lst:=[[sqrt(b*x^2+a)*(d*x^2+c)^(3/2)*(f*x^2+e),x,7,1/105*(8*a^3*d^3*f+3*b^3*c^2*(-2*c*f+7*d*e)+a*b^2*c*d*(9*c*f+49*d*e)-a^2*b*d^2*(19*c*f+14*d*e))*x*sqrt(d*x^2+c)/b^2/d^2/sqrt(b*x^2+a)-1/105*(4*a^2*d^2*f-3*b^2*c*(-2*c*f+7*d*e)-a*b*d*(6*c*f+7*d*e))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b^2/d+1/35*(a*d*f-2*b*c*f+7*b*d*e)*x*sqrt(b*x^2+a)*(d*x^2+c)^(3/2)/b/d+1/7*f*x*sqrt(b*x^2+a)*(d*x^2+c)^(5/2)/d-1/105*sqrt(a)*(8*a^3*d^3*f+3*b^3*c^2*(-2*c*f+7*d*e)+a*b^2*c*d*(9*c*f+49*d*e)-a^2*b*d^2*(19*c*f+14*d*e))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/b^(5/2)/d^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/105*a^(3/2)*(4*a^2*d^2*f+3*b^2*c*(-c*f+21*d*e)-a*b*d*(9*c*f+7*d*e))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(5/2)/d/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[sqrt(b*x^2+a)*sqrt(d*x^2+c)*(f*x^2+e),x,6,1/15*(5*b*c*e+5*a*d*e+2*a*c*f-2*b*c^2*f/d-2*a^2*d*f/b)*x*sqrt(d*x^2+c)/d/sqrt(b*x^2+a)+1/15*(a*d*f-2*b*c*f+5*b*d*e)*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b/d+1/5*f*x*sqrt(b*x^2+a)*(d*x^2+c)^(3/2)/d+1/15*sqrt(a)*(2*a^2*d^2*f-b^2*c*(-2*c*f+5*d*e)-a*b*d*(2*c*f+5*d*e))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/b^(3/2)/d^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/15*a^(3/2)*(-a*d*f-b*c*f+10*b*d*e)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(3/2)/d/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[sqrt(b*x^2+a)*(f*x^2+e)/sqrt(d*x^2+c),x,5,1/3*(a*d*f-2*b*c*f+3*b*d*e)*x*sqrt(d*x^2+c)/d^2/sqrt(b*x^2+a)+1/3*f*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/d-1/3*sqrt(a)*(a*d*f-2*b*c*f+3*b*d*e)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/sqrt(b)/d^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/3*a^(3/2)*(-c*f+3*d*e)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(b)/c/d/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[sqrt(b*x^2+a)*(f*x^2+e)/(d*x^2+c)^(3/2),x,2,f*x*sqrt(b*x^2+a)/d/sqrt(d*x^2+c)+(-2*c*f+d*e)*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/sqrt(c)/d^(3/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+sqrt(c)*f*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/d^(3/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[sqrt(b*x^2+a)*(f*x^2+e)/(d*x^2+c)^(5/2),x,2,1/3*(-c*f+d*e)*x*sqrt(b*x^2+a)/c/d/(d*x^2+c)^(3/2)-1/3*(a*d*(c*f+2*d*e)-b*c*(2*c*f+d*e))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/c^(3/2)/d^(3/2)/(-a*d+b*c)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+1/3*b*(-c*f+d*e)*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/sqrt(c)/d^(3/2)/(-a*d+b*c)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[sqrt(b*x^2+a)*(f*x^2+e)/(d*x^2+c)^(7/2),x,3,1/5*(-c*f+d*e)*x*sqrt(b*x^2+a)/c/d/(d*x^2+c)^(5/2)-1/15*(a*d*(c*f+4*d*e)-b*c*(2*c*f+3*d*e))*x*sqrt(b*x^2+a)/c^2/d/(-a*d+b*c)/(d*x^2+c)^(3/2)+1/15*(2*a^2*d^2*(c*f+4*d*e)+b^2*c^2*(2*c*f+3*d*e)-a*b*c*d*(2*c*f+13*d*e))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/c^(5/2)/d^(3/2)/(-a*d+b*c)^2/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+1/15*b*(b*c*(-c*f+6*d*e)-a*d*(c*f+4*d*e))*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/c^(3/2)/d^(3/2)/(-a*d+b*c)^2/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[sqrt(b*x^2+a)*(f*x^2+e)/(d*x^2+c)^(9/2),x,4,1/7*(-c*f+d*e)*x*sqrt(b*x^2+a)/c/d/(d*x^2+c)^(7/2)-1/35*(a*d*(c*f+6*d*e)-b*c*(2*c*f+5*d*e))*x*sqrt(b*x^2+a)/c^2/d/(-a*d+b*c)/(d*x^2+c)^(5/2)+1/105*(4*a^2*d^2*(c*f+6*d*e)+3*b^2*c^2*(2*c*f+5*d*e)-a*b*c*d*(6*c*f+43*d*e))*x*sqrt(b*x^2+a)/c^3/d/(-a*d+b*c)^2/(d*x^2+c)^(3/2)-1/105*(8*a^3*d^3*(c*f+6*d*e)-3*b^3*c^3*(2*c*f+5*d*e)+a*b^2*c^2*d*(9*c*f+103*d*e)-a^2*b*c*d^2*(19*c*f+128*d*e))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/c^(7/2)/d^(3/2)/(-a*d+b*c)^3/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+1/105*b*(3*b^2*c^2*(-c*f+15*d*e)+4*a^2*d^2*(c*f+6*d*e)-a*b*c*d*(9*c*f+61*d*e))*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/c^(5/2)/d^(3/2)/(-a*d+b*c)^3/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[(b*x^2+a)^(3/2)*(d*x^2+c)^(3/2)*(f*x^2+e),x,8,1/315*(8*a^4*d^4*f+5*a*b^3*c^2*d*(-5*c*f+18*d*e)-2*b^4*c^3*(-4*c*f+9*d*e)+18*a^2*b^2*c*d^2*(c*f+5*d*e)-a^3*b*d^3*(25*c*f+18*d*e))*x*sqrt(d*x^2+c)/b^2/d^3/sqrt(b*x^2+a)-1/315*(4*a^3*d^3*f-3*a*b^2*c*d*(-7*c*f+27*d*e)+2*b^3*c^2*(-4*c*f+9*d*e)-9*a^2*b*d^2*(c*f+d*e))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b^2/d^2-1/315*(18*b*c*e-72*a*d*e+17*a*c*f-8*b*c^2*f/d-3*a^2*d*f/b)*x*sqrt(b*x^2+a)*(d*x^2+c)^(3/2)/d+1/63*(3*a*d*f-4*b*c*f+9*b*d*e)*x*sqrt(b*x^2+a)*(d*x^2+c)^(5/2)/d^2+1/9*f*x*(b*x^2+a)^(3/2)*(d*x^2+c)^(5/2)/d-1/315*sqrt(a)*(8*a^4*d^4*f+5*a*b^3*c^2*d*(-5*c*f+18*d*e)-2*b^4*c^3*(-4*c*f+9*d*e)+18*a^2*b^2*c*d^2*(c*f+5*d*e)-a^3*b*d^3*(25*c*f+18*d*e))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/b^(5/2)/d^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/315*a^(3/2)*(4*a^3*d^3*f-b^3*c^2*(-4*c*f+9*d*e)+6*a*b^2*c*d*(-2*c*f+27*d*e)-3*a^2*b*d^2*(4*c*f+3*d*e))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(5/2)/d^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(b*x^2+a)^(3/2)*sqrt(d*x^2+c)*(f*x^2+e),x,7,-1/105*(6*a^3*d^3*f-a*b^2*c*d*(-19*c*f+49*d*e)+2*b^3*c^2*(-4*c*f+7*d*e)-3*a^2*b*d^2*(3*c*f+7*d*e))*x*sqrt(d*x^2+c)/b/d^3/sqrt(b*x^2+a)-1/105*(14*b*c*e-42*a*d*e+15*a*c*f-8*b*c^2*f/d-3*a^2*d*f/b)*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/d+1/35*(3*a*d*f-4*b*c*f+7*b*d*e)*x*sqrt(b*x^2+a)*(d*x^2+c)^(3/2)/d^2+1/7*f*x*(b*x^2+a)^(3/2)*(d*x^2+c)^(3/2)/d+1/105*sqrt(a)*(6*a^3*d^3*f-a*b^2*c*d*(-19*c*f+49*d*e)+2*b^3*c^2*(-4*c*f+7*d*e)-3*a^2*b*d^2*(3*c*f+7*d*e))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/b^(3/2)/d^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/105*a^(3/2)*(3*a^2*d^2*f+b^2*c*(-4*c*f+7*d*e)-9*a*b*d*(-c*f+7*d*e))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(3/2)/d^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(b*x^2+a)^(3/2)*(f*x^2+e)/sqrt(d*x^2+c),x,6,1/15*(3*a^2*d^2*f+a*b*d*(-13*c*f+20*d*e)-2*b^2*c*(-4*c*f+5*d*e))*x*sqrt(d*x^2+c)/d^3/sqrt(b*x^2+a)+1/15*(3*a*d*f-4*b*c*f+5*b*d*e)*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/d^2+1/5*f*x*(b*x^2+a)^(3/2)*sqrt(d*x^2+c)/d-1/15*sqrt(a)*(3*a^2*d^2*f+a*b*d*(-13*c*f+20*d*e)-2*b^2*c*(-4*c*f+5*d*e))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/sqrt(b)/d^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/15*a^(3/2)*(b*c*(-4*c*f+5*d*e)-3*a*d*(-2*c*f+5*d*e))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(b)/c/d^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(b*x^2+a)^(3/2)*(f*x^2+e)/(d*x^2+c)^(3/2),x,3,1/3*(3*a*d*f-4*b*c*f+3*b*d*e)*x*sqrt(b*x^2+a)/d^2/sqrt(d*x^2+c)+1/3*f*x*(b*x^2+a)^(3/2)/d/sqrt(d*x^2+c)+1/3*(a*d*(-7*c*f+3*d*e)-2*b*c*(-4*c*f+3*d*e))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/sqrt(c)/d^(5/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+1/3*sqrt(c)*(3*a*d*f-4*b*c*f+3*b*d*e)*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/d^(5/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[(b*x^2+a)^(3/2)*(f*x^2+e)/(d*x^2+c)^(5/2),x,3,1/3*(-c*f+d*e)*x*(b*x^2+a)^(3/2)/c/d/(d*x^2+c)^(3/2)-1/3*b*(-4*c*f+d*e)*x*sqrt(b*x^2+a)/c/d^2/sqrt(d*x^2+c)+1/3*(2*b*c*(-4*c*f+d*e)+a*d*(c*f+2*d*e))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/c^(3/2)/d^(5/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-1/3*b*(-4*c*f+d*e)*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/sqrt(c)/d^(5/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[(b*x^2+a)^(3/2)*(f*x^2+e)/(d*x^2+c)^(7/2),x,3,1/5*(-c*f+d*e)*x*(b*x^2+a)^(3/2)/c/d/(d*x^2+c)^(5/2)+1/15*(a*d*(c*f+4*d*e)-b*c*(4*c*f+d*e))*x*sqrt(b*x^2+a)/c^2/d^2/(d*x^2+c)^(3/2)+1/15*(3*a*b*c*d*(-c*f+d*e)-2*a^2*d^2*(c*f+4*d*e)+2*b^2*c^2*(4*c*f+d*e))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/c^(5/2)/d^(5/2)/(-a*d+b*c)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+1/15*b*(a*d*(c*f+4*d*e)-b*c*(4*c*f+d*e))*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/c^(3/2)/d^(5/2)/(-a*d+b*c)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[(b*x^2+a)^(3/2)*(f*x^2+e)/(d*x^2+c)^(9/2),x,4,1/7*(-c*f+d*e)*x*(b*x^2+a)^(3/2)/c/d/(d*x^2+c)^(7/2)+1/35*(a*d*(c*f+6*d*e)-b*c*(4*c*f+3*d*e))*x*sqrt(b*x^2+a)/c^2/d^2/(d*x^2+c)^(5/2)+1/105*(a*b*c*d*(-c*f+15*d*e)-4*a^2*d^2*(c*f+6*d*e)+2*b^2*c^2*(4*c*f+3*d*e))*x*sqrt(b*x^2+a)/c^3/d^2/(-a*d+b*c)/(d*x^2+c)^(3/2)+1/105*(a*b^2*c^2*d*(-5*c*f+12*d*e)+8*a^3*d^3*(c*f+6*d*e)+2*b^3*c^3*(4*c*f+3*d*e)-a^2*b*c*d^2*(5*c*f+72*d*e))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/c^(7/2)/d^(5/2)/(-a*d+b*c)^2/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-1/105*b*(4*a^2*d^2*(c*f+6*d*e)-a*b*c*d*(2*c*f+33*d*e)+b^2*c^2*(4*c*f+3*d*e))*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/c^(5/2)/d^(5/2)/(-a*d+b*c)^2/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[(b*x^2+a)^(5/2)*sqrt(d*x^2+c)*(f*x^2+e),x,8,-1/315*(10*a^4*d^4*f+a*b^3*c^2*d*(-56*c*f+99*d*e)-6*a^2*b^2*c*d^2*(-11*c*f+29*d*e)-8*b^4*c^3*(-2*c*f+3*d*e)-5*a^3*b*d^3*(4*c*f+9*d*e))*x*sqrt(d*x^2+c)/b/d^4/sqrt(b*x^2+a)+1/315*(5*a^3*d^3*f-3*a*b^2*c*d*(-16*c*f+29*d*e)+8*b^3*c^2*(-2*c*f+3*d*e)+45*a^2*b*d^2*(-c*f+3*d*e))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b/d^3+1/105*(5*a^2*d^2*f-4*b^2*c*(-2*c*f+3*d*e)+15*a*b*d*(-c*f+2*d*e))*x*sqrt(b*x^2+a)*(d*x^2+c)^(3/2)/d^3+1/63*(5*a*d*f-6*b*c*f+9*b*d*e)*x*(b*x^2+a)^(3/2)*(d*x^2+c)^(3/2)/d^2+1/9*f*x*(b*x^2+a)^(5/2)*(d*x^2+c)^(3/2)/d+1/315*sqrt(a)*(10*a^4*d^4*f+a*b^3*c^2*d*(-56*c*f+99*d*e)-6*a^2*b^2*c*d^2*(-11*c*f+29*d*e)-8*b^4*c^3*(-2*c*f+3*d*e)-5*a^3*b*d^3*(4*c*f+9*d*e))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/b^(3/2)/d^4/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/315*a^(3/2)*(5*a^3*d^3*f+3*a*b^2*c*d*(-9*c*f+16*d*e)-4*b^3*c^2*(-2*c*f+3*d*e)-30*a^2*b*d^2*(-c*f+6*d*e))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(3/2)/d^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(b*x^2+a)^(5/2)*(f*x^2+e)/sqrt(d*x^2+c),x,7,1/105*(15*a^3*d^3*f-a*b^2*c*d*(-128*c*f+161*d*e)+a^2*b*d^2*(-103*c*f+161*d*e)+8*b^3*c^2*(-6*c*f+7*d*e))*x*sqrt(d*x^2+c)/d^4/sqrt(b*x^2+a)+1/105*(15*a^2*d^2*f+a*b*d*(-43*c*f+56*d*e)-4*b^2*c*(-6*c*f+7*d*e))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/d^3+1/35*(5*a*d*f-6*b*c*f+7*b*d*e)*x*(b*x^2+a)^(3/2)*sqrt(d*x^2+c)/d^2+1/7*f*x*(b*x^2+a)^(5/2)*sqrt(d*x^2+c)/d-1/105*sqrt(a)*(15*a^3*d^3*f-a*b^2*c*d*(-128*c*f+161*d*e)+a^2*b*d^2*(-103*c*f+161*d*e)+8*b^3*c^2*(-6*c*f+7*d*e))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/sqrt(b)/d^4/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/105*a^(3/2)*(a*b*c*d*(-61*c*f+77*d*e)-4*b^2*c^2*(-6*c*f+7*d*e)-15*a^2*d^2*(-3*c*f+7*d*e))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(b)/c/d^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(b*x^2+a)^(5/2)*(f*x^2+e)/(d*x^2+c)^(3/2),x,4,1/15*(15*a^2*d^2*f+a*b*d*(-41*c*f+30*d*e)-4*b^2*c*(-6*c*f+5*d*e))*x*sqrt(b*x^2+a)/d^3/sqrt(d*x^2+c)+1/15*(5*a*d*f-6*b*c*f+5*b*d*e)*x*(b*x^2+a)^(3/2)/d^2/sqrt(d*x^2+c)+1/5*f*x*(b*x^2+a)^(5/2)/d/sqrt(d*x^2+c)-1/15*(a*b*c*d*(-88*c*f+65*d*e)-a^2*d^2*(-38*c*f+15*d*e)-8*b^2*c^2*(-6*c*f+5*d*e))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/sqrt(c)/d^(7/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+1/15*sqrt(c)*(15*a^2*d^2*f+a*b*d*(-41*c*f+30*d*e)-4*b^2*c*(-6*c*f+5*d*e))*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/d^(7/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[(b*x^2+a)^(5/2)*(f*x^2+e)/(d*x^2+c)^(5/2),x,4,1/3*(-c*f+d*e)*x*(b*x^2+a)^(5/2)/c/d/(d*x^2+c)^(3/2)-1/3*b*(a*d*(-7*c*f+d*e)-4*b*c*(-2*c*f+d*e))*x*sqrt(b*x^2+a)/c/d^3/sqrt(d*x^2+c)-1/3*b*(-2*c*f+d*e)*x*(b*x^2+a)^(3/2)/c/d^2/sqrt(d*x^2+c)+1/3*(a*b*c*d*(-16*c*f+3*d*e)-8*b^2*c^2*(-2*c*f+d*e)+a^2*d^2*(c*f+2*d*e))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/c^(3/2)/d^(7/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-1/3*b*(a*d*(-7*c*f+d*e)-4*b*c*(-2*c*f+d*e))*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/sqrt(c)/d^(7/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[(b*x^2+a)^(5/2)*(f*x^2+e)/(d*x^2+c)^(7/2),x,4,1/5*(-c*f+d*e)*x*(b*x^2+a)^(5/2)/c/d/(d*x^2+c)^(5/2)+1/15*(b*c*(-6*c*f+d*e)+a*d*(c*f+4*d*e))*x*(b*x^2+a)^(3/2)/c^2/d^2/(d*x^2+c)^(3/2)-1/15*b*(4*b*c*(-6*c*f+d*e)+a*d*(c*f+4*d*e))*x*sqrt(b*x^2+a)/c^2/d^3/sqrt(d*x^2+c)+1/15*(8*b^2*c^2*(-6*c*f+d*e)+2