*x)^1//3*(b*c+-1*a*d)^-4)
@test integrate((a+b*x)^7//3*(c+d*x)^-2//3, x) == :(3//8*d^-1*(a+b*x)^7//3*(c+d*x)^1//3+-1//40*d^-2*(a+b*x)^4//3*(c+d*x)^1//3*(-21*a*d+21*b*c)+21//20*d^-3*(a+b*x)^1//3*(c+d*x)^1//3*(b*c+-1*a*d)^2+-7//20*2^1//3*3^3//4*b^-1//3*d^-10//3*((a*d+b*(c+2*d*x))^2)^-1//2*((a*d+b*c+2*b*d*x)^2)^(1/2)*(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-2*((b*c+-1*a*d)^4//3+2*2^1//3*b^2//3*d^2//3*((a+b*x)*(c+d*x))^2//3+-1*2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3*(b*c+-1*a*d)^2//3))^(1/2)*((a+b*x)*(c+d*x))^2//3*((b*c+-1*a*d)^2//3*((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-2*((b*c+-1*a*d)^2//3+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x)^-2//3*(c+d*x)^-2//3*(b*c+-1*a*d)^3*(a*d+b*c+2*b*d*x)^-1*((b*c+-1*a*d)^2//3+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)*Elliptic.F(arcsin(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-1*((b*c+-1*a*d)^2//3*(1+-1*3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)),-7+-4*3^(1/2)))
@test integrate((a+b*x)^4//3*(c+d*x)^-2//3, x) == :(3//5*d^-1*(a+b*x)^4//3*(c+d*x)^1//3+-1//5*d^-2*(a+b*x)^1//3*(c+d*x)^1//3*(-6*a*d+6*b*c)+2//5*2^1//3*3^3//4*b^-1//3*d^-7//3*((a*d+b*(c+2*d*x))^2)^-1//2*((a*d+b*c+2*b*d*x)^2)^(1/2)*(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-2*((b*c+-1*a*d)^4//3+2*2^1//3*b^2//3*d^2//3*((a+b*x)*(c+d*x))^2//3+-1*2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3*(b*c+-1*a*d)^2//3))^(1/2)*((a+b*x)*(c+d*x))^2//3*((b*c+-1*a*d)^2//3*((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-2*((b*c+-1*a*d)^2//3+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x)^-2//3*(c+d*x)^-2//3*(b*c+-1*a*d)^2*(a*d+b*c+2*b*d*x)^-1*((b*c+-1*a*d)^2//3+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)*Elliptic.F(arcsin(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-1*((b*c+-1*a*d)^2//3*(1+-1*3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)),-7+-4*3^(1/2)))
@test integrate((a+b*x)^1//3*(c+d*x)^-2//3, x) == :(3//2*d^-1*(a+b*x)^1//3*(c+d*x)^1//3+-1//2*2^1//3*3^3//4*b^-1//3*d^-4//3*((a*d+b*(c+2*d*x))^2)^-1//2*((a*d+b*c+2*b*d*x)^2)^(1/2)*(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-2*((b*c+-1*a*d)^4//3+2*2^1//3*b^2//3*d^2//3*((a+b*x)*(c+d*x))^2//3+-1*2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3*(b*c+-1*a*d)^2//3))^(1/2)*((a+b*x)*(c+d*x))^2//3*((b*c+-1*a*d)^2//3*((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-2*((b*c+-1*a*d)^2//3+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x)^-2//3*(c+d*x)^-2//3*(a*d+b*c+2*b*d*x)^-1*((b*c+-1*a*d)^2//3+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)*(b*c+-1*a*d)*Elliptic.F(arcsin(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-1*((b*c+-1*a*d)^2//3*(1+-1*3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)),-7+-4*3^(1/2)))
@test integrate((a+b*x)^-2//3*(c+d*x)^-2//3, x) == :(2^1//3*3^3//4*b^-1//3*d^-1//3*((a*d+b*(c+2*d*x))^2)^-1//2*((a*d+b*c+2*b*d*x)^2)^(1/2)*(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-2*((b*c+-1*a*d)^4//3+2*2^1//3*b^2//3*d^2//3*((a+b*x)*(c+d*x))^2//3+-1*2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3*(b*c+-1*a*d)^2//3))^(1/2)*((a+b*x)*(c+d*x))^2//3*((b*c+-1*a*d)^2//3*((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-2*((b*c+-1*a*d)^2//3+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x)^-2//3*(c+d*x)^-2//3*(a*d+b*c+2*b*d*x)^-1*((b*c+-1*a*d)^2//3+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)*Elliptic.F(arcsin(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-1*((b*c+-1*a*d)^2//3*(1+-1*3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)),-7+-4*3^(1/2)))
@test integrate((a+b*x)^-5//3*(c+d*x)^-2//3, x) == :(-3*(a+b*x)^-2//3*(c+d*x)^1//3*(-2*a*d+2*b*c)^-1+-1//2*2^1//3*3^3//4*b^-1//3*d^2//3*((a*d+b*(c+2*d*x))^2)^-1//2*((a*d+b*c+2*b*d*x)^2)^(1/2)*(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-2*((b*c+-1*a*d)^4//3+2*2^1//3*b^2//3*d^2//3*((a+b*x)*(c+d*x))^2//3+-1*2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3*(b*c+-1*a*d)^2//3))^(1/2)*((a+b*x)*(c+d*x))^2//3*((b*c+-1*a*d)^2//3*((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-2*((b*c+-1*a*d)^2//3+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x)^-2//3*(c+d*x)^-2//3*(b*c+-1*a*d)^-1*(a*d+b*c+2*b*d*x)^-1*((b*c+-1*a*d)^2//3+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)*Elliptic.F(arcsin(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-1*((b*c+-1*a*d)^2//3*(1+-1*3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)),-7+-4*3^(1/2)))
@test integrate((a+b*x)^-8//3*(c+d*x)^-2//3, x) == :(-3*(a+b*x)^-5//3*(c+d*x)^1//3*(-5*a*d+5*b*c)^-1+6//5*d*(a+b*x)^-2//3*(c+d*x)^1//3*(b*c+-1*a*d)^-2+2//5*2^1//3*3^3//4*b^-1//3*d^5//3*((a*d+b*(c+2*d*x))^2)^-1//2*((a*d+b*c+2*b*d*x)^2)^(1/2)*(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-2*((b*c+-1*a*d)^4//3+2*2^1//3*b^2//3*d^2//3*((a+b*x)*(c+d*x))^2//3+-1*2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3*(b*c+-1*a*d)^2//3))^(1/2)*((a+b*x)*(c+d*x))^2//3*((b*c+-1*a*d)^2//3*((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-2*((b*c+-1*a*d)^2//3+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x)^-2//3*(c+d*x)^-2//3*(b*c+-1*a*d)^-2*(a*d+b*c+2*b*d*x)^-1*((b*c+-1*a*d)^2//3+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)*Elliptic.F(arcsin(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-1*((b*c+-1*a*d)^2//3*(1+-1*3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)),-7+-4*3^(1/2)))
@test integrate((a+b*x)^-11//3*(c+d*x)^-2//3, x) == :(-3*(a+b*x)^-8//3*(c+d*x)^1//3*(-8*a*d+8*b*c)^-1+-21//20*d^2*(a+b*x)^-2//3*(c+d*x)^1//3*(b*c+-1*a*d)^-3+21//40*d*(a+b*x)^-5//3*(c+d*x)^1//3*(b*c+-1*a*d)^-2+-7//20*2^1//3*3^3//4*b^-1//3*d^8//3*((a*d+b*(c+2*d*x))^2)^-1//2*((a*d+b*c+2*b*d*x)^2)^(1/2)*(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-2*((b*c+-1*a*d)^4//3+2*2^1//3*b^2//3*d^2//3*((a+b*x)*(c+d*x))^2//3+-1*2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3*(b*c+-1*a*d)^2//3))^(1/2)*((a+b*x)*(c+d*x))^2//3*((b*c+-1*a*d)^2//3*((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-2*((b*c+-1*a*d)^2//3+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x)^-2//3*(c+d*x)^-2//3*(b*c+-1*a*d)^-3*(a*d+b*c+2*b*d*x)^-1*((b*c+-1*a*d)^2//3+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)*Elliptic.F(arcsin(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-1*((b*c+-1*a*d)^2//3*(1+-1*3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)),-7+-4*3^(1/2)))
@test integrate((a+b*x)^7//3*(c+d*x)^-4//3, x) == :(-3*d^-1*(a+b*x)^7//3*(c+d*x)^-1//3+-7//3*b^1//3*d^-10//3*(b*c+-1*a*d)^2*log(-1+b^1//3*d^-1//3*(a+b*x)^-1//3*(c+d*x)^1//3)+-7//9*b^1//3*d^-10//3*(b*c+-1*a*d)^2*log(a+b*x)+7//2*b*d^-2*(a+b*x)^4//3*(c+d*x)^2//3+-14//3*b*d^-3*(a+b*x)^1//3*(c+d*x)^2//3*(b*c+-1*a*d)+-14//9*3^(1/2)*b^1//3*d^-10//3*(b*c+-1*a*d)^2*arctan(1//3*3^(1/2)+2//3*3^(1/2)*b^1//3*d^-1//3*(a+b*x)^-1//3*(c+d*x)^1//3))
@test integrate((a+b*x)^4//3*(c+d*x)^-4//3, x) == :(-3*d^-1*(a+b*x)^4//3*(c+d*x)^-1//3+2*b^1//3*d^-7//3*(b*c+-1*a*d)*log(-1+b^1//3*d^-1//3*(a+b*x)^-1//3*(c+d*x)^1//3)+4*b*d^-2*(a+b*x)^1//3*(c+d*x)^2//3+2//3*b^1//3*d^-7//3*(b*c+-1*a*d)*log(a+b*x)+4//3*3^(1/2)*b^1//3*d^-7//3*(b*c+-1*a*d)*arctan(1//3*3^(1/2)+2//3*3^(1/2)*b^1//3*d^-1//3*(a+b*x)^-1//3*(c+d*x)^1//3))
@test integrate((a+b*x)^1//3*(c+d*x)^-4//3, x) == :(-3*d^-1*(a+b*x)^1//3*(c+d*x)^-1//3+-3//2*b^1//3*d^-4//3*log(-1+b^1//3*d^-1//3*(a+b*x)^-1//3*(c+d*x)^1//3)+-1//2*b^1//3*d^-4//3*log(a+b*x)+-1*3^(1/2)*b^1//3*d^-4//3*arctan(1//3*3^(1/2)+2//3*3^(1/2)*b^1//3*d^-1//3*(a+b*x)^-1//3*(c+d*x)^1//3))
@test integrate((a+b*x)^-2//3*(c+d*x)^-4//3, x) == :(3*(a+b*x)^1//3*(c+d*x)^-1//3*(b*c+-1*a*d)^-1)
@test integrate((a+b*x)^-5//3*(c+d*x)^-4//3, x) == :(-3*(a+b*x)^-2//3*(c+d*x)^-1//3*(-2*a*d+2*b*c)^-1+-9//2*d*(a+b*x)^1//3*(c+d*x)^-1//3*(b*c+-1*a*d)^-2)
@test integrate((a+b*x)^-8//3*(c+d*x)^-4//3, x) == :(-3*(a+b*x)^-5//3*(c+d*x)^-1//3*(-5*a*d+5*b*c)^-1+9//5*d*(a+b*x)^-2//3*(c+d*x)^-1//3*(b*c+-1*a*d)^-2+27//5*d^2*(a+b*x)^1//3*(c+d*x)^-1//3*(b*c+-1*a*d)^-3)
@test integrate((a+b*x)^-11//3*(c+d*x)^-4//3, x) == :(-3*(a+b*x)^-8//3*(c+d*x)^-1//3*(-8*a*d+8*b*c)^-1+-243//40*d^3*(a+b*x)^1//3*(c+d*x)^-1//3*(b*c+-1*a*d)^-4+-81//40*d^2*(a+b*x)^-2//3*(c+d*x)^-1//3*(b*c+-1*a*d)^-3+27//40*d*(a+b*x)^-5//3*(c+d*x)^-1//3*(b*c+-1*a*d)^-2)
@test integrate((a+b*x)^8//3*(c+d*x)^-4//3, x) == :(-3*d^-1*(a+b*x)^8//3*(c+d*x)^-1//3+24//7*b*d^-2*(a+b*x)^5//3*(c+d*x)^2//3+-30//7*b*d^-3*(a+b*x)^2//3*(c+d*x)^2//3*(b*c+-1*a*d)+30//7*2^2//3*b^1//3*d^-11//3*((a*d+b*(c+2*d*x))^2)^(1/2)*((a*d+b*c+2*b*d*x)^2)^(1/2)*((a+b*x)*(c+d*x))^1//3*(a+b*x)^-1//3*(c+d*x)^-1//3*(b*c+-1*a*d)^2*((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-1*(a*d+b*c+2*b*d*x)^-1+20//7*2^1//6*3^3//4*b^1//3*d^-11//3*((a*d+b*(c+2*d*x))^2)^-1//2*((a*d+b*c+2*b*d*x)^2)^(1/2)*(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-2*((b*c+-1*a*d)^4//3+2*2^1//3*b^2//3*d^2//3*((a+b*x)*(c+d*x))^2//3+-1*2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3*(b*c+-1*a*d)^2//3))^(1/2)*((a+b*x)*(c+d*x))^1//3*((b*c+-1*a*d)^2//3*((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-2*((b*c+-1*a*d)^2//3+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3))^-1//2*(a+b*x)^-1//3*(c+d*x)^-1//3*(b*c+-1*a*d)^8//3*(a*d+b*c+2*b*d*x)^-1*((b*c+-1*a*d)^2//3+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)*Elliptic.F(arcsin(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-1*((b*c+-1*a*d)^2//3*(1+-1*3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)),-7+-4*3^(1/2))+-15//7*2^2//3*3^1//4*b^1//3*d^-11//3*((a*d+b*(c+2*d*x))^2)^-1//2*((a*d+b*c+2*b*d*x)^2)^(1/2)*(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-2*((b*c+-1*a*d)^4//3+2*2^1//3*b^2//3*d^2//3*((a+b*x)*(c+d*x))^2//3+-1*2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3*(b*c+-1*a*d)^2//3))^(1/2)*((a+b*x)*(c+d*x))^1//3*((b*c+-1*a*d)^2//3*((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-2*((b*c+-1*a*d)^2//3+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x)^-1//3*(c+d*x)^-1//3*(b*c+-1*a*d)^8//3*(a*d+b*c+2*b*d*x)^-1*((b*c+-1*a*d)^2//3+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)*Elliptic.E(arcsin(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-1*((b*c+-1*a*d)^2//3*(1+-1*3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)),-7+-4*3^(1/2)))
@test integrate((a+b*x)^5//3*(c+d*x)^-4//3, x) == :(-3*d^-1*(a+b*x)^5//3*(c+d*x)^-1//3+15//4*b*d^-2*(a+b*x)^2//3*(c+d*x)^2//3+-15//4*2^2//3*b^1//3*d^-8//3*((a*d+b*(c+2*d*x))^2)^(1/2)*((a*d+b*c+2*b*d*x)^2)^(1/2)*((a+b*x)*(c+d*x))^1//3*(a+b*x)^-1//3*(c+d*x)^-1//3*((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-1*(a*d+b*c+2*b*d*x)^-1*(b*c+-1*a*d)+-5//2*2^1//6*3^3//4*b^1//3*d^-8//3*((a*d+b*(c+2*d*x))^2)^-1//2*((a*d+b*c+2*b*d*x)^2)^(1/2)*(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-2*((b*c+-1*a*d)^4//3+2*2^1//3*b^2//3*d^2//3*((a+b*x)*(c+d*x))^2//3+-1*2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3*(b*c+-1*a*d)^2//3))^(1/2)*((a+b*x)*(c+d*x))^1//3*((b*c+-1*a*d)^2//3*((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-2*((b*c+-1*a*d)^2//3+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3))^-1//2*(a+b*x)^-1//3*(c+d*x)^-1//3*(b*c+-1*a*d)^5//3*(a*d+b*c+2*b*d*x)^-1*((b*c+-1*a*d)^2//3+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)*Elliptic.F(arcsin(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-1*((b*c+-1*a*d)^2//3*(1+-1*3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)),-7+-4*3^(1/2))+15//8*2^2//3*3^1//4*b^1//3*d^-8//3*((a*d+b*(c+2*d*x))^2)^-1//2*((a*d+b*c+2*b*d*x)^2)^(1/2)*(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-2*((b*c+-1*a*d)^4//3+2*2^1//3*b^2//3*d^2//3*((a+b*x)*(c+d*x))^2//3+-1*2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3*(b*c+-1*a*d)^2//3))^(1/2)*((a+b*x)*(c+d*x))^1//3*((b*c+-1*a*d)^2//3*((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-2*((b*c+-1*a*d)^2//3+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x)^-1//3*(c+d*x)^-1//3*(b*c+-1*a*d)^5//3*(a*d+b*c+2*b*d*x)^-1*((b*c+-1*a*d)^2//3+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)*Elliptic.E(arcsin(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-1*((b*c+-1*a*d)^2//3*(1+-1*3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)),-7+-4*3^(1/2)))
@test integrate((a+b*x)^2//3*(c+d*x)^-4//3, x) == :(-3*d^-1*(a+b*x)^2//3*(c+d*x)^-1//3+3*2^2//3*b^1//3*d^-5//3*((a*d+b*(c+2*d*x))^2)^(1/2)*((a*d+b*c+2*b*d*x)^2)^(1/2)*((a+b*x)*(c+d*x))^1//3*(a+b*x)^-1//3*(c+d*x)^-1//3*((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-1*(a*d+b*c+2*b*d*x)^-1+2*2^1//6*3^3//4*b^1//3*d^-5//3*((a*d+b*(c+2*d*x))^2)^-1//2*((a*d+b*c+2*b*d*x)^2)^(1/2)*(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-2*((b*c+-1*a*d)^4//3+2*2^1//3*b^2//3*d^2//3*((a+b*x)*(c+d*x))^2//3+-1*2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3*(b*c+-1*a*d)^2//3))^(1/2)*((a+b*x)*(c+d*x))^1//3*((b*c+-1*a*d)^2//3*((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-2*((b*c+-1*a*d)^2//3+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3))^-1//2*(a+b*x)^-1//3*(c+d*x)^-1//3*(b*c+-1*a*d)^2//3*(a*d+b*c+2*b*d*x)^-1*((b*c+-1*a*d)^2//3+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)*Elliptic.F(arcsin(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-1*((b*c+-1*a*d)^2//3*(1+-1*3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)),-7+-4*3^(1/2))+-3//2*2^2//3*3^1//4*b^1//3*d^-5//3*((a*d+b*(c+2*d*x))^2)^-1//2*((a*d+b*c+2*b*d*x)^2)^(1/2)*(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-2*((b*c+-1*a*d)^4//3+2*2^1//3*b^2//3*d^2//3*((a+b*x)*(c+d*x))^2//3+-1*2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3*(b*c+-1*a*d)^2//3))^(1/2)*((a+b*x)*(c+d*x))^1//3*((b*c+-1*a*d)^2//3*((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-2*((b*c+-1*a*d)^2//3+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x)^-1//3*(c+d*x)^-1//3*(b*c+-1*a*d)^2//3*(a*d+b*c+2*b*d*x)^-1*((b*c+-1*a*d)^2//3+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)*Elliptic.E(arcsin(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-1*((b*c+-1*a*d)^2//3*(1+-1*3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)),-7+-4*3^(1/2)))
@test integrate((a+b*x)^-1//3*(c+d*x)^-4//3, x) == :(3*(a+b*x)^2//3*(c+d*x)^-1//3*(b*c+-1*a*d)^-1+-3//2*2^2//3*b^1//3*d^-2//3*((a*d+b*(c+2*d*x))^2)^(1/2)*((a*d+b*c+2*b*d*x)^2)^(1/2)*((a+b*x)*(c+d*x))^1//3*(a+b*x)^-1//3*(c+d*x)^-1//3*(b*c+-1*a*d)^-1*((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-1*(a*d+b*c+2*b*d*x)^-1+-1*2^1//6*3^3//4*b^1//3*d^-2//3*((a*d+b*(c+2*d*x))^2)^-1//2*((a*d+b*c+2*b*d*x)^2)^(1/2)*(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-2*((b*c+-1*a*d)^4//3+2*2^1//3*b^2//3*d^2//3*((a+b*x)*(c+d*x))^2//3+-1*2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3*(b*c+-1*a*d)^2//3))^(1/2)*((a+b*x)*(c+d*x))^1//3*((b*c+-1*a*d)^2//3*((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-2*((b*c+-1*a*d)^2//3+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3))^-1//2*(a+b*x)^-1//3*(c+d*x)^-1//3*(b*c+-1*a*d)^-1//3*(a*d+b*c+2*b*d*x)^-1*((b*c+-1*a*d)^2//3+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)*Elliptic.F(arcsin(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-1*((b*c+-1*a*d)^2//3*(1+-1*3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)),-7+-4*3^(1/2))+3//4*2^2//3*3^1//4*b^1//3*d^-2//3*((a*d+b*(c+2*d*x))^2)^-1//2*((a*d+b*c+2*b*d*x)^2)^(1/2)*(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-2*((b*c+-1*a*d)^4//3+2*2^1//3*b^2//3*d^2//3*((a+b*x)*(c+d*x))^2//3+-1*2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3*(b*c+-1*a*d)^2//3))^(1/2)*((a+b*x)*(c+d*x))^1//3*((b*c+-1*a*d)^2//3*((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-2*((b*c+-1*a*d)^2//3+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x)^-1//3*(c+d*x)^-1//3*(b*c+-1*a*d)^-1//3*(a*d+b*c+2*b*d*x)^-1*((b*c+-1*a*d)^2//3+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)*Elliptic.E(arcsin(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-1*((b*c+-1*a*d)^2//3*(1+-1*3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)),-7+-4*3^(1/2)))
