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

@test integrate(x^3*(a+c*x^4)^5*(d+e*x^2), x) == :(1//4*d*a^5*x^4+1//6*e*a^5*x^6+1//24*d*c^5*x^24+1//26*e*c^5*x^26+(1/2)*c*e*a^4*x^10+1//4*a*d*c^4*x^20+5//6*d*a^3*c^2*x^12+5//7*e*a^3*c^2*x^14+5//8*c*d*a^4*x^8+5//8*d*a^2*c^3*x^16+5//9*e*a^2*c^3*x^18+5//22*a*e*c^4*x^22)
@test integrate(x^2*(a+c*x^4)^5*(d+e*x^2), x) == :(1//3*d*a^5*x^3+1//5*e*a^5*x^5+1//23*d*c^5*x^23+1//25*e*c^5*x^25+2//3*d*a^2*c^3*x^15+5//7*c*d*a^4*x^7+5//9*c*e*a^4*x^9+5//19*a*d*c^4*x^19+5//21*a*e*c^4*x^21+10//11*d*a^3*c^2*x^11+10//13*e*a^3*c^2*x^13+10//17*e*a^2*c^3*x^17)
@test integrate(x*(a+c*x^4)^5*(d+e*x^2), x) == :((1/2)*d*a^5*x^2+1//22*d*c^5*x^22+1//24*e*c^-1*(a+c*x^4)^6+d*a^3*c^2*x^10+5//6*c*d*a^4*x^6+5//7*d*a^2*c^3*x^14+5//18*a*d*c^4*x^18)
@test integrate((a+c*x^4)^5*(d+e*x^2), x) == :(d*x*a^5+1//3*e*a^5*x^3+1//21*d*c^5*x^21+1//23*e*c^5*x^23+c*d*a^4*x^5+2//3*e*a^2*c^3*x^15+5//7*c*e*a^4*x^7+5//17*a*d*c^4*x^17+5//19*a*e*c^4*x^19+10//9*d*a^3*c^2*x^9+10//11*e*a^3*c^2*x^11+10//13*d*a^2*c^3*x^13)
@test integrate(x^-1*(a+c*x^4)^5*(d+e*x^2), x) == :(d*a^5*log(x)+(1/2)*e*a^5*x^2+1//20*d*c^5*x^20+1//22*e*c^5*x^22+e*a^3*c^2*x^10+5//4*c*d*a^4*x^4+5//4*d*a^3*c^2*x^8+5//6*c*e*a^4*x^6+5//6*d*a^2*c^3*x^12+5//7*e*a^2*c^3*x^14+5//16*a*d*c^4*x^16+5//18*a*e*c^4*x^18)
@test integrate(x^-2*(a+c*x^4)^5*(d+e*x^2), x) == :(e*x*a^5+-1*d*a^5*x^-1+1//19*d*c^5*x^19+1//21*e*c^5*x^21+c*e*a^4*x^5+1//3*a*d*c^4*x^15+5//3*c*d*a^4*x^3+5//17*a*e*c^4*x^17+10//7*d*a^3*c^2*x^7+10//9*e*a^3*c^2*x^9+10//11*d*a^2*c^3*x^11+10//13*e*a^2*c^3*x^13)
@test integrate(x^-3*(a+c*x^4)^5*(d+e*x^2), x) == :(e*a^5*log(x)+-1//2*d*a^5*x^-2+1//18*d*c^5*x^18+1//20*e*c^5*x^20+d*a^2*c^3*x^10+5//2*c*d*a^4*x^2+5//3*d*a^3*c^2*x^6+5//4*c*e*a^4*x^4+5//4*e*a^3*c^2*x^8+5//6*e*a^2*c^3*x^12+5//14*a*d*c^4*x^14+5//16*a*e*c^4*x^16)
@test integrate(x^5*(5+x^4)^(1/2)*(2+3*x^2), x) == :(-25//8*arcsinh(1//5*5^(1/2)*x^2)+-5//8*x^2*(5+x^4)^(1/2)+-1//4*(5+x^4)^3//2*(4+-1*x^2)+3//10*x^4*(5+x^4)^3//2)
@test integrate(x^3*(5+x^4)^(1/2)*(2+3*x^2), x) == :(-75//16*arcsinh(1//5*5^(1/2)*x^2)+-15//16*x^2*(5+x^4)^(1/2)+1//24*(5+x^4)^3//2*(8+9*x^2))
@test integrate(x*(5+x^4)^(1/2)*(2+3*x^2), x) == :((1/2)*(5+x^4)^3//2+5//2*arcsinh(1//5*5^(1/2)*x^2)+(1/2)*x^2*(5+x^4)^(1/2))
@test integrate(x^-1*(5+x^4)^(1/2)*(2+3*x^2), x) == :(15//4*arcsinh(1//5*5^(1/2)*x^2)+-1*5^(1/2)*arctanh(1//5*5^(1/2)*(5+x^4)^(1/2))+1//4*(5+x^4)^(1/2)*(4+3*x^2))
@test integrate(x^-3*(5+x^4)^(1/2)*(2+3*x^2), x) == :(-3//2*5^(1/2)*arctanh(1//5*5^(1/2)*(5+x^4)^(1/2))+-1//2*x^-2*(5+x^4)^(1/2)*(2+-3*x^2)+arcsinh(1//5*5^(1/2)*x^2))
@test integrate(x^-5*(5+x^4)^(1/2)*(2+3*x^2), x) == :(3//2*arcsinh(1//5*5^(1/2)*x^2)+-1//10*5^(1/2)*arctanh(1//5*5^(1/2)*(5+x^4)^(1/2))+-1//2*x^-4*(5+x^4)^(1/2)*(1+3*x^2))
@test integrate(x^-7*(5+x^4)^(1/2)*(2+3*x^2), x) == :(-3//4*x^-4*(5+x^4)^(1/2)+-3//20*5^(1/2)*arctanh(1//5*5^(1/2)*(5+x^4)^(1/2))+-1//15*x^-6*(5+x^4)^3//2)
@test integrate(x^4*(5+x^4)^(1/2)*(2+3*x^2), x) == :(2//3*x^3*(5+x^4)^(1/2)+20//21*x*(5+x^4)^(1/2)+-10*x*(5+x^4)^(1/2)*(5^(1/2)+x^2)^-1+1//21*x^5*(5+x^4)^(1/2)*(6+7*x^2)+10*5^1//4*((5^(1/2)+x^2)^-2*(5+x^4))^(1/2)*(5+x^4)^-1//2*(5^(1/2)+x^2)*Elliptic.E(2*arctan(1//5*x*5^3//4),1/2)+-5//21*5^1//4*((5^(1/2)+x^2)^-2*(5+x^4))^(1/2)*(5+x^4)^-1//2*(21+2*5^(1/2))*(5^(1/2)+x^2)*Elliptic.F(2*arctan(1//5*x*5^3//4),1/2))
@test integrate(x^2*(5+x^4)^(1/2)*(2+3*x^2), x) == :(10//7*x*(5+x^4)^(1/2)+4*x*(5+x^4)^(1/2)*(5^(1/2)+x^2)^-1+1//35*x^3*(5+x^4)^(1/2)*(14+15*x^2)+-4*5^1//4*((5^(1/2)+x^2)^-2*(5+x^4))^(1/2)*(5+x^4)^-1//2*(5^(1/2)+x^2)*Elliptic.E(2*arctan(1//5*x*5^3//4),1/2)+1//7*5^1//4*((5^(1/2)+x^2)^-2*(5+x^4))^(1/2)*(5+x^4)^-1//2*(14+-5*5^(1/2))*(5^(1/2)+x^2)*Elliptic.F(2*arctan(1//5*x*5^3//4),1/2))
@test integrate((5+x^4)^(1/2)*(2+3*x^2), x) == :(6*x*(5+x^4)^(1/2)*(5^(1/2)+x^2)^-1+1//15*x*(5+x^4)^(1/2)*(10+9*x^2)+-6*5^1//4*((5^(1/2)+x^2)^-2*(5+x^4))^(1/2)*(5+x^4)^-1//2*(5^(1/2)+x^2)*Elliptic.E(2*arctan(1//5*x*5^3//4),1/2)+1//3*5^1//4*((5^(1/2)+x^2)^-2*(5+x^4))^(1/2)*(5+x^4)^-1//2*(9+2*5^(1/2))*(5^(1/2)+x^2)*Elliptic.F(2*arctan(1//5*x*5^3//4),1/2))
@test integrate(x^-2*(5+x^4)^(1/2)*(2+3*x^2), x) == :(-1*x^-1*(5+x^4)^(1/2)*(2+-1*x^2)+4*x*(5+x^4)^(1/2)*(5^(1/2)+x^2)^-1+-4*5^1//4*((5^(1/2)+x^2)^-2*(5+x^4))^(1/2)*(5+x^4)^-1//2*(5^(1/2)+x^2)*Elliptic.E(2*arctan(1//5*x*5^3//4),1/2)+5^1//4*((5^(1/2)+x^2)^-2*(5+x^4))^(1/2)*(5+x^4)^-1//2*(2+5^(1/2))*(5^(1/2)+x^2)*Elliptic.F(2*arctan(1//5*x*5^3//4),1/2))
@test integrate(x^-4*(5+x^4)^(1/2)*(2+3*x^2), x) == :(-6*x^-1*(5+x^4)^(1/2)+6*x*(5+x^4)^(1/2)*(5^(1/2)+x^2)^-1+-1//3*x^-3*(5+x^4)^(1/2)*(2+-9*x^2)+-6*5^1//4*((5^(1/2)+x^2)^-2*(5+x^4))^(1/2)*(5+x^4)^-1//2*(5^(1/2)+x^2)*Elliptic.E(2*arctan(1//5*x*5^3//4),1/2)+1//15*5^3//4*((5^(1/2)+x^2)^-2*(5+x^4))^(1/2)*(5+x^4)^-1//2*(2+9*5^(1/2))*(5^(1/2)+x^2)*Elliptic.F(2*arctan(1//5*x*5^3//4),1/2))
@test integrate(x^5*(5+x^4)^3//2*(2+3*x^2), x) == :(-125//16*arcsinh(1//5*5^(1/2)*x^2)+-1*(5+x^4)^5//2*(3//7+-1//6*x^2)+-25//16*x^2*(5+x^4)^(1/2)+-5//24*x^2*(5+x^4)^3//2+3//14*x^4*(5+x^4)^5//2)
@test integrate(x^3*(5+x^4)^3//2*(2+3*x^2), x) == :(-375//32*arcsinh(1//5*5^(1/2)*x^2)+(5+x^4)^5//2*(1//5+1//4*x^2)+-75//32*x^2*(5+x^4)^(1/2)+-5//16*x^2*(5+x^4)^3//2)
@test integrate(x*(5+x^4)^3//2*(2+3*x^2), x) == :(3//10*(5+x^4)^5//2+75//8*arcsinh(1//5*5^(1/2)*x^2)+1//4*x^2*(5+x^4)^3//2+15//8*x^2*(5+x^4)^(1/2))
@test integrate(x^-1*(5+x^4)^3//2*(2+3*x^2), x) == :(225//16*arcsinh(1//5*5^(1/2)*x^2)+(5+x^4)^(1/2)*(5+45//16*x^2)+(5+x^4)^3//2*(1//3+3//8*x^2)+-5*5^(1/2)*arctanh(1//5*5^(1/2)*(5+x^4)^(1/2)))
@test integrate(x^-3*(5+x^4)^3//2*(2+3*x^2), x) == :(15//2*arcsinh(1//5*5^(1/2)*x^2)+(5+x^4)^(1/2)*(15//2+3//2*x^2)+-15//2*5^(1/2)*arctanh(1//5*5^(1/2)*(5+x^4)^(1/2))+-1//2*x^-2*(5+x^4)^3//2*(2+-1*x^2))
@test integrate(x^-5*(5+x^4)^3//2*(2+3*x^2), x) == :(45//4*arcsinh(1//5*5^(1/2)*x^2)+-3//2*5^(1/2)*arctanh(1//5*5^(1/2)*(5+x^4)^(1/2))+-1//4*x^-4*(5+x^4)^3//2*(2+-3*x^2)+-1//4*x^-2*(5+x^4)^(1/2)*(45+-6*x^2))
@test integrate(x^-7*(5+x^4)^3//2*(2+3*x^2), x) == :(-9//4*5^(1/2)*arctanh(1//5*5^(1/2)*(5+x^4)^(1/2))+-1//4*x^-2*(5+x^4)^(1/2)*(4+-9*x^2)+-1//12*x^-6*(5+x^4)^3//2*(4+9*x^2)+arcsinh(1//5*5^(1/2)*x^2))
@test integrate(x^4*(5+x^4)^3//2*(2+3*x^2), x) == :(20//13*x^3*(5+x^4)^(1/2)+200//77*x*(5+x^4)^(1/2)+-300*x*(5+x^4)^(1/2)*(13*5^(1/2)+13*x^2)^-1+1//143*x^5*(5+x^4)^3//2*(26+33*x^2)+10//1001*x^5*(5+x^4)^(1/2)*(78+77*x^2)+300//13*5^1//4*((5^(1/2)+x^2)^-2*(5+x^4))^(1/2)*(5+x^4)^-1//2*(5^(1/2)+x^2)*Elliptic.E(2*arctan(1//5*x*5^3//4),1/2)+-50//1001*5^1//4*((5^(1/2)+x^2)^-2*(5+x^4))^(1/2)*(5+x^4)^-1//2*(231+26*5^(1/2))*(5^(1/2)+x^2)*Elliptic.F(2*arctan(1//5*x*5^3//4),1/2))
@test integrate(x^2*(5+x^4)^3//2*(2+3*x^2), x) == :(300//77*x*(5+x^4)^(1/2)+40*x*(5+x^4)^(1/2)*(3*5^(1/2)+3*x^2)^-1+1//99*x^3*(5+x^4)^3//2*(22+27*x^2)+2//231*x^3*(5+x^4)^(1/2)*(154+135*x^2)+-40//3*5^1//4*((5^(1/2)+x^2)^-2*(5+x^4))^(1/2)*(5+x^4)^-1//2*(5^(1/2)+x^2)*Elliptic.E(2*arctan(1//5*x*5^3//4),1/2)+10//231*5^1//4*((5^(1/2)+x^2)^-2*(5+x^4))^(1/2)*(5+x^4)^-1//2*(154+-45*5^(1/2))*(5^(1/2)+x^2)*Elliptic.F(2*arctan(1//5*x*5^3//4),1/2))
@test integrate((5+x^4)^3//2*(2+3*x^2), x) == :(20*x*(5+x^4)^(1/2)*(5^(1/2)+x^2)^-1+1//21*x*(5+x^4)^3//2*(6+7*x^2)+2//7*x*(5+x^4)^(1/2)*(10+7*x^2)+-20*5^1//4*((5^(1/2)+x^2)^-2*(5+x^4))^(1/2)*(5+x^4)^-1//2*(5^(1/2)+x^2)*Elliptic.E(2*arctan(1//5*x*5^3//4),1/2)+10//7*5^1//4*((5^(1/2)+x^2)^-2*(5+x^4))^(1/2)*(5+x^4)^-1//2*(7+2*5^(1/2))*(5^(1/2)+x^2)*Elliptic.F(2*arctan(1//5*x*5^3//4),1/2))
@test integrate(x^-2*(5+x^4)^3//2*(2+3*x^2), x) == :(24*x*(5+x^4)^(1/2)*(5^(1/2)+x^2)^-1+-1//7*x^-1*(5+x^4)^3//2*(14+-3*x^2)+6//35*x*(5+x^4)^(1/2)*(25+14*x^2)+-24*5^1//4*((5^(1/2)+x^2)^-2*(5+x^4))^(1/2)*(5+x^4)^-1//2*(5^(1/2)+x^2)*Elliptic.E(2*arctan(1//5*x*5^3//4),1/2)+6//7*5^1//4*((5^(1/2)+x^2)^-2*(5+x^4))^(1/2)*(5+x^4)^-1//2*(14+5*5^(1/2))*(5^(1/2)+x^2)*Elliptic.F(2*arctan(1//5*x*5^3//4),1/2))
@test integrate(x^-4*(5+x^4)^3//2*(2+3*x^2), x) == :(36*x*(5+x^4)^(1/2)*(5^(1/2)+x^2)^-1+-1//3*x^-1*(5+x^4)^(1/2)*(54+-4*x^2)+-1//15*x^-3*(5+x^4)^3//2*(10+-9*x^2)+-36*5^1//4*((5^(1/2)+x^2)^-2*(5+x^4))^(1/2)*(5+x^4)^-1//2*(5^(1/2)+x^2)*Elliptic.E(2*arctan(1//5*x*5^3//4),1/2)+2//3*5^1//4*((5^(1/2)+x^2)^-2*(5+x^4))^(1/2)*(5+x^4)^-1//2*(27+2*5^(1/2))*(5^(1/2)+x^2)*Elliptic.F(2*arctan(1//5*x*5^3//4),1/2))
@test integrate(x^7*(5+x^4)^-1//2*(2+3*x^2), x) == :(225//16*arcsinh(1//5*5^(1/2)*x^2)+-1*(5+x^4)^(1/2)*(10//3+45//16*x^2)+1//3*x^4*(5+x^4)^(1/2)+3//8*x^6*(5+x^4)^(1/2))
@test integrate(x^5*(5+x^4)^-1//2*(2+3*x^2), x) == :(-5//2*arcsinh(1//5*5^(1/2)*x^2)+(1/2)*x^4*(5+x^4)^(1/2)+-1//2*(5+x^4)^(1/2)*(10+-1*x^2))
@test integrate(x^3*(5+x^4)^-1//2*(2+3*x^2), x) == :(-15//4*arcsinh(1//5*5^(1/2)*x^2)+1//4*(5+x^4)^(1/2)*(4+3*x^2))
@test integrate(x*(5+x^4)^-1//2*(2+3*x^2), x) == :(3//2*(5+x^4)^(1/2)+arcsinh(1//5*5^(1/2)*x^2))
@test integrate(x^-1*(5+x^4)^-1//2*(2+3*x^2), x) == :(3//2*arcsinh(1//5*5^(1/2)*x^2)+-1//5*5^(1/2)*arctanh(1//5*5^(1/2)*(5+x^4)^(1/2)))
@test integrate(x^-3*(5+x^4)^-1//2*(2+3*x^2), x) == :(-3//10*5^(1/2)*arctanh(1//5*5^(1/2)*(5+x^4)^(1/2))+-1//5*x^-2*(5+x^4)^(1/2))
@test integrate(x^-5*(5+x^4)^-1//2*(2+3*x^2), x) == :(-3//10*x^-2*(5+x^4)^(1/2)+-1//10*x^-4*(5+x^4)^(1/2)+1//50*5^(1/2)*arctanh(1//5*5^(1/2)*(5+x^4)^(1/2)))
@test integrate(x^4*(5+x^4)^-1//2*(2+3*x^2), x) == :(2//3*x*(5+x^4)^(1/2)+3//5*x^3*(5+x^4)^(1/2)+-9*x*(5+x^4)^(1/2)*(5^(1/2)+x^2)^-1+9*5^1//4*((5^(1/2)+x^2)^-2*(5+x^4))^(1/2)*(5+x^4)^-1//2*(5^(1/2)+x^2)*Elliptic.E(2*arctan(1//5*x*5^3//4),1/2)+-1//6*5^1//4*((5^(1/2)+x^2)^-2*(5+x^4))^(1/2)*(5+x^4)^-1//2*(27+2*5^(1/2))*(5^(1/2)+x^2)*Elliptic.F(2*arctan(1//5*x*5^3//4),1/2))
@test integrate(x^2*(5+x^4)^-1//2*(2+3*x^2), x) == :(x*(5+x^4)^(1/2)+2*x*(5+x^4)^(1/2)*(5^(1/2)+x^2)^-1+-2*5^1//4*((5^(1/2)+x^2)^-2*(5+x^4))^(1/2)*(5+x^4)^-1//2*(5^(1/2)+x^2)*Elliptic.E(2*arctan(1//5*x*5^3//4),1/2)+(1/2)*5^1//4*((5^(1/2)+x^2)^-2*(5+x^4))^(1/2)*(5+x^4)^-1//2*(2+-1*5^(1/2))*(5^(1/2)+x^2)*Elliptic.F(2*arctan(1//5*x*5^3//4),1/2))
@test integrate((5+x^4)^-1//2*(2+3*x^2), x) == :(3*x*(5+x^4)^(1/2)*(5^(1/2)+x^2)^-1+-3*5^1//4*((5^(1/2)+x^2)^-2*(5+x^4))^(1/2)*(5+x^4)^-1//2*(5^(1/2)+x^2)*Elliptic.E(2*arctan(1//5*x*5^3//4),1/2)+1//10*5^3//4*((5^(1/2)+x^2)^-2*(5+x^4))^(1/2)*(5+x^4)^-1//2*(2+3*5^(1/2))*(5^(1/2)+x^2)*Elliptic.F(2*arctan(1//5*x*5^3//4),1/2))
@test integrate(x^-2*(5+x^4)^-1//2*(2+3*x^2), x) == :(-2//5*x^-1*(5+x^4)^(1/2)+2*x*(5+x^4)^(1/2)*(5*5^(1/2)+5*x^2)^-1+-1//5*5^1//4*((5^(1/2)+x^2)^-2*(5+x^4))^(1/2)*(5+x^4)^-1//2*(2*5^(1/2)+2*x^2)*Elliptic.E(2*arctan(1//5*x*5^3//4),1/2)+1//10*5^1//4*((5^(1/2)+x^2)^-2*(5+x^4))^(1/2)*(5+x^4)^-1//2*(2+3*5^(1/2))*(5^(1/2)+x^2)*Elliptic.F(2*arctan(1//5*x*5^3//4),1/2))
@test integrate(x^-4*(5+x^4)^-1//2*(2+3*x^2), x) == :(-3//5*x^-1*(5+x^4)^(1/2)+-2//15*x^-3*(5+x^4)^(1/2)+3*x*(5+x^4)^(1/2)*(5*5^(1/2)+5*x^2)^-1+-1//5*5^1//4*((5^(1/2)+x^2)^-2*(5+x^4))^(1/2)*(5+x^4)^-1//2*(3*5^(1/2)+3*x^2)*Elliptic.E(2*arctan(1//5*x*5^3//4),1/2)+-1//150*5^3//4*((5^(1/2)+x^2)^-2*(5+x^4))^(1/2)*(5+x^4)^-1//2*(2+-9*5^(1/2))*(5^(1/2)+x^2)*Elliptic.F(2*arctan(1//5*x*5^3//4),1/2))
@test integrate(x^7*(5+x^4)^-3//2*(2+3*x^2), x) == :(-45//4*arcsinh(1//5*5^(1/2)*x^2)+(5+x^4)^(1/2)*(2+9//4*x^2)+-1//2*x^4*(5+x^4)^-1//2*(2+3*x^2))
@test integrate(x^5*(5+x^4)^-3//2*(2+3*x^2), x) == :(3*(5+x^4)^(1/2)+-1//2*x^2*(5+x^4)^-1//2*(2+3*x^2)+arcsinh(1//5*5^(1/2)*x^2))
@test integrate(x^3*(5+x^4)^-3//2*(2+3*x^2), x) == :(3//2*arcsinh(1//5*5^(1/2)*x^2)+(1/2)*(5+x^4)^-1//2*(-2+-3*x^2))
@test integrate(x*(5+x^4)^-3//2*(2+3*x^2), x) == :(1//10*(5+x^4)^-1//2*(-15+2*x^2))
@test integrate(x^-1*(5+x^4)^-3//2*(2+3*x^2), x) == :(-1//25*5^(1/2)*arctanh(1//5*5^(1/2)*(5+x^4)^(1/2))+1//10*(5+x^4)^-1//2*(2+3*x^2))
@test integrate(x^-3*(5+x^4)^-3//2*(2+3*x^2), x) == :(-3//50*5^(1/2)*arctanh(1//5*5^(1/2)*(5+x^4)^(1/2))+-2//25*x^-2*(5+x^4)^(1/2)+1//10*x^-2*(5+x^4)^-1//2*(2+3*x^2))
@test integrate(x^4*(5+x^4)^-3//2*(2+3*x^2), x) == :(-1//5*x*(5+x^4)^(1/2)+9*x*(5+x^4)^(1/2)*(2*5^(1/2)+2*x^2)^-1+-1//10*x^3*(5+x^4)^-1//2*(15+-2*x^2)+-9//2*5^1//4*((5^(1/2)+x^2)^-2*(5+x^4))^(1/2)*(5+x^4)^-1//2*(5^(1/2)+x^2)*Elliptic.E(2*arctan(1//5*x*5^3//4),1/2)+1//20*5^3//4*((5^(1/2)+x^2)^-2*(5+x^4))^(1/2)*(5+x^4)^-1//2*(2+9*5^(1/2))*(5^(1/2)+x^2)*Elliptic.F(2*arctan(1//5*x*5^3//4),1/2))
@test integrate(x^2*(5+x^4)^-3//2*(2+3*x^2), x) == :(-1*x*(5+x^4)^(1/2)*(5*5^(1/2)+5*x^2)^-1+-1//10*x*(5+x^4)^-1//2*(15+-2*x^2)+1//5*5^1//4*((5^(1/2)+x^2)^-2*(5+x^4))^(1/2)*(5+x^4)^-1//2*(5^(1/2)+x^2)*Elliptic.E(2*arctan(1//5*x*5^3//4),1/2)+-1//20*5^1//4*((5^(1/2)+x^2)^-2*(5+x^4))^(1/2)*(5+x^4)^-1//2*(2+-3*5^(1/2))*(5^(1/2)+x^2)*Elliptic.F(2*arctan(1//5*x*5^3//4),1/2))
@test integrate((5+x^4)^-3//2*(2+3*x^2), x) == :(-3*x*(5+x^4)^(1/2)*(10*5^(1/2)+10*x^2)^-1+1//10*x*(5+x^4)^-1//2*(2+3*x^2)+1//10*5^1//4*((5^(1/2)+x^2)^-2*(5+x^4))^(1/2)*(5+x^4)^-1//2*(3*5^(1/2)+3*x^2)*Elliptic.E(2*arctan(1//5*x*5^3//4),1/2)+1//100*5^3//4*((5^(1/2)+x^2)^-2*(5+x^4))^(1/2)*(5+x^4)^-1//2*(2+-3*5^(1/2))*(5^(1/2)+x^2)*Elliptic.F(2*arctan(1//5*x*5^3//4),1/2))
@test integrate(x^-2*(5+x^4)^-3//2*(2+3*x^2), x) == :(-3//25*x^-1*(5+x^4)^(1/2)+3*x*(5+x^4)^(1/2)*(25*5^(1/2)+25*x^2)^-1+1//10*x^-1*(5+x^4)^-1//2*(2+3*x^2)+-1//25*5^1//4*((5^(1/2)+x^2)^-2*(5+x^4))^(1/2)*(5+x^4)^-1//2*(3*5^(1/2)+3*x^2)*Elliptic.E(2*arctan(1//5*x*5^3//4),1/2)+1//100*5^1//4*((5^(1/2)+x^2)^-2*(5+x^4))^(1/2)*(5+x^4)^-1//2*(6+3*5^(1/2))*(5^(1/2)+x^2)*Elliptic.F(2*arctan(1//5*x*5^3//4),1/2))
@test integrate(x^-4*(5+x^4)^-3//2*(2+3*x^2), x) == :(-9//50*x^-1*(5+x^4)^(1/2)+-1//15*x^-3*(5+x^4)^(1/2)+9*x*(5+x^4)^(1/2)*(50*5^(1/2)+50*x^2)^-1+1//10*x^-3*(5+x^4)^-1//2*(2+3*x^2)+-1//50*5^1//4*((5^(1/2)+x^2)^-2*(5+x^4))^(1/2)*(5+x^4)^-1//2*(9*5^(1/2)+9*x^2)*Elliptic.E(2*arctan(1//5*x*5^3//4),1/2)+1//300*5^1//4*((5^(1/2)+x^2)^-2*(5+x^4))^(1/2)*(5+x^4)^-1//2*(27+-2*5^(1/2))*(5^(1/2)+x^2)*Elliptic.F(2*arctan(1//5*x*5^3//4),1/2))
@test integrate((f*x)^m*(1+x^4+2*x^2)^5*(d+e*x^2), x) == :(d*f^-1*(f*x)^(1+m)*(1+m)^-1+e*f^-23*(f*x)^(23+m)*(23+m)^-1+f^-21*(f*x)^(21+m)*(21+m)^-1*(d+10*e)+f^-19*(f*x)^(19+m)*(19+m)^-1*(10d+45*e)+f^-17*(f*x)^(17+m)*(17+m)^-1*(45d+120*e)+f^-15*(f*x)^(15+m)*(15+m)^-1*(120d+210*e)+f^-13*(f*x)^(13+m)*(13+m)^-1*(210d+252*e)+f^-11*(f*x)^(11+m)*(11+m)^-1*(210*e+252d)+f^-9*(f*x)^(9+m)*(9+m)^-1*(120*e+210d)+f^-7*(f*x)^(7+m)*(7+m)^-1*(45*e+120d)+f^-5*(f*x)^(5+m)*(5+m)^-1*(10*e+45d)+f^-3*(f*x)^(3+m)*(3+m)^-1*(e+10d))
@test integrate(x^5*(1+x^4+2*x^2)^5*(d+e*x^2), x) == :((1+x^2)^11*(-1//22*e+1//22*d)+(1+x^2)^13*(-3//26*e+1//26*d)+-1*(1+x^2)^12*(-1//8*e+1//12*d)+1//28*e*(1+x^2)^14)
@test integrate(x^4*(1+x^4+2*x^2)^5*(d+e*x^2), x) == :(x^7*(1//7*e+10//7*d)+x^9*(5d+10//9*e)+x^11*(45//11*e+120//11*d)+x^13*(120//13*e+210//13*d)+x^15*(14*e+84//5*d)+x^17*(210//17*d+252//17*e)+x^19*(120//19*d+210//19*e)+x^21*(15//7*d+40//7*e)+x^23*(10//23*d+45//23*e)+x^25*(1//25*d+2//5*e)+1//5*d*x^5+1//27*e*x^27)
@test integrate(x^3*(1+x^4+2*x^2)^5*(d+e*x^2), x) == :((1+x^2)^11*(-1//22*d+1//22*e)+(1+x^2)^12*(-1//12*e+1//24*d)+1//26*e*(1+x^2)^13)
@test integrate(x^2*(1+x^4+2*x^2)^5*(d+e*x^2), x) == :(x^5*(2d+1//5*e)+x^7*(10//7*e+45//7*d)+x^9*(5*e+40//3*d)+x^11*(120//11*e+210//11*d)+x^13*(210//13*e+252//13*d)+x^15*(14d+84//5*e)+x^17*(120//17*d+210//17*e)+x^19*(45//19*d+120//19*e)+x^21*(10//21*d+15//7*e)+x^23*(1//23*d+10//23*e)+1//3*d*x^3+1//25*e*x^25)
@test integrate(x*(1+x^4+2*x^2)^5*(d+e*x^2), x) == :((1+x^2)^11*(-1//22*e+1//22*d)+1//24*e*(1+x^2)^12)
@test integrate((1+x^4+2*x^2)^5*(d+e*x^2), x) == :(d*x+x^3*(1//3*e+10//3*d)+x^5*(2*e+9d)+x^7*(45//7*e+120//7*d)+x^9*(40//3*e+70//3*d)+x^11*(210//11*e+252//11*d)+x^13*(210//13*d+252//13*e)+x^15*(8d+14*e)+x^17*(45//17*d+120//17*e)+x^19*(10//19*d+45//19*e)+x^21*(1//21*d+10//21*e)+1//23*e*x^23)
@test integrate(x^-1*(1+x^4+2*x^2)^5*(d+e*x^2), x) == :(d*log(x)+5*d*x^2+20*d*x^6+1//20*d*x^20+1//22*e*(1+x^2)^11+5//9*d*x^18+35//2*d*x^12+45//4*d*x^4+45//16*d*x^16+60//7*d*x^14+105//4*d*x^8+126//5*d*x^10)
@test integrate(x^-2*(1+x^4+2*x^2)^5*(d+e*x^2), x) == :(x*(e+10d)+x^3*(15d+10//3*e)+x^5*(9*e+24d)+x^7*(30d+120//7*e)+x^9*(28d+70//3*e)+x^11*(210//11*d+252//11*e)+x^13*(120//13*d+210//13*e)+x^15*(3d+8*e)+x^17*(10//17*d+45//17*e)+x^19*(1//19*d+10//19*e)+-1*d*x^-1+1//21*e*x^21)
@test integrate(x^-3*(1+x^4+2*x^2)^5*(d+e*x^2), x) == :(x^2*(5*e+45//2*d)+x^4*(30d+45//4*e)+x^6*(20*e+35d)+x^8*(63//2*d+105//4*e)+x^10*(21d+126//5*e)+x^12*(10d+35//2*e)+x^14*(45//14*d+60//7*e)+x^16*(5//8*d+45//16*e)+x^18*(1//18*d+5//9*e)+(e+10d)*log(x)+-1//2*d*x^-2+1//20*e*x^20)
@test integrate((f*x)^m*(1+x^4+2*x^2)^5*(1+x^2), x) == :(f^-1*(f*x)^(1+m)*(1+m)^-1+f^-23*(f*x)^(23+m)*(23+m)^-1+11*f^-21*(f*x)^(21+m)*(21+m)^-1+11*f^-3*(f*x)^(3+m)*(3+m)^-1+55*f^-19*(f*x)^(19+m)*(19+m)^-1+55*f^-5*(f*x)^(5+m)*(5+m)^-1+165*f^-17*(f*x)^(17+m)*(17+m)^-1+165*f^-7*(f*x)^(7+m)*(7+m)^-1+330*f^-15*(f*x)^(15+m)*(15+m)^-1+330*f^-9*(f*x)^(9+m)*(9+m)^-1+462*f^-13*(f*x)^(13+m)*(13+m)^-1+462*f^-11*(f*x)^(11+m)*(11+m)^-1)
@test integrate(x^5*(1+x^4+2*x^2)^5*(1+x^2), x) == :(-1//13*(1+x^2)^13+1//24*(1+x^2)^12+1//28*(1+x^2)^14)
@test integrate(x^4*(1+x^4+2*x^2)^5*(1+x^2), x) == :(15*x^11+1//5*x^5+1//27*x^27+11//7*x^7+11//25*x^25+55//7*x^21+55//9*x^9+55//23*x^23+154//5*x^15+330//13*x^13+330//19*x^19+462//17*x^17)
@test integrate(x^3*(1+x^4+2*x^2)^5*(1+x^2), x) == :(-1//24*(1+x^2)^12+1//26*(1+x^2)^13)
@test integrate(x^2*(1+x^4+2*x^2)^5*(1+x^2), x) == :(30*x^11+1//3*x^3+1//25*x^25+11//5*x^5+11//23*x^23+55//3*x^9+55//7*x^7+55//21*x^21+154//5*x^15+165//19*x^19+330//17*x^17+462//13*x^13)
@test integrate(x*(1+x^4+2*x^2)^5*(1+x^2), x) == :(1//24*(1+x^2)^12)
@test integrate((1+x^4+2*x^2)^5*(1+x^2), x) == :(x+11*x^5+22*x^15+42*x^11+1//23*x^23+11//3*x^3+11//21*x^21+55//19*x^19+110//3*x^9+165//7*x^7+165//17*x^17+462//13*x^13)
@test integrate(x^-1*(1+x^4+2*x^2)^5*(1+x^2), x) == :(1//22*x^22+11//2*x^2+11//20*x^20+55//2*x^6+55//4*x^4+55//18*x^18+77//2*x^12+165//4*x^8+165//7*x^14+165//16*x^16+231//5*x^10+log(x))
