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

@test integrate(x^2*(d^2+-1*e^2*x^2)^(1/2)*(d+e*x), x) == :(1//5*e^-3*(d^2+-1*e^2*x^2)^5//2+-1//3*d^2*e^-3*(d^2+-1*e^2*x^2)^3//2+1//8*d^5*e^-3*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+-1//4*d*x*e^-2*(d^2+-1*e^2*x^2)^3//2+1//8*x*d^3*e^-2*(d^2+-1*e^2*x^2)^(1/2))
@test integrate(x^4*(d^2+-1*e^2*x^2)^3//2*(d+e*x), x) == :(-1//9*e^-1*x^4*(d^2+-1*e^2*x^2)^5//2+3//128*d^9*e^-5*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+-4//63*d^2*e^-3*x^2*(d^2+-1*e^2*x^2)^5//2+-1//8*d*e^-2*x^3*(d^2+-1*e^2*x^2)^5//2+-1//5040*d^3*e^-5*(d^2+-1*e^2*x^2)^5//2*(128d+315*e*x)+1//64*x*d^5*e^-4*(d^2+-1*e^2*x^2)^3//2+3//128*x*d^7*e^-4*(d^2+-1*e^2*x^2)^(1/2))
@test integrate(x^3*(d^2+-1*e^2*x^2)^3//2*(d+e*x), x) == :(-1//8*e^-1*x^3*(d^2+-1*e^2*x^2)^5//2+3//128*d^8*e^-4*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+-1//7*d*e^-2*x^2*(d^2+-1*e^2*x^2)^5//2+-1//560*d^2*e^-4*(d^2+-1*e^2*x^2)^5//2*(32d+35*e*x)+1//64*x*d^4*e^-3*(d^2+-1*e^2*x^2)^3//2+3//128*x*d^6*e^-3*(d^2+-1*e^2*x^2)^(1/2))
@test integrate(x^2*(d^2+-1*e^2*x^2)^3//2*(d+e*x), x) == :(1//7*e^-3*(d^2+-1*e^2*x^2)^7//2+-1//5*d^2*e^-3*(d^2+-1*e^2*x^2)^5//2+1//16*d^7*e^-3*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+-1//6*d*x*e^-2*(d^2+-1*e^2*x^2)^5//2+1//16*x*d^5*e^-2*(d^2+-1*e^2*x^2)^(1/2)+1//24*x*d^3*e^-2*(d^2+-1*e^2*x^2)^3//2)
@test integrate(x*(d^2+-1*e^2*x^2)^3//2*(d+e*x), x) == :(-1//30*e^-2*(d^2+-1*e^2*x^2)^5//2*(6d+5*e*x)+1//16*d^6*e^-2*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+1//16*x*d^4*e^-1*(d^2+-1*e^2*x^2)^(1/2)+1//24*x*d^2*e^-1*(d^2+-1*e^2*x^2)^3//2)
@test integrate(x*(d^2+-1*e^2*x^2)^3//2*(d+e*x), x) == :(-1//30*e^-2*(d^2+-1*e^2*x^2)^5//2*(6d+5*e*x)+1//16*d^6*e^-2*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+1//16*x*d^4*e^-1*(d^2+-1*e^2*x^2)^(1/2)+1//24*x*d^2*e^-1*(d^2+-1*e^2*x^2)^3//2)
@test integrate(x^-1*(d^2+-1*e^2*x^2)^3//2*(d+e*x), x) == :((d^2+-1*e^2*x^2)^3//2*(1//3*d+1//4*e*x)+-1*d^4*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+3//8*d^4*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+1//8*d^2*(d^2+-1*e^2*x^2)^(1/2)*(8d+3*e*x))
@test integrate(x^-2*(d^2+-1*e^2*x^2)^3//2*(d+e*x), x) == :(-1*e*d^3*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+-3//2*e*d^3*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+-1//3*x^-1*(d^2+-1*e^2*x^2)^3//2*(3d+-1*e*x)+(1/2)*d*e*(d^2+-1*e^2*x^2)^(1/2)*(2d+-3*e*x))
@test integrate(x^-3*(d^2+-1*e^2*x^2)^3//2*(d+e*x), x) == :(-3//2*d^2*e^2*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+-1//2*x^-2*(d^2+-1*e^2*x^2)^3//2*(d+-1*e*x)+3//2*d^2*e^2*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+-3//2*d*e*x^-1*(d^2+-1*e^2*x^2)^(1/2)*(d+e*x))
@test integrate(x^-4*(d^2+-1*e^2*x^2)^3//2*(d+e*x), x) == :(d*e^3*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+-1//6*x^-3*(d^2+-1*e^2*x^2)^3//2*(2d+3*e*x)+3//2*d*e^3*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+(1/2)*e^2*x^-1*(d^2+-1*e^2*x^2)^(1/2)*(2d+-3*e*x))
@test integrate(x^-5*(d^2+-1*e^2*x^2)^3//2*(d+e*x), x) == :(e^4*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+-3//8*e^4*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+-1//12*x^-4*(d^2+-1*e^2*x^2)^3//2*(3d+4*e*x)+1//8*e^2*x^-2*(d^2+-1*e^2*x^2)^(1/2)*(3d+8*e*x))
@test integrate(x^-6*(d^2+-1*e^2*x^2)^3//2*(d+e*x), x) == :(-3//8*d^-1*e^5*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+-1//4*e*x^-4*(d^2+-1*e^2*x^2)^3//2+-1//5*d^-1*x^-5*(d^2+-1*e^2*x^2)^5//2+3//8*e^3*x^-2*(d^2+-1*e^2*x^2)^(1/2))
@test integrate(x^-7*(d^2+-1*e^2*x^2)^3//2*(d+e*x), x) == :(-1//6*d^-1*x^-6*(d^2+-1*e^2*x^2)^5//2+-1//16*d^-2*e^6*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+-1//5*e*d^-2*x^-5*(d^2+-1*e^2*x^2)^5//2+-1//24*d^-1*e^2*x^-4*(d^2+-1*e^2*x^2)^3//2+1//16*d^-1*e^4*x^-2*(d^2+-1*e^2*x^2)^(1/2))
@test integrate(x^-8*(d^2+-1*e^2*x^2)^3//2*(d+e*x), x) == :(-1//7*d^-1*x^-7*(d^2+-1*e^2*x^2)^5//2+-1//16*d^-3*e^7*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+-2//35*d^-3*e^2*x^-5*(d^2+-1*e^2*x^2)^5//2+-1//6*e*d^-2*x^-6*(d^2+-1*e^2*x^2)^5//2+-1//24*d^-2*e^3*x^-4*(d^2+-1*e^2*x^2)^3//2+1//16*d^-2*e^5*x^-2*(d^2+-1*e^2*x^2)^(1/2))
@test integrate(x^-9*(d^2+-1*e^2*x^2)^3//2*(d+e*x), x) == :(-3//128*d^-4*e^8*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+-1//8*d^-1*x^-8*(d^2+-1*e^2*x^2)^5//2+-2//35*d^-4*e^3*x^-5*(d^2+-1*e^2*x^2)^5//2+-1//7*e*d^-2*x^-7*(d^2+-1*e^2*x^2)^5//2+-1//16*d^-3*e^2*x^-6*(d^2+-1*e^2*x^2)^5//2+-1//64*d^-3*e^4*x^-4*(d^2+-1*e^2*x^2)^3//2+3//128*d^-3*e^6*x^-2*(d^2+-1*e^2*x^2)^(1/2))
@test integrate(x^2*(d^2+-1*e^2*x^2)^-1//2*(d+e*x), x) == :(1//3*e^-3*(d^2+-1*e^2*x^2)^3//2+(1/2)*d^3*e^-3*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+-1*d^2*e^-3*(d^2+-1*e^2*x^2)^(1/2)+-1//2*d*x*e^-2*(d^2+-1*e^2*x^2)^(1/2))
@test integrate(x^2*(d^2+-1*e^2*x^2)^-3//2*(d+e*x), x) == :(e^-3*(d^2+-1*e^2*x^2)^(1/2)+-1*d*e^-3*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+d*e^-3*(d^2+-1*e^2*x^2)^-1//2*(d+e*x))
@test integrate(x^2*(d^2+-1*e^2*x^2)^-5//2*(d+e*x), x) == :(-2//3*e^-3*(d^2+-1*e^2*x^2)^-1//2+1//3*d^-1*e^-1*x^2*(d^2+-1*e^2*x^2)^-3//2*(d+e*x))
@test integrate(x^7*(d^2+-1*e^2*x^2)^-7//2*(d+e*x), x) == :(-7//2*d^2*e^-8*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+1//10*e^-8*(d^2+-1*e^2*x^2)^(1/2)*(32d+35*e*x)+-1//15*e^-4*x^4*(d^2+-1*e^2*x^2)^-3//2*(6d+7*e*x)+1//5*e^-2*x^6*(d^2+-1*e^2*x^2)^-5//2*(d+e*x)+1//15*e^-6*x^2*(d^2+-1*e^2*x^2)^-1//2*(24d+35*e*x))
@test integrate(x^6*(d^2+-1*e^2*x^2)^-7//2*(d+e*x), x) == :(16//5*e^-7*(d^2+-1*e^2*x^2)^(1/2)+-1*d*e^-7*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+-1//15*e^-4*x^3*(d^2+-1*e^2*x^2)^-3//2*(5d+6*e*x)+1//5*x*e^-6*(d^2+-1*e^2*x^2)^-1//2*(5d+8*e*x)+1//5*e^-2*x^5*(d^2+-1*e^2*x^2)^-5//2*(d+e*x))
@test integrate(x^5*(d^2+-1*e^2*x^2)^-7//2*(d+e*x), x) == :(-1*e^-6*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+1//15*e^-6*(d^2+-1*e^2*x^2)^-1//2*(8d+15*e*x)+-1//15*e^-4*x^2*(d^2+-1*e^2*x^2)^-3//2*(4d+5*e*x)+1//5*e^-2*x^4*(d^2+-1*e^2*x^2)^-5//2*(d+e*x))
@test integrate(x^4*(d^2+-1*e^2*x^2)^-7//2*(d+e*x), x) == :(4//5*e^-5*(d^2+-1*e^2*x^2)^-1//2+-4//15*d^2*e^-5*(d^2+-1*e^2*x^2)^-3//2+1//5*d^-1*e^-1*x^4*(d^2+-1*e^2*x^2)^-5//2*(d+e*x))
@test integrate(x^3*(d^2+-1*e^2*x^2)^-7//2*(d+e*x), x) == :(-1//15*e^-4*(d^2+-1*e^2*x^2)^-3//2*(2d+3*e*x)+1//5*x*d^-2*e^-3*(d^2+-1*e^2*x^2)^-1//2+1//5*e^-2*x^2*(d^2+-1*e^2*x^2)^-5//2*(d+e*x))
@test integrate(x^2*(d^2+-1*e^2*x^2)^-7//2*(d+e*x), x) == :(-2//15*x*d^-3*e^-2*(d^2+-1*e^2*x^2)^-1//2+-1//15*d^-1*e^-3*(d^2+-1*e^2*x^2)^-3//2*(2d+-2*e*x)+1//5*d^-1*e^-1*x^2*(d^2+-1*e^2*x^2)^-5//2*(d+e*x))
@test integrate(x*(d^2+-1*e^2*x^2)^-7//2*(d+e*x), x) == :(1//5*e^-2*(d^2+-1*e^2*x^2)^-5//2*(d+e*x)+-2//15*x*d^-4*e^-1*(d^2+-1*e^2*x^2)^-1//2+-1//15*x*d^-2*e^-1*(d^2+-1*e^2*x^2)^-3//2)
@test integrate((d^2+-1*e^2*x^2)^-7//2*(d+e*x), x) == :(4//15*x*d^-3*(d^2+-1*e^2*x^2)^-3//2+8//15*x*d^-5*(d^2+-1*e^2*x^2)^-1//2+1//5*d^-1*e^-1*(d^2+-1*e^2*x^2)^-5//2*(d+e*x))
@test integrate(x^-1*(d^2+-1*e^2*x^2)^-7//2*(d+e*x), x) == :(-1*d^-6*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+1//5*d^-2*(d^2+-1*e^2*x^2)^-5//2*(d+e*x)+1//15*d^-6*(d^2+-1*e^2*x^2)^-1//2*(15d+8*e*x)+1//15*d^-4*(d^2+-1*e^2*x^2)^-3//2*(5d+4*e*x))
@test integrate(x^-2*(d^2+-1*e^2*x^2)^-7//2*(d+e*x), x) == :(-1*e*d^-7*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+-16//5*d^-7*x^-1*(d^2+-1*e^2*x^2)^(1/2)+1//5*d^-6*x^-1*(d^2+-1*e^2*x^2)^-1//2*(8d+5*e*x)+1//5*d^-2*x^-1*(d^2+-1*e^2*x^2)^-5//2*(d+e*x)+1//15*d^-4*x^-1*(d^2+-1*e^2*x^2)^-3//2*(6d+5*e*x))
@test integrate(x^-3*(d^2+-1*e^2*x^2)^-7//2*(d+e*x), x) == :(-7//2*d^-8*e^2*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+-7//2*d^-7*x^-2*(d^2+-1*e^2*x^2)^(1/2)+-16//5*e*d^-8*x^-1*(d^2+-1*e^2*x^2)^(1/2)+1//5*d^-2*x^-2*(d^2+-1*e^2*x^2)^-5//2*(d+e*x)+1//15*d^-6*x^-2*(d^2+-1*e^2*x^2)^-1//2*(35d+24*e*x)+1//15*d^-4*x^-2*(d^2+-1*e^2*x^2)^-3//2*(7d+6*e*x))
@test integrate(x^2*(d^2+-1*e^2*x^2)^-9//2*(d+e*x), x) == :(-8//105*x*d^-5*e^-2*(d^2+-1*e^2*x^2)^-1//2+-4//105*x*d^-3*e^-2*(d^2+-1*e^2*x^2)^-3//2+-1//35*d^-1*e^-3*(d^2+-1*e^2*x^2)^-5//2*(2d+-4*e*x)+1//7*d^-1*e^-1*x^2*(d^2+-1*e^2*x^2)^-7//2*(d+e*x))
@test integrate(x^2*(d^2+-1*e^2*x^2)^-11//2*(d+e*x), x) == :(-16//315*x*d^-7*e^-2*(d^2+-1*e^2*x^2)^-1//2+-8//315*x*d^-5*e^-2*(d^2+-1*e^2*x^2)^-3//2+-2//105*x*d^-3*e^-2*(d^2+-1*e^2*x^2)^-5//2+-1//63*d^-1*e^-3*(d^2+-1*e^2*x^2)^-7//2*(2d+-6*e*x)+1//9*d^-1*e^-1*x^2*(d^2+-1*e^2*x^2)^-9//2*(d+e*x))
@test integrate(x^2*(1+-1*a^2*x^2)^-3//2*(1+-1*a*x), x) == :(-1*a^-3*(1+-1*a^2*x^2)^(1/2)+-1*a^-3*arcsin(a*x)+-1*a^-3*(1+-1*a^2*x^2)^-1//2*(1+-1*a*x))
@test integrate(x^4*(d+e*x)^2*(d^2+-1*e^2*x^2)^-1//2, x) == :(-1//6*x^5*(d^2+-1*e^2*x^2)^(1/2)+11//16*d^6*e^-5*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+-11//24*d^2*e^-2*x^3*(d^2+-1*e^2*x^2)^(1/2)+-8//15*d^3*e^-3*x^2*(d^2+-1*e^2*x^2)^(1/2)+-2//5*d*e^-1*x^4*(d^2+-1*e^2*x^2)^(1/2)+-1//240*d^4*e^-5*(d^2+-1*e^2*x^2)^(1/2)*(256d+165*e*x))
@test integrate(x^3*(d+e*x)^2*(d^2+-1*e^2*x^2)^-1//2, x) == :(-1//5*x^4*(d^2+-1*e^2*x^2)^(1/2)+3//4*d^5*e^-4*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+-3//5*d^2*e^-2*x^2*(d^2+-1*e^2*x^2)^(1/2)+-3//20*d^3*e^-4*(d^2+-1*e^2*x^2)^(1/2)*(8d+5*e*x)+-1//2*d*e^-1*x^3*(d^2+-1*e^2*x^2)^(1/2))
@test integrate(x^2*(d+e*x)^2*(d^2+-1*e^2*x^2)^-1//2, x) == :(-1//4*x^3*(d^2+-1*e^2*x^2)^(1/2)+7//8*d^4*e^-3*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+-2//3*d*e^-1*x^2*(d^2+-1*e^2*x^2)^(1/2)+-1//24*d^2*e^-3*(d^2+-1*e^2*x^2)^(1/2)*(32d+21*e*x))
@test integrate(x*(d+e*x)^2*(d^2+-1*e^2*x^2)^-1//2, x) == :(-1//3*x^2*(d^2+-1*e^2*x^2)^(1/2)+d^3*e^-2*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+-1//3*d*e^-2*(d^2+-1*e^2*x^2)^(1/2)*(5d+3*e*x))
@test integrate((d+e*x)^2*(d^2+-1*e^2*x^2)^-1//2, x) == :(-3//2*d*e^-1*(d^2+-1*e^2*x^2)^(1/2)+-1//2*e^-1*(d^2+-1*e^2*x^2)^(1/2)*(d+e*x)+3//2*d^2*e^-1*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2))
@test integrate(x^-1*(d+e*x)^2*(d^2+-1*e^2*x^2)^-1//2, x) == :(-1*(d^2+-1*e^2*x^2)^(1/2)+-1*d*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+2*d*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2))
@test integrate(x^-2*(d+e*x)^2*(d^2+-1*e^2*x^2)^-1//2, x) == :(e*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+-1*x^-1*(d^2+-1*e^2*x^2)^(1/2)+-2*e*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2)))
@test integrate(x^-3*(d+e*x)^2*(d^2+-1*e^2*x^2)^-1//2, x) == :(-1//2*x^-2*(d^2+-1*e^2*x^2)^(1/2)+-3//2*d^-1*e^2*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+-2*e*d^-1*x^-1*(d^2+-1*e^2*x^2)^(1/2))
@test integrate(x^-4*(d+e*x)^2*(d^2+-1*e^2*x^2)^-1//2, x) == :(-1//3*x^-3*(d^2+-1*e^2*x^2)^(1/2)+-1*d^-2*e^3*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+-1*e*d^-1*x^-2*(d^2+-1*e^2*x^2)^(1/2)+-5//3*d^-2*e^2*x^-1*(d^2+-1*e^2*x^2)^(1/2))
@test integrate(x^-5*(d+e*x)^2*(d^2+-1*e^2*x^2)^-1//2, x) == :(-1//4*x^-4*(d^2+-1*e^2*x^2)^(1/2)+-7//8*d^-3*e^4*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+-7//8*d^-2*e^2*x^-2*(d^2+-1*e^2*x^2)^(1/2)+-4//3*d^-3*e^3*x^-1*(d^2+-1*e^2*x^2)^(1/2)+-2//3*e*d^-1*x^-3*(d^2+-1*e^2*x^2)^(1/2))
@test integrate(x^-6*(d+e*x)^2*(d^2+-1*e^2*x^2)^-1//2, x) == :(-1//5*x^-5*(d^2+-1*e^2*x^2)^(1/2)+-3//4*d^-4*e^5*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+-6//5*d^-4*e^4*x^-1*(d^2+-1*e^2*x^2)^(1/2)+-3//4*d^-3*e^3*x^-2*(d^2+-1*e^2*x^2)^(1/2)+-3//5*d^-2*e^2*x^-3*(d^2+-1*e^2*x^2)^(1/2)+-1//2*e*d^-1*x^-4*(d^2+-1*e^2*x^2)^(1/2))
@test integrate(x^5*(d+e*x)^2*(d^2+-1*e^2*x^2)^-7//2, x) == :(e^-6*(d^2+-1*e^2*x^2)^(1/2)+-2*d*e^-6*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+-22//15*d^3*e^-6*(d^2+-1*e^2*x^2)^-3//2*(d+e*x)+1//5*d^4*e^-6*(d+e*x)^2*(d^2+-1*e^2*x^2)^-5//2+2//15*d*e^-6*(d^2+-1*e^2*x^2)^-1//2*(30d+23*e*x))
@test integrate(x^4*(d+e*x)^2*(d^2+-1*e^2*x^2)^-7//2, x) == :(-1*e^-5*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+1//15*e^-5*(d^2+-1*e^2*x^2)^-1//2*(30d+26*e*x)+-17//15*d^2*e^-5*(d^2+-1*e^2*x^2)^-3//2*(d+e*x)+1//5*d^3*e^-5*(d+e*x)^2*(d^2+-1*e^2*x^2)^-5//2)
@test integrate(x^3*(d+e*x)^2*(d^2+-1*e^2*x^2)^-7//2, x) == :(-4//5*d*e^-4*(d^2+-1*e^2*x^2)^-3//2*(d+e*x)+1//5*d^-1*e^-4*(d^2+-1*e^2*x^2)^-1//2*(5d+2*e*x)+1//5*d^2*e^-4*(d+e*x)^2*(d^2+-1*e^2*x^2)^-5//2)
@test integrate(x^2*(d+e*x)^2*(d^2+-1*e^2*x^2)^-7//2, x) == :(-1//15*e^-3*(d^2+-1*e^2*x^2)^-3//2*(7d+7*e*x)+1//5*d*e^-3*(d+e*x)^2*(d^2+-1*e^2*x^2)^-5//2+1//15*x*d^-2*e^-2*(d^2+-1*e^2*x^2)^-1//2)
@test integrate(x*(d+e*x)^2*(d^2+-1*e^2*x^2)^-7//2, x) == :(1//5*e^-2*(d+e*x)^2*(d^2+-1*e^2*x^2)^-5//2+-4//15*x*d^-3*e^-1*(d^2+-1*e^2*x^2)^-1//2+-1//15*d^-1*e^-2*(d^2+-1*e^2*x^2)^-3//2*(2d+2*e*x))
@test integrate((d+e*x)^2*(d^2+-1*e^2*x^2)^-7//2, x) == :(1//5*x*d^-2*(d^2+-1*e^2*x^2)^-3//2+1//5*e^-1*(d^2+-1*e^2*x^2)^-5//2*(2d+2*e*x)+2//5*x*d^-4*(d^2+-1*e^2*x^2)^-1//2)
@test integrate(x^-1*(d+e*x)^2*(d^2+-1*e^2*x^2)^-7//2, x) == :(-1*d^-5*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+1//5*d^-1*(d^2+-1*e^2*x^2)^-5//2*(2d+2*e*x)+1//15*d^-5*(d^2+-1*e^2*x^2)^-1//2*(15d+16*e*x)+1//15*d^-3*(d^2+-1*e^2*x^2)^-3//2*(5d+8*e*x))
@test integrate(x^-2*(d+e*x)^2*(d^2+-1*e^2*x^2)^-7//2, x) == :(-1*d^-6*x^-1*(d^2+-1*e^2*x^2)^(1/2)+-2*e*d^-6*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+1//15*e*d^-6*(d^2+-1*e^2*x^2)^-1//2*(30d+41*e*x)+1//15*e*d^-4*(d^2+-1*e^2*x^2)^-3//2*(10d+13*e*x)+2//5*e*d^-2*(d^2+-1*e^2*x^2)^-5//2*(d+e*x))
@test integrate(x^-3*(d+e*x)^2*(d^2+-1*e^2*x^2)^-7//2, x) == :(-9//2*d^-7*e^2*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+-1//2*d^-6*x^-2*(d^2+-1*e^2*x^2)^(1/2)+-2*e*d^-7*x^-1*(d^2+-1*e^2*x^2)^(1/2)+1//5*d^-5*e^2*(d^2+-1*e^2*x^2)^-3//2*(5d+6*e*x)+2//5*d^-7*e^2*(d^2+-1*e^2*x^2)^-1//2*(10d+11*e*x)+2//5*d^-3*e^2*(d^2+-1*e^2*x^2)^-5//2*(d+e*x))
@test integrate(x^-4*(d+e*x)^2*(d^2+-1*e^2*x^2)^-7//2, x) == :(-7*d^-8*e^3*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+-1//3*d^-6*x^-3*(d^2+-1*e^2*x^2)^(1/2)+-1*e*d^-7*x^-2*(d^2+-1*e^2*x^2)^(1/2)+-14//3*d^-8*e^2*x^-1*(d^2+-1*e^2*x^2)^(1/2)+1//15*d^-6*e^3*(d^2+-1*e^2*x^2)^-3//2*(20d+23*e*x)+2//5*d^-4*e^3*(d^2+-1*e^2*x^2)^-5//2*(d+e*x)+2//15*d^-8*e^3*(d^2+-1*e^2*x^2)^-1//2*(45d+53*e*x))
@test integrate(x^3*(1+x)^2*(1+-1*x^2)^-1//2, x) == :(3//4*arcsin(x)+-1*(1+-1*x^2)^(1/2)*(6//5+3//4*x)+-3//5*x^2*(1+-1*x^2)^(1/2)+-1//2*x^3*(1+-1*x^2)^(1/2)+-1//5*x^4*(1+-1*x^2)^(1/2))
@test integrate(x^2*(1+x)^2*(1+-1*x^2)^-1//2, x) == :(7//8*arcsin(x)+-1*(1+-1*x^2)^(1/2)*(4//3+7//8*x)+-2//3*x^2*(1+-1*x^2)^(1/2)+-1//4*x^3*(1+-1*x^2)^(1/2))
@test integrate(x*(1+x)^2*(1+-1*x^2)^-1//2, x) == :(-1*(1+-1*x^2)^(1/2)*(5//3+x)+-1//3*x^2*(1+-1*x^2)^(1/2)+arcsin(x))
@test integrate((1+x)^2*(1+-1*x^2)^-1//2, x) == :(-3//2*(1+-1*x^2)^(1/2)+3//2*arcsin(x)+-1*(1+-1*x^2)^(1/2)*(1/2+(1/2)*x))
@test integrate(x^-1*(1+x)^2*(1+-1*x^2)^-1//2, x) == :(-1*(1+-1*x^2)^(1/2)+-1*arctanh((1+-1*x^2)^(1/2))+2*arcsin(x))
@test integrate(x^-2*(1+x)^2*(1+-1*x^2)^-1//2, x) == :(-2*arctanh((1+-1*x^2)^(1/2))+-1*x^-1*(1+-1*x^2)^(1/2)+arcsin(x))
@test integrate(x^-3*(1+x)^2*(1+-1*x^2)^-1//2, x) == :(-3//2*arctanh((1+-1*x^2)^(1/2))+-2*x^-1*(1+-1*x^2)^(1/2)+-1//2*x^-2*(1+-1*x^2)^(1/2))
@test integrate(x^-4*(1+x)^2*(1+-1*x^2)^-1//2, x) == :(-1*arctanh((1+-1*x^2)^(1/2))+-1*x^-2*(1+-1*x^2)^(1/2)+-5//3*x^-1*(1+-1*x^2)^(1/2)+-1//3*x^-3*(1+-1*x^2)^(1/2))
@test integrate(x^-5*(1+x)^2*(1+-1*x^2)^-1//2, x) == :(-7//8*arctanh((1+-1*x^2)^(1/2))+-7//8*x^-2*(1+-1*x^2)^(1/2)+-4//3*x^-1*(1+-1*x^2)^(1/2)+-2//3*x^-3*(1+-1*x^2)^(1/2)+-1//4*x^-4*(1+-1*x^2)^(1/2))
@test integrate(x^-6*(1+x)^2*(1+-1*x^2)^-1//2, x) == :(-3//4*arctanh((1+-1*x^2)^(1/2))+-6//5*x^-1*(1+-1*x^2)^(1/2)+-3//4*x^-2*(1+-1*x^2)^(1/2)+-3//5*x^-3*(1+-1*x^2)^(1/2)+-1//2*x^-4*(1+-1*x^2)^(1/2)+-1//5*x^-5*(1+-1*x^2)^(1/2))
@test integrate(x^-5*(d+e*x)^3*(d^2+-1*e^2*x^2)^(1/2), x) == :(-1*e^4*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+13//8*e^4*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+-1*e*x^-3*(d^2+-1*e^2*x^2)^3//2+-1//4*d*x^-4*(d^2+-1*e^2*x^2)^3//2+-1//8*e^2*x^-2*(d^2+-1*e^2*x^2)^(1/2)*(13d+8*e*x))
@test integrate(x^5*(d+e*x)^3*(d^2+-1*e^2*x^2)^5//2, x) == :(-3//13*d*x^6*(d^2+-1*e^2*x^2)^7//2+-1//14*e*x^7*(d^2+-1*e^2*x^2)^7//2+35//2048*d^14*e^-6*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+-124//1287*d^5*e^-4*x^2*(d^2+-1*e^2*x^2)^7//2+-31//143*d^3*e^-2*x^4*(d^2+-1*e^2*x^2)^7//2+-7//24*d^2*e^-1*x^5*(d^2+-1*e^2*x^2)^7//2+-7//48*d^4*e^-3*x^3*(d^2+-1*e^2*x^2)^7//2+-1//1153152*d^6*e^-6*(d^2+-1*e^2*x^2)^7//2*(31744d+63063*e*x)+7//768*x*d^8*e^-5*(d^2+-1*e^2*x^2)^5//2+35//2048*x*d^12*e^-5*(d^2+-1*e^2*x^2)^(1/2)+35//3072*x*d^10*e^-5*(d^2+-1*e^2*x^2)^3//2)
@test integrate(x^4*(d+e*x)^3*(d^2+-1*e^2*x^2)^5//2, x) == :(-1//4*d*x^5*(d^2+-1*e^2*x^2)^7//2+-1//13*e*x^6*(d^2+-1*e^2*x^2)^7//2+27//1024*d^13*e^-5*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+-45//143*d^2*e^-1*x^4*(d^2+-1*e^2*x^2)^7//2+-20//143*d^4*e^-3*x^2*(d^2+-1*e^2*x^2)^7//2+-9//40*d^3*e^-2*x^3*(d^2+-1*e^2*x^2)^7//2+-1//320320*d^5*e^-5*(d^2+-1*e^2*x^2)^7//2*(12800d+27027*e*x)+9//512*x*d^9*e^-4*(d^2+-1*e^2*x^2)^3//2+9//640*x*d^7*e^-4*(d^2+-1*e^2*x^2)^5//2+27//1024*x*d^11*e^-4*(d^2+-1*e^2*x^2)^(1/2))
@test integrate(x^3*(d+e*x)^3*(d^2+-1*e^2*x^2)^5//2, x) == :(-3//11*d*x^4*(d^2+-1*e^2*x^2)^7//2+-1//12*e*x^5*(d^2+-1*e^2*x^2)^7//2+41//1024*d^12*e^-4*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+-41//120*d^2*e^-1*x^3*(d^2+-1*e^2*x^2)^7//2+-23//99*d^3*e^-2*x^2*(d^2+-1*e^2*x^2)^7//2+-1//221760*d^4*e^-4*(d^2+-1*e^2*x^2)^7//2*(14720d+28413*e*x)+41//1024*x*d^10*e^-3*(d^2+-1*e^2*x^2)^(1/2)+41//1536*x*d^8*e^-3*(d^2+-1*e^2*x^2)^3//2+41//1920*x*d^6*e^-3*(d^2+-1*e^2*x^2)^5//2)
@test integrate(x^2*(d+e*x)^3*(d^2+-1*e^2*x^2)^5//2, x) == :(-3//10*d*x^3*(d^2+-1*e^2*x^2)^7//2+-1//11*e*x^4*(d^2+-1*e^2*x^2)^7//2+19//256*d^11*e^-3*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+-37//99*d^2*e^-1*x^2*(d^2+-1*e^2*x^2)^7//2+-1//55440*d^3*e^-3*(d^2+-1*e^2*x^2)^7//2*(5920d+13167*e*x)+19//256*x*d^9*e^-2*(d^2+-1*e^2*x^2)^(1/2)+19//384*x*d^7*e^-2*(d^2+-1*e^2*x^2)^3//2+19//480*x*d^5*e^-2*(d^2+-1*e^2*x^2)^5//2)
@test integrate(x*(d+e*x)^3*(d^2+-1*e^2*x^2)^5//2, x) == :(-33//560*d^3*e^-2*(d^2+-1*e^2*x^2)^7//2+-1//10*e^-2*(d+e*x)^3*(d^2+-1*e^2*x^2)^7//2+33//256*d^10*e^-2*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+-11//240*d^2*e^-2*(d^2+-1*e^2*x^2)^7//2*(d+e*x)+-1//30*d*e^-2*(d+e*x)^2*(d^2+-1*e^2*x^2)^7//2+11//128*x*d^6*e^-1*(d^2+-1*e^2*x^2)^3//2+11//160*x*d^4*e^-1*(d^2+-1*e^2*x^2)^5//2+33//256*x*d^8*e^-1*(d^2+-1*e^2*x^2)^(1/2))
@test integrate((d+e*x)^3*(d^2+-1*e^2*x^2)^5//2, x) == :(-11//56*d^2*e^-1*(d^2+-1*e^2*x^2)^7//2+-1//9*e^-1*(d+e*x)^2*(d^2+-1*e^2*x^2)^7//2+11//48*x*d^3*(d^2+-1*e^2*x^2)^5//2+55//128*x*d^7*(d^2+-1*e^2*x^2)^(1/2)+55//128*d^9*e^-1*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+55//192*x*d^5*(d^2+-1*e^2*x^2)^3//2+-11//72*d*e^-1*(d^2+-1*e^2*x^2)^7//2*(d+e*x))
@test integrate(x^-1*(d+e*x)^3*(d^2+-1*e^2*x^2)^5//2, x) == :(-1*d^8*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+-3//7*d*(d^2+-1*e^2*x^2)^7//2+125//128*d^8*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+-1//8*e*x*(d^2+-1*e^2*x^2)^7//2+1//128*d^6*(d^2+-1*e^2*x^2)^(1/2)*(128d+125*e*x)+1//192*d^4*(d^2+-1*e^2*x^2)^3//2*(64d+125*e*x)+1//240*d^2*(d^2+-1*e^2*x^2)^5//2*(48d+125*e*x))
@test integrate(x^-2*(d+e*x)^3*(d^2+-1*e^2*x^2)^5//2, x) == :(-1//7*e*(d^2+-1*e^2*x^2)^7//2+-1*d*x^-1*(d^2+-1*e^2*x^2)^7//2+-3*e*d^7*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+-15//16*e*d^7*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+1//8*e*d^3*(d^2+-1*e^2*x^2)^3//2*(8d+-5*e*x)+1//10*d*e*(d^2+-1*e^2*x^2)^5//2*(6d+-5*e*x)+3//16*e*d^5*(d^2+-1*e^2*x^2)^(1/2)*(16d+-5*e*x))
@test integrate(x^-3*(d+e*x)^3*(d^2+-1*e^2*x^2)^5//2, x) == :(-3*e*x^-1*(d^2+-1*e^2*x^2)^7//2+-85//16*d^6*e^2*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+-1//2*d*x^-2*(d^2+-1*e^2*x^2)^7//2+-1//2*d^6*e^2*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+1//30*e^2*(d^2+-1*e^2*x^2)^5//2*(3d+-85*e*x)+1//16*d^4*e^2*(d^2+-1*e^2*x^2)^(1/2)*(8d+-85*e*x)+1//24*d^2*e^2*(d^2+-1*e^2*x^2)^3//2*(4d+-85*e*x))
@test integrate(x^-4*(d+e*x)^3*(d^2+-1*e^2*x^2)^5//2, x) == :(-25//8*d^5*e^3*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+-3//2*e*x^-2*(d^2+-1*e^2*x^2)^7//2+-1//3*d*x^-3*(d^2+-1*e^2*x^2)^7//2+13//2*d^5*e^3*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+-1//8*d^3*e^3*(d^2+-1*e^2*x^2)^(1/2)*(52d+25*e*x)+-1//12*d*e^3*(d^2+-1*e^2*x^2)^3//2*(26d+25*e*x)+-1//30*e^2*x^-1*(d^2+-1*e^2*x^2)^5//2*(50d+39*e*x))
@test integrate(x^-5*(d+e*x)^3*(d^2+-1*e^2*x^2)^5//2, x) == :(-1*e*x^-3*(d^2+-1*e^2*x^2)^7//2+-1//4*d*x^-4*(d^2+-1*e^2*x^2)^7//2+45//8*d^4*e^4*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+45//8*d^4*e^4*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+-45//8*d^2*e^4*(d^2+-1*e^2*x^2)^(1/2)*(d+-1*e*x)+-3//8*e^2*x^-2*(d^2+-1*e^2*x^2)^5//2*(3d+2*e*x)+15//8*d*e^3*x^-1*(d^2+-1*e^2*x^2)^3//2*(2d+-1*e*x))
@test integrate(x^-6*(d+e*x)^3*(d^2+-1*e^2*x^2)^5//2, x) == :(-25//8*d^3*e^5*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+-3//4*e*x^-4*(d^2+-1*e^2*x^2)^7//2+-1//5*d*x^-5*(d^2+-1*e^2*x^2)^7//2+13//2*d^3*e^5*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+-1//60*e^2*x^-3*(d^2+-1*e^2*x^2)^5//2*(52d+25*e*x)+1//8*d^2*e^4*x^-1*(d^2+-1*e^2*x^2)^(1/2)*(52d+25*e*x)+1//24*d*e^3*x^-2*(d^2+-1*e^2*x^2)^3//2*(25d+-52*e*x))
@test integrate(x^-7*(d+e*x)^3*(d^2+-1*e^2*x^2)^5//2, x) == :(-85//16*d^2*e^6*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+-3//5*e*x^-5*(d^2+-1*e^2*x^2)^7//2+-1//2*d^2*e^6*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+-1//6*d*x^-6*(d^2+-1*e^2*x^2)^7//2+-1//120*e^2*x^-4*(d^2+-1*e^2*x^2)^5//2*(85d+12*e*x)+-1//16*d*e^5*x^-1*(d^2+-1*e^2*x^2)^(1/2)*(8d+-85*e*x)+1//48*d*e^3*x^-3*(d^2+-1*e^2*x^2)^3//2*(8d+85*e*x))
@test integrate(x^-8*(d+e*x)^3*(d^2+-1*e^2*x^2)^5//2, x) == :(-3*d*e^7*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+-15//16*d*e^7*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+-1//2*e*x^-6*(d^2+-1*e^2*x^2)^7//2+-1//7*d*x^-7*(d^2+-1*e^2*x^2)^7//2+-3//16*e^6*x^-1*(d^2+-1*e^2*x^2)^(1/2)*(16d+-5*e*x)+-1//40*e^2*x^-5*(d^2+-1*e^2*x^2)^5//2*(24d+5*e*x)+1//16*e^4*x^-3*(d^2+-1*e^2*x^2)^3//2*(16d+5*e*x))
@test integrate(x^-9*(d+e*x)^3*(d^2+-1*e^2*x^2)^5//2, x) == :(-1*e^8*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+125//128*e^8*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+-3//7*e*x^-7*(d^2+-1*e^2*x^2)^7//2+-1//8*d*x^-8*(d^2+-1*e^2*x^2)^7//2+-1//128*e^6*x^-2*(d^2+-1*e^2*x^2)^(1/2)*(125d+128*e*x)+-1//240*e^2*x^-6*(d^2+-1*e^2*x^2)^5//2*(125d+48*e*x)+1//192*e^4*x^-4*(d^2+-1*e^2*x^2)^3//2*(125d+64*e*x))
@test integrate(x^-10*(d+e*x)^3*(d^2+-1*e^2*x^2)^5//2, x) == :(-55//128*e^7*x^-2*(d^2+-1*e^2*x^2)^(1/2)+-11//48*e^3*x^-6*(d^2+-1*e^2*x^2)^5//2+-3//8*e*x^-8*(d^2+-1*e^2*x^2)^7//2+-1//9*d*x^-9*(d^2+-1*e^2*x^2)^7//2+55//128*d^-1*e^9*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+55//192*e^5*x^-4*(d^2+-1*e^2*x^2)^3//2+-29//63*d^-1*e^2*x^-7*(d^2+-1*e^2*x^2)^7//2)
@test integrate(x^-11*(d+e*x)^3*(d^2+-1*e^2*x^2)^5//2, x) == :(-1//3*e*x^-9*(d^2+-1*e^2*x^2)^7//2+-1//10*d*x^-10*(d^2+-1*e^2*x^2)^7//2+33//256*d^-2*e^10*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+-33//80*d^-1*e^2*x^-8*(d^2+-1*e^2*x^2)^7//2+-33//256*d^-1*e^8*x^-2*(d^2+-1*e^2*x^2)^(1/2)+-11//160*d^-1*e^4*x^-6*(d^2+-1*e^2*x^2)^5//2+-5//21*d^-2*e^3*x^-7*(d^2+-1*e^2*x^2)^7//2+11//128*d^-1*e^6*x^-4*(d^2+-1*e^2*x^2)^3//2)
@test integrate(x^-12*(d+e*x)^3*(d^2+-1*e^2*x^2)^5//2, x) == :(-3//10*e*x^-10*(d^2+-1*e^2*x^2)^7//2+-1//11*d*x^-11*(d^2+-1*e^2*x^2)^7//2+19//256*d^-3*e^11*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+-74//693*d^-3*e^4*x^-7*(d^2+-1*e^2*x^2)^7//2+-37//99*d^-1*e^2*x^-9*(d^2+-1*e^2*x^2)^7//2+-19//80*d^-2*e^3*x^-8*(d^2+-1*e^2*x^2)^7//2+-19//256*d^-2*e^9*x^-2*(d^2+-1*e^2*x^2)^(1/2)+-19//480*d^-2*e^5*x^-6*(d^2+-1*e^2*x^2)^5//2+19//384*d^-2*e^7*x^-4*(d^2+-1*e^2*x^2)^3//2)
@test integrate(x^5*(d+e*x)^3*(d^2+-1*e^2*x^2)^-7//2, x) == :((1/2)*x*e^-5*(d^2+-1*e^2*x^2)^(1/2)+3*d*e^-6*(d^2+-1*e^2*x^2)^(1/2)+-13//2*d^2*e^-6*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+-23//15*d^3*e^-6*(d+e*x)^2*(d^2+-1*e^2*x^2)^-3//2+1//5*d^4*e^-6*(d+e*x)^3*(d^2+-1*e^2*x^2)^-5//2+127//15*d^2*e^-6*(d^2+-1*e^2*x^2)^-1//2*(d+e*x))
@test integrate(x^4*(d+e*x)^3*(d^2+-1*e^2*x^2)^-7//2, x) == :(e^-5*(d^2+-1*e^2*x^2)^(1/2)+-3*d*e^-5*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+-6//5*d^2*e^-5*(d+e*x)^2*(d^2+-1*e^2*x^2)^-3//2+1//5*d^3*e^-5*(d+e*x)^3*(d^2+-1*e^2*x^2)^-5//2+24//5*d*e^-5*(d^2+-1*e^2*x^2)^-1//2*(d+e*x))
@test integrate(x^3*(d+e*x)^3*(d^2+-1*e^2*x^2)^-7//2, x) == :(-1*e^-4*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+1//15*e^-4*(d^2+-1*e^2*x^2)^-1//2*(32d+32*e*x)+-13//15*d*e^-4*(d+e*x)^2*(d^2+-1*e^2*x^2)^-3//2+1//5*d^2*e^-4*(d+e*x)^3*(d^2+-1*e^2*x^2)^-5//2)
@test integrate(x^2*(d+e*x)^3*(d^2+-1*e^2*x^2)^-7//2, x) == :(-8//15*e^-3*(d+e*x)^2*(d^2+-1*e^2*x^2)^-3//2+1//5*d*e^-3*(d+e*x)^3*(d^2+-1*e^2*x^2)^-5//2+1//15*d^-1*e^-3*(d^2+-1*e^2*x^2)^-1//2*(7d+7*e*x))
@test integrate(x*(d+e*x)^3*(d^2+-1*e^2*x^2)^-7//2, x) == :(-1//5*e^-2*(d^2+-1*e^2*x^2)^-3//2*(2d+2*e*x)+1//5*e^-2*(d+e*x)^3*(d^2+-1*e^2*x^2)^-5//2+-1//5*x*d^-2*e^-1*(d^2+-1*e^2*x^2)^-1//2)
@test integrate((d+e*x)^3*(d^2+-1*e^2*x^2)^-7//2, x) == :(1//5*d^-1*e^-1*(d+-1*e*x)^-3*(d^2+-1*e^2*x^2)^(1/2)+2//15*d^-3*e^-1*(d+-1*e*x)^-1*(d^2+-1*e^2*x^2)^(1/2)+2//15*d^-2*e^-1*(d+-1*e*x)^-2*(d^2+-1*e^2*x^2)^(1/2))
@test integrate(x^-1*(d+e*x)^3*(d^2+-1*e^2*x^2)^-7//2, x) == :(-1*d^-4*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+1//5*(d^2+-1*e^2*x^2)^-5//2*(4d+4*e*x)+1//15*d^-4*(d^2+-1*e^2*x^2)^-1//2*(15d+22*e*x)+1//15*d^-2*(d^2+-1*e^2*x^2)^-3//2*(5d+11*e*x))
@test integrate(x^-2*(d+e*x)^3*(d^2+-1*e^2*x^2)^-7//2, x) == :(-1*d^-5*x^-1*(d^2+-1*e^2*x^2)^(1/2)+-3*e*d^-5*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+1//5*e*d^-5*(d^2+-1*e^2*x^2)^-1//2*(15d+19*e*x)+1//5*e*d^-3*(d^2+-1*e^2*x^2)^-3//2*(5d+7*e*x)+4//5*e*d^-1*(d^2+-1*e^2*x^2)^-5//2*(d+e*x))
@test integrate(x^-3*(d+e*x)^3*(d^2+-1*e^2*x^2)^-7//2, x) == :(-13//2*d^-6*e^2*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+-1//2*d^-5*x^-2*(d^2+-1*e^2*x^2)^(1/2)+-3*e*d^-6*x^-1*(d^2+-1*e^2*x^2)^(1/2)+1//15*d^-6*e^2*(d^2+-1*e^2*x^2)^-1//2*(90d+107*e*x)+1//15*d^-4*e^2*(d^2+-1*e^2*x^2)^-3//2*(25d+31*e*x)+4//5*d^-2*e^2*(d^2+-1*e^2*x^2)^-5//2*(d+e*x))
@test integrate(x^4*(d+e*x)^-1*(d^2+-1*e^2*x^2)^(1/2), x) == :(1//5*e^-1*x^4*(d^2+-1*e^2*x^2)^(1/2)+3//8*d^5*e^-5*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+-1//4*d*e^-2*x^3*(d^2+-1*e^2*x^2)^(1/2)+1//120*d^3*e^-5*(d^2+-1*e^2*x^2)^(1/2)*(64d+-45*e*x)+4//15*d^2*e^-3*x^2*(d^2+-1*e^2*x^2)^(1/2))
@test integrate(x^3*(d+e*x)^-1*(d^2+-1*e^2*x^2)^(1/2), x) == :(-3//8*d^4*e^-4*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+1//4*e^-1*x^3*(d^2+-1*e^2*x^2)^(1/2)+-1//3*d*e^-2*x^2*(d^2+-1*e^2*x^2)^(1/2)+-1//24*d^2*e^-4*(d^2+-1*e^2*x^2)^(1/2)*(16d+-9*e*x))
@test integrate(x^2*(d+e*x)^-1*(d^2+-1*e^2*x^2)^(1/2), x) == :(-1//3*e^-3*(d^2+-1*e^2*x^2)^3//2+(1/2)*d^3*e^-3*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+(1/2)*d*e^-3*(d^2+-1*e^2*x^2)^(1/2)*(2d+-1*e*x))
@test integrate(x*(d+e*x)^-1*(d^2+-1*e^2*x^2)^(1/2), x) == :(-1//2*d^2*e^-2*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+-1//2*e^-2*(d^2+-1*e^2*x^2)^(1/2)*(2d+-1*e*x))
@test integrate((d+e*x)^-1*(d^2+-1*e^2*x^2)^(1/2), x) == :(e^-1*(d^2+-1*e^2*x^2)^(1/2)+d*e^-1*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2))
@test integrate(x^-1*(d+e*x)^-1*(d^2+-1*e^2*x^2)^(1/2), x) == :(-1*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+-1*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2)))
@test integrate(x^-2*(d+e*x)^-1*(d^2+-1*e^2*x^2)^(1/2), x) == :(e*d^-1*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+-1*d^-1*x^-1*(d^2+-1*e^2*x^2)^(1/2))
@test integrate(x^-3*(d+e*x)^-1*(d^2+-1*e^2*x^2)^(1/2), x) == :(-1//2*d^-1*x^-2*(d^2+-1*e^2*x^2)^(1/2)+-1//2*d^-2*e^2*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+e*d^-2*x^-1*(d^2+-1*e^2*x^2)^(1/2))
@test integrate(x^-4*(d+e*x)^-1*(d^2+-1*e^2*x^2)^(1/2), x) == :((1/2)*d^-3*e^3*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+-1//3*d^-1*x^-3*(d^2+-1*e^2*x^2)^(1/2)+(1/2)*e*d^-2*x^-2*(d^2+-1*e^2*x^2)^(1/2)+-2//3*d^-3*e^2*x^-1*(d^2+-1*e^2*x^2)^(1/2))
@test integrate(x^-5*(d+e*x)^-1*(d^2+-1*e^2*x^2)^(1/2), x) == :(-3//8*d^-4*e^4*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+-1//4*d^-1*x^-4*(d^2+-1*e^2*x^2)^(1/2)+-3//8*d^-3*e^2*x^-2*(d^2+-1*e^2*x^2)^(1/2)+1//3*e*d^-2*x^-3*(d^2+-1*e^2*x^2)^(1/2)+2//3*d^-4*e^3*x^-1*(d^2+-1*e^2*x^2)^(1/2))
@test integrate(x^2*(d+e*x)^-1*(d^2+-1*e^2*x^2)^3//2, x) == :(-1//5*e^-3*(d^2+-1*e^2*x^2)^5//2+1//8*d^5*e^-3*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+1//8*x*d^3*e^-2*(d^2+-1*e^2*x^2)^(1/2)+1//12*d*e^-3*(d^2+-1*e^2*x^2)^3//2*(4d+-3*e*x))
@test integrate(x^4*(d+e*x)^-1*(d^2+-1*e^2*x^2)^5//2, x) == :(1//9*e^-1*x^4*(d^2+-1*e^2*x^2)^5//2+3//128*d^9*e^-5*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+-1//8*d*e^-2*x^3*(d^2+-1*e^2*x^2)^5//2+1//64*x*d^5*e^-4*(d^2+-1*e^2*x^2)^3//2+1//5040*d^3*e^-5*(d^2+-1*e^2*x^2)^5//2*(128d+-315*e*x)+3//128*x*d^7*e^-4*(d^2+-1*e^2*x^2)^(1/2)+4//63*d^2*e^-3*x^2*(d^2+-1*e^2*x^2)^5//2)
@test integrate(x^3*(d+e*x)^-1*(d^2+-1*e^2*x^2)^5//2, x) == :(-3//128*d^8*e^-4*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+1//8*e^-1*x^3*(d^2+-1*e^2*x^2)^5//2+-3//128*x*d^6*e^-3*(d^2+-1*e^2*x^2)^(1/2)+-1//7*d*e^-2*x^2*(d^2+-1*e^2*x^2)^5//2+-1//64*x*d^4*e^-3*(d^2+-1*e^2*x^2)^3//2+-1//560*d^2*e^-4*(d^2+-1*e^2*x^2)^5//2*(32d+-35*e*x))
@test integrate(x^2*(d+e*x)^-1*(d^2+-1*e^2*x^2)^5//2, x) == :(-1//7*e^-3*(d^2+-1*e^2*x^2)^7//2+1//16*d^7*e^-3*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+1//16*x*d^5*e^-2*(d^2+-1*e^2*x^2)^(1/2)+1//24*x*d^3*e^-2*(d^2+-1*e^2*x^2)^3//2+1//30*d*e^-3*(d^2+-1*e^2*x^2)^5//2*(6d+-5*e*x))
@test integrate(x*(d+e*x)^-1*(d^2+-1*e^2*x^2)^5//2, x) == :(-1//16*d^6*e^-2*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+-1//30*e^-2*(d^2+-1*e^2*x^2)^5//2*(6d+-5*e*x)+-1//16*x*d^4*e^-1*(d^2+-1*e^2*x^2)^(1/2)+-1//24*x*d^2*e^-1*(d^2+-1*e^2*x^2)^3//2)
@test integrate((d+e*x)^-1*(d^2+-1*e^2*x^2)^5//2, x) == :(1//5*e^-1*(d^2+-1*e^2*x^2)^5//2+1//4*d*x*(d^2+-1*e^2*x^2)^3//2+3//8*x*d^3*(d^2+-1*e^2*x^2)^(1/2)+3//8*d^5*e^-1*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2))
@test integrate(x^-1*(d+e*x)^-1*(d^2+-1*e^2*x^2)^5//2, x) == :((d^2+-1*e^2*x^2)^3//2*(1//3*d+-1//4*e*x)+-1*d^4*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+-3//8*d^4*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+1//8*d^2*(d^2+-1*e^2*x^2)^(1/2)*(8d+-3*e*x))
@test integrate(x^-2*(d+e*x)^-1*(d^2+-1*e^2*x^2)^5//2, x) == :(e*d^3*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+-3//2*e*d^3*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+-1//3*x^-1*(d^2+-1*e^2*x^2)^3//2*(3d+e*x)+-1//2*d*e*(d^2+-1*e^2*x^2)^(1/2)*(2d+3*e*x))
@test integrate(x^-3*(d+e*x)^-1*(d^2+-1*e^2*x^2)^5//2, x) == :(-1//2*x^-2*(d^2+-1*e^2*x^2)^3//2*(d+e*x)+3//2*d^2*e^2*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+3//2*d^2*e^2*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+3//2*d*e*x^-1*(d^2+-1*e^2*x^2)^(1/2)*(d+-1*e*x))
@test integrate(x^-4*(d+e*x)^-1*(d^2+-1*e^2*x^2)^5//2, x) == :(d*e^3*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+-3//2*d*e^3*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+-1//6*x^-3*(d^2+-1*e^2*x^2)^3//2*(2d+-3*e*x)+(1/2)*e^2*x^-1*(d^2+-1*e^2*x^2)^(1/2)*(2d+3*e*x))
@test integrate(x^-5*(d+e*x)^-1*(d^2+-1*e^2*x^2)^5//2, x) == :(-1*e^4*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+-3//8*e^4*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+-1//12*x^-4*(d^2+-1*e^2*x^2)^3//2*(3d+-4*e*x)+1//8*e^2*x^-2*(d^2+-1*e^2*x^2)^(1/2)*(3d+-8*e*x))
@test integrate(x^-6*(d+e*x)^-1*(d^2+-1*e^2*x^2)^5//2, x) == :(-3//8*e^3*x^-2*(d^2+-1*e^2*x^2)^(1/2)+-1//5*d^-1*x^-5*(d^2+-1*e^2*x^2)^5//2+1//4*e*x^-4*(d^2+-1*e^2*x^2)^3//2+3//8*d^-1*e^5*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2)))
@test integrate(x^-7*(d+e*x)^-1*(d^2+-1*e^2*x^2)^5//2, x) == :(-1//6*d^-1*x^-6*(d^2+-1*e^2*x^2)^5//2+-1//16*d^-2*e^6*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+-1//24*d^-1*e^2*x^-4*(d^2+-1*e^2*x^2)^3//2+1//5*e*d^-2*x^-5*(d^2+-1*e^2*x^2)^5//2+1//16*d^-1*e^4*x^-2*(d^2+-1*e^2*x^2)^(1/2))
@test integrate(x^-8*(d+e*x)^-1*(d^2+-1*e^2*x^2)^5//2, x) == :(-1//7*d^-1*x^-7*(d^2+-1*e^2*x^2)^5//2+1//16*d^-3*e^7*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+-2//35*d^-3*e^2*x^-5*(d^2+-1*e^2*x^2)^5//2+-1//16*d^-2*e^5*x^-2*(d^2+-1*e^2*x^2)^(1/2)+1//6*e*d^-2*x^-6*(d^2+-1*e^2*x^2)^5//2+1//24*d^-2*e^3*x^-4*(d^2+-1*e^2*x^2)^3//2)
@test integrate(x^-9*(d+e*x)^-1*(d^2+-1*e^2*x^2)^5//2, x) == :(-3//128*d^-4*e^8*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+-1//8*d^-1*x^-8*(d^2+-1*e^2*x^2)^5//2+-1//16*d^-3*e^2*x^-6*(d^2+-1*e^2*x^2)^5//2+-1//64*d^-3*e^4*x^-4*(d^2+-1*e^2*x^2)^3//2+1//7*e*d^-2*x^-7*(d^2+-1*e^2*x^2)^5//2+2//35*d^-4*e^3*x^-5*(d^2+-1*e^2*x^2)^5//2+3//128*d^-3*e^6*x^-2*(d^2+-1*e^2*x^2)^(1/2))
@test integrate(x*(1+x)^-1*(1+-1*x^2)^(1/2), x) == :(-1//2*arcsin(x)+(1+-1*x^2)^(1/2)*(-1+(1/2)*x))
@test integrate(x^-2*(1+-1*a*x)^-1*(1+-1*a^2*x^2)^3//2, x) == :(-1*a*arcsin(a*x)+-1*a*arctanh((1+-1*a^2*x^2)^(1/2))+-1*x^-1*(1+-1*a^2*x^2)^(1/2)*(1+-1*a*x))
@test integrate(x^4*(d+e*x)^-1*(d^2+-1*e^2*x^2)^-1//2, x) == :(-4//3*e^-3*x^2*(d^2+-1*e^2*x^2)^(1/2)+-3//2*d^3*e^-5*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+e^-2*x^3*(d^2+-1*e^2*x^2)^-1//2*(d+-1*e*x)+-1//6*d*e^-5*(d^2+-1*e^2*x^2)^(1/2)*(16d+-9*e*x))
@test integrate(x^3*(d+e*x)^-1*(d^2+-1*e^2*x^2)^-1//2, x) == :((1/2)*e^-4*(d^2+-1*e^2*x^2)^(1/2)*(4d+-3*e*x)+3//2*d^2*e^-4*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+e^-2*x^2*(d^2+-1*e^2*x^2)^-1//2*(d+-1*e*x))
@test integrate(x^2*(d+e*x)^-1*(d^2+-1*e^2*x^2)^-1//2, x) == :(-1*e^-3*(d^2+-1*e^2*x^2)^(1/2)+-1*d*e^-3*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+-1*d*e^-3*(d+e*x)^-1*(d^2+-1*e^2*x^2)^(1/2))
@test integrate(x*(d+e*x)^-1*(d^2+-1*e^2*x^2)^-1//2, x) == :(e^-2*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+e^-2*(d+e*x)^-1*(d^2+-1*e^2*x^2)^(1/2))
@test integrate((d+e*x)^-1*(d^2+-1*e^2*x^2)^-1//2, x) == :(-1*d^-1*e^-1*(d+e*x)^-1*(d^2+-1*e^2*x^2)^(1/2))
@test integrate(x^-1*(d+e*x)^-1*(d^2+-1*e^2*x^2)^-1//2, x) == :(-1*d^-2*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+d^-2*(d+e*x)^-1*(d^2+-1*e^2*x^2)^(1/2))
@test integrate(x^-2*(d+e*x)^-1*(d^2+-1*e^2*x^2)^-1//2, x) == :(e*d^-3*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+-2*d^-3*x^-1*(d^2+-1*e^2*x^2)^(1/2)+d^-2*x^-1*(d+e*x)^-1*(d^2+-1*e^2*x^2)^(1/2))
@test integrate(x^-3*(d+e*x)^-1*(d^2+-1*e^2*x^2)^-1//2, x) == :(-3//2*d^-4*e^2*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+-3//2*d^-3*x^-2*(d^2+-1*e^2*x^2)^(1/2)+d^-2*x^-2*(d+e*x)^-1*(d^2+-1*e^2*x^2)^(1/2)+2*e*d^-4*x^-1*(d^2+-1*e^2*x^2)^(1/2))
@test integrate(x^5*(d+e*x)^-1*(d^2+-1*e^2*x^2)^-3//2, x) == :(-5//2*d^2*e^-6*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+-1//6*e^-6*(d^2+-1*e^2*x^2)^(1/2)*(16d+-15*e*x)+-1//3*e^-4*x^2*(d^2+-1*e^2*x^2)^-1//2*(4d+-5*e*x)+1//3*e^-2*x^4*(d^2+-1*e^2*x^2)^-3//2*(d+-1*e*x))
@test integrate(x^4*(d+e*x)^-1*(d^2+-1*e^2*x^2)^-3//2, x) == :(8//3*e^-5*(d^2+-1*e^2*x^2)^(1/2)+d*e^-5*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+-1//3*x*e^-4*(d^2+-1*e^2*x^2)^-1//2*(3d+-4*e*x)+1//3*e^-2*x^3*(d^2+-1*e^2*x^2)^-3//2*(d+-1*e*x))
@test integrate(x^3*(d+e*x)^-1*(d^2+-1*e^2*x^2)^-3//2, x) == :(-1*e^-4*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+-1//3*e^-4*(d^2+-1*e^2*x^2)^-1//2*(2d+-3*e*x)+1//3*e^-2*x^2*(d^2+-1*e^2*x^2)^-3//2*(d+-1*e*x))
@test integrate(x^2*(d+e*x)^-1*(d^2+-1*e^2*x^2)^-3//2, x) == :(2//3*e^-3*(d^2+-1*e^2*x^2)^-1//2+-1//3*d^-1*e^-1*x^2*(d+e*x)^-1*(d^2+-1*e^2*x^2)^-1//2)
@test integrate(x*(d+e*x)^-1*(d^2+-1*e^2*x^2)^-3//2, x) == :(1//3*e^-2*(d+e*x)^-1*(d^2+-1*e^2*x^2)^-1//2+1//3*x*d^-2*e^-1*(d^2+-1*e^2*x^2)^-1//2)
@test integrate((d+e*x)^-1*(d^2+-1*e^2*x^2)^-3//2, x) == :(2//3*x*d^-3*(d^2+-1*e^2*x^2)^-1//2+-1//3*d^-1*e^-1*(d+e*x)^-1*(d^2+-1*e^2*x^2)^-1//2)
@test integrate(x^-1*(d+e*x)^-1*(d^2+-1*e^2*x^2)^-3//2, x) == :(-1*d^-4*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+1//3*d^-4*(d^2+-1*e^2*x^2)^-1//2*(3d+-2*e*x)+1//3*d^-2*(d+e*x)^-1*(d^2+-1*e^2*x^2)^-1//2)
@test integrate(x^-2*(d+e*x)^-1*(d^2+-1*e^2*x^2)^-3//2, x) == :(e*d^-5*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+-8//3*d^-5*x^-1*(d^2+-1*e^2*x^2)^(1/2)+1//3*d^-4*x^-1*(d^2+-1*e^2*x^2)^-1//2*(4d+-3*e*x)+1//3*d^-2*x^-1*(d+e*x)^-1*(d^2+-1*e^2*x^2)^-1//2)
@test integrate(x^-3*(d+e*x)^-1*(d^2+-1*e^2*x^2)^-3//2, x) == :(-5//2*d^-6*e^2*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+-5//2*d^-5*x^-2*(d^2+-1*e^2*x^2)^(1/2)+1//3*d^-4*x^-2*(d^2+-1*e^2*x^2)^-1//2*(5d+-4*e*x)+1//3*d^-2*x^-2*(d+e*x)^-1*(d^2+-1*e^2*x^2)^-1//2+8//3*e*d^-6*x^-1*(d^2+-1*e^2*x^2)^(1/2))
@test integrate(x^7*(d+e*x)^-1*(d^2+-1*e^2*x^2)^-5//2, x) == :(1//10*e^-8*(d^2+-1*e^2*x^2)^(1/2)*(32d+-35*e*x)+7//2*d^2*e^-8*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+-1//15*e^-4*x^4*(d^2+-1*e^2*x^2)^-3//2*(6d+-7*e*x)+1//5*e^-2*x^6*(d^2+-1*e^2*x^2)^-5//2*(d+-1*e*x)+1//15*e^-6*x^2*(d^2+-1*e^2*x^2)^-1//2*(24d+-35*e*x))