@test integrate((a+b*x)^-4//3*(c+d*x)^-4//3, x) == :(-3*(a+b*x)^-1//3*(c+d*x)^-1//3*(b*c+-1*a*d)^-1+-6*d*(a+b*x)^2//3*(c+d*x)^-1//3*(b*c+-1*a*d)^-2+3*2^2//3*b^1//3*d^1//3*((a*d+b*(c+2*d*x))^2)^(1/2)*((a*d+b*c+2*b*d*x)^2)^(1/2)*((a+b*x)*(c+d*x))^1//3*(a+b*x)^-1//3*(c+d*x)^-1//3*(b*c+-1*a*d)^-2*((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-1*(a*d+b*c+2*b*d*x)^-1+2*2^1//6*3^3//4*b^1//3*d^1//3*((a*d+b*(c+2*d*x))^2)^-1//2*((a*d+b*c+2*b*d*x)^2)^(1/2)*(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-2*((b*c+-1*a*d)^4//3+2*2^1//3*b^2//3*d^2//3*((a+b*x)*(c+d*x))^2//3+-1*2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3*(b*c+-1*a*d)^2//3))^(1/2)*((a+b*x)*(c+d*x))^1//3*((b*c+-1*a*d)^2//3*((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-2*((b*c+-1*a*d)^2//3+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3))^-1//2*(a+b*x)^-1//3*(c+d*x)^-1//3*(b*c+-1*a*d)^-4//3*(a*d+b*c+2*b*d*x)^-1*((b*c+-1*a*d)^2//3+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)*Elliptic.F(arcsin(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-1*((b*c+-1*a*d)^2//3*(1+-1*3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)),-7+-4*3^(1/2))+-3//2*2^2//3*3^1//4*b^1//3*d^1//3*((a*d+b*(c+2*d*x))^2)^-1//2*((a*d+b*c+2*b*d*x)^2)^(1/2)*(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-2*((b*c+-1*a*d)^4//3+2*2^1//3*b^2//3*d^2//3*((a+b*x)*(c+d*x))^2//3+-1*2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3*(b*c+-1*a*d)^2//3))^(1/2)*((a+b*x)*(c+d*x))^1//3*((b*c+-1*a*d)^2//3*((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-2*((b*c+-1*a*d)^2//3+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x)^-1//3*(c+d*x)^-1//3*(b*c+-1*a*d)^-4//3*(a*d+b*c+2*b*d*x)^-1*((b*c+-1*a*d)^2//3+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)*Elliptic.E(arcsin(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-1*((b*c+-1*a*d)^2//3*(1+-1*3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)),-7+-4*3^(1/2)))
@test integrate((a+b*x)^-7//3*(c+d*x)^-4//3, x) == :(-3*(a+b*x)^-4//3*(c+d*x)^-1//3*(-4*a*d+4*b*c)^-1+15//2*d^2*(a+b*x)^2//3*(c+d*x)^-1//3*(b*c+-1*a*d)^-3+15//4*d*(a+b*x)^-1//3*(c+d*x)^-1//3*(b*c+-1*a*d)^-2+-15//4*2^2//3*b^1//3*d^4//3*((a*d+b*(c+2*d*x))^2)^(1/2)*((a*d+b*c+2*b*d*x)^2)^(1/2)*((a+b*x)*(c+d*x))^1//3*(a+b*x)^-1//3*(c+d*x)^-1//3*(b*c+-1*a*d)^-3*((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-1*(a*d+b*c+2*b*d*x)^-1+-5//2*2^1//6*3^3//4*b^1//3*d^4//3*((a*d+b*(c+2*d*x))^2)^-1//2*((a*d+b*c+2*b*d*x)^2)^(1/2)*(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-2*((b*c+-1*a*d)^4//3+2*2^1//3*b^2//3*d^2//3*((a+b*x)*(c+d*x))^2//3+-1*2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3*(b*c+-1*a*d)^2//3))^(1/2)*((a+b*x)*(c+d*x))^1//3*((b*c+-1*a*d)^2//3*((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-2*((b*c+-1*a*d)^2//3+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3))^-1//2*(a+b*x)^-1//3*(c+d*x)^-1//3*(b*c+-1*a*d)^-7//3*(a*d+b*c+2*b*d*x)^-1*((b*c+-1*a*d)^2//3+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)*Elliptic.F(arcsin(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-1*((b*c+-1*a*d)^2//3*(1+-1*3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)),-7+-4*3^(1/2))+15//8*2^2//3*3^1//4*b^1//3*d^4//3*((a*d+b*(c+2*d*x))^2)^-1//2*((a*d+b*c+2*b*d*x)^2)^(1/2)*(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-2*((b*c+-1*a*d)^4//3+2*2^1//3*b^2//3*d^2//3*((a+b*x)*(c+d*x))^2//3+-1*2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3*(b*c+-1*a*d)^2//3))^(1/2)*((a+b*x)*(c+d*x))^1//3*((b*c+-1*a*d)^2//3*((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-2*((b*c+-1*a*d)^2//3+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x)^-1//3*(c+d*x)^-1//3*(b*c+-1*a*d)^-7//3*(a*d+b*c+2*b*d*x)^-1*((b*c+-1*a*d)^2//3+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)*Elliptic.E(arcsin(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)^-1*((b*c+-1*a*d)^2//3*(1+-1*3^(1/2))+2^2//3*b^1//3*d^1//3*((a+b*x)*(c+d*x))^1//3)),-7+-4*3^(1/2)))
@test integrate((1+x)^-1//3*(-1+x)^1//3, x) == :(1//3*log(-1+x)+(1+x)^2//3*(-1+x)^1//3+2//3*3^(1/2)*arctan(1//3*3^(1/2)+2//3*3^(1/2)*(1+x)^1//3*(-1+x)^-1//3)+log(-1+(1+x)^1//3*(-1+x)^-1//3))
@test integrate((a+b*x)^3//2*(c+d*x)^1//4, x) == :(4//11*b^-1*(a+b*x)^5//2*(c+d*x)^1//4+-8//77*b^-1*d^-2*(a+b*x)^(1/2)*(c+d*x)^1//4*(b*c+-1*a*d)^2+1//77*b^-1*d^-1*(a+b*x)^3//2*(c+d*x)^1//4*(-4*a*d+4*b*c)+16//77*b^-5//4*d^-3*(-1*d*(b*c+-1*a*d)^-1*(a+b*x))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^13//4*Elliptic.F(arcsin(b^1//4*(c+d*x)^1//4*(b*c+-1*a*d)^-1//4),-1))
@test integrate((a+b*x)^(1/2)*(c+d*x)^1//4, x) == :(4//7*b^-1*(a+b*x)^3//2*(c+d*x)^1//4+1//21*b^-1*d^-1*(a+b*x)^(1/2)*(c+d*x)^1//4*(-4*a*d+4*b*c)+-8//21*b^-5//4*d^-2*(-1*d*(b*c+-1*a*d)^-1*(a+b*x))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^9//4*Elliptic.F(arcsin(b^1//4*(c+d*x)^1//4*(b*c+-1*a*d)^-1//4),-1))
@test integrate((a+b*x)^-1//2*(c+d*x)^1//4, x) == :(4//3*b^-1*(a+b*x)^(1/2)*(c+d*x)^1//4+4//3*b^-5//4*d^-1*(-1*d*(b*c+-1*a*d)^-1*(a+b*x))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^5//4*Elliptic.F(arcsin(b^1//4*(c+d*x)^1//4*(b*c+-1*a*d)^-1//4),-1))
@test integrate((a+b*x)^-3//2*(c+d*x)^1//4, x) == :(-2*b^-1*(a+b*x)^-1//2*(c+d*x)^1//4+2*b^-5//4*(-1*d*(b*c+-1*a*d)^-1*(a+b*x))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^1//4*Elliptic.F(arcsin(b^1//4*(c+d*x)^1//4*(b*c+-1*a*d)^-1//4),-1))
@test integrate((a+b*x)^-5//2*(c+d*x)^1//4, x) == :(-2//3*b^-1*(a+b*x)^-3//2*(c+d*x)^1//4+-1//3*d*b^-1*(a+b*x)^-1//2*(c+d*x)^1//4*(b*c+-1*a*d)^-1+-1//3*d*b^-5//4*(-1*d*(b*c+-1*a*d)^-1*(a+b*x))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^-3//4*Elliptic.F(arcsin(b^1//4*(c+d*x)^1//4*(b*c+-1*a*d)^-1//4),-1))
@test integrate((a+b*x)^-7//2*(c+d*x)^1//4, x) == :(-2//5*b^-1*(a+b*x)^-5//2*(c+d*x)^1//4+-1//15*d*b^-1*(a+b*x)^-3//2*(c+d*x)^1//4*(b*c+-1*a*d)^-1+1//6*b^-1*d^2*(a+b*x)^-1//2*(c+d*x)^1//4*(b*c+-1*a*d)^-2+1//6*b^-5//4*d^2*(-1*d*(b*c+-1*a*d)^-1*(a+b*x))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^-7//4*Elliptic.F(arcsin(b^1//4*(c+d*x)^1//4*(b*c+-1*a*d)^-1//4),-1))
@test integrate((a+b*x)^3//2*(c+d*x)^3//4, x) == :(4//13*b^-1*(a+b*x)^5//2*(c+d*x)^3//4+-8//65*b^-1*d^-2*(a+b*x)^(1/2)*(c+d*x)^3//4*(b*c+-1*a*d)^2+1//39*b^-1*d^-1*(a+b*x)^3//2*(c+d*x)^3//4*(-4*a*d+4*b*c)+-16//65*b^-7//4*d^-3*(-1*d*(b*c+-1*a*d)^-1*(a+b*x))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^15//4*Elliptic.F(arcsin(b^1//4*(c+d*x)^1//4*(b*c+-1*a*d)^-1//4),-1)+16//65*b^-7//4*d^-3*(-1*d*(b*c+-1*a*d)^-1*(a+b*x))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^15//4*Elliptic.E(arcsin(b^1//4*(c+d*x)^1//4*(b*c+-1*a*d)^-1//4),-1))
@test integrate((a+b*x)^(1/2)*(c+d*x)^3//4, x) == :(4//9*b^-1*(a+b*x)^3//2*(c+d*x)^3//4+1//15*b^-1*d^-1*(a+b*x)^(1/2)*(c+d*x)^3//4*(-4*a*d+4*b*c)+-8//15*b^-7//4*d^-2*(-1*d*(b*c+-1*a*d)^-1*(a+b*x))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^11//4*Elliptic.E(arcsin(b^1//4*(c+d*x)^1//4*(b*c+-1*a*d)^-1//4),-1)+8//15*b^-7//4*d^-2*(-1*d*(b*c+-1*a*d)^-1*(a+b*x))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^11//4*Elliptic.F(arcsin(b^1//4*(c+d*x)^1//4*(b*c+-1*a*d)^-1//4),-1))
@test integrate((a+b*x)^-1//2*(c+d*x)^3//4, x) == :(4//5*b^-1*(a+b*x)^(1/2)*(c+d*x)^3//4+-12//5*b^-7//4*d^-1*(-1*d*(b*c+-1*a*d)^-1*(a+b*x))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^7//4*Elliptic.F(arcsin(b^1//4*(c+d*x)^1//4*(b*c+-1*a*d)^-1//4),-1)+12//5*b^-7//4*d^-1*(-1*d*(b*c+-1*a*d)^-1*(a+b*x))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^7//4*Elliptic.E(arcsin(b^1//4*(c+d*x)^1//4*(b*c+-1*a*d)^-1//4),-1))
@test integrate((a+b*x)^-3//2*(c+d*x)^3//4, x) == :(-2*b^-1*(a+b*x)^-1//2*(c+d*x)^3//4+-6*b^-7//4*(-1*d*(b*c+-1*a*d)^-1*(a+b*x))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^3//4*Elliptic.F(arcsin(b^1//4*(c+d*x)^1//4*(b*c+-1*a*d)^-1//4),-1)+6*b^-7//4*(-1*d*(b*c+-1*a*d)^-1*(a+b*x))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^3//4*Elliptic.E(arcsin(b^1//4*(c+d*x)^1//4*(b*c+-1*a*d)^-1//4),-1))
@test integrate((a+b*x)^-5//2*(c+d*x)^3//4, x) == :(-2//3*b^-1*(a+b*x)^-3//2*(c+d*x)^3//4+-1*d*b^-1*(a+b*x)^-1//2*(c+d*x)^3//4*(b*c+-1*a*d)^-1+d*b^-7//4*(-1*d*(b*c+-1*a*d)^-1*(a+b*x))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^-1//4*Elliptic.E(arcsin(b^1//4*(c+d*x)^1//4*(b*c+-1*a*d)^-1//4),-1)+-1*d*b^-7//4*(-1*d*(b*c+-1*a*d)^-1*(a+b*x))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^-1//4*Elliptic.F(arcsin(b^1//4*(c+d*x)^1//4*(b*c+-1*a*d)^-1//4),-1))
@test integrate((a+b*x)^-7//2*(c+d*x)^3//4, x) == :(-2//5*b^-1*(a+b*x)^-5//2*(c+d*x)^3//4+-1//5*d*b^-1*(a+b*x)^-3//2*(c+d*x)^3//4*(b*c+-1*a*d)^-1+3//10*b^-1*d^2*(a+b*x)^-1//2*(c+d*x)^3//4*(b*c+-1*a*d)^-2+-3//10*b^-7//4*d^2*(-1*d*(b*c+-1*a*d)^-1*(a+b*x))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^-5//4*Elliptic.E(arcsin(b^1//4*(c+d*x)^1//4*(b*c+-1*a*d)^-1//4),-1)+3//10*b^-7//4*d^2*(-1*d*(b*c+-1*a*d)^-1*(a+b*x))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^-5//4*Elliptic.F(arcsin(b^1//4*(c+d*x)^1//4*(b*c+-1*a*d)^-1//4),-1))
@test integrate((a+b*x)^3//2*(c+d*x)^5//4, x) == :(4//15*b^-1*(a+b*x)^5//2*(c+d*x)^5//4+1//33*b^-2*(a+b*x)^5//2*(c+d*x)^1//4*(-4*a*d+4*b*c)+-8//231*b^-2*d^-2*(a+b*x)^(1/2)*(c+d*x)^1//4*(b*c+-1*a*d)^3+4//231*b^-2*d^-1*(a+b*x)^3//2*(c+d*x)^1//4*(b*c+-1*a*d)^2+16//231*b^-9//4*d^-3*(-1*d*(b*c+-1*a*d)^-1*(a+b*x))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^17//4*Elliptic.F(arcsin(b^1//4*(c+d*x)^1//4*(b*c+-1*a*d)^-1//4),-1))
@test integrate((a+b*x)^(1/2)*(c+d*x)^5//4, x) == :(4//11*b^-1*(a+b*x)^3//2*(c+d*x)^5//4+1//77*b^-2*(a+b*x)^3//2*(c+d*x)^1//4*(-20*a*d+20*b*c)+20//231*b^-2*d^-1*(a+b*x)^(1/2)*(c+d*x)^1//4*(b*c+-1*a*d)^2+-40//231*b^-9//4*d^-2*(-1*d*(b*c+-1*a*d)^-1*(a+b*x))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^13//4*Elliptic.F(arcsin(b^1//4*(c+d*x)^1//4*(b*c+-1*a*d)^-1//4),-1))
@test integrate((a+b*x)^-1//2*(c+d*x)^5//4, x) == :(4//7*b^-1*(a+b*x)^(1/2)*(c+d*x)^5//4+1//21*b^-2*(a+b*x)^(1/2)*(c+d*x)^1//4*(-20*a*d+20*b*c)+20//21*b^-9//4*d^-1*(-1*d*(b*c+-1*a*d)^-1*(a+b*x))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^9//4*Elliptic.F(arcsin(b^1//4*(c+d*x)^1//4*(b*c+-1*a*d)^-1//4),-1))
@test integrate((a+b*x)^-3//2*(c+d*x)^5//4, x) == :(-2*b^-1*(a+b*x)^-1//2*(c+d*x)^5//4+10//3*d*b^-2*(a+b*x)^(1/2)*(c+d*x)^1//4+10//3*b^-9//4*(-1*d*(b*c+-1*a*d)^-1*(a+b*x))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^5//4*Elliptic.F(arcsin(b^1//4*(c+d*x)^1//4*(b*c+-1*a*d)^-1//4),-1))
@test integrate((a+b*x)^-5//2*(c+d*x)^5//4, x) == :(-2//3*b^-1*(a+b*x)^-3//2*(c+d*x)^5//4+-5//3*d*b^-2*(a+b*x)^-1//2*(c+d*x)^1//4+5//3*d*b^-9//4*(-1*d*(b*c+-1*a*d)^-1*(a+b*x))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^1//4*Elliptic.F(arcsin(b^1//4*(c+d*x)^1//4*(b*c+-1*a*d)^-1//4),-1))
@test integrate((a+b*x)^-7//2*(c+d*x)^5//4, x) == :(-2//5*b^-1*(a+b*x)^-5//2*(c+d*x)^5//4+-1//3*d*b^-2*(a+b*x)^-3//2*(c+d*x)^1//4+-1//6*b^-2*d^2*(a+b*x)^-1//2*(c+d*x)^1//4*(b*c+-1*a*d)^-1+-1//6*b^-9//4*d^2*(-1*d*(b*c+-1*a*d)^-1*(a+b*x))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^-3//4*Elliptic.F(arcsin(b^1//4*(c+d*x)^1//4*(b*c+-1*a*d)^-1//4),-1))
@test integrate((a+b*x)^-9//2*(c+d*x)^5//4, x) == :(-2//7*b^-1*(a+b*x)^-7//2*(c+d*x)^5//4+-1//7*d*b^-2*(a+b*x)^-5//2*(c+d*x)^1//4+-1//42*b^-2*d^2*(a+b*x)^-3//2*(c+d*x)^1//4*(b*c+-1*a*d)^-1+5//84*b^-2*d^3*(a+b*x)^-1//2*(c+d*x)^1//4*(b*c+-1*a*d)^-2+5//84*b^-9//4*d^3*(-1*d*(b*c+-1*a*d)^-1*(a+b*x))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^-7//4*Elliptic.F(arcsin(b^1//4*(c+d*x)^1//4*(b*c+-1*a*d)^-1//4),-1))
@test integrate((a+b*x)^5//2*(c+d*x)^-1//4, x) == :(4//13*d^-1*(a+b*x)^5//2*(c+d*x)^3//4+-1//117*d^-2*(a+b*x)^3//2*(c+d*x)^3//4*(-40*a*d+40*b*c)+16//39*d^-3*(a+b*x)^(1/2)*(c+d*x)^3//4*(b*c+-1*a*d)^2+-32//39*b^-3//4*d^-4*(-1*d*(b*c+-1*a*d)^-1*(a+b*x))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^15//4*Elliptic.E(arcsin(b^1//4*(c+d*x)^1//4*(b*c+-1*a*d)^-1//4),-1)+32//39*b^-3//4*d^-4*(-1*d*(b*c+-1*a*d)^-1*(a+b*x))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^15//4*Elliptic.F(arcsin(b^1//4*(c+d*x)^1//4*(b*c+-1*a*d)^-1//4),-1))
@test integrate((a+b*x)^3//2*(c+d*x)^-1//4, x) == :(4//9*d^-1*(a+b*x)^3//2*(c+d*x)^3//4+1//15*d^-2*(a+b*x)^(1/2)*(c+d*x)^3//4*(-8*b*c+8*a*d)+-16//15*b^-3//4*d^-3*(-1*d*(b*c+-1*a*d)^-1*(a+b*x))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^11//4*Elliptic.F(arcsin(b^1//4*(c+d*x)^1//4*(b*c+-1*a*d)^-1//4),-1)+16//15*b^-3//4*d^-3*(-1*d*(b*c+-1*a*d)^-1*(a+b*x))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^11//4*Elliptic.E(arcsin(b^1//4*(c+d*x)^1//4*(b*c+-1*a*d)^-1//4),-1))
@test integrate((a+b*x)^(1/2)*(c+d*x)^-1//4, x) == :(4//5*d^-1*(a+b*x)^(1/2)*(c+d*x)^3//4+-8//5*b^-3//4*d^-2*(-1*d*(b*c+-1*a*d)^-1*(a+b*x))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^7//4*Elliptic.E(arcsin(b^1//4*(c+d*x)^1//4*(b*c+-1*a*d)^-1//4),-1)+8//5*b^-3//4*d^-2*(-1*d*(b*c+-1*a*d)^-1*(a+b*x))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^7//4*Elliptic.F(arcsin(b^1//4*(c+d*x)^1//4*(b*c+-1*a*d)^-1//4),-1))
@test integrate((a+b*x)^-1//2*(c+d*x)^-1//4, x) == :(-4*b^-3//4*d^-1*(-1*d*(b*c+-1*a*d)^-1*(a+b*x))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^3//4*Elliptic.F(arcsin(b^1//4*(c+d*x)^1//4*(b*c+-1*a*d)^-1//4),-1)+4*b^-3//4*d^-1*(-1*d*(b*c+-1*a*d)^-1*(a+b*x))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^3//4*Elliptic.E(arcsin(b^1//4*(c+d*x)^1//4*(b*c+-1*a*d)^-1//4),-1))
@test integrate((a+b*x)^-3//2*(c+d*x)^-1//4, x) == :(-2*(a+b*x)^-1//2*(c+d*x)^3//4*(b*c+-1*a*d)^-1+-2*b^-3//4*(-1*d*(b*c+-1*a*d)^-1*(a+b*x))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^-1//4*Elliptic.F(arcsin(b^1//4*(c+d*x)^1//4*(b*c+-1*a*d)^-1//4),-1)+2*b^-3//4*(-1*d*(b*c+-1*a*d)^-1*(a+b*x))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^-1//4*Elliptic.E(arcsin(b^1//4*(c+d*x)^1//4*(b*c+-1*a*d)^-1//4),-1))
@test integrate((a+b*x)^-5//2*(c+d*x)^-1//4, x) == :(-2*(a+b*x)^-3//2*(c+d*x)^3//4*(-3*a*d+3*b*c)^-1+d*(a+b*x)^-1//2*(c+d*x)^3//4*(b*c+-1*a*d)^-2+d*b^-3//4*(-1*d*(b*c+-1*a*d)^-1*(a+b*x))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^-5//4*Elliptic.F(arcsin(b^1//4*(c+d*x)^1//4*(b*c+-1*a*d)^-1//4),-1)+-1*d*b^-3//4*(-1*d*(b*c+-1*a*d)^-1*(a+b*x))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^-5//4*Elliptic.E(arcsin(b^1//4*(c+d*x)^1//4*(b*c+-1*a*d)^-1//4),-1))
@test integrate((a+b*x)^3//2*(c+d*x)^-3//4, x) == :(4//7*d^-1*(a+b*x)^3//2*(c+d*x)^1//4+1//7*d^-2*(a+b*x)^(1/2)*(c+d*x)^1//4*(-8*b*c+8*a*d)+16//7*b^-1//4*d^-3*(-1*d*(b*c+-1*a*d)^-1*(a+b*x))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^9//4*Elliptic.F(arcsin(b^1//4*(c+d*x)^1//4*(b*c+-1*a*d)^-1//4),-1))
@test integrate((a+b*x)^(1/2)*(c+d*x)^-3//4, x) == :(4//3*d^-1*(a+b*x)^(1/2)*(c+d*x)^1//4+-8//3*b^-1//4*d^-2*(-1*d*(b*c+-1*a*d)^-1*(a+b*x))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^5//4*Elliptic.F(arcsin(b^1//4*(c+d*x)^1//4*(b*c+-1*a*d)^-1//4),-1))