@test integrate(x^-2*(1+x^4+2*x^2)^5*(1+x^2), x) == :(-1*x^-1+11x+11*x^15+33*x^5+42*x^11+1//21*x^21+11//19*x^19+55//3*x^3+55//17*x^17+154//3*x^9+330//7*x^7+330//13*x^13)
@test integrate(x^-3*(1+x^4+2*x^2)^5*(1+x^2), x) == :(11*log(x)+55*x^6+-1//2*x^-2+1//20*x^20+11//18*x^18+55//2*x^2+55//2*x^12+55//16*x^16+165//4*x^4+165//14*x^14+231//4*x^8+231//5*x^10)
@test integrate(x^2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(d+e*x^2), x) == :(x*b^-2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*(b*d+-1*a*e)+1//3*e*b^-1*x^3*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)+-1*a^(1/2)*b^-5//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*(b*d+-1*a*e)*arctan(x*a^-1//2*b^(1/2)))
@test integrate(x*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(d+e*x^2), x) == :((1/2)*e*b^-2*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+(1/2)*b^-2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*(b*d+-1*a*e)*log(a+b*x^2))
@test integrate((a^2+b^2*x^4+2*a*b*x^2)^-1//2*(d+e*x^2), x) == :(e*x*b^-1*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)+a^-1//2*b^-3//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*(b*d+-1*a*e)*arctan(x*a^-1//2*b^(1/2)))
@test integrate(x^-1*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(d+e*x^2), x) == :(d*a^-1*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(x)+-1//2*a^-1*b^-1*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*(b*d+-1*a*e)*log(a+b*x^2))
@test integrate(x^-2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(d+e*x^2), x) == :(-1*d*a^-1*x^-1*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)+-1*a^-3//2*b^-1//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*(b*d+-1*a*e)*arctan(x*a^-1//2*b^(1/2)))
@test integrate(x^-3*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(d+e*x^2), x) == :((1/2)*a^-2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*(b*d+-1*a*e)*log(a+b*x^2)+-1*a^-2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*(b*d+-1*a*e)*log(x)+-1//2*d*a^-1*x^-2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2))
@test integrate(x^2*(a^2+b^2*x^4+2*a*b*x^2)^-3//2*(d+e*x^2), x) == :(-1//4*x*b^-2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(b*d+-1*a*e)+1//8*x*a^-1*b^-2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(b*d+-5*a*e)+1//8*a^-3//2*b^-5//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*(b*d+3*a*e)*arctan(x*a^-1//2*b^(1/2)))
@test integrate(x*(a^2+b^2*x^4+2*a*b*x^2)^-3//2*(d+e*x^2), x) == :(-1//2*e*b^-2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+-1//4*b^-2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(b*d+-1*a*e))
@test integrate((a^2+b^2*x^4+2*a*b*x^2)^-3//2*(d+e*x^2), x) == :(1//8*x*a^-2*b^-1*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a*e+3*b*d)+1//4*x*a^-1*b^-1*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(b*d+-1*a*e)+1//8*a^-5//2*b^-3//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*(a*e+3*b*d)*arctan(x*a^-1//2*b^(1/2)))
@test integrate(x^-1*(a^2+b^2*x^4+2*a*b*x^2)^-3//2*(d+e*x^2), x) == :((1/2)*d*a^-2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+d*a^-3*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(x)+-1//2*d*a^-3*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a+b*x^2)+1//4*a^-1*b^-1*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(b*d+-1*a*e))
@test integrate(x^-2*(a^2+b^2*x^4+2*a*b*x^2)^-3//2*(d+e*x^2), x) == :(-1//8*x*a^-3*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(-3*a*e+7*b*d)+-1*d*a^-3*x^-1*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)+-1//4*x*a^-2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(b*d+-1*a*e)+-1//8*a^-7//2*b^-1//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*(-3*a*e+15*b*d)*arctan(x*a^-1//2*b^(1/2)))
@test integrate(x^-3*(a^2+b^2*x^4+2*a*b*x^2)^-3//2*(d+e*x^2), x) == :(-1//2*a^-3*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(-1*a*e+2*b*d)+-1//4*a^-2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(b*d+-1*a*e)+(1/2)*a^-4*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*(-1*a*e+3*b*d)*log(a+b*x^2)+-1*a^-4*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*(-1*a*e+3*b*d)*log(x)+-1//2*d*a^-3*x^-2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2))
@test integrate((f*x)^m*(a^2+b^2*x^4+2*a*b*x^2)^5//2*(d+e*x^2), x) == :(d*a^5*f^-1*(f*x)^(1+m)*(1+m)^-1*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+e*b^5*f^-13*(f*x)^(13+m)*(13+m)^-1*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+a^4*f^-3*(f*x)^(3+m)*(3+m)^-1*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)*(a*e+5*b*d)+b^4*f^-11*(f*x)^(11+m)*(11+m)^-1*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)*(b*d+5*a*e)+5*a*b^3*f^-9*(f*x)^(9+m)*(9+m)^-1*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)*(b*d+2*a*e)+5*b*a^3*f^-5*(f*x)^(5+m)*(5+m)^-1*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)*(a*e+2*b*d)+10*a^2*b^2*f^-7*(f*x)^(7+m)*(7+m)^-1*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)*(a*e+b*d))
@test integrate((f*x)^m*(a^2+b^2*x^4+2*a*b*x^2)^3//2*(d+e*x^2), x) == :(d*a^3*f^-1*(f*x)^(1+m)*(1+m)^-1*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+e*b^3*f^-9*(f*x)^(9+m)*(9+m)^-1*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+a^2*f^-3*(f*x)^(3+m)*(3+m)^-1*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)*(a*e+3*b*d)+b^2*f^-7*(f*x)^(7+m)*(7+m)^-1*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)*(b*d+3*a*e)+3*a*b*f^-5*(f*x)^(5+m)*(5+m)^-1*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)*(a*e+b*d))
@test integrate((f*x)^m*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)*(d+e*x^2), x) == :(f^-3*(f*x)^(3+m)*(3+m)^-1*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)*(a*e+b*d)+a*d*f^-1*(f*x)^(1+m)*(1+m)^-1*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+b*e*f^-5*(f*x)^(5+m)*(5+m)^-1*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate(x*(a^2+b^2*x^4+2*a*b*x^2)^p*(a+b*x^2), x) == :(1//4*b^-1*(1+p)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1+p))
@test integrate(x^3*(a^2+b^2*x^4+2*a*b*x^2)^p*(a+b*x^2), x) == :((1/2)*b^-2*(3+2p)^-1*(a+b*x^2)^3*(a^2+b^2*x^4+2*a*b*x^2)^p+-1//4*a*b^-2*(1+p)^-1*(a+b*x^2)^2*(a^2+b^2*x^4+2*a*b*x^2)^p)
@test integrate(x^5*(a^2+b^2*x^4+2*a*b*x^2)^p*(a+b*x^2), x) == :(1//4*b^-3*(2+p)^-1*(a+b*x^2)^4*(a^2+b^2*x^4+2*a*b*x^2)^p+-1*a*b^-3*(3+2p)^-1*(a+b*x^2)^3*(a^2+b^2*x^4+2*a*b*x^2)^p+1//4*a^2*b^-3*(1+p)^-1*(a+b*x^2)^2*(a^2+b^2*x^4+2*a*b*x^2)^p)
@test integrate(x^3*(a+b*x^2+c*x^4)^3*(A+B*x^2), x) == :(x^10*(1//10*A*(b^3+6*a*b*c)+3//10*B*a*(b^2+a*c))+x^12*(1//12*B*b^3+1//4*A*a*c^2+1//4*A*c*b^2+(1/2)*B*a*b*c)+1//4*A*a^3*x^4+1//6*a^2*x^6*(B*a+3*A*b)+1//16*c^2*x^16*(A*c+3*B*b)+1//18*B*c^3*x^18+3//8*a*x^8*(A*(b^2+a*c)+B*a*b)+3//14*c*x^14*(B*b^2+A*b*c+B*a*c))
@test integrate(x^2*(a+b*x^2+c*x^4)^3*(A+B*x^2), x) == :(x^9*(1//9*A*(b^3+6*a*b*c)+1//3*B*a*(b^2+a*c))+x^11*(1//11*B*b^3+3//11*A*a*c^2+3//11*A*c*b^2+6//11*B*a*b*c)+1//3*A*a^3*x^3+1//5*a^2*x^5*(B*a+3*A*b)+1//15*c^2*x^15*(A*c+3*B*b)+1//17*B*c^3*x^17+3//7*a*x^7*(A*(b^2+a*c)+B*a*b)+3//13*c*x^13*(B*b^2+A*b*c+B*a*c))
@test integrate(x*(a+b*x^2+c*x^4)^3*(A+B*x^2), x) == :(x^8*(1//8*A*(b^3+6*a*b*c)+3//8*B*a*(b^2+a*c))+x^10*(1//10*B*b^3+3//10*A*a*c^2+3//10*A*c*b^2+3//5*B*a*b*c)+(1/2)*A*a^3*x^2+(1/2)*a*x^6*(A*(b^2+a*c)+B*a*b)+1//4*c*x^12*(B*b^2+A*b*c+B*a*c)+1//4*a^2*x^4*(B*a+3*A*b)+1//14*c^2*x^14*(A*c+3*B*b)+1//16*B*c^3*x^16)
@test integrate((a+b*x^2+c*x^4)^3*(A+B*x^2), x) == :(x^7*(1//7*A*(b^3+6*a*b*c)+3//7*B*a*(b^2+a*c))+x^9*(1//9*B*b^3+1//3*A*a*c^2+1//3*A*c*b^2+2//3*B*a*b*c)+A*x*a^3+1//3*a^2*x^3*(B*a+3*A*b)+1//13*c^2*x^13*(A*c+3*B*b)+1//15*B*c^3*x^15+3//5*a*x^5*(A*(b^2+a*c)+B*a*b)+3//11*c*x^11*(B*b^2+A*b*c+B*a*c))
@test integrate(x^-1*(a+b*x^2+c*x^4)^3*(A+B*x^2), x) == :(x^6*(1//6*A*(b^3+6*a*b*c)+(1/2)*B*a*(b^2+a*c))+x^8*(1//8*B*b^3+3//8*A*a*c^2+3//8*A*c*b^2+3//4*B*a*b*c)+A*a^3*log(x)+(1/2)*a^2*x^2*(B*a+3*A*b)+1//12*c^2*x^12*(A*c+3*B*b)+1//14*B*c^3*x^14+3//4*a*x^4*(A*(b^2+a*c)+B*a*b)+3//10*c*x^10*(B*b^2+A*b*c+B*a*c))
@test integrate(x^-2*(a+b*x^2+c*x^4)^3*(A+B*x^2), x) == :(x^5*(1//5*A*(b^3+6*a*b*c)+3//5*B*a*(b^2+a*c))+x^7*(1//7*B*b^3+3//7*A*a*c^2+3//7*A*c*b^2+6//7*B*a*b*c)+a*x^3*(A*(b^2+a*c)+B*a*b)+x*a^2*(B*a+3*A*b)+-1*A*a^3*x^-1+1//3*c*x^9*(B*b^2+A*b*c+B*a*c)+1//11*c^2*x^11*(A*c+3*B*b)+1//13*B*c^3*x^13)
@test integrate(x^-3*(a+b*x^2+c*x^4)^3*(A+B*x^2), x) == :(x^4*(1//4*A*(b^3+6*a*b*c)+3//4*B*a*(b^2+a*c))+x^6*(1//6*B*b^3+(1/2)*A*a*c^2+(1/2)*A*c*b^2+B*a*b*c)+a^2*(B*a+3*A*b)*log(x)+-1//2*A*a^3*x^-2+1//10*c^2*x^10*(A*c+3*B*b)+1//12*B*c^3*x^12+3//2*a*x^2*(A*(b^2+a*c)+B*a*b)+3//8*c*x^8*(B*b^2+A*b*c+B*a*c))
@test integrate(x^5*(a+b*x^2+c*x^4)^-1*(A+B*x^2), x) == :(-1//2*c^-2*x^2*(B*b+-1*A*c)+1//4*B*c^-1*x^4+1//4*c^-3*(B*b^2+-1*A*b*c+-1*B*a*c)*log(a+b*x^2+c*x^4)+(1/2)*c^-3*(b^2+-4*a*c)^-1//2*(B*b^3+-1*A*c*b^2+2*A*a*c^2+-3*B*a*b*c)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x^2)))
@test integrate(x^3*(a+b*x^2+c*x^4)^-1*(A+B*x^2), x) == :((1/2)*B*c^-1*x^2+-1//4*c^-2*(B*b+-1*A*c)*log(a+b*x^2+c*x^4)+-1//2*c^-2*(b^2+-4*a*c)^-1//2*(B*b^2+-1*A*b*c+-2*B*a*c)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x^2)))
@test integrate(x*(a+b*x^2+c*x^4)^-1*(A+B*x^2), x) == :(1//4*B*c^-1*log(a+b*x^2+c*x^4)+(1/2)*c^-1*(b^2+-4*a*c)^-1//2*(B*b+-2*A*c)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x^2)))
@test integrate(x^-1*(a+b*x^2+c*x^4)^-1*(A+B*x^2), x) == :(A*a^-1*log(x)+-1//4*A*a^-1*log(a+b*x^2+c*x^4)+(1/2)*a^-1*(b^2+-4*a*c)^-1//2*(A*b+-2*B*a)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x^2)))
@test integrate(x^-3*(a+b*x^2+c*x^4)^-1*(A+B*x^2), x) == :(-1*a^-2*(A*b+-1*B*a)*log(x)+-1//2*A*a^-1*x^-2+1//4*a^-2*(A*b+-1*B*a)*log(a+b*x^2+c*x^4)+-1//2*a^-2*(b^2+-4*a*c)^-1//2*(A*b^2+-1*B*a*b+-2*A*a*c)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x^2)))
@test integrate(x^4*(a+b*x^2+c*x^4)^-1*(A+B*x^2), x) == :(-1*x*c^-2*(B*b+-1*A*c)+1//3*B*c^-1*x^3+(1/2)*2^(1/2)*c^-5//2*(b+(b^2+-4*a*c)^(1/2))^-1//2*(B*b^2+(b^2+-4*a*c)^-1//2*(B*b^3+-1*A*c*b^2+2*A*a*c^2+-3*B*a*b*c)+-1*A*b*c+-1*B*a*c)*arctan(x*2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2)+(1/2)*2^(1/2)*c^-5//2*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(B*b^2+-1*(b^2+-4*a*c)^-1//2*(B*b^3+-1*A*c*b^2+2*A*a*c^2+-3*B*a*b*c)+-1*A*b*c+-1*B*a*c)*arctan(x*2^(1/2)*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2))
@test integrate(x^2*(a+b*x^2+c*x^4)^-1*(A+B*x^2), x) == :(B*x*c^-1+-1//2*2^(1/2)*c^-3//2*(b+(b^2+-4*a*c)^(1/2))^-1//2*(B*b+(b^2+-4*a*c)^-1//2*(B*b^2+-1*A*b*c+-2*B*a*c)+-1*A*c)*arctan(x*2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2)+-1//2*2^(1/2)*c^-3//2*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(B*b+-1*A*c+-1*(b^2+-4*a*c)^-1//2*(B*b^2+-1*A*b*c+-2*B*a*c))*arctan(x*2^(1/2)*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2))
@test integrate((a+b*x^2+c*x^4)^-1*(A+B*x^2), x) == :((1/2)*2^(1/2)*c^-1//2*(b+(b^2+-4*a*c)^(1/2))^-1//2*(B+(b^2+-4*a*c)^-1//2*(B*b+-2*A*c))*arctan(x*2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2)+(1/2)*2^(1/2)*c^-1//2*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(B+-1*(b^2+-4*a*c)^-1//2*(B*b+-2*A*c))*arctan(x*2^(1/2)*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2))
@test integrate(x^-2*(a+b*x^2+c*x^4)^-1*(A+B*x^2), x) == :(-1*A*a^-1*x^-1+-1//2*2^(1/2)*a^-1*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2*(A+-1*(b^2+-4*a*c)^-1//2*(A*b+-2*B*a))*arctan(x*2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2)+-1//2*2^(1/2)*a^-1*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(A+(b^2+-4*a*c)^-1//2*(A*b+-2*B*a))*arctan(x*2^(1/2)*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2))
@test integrate(x^-4*(a+b*x^2+c*x^4)^-1*(A+B*x^2), x) == :(a^-2*x^-1*(A*b+-1*B*a)+-1//3*A*a^-1*x^-3+(1/2)*2^(1/2)*a^-2*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-1//2*(-1*A*(b^2+-1*b*(b^2+-4*a*c)^(1/2)+-2*a*c)+B*a*(b+-1*(b^2+-4*a*c)^(1/2)))*arctan(x*2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2)+-1//2*2^(1/2)*a^-2*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-1//2*(-1*A*(b^2+b*(b^2+-4*a*c)^(1/2)+-2*a*c)+B*a*(b+(b^2+-4*a*c)^(1/2)))*arctan(x*2^(1/2)*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2))
@test integrate(x^7*(a+b*x^2+c*x^4)^-2*(A+B*x^2), x) == :(-1//4*c^-3*(-1*A*c+2*B*b)*log(a+b*x^2+c*x^4)+(1/2)*c^-2*x^2*(b^2+-4*a*c)^-1*(2*B*b^2+-1*A*b*c+-6*B*a*c)+-1//2*c^-3*(b^2+-4*a*c)^-3//2*(2*B*b^4+-1*A*c*b^3+12*B*a^2*c^2+-12*B*a*c*b^2+6*A*a*b*c^2)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x^2))+-1//2*c^-1*x^4*(b^2+-4*a*c)^-1*(a+b*x^2+c*x^4)^-1*(a*(B*b+-2*A*c)+x^2*(B*b^2+-1*A*b*c+-2*B*a*c)))
@test integrate(x^5*(a+b*x^2+c*x^4)^-2*(A+B*x^2), x) == :(1//4*B*c^-2*log(a+b*x^2+c*x^4)+(1/2)*c^-2*(b^2+-4*a*c)^-3//2*(B*b^3+4*A*a*c^2+-6*B*a*b*c)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x^2))+-1//2*c^-1*x^2*(b^2+-4*a*c)^-1*(a+b*x^2+c*x^4)^-1*(a*(B*b+-2*A*c)+x^2*(B*b^2+-1*A*b*c+-2*B*a*c)))
@test integrate(x^3*(a+b*x^2+c*x^4)^-2*(A+B*x^2), x) == :(-1*(b^2+-4*a*c)^-3//2*(A*b+-2*B*a)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x^2))+-1//2*c^-1*(b^2+-4*a*c)^-1*(a+b*x^2+c*x^4)^-1*(a*(B*b+-2*A*c)+x^2*(B*b^2+-1*A*b*c+-2*B*a*c)))
@test integrate(x*(a+b*x^2+c*x^4)^-2*(A+B*x^2), x) == :(-1*(b^2+-4*a*c)^-3//2*(B*b+-2*A*c)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x^2))+-1*(2*b^2+-8*a*c)^-1*(a+b*x^2+c*x^4)^-1*(A*b+-1*x^2*(B*b+-2*A*c)+-2*B*a))
@test integrate(x^-1*(a+b*x^2+c*x^4)^-2*(A+B*x^2), x) == :(A*a^-2*log(x)+-1//4*A*a^-2*log(a+b*x^2+c*x^4)+(1/2)*a^-2*(b^2+-4*a*c)^-3//2*(A*(b^3+-6*a*b*c)+4*B*c*a^2)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x^2))+-1//2*a^-1*(b^2+-4*a*c)^-1*(a+b*x^2+c*x^4)^-1*(-1*A*(b^2+-2*a*c)+B*a*b+-1*c*x^2*(A*b+-2*B*a)))
@test integrate(x^-3*(a+b*x^2+c*x^4)^-2*(A+B*x^2), x) == :(-1*a^-3*(-1*B*a+2*A*b)*log(x)+1//4*a^-3*(-1*B*a+2*A*b)*log(a+b*x^2+c*x^4)+(1/2)*a^-3*(b^2+-4*a*c)^-3//2*(-2*A*(b^4+6*a^2*c^2+-6*a*c*b^2)+B*a*b*(b^2+-6*a*c))*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x^2))+-1//2*a^-2*x^-2*(b^2+-4*a*c)^-1*(2*A*b^2+-1*B*a*b+-6*A*a*c)+-1//2*a^-1*x^-2*(b^2+-4*a*c)^-1*(a+b*x^2+c*x^4)^-1*(-1*A*(b^2+-2*a*c)+B*a*b+-1*c*x^2*(A*b+-2*B*a)))
@test integrate(x^6*(a+b*x^2+c*x^4)^-2*(A+B*x^2), x) == :((1/2)*x*c^-2*(b^2+-4*a*c)^-1*(3*B*b^2+-1*A*b*c+-10*B*a*c)+-1*x^5*(2*b^2+-8*a*c)^-1*(a+b*x^2+c*x^4)^-1*(A*b+-1*x^2*(B*b+-2*A*c)+-2*B*a)+-1//2*c^-1*x^3*(b^2+-4*a*c)^-1*(B*b+-2*A*c)+-1//4*2^(1/2)*c^-5//2*(b+(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-1*((b^2+-4*a*c)^-1//2*(3*B*b^4+-1*A*c*b^3+20*B*a^2*c^2+-19*B*a*c*b^2+8*A*a*b*c^2)+3*B*b^3+-1*A*c*b^2+6*A*a*c^2+-13*B*a*b*c)*arctan(x*2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2)+-1//4*2^(1/2)*c^-5//2*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-1*(-1*(b^2+-4*a*c)^-1//2*(3*B*b^4+-1*A*c*b^3+20*B*a^2*c^2+-19*B*a*c*b^2+8*A*a*b*c^2)+3*B*b^3+-1*A*c*b^2+6*A*a*c^2+-13*B*a*b*c)*arctan(x*2^(1/2)*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2))
@test integrate(x^4*(a+b*x^2+c*x^4)^-2*(A+B*x^2), x) == :(-1*x^3*(2*b^2+-8*a*c)^-1*(a+b*x^2+c*x^4)^-1*(A*b+-1*x^2*(B*b+-2*A*c)+-2*B*a)+-1//2*x*c^-1*(b^2+-4*a*c)^-1*(B*b+-2*A*c)+1//4*2^(1/2)*c^-3//2*(b+(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-1*(B*b^2+(b^2+-4*a*c)^-1//2*(B*b^3+A*c*b^2+4*A*a*c^2+-8*B*a*b*c)+A*b*c+-6*B*a*c)*arctan(x*2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2)+1//4*2^(1/2)*c^-3//2*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-1*(B*b^2+-1*(b^2+-4*a*c)^-1//2*(B*b^3+A*c*b^2+4*A*a*c^2+-8*B*a*b*c)+A*b*c+-6*B*a*c)*arctan(x*2^(1/2)*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2))
@test integrate(x^2*(a+b*x^2+c*x^4)^-2*(A+B*x^2), x) == :(-1*x*(2*b^2+-8*a*c)^-1*(a+b*x^2+c*x^4)^-1*(A*b+-1*x^2*(B*b+-2*A*c)+-2*B*a)+1//4*2^(1/2)*c^-1//2*(b+(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-1*(B*b+(b^2+-4*a*c)^-1//2*(B*b^2+-4*A*b*c+4*B*a*c)+-2*A*c)*arctan(x*2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2)+1//4*2^(1/2)*c^-1//2*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-1*(B*b+-1*(b^2+-4*a*c)^-1//2*(B*b^2+-4*A*b*c+4*B*a*c)+-2*A*c)*arctan(x*2^(1/2)*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2))
@test integrate((a+b*x^2+c*x^4)^-2*(A+B*x^2), x) == :((1/2)*x*a^-1*(b^2+-4*a*c)^-1*(a+b*x^2+c*x^4)^-1*(A*b^2+c*x^2*(A*b+-2*B*a)+-1*B*a*b+-2*A*a*c)+1//4*2^(1/2)*a^-1*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-1*(A*b+-1*(b^2+-4*a*c)^-1//2*(A*b^2+-12*A*a*c+4*B*a*b)+-2*B*a)*arctan(x*2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2)+1//4*2^(1/2)*a^-1*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-1*(A*b+(b^2+-4*a*c)^-1//2*(A*(b^2+-12*a*c)+4*B*a*b)+-2*B*a)*arctan(x*2^(1/2)*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2))
@test integrate(x^-2*(a+b*x^2+c*x^4)^-2*(A+B*x^2), x) == :(-1//2*a^-2*x^-1*(b^2+-4*a*c)^-1*(3*A*b^2+-1*B*a*b+-10*A*a*c)+-1//2*a^-1*x^-1*(b^2+-4*a*c)^-1*(a+b*x^2+c*x^4)^-1*(-1*A*(b^2+-2*a*c)+B*a*b+-1*c*x^2*(A*b+-2*B*a))+-1//4*2^(1/2)*a^-2*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-1*((b^2+-4*a*c)^-1//2*(-1*A*(3*b^3+-16*a*b*c)+B*a*(b^2+-12*a*c))+3*A*b^2+-1*B*a*b+-10*A*a*c)*arctan(x*2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2)+1//4*2^(1/2)*a^-2*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-3//2*(-1*A*(3*b^3+3*b^2*(b^2+-4*a*c)^(1/2)+-16*a*b*c+-10*a*c*(b^2+-4*a*c)^(1/2))+B*a*(b^2+b*(b^2+-4*a*c)^(1/2)+-12*a*c))*arctan(x*2^(1/2)*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2))