@test integrate(x^6*(d+e*x)^-1*(d^2+-1*e^2*x^2)^-5//2, x) == :(-16//5*e^-7*(d^2+-1*e^2*x^2)^(1/2)+-1*d*e^-7*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+-1//15*e^-4*x^3*(d^2+-1*e^2*x^2)^-3//2*(5d+-6*e*x)+1//5*x*e^-6*(d^2+-1*e^2*x^2)^-1//2*(5d+-8*e*x)+1//5*e^-2*x^5*(d^2+-1*e^2*x^2)^-5//2*(d+-1*e*x))
@test integrate(x^5*(d+e*x)^-1*(d^2+-1*e^2*x^2)^-5//2, x) == :(e^-6*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+1//15*e^-6*(d^2+-1*e^2*x^2)^-1//2*(8d+-15*e*x)+-1//15*e^-4*x^2*(d^2+-1*e^2*x^2)^-3//2*(4d+-5*e*x)+1//5*e^-2*x^4*(d^2+-1*e^2*x^2)^-5//2*(d+-1*e*x))
@test integrate(x^4*(d+e*x)^-1*(d^2+-1*e^2*x^2)^-5//2, x) == :(-4//5*e^-5*(d^2+-1*e^2*x^2)^-1//2+4//15*d^2*e^-5*(d^2+-1*e^2*x^2)^-3//2+-1//5*d^-1*e^-1*x^4*(d^2+-1*e^2*x^2)^-5//2*(d+-1*e*x))
@test integrate(x^3*(d+e*x)^-1*(d^2+-1*e^2*x^2)^-5//2, x) == :(-1//15*e^-4*(d^2+-1*e^2*x^2)^-3//2*(2d+-3*e*x)+-1//5*x*d^-2*e^-3*(d^2+-1*e^2*x^2)^-1//2+1//5*e^-2*x^2*(d^2+-1*e^2*x^2)^-5//2*(d+-1*e*x))
@test integrate(x^2*(d+e*x)^-1*(d^2+-1*e^2*x^2)^-5//2, x) == :(-2//15*x*d^-3*e^-2*(d^2+-1*e^2*x^2)^-1//2+1//15*d^-1*e^-3*(d^2+-1*e^2*x^2)^-3//2*(2d+2*e*x)+-1//5*d^-1*e^-1*x^2*(d+e*x)^-1*(d^2+-1*e^2*x^2)^-3//2)
@test integrate(x*(d+e*x)^-1*(d^2+-1*e^2*x^2)^-5//2, x) == :(1//5*e^-2*(d+e*x)^-1*(d^2+-1*e^2*x^2)^-3//2+1//15*x*d^-2*e^-1*(d^2+-1*e^2*x^2)^-3//2+2//15*x*d^-4*e^-1*(d^2+-1*e^2*x^2)^-1//2)
@test integrate((d+e*x)^-1*(d^2+-1*e^2*x^2)^-5//2, x) == :(4//15*x*d^-3*(d^2+-1*e^2*x^2)^-3//2+8//15*x*d^-5*(d^2+-1*e^2*x^2)^-1//2+-1//5*d^-1*e^-1*(d+e*x)^-1*(d^2+-1*e^2*x^2)^-3//2)
@test integrate(x^-1*(d+e*x)^-1*(d^2+-1*e^2*x^2)^-5//2, x) == :(-1*d^-6*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+1//5*d^-2*(d+e*x)^-1*(d^2+-1*e^2*x^2)^-3//2+1//15*d^-6*(d^2+-1*e^2*x^2)^-1//2*(15d+-8*e*x)+1//15*d^-4*(d^2+-1*e^2*x^2)^-3//2*(5d+-4*e*x))
@test integrate(x^-2*(d+e*x)^-1*(d^2+-1*e^2*x^2)^-5//2, x) == :(e*d^-7*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+-16//5*d^-7*x^-1*(d^2+-1*e^2*x^2)^(1/2)+1//5*d^-6*x^-1*(d^2+-1*e^2*x^2)^-1//2*(8d+-5*e*x)+1//5*d^-2*x^-1*(d+e*x)^-1*(d^2+-1*e^2*x^2)^-3//2+1//15*d^-4*x^-1*(d^2+-1*e^2*x^2)^-3//2*(6d+-5*e*x))
@test integrate(x^-3*(d+e*x)^-1*(d^2+-1*e^2*x^2)^-5//2, x) == :(-7//2*d^-8*e^2*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+-7//2*d^-7*x^-2*(d^2+-1*e^2*x^2)^(1/2)+1//5*d^-2*x^-2*(d+e*x)^-1*(d^2+-1*e^2*x^2)^-3//2+1//15*d^-6*x^-2*(d^2+-1*e^2*x^2)^-1//2*(35d+-24*e*x)+1//15*d^-4*x^-2*(d^2+-1*e^2*x^2)^-3//2*(7d+-6*e*x)+16//5*e*d^-8*x^-1*(d^2+-1*e^2*x^2)^(1/2))
@test integrate(x^-4*(d+e*x)^-1*(d^2+-1*e^2*x^2)^-5//2, x) == :(-64//15*d^-7*x^-3*(d^2+-1*e^2*x^2)^(1/2)+7//2*d^-9*e^3*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+-128//15*d^-9*e^2*x^-1*(d^2+-1*e^2*x^2)^(1/2)+1//5*d^-2*x^-3*(d+e*x)^-1*(d^2+-1*e^2*x^2)^-3//2+1//15*d^-6*x^-3*(d^2+-1*e^2*x^2)^-1//2*(48d+-35*e*x)+1//15*d^-4*x^-3*(d^2+-1*e^2*x^2)^-3//2*(8d+-7*e*x)+7//2*e*d^-8*x^-2*(d^2+-1*e^2*x^2)^(1/2))
@test integrate(x^3*(d+e*x)^-1*(d^2+-1*e^2*x^2)^-7//2, x) == :(-1//35*e^-4*(d^2+-1*e^2*x^2)^-5//2*(2d+-3*e*x)+-2//35*x*d^-4*e^-3*(d^2+-1*e^2*x^2)^-1//2+-1//35*x*d^-2*e^-3*(d^2+-1*e^2*x^2)^-3//2+1//7*e^-2*x^2*(d^2+-1*e^2*x^2)^-7//2*(d+-1*e*x))
@test integrate(x^2*(d+e*x)^-1*(d^2+-1*e^2*x^2)^-7//2, x) == :(-8//105*x*d^-5*e^-2*(d^2+-1*e^2*x^2)^-1//2+-4//105*x*d^-3*e^-2*(d^2+-1*e^2*x^2)^-3//2+1//35*d^-1*e^-3*(d^2+-1*e^2*x^2)^-5//2*(2d+4*e*x)+-1//7*d^-1*e^-1*x^2*(d+e*x)^-1*(d^2+-1*e^2*x^2)^-5//2)
@test integrate(x^3*(1+a*x)^-1*(1+-1*a^2*x^2)^-1//2, x) == :(3//2*a^-4*arcsin(a*x)+(1/2)*a^-4*(1+-1*a^2*x^2)^(1/2)*(4+-3*a*x)+a^-2*x^2*(1+-1*a^2*x^2)^-1//2*(1+-1*a*x))
@test integrate(x^2*(1+a*x)^-1*(1+-1*a^2*x^2)^-1//2, x) == :(-1*a^-3*(1+-1*a^2*x^2)^(1/2)+-1*a^-3*arcsin(a*x)+-1*a^-3*(1+a*x)^-1*(1+-1*a^2*x^2)^(1/2))
@test integrate(x*(1+a*x)^-1*(1+-1*a^2*x^2)^-1//2, x) == :(a^-2*arcsin(a*x)+a^-2*(1+a*x)^-1*(1+-1*a^2*x^2)^(1/2))
@test integrate((1+a*x)^-1*(1+-1*a^2*x^2)^-1//2, x) == :(-1*a^-1*(1+a*x)^-1*(1+-1*a^2*x^2)^(1/2))
@test integrate(x^-1*(1+-1*a*x)^-1*(1+-1*a^2*x^2)^-1//2, x) == :(-1*arctanh((1+-1*a^2*x^2)^(1/2))+(1+-1*a*x)^-1*(1+-1*a^2*x^2)^(1/2))
@test integrate(x^-2*(1+-1*a*x)^-1*(1+-1*a^2*x^2)^-1//2, x) == :(-1*a*arctanh((1+-1*a^2*x^2)^(1/2))+-2*x^-1*(1+-1*a^2*x^2)^(1/2)+x^-1*(1+-1*a*x)^-1*(1+-1*a^2*x^2)^(1/2))
@test integrate(x^-3*(1+-1*a*x)^-1*(1+-1*a^2*x^2)^-1//2, x) == :(-3//2*a^2*arctanh((1+-1*a^2*x^2)^(1/2))+-3//2*x^-2*(1+-1*a^2*x^2)^(1/2)+x^-2*(1+-1*a*x)^-1*(1+-1*a^2*x^2)^(1/2)+-2*a*x^-1*(1+-1*a^2*x^2)^(1/2))
@test integrate(x^5*(d+e*x)^-2*(d^2+-1*e^2*x^2)^5//2, x) == :(-1//9*x^6*(d^2+-1*e^2*x^2)^3//2+-5//64*d^9*e^-6*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+-5//21*d^2*e^-2*x^4*(d^2+-1*e^2*x^2)^3//2+-5//64*x*d^7*e^-5*(d^2+-1*e^2*x^2)^(1/2)+-4//21*d^4*e^-4*x^2*(d^2+-1*e^2*x^2)^3//2+-1//2016*d^5*e^-6*(d^2+-1*e^2*x^2)^3//2*(256d+-315*e*x)+1//4*d*e^-1*x^5*(d^2+-1*e^2*x^2)^3//2+5//24*d^3*e^-3*x^3*(d^2+-1*e^2*x^2)^3//2)
@test integrate(x^4*(d+e*x)^-2*(d^2+-1*e^2*x^2)^5//2, x) == :(-1//8*x^5*(d^2+-1*e^2*x^2)^3//2+13//128*d^8*e^-5*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+-13//48*d^2*e^-2*x^3*(d^2+-1*e^2*x^2)^3//2+1//6720*d^4*e^-5*(d^2+-1*e^2*x^2)^3//2*(1024d+-1365*e*x)+2//7*d*e^-1*x^4*(d^2+-1*e^2*x^2)^3//2+8//35*d^3*e^-3*x^2*(d^2+-1*e^2*x^2)^3//2+13//128*x*d^6*e^-4*(d^2+-1*e^2*x^2)^(1/2))
@test integrate(x^3*(d+e*x)^-2*(d^2+-1*e^2*x^2)^5//2, x) == :(-1//7*x^4*(d^2+-1*e^2*x^2)^3//2+-1//8*d^7*e^-4*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+-11//35*d^2*e^-2*x^2*(d^2+-1*e^2*x^2)^3//2+-1//8*x*d^5*e^-3*(d^2+-1*e^2*x^2)^(1/2)+-1//420*d^3*e^-4*(d^2+-1*e^2*x^2)^3//2*(88d+-105*e*x)+1//3*d*e^-1*x^3*(d^2+-1*e^2*x^2)^3//2)
@test integrate(x^2*(d+e*x)^-2*(d^2+-1*e^2*x^2)^5//2, x) == :(-1//6*x^3*(d^2+-1*e^2*x^2)^3//2+3//16*d^6*e^-3*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+1//120*d^2*e^-3*(d^2+-1*e^2*x^2)^3//2*(32d+-45*e*x)+2//5*d*e^-1*x^2*(d^2+-1*e^2*x^2)^3//2+3//16*x*d^4*e^-2*(d^2+-1*e^2*x^2)^(1/2))
@test integrate(x*(d+e*x)^-2*(d^2+-1*e^2*x^2)^5//2, x) == :(-2//15*e^-2*(d^2+-1*e^2*x^2)^5//2+-1//3*e^-2*(d+e*x)^-2*(d^2+-1*e^2*x^2)^7//2+-1//4*d^5*e^-2*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+-1//4*x*d^3*e^-1*(d^2+-1*e^2*x^2)^(1/2)+-1//6*d*x*e^-1*(d^2+-1*e^2*x^2)^3//2)
@test integrate((d+e*x)^-2*(d^2+-1*e^2*x^2)^5//2, x) == :(1//4*e^-1*(d^2+-1*e^2*x^2)^3//2*(d+-1*e*x)+5//8*x*d^2*(d^2+-1*e^2*x^2)^(1/2)+5//8*d^4*e^-1*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+5//12*d*e^-1*(d^2+-1*e^2*x^2)^3//2)
@test integrate(x^-1*(d+e*x)^-2*(d^2+-1*e^2*x^2)^5//2, x) == :(-1//3*(d^2+-1*e^2*x^2)^3//2+-1*d^3*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+-1*d^3*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+d*(d^2+-1*e^2*x^2)^(1/2)*(d+-1*e*x))
@test integrate(x^-2*(d+e*x)^-2*(d^2+-1*e^2*x^2)^5//2, x) == :(-1*x^-1*(d^2+-1*e^2*x^2)^3//2+2*e*d^2*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+-1//2*e*d^2*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+-1//2*e*(d^2+-1*e^2*x^2)^(1/2)*(4d+e*x))
@test integrate(x^-3*(d+e*x)^-2*(d^2+-1*e^2*x^2)^5//2, x) == :(-1//2*x^-2*(d^2+-1*e^2*x^2)^3//2+2*d*e^2*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+-1//2*d*e^2*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+(1/2)*e*x^-1*(d^2+-1*e^2*x^2)^(1/2)*(4d+e*x))
@test integrate(x^-4*(d+e*x)^-2*(d^2+-1*e^2*x^2)^5//2, x) == :(-1*e^3*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+-1*e^3*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+-1//3*x^-3*(d^2+-1*e^2*x^2)^3//2+e*x^-2*(d^2+-1*e^2*x^2)^(1/2)*(d+-1*e*x))
@test integrate(x^-5*(d+e*x)^-2*(d^2+-1*e^2*x^2)^5//2, x) == :(-1//4*x^-4*(d^2+-1*e^2*x^2)^3//2+-5//8*e^2*x^-2*(d^2+-1*e^2*x^2)^(1/2)+5//8*d^-1*e^4*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+2//3*e*d^-1*x^-3*(d^2+-1*e^2*x^2)^3//2)
@test integrate(x^-6*(d+e*x)^-2*(d^2+-1*e^2*x^2)^5//2, x) == :(-1//5*x^-5*(d^2+-1*e^2*x^2)^3//2+-1//4*d^-2*e^5*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+(1/2)*e*d^-1*x^-4*(d^2+-1*e^2*x^2)^3//2+-7//15*d^-2*e^2*x^-3*(d^2+-1*e^2*x^2)^3//2+1//4*d^-1*e^3*x^-2*(d^2+-1*e^2*x^2)^(1/2))
@test integrate(x^-7*(d+e*x)^-2*(d^2+-1*e^2*x^2)^5//2, x) == :(-1//6*x^-6*(d^2+-1*e^2*x^2)^3//2+3//16*d^-3*e^6*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+-3//8*d^-2*e^2*x^-4*(d^2+-1*e^2*x^2)^3//2+-3//16*d^-2*e^4*x^-2*(d^2+-1*e^2*x^2)^(1/2)+2//5*e*d^-1*x^-5*(d^2+-1*e^2*x^2)^3//2+4//15*d^-3*e^3*x^-3*(d^2+-1*e^2*x^2)^3//2)
@test integrate(x^-8*(d+e*x)^-2*(d^2+-1*e^2*x^2)^5//2, x) == :(-1//7*x^-7*(d^2+-1*e^2*x^2)^3//2+-1//8*d^-4*e^7*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+-22//105*d^-4*e^4*x^-3*(d^2+-1*e^2*x^2)^3//2+-11//35*d^-2*e^2*x^-5*(d^2+-1*e^2*x^2)^3//2+1//3*e*d^-1*x^-6*(d^2+-1*e^2*x^2)^3//2+1//4*d^-3*e^3*x^-4*(d^2+-1*e^2*x^2)^3//2+1//8*d^-3*e^5*x^-2*(d^2+-1*e^2*x^2)^(1/2))
@test integrate(x^4*(d+e*x)^-2*(d^2+-1*e^2*x^2)^-3//2, x) == :(-1*e^-5*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+-1//15*e^-5*(d^2+-1*e^2*x^2)^-1//2*(30d+-26*e*x)+-1//5*d^3*e^-5*(d+-1*e*x)^2*(d^2+-1*e^2*x^2)^-5//2+17//15*d^2*e^-5*(d^2+-1*e^2*x^2)^-3//2*(d+-1*e*x))
@test integrate(x^3*(d+e*x)^-2*(d^2+-1*e^2*x^2)^-3//2, x) == :(-4//5*d*e^-4*(d^2+-1*e^2*x^2)^-3//2*(d+-1*e*x)+1//5*d^-1*e^-4*(d^2+-1*e^2*x^2)^-1//2*(5d+-2*e*x)+1//5*d^2*e^-4*(d+-1*e*x)^2*(d^2+-1*e^2*x^2)^-5//2)
@test integrate(x*(d+e*x)^-2*(d^2+-1*e^2*x^2)^-3//2, x) == :(1//5*e^-2*(d+e*x)^-2*(d^2+-1*e^2*x^2)^-1//2+-2//15*d^-1*e^-2*(d+e*x)^-1*(d^2+-1*e^2*x^2)^-1//2+4//15*x*d^-3*e^-1*(d^2+-1*e^2*x^2)^-1//2)
@test integrate((d+e*x)^-2*(d^2+-1*e^2*x^2)^-3//2, x) == :(2//5*x*d^-4*(d^2+-1*e^2*x^2)^-1//2+-1//5*d^-1*e^-1*(d+e*x)^-2*(d^2+-1*e^2*x^2)^-1//2+-1//5*d^-2*e^-1*(d+e*x)^-1*(d^2+-1*e^2*x^2)^-1//2)
@test integrate(x^-1*(d+e*x)^-2*(d^2+-1*e^2*x^2)^-3//2, x) == :(-1*d^-5*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+1//5*d^-1*(d^2+-1*e^2*x^2)^-5//2*(2d+-2*e*x)+1//15*d^-5*(d^2+-1*e^2*x^2)^-1//2*(15d+-16*e*x)+1//15*d^-3*(d^2+-1*e^2*x^2)^-3//2*(5d+-8*e*x))
@test integrate(x^-2*(d+e*x)^-2*(d^2+-1*e^2*x^2)^-3//2, x) == :(-1*d^-6*x^-1*(d^2+-1*e^2*x^2)^(1/2)+2*e*d^-6*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+-2//5*e*d^-2*(d^2+-1*e^2*x^2)^-5//2*(d+-1*e*x)+-1//15*e*d^-6*(d^2+-1*e^2*x^2)^-1//2*(30d+-41*e*x)+-1//15*e*d^-4*(d^2+-1*e^2*x^2)^-3//2*(10d+-13*e*x))
@test integrate(x^-3*(d+e*x)^-2*(d^2+-1*e^2*x^2)^-3//2, x) == :(-9//2*d^-7*e^2*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+-1//2*d^-6*x^-2*(d^2+-1*e^2*x^2)^(1/2)+2*e*d^-7*x^-1*(d^2+-1*e^2*x^2)^(1/2)+1//5*d^-5*e^2*(d^2+-1*e^2*x^2)^-3//2*(5d+-6*e*x)+2//5*d^-7*e^2*(d^2+-1*e^2*x^2)^-1//2*(10d+-11*e*x)+2//5*d^-3*e^2*(d^2+-1*e^2*x^2)^-5//2*(d+-1*e*x))
@test integrate(x^5*(d+e*x)^-3*(d^2+-1*e^2*x^2)^-1//2, x) == :(3*d*e^-6*(d^2+-1*e^2*x^2)^(1/2)+-1//2*x*e^-5*(d^2+-1*e^2*x^2)^(1/2)+13//2*d^2*e^-6*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+-23//15*d^3*e^-6*(d+-1*e*x)^2*(d^2+-1*e^2*x^2)^-3//2+1//5*d^4*e^-6*(d+-1*e*x)^3*(d^2+-1*e^2*x^2)^-5//2+127//15*d^2*e^-6*(d^2+-1*e^2*x^2)^-1//2*(d+-1*e*x))
@test integrate(x^4*(d+e*x)^-3*(d^2+-1*e^2*x^2)^-1//2, x) == :(-1*e^-5*(d^2+-1*e^2*x^2)^(1/2)+-3*d*e^-5*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+-24//5*d*e^-5*(d^2+-1*e^2*x^2)^-1//2*(d+-1*e*x)+-1//5*d^3*e^-5*(d+-1*e*x)^3*(d^2+-1*e^2*x^2)^-5//2+6//5*d^2*e^-5*(d+-1*e*x)^2*(d^2+-1*e^2*x^2)^-3//2)
@test integrate(x^3*(d+e*x)^-3*(d^2+-1*e^2*x^2)^-1//2, x) == :(e^-4*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+1//15*e^-4*(d^2+-1*e^2*x^2)^-1//2*(32d+-32*e*x)+-13//15*d*e^-4*(d+-1*e*x)^2*(d^2+-1*e^2*x^2)^-3//2+1//5*d^2*e^-4*(d+-1*e*x)^3*(d^2+-1*e^2*x^2)^-5//2)
@test integrate(x^2*(d+e*x)^-3*(d^2+-1*e^2*x^2)^-1//2, x) == :(8//15*e^-3*(d+e*x)^-2*(d^2+-1*e^2*x^2)^(1/2)+-7//15*d^-1*e^-3*(d+e*x)^-1*(d^2+-1*e^2*x^2)^(1/2)+-1//5*d*e^-3*(d+e*x)^-3*(d^2+-1*e^2*x^2)^(1/2))
@test integrate(x*(d+e*x)^-3*(d^2+-1*e^2*x^2)^-1//2, x) == :(1//5*e^-2*(d+e*x)^-3*(d^2+-1*e^2*x^2)^(1/2)+-1//5*d^-1*e^-2*(d+e*x)^-2*(d^2+-1*e^2*x^2)^(1/2)+-1//5*d^-2*e^-2*(d+e*x)^-1*(d^2+-1*e^2*x^2)^(1/2))
@test integrate((d+e*x)^-3*(d^2+-1*e^2*x^2)^-1//2, x) == :(-2//15*d^-3*e^-1*(d+e*x)^-1*(d^2+-1*e^2*x^2)^(1/2)+-2//15*d^-2*e^-1*(d+e*x)^-2*(d^2+-1*e^2*x^2)^(1/2)+-1//5*d^-1*e^-1*(d+e*x)^-3*(d^2+-1*e^2*x^2)^(1/2))
@test integrate(x^-1*(d+e*x)^-3*(d^2+-1*e^2*x^2)^-1//2, x) == :(-1*d^-4*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+1//5*(d^2+-1*e^2*x^2)^-5//2*(4d+-4*e*x)+1//15*d^-4*(d^2+-1*e^2*x^2)^-1//2*(15d+-22*e*x)+1//15*d^-2*(d^2+-1*e^2*x^2)^-3//2*(5d+-11*e*x))
@test integrate(x^-2*(d+e*x)^-3*(d^2+-1*e^2*x^2)^-1//2, x) == :(-1*d^-5*x^-1*(d^2+-1*e^2*x^2)^(1/2)+3*e*d^-5*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+-4//5*e*d^-1*(d^2+-1*e^2*x^2)^-5//2*(d+-1*e*x)+-1//5*e*d^-5*(d^2+-1*e^2*x^2)^-1//2*(15d+-19*e*x)+-1//5*e*d^-3*(d^2+-1*e^2*x^2)^-3//2*(5d+-7*e*x))
@test integrate(x^-3*(d+e*x)^-3*(d^2+-1*e^2*x^2)^-1//2, x) == :(-13//2*d^-6*e^2*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+-1//2*d^-5*x^-2*(d^2+-1*e^2*x^2)^(1/2)+3*e*d^-6*x^-1*(d^2+-1*e^2*x^2)^(1/2)+1//15*d^-6*e^2*(d^2+-1*e^2*x^2)^-1//2*(90d+-107*e*x)+1//15*d^-4*e^2*(d^2+-1*e^2*x^2)^-3//2*(25d+-31*e*x)+4//5*d^-2*e^2*(d^2+-1*e^2*x^2)^-5//2*(d+-1*e*x))
@test integrate(x^5*(d+e*x)^-4*(d^2+-1*e^2*x^2)^(1/2), x) == :(18*d^3*e^-6*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+1//3*e^-4*x^2*(d^2+-1*e^2*x^2)^(1/2)+59//3*d^2*e^-6*(d^2+-1*e^2*x^2)^(1/2)+-2*d*x*e^-5*(d^2+-1*e^2*x^2)^(1/2)+10*d^2*e^-6*(d+-1*e*x)^2*(d^2+-1*e^2*x^2)^-1//2+-8//5*d^3*e^-6*(d+-1*e*x)^3*(d^2+-1*e^2*x^2)^-3//2+1//5*d^4*e^-6*(d+-1*e*x)^4*(d^2+-1*e^2*x^2)^-5//2)
@test integrate(x^4*(d+e*x)^-4*(d^2+-1*e^2*x^2)^(1/2), x) == :(-19//2*d^2*e^-5*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+-1//2*e^-5*(d^2+-1*e^2*x^2)^(1/2)*(20d+-1*e*x)+-6*d*e^-5*(d+-1*e*x)^2*(d^2+-1*e^2*x^2)^-1//2+-1//5*d^3*e^-5*(d+-1*e*x)^4*(d^2+-1*e^2*x^2)^-5//2+19//15*d^2*e^-5*(d+-1*e*x)^3*(d^2+-1*e^2*x^2)^-3//2)
@test integrate(x^3*(d+e*x)^-4*(d^2+-1*e^2*x^2)^(1/2), x) == :(-1*e^-4*(d+e*x)^-2*(d^2+-1*e^2*x^2)^3//2+4*d*e^-4*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+8*d*e^-4*(d+e*x)^-1*(d^2+-1*e^2*x^2)^(1/2)+-14//15*d*e^-4*(d+e*x)^-3*(d^2+-1*e^2*x^2)^3//2+1//5*d^2*e^-4*(d+e*x)^-4*(d^2+-1*e^2*x^2)^3//2)
@test integrate(x^2*(d+e*x)^-4*(d^2+-1*e^2*x^2)^(1/2), x) == :(-1*e^-3*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+-2*e^-3*(d+e*x)^-1*(d^2+-1*e^2*x^2)^(1/2)+3//5*e^-3*(d+e*x)^-3*(d^2+-1*e^2*x^2)^3//2+-1//5*d*e^-3*(d+e*x)^-4*(d^2+-1*e^2*x^2)^3//2)
@test integrate(x*(d+e*x)^-4*(d^2+-1*e^2*x^2)^(1/2), x) == :(1//5*e^-2*(d+e*x)^-4*(d^2+-1*e^2*x^2)^3//2+-4//15*d^-1*e^-2*(d+e*x)^-3*(d^2+-1*e^2*x^2)^3//2)
@test integrate((d+e*x)^-4*(d^2+-1*e^2*x^2)^(1/2), x) == :(-1//5*d^-1*e^-1*(d+e*x)^-4*(d^2+-1*e^2*x^2)^3//2+-1//15*d^-2*e^-1*(d+e*x)^-3*(d^2+-1*e^2*x^2)^3//2)
@test integrate(x^-1*(d+e*x)^-4*(d^2+-1*e^2*x^2)^(1/2), x) == :(-1*d^-3*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+1//5*d^-3*(d^2+-1*e^2*x^2)^-1//2*(5d+-8*e*x)+8//5*d*(d^2+-1*e^2*x^2)^-5//2*(d+-1*e*x)+-4//5*e*x*d^-1*(d^2+-1*e^2*x^2)^-3//2)
@test integrate(x^-2*(d+e*x)^-4*(d^2+-1*e^2*x^2)^(1/2), x) == :(-1*d^-4*x^-1*(d^2+-1*e^2*x^2)^(1/2)+4*e*d^-4*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+-8//5*e*(d^2+-1*e^2*x^2)^-5//2*(d+-1*e*x)+-4//15*e*d^-2*(d^2+-1*e^2*x^2)^-3//2*(5d+-8*e*x)+-1//15*e*d^-4*(d^2+-1*e^2*x^2)^-1//2*(60d+-79*e*x))
@test integrate(x^-3*(d+e*x)^-4*(d^2+-1*e^2*x^2)^(1/2), x) == :(-19//2*d^-5*e^2*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+-1//2*d^-4*x^-2*(d^2+-1*e^2*x^2)^(1/2)+4*e*d^-5*x^-1*(d^2+-1*e^2*x^2)^(1/2)+1//15*d^-5*e^2*(d^2+-1*e^2*x^2)^-1//2*(135d+-164*e*x)+4//15*d^-3*e^2*(d^2+-1*e^2*x^2)^-3//2*(10d+-13*e*x)+8//5*d^-1*e^2*(d^2+-1*e^2*x^2)^-5//2*(d+-1*e*x))
@test integrate(x^-4*(d+e*x)^-4*(d^2+-1*e^2*x^2)^(1/2), x) == :(18*d^-6*e^3*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+-1//3*d^-4*x^-3*(d^2+-1*e^2*x^2)^(1/2)+2*e*d^-5*x^-2*(d^2+-1*e^2*x^2)^(1/2)+-29//3*d^-6*e^2*x^-1*(d^2+-1*e^2*x^2)^(1/2)+-8//5*d^-2*e^3*(d^2+-1*e^2*x^2)^-5//2*(d+-1*e*x)+-4//5*d^-4*e^3*(d^2+-1*e^2*x^2)^-3//2*(5d+-6*e*x)+-1//5*d^-6*e^3*(d^2+-1*e^2*x^2)^-1//2*(80d+-93*e*x))
@test integrate(x^5*(d+e*x)^-4*(d^2+-1*e^2*x^2)^5//2, x) == :(1//7*x^6*(d^2+-1*e^2*x^2)^(1/2)+65//4*d^7*e^-6*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+515//21*d^6*e^-6*(d^2+-1*e^2*x^2)^(1/2)+d^4*e^-6*(d+-1*e*x)^4*(d^2+-1*e^2*x^2)^-1//2+-49//4*x*d^5*e^-5*(d^2+-1*e^2*x^2)^(1/2)+-17//6*d^3*e^-3*x^3*(d^2+-1*e^2*x^2)^(1/2)+-2//3*d*e^-1*x^5*(d^2+-1*e^2*x^2)^(1/2)+11//7*d^2*e^-2*x^4*(d^2+-1*e^2*x^2)^(1/2)+121//21*d^4*e^-4*x^2*(d^2+-1*e^2*x^2)^(1/2))
@test integrate(x^4*(d+e*x)^-4*(d^2+-1*e^2*x^2)^5//2, x) == :(1//6*x^5*(d^2+-1*e^2*x^2)^(1/2)+-337//15*d^5*e^-5*(d^2+-1*e^2*x^2)^(1/2)+-239//16*d^6*e^-5*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+-1*d^3*e^-5*(d+-1*e*x)^4*(d^2+-1*e^2*x^2)^-1//2+-71//15*d^3*e^-3*x^2*(d^2+-1*e^2*x^2)^(1/2)+-4//5*d*e^-1*x^4*(d^2+-1*e^2*x^2)^(1/2)+47//24*d^2*e^-2*x^3*(d^2+-1*e^2*x^2)^(1/2)+175//16*x*d^4*e^-4*(d^2+-1*e^2*x^2)^(1/2))
@test integrate(x^3*(d+e*x)^-4*(d^2+-1*e^2*x^2)^5//2, x) == :(1//5*x^4*(d^2+-1*e^2*x^2)^(1/2)+27//2*d^5*e^-4*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+101//5*d^4*e^-4*(d^2+-1*e^2*x^2)^(1/2)+d^2*e^-4*(d+-1*e*x)^4*(d^2+-1*e^2*x^2)^-1//2+-1*d*e^-1*x^3*(d^2+-1*e^2*x^2)^(1/2)+-19//2*x*d^3*e^-3*(d^2+-1*e^2*x^2)^(1/2)+18//5*d^2*e^-2*x^2*(d^2+-1*e^2*x^2)^(1/2))
@test integrate(x^2*(d+e*x)^-4*(d^2+-1*e^2*x^2)^5//2, x) == :(-95//8*d^3*e^-3*(d^2+-1*e^2*x^2)^(1/2)+-95//8*d^4*e^-3*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+-1//4*e^-3*(d+-1*e*x)^3*(d^2+-1*e^2*x^2)^(1/2)+-1*d*e^-3*(d+-1*e*x)^4*(d^2+-1*e^2*x^2)^-1//2+-95//24*d^2*e^-3*(d^2+-1*e^2*x^2)^(1/2)*(d+-1*e*x)+-19//12*d*e^-3*(d+-1*e*x)^2*(d^2+-1*e^2*x^2)^(1/2))
@test integrate(x*(d+e*x)^-4*(d^2+-1*e^2*x^2)^5//2, x) == :(20//3*e^-2*(d^2+-1*e^2*x^2)^3//2+e^-2*(d+e*x)^-4*(d^2+-1*e^2*x^2)^7//2+8*e^-2*(d+e*x)^-2*(d^2+-1*e^2*x^2)^5//2+10*d^3*e^-2*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+10*d*x*e^-1*(d^2+-1*e^2*x^2)^(1/2))
@test integrate((d+e*x)^-4*(d^2+-1*e^2*x^2)^5//2, x) == :(-2*e^-1*(d+e*x)^-3*(d^2+-1*e^2*x^2)^5//2+-15//2*d*e^-1*(d^2+-1*e^2*x^2)^(1/2)+-15//2*d^2*e^-1*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+-5//2*e^-1*(d+e*x)^-1*(d^2+-1*e^2*x^2)^3//2)
@test integrate(x^-1*(d+e*x)^-4*(d^2+-1*e^2*x^2)^5//2, x) == :((d^2+-1*e^2*x^2)^(1/2)+-1*d*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+4*d*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+8*d*(d^2+-1*e^2*x^2)^-1//2*(d+-1*e*x))
@test integrate(x^-2*(d+e*x)^-4*(d^2+-1*e^2*x^2)^5//2, x) == :(-1*e*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+-1*x^-1*(d^2+-1*e^2*x^2)^(1/2)+4*e*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+-8*e*(d^2+-1*e^2*x^2)^-1//2*(d+-1*e*x))
@test integrate(x^-3*(d+e*x)^-4*(d^2+-1*e^2*x^2)^5//2, x) == :(-1//2*x^-2*(d^2+-1*e^2*x^2)^(1/2)+-15//2*d^-1*e^2*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+4*e*d^-1*x^-1*(d^2+-1*e^2*x^2)^(1/2)+8*d^-1*e^2*(d^2+-1*e^2*x^2)^-1//2*(d+-1*e*x))
@test integrate(x^-4*(d+e*x)^-4*(d^2+-1*e^2*x^2)^5//2, x) == :(-1//3*x^-3*(d^2+-1*e^2*x^2)^(1/2)+10*d^-2*e^3*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+-8*d^-2*e^3*(d^2+-1*e^2*x^2)^-1//2*(d+-1*e*x)+2*e*d^-1*x^-2*(d^2+-1*e^2*x^2)^(1/2)+-23//3*d^-2*e^2*x^-1*(d^2+-1*e^2*x^2)^(1/2))
@test integrate(x^-5*(d+e*x)^-4*(d^2+-1*e^2*x^2)^5//2, x) == :(-1//4*x^-4*(d^2+-1*e^2*x^2)^(1/2)+-95//8*d^-3*e^4*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+8*d^-3*e^4*(d^2+-1*e^2*x^2)^-1//2*(d+-1*e*x)+-31//8*d^-2*e^2*x^-2*(d^2+-1*e^2*x^2)^(1/2)+4//3*e*d^-1*x^-3*(d^2+-1*e^2*x^2)^(1/2)+32//3*d^-3*e^3*x^-1*(d^2+-1*e^2*x^2)^(1/2))
@test integrate(x^-6*(d+e*x)^-4*(d^2+-1*e^2*x^2)^5//2, x) == :(-1//5*x^-5*(d^2+-1*e^2*x^2)^(1/2)+27//2*d^-4*e^5*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+e*d^-1*x^-4*(d^2+-1*e^2*x^2)^(1/2)+-8*d^-4*e^5*(d^2+-1*e^2*x^2)^-1//2*(d+-1*e*x)+-66//5*d^-4*e^4*x^-1*(d^2+-1*e^2*x^2)^(1/2)+-13//5*d^-2*e^2*x^-3*(d^2+-1*e^2*x^2)^(1/2)+11//2*d^-3*e^3*x^-2*(d^2+-1*e^2*x^2)^(1/2))
@test integrate(x^2*(1+-1*a*x)^-4*(1+-1*a^2*x^2)^(1/2), x) == :(-1*a^-3*arcsin(a*x)+2*a^-3*(1+-1*a*x)^-1*(1+-1*a^2*x^2)^(1/2)+-3//5*a^-3*(1+-1*a*x)^-3*(1+-1*a^2*x^2)^3//2+1//5*a^-3*(1+-1*a*x)^-4*(1+-1*a^2*x^2)^3//2)
@test integrate(x^2*(1+-1*a*x)^-5*(1+-1*a^2*x^2)^(1/2), x) == :(-12//35*a^-3*(1+-1*a*x)^-4*(1+-1*a^2*x^2)^3//2+1//7*a^-3*(1+-1*a*x)^-5*(1+-1*a^2*x^2)^3//2+23//105*a^-3*(1+-1*a*x)^-3*(1+-1*a^2*x^2)^3//2)
@test integrate(x^3*(d+e*x)^-4*(d^2+-1*e^2*x^2)^-7//2, x) == :(21//143*e^-4*(d+e*x)^-2*(d^2+-1*e^2*x^2)^-5//2+-64//5005*x*d^-7*e^-3*(d^2+-1*e^2*x^2)^-1//2+-32//5005*x*d^-5*e^-3*(d^2+-1*e^2*x^2)^-3//2+-30//143*d*e^-4*(d+e*x)^-3*(d^2+-1*e^2*x^2)^-5//2+-24//5005*x*d^-3*e^-3*(d^2+-1*e^2*x^2)^-5//2+1//13*d^2*e^-4*(d+e*x)^-4*(d^2+-1*e^2*x^2)^-5//2+4//1001*d^-1*e^-4*(d+e*x)^-1*(d^2+-1*e^2*x^2)^-5//2)
@test integrate(x^2*(d+e*x)^-4*(d^2+-1*e^2*x^2)^-7//2, x) == :(17//143*e^-3*(d+e*x)^-3*(d^2+-1*e^2*x^2)^-5//2+-7//1287*d^-1*e^-3*(d+e*x)^-2*(d^2+-1*e^2*x^2)^-5//2+-7//1287*d^-2*e^-3*(d+e*x)^-1*(d^2+-1*e^2*x^2)^-5//2+-1//13*d*e^-3*(d+e*x)^-4*(d^2+-1*e^2*x^2)^-5//2+14//2145*x*d^-4*e^-2*(d^2+-1*e^2*x^2)^-5//2+56//6435*x*d^-6*e^-2*(d^2+-1*e^2*x^2)^-3//2+112//6435*x*d^-8*e^-2*(d^2+-1*e^2*x^2)^-1//2)
@test integrate(x*(d+e*x)^-4*(d^2+-1*e^2*x^2)^-7//2, x) == :(1//13*e^-2*(d+e*x)^-4*(d^2+-1*e^2*x^2)^-5//2+-32//1287*d^-3*e^-2*(d+e*x)^-1*(d^2+-1*e^2*x^2)^-5//2+-32//1287*d^-2*e^-2*(d+e*x)^-2*(d^2+-1*e^2*x^2)^-5//2+-4//143*d^-1*e^-2*(d+e*x)^-3*(d^2+-1*e^2*x^2)^-5//2+64//2145*x*d^-5*e^-1*(d^2+-1*e^2*x^2)^-5//2+256//6435*x*d^-7*e^-1*(d^2+-1*e^2*x^2)^-3//2+512//6435*x*d^-9*e^-1*(d^2+-1*e^2*x^2)^-1//2)
@test integrate((d+e*x)^-4*(d^2+-1*e^2*x^2)^-7//2, x) == :(48//715*x*d^-6*(d^2+-1*e^2*x^2)^-5//2+64//715*x*d^-8*(d^2+-1*e^2*x^2)^-3//2+128//715*x*d^-10*(d^2+-1*e^2*x^2)^-1//2+-9//143*d^-2*e^-1*(d+e*x)^-3*(d^2+-1*e^2*x^2)^-5//2+-8//143*d^-4*e^-1*(d+e*x)^-1*(d^2+-1*e^2*x^2)^-5//2+-8//143*d^-3*e^-1*(d+e*x)^-2*(d^2+-1*e^2*x^2)^-5//2+-1//13*d^-1*e^-1*(d+e*x)^-4*(d^2+-1*e^2*x^2)^-5//2)
@test integrate(x^-1*(d+e*x)^-4*(d^2+-1*e^2*x^2)^-7//2, x) == :(-1*d^-11*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+1//117*d^-3*(d^2+-1*e^2*x^2)^-9//2*(13d+-40*e*x)+1//819*d^-11*(d^2+-1*e^2*x^2)^-1//2*(819d+-1024*e*x)+1//819*d^-9*(d^2+-1*e^2*x^2)^-3//2*(273d+-512*e*x)+1//819*d^-5*(d^2+-1*e^2*x^2)^-7//2*(117d+-320*e*x)+1//1365*d^-7*(d^2+-1*e^2*x^2)^-5//2*(273d+-640*e*x)+8//13*d*(d^2+-1*e^2*x^2)^-13//2*(d+-1*e*x)+-4//13*e*x*d^-1*(d^2+-1*e^2*x^2)^-11//2)
@test integrate(x^-2*(d+e*x)^-4*(d^2+-1*e^2*x^2)^-7//2, x) == :(-1*d^-12*x^-1*(d^2+-1*e^2*x^2)^(1/2)+4*e*d^-12*arctanh(d^-1*(d^2+-1*e^2*x^2)^(1/2))+-8//13*e*(d^2+-1*e^2*x^2)^-13//2*(d+-1*e*x)+-4//143*e*d^-2*(d^2+-1*e^2*x^2)^-11//2*(13d+-24*e*x)+-1//1287*e*d^-4*(d^2+-1*e^2*x^2)^-9//2*(572d+-1103*e*x)+-1//9009*e*d^-12*(d^2+-1*e^2*x^2)^-1//2*(36036d+-52175*e*x)+-1//9009*e*d^-10*(d^2+-1*e^2*x^2)^-3//2*(12012d+-21583*e*x)+-1//9009*e*d^-6*(d^2+-1*e^2*x^2)^-7//2*(5148d+-10111*e*x)+-1//15015*e*d^-8*(d^2+-1*e^2*x^2)^-5//2*(12012d+-23225*e*x))
@test integrate(x^-2*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^(1/2), x) == :(a*c^(1/2)*arctanh(c^(1/2)*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^-1//2)+-1*a*c*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^-1//2+-1*c^2*x^-1*(1+-1*a^2*x^2)^3//2*(c+-1*a*c*x)^-3//2)
@test integrate(x^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*a*c*x)^(1/2), x) == :(-2*c^(1/2)*arctanh(c^(1/2)*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^-1//2))
@test integrate(x^-1//2*(1+-1*a*x)^(1/2), x) == :(a^-1//2*arcsin(a^(1/2)*x^(1/2))+x^(1/2)*(1+-1*a*x)^(1/2))
@test integrate(x^-1//2*(1+a*x)^-1//2*(1+-1*a^2*x^2)^(1/2), x) == :(a^-1//2*arcsin(a^(1/2)*x^(1/2))+x^(1/2)*(1+-1*a*x)^(1/2))
@test integrate(x^-1//2*(1+a*x)^(1/2), x) == :(a^-1//2*arcsinh(a^(1/2)*x^(1/2))+x^(1/2)*(1+a*x)^(1/2))
@test integrate(x^-1//2*(1+-1*a*x)^-1//2*(1+-1*a^2*x^2)^(1/2), x) == :(a^-1//2*arcsinh(a^(1/2)*x^(1/2))+x^(1/2)*(1+a*x)^(1/2))
@test integrate(x^(1/2)*(1+-1*a*x)^(1/2), x) == :((1/2)*x^3//2*(1+-1*a*x)^(1/2)+1//4*a^-3//2*arcsin(a^(1/2)*x^(1/2))+-1//4*a^-1*x^(1/2)*(1+-1*a*x)^(1/2))
@test integrate(x^(1/2)*(1+a*x)^-1//2*(1+-1*a^2*x^2)^(1/2), x) == :((1/2)*x^3//2*(1+-1*a*x)^(1/2)+1//4*a^-3//2*arcsin(a^(1/2)*x^(1/2))+-1//4*a^-1*x^(1/2)*(1+-1*a*x)^(1/2))
@test integrate(x*(1+x)^(1/2)*(1+x^2)^-1, x) == :(2*(1+x)^(1/2)+(2+2*2^(1/2))^-1//2*arctan((-2+2*2^(1/2))^-1//2*((2+2*2^(1/2))^(1/2)+-2*(1+x)^(1/2)))+(1/2)*(1/2+(1/2)*2^(1/2))^(1/2)*log(1+x+2^(1/2)+-1*(1+x)^(1/2)*(2+2*2^(1/2))^(1/2))+-1*(2+2*2^(1/2))^-1//2*arctan((-2+2*2^(1/2))^-1//2*((2+2*2^(1/2))^(1/2)+2*(1+x)^(1/2)))+-1//2*(1/2+(1/2)*2^(1/2))^(1/2)*log(1+x+2^(1/2)+(1+x)^(1/2)*(2+2*2^(1/2))^(1/2)))
@test integrate(x^4*(a+c*x^2)^(1/2)*(d+e*x)^-1, x) == :(-1*d^4*e^-6*(a*e^2+c*d^2)^(1/2)*arctanh((a+c*x^2)^-1//2*(a*e^2+c*d^2)^-1//2*(a*e+-1*c*d*x))+1//5*c^-1*e^-3*(a+c*x^2)^3//2*(d+e*x)^2+1//60*c^-2*e^-3*(a+c*x^2)^3//2*(-8*a*e^2+47*c*d^2)+-13//20*d*c^-1*e^-3*(a+c*x^2)^3//2*(d+e*x)+-1//8*d*c^-3//2*e^-6*(-1*a^2*e^4+8*c^2*d^4+4*a*c*d^2*e^2)*arctanh(x*c^(1/2)*(a+c*x^2)^-1//2)+1//8*d*c^-1*e^-5*(a+c*x^2)^(1/2)*(8*c*d^3+-1*e*x*(-1*a*e^2+4*c*d^2)))
@test integrate(x^3*(a+c*x^2)^(1/2)*(d+e*x)^-1, x) == :(d^3*e^-5*(a*e^2+c*d^2)^(1/2)*arctanh((a+c*x^2)^-1//2*(a*e^2+c*d^2)^-1//2*(a*e+-1*c*d*x))+-7//12*d*c^-1*e^-2*(a+c*x^2)^3//2+-1//8*c^-1*e^-4*(a+c*x^2)^(1/2)*(8*c*d^3+-1*e*x*(-1*a*e^2+4*c*d^2))+1//4*c^-1*e^-2*(a+c*x^2)^3//2*(d+e*x)+1//8*c^-3//2*e^-5*(-1*a^2*e^4+8*c^2*d^4+4*a*c*d^2*e^2)*arctanh(x*c^(1/2)*(a+c*x^2)^-1//2))
@test integrate(x^2*(a+c*x^2)^(1/2)*(d+e*x)^-1, x) == :(1//3*c^-1*e^-1*(a+c*x^2)^3//2+(1/2)*d*e^-3*(a+c*x^2)^(1/2)*(2d+-1*e*x)+-1*d^2*e^-4*(a*e^2+c*d^2)^(1/2)*arctanh((a+c*x^2)^-1//2*(a*e^2+c*d^2)^-1//2*(a*e+-1*c*d*x))+-1//2*d*c^-1//2*e^-4*(a*e^2+2*c*d^2)*arctanh(x*c^(1/2)*(a+c*x^2)^-1//2))
@test integrate(x*(a+c*x^2)^(1/2)*(d+e*x)^-1, x) == :(-1//2*e^-2*(a+c*x^2)^(1/2)*(2d+-1*e*x)+d*e^-3*(a*e^2+c*d^2)^(1/2)*arctanh((a+c*x^2)^-1//2*(a*e^2+c*d^2)^-1//2*(a*e+-1*c*d*x))+(1/2)*c^-1//2*e^-3*(a*e^2+2*c*d^2)*arctanh(x*c^(1/2)*(a+c*x^2)^-1//2))
@test integrate((a+c*x^2)^(1/2)*(d+e*x)^-1, x) == :(e^-1*(a+c*x^2)^(1/2)+-1*e^-2*(a*e^2+c*d^2)^(1/2)*arctanh((a+c*x^2)^-1//2*(a*e^2+c*d^2)^-1//2*(a*e+-1*c*d*x))+-1*d*c^(1/2)*e^-2*arctanh(x*c^(1/2)*(a+c*x^2)^-1//2))
@test integrate(x^-1*(a+c*x^2)^(1/2)*(d+e*x)^-1, x) == :(c^(1/2)*e^-1*arctanh(x*c^(1/2)*(a+c*x^2)^-1//2)+-1*a^(1/2)*d^-1*arctanh(a^-1//2*(a+c*x^2)^(1/2))+d^-1*e^-1*(a*e^2+c*d^2)^(1/2)*arctanh((a+c*x^2)^-1//2*(a*e^2+c*d^2)^-1//2*(a*e+-1*c*d*x)))
@test integrate(x^-2*(a+c*x^2)^(1/2)*(d+e*x)^-1, x) == :(-1*d^-1*x^-1*(a+c*x^2)^(1/2)+-1*d^-2*(a*e^2+c*d^2)^(1/2)*arctanh((a+c*x^2)^-1//2*(a*e^2+c*d^2)^-1//2*(a*e+-1*c*d*x))+e*a^(1/2)*d^-2*arctanh(a^-1//2*(a+c*x^2)^(1/2)))
@test integrate(x^-3*(a+c*x^2)^(1/2)*(d+e*x)^-1, x) == :(-1//2*d^-1*x^-2*(a+c*x^2)^(1/2)+e*d^-3*(a*e^2+c*d^2)^(1/2)*arctanh((a+c*x^2)^-1//2*(a*e^2+c*d^2)^-1//2*(a*e+-1*c*d*x))+e*d^-2*x^-1*(a+c*x^2)^(1/2)+-1*a^(1/2)*d^-3*e^2*arctanh(a^-1//2*(a+c*x^2)^(1/2))+-1//2*c*a^-1//2*d^-1*arctanh(a^-1//2*(a+c*x^2)^(1/2)))
@test integrate(x^-4*(a+c*x^2)^(1/2)*(d+e*x)^-1, x) == :(a^(1/2)*d^-4*e^3*arctanh(a^-1//2*(a+c*x^2)^(1/2))+(1/2)*e*d^-2*x^-2*(a+c*x^2)^(1/2)+-1*d^-4*e^2*(a*e^2+c*d^2)^(1/2)*arctanh((a+c*x^2)^-1//2*(a*e^2+c*d^2)^-1//2*(a*e+-1*c*d*x))+-1*d^-3*e^2*x^-1*(a+c*x^2)^(1/2)+-1//3*a^-1*d^-1*x^-3*(a+c*x^2)^3//2+(1/2)*c*e*a^-1//2*d^-2*arctanh(a^-1//2*(a+c*x^2)^(1/2)))
@test integrate(x^-5*(a+c*x^2)^(1/2)*(d+e*x)^-1, x) == :(-1//4*d^-1*x^-4*(a+c*x^2)^(1/2)+d^-5*e^3*(a*e^2+c*d^2)^(1/2)*arctanh((a+c*x^2)^-1//2*(a*e^2+c*d^2)^-1//2*(a*e+-1*c*d*x))+d^-4*e^3*x^-1*(a+c*x^2)^(1/2)+-1*a^(1/2)*d^-5*e^4*arctanh(a^-1//2*(a+c*x^2)^(1/2))+-1//2*d^-3*e^2*x^-2*(a+c*x^2)^(1/2)+1//8*a^-3//2*c^2*d^-1*arctanh(a^-1//2*(a+c*x^2)^(1/2))+-1//2*c*a^-1//2*d^-3*e^2*arctanh(a^-1//2*(a+c*x^2)^(1/2))+-1//8*c*a^-1*d^-1*x^-2*(a+c*x^2)^(1/2)+1//3*e*a^-1*d^-2*x^-3*(a+c*x^2)^3//2)
@test integrate(x^4*(a+c*x^2)^-1//2*(d+e*x)^-1, x) == :(-1*d^4*e^-4*(a*e^2+c*d^2)^-1//2*arctanh((a+c*x^2)^-1//2*(a*e^2+c*d^2)^-1//2*(a*e+-1*c*d*x))+1//3*c^-1*e^-3*(a+c*x^2)^(1/2)*(d+e*x)^2+1//6*c^-2*e^-3*(a+c*x^2)^(1/2)*(-4*a*e^2+11*c*d^2)+-7//6*d*c^-1*e^-3*(a+c*x^2)^(1/2)*(d+e*x)+-1//2*d*c^-3//2*e^-4*(-1*a*e^2+2*c*d^2)*arctanh(x*c^(1/2)*(a+c*x^2)^-1//2))
@test integrate(x^3*(a+c*x^2)^-1//2*(d+e*x)^-1, x) == :(d^3*e^-3*(a*e^2+c*d^2)^-1//2*arctanh((a+c*x^2)^-1//2*(a*e^2+c*d^2)^-1//2*(a*e+-1*c*d*x))+(1/2)*c^-1*e^-2*(a+c*x^2)^(1/2)*(d+e*x)+(1/2)*c^-3//2*e^-3*(-1*a*e^2+2*c*d^2)*arctanh(x*c^(1/2)*(a+c*x^2)^-1//2)+-3//2*d*c^-1*e^-2*(a+c*x^2)^(1/2))
@test integrate(x^2*(a+c*x^2)^-1//2*(d+e*x)^-1, x) == :(c^-1*e^-1*(a+c*x^2)^(1/2)+-1*d*c^-1//2*e^-2*arctanh(x*c^(1/2)*(a+c*x^2)^-1//2)+-1*d^2*e^-2*(a*e^2+c*d^2)^-1//2*arctanh((a+c*x^2)^-1//2*(a*e^2+c*d^2)^-1//2*(a*e+-1*c*d*x)))
@test integrate(x*(a+c*x^2)^-1//2*(d+e*x)^-1, x) == :(c^-1//2*e^-1*arctanh(x*c^(1/2)*(a+c*x^2)^-1//2)+d*e^-1*(a*e^2+c*d^2)^-1//2*arctanh((a+c*x^2)^-1//2*(a*e^2+c*d^2)^-1//2*(a*e+-1*c*d*x)))
@test integrate((a+c*x^2)^-1//2*(d+e*x)^-1, x) == :(-1*(a*e^2+c*d^2)^-1//2*arctanh((a+c*x^2)^-1//2*(a*e^2+c*d^2)^-1//2*(a*e+-1*c*d*x)))
@test integrate(x^-1*(a+c*x^2)^-1//2*(d+e*x)^-1, x) == :(-1*a^-1//2*d^-1*arctanh(a^-1//2*(a+c*x^2)^(1/2))+e*d^-1*(a*e^2+c*d^2)^-1//2*arctanh((a+c*x^2)^-1//2*(a*e^2+c*d^2)^-1//2*(a*e+-1*c*d*x)))
@test integrate(x^-2*(a+c*x^2)^-1//2*(d+e*x)^-1, x) == :(e*a^-1//2*d^-2*arctanh(a^-1//2*(a+c*x^2)^(1/2))+-1*a^-1*d^-1*x^-1*(a+c*x^2)^(1/2)+-1*d^-2*e^2*(a*e^2+c*d^2)^-1//2*arctanh((a+c*x^2)^-1//2*(a*e^2+c*d^2)^-1//2*(a*e+-1*c*d*x)))
@test integrate(x^-3*(a+c*x^2)^-1//2*(d+e*x)^-1, x) == :(d^-3*e^3*(a*e^2+c*d^2)^-1//2*arctanh((a+c*x^2)^-1//2*(a*e^2+c*d^2)^-1//2*(a*e+-1*c*d*x))+(1/2)*c*a^-3//2*d^-1*arctanh(a^-1//2*(a+c*x^2)^(1/2))+-1*a^-1//2*d^-3*e^2*arctanh(a^-1//2*(a+c*x^2)^(1/2))+-1//2*a^-1*d^-1*x^-2*(a+c*x^2)^(1/2)+e*a^-1*d^-2*x^-1*(a+c*x^2)^(1/2))
@test integrate(x^4*(a+c*x^2)^-3//2*(d+e*x)^-1, x) == :(c^-2*e^-1*(a+c*x^2)^(1/2)+-1*d*c^-3//2*e^-2*arctanh(x*c^(1/2)*(a+c*x^2)^-1//2)+-1*d^4*e^-2*(a*e^2+c*d^2)^-3//2*arctanh((a+c*x^2)^-1//2*(a*e^2+c*d^2)^-1//2*(a*e+-1*c*d*x))+a*c^-2*(a+c*x^2)^-1//2*(a*e^2+c*d^2)^-1*(a*e+c*d*x))
@test integrate(x^3*(a+c*x^2)^-3//2*(d+e*x)^-1, x) == :(c^-3//2*e^-1*arctanh(x*c^(1/2)*(a+c*x^2)^-1//2)+d^3*e^-1*(a*e^2+c*d^2)^-3//2*arctanh((a+c*x^2)^-1//2*(a*e^2+c*d^2)^-1//2*(a*e+-1*c*d*x))+a*c^-1*(a+c*x^2)^-1//2*(a*e^2+c*d^2)^-1*(d+-1*e*x))
@test integrate(x^2*(a+c*x^2)^-3//2*(d+e*x)^-1, x) == :(-1*d^2*(a*e^2+c*d^2)^-3//2*arctanh((a+c*x^2)^-1//2*(a*e^2+c*d^2)^-1//2*(a*e+-1*c*d*x))+-1*c^-1*(a+c*x^2)^-1//2*(a*e^2+c*d^2)^-1*(a*e+c*d*x))
@test integrate(x*(a+c*x^2)^-3//2*(d+e*x)^-1, x) == :(-1*(a+c*x^2)^-1//2*(a*e^2+c*d^2)^-1*(d+-1*e*x)+d*e*(a*e^2+c*d^2)^-3//2*arctanh((a+c*x^2)^-1//2*(a*e^2+c*d^2)^-1//2*(a*e+-1*c*d*x)))
@test integrate((a+c*x^2)^-3//2*(d+e*x)^-1, x) == :(-1*e^2*(a*e^2+c*d^2)^-3//2*arctanh((a+c*x^2)^-1//2*(a*e^2+c*d^2)^-1//2*(a*e+-1*c*d*x))+a^-1*(a+c*x^2)^-1//2*(a*e^2+c*d^2)^-1*(a*e+c*d*x))
@test integrate(x^-1*(a+c*x^2)^-3//2*(d+e*x)^-1, x) == :(a^-1*d^-1*(a+c*x^2)^-1//2+-1*a^-3//2*d^-1*arctanh(a^-1//2*(a+c*x^2)^(1/2))+d^-1*e^3*(a*e^2+c*d^2)^-3//2*arctanh((a+c*x^2)^-1//2*(a*e^2+c*d^2)^-1//2*(a*e+-1*c*d*x))+-1*e*a^-1*d^-1*(a+c*x^2)^-1//2*(a*e^2+c*d^2)^-1*(a*e+c*d*x))
@test integrate(x^-2*(a+c*x^2)^-3//2*(d+e*x)^-1, x) == :(e*a^-3//2*d^-2*arctanh(a^-1//2*(a+c*x^2)^(1/2))+-1*e*a^-1*d^-2*(a+c*x^2)^-1//2+-1*a^-1*d^-1*x^-1*(a+c*x^2)^-1//2+-1*d^-2*e^4*(a*e^2+c*d^2)^-3//2*arctanh((a+c*x^2)^-1//2*(a*e^2+c*d^2)^-1//2*(a*e+-1*c*d*x))+-2*c*x*a^-2*d^-1*(a+c*x^2)^-1//2+a^-1*d^-2*e^2*(a+c*x^2)^-1//2*(a*e^2+c*d^2)^-1*(a*e+c*d*x))
@test integrate(x^-3*(a+c*x^2)^-3//2*(d+e*x)^-1, x) == :(a^-1*d^-3*e^2*(a+c*x^2)^-1//2+d^-3*e^5*(a*e^2+c*d^2)^-3//2*arctanh((a+c*x^2)^-1//2*(a*e^2+c*d^2)^-1//2*(a*e+-1*c*d*x))+-1*a^-3//2*d^-3*e^2*arctanh(a^-1//2*(a+c*x^2)^(1/2))+-3//2*c*a^-2*d^-1*(a+c*x^2)^-1//2+-1//2*a^-1*d^-1*x^-2*(a+c*x^2)^-1//2+3//2*c*a^-5//2*d^-1*arctanh(a^-1//2*(a+c*x^2)^(1/2))+e*a^-1*d^-2*x^-1*(a+c*x^2)^-1//2+-1*a^-1*d^-3*e^3*(a+c*x^2)^-1//2*(a*e^2+c*d^2)^-1*(a*e+c*d*x)+2*c*e*x*a^-2*d^-2*(a+c*x^2)^-1//2)
@test integrate(x^5*(a+c*x^2)^-1//2*(d+e*x)^-2, x) == :(1//3*c^-1*e^-4*(a+c*x^2)^(1/2)*(d+e*x)^2+1//3*c^-2*e^-4*(a+c*x^2)^(1/2)*(-2*a*e^2+13*c*d^2)+d^5*e^-4*(a+c*x^2)^(1/2)*(d+e*x)^-1*(a*e^2+c*d^2)^-1+-1*d*c^-3//2*e^-5*(-1*a*e^2+4*c*d^2)*arctanh(x*c^(1/2)*(a+c*x^2)^-1//2)+-1*d^4*e^-5*(a*e^2+c*d^2)^-3//2*(4*c*d^2+5*a*e^2)*arctanh((a+c*x^2)^-1//2*(a*e^2+c*d^2)^-1//2*(a*e+-1*c*d*x))+-5//3*d*c^-1*e^-4*(a+c*x^2)^(1/2)*(d+e*x))
@test integrate(x^4*(a+c*x^2)^-1//2*(d+e*x)^-2, x) == :((1/2)*c^-1*e^-3*(a+c*x^2)^(1/2)*(d+e*x)+(1/2)*c^-3//2*e^-4*(-1*a*e^2+6*c*d^2)*arctanh(x*c^(1/2)*(a+c*x^2)^-1//2)+-5//2*d*c^-1*e^-3*(a+c*x^2)^(1/2)+d^3*e^-4*(a*e^2+c*d^2)^-3//2*(3*c*d^2+4*a*e^2)*arctanh((a+c*x^2)^-1//2*(a*e^2+c*d^2)^-1//2*(a*e+-1*c*d*x))+-1*d^4*e^-3*(a+c*x^2)^(1/2)*(d+e*x)^-1*(a*e^2+c*d^2)^-1)
@test integrate(x^3*(a+c*x^2)^-1//2*(d+e*x)^-2, x) == :(c^-1*e^-2*(a+c*x^2)^(1/2)+-2*d*c^-1//2*e^-3*arctanh(x*c^(1/2)*(a+c*x^2)^-1//2)+d^3*e^-2*(a+c*x^2)^(1/2)*(d+e*x)^-1*(a*e^2+c*d^2)^-1+-1*d^2*e^-3*(a*e^2+c*d^2)^-3//2*(2*c*d^2+3*a*e^2)*arctanh((a+c*x^2)^-1//2*(a*e^2+c*d^2)^-1//2*(a*e+-1*c*d*x)))
@test integrate(x^2*(a+c*x^2)^-1//2*(d+e*x)^-2, x) == :(c^-1//2*e^-2*arctanh(x*c^(1/2)*(a+c*x^2)^-1//2)+d*e^-2*(a*e^2+c*d^2)^-3//2*(c*d^2+2*a*e^2)*arctanh((a+c*x^2)^-1//2*(a*e^2+c*d^2)^-1//2*(a*e+-1*c*d*x))+-1*d^2*e^-1*(a+c*x^2)^(1/2)*(d+e*x)^-1*(a*e^2+c*d^2)^-1)
@test integrate(x*(a+c*x^2)^-1//2*(d+e*x)^-2, x) == :(d*(a+c*x^2)^(1/2)*(d+e*x)^-1*(a*e^2+c*d^2)^-1+-1*a*e*(a*e^2+c*d^2)^-3//2*arctanh((a+c*x^2)^-1//2*(a*e^2+c*d^2)^-1//2*(a*e+-1*c*d*x)))
@test integrate((a+c*x^2)^-1//2*(d+e*x)^-2, x) == :(-1*c*d*(a*e^2+c*d^2)^-3//2*arctanh((a+c*x^2)^-1//2*(a*e^2+c*d^2)^-1//2*(a*e+-1*c*d*x))+-1*e*(a+c*x^2)^(1/2)*(d+e*x)^-1*(a*e^2+c*d^2)^-1)
@test integrate(x^-1*(a+c*x^2)^-1//2*(d+e*x)^-2, x) == :(-1*a^-1//2*d^-2*arctanh(a^-1//2*(a+c*x^2)^(1/2))+c*e*(a*e^2+c*d^2)^-3//2*arctanh((a+c*x^2)^-1//2*(a*e^2+c*d^2)^-1//2*(a*e+-1*c*d*x))+e*d^-2*(a*e^2+c*d^2)^-1//2*arctanh((a+c*x^2)^-1//2*(a*e^2+c*d^2)^-1//2*(a*e+-1*c*d*x))+d^-1*e^2*(a+c*x^2)^(1/2)*(d+e*x)^-1*(a*e^2+c*d^2)^-1)
@test integrate(x^-2*(a+c*x^2)^-1//2*(d+e*x)^-2, x) == :(-1*a^-1*d^-2*x^-1*(a+c*x^2)^(1/2)+-2*d^-3*e^2*(a*e^2+c*d^2)^-1//2*arctanh((a+c*x^2)^-1//2*(a*e^2+c*d^2)^-1//2*(a*e+-1*c*d*x))+2*e*a^-1//2*d^-3*arctanh(a^-1//2*(a+c*x^2)^(1/2))+-1*c*d^-1*e^2*(a*e^2+c*d^2)^-3//2*arctanh((a+c*x^2)^-1//2*(a*e^2+c*d^2)^-1//2*(a*e+-1*c*d*x))+-1*d^-2*e^3*(a+c*x^2)^(1/2)*(d+e*x)^-1*(a*e^2+c*d^2)^-1)
@test integrate(x^-3*(a+c*x^2)^-1//2*(d+e*x)^-2, x) == :((1/2)*c*a^-3//2*d^-2*arctanh(a^-1//2*(a+c*x^2)^(1/2))+-3*a^-1//2*d^-4*e^2*arctanh(a^-1//2*(a+c*x^2)^(1/2))+3*d^-4*e^3*(a*e^2+c*d^2)^-1//2*arctanh((a+c*x^2)^-1//2*(a*e^2+c*d^2)^-1//2*(a*e+-1*c*d*x))+-1//2*a^-1*d^-2*x^-2*(a+c*x^2)^(1/2)+c*d^-2*e^3*(a*e^2+c*d^2)^-3//2*arctanh((a+c*x^2)^-1//2*(a*e^2+c*d^2)^-1//2*(a*e+-1*c*d*x))+d^-3*e^4*(a+c*x^2)^(1/2)*(d+e*x)^-1*(a*e^2+c*d^2)^-1+2*e*a^-1*d^-3*x^-1*(a+c*x^2)^(1/2))
@test integrate(x^2*(a+b*x)^n*(c+d*x^2), x) == :(d*b^-5*(5+n)^-1*(a+b*x)^(5+n)+b^-5*(3+n)^-1*(a+b*x)^(3+n)*(c*b^2+6*d*a^2)+a^2*b^-5*(1+n)^-1*(a+b*x)^(1+n)*(c*b^2+d*a^2)+-4*a*d*b^-5*(4+n)^-1*(a+b*x)^(4+n)+-2*a*b^-5*(2+n)^-1*(a+b*x)^(2+n)*(c*b^2+2*d*a^2))
@test integrate(x*(a+b*x)^n*(c+d*x^2), x) == :(d*b^-4*(4+n)^-1*(a+b*x)^(4+n)+b^-4*(2+n)^-1*(a+b*x)^(2+n)*(c*b^2+3*d*a^2)+-1*a*b^-4*(1+n)^-1*(a+b*x)^(1+n)*(c*b^2+d*a^2)+-3*a*d*b^-4*(3+n)^-1*(a+b*x)^(3+n))
@test integrate((a+b*x)^n*(c+d*x^2), x) == :(d*b^-3*(3+n)^-1*(a+b*x)^(3+n)+b^-3*(1+n)^-1*(a+b*x)^(1+n)*(c*b^2+d*a^2)+-2*a*d*b^-3*(2+n)^-1*(a+b*x)^(2+n))
@test integrate(x^2*(a+b*x)^n*(c+d*x^2)^2, x) == :(b^-7*d^2*(7+n)^-1*(a+b*x)^(7+n)+b^-7*(3+n)^-1*(a+b*x)^(3+n)*(b^4*c^2+15*a^4*d^2+12*c*d*a^2*b^2)+d*b^-7*(5+n)^-1*(a+b*x)^(5+n)*(2*c*b^2+15*d*a^2)+a^2*b^-7*(1+n)^-1*(a+b*x)^(1+n)*(c*b^2+d*a^2)^2+-6*a*b^-7*d^2*(6+n)^-1*(a+b*x)^(6+n)+-4*a*d*b^-7*(4+n)^-1*(a+b*x)^(4+n)*(2*c*b^2+5*d*a^2)+-2*a*b^-7*(2+n)^-1*(a+b*x)^(2+n)*(c*b^2+d*a^2)*(c*b^2+3*d*a^2))
@test integrate(x*(a+b*x)^n*(c+d*x^2)^2, x) == :(b^-6*d^2*(6+n)^-1*(a+b*x)^(6+n)+b^-6*(2+n)^-1*(a+b*x)^(2+n)*(c*b^2+d*a^2)*(c*b^2+5*d*a^2)+-1*a*b^-6*(1+n)^-1*(a+b*x)^(1+n)*(c*b^2+d*a^2)^2+-5*a*b^-6*d^2*(5+n)^-1*(a+b*x)^(5+n)+2*d*b^-6*(4+n)^-1*(a+b*x)^(4+n)*(c*b^2+5*d*a^2)+-2*a*d*b^-6*(3+n)^-1*(a+b*x)^(3+n)*(3*c*b^2+5*d*a^2))
@test integrate((a+b*x)^n*(c+d*x^2)^2, x) == :(b^-5*d^2*(5+n)^-1*(a+b*x)^(5+n)+b^-5*(1+n)^-1*(a+b*x)^(1+n)*(c*b^2+d*a^2)^2+-4*a*b^-5*d^2*(4+n)^-1*(a+b*x)^(4+n)+2*d*b^-5*(3+n)^-1*(a+b*x)^(3+n)*(c*b^2+3*d*a^2)+-4*a*d*b^-5*(2+n)^-1*(a+b*x)^(2+n)*(c*b^2+d*a^2))
@test integrate(x^2*(a+b*x)^n*(c+d*x^2)^3, x) == :(b^-9*d^3*(9+n)^-1*(a+b*x)^(9+n)+d*b^-9*(5+n)^-1*(a+b*x)^(5+n)*(3*b^4*c^2+70*a^4*d^2+45*c*d*a^2*b^2)+a^2*b^-9*(1+n)^-1*(a+b*x)^(1+n)*(c*b^2+d*a^2)^3+b^-9*d^2*(7+n)^-1*(a+b*x)^(7+n)*(3*c*b^2+28*d*a^2)+b^-9*(3+n)^-1*(a+b*x)^(3+n)*(c*b^2+d*a^2)*(b^4*c^2+28*a^4*d^2+17*c*d*a^2*b^2)+-8*a*b^-9*d^3*(8+n)^-1*(a+b*x)^(8+n)+-4*a*d*b^-9*(4+n)^-1*(a+b*x)^(4+n)*(3*b^4*c^2+14*a^4*d^2+15*c*d*a^2*b^2)+-2*a*b^-9*d^2*(6+n)^-1*(a+b*x)^(6+n)*(9*c*b^2+28*d*a^2)+-2*a*b^-9*(2+n)^-1*(a+b*x)^(2+n)*(c*b^2+d*a^2)^2*(c*b^2+4*d*a^2))