@test integrate((a+b*x)^-1//2*(c+d*x)^-3//4, x) == :(4*b^-1//4*d^-1*(-1*d*(b*c+-1*a*d)^-1*(a+b*x))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^1//4*Elliptic.F(arcsin(b^1//4*(c+d*x)^1//4*(b*c+-1*a*d)^-1//4),-1))
@test integrate((a+b*x)^-3//2*(c+d*x)^-3//4, x) == :(-2*(a+b*x)^-1//2*(c+d*x)^1//4*(b*c+-1*a*d)^-1+-2*b^-1//4*(-1*d*(b*c+-1*a*d)^-1*(a+b*x))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^-3//4*Elliptic.F(arcsin(b^1//4*(c+d*x)^1//4*(b*c+-1*a*d)^-1//4),-1))
@test integrate((a+b*x)^-5//2*(c+d*x)^-3//4, x) == :(-2*(a+b*x)^-3//2*(c+d*x)^1//4*(-3*a*d+3*b*c)^-1+5//3*d*(a+b*x)^-1//2*(c+d*x)^1//4*(b*c+-1*a*d)^-2+5//3*d*b^-1//4*(-1*d*(b*c+-1*a*d)^-1*(a+b*x))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^-7//4*Elliptic.F(arcsin(b^1//4*(c+d*x)^1//4*(b*c+-1*a*d)^-1//4),-1))
@test integrate((a+b*x)^5//2*(c+d*x)^-5//4, x) == :(-4*d^-1*(a+b*x)^5//2*(c+d*x)^-1//4+40//9*b*d^-2*(a+b*x)^3//2*(c+d*x)^3//4+-16//3*b*d^-3*(a+b*x)^(1/2)*(c+d*x)^3//4*(b*c+-1*a*d)+-32//3*b^1//4*d^-4*(-1*d*(b*c+-1*a*d)^-1*(a+b*x))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^11//4*Elliptic.F(arcsin(b^1//4*(c+d*x)^1//4*(b*c+-1*a*d)^-1//4),-1)+32//3*b^1//4*d^-4*(-1*d*(b*c+-1*a*d)^-1*(a+b*x))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^11//4*Elliptic.E(arcsin(b^1//4*(c+d*x)^1//4*(b*c+-1*a*d)^-1//4),-1))
@test integrate((a+b*x)^3//2*(c+d*x)^-5//4, x) == :(-4*d^-1*(a+b*x)^3//2*(c+d*x)^-1//4+24//5*b*d^-2*(a+b*x)^(1/2)*(c+d*x)^3//4+-48//5*b^1//4*d^-3*(-1*d*(b*c+-1*a*d)^-1*(a+b*x))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^7//4*Elliptic.E(arcsin(b^1//4*(c+d*x)^1//4*(b*c+-1*a*d)^-1//4),-1)+48//5*b^1//4*d^-3*(-1*d*(b*c+-1*a*d)^-1*(a+b*x))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^7//4*Elliptic.F(arcsin(b^1//4*(c+d*x)^1//4*(b*c+-1*a*d)^-1//4),-1))
@test integrate((a+b*x)^(1/2)*(c+d*x)^-5//4, x) == :(-4*d^-1*(a+b*x)^(1/2)*(c+d*x)^-1//4+-8*b^1//4*d^-2*(-1*d*(b*c+-1*a*d)^-1*(a+b*x))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^3//4*Elliptic.F(arcsin(b^1//4*(c+d*x)^1//4*(b*c+-1*a*d)^-1//4),-1)+8*b^1//4*d^-2*(-1*d*(b*c+-1*a*d)^-1*(a+b*x))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^3//4*Elliptic.E(arcsin(b^1//4*(c+d*x)^1//4*(b*c+-1*a*d)^-1//4),-1))
@test integrate((a+b*x)^-1//2*(c+d*x)^-5//4, x) == :(4*(a+b*x)^(1/2)*(c+d*x)^-1//4*(b*c+-1*a*d)^-1+-4*b^1//4*d^-1*(-1*d*(b*c+-1*a*d)^-1*(a+b*x))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^-1//4*Elliptic.E(arcsin(b^1//4*(c+d*x)^1//4*(b*c+-1*a*d)^-1//4),-1)+4*b^1//4*d^-1*(-1*d*(b*c+-1*a*d)^-1*(a+b*x))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^-1//4*Elliptic.F(arcsin(b^1//4*(c+d*x)^1//4*(b*c+-1*a*d)^-1//4),-1))
@test integrate((a+b*x)^-3//2*(c+d*x)^-5//4, x) == :(-2*(a+b*x)^-1//2*(c+d*x)^-1//4*(b*c+-1*a*d)^-1+-6*d*(a+b*x)^(1/2)*(c+d*x)^-1//4*(b*c+-1*a*d)^-2+-6*b^1//4*(-1*d*(b*c+-1*a*d)^-1*(a+b*x))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^-5//4*Elliptic.F(arcsin(b^1//4*(c+d*x)^1//4*(b*c+-1*a*d)^-1//4),-1)+6*b^1//4*(-1*d*(b*c+-1*a*d)^-1*(a+b*x))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^-5//4*Elliptic.E(arcsin(b^1//4*(c+d*x)^1//4*(b*c+-1*a*d)^-1//4),-1))
@test integrate((a+b*x)^-5//2*(c+d*x)^-5//4, x) == :(-2*(a+b*x)^-3//2*(c+d*x)^-1//4*(-3*a*d+3*b*c)^-1+7*d^2*(a+b*x)^(1/2)*(c+d*x)^-1//4*(b*c+-1*a*d)^-3+7//3*d*(a+b*x)^-1//2*(c+d*x)^-1//4*(b*c+-1*a*d)^-2+-7*d*b^1//4*(-1*d*(b*c+-1*a*d)^-1*(a+b*x))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^-9//4*Elliptic.E(arcsin(b^1//4*(c+d*x)^1//4*(b*c+-1*a*d)^-1//4),-1)+7*d*b^1//4*(-1*d*(b*c+-1*a*d)^-1*(a+b*x))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^-9//4*Elliptic.F(arcsin(b^1//4*(c+d*x)^1//4*(b*c+-1*a*d)^-1//4),-1))
@test integrate((a+b*x)^7//2*(c+d*x)^-7//4, x) == :(-4//3*d^-1*(a+b*x)^7//2*(c+d*x)^-3//4+56//33*b*d^-2*(a+b*x)^5//2*(c+d*x)^1//4+-80//33*b*d^-3*(a+b*x)^3//2*(c+d*x)^1//4*(b*c+-1*a*d)+160//33*b*d^-4*(a+b*x)^(1/2)*(c+d*x)^1//4*(b*c+-1*a*d)^2+-320//33*b^3//4*d^-5*(-1*d*(b*c+-1*a*d)^-1*(a+b*x))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^13//4*Elliptic.F(arcsin(b^1//4*(c+d*x)^1//4*(b*c+-1*a*d)^-1//4),-1))
@test integrate((a+b*x)^3//2*(c+d*x)^-7//4, x) == :(-4//3*d^-1*(a+b*x)^3//2*(c+d*x)^-3//4+8//3*b*d^-2*(a+b*x)^(1/2)*(c+d*x)^1//4+-16//3*b^3//4*d^-3*(-1*d*(b*c+-1*a*d)^-1*(a+b*x))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^5//4*Elliptic.F(arcsin(b^1//4*(c+d*x)^1//4*(b*c+-1*a*d)^-1//4),-1))
@test integrate((a+b*x)^(1/2)*(c+d*x)^-7//4, x) == :(-4//3*d^-1*(a+b*x)^(1/2)*(c+d*x)^-3//4+8//3*b^3//4*d^-2*(-1*d*(b*c+-1*a*d)^-1*(a+b*x))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^1//4*Elliptic.F(arcsin(b^1//4*(c+d*x)^1//4*(b*c+-1*a*d)^-1//4),-1))
@test integrate((a+b*x)^-1//2*(c+d*x)^-7//4, x) == :(4*(a+b*x)^(1/2)*(c+d*x)^-3//4*(-3*a*d+3*b*c)^-1+4//3*b^3//4*d^-1*(-1*d*(b*c+-1*a*d)^-1*(a+b*x))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^-3//4*Elliptic.F(arcsin(b^1//4*(c+d*x)^1//4*(b*c+-1*a*d)^-1//4),-1))
@test integrate((a+b*x)^-3//2*(c+d*x)^-7//4, x) == :(-2*(a+b*x)^-1//2*(c+d*x)^-3//4*(b*c+-1*a*d)^-1+-10//3*d*(a+b*x)^(1/2)*(c+d*x)^-3//4*(b*c+-1*a*d)^-2+-10//3*b^3//4*(-1*d*(b*c+-1*a*d)^-1*(a+b*x))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^-7//4*Elliptic.F(arcsin(b^1//4*(c+d*x)^1//4*(b*c+-1*a*d)^-1//4),-1))
@test integrate((a+b*x)^-5//2*(c+d*x)^-7//4, x) == :(-2*(a+b*x)^-3//2*(c+d*x)^-3//4*(-3*a*d+3*b*c)^-1+3*d*(a+b*x)^-1//2*(c+d*x)^-3//4*(b*c+-1*a*d)^-2+5*d^2*(a+b*x)^(1/2)*(c+d*x)^-3//4*(b*c+-1*a*d)^-3+5*d*b^3//4*(-1*d*(b*c+-1*a*d)^-1*(a+b*x))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^-11//4*Elliptic.F(arcsin(b^1//4*(c+d*x)^1//4*(b*c+-1*a*d)^-1//4),-1))
@test integrate((a+b*x)^7//2*(c+d*x)^-9//4, x) == :(-4//5*d^-1*(a+b*x)^7//2*(c+d*x)^-5//4+-56//5*b*d^-2*(a+b*x)^5//2*(c+d*x)^-1//4+112//9*b^2*d^-3*(a+b*x)^3//2*(c+d*x)^3//4+-224//15*b^2*d^-4*(a+b*x)^(1/2)*(c+d*x)^3//4*(b*c+-1*a*d)+-448//15*b^5//4*d^-5*(-1*d*(b*c+-1*a*d)^-1*(a+b*x))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^11//4*Elliptic.F(arcsin(b^1//4*(c+d*x)^1//4*(b*c+-1*a*d)^-1//4),-1)+448//15*b^5//4*d^-5*(-1*d*(b*c+-1*a*d)^-1*(a+b*x))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^11//4*Elliptic.E(arcsin(b^1//4*(c+d*x)^1//4*(b*c+-1*a*d)^-1//4),-1))
@test integrate((a+b*x)^5//2*(c+d*x)^-9//4, x) == :(-4//5*d^-1*(a+b*x)^5//2*(c+d*x)^-5//4+-8*b*d^-2*(a+b*x)^3//2*(c+d*x)^-1//4+48//5*b^2*d^-3*(a+b*x)^(1/2)*(c+d*x)^3//4+-96//5*b^5//4*d^-4*(-1*d*(b*c+-1*a*d)^-1*(a+b*x))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^7//4*Elliptic.E(arcsin(b^1//4*(c+d*x)^1//4*(b*c+-1*a*d)^-1//4),-1)+96//5*b^5//4*d^-4*(-1*d*(b*c+-1*a*d)^-1*(a+b*x))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^7//4*Elliptic.F(arcsin(b^1//4*(c+d*x)^1//4*(b*c+-1*a*d)^-1//4),-1))
@test integrate((a+b*x)^3//2*(c+d*x)^-9//4, x) == :(-4//5*d^-1*(a+b*x)^3//2*(c+d*x)^-5//4+-24//5*b*d^-2*(a+b*x)^(1/2)*(c+d*x)^-1//4+-48//5*b^5//4*d^-3*(-1*d*(b*c+-1*a*d)^-1*(a+b*x))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^3//4*Elliptic.F(arcsin(b^1//4*(c+d*x)^1//4*(b*c+-1*a*d)^-1//4),-1)+48//5*b^5//4*d^-3*(-1*d*(b*c+-1*a*d)^-1*(a+b*x))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^3//4*Elliptic.E(arcsin(b^1//4*(c+d*x)^1//4*(b*c+-1*a*d)^-1//4),-1))
@test integrate((a+b*x)^(1/2)*(c+d*x)^-9//4, x) == :(-4//5*d^-1*(a+b*x)^(1/2)*(c+d*x)^-5//4+8//5*b*d^-1*(a+b*x)^(1/2)*(c+d*x)^-1//4*(b*c+-1*a*d)^-1+-8//5*b^5//4*d^-2*(-1*d*(b*c+-1*a*d)^-1*(a+b*x))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^-1//4*Elliptic.E(arcsin(b^1//4*(c+d*x)^1//4*(b*c+-1*a*d)^-1//4),-1)+8//5*b^5//4*d^-2*(-1*d*(b*c+-1*a*d)^-1*(a+b*x))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^-1//4*Elliptic.F(arcsin(b^1//4*(c+d*x)^1//4*(b*c+-1*a*d)^-1//4),-1))
@test integrate((a+b*x)^-1//2*(c+d*x)^-9//4, x) == :(4*(a+b*x)^(1/2)*(c+d*x)^-5//4*(-5*a*d+5*b*c)^-1+12//5*b*(a+b*x)^(1/2)*(c+d*x)^-1//4*(b*c+-1*a*d)^-2+-12//5*b^5//4*d^-1*(-1*d*(b*c+-1*a*d)^-1*(a+b*x))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^-5//4*Elliptic.E(arcsin(b^1//4*(c+d*x)^1//4*(b*c+-1*a*d)^-1//4),-1)+12//5*b^5//4*d^-1*(-1*d*(b*c+-1*a*d)^-1*(a+b*x))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^-5//4*Elliptic.F(arcsin(b^1//4*(c+d*x)^1//4*(b*c+-1*a*d)^-1//4),-1))
@test integrate((a+b*x)^-3//2*(c+d*x)^-9//4, x) == :(-2*(a+b*x)^-1//2*(c+d*x)^-5//4*(b*c+-1*a*d)^-1+-14//5*d*(a+b*x)^(1/2)*(c+d*x)^-5//4*(b*c+-1*a*d)^-2+-42//5*b*d*(a+b*x)^(1/2)*(c+d*x)^-1//4*(b*c+-1*a*d)^-3+-42//5*b^5//4*(-1*d*(b*c+-1*a*d)^-1*(a+b*x))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^-9//4*Elliptic.F(arcsin(b^1//4*(c+d*x)^1//4*(b*c+-1*a*d)^-1//4),-1)+42//5*b^5//4*(-1*d*(b*c+-1*a*d)^-1*(a+b*x))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^-9//4*Elliptic.E(arcsin(b^1//4*(c+d*x)^1//4*(b*c+-1*a*d)^-1//4),-1))
@test integrate((a+b*x)^-5//2*(c+d*x)^-9//4, x) == :(-2*(a+b*x)^-3//2*(c+d*x)^-5//4*(-3*a*d+3*b*c)^-1+11//3*d*(a+b*x)^-1//2*(c+d*x)^-5//4*(b*c+-1*a*d)^-2+77//15*d^2*(a+b*x)^(1/2)*(c+d*x)^-5//4*(b*c+-1*a*d)^-3+77//5*b*d^2*(a+b*x)^(1/2)*(c+d*x)^-1//4*(b*c+-1*a*d)^-4+-77//5*d*b^5//4*(-1*d*(b*c+-1*a*d)^-1*(a+b*x))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^-13//4*Elliptic.E(arcsin(b^1//4*(c+d*x)^1//4*(b*c+-1*a*d)^-1//4),-1)+77//5*d*b^5//4*(-1*d*(b*c+-1*a*d)^-1*(a+b*x))^(1/2)*(a+b*x)^-1//2*(b*c+-1*a*d)^-13//4*Elliptic.F(arcsin(b^1//4*(c+d*x)^1//4*(b*c+-1*a*d)^-1//4),-1))
@test integrate((a+b*x)^3//4*(c+d*x)^5//4, x) == :(1//3*b^-1*(a+b*x)^7//4*(c+d*x)^5//4+-5//64*b^-9//4*d^-7//4*(b*c+-1*a*d)^3*arctanh(b^-1//4*d^1//4*(a+b*x)^1//4*(c+d*x)^-1//4)+1//24*b^-2*(a+b*x)^7//4*(c+d*x)^1//4*(-5*a*d+5*b*c)+5//64*b^-9//4*d^-7//4*(b*c+-1*a*d)^3*arctan(b^-1//4*d^1//4*(a+b*x)^1//4*(c+d*x)^-1//4)+5//96*b^-2*d^-1*(a+b*x)^3//4*(c+d*x)^1//4*(b*c+-1*a*d)^2)
@test integrate((a+b*x)^-1//4*(c+d*x)^5//4, x) == :((1/2)*b^-1*(a+b*x)^3//4*(c+d*x)^5//4+-5//16*b^-9//4*d^-3//4*(b*c+-1*a*d)^2*arctan(b^-1//4*d^1//4*(a+b*x)^1//4*(c+d*x)^-1//4)+1//8*b^-2*(a+b*x)^3//4*(c+d*x)^1//4*(-5*a*d+5*b*c)+5//16*b^-9//4*d^-3//4*(b*c+-1*a*d)^2*arctanh(b^-1//4*d^1//4*(a+b*x)^1//4*(c+d*x)^-1//4))
@test integrate((a+b*x)^-5//4*(c+d*x)^5//4, x) == :(-4*b^-1*(a+b*x)^-1//4*(c+d*x)^5//4+5*d*b^-2*(a+b*x)^3//4*(c+d*x)^1//4+-5//2*b^-9//4*d^1//4*(b*c+-1*a*d)*arctan(b^-1//4*d^1//4*(a+b*x)^1//4*(c+d*x)^-1//4)+5//2*b^-9//4*d^1//4*(b*c+-1*a*d)*arctanh(b^-1//4*d^1//4*(a+b*x)^1//4*(c+d*x)^-1//4))
@test integrate((a+b*x)^-9//4*(c+d*x)^5//4, x) == :(-2*b^-9//4*d^5//4*arctan(b^-1//4*d^1//4*(a+b*x)^1//4*(c+d*x)^-1//4)+2*b^-9//4*d^5//4*arctanh(b^-1//4*d^1//4*(a+b*x)^1//4*(c+d*x)^-1//4)+-4//5*b^-1*(a+b*x)^-5//4*(c+d*x)^5//4+-4*d*b^-2*(a+b*x)^-1//4*(c+d*x)^1//4)
@test integrate((a+b*x)^-13//4*(c+d*x)^5//4, x) == :(-4*(a+b*x)^-9//4*(c+d*x)^9//4*(-9*a*d+9*b*c)^-1)
@test integrate((a+b*x)^-17//4*(c+d*x)^5//4, x) == :(-4*(a+b*x)^-13//4*(c+d*x)^9//4*(-13*a*d+13*b*c)^-1+16//117*d*(a+b*x)^-9//4*(c+d*x)^9//4*(b*c+-1*a*d)^-2)
@test integrate((a+b*x)^-21//4*(c+d*x)^5//4, x) == :(-4*(a+b*x)^-17//4*(c+d*x)^9//4*(-17*a*d+17*b*c)^-1+-128//1989*d^2*(a+b*x)^-9//4*(c+d*x)^9//4*(b*c+-1*a*d)^-3+32//221*d*(a+b*x)^-13//4*(c+d*x)^9//4*(b*c+-1*a*d)^-2)
@test integrate((a+b*x)^-25//4*(c+d*x)^5//4, x) == :(-4*(a+b*x)^-21//4*(c+d*x)^9//4*(-21*a*d+21*b*c)^-1+-128//1547*d^2*(a+b*x)^-13//4*(c+d*x)^9//4*(b*c+-1*a*d)^-3+16//119*d*(a+b*x)^-17//4*(c+d*x)^9//4*(b*c+-1*a*d)^-2+512//13923*d^3*(a+b*x)^-9//4*(c+d*x)^9//4*(b*c+-1*a*d)^-4)
@test integrate((a+b*x)^5//4*(c+d*x)^5//4, x) == :(2//7*b^-1*(a+b*x)^9//4*(c+d*x)^5//4+1//7*b^-2*(a+b*x)^9//4*(c+d*x)^1//4*(b*c+-1*a*d)+-5//84*b^-2*d^-2*(a+b*x)^1//4*(c+d*x)^1//4*(b*c+-1*a*d)^3+1//42*b^-2*d^-1*(a+b*x)^5//4*(c+d*x)^1//4*(b*c+-1*a*d)^2+5//336*2^(1/2)*b^-9//4*d^-9//4*((a*d+b*(c+2*d*x))^2)^-1//2*((a*d+b*c+2*b*d*x)^2)^(1/2)*((a+b*x)*(c+d*x))^3//4*((1+2*b^(1/2)*d^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(b*c+-1*a*d)^-1)^-2*(a*d+b*(c+2*d*x))^2*(b*c+-1*a*d)^-2)^(1/2)*(a+b*x)^-3//4*(c+d*x)^-3//4*(b*c+-1*a*d)^9//2*(a*d+b*c+2*b*d*x)^-1*(1+2*b^(1/2)*d^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(b*c+-1*a*d)^-1)*Elliptic.F(2*arctan(2^(1/2)*b^1//4*d^1//4*((a+b*x)*(c+d*x))^1//4*(b*c+-1*a*d)^-1//2),1/2))
@test integrate((a+b*x)^1//4*(c+d*x)^5//4, x) == :(2//5*b^-1*(a+b*x)^5//4*(c+d*x)^5//4+1//3*b^-2*(a+b*x)^5//4*(c+d*x)^1//4*(b*c+-1*a*d)+1//6*b^-2*d^-1*(a+b*x)^1//4*(c+d*x)^1//4*(b*c+-1*a*d)^2+-1//24*2^(1/2)*b^-9//4*d^-5//4*((a*d+b*(c+2*d*x))^2)^-1//2*((a*d+b*c+2*b*d*x)^2)^(1/2)*((a+b*x)*(c+d*x))^3//4*((1+2*b^(1/2)*d^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(b*c+-1*a*d)^-1)^-2*(a*d+b*(c+2*d*x))^2*(b*c+-1*a*d)^-2)^(1/2)*(a+b*x)^-3//4*(c+d*x)^-3//4*(b*c+-1*a*d)^7//2*(a*d+b*c+2*b*d*x)^-1*(1+2*b^(1/2)*d^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(b*c+-1*a*d)^-1)*Elliptic.F(2*arctan(2^(1/2)*b^1//4*d^1//4*((a+b*x)*(c+d*x))^1//4*(b*c+-1*a*d)^-1//2),1/2))
@test integrate((a+b*x)^-3//4*(c+d*x)^5//4, x) == :(2//3*b^-1*(a+b*x)^1//4*(c+d*x)^5//4+1//3*b^-2*(a+b*x)^1//4*(c+d*x)^1//4*(-5*a*d+5*b*c)+5//12*2^(1/2)*b^-9//4*d^-1//4*((a*d+b*(c+2*d*x))^2)^-1//2*((a*d+b*c+2*b*d*x)^2)^(1/2)*((a+b*x)*(c+d*x))^3//4*((1+2*b^(1/2)*d^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(b*c+-1*a*d)^-1)^-2*(a*d+b*(c+2*d*x))^2*(b*c+-1*a*d)^-2)^(1/2)*(a+b*x)^-3//4*(c+d*x)^-3//4*(b*c+-1*a*d)^5//2*(a*d+b*c+2*b*d*x)^-1*(1+2*b^(1/2)*d^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(b*c+-1*a*d)^-1)*Elliptic.F(2*arctan(2^(1/2)*b^1//4*d^1//4*((a+b*x)*(c+d*x))^1//4*(b*c+-1*a*d)^-1//2),1/2))
@test integrate((a+b*x)^-7//4*(c+d*x)^5//4, x) == :(-4//3*b^-1*(a+b*x)^-3//4*(c+d*x)^5//4+10//3*d*b^-2*(a+b*x)^1//4*(c+d*x)^1//4+5//6*2^(1/2)*b^-9//4*d^3//4*((a*d+b*(c+2*d*x))^2)^-1//2*((a*d+b*c+2*b*d*x)^2)^(1/2)*((a+b*x)*(c+d*x))^3//4*((1+2*b^(1/2)*d^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(b*c+-1*a*d)^-1)^-2*(a*d+b*(c+2*d*x))^2*(b*c+-1*a*d)^-2)^(1/2)*(a+b*x)^-3//4*(c+d*x)^-3//4*(b*c+-1*a*d)^3//2*(a*d+b*c+2*b*d*x)^-1*(1+2*b^(1/2)*d^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(b*c+-1*a*d)^-1)*Elliptic.F(2*arctan(2^(1/2)*b^1//4*d^1//4*((a+b*x)*(c+d*x))^1//4*(b*c+-1*a*d)^-1//2),1/2))
@test integrate((a+b*x)^-11//4*(c+d*x)^5//4, x) == :(-4//7*b^-1*(a+b*x)^-7//4*(c+d*x)^5//4+-20//21*d*b^-2*(a+b*x)^-3//4*(c+d*x)^1//4+5//21*2^(1/2)*b^-9//4*d^7//4*((a*d+b*(c+2*d*x))^2)^-1//2*((a*d+b*c+2*b*d*x)^2)^(1/2)*((a+b*x)*(c+d*x))^3//4*((1+2*b^(1/2)*d^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(b*c+-1*a*d)^-1)^-2*(a*d+b*(c+2*d*x))^2*(b*c+-1*a*d)^-2)^(1/2)*(a+b*x)^-3//4*(c+d*x)^-3//4*(b*c+-1*a*d)^(1/2)*(a*d+b*c+2*b*d*x)^-1*(1+2*b^(1/2)*d^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(b*c+-1*a*d)^-1)*Elliptic.F(2*arctan(2^(1/2)*b^1//4*d^1//4*((a+b*x)*(c+d*x))^1//4*(b*c+-1*a*d)^-1//2),1/2))
@test integrate((a+b*x)^-15//4*(c+d*x)^5//4, x) == :(-4//11*b^-1*(a+b*x)^-11//4*(c+d*x)^5//4+-20//77*d*b^-2*(a+b*x)^-7//4*(c+d*x)^1//4+-20//231*b^-2*d^2*(a+b*x)^-3//4*(c+d*x)^1//4*(b*c+-1*a*d)^-1+-10//231*2^(1/2)*b^-9//4*d^11//4*((a*d+b*(c+2*d*x))^2)^-1//2*((a*d+b*c+2*b*d*x)^2)^(1/2)*((a+b*x)*(c+d*x))^3//4*((1+2*b^(1/2)*d^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(b*c+-1*a*d)^-1)^-2*(a*d+b*(c+2*d*x))^2*(b*c+-1*a*d)^-2)^(1/2)*(a+b*x)^-3//4*(c+d*x)^-3//4*(b*c+-1*a*d)^-1//2*(a*d+b*c+2*b*d*x)^-1*(1+2*b^(1/2)*d^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(b*c+-1*a*d)^-1)*Elliptic.F(2*arctan(2^(1/2)*b^1//4*d^1//4*((a+b*x)*(c+d*x))^1//4*(b*c+-1*a*d)^-1//2),1/2))