*a^2*d^2*(c*f+4*d*e)+a*b*c*d*(8*c*f+7*d*e))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/c^(5/2)/d^(7/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-1/15*b*(4*b*c*(-6*c*f+d*e)+a*d*(c*f+4*d*e))*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/c^(3/2)/d^(7/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[(b*x^2+a)^(5/2)*(f*x^2+e)/(d*x^2+c)^(9/2),x,4,1/7*(-c*f+d*e)*x*(b*x^2+a)^(5/2)/c/d/(d*x^2+c)^(7/2)+1/35*(a*d*(c*f+6*d*e)-b*c*(6*c*f+d*e))*x*(b*x^2+a)^(3/2)/c^2/d^2/(d*x^2+c)^(5/2)-1/105*(5*a*b*c*d*(-c*f+d*e)-4*a^2*d^2*(c*f+6*d*e)+4*b^2*c^2*(6*c*f+d*e))*x*sqrt(b*x^2+a)/c^3/d^3/(d*x^2+c)^(3/2)+1/105*(a*b^2*c^2*d*(-16*c*f+9*d*e)+a^2*b*c*d^2*(-9*c*f+16*d*e)-8*a^3*d^3*(c*f+6*d*e)+8*b^3*c^3*(6*c*f+d*e))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/c^(7/2)/d^(7/2)/(-a*d+b*c)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-1/105*b*(5*a*b*c*d*(-c*f+d*e)-4*a^2*d^2*(c*f+6*d*e)+4*b^2*c^2*(6*c*f+d*e))*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/c^(5/2)/d^(7/2)/(-a*d+b*c)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[(d*x^2+c)^(3/2)*(f*x^2+e)/sqrt(b*x^2+a),x,6,1/15*(20*b*c*e-10*a*d*e-13*a*c*f+3*b*c^2*f/d+8*a^2*d*f/b)*x*sqrt(d*x^2+c)/b/sqrt(b*x^2+a)+1/15*(-4*a*d*f+3*b*c*f+5*b*d*e)*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b^2+1/5*f*x*sqrt(b*x^2+a)*(d*x^2+c)^(3/2)/b-1/15*sqrt(a)*(8*a^2*d^2*f+b^2*c*(3*c*f+20*d*e)-a*b*d*(13*c*f+10*d*e))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/b^(5/2)/d/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/15*sqrt(a)*(4*a^2*d*f-6*a*b*c*f-5*a*b*d*e+15*b^2*c*e)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(5/2)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[sqrt(d*x^2+c)*(f*x^2+e)/sqrt(b*x^2+a),x,5,1/3*(-2*a*d*f+b*c*f+3*b*d*e)*x*sqrt(d*x^2+c)/b/d/sqrt(b*x^2+a)+1/3*f*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b-1/3*sqrt(a)*(-2*a*d*f+b*c*f+3*b*d*e)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/b^(3/2)/d/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/3*sqrt(a)*(-a*f+3*b*e)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(3/2)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(f*x^2+e)/sqrt(b*x^2+a)/sqrt(d*x^2+c),x,4,f*x*sqrt(d*x^2+c)/d/sqrt(b*x^2+a)-sqrt(a)*f*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/sqrt(b)/d/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+sqrt(a)*e*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(b)/c/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(f*x^2+e)/sqrt(b*x^2+a)/(d*x^2+c)^(3/2),x,1,-(-c*f+d*e)*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/sqrt(c)/sqrt(d)/(-a*d+b*c)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+sqrt(c)*(-a*f+b*e)*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a/sqrt(d)/(-a*d+b*c)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[(f*x^2+e)/sqrt(b*x^2+a)/(d*x^2+c)^(5/2),x,2,-1/3*(-c*f+d*e)*x*sqrt(b*x^2+a)/c/(-a*d+b*c)/(d*x^2+c)^(3/2)-1/3*(b*c*(-c*f+4*d*e)-a*d*(c*f+2*d*e))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/c^(3/2)/sqrt(d)/(-a*d+b*c)^2/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+1/3*b*(-2*a*c*f-a*d*e+3*b*c*e)*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a/sqrt(c)/sqrt(d)/(-a*d+b*c)^2/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[(f*x^2+e)/sqrt(b*x^2+a)/(d*x^2+c)^(7/2),x,3,-1/5*(-c*f+d*e)*x*sqrt(b*x^2+a)/c/(-a*d+b*c)/(d*x^2+c)^(5/2)-1/15*(b*c*(-3*c*f+8*d*e)-a*d*(c*f+4*d*e))*x*sqrt(b*x^2+a)/c^2/(-a*d+b*c)^2/(d*x^2+c)^(3/2)-1/15*(b^2*c^2*(-3*c*f+23*d*e)+2*a^2*d^2*(c*f+4*d*e)-a*b*c*d*(7*c*f+23*d*e))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/c^(5/2)/sqrt(d)/(-a*d+b*c)^3/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+1/15*b*(15*b^2*c^2*e+a^2*d*(c*f+4*d*e)-a*b*c*(9*c*f+11*d*e))*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a/c^(3/2)/sqrt(d)/(-a*d+b*c)^3/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[(d*x^2+c)^(5/2)*(f*x^2+e)/(b*x^2+a)^(3/2),x,4,1/15*(24*a^2*d^2*f+15*b^2*c*(c*f+2*d*e)-a*b*d*(41*c*f+20*d*e))*x*sqrt(d*x^2+c)/b^3/sqrt(b*x^2+a)-1/15*(6*a*d*f-5*b*(c*f+d*e))*x*(d*x^2+c)^(3/2)/b^2/sqrt(b*x^2+a)+1/5*f*x*(d*x^2+c)^(5/2)/b/sqrt(b*x^2+a)+1/15*(15*b^3*c^2*e-48*a^3*d^2*f+8*a^2*b*d*(11*c*f+5*d*e)-a*b^2*c*(38*c*f+65*d*e))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/sqrt(a)/b^(7/2)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/15*sqrt(a)*(24*a^2*d^2*f+15*b^2*c*(c*f+2*d*e)-a*b*d*(41*c*f+20*d*e))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(7/2)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(d*x^2+c)^(3/2)*(f*x^2+e)/(b*x^2+a)^(3/2),x,3,-1/3*(4*a*d*f-3*b*(c*f+d*e))*x*sqrt(d*x^2+c)/b^2/sqrt(b*x^2+a)+1/3*f*x*(d*x^2+c)^(3/2)/b/sqrt(b*x^2+a)+1/3*(8*a^2*d*f-7*a*b*c*f-6*a*b*d*e+3*b^2*c*e)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/sqrt(a)/b^(5/2)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/3*sqrt(a)*(4*a*d*f-3*b*(c*f+d*e))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(5/2)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[sqrt(d*x^2+c)*(f*x^2+e)/(b*x^2+a)^(3/2),x,2,f*x*sqrt(d*x^2+c)/b/sqrt(b*x^2+a)+(-2*a*f+b*e)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/sqrt(a)/b^(3/2)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+sqrt(a)*f*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(3/2)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(f*x^2+e)/(b*x^2+a)^(3/2)/sqrt(d*x^2+c),x,1,(-a*f+b*e)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/sqrt(a)/sqrt(b)/(-a*d+b*c)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-sqrt(a)*(-c*f+d*e)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(b)/c/(-a*d+b*c)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(f*x^2+e)/(b*x^2+a)^(3/2)/(d*x^2+c)^(3/2),x,2,(-a*f+b*e)*x/a/(-a*d+b*c)/sqrt(b*x^2+a)/sqrt(d*x^2+c)+sqrt(d)*(-2*a*c*f+a*d*e+b*c*e)*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/a/sqrt(c)/(-a*d+b*c)^2/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-sqrt(c)*(-a*d*f-b*c*f+2*b*d*e)*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a/sqrt(d)/(-a*d+b*c)^2/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[(f*x^2+e)/(b*x^2+a)^(3/2)/(d*x^2+c)^(5/2),x,3,(-a*f+b*e)*x/a/(-a*d+b*c)/sqrt(b*x^2+a)/(d*x^2+c)^(3/2)+1/3*d*(-4*a*c*f+a*d*e+3*b*c*e)*x*sqrt(b*x^2+a)/a/c/(-a*d+b*c)^2/(d*x^2+c)^(3/2)+1/3*sqrt(d)*(3*b^2*c^2*e+7*a*b*c*(-c*f+d*e)-a^2*d*(c*f+2*d*e))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/a/c^(3/2)/(-a*d+b*c)^3/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-1/3*b*(3*b*c*(-c*f+3*d*e)-a*d*(5*c*f+d*e))*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a/sqrt(c)/sqrt(d)/(-a*d+b*c)^3/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[(d*x^2+c)^(5/2)*(f*x^2+e)/(b*x^2+a)^(5/2),x,4,-1/3*d*(8*a^2*d*f-7*a*b*c*f-4*a*b*d*e+b^2*c*e)*x*sqrt(d*x^2+c)/a/b^3/sqrt(b*x^2+a)-1/3*d*(-2*a*f+b*e)*x*(d*x^2+c)^(3/2)/a/b^2/sqrt(b*x^2+a)+1/3*(-a*f+b*e)*x*(d*x^2+c)^(5/2)/a/b/(b*x^2+a)^(3/2)+1/3*(2*b^3*c^2*e+16*a^3*d^2*f+a*b^2*c*(c*f+3*d*e)-8*a^2*b*d*(2*c*f+d*e))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/a^(3/2)/b^(7/2)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/3*d*(8*a^2*d*f-7*a*b*c*f-4*a*b*d*e+b^2*c*e)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(a)/b^(7/2)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(d*x^2+c)^(3/2)*(f*x^2+e)/(b*x^2+a)^(5/2),x,3,-1/3*d*(-4*a*f+b*e)*x*sqrt(d*x^2+c)/a/b^2/sqrt(b*x^2+a)+1/3*(-a*f+b*e)*x*(d*x^2+c)^(3/2)/a/b/(b*x^2+a)^(3/2)+1/3*(2*b^2*c*e-8*a^2*d*f+a*b*(c*f+2*d*e))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/a^(3/2)/b^(5/2)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/3*d*(-4*a*f+b*e)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(a)/b^(5/2)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[sqrt(d*x^2+c)*(f*x^2+e)/(b*x^2+a)^(5/2),x,2,1/3*(-a*f+b*e)*x*sqrt(d*x^2+c)/a/b/(b*x^2+a)^(3/2)+1/3*(2*b^2*c*e-2*a^2*d*f-a*b*(-c*f+d*e))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/a^(3/2)/b^(3/2)/(-a*d+b*c)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/3*d*(-a*f+b*e)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(a)/b^(3/2)/(-a*d+b*c)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(f*x^2+e)/(b*x^2+a)^(5/2)/sqrt(d*x^2+c),x,2,1/3*(-a*f+b*e)*x*sqrt(d*x^2+c)/a/(-a*d+b*c)/(b*x^2+a)^(3/2)+1/3*(2*b^2*c*e+a^2*d*f-a*b*(-c*f+4*d*e))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/a^(3/2)/sqrt(b)/(-a*d+b*c)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/3*d*(2*a*c*f-3*a*d*e+b*c*e)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(a)/sqrt(b)/c/(-a*d+b*c)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(f*x^2+e)/(b*x^2+a)^(5/2)/(d*x^2+c)^(3/2),x,3,1/3*(-a*f+b*e)*x/a/(-a*d+b*c)/(b*x^2+a)^(3/2)/sqrt(d*x^2+c)+1/3*(2*b^2*c*e+3*a^2*d*f-a*b*(-c*f+6*d*e))*x/a^2/(-a*d+b*c)^2/sqrt(b*x^2+a)/sqrt(d*x^2+c)+1/3*sqrt(d)*(2*b^2*c^2*e-a^2*d*(-7*c*f+3*d*e)-a*b*c*(-c*f+7*d*e))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/a^2/sqrt(c)/(-a*d+b*c)^3/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-1/3*sqrt(c)*sqrt(d)*(b^2*c*e+3*a^2*d*f-a*b*(-5*c*f+9*d*e))*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a^2/(-a*d+b*c)^3/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[(f*x^2+e)/(b*x^2+a)^(5/2)/(d*x^2+c)^(5/2),x,4,1/3*(-a*f+b*e)*x/a/(-a*d+b*c)/(b*x^2+a)^(3/2)/(d*x^2+c)^(3/2)+1/3*(2*b^2*c*e+5*a^2*d*f-a*b*(-c*f+8*d*e))*x/a^2/(-a*d+b*c)^2/sqrt(b*x^2+a)/(d*x^2+c)^(3/2)+1/3*d*(2*b^2*c^2*e-a^2*d*(-7*c*f+d*e)-a*b*c*(-c*f+9*d*e))*x*sqrt(b*x^2+a)/a^2/c/(-a*d+b*c)^3/(d*x^2+c)^(3/2)+1/3*sqrt(d)*(2*b^3*c^3*e-2*a^2*b*c*d*(-7*c*f+5*d*e)-a*b^2*c^2*(-c*f+10*d*e)+a^3*d^2*(c*f+2*d*e))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/a^2/c^(3/2)/(-a*d+b*c)^4/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-1/3*b*sqrt(d)*(b^2*c^2*e-2*a*b*c*(-4*c*f+9*d*e)+a^2*d*(8*c*f+d*e))*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a^2/sqrt(c)/(-a*d+b*c)^4/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[(f*x^2+e)/sqrt(b*x^2+a)/sqrt(d*x^2+c),x,4,f*x*sqrt(d*x^2+c)/d/sqrt(b*x^2+a)-sqrt(a)*f*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/sqrt(b)/d/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+sqrt(a)*e*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(b)/c/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(f*x^2+e)/sqrt(b*x^2+a)/sqrt(-d*x^2+c),x,7,sqrt(c)*f*sqrt(b*x^2+a)*sqrt(1-d*x^2/c)*EllipticE(sin(arcsin(sqrt(d)*x/sqrt(c))),sqrt(-b*c/a/d))/b/sqrt(d)/sqrt(1+b*x^2/a)/sqrt(-d*x^2+c)+sqrt(c)*(-a*f+b*e)*sqrt(1+b*x^2/a)*sqrt(1-d*x^2/c)*InverseJacobiAM(arcsin(sqrt(d)*x/sqrt(c)),sqrt(-b*c/a/d))/b/sqrt(d)/sqrt(b*x^2+a)/sqrt(-d*x^2+c),1],
[(f*x^2+e)/sqrt(-b*x^2+a)/sqrt(d*x^2+c),x,7,sqrt(a)*f*sqrt(1-b*x^2/a)*sqrt(d*x^2+c)*EllipticE(sin(arcsin(sqrt(b)*x/sqrt(a))),sqrt(-a*d/b/c))/sqrt(b)/d/sqrt(-b*x^2+a)/sqrt(1+d*x^2/c)+sqrt(a)*(-c*f+d*e)*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*InverseJacobiAM(arcsin(sqrt(b)*x/sqrt(a)),sqrt(-a*d/b/c))/sqrt(b)/d/sqrt(-b*x^2+a)/sqrt(d*x^2+c),1],
[(f*x^2+e)/sqrt(-b*x^2+a)/sqrt(-d*x^2+c),x,7,-sqrt(a)*f*sqrt(1-b*x^2/a)*sqrt(-d*x^2+c)*EllipticE(sin(arcsin(sqrt(b)*x/sqrt(a))),sqrt(a*d/b/c))/sqrt(b)/d/sqrt(-b*x^2+a)/sqrt(1-d*x^2/c)+sqrt(a)*(c*f+d*e)*sqrt(1-b*x^2/a)*sqrt(1-d*x^2/c)*InverseJacobiAM(arcsin(sqrt(b)*x/sqrt(a)),sqrt(a*d/b/c))/sqrt(b)/d/sqrt(-b*x^2+a)/sqrt(-d*x^2+c),1],
[(f*x^2+e)/sqrt(b*x^2+a)/(d*x^2+c)^(3/2),x,1,-(-c*f+d*e)*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/sqrt(c)/sqrt(d)/(-a*d+b*c)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+sqrt(c)*(-a*f+b*e)*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a/sqrt(d)/(-a*d+b*c)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[(f*x^2+e)/sqrt(-b*x^2+a)/(d*x^2+c)^(3/2),x,1,(-c*f+d*e)*sqrt(-b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1+b*c/a/d))/sqrt(c)/sqrt(d)/(a*d+b*c)/sqrt(c*(-b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+sqrt(c)*(a*f+b*e)*sqrt(-b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1+b*c/a/d))/a/sqrt(d)/(a*d+b*c)/sqrt(c*(-b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[(f*x^2+e)/sqrt(b*x^2+a)/(-d*x^2+c)^(3/2),x,8,(c*f+d*e)*x*sqrt(b*x^2+a)/c/(a*d+b*c)/sqrt(-d*x^2+c)-(c*f+d*e)*sqrt(b*x^2+a)*sqrt(1-d*x^2/c)*EllipticE(sin(arcsin(sqrt(d)*x/sqrt(c))),sqrt(-b*c/a/d))/sqrt(c)/sqrt(d)/(a*d+b*c)/sqrt(1+b*x^2/a)/sqrt(-d*x^2+c)+e*sqrt(1+b*x^2/a)*sqrt(1-d*x^2/c)*InverseJacobiAM(arcsin(sqrt(d)*x/sqrt(c)),sqrt(-b*c/a/d))/sqrt(c)/sqrt(d)/sqrt(b*x^2+a)/sqrt(-d*x^2+c),1],