@test integrate(x*(a+b*x)^n*(c+d*x^2)^3, x) == :(b^-8*d^3*(8+n)^-1*(a+b*x)^(8+n)+d*b^-8*(4+n)^-1*(a+b*x)^(4+n)*(3*b^4*c^2+35*a^4*d^2+30*c*d*a^2*b^2)+b^-8*(2+n)^-1*(a+b*x)^(2+n)*(c*b^2+d*a^2)^2*(c*b^2+7*d*a^2)+-1*a*b^-8*(1+n)^-1*(a+b*x)^(1+n)*(c*b^2+d*a^2)^3+-7*a*b^-8*d^3*(7+n)^-1*(a+b*x)^(7+n)+3*b^-8*d^2*(6+n)^-1*(a+b*x)^(6+n)*(c*b^2+7*d*a^2)+-5*a*b^-8*d^2*(5+n)^-1*(a+b*x)^(5+n)*(3*c*b^2+7*d*a^2)+-3*a*d*b^-8*(3+n)^-1*(a+b*x)^(3+n)*(c*b^2+d*a^2)*(3*c*b^2+7*d*a^2))
@test integrate((a+b*x)^n*(c+d*x^2)^3, x) == :(b^-7*d^3*(7+n)^-1*(a+b*x)^(7+n)+b^-7*(1+n)^-1*(a+b*x)^(1+n)*(c*b^2+d*a^2)^3+-6*a*b^-7*d^3*(6+n)^-1*(a+b*x)^(6+n)+3*b^-7*d^2*(5+n)^-1*(a+b*x)^(5+n)*(c*b^2+5*d*a^2)+-6*a*d*b^-7*(2+n)^-1*(a+b*x)^(2+n)*(c*b^2+d*a^2)^2+-4*a*b^-7*d^2*(4+n)^-1*(a+b*x)^(4+n)*(3*c*b^2+5*d*a^2)+3*d*b^-7*(3+n)^-1*(a+b*x)^(3+n)*(c*b^2+d*a^2)*(c*b^2+5*d*a^2))
@test integrate(x^3*(d+e*x)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2), x) == :(x^2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(-7//24*d*e^-2+1//24*a*c^-1*d^-1)+1//4*e^-1*x^3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+-1//192*c^-3*d^-3*e^-4*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(-15*a^3*e^6+105*c^3*d^6+-25*a*c^2*d^4*e^2+-17*c*a^2*d^2*e^4+-2*c*d*e*x*(-5*a^2*e^4+35*c^2*d^4+-6*a*c*d^2*e^2))+1//128*c^-7//2*d^-7//2*e^-9//2*(c*d^2+-1*a*e^2)*(5*a^3*e^6+35*c^3*d^6+9*c*a^2*d^2*e^4+15*a*c^2*d^4*e^2)*arctanh((1/2)*c^-1//2*d^-1//2*e^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*(a*e^2+c*d^2+2*c*d*e*x)))
@test integrate(x^2*(d+e*x)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2), x) == :(1//3*e^-1*x^2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+1//24*c^-2*d^-2*e^-3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*((a*e^2+3*c*d^2)*(-3*a*e^2+5*c*d^2)+-2*c*d*e*x*(-1*a*e^2+5*c*d^2))+-1//16*c^-5//2*d^-5//2*e^-7//2*(c*d^2+-1*a*e^2)*(a^2*e^4+5*c^2*d^4+2*a*c*d^2*e^2)*arctanh((1/2)*c^-1//2*d^-1//2*e^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*(a*e^2+c*d^2+2*c*d*e*x)))
@test integrate(x*(d+e*x)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2), x) == :((x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(-3//4*d*e^-2+-1//4*a*c^-1*d^-1)+(1/2)*c^-1*d^-1*e^-1*(d+e*x)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2+1//8*c^-3//2*d^-3//2*e^-5//2*(a*e^2+3*c*d^2)*(c*d^2+-1*a*e^2)*arctanh((1/2)*c^-1//2*d^-1//2*e^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*(a*e^2+c*d^2+2*c*d*e*x)))
@test integrate((d+e*x)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2), x) == :(e^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+-1//2*c^-1//2*d^-1//2*e^-3//2*(c*d^2+-1*a*e^2)*arctanh((1/2)*c^-1//2*d^-1//2*e^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*(a*e^2+c*d^2+2*c*d*e*x)))
@test integrate(x^-1*(d+e*x)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2), x) == :(c^(1/2)*d^(1/2)*e^-1//2*arctanh((1/2)*c^-1//2*d^-1//2*e^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*(a*e^2+c*d^2+2*c*d*e*x))+-1*a^(1/2)*d^-1//2*e^(1/2)*arctanh((1/2)*a^-1//2*d^-1//2*e^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*(x*(a*e^2+c*d^2)+2*a*d*e)))
@test integrate(x^-2*(d+e*x)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2), x) == :(-1*d^-1*x^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+-1//2*a^-1//2*d^-3//2*e^-1//2*(c*d^2+-1*a*e^2)*arctanh((1/2)*a^-1//2*d^-1//2*e^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*(x*(a*e^2+c*d^2)+2*a*d*e)))
@test integrate(x^-3*(d+e*x)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2), x) == :(-1//2*d^-1*x^-2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+-1//4*x^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(-3*e*d^-2+c*a^-1*e^-1)+1//8*a^-3//2*d^-5//2*e^-3//2*(c*d^2+-1*a*e^2)*(c*d^2+3*a*e^2)*arctanh((1/2)*a^-1//2*d^-1//2*e^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*(x*(a*e^2+c*d^2)+2*a*d*e)))
@test integrate(x^-4*(d+e*x)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2), x) == :(-1//3*d^-1*x^-3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+-1//12*x^-2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(-5*e*d^-2+c*a^-1*e^-1)+-1//16*a^-5//2*d^-7//2*e^-5//2*(c*d^2+-1*a*e^2)*(c^2*d^4+5*a^2*e^4+2*a*c*d^2*e^2)*arctanh((1/2)*a^-1//2*d^-1//2*e^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*(x*(a*e^2+c*d^2)+2*a*d*e))+1//24*a^-2*d^-3*e^-2*x^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(c*d^2+3*a*e^2)*(-5*a*e^2+3*c*d^2))
@test integrate(x^-5*(d+e*x)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2), x) == :(-1//4*d^-1*x^-4*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+-1//24*x^-3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(-7*e*d^-2+c*a^-1*e^-1)+-1//192*a^-3*d^-4*e^-3*x^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(-105*a^3*e^6+15*c^3*d^6+17*a*c^2*d^4*e^2+25*c*a^2*d^2*e^4)+1//96*a^-2*d^-3*e^-2*x^-2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(-35*a^2*e^4+5*c^2*d^4+6*a*c*d^2*e^2)+1//128*a^-7//2*d^-9//2*e^-7//2*(c*d^2+-1*a*e^2)*(5*c^3*d^6+35*a^3*e^6+9*a*c^2*d^4*e^2+15*c*a^2*d^2*e^4)*arctanh((1/2)*a^-1//2*d^-1//2*e^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*(x*(a*e^2+c*d^2)+2*a*d*e)))
@test integrate(x^3*(d+e*x)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2, x) == :(x^2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2*(-3//20*d*e^-2+1//20*a*c^-1*d^-1)+1//6*e^-1*x^3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2+-1//960*c^-3*d^-3*e^-4*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2*(-35*a^3*e^6+105*c^3*d^6+-33*c*a^2*d^2*e^4+-21*a*c^2*d^4*e^2+-6*c*d*e*x*(-7*a^2*e^4+21*c^2*d^4+-6*a*c*d^2*e^2))+-1//1024*c^-9//2*d^-9//2*e^-11//2*(c*d^2+-1*a*e^2)^3*(7*a^3*e^6+21*c^3*d^6+15*c*a^2*d^2*e^4+21*a*c^2*d^4*e^2)*arctanh((1/2)*c^-1//2*d^-1//2*e^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*(a*e^2+c*d^2+2*c*d*e*x))+1//512*c^-4*d^-4*e^-5*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(a*e^2+c*d^2+2*c*d*e*x)*(-7*a^4*e^8+21*c^4*d^8+-8*c*a^3*d^2*e^6+-6*a^2*c^2*d^4*e^4))
@test integrate(x^2*(d+e*x)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2, x) == :(1//5*e^-1*x^2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2+1//240*c^-2*d^-2*e^-3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2*(-15*a^2*e^4+35*c^2*d^4+-12*a*c*d^2*e^2+-6*c*d*e*x*(-3*a*e^2+7*c*d^2))+1//256*c^-7//2*d^-7//2*e^-9//2*(c*d^2+-1*a*e^2)^3*(3*a^2*e^4+7*c^2*d^4+6*a*c*d^2*e^2)*arctanh((1/2)*c^-1//2*d^-1//2*e^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*(a*e^2+c*d^2+2*c*d*e*x))+-1//128*c^-3*d^-3*e^-4*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(c*d^2+-1*a*e^2)*(a*e^2+c*d^2+2*c*d*e*x)*(3*a^2*e^4+7*c^2*d^4+6*a*c*d^2*e^2))
@test integrate(x*(d+e*x)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2, x) == :(-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2*(5//24*d*e^-2+1//8*a*c^-1*d^-1)+1//4*c^-1*d^-1*e^-1*(d+e*x)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2+-1//128*c^-5//2*d^-5//2*e^-7//2*(c*d^2+-1*a*e^2)^3*(3*a*e^2+5*c*d^2)*arctanh((1/2)*c^-1//2*d^-1//2*e^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*(a*e^2+c*d^2+2*c*d*e*x))+1//64*c^-2*d^-2*e^-3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(c*d^2+-1*a*e^2)*(3*a*e^2+5*c*d^2)*(a*e^2+c*d^2+2*c*d*e*x))
@test integrate((d+e*x)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2, x) == :(1//3*e^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2+(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(-1//8*d*e^-2+1//8*a*c^-1*d^-1)*(a*e^2+c*d^2+2*c*d*e*x)+1//16*c^-3//2*d^-3//2*e^-5//2*(c*d^2+-1*a*e^2)^3*arctanh((1/2)*c^-1//2*d^-1//2*e^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*(a*e^2+c*d^2+2*c*d*e*x)))
@test integrate(x^-1*(d+e*x)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2, x) == :(1//4*e^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(c*d^2+5*a*e^2+2*c*d*e*x)+-1*a^3//2*d^(1/2)*e^3//2*arctanh((1/2)*a^-1//2*d^-1//2*e^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*(x*(a*e^2+c*d^2)+2*a*d*e))+-1//8*c^-1//2*d^-1//2*e^-3//2*(c^2*d^4+-3*a^2*e^4+-6*a*c*d^2*e^2)*arctanh((1/2)*c^-1//2*d^-1//2*e^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*(a*e^2+c*d^2+2*c*d*e*x)))
@test integrate(x^-2*(d+e*x)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2, x) == :(-1*x^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(a*e+-1*c*d*x)+(1/2)*c^(1/2)*d^(1/2)*e^-1//2*(c*d^2+3*a*e^2)*arctanh((1/2)*c^-1//2*d^-1//2*e^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*(a*e^2+c*d^2+2*c*d*e*x))+-1//2*a^(1/2)*d^-1//2*e^(1/2)*(a*e^2+3*c*d^2)*arctanh((1/2)*a^-1//2*d^-1//2*e^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*(x*(a*e^2+c*d^2)+2*a*d*e)))
@test integrate(x^-3*(d+e*x)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2, x) == :(c^3//2*d^3//2*e^(1/2)*arctanh((1/2)*c^-1//2*d^-1//2*e^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*(a*e^2+c*d^2+2*c*d*e*x))+-1//4*d^-1*x^-2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(x*(a*e^2+5*c*d^2)+2*a*d*e)+-1//8*a^-1//2*d^-3//2*e^-1//2*(-1*a^2*e^4+3*c^2*d^4+6*a*c*d^2*e^2)*arctanh((1/2)*a^-1//2*d^-1//2*e^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*(x*(a*e^2+c*d^2)+2*a*d*e)))
@test integrate(x^-4*(d+e*x)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2, x) == :(-1//3*d^-1*x^-3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2+-1//8*x^-2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(x*(a*e^2+c*d^2)+2*a*d*e)*(-1*e*d^-2+c*a^-1*e^-1)+1//16*a^-3//2*d^-5//2*e^-3//2*(c*d^2+-1*a*e^2)^3*arctanh((1/2)*a^-1//2*d^-1//2*e^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*(x*(a*e^2+c*d^2)+2*a*d*e)))
@test integrate(x^-5*(d+e*x)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2, x) == :(-1//4*d^-1*x^-4*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2+-1//24*x^-3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2*(-5*e*d^-2+3*c*a^-1*e^-1)+-1//128*a^-5//2*d^-7//2*e^-5//2*(c*d^2+-1*a*e^2)^3*(3*c*d^2+5*a*e^2)*arctanh((1/2)*a^-1//2*d^-1//2*e^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*(x*(a*e^2+c*d^2)+2*a*d*e))+1//64*a^-2*d^-3*e^-2*x^-2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(c*d^2+-1*a*e^2)*(x*(a*e^2+c*d^2)+2*a*d*e)*(3*c*d^2+5*a*e^2))
@test integrate(x^-6*(d+e*x)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2, x) == :(-1//5*d^-1*x^-5*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2+-1//40*x^-4*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2*(-7*e*d^-2+3*c*a^-1*e^-1)+1//240*a^-2*d^-3*e^-2*x^-3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2*(-35*a^2*e^4+15*c^2*d^4+12*a*c*d^2*e^2)+1//256*a^-7//2*d^-9//2*e^-7//2*(c*d^2+-1*a*e^2)^3*(3*c^2*d^4+7*a^2*e^4+6*a*c*d^2*e^2)*arctanh((1/2)*a^-1//2*d^-1//2*e^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*(x*(a*e^2+c*d^2)+2*a*d*e))+-1//128*a^-3*d^-4*e^-3*x^-2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(c*d^2+-1*a*e^2)*(x*(a*e^2+c*d^2)+2*a*d*e)*(3*c^2*d^4+7*a^2*e^4+6*a*c*d^2*e^2))
@test integrate(x^-7*(d+e*x)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2, x) == :(-1//6*d^-1*x^-6*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2+-1//20*x^-5*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2*(-3*e*d^-2+c*a^-1*e^-1)+-1//960*a^-3*d^-4*e^-3*x^-3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2*(-105*a^3*e^6+35*c^3*d^6+21*c*a^2*d^2*e^4+33*a*c^2*d^4*e^2)+-1//1024*a^-9//2*d^-11//2*e^-9//2*(c*d^2+-1*a*e^2)^3*(7*c^3*d^6+21*a^3*e^6+15*a*c^2*d^4*e^2+21*c*a^2*d^2*e^4)*arctanh((1/2)*a^-1//2*d^-1//2*e^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*(x*(a*e^2+c*d^2)+2*a*d*e))+1//160*a^-2*d^-3*e^-2*x^-4*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2*(-21*a^2*e^4+7*c^2*d^4+6*a*c*d^2*e^2)+1//512*a^-4*d^-5*e^-4*x^-2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(x*(a*e^2+c*d^2)+2*a*d*e)*(-21*a^4*e^8+7*c^4*d^8+6*a^2*c^2*d^4*e^4+8*a*c^3*d^6*e^2))
@test integrate(x^3*(d+e*x)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2, x) == :(x^2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2*(-11//112*d*e^-2+5//112*a*c^-1*d^-1)+1//8*e^-1*x^3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2+-1//4480*c^-3*d^-3*e^-4*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2*(-105*a^3*e^6+231*c^3*d^6+-95*c*a^2*d^2*e^4+-15*a*c^2*d^4*e^2+-10*c*d*e*x*(-15*a^2*e^4+33*c^2*d^4+-10*a*c*d^2*e^2))+3//32768*c^-11//2*d^-11//2*e^-13//2*(c*d^2+-1*a*e^2)^5*(15*a^3*e^6+33*c^3*d^6+35*c*a^2*d^2*e^4+45*a*c^2*d^4*e^2)*arctanh((1/2)*c^-1//2*d^-1//2*e^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*(a*e^2+c*d^2+2*c*d*e*x))+-3//16384*c^-5*d^-5*e^-6*(c*d^2+-1*a*e^2)^3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(a*e^2+c*d^2+2*c*d*e*x)*(15*a^3*e^6+33*c^3*d^6+35*c*a^2*d^2*e^4+45*a*c^2*d^4*e^2)+1//2048*c^-4*d^-4*e^-5*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2*(c*d^2+-1*a*e^2)*(a*e^2+c*d^2+2*c*d*e*x)*(15*a^3*e^6+33*c^3*d^6+35*c*a^2*d^2*e^4+45*a*c^2*d^4*e^2))
@test integrate(x^2*(d+e*x)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2, x) == :(1//7*e^-1*x^2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2+1//840*c^-2*d^-2*e^-3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2*(-35*a^2*e^4+63*c^2*d^4+-20*a*c*d^2*e^2+-10*c*d*e*x*(-5*a*e^2+9*c*d^2))+-1//2048*c^-9//2*d^-9//2*e^-11//2*(c*d^2+-1*a*e^2)^5*(5*a^2*e^4+9*c^2*d^4+10*a*c*d^2*e^2)*arctanh((1/2)*c^-1//2*d^-1//2*e^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*(a*e^2+c*d^2+2*c*d*e*x))+-1//384*c^-3*d^-3*e^-4*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2*(c*d^2+-1*a*e^2)*(a*e^2+c*d^2+2*c*d*e*x)*(5*a^2*e^4+9*c^2*d^4+10*a*c*d^2*e^2)+1//1024*c^-4*d^-4*e^-5*(c*d^2+-1*a*e^2)^3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(a*e^2+c*d^2+2*c*d*e*x)*(5*a^2*e^4+9*c^2*d^4+10*a*c*d^2*e^2))
@test integrate(x*(d+e*x)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2, x) == :(-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2*(7//60*d*e^-2+1//12*a*c^-1*d^-1)+1//6*c^-1*d^-1*e^-1*(d+e*x)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^7//2+1//1024*c^-7//2*d^-7//2*e^-9//2*(c*d^2+-1*a*e^2)^5*(5*a*e^2+7*c*d^2)*arctanh((1/2)*c^-1//2*d^-1//2*e^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*(a*e^2+c*d^2+2*c*d*e*x))+-1//512*c^-3*d^-3*e^-4*(c*d^2+-1*a*e^2)^3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(5*a*e^2+7*c*d^2)*(a*e^2+c*d^2+2*c*d*e*x)+1//192*c^-2*d^-2*e^-3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2*(c*d^2+-1*a*e^2)*(5*a*e^2+7*c*d^2)*(a*e^2+c*d^2+2*c*d*e*x))
@test integrate((d+e*x)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2, x) == :(1//5*e^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2+(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2*(-1//16*d*e^-2+1//16*a*c^-1*d^-1)*(a*e^2+c*d^2+2*c*d*e*x)+-3//256*c^-5//2*d^-5//2*e^-7//2*(c*d^2+-1*a*e^2)^5*arctanh((1/2)*c^-1//2*d^-1//2*e^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*(a*e^2+c*d^2+2*c*d*e*x))+3//128*c^-2*d^-2*e^-3*(c*d^2+-1*a*e^2)^3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(a*e^2+c*d^2+2*c*d*e*x))
@test integrate(x^-1*(d+e*x)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2, x) == :(1//24*e^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2*(3*c*d^2+11*a*e^2+6*c*d*e*x)+-1*a^5//2*d^3//2*e^5//2*arctanh((1/2)*a^-1//2*d^-1//2*e^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*(x*(a*e^2+c*d^2)+2*a*d*e))+-1//64*c^-1*d^-1*e^-2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(-5*a^3*e^6+3*c^3*d^6+-83*c*a^2*d^2*e^4+-11*a*c^2*d^4*e^2+2*c*d*e*x*(a*e^2+3*c*d^2)*(c*d^2+-5*a*e^2))+1//128*c^-3//2*d^-3//2*e^-5//2*(-5*a^4*e^8+3*c^4*d^8+-20*a*c^3*d^6*e^2+60*c*a^3*d^2*e^6+90*a^2*c^2*d^4*e^4)*arctanh((1/2)*c^-1//2*d^-1//2*e^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*(a*e^2+c*d^2+2*c*d*e*x)))
@test integrate(x^-2*(d+e*x)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2, x) == :(-1//3*x^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2*(3*a*e+-1*c*d*x)+1//8*e^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(c^2*d^4+19*a^2*e^4+28*a*c*d^2*e^2+2*c*d*e*x*(c*d^2+7*a*e^2))+-1//2*a^3//2*d^(1/2)*e^3//2*(3*a*e^2+5*c*d^2)*arctanh((1/2)*a^-1//2*d^-1//2*e^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*(x*(a*e^2+c*d^2)+2*a*d*e))+-1//16*c^-1//2*d^-1//2*e^-3//2*(c^3*d^6+-5*a^3*e^6+-45*c*a^2*d^2*e^4+-15*a*c^2*d^4*e^2)*arctanh((1/2)*c^-1//2*d^-1//2*e^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*(a*e^2+c*d^2+2*c*d*e*x)))
@test integrate(x^-3*(d+e*x)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2, x) == :(-1//2*x^-2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2*(a*e+-1*c*d*x)+-1//4*x^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(3*a*e*(a*e^2+3*c*d^2)+-3*c*d*x*(c*d^2+3*a*e^2))+-3//8*a^(1/2)*d^-1//2*e^(1/2)*(a^2*e^4+5*c^2*d^4+10*a*c*d^2*e^2)*arctanh((1/2)*a^-1//2*d^-1//2*e^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*(x*(a*e^2+c*d^2)+2*a*d*e))+3//8*c^(1/2)*d^(1/2)*e^-1//2*(c^2*d^4+5*a^2*e^4+10*a*c*d^2*e^2)*arctanh((1/2)*c^-1//2*d^-1//2*e^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*(a*e^2+c*d^2+2*c*d*e*x)))
@test integrate(x^-4*(d+e*x)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2, x) == :(-1//8*d^-1*x^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(-1*a^2*e^4+5*c^2*d^4+12*a*c*d^2*e^2+-2*c*d*e*x*(a*e^2+7*c*d^2))+-1//12*d^-1*x^-3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2*(x*(3*a*e^2+9*c*d^2)+4*a*d*e)+(1/2)*c^3//2*d^3//2*e^(1/2)*(3*c*d^2+5*a*e^2)*arctanh((1/2)*c^-1//2*d^-1//2*e^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*(a*e^2+c*d^2+2*c*d*e*x))+-1//16*a^-1//2*d^-3//2*e^-1//2*(-1*a^3*e^6+5*c^3*d^6+15*c*a^2*d^2*e^4+45*a*c^2*d^4*e^2)*arctanh((1/2)*a^-1//2*d^-1//2*e^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*(x*(a*e^2+c*d^2)+2*a*d*e)))
@test integrate(x^-5*(d+e*x)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2, x) == :(c^5//2*d^5//2*e^3//2*arctanh((1/2)*c^-1//2*d^-1//2*e^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*(a*e^2+c*d^2+2*c*d*e*x))+-1//24*d^-1*x^-4*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2*(x*(3*a*e^2+11*c*d^2)+6*a*d*e)+1//128*a^-3//2*d^-5//2*e^-3//2*(-3*a^4*e^8+5*c^4*d^8+-90*a^2*c^2*d^4*e^4+-60*a*c^3*d^6*e^2+20*c*a^3*d^2*e^6)*arctanh((1/2)*a^-1//2*d^-1//2*e^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*(x*(a*e^2+c*d^2)+2*a*d*e))+-1//64*a^-1*d^-2*e^-1*x^-2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(x*(-3*a^3*e^6+5*c^3*d^6+11*c*a^2*d^2*e^4+83*a*c^2*d^4*e^2)+2*a*d*e*(c*d^2+3*a*e^2)*(-1*a*e^2+5*c*d^2)))
@test integrate(x^-6*(d+e*x)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2, x) == :(-1//5*d^-1*x^-5*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2+-1//16*x^-4*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2*(x*(a*e^2+c*d^2)+2*a*d*e)*(-1*e*d^-2+c*a^-1*e^-1)+-3//256*a^-5//2*d^-7//2*e^-5//2*(c*d^2+-1*a*e^2)^5*arctanh((1/2)*a^-1//2*d^-1//2*e^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*(x*(a*e^2+c*d^2)+2*a*d*e))+3//128*a^-2*d^-3*e^-2*x^-2*(c*d^2+-1*a*e^2)^3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(x*(a*e^2+c*d^2)+2*a*d*e))
@test integrate(x^-7*(d+e*x)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2, x) == :(-1//6*d^-1*x^-6*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2+-1//60*x^-5*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2*(-7*e*d^-2+5*c*a^-1*e^-1)+1//1024*a^-7//2*d^-9//2*e^-7//2*(c*d^2+-1*a*e^2)^5*(5*c*d^2+7*a*e^2)*arctanh((1/2)*a^-1//2*d^-1//2*e^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*(x*(a*e^2+c*d^2)+2*a*d*e))+-1//512*a^-3*d^-4*e^-3*x^-2*(c*d^2+-1*a*e^2)^3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(x*(a*e^2+c*d^2)+2*a*d*e)*(5*c*d^2+7*a*e^2)+1//192*a^-2*d^-3*e^-2*x^-4*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2*(c*d^2+-1*a*e^2)*(x*(a*e^2+c*d^2)+2*a*d*e)*(5*c*d^2+7*a*e^2))
@test integrate(x^-8*(d+e*x)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2, x) == :(-1//7*d^-1*x^-7*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2+-1//84*x^-6*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2*(-9*e*d^-2+5*c*a^-1*e^-1)+-1//2048*a^-9//2*d^-11//2*e^-9//2*(c*d^2+-1*a*e^2)^5*(5*c^2*d^4+9*a^2*e^4+10*a*c*d^2*e^2)*arctanh((1/2)*a^-1//2*d^-1//2*e^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*(x*(a*e^2+c*d^2)+2*a*d*e))+1//840*a^-2*d^-3*e^-2*x^-5*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2*(-63*a^2*e^4+35*c^2*d^4+20*a*c*d^2*e^2)+-1//384*a^-3*d^-4*e^-3*x^-4*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2*(c*d^2+-1*a*e^2)*(x*(a*e^2+c*d^2)+2*a*d*e)*(5*c^2*d^4+9*a^2*e^4+10*a*c*d^2*e^2)+1//1024*a^-4*d^-5*e^-4*x^-2*(c*d^2+-1*a*e^2)^3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(x*(a*e^2+c*d^2)+2*a*d*e)*(5*c^2*d^4+9*a^2*e^4+10*a*c*d^2*e^2))
@test integrate(x^-9*(d+e*x)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2, x) == :(-1//8*d^-1*x^-8*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2+-1//112*x^-7*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2*(-11*e*d^-2+5*c*a^-1*e^-1)+-1//4480*a^-3*d^-4*e^-3*x^-5*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2*(-231*a^3*e^6+105*c^3*d^6+15*c*a^2*d^2*e^4+95*a*c^2*d^4*e^2)+1//448*a^-2*d^-3*e^-2*x^-6*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2*(-33*a^2*e^4+15*c^2*d^4+10*a*c*d^2*e^2)+3//32768*a^-11//2*d^-13//2*e^-11//2*(c*d^2+-1*a*e^2)^5*(15*c^3*d^6+33*a^3*e^6+35*a*c^2*d^4*e^2+45*c*a^2*d^2*e^4)*arctanh((1/2)*a^-1//2*d^-1//2*e^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*(x*(a*e^2+c*d^2)+2*a*d*e))+-3//16384*a^-5*d^-6*e^-5*x^-2*(c*d^2+-1*a*e^2)^3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(x*(a*e^2+c*d^2)+2*a*d*e)*(15*c^3*d^6+33*a^3*e^6+35*a*c^2*d^4*e^2+45*c*a^2*d^2*e^4)+1//2048*a^-4*d^-5*e^-4*x^-4*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2*(c*d^2+-1*a*e^2)*(x*(a*e^2+c*d^2)+2*a*d*e)*(15*c^3*d^6+33*a^3*e^6+35*a*c^2*d^4*e^2+45*c*a^2*d^2*e^4))
@test integrate(x^2*(d+e*x)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2, x) == :(c^-1*d^-1*e^-2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+2*d^2*e^-2*(d+e*x)^-1*(c*d^2+-1*a*e^2)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+-1//2*c^-3//2*d^-3//2*e^-5//2*(a*e^2+3*c*d^2)*arctanh((1/2)*c^-1//2*d^-1//2*e^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*(a*e^2+c*d^2+2*c*d*e*x)))
@test integrate(x*(d+e*x)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2, x) == :(c^-1//2*d^-1//2*e^-3//2*arctanh((1/2)*c^-1//2*d^-1//2*e^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*(a*e^2+c*d^2+2*c*d*e*x))+-2*d*e^-1*(d+e*x)^-1*(c*d^2+-1*a*e^2)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2))
@test integrate((d+e*x)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2, x) == :(2*(d+e*x)^-1*(c*d^2+-1*a*e^2)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2))
@test integrate(x^-1*(d+e*x)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2, x) == :(-1*a^-1//2*d^-3//2*e^-1//2*arctanh((1/2)*a^-1//2*d^-1//2*e^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*(x*(a*e^2+c*d^2)+2*a*d*e))+-2*e*d^-1*(c*d^2+-1*a*e^2)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*(a*e+c*d*x))
@test integrate(x^-2*(d+e*x)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2, x) == :((1/2)*a^-3//2*d^-5//2*e^-3//2*(c*d^2+3*a*e^2)*arctanh((1/2)*a^-1//2*d^-1//2*e^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*(x*(a*e^2+c*d^2)+2*a*d*e))+-2*e*d^-1*x^-1*(c*d^2+-1*a*e^2)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*(a*e+c*d*x)+-1*a^-1*d^-2*e^-1*x^-1*(c*d^2+-1*a*e^2)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(c*d^2+-3*a*e^2))
@test integrate(x^-3*(d+e*x)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2, x) == :(-1//8*a^-5//2*d^-7//2*e^-5//2*(3*c^2*d^4+15*a^2*e^4+6*a*c*d^2*e^2)*arctanh((1/2)*a^-1//2*d^-1//2*e^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*(x*(a*e^2+c*d^2)+2*a*d*e))+-2*e*d^-1*x^-2*(c*d^2+-1*a*e^2)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*(a*e+c*d*x)+-1//2*a^-1*d^-2*e^-1*x^-2*(c*d^2+-1*a*e^2)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(c*d^2+-5*a*e^2)+1//4*a^-2*d^-3*e^-2*x^-1*(c*d^2+-1*a*e^2)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(c*d^2+3*a*e^2)*(-5*a*e^2+3*c*d^2))
@test integrate(x^5*(d+e*x)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-3//2, x) == :(1//8*c^-7//2*d^-7//2*e^-9//2*(15*a^2*e^4+35*c^2*d^4+30*a*c*d^2*e^2)*arctanh((1/2)*c^-1//2*d^-1//2*e^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*(a*e^2+c*d^2+2*c*d*e*x))+-2//3*d*e^-1*x^4*(c*d^2+-1*a*e^2)^-2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-3//2*(a*e*(c*d^2+-1*a*e^2)+c*d*x*(c*d^2+-1*a*e^2))+-1//12*c^-3*d^-3*e^-4*(c*d^2+-1*a*e^2)^-3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(-45*a^4*e^8+105*c^4*d^8+-190*a*c^3*d^6*e^2+30*c*a^3*d^2*e^6+36*a^2*c^2*d^4*e^4+-2*c*d*e*x*(-15*a^3*e^6+35*c^3*d^6+-61*a*c^2*d^4*e^2+9*c*a^2*d^2*e^4))+-2//3*c^-1*d^-1*e^-2*x^2*(c*d^2+-1*a*e^2)^-4*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*(x*(c*d^2+-1*a*e^2)*(-3*a^3*e^6+7*c^3*d^6+-1*c*a^2*d^2*e^4+-11*a*c^2*d^4*e^2)+a*d*e*(c*d^2+-1*a*e^2)*(-3*a^2*e^4+7*c^2*d^4+-12*a*c*d^2*e^2)))
@test integrate(x^4*(d+e*x)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-3//2, x) == :(-1//2*c^-5//2*d^-5//2*e^-7//2*(3*a*e^2+5*c*d^2)*arctanh((1/2)*c^-1//2*d^-1//2*e^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*(a*e^2+c*d^2+2*c*d*e*x))+-2//3*d*e^-1*x^3*(c*d^2+-1*a*e^2)^-2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-3//2*(a*e*(c*d^2+-1*a*e^2)+c*d*x*(c*d^2+-1*a*e^2))+1//3*c^-2*d^-2*e^-3*(c*d^2+-1*a*e^2)^-3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(-9*a^3*e^6+15*c^3*d^6+-31*a*c^2*d^4*e^2+9*c*a^2*d^2*e^4)+-2//3*x*c^-1*d^-1*e^-2*(c*d^2+-1*a*e^2)^-4*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*(x*(c*d^2+-1*a*e^2)*(-3*a^3*e^6+5*c^3*d^6+-1*c*a^2*d^2*e^4+-9*a*c^2*d^4*e^2)+a*d*e*(c*d^2+-1*a*e^2)*(-3*a^2*e^4+5*c^2*d^4+-10*a*c*d^2*e^2)))
@test integrate(x^3*(d+e*x)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-3//2, x) == :(c^-3//2*d^-3//2*e^-5//2*arctanh((1/2)*c^-1//2*d^-1//2*e^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*(a*e^2+c*d^2+2*c*d*e*x))+-2//3*d*e^-1*x^2*(c*d^2+-1*a*e^2)^-2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-3//2*(a*e*(c*d^2+-1*a*e^2)+c*d*x*(c*d^2+-1*a*e^2))+-1//3*c^-1*d^-1*e^-2*(c*d^2+-1*a*e^2)^-3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*(2*x*(-3*a^3*e^6+3*c^3*d^6+-1*c*a^2*d^2*e^4+-7*a*c^2*d^4*e^2)+2*a*d*e*(a*e^2+3*c*d^2)*(c*d^2+-3*a*e^2)))
@test integrate(x^2*(d+e*x)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-3//2, x) == :(2*x^2*(d+e*x)^-1*(-3*a*e^2+3*c*d^2)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2+-8//3*a*e*(c*d^2+-1*a*e^2)^-3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*(x*(a*e^2+c*d^2)+2*a*d*e))
@test integrate(x*(d+e*x)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-3//2, x) == :(-2//3*d*e^-1*(d+e*x)^-1*(c*d^2+-1*a*e^2)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2+1//3*e^-1*(c*d^2+-1*a*e^2)^-3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*(2*c*d^2+6*a*e^2)*(a*e^2+c*d^2+2*c*d*e*x))
@test integrate((d+e*x)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-3//2, x) == :(2*(d+e*x)^-1*(-3*a*e^2+3*c*d^2)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2+-8//3*c*d*(c*d^2+-1*a*e^2)^-3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*(a*e^2+c*d^2+2*c*d*e*x))
@test integrate(x^-1*(d+e*x)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-3//2, x) == :(-1*a^-3//2*d^-5//2*e^-3//2*arctanh((1/2)*a^-1//2*d^-1//2*e^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*(x*(a*e^2+c*d^2)+2*a*d*e))+-2//3*e*d^-1*(c*d^2+-1*a*e^2)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-3//2*(a*e+c*d*x)+1//3*a^-1*d^-2*e^-1*(c*d^2+-1*a*e^2)^-3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*(-6*a^3*e^6+6*c^3*d^6+2*a*c^2*d^4*e^2+14*c*a^2*d^2*e^4+2*c*d*e*x*(c*d^2+3*a*e^2)*(-1*a*e^2+3*c*d^2)))
@test integrate(x^-2*(d+e*x)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-3//2, x) == :((1/2)*a^-5//2*d^-7//2*e^-5//2*(3*c*d^2+5*a*e^2)*arctanh((1/2)*a^-1//2*d^-1//2*e^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*(x*(a*e^2+c*d^2)+2*a*d*e))+-2//3*e*d^-1*x^-1*(c*d^2+-1*a*e^2)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-3//2*(a*e+c*d*x)+-1//3*a^-2*d^-3*e^-2*x^-1*(c*d^2+-1*a*e^2)^-3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(-15*a^3*e^6+9*c^3*d^6+-9*a*c^2*d^4*e^2+31*c*a^2*d^2*e^4)+1//3*a^-1*d^-2*e^-1*x^-1*(c*d^2+-1*a*e^2)^-3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*(-10*a^3*e^6+6*c^3*d^6+2*a*c^2*d^4*e^2+18*c*a^2*d^2*e^4+2*c*d*e*x*(-5*a^2*e^4+3*c^2*d^4+10*a*c*d^2*e^2)))
@test integrate(x^-3*(d+e*x)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-3//2, x) == :(-1//8*a^-7//2*d^-9//2*e^-7//2*(15*c^2*d^4+35*a^2*e^4+30*a*c*d^2*e^2)*arctanh((1/2)*a^-1//2*d^-1//2*e^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*(x*(a*e^2+c*d^2)+2*a*d*e))+-2//3*e*d^-1*x^-2*(c*d^2+-1*a*e^2)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-3//2*(a*e+c*d*x)+-1//6*a^-2*d^-3*e^-2*x^-2*(c*d^2+-1*a*e^2)^-3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(-35*a^3*e^6+15*c^3*d^6+-9*a*c^2*d^4*e^2+61*c*a^2*d^2*e^4)+1//3*a^-1*d^-2*e^-1*x^-2*(c*d^2+-1*a*e^2)^-3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*(-14*a^3*e^6+6*c^3*d^6+2*a*c^2*d^4*e^2+22*c*a^2*d^2*e^4+2*c*d*e*x*(-7*a^2*e^4+3*c^2*d^4+12*a*c*d^2*e^2))+1//12*a^-3*d^-4*e^-3*x^-1*(c*d^2+-1*a*e^2)^-3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(-105*a^4*e^8+45*c^4*d^8+-36*a^2*c^2*d^4*e^4+-30*a*c^3*d^6*e^2+190*c*a^3*d^2*e^6))
@test integrate(x^-4*(d+e*x)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-3//2, x) == :(1//16*a^-9//2*d^-11//2*e^-9//2*(35*c^3*d^6+105*a^3*e^6+75*a*c^2*d^4*e^2+105*c*a^2*d^2*e^4)*arctanh((1/2)*a^-1//2*d^-1//2*e^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*(x*(a*e^2+c*d^2)+2*a*d*e))+-2//3*e*d^-1*x^-3*(c*d^2+-1*a*e^2)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-3//2*(a*e+c*d*x)+-1//3*a^-2*d^-3*e^-2*x^-3*(c*d^2+-1*a*e^2)^-3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(-21*a^3*e^6+7*c^3*d^6+-3*a*c^2*d^4*e^2+33*c*a^2*d^2*e^4)+-1//24*a^-4*d^-5*e^-4*x^-1*(c*d^2+-1*a*e^2)^-3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(-315*a^5*e^10+105*c^5*d^10+-78*a^3*c^2*d^4*e^6+-55*a*c^4*d^8*e^2+-54*a^2*c^3*d^6*e^4+525*c*a^4*d^2*e^8)+1//3*a^-1*d^-2*e^-1*x^-3*(c*d^2+-1*a*e^2)^-3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*(-18*a^3*e^6+6*c^3*d^6+2*a*c^2*d^4*e^2+26*c*a^2*d^2*e^4+2*c*d*e*x*(-9*a^2*e^4+3*c^2*d^4+14*a*c*d^2*e^2))+1//12*a^-3*d^-4*e^-3*x^-2*(c*d^2+-1*a*e^2)^-3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(-105*a^4*e^8+35*c^4*d^8+-18*a^2*c^2*d^4*e^4+-16*a*c^3*d^6*e^2+168*c*a^3*d^2*e^6))
@test integrate(x^2*(d+e*x)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-5//2, x) == :(2*x^2*(d+e*x)^-1*(-5*a*e^2+5*c*d^2)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-3//2+-1//15*e^-1*(c*d^2+-1*a*e^2)^-4*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-3//2*(8*x*(c^3*d^6+-2*a^3*e^6+c*a^2*d^2*e^4)+8*a*d*e*(c*d^2+-1*a*e^2)*(c*d^2+3*a*e^2))+1//15*e^-1*(c*d^2+-1*a*e^2)^-5*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*(a*e^2+c*d^2+2*c*d*e*x)*(8*c^2*d^4+40*a^2*e^4+80*a*c*d^2*e^2))
@test integrate(x^2*(d+e*x)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-7//2, x) == :(2*x^2*(d+e*x)^-1*(-7*a*e^2+7*c*d^2)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-5//2+-1//35*e^-1*(c*d^2+-1*a*e^2)^-3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-5//2*(8*x*(2*c^2*d^4+3*a^2*e^4+a*c*d^2*e^2)+16*a*d*e*(c*d^2+2*a*e^2))+1//105*e^-1*(c*d^2+-1*a*e^2)^-5*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-3//2*(a*e^2+c*d^2+2*c*d*e*x)*(48*c^2*d^4+112*a^2*e^4+224*a*c*d^2*e^2)+-128//105*c*d*(c*d^2+-1*a*e^2)^-7*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*(a*e^2+c*d^2+2*c*d*e*x)*(3*c^2*d^4+7*a^2*e^4+14*a*c*d^2*e^2))
@test integrate(x^3*(1+x)^(1/2)*(1+x^2+-1x)^(1/2), x) == :(2//11*x^4*(1+x)^(1/2)*(1+x^2+-1x)^(1/2)+6//55*x*(1+x)^(1/2)*(1+x^2+-1x)^(1/2)+-4//55*3^3//4*((1+x+3^(1/2))^-2*(1+x))^-1//2*((1+x+3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(1+x)^3//2*(1+x^3)^-1*(2+3^(1/2))^(1/2)*(1+x^2+-1x)^(1/2)*Elliptic.F(arcsin((1+x+3^(1/2))^-1*(1+x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate(x^2*(1+x)^(1/2)*(1+x^2+-1x)^(1/2), x) == :(2//9*(1+x)^3//2*(1+x^2+-1x)^3//2)
@test integrate(x*(1+x)^(1/2)*(1+x^2+-1x)^(1/2), x) == :(6*(1+x)^(1/2)*(1+x^2+-1x)^(1/2)*(7+7x+7*3^(1/2))^-1+2//7*x^2*(1+x)^(1/2)*(1+x^2+-1x)^(1/2)+-3//7*3^1//4*((1+x+3^(1/2))^-2*(1+x))^-1//2*((1+x+3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(1+x)^3//2*(1+x^3)^-1*(2+-1*3^(1/2))^(1/2)*(1+x^2+-1x)^(1/2)*Elliptic.E(arcsin((1+x+3^(1/2))^-1*(1+x+-1*3^(1/2))),-7+-4*3^(1/2))+2//7*2^(1/2)*3^3//4*((1+x+3^(1/2))^-2*(1+x))^-1//2*((1+x+3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(1+x)^3//2*(1+x^3)^-1*(1+x^2+-1x)^(1/2)*Elliptic.F(arcsin((1+x+3^(1/2))^-1*(1+x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate((1+x)^(1/2)*(1+x^2+-1x)^(1/2), x) == :(2//5*x*(1+x)^(1/2)*(1+x^2+-1x)^(1/2)+2//5*3^3//4*((1+x+3^(1/2))^-2*(1+x))^-1//2*((1+x+3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(1+x)^3//2*(1+x^3)^-1*(2+3^(1/2))^(1/2)*(1+x^2+-1x)^(1/2)*Elliptic.F(arcsin((1+x+3^(1/2))^-1*(1+x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate(x^-1*(1+x)^(1/2)*(1+x^2+-1x)^(1/2), x) == :(2//3*(1+x)^(1/2)*(1+x^2+-1x)^(1/2)+-2//3*(1+x)^(1/2)*(1+x^3)^-1//2*(1+x^2+-1x)^(1/2)*arctanh((1+x^3)^(1/2)))
@test integrate(x^-2*(1+x)^(1/2)*(1+x^2+-1x)^(1/2), x) == :(-1*x^-1*(1+x)^(1/2)*(1+x^2+-1x)^(1/2)+3*(1+x)^(1/2)*(1+x+3^(1/2))^-1*(1+x^2+-1x)^(1/2)+2^(1/2)*3^3//4*((1+x+3^(1/2))^-2*(1+x))^-1//2*((1+x+3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(1+x)^3//2*(1+x^3)^-1*(1+x^2+-1x)^(1/2)*Elliptic.F(arcsin((1+x+3^(1/2))^-1*(1+x+-1*3^(1/2))),-7+-4*3^(1/2))+-3//2*3^1//4*((1+x+3^(1/2))^-2*(1+x))^-1//2*((1+x+3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(1+x)^3//2*(1+x^3)^-1*(2+-1*3^(1/2))^(1/2)*(1+x^2+-1x)^(1/2)*Elliptic.E(arcsin((1+x+3^(1/2))^-1*(1+x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate(x^-3*(1+x)^(1/2)*(1+x^2+-1x)^(1/2), x) == :(-1//2*x^-2*(1+x)^(1/2)*(1+x^2+-1x)^(1/2)+(1/2)*3^3//4*((1+x+3^(1/2))^-2*(1+x))^-1//2*((1+x+3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(1+x)^3//2*(1+x^3)^-1*(2+3^(1/2))^(1/2)*(1+x^2+-1x)^(1/2)*Elliptic.F(arcsin((1+x+3^(1/2))^-1*(1+x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate(x^3*(1+x)^3//2*(1+x^2+-1x)^3//2, x) == :(18//187*x^4*(1+x)^(1/2)*(1+x^2+-1x)^(1/2)+54//935*x*(1+x)^(1/2)*(1+x^2+-1x)^(1/2)+2//17*x^4*(1+x)^(1/2)*(1+x^2+-1x)^(1/2)*(1+x^3)+-36//935*3^3//4*((1+x+3^(1/2))^-2*(1+x))^-1//2*((1+x+3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(1+x)^3//2*(1+x^3)^-1*(2+3^(1/2))^(1/2)*(1+x^2+-1x)^(1/2)*Elliptic.F(arcsin((1+x+3^(1/2))^-1*(1+x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate(x^2*(1+x)^3//2*(1+x^2+-1x)^3//2, x) == :(2//15*(1+x)^5//2*(1+x^2+-1x)^5//2)
@test integrate(x*(1+x)^3//2*(1+x^2+-1x)^3//2, x) == :(54*(1+x)^(1/2)*(1+x^2+-1x)^(1/2)*(91+91x+91*3^(1/2))^-1+18//91*x^2*(1+x)^(1/2)*(1+x^2+-1x)^(1/2)+2//13*x^2*(1+x)^(1/2)*(1+x^2+-1x)^(1/2)*(1+x^3)+-27//91*3^1//4*((1+x+3^(1/2))^-2*(1+x))^-1//2*((1+x+3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(1+x)^3//2*(1+x^3)^-1*(2+-1*3^(1/2))^(1/2)*(1+x^2+-1x)^(1/2)*Elliptic.E(arcsin((1+x+3^(1/2))^-1*(1+x+-1*3^(1/2))),-7+-4*3^(1/2))+18//91*2^(1/2)*3^3//4*((1+x+3^(1/2))^-2*(1+x))^-1//2*((1+x+3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(1+x)^3//2*(1+x^3)^-1*(1+x^2+-1x)^(1/2)*Elliptic.F(arcsin((1+x+3^(1/2))^-1*(1+x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate((1+x)^3//2*(1+x^2+-1x)^3//2, x) == :(18//55*x*(1+x)^(1/2)*(1+x^2+-1x)^(1/2)+2//11*x*(1+x)^(1/2)*(1+x^2+-1x)^(1/2)*(1+x^3)+18//55*3^3//4*((1+x+3^(1/2))^-2*(1+x))^-1//2*((1+x+3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(1+x)^3//2*(1+x^3)^-1*(2+3^(1/2))^(1/2)*(1+x^2+-1x)^(1/2)*Elliptic.F(arcsin((1+x+3^(1/2))^-1*(1+x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate(x^-1*(1+x)^3//2*(1+x^2+-1x)^3//2, x) == :(2//3*(1+x)^(1/2)*(1+x^2+-1x)^(1/2)+2//9*(1+x)^(1/2)*(1+x^2+-1x)^(1/2)*(1+x^3)+-2//3*(1+x)^(1/2)*(1+x^3)^-1//2*(1+x^2+-1x)^(1/2)*arctanh((1+x^3)^(1/2)))
@test integrate(x^-2*(1+x)^3//2*(1+x^2+-1x)^3//2, x) == :(27*(1+x)^(1/2)*(1+x^2+-1x)^(1/2)*(7+7x+7*3^(1/2))^-1+9//7*x^2*(1+x)^(1/2)*(1+x^2+-1x)^(1/2)+-1*x^-1*(1+x)^(1/2)*(1+x^2+-1x)^(1/2)*(1+x^3)+-27//14*3^1//4*((1+x+3^(1/2))^-2*(1+x))^-1//2*((1+x+3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(1+x)^3//2*(1+x^3)^-1*(2+-1*3^(1/2))^(1/2)*(1+x^2+-1x)^(1/2)*Elliptic.E(arcsin((1+x+3^(1/2))^-1*(1+x+-1*3^(1/2))),-7+-4*3^(1/2))+9//7*2^(1/2)*3^3//4*((1+x+3^(1/2))^-2*(1+x))^-1//2*((1+x+3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(1+x)^3//2*(1+x^3)^-1*(1+x^2+-1x)^(1/2)*Elliptic.F(arcsin((1+x+3^(1/2))^-1*(1+x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate(x^-3*(1+x)^3//2*(1+x^2+-1x)^3//2, x) == :(9//10*x*(1+x)^(1/2)*(1+x^2+-1x)^(1/2)+-1//2*x^-2*(1+x)^(1/2)*(1+x^2+-1x)^(1/2)*(1+x^3)+9//10*3^3//4*((1+x+3^(1/2))^-2*(1+x))^-1//2*((1+x+3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(1+x)^3//2*(1+x^3)^-1*(2+3^(1/2))^(1/2)*(1+x^2+-1x)^(1/2)*Elliptic.F(arcsin((1+x+3^(1/2))^-1*(1+x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate(x^3*(1+x)^-1//2*(1+x^2+-1x)^-1//2, x) == :(2//5*x*(1+x)^-1//2*(1+x^2+-1x)^-1//2*(1+x^3)+-4//15*3^3//4*((1+x+3^(1/2))^-2*(1+x))^-1//2*((1+x+3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(1+x)^(1/2)*(2+3^(1/2))^(1/2)*(1+x^2+-1x)^-1//2*Elliptic.F(arcsin((1+x+3^(1/2))^-1*(1+x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate(x^2*(1+x)^-1//2*(1+x^2+-1x)^-1//2, x) == :(2//3*(1+x)^(1/2)*(1+x^2+-1x)^(1/2))