@test integrate((a+b*x)^-19//4*(c+d*x)^5//4, x) == :(-4//15*b^-1*(a+b*x)^-15//4*(c+d*x)^5//4+-4//33*d*b^-2*(a+b*x)^-11//4*(c+d*x)^1//4+-4//231*b^-2*d^2*(a+b*x)^-7//4*(c+d*x)^1//4*(b*c+-1*a*d)^-1+8//231*b^-2*d^3*(a+b*x)^-3//4*(c+d*x)^1//4*(b*c+-1*a*d)^-2+4//231*2^(1/2)*b^-9//4*d^15//4*((a*d+b*(c+2*d*x))^2)^-1//2*((a*d+b*c+2*b*d*x)^2)^(1/2)*((a+b*x)*(c+d*x))^3//4*((1+2*b^(1/2)*d^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(b*c+-1*a*d)^-1)^-2*(a*d+b*(c+2*d*x))^2*(b*c+-1*a*d)^-2)^(1/2)*(a+b*x)^-3//4*(c+d*x)^-3//4*(b*c+-1*a*d)^-3//2*(a*d+b*c+2*b*d*x)^-1*(1+2*b^(1/2)*d^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(b*c+-1*a*d)^-1)*Elliptic.F(2*arctan(2^(1/2)*b^1//4*d^1//4*((a+b*x)*(c+d*x))^1//4*(b*c+-1*a*d)^-1//2),1/2))
@test integrate((a+b*x)^5//4*(c+d*x)^-1//4, x) == :((1/2)*d^-1*(a+b*x)^5//4*(c+d*x)^3//4+1//8*d^-2*(a+b*x)^1//4*(c+d*x)^3//4*(-5*b*c+5*a*d)+5//16*b^-3//4*d^-9//4*(b*c+-1*a*d)^2*arctan(b^-1//4*d^1//4*(a+b*x)^1//4*(c+d*x)^-1//4)+5//16*b^-3//4*d^-9//4*(b*c+-1*a*d)^2*arctanh(b^-1//4*d^1//4*(a+b*x)^1//4*(c+d*x)^-1//4))
@test integrate((a+b*x)^1//4*(c+d*x)^-1//4, x) == :(d^-1*(a+b*x)^1//4*(c+d*x)^3//4+-1//2*b^-3//4*d^-5//4*(b*c+-1*a*d)*arctan(b^-1//4*d^1//4*(a+b*x)^1//4*(c+d*x)^-1//4)+-1//2*b^-3//4*d^-5//4*(b*c+-1*a*d)*arctanh(b^-1//4*d^1//4*(a+b*x)^1//4*(c+d*x)^-1//4))
@test integrate((a+b*x)^-3//4*(c+d*x)^-1//4, x) == :(2*b^-3//4*d^-1//4*arctan(b^-1//4*d^1//4*(a+b*x)^1//4*(c+d*x)^-1//4)+2*b^-3//4*d^-1//4*arctanh(b^-1//4*d^1//4*(a+b*x)^1//4*(c+d*x)^-1//4))
@test integrate((a+b*x)^-7//4*(c+d*x)^-1//4, x) == :(-4*(a+b*x)^-3//4*(c+d*x)^3//4*(-3*a*d+3*b*c)^-1)
@test integrate((a+b*x)^-11//4*(c+d*x)^-1//4, x) == :(-4*(a+b*x)^-7//4*(c+d*x)^3//4*(-7*a*d+7*b*c)^-1+16//21*d*(a+b*x)^-3//4*(c+d*x)^3//4*(b*c+-1*a*d)^-2)
@test integrate((a+b*x)^-15//4*(c+d*x)^-1//4, x) == :(-4*(a+b*x)^-11//4*(c+d*x)^3//4*(-11*a*d+11*b*c)^-1+-128//231*d^2*(a+b*x)^-3//4*(c+d*x)^3//4*(b*c+-1*a*d)^-3+32//77*d*(a+b*x)^-7//4*(c+d*x)^3//4*(b*c+-1*a*d)^-2)
@test integrate((a+b*x)^-19//4*(c+d*x)^-1//4, x) == :(-4*(a+b*x)^-15//4*(c+d*x)^3//4*(-15*a*d+15*b*c)^-1+-128//385*d^2*(a+b*x)^-7//4*(c+d*x)^3//4*(b*c+-1*a*d)^-3+16//55*d*(a+b*x)^-11//4*(c+d*x)^3//4*(b*c+-1*a*d)^-2+512//1155*d^3*(a+b*x)^-3//4*(c+d*x)^3//4*(b*c+-1*a*d)^-4)
@test integrate((a+b*x)^7//4*(c+d*x)^-1//4, x) == :(2//5*d^-1*(a+b*x)^7//4*(c+d*x)^3//4+-1//15*d^-2*(a+b*x)^3//4*(c+d*x)^3//4*(-7*a*d+7*b*c)+1//10*b^-1//2*d^-5//2*((a*d+b*(c+2*d*x))^2)^(1/2)*((a*d+b*c+2*b*d*x)^2)^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(1+2*b^(1/2)*d^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(b*c+-1*a*d)^-1)^-1*(a+b*x)^-1//4*(c+d*x)^-1//4*(a*d+b*c+2*b*d*x)^-1*(-7*a*d+7*b*c)+-7//20*2^(1/2)*b^-3//4*d^-11//4*((a*d+b*(c+2*d*x))^2)^-1//2*((a*d+b*c+2*b*d*x)^2)^(1/2)*((a+b*x)*(c+d*x))^1//4*((1+2*b^(1/2)*d^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(b*c+-1*a*d)^-1)^-2*(a*d+b*(c+2*d*x))^2*(b*c+-1*a*d)^-2)^(1/2)*(a+b*x)^-1//4*(c+d*x)^-1//4*(b*c+-1*a*d)^7//2*(a*d+b*c+2*b*d*x)^-1*(1+2*b^(1/2)*d^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(b*c+-1*a*d)^-1)*Elliptic.E(2*arctan(2^(1/2)*b^1//4*d^1//4*((a+b*x)*(c+d*x))^1//4*(b*c+-1*a*d)^-1//2),1/2)+7//40*2^(1/2)*b^-3//4*d^-11//4*((a*d+b*(c+2*d*x))^2)^-1//2*((a*d+b*c+2*b*d*x)^2)^(1/2)*((a+b*x)*(c+d*x))^1//4*((1+2*b^(1/2)*d^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(b*c+-1*a*d)^-1)^-2*(a*d+b*(c+2*d*x))^2*(b*c+-1*a*d)^-2)^(1/2)*(a+b*x)^-1//4*(c+d*x)^-1//4*(b*c+-1*a*d)^7//2*(a*d+b*c+2*b*d*x)^-1*(1+2*b^(1/2)*d^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(b*c+-1*a*d)^-1)*Elliptic.F(2*arctan(2^(1/2)*b^1//4*d^1//4*((a+b*x)*(c+d*x))^1//4*(b*c+-1*a*d)^-1//2),1/2))
@test integrate((a+b*x)^3//4*(c+d*x)^-1//4, x) == :(2//3*d^-1*(a+b*x)^3//4*(c+d*x)^3//4+-1*b^-1//2*d^-3//2*((a*d+b*(c+2*d*x))^2)^(1/2)*((a*d+b*c+2*b*d*x)^2)^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(1+2*b^(1/2)*d^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(b*c+-1*a*d)^-1)^-1*(a+b*x)^-1//4*(c+d*x)^-1//4*(a*d+b*c+2*b*d*x)^-1+(1/2)*2^(1/2)*b^-3//4*d^-7//4*((a*d+b*(c+2*d*x))^2)^-1//2*((a*d+b*c+2*b*d*x)^2)^(1/2)*((a+b*x)*(c+d*x))^1//4*((1+2*b^(1/2)*d^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(b*c+-1*a*d)^-1)^-2*(a*d+b*(c+2*d*x))^2*(b*c+-1*a*d)^-2)^(1/2)*(a+b*x)^-1//4*(c+d*x)^-1//4*(b*c+-1*a*d)^5//2*(a*d+b*c+2*b*d*x)^-1*(1+2*b^(1/2)*d^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(b*c+-1*a*d)^-1)*Elliptic.E(2*arctan(2^(1/2)*b^1//4*d^1//4*((a+b*x)*(c+d*x))^1//4*(b*c+-1*a*d)^-1//2),1/2)+-1//4*2^(1/2)*b^-3//4*d^-7//4*((a*d+b*(c+2*d*x))^2)^-1//2*((a*d+b*c+2*b*d*x)^2)^(1/2)*((a+b*x)*(c+d*x))^1//4*((1+2*b^(1/2)*d^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(b*c+-1*a*d)^-1)^-2*(a*d+b*(c+2*d*x))^2*(b*c+-1*a*d)^-2)^(1/2)*(a+b*x)^-1//4*(c+d*x)^-1//4*(b*c+-1*a*d)^5//2*(a*d+b*c+2*b*d*x)^-1*(1+2*b^(1/2)*d^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(b*c+-1*a*d)^-1)*Elliptic.F(2*arctan(2^(1/2)*b^1//4*d^1//4*((a+b*x)*(c+d*x))^1//4*(b*c+-1*a*d)^-1//2),1/2))
@test integrate((a+b*x)^-1//4*(c+d*x)^-1//4, x) == :(2*b^-1//2*d^-1//2*((a*d+b*(c+2*d*x))^2)^(1/2)*((a*d+b*c+2*b*d*x)^2)^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(1+2*b^(1/2)*d^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(b*c+-1*a*d)^-1)^-1*(a+b*x)^-1//4*(c+d*x)^-1//4*(b*c+-1*a*d)^-1*(a*d+b*c+2*b*d*x)^-1+(1/2)*2^(1/2)*b^-3//4*d^-3//4*((a*d+b*(c+2*d*x))^2)^-1//2*((a*d+b*c+2*b*d*x)^2)^(1/2)*((a+b*x)*(c+d*x))^1//4*((1+2*b^(1/2)*d^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(b*c+-1*a*d)^-1)^-2*(a*d+b*(c+2*d*x))^2*(b*c+-1*a*d)^-2)^(1/2)*(a+b*x)^-1//4*(c+d*x)^-1//4*(b*c+-1*a*d)^3//2*(a*d+b*c+2*b*d*x)^-1*(1+2*b^(1/2)*d^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(b*c+-1*a*d)^-1)*Elliptic.F(2*arctan(2^(1/2)*b^1//4*d^1//4*((a+b*x)*(c+d*x))^1//4*(b*c+-1*a*d)^-1//2),1/2)+-1*2^(1/2)*b^-3//4*d^-3//4*((a*d+b*(c+2*d*x))^2)^-1//2*((a*d+b*c+2*b*d*x)^2)^(1/2)*((a+b*x)*(c+d*x))^1//4*((1+2*b^(1/2)*d^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(b*c+-1*a*d)^-1)^-2*(a*d+b*(c+2*d*x))^2*(b*c+-1*a*d)^-2)^(1/2)*(a+b*x)^-1//4*(c+d*x)^-1//4*(b*c+-1*a*d)^3//2*(a*d+b*c+2*b*d*x)^-1*(1+2*b^(1/2)*d^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(b*c+-1*a*d)^-1)*Elliptic.E(2*arctan(2^(1/2)*b^1//4*d^1//4*((a+b*x)*(c+d*x))^1//4*(b*c+-1*a*d)^-1//2),1/2))
@test integrate((a+b*x)^-5//4*(c+d*x)^-1//4, x) == :(-4*(a+b*x)^-1//4*(c+d*x)^3//4*(b*c+-1*a*d)^-1+4*b^-1//2*d^(1/2)*((a*d+b*(c+2*d*x))^2)^(1/2)*((a*d+b*c+2*b*d*x)^2)^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(1+2*b^(1/2)*d^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(b*c+-1*a*d)^-1)^-1*(a+b*x)^-1//4*(c+d*x)^-1//4*(b*c+-1*a*d)^-2*(a*d+b*c+2*b*d*x)^-1+2^(1/2)*b^-3//4*d^1//4*((a*d+b*(c+2*d*x))^2)^-1//2*((a*d+b*c+2*b*d*x)^2)^(1/2)*((a+b*x)*(c+d*x))^1//4*((1+2*b^(1/2)*d^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(b*c+-1*a*d)^-1)^-2*(a*d+b*(c+2*d*x))^2*(b*c+-1*a*d)^-2)^(1/2)*(a+b*x)^-1//4*(c+d*x)^-1//4*(b*c+-1*a*d)^(1/2)*(a*d+b*c+2*b*d*x)^-1*(1+2*b^(1/2)*d^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(b*c+-1*a*d)^-1)*Elliptic.F(2*arctan(2^(1/2)*b^1//4*d^1//4*((a+b*x)*(c+d*x))^1//4*(b*c+-1*a*d)^-1//2),1/2)+-2*2^(1/2)*b^-3//4*d^1//4*((a*d+b*(c+2*d*x))^2)^-1//2*((a*d+b*c+2*b*d*x)^2)^(1/2)*((a+b*x)*(c+d*x))^1//4*((1+2*b^(1/2)*d^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(b*c+-1*a*d)^-1)^-2*(a*d+b*(c+2*d*x))^2*(b*c+-1*a*d)^-2)^(1/2)*(a+b*x)^-1//4*(c+d*x)^-1//4*(b*c+-1*a*d)^(1/2)*(a*d+b*c+2*b*d*x)^-1*(1+2*b^(1/2)*d^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(b*c+-1*a*d)^-1)*Elliptic.E(2*arctan(2^(1/2)*b^1//4*d^1//4*((a+b*x)*(c+d*x))^1//4*(b*c+-1*a*d)^-1//2),1/2))
@test integrate((a+b*x)^-9//4*(c+d*x)^-1//4, x) == :(-4*(a+b*x)^-5//4*(c+d*x)^3//4*(-5*a*d+5*b*c)^-1+8//5*d*(a+b*x)^-1//4*(c+d*x)^3//4*(b*c+-1*a*d)^-2+-8//5*b^-1//2*d^3//2*((a*d+b*(c+2*d*x))^2)^(1/2)*((a*d+b*c+2*b*d*x)^2)^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(1+2*b^(1/2)*d^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(b*c+-1*a*d)^-1)^-1*(a+b*x)^-1//4*(c+d*x)^-1//4*(b*c+-1*a*d)^-3*(a*d+b*c+2*b*d*x)^-1+-2//5*2^(1/2)*b^-3//4*d^5//4*((a*d+b*(c+2*d*x))^2)^-1//2*((a*d+b*c+2*b*d*x)^2)^(1/2)*((a+b*x)*(c+d*x))^1//4*((1+2*b^(1/2)*d^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(b*c+-1*a*d)^-1)^-2*(a*d+b*(c+2*d*x))^2*(b*c+-1*a*d)^-2)^(1/2)*(a+b*x)^-1//4*(c+d*x)^-1//4*(b*c+-1*a*d)^-1//2*(a*d+b*c+2*b*d*x)^-1*(1+2*b^(1/2)*d^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(b*c+-1*a*d)^-1)*Elliptic.F(2*arctan(2^(1/2)*b^1//4*d^1//4*((a+b*x)*(c+d*x))^1//4*(b*c+-1*a*d)^-1//2),1/2)+4//5*2^(1/2)*b^-3//4*d^5//4*((a*d+b*(c+2*d*x))^2)^-1//2*((a*d+b*c+2*b*d*x)^2)^(1/2)*((a+b*x)*(c+d*x))^1//4*((1+2*b^(1/2)*d^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(b*c+-1*a*d)^-1)^-2*(a*d+b*(c+2*d*x))^2*(b*c+-1*a*d)^-2)^(1/2)*(a+b*x)^-1//4*(c+d*x)^-1//4*(b*c+-1*a*d)^-1//2*(a*d+b*c+2*b*d*x)^-1*(1+2*b^(1/2)*d^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(b*c+-1*a*d)^-1)*Elliptic.E(2*arctan(2^(1/2)*b^1//4*d^1//4*((a+b*x)*(c+d*x))^1//4*(b*c+-1*a*d)^-1//2),1/2))
@test integrate((a+b*x)^7//4*(c+d*x)^-3//4, x) == :((1/2)*d^-1*(a+b*x)^7//4*(c+d*x)^1//4+-21//16*b^-1//4*d^-11//4*(b*c+-1*a*d)^2*arctan(b^-1//4*d^1//4*(a+b*x)^1//4*(c+d*x)^-1//4)+1//8*d^-2*(a+b*x)^3//4*(c+d*x)^1//4*(-7*b*c+7*a*d)+21//16*b^-1//4*d^-11//4*(b*c+-1*a*d)^2*arctanh(b^-1//4*d^1//4*(a+b*x)^1//4*(c+d*x)^-1//4))
@test integrate((a+b*x)^3//4*(c+d*x)^-3//4, x) == :(d^-1*(a+b*x)^3//4*(c+d*x)^1//4+(1/2)*b^-1//4*d^-7//4*(-3*a*d+3*b*c)*arctan(b^-1//4*d^1//4*(a+b*x)^1//4*(c+d*x)^-1//4)+-1//2*b^-1//4*d^-7//4*(-3*a*d+3*b*c)*arctanh(b^-1//4*d^1//4*(a+b*x)^1//4*(c+d*x)^-1//4))
@test integrate((a+b*x)^-1//4*(c+d*x)^-3//4, x) == :(-2*b^-1//4*d^-3//4*arctan(b^-1//4*d^1//4*(a+b*x)^1//4*(c+d*x)^-1//4)+2*b^-1//4*d^-3//4*arctanh(b^-1//4*d^1//4*(a+b*x)^1//4*(c+d*x)^-1//4))
@test integrate((a+b*x)^-5//4*(c+d*x)^-3//4, x) == :(-4*(a+b*x)^-1//4*(c+d*x)^1//4*(b*c+-1*a*d)^-1)
@test integrate((a+b*x)^-9//4*(c+d*x)^-3//4, x) == :(-4*(a+b*x)^-5//4*(c+d*x)^1//4*(-5*a*d+5*b*c)^-1+16//5*d*(a+b*x)^-1//4*(c+d*x)^1//4*(b*c+-1*a*d)^-2)
@test integrate((a+b*x)^-13//4*(c+d*x)^-3//4, x) == :(-4*(a+b*x)^-9//4*(c+d*x)^1//4*(-9*a*d+9*b*c)^-1+-128//45*d^2*(a+b*x)^-1//4*(c+d*x)^1//4*(b*c+-1*a*d)^-3+32//45*d*(a+b*x)^-5//4*(c+d*x)^1//4*(b*c+-1*a*d)^-2)
@test integrate((a+b*x)^-17//4*(c+d*x)^-3//4, x) == :(-4*(a+b*x)^-13//4*(c+d*x)^1//4*(-13*a*d+13*b*c)^-1+-128//195*d^2*(a+b*x)^-5//4*(c+d*x)^1//4*(b*c+-1*a*d)^-3+16//39*d*(a+b*x)^-9//4*(c+d*x)^1//4*(b*c+-1*a*d)^-2+512//195*d^3*(a+b*x)^-1//4*(c+d*x)^1//4*(b*c+-1*a*d)^-4)
@test integrate((a+b*x)^5//4*(c+d*x)^-3//4, x) == :(2//3*d^-1*(a+b*x)^5//4*(c+d*x)^1//4+-1//3*d^-2*(a+b*x)^1//4*(c+d*x)^1//4*(-5*a*d+5*b*c)+5//12*2^(1/2)*b^-1//4*d^-9//4*((a*d+b*(c+2*d*x))^2)^-1//2*((a*d+b*c+2*b*d*x)^2)^(1/2)*((a+b*x)*(c+d*x))^3//4*((1+2*b^(1/2)*d^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(b*c+-1*a*d)^-1)^-2*(a*d+b*(c+2*d*x))^2*(b*c+-1*a*d)^-2)^(1/2)*(a+b*x)^-3//4*(c+d*x)^-3//4*(b*c+-1*a*d)^5//2*(a*d+b*c+2*b*d*x)^-1*(1+2*b^(1/2)*d^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(b*c+-1*a*d)^-1)*Elliptic.F(2*arctan(2^(1/2)*b^1//4*d^1//4*((a+b*x)*(c+d*x))^1//4*(b*c+-1*a*d)^-1//2),1/2))
@test integrate((a+b*x)^1//4*(c+d*x)^-3//4, x) == :(2*d^-1*(a+b*x)^1//4*(c+d*x)^1//4+-1//2*2^(1/2)*b^-1//4*d^-5//4*((a*d+b*(c+2*d*x))^2)^-1//2*((a*d+b*c+2*b*d*x)^2)^(1/2)*((a+b*x)*(c+d*x))^3//4*((1+2*b^(1/2)*d^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(b*c+-1*a*d)^-1)^-2*(a*d+b*(c+2*d*x))^2*(b*c+-1*a*d)^-2)^(1/2)*(a+b*x)^-3//4*(c+d*x)^-3//4*(b*c+-1*a*d)^3//2*(a*d+b*c+2*b*d*x)^-1*(1+2*b^(1/2)*d^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(b*c+-1*a*d)^-1)*Elliptic.F(2*arctan(2^(1/2)*b^1//4*d^1//4*((a+b*x)*(c+d*x))^1//4*(b*c+-1*a*d)^-1//2),1/2))
@test integrate((a+b*x)^-3//4*(c+d*x)^-3//4, x) == :(2^(1/2)*b^-1//4*d^-1//4*((a*d+b*(c+2*d*x))^2)^-1//2*((a*d+b*c+2*b*d*x)^2)^(1/2)*((a+b*x)*(c+d*x))^3//4*((1+2*b^(1/2)*d^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(b*c+-1*a*d)^-1)^-2*(a*d+b*(c+2*d*x))^2*(b*c+-1*a*d)^-2)^(1/2)*(a+b*x)^-3//4*(c+d*x)^-3//4*(b*c+-1*a*d)^(1/2)*(a*d+b*c+2*b*d*x)^-1*(1+2*b^(1/2)*d^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(b*c+-1*a*d)^-1)*Elliptic.F(2*arctan(2^(1/2)*b^1//4*d^1//4*((a+b*x)*(c+d*x))^1//4*(b*c+-1*a*d)^-1//2),1/2))
@test integrate((a+b*x)^-7//4*(c+d*x)^-3//4, x) == :(-4*(a+b*x)^-3//4*(c+d*x)^1//4*(-3*a*d+3*b*c)^-1+-2//3*2^(1/2)*b^-1//4*d^3//4*((a*d+b*(c+2*d*x))^2)^-1//2*((a*d+b*c+2*b*d*x)^2)^(1/2)*((a+b*x)*(c+d*x))^3//4*((1+2*b^(1/2)*d^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(b*c+-1*a*d)^-1)^-2*(a*d+b*(c+2*d*x))^2*(b*c+-1*a*d)^-2)^(1/2)*(a+b*x)^-3//4*(c+d*x)^-3//4*(b*c+-1*a*d)^-1//2*(a*d+b*c+2*b*d*x)^-1*(1+2*b^(1/2)*d^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(b*c+-1*a*d)^-1)*Elliptic.F(2*arctan(2^(1/2)*b^1//4*d^1//4*((a+b*x)*(c+d*x))^1//4*(b*c+-1*a*d)^-1//2),1/2))
@test integrate((a+b*x)^-11//4*(c+d*x)^-3//4, x) == :(-4*(a+b*x)^-7//4*(c+d*x)^1//4*(-7*a*d+7*b*c)^-1+8//7*d*(a+b*x)^-3//4*(c+d*x)^1//4*(b*c+-1*a*d)^-2+4//7*2^(1/2)*b^-1//4*d^7//4*((a*d+b*(c+2*d*x))^2)^-1//2*((a*d+b*c+2*b*d*x)^2)^(1/2)*((a+b*x)*(c+d*x))^3//4*((1+2*b^(1/2)*d^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(b*c+-1*a*d)^-1)^-2*(a*d+b*(c+2*d*x))^2*(b*c+-1*a*d)^-2)^(1/2)*(a+b*x)^-3//4*(c+d*x)^-3//4*(b*c+-1*a*d)^-3//2*(a*d+b*c+2*b*d*x)^-1*(1+2*b^(1/2)*d^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(b*c+-1*a*d)^-1)*Elliptic.F(2*arctan(2^(1/2)*b^1//4*d^1//4*((a+b*x)*(c+d*x))^1//4*(b*c+-1*a*d)^-1//2),1/2))
@test integrate((a+b*x)^5//4*(c+d*x)^-5//4, x) == :(-4*d^-1*(a+b*x)^5//4*(c+d*x)^-1//4+5*b*d^-2*(a+b*x)^1//4*(c+d*x)^3//4+-5//2*b^1//4*d^-9//4*(b*c+-1*a*d)*arctan(b^-1//4*d^1//4*(a+b*x)^1//4*(c+d*x)^-1//4)+-5//2*b^1//4*d^-9//4*(b*c+-1*a*d)*arctanh(b^-1//4*d^1//4*(a+b*x)^1//4*(c+d*x)^-1//4))
@test integrate((a+b*x)^1//4*(c+d*x)^-5//4, x) == :(-4*d^-1*(a+b*x)^1//4*(c+d*x)^-1//4+2*b^1//4*d^-5//4*arctan(b^-1//4*d^1//4*(a+b*x)^1//4*(c+d*x)^-1//4)+2*b^1//4*d^-5//4*arctanh(b^-1//4*d^1//4*(a+b*x)^1//4*(c+d*x)^-1//4))
@test integrate((a+b*x)^-3//4*(c+d*x)^-5//4, x) == :(4*(a+b*x)^1//4*(c+d*x)^-1//4*(b*c+-1*a*d)^-1)
@test integrate((a+b*x)^-7//4*(c+d*x)^-5//4, x) == :(-4*(a+b*x)^-3//4*(c+d*x)^-1//4*(-3*a*d+3*b*c)^-1+-16//3*d*(a+b*x)^1//4*(c+d*x)^-1//4*(b*c+-1*a*d)^-2)
@test integrate((a+b*x)^-11//4*(c+d*x)^-5//4, x) == :(-4*(a+b*x)^-7//4*(c+d*x)^-1//4*(-7*a*d+7*b*c)^-1+32//21*d*(a+b*x)^-3//4*(c+d*x)^-1//4*(b*c+-1*a*d)^-2+128//21*d^2*(a+b*x)^1//4*(c+d*x)^-1//4*(b*c+-1*a*d)^-3)
@test integrate((a+b*x)^-15//4*(c+d*x)^-5//4, x) == :(-4*(a+b*x)^-11//4*(c+d*x)^-1//4*(-11*a*d+11*b*c)^-1+-512//77*d^3*(a+b*x)^1//4*(c+d*x)^-1//4*(b*c+-1*a*d)^-4+-128//77*d^2*(a+b*x)^-3//4*(c+d*x)^-1//4*(b*c+-1*a*d)^-3+48//77*d*(a+b*x)^-7//4*(c+d*x)^-1//4*(b*c+-1*a*d)^-2)
