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

@test integrate((d+e*x)^2*(d^2+-1*e^2*x^2)^(1/2)*(A+B*x+C*x^2), x) == :(-1//6*C*x^3*(d^2+-1*e^2*x^2)^3//2+-1//5*e^-1*x^2*(d^2+-1*e^2*x^2)^3//2*(B*e+2*C*d)+-1//8*x*e^-2*(d^2+-1*e^2*x^2)^3//2*(2*e*(A*e+2*B*d)+3*C*d^2)+-1//15*d*e^-3*(d^2+-1*e^2*x^2)^3//2*(e*(7*B*d+10*A*e)+4*C*d^2)+1//16*d^4*e^-3*(3*C*d^2+10*A*e^2+4*B*d*e)*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+1//16*x*d^2*e^-2*(d^2+-1*e^2*x^2)^(1/2)*(3*C*d^2+10*A*e^2+4*B*d*e))
@test integrate((d^2+-1*e^2*x^2)^(1/2)*(d+e*x)*(A+B*x+C*x^2), x) == :(-1//15*e^-3*(d^2+-1*e^2*x^2)^3//2*(2*C*d^2+5*e*(A*e+B*d))+-1//4*x*e^-2*(d^2+-1*e^2*x^2)^3//2*(B*e+C*d)+-1//5*C*e^-1*x^2*(d^2+-1*e^2*x^2)^3//2+1//8*d^3*e^-3*(C*d^2+e*(B*d+4*A*e))*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+1//8*d*x*e^-2*(d^2+-1*e^2*x^2)^(1/2)*(C*d^2+e*(B*d+4*A*e)))
@test integrate((d^2+-1*e^2*x^2)^(1/2)*(A+B*x+C*x^2), x) == :(x*(d^2+-1*e^2*x^2)^(1/2)*((1/2)*A+1//8*C*d^2*e^-2)+-1//3*B*e^-2*(d^2+-1*e^2*x^2)^3//2+-1//4*C*x*e^-2*(d^2+-1*e^2*x^2)^3//2+1//8*d^2*e^-3*(C*d^2+4*A*e^2)*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2))
@test integrate((d+e*x)^-1*(d^2+-1*e^2*x^2)^(1/2)*(A+B*x+C*x^2), x) == :((1/2)*e^-3*(d^2+-1*e^2*x^2)^(1/2)*(C*d^2+-1*e*(B*d+-2*A*e))+-1//3*C*e^-3*(d^2+-1*e^2*x^2)^3//2+(1/2)*d*e^-3*(C*d^2+-1*e*(B*d+-2*A*e))*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+(1/2)*e^-3*(d+e*x)^-1*(d^2+-1*e^2*x^2)^3//2*(C*d+-1*B*e))
@test integrate((d+e*x)^-2*(d^2+-1*e^2*x^2)^(1/2)*(A+B*x+C*x^2), x) == :(-1//2*e^-3*(-2*e*(-1*A*e+2*B*d)+5*C*d^2)*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+-1//2*C*e^-3*(d+e*x)^-1*(d^2+-1*e^2*x^2)^3//2+-1//2*d^-1*e^-3*(d^2+-1*e^2*x^2)^(1/2)*(-2*e*(-1*A*e+2*B*d)+5*C*d^2)+-1*d^-1*e^-3*(d+e*x)^-2*(d^2+-1*e^2*x^2)^3//2*(A*e^2+C*d^2+-1*B*d*e))
@test integrate((d+e*x)^-3*(d^2+-1*e^2*x^2)^(1/2)*(A+B*x+C*x^2), x) == :(e^-3*(-1*B*e+3*C*d)*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+e^-3*(d+e*x)^-1*(d^2+-1*e^2*x^2)^(1/2)*(-2*B*e+6*C*d)+-1*C*e^-3*(d+e*x)^-2*(d^2+-1*e^2*x^2)^3//2+-1//3*d^-1*e^-3*(d+e*x)^-3*(d^2+-1*e^2*x^2)^3//2*(A*e^2+C*d^2+-1*B*d*e))
@test integrate((d+e*x)^-4*(d^2+-1*e^2*x^2)^(1/2)*(A+B*x+C*x^2), x) == :(-1*C*e^-3*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+-2*C*e^-3*(d+e*x)^-1*(d^2+-1*e^2*x^2)^(1/2)+-1//5*d^-1*e^-3*(d+e*x)^-4*(d^2+-1*e^2*x^2)^3//2*(A*e^2+C*d^2+-1*B*d*e)+-1//15*d^-2*e^-3*(d+e*x)^-3*(d^2+-1*e^2*x^2)^3//2*(A*e^2+C*d^2+-1*B*d*e)+1//3*d^-1*e^-3*(d+e*x)^-3*(d^2+-1*e^2*x^2)^3//2*(-1*B*e+2*C*d))
@test integrate((d+e*x)^-5*(d^2+-1*e^2*x^2)^(1/2)*(A+B*x+C*x^2), x) == :(C*e^-3*(d+e*x)^-4*(d^2+-1*e^2*x^2)^3//2+-1//7*d^-1*e^-3*(d+e*x)^-5*(d^2+-1*e^2*x^2)^3//2*(A*e^2+C*d^2+-1*B*d*e)+-1//35*d^-2*e^-3*(d+e*x)^-4*(d^2+-1*e^2*x^2)^3//2*(e*(2*A*e+5*B*d)+23*C*d^2)+-1//105*d^-3*e^-3*(d+e*x)^-3*(d^2+-1*e^2*x^2)^3//2*(e*(2*A*e+5*B*d)+23*C*d^2))
@test integrate((d+e*x)^-6*(d^2+-1*e^2*x^2)^(1/2)*(A+B*x+C*x^2), x) == :((1/2)*C*e^-3*(d+e*x)^-5*(d^2+-1*e^2*x^2)^3//2+-1//9*d^-1*e^-3*(d+e*x)^-6*(d^2+-1*e^2*x^2)^3//2*(A*e^2+C*d^2+-1*B*d*e)+-1//42*d^-2*e^-3*(d+e*x)^-5*(d^2+-1*e^2*x^2)^3//2*(2*e*(A*e+2*B*d)+11*C*d^2)+-1//105*d^-3*e^-3*(d+e*x)^-4*(d^2+-1*e^2*x^2)^3//2*(2*e*(A*e+2*B*d)+11*C*d^2)+-1//315*d^-4*e^-3*(d+e*x)^-3*(d^2+-1*e^2*x^2)^3//2*(2*e*(A*e+2*B*d)+11*C*d^2))
@test integrate((d+e*x)^3*(d^2+-1*e^2*x^2)^-1//2*(A+B*x+C*x^2), x) == :(-1*x^3*(d^2+-1*e^2*x^2)^(1/2)*(1//4*B*e+3//4*C*d)+-1//5*C*e*x^4*(d^2+-1*e^2*x^2)^(1/2)+-1//15*d^2*e^-3*(d^2+-1*e^2*x^2)^(1/2)*(38*C*d^2+55*A*e^2+45*B*d*e)+-1//15*e^-1*x^2*(d^2+-1*e^2*x^2)^(1/2)*(5*e*(A*e+3*B*d)+19*C*d^2)+1//8*d^3*e^-3*(13*C*d^2+20*A*e^2+15*B*d*e)*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+-1//8*d*x*e^-2*(d^2+-1*e^2*x^2)^(1/2)*(12*A*e^2+13*C*d^2+15*B*d*e))
@test integrate((d+e*x)^2*(d^2+-1*e^2*x^2)^-1//2*(A+B*x+C*x^2), x) == :(-1//4*C*x^3*(d^2+-1*e^2*x^2)^(1/2)+-1//3*d*e^-3*(d^2+-1*e^2*x^2)^(1/2)*(e*(5*B*d+6*A*e)+4*C*d^2)+-1//3*e^-1*x^2*(d^2+-1*e^2*x^2)^(1/2)*(B*e+2*C*d)+-1//8*x*e^-2*(d^2+-1*e^2*x^2)^(1/2)*(4*e*(A*e+2*B*d)+7*C*d^2)+1//8*d^2*e^-3*(7*C*d^2+12*A*e^2+8*B*d*e)*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2))
@test integrate((d^2+-1*e^2*x^2)^-1//2*(d+e*x)*(A+B*x+C*x^2), x) == :(-1//3*e^-3*(d^2+-1*e^2*x^2)^(1/2)*(2*C*d^2+3*e*(A*e+B*d))+(1/2)*d*e^-3*(C*d^2+e*(B*d+2*A*e))*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+-1//2*x*e^-2*(d^2+-1*e^2*x^2)^(1/2)*(B*e+C*d)+-1//3*C*e^-1*x^2*(d^2+-1*e^2*x^2)^(1/2))
@test integrate((d^2+-1*e^2*x^2)^-1//2*(A+B*x+C*x^2), x) == :((1/2)*e^-3*(C*d^2+2*A*e^2)*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+-1*B*e^-2*(d^2+-1*e^2*x^2)^(1/2)+-1//2*C*x*e^-2*(d^2+-1*e^2*x^2)^(1/2))
@test integrate((d+e*x)^-1*(d^2+-1*e^2*x^2)^-1//2*(A+B*x+C*x^2), x) == :(-1*C*e^-3*(d^2+-1*e^2*x^2)^(1/2)+-1*e^-3*(C*d+-1*B*e)*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+-1*d^-1*e^-3*(d+e*x)^-1*(d^2+-1*e^2*x^2)^(1/2)*(A*e^2+C*d^2+-1*B*d*e))
@test integrate((d+e*x)^-2*(d^2+-1*e^2*x^2)^-1//2*(A+B*x+C*x^2), x) == :(C*e^-3*arctan(e*x*(d^2+-1*e^2*x^2)^-1//2)+d^-1*e^-3*(d+e*x)^-1*(d^2+-1*e^2*x^2)^(1/2)*(-1*B*e+2*C*d)+-1//3*d^-1*e^-3*(d+e*x)^-2*(d^2+-1*e^2*x^2)^(1/2)*(A*e^2+C*d^2+-1*B*d*e)+-1//3*d^-2*e^-3*(d+e*x)^-1*(d^2+-1*e^2*x^2)^(1/2)*(A*e^2+C*d^2+-1*B*d*e))
@test integrate((d+e*x)^-3*(d^2+-1*e^2*x^2)^-1//2*(A+B*x+C*x^2), x) == :(C*e^-3*(d+e*x)^-2*(d^2+-1*e^2*x^2)^(1/2)+-1//5*d^-1*e^-3*(d+e*x)^-3*(d^2+-1*e^2*x^2)^(1/2)*(A*e^2+C*d^2+-1*B*d*e)+-1//15*d^-3*e^-3*(d+e*x)^-1*(d^2+-1*e^2*x^2)^(1/2)*(e*(2*A*e+3*B*d)+7*C*d^2)+-1//15*d^-2*e^-3*(d+e*x)^-2*(d^2+-1*e^2*x^2)^(1/2)*(e*(2*A*e+3*B*d)+7*C*d^2))
@test integrate((d+e*x)^-4*(d^2+-1*e^2*x^2)^-1//2*(A+B*x+C*x^2), x) == :((1/2)*C*e^-3*(d+e*x)^-3*(d^2+-1*e^2*x^2)^(1/2)+-1//7*d^-1*e^-3*(d+e*x)^-4*(d^2+-1*e^2*x^2)^(1/2)*(A*e^2+C*d^2+-1*B*d*e)+-1//70*d^-2*e^-3*(d+e*x)^-3*(d^2+-1*e^2*x^2)^(1/2)*(6*A*e^2+13*C*d^2+8*B*d*e)+-1//105*d^-4*e^-3*(d+e*x)^-1*(d^2+-1*e^2*x^2)^(1/2)*(6*A*e^2+13*C*d^2+8*B*d*e)+-1//105*d^-3*e^-3*(d+e*x)^-2*(d^2+-1*e^2*x^2)^(1/2)*(6*A*e^2+13*C*d^2+8*B*d*e))
@test integrate((d+e*x)^3*(a+c*x^2)*(A+B*x+C*x^2), x) == :(-1//5*e^-5*(d+e*x)^5*(a*e^2*(-1*B*e+2*C*d)+c*d*(-1*e*(-2*A*e+3*B*d)+4*C*d^2))+1//6*e^-5*(d+e*x)^6*(c*(-1*e*(-1*A*e+3*B*d)+6*C*d^2)+C*a*e^2)+-1//7*c*e^-5*(d+e*x)^7*(-1*B*e+4*C*d)+1//4*e^-5*(d+e*x)^4*(a*e^2+c*d^2)*(A*e^2+C*d^2+-1*B*d*e)+1//8*C*c*e^-5*(d+e*x)^8)
@test integrate((d+e*x)^2*(a+c*x^2)*(A+B*x+C*x^2), x) == :(-1//4*e^-5*(d+e*x)^4*(a*e^2*(-1*B*e+2*C*d)+c*d*(-1*e*(-2*A*e+3*B*d)+4*C*d^2))+1//5*e^-5*(d+e*x)^5*(c*(-1*e*(-1*A*e+3*B*d)+6*C*d^2)+C*a*e^2)+-1//6*c*e^-5*(d+e*x)^6*(-1*B*e+4*C*d)+1//3*e^-5*(d+e*x)^3*(a*e^2+c*d^2)*(A*e^2+C*d^2+-1*B*d*e)+1//7*C*c*e^-5*(d+e*x)^7)
@test integrate((a+c*x^2)*(d+e*x)*(A+B*x+C*x^2), x) == :(x^3*(1//3*A*c*d+1//3*B*a*e+1//3*C*a*d)+x^4*(1//4*A*c*e+1//4*B*c*d+1//4*C*a*e)+(1/2)*a*x^2*(A*e+B*d)+1//5*c*x^5*(B*e+C*d)+A*a*d*x+1//6*C*c*e*x^6)
@test integrate((a+c*x^2)*(A+B*x+C*x^2), x) == :(x^3*(1//3*A*c+1//3*C*a)+A*a*x+(1/2)*B*a*x^2+1//4*B*c*x^4+1//5*C*c*x^5)
@test integrate((d+e*x)^-1*(a+c*x^2)*(A+B*x+C*x^2), x) == :((1/2)*e^-3*x^2*(c*(C*d^2+-1*e*(B*d+-1*A*e))+C*a*e^2)+-1*x*e^-4*(a*e^2*(C*d+-1*B*e)+c*d*(C*d^2+-1*e*(B*d+-1*A*e)))+e^-5*(a*e^2+c*d^2)*(A*e^2+C*d^2+-1*B*d*e)*log(d+e*x)+-1//3*c*e^-2*x^3*(C*d+-1*B*e)+1//4*C*c*e^-1*x^4)
@test integrate((d+e*x)^-2*(a+c*x^2)*(A+B*x+C*x^2), x) == :(x*e^-4*(c*(-1*e*(-1*A*e+2*B*d)+3*C*d^2)+C*a*e^2)+-1*e^-5*(a*e^2*(-1*B*e+2*C*d)+c*d*(-1*e*(-2*A*e+3*B*d)+4*C*d^2))*log(d+e*x)+-1*e^-5*(d+e*x)^-1*(a*e^2+c*d^2)*(A*e^2+C*d^2+-1*B*d*e)+-1//2*c*e^-3*x^2*(-1*B*e+2*C*d)+1//3*C*c*e^-2*x^3)
@test integrate((d+e*x)^-3*(a+c*x^2)*(A+B*x+C*x^2), x) == :(e^-5*(d+e*x)^-1*(a*e^2*(-1*B*e+2*C*d)+c*d*(-1*e*(-2*A*e+3*B*d)+4*C*d^2))+e^-5*(c*(-1*e*(-1*A*e+3*B*d)+6*C*d^2)+C*a*e^2)*log(d+e*x)+(1/2)*C*c*e^-3*x^2+-1*c*x*e^-4*(-1*B*e+3*C*d)+-1//2*e^-5*(d+e*x)^-2*(a*e^2+c*d^2)*(A*e^2+C*d^2+-1*B*d*e))
@test integrate((a+c*x^2)^2*(d+e*x)^3*(A+B*x+C*x^2), x) == :(x^5*(1//5*a*(a*e^2*(B*e+3*C*d)+2*c*d^2*(C*d+3*B*e))+1//5*A*c*d*(c*d^2+6*a*e^2))+1//7*c*x^7*(c*d*(C*d^2+3*e*(A*e+B*d))+2*a*e^2*(B*e+3*C*d))+A*x*a^2*d^3+1//3*a*d*x^3*(A*(2*c*d^2+3*a*e^2)+a*d*(C*d+3*B*e))+1//4*e*a^2*x^4*(e*(A*e+3*B*d)+3*C*d^2)+1//6*a*e*x^6*(2*c*(e*(A*e+3*B*d)+3*C*d^2)+C*a*e^2)+1//6*c^-1*d^2*(a+c*x^2)^3*(B*d+3*A*e)+1//8*c*e*x^8*(c*(e*(A*e+3*B*d)+3*C*d^2)+2*C*a*e^2)+1//9*c^2*e^2*x^9*(B*e+3*C*d)+1//10*C*c^2*e^3*x^10)
@test integrate((a+c*x^2)^2*(d+e*x)^2*(A+B*x+C*x^2), x) == :(x^5*(1//5*a*(C*a*e^2+2*c*d*(C*d+2*B*e))+1//5*A*c*(c*d^2+2*a*e^2))+1//3*a*x^3*(A*(a*e^2+2*c*d^2)+a*d*(C*d+2*B*e))+1//7*c*x^7*(c*(C*d^2+e*(A*e+2*B*d))+2*C*a*e^2)+A*x*a^2*d^2+1//4*e*a^2*x^4*(B*e+2*C*d)+1//6*d*c^-1*(a+c*x^2)^3*(B*d+2*A*e)+1//8*e*c^2*x^8*(B*e+2*C*d)+1//9*C*c^2*e^2*x^9+1//3*a*c*e*x^6*(B*e+2*C*d))
@test integrate((a+c*x^2)^2*(d+e*x)*(A+B*x+C*x^2), x) == :(1//3*a*x^3*(B*a*e+C*a*d+2*A*c*d)+1//5*c*x^5*(2*a*(B*e+C*d)+A*c*d)+1//6*c^-1*(a+c*x^2)^3*(A*e+B*d)+1//7*c^2*x^7*(B*e+C*d)+A*d*x*a^2+1//4*C*e*a^2*x^4+1//8*C*e*c^2*x^8+1//3*C*a*c*e*x^6)
@test integrate((a+c*x^2)^2*(A+B*x+C*x^2), x) == :(A*x*a^2+1//3*a*x^3*(C*a+2*A*c)+1//5*c*x^5*(A*c+2*C*a)+1//6*B*c^-1*(a+c*x^2)^3+1//7*C*c^2*x^7)
@test integrate((a+c*x^2)^2*(d+e*x)^-1*(A+B*x+C*x^2), x) == :((1/2)*e^-5*x^2*(C*a^2*e^4+c^2*d^2*(C*d^2+-1*e*(B*d+-1*A*e))+2*a*c*e^2*(C*d^2+-1*e*(B*d+-1*A*e)))+-1*x*e^-6*(a^2*e^4*(C*d+-1*B*e)+c^2*d^3*(C*d^2+-1*e*(B*d+-1*A*e))+2*a*c*d*e^2*(C*d^2+-1*e*(B*d+-1*A*e)))+e^-7*(a*e^2+c*d^2)^2*(A*e^2+C*d^2+-1*B*d*e)*log(d+e*x)+-1//3*c*e^-4*x^3*(c*d*(C*d^2+-1*e*(B*d+-1*A*e))+2*a*e^2*(C*d+-1*B*e))+-1//5*c^2*e^-2*x^5*(C*d+-1*B*e)+1//4*c*e^-3*x^4*(c*(C*d^2+-1*e*(B*d+-1*A*e))+2*C*a*e^2)+1//6*C*c^2*e^-1*x^6)
@test integrate((a+c*x^2)^2*(d+e*x)^-2*(A+B*x+C*x^2), x) == :(x*e^-6*(C*a^2*e^4+c^2*d^2*(-1*e*(-3*A*e+4*B*d)+5*C*d^2)+2*a*c*e^2*(-1*e*(-1*A*e+2*B*d)+3*C*d^2))+-1*e^-7*(d+e*x)^-1*(a*e^2+c*d^2)^2*(A*e^2+C*d^2+-1*B*d*e)+-1*e^-7*(a*e^2+c*d^2)*(a*e^2*(-1*B*e+2*C*d)+c*d*(-1*e*(-4*A*e+5*B*d)+6*C*d^2))*log(d+e*x)+-1//2*c*e^-5*x^2*(c*d*(-1*e*(-2*A*e+3*B*d)+4*C*d^2)+2*a*e^2*(-1*B*e+2*C*d))+-1//4*c^2*e^-3*x^4*(-1*B*e+2*C*d)+1//3*c*e^-4*x^3*(c*(-1*e*(-1*A*e+2*B*d)+3*C*d^2)+2*C*a*e^2)+1//5*C*c^2*e^-2*x^5)
@test integrate((a+c*x^2)^2*(d+e*x)^-3*(A+B*x+C*x^2), x) == :(e^-7*(C*a^2*e^4+c^2*d^2*(-2*e*(-3*A*e+5*B*d)+15*C*d^2)+2*a*c*e^2*(-1*e*(-1*A*e+3*B*d)+6*C*d^2))*log(d+e*x)+e^-7*(d+e*x)^-1*(a*e^2+c*d^2)*(a*e^2*(-1*B*e+2*C*d)+c*d*(-1*e*(-4*A*e+5*B*d)+6*C*d^2))+(1/2)*c*e^-5*x^2*(c*(-1*e*(-1*A*e+3*B*d)+6*C*d^2)+2*C*a*e^2)+-1*c*x*e^-6*(c*d*(-3*e*(-1*A*e+2*B*d)+10*C*d^2)+2*a*e^2*(-1*B*e+3*C*d))+-1//2*e^-7*(d+e*x)^-2*(a*e^2+c*d^2)^2*(A*e^2+C*d^2+-1*B*d*e)+-1//3*c^2*e^-4*x^3*(-1*B*e+3*C*d)+1//4*C*c^2*e^-3*x^4)
@test integrate((a+c*x^2)^3*(d+e*x)^3*(A+B*x+C*x^2), x) == :(1//5*a*x^5*(a*(a*e^2*(B*e+3*C*d)+3*c*d^2*(C*d+3*B*e))+3*A*c*d*(c*d^2+3*a*e^2))+1//7*c*x^7*(3*a*(a*e^2*(B*e+3*C*d)+c*d^2*(C*d+3*B*e))+A*c*d*(c*d^2+9*a*e^2))+1//9*c^2*x^9*(c*d*(C*d^2+3*e*(A*e+B*d))+3*a*e^2*(B*e+3*C*d))+A*x*a^3*d^3+1//3*d*a^2*x^3*(3*A*(a*e^2+c*d^2)+a*d*(C*d+3*B*e))+1//4*e*a^3*x^4*(e*(A*e+3*B*d)+3*C*d^2)+1//6*e*a^2*x^6*(3*c*(e*(A*e+3*B*d)+3*C*d^2)+C*a*e^2)+1//8*c^-1*d^2*(a+c*x^2)^4*(B*d+3*A*e)+1//10*e*c^2*x^10*(c*(e*(A*e+3*B*d)+3*C*d^2)+3*C*a*e^2)+1//11*c^3*e^2*x^11*(B*e+3*C*d)+1//12*C*c^3*e^3*x^12+3//8*a*c*e*x^8*(c*(e*(A*e+3*B*d)+3*C*d^2)+C*a*e^2))
@test integrate((a+c*x^2)^3*(d+e*x)^2*(A+B*x+C*x^2), x) == :(1//3*a^2*x^3*(A*(a*e^2+3*c*d^2)+a*d*(C*d+2*B*e))+1//5*a*x^5*(a*(C*a*e^2+3*c*d*(C*d+2*B*e))+3*A*c*(a*e^2+c*d^2))+1//7*c*x^7*(3*a*(C*a*e^2+c*d*(C*d+2*B*e))+A*c*(c*d^2+3*a*e^2))+1//9*c^2*x^9*(c*(C*d^2+e*(A*e+2*B*d))+3*C*a*e^2)+A*x*a^3*d^2+1//4*e*a^3*x^4*(B*e+2*C*d)+1//8*d*c^-1*(a+c*x^2)^4*(B*d+2*A*e)+1//10*e*c^3*x^10*(B*e+2*C*d)+1//11*C*c^3*e^2*x^11+(1/2)*c*e*a^2*x^6*(B*e+2*C*d)+3//8*a*e*c^2*x^8*(B*e+2*C*d))
@test integrate((a+c*x^2)^3*(d+e*x)*(A+B*x+C*x^2), x) == :(1//3*a^2*x^3*(B*a*e+C*a*d+3*A*c*d)+1//7*c^2*x^7*(3*a*(B*e+C*d)+A*c*d)+1//8*c^-1*(a+c*x^2)^4*(A*e+B*d)+1//9*c^3*x^9*(B*e+C*d)+A*d*x*a^3+1//4*C*e*a^3*x^4+1//10*C*e*c^3*x^10+3//5*a*c*x^5*(A*c*d+B*a*e+C*a*d)+(1/2)*C*c*e*a^2*x^6+3//8*C*a*e*c^2*x^8)
@test integrate((a+c*x^2)^3*(A+B*x+C*x^2), x) == :(A*x*a^3+1//3*a^2*x^3*(C*a+3*A*c)+1//7*c^2*x^7*(A*c+3*C*a)+1//8*B*c^-1*(a+c*x^2)^4+1//9*C*c^3*x^9+3//5*a*c*x^5*(A*c+C*a))
@test integrate((a+c*x^2)^3*(d+e*x)^-1*(A+B*x+C*x^2), x) == :(e^-9*(a*e^2+c*d^2)^3*(A*e^2+C*d^2+-1*B*d*e)*log(d+e*x)+(1/2)*e^-9*(d+e*x)^2*(a*e^2+c*d^2)*(C*a^2*e^4+c^2*d^2*(-3*e*(-5*A*e+7*B*d)+28*C*d^2)+a*c*e^2*(-3*e*(-1*A*e+3*B*d)+17*C*d^2))+-1*x*e^-8*(a*e^2+c*d^2)^2*(a*e^2*(-1*B*e+2*C*d)+c*d*(-1*e*(-6*A*e+7*B*d)+8*C*d^2))+-1//3*c*e^-9*(d+e*x)^3*(c^2*d^3*(-5*e*(-4*A*e+7*B*d)+56*C*d^2)+3*a^2*e^4*(-1*B*e+4*C*d)+6*a*c*d*e^2*(-1*e*(-2*A*e+5*B*d)+10*C*d^2))+-1//5*c^2*e^-9*(d+e*x)^5*(c*d*(-3*e*(-2*A*e+7*B*d)+56*C*d^2)+3*a*e^2*(-1*B*e+6*C*d))+-1//7*c^3*e^-9*(d+e*x)^7*(-1*B*e+8*C*d)+1//4*c*e^-9*(d+e*x)^4*(3*C*a^2*e^4+5*c^2*d^2*(-1*e*(-3*A*e+7*B*d)+14*C*d^2)+3*a*c*e^2*(-1*e*(-1*A*e+5*B*d)+15*C*d^2))+1//6*c^2*e^-9*(d+e*x)^6*(c*(-1*e*(-1*A*e+7*B*d)+28*C*d^2)+3*C*a*e^2)+1//8*C*c^3*e^-9*(d+e*x)^8)
@test integrate((a+c*x^2)^3*(d+e*x)^-2*(A+B*x+C*x^2), x) == :(x*e^-8*(C*a^3*e^6+c^3*d^4*(-1*e*(-5*A*e+6*B*d)+7*C*d^2)+3*c*a^2*e^4*(-1*e*(-1*A*e+2*B*d)+3*C*d^2)+3*a*c^2*d^2*e^2*(-1*e*(-3*A*e+4*B*d)+5*C*d^2))+-1*e^-9*(d+e*x)^-1*(a*e^2+c*d^2)^3*(A*e^2+C*d^2+-1*B*d*e)+-1*e^-9*(a*e^2+c*d^2)^2*(a*e^2*(-1*B*e+2*C*d)+c*d*(-1*e*(-6*A*e+7*B*d)+8*C*d^2))*log(d+e*x)+-1//2*c*e^-7*x^2*(c^2*d^3*(-1*e*(-4*A*e+5*B*d)+6*C*d^2)+3*a^2*e^4*(-1*B*e+2*C*d)+3*a*c*d*e^2*(-1*e*(-2*A*e+3*B*d)+4*C*d^2))+-1//4*c^2*e^-5*x^4*(c*d*(-1*e*(-2*A*e+3*B*d)+4*C*d^2)+3*a*e^2*(-1*B*e+2*C*d))+-1//6*c^3*e^-3*x^6*(-1*B*e+2*C*d)+1//3*c*e^-6*x^3*(c^2*d^2*(-1*e*(-3*A*e+4*B*d)+5*C*d^2)+3*C*a^2*e^4+3*a*c*e^2*(-1*e*(-1*A*e+2*B*d)+3*C*d^2))+1//5*c^2*e^-4*x^5*(c*(-1*e*(-1*A*e+2*B*d)+3*C*d^2)+3*C*a*e^2)+1//7*C*c^3*e^-2*x^7)
@test integrate((a+c*x^2)^3*(d+e*x)^-3*(A+B*x+C*x^2), x) == :(e^-9*(d+e*x)^-1*(a*e^2+c*d^2)^2*(a*e^2*(-1*B*e+2*C*d)+c*d*(-1*e*(-6*A*e+7*B*d)+8*C*d^2))+e^-9*(a*e^2+c*d^2)*(C*a^2*e^4+c^2*d^2*(-3*e*(-5*A*e+7*B*d)+28*C*d^2)+a*c*e^2*(-3*e*(-1*A*e+3*B*d)+17*C*d^2))*log(d+e*x)+(1/2)*c*e^-7*x^2*(c^2*d^2*(-2*e*(-3*A*e+5*B*d)+15*C*d^2)+3*C*a^2*e^4+3*a*c*e^2*(-1*e*(-1*A*e+3*B*d)+6*C*d^2))+-1*c*x*e^-8*(c^2*d^3*(-5*e*(-2*A*e+3*B*d)+21*C*d^2)+3*a^2*e^4*(-1*B*e+3*C*d)+3*a*c*d*e^2*(-3*e*(-1*A*e+2*B*d)+10*C*d^2))+-1//2*e^-9*(d+e*x)^-2*(a*e^2+c*d^2)^3*(A*e^2+C*d^2+-1*B*d*e)+-1//3*c^2*e^-6*x^3*(c*d*(-3*e*(-1*A*e+2*B*d)+10*C*d^2)+3*a*e^2*(-1*B*e+3*C*d))+-1//5*c^3*e^-4*x^5*(-1*B*e+3*C*d)+1//4*c^2*e^-5*x^4*(c*(-1*e*(-1*A*e+3*B*d)+6*C*d^2)+3*C*a*e^2)+1//6*C*c^3*e^-3*x^6)
@test integrate((c+d*x)^-2*(a+b*x^2)*(-1*a*d+3*b*d*x^2+4*b*c*x), x) == :((a+b*x^2)^2*(c+d*x)^-1)
@test integrate((c+d*x)^-2*(a+b*x^2)*(-1*a*d+b*x*(4c+3*d*x)), x) == :((a+b*x^2)^2*(c+d*x)^-1)
@test integrate((a+b*x^2)^2*(c+d*x)^-2*(-1*a*d+5*b*d*x^2+6*b*c*x), x) == :((a+b*x^2)^3*(c+d*x)^-1)
@test integrate((a+b*x^2)^2*(c+d*x)^-2*(-1*a*d+b*x*(6c+5*d*x)), x) == :((a+b*x^2)^3*(c+d*x)^-1)
@test integrate((a+c*x^2)^-1*(d+e*x)^3*(A+B*x+C*x^2), x) == :((1/2)*c^-3*(e*(A*c+-1*C*a)*(-1*a*e^2+3*c*d^2)+B*c*d*(c*d^2+-3*a*e^2))*log(a+c*x^2)+-1*x*c^-2*(a*e^2*(B*e+3*C*d)+-1*c*d*(C*d^2+3*e*(A*e+B*d)))+a^-1//2*c^-5//2*(a*(a*e^2*(B*e+3*C*d)+-1*c*d^2*(C*d+3*B*e))+A*c*d*(c*d^2+-3*a*e^2))*arctan(x*a^-1//2*c^(1/2))+-1//2*e*c^-2*x^2*(-1*c*(e*(A*e+3*B*d)+3*C*d^2)+C*a*e^2)+1//3*c^-1*e^2*x^3*(B*e+3*C*d)+1//4*C*c^-1*e^3*x^4)
@test integrate((a+c*x^2)^-1*(d+e*x)^2*(A+B*x+C*x^2), x) == :((1/2)*c^-2*(B*c*d^2+-1*B*a*e^2+-2*C*a*d*e+2*A*c*d*e)*log(a+c*x^2)+-1*x*c^-2*(-1*c*(C*d^2+e*(A*e+2*B*d))+C*a*e^2)+a^-1//2*c^-5//2*(a*(C*a*e^2+-1*c*d*(C*d+2*B*e))+A*c*(c*d^2+-1*a*e^2))*arctan(x*a^-1//2*c^(1/2))+(1/2)*e*c^-1*x^2*(B*e+2*C*d)+1//3*C*c^-1*e^2*x^3)
@test integrate((a+c*x^2)^-1*(d+e*x)*(A+B*x+C*x^2), x) == :(x*c^-1*(B*e+C*d)+(1/2)*c^-2*(A*c*e+B*c*d+-1*C*a*e)*log(a+c*x^2)+a^-1//2*c^-3//2*(-1*a*(B*e+C*d)+A*c*d)*arctan(x*a^-1//2*c^(1/2))+(1/2)*C*e*c^-1*x^2)
@test integrate((a+c*x^2)^-1*(A+B*x+C*x^2), x) == :(C*x*c^-1+(1/2)*B*c^-1*log(a+c*x^2)+a^-1//2*c^-3//2*(A*c+-1*C*a)*arctan(x*a^-1//2*c^(1/2)))
@test integrate((a+c*x^2)^-1*(d+e*x)^-1*(A+B*x+C*x^2), x) == :(e^-1*(a*e^2+c*d^2)^-1*(A*e^2+C*d^2+-1*B*d*e)*log(d+e*x)+(1/2)*c^-1*(a*e^2+c*d^2)^-1*(B*c*d+C*a*e+-1*A*c*e)*log(a+c*x^2)+a^-1//2*c^-1//2*(a*e^2+c*d^2)^-1*(A*c*d+B*a*e+-1*C*a*d)*arctan(x*a^-1//2*c^(1/2)))
@test integrate((a+c*x^2)^-1*(d+e*x)^-2*(A+B*x+C*x^2), x) == :((1/2)*(a*e^2+c*d^2)^-2*(B*c*d^2+-1*B*a*e^2+-2*A*c*d*e+2*C*a*d*e)*log(a+c*x^2)+-1*(a*e^2+c*d^2)^-2*(B*c*d^2+-1*B*a*e^2+-2*A*c*d*e+2*C*a*d*e)*log(d+e*x)+-1*e^-1*(d+e*x)^-1*(a*e^2+c*d^2)^-1*(A*e^2+C*d^2+-1*B*d*e)+a^-1//2*c^-1//2*(a*e^2+c*d^2)^-2*(a*(C*a*e^2+-1*c*d*(C*d+-2*B*e))+A*c*(c*d^2+-1*a*e^2))*arctan(x*a^-1//2*c^(1/2)))
@test integrate((a+c*x^2)^-1*(d+e*x)^-3*(A+B*x+C*x^2), x) == :((d+e*x)^-1*(a*e^2+c*d^2)^-2*(B*c*d^2+-1*B*a*e^2+-2*A*c*d*e+2*C*a*d*e)+(1/2)*(a*e^2+c*d^2)^-3*(-1*e*(A*c+-1*C*a)*(-1*a*e^2+3*c*d^2)+B*c*d*(c*d^2+-3*a*e^2))*log(a+c*x^2)+-1*(a*e^2+c*d^2)^-3*(-1*e*(A*c+-1*C*a)*(-1*a*e^2+3*c*d^2)+B*c*d*(c*d^2+-3*a*e^2))*log(d+e*x)+-1//2*e^-1*(d+e*x)^-2*(a*e^2+c*d^2)^-1*(A*e^2+C*d^2+-1*B*d*e)+a^-1//2*c^(1/2)*(a*e^2+c*d^2)^-3*(-1*a*(c*d^2*(C*d+-3*B*e)+-1*a*e^2*(-1*B*e+3*C*d))+A*c*d*(c*d^2+-3*a*e^2))*arctan(x*a^-1//2*c^(1/2)))
@test integrate((a+c*x^2)^-2*(d+e*x)^3*(A+B*x+C*x^2), x) == :((1/2)*a^-3//2*c^-5//2*(-1*a*(-1*c*d^2*(C*d+3*B*e)+3*a*e^2*(B*e+3*C*d))+A*c*d*(c*d^2+3*a*e^2))*arctan(x*a^-1//2*c^(1/2))+-1//2*e*c^-3*(-1*c*(e*(A*e+3*B*d)+3*C*d^2)+2*C*a*e^2)*log(a+c*x^2)+-3//2*x*a^-1*c^-2*e^2*(-1*a*(B*e+3*C*d)+A*c*d)+-1//2*a^-1*c^-1*(a+c*x^2)^-1*(d+e*x)^3*(B*a+-1*x*(A*c+-1*C*a))+-1//2*a^-1*c^-2*e^3*x^2*(A*c+-2*C*a))
@test integrate((a+c*x^2)^-2*(d+e*x)^2*(A+B*x+C*x^2), x) == :((1/2)*e*c^-2*(B*e+2*C*d)*log(a+c*x^2)+(1/2)*a^-3//2*c^-5//2*(a*e^2*(A*c+-3*C*a)+c*d*(A*c*d+C*a*d+2*B*a*e))*arctan(x*a^-1//2*c^(1/2))+-1//2*x*a^-1*c^-2*e^2*(A*c+-3*C*a)+-1//2*a^-1*c^-1*(a+c*x^2)^-1*(d+e*x)^2*(B*a+-1*x*(A*c+-1*C*a)))
@test integrate((a+c*x^2)^-2*(d+e*x)*(A+B*x+C*x^2), x) == :((1/2)*C*e*c^-2*log(a+c*x^2)+(1/2)*a^-3//2*c^-3//2*(A*c*d+B*a*e+C*a*d)*arctan(x*a^-1//2*c^(1/2))+-1//2*a^-1*c^-1*(a+c*x^2)^-1*(d+e*x)*(B*a+-1*x*(A*c+-1*C*a)))
@test integrate((a+c*x^2)^-2*(A+B*x+C*x^2), x) == :((1/2)*a^-3//2*c^-3//2*(A*c+C*a)*arctan(x*a^-1//2*c^(1/2))+-1//2*a^-1*c^-1*(a+c*x^2)^-1*(B*a+-1*x*(A*c+-1*C*a)))
@test integrate((a+c*x^2)^-2*(d+e*x)^-1*(A+B*x+C*x^2), x) == :(e*(a*e^2+c*d^2)^-2*(A*e^2+C*d^2+-1*B*d*e)*log(d+e*x)+-1//2*e*(a*e^2+c*d^2)^-2*(A*e^2+C*d^2+-1*B*d*e)*log(a+c*x^2)+(1/2)*a^-3//2*c^-1//2*(a*e^2+c*d^2)^-2*(a*(C*d+-1*B*e)*(c*d^2+-1*a*e^2)+A*c*d*(c*d^2+3*a*e^2))*arctan(x*a^-1//2*c^(1/2))+-1//2*a^-1*c^-1*(a+c*x^2)^-1*(a*e^2+c*d^2)^-1*(a*(B*c*d+C*a*e+-1*A*c*e)+-1*c*x*(A*c*d+B*a*e+-1*C*a*d)))
@test integrate((a+c*x^2)^-2*(d+e*x)^-2*(A+B*x+C*x^2), x) == :((1/2)*e*(a*e^2+c*d^2)^-3*(a*e^2*(-1*B*e+2*C*d)+-1*c*d*(-1*e*(-4*A*e+3*B*d)+2*C*d^2))*log(a+c*x^2)+-1*e*(d+e*x)^-1*(a*e^2+c*d^2)^-2*(A*e^2+C*d^2+-1*B*d*e)+-1*e*(a*e^2+c*d^2)^-3*(a*e^2*(-1*B*e+2*C*d)+-1*c*d*(-1*e*(-4*A*e+3*B*d)+2*C*d^2))*log(d+e*x)+-1//2*a^-1*(a+c*x^2)^-1*(a*e^2+c*d^2)^-2*(a*(B*c*d^2+-1*B*a*e^2+-2*A*c*d*e+2*C*a*d*e)+-1*x*(a*(C*a*e^2+-1*c*d*(C*d+-2*B*e))+A*c*(c*d^2+-1*a*e^2)))+(1/2)*a^-3//2*c^-1//2*(a*e^2+c*d^2)^-3*(a*(C*a^2*e^4+c^2*d^3*(C*d+-2*B*e)+-6*a*c*d*e^2*(C*d+-1*B*e))+A*c*(c^2*d^4+-3*a^2*e^4+6*a*c*d^2*e^2))*arctan(x*a^-1//2*c^(1/2)))
@test integrate((a+c*x^2)^-2*(d+e*x)^-3*(A+B*x+C*x^2), x) == :(e*(d+e*x)^-1*(a*e^2+c*d^2)^-3*(a*e^2*(-1*B*e+2*C*d)+-1*c*d*(-1*e*(-4*A*e+3*B*d)+2*C*d^2))+e*(a*e^2+c*d^2)^-4*(C*a^2*e^4+c^2*d^2*(-2*e*(-5*A*e+3*B*d)+3*C*d^2)+-2*a*c*e^2*(-1*e*(-1*A*e+3*B*d)+4*C*d^2))*log(d+e*x)+-1//2*e*(d+e*x)^-2*(a*e^2+c*d^2)^-2*(A*e^2+C*d^2+-1*B*d*e)+-1//2*e*(a*e^2+c*d^2)^-4*(C*a^2*e^4+c^2*d^2*(-2*e*(-5*A*e+3*B*d)+3*C*d^2)+-2*a*c*e^2*(-1*e*(-1*A*e+3*B*d)+4*C*d^2))*log(a+c*x^2)+-1//2*a^-1*(a+c*x^2)^-1*(a*e^2+c*d^2)^-3*(a*(-1*e*(A*c+-1*C*a)*(-1*a*e^2+3*c*d^2)+B*c*d*(c*d^2+-3*a*e^2))+-1*c*x*(-1*a*(c*d^2*(C*d+-3*B*e)+-1*a*e^2*(-1*B*e+3*C*d))+A*c*d*(c*d^2+-3*a*e^2)))+(1/2)*a^-3//2*c^(1/2)*(a*e^2+c*d^2)^-4*(-1*a*(-1*c^2*d^4*(C*d+-3*B*e)+-3*a^2*e^4*(-1*B*e+3*C*d)+2*a*c*d^2*e^2*(-9*B*e+7*C*d))+A*c*d*(c^2*d^4+-15*a^2*e^4+10*a*c*d^2*e^2))*arctan(x*a^-1//2*c^(1/2)))
@test integrate((a+c*x^2)^-3*(d+e*x)*(A+B*x+C*x^2), x) == :(-1//8*a^-2*c^-2*(a+c*x^2)^-1*(-1*c*x*(B*a*e+C*a*d+3*A*c*d)+2*a*e*(A*c+C*a))+1//8*a^-5//2*c^-3//2*(B*a*e+C*a*d+3*A*c*d)*arctan(x*a^-1//2*c^(1/2))+-1//4*a^-1*c^-1*(a+c*x^2)^-2*(d+e*x)*(B*a+-1*x*(A*c+-1*C*a)))
@test integrate((a+c*x^2)^-3*(A+B*x+C*x^2), x) == :(-1//4*a^-1*c^-1*(a+c*x^2)^-2*(B*a+-1*x*(A*c+-1*C*a))+1//8*a^-5//2*c^-3//2*(C*a+3*A*c)*arctan(x*a^-1//2*c^(1/2))+1//8*x*a^-2*c^-1*(a+c*x^2)^-1*(C*a+3*A*c))
@test integrate((a+c*x^2)^-3*(d+e*x)^-1*(A+B*x+C*x^2), x) == :(e^3*(a*e^2+c*d^2)^-3*(A*e^2+C*d^2+-1*B*d*e)*log(d+e*x)+-1//2*e^3*(a*e^2+c*d^2)^-3*(A*e^2+C*d^2+-1*B*d*e)*log(a+c*x^2)+1//8*a^-2*(a+c*x^2)^-1*(a*e^2+c*d^2)^-2*(x*(a*(C*d+-1*B*e)*(c*d^2+-3*a*e^2)+A*c*d*(3*c*d^2+7*a*e^2))+4*e*a^2*(A*e^2+C*d^2+-1*B*d*e))+-1//4*a^-1*c^-1*(a+c*x^2)^-2*(a*e^2+c*d^2)^-1*(a*(B*c*d+C*a*e+-1*A*c*e)+-1*c*x*(A*c*d+B*a*e+-1*C*a*d))+1//8*a^-5//2*c^-1//2*(a*e^2+c*d^2)^-3*(a*(C*d+-1*B*e)*(c^2*d^4+-3*a^2*e^4+6*a*c*d^2*e^2)+A*c*d*(3*c^2*d^4+15*a^2*e^4+10*a*c*d^2*e^2))*arctan(x*a^-1//2*c^(1/2)))