@test integrate(x*(1+x)^-1//2*(1+x^2+-1x)^-1//2, x) == :((1+x)^-1//2*(1+x+3^(1/2))^-1*(1+x^2+-1x)^-1//2*(2+2*x^3)+-1*3^1//4*((1+x+3^(1/2))^-2*(1+x))^-1//2*((1+x+3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(1+x)^(1/2)*(2+-1*3^(1/2))^(1/2)*(1+x^2+-1x)^-1//2*Elliptic.E(arcsin((1+x+3^(1/2))^-1*(1+x+-1*3^(1/2))),-7+-4*3^(1/2))+2//3*2^(1/2)*3^3//4*((1+x+3^(1/2))^-2*(1+x))^-1//2*((1+x+3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(1+x)^(1/2)*(1+x^2+-1x)^-1//2*Elliptic.F(arcsin((1+x+3^(1/2))^-1*(1+x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate((1+x)^-1//2*(1+x^2+-1x)^-1//2, x) == :(2//3*3^3//4*((1+x+3^(1/2))^-2*(1+x))^-1//2*((1+x+3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(1+x)^(1/2)*(2+3^(1/2))^(1/2)*(1+x^2+-1x)^-1//2*Elliptic.F(arcsin((1+x+3^(1/2))^-1*(1+x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate(x^-1*(1+x)^-1//2*(1+x^2+-1x)^-1//2, x) == :(-2//3*(1+x)^-1//2*(1+x^3)^(1/2)*(1+x^2+-1x)^-1//2*arctanh((1+x^3)^(1/2)))
@test integrate(x^-2*(1+x)^-1//2*(1+x^2+-1x)^-1//2, x) == :((1+x)^-1//2*(1+x+3^(1/2))^-1*(1+x^2+-1x)^-1//2*(1+x^3)+-1*x^-1*(1+x)^-1//2*(1+x^2+-1x)^-1//2*(1+x^3)+-1//2*3^1//4*((1+x+3^(1/2))^-2*(1+x))^-1//2*((1+x+3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(1+x)^(1/2)*(2+-1*3^(1/2))^(1/2)*(1+x^2+-1x)^-1//2*Elliptic.E(arcsin((1+x+3^(1/2))^-1*(1+x+-1*3^(1/2))),-7+-4*3^(1/2))+1//3*2^(1/2)*3^3//4*((1+x+3^(1/2))^-2*(1+x))^-1//2*((1+x+3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(1+x)^(1/2)*(1+x^2+-1x)^-1//2*Elliptic.F(arcsin((1+x+3^(1/2))^-1*(1+x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate(x^-3*(1+x)^-1//2*(1+x^2+-1x)^-1//2, x) == :((1/2)*x^-2*(1+x)^-1//2*(1+x^2+-1x)^-1//2*(-1+-1*x^3)+-1//6*3^3//4*((1+x+3^(1/2))^-2*(1+x))^-1//2*((1+x+3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(1+x)^(1/2)*(2+3^(1/2))^(1/2)*(1+x^2+-1x)^-1//2*Elliptic.F(arcsin((1+x+3^(1/2))^-1*(1+x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate(x^3*(1+x)^-3//2*(1+x^2+-1x)^-3//2, x) == :(-2//3*x*(1+x)^-1//2*(1+x^2+-1x)^-1//2+4//9*3^3//4*((1+x+3^(1/2))^-2*(1+x))^-1//2*((1+x+3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(1+x)^(1/2)*(2+3^(1/2))^(1/2)*(1+x^2+-1x)^-1//2*Elliptic.F(arcsin((1+x+3^(1/2))^-1*(1+x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate(x^2*(1+x)^-3//2*(1+x^2+-1x)^-3//2, x) == :(-2//3*(1+x)^-1//2*(1+x^2+-1x)^-1//2)
@test integrate(x*(1+x)^-3//2*(1+x^2+-1x)^-3//2, x) == :(2//3*x^2*(1+x)^-1//2*(1+x^2+-1x)^-1//2+-1//3*(1+x)^-1//2*(1+x+3^(1/2))^-1*(1+x^2+-1x)^-1//2*(2+2*x^3)+-2//9*2^(1/2)*3^3//4*((1+x+3^(1/2))^-2*(1+x))^-1//2*((1+x+3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(1+x)^(1/2)*(1+x^2+-1x)^-1//2*Elliptic.F(arcsin((1+x+3^(1/2))^-1*(1+x+-1*3^(1/2))),-7+-4*3^(1/2))+1//3*3^1//4*((1+x+3^(1/2))^-2*(1+x))^-1//2*((1+x+3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(1+x)^(1/2)*(2+-1*3^(1/2))^(1/2)*(1+x^2+-1x)^-1//2*Elliptic.E(arcsin((1+x+3^(1/2))^-1*(1+x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate((1+x)^-3//2*(1+x^2+-1x)^-3//2, x) == :(2//3*x*(1+x)^-1//2*(1+x^2+-1x)^-1//2+2//9*3^3//4*((1+x+3^(1/2))^-2*(1+x))^-1//2*((1+x+3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(1+x)^(1/2)*(2+3^(1/2))^(1/2)*(1+x^2+-1x)^-1//2*Elliptic.F(arcsin((1+x+3^(1/2))^-1*(1+x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate(x^-1*(1+x)^-3//2*(1+x^2+-1x)^-3//2, x) == :(2//3*(1+x)^-1//2*(1+x^2+-1x)^-1//2+-2//3*(1+x)^-1//2*(1+x^3)^(1/2)*(1+x^2+-1x)^-1//2*arctanh((1+x^3)^(1/2)))
@test integrate(x^-2*(1+x)^-3//2*(1+x^2+-1x)^-3//2, x) == :(2//3*x^-1*(1+x)^-1//2*(1+x^2+-1x)^-1//2+-1//3*x^-1*(1+x)^-1//2*(1+x^2+-1x)^-1//2*(5+5*x^3)+1//3*(1+x)^-1//2*(1+x+3^(1/2))^-1*(1+x^2+-1x)^-1//2*(5+5*x^3)+-5//6*3^1//4*((1+x+3^(1/2))^-2*(1+x))^-1//2*((1+x+3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(1+x)^(1/2)*(2+-1*3^(1/2))^(1/2)*(1+x^2+-1x)^-1//2*Elliptic.E(arcsin((1+x+3^(1/2))^-1*(1+x+-1*3^(1/2))),-7+-4*3^(1/2))+5//9*2^(1/2)*3^3//4*((1+x+3^(1/2))^-2*(1+x))^-1//2*((1+x+3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(1+x)^(1/2)*(1+x^2+-1x)^-1//2*Elliptic.F(arcsin((1+x+3^(1/2))^-1*(1+x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate(x^-3*(1+x)^-3//2*(1+x^2+-1x)^-3//2, x) == :(2//3*x^-2*(1+x)^-1//2*(1+x^2+-1x)^-1//2+-1//6*x^-2*(1+x)^-1//2*(1+x^2+-1x)^-1//2*(7+7*x^3)+-7//18*3^3//4*((1+x+3^(1/2))^-2*(1+x))^-1//2*((1+x+3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(1+x)^(1/2)*(2+3^(1/2))^(1/2)*(1+x^2+-1x)^-1//2*Elliptic.F(arcsin((1+x+3^(1/2))^-1*(1+x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate(x^3*(1+x)^-5//2*(1+x^2+-1x)^-5//2, x) == :(4//27*x*(1+x)^-1//2*(1+x^2+-1x)^-1//2+-2//9*x*(1+x)^-1//2*(1+x^3)^-1*(1+x^2+-1x)^-1//2+4//81*3^3//4*((1+x+3^(1/2))^-2*(1+x))^-1//2*((1+x+3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(1+x)^(1/2)*(2+3^(1/2))^(1/2)*(1+x^2+-1x)^-1//2*Elliptic.F(arcsin((1+x+3^(1/2))^-1*(1+x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate(x^2*(1+x)^-5//2*(1+x^2+-1x)^-5//2, x) == :(-2//9*(1+x)^-3//2*(1+x^2+-1x)^-3//2)
@test integrate(x*(1+x)^-5//2*(1+x^2+-1x)^-5//2, x) == :(10//27*x^2*(1+x)^-1//2*(1+x^2+-1x)^-1//2+-1//27*(1+x)^-1//2*(1+x+3^(1/2))^-1*(1+x^2+-1x)^-1//2*(10+10*x^3)+2//9*x^2*(1+x)^-1//2*(1+x^3)^-1*(1+x^2+-1x)^-1//2+-10//81*2^(1/2)*3^3//4*((1+x+3^(1/2))^-2*(1+x))^-1//2*((1+x+3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(1+x)^(1/2)*(1+x^2+-1x)^-1//2*Elliptic.F(arcsin((1+x+3^(1/2))^-1*(1+x+-1*3^(1/2))),-7+-4*3^(1/2))+5//27*3^1//4*((1+x+3^(1/2))^-2*(1+x))^-1//2*((1+x+3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(1+x)^(1/2)*(2+-1*3^(1/2))^(1/2)*(1+x^2+-1x)^-1//2*Elliptic.E(arcsin((1+x+3^(1/2))^-1*(1+x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate((1+x)^-5//2*(1+x^2+-1x)^-5//2, x) == :(14//27*x*(1+x)^-1//2*(1+x^2+-1x)^-1//2+2//9*x*(1+x)^-1//2*(1+x^3)^-1*(1+x^2+-1x)^-1//2+14//81*3^3//4*((1+x+3^(1/2))^-2*(1+x))^-1//2*((1+x+3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(1+x)^(1/2)*(2+3^(1/2))^(1/2)*(1+x^2+-1x)^-1//2*Elliptic.F(arcsin((1+x+3^(1/2))^-1*(1+x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate(x^-1*(1+x)^-5//2*(1+x^2+-1x)^-5//2, x) == :(2//3*(1+x)^-1//2*(1+x^2+-1x)^-1//2+2//9*(1+x)^-1//2*(1+x^3)^-1*(1+x^2+-1x)^-1//2+-2//3*(1+x)^-1//2*(1+x^3)^(1/2)*(1+x^2+-1x)^-1//2*arctanh((1+x^3)^(1/2)))
@test integrate(x^-2*(1+x)^-5//2*(1+x^2+-1x)^-5//2, x) == :(22//27*x^-1*(1+x)^-1//2*(1+x^2+-1x)^-1//2+-1//27*x^-1*(1+x)^-1//2*(1+x^2+-1x)^-1//2*(55+55*x^3)+1//27*(1+x)^-1//2*(1+x+3^(1/2))^-1*(1+x^2+-1x)^-1//2*(55+55*x^3)+2//9*x^-1*(1+x)^-1//2*(1+x^3)^-1*(1+x^2+-1x)^-1//2+-55//54*3^1//4*((1+x+3^(1/2))^-2*(1+x))^-1//2*((1+x+3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(1+x)^(1/2)*(2+-1*3^(1/2))^(1/2)*(1+x^2+-1x)^-1//2*Elliptic.E(arcsin((1+x+3^(1/2))^-1*(1+x+-1*3^(1/2))),-7+-4*3^(1/2))+55//81*2^(1/2)*3^3//4*((1+x+3^(1/2))^-2*(1+x))^-1//2*((1+x+3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(1+x)^(1/2)*(1+x^2+-1x)^-1//2*Elliptic.F(arcsin((1+x+3^(1/2))^-1*(1+x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate(x^-3*(1+x)^-5//2*(1+x^2+-1x)^-5//2, x) == :(26//27*x^-2*(1+x)^-1//2*(1+x^2+-1x)^-1//2+-1//54*x^-2*(1+x)^-1//2*(1+x^2+-1x)^-1//2*(91+91*x^3)+2//9*x^-2*(1+x)^-1//2*(1+x^3)^-1*(1+x^2+-1x)^-1//2+-91//162*3^3//4*((1+x+3^(1/2))^-2*(1+x))^-1//2*((1+x+3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(1+x)^(1/2)*(2+3^(1/2))^(1/2)*(1+x^2+-1x)^-1//2*Elliptic.F(arcsin((1+x+3^(1/2))^-1*(1+x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate(x*(-1+x)^-3*(3+4*x^2+5x)^-2, x) == :(-97*(4416+-4416x)^-1+-21//736*(1+-1x)^-2+-11//4608*log(3+4*x^2+5x)+11//2304*log(1+-1x)+6023//1218816*23^(1/2)*arctan(1//23*23^(1/2)*(5+8x))+1//276*(1+-1x)^-2*(3+4*x^2+5x)^-1*(39+44x))
@test integrate(x^4*(d+e*x)^(1/2)*(a+b*x+c*x^2)^-1, x) == :(2//7*c^-1*e^-3*(d+e*x)^7//2+-2*b*c^-4*(d+e*x)^(1/2)*(b^2+-2*a*c)+-1//5*c^-2*e^-3*(d+e*x)^5//2*(2*b*e+4*c*d)+1//3*c^-3*e^-3*(d+e*x)^3//2*(2*b^2*e^2+2*c^2*d^2+2*c*e*(b*d+-1*a*e))+2^(1/2)*c^-9//2*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*((b^2+-4*a*c)^-1//2*(-1*e*b^5+c*d*b^4+2*d*a^2*c^3+-5*b*e*a^2*c^2+-4*a*d*b^2*c^2+5*a*c*e*b^3)+-1*e*b^4+c*d*b^3+-1*e*a^2*c^2+-2*a*b*d*c^2+3*a*c*e*b^2)*arctanh(2^(1/2)*c^(1/2)*(d+e*x)^(1/2)*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2)+2^(1/2)*c^-9//2*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*(-1*e*b^4+-1*(b^2+-4*a*c)^-1//2*(-1*e*b^5+c*d*b^4+2*d*a^2*c^3+-5*b*e*a^2*c^2+-4*a*d*b^2*c^2+5*a*c*e*b^3)+c*d*b^3+-1*e*a^2*c^2+-2*a*b*d*c^2+3*a*c*e*b^2)*arctanh(2^(1/2)*c^(1/2)*(d+e*x)^(1/2)*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2))
@test integrate(x^2*(d+e*x)^(1/2)*(a+b*x+c*x^2)^-1, x) == :(-2*b*c^-2*(d+e*x)^(1/2)+2//3*c^-1*e^-1*(d+e*x)^3//2+2^(1/2)*c^-5//2*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*((b^2+-4*a*c)^-1//2*(-1*e*b^3+c*d*b^2+-2*a*d*c^2+3*a*b*c*e)+-1*e*b^2+a*c*e+b*c*d)*arctanh(2^(1/2)*c^(1/2)*(d+e*x)^(1/2)*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2)+2^(1/2)*c^-5//2*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*(-1*e*b^2+-1*(b^2+-4*a*c)^-1//2*(-1*e*b^3+c*d*b^2+-2*a*d*c^2+3*a*b*c*e)+a*c*e+b*c*d)*arctanh(2^(1/2)*c^(1/2)*(d+e*x)^(1/2)*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2))
@test integrate(x*(d+e*x)^(1/2)*(a+b*x+c*x^2)^-1, x) == :(2*c^-1*(d+e*x)^(1/2)+2^(1/2)*c^-3//2*(b^2+-4*a*c)^-1//2*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*(-1*e*b^2+-1*(b^2+-4*a*c)^(1/2)*(c*d+-1*b*e)+b*c*d+2*a*c*e)*arctanh(2^(1/2)*c^(1/2)*(d+e*x)^(1/2)*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2)+-1*2^(1/2)*c^-3//2*(b^2+-4*a*c)^-1//2*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*((b^2+-4*a*c)^(1/2)*(c*d+-1*b*e)+-1*e*b^2+b*c*d+2*a*c*e)*arctanh(2^(1/2)*c^(1/2)*(d+e*x)^(1/2)*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2))
@test integrate((d+e*x)^(1/2)*(a+b*x+c*x^2)^-1, x) == :(2^(1/2)*c^-1//2*(b^2+-4*a*c)^-1//2*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^(1/2)*arctanh(2^(1/2)*c^(1/2)*(d+e*x)^(1/2)*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2)+-1*2^(1/2)*c^-1//2*(b^2+-4*a*c)^-1//2*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^(1/2)*arctanh(2^(1/2)*c^(1/2)*(d+e*x)^(1/2)*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2))
@test integrate(x^-1*(d+e*x)^(1/2)*(a+b*x+c*x^2)^-1, x) == :(-2*a^-1*d^(1/2)*arctanh(d^-1//2*(d+e*x)^(1/2))+2^(1/2)*a^-1*c^(1/2)*(b^2+-4*a*c)^-1//2*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*(b*d+d*(b^2+-4*a*c)^(1/2)+-2*a*e)*arctanh(2^(1/2)*c^(1/2)*(d+e*x)^(1/2)*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2)+-1*2^(1/2)*a^-1*c^(1/2)*(b^2+-4*a*c)^-1//2*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*(b*d+-1*d*(b^2+-4*a*c)^(1/2)+-2*a*e)*arctanh(2^(1/2)*c^(1/2)*(d+e*x)^(1/2)*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2))
@test integrate(x^-3*(d+e*x)^(1/2)*(a+b*x+c*x^2)^-1, x) == :(-1//2*a^-1*x^-2*(d+e*x)^(1/2)+-1*a^-3*d^-1//2*(2*d*b^2+-2*a*b*e+-2*a*c*d)*arctanh(d^-1//2*(d+e*x)^(1/2))+-3//4*a^-1*d^-3//2*e^2*arctanh(d^-1//2*(d+e*x)^(1/2))+a^-2*d^-1*x^-1*(d+e*x)^(1/2)*(b*d+-1*a*e)+-1*e*a^-2*d^-3//2*(b*d+-1*a*e)*arctanh(d^-1//2*(d+e*x)^(1/2))+3//4*e*a^-1*d^-1*x^-1*(d+e*x)^(1/2)+2^(1/2)*a^-3*c^(1/2)*(b^2+-4*a*c)^-1//2*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*(d*b^3+b^2*(d*(b^2+-4*a*c)^(1/2)+-1*a*e)+-1*a*b*(e*(b^2+-4*a*c)^(1/2)+3*c*d)+-1*a*c*(d*(b^2+-4*a*c)^(1/2)+-2*a*e))*arctanh(2^(1/2)*c^(1/2)*(d+e*x)^(1/2)*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2)+-1*2^(1/2)*a^-3*c^(1/2)*(b^2+-4*a*c)^-1//2*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*(d*b^3+-1*b^2*(a*e+d*(b^2+-4*a*c)^(1/2))+a*c*(d*(b^2+-4*a*c)^(1/2)+2*a*e)+-1*a*b*(-1*e*(b^2+-4*a*c)^(1/2)+3*c*d))*arctanh(2^(1/2)*c^(1/2)*(d+e*x)^(1/2)*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2))
@test integrate(x^4*(d+e*x)^3//2*(a+b*x+c*x^2)^-1, x) == :(-1*c^-5*(d+e*x)^(1/2)*(-2*e*b^4+-2*e*a^2*c^2+2*c*d*b^3+-4*a*b*d*c^2+6*a*c*e*b^2)+2//9*c^-1*e^-3*(d+e*x)^9//2+-2//3*b*c^-4*(d+e*x)^3//2*(b^2+-2*a*c)+-1//7*c^-2*e^-3*(d+e*x)^7//2*(2*b*e+4*c*d)+1//5*c^-3*e^-3*(d+e*x)^5//2*(2*b^2*e^2+2*c^2*d^2+2*c*e*(b*d+-1*a*e))+2^(1/2)*c^-11//2*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*((-1*e*b^2+a*c*e+b*c*d)*(-1*e*b^3+c*d*b^2+-2*a*d*c^2+3*a*b*c*e)+-1*(b^2+-4*a*c)^-1//2*(-1*b^6*e^2+-1*c*b^4*(c*d^2+-6*a*e^2)+-2*a^2*c^3*(c*d^2+-1*a*e^2)+a*b^2*c^2*(-9*a*e^2+4*c*d^2)+2*c*d*e*b^5+-10*a*d*e*b^3*c^2+10*b*d*e*a^2*c^3))*arctanh(2^(1/2)*c^(1/2)*(d+e*x)^(1/2)*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2)+2^(1/2)*c^-11//2*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*((b^2+-4*a*c)^-1//2*(-1*b^6*e^2+-1*c*b^4*(c*d^2+-6*a*e^2)+-2*a^2*c^3*(c*d^2+-1*a*e^2)+a*b^2*c^2*(-9*a*e^2+4*c*d^2)+2*c*d*e*b^5+-10*a*d*e*b^3*c^2+10*b*d*e*a^2*c^3)+(-1*e*b^2+a*c*e+b*c*d)*(-1*e*b^3+c*d*b^2+-2*a*d*c^2+3*a*b*c*e))*arctanh(2^(1/2)*c^(1/2)*(d+e*x)^(1/2)*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2))
@test integrate(x^3*(d+e*x)^3//2*(a+b*x+c*x^2)^-1, x) == :(c^-4*(d+e*x)^(1/2)*(-2*e*b^3+-2*a*d*c^2+2*c*d*b^2+4*a*b*c*e)+1//3*c^-3*(d+e*x)^3//2*(2*b^2+-2*a*c)+2//7*c^-1*e^-2*(d+e*x)^7//2+-1//5*c^-2*e^-2*(d+e*x)^5//2*(2*b*e+2*c*d)+2^(1/2)*c^-9//2*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*((b^2+-4*a*c)^-1//2*(-1*b^5*e^2+-1*c*b^3*(c*d^2+-5*a*e^2)+a*b*c^2*(-5*a*e^2+3*c*d^2)+2*c*d*e*b^4+4*d*e*a^2*c^3+-8*a*d*e*b^2*c^2)+-1*b^4*e^2+a*c^2*(c*d^2+-1*a*e^2)+-1*c*b^2*(c*d^2+-3*a*e^2)+2*c*d*e*b^3+-4*a*b*d*e*c^2)*arctanh(2^(1/2)*c^(1/2)*(d+e*x)^(1/2)*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2)+2^(1/2)*c^-9//2*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*(-1*b^4*e^2+-1*(b^2+-4*a*c)^-1//2*(-1*b^5*e^2+-1*c*b^3*(c*d^2+-5*a*e^2)+a*b*c^2*(-5*a*e^2+3*c*d^2)+2*c*d*e*b^4+4*d*e*a^2*c^3+-8*a*d*e*b^2*c^2)+a*c^2*(c*d^2+-1*a*e^2)+-1*c*b^2*(c*d^2+-3*a*e^2)+2*c*d*e*b^3+-4*a*b*d*e*c^2)*arctanh(2^(1/2)*c^(1/2)*(d+e*x)^(1/2)*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2))
@test integrate(x^2*(d+e*x)^3//2*(a+b*x+c*x^2)^-1, x) == :(-1*c^-3*(d+e*x)^(1/2)*(-2*e*b^2+2*a*c*e+2*b*c*d)+-2//3*b*c^-2*(d+e*x)^3//2+2//5*c^-1*e^-1*(d+e*x)^5//2+2^(1/2)*c^-7//2*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*((c*d+-1*b*e)*(-1*e*b^2+b*c*d+2*a*c*e)+-1*(b^2+-4*a*c)^-1//2*(-1*b^4*e^2+-1*c*b^2*(c*d^2+-4*a*e^2)+2*a*c^2*(c*d^2+-1*a*e^2)+2*c*d*e*b^3+-6*a*b*d*e*c^2))*arctanh(2^(1/2)*c^(1/2)*(d+e*x)^(1/2)*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2)+2^(1/2)*c^-7//2*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*((b^2+-4*a*c)^-1//2*(-1*b^4*e^2+-1*c*b^2*(c*d^2+-4*a*e^2)+2*a*c^2*(c*d^2+-1*a*e^2)+2*c*d*e*b^3+-6*a*b*d*e*c^2)+(c*d+-1*b*e)*(-1*e*b^2+b*c*d+2*a*c*e))*arctanh(2^(1/2)*c^(1/2)*(d+e*x)^(1/2)*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2))
@test integrate(x*(d+e*x)^3//2*(a+b*x+c*x^2)^-1, x) == :(2//3*c^-1*(d+e*x)^3//2+c^-2*(d+e*x)^(1/2)*(-2*b*e+2*c*d)+2^(1/2)*c^-5//2*(b^2+-4*a*c)^-1//2*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*(c*(a*e^2*(b^2+-4*a*c)^(1/2)+-1*c*d*(d*(b^2+-4*a*c)^(1/2)+-4*a*e))+b^3*e^2+b*c*(c*d^2+e*(-3*a*e+2*d*(b^2+-4*a*c)^(1/2)))+-1*e*b^2*(e*(b^2+-4*a*c)^(1/2)+2*c*d))*arctanh(2^(1/2)*c^(1/2)*(d+e*x)^(1/2)*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2)+-1*2^(1/2)*c^-5//2*(b^2+-4*a*c)^-1//2*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*(b^3*e^2+-1*c*(a*e^2*(b^2+-4*a*c)^(1/2)+-1*c*d*(d*(b^2+-4*a*c)^(1/2)+4*a*e))+b*c*(c*d^2+-1*e*(2*d*(b^2+-4*a*c)^(1/2)+3*a*e))+-1*e*b^2*(-1*e*(b^2+-4*a*c)^(1/2)+2*c*d))*arctanh(2^(1/2)*c^(1/2)*(d+e*x)^(1/2)*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2))
@test integrate((d+e*x)^3//2*(a+b*x+c*x^2)^-1, x) == :(2*e*c^-1*(d+e*x)^(1/2)+2^(1/2)*c^-3//2*(b^2+-4*a*c)^-1//2*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*(2*c^2*d^2+b*e^2*(b+(b^2+-4*a*c)^(1/2))+-2*c*e*(a*e+b*d+d*(b^2+-4*a*c)^(1/2)))*arctanh(2^(1/2)*c^(1/2)*(d+e*x)^(1/2)*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2)+-1*2^(1/2)*c^-3//2*(b^2+-4*a*c)^-1//2*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*(2*c^2*d^2+b*e^2*(b+-1*(b^2+-4*a*c)^(1/2))+-2*c*e*(a*e+b*d+-1*d*(b^2+-4*a*c)^(1/2)))*arctanh(2^(1/2)*c^(1/2)*(d+e*x)^(1/2)*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2))
@test integrate(x^-1*(d+e*x)^3//2*(a+b*x+c*x^2)^-1, x) == :(-2*a^-1*d^3//2*arctanh(d^-1//2*(d+e*x)^(1/2))+-1*2^(1/2)*a^-1*c^-1//2*(b^2+-4*a*c)^-1//2*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*(b*(a*e^2+c*d^2)+a*e^2*(b^2+-4*a*c)^(1/2)+-1*c*d*(d*(b^2+-4*a*c)^(1/2)+4*a*e))*arctanh(2^(1/2)*c^(1/2)*(d+e*x)^(1/2)*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2)+-1*2^(1/2)*a^-1*c^-1//2*(b^2+-4*a*c)^-1//2*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*(-1*b*(a*e^2+c*d^2)+a*e^2*(b^2+-4*a*c)^(1/2)+-1*c*d*(d*(b^2+-4*a*c)^(1/2)+-4*a*e))*arctanh(2^(1/2)*c^(1/2)*(d+e*x)^(1/2)*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2))
@test integrate(x^-2*(d+e*x)^3//2*(a+b*x+c*x^2)^-1, x) == :(e*a^-1*d^(1/2)*arctanh(d^-1//2*(d+e*x)^(1/2))+-1*d*a^-1*x^-1*(d+e*x)^(1/2)+2*a^-2*d^(1/2)*(b*d+-2*a*e)*arctanh(d^-1//2*(d+e*x)^(1/2))+2^(1/2)*a^-2*c^(1/2)*(b^2+-4*a*c)^-1//2*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*(b^2*d^2+-2*a*(c*d^2+-1*e*(a*e+d*(b^2+-4*a*c)^(1/2)))+-1*b*d*(d*(b^2+-4*a*c)^(1/2)+2*a*e))*arctanh(2^(1/2)*c^(1/2)*(d+e*x)^(1/2)*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2)+-1*2^(1/2)*a^-2*c^(1/2)*(b^2+-4*a*c)^-1//2*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*(b^2*d^2+-2*a*(c*d^2+e*(d*(b^2+-4*a*c)^(1/2)+-1*a*e))+b*d*(d*(b^2+-4*a*c)^(1/2)+-2*a*e))*arctanh(2^(1/2)*c^(1/2)*(d+e*x)^(1/2)*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2))
@test integrate(x^-3*(d+e*x)^3//2*(a+b*x+c*x^2)^-1, x) == :(a^-2*x^-1*(d+e*x)^(1/2)*(b*d+-2*a*e)+-1*a^-3*d^-1//2*(-2*a*(c*d^2+-1*a*e^2)+2*b^2*d^2+-4*a*b*d*e)*arctanh(d^-1//2*(d+e*x)^(1/2))+-3//4*a^-1*d^-1//2*e^2*arctanh(d^-1//2*(d+e*x)^(1/2))+-1//2*d*a^-1*x^-2*(d+e*x)^(1/2)+3//4*e*a^-1*x^-1*(d+e*x)^(1/2)+-1*e*a^-2*d^-1//2*(b*d+-2*a*e)*arctanh(d^-1//2*(d+e*x)^(1/2))+2^(1/2)*a^-3*c^(1/2)*(b^2+-4*a*c)^-1//2*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*(a*(a*e^2*(b^2+-4*a*c)^(1/2)+-1*c*d*(d*(b^2+-4*a*c)^(1/2)+-4*a*e))+b^3*d^2+d*b^2*(d*(b^2+-4*a*c)^(1/2)+-2*a*e)+-1*a*b*(e*(-1*a*e+2*d*(b^2+-4*a*c)^(1/2))+3*c*d^2))*arctanh(2^(1/2)*c^(1/2)*(d+e*x)^(1/2)*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2)+-1*2^(1/2)*a^-3*c^(1/2)*(b^2+-4*a*c)^-1//2*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*(b^3*d^2+-1*a*(a*e^2*(b^2+-4*a*c)^(1/2)+-1*c*d*(d*(b^2+-4*a*c)^(1/2)+4*a*e))+-1*a*b*(-1*e*(a*e+2*d*(b^2+-4*a*c)^(1/2))+3*c*d^2)+-1*d*b^2*(d*(b^2+-4*a*c)^(1/2)+2*a*e))*arctanh(2^(1/2)*c^(1/2)*(d+e*x)^(1/2)*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2))
@test integrate((d+e*x)^4*(f+g*x)^2*(d^2+-1*e^2*x^2)^-1, x) == :(-1*x^3*(e*f+7*d*g)*(1//3*d*g+1//3*e*f)+-1//5*e^2*g^2*x^5+-1*d*e^-1*x^2*(2*e^2*f^2+4*d^2*g^2+7*d*e*f*g)+-1*x*d^2*e^-2*(7*e^2*f^2+8*d^2*g^2+16*d*e*f*g)+-8*d^3*e^-3*(d*g+e*f)^2*log(d+-1*e*x)+-1//2*e*g*x^4*(e*f+2*d*g))
@test integrate((d+e*x)^3*(f+g*x)^2*(d^2+-1*e^2*x^2)^-1, x) == :(-1//2*e^-1*x^2*(e^2*f^2+4*d^2*g^2+6*d*e*f*g)+-1//3*g*x^3*(2*e*f+3*d*g)+-1//4*e*g^2*x^4+-4*d^2*e^-3*(d*g+e*f)^2*log(d+-1*e*x)+-1*d*x*e^-2*(e*f+2*d*g)*(2*d*g+3*e*f))
@test integrate((d+e*x)^2*(f+g*x)^2*(d^2+-1*e^2*x^2)^-1, x) == :(-1//3*g^-1*(f+g*x)^3+-1*d*e^-1*(f+g*x)^2+-2*d*e^-3*(d*g+e*f)^2*log(d+-1*e*x)+-2*d*g*x*e^-2*(d*g+e*f))
@test integrate((f+g*x)^2*(d^2+-1*e^2*x^2)^-1*(d+e*x), x) == :(-1//2*e^-1*(f+g*x)^2+-1*e^-3*(d*g+e*f)^2*log(d+-1*e*x)+-1*g*x*e^-2*(d*g+e*f))
@test integrate((f+g*x)^2*(d^2+-1*e^2*x^2)^-1, x) == :(-1*x*e^-2*g^2+(1/2)*d^-1*e^-3*(e*f+-1*d*g)^2*log(d+e*x)+-1//2*d^-1*e^-3*(d*g+e*f)^2*log(d+-1*e*x))
@test integrate((d+e*x)^-1*(f+g*x)^2*(d^2+-1*e^2*x^2)^-1, x) == :(-1//2*d^-1*e^-3*(d+e*x)^-1*(e*f+-1*d*g)^2+-1//4*d^-2*e^-3*(d*g+e*f)^2*log(d+-1*e*x)+1//4*d^-2*e^-3*(e*f+-1*d*g)*(e*f+3*d*g)*log(d+e*x))
@test integrate((d+e*x)^-2*(f+g*x)^2*(d^2+-1*e^2*x^2)^-1, x) == :(-1//4*d^-1*e^-3*(d+e*x)^-2*(e*f+-1*d*g)^2+1//4*d^-3*e^-3*(d*g+e*f)^2*arctanh(e*x*d^-1)+-1//4*d^-2*e^-3*(d+e*x)^-1*(e*f+-1*d*g)*(e*f+3*d*g))
@test integrate((d+e*x)^-3*(f+g*x)^2*(d^2+-1*e^2*x^2)^-1, x) == :(-1//6*d^-1*e^-3*(d+e*x)^-3*(e*f+-1*d*g)^2+-1//8*d^-3*e^-3*(d+e*x)^-1*(d*g+e*f)^2+1//8*d^-4*e^-3*(d*g+e*f)^2*arctanh(e*x*d^-1)+-1//8*d^-2*e^-3*(d+e*x)^-2*(e*f+-1*d*g)*(e*f+3*d*g))
@test integrate((d+e*x)^-4*(f+g*x)^2*(d^2+-1*e^2*x^2)^-1, x) == :(-1//8*d^-1*e^-3*(d+e*x)^-4*(e*f+-1*d*g)^2+-1//16*d^-4*e^-3*(d+e*x)^-1*(d*g+e*f)^2+-1//16*d^-3*e^-3*(d+e*x)^-2*(d*g+e*f)^2+1//16*d^-5*e^-3*(d*g+e*f)^2*arctanh(e*x*d^-1)+-1//12*d^-2*e^-3*(d+e*x)^-3*(e*f+-1*d*g)*(e*f+3*d*g))
@test integrate((d+e*x)^7*(f+g*x)^2*(d^2+-1*e^2*x^2)^-2, x) == :(1//3*d*x^3*(7*e^2*f^2+49*d^2*g^2+46*d*e*f*g)+1//4*e*x^4*(e^2*f^2+23*d^2*g^2+14*d*e*f*g)+1//6*e^3*g^2*x^6+x*d^3*e^-2*(49*e^2*f^2+112*d^2*g^2+160*d*e*f*g)+(1/2)*d^2*e^-1*x^2*(23*e^2*f^2+80*d^2*g^2+98*d*e*f*g)+32*d^5*e^-3*(d+-1*e*x)^-1*(d*g+e*f)^2+1//5*g*e^2*x^5*(2*e*f+7*d*g)+16*d^4*e^-3*(d*g+e*f)*(5*e*f+9*d*g)*log(d+-1*e*x))
@test integrate((d+e*x)^6*(f+g*x)^2*(d^2+-1*e^2*x^2)^-2, x) == :(x^3*(1//3*e^2*f^2+17//3*d^2*g^2+4*d*e*f*g)+1//5*e^2*g^2*x^5+d*e^-1*x^2*(3*e^2*f^2+16*d^2*g^2+17*d*e*f*g)+x*d^2*e^-2*(17*e^2*f^2+48*d^2*g^2+64*d*e*f*g)+(1/2)*e*g*x^4*(e*f+3*d*g)+16*d^4*e^-3*(d+-1*e*x)^-1*(d*g+e*f)^2+32*d^3*e^-3*(d*g+e*f)*(e*f+2*d*g)*log(d+-1*e*x))
@test integrate((d+e*x)^5*(f+g*x)^2*(d^2+-1*e^2*x^2)^-2, x) == :((1/2)*e^-1*x^2*(e^2*f^2+12*d^2*g^2+10*d*e*f*g)+1//3*g*x^3*(2*e*f+5*d*g)+1//4*e*g^2*x^4+d*x*e^-2*(5*e^2*f^2+20*d^2*g^2+24*d*e*f*g)+8*d^3*e^-3*(d+-1*e*x)^-1*(d*g+e*f)^2+4*d^2*e^-3*(d*g+e*f)*(3*e*f+7*d*g)*log(d+-1*e*x))
@test integrate((d+e*x)^4*(f+g*x)^2*(d^2+-1*e^2*x^2)^-2, x) == :(1//3*g^2*x^3+x*e^-2*(e^2*f^2+8*d^2*g^2+8*d*e*f*g)+g*e^-1*x^2*(e*f+2*d*g)+4*d^2*e^-3*(d+-1*e*x)^-1*(d*g+e*f)^2+4*d*e^-3*(d*g+e*f)*(e*f+3*d*g)*log(d+-1*e*x))
@test integrate((d+e*x)^3*(f+g*x)^2*(d^2+-1*e^2*x^2)^-2, x) == :((1/2)*e^-1*g^2*x^2+g*x*e^-2*(2*e*f+3*d*g)+e^-3*(d*g+e*f)*(e*f+5*d*g)*log(d+-1*e*x)+2*d*e^-3*(d+-1*e*x)^-1*(d*g+e*f)^2)
@test integrate((d+e*x)^2*(f+g*x)^2*(d^2+-1*e^2*x^2)^-2, x) == :(x*e^-2*g^2+e^-3*(d+-1*e*x)^-1*(d*g+e*f)^2+2*g*e^-3*(d*g+e*f)*log(d+-1*e*x))
@test integrate((f+g*x)^2*(d^2+-1*e^2*x^2)^-2*(d+e*x), x) == :((1/2)*d^-1*e^-3*(d+-1*e*x)^-1*(d*g+e*f)^2+1//4*d^-2*e^-3*(e*f+-1*d*g)^2*log(d+e*x)+-1//4*d^-2*e^-3*(d*g+e*f)*(e*f+-3*d*g)*log(d+-1*e*x))
@test integrate((f+g*x)^2*(d^2+-1*e^2*x^2)^-2, x) == :((1/2)*d^-3*e^-3*(d*g+e*f)*(e*f+-1*d*g)*arctanh(e*x*d^-1)+(1/2)*d^-2*e^-2*(d^2+-1*e^2*x^2)^-1*(f+g*x)*(g*d^2+f*x*e^2))
@test integrate((d+e*x)^-1*(f+g*x)^2*(d^2+-1*e^2*x^2)^-2, x) == :(-1//4*d^-3*e^-3*(d+e*x)^-1*(e^2*f^2+-1*d^2*g^2)+-1//8*d^-2*e^-3*(d+e*x)^-2*(e*f+-1*d*g)^2+1//8*d^-3*e^-3*(d+-1*e*x)^-1*(d*g+e*f)^2+1//8*d^-4*e^-3*(d*g+e*f)*(-1*d*g+3*e*f)*arctanh(e*x*d^-1))
@test integrate((d+e*x)^-2*(f+g*x)^2*(d^2+-1*e^2*x^2)^-2, x) == :(-1//8*d^-3*e^-3*(d+e*x)^-2*(e^2*f^2+-1*d^2*g^2)+-1//12*d^-2*e^-3*(d+e*x)^-3*(e*f+-1*d*g)^2+1//16*d^-4*e^-3*(d+-1*e*x)^-1*(d*g+e*f)^2+-1//16*d^-4*e^-3*(d+e*x)^-1*(d*g+e*f)*(-1*d*g+3*e*f)+1//4*f*d^-5*e^-2*(d*g+e*f)*arctanh(e*x*d^-1))
@test integrate((d+e*x)^-3*(f+g*x)^2*(d^2+-1*e^2*x^2)^-2, x) == :(-1//12*d^-3*e^-3*(d+e*x)^-3*(e^2*f^2+-1*d^2*g^2)+-1//16*d^-2*e^-3*(d+e*x)^-4*(e*f+-1*d*g)^2+1//32*d^-5*e^-3*(d+-1*e*x)^-1*(d*g+e*f)^2+-1//8*f*d^-5*e^-2*(d+e*x)^-1*(d*g+e*f)+-1//32*d^-4*e^-3*(d+e*x)^-2*(d*g+e*f)*(-1*d*g+3*e*f)+1//32*d^-6*e^-3*(d*g+e*f)*(d*g+5*e*f)*arctanh(e*x*d^-1))
@test integrate((d+e*x)^-4*(f+g*x)^2*(d^2+-1*e^2*x^2)^-2, x) == :(-1//16*d^-3*e^-3*(d+e*x)^-4*(e^2*f^2+-1*d^2*g^2)+-1//20*d^-2*e^-3*(d+e*x)^-5*(e*f+-1*d*g)^2+1//64*d^-6*e^-3*(d+-1*e*x)^-1*(d*g+e*f)^2+-1//16*f*d^-5*e^-2*(d+e*x)^-2*(d*g+e*f)+-1//48*d^-4*e^-3*(d+e*x)^-3*(d*g+e*f)*(-1*d*g+3*e*f)+-1//64*d^-6*e^-3*(d+e*x)^-1*(d*g+e*f)*(d*g+5*e*f)+1//32*d^-7*e^-3*(d*g+e*f)*(d*g+3*e*f)*arctanh(e*x*d^-1))
@test integrate((d+e*x)^7*(f+g*x)^2*(d^2+-1*e^2*x^2)^-3, x) == :(-1//3*g*x^3*(2*e*f+7*d*g)+-1//4*e*g^2*x^4+-1*d*x*e^-2*(7*e^2*f^2+56*d^2*g^2+48*d*e*f*g)+-8*d^2*e^-3*(3*e^2*f^2+13*d^2*g^2+14*d*e*f*g)*log(d+-1*e*x)+8*d^4*e^-3*(d+-1*e*x)^-2*(d*g+e*f)^2+-1//2*e^-1*x^2*(e*f+2*d*g)*(e*f+12*d*g)+-32*d^3*e^-3*(d+-1*e*x)^-1*(d*g+e*f)*(e*f+2*d*g))
@test integrate((d+e*x)^6*(f+g*x)^2*(d^2+-1*e^2*x^2)^-3, x) == :(-1//3*g^2*x^3+-1*x*e^-2*(e^2*f^2+18*d^2*g^2+12*d*e*f*g)+-1*g*e^-1*x^2*(e*f+3*d*g)+-2*d*e^-3*(3*e^2*f^2+19*d^2*g^2+18*d*e*f*g)*log(d+-1*e*x)+4*d^3*e^-3*(d+-1*e*x)^-2*(d*g+e*f)^2+-4*d^2*e^-3*(d+-1*e*x)^-1*(d*g+e*f)*(3*e*f+7*d*g))
@test integrate((d+e*x)^5*(f+g*x)^2*(d^2+-1*e^2*x^2)^-3, x) == :(-1*e^-3*(e^2*f^2+13*d^2*g^2+10*d*e*f*g)*log(d+-1*e*x)+-1//2*e^-1*g^2*x^2+-1*g*x*e^-2*(2*e*f+5*d*g)+2*d^2*e^-3*(d+-1*e*x)^-2*(d*g+e*f)^2+-4*d*e^-3*(d+-1*e*x)^-1*(d*g+e*f)*(e*f+3*d*g))
@test integrate((d+e*x)^4*(f+g*x)^2*(d^2+-1*e^2*x^2)^-3, x) == :(-1*x*e^-2*g^2+d*e^-3*(d+-1*e*x)^-2*(d*g+e*f)^2+-1*e^-3*(d+-1*e*x)^-1*(d*g+e*f)*(e*f+5*d*g)+-2*g*e^-3*(e*f+2*d*g)*log(d+-1*e*x))
@test integrate((d+e*x)^3*(f+g*x)^2*(d^2+-1*e^2*x^2)^-3, x) == :((1/2)*e^-3*(d+-1*e*x)^-2*(d*g+e*f)^2+-1*e^-3*g^2*log(d+-1*e*x)+-2*g*e^-3*(d+-1*e*x)^-1*(d*g+e*f))
@test integrate((d+e*x)^2*(f+g*x)^2*(d^2+-1*e^2*x^2)^-3, x) == :(1//4*d^-1*e^-3*(d+-1*e*x)^-2*(d*g+e*f)^2+1//4*d^-3*e^-3*(e*f+-1*d*g)^2*arctanh(e*x*d^-1)+1//4*d^-2*e^-3*(d+-1*e*x)^-1*(d*g+e*f)*(e*f+-3*d*g))
@test integrate((f+g*x)^2*(d^2+-1*e^2*x^2)^-3*(d+e*x), x) == :(-1//8*d^-3*e^-3*(d+e*x)^-1*(e*f+-1*d*g)^2+1//4*d^-3*e^-3*(d+-1*e*x)^-1*(e^2*f^2+-1*d^2*g^2)+1//8*d^-2*e^-3*(d+-1*e*x)^-2*(d*g+e*f)^2+1//8*d^-4*e^-3*(d*g+3*e*f)*(e*f+-1*d*g)*arctanh(e*x*d^-1))
@test integrate((f+g*x)^2*(d^2+-1*e^2*x^2)^-3, x) == :(1//8*d^-5*e^-3*(-1*d^2*g^2+3*e^2*f^2)*arctanh(e*x*d^-1)+1//8*d^-4*e^-2*(d^2+-1*e^2*x^2)^-1*(x*(-1*d^2*g^2+3*e^2*f^2)+2*f*g*d^2)+1//4*d^-2*e^-2*(d^2+-1*e^2*x^2)^-2*(f+g*x)*(g*d^2+f*x*e^2))
@test integrate((d+e*x)^-1*(f+g*x)^2*(d^2+-1*e^2*x^2)^-3, x) == :(-1//16*d^-5*e^-3*(d+e*x)^-1*(-1*d^2*g^2+3*e^2*f^2)+-1//24*d^-3*e^-3*(d+e*x)^-3*(e*f+-1*d*g)^2+1//16*d^-6*e^-3*(-1*d^2*g^2+5*e^2*f^2+2*d*e*f*g)*arctanh(e*x*d^-1)+1//32*d^-4*e^-3*(d+-1*e*x)^-2*(d*g+e*f)^2+-1//32*d^-4*e^-3*(d+e*x)^-2*(d*g+3*e*f)*(e*f+-1*d*g)+1//8*f*d^-5*e^-2*(d+-1*e*x)^-1*(d*g+e*f))
@test integrate((d+e*x)^-2*(f+g*x)^2*(d^2+-1*e^2*x^2)^-3, x) == :(-1//32*d^-6*e^-3*(d+e*x)^-1*(-1*d^2*g^2+5*e^2*f^2+2*d*e*f*g)+-1//32*d^-5*e^-3*(d+e*x)^-2*(-1*d^2*g^2+3*e^2*f^2)+-1//32*d^-3*e^-3*(d+e*x)^-4*(e*f+-1*d*g)^2+1//64*d^-7*e^-3*(-1*d^2*g^2+15*e^2*f^2+10*d*e*f*g)*arctanh(e*x*d^-1)+1//64*d^-5*e^-3*(d+-1*e*x)^-2*(d*g+e*f)^2+-1//48*d^-4*e^-3*(d+e*x)^-3*(d*g+3*e*f)*(e*f+-1*d*g)+1//64*d^-6*e^-3*(d+-1*e*x)^-1*(d*g+e*f)*(d*g+5*e*f))
@test integrate((d+e*x)^3*(f+g*x)^5*(d^2+-1*e^2*x^2)^-7//2, x) == :(e^-6*g^4*(d^2+-1*e^2*x^2)^(1/2)*(3*d*g+5*e*f)+(1/2)*x*e^-5*g^5*(d^2+-1*e^2*x^2)^(1/2)+-1//2*e^-6*g^3*(13*d^2*g^2+20*e^2*f^2+30*d*e*f*g)*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+1//5*d^-1*e^-6*(d+e*x)^3*(d^2+-1*e^2*x^2)^-5//2*(d*g+e*f)^5+1//15*d^-3*e^-6*(d^2+-1*e^2*x^2)^-1//2*(d*g+e*f)^3*(d+e*x)*(2*e^2*f^2+127*d^2*g^2+-21*d*e*f*g)+1//15*d^-2*e^-6*(d+e*x)^2*(d^2+-1*e^2*x^2)^-3//2*(d*g+e*f)^4*(-23*d*g+2*e*f))
@test integrate((d+e*x)^3*(f+g*x)^4*(d^2+-1*e^2*x^2)^-7//2, x) == :(e^-5*g^4*(d^2+-1*e^2*x^2)^(1/2)+-1*e^-5*g^3*(3*d*g+4*e*f)*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+1//5*d^-1*e^-5*(d+e*x)^3*(d^2+-1*e^2*x^2)^-5//2*(d*g+e*f)^4+1//15*d^-2*e^-5*(d+e*x)^2*(d^2+-1*e^2*x^2)^-3//2*(d*g+e*f)^3*(-18*d*g+2*e*f)+2//15*d^-3*e^-5*(d^2+-1*e^2*x^2)^-1//2*(d*g+e*f)^2*(d+e*x)*(e^2*f^2+36*d^2*g^2+-8*d*e*f*g))
@test integrate((d+e*x)^3*(f+g*x)^3*(d^2+-1*e^2*x^2)^-7//2, x) == :(-1*e^-4*g^3*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+1//5*d^-1*e^-4*(d+e*x)^3*(d^2+-1*e^2*x^2)^-5//2*(d*g+e*f)^3+1//15*d^-3*e^-4*(d^2+-1*e^2*x^2)^-1//2*(d+e*x)*(d*g+e*f)*(2*e^2*f^2+32*d^2*g^2+-11*d*e*f*g)+1//15*d^-2*e^-4*(d+e*x)^2*(d^2+-1*e^2*x^2)^-3//2*(d*g+e*f)^2*(-13*d*g+2*e*f))
@test integrate((d+e*x)^3*(f+g*x)^2*(d^2+-1*e^2*x^2)^-7//2, x) == :(1//5*d^-1*e^-3*(d+e*x)^3*(d^2+-1*e^2*x^2)^-5//2*(d*g+e*f)^2+1//15*d^-3*e^-3*(d^2+-1*e^2*x^2)^-1//2*(d+e*x)*(2*e^2*f^2+7*d^2*g^2+-6*d*e*f*g)+1//15*d^-2*e^-3*(d+e*x)^2*(d^2+-1*e^2*x^2)^-3//2*(d*g+e*f)*(-8*d*g+2*e*f))
@test integrate((d+e*x)^3*(d^2+-1*e^2*x^2)^-7//2*(f+g*x), x) == :(1//5*d^-1*e^-2*(d+e*x)^3*(d^2+-1*e^2*x^2)^-5//2*(d*g+e*f)+1//15*x*d^-3*e^-1*(d^2+-1*e^2*x^2)^-1//2*(-3*d*g+2*e*f)+1//15*d^-1*e^-2*(d^2+-1*e^2*x^2)^-3//2*(d+e*x)*(-6*d*g+4*e*f))
@test integrate((d+e*x)^3*(d^2+-1*e^2*x^2)^-7//2, x) == :(1//5*d^-1*e^-1*(d+-1*e*x)^-3*(d^2+-1*e^2*x^2)^(1/2)+2//15*d^-3*e^-1*(d+-1*e*x)^-1*(d^2+-1*e^2*x^2)^(1/2)+2//15*d^-2*e^-1*(d+-1*e*x)^-2*(d^2+-1*e^2*x^2)^(1/2))
@test integrate((d+e*x)^3*(f+g*x)^-1*(d^2+-1*e^2*x^2)^-7//2, x) == :(g^3*(d*g+e*f)^-3*(e^2*f^2+-1*d^2*g^2)^-1//2*arctan((d^2+-1*e^2*x^2)^-1//2*(e^2*f^2+-1*d^2*g^2)^-1//2*(g*d^2+f*x*e^2))+4*d*(d^2+-1*e^2*x^2)^-5//2*(5*d*g+5*e*f)^-1*(d+e*x)+-1//15*d^-1*(d^2+-1*e^2*x^2)^-3//2*(d*g+e*f)^-2*(5*d*(e*f+-1*d*g)+-1*e*x*(e*f+11*d*g))+1//15*d^-3*(d^2+-1*e^2*x^2)^-1//2*(d*g+e*f)^-3*(15*d^3*g^2+e*x*(2*e^2*f^2+22*d^2*g^2+9*d*e*f*g)))
@test integrate((d+e*x)^3*(f+g*x)^-2*(d^2+-1*e^2*x^2)^-7//2, x) == :(g^4*(f+g*x)^-1*(d^2+-1*e^2*x^2)^(1/2)*(d*g+e*f)^-4*(e*f+-1*d*g)^-1+-1//15*e*d^-1*(d^2+-1*e^2*x^2)^-3//2*(d*g+e*f)^-3*(5*d*(e*f+-3*d*g)+-1*e*x*(e*f+21*d*g))+1//15*e*d^-3*(d^2+-1*e^2*x^2)^-1//2*(d*g+e*f)^-4*(45*d^3*g^2+e*x*(2*e^2*f^2+57*d^2*g^2+14*d*e*f*g))+4//5*d*e*(d^2+-1*e^2*x^2)^-5//2*(d*g+e*f)^-2*(d+e*x)+e*g^3*(d*g+e*f)^-4*(e*f+-1*d*g)^-1*(e^2*f^2+-1*d^2*g^2)^-1//2*(-3*d*g+4*e*f)*arctan((d^2+-1*e^2*x^2)^-1//2*(e^2*f^2+-1*d^2*g^2)^-1//2*(g*d^2+f*x*e^2)))
@test integrate((d+e*x)^3*(f+g*x)^-3*(d^2+-1*e^2*x^2)^-7//2, x) == :(g^4*(f+g*x)^-2*(d^2+-1*e^2*x^2)^(1/2)*(d*g+e*f)^-4*(-2*d*g+2*e*f)^-1+-1//15*d^-1*e^2*(d^2+-1*e^2*x^2)^-3//2*(d*g+e*f)^-4*(5*d*(e*f+-5*d*g)+-1*e*x*(e*f+31*d*g))+1//15*d^-3*e^2*(d^2+-1*e^2*x^2)^-1//2*(d*g+e*f)^-5*(90*d^3*g^2+e*x*(2*e^2*f^2+107*d^2*g^2+19*d*e*f*g))+4//5*d*e^2*(d^2+-1*e^2*x^2)^-5//2*(d*g+e*f)^-3*(d+e*x)+(1/2)*e^2*g^3*(d*g+e*f)^-5*(e*f+-1*d*g)^-2*(e^2*f^2+-1*d^2*g^2)^-1//2*(13*d^2*g^2+20*e^2*f^2+-30*d*e*f*g)*arctan((d^2+-1*e^2*x^2)^-1//2*(e^2*f^2+-1*d^2*g^2)^-1//2*(g*d^2+f*x*e^2))+3//2*e*g^4*(f+g*x)^-1*(d^2+-1*e^2*x^2)^(1/2)*(d*g+e*f)^-5*(e*f+-1*d*g)^-2*(-2*d*g+3*e*f))
@test integrate((d+e*x)^-3//2*(f+g*x)^-1*(a+c*x^2), x) == :(-1*e^-2*(d+e*x)^-1//2*(e*f+-1*d*g)^-1*(2*a*e^2+2*c*d^2)+-1*g^-3//2*(e*f+-1*d*g)^-3//2*(2*a*g^2+2*c*f^2)*arctan(g^(1/2)*(d+e*x)^(1/2)*(e*f+-1*d*g)^-1//2)+2*c*e^-2*g^-1*(d+e*x)^(1/2))
@test integrate((d+e*x)^3*(f+g*x)^-1//2*(a+c*x^2), x) == :(-2*g^-6*(f+g*x)^(1/2)*(e*f+-1*d*g)^3*(a*g^2+c*f^2)+-1//5*g^-6*(f+g*x)^5//2*(c*(d^2*g^2+10*e^2*f^2+-8*d*e*f*g)+3*a*e^2*g^2)*(-2*d*g+2*e*f)+2//3*g^-6*(f+g*x)^3//2*(e*f+-1*d*g)^2*(c*f*(-2*d*g+5*e*f)+3*a*e*g^2)+2//7*e*g^-6*(f+g*x)^7//2*(c*(3*d^2*g^2+10*e^2*f^2+-12*d*e*f*g)+a*e^2*g^2)+2//11*c*e^3*g^-6*(f+g*x)^11//2+-2//9*c*e^2*g^-6*(f+g*x)^9//2*(-3*d*g+5*e*f))
@test integrate((d+e*x)^2*(f+g*x)^-1//2*(a+c*x^2), x) == :(1//5*g^-5*(f+g*x)^5//2*(2*c*(d^2*g^2+6*e^2*f^2+-6*d*e*f*g)+2*a*e^2*g^2)+2*g^-5*(f+g*x)^(1/2)*(e*f+-1*d*g)^2*(a*g^2+c*f^2)+-1//3*g^-5*(f+g*x)^3//2*(-4*d*g+4*e*f)*(a*e*g^2+c*f*(-1*d*g+2*e*f))+2//9*c*e^2*g^-5*(f+g*x)^9//2+-4//7*c*e*g^-5*(f+g*x)^7//2*(-1*d*g+2*e*f))
@test integrate((f+g*x)^-1//2*(a+c*x^2)*(d+e*x), x) == :(1//3*g^-4*(f+g*x)^3//2*(2*a*e*g^2+2*c*f*(-2*d*g+3*e*f))+-1*g^-4*(f+g*x)^(1/2)*(a*g^2+c*f^2)*(-2*d*g+2*e*f)+-2//5*c*g^-4*(f+g*x)^5//2*(-1*d*g+3*e*f)+2//7*c*e*g^-4*(f+g*x)^7//2)
@test integrate((f+g*x)^-1//2*(a+c*x^2), x) == :(g^-3*(f+g*x)^(1/2)*(2*a*g^2+2*c*f^2)+2//5*c*g^-3*(f+g*x)^5//2+-4//3*c*f*g^-3*(f+g*x)^3//2)
@test integrate((d+e*x)^-1*(f+g*x)^-1//2*(a+c*x^2), x) == :(-1*e^-5//2*(e*f+-1*d*g)^-1//2*(2*a*e^2+2*c*d^2)*arctanh(e^(1/2)*(f+g*x)^(1/2)*(e*f+-1*d*g)^-1//2)+2//3*c*e^-1*g^-2*(f+g*x)^3//2+-2*c*e^-2*g^-2*(f+g*x)^(1/2)*(d*g+e*f))
@test integrate((d+e*x)^-2*(f+g*x)^-1//2*(a+c*x^2), x) == :(e^-5//2*(e*f+-1*d*g)^-3//2*(a*g*e^2+c*d*(-3*d*g+4*e*f))*arctanh(e^(1/2)*(f+g*x)^(1/2)*(e*f+-1*d*g)^-1//2)+-1*(d+e*x)^-1*(f+g*x)^(1/2)*(e*f+-1*d*g)^-1*(a+c*d^2*e^-2)+2*c*e^-2*g^-1*(f+g*x)^(1/2))
@test integrate((d+e*x)^-3*(f+g*x)^-1//2*(a+c*x^2), x) == :(-1*(d+e*x)^-2*(f+g*x)^(1/2)*(-2*d*g+2*e*f)^-1*(a+c*d^2*e^-2)+-1//4*e^-5//2*(e*f+-1*d*g)^-5//2*(c*(3*d^2*g^2+8*e^2*f^2+-8*d*e*f*g)+3*a*e^2*g^2)*arctanh(e^(1/2)*(f+g*x)^(1/2)*(e*f+-1*d*g)^-1//2)+1//4*e^-2*(d+e*x)^-1*(f+g*x)^(1/2)*(e*f+-1*d*g)^-2*(c*d*(-5*d*g+8*e*f)+3*a*g*e^2))
@test integrate((d+e*x)^3*(f+g*x)^-3//2*(a+c*x^2), x) == :(2*g^-6*(f+g*x)^(1/2)*(e*f+-1*d*g)^2*(c*f*(-2*d*g+5*e*f)+3*a*e*g^2)+2*g^-6*(f+g*x)^-1//2*(e*f+-1*d*g)^3*(a*g^2+c*f^2)+-1//3*g^-6*(f+g*x)^3//2*(c*(d^2*g^2+10*e^2*f^2+-8*d*e*f*g)+3*a*e^2*g^2)*(-2*d*g+2*e*f)+2//5*e*g^-6*(f+g*x)^5//2*(c*(3*d^2*g^2+10*e^2*f^2+-12*d*e*f*g)+a*e^2*g^2)+2//9*c*e^3*g^-6*(f+g*x)^9//2+-2//7*c*e^2*g^-6*(f+g*x)^7//2*(-3*d*g+5*e*f))
@test integrate((d+e*x)^2*(f+g*x)^-3//2*(a+c*x^2), x) == :(1//3*g^-5*(f+g*x)^3//2*(2*c*(d^2*g^2+6*e^2*f^2+-6*d*e*f*g)+2*a*e^2*g^2)+-1*g^-5*(f+g*x)^(1/2)*(-4*d*g+4*e*f)*(a*e*g^2+c*f*(-1*d*g+2*e*f))+-2*g^-5*(f+g*x)^-1//2*(e*f+-1*d*g)^2*(a*g^2+c*f^2)+2//7*c*e^2*g^-5*(f+g*x)^7//2+-4//5*c*e*g^-5*(f+g*x)^5//2*(-1*d*g+2*e*f))
@test integrate((f+g*x)^-3//2*(a+c*x^2)*(d+e*x), x) == :(g^-4*(f+g*x)^(1/2)*(2*a*e*g^2+2*c*f*(-2*d*g+3*e*f))+g^-4*(f+g*x)^-1//2*(a*g^2+c*f^2)*(-2*d*g+2*e*f)+-2//3*c*g^-4*(f+g*x)^3//2*(-1*d*g+3*e*f)+2//5*c*e*g^-4*(f+g*x)^5//2)
@test integrate((f+g*x)^-3//2*(a+c*x^2), x) == :(-1*g^-3*(f+g*x)^-1//2*(2*a*g^2+2*c*f^2)+2//3*c*g^-3*(f+g*x)^3//2+-4*c*f*g^-3*(f+g*x)^(1/2))
@test integrate((d+e*x)^-1*(f+g*x)^-3//2*(a+c*x^2), x) == :(g^-2*(f+g*x)^-1//2*(e*f+-1*d*g)^-1*(2*a*g^2+2*c*f^2)+-1*e^-3//2*(e*f+-1*d*g)^-3//2*(2*a*e^2+2*c*d^2)*arctanh(e^(1/2)*(f+g*x)^(1/2)*(e*f+-1*d*g)^-1//2)+2*c*e^-1*g^-2*(f+g*x)^(1/2))
@test integrate((d+e*x)^-2*(f+g*x)^-3//2*(a+c*x^2), x) == :(e^-3//2*(e*f+-1*d*g)^-5//2*(c*d*(-1*d*g+4*e*f)+3*a*g*e^2)*arctanh(e^(1/2)*(f+g*x)^(1/2)*(e*f+-1*d*g)^-1//2)+-1*g^-1*(f+g*x)^-1//2*(e*f+-1*d*g)^-2*(2*a*g^2+2*c*f^2)+-1*e^-1*(d+e*x)^-1*(f+g*x)^(1/2)*(e*f+-1*d*g)^-2*(a*e^2+c*d^2))
@test integrate((d+e*x)^-3*(f+g*x)^-3//2*(a+c*x^2), x) == :((f+g*x)^-1//2*(e*f+-1*d*g)^-3*(2*a*g^2+2*c*f^2)+-1//4*e^-3//2*(e*f+-1*d*g)^-7//2*(c*(-1*d^2*g^2+8*e^2*f^2+8*d*e*f*g)+15*a*e^2*g^2)*arctanh(e^(1/2)*(f+g*x)^(1/2)*(e*f+-1*d*g)^-1//2)+-1//2*e^-1*(d+e*x)^-2*(f+g*x)^(1/2)*(e*f+-1*d*g)^-2*(a*e^2+c*d^2)+1//4*e^-1*(d+e*x)^-1*(f+g*x)^(1/2)*(e*f+-1*d*g)^-3*(c*d*(-1*d*g+8*e*f)+7*a*g*e^2))
@test integrate((d+e*x)^-1//2*(f+g*x)^-1//2*(a+c*x^2), x) == :(1//4*e^-5//2*g^-5//2*(c*(3*d^2*g^2+3*e^2*f^2+2*d*e*f*g)+8*a*e^2*g^2)*arctanh(e^-1//2*g^(1/2)*(d+e*x)^(1/2)*(f+g*x)^-1//2)+(1/2)*c*e^-2*g^-1*(d+e*x)^3//2*(f+g*x)^(1/2)+-1//4*c*e^-2*g^-2*(d+e*x)^(1/2)*(f+g*x)^(1/2)*(3*e*f+5*d*g))
@test integrate((1+x)^-1//2*(-1+x)^-1//2*(-1+2*x^2), x) == :(x*(1+x)^(1/2)*(-1+x)^(1/2))
@test integrate((a+c*x^2)^-1*(d+e*x)^3//2*(f+g*x)^(1/2), x) == :(e*c^-1*(d+e*x)^(1/2)*(f+g*x)^(1/2)+c^-1*e^(1/2)*g^-1//2*(e*f+3*d*g)*arctanh(e^-1//2*g^(1/2)*(d+e*x)^(1/2)*(f+g*x)^-1//2)+a^-1*c^-1*(d*c^(1/2)+e*(-1a)^(1/2))^-1//2*(f*c^(1/2)+g*(-1a)^(1/2))^-1//2*((-1a)^(1/2)*(c*f*d^2+-1*a*e*(e*f+2*d*g))+a*c^-1//2*(a*g*e^2+-1*c*d*(d*g+2*e*f)))*arctanh((d+e*x)^(1/2)*(f+g*x)^-1//2*(d*c^(1/2)+e*(-1a)^(1/2))^-1//2*(f*c^(1/2)+g*(-1a)^(1/2))^(1/2))+a^-1*c^-1*(d*c^(1/2)+-1*e*(-1a)^(1/2))^-1//2*(f*c^(1/2)+-1*g*(-1a)^(1/2))^-1//2*(-1*(-1a)^(1/2)*(c*f*d^2+-1*a*e*(e*f+2*d*g))+a*c^-1//2*(a*g*e^2+-1*c*d*(d*g+2*e*f)))*arctanh((d+e*x)^(1/2)*(f+g*x)^-1//2*(d*c^(1/2)+-1*e*(-1a)^(1/2))^-1//2*(f*c^(1/2)+-1*g*(-1a)^(1/2))^(1/2)))
@test integrate((a+c*x^2)^-1*(d+e*x)^(1/2)*(f+g*x)^(1/2), x) == :(2*c^-1*e^(1/2)*g^(1/2)*arctanh(e^-1//2*g^(1/2)*(d+e*x)^(1/2)*(f+g*x)^-1//2)+c^-1*(-1a)^-1//2*(d*c^(1/2)+-1*e*(-1a)^(1/2))^-1//2*(f*c^(1/2)+-1*g*(-1a)^(1/2))^-1//2*(c*d*f+-1*a*e*g+-1*c^(1/2)*(-1a)^(1/2)*(d*g+e*f))*arctanh((d+e*x)^(1/2)*(f+g*x)^-1//2*(d*c^(1/2)+-1*e*(-1a)^(1/2))^-1//2*(f*c^(1/2)+-1*g*(-1a)^(1/2))^(1/2))+-1*c^-1*(-1a)^-1//2*(d*c^(1/2)+e*(-1a)^(1/2))^-1//2*(f*c^(1/2)+g*(-1a)^(1/2))^-1//2*(c*d*f+c^(1/2)*(-1a)^(1/2)*(d*g+e*f)+-1*a*e*g)*arctanh((d+e*x)^(1/2)*(f+g*x)^-1//2*(d*c^(1/2)+e*(-1a)^(1/2))^-1//2*(f*c^(1/2)+g*(-1a)^(1/2))^(1/2)))
@test integrate((a+c*x^2)^-1*(d+e*x)^-1//2*(f+g*x)^(1/2), x) == :(c^-1//2*(-1a)^-1//2*(d*c^(1/2)+-1*e*(-1a)^(1/2))^-1//2*(f*c^(1/2)+-1*g*(-1a)^(1/2))^(1/2)*arctanh((d+e*x)^(1/2)*(f+g*x)^-1//2*(d*c^(1/2)+-1*e*(-1a)^(1/2))^-1//2*(f*c^(1/2)+-1*g*(-1a)^(1/2))^(1/2))+-1*c^-1//2*(-1a)^-1//2*(d*c^(1/2)+e*(-1a)^(1/2))^-1//2*(f*c^(1/2)+g*(-1a)^(1/2))^(1/2)*arctanh((d+e*x)^(1/2)*(f+g*x)^-1//2*(d*c^(1/2)+e*(-1a)^(1/2))^-1//2*(f*c^(1/2)+g*(-1a)^(1/2))^(1/2)))