@test integrate((a+b*x)^11//4*(c+d*x)^-5//4, x) == :(-4*d^-1*(a+b*x)^11//4*(c+d*x)^-1//4+22//5*b*d^-2*(a+b*x)^7//4*(c+d*x)^3//4+-77//15*b*d^-3*(a+b*x)^3//4*(c+d*x)^3//4*(b*c+-1*a*d)+77//10*b^(1/2)*d^-7//2*((a*d+b*(c+2*d*x))^2)^(1/2)*((a*d+b*c+2*b*d*x)^2)^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(1+2*b^(1/2)*d^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(b*c+-1*a*d)^-1)^-1*(a+b*x)^-1//4*(c+d*x)^-1//4*(a*d+b*c+2*b*d*x)^-1*(b*c+-1*a*d)+-77//20*2^(1/2)*b^1//4*d^-15//4*((a*d+b*(c+2*d*x))^2)^-1//2*((a*d+b*c+2*b*d*x)^2)^(1/2)*((a+b*x)*(c+d*x))^1//4*((1+2*b^(1/2)*d^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(b*c+-1*a*d)^-1)^-2*(a*d+b*(c+2*d*x))^2*(b*c+-1*a*d)^-2)^(1/2)*(a+b*x)^-1//4*(c+d*x)^-1//4*(b*c+-1*a*d)^7//2*(a*d+b*c+2*b*d*x)^-1*(1+2*b^(1/2)*d^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(b*c+-1*a*d)^-1)*Elliptic.E(2*arctan(2^(1/2)*b^1//4*d^1//4*((a+b*x)*(c+d*x))^1//4*(b*c+-1*a*d)^-1//2),1/2)+77//40*2^(1/2)*b^1//4*d^-15//4*((a*d+b*(c+2*d*x))^2)^-1//2*((a*d+b*c+2*b*d*x)^2)^(1/2)*((a+b*x)*(c+d*x))^1//4*((1+2*b^(1/2)*d^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(b*c+-1*a*d)^-1)^-2*(a*d+b*(c+2*d*x))^2*(b*c+-1*a*d)^-2)^(1/2)*(a+b*x)^-1//4*(c+d*x)^-1//4*(b*c+-1*a*d)^7//2*(a*d+b*c+2*b*d*x)^-1*(1+2*b^(1/2)*d^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(b*c+-1*a*d)^-1)*Elliptic.F(2*arctan(2^(1/2)*b^1//4*d^1//4*((a+b*x)*(c+d*x))^1//4*(b*c+-1*a*d)^-1//2),1/2))
@test integrate((a+b*x)^7//4*(c+d*x)^-5//4, x) == :(-4*d^-1*(a+b*x)^7//4*(c+d*x)^-1//4+14//3*b*d^-2*(a+b*x)^3//4*(c+d*x)^3//4+-7*b^(1/2)*d^-5//2*((a*d+b*(c+2*d*x))^2)^(1/2)*((a*d+b*c+2*b*d*x)^2)^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(1+2*b^(1/2)*d^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(b*c+-1*a*d)^-1)^-1*(a+b*x)^-1//4*(c+d*x)^-1//4*(a*d+b*c+2*b*d*x)^-1+-7//4*2^(1/2)*b^1//4*d^-11//4*((a*d+b*(c+2*d*x))^2)^-1//2*((a*d+b*c+2*b*d*x)^2)^(1/2)*((a+b*x)*(c+d*x))^1//4*((1+2*b^(1/2)*d^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(b*c+-1*a*d)^-1)^-2*(a*d+b*(c+2*d*x))^2*(b*c+-1*a*d)^-2)^(1/2)*(a+b*x)^-1//4*(c+d*x)^-1//4*(b*c+-1*a*d)^5//2*(a*d+b*c+2*b*d*x)^-1*(1+2*b^(1/2)*d^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(b*c+-1*a*d)^-1)*Elliptic.F(2*arctan(2^(1/2)*b^1//4*d^1//4*((a+b*x)*(c+d*x))^1//4*(b*c+-1*a*d)^-1//2),1/2)+7//2*2^(1/2)*b^1//4*d^-11//4*((a*d+b*(c+2*d*x))^2)^-1//2*((a*d+b*c+2*b*d*x)^2)^(1/2)*((a+b*x)*(c+d*x))^1//4*((1+2*b^(1/2)*d^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(b*c+-1*a*d)^-1)^-2*(a*d+b*(c+2*d*x))^2*(b*c+-1*a*d)^-2)^(1/2)*(a+b*x)^-1//4*(c+d*x)^-1//4*(b*c+-1*a*d)^5//2*(a*d+b*c+2*b*d*x)^-1*(1+2*b^(1/2)*d^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(b*c+-1*a*d)^-1)*Elliptic.E(2*arctan(2^(1/2)*b^1//4*d^1//4*((a+b*x)*(c+d*x))^1//4*(b*c+-1*a*d)^-1//2),1/2))
@test integrate((a+b*x)^3//4*(c+d*x)^-5//4, x) == :(-4*d^-1*(a+b*x)^3//4*(c+d*x)^-1//4+6*b^(1/2)*d^-3//2*((a*d+b*(c+2*d*x))^2)^(1/2)*((a*d+b*c+2*b*d*x)^2)^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(1+2*b^(1/2)*d^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(b*c+-1*a*d)^-1)^-1*(a+b*x)^-1//4*(c+d*x)^-1//4*(b*c+-1*a*d)^-1*(a*d+b*c+2*b*d*x)^-1+-3*2^(1/2)*b^1//4*d^-7//4*((a*d+b*(c+2*d*x))^2)^-1//2*((a*d+b*c+2*b*d*x)^2)^(1/2)*((a+b*x)*(c+d*x))^1//4*((1+2*b^(1/2)*d^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(b*c+-1*a*d)^-1)^-2*(a*d+b*(c+2*d*x))^2*(b*c+-1*a*d)^-2)^(1/2)*(a+b*x)^-1//4*(c+d*x)^-1//4*(b*c+-1*a*d)^3//2*(a*d+b*c+2*b*d*x)^-1*(1+2*b^(1/2)*d^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(b*c+-1*a*d)^-1)*Elliptic.E(2*arctan(2^(1/2)*b^1//4*d^1//4*((a+b*x)*(c+d*x))^1//4*(b*c+-1*a*d)^-1//2),1/2)+3//2*2^(1/2)*b^1//4*d^-7//4*((a*d+b*(c+2*d*x))^2)^-1//2*((a*d+b*c+2*b*d*x)^2)^(1/2)*((a+b*x)*(c+d*x))^1//4*((1+2*b^(1/2)*d^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(b*c+-1*a*d)^-1)^-2*(a*d+b*(c+2*d*x))^2*(b*c+-1*a*d)^-2)^(1/2)*(a+b*x)^-1//4*(c+d*x)^-1//4*(b*c+-1*a*d)^3//2*(a*d+b*c+2*b*d*x)^-1*(1+2*b^(1/2)*d^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(b*c+-1*a*d)^-1)*Elliptic.F(2*arctan(2^(1/2)*b^1//4*d^1//4*((a+b*x)*(c+d*x))^1//4*(b*c+-1*a*d)^-1//2),1/2))
@test integrate((a+b*x)^-1//4*(c+d*x)^-5//4, x) == :(4*(a+b*x)^3//4*(c+d*x)^-1//4*(b*c+-1*a*d)^-1+-4*b^(1/2)*d^-1//2*((a*d+b*(c+2*d*x))^2)^(1/2)*((a*d+b*c+2*b*d*x)^2)^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(1+2*b^(1/2)*d^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(b*c+-1*a*d)^-1)^-1*(a+b*x)^-1//4*(c+d*x)^-1//4*(b*c+-1*a*d)^-2*(a*d+b*c+2*b*d*x)^-1+-1*2^(1/2)*b^1//4*d^-3//4*((a*d+b*(c+2*d*x))^2)^-1//2*((a*d+b*c+2*b*d*x)^2)^(1/2)*((a+b*x)*(c+d*x))^1//4*((1+2*b^(1/2)*d^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(b*c+-1*a*d)^-1)^-2*(a*d+b*(c+2*d*x))^2*(b*c+-1*a*d)^-2)^(1/2)*(a+b*x)^-1//4*(c+d*x)^-1//4*(b*c+-1*a*d)^(1/2)*(a*d+b*c+2*b*d*x)^-1*(1+2*b^(1/2)*d^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(b*c+-1*a*d)^-1)*Elliptic.F(2*arctan(2^(1/2)*b^1//4*d^1//4*((a+b*x)*(c+d*x))^1//4*(b*c+-1*a*d)^-1//2),1/2)+2*2^(1/2)*b^1//4*d^-3//4*((a*d+b*(c+2*d*x))^2)^-1//2*((a*d+b*c+2*b*d*x)^2)^(1/2)*((a+b*x)*(c+d*x))^1//4*((1+2*b^(1/2)*d^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(b*c+-1*a*d)^-1)^-2*(a*d+b*(c+2*d*x))^2*(b*c+-1*a*d)^-2)^(1/2)*(a+b*x)^-1//4*(c+d*x)^-1//4*(b*c+-1*a*d)^(1/2)*(a*d+b*c+2*b*d*x)^-1*(1+2*b^(1/2)*d^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(b*c+-1*a*d)^-1)*Elliptic.E(2*arctan(2^(1/2)*b^1//4*d^1//4*((a+b*x)*(c+d*x))^1//4*(b*c+-1*a*d)^-1//2),1/2))
@test integrate((a+b*x)^-5//4*(c+d*x)^-5//4, x) == :(-4*(a+b*x)^-1//4*(c+d*x)^-1//4*(b*c+-1*a*d)^-1+-8*d*(a+b*x)^3//4*(c+d*x)^-1//4*(b*c+-1*a*d)^-2+8*b^(1/2)*d^(1/2)*((a*d+b*(c+2*d*x))^2)^(1/2)*((a*d+b*c+2*b*d*x)^2)^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(1+2*b^(1/2)*d^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(b*c+-1*a*d)^-1)^-1*(a+b*x)^-1//4*(c+d*x)^-1//4*(b*c+-1*a*d)^-3*(a*d+b*c+2*b*d*x)^-1+-4*2^(1/2)*b^1//4*d^1//4*((a*d+b*(c+2*d*x))^2)^-1//2*((a*d+b*c+2*b*d*x)^2)^(1/2)*((a+b*x)*(c+d*x))^1//4*((1+2*b^(1/2)*d^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(b*c+-1*a*d)^-1)^-2*(a*d+b*(c+2*d*x))^2*(b*c+-1*a*d)^-2)^(1/2)*(a+b*x)^-1//4*(c+d*x)^-1//4*(b*c+-1*a*d)^-1//2*(a*d+b*c+2*b*d*x)^-1*(1+2*b^(1/2)*d^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(b*c+-1*a*d)^-1)*Elliptic.E(2*arctan(2^(1/2)*b^1//4*d^1//4*((a+b*x)*(c+d*x))^1//4*(b*c+-1*a*d)^-1//2),1/2)+2*2^(1/2)*b^1//4*d^1//4*((a*d+b*(c+2*d*x))^2)^-1//2*((a*d+b*c+2*b*d*x)^2)^(1/2)*((a+b*x)*(c+d*x))^1//4*((1+2*b^(1/2)*d^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(b*c+-1*a*d)^-1)^-2*(a*d+b*(c+2*d*x))^2*(b*c+-1*a*d)^-2)^(1/2)*(a+b*x)^-1//4*(c+d*x)^-1//4*(b*c+-1*a*d)^-1//2*(a*d+b*c+2*b*d*x)^-1*(1+2*b^(1/2)*d^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(b*c+-1*a*d)^-1)*Elliptic.F(2*arctan(2^(1/2)*b^1//4*d^1//4*((a+b*x)*(c+d*x))^1//4*(b*c+-1*a*d)^-1//2),1/2))
@test integrate((a+b*x)^-9//4*(c+d*x)^-5//4, x) == :(-4*(a+b*x)^-5//4*(c+d*x)^-1//4*(-5*a*d+5*b*c)^-1+24//5*d*(a+b*x)^-1//4*(c+d*x)^-1//4*(b*c+-1*a*d)^-2+48//5*d^2*(a+b*x)^3//4*(c+d*x)^-1//4*(b*c+-1*a*d)^-3+-48//5*b^(1/2)*d^3//2*((a*d+b*(c+2*d*x))^2)^(1/2)*((a*d+b*c+2*b*d*x)^2)^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(1+2*b^(1/2)*d^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(b*c+-1*a*d)^-1)^-1*(a+b*x)^-1//4*(c+d*x)^-1//4*(b*c+-1*a*d)^-4*(a*d+b*c+2*b*d*x)^-1+-12//5*2^(1/2)*b^1//4*d^5//4*((a*d+b*(c+2*d*x))^2)^-1//2*((a*d+b*c+2*b*d*x)^2)^(1/2)*((a+b*x)*(c+d*x))^1//4*((1+2*b^(1/2)*d^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(b*c+-1*a*d)^-1)^-2*(a*d+b*(c+2*d*x))^2*(b*c+-1*a*d)^-2)^(1/2)*(a+b*x)^-1//4*(c+d*x)^-1//4*(b*c+-1*a*d)^-3//2*(a*d+b*c+2*b*d*x)^-1*(1+2*b^(1/2)*d^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(b*c+-1*a*d)^-1)*Elliptic.F(2*arctan(2^(1/2)*b^1//4*d^1//4*((a+b*x)*(c+d*x))^1//4*(b*c+-1*a*d)^-1//2),1/2)+24//5*2^(1/2)*b^1//4*d^5//4*((a*d+b*(c+2*d*x))^2)^-1//2*((a*d+b*c+2*b*d*x)^2)^(1/2)*((a+b*x)*(c+d*x))^1//4*((1+2*b^(1/2)*d^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(b*c+-1*a*d)^-1)^-2*(a*d+b*(c+2*d*x))^2*(b*c+-1*a*d)^-2)^(1/2)*(a+b*x)^-1//4*(c+d*x)^-1//4*(b*c+-1*a*d)^-3//2*(a*d+b*c+2*b*d*x)^-1*(1+2*b^(1/2)*d^(1/2)*((a+b*x)*(c+d*x))^(1/2)*(b*c+-1*a*d)^-1)*Elliptic.E(2*arctan(2^(1/2)*b^1//4*d^1//4*((a+b*x)*(c+d*x))^1//4*(b*c+-1*a*d)^-1//2),1/2))
@test integrate((1+b*x)^-3//4*(1+-1*a*x)^-1//4, x) == :(2^(1/2)*a^-1//4*b^-3//4*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*(1+b*x)^-1//4*(1+-1*a*x)^1//4)+(1/2)*2^(1/2)*a^-1//4*b^-3//4*log(a^(1/2)+b^(1/2)*(1+b*x)^-1//2*(1+-1*a*x)^(1/2)+2^(1/2)*a^1//4*b^1//4*(1+b*x)^-1//4*(1+-1*a*x)^1//4)+-1*2^(1/2)*a^-1//4*b^-3//4*arctan(1+2^(1/2)*a^-1//4*b^1//4*(1+b*x)^-1//4*(1+-1*a*x)^1//4)+-1//2*2^(1/2)*a^-1//4*b^-3//4*log(a^(1/2)+b^(1/2)*(1+b*x)^-1//2*(1+-1*a*x)^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*(1+b*x)^-1//4*(1+-1*a*x)^1//4))
@test integrate((1+a*x)^-3//4*(1+-1*a*x)^-1//4, x) == :(2^(1/2)*a^-1*arctan(1+-1*2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+(1/2)*2^(1/2)*a^-1*log(1+(1+a*x)^-1//2*(1+-1*a*x)^(1/2)+2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+-1*2^(1/2)*a^-1*arctan(1+2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+-1//2*2^(1/2)*a^-1*log(1+(1+a*x)^-1//2*(1+-1*a*x)^(1/2)+-1*2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4))
@test integrate((a+b*x)^5//2*(c+d*x)^1//6, x) == :(3//11*b^-1*(a+b*x)^7//2*(c+d*x)^1//6+-9//352*b^-1*d^-2*(a+b*x)^3//2*(c+d*x)^1//6*(b*c+-1*a*d)^2+1//176*b^-1*d^-1*(a+b*x)^5//2*(c+d*x)^1//6*(-3*a*d+3*b*c)+81//1408*b^-1*d^-3*(a+b*x)^(1/2)*(c+d*x)^1//6*(b*c+-1*a*d)^3+-81//2816*3^3//4*b^-1*d^-4*(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^2//3+b^2//3*(c+d*x)^2//3+b^1//3*(c+d*x)^1//3*(b*c+-1*a*d)^1//3))^(1/2)*(-1*b^1//3*(c+d*x)^1//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3))^-1//2*(a+b*x)^-1//2*(c+d*x)^1//6*(b*c+-1*a*d)^11//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3)*Elliptic.F(arccos(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-1*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate((a+b*x)^3//2*(c+d*x)^1//6, x) == :(3//8*b^-1*(a+b*x)^5//2*(c+d*x)^1//6+-27//320*b^-1*d^-2*(a+b*x)^(1/2)*(c+d*x)^1//6*(b*c+-1*a*d)^2+1//80*b^-1*d^-1*(a+b*x)^3//2*(c+d*x)^1//6*(-3*a*d+3*b*c)+27//640*3^3//4*b^-1*d^-3*(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^2//3+b^2//3*(c+d*x)^2//3+b^1//3*(c+d*x)^1//3*(b*c+-1*a*d)^1//3))^(1/2)*(-1*b^1//3*(c+d*x)^1//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3))^-1//2*(a+b*x)^-1//2*(c+d*x)^1//6*(b*c+-1*a*d)^8//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3)*Elliptic.F(arccos(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-1*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate((a+b*x)^(1/2)*(c+d*x)^1//6, x) == :(3//5*b^-1*(a+b*x)^3//2*(c+d*x)^1//6+1//20*b^-1*d^-1*(a+b*x)^(1/2)*(c+d*x)^1//6*(-3*a*d+3*b*c)+-3//40*3^3//4*b^-1*d^-2*(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^2//3+b^2//3*(c+d*x)^2//3+b^1//3*(c+d*x)^1//3*(b*c+-1*a*d)^1//3))^(1/2)*(-1*b^1//3*(c+d*x)^1//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3))^-1//2*(a+b*x)^-1//2*(c+d*x)^1//6*(b*c+-1*a*d)^5//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3)*Elliptic.F(arccos(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-1*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate((a+b*x)^-1//2*(c+d*x)^1//6, x) == :(3//2*b^-1*(a+b*x)^(1/2)*(c+d*x)^1//6+1//4*3^3//4*b^-1*d^-1*(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^2//3+b^2//3*(c+d*x)^2//3+b^1//3*(c+d*x)^1//3*(b*c+-1*a*d)^1//3))^(1/2)*(-1*b^1//3*(c+d*x)^1//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3))^-1//2*(a+b*x)^-1//2*(c+d*x)^1//6*(b*c+-1*a*d)^2//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3)*Elliptic.F(arccos(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-1*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate((a+b*x)^-3//2*(c+d*x)^1//6, x) == :(-2*b^-1*(a+b*x)^-1//2*(c+d*x)^1//6+1//3*3^3//4*b^-1*(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^2//3+b^2//3*(c+d*x)^2//3+b^1//3*(c+d*x)^1//3*(b*c+-1*a*d)^1//3))^(1/2)*(-1*b^1//3*(c+d*x)^1//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3))^-1//2*(a+b*x)^-1//2*(c+d*x)^1//6*(b*c+-1*a*d)^-1//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3)*Elliptic.F(arccos(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-1*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate((a+b*x)^-5//2*(c+d*x)^1//6, x) == :(-2//3*b^-1*(a+b*x)^-3//2*(c+d*x)^1//6+-2//9*d*b^-1*(a+b*x)^-1//2*(c+d*x)^1//6*(b*c+-1*a*d)^-1+-2//27*d*3^3//4*b^-1*(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^2//3+b^2//3*(c+d*x)^2//3+b^1//3*(c+d*x)^1//3*(b*c+-1*a*d)^1//3))^(1/2)*(-1*b^1//3*(c+d*x)^1//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3))^-1//2*(a+b*x)^-1//2*(c+d*x)^1//6*(b*c+-1*a*d)^-4//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3)*Elliptic.F(arccos(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-1*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate((a+b*x)^3//2*(c+d*x)^5//6, x) == :(3//10*b^-1*(a+b*x)^5//2*(c+d*x)^5//6+-27//224*b^-1*d^-2*(a+b*x)^(1/2)*(c+d*x)^5//6*(b*c+-1*a*d)^2+1//28*b^-1*d^-1*(a+b*x)^3//2*(c+d*x)^5//6*(-3*a*d+3*b*c)+-1//448*b^-5//3*d^-2*(a+b*x)^(1/2)*(c+d*x)^1//6*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-1*(b*c+-1*a*d)^3*(81+81*3^(1/2))+-81//448*3^1//4*b^-5//3*d^-3*(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^2//3+b^2//3*(c+d*x)^2//3+b^1//3*(c+d*x)^1//3*(b*c+-1*a*d)^1//3))^(1/2)*(-1*b^1//3*(c+d*x)^1//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3))^-1//2*(a+b*x)^-1//2*(c+d*x)^1//6*(b*c+-1*a*d)^10//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3)*Elliptic.E(arccos(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-1*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2))+-27//896*3^3//4*b^-5//3*d^-3*(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^2//3+b^2//3*(c+d*x)^2//3+b^1//3*(c+d*x)^1//3*(b*c+-1*a*d)^1//3))^(1/2)*(-1*b^1//3*(c+d*x)^1//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3))^-1//2*(a+b*x)^-1//2*(c+d*x)^1//6*(b*c+-1*a*d)^10//3*(1+-1*3^(1/2))*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3)*Elliptic.F(arccos(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-1*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate((a+b*x)^(1/2)*(c+d*x)^5//6, x) == :(3//7*b^-1*(a+b*x)^3//2*(c+d*x)^5//6+1//56*b^-1*d^-1*(a+b*x)^(1/2)*(c+d*x)^5//6*(-15*a*d+15*b*c)+1//112*b^-5//3*d^-1*(a+b*x)^(1/2)*(c+d*x)^1//6*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-1*(b*c+-1*a*d)^2*(45+45*3^(1/2))+45//112*3^1//4*b^-5//3*d^-2*(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^2//3+b^2//3*(c+d*x)^2//3+b^1//3*(c+d*x)^1//3*(b*c+-1*a*d)^1//3))^(1/2)*(-1*b^1//3*(c+d*x)^1//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3))^-1//2*(a+b*x)^-1//2*(c+d*x)^1//6*(b*c+-1*a*d)^7//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3)*Elliptic.E(arccos(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-1*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2))+15//224*3^3//4*b^-5//3*d^-2*(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^2//3+b^2//3*(c+d*x)^2//3+b^1//3*(c+d*x)^1//3*(b*c+-1*a*d)^1//3))^(1/2)*(-1*b^1//3*(c+d*x)^1//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3))^-1//2*(a+b*x)^-1//2*(c+d*x)^1//6*(b*c+-1*a*d)^7//3*(1+-1*3^(1/2))*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3)*Elliptic.F(arccos(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-1*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate((a+b*x)^-1//2*(c+d*x)^5//6, x) == :(3//4*b^-1*(a+b*x)^(1/2)*(c+d*x)^5//6+-1//8*b^-5//3*(a+b*x)^(1/2)*(c+d*x)^1//6*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-1*(15+15*3^(1/2))*(b*c+-1*a*d)+-15//8*3^1//4*b^-5//3*d^-1*(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^2//3+b^2//3*(c+d*x)^2//3+b^1//3*(c+d*x)^1//3*(b*c+-1*a*d)^1//3))^(1/2)*(-1*b^1//3*(c+d*x)^1//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3))^-1//2*(a+b*x)^-1//2*(c+d*x)^1//6*(b*c+-1*a*d)^4//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3)*Elliptic.E(arccos(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-1*