@test integrate((a+c*x^2)^-3*(d+e*x)^-2*(A+B*x+C*x^2), x) == :((1/2)*e^3*(a*e^2+c*d^2)^-4*(a*e^2*(-1*B*e+2*C*d)+-1*c*d*(-1*e*(-6*A*e+5*B*d)+4*C*d^2))*log(a+c*x^2)+-1*e^3*(d+e*x)^-1*(a*e^2+c*d^2)^-3*(A*e^2+C*d^2+-1*B*d*e)+-1*e^3*(a*e^2+c*d^2)^-4*(a*e^2*(-1*B*e+2*C*d)+-1*c*d*(-1*e*(-6*A*e+5*B*d)+4*C*d^2))*log(d+e*x)+-1//4*a^-1*(a+c*x^2)^-2*(a*e^2+c*d^2)^-2*(a*(B*c*d^2+-1*B*a*e^2+-2*A*c*d*e+2*C*a*d*e)+-1*x*(a*(C*a*e^2+-1*c*d*(C*d+-2*B*e))+A*c*(c*d^2+-1*a*e^2)))+-1//8*a^-2*(a+c*x^2)^-1*(a*e^2+c*d^2)^-3*(-1*x*(a*(c^2*d^3*(C*d+-2*B*e)+3*C*a^2*e^4+-2*a*c*d*e^2*(-7*B*e+6*C*d))+A*c*(-7*a^2*e^4+3*c^2*d^4+12*a*c*d^2*e^2))+4*e*a^2*(a*e^2*(-1*B*e+2*C*d)+-1*c*d*(-1*e*(-4*A*e+3*B*d)+2*C*d^2)))+1//8*a^-5//2*c^-1//2*(a*e^2+c*d^2)^-4*(a*(c^3*d^5*(C*d+-2*B*e)+3*C*a^3*e^6+a*c^2*d^3*e^2*(-20*B*e+13*C*d)+-3*c*d*a^2*e^4*(-10*B*e+11*C*d))+3*A*c*(c^3*d^6+-5*a^3*e^6+5*a*c^2*d^4*e^2+15*c*a^2*d^2*e^4))*arctan(x*a^-1//2*c^(1/2)))
@test integrate((a+c*x^2)^-3*(d+e*x)^-3*(A+B*x+C*x^2), x) == :(e^3*(d+e*x)^-1*(a*e^2+c*d^2)^-4*(a*e^2*(-1*B*e+2*C*d)+-1*c*d*(-1*e*(-6*A*e+5*B*d)+4*C*d^2))+e^3*(a*e^2+c*d^2)^-5*(C*a^2*e^4+c^2*d^2*(-3*e*(-7*A*e+5*B*d)+10*C*d^2)+-1*a*c*e^2*(3*A*e^2+13*C*d^2+-9*B*d*e))*log(d+e*x)+-1//2*e^3*(d+e*x)^-2*(a*e^2+c*d^2)^-3*(A*e^2+C*d^2+-1*B*d*e)+-1//2*e^3*(a*e^2+c*d^2)^-5*(C*a^2*e^4+c^2*d^2*(-3*e*(-7*A*e+5*B*d)+10*C*d^2)+-1*a*c*e^2*(3*A*e^2+13*C*d^2+-9*B*d*e))*log(a+c*x^2)+-1//4*a^-1*(a+c*x^2)^-2*(a*e^2+c*d^2)^-3*(a*(-1*e*(A*c+-1*C*a)*(-1*a*e^2+3*c*d^2)+B*c*d*(c*d^2+-3*a*e^2))+-1*c*x*(-1*a*(c*d^2*(C*d+-3*B*e)+-1*a*e^2*(-1*B*e+3*C*d))+A*c*d*(c*d^2+-3*a*e^2)))+1//8*a^-2*(a+c*x^2)^-1*(a*e^2+c*d^2)^-4*(c*x*(-1*a*(-1*c^2*d^4*(C*d+-3*B*e)+-7*a^2*e^4*(-1*B*e+3*C*d)+2*a*c*d^2*e^2*(-19*B*e+13*C*d))+3*A*c*d*(c^2*d^4+-11*a^2*e^4+6*a*c*d^2*e^2))+4*e*a^2*(C*a^2*e^4+c^2*d^2*(-2*e*(-5*A*e+3*B*d)+3*C*d^2)+-2*a*c*e^2*(-1*e*(-1*A*e+3*B*d)+4*C*d^2)))+1//8*a^-5//2*c^(1/2)*(a*e^2+c*d^2)^-5*(a*(c^3*d^6*(C*d+-3*B*e)+15*a^3*e^6*(-1*B*e+3*C*d)+a*c^2*d^4*e^2*(-45*B*e+23*C*d)+-5*c*a^2*d^2*e^4*(-27*B*e+25*C*d))+3*A*c*d*(c^3*d^6+-35*a^3*e^6+7*a*c^2*d^4*e^2+35*c*a^2*d^2*e^4))*arctan(x*a^-1//2*c^(1/2)))
@test integrate((a+c*x^2)^-4*(d+e*x)^4*(A+B*x+C*x^2), x) == :(-1//6*a^-1*c^-1*(a+c*x^2)^-3*(d+e*x)^4*(B*a+-1*x*(A*c+-1*C*a))+-1//24*a^-2*c^-2*(a+c*x^2)^-2*(d+e*x)^3*(a*e*(A*c+5*C*a)+-1*c*x*(C*a*d+4*B*a*e+5*A*c*d))+1//16*a^-7//2*c^-7//2*(a*e^2+c*d^2)*(a*e^2*(A*c+5*C*a)+c*d*(C*a*d+4*B*a*e+5*A*c*d))*arctan(x*a^-1//2*c^(1/2))+-1//16*a^-3*c^-3*(a+c*x^2)^-1*(d+e*x)*(a*e+-1*c*d*x)*(a*e^2*(A*c+5*C*a)+c*d*(C*a*d+4*B*a*e+5*A*c*d)))
@test integrate((a+c*x^2)^-4*(d+e*x)^2*(A+B*x+C*x^2), x) == :(-1//24*a^-2*c^-2*(a+c*x^2)^-2*(x*(-1*c*d*(C*a*d+2*B*a*e+5*A*c*d)+3*a*e^2*(A*c+C*a))+2*a*e*(B*a*e+2*C*a*d+4*A*c*d))+1//16*a^-7//2*c^-5//2*(a*e^2*(A*c+C*a)+c*d*(C*a*d+2*B*a*e+5*A*c*d))*arctan(x*a^-1//2*c^(1/2))+-1//6*a^-1*c^-1*(a+c*x^2)^-3*(d+e*x)^2*(B*a+-1*x*(A*c+-1*C*a))+1//16*x*a^-3*c^-2*(a+c*x^2)^-1*(a*e^2*(A*c+C*a)+c*d*(C*a*d+2*B*a*e+5*A*c*d)))
@test integrate((a+c*x^2)^-4*(d+e*x)*(A+B*x+C*x^2), x) == :(-1//24*a^-2*c^-2*(a+c*x^2)^-2*(-1*c*x*(B*a*e+C*a*d+5*A*c*d)+2*a*e*(C*a+2*A*c))+1//16*a^-7//2*c^-3//2*(B*a*e+C*a*d+5*A*c*d)*arctan(x*a^-1//2*c^(1/2))+-1//6*a^-1*c^-1*(a+c*x^2)^-3*(d+e*x)*(B*a+-1*x*(A*c+-1*C*a))+1//16*x*a^-3*c^-1*(a+c*x^2)^-1*(B*a*e+C*a*d+5*A*c*d))
@test integrate((a+c*x^2)^-4*(A+B*x+C*x^2), x) == :(-1//6*a^-1*c^-1*(a+c*x^2)^-3*(B*a+-1*x*(A*c+-1*C*a))+1//16*a^-7//2*c^-3//2*(C*a+5*A*c)*arctan(x*a^-1//2*c^(1/2))+1//16*x*a^-3*c^-1*(a+c*x^2)^-1*(C*a+5*A*c)+1//24*x*a^-2*c^-1*(a+c*x^2)^-2*(C*a+5*A*c))
@test integrate(x^3*(1+x^2)^-2*(1+x+x^2), x) == :((1/2)*x^2+-3//2*arctan(x)+-1//2*log(1+x^2)+3//2*x+-1*x^3*(2+2*x^2)^-1)
@test integrate(x^2*(1+x^2)^-2*(1+x+x^2), x) == :(x+(1/2)*log(1+x^2)+-1*arctan(x)+-1*x^2*(2+2*x^2)^-1)
@test integrate(x*(1+x^2)^-2*(1+x+x^2), x) == :((1/2)*arctan(x)+(1/2)*log(1+x^2)+-1*x*(2+2*x^2)^-1)
@test integrate((1+x^2)^-2*(1+x+x^2), x) == :(-1*(2+2*x^2)^-1+arctan(x))
@test integrate(x^-1*(1+x^2)^-2*(1+x+x^2), x) == :((1/2)*arctan(x)+-1//2*log(1+x^2)+x*(2+2*x^2)^-1+log(x))
@test integrate(x^-2*(1+x^2)^-2*(1+x+x^2), x) == :((2+2*x^2)^-1+-1*x^-1+-1*arctan(x)+-1//2*log(1+x^2)+log(x))
@test integrate(x^-3*(1+x^2)^-2*(1+x+x^2), x) == :((1/2)*log(1+x^2)+-1*x^-1+-1*log(x)+-3//2*arctan(x)+-1//2*x^-2+-1*x*(2+2*x^2)^-1)
@test integrate((4+x^2)^-2*(2+3*x^2+12x), x) == :(7//8*arctan((1/2)*x)+-1*(16+4*x^2)^-1*(24+5x))
@test integrate((a+c*x^2)^(1/2)*(g+h*x)^3*(d+e*x+f*x^2), x) == :(1//16*a*c^-5//2*(a^2*h^2*(e*h+3*f*g)+8*d*c^2*g^3+-2*a*c*g*(f*g^2+3*h*(d*h+e*g)))*arctanh(x*c^(1/2)*(a+c*x^2)^-1//2)+1//16*x*c^-2*(a+c*x^2)^(1/2)*(a^2*h^2*(e*h+3*f*g)+8*d*c^2*g^3+-2*a*c*g*(f*g^2+3*h*(d*h+e*g)))+1//840*c^-3*h^-1*(a+c*x^2)^3//2*(-8*c^2*g^2*(-7*h*(e*g+12*d*h)+3*f*g^2)+64*f*a^2*h^4+-16*a*c*h^2*(7*h*(d*h+3*e*g)+15*f*g^2)+-3*c*h*x*(a*h^2*(35*e*h+41*f*g)+2*c*g*(-7*h*(e*g+7*d*h)+3*f*g^2)))+-1//42*c^-1*h^-1*(a+c*x^2)^3//2*(g+h*x)^3*(-7*e*h+3*f*g)+-1//70*c^-2*h^-1*(a+c*x^2)^3//2*(g+h*x)^2*(c*(-7*h*(e*g+2*d*h)+3*f*g^2)+8*a*f*h^2)+1//7*f*c^-1*h^-1*(a+c*x^2)^3//2*(g+h*x)^4)
@test integrate((a+c*x^2)^(1/2)*(g+h*x)^2*(d+e*x+f*x^2), x) == :(-1//120*c^-2*h^-1*(a+c*x^2)^3//2*(-3*h*x*(h^2*(-5*a*f+10*c*d)+-2*c*g*(f*g+-2*e*h))+8*c*g*(f*g^2+-2*h*(e*g+5*d*h))+16*a*h^2*(e*h+2*f*g))+1//16*a*c^-5//2*(f*a^2*h^2+-2*a*c*(f*g^2+h*(d*h+2*e*g))+8*d*c^2*g^2)*arctanh(x*c^(1/2)*(a+c*x^2)^-1//2)+1//16*x*c^-2*(a+c*x^2)^(1/2)*(f*a^2*h^2+-2*a*c*(f*g^2+h*(d*h+2*e*g))+8*d*c^2*g^2)+-1//10*c^-1*h^-1*(a+c*x^2)^3//2*(g+h*x)^2*(f*g+-2*e*h)+1//6*f*c^-1*h^-1*(a+c*x^2)^3//2*(g+h*x)^3)
@test integrate((a+c*x^2)^(1/2)*(g+h*x)*(d+e*x+f*x^2), x) == :(-1//60*c^-2*h^-1*(a+c*x^2)^3//2*(4*c*(-5*h*(d*h+e*g)+3*f*g^2)+8*a*f*h^2+3*c*h*x*(-5*e*h+3*f*g))+1//8*a*c^-3//2*(-1*a*e*h+-1*a*f*g+4*c*d*g)*arctanh(x*c^(1/2)*(a+c*x^2)^-1//2)+1//8*x*c^-1*(a+c*x^2)^(1/2)*(-1*a*(e*h+f*g)+4*c*d*g)+1//5*f*c^-1*h^-1*(a+c*x^2)^3//2*(g+h*x)^2)
@test integrate((a+c*x^2)^(1/2)*(d+e*x+f*x^2), x) == :(1//3*e*c^-1*(a+c*x^2)^3//2+1//4*f*x*c^-1*(a+c*x^2)^3//2+1//8*a*c^-3//2*(-1*a*f+4*c*d)*arctanh(x*c^(1/2)*(a+c*x^2)^-1//2)+1//8*x*c^-1*(a+c*x^2)^(1/2)*(-1*a*f+4*c*d))
@test integrate((a+c*x^2)^(1/2)*(g+h*x)^-1*(d+e*x+f*x^2), x) == :((1/2)*h^-3*(a+c*x^2)^(1/2)*(2*d*h^2+2*f*g^2+-1*h*x*(f*g+-1*e*h)+-2*e*g*h)+-1*h^-4*(a*h^2+c*g^2)^(1/2)*(d*h^2+f*g^2+-1*e*g*h)*arctanh((a+c*x^2)^-1//2*(a*h^2+c*g^2)^-1//2*(a*h+-1*c*g*x))+-1//2*c^-1//2*h^-4*((a*h^2+2*c*g^2)*(f*g+-1*e*h)+2*c*d*g*h^2)*arctanh(x*c^(1/2)*(a+c*x^2)^-1//2)+1//3*f*c^-1*h^-1*(a+c*x^2)^3//2)
@test integrate((a+c*x^2)^(1/2)*(g+h*x)^-2*(d+e*x+f*x^2), x) == :(h^-4*(a*h^2+c*g^2)^-1//2*(a*h^2*(-1*e*h+2*f*g)+c*g*(-1*h*(-1*d*h+2*e*g)+3*f*g^2))*arctanh((a+c*x^2)^-1//2*(a*h^2+c*g^2)^-1//2*(a*h+-1*c*g*x))+(1/2)*c^-1//2*h^-4*(2*c*(-1*h*(-1*d*h+2*e*g)+3*f*g^2)+a*f*h^2)*arctanh(x*c^(1/2)*(a+c*x^2)^-1//2)+-1//2*h^-3*(a+c*x^2)^(1/2)*(a*h^2+c*g^2)^-1*(-1*h*x*(c*(-2*h*(e*g+-1*d*h)+3*f*g^2)+a*f*h^2)+2*a*h^2*(-1*e*h+2*f*g)+2*c*g*(-1*h*(-1*d*h+2*e*g)+3*f*g^2))+-1*h^-1*(a+c*x^2)^3//2*(g+h*x)^-1*(a*h^2+c*g^2)^-1*(d*h^2+f*g^2+-1*e*g*h))
@test integrate((a+c*x^2)^(1/2)*(g+h*x)^-3*(d+e*x+f*x^2), x) == :(-1*c^(1/2)*h^-4*(-1*e*h+3*f*g)*arctanh(x*c^(1/2)*(a+c*x^2)^-1//2)+-1//2*h^-4*(a*h^2+c*g^2)^-3//2*(2*f*a^2*h^4+2*c^2*g^3*(-1*e*h+3*f*g)+a*c*h^2*(-1*h*(-1*d*h+3*e*g)+9*f*g^2))*arctanh((a+c*x^2)^-1//2*(a*h^2+c*g^2)^-1//2*(a*h+-1*c*g*x))+(1/2)*h^-3*(a+c*x^2)^(1/2)*(g+h*x)^-1*(a*h^2+c*g^2)^-1*((a*h^2+c*g^2)*(-2*e*h+6*f*g)+h*x*(c*(-1*h*(e*g+-1*d*h)+3*f*g^2)+2*a*f*h^2))+-1//2*h^-1*(a+c*x^2)^3//2*(g+h*x)^-2*(a*h^2+c*g^2)^-1*(d*h^2+f*g^2+-1*e*g*h))
@test integrate((a+c*x^2)^(1/2)*(g+h*x)^-4*(d+e*x+f*x^2), x) == :(f*c^(1/2)*h^-4*arctanh(x*c^(1/2)*(a+c*x^2)^-1//2)+(1/2)*c*h^-4*(a*h^2+c*g^2)^-5//2*(a^2*h^4*(-1*e*h+4*f*g)+2*f*c^2*g^5+a*c*g*h^2*(-1*d*h^2+5*f*g^2))*arctanh((a+c*x^2)^-1//2*(a*h^2+c*g^2)^-1//2*(a*h+-1*c*g*x))+-1//2*h^-3*(a+c*x^2)^(1/2)*(g+h*x)^-2*(a*h^2+c*g^2)^-2*(e*a^2*h^5+h*x*(c^2*(3*f*g^4+-1*d*g^2*h^2)+2*f*a^2*h^4+a*c*g*h^2*(-1*e*h+6*f*g))+2*f*c^2*g^5+a*c*g*h^2*(d*h^2+3*f*g^2))+-1//3*h^-1*(a+c*x^2)^3//2*(g+h*x)^-3*(a*h^2+c*g^2)^-1*(d*h^2+f*g^2+-1*e*g*h))
@test integrate((a+c*x^2)^(1/2)*(g+h*x)^-5*(d+e*x+f*x^2), x) == :(-1//4*h^-1*(a+c*x^2)^3//2*(g+h*x)^-4*(a*h^2+c*g^2)^-1*(d*h^2+f*g^2+-1*e*g*h)+-1//8*a*c*(a*h^2+c*g^2)^-7//2*(-1*a*c*(f*g^2+-1*h*(-1*d*h+5*e*g))+4*d*c^2*g^2+4*f*a^2*h^2)*arctanh((a+c*x^2)^-1//2*(a*h^2+c*g^2)^-1//2*(a*h+-1*c*g*x))+-1//8*(a+c*x^2)^(1/2)*(g+h*x)^-2*(a*h^2+c*g^2)^-3*(a*h+-1*c*g*x)*(-1*a*c*(f*g^2+-1*h*(-1*d*h+5*e*g))+4*d*c^2*g^2+4*f*a^2*h^2)+1//12*h^-1*(a+c*x^2)^3//2*(g+h*x)^-3*(a*h^2+c*g^2)^-2*(c*g*(h*(e*g+-5*d*h)+3*f*g^2)+4*a*h^2*(-1*e*h+2*f*g)))
@test integrate((a+c*x^2)^(1/2)*(g+h*x)^-6*(d+e*x+f*x^2), x) == :(-1//5*h^-1*(a+c*x^2)^3//2*(g+h*x)^-5*(a*h^2+c*g^2)^-1*(d*h^2+f*g^2+-1*e*g*h)+-1//8*a*c^2*(a*h^2+c*g^2)^-9//2*(a^2*h^2*(-1*e*h+6*f*g)+4*d*c^2*g^3+-1*a*c*g*(f*g^2+-3*h*(-1*d*h+2*e*g)))*arctanh((a+c*x^2)^-1//2*(a*h^2+c*g^2)^-1//2*(a*h+-1*c*g*x))+-1//60*h^-1*(a+c*x^2)^3//2*(g+h*x)^-3*(a*h^2+c*g^2)^-3*(-1*c^2*g^2*(h*(-27*d*h+2*e*g)+3*f*g^2)+20*f*a^2*h^4+-1*a*c*h^2*(-1*h*(-8*d*h+33*e*g)+18*f*g^2))+1//20*h^-1*(a+c*x^2)^3//2*(g+h*x)^-4*(a*h^2+c*g^2)^-2*(c*g*(h*(-7*d*h+2*e*g)+3*f*g^2)+5*a*h^2*(-1*e*h+2*f*g))+-1//8*c*(a+c*x^2)^(1/2)*(g+h*x)^-2*(a*h^2+c*g^2)^-4*(a*h+-1*c*g*x)*(a^2*h^2*(-1*e*h+6*f*g)+4*d*c^2*g^3+-1*a*c*g*(f*g^2+-3*h*(-1*d*h+2*e*g))))
@test integrate((a+c*x^2)^3//2*(g+h*x)^3*(d+e*x+f*x^2), x) == :(1//128*a^2*c^-5//2*(3*a^2*h^2*(e*h+3*f*g)+48*d*c^2*g^3+-8*a*c*g*(f*g^2+3*h*(d*h+e*g)))*arctanh(x*c^(1/2)*(a+c*x^2)^-1//2)+1//192*x*c^-2*(a+c*x^2)^3//2*(3*a^2*h^2*(e*h+3*f*g)+48*d*c^2*g^3+-8*a*c*g*(f*g^2+3*h*(d*h+e*g)))+1//5040*c^-3*h^-1*(a+c*x^2)^5//2*(-12*c^2*g^2*(-3*h*(3*e*g+64*d*h)+5*f*g^2)+128*f*a^2*h^4+-32*a*c*h^2*(9*h*(d*h+3*e*g)+17*f*g^2)+-5*c*h*x*(a*h^2*(61*f*g+63*e*h)+2*c*g*(-9*h*(e*g+12*d*h)+5*f*g^2)))+-1//72*c^-1*h^-1*(a+c*x^2)^5//2*(g+h*x)^3*(-9*e*h+5*f*g)+1//9*f*c^-1*h^-1*(a+c*x^2)^5//2*(g+h*x)^4+1//128*a*x*c^-2*(a+c*x^2)^(1/2)*(3*a^2*h^2*(e*h+3*f*g)+48*d*c^2*g^3+-8*a*c*g*(f*g^2+3*h*(d*h+e*g)))+1//504*c^-2*h^-1*(a+c*x^2)^5//2*(g+h*x)^2*(h^2*(-32*a*f+72*c*d)+-3*c*g*(-9*e*h+5*f*g)))
@test integrate((a+c*x^2)^3//2*(g+h*x)^2*(d+e*x+f*x^2), x) == :(-1//1680*c^-2*h^-1*(a+c*x^2)^5//2*(-5*h*x*(h^2*(-21*a*f+56*c*d)+-2*c*g*(-8*e*h+5*f*g))+12*c*g*(-8*h*(e*g+7*d*h)+5*f*g^2)+96*a*h^2*(e*h+2*f*g))+1//128*a^2*c^-5//2*(-8*a*c*(f*g^2+h*(d*h+2*e*g))+3*f*a^2*h^2+48*d*c^2*g^2)*arctanh(x*c^(1/2)*(a+c*x^2)^-1//2)+1//192*x*c^-2*(a+c*x^2)^3//2*(-8*a*c*(f*g^2+h*(d*h+2*e*g))+3*f*a^2*h^2+48*d*c^2*g^2)+-1//56*c^-1*h^-1*(a+c*x^2)^5//2*(g+h*x)^2*(-8*e*h+5*f*g)+1//8*f*c^-1*h^-1*(a+c*x^2)^5//2*(g+h*x)^3+1//128*a*x*c^-2*(a+c*x^2)^(1/2)*(-8*a*c*(f*g^2+h*(d*h+2*e*g))+3*f*a^2*h^2+48*d*c^2*g^2))
@test integrate((a+c*x^2)^3//2*(g+h*x)*(d+e*x+f*x^2), x) == :(-1//210*c^-2*h^-1*(a+c*x^2)^5//2*(6*c*(-7*h*(d*h+e*g)+5*f*g^2)+12*a*f*h^2+5*c*h*x*(-7*e*h+5*f*g))+1//16*a^2*c^-3//2*(-1*a*e*h+-1*a*f*g+6*c*d*g)*arctanh(x*c^(1/2)*(a+c*x^2)^-1//2)+1//24*x*c^-1*(a+c*x^2)^3//2*(-1*a*(e*h+f*g)+6*c*d*g)+1//7*f*c^-1*h^-1*(a+c*x^2)^5//2*(g+h*x)^2+1//16*a*x*c^-1*(a+c*x^2)^(1/2)*(-1*a*e*h+-1*a*f*g+6*c*d*g))
@test integrate((a+c*x^2)^3//2*(d+e*x+f*x^2), x) == :(1//5*e*c^-1*(a+c*x^2)^5//2+1//6*f*x*c^-1*(a+c*x^2)^5//2+1//16*a^2*c^-3//2*(-1*a*f+6*c*d)*arctanh(x*c^(1/2)*(a+c*x^2)^-1//2)+1//24*x*c^-1*(a+c*x^2)^3//2*(-1*a*f+6*c*d)+1//16*a*x*c^-1*(a+c*x^2)^(1/2)*(-1*a*f+6*c*d))
@test integrate((a+c*x^2)^3//2*(g+h*x)^-1*(d+e*x+f*x^2), x) == :(1//8*h^-5*(a+c*x^2)^(1/2)*((8*a*h^2+8*c*g^2)*(d*h^2+f*g^2+-1*e*g*h)+-1*h*x*((f*g+-1*e*h)*(3*a*h^2+4*c*g^2)+4*c*d*g*h^2))+1//12*h^-3*(a+c*x^2)^3//2*(4*d*h^2+4*f*g^2+-4*e*g*h+-3*h*x*(f*g+-1*e*h))+-1*h^-6*(a*h^2+c*g^2)^3//2*(d*h^2+f*g^2+-1*e*g*h)*arctanh((a+c*x^2)^-1//2*(a*h^2+c*g^2)^-1//2*(a*h+-1*c*g*x))+-1//8*c^-1//2*h^-6*(3*a^2*h^4*(f*g+-1*e*h)+8*c^2*g^3*(f*g^2+-1*h*(e*g+-1*d*h))+12*a*c*g*h^2*(f*g^2+-1*h*(e*g+-1*d*h)))*arctanh(x*c^(1/2)*(a+c*x^2)^-1//2)+1//5*f*c^-1*h^-1*(a+c*x^2)^5//2)
@test integrate((a+c*x^2)^3//2*(g+h*x)^-2*(d+e*x+f*x^2), x) == :(-1//8*h^-5*(a+c*x^2)^(1/2)*(-1*h*x*(3*a*f*h^2+12*c*d*h^2+20*c*f*g^2+-16*c*e*g*h)+8*a*h^2*(-1*e*h+2*f*g)+8*c*g*(-1*h*(-3*d*h+4*e*g)+5*f*g^2))+h^-6*(a*h^2+c*g^2)^(1/2)*(a*h^2*(-1*e*h+2*f*g)+c*g*(-1*h*(-3*d*h+4*e*g)+5*f*g^2))*arctanh((a+c*x^2)^-1//2*(a*h^2+c*g^2)^-1//2*(a*h+-1*c*g*x))+-1//12*h^-3*(a+c*x^2)^3//2*(a*h^2+c*g^2)^-1*(-3*h*x*(c*(-4*h*(e*g+-1*d*h)+5*f*g^2)+a*f*h^2)+4*a*h^2*(-1*e*h+2*f*g)+4*c*g*(-1*h*(-3*d*h+4*e*g)+5*f*g^2))+1//8*c^-1//2*h^-6*(3*f*a^2*h^4+8*c^2*g^2*(-1*h*(-3*d*h+4*e*g)+5*f*g^2)+12*a*c*h^2*(-1*h*(-1*d*h+2*e*g)+3*f*g^2))*arctanh(x*c^(1/2)*(a+c*x^2)^-1//2)+-1*h^-1*(a+c*x^2)^5//2*(g+h*x)^-1*(a*h^2+c*g^2)^-1*(d*h^2+f*g^2+-1*e*g*h))
@test integrate((a+c*x^2)^3//2*(g+h*x)^-3*(d+e*x+f*x^2), x) == :((1/2)*h^-5*(a+c*x^2)^(1/2)*(a*h^2+c*g^2)^-1*(2*f*a^2*h^4+2*c^2*g^2*(-3*h*(-1*d*h+2*e*g)+10*f*g^2)+a*c*h^2*(-3*h*(-1*d*h+3*e*g)+19*f*g^2)+-1*c*h*x*(a*h^2*(-3*e*h+7*f*g)+c*g*(-3*h*(-1*d*h+2*e*g)+10*f*g^2)))+-1//2*c^(1/2)*h^-6*(2*c*g*(-3*h*(-1*d*h+2*e*g)+10*f*g^2)+3*a*h^2*(-1*e*h+3*f*g))*arctanh(x*c^(1/2)*(a+c*x^2)^-1//2)+-1//2*h^-6*(a*h^2+c*g^2)^-1//2*(2*f*a^2*h^4+2*c^2*g^2*(-3*h*(-1*d*h+2*e*g)+10*f*g^2)+a*c*h^2*(-3*h*(-1*d*h+3*e*g)+19*f*g^2))*arctanh((a+c*x^2)^-1//2*(a*h^2+c*g^2)^-1//2*(a*h+-1*c*g*x))+-1//2*h^-1*(a+c*x^2)^5//2*(g+h*x)^-2*(a*h^2+c*g^2)^-1*(d*h^2+f*g^2+-1*e*g*h)+-1//6*h^-2*(a+c*x^2)^3//2*(g+h*x)^-1*(a*h^2+c*g^2)^-1*(-1*x*(c*(-3*h*(e*g+-1*d*h)+5*f*g^2)+2*a*f*h^2)+-2*a*h*(-3*e*h+7*f*g)+2*c*g*(-3*d*h+6*e*g+-10*f*g^2*h^-1)))
@test integrate((a+c*x^2)^3//2*(g+h*x)^-4*(d+e*x+f*x^2), x) == :((1/2)*c^(1/2)*h^-6*(2*c*(-1*h*(-1*d*h+4*e*g)+10*f*g^2)+3*a*f*h^2)*arctanh(x*c^(1/2)*(a+c*x^2)^-1//2)+(1/2)*c*h^-6*(a*h^2+c*g^2)^-3//2*(2*c^2*g^3*(-1*h*(-1*d*h+4*e*g)+10*f*g^2)+3*a^2*h^4*(-1*e*h+4*f*g)+3*a*c*g*h^2*(-1*h*(-1*d*h+4*e*g)+11*f*g^2))*arctanh((a+c*x^2)^-1//2*(a*h^2+c*g^2)^-1//2*(a*h+-1*c*g*x))+-1//2*h^-5*(a+c*x^2)^(1/2)*(g+h*x)^-1*(a*h^2+c*g^2)^-1*((a*h^2+c*g^2)*(2*c*(-1*h*(-1*d*h+4*e*g)+10*f*g^2)+3*a*f*h^2)+c*h*x*(c*g*(-1*h*(-1*d*h+4*e*g)+10*f*g^2)+3*a*h^2*(-1*e*h+3*f*g)))+-1//3*h^-1*(a+c*x^2)^5//2*(g+h*x)^-3*(a*h^2+c*g^2)^-1*(d*h^2+f*g^2+-1*e*g*h)+-1//6*h^-2*(a+c*x^2)^3//2*(g+h*x)^-2*(a*h^2+c*g^2)^-1*(-1*x*(c*(-2*h*(e*g+-1*d*h)+5*f*g^2)+3*a*f*h^2)+c*g*(-1*d*h+4*e*g+-10*f*g^2*h^-1)+-3*a*h*(-1*e*h+3*f*g)))
@test integrate((a+c*x^2)^3//2*(g+h*x)^-5*(d+e*x+f*x^2), x) == :(-1*c^3//2*h^-6*(-1*e*h+5*f*g)*arctanh(x*c^(1/2)*(a+c*x^2)^-1//2)+-1//4*h^-1*(a+c*x^2)^5//2*(g+h*x)^-4*(a*h^2+c*g^2)^-1*(d*h^2+f*g^2+-1*e*g*h)+-1//8*c*h^-6*(a*h^2+c*g^2)^-5//2*(8*c^3*g^5*(-1*e*h+5*f*g)+12*f*a^3*h^6+3*c*a^2*h^4*(-1*h*(-1*d*h+5*e*g)+25*f*g^2)+20*a*c^2*g^3*h^2*(-1*e*h+5*f*g))*arctanh((a+c*x^2)^-1//2*(a*h^2+c*g^2)^-1//2*(a*h+-1*c*g*x))+1//24*h^-3*(a+c*x^2)^3//2*(g+h*x)^-3*(a*h^2+c*g^2)^-2*(-4*c^2*g^4*(-1*e*h+5*f*g)+-3*h*x*(2*c^2*g^2*(-1*h*(d*h+e*g)+5*f*g^2)+4*f*a^2*h^4+a*c*h^2*(-1*h*(-1*d*h+5*e*g)+17*f*g^2))+4*a^2*h^4*(f*g+-2*e*h)+-1*a*c*g*h^2*(-1*h*(-9*d*h+5*e*g)+25*f*g^2))+1//8*c*h^-5*(a+c*x^2)^(1/2)*(g+h*x)^-1*(a*h^2+c*g^2)^-2*((a*h^2+c*g^2)^2*(-8*e*h+40*f*g)+h*x*(4*c^2*g^3*(-1*e*h+5*f*g)+12*f*a^2*h^4+a*c*h^2*(-1*h*(-3*d*h+7*e*g)+35*f*g^2))))
@test integrate((a+c*x^2)^3//2*(g+h*x)^-6*(d+e*x+f*x^2), x) == :(f*c^3//2*h^-6*arctanh(x*c^(1/2)*(a+c*x^2)^-1//2)+-1//5*h^-1*(a+c*x^2)^5//2*(g+h*x)^-5*(a*h^2+c*g^2)^-1*(d*h^2+f*g^2+-1*e*g*h)+-1//12*h^-3*(a+c*x^2)^3//2*(g+h*x)^-4*(a*h^2+c*g^2)^-2*(h*x*(c^2*(7*f*g^4+-3*d*g^2*h^2)+4*f*a^2*h^4+a*c*g*h^2*(-3*e*h+14*f*g))+-1*a^2*h^4*(-3*e*h+2*f*g)+4*f*c^2*g^5+a*c*g*h^2*(3*d*h^2+5*f*g^2))+1//8*c^2*h^-6*(a*h^2+c*g^2)^-7//2*(3*a^3*h^6*(-1*e*h+6*f*g)+8*f*c^3*g^7+c*g*a^2*h^4*(-3*d*h^2+35*f*g^2)+28*a*f*c^2*g^5*h^2)*arctanh((a+c*x^2)^-1//2*(a*h^2+c*g^2)^-1//2*(a*h+-1*c*g*x))+-1//8*c*h^-5*(a+c*x^2)^(1/2)*(g+h*x)^-2*(a*h^2+c*g^2)^-3*(h*x*(8*f*a^3*h^6+12*f*c^3*g^6+a*c^2*g^2*h^2*(-3*d*h^2+35*f*g^2)+c*g*a^2*h^4*(-3*e*h+34*f*g))+-1*a^3*h^6*(-3*e*h+2*f*g)+8*f*c^3*g^7+c*g*a^2*h^4*(3*d*h^2+13*f*g^2)+20*a*f*c^2*g^5*h^2))
@test integrate((a+c*x^2)^3//2*(g+h*x)^-7*(d+e*x+f*x^2), x) == :(-1//6*h^-1*(a+c*x^2)^5//2*(g+h*x)^-6*(a*h^2+c*g^2)^-1*(d*h^2+f*g^2+-1*e*g*h)+-1//16*a^2*c^2*(a*h^2+c*g^2)^-9//2*(-1*a*c*(f*g^2+-1*h*(-1*d*h+7*e*g))+6*d*c^2*g^2+6*f*a^2*h^2)*arctanh((a+c*x^2)^-1//2*(a*h^2+c*g^2)^-1//2*(a*h+-1*c*g*x))+-1//24*(a+c*x^2)^3//2*(g+h*x)^-4*(a*h^2+c*g^2)^-3*(a*h+-1*c*g*x)*(-1*a*c*(f*g^2+-1*h*(-1*d*h+7*e*g))+6*d*c^2*g^2+6*f*a^2*h^2)+1//30*h^-1*(a+c*x^2)^5//2*(g+h*x)^-5*(a*h^2+c*g^2)^-2*(c*g*(h*(e*g+-7*d*h)+5*f*g^2)+6*a*h^2*(-1*e*h+2*f*g))+-1//16*a*c*(a+c*x^2)^(1/2)*(g+h*x)^-2*(a*h^2+c*g^2)^-4*(a*h+-1*c*g*x)*(-1*a*c*(f*g^2+-1*h*(-1*d*h+7*e*g))+6*d*c^2*g^2+6*f*a^2*h^2))
@test integrate((a+c*x^2)^3//2*(g+h*x)^-8*(d+e*x+f*x^2), x) == :(-1//7*h^-1*(a+c*x^2)^5//2*(g+h*x)^-7*(a*h^2+c*g^2)^-1*(d*h^2+f*g^2+-1*e*g*h)+-1//16*a^2*c^3*(a*h^2+c*g^2)^-11//2*(a^2*h^2*(-1*e*h+8*f*g)+6*d*c^2*g^3+-1*a*c*g*(f*g^2+-1*h*(-3*d*h+8*e*g)))*arctanh((a+c*x^2)^-1//2*(a*h^2+c*g^2)^-1//2*(a*h+-1*c*g*x))+-1//210*h^-1*(a+c*x^2)^5//2*(g+h*x)^-5*(a*h^2+c*g^2)^-3*(-1*c^2*g^2*(h*(-51*d*h+2*e*g)+5*f*g^2)+42*f*a^2*h^4+-1*a*c*h^2*(-1*h*(-12*d*h+61*e*g)+26*f*g^2))+1//42*h^-1*(a+c*x^2)^5//2*(g+h*x)^-6*(a*h^2+c*g^2)^-2*(c*g*(h*(-9*d*h+2*e*g)+5*f*g^2)+7*a*h^2*(-1*e*h+2*f*g))+-1//24*c*(a+c*x^2)^3//2*(g+h*x)^-4*(a*h^2+c*g^2)^-4*(a*h+-1*c*g*x)*(a^2*h^2*(-1*e*h+8*f*g)+6*d*c^2*g^3+-1*a*c*g*(f*g^2+-1*h*(-3*d*h+8*e*g)))+-1//16*a*c^2*(a+c*x^2)^(1/2)*(g+h*x)^-2*(a*h^2+c*g^2)^-5*(a*h+-1*c*g*x)*(a^2*h^2*(-1*e*h+8*f*g)+6*d*c^2*g^3+-1*a*c*g*(f*g^2+-1*h*(-3*d*h+8*e*g))))
@test integrate((a+c*x^2)^5//2*(A+B*x+C*x^2), x) == :(1//7*B*c^-1*(a+c*x^2)^7//2+1//8*C*x*c^-1*(a+c*x^2)^7//2+1//48*x*c^-1*(a+c*x^2)^5//2*(-1*C*a+8*A*c)+5//128*a^3*c^-3//2*(-1*C*a+8*A*c)*arctanh(x*c^(1/2)*(a+c*x^2)^-1//2)+5//128*x*a^2*c^-1*(a+c*x^2)^(1/2)*(-1*C*a+8*A*c)+5//192*a*x*c^-1*(a+c*x^2)^3//2*(-1*C*a+8*A*c))
@test integrate((a+c*x^2)^-1//2*(g+h*x)^3*(d+e*x+f*x^2), x) == :(1//8*c^-5//2*(3*a^2*h^2*(e*h+3*f*g)+8*d*c^2*g^3+-4*a*c*g*(f*g^2+3*h*(d*h+e*g)))*arctanh(x*c^(1/2)*(a+c*x^2)^-1//2)+1//120*c^-3*h^-1*(a+c*x^2)^(1/2)*(-4*c^2*g^2*(-5*h*(3*e*g+16*d*h)+3*f*g^2)+64*f*a^2*h^4+-1*c*h*x*(a*h^2*(45*e*h+71*f*g)+2*c*g*(-5*h*(3*e*g+10*d*h)+3*f*g^2))+-16*a*c*h^2*(5*h*(d*h+3*e*g)+13*f*g^2))+-1//20*c^-1*h^-1*(a+c*x^2)^(1/2)*(g+h*x)^3*(f*g+-5*e*h)+1//5*f*c^-1*h^-1*(a+c*x^2)^(1/2)*(g+h*x)^4+1//60*c^-2*h^-1*(a+c*x^2)^(1/2)*(g+h*x)^2*(h^2*(-16*a*f+20*c*d)+-3*c*g*(f*g+-5*e*h)))
@test integrate((a+c*x^2)^-1//2*(g+h*x)^2*(d+e*x+f*x^2), x) == :(1//8*c^-5//2*(-4*a*c*(f*g^2+h*(d*h+2*e*g))+3*f*a^2*h^2+8*d*c^2*g^2)*arctanh(x*c^(1/2)*(a+c*x^2)^-1//2)+-1//24*c^-2*h^-1*(a+c*x^2)^(1/2)*(-1*h*x*(h^2*(-9*a*f+12*c*d)+-2*c*g*(f*g+-4*e*h))+4*c*g*(f*g^2+-4*h*(e*g+3*d*h))+16*a*h^2*(e*h+2*f*g))+-1//12*c^-1*h^-1*(a+c*x^2)^(1/2)*(g+h*x)^2*(f*g+-4*e*h)+1//4*f*c^-1*h^-1*(a+c*x^2)^(1/2)*(g+h*x)^3)
@test integrate((a+c*x^2)^-1//2*(g+h*x)*(d+e*x+f*x^2), x) == :((1/2)*c^-3//2*(-1*a*(e*h+f*g)+2*c*d*g)*arctanh(x*c^(1/2)*(a+c*x^2)^-1//2)+-1//6*c^-2*h^-1*(a+c*x^2)^(1/2)*(2*c*(f*g^2+-3*h*(d*h+e*g))+4*a*f*h^2+c*h*x*(f*g+-3*e*h))+1//3*f*c^-1*h^-1*(a+c*x^2)^(1/2)*(g+h*x)^2)
@test integrate((a+c*x^2)^-1//2*(d+e*x+f*x^2), x) == :(e*c^-1*(a+c*x^2)^(1/2)+(1/2)*c^-3//2*(-1*a*f+2*c*d)*arctanh(x*c^(1/2)*(a+c*x^2)^-1//2)+(1/2)*f*x*c^-1*(a+c*x^2)^(1/2))
@test integrate((a+c*x^2)^-1//2*(g+h*x)^-1*(d+e*x+f*x^2), x) == :(f*c^-1*h^-1*(a+c*x^2)^(1/2)+-1*c^-1//2*h^-2*(f*g+-1*e*h)*arctanh(x*c^(1/2)*(a+c*x^2)^-1//2)+-1*h^-2*(a*h^2+c*g^2)^-1//2*(d*h^2+f*g^2+-1*e*g*h)*arctanh((a+c*x^2)^-1//2*(a*h^2+c*g^2)^-1//2*(a*h+-1*c*g*x)))
@test integrate((a+c*x^2)^-1//2*(g+h*x)^-2*(d+e*x+f*x^2), x) == :(f*c^-1//2*h^-2*arctanh(x*c^(1/2)*(a+c*x^2)^-1//2)+h^-2*(a*h^2+c*g^2)^-3//2*(c*(f*g^3+-1*d*g*h^2)+a*h^2*(-1*e*h+2*f*g))*arctanh((a+c*x^2)^-1//2*(a*h^2+c*g^2)^-1//2*(a*h+-1*c*g*x))+-1*h^-1*(a+c*x^2)^(1/2)*(g+h*x)^-1*(a*h^2+c*g^2)^-1*(d*h^2+f*g^2+-1*e*g*h))
@test integrate((a+c*x^2)^-1//2*(g+h*x)^-3*(d+e*x+f*x^2), x) == :(-1//2*(a*h^2+c*g^2)^-5//2*(-1*a*c*(f*g^2+-1*h*(-1*d*h+3*e*g))+2*d*c^2*g^2+2*f*a^2*h^2)*arctanh((a+c*x^2)^-1//2*(a*h^2+c*g^2)^-1//2*(a*h+-1*c*g*x))+(1/2)*h^-1*(a+c*x^2)^(1/2)*(g+h*x)^-1*(a*h^2+c*g^2)^-2*(c*g*(f*g^2+h*(e*g+-3*d*h))+2*a*h^2*(-1*e*h+2*f*g))+-1//2*h^-1*(a+c*x^2)^(1/2)*(g+h*x)^-2*(a*h^2+c*g^2)^-1*(d*h^2+f*g^2+-1*e*g*h))
@test integrate((a+c*x^2)^-3//2*(g+h*x)^3*(d+e*x+f*x^2), x) == :(-1//2*c^-5//2*(-2*c*g*(f*g^2+3*h*(d*h+e*g))+3*a*h^2*(e*h+3*f*g))*arctanh(x*c^(1/2)*(a+c*x^2)^-1//2)+-1*a^-1*c^-1*(a+c*x^2)^-1//2*(g+h*x)^3*(a*e+-1*x*(c*d+-1*a*f))+-1//6*h*a^-1*c^-3*(a+c*x^2)^(1/2)*(-4*a*c*(3*h*(d*h+3*e*g)+7*f*g^2)+12*d*c^2*g^2+16*f*a^2*h^2+c*h*x*(-11*a*f*g+-9*a*e*h+6*c*d*g))+-1//3*h*a^-1*c^-2*(a+c*x^2)^(1/2)*(g+h*x)^2*(-4*a*f+3*c*d))
@test integrate((a+c*x^2)^-3//2*(g+h*x)^2*(d+e*x+f*x^2), x) == :((1/2)*c^-5//2*(h^2*(-3*a*f+2*c*d)+2*c*g*(f*g+2*e*h))*arctanh(x*c^(1/2)*(a+c*x^2)^-1//2)+-1*a^-1*c^-1*(a+c*x^2)^-1//2*(g+h*x)^2*(a*e+-1*x*(c*d+-1*a*f))+-1//2*h*a^-1*c^-2*(a+c*x^2)^(1/2)*(-4*a*(e*h+2*f*g)+h*x*(-3*a*f+2*c*d)+4*c*d*g))
@test integrate((a+c*x^2)^-3//2*(g+h*x)*(d+e*x+f*x^2), x) == :(c^-3//2*(e*h+f*g)*arctanh(x*c^(1/2)*(a+c*x^2)^-1//2)+-1*h*a^-1*c^-2*(a+c*x^2)^(1/2)*(c*d+-2*a*f)+-1*a^-1*c^-1*(a+c*x^2)^-1//2*(g+h*x)*(a*e+-1*x*(c*d+-1*a*f)))
@test integrate((a+c*x^2)^-3//2*(d+e*x+f*x^2), x) == :(f*c^-3//2*arctanh(x*c^(1/2)*(a+c*x^2)^-1//2)+-1*a^-1*c^-1*(a+c*x^2)^-1//2*(a*e+-1*x*(c*d+-1*a*f)))
@test integrate((a+c*x^2)^-3//2*(g+h*x)^-1*(d+e*x+f*x^2), x) == :(-1*(a*h^2+c*g^2)^-3//2*(d*h^2+f*g^2+-1*e*g*h)*arctanh((a+c*x^2)^-1//2*(a*h^2+c*g^2)^-1//2*(a*h+-1*c*g*x))+-1*a^-1*c^-1*(a+c*x^2)^-1//2*(a*h^2+c*g^2)^-1*(a*(a*f*h+c*e*g+-1*c*d*h)+-1*c*x*(a*e*h+c*d*g+-1*a*f*g)))
@test integrate((a+c*x^2)^-3//2*(g+h*x)^-2*(d+e*x+f*x^2), x) == :((a*h^2+c*g^2)^-5//2*(a*h^2*(-1*e*h+2*f*g)+-1*c*g*(f*g^2+-1*h*(-3*d*h+2*e*g)))*arctanh((a+c*x^2)^-1//2*(a*h^2+c*g^2)^-1//2*(a*h+-1*c*g*x))+-1*a^-1*(a+c*x^2)^-1//2*(a*h^2+c*g^2)^-2*(a*(a*h*(-1*e*h+2*f*g)+c*g*(e*g+-2*d*h))+-1*x*(d*c^2*g^2+f*a^2*h^2+-1*a*c*(f*g^2+-1*h*(-1*d*h+2*e*g))))+-1*h*(a+c*x^2)^(1/2)*(g+h*x)^-1*(a*h^2+c*g^2)^-2*(d*h^2+f*g^2+-1*e*g*h))