@test integrate((a+c*x^2)^-1*(d+e*x)^-3//2*(f+g*x)^(1/2), x) == :(-2*e*(d+e*x)^-1//2*(f+g*x)^(1/2)*(a*e^2+c*d^2)^-1+(-1a)^-1//2*(a*e^2+c*d^2)^-1*(d*c^(1/2)+-1*e*(-1a)^(1/2))^-1//2*(f*c^(1/2)+-1*g*(-1a)^(1/2))^-1//2*(a*e*g+c*d*f+c^(1/2)*(-1a)^(1/2)*(e*f+-1*d*g))*arctanh((d+e*x)^(1/2)*(f+g*x)^-1//2*(d*c^(1/2)+-1*e*(-1a)^(1/2))^-1//2*(f*c^(1/2)+-1*g*(-1a)^(1/2))^(1/2))+-1*(-1a)^-1//2*(a*e^2+c*d^2)^-1*(d*c^(1/2)+e*(-1a)^(1/2))^-1//2*(f*c^(1/2)+g*(-1a)^(1/2))^-1//2*(a*e*g+c*d*f+-1*c^(1/2)*(-1a)^(1/2)*(e*f+-1*d*g))*arctanh((d+e*x)^(1/2)*(f+g*x)^-1//2*(d*c^(1/2)+e*(-1a)^(1/2))^-1//2*(f*c^(1/2)+g*(-1a)^(1/2))^(1/2)))
@test integrate((a+c*x^2)^-1*(d+e*x)^-5//2*(f+g*x)^(1/2), x) == :(-2*e*(d+e*x)^-3//2*(f+g*x)^(1/2)*(3*a*e^2+3*c*d^2)^-1+4*e*g*(d+e*x)^-1//2*(f+g*x)^(1/2)*(e*f+-1*d*g)^-1*(3*a*e^2+3*c*d^2)^-1+a^-1*c^(1/2)*(a*e^2+c*d^2)^-1*(d*c^(1/2)+e*(-1a)^(1/2))^-3//2*(f*c^(1/2)+g*(-1a)^(1/2))^-1//2*(a*c^(1/2)*(e*f+-1*d*g)+a*e*g*(-1a)^(1/2)+c*d*f*(-1a)^(1/2))*arctanh((d+e*x)^(1/2)*(f+g*x)^-1//2*(d*c^(1/2)+e*(-1a)^(1/2))^-1//2*(f*c^(1/2)+g*(-1a)^(1/2))^(1/2))+c^(1/2)*(-1a)^-1//2*(a*e^2+c*d^2)^-1*(d*c^(1/2)+-1*e*(-1a)^(1/2))^-3//2*(f*c^(1/2)+-1*g*(-1a)^(1/2))^-1//2*(a*e*g+c*d*f+c^(1/2)*(-1a)^(1/2)*(e*f+-1*d*g))*arctanh((d+e*x)^(1/2)*(f+g*x)^-1//2*(d*c^(1/2)+-1*e*(-1a)^(1/2))^-1//2*(f*c^(1/2)+-1*g*(-1a)^(1/2))^(1/2))+e*(-1a)^-1//2*(d+e*x)^-1//2*(f+g*x)^(1/2)*(a*e^2+c*d^2)^-1*(d*c^(1/2)+e*(-1a)^(1/2))^-1*(e*f+-1*d*g)^-1*(a*e*g+c*d*f+-1*c^(1/2)*(-1a)^(1/2)*(e*f+-1*d*g))+-1*e*(-1a)^-1//2*(d+e*x)^-1//2*(f+g*x)^(1/2)*(a*e^2+c*d^2)^-1*(d*c^(1/2)+-1*e*(-1a)^(1/2))^-1*(e*f+-1*d*g)^-1*(a*e*g+c*d*f+c^(1/2)*(-1a)^(1/2)*(e*f+-1*d*g)))
@test integrate((a+c*x^2)^-1*(d+e*x)^3//2*(f+g*x)^-1//2, x) == :(2*c^-1*e^3//2*g^-1//2*arctanh(e^-1//2*g^(1/2)*(d+e*x)^(1/2)*(f+g*x)^-1//2)+c^-1*(-1a)^-1//2*(d*c^(1/2)+-1*e*(-1a)^(1/2))^-1//2*(f*c^(1/2)+-1*g*(-1a)^(1/2))^-1//2*(c*d^2+-1*a*e^2+-2*d*e*c^(1/2)*(-1a)^(1/2))*arctanh((d+e*x)^(1/2)*(f+g*x)^-1//2*(d*c^(1/2)+-1*e*(-1a)^(1/2))^-1//2*(f*c^(1/2)+-1*g*(-1a)^(1/2))^(1/2))+-1*c^-1*(-1a)^-1//2*(d*c^(1/2)+e*(-1a)^(1/2))^-1//2*(f*c^(1/2)+g*(-1a)^(1/2))^-1//2*(c*d^2+-1*a*e^2+2*d*e*c^(1/2)*(-1a)^(1/2))*arctanh((d+e*x)^(1/2)*(f+g*x)^-1//2*(d*c^(1/2)+e*(-1a)^(1/2))^-1//2*(f*c^(1/2)+g*(-1a)^(1/2))^(1/2)))
@test integrate((a+c*x^2)^-1*(d+e*x)^(1/2)*(f+g*x)^-1//2, x) == :(c^-1//2*(-1a)^-1//2*(d*c^(1/2)+-1*e*(-1a)^(1/2))^(1/2)*(f*c^(1/2)+-1*g*(-1a)^(1/2))^-1//2*arctanh((d+e*x)^(1/2)*(f+g*x)^-1//2*(d*c^(1/2)+-1*e*(-1a)^(1/2))^-1//2*(f*c^(1/2)+-1*g*(-1a)^(1/2))^(1/2))+-1*c^-1//2*(-1a)^-1//2*(d*c^(1/2)+e*(-1a)^(1/2))^(1/2)*(f*c^(1/2)+g*(-1a)^(1/2))^-1//2*arctanh((d+e*x)^(1/2)*(f+g*x)^-1//2*(d*c^(1/2)+e*(-1a)^(1/2))^-1//2*(f*c^(1/2)+g*(-1a)^(1/2))^(1/2)))
@test integrate((a+c*x^2)^-1*(d+e*x)^-1//2*(f+g*x)^-1//2, x) == :((-1a)^-1//2*(d*c^(1/2)+-1*e*(-1a)^(1/2))^-1//2*(f*c^(1/2)+-1*g*(-1a)^(1/2))^-1//2*arctanh((d+e*x)^(1/2)*(f+g*x)^-1//2*(d*c^(1/2)+-1*e*(-1a)^(1/2))^-1//2*(f*c^(1/2)+-1*g*(-1a)^(1/2))^(1/2))+-1*(-1a)^-1//2*(d*c^(1/2)+e*(-1a)^(1/2))^-1//2*(f*c^(1/2)+g*(-1a)^(1/2))^-1//2*arctanh((d+e*x)^(1/2)*(f+g*x)^-1//2*(d*c^(1/2)+e*(-1a)^(1/2))^-1//2*(f*c^(1/2)+g*(-1a)^(1/2))^(1/2)))
@test integrate((a+c*x^2)^-1*(d+e*x)^-3//2*(f+g*x)^-1//2, x) == :(c^(1/2)*(-1a)^-1//2*(d*c^(1/2)+-1*e*(-1a)^(1/2))^-3//2*(f*c^(1/2)+-1*g*(-1a)^(1/2))^-1//2*arctanh((d+e*x)^(1/2)*(f+g*x)^-1//2*(d*c^(1/2)+-1*e*(-1a)^(1/2))^-1//2*(f*c^(1/2)+-1*g*(-1a)^(1/2))^(1/2))+-1*c^(1/2)*(-1a)^-1//2*(d*c^(1/2)+e*(-1a)^(1/2))^-3//2*(f*c^(1/2)+g*(-1a)^(1/2))^-1//2*arctanh((d+e*x)^(1/2)*(f+g*x)^-1//2*(d*c^(1/2)+e*(-1a)^(1/2))^-1//2*(f*c^(1/2)+g*(-1a)^(1/2))^(1/2))+e*(-1a)^-1//2*(d+e*x)^-1//2*(f+g*x)^(1/2)*(d*c^(1/2)+e*(-1a)^(1/2))^-1*(e*f+-1*d*g)^-1+-1*e*(-1a)^-1//2*(d+e*x)^-1//2*(f+g*x)^(1/2)*(d*c^(1/2)+-1*e*(-1a)^(1/2))^-1*(e*f+-1*d*g)^-1)
@test integrate((a+c*x^2)^-1*(d+e*x)^3//2*(f+g*x)^-3//2, x) == :((d+e*x)^(1/2)*(f+g*x)^-1//2*(a*g^2+c*f^2)^-1*(-2*d*g+2*e*f)+-2*e^(1/2)*g^-1//2*(a*g^2+c*f^2)^-1*(e*f+-1*d*g)*arctanh(e^-1//2*g^(1/2)*(d+e*x)^(1/2)*(f+g*x)^-1//2)+c^-1//2*e^(1/2)*g^-1//2*(-1a)^-1//2*(a*g^2+c*f^2)^-1*(a*e*g+c*d*f+c^(1/2)*(-1a)^(1/2)*(e*f+-1*d*g))*arctanh(e^-1//2*g^(1/2)*(d+e*x)^(1/2)*(f+g*x)^-1//2)+c^-1//2*(-1a)^-1//2*(a*g^2+c*f^2)^-1*(d*c^(1/2)+-1*e*(-1a)^(1/2))^(1/2)*(f*c^(1/2)+-1*g*(-1a)^(1/2))^-1//2*(a*e*g+c*d*f+-1*c^(1/2)*(-1a)^(1/2)*(e*f+-1*d*g))*arctanh((d+e*x)^(1/2)*(f+g*x)^-1//2*(d*c^(1/2)+-1*e*(-1a)^(1/2))^-1//2*(f*c^(1/2)+-1*g*(-1a)^(1/2))^(1/2))+-1*c^-1//2*e^(1/2)*g^-1//2*(-1a)^-1//2*(a*g^2+c*f^2)^-1*(a*e*g+c*d*f+-1*c^(1/2)*(-1a)^(1/2)*(e*f+-1*d*g))*arctanh(e^-1//2*g^(1/2)*(d+e*x)^(1/2)*(f+g*x)^-1//2)+-1*c^-1//2*(-1a)^-1//2*(a*g^2+c*f^2)^-1*(d*c^(1/2)+e*(-1a)^(1/2))^(1/2)*(f*c^(1/2)+g*(-1a)^(1/2))^-1//2*(a*e*g+c*d*f+c^(1/2)*(-1a)^(1/2)*(e*f+-1*d*g))*arctanh((d+e*x)^(1/2)*(f+g*x)^-1//2*(d*c^(1/2)+e*(-1a)^(1/2))^-1//2*(f*c^(1/2)+g*(-1a)^(1/2))^(1/2)))
@test integrate((a+c*x^2)^-1*(d+e*x)^(1/2)*(f+g*x)^-3//2, x) == :(-2*g*(d+e*x)^(1/2)*(f+g*x)^-1//2*(a*g^2+c*f^2)^-1+(-1a)^-1//2*(a*g^2+c*f^2)^-1*(d*c^(1/2)+-1*e*(-1a)^(1/2))^-1//2*(f*c^(1/2)+-1*g*(-1a)^(1/2))^-1//2*(a*e*g+c*d*f+-1*c^(1/2)*(-1a)^(1/2)*(e*f+-1*d*g))*arctanh((d+e*x)^(1/2)*(f+g*x)^-1//2*(d*c^(1/2)+-1*e*(-1a)^(1/2))^-1//2*(f*c^(1/2)+-1*g*(-1a)^(1/2))^(1/2))+-1*(-1a)^-1//2*(a*g^2+c*f^2)^-1*(d*c^(1/2)+e*(-1a)^(1/2))^-1//2*(f*c^(1/2)+g*(-1a)^(1/2))^-1//2*(a*e*g+c*d*f+c^(1/2)*(-1a)^(1/2)*(e*f+-1*d*g))*arctanh((d+e*x)^(1/2)*(f+g*x)^-1//2*(d*c^(1/2)+e*(-1a)^(1/2))^-1//2*(f*c^(1/2)+g*(-1a)^(1/2))^(1/2)))
@test integrate((a+c*x^2)^-1*(d+e*x)^-1//2*(f+g*x)^-3//2, x) == :(c^(1/2)*(-1a)^-1//2*(d*c^(1/2)+-1*e*(-1a)^(1/2))^-1//2*(f*c^(1/2)+-1*g*(-1a)^(1/2))^-3//2*arctanh((d+e*x)^(1/2)*(f+g*x)^-1//2*(d*c^(1/2)+-1*e*(-1a)^(1/2))^-1//2*(f*c^(1/2)+-1*g*(-1a)^(1/2))^(1/2))+-1*c^(1/2)*(-1a)^-1//2*(d*c^(1/2)+e*(-1a)^(1/2))^-1//2*(f*c^(1/2)+g*(-1a)^(1/2))^-3//2*arctanh((d+e*x)^(1/2)*(f+g*x)^-1//2*(d*c^(1/2)+e*(-1a)^(1/2))^-1//2*(f*c^(1/2)+g*(-1a)^(1/2))^(1/2))+g*(-1a)^-1//2*(d+e*x)^(1/2)*(f+g*x)^-1//2*(e*f+-1*d*g)^-1*(f*c^(1/2)+-1*g*(-1a)^(1/2))^-1+-1*g*(-1a)^-1//2*(d+e*x)^(1/2)*(f+g*x)^-1//2*(e*f+-1*d*g)^-1*(f*c^(1/2)+g*(-1a)^(1/2))^-1)
@test integrate((a+c*x^2)^-1*(d+e*x)^-3//2*(f+g*x)^-3//2, x) == :(c*(-1a)^-1//2*(d*c^(1/2)+-1*e*(-1a)^(1/2))^-3//2*(f*c^(1/2)+-1*g*(-1a)^(1/2))^-3//2*arctanh((d+e*x)^(1/2)*(f+g*x)^-1//2*(d*c^(1/2)+-1*e*(-1a)^(1/2))^-1//2*(f*c^(1/2)+-1*g*(-1a)^(1/2))^(1/2))+-1*c*(-1a)^-1//2*(d*c^(1/2)+e*(-1a)^(1/2))^-3//2*(f*c^(1/2)+g*(-1a)^(1/2))^-3//2*arctanh((d+e*x)^(1/2)*(f+g*x)^-1//2*(d*c^(1/2)+e*(-1a)^(1/2))^-1//2*(f*c^(1/2)+g*(-1a)^(1/2))^(1/2))+e*(-1a)^-1//2*(d+e*x)^-1//2*(f+g*x)^-1//2*(d*c^(1/2)+e*(-1a)^(1/2))^-1*(e*f+-1*d*g)^-1+-1*e*(-1a)^-1//2*(d+e*x)^-1//2*(f+g*x)^-1//2*(d*c^(1/2)+-1*e*(-1a)^(1/2))^-1*(e*f+-1*d*g)^-1+g*(-1a)^-1//2*(d+e*x)^(1/2)*(f+g*x)^-1//2*(d*c^(1/2)+e*(-1a)^(1/2))^-1*(e*f+-1*d*g)^-2*(f*c^(1/2)+g*(-1a)^(1/2))^-1*(c^(1/2)*(d*g+e*f)+2*e*g*(-1a)^(1/2))+g*(-1a)^-1//2*(d+e*x)^(1/2)*(f+g*x)^-1//2*(d*c^(1/2)+-1*e*(-1a)^(1/2))^-1*(e*f+-1*d*g)^-2*(f*c^(1/2)+-1*g*(-1a)^(1/2))^-1*(-1*c^(1/2)*(d*g+e*f)+2*e*g*(-1a)^(1/2)))
@test integrate(x^(1/2)*(1+x)^-1//2*(1+x^2)^-1, x) == :(-1//2*(1+im)^3//2*arctanh(x^(1/2)*(1+im)^(1/2)*(1+x)^-1//2)+-1//2*(1+-1im)^3//2*arctanh(x^(1/2)*(1+x)^-1//2*(1+-1im)^(1/2)))
@test integrate((1+-1x)^-4*(1+-1*x^2)^(1/2)*(f+g*x)^2, x) == :(-1*g^2*arcsin(x)+2*g^2*(1+-1*x^2)^-1//2*(1+x)+1//5*(1+x)^4*(1+-1*x^2)^-5//2*(f+g)^2+1//15*(1+x)^3*(1+-1*x^2)^-3//2*(f+g)*(f+-9g))
@test integrate((1+-1*a*x)^-2*(1+-1*a^2*x^2)^3//2*(c+d*x)^-1, x) == :(-1*d^-1*(1+-1*a^2*x^2)^(1/2)+-1*d^-2*(-2d+a*c)*arcsin(a*x)+d^-2*(-1d+a*c)^2*(-1*d^2+a^2*c^2)^-1//2*arctan((1+-1*a^2*x^2)^-1//2*(-1*d^2+a^2*c^2)^-1//2*(d+c*x*a^2)))
@test integrate((1+a*x)^2*(1+-1*a^2*x^2)^-1//2*(c+d*x)^-1, x) == :(-1*d^-1*(1+-1*a^2*x^2)^(1/2)+-1*d^-2*(-2d+a*c)*arcsin(a*x)+d^-2*(-1d+a*c)^2*(-1*d^2+a^2*c^2)^-1//2*arctan((1+-1*a^2*x^2)^-1//2*(-1*d^2+a^2*c^2)^-1//2*(d+c*x*a^2)))
@test integrate((a+c*x^2)^(1/2)*(d+e*x)^3*(f+g*x)^(1/2), x) == :(2//11*e^-1*(a+c*x^2)^(1/2)*(d+e*x)^4*(f+g*x)^(1/2)+-1//3465*c^-1*g^-4*(a+c*x^2)^(1/2)*(f+g*x)^3//2*(-2*c*(-567*d^3*g^3+233*e^3*f^3+-843*d*g*e^2*f^2+1107*e*f*d^2*g^2)+4*a*e^2*g^2*(-231*d*g+74*e*f))+2//99*e^2*g^-4*(a+c*x^2)^(1/2)*(f+g*x)^7//2*(e*f+-3*d*g)+1//3465*c^-2*e^-1*g^-4*(a+c*x^2)^(1/2)*(f+g*x)^(1/2)*(-2*c^2*(187*e^4*f^4+315*d^4*g^4+-798*e*f*d^3*g^3+-732*d*g*e^3*f^3+1098*d^2*e^2*f^2*g^2)+-300*a^2*e^4*g^4+12*a*c*e^2*g^2*(2*e^2*f^2+165*d^2*g^2+-33*d*e*f*g))+2//693*e*c^-1*g^-4*(a+c*x^2)^(1/2)*(f+g*x)^5//2*(-1*c*(29*e^2*f^2+81*d^2*g^2+-96*d*e*f*g)+18*a*e^2*g^2)+4//3465*c^-3//2*g^-5*(-1a)^(1/2)*(c^(1/2)*(f*c^(1/2)+g*(-1a)^(1/2))^-1*(f+g*x))^-1//2*(1+c*a^-1*x^2)^(1/2)*(a+c*x^2)^-1//2*(f+g*x)^(1/2)*(-1*c^2*f^2*(-231*d^3*g^3+64*e^3*f^3+-264*d*g*e^2*f^2+396*e*f*d^2*g^2)+-9*a*c*g^2*(6*e^3*f^3+77*d^3*g^3+-33*d*g*e^2*f^2+88*e*f*d^2*g^2)+3*a^2*e^2*g^4*(26*e*f+231*d*g))*Elliptic.E(arcsin((1/2)*2^(1/2)*(1+-1*x*c^(1/2)*(-1a)^-1//2)^(1/2)),-2*a*g*(-1*a*g+f*c^(1/2)*(-1a)^(1/2))^-1)+-4//3465*c^-5//2*g^-5*(-1a)^(1/2)*(c^(1/2)*(f*c^(1/2)+g*(-1a)^(1/2))^-1*(f+g*x))^(1/2)*(1+c*a^-1*x^2)^(1/2)*(a+c*x^2)^-1//2*(f+g*x)^-1//2*(a*g^2+c*f^2)*(-1*f*c^2*(-231*d^3*g^3+64*e^3*f^3+-264*d*g*e^2*f^2+396*e*f*d^2*g^2)+75*a^2*e^3*g^4+-3*a*c*e*g^2*(2*e^2*f^2+165*d^2*g^2+-33*d*e*f*g))*Elliptic.F(arcsin((1/2)*2^(1/2)*(1+-1*x*c^(1/2)*(-1a)^-1//2)^(1/2)),-2*a*g*(-1*a*g+f*c^(1/2)*(-1a)^(1/2))^-1))
@test integrate((a+c*x^2)^(1/2)*(d+e*x)^2*(f+g*x)^(1/2), x) == :(2//9*e^-1*(a+c*x^2)^(1/2)*(d+e*x)^3*(f+g*x)^(1/2)+1//315*c^-1*g^-3*(a+c*x^2)^(1/2)*(f+g*x)^3//2*(-4*c*(8*e^2*f^2+21*d^2*g^2+-24*d*e*f*g)+28*a*e^2*g^2)+2//63*e*g^-3*(a+c*x^2)^(1/2)*(f+g*x)^5//2*(e*f+-3*d*g)+1//315*c^-1*e^-1*g^-3*(a+c*x^2)^(1/2)*(f+g*x)^(1/2)*(2*c*(-35*d^3*g^3+19*e^3*f^3+-57*d*g*e^2*f^2+63*e*f*d^2*g^2)+-12*a*e^2*g^2*(e*f+-10*d*g))+4//315*c^-3//2*g^-4*(-1a)^(1/2)*(c^(1/2)*(f*c^(1/2)+g*(-1a)^(1/2))^-1*(f+g*x))^-1//2*(1+c*a^-1*x^2)^(1/2)*(a+c*x^2)^-1//2*(f+g*x)^(1/2)*(c^2*f^2*(8*e^2*f^2+21*d^2*g^2+-24*d*e*f*g)+21*a^2*e^2*g^4+3*a*c*g^2*(-21*d^2*g^2+3*e^2*f^2+-16*d*e*f*g))*Elliptic.E(arcsin((1/2)*2^(1/2)*(1+-1*x*c^(1/2)*(-1a)^-1//2)^(1/2)),-2*a*g*(-1*a*g+f*c^(1/2)*(-1a)^(1/2))^-1)+-4//315*c^-3//2*g^-4*(-1a)^(1/2)*(c^(1/2)*(f*c^(1/2)+g*(-1a)^(1/2))^-1*(f+g*x))^(1/2)*(1+c*a^-1*x^2)^(1/2)*(a+c*x^2)^-1//2*(f+g*x)^-1//2*(a*g^2+c*f^2)*(c*f*(8*e^2*f^2+21*d^2*g^2+-24*d*e*f*g)+3*a*e*g^2*(e*f+-10*d*g))*Elliptic.F(arcsin((1/2)*2^(1/2)*(1+-1*x*c^(1/2)*(-1a)^-1//2)^(1/2)),-2*a*g*(-1*a*g+f*c^(1/2)*(-1a)^(1/2))^-1))
@test integrate((a+c*x^2)^(1/2)*(f+g*x)^(1/2)*(d+e*x), x) == :(2//7*e*c^-1*(a+c*x^2)^3//2*(f+g*x)^(1/2)+-2//105*c^-1*g^-2*(a+c*x^2)^(1/2)*(f+g*x)^(1/2)*(c*f*(-7*d*g+4*e*f)+5*a*e*g^2+-3*c*g*x*(e*f+7*d*g))+-4//105*c^-1//2*g^-3*(-1a)^(1/2)*(c^(1/2)*(f*c^(1/2)+g*(-1a)^(1/2))^-1*(f+g*x))^-1//2*(1+c*a^-1*x^2)^(1/2)*(a+c*x^2)^-1//2*(f+g*x)^(1/2)*(a*g^2*(8*e*f+21*d*g)+c*f^2*(-7*d*g+4*e*f))*Elliptic.E(arcsin((1/2)*2^(1/2)*(1+-1*x*c^(1/2)*(-1a)^-1//2)^(1/2)),-2*a*g*(-1*a*g+f*c^(1/2)*(-1a)^(1/2))^-1)+4//105*c^-3//2*g^-3*(-1a)^(1/2)*(c^(1/2)*(f*c^(1/2)+g*(-1a)^(1/2))^-1*(f+g*x))^(1/2)*(1+c*a^-1*x^2)^(1/2)*(a+c*x^2)^-1//2*(f+g*x)^-1//2*(a*g^2+c*f^2)*(c*f*(-7*d*g+4*e*f)+5*a*e*g^2)*Elliptic.F(arcsin((1/2)*2^(1/2)*(1+-1*x*c^(1/2)*(-1a)^-1//2)^(1/2)),-2*a*g*(-1*a*g+f*c^(1/2)*(-1a)^(1/2))^-1))
@test integrate((a+c*x^2)^(1/2)*(f+g*x)^(1/2), x) == :(2//5*g^-1*(a+c*x^2)^(1/2)*(f+g*x)^3//2+-4//15*f*g^-1*(a+c*x^2)^(1/2)*(f+g*x)^(1/2)+4//15*c^-1//2*g^-2*(-1a)^(1/2)*(c^(1/2)*(f*c^(1/2)+g*(-1a)^(1/2))^-1*(f+g*x))^-1//2*(1+c*a^-1*x^2)^(1/2)*(a+c*x^2)^-1//2*(f+g*x)^(1/2)*(c*f^2+-3*a*g^2)*Elliptic.E(arcsin((1/2)*2^(1/2)*(1+-1*x*c^(1/2)*(-1a)^-1//2)^(1/2)),-2*a*g*(-1*a*g+f*c^(1/2)*(-1a)^(1/2))^-1)+-4//15*f*c^-1//2*g^-2*(-1a)^(1/2)*(c^(1/2)*(f*c^(1/2)+g*(-1a)^(1/2))^-1*(f+g*x))^(1/2)*(1+c*a^-1*x^2)^(1/2)*(a+c*x^2)^-1//2*(f+g*x)^-1//2*(a*g^2+c*f^2)*Elliptic.F(arcsin((1/2)*2^(1/2)*(1+-1*x*c^(1/2)*(-1a)^-1//2)^(1/2)),-2*a*g*(-1*a*g+f*c^(1/2)*(-1a)^(1/2))^-1))
@test integrate((a+c*x^2)^(1/2)*(d+e*x)^3*(f+g*x)^-1//2, x) == :(2//9*g^-1*(a+c*x^2)^(1/2)*(d+e*x)^3*(f+g*x)^(1/2)+-4//63*e^2*g^-4*(a+c*x^2)^(1/2)*(f+g*x)^5//2*(-3*d*g+4*e*f)+1//315*c^-1*g^-4*(a+c*x^2)^(1/2)*(f+g*x)^(1/2)*(-4*c*(-35*d^3*g^3+76*e^3*f^3+-204*d*g*e^2*f^2+168*e*f*d^2*g^2)+-36*a*e^2*g^2*(-5*d*g+2*e*f))+4//315*e*c^-1*g^-4*(a+c*x^2)^(1/2)*(f+g*x)^3//2*(c*(42*d^2*g^2+64*e^2*f^2+-111*d*e*f*g)+7*a*e^2*g^2)+4//315*c^-3//2*g^-5*(-1a)^(1/2)*(c^(1/2)*(f*c^(1/2)+g*(-1a)^(1/2))^-1*(f+g*x))^-1//2*(1+c*a^-1*x^2)^(1/2)*(a+c*x^2)^-1//2*(f+g*x)^(1/2)*(-1*f*c^2*(-105*d^3*g^3+64*e^3*f^3+-216*d*g*e^2*f^2+252*e*f*d^2*g^2)+21*a^2*e^3*g^4+-3*a*c*e*g^2*(10*e^2*f^2+63*d^2*g^2+-39*d*e*f*g))*Elliptic.E(arcsin((1/2)*2^(1/2)*(1+-1*x*c^(1/2)*(-1a)^-1//2)^(1/2)),-2*a*g*(-1*a*g+f*c^(1/2)*(-1a)^(1/2))^-1)+-4//315*c^-3//2*g^-5*(-1a)^(1/2)*(c^(1/2)*(f*c^(1/2)+g*(-1a)^(1/2))^-1*(f+g*x))^(1/2)*(1+c*a^-1*x^2)^(1/2)*(a+c*x^2)^-1//2*(f+g*x)^-1//2*(a*g^2+c*f^2)*(-1*c*(-105*d^3*g^3+64*e^3*f^3+-216*d*g*e^2*f^2+252*e*f*d^2*g^2)+9*a*e^2*g^2*(-5*d*g+2*e*f))*Elliptic.F(arcsin((1/2)*2^(1/2)*(1+-1*x*c^(1/2)*(-1a)^-1//2)^(1/2)),-2*a*g*(-1*a*g+f*c^(1/2)*(-1a)^(1/2))^-1))
@test integrate((a+c*x^2)^(1/2)*(d+e*x)^2*(f+g*x)^-1//2, x) == :(2//7*g^-1*(a+c*x^2)^(1/2)*(d+e*x)^2*(f+g*x)^(1/2)+-4//35*e*g^-3*(a+c*x^2)^(1/2)*(f+g*x)^3//2*(-2*d*g+3*e*f)+1//105*c^-1*g^-3*(a+c*x^2)^(1/2)*(f+g*x)^(1/2)*(4*c*(10*d^2*g^2+21*e^2*f^2+-34*d*e*f*g)+20*a*e^2*g^2)+4//105*c^-1//2*g^-4*(-1a)^(1/2)*(c^(1/2)*(f*c^(1/2)+g*(-1a)^(1/2))^-1*(f+g*x))^-1//2*(1+c*a^-1*x^2)^(1/2)*(a+c*x^2)^-1//2*(f+g*x)^(1/2)*(c*f*(24*e^2*f^2+35*d^2*g^2+-56*d*e*f*g)+a*e*g^2*(-42*d*g+13*e*f))*Elliptic.E(arcsin((1/2)*2^(1/2)*(1+-1*x*c^(1/2)*(-1a)^-1//2)^(1/2)),-2*a*g*(-1*a*g+f*c^(1/2)*(-1a)^(1/2))^-1)+4//105*c^-3//2*g^-4*(-1a)^(1/2)*(c^(1/2)*(f*c^(1/2)+g*(-1a)^(1/2))^-1*(f+g*x))^(1/2)*(1+c*a^-1*x^2)^(1/2)*(a+c*x^2)^-1//2*(f+g*x)^-1//2*(a*g^2+c*f^2)*(-1*c*(24*e^2*f^2+35*d^2*g^2+-56*d*e*f*g)+5*a*e^2*g^2)*Elliptic.F(arcsin((1/2)*2^(1/2)*(1+-1*x*c^(1/2)*(-1a)^-1//2)^(1/2)),-2*a*g*(-1*a*g+f*c^(1/2)*(-1a)^(1/2))^-1))
@test integrate((a+c*x^2)^(1/2)*(f+g*x)^-1//2*(d+e*x), x) == :(-2//15*g^-2*(a+c*x^2)^(1/2)*(f+g*x)^(1/2)*(-5*d*g+4*e*f+-3*e*g*x)+-4//15*c^-1//2*g^-3*(-1a)^(1/2)*(c^(1/2)*(f*c^(1/2)+g*(-1a)^(1/2))^-1*(f+g*x))^-1//2*(1+c*a^-1*x^2)^(1/2)*(a+c*x^2)^-1//2*(f+g*x)^(1/2)*(c*f*(-5*d*g+4*e*f)+3*a*e*g^2)*Elliptic.E(arcsin((1/2)*2^(1/2)*(1+-1*x*c^(1/2)*(-1a)^-1//2)^(1/2)),-2*a*g*(-1*a*g+f*c^(1/2)*(-1a)^(1/2))^-1)+4//15*c^-1//2*g^-3*(-1a)^(1/2)*(c^(1/2)*(f*c^(1/2)+g*(-1a)^(1/2))^-1*(f+g*x))^(1/2)*(1+c*a^-1*x^2)^(1/2)*(a+c*x^2)^-1//2*(f+g*x)^-1//2*(a*g^2+c*f^2)*(-5*d*g+4*e*f)*Elliptic.F(arcsin((1/2)*2^(1/2)*(1+-1*x*c^(1/2)*(-1a)^-1//2)^(1/2)),-2*a*g*(-1*a*g+f*c^(1/2)*(-1a)^(1/2))^-1))
@test integrate((a+c*x^2)^(1/2)*(f+g*x)^-1//2, x) == :(2//3*g^-1*(a+c*x^2)^(1/2)*(f+g*x)^(1/2)+-4//3*c^-1//2*g^-2*(-1a)^(1/2)*(c^(1/2)*(f*c^(1/2)+g*(-1a)^(1/2))^-1*(f+g*x))^(1/2)*(1+c*a^-1*x^2)^(1/2)*(a+c*x^2)^-1//2*(f+g*x)^-1//2*(a*g^2+c*f^2)*Elliptic.F(arcsin((1/2)*2^(1/2)*(1+-1*x*c^(1/2)*(-1a)^-1//2)^(1/2)),-2*a*g*(-1*a*g+f*c^(1/2)*(-1a)^(1/2))^-1)+4//3*f*c^(1/2)*g^-2*(-1a)^(1/2)*(c^(1/2)*(f*c^(1/2)+g*(-1a)^(1/2))^-1*(f+g*x))^-1//2*(1+c*a^-1*x^2)^(1/2)*(a+c*x^2)^-1//2*(f+g*x)^(1/2)*Elliptic.E(arcsin((1/2)*2^(1/2)*(1+-1*x*c^(1/2)*(-1a)^-1//2)^(1/2)),-2*a*g*(-1*a*g+f*c^(1/2)*(-1a)^(1/2))^-1))
@test integrate((a+c*x^2)^-1//2*(d+e*x)^3*(f+g*x)^(1/2), x) == :(2//7*e*c^-1*(a+c*x^2)^(1/2)*(d+e*x)^2*(f+g*x)^(1/2)+-2//105*e*c^-2*g^-2*(a+c*x^2)^(1/2)*(f+g*x)^(1/2)*(c*(-90*d^2*g^2+7*e^2*f^2+12*d*e*f*g)+25*a*e^2*g^2)+2//35*c^-1*e^2*g^-2*(a+c*x^2)^(1/2)*(f+g*x)^3//2*(e*f+11*d*g)+2//105*c^-3//2*g^-3*(-1a)^(1/2)*(c^(1/2)*(f*c^(1/2)+g*(-1a)^(1/2))^-1*(f+g*x))^-1//2*(1+c*a^-1*x^2)^(1/2)*(a+c*x^2)^-1//2*(f+g*x)^(1/2)*(-1*c*(8*e^3*f^3+105*d^3*g^3+-42*d*g*e^2*f^2+105*e*f*d^2*g^2)+a*e^2*g^2*(19*e*f+189*d*g))*Elliptic.E(arcsin((1/2)*2^(1/2)*(1+-1*x*c^(1/2)*(-1a)^-1//2)^(1/2)),-2*a*g*(-1*a*g+f*c^(1/2)*(-1a)^(1/2))^-1)+-2//105*e*c^-5//2*g^-3*(-1a)^(1/2)*(c^(1/2)*(f*c^(1/2)+g*(-1a)^(1/2))^-1*(f+g*x))^(1/2)*(1+c*a^-1*x^2)^(1/2)*(a+c*x^2)^-1//2*(f+g*x)^-1//2*(a*g^2+c*f^2)*(-1*c*(8*e^2*f^2+105*d^2*g^2+-42*d*e*f*g)+25*a*e^2*g^2)*Elliptic.F(arcsin((1/2)*2^(1/2)*(1+-1*x*c^(1/2)*(-1a)^-1//2)^(1/2)),-2*a*g*(-1*a*g+f*c^(1/2)*(-1a)^(1/2))^-1))
@test integrate((a+c*x^2)^-1//2*(d+e*x)^2*(f+g*x)^(1/2), x) == :(2//5*e*c^-1*(a+c*x^2)^(1/2)*(f+g*x)^(1/2)*(d+e*x)+2//15*e*c^-1*g^-1*(a+c*x^2)^(1/2)*(f+g*x)^(1/2)*(e*f+7*d*g)+2//15*c^-3//2*g^-2*(-1a)^(1/2)*(c^(1/2)*(f*c^(1/2)+g*(-1a)^(1/2))^-1*(f+g*x))^-1//2*(1+c*a^-1*x^2)^(1/2)*(a+c*x^2)^-1//2*(f+g*x)^(1/2)*(c*(-15*d^2*g^2+2*e^2*f^2+-10*d*e*f*g)+9*a*e^2*g^2)*Elliptic.E(arcsin((1/2)*2^(1/2)*(1+-1*x*c^(1/2)*(-1a)^-1//2)^(1/2)),-2*a*g*(-1*a*g+f*c^(1/2)*(-1a)^(1/2))^-1)+-4//15*e*c^-3//2*g^-2*(-1a)^(1/2)*(c^(1/2)*(f*c^(1/2)+g*(-1a)^(1/2))^-1*(f+g*x))^(1/2)*(1+c*a^-1*x^2)^(1/2)*(a+c*x^2)^-1//2*(f+g*x)^-1//2*(a*g^2+c*f^2)*(e*f+-5*d*g)*Elliptic.F(arcsin((1/2)*2^(1/2)*(1+-1*x*c^(1/2)*(-1a)^-1//2)^(1/2)),-2*a*g*(-1*a*g+f*c^(1/2)*(-1a)^(1/2))^-1))
@test integrate((a+c*x^2)^-1//2*(f+g*x)^(1/2)*(d+e*x), x) == :(2//3*e*c^-1*(a+c*x^2)^(1/2)*(f+g*x)^(1/2)+-2//3*c^-1//2*g^-1*(-1a)^(1/2)*(c^(1/2)*(f*c^(1/2)+g*(-1a)^(1/2))^-1*(f+g*x))^-1//2*(1+c*a^-1*x^2)^(1/2)*(a+c*x^2)^-1//2*(f+g*x)^(1/2)*(e*f+3*d*g)*Elliptic.E(arcsin((1/2)*2^(1/2)*(1+-1*x*c^(1/2)*(-1a)^-1//2)^(1/2)),-2*a*g*(-1*a*g+f*c^(1/2)*(-1a)^(1/2))^-1)+2//3*e*c^-3//2*g^-1*(-1a)^(1/2)*(c^(1/2)*(f*c^(1/2)+g*(-1a)^(1/2))^-1*(f+g*x))^(1/2)*(1+c*a^-1*x^2)^(1/2)*(a+c*x^2)^-1//2*(f+g*x)^-1//2*(a*g^2+c*f^2)*Elliptic.F(arcsin((1/2)*2^(1/2)*(1+-1*x*c^(1/2)*(-1a)^-1//2)^(1/2)),-2*a*g*(-1*a*g+f*c^(1/2)*(-1a)^(1/2))^-1))
@test integrate((a+c*x^2)^-1//2*(f+g*x)^(1/2), x) == :(-2*c^-1//2*(-1a)^(1/2)*(c^(1/2)*(f*c^(1/2)+g*(-1a)^(1/2))^-1*(f+g*x))^-1//2*(1+c*a^-1*x^2)^(1/2)*(a+c*x^2)^-1//2*(f+g*x)^(1/2)*Elliptic.E(arcsin((1/2)*2^(1/2)*(1+-1*x*c^(1/2)*(-1a)^-1//2)^(1/2)),-2*a*g*(-1*a*g+f*c^(1/2)*(-1a)^(1/2))^-1))
@test integrate((a+c*x^2)^-1//2*(d+e*x)^3*(f+g*x)^-1//2, x) == :(-8//15*c^-1*e^2*g^-2*(a+c*x^2)^(1/2)*(f+g*x)^(1/2)*(e*f+-3*d*g)+2//5*c^-1*e^2*g^-1*(a+c*x^2)^(1/2)*(f+g*x)^(1/2)*(d+e*x)+-2//15*c^-3//2*g^-3*(-1a)^(1/2)*(c^(1/2)*(f*c^(1/2)+g*(-1a)^(1/2))^-1*(f+g*x))^(1/2)*(1+c*a^-1*x^2)^(1/2)*(a+c*x^2)^-1//2*(f+g*x)^-1//2*(-1*c*(-15*d^3*g^3+8*e^3*f^3+-30*d*g*e^2*f^2+45*e*f*d^2*g^2)+a*e^2*g^2*(-15*d*g+7*e*f))*Elliptic.F(arcsin((1/2)*2^(1/2)*(1+-1*x*c^(1/2)*(-1a)^-1//2)^(1/2)),-2*a*g*(-1*a*g+f*c^(1/2)*(-1a)^(1/2))^-1)+2//15*e*c^-3//2*g^-3*(-1a)^(1/2)*(c^(1/2)*(f*c^(1/2)+g*(-1a)^(1/2))^-1*(f+g*x))^-1//2*(1+c*a^-1*x^2)^(1/2)*(a+c*x^2)^-1//2*(f+g*x)^(1/2)*(-1*c*(8*e^2*f^2+45*d^2*g^2+-30*d*e*f*g)+9*a*e^2*g^2)*Elliptic.E(arcsin((1/2)*2^(1/2)*(1+-1*x*c^(1/2)*(-1a)^-1//2)^(1/2)),-2*a*g*(-1*a*g+f*c^(1/2)*(-1a)^(1/2))^-1))
@test integrate((a+c*x^2)^-1//2*(d+e*x)^2*(f+g*x)^-1//2, x) == :(2//3*c^-1*e^2*g^-1*(a+c*x^2)^(1/2)*(f+g*x)^(1/2)+-2//3*c^-3//2*g^-2*(-1a)^(1/2)*(c^(1/2)*(f*c^(1/2)+g*(-1a)^(1/2))^-1*(f+g*x))^(1/2)*(1+c*a^-1*x^2)^(1/2)*(a+c*x^2)^-1//2*(f+g*x)^-1//2*(g^2*(-1*a*e^2+3*c*d^2)+2*c*e*f*(e*f+-3*d*g))*Elliptic.F(arcsin((1/2)*2^(1/2)*(1+-1*x*c^(1/2)*(-1a)^-1//2)^(1/2)),-2*a*g*(-1*a*g+f*c^(1/2)*(-1a)^(1/2))^-1)+4//3*e*c^-1//2*g^-2*(-1a)^(1/2)*(c^(1/2)*(f*c^(1/2)+g*(-1a)^(1/2))^-1*(f+g*x))^-1//2*(1+c*a^-1*x^2)^(1/2)*(a+c*x^2)^-1//2*(f+g*x)^(1/2)*(e*f+-3*d*g)*Elliptic.E(arcsin((1/2)*2^(1/2)*(1+-1*x*c^(1/2)*(-1a)^-1//2)^(1/2)),-2*a*g*(-1*a*g+f*c^(1/2)*(-1a)^(1/2))^-1))
@test integrate((a+c*x^2)^-1//2*(f+g*x)^-1//2*(d+e*x), x) == :(-2*e*c^-1//2*g^-1*(-1a)^(1/2)*(c^(1/2)*(f*c^(1/2)+g*(-1a)^(1/2))^-1*(f+g*x))^-1//2*(1+c*a^-1*x^2)^(1/2)*(a+c*x^2)^-1//2*(f+g*x)^(1/2)*Elliptic.E(arcsin((1/2)*2^(1/2)*(1+-1*x*c^(1/2)*(-1a)^-1//2)^(1/2)),-2*a*g*(-1*a*g+f*c^(1/2)*(-1a)^(1/2))^-1)+2*c^-1//2*g^-1*(-1a)^(1/2)*(c^(1/2)*(f*c^(1/2)+g*(-1a)^(1/2))^-1*(f+g*x))^(1/2)*(1+c*a^-1*x^2)^(1/2)*(a+c*x^2)^-1//2*(f+g*x)^-1//2*(e*f+-1*d*g)*Elliptic.F(arcsin((1/2)*2^(1/2)*(1+-1*x*c^(1/2)*(-1a)^-1//2)^(1/2)),-2*a*g*(-1*a*g+f*c^(1/2)*(-1a)^(1/2))^-1))
@test integrate((a+c*x^2)^-1//2*(f+g*x)^-1//2, x) == :(-2*c^-1//2*(-1a)^(1/2)*(c^(1/2)*(f*c^(1/2)+g*(-1a)^(1/2))^-1*(f+g*x))^(1/2)*(1+c*a^-1*x^2)^(1/2)*(a+c*x^2)^-1//2*(f+g*x)^-1//2*Elliptic.F(arcsin((1/2)*2^(1/2)*(1+-1*x*c^(1/2)*(-1a)^-1//2)^(1/2)),-2*a*g*(-1*a*g+f*c^(1/2)*(-1a)^(1/2))^-1))
@test integrate((a+c*x^2)^-1//2*(d+e*x)^-1//2*(f+g*x)^-1//2, x) == :(-1*((1+(d+e*x)^-1*(a*e^2+c*d^2)^(1/2)*(a*g^2+c*f^2)^-1//2*(f+g*x))^-2*(1+(d+e*x)^-2*(f+g*x)^2*(a*g^2+c*f^2)^-1*(a*e^2+c*d^2)+-1*(d+e*x)^-1*(a*g^2+c*f^2)^-1*(f+g*x)*(2*a*e*g+2*c*d*f)))^(1/2)*((d+e*x)^-2*(a*g^2+c*f^2)^-1*(e*f+-1*d*g)^2*(a+c*x^2))^(1/2)*(a+c*x^2)^-1//2*(a*e^2+c*d^2)^-1//4*(a*g^2+c*f^2)^1//4*(e*f+-1*d*g)^-1*(1+(d+e*x)^-2*(f+g*x)^2*(a*g^2+c*f^2)^-1*(a*e^2+c*d^2)+-1*(d+e*x)^-1*(a*g^2+c*f^2)^-1*(f+g*x)*(2*a*e*g+2*c*d*f))^-1//2*(1+(d+e*x)^-1*(a*e^2+c*d^2)^(1/2)*(a*g^2+c*f^2)^-1//2*(f+g*x))*(d+e*x)*Elliptic.F(2*arctan((d+e*x)^-1//2*(f+g*x)^(1/2)*(a*e^2+c*d^2)^1//4*(a*g^2+c*f^2)^-1//4),1/2+(1/2)*(a*e^2+c*d^2)^-1//2*(a*g^2+c*f^2)^-1//2*(a*e*g+c*d*f)))
@test integrate((1+x)^-1//2*(-1+x)^-1//2*(-1+2*x^2)^-1//2, x) == :((1+x)^-1//2*(1+-1*x^2)^(1/2)*(1+-2*x^2)^(1/2)*(-1+x)^-1//2*(-1+2*x^2)^-1//2*Elliptic.F(arcsin(x),2))
@test integrate((d+e*x)^(1/2)*(f+g*x)^3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2, x) == :(2//7*c^-1*d^-1*(d+e*x)^-1//2*(f+g*x)^3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+1//35*c^-2*d^-2*(d+e*x)^-1//2*(f+g*x)^2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(-12*a*e*g+12*c*d*f)+-16//35*c^-4*d^-4*e^-1*(d+e*x)^-1//2*(c*d*f+-1*a*e*g)^2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(-1*c*d*(-1*d*g+3*e*f)+2*a*g*e^2)+16//35*g*c^-3*d^-3*e^-1*(d+e*x)^(1/2)*(c*d*f+-1*a*e*g)^2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2))
@test integrate((d+e*x)^(1/2)*(f+g*x)^2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2, x) == :(2//5*c^-1*d^-1*(d+e*x)^-1//2*(f+g*x)^2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+-1//15*c^-3*d^-3*e^-1*(d+e*x)^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(-1*c*d*(-1*d*g+3*e*f)+2*a*g*e^2)*(-8*a*e*g+8*c*d*f)+8//15*g*c^-2*d^-2*e^-1*(d+e*x)^(1/2)*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(c*d*f+-1*a*e*g))
@test integrate((d+e*x)^(1/2)*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*(f+g*x), x) == :(-1//3*c^-2*d^-2*e^-1*(d+e*x)^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(-2*c*d*(-1*d*g+3*e*f)+4*a*g*e^2)+2//3*g*c^-1*d^-1*e^-1*(d+e*x)^(1/2)*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2))
@test integrate((d+e*x)^(1/2)*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2, x) == :(2*c^-1*d^-1*(d+e*x)^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2))
@test integrate((d+e*x)^(1/2)*(f+g*x)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2, x) == :(2*g^-1//2*(c*d*f+-1*a*e*g)^-1//2*arctan(g^(1/2)*(d+e*x)^-1//2*(c*d*f+-1*a*e*g)^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)))
@test integrate((d+e*x)^(1/2)*(f+g*x)^-2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2, x) == :((d+e*x)^-1//2*(f+g*x)^-1*(c*d*f+-1*a*e*g)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+c*d*g^-1//2*(c*d*f+-1*a*e*g)^-3//2*arctan(g^(1/2)*(d+e*x)^-1//2*(c*d*f+-1*a*e*g)^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)))
@test integrate((d+e*x)^(1/2)*(f+g*x)^-3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2, x) == :((d+e*x)^-1//2*(f+g*x)^-2*(-2*a*e*g+2*c*d*f)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+3//4*c^2*d^2*g^-1//2*(c*d*f+-1*a*e*g)^-5//2*arctan(g^(1/2)*(d+e*x)^-1//2*(c*d*f+-1*a*e*g)^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2))+3//4*c*d*(d+e*x)^-1//2*(f+g*x)^-1*(c*d*f+-1*a*e*g)^-2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2))
@test integrate((d+e*x)^(1/2)*(f+g*x)^-4*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2, x) == :((d+e*x)^-1//2*(f+g*x)^-3*(-3*a*e*g+3*c*d*f)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+5//8*c^3*d^3*g^-1//2*(c*d*f+-1*a*e*g)^-7//2*arctan(g^(1/2)*(d+e*x)^-1//2*(c*d*f+-1*a*e*g)^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2))+5//8*c^2*d^2*(d+e*x)^-1//2*(f+g*x)^-1*(c*d*f+-1*a*e*g)^-3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+5//12*c*d*(d+e*x)^-1//2*(f+g*x)^-2*(c*d*f+-1*a*e*g)^-2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2))
@test integrate((d+e*x)^3//2*(f+g*x)^3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-3//2, x) == :(-2*c^-1*d^-1*(d+e*x)^(1/2)*(f+g*x)^3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2+12//5*g*c^-2*d^-2*(d+e*x)^-1//2*(f+g*x)^2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+16//5*c^-3*d^-3*e^-1*g^2*(d+e*x)^(1/2)*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(c*d*f+-1*a*e*g)+-16//5*g*c^-4*d^-4*e^-1*(d+e*x)^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(c*d*f+-1*a*e*g)*(-1*c*d*(-1*d*g+3*e*f)+2*a*g*e^2))
@test integrate((d+e*x)^3//2*(f+g*x)^2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-3//2, x) == :(-2*c^-1*d^-1*(d+e*x)^(1/2)*(f+g*x)^2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2+8//3*c^-2*d^-2*e^-1*g^2*(d+e*x)^(1/2)*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+-8//3*g*c^-3*d^-3*e^-1*(d+e*x)^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(-1*c*d*(-1*d*g+3*e*f)+2*a*g*e^2))
@test integrate((d+e*x)^3//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-3//2*(f+g*x), x) == :(-1*c^-1*d^-1*(d+e*x)^3//2*(c*d^2+-1*a*e^2)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*(-2*a*e*g+2*c*d*f)+-1*c^-2*d^-2*(d+e*x)^-1//2*(c*d^2+-1*a*e^2)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(-2*c*d*(d*g+e*f)+4*a*g*e^2))
@test integrate((d+e*x)^3//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-3//2, x) == :(-2*c^-1*d^-1*(d+e*x)^(1/2)*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2)
@test integrate((d+e*x)^3//2*(f+g*x)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-3//2, x) == :(-2*g^(1/2)*(c*d*f+-1*a*e*g)^-3//2*arctan(g^(1/2)*(d+e*x)^-1//2*(c*d*f+-1*a*e*g)^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2))+-2*(d+e*x)^(1/2)*(c*d*f+-1*a*e*g)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2)
@test integrate((d+e*x)^3//2*(f+g*x)^-2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-3//2, x) == :(-2*(d+e*x)^(1/2)*(f+g*x)^-1*(c*d*f+-1*a*e*g)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2+-3*c*d*g^(1/2)*(c*d*f+-1*a*e*g)^-5//2*arctan(g^(1/2)*(d+e*x)^-1//2*(c*d*f+-1*a*e*g)^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2))+-3*g*(d+e*x)^-1//2*(f+g*x)^-1*(c*d*f+-1*a*e*g)^-2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2))
@test integrate((d+e*x)^3//2*(f+g*x)^-3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-3//2, x) == :(-2*(d+e*x)^(1/2)*(f+g*x)^-2*(c*d*f+-1*a*e*g)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2+-15//4*c^2*d^2*g^(1/2)*(c*d*f+-1*a*e*g)^-7//2*arctan(g^(1/2)*(d+e*x)^-1//2*(c*d*f+-1*a*e*g)^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2))+-5//2*g*(d+e*x)^-1//2*(f+g*x)^-2*(c*d*f+-1*a*e*g)^-2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+-15//4*c*d*g*(d+e*x)^-1//2*(f+g*x)^-1*(c*d*f+-1*a*e*g)^-3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2))
@test integrate((d+e*x)^5//2*(f+g*x)^3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-5//2, x) == :(-2//3*c^-1*d^-1*(d+e*x)^3//2*(f+g*x)^3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-3//2+-4*g*c^-2*d^-2*(d+e*x)^(1/2)*(f+g*x)^2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2+16//3*c^-3*d^-3*e^-1*g^3*(d+e*x)^(1/2)*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+-16//3*c^-4*d^-4*e^-1*g^2*(d+e*x)^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(-1*c*d*(-1*d*g+3*e*f)+2*a*g*e^2))
@test integrate((d+e*x)^5//2*(f+g*x)^2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-5//2, x) == :(-2//3*c^-1*d^-1*(d+e*x)^3//2*(f+g*x)^2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-3//2+-8//3*g*c^-3*d^-3*(d+e*x)^-1//2*(c*d^2+-1*a*e^2)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(-1*c*d*(d*g+e*f)+2*a*g*e^2)+-8//3*g*c^-2*d^-2*(d+e*x)^3//2*(c*d^2+-1*a*e^2)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*(c*d*f+-1*a*e*g))
@test integrate((d+e*x)^5//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-5//2*(f+g*x), x) == :(-1//3*c^-1*d^-1*(d+e*x)^5//2*(c*d^2+-1*a*e^2)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-3//2*(-2*a*e*g+2*c*d*f)+1//3*c^-2*d^-2*(d+e*x)^(1/2)*(c*d^2+-1*a*e^2)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*(2*c*d*(e*f+-3*d*g)+4*a*g*e^2))
@test integrate((d+e*x)^5//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-5//2, x) == :(-2//3*c^-1*d^-1*(d+e*x)^3//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-3//2)
@test integrate((d+e*x)^5//2*(f+g*x)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-5//2, x) == :(-2*(d+e*x)^3//2*(-3*a*e*g+3*c*d*f)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-3//2+2*g^3//2*(c*d*f+-1*a*e*g)^-5//2*arctan(g^(1/2)*(d+e*x)^-1//2*(c*d*f+-1*a*e*g)^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2))+2*g*(d+e*x)^(1/2)*(c*d*f+-1*a*e*g)^-2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2)
@test integrate((d+e*x)^5//2*(f+g*x)^-2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-5//2, x) == :(-2*(d+e*x)^3//2*(f+g*x)^-1*(-3*a*e*g+3*c*d*f)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-3//2+5*c*d*g^3//2*(c*d*f+-1*a*e*g)^-7//2*arctan(g^(1/2)*(d+e*x)^-1//2*(c*d*f+-1*a*e*g)^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2))+5*g^2*(d+e*x)^-1//2*(f+g*x)^-1*(c*d*f+-1*a*e*g)^-3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+10//3*g*(d+e*x)^(1/2)*(f+g*x)^-1*(c*d*f+-1*a*e*g)^-2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2)
@test integrate((d+e*x)^5//2*(f+g*x)^-3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-5//2, x) == :(-2*(d+e*x)^3//2*(f+g*x)^-2*(-3*a*e*g+3*c*d*f)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-3//2+14//3*g*(d+e*x)^(1/2)*(f+g*x)^-2*(c*d*f+-1*a*e*g)^-2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2+35//4*c^2*d^2*g^3//2*(c*d*f+-1*a*e*g)^-9//2*arctan(g^(1/2)*(d+e*x)^-1//2*(c*d*f+-1*a*e*g)^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2))+35//6*g^2*(d+e*x)^-1//2*(f+g*x)^-2*(c*d*f+-1*a*e*g)^-3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+35//4*c*d*g^2*(d+e*x)^-1//2*(f+g*x)^-1*(c*d*f+-1*a*e*g)^-4*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2))
@test integrate((d+e*x)^-1//2*(f+g*x)^4*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2), x) == :(2//11*c^-1*d^-1*(d+e*x)^-3//2*(f+g*x)^4*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2+1//99*c^-2*d^-2*(d+e*x)^-3//2*(f+g*x)^3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2*(-16*a*e*g+16*c*d*f)+32//231*c^-3*d^-3*(d+e*x)^-3//2*(f+g*x)^2*(c*d*f+-1*a*e*g)^2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2+-128//3465*c^-5*d^-5*e^-1*(d+e*x)^-3//2*(c*d*f+-1*a*e*g)^3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2*(-1*c*d*(-3*d*g+5*e*f)+2*a*g*e^2)+128//1155*g*c^-4*d^-4*e^-1*(d+e*x)^-1//2*(c*d*f+-1*a*e*g)^3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2)
@test integrate((d+e*x)^-1//2*(f+g*x)^3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2), x) == :(2//9*c^-1*d^-1*(d+e*x)^-3//2*(f+g*x)^3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2+1//21*c^-2*d^-2*(d+e*x)^-3//2*(f+g*x)^2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2*(-4*a*e*g+4*c*d*f)+-16//315*c^-4*d^-4*e^-1*(d+e*x)^-3//2*(c*d*f+-1*a*e*g)^2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2*(-1*c*d*(-3*d*g+5*e*f)+2*a*g*e^2)+16//105*g*c^-3*d^-3*e^-1*(d+e*x)^-1//2*(c*d*f+-1*a*e*g)^2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2)
@test integrate((d+e*x)^-1//2*(f+g*x)^2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2), x) == :(2//7*c^-1*d^-1*(d+e*x)^-3//2*(f+g*x)^2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2+-1//105*c^-3*d^-3*e^-1*(d+e*x)^-3//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2*(-1*c*d*(-3*d*g+5*e*f)+2*a*g*e^2)*(-8*a*e*g+8*c*d*f)+8//35*g*c^-2*d^-2*e^-1*(d+e*x)^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2*(c*d*f+-1*a*e*g))
@test integrate((d+e*x)^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(f+g*x), x) == :(-1//15*c^-2*d^-2*e^-1*(d+e*x)^-3//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2*(-2*c*d*(-3*d*g+5*e*f)+4*a*g*e^2)+2//5*g*c^-1*d^-1*e^-1*(d+e*x)^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2)
@test integrate((d+e*x)^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2), x) == :(2//3*c^-1*d^-1*(d+e*x)^-3//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2)
@test integrate((d+e*x)^-1//2*(f+g*x)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2), x) == :(-2*g^-3//2*(c*d*f+-1*a*e*g)^(1/2)*arctan(g^(1/2)*(d+e*x)^-1//2*(c*d*f+-1*a*e*g)^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2))+2*g^-1*(d+e*x)^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2))
@test integrate((d+e*x)^-1//2*(f+g*x)^-2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2), x) == :(-1*g^-1*(d+e*x)^-1//2*(f+g*x)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+c*d*g^-3//2*(c*d*f+-1*a*e*g)^-1//2*arctan(g^(1/2)*(d+e*x)^-1//2*(c*d*f+-1*a*e*g)^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)))
@test integrate((d+e*x)^-1//2*(f+g*x)^-3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2), x) == :(-1//2*g^-1*(d+e*x)^-1//2*(f+g*x)^-2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+1//4*c^2*d^2*g^-3//2*(c*d*f+-1*a*e*g)^-3//2*arctan(g^(1/2)*(d+e*x)^-1//2*(c*d*f+-1*a*e*g)^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2))+1//4*c*d*g^-1*(d+e*x)^-1//2*(f+g*x)^-1*(c*d*f+-1*a*e*g)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2))
@test integrate((d+e*x)^-1//2*(f+g*x)^-4*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2), x) == :(-1//3*g^-1*(d+e*x)^-1//2*(f+g*x)^-3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+1//8*c^3*d^3*g^-3//2*(c*d*f+-1*a*e*g)^-5//2*arctan(g^(1/2)*(d+e*x)^-1//2*(c*d*f+-1*a*e*g)^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2))+1//8*c^2*d^2*g^-1*(d+e*x)^-1//2*(f+g*x)^-1*(c*d*f+-1*a*e*g)^-2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+1//12*c*d*g^-1*(d+e*x)^-1//2*(f+g*x)^-2*(c*d*f+-1*a*e*g)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2))
@test integrate((d+e*x)^-1//2*(f+g*x)^-5*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2), x) == :(-1//4*g^-1*(d+e*x)^-1//2*(f+g*x)^-4*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+5//64*c^4*d^4*g^-3//2*(c*d*f+-1*a*e*g)^-7//2*arctan(g^(1/2)*(d+e*x)^-1//2*(c*d*f+-1*a*e*g)^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2))+1//24*c*d*g^-1*(d+e*x)^-1//2*(f+g*x)^-3*(c*d*f+-1*a*e*g)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+5//64*c^3*d^3*g^-1*(d+e*x)^-1//2*(f+g*x)^-1*(c*d*f+-1*a*e*g)^-3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+5//96*c^2*d^2*g^-1*(d+e*x)^-1//2*(f+g*x)^-2*(c*d*f+-1*a*e*g)^-2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2))
@test integrate((d+e*x)^-3//2*(f+g*x)^4*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2, x) == :(2//13*c^-1*d^-1*(d+e*x)^-5//2*(f+g*x)^4*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2+1//143*c^-2*d^-2*(d+e*x)^-5//2*(f+g*x)^3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2*(-16*a*e*g+16*c*d*f)+32//429*c^-3*d^-3*(d+e*x)^-5//2*(f+g*x)^2*(c*d*f+-1*a*e*g)^2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2+-128//15015*c^-5*d^-5*e^-1*(d+e*x)^-5//2*(c*d*f+-1*a*e*g)^3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2*(-1*c*d*(-5*d*g+7*e*f)+2*a*g*e^2)+128//3003*g*c^-4*d^-4*e^-1*(d+e*x)^-3//2*(c*d*f+-1*a*e*g)^3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2)
@test integrate((d+e*x)^-3//2*(f+g*x)^3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2, x) == :(2//11*c^-1*d^-1*(d+e*x)^-5//2*(f+g*x)^3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2+1//33*c^-2*d^-2*(d+e*x)^-5//2*(f+g*x)^2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2*(-4*a*e*g+4*c*d*f)+-16//1155*c^-4*d^-4*e^-1*(d+e*x)^-5//2*(c*d*f+-1*a*e*g)^2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2*(-1*c*d*(-5*d*g+7*e*f)+2*a*g*e^2)+16//231*g*c^-3*d^-3*e^-1*(d+e*x)^-3//2*(c*d*f+-1*a*e*g)^2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2)
@test integrate((d+e*x)^-3//2*(f+g*x)^2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2, x) == :(2//9*c^-1*d^-1*(d+e*x)^-5//2*(f+g*x)^2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2+-1//315*c^-3*d^-3*e^-1*(d+e*x)^-5//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2*(-1*c*d*(-5*d*g+7*e*f)+2*a*g*e^2)*(-8*a*e*g+8*c*d*f)+8//63*g*c^-2*d^-2*e^-1*(d+e*x)^-3//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2*(c*d*f+-1*a*e*g))
@test integrate((d+e*x)^-3//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2*(f+g*x), x) == :(-1//35*c^-2*d^-2*e^-1*(d+e*x)^-5//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2*(-2*c*d*(-5*d*g+7*e*f)+4*a*g*e^2)+2//7*g*c^-1*d^-1*e^-1*(d+e*x)^-3//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2)
@test integrate((d+e*x)^-3//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2, x) == :(2//5*c^-1*d^-1*(d+e*x)^-5//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2)