[(f*x^2+e)/sqrt(-b*x^2+a)/(-d*x^2+c)^(3/2),x,8,-(c*f+d*e)*x*sqrt(-b*x^2+a)/c/(-a*d+b*c)/sqrt(-d*x^2+c)+sqrt(a)*sqrt(b)*(c*f+d*e)*sqrt(1-b*x^2/a)*sqrt(-d*x^2+c)*EllipticE(sin(arcsin(sqrt(b)*x/sqrt(a))),sqrt(a*d/b/c))/c/d/(-a*d+b*c)/sqrt(-b*x^2+a)/sqrt(1-d*x^2/c)-sqrt(a)*f*sqrt(1-b*x^2/a)*sqrt(1-d*x^2/c)*InverseJacobiAM(arcsin(sqrt(b)*x/sqrt(a)),sqrt(a*d/b/c))/sqrt(b)/d/sqrt(-b*x^2+a)/sqrt(-d*x^2+c),1],
[(b*x^2+a)/sqrt(d*x^2+2)/sqrt(f*x^2+3),x,4,b*x*sqrt(f*x^2+3)/f/sqrt(d*x^2+2)-sqrt(3)*b*sqrt(f*x^2+3)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(2))),sqrt(1-2/3*f/d))/sqrt(d)/f/sqrt(d*x^2+2)/sqrt((f*x^2+3)/(d*x^2+2))+a*sqrt(f*x^2+3)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(2)),sqrt(1-2/3*f/d))/sqrt(3)/sqrt(d)/sqrt(d*x^2+2)/sqrt((f*x^2+3)/(d*x^2+2)),1],
[(b*x^2+a)*sqrt(d*x^2+2)/sqrt(f*x^2+3),x,5,-1/3*(-3*a*d*f+6*b*d-2*b*f)*x*sqrt(f*x^2+3)/f^2/sqrt(d*x^2+2)+1/3*b*x*sqrt(d*x^2+2)*sqrt(f*x^2+3)/f+(-3*a*d*f+6*b*d-2*b*f)*sqrt(f*x^2+3)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(2))),sqrt(1-2/3*f/d))/sqrt(3)/sqrt(d)/f^2/sqrt(d*x^2+2)/sqrt((f*x^2+3)/(d*x^2+2))-2*(-a*f+b)*sqrt(f*x^2+3)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(2)),sqrt(1-2/3*f/d))/sqrt(3)/sqrt(d)/f/sqrt(d*x^2+2)/sqrt((f*x^2+3)/(d*x^2+2)),1],
[(b*x^2+a)*sqrt(d*x^2+2)*sqrt(f*x^2+3),x,6,1/15*(5*a*d*f*(3*d+2*f)-2*b*(9*d^2-6*d*f+4*f^2))*x*sqrt(f*x^2+3)/d/f^2/sqrt(d*x^2+2)-1/15*(-5*a*d*f+6*b*d-2*b*f)*x*sqrt(d*x^2+2)*sqrt(f*x^2+3)/d/f+1/5*b*x*sqrt(d*x^2+2)*(f*x^2+3)^(3/2)/f-1/5*(5*a*d*f*(3*d+2*f)-2*b*(9*d^2-6*d*f+4*f^2))*sqrt(f*x^2+3)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(2))),sqrt(1-2/3*f/d))/sqrt(3)/d^(3/2)/f^2/sqrt(d*x^2+2)/sqrt((f*x^2+3)/(d*x^2+2))-2/5*(-10*a*d*f+3*b*d+2*b*f)*sqrt(f*x^2+3)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(2)),sqrt(1-2/3*f/d))/sqrt(3)/d^(3/2)/f/sqrt(d*x^2+2)/sqrt((f*x^2+3)/(d*x^2+2)),1],
[(-b-sqrt(-4*a*c+b^2)+2*c*x^2)/sqrt(1+2*c*x^2/(-b-sqrt(-4*a*c+b^2)))/sqrt(1+2*c*x^2/(-b+sqrt(-4*a*c+b^2))),x,2,-sqrt(b-sqrt(-4*a*c+b^2))*(b+sqrt(-4*a*c+b^2))*EllipticE(sin(arcsin(sqrt(2)*sqrt(c)*x/sqrt(b-sqrt(-4*a*c+b^2)))),sqrt((b-sqrt(-4*a*c+b^2))/(b+sqrt(-4*a*c+b^2))))/sqrt(2)/sqrt(c),1],
[(b-sqrt(-4*a*c+b^2)+2*c*x^2)/sqrt(1+2*c*x^2/(b-sqrt(-4*a*c+b^2)))/sqrt(1+2*c*x^2/(b+sqrt(-4*a*c+b^2))),x,4,sqrt(-b+sqrt(-4*a*c+b^2))*(b+sqrt(-4*a*c+b^2))*EllipticE(sin(arcsin(sqrt(2)*sqrt(c)*x/sqrt(-b+sqrt(-4*a*c+b^2)))),sqrt((b-sqrt(-4*a*c+b^2))/(b+sqrt(-4*a*c+b^2))))/sqrt(2)/sqrt(c)-sqrt(2)*sqrt(-4*a*c+b^2)*sqrt(-b+sqrt(-4*a*c+b^2))*InverseJacobiAM(arcsin(sqrt(2)*sqrt(c)*x/sqrt(-b+sqrt(-4*a*c+b^2))),sqrt((b-sqrt(-4*a*c+b^2))/(b+sqrt(-4*a*c+b^2))))/sqrt(c),1],
[(10*x^2+7)/sqrt(3*x^2+2)/(7*x^2+5)^(3/2),x,3,1/5*sqrt(2/7)*EllipticE(sin(arctan(sqrt(7/5)*x)),sqrt(-1/14))+InverseJacobiAM(arctan(sqrt(7/5)*x),sqrt(-1/14))/sqrt(14),1],
[(10*x^2+7)/sqrt((3*x^2+2)/(7*x^2+5))/(7*x^2+5)^2,x,4,1/5*sqrt(2/7)*EllipticE(sin(arctan(sqrt(7/5)*x)),sqrt(-1/14))+InverseJacobiAM(arctan(sqrt(7/5)*x),sqrt(-1/14))/sqrt(14),1],
[sqrt(3*x^2+2)/(7*x^2+5)^(3/2)+1/sqrt(3*x^2+2)/sqrt(7*x^2+5),x,3,1/5*sqrt(2/7)*EllipticE(sin(arctan(sqrt(7/5)*x)),sqrt(-1/14))+InverseJacobiAM(arctan(sqrt(7/5)*x),sqrt(-1/14))/sqrt(14),1],
[sqrt(b*x^2+a)*(d*x^2+c)^(3/2)*(f*x^2+e)^2,x,8,-1/315*(16*a^4*d^4*f^2-16*a^3*b*d^3*f*(2*c*f+3*d*e)-a*b^3*c*d*(-7*c^2*f^2+54*c*d*e*f+147*d^2*e^2)+3*a^2*b^2*d^2*(3*c^2*f^2+38*c*d*e*f+14*d^2*e^2)-b^4*c^2*(8*c^2*f^2-36*c*d*e*f+63*d^2*e^2))*x*sqrt(d*x^2+c)/b^3/d^3/sqrt(b*x^2+a)+1/315*(8*a^3*d^3*f^2-3*a^2*b*d^2*f*(5*c*f+8*d*e)+2*b^3*c*(-2*c^2*f^2+9*c*d*e*f+63*d^2*e^2)+3*a*b^2*d*(c^2*f^2+18*c*d*e*f+7*d^2*e^2))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b^3/d^2-1/315*(6*a^2*d^2*f^2-a*b*d*f*(11*c*f+18*d*e)-3*b^2*(c^2*f^2+48*c*d*e*f+21*d^2*e^2))*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b^2/d+1/63*f*(a*d*f+10*b*c*f+18*b*d*e)*x^5*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b+1/9*d*f^2*x^7*sqrt(b*x^2+a)*sqrt(d*x^2+c)+1/315*sqrt(a)*(16*a^4*d^4*f^2-16*a^3*b*d^3*f*(2*c*f+3*d*e)-a*b^3*c*d*(-7*c^2*f^2+54*c*d*e*f+147*d^2*e^2)+3*a^2*b^2*d^2*(3*c^2*f^2+38*c*d*e*f+14*d^2*e^2)-b^4*c^2*(8*c^2*f^2-36*c*d*e*f+63*d^2*e^2))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/b^(7/2)/d^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/315*a^(3/2)*(8*a^3*d^3*f^2-3*a^2*b*d^2*f*(5*c*f+8*d*e)+3*a*b^2*d*(c^2*f^2+18*c*d*e*f+7*d^2*e^2)-b^3*c*(4*c^2*f^2-18*c*d*e*f+189*d^2*e^2))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(7/2)/d^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[sqrt(b*x^2+a)*sqrt(d*x^2+c)*(f*x^2+e)^2,x,7,1/105*(8*a^3*d^3*f^2-a^2*b*d^2*f*(5*c*f+28*d*e)+a*b^2*d*(-5*c^2*f^2+28*c*d*e*f+35*d^2*e^2)+b^3*c*(8*c^2*f^2-28*c*d*e*f+35*d^2*e^2))*x*sqrt(d*x^2+c)/b^2/d^3/sqrt(b*x^2+a)-1/105*(4*a^2*d*f^2/b-2*a*f*(c*f+7*d*e)-b*(35*d*e^2+14*c*e*f-4*c^2*f^2/d))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b/d+1/35*f*(a*d*f+b*c*f+14*b*d*e)*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b/d+1/7*f^2*x^5*sqrt(b*x^2+a)*sqrt(d*x^2+c)-1/105*sqrt(a)*(8*a^3*d^3*f^2-a^2*b*d^2*f*(5*c*f+28*d*e)+a*b^2*d*(-5*c^2*f^2+28*c*d*e*f+35*d^2*e^2)+b^3*c*(8*c^2*f^2-28*c*d*e*f+35*d^2*e^2))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/b^(5/2)/d^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+2/105*a^(3/2)*(2*a^2*d^2*f^2-a*b*d*f*(c*f+7*d*e)+b^2*(2*c^2*f^2-7*c*d*e*f+35*d^2*e^2))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(5/2)/d^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[sqrt(b*x^2+a)*(f*x^2+e)^2/sqrt(d*x^2+c),x,6,-1/15*(2*a^2*d^2*f^2-a*b*d*f*(-3*c*f+10*d*e)-b^2*(8*c^2*f^2-20*c*d*e*f+15*d^2*e^2))*x*sqrt(d*x^2+c)/b/d^3/sqrt(b*x^2+a)+1/15*f*(a*d*f-4*b*c*f+10*b*d*e)*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b/d^2+1/5*f^2*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/d+1/15*sqrt(a)*(2*a^2*d^2*f^2-a*b*d*f*(-3*c*f+10*d*e)-b^2*(8*c^2*f^2-20*c*d*e*f+15*d^2*e^2))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/b^(3/2)/d^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/15*a^(3/2)*(a*c*d*f^2-b*(4*c^2*f^2-10*c*d*e*f+15*d^2*e^2))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(3/2)/c/d^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[sqrt(b*x^2+a)*(f*x^2+e)^2/(d*x^2+c)^(3/2),x,3,1/3*f*(a*d*f-4*b*c*f+6*b*d*e)*x*sqrt(b*x^2+a)/b/d^2/sqrt(d*x^2+c)+1/3*f^2*x^3*sqrt(b*x^2+a)/d/sqrt(d*x^2+c)-1/3*(a*c*d*f^2-b*(8*c^2*f^2-12*c*d*e*f+3*d^2*e^2))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/b/sqrt(c)/d^(5/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+2/3*sqrt(c)*f*(-2*c*f+3*d*e)*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/d^(5/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[sqrt(b*x^2+a)*(f*x^2+e)^2/(d*x^2+c)^(5/2),x,3,1/3*(4*c^2*f^2-2*c*d*e*f+d^2*e^2)*x*sqrt(b*x^2+a)/c/d^2/(d*x^2+c)^(3/2)+f^2*x^3*sqrt(b*x^2+a)/d/(d*x^2+c)^(3/2)+1/3*(b*c*(-8*c^2*f^2+4*c*d*e*f+d^2*e^2)-a*d*(-7*c^2*f^2+2*c*d*e*f+2*d^2*e^2))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/c^(3/2)/d^(5/2)/(-a*d+b*c)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-1/3*(3*a*c*d*f^2-b*(4*c^2*f^2-2*c*d*e*f+d^2*e^2))*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/sqrt(c)/d^(5/2)/(-a*d+b*c)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[sqrt(b*x^2+a)*(f*x^2+e)^2/(d*x^2+c)^(7/2),x,4,1/5*(-4*c^2*f^2-2*c*d*e*f+d^2*e^2)*x*sqrt(b*x^2+a)/c/d^2/(d*x^2+c)^(5/2)-f^2*x^3*sqrt(b*x^2+a)/d/(d*x^2+c)^(5/2)+1/15*(b*c*(8*c^2*f^2+4*c*d*e*f+3*d^2*e^2)-a*d*(9*c^2*f^2+2*c*d*e*f+4*d^2*e^2))*x*sqrt(b*x^2+a)/c^2/d^2/(-a*d+b*c)/(d*x^2+c)^(3/2)+1/15*(a^2*d^2*(3*c^2*f^2+4*c*d*e*f+8*d^2*e^2)+b^2*c^2*(8*c^2*f^2+4*c*d*e*f+3*d^2*e^2)-a*b*c*d*(13*c^2*f^2+4*c*d*e*f+13*d^2*e^2))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/c^(5/2)/d^(5/2)/(-a*d+b*c)^2/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+2/15*b*(-c*f+d*e)*(b*c*(2*c*f+3*d*e)-a*d*(3*c*f+2*d*e))*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/c^(3/2)/d^(5/2)/(-a*d+b*c)^2/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[sqrt(b*x^2+a)*(f*x^2+e)^2/(d*x^2+c)^(9/2),x,5,1/21*(-4*c^2*f^2-6*c*d*e*f+3*d^2*e^2)*x*sqrt(b*x^2+a)/c/d^2/(d*x^2+c)^(7/2)-1/3*f^2*x^3*sqrt(b*x^2+a)/d/(d*x^2+c)^(7/2)+1/105*(b*c*(8*c^2*f^2+12*c*d*e*f+15*d^2*e^2)-a*d*(11*c^2*f^2+6*c*d*e*f+18*d^2*e^2))*x*sqrt(b*x^2+a)/c^2/d^2/(-a*d+b*c)/(d*x^2+c)^(5/2)+1/105*(a^2*d^2*(3*c^2*f^2+8*c*d*e*f+24*d^2*e^2)+b^2*c^2*(8*c^2*f^2+12*c*d*e*f+15*d^2*e^2)-a*b*c*d*(15*c^2*f^2+12*c*d*e*f+43*d^2*e^2))*x*sqrt(b*x^2+a)/c^3/d^2/(-a*d+b*c)^2/(d*x^2+c)^(3/2)-1/105*(2*a^3*d^3*(3*c^2*f^2+8*c*d*e*f+24*d^2*e^2)-b^3*c^3*(8*c^2*f^2+12*c*d*e*f+15*d^2*e^2)-a^2*b*c*d^2*(9*c^2*f^2+38*c*d*e*f+128*d^2*e^2)+a*b^2*c^2*d*(19*c^2*f^2+18*c*d*e*f+103*d^2*e^2))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/c^(7/2)/d^(5/2)/(-a*d+b*c)^3/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-1/105*b*(a*b*c*d*(-9*c^2*f^2+18*c*d*e*f+61*d^2*e^2)-b^2*c^2*(-4*c^2*f^2-6*c*d*e*f+45*d^2*e^2)-a^2*d^2*(3*c^2*f^2+8*c*d*e*f+24*d^2*e^2))*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/c^(5/2)/d^(5/2)/(-a*d+b*c)^3/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[(b*x^2+a)^(3/2)*sqrt(d*x^2+c)*(f*x^2+e)^2,x,8,1/315*(8*a^4*d^4*f^2-a^3*b*d^3*f*(7*c*f+36*d*e)+9*a^2*b^2*d^2*(-c^2*f^2+6*c*d*e*f+7*d^2*e^2)-2*b^4*c^2*(8*c^2*f^2-24*c*d*e*f+21*d^2*e^2)+a*b^3*c*d*(32*c^2*f^2-114*c*d*e*f+147*d^2*e^2))*x*sqrt(d*x^2+c)/b^2/d^4/sqrt(b*x^2+a)-1/315*(4*a^3*d^3*f^2-3*a^2*b*d^2*f*(c*f+6*d*e)-3*a*b^2*d*(-5*c^2*f^2+18*c*d*e*f+42*d^2*e^2)-b^3*c*(8*c^2*f^2-24*c*d*e*f+21*d^2*e^2))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b^2/d^3+1/315*(3*a^2*d^2*f^2+a*b*d*f*(11*c*f+144*d*e)+3*b^2*(-2*c^2*f^2+6*c*d*e*f+21*d^2*e^2))*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b/d^2+1/63*f*(10*a*d*f+b*c*f+18*b*d*e)*x^5*sqrt(b*x^2+a)*sqrt(d*x^2+c)/d+1/9*b*f^2*x^7*sqrt(b*x^2+a)*sqrt(d*x^2+c)-1/315*sqrt(a)*(8*a^4*d^4*f^2-a^3*b*d^3*f*(7*c*f+36*d*e)+9*a^2*b^2*d^2*(-c^2*f^2+6*c*d*e*f+7*d^2*e^2)-2*b^4*c^2*(8*c^2*f^2-24*c*d*e*f+21*d^2*e^2)+a*b^3*c*d*(32*c^2*f^2-114*c*d*e*f+147*d^2*e^2))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/b^(5/2)/d^4/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/315*a^(3/2)*(4*a^3*d^3*f^2-3*a^2*b*d^2*f*(c*f+6*d*e)+3*a*b^2*d*(5*c^2*f^2-18*c*d*e*f+63*d^2*e^2)-b^3*c*(8*c^2*f^2-24*c*d*e*f+21*d^2*e^2))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(5/2)/d^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(b*x^2+a)^(3/2)*(f*x^2+e)^2/sqrt(d*x^2+c),x,7,-2/105*(3*a^3*d^3*f^2-3*a^2*b*d^2*f*(-2*c*f+7*d*e)+b^3*c*(24*c^2*f^2-56*c*d*e*f+35*d^2*e^2)-a*b^2*d*(36*c^2*f^2-91*c*d*e*f+70*d^2*e^2))*x*sqrt(d*x^2+c)/b/d^4/sqrt(b*x^2+a)+1/105*(3*a^2*d^2*f^2+3*a*b*d*f*(-11*c*f+28*d*e)+b^2*(24*c^2*f^2-56*c*d*e*f+35*d^2*e^2))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b/d^3+2/35*f*(4*a*d*f-3*b*c*f+7*b*d*e)*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/d^2+1/7*b*f^2*x^5*sqrt(b*x^2+a)*sqrt(d*x^2+c)/d+2/105*sqrt(a)*(3*a^3*d^3*f^2-3*a^2*b*d^2*f*(-2*c*f+7*d*e)+b^3*c*(24*c^2*f^2-56*c*d*e*f+35*d^2*e^2)-a*b^2*d*(36*c^2*f^2-91*c*d*e*f+70*d^2*e^2))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/b^(3/2)/d^4/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/105*a^(3/2)*(3*a^2*c*d^2*f^2-3*a*b*d*(11*c^2*f^2-28*c*d*e*f+35*d^2*e^2)+b^2*c*(24*c^2*f^2-56*c*d*e*f+35*d^2*e^2))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(3/2)/c/d^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(b*x^2+a)^(3/2)*(f*x^2+e)^2/(d*x^2+c)^(3/2),x,4,1/15*(3*a^2*d^2*f^2+a*b*d*f*(-27*c*f+40*d*e)+b^2*(24*c^2*f^2-40*c*d*e*f+15*d^2*e^2))*x*sqrt(b*x^2+a)/b/d^3/sqrt(d*x^2+c)+2/15*f*(3*a*d*f-3*b*c*f+5*b*d*e)*x^3*sqrt(b*x^2+a)/d^2/sqrt(d*x^2+c)+1/5*b*f^2*x^5*sqrt(b*x^2+a)/d/sqrt(d*x^2+c)-1/15*(3*a^2*c*d^2*f^2+2*b^2*c*(24*c^2*f^2-40*c*d*e*f+15*d^2*e^2)-a*b*d*(48*c^2*f^2-70*c*d*e*f+15*d^2*e^2))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/b/sqrt(c)/d^(7/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+1/15*sqrt(c)*(3*a*d*f*(-7*c*f+10*d*e)+b*(24*c^2*f^2-40*c*d*e*f+15*d^2*e^2))*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/d^(7/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[(b*x^2+a)^(3/2)*(f*x^2+e)^2/(d*x^2+c)^(5/2),x,4,1/3*(a