@test integrate((a+c*x^2)^-3//2*(g+h*x)^-3*(d+e*x+f*x^2), x) == :(-1//2*(a*h^2+c*g^2)^-7//2*(2*f*a^2*h^4+2*c^2*g^2*(f*g^2+6*d*h^2+-3*e*g*h)+-1*a*c*h^2*(3*d*h^2+11*f*g^2+-9*e*g*h))*arctanh((a+c*x^2)^-1//2*(a*h^2+c*g^2)^-1//2*(a*h+-1*c*g*x))+a^-1*(a+c*x^2)^-1//2*(a*h^2+c*g^2)^-3*(a*(f*a^2*h^3+-1*c^2*g^2*(e*g+-3*d*h)+-1*a*c*h*(-1*h*(-1*d*h+3*e*g)+3*f*g^2))+c*x*(d*c^2*g^3+a^2*h^2*(-1*e*h+3*f*g)+-1*a*c*g*(f*g^2+-3*h*(e*g+-1*d*h))))+(1/2)*h*(a+c*x^2)^(1/2)*(g+h*x)^-1*(a*h^2+c*g^2)^-3*(-1*c*g*(-1*h*(-7*d*h+5*e*g)+3*f*g^2)+2*a*h^2*(-1*e*h+2*f*g))+-1//2*h*(a+c*x^2)^(1/2)*(g+h*x)^-2*(a*h^2+c*g^2)^-2*(d*h^2+f*g^2+-1*e*g*h))
@test integrate((a+c*x^2)^-5//2*(A+B*x+C*x^2), x) == :(-1//3*a^-1*c^-1*(a+c*x^2)^-3//2*(B*a+-1*x*(A*c+-1*C*a))+1//3*x*a^-2*c^-1*(a+c*x^2)^-1//2*(C*a+2*A*c))
@test integrate((a+c*x^2)^-7//2*(A+B*x+C*x^2), x) == :(-1//5*a^-1*c^-1*(a+c*x^2)^-5//2*(B*a+-1*x*(A*c+-1*C*a))+1//15*x*a^-3*c^-1*(a+c*x^2)^-1//2*(2*C*a+8*A*c)+1//15*x*a^-2*c^-1*(a+c*x^2)^-3//2*(C*a+4*A*c))
@test integrate((a+c*x^2)^-9//2*(A+B*x+C*x^2), x) == :(-1//7*a^-1*c^-1*(a+c*x^2)^-7//2*(B*a+-1*x*(A*c+-1*C*a))+1//35*x*a^-2*c^-1*(a+c*x^2)^-5//2*(C*a+6*A*c)+1//105*x*a^-4*c^-1*(a+c*x^2)^-1//2*(8*C*a+48*A*c)+1//105*x*a^-3*c^-1*(a+c*x^2)^-3//2*(4*C*a+24*A*c))
@test integrate((1+2x)^3*(2+3*x^2)^-1//2*(1+3x+4*x^2), x) == :(-1*(2+3*x^2)^(1/2)*(3937//810+691//270*x)+-19//540*(1+2x)^2*(2+3*x^2)^(1/2)+2//15*(1+2x)^4*(2+3*x^2)^(1/2)+5//9*3^(1/2)*arcsinh((1/2)*x*6^(1/2))+13//60*(1+2x)^3*(2+3*x^2)^(1/2))
@test integrate((1+2x)^2*(2+3*x^2)^-1//2*(1+3x+4*x^2), x) == :(-1*3^(1/2)*arcsinh((1/2)*x*6^(1/2))+-1*(2+3*x^2)^(1/2)*(61//27+1//9*x)+1//6*(1+2x)^3*(2+3*x^2)^(1/2)+5//18*(1+2x)^2*(2+3*x^2)^(1/2))
@test integrate((2+3*x^2)^-1//2*(1+2x)*(1+3x+4*x^2), x) == :((2+3*x^2)^(1/2)*(7//27+7//9*x)+-7//9*3^(1/2)*arcsinh((1/2)*x*6^(1/2))+2//9*(1+2x)^2*(2+3*x^2)^(1/2))
@test integrate((1+2x)^-1*(2+3*x^2)^-1//2*(1+3x+4*x^2), x) == :(2//3*(2+3*x^2)^(1/2)+-1//22*11^(1/2)*arctanh(1//11*11^(1/2)*(2+3*x^2)^-1//2*(4+-3x))+1//6*3^(1/2)*arcsinh((1/2)*x*6^(1/2)))
@test integrate((1+2x)^-2*(2+3*x^2)^-1//2*(1+3x+4*x^2), x) == :(-1*(2+3*x^2)^(1/2)*(11+22x)^-1+1//3*3^(1/2)*arcsinh((1/2)*x*6^(1/2))+4//121*11^(1/2)*arctanh(1//11*11^(1/2)*(2+3*x^2)^-1//2*(4+-3x)))
@test integrate((1+2x)^-3*(2+3*x^2)^-1//2*(1+3x+4*x^2), x) == :(13*(2+3*x^2)^(1/2)*(242+484x)^-1+-103//1331*11^(1/2)*arctanh(1//11*11^(1/2)*(2+3*x^2)^-1//2*(4+-3x))+-1//22*(1+2x)^-2*(2+3*x^2)^(1/2))
@test integrate((1+2x)^3*(2+3*x^2)^-3//2*(1+3x+4*x^2), x) == :(292//81*(2+3*x^2)^(1/2)+4*x*(2+3*x^2)^(1/2)+-38//9*3^(1/2)*arcsinh((1/2)*x*6^(1/2))+1//54*(2+3*x^2)^-1//2*(398+279x)+32//27*x^2*(2+3*x^2)^(1/2))
@test integrate((1+2x)^2*(2+3*x^2)^-3//2*(1+3x+4*x^2), x) == :(28//9*(2+3*x^2)^(1/2)+1//18*(2+3*x^2)^-1//2*(70+-47x)+4//9*3^(1/2)*arcsinh((1/2)*x*6^(1/2))+8//9*x*(2+3*x^2)^(1/2))
@test integrate((2+3*x^2)^-3//2*(1+2x)*(1+3x+4*x^2), x) == :(8//9*(2+3*x^2)^(1/2)+1//18*(2+3*x^2)^-1//2*(2+-51x)+10//9*3^(1/2)*arcsinh((1/2)*x*6^(1/2)))
@test integrate((1+2x)^-1*(2+3*x^2)^-3//2*(1+3x+4*x^2), x) == :(-2//121*11^(1/2)*arctanh(1//11*11^(1/2)*(2+3*x^2)^-1//2*(4+-3x))+1//66*(2+3*x^2)^-1//2*(-38+21x))
@test integrate((1+2x)^-2*(2+3*x^2)^-3//2*(1+3x+4*x^2), x) == :(-4*(2+3*x^2)^(1/2)*(121+242x)^-1+1//242*(2+3*x^2)^-1//2*(-10+97x)+4//1331*11^(1/2)*arctanh(1//11*11^(1/2)*(2+3*x^2)^-1//2*(4+-3x)))
@test integrate((1+2x)^-3*(2+3*x^2)^-3//2*(1+3x+4*x^2), x) == :(2*(2+3*x^2)^(1/2)*(1331+2662x)^-1+-322//14641*11^(1/2)*arctanh(1//11*11^(1/2)*(2+3*x^2)^-1//2*(4+-3x))+-2//121*(1+2x)^-2*(2+3*x^2)^(1/2)+1//2662*(2+3*x^2)^-1//2*(358+351x))
@test integrate((1+2x)^3*(2+3*x^2)^-5//2*(1+3x+4*x^2), x) == :(32//27*(2+3*x^2)^(1/2)+-1//54*(2+3*x^2)^-1//2*(152+465x)+1//162*(2+3*x^2)^-3//2*(398+279x)+8//3*3^(1/2)*arcsinh((1/2)*x*6^(1/2)))
@test integrate((1+2x)^2*(2+3*x^2)^-5//2*(1+3x+4*x^2), x) == :(-1//54*(2+3*x^2)^-1//2*(168+59x)+1//54*(2+3*x^2)^-3//2*(70+-47x)+16//27*3^(1/2)*arcsinh((1/2)*x*6^(1/2)))
@test integrate((2+3*x^2)^-5//2*(1+2x)*(1+3x+4*x^2), x) == :(-1//18*(2+3*x^2)^-1//2*(16+-13x)+1//54*(2+3*x^2)^-3//2*(2+-51x))
@test integrate((1+2x)^-1*(2+3*x^2)^-5//2*(1+3x+4*x^2), x) == :(-8//1331*11^(1/2)*arctanh(1//11*11^(1/2)*(2+3*x^2)^-1//2*(4+-3x))+1//198*(2+3*x^2)^-3//2*(-38+21x)+1//726*(2+3*x^2)^-1//2*(24+95x))
@test integrate((1+2x)^-2*(2+3*x^2)^-5//2*(1+3x+4*x^2), x) == :(-16*(2+3*x^2)^(1/2)*(1331+2662x)^-1+-32//14641*11^(1/2)*arctanh(1//11*11^(1/2)*(2+3*x^2)^-1//2*(4+-3x))+1//726*(2+3*x^2)^-3//2*(-10+97x)+1//7986*(2+3*x^2)^-1//2*(24+887x))
@test integrate((1+2x)^-3*(2+3*x^2)^-5//2*(1+3x+4*x^2), x) == :(-8*(2+3*x^2)^(1/2)*(1331+2662x)^-1+-1216//161051*11^(1/2)*arctanh(1//11*11^(1/2)*(2+3*x^2)^-1//2*(4+-3x))+-8//1331*(1+2x)^-2*(2+3*x^2)^(1/2)+1//7986*(2+3*x^2)^-3//2*(358+351x)+1//29282*(2+3*x^2)^-1//2*(1216+2133x))
@test integrate((a+b*x+c*x^2)^4*(A+C*x^2), x) == :(x^5*(1//5*A*(b^4+6*a^2*c^2+12*a*c*b^2)+2//5*C*a^2*(3*b^2+2*a*c))+x^7*(1//7*C*(b^4+6*a^2*c^2+12*a*c*b^2)+2//7*A*c^2*(3*b^2+2*a*c))+A*x*a^4+1//3*a^2*x^3*(C*a^2+6*A*b^2+4*A*a*c)+1//9*c^2*x^9*(A*c^2+6*C*b^2+4*C*a*c)+1//11*C*c^4*x^11+a*b*x^4*(A*(b^2+3*a*c)+C*a^2)+(1/2)*b*c*x^8*(A*c^2+C*(b^2+3*a*c))+2*A*b*a^3*x^2+2//3*b*x^6*(b^2+3*a*c)*(A*c+C*a)+2//5*C*b*c^3*x^10)
@test integrate((a+b*x+c*x^2)^3*(A+C*x^2), x) == :(A*x*a^3+x^5*(3//5*b^2+3//5*a*c)*(A*c+C*a)+1//3*a*x^3*(C*a^2+3*A*(b^2+a*c))+1//4*b*x^4*(A*(b^2+6*a*c)+3*C*a^2)+1//6*b*x^6*(C*(b^2+6*a*c)+3*A*c^2)+1//7*c*x^7*(A*c^2+C*(3*b^2+3*a*c))+1//9*C*c^3*x^9+3//2*A*b*a^2*x^2+3//8*C*b*c^2*x^8)
@test integrate((a+b*x+c*x^2)^2*(A+C*x^2), x) == :(x^3*(1//3*A*(b^2+2*a*c)+1//3*C*a^2)+x^5*(1//5*A*c^2+1//5*C*(b^2+2*a*c))+A*x*a^2+(1/2)*b*x^4*(A*c+C*a)+1//7*C*c^2*x^7+A*a*b*x^2+1//3*C*b*c*x^6)
@test integrate((A+C*x^2)*(a+b*x+c*x^2), x) == :(x^3*(1//3*A*c+1//3*C*a)+A*a*x+(1/2)*A*b*x^2+1//4*C*b*x^4+1//5*C*c*x^5)
@test integrate((a+b*x+c*x^2)^-1*(A+C*x^2), x) == :(C*x*c^-1+-1*c^-2*(b^2+-4*a*c)^-1//2*(C*(b^2+-2*a*c)+2*A*c^2)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x))+-1//2*C*b*c^-2*log(a+b*x+c*x^2))
@test integrate((a+b*x+c*x^2)^-2*(A+C*x^2), x) == :((b^2+-4*a*c)^-3//2*(4*A*c+4*C*a)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x))+-1*c^-1*(b^2+-4*a*c)^-1*(a+b*x+c*x^2)^-1*(x*(C*(b^2+-2*a*c)+2*A*c^2)+b*c*(A+C*a*c^-1)))
@test integrate((a+b*x+c*x^2)^-3*(A+C*x^2), x) == :(-1*(b^2+-4*a*c)^-5//2*(2*C*(b^2+2*a*c)+12*A*c^2)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x))+(1/2)*(b^2+-4*a*c)^-2*(a+b*x+c*x^2)^-1*(b+2*c*x)*(2*C*a+6*A*c+C*b^2*c^-1)+-1//2*c^-1*(b^2+-4*a*c)^-1*(a+b*x+c*x^2)^-2*(x*(C*(b^2+-2*a*c)+2*A*c^2)+b*c*(A+C*a*c^-1)))
@test integrate((a+b*x+c*x^2)^-4*(A+C*x^2), x) == :(-1*(b^2+-4*a*c)^-3*(a+b*x+c*x^2)^-1*(b+2*c*x)*(2*C*(b^2+a*c)+10*A*c^2)+8*c*(b^2+-4*a*c)^-7//2*(C*(b^2+a*c)+5*A*c^2)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x))+-1//3*c^-1*(b^2+-4*a*c)^-1*(a+b*x+c*x^2)^-3*(x*(C*(b^2+-2*a*c)+2*A*c^2)+b*c*(A+C*a*c^-1))+1//3*(b^2+-4*a*c)^-2*(a+b*x+c*x^2)^-2*(b+2*c*x)*(C*(a+b^2*c^-1)+5*A*c))
@test integrate((d+e*x)^3*(a+b*x+c*x^2)^-1*(f+g*x+h*x^2), x) == :((1/2)*c^-5*(-1*c^3*(a*e*(f*e^2+3*h*d^2+3*d*e*g)+b*d*(h*d^2+3*f*e^2+3*d*e*g))+e*c^2*(b^2*(f*e^2+3*h*d^2+3*d*e*g)+h*a^2*e^2+2*a*b*e*(e*g+3*d*h))+h*b^4*e^3+c^4*d^2*(d*g+3*e*f)+-1*c*b^2*e^2*(b*e*g+3*a*e*h+3*b*d*h))*log(a+b*x+c*x^2)+-1*x*c^-4*(e*c^2*(b*(f*e^2+3*h*d^2+3*d*e*g)+a*e*(e*g+3*d*h))+h*b^3*e^3+-1*d*c^3*(h*d^2+3*f*e^2+3*d*e*g)+-1*b*c*e^2*(b*e*g+2*a*e*h+3*b*d*h))+(1/2)*e*c^-3*x^2*(c^2*(f*e^2+3*h*d^2+3*d*e*g)+h*b^2*e^2+-1*c*e*(a*e*h+b*e*g+3*b*d*h))+-1*c^-5*(b^2+-4*a*c)^-1//2*(c^3*(d*b^2*(h*d^2+3*f*e^2+3*d*e*g)+2*a^2*e^2*(e*g+3*d*h)+3*a*b*e*(f*e^2+3*h*d^2+3*d*e*g))+-1*d*c^4*(2*a*(h*d^2+3*f*e^2+3*d*e*g)+b*d*(d*g+3*e*f))+-1*h*b^5*e^3+2*f*c^5*d^3+c*b^3*e^2*(b*e*g+3*b*d*h+5*a*e*h)+-1*b*e*c^2*(b^2*(f*e^2+3*h*d^2+3*d*e*g)+5*h*a^2*e^2+4*a*b*e*(e*g+3*d*h)))*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x))+1//3*c^-2*e^2*x^3*(c*e*g+-1*b*e*h+3*c*d*h)+1//4*h*c^-1*e^3*x^4)
@test integrate((d+e*x)^2*(a+b*x+c*x^2)^-1*(f+g*x+h*x^2), x) == :(x*c^-3*(c^2*(f*e^2+h*d^2+2*d*e*g)+h*b^2*e^2+-1*c*e*(a*e*h+b*e*g+2*b*d*h))+(1/2)*c^-4*(-1*c^2*(b*(f*e^2+h*d^2+2*d*e*g)+a*e*(e*g+2*d*h))+d*c^3*(d*g+2*e*f)+-1*h*b^3*e^2+b*c*e*(b*e*g+2*a*e*h+2*b*d*h))*log(a+b*x+c*x^2)+(1/2)*e*c^-2*x^2*(c*e*g+-1*b*e*h+2*c*d*h)+-1*c^-4*(b^2+-4*a*c)^-1//2*(c^2*(b^2*(f*e^2+h*d^2+2*d*e*g)+2*h*a^2*e^2+3*a*b*e*(e*g+2*d*h))+-1*c^3*(2*a*(f*e^2+h*d^2+2*d*e*g)+b*d*(d*g+2*e*f))+h*b^4*e^2+2*f*c^4*d^2+-1*c*e*b^2*(b*e*g+2*b*d*h+4*a*e*h))*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x))+1//3*h*c^-1*e^2*x^3)
@test integrate((a+b*x+c*x^2)^-1*(d+e*x)*(f+g*x+h*x^2), x) == :(x*c^-2*(c*d*h+c*e*g+-1*b*e*h)+(1/2)*c^-3*(c^2*(d*g+e*f)+-1*c*(a*e*h+b*d*h+b*e*g)+e*h*b^2)*log(a+b*x+c*x^2)+(1/2)*e*h*c^-1*x^2+-1*c^-3*(b^2+-4*a*c)^-1//2*(-1*c^2*(b*d*g+b*e*f+2*a*d*h+2*a*e*g)+b*c*(b*d*h+b*e*g+3*a*e*h)+-1*e*h*b^3+2*d*f*c^3)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x)))
@test integrate((a+b*x+c*x^2)^-1*(f+g*x+h*x^2), x) == :(h*x*c^-1+(1/2)*c^-2*(c*g+-1*b*h)*log(a+b*x+c*x^2)+-1*c^-2*(b^2+-4*a*c)^-1//2*(h*b^2+2*f*c^2+-1*b*c*g+-2*a*c*h)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x)))
@test integrate((d+e*x)^-1*(a+b*x+c*x^2)^-1*(f+g*x+h*x^2), x) == :(e^-1*(a*e^2+c*d^2+-1*b*d*e)^-1*(f*e^2+h*d^2+-1*d*e*g)*log(d+e*x)+-1//2*c^-1*(a*e^2+c*d^2+-1*b*d*e)^-1*(b*d*h+c*e*f+-1*a*e*h+-1*c*d*g)*log(a+b*x+c*x^2)+-1*c^-1*(b^2+-4*a*c)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1*(-1*c*(b*d*g+b*e*f+-2*a*e*g+2*a*d*h)+b*h*(b*d+-1*a*e)+2*d*f*c^2)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x)))
@test integrate((d+e*x)^-2*(a+b*x+c*x^2)^-1*(f+g*x+h*x^2), x) == :((a*e^2+c*d^2+-1*b*d*e)^-2*(-1*b*(f*e^2+-1*h*d^2)+a*e*(e*g+-2*d*h)+c*d*(-1*d*g+2*e*f))*log(d+e*x)+-1//2*(a*e^2+c*d^2+-1*b*d*e)^-2*(-1*b*(f*e^2+-1*h*d^2)+a*e*(e*g+-2*d*h)+c*d*(-1*d*g+2*e*f))*log(a+b*x+c*x^2)+-1*e^-1*(d+e*x)^-1*(a*e^2+c*d^2+-1*b*d*e)^-1*(f*e^2+h*d^2+-1*d*e*g)+-1*(b^2+-4*a*c)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-2*(b^2*(f*e^2+h*d^2)+-1*c*(2*a*(f*e^2+h*d^2+-2*d*e*g)+b*d*(d*g+2*e*f))+2*f*c^2*d^2+2*h*a^2*e^2+-1*a*b*e*(e*g+2*d*h))*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x)))
@test integrate((d+e*x)^-3*(a+b*x+c*x^2)^-1*(f+g*x+h*x^2), x) == :((a*e^2+c*d^2+-1*b*d*e)^-3*(e^3*(f*b^2+h*a^2+-1*a*b*g)+-1*c*(b*(-1*h*d^3+3*d*f*e^2)+a*e*(f*e^2+3*h*d^2+-3*d*e*g))+c^2*d^2*(-1*d*g+3*e*f))*log(d+e*x)+-1*(d+e*x)^-1*(a*e^2+c*d^2+-1*b*d*e)^-2*(-1*b*(f*e^2+-1*h*d^2)+a*e*(e*g+-2*d*h)+c*d*(-1*d*g+2*e*f))+-1//2*(a*e^2+c*d^2+-1*b*d*e)^-3*(e^3*(f*b^2+h*a^2+-1*a*b*g)+-1*c*(b*(-1*h*d^3+3*d*f*e^2)+a*e*(f*e^2+3*h*d^2+-3*d*e*g))+c^2*d^2*(-1*d*g+3*e*f))*log(a+b*x+c*x^2)+-1*(b^2+-4*a*c)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-3*(-1*c*(-1*b^2*(h*d^3+3*d*f*e^2)+2*a^2*e^2*(e*g+-3*d*h)+-3*a*b*e*(f*e^2+-1*h*d^2+-1*d*e*g))+-1*b*e^3*(f*b^2+h*a^2+-1*a*b*g)+-1*d*c^2*(2*a*(h*d^2+3*f*e^2+-3*d*e*g)+b*d*(d*g+3*e*f))+2*f*c^3*d^3)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x))+-1//2*e^-1*(d+e*x)^-2*(a*e^2+c*d^2+-1*b*d*e)^-1*(f*e^2+h*d^2+-1*d*e*g))
@test integrate((a+b*x+c*x^2)^-2*(d+e*x)*(f+g*x+h*x^2), x) == :(c^-2*(b^2+-4*a*c)^-3//2*(-2*c^2*(b*(d*g+e*f)+-2*a*(d*h+e*g))+e*h*b^3+4*d*f*c^3+-6*a*b*c*e*h)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x))+(1/2)*e*h*c^-2*log(a+b*x+c*x^2)+c^-1*(b^2+-4*a*c)^-1*(a+b*x+c*x^2)^-1*(d+e*x)*(c*(-1*b*(f+a*h*c^-1)+2*a*g)+-1*x*(h*b^2+2*f*c^2+-1*b*c*g+-2*a*c*h)))
@test integrate((a+b*x+c*x^2)^-2*(f+g*x+h*x^2), x) == :((b^2+-4*a*c)^-3//2*(-2*b*g+4*a*h+4*c*f)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x))+c^-1*(b^2+-4*a*c)^-1*(a+b*x+c*x^2)^-1*(c*(-1*b*(f+a*h*c^-1)+2*a*g)+-1*x*(h*b^2+2*f*c^2+-1*b*c*g+-2*a*c*h)))
@test integrate((d+e*x)^-1*(a+b*x+c*x^2)^-2*(f+g*x+h*x^2), x) == :(e*(a*e^2+c*d^2+-1*b*d*e)^-2*(f*e^2+h*d^2+-1*d*e*g)*log(d+e*x)+(b^2+-4*a*c)^-1*(a+b*x+c*x^2)^-1*(a*e^2+c*d^2+-1*b*d*e)^-1*(-1*b*(a*d*h+a*e*g+c*d*f)+-1*x*(-1*c*(b*d*g+b*e*f+-2*a*e*g+2*a*d*h)+b*h*(b*d+-1*a*e)+2*d*f*c^2)+-2*a*(c*e*f+-1*a*e*h+-1*c*d*g)+e*f*b^2)+(b^2+-4*a*c)^-3//2*(a*e^2+c*d^2+-1*b*d*e)^-2*(b*e*(b^2*(f*e^2+-1*h*d^2+-1*d*e*g)+-2*h*a^2*e^2+4*a*b*d*e*h)+-2*d*c^2*(-2*a*(h*d^2+3*f*e^2+-1*d*e*g)+b*d*(d*g+3*e*f))+2*c*e*(-1*a*b*(h*d^2+3*f*e^2+d*e*g)+2*e*a^2*(e*g+-1*d*h)+2*g*b^2*d^2)+4*f*c^3*d^3)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x))+-1//2*e*(a*e^2+c*d^2+-1*b*d*e)^-2*(f*e^2+h*d^2+-1*d*e*g)*log(a+b*x+c*x^2))
@test integrate((d+e*x)^-2*(a+b*x+c*x^2)^-2*(f+g*x+h*x^2), x) == :((b^2+-4*a*c)^-3//2*(a*e^2+c*d^2+-1*b*d*e)^-3*(-1*c*e*(-1*d*b^3*(-2*h*d^2+4*f*e^2+-3*d*e*g)+-4*h*a^3*e^3+-6*a*e*b^2*(2*f*e^2+2*h*d^2+-1*d*e*g)+6*b*g*a^2*e^3)+-1*b^3*e^3*(-1*a*e*g+-1*b*d*g+2*a*d*h+2*b*e*f)+-6*e*c^2*(-1*g*b^2*d^3+2*e*a^2*(f*e^2+2*h*d^2+-2*d*e*g)+4*a*b*d*f*e^2)+-2*c^3*d^2*(-2*a*(h*d^2+6*f*e^2+-2*d*e*g)+b*d*(d*g+4*e*f))+4*f*c^4*d^4)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x))+(1/2)*e*(a*e^2+c*d^2+-1*b*d*e)^-3*(e^2*(-1*a*e*g+-1*b*d*g+2*a*d*h+2*b*e*f)+-1*c*d*(2*h*d^2+4*f*e^2+-3*d*e*g))*log(a+b*x+c*x^2)+-1*e*(d+e*x)^-1*(a*e^2+c*d^2+-1*b*d*e)^-2*(f*e^2+h*d^2+-1*d*e*g)+-1*e*(a*e^2+c*d^2+-1*b*d*e)^-3*(e^2*(-1*a*e*g+-1*b*d*g+2*a*d*h+2*b*e*f)+-1*c*d*(2*h*d^2+4*f*e^2+-3*d*e*g))*log(d+e*x)+-1*(b^2+-4*a*c)^-1*(a+b*x+c*x^2)^-1*(a*e^2+c*d^2+-1*b*d*e)^-2*(b*(f*c^2*d^2+h*a^2*e^2+-1*a*c*(-1*h*d^2+3*f*e^2+-2*d*e*g))+c*x*(b^2*(f*e^2+h*d^2)+-1*c*(2*a*(f*e^2+h*d^2+-2*d*e*g)+b*d*(d*g+2*e*f))+2*f*c^2*d^2+2*h*a^2*e^2+-1*a*b*e*(e*g+2*d*h))+f*b^3*e^2+-1*e*b^2*(a*e*g+2*c*d*f)+2*a*c*(a*e*(e*g+-2*d*h)+c*d*(-1*d*g+2*e*f))))
@test integrate(x^3*(1+x^2+-1x)^-2*(1+x+x^2), x) == :((1/2)*x^2+2*log(1+x^2+-1x)+3x+(3+-3x+3*x^2)^-1*(4+-2x)+10//9*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2x)))
@test integrate(x^2*(1+x^2+-1x)^-2*(1+x+x^2), x) == :(x+3//2*log(1+x^2+-1x)+(3+-3x+3*x^2)^-1*(2+-4x)+-7//9*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2x)))
@test integrate(x*(1+x^2+-1x)^-2*(1+x+x^2), x) == :((1/2)*log(1+x^2+-1x)+-1*(3+-3x+3*x^2)^-1*(2+2x)+-11//9*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2x)))
@test integrate((1+x^2+-1x)^-2*(1+x+x^2), x) == :(-1*(3+-3x+3*x^2)^-1*(4+-2x)+-10//9*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2x)))
@test integrate(x^-1*(1+x^2+-1x)^-2*(1+x+x^2), x) == :(-1//2*log(1+x^2+-1x)+-1*(3+-3x+3*x^2)^-1*(2+-4x)+-11//9*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2x))+log(x))
@test integrate(x^-2*(1+x^2+-1x)^-2*(1+x+x^2), x) == :(-1*x^-1+3*log(x)+-3//2*log(1+x^2+-1x)+(3+-3x+3*x^2)^-1*(2+2x)+-7//9*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2x)))
@test integrate(x^-3*(1+x^2+-1x)^-2*(1+x+x^2), x) == :(-3*x^-1+-2*log(1+x^2+-1x)+4*log(x)+-1//2*x^-2+(3+-3x+3*x^2)^-1*(4+-2x)+10//9*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2x)))
@test integrate((1+x+x^2)^-2*(1+-1*x^2), x) == :(x*(1+x+x^2)^-1)
@test integrate((1+x+x^2)^-1*(1+x^2), x) == :(x+-1//2*log(1+x+x^2)+1//3*3^(1/2)*arctan(1//3*3^(1/2)*(1+2x)))
@test integrate((25+x^2+-6x)^-1*(-1+x^2), x) == :(x+-2*arctan(-3//4+1//4*x)+3*log(25+x^2+-6x))
@test integrate((4+x^2+-4x)^-1*(-10+3*x^2), x) == :(2*(2+-1x)^-1+3x+12*log(2+-1x))
@test integrate((6+x^2+-5x)^-1*(8+x^2), x) == :(x+-12*log(2+-1x)+17*log(3+-1x))
@test integrate((-8+x^2+-2x)^-1*(-4+x^2+3x), x) == :(x+4*log(4+-1x)+log(2+x))
@test integrate((5+4x+4*x^2)^-1*(7+4*x^2+5x), x) == :(x+1//8*log(5+4x+4*x^2)+3//8*arctan(1/2+x))
@test integrate((-5+x^2+2x)^-1*(2+x^2+-1x), x) == :(x+-1*(3//2+-5//6*6^(1/2))*log(1+x+-1*6^(1/2))+-1*(3//2+5//6*6^(1/2))*log(1+x+6^(1/2)))
@test integrate((4+2*x^2+7x)^-2*(1+3*x^2+4x), x) == :(-1*(8+4*x^2+14x)^-1*(2+3x))
@test integrate((3+x^2+2x)^-2*(1+x+x^2), x) == :((12+4*x^2+8x)^-1*(1+-1x)+3//8*2^(1/2)*arctan((1/2)*2^(1/2)*(1+x)))
@test integrate((1+x+x^2)^-4*(-1+2x+5*x^2), x) == :(-1*x*(1+x+x^2)^-3)
@test integrate((a+b*x+c*x^2)^5//2*(A+C*x^2), x) == :(-9//112*C*b*c^-2*(a+b*x+c*x^2)^7//2+-5//32768*c^-11//2*(b^2+-4*a*c)^3*(9*C*b^2+32*A*c^2+-4*C*a*c)*arctanh((1/2)*c^-1//2*(a+b*x+c*x^2)^-1//2*(b+2*c*x))+1//8*C*x*c^-1*(a+b*x+c*x^2)^7//2+1//384*c^-3*(a+b*x+c*x^2)^5//2*(b+2*c*x)*(9*C*b^2+32*A*c^2+-4*C*a*c)+-1//6144*c^-4*(a+b*x+c*x^2)^3//2*(b+2*c*x)*(5*b^2+-20*a*c)*(9*C*b^2+32*A*c^2+-4*C*a*c)+5//16384*c^-5*(b^2+-4*a*c)^2*(a+b*x+c*x^2)^(1/2)*(b+2*c*x)*(9*C*b^2+32*A*c^2+-4*C*a*c))
@test integrate((a+b*x+c*x^2)^3//2*(A+C*x^2), x) == :(-7//60*C*b*c^-2*(a+b*x+c*x^2)^5//2+1//6*C*x*c^-1*(a+b*x+c*x^2)^5//2+1//192*c^-3*(a+b*x+c*x^2)^3//2*(b+2*c*x)*(7*C*b^2+24*A*c^2+-4*C*a*c)+1//1024*c^-9//2*(b^2+-4*a*c)^2*(7*C*b^2+24*A*c^2+-4*C*a*c)*arctanh((1/2)*c^-1//2*(a+b*x+c*x^2)^-1//2*(b+2*c*x))+-1//512*c^-4*(a+b*x+c*x^2)^(1/2)*(b+2*c*x)*(b^2+-4*a*c)*(7*C*b^2+24*A*c^2+-4*C*a*c))
@test integrate((a+b*x+c*x^2)^(1/2)*(A+C*x^2), x) == :(-5//24*C*b*c^-2*(a+b*x+c*x^2)^3//2+-1//128*c^-7//2*(b^2+-4*a*c)*(5*C*b^2+16*A*c^2+-4*C*a*c)*arctanh((1/2)*c^-1//2*(a+b*x+c*x^2)^-1//2*(b+2*c*x))+1//4*C*x*c^-1*(a+b*x+c*x^2)^3//2+1//64*c^-3*(a+b*x+c*x^2)^(1/2)*(b+2*c*x)*(5*C*b^2+16*A*c^2+-4*C*a*c))
@test integrate((a+b*x+c*x^2)^-1//2*(A+C*x^2), x) == :(1//8*c^-5//2*(3*C*b^2+8*A*c^2+-4*C*a*c)*arctanh((1/2)*c^-1//2*(a+b*x+c*x^2)^-1//2*(b+2*c*x))+(1/2)*C*x*c^-1*(a+b*x+c*x^2)^(1/2)+-3//4*C*b*c^-2*(a+b*x+c*x^2)^(1/2))
@test integrate((a+b*x+c*x^2)^-3//2*(A+C*x^2), x) == :(C*c^-3//2*arctanh((1/2)*c^-1//2*(a+b*x+c*x^2)^-1//2*(b+2*c*x))+-1*c^-1*(b^2+-4*a*c)^-1*(a+b*x+c*x^2)^-1//2*(2*x*(C*(b^2+-2*a*c)+2*A*c^2)+2*b*c*(A+C*a*c^-1)))
@test integrate((a+b*x+c*x^2)^-5//2*(A+C*x^2), x) == :(-1//3*c^-1*(b^2+-4*a*c)^-1*(a+b*x+c*x^2)^-3//2*(2*x*(C*(b^2+-2*a*c)+2*A*c^2)+2*b*c*(A+C*a*c^-1))+1//3*(b^2+-4*a*c)^-2*(a+b*x+c*x^2)^-1//2*(b+2*c*x)*(8*C*a+16*A*c+2*C*b^2*c^-1))
@test integrate((a+b*x+c*x^2)^-7//2*(A+C*x^2), x) == :(-1//5*c^-1*(b^2+-4*a*c)^-1*(a+b*x+c*x^2)^-5//2*(2*x*(C*(b^2+-2*a*c)+2*A*c^2)+2*b*c*(A+C*a*c^-1))+-1//15*(b^2+-4*a*c)^-3*(a+b*x+c*x^2)^-1//2*(b+2*c*x)*(48*C*b^2+256*A*c^2+64*C*a*c)+1//15*(b^2+-4*a*c)^-2*(a+b*x+c*x^2)^-3//2*(b+2*c*x)*(8*C*a+32*A*c+6*C*b^2*c^-1))
@test integrate((a+b*x+c*x^2)^-9//2*(A+C*x^2), x) == :(-1//7*c^-1*(b^2+-4*a*c)^-1*(a+b*x+c*x^2)^-7//2*(2*x*(C*(b^2+-2*a*c)+2*A*c^2)+2*b*c*(A+C*a*c^-1))+-1//105*(b^2+-4*a*c)^-3*(a+b*x+c*x^2)^-3//2*(b+2*c*x)*(160*C*b^2+768*A*c^2+128*C*a*c)+1//35*(b^2+-4*a*c)^-2*(a+b*x+c*x^2)^-5//2*(b+2*c*x)*(8*C*a+48*A*c+10*C*b^2*c^-1)+256//105*c*(b^2+-4*a*c)^-4*(a+b*x+c*x^2)^-1//2*(b+2*c*x)*(5*C*b^2+24*A*c^2+4*C*a*c))
@test integrate((g+h*x)^3*(a+b*x+c*x^2)^(1/2)*(d+e*x+f*x^2), x) == :(-1//2048*c^-13//2*(b^2+-4*a*c)*(16*c^3*(2*a^2*h^2*(e*h+3*f*g)+5*g*b^2*(f*g^2+3*h*(d*h+e*g))+6*a*b*h*(h*(d*h+3*e*g)+3*f*g^2))+-64*g*c^4*(a*(f*g^2+3*h*(d*h+e*g))+2*b*g*(e*g+3*d*h))+-33*f*b^5*h^3+256*d*c^5*g^3+-8*b*h*c^2*(7*b^2*(d*h^2+3*f*g^2+3*e*g*h)+10*f*a^2*h^2+14*a*b*h*(e*h+3*f*g))+6*c*b^3*h^2*(7*b*(e*h+3*f*g)+20*a*f*h))*arctanh((1/2)*c^-1//2*(a+b*x+c*x^2)^-1//2*(b+2*c*x))+1//1024*c^-6*(a+b*x+c*x^2)^(1/2)*(b+2*c*x)*(16*c^3*(2*a^2*h^2*(e*h+3*f*g)+5*g*b^2*(f*g^2+3*h*(d*h+e*g))+6*a*b*h*(h*(d*h+3*e*g)+3*f*g^2))+-64*g*c^4*(a*(f*g^2+3*h*(d*h+e*g))+2*b*g*(e*g+3*d*h))+-33*f*b^5*h^3+256*d*c^5*g^3+-8*b*h*c^2*(7*b^2*(d*h^2+3*f*g^2+3*e*g*h)+10*f*a^2*h^2+14*a*b*h*(e*h+3*f*g))+6*c*b^3*h^2*(7*b*(e*h+3*f*g)+20*a*f*h))+1//13440*c^-5*h^-1*(a+b*x+c*x^2)^3//2*(-128*c^4*g^2*(-7*h*(e*g+12*d*h)+3*f*g^2)+-16*h*c^3*(b*g*(17*f*g^2+21*h*(19*e*g+25*d*h))+16*a*h*(7*h*(d*h+3*e*g)+15*f*g^2))+8*c^2*h^2*(b^2*(245*h*(d*h+3*e*g)+537*f*g^2)+128*f*a^2*h^2+343*a*b*h*(e*h+3*f*g))+1155*f*b^4*h^4+-42*c*b^2*h^3*(35*b*(e*h+3*f*g)+78*a*f*h)+-6*c*h*x*(8*h*c^2*(b*(5*f*g^2+7*h*(7*d*h+9*e*g))+a*h*(35*e*h+41*f*g))+16*g*c^3*(-7*h*(e*g+7*d*h)+3*f*g^2)+231*f*b^3*h^3+-6*b*c*h^2*(49*b*e*h+59*b*f*g+74*a*f*h)))+-1//84*c^-2*h^-1*(g+h*x)^3*(a+b*x+c*x^2)^3//2*(-14*c*e*h+6*c*f*g+11*b*f*h)+1//7*f*c^-1*h^-1*(g+h*x)^4*(a+b*x+c*x^2)^3//2+1//280*c^-3*h^-1*(g+h*x)^2*(a+b*x+c*x^2)^3//2*(-4*c^2*(-7*h*(e*g+2*d*h)+3*f*g^2)+-2*c*h*(8*b*f*g+16*a*f*h+21*b*e*h)+33*f*b^2*h^2))
@test integrate((g+h*x)^2*(a+b*x+c*x^2)^(1/2)*(d+e*x+f*x^2), x) == :(-1//960*c^-4*h^-1*(a+b*x+c*x^2)^3//2*(8*h*c^2*(b*(7*f*g^2+25*h*(d*h+2*e*g))+16*a*h*(e*h+2*f*g))+64*g*c^3*(f*g^2+-2*h*(e*g+5*d*h))+105*f*b^3*h^3+-28*b*c*h^2*(5*b*(e*h+2*f*g)+7*a*f*h)+-6*c*h*x*(-8*c^2*(f*g^2+-1*h*(2*e*g+5*d*h))+-4*c*h*(2*b*f*g+5*a*f*h+7*b*e*h)+21*f*b^2*h^2))+-1//1024*c^-11//2*(b^2+-4*a*c)*(-32*c^3*(a*(d*h^2+f*g^2+2*e*g*h)+2*b*g*(e*g+2*d*h))+8*c^2*(5*b^2*(d*h^2+f*g^2+2*e*g*h)+2*f*a^2*h^2+6*a*b*h*(e*h+2*f*g))+21*f*b^4*h^2+128*d*c^4*g^2+-28*c*h*b^2*(b*e*h+2*a*f*h+2*b*f*g))*arctanh((1/2)*c^-1//2*(a+b*x+c*x^2)^-1//2*(b+2*c*x))+1//512*c^-5*(a+b*x+c*x^2)^(1/2)*(b+2*c*x)*(-32*c^3*(a*(d*h^2+f*g^2+2*e*g*h)+2*b*g*(e*g+2*d*h))+8*c^2*(5*b^2*(d*h^2+f*g^2+2*e*g*h)+2*f*a^2*h^2+6*a*b*h*(e*h+2*f*g))+21*f*b^4*h^2+128*d*c^4*g^2+-28*c*h*b^2*(b*e*h+2*a*f*h+2*b*f*g))+-1//20*c^-2*h^-1*(g+h*x)^2*(a+b*x+c*x^2)^3//2*(-4*c*e*h+2*c*f*g+3*b*f*h)+1//6*f*c^-1*h^-1*(g+h*x)^3*(a+b*x+c*x^2)^3//2)
@test integrate((a+b*x+c*x^2)^(1/2)*(g+h*x)*(d+e*x+f*x^2), x) == :(-1//256*c^-9//2*(b^2+-4*a*c)*(-8*c^2*(a*e*h+a*f*g+2*b*d*h+2*b*e*g)+-7*f*h*b^3+2*b*c*(5*b*(e*h+f*g)+6*a*f*h)+32*d*g*c^3)*arctanh((1/2)*c^-1//2*(a+b*x+c*x^2)^-1//2*(b+2*c*x))+1//128*c^-4*(a+b*x+c*x^2)^(1/2)*(b+2*c*x)*(-8*c^2*(a*e*h+a*f*g+2*b*d*h+2*b*e*g)+-7*f*h*b^3+2*b*c*(5*b*(e*h+f*g)+6*a*f*h)+32*d*g*c^3)+1//240*c^-3*h^-1*(a+b*x+c*x^2)^3//2*(-16*c^2*(-5*h*(d*h+e*g)+3*f*g^2)+-2*c*h*(25*b*(e*h+f*g)+16*a*f*h)+35*f*b^2*h^2+-6*c*h*x*(-10*c*e*h+6*c*f*g+7*b*f*h))+1//5*f*c^-1*h^-1*(g+h*x)^2*(a+b*x+c*x^2)^3//2)
@test integrate((a+b*x+c*x^2)^(1/2)*(d+e*x+f*x^2), x) == :(1//24*c^-2*(a+b*x+c*x^2)^3//2*(-5*b*f+8*c*e)+-1//128*c^-7//2*(b^2+-4*a*c)*(-4*c*(a*f+2*b*e)+5*f*b^2+16*d*c^2)*arctanh((1/2)*c^-1//2*(a+b*x+c*x^2)^-1//2*(b+2*c*x))+1//4*f*x*c^-1*(a+b*x+c*x^2)^3//2+1//64*c^-3*(a+b*x+c*x^2)^(1/2)*(b+2*c*x)*(5*f*b^2+16*d*c^2+-8*b*c*e+-4*a*c*f))