@test integrate((d+e*x)^-3//2*(f+g*x)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2, x) == :(2*g^-5//2*(c*d*f+-1*a*e*g)^3//2*arctan(g^(1/2)*(d+e*x)^-1//2*(c*d*f+-1*a*e*g)^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2))+2//3*g^-1*(d+e*x)^-3//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2+-1*g^-2*(d+e*x)^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(-2*a*e*g+2*c*d*f))
@test integrate((d+e*x)^-3//2*(f+g*x)^-2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2, x) == :(-1*g^-1*(d+e*x)^-3//2*(f+g*x)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2+-3*c*d*g^-5//2*(c*d*f+-1*a*e*g)^(1/2)*arctan(g^(1/2)*(d+e*x)^-1//2*(c*d*f+-1*a*e*g)^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2))+3*c*d*g^-2*(d+e*x)^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2))
@test integrate((d+e*x)^-3//2*(f+g*x)^-3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2, x) == :(-1//2*g^-1*(d+e*x)^-3//2*(f+g*x)^-2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2+3//4*c^2*d^2*g^-5//2*(c*d*f+-1*a*e*g)^-1//2*arctan(g^(1/2)*(d+e*x)^-1//2*(c*d*f+-1*a*e*g)^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2))+-3//4*c*d*g^-2*(d+e*x)^-1//2*(f+g*x)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2))
@test integrate((d+e*x)^-3//2*(f+g*x)^-4*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2, x) == :(-1//3*g^-1*(d+e*x)^-3//2*(f+g*x)^-3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2+1//8*c^3*d^3*g^-5//2*(c*d*f+-1*a*e*g)^-3//2*arctan(g^(1/2)*(d+e*x)^-1//2*(c*d*f+-1*a*e*g)^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2))+-1//4*c*d*g^-2*(d+e*x)^-1//2*(f+g*x)^-2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+1//8*c^2*d^2*g^-2*(d+e*x)^-1//2*(f+g*x)^-1*(c*d*f+-1*a*e*g)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2))
@test integrate((d+e*x)^-3//2*(f+g*x)^-5*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2, x) == :(-1//4*g^-1*(d+e*x)^-3//2*(f+g*x)^-4*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2+3//64*c^4*d^4*g^-5//2*(c*d*f+-1*a*e*g)^-5//2*arctan(g^(1/2)*(d+e*x)^-1//2*(c*d*f+-1*a*e*g)^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2))+-1//8*c*d*g^-2*(d+e*x)^-1//2*(f+g*x)^-3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+1//32*c^2*d^2*g^-2*(d+e*x)^-1//2*(f+g*x)^-2*(c*d*f+-1*a*e*g)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+3//64*c^3*d^3*g^-2*(d+e*x)^-1//2*(f+g*x)^-1*(c*d*f+-1*a*e*g)^-2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2))
@test integrate((d+e*x)^-3//2*(f+g*x)^-6*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2, x) == :(-1//5*g^-1*(d+e*x)^-3//2*(f+g*x)^-5*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2+3//128*c^5*d^5*g^-5//2*(c*d*f+-1*a*e*g)^-7//2*arctan(g^(1/2)*(d+e*x)^-1//2*(c*d*f+-1*a*e*g)^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2))+-3//40*c*d*g^-2*(d+e*x)^-1//2*(f+g*x)^-4*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+1//64*c^3*d^3*g^-2*(d+e*x)^-1//2*(f+g*x)^-2*(c*d*f+-1*a*e*g)^-2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+1//80*c^2*d^2*g^-2*(d+e*x)^-1//2*(f+g*x)^-3*(c*d*f+-1*a*e*g)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+3//128*c^4*d^4*g^-2*(d+e*x)^-1//2*(f+g*x)^-1*(c*d*f+-1*a*e*g)^-3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2))
@test integrate((d+e*x)^-5//2*(f+g*x)^4*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2, x) == :(2//15*c^-1*d^-1*(d+e*x)^-7//2*(f+g*x)^4*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^7//2+1//195*c^-2*d^-2*(d+e*x)^-7//2*(f+g*x)^3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^7//2*(-16*a*e*g+16*c*d*f)+32//715*c^-3*d^-3*(d+e*x)^-7//2*(f+g*x)^2*(c*d*f+-1*a*e*g)^2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^7//2+-128//45045*c^-5*d^-5*e^-1*(d+e*x)^-7//2*(c*d*f+-1*a*e*g)^3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^7//2*(-1*c*d*(-7*d*g+9*e*f)+2*a*g*e^2)+128//6435*g*c^-4*d^-4*e^-1*(d+e*x)^-5//2*(c*d*f+-1*a*e*g)^3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^7//2)
@test integrate((d+e*x)^-5//2*(f+g*x)^3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2, x) == :(2//13*c^-1*d^-1*(d+e*x)^-7//2*(f+g*x)^3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^7//2+1//143*c^-2*d^-2*(d+e*x)^-7//2*(f+g*x)^2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^7//2*(-12*a*e*g+12*c*d*f)+-16//3003*c^-4*d^-4*e^-1*(d+e*x)^-7//2*(c*d*f+-1*a*e*g)^2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^7//2*(-1*c*d*(-7*d*g+9*e*f)+2*a*g*e^2)+16//429*g*c^-3*d^-3*e^-1*(d+e*x)^-5//2*(c*d*f+-1*a*e*g)^2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^7//2)
@test integrate((d+e*x)^-5//2*(f+g*x)^2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2, x) == :(2//11*c^-1*d^-1*(d+e*x)^-7//2*(f+g*x)^2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^7//2+-1//693*c^-3*d^-3*e^-1*(d+e*x)^-7//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^7//2*(-1*c*d*(-7*d*g+9*e*f)+2*a*g*e^2)*(-8*a*e*g+8*c*d*f)+8//99*g*c^-2*d^-2*e^-1*(d+e*x)^-5//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^7//2*(c*d*f+-1*a*e*g))
@test integrate((d+e*x)^-5//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2*(f+g*x), x) == :(-1//63*c^-2*d^-2*e^-1*(d+e*x)^-7//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^7//2*(-2*c*d*(-7*d*g+9*e*f)+4*a*g*e^2)+2//9*g*c^-1*d^-1*e^-1*(d+e*x)^-5//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^7//2)
@test integrate((d+e*x)^-5//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2, x) == :(2//7*c^-1*d^-1*(d+e*x)^-7//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^7//2)
@test integrate((d+e*x)^-5//2*(f+g*x)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2, x) == :(-2*g^-7//2*(c*d*f+-1*a*e*g)^5//2*arctan(g^(1/2)*(d+e*x)^-1//2*(c*d*f+-1*a*e*g)^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2))+2//5*g^-1*(d+e*x)^-5//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2+2*g^-3*(d+e*x)^-1//2*(c*d*f+-1*a*e*g)^2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+-1//3*g^-2*(d+e*x)^-3//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2*(-2*a*e*g+2*c*d*f))
@test integrate((d+e*x)^-5//2*(f+g*x)^-2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2, x) == :(-1*g^-1*(d+e*x)^-5//2*(f+g*x)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2+5*c*d*g^-7//2*(c*d*f+-1*a*e*g)^3//2*arctan(g^(1/2)*(d+e*x)^-1//2*(c*d*f+-1*a*e*g)^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2))+5//3*c*d*g^-2*(d+e*x)^-3//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2+-5*c*d*g^-3*(d+e*x)^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(c*d*f+-1*a*e*g))
@test integrate((d+e*x)^-5//2*(f+g*x)^-3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2, x) == :(-1//2*g^-1*(d+e*x)^-5//2*(f+g*x)^-2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2+-15//4*c^2*d^2*g^-7//2*(c*d*f+-1*a*e*g)^(1/2)*arctan(g^(1/2)*(d+e*x)^-1//2*(c*d*f+-1*a*e*g)^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2))+15//4*c^2*d^2*g^-3*(d+e*x)^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+-5//4*c*d*g^-2*(d+e*x)^-3//2*(f+g*x)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2)
@test integrate((d+e*x)^-5//2*(f+g*x)^-4*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2, x) == :(-1//3*g^-1*(d+e*x)^-5//2*(f+g*x)^-3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2+5//8*c^3*d^3*g^-7//2*(c*d*f+-1*a*e*g)^-1//2*arctan(g^(1/2)*(d+e*x)^-1//2*(c*d*f+-1*a*e*g)^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2))+-5//8*c^2*d^2*g^-3*(d+e*x)^-1//2*(f+g*x)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+-5//12*c*d*g^-2*(d+e*x)^-3//2*(f+g*x)^-2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2)
@test integrate((d+e*x)^-5//2*(f+g*x)^-5*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2, x) == :(-1//4*g^-1*(d+e*x)^-5//2*(f+g*x)^-4*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2+5//64*c^4*d^4*g^-7//2*(c*d*f+-1*a*e*g)^-3//2*arctan(g^(1/2)*(d+e*x)^-1//2*(c*d*f+-1*a*e*g)^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2))+-5//24*c*d*g^-2*(d+e*x)^-3//2*(f+g*x)^-3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2+-5//32*c^2*d^2*g^-3*(d+e*x)^-1//2*(f+g*x)^-2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+5//64*c^3*d^3*g^-3*(d+e*x)^-1//2*(f+g*x)^-1*(c*d*f+-1*a*e*g)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2))
@test integrate((d+e*x)^-5//2*(f+g*x)^-6*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2, x) == :(-1//5*g^-1*(d+e*x)^-5//2*(f+g*x)^-5*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2+3//128*c^5*d^5*g^-7//2*(c*d*f+-1*a*e*g)^-5//2*arctan(g^(1/2)*(d+e*x)^-1//2*(c*d*f+-1*a*e*g)^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2))+-1//8*c*d*g^-2*(d+e*x)^-3//2*(f+g*x)^-4*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2+-1//16*c^2*d^2*g^-3*(d+e*x)^-1//2*(f+g*x)^-3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+1//64*c^3*d^3*g^-3*(d+e*x)^-1//2*(f+g*x)^-2*(c*d*f+-1*a*e*g)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+3//128*c^4*d^4*g^-3*(d+e*x)^-1//2*(f+g*x)^-1*(c*d*f+-1*a*e*g)^-2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2))
@test integrate((d+e*x)^-5//2*(f+g*x)^-7*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2, x) == :(-1//6*g^-1*(d+e*x)^-5//2*(f+g*x)^-6*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2+5//512*c^6*d^6*g^-7//2*(c*d*f+-1*a*e*g)^-7//2*arctan(g^(1/2)*(d+e*x)^-1//2*(c*d*f+-1*a*e*g)^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2))+-1//12*c*d*g^-2*(d+e*x)^-3//2*(f+g*x)^-5*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2+-1//32*c^2*d^2*g^-3*(d+e*x)^-1//2*(f+g*x)^-4*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+1//192*c^3*d^3*g^-3*(d+e*x)^-1//2*(f+g*x)^-3*(c*d*f+-1*a*e*g)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+5//512*c^5*d^5*g^-3*(d+e*x)^-1//2*(f+g*x)^-1*(c*d*f+-1*a*e*g)^-3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+5//768*c^4*d^4*g^-3*(d+e*x)^-1//2*(f+g*x)^-2*(c*d*f+-1*a*e*g)^-2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2))
@test integrate((d+e*x)^(1/2)*(f+g*x)^5//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2, x) == :(1//3*c^-1*d^-1*(d+e*x)^-1//2*(f+g*x)^5//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+1//12*c^-2*d^-2*(d+e*x)^-1//2*(f+g*x)^3//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(-5*a*e*g+5*c*d*f)+5//8*c^-3*d^-3*(d+e*x)^-1//2*(f+g*x)^(1/2)*(c*d*f+-1*a*e*g)^2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+5//8*c^-7//2*d^-7//2*g^-1//2*(d+e*x)^(1/2)*(a*e+c*d*x)^(1/2)*(c*d*f+-1*a*e*g)^3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*arctanh(c^-1//2*d^-1//2*g^(1/2)*(f+g*x)^-1//2*(a*e+c*d*x)^(1/2)))
@test integrate((d+e*x)^(1/2)*(f+g*x)^3//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2, x) == :((1/2)*c^-1*d^-1*(d+e*x)^-1//2*(f+g*x)^3//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+1//4*c^-2*d^-2*(d+e*x)^-1//2*(f+g*x)^(1/2)*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(-3*a*e*g+3*c*d*f)+3//4*c^-5//2*d^-5//2*g^-1//2*(d+e*x)^(1/2)*(a*e+c*d*x)^(1/2)*(c*d*f+-1*a*e*g)^2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*arctanh(c^-1//2*d^-1//2*g^(1/2)*(f+g*x)^-1//2*(a*e+c*d*x)^(1/2)))
@test integrate((d+e*x)^(1/2)*(f+g*x)^(1/2)*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2, x) == :(c^-1*d^-1*(d+e*x)^-1//2*(f+g*x)^(1/2)*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+c^-3//2*d^-3//2*g^-1//2*(d+e*x)^(1/2)*(a*e+c*d*x)^(1/2)*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*(c*d*f+-1*a*e*g)*arctanh(c^-1//2*d^-1//2*g^(1/2)*(f+g*x)^-1//2*(a*e+c*d*x)^(1/2)))
@test integrate((d+e*x)^(1/2)*(f+g*x)^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2, x) == :(2*c^-1//2*d^-1//2*g^-1//2*(d+e*x)^(1/2)*(a*e+c*d*x)^(1/2)*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*arctanh(c^-1//2*d^-1//2*g^(1/2)*(f+g*x)^-1//2*(a*e+c*d*x)^(1/2)))
@test integrate((d+e*x)^(1/2)*(f+g*x)^-3//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2, x) == :(2*(d+e*x)^-1//2*(f+g*x)^-1//2*(c*d*f+-1*a*e*g)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2))
@test integrate((d+e*x)^(1/2)*(f+g*x)^-5//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2, x) == :(2*(d+e*x)^-1//2*(f+g*x)^-3//2*(-3*a*e*g+3*c*d*f)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+4//3*c*d*(d+e*x)^-1//2*(f+g*x)^-1//2*(c*d*f+-1*a*e*g)^-2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2))
@test integrate((d+e*x)^(1/2)*(f+g*x)^-7//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2, x) == :(2*(d+e*x)^-1//2*(f+g*x)^-5//2*(-5*a*e*g+5*c*d*f)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+8//15*c*d*(d+e*x)^-1//2*(f+g*x)^-3//2*(c*d*f+-1*a*e*g)^-2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+16//15*c^2*d^2*(d+e*x)^-1//2*(f+g*x)^-1//2*(c*d*f+-1*a*e*g)^-3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2))
@test integrate((d+e*x)^(1/2)*(f+g*x)^-9//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2, x) == :(2*(d+e*x)^-1//2*(f+g*x)^-7//2*(-7*a*e*g+7*c*d*f)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+12//35*c*d*(d+e*x)^-1//2*(f+g*x)^-5//2*(c*d*f+-1*a*e*g)^-2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+16//35*c^2*d^2*(d+e*x)^-1//2*(f+g*x)^-3//2*(c*d*f+-1*a*e*g)^-3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+32//35*c^3*d^3*(d+e*x)^-1//2*(f+g*x)^-1//2*(c*d*f+-1*a*e*g)^-4*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2))
@test integrate((d+e*x)^3//2*(f+g*x)^5//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-3//2, x) == :(-2*c^-1*d^-1*(d+e*x)^(1/2)*(f+g*x)^5//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2+5//2*g*c^-2*d^-2*(d+e*x)^-1//2*(f+g*x)^3//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+15//4*g*c^-3*d^-3*(d+e*x)^-1//2*(f+g*x)^(1/2)*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(c*d*f+-1*a*e*g)+15//4*c^-7//2*d^-7//2*g^(1/2)*(d+e*x)^(1/2)*(a*e+c*d*x)^(1/2)*(c*d*f+-1*a*e*g)^2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*arctanh(c^-1//2*d^-1//2*g^(1/2)*(f+g*x)^-1//2*(a*e+c*d*x)^(1/2)))
@test integrate((d+e*x)^3//2*(f+g*x)^3//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-3//2, x) == :(-2*c^-1*d^-1*(d+e*x)^(1/2)*(f+g*x)^3//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2+3*g*c^-2*d^-2*(d+e*x)^-1//2*(f+g*x)^(1/2)*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+3*c^-5//2*d^-5//2*g^(1/2)*(d+e*x)^(1/2)*(a*e+c*d*x)^(1/2)*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*(c*d*f+-1*a*e*g)*arctanh(c^-1//2*d^-1//2*g^(1/2)*(f+g*x)^-1//2*(a*e+c*d*x)^(1/2)))
@test integrate((d+e*x)^3//2*(f+g*x)^(1/2)*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-3//2, x) == :(-2*c^-1*d^-1*(d+e*x)^(1/2)*(f+g*x)^(1/2)*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2+2*c^-3//2*d^-3//2*g^(1/2)*(d+e*x)^(1/2)*(a*e+c*d*x)^(1/2)*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*arctanh(c^-1//2*d^-1//2*g^(1/2)*(f+g*x)^-1//2*(a*e+c*d*x)^(1/2)))
@test integrate((d+e*x)^3//2*(f+g*x)^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-3//2, x) == :(-2*(d+e*x)^(1/2)*(f+g*x)^(1/2)*(c*d*f+-1*a*e*g)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2)
@test integrate((d+e*x)^3//2*(f+g*x)^-3//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-3//2, x) == :(-2*(d+e*x)^(1/2)*(f+g*x)^-1//2*(c*d*f+-1*a*e*g)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2+-4*g*(d+e*x)^-1//2*(f+g*x)^-1//2*(c*d*f+-1*a*e*g)^-2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2))
@test integrate((d+e*x)^3//2*(f+g*x)^-5//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-3//2, x) == :(-2*(d+e*x)^(1/2)*(f+g*x)^-3//2*(c*d*f+-1*a*e*g)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2+-8//3*g*(d+e*x)^-1//2*(f+g*x)^-3//2*(c*d*f+-1*a*e*g)^-2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+-16//3*c*d*g*(d+e*x)^-1//2*(f+g*x)^-1//2*(c*d*f+-1*a*e*g)^-3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2))
@test integrate((d+e*x)^3//2*(f+g*x)^-7//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-3//2, x) == :(-2*(d+e*x)^(1/2)*(f+g*x)^-5//2*(c*d*f+-1*a*e*g)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2+-12//5*g*(d+e*x)^-1//2*(f+g*x)^-5//2*(c*d*f+-1*a*e*g)^-2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+-32//5*g*c^2*d^2*(d+e*x)^-1//2*(f+g*x)^-1//2*(c*d*f+-1*a*e*g)^-4*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+-16//5*c*d*g*(d+e*x)^-1//2*(f+g*x)^-3//2*(c*d*f+-1*a*e*g)^-3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2))
@test integrate((d+e*x)^5//2*(f+g*x)^5//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-5//2, x) == :(-2//3*c^-1*d^-1*(d+e*x)^3//2*(f+g*x)^5//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-3//2+5*c^-3*d^-3*g^2*(d+e*x)^-1//2*(f+g*x)^(1/2)*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+-10//3*g*c^-2*d^-2*(d+e*x)^(1/2)*(f+g*x)^3//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2+5*c^-7//2*d^-7//2*g^3//2*(d+e*x)^(1/2)*(a*e+c*d*x)^(1/2)*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*(c*d*f+-1*a*e*g)*arctanh(c^-1//2*d^-1//2*g^(1/2)*(f+g*x)^-1//2*(a*e+c*d*x)^(1/2)))
@test integrate((d+e*x)^5//2*(f+g*x)^3//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-5//2, x) == :(-2//3*c^-1*d^-1*(d+e*x)^3//2*(f+g*x)^3//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-3//2+-2*g*c^-2*d^-2*(d+e*x)^(1/2)*(f+g*x)^(1/2)*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2+2*c^-5//2*d^-5//2*g^3//2*(d+e*x)^(1/2)*(a*e+c*d*x)^(1/2)*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*arctanh(c^-1//2*d^-1//2*g^(1/2)*(f+g*x)^-1//2*(a*e+c*d*x)^(1/2)))
@test integrate((d+e*x)^5//2*(f+g*x)^(1/2)*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-5//2, x) == :(-2*(d+e*x)^3//2*(f+g*x)^3//2*(-3*a*e*g+3*c*d*f)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-3//2)
@test integrate((d+e*x)^5//2*(f+g*x)^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-5//2, x) == :(-2*(d+e*x)^3//2*(f+g*x)^(1/2)*(-3*a*e*g+3*c*d*f)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-3//2+4//3*g*(d+e*x)^(1/2)*(f+g*x)^(1/2)*(c*d*f+-1*a*e*g)^-2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2)
@test integrate((d+e*x)^5//2*(f+g*x)^-3//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-5//2, x) == :(-2*(d+e*x)^3//2*(f+g*x)^-1//2*(-3*a*e*g+3*c*d*f)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-3//2+8//3*g*(d+e*x)^(1/2)*(f+g*x)^-1//2*(c*d*f+-1*a*e*g)^-2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2+16//3*g^2*(d+e*x)^-1//2*(f+g*x)^-1//2*(c*d*f+-1*a*e*g)^-3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2))
@test integrate((d+e*x)^5//2*(f+g*x)^-5//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-5//2, x) == :(-2*(d+e*x)^3//2*(f+g*x)^-3//2*(-3*a*e*g+3*c*d*f)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-3//2+4*g*(d+e*x)^(1/2)*(f+g*x)^-3//2*(c*d*f+-1*a*e*g)^-2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2+16//3*g^2*(d+e*x)^-1//2*(f+g*x)^-3//2*(c*d*f+-1*a*e*g)^-3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+32//3*c*d*g^2*(d+e*x)^-1//2*(f+g*x)^-1//2*(c*d*f+-1*a*e*g)^-4*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2))
@test integrate((d+e*x)^-1//2*(f+g*x)^5//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2), x) == :(1//4*g^-1*(d+e*x)^-1//2*(f+g*x)^7//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+1//24*(d+e*x)^-1//2*(f+g*x)^5//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(-1*f*g^-1+a*e*c^-1*d^-1)+-5//64*c^-3*d^-3*g^-1*(d+e*x)^-1//2*(f+g*x)^(1/2)*(c*d*f+-1*a*e*g)^3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+-5//96*c^-2*d^-2*g^-1*(d+e*x)^-1//2*(f+g*x)^3//2*(c*d*f+-1*a*e*g)^2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+-5//64*c^-7//2*d^-7//2*g^-3//2*(d+e*x)^(1/2)*(a*e+c*d*x)^(1/2)*(c*d*f+-1*a*e*g)^4*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*arctanh(c^-1//2*d^-1//2*g^(1/2)*(f+g*x)^-1//2*(a*e+c*d*x)^(1/2)))
@test integrate((d+e*x)^-1//2*(f+g*x)^3//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2), x) == :(1//3*g^-1*(d+e*x)^-1//2*(f+g*x)^5//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+1//12*(d+e*x)^-1//2*(f+g*x)^3//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(-1*f*g^-1+a*e*c^-1*d^-1)+-1//8*c^-2*d^-2*g^-1*(d+e*x)^-1//2*(f+g*x)^(1/2)*(c*d*f+-1*a*e*g)^2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+-1//8*c^-5//2*d^-5//2*g^-3//2*(d+e*x)^(1/2)*(a*e+c*d*x)^(1/2)*(c*d*f+-1*a*e*g)^3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*arctanh(c^-1//2*d^-1//2*g^(1/2)*(f+g*x)^-1//2*(a*e+c*d*x)^(1/2)))
@test integrate((d+e*x)^-1//2*(f+g*x)^(1/2)*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2), x) == :((1/2)*g^-1*(d+e*x)^-1//2*(f+g*x)^3//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+1//4*(d+e*x)^-1//2*(f+g*x)^(1/2)*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(-1*f*g^-1+a*e*c^-1*d^-1)+-1//4*c^-3//2*d^-3//2*g^-3//2*(d+e*x)^(1/2)*(a*e+c*d*x)^(1/2)*(c*d*f+-1*a*e*g)^2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*arctanh(c^-1//2*d^-1//2*g^(1/2)*(f+g*x)^-1//2*(a*e+c*d*x)^(1/2)))
@test integrate((d+e*x)^-1//2*(f+g*x)^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2), x) == :(g^-1*(d+e*x)^-1//2*(f+g*x)^(1/2)*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+-1*c^-1//2*d^-1//2*g^-3//2*(d+e*x)^(1/2)*(a*e+c*d*x)^(1/2)*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*(c*d*f+-1*a*e*g)*arctanh(c^-1//2*d^-1//2*g^(1/2)*(f+g*x)^-1//2*(a*e+c*d*x)^(1/2)))
@test integrate((d+e*x)^-1//2*(f+g*x)^-3//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2), x) == :(-2*g^-1*(d+e*x)^-1//2*(f+g*x)^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+2*c^(1/2)*d^(1/2)*g^-3//2*(d+e*x)^(1/2)*(a*e+c*d*x)^(1/2)*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*arctanh(c^-1//2*d^-1//2*g^(1/2)*(f+g*x)^-1//2*(a*e+c*d*x)^(1/2)))
@test integrate((d+e*x)^-1//2*(f+g*x)^-5//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2), x) == :(2*(d+e*x)^-3//2*(f+g*x)^-3//2*(-3*a*e*g+3*c*d*f)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2)
@test integrate((d+e*x)^-1//2*(f+g*x)^-7//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2), x) == :(2*(d+e*x)^-3//2*(f+g*x)^-5//2*(-5*a*e*g+5*c*d*f)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2+4//15*c*d*(d+e*x)^-3//2*(f+g*x)^-3//2*(c*d*f+-1*a*e*g)^-2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2)
@test integrate((d+e*x)^-1//2*(f+g*x)^-9//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2), x) == :(2*(d+e*x)^-3//2*(f+g*x)^-7//2*(-7*a*e*g+7*c*d*f)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2+8//35*c*d*(d+e*x)^-3//2*(f+g*x)^-5//2*(c*d*f+-1*a*e*g)^-2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2+16//105*c^2*d^2*(d+e*x)^-3//2*(f+g*x)^-3//2*(c*d*f+-1*a*e*g)^-3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2)
@test integrate((d+e*x)^-1//2*(f+g*x)^-11//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2), x) == :(2*(d+e*x)^-3//2*(f+g*x)^-9//2*(-9*a*e*g+9*c*d*f)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2+4//21*c*d*(d+e*x)^-3//2*(f+g*x)^-7//2*(c*d*f+-1*a*e*g)^-2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2+16//105*c^2*d^2*(d+e*x)^-3//2*(f+g*x)^-5//2*(c*d*f+-1*a*e*g)^-3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2+32//315*c^3*d^3*(d+e*x)^-3//2*(f+g*x)^-3//2*(c*d*f+-1*a*e*g)^-4*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2)
@test integrate((d+e*x)^-3//2*(f+g*x)^3//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2, x) == :(1//4*g^-1*(d+e*x)^-3//2*(f+g*x)^5//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2+-1//8*g^-2*(d+e*x)^-1//2*(f+g*x)^5//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(c*d*f+-1*a*e*g)+1//32*c^-1*d^-1*g^-2*(d+e*x)^-1//2*(f+g*x)^3//2*(c*d*f+-1*a*e*g)^2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+3//64*c^-2*d^-2*g^-2*(d+e*x)^-1//2*(f+g*x)^(1/2)*(c*d*f+-1*a*e*g)^3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+3//64*c^-5//2*d^-5//2*g^-5//2*(d+e*x)^(1/2)*(a*e+c*d*x)^(1/2)*(c*d*f+-1*a*e*g)^4*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*arctanh(c^-1//2*d^-1//2*g^(1/2)*(f+g*x)^-1//2*(a*e+c*d*x)^(1/2)))
@test integrate((d+e*x)^-3//2*(f+g*x)^(1/2)*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2, x) == :(1//3*g^-1*(d+e*x)^-3//2*(f+g*x)^3//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2+-1//4*g^-2*(d+e*x)^-1//2*(f+g*x)^3//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(c*d*f+-1*a*e*g)+1//8*c^-1*d^-1*g^-2*(d+e*x)^-1//2*(f+g*x)^(1/2)*(c*d*f+-1*a*e*g)^2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+1//8*c^-3//2*d^-3//2*g^-5//2*(d+e*x)^(1/2)*(a*e+c*d*x)^(1/2)*(c*d*f+-1*a*e*g)^3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*arctanh(c^-1//2*d^-1//2*g^(1/2)*(f+g*x)^-1//2*(a*e+c*d*x)^(1/2)))
@test integrate((d+e*x)^-3//2*(f+g*x)^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2, x) == :((1/2)*g^-1*(d+e*x)^-3//2*(f+g*x)^(1/2)*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2+-1//4*g^-2*(d+e*x)^-1//2*(f+g*x)^(1/2)*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(-3*a*e*g+3*c*d*f)+3//4*c^-1//2*d^-1//2*g^-5//2*(d+e*x)^(1/2)*(a*e+c*d*x)^(1/2)*(c*d*f+-1*a*e*g)^2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*arctanh(c^-1//2*d^-1//2*g^(1/2)*(f+g*x)^-1//2*(a*e+c*d*x)^(1/2)))
@test integrate((d+e*x)^-3//2*(f+g*x)^-3//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2, x) == :(-2*g^-1*(d+e*x)^-3//2*(f+g*x)^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2+3*c*d*g^-2*(d+e*x)^-1//2*(f+g*x)^(1/2)*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+-3*c^(1/2)*d^(1/2)*g^-5//2*(d+e*x)^(1/2)*(a*e+c*d*x)^(1/2)*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*(c*d*f+-1*a*e*g)*arctanh(c^-1//2*d^-1//2*g^(1/2)*(f+g*x)^-1//2*(a*e+c*d*x)^(1/2)))
@test integrate((d+e*x)^-3//2*(f+g*x)^-5//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2, x) == :(-2//3*g^-1*(d+e*x)^-3//2*(f+g*x)^-3//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2+-2*c*d*g^-2*(d+e*x)^-1//2*(f+g*x)^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+2*c^3//2*d^3//2*g^-5//2*(d+e*x)^(1/2)*(a*e+c*d*x)^(1/2)*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*arctanh(c^-1//2*d^-1//2*g^(1/2)*(f+g*x)^-1//2*(a*e+c*d*x)^(1/2)))
@test integrate((d+e*x)^-3//2*(f+g*x)^-7//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2, x) == :(2*(d+e*x)^-5//2*(f+g*x)^-5//2*(-5*a*e*g+5*c*d*f)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2)
@test integrate((d+e*x)^-3//2*(f+g*x)^-9//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2, x) == :(2*(d+e*x)^-5//2*(f+g*x)^-7//2*(-7*a*e*g+7*c*d*f)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2+4//35*c*d*(d+e*x)^-5//2*(f+g*x)^-5//2*(c*d*f+-1*a*e*g)^-2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2)
@test integrate((d+e*x)^-3//2*(f+g*x)^-11//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2, x) == :(2*(d+e*x)^-5//2*(f+g*x)^-9//2*(-9*a*e*g+9*c*d*f)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2+8//63*c*d*(d+e*x)^-5//2*(f+g*x)^-7//2*(c*d*f+-1*a*e*g)^-2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2+16//315*c^2*d^2*(d+e*x)^-5//2*(f+g*x)^-5//2*(c*d*f+-1*a*e*g)^-3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2)
@test integrate((d+e*x)^-3//2*(f+g*x)^-13//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2, x) == :(2*(d+e*x)^-5//2*(f+g*x)^-11//2*(-11*a*e*g+11*c*d*f)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2+4//33*c*d*(d+e*x)^-5//2*(f+g*x)^-9//2*(c*d*f+-1*a*e*g)^-2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2+16//231*c^2*d^2*(d+e*x)^-5//2*(f+g*x)^-7//2*(c*d*f+-1*a*e*g)^-3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2+32//1155*c^3*d^3*(d+e*x)^-5//2*(f+g*x)^-5//2*(c*d*f+-1*a*e*g)^-4*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2)
@test integrate((d+e*x)^-5//2*(f+g*x)^3//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2, x) == :(1//5*g^-1*(d+e*x)^-5//2*(f+g*x)^5//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2+-1//8*g^-2*(d+e*x)^-3//2*(f+g*x)^5//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2*(c*d*f+-1*a*e*g)+1//16*g^-3*(d+e*x)^-1//2*(f+g*x)^5//2*(c*d*f+-1*a*e*g)^2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+-3//128*c^-2*d^-2*g^-3*(d+e*x)^-1//2*(f+g*x)^(1/2)*(c*d*f+-1*a*e*g)^4*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+-1//64*c^-1*d^-1*g^-3*(d+e*x)^-1//2*(f+g*x)^3//2*(c*d*f+-1*a*e*g)^3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+-3//128*c^-5//2*d^-5//2*g^-7//2*(d+e*x)^(1/2)*(a*e+c*d*x)^(1/2)*(c*d*f+-1*a*e*g)^5*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*arctanh(c^-1//2*d^-1//2*g^(1/2)*(f+g*x)^-1//2*(a*e+c*d*x)^(1/2)))
@test integrate((d+e*x)^-5//2*(f+g*x)^(1/2)*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2, x) == :(1//4*g^-1*(d+e*x)^-5//2*(f+g*x)^3//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2+-1//24*g^-2*(d+e*x)^-3//2*(f+g*x)^3//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2*(-5*a*e*g+5*c*d*f)+5//32*g^-3*(d+e*x)^-1//2*(f+g*x)^3//2*(c*d*f+-1*a*e*g)^2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+-5//64*c^-1*d^-1*g^-3*(d+e*x)^-1//2*(f+g*x)^(1/2)*(c*d*f+-1*a*e*g)^3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+-5//64*c^-3//2*d^-3//2*g^-7//2*(d+e*x)^(1/2)*(a*e+c*d*x)^(1/2)*(c*d*f+-1*a*e*g)^4*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*arctanh(c^-1//2*d^-1//2*g^(1/2)*(f+g*x)^-1//2*(a*e+c*d*x)^(1/2)))
@test integrate((d+e*x)^-5//2*(f+g*x)^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2, x) == :(1//3*g^-1*(d+e*x)^-5//2*(f+g*x)^(1/2)*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2+-1//12*g^-2*(d+e*x)^-3//2*(f+g*x)^(1/2)*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2*(-5*a*e*g+5*c*d*f)+5//8*g^-3*(d+e*x)^-1//2*(f+g*x)^(1/2)*(c*d*f+-1*a*e*g)^2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+-5//8*c^-1//2*d^-1//2*g^-7//2*(d+e*x)^(1/2)*(a*e+c*d*x)^(1/2)*(c*d*f+-1*a*e*g)^3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*arctanh(c^-1//2*d^-1//2*g^(1/2)*(f+g*x)^-1//2*(a*e+c*d*x)^(1/2)))
@test integrate((d+e*x)^-5//2*(f+g*x)^-3//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2, x) == :(-2*g^-1*(d+e*x)^-5//2*(f+g*x)^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2+5//2*c*d*g^-2*(d+e*x)^-3//2*(f+g*x)^(1/2)*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2+-15//4*c*d*g^-3*(d+e*x)^-1//2*(f+g*x)^(1/2)*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(c*d*f+-1*a*e*g)+15//4*c^(1/2)*d^(1/2)*g^-7//2*(d+e*x)^(1/2)*(a*e+c*d*x)^(1/2)*(c*d*f+-1*a*e*g)^2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*arctanh(c^-1//2*d^-1//2*g^(1/2)*(f+g*x)^-1//2*(a*e+c*d*x)^(1/2)))
@test integrate((d+e*x)^-5//2*(f+g*x)^-5//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2, x) == :(-2//3*g^-1*(d+e*x)^-5//2*(f+g*x)^-3//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2+5*c^2*d^2*g^-3*(d+e*x)^-1//2*(f+g*x)^(1/2)*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+-10//3*c*d*g^-2*(d+e*x)^-3//2*(f+g*x)^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2+-5*c^3//2*d^3//2*g^-7//2*(d+e*x)^(1/2)*(a*e+c*d*x)^(1/2)*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*(c*d*f+-1*a*e*g)*arctanh(c^-1//2*d^-1//2*g^(1/2)*(f+g*x)^-1//2*(a*e+c*d*x)^(1/2)))
@test integrate((d+e*x)^-5//2*(f+g*x)^-7//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2, x) == :(-2//5*g^-1*(d+e*x)^-5//2*(f+g*x)^-5//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2+-2*c^2*d^2*g^-3*(d+e*x)^-1//2*(f+g*x)^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+-2//3*c*d*g^-2*(d+e*x)^-3//2*(f+g*x)^-3//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^3//2+2*c^5//2*d^5//2*g^-7//2*(d+e*x)^(1/2)*(a*e+c*d*x)^(1/2)*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*arctanh(c^-1//2*d^-1//2*g^(1/2)*(f+g*x)^-1//2*(a*e+c*d*x)^(1/2)))
@test integrate((d+e*x)^-5//2*(f+g*x)^-9//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2, x) == :(2*(d+e*x)^-7//2*(f+g*x)^-7//2*(-7*a*e*g+7*c*d*f)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^7//2)
@test integrate((d+e*x)^-5//2*(f+g*x)^-11//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2, x) == :(2*(d+e*x)^-7//2*(f+g*x)^-9//2*(-9*a*e*g+9*c*d*f)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^7//2+4//63*c*d*(d+e*x)^-7//2*(f+g*x)^-7//2*(c*d*f+-1*a*e*g)^-2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^7//2)
@test integrate((d+e*x)^-5//2*(f+g*x)^-13//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2, x) == :(2*(d+e*x)^-7//2*(f+g*x)^-11//2*(-11*a*e*g+11*c*d*f)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^7//2+8//99*c*d*(d+e*x)^-7//2*(f+g*x)^-9//2*(c*d*f+-1*a*e*g)^-2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^7//2+16//693*c^2*d^2*(d+e*x)^-7//2*(f+g*x)^-7//2*(c*d*f+-1*a*e*g)^-3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^7//2)
@test integrate((d+e*x)^-5//2*(f+g*x)^-15//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^5//2, x) == :(2*(d+e*x)^-7//2*(f+g*x)^-13//2*(-13*a*e*g+13*c*d*f)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^7//2+12//143*c*d*(d+e*x)^-7//2*(f+g*x)^-11//2*(c*d*f+-1*a*e*g)^-2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^7//2+16//429*c^2*d^2*(d+e*x)^-7//2*(f+g*x)^-9//2*(c*d*f+-1*a*e*g)^-3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^7//2+32//3003*c^3*d^3*(d+e*x)^-7//2*(f+g*x)^-7//2*(c*d*f+-1*a*e*g)^-4*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^7//2)
@test integrate((d+e*x)^m*(f+g*x)^2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(-1m), x) == :(c^-1*d^-1*(3+-1m)^-1*(d+e*x)^(-1+m)*(f+g*x)^2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1+-1m)+2*g*c^-2*d^-2*e^-1*(2+-1m)^-1*(3+-1m)^-1*(d+e*x)^m*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1+-1m)*(c*d*f+-1*a*e*g)+-1*c^-3*d^-3*e^-1*(1+-1m)^-1*(2+-1m)^-1*(3+-1m)^-1*(d+e*x)^(-1+m)*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1+-1m)*(a*g*e^2+c*d*(d*g*(1+-1m)+-1*e*f*(2+-1m)))*(-2*a*e*g+2*c*d*f))
@test integrate((d+e*x)^m*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(-1m)*(f+g*x), x) == :(g*c^-1*d^-1*e^-1*(2+-1m)^-1*(d+e*x)^m*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1+-1m)+-1*c^-2*d^-2*e^-1*(1+-1m)^-1*(2+-1m)^-1*(d+e*x)^(-1+m)*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1+-1m)*(a*g*e^2+c*d*(d*g*(1+-1m)+-1*e*f*(2+-1m))))
@test integrate((d+e*x)^m*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(-1m), x) == :(c^-1*d^-1*(1+-1m)^-1*(d+e*x)^(-1+m)*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1+-1m))
@test integrate((d+e*x)^m*(a*e+c*d*x)^n*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(-1m), x) == :(c^-1*d^-1*(d+e*x)^(-1+m)*(a*e+c*d*x)^n*(1+n+-1m)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1+-1m))
@test integrate((d+e*x)^m*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(-1m)*(-1*e*g*(a*e^2+c*d^2)+c*e*g*d^2+-1*c*d*g*x*e^2)^(-1+m), x) == :(-1*c^-1*d^-1*e^-2*g^-1*(d+e*x)^m*(-1*a*g*e^3+-1*c*d*g*x*e^2)^m*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(-1m)*log(a*e+c*d*x))
@test integrate((d+e*x)^3//2*(f+g*x)^4*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2, x) == :(-128//3465*c^-5*d^-5*e^-1*(d+e*x)^(1/2)*(c*d*f+-1*a*e*g)^3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(c*d*(e*f+-11*d*g)+10*a*g*e^2)+-1//99*c^-2*d^-2*g^-1*(d+e*x)^-1//2*(f+g*x)^4*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(2*c*d*(e*f+-11*d*g)+20*a*g*e^2)+2//11*e*c^-1*d^-1*g^-1*(d+e*x)^-1//2*(f+g*x)^5*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+-32//1155*c^-4*d^-4*g^-1*(d+e*x)^-1//2*(f+g*x)^2*(c*d*f+-1*a*e*g)^2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(c*d*(e*f+-11*d*g)+10*a*g*e^2)+-1//693*c^-3*d^-3*g^-1*(d+e*x)^-1//2*(f+g*x)^3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(c*d*(e*f+-11*d*g)+10*a*g*e^2)*(-16*a*e*g+16*c*d*f)+128//3465*c^-6*d^-6*e^-1*g^-1*(d+e*x)^-1//2*(c*d*f+-1*a*e*g)^3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(c*d*(e*f+-11*d*g)+10*a*g*e^2)*(-1*c*d*(-1*d*g+3*e*f)+2*a*g*e^2))
@test integrate((d+e*x)^3//2*(f+g*x)^3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2, x) == :(-16//315*c^-4*d^-4*e^-1*(d+e*x)^(1/2)*(c*d*f+-1*a*e*g)^2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(c*d*(e*f+-9*d*g)+8*a*g*e^2)+-1//63*c^-2*d^-2*g^-1*(d+e*x)^-1//2*(f+g*x)^3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(2*c*d*(e*f+-9*d*g)+16*a*g*e^2)+2//9*e*c^-1*d^-1*g^-1*(d+e*x)^-1//2*(f+g*x)^4*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+-1//105*c^-3*d^-3*g^-1*(d+e*x)^-1//2*(f+g*x)^2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(c*d*(e*f+-9*d*g)+8*a*g*e^2)*(-4*a*e*g+4*c*d*f)+16//315*c^-5*d^-5*e^-1*g^-1*(d+e*x)^-1//2*(c*d*f+-1*a*e*g)^2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(c*d*(e*f+-9*d*g)+8*a*g*e^2)*(-1*c*d*(-1*d*g+3*e*f)+2*a*g*e^2))
@test integrate((d+e*x)^3//2*(f+g*x)^2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2, x) == :(-1//35*c^-2*d^-2*g^-1*(d+e*x)^-1//2*(f+g*x)^2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(2*c*d*(e*f+-7*d*g)+12*a*g*e^2)+-1//105*c^-3*d^-3*e^-1*(d+e*x)^(1/2)*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(c*d*(e*f+-7*d*g)+6*a*g*e^2)*(-8*a*e*g+8*c*d*f)+2//7*e*c^-1*d^-1*g^-1*(d+e*x)^-1//2*(f+g*x)^3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+1//105*c^-4*d^-4*e^-1*g^-1*(d+e*x)^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(c*d*(e*f+-7*d*g)+6*a*g*e^2)*(-1*c*d*(-1*d*g+3*e*f)+2*a*g*e^2)*(-8*a*e*g+8*c*d*f))