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2))+-5//16*3^3//4*b^-5//3*d^-1*(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^2//3+b^2//3*(c+d*x)^2//3+b^1//3*(c+d*x)^1//3*(b*c+-1*a*d)^1//3))^(1/2)*(-1*b^1//3*(c+d*x)^1//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3))^-1//2*(a+b*x)^-1//2*(c+d*x)^1//6*(b*c+-1*a*d)^4//3*(1+-1*3^(1/2))*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3)*Elliptic.F(arccos(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-1*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate((a+b*x)^-3//2*(c+d*x)^5//6, x) == :(-2*b^-1*(a+b*x)^-1//2*(c+d*x)^5//6+-1*d*b^-5//3*(a+b*x)^(1/2)*(c+d*x)^1//6*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-1*(5+5*3^(1/2))+-5*3^1//4*b^-5//3*(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^2//3+b^2//3*(c+d*x)^2//3+b^1//3*(c+d*x)^1//3*(b*c+-1*a*d)^1//3))^(1/2)*(-1*b^1//3*(c+d*x)^1//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3))^-1//2*(a+b*x)^-1//2*(c+d*x)^1//6*(b*c+-1*a*d)^1//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3)*Elliptic.E(arccos(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-1*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2))+-1//6*3^3//4*b^-5//3*(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^2//3+b^2//3*(c+d*x)^2//3+b^1//3*(c+d*x)^1//3*(b*c+-1*a*d)^1//3))^(1/2)*(-1*b^1//3*(c+d*x)^1//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3))^-1//2*(a+b*x)^-1//2*(c+d*x)^1//6*(b*c+-1*a*d)^1//3*(5+-5*3^(1/2))*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3)*Elliptic.F(arccos(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-1*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate((a+b*x)^-5//2*(c+d*x)^5//6, x) == :(-2//3*b^-1*(a+b*x)^-3//2*(c+d*x)^5//6+-10//9*d*b^-1*(a+b*x)^-1//2*(c+d*x)^5//6*(b*c+-1*a*d)^-1+-1//9*b^-5//3*d^2*(a+b*x)^(1/2)*(c+d*x)^1//6*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-1*(b*c+-1*a*d)^-1*(10+10*3^(1/2))+-10//9*d*3^1//4*b^-5//3*(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^2//3+b^2//3*(c+d*x)^2//3+b^1//3*(c+d*x)^1//3*(b*c+-1*a*d)^1//3))^(1/2)*(-1*b^1//3*(c+d*x)^1//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3))^-1//2*(a+b*x)^-1//2*(c+d*x)^1//6*(b*c+-1*a*d)^-2//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3)*Elliptic.E(arccos(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-1*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2))+-1//27*d*3^3//4*b^-5//3*(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^2//3+b^2//3*(c+d*x)^2//3+b^1//3*(c+d*x)^1//3*(b*c+-1*a*d)^1//3))^(1/2)*(-1*b^1//3*(c+d*x)^1//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3))^-1//2*(a+b*x)^-1//2*(c+d*x)^1//6*(b*c+-1*a*d)^-2//3*(5+-5*3^(1/2))*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3)*Elliptic.F(arccos(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-1*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate((a+b*x)^-7//2*(c+d*x)^5//6, x) == :(-2//5*b^-1*(a+b*x)^-5//2*(c+d*x)^5//6+-2//9*d*b^-1*(a+b*x)^-3//2*(c+d*x)^5//6*(b*c+-1*a*d)^-1+8//27*b^-1*d^2*(a+b*x)^-1//2*(c+d*x)^5//6*(b*c+-1*a*d)^-2+1//27*b^-5//3*d^3*(a+b*x)^(1/2)*(c+d*x)^1//6*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-1*(b*c+-1*a*d)^-2*(8+8*3^(1/2))+8//27*3^1//4*b^-5//3*d^2*(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^2//3+b^2//3*(c+d*x)^2//3+b^1//3*(c+d*x)^1//3*(b*c+-1*a*d)^1//3))^(1/2)*(-1*b^1//3*(c+d*x)^1//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3))^-1//2*(a+b*x)^-1//2*(c+d*x)^1//6*(b*c+-1*a*d)^-5//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3)*Elliptic.E(arccos(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-1*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2))+1//81*3^3//4*b^-5//3*d^2*(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^2//3+b^2//3*(c+d*x)^2//3+b^1//3*(c+d*x)^1//3*(b*c+-1*a*d)^1//3))^(1/2)*(-1*b^1//3*(c+d*x)^1//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3))^-1//2*(a+b*x)^-1//2*(c+d*x)^1//6*(b*c+-1*a*d)^-5//3*(4+-4*3^(1/2))*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3)*Elliptic.F(arccos(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-1*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate((a+b*x)^5//2*(c+d*x)^-1//6, x) == :(3//10*d^-1*(a+b*x)^5//2*(c+d*x)^5//6+-1//28*d^-2*(a+b*x)^3//2*(c+d*x)^5//6*(-9*a*d+9*b*c)+81//224*d^-3*(a+b*x)^(1/2)*(c+d*x)^5//6*(b*c+-1*a*d)^2+1//448*b^-2//3*d^-3*(a+b*x)^(1/2)*(c+d*x)^1//6*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-1*(b*c+-1*a*d)^3*(243+243*3^(1/2))+243//448*3^1//4*b^-2//3*d^-4*(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^2//3+b^2//3*(c+d*x)^2//3+b^1//3*(c+d*x)^1//3*(b*c+-1*a*d)^1//3))^(1/2)*(-1*b^1//3*(c+d*x)^1//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3))^-1//2*(a+b*x)^-1//2*(c+d*x)^1//6*(b*c+-1*a*d)^10//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3)*Elliptic.E(arccos(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-1*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2))+81//896*3^3//4*b^-2//3*d^-4*(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^2//3+b^2//3*(c+d*x)^2//3+b^1//3*(c+d*x)^1//3*(b*c+-1*a*d)^1//3))^(1/2)*(-1*b^1//3*(c+d*x)^1//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3))^-1//2*(a+b*x)^-1//2*(c+d*x)^1//6*(b*c+-1*a*d)^10//3*(1+-1*3^(1/2))*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3)*Elliptic.F(arccos(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-1*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate((a+b*x)^3//2*(c+d*x)^-1//6, x) == :(3//7*d^-1*(a+b*x)^3//2*(c+d*x)^5//6+-1//56*d^-2*(a+b*x)^(1/2)*(c+d*x)^5//6*(-27*a*d+27*b*c)+-1//112*b^-2//3*d^-2*(a+b*x)^(1/2)*(c+d*x)^1//6*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-1*(b*c+-1*a*d)^2*(81+81*3^(1/2))+-81//112*3^1//4*b^-2//3*d^-3*(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^2//3+b^2//3*(c+d*x)^2//3+b^1//3*(c+d*x)^1//3*(b*c+-1*a*d)^1//3))^(1/2)*(-1*b^1//3*(c+d*x)^1//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3))^-1//2*(a+b*x)^-1//2*(c+d*x)^1//6*(b*c+-1*a*d)^7//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3)*Elliptic.E(arccos(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-1*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2))+-27//224*3^3//4*b^-2//3*d^-3*(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^2//3+b^2//3*(c+d*x)^2//3+b^1//3*(c+d*x)^1//3*(b*c+-1*a*d)^1//3))^(1/2)*(-1*b^1//3*(c+d*x)^1//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3))^-1//2*(a+b*x)^-1//2*(c+d*x)^1//6*(b*c+-1*a*d)^7//3*(1+-1*3^(1/2))*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3)*Elliptic.F(arccos(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-1*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate((a+b*x)^(1/2)*(c+d*x)^-1//6, x) == :(3//4*d^-1*(a+b*x)^(1/2)*(c+d*x)^5//6+1//8*b^-2//3*d^-1*(a+b*x)^(1/2)*(c+d*x)^1//6*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-1*(9+9*3^(1/2))*(b*c+-1*a*d)+9//8*3^1//4*b^-2//3*d^-2*(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^2//3+b^2//3*(c+d*x)^2//3+b^1//3*(c+d*x)^1//3*(b*c+-1*a*d)^1//3))^(1/2)*(-1*b^1//3*(c+d*x)^1//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3))^-1//2*(a+b*x)^-1//2*(c+d*x)^1//6*(b*c+-1*a*d)^4//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3)*Elliptic.E(arccos(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-1*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2))+3//16*3^3//4*b^-2//3*d^-2*(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^2//3+b^2//3*(c+d*x)^2//3+b^1//3*(c+d*x)^1//3*(b*c+-1*a*d)^1//3))^(1/2)*(-1*b^1//3*(c+d*x)^1//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3))^-1//2*(a+b*x)^-1//2*(c+d*x)^1//6*(b*c+-1*a*d)^4//3*(1+-1*3^(1/2))*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3)*Elliptic.F(arccos(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-1*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate((a+b*x)^-1//2*(c+d*x)^-1//6, x) == :(-1*b^-2//3*(a+b*x)^(1/2)*(c+d*x)^1//6*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-1*(3+3*3^(1/2))+-3*3^1//4*b^-2//3*d^-1*(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^2//3+b^2//3*(c+d*x)^2//3+b^1//3*(c+d*x)^1//3*(b*c+-1*a*d)^1//3))^(1/2)*(-1*b^1//3*(c+d*x)^1//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3))^-1//2*(a+b*x)^-1//2*(c+d*x)^1//6*(b*c+-1*a*d)^1//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3)*Elliptic.E(arccos(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-1*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2))+-1//2*3^3//4*b^-2//3*d^-1*(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^2//3+b^2//3*(c+d*x)^2//3+b^1//3*(c+d*x)^1//3*(b*c+-1*a*d)^1//3))^(1/2)*(-1*b^1//3*(c+d*x)^1//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3))^-1//2*(a+b*x)^-1//2*(c+d*x)^1//6*(b*c+-1*a*d)^1//3*(1+-1*3^(1/2))*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3)*Elliptic.F(arccos(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-1*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate((a+b*x)^-3//2*(c+d*x)^-1//6, x) == :(-2*(a+b*x)^-1//2*(c+d*x)^5//6*(b*c+-1*a*d)^-1+-1*d*b^-2//3*(a+b*x)^(1/2)*(c+d*x)^1//6*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-1*(b*c+-1*a*d)^-1*(2+2*3^(1/2))+-2*3^1//4*b^-2//3*(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^2//3+b^2//3*(c+d*x)^2//3+b^1//3*(c+d*x)^1//3*(b*c+-1*a*d)^1//3))^(1/2)*(-1*b^1//3*(c+d*x)^1//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3))^-1//2*(a+b*x)^-1//2*(c+d*x)^1//6*(b*c+-1*a*d)^-2//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3)*Elliptic.E(arccos(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-1*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2))+-1//3*3^3//4*b^-2//3*(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^2//3+b^2//3*(c+d*x)^2//3+b^1//3*(c+d*x)^1//3*(b*c+-1*a*d)^1//3))^(1/2)*(-1*b^1//3*(c+d*x)^1//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3))^-1//2*(a+b*x)^-1//2*(c+d*x)^1//6*(b*c+-1*a*d)^-2//3*(1+-1*3^(1/2))*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3)*Elliptic.F(arccos(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-1*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate((a+b*x)^-5//2*(c+d*x)^-1//6, x) == :(-2*(a+b*x)^-3//2*(c+d*x)^5//6*(-3*a*d+3*b*c)^-1+8//9*d*(a+b*x)^-1//2*(c+d*x)^5//6*(b*c+-1*a*d)^-2+1//9*b^-2//3*d^2*(a+b*x)^(1/2)*(c+d*x)^1//6*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-1*(b*c+-1*a*d)^-2*(8+8*3^(1/2))+8//9*d*3^1//4*b^-2//3*(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^2//3+b^2//3*(c+d*x)^2//3+b^1//3*(c+d*x)^1//3*(b*c+-1*a*d)^1//3))^(1/2)*(-1*b^1//3*(c+d*x)^1//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3))^-1//2*(a+b*x)^-1//2*(c+d*x)^1//6*(b*c+-1*a*d)^-5//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3)*Elliptic.E(arccos(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-1*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2))+1//27*d*3^3//4*b^-2//3*(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^2//3+b^2//3*(c+d*x)^2//3+b^1//3*(c+d*x)^1//3*(b*c+-1*a*d)^1//3))^(1/2)*(-1*b^1//3*(c+d*x)^1//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3))^-1//2*(a+b*x)^-1//2*(c+d*x)^1//6*(b*c+-1*a*d)^-5//3*(4+-4*3^(1/2))*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3)*Elliptic.F(arccos(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-1*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate((a+b*x)^5//2*(c+d*x)^-5//6, x) == :(3//8*d^-1*(a+b*x)^5//2*(c+d*x)^1//6+-1//16*d^-2*(a+b*x)^3//2*(c+d*x)^1//6*(-9*a*d+9*b*c)+81//64*d^-3*(a+b*x)^(1/2)*(c+d*x)^1//6*(b*c+-1*a*d)^2+-81//128*3^3//4*d^-4*(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^2//3+b^2//3*(c+d*x)^2//3+b^1//3*(c+d*x)^1//3*(b*c+-1*a*d)^1//3))^(1/2)*(-1*b^1//3*(c+d*x)^1//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3))^-1//2*(a+b*x)^-1//2*(c+d*x)^1//6*(b*c+-1*a*d)^8//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3)*Elliptic.F(arccos(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-1*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate((a+b*x)^3//2*(c+d*x)^-5//6, x) == :(3//5*d^-1*(a+b*x)^3//2*(c+d*x)^1//6+-1//20*d^-2*(a+b*x)^(1/2)*(c+d*x)^1//6*(-27*a*d+27*b*c)+27//40*3^3//4*d^-3*(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^2//3+b^2//3*(c+d*x)^2//3+b^1//3*(c+d*x)^1//3*(b*c+-1*a*d)^1//3))^(1/2)*(-1*b^1//3*(c+d*x)^1//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3))^-1//2*(a+b*x)^-1//2*(c+d*x)^1//6*(b*c+-1*a*d)^5//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3)*Elliptic.F(arccos(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-1*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate((a+b*x)^(1/2)*(c+d*x)^-5//6, x) == :(3//2*d^-1*(a+b*x)^(1/2)*(c+d*x)^1//6+-3//4*3^3//4*d^-2*(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^2//3+b^2//3*(c+d*x)^2//3+b^1//3*(c+d*x)^1//3*(b*c+-1*a*d)^1//3))^(1/2)*(-1*b^1//3*(c+d*x)^1//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3))^-1//2*(a+b*x)^-1//2*(c+d*x)^1//6*(b*c+-1*a*d)^2//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3)*Elliptic.F(arccos(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-1*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate((a+b*x)^-1//2*(c+d*x)^-5//6, x) == :(3^3//4*d^-1*(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^2//3+b^2//3*(c+d*x)^2//3+b^1//3*(c+d*x)^1//3*(b*c+-1*a*d)^1//3))^(1/2)*(-1*b^1//3*(c+d*x)^1//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3))^-1//2*(a+b*x)^-1//2*(c+d*x)^1//6*(b*c+-1*a*d)^-1//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3)*Elliptic.F(arccos(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-1*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate((a+b*x)^-3//2*(c+d*x)^-5//6, x) == :(-2*(a+b*x)^-1//2*(c+d*x)^1//6*(b*c+-1*a*d)^-1+-2//3*3^3//4*(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^2//3+b^2//3*(c+d*x)^2//3+b^1//3*(c+d*x)^1//3*(b*c+-1*a*d)^1//3))^(1/2)*(-1*b^1//3*(c+d*x)^1//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3))^-1//2*(a+b*x)^-1//2*(c+d*x)^1//6*(b*c+-1*a*d)^-4//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3)*Elliptic.F(arccos(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-1*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate((a+b*x)^-5//2*(c+d*x)^-5//6, x) == :(-2*(a+b*x)^-3//2*(c+d*x)^1//6*(-3*a*d+3*b*c)^-1+16//9*d*(a+b*x)^-1//2*(c+d*x)^1//6*(b*c+-1*a*d)^-2+16//27*d*3^3//4*(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^2//3+b^2//3*(c+d*x)^2//3+b^1//3*(c+d*x)^1//3*(b*c+-1*a*d)^1//3))^(1/2)*(-1*b^1//3*(c+d*x)^1//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3))^-1//2*(a+b*x)^-1//2*(c+d*x)^1//6*(b*c+-1*a*d)^-7//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3)*Elliptic.F(arccos(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-1*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate((a+b*x)^5//2*(c+d*x)^-7//6, x) == :(-6*d^-1*(a+b*x)^5//2*(c+d*x)^-1//6+45//7*b*d^-2*(a+b*x)^3//2*(c+d*x)^5//6+-405//56*b*d^-3*(a+b*x)^(1/2)*(c+d*x)^5//6*(b*c+-1*a*d)+-1//112*b^1//3*d^-3*(a+b*x)^(1/2)*(c+d*x)^1//6*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-1*(b*c+-1*a*d)^2*(1215+1215*3^(1/2))+-1215//112*3^1//4*b^1//3*d^-4*(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^2//3+b^2//3*(c+d*x)^2//3+b^1//3*(c+d*x)^1//3*(b*c+-1*a*d)^1//3))^(1/2)*(-1*b^1//3*(c+d*x)^1//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3))^-1//2*(a+b*x)^-1//2*(c+d*x)^1//6*(b*c+-1*a*d)^7//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3)*Elliptic.E(arccos(