@test integrate((g+h*x)^-1*(a+b*x+c*x^2)^(1/2)*(d+e*x+f*x^2), x) == :(h^-4*(a*h^2+c*g^2+-1*b*g*h)^(1/2)*(d*h^2+f*g^2+-1*e*g*h)*arctanh((1/2)*(a+b*x+c*x^2)^-1//2*(a*h^2+c*g^2+-1*b*g*h)^-1//2*(b*g+x*(-1*b*h+2*c*g)+-2*a*h))+-1//8*c^-2*h^-3*(a+b*x+c*x^2)^(1/2)*(-1*(-1*b*h+4*c*g)*(b*f*h+-2*c*e*h+2*c*f*g)+4*c*h*(b*f*g+-2*c*d*h)+2*c*h*x*(b*f*h+-2*c*e*h+2*c*f*g))+1//3*f*c^-1*h^-1*(a+b*x+c*x^2)^3//2+1//16*c^-5//2*h^-4*(-1*(-1*b^2*h^2+8*c^2*g^2+-4*c*h*(b*g+-1*a*h))*(b*f*h+-2*c*e*h+2*c*f*g)+4*c*h*(-1*b*h+2*c*g)*(b*f*g+-2*c*d*h))*arctanh((1/2)*c^-1//2*(a+b*x+c*x^2)^-1//2*(b+2*c*x)))
@test integrate((g+h*x)^-2*(a+b*x+c*x^2)^(1/2)*(d+e*x+f*x^2), x) == :(-1//2*h^-4*(a*h^2+c*g^2+-1*b*g*h)^-1//2*(h*(-1*b*(d*h^2+5*f*g^2+-3*e*g*h)+2*a*h*(-1*e*h+2*f*g))+2*c*g*(-1*h*(-1*d*h+2*e*g)+3*f*g^2))*arctanh((1/2)*(a+b*x+c*x^2)^-1//2*(a*h^2+c*g^2+-1*b*g*h)^-1//2*(b*g+x*(-1*b*h+2*c*g)+-2*a*h))+-1//8*c^-3//2*h^-4*(-8*c^2*(-1*h*(-1*d*h+2*e*g)+3*f*g^2)+f*b^2*h^2+4*c*h*(-1*a*f*h+-1*b*e*h+2*b*f*g))*arctanh((1/2)*c^-1//2*(a+b*x+c*x^2)^-1//2*(b+2*c*x))+-1*h^-1*(g+h*x)^-1*(a+b*x+c*x^2)^3//2*(a*h^2+c*g^2+-1*b*g*h)^-1*(f*g^2+-1*h*(e*g+-1*d*h))+-1//4*c^-1*h^-3*(a+b*x+c*x^2)^(1/2)*(a*h^2+c*g^2+-1*b*g*h)^-1*(c*h*(-1*b*(4*d*h^2+13*f*g^2+-8*e*g*h)+4*a*h*(-1*e*h+2*f*g))+4*g*c^2*(-1*h*(-1*d*h+2*e*g)+3*f*g^2)+b*f*h^2*(b*g+-1*a*h)+2*c*x*h^2*(b*f*g+-1*a*f*h+-2*c*d*h+2*c*e*g+-3*c*f*g^2*h^-1)))
@test integrate((g+h*x)^-3*(a+b*x+c*x^2)^(1/2)*(d+e*x+f*x^2), x) == :(-1//2*c^-1//2*h^-4*(-1*b*f*h+-2*c*e*h+6*c*f*g)*arctanh((1/2)*c^-1//2*(a+b*x+c*x^2)^-1//2*(b+2*c*x))+1//8*h^-4*(a*h^2+c*g^2+-1*b*g*h)^-3//2*(h^2*(b^2*(-1*h*(d*h+3*e*g)+15*f*g^2)+8*f*a^2*h^2+-4*a*b*h*(-1*e*h+6*f*g))+-4*c*h*(b*g^2*(-3*e*h+10*f*g)+-1*a*h*(d*h^2+9*f*g^2+-3*e*g*h))+8*c^2*g^3*(-1*e*h+3*f*g))*arctanh((1/2)*(a+b*x+c*x^2)^-1//2*(a*h^2+c*g^2+-1*b*g*h)^-1//2*(b*g+x*(-1*b*h+2*c*g)+-2*a*h))+-1//2*h^-1*(g+h*x)^-2*(a+b*x+c*x^2)^3//2*(a*h^2+c*g^2+-1*b*g*h)^-1*(f*g^2+-1*h*(e*g+-1*d*h))+1//4*h^-2*(g+h*x)^-1*(a+b*x+c*x^2)^(1/2)*(a*h^2+c*g^2+-1*b*g*h)^-1*(-1*b*(-1*d*h^2+11*f*g^2+-3*e*g*h)+-2*h*x*(c*e*g+-1*c*d*h+-2*a*f*h+2*b*f*g+-3*c*f*g^2*h^-1)+4*a*h*(-1*e*h+3*f*g)+4*c*g^2*h^-1*(-1*e*h+3*f*g)))
@test integrate((g+h*x)^-4*(a+b*x+c*x^2)^(1/2)*(d+e*x+f*x^2), x) == :(f*c^(1/2)*h^-4*arctanh((1/2)*c^-1//2*(a+b*x+c*x^2)^-1//2*(b+2*c*x))+-1//16*h^-4*(a*h^2+c*g^2+-1*b*g*h)^-5//2*(-1*b*h^3*(b^2*(d*h^2+5*f*g^2+e*g*h)+8*f*a^2*h^2+-2*a*b*h*(e*h+6*f*g))+2*c*h^2*(b^2*(15*f*g^3+d*g*h^2)+4*a^2*h^2*(-1*e*h+4*f*g)+-2*a*b*h*(-1*d*h^2+15*f*g^2+-1*e*g*h))+16*f*c^3*g^5+-8*g*h*c^2*(a*d*h^3+5*b*f*g^3+-5*a*f*h*g^2))*arctanh((1/2)*(a+b*x+c*x^2)^-1//2*(a*h^2+c*g^2+-1*b*g*h)^-1//2*(b*g+x*(-1*b*h+2*c*g)+-2*a*h))+-1//3*h^-1*(g+h*x)^-3*(a+b*x+c*x^2)^3//2*(a*h^2+c*g^2+-1*b*g*h)^-1*(f*g^2+-1*h*(e*g+-1*d*h))+-1//8*h^-3*(g+h*x)^-2*(a+b*x+c*x^2)^(1/2)*(a*h^2+c*g^2+-1*b*g*h)^-2*(h^2*(g*b^2*(d*h^2+5*f*g^2+e*g*h)+4*e*a^2*h^3+-2*a*b*h*(d*h^2+3*f*g^2+2*e*g*h))+h*x*(h^2*(b^2*(-1*h*(d*h+e*g)+11*f*g^2)+8*f*a^2*h^2+-2*a*b*h*(-1*e*h+10*f*g))+4*c^2*(3*f*g^4+-1*d*g^2*h^2)+2*c*g*h*(-1*b*(-1*h*(e*g+2*d*h)+12*f*g^2)+2*a*h*(-1*e*h+6*f*g)))+8*f*c^2*g^5+-2*c*g*h*(-2*a*d*h^3+7*b*f*g^3+b*d*g*h^2+-6*a*f*h*g^2)))
@test integrate((g+h*x)^-5*(a+b*x+c*x^2)^(1/2)*(d+e*x+f*x^2), x) == :(-1//128*(a*h^2+c*g^2+-1*b*g*h)^-7//2*(b^2+-4*a*c)*(b^2*(5*d*h^2+5*f*g^2+3*e*g*h)+-4*c*(a*(d*h^2+f*g^2+-5*e*g*h)+2*b*g*(e*g+2*d*h))+16*d*c^2*g^2+16*f*a^2*h^2+-8*a*b*h*(e*h+2*f*g))*arctanh((1/2)*(a+b*x+c*x^2)^-1//2*(a*h^2+c*g^2+-1*b*g*h)^-1//2*(b*g+x*(-1*b*h+2*c*g)+-2*a*h))+-1//4*h^-1*(g+h*x)^-4*(a+b*x+c*x^2)^3//2*(a*h^2+c*g^2+-1*b*g*h)^-1*(f*g^2+-1*h*(e*g+-1*d*h))+1//24*h^-1*(g+h*x)^-3*(a+b*x+c*x^2)^3//2*(a*h^2+c*g^2+-1*b*g*h)^-2*(h*(-1*b*(-5*d*h^2+11*f*g^2+-3*e*g*h)+8*a*h*(-1*e*h+2*f*g))+2*c*g*(h*(e*g+-5*d*h)+3*f*g^2))+1//64*(g+h*x)^-2*(a+b*x+c*x^2)^(1/2)*(a*h^2+c*g^2+-1*b*g*h)^-3*(b*g+x*(-1*b*h+2*c*g)+-2*a*h)*(b^2*(5*d*h^2+5*f*g^2+3*e*g*h)+-4*c*(a*(d*h^2+f*g^2+-5*e*g*h)+2*b*g*(e*g+2*d*h))+16*d*c^2*g^2+16*f*a^2*h^2+-8*a*b*h*(e*h+2*f*g)))
@test integrate((g+h*x)^-6*(a+b*x+c*x^2)^(1/2)*(d+e*x+f*x^2), x) == :(-1//256*(a*h^2+c*g^2+-1*b*g*h)^-9//2*(b^2+-4*a*c)*(2*c*(g*b^2*(5*f*g^2+15*d*h^2+6*e*g*h)+4*a^2*h^2*(-1*e*h+6*f*g)+-6*a*b*h*(-1*d*h^2+3*f*g^2+3*e*g*h))+-1*b*h*(b^2*(3*f*g^2+7*d*h^2+3*e*g*h)+16*f*a^2*h^2+-2*a*b*h*(5*e*h+6*f*g))+-8*g*c^2*(a*(f*g^2+3*d*h^2+-6*e*g*h)+2*b*g*(e*g+3*d*h))+32*d*c^3*g^3)*arctanh((1/2)*(a+b*x+c*x^2)^-1//2*(a*h^2+c*g^2+-1*b*g*h)^-1//2*(b*g+x*(-1*b*h+2*c*g)+-2*a*h))+-1//5*h^-1*(g+h*x)^-5*(a+b*x+c*x^2)^3//2*(a*h^2+c*g^2+-1*b*g*h)^-1*(f*g^2+-1*h*(e*g+-1*d*h))+1//40*h^-1*(g+h*x)^-4*(a+b*x+c*x^2)^3//2*(a*h^2+c*g^2+-1*b*g*h)^-2*(h*(-1*b*(-7*d*h^2+13*f*g^2+-3*e*g*h)+10*a*h*(-1*e*h+2*f*g))+2*c*g*(h*(-7*d*h+2*e*g)+3*f*g^2))+1//128*(g+h*x)^-2*(a+b*x+c*x^2)^(1/2)*(a*h^2+c*g^2+-1*b*g*h)^-4*(b*g+x*(-1*b*h+2*c*g)+-2*a*h)*(2*c*(g*b^2*(5*f*g^2+15*d*h^2+6*e*g*h)+4*a^2*h^2*(-1*e*h+6*f*g)+-6*a*b*h*(-1*d*h^2+3*f*g^2+3*e*g*h))+-1*b*h*(b^2*(3*f*g^2+7*d*h^2+3*e*g*h)+16*f*a^2*h^2+-2*a*b*h*(5*e*h+6*f*g))+-8*g*c^2*(a*(f*g^2+3*d*h^2+-6*e*g*h)+2*b*g*(e*g+3*d*h))+32*d*c^3*g^3)+1//240*h^-1*(g+h*x)^-3*(a+b*x+c*x^2)^3//2*(a*h^2+c*g^2+-1*b*g*h)^-3*(-5*h^2*(b^2*(3*f*g^2+7*d*h^2+3*e*g*h)+16*f*a^2*h^2+-2*a*b*h*(5*e*h+6*f*g))+-2*c*h*(b*g*(-54*d*h^2+16*f*g^2+-21*e*g*h)+-2*a*h*(8*d*h^2+18*f*g^2+-33*e*g*h))+4*c^2*g^2*(h*(-27*d*h+2*e*g)+3*f*g^2)))
@test integrate((g+h*x)^3*(a+b*x+c*x^2)^3//2*(d+e*x+f*x^2), x) == :(1//12288*c^-6*(a+b*x+c*x^2)^3//2*(b+2*c*x)*(32*c^3*(3*a^2*h^2*(e*h+3*f*g)+14*g*b^2*(f*g^2+3*h*(d*h+e*g))+12*a*b*h*(h*(d*h+3*e*g)+3*f*g^2))+-256*g*c^4*(a*(f*g^2+3*h*(d*h+e*g))+3*b*g*(e*g+3*d*h))+-143*f*b^5*h^3+1536*d*c^5*g^3+-48*b*h*c^2*(6*b^2*(d*h^2+3*f*g^2+3*e*g*h)+5*f*a^2*h^2+9*a*b*h*(e*h+3*f*g))+22*c*b^3*h^2*(9*b*(e*h+3*f*g)+20*a*f*h))+1//65536*c^-15//2*(b^2+-4*a*c)^2*(32*c^3*(3*a^2*h^2*(e*h+3*f*g)+14*g*b^2*(f*g^2+3*h*(d*h+e*g))+12*a*b*h*(h*(d*h+3*e*g)+3*f*g^2))+-256*g*c^4*(a*(f*g^2+3*h*(d*h+e*g))+3*b*g*(e*g+3*d*h))+-143*f*b^5*h^3+1536*d*c^5*g^3+-48*b*h*c^2*(6*b^2*(d*h^2+3*f*g^2+3*e*g*h)+5*f*a^2*h^2+9*a*b*h*(e*h+3*f*g))+22*c*b^3*h^2*(9*b*(e*h+3*f*g)+20*a*f*h))*arctanh((1/2)*c^-1//2*(a+b*x+c*x^2)^-1//2*(b+2*c*x))+1//80640*c^-5*h^-1*(a+b*x+c*x^2)^5//2*(-192*c^4*g^2*(-3*h*(3*e*g+64*d*h)+5*f*g^2)+-16*h*c^3*(b*g*(9*h*(141*e*g+196*d*h)+13*f*g^2)+32*a*h*(9*h*(d*h+3*e*g)+17*f*g^2))+8*c^2*h^2*(b^2*(756*h*(d*h+3*e*g)+1553*f*g^2)+256*f*a^2*h^2+837*a*b*h*(e*h+3*f*g))+3003*f*b^4*h^4+-198*c*b^2*h^3*(21*b*(e*h+3*f*g)+38*a*f*h)+-10*c*h*x*(8*h*c^2*(3*b*(f*g^2+6*h*(6*d*h+7*e*g))+a*h*(61*f*g+63*e*h))+16*g*c^3*(-9*h*(e*g+12*d*h)+5*f*g^2)+429*f*b^3*h^3+-22*b*c*h^2*(27*b*e*h+29*b*f*g+34*a*f*h)))+-1//144*c^-2*h^-1*(g+h*x)^3*(a+b*x+c*x^2)^5//2*(-18*c*e*h+10*c*f*g+13*b*f*h)+-1//32768*c^-7*(a+b*x+c*x^2)^(1/2)*(b+2*c*x)*(b^2+-4*a*c)*(32*c^3*(3*a^2*h^2*(e*h+3*f*g)+14*g*b^2*(f*g^2+3*h*(d*h+e*g))+12*a*b*h*(h*(d*h+3*e*g)+3*f*g^2))+-256*g*c^4*(a*(f*g^2+3*h*(d*h+e*g))+3*b*g*(e*g+3*d*h))+-143*f*b^5*h^3+1536*d*c^5*g^3+-48*b*h*c^2*(6*b^2*(d*h^2+3*f*g^2+3*e*g*h)+5*f*a^2*h^2+9*a*b*h*(e*h+3*f*g))+22*c*b^3*h^2*(9*b*(e*h+3*f*g)+20*a*f*h))+1//9*f*c^-1*h^-1*(g+h*x)^4*(a+b*x+c*x^2)^5//2+1//2016*c^-3*h^-1*(g+h*x)^2*(a+b*x+c*x^2)^5//2*(-12*c^2*(-3*h*(3*e*g+8*d*h)+5*f*g^2)+-2*c*h*(24*b*f*g+64*a*f*h+99*b*e*h)+143*f*b^2*h^2))
@test integrate((g+h*x)^2*(a+b*x+c*x^2)^3//2*(d+e*x+f*x^2), x) == :(-1//13440*c^-4*h^-1*(a+b*x+c*x^2)^5//2*(8*h*c^2*(b*(31*f*g^2+196*h*(d*h+2*e*g))+96*a*h*(e*h+2*f*g))+96*g*c^3*(-8*h*(e*g+7*d*h)+5*f*g^2)+693*f*b^3*h^3+-36*b*c*h^2*(28*b*(e*h+2*f*g)+31*a*f*h)+-10*c*h*x*(-8*c^2*(-4*h*(2*e*g+7*d*h)+5*f*g^2)+-12*c*h*(2*b*(f*g+6*e*h)+7*a*f*h)+99*f*b^2*h^2))+1//6144*c^-5*(a+b*x+c*x^2)^3//2*(b+2*c*x)*(-128*c^3*(a*(d*h^2+f*g^2+2*e*g*h)+3*b*g*(e*g+2*d*h))+16*c^2*(14*b^2*(d*h^2+f*g^2+2*e*g*h)+3*f*a^2*h^2+12*a*b*h*(e*h+2*f*g))+99*f*b^4*h^2+768*d*c^4*g^2+-72*c*h*b^2*(2*b*e*h+3*a*f*h+4*b*f*g))+1//32768*c^-13//2*(b^2+-4*a*c)^2*(-128*c^3*(a*(d*h^2+f*g^2+2*e*g*h)+3*b*g*(e*g+2*d*h))+16*c^2*(14*b^2*(d*h^2+f*g^2+2*e*g*h)+3*f*a^2*h^2+12*a*b*h*(e*h+2*f*g))+99*f*b^4*h^2+768*d*c^4*g^2+-72*c*h*b^2*(2*b*e*h+3*a*f*h+4*b*f*g))*arctanh((1/2)*c^-1//2*(a+b*x+c*x^2)^-1//2*(b+2*c*x))+-1//112*c^-2*h^-1*(g+h*x)^2*(a+b*x+c*x^2)^5//2*(-16*c*e*h+10*c*f*g+11*b*f*h)+-1//16384*c^-6*(a+b*x+c*x^2)^(1/2)*(b+2*c*x)*(b^2+-4*a*c)*(-128*c^3*(a*(d*h^2+f*g^2+2*e*g*h)+3*b*g*(e*g+2*d*h))+16*c^2*(14*b^2*(d*h^2+f*g^2+2*e*g*h)+3*f*a^2*h^2+12*a*b*h*(e*h+2*f*g))+99*f*b^4*h^2+768*d*c^4*g^2+-72*c*h*b^2*(2*b*e*h+3*a*f*h+4*b*f*g))+1//8*f*c^-1*h^-1*(g+h*x)^3*(a+b*x+c*x^2)^5//2)
@test integrate((a+b*x+c*x^2)^3//2*(g+h*x)*(d+e*x+f*x^2), x) == :(1//384*c^-4*(a+b*x+c*x^2)^3//2*(b+2*c*x)*(-8*c^2*(a*e*h+a*f*g+3*b*d*h+3*b*e*g)+-9*f*h*b^3+2*b*c*(7*b*(e*h+f*g)+6*a*f*h)+48*d*g*c^3)+1//840*c^-3*h^-1*(a+b*x+c*x^2)^5//2*(-24*c^2*(-7*h*(d*h+e*g)+5*f*g^2)+-2*c*h*(49*b*(e*h+f*g)+24*a*f*h)+63*f*b^2*h^2+-10*c*h*x*(-14*c*e*h+9*b*f*h+10*c*f*g))+1//2048*c^-11//2*(b^2+-4*a*c)^2*(-8*c^2*(a*e*h+a*f*g+3*b*d*h+3*b*e*g)+-9*f*h*b^3+2*b*c*(7*b*(e*h+f*g)+6*a*f*h)+48*d*g*c^3)*arctanh((1/2)*c^-1//2*(a+b*x+c*x^2)^-1//2*(b+2*c*x))+-1//1024*c^-5*(a+b*x+c*x^2)^(1/2)*(b+2*c*x)*(b^2+-4*a*c)*(-8*c^2*(a*e*h+a*f*g+3*b*d*h+3*b*e*g)+-9*f*h*b^3+2*b*c*(7*b*(e*h+f*g)+6*a*f*h)+48*d*g*c^3)+1//7*f*c^-1*h^-1*(g+h*x)^2*(a+b*x+c*x^2)^5//2)
@test integrate((a+b*x+c*x^2)^3//2*(d+e*x+f*x^2), x) == :(1//60*c^-2*(a+b*x+c*x^2)^5//2*(-7*b*f+12*c*e)+1//6*f*x*c^-1*(a+b*x+c*x^2)^5//2+1//192*c^-3*(a+b*x+c*x^2)^3//2*(b+2*c*x)*(7*f*b^2+24*d*c^2+-12*b*c*e+-4*a*c*f)+1//1024*c^-9//2*(b^2+-4*a*c)^2*(-4*c*(a*f+3*b*e)+7*f*b^2+24*d*c^2)*arctanh((1/2)*c^-1//2*(a+b*x+c*x^2)^-1//2*(b+2*c*x))+-1//512*c^-4*(a+b*x+c*x^2)^(1/2)*(b+2*c*x)*(b^2+-4*a*c)*(-4*c*(a*f+3*b*e)+7*f*b^2+24*d*c^2))
@test integrate((g+h*x)^-1*(a+b*x+c*x^2)^3//2*(d+e*x+f*x^2), x) == :(h^-6*(a*h^2+c*g^2+-1*b*g*h)^3//2*(f*g^2+-1*h*(e*g+-1*d*h))*arctanh((1/2)*(a+b*x+c*x^2)^-1//2*(a*h^2+c*g^2+-1*b*g*h)^-1//2*(b*g+x*(-1*b*h+2*c*g)+-2*a*h))+-1//48*c^-2*h^-3*(a+b*x+c*x^2)^3//2*(-1*(-3*b*h+8*c*g)*(b*f*h+-2*c*e*h+2*c*f*g)+8*c*h*(b*f*g+-2*c*d*h)+6*c*h*x*(b*f*h+-2*c*e*h+2*c*f*g))+-1//256*c^-7//2*h^-6*(-1*(-1*(-3*b^2*h^2+16*c^2*g^2+-4*c*h*(-3*a*h+2*b*g))*(b*f*h+-2*c*e*h+2*c*f*g)+8*c*h*(-1*b*h+2*c*g)*(b*f*g+-2*c*d*h))*(-1*b^2*h^2+8*c^2*g^2+-4*c*h*(b*g+-1*a*h))+4*c*h*(-1*b*h+2*c*g)*(-1*g*(-3*h*b^2+-4*a*c*h+8*b*c*g)*(b*f*h+-2*c*e*h+2*c*f*g)+8*c*h*(b*g+-2*a*h)*(b*f*g+-2*c*d*h)))*arctanh((1/2)*c^-1//2*(a+b*x+c*x^2)^-1//2*(b+2*c*x))+1//5*f*c^-1*h^-1*(a+b*x+c*x^2)^5//2+1//128*c^-3*h^-5*(a+b*x+c*x^2)^(1/2)*(3*f*b^4*h^4+128*c^4*g^2*(f*g^2+-1*h*(e*g+-1*d*h))+-32*h*c^3*(f*g^2+-1*h*(e*g+-1*d*h))*(-4*a*h+5*b*g)+-8*b*c^2*h^2*(-2*b*(d*h^2+f*g^2+-1*e*g*h)+3*a*h*(f*g+-1*e*h))+2*c*h*x*(-1*(-3*b^2*h^2+16*c^2*g^2+-4*c*h*(-3*a*h+2*b*g))*(b*f*h+-2*c*e*h+2*c*f*g)+8*c*h*(-1*b*h+2*c*g)*(b*f*g+-2*c*d*h))+6*c*b^2*h^3*(b*f*g+-1*b*e*h+-2*a*f*h)))
@test integrate((g+h*x)^-2*(a+b*x+c*x^2)^3//2*(d+e*x+f*x^2), x) == :(-1//2*h^-6*(a*h^2+c*g^2+-1*b*g*h)^(1/2)*(h*(-1*b*(3*d*h^2+7*f*g^2+-5*e*g*h)+2*a*h*(-1*e*h+2*f*g))+2*c*g*(-1*h*(-3*d*h+4*e*g)+5*f*g^2))*arctanh((1/2)*(a+b*x+c*x^2)^-1//2*(a*h^2+c*g^2+-1*b*g*h)^-1//2*(b*g+x*(-1*b*h+2*c*g)+-2*a*h))+-1//64*c^-2*h^-5*(a+b*x+c*x^2)^(1/2)*(3*f*b^3*h^3+16*h*c^2*(-1*b*(9*d*h^2+19*f*g^2+-14*e*g*h)+4*a*h*(-1*e*h+2*f*g))+64*g*c^3*(-1*h*(-3*d*h+4*e*g)+5*f*g^2)+2*c*h*x*(-16*c^2*(-1*h*(-3*d*h+4*e*g)+5*f*g^2)+3*f*b^2*h^2+4*c*h*(-3*a*f*h+-2*b*e*h+4*b*f*g))+4*b*c*h^2*(-3*a*f*h+-2*b*e*h+4*b*f*g))+1//128*c^-5//2*h^-6*(3*f*b^4*h^4+48*c^2*h^2*(b^2*(d*h^2+3*f*g^2+-2*e*g*h)+f*a^2*h^2+-2*a*b*h*(-1*e*h+2*f*g))+128*c^4*g^2*(-1*h*(-3*d*h+4*e*g)+5*f*g^2)+192*h*c^3*(a*h*(d*h^2+3*f*g^2+-2*e*g*h)+-1*b*g*(2*d*h^2+4*f*g^2+-3*e*g*h))+8*c*b^2*h^3*(-1*b*e*h+-3*a*f*h+2*b*f*g))*arctanh((1/2)*c^-1//2*(a+b*x+c*x^2)^-1//2*(b+2*c*x))+-1*h^-1*(g+h*x)^-1*(a+b*x+c*x^2)^5//2*(a*h^2+c*g^2+-1*b*g*h)^-1*(f*g^2+-1*h*(e*g+-1*d*h))+-1//24*c^-1*h^-3*(a+b*x+c*x^2)^3//2*(a*h^2+c*g^2+-1*b*g*h)^-1*(c*h*(-1*b*(-8*h*(-3*d*h+4*e*g)+43*f*g^2)+8*a*h*(-1*e*h+2*f*g))+8*g*c^2*(-1*h*(-3*d*h+4*e*g)+5*f*g^2)+3*b*f*h^2*(b*g+-1*a*h)+6*c*x*h^2*(b*f*g+-1*a*f*h+-4*c*d*h+4*c*e*g+-5*c*f*g^2*h^-1)))
@test integrate((g+h*x)^-3*(a+b*x+c*x^2)^3//2*(d+e*x+f*x^2), x) == :(-1//16*c^-3//2*h^-6*(f*b^3*h^3+16*g*c^3*(-3*h*(-1*d*h+2*e*g)+10*f*g^2)+24*h*c^2*(-1*b*(d*h^2+6*f*g^2+-3*e*g*h)+a*h*(-1*e*h+3*f*g))+6*b*c*h^2*(-1*b*e*h+-2*a*f*h+3*b*f*g))*arctanh((1/2)*c^-1//2*(a+b*x+c*x^2)^-1//2*(b+2*c*x))+1//8*h^-6*(a*h^2+c*g^2+-1*b*g*h)^-1//2*(h^2*(b^2*(-3*h*(-1*d*h+5*e*g)+35*f*g^2)+8*f*a^2*h^2+-4*a*b*h*(-3*e*h+10*f*g))+4*c*h*(a*h*(3*d*h^2+19*f*g^2+-9*e*g*h)+-1*b*g*(6*d*h^2+28*f*g^2+-15*e*g*h))+8*c^2*g^2*(-3*h*(-1*d*h+2*e*g)+10*f*g^2))*arctanh((1/2)*(a+b*x+c*x^2)^-1//2*(a*h^2+c*g^2+-1*b*g*h)^-1//2*(b*g+x*(-1*b*h+2*c*g)+-2*a*h))+-1//2*h^-1*(g+h*x)^-2*(a+b*x+c*x^2)^5//2*(a*h^2+c*g^2+-1*b*g*h)^-1*(f*g^2+-1*h*(e*g+-1*d*h))+-1//8*c^-1*h^-5*(a+b*x+c*x^2)^(1/2)*(a*h^2+c*g^2+-1*b*g*h)^-1*(-1*c*h^2*(b^2*(-6*h*(-1*d*h+4*e*g)+53*f*g^2)+8*f*a^2*h^2+-18*a*b*h*(-1*e*h+3*f*g))+-8*c^3*g^2*(-3*h*(-1*d*h+2*e*g)+10*f*g^2)+-2*h*c^2*(-3*b*g*(5*d*h^2+22*f*g^2+-12*e*g*h)+2*a*h*(3*d*h^2+19*f*g^2+-9*e*g*h))+f*b^2*h^3*(b*g+-1*a*h)+2*c*h*x*(c*h*(-3*b*(d*h^2+6*f*g^2+-3*e*g*h)+2*a*h*(-3*e*h+7*f*g))+2*g*c^2*(-3*h*(-1*d*h+2*e*g)+10*f*g^2)+b*f*h^2*(b*g+-1*a*h)))+-1//12*h^-2*(g+h*x)^-1*(a+b*x+c*x^2)^3//2*(a*h^2+c*g^2+-1*b*g*h)^-1*(b*(-3*h*(-1*d*h+5*e*g)+31*f*g^2)+-4*a*h*(-3*e*h+7*f*g)+2*h*x*(-3*c*d*h+-2*a*f*h+2*b*f*g+3*c*e*g+-5*c*f*g^2*h^-1)+4*c*g*(-3*d*h+6*e*g+-10*f*g^2*h^-1)))
@test integrate((g+h*x)^-4*(a+b*x+c*x^2)^3//2*(d+e*x+f*x^2), x) == :(-1//16*h^-6*(a*h^2+c*g^2+-1*b*g*h)^-3//2*(-1*b*h^3*(b^2*(-1*d*h^2+35*f*g^2+-5*e*g*h)+24*f*a^2*h^2+-6*a*b*h*(-1*e*h+10*f*g))+6*c*h^2*(g*b^2*(d*h^2+35*f*g^2+-10*e*g*h)+4*a^2*h^2*(-1*e*h+4*f*g)+-2*a*b*h*(d*h^2+25*f*g^2+-7*e*g*h))+16*c^3*g^3*(-1*h*(-1*d*h+4*e*g)+10*f*g^2)+-24*g*h*c^2*(b*g*(d*h^2+14*f*g^2+-5*e*g*h)+-1*a*h*(d*h^2+11*f*g^2+-4*e*g*h)))*arctanh((1/2)*(a+b*x+c*x^2)^-1//2*(a*h^2+c*g^2+-1*b*g*h)^-1//2*(b*g+x*(-1*b*h+2*c*g)+-2*a*h))+1//8*c^-1//2*h^-6*(8*c^2*(-1*h*(-1*d*h+4*e*g)+10*f*g^2)+-12*c*h*(-1*a*f*h+-1*b*e*h+4*b*f*g)+3*f*b^2*h^2)*arctanh((1/2)*c^-1//2*(a+b*x+c*x^2)^-1//2*(b+2*c*x))+-1//3*h^-1*(g+h*x)^-3*(a+b*x+c*x^2)^5//2*(a*h^2+c*g^2+-1*b*g*h)^-1*(f*g^2+-1*h*(e*g+-1*d*h))+-1//8*h^-5*(g+h*x)^-1*(a+b*x+c*x^2)^(1/2)*(a*h^2+c*g^2+-1*b*g*h)^-1*(h^2*(b^2*(-1*h*(d*h+5*e*g)+29*f*g^2)+12*f*a^2*h^2+-6*a*b*h*(-1*e*h+7*f*g))+-2*c*h*(-2*a*h*(2*d*h^2+23*f*g^2+-8*e*g*h)+3*b*g*(d*h^2+18*f*g^2+-6*e*g*h))+2*h*x*(c*h*(-1*b*(d*h^2+22*f*g^2+-7*e*g*h)+6*a*h*(-1*e*h+3*f*g))+2*g*c^2*(-1*h*(-1*d*h+4*e*g)+10*f*g^2)+3*b*f*h^2*(b*g+-1*a*h))+8*c^2*g^2*(-1*h*(-1*d*h+4*e*g)+10*f*g^2))+-1//12*h^-2*(g+h*x)^-2*(a+b*x+c*x^2)^3//2*(a*h^2+c*g^2+-1*b*g*h)^-1*(b*(-1*h*(d*h+5*e*g)+17*f*g^2)+-6*a*h*(-1*e*h+3*f*g)+2*c*g*(-1*d*h+4*e*g+-10*f*g^2*h^-1)+2*h*x*(-3*a*f*h+-2*c*d*h+2*c*e*g+3*b*f*g+-5*c*f*g^2*h^-1)))
@test integrate((g+h*x)^-5*(a+b*x+c*x^2)^3//2*(d+e*x+f*x^2), x) == :(-1//2*c^(1/2)*h^-6*(-3*b*f*h+-2*c*e*h+10*c*f*g)*arctanh((1/2)*c^-1//2*(a+b*x+c*x^2)^-1//2*(b+2*c*x))+1//128*h^-6*(a*h^2+c*g^2+-1*b*g*h)^-5//2*(b^2*h^4*(b^2*(3*d*h^2+35*f*g^2+5*e*g*h)+48*f*a^2*h^2+-8*a*b*h*(e*h+10*f*g))+-48*c^2*h^2*(-1*a^2*h^2*(d*h^2+25*f*g^2+-5*e*g*h)+-5*b^2*g^3*(-1*e*h+7*f*g)+10*a*b*h*g^2*(-1*e*h+6*f*g))+8*c*h^3*(-5*b^3*g^2*(-1*e*h+14*f*g)+24*f*a^3*h^3+-12*b*a^2*h^2*(-1*e*h+10*f*g)+3*a*h*b^2*(-1*d*h^2+55*f*g^2+-5*e*g*h))+128*c^4*g^5*(-1*e*h+5*f*g)+-64*h*c^3*g^3*(b*g*(-5*e*h+28*f*g)+-5*a*h*(-1*e*h+5*f*g)))*arctanh((1/2)*(a+b*x+c*x^2)^-1//2*(a*h^2+c*g^2+-1*b*g*h)^-1//2*(b*g+x*(-1*b*h+2*c*g)+-2*a*h))+-1//4*h^-1*(g+h*x)^-4*(a+b*x+c*x^2)^5//2*(a*h^2+c*g^2+-1*b*g*h)^-1*(f*g^2+-1*h*(e*g+-1*d*h))+-1//96*h^-3*(g+h*x)^-3*(a+b*x+c*x^2)^3//2*(a*h^2+c*g^2+-1*b*g*h)^-2*(-1*h^2*(-1*g*b^2*(3*d*h^2+35*f*g^2+5*e*g*h)+16*a^2*h^2*(f*g+-2*e*h)+4*a*b*h*(3*d*h^2+7*f*g^2+7*e*g*h))+3*h*x*(h^2*(b^2*(-3*d*h^2+29*f*g^2+-5*e*g*h)+16*f*a^2*h^2+-8*a*b*h*(-1*e*h+6*f*g))+-4*c*h*(-1*a*h*(d*h^2+17*f*g^2+-5*e*g*h)+2*b*g*(-1*d*h^2+9*f*g^2+-2*e*g*h))+8*c^2*g^2*(-1*h*(d*h+e*g)+5*f*g^2))+16*c^2*g^4*(-1*e*h+5*f*g)+-4*c*g*h*(b*g*(3*d*h^2+31*f*g^2+-5*e*g*h)+-1*a*h*(9*d*h^2+25*f*g^2+-5*e*g*h)))+1//64*h^-5*(g+h*x)^-1*(a+b*x+c*x^2)^(1/2)*(a*h^2+c*g^2+-1*b*g*h)^-2*(-1*b*h^3*(b^2*(3*d*h^2+35*f*g^2+5*e*g*h)+48*f*a^2*h^2+-8*a*b*h*(e*h+10*f*g))+4*c*h^2*(2*b^2*g^2*(-5*e*h+46*f*g)+16*a^2*h^2*(-1*e*h+5*f*g)+-1*a*b*h*(-3*d*h^2+173*f*g^2+-25*e*g*h))+64*c^3*g^4*(-1*e*h+5*f*g)+-16*h*c^2*g^2*(b*g*(-7*e*h+41*f*g)+-8*a*h*(-1*e*h+5*f*g))+2*c*h*x*(h^2*(b^2*(-1*h*(3*d*h+5*e*g)+61*f*g^2)+48*f*a^2*h^2+-8*a*b*h*(-1*e*h+14*f*g))+-4*c*h*(-1*a*h*(-1*h*(-3*d*h+7*e*g)+35*f*g^2)+6*b*g^2*(-1*e*h+6*f*g))+16*c^2*g^3*(-1*e*h+5*f*g))))
@test integrate((g+h*x)^-6*(a+b*x+c*x^2)^3//2*(d+e*x+f*x^2), x) == :(f*c^3//2*h^-6*arctanh((1/2)*c^-1//2*(a+b*x+c*x^2)^-1//2*(b+2*c*x))+-1//256*h^-6*(a*h^2+c*g^2+-1*b*g*h)^-7//2*(b^3*h^5*(b^2*(3*h*(d*h+e*g)+7*f*g^2)+16*f*a^2*h^2+-2*a*b*h*(3*e*h+10*f*g))+-16*c^2*h^3*(-6*a^3*h^3*(-1*e*h+6*f*g)+35*f*b^3*g^4+3*b*a^2*h^2*(-1*d*h^2+35*f*g^2+-1*e*g*h)+-3*a*g*h*b^2*(d*h^2+35*f*g^2))+256*f*c^5*g^7+-2*b*c*h^4*(-1*b^3*(35*f*g^3+-3*d*g*h^2)+96*f*a^3*h^3+-24*b*a^2*h^2*(e*h+8*f*g)+4*a*h*b^2*(3*h*(d*h+e*g)+35*f*g^2))+32*g*c^3*h^2*(a^2*h^2*(-3*d*h^2+35*f*g^2)+35*f*b^2*g^4+-70*a*b*f*h*g^3)+-896*f*h*c^4*g^5*(b*g+-1*a*h))*arctanh((1/2)*(a+b*x+c*x^2)^-1//2*(a*h^2+c*g^2+-1*b*g*h)^-1//2*(b*g+x*(-1*b*h+2*c*g)+-2*a*h))+-1//5*h^-1*(g+h*x)^-5*(a+b*x+c*x^2)^5//2*(a*h^2+c*g^2+-1*b*g*h)^-1*(f*g^2+-1*h*(e*g+-1*d*h))+-1//48*h^-3*(g+h*x)^-4*(a+b*x+c*x^2)^3//2*(a*h^2+c*g^2+-1*b*g*h)^-2*(-1*h^2*(-1*g*b^2*(3*h*(d*h+e*g)+7*f*g^2)+4*a^2*h^2*(-3*e*h+2*f*g)+2*a*b*h*(f*g^2+3*h*(d*h+2*e*g)))+h*x*(h^2*(b^2*(-3*h*(d*h+e*g)+25*f*g^2)+16*f*a^2*h^2+-2*a*b*h*(-3*e*h+22*f*g))+4*c^2*(7*f*g^4+-3*d*g^2*h^2)+2*c*g*h*(-1*b*(-6*d*h^2+28*f*g^2+-3*e*g*h)+2*a*h*(-3*e*h+14*f*g)))+16*f*c^2*g^5+-2*c*g*h*(-6*a*d*h^3+13*b*f*g^3+-10*a*f*h*g^2+3*b*d*g*h^2))+-1//128*h^-5*(g+h*x)^-2*(a+b*x+c*x^2)^(1/2)*(a*h^2+c*g^2+-1*b*g*h)^-3*(h*x*((-1*b*h+2*c*g)*(-1*b*h^3*(b^2*(3*h*(d*h+e*g)+7*f*g^2)+16*f*a^2*h^2+-2*a*b*h*(3*e*h+10*f*g))+2*c*h^2*(b^2*(29*f*g^3+3*d*g*h^2)+4*a^2*h^2*(-3*e*h+10*f*g)+-6*a*b*h*(-1*d*h^2+11*f*g^2+-1*e*g*h))+32*f*c^3*g^5+-8*g*h*c^2*(3*a*d*h^3+10*b*f*g^3+-11*a*f*h*g^2))+128*c*f*(c*g^2+-1*h*(b*g+-1*a*h))^3)+-2*c*h^3*(b^3*(35*f*g^4+-3*d*g^2*h^2)+8*a^3*h^3*(-3*e*h+2*f*g)+4*b*a^2*h^2*(3*d*h^2+5*f*g^2+6*e*g*h)+-2*a*h*b^2*g^2*(3*e*h+34*f*g))+128*f*c^4*g^7+-1*b*h^4*(b*g+-2*a*h)*(b^2*(3*h*(d*h+e*g)+7*f*g^2)+16*f*a^2*h^2+-2*a*b*h*(3*e*h+10*f*g))+8*g*c^2*h^2*(2*a^2*h^2*(3*d*h^2+13*f*g^2)+38*f*b^2*g^4+-1*a*b*g*h*(3*d*h^2+65*f*g^2))+-32*f*h*c^3*g^5*(-10*a*h+11*b*g)))
@test integrate((g+h*x)^-7*(a+b*x+c*x^2)^3//2*(d+e*x+f*x^2), x) == :(1//1024*(b^2+-4*a*c)^2*(a*h^2+c*g^2+-1*b*g*h)^-9//2*(b^2*(7*d*h^2+7*f*g^2+5*e*g*h)+-4*c*(a*(d*h^2+f*g^2+-7*e*g*h)+3*b*g*(e*g+2*d*h))+24*d*c^2*g^2+24*f*a^2*h^2+-12*a*b*h*(e*h+2*f*g))*arctanh((1/2)*(a+b*x+c*x^2)^-1//2*(a*h^2+c*g^2+-1*b*g*h)^-1//2*(b*g+x*(-1*b*h+2*c*g)+-2*a*h))+-1//6*h^-1*(g+h*x)^-6*(a+b*x+c*x^2)^5//2*(a*h^2+c*g^2+-1*b*g*h)^-1*(f*g^2+-1*h*(e*g+-1*d*h))+1//60*h^-1*(g+h*x)^-5*(a+b*x+c*x^2)^5//2*(a*h^2+c*g^2+-1*b*g*h)^-2*(h*(-1*b*(-7*d*h^2+17*f*g^2+-5*e*g*h)+12*a*h*(-1*e*h+2*f*g))+2*c*g*(h*(e*g+-7*d*h)+5*f*g^2))+1//192*(g+h*x)^-4*(a+b*x+c*x^2)^3//2*(a*h^2+c*g^2+-1*b*g*h)^-3*(b*g+x*(-1*b*h+2*c*g)+-2*a*h)*(b^2*(7*d*h^2+7*f*g^2+5*e*g*h)+-4*c*(a*(d*h^2+f*g^2+-7*e*g*h)+3*b*g*(e*g+2*d*h))+24*d*c^2*g^2+24*f*a^2*h^2+-12*a*b*h*(e*h+2*f*g))+-1//512*(g+h*x)^-2*(a+b*x+c*x^2)^(1/2)*(a*h^2+c*g^2+-1*b*g*h)^-4*(b^2+-4*a*c)*(b*g+x*(-1*b*h+2*c*g)+-2*a*h)*(b^2*(7*d*h^2+7*f*g^2+5*e*g*h)+-4*c*(a*(d*h^2+f*g^2+-7*e*g*h)+3*b*g*(e*g+2*d*h))+24*d*c^2*g^2+24*f*a^2*h^2+-12*a*b*h*(e*h+2*f*g)))
@test integrate((g+h*x)^-8*(a+b*x+c*x^2)^3//2*(d+e*x+f*x^2), x) == :(1//2048*(b^2+-4*a*c)^2*(a*h^2+c*g^2+-1*b*g*h)^-11//2*(2*c*(g*b^2*(7*f*g^2+21*d*h^2+10*e*g*h)+4*a^2*h^2*(-1*e*h+8*f*g)+-2*a*b*h*(-3*d*h^2+13*f*g^2+13*e*g*h))+-1*b*h*(b^2*(5*f*g^2+9*d*h^2+5*e*g*h)+24*f*a^2*h^2+-2*a*b*h*(7*e*h+10*f*g))+-8*g*c^2*(a*(f*g^2+3*d*h^2+-8*e*g*h)+3*b*g*(e*g+3*d*h))+48*d*c^3*g^3)*arctanh((1/2)*(a+b*x+c*x^2)^-1//2*(a*h^2+c*g^2+-1*b*g*h)^-1//2*(b*g+x*(-1*b*h+2*c*g)+-2*a*h))+-1//7*h^-1*(g+h*x)^-7*(a+b*x+c*x^2)^5//2*(a*h^2+c*g^2+-1*b*g*h)^-1*(f*g^2+-1*h*(e*g+-1*d*h))+1//84*h^-1*(g+h*x)^-6*(a+b*x+c*x^2)^5//2*(a*h^2+c*g^2+-1*b*g*h)^-2*(h*(-1*b*(-9*d*h^2+19*f*g^2+-5*e*g*h)+14*a*h*(-1*e*h+2*f*g))+2*c*g*(h*(-9*d*h+2*e*g)+5*f*g^2))+1//384*(g+h*x)^-4*(a+b*x+c*x^2)^3//2*(a*h^2+c*g^2+-1*b*g*h)^-4*(b*g+x*(-1*b*h+2*c*g)+-2*a*h)*(2*c*(g*b^2*(7*f*g^2+21*d*h^2+10*e*g*h)+4*a^2*h^2*(-1*e*h+8*f*g)+-2*a*b*h*(-3*d*h^2+13*f*g^2+13*e*g*h))+-1*b*h*(b^2*(5*f*g^2+9*d*h^2+5*e*g*h)+24*f*a^2*h^2+-2*a*b*h*(7*e*h+10*f*g))+-8*g*c^2*(a*(f*g^2+3*d*h^2+-8*e*g*h)+3*b*g*(e*g+3*d*h))+48*d*c^3*g^3)+1//840*h^-1*(g+h*x)^-5*(a+b*x+c*x^2)^5//2*(a*h^2+c*g^2+-1*b*g*h)^-3*(-7*h^2*(b^2*(5*f*g^2+9*d*h^2+5*e*g*h)+24*f*a^2*h^2+-2*a*b*h*(7*e*h+10*f*g))+-2*c*h*(-2*a*h*(12*d*h^2+26*f*g^2+-61*e*g*h)+3*b*g*(-34*d*h^2+8*f*g^2+-15*e*g*h))+4*c^2*g^2*(h*(-51*d*h+2*e*g)+5*f*g^2))+-1//1024*(g+h*x)^-2*(a+b*x+c*x^2)^(1/2)*(a*h^2+c*g^2+-1*b*g*h)^-5*(b^2+-4*a*c)*(b*g+x*(-1*b*h+2*c*g)+-2*a*h)*(2*c*(g*b^2*(7*f*g^2+21*d*h^2+10*e*g*h)+4*a^2*h^2*(-1*e*h+8*f*g)+-2*a*b*h*(-3*d*h^2+13*f*g^2+13*e*g*h))+-1*b*h*(b^2*(5*f*g^2+9*d*h^2+5*e*g*h)+24*f*a^2*h^2+-2*a*b*h*(7*e*h+10*f*g))+-8*g*c^2*(a*(f*g^2+3*d*h^2+-8*e*g*h)+3*b*g*(e*g+3*d*h))+48*d*c^3*g^3))
@test integrate((1+2x)^3*(2+-1x+3*x^2)^(1/2)*(1+3x+4*x^2), x) == :(-1//68040*(2+-1x+3*x^2)^3//2*(75295+26982x)+1//15552*(2+-1x+3*x^2)^(1/2)*(5393+-32358x)+2//21*(1+2x)^4*(2+-1x+3*x^2)^3//2+17//105*(1+2x)^2*(2+-1x+3*x^2)^3//2+67//378*(1+2x)^3*(2+-1x+3*x^2)^3//2+124039//93312*3^(1/2)*arcsinh(1//23*23^(1/2)*(1+-6x)))
@test integrate((1+2x)^2*(2+-1x+3*x^2)^(1/2)*(1+3x+4*x^2), x) == :(1//5*(1+2x)^2*(2+-1x+3*x^2)^3//2+1//9*(1+2x)^3*(2+-1x+3*x^2)^3//2+1//810*(2+-1x+3*x^2)^3//2*(25+306x)+1//1296*(2+-1x+3*x^2)^(1/2)*(235+-1410x)+5405//7776*3^(1/2)*arcsinh(1//23*23^(1/2)*(1+-6x)))