*d*(-c*f+d*e)^2-b*c*(2*c^2*f^2-2*c*d*e*f+d^2*e^2))*x*sqrt(b*x^2+a)/c/d^3/(d*x^2+c)^(3/2)+1/3*b*f^2*x^5*sqrt(b*x^2+a)/d/(d*x^2+c)^(3/2)+2/3*f*(2*a*d*f-3*b*c*f+3*b*d*e)*x*sqrt(b*x^2+a)/d^3/sqrt(d*x^2+c)+2/3*(a*d*(-4*c^2*f^2+c*d*e*f+d^2*e^2)+b*c*(8*c^2*f^2-8*c*d*e*f+d^2*e^2))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/c^(3/2)/d^(7/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+1/3*(3*a*c*d*f^2-b*(8*c^2*f^2-8*c*d*e*f+d^2*e^2))*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/sqrt(c)/d^(7/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[(b*x^2+a)^(3/2)*(f*x^2+e)^2/(d*x^2+c)^(7/2),x,4,1/5*(a*d*(-c*f+d*e)^2-b*c*(6*c^2*f^2-2*c*d*e*f+d^2*e^2))*x*sqrt(b*x^2+a)/c/d^3/(d*x^2+c)^(5/2)+b*f^2*x^5*sqrt(b*x^2+a)/d/(d*x^2+c)^(5/2)+2/15*(a*d*(-3*c^2*f^2+c*d*e*f+2*d^2*e^2)+b*c*(21*c^2*f^2-7*c*d*e*f+d^2*e^2))*x*sqrt(b*x^2+a)/c^2/d^3/(d*x^2+c)^(3/2)+1/15*(2*b^2*c^2*(-24*c^2*f^2+8*c*d*e*f+d^2*e^2)-a^2*d^2*(3*c^2*f^2+4*c*d*e*f+8*d^2*e^2)+3*a*b*c*d*(16*c^2*f^2-2*c*d*e*f+d^2*e^2))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/c^(5/2)/d^(7/2)/(-a*d+b*c)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-1/15*b*(b*c*(-24*c^2*f^2+8*c*d*e*f+d^2*e^2)-a*d*(-21*c^2*f^2+2*c*d*e*f+4*d^2*e^2))*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/c^(3/2)/d^(7/2)/(-a*d+b*c)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[(b*x^2+a)^(3/2)*(f*x^2+e)^2/(d*x^2+c)^(9/2),x,5,1/7*(a*d*(-c*f+d*e)^2-b*c*(-6*c^2*f^2-2*c*d*e*f+d^2*e^2))*x*sqrt(b*x^2+a)/c/d^3/(d*x^2+c)^(7/2)-b*f^2*x^5*sqrt(b*x^2+a)/d/(d*x^2+c)^(7/2)+2/35*(b*c*(-27*c^2*f^2-9*c*d*e*f+d^2*e^2)+a*d*(-4*c^2*f^2+c*d*e*f+3*d^2*e^2))*x*sqrt(b*x^2+a)/c^2/d^3/(d*x^2+c)^(5/2)+1/105*(a*b*c*d*(-48*c^2*f^2-2*c*d*e*f+15*d^2*e^2)-a^2*d^2*(3*c^2*f^2+8*c*d*e*f+24*d^2*e^2)+2*b^2*c^2*(24*c^2*f^2+8*c*d*e*f+3*d^2*e^2))*x*sqrt(b*x^2+a)/c^3/d^3/(-a*d+b*c)/(d*x^2+c)^(3/2)+2/105*(a*b^2*c^2*d*(-36*c^2*f^2-5*c*d*e*f+6*d^2*e^2)-a^2*b*c*d^2*(-6*c^2*f^2+5*c*d*e*f+36*d^2*e^2)+a^3*d^3*(3*c^2*f^2+8*c*d*e*f+24*d^2*e^2)+b^3*c^3*(24*c^2*f^2+8*c*d*e*f+3*d^2*e^2))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/c^(7/2)/d^(7/2)/(-a*d+b*c)^2/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-1/105*b*(a^2*d^2*(3*c^2*f^2+8*c*d*e*f+24*d^2*e^2)+b^2*c^2*(24*c^2*f^2+8*c*d*e*f+3*d^2*e^2)-a*b*c*d*(33*c^2*f^2+4*c*d*e*f+33*d^2*e^2))*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/c^(5/2)/d^(7/2)/(-a*d+b*c)^2/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[(b*x^2+a)^(5/2)*sqrt(d*x^2+c)*(f*x^2+e)^2,x,9,1/3465*(40*a^5*d^5*f^2-5*a^4*b*d^4*f*(9*c*f+44*d*e)+5*a^3*b^2*d^3*(-14*c^2*f^2+88*c*d*e*f+99*d^2*e^2)+8*b^5*c^3*(16*c^2*f^2-44*c*d*e*f+33*d^2*e^2)+a^2*b^3*c*d^2*(403*c^2*f^2-1452*c*d*e*f+1914*d^2*e^2)-a*b^4*c^2*d*(408*c^2*f^2-1232*c*d*e*f+1089*d^2*e^2))*x*sqrt(d*x^2+c)/b^2/d^5/sqrt(b*x^2+a)-1/3465*(20*a^4*d^4*f^2-10*a^3*b*d^3*f*(2*c*f+11*d*e)-15*a^2*b^2*d^2*(-12*c^2*f^2+44*c*d*e*f+99*d^2*e^2)+4*b^4*c^2*(16*c^2*f^2-44*c*d*e*f+33*d^2*e^2)-2*a*b^3*c*d*(98*c^2*f^2-297*c*d*e*f+264*d^2*e^2))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b^2/d^4+1/3465*(15*a^3*d^3*f^2+10*a^2*b*d^2*f*(13*c*f+165*d*e)+5*a*b^2*d*(-29*c^2*f^2+88*c*d*e*f+297*d^2*e^2)+3*b^3*c*(16*c^2*f^2-44*c*d*e*f+33*d^2*e^2))*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b/d^3+1/693*(113*a^2*d^2*f^2+2*a*b*d*f*(12*c*f+209*d*e)+b^2*(-8*c^2*f^2+22*c*d*e*f+99*d^2*e^2))*x^5*sqrt(b*x^2+a)*sqrt(d*x^2+c)/d^2+1/99*b*f*(23*a*d*f+b*c*f+22*b*d*e)*x^7*sqrt(b*x^2+a)*sqrt(d*x^2+c)/d+1/11*b^2*f^2*x^9*sqrt(b*x^2+a)*sqrt(d*x^2+c)-1/3465*sqrt(a)*(40*a^5*d^5*f^2-5*a^4*b*d^4*f*(9*c*f+44*d*e)+5*a^3*b^2*d^3*(-14*c^2*f^2+88*c*d*e*f+99*d^2*e^2)+8*b^5*c^3*(16*c^2*f^2-44*c*d*e*f+33*d^2*e^2)+a^2*b^3*c*d^2*(403*c^2*f^2-1452*c*d*e*f+1914*d^2*e^2)-a*b^4*c^2*d*(408*c^2*f^2-1232*c*d*e*f+1089*d^2*e^2))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/b^(5/2)/d^5/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+2/3465*a^(3/2)*(10*a^4*d^4*f^2-5*a^3*b*d^3*f*(2*c*f+11*d*e)+30*a^2*b^2*d^2*(3*c^2*f^2-11*c*d*e*f+33*d^2*e^2)+2*b^4*c^2*(16*c^2*f^2-44*c*d*e*f+33*d^2*e^2)-a*b^3*c*d*(98*c^2*f^2-297*c*d*e*f+264*d^2*e^2))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(5/2)/d^4/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(b*x^2+a)^(5/2)*(f*x^2+e)^2/sqrt(d*x^2+c),x,8,-1/315*(10*a^4*d^4*f^2-5*a^3*b*d^3*f*(-5*c*f+18*d*e)-8*b^4*c^2*(16*c^2*f^2-36*c*d*e*f+21*d^2*e^2)-3*a^2*b^2*d^2*(81*c^2*f^2-206*c*d*e*f+161*d^2*e^2)+a*b^3*c*d*(328*c^2*f^2-768*c*d*e*f+483*d^2*e^2))*x*sqrt(d*x^2+c)/b/d^5/sqrt(b*x^2+a)+1/315*(5*a^3*d^3*f^2+15*a^2*b*d^2*f*(-7*c*f+18*d*e)-4*b^3*c*(16*c^2*f^2-36*c*d*e*f+21*d^2*e^2)+3*a*b^2*d*(52*c^2*f^2-122*c*d*e*f+77*d^2*e^2))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b/d^4+1/315*(75*a^2*d^2*f^2+5*a*b*d*f*(-23*c*f+54*d*e)+3*b^2*(16*c^2*f^2-36*c*d*e*f+21*d^2*e^2))*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/d^3+1/63*b*f*(19*a*d*f-8*b*c*f+18*b*d*e)*x^5*sqrt(b*x^2+a)*sqrt(d*x^2+c)/d^2+1/9*b^2*f^2*x^7*sqrt(b*x^2+a)*sqrt(d*x^2+c)/d+1/315*sqrt(a)*(10*a^4*d^4*f^2-5*a^3*b*d^3*f*(-5*c*f+18*d*e)-8*b^4*c^2*(16*c^2*f^2-36*c*d*e*f+21*d^2*e^2)-3*a^2*b^2*d^2*(81*c^2*f^2-206*c*d*e*f+161*d^2*e^2)+a*b^3*c*d*(328*c^2*f^2-768*c*d*e*f+483*d^2*e^2))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/b^(3/2)/d^5/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/315*a^(3/2)*(5*a^3*c*d^3*f^2-15*a^2*b*d^2*(7*c^2*f^2-18*c*d*e*f+21*d^2*e^2)-4*b^3*c^2*(16*c^2*f^2-36*c*d*e*f+21*d^2*e^2)+3*a*b^2*c*d*(52*c^2*f^2-122*c*d*e*f+77*d^2*e^2))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(3/2)/c/d^4/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(b*x^2+a)^(5/2)*(f*x^2+e)^2/(d*x^2+c)^(3/2),x,5,1/105*(15*a^3*d^3*f^2+a^2*b*d^2*f*(-219*c*f+322*d*e)-4*b^3*c*(48*c^2*f^2-84*c*d*e*f+35*d^2*e^2)+a*b^2*d*(396*c^2*f^2-658*c*d*e*f+245*d^2*e^2))*x*sqrt(b*x^2+a)/b/d^4/sqrt(d*x^2+c)+1/105*(45*a^2*d^2*f^2+a*b*d*f*(-93*c*f+154*d*e)+b^2*(48*c^2*f^2-84*c*d*e*f+35*d^2*e^2))*x^3*sqrt(b*x^2+a)/d^3/sqrt(d*x^2+c)+1/35*b*f*(15*a*d*f-8*b*c*f+14*b*d*e)*x^5*sqrt(b*x^2+a)/d^2/sqrt(d*x^2+c)+1/7*b^2*f^2*x^7*sqrt(b*x^2+a)/d/sqrt(d*x^2+c)-1/105*(15*a^3*c*d^3*f^2-8*b^3*c^2*(48*c^2*f^2-84*c*d*e*f+35*d^2*e^2)-a^2*b*d^2*(369*c^2*f^2-532*c*d*e*f+105*d^2*e^2)+a*b^2*c*d*(744*c^2*f^2-1232*c*d*e*f+455*d^2*e^2))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/b/sqrt(c)/d^(9/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+2/105*sqrt(c)*(15*a^2*d^2*f*(-5*c*f+7*d*e)-2*b^2*c*(48*c^2*f^2-84*c*d*e*f+35*d^2*e^2)+a*b*d*(174*c^2*f^2-287*c*d*e*f+105*d^2*e^2))*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/d^(9/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[(b*x^2+a)^(5/2)*(f*x^2+e)^2/(d*x^2+c)^(5/2),x,5,-1/15*(10*a*b*c*d*(-c*f+d*e)^2-5*a^2*d^2*(-c*f+d*e)^2-b^2*c^2*(8*c^2*f^2-10*c*d*e*f+5*d^2*e^2))*x*sqrt(b*x^2+a)/c/d^4/(d*x^2+c)^(3/2)+1/5*b^2*f^2*x^7*sqrt(b*x^2+a)/d/(d*x^2+c)^(3/2)+1/15*(23*a^2*d^2*f^2+2*a*b*d*f*(-41*c*f+35*d*e)+b^2*(56*c^2*f^2-70*c*d*e*f+15*d^2*e^2))*x*sqrt(b*x^2+a)/d^4/sqrt(d*x^2+c)+1/15*b*f*(11*a*d*f-8*b*c*f+10*b*d*e)*x^3*sqrt(b*x^2+a)/d^3/sqrt(d*x^2+c)+1/15*(a^2*d^2*(-43*c^2*f^2+10*c*d*e*f+10*d^2*e^2)-8*b^2*c^2*(16*c^2*f^2-20*c*d*e*f+5*d^2*e^2)+a*b*c*d*(168*c^2*f^2-160*c*d*e*f+15*d^2*e^2))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/c^(3/2)/d^(9/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+1/15*(15*a^2*c*d^2*f^2+4*b^2*c*(16*c^2*f^2-20*c*d*e*f+5*d^2*e^2)-a*b*d*(76*c^2*f^2-70*c*d*e*f+5*d^2*e^2))*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/sqrt(c)/d^(9/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[(b*x^2+a)^(5/2)*(f*x^2+e)^2/(d*x^2+c)^(7/2),x,5,-1/15*(6*a*b*c*d*(-c*f+d*e)^2-3*a^2*d^2*(-c*f+d*e)^2-b^2*c^2*(8*c^2*f^2-6*c*d*e*f+3*d^2*e^2))*x*sqrt(b*x^2+a)/c/d^4/(d*x^2+c)^(5/2)+1/3*b^2*f^2*x^7*sqrt(b*x^2+a)/d/(d*x^2+c)^(5/2)+1/15*(2*a^2*d^2*(-3*c^2*f^2+c*d*e*f+2*d^2*e^2)+a*b*c*d*(23*c^2*f^2-26*c*d*e*f+3*d^2*e^2)-b^2*c^2*(32*c^2*f^2-24*c*d*e*f+7*d^2*e^2))*x*sqrt(b*x^2+a)/c^2/d^4/(d*x^2+c)^(3/2)+1/3*b*f*(7*a*d*f-8*b*c*f+6*b*d*e)*x*sqrt(b*x^2+a)/d^4/sqrt(d*x^2+c)+1/15*(a*b*c*d*(-88*c^2*f^2+16*c*d*e*f+7*d^2*e^2)+a^2*d^2*(3*c^2*f^2+4*c*d*e*f+8*d^2*e^2)+8*b^2*c^2*(16*c^2*f^2-12*c*d*e*f+d^2*e^2))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/c^(5/2)/d^(9/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-2/15*b*(a*d*(-18*c^2*f^2+c*d*e*f+2*d^2*e^2)+2*b*c*(16*c^2*f^2-12*c*d*e*f+d^2*e^2))*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/c^(3/2)/d^(9/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[(b*x^2+a)^(5/2)*(f*x^2+e)^2/(d*x^2+c)^(9/2),x,5,-1/7*(2*a*b*c*d*(-c*f+d*e)^2-a^2*d^2*(-c*f+d*e)^2-b^2*c^2*(8*c^2*f^2-2*c*d*e*f+d^2*e^2))*x*sqrt(b*x^2+a)/c/d^4/(d*x^2+c)^(7/2)+b^2*f^2*x^7*sqrt(b*x^2+a)/d/(d*x^2+c)^(7/2)+1/35*(2*a^2*d^2*(-4*c^2*f^2+c*d*e*f+3*d^2*e^2)+a*b*c*d*(31*c^2*f^2-34*c*d*e*f+3*d^2*e^2)-b^2*c^2*(128*c^2*f^2-32*c*d*e*f+9*d^2*e^2))*x*sqrt(b*x^2+a)/c^2/d^4/(d*x^2+c)^(5/2)+1/105*(a*b*c*d*(-99*c^2*f^2+16*c*d*e*f+13*d^2*e^2)+a^2*d^2*(3*c^2*f^2+8*c*d*e*f+24*d^2*e^2)+2*b^2*c^2*(228*c^2*f^2-57*c*d*e*f+4*d^2*e^2))*x*sqrt(b*x^2+a)/c^3/d^4/(d*x^2+c)^(3/2)+1/105*(8*b^3*c^3*(-48*c^2*f^2+12*c*d*e*f+d^2*e^2)+a^2*b*c*d^2*(-33*c^2*f^2-18*c*d*e*f+16*d^2*e^2)-2*a^3*d^3*(3*c^2*f^2+8*c*d*e*f+24*d^2*e^2)+a*b^2*c^2*d*(408*c^2*f^2-32*c*d*e*f+9*d^2*e^2))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/c^(7/2)/d^(9/2)/(-a*d+b*c)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-1/105*b*(4*b^2*c^2*(-48*c^2*f^2+12*c*d*e*f+d^2*e^2)-a^2*d^2*(3*c^2*f^2+8*c*d*e*f+24*d^2*e^2)+5*a*b*c*d*(36*c^2*f^2-2*c*d*e*f+d^2*e^2))*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/c^(5/2)/d^(9/2)/(-a*d+b*c)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[(d*x^2+c)^(3/2)*(f*x^2+e)^2/sqrt(b*x^2+a),x,7,-2/105*(24*a^3*d^3*f^2-4*a^2*b*d^2*f*(9*c*f+14*d*e)-b^3*c*(-3*c^2*f^2+21*c*d*e*f+70*d^2*e^2)+a*b^2*d*(6*c^2*f^2+91*c*d*e*f+35*d^2*e^2))*x*sqrt(d*x^2+c)/b^3/d^2/sqrt(b*x^2+a)+1/105*(24*a^2*d^2*f^2-a*b*d*f*(33*c*f+56*d*e)+b^2*(3*c^2*f^2+84*c*d*e*f+35*d^2*e^2))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b^3/d+2/35*f*(-3*a*d*f+4*b*c*f+7*b*d*e)*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b^2+1/7*d*f^2*x^5*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b+2/105*sqrt(a)*(24*a^3*d^3*f^2-4*a^2*b*d^2*f*(9*c*f+14*d*e)-b^3*c*(-3*c^2*f^2+21*c*d*e*f+70*d^2*e^2)+a*b^2*d*(6*c^2*f^2+91*c*d*e*f+35*d^2*e^2))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/b^(7/2)/d^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/105*sqrt(a)*(105*b^3*c*d*e^2-24*a^3*d^2*f^2+a^2*b*d*f*(33*c*f+56*d*e)-a*b^2*(3*c^2*f^2+84*c*d*e*f+35*d^2*e^2))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(7/2)/d/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[sqrt(d*x^2+c)*(f*x^2+e)^2/sqrt(b*x^2+a),x,6,1/15*(8*a^2*d*f^2/b-a*f*(3*c*f+20*d*e)+b*(15*d*e^2+10*c*e*f-2*c^2*f^2/d))*x*sqrt(d*x^2+c)/b/d/sqrt(b*x^2+a)+1/15*f*(-4*a*d*f+b*c*f+10*b*d*e)*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b^2/d+1/5*f^2*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b-1/15*sqrt(a)*(8*a^2*d^2*f^2-a*b*d*f*(3*c*f+20*d*e)+b^2*(-2*c^2*f^2+10*c*d*e*f+15*d^2*e^2))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/b^(5/2)/d^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/15*sqrt(a)*(15*b^2*d*e^2+4*a^2*d*f^2-a*b*f*(c*f+10*d*e))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(5/2)/d/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(f*x^2+e)^2/sqrt(b*x^2+a)/sqrt(d*x^2+c),x,5,2/3*f*(-a*d*f-b*c*f+3*b*d*e)*x*sqrt(d*x^2+c)/b/d^2/sqrt(b*x^2+a)+1/3*f^2*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b/d-2/3*sqrt(a)*f*(-a*d*f-b*c*f+3*b*d*e)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/b^(3/2)/d^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/3*sqrt(a)*(-a*c*f^2+3*b*d*e^2)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(3/2)/c/d/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(f*x^2+e)^2/sqrt(b*x^2+a)/(d*x^2+c)^(3/2),x,2,f^2*x*sqrt(b*x^2+a)/b/d/sqrt(d*x^2+c)+(2*b*c*f*(-c*f+d*e)-d*(-a*c*f^2+b*d*e^2))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/b/sqrt(c)/d^(3/2)/(-a*d+b*c)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+sqrt(c)*(b*d*e^2-a*f*(-c*f+2*d*e))*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a/d^(3/2)/(-a*d+b*c)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[(f*x^2+e)