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-1*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2))+-405//224*3^3//4*b^1//3*d^-4*(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^2//3+b^2//3*(c+d*x)^2//3+b^1//3*(c+d*x)^1//3*(b*c+-1*a*d)^1//3))^(1/2)*(-1*b^1//3*(c+d*x)^1//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3))^-1//2*(a+b*x)^-1//2*(c+d*x)^1//6*(b*c+-1*a*d)^7//3*(1+-1*3^(1/2))*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3)*Elliptic.F(arccos(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-1*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate((a+b*x)^3//2*(c+d*x)^-7//6, x) == :(-6*d^-1*(a+b*x)^3//2*(c+d*x)^-1//6+27//4*b*d^-2*(a+b*x)^(1/2)*(c+d*x)^5//6+1//8*b^1//3*d^-2*(a+b*x)^(1/2)*(c+d*x)^1//6*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-1*(81+81*3^(1/2))*(b*c+-1*a*d)+81//8*3^1//4*b^1//3*d^-3*(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^2//3+b^2//3*(c+d*x)^2//3+b^1//3*(c+d*x)^1//3*(b*c+-1*a*d)^1//3))^(1/2)*(-1*b^1//3*(c+d*x)^1//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3))^-1//2*(a+b*x)^-1//2*(c+d*x)^1//6*(b*c+-1*a*d)^4//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3)*Elliptic.E(arccos(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-1*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2))+27//16*3^3//4*b^1//3*d^-3*(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^2//3+b^2//3*(c+d*x)^2//3+b^1//3*(c+d*x)^1//3*(b*c+-1*a*d)^1//3))^(1/2)*(-1*b^1//3*(c+d*x)^1//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3))^-1//2*(a+b*x)^-1//2*(c+d*x)^1//6*(b*c+-1*a*d)^4//3*(1+-1*3^(1/2))*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3)*Elliptic.F(arccos(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-1*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate((a+b*x)^(1/2)*(c+d*x)^-7//6, x) == :(-6*d^-1*(a+b*x)^(1/2)*(c+d*x)^-1//6+-1*b^1//3*d^-1*(a+b*x)^(1/2)*(c+d*x)^1//6*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-1*(9+9*3^(1/2))+-9*3^1//4*b^1//3*d^-2*(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^2//3+b^2//3*(c+d*x)^2//3+b^1//3*(c+d*x)^1//3*(b*c+-1*a*d)^1//3))^(1/2)*(-1*b^1//3*(c+d*x)^1//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3))^-1//2*(a+b*x)^-1//2*(c+d*x)^1//6*(b*c+-1*a*d)^1//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3)*Elliptic.E(arccos(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-1*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2))+-3//2*3^3//4*b^1//3*d^-2*(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^2//3+b^2//3*(c+d*x)^2//3+b^1//3*(c+d*x)^1//3*(b*c+-1*a*d)^1//3))^(1/2)*(-1*b^1//3*(c+d*x)^1//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3))^-1//2*(a+b*x)^-1//2*(c+d*x)^1//6*(b*c+-1*a*d)^1//3*(1+-1*3^(1/2))*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3)*Elliptic.F(arccos(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-1*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate((a+b*x)^-1//2*(c+d*x)^-7//6, x) == :(6*(a+b*x)^(1/2)*(c+d*x)^-1//6*(b*c+-1*a*d)^-1+b^1//3*(a+b*x)^(1/2)*(c+d*x)^1//6*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-1*(b*c+-1*a*d)^-1*(6+6*3^(1/2))+6*3^1//4*b^1//3*d^-1*(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^2//3+b^2//3*(c+d*x)^2//3+b^1//3*(c+d*x)^1//3*(b*c+-1*a*d)^1//3))^(1/2)*(-1*b^1//3*(c+d*x)^1//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3))^-1//2*(a+b*x)^-1//2*(c+d*x)^1//6*(b*c+-1*a*d)^-2//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3)*Elliptic.E(arccos(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-1*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2))+3^3//4*b^1//3*d^-1*(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^2//3+b^2//3*(c+d*x)^2//3+b^1//3*(c+d*x)^1//3*(b*c+-1*a*d)^1//3))^(1/2)*(-1*b^1//3*(c+d*x)^1//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3))^-1//2*(a+b*x)^-1//2*(c+d*x)^1//6*(b*c+-1*a*d)^-2//3*(1+-1*3^(1/2))*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3)*Elliptic.F(arccos(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-1*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate((a+b*x)^-3//2*(c+d*x)^-7//6, x) == :(-2*(a+b*x)^-1//2*(c+d*x)^-1//6*(b*c+-1*a*d)^-1+-8*d*(a+b*x)^(1/2)*(c+d*x)^-1//6*(b*c+-1*a*d)^-2+-1*d*b^1//3*(a+b*x)^(1/2)*(c+d*x)^1//6*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-1*(b*c+-1*a*d)^-2*(8+8*3^(1/2))+-8*3^1//4*b^1//3*(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^2//3+b^2//3*(c+d*x)^2//3+b^1//3*(c+d*x)^1//3*(b*c+-1*a*d)^1//3))^(1/2)*(-1*b^1//3*(c+d*x)^1//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3))^-1//2*(a+b*x)^-1//2*(c+d*x)^1//6*(b*c+-1*a*d)^-5//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3)*Elliptic.E(arccos(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-1*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2))+-1//3*3^3//4*b^1//3*(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^2//3+b^2//3*(c+d*x)^2//3+b^1//3*(c+d*x)^1//3*(b*c+-1*a*d)^1//3))^(1/2)*(-1*b^1//3*(c+d*x)^1//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3))^-1//2*(a+b*x)^-1//2*(c+d*x)^1//6*(b*c+-1*a*d)^-5//3*(4+-4*3^(1/2))*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3)*Elliptic.F(arccos(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-1*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate((a+b*x)^-5//2*(c+d*x)^-7//6, x) == :(-2*(a+b*x)^-3//2*(c+d*x)^-1//6*(-3*a*d+3*b*c)^-1+20//9*d*(a+b*x)^-1//2*(c+d*x)^-1//6*(b*c+-1*a*d)^-2+80//9*d^2*(a+b*x)^(1/2)*(c+d*x)^-1//6*(b*c+-1*a*d)^-3+1//9*b^1//3*d^2*(a+b*x)^(1/2)*(c+d*x)^1//6*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-1*(b*c+-1*a*d)^-3*(80+80*3^(1/2))+80//9*d*3^1//4*b^1//3*(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^2//3+b^2//3*(c+d*x)^2//3+b^1//3*(c+d*x)^1//3*(b*c+-1*a*d)^1//3))^(1/2)*(-1*b^1//3*(c+d*x)^1//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3))^-1//2*(a+b*x)^-1//2*(c+d*x)^1//6*(b*c+-1*a*d)^-8//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3)*Elliptic.E(arccos(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-1*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2))+1//27*d*3^3//4*b^1//3*(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^2//3+b^2//3*(c+d*x)^2//3+b^1//3*(c+d*x)^1//3*(b*c+-1*a*d)^1//3))^(1/2)*(-1*b^1//3*(c+d*x)^1//3*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-2*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3))^-1//2*(a+b*x)^-1//2*(c+d*x)^1//6*(b*c+-1*a*d)^-8//3*(40+-40*3^(1/2))*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3)*Elliptic.F(arccos(((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+3^(1/2)))^-1*((b*c+-1*a*d)^1//3+-1*b^1//3*(c+d*x)^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate((a+b*x)^1//6*(c+d*x)^5//6, x) == :((1/2)*b^-1*(a+b*x)^7//6*(c+d*x)^5//6+-5//36*b^-11//6*d^-7//6*(b*c+-1*a*d)^2*arctanh(b^-1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6)+-5//144*b^-11//6*d^-7//6*(b*c+-1*a*d)^2*log(b^1//3+d^1//3*(a+b*x)^1//3*(c+d*x)^-1//3+b^1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6)+5//144*b^-11//6*d^-7//6*(b*c+-1*a*d)^2*log(b^1//3+d^1//3*(a+b*x)^1//3*(c+d*x)^-1//3+-1*b^1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6)+-5//72*3^(1/2)*b^-11//6*d^-7//6*(b*c+-1*a*d)^2*arctan(1//3*3^(1/2)+2//3*3^(1/2)*b^-1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6)+1//12*b^-1*d^-1*(a+b*x)^1//6*(c+d*x)^5//6*(-5*a*d+5*b*c)+5//72*3^(1/2)*b^-11//6*d^-7//6*(b*c+-1*a*d)^2*arctan(1//3*3^(1/2)+-2//3*3^(1/2)*b^-1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6))
@test integrate((a+b*x)^1//6*(c+d*x)^-1//6, x) == :(d^-1*(a+b*x)^1//6*(c+d*x)^5//6+-1//3*b^-5//6*d^-7//6*(b*c+-1*a*d)*arctanh(b^-1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6)+-1//12*b^-5//6*d^-7//6*(b*c+-1*a*d)*log(b^1//3+d^1//3*(a+b*x)^1//3*(c+d*x)^-1//3+b^1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6)+1//12*b^-5//6*d^-7//6*(b*c+-1*a*d)*log(b^1//3+d^1//3*(a+b*x)^1//3*(c+d*x)^-1//3+-1*b^1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6)+-1//6*3^(1/2)*b^-5//6*d^-7//6*(b*c+-1*a*d)*arctan(1//3*3^(1/2)+2//3*3^(1/2)*b^-1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6)+1//6*3^(1/2)*b^-5//6*d^-7//6*(b*c+-1*a*d)*arctan(1//3*3^(1/2)+-2//3*3^(1/2)*b^-1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6))
@test integrate((a+b*x)^1//6*(c+d*x)^-7//6, x) == :((1/2)*b^1//6*d^-7//6*log(b^1//3+d^1//3*(a+b*x)^1//3*(c+d*x)^-1//3+b^1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6)+-6*d^-1*(a+b*x)^1//6*(c+d*x)^-1//6+2*b^1//6*d^-7//6*arctanh(b^-1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6)+-1//2*b^1//6*d^-7//6*log(b^1//3+d^1//3*(a+b*x)^1//3*(c+d*x)^-1//3+-1*b^1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6)+3^(1/2)*b^1//6*d^-7//6*arctan(1//3*3^(1/2)+2//3*3^(1/2)*b^-1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6)+-1*3^(1/2)*b^1//6*d^-7//6*arctan(1//3*3^(1/2)+-2//3*3^(1/2)*b^-1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6))
@test integrate((a+b*x)^1//6*(c+d*x)^-13//6, x) == :(6*(a+b*x)^7//6*(c+d*x)^-7//6*(-7*a*d+7*b*c)^-1)
@test integrate((a+b*x)^1//6*(c+d*x)^-19//6, x) == :(6*(a+b*x)^7//6*(c+d*x)^-13//6*(-13*a*d+13*b*c)^-1+36//91*b*(a+b*x)^7//6*(c+d*x)^-7//6*(b*c+-1*a*d)^-2)
@test integrate((a+b*x)^1//6*(c+d*x)^-25//6, x) == :(6*(a+b*x)^7//6*(c+d*x)^-19//6*(-19*a*d+19*b*c)^-1+72//247*b*(a+b*x)^7//6*(c+d*x)^-13//6*(b*c+-1*a*d)^-2+432//1729*b^2*(a+b*x)^7//6*(c+d*x)^-7//6*(b*c+-1*a*d)^-3)
@test integrate((a+b*x)^1//6*(c+d*x)^-31//6, x) == :(6*(a+b*x)^7//6*(c+d*x)^-25//6*(-25*a*d+25*b*c)^-1+108//475*b*(a+b*x)^7//6*(c+d*x)^-19//6*(b*c+-1*a*d)^-2+1296//6175*b^2*(a+b*x)^7//6*(c+d*x)^-13//6*(b*c+-1*a*d)^-3+7776//43225*b^3*(a+b*x)^7//6*(c+d*x)^-7//6*(b*c+-1*a*d)^-4)
@test integrate((a+b*x)^5//6*(c+d*x)^1//6, x) == :((1/2)*b^-1*(a+b*x)^11//6*(c+d*x)^1//6+-5//36*b^-7//6*d^-11//6*(b*c+-1*a*d)^2*arctanh(b^-1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6)+-5//144*b^-7//6*d^-11//6*(b*c+-1*a*d)^2*log(b^1//3+d^1//3*(a+b*x)^1//3*(c+d*x)^-1//3+b^1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6)+5//144*b^-7//6*d^-11//6*(b*c+-1*a*d)^2*log(b^1//3+d^1//3*(a+b*x)^1//3*(c+d*x)^-1//3+-1*b^1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6)+-5//72*3^(1/2)*b^-7//6*d^-11//6*(b*c+-1*a*d)^2*arctan(1//3*3^(1/2)+-2//3*3^(1/2)*b^-1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6)+1//12*b^-1*d^-1*(a+b*x)^5//6*(c+d*x)^1//6*(b*c+-1*a*d)+5//72*3^(1/2)*b^-7//6*d^-11//6*(b*c+-1*a*d)^2*arctan(1//3*3^(1/2)+2//3*3^(1/2)*b^-1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6))
@test integrate((a+b*x)^5//6*(c+d*x)^-5//6, x) == :(d^-1*(a+b*x)^5//6*(c+d*x)^1//6+-1//3*b^-1//6*d^-11//6*(-5*a*d+5*b*c)*arctanh(b^-1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6)+-1//12*b^-1//6*d^-11//6*(-5*a*d+5*b*c)*log(b^1//3+d^1//3*(a+b*x)^1//3*(c+d*x)^-1//3+b^1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6)+1//12*b^-1//6*d^-11//6*(-5*a*d+5*b*c)*log(b^1//3+d^1//3*(a+b*x)^1//3*(c+d*x)^-1//3+-1*b^1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6)+-1//6*3^(1/2)*b^-1//6*d^-11//6*(-5*a*d+5*b*c)*arctan(1//3*3^(1/2)+-2//3*3^(1/2)*b^-1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6)+1//6*3^(1/2)*b^-1//6*d^-11//6*(-5*a*d+5*b*c)*arctan(1//3*3^(1/2)+2//3*3^(1/2)*b^-1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6))
@test integrate((a+b*x)^5//6*(c+d*x)^-11//6, x) == :((1/2)*b^5//6*d^-11//6*log(b^1//3+d^1//3*(a+b*x)^1//3*(c+d*x)^-1//3+b^1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6)+2*b^5//6*d^-11//6*arctanh(b^-1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6)+-6//5*d^-1*(a+b*x)^5//6*(c+d*x)^-5//6+-1//2*b^5//6*d^-11//6*log(b^1//3+d^1//3*(a+b*x)^1//3*(c+d*x)^-1//3+-1*b^1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6)+3^(1/2)*b^5//6*d^-11//6*arctan(1//3*3^(1/2)+-2//3*3^(1/2)*b^-1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6)+-1*3^(1/2)*b^5//6*d^-11//6*arctan(1//3*3^(1/2)+2//3*3^(1/2)*b^-1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6))
@test integrate((a+b*x)^5//6*(c+d*x)^-17//6, x) == :(6*(a+b*x)^11//6*(c+d*x)^-11//6*(-11*a*d+11*b*c)^-1)
@test integrate((a+b*x)^5//6*(c+d*x)^-23//6, x) == :(6*(a+b*x)^11//6*(c+d*x)^-17//6*(-17*a*d+17*b*c)^-1+36//187*b*(a+b*x)^11//6*(c+d*x)^-11//6*(b*c+-1*a*d)^-2)
@test integrate((a+b*x)^5//6*(c+d*x)^-29//6, x) == :(6*(a+b*x)^11//6*(c+d*x)^-23//6*(-23*a*d+23*b*c)^-1+72//391*b*(a+b*x)^11//6*(c+d*x)^-17//6*(b*c+-1*a*d)^-2+432//4301*b^2*(a+b*x)^11//6*(c+d*x)^-11//6*(b*c+-1*a*d)^-3)
@test integrate((a+b*x)^5//6*(c+d*x)^-35//6, x) == :(6*(a+b*x)^11//6*(c+d*x)^-29//6*(-29*a*d+29*b*c)^-1+108//667*b*(a+b*x)^11//6*(c+d*x)^-23//6*(b*c+-1*a*d)^-2+1296//11339*b^2*(a+b*x)^11//6*(c+d*x)^-17//6*(b*c+-1*a*d)^-3+7776//124729*b^3*(a+b*x)^11//6*(c+d*x)^-11//6*(b*c+-1*a*d)^-4)
@test integrate((a+b*x)^7//6*(c+d*x)^-1//6, x) == :((1/2)*d^-1*(a+b*x)^7//6*(c+d*x)^5//6+-7//144*b^-5//6*d^-13//6*(b*c+-1*a*d)^2*log(b^1//3+d^1//3*(a+b*x)^1//3*(c+d*x)^-1//3+-1*b^1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6)+-1//12*d^-2*(a+b*x)^1//6*(c+d*x)^5//6*(-7*a*d+7*b*c)+7//36*b^-5//6*d^-13//6*(b*c+-1*a*d)^2*arctanh(b^-1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6)+7//144*b^-5//6*d^-13//6*(b*c+-1*a*d)^2*log(b^1//3+d^1//3*(a+b*x)^1//3*(c+d*x)^-1//3+b^1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6)+-7//72*3^(1/2)*b^-5//6*d^-13//6*(b*c+-1*a*d)^2*arctan(1//3*3^(1/2)+-2//3*3^(1/2)*b^-1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6)+7//72*3^(1/2)*b^-5//6*d^-13//6*(b*c+-1*a*d)^2*arctan(1//3*3^(1/2)+2//3*3^(1/2)*b^-1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6))
@test integrate((a+b*x)^7//6*(c+d*x)^-7//6, x) == :(-6*d^-1*(a+b*x)^7//6*(c+d*x)^-1//6+7*b*d^-2*(a+b*x)^1//6*(c+d*x)^5//6+-7//3*b^1//6*d^-13//6*(b*c+-1*a*d)*arctanh(b^-1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6)+-7//12*b^1//6*d^-13//6*(b*c+-1*a*d)*log(b^1//3+d^1//3*(a+b*x)^1//3*(c+d*x)^-1//3+b^1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6)+7//12*b^1//6*d^-13//6*(b*c+-1*a*d)*log(b^1//3+d^1//3*(a+b*x)^1//3*(c+d*x)^-1//3+-1*b^1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6)+-7//6*3^(1/2)*b^1//6*d^-13//6*(b*c+-1*a*d)*arctan(1//3*3^(1/2)+2//3*3^(1/2)*b^-1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6)+7//6*3^(1/2)*b^1//6*d^-13//6*(b*c+-1*a*d)*arctan(1//3*3^(1/2)+-2//3*3^(1/2)*b^-1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6))
@test integrate((a+b*x)^7//6*(c+d*x)^-13//6, x) == :((1/2)*b^7//6*d^-13//6*log(b^1//3+d^1//3*(a+b*x)^1//3*(c+d*x)^-1//3+b^1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6)+2*b^7//6*d^-13//6*arctanh(b^-1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6)+-6//7*d^-1*(a+b*x)^7//6*(c+d*x)^-7//6+-1//2*b^7//6*d^-13//6*log(b^1//3+d^1//3*(a+b*x)^1//3*(c+d*x)^-1//3+-1*b^1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6)+3^(1/2)*b^7//6*d^-13//6*arctan(1//3*3^(1/2)+2//3*3^(1/2)*b^-1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6)+-1*3^(1/2)*b^7//6*d^-13//6*arctan(1//3*3^(1/2)+-2//3*3^(1/2)*b^-1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6)+-6*b*d^-2*(a+b*x)^1//6*(c+d*x)^-1//6)
@test integrate((a+b*x)^7//6*(c+d*x)^-19//6, x) == :(6*(a+b*x)^13//6*(c+d*x)^-13//6*(-13*a*d+13*b*c)^-1)
@test integrate((a+b*x)^7//6*(c+d*x)^-25//6, x) == :(6*(a+b*x)^13//6*(c+d*x)^-19//6*(-19*a*d+19*b*c)^-1+36//247*b*(a+b*x)^13//6*(c+d*x)^-13//6*(b*c+-1*a*d)^-2)
@test integrate((a+b*x)^7//6*(c+d*x)^-31//6, x) == :(6*(a+b*x)^13//6*(c+d*x)^-25//6*(-25*a*d+25*b*c)^-1+72//475*b*(a+b*x)^13//6*(c+d*x)^-19//6*(b*c+-1*a*d)^-2+432//6175*b^2*(a+b*x)^13//6*(c+d*x)^-13//6*(b*c+-1*a*d)^-3)