@test integrate((2+-1x+3*x^2)^(1/2)*(1+2x)*(1+3x+4*x^2), x) == :(1//1620*(2+-1x+3*x^2)^3//2*(745+738x)+1//2592*(2+-1x+3*x^2)^(1/2)*(19+-114x)+2//15*(1+2x)^2*(2+-1x+3*x^2)^3//2+437//15552*3^(1/2)*arcsinh(1//23*23^(1/2)*(1+-6x)))
@test integrate((1+2x)^-1*(2+-1x+3*x^2)^(1/2)*(1+3x+4*x^2), x) == :(2//9*(2+-1x+3*x^2)^3//2+-43//432*3^(1/2)*arcsinh(1//23*23^(1/2)*(1+-6x))+-1//8*13^(1/2)*arctanh(1//26*13^(1/2)*(2+-1x+3*x^2)^-1//2*(9+-8x))+1//72*(2+-1x+3*x^2)^(1/2)*(13+30x))
@test integrate((1+2x)^-2*(2+-1x+3*x^2)^(1/2)*(1+3x+4*x^2), x) == :(-1*(13+26x)^-1*(2+-1x+3*x^2)^3//2+-11//18*3^(1/2)*arcsinh(1//23*23^(1/2)*(1+-6x))+-1//156*(2+-1x+3*x^2)^(1/2)*(67+-96x)+17//104*13^(1/2)*arctanh(1//26*13^(1/2)*(2+-1x+3*x^2)^-1//2*(9+-8x)))
@test integrate((1+2x)^-3*(2+-1x+3*x^2)^(1/2)*(1+3x+4*x^2), x) == :(-803//2704*13^(1/2)*arctanh(1//26*13^(1/2)*(2+-1x+3*x^2)^-1//2*(9+-8x))+-1//26*(1+2x)^-2*(2+-1x+3*x^2)^3//2+11//24*3^(1/2)*arcsinh(1//23*23^(1/2)*(1+-6x))+(104+208x)^-1*(2+-1x+3*x^2)^(1/2)*(77+110x))
@test integrate((1+2x)^3*(2+-1x+3*x^2)^3//2*(1+3x+4*x^2), x) == :(-1//58320*(2+-1x+3*x^2)^5//2*(3113+-64350x)+1//559872*(2+-1x+3*x^2)^3//2*(54593+-327558x)+1//4478976*(2+-1x+3*x^2)^(1/2)*(1255639+-7533834x)+2//27*(1+2x)^4*(2+-1x+3*x^2)^5//2+77//81*x^3*(2+-1x+3*x^2)^5//2+913//486*x^2*(2+-1x+3*x^2)^5//2+28879697//26873856*3^(1/2)*arcsinh(1//23*23^(1/2)*(1+-6x)))
@test integrate((1+2x)^2*(2+-1x+3*x^2)^3//2*(1+3x+4*x^2), x) == :(1//12*(1+2x)^3*(2+-1x+3*x^2)^5//2+1//2520*(2+-1x+3*x^2)^5//2*(377+650x)+1//3456*(2+-1x+3*x^2)^3//2*(91+-546x)+1//27648*(2+-1x+3*x^2)^(1/2)*(2093+-12558x)+8//63*(1+2x)^2*(2+-1x+3*x^2)^5//2+48139//165888*3^(1/2)*arcsinh(1//23*23^(1/2)*(1+-6x)))
@test integrate((2+-1x+3*x^2)^3//2*(1+2x)*(1+3x+4*x^2), x) == :(-37559//124416*3^(1/2)*arcsinh(1//23*23^(1/2)*(1+-6x))+-1//2592*(2+-1x+3*x^2)^3//2*(71+-426x)+1//378*(2+-1x+3*x^2)^5//2*(109+102x)+1//20736*(2+-1x+3*x^2)^(1/2)*(-1633+9798x)+2//21*(1+2x)^2*(2+-1x+3*x^2)^5//2)
@test integrate((1+2x)^-1*(2+-1x+3*x^2)^3//2*(1+3x+4*x^2), x) == :(2//15*(2+-1x+3*x^2)^5//2+-13//32*13^(1/2)*arctanh(1//26*13^(1/2)*(2+-1x+3*x^2)^-1//2*(9+-8x))+1//144*(2+-1x+3*x^2)^3//2*(7+30x)+1//1152*(2+-1x+3*x^2)^(1/2)*(869+402x)+2203//6912*3^(1/2)*arcsinh(1//23*23^(1/2)*(1+-6x)))
@test integrate((1+2x)^-2*(2+-1x+3*x^2)^3//2*(1+3x+4*x^2), x) == :(-1*(13+26x)^-1*(2+-1x+3*x^2)^5//2+-2327//1152*3^(1/2)*arcsinh(1//23*23^(1/2)*(1+-6x))+-1//104*(2+-1x+3*x^2)^3//2*(23+-38x)+-1//192*(2+-1x+3*x^2)^(1/2)*(349+-294x)+25//32*13^(1/2)*arctanh(1//26*13^(1/2)*(2+-1x+3*x^2)^-1//2*(9+-8x)))
@test integrate((1+2x)^-3*(2+-1x+3*x^2)^3//2*(1+3x+4*x^2), x) == :(-1153//832*13^(1/2)*arctanh(1//26*13^(1/2)*(2+-1x+3*x^2)^-1//2*(9+-8x))+-1//26*(1+2x)^-2*(2+-1x+3*x^2)^5//2+1//624*(2+-1x+3*x^2)^(1/2)*(1858+-771x)+1519//576*3^(1/2)*arcsinh(1//23*23^(1/2)*(1+-6x))+(312+624x)^-1*(2+-1x+3*x^2)^3//2*(151+122x))
@test integrate((1+2x)^3*(2+-1x+3*x^2)^5//2*(1+3x+4*x^2), x) == :(-1//498960*(2+-1x+3*x^2)^7//2*(26353+-21350x)+1//155520*(2+-1x+3*x^2)^5//2*(5089+-30534x)+1//1492992*(2+-1x+3*x^2)^3//2*(117047+-702282x)+1//11943936*(2+-1x+3*x^2)^(1/2)*(2692081+-16152486x)+2//33*(1+2x)^4*(2+-1x+3*x^2)^7//2+29//330*(1+2x)^3*(2+-1x+3*x^2)^7//2+133//1485*(1+2x)^2*(2+-1x+3*x^2)^7//2+61917863//71663616*3^(1/2)*arcsinh(1//23*23^(1/2)*(1+-6x)))
@test integrate((1+2x)^2*(2+-1x+3*x^2)^5//2*(1+3x+4*x^2), x) == :(-3564931//26873856*3^(1/2)*arcsinh(1//23*23^(1/2)*(1+-6x))+-1//58320*(2+-1x+3*x^2)^5//2*(293+-1758x)+-1//559872*(2+-1x+3*x^2)^3//2*(6739+-40434x)+1//15*(1+2x)^3*(2+-1x+3*x^2)^7//2+1//17010*(2+-1x+3*x^2)^7//2*(2731+3430x)+1//4478976*(2+-1x+3*x^2)^(1/2)*(-154997+929982x)+37//405*(1+2x)^2*(2+-1x+3*x^2)^7//2)
@test integrate((2+-1x+3*x^2)^5//2*(1+2x)*(1+3x+4*x^2), x) == :(-27071575//35831808*3^(1/2)*arcsinh(1//23*23^(1/2)*(1+-6x))+-1//15552*(2+-1x+3*x^2)^5//2*(445+-2670x)+-1//746496*(2+-1x+3*x^2)^3//2*(51175+-307050x)+1//648*(2+-1x+3*x^2)^7//2*(137+122x)+1//5971968*(2+-1x+3*x^2)^(1/2)*(-1177025+7062150x)+2//27*(1+2x)^2*(2+-1x+3*x^2)^7//2)
@test integrate((1+2x)^-1*(2+-1x+3*x^2)^5//2*(1+3x+4*x^2), x) == :(2//21*(2+-1x+3*x^2)^7//2+-169//128*13^(1/2)*arctanh(1//26*13^(1/2)*(2+-1x+3*x^2)^-1//2*(9+-8x))+1//1080*(2+-1x+3*x^2)^5//2*(29+150x)+1//10368*(2+-1x+3*x^2)^3//2*(2449+2154x)+1//82944*(2+-1x+3*x^2)^(1/2)*(221999+-17850x)+944521//497664*3^(1/2)*arcsinh(1//23*23^(1/2)*(1+-6x)))
@test integrate((1+2x)^-2*(2+-1x+3*x^2)^5//2*(1+3x+4*x^2), x) == :(-1*(13+26x)^-1*(2+-1x+3*x^2)^7//2+-315623//41472*3^(1/2)*arcsinh(1//23*23^(1/2)*(1+-6x))+-1//864*(2+-1x+3*x^2)^3//2*(737+-858x)+-1//2340*(2+-1x+3*x^2)^5//2*(407+-660x)+1//6912*(2+-1x+3*x^2)^(1/2)*(-51997+33990x)+429//128*13^(1/2)*arctanh(1//26*13^(1/2)*(2+-1x+3*x^2)^-1//2*(9+-8x)))
@test integrate((1+2x)^-3*(2+-1x+3*x^2)^5//2*(1+3x+4*x^2), x) == :(-1631//256*13^(1/2)*arctanh(1//26*13^(1/2)*(2+-1x+3*x^2)^-1//2*(9+-8x))+-1//26*(1+2x)^-2*(2+-1x+3*x^2)^7//2+1//832*(2+-1x+3*x^2)^3//2*(1227+-838x)+1//1536*(2+-1x+3*x^2)^(1/2)*(21317+-10470x)+118423//9216*3^(1/2)*arcsinh(1//23*23^(1/2)*(1+-6x))+(520+1040x)^-1*(2+-1x+3*x^2)^5//2*(257+134x))
@test integrate((g+h*x)^3*(a+b*x+c*x^2)^-1//2*(d+e*x+f*x^2), x) == :(1//256*c^-11//2*(96*c^3*(g*b^2*(f*g^2+3*h*(d*h+e*g))+a^2*h^2*(e*h+3*f*g)+2*a*b*h*(h*(d*h+3*e*g)+3*f*g^2))+-128*g*c^4*(a*(f*g^2+3*h*(d*h+e*g))+b*g*(e*g+3*d*h))+-63*f*b^5*h^3+256*d*c^5*g^3+-80*b*h*c^2*(b^2*(d*h^2+3*f*g^2+3*e*g*h)+3*f*a^2*h^2+3*a*b*h*(e*h+3*f*g))+70*c*b^3*h^2*(b*e*h+3*b*f*g+4*a*f*h))*arctanh((1/2)*c^-1//2*(a+b*x+c*x^2)^-1//2*(b+2*c*x))+1//1920*c^-5*h^-1*(a+b*x+c*x^2)^(1/2)*(-64*c^4*g^2*(-5*h*(3*e*g+16*d*h)+3*f*g^2)+-16*h*c^3*(b*g*(5*h*(47*e*g+54*d*h)+39*f*g^2)+16*a*h*(5*h*(d*h+3*e*g)+13*f*g^2))+8*c^2*h^2*(3*b^2*(50*h*(d*h+3*e*g)+129*f*g^2)+128*f*a^2*h^2+275*a*b*h*(e*h+3*f*g))+945*f*b^4*h^4+-210*c*b^2*h^3*(5*b*(e*h+3*f*g)+14*a*f*h)+-2*c*h*x*(8*h*c^2*(b*(21*f*g^2+50*d*h^2+80*e*g*h)+a*h*(45*e*h+71*f*g))+16*g*c^3*(-5*h*(3*e*g+10*d*h)+3*f*g^2)+315*f*b^3*h^3+-14*b*c*h^2*(25*b*e*h+39*b*f*g+46*a*f*h)))+-1//40*c^-2*h^-1*(g+h*x)^3*(a+b*x+c*x^2)^(1/2)*(2*c*(f*g+-5*e*h)+9*b*f*h)+1//5*f*c^-1*h^-1*(g+h*x)^4*(a+b*x+c*x^2)^(1/2)+1//240*c^-3*h^-1*(g+h*x)^2*(a+b*x+c*x^2)^(1/2)*(-1*c^2*(-20*h*(3*e*g+4*d*h)+12*f*g^2)+-2*c*h*(24*b*f*g+32*a*f*h+35*b*e*h)+63*f*b^2*h^2))
@test integrate((g+h*x)^2*(a+b*x+c*x^2)^-1//2*(d+e*x+f*x^2), x) == :(1//128*c^-9//2*(-64*c^3*(a*(d*h^2+f*g^2+2*e*g*h)+b*g*(e*g+2*d*h))+48*c^2*(b^2*(d*h^2+f*g^2+2*e*g*h)+f*a^2*h^2+2*a*b*h*(e*h+2*f*g))+35*f*b^4*h^2+128*d*c^4*g^2+-40*c*h*b^2*(b*e*h+2*b*f*g+3*a*f*h))*arctanh((1/2)*c^-1//2*(a+b*x+c*x^2)^-1//2*(b+2*c*x))+-1//192*c^-4*h^-1*(a+b*x+c*x^2)^(1/2)*(8*h*c^2*(b*(11*f*g^2+18*h*(d*h+2*e*g))+16*a*h*(e*h+2*f*g))+32*g*c^3*(f*g^2+-4*h*(e*g+3*d*h))+105*f*b^3*h^3+-20*b*c*h^2*(6*b*(e*h+2*f*g)+11*a*f*h)+-2*c*h*x*(-8*c^2*(f*g^2+-2*h*(2*e*g+3*d*h))+-4*c*h*(6*b*f*g+9*a*f*h+10*b*e*h)+35*f*b^2*h^2))+-1//24*c^-2*h^-1*(g+h*x)^2*(a+b*x+c*x^2)^(1/2)*(-8*c*e*h+2*c*f*g+7*b*f*h)+1//4*f*c^-1*h^-1*(g+h*x)^3*(a+b*x+c*x^2)^(1/2))
@test integrate((a+b*x+c*x^2)^-1//2*(g+h*x)*(d+e*x+f*x^2), x) == :(1//16*c^-7//2*(-8*c^2*(a*e*h+a*f*g+b*d*h+b*e*g)+-5*f*h*b^3+6*b*c*(b*e*h+b*f*g+2*a*f*h)+16*d*g*c^3)*arctanh((1/2)*c^-1//2*(a+b*x+c*x^2)^-1//2*(b+2*c*x))+1//24*c^-3*h^-1*(a+b*x+c*x^2)^(1/2)*(-8*c^2*(f*g^2+-3*h*(d*h+e*g))+-2*c*h*(9*b*(e*h+f*g)+8*a*f*h)+15*f*b^2*h^2+-2*c*h*x*(-6*c*e*h+2*c*f*g+5*b*f*h))+1//3*f*c^-1*h^-1*(g+h*x)^2*(a+b*x+c*x^2)^(1/2))
@test integrate((a+b*x+c*x^2)^-1//2*(d+e*x+f*x^2), x) == :(1//4*c^-2*(a+b*x+c*x^2)^(1/2)*(-3*b*f+4*c*e)+1//8*c^-5//2*(-4*c*(a*f+b*e)+3*f*b^2+8*d*c^2)*arctanh((1/2)*c^-1//2*(a+b*x+c*x^2)^-1//2*(b+2*c*x))+(1/2)*f*x*c^-1*(a+b*x+c*x^2)^(1/2))
@test integrate((g+h*x)^-1*(a+b*x+c*x^2)^-1//2*(d+e*x+f*x^2), x) == :(f*c^-1*h^-1*(a+b*x+c*x^2)^(1/2)+h^-2*(a*h^2+c*g^2+-1*b*g*h)^-1//2*(f*g^2+-1*h*(e*g+-1*d*h))*arctanh((1/2)*(a+b*x+c*x^2)^-1//2*(a*h^2+c*g^2+-1*b*g*h)^-1//2*(b*g+x*(-1*b*h+2*c*g)+-2*a*h))+-1//2*c^-3//2*h^-2*(b*f*h+-2*c*e*h+2*c*f*g)*arctanh((1/2)*c^-1//2*(a+b*x+c*x^2)^-1//2*(b+2*c*x)))
@test integrate((g+h*x)^-2*(a+b*x+c*x^2)^-1//2*(d+e*x+f*x^2), x) == :(f*c^-1//2*h^-2*arctanh((1/2)*c^-1//2*(a+b*x+c*x^2)^-1//2*(b+2*c*x))+-1//2*h^-2*(a*h^2+c*g^2+-1*b*g*h)^-3//2*(h*(-1*b*(-1*d*h^2+3*f*g^2+-1*e*g*h)+2*a*h*(-1*e*h+2*f*g))+2*c*(f*g^3+-1*d*g*h^2))*arctanh((1/2)*(a+b*x+c*x^2)^-1//2*(a*h^2+c*g^2+-1*b*g*h)^-1//2*(b*g+x*(-1*b*h+2*c*g)+-2*a*h))+-1*h^-1*(g+h*x)^-1*(a+b*x+c*x^2)^(1/2)*(a*h^2+c*g^2+-1*b*g*h)^-1*(f*g^2+-1*h*(e*g+-1*d*h)))
@test integrate((g+h*x)^-3*(a+b*x+c*x^2)^-1//2*(d+e*x+f*x^2), x) == :(1//8*(a*h^2+c*g^2+-1*b*g*h)^-5//2*(b^2*(3*d*h^2+3*f*g^2+e*g*h)+-4*c*(a*(d*h^2+f*g^2+-3*e*g*h)+b*g*(e*g+2*d*h))+8*d*c^2*g^2+8*f*a^2*h^2+-4*a*b*h*(e*h+2*f*g))*arctanh((1/2)*(a+b*x+c*x^2)^-1//2*(a*h^2+c*g^2+-1*b*g*h)^-1//2*(b*g+x*(-1*b*h+2*c*g)+-2*a*h))+-1//2*h^-1*(g+h*x)^-2*(a+b*x+c*x^2)^(1/2)*(a*h^2+c*g^2+-1*b*g*h)^-1*(f*g^2+-1*h*(e*g+-1*d*h))+1//4*h^-1*(g+h*x)^-1*(a+b*x+c*x^2)^(1/2)*(a*h^2+c*g^2+-1*b*g*h)^-2*(h*(-1*b*(-3*d*h^2+5*f*g^2+-1*e*g*h)+4*a*h*(-1*e*h+2*f*g))+2*c*g*(f*g^2+h*(e*g+-3*d*h))))
@test integrate((g+h*x)^3*(a+b*x+c*x^2)^-3//2*(d+e*x+f*x^2), x) == :(-1//16*c^-9//2*(-16*g*c^3*(f*g^2+3*h*(d*h+e*g))+24*h*c^2*(b*(d*h^2+3*f*g^2+3*e*g*h)+a*h*(e*h+3*f*g))+35*f*b^3*h^3+-30*b*c*h^2*(b*e*h+2*a*f*h+3*b*f*g))*arctanh((1/2)*c^-1//2*(a+b*x+c*x^2)^-1//2*(b+2*c*x))+c^-1*(g+h*x)^3*(b^2+-4*a*c)^-1*(a+b*x+c*x^2)^-1//2*(-2*x*(f*b^2+2*d*c^2+-1*b*c*e+-2*a*c*f)+2*c*(-1*b*(d+a*f*c^-1)+2*a*e))+1//24*h*c^-4*(b^2+-4*a*c)^-1*(a+b*x+c*x^2)^(1/2)*(-16*c^3*(4*a*(3*d*h^2+7*f*g^2+9*e*g*h)+3*b*g*(2*e*g+3*d*h))+8*c^2*(b^2*(9*h*(d*h+3*e*g)+20*f*g^2)+32*f*a^2*h^2+39*a*b*h*(e*h+3*f*g))+105*f*b^4*h^2+192*d*c^4*g^2+-10*c*h*b^2*(9*b*(e*h+3*f*g)+46*a*f*h)+2*c*h*x*(-8*c^2*(3*b*d*h+3*b*e*g+9*a*e*h+11*a*f*g)+-35*f*h*b^3+2*b*c*(15*b*e*h+17*b*f*g+58*a*f*h)+48*d*g*c^3))+1//3*h*c^-2*(g+h*x)^2*(b^2+-4*a*c)^-1*(a+b*x+c*x^2)^(1/2)*(7*f*b^2+12*d*c^2+-16*a*c*f+-6*b*c*e))
@test integrate((g+h*x)^2*(a+b*x+c*x^2)^-3//2*(d+e*x+f*x^2), x) == :(1//8*c^-7//2*(8*c^2*(f*g^2+h*(d*h+2*e*g))+-12*c*h*(a*f*h+b*e*h+2*b*f*g)+15*f*b^2*h^2)*arctanh((1/2)*c^-1//2*(a+b*x+c*x^2)^-1//2*(b+2*c*x))+c^-1*(g+h*x)^2*(b^2+-4*a*c)^-1*(a+b*x+c*x^2)^-1//2*(-2*x*(f*b^2+2*d*c^2+-1*b*c*e+-2*a*c*f)+2*c*(-1*b*(d+a*f*c^-1)+2*a*e))+1//4*h*c^-3*(b^2+-4*a*c)^-1*(a+b*x+c*x^2)^(1/2)*(-8*c^2*(b*d*h+2*b*e*g+4*a*e*h+8*a*f*g)+-15*f*h*b^3+4*b*c*(3*b*e*h+6*b*f*g+13*a*f*h)+32*d*g*c^3+2*c*h*x*(5*f*b^2+8*d*c^2+-12*a*c*f+-4*b*c*e)))
@test integrate((a+b*x+c*x^2)^-3//2*(d+e*x+f*x^2), x) == :(f*c^-3//2*arctanh((1/2)*c^-1//2*(a+b*x+c*x^2)^-1//2*(b+2*c*x))+c^-1*(b^2+-4*a*c)^-1*(a+b*x+c*x^2)^-1//2*(-2*x*(f*b^2+2*d*c^2+-1*b*c*e+-2*a*c*f)+2*c*(-1*b*(d+a*f*c^-1)+2*a*e)))
@test integrate((g+h*x)^-1*(a+b*x+c*x^2)^-3//2*(d+e*x+f*x^2), x) == :((a*h^2+c*g^2+-1*b*g*h)^-3//2*(f*g^2+-1*h*(e*g+-1*d*h))*arctanh((1/2)*(a+b*x+c*x^2)^-1//2*(a*h^2+c*g^2+-1*b*g*h)^-1//2*(b*g+x*(-1*b*h+2*c*g)+-2*a*h))+(b^2+-4*a*c)^-1*(a+b*x+c*x^2)^-1//2*(a*h^2+c*g^2+-1*b*g*h)^-1*(-2*b*(a*e*h+a*f*g+c*d*g)+-2*x*(-1*c*(b*d*h+b*e*g+-2*a*e*h+2*a*f*g)+b*f*(b*g+-1*a*h)+2*d*g*c^2)+4*a*(a*f*h+c*e*g+-1*c*d*h)+2*d*h*b^2))
@test integrate((g+h*x)^-2*(a+b*x+c*x^2)^-3//2*(d+e*x+f*x^2), x) == :((1/2)*(a*h^2+c*g^2+-1*b*g*h)^-5//2*(-1*h*(-1*b*(f*g^2+-3*d*h^2+e*g*h)+2*a*h*(-1*e*h+2*f*g))+2*c*g*(f*g^2+-1*h*(-3*d*h+2*e*g)))*arctanh((1/2)*(a+b*x+c*x^2)^-1//2*(a*h^2+c*g^2+-1*b*g*h)^-1//2*(b*g+x*(-1*b*h+2*c*g)+-2*a*h))+-1*(b^2+-4*a*c)^-1*(a+b*x+c*x^2)^-1//2*(a*h^2+c*g^2+-1*b*g*h)^-2*(2*b*(a*c*(f*g^2+-3*d*h^2+2*e*g*h)+d*c^2*g^2+f*a^2*h^2)+-4*a*c*(a*h*(-1*e*h+2*f*g)+c*g*(e*g+-2*d*h))+-2*h*b^2*(a*e*h+2*c*d*g)+2*c*x*(b^2*(d*h^2+f*g^2)+-1*c*(2*a*(d*h^2+f*g^2+-2*e*g*h)+b*g*(e*g+2*d*h))+2*d*c^2*g^2+2*f*a^2*h^2+-1*a*b*h*(e*h+2*f*g))+2*d*b^3*h^2)+-1*h*(g+h*x)^-1*(a+b*x+c*x^2)^(1/2)*(a*h^2+c*g^2+-1*b*g*h)^-2*(f*g^2+-1*h*(e*g+-1*d*h)))
@test integrate((g+h*x)^-3*(a+b*x+c*x^2)^-3//2*(d+e*x+f*x^2), x) == :(1//8*(a*h^2+c*g^2+-1*b*g*h)^-7//2*(h^2*(-1*b^2*(f*g^2+3*h*(e*g+-5*d*h))+8*f*a^2*h^2+4*a*b*h*(-3*e*h+2*f*g))+-4*c*h*(a*h*(3*d*h^2+11*f*g^2+-9*e*g*h)+-1*b*g*(2*f*g^2+3*h*(e*g+-4*d*h)))+8*c^2*g^2*(f*g^2+6*d*h^2+-3*e*g*h))*arctanh((1/2)*(a+b*x+c*x^2)^-1//2*(a*h^2+c*g^2+-1*b*g*h)^-1//2*(b*g+x*(-1*b*h+2*c*g)+-2*a*h))+(b^2+-4*a*c)^-1*(a+b*x+c*x^2)^-1//2*(a*h^2+c*g^2+-1*b*g*h)^-3*(-4*a*c*(f*a^2*h^3+-1*c^2*g^2*(e*g+-3*d*h)+-1*a*c*h*(d*h^2+3*f*g^2+-3*e*g*h))+-2*b*c*(d*c^2*g^3+3*a^2*h^2*(f*g+-1*e*h)+a*c*g*(f*g^2+-9*d*h^2+3*e*g*h))+-2*c*x*(c*(b^2*(f*g^3+3*d*g*h^2)+2*a^2*h^2*(-1*e*h+3*f*g)+-3*a*b*h*(f*g^2+-1*d*h^2+e*g*h))+-1*b*h^3*(d*b^2+f*a^2+-1*a*b*e)+-1*g*c^2*(2*a*(f*g^2+3*d*h^2+-3*e*g*h)+b*g*(e*g+3*d*h))+2*d*c^3*g^3)+-2*b^3*h^2*(a*e*h+3*c*d*g)+2*d*b^4*h^3+2*h*b^2*(f*a^2*h^2+3*d*c^2*g^2+a*c*h*(-4*d*h+3*e*g)))+-1//2*h*(g+h*x)^-2*(a+b*x+c*x^2)^(1/2)*(a*h^2+c*g^2+-1*b*g*h)^-2*(f*g^2+-1*h*(e*g+-1*d*h))+-1//4*h*(g+h*x)^-1*(a+b*x+c*x^2)^(1/2)*(a*h^2+c*g^2+-1*b*g*h)^-3*(-1*h*(-1*b*(f*g^2+-7*d*h^2+3*e*g*h)+4*a*h*(-1*e*h+2*f*g))+2*c*g*(-1*h*(-7*d*h+5*e*g)+3*f*g^2)))
@test integrate((1+2x)^3*(2+-1x+3*x^2)^-1//2*(1+3x+4*x^2), x) == :(-1//3240*(2+-1x+3*x^2)^(1/2)*(24897+6298x)+2//15*(1+2x)^4*(2+-1x+3*x^2)^(1/2)+19//60*(1+2x)^3*(2+-1x+3*x^2)^(1/2)+44//135*(1+2x)^2*(2+-1x+3*x^2)^(1/2)+9211//3888*3^(1/2)*arcsinh(1//23*23^(1/2)*(1+-6x)))
@test integrate((1+2x)^2*(2+-1x+3*x^2)^-1//2*(1+3x+4*x^2), x) == :(1//6*(1+2x)^3*(2+-1x+3*x^2)^(1/2)+1//324*(2+-1x+3*x^2)^(1/2)*(-429+286x)+11//27*(1+2x)^2*(2+-1x+3*x^2)^(1/2)+4147//1944*3^(1/2)*arcsinh(1//23*23^(1/2)*(1+-6x)))
@test integrate((2+-1x+3*x^2)^-1//2*(1+2x)*(1+3x+4*x^2), x) == :(1//54*(2+-1x+3*x^2)^(1/2)*(69+62x)+2//9*(1+2x)^2*(2+-1x+3*x^2)^(1/2)+251//324*3^(1/2)*arcsinh(1//23*23^(1/2)*(1+-6x)))
@test integrate((1+2x)^-1*(2+-1x+3*x^2)^-1//2*(1+3x+4*x^2), x) == :(2//3*(2+-1x+3*x^2)^(1/2)+-5//18*3^(1/2)*arcsinh(1//23*23^(1/2)*(1+-6x))+-1//26*13^(1/2)*arctanh(1//26*13^(1/2)*(2+-1x+3*x^2)^-1//2*(9+-8x)))
@test integrate((1+2x)^-2*(2+-1x+3*x^2)^-1//2*(1+3x+4*x^2), x) == :(-1*(13+26x)^-1*(2+-1x+3*x^2)^(1/2)+-1//3*3^(1/2)*arcsinh(1//23*23^(1/2)*(1+-6x))+9//338*13^(1/2)*arctanh(1//26*13^(1/2)*(2+-1x+3*x^2)^-1//2*(9+-8x)))
@test integrate((1+2x)^-3*(2+-1x+3*x^2)^-1//2*(1+3x+4*x^2), x) == :(7*(169+338x)^-1*(2+-1x+3*x^2)^(1/2)+-581//8788*13^(1/2)*arctanh(1//26*13^(1/2)*(2+-1x+3*x^2)^-1//2*(9+-8x))+-1//26*(1+2x)^-2*(2+-1x+3*x^2)^(1/2))
@test integrate((1+2x)^3*(2+-1x+3*x^2)^-3//2*(1+3x+4*x^2), x) == :(746//81*(2+-1x+3*x^2)^(1/2)+1//1863*(2+-1x+3*x^2)^-1//2*(25678+-7742x)+32//27*x^2*(2+-1x+3*x^2)^(1/2)+353//243*3^(1/2)*arcsinh(1//23*23^(1/2)*(1+-6x))+412//81*x*(2+-1x+3*x^2)^(1/2))
@test integrate((1+2x)^2*(2+-1x+3*x^2)^-3//2*(1+3x+4*x^2), x) == :(112//27*(2+-1x+3*x^2)^(1/2)+-64//27*3^(1/2)*arcsinh(1//23*23^(1/2)*(1+-6x))+1//621*(2+-1x+3*x^2)^-1//2*(2498+-4546x)+8//9*x*(2+-1x+3*x^2)^(1/2))
@test integrate((2+-1x+3*x^2)^-3//2*(1+2x)*(1+3x+4*x^2), x) == :(8//9*(2+-1x+3*x^2)^(1/2)+-14//9*3^(1/2)*arcsinh(1//23*23^(1/2)*(1+-6x))+-1//207*(2+-1x+3*x^2)^-1//2*(146+734x))
@test integrate((1+2x)^-1*(2+-1x+3*x^2)^-3//2*(1+3x+4*x^2), x) == :(-2//169*13^(1/2)*arctanh(1//26*13^(1/2)*(2+-1x+3*x^2)^-1//2*(9+-8x))+1//299*(2+-1x+3*x^2)^-1//2*(-202+154x))
@test integrate((1+2x)^-2*(2+-1x+3*x^2)^-3//2*(1+3x+4*x^2), x) == :(-4*(169+338x)^-1*(2+-1x+3*x^2)^(1/2)+-1//3887*(2+-1x+3*x^2)^-1//2*(394+-1674x)+2//2197*13^(1/2)*arctanh(1//26*13^(1/2)*(2+-1x+3*x^2)^-1//2*(9+-8x)))
@test integrate((1+2x)^-3*(2+-1x+3*x^2)^-3//2*(1+3x+4*x^2), x) == :(-4*(2197+4394x)^-1*(2+-1x+3*x^2)^(1/2)+-487//28561*13^(1/2)*arctanh(1//26*13^(1/2)*(2+-1x+3*x^2)^-1//2*(9+-8x))+-2//169*(1+2x)^-2*(2+-1x+3*x^2)^(1/2)+1//50531*(2+-1x+3*x^2)^-1//2*(4726+7386x))
@test integrate((1+2x)^3*(2+-1x+3*x^2)^-5//2*(1+3x+4*x^2), x) == :(32//27*(2+-1x+3*x^2)^(1/2)+-296//81*3^(1/2)*arcsinh(1//23*23^(1/2)*(1+-6x))+-1//128547*(2+-1x+3*x^2)^-1//2*(1002652+1182720x)+1//5589*(2+-1x+3*x^2)^-3//2*(25678+-7742x))
@test integrate((1+2x)^2*(2+-1x+3*x^2)^-5//2*(1+3x+4*x^2), x) == :(-16//27*3^(1/2)*arcsinh(1//23*23^(1/2)*(1+-6x))+-1//42849*(2+-1x+3*x^2)^-1//2*(186056+-11784x)+1//1863*(2+-1x+3*x^2)^-3//2*(2498+-4546x))
@test integrate((2+-1x+3*x^2)^-5//2*(1+2x)*(1+3x+4*x^2), x) == :(-1//621*(2+-1x+3*x^2)^-3//2*(146+734x)+-1//14283*(2+-1x+3*x^2)^-1//2*(15556+-17160x))
@test integrate((1+2x)^-1*(2+-1x+3*x^2)^-5//2*(1+3x+4*x^2), x) == :(-8//2197*13^(1/2)*arctanh(1//26*13^(1/2)*(2+-1x+3*x^2)^-1//2*(9+-8x))+-1//268203*(2+-1x+3*x^2)^-1//2*(2764+-54672x)+1//897*(2+-1x+3*x^2)^-3//2*(-202+154x))
@test integrate((1+2x)^-2*(2+-1x+3*x^2)^-5//2*(1+3x+4*x^2), x) == :(-16*(2197+4394x)^-1*(2+-1x+3*x^2)^(1/2)+-56//28561*13^(1/2)*arctanh(1//26*13^(1/2)*(2+-1x+3*x^2)^-1//2*(9+-8x))+-1//11661*(2+-1x+3*x^2)^-3//2*(394+-1674x)+-1//1162213*(2+-1x+3*x^2)^-1//2*(20184+-159192x))
@test integrate((1+2x)^-3*(2+-1x+3*x^2)^-5//2*(1+3x+4*x^2), x) == :(-144*(28561+57122x)^-1*(2+-1x+3*x^2)^(1/2)+-2084//371293*13^(1/2)*arctanh(1//26*13^(1/2)*(2+-1x+3*x^2)^-1//2*(9+-8x))+-8//2197*(1+2x)^-2*(2+-1x+3*x^2)^(1/2)+1//151593*(2+-1x+3*x^2)^-3//2*(4726+7386x)+1//15108769*(2+-1x+3*x^2)^-1//2*(309252+1242312x))
@test integrate((g+h*x)^-1*(-1*c*g^2+b*g*h+b*x*h^2+c*h^2*x^2)^-3//2*(d+e*x+f*x^2), x) == :(-1*f*c^-1*h^-3*(-1*g*(c*g+-1*b*h)+b*x*h^2+c*h^2*x^2)^-1//2+1//3*h^-3*(g+h*x)^-1*(-1*b*h+2*c*g)^-1*(-1*g*(c*g+-1*b*h)+b*x*h^2+c*h^2*x^2)^-1//2*(2*d*h^2+2*f*g^2+-2*e*g*h)+1//3*c^-1*h^-2*(-1*b*h+2*c*g)^-3*(-1*g*(c*g+-1*b*h)+b*x*h^2+c*h^2*x^2)^-1//2*(b+2*c*x)*(4*c^2*(f*g^2+-1*h*(e*g+2*d*h))+-3*f*b^2*h^2+6*b*c*e*h^2))
@test integrate((d+e*x)^(1/2)*(a+b*x+c*x^2)^(1/2)*(A+B*x+C*x^2), x) == :(-1//21*c^-2*e^-1*(d+e*x)^(1/2)*(a+b*x+c*x^2)^3//2*(-6*B*c*e+4*C*b*e+4*C*c*d)+2//9*C*c^-1*e^-1*(d+e*x)^3//2*(a+b*x+c*x^2)^3//2+2//315*c^-3*e^-3*(d+e*x)^(1/2)*(a+b*x+c*x^2)^(1/2)*(d*c^3*(-3*e*(-7*A*e+4*B*d)+8*C*d^2)+3*e*c^2*(-1*b*(C*d^2+-7*A*e^2+-2*B*d*e)+a*e*(C*d+-5*B*e))+8*C*b^3*e^3+-3*b*c*e^2*(C*b*d+-1*C*a*e+4*B*b*e)+3*c*e*x*(-1*c^2*(-3*e*(B*d+7*A*e)+2*C*d^2)+-1*c*e*(C*b*d+7*C*a*e+12*B*b*e)+8*C*b^2*e^2))+1//315*2^(1/2)*c^-4*e^-4*(c*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1*(d+e*x))^-1//2*(-1*c*(b^2+-4*a*c)^-1*(a+b*x+c*x^2))^(1/2)*(d+e*x)^(1/2)*(b^2+-4*a*c)^(1/2)*(a+b*x+c*x^2)^-1//2*((-1*c^2*(-3*e*(B*d+7*A*e)+2*C*d^2)+-1*c*e*(C*b*d+7*C*a*e+12*B*b*e)+8*C*b^2*e^2)*(-2*b^2*e^2+8*c^2*d^2+-3*c*e*(b*d+-2*a*e))+-5*c*e*(-1*b*e+2*c*d)*(b*(-1*c*d*(C*d+9*B*e)+2*C*a*e^2)+c*e*(-5*C*a*d+-3*B*a*e+21*A*c*d)+6*C*d*e*b^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*e*(b^2+-4*a*c)^(1/2)*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1)+-2//315*2^(1/2)*c^-4*e^-4*(c*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1*(d+e*x))^(1/2)*(-1*c*(b^2+-4*a*c)^-1*(a+b*x+c*x^2))^(1/2)*(d+e*x)^-1//2*(b^2+-4*a*c)^(1/2)*(a+b*x+c*x^2)^-1//2*(a*e^2+c*d^2+-1*b*d*e)*(-3*c^2*e^2*(B*b*d+-10*B*a*e+-7*A*b*e+2*C*a*d)+-2*d*c^3*(-3*e*(-7*A*e+4*B*d)+8*C*d^2)+8*C*b^3*e^3+3*b*c*e^2*(C*b*d+-9*C*a*e+-4*B*b*e))*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*e*(b^2+-4*a*c)^(1/2)*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1))
@test integrate((d+e*x)^-1//2*(a+b*x+c*x^2)^(1/2)*(A+B*x+C*x^2), x) == :(-2//105*c^-2*e^-3*(d+e*x)^(1/2)*(a+b*x+c*x^2)^(1/2)*(-1*(-1*b*e+4*c*d)*(-7*B*c*e+4*C*b*e+6*C*c*d)+5*c*e*(C*a*e+-7*A*c*e+3*C*b*d)+3*c*e*x*(-7*B*c*e+4*C*b*e+6*C*c*d))+2//7*C*c^-1*e^-1*(d+e*x)^(1/2)*(a+b*x+c*x^2)^3//2+1//105*2^(1/2)*c^-3*e^-4*(c*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1*(d+e*x))^-1//2*(-1*c*(b^2+-4*a*c)^-1*(a+b*x+c*x^2))^(1/2)*(d+e*x)^(1/2)*(b^2+-4*a*c)^(1/2)*(a+b*x+c*x^2)^-1//2*(-1*(-2*b^2*e^2+8*c^2*d^2+-3*c*e*(b*d+-2*a*e))*(-7*B*c*e+4*C*b*e+6*C*c*d)+5*c*e*(-1*b*e+2*c*d)*(C*a*e+-7*A*c*e+3*C*b*d))*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*e*(b^2+-4*a*c)^(1/2)*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1)+2//105*2^(1/2)*c^-3*e^-4*(c*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1*(d+e*x))^(1/2)*(-1*c*(b^2+-4*a*c)^-1*(a+b*x+c*x^2))^(1/2)*(d+e*x)^-1//2*(b^2+-4*a*c)^(1/2)*(a+b*x+c*x^2)^-1//2*(a*e^2+c*d^2+-1*b*d*e)*(c^2*(-14*e*(-5*A*e+4*B*d)+48*C*d^2)+c*e*(-10*C*a*e+-7*B*b*e+8*C*b*d)+4*C*b^2*e^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*e*(b^2+-4*a*c)^(1/2)*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1))
@test integrate((d+e*x)^-3//2*(a+b*x+c*x^2)^(1/2)*(A+B*x+C*x^2), x) == :(-1*e^-1*(d+e*x)^-1//2*(a+b*x+c*x^2)^3//2*(a*e^2+c*d^2+-1*b*d*e)^-1*(-2*e*(B*d+-1*A*e)+2*C*d^2)+-2//15*c^-1*e^-3*(d+e*x)^(1/2)*(a+b*x+c*x^2)^(1/2)*(a*e^2+c*d^2+-1*b*d*e)^-1*(c*e*(-5*b*(3*A*e^2+5*C*d^2+-4*B*d*e)+a*e*(-5*B*e+9*C*d))+d*c^2*(-5*e*(-3*A*e+4*B*d)+24*C*d^2)+C*b*e^2*(b*d+-1*a*e)+3*c*x*e^2*(C*b*d+-1*C*a*e+-5*A*c*e+5*B*c*d+-6*C*c*d^2*e^-1))+-1//15*2^(1/2)*c^-2*e^-4*(c*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1*(d+e*x))^-1//2*(-1*c*(b^2+-4*a*c)^-1*(a+b*x+c*x^2))^(1/2)*(d+e*x)^(1/2)*(b^2+-4*a*c)^(1/2)*(a+b*x+c*x^2)^-1//2*(-1*c^2*(-10*e*(-3*A*e+4*B*d)+48*C*d^2)+c*e*(-6*C*a*e+-5*B*b*e+8*C*b*d)+2*C*b^2*e^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*e*(b^2+-4*a*c)^(1/2)*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1)+2//15*2^(1/2)*c^-2*e^-4*(c*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1*(d+e*x))^(1/2)*(-1*c*(b^2+-4*a*c)^-1*(a+b*x+c*x^2))^(1/2)*(d+e*x)^-1//2*(b^2+-4*a*c)^(1/2)*(a+b*x+c*x^2)^-1//2*(-1*c*e*(-1*b*(-5*e*(-3*A*e+5*B*d)+32*C*d^2)+2*a*e*(-5*B*e+9*C*d))+-2*d*c^2*(-5*e*(-3*A*e+4*B*d)+24*C*d^2)+C*b*e^2*(b*d+-1*a*e))*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*e*(b^2+-4*a*c)^(1/2)*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1))