@test integrate(x^-4*(a+b*x^2+c*x^4)^-2*(A+B*x^2), x) == :(-1//2*a^-3*x^-1*(b^2+-4*a*c)^-1*(-1*A*(5*b^3+-19*a*b*c)+B*a*(3*b^2+-10*a*c))+-1//6*a^-2*x^-3*(b^2+-4*a*c)^-1*(5*A*b^2+-14*A*a*c+-3*B*a*b)+-1//2*a^-1*x^-3*(b^2+-4*a*c)^-1*(a+b*x^2+c*x^4)^-1*(-1*A*(b^2+-2*a*c)+B*a*b+-1*c*x^2*(A*b+-2*B*a))+-1//4*2^(1/2)*a^-3*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-3//2*(-1*A*(5*b^4+5*b^3*(b^2+-4*a*c)^(1/2)+28*a^2*c^2+-29*a*c*b^2+-19*a*b*c*(b^2+-4*a*c)^(1/2))+B*a*(3*b^3+3*b^2*(b^2+-4*a*c)^(1/2)+-16*a*b*c+-10*a*c*(b^2+-4*a*c)^(1/2)))*arctan(x*2^(1/2)*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2)+1//4*2^(1/2)*a^-3*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-3//2*(-1*A*(5*b^4+-5*b^3*(b^2+-4*a*c)^(1/2)+28*a^2*c^2+-29*a*c*b^2+19*a*b*c*(b^2+-4*a*c)^(1/2))+B*a*(3*b^3+-3*b^2*(b^2+-4*a*c)^(1/2)+-16*a*b*c+10*a*c*(b^2+-4*a*c)^(1/2)))*arctan(x*2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2))
@test integrate(x^11*(a+b*x^2+c*x^4)^-3*(A+B*x^2), x) == :(-1//4*c^-4*(-1*A*c+3*B*b)*log(a+b*x^2+c*x^4)+(1/2)*c^-3*x^2*(b^2+-4*a*c)^-2*(3*B*b^4+-1*A*c*b^3+30*B*a^2*c^2+-21*B*a*c*b^2+7*A*a*b*c^2)+-1//2*c^-4*(b^2+-4*a*c)^-5//2*(3*B*b^6+-1*A*c*b^5+-60*B*a^3*c^3+-30*A*b*a^2*c^3+-30*B*a*c*b^4+10*A*a*b^3*c^2+90*B*a^2*b^2*c^2)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x^2))+-1//4*c^-1*x^8*(b^2+-4*a*c)^-1*(a+b*x^2+c*x^4)^-2*(a*(B*b+-2*A*c)+x^2*(B*b^2+-1*A*b*c+-2*B*a*c))+-1//4*c^-2*x^4*(b^2+-4*a*c)^-2*(a+b*x^2+c*x^4)^-1*(a*(3*B*b^3+-1*A*c*b^2+16*A*a*c^2+-18*B*a*b*c)+x^2*(3*B*b^4+-1*A*c*b^3+20*B*a^2*c^2+-20*B*a*c*b^2+10*A*a*b*c^2)))
@test integrate(x^9*(a+b*x^2+c*x^4)^-3*(A+B*x^2), x) == :(1//4*B*c^-3*log(a+b*x^2+c*x^4)+(1/2)*c^-3*(b^2+-4*a*c)^-5//2*(B*b^5+-12*A*a^2*c^3+-10*B*a*c*b^3+30*B*b*a^2*c^2)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x^2))+-1//4*c^-1*x^6*(b^2+-4*a*c)^-1*(a+b*x^2+c*x^4)^-2*(a*(B*b+-2*A*c)+x^2*(B*b^2+-1*A*b*c+-2*B*a*c))+-1//4*c^-2*x^2*(b^2+-4*a*c)^-2*(a+b*x^2+c*x^4)^-1*(x^2*(2*B*b^4+16*B*a^2*c^2+-15*B*a*c*b^2+6*A*a*b*c^2)+2*a*(B*b^3+6*A*a*c^2+-7*B*a*b*c)))
@test integrate(x^7*(a+b*x^2+c*x^4)^-3*(A+B*x^2), x) == :(-1*x^6*(4*b^2+-16*a*c)^-1*(a+b*x^2+c*x^4)^-2*(A*b+-1*x^2*(B*b+-2*A*c)+-2*B*a)+3*a*(b^2+-4*a*c)^-5//2*(A*b+-2*B*a)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x^2))+1//4*x^2*(b^2+-4*a*c)^-2*(a+b*x^2+c*x^4)^-1*(2a+b*x^2)*(-6*B*a+3*A*b))
@test integrate(x^5*(a+b*x^2+c*x^4)^-3*(A+B*x^2), x) == :((b^2+-4*a*c)^-5//2*(-1*A*(b^2+2*a*c)+3*B*a*b)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x^2))+-1*x^4*(4*b^2+-16*a*c)^-1*(a+b*x^2+c*x^4)^-2*(A*b+-1*x^2*(B*b+-2*A*c)+-2*B*a)+-1//4*c^-1*(b^2+-4*a*c)^-2*(a+b*x^2+c*x^4)^-1*(a*(B*b^2+-6*A*b*c+8*B*a*c)+x^2*(B*b^3+-4*A*c*b^2+4*A*a*c^2+2*B*a*b*c)))
@test integrate(x^3*(a+b*x^2+c*x^4)^-3*(A+B*x^2), x) == :(-1*(b^2+-4*a*c)^-5//2*(B*b^2+-3*A*b*c+2*B*a*c)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x^2))+-1//4*c^-1*(b^2+-4*a*c)^-1*(a+b*x^2+c*x^4)^-2*(a*(B*b+-2*A*c)+x^2*(B*b^2+-1*A*b*c+-2*B*a*c))+1//4*c^-1*(b^2+-4*a*c)^-2*(a+b*x^2+c*x^4)^-1*(b+2*c*x^2)*(B*b^2+-3*A*b*c+2*B*a*c))
@test integrate(x*(a+b*x^2+c*x^4)^-3*(A+B*x^2), x) == :(-1*(4*b^2+-16*a*c)^-1*(a+b*x^2+c*x^4)^-2*(A*b+-1*x^2*(B*b+-2*A*c)+-2*B*a)+3*c*(b^2+-4*a*c)^-5//2*(B*b+-2*A*c)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x^2))+-1//4*(b^2+-4*a*c)^-2*(a+b*x^2+c*x^4)^-1*(b+2*c*x^2)*(-6*A*c+3*B*b))
@test integrate(x^-1*(a+b*x^2+c*x^4)^-3*(A+B*x^2), x) == :(A*a^-3*log(x)+-1//4*A*a^-3*log(a+b*x^2+c*x^4)+-1//2*a^-3*(b^2+-4*a*c)^-5//2*(-1*A*(b^5+-10*a*c*b^3+30*b*a^2*c^2)+12*B*a^3*c^2)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x^2))+-1//4*a^-1*(b^2+-4*a*c)^-1*(a+b*x^2+c*x^4)^-2*(-1*A*(b^2+-2*a*c)+B*a*b+-1*c*x^2*(A*b+-2*B*a))+1//4*a^-2*(b^2+-4*a*c)^-2*(a+b*x^2+c*x^4)^-1*(A*(2*b^4+16*a^2*c^2+-15*a*c*b^2)+2*c*x^2*(A*(b^3+-7*a*b*c)+6*B*c*a^2)+6*B*b*c*a^2))
@test integrate(x^-3*(a+b*x^2+c*x^4)^-3*(A+B*x^2), x) == :(-1*a^-4*(-1*B*a+3*A*b)*log(x)+1//4*a^-4*(-1*B*a+3*A*b)*log(a+b*x^2+c*x^4)+(1/2)*a^-4*(b^2+-4*a*c)^-5//2*(-3*A*(b^6+-20*a^3*c^3+-10*a*c*b^4+30*a^2*b^2*c^2)+B*a*b*(b^4+30*a^2*c^2+-10*a*c*b^2))*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x^2))+(1/2)*a^-3*x^-2*(b^2+-4*a*c)^-2*(-3*A*(b^4+10*a^2*c^2+-7*a*c*b^2)+B*a*b*(b^2+-7*a*c))+-1//4*a^-1*x^-2*(b^2+-4*a*c)^-1*(a+b*x^2+c*x^4)^-2*(-1*A*(b^2+-2*a*c)+B*a*b+-1*c*x^2*(A*b+-2*B*a))+-1//4*a^-2*x^-2*(b^2+-4*a*c)^-2*(a+b*x^2+c*x^4)^-1*(-1*A*(3*b^4+20*a^2*c^2+-20*a*c*b^2)+c*x^2*(-3*A*(b^3+-6*a*b*c)+B*a*(b^2+-16*a*c))+B*a*b*(b^2+-10*a*c)))
@test integrate(x^8*(a+b*x^2+c*x^4)^-3*(A+B*x^2), x) == :(-1*x^7*(4*b^2+-16*a*c)^-1*(a+b*x^2+c*x^4)^-2*(A*b+-1*x^2*(B*b+-2*A*c)+-2*B*a)+-1//8*x*c^-2*(b^2+-4*a*c)^-2*(3*B*b^3+A*c*b^2+20*A*a*c^2+-24*B*a*b*c)+-1//8*x^5*(b^2+-4*a*c)^-2*(a+b*x^2+c*x^4)^-1*(x^2*(B*b^2+-28*B*a*c+12*A*b*c)+7*A*b^2+-12*B*a*b+-4*A*a*c)+1//8*c^-1*x^3*(b^2+-4*a*c)^-2*(B*b^2+-28*B*a*c+12*A*b*c)+1//16*2^(1/2)*c^-5//2*(b+(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-2*((b^2+-4*a*c)^-1//2*(3*B*b^5+A*c*b^4+-40*A*a^2*c^3+-33*B*a*c*b^3+-18*A*a*b^2*c^2+132*B*b*a^2*c^2)+3*B*b^4+A*c*b^3+84*B*a^2*c^2+-27*B*a*c*b^2+-16*A*a*b*c^2)*arctan(x*2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2)+1//16*2^(1/2)*c^-5//2*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-2*(-1*(b^2+-4*a*c)^-1//2*(3*B*b^5+A*c*b^4+-40*A*a^2*c^3+-33*B*a*c*b^3+-18*A*a*b^2*c^2+132*B*b*a^2*c^2)+3*B*b^4+A*c*b^3+84*B*a^2*c^2+-27*B*a*c*b^2+-16*A*a*b*c^2)*arctan(x*2^(1/2)*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2))
@test integrate(x^6*(a+b*x^2+c*x^4)^-3*(A+B*x^2), x) == :(-1*x^5*(4*b^2+-16*a*c)^-1*(a+b*x^2+c*x^4)^-2*(A*b+-1*x^2*(B*b+-2*A*c)+-2*B*a)+-1//8*x*c^-1*(b^2+-4*a*c)^-2*(B*b^2+-12*A*b*c+20*B*a*c)+-1//8*x^3*(b^2+-4*a*c)^-2*(a+b*x^2+c*x^4)^-1*(-1*x^2*(B*b^2+-12*A*b*c+20*B*a*c)+5*A*b^2+-12*B*a*b+4*A*a*c)+1//16*2^(1/2)*c^-3//2*(b+(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-2*(B*b^3+(b^2+-4*a*c)^-1//2*(B*b^4+-40*B*a^2*c^2+3*A*c*b^3+-18*B*a*c*b^2+36*A*a*b*c^2)+3*A*c*b^2+12*A*a*c^2+-16*B*a*b*c)*arctan(x*2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2)+1//16*2^(1/2)*c^-3//2*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-2*(B*b^3+-1*(b^2+-4*a*c)^-1//2*(B*b^4+-40*B*a^2*c^2+3*A*c*b^3+-18*B*a*c*b^2+36*A*a*b*c^2)+3*A*c*b^2+12*A*a*c^2+-16*B*a*b*c)*arctan(x*2^(1/2)*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2))
@test integrate(x^4*(a+b*x^2+c*x^4)^-3*(A+B*x^2), x) == :(-1*x^3*(4*b^2+-16*a*c)^-1*(a+b*x^2+c*x^4)^-2*(A*b+-1*x^2*(B*b+-2*A*c)+-2*B*a)+3//8*x*(b^2+-4*a*c)^-2*(a+b*x^2+c*x^4)^-1*(x^2*(B*b^2+-4*A*b*c+4*B*a*c)+-1*A*(b^2+4*a*c)+4*B*a*b)+1//16*2^(1/2)*c^-1//2*(b+(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-2*(3*B*b^2+3*(b^2+-4*a*c)^-1//2*(B*b^3+-8*A*a*c^2+-6*A*c*b^2+12*B*a*b*c)+-12*A*b*c+12*B*a*c)*arctan(x*2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2)+1//16*2^(1/2)*c^-1//2*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-2*(-3*(b^2+-4*a*c)^-1//2*(B*b^3+-8*A*a*c^2+-6*A*c*b^2+12*B*a*b*c)+3*B*b^2+-12*A*b*c+12*B*a*c)*arctan(x*2^(1/2)*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2))
@test integrate(x^2*(a+b*x^2+c*x^4)^-3*(A+B*x^2), x) == :(-1*x*(4*b^2+-16*a*c)^-1*(a+b*x^2+c*x^4)^-2*(A*b+-1*x^2*(B*b+-2*A*c)+-2*B*a)+-1//8*x*a^-1*(b^2+-4*a*c)^-2*(a+b*x^2+c*x^4)^-1*(-1*A*(b^3+8*a*b*c)+B*a*(7*b^2+-4*a*c)+c*x^2*(-1*A*(b^2+20*a*c)+12*B*a*b))+-1//16*2^(1/2)*a^-1*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-5//2*(A*(b^3+-1*b^2*(b^2+-4*a*c)^(1/2)+-52*a*b*c+-20*a*c*(b^2+-4*a*c)^(1/2))+6*B*a*(3*b^2+2*b*(b^2+-4*a*c)^(1/2)+4*a*c))*arctan(x*2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2)+1//16*2^(1/2)*a^-1*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-5//2*(A*(b^3+b^2*(b^2+-4*a*c)^(1/2)+-52*a*b*c+20*a*c*(b^2+-4*a*c)^(1/2))+6*B*a*(3*b^2+-2*b*(b^2+-4*a*c)^(1/2)+4*a*c))*arctan(x*2^(1/2)*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2))
@test integrate((a+b*x^2+c*x^4)^-3*(A+B*x^2), x) == :(1//4*x*a^-1*(b^2+-4*a*c)^-1*(a+b*x^2+c*x^4)^-2*(A*b^2+c*x^2*(A*b+-2*B*a)+-1*B*a*b+-2*A*a*c)+1//8*x*a^-2*(b^2+-4*a*c)^-2*(a+b*x^2+c*x^4)^-1*(A*(3*b^4+28*a^2*c^2+-25*a*c*b^2)+c*x^2*(3*A*(b^3+-8*a*b*c)+B*a*(b^2+20*a*c))+B*a*b*(b^2+8*a*c))+1//16*2^(1/2)*a^-2*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-2*(-1*(b^2+-4*a*c)^-1//2*(3*A*(b^4+56*a^2*c^2+-10*a*c*b^2)+B*a*b*(b^2+-52*a*c))+3*A*(b^3+-8*a*b*c)+B*a*(b^2+20*a*c))*arctan(x*2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2)+1//16*2^(1/2)*a^-2*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-2*((b^2+-4*a*c)^-1//2*(3*A*(b^4+56*a^2*c^2+-10*a*c*b^2)+B*a*b*(b^2+-52*a*c))+3*A*(b^3+-8*a*b*c)+B*a*(b^2+20*a*c))*arctan(x*2^(1/2)*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2))
@test integrate(x*(4+x^4+-5*x^2)^-1*(-7+4*x^2), x) == :((1/2)*log(1+-1*x^2)+3//2*log(4+-1*x^2))
@test integrate((4+x^4+-5*x^2)^-1*(-7x+4*x^3), x) == :((1/2)*log(1+-1*x^2)+3//2*log(4+-1*x^2))
@test integrate(x*(1+x^2+x^4)^-1*(2+x^2), x) == :(1//4*log(1+x^2+x^4)+(1/2)*3^(1/2)*arctan(1//3*3^(1/2)*(1+2*x^2)))
@test integrate((1+x^2+x^4)^-1*(x^3+2x), x) == :(1//4*log(1+x^2+x^4)+(1/2)*3^(1/2)*arctan(1//3*3^(1/2)*(1+2*x^2)))
@test integrate((3+x^4+2*x^2)^-2*(2*x^3+11x), x) == :((24+8*x^4+16*x^2)^-1*(5+9*x^2)+9//16*2^(1/2)*arctan((1/2)*2^(1/2)*(1+x^2)))
@test integrate(x^5*(3+x^4+5*x^2)^(1/2)*(2+3*x^2), x) == :(21229//512*arctanh((1/2)*(3+x^4+5*x^2)^-1//2*(5+2*x^2))+(3+x^4+5*x^2)^(1/2)*(-8165//256+-1633//128*x^2)+(3+x^4+5*x^2)^3//2*(1837//480+-17//16*x^2)+3//10*x^4*(3+x^4+5*x^2)^3//2)
@test integrate(x^3*(3+x^4+5*x^2)^(1/2)*(2+3*x^2), x) == :(-3367//256*arctanh((1/2)*(3+x^4+5*x^2)^-1//2*(5+2*x^2))+-1//48*(3+x^4+5*x^2)^3//2*(59+-18*x^2)+1//128*(3+x^4+5*x^2)^(1/2)*(1295+518*x^2))
@test integrate(x*(3+x^4+5*x^2)^(1/2)*(2+3*x^2), x) == :((1/2)*(3+x^4+5*x^2)^3//2+143//32*arctanh((1/2)*(3+x^4+5*x^2)^-1//2*(5+2*x^2))+1//16*(3+x^4+5*x^2)^(1/2)*(-55+-22*x^2))
@test integrate(x^-1*(3+x^4+5*x^2)^(1/2)*(2+3*x^2), x) == :(1//16*arctanh((1/2)*(3+x^4+5*x^2)^-1//2*(5+2*x^2))+-1*3^(1/2)*arctanh(1//6*3^(1/2)*(3+x^4+5*x^2)^-1//2*(6+5*x^2))+1//8*(3+x^4+5*x^2)^(1/2)*(23+6*x^2))
@test integrate(x^-3*(3+x^4+5*x^2)^(1/2)*(2+3*x^2), x) == :(19//4*arctanh((1/2)*(3+x^4+5*x^2)^-1//2*(5+2*x^2))+-7//3*3^(1/2)*arctanh(1//6*3^(1/2)*(3+x^4+5*x^2)^-1//2*(6+5*x^2))+-1//2*x^-2*(3+x^4+5*x^2)^(1/2)*(2+-3*x^2))
@test integrate(x^-5*(3+x^4+5*x^2)^(1/2)*(2+3*x^2), x) == :(3//2*arctanh((1/2)*(3+x^4+5*x^2)^-1//2*(5+2*x^2))+-77//72*3^(1/2)*arctanh(1//6*3^(1/2)*(3+x^4+5*x^2)^-1//2*(6+5*x^2))+-1//12*x^-4*(3+x^4+5*x^2)^(1/2)*(6+23*x^2))
@test integrate(x^-7*(3+x^4+5*x^2)^(1/2)*(2+3*x^2), x) == :(-1//9*x^-6*(3+x^4+5*x^2)^3//2+13//108*3^(1/2)*arctanh(1//6*3^(1/2)*(3+x^4+5*x^2)^-1//2*(6+5*x^2))+-1//18*x^-4*(3+x^4+5*x^2)^(1/2)*(6+5*x^2))
@test integrate(x^-9*(3+x^4+5*x^2)^(1/2)*(2+3*x^2), x) == :(-871//10368*3^(1/2)*arctanh(1//6*3^(1/2)*(3+x^4+5*x^2)^-1//2*(6+5*x^2))+-11//216*x^-6*(3+x^4+5*x^2)^3//2+-1//12*x^-8*(3+x^4+5*x^2)^3//2+1//1728*x^-4*(3+x^4+5*x^2)^(1/2)*(402+335*x^2))
@test integrate(x^-11*(3+x^4+5*x^2)^(1/2)*(2+3*x^2), x) == :(-1//15*x^-10*(3+x^4+5*x^2)^3//2+-1//36*x^-8*(3+x^4+5*x^2)^3//2+173//3240*x^-6*(3+x^4+5*x^2)^3//2+2093//31104*3^(1/2)*arctanh(1//6*3^(1/2)*(3+x^4+5*x^2)^-1//2*(6+5*x^2))+-1//5184*x^-4*(3+x^4+5*x^2)^(1/2)*(966+805*x^2))
@test integrate(x^4*(3+x^4+5*x^2)^(1/2)*(2+3*x^2), x) == :(-26//35*x^3*(3+x^4+5*x^2)^(1/2)+13//3*x*(3+x^4+5*x^2)^(1/2)+-1924//105*x*(3+x^4+5*x^2)^-1//2*(5+13^(1/2)+2*x^2)+1//21*x^5*(3+x^4+5*x^2)^(1/2)*(11+7*x^2)+-13*((6+x^2*(5+13^(1/2)))^-1*(6+x^2*(5+-1*13^(1/2))))^(1/2)*(30+6*13^(1/2))^-1//2*(3+x^4+5*x^2)^-1//2*(6+x^2*(5+13^(1/2)))*Elliptic.F(arctan(x*(5//6+1//6*13^(1/2))^(1/2)),-13//6+5//6*13^(1/2))+962//105*((6+x^2*(5+13^(1/2)))^-1*(6+x^2*(5+-1*13^(1/2))))^(1/2)*(10//3+2//3*13^(1/2))^(1/2)*(3+x^4+5*x^2)^-1//2*(6+x^2*(5+13^(1/2)))*Elliptic.E(arctan(x*(5//6+1//6*13^(1/2))^(1/2)),-13//6+5//6*13^(1/2)))
@test integrate(x^2*(3+x^4+5*x^2)^(1/2)*(2+3*x^2), x) == :(-4//3*x*(3+x^4+5*x^2)^(1/2)+1//35*x^3*(3+x^4+5*x^2)^(1/2)*(29+15*x^2)+1247//210*x*(3+x^4+5*x^2)^-1//2*(5+13^(1/2)+2*x^2)+-1247//210*((6+x^2*(5+13^(1/2)))^-1*(6+x^2*(5+-1*13^(1/2))))^(1/2)*(5//6+1//6*13^(1/2))^(1/2)*(3+x^4+5*x^2)^-1//2*(6+x^2*(5+13^(1/2)))*Elliptic.E(arctan(x*(5//6+1//6*13^(1/2))^(1/2)),-13//6+5//6*13^(1/2))+2*2^(1/2)*((6+x^2*(5+13^(1/2)))^-1*(6+x^2*(5+-1*13^(1/2))))^(1/2)*(15+3*13^(1/2))^-1//2*(3+x^4+5*x^2)^-1//2*(6+x^2*(5+13^(1/2)))*Elliptic.F(arctan(x*(5//6+1//6*13^(1/2))^(1/2)),-13//6+5//6*13^(1/2)))
@test integrate((3+x^4+5*x^2)^(1/2)*(2+3*x^2), x) == :(-23//15*x*(3+x^4+5*x^2)^-1//2*(5+13^(1/2)+2*x^2)+1//15*x*(3+x^4+5*x^2)^(1/2)*(25+9*x^2)+((6+x^2*(5+13^(1/2)))^-1*(6+x^2*(5+-1*13^(1/2))))^(1/2)*(30+6*13^(1/2))^-1//2*(3+x^4+5*x^2)^-1//2*(6+x^2*(5+13^(1/2)))*Elliptic.F(arctan(x*(5//6+1//6*13^(1/2))^(1/2)),-13//6+5//6*13^(1/2))+23//15*((6+x^2*(5+13^(1/2)))^-1*(6+x^2*(5+-1*13^(1/2))))^(1/2)*(5//6+1//6*13^(1/2))^(1/2)*(3+x^4+5*x^2)^-1//2*(6+x^2*(5+13^(1/2)))*Elliptic.E(arctan(x*(5//6+1//6*13^(1/2))^(1/2)),-13//6+5//6*13^(1/2)))
@test integrate(x^-2*(3+x^4+5*x^2)^(1/2)*(2+3*x^2), x) == :(-1*x^-1*(3+x^4+5*x^2)^(1/2)*(2+-1*x^2)+9//2*x*(3+x^4+5*x^2)^-1//2*(5+13^(1/2)+2*x^2)+-3//2*((6+x^2*(5+13^(1/2)))^-1*(6+x^2*(5+-1*13^(1/2))))^(1/2)*(15//2+3//2*13^(1/2))^(1/2)*(3+x^4+5*x^2)^-1//2*(6+x^2*(5+13^(1/2)))*Elliptic.E(arctan(x*(5//6+1//6*13^(1/2))^(1/2)),-13//6+5//6*13^(1/2))+8*2^(1/2)*((6+x^2*(5+13^(1/2)))^-1*(6+x^2*(5+-1*13^(1/2))))^(1/2)*(15+3*13^(1/2))^-1//2*(3+x^4+5*x^2)^-1//2*(6+x^2*(5+13^(1/2)))*Elliptic.F(arctan(x*(5//6+1//6*13^(1/2))^(1/2)),-13//6+5//6*13^(1/2)))
@test integrate(x^-4*(3+x^4+5*x^2)^(1/2)*(2+3*x^2), x) == :(-64//9*x^-1*(3+x^4+5*x^2)^(1/2)+-1//3*x^-3*(3+x^4+5*x^2)^(1/2)*(2+-9*x^2)+32//9*x*(3+x^4+5*x^2)^-1//2*(5+13^(1/2)+2*x^2)+-16//9*((6+x^2*(5+13^(1/2)))^-1*(6+x^2*(5+-1*13^(1/2))))^(1/2)*(10//3+2//3*13^(1/2))^(1/2)*(3+x^4+5*x^2)^-1//2*(6+x^2*(5+13^(1/2)))*Elliptic.E(arctan(x*(5//6+1//6*13^(1/2))^(1/2)),-13//6+5//6*13^(1/2))+49//3*((6+x^2*(5+13^(1/2)))^-1*(6+x^2*(5+-1*13^(1/2))))^(1/2)*(30+6*13^(1/2))^-1//2*(3+x^4+5*x^2)^-1//2*(6+x^2*(5+13^(1/2)))*Elliptic.F(arctan(x*(5//6+1//6*13^(1/2))^(1/2)),-13//6+5//6*13^(1/2)))
@test integrate(x^5*(3+x^4+5*x^2)^3//2*(2+3*x^2), x) == :(-368927//4096*arctanh((1/2)*(3+x^4+5*x^2)^-1//2*(5+2*x^2))+-1*(3+x^4+5*x^2)^3//2*(10915//768+2183//384*x^2)+1//1680*(3+x^4+5*x^2)^5//2*(3313+-1070*x^2)+1//2048*(3+x^4+5*x^2)^(1/2)*(141895+56758*x^2)+3//14*x^4*(3+x^4+5*x^2)^5//2)
@test integrate(x^3*(3+x^4+5*x^2)^3//2*(2+3*x^2), x) == :(62361//2048*arctanh((1/2)*(3+x^4+5*x^2)^-1//2*(5+2*x^2))+(3+x^4+5*x^2)^3//2*(615//128+123//64*x^2)+-1*(3+x^4+5*x^2)^5//2*(27//40+-1//4*x^2)+-1//1024*(3+x^4+5*x^2)^(1/2)*(23985+9594*x^2))
@test integrate(x*(3+x^4+5*x^2)^3//2*(2+3*x^2), x) == :(-5577//512*arctanh((1/2)*(3+x^4+5*x^2)^-1//2*(5+2*x^2))+3//10*(3+x^4+5*x^2)^5//2+(3+x^4+5*x^2)^(1/2)*(2145//256+429//128*x^2)+-1*(3+x^4+5*x^2)^3//2*(55//32+11//16*x^2))
@test integrate(x^-1*(3+x^4+5*x^2)^3//2*(2+3*x^2), x) == :(2401//256*arctanh((1/2)*(3+x^4+5*x^2)^-1//2*(5+2*x^2))+(3+x^4+5*x^2)^(1/2)*(199//128+-37//64*x^2)+(3+x^4+5*x^2)^3//2*(61//48+3//8*x^2)+-3*3^(1/2)*arctanh(1//6*3^(1/2)*(3+x^4+5*x^2)^-1//2*(6+5*x^2)))
@test integrate(x^-3*(3+x^4+5*x^2)^3//2*(2+3*x^2), x) == :(609//32*arctanh((1/2)*(3+x^4+5*x^2)^-1//2*(5+2*x^2))+(3+x^4+5*x^2)^(1/2)*(327//16+27//8*x^2)+-12*3^(1/2)*arctanh(1//6*3^(1/2)*(3+x^4+5*x^2)^-1//2*(6+5*x^2))+-1//2*x^-2*(3+x^4+5*x^2)^3//2*(2+-1*x^2))
@test integrate(x^-5*(3+x^4+5*x^2)^3//2*(2+3*x^2), x) == :(453//16*arctanh((1/2)*(3+x^4+5*x^2)^-1//2*(5+2*x^2))+-127//8*3^(1/2)*arctanh(1//6*3^(1/2)*(3+x^4+5*x^2)^-1//2*(6+5*x^2))+-1//4*x^-4*(3+x^4+5*x^2)^3//2*(2+-3*x^2)+-1//8*x^-2*(3+x^4+5*x^2)^(1/2)*(84+-57*x^2))
@test integrate(x^-7*(3+x^4+5*x^2)^3//2*(2+3*x^2), x) == :(49//4*arctanh((1/2)*(3+x^4+5*x^2)^-1//2*(5+2*x^2))+-527//72*3^(1/2)*arctanh(1//6*3^(1/2)*(3+x^4+5*x^2)^-1//2*(6+5*x^2))+-1//6*x^-6*(3+x^4+5*x^2)^3//2*(2+7*x^2)+-1//12*x^-2*(3+x^4+5*x^2)^(1/2)*(67+-32*x^2))
@test integrate(x^4*(3+x^4+5*x^2)^3//2*(2+3*x^2), x) == :(-4210//429*x*(3+x^4+5*x^2)^(1/2)+1251//715*x^3*(3+x^4+5*x^2)^(1/2)+-1//429*x^5*(3+x^4+5*x^2)^(1/2)*(283+272*x^2)+1//143*x^5*(3+x^4+5*x^2)^3//2*(71+33*x^2)+176723//4290*x*(3+x^4+5*x^2)^-1//2*(5+13^(1/2)+2*x^2)+-176723//4290*((6+x^2*(5+13^(1/2)))^-1*(6+x^2*(5+-1*13^(1/2))))^(1/2)*(5//6+1//6*13^(1/2))^(1/2)*(3+x^4+5*x^2)^-1//2*(6+x^2*(5+13^(1/2)))*Elliptic.E(arctan(x*(5//6+1//6*13^(1/2))^(1/2)),-13//6+5//6*13^(1/2))+2105//143*2^(1/2)*((6+x^2*(5+13^(1/2)))^-1*(6+x^2*(5+-1*13^(1/2))))^(1/2)*(15+3*13^(1/2))^-1//2*(3+x^4+5*x^2)^-1//2*(6+x^2*(5+13^(1/2)))*Elliptic.F(arctan(x*(5//6+1//6*13^(1/2))^(1/2)),-13//6+5//6*13^(1/2)))
@test integrate(x^2*(3+x^4+5*x^2)^3//2*(2+3*x^2), x) == :(353//99*x*(3+x^4+5*x^2)^(1/2)+-49949//3465*x*(3+x^4+5*x^2)^-1//2*(5+13^(1/2)+2*x^2)+-1//1155*x^3*(3+x^4+5*x^2)^(1/2)*(911+890*x^2)+1//99*x^3*(3+x^4+5*x^2)^3//2*(67+27*x^2)+-353//33*((6+x^2*(5+13^(1/2)))^-1*(6+x^2*(5+-1*13^(1/2))))^(1/2)*(30+6*13^(1/2))^-1//2*(3+x^4+5*x^2)^-1//2*(6+x^2*(5+13^(1/2)))*Elliptic.F(arctan(x*(5//6+1//6*13^(1/2))^(1/2)),-13//6+5//6*13^(1/2))+49949//3465*((6+x^2*(5+13^(1/2)))^-1*(6+x^2*(5+-1*13^(1/2))))^(1/2)*(5//6+1//6*13^(1/2))^(1/2)*(3+x^4+5*x^2)^-1//2*(6+x^2*(5+13^(1/2)))*Elliptic.E(arctan(x*(5//6+1//6*13^(1/2))^(1/2)),-13//6+5//6*13^(1/2)))
@test integrate((3+x^4+5*x^2)^3//2*(2+3*x^2), x) == :(-1//15*x*(3+x^4+5*x^2)^(1/2)*(5+12*x^2)+1//3*x*(3+x^4+5*x^2)^3//2*(3+x^2)+203//30*x*(3+x^4+5*x^2)^-1//2*(5+13^(1/2)+2*x^2)+-203//30*((6+x^2*(5+13^(1/2)))^-1*(6+x^2*(5+-1*13^(1/2))))^(1/2)*(5//6+1//6*13^(1/2))^(1/2)*(3+x^4+5*x^2)^-1//2*(6+x^2*(5+13^(1/2)))*Elliptic.E(arctan(x*(5//6+1//6*13^(1/2))^(1/2)),-13//6+5//6*13^(1/2))+5*2^(1/2)*((6+x^2*(5+13^(1/2)))^-1*(6+x^2*(5+-1*13^(1/2))))^(1/2)*(15+3*13^(1/2))^-1//2*(3+x^4+5*x^2)^-1//2*(6+x^2*(5+13^(1/2)))*Elliptic.F(arctan(x*(5//6+1//6*13^(1/2))^(1/2)),-13//6+5//6*13^(1/2)))
@test integrate(x^-2*(3+x^4+5*x^2)^3//2*(2+3*x^2), x) == :(-1//7*x^-1*(3+x^4+5*x^2)^3//2*(14+-3*x^2)+1//35*x*(3+x^4+5*x^2)^(1/2)*(655+129*x^2)+412//35*x*(3+x^4+5*x^2)^-1//2*(5+13^(1/2)+2*x^2)+-206//35*((6+x^2*(5+13^(1/2)))^-1*(6+x^2*(5+-1*13^(1/2))))^(1/2)*(10//3+2//3*13^(1/2))^(1/2)*(3+x^4+5*x^2)^-1//2*(6+x^2*(5+13^(1/2)))*Elliptic.E(arctan(x*(5//6+1//6*13^(1/2))^(1/2)),-13//6+5//6*13^(1/2))+19*3^(1/2)*((6+x^2*(5+13^(1/2)))^-1*(6+x^2*(5+-1*13^(1/2))))^(1/2)*(10+2*13^(1/2))^-1//2*(3+x^4+5*x^2)^-1//2*(6+x^2*(5+13^(1/2)))*Elliptic.F(arctan(x*(5//6+1//6*13^(1/2))^(1/2)),-13//6+5//6*13^(1/2)))