^2/sqrt(b*x^2+a)/(d*x^2+c)^(5/2),x,2,-1/3*(-c*f+d*e)^2*x*sqrt(b*x^2+a)/c/d/(-a*d+b*c)/(d*x^2+c)^(3/2)-2/3*(-c*f+d*e)*(b*c*(c*f+2*d*e)-a*d*(2*c*f+d*e))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/c^(3/2)/d^(3/2)/(-a*d+b*c)^2/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+1/3*(3*b^2*c*d*e^2+3*a^2*c*d*f^2-a*b*(c^2*f^2+4*c*d*e*f+d^2*e^2))*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a/sqrt(c)/d^(3/2)/(-a*d+b*c)^2/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[(f*x^2+e)^2/sqrt(b*x^2+a)/(d*x^2+c)^(7/2),x,3,-1/5*(-c*f+d*e)^2*x*sqrt(b*x^2+a)/c/d/(-a*d+b*c)/(d*x^2+c)^(5/2)-2/15*(-c*f+d*e)*(b*c*(c*f+4*d*e)-a*d*(3*c*f+2*d*e))*x*sqrt(b*x^2+a)/c^2/d/(-a*d+b*c)^2/(d*x^2+c)^(3/2)+1/15*(a*b*c*d*(-7*c^2*f^2+14*c*d*e*f+23*d^2*e^2)-b^2*c^2*(-2*c^2*f^2-6*c*d*e*f+23*d^2*e^2)-a^2*d^2*(3*c^2*f^2+4*c*d*e*f+8*d^2*e^2))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/c^(5/2)/d^(3/2)/(-a*d+b*c)^3/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+1/15*b*(15*b^2*c^2*d*e^2-a*b*c*(c^2*f^2+18*c*d*e*f+11*d^2*e^2)+a^2*d*(9*c^2*f^2+2*c*d*e*f+4*d^2*e^2))*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a/c^(3/2)/d^(3/2)/(-a*d+b*c)^3/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[(d*x^2+c)^(5/2)*(f*x^2+e)^2/(b*x^2+a)^(3/2),x,5,-1/105*(192*a^3*d^3*f^2-12*a^2*b*d^2*f*(33*c*f+28*d*e)-b^3*c*(15*c^2*f^2+322*c*d*e*f+245*d^2*e^2)+a*b^2*d*(219*c^2*f^2+658*c*d*e*f+140*d^2*e^2))*x*sqrt(d*x^2+c)/b^4/d/sqrt(b*x^2+a)+1/105*(48*a^2*d^2*f^2-3*a*b*d*f*(31*c*f+28*d*e)+b^2*(45*c^2*f^2+154*c*d*e*f+35*d^2*e^2))*x^3*sqrt(d*x^2+c)/b^3/sqrt(b*x^2+a)+1/35*d*f*(-8*a*d*f+15*b*c*f+14*b*d*e)*x^5*sqrt(d*x^2+c)/b^2/sqrt(b*x^2+a)+1/7*d^2*f^2*x^7*sqrt(d*x^2+c)/b/sqrt(b*x^2+a)+1/105*(105*b^4*c^2*d*e^2+384*a^4*d^3*f^2-24*a^3*b*d^2*f*(31*c*f+28*d*e)-a*b^3*c*(15*c^2*f^2+532*c*d*e*f+455*d^2*e^2)+a^2*b^2*d*(369*c^2*f^2+1232*c*d*e*f+280*d^2*e^2))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/sqrt(a)/b^(9/2)/d/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-2/105*sqrt(a)*(96*a^3*d^2*f^2-105*b^3*c*e*(c*f+d*e)-6*a^2*b*d*f*(29*c*f+28*d*e)+a*b^2*(75*c^2*f^2+287*c*d*e*f+70*d^2*e^2))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(9/2)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(d*x^2+c)^(3/2)*(f*x^2+e)^2/(b*x^2+a)^(3/2),x,4,1/15*(24*a^2*d^2*f^2-a*b*d*f*(27*c*f+40*d*e)+b^2*(3*c^2*f^2+40*c*d*e*f+15*d^2*e^2))*x*sqrt(d*x^2+c)/b^3/d/sqrt(b*x^2+a)+2/15*f*(-3*a*d*f+3*b*c*f+5*b*d*e)*x^3*sqrt(d*x^2+c)/b^2/sqrt(b*x^2+a)+1/5*d*f^2*x^5*sqrt(d*x^2+c)/b/sqrt(b*x^2+a)+1/15*(15*b^3*c*d*e^2-48*a^3*d^2*f^2+16*a^2*b*d*f*(3*c*f+5*d*e)-a*b^2*(3*c^2*f^2+70*c*d*e*f+30*d^2*e^2))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/sqrt(a)/b^(7/2)/d/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/15*sqrt(a)*(24*a^2*d*f^2+15*b^2*e*(2*c*f+d*e)-a*b*f*(21*c*f+40*d*e))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(7/2)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[sqrt(d*x^2+c)*(f*x^2+e)^2/(b*x^2+a)^(3/2),x,3,1/3*f*(-4*a*d*f+b*c*f+6*b*d*e)*x*sqrt(d*x^2+c)/b^2/d/sqrt(b*x^2+a)+1/3*f^2*x^3*sqrt(d*x^2+c)/b/sqrt(b*x^2+a)+1/3*(3*b^2*d*e^2+8*a^2*d*f^2-a*b*f*(c*f+12*d*e))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/sqrt(a)/b^(5/2)/d/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+2/3*sqrt(a)*f*(-2*a*f+3*b*e)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(5/2)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(f*x^2+e)^2/(b*x^2+a)^(3/2)/sqrt(d*x^2+c),x,2,f^2*x*sqrt(d*x^2+c)/b/d/sqrt(b*x^2+a)+(b^2*d*e^2+2*a^2*d*f^2-a*b*f*(c*f+2*d*e))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/sqrt(a)/b^(3/2)/d/(-a*d+b*c)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-sqrt(a)*(a*c*f^2+b*e*(-2*c*f+d*e))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(3/2)/c/(-a*d+b*c)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(f*x^2+e)^2/(b*x^2+a)^(3/2)/(d*x^2+c)^(3/2),x,2,(-a*f+b*e)^2*x/a/b/(-a*d+b*c)/sqrt(b*x^2+a)/sqrt(d*x^2+c)+(b^2*c*d*e^2+a^2*c*d*f^2+a*b*(c^2*f^2-4*c*d*e*f+d^2*e^2))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/a/b/sqrt(c)/sqrt(d)/(-a*d+b*c)^2/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-2*sqrt(c)*(-a*f+b*e)*(-c*f+d*e)*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a/sqrt(d)/(-a*d+b*c)^2/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[(f*x^2+e)^2/(b*x^2+a)^(3/2)/(d*x^2+c)^(5/2),x,3,(-a*f+b*e)^2*x/a/b/(-a*d+b*c)/sqrt(b*x^2+a)/(d*x^2+c)^(3/2)+1/3*(3*b^2*c*d*e^2+3*a^2*c*d*f^2+a*b*(c^2*f^2-8*c*d*e*f+d^2*e^2))*x*sqrt(b*x^2+a)/a/b/c/(-a*d+b*c)^2/(d*x^2+c)^(3/2)+1/3*(3*b^2*c^2*d*e^2-a^2*d*(-7*c^2*f^2+2*c*d*e*f+2*d^2*e^2)+a*b*c*(c^2*f^2-14*c*d*e*f+7*d^2*e^2))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/a/c^(3/2)/sqrt(d)/(-a*d+b*c)^3/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-1/3*(3*a^2*c*d*f^2+3*b^2*c*e*(-2*c*f+3*d*e)-a*b*(-5*c^2*f^2+10*c*d*e*f+d^2*e^2))*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a/sqrt(c)/sqrt(d)/(-a*d+b*c)^3/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[(d*x^2+c)^(5/2)*(f*x^2+e)^2/(b*x^2+a)^(5/2),x,5,1/15*(5*b^4*c^2*e^2+8*a^4*d^2*f^2-10*a*b^3*c*e*(c*f+d*e)-10*a^3*b*d*f*(c*f+d*e)+5*a^2*b^2*(c^2*f^2+4*c*d*e*f+d^2*e^2))*x*sqrt(d*x^2+c)/a/b^4/(b*x^2+a)^(3/2)+1/5*d^2*f^2*x^7*sqrt(d*x^2+c)/b/(b*x^2+a)^(3/2)+1/15*(56*a^2*d^2*f^2-2*a*b*d*f*(41*c*f+35*d*e)+b^2*(23*c^2*f^2+70*c*d*e*f+15*d^2*e^2))*x*sqrt(d*x^2+c)/b^4/sqrt(b*x^2+a)+1/15*d*f*(-8*a*d*f+11*b*c*f+10*b*d*e)*x^3*sqrt(d*x^2+c)/b^3/sqrt(b*x^2+a)+1/15*(10*b^4*c^2*e^2-128*a^4*d^2*f^2+5*a*b^3*c*e*(2*c*f+3*d*e)+8*a^3*b*d*f*(21*c*f+20*d*e)-a^2*b^2*(43*c^2*f^2+160*c*d*e*f+40*d^2*e^2))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/a^(3/2)/b^(9/2)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/15*(5*b^3*c*d*e^2-64*a^3*d^2*f^2+4*a^2*b*d*f*(19*c*f+20*d*e)-5*a*b^2*(3*c^2*f^2+14*c*d*e*f+4*d^2*e^2))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(a)/b^(9/2)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(d*x^2+c)^(3/2)*(f*x^2+e)^2/(b*x^2+a)^(5/2),x,4,1/3*(b^3*c*e^2-2*a^3*d*f^2+a^2*b*f*(c*f+2*d*e)-a*b^2*e*(2*c*f+d*e))*x*sqrt(d*x^2+c)/a/b^3/(b*x^2+a)^(3/2)+1/3*d*f^2*x^5*sqrt(d*x^2+c)/b/(b*x^2+a)^(3/2)+2/3*f*(-3*a*d*f+2*b*c*f+3*b*d*e)*x*sqrt(d*x^2+c)/b^3/sqrt(b*x^2+a)+2/3*(b^3*c*e^2+8*a^3*d*f^2+a*b^2*e*(c*f+d*e)-4*a^2*b*f*(c*f+2*d*e))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/a^(3/2)/b^(7/2)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/3*(b^2*d*e^2+8*a^2*d*f^2-a*b*f*(3*c*f+8*d*e))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(a)/b^(7/2)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[sqrt(d*x^2+c)*(f*x^2+e)^2/(b*x^2+a)^(5/2),x,3,1/3*(4*a^2*f^2-2*a*b*e*f+b^2*e^2)*x*sqrt(d*x^2+c)/a/b^2/(b*x^2+a)^(3/2)+f^2*x^3*sqrt(d*x^2+c)/b/(b*x^2+a)^(3/2)+1/3*(2*b^3*c*e^2+8*a^3*d*f^2-a*b^2*e*(-2*c*f+d*e)-a^2*b*f*(7*c*f+4*d*e))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/a^(3/2)/b^(5/2)/(-a*d+b*c)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/3*(b^2*d*e^2+4*a^2*d*f^2-a*b*f*(3*c*f+2*d*e))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(a)/b^(5/2)/(-a*d+b*c)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(f*x^2+e)^2/(b*x^2+a)^(5/2)/sqrt(d*x^2+c),x,2,1/3*(-a*f+b*e)^2*x*sqrt(d*x^2+c)/a/b/(-a*d+b*c)/(b*x^2+a)^(3/2)+2/3*(-a*f+b*e)*(b^2*c*e-a^2*d*f-2*a*b*(-c*f+d*e))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/a^(3/2)/b^(3/2)/(-a*d+b*c)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/3*(b^2*c*d*e^2+a^2*c*d*f^2-a*b*(3*c^2*f^2-4*c*d*e*f+3*d^2*e^2))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(a)/b^(3/2)/c/(-a*d+b*c)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(f*x^2+e)^2/(b*x^2+a)^(5/2)/(d*x^2+c)^(3/2),x,3,1/3*(-a*f+b*e)^2*x/a/b/(-a*d+b*c)/(b*x^2+a)^(3/2)/sqrt(d*x^2+c)+2/3*(-a*f+b*e)*(2*a*c*f-3*a*d*e+b*c*e)*x/a^2/(-a*d+b*c)^2/sqrt(b*x^2+a)/sqrt(d*x^2+c)+1/3*sqrt(d)*(2*b^3*c^2*e^2-a^3*c*d*f^2-a*b^2*c*e*(-2*c*f+7*d*e)-a^2*b*(7*c^2*f^2-14*c*d*e*f+3*d^2*e^2))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/a^2/b/sqrt(c)/(-a*d+b*c)^3/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-1/3*sqrt(c)*(b^2*c*d*e^2+a^2*d*f*(-5*c*f+6*d*e)-a*b*(3*c^2*f^2-10*c*d*e*f+9*d^2*e^2))*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a^2/sqrt(d)/(-a*d+b*c)^3/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[(f*x^2+e)^2/(b*x^2+a)^(5/2)/(d*x^2+c)^(5/2),x,4,1/3*(-a*f+b*e)^2*x/a/b/(-a*d+b*c)/(b*x^2+a)^(3/2)/(d*x^2+c)^(3/2)+2/3*(-a*f+b*e)*(b^2*c*e+a^2*d*f-a*b*(-2*c*f+4*d*e))*x/a^2/b/(-a*d+b*c)^2/sqrt(b*x^2+a)/(d*x^2+c)^(3/2)+1/3*d*(2*b^3*c^2*e^2-3*a^3*c*d*f^2-a*b^2*c*e*(-2*c*f+9*d*e)-a^2*b*(5*c^2*f^2-14*c*d*e*f+d^2*e^2))*x*sqrt(b*x^2+a)/a^2/b/c/(-a*d+b*c)^3/(d*x^2+c)^(3/2)+2/3*sqrt(d)*(b^3*c^3*e^2-a*b^2*c^2*e*(-c*f+5*d*e)+a^3*d*(-4*c^2*f^2+c*d*e*f+d^2*e^2)-a^2*b*c*(4*c^2*f^2-14*c*d*e*f+5*d^2*e^2))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/a^2/c^(3/2)/(-a*d+b*c)^4/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-1/3*(b^3*c^2*d*e^2-3*a^3*c*d^2*f^2+a^2*b*d*(-10*c^2*f^2+16*c*d*e*f+d^2*e^2)-a*b^2*c*(3*c^2*f^2-16*c*d*e*f+18*d^2*e^2))*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a^2/sqrt(c)/sqrt(d)/(-a*d+b*c)^4/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[sqrt(b*x^2+a)*(d*x^2+c)^(5/2)/(f*x^2+e),x,6,-1/15*(2*a^2*d^2*f^2+a*b*d*f*(-12*c*f+5*d*e)-b^2*(23*c^2*f^2-35*c*d*e*f+15*d^2*e^2))*x*sqrt(d*x^2+c)/b/f^3/sqrt(b*x^2+a)-1/15*d*(-a*d*f-11*b*c*f+5*b*d*e)*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b/f^2+1/5*d^2*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/f+1/15*sqrt(a)*(2*a^2*d^2*f^2+a*b*d*f*(-12*c*f+5*d*e)-b^2*(23*c^2*f^2-35*c*d*e*f+15*d^2*e^2))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/b^(3/2)/f^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/15*a^(3/2)*d*(a*c*d*f^2-b*(34*c^2*f^2-40*c*d*e*f+15*d^2*e^2))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(3/2)/c/f^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-a^(3/2)*(-c*f+d*e)^3*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e/f^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[sqrt(b*x^2+a)*(d*x^2+c)^(3/2)/(f*x^2+e),x,5,-1/3*(-a*d*f-4*b*c*f+3*b*d*e)*x*sqrt(d*x^2+c)/f^2/sqrt(b*x^2+a)+1/3*d*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/f+1/3*sqrt(a)*(-a*d*f-4*b*c*f+3*b*d*e)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/sqrt(b)/f^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/3*a^(3/2)*d*(-5*c*f+3*d*e)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(b)/c/f^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+a^(3/2)*(-c*f+d*e)^2*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e/f^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[sqrt(b*x^2+a)*sqrt(d*x^2+c)/(f*x^2+e),x,5,b*x*sqrt(d*x^2+c)/f/sqrt(b*x^2+a)-sqrt(a)*sqrt(b)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/f/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+a^(3/2)*d*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(b)/c/f/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-a^(3/2)*(-c*f+d*e)*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e/f/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[sqrt(b*x^2+a)/sqrt(d*x^2+c)/(f*x^2+e),x,1,a^(3/2)*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[sqrt(b*x^2+a)/(d*x^2+c)^(3/2)/(f*x^2+e),x,3,sqrt(d)*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/sqrt(c)/(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-a^(3/2)*f*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[sqrt(b*x^2+a)/(d*x^2+c)^(5/2)/(f*x^2+e),x,4,1/3*d*x*sqrt(b*x^2+a)/c/(-c*f+d*e)/(d*x^2+c)^(3/2)-1/3*sqrt(d)*(a*d*(-5*c*f+2*d*e)-b*c*(-4*c*f+d*e))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/c^(3/2)/(-a*d+b*c)/(-c*f+d*e)^2/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-1/3*(3*b^2*c^3*f^2+3*a^2*c*d^2*f^2-a*b*d*(7*c^2*f^2-2*c*d*e*f+d^2*e^2))*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a/sqrt(c)/sqrt(d)/(-a*d+b*c)/(-c*f+d*e)^3/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+c^(3/2)*f^2*(-a*f+b*e)*sqrt(b*x^2+a)*EllipticPi(sin(arctan(sqrt(d)*x/sqrt(c))),1-c*f/d/e,sqrt(1-b*c/a/d))/a/sqrt(d)/e/(-c*f+d*e)^3/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[(b*x^2+a)^(3/2)*(d*x^2+c)^(3/2)/(f*x^2+e),x,6,1/15*(3*a^2*d^2*f^2-a*b*d*f*(-27*c*f+20*d*e)+b^2*(3*c^2*f^2-20*c*d*e*f+15*d^2*e^2))*x*sqrt(d*x^2+c)/d/f^3/sqrt(b*