@test integrate((d+e*x)^-5//2*(a+b*x+c*x^2)^(1/2)*(A+B*x+C*x^2), x) == :(-1//3*e^-1*(d+e*x)^-3//2*(a+b*x+c*x^2)^3//2*(a*e^2+c*d^2+-1*b*d*e)^-1*(-2*e*(B*d+-1*A*e)+2*C*d^2)+-1//3*e^-3*(d+e*x)^-1//2*(a+b*x+c*x^2)^(1/2)*(a*e^2+c*d^2+-1*b*d*e)^-1*(-2*c*d*(-1*e*(-1*A*e+4*B*d)+8*C*d^2)+2*e*(b*d+-1*a*e)*(-3*B*e+7*C*d)+2*x*e^2*(B*c*d+C*b*d+-1*A*c*e+-1*C*a*e+-2*C*c*d^2*e^-1))+-2//3*2^(1/2)*c^-1*e^-4*(c*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1*(d+e*x))^(1/2)*(-1*c*(b^2+-4*a*c)^-1*(a+b*x+c*x^2))^(1/2)*(d+e*x)^-1//2*(b^2+-4*a*c)^(1/2)*(a+b*x+c*x^2)^-1//2*(e*(-3*B*b*e+-2*C*a*e+8*C*b*d)+-2*c*(-1*e*(-1*A*e+4*B*d)+8*C*d^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*e*(b^2+-4*a*c)^(1/2)*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1)+1//3*2^(1/2)*c^-1*e^-3*(c*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1*(d+e*x))^-1//2*(-1*c*(b^2+-4*a*c)^-1*(a+b*x+c*x^2))^(1/2)*(d+e*x)^(1/2)*(b^2+-4*a*c)^(1/2)*(a+b*x+c*x^2)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1*((-1*b*e+8*c*d)*(B*c*d+C*b*d+-1*A*c*e+-1*C*a*e+-2*C*c*d^2*e^-1)+6*c*(e*(A*c*d+B*a*e+-1*C*a*d)+b*d*(C*d+-1*B*e)))*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*e*(b^2+-4*a*c)^(1/2)*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1))
@test integrate((d+e*x)^-7//2*(a+b*x+c*x^2)^(1/2)*(A+B*x+C*x^2), x) == :(-1//5*e^-1*(d+e*x)^-5//2*(a+b*x+c*x^2)^3//2*(a*e^2+c*d^2+-1*b*d*e)^-1*(-2*e*(B*d+-1*A*e)+2*C*d^2)+-1//15*e^-3*(d+e*x)^-3//2*(a+b*x+c*x^2)^(1/2)*(a*e^2+c*d^2+-1*b*d*e)^-2*(2*e^2*(5*a^2*e^2*(B*e+C*d)+15*C*b^2*d^3+-1*a*b*e*(2*A*e^2+22*C*d^2+3*B*d*e))+2*e*x*(e^2*(b^2*(-2*A*e^2+23*C*d^2+-3*B*d*e)+15*C*a^2*e^2+-5*a*b*e*(-1*B*e+8*C*d))+-1*c*e*(-1*a*e*(3*A*e^2+53*C*d^2+-13*B*d*e)+5*b*d*(-1*A*e^2+11*C*d^2+-2*B*d*e))+5*c^2*d^2*(-1*e*(A*e+B*d)+6*C*d^2))+2*c^2*d^3*(-1*e*(A*e+4*B*d)+24*C*d^2)+-2*c*d*e*(b*d*(A*e^2+41*C*d^2+-6*B*d*e)+-1*a*e*(7*A*e^2+37*C*d^2+-7*B*d*e)))+1//15*2^(1/2)*e^-4*(c*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1*(d+e*x))^-1//2*(-1*c*(b^2+-4*a*c)^-1*(a+b*x+c*x^2))^(1/2)*(d+e*x)^(1/2)*(b^2+-4*a*c)^(1/2)*(a+b*x+c*x^2)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-2*(e^2*(b^2*(-2*A*e^2+38*C*d^2+-3*B*d*e)+30*C*a^2*e^2+-5*a*b*e*(-1*B*e+14*C*d))+-1*c*e*(b*d*(-2*A*e^2+88*C*d^2+-13*B*d*e)+-2*a*e*(3*A*e^2+43*C*d^2+-8*B*d*e))+2*c^2*d^2*(-1*e*(A*e+4*B*d)+24*C*d^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*e*(b^2+-4*a*c)^(1/2)*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1)+-2//15*2^(1/2)*c^-1*e^-4*(c*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1*(d+e*x))^(1/2)*(-1*c*(b^2+-4*a*c)^-1*(a+b*x+c*x^2))^(1/2)*(d+e*x)^-1//2*(b^2+-4*a*c)^(1/2)*(a+b*x+c*x^2)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1*(c*e*(-1*b*(-1*A*e^2+64*C*d^2+-9*B*d*e)+10*a*e*(-1*B*e+5*C*d))+2*d*c^2*(-1*e*(A*e+4*B*d)+24*C*d^2)+15*C*b*e^2*(b*d+-1*a*e))*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*e*(b^2+-4*a*c)^(1/2)*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1))
@test integrate((d+e*x)^-9//2*(a+b*x+c*x^2)^(1/2)*(A+B*x+C*x^2), x) == :(-1//7*e^-1*(d+e*x)^-7//2*(a+b*x+c*x^2)^3//2*(a*e^2+c*d^2+-1*b*d*e)^-1*(-2*e*(B*d+-1*A*e)+2*C*d^2)+-1//105*e^-3*(d+e*x)^-5//2*(a+b*x+c*x^2)^(1/2)*(a*e^2+c*d^2+-1*b*d*e)^-2*(-2*e^2*(-1*d*b^2*(8*A*e^2+15*C*d^2+6*B*d*e)+7*a^2*e^2*(C*d+-3*B*e)+a*b*e*(12*A*e^2+12*C*d^2+23*B*d*e))+2*e*x*(e^2*(b^2*(-4*A*e^2+45*C*d^2+-3*B*d*e)+35*C*a^2*e^2+-7*a*b*e*(-1*B*e+12*C*d))+c*e*(-1*b*(91*C*d^3+-21*A*d*e^2)+a*e*(-5*A*e^2+93*C*d^2+-9*B*d*e))+7*c^2*d^2*(e*(B*d+-3*A*e)+6*C*d^2))+2*c^2*d^3*(e*(3*A*e+4*B*d)+24*C*d^2)+-2*c*d*e*(b*d*(15*A*e^2+43*C*d^2+6*B*d*e)+-1*a*e*(19*A*e^2+33*C*d^2+9*B*d*e)))+1//105*e^-3*(d+e*x)^-1//2*(a+b*x+c*x^2)^(1/2)*(a*e^2+c*d^2+-1*b*d*e)^-3*(-2*b*e^3*(b^2*(8*A*e^2+15*C*d^2+6*B*d*e)+35*C*a^2*e^2+-14*a*b*e*(B*e+3*C*d))+2*c*e^2*(d*b^2*(e*(9*B*d+19*A*e)+103*C*d^2)+14*a^2*e^2*(-3*B*e+11*C*d)+-1*a*b*e*(e*(B*d+-29*A*e)+237*C*d^2))+4*c^3*d^3*(e*(3*A*e+4*B*d)+24*C*d^2)+2*d*e*c^2*(-1*b*d*(e*(9*A*e+19*B*d)+128*C*d^2)+2*a*e*(e*(-29*A*e+15*B*d)+69*C*d^2)))+-1//105*2^(1/2)*e^-4*(c*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1*(d+e*x))^-1//2*(-1*c*(b^2+-4*a*c)^-1*(a+b*x+c*x^2))^(1/2)*(d+e*x)^(1/2)*(b^2+-4*a*c)^(1/2)*(a+b*x+c*x^2)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-3*(c*e^2*(d*b^2*(e*(9*B*d+19*A*e)+103*C*d^2)+14*a^2*e^2*(-3*B*e+11*C*d)+-1*a*b*e*(e*(B*d+-29*A*e)+237*C*d^2))+-1*b*e^3*(b^2*(8*A*e^2+15*C*d^2+6*B*d*e)+35*C*a^2*e^2+-14*a*b*e*(B*e+3*C*d))+2*c^3*d^3*(e*(3*A*e+4*B*d)+24*C*d^2)+d*e*c^2*(-1*b*d*(e*(9*A*e+19*B*d)+128*C*d^2)+2*a*e*(e*(-29*A*e+15*B*d)+69*C*d^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*e*(b^2+-4*a*c)^(1/2)*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1)+2//105*2^(1/2)*e^-4*(c*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1*(d+e*x))^(1/2)*(-1*c*(b^2+-4*a*c)^-1*(a+b*x+c*x^2))^(1/2)*(d+e*x)^-1//2*(b^2+-4*a*c)^(1/2)*(a+b*x+c*x^2)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-2*(e^2*(b^2*(e*(3*B*d+4*A*e)+60*C*d^2)+70*C*a^2*e^2+-7*a*b*e*(B*e+18*C*d))+c*e*(-1*b*d*(3*e*(2*A*e+5*B*d)+104*C*d^2)+2*a*e*(e*(-5*A*e+12*B*d)+51*C*d^2))+2*c^2*d^2*(e*(3*A*e+4*B*d)+24*C*d^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*e*(b^2+-4*a*c)^(1/2)*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1))
@test integrate((d+e*x)^-11//2*(a+b*x+c*x^2)^(1/2)*(A+B*x+C*x^2), x) == :(-1//9*e^-1*(d+e*x)^-9//2*(a+b*x+c*x^2)^3//2*(a*e^2+c*d^2+-1*b*d*e)^-1*(-2*e*(B*d+-1*A*e)+2*C*d^2)+-1//105*e^-3*(d+e*x)^-7//2*(a+b*x+c*x^2)^(1/2)*(a*e^2+c*d^2+-1*b*d*e)^-2*(-2*e^2*(-1*d*b^2*(5*C*d^2+8*A*e^2+4*B*d*e)+3*a^2*e^2*(-5*B*e+3*C*d)+-1*a*b*e*(-10*A*e^2+2*C*d^2+-17*B*d*e))+2*e*x*(e^2*(b^2*(-1*e*(B*d+2*A*e)+25*C*d^2)+21*C*a^2*e^2+-3*a*b*e*(-1*B*e+16*C*d))+c*e*(a*e*(-7*A*e^2+47*C*d^2+B*d*e)+-3*b*d*(-5*A*e^2+15*C*d^2+2*B*d*e))+3*c^2*d^2*(e*(-5*A*e+3*B*d)+6*C*d^2))+2*c^2*d^3*(e*(4*B*d+5*A*e)+8*C*d^2)+-2*c*d*e*(-1*a*e*(7*C*d^2+13*A*e^2+11*B*d*e)+3*b*d*(5*A*e^2+5*C*d^2+2*B*d*e)))+1//315*e^-3*(d+e*x)^-3//2*(a+b*x+c*x^2)^(1/2)*(a*e^2+c*d^2+-1*b*d*e)^-3*(-2*b*e^3*(b^2*(5*C*d^2+8*A*e^2+4*B*d*e)+21*C*a^2*e^2+-6*a*b*e*(2*B*e+3*C*d))+4*c^3*d^3*(e*(4*B*d+5*A*e)+8*C*d^2)+6*c*e^2*(d*b^2*(7*A*e^2+15*C*d^2+3*B*d*e)+2*a^2*e^2*(-5*B*e+17*C*d)+-1*a*b*e*(-9*A*e^2+41*C*d^2+5*B*d*e))+6*d*e*c^2*(-1*b*d*(5*A*e^2+16*C*d^2+7*B*d*e)+2*a*e*(-9*A*e^2+9*C*d^2+7*B*d*e)))+1//315*e^-3*(d+e*x)^-1//2*(a+b*x+c*x^2)^(1/2)*(a*e^2+c*d^2+-1*b*d*e)^-4*(-12*c^2*e^2*(-1*a^2*e^2*(7*A*e^2+30*C*d^2+-36*B*d*e)+-1*b^2*d^2*(11*A*e^2+11*C*d^2+3*B*d*e)+a*b*d*e*(-34*A*e^2+30*C*d^2+-5*B*d*e))+-2*c*e^3*(d*b^3*(20*C*d^2+56*A*e^2+25*B*d*e)+126*C*a^3*e^3+-6*a*e*b^2*(-12*A*e^2+5*C*d^2+7*B*d*e)+-3*b*a^2*e^2*(12*C*d+29*B*e))+4*b^2*e^4*(b^2*(5*C*d^2+8*A*e^2+4*B*d*e)+21*C*a^2*e^2+-6*a*b*e*(2*B*e+3*C*d))+4*c^4*d^4*(e*(4*B*d+5*A*e)+8*C*d^2)+2*e*c^3*d^2*(-1*b*d*(5*e*(4*A*e+5*B*d)+56*C*d^2)+6*a*e*(-34*A*e^2+11*C*d^2+8*B*d*e)))+-1//315*2^(1/2)*e^-4*(c*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1*(d+e*x))^-1//2*(-1*c*(b^2+-4*a*c)^-1*(a+b*x+c*x^2))^(1/2)*(d+e*x)^(1/2)*(b^2+-4*a*c)^(1/2)*(a+b*x+c*x^2)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-4*(-1*c*e^3*(d*b^3*(20*C*d^2+56*A*e^2+25*B*d*e)+126*C*a^3*e^3+-6*a*e*b^2*(-12*A*e^2+5*C*d^2+7*B*d*e)+-3*b*a^2*e^2*(12*C*d+29*B*e))+-6*c^2*e^2*(-1*a^2*e^2*(7*A*e^2+30*C*d^2+-36*B*d*e)+-1*b^2*d^2*(11*A*e^2+11*C*d^2+3*B*d*e)+a*b*d*e*(-34*A*e^2+30*C*d^2+-5*B*d*e))+2*b^2*e^4*(b^2*(5*C*d^2+8*A*e^2+4*B*d*e)+21*C*a^2*e^2+-6*a*b*e*(2*B*e+3*C*d))+2*c^4*d^4*(e*(4*B*d+5*A*e)+8*C*d^2)+e*c^3*d^2*(-1*b*d*(5*e*(4*A*e+5*B*d)+56*C*d^2)+6*a*e*(-34*A*e^2+11*C*d^2+8*B*d*e)))*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*e*(b^2+-4*a*c)^(1/2)*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1)+2//315*2^(1/2)*e^-4*(c*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1*(d+e*x))^(1/2)*(-1*c*(b^2+-4*a*c)^-1*(a+b*x+c*x^2))^(1/2)*(d+e*x)^-1//2*(b^2+-4*a*c)^(1/2)*(a+b*x+c*x^2)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-3*(-1*b*e^3*(b^2*(5*C*d^2+8*A*e^2+4*B*d*e)+21*C*a^2*e^2+-6*a*b*e*(2*B*e+3*C*d))+2*c^3*d^3*(e*(4*B*d+5*A*e)+8*C*d^2)+3*c*e^2*(d*b^2*(7*A*e^2+15*C*d^2+3*B*d*e)+2*a^2*e^2*(-5*B*e+17*C*d)+-1*a*b*e*(-9*A*e^2+41*C*d^2+5*B*d*e))+3*d*e*c^2*(-1*b*d*(5*A*e^2+16*C*d^2+7*B*d*e)+2*a*e*(-9*A*e^2+9*C*d^2+7*B*d*e)))*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*e*(b^2+-4*a*c)^(1/2)*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1))
@test integrate((d+e*x)^3//2*(a+b*x+c*x^2)^-1//2*(A+B*x+C*x^2), x) == :(-1//35*c^-2*e^-1*(d+e*x)^3//2*(a+b*x+c*x^2)^(1/2)*(-14*B*c*e+4*C*c*d+12*C*b*e)+1//105*c^-3*e^-1*(d+e*x)^(1/2)*(a+b*x+c*x^2)^(1/2)*(-2*c^2*(-7*e*(3*B*d+5*A*e)+6*C*d^2)+-2*c*e*(15*C*b*d+25*C*a*e+28*B*b*e)+48*C*b^2*e^2)+2//7*C*c^-1*e^-1*(d+e*x)^5//2*(a+b*x+c*x^2)^(1/2)+-1//105*2^(1/2)*c^-4*e^-2*(c*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1*(d+e*x))^-1//2*(-1*c*(b^2+-4*a*c)^-1*(a+b*x+c*x^2))^(1/2)*(d+e*x)^(1/2)*(b^2+-4*a*c)^(1/2)*(a+b*x+c*x^2)^-1//2*(d*c^3*(-7*e*(3*B*d+20*A*e)+6*C*d^2)+e*c^2*(b*(12*C*d^2+70*A*e^2+91*B*d*e)+a*e*(63*B*e+82*C*d))+48*C*b^3*e^3+-8*b*c*e^2*(7*B*b*e+9*C*b*d+13*C*a*e))*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*e*(b^2+-4*a*c)^(1/2)*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1)+-2//105*2^(1/2)*c^-4*e^-2*(c*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1*(d+e*x))^(1/2)*(-1*c*(b^2+-4*a*c)^-1*(a+b*x+c*x^2))^(1/2)*(d+e*x)^-1//2*(b^2+-4*a*c)^(1/2)*(a+b*x+c*x^2)^-1//2*(a*e^2+c*d^2+-1*b*d*e)*(-1*c^2*(-7*e*(3*B*d+5*A*e)+6*C*d^2)+-1*c*e*(15*C*b*d+25*C*a*e+28*B*b*e)+24*C*b^2*e^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*e*(b^2+-4*a*c)^(1/2)*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1))
@test integrate((d+e*x)^(1/2)*(a+b*x+c*x^2)^-1//2*(A+B*x+C*x^2), x) == :(-1//15*c^-2*e^-1*(d+e*x)^(1/2)*(a+b*x+c*x^2)^(1/2)*(-10*B*c*e+4*C*c*d+8*C*b*e)+2//5*C*c^-1*e^-1*(d+e*x)^3//2*(a+b*x+c*x^2)^(1/2)+1//15*2^(1/2)*c^-3*e^-2*(c*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1*(d+e*x))^-1//2*(-1*c*(b^2+-4*a*c)^-1*(a+b*x+c*x^2))^(1/2)*(d+e*x)^(1/2)*(b^2+-4*a*c)^(1/2)*(a+b*x+c*x^2)^-1//2*(-1*c^2*(-5*e*(B*d+3*A*e)+2*C*d^2)+-1*c*e*(3*C*b*d+9*C*a*e+10*B*b*e)+8*C*b^2*e^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*e*(b^2+-4*a*c)^(1/2)*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1)+2//15*2^(1/2)*c^-3*e^-2*(c*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1*(d+e*x))^(1/2)*(-1*c*(b^2+-4*a*c)^-1*(a+b*x+c*x^2))^(1/2)*(d+e*x)^-1//2*(b^2+-4*a*c)^(1/2)*(a+b*x+c*x^2)^-1//2*(a*e^2+c*d^2+-1*b*d*e)*(-5*B*c*e+2*C*c*d+4*C*b*e)*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*e*(b^2+-4*a*c)^(1/2)*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1))
@test integrate((d+e*x)^-1//2*(a+b*x+c*x^2)^-1//2*(A+B*x+C*x^2), x) == :(2//3*C*c^-1*e^-1*(d+e*x)^(1/2)*(a+b*x+c*x^2)^(1/2)+-1//3*2^(1/2)*c^-2*e^-2*(c*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1*(d+e*x))^-1//2*(-1*c*(b^2+-4*a*c)^-1*(a+b*x+c*x^2))^(1/2)*(d+e*x)^(1/2)*(b^2+-4*a*c)^(1/2)*(a+b*x+c*x^2)^-1//2*(-3*B*c*e+2*C*b*e+2*C*c*d)*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*e*(b^2+-4*a*c)^(1/2)*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1)+2//3*2^(1/2)*c^-2*e^-2*(c*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1*(d+e*x))^(1/2)*(-1*c*(b^2+-4*a*c)^-1*(a+b*x+c*x^2))^(1/2)*(d+e*x)^-1//2*(b^2+-4*a*c)^(1/2)*(a+b*x+c*x^2)^-1//2*(c*(-3*e*(B*d+-1*A*e)+2*C*d^2)+C*e*(b*d+-1*a*e))*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*e*(b^2+-4*a*c)^(1/2)*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1))
@test integrate((d+e*x)^-3//2*(a+b*x+c*x^2)^-1//2*(A+B*x+C*x^2), x) == :(-1*e^-1*(d+e*x)^-1//2*(a+b*x+c*x^2)^(1/2)*(a*e^2+c*d^2+-1*b*d*e)^-1*(-2*e*(B*d+-1*A*e)+2*C*d^2)+-2*2^(1/2)*c^-1*e^-2*(c*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1*(d+e*x))^(1/2)*(-1*c*(b^2+-4*a*c)^-1*(a+b*x+c*x^2))^(1/2)*(d+e*x)^-1//2*(b^2+-4*a*c)^(1/2)*(a+b*x+c*x^2)^-1//2*(-1*B*e+2*C*d)*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*e*(b^2+-4*a*c)^(1/2)*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1)+-1*2^(1/2)*c^-1*e^-2*(c*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1*(d+e*x))^-1//2*(-1*c*(b^2+-4*a*c)^-1*(a+b*x+c*x^2))^(1/2)*(d+e*x)^(1/2)*(b^2+-4*a*c)^(1/2)*(a+b*x+c*x^2)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1*(-1*c*(-1*e*(B*d+-1*A*e)+2*C*d^2)+C*e*(b*d+-1*a*e))*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*e*(b^2+-4*a*c)^(1/2)*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1))
@test integrate((d+e*x)^-5//2*(a+b*x+c*x^2)^-1//2*(A+B*x+C*x^2), x) == :(-1//3*e^-1*(d+e*x)^-3//2*(a+b*x+c*x^2)^(1/2)*(a*e^2+c*d^2+-1*b*d*e)^-1*(-2*e*(B*d+-1*A*e)+2*C*d^2)+1//3*e^-1*(d+e*x)^-1//2*(a+b*x+c*x^2)^(1/2)*(a*e^2+c*d^2+-1*b*d*e)^-2*(2*e*(-1*b*(-2*A*e^2+4*C*d^2+-1*B*d*e)+3*a*e*(-1*B*e+2*C*d))+2*c*d*(e*(B*d+-4*A*e)+2*C*d^2))+-1//3*2^(1/2)*e^-2*(c*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1*(d+e*x))^-1//2*(-1*c*(b^2+-4*a*c)^-1*(a+b*x+c*x^2))^(1/2)*(d+e*x)^(1/2)*(b^2+-4*a*c)^(1/2)*(a+b*x+c*x^2)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-2*(e*(-1*b*(-2*A*e^2+4*C*d^2+-1*B*d*e)+3*a*e*(-1*B*e+2*C*d))+c*d*(e*(B*d+-4*A*e)+2*C*d^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*e*(b^2+-4*a*c)^(1/2)*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1)+-2//3*2^(1/2)*c^-1*e^-2*(c*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1*(d+e*x))^(1/2)*(-1*c*(b^2+-4*a*c)^-1*(a+b*x+c*x^2))^(1/2)*(d+e*x)^-1//2*(b^2+-4*a*c)^(1/2)*(a+b*x+c*x^2)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1*(-1*c*(e*(B*d+-1*A*e)+2*C*d^2)+3*C*e*(b*d+-1*a*e))*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*e*(b^2+-4*a*c)^(1/2)*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1))
@test integrate((d+e*x)^-7//2*(a+b*x+c*x^2)^-1//2*(A+B*x+C*x^2), x) == :(-1//5*e^-1*(d+e*x)^-5//2*(a+b*x+c*x^2)^(1/2)*(a*e^2+c*d^2+-1*b*d*e)^-1*(-2*e*(B*d+-1*A*e)+2*C*d^2)+1//15*e^-1*(d+e*x)^-3//2*(a+b*x+c*x^2)^(1/2)*(a*e^2+c*d^2+-1*b*d*e)^-2*(2*e*(-1*b*(-4*A*e^2+6*C*d^2+-1*B*d*e)+5*a*e*(-1*B*e+2*C*d))+2*c*d*(e*(-8*A*e+3*B*d)+2*C*d^2))+1//15*e^-1*(d+e*x)^-1//2*(a+b*x+c*x^2)^(1/2)*(a*e^2+c*d^2+-1*b*d*e)^-3*(-2*e^2*(b^2*(3*C*d^2+8*A*e^2+2*B*d*e)+15*C*a^2*e^2+-10*a*b*e*(B*e+C*d))+-2*c*e*(b*d*(-23*A*e^2+7*C*d^2+-7*B*d*e)+-1*a*e*(9*A*e^2+19*C*d^2+-29*B*d*e))+2*c^2*d^2*(e*(-23*A*e+3*B*d)+2*C*d^2))+-1//15*2^(1/2)*e^-2*(c*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1*(d+e*x))^-1//2*(-1*c*(b^2+-4*a*c)^-1*(a+b*x+c*x^2))^(1/2)*(d+e*x)^(1/2)*(b^2+-4*a*c)^(1/2)*(a+b*x+c*x^2)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-3*(-1*e^2*(b^2*(3*C*d^2+8*A*e^2+2*B*d*e)+15*C*a^2*e^2+-10*a*b*e*(B*e+C*d))+c^2*d^2*(e*(-23*A*e+3*B*d)+2*C*d^2)+-1*c*e*(b*d*(-23*A*e^2+7*C*d^2+-7*B*d*e)+-1*a*e*(9*A*e^2+19*C*d^2+-29*B*d*e)))*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*e*(b^2+-4*a*c)^(1/2)*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1)+2//15*2^(1/2)*e^-2*(c*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1*(d+e*x))^(1/2)*(-1*c*(b^2+-4*a*c)^-1*(a+b*x+c*x^2))^(1/2)*(d+e*x)^-1//2*(b^2+-4*a*c)^(1/2)*(a+b*x+c*x^2)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-2*(e*(-1*b*(-4*A*e^2+6*C*d^2+-1*B*d*e)+5*a*e*(-1*B*e+2*C*d))+c*d*(e*(-8*A*e+3*B*d)+2*C*d^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*e*(b^2+-4*a*c)^(1/2)*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1))
@test integrate((d+f*x^2)^p*(2*c*d*f+2*b*x*f^2*(3+2p)+2*c*f^2*x^2*(3+2p)), x) == :(2*c*f*x*(d+f*x^2)^(1+p)+b*f*(1+p)^-1*(d+f*x^2)^(1+p)*(3+2p))
@test integrate((d+e*x+f*x^2)^p*(-2*c*e^2+-1*c*p*e^2+2*c*d*f+2*c*f^2*x^2*(3+2p)), x) == :(2*c*f*x*(d+e*x+f*x^2)^(1+p)+-1*c*e*(1+p)^-1*(d+e*x+f*x^2)^(1+p)*(2+p))
@test integrate((d+e*x+f*x^2)^p*(-2*c*e^2+-1*c*p*e^2+2*c*d*f+3*b*e*f+2*b*e*f*p+2*b*x*f^2*(3+2p)+2*c*f^2*x^2*(3+2p)), x) == :(-1*(1+p)^-1*(d+e*x+f*x^2)^(1+p)*(c*e*(2+p)+-1*b*f*(3+2p))+2*c*f*x*(d+e*x+f*x^2)^(1+p))
@test integrate((d+e*x)^3*(a+b*x+c*x^2)^5*(d*(5*a*e+6*b*d)+x*(5*a*e^2+12*c*d^2+17*b*d*e)+e*x^2*(11*b*e+29*c*d)+17*c*e^2*x^3), x) == :((d+e*x)^5*(a+b*x+c*x^2)^6)
@test integrate((-2+x+x^2)^-1*(x^2+x^3), x) == :((1/2)*x^2+2//3*log(1+-1x)+4//3*log(2+x))
@test integrate(x^2*(a+b*x+c*x^2)^-1//2*(d+e*x+f*x^2+g*x^3), x) == :(-1//1920*c^-5*(a+b*x+c*x^2)^(1/2)*(-945*g*b^4+-60*c*b^2*(-49*a*g+20*c*e)+-2*c*x*(-315*g*b^3+-40*c^2*(9*a*f+10*b*e)+480*d*c^3+14*b*c*(25*b*f+46*a*g))+40*b*c^2*(-55*a*f+36*c*d)+256*a*c^2*(-4*a*g+5*c*e)+1050*c*f*b^3)+1//256*c^-11//2*(-63*g*b^5+-40*c*b^3*(-7*a*g+2*c*e)+-32*a*c^3*(-3*a*f+4*c*d)+48*b^2*c^2*(-5*a*f+2*c*d)+70*c*f*b^4+48*a*b*c^2*(-5*a*g+4*c*e))*arctanh((1/2)*c^-1//2*(a+b*x+c*x^2)^-1//2*(b+2*c*x))+1//5*g*c^-1*x^4*(a+b*x+c*x^2)^(1/2)+1//40*c^-2*x^3*(a+b*x+c*x^2)^(1/2)*(-9*b*g+10*c*f)+1//240*c^-3*x^2*(a+b*x+c*x^2)^(1/2)*(63*g*b^2+80*e*c^2+-70*b*c*f+-64*a*c*g))
@test integrate(x*(a+b*x+c*x^2)^-1//2*(d+e*x+f*x^2+g*x^3), x) == :(-1//128*c^-9//2*(-35*g*b^4+-24*c*b^2*(-5*a*g+2*c*e)+16*a*c^2*(-3*a*g+4*c*e)+32*b*c^2*(-3*a*f+2*c*d)+40*c*f*b^3)*arctanh((1/2)*c^-1//2*(a+b*x+c*x^2)^-1//2*(b+2*c*x))+1//192*c^-4*(a+b*x+c*x^2)^(1/2)*(-105*g*b^3+-16*c^2*(8*a*f+9*b*e)+192*d*c^3+2*c*x*(35*g*b^2+48*e*c^2+-40*b*c*f+-36*a*c*g)+20*b*c*(6*b*f+11*a*g))+1//4*g*c^-1*x^3*(a+b*x+c*x^2)^(1/2)+1//24*c^-2*x^2*(a+b*x+c*x^2)^(1/2)*(-7*b*g+8*c*f))
@test integrate((a+b*x+c*x^2)^-1//2*(d+e*x+f*x^2+g*x^3), x) == :(1//16*c^-7//2*(-8*c^2*(a*f+b*e)+-5*g*b^3+16*d*c^3+6*b*c*(b*f+2*a*g))*arctanh((1/2)*c^-1//2*(a+b*x+c*x^2)^-1//2*(b+2*c*x))+1//24*c^-3*(a+b*x+c*x^2)^(1/2)*(15*g*b^2+24*e*c^2+-18*b*c*f+-16*a*c*g)+1//3*g*c^-1*x^2*(a+b*x+c*x^2)^(1/2)+1//12*x*c^-2*(a+b*x+c*x^2)^(1/2)*(-5*b*g+6*c*f))
@test integrate(x^-1*(a+b*x+c*x^2)^-1//2*(d+e*x+f*x^2+g*x^3), x) == :(-1*d*a^-1//2*arctanh((1/2)*a^-1//2*(a+b*x+c*x^2)^-1//2*(2a+b*x))+1//4*c^-2*(a+b*x+c*x^2)^(1/2)*(-3*b*g+4*c*f)+1//8*c^-5//2*(-4*c*(a*g+b*f)+3*g*b^2+8*e*c^2)*arctanh((1/2)*c^-1//2*(a+b*x+c*x^2)^-1//2*(b+2*c*x))+(1/2)*g*x*c^-1*(a+b*x+c*x^2)^(1/2))
@test integrate(x^-2*(a+b*x+c*x^2)^-1//2*(d+e*x+f*x^2+g*x^3), x) == :(g*c^-1*(a+b*x+c*x^2)^(1/2)+(1/2)*a^-3//2*(b*d+-2*a*e)*arctanh((1/2)*a^-1//2*(a+b*x+c*x^2)^-1//2*(2a+b*x))+(1/2)*c^-3//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))+-1*d*a^-1*x^-1*(a+b*x+c*x^2)^(1/2))
@test integrate(x^-3*(a+b*x+c*x^2)^-1//2*(d+e*x+f*x^2+g*x^3), x) == :(g*c^-1//2*arctanh((1/2)*c^-1//2*(a+b*x+c*x^2)^-1//2*(b+2*c*x))+-1//8*a^-5//2*(3*d*b^2+8*f*a^2+-4*a*b*e+-4*a*c*d)*arctanh((1/2)*a^-1//2*(a+b*x+c*x^2)^-1//2*(2a+b*x))+-1//2*d*a^-1*x^-2*(a+b*x+c*x^2)^(1/2)+1//4*a^-2*x^-1*(a+b*x+c*x^2)^(1/2)*(-4*a*e+3*b*d))
@test integrate(x^-4*(a+b*x+c*x^2)^-1//2*(d+e*x+f*x^2+g*x^3), x) == :(1//16*a^-7//2*(5*d*b^3+8*a^2*(c*e+-2*a*g)+-6*a*e*b^2+-4*a*b*(-2*a*f+3*c*d))*arctanh((1/2)*a^-1//2*(a+b*x+c*x^2)^-1//2*(2a+b*x))+-1//3*d*a^-1*x^-3*(a+b*x+c*x^2)^(1/2)+-1//24*a^-3*x^-1*(a+b*x+c*x^2)^(1/2)*(15*d*b^2+24*f*a^2+-18*a*b*e+-16*a*c*d)+1//12*a^-2*x^-2*(a+b*x+c*x^2)^(1/2)*(-6*a*e+5*b*d))
@test integrate(x^-5*(a+b*x+c*x^2)^-1//2*(d+e*x+f*x^2+g*x^3), x) == :(-1//128*a^-9//2*(35*d*b^4+-40*a*e*b^3+-24*a*b^2*(-2*a*f+5*c*d)+16*c*a^2*(-4*a*f+3*c*d)+32*b*a^2*(-2*a*g+3*c*e))*arctanh((1/2)*a^-1//2*(a+b*x+c*x^2)^-1//2*(2a+b*x))+-1//4*d*a^-1*x^-4*(a+b*x+c*x^2)^(1/2)+-1//96*a^-3*x^-2*(a+b*x+c*x^2)^(1/2)*(35*d*b^2+48*f*a^2+-40*a*b*e+-36*a*c*d)+1//24*a^-2*x^-3*(a+b*x+c*x^2)^(1/2)*(-8*a*e+7*b*d)+1//192*a^-4*x^-1*(a+b*x+c*x^2)^(1/2)*(64*a^2*(-3*a*g+2*c*e)+105*d*b^3+-120*a*e*b^2+-4*a*b*(-36*a*f+55*c*d)))
@test integrate(x^-6*(a+b*x+c*x^2)^-1//2*(d+e*x+f*x^2+g*x^3), x) == :(1//256*a^-11//2*(63*d*b^5+-70*a*e*b^4+-40*a*b^3*(-2*a*f+7*c*d)+-32*c*a^3*(-4*a*g+3*c*e)+48*a^2*b^2*(-2*a*g+5*c*e)+48*b*c*a^2*(-4*a*f+5*c*d))*arctanh((1/2)*a^-1//2*(a+b*x+c*x^2)^-1//2*(2a+b*x))+-1//5*d*a^-1*x^-5*(a+b*x+c*x^2)^(1/2)+-1//240*a^-3*x^-3*(a+b*x+c*x^2)^(1/2)*(63*d*b^2+80*f*a^2+-70*a*b*e+-64*a*c*d)+-1//1920*a^-5*x^-1*(a+b*x+c*x^2)^(1/2)*(945*d*b^4+-1050*a*e*b^3+-60*a*b^2*(-20*a*f+49*c*d)+40*b*a^2*(-36*a*g+55*c*e)+256*c*a^2*(-5*a*f+4*c*d))+1//40*a^-2*x^-4*(a+b*x+c*x^2)^(1/2)*(-10*a*e+9*b*d)+1//960*a^-4*x^-2*(a+b*x+c*x^2)^(1/2)*(120*a^2*(-4*a*g+3*c*e)+315*d*b^3+-350*a*e*b^2+-4*a*b*(-100*a*f+161*c*d)))
@test integrate((d+e*x)^3*(3+2x+5*x^2)*(2+x+-5*x^3+3*x^2+4*x^4), x) == :(2*e^-7*(d+e*x)^10+-1//5*e^-7*(d+e*x)^5*(-7*e^5+120*d^5+12*d^2*e^3+42*d*e^4+68*d^3*e^2+85*e*d^4)+-1//7*e^-7*(d+e*x)^7*(4*e^3+400*d^3+68*d*e^2+170*e*d^2)+-1//9*e^-7*(d+e*x)^9*(17*e+120d)+1//6*e^-7*(d+e*x)^6*(21*e^4+300*d^4+12*d*e^3+102*d^2*e^2+170*e*d^3)+1//8*e^-7*(d+e*x)^8*(17*e^2+300*d^2+85*d*e)+1//4*e^-7*(d+e*x)^4*(3*e^2+5*d^2+-2*d*e)*(2*e^4+4*d^4+-1*d*e^3+3*d^2*e^2+5*e*d^3))
@test integrate((d+e*x)^2*(3+2x+5*x^2)*(2+x+-5*x^3+3*x^2+4*x^4), x) == :(x^3*(2*e^2+7*d^2+14//3*d*e)+x^5*(17//5*d^2+21//5*e^2+-8//5*d*e)+x^7*(17//7*e^2+20//7*d^2+-34//7*d*e)+-1*x^4*(d^2+-7//4*e^2+-21//2*d*e)+-1*x^6*(2//3*e^2+17//6*d^2+-17//3*d*e)+6*x*d^2+20//9*e^2*x^9+e*x^8*(5d+-17//8*e)+(1/2)*d*x^2*(7d+12*e))
@test integrate((d+e*x)*(3+2x+5*x^2)*(2+x+-5*x^3+3*x^2+4*x^4), x) == :(x^2*(3*e+7//2*d)+x^3*(7d+7//3*e)+x^5*(-4//5*e+17//5*d)+x^7*(-17//7*e+20//7*d)+-1*x^4*(d+-21//4*e)+-1*x^6*(-17//6*e+17//6*d)+6*d*x+5//2*e*x^8)
@test integrate((3+2x+5*x^2)*(2+x+-5*x^3+3*x^2+4*x^4), x) == :(-1*x^4+6x+7*x^3+-17//6*x^6+7//2*x^2+17//5*x^5+20//7*x^7)
@test integrate((d+e*x)^-1*(3+2x+5*x^2)*(2+x+-5*x^3+3*x^2+4*x^4), x) == :(10//3*e^-1*x^6+(1/2)*e^-5*x^2*(20*d^4+21*e^4+4*d*e^3+17*e*d^3+17*d^2*e^2)+-1*x*e^-6*(-7*e^5+20*d^5+4*d^2*e^3+17*e*d^4+17*d^3*e^2+21*d*e^4)+-1//3*e^-4*x^3*(4*e^3+20*d^3+17*d*e^2+17*e*d^2)+-1//5*e^-2*x^5*(17*e+20d)+1//4*e^-3*x^4*(17*e^2+20*d^2+17*d*e)+e^-7*(3*e^2+5*d^2+-2*d*e)*(2*e^4+4*d^4+-1*d*e^3+3*d^2*e^2+5*e*d^3)*log(d+e*x))
@test integrate((d+e*x)^-2*(3+2x+5*x^2)*(2+x+-5*x^3+3*x^2+4*x^4), x) == :(4*e^-2*x^5+x*e^-6*(21*e^4+100*d^4+8*d*e^3+51*d^2*e^2+68*e*d^3)+-1*e^-7*(-7*e^5+120*d^5+12*d^2*e^3+42*d*e^4+68*d^3*e^2+85*e*d^4)*log(d+e*x)+-1//2*e^-5*x^2*(4*e^3+80*d^3+34*d*e^2+51*e*d^2)+-1//4*e^-3*x^4*(17*e+40d)+1//3*e^-4*x^3*(17*e^2+60*d^2+34*d*e)+-1*e^-7*(d+e*x)^-1*(3*e^2+5*d^2+-2*d*e)*(2*e^4+4*d^4+-1*d*e^3+3*d^2*e^2+5*e*d^3))