@test integrate(x^-4*(3+x^4+5*x^2)^3//2*(2+3*x^2), x) == :(-1//15*x^-1*(3+x^4+5*x^2)^(1/2)*(312+-65*x^2)+-1//15*x^-3*(3+x^4+5*x^2)^3//2*(10+-9*x^2)+949//30*x*(3+x^4+5*x^2)^-1//2*(5+13^(1/2)+2*x^2)+-949//30*((6+x^2*(5+13^(1/2)))^-1*(6+x^2*(5+-1*13^(1/2))))^(1/2)*(5//6+1//6*13^(1/2))^(1/2)*(3+x^4+5*x^2)^-1//2*(6+x^2*(5+13^(1/2)))*Elliptic.E(arctan(x*(5//6+1//6*13^(1/2))^(1/2)),-13//6+5//6*13^(1/2))+65*2^(1/2)*((6+x^2*(5+13^(1/2)))^-1*(6+x^2*(5+-1*13^(1/2))))^(1/2)*(15+3*13^(1/2))^-1//2*(3+x^4+5*x^2)^-1//2*(6+x^2*(5+13^(1/2)))*Elliptic.F(arctan(x*(5//6+1//6*13^(1/2))^(1/2)),-13//6+5//6*13^(1/2)))
@test integrate(x^-6*(3+x^4+5*x^2)^3//2*(2+3*x^2), x) == :(-722//15*x^-1*(3+x^4+5*x^2)^(1/2)+-1//5*x^-5*(3+x^4+5*x^2)^3//2*(2+-5*x^2)+-1//5*x^-3*(3+x^4+5*x^2)^(1/2)*(40+-87*x^2)+361//15*x*(3+x^4+5*x^2)^-1//2*(5+13^(1/2)+2*x^2)+103*((6+x^2*(5+13^(1/2)))^-1*(6+x^2*(5+-1*13^(1/2))))^(1/2)*(30+6*13^(1/2))^-1//2*(3+x^4+5*x^2)^-1//2*(6+x^2*(5+13^(1/2)))*Elliptic.F(arctan(x*(5//6+1//6*13^(1/2))^(1/2)),-13//6+5//6*13^(1/2))+-361//15*((6+x^2*(5+13^(1/2)))^-1*(6+x^2*(5+-1*13^(1/2))))^(1/2)*(5//6+1//6*13^(1/2))^(1/2)*(3+x^4+5*x^2)^-1//2*(6+x^2*(5+13^(1/2)))*Elliptic.E(arctan(x*(5//6+1//6*13^(1/2))^(1/2)),-13//6+5//6*13^(1/2)))
@test integrate(x^5*(a+b*x^2+c*x^4)^-1//2*(A+B*x^2), x) == :(-1//32*c^-7//2*(5*B*b^3+-6*A*c*b^2+8*A*a*c^2+-12*B*a*b*c)*arctanh((1/2)*c^-1//2*(a+b*x^2+c*x^4)^-1//2*(b+2*c*x^2))+1//48*c^-3*(a+b*x^2+c*x^4)^(1/2)*(15*B*b^2+-18*A*b*c+-16*B*a*c+-2*c*x^2*(-6*A*c+5*B*b))+1//6*B*c^-1*x^4*(a+b*x^2+c*x^4)^(1/2))
@test integrate(x^3*(a+b*x^2+c*x^4)^-1//2*(A+B*x^2), x) == :(-1//8*c^-2*(a+b*x^2+c*x^4)^(1/2)*(-4*A*c+3*B*b+-2*B*c*x^2)+1//16*c^-5//2*(3*B*b^2+-4*A*b*c+-4*B*a*c)*arctanh((1/2)*c^-1//2*(a+b*x^2+c*x^4)^-1//2*(b+2*c*x^2)))
@test integrate(x*(a+b*x^2+c*x^4)^-1//2*(A+B*x^2), x) == :((1/2)*B*c^-1*(a+b*x^2+c*x^4)^(1/2)+-1//4*c^-3//2*(B*b+-2*A*c)*arctanh((1/2)*c^-1//2*(a+b*x^2+c*x^4)^-1//2*(b+2*c*x^2)))
@test integrate(x^-1*(a+b*x^2+c*x^4)^-1//2*(A+B*x^2), x) == :((1/2)*B*c^-1//2*arctanh((1/2)*c^-1//2*(a+b*x^2+c*x^4)^-1//2*(b+2*c*x^2))+-1//2*A*a^-1//2*arctanh((1/2)*a^-1//2*(a+b*x^2+c*x^4)^-1//2*(2a+b*x^2)))
@test integrate(x^-3*(a+b*x^2+c*x^4)^-1//2*(A+B*x^2), x) == :(1//4*a^-3//2*(A*b+-2*B*a)*arctanh((1/2)*a^-1//2*(a+b*x^2+c*x^4)^-1//2*(2a+b*x^2))+-1//2*A*a^-1*x^-2*(a+b*x^2+c*x^4)^(1/2))
@test integrate(x^-5*(a+b*x^2+c*x^4)^-1//2*(A+B*x^2), x) == :(-1//16*a^-5//2*(3*A*b^2+-4*A*a*c+-4*B*a*b)*arctanh((1/2)*a^-1//2*(a+b*x^2+c*x^4)^-1//2*(2a+b*x^2))+-1//4*A*a^-1*x^-4*(a+b*x^2+c*x^4)^(1/2)+1//8*a^-2*x^-2*(a+b*x^2+c*x^4)^(1/2)*(-4*B*a+3*A*b))
@test integrate(x^-7*(a+b*x^2+c*x^4)^-1//2*(A+B*x^2), x) == :(1//32*a^-7//2*(5*A*b^3+-6*B*a*b^2+8*B*c*a^2+-12*A*a*b*c)*arctanh((1/2)*a^-1//2*(a+b*x^2+c*x^4)^-1//2*(2a+b*x^2))+-1//6*A*a^-1*x^-6*(a+b*x^2+c*x^4)^(1/2)+-1//48*a^-3*x^-2*(a+b*x^2+c*x^4)^(1/2)*(15*A*b^2+-18*B*a*b+-16*A*a*c)+1//24*a^-2*x^-4*(a+b*x^2+c*x^4)^(1/2)*(-6*B*a+5*A*b))
@test integrate(x^4*(a+b*x^2+c*x^4)^-1//2*(A+B*x^2), x) == :(-1//15*x*c^-2*(a+b*x^2+c*x^4)^(1/2)*(-5*A*c+4*B*b)+1//5*B*c^-1*x^3*(a+b*x^2+c*x^4)^(1/2)+1//15*x*c^-5//2*(a^(1/2)+c^(1/2)*x^2)^-1*(a+b*x^2+c*x^4)^(1/2)*(8*B*b^2+-10*A*b*c+-9*B*a*c)+-1//15*a^1//4*c^-11//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+b*x^2+c*x^4))^(1/2)*(a+b*x^2+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*(8*B*b^2+-10*A*b*c+-9*B*a*c)*Elliptic.E(2*arctan(x*a^-1//4*c^1//4),1/2+-1//4*b*a^-1//2*c^-1//2)+1//30*a^1//4*c^-11//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+b*x^2+c*x^4))^(1/2)*(a+b*x^2+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*(8*B*b^2+a^(1/2)*c^(1/2)*(-5*A*c+4*B*b)+-10*A*b*c+-9*B*a*c)*Elliptic.F(2*arctan(x*a^-1//4*c^1//4),1/2+-1//4*b*a^-1//2*c^-1//2))
@test integrate(x^2*(a+b*x^2+c*x^4)^-1//2*(A+B*x^2), x) == :(1//3*B*x*c^-1*(a+b*x^2+c*x^4)^(1/2)+-1//3*x*c^-3//2*(a^(1/2)+c^(1/2)*x^2)^-1*(a+b*x^2+c*x^4)^(1/2)*(-3*A*c+2*B*b)+-1//6*a^1//4*c^-7//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+b*x^2+c*x^4))^(1/2)*(a+b*x^2+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*(-3*A*c+2*B*b+B*a^(1/2)*c^(1/2))*Elliptic.F(2*arctan(x*a^-1//4*c^1//4),1/2+-1//4*b*a^-1//2*c^-1//2)+1//3*a^1//4*c^-7//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+b*x^2+c*x^4))^(1/2)*(a+b*x^2+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*(-3*A*c+2*B*b)*Elliptic.E(2*arctan(x*a^-1//4*c^1//4),1/2+-1//4*b*a^-1//2*c^-1//2))
@test integrate((a+b*x^2+c*x^4)^-1//2*(A+B*x^2), x) == :(B*x*c^-1//2*(a^(1/2)+c^(1/2)*x^2)^-1*(a+b*x^2+c*x^4)^(1/2)+(1/2)*a^1//4*c^-3//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+b*x^2+c*x^4))^(1/2)*(a+b*x^2+c*x^4)^-1//2*(B+A*a^-1//2*c^(1/2))*(a^(1/2)+c^(1/2)*x^2)*Elliptic.F(2*arctan(x*a^-1//4*c^1//4),1/2+-1//4*b*a^-1//2*c^-1//2)+-1*B*a^1//4*c^-3//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+b*x^2+c*x^4))^(1/2)*(a+b*x^2+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*c^1//4),1/2+-1//4*b*a^-1//2*c^-1//2))
@test integrate(x^-2*(a+b*x^2+c*x^4)^-1//2*(A+B*x^2), x) == :(-1*A*a^-1*x^-1*(a+b*x^2+c*x^4)^(1/2)+A*x*a^-1*c^(1/2)*(a^(1/2)+c^(1/2)*x^2)^-1*(a+b*x^2+c*x^4)^(1/2)+(1/2)*a^-3//4*c^-1//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+b*x^2+c*x^4))^(1/2)*(a+b*x^2+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*(A*c^(1/2)+B*a^(1/2))*Elliptic.F(2*arctan(x*a^-1//4*c^1//4),1/2+-1//4*b*a^-1//2*c^-1//2)+-1*A*a^-3//4*c^1//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+b*x^2+c*x^4))^(1/2)*(a+b*x^2+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*c^1//4),1/2+-1//4*b*a^-1//2*c^-1//2))
@test integrate(x^-4*(a+b*x^2+c*x^4)^-1//2*(A+B*x^2), x) == :(-1//3*A*a^-1*x^-3*(a+b*x^2+c*x^4)^(1/2)+1//3*a^-2*x^-1*(a+b*x^2+c*x^4)^(1/2)*(-3*B*a+2*A*b)+-1//3*x*a^-2*c^(1/2)*(a^(1/2)+c^(1/2)*x^2)^-1*(a+b*x^2+c*x^4)^(1/2)*(-3*B*a+2*A*b)+-1//6*a^-7//4*c^1//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+b*x^2+c*x^4))^(1/2)*(a+b*x^2+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*(-3*B*a+2*A*b+A*a^(1/2)*c^(1/2))*Elliptic.F(2*arctan(x*a^-1//4*c^1//4),1/2+-1//4*b*a^-1//2*c^-1//2)+1//3*a^-7//4*c^1//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+b*x^2+c*x^4))^(1/2)*(a+b*x^2+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*(-3*B*a+2*A*b)*Elliptic.E(2*arctan(x*a^-1//4*c^1//4),1/2+-1//4*b*a^-1//2*c^-1//2))
@test integrate(x^7*(3+x^4+5*x^2)^-1//2*(2+3*x^2), x) == :(32801//256*arctanh((1/2)*(3+x^4+5*x^2)^-1//2*(5+2*x^2))+-1*(3+x^4+5*x^2)^(1/2)*(8081//128+-1901//192*x^2)+-89//48*x^4*(3+x^4+5*x^2)^(1/2)+3//8*x^6*(3+x^4+5*x^2)^(1/2))
@test integrate(x^5*(3+x^4+5*x^2)^-1//2*(2+3*x^2), x) == :(-1083//32*arctanh((1/2)*(3+x^4+5*x^2)^-1//2*(5+2*x^2))+(3+x^4+5*x^2)^(1/2)*(267//16+-21//8*x^2)+(1/2)*x^4*(3+x^4+5*x^2)^(1/2))
@test integrate(x^3*(3+x^4+5*x^2)^-1//2*(2+3*x^2), x) == :(149//16*arctanh((1/2)*(3+x^4+5*x^2)^-1//2*(5+2*x^2))+-1//8*(3+x^4+5*x^2)^(1/2)*(37+-6*x^2))
@test integrate(x*(3+x^4+5*x^2)^-1//2*(2+3*x^2), x) == :(-11//4*arctanh((1/2)*(3+x^4+5*x^2)^-1//2*(5+2*x^2))+3//2*(3+x^4+5*x^2)^(1/2))
@test integrate(x^-1*(3+x^4+5*x^2)^-1//2*(2+3*x^2), x) == :(3//2*arctanh((1/2)*(3+x^4+5*x^2)^-1//2*(5+2*x^2))+-1//3*3^(1/2)*arctanh(1//6*3^(1/2)*(3+x^4+5*x^2)^-1//2*(6+5*x^2)))
@test integrate(x^-3*(3+x^4+5*x^2)^-1//2*(2+3*x^2), x) == :(-2//9*3^(1/2)*arctanh(1//6*3^(1/2)*(3+x^4+5*x^2)^-1//2*(6+5*x^2))+-1//3*x^-2*(3+x^4+5*x^2)^(1/2))
@test integrate(x^-5*(3+x^4+5*x^2)^-1//2*(2+3*x^2), x) == :(-1//6*x^-4*(3+x^4+5*x^2)^(1/2)+-1//12*x^-2*(3+x^4+5*x^2)^(1/2)+1//8*3^(1/2)*arctanh(1//6*3^(1/2)*(3+x^4+5*x^2)^-1//2*(6+5*x^2)))
@test integrate(x^-7*(3+x^4+5*x^2)^-1//2*(2+3*x^2), x) == :(-61//648*3^(1/2)*arctanh(1//6*3^(1/2)*(3+x^4+5*x^2)^-1//2*(6+5*x^2))+-1//9*x^-6*(3+x^4+5*x^2)^(1/2)+-1//54*x^-4*(3+x^4+5*x^2)^(1/2)+13//108*x^-2*(3+x^4+5*x^2)^(1/2))
@test integrate(x^4*(3+x^4+5*x^2)^-1//2*(2+3*x^2), x) == :(-10//3*x*(3+x^4+5*x^2)^(1/2)+3//5*x^3*(3+x^4+5*x^2)^(1/2)+419//30*x*(3+x^4+5*x^2)^-1//2*(5+13^(1/2)+2*x^2)+-419//30*((6+x^2*(5+13^(1/2)))^-1*(6+x^2*(5+-1*13^(1/2))))^(1/2)*(5//6+1//6*13^(1/2))^(1/2)*(3+x^4+5*x^2)^-1//2*(6+x^2*(5+13^(1/2)))*Elliptic.E(arctan(x*(5//6+1//6*13^(1/2))^(1/2)),-13//6+5//6*13^(1/2))+5*2^(1/2)*((6+x^2*(5+13^(1/2)))^-1*(6+x^2*(5+-1*13^(1/2))))^(1/2)*(15+3*13^(1/2))^-1//2*(3+x^4+5*x^2)^-1//2*(6+x^2*(5+13^(1/2)))*Elliptic.F(arctan(x*(5//6+1//6*13^(1/2))^(1/2)),-13//6+5//6*13^(1/2)))
@test integrate(x^2*(3+x^4+5*x^2)^-1//2*(2+3*x^2), x) == :(x*(3+x^4+5*x^2)^(1/2)+-4*x*(3+x^4+5*x^2)^-1//2*(5+13^(1/2)+2*x^2)+2*((6+x^2*(5+13^(1/2)))^-1*(6+x^2*(5+-1*13^(1/2))))^(1/2)*(10//3+2//3*13^(1/2))^(1/2)*(3+x^4+5*x^2)^-1//2*(6+x^2*(5+13^(1/2)))*Elliptic.E(arctan(x*(5//6+1//6*13^(1/2))^(1/2)),-13//6+5//6*13^(1/2))+-1*3^(1/2)*((6+x^2*(5+13^(1/2)))^-1*(6+x^2*(5+-1*13^(1/2))))^(1/2)*(10+2*13^(1/2))^-1//2*(3+x^4+5*x^2)^-1//2*(6+x^2*(5+13^(1/2)))*Elliptic.F(arctan(x*(5//6+1//6*13^(1/2))^(1/2)),-13//6+5//6*13^(1/2)))
@test integrate((3+x^4+5*x^2)^-1//2*(2+3*x^2), x) == :(3//2*x*(3+x^4+5*x^2)^-1//2*(5+13^(1/2)+2*x^2)+-1//2*((6+x^2*(5+13^(1/2)))^-1*(6+x^2*(5+-1*13^(1/2))))^(1/2)*(15//2+3//2*13^(1/2))^(1/2)*(3+x^4+5*x^2)^-1//2*(6+x^2*(5+13^(1/2)))*Elliptic.E(arctan(x*(5//6+1//6*13^(1/2))^(1/2)),-13//6+5//6*13^(1/2))+2^(1/2)*((6+x^2*(5+13^(1/2)))^-1*(6+x^2*(5+-1*13^(1/2))))^(1/2)*(15+3*13^(1/2))^-1//2*(3+x^4+5*x^2)^-1//2*(6+x^2*(5+13^(1/2)))*Elliptic.F(arctan(x*(5//6+1//6*13^(1/2))^(1/2)),-13//6+5//6*13^(1/2)))
@test integrate(x^-2*(3+x^4+5*x^2)^-1//2*(2+3*x^2), x) == :(-2//3*x^-1*(3+x^4+5*x^2)^(1/2)+1//3*x*(3+x^4+5*x^2)^-1//2*(5+13^(1/2)+2*x^2)+-1//3*((6+x^2*(5+13^(1/2)))^-1*(6+x^2*(5+-1*13^(1/2))))^(1/2)*(5//6+1//6*13^(1/2))^(1/2)*(3+x^4+5*x^2)^-1//2*(6+x^2*(5+13^(1/2)))*Elliptic.E(arctan(x*(5//6+1//6*13^(1/2))^(1/2)),-13//6+5//6*13^(1/2))+3^(1/2)*((6+x^2*(5+13^(1/2)))^-1*(6+x^2*(5+-1*13^(1/2))))^(1/2)*(10+2*13^(1/2))^-1//2*(3+x^4+5*x^2)^-1//2*(6+x^2*(5+13^(1/2)))*Elliptic.F(arctan(x*(5//6+1//6*13^(1/2))^(1/2)),-13//6+5//6*13^(1/2)))
@test integrate(x^-4*(3+x^4+5*x^2)^-1//2*(2+3*x^2), x) == :(-7//27*x^-1*(3+x^4+5*x^2)^(1/2)+-2//9*x^-3*(3+x^4+5*x^2)^(1/2)+7//54*x*(3+x^4+5*x^2)^-1//2*(5+13^(1/2)+2*x^2)+-7//54*((6+x^2*(5+13^(1/2)))^-1*(6+x^2*(5+-1*13^(1/2))))^(1/2)*(5//6+1//6*13^(1/2))^(1/2)*(3+x^4+5*x^2)^-1//2*(6+x^2*(5+13^(1/2)))*Elliptic.E(arctan(x*(5//6+1//6*13^(1/2))^(1/2)),-13//6+5//6*13^(1/2))+-1//9*2^(1/2)*((6+x^2*(5+13^(1/2)))^-1*(6+x^2*(5+-1*13^(1/2))))^(1/2)*(15+3*13^(1/2))^-1//2*(3+x^4+5*x^2)^-1//2*(6+x^2*(5+13^(1/2)))*Elliptic.F(arctan(x*(5//6+1//6*13^(1/2))^(1/2)),-13//6+5//6*13^(1/2)))
@test integrate(x^5*(3+x^4+5*x^2)^-3//2*(2+3*x^2), x) == :(-41//4*arctanh((1/2)*(3+x^4+5*x^2)^-1//2*(5+2*x^2))+133//26*(3+x^4+5*x^2)^(1/2)+-1//13*x^2*(3+x^4+5*x^2)^-1//2*(33+47*x^2))
@test integrate(x^3*(3+x^4+5*x^2)^-3//2*(2+3*x^2), x) == :(3//2*arctanh((1/2)*(3+x^4+5*x^2)^-1//2*(5+2*x^2))+1//13*(3+x^4+5*x^2)^-1//2*(-33+-47*x^2))
@test integrate(x*(3+x^4+5*x^2)^-3//2*(2+3*x^2), x) == :(1//13*(3+x^4+5*x^2)^-1//2*(8+11*x^2))
@test integrate(x^-1*(3+x^4+5*x^2)^-3//2*(2+3*x^2), x) == :(-1//9*3^(1/2)*arctanh(1//6*3^(1/2)*(3+x^4+5*x^2)^-1//2*(6+5*x^2))+1//39*(3+x^4+5*x^2)^-1//2*(-7+-8*x^2))
@test integrate(x^-3*(3+x^4+5*x^2)^-3//2*(2+3*x^2), x) == :(-2//39*x^-2*(3+x^4+5*x^2)^(1/2)+1//9*3^(1/2)*arctanh(1//6*3^(1/2)*(3+x^4+5*x^2)^-1//2*(6+5*x^2))+1//39*x^-2*(3+x^4+5*x^2)^-1//2*(-7+-8*x^2))
@test integrate(x^4*(3+x^4+5*x^2)^-3//2*(2+3*x^2), x) == :(-11//13*x*(3+x^4+5*x^2)^(1/2)+1//13*x^3*(3+x^4+5*x^2)^-1//2*(8+11*x^2)+43//13*x*(3+x^4+5*x^2)^-1//2*(5+13^(1/2)+2*x^2)+-43//13*((6+x^2*(5+13^(1/2)))^-1*(6+x^2*(5+-1*13^(1/2))))^(1/2)*(5//6+1//6*13^(1/2))^(1/2)*(3+x^4+5*x^2)^-1//2*(6+x^2*(5+13^(1/2)))*Elliptic.E(arctan(x*(5//6+1//6*13^(1/2))^(1/2)),-13//6+5//6*13^(1/2))+11//13*3^(1/2)*((6+x^2*(5+13^(1/2)))^-1*(6+x^2*(5+-1*13^(1/2))))^(1/2)*(10+2*13^(1/2))^-1//2*(3+x^4+5*x^2)^-1//2*(6+x^2*(5+13^(1/2)))*Elliptic.F(arctan(x*(5//6+1//6*13^(1/2))^(1/2)),-13//6+5//6*13^(1/2)))
@test integrate(x^2*(3+x^4+5*x^2)^-3//2*(2+3*x^2), x) == :(-11//26*x*(3+x^4+5*x^2)^-1//2*(5+13^(1/2)+2*x^2)+1//13*x*(3+x^4+5*x^2)^-1//2*(8+11*x^2)+11//26*((6+x^2*(5+13^(1/2)))^-1*(6+x^2*(5+-1*13^(1/2))))^(1/2)*(5//6+1//6*13^(1/2))^(1/2)*(3+x^4+5*x^2)^-1//2*(6+x^2*(5+13^(1/2)))*Elliptic.E(arctan(x*(5//6+1//6*13^(1/2))^(1/2)),-13//6+5//6*13^(1/2))+-4//13*2^(1/2)*((6+x^2*(5+13^(1/2)))^-1*(6+x^2*(5+-1*13^(1/2))))^(1/2)*(15+3*13^(1/2))^-1//2*(3+x^4+5*x^2)^-1//2*(6+x^2*(5+13^(1/2)))*Elliptic.F(arctan(x*(5//6+1//6*13^(1/2))^(1/2)),-13//6+5//6*13^(1/2)))
@test integrate((3+x^4+5*x^2)^-3//2*(2+3*x^2), x) == :(-1//39*x*(3+x^4+5*x^2)^-1//2*(7+8*x^2)+4//39*x*(3+x^4+5*x^2)^-1//2*(5+13^(1/2)+2*x^2)+-2//39*((6+x^2*(5+13^(1/2)))^-1*(6+x^2*(5+-1*13^(1/2))))^(1/2)*(10//3+2//3*13^(1/2))^(1/2)*(3+x^4+5*x^2)^-1//2*(6+x^2*(5+13^(1/2)))*Elliptic.E(arctan(x*(5//6+1//6*13^(1/2))^(1/2)),-13//6+5//6*13^(1/2))+11//13*((6+x^2*(5+13^(1/2)))^-1*(6+x^2*(5+-1*13^(1/2))))^(1/2)*(30+6*13^(1/2))^-1//2*(3+x^4+5*x^2)^-1//2*(6+x^2*(5+13^(1/2)))*Elliptic.F(arctan(x*(5//6+1//6*13^(1/2))^(1/2)),-13//6+5//6*13^(1/2)))
@test integrate(x^-2*(3+x^4+5*x^2)^-3//2*(2+3*x^2), x) == :(-19//117*x^-1*(3+x^4+5*x^2)^(1/2)+-1//39*x^-1*(3+x^4+5*x^2)^-1//2*(7+8*x^2)+19//234*x*(3+x^4+5*x^2)^-1//2*(5+13^(1/2)+2*x^2)+-19//234*((6+x^2*(5+13^(1/2)))^-1*(6+x^2*(5+-1*13^(1/2))))^(1/2)*(5//6+1//6*13^(1/2))^(1/2)*(3+x^4+5*x^2)^-1//2*(6+x^2*(5+13^(1/2)))*Elliptic.E(arctan(x*(5//6+1//6*13^(1/2))^(1/2)),-13//6+5//6*13^(1/2))+-4//39*2^(1/2)*((6+x^2*(5+13^(1/2)))^-1*(6+x^2*(5+-1*13^(1/2))))^(1/2)*(15+3*13^(1/2))^-1//2*(3+x^4+5*x^2)^-1//2*(6+x^2*(5+13^(1/2)))*Elliptic.F(arctan(x*(5//6+1//6*13^(1/2))^(1/2)),-13//6+5//6*13^(1/2)))
@test integrate(x^-4*(3+x^4+5*x^2)^-3//2*(2+3*x^2), x) == :(-5//351*x^-3*(3+x^4+5*x^2)^(1/2)+266//1053*x^-1*(3+x^4+5*x^2)^(1/2)+-133//1053*x*(3+x^4+5*x^2)^-1//2*(5+13^(1/2)+2*x^2)+-1//39*x^-3*(3+x^4+5*x^2)^-1//2*(7+8*x^2)+-5//351*((6+x^2*(5+13^(1/2)))^-1*(6+x^2*(5+-1*13^(1/2))))^(1/2)*(30+6*13^(1/2))^-1//2*(3+x^4+5*x^2)^-1//2*(6+x^2*(5+13^(1/2)))*Elliptic.F(arctan(x*(5//6+1//6*13^(1/2))^(1/2)),-13//6+5//6*13^(1/2))+133//1053*((6+x^2*(5+13^(1/2)))^-1*(6+x^2*(5+-1*13^(1/2))))^(1/2)*(5//6+1//6*13^(1/2))^(1/2)*(3+x^4+5*x^2)^-1//2*(6+x^2*(5+13^(1/2)))*Elliptic.E(arctan(x*(5//6+1//6*13^(1/2))^(1/2)),-13//6+5//6*13^(1/2)))
@test integrate((f*x)^m*(a+b*x^2+c*x^4)^3*(d+e*x^2), x) == :(f^-9*(f*x)^(9+m)*(9+m)^-1*(e*b^3+3*a*d*c^2+3*c*d*b^2+6*a*b*c*e)+f^-7*(f*x)^(7+m)*(7+m)^-1*(d*b^3+3*a*e*b^2+3*c*e*a^2+6*a*b*c*d)+d*a^3*f^-1*(f*x)^(1+m)*(1+m)^-1+e*c^3*f^-15*(f*x)^(15+m)*(15+m)^-1+a^2*f^-3*(f*x)^(3+m)*(3+m)^-1*(a*e+3*b*d)+c^2*f^-13*(f*x)^(13+m)*(13+m)^-1*(c*d+3*b*e)+3*a*f^-5*(f*x)^(5+m)*(5+m)^-1*(d*b^2+a*b*e+a*c*d)+3*c*f^-11*(f*x)^(11+m)*(11+m)^-1*(e*b^2+a*c*e+b*c*d))
@test integrate((f*x)^m*(a+b*x^2+c*x^4)^2*(d+e*x^2), x) == :(f^-7*(f*x)^(7+m)*(7+m)^-1*(e*b^2+2*a*c*e+2*b*c*d)+f^-5*(f*x)^(5+m)*(5+m)^-1*(d*b^2+2*a*b*e+2*a*c*d)+a*f^-3*(f*x)^(3+m)*(3+m)^-1*(a*e+2*b*d)+c*f^-9*(f*x)^(9+m)*(9+m)^-1*(c*d+2*b*e)+d*a^2*f^-1*(f*x)^(1+m)*(1+m)^-1+e*c^2*f^-11*(f*x)^(11+m)*(11+m)^-1)
@test integrate((f*x)^m*(d+e*x^2)*(a+b*x^2+c*x^4), x) == :(f^-5*(f*x)^(5+m)*(5+m)^-1*(b*e+c*d)+f^-3*(f*x)^(3+m)*(3+m)^-1*(a*e+b*d)+a*d*f^-1*(f*x)^(1+m)*(1+m)^-1+c*e*f^-7*(f*x)^(7+m)*(7+m)^-1)
@test integrate(x^9*(a+c*x^4)^-1*(d+e*x^2)^-1, x) == :(1//4*c^-1*e^-1*x^4+(1/2)*d^4*e^-3*(a*e^2+c*d^2)^-1*log(d+e*x^2)+-1//2*d*c^-1*e^-2*x^2+(1/2)*d*a^3//2*c^-3//2*(a*e^2+c*d^2)^-1*arctan(a^-1//2*c^(1/2)*x^2)+-1//4*e*a^2*c^-2*(a*e^2+c*d^2)^-1*log(a+c*x^4))
@test integrate(x^7*(a+c*x^4)^-1*(d+e*x^2)^-1, x) == :((1/2)*c^-1*e^-1*x^2+-1//2*d^3*e^-2*(a*e^2+c*d^2)^-1*log(d+e*x^2)+-1//2*e*a^3//2*c^-3//2*(a*e^2+c*d^2)^-1*arctan(a^-1//2*c^(1/2)*x^2)+-1//4*a*d*c^-1*(a*e^2+c*d^2)^-1*log(a+c*x^4))
@test integrate(x^5*(a+c*x^4)^-1*(d+e*x^2)^-1, x) == :((1/2)*d^2*e^-1*(a*e^2+c*d^2)^-1*log(d+e*x^2)+-1//2*d*a^(1/2)*c^-1//2*(a*e^2+c*d^2)^-1*arctan(a^-1//2*c^(1/2)*x^2)+1//4*a*e*c^-1*(a*e^2+c*d^2)^-1*log(a+c*x^4))
@test integrate(x^3*(a+c*x^4)^-1*(d+e*x^2)^-1, x) == :(d*(4*a*e^2+4*c*d^2)^-1*log(a+c*x^4)+-1*d*(2*a*e^2+2*c*d^2)^-1*log(d+e*x^2)+(1/2)*e*a^(1/2)*c^-1//2*(a*e^2+c*d^2)^-1*arctan(a^-1//2*c^(1/2)*x^2))
@test integrate(x*(a+c*x^4)^-1*(d+e*x^2)^-1, x) == :(e*(2*a*e^2+2*c*d^2)^-1*log(d+e*x^2)+-1*e*(4*a*e^2+4*c*d^2)^-1*log(a+c*x^4)+(1/2)*d*a^-1//2*c^(1/2)*(a*e^2+c*d^2)^-1*arctan(a^-1//2*c^(1/2)*x^2))
@test integrate(x^-1*(a+c*x^4)^-1*(d+e*x^2)^-1, x) == :(a^-1*d^-1*log(x)+-1//2*d^-1*e^2*(a*e^2+c*d^2)^-1*log(d+e*x^2)+-1//2*e*a^-1//2*c^(1/2)*(a*e^2+c*d^2)^-1*arctan(a^-1//2*c^(1/2)*x^2)+-1//4*c*d*a^-1*(a*e^2+c*d^2)^-1*log(a+c*x^4))
@test integrate(x^-3*(a+c*x^4)^-1*(d+e*x^2)^-1, x) == :(-1//2*a^-1*d^-1*x^-2+(1/2)*d^-2*e^3*(a*e^2+c*d^2)^-1*log(d+e*x^2)+-1*e*a^-1*d^-2*log(x)+-1//2*d*a^-3//2*c^3//2*(a*e^2+c*d^2)^-1*arctan(a^-1//2*c^(1/2)*x^2)+1//4*c*e*a^-1*(a*e^2+c*d^2)^-1*log(a+c*x^4))
@test integrate(x^-5*(a+c*x^4)^-1*(d+e*x^2)^-1, x) == :(-1//4*a^-1*d^-1*x^-4+(1/2)*e*a^-1*d^-2*x^-2+-1*a^-2*d^-3*(c*d^2+-1*a*e^2)*log(x)+-1//2*d^-3*e^4*(a*e^2+c*d^2)^-1*log(d+e*x^2)+(1/2)*e*a^-3//2*c^3//2*(a*e^2+c*d^2)^-1*arctan(a^-1//2*c^(1/2)*x^2)+1//4*d*a^-2*c^2*(a*e^2+c*d^2)^-1*log(a+c*x^4))
@test integrate(x^8*(a+c*x^4)^-1*(d+e*x^2)^-1, x) == :(1//3*c^-1*e^-1*x^3+d^7//2*e^-5//2*(a*e^2+c*d^2)^-1*arctan(x*d^-1//2*e^(1/2))+-1*d*x*c^-1*e^-2+-1//4*2^(1/2)*a^5//4*c^-7//4*(a*e^2+c*d^2)^-1*(d*c^(1/2)+-1*e*a^(1/2))*arctan(1+-1*x*2^(1/2)*a^-1//4*c^1//4)+-1//8*2^(1/2)*a^5//4*c^-7//4*(a*e^2+c*d^2)^-1*(d*c^(1/2)+e*a^(1/2))*log(a^(1/2)+c^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*c^1//4)+1//4*2^(1/2)*a^5//4*c^-7//4*(a*e^2+c*d^2)^-1*(d*c^(1/2)+-1*e*a^(1/2))*arctan(1+x*2^(1/2)*a^-1//4*c^1//4)+1//8*2^(1/2)*a^5//4*c^-7//4*(a*e^2+c*d^2)^-1*(d*c^(1/2)+e*a^(1/2))*log(a^(1/2)+c^(1/2)*x^2+x*2^(1/2)*a^1//4*c^1//4))