@test integrate((d+e*x)^3//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2*(f+g*x), x) == :(-1//15*c^-2*d^-2*e^-1*(d+e*x)^(1/2)*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(-2*c*d*(-1*d*g+5*e*f)+8*a*g*e^2)+2//5*g*c^-1*d^-1*e^-1*(d+e*x)^3//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+-1//15*c^-3*d^-3*e^-1*(d+e*x)^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(-4*a*e^2+4*c*d^2)*(-1*c*d*(-1*d*g+5*e*f)+4*a*g*e^2))
@test integrate((d+e*x)^3//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2, x) == :(2//3*c^-1*d^-1*(d+e*x)^(1/2)*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)+1//3*c^-2*d^-2*(d+e*x)^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(-4*a*e^2+4*c*d^2))
@test integrate((d+e*x)^3//2*(f+g*x)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2, x) == :(-1*g^-3//2*(c*d*f+-1*a*e*g)^-1//2*(-2*d*g+2*e*f)*arctan(g^(1/2)*(d+e*x)^-1//2*(c*d*f+-1*a*e*g)^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2))+2*e*c^-1*d^-1*g^-1*(d+e*x)^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2))
@test integrate((d+e*x)^3//2*(f+g*x)^-2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2, x) == :(-1*g^-3//2*(c*d*f+-1*a*e*g)^-3//2*(-1*c*d*(d*g+e*f)+2*a*g*e^2)*arctan(g^(1/2)*(d+e*x)^-1//2*(c*d*f+-1*a*e*g)^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2))+-1*g^-1*(d+e*x)^-1//2*(f+g*x)^-1*(c*d*f+-1*a*e*g)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(e*f+-1*d*g))
@test integrate((d+e*x)^3//2*(f+g*x)^-3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2, x) == :(-1//2*g^-1*(d+e*x)^-1//2*(f+g*x)^-2*(c*d*f+-1*a*e*g)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(e*f+-1*d*g)+-1//4*c*d*g^-3//2*(c*d*f+-1*a*e*g)^-5//2*(-1*c*d*(e*f+3*d*g)+4*a*g*e^2)*arctan(g^(1/2)*(d+e*x)^-1//2*(c*d*f+-1*a*e*g)^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2))+-1//4*g^-1*(d+e*x)^-1//2*(f+g*x)^-1*(c*d*f+-1*a*e*g)^-2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(-1*c*d*(e*f+3*d*g)+4*a*g*e^2))
@test integrate((d+e*x)^3//2*(f+g*x)^-4*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^-1//2, x) == :(-1//3*g^-1*(d+e*x)^-1//2*(f+g*x)^-3*(c*d*f+-1*a*e*g)^-1*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(e*f+-1*d*g)+-1//8*c^2*d^2*g^-3//2*(c*d*f+-1*a*e*g)^-7//2*(-1*c*d*(e*f+5*d*g)+6*a*g*e^2)*arctan(g^(1/2)*(d+e*x)^-1//2*(c*d*f+-1*a*e*g)^-1//2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2))+-1//12*g^-1*(d+e*x)^-1//2*(f+g*x)^-2*(c*d*f+-1*a*e*g)^-2*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(-1*c*d*(e*f+5*d*g)+6*a*g*e^2)+-1//8*c*d*g^-1*(d+e*x)^-1//2*(f+g*x)^-1*(c*d*f+-1*a*e*g)^-3*(x*(a*e^2+c*d^2)+a*d*e+c*d*e*x^2)^(1/2)*(-1*c*d*(e*f+5*d*g)+6*a*g*e^2))
@test integrate((1+d*x)^-1//2*(1+-1*d*x)^-1//2*(a+b*x+c*x^2)^3, x) == :(1//16*d^-7*(5*c^3+16*a^3*d^6+18*a*c^2*d^2+18*c*b^2*d^2+24*a*b^2*d^4+24*c*a^2*d^4)*arcsin(d*x)+-1//6*c^3*d^-2*x^5*(1+-1*d^2*x^2)^(1/2)+-1//15*b*d^-6*(1+-1*d^2*x^2)^(1/2)*(24*c^2+10*b^2*d^2+45*a^2*d^4+60*a*c*d^2)+-1//16*x*d^-6*(1+-1*d^2*x^2)^(1/2)*(5*c^3+18*a*c^2*d^2+18*c*b^2*d^2+24*a*b^2*d^4+24*c*a^2*d^4)+-3//5*b*c^2*d^-2*x^4*(1+-1*d^2*x^2)^(1/2)+-1//15*b*d^-4*x^2*(1+-1*d^2*x^2)^(1/2)*(12*c^2+5*b^2*d^2+30*a*c*d^2)+-1//24*c*d^-4*x^3*(1+-1*d^2*x^2)^(1/2)*(5*c^2+18*b^2*d^2+18*a*c*d^2))
@test integrate((1+d*x)^-1//2*(1+-1*d*x)^-1//2*(a+b*x+c*x^2)^2, x) == :(1//8*d^-5*(3*c^2+4*b^2*d^2+8*a^2*d^4+8*a*c*d^2)*arcsin(d*x)+-2//3*b*d^-4*(1+-1*d^2*x^2)^(1/2)*(2c+3*a*d^2)+-1//4*c^2*d^-2*x^3*(1+-1*d^2*x^2)^(1/2)+-1//8*x*d^-2*(1+-1*d^2*x^2)^(1/2)*(4*b^2+c*(8a+3*c*d^-2))+-2//3*b*c*d^-2*x^2*(1+-1*d^2*x^2)^(1/2))
@test integrate((1+d*x)^-1//2*(1+-1*d*x)^-1//2*(a+b*x+c*x^2), x) == :((1/2)*d^-3*(c+2*a*d^2)*arcsin(d*x)+-1*b*d^-2*(1+-1*d^2*x^2)^(1/2)+-1//2*c*x*d^-2*(1+-1*d^2*x^2)^(1/2))
@test integrate((1+d*x)^-1//2*(1+-1*d*x)^-1//2*(a+b*x+c*x^2)^-1, x) == :(c*2^(1/2)*(b^2+-4*a*c)^-1//2*(2*c^2+-1*b*d^2*(b+(b^2+-4*a*c)^(1/2))+2*a*c*d^2)^-1//2*arctanh((1/2)*2^(1/2)*(1+-1*d^2*x^2)^-1//2*(2*c^2+-1*b*d^2*(b+(b^2+-4*a*c)^(1/2))+2*a*c*d^2)^-1//2*(2c+x*d^2*(b+(b^2+-4*a*c)^(1/2))))+-1*c*2^(1/2)*(b^2+-4*a*c)^-1//2*(2*c^2+-1*b*d^2*(b+-1*(b^2+-4*a*c)^(1/2))+2*a*c*d^2)^-1//2*arctanh((1/2)*2^(1/2)*(1+-1*d^2*x^2)^-1//2*(2*c^2+-1*b*d^2*(b+-1*(b^2+-4*a*c)^(1/2))+2*a*c*d^2)^-1//2*(2c+x*d^2*(b+-1*(b^2+-4*a*c)^(1/2)))))
@test integrate((1+d*x)^-1//2*(1+-1*d*x)^-1//2*(a+b*x+c*x^2)^-2, x) == :(-1*(1+-1*d^2*x^2)^(1/2)*(b^2+-4*a*c)^-1*(-1*(c+a*d^2)^2+b^2*d^2)^-1*(a+b*x+c*x^2)^-1*(b*(b^2*d^2+-1*c*(c+3*a*d^2))+-1*c*x*(2*c^2+-1*b^2*d^2+2*a*c*d^2))+(1/2)*c*2^(1/2)*(b^2+-4*a*c)^-3//2*(-1*(c+a*d^2)^2+b^2*d^2)^-1*(2*c^2+-1*b*d^2*(b+(b^2+-4*a*c)^(1/2))+2*a*c*d^2)^-1//2*(4*c^3+-4*c*d^2*(b^2+-2*a^2*d^2)+-2*a*b^2*d^4+12*a*c^2*d^2+-1*b*d^2*(b+(b^2+-4*a*c)^(1/2))*(c+-1*a*d^2))*arctanh((1/2)*2^(1/2)*(1+-1*d^2*x^2)^-1//2*(2*c^2+-1*b*d^2*(b+(b^2+-4*a*c)^(1/2))+2*a*c*d^2)^-1//2*(2c+x*d^2*(b+(b^2+-4*a*c)^(1/2))))+-1//2*c*2^(1/2)*(b^2+-4*a*c)^-3//2*(-1*(c+a*d^2)^2+b^2*d^2)^-1*(2*c^2+-1*b*d^2*(b+-1*(b^2+-4*a*c)^(1/2))+2*a*c*d^2)^-1//2*(4*c^3+-1*c*d^2*(5*b^2+-1*b*(b^2+-4*a*c)^(1/2)+-8*a^2*d^2)+12*a*c^2*d^2+-1*a*b*d^4*(b+(b^2+-4*a*c)^(1/2)))*arctanh((1/2)*2^(1/2)*(1+-1*d^2*x^2)^-1//2*(2*c^2+-1*b*d^2*(b+-1*(b^2+-4*a*c)^(1/2))+2*a*c*d^2)^-1//2*(2c+x*d^2*(b+-1*(b^2+-4*a*c)^(1/2)))))
@test integrate((1+d*x)^-3//2*(1+-1*d*x)^-3//2*(a+b*x+c*x^2)^3, x) == :(d^-6*(1+-1*d^2*x^2)^-1//2*(b*d^4*(3*a^2+b^2*d^-2+3*c^2*d^-4+6*a*c*d^-2)+x*(c+a*d^2)*(c^2+a^2*d^4+3*b^2*d^2+2*a*c*d^2))+-1//8*d^-7*(15*c^3+24*a*b^2*d^4+24*c*a^2*d^4+36*a*c^2*d^2+36*c*b^2*d^2)*arcsin(d*x)+b*d^-6*(1+-1*d^2*x^2)^(1/2)*(5*c^2+b^2*d^2+6*a*c*d^2)+1//4*c^3*d^-4*x^3*(1+-1*d^2*x^2)^(1/2)+b*c^2*d^-4*x^2*(1+-1*d^2*x^2)^(1/2)+1//8*c*x*d^-6*(1+-1*d^2*x^2)^(1/2)*(7*c^2+12*b^2*d^2+12*a*c*d^2))
@test integrate((1+d*x)^-3//2*(1+-1*d*x)^-3//2*(a+b*x+c*x^2)^2, x) == :(d^-4*(1+-1*d^2*x^2)^-1//2*(x*(c^2+a^2*d^4+b^2*d^2+2*a*c*d^2)+2*b*d^2*(a+c*d^-2))+-1//2*d^-3*(2*b^2+c*(4a+3*c*d^-2))*arcsin(d*x)+(1/2)*x*c^2*d^-4*(1+-1*d^2*x^2)^(1/2)+2*b*c*d^-4*(1+-1*d^2*x^2)^(1/2))
@test integrate((1+d*x)^-3//2*(1+-1*d*x)^-3//2*(a+b*x+c*x^2), x) == :(d^-2*(1+-1*d^2*x^2)^-1//2*(b+x*(c+a*d^2))+-1*c*d^-3*arcsin(d*x))
@test integrate((1+d*x)^-3//2*(1+-1*d*x)^-3//2*(a+b*x+c*x^2)^-1, x) == :(d^2*(1+-1*d^2*x^2)^-1//2*(-1*(c+a*d^2)^2+b^2*d^2)^-1*(b+-1*x*(c+a*d^2))+(1/2)*c*2^(1/2)*(b^2+-4*a*c)^-1//2*(-1*(c+a*d^2)^2+b^2*d^2)^-1*(2*c^2+-1*b*d^2*(b+-1*(b^2+-4*a*c)^(1/2))+2*a*c*d^2)^-1//2*(2*c^2+-1*b*d^2*(b+(b^2+-4*a*c)^(1/2))+2*a*c*d^2)*arctanh((1/2)*2^(1/2)*(1+-1*d^2*x^2)^-1//2*(2*c^2+-1*b*d^2*(b+-1*(b^2+-4*a*c)^(1/2))+2*a*c*d^2)^-1//2*(2c+x*d^2*(b+-1*(b^2+-4*a*c)^(1/2))))+-1//2*c*2^(1/2)*(b^2+-4*a*c)^-1//2*(-1*(c+a*d^2)^2+b^2*d^2)^-1*(2*c^2+-1*b*d^2*(b+(b^2+-4*a*c)^(1/2))+2*a*c*d^2)^-1//2*(2*c^2+-1*b*d^2*(b+-1*(b^2+-4*a*c)^(1/2))+2*a*c*d^2)*arctanh((1/2)*2^(1/2)*(1+-1*d^2*x^2)^-1//2*(2*c^2+-1*b*d^2*(b+(b^2+-4*a*c)^(1/2))+2*a*c*d^2)^-1//2*(2c+x*d^2*(b+(b^2+-4*a*c)^(1/2)))))
@test integrate((1+d*x)^-3//2*(1+-1*d*x)^-3//2*(a+b*x+c*x^2)^-2, x) == :(-1*(1+-1*d^2*x^2)^-1//2*(b^2+-4*a*c)^-1*(-1*(c+a*d^2)^2+b^2*d^2)^-1*(a+b*x+c*x^2)^-1*(b*(b^2*d^2+-1*c*(c+3*a*d^2))+-1*c*x*(2*c^2+-1*b^2*d^2+2*a*c*d^2))+-1*d^2*(1+-1*d^2*x^2)^-1//2*(b^2+-4*a*c)^-1*(c+a*d^2+b*d)^-2*(c+a*d^2+-1*b*d)^-2*(b*(c^3+-11*c*a^2*d^4+-10*a*c^2*d^2+2*c*b^2*d^2+3*a*b^2*d^4)+-1*x*(2*c^4+-1*c*(4*a^3*d^6+6*a*b^2*d^4)+b^2*d^4*(2*b^2+a^2*d^2)+-1*c^2*d^2*(b^2+6*a^2*d^2)))+(1/2)*c*2^(1/2)*(b^2+-4*a*c)^-3//2*(2*c^2+-1*b*d^2*(b+-1*(b^2+-4*a*c)^(1/2))+2*a*c*d^2)^-1//2*(c^2+a^2*d^4+-1*b^2*d^2+2*a*c*d^2)^-2*(4*c^5+-1*c^3*d^2*(9*b^2+-1*b*(b^2+-4*a*c)^(1/2)+-36*a^2*d^2)+24*a*c^4*d^2+b*c*d^4*(2*b^3+2*b^2*(b^2+-4*a*c)^(1/2)+-17*b*a^2*d^2+-11*a^2*d^2*(b^2+-4*a*c)^(1/2))+-2*a*c^2*d^4*(7*b^2+-8*a^2*d^2+5*b*(b^2+-4*a*c)^(1/2))+3*a*b^3*d^6*(b+(b^2+-4*a*c)^(1/2)))*arctanh((1/2)*2^(1/2)*(1+-1*d^2*x^2)^-1//2*(2*c^2+-1*b*d^2*(b+-1*(b^2+-4*a*c)^(1/2))+2*a*c*d^2)^-1//2*(2c+x*d^2*(b+-1*(b^2+-4*a*c)^(1/2))))+(1/2)*c*2^(1/2)*d^-2*(b^2+-4*a*c)^-3//2*(2*c^2+-1*b*d^2*(b+(b^2+-4*a*c)^(1/2))+2*a*c*d^2)^-1//2*(c^2+a^2*d^4+-1*b^2*d^2+2*a*c*d^2)^-2*(-4*c^5*d^2+2*c^3*(-18*a^2*d^6+4*b^2*d^4)+8*c^2*(-2*a^3*d^8+3*a*b^2*d^6)+-24*a*c^4*d^4+-6*a*b^4*d^8+b*d^4*(b+(b^2+-4*a*c)^(1/2))*(c^3+-11*c*a^2*d^4+-10*a*c^2*d^2+2*c*b^2*d^2+3*a*b^2*d^4)+-4*c*b^2*d^6*(b^2+-7*a^2*d^2))*arctanh((1/2)*2^(1/2)*(1+-1*d^2*x^2)^-1//2*(2*c^2+-1*b*d^2*(b+(b^2+-4*a*c)^(1/2))+2*a*c*d^2)^-1//2*(2c+x*d^2*(b+(b^2+-4*a*c)^(1/2)))))
@test integrate((d+e*x)^3*(f+g*x)^n*(a+c*e*x^2+2*c*d*x), x) == :(c*e^4*g^-6*(6+n)^-1*(f+g*x)^(6+n)+e^2*g^-6*(4+n)^-1*(f+g*x)^(4+n)*(c*(9*d^2*g^2+10*e^2*f^2+-20*d*e*f*g)+a*e*g^2)+g^-6*(2+n)^-1*(f+g*x)^(2+n)*(e*f+-1*d*g)^2*(c*(2*d^2*g^2+5*e^2*f^2+-10*d*e*f*g)+3*a*e*g^2)+-1*g^-6*(1+n)^-1*(f+g*x)^(1+n)*(e*f+-1*d*g)^3*(a*g^2+c*f*(e*f+-2*d*g))+-1*e*g^-6*(3+n)^-1*(f+g*x)^(3+n)*(c*(7*d^2*g^2+10*e^2*f^2+-20*d*e*f*g)+3*a*e*g^2)*(e*f+-1*d*g)+-5*c*e^3*g^-6*(5+n)^-1*(f+g*x)^(5+n)*(e*f+-1*d*g))
@test integrate((d+e*x)^2*(f+g*x)^n*(a+c*e*x^2+2*c*d*x), x) == :(c*e^3*g^-5*(5+n)^-1*(f+g*x)^(5+n)+e*g^-5*(3+n)^-1*(f+g*x)^(3+n)*(c*(5*d^2*g^2+6*e^2*f^2+-12*d*e*f*g)+a*e*g^2)+g^-5*(1+n)^-1*(f+g*x)^(1+n)*(e*f+-1*d*g)^2*(a*g^2+c*f*(e*f+-2*d*g))+-1*g^-5*(2+n)^-1*(f+g*x)^(2+n)*(c*(d^2*g^2+2*e^2*f^2+-4*d*e*f*g)+a*e*g^2)*(-2*d*g+2*e*f)+-4*c*e^2*g^-5*(4+n)^-1*(f+g*x)^(4+n)*(e*f+-1*d*g))
@test integrate((f+g*x)^n*(d+e*x)*(a+c*e*x^2+2*c*d*x), x) == :(g^-4*(2+n)^-1*(f+g*x)^(2+n)*(c*(2*d^2*g^2+3*e^2*f^2+-6*d*e*f*g)+a*e*g^2)+c*e^2*g^-4*(4+n)^-1*(f+g*x)^(4+n)+-1*g^-4*(1+n)^-1*(f+g*x)^(1+n)*(a*g^2+c*f*(e*f+-2*d*g))*(e*f+-1*d*g)+-3*c*e*g^-4*(3+n)^-1*(f+g*x)^(3+n)*(e*f+-1*d*g))
@test integrate((f+g*x)^n*(a+c*e*x^2+2*c*d*x), x) == :(g^-3*(1+n)^-1*(f+g*x)^(1+n)*(a*g^2+c*f*(e*f+-2*d*g))+c*e*g^-3*(3+n)^-1*(f+g*x)^(3+n)+-2*c*g^-3*(2+n)^-1*(f+g*x)^(2+n)*(e*f+-1*d*g))
@test integrate((d+e*x)^-1*(f+g*x)^-1*(a+b*x+c*x^2), x) == :(c*x*e^-1*g^-1+e^-2*(e*f+-1*d*g)^-1*(a*e^2+c*d^2+-1*b*d*e)*log(d+e*x)+-1*g^-2*(e*f+-1*d*g)^-1*(a*g^2+c*f^2+-1*b*f*g)*log(f+g*x))
@test integrate((d+e*x)^-1*(f+g*x)^-1*(a+b*x+c*x^2)^2, x) == :(x*e^-3*g^-3*(c^2*(d^2*g^2+e^2*f^2+d*e*f*g)+b^2*e^2*g^2+-2*c*e*g*(b*d*g+b*e*f+-1*a*e*g))+e^-4*(e*f+-1*d*g)^-1*(a*e^2+c*d^2+-1*b*d*e)^2*log(d+e*x)+-1*g^-4*(e*f+-1*d*g)^-1*(a*g^2+c*f^2+-1*b*f*g)^2*log(f+g*x)+1//3*c^2*e^-1*g^-1*x^3+-1//2*c*e^-2*g^-2*x^2*(c*d*g+c*e*f+-2*b*e*g))
@test integrate((d+e*x)^-1*(f+g*x)^-1*(a+b*x+c*x^2)^3, x) == :(e^-6*(e*f+-1*d*g)^-1*(a*e^2+c*d^2+-1*b*d*e)^3*log(d+e*x)+(1/2)*e^-4*g^-4*x^2*(-1*c^3*(d^3*g^3+e^3*f^3+d*g*e^2*f^2+e*f*d^2*g^2)+b^3*e^3*g^3+-3*e*g*c^2*(-1*b*(d^2*g^2+e^2*f^2+d*e*f*g)+a*e*g*(d*g+e*f))+-3*b*c*e^2*g^2*(b*d*g+b*e*f+-2*a*e*g))+-1*x*e^-5*g^-5*(-1*c^3*(d^4*g^4+e^4*f^4+d*g*e^3*f^3+e*f*d^3*g^3+d^2*e^2*f^2*g^2)+b^2*e^3*g^3*(b*d*g+b*e*f+-3*a*e*g)+-3*c*e^2*g^2*(b^2*(d^2*g^2+e^2*f^2+d*e*f*g)+a^2*e^2*g^2+-2*a*b*e*g*(d*g+e*f))+-3*e*g*c^2*(-1*b*(d^3*g^3+e^3*f^3+d*g*e^2*f^2+e*f*d^2*g^2)+a*e*g*(d^2*g^2+e^2*f^2+d*e*f*g)))+-1*g^-6*(e*f+-1*d*g)^-1*(a*g^2+c*f^2+-1*b*f*g)^3*log(f+g*x)+1//5*c^3*e^-1*g^-1*x^5+-1//4*c^2*e^-2*g^-2*x^4*(c*d*g+c*e*f+-3*b*e*g)+1//3*c*e^-3*g^-3*x^3*(c^2*(d^2*g^2+e^2*f^2+d*e*f*g)+3*b^2*e^2*g^2+-3*c*e*g*(b*d*g+b*e*f+-1*a*e*g)))
@test integrate((d+e*x)^-1*(f+g*x)^-1*(a+b*x+c*x^2)^-1, x) == :(e^2*(e*f+-1*d*g)^-1*(a*e^2+c*d^2+-1*b*d*e)^-1*log(d+e*x)+-1*g^2*(e*f+-1*d*g)^-1*(a*g^2+c*f^2+-1*b*f*g)^-1*log(f+g*x)+-1*(c*f^2+-1*g*(b*f+-1*a*g))^-1*(2*a*e^2+2*c*d^2+-2*b*d*e)^-1*(c*d*g+c*e*f+-1*b*e*g)*log(a+b*x+c*x^2)+-1*(b^2+-4*a*c)^-1//2*(c*f^2+-1*g*(b*f+-1*a*g))^-1*(a*e^2+c*d^2+-1*b*d*e)^-1*(-1*c*(b*d*g+b*e*f+2*a*e*g)+e*g*b^2+2*d*f*c^2)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x)))
@test integrate((d+e*x)^-1*(f+g*x)^-1*(a+b*x+c*x^2)^-2, x) == :(e^4*(e*f+-1*d*g)^-1*(a*e^2+c*d^2+-1*b*d*e)^-2*log(d+e*x)+-1*g^4*(e*f+-1*d*g)^-1*(a*g^2+c*f^2+-1*b*f*g)^-2*log(f+g*x)+(b^2+-4*a*c)^-1//2*(c*f^2+-1*g*(b*f+-1*a*g))^-2*(a*e^2+c*d^2+-1*b*d*e)^-2*(-1*c^2*(-1*b*(d^3*g^3+e^3*f^3+5*d*g*e^2*f^2+5*e*f*d^2*g^2)+4*a*d*f*e^2*g^2)+b^2*e^2*g^2*(b*d*g+b*e*f+-2*a*e*g)+-2*d*f*c^3*(d^2*g^2+e^2*f^2+d*e*f*g)+2*c*e*g*(-1*b^2*(d*g+e*f)^2+a^2*e^2*g^2+a*b*e*g*(d*g+e*f)))*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x))+-1*(b^2+-4*a*c)^-1*(c*f^2+-1*g*(b*f+-1*a*g))^-1*(a+b*x+c*x^2)^-1*(a*e^2+c*d^2+-1*b*d*e)^-1*(b*c*(c*d*f+-3*a*e*g)+c*x*(-1*c*(b*d*g+b*e*f+2*a*e*g)+e*g*b^2+2*d*f*c^2)+e*g*b^3+-1*c*b^2*(d*g+e*f)+2*a*c^2*(d*g+e*f))+-1//2*(c*f^2+-1*g*(b*f+-1*a*g))^-2*(a*e^2+c*d^2+-1*b*d*e)^-2*(c*(d^2*g^2+e^2*f^2)+e*g*(-1*b*(d*g+e*f)+2*a*e*g))*(c*d*g+c*e*f+-1*b*e*g)*log(a+b*x+c*x^2)+2*c*(b^2+-4*a*c)^-3//2*(c*f^2+-1*g*(b*f+-1*a*g))^-1*(a*e^2+c*d^2+-1*b*d*e)^-1*(-1*c*(b*d*g+b*e*f+2*a*e*g)+e*g*b^2+2*d*f*c^2)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x)))
@test integrate((d+e*x)^3*(f+g*x)^-1//2*(a+b*x+c*x^2), x) == :(-2*g^-6*(f+g*x)^(1/2)*(e*f+-1*d*g)^3*(a*g^2+c*f^2+-1*b*f*g)+-2//7*e*g^-6*(f+g*x)^7//2*(-1*c*(3*d^2*g^2+10*e^2*f^2+-12*d*e*f*g)+e*g*(-1*a*e*g+-3*b*d*g+4*b*e*f))+-2//9*e^2*g^-6*(f+g*x)^9//2*(-1*b*e*g+-3*c*d*g+5*c*e*f)+1//5*g^-6*(f+g*x)^5//2*(-1*c*(d^2*g^2+10*e^2*f^2+-8*d*e*f*g)+3*e*g*(-1*a*e*g+-1*b*d*g+2*b*e*f))*(-2*d*g+2*e*f)+2//3*g^-6*(f+g*x)^3//2*(e*f+-1*d*g)^2*(-1*g*(-1*b*d*g+-3*a*e*g+4*b*e*f)+c*f*(-2*d*g+5*e*f))+2//11*c*e^3*g^-6*(f+g*x)^11//2)
@test integrate((d+e*x)^2*(f+g*x)^-1//2*(a+b*x+c*x^2), x) == :(-1//5*g^-5*(f+g*x)^5//2*(-2*c*(d^2*g^2+6*e^2*f^2+-6*d*e*f*g)+2*e*g*(-1*a*e*g+-2*b*d*g+3*b*e*f))+2*g^-5*(f+g*x)^(1/2)*(e*f+-1*d*g)^2*(a*g^2+c*f^2+-1*b*f*g)+-2//7*e*g^-5*(f+g*x)^7//2*(-1*b*e*g+-2*c*d*g+4*c*e*f)+-1//3*g^-5*(f+g*x)^3//2*(-1*g*(-1*b*d*g+-2*a*e*g+3*b*e*f)+2*c*f*(-1*d*g+2*e*f))*(-2*d*g+2*e*f)+2//9*c*e^2*g^-5*(f+g*x)^9//2)
@test integrate((f+g*x)^-1//2*(d+e*x)*(a+b*x+c*x^2), x) == :(-1//5*g^-4*(f+g*x)^5//2*(-2*b*e*g+-2*c*d*g+6*c*e*f)+1//3*g^-4*(f+g*x)^3//2*(-2*g*(-1*a*e*g+-1*b*d*g+2*b*e*f)+2*c*f*(-2*d*g+3*e*f))+-1*g^-4*(f+g*x)^(1/2)*(-2*d*g+2*e*f)*(a*g^2+c*f^2+-1*b*f*g)+2//7*c*e*g^-4*(f+g*x)^7//2)
@test integrate((f+g*x)^-1//2*(a+b*x+c*x^2), x) == :(g^-3*(f+g*x)^(1/2)*(2*a*g^2+2*c*f^2+-2*b*f*g)+-1//3*g^-3*(f+g*x)^3//2*(-2*b*g+4*c*f)+2//5*c*g^-3*(f+g*x)^5//2)
@test integrate((d+e*x)^-1*(f+g*x)^-1//2*(a+b*x+c*x^2), x) == :(e^-2*g^-2*(f+g*x)^(1/2)*(-2*c*(d*g+e*f)+2*b*e*g)+-1*e^-5//2*(e*f+-1*d*g)^-1//2*(2*a*e^2+2*c*d^2+-2*b*d*e)*arctanh(e^(1/2)*(f+g*x)^(1/2)*(e*f+-1*d*g)^-1//2)+2//3*c*e^-1*g^-2*(f+g*x)^3//2)
@test integrate((d+e*x)^-2*(f+g*x)^-1//2*(a+b*x+c*x^2), x) == :(e^-5//2*(e*f+-1*d*g)^-3//2*(-1*e*(-1*a*e*g+-1*b*d*g+2*b*e*f)+c*d*(-3*d*g+4*e*f))*arctanh(e^(1/2)*(f+g*x)^(1/2)*(e*f+-1*d*g)^-1//2)+-1*(d+e*x)^-1*(f+g*x)^(1/2)*(e*f+-1*d*g)^-1*(a+d*e^-2*(c*d+-1*b*e))+2*c*e^-2*g^-1*(f+g*x)^(1/2))
@test integrate((d+e*x)^-3*(f+g*x)^-1//2*(a+b*x+c*x^2), x) == :(-1*(d+e*x)^-2*(f+g*x)^(1/2)*(-2*d*g+2*e*f)^-1*(a+d*e^-2*(c*d+-1*b*e))+1//4*e^-5//2*(e*f+-1*d*g)^-5//2*(-1*c*(3*d^2*g^2+8*e^2*f^2+-8*d*e*f*g)+e*g*(-1*b*d*g+-3*a*e*g+4*b*e*f))*arctanh(e^(1/2)*(f+g*x)^(1/2)*(e*f+-1*d*g)^-1//2)+1//4*e^-2*(d+e*x)^-1*(f+g*x)^(1/2)*(e*f+-1*d*g)^-2*(-1*e*(-1*b*d*g+-3*a*e*g+4*b*e*f)+c*d*(-5*d*g+8*e*f)))
@test integrate((d+e*x)^3*(f+g*x)^-3//2*(a+b*x+c*x^2), x) == :(2*g^-6*(f+g*x)^(1/2)*(e*f+-1*d*g)^2*(-1*g*(-1*b*d*g+-3*a*e*g+4*b*e*f)+c*f*(-2*d*g+5*e*f))+2*g^-6*(f+g*x)^-1//2*(e*f+-1*d*g)^3*(a*g^2+c*f^2+-1*b*f*g)+-2//5*e*g^-6*(f+g*x)^5//2*(-1*c*(3*d^2*g^2+10*e^2*f^2+-12*d*e*f*g)+e*g*(-1*a*e*g+-3*b*d*g+4*b*e*f))+-2//7*e^2*g^-6*(f+g*x)^7//2*(-1*b*e*g+-3*c*d*g+5*c*e*f)+1//3*g^-6*(f+g*x)^3//2*(-1*c*(d^2*g^2+10*e^2*f^2+-8*d*e*f*g)+3*e*g*(-1*a*e*g+-1*b*d*g+2*b*e*f))*(-2*d*g+2*e*f)+2//9*c*e^3*g^-6*(f+g*x)^9//2)
@test integrate((d+e*x)^2*(f+g*x)^-3//2*(a+b*x+c*x^2), x) == :(-1//3*g^-5*(f+g*x)^3//2*(-2*c*(d^2*g^2+6*e^2*f^2+-6*d*e*f*g)+2*e*g*(-1*a*e*g+-2*b*d*g+3*b*e*f))+-1*g^-5*(f+g*x)^(1/2)*(-1*g*(-1*b*d*g+-2*a*e*g+3*b*e*f)+2*c*f*(-1*d*g+2*e*f))*(-2*d*g+2*e*f)+-2*g^-5*(f+g*x)^-1//2*(e*f+-1*d*g)^2*(a*g^2+c*f^2+-1*b*f*g)+-2//5*e*g^-5*(f+g*x)^5//2*(-1*b*e*g+-2*c*d*g+4*c*e*f)+2//7*c*e^2*g^-5*(f+g*x)^7//2)
@test integrate((f+g*x)^-3//2*(d+e*x)*(a+b*x+c*x^2), x) == :(g^-4*(f+g*x)^(1/2)*(-2*g*(-1*a*e*g+-1*b*d*g+2*b*e*f)+2*c*f*(-2*d*g+3*e*f))+-1//3*g^-4*(f+g*x)^3//2*(-2*b*e*g+-2*c*d*g+6*c*e*f)+g^-4*(f+g*x)^-1//2*(-2*d*g+2*e*f)*(a*g^2+c*f^2+-1*b*f*g)+2//5*c*e*g^-4*(f+g*x)^5//2)
@test integrate((f+g*x)^-3//2*(a+b*x+c*x^2), x) == :(-1*g^-3*(f+g*x)^(1/2)*(-2*b*g+4*c*f)+-1*g^-3*(f+g*x)^-1//2*(2*a*g^2+2*c*f^2+-2*b*f*g)+2//3*c*g^-3*(f+g*x)^3//2)
@test integrate((d+e*x)^-1*(f+g*x)^-3//2*(a+b*x+c*x^2), x) == :(g^-2*(f+g*x)^-1//2*(e*f+-1*d*g)^-1*(2*a*g^2+2*c*f^2+-2*b*f*g)+-1*e^-3//2*(e*f+-1*d*g)^-3//2*(2*a*e^2+2*c*d^2+-2*b*d*e)*arctanh(e^(1/2)*(f+g*x)^(1/2)*(e*f+-1*d*g)^-1//2)+2*c*e^-1*g^-2*(f+g*x)^(1/2))
@test integrate((d+e*x)^-2*(f+g*x)^-3//2*(a+b*x+c*x^2), x) == :(e^-3//2*(e*f+-1*d*g)^-5//2*(-1*e*(b*d*g+-3*a*e*g+2*b*e*f)+c*d*(-1*d*g+4*e*f))*arctanh(e^(1/2)*(f+g*x)^(1/2)*(e*f+-1*d*g)^-1//2)+-1*g^-1*(f+g*x)^-1//2*(e*f+-1*d*g)^-2*(2*a*g^2+2*c*f^2+-2*b*f*g)+-1*e^-1*(d+e*x)^-1*(f+g*x)^(1/2)*(e*f+-1*d*g)^-2*(a*e^2+c*d^2+-1*b*d*e))
@test integrate((d+e*x)^-3*(f+g*x)^-3//2*(a+b*x+c*x^2), x) == :((f+g*x)^-1//2*(e*f+-1*d*g)^-3*(2*a*g^2+2*c*f^2+-2*b*f*g)+-1//4*e^-3//2*(e*f+-1*d*g)^-7//2*(c*(-1*d^2*g^2+8*e^2*f^2+8*d*e*f*g)+3*e*g*(-1*b*(d*g+4*e*f)+5*a*e*g))*arctanh(e^(1/2)*(f+g*x)^(1/2)*(e*f+-1*d*g)^-1//2)+-1//2*e^-1*(d+e*x)^-2*(f+g*x)^(1/2)*(e*f+-1*d*g)^-2*(a*e^2+c*d^2+-1*b*d*e)+1//4*e^-1*(d+e*x)^-1*(f+g*x)^(1/2)*(e*f+-1*d*g)^-3*(-1*e*(-7*a*e*g+3*b*d*g+4*b*e*f)+c*d*(-1*d*g+8*e*f)))
@test integrate((1+x)^(1/2)*(-1+x)^(1/2)*(1+x+-1*x^2)^-1, x) == :(-1*arccosh(x)+(-2//5+2//5*5^(1/2))^(1/2)*arctan((1+x)^(1/2)*(-1+x)^-1//2*(-2+5^(1/2))^-1//2)+(2//5+2//5*5^(1/2))^(1/2)*arctanh((1+x)^(1/2)*(-1+x)^-1//2*(2+5^(1/2))^-1//2))
@test integrate((d+e*x)^-1//2*(f+g*x)^-1//2*(a+b*x+c*x^2), x) == :(1//4*e^-5//2*g^-5//2*(c*(3*d^2*g^2+3*e^2*f^2+2*d*e*f*g)+4*e*g*(-1*b*(d*g+e*f)+2*a*e*g))*arctanh(e^-1//2*g^(1/2)*(d+e*x)^(1/2)*(f+g*x)^-1//2)+(1/2)*c*e^-2*g^-1*(d+e*x)^3//2*(f+g*x)^(1/2)+-1//4*e^-2*g^-2*(d+e*x)^(1/2)*(f+g*x)^(1/2)*(-4*b*e*g+3*c*e*f+5*c*d*g))
@test integrate((d+e*x)^3//2*(f+g*x)^-1//2*(a+b*x+c*x^2), x) == :(-1//24*e^-2*g^-2*(d+e*x)^5//2*(f+g*x)^(1/2)*(-8*b*e*g+7*c*e*f+9*c*d*g)+1//4*c*e^-2*g^-1*(d+e*x)^7//2*(f+g*x)^(1/2)+1//64*e^-5//2*g^-9//2*(e*f+-1*d*g)^2*(c*(3*d^2*g^2+35*e^2*f^2+10*d*e*f*g)+8*e*g*(-1*b*(d*g+5*e*f)+6*a*e*g))*arctanh(e^-1//2*g^(1/2)*(d+e*x)^(1/2)*(f+g*x)^-1//2)+1//96*e^-2*g^-3*(d+e*x)^3//2*(f+g*x)^(1/2)*(c*(3*d^2*g^2+35*e^2*f^2+10*d*e*f*g)+8*e*g*(-1*b*(d*g+5*e*f)+6*a*e*g))+-1//64*e^-2*g^-4*(d+e*x)^(1/2)*(f+g*x)^(1/2)*(c*(3*d^2*g^2+35*e^2*f^2+10*d*e*f*g)+8*e*g*(-1*b*(d*g+5*e*f)+6*a*e*g))*(e*f+-1*d*g))
@test integrate((d+e*x)^(1/2)*(f+g*x)^-1//2*(a+b*x+c*x^2), x) == :(-1//8*e^-5//2*g^-7//2*(c*(d^2*g^2+5*e^2*f^2+2*d*e*f*g)+2*e*g*(-1*b*(d*g+3*e*f)+4*a*e*g))*(e*f+-1*d*g)*arctanh(e^-1//2*g^(1/2)*(d+e*x)^(1/2)*(f+g*x)^-1//2)+-1//12*e^-2*g^-2*(d+e*x)^3//2*(f+g*x)^(1/2)*(-6*b*e*g+5*c*e*f+7*c*d*g)+1//3*c*e^-2*g^-1*(d+e*x)^5//2*(f+g*x)^(1/2)+1//8*e^-2*g^-3*(d+e*x)^(1/2)*(f+g*x)^(1/2)*(c*(d^2*g^2+5*e^2*f^2+2*d*e*f*g)+2*e*g*(-1*b*(d*g+3*e*f)+4*a*e*g)))
@test integrate((d+e*x)^-1//2*(f+g*x)^-1//2*(a+b*x+c*x^2), x) == :(1//4*e^-5//2*g^-5//2*(c*(3*d^2*g^2+3*e^2*f^2+2*d*e*f*g)+4*e*g*(-1*b*(d*g+e*f)+2*a*e*g))*arctanh(e^-1//2*g^(1/2)*(d+e*x)^(1/2)*(f+g*x)^-1//2)+(1/2)*c*e^-2*g^-1*(d+e*x)^3//2*(f+g*x)^(1/2)+-1//4*e^-2*g^-2*(d+e*x)^(1/2)*(f+g*x)^(1/2)*(-4*b*e*g+3*c*e*f+5*c*d*g))
@test integrate((d+e*x)^-3//2*(f+g*x)^-1//2*(a+b*x+c*x^2), x) == :(-1*e^-5//2*g^-3//2*(c*e*f+-2*b*e*g+3*c*d*g)*arctanh(e^-1//2*g^(1/2)*(d+e*x)^(1/2)*(f+g*x)^-1//2)+-1*(d+e*x)^-1//2*(f+g*x)^(1/2)*(e*f+-1*d*g)^-1*(2a+2*d*e^-2*(c*d+-1*b*e))+c*e^-2*g^-1*(d+e*x)^(1/2)*(f+g*x)^(1/2))
@test integrate((d+e*x)^-5//2*(f+g*x)^-1//2*(a+b*x+c*x^2), x) == :(-1*(d+e*x)^-3//2*(f+g*x)^(1/2)*(-3*d*g+3*e*f)^-1*(2a+2*d*e^-2*(c*d+-1*b*e))+2*c*e^-5//2*g^-1//2*arctanh(e^-1//2*g^(1/2)*(d+e*x)^(1/2)*(f+g*x)^-1//2)+1//3*e^-2*(d+e*x)^-1//2*(f+g*x)^(1/2)*(e*f+-1*d*g)^-2*(-2*e*(-1*b*d*g+-2*a*e*g+3*b*e*f)+2*c*(-4*g*d^2+6*d*e*f)))
@test integrate((d+e*x)^-7//2*(f+g*x)^-1//2*(a+b*x+c*x^2), x) == :(-1*(d+e*x)^-5//2*(f+g*x)^(1/2)*(-5*d*g+5*e*f)^-1*(2a+2*d*e^-2*(c*d+-1*b*e))+1//15*e^-2*(d+e*x)^-3//2*(f+g*x)^(1/2)*(e*f+-1*d*g)^-2*(-2*e*(-1*b*d*g+-4*a*e*g+5*b*e*f)+4*c*d*(-3*d*g+5*e*f))+1//15*e^-2*(d+e*x)^-1//2*(f+g*x)^(1/2)*(e*f+-1*d*g)^-3*(-2*c*(3*d^2*g^2+15*e^2*f^2+-10*d*e*f*g)+4*e*g*(-1*b*d*g+-4*a*e*g+5*b*e*f)))
@test integrate((d+e*x)^-9//2*(f+g*x)^-1//2*(a+b*x+c*x^2), x) == :(-1*(d+e*x)^-7//2*(f+g*x)^(1/2)*(-7*d*g+7*e*f)^-1*(2a+2*d*e^-2*(c*d+-1*b*e))+1//35*e^-2*(d+e*x)^-5//2*(f+g*x)^(1/2)*(e*f+-1*d*g)^-2*(-2*e*(-1*b*d*g+-6*a*e*g+7*b*e*f)+4*c*d*(-4*d*g+7*e*f))+1//105*e^-2*(d+e*x)^-3//2*(f+g*x)^(1/2)*(e*f+-1*d*g)^-3*(-2*c*(3*d^2*g^2+35*e^2*f^2+-14*d*e*f*g)+8*e*g*(-1*b*d*g+-6*a*e*g+7*b*e*f))+-4//105*g*e^-2*(d+e*x)^-1//2*(f+g*x)^(1/2)*(e*f+-1*d*g)^-4*(-1*c*(3*d^2*g^2+35*e^2*f^2+-14*d*e*f*g)+4*e*g*(-1*b*d*g+-6*a*e*g+7*b*e*f)))
@test integrate((d+e*x)^(1/2)*(e+f*x)^-3//2*(a+b*x+c*x^2), x) == :((d+e*x)^3//2*(e+f*x)^-1//2*(e^2+-1*d*f)^-1*(2a+2*e*f^-2*(c*e+-1*b*f))+-1//4*e^-3//2*f^-7//2*(-1*c*(15*e^4+-1*d^2*f^2+-6*d*f*e^2)+4*e*f*(3*b*e^2+-1*b*d*f+-2*a*e*f))*arctanh(e^-1//2*f^(1/2)*(d+e*x)^(1/2)*(e+f*x)^-1//2)+(1/2)*c*e^-1*f^-2*(d+e*x)^3//2*(e+f*x)^(1/2)+1//4*e^-1*f^-3*(d+e*x)^(1/2)*(e+f*x)^(1/2)*(e^2+-1*d*f)^-1*(-1*c*(15*e^4+-1*d^2*f^2+-6*d*f*e^2)+4*e*f*(3*b*e^2+-1*b*d*f+-2*a*e*f)))
@test integrate((a+b*x)^-1//2*(d+e*x)^3//2*(15*d^2+8*e^2*x^2+20*d*e*x), x) == :(2*e*b^-2*(a+b*x)^3//2*(d+e*x)^5//2+1//3*b^-2*(a+b*x)^(1/2)*(d+e*x)^5//2*(-13*a*e+17*b*d)+1//12*b^-3*(a+b*x)^(1/2)*(d+e*x)^3//2*(35*a^2*e^2+73*b^2*d^2+-90*a*b*d*e)+1//8*b^-4*(a+b*x)^(1/2)*(d+e*x)^(1/2)*(b*d+-1*a*e)*(35*a^2*e^2+73*b^2*d^2+-90*a*b*d*e)+1//8*b^-9//2*e^-1//2*(b*d+-1*a*e)^2*(35*a^2*e^2+73*b^2*d^2+-90*a*b*d*e)*arctanh(b^-1//2*e^(1/2)*(a+b*x)^(1/2)*(d+e*x)^-1//2))
@test integrate((a+b*x)^-1//2*(d+e*x)^(1/2)*(15*d^2+8*e^2*x^2+20*d*e*x), x) == :(b^-3*(a+b*x)^(1/2)*(d+e*x)^(1/2)*(5*a^2*e^2+11*b^2*d^2+-13*a*b*d*e)+b^-2*(a+b*x)^(1/2)*(d+e*x)^3//2*(-6*a*e+8*b*d)+8//3*e*b^-2*(a+b*x)^3//2*(d+e*x)^3//2+b^-7//2*e^-1//2*(b*d+-1*a*e)*(5*a^2*e^2+11*b^2*d^2+-13*a*b*d*e)*arctanh(b^-1//2*e^(1/2)*(a+b*x)^(1/2)*(d+e*x)^-1//2))
@test integrate((a+b*x)^-1//2*(d+e*x)^-1//2*(15*d^2+8*e^2*x^2+20*d*e*x), x) == :(b^-2*(a+b*x)^(1/2)*(d+e*x)^(1/2)*(-10*a*e+14*b*d)+b^-5//2*e^-1//2*(6*a^2*e^2+16*b^2*d^2+-16*a*b*d*e)*arctanh(b^-1//2*e^(1/2)*(a+b*x)^(1/2)*(d+e*x)^-1//2)+4*e*b^-2*(a+b*x)^3//2*(d+e*x)^(1/2))
@test integrate((a+b*x)^-1//2*(d+e*x)^-3//2*(15*d^2+8*e^2*x^2+20*d*e*x), x) == :(8*b^-1*(a+b*x)^(1/2)*(d+e*x)^(1/2)+b^-3//2*e^-1//2*(-8*a*e+16*b*d)*arctanh(b^-1//2*e^(1/2)*(a+b*x)^(1/2)*(d+e*x)^-1//2)+6*d^2*(a+b*x)^(1/2)*(d+e*x)^-1//2*(b*d+-1*a*e)^-1)
@test integrate((a+b*x)^-1//2*(d+e*x)^-5//2*(15*d^2+8*e^2*x^2+20*d*e*x), x) == :(16*b^-1//2*e^-1//2*arctanh(b^-1//2*e^(1/2)*(a+b*x)^(1/2)*(d+e*x)^-1//2)+2*d^2*(a+b*x)^(1/2)*(d+e*x)^-3//2*(b*d+-1*a*e)^-1+4*d*(a+b*x)^(1/2)*(d+e*x)^-1//2*(b*d+-1*a*e)^-2*(-2*a*e+3*b*d))
@test integrate((a+b*x)^-1//2*(d+e*x)^-7//2*(15*d^2+8*e^2*x^2+20*d*e*x), x) == :(6*d^2*(a+b*x)^(1/2)*(d+e*x)^-5//2*(-5*a*e+5*b*d)^-1+1//15*(a+b*x)^(1/2)*(d+e*x)^-1//2*(b*d+-1*a*e)^-3*(240*a^2*e^2+368*b^2*d^2+-560*a*b*d*e)+8//15*d*(a+b*x)^(1/2)*(d+e*x)^-3//2*(b*d+-1*a*e)^-2*(-5*a*e+8*b*d))
@test integrate((a+b*x)^-1//2*(d+e*x)^-9//2*(15*d^2+8*e^2*x^2+20*d*e*x), x) == :(6*d^2*(a+b*x)^(1/2)*(d+e*x)^-7//2*(-7*a*e+7*b*d)^-1+1//105*(a+b*x)^(1/2)*(d+e*x)^-3//2*(b*d+-1*a*e)^-3*(560*a^2*e^2+928*b^2*d^2+-1344*a*b*d*e)+4//35*d*(a+b*x)^(1/2)*(d+e*x)^-5//2*(b*d+-1*a*e)^-2*(-14*a*e+23*b*d)+32//105*b*(a+b*x)^(1/2)*(d+e*x)^-1//2*(b*d+-1*a*e)^-4*(35*a^2*e^2+58*b^2*d^2+-84*a*b*d*e))
@test integrate((d+e*x)^3//2*(f+g*x)^-1//2*(a+b*x+c*x^2)^-1, x) == :(2*c^-1*e^3//2*g^-1//2*arctanh(e^-1//2*g^(1/2)*(d+e*x)^(1/2)*(f+g*x)^-1//2)+-1*c^-1*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*(-1*g*(b+(b^2+-4*a*c)^(1/2))+2*c*f)^-1//2*(-2*(b^2+-4*a*c)^-1//2*(b^2*e^2+2*c^2*d^2+-2*c*e*(a*e+b*d))+2*e*(-1*b*e+2*c*d))*arctanh((d+e*x)^(1/2)*(f+g*x)^-1//2*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*(-1*g*(b+(b^2+-4*a*c)^(1/2))+2*c*f)^(1/2))+-1*c^-1*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*(-1*g*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*f)^-1//2*(2*e*(-1*b*e+2*c*d)+2*(b^2+-4*a*c)^-1//2*(b^2*e^2+2*c^2*d^2+-2*c*e*(a*e+b*d)))*arctanh((d+e*x)^(1/2)*(f+g*x)^-1//2*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*(-1*g*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*f)^(1/2)))
@test integrate((d+e*x)^(1/2)*(f+g*x)^-1//2*(a+b*x+c*x^2)^-1, x) == :(-2*(b^2+-4*a*c)^-1//2*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^(1/2)*(-1*g*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*f)^-1//2*arctanh((d+e*x)^(1/2)*(f+g*x)^-1//2*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*(-1*g*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*f)^(1/2))+2*(b^2+-4*a*c)^-1//2*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^(1/2)*(-1*g*(b+(b^2+-4*a*c)^(1/2))+2*c*f)^-1//2*arctanh((d+e*x)^(1/2)*(f+g*x)^-1//2*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*(-1*g*(b+(b^2+-4*a*c)^(1/2))+2*c*f)^(1/2)))
@test integrate((d+e*x)^-1//2*(f+g*x)^-1//2*(a+b*x+c*x^2)^-1, x) == :(-4*c*(b^2+-4*a*c)^-1//2*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*(-1*g*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*f)^-1//2*arctanh((d+e*x)^(1/2)*(f+g*x)^-1//2*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*(-1*g*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*f)^(1/2))+4*c*(b^2+-4*a*c)^-1//2*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*(-1*g*(b+(b^2+-4*a*c)^(1/2))+2*c*f)^-1//2*arctanh((d+e*x)^(1/2)*(f+g*x)^-1//2*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*(-1*g*(b+(b^2+-4*a*c)^(1/2))+2*c*f)^(1/2)))
@test integrate((d+e*x)^-3//2*(f+g*x)^-1//2*(a+b*x+c*x^2)^-1, x) == :(-8*c^2*(b^2+-4*a*c)^-1//2*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^-3//2*(-1*g*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*f)^-1//2*arctanh((d+e*x)^(1/2)*(f+g*x)^-1//2*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*(-1*g*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*f)^(1/2))+8*c^2*(b^2+-4*a*c)^-1//2*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-3//2*(-1*g*(b+(b^2+-4*a*c)^(1/2))+2*c*f)^-1//2*arctanh((d+e*x)^(1/2)*(f+g*x)^-1//2*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*(-1*g*(b+(b^2+-4*a*c)^(1/2))+2*c*f)^(1/2))+-4*c*e*(d+e*x)^-1//2*(f+g*x)^(1/2)*(b^2+-4*a*c)^-1//2*(e*f+-1*d*g)^-1*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1+4*c*e*(d+e*x)^-1//2*(f+g*x)^(1/2)*(b^2+-4*a*c)^-1//2*(e*f+-1*d*g)^-1*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^-1)
@test integrate((d+e*x)^-1*(f+g*x)^3*(a+b*x+c*x^2)^(1/2), x) == :(e^-5*(e*f+-1*d*g)^3*(a*e^2+c*d^2+-1*b*d*e)^(1/2)*arctanh((1/2)*(a+b*x+c*x^2)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1//2*(b*d+x*(-1*b*e+2*c*d)+-2*a*e))+-1//128*c^-7//2*e^-5*(-1*g*(-1*b^2*e^2+8*c^2*d^2+-4*c*e*(b*d+-1*a*e))*(16*c^2*(d^2*g^2+3*e^2*f^2+-3*d*e*f*g)+5*b^2*e^2*g^2+-4*c*e*g*(a*e*g+-2*b*d*g+6*b*e*f))+4*c*e*(-1*b*e+2*c*d)*(16*c^2*e^2*f^3+-4*c*d*g^2*(a*e*g+-2*b*d*g+6*b*e*f)+5*d*e*b^2*g^3))*arctanh((1/2)*c^-1//2*(a+b*x+c*x^2)^-1//2*(b+2*c*x))+1//64*c^-3*e^-4*(a+b*x+c*x^2)^(1/2)*(64*c^3*(e*f+-1*d*g)^3+5*b^3*e^3*g^3+-4*b*c*e^2*g^2*(a*e*g+-2*b*d*g+6*b*e*f)+2*c*e*g*x*(16*c^2*(d^2*g^2+3*e^2*f^2+-3*d*e*f*g)+5*b^2*e^2*g^2+-4*c*e*g*(a*e*g+-2*b*d*g+6*b*e*f))+16*b*e*g*c^2*(d^2*g^2+3*e^2*f^2+-3*d*e*f*g))+1//4*c^-1*e^-2*g^3*(a+b*x+c*x^2)^3//2*(d+e*x)+1//24*c^-2*e^-2*g^2*(a+b*x+c*x^2)^3//2*(-14*c*d*g+-5*b*e*g+24*c*e*f))
@test integrate((d+e*x)^-1*(f+g*x)^2*(a+b*x+c*x^2)^(1/2), x) == :(e^-4*(e*f+-1*d*g)^2*(a*e^2+c*d^2+-1*b*d*e)^(1/2)*arctanh((1/2)*(a+b*x+c*x^2)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1//2*(b*d+x*(-1*b*e+2*c*d)+-2*a*e))+-1//8*c^-2*e^-3*(a+b*x+c*x^2)^(1/2)*(-8*c^2*(e*f+-1*d*g)^2+b^2*e^2*g^2+-2*b*c*e*g*(-1*d*g+2*e*f)+-2*c*e*g*x*(-1*b*e*g+-2*c*d*g+4*c*e*f))+1//3*c^-1*e^-1*g^2*(a+b*x+c*x^2)^3//2+1//16*c^-5//2*e^-4*(g*(-1*b^2*e^2+8*c^2*d^2+-4*c*e*(b*d+-1*a*e))*(-1*b*e*g+-2*c*d*g+4*c*e*f)+-4*c*e*(-1*b*e+2*c*d)*(-1*b*d*g^2+2*c*e*f^2))*arctanh((1/2)*c^-1//2*(a+b*x+c*x^2)^-1//2*(b+2*c*x)))
@test integrate((d+e*x)^-1*(a+b*x+c*x^2)^(1/2)*(f+g*x), x) == :(e^-3*(a*e^2+c*d^2+-1*b*d*e)^(1/2)*(e*f+-1*d*g)*arctanh((1/2)*(a+b*x+c*x^2)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1//2*(b*d+x*(-1*b*e+2*c*d)+-2*a*e))+-1//8*c^-3//2*e^-3*(g*b^2*e^2+-4*c*e*(a*e*g+b*e*f+-1*b*d*g)+8*d*c^2*(e*f+-1*d*g))*arctanh((1/2)*c^-1//2*(a+b*x+c*x^2)^-1//2*(b+2*c*x))+1//4*c^-1*e^-2*(a+b*x+c*x^2)^(1/2)*(b*e*g+-4*c*d*g+4*c*e*f+2*c*e*g*x))
@test integrate((d+e*x)^-1*(a+b*x+c*x^2)^(1/2), x) == :(e^-1*(a+b*x+c*x^2)^(1/2)+e^-2*(a*e^2+c*d^2+-1*b*d*e)^(1/2)*arctanh((1/2)*(a+b*x+c*x^2)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1//2*(b*d+x*(-1*b*e+2*c*d)+-2*a*e))+-1//2*c^-1//2*e^-2*(-1*b*e+2*c*d)*arctanh((1/2)*c^-1//2*(a+b*x+c*x^2)^-1//2*(b+2*c*x)))
@test integrate((d+e*x)^-1*(f+g*x)^-1*(a+b*x+c*x^2)^(1/2), x) == :(c^(1/2)*e^-1*g^-1*arctanh((1/2)*c^-1//2*(a+b*x+c*x^2)^-1//2*(b+2*c*x))+e^-1*(e*f+-1*d*g)^-1*(a*e^2+c*d^2+-1*b*d*e)^(1/2)*arctanh((1/2)*(a+b*x+c*x^2)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1//2*(b*d+x*(-1*b*e+2*c*d)+-2*a*e))+-1*g^-1*(e*f+-1*d*g)^-1*(a*g^2+c*f^2+-1*b*f*g)^(1/2)*arctanh((1/2)*(a+b*x+c*x^2)^-1//2*(a*g^2+c*f^2+-1*b*f*g)^-1//2*(b*f+x*(-1*b*g+2*c*f)+-2*a*g)))
@test integrate((d+e*x)^-1*(f+g*x)^-2*(a+b*x+c*x^2)^(1/2), x) == :((f+g*x)^-1*(e*f+-1*d*g)^-1*(a+b*x+c*x^2)^(1/2)+(e*f+-1*d*g)^-2*(a*e^2+c*d^2+-1*b*d*e)^(1/2)*arctanh((1/2)*(a+b*x+c*x^2)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1//2*(b*d+x*(-1*b*e+2*c*d)+-2*a*e))+-1*c^(1/2)*g^-1*(e*f+-1*d*g)^-1*arctanh((1/2)*c^-1//2*(a+b*x+c*x^2)^-1//2*(b+2*c*x))+-1//2*c^-1//2*(e*f+-1*d*g)^-2*(-1*b*e+2*c*d)*arctanh((1/2)*c^-1//2*(a+b*x+c*x^2)^-1//2*(b+2*c*x))+(1/2)*g^-1*(e*f+-1*d*g)^-1*(a*g^2+c*f^2+-1*b*f*g)^-1//2*(-1*b*g+2*c*f)*arctanh((1/2)*(a+b*x+c*x^2)^-1//2*(a*g^2+c*f^2+-1*b*f*g)^-1//2*(b*f+x*(-1*b*g+2*c*f)+-2*a*g))+-1*e*g^-1*(e*f+-1*d*g)^-2*(a*g^2+c*f^2+-1*b*f*g)^(1/2)*arctanh((1/2)*(a+b*x+c*x^2)^-1//2*(a*g^2+c*f^2+-1*b*f*g)^-1//2*(b*f+x*(-1*b*g+2*c*f)+-2*a*g))+(1/2)*e*c^-1//2*g^-1*(e*f+-1*d*g)^-2*(-1*b*g+2*c*f)*arctanh((1/2)*c^-1//2*(a+b*x+c*x^2)^-1//2*(b+2*c*x)))
@test integrate((d+e*x)^-1*(f+g*x)^-3*(a+b*x+c*x^2)^(1/2), x) == :(e*(f+g*x)^-1*(e*f+-1*d*g)^-2*(a+b*x+c*x^2)^(1/2)+e*(e*f+-1*d*g)^-3*(a*e^2+c*d^2+-1*b*d*e)^(1/2)*arctanh((1/2)*(a+b*x+c*x^2)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1//2*(b*d+x*(-1*b*e+2*c*d)+-2*a*e))+g*(-8*d*g+8*e*f)^-1*(a*g^2+c*f^2+-1*b*f*g)^-3//2*(b^2+-4*a*c)*arctanh((1/2)*(a+b*x+c*x^2)^-1//2*(a*g^2+c*f^2+-1*b*f*g)^-1//2*(b*f+x*(-1*b*g+2*c*f)+-2*a*g))+-1*e*c^(1/2)*g^-1*(e*f+-1*d*g)^-2*arctanh((1/2)*c^-1//2*(a+b*x+c*x^2)^-1//2*(b+2*c*x))+-1*e^2*g^-1*(e*f+-1*d*g)^-3*(a*g^2+c*f^2+-1*b*f*g)^(1/2)*arctanh((1/2)*(a+b*x+c*x^2)^-1//2*(a*g^2+c*f^2+-1*b*f*g)^-1//2*(b*f+x*(-1*b*g+2*c*f)+-2*a*g))+-1//2*e*c^-1//2*(e*f+-1*d*g)^-3*(-1*b*e+2*c*d)*arctanh((1/2)*c^-1//2*(a+b*x+c*x^2)^-1//2*(b+2*c*x))+(1/2)*e*g^-1*(e*f+-1*d*g)^-2*(a*g^2+c*f^2+-1*b*f*g)^-1//2*(-1*b*g+2*c*f)*arctanh((1/2)*(a+b*x+c*x^2)^-1//2*(a*g^2+c*f^2+-1*b*f*g)^-1//2*(b*f+x*(-1*b*g+2*c*f)+-2*a*g))+(1/2)*c^-1//2*e^2*g^-1*(e*f+-1*d*g)^-3*(-1*b*g+2*c*f)*arctanh((1/2)*c^-1//2*(a+b*x+c*x^2)^-1//2*(b+2*c*x))+-1*g*(f+g*x)^-2*(-4*d*g+4*e*f)^-1*(a+b*x+c*x^2)^(1/2)*(a*g^2+c*f^2+-1*b*f*g)^-1*(b*f+x*(-1*b*g+2*c*f)+-2*a*g))
@test integrate((d+e*x)^-1*(f+g*x)^-4*(a+b*x+c*x^2)^(1/2), x) == :(e^2*(f+g*x)^-1*(e*f+-1*d*g)^-3*(a+b*x+c*x^2)^(1/2)+e^2*(e*f+-1*d*g)^-4*(a*e^2+c*d^2+-1*b*d*e)^(1/2)*arctanh((1/2)*(a+b*x+c*x^2)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1//2*(b*d+x*(-1*b*e+2*c*d)+-2*a*e))+g^2*(f+g*x)^-3*(-3*d*g+3*e*f)^-1*(a+b*x+c*x^2)^3//2*(a*g^2+c*f^2+-1*b*f*g)^-1+-1*c^(1/2)*e^2*g^-1*(e*f+-1*d*g)^-3*arctanh((1/2)*c^-1//2*(a+b*x+c*x^2)^-1//2*(b+2*c*x))+-1*e^3*g^-1*(e*f+-1*d*g)^-4*(a*g^2+c*f^2+-1*b*f*g)^(1/2)*arctanh((1/2)*(a+b*x+c*x^2)^-1//2*(a*g^2+c*f^2+-1*b*f*g)^-1//2*(b*f+x*(-1*b*g+2*c*f)+-2*a*g))+-1//2*c^-1//2*e^2*(e*f+-1*d*g)^-4*(-1*b*e+2*c*d)*arctanh((1/2)*c^-1//2*(a+b*x+c*x^2)^-1//2*(b+2*c*x))+g*(-16*d*g+16*e*f)^-1*(a*g^2+c*f^2+-1*b*f*g)^-5//2*(b^2+-4*a*c)*(-1*b*g+2*c*f)*arctanh((1/2)*(a+b*x+c*x^2)^-1//2*(a*g^2+c*f^2+-1*b*f*g)^-1//2*(b*f+x*(-1*b*g+2*c*f)+-2*a*g))+(1/2)*c^-1//2*e^3*g^-1*(e*f+-1*d*g)^-4*(-1*b*g+2*c*f)*arctanh((1/2)*c^-1//2*(a+b*x+c*x^2)^-1//2*(b+2*c*x))+(1/2)*e^2*g^-1*(e*f+-1*d*g)^-3*(a*g^2+c*f^2+-1*b*f*g)^-1//2*(-1*b*g+2*c*f)*arctanh((1/2)*(a+b*x+c*x^2)^-1//2*(a*g^2+c*f^2+-1*b*f*g)^-1//2*(b*f+x*(-1*b*g+2*c*f)+-2*a*g))+1//8*e*g*(e*f+-1*d*g)^-2*(a*g^2+c*f^2+-1*b*f*g)^-3//2*(b^2+-4*a*c)*arctanh((1/2)*(a+b*x+c*x^2)^-1//2*(a*g^2+c*f^2+-1*b*f*g)^-1//2*(b*f+x*(-1*b*g+2*c*f)+-2*a*g))+-1*g*(f+g*x)^-2*(-8*d*g+8*e*f)^-1*(a+b*x+c*x^2)^(1/2)*(a*g^2+c*f^2+-1*b*f*g)^-2*(-1*b*g+2*c*f)*(b*f+x*(-1*b*g+2*c*f)+-2*a*g)+-1//4*e*g*(f+g*x)^-2*(e*f+-1*d*g)^-2*(a+b*x+c*x^2)^(1/2)*(a*g^2+c*f^2+-1*b*f*g)^-1*(b*f+x*(-1*b*g+2*c*f)+-2*a*g))
@test integrate((d+e*x)^-1*(f+g*x)^3*(a+b*x+c*x^2)^3//2, x) == :(e^-7*(e*f+-1*d*g)^3*(a*e^2+c*d^2+-1*b*d*e)^3//2*arctanh((1/2)*(a+b*x+c*x^2)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1//2*(b*d+x*(-1*b*e+2*c*d)+-2*a*e))+-1//1536*c^-4*e^-6*(a+b*x+c*x^2)^(1/2)*(-1536*c^5*d^2*(e*f+-1*d*g)^3+21*b^5*e^5*g^3+-96*b*c^3*e^2*(2*b*(e*f+-1*d*g)^3+3*a*e*g*(d^2*g^2+3*e^2*f^2+-3*d*e*f*g))+2*c*e*x*(-1*g*(24*c^2*(d^2*g^2+3*e^2*f^2+-3*d*e*f*g)+7*b^2*e^2*g^2+-4*c*e*g*(a*e*g+-3*b*d*g+9*b*e*f))*(-3*b^2*e^2+16*c^2*d^2+12*a*c*e^2+-8*b*c*d*e)+8*c*e*(-1*b*e+2*c*d)*(24*c^2*e^2*f^3+-4*c*d*g^2*(a*e*g+-3*b*d*g+9*b*e*f)+7*d*e*b^2*g^3))+384*e*c^4*(e*f+-1*d*g)^3*(-4*a*e+5*b*d)+-12*c*b^3*e^4*g^2*(-3*b*d*g+8*a*e*g+9*b*e*f)+24*b*g*c^2*e^3*(3*b^2*(d^2*g^2+3*e^2*f^2+-3*d*e*f*g)+2*a^2*e^2*g^2+6*a*b*e*g*(-1*d*g+3*e*f)))+1//192*c^-3*e^-4*(a+b*x+c*x^2)^3//2*(64*c^3*(e*f+-1*d*g)^3+7*b^3*e^3*g^3+-4*b*c*e^2*g^2*(a*e*g+-3*b*d*g+9*b*e*f)+2*c*e*g*x*(24*c^2*(d^2*g^2+3*e^2*f^2+-3*d*e*f*g)+7*b^2*e^2*g^2+-4*c*e*g*(a*e*g+-3*b*d*g+9*b*e*f))+24*b*e*g*c^2*(d^2*g^2+3*e^2*f^2+-3*d*e*f*g))+1//3072*c^-9//2*e^-7*(-1*(-1*g*(24*c^2*(d^2*g^2+3*e^2*f^2+-3*d*e*f*g)+7*b^2*e^2*g^2+-4*c*e*g*(a*e*g+-3*b*d*g+9*b*e*f))*(-3*b^2*e^2+16*c^2*d^2+12*a*c*e^2+-8*b*c*d*e)+8*c*e*(-1*b*e+2*c*d)*(24*c^2*e^2*f^3+-4*c*d*g^2*(a*e*g+-3*b*d*g+9*b*e*f)+7*d*e*b^2*g^3))*(-1*b^2*e^2+8*c^2*d^2+-4*c*e*(b*d+-1*a*e))+4*c*e*(-1*b*e+2*c*d)*(-1*d*g*(-3*e*b^2+-4*a*c*e+8*b*c*d)*(24*c^2*(d^2*g^2+3*e^2*f^2+-3*d*e*f*g)+7*b^2*e^2*g^2+-4*c*e*g*(a*e*g+-3*b*d*g+9*b*e*f))+8*c*e*(b*d+-2*a*e)*(24*c^2*e^2*f^3+-4*c*d*g^2*(a*e*g+-3*b*d*g+9*b*e*f)+7*d*e*b^2*g^3)))*arctanh((1/2)*c^-1//2*(a+b*x+c*x^2)^-1//2*(b+2*c*x))+1//6*c^-1*e^-2*g^3*(a+b*x+c*x^2)^5//2*(d+e*x)+1//60*c^-2*e^-2*g^2*(a+b*x+c*x^2)^5//2*(-22*c*d*g+-7*b*e*g+36*c*e*f))
@test integrate((d+e*x)^-1*(f+g*x)^2*(a+b*x+c*x^2)^3//2, x) == :(e^-6*(e*f+-1*d*g)^2*(a*e^2+c*d^2+-1*b*d*e)^3//2*arctanh((1/2)*(a+b*x+c*x^2)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1//2*(b*d+x*(-1*b*e+2*c*d)+-2*a*e))+-1//48*c^-2*e^-3*(a+b*x+c*x^2)^3//2*(-16*c^2*(e*f+-1*d*g)^2+3*b^2*e^2*g^2+-6*b*c*e*g*(-1*d*g+2*e*f)+-6*c*e*g*x*(-1*b*e*g+-2*c*d*g+4*c*e*f))+-1//256*c^-7//2*e^-6*(3*b^5*e^5*g^2+96*c^3*e^2*(d*b^2*(e*f+-1*d*g)^2+-1*g*a^2*e^2*(-1*d*g+2*e*f)+-2*a*b*e*(e*f+-1*d*g)^2)+256*c^5*d^3*(e*f+-1*d*g)^2+16*b*c^2*e^3*(b^2*(e*f+-1*d*g)^2+3*a^2*e^2*g^2+3*a*b*e*g*(-1*d*g+2*e*f))+-384*d*e*c^4*(e*f+-1*d*g)^2*(b*d+-1*a*e)+-6*c*g*b^3*e^4*(-1*b*d*g+2*b*e*f+4*a*e*g))*arctanh((1/2)*c^-1//2*(a+b*x+c*x^2)^-1//2*(b+2*c*x))+1//5*c^-1*e^-1*g^2*(a+b*x+c*x^2)^5//2+1//128*c^-3*e^-5*(a+b*x+c*x^2)^(1/2)*(3*b^4*e^4*g^2+128*c^4*d^2*(e*f+-1*d*g)^2+-32*e*c^3*(e*f+-1*d*g)^2*(-4*a*e+5*b*d)+2*c*e*x*(g*(-3*b^2*e^2+16*c^2*d^2+-4*c*e*(-3*a*e+2*b*d))*(-1*b*e*g+-2*c*d*g+4*c*e*f)+-8*c*e*(-1*b*e+2*c*d)*(-1*b*d*g^2+2*c*e*f^2))+8*b*c^2*e^2*(2*b*(e*f+-1*d*g)^2+3*a*e*g*(-1*d*g+2*e*f))+-6*c*g*b^2*e^3*(-1*b*d*g+2*a*e*g+2*b*e*f)))
@test integrate((d+e*x)^-1*(a+b*x+c*x^2)^3//2*(f+g*x), x) == :(e^-5*(a*e^2+c*d^2+-1*b*d*e)^3//2*(e*f+-1*d*g)*arctanh((1/2)*(a+b*x+c*x^2)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1//2*(b*d+x*(-1*b*e+2*c*d)+-2*a*e))+-1//64*c^-2*e^-4*(a+b*x+c*x^2)^(1/2)*(-64*c^3*d^2*(e*f+-1*d*g)+3*g*b^3*e^3+-4*b*c*e^2*(-2*b*d*g+2*b*e*f+3*a*e*g)+2*c*e*x*(-4*c*e*(-2*b*d*g+2*b*e*f+3*a*e*g)+3*g*b^2*e^2+16*d*c^2*(e*f+-1*d*g))+16*e*c^2*(e*f+-1*d*g)*(-4*a*e+5*b*d))+1//24*c^-1*e^-2*(a+b*x+c*x^2)^3//2*(-8*c*d*g+3*b*e*g+8*c*e*f+6*c*e*g*x)+1//128*c^-5//2*e^-5*(-128*c^4*d^3*(e*f+-1*d*g)+3*g*b^4*e^4+48*c^2*e^2*(g*a^2*e^2+-1*d*b^2*(e*f+-1*d*g)+2*a*b*e*(e*f+-1*d*g))+-8*c*b^2*e^3*(b*e*f+-1*b*d*g+3*a*e*g)+192*d*e*c^3*(b*d+-1*a*e)*(e*f+-1*d*g))*arctanh((1/2)*c^-1//2*(a+b*x+c*x^2)^-1//2*(b+2*c*x)))
@test integrate((d+e*x)^-1*(a+b*x+c*x^2)^3//2, x) == :(1//3*e^-1*(a+b*x+c*x^2)^3//2+e^-4*(a*e^2+c*d^2+-1*b*d*e)^3//2*arctanh((1/2)*(a+b*x+c*x^2)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1//2*(b*d+x*(-1*b*e+2*c*d)+-2*a*e))+1//8*c^-1*e^-3*(a+b*x+c*x^2)^(1/2)*(b^2*e^2+8*c^2*d^2+-2*c*e*(-4*a*e+5*b*d)+-2*c*e*x*(-1*b*e+2*c*d))+-1//16*c^-3//2*e^-4*(-1*b*e+2*c*d)*(-1*b^2*e^2+8*c^2*d^2+-4*c*e*(-3*a*e+2*b*d))*arctanh((1/2)*c^-1//2*(a+b*x+c*x^2)^-1//2*(b+2*c*x)))