x^2+a)-1/15*(-6*a*d*f-6*b*c*f+5*b*d*e)*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/f^2+1/5*b*d*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/f-1/15*sqrt(a)*(3*a^2*d^2*f^2-a*b*d*f*(-27*c*f+20*d*e)+b^2*(3*c^2*f^2-20*c*d*e*f+15*d^2*e^2))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/sqrt(b)/d/f^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/15*a^(3/2)*(3*a*d*f*(-8*c*f+5*d*e)-b*(9*c^2*f^2-25*c*d*e*f+15*d^2*e^2))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(b)/c/f^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-a^(3/2)*(-a*f+b*e)*(-c*f+d*e)^2*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e/f^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(b*x^2+a)^(3/2)*sqrt(d*x^2+c)/(f*x^2+e),x,5,-1/3*b*(-4*a*d*f-b*c*f+3*b*d*e)*x*sqrt(d*x^2+c)/d/f^2/sqrt(b*x^2+a)+1/3*b*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/f+1/3*sqrt(a)*sqrt(b)*(-4*a*d*f-b*c*f+3*b*d*e)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/d/f^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/3*a^(3/2)*(-3*a*d*f-2*b*c*f+3*b*d*e)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(b)/c/f^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+a^(3/2)*(-a*f+b*e)*(-c*f+d*e)*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e/f^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(b*x^2+a)^(3/2)/sqrt(d*x^2+c)/(f*x^2+e),x,4,b*x*sqrt(b*x^2+a)/f/sqrt(d*x^2+c)-b*sqrt(c)*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/sqrt(d)/f/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+sqrt(c)*(a^2*d*f-2*a*b*c*f+b^2*c*e)*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a/sqrt(d)/f/(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-c^(3/2)*(-a*f+b*e)^2*sqrt(b*x^2+a)*EllipticPi(sin(arctan(sqrt(d)*x/sqrt(c))),1-c*f/d/e,sqrt(1-b*c/a/d))/a/sqrt(d)/e/f/(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[(b*x^2+a)^(3/2)/(d*x^2+c)^(3/2)/(f*x^2+e),x,5,(-a*d+b*c)^2*x/c/d/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(d*x^2+c)-sqrt(a)*sqrt(b)*(-a*d+b*c)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/c/d/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+a^(3/2)*(-a*f+b*e)*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(b*x^2+a)^(3/2)/(d*x^2+c)^(5/2)/(f*x^2+e),x,4,-1/3*(-a*d+b*c)*x*sqrt(b*x^2+a)/c/(-c*f+d*e)/(d*x^2+c)^(3/2)+1/3*(a*d*(-5*c*f+2*d*e)+b*c*(c*f+2*d*e))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/c^(3/2)/sqrt(d)/(-c*f+d*e)^2/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+1/3*(3*b^2*c^2*e*f+3*a^2*c*d*f^2-a*b*(4*c^2*f^2+c*d*e*f+d^2*e^2))*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a/sqrt(c)/sqrt(d)/(-c*f+d*e)^3/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-c^(3/2)*f*(-a*f+b*e)^2*sqrt(b*x^2+a)*EllipticPi(sin(arctan(sqrt(d)*x/sqrt(c))),1-c*f/d/e,sqrt(1-b*c/a/d))/a/sqrt(d)/e/(-c*f+d*e)^3/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[(b*x^2+a)^(3/2)/(d*x^2+c)^(7/2)/(f*x^2+e),x,5,-1/5*(-a*d+b*c)*x*sqrt(b*x^2+a)/c/(-c*f+d*e)/(d*x^2+c)^(5/2)+1/15*(a*d*(-9*c*f+4*d*e)+b*c*(3*c*f+2*d*e))*x*sqrt(b*x^2+a)/c^2/(-c*f+d*e)^2/(d*x^2+c)^(3/2)+1/15*(b^2*c^2*(-3*c^2*f^2-14*c*d*e*f+2*d^2*e^2)+3*a*b*c*d*(11*c^2*f^2-2*c*d*e*f+d^2*e^2)-a^2*d^2*(33*c^2*f^2-26*c*d*e*f+8*d^2*e^2))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/c^(5/2)/sqrt(d)/(-a*d+b*c)/(-c*f+d*e)^3/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-1/15*(15*b^3*c^4*e*f^2-15*a^3*c^2*d^2*f^3-a^2*b*d*(-39*c^3*f^3+7*c^2*d*e*f^2-17*c*d^2*e^2*f+4*d^3*e^3)+a*b^2*c*(-21*c^3*f^3-17*c^2*d*e*f^2-8*c*d^2*e^2*f+d^3*e^3))*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a/c^(3/2)/sqrt(d)/(-a*d+b*c)/(-c*f+d*e)^4/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+c^(3/2)*f^2*(-a*f+b*e)^2*sqrt(b*x^2+a)*EllipticPi(sin(arctan(sqrt(d)*x/sqrt(c))),1-c*f/d/e,sqrt(1-b*c/a/d))/a/sqrt(d)/e/(-c*f+d*e)^4/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[(b*x^2+a)^(5/2)*(d*x^2+c)^(3/2)/(f*x^2+e),x,7,1/105*(15*a^3*d^3*f^3-a^2*b*d^2*f^2*(-219*c*f+161*d*e)+a*b^2*d*f*(51*c^2*f^2-329*c*d*e*f+245*d^2*e^2)-b^3*(6*c^3*f^3+21*c^2*d*e*f^2-140*c*d^2*e^2*f+105*d^3*e^3))*x*sqrt(d*x^2+c)/d^2/f^4/sqrt(b*x^2+a)+1/105*(45*a^2*d^2*f^2-a*b*d*f*(-93*c*f+77*d*e)+b^2*(3*c^2*f^2-42*c*d*e*f+35*d^2*e^2))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/d/f^3-1/35*b*(-15*a*d*f-8*b*c*f+7*b*d*e)*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/f^2+1/7*b^2*d*x^5*sqrt(b*x^2+a)*sqrt(d*x^2+c)/f-1/105*sqrt(a)*(15*a^3*d^3*f^3-a^2*b*d^2*f^2*(-219*c*f+161*d*e)+a*b^2*d*f*(51*c^2*f^2-329*c*d*e*f+245*d^2*e^2)-b^3*(6*c^3*f^3+21*c^2*d*e*f^2-140*c*d^2*e^2*f+105*d^3*e^3))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/sqrt(b)/d^2/f^4/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/105*a^(3/2)*(15*a^2*d^2*f^2*(-11*c*f+7*d*e)-a*b*d*f*(117*c^2*f^2-343*c*d*e*f+210*d^2*e^2)+b^2*(3*c^3*f^3+63*c^2*d*e*f^2-175*c*d^2*e^2*f+105*d^3*e^3))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(b)/c/d/f^4/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+a^(3/2)*(-a*f+b*e)^2*(-c*f+d*e)^2*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e/f^4/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(b*x^2+a)^(5/2)*sqrt(d*x^2+c)/(f*x^2+e),x,6,1/15*b*(23*a^2*d^2*f^2-a*b*d*f*(-12*c*f+35*d*e)+b^2*(-2*c^2*f^2-5*c*d*e*f+15*d^2*e^2))*x*sqrt(d*x^2+c)/d^2/f^3/sqrt(b*x^2+a)-1/15*b*(-11*a*d*f-b*c*f+5*b*d*e)*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/d/f^2+1/5*b^2*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/f-1/15*sqrt(a)*sqrt(b)*(23*a^2*d^2*f^2-a*b*d*f*(-12*c*f+35*d*e)+b^2*(-2*c^2*f^2-5*c*d*e*f+15*d^2*e^2))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/d^2/f^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/15*a^(3/2)*(15*a^2*d^2*f^2-a*b*d*f*(-19*c*f+30*d*e)+b^2*(-c^2*f^2-10*c*d*e*f+15*d^2*e^2))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(b)/c/d/f^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-a^(3/2)*(-a*f+b*e)^2*(-c*f+d*e)*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e/f^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(b*x^2+a)^(5/2)/sqrt(d*x^2+c)/(f*x^2+e),x,5,-1/3*b^2*(-7*a*d*f+2*b*c*f+3*b*d*e)*x*sqrt(d*x^2+c)/d^2/f^2/sqrt(b*x^2+a)+1/3*b^2*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/d/f+1/3*sqrt(a)*b^(3/2)*(-7*a*d*f+2*b*c*f+3*b*d*e)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/d^2/f^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/3*a^(3/2)*sqrt(b)*(-6*a*d*f+b*c*f+3*b*d*e)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/c/d/f^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+a^(3/2)*(-a*f+b*e)^2*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e/f^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(b*x^2+a)^(5/2)/(d*x^2+c)^(3/2)/(f*x^2+e),x,4,b^2*x*sqrt(b*x^2+a)/d/f/sqrt(d*x^2+c)-(2*a*b*c*d*f-a^2*d^2*f+b^2*c*(-2*c*f+d*e))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/sqrt(c)/d^(3/2)/f/(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+sqrt(c)*(b^3*c*d*e^2-a^3*d^2*f^2-a*b^2*c*f*(-c*f+4*d*e)+a^2*b*d*f*(c*f+2*d*e))*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a/d^(3/2)/f/(-c*f+d*e)^2/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-c^(3/2)*(-a*f+b*e)^3*sqrt(b*x^2+a)*EllipticPi(sin(arctan(sqrt(d)*x/sqrt(c))),1-c*f/d/e,sqrt(1-b*c/a/d))/a/sqrt(d)/e/f/(-c*f+d*e)^2/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[(b*x^2+a)^(5/2)/(d*x^2+c)^(5/2)/(f*x^2+e),x,4,1/3*(-a*d+b*c)^2*x*sqrt(b*x^2+a)/c/d/(-c*f+d*e)/(d*x^2+c)^(3/2)-1/3*(-a*d+b*c)*(a*d*(-5*c*f+2*d*e)+b*c*(-2*c*f+5*d*e))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/c^(3/2)/d^(3/2)/(-c*f+d*e)^2/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-1/3*(-a*d+b*c)*(3*b^2*c*d*e^2+3*a^2*c*d*f^2-a*b*(c^2*f^2+4*c*d*e*f+d^2*e^2))*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a/sqrt(c)/d^(3/2)/(-c*f+d*e)^3/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+c^(3/2)*(-a*f+b*e)^3*sqrt(b*x^2+a)*EllipticPi(sin(arctan(sqrt(d)*x/sqrt(c))),1-c*f/d/e,sqrt(1-b*c/a/d))/a/sqrt(d)/e/(-c*f+d*e)^3/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[(b*x^2+a)^(5/2)/(d*x^2+c)^(7/2)/(f*x^2+e),x,5,1/5*(-a*d+b*c)^2*x*sqrt(b*x^2+a)/c/d/(-c*f+d*e)/(d*x^2+c)^(5/2)-1/15*(-a*d+b*c)*(a*d*(-9*c*f+4*d*e)+b*c*(-2*c*f+7*d*e))*x*sqrt(b*x^2+a)/c^2/d/(-c*f+d*e)^2/(d*x^2+c)^(3/2)+1/15*(a*b*c*d*(-8*c^2*f^2-29*c*d*e*f+7*d^2*e^2)+b^2*c^2*(-2*c^2*f^2+9*c*d*e*f+8*d^2*e^2)+a^2*d^2*(33*c^2*f^2-26*c*d*e*f+8*d^2*e^2))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/c^(5/2)/d^(3/2)/(-c*f+d*e)^3/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+1/15*(15*b^3*c^3*d*e^2*f-15*a^3*c^2*d^2*f^3-a^2*b*d*(-24*c^3*f^3-8*c^2*d*e*f^2-17*c*d^2*e^2*f+4*d^3*e^3)-a*b^2*c*(c^3*f^3+32*c^2*d*e*f^2+8*c*d^2*e^2*f+4*d^3*e^3))*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a/c^(3/2)/d^(3/2)/(-c*f+d*e)^4/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-c^(3/2)*f*(-a*f+b*e)^3*sqrt(b*x^2+a)*EllipticPi(sin(arctan(sqrt(d)*x/sqrt(c))),1-c*f/d/e,sqrt(1-b*c/a/d))/a/sqrt(d)/e/(-c*f+d*e)^4/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[(b*x^2+a)^(5/2)/(d*x^2+c)^(9/2)/(f*x^2+e),x,6,1/7*(-a*d+b*c)^2*x*sqrt(b*x^2+a)/c/d/(-c*f+d*e)/(d*x^2+c)^(7/2)-1/35*(-a*d+b*c)*(a*d*(-13*c*f+6*d*e)+b*c*(-2*c*f+9*d*e))*x*sqrt(b*x^2+a)/c^2/d/(-c*f+d*e)^2/(d*x^2+c)^(5/2)+1/105*(a*b*c*d*(-36*c^2*f^2-47*c*d*e*f+13*d^2*e^2)+b^2*c^2*(-6*c^2*f^2+33*c*d*e*f+8*d^2*e^2)+a^2*d^2*(87*c^2*f^2-76*c*d*e*f+24*d^2*e^2))*x*sqrt(b*x^2+a)/c^3/d/(-c*f+d*e)^3/(d*x^2+c)^(3/2)+1/105*(a^2*b*c*d^2*(-303*c^3*f^3+27*c^2*d*e*f^2-55*c*d^2*e^2*f+16*d^3*e^3)-a^3*d^3*(-279*c^3*f^3+326*c^2*d*e*f^2-200*c*d^2*e^2*f+48*d^3*e^3)+b^3*c^3*(6*c^3*f^3-39*c^2*d*e*f^2-80*c*d^2*e^2*f+8*d^3*e^3)+a*b^2*c^2*d*(33*c^3*f^3+293*c^2*d*e*f^2-20*c*d^2*e^2*f+9*d^3*e^3))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/c^(7/2)/d^(3/2)/(-a*d+b*c)/(-c*f+d*e)^4/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-1/105*(105*b^4*c^5*d*e^2*f^2+105*a^4*c^3*d^3*f^4+a*b^3*c^2*(-3*c^4*f^4-240*c^3*d*e*f^3-137*c^2*d^2*e^2*f^2-44*c*d^3*e^3*f+4*d^4*e^4)+5*a^2*b^2*c*d*(36*c^4*f^4+52*c^3*d*e*f^3+41*c^2*d^2*e^2*f^2-4*c*d^3*e^3*f+d^4*e^4)-a^3*b*d^2*(297*c^4*f^4-40*c^3*d*e*f^3+263*c^2*d^2*e^2*f^2-124*c*d^3*e^3*f+24*d^4*e^4))*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a/c^(5/2)/d^(3/2)/(-a*d+b*c)/(-c*f+d*e)^5/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+c^(3/2)*f^2*(-a*f+b*e)^3*sqrt(b*x^2+a)*EllipticPi(sin(arctan(sqrt(d)*x/sqrt(c))),1-c*f/d/e,sqrt(1-b*c/a/d))/a/sqrt(d)/e/(-c*f+d*e)^5/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[(b*x^2+a)^(3/2)/sqrt(d*x^2+c)/(f*x^2+e),x,4,b*x*sqrt(b*x^2+a)/f/sqrt(d*x^2+c)-b*sqrt(c)*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/sqrt(d)/f/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+sqrt(c)*(a^2*d*f-2*a*b*c*f+b^2*c*e)*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a/sqrt(d)/f/(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-c^(3/2)*(-a*f+b*e)^2*sqrt(b*x^2+a)*EllipticPi(sin(arctan(sqrt(d)*x/sqrt(c))),1-c*f/d/e,sqrt(1-b*c/a/d))/a/sqrt(d)/e/f/(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[(b*x^2+a)^(3/2)/sqrt(-d*x^2+c)/(f*x^2+e),x,10,b*sqrt(c)*sqrt(b*x^2+a)*sqrt(1-d*x^2/c)*EllipticE(sin(arcsin(sqrt(d)*x/sqrt(c))),sqrt(-b*c/a/d))/sqrt(d)/f/sqrt(1+b*x^2/a)/sqrt(-d*x^2+c)-b*sqrt(c)*(-a*f+b*e)*sqrt(1+b*x^2/a)*sqrt(1-d*x^2/c)*InverseJacobiAM(arcsin(sqrt(d)*x/sqrt(c)),sqrt(-b*c/a/d))/sqrt(d)/f^2/sqrt(b*x^2+a)/sqrt(-d*x^2+c)+sqrt(c)*(-a*f+b*e)^2*sqrt(1+b*x^2/a)*sqrt(1-d*x^2/c)*EllipticPi(sin(arcsin(sqrt(d)*x/sqrt(c))),-c*f/d/e,sqrt(-b*c/a/d))/sqrt(d)/e/f^2/sqrt(b*x^2+a)/sqrt(-d*x^2+c),1],
[(-b*x^2+a)^(3/2)/sqrt(d*x^2+c)/(f*x^2+e),x,10,sqrt(a)*b^(3/2)*sqrt(1-b*x^2/a)*sqrt(d*x^2+c)*EllipticE(sin(arcsin(sqrt(b)*x/sqrt(a))),sqrt(-a*d/b/c))/d/f/sqrt(-b*x^2+a)/sqrt(1+d*x^2/c)-sqrt(a)*sqrt(b)*(2*a*d*f+b*c*f+b*d*e)*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*InverseJacobiAM(arcsin(sqrt(b)*x/sqrt(a)),sqrt(-a*d/b/c))/d/f^2/sqrt(-b*x^2+a)/sqrt(d*x^2+c)+sqrt(a)*(a*f+b*e)^2*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*EllipticPi(sin(arcsin(sqrt(b)*x/sqrt(a))),-a*f/b/e,sqrt(-a*d/b/c))/sqrt(b)/e/f^2/sqrt(-b*x^2+a)/sqrt(d*x^2+c),1],