@test integrate(x^6*(a+c*x^4)^-1*(d+e*x^2)^-1, x) == :(x*c^-1*e^-1+-1*d^5//2*e^-3//2*(a*e^2+c*d^2)^-1*arctan(x*d^-1//2*e^(1/2))+-1//4*2^(1/2)*a^3//4*c^-5//4*(a*e^2+c*d^2)^-1*(d*c^(1/2)+e*a^(1/2))*arctan(1+x*2^(1/2)*a^-1//4*c^1//4)+-1//8*2^(1/2)*a^3//4*c^-5//4*(a*e^2+c*d^2)^-1*(d*c^(1/2)+-1*e*a^(1/2))*log(a^(1/2)+c^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*c^1//4)+1//4*2^(1/2)*a^3//4*c^-5//4*(a*e^2+c*d^2)^-1*(d*c^(1/2)+e*a^(1/2))*arctan(1+-1*x*2^(1/2)*a^-1//4*c^1//4)+1//8*2^(1/2)*a^3//4*c^-5//4*(a*e^2+c*d^2)^-1*(d*c^(1/2)+-1*e*a^(1/2))*log(a^(1/2)+c^(1/2)*x^2+x*2^(1/2)*a^1//4*c^1//4))
@test integrate(x^4*(a+c*x^4)^-1*(d+e*x^2)^-1, x) == :(d^3//2*e^-1//2*(a*e^2+c*d^2)^-1*arctan(x*d^-1//2*e^(1/2))+-1//4*2^(1/2)*a^1//4*c^-3//4*(a*e^2+c*d^2)^-1*(d*c^(1/2)+-1*e*a^(1/2))*arctan(1+x*2^(1/2)*a^-1//4*c^1//4)+-1//8*2^(1/2)*a^1//4*c^-3//4*(a*e^2+c*d^2)^-1*(d*c^(1/2)+e*a^(1/2))*log(a^(1/2)+c^(1/2)*x^2+x*2^(1/2)*a^1//4*c^1//4)+1//4*2^(1/2)*a^1//4*c^-3//4*(a*e^2+c*d^2)^-1*(d*c^(1/2)+-1*e*a^(1/2))*arctan(1+-1*x*2^(1/2)*a^-1//4*c^1//4)+1//8*2^(1/2)*a^1//4*c^-3//4*(a*e^2+c*d^2)^-1*(d*c^(1/2)+e*a^(1/2))*log(a^(1/2)+c^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*c^1//4))
@test integrate(x^2*(a+c*x^4)^-1*(d+e*x^2)^-1, x) == :(-1*d^(1/2)*e^(1/2)*(a*e^2+c*d^2)^-1*arctan(x*d^-1//2*e^(1/2))+-1//4*2^(1/2)*a^-1//4*c^-1//4*(a*e^2+c*d^2)^-1*(d*c^(1/2)+e*a^(1/2))*arctan(1+-1*x*2^(1/2)*a^-1//4*c^1//4)+-1//8*2^(1/2)*a^-1//4*c^-1//4*(a*e^2+c*d^2)^-1*(d*c^(1/2)+-1*e*a^(1/2))*log(a^(1/2)+c^(1/2)*x^2+x*2^(1/2)*a^1//4*c^1//4)+1//4*2^(1/2)*a^-1//4*c^-1//4*(a*e^2+c*d^2)^-1*(d*c^(1/2)+e*a^(1/2))*arctan(1+x*2^(1/2)*a^-1//4*c^1//4)+1//8*2^(1/2)*a^-1//4*c^-1//4*(a*e^2+c*d^2)^-1*(d*c^(1/2)+-1*e*a^(1/2))*log(a^(1/2)+c^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*c^1//4))
@test integrate((a+c*x^4)^-1*(d+e*x^2)^-1, x) == :(d^-1//2*e^3//2*(a*e^2+c*d^2)^-1*arctan(x*d^-1//2*e^(1/2))+-1//4*2^(1/2)*a^-3//4*c^1//4*(a*e^2+c*d^2)^-1*(d*c^(1/2)+-1*e*a^(1/2))*arctan(1+-1*x*2^(1/2)*a^-1//4*c^1//4)+-1//8*2^(1/2)*a^-3//4*c^1//4*(a*e^2+c*d^2)^-1*(d*c^(1/2)+e*a^(1/2))*log(a^(1/2)+c^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*c^1//4)+1//4*2^(1/2)*a^-3//4*c^1//4*(a*e^2+c*d^2)^-1*(d*c^(1/2)+-1*e*a^(1/2))*arctan(1+x*2^(1/2)*a^-1//4*c^1//4)+1//8*2^(1/2)*a^-3//4*c^1//4*(a*e^2+c*d^2)^-1*(d*c^(1/2)+e*a^(1/2))*log(a^(1/2)+c^(1/2)*x^2+x*2^(1/2)*a^1//4*c^1//4))
@test integrate(x^-2*(a+c*x^4)^-1*(d+e*x^2)^-1, x) == :(-1*a^-1*d^-1*x^-1+-1*d^-3//2*e^5//2*(a*e^2+c*d^2)^-1*arctan(x*d^-1//2*e^(1/2))+-1//4*2^(1/2)*a^-5//4*c^3//4*(a*e^2+c*d^2)^-1*(d*c^(1/2)+e*a^(1/2))*arctan(1+x*2^(1/2)*a^-1//4*c^1//4)+-1//8*2^(1/2)*a^-5//4*c^3//4*(a*e^2+c*d^2)^-1*(d*c^(1/2)+-1*e*a^(1/2))*log(a^(1/2)+c^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*c^1//4)+1//4*2^(1/2)*a^-5//4*c^3//4*(a*e^2+c*d^2)^-1*(d*c^(1/2)+e*a^(1/2))*arctan(1+-1*x*2^(1/2)*a^-1//4*c^1//4)+1//8*2^(1/2)*a^-5//4*c^3//4*(a*e^2+c*d^2)^-1*(d*c^(1/2)+-1*e*a^(1/2))*log(a^(1/2)+c^(1/2)*x^2+x*2^(1/2)*a^1//4*c^1//4))
@test integrate(x^-4*(a+c*x^4)^-1*(d+e*x^2)^-1, x) == :(-1//3*a^-1*d^-1*x^-3+e*a^-1*d^-2*x^-1+d^-5//2*e^7//2*(a*e^2+c*d^2)^-1*arctan(x*d^-1//2*e^(1/2))+-1//4*2^(1/2)*a^-7//4*c^5//4*(a*e^2+c*d^2)^-1*(d*c^(1/2)+-1*e*a^(1/2))*arctan(1+x*2^(1/2)*a^-1//4*c^1//4)+-1//8*2^(1/2)*a^-7//4*c^5//4*(a*e^2+c*d^2)^-1*(d*c^(1/2)+e*a^(1/2))*log(a^(1/2)+c^(1/2)*x^2+x*2^(1/2)*a^1//4*c^1//4)+1//4*2^(1/2)*a^-7//4*c^5//4*(a*e^2+c*d^2)^-1*(d*c^(1/2)+-1*e*a^(1/2))*arctan(1+-1*x*2^(1/2)*a^-1//4*c^1//4)+1//8*2^(1/2)*a^-7//4*c^5//4*(a*e^2+c*d^2)^-1*(d*c^(1/2)+e*a^(1/2))*log(a^(1/2)+c^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*c^1//4))
@test integrate(x^9*(a+c*x^4)^-2*(d+e*x^2)^-1, x) == :((1/2)*d^4*e^-1*(a*e^2+c*d^2)^-2*log(d+e*x^2)+1//4*a*c^-2*(a+c*x^4)^-1*(a*e^2+c*d^2)^-1*(a*e+c*d*x^2)+-1//4*d*a^(1/2)*c^-3//2*(a*e^2+c*d^2)^-2*(a*e^2+3*c*d^2)*arctan(a^-1//2*c^(1/2)*x^2)+1//4*a*e*c^-2*(a*e^2+c*d^2)^-2*(a*e^2+2*c*d^2)*log(a+c*x^4))
@test integrate(x^7*(a+c*x^4)^-2*(d+e*x^2)^-1, x) == :(-1//2*d^3*(a*e^2+c*d^2)^-2*log(d+e*x^2)+1//4*d^3*(a*e^2+c*d^2)^-2*log(a+c*x^4)+1//4*a*c^-1*(a+c*x^4)^-1*(a*e^2+c*d^2)^-1*(d+-1*e*x^2)+1//4*e*a^(1/2)*c^-3//2*(a*e^2+c*d^2)^-2*(a*e^2+3*c*d^2)*arctan(a^-1//2*c^(1/2)*x^2))
@test integrate(x^5*(a+c*x^4)^-2*(d+e*x^2)^-1, x) == :((1/2)*e*d^2*(a*e^2+c*d^2)^-2*log(d+e*x^2)+-1//4*e*d^2*(a*e^2+c*d^2)^-2*log(a+c*x^4)+1//4*c^-1*(a+c*x^4)^-1*(a*e^2+c*d^2)^-1*(-1*a*e+-1*c*d*x^2)+1//4*d*a^-1//2*c^-1//2*(a*e^2+c*d^2)^-2*(c*d^2+-1*a*e^2)*arctan(a^-1//2*c^(1/2)*x^2))
@test integrate(x^3*(a+c*x^4)^-2*(d+e*x^2)^-1, x) == :((a+c*x^4)^-1*(4*a*e^2+4*c*d^2)^-1*(-1d+e*x^2)+-1//2*d*e^2*(a*e^2+c*d^2)^-2*log(d+e*x^2)+1//4*d*e^2*(a*e^2+c*d^2)^-2*log(a+c*x^4)+-1//4*e*a^-1//2*c^-1//2*(a*e^2+c*d^2)^-2*(c*d^2+-1*a*e^2)*arctan(a^-1//2*c^(1/2)*x^2))
@test integrate(x*(a+c*x^4)^-2*(d+e*x^2)^-1, x) == :((1/2)*e^3*(a*e^2+c*d^2)^-2*log(d+e*x^2)+-1//4*e^3*(a*e^2+c*d^2)^-2*log(a+c*x^4)+1//4*a^-1*(a+c*x^4)^-1*(a*e^2+c*d^2)^-1*(a*e+c*d*x^2)+1//4*d*a^-3//2*c^(1/2)*(a*e^2+c*d^2)^-2*(c*d^2+3*a*e^2)*arctan(a^-1//2*c^(1/2)*x^2))
@test integrate(x^-1*(a+c*x^4)^-2*(d+e*x^2)^-1, x) == :(a^-2*d^-1*log(x)+-1//2*d^-1*e^4*(a*e^2+c*d^2)^-2*log(d+e*x^2)+-1//2*a^-1//2*c^(1/2)*e^3*(a*e^2+c*d^2)^-2*arctan(a^-1//2*c^(1/2)*x^2)+-1//4*e*a^-3//2*c^(1/2)*(a*e^2+c*d^2)^-1*arctan(a^-1//2*c^(1/2)*x^2)+1//4*c*a^-1*(a+c*x^4)^-1*(a*e^2+c*d^2)^-1*(d+-1*e*x^2)+-1//4*c*d*a^-2*(a*e^2+c*d^2)^-2*(c*d^2+2*a*e^2)*log(a+c*x^4))
@test integrate(x^-3*(a+c*x^4)^-2*(d+e*x^2)^-1, x) == :(-1//2*a^-2*d^-1*x^-2+(1/2)*d^-2*e^5*(a*e^2+c*d^2)^-2*log(d+e*x^2)+-1*e*a^-2*d^-2*log(x)+-1//4*c*a^-2*(a+c*x^4)^-1*(a*e^2+c*d^2)^-1*(a*e+c*d*x^2)+-1//4*d*a^-5//2*c^3//2*(a*e^2+c*d^2)^-1*arctan(a^-1//2*c^(1/2)*x^2)+-1//2*d*a^-5//2*c^3//2*(a*e^2+c*d^2)^-2*(c*d^2+2*a*e^2)*arctan(a^-1//2*c^(1/2)*x^2)+1//4*c*e*a^-2*(a*e^2+c*d^2)^-2*(c*d^2+2*a*e^2)*log(a+c*x^4))
@test integrate(x^-5*(a+c*x^4)^-2*(d+e*x^2)^-1, x) == :(-1//4*a^-2*d^-1*x^-4+(1/2)*e*a^-2*d^-2*x^-2+-1*a^-3*d^-3*(-1*a*e^2+2*c*d^2)*log(x)+-1//2*d^-3*e^6*(a*e^2+c*d^2)^-2*log(d+e*x^2)+-1//4*a^-2*c^2*(a+c*x^4)^-1*(a*e^2+c*d^2)^-1*(d+-1*e*x^2)+1//4*e*a^-5//2*c^3//2*(a*e^2+c*d^2)^-1*arctan(a^-1//2*c^(1/2)*x^2)+(1/2)*e*a^-5//2*c^3//2*(a*e^2+c*d^2)^-2*(c*d^2+2*a*e^2)*arctan(a^-1//2*c^(1/2)*x^2)+1//4*d*a^-3*c^2*(a*e^2+c*d^2)^-2*(2*c*d^2+3*a*e^2)*log(a+c*x^4))
@test integrate(x^8*(a+c*x^4)^-2*(d+e*x^2)^-1, x) == :(d^7//2*e^-1//2*(a*e^2+c*d^2)^-2*arctan(x*d^-1//2*e^(1/2))+1//4*d*x*c^-1*(a*e^2+c*d^2)^-1+-1//4*c^-1*x^3*(a+c*x^4)^-1*(a*e^2+c*d^2)^-1*(a*e+c*d*x^2)+-1//16*2^(1/2)*a^1//4*c^-7//4*(a*e^2+c*d^2)^-1*(d*c^(1/2)+-3*e*a^(1/2))*arctan(1+x*2^(1/2)*a^-1//4*c^1//4)+-1//32*2^(1/2)*a^1//4*c^-7//4*(a*e^2+c*d^2)^-1*(d*c^(1/2)+3*e*a^(1/2))*log(a^(1/2)+c^(1/2)*x^2+x*2^(1/2)*a^1//4*c^1//4)+1//16*2^(1/2)*a^1//4*c^-7//4*(a*e^2+c*d^2)^-1*(d*c^(1/2)+-3*e*a^(1/2))*arctan(1+-1*x*2^(1/2)*a^-1//4*c^1//4)+1//32*2^(1/2)*a^1//4*c^-7//4*(a*e^2+c*d^2)^-1*(d*c^(1/2)+3*e*a^(1/2))*log(a^(1/2)+c^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*c^1//4)+-1//4*2^(1/2)*a^1//4*c^-3//4*d^2*(a*e^2+c*d^2)^-2*(d*c^(1/2)+-1*e*a^(1/2))*arctan(1+x*2^(1/2)*a^-1//4*c^1//4)+-1//8*2^(1/2)*a^1//4*c^-3//4*d^2*(a*e^2+c*d^2)^-2*(d*c^(1/2)+e*a^(1/2))*log(a^(1/2)+c^(1/2)*x^2+x*2^(1/2)*a^1//4*c^1//4)+1//4*2^(1/2)*a^1//4*c^-3//4*d^2*(a*e^2+c*d^2)^-2*(d*c^(1/2)+-1*e*a^(1/2))*arctan(1+-1*x*2^(1/2)*a^-1//4*c^1//4)+1//8*2^(1/2)*a^1//4*c^-3//4*d^2*(a*e^2+c*d^2)^-2*(d*c^(1/2)+e*a^(1/2))*log(a^(1/2)+c^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*c^1//4))
@test integrate(x^6*(a+c*x^4)^-2*(d+e*x^2)^-1, x) == :(-1*d^5//2*e^(1/2)*(a*e^2+c*d^2)^-2*arctan(x*d^-1//2*e^(1/2))+-1//4*x*c^-1*(a+c*x^4)^-1*(a*e^2+c*d^2)^-1*(a*e+c*d*x^2)+-1//16*2^(1/2)*a^-1//4*c^-5//4*(a*e^2+c*d^2)^-1*(d*c^(1/2)+-1*e*a^(1/2))*arctan(1+x*2^(1/2)*a^-1//4*c^1//4)+-1//32*2^(1/2)*a^-1//4*c^-5//4*(a*e^2+c*d^2)^-1*(d*c^(1/2)+e*a^(1/2))*log(a^(1/2)+c^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*c^1//4)+1//16*2^(1/2)*a^-1//4*c^-5//4*(a*e^2+c*d^2)^-1*(d*c^(1/2)+-1*e*a^(1/2))*arctan(1+-1*x*2^(1/2)*a^-1//4*c^1//4)+1//32*2^(1/2)*a^-1//4*c^-5//4*(a*e^2+c*d^2)^-1*(d*c^(1/2)+e*a^(1/2))*log(a^(1/2)+c^(1/2)*x^2+x*2^(1/2)*a^1//4*c^1//4)+-1//4*2^(1/2)*a^-1//4*c^-1//4*d^2*(a*e^2+c*d^2)^-2*(d*c^(1/2)+e*a^(1/2))*arctan(1+-1*x*2^(1/2)*a^-1//4*c^1//4)+-1//8*2^(1/2)*a^-1//4*c^-1//4*d^2*(a*e^2+c*d^2)^-2*(d*c^(1/2)+-1*e*a^(1/2))*log(a^(1/2)+c^(1/2)*x^2+x*2^(1/2)*a^1//4*c^1//4)+1//4*2^(1/2)*a^-1//4*c^-1//4*d^2*(a*e^2+c*d^2)^-2*(d*c^(1/2)+e*a^(1/2))*arctan(1+x*2^(1/2)*a^-1//4*c^1//4)+1//8*2^(1/2)*a^-1//4*c^-1//4*d^2*(a*e^2+c*d^2)^-2*(d*c^(1/2)+-1*e*a^(1/2))*log(a^(1/2)+c^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*c^1//4))
@test integrate(x^4*(a+c*x^4)^-2*(d+e*x^2)^-1, x) == :(d^3//2*e^3//2*(a*e^2+c*d^2)^-2*arctan(x*d^-1//2*e^(1/2))+-1*x*(a+c*x^4)^-1*(4*a*e^2+4*c*d^2)^-1*(d+-1*e*x^2)+-1//16*2^(1/2)*a^-3//4*c^-3//4*(a*e^2+c*d^2)^-1*(-1*e*a^(1/2)+3*d*c^(1/2))*arctan(1+x*2^(1/2)*a^-1//4*c^1//4)+-1//32*2^(1/2)*a^-3//4*c^-3//4*(a*e^2+c*d^2)^-1*(e*a^(1/2)+3*d*c^(1/2))*log(a^(1/2)+c^(1/2)*x^2+x*2^(1/2)*a^1//4*c^1//4)+1//16*2^(1/2)*a^-3//4*c^-3//4*(a*e^2+c*d^2)^-1*(-1*e*a^(1/2)+3*d*c^(1/2))*arctan(1+-1*x*2^(1/2)*a^-1//4*c^1//4)+1//32*2^(1/2)*a^-3//4*c^-3//4*(a*e^2+c*d^2)^-1*(e*a^(1/2)+3*d*c^(1/2))*log(a^(1/2)+c^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*c^1//4)+-1//4*2^(1/2)*a^-3//4*c^1//4*d^2*(a*e^2+c*d^2)^-2*(d*c^(1/2)+-1*e*a^(1/2))*arctan(1+-1*x*2^(1/2)*a^-1//4*c^1//4)+-1//8*2^(1/2)*a^-3//4*c^1//4*d^2*(a*e^2+c*d^2)^-2*(d*c^(1/2)+e*a^(1/2))*log(a^(1/2)+c^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*c^1//4)+1//4*2^(1/2)*a^-3//4*c^1//4*d^2*(a*e^2+c*d^2)^-2*(d*c^(1/2)+-1*e*a^(1/2))*arctan(1+x*2^(1/2)*a^-1//4*c^1//4)+1//8*2^(1/2)*a^-3//4*c^1//4*d^2*(a*e^2+c*d^2)^-2*(d*c^(1/2)+e*a^(1/2))*log(a^(1/2)+c^(1/2)*x^2+x*2^(1/2)*a^1//4*c^1//4))
@test integrate(x^2*(a+c*x^4)^-2*(d+e*x^2)^-1, x) == :(-1*d^(1/2)*e^5//2*(a*e^2+c*d^2)^-2*arctan(x*d^-1//2*e^(1/2))+1//4*x*a^-1*(a+c*x^4)^-1*(a*e^2+c*d^2)^-1*(a*e+c*d*x^2)+-1//16*2^(1/2)*a^-5//4*c^-1//4*(a*e^2+c*d^2)^-1*(d*c^(1/2)+3*e*a^(1/2))*arctan(1+-1*x*2^(1/2)*a^-1//4*c^1//4)+-1//32*2^(1/2)*a^-5//4*c^-1//4*(a*e^2+c*d^2)^-1*(d*c^(1/2)+-3*e*a^(1/2))*log(a^(1/2)+c^(1/2)*x^2+x*2^(1/2)*a^1//4*c^1//4)+1//16*2^(1/2)*a^-5//4*c^-1//4*(a*e^2+c*d^2)^-1*(d*c^(1/2)+3*e*a^(1/2))*arctan(1+x*2^(1/2)*a^-1//4*c^1//4)+1//32*2^(1/2)*a^-5//4*c^-1//4*(a*e^2+c*d^2)^-1*(d*c^(1/2)+-3*e*a^(1/2))*log(a^(1/2)+c^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*c^1//4)+-1//4*d*e*2^(1/2)*a^-3//4*c^1//4*(a*e^2+c*d^2)^-2*(d*c^(1/2)+-1*e*a^(1/2))*arctan(1+x*2^(1/2)*a^-1//4*c^1//4)+-1//8*d*e*2^(1/2)*a^-3//4*c^1//4*(a*e^2+c*d^2)^-2*(d*c^(1/2)+e*a^(1/2))*log(a^(1/2)+c^(1/2)*x^2+x*2^(1/2)*a^1//4*c^1//4)+1//4*d*e*2^(1/2)*a^-3//4*c^1//4*(a*e^2+c*d^2)^-2*(d*c^(1/2)+-1*e*a^(1/2))*arctan(1+-1*x*2^(1/2)*a^-1//4*c^1//4)+1//8*d*e*2^(1/2)*a^-3//4*c^1//4*(a*e^2+c*d^2)^-2*(d*c^(1/2)+e*a^(1/2))*log(a^(1/2)+c^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*c^1//4))
@test integrate((a+c*x^4)^-2*(d+e*x^2)^-1, x) == :(d^-1//2*e^7//2*(a*e^2+c*d^2)^-2*arctan(x*d^-1//2*e^(1/2))+-1//16*2^(1/2)*a^-7//4*c^1//4*(a*e^2+c*d^2)^-1*(-1*e*a^(1/2)+3*d*c^(1/2))*arctan(1+-1*x*2^(1/2)*a^-1//4*c^1//4)+-1//32*2^(1/2)*a^-7//4*c^1//4*(a*e^2+c*d^2)^-1*(e*a^(1/2)+3*d*c^(1/2))*log(a^(1/2)+c^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*c^1//4)+1//4*c*x*a^-1*(a+c*x^4)^-1*(a*e^2+c*d^2)^-1*(d+-1*e*x^2)+1//16*2^(1/2)*a^-7//4*c^1//4*(a*e^2+c*d^2)^-1*(-1*e*a^(1/2)+3*d*c^(1/2))*arctan(1+x*2^(1/2)*a^-1//4*c^1//4)+1//32*2^(1/2)*a^-7//4*c^1//4*(a*e^2+c*d^2)^-1*(e*a^(1/2)+3*d*c^(1/2))*log(a^(1/2)+c^(1/2)*x^2+x*2^(1/2)*a^1//4*c^1//4)+-1//4*2^(1/2)*a^-3//4*c^1//4*e^2*(a*e^2+c*d^2)^-2*(d*c^(1/2)+-1*e*a^(1/2))*arctan(1+-1*x*2^(1/2)*a^-1//4*c^1//4)+-1//8*2^(1/2)*a^-3//4*c^1//4*e^2*(a*e^2+c*d^2)^-2*(d*c^(1/2)+e*a^(1/2))*log(a^(1/2)+c^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*c^1//4)+1//4*2^(1/2)*a^-3//4*c^1//4*e^2*(a*e^2+c*d^2)^-2*(d*c^(1/2)+-1*e*a^(1/2))*arctan(1+x*2^(1/2)*a^-1//4*c^1//4)+1//8*2^(1/2)*a^-3//4*c^1//4*e^2*(a*e^2+c*d^2)^-2*(d*c^(1/2)+e*a^(1/2))*log(a^(1/2)+c^(1/2)*x^2+x*2^(1/2)*a^1//4*c^1//4))
@test integrate(x^-2*(a+c*x^4)^-2*(d+e*x^2)^-1, x) == :(-1*a^-2*d^-1*x^-1+-1*d^-3//2*e^9//2*(a*e^2+c*d^2)^-2*arctan(x*d^-1//2*e^(1/2))+-1//4*c*x*a^-2*(a+c*x^4)^-1*(a*e^2+c*d^2)^-1*(a*e+c*d*x^2)+-1//4*2^(1/2)*a^-9//4*c^3//4*(a*e^2+c*d^2)^-2*(a^3//2*e^3+d*c^(1/2)*(c*d^2+2*a*e^2))*arctan(1+x*2^(1/2)*a^-1//4*c^1//4)+-1//8*2^(1/2)*a^-9//4*c^3//4*(a*e^2+c*d^2)^-2*(a^3//2*e^3+-1*d*c^(1/2)*(c*d^2+2*a*e^2))*log(a^(1/2)+c^(1/2)*x^2+x*2^(1/2)*a^1//4*c^1//4)+-1//16*2^(1/2)*a^-9//4*c^3//4*(a*e^2+c*d^2)^-1*(d*c^(1/2)+3*e*a^(1/2))*arctan(1+x*2^(1/2)*a^-1//4*c^1//4)+-1//32*2^(1/2)*a^-9//4*c^3//4*(a*e^2+c*d^2)^-1*(d*c^(1/2)+-3*e*a^(1/2))*log(a^(1/2)+c^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*c^1//4)+1//4*2^(1/2)*a^-9//4*c^3//4*(a*e^2+c*d^2)^-2*(a^3//2*e^3+d*c^(1/2)*(c*d^2+2*a*e^2))*arctan(1+-1*x*2^(1/2)*a^-1//4*c^1//4)+1//8*2^(1/2)*a^-9//4*c^3//4*(a*e^2+c*d^2)^-2*(a^3//2*e^3+-1*d*c^(1/2)*(c*d^2+2*a*e^2))*log(a^(1/2)+c^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*c^1//4)+1//16*2^(1/2)*a^-9//4*c^3//4*(a*e^2+c*d^2)^-1*(d*c^(1/2)+3*e*a^(1/2))*arctan(1+-1*x*2^(1/2)*a^-1//4*c^1//4)+1//32*2^(1/2)*a^-9//4*c^3//4*(a*e^2+c*d^2)^-1*(d*c^(1/2)+-3*e*a^(1/2))*log(a^(1/2)+c^(1/2)*x^2+x*2^(1/2)*a^1//4*c^1//4))
@test integrate(x^-4*(a+c*x^4)^-2*(d+e*x^2)^-1, x) == :(-1//3*a^-2*d^-1*x^-3+e*a^-2*d^-2*x^-1+d^-5//2*e^11//2*(a*e^2+c*d^2)^-2*arctan(x*d^-1//2*e^(1/2))+-1//4*x*a^-2*c^2*(a+c*x^4)^-1*(a*e^2+c*d^2)^-1*(d+-1*e*x^2)+-1//16*2^(1/2)*a^-11//4*c^5//4*(a*e^2+c*d^2)^-1*(-1*e*a^(1/2)+3*d*c^(1/2))*arctan(1+x*2^(1/2)*a^-1//4*c^1//4)+-1//32*2^(1/2)*a^-11//4*c^5//4*(a*e^2+c*d^2)^-1*(e*a^(1/2)+3*d*c^(1/2))*log(a^(1/2)+c^(1/2)*x^2+x*2^(1/2)*a^1//4*c^1//4)+1//16*2^(1/2)*a^-11//4*c^5//4*(a*e^2+c*d^2)^-1*(-1*e*a^(1/2)+3*d*c^(1/2))*arctan(1+-1*x*2^(1/2)*a^-1//4*c^1//4)+1//32*2^(1/2)*a^-11//4*c^5//4*(a*e^2+c*d^2)^-1*(e*a^(1/2)+3*d*c^(1/2))*log(a^(1/2)+c^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*c^1//4)+-1//4*2^(1/2)*a^-11//4*c^5//4*(a*e^2+c*d^2)^-2*(c*d^2+2*a*e^2)*(d*c^(1/2)+-1*e*a^(1/2))*arctan(1+x*2^(1/2)*a^-1//4*c^1//4)+-1//8*2^(1/2)*a^-11//4*c^5//4*(a*e^2+c*d^2)^-2*(c*d^2+2*a*e^2)*(d*c^(1/2)+e*a^(1/2))*log(a^(1/2)+c^(1/2)*x^2+x*2^(1/2)*a^1//4*c^1//4)+1//4*2^(1/2)*a^-11//4*c^5//4*(a*e^2+c*d^2)^-2*(c*d^2+2*a*e^2)*(d*c^(1/2)+-1*e*a^(1/2))*arctan(1+-1*x*2^(1/2)*a^-1//4*c^1//4)+1//8*2^(1/2)*a^-11//4*c^5//4*(a*e^2+c*d^2)^-2*(c*d^2+2*a*e^2)*(d*c^(1/2)+e*a^(1/2))*log(a^(1/2)+c^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*c^1//4))
@test integrate(x^2*(1+x^2)^-1*(1+x^4)^-1//2, x) == :(-1//4*2^(1/2)*arctan(x*2^(1/2)*(1+x^4)^-1//2)+1//4*((1+x^2)^-2*(1+x^4))^(1/2)*(1+x^4)^-1//2*(1+x^2)*Elliptic.F(2*arctan(x),1/2))
@test integrate(x^2*(1+x^4)^-1//2*(1+-1*x^2)^-1, x) == :(1//4*2^(1/2)*arctanh(x*2^(1/2)*(1+x^4)^-1//2)+-1//4*((1+x^2)^-2*(1+x^4))^(1/2)*(1+x^4)^-1//2*(1+x^2)*Elliptic.F(2*arctan(x),1/2))
@test integrate(x^2*(1+x^2)^-1*(1+-1*x^4)^-1//2, x) == :(-1//2*x*(1+-1*x^4)^-1//2*(1+-1*x^2)+(1+x^2)^(1/2)*(1+-1*x^2)^(1/2)*(1+-1*x^4)^-1//2*Elliptic.F(arcsin(x),-1)+-1//2*(1+x^2)^(1/2)*(1+-1*x^2)^(1/2)*(1+-1*x^4)^-1//2*Elliptic.E(arcsin(x),-1))
@test integrate(x^2*(1+-1*x^2)^-1*(1+-1*x^4)^-1//2, x) == :((1/2)*x*(1+-1*x^4)^-1//2*(1+x^2)+-1//2*(1+x^2)^(1/2)*(1+-1*x^2)^(1/2)*(1+-1*x^4)^-1//2*Elliptic.E(arcsin(x),-1))
@test integrate(x^2*(1+x^2)^-1*(-1+x^4)^-1//2, x) == :(-1//2*x*(-1+x^4)^-1//2*(1+-1*x^2)+-1//2*(1+x^2)^(1/2)*(1+-1*x^2)^(1/2)*(-1+x^4)^-1//2*Elliptic.E(arcsin(x),-1)+(1/2)*2^(1/2)*(1+x^2)^(1/2)*(-1+x^2)^(1/2)*(-1+x^4)^-1//2*Elliptic.F(arcsin(x*2^(1/2)*(-1+x^2)^-1//2),1/2))
@test integrate(x^2*(1+-1*x^2)^-1*(-1+x^4)^-1//2, x) == :((1/2)*x*(-1+x^4)^-1//2*(1+x^2)+-1//2*(1+x^2)^(1/2)*(1+-1*x^2)^(1/2)*(-1+x^4)^-1//2*Elliptic.E(arcsin(x),-1))
@test integrate(x^2*(1+x^2)^-1*(-1+-1*x^4)^-1//2, x) == :(-1//4*2^(1/2)*arctanh(x*2^(1/2)*(-1+-1*x^4)^-1//2)+1//4*((1+x^2)^-2*(1+x^4))^(1/2)*(-1+-1*x^4)^-1//2*(1+x^2)*Elliptic.F(2*arctan(x),1/2))
@test integrate(x^2*(1+-1*x^2)^-1*(-1+-1*x^4)^-1//2, x) == :(1//4*2^(1/2)*arctan(x*2^(1/2)*(-1+-1*x^4)^-1//2)+-1//4*((1+x^2)^-2*(1+x^4))^(1/2)*(-1+-1*x^4)^-1//2*(1+x^2)*Elliptic.F(2*arctan(x),1/2))
@test integrate(x^2*(c+d*x^2)^(1/2)*(a^2+b^2*x^4+2*a*b*x^2)^(1/2), x) == :(-1//8*d^-1*x^3*(a+b*x^2)^-1*(c+d*x^2)^(1/2)*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)*(b*c+-2*a*d)+1//6*b*d^-1*x^3*(a+b*x^2)^-1*(c+d*x^2)^3//2*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+1//16*c^2*d^-5//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)*(b*c+-2*a*d)*arctanh(x*d^(1/2)*(c+d*x^2)^-1//2)+-1//16*c*x*d^-2*(a+b*x^2)^-1*(c+d*x^2)^(1/2)*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)*(b*c+-2*a*d))
@test integrate(x*(c+d*x^2)^(1/2)*(a^2+b^2*x^4+2*a*b*x^2)^(1/2), x) == :(-1//3*d^-2*(a+b*x^2)^-1*(c+d*x^2)^3//2*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)*(b*c+-1*a*d)+1//5*b*d^-2*(a+b*x^2)^-1*(c+d*x^2)^5//2*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate((c+d*x^2)^(1/2)*(a^2+b^2*x^4+2*a*b*x^2)^(1/2), x) == :(-1//8*c*d^-3//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)*(b*c+-4*a*d)*arctanh(x*d^(1/2)*(c+d*x^2)^-1//2)+-1//8*x*d^-1*(a+b*x^2)^-1*(c+d*x^2)^(1/2)*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)*(b*c+-4*a*d)+1//4*b*x*d^-1*(a+b*x^2)^-1*(c+d*x^2)^3//2*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate(x^-1*(c+d*x^2)^(1/2)*(a^2+b^2*x^4+2*a*b*x^2)^(1/2), x) == :(a*(a+b*x^2)^-1*(c+d*x^2)^(1/2)*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-1*a*c^(1/2)*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)*arctanh(c^-1//2*(c+d*x^2)^(1/2))+1//3*b*d^-1*(a+b*x^2)^-1*(c+d*x^2)^3//2*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate(x^-2*(c+d*x^2)^(1/2)*(a^2+b^2*x^4+2*a*b*x^2)^(1/2), x) == :((1/2)*d^-1//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)*(b*c+2*a*d)*arctanh(x*d^(1/2)*(c+d*x^2)^-1//2)+(1/2)*x*c^-1*(a+b*x^2)^-1*(c+d*x^2)^(1/2)*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)*(b*c+2*a*d)+-1*a*c^-1*x^-1*(a+b*x^2)^-1*(c+d*x^2)^3//2*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate(x^-3*(c+d*x^2)^(1/2)*(a^2+b^2*x^4+2*a*b*x^2)^(1/2), x) == :((1/2)*c^-1*(a+b*x^2)^-1*(c+d*x^2)^(1/2)*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)*(a*d+2*b*c)+-1//2*c^-1//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)*(a*d+2*b*c)*arctanh(c^-1//2*(c+d*x^2)^(1/2))+-1//2*a*c^-1*x^-2*(a+b*x^2)^-1*(c+d*x^2)^3//2*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate(x^3*(d+e*x^2)^2*(a+b*x^2+c*x^4), x) == :(x^8*(1//8*c*d^2+1//8*e*(a*e+2*b*d))+1//4*a*d^2*x^4+1//6*d*x^6*(b*d+2*a*e)+1//10*e*x^10*(b*e+2*c*d)+1//12*c*e^2*x^12)