@test integrate((d+e*x)^-3*(3+2x+5*x^2)*(2+x+-5*x^3+3*x^2+4*x^4), x) == :(5*e^-3*x^4+e^-7*(d+e*x)^-1*(-7*e^5+120*d^5+12*d^2*e^3+42*d*e^4+68*d^3*e^2+85*e*d^4)+e^-7*(21*e^4+300*d^4+12*d*e^3+102*d^2*e^2+170*e*d^3)*log(d+e*x)+(1/2)*e^-5*x^2*(17*e^2+120*d^2+51*d*e)+-1*x*e^-6*(4*e^3+200*d^3+51*d*e^2+102*e*d^2)+-1//3*e^-4*x^3*(17*e+60d)+-1//2*e^-7*(d+e*x)^-2*(3*e^2+5*d^2+-2*d*e)*(2*e^4+4*d^4+-1*d*e^3+3*d^2*e^2+5*e*d^3))
@test integrate((d+e*x)^3*(3+2x+5*x^2)^2*(2+x+-5*x^3+3*x^2+4*x^4), x) == :(25//3*e^-9*(d+e*x)^12+-1//7*e^-9*(d+e*x)^7*(-65*e^5+5600*d^5+370*d^2*e^3+592*d*e^4+1575*e*d^4+2220*d^3*e^2)+-1//9*e^-9*(d+e*x)^9*(37*e^3+5600*d^3+666*d*e^2+945*e*d^2)+-1//11*e^-9*(d+e*x)^11*(45*e+800d)+1//6*e^-9*(d+e*x)^6*(107*e^6+2800*d^6+-195*d*e^5+370*d^3*e^3+888*d^2*e^4+945*e*d^5+1665*d^4*e^2)+1//8*e^-9*(d+e*x)^8*(148*e^4+7000*d^4+185*d*e^3+1575*e*d^3+1665*d^2*e^2)+1//10*e^-9*(d+e*x)^10*(111*e^2+2800*d^2+315*d*e)+-1//5*e^-9*(d+e*x)^5*(3*e^2+5*d^2+-2*d*e)*(-11*e^5+160*d^5+-4*d^2*e^3+64*d*e^4+88*d^3*e^2+127*e*d^4)+1//4*e^-9*(d+e*x)^4*(3*e^2+5*d^2+-2*d*e)^2*(2*e^4+4*d^4+-1*d*e^3+3*d^2*e^2+5*e*d^3))
@test integrate((d+e*x)^2*(3+2x+5*x^2)^2*(2+x+-5*x^3+3*x^2+4*x^4), x) == :(x^3*(6*e^2+107//3*d^2+22*d*e)+x^4*(33//4*e^2+65//4*d^2+107//2*d*e)+x^5*(107//5*e^2+148//5*d^2+26*d*e)+x^7*(111//7*d^2+148//7*e^2+-74//7*d*e)+x^9*(37//3*e^2+100//9*d^2+-10*d*e)+-1*x^6*(-65//6*e^2+37//6*d^2+-148//3*d*e)+-1*x^8*(37//8*e^2+45//8*d^2+-111//4*d*e)+18*x*d^2+100//11*e^2*x^11+e*x^10*(20d+-9//2*e)+3//2*d*x^2*(11d+12*e))
@test integrate((3+2x+5*x^2)^2*(d+e*x)*(2+x+-5*x^3+3*x^2+4*x^4), x) == :(x^2*(9*e+33//2*d)+x^3*(11*e+107//3*d)+x^4*(65//4*d+107//4*e)+x^5*(13*e+148//5*d)+x^7*(-37//7*e+111//7*d)+x^9*(-5*e+100//9*d)+-1*x^6*(-74//3*e+37//6*d)+-1*x^8*(-111//8*e+45//8*d)+10*e*x^10+18*d*x)
@test integrate((3+2x+5*x^2)^2*(2+x+-5*x^3+3*x^2+4*x^4), x) == :(18x+-45//8*x^8+-37//6*x^6+33//2*x^2+65//4*x^4+100//9*x^9+107//3*x^3+111//7*x^7+148//5*x^5)
@test integrate((d+e*x)^-1*(3+2x+5*x^2)^2*(2+x+-5*x^3+3*x^2+4*x^4), x) == :(25//2*e^-1*x^8+(1/2)*e^-7*x^2*(100*d^6+107*e^6+-65*d*e^5+37*d^3*e^3+45*e*d^5+111*d^4*e^2+148*d^2*e^4)+-1*x*e^-8*(-33*e^7+100*d^7+-65*d^2*e^5+37*d^4*e^3+45*e*d^6+107*d*e^6+111*d^5*e^2+148*d^3*e^4)+-1//3*e^-6*x^3*(-65*e^5+100*d^5+37*d^2*e^3+45*e*d^4+111*d^3*e^2+148*d*e^4)+-1//5*e^-4*x^5*(37*e^3+100*d^3+45*e*d^2+111*d*e^2)+-1//7*e^-2*x^7*(45*e+100d)+1//4*e^-5*x^4*(100*d^4+148*e^4+37*d*e^3+45*e*d^3+111*d^2*e^2)+1//6*e^-3*x^6*(100*d^2+111*e^2+45*d*e)+e^-9*(3*e^2+5*d^2+-2*d*e)^2*(2*e^4+4*d^4+-1*d*e^3+3*d^2*e^2+5*e*d^3)*log(d+e*x))
@test integrate((d+e*x)^-2*(3+2x+5*x^2)^2*(2+x+-5*x^3+3*x^2+4*x^4), x) == :(100//7*e^-2*x^7+x*e^-8*(107*e^6+700*d^6+-130*d*e^5+148*d^3*e^3+270*e*d^5+444*d^2*e^4+555*d^4*e^2)+-1//2*e^-7*x^2*(-65*e^5+600*d^5+111*d^2*e^3+225*e*d^4+296*d*e^4+444*d^3*e^2)+-1//4*e^-5*x^4*(37*e^3+400*d^3+135*e*d^2+222*d*e^2)+-1//6*e^-3*x^6*(45*e+200d)+1//3*e^-6*x^3*(148*e^4+500*d^4+74*d*e^3+180*e*d^3+333*d^2*e^2)+1//5*e^-4*x^5*(111*e^2+300*d^2+90*d*e)+-1*e^-9*(d+e*x)^-1*(3*e^2+5*d^2+-2*d*e)^2*(2*e^4+4*d^4+-1*d*e^3+3*d^2*e^2+5*e*d^3)+-1*e^-9*(3*e^2+5*d^2+-2*d*e)*(-11*e^5+160*d^5+-4*d^2*e^3+64*d*e^4+88*d^3*e^2+127*e*d^4)*log(d+e*x))
@test integrate((d+e*x)^-3*(3+2x+5*x^2)^2*(2+x+-5*x^3+3*x^2+4*x^4), x) == :(50//3*e^-3*x^6+e^-9*(107*e^6+2800*d^6+-195*d*e^5+370*d^3*e^3+888*d^2*e^4+945*e*d^5+1665*d^4*e^2)*log(d+e*x)+(1/2)*e^-7*x^2*(148*e^4+1500*d^4+111*d*e^3+450*e*d^3+666*d^2*e^2)+-1*x*e^-8*(-65*e^5+2100*d^5+222*d^2*e^3+444*d*e^4+675*e*d^4+1110*d^3*e^2)+-1*e^-4*x^5*(9*e+60d)+-1//3*e^-6*x^3*(37*e^3+1000*d^3+270*e*d^2+333*d*e^2)+1//4*e^-5*x^4*(111*e^2+600*d^2+135*d*e)+e^-9*(d+e*x)^-1*(3*e^2+5*d^2+-2*d*e)*(-11*e^5+160*d^5+-4*d^2*e^3+64*d*e^4+88*d^3*e^2+127*e*d^4)+-1//2*e^-9*(d+e*x)^-2*(3*e^2+5*d^2+-2*d*e)^2*(2*e^4+4*d^4+-1*d*e^3+3*d^2*e^2+5*e*d^3))
@test integrate((d+e*x)^-4*(3+2x+5*x^2)^2*(2+x+-5*x^3+3*x^2+4*x^4), x) == :(20*e^-4*x^5+x*e^-8*(148*e^4+3500*d^4+148*d*e^3+900*e*d^3+1110*d^2*e^2)+-1*e^-9*(d+e*x)^-1*(107*e^6+2800*d^6+-195*d*e^5+370*d^3*e^3+888*d^2*e^4+945*e*d^5+1665*d^4*e^2)+-1*e^-9*(-65*e^5+5600*d^5+370*d^2*e^3+592*d*e^4+1575*e*d^4+2220*d^3*e^2)*log(d+e*x)+-1//2*e^-7*x^2*(37*e^3+2000*d^3+444*d*e^2+450*e*d^2)+-1//4*e^-5*x^4*(45*e+400d)+1//3*e^-6*x^3*(111*e^2+1000*d^2+180*d*e)+(1/2)*e^-9*(d+e*x)^-2*(3*e^2+5*d^2+-2*d*e)*(-11*e^5+160*d^5+-4*d^2*e^3+64*d*e^4+88*d^3*e^2+127*e*d^4)+-1//3*e^-9*(d+e*x)^-3*(3*e^2+5*d^2+-2*d*e)^2*(2*e^4+4*d^4+-1*d*e^3+3*d^2*e^2+5*e*d^3))
@test integrate((d+e*x)^3*(3+2x+5*x^2)^-1*(2+x+-5*x^3+3*x^2+4*x^4), x) == :(-1//6250*x^2*(881*e^3+4125*d^3+-6870*d*e^2+-6075*e*d^2)+1//1875*x^3*(458*e^3+500*d^3+-2475*e*d^2+1215*d*e^2)+1//15625*x*(-5108*e^3+10125*d^3+-13215*d*e^2+34350*e*d^2)+1//156250*(23431*e^3+57250*d^3+-76620*d*e^2+-66075*e*d^2)*log(3+2x+5*x^2)+2//15*e^3*x^6+e^2*x^5*(-33//125*e+12//25*d)+-1//1093750*14^(1/2)*(-53189*e^3+52875*d^3+-274845*d*e^2+449175*e*d^2)*arctan(1//14*14^(1/2)*(1+5x))+3//500*e*x^4*(27*e^2+100*d^2+-165*d*e))
@test integrate((d+e*x)^2*(3+2x+5*x^2)^-1*(2+x+-5*x^3+3*x^2+4*x^4), x) == :(x^3*(4//15*d^2+27//125*e^2+-22//25*d*e)+-1//1250*x^2*(-458*e^2+825*d^2+-810*d*e)+1//3125*x*(-881*e^2+2025*d^2+4580*d*e)+1//15625*(-2554*e^2+5725*d^2+-4405*d*e)*log(3+2x+5*x^2)+4//25*e^2*x^5+e*x^4*(-33//100*e+2//5*d)+-1//218750*14^(1/2)*(-18323*e^2+10575*d^2+59890*d*e)*arctan(1//14*14^(1/2)*(1+5x)))
@test integrate((3+2x+5*x^2)^-1*(d+e*x)*(2+x+-5*x^3+3*x^2+4*x^4), x) == :(x*(81//125*d+458//625*e)+x^3*(-11//25*e+4//15*d)+-1*x^2*(-81//250*e+33//50*d)+1//5*e*x^4+1//6250*(-881*e+2290d)*log(3+2x+5*x^2)+-1//43750*14^(1/2)*(2115d+5989*e)*arctan(1//14*14^(1/2)*(1+5x)))
@test integrate((3+2x+5*x^2)^-1*(2+x+-5*x^3+3*x^2+4*x^4), x) == :(-33//50*x^2+4//15*x^3+81//125*x+229//625*log(3+2x+5*x^2)+-423//8750*14^(1/2)*arctan(1//14*14^(1/2)*(1+5x)))
@test integrate((d+e*x)^-1*(3+2x+5*x^2)^-1*(2+x+-5*x^3+3*x^2+4*x^4), x) == :(2//5*e^-1*x^2+(750*e^2+1250*d^2+-500*d*e)^-1*(-7*e+458d)*log(3+2x+5*x^2)+-1//25*x*e^-2*(20d+33*e)+e^-3*(3*e^2+5*d^2+-2*d*e)^-1*(2*e^4+4*d^4+-1*d*e^3+3*d^2*e^2+5*e*d^3)*log(d+e*x)+-1//1750*14^(1/2)*(3*e^2+5*d^2+-2*d*e)^-1*(-1367*e+423d)*arctan(1//14*14^(1/2)*(1+5x)))
@test integrate((d+e*x)^-2*(3+2x+5*x^2)^-1*(2+x+-5*x^3+3*x^2+4*x^4), x) == :(4//5*x*e^-2+1//25*(3*e^2+5*d^2+-2*d*e)^-2*(-136*e^2+229*d^2+-7*d*e)*log(3+2x+5*x^2)+-1*e^-3*(d+e*x)^-1*(3*e^2+5*d^2+-2*d*e)^-1*(2*e^4+4*d^4+-1*d*e^3+3*d^2*e^2+5*e*d^3)+-1*e^-3*(3*e^2+5*d^2+-2*d*e)^-2*(e^5+40*d^5+e*d^4+-2*d*e^4+28*d^3*e^2+44*d^2*e^3)*log(d+e*x)+-1//350*14^(1/2)*(3*e^2+5*d^2+-2*d*e)^-2*(293*e^2+423*d^2+-2734*d*e)*arctan(1//14*14^(1/2)*(1+5x)))
@test integrate((d+e*x)^-3*(3+2x+5*x^2)^-1*(2+x+-5*x^3+3*x^2+4*x^4), x) == :(1//10*(3*e^2+5*d^2+-2*d*e)^-3*(113*e^3+458*d^3+-816*d*e^2+-21*e*d^2)*log(3+2x+5*x^2)+e^-3*(d+e*x)^-1*(3*e^2+5*d^2+-2*d*e)^-2*(e^5+40*d^5+e*d^4+-2*d*e^4+28*d^3*e^2+44*d^2*e^3)+e^-3*(3*e^2+5*d^2+-2*d*e)^-3*(-1*e^6+100*d^6+-242*d^3*e^3+-120*e*d^5+120*d*e^5+141*d^2*e^4+228*d^4*e^2)*log(d+e*x)+-1//2*e^-3*(d+e*x)^-2*(3*e^2+5*d^2+-2*d*e)^-1*(2*e^4+4*d^4+-1*d*e^3+3*d^2*e^2+5*e*d^3)+-1//70*14^(1/2)*(3*e^2+5*d^2+-2*d*e)^-3*(423*d^3+703*e^3+-4101*e*d^2+879*d*e^2)*arctan(1//14*14^(1/2)*(1+5x)))
@test integrate((d+e*x)^3*(3+2x+5*x^2)^-2*(2+x+-5*x^3+3*x^2+4*x^4), x) == :(-1//6250*(832*e^3+1025*d^3+-2601*d*e^2+-1545*e*d^2)*log(3+2x+5*x^2)+1//25*e^3*x^4+1//17500*x*(2800*d^3+6053*e^3+-17220*e*d^2+9921*d*e^2)+e^2*x^3*(-41//375*e+4//25*d)+-1*(d+e*x)^3*(10500+7000x+17500*x^2)^-1*(1367+423x)+1//3500*e*x^2*(373*e^2+840*d^2+-1722*d*e)+1//1225000*14^(1/2)*(-67499*e^3+32825*d^3+-221643*d*e^2+317565*e*d^2)*arctan(1//14*14^(1/2)*(1+5x)))
@test integrate((d+e*x)^2*(3+2x+5*x^2)^-2*(2+x+-5*x^3+3*x^2+4*x^4), x) == :(-1//6250*(-867*e^2+1025*d^2+-1030*d*e)*log(3+2x+5*x^2)+1//17500*x*(2800*d^2+3307*e^2+-11480*d*e)+4//75*e^2*x^3+e*x^2*(-41//250*e+4//25*d)+-1*(d+e*x)^2*(10500+7000x+17500*x^2)^-1*(1367+423x)+1//1225000*14^(1/2)*(-73881*e^2+32825*d^2+211710*d*e)*arctan(1//14*14^(1/2)*(1+5x)))
@test integrate((3+2x+5*x^2)^-2*(d+e*x)*(2+x+-5*x^3+3*x^2+4*x^4), x) == :(x*(-41//125*e+4//25*d)+-1//1250*(-103*e+205d)*log(3+2x+5*x^2)+2//25*e*x^2+-1*(10500+7000x+17500*x^2)^-1*(1367+423x)*(d+e*x)+1//245000*14^(1/2)*(6565d+21171*e)*arctan(1//14*14^(1/2)*(1+5x)))
@test integrate((3+2x+5*x^2)^-2*(2+x+-5*x^3+3*x^2+4*x^4), x) == :(-41//250*log(3+2x+5*x^2)+4//25*x+-1*(10500+7000x+17500*x^2)^-1*(1367+423x)+1313//49000*14^(1/2)*arctan(1//14*14^(1/2)*(1+5x)))
@test integrate((d+e*x)^-1*(3+2x+5*x^2)^-2*(2+x+-5*x^3+3*x^2+4*x^4), x) == :(-1*(3+2x+5*x^2)^-1*(2100*e^2+3500*d^2+-1400*d*e)^-1*(-293*e+1367d+x*(-1367*e+423d))+-1//50*(3*e^2+5*d^2+-2*d*e)^-2*(14*e^3+205*d^3+-61*e*d^2+23*d*e^2)*log(3+2x+5*x^2)+e^-1*(3*e^2+5*d^2+-2*d*e)^-2*(2*e^4+4*d^4+-1*d*e^3+3*d^2*e^2+5*e*d^3)*log(d+e*x)+1//9800*14^(1/2)*(3*e^2+5*d^2+-2*d*e)^-2*(-6623*e^3+6565*d^3+-26423*e*d^2+11089*d*e^2)*arctan(1//14*14^(1/2)*(1+5x)))
@test integrate((d+e*x)^-2*(3+2x+5*x^2)^-2*(2+x+-5*x^3+3*x^2+4*x^4), x) == :((3*e^2+5*d^2+-2*d*e)^-3*(-5*e^4+41*d^4+-60*d^2*e^2+-8*e*d^3+24*d*e^3)*log(d+e*x)+-1//2*(3*e^2+5*d^2+-2*d*e)^-3*(-5*e^4+41*d^4+-60*d^2*e^2+-8*e*d^3+24*d*e^3)*log(3+2x+5*x^2)+-1//140*(3+2x+5*x^2)^-1*(3*e^2+5*d^2+-2*d*e)^-2*(-703*e^2+1367*d^2+x*(293*e^2+423*d^2+-2734*d*e)+-586*d*e)+-1*e^-1*(d+e*x)^-1*(3*e^2+5*d^2+-2*d*e)^-2*(2*e^4+4*d^4+-1*d*e^3+3*d^2*e^2+5*e*d^3)+1//392*14^(1/2)*(3*e^2+5*d^2+-2*d*e)^-3*(-271*e^4+1313*d^4+-10044*e*d^3+156*d*e^3+4290*d^2*e^2)*arctan(1//14*14^(1/2)*(1+5x)))
@test integrate((d+e*x)^-3*(3+2x+5*x^2)^-2*(2+x+-5*x^3+3*x^2+4*x^4), x) == :((3*e^2+5*d^2+-2*d*e)^-4*(-21*e^5+205*d^5+-846*d^3*e^2+-19*e*d^4+57*d*e^4+396*d^2*e^3)*log(d+e*x)+-1*(d+e*x)^-1*(3*e^2+5*d^2+-2*d*e)^-3*(-5*e^4+41*d^4+-60*d^2*e^2+-8*e*d^3+24*d*e^3)+-1//2*(3*e^2+5*d^2+-2*d*e)^-4*(-21*e^5+205*d^5+-846*d^3*e^2+-19*e*d^4+57*d*e^4+396*d^2*e^3)*log(3+2x+5*x^2)+-1//28*(3+2x+5*x^2)^-1*(3*e^2+5*d^2+-2*d*e)^-3*(457*e^3+1367*d^3+x*(423*d^3+703*e^3+-4101*e*d^2+879*d*e^2)+-2109*d*e^2+-879*e*d^2)+-1//2*e^-1*(d+e*x)^-2*(3*e^2+5*d^2+-2*d*e)^-2*(2*e^4+4*d^4+-1*d*e^3+3*d^2*e^2+5*e*d^3)+1//392*14^(1/2)*(3*e^2+5*d^2+-2*d*e)^-4*(579*e^5+6565*d^5+-74017*e*d^4+-17247*d*e^4+35022*d^3*e^2+42858*d^2*e^3)*arctan(1//14*14^(1/2)*(1+5x)))
@test integrate((d+e*x)^3*(3+2x+5*x^2)^-3*(2+x+-5*x^3+3*x^2+4*x^4), x) == :(2//125*e^3*x^2+(d+e*x)^2*(588000+392000x+980000*x^2)^-1*(-6315*e+34347d+x*(11015d+49177*e))+-1//7000*(d+e*x)^3*(3+2x+5*x^2)^-2*(1367+423x)+1//980000*x*e^2*(-126009*e+83065d)+1//68600000*14^(1/2)*(1059375*d^3+1669047*e^3+-2565525*e*d^2+222255*d*e^2)*arctan(1//14*14^(1/2)*(1+5x))+3//6250*e*(47*e^2+100*d^2+-245*d*e)*log(3+2x+5*x^2))
@test integrate((d+e*x)^2*(3+2x+5*x^2)^-3*(2+x+-5*x^3+3*x^2+4*x^4), x) == :(4//125*x*e^2+(588000+392000x+980000*x^2)^-1*(d+e*x)*(-6413*e+34347d+x*(11015d+42765*e))+-1//7000*(d+e*x)^2*(3+2x+5*x^2)^-2*(1367+423x)+1//1250*e*(-49*e+40d)*log(3+2x+5*x^2)+1//13720000*14^(1/2)*(14817*e^2+211875*d^2+-342070*d*e)*arctan(1//14*14^(1/2)*(1+5x)))
@test integrate((3+2x+5*x^2)^-3*(d+e*x)*(2+x+-5*x^3+3*x^2+4*x^4), x) == :((588000+392000x+980000*x^2)^-1*(-6511*e+34347d+x*(11015d+36353*e))+2//125*e*log(3+2x+5*x^2)+-1//7000*(3+2x+5*x^2)^-2*(1367+423x)*(d+e*x)+1//2744000*14^(1/2)*(-34207*e+42375d)*arctan(1//14*14^(1/2)*(1+5x)))
@test integrate((3+2x+5*x^2)^-3*(2+x+-5*x^3+3*x^2+4*x^4), x) == :((588000+392000x+980000*x^2)^-1*(34347+11015x)+-1//7000*(3+2x+5*x^2)^-2*(1367+423x)+339//21952*14^(1/2)*arctan(1//14*14^(1/2)*(1+5x)))
@test integrate((d+e*x)^-1*(3+2x+5*x^2)^-3*(2+x+-5*x^3+3*x^2+4*x^4), x) == :(-1*(3+2x+5*x^2)^-2*(4200*e^2+7000*d^2+-2800*d*e)^-1*(-293*e+1367d+x*(-1367*e+423d))+1//39200*(3+2x+5*x^2)^-1*(3*e^2+5*d^2+-2*d*e)^-2*(1831*e^3+171735*d^3+x*(-45725*e^3+55075*d^3+-225825*e*d^2+90875*d*e^2)+-92989*e*d^2+36207*d*e^2)+e*(3*e^2+5*d^2+-2*d*e)^-3*(2*e^4+4*d^4+-1*d*e^3+3*d^2*e^2+5*e*d^3)*log(d+e*x)+-1//2*e*(3*e^2+5*d^2+-2*d*e)^-3*(2*e^4+4*d^4+-1*d*e^3+3*d^2*e^2+5*e*d^3)*log(3+2x+5*x^2)+1//21952*14^(1/2)*(3*e^2+5*d^2+-2*d*e)^-3*(-8623*e^5+42375*d^5+-56058*d^2*e^3+-16643*e*d^4+31811*d*e^4+58530*d^3*e^2)*arctan(1//14*14^(1/2)*(1+5x)))
@test integrate((d+e*x)^-2*(3+2x+5*x^2)^-3*(2+x+-5*x^3+3*x^2+4*x^4), x) == :(-1//280*(3+2x+5*x^2)^-2*(3*e^2+5*d^2+-2*d*e)^-2*(-703*e^2+1367*d^2+x*(293*e^2+423*d^2+-2734*d*e)+-586*d*e)+1//7840*(3+2x+5*x^2)^-1*(3*e^2+5*d^2+-2*d*e)^-3*(-23189*e^4+171735*d^4+x*(-17945*e^4+55075*d^4+-429620*e*d^3+51740*d*e^3+173490*d^2*e^2)+-200502*d^2*e^2+-117284*e*d^3+104428*d*e^3)+e*(3*e^2+5*d^2+-2*d*e)^-4*(-9*e^5+40*d^5+-76*d^2*e^3+12*d^3*e^2+46*d*e^4+83*e*d^4)*log(d+e*x)+-1*e*(d+e*x)^-1*(3*e^2+5*d^2+-2*d*e)^-3*(2*e^4+4*d^4+-1*d*e^3+3*d^2*e^2+5*e*d^3)+-1//2*e*(3*e^2+5*d^2+-2*d*e)^-4*(-9*e^5+40*d^5+-76*d^2*e^3+12*d^3*e^2+46*d*e^4+83*e*d^4)*log(3+2x+5*x^2)+1//21952*14^(1/2)*(3*e^2+5*d^2+-2*d*e)^-4*(-43695*e^6+211875*d^6+-921444*d^3*e^3+-49586*d*e^5+3070*e*d^5+209039*d^4*e^2+380621*d^2*e^4)*arctan(1//14*14^(1/2)*(1+5x)))
@test integrate((3+-1x+2*x^2)^(1/2)*(5+2x)*(2+x+-1*x^3+3*x^2+5*x^4), x) == :(-1183005//131072*2^(1/2)*arcsinh(1//23*23^(1/2)*(1+-4x))+-823//1344*(5+2x)^3*(3+-1x+2*x^2)^3//2+-1//71680*(3+-1x+2*x^2)^3//2*(1005757+295276x)+1//32768*(3+-1x+2*x^2)^(1/2)*(-51435+205740x)+5//112*(5+2x)^4*(3+-1x+2*x^2)^3//2+11433//4480*(5+2x)^2*(3+-1x+2*x^2)^3//2)
@test integrate((3+-1x+2*x^2)^(1/2)*(2+x+-1*x^3+3*x^2+5*x^4), x) == :(287//5120*(3+-1x+2*x^2)^3//2+-106007//65536*2^(1/2)*arcsinh(1//23*23^(1/2)*(1+-4x))+-71//1280*x*(3+-1x+2*x^2)^3//2+1//16384*(3+-1x+2*x^2)^(1/2)*(-4609+18436x)+5//12*x^3*(3+-1x+2*x^2)^3//2+7//80*x^2*(3+-1x+2*x^2)^3//2)
@test integrate((5+2x)^-1*(3+-1x+2*x^2)^(1/2)*(2+x+-1*x^3+3*x^2+5*x^4), x) == :(4535//768*(3+-1x+2*x^2)^3//2+-11001//32*2^(1/2)*arctanh(1//24*2^(1/2)*(3+-1x+2*x^2)^-1//2*(17+-22x))+-1//128*(3+-1x+2*x^2)^3//2*(635+254x)+1//16*(5+2x)^2*(3+-1x+2*x^2)^3//2+1//4096*(3+-1x+2*x^2)^(1/2)*(489587+-80844x)+5627989//16384*2^(1/2)*arcsinh(1//23*23^(1/2)*(1+-4x)))
@test integrate((5+2x)^-2*(3+-1x+2*x^2)^(1/2)*(2+x+-1*x^3+3*x^2+5*x^4), x) == :(-541//384*(3+-1x+2*x^2)^3//2+-3667*(2880+1152x)^-1*(3+-1x+2*x^2)^3//2+-2551847//8192*2^(1/2)*arcsinh(1//23*23^(1/2)*(1+-4x))+-1//18432*(3+-1x+2*x^2)^(1/2)*(1996953+-333380x)+1//64*(3+-1x+2*x^2)^3//2*(25+10x)+239201//768*2^(1/2)*arctanh(1//24*2^(1/2)*(3+-1x+2*x^2)^-1//2*(17+-22x)))
@test integrate((5+2x)^-3*(3+-1x+2*x^2)^(1/2)*(2+x+-1*x^3+3*x^2+5*x^4), x) == :(5//48*(3+-1x+2*x^2)^3//2+357391*(414720+165888x)^-1*(3+-1x+2*x^2)^3//2+-12670805//110592*2^(1/2)*arctanh(1//24*2^(1/2)*(3+-1x+2*x^2)^-1//2*(17+-22x))+-3667//1152*(5+2x)^-2*(3+-1x+2*x^2)^3//2+1//82944*(3+-1x+2*x^2)^(1/2)*(3305325+-550495x)+117315//1024*2^(1/2)*arcsinh(1//23*23^(1/2)*(1+-4x)))
@test integrate((5+2x)^-4*(3+-1x+2*x^2)^(1/2)*(2+x+-1*x^3+3*x^2+5*x^4), x) == :(-6467659*(29859840+11943936x)^-1*(3+-1x+2*x^2)^3//2+-10939//512*2^(1/2)*arcsinh(1//23*23^(1/2)*(1+-4x))+-3667//1728*(5+2x)^-3*(3+-1x+2*x^2)^3//2+-1//5971968*(3+-1x+2*x^2)^(1/2)*(44378877+-7400779x)+158527//82944*(5+2x)^-2*(3+-1x+2*x^2)^3//2+170114729//7962624*2^(1/2)*arctanh(1//24*2^(1/2)*(3+-1x+2*x^2)^-1//2*(17+-22x)))
@test integrate((5+2x)^-5*(3+-1x+2*x^2)^(1/2)*(2+x+-1*x^3+3*x^2+5*x^4), x) == :(-4640586097//2293235712*2^(1/2)*arctanh(1//24*2^(1/2)*(3+-1x+2*x^2)^-1//2*(17+-22x))+-9363383//23887872*(5+2x)^-2*(3+-1x+2*x^2)^3//2+-3667//2304*(5+2x)^-4*(3+-1x+2*x^2)^3//2+259//128*2^(1/2)*arcsinh(1//23*23^(1/2)*(1+-4x))+593771//497664*(5+2x)^-3*(3+-1x+2*x^2)^3//2+(477757440+191102976x)^-1*(3+-1x+2*x^2)^(1/2)*(369856585+67313372x))
@test integrate((5+2x)^-6*(3+-1x+2*x^2)^(1/2)*(2+x+-1*x^3+3*x^2+5*x^4), x) == :(-38732321//179159040*(5+2x)^-3*(3+-1x+2*x^2)^3//2+-3667//2880*(5+2x)^-5*(3+-1x+2*x^2)^3//2+-5//64*2^(1/2)*arcsinh(1//23*23^(1/2)*(1+-4x))+711961//829440*(5+2x)^-4*(3+-1x+2*x^2)^3//2+12895597463//165112971264*2^(1/2)*arctanh(1//24*2^(1/2)*(3+-1x+2*x^2)^-1//2*(17+-22x))+-1//6879707136*(5+2x)^-2*(3+-1x+2*x^2)^(1/2)*(4583087983+3174439702x))
@test integrate((5+2x)^-7*(3+-1x+2*x^2)^(1/2)*(2+x+-1*x^3+3*x^2+5*x^4), x) == :(-26972675//7925422620672*2^(1/2)*arctanh(1//24*2^(1/2)*(3+-1x+2*x^2)^-1//2*(17+-22x))+-5703277//39813120*(5+2x)^-4*(3+-1x+2*x^2)^3//2+-3667//3456*(5+2x)^-6*(3+-1x+2*x^2)^3//2+92239//138240*(5+2x)^-5*(3+-1x+2*x^2)^3//2+87677717//8599633920*(5+2x)^-3*(3+-1x+2*x^2)^3//2+1//330225942528*(5+2x)^-2*(3+-1x+2*x^2)^(1/2)*(-19936325+25799950x))
@test integrate((5+2x)^-8*(3+-1x+2*x^2)^(1/2)*(2+x+-1*x^3+3*x^2+5*x^4), x) == :(-289071245//570630428688384*2^(1/2)*arctanh(1//24*2^(1/2)*(3+-1x+2*x^2)^-1//2*(17+-22x))+-1464037//13934592*(5+2x)^-5*(3+-1x+2*x^2)^3//2+-3667//4032*(5+2x)^-7*(3+-1x+2*x^2)^3//2+948341//1741824*(5+2x)^-6*(3+-1x+2*x^2)^3//2+19414831//4013162496*(5+2x)^-4*(3+-1x+2*x^2)^3//2+246159769//866843099136*(5+2x)^-3*(3+-1x+2*x^2)^3//2+1//23776267862016*(5+2x)^-2*(3+-1x+2*x^2)^(1/2)*(-213661355+276502930x))
@test integrate((3+-1x+2*x^2)^3//2*(5+2x)*(2+x+-1*x^3+3*x^2+5*x^4), x) == :(-147157749//8388608*2^(1/2)*arcsinh(1//23*23^(1/2)*(1+-4x))+-1121//2304*(5+2x)^3*(3+-1x+2*x^2)^5//2+-1//131072*(3+-1x+2*x^2)^3//2*(92727+-370908x)+-1//143360*(3+-1x+2*x^2)^5//2*(1984191+647700x)+1//2097152*(3+-1x+2*x^2)^(1/2)*(-6398163+25592652x)+5//144*(5+2x)^4*(3+-1x+2*x^2)^5//2+69415//32256*(5+2x)^2*(3+-1x+2*x^2)^5//2)
@test integrate((3+-1x+2*x^2)^3//2*(2+x+-1*x^3+3*x^2+5*x^4), x) == :(1167//14336*(3+-1x+2*x^2)^5//2+-13643439//4194304*2^(1/2)*arcsinh(1//23*23^(1/2)*(1+-4x))+-1//65536*(3+-1x+2*x^2)^3//2*(8597+-34388x)+1//1048576*(3+-1x+2*x^2)^(1/2)*(-593193+2372772x)+5//16*x^3*(3+-1x+2*x^2)^5//2+23//448*x^2*(3+-1x+2*x^2)^5//2+125//3584*x*(3+-1x+2*x^2)^5//2)
@test integrate((5+2x)^-1*(3+-1x+2*x^2)^3//2*(2+x+-1*x^3+3*x^2+5*x^4), x) == :(3505//896*(3+-1x+2*x^2)^5//2+-99009//16*2^(1/2)*arctanh(1//24*2^(1/2)*(3+-1x+2*x^2)^-1//2*(17+-22x))+-1//448*(3+-1x+2*x^2)^5//2*(1555+622x)+1//12288*(3+-1x+2*x^2)^3//2*(500141+-123060x)+1//65536*(3+-1x+2*x^2)^(1/2)*(141051019+-23482924x)+5//112*(5+2x)^2*(3+-1x+2*x^2)^5//2+1622009981//262144*2^(1/2)*arcsinh(1//23*23^(1/2)*(1+-4x)))
@test integrate((5+2x)^-2*(3+-1x+2*x^2)^3//2*(2+x+-1*x^3+3*x^2+5*x^4), x) == :(-839//960*(3+-1x+2*x^2)^5//2+-3667*(2880+1152x)^-1*(3+-1x+2*x^2)^5//2+-982669459//131072*2^(1/2)*arcsinh(1//23*23^(1/2)*(1+-4x))+-1//18432*(3+-1x+2*x^2)^3//2*(909513+-226052x)+-1//32768*(3+-1x+2*x^2)^(1/2)*(85448933+-14243732x)+1//96*(3+-1x+2*x^2)^5//2*(25+10x)+959625//128*2^(1/2)*arctanh(1//24*2^(1/2)*(3+-1x+2*x^2)^-1//2*(17+-22x)))
@test integrate((5+2x)^-3*(3+-1x+2*x^2)^3//2*(2+x+-1*x^3+3*x^2+5*x^4), x) == :(1//16*(3+-1x+2*x^2)^5//2+438065*(414720+165888x)^-1*(3+-1x+2*x^2)^5//2+-8083915//2048*2^(1/2)*arctanh(1//24*2^(1/2)*(3+-1x+2*x^2)^-1//2*(17+-22x))+-3667//1152*(5+2x)^-2*(3+-1x+2*x^2)^5//2+1//24576*(3+-1x+2*x^2)^(1/2)*(33741483+-5623292x)+1//82944*(3+-1x+2*x^2)^3//2*(2154633+-534617x)+129342063//32768*2^(1/2)*arcsinh(1//23*23^(1/2)*(1+-4x)))
@test integrate((5+2x)^-4*(3+-1x+2*x^2)^3//2*(2+x+-1*x^3+3*x^2+5*x^4), x) == :(-32865365*(89579520+35831808x)^-1*(3+-1x+2*x^2)^5//2+-19176431//16384*2^(1/2)*arcsinh(1//23*23^(1/2)*(1+-4x))+-3667//1728*(5+2x)^-3*(3+-1x+2*x^2)^5//2+-1//331776*(3+-1x+2*x^2)^(1/2)*(135068604+-22512089x)+-1//17915904*(3+-1x+2*x^2)^3//2*(138006843+-34265045x)+556255//248832*(5+2x)^-2*(3+-1x+2*x^2)^5//2+517762327//442368*2^(1/2)*arctanh(1//24*2^(1/2)*(3+-1x+2*x^2)^-1//2*(17+-22x)))
@test integrate((5+2x)^-5*(3+-1x+2*x^2)^3//2*(2+x+-1*x^3+3*x^2+5*x^4), x) == :(-8969688643//42467328*2^(1/2)*arctanh(1//24*2^(1/2)*(3+-1x+2*x^2)^-1//2*(17+-22x))+-14477995//23887872*(5+2x)^-2*(3+-1x+2*x^2)^5//2+-3667//2304*(5+2x)^-4*(3+-1x+2*x^2)^5//2+1//31850496*(3+-1x+2*x^2)^(1/2)*(2339916063+-389975609x)+224815//165888*(5+2x)^-3*(3+-1x+2*x^2)^5//2+432565//2048*2^(1/2)*arcsinh(1//23*23^(1/2)*(1+-4x))+(477757440+191102976x)^-1*(3+-1x+2*x^2)^3//2*(762984903+67865260x))
@test integrate((5+2x)^-6*(3+-1x+2*x^2)^3//2*(2+x+-1*x^3+3*x^2+5*x^4), x) == :(-3730507//11943936*(5+2x)^-3*(3+-1x+2*x^2)^5//2+-23775//1024*2^(1/2)*arcsinh(1//23*23^(1/2)*(1+-4x))+-3667//2880*(5+2x)^-5*(3+-1x+2*x^2)^5//2+158527//165888*(5+2x)^-4*(3+-1x+2*x^2)^5//2+70991525167//3057647616*2^(1/2)*arctanh(1//24*2^(1/2)*(3+-1x+2*x^2)^-1//2*(17+-22x))+-1*(637009920+254803968x)^-1*(3+-1x+2*x^2)^(1/2)*(5658774871+1028823716x)+1//95551488*(5+2x)^-2*(3+-1x+2*x^2)^3//2*(246012435+44773976x))
@test integrate((5+2x)^-7*(3+-1x+2*x^2)^3//2*(2+x+-1*x^3+3*x^2+5*x^4), x) == :(-1903976002333//1320903770112*2^(1/2)*arctanh(1//24*2^(1/2)*(3+-1x+2*x^2)^-1//2*(17+-22x))+-14087245//71663616*(5+2x)^-4*(3+-1x+2*x^2)^5//2+-3667//3456*(5+2x)^-6*(3+-1x+2*x^2)^5//2+369//256*2^(1/2)*arcsinh(1//23*23^(1/2)*(1+-4x))+182165//248832*(5+2x)^-5*(3+-1x+2*x^2)^5//2+(275188285440+110075314176x)^-1*(3+-1x+2*x^2)^(1/2)*(151764102421+27596573612x)+-1//13759414272*(5+2x)^-3*(3+-1x+2*x^2)^3//2*(9802984711+6793718806x))
@test integrate((5+2x)^-8*(3+-1x+2*x^2)^3//2*(2+x+-1*x^3+3*x^2+5*x^4), x) == :(-1930441//13934592*(5+2x)^-5*(3+-1x+2*x^2)^5//2+-3667//4032*(5+2x)^-7*(3+-1x+2*x^2)^5//2+-5//128*2^(1/2)*arcsinh(1//23*23^(1/2)*(1+-4x))+114335//193536*(5+2x)^-6*(3+-1x+2*x^2)^5//2+412760561351//10567230160896*2^(1/2)*arctanh(1//24*2^(1/2)*(3+-1x+2*x^2)^-1//2*(17+-22x))+-1//2293235712*(5+2x)^-4*(3+-1x+2*x^2)^3//2*(463558457+411822458x)+-1//440301256704*(5+2x)^-2*(3+-1x+2*x^2)^(1/2)*(146583836191+101679102454x))
@test integrate((3+-1x+2*x^2)^-1//2*(5+2x)*(2+x+-1*x^3+3*x^2+5*x^4), x) == :(-85429//8192*2^(1/2)*arcsinh(1//23*23^(1/2)*(1+-4x))+-105//128*(5+2x)^3*(3+-1x+2*x^2)^(1/2)+-1//2048*(3+-1x+2*x^2)^(1/2)*(19227+4676x)+1//16*(5+2x)^4*(3+-1x+2*x^2)^(1/2)+761//256*(5+2x)^2*(3+-1x+2*x^2)^(1/2))
@test integrate((3+-1x+2*x^2)^-1//2*(2+x+-1*x^3+3*x^2+5*x^4), x) == :(-505//1024*(3+-1x+2*x^2)^(1/2)+-6863//4096*2^(1/2)*arcsinh(1//23*23^(1/2)*(1+-4x))+-409//768*x*(3+-1x+2*x^2)^(1/2)+5//8*x^3*(3+-1x+2*x^2)^(1/2)+19//96*x^2*(3+-1x+2*x^2)^(1/2))