[(-b*x^2+a)^(3/2)/sqrt(-d*x^2+c)/(f*x^2+e),x,10,-sqrt(a)*b^(3/2)*sqrt(1-b*x^2/a)*sqrt(-d*x^2+c)*EllipticE(sin(arcsin(sqrt(b)*x/sqrt(a))),sqrt(a*d/b/c))/d/f/sqrt(-b*x^2+a)/sqrt(1-d*x^2/c)-sqrt(a)*sqrt(b)*(2*a*d*f-b*c*f+b*d*e)*sqrt(1-b*x^2/a)*sqrt(1-d*x^2/c)*InverseJacobiAM(arcsin(sqrt(b)*x/sqrt(a)),sqrt(a*d/b/c))/d/f^2/sqrt(-b*x^2+a)/sqrt(-d*x^2+c)+sqrt(a)*(a*f+b*e)^2*sqrt(1-b*x^2/a)*sqrt(1-d*x^2/c)*EllipticPi(sin(arcsin(sqrt(b)*x/sqrt(a))),-a*f/b/e,sqrt(a*d/b/c))/sqrt(b)/e/f^2/sqrt(-b*x^2+a)/sqrt(-d*x^2+c),1],
[1/sqrt(b*x^2+a)/sqrt(d*x^2+c)/(f*x^2+e),x,3,sqrt(a)*sqrt(b)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/c/(-a*f+b*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-a^(3/2)*f*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e/(-a*f+b*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[1/sqrt(b*x^2+a)/(d*x^2+c)^(3/2)/(f*x^2+e),x,3,-d^(3/2)*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/sqrt(c)/(-a*d+b*c)/(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+sqrt(c)*sqrt(d)*(a*d*f-2*b*c*f+b*d*e)*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a/(-a*d+b*c)/(-c*f+d*e)^2/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+c^(3/2)*f^2*sqrt(b*x^2+a)*EllipticPi(sin(arctan(sqrt(d)*x/sqrt(c))),1-c*f/d/e,sqrt(1-b*c/a/d))/a/sqrt(d)/e/(-c*f+d*e)^2/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[1/sqrt(b*x^2+a)/(d*x^2+c)^(5/2)/(f*x^2+e),x,4,-1/3*d^2*x*sqrt(b*x^2+a)/c/(-a*d+b*c)/(-c*f+d*e)/(d*x^2+c)^(3/2)-1/3*d^(3/2)*(b*c*(-7*c*f+4*d*e)-a*d*(-5*c*f+2*d*e))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/c^(3/2)/(-a*d+b*c)^2/(-c*f+d*e)^2/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+1/3*sqrt(d)*(3*a^2*c*d^2*f^2+3*b^2*c*(3*c^2*f^2-3*c*d*e*f+d^2*e^2)-a*b*d*(10*c^2*f^2-5*c*d*e*f+d^2*e^2))*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a/sqrt(c)/(-a*d+b*c)^2/(-c*f+d*e)^3/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-c^(3/2)*f^3*sqrt(b*x^2+a)*EllipticPi(sin(arctan(sqrt(d)*x/sqrt(c))),1-c*f/d/e,sqrt(1-b*c/a/d))/a/sqrt(d)/e/(-c*f+d*e)^3/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[1/(b*x^2+a)^(3/2)/sqrt(d*x^2+c)/(f*x^2+e),x,3,b^(3/2)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/sqrt(a)/(-a*d+b*c)/(-a*f+b*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-sqrt(a)*sqrt(b)*(-2*a*d*f+b*c*f+b*d*e)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/c/(-a*d+b*c)/(-a*f+b*e)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+a^(3/2)*f^2*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e/(-a*f+b*e)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[1/(b*x^2+a)^(3/2)/(d*x^2+c)^(3/2)/(f*x^2+e),x,4,b^2*x/a/(-a*d+b*c)/(-a*f+b*e)/sqrt(b*x^2+a)/sqrt(d*x^2+c)+sqrt(d)*(a*b*d^2*e-a^2*d^2*f+b^2*c*(-c*f+d*e))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/a/sqrt(c)/(-a*d+b*c)^2/(-a*f+b*e)/(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-sqrt(c)*d^(3/2)*(a*d*f-3*b*c*f+2*b*d*e)*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a/(-a*d+b*c)^2/(-c*f+d*e)^2/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-c^(3/2)*f^3*sqrt(b*x^2+a)*EllipticPi(sin(arctan(sqrt(d)*x/sqrt(c))),1-c*f/d/e,sqrt(1-b*c/a/d))/a/sqrt(d)/e/(-a*f+b*e)/(-c*f+d*e)^2/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[1/(b*x^2+a)^(3/2)/(d*x^2+c)^(5/2)/(f*x^2+e),x,5,-1/3*d^2*x/c/(-a*d+b*c)/(-c*f+d*e)/sqrt(b*x^2+a)/(d*x^2+c)^(3/2)+1/3*b*(a*b*d^2*e-a^2*d^2*f+3*b^2*c*(-c*f+d*e))*x/a/c/(-a*d+b*c)^2/(-a*f+b*e)/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(d*x^2+c)+1/3*sqrt(d)*(a*b^2*c*d^2*e*(-10*c*f+7*d*e)+a^3*d^3*f*(-5*c*f+2*d*e)+3*b^3*c^2*(-c*f+d*e)^2-2*a^2*b*d^2*(-5*c^2*f^2+c*d*e*f+d^2*e^2))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/a/c^(3/2)/(-a*d+b*c)^3/(-a*f+b*e)/(-c*f+d*e)^2/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-1/3*d^(3/2)*(3*a^2*c*d^2*f^2+3*b^2*c*(6*c^2*f^2-8*c*d*e*f+3*d^2*e^2)-a*b*d*(13*c^2*f^2-8*c*d*e*f+d^2*e^2))*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a/sqrt(c)/(-a*d+b*c)^3/(-c*f+d*e)^3/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+c^(3/2)*f^4*sqrt(b*x^2+a)*EllipticPi(sin(arctan(sqrt(d)*x/sqrt(c))),1-c*f/d/e,sqrt(1-b*c/a/d))/a/sqrt(d)/e/(-a*f+b*e)/(-c*f+d*e)^3/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[1/(b*x^2+a)^(5/2)/sqrt(d*x^2+c)/(f*x^2+e),x,4,1/3*b^2*x*sqrt(d*x^2+c)/a/(-a*d+b*c)/(-a*f+b*e)/(b*x^2+a)^(3/2)+1/3*b^(3/2)*(7*a^2*d*f-5*a*b*c*f-4*a*b*d*e+2*b^2*c*e)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/a^(3/2)/(-a*d+b*c)^2/(-a*f+b*e)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/3*sqrt(b)*(b^3*c*d*e^2-9*a^3*d^2*f^2+a^2*b*d*f*(10*c*f+9*d*e)-a*b^2*(3*c^2*f^2+5*c*d*e*f+3*d^2*e^2))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(a)/c/(-a*d+b*c)^2/(-a*f+b*e)^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-a^(3/2)*f^3*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e/(-a*f+b*e)^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[1/(b*x^2+a)^(5/2)/(d*x^2+c)^(3/2)/(f*x^2+e),x,5,1/3*b^2*x/a/(-a*d+b*c)/(-a*f+b*e)/(b*x^2+a)^(3/2)/sqrt(d*x^2+c)+1/3*b^2*(9*a^2*d*f-5*a*b*c*f-6*a*b*d*e+2*b^2*c*e)*x/a^2/(-a*d+b*c)^2/(-a*f+b*e)^2/sqrt(b*x^2+a)/sqrt(d*x^2+c)+1/3*sqrt(d)*(6*a^3*b*d^3*e*f-3*a^4*d^3*f^2+2*b^4*c^2*e*(-c*f+d*e)-a*b^3*c*(-5*c^2*f^2-2*c*d*e*f+7*d^2*e^2)-a^2*b^2*d*(10*c^2*f^2-10*c*d*e*f+3*d^2*e^2))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/a^2/sqrt(c)/(-a*d+b*c)^3/(-a*f+b*e)^2/(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-1/3*sqrt(c)*sqrt(d)*(3*a^3*d^3*f^2-3*a*b^2*d^2*e*(-4*c*f+3*d*e)+6*a^2*b*d^2*f*(-2*c*f+d*e)+b^3*c*(-c*f+d*e)^2)*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a^2/(-a*d+b*c)^3/(-a*f+b*e)/(-c*f+d*e)^2/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+c^(3/2)*f^4*sqrt(b*x^2+a)*EllipticPi(sin(arctan(sqrt(d)*x/sqrt(c))),1-c*f/d/e,sqrt(1-b*c/a/d))/a/sqrt(d)/e/(-a*f+b*e)^2/(-c*f+d*e)^2/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[1/(b*x^2+a)^(5/2)/(d*x^2+c)^(5/2)/(f*x^2+e),x,6,1/3*b^2*x/a/(-a*d+b*c)/(-a*f+b*e)/(b*x^2+a)^(3/2)/(d*x^2+c)^(3/2)+1/3*d*(a*b*d^2*e-a^2*d^2*f+b^2*c*(-c*f+d*e))*x/a/c/(-a*d+b*c)^2/(-a*f+b*e)/(-c*f+d*e)/sqrt(b*x^2+a)/(d*x^2+c)^(3/2)+1/3*b*(2*a^3*b*d^3*e*f-a^4*d^3*f^2+2*b^4*c^2*e*(-c*f+d*e)-a*b^3*c*(-5*c^2*f^2-4*c*d*e*f+9*d^2*e^2)-a^2*b^2*d*(12*c^2*f^2-12*c*d*e*f+d^2*e^2))*x/a^2/c/(-a*d+b*c)^3/(-a*f+b*e)^2/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(d*x^2+c)+1/3*sqrt(d)*(a^5*d^4*f^2*(-5*c*f+2*d*e)+2*b^5*c^3*e*(-c*f+d*e)^2-5*a*b^4*c^2*(-c*f+d*e)^2*(c*f+2*d*e)+a^3*b^2*d^3*e*(-26*c^2*f^2+15*c*d*e*f+2*d^2*e^2)-a^4*b*d^3*f*(-13*c^2*f^2+4*d^2*e^2)-a^2*b^3*c*d*(-13*c^3*f^3+26*c^2*d*e*f^2-26*c*d^2*e^2*f+10*d^3*e^3))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/a^2/c^(3/2)/(-a*d+b*c)^4/(-a*f+b*e)^2/(-c*f+d*e)^2/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-1/3*sqrt(d)*(3*a^4*c*d^4*f^3-a^3*b*d^3*f*(-4*c*f+d*e)^2+b^4*c^2*(-c*f+d*e)^3-3*a*b^3*c*d^2*e*(10*c^2*f^2-15*c*d*e*f+6*d^2*e^2)+a^2*b^2*d^2*(30*c^3*f^3-29*c^2*d*e*f^2+7*c*d^2*e^2*f+d^3*e^3))*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a^2/sqrt(c)/(-a*d+b*c)^4/(-a*f+b*e)/(-c*f+d*e)^3/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-c^(3/2)*f^5*sqrt(b*x^2+a)*EllipticPi(sin(arctan(sqrt(d)*x/sqrt(c))),1-c*f/d/e,sqrt(1-b*c/a/d))/a/sqrt(d)/e/(-a*f+b*e)^2/(-c*f+d*e)^3/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[(d*x^2+c)^(5/2)/(-b*x^2+a)^(3/2)/(f*x^2+e),x,11,(a*d+b*c)^2*x*sqrt(d*x^2+c)/a/b/(a*f+b*e)/sqrt(-b*x^2+a)-(b^2*c^2*f+2*a^2*d^2*f+a*b*d*(2*c*f+d*e))*sqrt(1-b*x^2/a)*sqrt(d*x^2+c)*EllipticE(sin(arcsin(sqrt(b)*x/sqrt(a))),sqrt(-a*d/b/c))/sqrt(a)/b^(3/2)/f/(a*f+b*e)/sqrt(-b*x^2+a)/sqrt(1+d*x^2/c)+(b^2*c^3*f^2+a^2*c*d^2*f^2+a*b*d*(3*c^2*f^2-2*c*d*e*f+d^2*e^2))*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*InverseJacobiAM(arcsin(sqrt(b)*x/sqrt(a)),sqrt(-a*d/b/c))/sqrt(a)/b^(3/2)/f^2/(a*f+b*e)/sqrt(-b*x^2+a)/sqrt(d*x^2+c)-sqrt(a)*(-c*f+d*e)^3*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*EllipticPi(sin(arcsin(sqrt(b)*x/sqrt(a))),-a*f/b/e,sqrt(-a*d/b/c))/sqrt(b)/e/f^2/(a*f+b*e)/sqrt(-b*x^2+a)/sqrt(d*x^2+c),1],
[(d*x^2+c)^(3/2)/(-b*x^2+a)^(3/2)/(f*x^2+e),x,11,(a*d+b*c)*x*sqrt(d*x^2+c)/a/(a*f+b*e)/sqrt(-b*x^2+a)-(a*d+b*c)*sqrt(1-b*x^2/a)*sqrt(d*x^2+c)*EllipticE(sin(arcsin(sqrt(b)*x/sqrt(a))),sqrt(-a*d/b/c))/sqrt(a)/sqrt(b)/(a*f+b*e)/sqrt(-b*x^2+a)/sqrt(1+d*x^2/c)+(b*c^2*f-a*d*(-2*c*f+d*e))*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*InverseJacobiAM(arcsin(sqrt(b)*x/sqrt(a)),sqrt(-a*d/b/c))/sqrt(a)/sqrt(b)/f/(a*f+b*e)/sqrt(-b*x^2+a)/sqrt(d*x^2+c)+sqrt(a)*(-c*f+d*e)^2*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*EllipticPi(sin(arcsin(sqrt(b)*x/sqrt(a))),-a*f/b/e,sqrt(-a*d/b/c))/sqrt(b)/e/f/(a*f+b*e)/sqrt(-b*x^2+a)/sqrt(d*x^2+c),1],
[sqrt(d*x^2+c)/(-b*x^2+a)^(3/2)/(f*x^2+e),x,10,b*x*sqrt(d*x^2+c)/a/(a*f+b*e)/sqrt(-b*x^2+a)-sqrt(b)*c*sqrt(-b*x^2+a)*sqrt(1+d*x^2/c)*EllipticE(sin(arcsin(sqrt(b)*x/sqrt(a))),sqrt(-a*d/b/c))/a^(3/2)/(a*f+b*e)/sqrt(1-b*x^2/a)/sqrt(d*x^2+c)+(a*d+b*c)*sqrt(-b*x^2+a)*sqrt(1+d*x^2/c)*InverseJacobiAM(arcsin(sqrt(b)*x/sqrt(a)),sqrt(-a*d/b/c))/a^(3/2)/sqrt(b)/(a*f+b*e)/sqrt(1-b*x^2/a)/sqrt(d*x^2+c)-sqrt(a)*(-c*f+d*e)*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*EllipticPi(sin(arcsin(sqrt(b)*x/sqrt(a))),-a*f/b/e,sqrt(-a*d/b/c))/sqrt(b)/e/(a*f+b*e)/sqrt(-b*x^2+a)/sqrt(d*x^2+c),1],
[1/(-b*x^2+a)^(3/2)/sqrt(d*x^2+c)/(f*x^2+e),x,10,b^2*x*sqrt(d*x^2+c)/a/(a*d+b*c)/(a*f+b*e)/sqrt(-b*x^2+a)-b^(3/2)*c*sqrt(-b*x^2+a)*sqrt(1+d*x^2/c)*EllipticE(sin(arcsin(sqrt(b)*x/sqrt(a))),sqrt(-a*d/b/c))/a^(3/2)/(a*d+b*c)/(a*f+b*e)/sqrt(1-b*x^2/a)/sqrt(d*x^2+c)+sqrt(b)*sqrt(-b*x^2+a)*sqrt(1+d*x^2/c)*InverseJacobiAM(arcsin(sqrt(b)*x/sqrt(a)),sqrt(-a*d/b/c))/a^(3/2)/(a*f+b*e)/sqrt(1-b*x^2/a)/sqrt(d*x^2+c)+sqrt(a)*f*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*EllipticPi(sin(arcsin(sqrt(b)*x/sqrt(a))),-a*f/b/e,sqrt(-a*d/b/c))/sqrt(b)/e/(a*f+b*e)/sqrt(-b*x^2+a)/sqrt(d*x^2+c),1],
[1/(-b*x^2+a)^(3/2)/(d*x^2+c)^(3/2)/(f*x^2+e),x,12,b^2*x/a/(a*d+b*c)/(a*f+b*e)/sqrt(-b*x^2+a)/sqrt(d*x^2+c)+d*(a*b*d^2*e+a^2*d^2*f-b^2*c*(-c*f+d*e))*x*sqrt(-b*x^2+a)/a/c/(a*d+b*c)^2/(a*f+b*e)/(-c*f+d*e)/sqrt(d*x^2+c)+sqrt(b)*(a*b*d^2*e+a^2*d^2*f-b^2*c*(-c*f+d*e))*sqrt(1-b*x^2/a)*sqrt(d*x^2+c)*EllipticE(sin(arcsin(sqrt(b)*x/sqrt(a))),sqrt(-a*d/b/c))/sqrt(a)/c/(a*d+b*c)^2/(a*f+b*e)/(-c*f+d*e)/sqrt(-b*x^2+a)/sqrt(1+d*x^2/c)+b^(3/2)*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*InverseJacobiAM(arcsin(sqrt(b)*x/sqrt(a)),sqrt(-a*d/b/c))/sqrt(a)/(a*d+b*c)/(a*f+b*e)/sqrt(-b*x^2+a)/sqrt(d*x^2+c)-sqrt(a)*f^2*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*EllipticPi(sin(arcsin(sqrt(b)*x/sqrt(a))),-a*f/b/e,sqrt(-a*d/b/c))/sqrt(b)/e/(a*f+b*e)/(-c*f+d*e)/sqrt(-b*x^2+a)/sqrt(d*x^2+c),1],
[1/(-b*x^2+a)^(3/2)/(d*x^2+c)^(5/2)/(f*x^2+e),x,13,1/3*d^2*x/c/(a*d+b*c)/(-c*f+d*e)/sqrt(-b*x^2+a)/(d*x^2+c)^(3/2)-1/3*b*(a*b*d^2*e+a^2*d^2*f-3*b^2*c*(-c*f+d*e))*x/a/c/(a*d+b*c)^2/(a*f+b*e)/(-c*f+d*e)/sqrt(-b*x^2+a)/sqrt(d*x^2+c)+1/3*d*(a*b^2*c*d^2*e*(-10*c*f+7*d*e)+a^3*d^3*f*(-5*c*f+2*d*e)-3*b^3*c^2*(-c*f+d*e)^2+2*a^2*b*d^2*(-5*c^2*f^2+c*d*e*f+d^2*e^2))*x*sqrt(-b*x^2+a)/a/c^2/(a*d+b*c)^3/(a*f+b*e)/(-c*f+d*e)^2/sqrt(d*x^2+c)+1/3*sqrt(b)*(a*b^2*c*d^2*e*(-10*c*f+7*d*e)+a^3*d^3*f*(-5*c*f+2*d*e)-3*b^3*c^2*(-c*f+d*e)^2+2*a^2*b*d^2*(-5*c^2*f^2+c*d*e*f+d^2*e^2))*sqrt(1-b*x^2/a)*sqrt(d*x^2+c)*EllipticE(sin(arcsin(sqrt(b)*x/sqrt(a))),sqrt(-a*d/b/c))/sqrt(a)/c^2/(a*d+b*c)^3/(a*f+b*e)/(-c*f+d*e)^2/sqrt(-b*x^2+a)/sqrt(1+d*x^2/c)-1/3*sqrt(b)*(a*b*d^2*e+a^2*d^2*f-3*b^2*c*(-c*f+d*e))*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*InverseJacobiAM(arcsin(sqrt(b)*x/sqrt(a)),sqrt(-a*d/b/c))/sqrt(a)/c/(a*d+b*c)^2/(a*f+b*e)/(-c*f+d*e)/sqrt(-b*x^2+a)/sqrt(d*x^2+c)+sqrt(a)*f^3*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*EllipticPi(sin(arcsin(sqrt(b)*x/sqrt(a))),-a*f/b/e,sqrt(-a*d/b/c))/sqrt(b)/e/(a*f+b*e)/(-c*f+d*e)^2/sqrt(-b*x^2+a)/sqrt(d*x^2+c),1],
[(x^2+1)^(3/2)*sqrt(x^2+2)/(b*x^2+a),x,5,-(a-2*b)*x*sqrt(x^2+2)/b^2/sqrt(x^2+1)+1/3*x*sqrt(x^2+1)*sqrt(x^2+2)/b+sqrt(2)*(a-2*b)*sqrt(x^2+2)*EllipticE(sin(arctan(x)),sqrt(1/2))/b^2/sqrt(x^2+1)/sqrt((x^2+2)/(x^2+1))-1/3*(3*a-7*b)*sqrt(x^2+2)*InverseJacobiAM(arctan(x),sqrt(1/2))/sqrt(2)/b^2/sqrt(x^2+1)/sqrt((x^2+2)/(x^2+1))+(a-2*b)*(a-b)*sqrt(x^2+2)*EllipticPi(sin(arctan(x)),1-b/a,sqrt(1/2))/sqrt(2)/a/b^2/sqrt(x^2+1)/sqrt((x^2+2)/(x^2+1)),1],