@test integrate(x^2*(d+e*x^2)^2*(a+b*x^2+c*x^4), x) == :(x^7*(1//7*c*d^2+1//7*e*(a*e+2*b*d))+1//3*a*d^2*x^3+1//5*d*x^5*(b*d+2*a*e)+1//9*e*x^9*(b*e+2*c*d)+1//11*c*e^2*x^11)
@test integrate(x*(d+e*x^2)^2*(a+b*x^2+c*x^4), x) == :(-1//8*e^-3*(d+e*x^2)^4*(-1*b*e+2*c*d)+1//6*e^-3*(d+e*x^2)^3*(a*e^2+c*d^2+-1*b*d*e)+1//10*c*e^-3*(d+e*x^2)^5)
@test integrate((d+e*x^2)^2*(a+b*x^2+c*x^4), x) == :(x^5*(1//5*c*d^2+1//5*e*(a*e+2*b*d))+a*x*d^2+1//3*d*x^3*(b*d+2*a*e)+1//7*e*x^7*(b*e+2*c*d)+1//9*c*e^2*x^9)
@test integrate(x^-1*(d+e*x^2)^2*(a+b*x^2+c*x^4), x) == :(x^4*(1//4*c*d^2+1//4*e*(a*e+2*b*d))+a*d^2*log(x)+(1/2)*d*x^2*(b*d+2*a*e)+1//6*e*x^6*(b*e+2*c*d)+1//8*c*e^2*x^8)
@test integrate(x^-2*(d+e*x^2)^2*(a+b*x^2+c*x^4), x) == :(x^3*(1//3*c*d^2+1//3*e*(a*e+2*b*d))+d*x*(b*d+2*a*e)+-1*a*d^2*x^-1+1//5*e*x^5*(b*e+2*c*d)+1//7*c*e^2*x^7)
@test integrate(x^-3*(d+e*x^2)^2*(a+b*x^2+c*x^4), x) == :(x^2*((1/2)*c*d^2+(1/2)*e*(a*e+2*b*d))+d*(b*d+2*a*e)*log(x)+-1//2*a*d^2*x^-2+1//4*e*x^4*(b*e+2*c*d)+1//6*c*e^2*x^6)
@test integrate(x^6*(d+e*x^2)^-2*(a+b*x^2+c*x^4), x) == :(-1//5*e^-3*x^5*(-1*b*e+2*c*d)+1//3*e^-4*x^3*(-1*e*(-1*a*e+2*b*d)+3*c*d^2)+1//7*c*e^-2*x^7+(1/2)*d^3//2*e^-11//2*(-1*e*(-5*a*e+7*b*d)+9*c*d^2)*arctan(x*d^-1//2*e^(1/2))+-1*d*x*e^-5*(-1*e*(-2*a*e+3*b*d)+4*c*d^2)+-1//2*x*d^2*e^-5*(d+e*x^2)^-1*(a*e^2+c*d^2+-1*b*d*e))
@test integrate(x^4*(d+e*x^2)^-2*(a+b*x^2+c*x^4), x) == :(x*e^-4*(-1*e*(-1*a*e+2*b*d)+3*c*d^2)+-1//3*e^-3*x^3*(-1*b*e+2*c*d)+1//5*c*e^-2*x^5+-1//2*d^(1/2)*e^-9//2*(-1*e*(-3*a*e+5*b*d)+7*c*d^2)*arctan(x*d^-1//2*e^(1/2))+(1/2)*d*x*e^-4*(d+e*x^2)^-1*(a*e^2+c*d^2+-1*b*d*e))
@test integrate(x^2*(d+e*x^2)^-2*(a+b*x^2+c*x^4), x) == :(-1*x*e^-3*(-1*b*e+2*c*d)+1//3*c*e^-2*x^3+(1/2)*d^-1//2*e^-7//2*(-1*e*(-1*a*e+3*b*d)+5*c*d^2)*arctan(x*d^-1//2*e^(1/2))+-1//2*x*e^-3*(d+e*x^2)^-1*(a*e^2+c*d^2+-1*b*d*e))
@test integrate((d+e*x^2)^-2*(a+b*x^2+c*x^4), x) == :(c*x*e^-2+(1/2)*x*d^-1*(d+e*x^2)^-1*(a+d*e^-2*(c*d+-1*b*e))+-1//2*d^-3//2*e^-5//2*(-1*e*(a*e+b*d)+3*c*d^2)*arctan(x*d^-1//2*e^(1/2)))
@test integrate(x^-2*(d+e*x^2)^-2*(a+b*x^2+c*x^4), x) == :(-1*a*d^-2*x^-1+(1/2)*d^-5//2*e^-3//2*(c*d^2+e*(b*d+-3*a*e))*arctan(x*d^-1//2*e^(1/2))+-1//2*x*d^-2*e^-1*(d+e*x^2)^-1*(a*e^2+c*d^2+-1*b*d*e))
@test integrate(x^-4*(d+e*x^2)^-2*(a+b*x^2+c*x^4), x) == :(-1*d^-3*x^-1*(b*d+-2*a*e)+-1//3*a*d^-2*x^-3+(1/2)*x*d^-3*(d+e*x^2)^-1*(a*e^2+c*d^2+-1*b*d*e)+(1/2)*d^-7//2*e^-1//2*(c*d^2+-1*e*(-5*a*e+3*b*d))*arctan(x*d^-1//2*e^(1/2)))
@test integrate(x^-6*(d+e*x^2)^-2*(a+b*x^2+c*x^4), x) == :(-1*d^-4*x^-1*(c*d^2+-1*e*(-3*a*e+2*b*d))+-1//3*d^-3*x^-3*(b*d+-2*a*e)+-1//5*a*d^-2*x^-5+-1//2*d^-9//2*e^(1/2)*(-1*e*(-7*a*e+5*b*d)+3*c*d^2)*arctan(x*d^-1//2*e^(1/2))+-1//2*e*x*d^-4*(d+e*x^2)^-1*(a*e^2+c*d^2+-1*b*d*e))
@test integrate(x^-8*(d+e*x^2)^-2*(a+b*x^2+c*x^4), x) == :(-1//3*d^-4*x^-3*(c*d^2+-1*e*(-3*a*e+2*b*d))+-1//5*d^-3*x^-5*(b*d+-2*a*e)+-1//7*a*d^-2*x^-7+e*d^-5*x^-1*(-1*e*(-4*a*e+3*b*d)+2*c*d^2)+(1/2)*d^-11//2*e^3//2*(-1*e*(-9*a*e+7*b*d)+5*c*d^2)*arctan(x*d^-1//2*e^(1/2))+(1/2)*x*d^-5*e^2*(d+e*x^2)^-1*(a*e^2+c*d^2+-1*b*d*e))
@test integrate(x^6*(d+e*x^2)^-3*(a+b*x^2+c*x^4), x) == :(x*e^-5*(-1*e*(-1*a*e+3*b*d)+6*c*d^2)+-1//3*e^-4*x^3*(-1*b*e+3*c*d)+1//5*c*e^-3*x^5+-1//8*d^(1/2)*e^-11//2*(15*a*e^2+63*c*d^2+-35*b*d*e)*arctan(x*d^-1//2*e^(1/2))+-1//4*x*d^2*e^-5*(d+e*x^2)^-2*(a*e^2+c*d^2+-1*b*d*e)+1//8*d*x*e^-5*(d+e*x^2)^-1*(-1*e*(-9*a*e+13*b*d)+17*c*d^2))
@test integrate(x^4*(d+e*x^2)^-3*(a+b*x^2+c*x^4), x) == :(-1*x*e^-4*(-1*b*e+3*c*d)+1//3*c*e^-3*x^3+-1//8*x*e^-4*(d+e*x^2)^-1*(-1*e*(-5*a*e+9*b*d)+13*c*d^2)+1//8*d^-1//2*e^-9//2*(-3*e*(-1*a*e+5*b*d)+35*c*d^2)*arctan(x*d^-1//2*e^(1/2))+1//4*d*x*e^-4*(d+e*x^2)^-2*(a*e^2+c*d^2+-1*b*d*e))
@test integrate(x^2*(d+e*x^2)^-3*(a+b*x^2+c*x^4), x) == :(c*x*e^-3+-1//4*x*e^-3*(d+e*x^2)^-2*(a*e^2+c*d^2+-1*b*d*e)+-1//8*d^-3//2*e^-7//2*(-1*e*(a*e+3*b*d)+15*c*d^2)*arctan(x*d^-1//2*e^(1/2))+1//8*x*d^-1*e^-3*(d+e*x^2)^-1*(-1*e*(-1*a*e+5*b*d)+9*c*d^2))
@test integrate((d+e*x^2)^-3*(a+b*x^2+c*x^4), x) == :(1//4*x*d^-1*(d+e*x^2)^-2*(a+d*e^-2*(c*d+-1*b*e))+1//8*d^-5//2*e^-5//2*(e*(b*d+3*a*e)+3*c*d^2)*arctan(x*d^-1//2*e^(1/2))+-1//8*x*d^-2*e^-2*(d+e*x^2)^-1*(-1*e*(b*d+3*a*e)+5*c*d^2))
@test integrate(x^-2*(d+e*x^2)^-3*(a+b*x^2+c*x^4), x) == :(-1*a*d^-3*x^-1+1//8*d^-7//2*e^-3//2*(c*d^2+3*e*(b*d+-5*a*e))*arctan(x*d^-1//2*e^(1/2))+-1//4*x*d^-2*e^-1*(d+e*x^2)^-2*(a*e^2+c*d^2+-1*b*d*e)+1//8*x*d^-3*e^-1*(d+e*x^2)^-1*(c*d^2+e*(-7*a*e+3*b*d)))
@test integrate(x^-4*(d+e*x^2)^-3*(a+b*x^2+c*x^4), x) == :(-1*d^-4*x^-1*(b*d+-3*a*e)+-1//3*a*d^-3*x^-3+1//4*x*d^-3*(d+e*x^2)^-2*(a*e^2+c*d^2+-1*b*d*e)+1//8*x*d^-4*(d+e*x^2)^-1*(-1*e*(-11*a*e+7*b*d)+3*c*d^2)+1//8*d^-9//2*e^-1//2*(3*c*d^2+35*a*e^2+-15*b*d*e)*arctan(x*d^-1//2*e^(1/2)))
@test integrate(x^-6*(d+e*x^2)^-3*(a+b*x^2+c*x^4), x) == :(-1*d^-5*x^-1*(c*d^2+6*a*e^2+-3*b*d*e)+-1//3*d^-4*x^-3*(b*d+-3*a*e)+-1//5*a*d^-3*x^-5+-1//8*d^-11//2*e^(1/2)*(15*c*d^2+63*a*e^2+-35*b*d*e)*arctan(x*d^-1//2*e^(1/2))+-1//4*e*x*d^-4*(d+e*x^2)^-2*(a*e^2+c*d^2+-1*b*d*e)+-1//8*e*x*d^-5*(d+e*x^2)^-1*(-1*e*(-15*a*e+11*b*d)+7*c*d^2))
@test integrate(x^9*(d+e*x^2)^-1*(a+b*x^2+c*x^4)^-1, x) == :(1//4*c^-1*e^-1*x^4+(1/2)*d^4*e^-3*(a*e^2+c*d^2+-1*b*d*e)^-1*log(d+e*x^2)+-1//2*c^-2*e^-2*x^2*(b*e+c*d)+-1//4*c^-3*(a*e^2+c*d^2+-1*b*d*e)^-1*(d*b^3+c*e*a^2+-1*a*e*b^2+-2*a*b*c*d)*log(a+b*x^2+c*x^4)+-1//2*c^-3*(b^2+-4*a*c)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1*(d*b^4+-1*a*e*b^3+2*d*a^2*c^2+-4*a*c*d*b^2+3*b*c*e*a^2)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x^2)))
@test integrate(x^7*(d+e*x^2)^-1*(a+b*x^2+c*x^4)^-1, x) == :((1/2)*c^-1*e^-1*x^2+-1//2*d^3*e^-2*(a*e^2+c*d^2+-1*b*d*e)^-1*log(d+e*x^2)+1//4*c^-2*(a*e^2+c*d^2+-1*b*d*e)^-1*(d*b^2+-1*a*b*e+-1*a*c*d)*log(a+b*x^2+c*x^4)+(1/2)*c^-2*(b^2+-4*a*c)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1*(d*b^3+-1*a*e*b^2+2*c*e*a^2+-3*a*b*c*d)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x^2)))
@test integrate(x^5*(d+e*x^2)^-1*(a+b*x^2+c*x^4)^-1, x) == :((1/2)*d^2*e^-1*(a*e^2+c*d^2+-1*b*d*e)^-1*log(d+e*x^2)+-1//4*c^-1*(a*e^2+c*d^2+-1*b*d*e)^-1*(b*d+-1*a*e)*log(a+b*x^2+c*x^4)+-1//2*c^-1*(b^2+-4*a*c)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1*(d*b^2+-1*a*b*e+-2*a*c*d)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x^2)))
@test integrate(x^3*(d+e*x^2)^-1*(a+b*x^2+c*x^4)^-1, x) == :(d*(4*a*e^2+4*c*d^2+-4*b*d*e)^-1*log(a+b*x^2+c*x^4)+-1*d*(2*a*e^2+2*c*d^2+-2*b*d*e)^-1*log(d+e*x^2)+(1/2)*(b^2+-4*a*c)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1*(b*d+-2*a*e)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x^2)))
@test integrate(x*(d+e*x^2)^-1*(a+b*x^2+c*x^4)^-1, x) == :(e*(2*a*e^2+2*c*d^2+-2*b*d*e)^-1*log(d+e*x^2)+-1*e*(4*a*e^2+4*c*d^2+-4*b*d*e)^-1*log(a+b*x^2+c*x^4)+-1//2*(b^2+-4*a*c)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1*(-1*b*e+2*c*d)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x^2)))
@test integrate(x^-1*(d+e*x^2)^-1*(a+b*x^2+c*x^4)^-1, x) == :(a^-1*d^-1*log(x)+-1//2*d^-1*e^2*(a*e^2+c*d^2+-1*b*d*e)^-1*log(d+e*x^2)+-1//4*a^-1*(a*e^2+c*d^2+-1*b*d*e)^-1*(c*d+-1*b*e)*log(a+b*x^2+c*x^4)+(1/2)*a^-1*(b^2+-4*a*c)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1*(-1*e*b^2+b*c*d+2*a*c*e)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x^2)))
@test integrate(x^-3*(d+e*x^2)^-1*(a+b*x^2+c*x^4)^-1, x) == :(-1//2*a^-1*d^-1*x^-2+(1/2)*d^-2*e^3*(a*e^2+c*d^2+-1*b*d*e)^-1*log(d+e*x^2)+-1*a^-2*d^-2*(a*e+b*d)*log(x)+1//4*a^-2*(a*e^2+c*d^2+-1*b*d*e)^-1*(-1*e*b^2+a*c*e+b*c*d)*log(a+b*x^2+c*x^4)+-1//2*a^-2*(b^2+-4*a*c)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1*(-1*e*b^3+c*d*b^2+-2*a*d*c^2+3*a*b*c*e)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x^2)))
@test integrate(x^-5*(d+e*x^2)^-1*(a+b*x^2+c*x^4)^-1, x) == :(-1//4*a^-1*d^-1*x^-4+a^-3*d^-3*(b^2*d^2+-1*a*(c*d^2+-1*a*e^2)+a*b*d*e)*log(x)+(1/2)*a^-2*d^-2*x^-2*(a*e+b*d)+-1//2*d^-3*e^4*(a*e^2+c*d^2+-1*b*d*e)^-1*log(d+e*x^2)+-1//4*a^-3*(a*e^2+c*d^2+-1*b*d*e)^-1*(-1*e*b^3+c*d*b^2+-1*a*d*c^2+2*a*b*c*e)*log(a+b*x^2+c*x^4)+(1/2)*a^-3*(b^2+-4*a*c)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1*(-1*e*b^4+c*d*b^3+-2*e*a^2*c^2+-3*a*b*d*c^2+4*a*c*e*b^2)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x^2)))
@test integrate(x^8*(d+e*x^2)^-1*(a+b*x^2+c*x^4)^-1, x) == :(1//3*c^-1*e^-1*x^3+d^7//2*e^-5//2*(a*e^2+c*d^2+-1*b*d*e)^-1*arctan(x*d^-1//2*e^(1/2))+-1*x*c^-2*e^-2*(b*e+c*d)+-1//2*2^(1/2)*c^-5//2*(b+(b^2+-4*a*c)^(1/2))^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1*(d*b^3+(b^2+-4*a*c)^-1//2*(d*b^4+-1*a*e*b^3+2*d*a^2*c^2+-4*a*c*d*b^2+3*b*c*e*a^2)+c*e*a^2+-1*a*e*b^2+-2*a*b*c*d)*arctan(x*2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2)+-1//2*2^(1/2)*c^-5//2*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1*(d*b^3+-1*(b^2+-4*a*c)^-1//2*(d*b^4+-1*a*e*b^3+2*d*a^2*c^2+-4*a*c*d*b^2+3*b*c*e*a^2)+c*e*a^2+-1*a*e*b^2+-2*a*b*c*d)*arctan(x*2^(1/2)*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2))
@test integrate(x^6*(d+e*x^2)^-1*(a+b*x^2+c*x^4)^-1, x) == :(x*c^-1*e^-1+-1*d^5//2*e^-3//2*(a*e^2+c*d^2+-1*b*d*e)^-1*arctan(x*d^-1//2*e^(1/2))+(1/2)*2^(1/2)*c^-3//2*(b+(b^2+-4*a*c)^(1/2))^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1*(d*b^2+(b^2+-4*a*c)^-1//2*(d*b^3+-1*a*e*b^2+2*c*e*a^2+-3*a*b*c*d)+-1*a*b*e+-1*a*c*d)*arctan(x*2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2)+(1/2)*2^(1/2)*c^-3//2*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1*(d*b^2+-1*(b^2+-4*a*c)^-1//2*(d*b^3+-1*a*e*b^2+2*c*e*a^2+-3*a*b*c*d)+-1*a*b*e+-1*a*c*d)*arctan(x*2^(1/2)*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2))
@test integrate(x^4*(d+e*x^2)^-1*(a+b*x^2+c*x^4)^-1, x) == :(d^3//2*e^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1*arctan(x*d^-1//2*e^(1/2))+-1//2*2^(1/2)*c^-1//2*(b+(b^2+-4*a*c)^(1/2))^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1*(b*d+(b^2+-4*a*c)^-1//2*(d*b^2+-1*a*b*e+-2*a*c*d)+-1*a*e)*arctan(x*2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2)+-1//2*2^(1/2)*c^-1//2*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1*(b*d+-1*a*e+-1*(b^2+-4*a*c)^-1//2*(d*b^2+-1*a*b*e+-2*a*c*d))*arctan(x*2^(1/2)*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2))
@test integrate(x^2*(d+e*x^2)^-1*(a+b*x^2+c*x^4)^-1, x) == :(-1*d^(1/2)*e^(1/2)*(a*e^2+c*d^2+-1*b*d*e)^-1*arctan(x*d^-1//2*e^(1/2))+(1/2)*2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1*(d+(b^2+-4*a*c)^-1//2*(b*d+-2*a*e))*arctan(x*2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2)+(1/2)*2^(1/2)*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1*(d+-1*(b^2+-4*a*c)^-1//2*(b*d+-2*a*e))*arctan(x*2^(1/2)*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2))
@test integrate((d+e*x^2)^-1*(a+b*x^2+c*x^4)^-1, x) == :(d^-1//2*e^3//2*(a*e^2+c*d^2+-1*b*d*e)^-1*arctan(x*d^-1//2*e^(1/2))+-1//2*2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1*(e+(b^2+-4*a*c)^-1//2*(-1*b*e+2*c*d))*arctan(x*2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2)+-1//2*2^(1/2)*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1*(e+-1*(b^2+-4*a*c)^-1//2*(-1*b*e+2*c*d))*arctan(x*2^(1/2)*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2))
@test integrate(x^-2*(d+e*x^2)^-1*(a+b*x^2+c*x^4)^-1, x) == :(-1*a^-1*d^-1*x^-1+-1*d^-3//2*e^5//2*(a*e^2+c*d^2+-1*b*d*e)^-1*arctan(x*d^-1//2*e^(1/2))+-1//2*2^(1/2)*a^-1*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1*(c*d+-1*b*e+-1*(b^2+-4*a*c)^-1//2*(-1*e*b^2+b*c*d+2*a*c*e))*arctan(x*2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2)+-1//2*2^(1/2)*a^-1*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1*(c*d+(b^2+-4*a*c)^-1//2*(-1*e*b^2+b*c*d+2*a*c*e)+-1*b*e)*arctan(x*2^(1/2)*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2))
@test integrate(x^-4*(d+e*x^2)^-1*(a+b*x^2+c*x^4)^-1, x) == :(-1//3*a^-1*d^-1*x^-3+a^-2*d^-2*x^-1*(a*e+b*d)+d^-5//2*e^7//2*(a*e^2+c*d^2+-1*b*d*e)^-1*arctan(x*d^-1//2*e^(1/2))+(1/2)*2^(1/2)*a^-2*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1*(-1*e*b^2+-1*(b^2+-4*a*c)^-1//2*(-1*e*b^3+c*d*b^2+-2*a*d*c^2+3*a*b*c*e)+a*c*e+b*c*d)*arctan(x*2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2)+(1/2)*2^(1/2)*a^-2*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1*((b^2+-4*a*c)^-1//2*(-1*e*b^3+c*d*b^2+-2*a*d*c^2+3*a*b*c*e)+-1*e*b^2+a*c*e+b*c*d)*arctan(x*2^(1/2)*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2))
@test integrate((f*x)^-1//2*(d+e*x^2)^-1*(a+b*x^2+c*x^4)^-1, x) == :((1/2)*2^(1/2)*d^-3//4*e^7//4*f^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1*arctan(1+2^(1/2)*d^-1//4*e^1//4*f^-1//2*(f*x)^(1/2))+-1//2*2^(1/2)*d^-3//4*e^7//4*f^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1*arctan(1+-1*2^(1/2)*d^-1//4*e^1//4*f^-1//2*(f*x)^(1/2))+-1//4*2^(1/2)*d^-3//4*e^7//4*f^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1*log(d^(1/2)*f^(1/2)+x*e^(1/2)*f^(1/2)+-1*2^(1/2)*d^1//4*e^1//4*(f*x)^(1/2))+1//4*2^(1/2)*d^-3//4*e^7//4*f^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1*log(d^(1/2)*f^(1/2)+x*e^(1/2)*f^(1/2)+2^(1/2)*d^1//4*e^1//4*(f*x)^(1/2))+(1/2)*2^3//4*c^3//4*f^-1//2*(b^2+-4*a*c)^-1//2*(-1b+-1*(b^2+-4*a*c)^(1/2))^-3//4*(a*e^2+c*d^2+-1*b*d*e)^-1*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)*arctan(2^1//4*c^1//4*f^-1//2*(f*x)^(1/2)*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4)+(1/2)*2^3//4*c^3//4*f^-1//2*(b^2+-4*a*c)^-1//2*(-1b+-1*(b^2+-4*a*c)^(1/2))^-3//4*(a*e^2+c*d^2+-1*b*d*e)^-1*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)*arctanh(2^1//4*c^1//4*f^-1//2*(f*x)^(1/2)*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4)+-1//2*2^3//4*c^3//4*f^-1//2*(b^2+-4*a*c)^-1//2*((b^2+-4*a*c)^(1/2)+-1b)^-3//4*(a*e^2+c*d^2+-1*b*d*e)^-1*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)*arctan(2^1//4*c^1//4*f^-1//2*(f*x)^(1/2)*((b^2+-4*a*c)^(1/2)+-1b)^-1//4)+-1//2*2^3//4*c^3//4*f^-1//2*(b^2+-4*a*c)^-1//2*((b^2+-4*a*c)^(1/2)+-1b)^-3//4*(a*e^2+c*d^2+-1*b*d*e)^-1*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)*arctanh(2^1//4*c^1//4*f^-1//2*(f*x)^(1/2)*((b^2+-4*a*c)^(1/2)+-1b)^-1//4))
@test integrate(x^5*(d+e*x^2)^-1*(a+b*x^2+c*x^4)^(1/2), x) == :(1//6*c^-1*e^-1*(a+b*x^2+c*x^4)^3//2+(1/2)*d^2*e^-4*(a*e^2+c*d^2+-1*b*d*e)^(1/2)*arctanh((1/2)*(a+b*x^2+c*x^4)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1//2*(b*d+x^2*(-1*b*e+2*c*d)+-2*a*e))+-1//32*c^-5//2*e^-4*(-1*b^3*e^3+16*c^3*d^3+-8*d*e*c^2*(b*d+-1*a*e)+-2*b*c*e^2*(b*d+-2*a*e))*arctanh((1/2)*c^-1//2*(a+b*x^2+c*x^4)^-1//2*(b+2*c*x^2))+1//16*c^-2*e^-3*(a+b*x^2+c*x^4)^(1/2)*((b*e+4*c*d)*(-1*b*e+2*c*d)+-2*c*e*x^2*(b*e+2*c*d)))
@test integrate(x^3*(d+e*x^2)^-1*(a+b*x^2+c*x^4)^(1/2), x) == :(-1//2*d*e^-3*(a*e^2+c*d^2+-1*b*d*e)^(1/2)*arctanh((1/2)*(a+b*x^2+c*x^4)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1//2*(b*d+x^2*(-1*b*e+2*c*d)+-2*a*e))+-1//8*c^-1*e^-2*(a+b*x^2+c*x^4)^(1/2)*(-1*b*e+4*c*d+-2*c*e*x^2)+1//16*c^-3//2*e^-3*(-1*b^2*e^2+8*c^2*d^2+-4*c*e*(b*d+-1*a*e))*arctanh((1/2)*c^-1//2*(a+b*x^2+c*x^4)^-1//2*(b+2*c*x^2)))
@test integrate(x*(d+e*x^2)^-1*(a+b*x^2+c*x^4)^(1/2), x) == :((1/2)*e^-1*(a+b*x^2+c*x^4)^(1/2)+(1/2)*e^-2*(a*e^2+c*d^2+-1*b*d*e)^(1/2)*arctanh((1/2)*(a+b*x^2+c*x^4)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1//2*(b*d+x^2*(-1*b*e+2*c*d)+-2*a*e))+-1//4*c^-1//2*e^-2*(-1*b*e+2*c*d)*arctanh((1/2)*c^-1//2*(a+b*x^2+c*x^4)^-1//2*(b+2*c*x^2)))
@test integrate(x^-1*(d+e*x^2)^-1*(a+b*x^2+c*x^4)^(1/2), x) == :((1/2)*c^(1/2)*e^-1*arctanh((1/2)*c^-1//2*(a+b*x^2+c*x^4)^-1//2*(b+2*c*x^2))+-1//2*a^(1/2)*d^-1*arctanh((1/2)*a^-1//2*(a+b*x^2+c*x^4)^-1//2*(2a+b*x^2))+-1//2*d^-1*e^-1*(a*e^2+c*d^2+-1*b*d*e)^(1/2)*arctanh((1/2)*(a+b*x^2+c*x^4)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1//2*(b*d+x^2*(-1*b*e+2*c*d)+-2*a*e)))
@test integrate(x^-3*(d+e*x^2)^-1*(a+b*x^2+c*x^4)^(1/2), x) == :((1/2)*c^(1/2)*d^-1*arctanh((1/2)*c^-1//2*(a+b*x^2+c*x^4)^-1//2*(b+2*c*x^2))+(1/2)*d^-2*(a*e^2+c*d^2+-1*b*d*e)^(1/2)*arctanh((1/2)*(a+b*x^2+c*x^4)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1//2*(b*d+x^2*(-1*b*e+2*c*d)+-2*a*e))+-1//2*d^-1*x^-2*(a+b*x^2+c*x^4)^(1/2)+(1/2)*e*a^(1/2)*d^-2*arctanh((1/2)*a^-1//2*(a+b*x^2+c*x^4)^-1//2*(2a+b*x^2))+-1//4*b*a^-1//2*d^-1*arctanh((1/2)*a^-1//2*(a+b*x^2+c*x^4)^-1//2*(2a+b*x^2))+-1//4*c^-1//2*d^-2*(-1*b*e+2*c*d)*arctanh((1/2)*c^-1//2*(a+b*x^2+c*x^4)^-1//2*(b+2*c*x^2))+-1//4*b*e*c^-1//2*d^-2*arctanh((1/2)*c^-1//2*(a+b*x^2+c*x^4)^-1//2*(b+2*c*x^2)))
@test integrate(x^5*(d+e*x^2)^-1*(a+b*x^2+c*x^4)^3//2, x) == :(1//10*c^-1*e^-1*(a+b*x^2+c*x^4)^5//2+(1/2)*d^2*e^-6*(a*e^2+c*d^2+-1*b*d*e)^3//2*arctanh((1/2)*(a+b*x^2+c*x^4)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1//2*(b*d+x^2*(-1*b*e+2*c*d)+-2*a*e))+-1//512*c^-7//2*e^-6*(3*b^5*e^5+256*c^5*d^5+-384*e*c^4*d^3*(b*d+-1*a*e)+6*c*b^3*e^4*(b*d+-4*a*e)+16*b*c^2*e^3*(b^2*d^2+3*a^2*e^2+-3*a*b*d*e)+96*d*c^3*e^2*(b*d+-1*a*e)^2)*arctanh((1/2)*c^-1//2*(a+b*x^2+c*x^4)^-1//2*(b+2*c*x^2))+1//96*c^-2*e^-3*(a+b*x^2+c*x^4)^3//2*(-3*b^2*e^2+16*c^2*d^2+-6*b*c*d*e+-6*c*e*x^2*(b*e+2*c*d))+1//256*c^-3*e^-5*(a+b*x^2+c*x^4)^(1/2)*(3*b^4*e^4+128*c^4*d^4+-32*e*c^3*d^2*(-4*a*e+5*b*d)+-2*c*e*x^2*(-3*b^3*e^3+32*c^3*d^3+-8*d*e*c^2*(-3*a*e+2*b*d)+-6*b*c*e^2*(b*d+-2*a*e))+6*c*b^2*e^3*(b*d+-2*a*e)+8*b*d*c^2*e^2*(-3*a*e+2*b*d)))