@test integrate((a+b*x)^7//6*(c+d*x)^-37//6, x) == :(6*(a+b*x)^13//6*(c+d*x)^-31//6*(-31*a*d+31*b*c)^-1+108//775*b*(a+b*x)^13//6*(c+d*x)^-25//6*(b*c+-1*a*d)^-2+1296//14725*b^2*(a+b*x)^13//6*(c+d*x)^-19//6*(b*c+-1*a*d)^-3+7776//191425*b^3*(a+b*x)^13//6*(c+d*x)^-13//6*(b*c+-1*a*d)^-4)
@test integrate((a+b*x)^-1//6*(c+d*x)^7//6, x) == :((1/2)*b^-1*(a+b*x)^5//6*(c+d*x)^7//6+-7//144*b^-13//6*d^-5//6*(b*c+-1*a*d)^2*log(b^1//3+d^1//3*(a+b*x)^1//3*(c+d*x)^-1//3+-1*b^1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6)+1//12*b^-2*(a+b*x)^5//6*(c+d*x)^1//6*(-7*a*d+7*b*c)+7//36*b^-13//6*d^-5//6*(b*c+-1*a*d)^2*arctanh(b^-1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6)+7//144*b^-13//6*d^-5//6*(b*c+-1*a*d)^2*log(b^1//3+d^1//3*(a+b*x)^1//3*(c+d*x)^-1//3+b^1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6)+-7//72*3^(1/2)*b^-13//6*d^-5//6*(b*c+-1*a*d)^2*arctan(1//3*3^(1/2)+2//3*3^(1/2)*b^-1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6)+7//72*3^(1/2)*b^-13//6*d^-5//6*(b*c+-1*a*d)^2*arctan(1//3*3^(1/2)+-2//3*3^(1/2)*b^-1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6))
@test integrate((a+b*x)^-1//6*(c+d*x)^1//6, x) == :(b^-1*(a+b*x)^5//6*(c+d*x)^1//6+-1//12*b^-7//6*d^-5//6*(b*c+-1*a*d)*log(b^1//3+d^1//3*(a+b*x)^1//3*(c+d*x)^-1//3+-1*b^1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6)+1//3*b^-7//6*d^-5//6*(b*c+-1*a*d)*arctanh(b^-1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6)+1//12*b^-7//6*d^-5//6*(b*c+-1*a*d)*log(b^1//3+d^1//3*(a+b*x)^1//3*(c+d*x)^-1//3+b^1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6)+-1//6*3^(1/2)*b^-7//6*d^-5//6*(b*c+-1*a*d)*arctan(1//3*3^(1/2)+2//3*3^(1/2)*b^-1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6)+1//6*3^(1/2)*b^-7//6*d^-5//6*(b*c+-1*a*d)*arctan(1//3*3^(1/2)+-2//3*3^(1/2)*b^-1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6))
@test integrate((a+b*x)^-1//6*(c+d*x)^-5//6, x) == :((1/2)*b^-1//6*d^-5//6*log(b^1//3+d^1//3*(a+b*x)^1//3*(c+d*x)^-1//3+b^1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6)+2*b^-1//6*d^-5//6*arctanh(b^-1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6)+-1//2*b^-1//6*d^-5//6*log(b^1//3+d^1//3*(a+b*x)^1//3*(c+d*x)^-1//3+-1*b^1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6)+3^(1/2)*b^-1//6*d^-5//6*arctan(1//3*3^(1/2)+-2//3*3^(1/2)*b^-1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6)+-1*3^(1/2)*b^-1//6*d^-5//6*arctan(1//3*3^(1/2)+2//3*3^(1/2)*b^-1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6))
@test integrate((a+b*x)^-1//6*(c+d*x)^-11//6, x) == :(6*(a+b*x)^5//6*(c+d*x)^-5//6*(-5*a*d+5*b*c)^-1)
@test integrate((a+b*x)^-1//6*(c+d*x)^-17//6, x) == :(6*(a+b*x)^5//6*(c+d*x)^-11//6*(-11*a*d+11*b*c)^-1+36//55*b*(a+b*x)^5//6*(c+d*x)^-5//6*(b*c+-1*a*d)^-2)
@test integrate((a+b*x)^-1//6*(c+d*x)^-23//6, x) == :(6*(a+b*x)^5//6*(c+d*x)^-17//6*(-17*a*d+17*b*c)^-1+72//187*b*(a+b*x)^5//6*(c+d*x)^-11//6*(b*c+-1*a*d)^-2+432//935*b^2*(a+b*x)^5//6*(c+d*x)^-5//6*(b*c+-1*a*d)^-3)
@test integrate((a+b*x)^-1//6*(c+d*x)^-29//6, x) == :(6*(a+b*x)^5//6*(c+d*x)^-23//6*(-23*a*d+23*b*c)^-1+108//391*b*(a+b*x)^5//6*(c+d*x)^-17//6*(b*c+-1*a*d)^-2+1296//4301*b^2*(a+b*x)^5//6*(c+d*x)^-11//6*(b*c+-1*a*d)^-3+7776//21505*b^3*(a+b*x)^5//6*(c+d*x)^-5//6*(b*c+-1*a*d)^-4)
@test integrate((a+b*x)^-5//6*(c+d*x)^11//6, x) == :((1/2)*b^-1*(a+b*x)^1//6*(c+d*x)^11//6+-55//144*b^-17//6*d^-1//6*(b*c+-1*a*d)^2*log(b^1//3+d^1//3*(a+b*x)^1//3*(c+d*x)^-1//3+-1*b^1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6)+1//12*b^-2*(a+b*x)^1//6*(c+d*x)^5//6*(-11*a*d+11*b*c)+55//36*b^-17//6*d^-1//6*(b*c+-1*a*d)^2*arctanh(b^-1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6)+55//144*b^-17//6*d^-1//6*(b*c+-1*a*d)^2*log(b^1//3+d^1//3*(a+b*x)^1//3*(c+d*x)^-1//3+b^1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6)+-55//72*3^(1/2)*b^-17//6*d^-1//6*(b*c+-1*a*d)^2*arctan(1//3*3^(1/2)+-2//3*3^(1/2)*b^-1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6)+55//72*3^(1/2)*b^-17//6*d^-1//6*(b*c+-1*a*d)^2*arctan(1//3*3^(1/2)+2//3*3^(1/2)*b^-1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6))
@test integrate((a+b*x)^-5//6*(c+d*x)^5//6, x) == :(b^-1*(a+b*x)^1//6*(c+d*x)^5//6+-1//12*b^-11//6*d^-1//6*(-5*a*d+5*b*c)*log(b^1//3+d^1//3*(a+b*x)^1//3*(c+d*x)^-1//3+-1*b^1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6)+1//3*b^-11//6*d^-1//6*(-5*a*d+5*b*c)*arctanh(b^-1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6)+1//12*b^-11//6*d^-1//6*(-5*a*d+5*b*c)*log(b^1//3+d^1//3*(a+b*x)^1//3*(c+d*x)^-1//3+b^1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6)+-1//6*3^(1/2)*b^-11//6*d^-1//6*(-5*a*d+5*b*c)*arctan(1//3*3^(1/2)+-2//3*3^(1/2)*b^-1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6)+1//6*3^(1/2)*b^-11//6*d^-1//6*(-5*a*d+5*b*c)*arctan(1//3*3^(1/2)+2//3*3^(1/2)*b^-1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6))
@test integrate((a+b*x)^-5//6*(c+d*x)^-1//6, x) == :((1/2)*b^-5//6*d^-1//6*log(b^1//3+d^1//3*(a+b*x)^1//3*(c+d*x)^-1//3+b^1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6)+2*b^-5//6*d^-1//6*arctanh(b^-1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6)+-1//2*b^-5//6*d^-1//6*log(b^1//3+d^1//3*(a+b*x)^1//3*(c+d*x)^-1//3+-1*b^1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6)+3^(1/2)*b^-5//6*d^-1//6*arctan(1//3*3^(1/2)+2//3*3^(1/2)*b^-1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6)+-1*3^(1/2)*b^-5//6*d^-1//6*arctan(1//3*3^(1/2)+-2//3*3^(1/2)*b^-1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6))
@test integrate((a+b*x)^-5//6*(c+d*x)^-7//6, x) == :(6*(a+b*x)^1//6*(c+d*x)^-1//6*(b*c+-1*a*d)^-1)
@test integrate((a+b*x)^-5//6*(c+d*x)^-13//6, x) == :(6*(a+b*x)^1//6*(c+d*x)^-7//6*(-7*a*d+7*b*c)^-1+36//7*b*(a+b*x)^1//6*(c+d*x)^-1//6*(b*c+-1*a*d)^-2)
@test integrate((a+b*x)^-5//6*(c+d*x)^-19//6, x) == :(6*(a+b*x)^1//6*(c+d*x)^-13//6*(-13*a*d+13*b*c)^-1+72//91*b*(a+b*x)^1//6*(c+d*x)^-7//6*(b*c+-1*a*d)^-2+432//91*b^2*(a+b*x)^1//6*(c+d*x)^-1//6*(b*c+-1*a*d)^-3)
@test integrate((a+b*x)^-5//6*(c+d*x)^-25//6, x) == :(6*(a+b*x)^1//6*(c+d*x)^-19//6*(-19*a*d+19*b*c)^-1+108//247*b*(a+b*x)^1//6*(c+d*x)^-13//6*(b*c+-1*a*d)^-2+1296//1729*b^2*(a+b*x)^1//6*(c+d*x)^-7//6*(b*c+-1*a*d)^-3+7776//1729*b^3*(a+b*x)^1//6*(c+d*x)^-1//6*(b*c+-1*a*d)^-4)
@test integrate((a+b*x)^-7//6*(c+d*x)^13//6, x) == :(-6*b^-1*(a+b*x)^-1//6*(c+d*x)^13//6+-91//144*b^-19//6*d^1//6*(b*c+-1*a*d)^2*log(b^1//3+d^1//3*(a+b*x)^1//3*(c+d*x)^-1//3+-1*b^1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6)+13//2*d*b^-2*(a+b*x)^5//6*(c+d*x)^7//6+91//36*b^-19//6*d^1//6*(b*c+-1*a*d)^2*arctanh(b^-1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6)+91//144*b^-19//6*d^1//6*(b*c+-1*a*d)^2*log(b^1//3+d^1//3*(a+b*x)^1//3*(c+d*x)^-1//3+b^1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6)+-91//72*3^(1/2)*b^-19//6*d^1//6*(b*c+-1*a*d)^2*arctan(1//3*3^(1/2)+2//3*3^(1/2)*b^-1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6)+91//12*d*b^-3*(a+b*x)^5//6*(c+d*x)^1//6*(b*c+-1*a*d)+91//72*3^(1/2)*b^-19//6*d^1//6*(b*c+-1*a*d)^2*arctan(1//3*3^(1/2)+-2//3*3^(1/2)*b^-1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6))
@test integrate((a+b*x)^-7//6*(c+d*x)^7//6, x) == :(-6*b^-1*(a+b*x)^-1//6*(c+d*x)^7//6+7*d*b^-2*(a+b*x)^5//6*(c+d*x)^1//6+-7//12*b^-13//6*d^1//6*(b*c+-1*a*d)*log(b^1//3+d^1//3*(a+b*x)^1//3*(c+d*x)^-1//3+-1*b^1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6)+7//3*b^-13//6*d^1//6*(b*c+-1*a*d)*arctanh(b^-1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6)+7//12*b^-13//6*d^1//6*(b*c+-1*a*d)*log(b^1//3+d^1//3*(a+b*x)^1//3*(c+d*x)^-1//3+b^1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6)+-7//6*3^(1/2)*b^-13//6*d^1//6*(b*c+-1*a*d)*arctan(1//3*3^(1/2)+2//3*3^(1/2)*b^-1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6)+7//6*3^(1/2)*b^-13//6*d^1//6*(b*c+-1*a*d)*arctan(1//3*3^(1/2)+-2//3*3^(1/2)*b^-1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6))
@test integrate((a+b*x)^-7//6*(c+d*x)^1//6, x) == :((1/2)*b^-7//6*d^1//6*log(b^1//3+d^1//3*(a+b*x)^1//3*(c+d*x)^-1//3+b^1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6)+-6*b^-1*(a+b*x)^-1//6*(c+d*x)^1//6+2*b^-7//6*d^1//6*arctanh(b^-1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6)+-1//2*b^-7//6*d^1//6*log(b^1//3+d^1//3*(a+b*x)^1//3*(c+d*x)^-1//3+-1*b^1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6)+3^(1/2)*b^-7//6*d^1//6*arctan(1//3*3^(1/2)+-2//3*3^(1/2)*b^-1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6)+-1*3^(1/2)*b^-7//6*d^1//6*arctan(1//3*3^(1/2)+2//3*3^(1/2)*b^-1//6*d^1//6*(a+b*x)^1//6*(c+d*x)^-1//6))
@test integrate((a+b*x)^-7//6*(c+d*x)^-5//6, x) == :(-6*(a+b*x)^-1//6*(c+d*x)^1//6*(b*c+-1*a*d)^-1)
@test integrate((a+b*x)^-7//6*(c+d*x)^-11//6, x) == :(-6*(a+b*x)^-1//6*(c+d*x)^-5//6*(b*c+-1*a*d)^-1+-36//5*d*(a+b*x)^5//6*(c+d*x)^-5//6*(b*c+-1*a*d)^-2)
@test integrate((a+b*x)^-7//6*(c+d*x)^-17//6, x) == :(-6*(a+b*x)^-1//6*(c+d*x)^-11//6*(b*c+-1*a*d)^-1+-72//11*d*(a+b*x)^5//6*(c+d*x)^-11//6*(b*c+-1*a*d)^-2+-432//55*b*d*(a+b*x)^5//6*(c+d*x)^-5//6*(b*c+-1*a*d)^-3)
@test integrate((a+b*x)^-7//6*(c+d*x)^-23//6, x) == :(-6*(a+b*x)^-1//6*(c+d*x)^-17//6*(b*c+-1*a*d)^-1+-108//17*d*(a+b*x)^5//6*(c+d*x)^-17//6*(b*c+-1*a*d)^-2+-7776//935*d*b^2*(a+b*x)^5//6*(c+d*x)^-5//6*(b*c+-1*a*d)^-4+-1296//187*b*d*(a+b*x)^5//6*(c+d*x)^-11//6*(b*c+-1*a*d)^-3)
@test integrate((a+b*x)^m*(a+b*x*(2+m)), x) == :(x*(a+b*x)^(1+m))
@test integrate((a+b*x)^m*(c+d*x)^3, x) == :(b^-4*d^3*(4+m)^-1*(a+b*x)^(4+m)+b^-4*(1+m)^-1*(a+b*x)^(1+m)*(b*c+-1*a*d)^3+3*d*b^-4*(2+m)^-1*(a+b*x)^(2+m)*(b*c+-1*a*d)^2+3*b^-4*d^2*(3+m)^-1*(a+b*x)^(3+m)*(b*c+-1*a*d))
@test integrate((a+b*x)^m*(c+d*x)^2, x) == :(b^-3*d^2*(3+m)^-1*(a+b*x)^(3+m)+b^-3*(1+m)^-1*(a+b*x)^(1+m)*(b*c+-1*a*d)^2+2*d*b^-3*(2+m)^-1*(a+b*x)^(2+m)*(b*c+-1*a*d))
@test integrate((a+b*x)^m*(c+d*x), x) == :(d*b^-2*(2+m)^-1*(a+b*x)^(2+m)+b^-2*(1+m)^-1*(a+b*x)^(1+m)*(b*c+-1*a*d))
@test integrate((a+b*x)^3*(c+d*x)^n, x) == :(b^3*d^-4*(4+n)^-1*(c+d*x)^(4+n)+-1*d^-4*(1+n)^-1*(c+d*x)^(1+n)*(b*c+-1*a*d)^3+-3*b^2*d^-4*(3+n)^-1*(c+d*x)^(3+n)*(b*c+-1*a*d)+3*b*d^-4*(2+n)^-1*(c+d*x)^(2+n)*(b*c+-1*a*d)^2)
@test integrate((a+b*x)^2*(c+d*x)^n, x) == :(b^2*d^-3*(3+n)^-1*(c+d*x)^(3+n)+d^-3*(1+n)^-1*(c+d*x)^(1+n)*(b*c+-1*a*d)^2+-2*b*d^-3*(2+n)^-1*(c+d*x)^(2+n)*(b*c+-1*a*d))
@test integrate((c+d*x)^n*(a+b*x), x) == :(b*d^-2*(2+n)^-1*(c+d*x)^(2+n)+-1*d^-2*(1+n)^-1*(c+d*x)^(1+n)*(b*c+-1*a*d))
@test integrate((c+d*x)^n, x) == :(d^-1*(1+n)^-1*(c+d*x)^(1+n))
@test integrate((a+b*x)^(-4+n)*(c+d*x)^(-1n), x) == :(-1*(3+-1n)^-1*(a+b*x)^(-3+n)*(c+d*x)^(1+-1n)*(b*c+-1*a*d)^-1+2*d*(2+-1n)^-1*(3+-1n)^-1*(a+b*x)^(-2+n)*(c+d*x)^(1+-1n)*(b*c+-1*a*d)^-2+-2*d^2*(1+-1n)^-1*(2+-1n)^-1*(3+-1n)^-1*(a+b*x)^(-1+n)*(c+d*x)^(1+-1n)*(b*c+-1*a*d)^-3)
@test integrate((a+b*x)^(-3+n)*(c+d*x)^(-1n), x) == :(-1*(2+-1n)^-1*(a+b*x)^(-2+n)*(c+d*x)^(1+-1n)*(b*c+-1*a*d)^-1+d*(1+-1n)^-1*(2+-1n)^-1*(a+b*x)^(-1+n)*(c+d*x)^(1+-1n)*(b*c+-1*a*d)^-2)
@test integrate((a+b*x)^(-2+n)*(c+d*x)^(-1n), x) == :(-1*(1+-1n)^-1*(a+b*x)^(-1+n)*(c+d*x)^(1+-1n)*(b*c+-1*a*d)^-1)
@test integrate((a+b*x)^(-2+-1n)*(c+d*x)^n, x) == :(-1*(1+n)^-1*(a+b*x)^(-1+-1n)*(c+d*x)^(1+n)*(b*c+-1*a*d)^-1)
@test integrate((a+b*x)^(-3+-1n)*(c+d*x)^n, x) == :(-1*(2+n)^-1*(a+b*x)^(-2+-1n)*(c+d*x)^(1+n)*(b*c+-1*a*d)^-1+d*(1+n)^-1*(2+n)^-1*(a+b*x)^(-1+-1n)*(c+d*x)^(1+n)*(b*c+-1*a*d)^-2)
@test integrate((a+b*x)^(-4+-1n)*(c+d*x)^n, x) == :(-1*(3+n)^-1*(a+b*x)^(-3+-1n)*(c+d*x)^(1+n)*(b*c+-1*a*d)^-1+2*d*(2+n)^-1*(3+n)^-1*(a+b*x)^(-2+-1n)*(c+d*x)^(1+n)*(b*c+-1*a*d)^-2+-2*d^2*(1+n)^-1*(2+n)^-1*(3+n)^-1*(a+b*x)^(-1+-1n)*(c+d*x)^(1+n)*(b*c+-1*a*d)^-3)
@test integrate((a+b*x)^(-5+-1n)*(c+d*x)^n, x) == :(-1*(4+n)^-1*(a+b*x)^(-4+-1n)*(c+d*x)^(1+n)*(b*c+-1*a*d)^-1+3*d*(3+n)^-1*(4+n)^-1*(a+b*x)^(-3+-1n)*(c+d*x)^(1+n)*(b*c+-1*a*d)^-2+-6*d^2*(2+n)^-1*(3+n)^-1*(4+n)^-1*(a+b*x)^(-2+-1n)*(c+d*x)^(1+n)*(b*c+-1*a*d)^-3+6*d^3*(1+n)^-1*(2+n)^-1*(3+n)^-1*(4+n)^-1*(a+b*x)^(-1+-1n)*(c+d*x)^(1+n)*(b*c+-1*a*d)^-4)
@test integrate((a+b*x)^n*(c+d*x)^(-2+-1n), x) == :((1+n)^-1*(a+b*x)^(1+n)*(c+d*x)^(-1+-1n)*(b*c+-1*a*d)^-1)
@test integrate((a+b*x)^n*(c+d*x)^(-3+-1n), x) == :((2+n)^-1*(a+b*x)^(1+n)*(c+d*x)^(-2+-1n)*(b*c+-1*a*d)^-1+b*(1+n)^-1*(2+n)^-1*(a+b*x)^(1+n)*(c+d*x)^(-1+-1n)*(b*c+-1*a*d)^-2)
@test integrate((a+b*x)^n*(c+d*x)^(-4+-1n), x) == :((3+n)^-1*(a+b*x)^(1+n)*(c+d*x)^(-3+-1n)*(b*c+-1*a*d)^-1+2*b*(2+n)^-1*(3+n)^-1*(a+b*x)^(1+n)*(c+d*x)^(-2+-1n)*(b*c+-1*a*d)^-2+2*b^2*(1+n)^-1*(2+n)^-1*(3+n)^-1*(a+b*x)^(1+n)*(c+d*x)^(-1+-1n)*(b*c+-1*a*d)^-3)
@test integrate((a+b*x)^n*(c+d*x)^(-5+-1n), x) == :((4+n)^-1*(a+b*x)^(1+n)*(c+d*x)^(-4+-1n)*(b*c+-1*a*d)^-1+3*b*(3+n)^-1*(4+n)^-1*(a+b*x)^(1+n)*(c+d*x)^(-3+-1n)*(b*c+-1*a*d)^-2+6*b^2*(2+n)^-1*(3+n)^-1*(4+n)^-1*(a+b*x)^(1+n)*(c+d*x)^(-2+-1n)*(b*c+-1*a*d)^-3+6*b^3*(1+n)^-1*(2+n)^-1*(3+n)^-1*(4+n)^-1*(a+b*x)^(1+n)*(c+d*x)^(-1+-1n)*(b*c+-1*a*d)^-4)
@test integrate((a+b*x)^-2*(c+d*x)^-1, x) == :(-1*(a+b*x)^-1*(b*c+-1*a*d)^-1+d*(b*c+-1*a*d)^-2*log(c+d*x)+-1*d*(b*c+-1*a*d)^-2*log(a+b*x))
@test integrate((a+b*x)^(-1+-1*b*c*(b*c+-1*a*d)^-1)*(c+d*x)^(-1+a*d*(b*c+-1*a*d)^-1), x) == :(-1*b^-1*c^-1*(a+b*x)^(-1*b*c*(b*c+-1*a*d)^-1)*(c+d*x)^(a*d*(b*c+-1*a*d)^-1)+a^-1*b^-1*c^-1*(a+b*x)^(-1*a*d*(b*c+-1*a*d)^-1)*(c+d*x)^(a*d*(b*c+-1*a*d)^-1))
@test integrate((a+b*x)^((b*c+-1*a*d)^-1*(a*d+-2*b*c))*(c+d*x)^((a*d+-1*b*c)^-1*(b*c+-2*a*d)), x) == :(-1*b^-1*c^-1*(a+b*x)^(-1*b*c*(b*c+-1*a*d)^-1)*(c+d*x)^(a*d*(b*c+-1*a*d)^-1)+a^-1*b^-1*c^-1*(a+b*x)^(-1*a*d*(b*c+-1*a*d)^-1)*(c+d*x)^(a*d*(b*c+-1*a*d)^-1))
@test integrate(a+b*x+c*x^2+d*x^3, x) == :(a*x+(1/2)*b*x^2+1//3*c*x^3+1//4*d*x^4)
@test integrate(x^4+-1*x^3, x) == :(-1//4*x^4+1//5*x^5)
@test integrate(-1+x^5, x) == :(-1x+1//6*x^6)
@test integrate(7+4x, x) == :(2*x^2+7x)
@test integrate(4x+pi*x^3, x) == :(2*x^2+1//4*pi*x^4)
@test integrate(2x+5*x^2, x) == :(x^2+5//3*x^3)
@test integrate((1/2)*x^2+1//3*x^3, x) == :(1//6*x^3+1//12*x^4)
@test integrate(3+-5x+2*x^2, x) == :(3x+-5//2*x^2+2//3*x^3)
@test integrate(x^2+x^3+-2x, x) == :(-1*x^2+1//3*x^3+1//4*x^4)
@test integrate(1+-1*x^2+-3*x^5, x) == :(x+-1//2*x^6+-1//3*x^3)
@test integrate(5+2x+3*x^2+4*x^3, x) == :(x^2+x^3+x^4+5x)
@test integrate(a+b*x^-1+c*x^-2+d*x^-3, x) == :(a*x+b*log(x)+-1*c*x^-1+-1//2*d*x^-2)
@test integrate(x+x^-5+x^5, x) == :((1/2)*x^2+-1//4*x^-4+1//6*x^6)
@test integrate(x^-1+x^-3+x^-2, x) == :(-1*x^-1+-1//2*x^-2+log(x))
@test integrate(-2*x^-2+3*x^-1, x) == :(2*x^-1+3*log(x))
@test integrate(x^6+-1//7*x^-6, x) == :(1//7*x^7+1//35*x^-5)
@test integrate(1+x+x^-1, x) == :(x+(1/2)*x^2+log(x))
@test integrate(-3*x^-3+4*x^-2, x) == :(-4*x^-1+3//2*x^-2)
@test integrate(x^-1+x^2+2x, x) == :(x^2+1//3*x^3+log(x))
@test integrate(x^5//6+-1*x^3, x) == :(-1//4*x^4+6//11*x^11//6)
@test integrate(33+x^1//33, x) == :(33x+33//34*x^34//33)
@test integrate((1/2)*x^-1//2+2*x^(1/2), x) == :(x^(1/2)+4//3*x^3//2)
@test integrate(-1*x^-2+6*x^(1/2)+10*x^-1, x) == :(x^-1+4*x^3//2+10*log(x))
@test integrate(x^-3//2+x^3//2, x) == :(-2*x^-1//2+2//5*x^5//2)
@test integrate(-5*x^3//2+7*x^5//2, x) == :(-2*x^5//2+2*x^7//2)
@test integrate(x^(1/2)+2*x^-1//2+-1//2*x, x) == :(4*x^(1/2)+-1//4*x^2+2//3*x^3//2)
@test integrate(x^3//2+-2*x^-1+1//5*x^(1/2), x) == :(-2*log(x)+2//5*x^5//2+2//15*x^3//2)

ext: jl

max_stars_repo_path: test/1 Algebraic functions/1.1 Binomial products/1.1.1 Linear/1.1.1.2 (a+b x)^m (c+d x)^n.jl