@test integrate((5+2x)^-1*(3+-1x+2*x^2)^-1//2*(2+x+-1*x^3+3*x^2+5*x^4), x) == :(1669//128*(3+-1x+2*x^2)^(1/2)+-3667//192*2^(1/2)*arctanh(1//24*2^(1/2)*(3+-1x+2*x^2)^-1//2*(17+-22x))+-1//192*(3+-1x+2*x^2)^(1/2)*(1685+674x)+5//48*(5+2x)^2*(3+-1x+2*x^2)^(1/2)+9657//512*2^(1/2)*arcsinh(1//23*23^(1/2)*(1+-4x)))
@test integrate((5+2x)^-2*(3+-1x+2*x^2)^-1//2*(2+x+-1*x^3+3*x^2+5*x^4), x) == :(-243//64*(3+-1x+2*x^2)^(1/2)+-3667*(2880+1152x)^-1*(3+-1x+2*x^2)^(1/2)+-2943//256*2^(1/2)*arcsinh(1//23*23^(1/2)*(1+-4x))+1//32*(3+-1x+2*x^2)^(1/2)*(25+10x)+158527//13824*2^(1/2)*arctanh(1//24*2^(1/2)*(3+-1x+2*x^2)^-1//2*(17+-22x)))
@test integrate((5+2x)^-3*(3+-1x+2*x^2)^-1//2*(2+x+-1*x^3+3*x^2+5*x^4), x) == :(5//16*(3+-1x+2*x^2)^(1/2)+92239*(138240+55296x)^-1*(3+-1x+2*x^2)^(1/2)+-1546507//663552*2^(1/2)*arctanh(1//24*2^(1/2)*(3+-1x+2*x^2)^-1//2*(17+-22x))+-3667//1152*(5+2x)^-2*(3+-1x+2*x^2)^(1/2)+149//64*2^(1/2)*arcsinh(1//23*23^(1/2)*(1+-4x)))
@test integrate((5+2x)^-4*(3+-1x+2*x^2)^-1//2*(2+x+-1*x^3+3*x^2+5*x^4), x) == :(-3163415*(29859840+11943936x)^-1*(3+-1x+2*x^2)^(1/2)+-3667//1728*(5+2x)^-3*(3+-1x+2*x^2)^(1/2)+-5//32*2^(1/2)*arcsinh(1//23*23^(1/2)*(1+-4x))+394907//248832*(5+2x)^-2*(3+-1x+2*x^2)^(1/2)+22389491//143327232*2^(1/2)*arctanh(1//24*2^(1/2)*(3+-1x+2*x^2)^-1//2*(17+-22x)))
@test integrate((5+2x)^-5*(3+-1x+2*x^2)^-1//2*(2+x+-1*x^3+3*x^2+5*x^4), x) == :(26800085*(8599633920+3439853568x)^-1*(3+-1x+2*x^2)^(1/2)+-16295969//71663616*(5+2x)^-2*(3+-1x+2*x^2)^(1/2)+-3667//2304*(5+2x)^-4*(3+-1x+2*x^2)^(1/2)+513097//497664*(5+2x)^-3*(3+-1x+2*x^2)^(1/2)+2053207//41278242816*2^(1/2)*arctanh(1//24*2^(1/2)*(3+-1x+2*x^2)^-1//2*(17+-22x)))
@test integrate((5+2x)^2*(3+-1x+2*x^2)^-3//2*(2+x+-1*x^3+3*x^2+5*x^4), x) == :(-13153//512*(3+-1x+2*x^2)^(1/2)+1//23*(3+-1x+2*x^2)^-1//2*(-1384+2132x)+5//4*x^3*(3+-1x+2*x^2)^(1/2)+153//16*x^2*(3+-1x+2*x^2)^(1/2)+2645//128*x*(3+-1x+2*x^2)^(1/2)+144217//2048*2^(1/2)*arcsinh(1//23*23^(1/2)*(1+-4x)))
@test integrate((3+-1x+2*x^2)^-3//2*(5+2x)*(2+x+-1*x^3+3*x^2+5*x^4), x) == :(33//64*(3+-1x+2*x^2)^(1/2)+1//23*(3+-1x+2*x^2)^-1//2*(-53+373x)+5//6*x^2*(3+-1x+2*x^2)^(1/2)+193//48*x*(3+-1x+2*x^2)^(1/2)+3111//256*2^(1/2)*arcsinh(1//23*23^(1/2)*(1+-4x)))
@test integrate((3+-1x+2*x^2)^-3//2*(2+x+-1*x^3+3*x^2+5*x^4), x) == :(27//32*(3+-1x+2*x^2)^(1/2)+1//92*(3+-1x+2*x^2)^-1//2*(89+219x)+5//8*x*(3+-1x+2*x^2)^(1/2)+213//128*2^(1/2)*arcsinh(1//23*23^(1/2)*(1+-4x)))
@test integrate((5+2x)^-1*(3+-1x+2*x^2)^-3//2*(2+x+-1*x^3+3*x^2+5*x^4), x) == :(5//8*(3+-1x+2*x^2)^(1/2)+-3667//3456*2^(1/2)*arctanh(1//24*2^(1/2)*(3+-1x+2*x^2)^-1//2*(17+-22x))+1//3312*(3+-1x+2*x^2)^-1//2*(1191+917x)+39//32*2^(1/2)*arcsinh(1//23*23^(1/2)*(1+-4x)))
@test integrate((5+2x)^-2*(3+-1x+2*x^2)^-3//2*(2+x+-1*x^3+3*x^2+5*x^4), x) == :(-3667*(51840+20736x)^-1*(3+-1x+2*x^2)^(1/2)+-5//16*2^(1/2)*arcsinh(1//23*23^(1/2)*(1+-4x))+1//119232*(3+-1x+2*x^2)^-1//2*(9897+2203x)+25951//82944*2^(1/2)*arctanh(1//24*2^(1/2)*(3+-1x+2*x^2)^-1//2*(17+-22x)))
@test integrate((5+2x)^-3*(3+-1x+2*x^2)^-3//2*(2+x+-1*x^3+3*x^2+5*x^4), x) == :(115369*(7464960+2985984x)^-1*(3+-1x+2*x^2)^(1/2)+-52631//11943936*2^(1/2)*arctanh(1//24*2^(1/2)*(3+-1x+2*x^2)^-1//2*(17+-22x))+-3667//20736*(5+2x)^-2*(3+-1x+2*x^2)^(1/2)+1//4292352*(3+-1x+2*x^2)^-1//2*(65991+-8779x))
@test integrate((5+2x)^-4*(3+-1x+2*x^2)^-3//2*(2+x+-1*x^3+3*x^2+5*x^4), x) == :(430799*(537477120+214990848x)^-1*(3+-1x+2*x^2)^(1/2)+-3505819//2579890176*2^(1/2)*arctanh(1//24*2^(1/2)*(3+-1x+2*x^2)^-1//2*(17+-22x))+-3667//31104*(5+2x)^-3*(3+-1x+2*x^2)^(1/2)+1//154524672*(3+-1x+2*x^2)^-1//2*(369609+-175877x)+152885//4478976*(5+2x)^-2*(3+-1x+2*x^2)^(1/2))
@test integrate((5+2x)^2*(3+-1x+2*x^2)^-5//2*(2+x+-1*x^3+3*x^2+5*x^4), x) == :(247//16*(3+-1x+2*x^2)^(1/2)+-1471//64*2^(1/2)*arcsinh(1//23*23^(1/2)*(1+-4x))+1//69*(3+-1x+2*x^2)^-3//2*(-1384+2132x)+1//1587*(3+-1x+2*x^2)^-1//2*(75928+-81532x)+5//4*x*(3+-1x+2*x^2)^(1/2))
@test integrate((3+-1x+2*x^2)^-5//2*(5+2x)*(2+x+-1*x^3+3*x^2+5*x^4), x) == :(5//4*(3+-1x+2*x^2)^(1/2)+-71//16*2^(1/2)*arcsinh(1//23*23^(1/2)*(1+-4x))+1//69*(3+-1x+2*x^2)^-3//2*(-53+373x)+1//3174*(3+-1x+2*x^2)^-1//2*(6055+-28981x))
@test integrate((3+-1x+2*x^2)^-5//2*(2+x+-1*x^3+3*x^2+5*x^4), x) == :(-5//8*2^(1/2)*arcsinh(1//23*23^(1/2)*(1+-4x))+-1//2116*(3+-1x+2*x^2)^-1//2*(1465+2604x)+1//276*(3+-1x+2*x^2)^-3//2*(89+219x))
@test integrate((5+2x)^-1*(3+-1x+2*x^2)^-5//2*(2+x+-1*x^3+3*x^2+5*x^4), x) == :(-3667//62208*2^(1/2)*arctanh(1//24*2^(1/2)*(3+-1x+2*x^2)^-1//2*(17+-22x))+-1//1371168*(3+-1x+2*x^2)^-1//2*(335337+146729x)+1//9936*(3+-1x+2*x^2)^-3//2*(1191+917x))
@test integrate((5+2x)^-2*(3+-1x+2*x^2)^-5//2*(2+x+-1*x^3+3*x^2+5*x^4), x) == :(-3667*(933120+373248x)^-1*(3+-1x+2*x^2)^(1/2)+-2821//4478976*2^(1/2)*arctanh(1//24*2^(1/2)*(3+-1x+2*x^2)^-1//2*(17+-22x))+-1//24681024*(3+-1x+2*x^2)^-1//2*(1255878+-62021x)+1//357696*(3+-1x+2*x^2)^-3//2*(9897+2203x))
@test integrate((5+2x)^-3*(3+-1x+2*x^2)^-5//2*(2+x+-1*x^3+3*x^2+5*x^4), x) == :(-45979*(134369280+53747712x)^-1*(3+-1x+2*x^2)^(1/2)+-3667//373248*(5+2x)^-2*(3+-1x+2*x^2)^(1/2)+-1//592344576*(3+-1x+2*x^2)^-1//2*(4679797+-2148263x)+1//12877056*(3+-1x+2*x^2)^-3//2*(65991+-8779x)+774079//644972544*2^(1/2)*arctanh(1//24*2^(1/2)*(3+-1x+2*x^2)^-1//2*(17+-22x)))
@test integrate((5+2x)^-4*(3+-1x+2*x^2)^-5//2*(2+x+-1*x^3+3*x^2+5*x^4), x) == :(475357*(9674588160+3869835264x)^-1*(3+-1x+2*x^2)^(1/2)+-89137//80621568*(5+2x)^-2*(3+-1x+2*x^2)^(1/2)+-3667//559872*(5+2x)^-3*(3+-1x+2*x^2)^(1/2)+-1//31986607104*(3+-1x+2*x^2)^-1//2*(27754539+-31190998x)+1//463574016*(3+-1x+2*x^2)^-3//2*(369609+-175877x)+4778789//15479341056*2^(1/2)*arctanh(1//24*2^(1/2)*(3+-1x+2*x^2)^-1//2*(17+-22x)))
@test integrate((a+b*x+c*x^2)^-5//2*(f+g*x+h*x^2+i*x^3+j*x^4), x) == :(j*c^-5//2*arctanh((1/2)*c^-1//2*(a+b*x+c*x^2)^-1//2*(b+2*c*x))+-1//3*c^-3*(b^2+-4*a*c)^-2*(a+b*x+c*x^2)^-1//2*(-2*j*b^5+-8*b*c^2*(2*f*c^2+8*j*a^2+a*c*h)+-2*c*x*(-1*c^3*(-8*a*h+8*b*g)+-4*j*b^4+2*c^2*(h*b^2+-16*j*a^2+-6*a*b*i)+16*f*c^4+c*b^2*(b*i+28*a*j))+-2*c*b^3*(c*h+-10*a*j)+2*c*i*b^4+4*b^2*c^2*(-3*a*i+2*c*g)+48*i*a^2*c^3)+1//3*c^-3*(b^2+-4*a*c)^-1*(a+b*x+c*x^2)^-3//2*(-2*x*(j*b^4+c^2*(h*b^2+2*j*a^2+3*a*b*i)+-1*c^3*(b*g+2*a*h)+2*f*c^4+-1*c*b^2*(b*i+4*a*j))+-2*a*j*b^3+-2*b*c*(f*c^2+-3*j*a^2+a*c*h)+4*a*c^2*(c*g+-1*a*i)+2*a*c*i*b^2))
@test integrate((a+b*x+-1*c*x^2)^-5//2*(f+g*x+h*x^2+i*x^3+j*x^4), x) == :(-1*j*c^-5//2*arctan((1/2)*c^-1//2*(a+b*x+-1*c*x^2)^-1//2*(b+-2*c*x))+-1//3*c^-3*(b^2+4*a*c)^-2*(a+b*x+-1*c*x^2)^-1//2*(2*j*b^5+-2*c*x*(-4*j*b^4+2*c^2*(h*b^2+-16*j*a^2+-6*a*b*i)+8*c^3*(b*g+-1*a*h)+16*f*c^4+-1*c*b^2*(b*i+28*a*j))+2*c*i*b^4+2*c*b^3*(c*h+10*a*j)+4*b^2*c^2*(2*c*g+3*a*i)+8*b*c^2*(2*f*c^2+8*j*a^2+-1*a*c*h)+48*i*a^2*c^3)+1//3*c^-3*(b^2+4*a*c)^-1*(a+b*x+-1*c*x^2)^-3//2*(2*x*(j*b^4+c^2*(h*b^2+2*j*a^2+3*a*b*i)+c^3*(b*g+2*a*h)+2*f*c^4+c*b^2*(b*i+4*a*j))+-2*b*c*(f*c^2+-3*j*a^2+-1*a*c*h)+2*a*j*b^3+4*a*c^2*(a*i+c*g)+2*a*c*i*b^2))
@test integrate((d+e*x)^m*(3+2x+5*x^2)^3*(2+x+-5*x^3+3*x^2+4*x^4), x) == :(500*e^-11*(11+m)^-1*(d+e*x)^(11+m)+e^-11*(5+m)^-1*(d+e*x)^(5+m)*(1109*e^6+105000*d^6+-2550*d*e^5+3150*e*d^5+3430*d^3*e^3+14985*d^2*e^4+53550*d^4*e^2)+e^-11*(7+m)^-1*(d+e*x)^(7+m)*(999*e^4+105000*d^4+686*d*e^3+2100*e*d^3+21420*d^2*e^2)+e^-11*(9+m)^-1*(d+e*x)^(9+m)*(765*e^2+22500*d^2+225*d*e)+-1*e^-11*(4+m)^-1*(d+e*x)^(4+m)*(-574*e^7+60000*d^7+-5100*d^2*e^5+2100*e*d^6+3430*d^4*e^3+4436*d*e^6+19980*d^3*e^4+42840*d^5*e^2)+-1*e^-11*(6+m)^-1*(d+e*x)^(6+m)*(-510*e^5+126000*d^5+2058*d^2*e^3+3150*e*d^4+5994*d*e^4+42840*d^3*e^2)+-1*e^-11*(8+m)^-1*(d+e*x)^(8+m)*(98*e^3+60000*d^3+900*e*d^2+6120*d*e^2)+-1*e^-11*(10+m)^-1*(d+e*x)^(10+m)*(25*e+5000d)+e^-11*(1+m)^-1*(d+e*x)^(1+m)*(3*e^2+5*d^2+-2*d*e)^3*(2*e^4+4*d^4+-1*d*e^3+3*d^2*e^2+5*e*d^3)+e^-11*(3+m)^-1*(d+e*x)^(3+m)*(9*e^2+15*d^2+-6*d*e)*(53*e^6+1500*d^6+-156*d*e^5+58*d^3*e^3+547*d^2*e^4+660*e*d^5+792*d^4*e^2)+-1*e^-11*(2+m)^-1*(d+e*x)^(2+m)*(3*e^2+5*d^2+-2*d*e)^2*(-15*e^5+200*d^5+-20*d^2*e^3+86*d*e^4+108*d^3*e^2+169*e*d^4))
@test integrate((d+e*x)^m*(3+2x+5*x^2)^2*(2+x+-5*x^3+3*x^2+4*x^4), x) == :(100*e^-9*(9+m)^-1*(d+e*x)^(9+m)+e^-9*(3+m)^-1*(d+e*x)^(3+m)*(107*e^6+2800*d^6+-195*d*e^5+370*d^3*e^3+888*d^2*e^4+945*e*d^5+1665*d^4*e^2)+e^-9*(5+m)^-1*(d+e*x)^(5+m)*(148*e^4+7000*d^4+185*d*e^3+1575*e*d^3+1665*d^2*e^2)+e^-9*(7+m)^-1*(d+e*x)^(7+m)*(111*e^2+2800*d^2+315*d*e)+-1*e^-9*(4+m)^-1*(d+e*x)^(4+m)*(-65*e^5+5600*d^5+370*d^2*e^3+592*d*e^4+1575*e*d^4+2220*d^3*e^2)+-1*e^-9*(6+m)^-1*(d+e*x)^(6+m)*(37*e^3+5600*d^3+666*d*e^2+945*e*d^2)+-1*e^-9*(8+m)^-1*(d+e*x)^(8+m)*(45*e+800d)+e^-9*(1+m)^-1*(d+e*x)^(1+m)*(3*e^2+5*d^2+-2*d*e)^2*(2*e^4+4*d^4+-1*d*e^3+3*d^2*e^2+5*e*d^3)+-1*e^-9*(2+m)^-1*(d+e*x)^(2+m)*(3*e^2+5*d^2+-2*d*e)*(-11*e^5+160*d^5+-4*d^2*e^3+64*d*e^4+88*d^3*e^2+127*e*d^4))
@test integrate((d+e*x)^m*(3+2x+5*x^2)*(2+x+-5*x^3+3*x^2+4*x^4), x) == :(20*e^-7*(7+m)^-1*(d+e*x)^(7+m)+e^-7*(3+m)^-1*(d+e*x)^(3+m)*(21*e^4+300*d^4+12*d*e^3+102*d^2*e^2+170*e*d^3)+e^-7*(5+m)^-1*(d+e*x)^(5+m)*(17*e^2+300*d^2+85*d*e)+-1*e^-7*(2+m)^-1*(d+e*x)^(2+m)*(-7*e^5+120*d^5+12*d^2*e^3+42*d*e^4+68*d^3*e^2+85*e*d^4)+-1*e^-7*(4+m)^-1*(d+e*x)^(4+m)*(4*e^3+400*d^3+68*d*e^2+170*e*d^2)+-1*e^-7*(6+m)^-1*(d+e*x)^(6+m)*(17*e+120d)+e^-7*(1+m)^-1*(d+e*x)^(1+m)*(3*e^2+5*d^2+-2*d*e)*(2*e^4+4*d^4+-1*d*e^3+3*d^2*e^2+5*e*d^3))
@test integrate((a+b*x+c*x^2)^-3*(d+e*x+f*x^2+g*x^3+h*x^4+i*x^5), x) == :((1/2)*i*c^-3*log(a+b*x+c*x^2)+(1/2)*c^-4*(b^2+-4*a*c)^-2*(a+b*x+c*x^2)^-1*(-1*i*b^6+c*h*b^5+b^3*c^2*(c*f+-8*a*h)+-1*c*b^4*(c*g+-11*a*i)+-1*b^2*c^2*(3*e*c^2+39*i*a^2+-5*a*c*g)+-16*a^2*c^3*(c*g+-2*a*i)+2*b*c^3*(3*d*c^2+11*h*a^2+a*c*f)+2*c*x*(c^3*(f*b^2+-10*h*a^2+-3*a*b*g)+-1*c^4*(-2*a*f+3*b*e)+2*i*b^5+6*d*c^5+-1*c*b^3*(b*h+15*a*i)+a*b*c^2*(8*b*h+25*a*i)))+-1*c^-3*(b^2+-4*a*c)^-5//2*(-1*i*b^5+-1*c^4*(-4*a*f+6*b*e)+2*c^3*(f*b^2+6*h*a^2+-3*a*b*g)+12*d*c^5+-30*b*i*a^2*c^2+10*a*c*i*b^3)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x))+-1//2*c^-4*(b^2+-4*a*c)^-1*(a+b*x+c*x^2)^-2*(x*(c^3*(f*b^2+2*h*a^2+3*a*b*g)+-1*i*b^5+-1*c^4*(b*e+2*a*f)+2*d*c^5+c*b^3*(b*h+5*a*i)+-1*b*c^2*(g*b^2+5*i*a^2+4*a*b*h))+b*c^2*(d*c^2+-3*h*a^2+a*c*f)+-1*a*i*b^4+-2*a*c^2*(e*c^2+i*a^2+-1*a*c*g)+a*c*h*b^3+-1*a*c*b^2*(c*g+-4*a*i)))
@test integrate((a+b*x+c*x^2)^-1*(d+e*x+f*x^2+g*x^3+h*x^4+j*x^5+k*x^6+l*x^7+m*x^8), x) == :(x*c^-7*(f*c^6+m*b^6+c^4*(h*b^2+k*a^2+2*a*b*j)+-1*c^3*(j*b^3+m*a^3+3*a*k*b^2+3*b*l*a^2)+-1*c^5*(a*h+b*g)+b^2*c^2*(k*b^2+6*m*a^2+4*a*b*l)+-1*c*b^4*(b*l+5*a*m))+(1/2)*c^-8*(e*c^7+c^5*(g*b^2+j*a^2+2*a*b*h)+-1*m*b^7+-1*c^4*(h*b^3+l*a^3+3*a*j*b^2+3*b*k*a^2)+-1*c^6*(a*g+b*f)+b*c^3*(j*b^3+4*m*a^3+4*a*k*b^2+6*b*l*a^2)+c*b^5*(b*l+6*a*m)+-1*b^3*c^2*(k*b^2+10*m*a^2+5*a*b*l))*log(a+b*x+c*x^2)+(1/2)*c^-6*x^2*(g*c^5+c^3*(j*b^2+l*a^2+2*a*b*k)+-1*m*b^5+-1*c^4*(a*j+b*h)+c*b^3*(b*l+4*a*m)+-1*b*c^2*(k*b^2+3*m*a^2+3*a*b*l))+1//3*c^-5*x^3*(h*c^4+m*b^4+c^2*(k*b^2+m*a^2+2*a*b*l)+-1*c^3*(a*k+b*j)+-1*c*b^2*(b*l+3*a*m))+1//4*c^-4*x^4*(j*c^3+-1*m*b^3+-1*c^2*(a*l+b*k)+b*c*(b*l+2*a*m))+1//5*c^-3*x^5*(k*c^2+m*b^2+-1*c*(a*m+b*l))+1//6*c^-2*x^6*(c*l+-1*b*m)+1//7*m*c^-1*x^7+-1*c^-8*(b^2+-4*a*c)^-1//2*(m*b^8+c^4*(h*b^4+2*m*a^4+5*a*j*b^3+7*b*l*a^3+9*k*a^2*b^2)+c^6*(f*b^2+2*h*a^2+3*a*b*g)+-1*c^5*(g*b^3+2*k*a^3+4*a*h*b^2+5*b*j*a^2)+-1*c^7*(b*e+2*a*f)+2*d*c^8+b^4*c^2*(k*b^2+20*m*a^2+7*a*b*l)+-1*c*b^6*(b*l+8*a*m)+-1*b^2*c^3*(j*b^3+16*m*a^3+6*a*k*b^2+14*b*l*a^2))*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x)))
@test integrate((1+-7*x^2+4x)^3*(3+2x+5*x^2)^(1/2)*(2+x^2+5x), x) == :(-1968340667//131250000*(3+2x+5*x^2)^3//2+-540119881//78125000*5^(1/2)*arcsinh(1//14*14^(1/2)*(1+5x))+-90960857//1575000*x^3*(3+2x+5*x^2)^3//2+-888751//105000*x^4*(3+2x+5*x^2)^3//2+-50519//2250*x^6*(3+2x+5*x^2)^3//2+-343//50*x^7*(3+2x+5*x^2)^3//2+-1//31250000*(3+2x+5*x^2)^(1/2)*(77159983+385799915x)+190939//3000*x^5*(3+2x+5*x^2)^3//2+98060877//4375000*x^2*(3+2x+5*x^2)^3//2+1045360143//43750000*x*(3+2x+5*x^2)^3//2)
@test integrate((1+-7*x^2+4x)^2*(3+2x+5*x^2)^(1/2)*(2+x^2+5x), x) == :(198439//750000*(3+2x+5*x^2)^3//2+-17652061//3125000*5^(1/2)*arcsinh(1//14*14^(1/2)*(1+5x))+-77509//25000*x^2*(3+2x+5*x^2)^3//2+-25277//3000*x^3*(3+2x+5*x^2)^3//2+-1//1250000*(3+2x+5*x^2)^(1/2)*(2521723+12608615x)+49//40*x^5*(3+2x+5*x^2)^3//2+989//200*x^4*(3+2x+5*x^2)^3//2+1781669//250000*x*(3+2x+5*x^2)^3//2)
@test integrate((3+2x+5*x^2)^(1/2)*(1+-7*x^2+4x)*(2+x^2+5x), x) == :(7819//7500*(3+2x+5*x^2)^3//2+-32431//31250*5^(1/2)*arcsinh(1//14*14^(1/2)*(1+5x))+-289//250*x^2*(3+2x+5*x^2)^3//2+-7//30*x^3*(3+2x+5*x^2)^3//2+-1//12500*(3+2x+5*x^2)^(1/2)*(4633+23165x)+2149//2500*x*(3+2x+5*x^2)^3//2)
@test integrate((1+-7*x^2+4x)^-1*(3+2x+5*x^2)^(1/2)*(2+x^2+5x), x) == :((3+2x+5*x^2)^(1/2)*(-397//490+-1//14*x)+-8233//8575*5^(1/2)*arcsinh(1//14*14^(1/2)*(1+5x))+-3//343*(497041//11+-146555//11*11^(1/2))^(1/2)*arctanh((250+-34*11^(1/2))^-1//2*(3+2x+5*x^2)^-1//2*(23+-1*11^(1/2)+x*(17+-5*11^(1/2))))+3//343*(497041//11+146555//11*11^(1/2))^(1/2)*arctanh((250+34*11^(1/2))^-1//2*(3+2x+5*x^2)^-1//2*(23+11^(1/2)+x*(17+5*11^(1/2)))))
@test integrate((1+-7*x^2+4x)^-2*(3+2x+5*x^2)^(1/2)*(2+x^2+5x), x) == :(-1//2156*(325022311//1397+3557521//127*11^(1/2))^(1/2)*arctanh((250+-34*11^(1/2))^-1//2*(3+2x+5*x^2)^-1//2*(23+-1*11^(1/2)+x*(17+-5*11^(1/2))))+1//49*5^(1/2)*arcsinh(1//14*14^(1/2)*(1+5x))+1//2156*(325022311//1397+-3557521//127*11^(1/2))^(1/2)*arctanh((250+34*11^(1/2))^-1//2*(3+2x+5*x^2)^-1//2*(23+11^(1/2)+x*(17+5*11^(1/2))))+(3+2x+5*x^2)^(1/2)*(154+-1078*x^2+616x)^-1*(9+183x))
@test integrate((1+-7*x^2+4x)^-3*(3+2x+5*x^2)^(1/2)*(2+x^2+5x), x) == :(-1//491744*(6492253020949//1397+-1079924461//127*11^(1/2))^(1/2)*arctanh((250+-34*11^(1/2))^-1//2*(3+2x+5*x^2)^-1//2*(23+-1*11^(1/2)+x*(17+-5*11^(1/2))))+1//491744*(6492253020949//1397+1079924461//127*11^(1/2))^(1/2)*arctanh((250+34*11^(1/2))^-1//2*(3+2x+5*x^2)^-1//2*(23+11^(1/2)+x*(17+5*11^(1/2))))+-1*(3+2x+5*x^2)^(1/2)*(1721104+-12047728*x^2+6884416x)^-1*(272941+-813113x)+1//308*(1+-7*x^2+4x)^-2*(3+2x+5*x^2)^(1/2)*(9+183x))
@test integrate((1+-7*x^2+4x)^3*(3+2x+5*x^2)^3//2*(2+x^2+5x), x) == :(-6133820867//1203125000*(3+2x+5*x^2)^5//2+-3357568053//781250000*5^(1/2)*arcsinh(1//14*14^(1/2)*(1+5x))+-190236913//4950000*x^3*(3+2x+5*x^2)^5//2+-796559//123750*x^4*(3+2x+5*x^2)^5//2+-61103//3300*x^6*(3+2x+5*x^2)^5//2+-343//60*x^7*(3+2x+5*x^2)^5//2+-1//62500000*(3+2x+5*x^2)^3//2*(22840599+114202995x)+-1//312500000*(3+2x+5*x^2)^(1/2)*(479652579+2398262895x)+1031177//20625*x^5*(3+2x+5*x^2)^5//2+837379699//72187500*x*(3+2x+5*x^2)^5//2+2173004363//173250000*x^2*(3+2x+5*x^2)^5//2)
@test integrate((1+-7*x^2+4x)^2*(3+2x+5*x^2)^3//2*(2+x^2+5x), x) == :(505667//2187500*(3+2x+5*x^2)^5//2+-101512467//15625000*5^(1/2)*arcsinh(1//14*14^(1/2)*(1+5x))+-219271//105000*x^2*(3+2x+5*x^2)^5//2+-18379//3000*x^3*(3+2x+5*x^2)^5//2+-1//1250000*(3+2x+5*x^2)^3//2*(690561+3452805x)+-1//6250000*(3+2x+5*x^2)^(1/2)*(14501781+72508905x)+49//50*x^5*(3+2x+5*x^2)^5//2+581//150*x^4*(3+2x+5*x^2)^5//2+86721//21875*x*(3+2x+5*x^2)^5//2)
@test integrate((3+2x+5*x^2)^3//2*(1+-7*x^2+4x)*(2+x^2+5x), x) == :(149509//262500*(3+2x+5*x^2)^5//2+-901453//625000*5^(1/2)*arcsinh(1//14*14^(1/2)*(1+5x))+-1163//1400*x^2*(3+2x+5*x^2)^5//2+-7//40*x^3*(3+2x+5*x^2)^5//2+-1//150000*(3+2x+5*x^2)^3//2*(18397+91985x)+-1//250000*(3+2x+5*x^2)^(1/2)*(128779+643895x)+2809//5250*x*(3+2x+5*x^2)^5//2)
@test integrate((1+-7*x^2+4x)^-1*(3+2x+5*x^2)^3//2*(2+x^2+5x), x) == :(-1*(3+2x+5*x^2)^3//2*(267//980+1//28*x)+-34425687//4201750*5^(1/2)*arcsinh(1//14*14^(1/2)*(1+5x))+-6//16807*(16197805214//11+-4868244470//11*11^(1/2))^(1/2)*arctanh((250+-34*11^(1/2))^-1//2*(3+2x+5*x^2)^-1//2*(23+-1*11^(1/2)+x*(17+-5*11^(1/2))))+-1//240100*(3+2x+5*x^2)^(1/2)*(1714863+588315x)+6//16807*(16197805214//11+4868244470//11*11^(1/2))^(1/2)*arctanh((250+34*11^(1/2))^-1//2*(3+2x+5*x^2)^-1//2*(23+11^(1/2)+x*(17+5*11^(1/2)))))
@test integrate((1+-7*x^2+4x)^-2*(3+2x+5*x^2)^3//2*(2+x^2+5x), x) == :(-1//26411*(52175400311//22+-1195943321//2*11^(1/2))^(1/2)*arctanh((250+-34*11^(1/2))^-1//2*(3+2x+5*x^2)^-1//2*(23+-1*11^(1/2)+x*(17+-5*11^(1/2))))+-1//26411*(52175400311//22+1195943321//2*11^(1/2))^(1/2)*arctanh((250+34*11^(1/2))^-1//2*(3+2x+5*x^2)^-1//2*(23+11^(1/2)+x*(17+5*11^(1/2))))+1//3773*(3+2x+5*x^2)^(1/2)*(5826+3395x)+16691//12005*5^(1/2)*arcsinh(1//14*14^(1/2)*(1+5x))+(3+2x+5*x^2)^3//2*(154+-1078*x^2+616x)^-1*(9+183x))
@test integrate((1+-7*x^2+4x)^-3*(3+2x+5*x^2)^3//2*(2+x^2+5x), x) == :(-5//343*5^(1/2)*arcsinh(1//14*14^(1/2)*(1+5x))+-1//332024*(62294197250171//2794+-189585522005//254*11^(1/2))^(1/2)*arctanh((250+-34*11^(1/2))^-1//2*(3+2x+5*x^2)^-1//2*(23+-1*11^(1/2)+x*(17+-5*11^(1/2))))+1//332024*(62294197250171//2794+189585522005//254*11^(1/2))^(1/2)*arctanh((250+34*11^(1/2))^-1//2*(3+2x+5*x^2)^-1//2*(23+11^(1/2)+x*(17+5*11^(1/2))))+-1*(3+2x+5*x^2)^(1/2)*(23716+-166012*x^2+94864x)^-1*(9495+-37088x)+1//308*(1+-7*x^2+4x)^-2*(3+2x+5*x^2)^3//2*(9+183x))
@test integrate((1+-7*x^2+4x)^3*(3+2x+5*x^2)^-1//2*(2+x^2+5x), x) == :(-16515809//156250*(3+2x+5*x^2)^(1/2)+-77513689//3125000*5^(1/2)*arcsinh(1//14*14^(1/2)*(1+5x))+-5160533//50000*x^3*(3+2x+5*x^2)^(1/2)+-47807//3750*x^4*(3+2x+5*x^2)^(1/2)+-1141//40*x^6*(3+2x+5*x^2)^(1/2)+-343//40*x^7*(3+2x+5*x^2)^(1/2)+26159//300*x^5*(3+2x+5*x^2)^(1/2)+5793077//75000*x*(3+2x+5*x^2)^(1/2)+40722851//750000*x^2*(3+2x+5*x^2)^(1/2))
@test integrate((1+-7*x^2+4x)^2*(3+2x+5*x^2)^-1//2*(2+x^2+5x), x) == :(-22053//31250*(3+2x+5*x^2)^(1/2)+-1719097//156250*5^(1/2)*arcsinh(1//14*14^(1/2)*(1+5x))+-207427//37500*x^2*(3+2x+5*x^2)^(1/2)+-33259//2500*x^3*(3+2x+5*x^2)^(1/2)+49//30*x^5*(3+2x+5*x^2)^(1/2)+5131//750*x^4*(3+2x+5*x^2)^(1/2)+36073//1875*x*(3+2x+5*x^2)^(1/2))
@test integrate((3+2x+5*x^2)^-1//2*(1+-7*x^2+4x)*(2+x^2+5x), x) == :(463//125*(3+2x+5*x^2)^(1/2)+-1901//1250*5^(1/2)*arcsinh(1//14*14^(1/2)*(1+5x))+-571//300*x^2*(3+2x+5*x^2)^(1/2)+-7//20*x^3*(3+2x+5*x^2)^(1/2)+59//30*x*(3+2x+5*x^2)^(1/2))
@test integrate((1+-7*x^2+4x)^-1*(3+2x+5*x^2)^-1//2*(2+x^2+5x), x) == :(-3//14*(4091//2794+-1055//2794*11^(1/2))^(1/2)*arctanh((250+-34*11^(1/2))^-1//2*(3+2x+5*x^2)^-1//2*(23+-1*11^(1/2)+x*(17+-5*11^(1/2))))+-1//35*5^(1/2)*arcsinh(1//14*14^(1/2)*(1+5x))+3//14*(4091//2794+1055//2794*11^(1/2))^(1/2)*arctanh((250+34*11^(1/2))^-1//2*(3+2x+5*x^2)^-1//2*(23+11^(1/2)+x*(17+5*11^(1/2)))))
@test integrate((1+-7*x^2+4x)^-2*(3+2x+5*x^2)^-1//2*(2+x^2+5x), x) == :(-1//11176*(3027900955//2794+1275971//254*11^(1/2))^(1/2)*arctanh((250+-34*11^(1/2))^-1//2*(3+2x+5*x^2)^-1//2*(23+-1*11^(1/2)+x*(17+-5*11^(1/2))))+1//11176*(3027900955//2794+-1275971//254*11^(1/2))^(1/2)*arctanh((250+34*11^(1/2))^-1//2*(3+2x+5*x^2)^-1//2*(23+11^(1/2)+x*(17+5*11^(1/2))))+-1*(3+2x+5*x^2)^(1/2)*(5588+-39116*x^2+22352x)^-1*(120+-1113x))
@test integrate((1+-7*x^2+4x)^-3*(3+2x+5*x^2)^-1//2*(2+x^2+5x), x) == :(-1*(3+2x+5*x^2)^(1/2)*(62451488+-437160416*x^2+249805952x)^-1*(2868383+-8325590x)+-1//11176*(1+-7*x^2+4x)^-2*(3+2x+5*x^2)^(1/2)*(120+-1113x)+-1//124902976*(2750+-374*11^(1/2))^-1//2*(275591617+-17771075*11^(1/2))*arctanh((250+-34*11^(1/2))^-1//2*(3+2x+5*x^2)^-1//2*(23+-1*11^(1/2)+x*(17+-5*11^(1/2))))+1//124902976*(2750+374*11^(1/2))^-1//2*(275591617+17771075*11^(1/2))*arctanh((250+34*11^(1/2))^-1//2*(3+2x+5*x^2)^-1//2*(23+11^(1/2)+x*(17+5*11^(1/2)))))
@test integrate((1+-7*x^2+4x)^3*(3+2x+5*x^2)^-3//2*(2+x^2+5x), x) == :(15715799//156250*(3+2x+5*x^2)^(1/2)+-3192602//46875*x*(3+2x+5*x^2)^(1/2)+-2583293//187500*x^2*(3+2x+5*x^2)^(1/2)+-25921//3750*x^4*(3+2x+5*x^2)^(1/2)+-343//150*x^5*(3+2x+5*x^2)^(1/2)+1//546875*(3+2x+5*x^2)^-1//2*(97964912+-85411472x)+393659//12500*x^3*(3+2x+5*x^2)^(1/2)+50047657//781250*5^(1/2)*arcsinh(1//14*14^(1/2)*(1+5x)))
@test integrate((1+-7*x^2+4x)^2*(3+2x+5*x^2)^-3//2*(2+x^2+5x), x) == :(-5086//3125*(3+2x+5*x^2)^(1/2)+-8749//1250*x*(3+2x+5*x^2)^(1/2)+-1//21875*(3+2x+5*x^2)^-1//2*(103864+1092816x)+49//100*x^3*(3+2x+5*x^2)^(1/2)+203//100*x^2*(3+2x+5*x^2)^(1/2)+89583//6250*5^(1/2)*arcsinh(1//14*14^(1/2)*(1+5x)))
@test integrate((3+2x+5*x^2)^-3//2*(1+-7*x^2+4x)*(2+x^2+5x), x) == :(-261//250*(3+2x+5*x^2)^(1/2)+-7//50*x*(3+2x+5*x^2)^(1/2)+-1//875*(3+2x+5*x^2)^-1//2*(4642+4898x)+149//125*5^(1/2)*arcsinh(1//14*14^(1/2)*(1+5x)))
@test integrate((1+-7*x^2+4x)^-1*(3+2x+5*x^2)^-3//2*(2+x^2+5x), x) == :(-3//1016*(281693//1397+-25015//1397*11^(1/2))^(1/2)*arctanh((250+-34*11^(1/2))^-1//2*(3+2x+5*x^2)^-1//2*(23+-1*11^(1/2)+x*(17+-5*11^(1/2))))+-1//3556*(3+2x+5*x^2)^-1//2*(131+-605x)+3//1016*(281693//1397+25015//1397*11^(1/2))^(1/2)*arctanh((250+34*11^(1/2))^-1//2*(3+2x+5*x^2)^-1//2*(23+11^(1/2)+x*(17+5*11^(1/2)))))
@test integrate((1+-7*x^2+4x)^-2*(3+2x+5*x^2)^-3//2*(2+x^2+5x), x) == :(-1//19870928*(3+2x+5*x^2)^-1//2*(76567+22755x)+-1*(3+2x+5*x^2)^-1//2*(5588+-39116*x^2+22352x)^-1*(120+-1113x)+-1//2838704*(2750+-374*11^(1/2))^-1//2*(3790801+-36008*11^(1/2))*arctanh((250+-34*11^(1/2))^-1//2*(3+2x+5*x^2)^-1//2*(23+-1*11^(1/2)+x*(17+-5*11^(1/2))))+1//2838704*(2750+374*11^(1/2))^-1//2*(3790801+36008*11^(1/2))*arctanh((250+34*11^(1/2))^-1//2*(3+2x+5*x^2)^-1//2*(23+11^(1/2)+x*(17+5*11^(1/2)))))
@test integrate((1+-7*x^2+4x)^-3*(3+2x+5*x^2)^-3//2*(2+x^2+5x), x) == :(-1//222077491328*(3+2x+5*x^2)^-1//2*(2306853905+5593656875x)+-1*(3+2x+5*x^2)^-1//2*(62451488+-437160416*x^2+249805952x)^-1*(2701733+-9148874x)+-1//11176*(1+-7*x^2+4x)^-2*(3+2x+5*x^2)^-1//2*(120+-1113x)+-1//31725355904*(2750+-374*11^(1/2))^-1//2*(19550020168+-594061265*11^(1/2))*arctanh((250+-34*11^(1/2))^-1//2*(3+2x+5*x^2)^-1//2*(23+-1*11^(1/2)+x*(17+-5*11^(1/2))))+1//31725355904*(2750+374*11^(1/2))^-1//2*(19550020168+594061265*11^(1/2))*arctanh((250+34*11^(1/2))^-1//2*(3+2x+5*x^2)^-1//2*(23+11^(1/2)+x*(17+5*11^(1/2)))))

max_stars_repo_path: test/1 Algebraic functions/1.2 Trinomial products/1.2.1 Quadratic/1.2.1.9 P(x) (d+e x)^m (a+b x+c x^2)^p.jl