@test integrate(x^3*(d+e*x^2)^-1*(a+b*x^2+c*x^4)^3//2, x) == :(-1//2*d*e^-5*(a*e^2+c*d^2+-1*b*d*e)^3//2*arctanh((1/2)*(a+b*x^2+c*x^4)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1//2*(b*d+x^2*(-1*b*e+2*c*d)+-2*a*e))+-1//48*c^-1*e^-2*(a+b*x^2+c*x^4)^3//2*(-3*b*e+8*c*d+-6*c*e*x^2)+-1//128*c^-2*e^-4*(a+b*x^2+c*x^4)^(1/2)*(3*b^3*e^3+64*c^3*d^3+-16*d*e*c^2*(-4*a*e+5*b*d)+-2*c*e*x^2*(-3*b^2*e^2+16*c^2*d^2+-4*c*e*(-3*a*e+2*b*d))+4*b*c*e^2*(-3*a*e+2*b*d))+1//256*c^-5//2*e^-5*(3*b^4*e^4+128*c^4*d^4+48*c^2*e^2*(b*d+-1*a*e)^2+-192*e*c^3*d^2*(b*d+-1*a*e)+8*c*b^2*e^3*(b*d+-3*a*e))*arctanh((1/2)*c^-1//2*(a+b*x^2+c*x^4)^-1//2*(b+2*c*x^2)))
@test integrate(x*(d+e*x^2)^-1*(a+b*x^2+c*x^4)^3//2, x) == :(1//6*e^-1*(a+b*x^2+c*x^4)^3//2+(1/2)*e^-4*(a*e^2+c*d^2+-1*b*d*e)^3//2*arctanh((1/2)*(a+b*x^2+c*x^4)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1//2*(b*d+x^2*(-1*b*e+2*c*d)+-2*a*e))+1//16*c^-1*e^-3*(a+b*x^2+c*x^4)^(1/2)*(b^2*e^2+8*c^2*d^2+-2*c*e*(-4*a*e+5*b*d)+-2*c*e*x^2*(-1*b*e+2*c*d))+-1//32*c^-3//2*e^-4*(-1*b*e+2*c*d)*(-1*b^2*e^2+8*c^2*d^2+-4*c*e*(-3*a*e+2*b*d))*arctanh((1/2)*c^-1//2*(a+b*x^2+c*x^4)^-1//2*(b+2*c*x^2)))
@test integrate(x^-1*(d+e*x^2)^-1*(a+b*x^2+c*x^4)^3//2, x) == :((1/2)*a*d^-1*(a+b*x^2+c*x^4)^(1/2)+-1//2*a^3//2*d^-1*arctanh((1/2)*a^-1//2*(a+b*x^2+c*x^4)^-1//2*(2a+b*x^2))+-1//2*d^-1*e^-3*(a*e^2+c*d^2+-1*b*d*e)^3//2*arctanh((1/2)*(a+b*x^2+c*x^4)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1//2*(b*d+x^2*(-1*b*e+2*c*d)+-2*a*e))+-1//8*d^-1*e^-2*(a+b*x^2+c*x^4)^(1/2)*(-1*e*(-4*a*e+5*b*d)+4*c*d^2+-2*c*d*e*x^2)+1//4*a*b*c^-1//2*d^-1*arctanh((1/2)*c^-1//2*(a+b*x^2+c*x^4)^-1//2*(b+2*c*x^2))+1//16*c^-1//2*d^-1*e^-3*(8*c^2*d^3+b*e^2*(-4*a*e+3*b*d)+-12*c*d*e*(b*d+-1*a*e))*arctanh((1/2)*c^-1//2*(a+b*x^2+c*x^4)^-1//2*(b+2*c*x^2)))
@test integrate(x^-3*(d+e*x^2)^-1*(a+b*x^2+c*x^4)^3//2, x) == :(-1//2*d^-1*x^-2*(a+b*x^2+c*x^4)^3//2+1//8*d^-1*(a+b*x^2+c*x^4)^(1/2)*(9b+6*c*x^2)+(1/2)*e*a^3//2*d^-2*arctanh((1/2)*a^-1//2*(a+b*x^2+c*x^4)^-1//2*(2a+b*x^2))+(1/2)*d^-2*e^-2*(a*e^2+c*d^2+-1*b*d*e)^3//2*arctanh((1/2)*(a+b*x^2+c*x^4)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1//2*(b*d+x^2*(-1*b*e+2*c*d)+-2*a*e))+-3//4*b*a^(1/2)*d^-1*arctanh((1/2)*a^-1//2*(a+b*x^2+c*x^4)^-1//2*(2a+b*x^2))+1//16*c^-1//2*d^-1*(3*b^2+12*a*c)*arctanh((1/2)*c^-1//2*(a+b*x^2+c*x^4)^-1//2*(b+2*c*x^2))+-1//16*e*c^-1*d^-2*(a+b*x^2+c*x^4)^(1/2)*(b^2+8*a*c+2*b*c*x^2)+1//16*c^-1*d^-2*e^-1*(a+b*x^2+c*x^4)^(1/2)*(b^2*e^2+8*c^2*d^2+-2*c*e*(-4*a*e+5*b*d)+-2*c*e*x^2*(-1*b*e+2*c*d))+-1//32*c^-3//2*d^-2*e^-2*(-1*b*e+2*c*d)*(-1*b^2*e^2+8*c^2*d^2+-4*c*e*(-3*a*e+2*b*d))*arctanh((1/2)*c^-1//2*(a+b*x^2+c*x^4)^-1//2*(b+2*c*x^2))+1//32*b*e*c^-3//2*d^-2*(b^2+-12*a*c)*arctanh((1/2)*c^-1//2*(a+b*x^2+c*x^4)^-1//2*(b+2*c*x^2)))
@test integrate(x^5*(d+e*x^2)^-1*(a+b*x^2+c*x^4)^-1//2, x) == :((1/2)*c^-1*e^-1*(a+b*x^2+c*x^4)^(1/2)+(1/2)*d^2*e^-2*(a*e^2+c*d^2+-1*b*d*e)^-1//2*arctanh((1/2)*(a+b*x^2+c*x^4)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1//2*(b*d+x^2*(-1*b*e+2*c*d)+-2*a*e))+-1//4*c^-3//2*e^-2*(b*e+2*c*d)*arctanh((1/2)*c^-1//2*(a+b*x^2+c*x^4)^-1//2*(b+2*c*x^2)))
@test integrate(x^3*(d+e*x^2)^-1*(a+b*x^2+c*x^4)^-1//2, x) == :((1/2)*c^-1//2*e^-1*arctanh((1/2)*c^-1//2*(a+b*x^2+c*x^4)^-1//2*(b+2*c*x^2))+-1//2*d*e^-1*(a*e^2+c*d^2+-1*b*d*e)^-1//2*arctanh((1/2)*(a+b*x^2+c*x^4)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1//2*(b*d+x^2*(-1*b*e+2*c*d)+-2*a*e)))
@test integrate(x*(d+e*x^2)^-1*(a+b*x^2+c*x^4)^-1//2, x) == :((1/2)*(a*e^2+c*d^2+-1*b*d*e)^-1//2*arctanh((1/2)*(a+b*x^2+c*x^4)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1//2*(b*d+x^2*(-1*b*e+2*c*d)+-2*a*e)))
@test integrate(x^-1*(d+e*x^2)^-1*(a+b*x^2+c*x^4)^-1//2, x) == :(-1//2*a^-1//2*d^-1*arctanh((1/2)*a^-1//2*(a+b*x^2+c*x^4)^-1//2*(2a+b*x^2))+-1//2*e*d^-1*(a*e^2+c*d^2+-1*b*d*e)^-1//2*arctanh((1/2)*(a+b*x^2+c*x^4)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1//2*(b*d+x^2*(-1*b*e+2*c*d)+-2*a*e)))
@test integrate(x^-3*(d+e*x^2)^-1*(a+b*x^2+c*x^4)^-1//2, x) == :((1/2)*e*a^-1//2*d^-2*arctanh((1/2)*a^-1//2*(a+b*x^2+c*x^4)^-1//2*(2a+b*x^2))+(1/2)*d^-2*e^2*(a*e^2+c*d^2+-1*b*d*e)^-1//2*arctanh((1/2)*(a+b*x^2+c*x^4)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1//2*(b*d+x^2*(-1*b*e+2*c*d)+-2*a*e))+-1//2*a^-1*d^-1*x^-2*(a+b*x^2+c*x^4)^(1/2)+1//4*b*a^-3//2*d^-1*arctanh((1/2)*a^-1//2*(a+b*x^2+c*x^4)^-1//2*(2a+b*x^2)))
@test integrate(x^7*(d+e*x^2)^-1*(a+b*x^2+c*x^4)^-3//2, x) == :((1/2)*c^-3//2*e^-1*arctanh((1/2)*c^-1//2*(a+b*x^2+c*x^4)^-1//2*(b+2*c*x^2))+-1//2*d^3*e^-1*(a*e^2+c*d^2+-1*b*d*e)^-3//2*arctanh((1/2)*(a+b*x^2+c*x^4)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1//2*(b*d+x^2*(-1*b*e+2*c*d)+-2*a*e))+c^-1*(b^2+-4*a*c)^-1*(a+b*x^2+c*x^4)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1*(a*(d*b^2+-1*a*b*e+-2*a*c*d)+x^2*(d*b^3+-1*a*e*b^2+2*c*e*a^2+-3*a*b*c*d)))
@test integrate(x^5*(d+e*x^2)^-1*(a+b*x^2+c*x^4)^-3//2, x) == :((1/2)*d^2*(a*e^2+c*d^2+-1*b*d*e)^-3//2*arctanh((1/2)*(a+b*x^2+c*x^4)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1//2*(b*d+x^2*(-1*b*e+2*c*d)+-2*a*e))+-1*(b^2+-4*a*c)^-1*(a+b*x^2+c*x^4)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1*(a*(b*d+-2*a*e)+x^2*(d*b^2+-1*a*b*e+-2*a*c*d)))
@test integrate(x^3*(d+e*x^2)^-1*(a+b*x^2+c*x^4)^-3//2, x) == :((b^2+-4*a*c)^-1*(a+b*x^2+c*x^4)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1*(a*(-1*b*e+2*c*d)+c*x^2*(b*d+-2*a*e))+-1//2*d*e*(a*e^2+c*d^2+-1*b*d*e)^-3//2*arctanh((1/2)*(a+b*x^2+c*x^4)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1//2*(b*d+x^2*(-1*b*e+2*c*d)+-2*a*e)))
@test integrate(x*(d+e*x^2)^-1*(a+b*x^2+c*x^4)^-3//2, x) == :((1/2)*e^2*(a*e^2+c*d^2+-1*b*d*e)^-3//2*arctanh((1/2)*(a+b*x^2+c*x^4)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1//2*(b*d+x^2*(-1*b*e+2*c*d)+-2*a*e))+-1*(b^2+-4*a*c)^-1*(a+b*x^2+c*x^4)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1*(-1*e*b^2+b*c*d+c*x^2*(-1*b*e+2*c*d)+2*a*c*e))
@test integrate(x^-1*(d+e*x^2)^-1*(a+b*x^2+c*x^4)^-3//2, x) == :(-1//2*a^-3//2*d^-1*arctanh((1/2)*a^-1//2*(a+b*x^2+c*x^4)^-1//2*(2a+b*x^2))+-1//2*d^-1*e^3*(a*e^2+c*d^2+-1*b*d*e)^-3//2*arctanh((1/2)*(a+b*x^2+c*x^4)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1//2*(b*d+x^2*(-1*b*e+2*c*d)+-2*a*e))+a^-1*d^-1*(b^2+-4*a*c)^-1*(a+b*x^2+c*x^4)^-1//2*(b^2+-2*a*c+b*c*x^2)+e*d^-1*(b^2+-4*a*c)^-1*(a+b*x^2+c*x^4)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1*(-1*e*b^2+b*c*d+c*x^2*(-1*b*e+2*c*d)+2*a*c*e))
@test integrate(x^-3*(d+e*x^2)^-1*(a+b*x^2+c*x^4)^-3//2, x) == :((1/2)*e*a^-3//2*d^-2*arctanh((1/2)*a^-1//2*(a+b*x^2+c*x^4)^-1//2*(2a+b*x^2))+(1/2)*d^-2*e^4*(a*e^2+c*d^2+-1*b*d*e)^-3//2*arctanh((1/2)*(a+b*x^2+c*x^4)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1//2*(b*d+x^2*(-1*b*e+2*c*d)+-2*a*e))+3//4*b*a^-5//2*d^-1*arctanh((1/2)*a^-1//2*(a+b*x^2+c*x^4)^-1//2*(2a+b*x^2))+a^-1*d^-1*x^-2*(b^2+-4*a*c)^-1*(a+b*x^2+c*x^4)^-1//2*(b^2+-2*a*c+b*c*x^2)+-1*e*a^-1*d^-2*(b^2+-4*a*c)^-1*(a+b*x^2+c*x^4)^-1//2*(b^2+-2*a*c+b*c*x^2)+-1*d^-2*e^2*(b^2+-4*a*c)^-1*(a+b*x^2+c*x^4)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1*(-1*e*b^2+b*c*d+c*x^2*(-1*b*e+2*c*d)+2*a*c*e)+-1//2*a^-2*d^-1*x^-2*(b^2+-4*a*c)^-1*(a+b*x^2+c*x^4)^(1/2)*(3*b^2+-8*a*c))
@test integrate(x^7*(d+e*x^2)^(1/2)*(a+b*x^2+c*x^4)^-1, x) == :(c^-3*(d+e*x^2)^(1/2)*(b^2+-1*a*c)+1//5*c^-1*e^-2*(d+e*x^2)^5//2+-1//3*c^-2*e^-2*(d+e*x^2)^3//2*(b*e+c*d)+-1//2*2^(1/2)*c^-7//2*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*((b^2+-4*a*c)^-1//2*(-1*e*b^4+c*d*b^3+-2*e*a^2*c^2+-3*a*b*d*c^2+4*a*c*e*b^2)+-1*e*b^3+c*d*b^2+-1*a*d*c^2+2*a*b*c*e)*arctanh(2^(1/2)*c^(1/2)*(d+e*x^2)^(1/2)*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2)+-1//2*2^(1/2)*c^-7//2*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*(-1*e*b^3+-1*(b^2+-4*a*c)^-1//2*(-1*e*b^4+c*d*b^3+-2*e*a^2*c^2+-3*a*b*d*c^2+4*a*c*e*b^2)+c*d*b^2+-1*a*d*c^2+2*a*b*c*e)*arctanh(2^(1/2)*c^(1/2)*(d+e*x^2)^(1/2)*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2))
@test integrate(x^5*(d+e*x^2)^(1/2)*(a+b*x^2+c*x^4)^-1, x) == :(-1*b*c^-2*(d+e*x^2)^(1/2)+1//3*c^-1*e^-1*(d+e*x^2)^3//2+(1/2)*2^(1/2)*c^-5//2*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*((b^2+-4*a*c)^-1//2*(-1*e*b^3+c*d*b^2+-2*a*d*c^2+3*a*b*c*e)+-1*e*b^2+a*c*e+b*c*d)*arctanh(2^(1/2)*c^(1/2)*(d+e*x^2)^(1/2)*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2)+(1/2)*2^(1/2)*c^-5//2*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*(-1*e*b^2+-1*(b^2+-4*a*c)^-1//2*(-1*e*b^3+c*d*b^2+-2*a*d*c^2+3*a*b*c*e)+a*c*e+b*c*d)*arctanh(2^(1/2)*c^(1/2)*(d+e*x^2)^(1/2)*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2))
@test integrate(x^3*(d+e*x^2)^(1/2)*(a+b*x^2+c*x^4)^-1, x) == :(c^-1*(d+e*x^2)^(1/2)+(1/2)*2^(1/2)*c^-3//2*(b^2+-4*a*c)^-1//2*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*(-1*e*b^2+-1*(b^2+-4*a*c)^(1/2)*(c*d+-1*b*e)+b*c*d+2*a*c*e)*arctanh(2^(1/2)*c^(1/2)*(d+e*x^2)^(1/2)*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2)+-1//2*2^(1/2)*c^-3//2*(b^2+-4*a*c)^-1//2*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*((b^2+-4*a*c)^(1/2)*(c*d+-1*b*e)+-1*e*b^2+b*c*d+2*a*c*e)*arctanh(2^(1/2)*c^(1/2)*(d+e*x^2)^(1/2)*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2))
@test integrate(x*(d+e*x^2)^(1/2)*(a+b*x^2+c*x^4)^-1, x) == :((1/2)*2^(1/2)*c^-1//2*(b^2+-4*a*c)^-1//2*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^(1/2)*arctanh(2^(1/2)*c^(1/2)*(d+e*x^2)^(1/2)*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2)+-1//2*2^(1/2)*c^-1//2*(b^2+-4*a*c)^-1//2*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^(1/2)*arctanh(2^(1/2)*c^(1/2)*(d+e*x^2)^(1/2)*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2))
@test integrate(x^-1*(d+e*x^2)^(1/2)*(a+b*x^2+c*x^4)^-1, x) == :(-1*a^-1*d^(1/2)*arctanh(d^-1//2*(d+e*x^2)^(1/2))+(1/2)*2^(1/2)*a^-1*c^(1/2)*(b^2+-4*a*c)^-1//2*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*(b*d+d*(b^2+-4*a*c)^(1/2)+-2*a*e)*arctanh(2^(1/2)*c^(1/2)*(d+e*x^2)^(1/2)*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2)+-1//2*2^(1/2)*a^-1*c^(1/2)*(b^2+-4*a*c)^-1//2*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*(b*d+-1*d*(b^2+-4*a*c)^(1/2)+-2*a*e)*arctanh(2^(1/2)*c^(1/2)*(d+e*x^2)^(1/2)*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2))
@test integrate(x^-5*(d+e*x^2)^(1/2)*(a+b*x^2+c*x^4)^-1, x) == :(-1//4*a^-1*x^-4*(d+e*x^2)^(1/2)+-1*a^-3*d^-1//2*(d*b^2+-1*a*b*e+-1*a*c*d)*arctanh(d^-1//2*(d+e*x^2)^(1/2))+-3//8*a^-1*d^-3//2*e^2*arctanh(d^-1//2*(d+e*x^2)^(1/2))+(1/2)*a^-2*d^-1*x^-2*(d+e*x^2)^(1/2)*(b*d+-1*a*e)+-1//2*e*a^-2*d^-3//2*(b*d+-1*a*e)*arctanh(d^-1//2*(d+e*x^2)^(1/2))+3//8*e*a^-1*d^-1*x^-2*(d+e*x^2)^(1/2)+(1/2)*2^(1/2)*a^-3*c^(1/2)*(b^2+-4*a*c)^-1//2*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*(d*b^3+b^2*(d*(b^2+-4*a*c)^(1/2)+-1*a*e)+-1*a*b*(e*(b^2+-4*a*c)^(1/2)+3*c*d)+-1*a*c*(d*(b^2+-4*a*c)^(1/2)+-2*a*e))*arctanh(2^(1/2)*c^(1/2)*(d+e*x^2)^(1/2)*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2)+-1//2*2^(1/2)*a^-3*c^(1/2)*(b^2+-4*a*c)^-1//2*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*(d*b^3+-1*b^2*(a*e+d*(b^2+-4*a*c)^(1/2))+a*c*(d*(b^2+-4*a*c)^(1/2)+2*a*e)+-1*a*b*(-1*e*(b^2+-4*a*c)^(1/2)+3*c*d))*arctanh(2^(1/2)*c^(1/2)*(d+e*x^2)^(1/2)*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2))
@test integrate(x^4*(d+e*x^2)^(1/2)*(a+b*x^2+c*x^4)^-1, x) == :((1/2)*x*c^-1*(d+e*x^2)^(1/2)+(1/2)*c^-2*e^-1//2*(c*d+-2*b*e)*arctanh(x*e^(1/2)*(d+e*x^2)^-1//2)+-1*c^-2*(b+(b^2+-4*a*c)^(1/2))^-1//2*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*((b^2+-4*a*c)^-1//2*(-1*e*b^3+c*d*b^2+-2*a*d*c^2+3*a*b*c*e)+-1*e*b^2+a*c*e+b*c*d)*arctan(x*(b+(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x^2)^-1//2*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^(1/2))+-1*c^-2*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*(-1*e*b^2+-1*(b^2+-4*a*c)^-1//2*(-1*e*b^3+c*d*b^2+-2*a*d*c^2+3*a*b*c*e)+a*c*e+b*c*d)*arctan(x*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x^2)^-1//2*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^(1/2)))
@test integrate(x^2*(d+e*x^2)^(1/2)*(a+b*x^2+c*x^4)^-1, x) == :(c^-1*e^(1/2)*arctanh(x*e^(1/2)*(d+e*x^2)^-1//2)+c^-1*(b+(b^2+-4*a*c)^(1/2))^-1//2*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*(c*d+(b^2+-4*a*c)^-1//2*(-1*e*b^2+b*c*d+2*a*c*e)+-1*b*e)*arctan(x*(b+(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x^2)^-1//2*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^(1/2))+c^-1*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*(c*d+-1*b*e+-1*(b^2+-4*a*c)^-1//2*(-1*e*b^2+b*c*d+2*a*c*e))*arctan(x*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x^2)^-1//2*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^(1/2)))
@test integrate((d+e*x^2)^(1/2)*(a+b*x^2+c*x^4)^-1, x) == :((b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-1//2*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^(1/2)*arctan(x*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x^2)^-1//2*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^(1/2))+-1*(b+(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-1//2*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^(1/2)*arctan(x*(b+(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x^2)^-1//2*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^(1/2)))
@test integrate(x^-2*(d+e*x^2)^(1/2)*(a+b*x^2+c*x^4)^-1, x) == :(-1*a^-1*x^-1*(d+e*x^2)^(1/2)+-1*c*a^-1*(b+(b^2+-4*a*c)^(1/2))^-1//2*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*(d+-1*(b^2+-4*a*c)^-1//2*(b*d+-2*a*e))*arctan(x*(b+(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x^2)^-1//2*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^(1/2))+-1*c*a^-1*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*(d+(b^2+-4*a*c)^-1//2*(b*d+-2*a*e))*arctan(x*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x^2)^-1//2*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^(1/2)))
@test integrate(x^-4*(d+e*x^2)^(1/2)*(a+b*x^2+c*x^4)^-1, x) == :(-1//3*a^-1*x^-3*(d+e*x^2)^(1/2)+a^-2*d^-1*x^-1*(d+e*x^2)^(1/2)*(b*d+-1*a*e)+2//3*e*a^-1*d^-1*x^-1*(d+e*x^2)^(1/2)+c*a^-2*(b+(b^2+-4*a*c)^(1/2))^-1//2*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*(b*d+-1*a*e+-1*(b^2+-4*a*c)^-1//2*(d*b^2+-1*a*b*e+-2*a*c*d))*arctan(x*(b+(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x^2)^-1//2*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^(1/2))+c*a^-2*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*(b*d+(b^2+-4*a*c)^-1//2*(d*b^2+-1*a*b*e+-2*a*c*d)+-1*a*e)*arctan(x*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x^2)^-1//2*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^(1/2)))
@test integrate(x^-6*(d+e*x^2)^(1/2)*(a+b*x^2+c*x^4)^-1, x) == :(-1//5*a^-1*x^-5*(d+e*x^2)^(1/2)+-1*a^-3*d^-1*x^-1*(d+e*x^2)^(1/2)*(d*b^2+-1*a*b*e+-1*a*c*d)+-8//15*a^-1*d^-2*e^2*x^-1*(d+e*x^2)^(1/2)+1//3*a^-2*d^-1*x^-3*(d+e*x^2)^(1/2)*(b*d+-1*a*e)+4//15*e*a^-1*d^-1*x^-3*(d+e*x^2)^(1/2)+-1*c*a^-3*(b+(b^2+-4*a*c)^(1/2))^-1//2*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*(d*b^2+-1*(b^2+-4*a*c)^-1//2*(d*b^3+-1*a*e*b^2+2*c*e*a^2+-3*a*b*c*d)+-1*a*b*e+-1*a*c*d)*arctan(x*(b+(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x^2)^-1//2*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^(1/2))+-1*c*a^-3*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*(d*b^2+(b^2+-4*a*c)^-1//2*(d*b^3+-1*a*e*b^2+2*c*e*a^2+-3*a*b*c*d)+-1*a*b*e+-1*a*c*d)*arctan(x*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x^2)^-1//2*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^(1/2))+-2//3*e*a^-2*d^-2*x^-1*(d+e*x^2)^(1/2)*(b*d+-1*a*e))
@test integrate(x^3*(d+e*x^2)^3//2*(a+b*x^2+c*x^4)^-1, x) == :(1//3*c^-1*(d+e*x^2)^3//2+c^-2*(d+e*x^2)^(1/2)*(c*d+-1*b*e)+(1/2)*2^(1/2)*c^-5//2*(b^2+-4*a*c)^-1//2*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*(c*(a*e^2*(b^2+-4*a*c)^(1/2)+-1*c*d*(d*(b^2+-4*a*c)^(1/2)+-4*a*e))+b^3*e^2+b*c*(c*d^2+e*(-3*a*e+2*d*(b^2+-4*a*c)^(1/2)))+-1*e*b^2*(e*(b^2+-4*a*c)^(1/2)+2*c*d))*arctanh(2^(1/2)*c^(1/2)*(d+e*x^2)^(1/2)*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2)+-1//2*2^(1/2)*c^-5//2*(b^2+-4*a*c)^-1//2*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*(b^3*e^2+-1*c*(a*e^2*(b^2+-4*a*c)^(1/2)+-1*c*d*(d*(b^2+-4*a*c)^(1/2)+4*a*e))+b*c*(c*d^2+-1*e*(2*d*(b^2+-4*a*c)^(1/2)+3*a*e))+-1*e*b^2*(-1*e*(b^2+-4*a*c)^(1/2)+2*c*d))*arctanh(2^(1/2)*c^(1/2)*(d+e*x^2)^(1/2)*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2))
@test integrate(x*(d+e*x^2)^3//2*(a+b*x^2+c*x^4)^-1, x) == :(e*c^-1*(d+e*x^2)^(1/2)+(1/2)*2^(1/2)*c^-3//2*(b^2+-4*a*c)^-1//2*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*(2*c^2*d^2+b*e^2*(b+(b^2+-4*a*c)^(1/2))+-2*c*e*(a*e+b*d+d*(b^2+-4*a*c)^(1/2)))*arctanh(2^(1/2)*c^(1/2)*(d+e*x^2)^(1/2)*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2)+-1//2*2^(1/2)*c^-3//2*(b^2+-4*a*c)^-1//2*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*(2*c^2*d^2+b*e^2*(b+-1*(b^2+-4*a*c)^(1/2))+-2*c*e*(a*e+b*d+-1*d*(b^2+-4*a*c)^(1/2)))*arctanh(2^(1/2)*c^(1/2)*(d+e*x^2)^(1/2)*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2))
@test integrate(x^-1*(d+e*x^2)^3//2*(a+b*x^2+c*x^4)^-1, x) == :(-1*a^-1*d^3//2*arctanh(d^-1//2*(d+e*x^2)^(1/2))+-1//2*2^(1/2)*a^-1*c^-1//2*(b^2+-4*a*c)^-1//2*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*(b*(a*e^2+c*d^2)+a*e^2*(b^2+-4*a*c)^(1/2)+-1*c*d*(d*(b^2+-4*a*c)^(1/2)+4*a*e))*arctanh(2^(1/2)*c^(1/2)*(d+e*x^2)^(1/2)*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2)+-1//2*2^(1/2)*a^-1*c^-1//2*(b^2+-4*a*c)^-1//2*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*(-1*b*(a*e^2+c*d^2)+a*e^2*(b^2+-4*a*c)^(1/2)+-1*c*d*(d*(b^2+-4*a*c)^(1/2)+-4*a*e))*arctanh(2^(1/2)*c^(1/2)*(d+e*x^2)^(1/2)*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2))