@test integrate((d+e*x)^-1*(f+g*x)^-1*(a+b*x+c*x^2)^3//2, x) == :(e^-3*(e*f+-1*d*g)^-1*(a*e^2+c*d^2+-1*b*d*e)^3//2*arctanh((1/2)*(a+b*x+c*x^2)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1//2*(b*d+x*(-1*b*e+2*c*d)+-2*a*e))+e^-2*(e*f+-1*d*g)^-1*(a+b*x+c*x^2)^(1/2)*(a*e^2+c*d^2+-1*b*d*e)+-1*g^-3*(e*f+-1*d*g)^-1*(a*g^2+c*f^2+-1*b*f*g)^3//2*arctanh((1/2)*(a+b*x+c*x^2)^-1//2*(a*g^2+c*f^2+-1*b*f*g)^-1//2*(b*f+x*(-1*b*g+2*c*f)+-2*a*g))+-1//4*e^-1*g^-2*(e*f+-1*d*g)^-1*(a+b*x+c*x^2)^(1/2)*(-1*g*(-1*b*d*g+-4*a*e*g+5*b*e*f)+4*c*e*f^2+-2*c*g*x*(e*f+-1*d*g))+-1//2*c^-1//2*e^-3*(e*f+-1*d*g)^-1*(-1*b*e+2*c*d)*(a*e^2+c*d^2+-1*b*d*e)*arctanh((1/2)*c^-1//2*(a+b*x+c*x^2)^-1//2*(b+2*c*x))+1//8*c^-1//2*e^-1*g^-3*(e*f+-1*d*g)^-1*(b*g^2*(b*d*g+-4*a*e*g+3*b*e*f)+-4*c*g*(-1*a*g*(-1*d*g+3*e*f)+3*b*e*f^2)+8*e*c^2*f^3)*arctanh((1/2)*c^-1//2*(a+b*x+c*x^2)^-1//2*(b+2*c*x)))
@test integrate((d+e*x)^-1*(f+g*x)^-2*(a+b*x+c*x^2)^3//2, x) == :((f+g*x)^-1*(e*f+-1*d*g)^-1*(a+b*x+c*x^2)^3//2+e^-2*(e*f+-1*d*g)^-2*(a*e^2+c*d^2+-1*b*d*e)^3//2*arctanh((1/2)*(a+b*x+c*x^2)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1//2*(b*d+x*(-1*b*e+2*c*d)+-2*a*e))+1//4*g^-2*(e*f+-1*d*g)^-1*(a+b*x+c*x^2)^(1/2)*(-9*b*g+12*c*f+-6*c*g*x)+(1/2)*g^-3*(e*f+-1*d*g)^-1*(a*g^2+c*f^2+-1*b*f*g)^(1/2)*(-3*b*g+6*c*f)*arctanh((1/2)*(a+b*x+c*x^2)^-1//2*(a*g^2+c*f^2+-1*b*f*g)^-1//2*(b*f+x*(-1*b*g+2*c*f)+-2*a*g))+-1*e*g^-3*(e*f+-1*d*g)^-2*(a*g^2+c*f^2+-1*b*f*g)^3//2*arctanh((1/2)*(a+b*x+c*x^2)^-1//2*(a*g^2+c*f^2+-1*b*f*g)^-1//2*(b*f+x*(-1*b*g+2*c*f)+-2*a*g))+-1//8*c^-1//2*g^-3*(e*f+-1*d*g)^-1*(3*b^2*g^2+24*c^2*f^2+-12*c*g*(-1*a*g+2*b*f))*arctanh((1/2)*c^-1//2*(a+b*x+c*x^2)^-1//2*(b+2*c*x))+1//8*c^-1*e^-1*(e*f+-1*d*g)^-2*(a+b*x+c*x^2)^(1/2)*(b^2*e^2+8*c^2*d^2+-2*c*e*(-4*a*e+5*b*d)+-2*c*e*x*(-1*b*e+2*c*d))+-1//8*e*c^-1*g^-2*(e*f+-1*d*g)^-2*(a+b*x+c*x^2)^(1/2)*(b^2*g^2+8*c^2*f^2+-2*c*g*(-4*a*g+5*b*f)+-2*c*g*x*(-1*b*g+2*c*f))+-1//16*c^-3//2*e^-2*(e*f+-1*d*g)^-2*(-1*b*e+2*c*d)*(-1*b^2*e^2+8*c^2*d^2+-4*c*e*(-3*a*e+2*b*d))*arctanh((1/2)*c^-1//2*(a+b*x+c*x^2)^-1//2*(b+2*c*x))+1//16*e*c^-3//2*g^-3*(e*f+-1*d*g)^-2*(-1*b*g+2*c*f)*(-1*b^2*g^2+8*c^2*f^2+-4*c*g*(-3*a*g+2*b*f))*arctanh((1/2)*c^-1//2*(a+b*x+c*x^2)^-1//2*(b+2*c*x)))
@test integrate((d+e*x)^-1*(f+g*x)^-3*(a+b*x+c*x^2)^3//2, x) == :((f+g*x)^-2*(-2*d*g+2*e*f)^-1*(a+b*x+c*x^2)^3//2+e*(f+g*x)^-1*(e*f+-1*d*g)^-2*(a+b*x+c*x^2)^3//2+e^-1*(e*f+-1*d*g)^-3*(a*e^2+c*d^2+-1*b*d*e)^3//2*arctanh((1/2)*(a+b*x+c*x^2)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1//2*(b*d+x*(-1*b*e+2*c*d)+-2*a*e))+1//8*c^-1*(e*f+-1*d*g)^-3*(a+b*x+c*x^2)^(1/2)*(b^2*e^2+8*c^2*d^2+-2*c*e*(-4*a*e+5*b*d)+-2*c*e*x*(-1*b*e+2*c*d))+-1*e^2*g^-3*(e*f+-1*d*g)^-3*(a*g^2+c*f^2+-1*b*f*g)^3//2*arctanh((1/2)*(a+b*x+c*x^2)^-1//2*(a*g^2+c*f^2+-1*b*f*g)^-1//2*(b*f+x*(-1*b*g+2*c*f)+-2*a*g))+-1//4*g^-2*(f+g*x)^-1*(e*f+-1*d*g)^-1*(a+b*x+c*x^2)^(1/2)*(-3*b*g+12*c*f+6*c*g*x)+-1//8*g^-3*(e*f+-1*d*g)^-1*(a*g^2+c*f^2+-1*b*f*g)^-1//2*(3*b^2*g^2+24*c^2*f^2+-12*c*g*(-1*a*g+2*b*f))*arctanh((1/2)*(a+b*x+c*x^2)^-1//2*(a*g^2+c*f^2+-1*b*f*g)^-1//2*(b*f+x*(-1*b*g+2*c*f)+-2*a*g))+3//2*c^(1/2)*g^-3*(e*f+-1*d*g)^-1*(-1*b*g+2*c*f)*arctanh((1/2)*c^-1//2*(a+b*x+c*x^2)^-1//2*(b+2*c*x))+3//4*e*g^-2*(e*f+-1*d*g)^-2*(a+b*x+c*x^2)^(1/2)*(-3*b*g+4*c*f+-2*c*g*x)+-3//8*e*c^-1//2*g^-3*(e*f+-1*d*g)^-2*(b^2*g^2+8*c^2*f^2+-4*c*g*(-1*a*g+2*b*f))*arctanh((1/2)*c^-1//2*(a+b*x+c*x^2)^-1//2*(b+2*c*x))+-1//8*c^-1*e^2*g^-2*(e*f+-1*d*g)^-3*(a+b*x+c*x^2)^(1/2)*(b^2*g^2+8*c^2*f^2+-2*c*g*(-4*a*g+5*b*f)+-2*c*g*x*(-1*b*g+2*c*f))+-1//16*c^-3//2*e^-1*(e*f+-1*d*g)^-3*(-1*b*e+2*c*d)*(-1*b^2*e^2+8*c^2*d^2+-4*c*e*(-3*a*e+2*b*d))*arctanh((1/2)*c^-1//2*(a+b*x+c*x^2)^-1//2*(b+2*c*x))+3//2*e*g^-3*(e*f+-1*d*g)^-2*(a*g^2+c*f^2+-1*b*f*g)^(1/2)*(-1*b*g+2*c*f)*arctanh((1/2)*(a+b*x+c*x^2)^-1//2*(a*g^2+c*f^2+-1*b*f*g)^-1//2*(b*f+x*(-1*b*g+2*c*f)+-2*a*g))+1//16*c^-3//2*e^2*g^-3*(e*f+-1*d*g)^-3*(-1*b*g+2*c*f)*(-1*b^2*g^2+8*c^2*f^2+-4*c*g*(-3*a*g+2*b*f))*arctanh((1/2)*c^-1//2*(a+b*x+c*x^2)^-1//2*(b+2*c*x)))
@test integrate((d+e*x)^-1*(f+g*x)^-1*(a+b*x+c*x^2)^5//2, x) == :(e^-5*(e*f+-1*d*g)^-1*(a*e^2+c*d^2+-1*b*d*e)^5//2*arctanh((1/2)*(a+b*x+c*x^2)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1//2*(b*d+x*(-1*b*e+2*c*d)+-2*a*e))+-1*g^-5*(e*f+-1*d*g)^-1*(a*g^2+c*f^2+-1*b*f*g)^5//2*arctanh((1/2)*(a+b*x+c*x^2)^-1//2*(a*g^2+c*f^2+-1*b*f*g)^-1//2*(b*f+x*(-1*b*g+2*c*f)+-2*a*g))+1//3*e^-2*(e*f+-1*d*g)^-1*(a+b*x+c*x^2)^3//2*(a*e^2+c*d^2+-1*b*d*e)+-1//24*e^-1*g^-2*(e*f+-1*d*g)^-1*(a+b*x+c*x^2)^3//2*(-1*g*(-8*a*e*g+-3*b*d*g+11*b*e*f)+8*c*e*f^2+-6*c*g*x*(e*f+-1*d*g))+-1//64*c^-1*e^-1*g^-4*(e*f+-1*d*g)^-1*(a+b*x+c*x^2)^(1/2)*(-1*b^2*g^3*(-8*a*e*g+3*b*d*g+5*b*e*f)+4*c*g^2*(16*e*a^2*g^2+22*e*b^2*f^2+-3*a*b*g*(-1*d*g+13*e*f))+64*e*c^3*f^4+-2*c*g*x*(b*g^2*(-8*a*e*g+3*b*d*g+5*b*e*f)+-4*c*g*(-1*a*g*(-3*d*g+7*e*f)+6*b*e*f^2)+16*e*c^2*f^3)+-16*e*g*c^2*f^2*(-8*a*g+9*b*f))+1//8*c^-1*e^-4*(e*f+-1*d*g)^-1*(a+b*x+c*x^2)^(1/2)*(a*e^2+c*d^2+-1*b*d*e)*(b^2*e^2+8*c^2*d^2+-2*c*e*(-4*a*e+5*b*d)+-2*c*e*x*(-1*b*e+2*c*d))+1//128*c^-3//2*e^-1*g^-5*(e*f+-1*d*g)^-1*(-1*b^3*g^4*(-8*a*e*g+3*b*d*g+5*b*e*f)+48*c^2*g^2*(a^2*g^2*(-1*d*g+5*e*f)+5*e*b^2*f^3+-10*a*b*e*g*f^2)+128*e*c^4*f^5+-8*b*c*g^3*(5*e*b^2*f^2+12*e*a^2*g^2+-3*a*b*g*(d*g+5*e*f))+-320*e*g*c^3*f^3*(b*f+-1*a*g))*arctanh((1/2)*c^-1//2*(a+b*x+c*x^2)^-1//2*(b+2*c*x))+-1//16*c^-3//2*e^-5*(e*f+-1*d*g)^-1*(-1*b*e+2*c*d)*(a*e^2+c*d^2+-1*b*d*e)*(-1*b^2*e^2+8*c^2*d^2+-4*c*e*(-3*a*e+2*b*d))*arctanh((1/2)*c^-1//2*(a+b*x+c*x^2)^-1//2*(b+2*c*x)))
@test integrate((d+e*x)^-1*(f+g*x)^4*(a+b*x+c*x^2)^-1//2, x) == :(e^-4*(e*f+-1*d*g)^4*(a*e^2+c*d^2+-1*b*d*e)^-1//2*arctanh((1/2)*(a+b*x+c*x^2)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1//2*(b*d+x*(-1*b*e+2*c*d)+-2*a*e))+-1//16*g*c^-7//2*e^-4*(-16*c^3*(-1*d^3*g^3+4*e^3*f^3+-6*d*g*e^2*f^2+4*e*f*d^2*g^2)+5*b^3*e^3*g^3+8*e*g*c^2*(b*(d^2*g^2+6*e^2*f^2+-4*d*e*f*g)+a*e*g*(-1*d*g+4*e*f))+-6*b*c*e^2*g^2*(-1*b*d*g+2*a*e*g+4*b*e*f))*arctanh((1/2)*c^-1//2*(a+b*x+c*x^2)^-1//2*(b+2*c*x))+1//3*c^-1*e^-3*g^4*(d+e*x)^2*(a+b*x+c*x^2)^(1/2)+1//24*c^-3*e^-3*g^2*(a+b*x+c*x^2)^(1/2)*(4*c^2*(11*d^2*g^2+36*e^2*f^2+-36*d*e*f*g)+15*b^2*e^2*g^2+-4*c*e*g*(-7*b*d*g+4*a*e*g+18*b*e*f))+1//12*c^-2*e^-3*g^3*(a+b*x+c*x^2)^(1/2)*(d+e*x)*(-14*c*d*g+-5*b*e*g+24*c*e*f))
@test integrate((d+e*x)^-1*(f+g*x)^3*(a+b*x+c*x^2)^-1//2, x) == :(e^-3*(e*f+-1*d*g)^3*(a*e^2+c*d^2+-1*b*d*e)^-1//2*arctanh((1/2)*(a+b*x+c*x^2)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1//2*(b*d+x*(-1*b*e+2*c*d)+-2*a*e))+(1/2)*c^-1*e^-2*g^3*(a+b*x+c*x^2)^(1/2)*(d+e*x)+1//8*g*c^-5//2*e^-3*(8*c^2*(d^2*g^2+3*e^2*f^2+-3*d*e*f*g)+3*b^2*e^2*g^2+-4*c*e*g*(a*e*g+-1*b*d*g+3*b*e*f))*arctanh((1/2)*c^-1//2*(a+b*x+c*x^2)^-1//2*(b+2*c*x))+3//4*c^-2*e^-2*g^2*(a+b*x+c*x^2)^(1/2)*(-1*b*e*g+-2*c*d*g+4*c*e*f))
@test integrate((d+e*x)^-1*(f+g*x)^2*(a+b*x+c*x^2)^-1//2, x) == :(c^-1*e^-1*g^2*(a+b*x+c*x^2)^(1/2)+e^-2*(e*f+-1*d*g)^2*(a*e^2+c*d^2+-1*b*d*e)^-1//2*arctanh((1/2)*(a+b*x+c*x^2)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1//2*(b*d+x*(-1*b*e+2*c*d)+-2*a*e))+(1/2)*g*c^-3//2*e^-2*(-1*b*e*g+-2*c*d*g+4*c*e*f)*arctanh((1/2)*c^-1//2*(a+b*x+c*x^2)^-1//2*(b+2*c*x)))
@test integrate((d+e*x)^-1*(a+b*x+c*x^2)^-1//2*(f+g*x), x) == :(g*c^-1//2*e^-1*arctanh((1/2)*c^-1//2*(a+b*x+c*x^2)^-1//2*(b+2*c*x))+e^-1*(a*e^2+c*d^2+-1*b*d*e)^-1//2*(e*f+-1*d*g)*arctanh((1/2)*(a+b*x+c*x^2)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1//2*(b*d+x*(-1*b*e+2*c*d)+-2*a*e)))
@test integrate((d+e*x)^-1*(a+b*x+c*x^2)^-1//2, x) == :((a*e^2+c*d^2+-1*b*d*e)^-1//2*arctanh((1/2)*(a+b*x+c*x^2)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1//2*(b*d+x*(-1*b*e+2*c*d)+-2*a*e)))
@test integrate((d+e*x)^-1*(f+g*x)^-1*(a+b*x+c*x^2)^-1//2, x) == :(e*(e*f+-1*d*g)^-1*(a*e^2+c*d^2+-1*b*d*e)^-1//2*arctanh((1/2)*(a+b*x+c*x^2)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1//2*(b*d+x*(-1*b*e+2*c*d)+-2*a*e))+-1*g*(e*f+-1*d*g)^-1*(a*g^2+c*f^2+-1*b*f*g)^-1//2*arctanh((1/2)*(a+b*x+c*x^2)^-1//2*(a*g^2+c*f^2+-1*b*f*g)^-1//2*(b*f+x*(-1*b*g+2*c*f)+-2*a*g)))
@test integrate((d+e*x)^-1*(f+g*x)^-2*(a+b*x+c*x^2)^-1//2, x) == :(e^2*(e*f+-1*d*g)^-2*(a*e^2+c*d^2+-1*b*d*e)^-1//2*arctanh((1/2)*(a+b*x+c*x^2)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1//2*(b*d+x*(-1*b*e+2*c*d)+-2*a*e))+g^2*(f+g*x)^-1*(e*f+-1*d*g)^-1*(a+b*x+c*x^2)^(1/2)*(a*g^2+c*f^2+-1*b*f*g)^-1+-1*e*g*(e*f+-1*d*g)^-2*(a*g^2+c*f^2+-1*b*f*g)^-1//2*arctanh((1/2)*(a+b*x+c*x^2)^-1//2*(a*g^2+c*f^2+-1*b*f*g)^-1//2*(b*f+x*(-1*b*g+2*c*f)+-2*a*g))+-1*g*(-2*d*g+2*e*f)^-1*(a*g^2+c*f^2+-1*b*f*g)^-3//2*(-1*b*g+2*c*f)*arctanh((1/2)*(a+b*x+c*x^2)^-1//2*(a*g^2+c*f^2+-1*b*f*g)^-1//2*(b*f+x*(-1*b*g+2*c*f)+-2*a*g)))
@test integrate((d+e*x)^-1*(f+g*x)^-3*(a+b*x+c*x^2)^-1//2, x) == :(e^3*(e*f+-1*d*g)^-3*(a*e^2+c*d^2+-1*b*d*e)^-1//2*arctanh((1/2)*(a+b*x+c*x^2)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1//2*(b*d+x*(-1*b*e+2*c*d)+-2*a*e))+g^2*(f+g*x)^-2*(-2*d*g+2*e*f)^-1*(a+b*x+c*x^2)^(1/2)*(a*g^2+c*f^2+-1*b*f*g)^-1+-1*g*e^2*(e*f+-1*d*g)^-3*(a*g^2+c*f^2+-1*b*f*g)^-1//2*arctanh((1/2)*(a+b*x+c*x^2)^-1//2*(a*g^2+c*f^2+-1*b*f*g)^-1//2*(b*f+x*(-1*b*g+2*c*f)+-2*a*g))+-1*g*(-8*d*g+8*e*f)^-1*(a*g^2+c*f^2+-1*b*f*g)^-5//2*(3*b^2*g^2+8*c^2*f^2+-4*c*g*(a*g+2*b*f))*arctanh((1/2)*(a+b*x+c*x^2)^-1//2*(a*g^2+c*f^2+-1*b*f*g)^-1//2*(b*f+x*(-1*b*g+2*c*f)+-2*a*g))+e*g^2*(f+g*x)^-1*(e*f+-1*d*g)^-2*(a+b*x+c*x^2)^(1/2)*(a*g^2+c*f^2+-1*b*f*g)^-1+3*g^2*(f+g*x)^-1*(-4*d*g+4*e*f)^-1*(a+b*x+c*x^2)^(1/2)*(a*g^2+c*f^2+-1*b*f*g)^-2*(-1*b*g+2*c*f)+-1//2*e*g*(e*f+-1*d*g)^-2*(a*g^2+c*f^2+-1*b*f*g)^-3//2*(-1*b*g+2*c*f)*arctanh((1/2)*(a+b*x+c*x^2)^-1//2*(a*g^2+c*f^2+-1*b*f*g)^-1//2*(b*f+x*(-1*b*g+2*c*f)+-2*a*g)))
@test integrate((d+e*x)^-1*(f+g*x)^4*(a+b*x+c*x^2)^-3//2, x) == :(c^-2*e^-1*g^4*(a+b*x+c*x^2)^(1/2)+e^-2*(e*f+-1*d*g)^4*(a*e^2+c*d^2+-1*b*d*e)^-3//2*arctanh((1/2)*(a+b*x+c*x^2)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1//2*(b*d+x*(-1*b*e+2*c*d)+-2*a*e))+(1/2)*c^-5//2*e^-2*g^3*(-3*b*e*g+-2*c*d*g+8*c*e*f)*arctanh((1/2)*c^-1//2*(a+b*x+c*x^2)^-1//2*(b+2*c*x))+-1*c^-2*(b^2+-4*a*c)^-1*(a+b*x+c*x^2)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1*(-2*b^2*(e*a^2*g^4+e*c^2*f^4+4*a*c*d*f*g^3)+2*x*(b^3*g^4*(b*d+-1*a*e)+c^3*f^2*(-1*b*f*(e*f+4*d*g)+4*a*g*(-3*d*g+2*e*f))+2*d*c^4*f^4+2*c^2*g^2*(-1*g*a^2*(-1*d*g+4*e*f)+3*d*b^2*f^2+-3*a*b*f*(e*f+-2*d*g))+-1*b*c*g^3*(-4*a*b*(e*f+-1*d*g)+-3*e*g*a^2+4*d*f*b^2))+2*b*c*(d*c^2*f^4+a^2*g^3*(-3*d*g+4*e*f)+2*a*c*g*f^2*(2*e*f+3*d*g))+4*a*c*(e*a^2*g^4+c^2*f^3*(e*f+-4*d*g)+-2*a*c*f*g^2*(-2*d*g+3*e*f))+2*a*d*b^3*g^4))
@test integrate((d+e*x)^-1*(f+g*x)^3*(a+b*x+c*x^2)^-3//2, x) == :(c^-3//2*e^-1*g^3*arctanh((1/2)*c^-1//2*(a+b*x+c*x^2)^-1//2*(b+2*c*x))+e^-1*(e*f+-1*d*g)^3*(a*e^2+c*d^2+-1*b*d*e)^-3//2*arctanh((1/2)*(a+b*x+c*x^2)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1//2*(b*d+x*(-1*b*e+2*c*d)+-2*a*e))+c^-1*(b^2+-4*a*c)^-1*(a+b*x+c*x^2)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1*(-2*b*(d*c^2*f^3+e*a^2*g^3+3*a*c*f*g*(d*g+e*f))+-2*x*(c*g^2*(-2*e*g*a^2+3*d*f*b^2+-3*a*b*e*f+3*a*b*d*g)+f*c^2*(-1*b*f*(e*f+3*d*g)+6*a*g*(e*f+-1*d*g))+-1*b^2*g^3*(b*d+-1*a*e)+2*d*c^3*f^3)+2*b^2*(a*d*g^3+c*e*f^3)+-4*a*c*(c*f^2*(e*f+-3*d*g)+-1*a*g^2*(-1*d*g+3*e*f))))
@test integrate((d+e*x)^-1*(f+g*x)^2*(a+b*x+c*x^2)^-3//2, x) == :((e*f+-1*d*g)^2*(a*e^2+c*d^2+-1*b*d*e)^-3//2*arctanh((1/2)*(a+b*x+c*x^2)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1//2*(b*d+x*(-1*b*e+2*c*d)+-2*a*e))+(b^2+-4*a*c)^-1*(a+b*x+c*x^2)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1*(-2*b*(a*g*(d*g+2*e*f)+c*d*f^2)+-2*x*(c*(-1*b*f*(e*f+2*d*g)+2*a*g*(-1*d*g+2*e*f))+b*g^2*(b*d+-1*a*e)+2*d*c^2*f^2)+4*a*(a*e*g^2+-1*c*f*(e*f+-2*d*g))+2*e*b^2*f^2))
@test integrate((d+e*x)^-1*(a+b*x+c*x^2)^-3//2*(f+g*x), x) == :(e*(a*e^2+c*d^2+-1*b*d*e)^-3//2*(e*f+-1*d*g)*arctanh((1/2)*(a+b*x+c*x^2)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1//2*(b*d+x*(-1*b*e+2*c*d)+-2*a*e))+-1*(b^2+-4*a*c)^-1*(a+b*x+c*x^2)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1*(-2*e*f*b^2+2*c*x*(-1*b*(d*g+e*f)+2*a*e*g+2*c*d*f)+-4*a*c*d*g+2*a*b*e*g+2*b*c*d*f+4*a*c*e*f))
@test integrate((d+e*x)^-1*(a+b*x+c*x^2)^-3//2, x) == :(e^2*(a*e^2+c*d^2+-1*b*d*e)^-3//2*arctanh((1/2)*(a+b*x+c*x^2)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1//2*(b*d+x*(-1*b*e+2*c*d)+-2*a*e))+-1*(b^2+-4*a*c)^-1*(a+b*x+c*x^2)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1*(-2*e*b^2+2*b*c*d+2*c*x*(-1*b*e+2*c*d)+4*a*c*e))
@test integrate((d+e*x)^-1*(f+g*x)^-1*(a+b*x+c*x^2)^-3//2, x) == :(e^3*(e*f+-1*d*g)^-1*(a*e^2+c*d^2+-1*b*d*e)^-3//2*arctanh((1/2)*(a+b*x+c*x^2)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1//2*(b*d+x*(-1*b*e+2*c*d)+-2*a*e))+-1*g^3*(e*f+-1*d*g)^-1*(a*g^2+c*f^2+-1*b*f*g)^-3//2*arctanh((1/2)*(a+b*x+c*x^2)^-1//2*(a*g^2+c*f^2+-1*b*f*g)^-1//2*(b*f+x*(-1*b*g+2*c*f)+-2*a*g))+-2*e*(b^2+-4*a*c)^-1*(e*f+-1*d*g)^-1*(a+b*x+c*x^2)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1*(-1*e*b^2+b*c*d+c*x*(-1*b*e+2*c*d)+2*a*c*e)+2*g*(b^2+-4*a*c)^-1*(e*f+-1*d*g)^-1*(a+b*x+c*x^2)^-1//2*(a*g^2+c*f^2+-1*b*f*g)^-1*(-1*g*b^2+b*c*f+c*x*(-1*b*g+2*c*f)+2*a*c*g))
@test integrate((d+e*x)^-1*(f+g*x)^-2*(a+b*x+c*x^2)^-3//2, x) == :(e^4*(e*f+-1*d*g)^-2*(a*e^2+c*d^2+-1*b*d*e)^-3//2*arctanh((1/2)*(a+b*x+c*x^2)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1//2*(b*d+x*(-1*b*e+2*c*d)+-2*a*e))+-1*e*g^3*(e*f+-1*d*g)^-2*(a*g^2+c*f^2+-1*b*f*g)^-3//2*arctanh((1/2)*(a+b*x+c*x^2)^-1//2*(a*g^2+c*f^2+-1*b*f*g)^-1//2*(b*f+x*(-1*b*g+2*c*f)+-2*a*g))+-3*g^3*(-2*d*g+2*e*f)^-1*(a*g^2+c*f^2+-1*b*f*g)^-5//2*(-1*b*g+2*c*f)*arctanh((1/2)*(a+b*x+c*x^2)^-1//2*(a*g^2+c*f^2+-1*b*f*g)^-1//2*(b*f+x*(-1*b*g+2*c*f)+-2*a*g))+-2*e^2*(b^2+-4*a*c)^-1*(e*f+-1*d*g)^-2*(a+b*x+c*x^2)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1*(-1*e*b^2+b*c*d+c*x*(-1*b*e+2*c*d)+2*a*c*e)+g^2*(f+g*x)^-1*(b^2+-4*a*c)^-1*(e*f+-1*d*g)^-1*(a+b*x+c*x^2)^(1/2)*(a*g^2+c*f^2+-1*b*f*g)^-2*(3*b^2*g^2+4*c^2*f^2+-4*c*g*(b*f+2*a*g))+2*e*g*(b^2+-4*a*c)^-1*(e*f+-1*d*g)^-2*(a+b*x+c*x^2)^-1//2*(a*g^2+c*f^2+-1*b*f*g)^-1*(-1*g*b^2+b*c*f+c*x*(-1*b*g+2*c*f)+2*a*c*g)+2*g*(f+g*x)^-1*(b^2+-4*a*c)^-1*(e*f+-1*d*g)^-1*(a+b*x+c*x^2)^-1//2*(a*g^2+c*f^2+-1*b*f*g)^-1*(-1*g*b^2+b*c*f+c*x*(-1*b*g+2*c*f)+2*a*c*g))
@test integrate((d+e*x)^-1*(f+g*x)^-3*(a+b*x+c*x^2)^-3//2, x) == :(e^5*(e*f+-1*d*g)^-3*(a*e^2+c*d^2+-1*b*d*e)^-3//2*arctanh((1/2)*(a+b*x+c*x^2)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1//2*(b*d+x*(-1*b*e+2*c*d)+-2*a*e))+-1*e^2*g^3*(e*f+-1*d*g)^-3*(a*g^2+c*f^2+-1*b*f*g)^-3//2*arctanh((1/2)*(a+b*x+c*x^2)^-1//2*(a*g^2+c*f^2+-1*b*f*g)^-1//2*(b*f+x*(-1*b*g+2*c*f)+-2*a*g))+-3*g^3*(-8*d*g+8*e*f)^-1*(a*g^2+c*f^2+-1*b*f*g)^-7//2*(5*b^2*g^2+16*c^2*f^2+-4*c*g*(a*g+4*b*f))*arctanh((1/2)*(a+b*x+c*x^2)^-1//2*(a*g^2+c*f^2+-1*b*f*g)^-1//2*(b*f+x*(-1*b*g+2*c*f)+-2*a*g))+-2*e^3*(b^2+-4*a*c)^-1*(e*f+-1*d*g)^-3*(a+b*x+c*x^2)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1*(-1*e*b^2+b*c*d+c*x*(-1*b*e+2*c*d)+2*a*c*e)+-3//2*e*g^3*(e*f+-1*d*g)^-2*(a*g^2+c*f^2+-1*b*f*g)^-5//2*(-1*b*g+2*c*f)*arctanh((1/2)*(a+b*x+c*x^2)^-1//2*(a*g^2+c*f^2+-1*b*f*g)^-1//2*(b*f+x*(-1*b*g+2*c*f)+-2*a*g))+g^2*(f+g*x)^-2*(2*b^2+-8*a*c)^-1*(e*f+-1*d*g)^-1*(a+b*x+c*x^2)^(1/2)*(a*g^2+c*f^2+-1*b*f*g)^-2*(5*b^2*g^2+8*c^2*f^2+-4*c*g*(2*b*f+3*a*g))+2*g*e^2*(b^2+-4*a*c)^-1*(e*f+-1*d*g)^-3*(a+b*x+c*x^2)^-1//2*(a*g^2+c*f^2+-1*b*f*g)^-1*(-1*g*b^2+b*c*f+c*x*(-1*b*g+2*c*f)+2*a*c*g)+2*g*(f+g*x)^-2*(b^2+-4*a*c)^-1*(e*f+-1*d*g)^-1*(a+b*x+c*x^2)^-1//2*(a*g^2+c*f^2+-1*b*f*g)^-1*(-1*g*b^2+b*c*f+c*x*(-1*b*g+2*c*f)+2*a*c*g)+e*g^2*(f+g*x)^-1*(b^2+-4*a*c)^-1*(e*f+-1*d*g)^-2*(a+b*x+c*x^2)^(1/2)*(a*g^2+c*f^2+-1*b*f*g)^-2*(3*b^2*g^2+4*c^2*f^2+-4*c*g*(b*f+2*a*g))+g^2*(f+g*x)^-1*(4*b^2+-16*a*c)^-1*(e*f+-1*d*g)^-1*(a+b*x+c*x^2)^(1/2)*(a*g^2+c*f^2+-1*b*f*g)^-3*(-1*b*g+2*c*f)*(8*c^2*f^2+15*b^2*g^2+-4*c*g*(2*b*f+13*a*g))+2*e*g*(f+g*x)^-1*(b^2+-4*a*c)^-1*(e*f+-1*d*g)^-2*(a+b*x+c*x^2)^-1//2*(a*g^2+c*f^2+-1*b*f*g)^-1*(-1*g*b^2+b*c*f+c*x*(-1*b*g+2*c*f)+2*a*c*g))
@test integrate((d+e*x)^3*(f+g*x)^(1/2)*(a+b*x+c*x^2)^(1/2), x) == :(2//11*e^-1*(d+e*x)^4*(f+g*x)^(1/2)*(a+b*x+c*x^2)^(1/2)+1//3465*c^-3*g^-4*(f+g*x)^3//2*(a+b*x+c*x^2)^(1/2)*(2*c^3*(-567*d^3*g^3+233*e^3*f^3+-843*d*g*e^2*f^2+1107*e*f*d^2*g^2)+96*b^3*e^3*g^3+-2*e*g*c^2*(-3*b*(24*e^2*f^2+99*d^2*g^2+-88*d*e*f*g)+2*a*e*g*(-231*d*g+74*e*f))+2*b*c*e^2*g^2*(-198*b*d*g+-157*a*e*g+67*b*e*f))+-2//693*e*c^-2*g^-4*(f+g*x)^5//2*(a+b*x+c*x^2)^(1/2)*(c^2*(29*e^2*f^2+81*d^2*g^2+-96*d*e*f*g)+8*b^2*e^2*g^2+c*e*g*(-33*b*d*g+-18*a*e*g+19*b*e*f))+1//3465*c^-4*e^-1*g^-4*(f+g*x)^(1/2)*(a+b*x+c*x^2)^(1/2)*(-2*c^4*(187*e^4*f^4+315*d^4*g^4+-798*e*f*d^3*g^3+-732*d*g*e^3*f^3+1098*d^2*e^2*f^2*g^2)+-128*b^4*e^4*g^4+-6*c^2*e^2*g^2*(3*b^2*(e^2*f^2+44*d^2*g^2+-11*d*e*f*g)+50*a^2*e^2*g^2+-1*a*b*e*g*(-297*d*g+29*e*f))+2*e*g*c^3*(b*(8*e^3*f^3+231*d^3*g^3+-99*e*f*d^2*g^2)+6*a*e*g*(2*e^2*f^2+165*d^2*g^2+-33*d*e*f*g))+-8*c*b^2*e^3*g^3*(-69*a*e*g+-66*b*d*g+7*b*e*f))+2//99*c^-1*e^2*g^-4*(f+g*x)^7//2*(a+b*x+c*x^2)^(1/2)*(b*e*g+c*e*f+-3*c*d*g)+1//3465*2^(1/2)*c^-5*g^-5*(c*(-1*g*(b+(b^2+-4*a*c)^(1/2))+2*c*f)^-1*(f+g*x))^-1//2*(-1*c*(b^2+-4*a*c)^-1*(a+b*x+c*x^2))^(1/2)*(f+g*x)^(1/2)*(b^2+-4*a*c)^(1/2)*(a+b*x+c*x^2)^-1//2*(-1*g*c^4*(b*f*(-462*d^3*g^3+56*e^3*f^3+-264*d*g*e^2*f^2+495*e*f*d^2*g^2)+-18*a*g*(6*e^3*f^3+77*d^3*g^3+-33*d*g*e^2*f^2+88*e*f*d^2*g^2))+-1*c^3*g^2*(b^2*(37*e^3*f^3+462*d^3*g^3+-198*d*g*e^2*f^2+495*e*f*d^2*g^2)+6*a^2*e^2*g^2*(26*e*f+231*d*g)+-9*a*b*e*g*(-319*d^2*g^2+15*e^2*f^2+-110*d*e*f*g))+2*c^5*f^2*(-231*d^3*g^3+64*e^3*f^3+-264*d*g*e^2*f^2+396*e*f*d^2*g^2)+128*b^5*e^3*g^5+b*e*c^2*g^3*(-1*b^2*(-792*d^2*g^2+37*e^2*f^2+-264*d*e*f*g)+771*a^2*e^2*g^2+6*a*b*e*g*(43*e*f+396*d*g))+-8*c*b^3*e^2*g^4*(7*b*e*f+66*b*d*g+87*a*e*g))*Elliptic.E(arcsin((1/2)*2^(1/2)*((b^2+-4*a*c)^-1//2*(b+(b^2+-4*a*c)^(1/2)+2*c*x))^(1/2)),-2*g*(b^2+-4*a*c)^(1/2)*(-1*g*(b+(b^2+-4*a*c)^(1/2))+2*c*f)^-1)+2//3465*2^(1/2)*c^-5*g^-5*(c*(-1*g*(b+(b^2+-4*a*c)^(1/2))+2*c*f)^-1*(f+g*x))^(1/2)*(-1*c*(b^2+-4*a*c)^-1*(a+b*x+c*x^2))^(1/2)*(f+g*x)^-1//2*(b^2+-4*a*c)^(1/2)*(a+b*x+c*x^2)^-1//2*(a*g^2+c*f^2+-1*b*f*g)*(-1*g*c^3*(b*(8*e^3*f^3+231*d^3*g^3+-99*e*f*d^2*g^2)+6*a*e*g*(2*e^2*f^2+165*d^2*g^2+-33*d*e*f*g))+-2*f*c^4*(-231*d^3*g^3+64*e^3*f^3+-264*d*g*e^2*f^2+396*e*f*d^2*g^2)+64*b^4*e^3*g^4+3*e*c^2*g^2*(3*b^2*(e^2*f^2+44*d^2*g^2+-11*d*e*f*g)+50*a^2*e^2*g^2+-1*a*b*e*g*(-297*d*g+29*e*f))+4*c*b^2*e^2*g^3*(-69*a*e*g+-66*b*d*g+7*b*e*f))*Elliptic.F(arcsin((1/2)*2^(1/2)*((b^2+-4*a*c)^-1//2*(b+(b^2+-4*a*c)^(1/2)+2*c*x))^(1/2)),-2*g*(b^2+-4*a*c)^(1/2)*(-1*g*(b+(b^2+-4*a*c)^(1/2))+2*c*f)^-1))
@test integrate((d+e*x)^2*(f+g*x)^(1/2)*(a+b*x+c*x^2)^(1/2), x) == :(2//9*e^-1*(d+e*x)^3*(f+g*x)^(1/2)*(a+b*x+c*x^2)^(1/2)+-1//315*c^-2*g^-3*(f+g*x)^3//2*(a+b*x+c*x^2)^(1/2)*(4*c^2*(8*e^2*f^2+21*d^2*g^2+-24*d*e*f*g)+12*b^2*e^2*g^2+4*c*e*g*(-9*b*d*g+-7*a*e*g+4*b*e*f))+1//315*c^-3*e^-1*g^-3*(f+g*x)^(1/2)*(a+b*x+c*x^2)^(1/2)*(2*c^3*(-35*d^3*g^3+19*e^3*f^3+-57*d*g*e^2*f^2+63*e*f*d^2*g^2)+16*b^3*e^3*g^3+-6*e*c^2*g^2*(b*d*(-7*d*g+2*e*f)+2*a*e*(e*f+-10*d*g))+6*b*c*e^2*g^2*(b*e*f+-9*a*e*g+-8*b*d*g))+2//63*e*c^-1*g^-3*(f+g*x)^5//2*(a+b*x+c*x^2)^(1/2)*(b*e*g+c*e*f+-3*c*d*g)+-2//315*2^(1/2)*c^-4*g^-4*(c*(-1*g*(b+(b^2+-4*a*c)^(1/2))+2*c*f)^-1*(f+g*x))^-1//2*(-1*c*(b^2+-4*a*c)^-1*(a+b*x+c*x^2))^(1/2)*(f+g*x)^(1/2)*(b^2+-4*a*c)^(1/2)*(a+b*x+c*x^2)^-1//2*(g*c^3*(-1*b*f*(4*e^2*f^2+21*d^2*g^2+-15*d*e*f*g)+3*a*g*(-21*d^2*g^2+3*e^2*f^2+-16*d*e*f*g))+c^4*f^2*(8*e^2*f^2+21*d^2*g^2+-24*d*e*f*g)+3*c^2*g^2*(-1*b^2*(e^2*f^2+-7*d^2*g^2+-5*d*e*f*g)+7*a^2*e^2*g^2+a*b*e*g*(5*e*f+29*d*g))+8*b^4*e^2*g^4+-4*c*e*b^2*g^3*(b*e*f+6*b*d*g+9*a*e*g))*Elliptic.E(arcsin((1/2)*2^(1/2)*((b^2+-4*a*c)^-1//2*(b+(b^2+-4*a*c)^(1/2)+2*c*x))^(1/2)),-2*g*(b^2+-4*a*c)^(1/2)*(-1*g*(b+(b^2+-4*a*c)^(1/2))+2*c*f)^-1)+-2//315*2^(1/2)*c^-4*g^-4*(c*(-1*g*(b+(b^2+-4*a*c)^(1/2))+2*c*f)^-1*(f+g*x))^(1/2)*(-1*c*(b^2+-4*a*c)^-1*(a+b*x+c*x^2))^(1/2)*(f+g*x)^-1//2*(b^2+-4*a*c)^(1/2)*(a+b*x+c*x^2)^-1//2*(a*g^2+c*f^2+-1*b*f*g)*(-3*c^2*g^2*(b*d*(-7*d*g+2*e*f)+2*a*e*(e*f+-10*d*g))+-2*f*c^3*(8*e^2*f^2+21*d^2*g^2+-24*d*e*f*g)+8*b^3*e^2*g^3+3*b*c*e*g^2*(b*e*f+-9*a*e*g+-8*b*d*g))*Elliptic.F(arcsin((1/2)*2^(1/2)*((b^2+-4*a*c)^-1//2*(b+(b^2+-4*a*c)^(1/2)+2*c*x))^(1/2)),-2*g*(b^2+-4*a*c)^(1/2)*(-1*g*(b+(b^2+-4*a*c)^(1/2))+2*c*f)^-1))
@test integrate((f+g*x)^(1/2)*(a+b*x+c*x^2)^(1/2)*(d+e*x), x) == :(2//7*e*c^-1*(f+g*x)^(1/2)*(a+b*x+c*x^2)^3//2+-2//105*c^-2*g^-2*(f+g*x)^(1/2)*(a+b*x+c*x^2)^(1/2)*(f*c^2*(-7*d*g+4*e*f)+-1*c*g*(-5*a*e*g+2*b*e*f+7*b*d*g)+4*e*b^2*g^2+-3*c*g*x*(c*e*f+-4*b*e*g+7*c*d*g))+1//105*2^(1/2)*c^-3*g^-3*(c*(-1*g*(b+(b^2+-4*a*c)^(1/2))+2*c*f)^-1*(f+g*x))^-1//2*(-1*c*(b^2+-4*a*c)^-1*(a+b*x+c*x^2))^(1/2)*(f+g*x)^(1/2)*(b^2+-4*a*c)^(1/2)*(a+b*x+c*x^2)^-1//2*((-2*b^2*g^2+8*c^2*f^2+-3*c*g*(b*f+-2*a*g))*(c*e*f+-4*b*e*g+7*c*d*g)+-5*c*g*(-1*b*g+2*c*f)*(-1*e*(a*g+3*b*f)+7*c*d*f))*Elliptic.E(arcsin((1/2)*2^(1/2)*((b^2+-4*a*c)^-1//2*(b+(b^2+-4*a*c)^(1/2)+2*c*x))^(1/2)),-2*g*(b^2+-4*a*c)^(1/2)*(-1*g*(b+(b^2+-4*a*c)^(1/2))+2*c*f)^-1)+2//105*2^(1/2)*c^-3*g^-3*(c*(-1*g*(b+(b^2+-4*a*c)^(1/2))+2*c*f)^-1*(f+g*x))^(1/2)*(-1*c*(b^2+-4*a*c)^-1*(a+b*x+c*x^2))^(1/2)*(f+g*x)^-1//2*(b^2+-4*a*c)^(1/2)*(a+b*x+c*x^2)^-1//2*(a*g^2+c*f^2+-1*b*f*g)*(c*g*(b*e*f+-10*a*e*g+-7*b*d*g)+-2*f*c^2*(-7*d*g+4*e*f)+4*e*b^2*g^2)*Elliptic.F(arcsin((1/2)*2^(1/2)*((b^2+-4*a*c)^-1//2*(b+(b^2+-4*a*c)^(1/2)+2*c*x))^(1/2)),-2*g*(b^2+-4*a*c)^(1/2)*(-1*g*(b+(b^2+-4*a*c)^(1/2))+2*c*f)^-1))
@test integrate((f+g*x)^(1/2)*(a+b*x+c*x^2)^(1/2), x) == :(2//5*g^-1*(f+g*x)^3//2*(a+b*x+c*x^2)^(1/2)+1//15*c^-1*g^-1*(f+g*x)^(1/2)*(a+b*x+c*x^2)^(1/2)*(-4*c*f+2*b*g)+-2//15*2^(1/2)*c^-2*g^-2*(c*(-1*g*(b+(b^2+-4*a*c)^(1/2))+2*c*f)^-1*(f+g*x))^-1//2*(-1*c*(b^2+-4*a*c)^-1*(a+b*x+c*x^2))^(1/2)*(f+g*x)^(1/2)*(b^2+-4*a*c)^(1/2)*(a+b*x+c*x^2)^-1//2*(b^2*g^2+c^2*f^2+-1*c*g*(b*f+3*a*g))*Elliptic.E(arcsin((1/2)*2^(1/2)*((b^2+-4*a*c)^-1//2*(b+(b^2+-4*a*c)^(1/2)+2*c*x))^(1/2)),-2*g*(b^2+-4*a*c)^(1/2)*(-1*g*(b+(b^2+-4*a*c)^(1/2))+2*c*f)^-1)+2//15*2^(1/2)*c^-2*g^-2*(c*(-1*g*(b+(b^2+-4*a*c)^(1/2))+2*c*f)^-1*(f+g*x))^(1/2)*(-1*c*(b^2+-4*a*c)^-1*(a+b*x+c*x^2))^(1/2)*(f+g*x)^-1//2*(b^2+-4*a*c)^(1/2)*(a+b*x+c*x^2)^-1//2*(-1*b*g+2*c*f)*(a*g^2+c*f^2+-1*b*f*g)*Elliptic.F(arcsin((1/2)*2^(1/2)*((b^2+-4*a*c)^-1//2*(b+(b^2+-4*a*c)^(1/2)+2*c*x))^(1/2)),-2*g*(b^2+-4*a*c)^(1/2)*(-1*g*(b+(b^2+-4*a*c)^(1/2))+2*c*f)^-1))
@test integrate((d+e*x)^3*(f+g*x)^-1//2*(a+b*x+c*x^2)^(1/2), x) == :(2//9*g^-1*(d+e*x)^3*(f+g*x)^(1/2)*(a+b*x+c*x^2)^(1/2)+1//315*c^-3*g^-4*(f+g*x)^(1/2)*(a+b*x+c*x^2)^(1/2)*(-2*c^3*(-70*d^3*g^3+152*e^3*f^3+-408*d*g*e^2*f^2+336*e*f*d^2*g^2)+16*b^3*e^3*g^3+-6*e*g*c^2*(-1*b*(8*e^2*f^2+21*d^2*g^2+-24*d*e*f*g)+6*a*e*g*(-5*d*g+2*e*f))+6*b*c*e^2*g^2*(-12*b*d*g+-9*a*e*g+5*b*e*f))+-2//63*c^-1*e^2*g^-4*(f+g*x)^5//2*(a+b*x+c*x^2)^(1/2)*(-1*b*e*g+-6*c*d*g+8*c*e*f)+-2//315*e*c^-2*g^-4*(f+g*x)^3//2*(a+b*x+c*x^2)^(1/2)*(-2*c^2*(42*d^2*g^2+64*e^2*f^2+-111*d*e*f*g)+6*b^2*e^2*g^2+c*e*g*(-27*b*d*g+-14*a*e*g+17*b*e*f))+-1//315*2^(1/2)*c^-4*g^-5*(c*(-1*g*(b+(b^2+-4*a*c)^(1/2))+2*c*f)^-1*(f+g*x))^-1//2*(-1*c*(b^2+-4*a*c)^-1*(a+b*x+c*x^2))^(1/2)*(f+g*x)^(1/2)*(b^2+-4*a*c)^(1/2)*(a+b*x+c*x^2)^-1//2*(-1*g*c^3*(-1*b*(-105*d^3*g^3+40*e^3*f^3+-144*d*g*e^2*f^2+189*e*f*d^2*g^2)+6*a*e*g*(10*e^2*f^2+63*d^2*g^2+-39*d*e*f*g))+-2*f*c^4*(-105*d^3*g^3+64*e^3*f^3+-216*d*g*e^2*f^2+252*e*f*d^2*g^2)+16*b^4*e^3*g^4+3*e*c^2*g^2*(b^2*(7*e^2*f^2+42*d^2*g^2+-27*d*e*f*g)+14*a^2*e^2*g^2+-1*a*b*e*g*(-87*d*g+19*e*f))+8*c*b^2*e^2*g^3*(-9*a*e*g+-9*b*d*g+2*b*e*f))*Elliptic.E(arcsin((1/2)*2^(1/2)*((b^2+-4*a*c)^-1//2*(b+(b^2+-4*a*c)^(1/2)+2*c*x))^(1/2)),-2*g*(b^2+-4*a*c)^(1/2)*(-1*g*(b+(b^2+-4*a*c)^(1/2))+2*c*f)^-1)+-2//315*2^(1/2)*c^-4*g^-5*(c*(-1*g*(b+(b^2+-4*a*c)^(1/2))+2*c*f)^-1*(f+g*x))^(1/2)*(-1*c*(b^2+-4*a*c)^-1*(a+b*x+c*x^2))^(1/2)*(f+g*x)^-1//2*(b^2+-4*a*c)^(1/2)*(a+b*x+c*x^2)^-1//2*(a*g^2+c*f^2+-1*b*f*g)*(2*c^3*(-105*d^3*g^3+64*e^3*f^3+-216*d*g*e^2*f^2+252*e*f*d^2*g^2)+8*b^3*e^3*g^3+-3*e*g*c^2*(-1*b*(8*e^2*f^2+21*d^2*g^2+-24*d*e*f*g)+6*a*e*g*(-5*d*g+2*e*f))+3*b*c*e^2*g^2*(-12*b*d*g+-9*a*e*g+5*b*e*f))*Elliptic.F(arcsin((1/2)*2^(1/2)*((b^2+-4*a*c)^-1//2*(b+(b^2+-4*a*c)^(1/2)+2*c*x))^(1/2)),-2*g*(b^2+-4*a*c)^(1/2)*(-1*g*(b+(b^2+-4*a*c)^(1/2))+2*c*f)^-1))
@test integrate((d+e*x)^2*(f+g*x)^-1//2*(a+b*x+c*x^2)^(1/2), x) == :(2//7*g^-1*(d+e*x)^2*(f+g*x)^(1/2)*(a+b*x+c*x^2)^(1/2)+1//105*c^-2*g^-3*(f+g*x)^(1/2)*(a+b*x+c*x^2)^(1/2)*(4*c^2*(10*d^2*g^2+21*e^2*f^2+-34*d*e*f*g)+-8*b^2*e^2*g^2+-4*c*e*g*(-7*b*d*g+-5*a*e*g+4*b*e*f))+-2//35*e*c^-1*g^-3*(f+g*x)^3//2*(a+b*x+c*x^2)^(1/2)*(-1*b*e*g+-4*c*d*g+6*c*e*f)+1//105*2^(1/2)*c^-3*g^-4*(c*(-1*g*(b+(b^2+-4*a*c)^(1/2))+2*c*f)^-1*(f+g*x))^-1//2*(-1*c*(b^2+-4*a*c)^-1*(a+b*x+c*x^2))^(1/2)*(f+g*x)^(1/2)*(b^2+-4*a*c)^(1/2)*(a+b*x+c*x^2)^-1//2*(-1*g*c^2*(-1*b*(16*e^2*f^2+35*d^2*g^2+-42*d*e*f*g)+2*a*e*g*(-42*d*g+13*e*f))+-2*f*c^3*(24*e^2*f^2+35*d^2*g^2+-56*d*e*f*g)+8*b^3*e^2*g^3+b*c*e*g^2*(-29*a*e*g+-28*b*d*g+9*b*e*f))*Elliptic.E(arcsin((1/2)*2^(1/2)*((b^2+-4*a*c)^-1//2*(b+(b^2+-4*a*c)^(1/2)+2*c*x))^(1/2)),-2*g*(b^2+-4*a*c)^(1/2)*(-1*g*(b+(b^2+-4*a*c)^(1/2))+2*c*f)^-1)+4//105*2^(1/2)*c^-3*g^-4*(c*(-1*g*(b+(b^2+-4*a*c)^(1/2))+2*c*f)^-1*(f+g*x))^(1/2)*(-1*c*(b^2+-4*a*c)^-1*(a+b*x+c*x^2))^(1/2)*(f+g*x)^-1//2*(b^2+-4*a*c)^(1/2)*(a+b*x+c*x^2)^-1//2*(a*g^2+c*f^2+-1*b*f*g)*(c^2*(24*e^2*f^2+35*d^2*g^2+-56*d*e*f*g)+2*b^2*e^2*g^2+c*e*g*(-7*b*d*g+-5*a*e*g+4*b*e*f))*Elliptic.F(arcsin((1/2)*2^(1/2)*((b^2+-4*a*c)^-1//2*(b+(b^2+-4*a*c)^(1/2)+2*c*x))^(1/2)),-2*g*(b^2+-4*a*c)^(1/2)*(-1*g*(b+(b^2+-4*a*c)^(1/2))+2*c*f)^-1))
@test integrate((f+g*x)^-1//2*(a+b*x+c*x^2)^(1/2)*(d+e*x), x) == :(-2//15*c^-1*g^-2*(f+g*x)^(1/2)*(a+b*x+c*x^2)^(1/2)*(-1*b*e*g+-5*c*d*g+4*c*e*f+-3*c*e*g*x)+-1//15*2^(1/2)*c^-2*g^-3*(c*(-1*g*(b+(b^2+-4*a*c)^(1/2))+2*c*f)^-1*(f+g*x))^-1//2*(-1*c*(b^2+-4*a*c)^-1*(a+b*x+c*x^2))^(1/2)*(f+g*x)^(1/2)*(b^2+-4*a*c)^(1/2)*(a+b*x+c*x^2)^-1//2*(c*g*(-6*a*e*g+-5*b*d*g+3*b*e*f)+-2*f*c^2*(-5*d*g+4*e*f)+2*e*b^2*g^2)*Elliptic.E(arcsin((1/2)*2^(1/2)*((b^2+-4*a*c)^-1//2*(b+(b^2+-4*a*c)^(1/2)+2*c*x))^(1/2)),-2*g*(b^2+-4*a*c)^(1/2)*(-1*g*(b+(b^2+-4*a*c)^(1/2))+2*c*f)^-1)+-2//15*2^(1/2)*c^-2*g^-3*(c*(-1*g*(b+(b^2+-4*a*c)^(1/2))+2*c*f)^-1*(f+g*x))^(1/2)*(-1*c*(b^2+-4*a*c)^-1*(a+b*x+c*x^2))^(1/2)*(f+g*x)^-1//2*(b^2+-4*a*c)^(1/2)*(a+b*x+c*x^2)^-1//2*(a*g^2+c*f^2+-1*b*f*g)*(b*e*g+-10*c*d*g+8*c*e*f)*Elliptic.F(arcsin((1/2)*2^(1/2)*((b^2+-4*a*c)^-1//2*(b+(b^2+-4*a*c)^(1/2)+2*c*x))^(1/2)),-2*g*(b^2+-4*a*c)^(1/2)*(-1*g*(b+(b^2+-4*a*c)^(1/2))+2*c*f)^-1))
@test integrate((f+g*x)^-1//2*(a+b*x+c*x^2)^(1/2), x) == :(2//3*g^-1*(f+g*x)^(1/2)*(a+b*x+c*x^2)^(1/2)+-1//3*2^(1/2)*c^-1*g^-2*(c*(-1*g*(b+(b^2+-4*a*c)^(1/2))+2*c*f)^-1*(f+g*x))^-1//2*(-1*c*(b^2+-4*a*c)^-1*(a+b*x+c*x^2))^(1/2)*(f+g*x)^(1/2)*(b^2+-4*a*c)^(1/2)*(a+b*x+c*x^2)^-1//2*(-1*b*g+2*c*f)*Elliptic.E(arcsin((1/2)*2^(1/2)*((b^2+-4*a*c)^-1//2*(b+(b^2+-4*a*c)^(1/2)+2*c*x))^(1/2)),-2*g*(b^2+-4*a*c)^(1/2)*(-1*g*(b+(b^2+-4*a*c)^(1/2))+2*c*f)^-1)+4//3*2^(1/2)*c^-1*g^-2*(c*(-1*g*(b+(b^2+-4*a*c)^(1/2))+2*c*f)^-1*(f+g*x))^(1/2)*(-1*c*(b^2+-4*a*c)^-1*(a+b*x+c*x^2))^(1/2)*(f+g*x)^-1//2*(b^2+-4*a*c)^(1/2)*(a+b*x+c*x^2)^-1//2*(a*g^2+c*f^2+-1*b*f*g)*Elliptic.F(arcsin((1/2)*2^(1/2)*((b^2+-4*a*c)^-1//2*(b+(b^2+-4*a*c)^(1/2)+2*c*x))^(1/2)),-2*g*(b^2+-4*a*c)^(1/2)*(-1*g*(b+(b^2+-4*a*c)^(1/2))+2*c*f)^-1))
@test integrate((d+e*x)^3*(f+g*x)^(1/2)*(a+b*x+c*x^2)^-1//2, x) == :(2//7*e*c^-1*(d+e*x)^2*(f+g*x)^(1/2)*(a+b*x+c*x^2)^(1/2)+2//35*c^-2*e^2*g^-2*(f+g*x)^3//2*(a+b*x+c*x^2)^(1/2)*(c*e*f+-6*b*e*g+11*c*d*g)+2//105*e*c^-3*g^-2*(f+g*x)^(1/2)*(a+b*x+c*x^2)^(1/2)*(-1*c^2*(-90*d^2*g^2+7*e^2*f^2+12*d*e*f*g)+24*b^2*e^2*g^2+c*e*g*(-84*b*d*g+-25*a*e*g+13*b*e*f))+-1//105*2^(1/2)*c^-4*g^-3*(c*(-1*g*(b+(b^2+-4*a*c)^(1/2))+2*c*f)^-1*(f+g*x))^-1//2*(-1*c*(b^2+-4*a*c)^-1*(a+b*x+c*x^2))^(1/2)*(f+g*x)^(1/2)*(b^2+-4*a*c)^(1/2)*(a+b*x+c*x^2)^-1//2*(-1*c^3*(8*e^3*f^3+105*d^3*g^3+-42*d*g*e^2*f^2+105*e*f*d^2*g^2)+48*b^3*e^3*g^3+e*g*c^2*(-1*b*(-210*d^2*g^2+9*e^2*f^2+-63*d*e*f*g)+a*e*g*(19*e*f+189*d*g))+-8*b*c*e^2*g^2*(2*b*e*f+13*a*e*g+21*b*d*g))*Elliptic.E(arcsin((1/2)*2^(1/2)*((b^2+-4*a*c)^-1//2*(b+(b^2+-4*a*c)^(1/2)+2*c*x))^(1/2)),-2*g*(b^2+-4*a*c)^(1/2)*(-1*g*(b+(b^2+-4*a*c)^(1/2))+2*c*f)^-1)+-2//105*e*2^(1/2)*c^-4*g^-3*(c*(-1*g*(b+(b^2+-4*a*c)^(1/2))+2*c*f)^-1*(f+g*x))^(1/2)*(-1*c*(b^2+-4*a*c)^-1*(a+b*x+c*x^2))^(1/2)*(f+g*x)^-1//2*(b^2+-4*a*c)^(1/2)*(a+b*x+c*x^2)^-1//2*(a*g^2+c*f^2+-1*b*f*g)*(c^2*(8*e^2*f^2+105*d^2*g^2+-42*d*e*f*g)+24*b^2*e^2*g^2+c*e*g*(-84*b*d*g+-25*a*e*g+13*b*e*f))*Elliptic.F(arcsin((1/2)*2^(1/2)*((b^2+-4*a*c)^-1//2*(b+(b^2+-4*a*c)^(1/2)+2*c*x))^(1/2)),-2*g*(b^2+-4*a*c)^(1/2)*(-1*g*(b+(b^2+-4*a*c)^(1/2))+2*c*f)^-1))
@test integrate((d+e*x)^2*(f+g*x)^(1/2)*(a+b*x+c*x^2)^-1//2, x) == :(2//5*e*c^-1*(f+g*x)^(1/2)*(a+b*x+c*x^2)^(1/2)*(d+e*x)+2//15*e*c^-2*g^-1*(f+g*x)^(1/2)*(a+b*x+c*x^2)^(1/2)*(c*e*f+-4*b*e*g+7*c*d*g)+1//15*2^(1/2)*c^-3*g^-2*(c*(-1*g*(b+(b^2+-4*a*c)^(1/2))+2*c*f)^-1*(f+g*x))^-1//2*(-1*c*(b^2+-4*a*c)^-1*(a+b*x+c*x^2))^(1/2)*(f+g*x)^(1/2)*(b^2+-4*a*c)^(1/2)*(a+b*x+c*x^2)^-1//2*(-1*c^2*(-15*d^2*g^2+2*e^2*f^2+-10*d*e*f*g)+8*b^2*e^2*g^2+-1*c*e*g*(3*b*e*f+9*a*e*g+20*b*d*g))*Elliptic.E(arcsin((1/2)*2^(1/2)*((b^2+-4*a*c)^-1//2*(b+(b^2+-4*a*c)^(1/2)+2*c*x))^(1/2)),-2*g*(b^2+-4*a*c)^(1/2)*(-1*g*(b+(b^2+-4*a*c)^(1/2))+2*c*f)^-1)+4//15*e*2^(1/2)*c^-3*g^-2*(c*(-1*g*(b+(b^2+-4*a*c)^(1/2))+2*c*f)^-1*(f+g*x))^(1/2)*(-1*c*(b^2+-4*a*c)^-1*(a+b*x+c*x^2))^(1/2)*(f+g*x)^-1//2*(b^2+-4*a*c)^(1/2)*(a+b*x+c*x^2)^-1//2*(a*g^2+c*f^2+-1*b*f*g)*(c*e*f+-5*c*d*g+2*b*e*g)*Elliptic.F(arcsin((1/2)*2^(1/2)*((b^2+-4*a*c)^-1//2*(b+(b^2+-4*a*c)^(1/2)+2*c*x))^(1/2)),-2*g*(b^2+-4*a*c)^(1/2)*(-1*g*(b+(b^2+-4*a*c)^(1/2))+2*c*f)^-1))
@test integrate((f+g*x)^(1/2)*(a+b*x+c*x^2)^-1//2*(d+e*x), x) == :(2//3*e*c^-1*(f+g*x)^(1/2)*(a+b*x+c*x^2)^(1/2)+1//3*2^(1/2)*c^-2*g^-1*(c*(-1*g*(b+(b^2+-4*a*c)^(1/2))+2*c*f)^-1*(f+g*x))^-1//2*(-1*c*(b^2+-4*a*c)^-1*(a+b*x+c*x^2))^(1/2)*(f+g*x)^(1/2)*(b^2+-4*a*c)^(1/2)*(a+b*x+c*x^2)^-1//2*(c*e*f+-2*b*e*g+3*c*d*g)*Elliptic.E(arcsin((1/2)*2^(1/2)*((b^2+-4*a*c)^-1//2*(b+(b^2+-4*a*c)^(1/2)+2*c*x))^(1/2)),-2*g*(b^2+-4*a*c)^(1/2)*(-1*g*(b+(b^2+-4*a*c)^(1/2))+2*c*f)^-1)+-2//3*e*2^(1/2)*c^-2*g^-1*(c*(-1*g*(b+(b^2+-4*a*c)^(1/2))+2*c*f)^-1*(f+g*x))^(1/2)*(-1*c*(b^2+-4*a*c)^-1*(a+b*x+c*x^2))^(1/2)*(f+g*x)^-1//2*(b^2+-4*a*c)^(1/2)*(a+b*x+c*x^2)^-1//2*(a*g^2+c*f^2+-1*b*f*g)*Elliptic.F(arcsin((1/2)*2^(1/2)*((b^2+-4*a*c)^-1//2*(b+(b^2+-4*a*c)^(1/2)+2*c*x))^(1/2)),-2*g*(b^2+-4*a*c)^(1/2)*(-1*g*(b+(b^2+-4*a*c)^(1/2))+2*c*f)^-1))
@test integrate((f+g*x)^(1/2)*(a+b*x+c*x^2)^-1//2, x) == :(2^(1/2)*c^-1*(c*(-1*g*(b+(b^2+-4*a*c)^(1/2))+2*c*f)^-1*(f+g*x))^-1//2*(-1*c*(b^2+-4*a*c)^-1*(a+b*x+c*x^2))^(1/2)*(f+g*x)^(1/2)*(b^2+-4*a*c)^(1/2)*(a+b*x+c*x^2)^-1//2*Elliptic.E(arcsin((1/2)*2^(1/2)*((b^2+-4*a*c)^-1//2*(b+(b^2+-4*a*c)^(1/2)+2*c*x))^(1/2)),-2*g*(b^2+-4*a*c)^(1/2)*(-1*g*(b+(b^2+-4*a*c)^(1/2))+2*c*f)^-1))
@test integrate((d+e*x)^3*(f+g*x)^-1//2*(a+b*x+c*x^2)^-1//2, x) == :(-8//15*c^-2*e^2*g^-2*(f+g*x)^(1/2)*(a+b*x+c*x^2)^(1/2)*(b*e*g+c*e*f+-3*c*d*g)+2//5*c^-1*e^2*g^-1*(f+g*x)^(1/2)*(a+b*x+c*x^2)^(1/2)*(d+e*x)+-2//15*2^(1/2)*c^-3*g^-3*(c*(-1*g*(b+(b^2+-4*a*c)^(1/2))+2*c*f)^-1*(f+g*x))^(1/2)*(-1*c*(b^2+-4*a*c)^-1*(a+b*x+c*x^2))^(1/2)*(f+g*x)^-1//2*(b^2+-4*a*c)^(1/2)*(a+b*x+c*x^2)^-1//2*(c^2*(-15*d^3*g^3+8*e^3*f^3+-30*d*g*e^2*f^2+45*e*f*d^2*g^2)+-1*c*g*e^2*(a*g*(-15*d*g+7*e*f)+-3*b*f*(e*f+-5*d*g))+4*b*e^3*g^2*(b*f+-1*a*g))*Elliptic.F(arcsin((1/2)*2^(1/2)*((b^2+-4*a*c)^-1//2*(b+(b^2+-4*a*c)^(1/2)+2*c*x))^(1/2)),-2*g*(b^2+-4*a*c)^(1/2)*(-1*g*(b+(b^2+-4*a*c)^(1/2))+2*c*f)^-1)+1//15*e*2^(1/2)*c^-3*g^-3*(c*(-1*g*(b+(b^2+-4*a*c)^(1/2))+2*c*f)^-1*(f+g*x))^-1//2*(-1*c*(b^2+-4*a*c)^-1*(a+b*x+c*x^2))^(1/2)*(f+g*x)^(1/2)*(b^2+-4*a*c)^(1/2)*(a+b*x+c*x^2)^-1//2*(c^2*(8*e^2*f^2+45*d^2*g^2+-30*d*e*f*g)+8*b^2*e^2*g^2+c*e*g*(-30*b*d*g+-9*a*e*g+7*b*e*f))*Elliptic.E(arcsin((1/2)*2^(1/2)*((b^2+-4*a*c)^-1//2*(b+(b^2+-4*a*c)^(1/2)+2*c*x))^(1/2)),-2*g*(b^2+-4*a*c)^(1/2)*(-1*g*(b+(b^2+-4*a*c)^(1/2))+2*c*f)^-1))
@test integrate((d+e*x)^2*(f+g*x)^-1//2*(a+b*x+c*x^2)^-1//2, x) == :(2//3*c^-1*e^2*g^-1*(f+g*x)^(1/2)*(a+b*x+c*x^2)^(1/2)+2//3*2^(1/2)*c^-2*g^-2*(c*(-1*g*(b+(b^2+-4*a*c)^(1/2))+2*c*f)^-1*(f+g*x))^(1/2)*(-1*c*(b^2+-4*a*c)^-1*(a+b*x+c*x^2))^(1/2)*(f+g*x)^-1//2*(b^2+-4*a*c)^(1/2)*(a+b*x+c*x^2)^-1//2*(c*(2*e^2*f^2+3*d^2*g^2+-6*d*e*f*g)+g*e^2*(b*f+-1*a*g))*Elliptic.F(arcsin((1/2)*2^(1/2)*((b^2+-4*a*c)^-1//2*(b+(b^2+-4*a*c)^(1/2)+2*c*x))^(1/2)),-2*g*(b^2+-4*a*c)^(1/2)*(-1*g*(b+(b^2+-4*a*c)^(1/2))+2*c*f)^-1)+-2//3*e*2^(1/2)*c^-2*g^-2*(c*(-1*g*(b+(b^2+-4*a*c)^(1/2))+2*c*f)^-1*(f+g*x))^-1//2*(-1*c*(b^2+-4*a*c)^-1*(a+b*x+c*x^2))^(1/2)*(f+g*x)^(1/2)*(b^2+-4*a*c)^(1/2)*(a+b*x+c*x^2)^-1//2*(b*e*g+c*e*f+-3*c*d*g)*Elliptic.E(arcsin((1/2)*2^(1/2)*((b^2+-4*a*c)^-1//2*(b+(b^2+-4*a*c)^(1/2)+2*c*x))^(1/2)),-2*g*(b^2+-4*a*c)^(1/2)*(-1*g*(b+(b^2+-4*a*c)^(1/2))+2*c*f)^-1))
@test integrate((f+g*x)^-1//2*(a+b*x+c*x^2)^-1//2*(d+e*x), x) == :(e*2^(1/2)*c^-1*g^-1*(c*(-1*g*(b+(b^2+-4*a*c)^(1/2))+2*c*f)^-1*(f+g*x))^-1//2*(-1*c*(b^2+-4*a*c)^-1*(a+b*x+c*x^2))^(1/2)*(f+g*x)^(1/2)*(b^2+-4*a*c)^(1/2)*(a+b*x+c*x^2)^-1//2*Elliptic.E(arcsin((1/2)*2^(1/2)*((b^2+-4*a*c)^-1//2*(b+(b^2+-4*a*c)^(1/2)+2*c*x))^(1/2)),-2*g*(b^2+-4*a*c)^(1/2)*(-1*g*(b+(b^2+-4*a*c)^(1/2))+2*c*f)^-1)+-2*2^(1/2)*c^-1*g^-1*(c*(-1*g*(b+(b^2+-4*a*c)^(1/2))+2*c*f)^-1*(f+g*x))^(1/2)*(-1*c*(b^2+-4*a*c)^-1*(a+b*x+c*x^2))^(1/2)*(f+g*x)^-1//2*(b^2+-4*a*c)^(1/2)*(a+b*x+c*x^2)^-1//2*(e*f+-1*d*g)*Elliptic.F(arcsin((1/2)*2^(1/2)*((b^2+-4*a*c)^-1//2*(b+(b^2+-4*a*c)^(1/2)+2*c*x))^(1/2)),-2*g*(b^2+-4*a*c)^(1/2)*(-1*g*(b+(b^2+-4*a*c)^(1/2))+2*c*f)^-1))
@test integrate((f+g*x)^-1//2*(a+b*x+c*x^2)^-1//2, x) == :(2*2^(1/2)*c^-1*(c*(-1*g*(b+(b^2+-4*a*c)^(1/2))+2*c*f)^-1*(f+g*x))^(1/2)*(-1*c*(b^2+-4*a*c)^-1*(a+b*x+c*x^2))^(1/2)*(f+g*x)^-1//2*(b^2+-4*a*c)^(1/2)*(a+b*x+c*x^2)^-1//2*Elliptic.F(arcsin((1/2)*2^(1/2)*((b^2+-4*a*c)^-1//2*(b+(b^2+-4*a*c)^(1/2)+2*c*x))^(1/2)),-2*g*(b^2+-4*a*c)^(1/2)*(-1*g*(b+(b^2+-4*a*c)^(1/2))+2*c*f)^-1))
@test integrate((d+e*x)^-1//2*(f+g*x)^-1//2*(a+b*x+c*x^2)^-1//2, x) == :(-1*((1+(d+e*x)^-1*(c*f^2+-1*g*(b*f+-1*a*g))^-1//2*(a*e^2+c*d^2+-1*b*d*e)^(1/2)*(f+g*x))^-2*(1+(d+e*x)^-2*(f+g*x)^2*(c*f^2+-1*g*(b*f+-1*a*g))^-1*(a*e^2+c*d^2+-1*b*d*e)+-1*(d+e*x)^-1*(a*g^2+c*f^2+-1*b*f*g)^-1*(f+g*x)*(-1*b*(d*g+e*f)+2*a*e*g+2*c*d*f)))^(1/2)*((d+e*x)^-2*(e*f+-1*d*g)^2*(a*g^2+c*f^2+-1*b*f*g)^-1*(a+b*x+c*x^2))^(1/2)*(c*f^2+-1*g*(b*f+-1*a*g))^1//4*(e*f+-1*d*g)^-1*(1+(d+e*x)^-2*(f+g*x)^2*(c*f^2+-1*g*(b*f+-1*a*g))^-1*(a*e^2+c*d^2+-1*b*d*e)+-1*(d+e*x)^-1*(a*g^2+c*f^2+-1*b*f*g)^-1*(f+g*x)*(-1*b*(d*g+e*f)+2*a*e*g+2*c*d*f))^-1//2*(a+b*x+c*x^2)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1//4*(1+(d+e*x)^-1*(c*f^2+-1*g*(b*f+-1*a*g))^-1//2*(a*e^2+c*d^2+-1*b*d*e)^(1/2)*(f+g*x))*(d+e*x)*Elliptic.F(2*arctan((d+e*x)^-1//2*(f+g*x)^(1/2)*(a*e^2+c*d^2+-1*b*d*e)^1//4*(a*g^2+c*f^2+-1*b*f*g)^-1//4),1/2+1//4*(c*d^2+-1*e*(b*d+-1*a*e))^-1//2*(c*f^2+-1*g*(b*f+-1*a*g))^-1//2*(-1*b*(d*g+e*f)+2*a*e*g+2*c*d*f)))
@test integrate((d+e*x)^m*(f+g*x)^2*(a+b*x+c*x^2), x) == :(e^-5*(3+m)^-1*(d+e*x)^(3+m)*(c*(e^2*f^2+6*d^2*g^2+-6*d*e*f*g)+e*g*(a*e*g+-3*b*d*g+2*b*e*f))+c*e^-5*g^2*(5+m)^-1*(d+e*x)^(5+m)+g*e^-5*(4+m)^-1*(d+e*x)^(4+m)*(b*e*g+-4*c*d*g+2*c*e*f)+e^-5*(1+m)^-1*(d+e*x)^(1+m)*(e*f+-1*d*g)^2*(a*e^2+c*d^2+-1*b*d*e)+-1*e^-5*(2+m)^-1*(d+e*x)^(2+m)*(e*f+-1*d*g)*(-1*e*(b*e*f+-3*b*d*g+2*a*e*g)+2*c*d*(e*f+-2*d*g)))
@test integrate((d+e*x)^m*(f+g*x)*(a+b*x+c*x^2), x) == :(e^-4*(3+m)^-1*(d+e*x)^(3+m)*(b*e*g+c*e*f+-3*c*d*g)+-1*e^-4*(2+m)^-1*(d+e*x)^(2+m)*(-1*e*(a*e*g+b*e*f+-2*b*d*g)+c*d*(-3*d*g+2*e*f))+c*g*e^-4*(4+m)^-1*(d+e*x)^(4+m)+e^-4*(1+m)^-1*(d+e*x)^(1+m)*(e*f+-1*d*g)*(a*e^2+c*d^2+-1*b*d*e))
@test integrate((d+e*x)^m*(f+g*x)^2*(a+b*x+c*x^2)^2, x) == :(e^-7*(3+m)^-1*(d+e*x)^(3+m)*(e^2*(b^2*(e^2*f^2+6*d^2*g^2+-6*d*e*f*g)+a^2*e^2*g^2+2*a*b*e*g*(-3*d*g+2*e*f))+c^2*d^2*(6*e^2*f^2+15*d^2*g^2+-20*d*e*f*g)+2*c*e*(a*e*(e^2*f^2+6*d^2*g^2+-6*d*e*f*g)+-1*b*d*(3*e^2*f^2+10*d^2*g^2+-12*d*e*f*g)))+e^-7*(4+m)^-1*(d+e*x)^(4+m)*(-4*d*c^2*(e^2*f^2+5*d^2*g^2+-5*d*e*f*g)+2*c*e*(b*(e^2*f^2+10*d^2*g^2+-8*d*e*f*g)+2*a*e*g*(e*f+-2*d*g))+2*b*g*e^2*(a*e*g+b*e*f+-2*b*d*g))+e^-7*(5+m)^-1*(d+e*x)^(5+m)*(c^2*(e^2*f^2+15*d^2*g^2+-10*d*e*f*g)+b^2*e^2*g^2+2*c*e*g*(a*e*g+-5*b*d*g+2*b*e*f))+c^2*e^-7*g^2*(7+m)^-1*(d+e*x)^(7+m)+e^-7*(1+m)^-1*(d+e*x)^(1+m)*(e*f+-1*d*g)^2*(a*e^2+c*d^2+-1*b*d*e)^2+-1*e^-7*(2+m)^-1*(d+e*x)^(2+m)*(e*f+-1*d*g)*(-1*e*(a*e*g+b*e*f+-2*b*d*g)+c*d*(-3*d*g+2*e*f))*(2*a*e^2+2*c*d^2+-2*b*d*e)+2*c*g*e^-7*(6+m)^-1*(d+e*x)^(6+m)*(b*e*g+c*e*f+-3*c*d*g))
@test integrate((d+e*x)^m*(a+b*x+c*x^2)^2*(f+g*x), x) == :(e^-6*(3+m)^-1*(d+e*x)^(3+m)*(b*e^2*(b*e*f+-3*b*d*g+2*a*e*g)+2*c*e*(a*e*(e*f+-3*d*g)+-3*b*d*(e*f+-2*d*g))+2*c^2*d^2*(-5*d*g+3*e*f))+e^-6*(4+m)^-1*(d+e*x)^(4+m)*(g*b^2*e^2+-2*d*c^2*(-5*d*g+2*e*f)+2*c*e*(a*e*g+b*e*f+-4*b*d*g))+c*e^-6*(5+m)^-1*(d+e*x)^(5+m)*(c*e*f+-5*c*d*g+2*b*e*g)+g*c^2*e^-6*(6+m)^-1*(d+e*x)^(6+m)+e^-6*(1+m)^-1*(d+e*x)^(1+m)*(a*e^2+c*d^2+-1*b*d*e)^2*(e*f+-1*d*g)+-1*e^-6*(2+m)^-1*(d+e*x)^(2+m)*(-1*e*(a*e*g+-3*b*d*g+2*b*e*f)+c*d*(-5*d*g+4*e*f))*(a*e^2+c*d^2+-1*b*d*e))

max_stars_repo_path: test/1 Algebraic functions/1.2 Trinomial products/1.2.1 Quadratic/1.2.1.4 (d+e x)^m (f+g x)^n (a+b x+c x^2)^p.jl