@test integrate(x^-3*(d+e*x^2)^3//2*(a+b*x^2+c*x^4)^-1, x) == :(a^-2*d^(1/2)*(b*d+-2*a*e)*arctanh(d^-1//2*(d+e*x^2)^(1/2))+(1/2)*e*a^-1*d^(1/2)*arctanh(d^-1//2*(d+e*x^2)^(1/2))+-1//2*d*a^-1*x^-2*(d+e*x^2)^(1/2)+(1/2)*2^(1/2)*a^-2*c^(1/2)*(b^2+-4*a*c)^-1//2*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*(b^2*d^2+-2*a*(c*d^2+-1*e*(a*e+d*(b^2+-4*a*c)^(1/2)))+-1*b*d*(d*(b^2+-4*a*c)^(1/2)+2*a*e))*arctanh(2^(1/2)*c^(1/2)*(d+e*x^2)^(1/2)*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2)+-1//2*2^(1/2)*a^-2*c^(1/2)*(b^2+-4*a*c)^-1//2*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*(b^2*d^2+-2*a*(c*d^2+e*(d*(b^2+-4*a*c)^(1/2)+-1*a*e))+b*d*(d*(b^2+-4*a*c)^(1/2)+-2*a*e))*arctanh(2^(1/2)*c^(1/2)*(d+e*x^2)^(1/2)*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2))
@test integrate(x^4*(d+e*x^2)^3//2*(a+b*x^2+c*x^4)^-1, x) == :(1//4*x*c^-1*(d+e*x^2)^3//2+-1//2*c^-3*e^(1/2)*((b^2+-4*a*c)^-1//2*(-1*e*b^3+c*d*b^2+-2*a*d*c^2+3*a*b*c*e)+-1*e*b^2+a*c*e+b*c*d)*arctanh(x*e^(1/2)*(d+e*x^2)^-1//2)+-1//2*c^-3*e^(1/2)*(-1*e*b^2+-1*(b^2+-4*a*c)^-1//2*(-1*e*b^3+c*d*b^2+-2*a*d*c^2+3*a*b*c*e)+a*c*e+b*c*d)*arctanh(x*e^(1/2)*(d+e*x^2)^-1//2)+1//8*x*c^-2*(d+e*x^2)^(1/2)*(-4*b*e+3*c*d)+-1//2*c^-3*(b+(b^2+-4*a*c)^(1/2))^-1//2*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^(1/2)*((b^2+-4*a*c)^-1//2*(-1*e*b^3+c*d*b^2+-2*a*d*c^2+3*a*b*c*e)+-1*e*b^2+a*c*e+b*c*d)*arctan(x*(b+(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x^2)^-1//2*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^(1/2))+-1//2*c^-3*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^(1/2)*(-1*e*b^2+-1*(b^2+-4*a*c)^-1//2*(-1*e*b^3+c*d*b^2+-2*a*d*c^2+3*a*b*c*e)+a*c*e+b*c*d)*arctan(x*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x^2)^-1//2*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^(1/2))+1//8*d*c^-2*e^-1//2*(-4*b*e+3*c*d)*arctanh(x*e^(1/2)*(d+e*x^2)^-1//2))
@test integrate(x^2*(d+e*x^2)^3//2*(a+b*x^2+c*x^4)^-1, x) == :((1/2)*d*c^-1*e^(1/2)*arctanh(x*e^(1/2)*(d+e*x^2)^-1//2)+(1/2)*e*x*c^-1*(d+e*x^2)^(1/2)+(1/2)*c^-2*e^(1/2)*(c*d+(b^2+-4*a*c)^-1//2*(-1*e*b^2+b*c*d+2*a*c*e)+-1*b*e)*arctanh(x*e^(1/2)*(d+e*x^2)^-1//2)+(1/2)*c^-2*e^(1/2)*(c*d+-1*b*e+-1*(b^2+-4*a*c)^-1//2*(-1*e*b^2+b*c*d+2*a*c*e))*arctanh(x*e^(1/2)*(d+e*x^2)^-1//2)+(1/2)*c^-2*(b+(b^2+-4*a*c)^(1/2))^-1//2*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^(1/2)*(c*d+(b^2+-4*a*c)^-1//2*(-1*e*b^2+b*c*d+2*a*c*e)+-1*b*e)*arctan(x*(b+(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x^2)^-1//2*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^(1/2))+(1/2)*c^-2*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^(1/2)*(c*d+-1*b*e+-1*(b^2+-4*a*c)^-1//2*(-1*e*b^2+b*c*d+2*a*c*e))*arctan(x*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x^2)^-1//2*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^(1/2)))
@test integrate((d+e*x^2)^3//2*(a+b*x^2+c*x^4)^-1, x) == :((1/2)*c^-1*e^(1/2)*(b^2+-4*a*c)^-1//2*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+3*c*d)*arctanh(x*e^(1/2)*(d+e*x^2)^-1//2)+-1//2*c^-1*e^(1/2)*(b^2+-4*a*c)^-1//2*(-1*e*(b+(b^2+-4*a*c)^(1/2))+3*c*d)*arctanh(x*e^(1/2)*(d+e*x^2)^-1//2)+c^-1*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-1//2*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*(2*c^2*d^2+b*e^2*(b+-1*(b^2+-4*a*c)^(1/2))+-2*c*e*(a*e+b*d+-1*d*(b^2+-4*a*c)^(1/2)))*arctan(x*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x^2)^-1//2*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^(1/2))+-1*c^-1*(b+(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-1//2*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*(2*c^2*d^2+b*e^2*(b+(b^2+-4*a*c)^(1/2))+-2*c*e*(a*e+b*d+d*(b^2+-4*a*c)^(1/2)))*arctan(x*(b+(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x^2)^-1//2*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^(1/2)))
@test integrate(x^-2*(d+e*x^2)^3//2*(a+b*x^2+c*x^4)^-1, x) == :((b+(b^2+-4*a*c)^(1/2))^-3//2*(b^2+-4*a*c)^-1//2*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^3//2*arctan(x*(b+(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x^2)^-1//2*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^(1/2))+-1*d*a^-1*x^-1*(d+e*x^2)^(1/2)+-1*(b+-1*(b^2+-4*a*c)^(1/2))^-3//2*(b^2+-4*a*c)^-1//2*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^3//2*arctan(x*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x^2)^-1//2*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^(1/2)))
@test integrate(x^-4*(d+e*x^2)^3//2*(a+b*x^2+c*x^4)^-1, x) == :(-1//3*a^-1*x^-3*(d+e*x^2)^3//2+a^-2*x^-1*(d+e*x^2)^(1/2)*(b*d+-1*a*e)+(1/2)*a^-2*e^(1/2)*(b*d+(b^2+-4*a*c)^-1//2*(d*b^2+-1*a*b*e+-2*a*c*d)+-1*a*e)*arctanh(x*e^(1/2)*(d+e*x^2)^-1//2)+(1/2)*a^-2*e^(1/2)*(b*d+-1*a*e+-1*(b^2+-4*a*c)^-1//2*(d*b^2+-1*a*b*e+-2*a*c*d))*arctanh(x*e^(1/2)*(d+e*x^2)^-1//2)+-1*a^-2*e^(1/2)*(b*d+-1*a*e)*arctanh(x*e^(1/2)*(d+e*x^2)^-1//2)+(1/2)*a^-2*(b+(b^2+-4*a*c)^(1/2))^-1//2*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^(1/2)*(b*d+-1*a*e+-1*(b^2+-4*a*c)^-1//2*(d*b^2+-1*a*b*e+-2*a*c*d))*arctan(x*(b+(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x^2)^-1//2*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^(1/2))+(1/2)*a^-2*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^(1/2)*(b*d+(b^2+-4*a*c)^-1//2*(d*b^2+-1*a*b*e+-2*a*c*d)+-1*a*e)*arctan(x*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x^2)^-1//2*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^(1/2)))
@test integrate(x^5*(1+-1*x^2)^(1/2)*(a+b*x^2+c*x^4)^-1, x) == :(-1//3*c^-1*(1+-1*x^2)^3//2+-1*b*c^-2*(1+-1*x^2)^(1/2)+(1/2)*2^(1/2)*c^-5//2*(b+(b^2+-4*a*c)^(1/2)+2c)^-1//2*(b^2+b*c+(b^2+-4*a*c)^-1//2*(b^3+c*b^2+-2*a*c^2+-3*a*b*c)+-1*a*c)*arctanh(2^(1/2)*c^(1/2)*(1+-1*x^2)^(1/2)*(b+(b^2+-4*a*c)^(1/2)+2c)^-1//2)+(1/2)*2^(1/2)*c^-5//2*(b+-1*(b^2+-4*a*c)^(1/2)+2c)^-1//2*(b^2+b*c+-1*a*c+-1*(b^2+-4*a*c)^-1//2*(b^3+c*b^2+-2*a*c^2+-3*a*b*c))*arctanh(2^(1/2)*c^(1/2)*(1+-1*x^2)^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2)+2c)^-1//2))
@test integrate(x^3*(1+-1*x^2)^(1/2)*(a+b*x^2+c*x^4)^-1, x) == :(c^-1*(1+-1*x^2)^(1/2)+-1//2*2^(1/2)*c^-3//2*(b+(b^2+-4*a*c)^(1/2)+2c)^-1//2*(b+c+(b^2+-4*a*c)^-1//2*(b^2+b*c+-2*a*c))*arctanh(2^(1/2)*c^(1/2)*(1+-1*x^2)^(1/2)*(b+(b^2+-4*a*c)^(1/2)+2c)^-1//2)+-1//2*2^(1/2)*c^-3//2*(b+-1*(b^2+-4*a*c)^(1/2)+2c)^-1//2*(b+c+-1*(b^2+-4*a*c)^-1//2*(b^2+b*c+-2*a*c))*arctanh(2^(1/2)*c^(1/2)*(1+-1*x^2)^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2)+2c)^-1//2))
@test integrate(x*(1+-1*x^2)^(1/2)*(a+b*x^2+c*x^4)^-1, x) == :((1/2)*2^(1/2)*c^-1//2*(b^2+-4*a*c)^-1//2*(b+(b^2+-4*a*c)^(1/2)+2c)^(1/2)*arctanh(2^(1/2)*c^(1/2)*(1+-1*x^2)^(1/2)*(b+(b^2+-4*a*c)^(1/2)+2c)^-1//2)+-1//2*2^(1/2)*c^-1//2*(b^2+-4*a*c)^-1//2*(b+-1*(b^2+-4*a*c)^(1/2)+2c)^(1/2)*arctanh(2^(1/2)*c^(1/2)*(1+-1*x^2)^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2)+2c)^-1//2))
@test integrate(x^-1*(1+-1*x^2)^(1/2)*(a+b*x^2+c*x^4)^-1, x) == :(-1*a^-1*arctanh((1+-1*x^2)^(1/2))+(1/2)*2^(1/2)*a^-1*c^(1/2)*(b^2+-4*a*c)^-1//2*(b+-1*(b^2+-4*a*c)^(1/2)+2c)^-1//2*(b+(b^2+-4*a*c)^(1/2)+2a)*arctanh(2^(1/2)*c^(1/2)*(1+-1*x^2)^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2)+2c)^-1//2)+-1//2*2^(1/2)*a^-1*c^(1/2)*(b^2+-4*a*c)^-1//2*(b+(b^2+-4*a*c)^(1/2)+2c)^-1//2*(b+-1*(b^2+-4*a*c)^(1/2)+2a)*arctanh(2^(1/2)*c^(1/2)*(1+-1*x^2)^(1/2)*(b+(b^2+-4*a*c)^(1/2)+2c)^-1//2))
@test integrate(x^-3*(1+-1*x^2)^(1/2)*(a+b*x^2+c*x^4)^-1, x) == :(-1//4*a^-1*(1+-1*(1+-1*x^2)^(1/2))^-1+1//4*a^-1*(1+(1+-1*x^2)^(1/2))^-1+(1/2)*a^-2*(a+2b)*arctanh((1+-1*x^2)^(1/2))+-1//2*2^(1/2)*a^-2*c^(1/2)*(b+(b^2+-4*a*c)^(1/2)+2c)^-1//2*(a+b+-1*(b^2+-4*a*c)^-1//2*(b^2+a*(b+-2c)))*arctanh(2^(1/2)*c^(1/2)*(1+-1*x^2)^(1/2)*(b+(b^2+-4*a*c)^(1/2)+2c)^-1//2)+-1//2*2^(1/2)*a^-2*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2)+2c)^-1//2*(a+b+(b^2+-4*a*c)^-1//2*(b^2+a*(b+-2c)))*arctanh(2^(1/2)*c^(1/2)*(1+-1*x^2)^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2)+2c)^-1//2))
@test integrate(x^4*(1+-1*x^2)^(1/2)*(a+b*x^2+c*x^4)^-1, x) == :((1/2)*x*c^-1*(1+-1*x^2)^(1/2)+(1/2)*c^-2*(c+2b)*arcsin(x)+-1*c^-2*(b+(b^2+-4*a*c)^(1/2))^-1//2*(b+(b^2+-4*a*c)^(1/2)+2c)^-1//2*(b^2+b*c+(b^2+-4*a*c)^-1//2*(b^3+c*b^2+-2*a*c^2+-3*a*b*c)+-1*a*c)*arctan(x*(1+-1*x^2)^-1//2*(b+(b^2+-4*a*c)^(1/2))^-1//2*(b+(b^2+-4*a*c)^(1/2)+2c)^(1/2))+-1*c^-2*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(b+-1*(b^2+-4*a*c)^(1/2)+2c)^-1//2*(b^2+b*c+-1*a*c+-1*(b^2+-4*a*c)^-1//2*(b^3+c*b^2+-2*a*c^2+-3*a*b*c))*arctan(x*(1+-1*x^2)^-1//2*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(b+-1*(b^2+-4*a*c)^(1/2)+2c)^(1/2)))
@test integrate(x^2*(1+-1*x^2)^(1/2)*(a+b*x^2+c*x^4)^-1, x) == :(-1*c^-1*arcsin(x)+c^-1*(b+(b^2+-4*a*c)^(1/2))^-1//2*(b+(b^2+-4*a*c)^(1/2)+2c)^-1//2*(b+c+(b^2+-4*a*c)^-1//2*(b^2+b*c+-2*a*c))*arctan(x*(1+-1*x^2)^-1//2*(b+(b^2+-4*a*c)^(1/2))^-1//2*(b+(b^2+-4*a*c)^(1/2)+2c)^(1/2))+c^-1*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(b+-1*(b^2+-4*a*c)^(1/2)+2c)^-1//2*(b+c+-1*(b^2+-4*a*c)^-1//2*(b^2+b*c+-2*a*c))*arctan(x*(1+-1*x^2)^-1//2*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(b+-1*(b^2+-4*a*c)^(1/2)+2c)^(1/2)))
@test integrate((1+-1*x^2)^(1/2)*(a+b*x^2+c*x^4)^-1, x) == :((b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-1//2*(b+-1*(b^2+-4*a*c)^(1/2)+2c)^(1/2)*arctan(x*(1+-1*x^2)^-1//2*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(b+-1*(b^2+-4*a*c)^(1/2)+2c)^(1/2))+-1*(b+(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-1//2*(b+(b^2+-4*a*c)^(1/2)+2c)^(1/2)*arctan(x*(1+-1*x^2)^-1//2*(b+(b^2+-4*a*c)^(1/2))^-1//2*(b+(b^2+-4*a*c)^(1/2)+2c)^(1/2)))
@test integrate(x^-2*(1+-1*x^2)^(1/2)*(a+b*x^2+c*x^4)^-1, x) == :(-1*a^-1*x^-1*(1+-1*x^2)^(1/2)+-1*c*a^-1*(b+(b^2+-4*a*c)^(1/2))^-1//2*(b+(b^2+-4*a*c)^(1/2)+2c)^-1//2*(1+-1*(b^2+-4*a*c)^-1//2*(b+2a))*arctan(x*(1+-1*x^2)^-1//2*(b+(b^2+-4*a*c)^(1/2))^-1//2*(b+(b^2+-4*a*c)^(1/2)+2c)^(1/2))+-1*c*a^-1*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(b+-1*(b^2+-4*a*c)^(1/2)+2c)^-1//2*(1+(b^2+-4*a*c)^-1//2*(b+2a))*arctan(x*(1+-1*x^2)^-1//2*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(b+-1*(b^2+-4*a*c)^(1/2)+2c)^(1/2)))
@test integrate(x^2*(1+-1*x^2)^(1/2)*(-1+x^2+x^4)^-1, x) == :(-1*arcsin(x)+(2//5+1//5*5^(1/2))^(1/2)*arctan(x*(1+-1*x^2)^-1//2*(1/2+(1/2)*5^(1/2))^(1/2))+-1*(-2//5+1//5*5^(1/2))^(1/2)*arctanh(x*(1+-1*x^2)^-1//2*(-1//2+(1/2)*5^(1/2))^(1/2)))
@test integrate(x^8*(d+e*x^2)^-1//2*(a+b*x^2+c*x^4)^-1, x) == :(c^-3*e^-1//2*(b^2+-1*a*c)*arctanh(x*e^(1/2)*(d+e*x^2)^-1//2)+1//4*c^-1*e^-1*x^3*(d+e*x^2)^(1/2)+3//8*c^-1*d^2*e^-5//2*arctanh(x*e^(1/2)*(d+e*x^2)^-1//2)+(1/2)*b*d*c^-2*e^-3//2*arctanh(x*e^(1/2)*(d+e*x^2)^-1//2)+-1*c^-3*(b+(b^2+-4*a*c)^(1/2))^-1//2*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*(b^3+(b^2+-4*a*c)^-1//2*(b^4+2*a^2*c^2+-4*a*c*b^2)+-2*a*b*c)*arctan(x*(b+(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x^2)^-1//2*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^(1/2))+-1*c^-3*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*(b^3+-1*(b^2+-4*a*c)^-1//2*(b^4+2*a^2*c^2+-4*a*c*b^2)+-2*a*b*c)*arctan(x*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x^2)^-1//2*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^(1/2))+-3//8*d*x*c^-1*e^-2*(d+e*x^2)^(1/2)+-1//2*b*x*c^-2*e^-1*(d+e*x^2)^(1/2))
@test integrate(x^6*(d+e*x^2)^-1//2*(a+b*x^2+c*x^4)^-1, x) == :((1/2)*x*c^-1*e^-1*(d+e*x^2)^(1/2)+-1*b*c^-2*e^-1//2*arctanh(x*e^(1/2)*(d+e*x^2)^-1//2)+-1//2*d*c^-1*e^-3//2*arctanh(x*e^(1/2)*(d+e*x^2)^-1//2)+c^-2*(b+(b^2+-4*a*c)^(1/2))^-1//2*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*(b^2+-1*a*c+b*(b^2+-4*a*c)^-1//2*(b^2+-3*a*c))*arctan(x*(b+(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x^2)^-1//2*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^(1/2))+c^-2*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*(b^2+-1*a*c+-1*b*(b^2+-4*a*c)^-1//2*(b^2+-3*a*c))*arctan(x*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x^2)^-1//2*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^(1/2)))
@test integrate(x^4*(d+e*x^2)^-1//2*(a+b*x^2+c*x^4)^-1, x) == :(c^-1*e^-1//2*arctanh(x*e^(1/2)*(d+e*x^2)^-1//2)+-1*c^-1*(b+(b^2+-4*a*c)^(1/2))^-1//2*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*(b+(b^2+-4*a*c)^-1//2*(b^2+-2*a*c))*arctan(x*(b+(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x^2)^-1//2*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^(1/2))+-1*c^-1*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*(b+-1*(b^2+-4*a*c)^-1//2*(b^2+-2*a*c))*arctan(x*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x^2)^-1//2*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^(1/2)))
@test integrate(x^2*(d+e*x^2)^-1//2*(a+b*x^2+c*x^4)^-1, x) == :((b+(b^2+-4*a*c)^(1/2))^(1/2)*(b^2+-4*a*c)^-1//2*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*arctan(x*(b+(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x^2)^-1//2*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^(1/2))+-1*(b+-1*(b^2+-4*a*c)^(1/2))^(1/2)*(b^2+-4*a*c)^-1//2*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*arctan(x*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x^2)^-1//2*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^(1/2)))
@test integrate((d+e*x^2)^-1//2*(a+b*x^2+c*x^4)^-1, x) == :(-2*c*(b+(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-1//2*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*arctan(x*(b+(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x^2)^-1//2*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^(1/2))+2*c*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-1//2*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*arctan(x*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x^2)^-1//2*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^(1/2)))
@test integrate(x^-2*(d+e*x^2)^-1//2*(a+b*x^2+c*x^4)^-1, x) == :(-1*a^-1*d^-1*x^-1*(d+e*x^2)^(1/2)+-1*c*a^-1*(b+(b^2+-4*a*c)^(1/2))^-1//2*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*(1+-1*b*(b^2+-4*a*c)^-1//2)*arctan(x*(b+(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x^2)^-1//2*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^(1/2))+-1*c*a^-1*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*(1+b*(b^2+-4*a*c)^-1//2)*arctan(x*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x^2)^-1//2*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^(1/2)))
@test integrate(x^-4*(d+e*x^2)^-1//2*(a+b*x^2+c*x^4)^-1, x) == :(-1//3*a^-1*d^-1*x^-3*(d+e*x^2)^(1/2)+b*a^-2*d^-1*x^-1*(d+e*x^2)^(1/2)+2//3*e*a^-1*d^-2*x^-1*(d+e*x^2)^(1/2)+c*a^-2*(b+(b^2+-4*a*c)^(1/2))^-1//2*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*(b+-1*(b^2+-4*a*c)^-1//2*(b^2+-2*a*c))*arctan(x*(b+(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x^2)^-1//2*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^(1/2))+c*a^-2*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*(b+(b^2+-4*a*c)^-1//2*(b^2+-2*a*c))*arctan(x*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x^2)^-1//2*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^(1/2)))
@test integrate(x^-6*(d+e*x^2)^-1//2*(a+b*x^2+c*x^4)^-1, x) == :(-1//5*a^-1*d^-1*x^-5*(d+e*x^2)^(1/2)+-1*a^-3*d^-1*x^-1*(d+e*x^2)^(1/2)*(b^2+-1*a*c)+-8//15*a^-1*d^-3*e^2*x^-1*(d+e*x^2)^(1/2)+1//3*b*a^-2*d^-1*x^-3*(d+e*x^2)^(1/2)+4//15*e*a^-1*d^-2*x^-3*(d+e*x^2)^(1/2)+-1*c*a^-3*(b+(b^2+-4*a*c)^(1/2))^-1//2*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*(b^2+-1*a*c+-1*b*(b^2+-4*a*c)^-1//2*(b^2+-3*a*c))*arctan(x*(b+(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x^2)^-1//2*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^(1/2))+-1*c*a^-3*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*(b^2+-1*a*c+b*(b^2+-4*a*c)^-1//2*(b^2+-3*a*c))*arctan(x*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x^2)^-1//2*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^(1/2))+-2//3*b*e*a^-2*d^-2*x^-1*(d+e*x^2)^(1/2))
@test integrate(x^4*(d+e*x^2)^-3//2*(a+b*x^2+c*x^4)^-1, x) == :(d*x*(d+e*x^2)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1+-1*(b+(b^2+-4*a*c)^(1/2))^-1//2*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1*(b*d+(b^2+-4*a*c)^-1//2*(d*b^2+-1*a*b*e+-2*a*c*d)+-1*a*e)*arctan(x*(b+(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x^2)^-1//2*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^(1/2))+-1*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1*(b*d+-1*a*e+-1*(b^2+-4*a*c)^-1//2*(d*b^2+-1*a*b*e+-2*a*c*d))*arctan(x*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x^2)^-1//2*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^(1/2)))
@test integrate(x^2*(d+e*x^2)^-3//2*(a+b*x^2+c*x^4)^-1, x) == :(-1*e*x*(d+e*x^2)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1+c*(b+(b^2+-4*a*c)^(1/2))^-1//2*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1*(d+(b^2+-4*a*c)^-1//2*(b*d+-2*a*e))*arctan(x*(b+(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x^2)^-1//2*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^(1/2))+c*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1*(d+-1*(b^2+-4*a*c)^-1//2*(b*d+-2*a*e))*arctan(x*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x^2)^-1//2*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^(1/2)))
@test integrate((d+e*x^2)^-3//2*(a+b*x^2+c*x^4)^-1, x) == :(x*d^-1*e^2*(d+e*x^2)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1+-1*c*(b+(b^2+-4*a*c)^(1/2))^-1//2*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1*(e+(b^2+-4*a*c)^-1//2*(-1*b*e+2*c*d))*arctan(x*(b+(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x^2)^-1//2*(-1*e*(b+(b^2+-4*a*c)^(1/2))+2*c*d)^(1/2))+-1*c*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1*(e+-1*(b^2+-4*a*c)^-1//2*(-1*b*e+2*c*d))*arctan(x*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x^2)^-1//2*(-1*e*(b+-1*(b^2+-4*a*c)^(1/2))+2*c*d)^(1/2)))

max_stars_repo_path: test/1 Algebraic functions/1.2 Trinomial products/1.2.2 Quartic/1.2.2.4 (f x)^m (d+e x^2)^q (a+b x^2+c x^4)^p.jl