[sqrt(x^2+1)*sqrt(x^2+2)/(b*x^2+a),x,5,x*sqrt(x^2+2)/b/sqrt(x^2+1)-sqrt(2)*sqrt(x^2+2)*EllipticE(sin(arctan(x)),sqrt(1/2))/b/sqrt(x^2+1)/sqrt((x^2+2)/(x^2+1))+sqrt(x^2+2)*InverseJacobiAM(arctan(x),sqrt(1/2))/sqrt(2)/b/sqrt(x^2+1)/sqrt((x^2+2)/(x^2+1))-(a-2*b)*sqrt(x^2+2)*EllipticPi(sin(arctan(x)),1-b/a,sqrt(1/2))/sqrt(2)/a/b/sqrt(x^2+1)/sqrt((x^2+2)/(x^2+1)),1],
[sqrt(x^2+2)/sqrt(x^2+1)/(b*x^2+a),x,1,2*EllipticPi(sin(arctan(x/sqrt(2))),1-2*b/a,sqrt(-1))/a,1],
[sqrt(x^2+2)/(x^2+1)^(3/2)/(b*x^2+a),x,3,sqrt(2)*sqrt(x^2+2)*EllipticE(sin(arctan(x)),sqrt(1/2))/(a-b)/sqrt(x^2+1)/sqrt((x^2+2)/(x^2+1))-2*b*EllipticPi(sin(arctan(x/sqrt(2))),1-2*b/a,sqrt(-1))/a/(a-b),1],
[sqrt(x^2+2)/(x^2+1)^(5/2)/(b*x^2+a),x,4,1/3*x*sqrt(x^2+2)/(a-b)/(x^2+1)^(3/2)+sqrt(2)*(a-2*b)*sqrt(x^2+2)*EllipticE(sin(arctan(x)),sqrt(1/2))/(a-b)^2/sqrt(x^2+1)/sqrt((x^2+2)/(x^2+1))-1/3*(2*a^2-4*a*b-b^2)*sqrt(x^2+2)*InverseJacobiAM(arctan(x),sqrt(1/2))/sqrt(2)/(a-b)^3/sqrt(x^2+1)/sqrt((x^2+2)/(x^2+1))+(a-2*b)*b^2*sqrt(x^2+2)*EllipticPi(sin(arctan(x)),1-b/a,sqrt(1/2))/sqrt(2)/a/(a-b)^3/sqrt(x^2+1)/sqrt((x^2+2)/(x^2+1)),1],
[sqrt(d*x^2+2)*sqrt(f*x^2+3)/(b*x^2+a),x,5,d*x*sqrt(f*x^2+3)/b/sqrt(d*x^2+2)-sqrt(3)*sqrt(d)*sqrt(f*x^2+3)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(2))),sqrt(1-2/3*f/d))/b/sqrt(d*x^2+2)/sqrt((f*x^2+3)/(d*x^2+2))+2*f*sqrt(f*x^2+3)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(2)),sqrt(1-2/3*f/d))/sqrt(3)/b/sqrt(d)/sqrt(d*x^2+2)/sqrt((f*x^2+3)/(d*x^2+2))+2*(-a*f+3*b)*sqrt(f*x^2+3)*EllipticPi(sin(arctan(sqrt(d)*x/sqrt(2))),1-2*b/a/d,sqrt(1-2/3*f/d))/sqrt(3)/a/b/sqrt(d)/sqrt(d*x^2+2)/sqrt((f*x^2+3)/(d*x^2+2)),1],
[sqrt(d*x^2+2)/(b*x^2+a)/sqrt(f*x^2+3),x,1,2*sqrt(f*x^2+3)*EllipticPi(sin(arctan(sqrt(d)*x/sqrt(2))),1-2*b/a/d,sqrt(1-2/3*f/d))/sqrt(3)/a/sqrt(d)/sqrt(d*x^2+2)/sqrt((f*x^2+3)/(d*x^2+2)),1],
[1/(b*x^2+a)/sqrt(d*x^2+2)/sqrt(f*x^2+3),x,3,-sqrt(d)*sqrt(f*x^2+3)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(2)),sqrt(1-2/3*f/d))/sqrt(3)/(-a*d+2*b)/sqrt(d*x^2+2)/sqrt((f*x^2+3)/(d*x^2+2))+2*b*sqrt(f*x^2+3)*EllipticPi(sin(arctan(sqrt(d)*x/sqrt(2))),1-2*b/a/d,sqrt(1-2/3*f/d))/sqrt(3)/a/sqrt(d)/(-a*d+2*b)/sqrt(d*x^2+2)/sqrt((f*x^2+3)/(d*x^2+2)),1],
[sqrt(-x^2+1)/(x^2-1)/sqrt(b*x^2+a),x,3,-sqrt(1+b*x^2/a)*InverseJacobiAM(arcsin(x),sqrt(-b/a))/sqrt(b*x^2+a),1],
[1/sqrt(-5*x^2+3)/sqrt(2*x^2+2)/(3*x^2+1),x,1,EllipticPi(sin(arcsin(sqrt(5/3)*x)),-9/5,sqrt(-3/5))/sqrt(10),1],
[1/sqrt(-5*x^2+3)/sqrt(2*x^2+1)/(3*x^2+1),x,1,EllipticPi(sin(arcsin(sqrt(5/3)*x)),-9/5,sqrt(-6/5))/sqrt(5),1],
[1/sqrt(-5*x^2+3)/sqrt(2*x^2-1)/(3*x^2+1),x,1,-5/14*EllipticPi(sin(arccos(sqrt(5/3)*x)),9/14,sqrt(6)),1],
[1/sqrt(-5*x^2+3)/sqrt(2*x^2-2)/(3*x^2+1),x,2,sqrt(-x^2+1)*EllipticPi(sin(arcsin(x)),-3,sqrt(5/3))/sqrt(6)/sqrt(x^2-1),1],
[sqrt(b*x^2+a)*(d*x^2+c)^(5/2)/(f*x^2+e)^2,x,6,1/6*(2*a*d^2*e*f-b*(3*c^2*f^2-20*c*d*e*f+15*d^2*e^2))*x*sqrt(d*x^2+c)/e/f^3/sqrt(b*x^2+a)+1/3*d^2*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/f^2+1/2*(-c*f+d*e)^2*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/e/f^2/(f*x^2+e)-1/6*sqrt(a)*(2*a*d^2*e*f-b*(3*c^2*f^2-20*c*d*e*f+15*d^2*e^2))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/sqrt(b)/e/f^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/6*a^(3/2)*(4*a*d^2*e*f*(-4*c*f+3*d*e)-b*(-3*c^3*f^3+9*c^2*d*e*f^2-25*c*d^2*e^2*f+15*d^3*e^3))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(b)/c/e/f^3/(-a*f+b*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/2*a^(3/2)*(-c*f+d*e)^2*(5*b*d*e^2-a*f*(c*f+4*d*e))*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e^2/f^3/(-a*f+b*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[sqrt(b*x^2+a)*(d*x^2+c)^(3/2)/(f*x^2+e)^2,x,5,1/2*d*(-c*f+3*d*e)*x*sqrt(b*x^2+a)/e/f^2/sqrt(d*x^2+c)-1/2*(-c*f+d*e)*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/e/f/(f*x^2+e)-1/2*sqrt(c)*sqrt(d)*(-c*f+3*d*e)*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/e/f^2/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+1/2*c^(3/2)*sqrt(d)*(-a*f+3*b*e)*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a/e/f^2/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-1/2*c^(3/2)*(3*b*d*e^2-a*f*(c*f+2*d*e))*sqrt(b*x^2+a)*EllipticPi(sin(arctan(sqrt(d)*x/sqrt(c))),1-c*f/d/e,sqrt(1-b*c/a/d))/a/sqrt(d)/e^2/f^2/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[sqrt(b*x^2+a)*sqrt(d*x^2+c)/(f*x^2+e)^2,x,5,-1/2*b*x*sqrt(d*x^2+c)/e/f/sqrt(b*x^2+a)+1/2*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/e/(f*x^2+e)+1/2*sqrt(a)*sqrt(b)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/e/f/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/2*a^(3/2)*sqrt(b)*(-c*f+d*e)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/c/e/f/(-a*f+b*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/2*a^(3/2)*(-a*c*f^2+b*d*e^2)*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e^2/f/(-a*f+b*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[sqrt(b*x^2+a)/sqrt(d*x^2+c)/(f*x^2+e)^2,x,5,1/2*b*x*sqrt(d*x^2+c)/e/(-c*f+d*e)/sqrt(b*x^2+a)-1/2*f*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/e/(-c*f+d*e)/(f*x^2+e)-1/2*sqrt(a)*sqrt(b)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/e/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/2*a^(3/2)*sqrt(b)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/c/e/(-a*f+b*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/2*a^(3/2)*(b*d*e^2-a*f*(-c*f+2*d*e))*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e^2/(-a*f+b*e)/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[sqrt(b*x^2+a)/(d*x^2+c)^(3/2)/(f*x^2+e)^2,x,4,-1/2*f*x*sqrt(b*x^2+a)/e/(-c*f+d*e)/sqrt(d*x^2+c)/(f*x^2+e)+1/2*sqrt(d)*(c*f+2*d*e)*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/sqrt(c)/e/(-c*f+d*e)^2/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+1/2*sqrt(c)*sqrt(d)*f*(a*c*f-4*a*d*e+3*b*c*e)*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a/e/(-c*f+d*e)^3/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-1/2*c^(3/2)*f*(3*b*d*e^2-a*f*(-c*f+4*d*e))*sqrt(b*x^2+a)*EllipticPi(sin(arctan(sqrt(d)*x/sqrt(c))),1-c*f/d/e,sqrt(1-b*c/a/d))/a/sqrt(d)/e^2/(-c*f+d*e)^3/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[sqrt(b*x^2+a)/(d*x^2+c)^(5/2)/(f*x^2+e)^2,x,5,1/6*d*(3*c*f+2*d*e)*x*sqrt(b*x^2+a)/c/e/(-c*f+d*e)^2/(d*x^2+c)^(3/2)-1/2*f*x*sqrt(b*x^2+a)/e/(-c*f+d*e)/(d*x^2+c)^(3/2)/(f*x^2+e)-1/6*sqrt(d)*(a*d*(-3*c^2*f^2-16*c*d*e*f+4*d^2*e^2)-b*c*(-3*c^2*f^2-14*c*d*e*f+2*d^2*e^2))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/c^(3/2)/(-a*d+b*c)/e/(-c*f+d*e)^3/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-1/6*sqrt(d)*(15*b^2*c^3*e*f^2+3*a^2*c*d*f^2*(-c*f+6*d*e)-a*b*(-3*c^3*f^3+35*c^2*d*e*f^2-4*c*d^2*e^2*f+2*d^3*e^3))*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a/sqrt(c)/(-a*d+b*c)/e/(-c*f+d*e)^4/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+1/2*c^(3/2)*f^2*(5*b*d*e^2-a*f*(-c*f+6*d*e))*sqrt(b*x^2+a)*EllipticPi(sin(arctan(sqrt(d)*x/sqrt(c))),1-c*f/d/e,sqrt(1-b*c/a/d))/a/sqrt(d)/e^2/(-c*f+d*e)^4/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[(b*x^2+a)^(3/2)*(d*x^2+c)^(5/2)/(f*x^2+e)^2,x,7,1/30*(6*a^2*d^2*e*f^2-a*b*f*(15*c^2*f^2-124*c*d*e*f+95*d^2*e^2)+b^2*e*(61*c^2*f^2-170*c*d*e*f+105*d^2*e^2))*x*sqrt(d*x^2+c)/e/f^4/sqrt(b*x^2+a)-1/15*d*(-6*a*d*f-11*b*c*f+10*b*d*e)*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/f^3+1/5*b*d^2*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/f^2-1/2*(-a*f+b*e)*(-c*f+d*e)^2*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/e/f^3/(f*x^2+e)-1/30*sqrt(a)*(6*a^2*d^2*e*f^2-a*b*f*(15*c^2*f^2-124*c*d*e*f+95*d^2*e^2)+b^2*e*(61*c^2*f^2-170*c*d*e*f+105*d^2*e^2))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/sqrt(b)/e/f^4/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/30*a^(3/2)*(6*a*d^2*e*f*(-13*c*f+10*d*e)-b*(-15*c^3*f^3+113*c^2*d*e*f^2-205*c*d^2*e^2*f+105*d^3*e^3))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(b)/c/e/f^4/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/2*a^(3/2)*(-c*f+d*e)^2*(b*e*(-2*c*f+7*d*e)-a*f*(c*f+4*d*e))*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e^2/f^4/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(b*x^2+a)^(3/2)*(d*x^2+c)^(3/2)/(f*x^2+e)^2,x,6,-1/6*b*(b*e*(-11*c*f+15*d*e)-a*f*(-3*c*f+11*d*e))*x*sqrt(d*x^2+c)/e/f^3/sqrt(b*x^2+a)+1/3*b*d*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/f^2+1/2*(-a*f+b*e)*(-c*f+d*e)*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/e/f^2/(f*x^2+e)+1/6*sqrt(a)*sqrt(b)*(b*e*(-11*c*f+15*d*e)-a*f*(-3*c*f+11*d*e))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/e/f^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/6*a^(3/2)*(6*a*d^2*e*f-b*(3*c^2*f^2-16*c*d*e*f+15*d^2*e^2))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(b)/c/e/f^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/2*a^(3/2)*(-c*f+d*e)*(b*e*(-2*c*f+5*d*e)-a*f*(c*f+2*d*e))*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e^2/f^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(b*x^2+a)^(3/2)*sqrt(d*x^2+c)/(f*x^2+e)^2,x,5,1/2*b*(-a*f+3*b*e)*x*sqrt(d*x^2+c)/e/f^2/sqrt(b*x^2+a)-1/2*(-a*f+b*e)*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/e/f/(f*x^2+e)-1/2*sqrt(a)*sqrt(b)*(-a*f+3*b*e)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/e/f^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/2*a^(3/2)*sqrt(b)*(-c*f+3*d*e)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/c/e/f^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/2*a^(3/2)*(a*c*f^2-b*e*(-2*c*f+3*d*e))*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e^2/f^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(b*x^2+a)^(3/2)/sqrt(d*x^2+c)/(f*x^2+e)^2,x,6,-1/2*b*(-a*f+b*e)*x*sqrt(d*x^2+c)/e/f/(-c*f+d*e)/sqrt(b*x^2+a)+1/2*b*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/e/(-c*f+d*e)-1/2*f*x*(b*x^2+a)^(3/2)*sqrt(d*x^2+c)/e/(-c*f+d*e)/(f*x^2+e)+1/2*sqrt(a)*sqrt(b)*(-a*f+b*e)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/e/f/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/2*a^(3/2)*sqrt(b)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/c/e/f/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/2*a^(3/2)*(b*e*(-2*c*f+d*e)+a*f*(-c*f+2*d*e))*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e^2/f/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(b*x^2+a)^(3/2)/(d*x^2+c)^(3/2)/(f*x^2+e)^2,x,6,-1/2*(-a*d+b*c)*(c*f+2*d*e)*x*sqrt(b*x^2+a)/c/e/(-c*f+d*e)^2/sqrt(d*x^2+c)+1/2*b*(-a*c*f-2*a*d*e+3*b*c*e)*x*sqrt(d*x^2+c)/c/e/(-c*f+d*e)^2/sqrt(b*x^2+a)-1/2*f*x*(b*x^2+a)^(3/2)/e/(-c*f+d*e)/sqrt(d*x^2+c)/(f*x^2+e)-1/2*sqrt(a)*sqrt(b)*(-a*c*f-2*a*d*e+3*b*c*e)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/c/e/(-c*f+d*e)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/2*a^(3/2)*sqrt(b)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/c/e/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/2*a^(3/2)*(a*f*(-c*f+4*d*e)-b*e*(2*c*f+d*e))*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e^2/(-c*f+d*e)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(b*x^2+a)^(3/2)/(d*x^2+c)^(5/2)/(f*x^2+e)^2,x,5,-1/6*(-a*d+b*c)*(3*c*f+2*d*e)*x*sqrt(b*x^2+a)/c/e/(-c*f+d*e)^2/(d*x^2+c)^(3/2)-1/2*f*x*(b*x^2+a)^(3/2)/e/(-c*f+d*e)/(d*x^2+c)^(3/2)/(f*x^2+e)+1/6*sqrt(d)*(b*c*e*(11*c*f+4*d*e)+a*(-3*c^2*f^2-16*c*d*e*f+4*d^2*e^2))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/c^(3/2)/e/(-c*f+d*e)^3/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+1/6*(3*a^2*c*d*f^2*(-c*f+6*d*e)+3*b^2*c^2*e*f*(2*c*f+3*d*e)-2*a*b*d*e*(10*c^2*f^2+4*c*d*e*f+d^2*e^2))*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a/sqrt(c)/sqrt(d)/e/(-c*f+d*e)^4/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+1/2*c^(3/2)*f*(-a*f+b*e)*(a*f*(-c*f+6*d*e)-b*e*(2*c*f+3*d*e))*sqrt(b*x^2+a)*EllipticPi(sin(arctan(sqrt(d)*x/sqrt(c))),1-c*f/d/e,sqrt(1-b*c/a/d))/a/sqrt(d)/e^2/(-c*f+d*e)^4/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[(b*x^2+a)^(5/2)*(d*x^2+c)^(5/2)/(f*x^2+e)^2,x,8,1/210*(30*a^3*d^3*e*f^3-a^2*b*d*f^2*(105*c^2*f^2-970*c*d*e*f+749*d^2*e^2)+2*a*b^2*d*e*f*(485*c^2*f^2-1358*c*d*e*f+840*d^2*e^2)-b^3*e*(-30*c^3*f^3+749*c^2*d*e*f^2-1680*c*d^2*e^2*f+945*d^3*e^3))*x*sqrt(d*x^2+c)/d/e/f^5/sqrt(b*x^2+a)+1/105*(45*a^2*d^2*f^2-2*a*b*d*f*(-85*c*f+77*d*e)+b^2*(45*c^2*f^2-154*c*d*e*f+105*d^2*e^2))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/f^4-1/35*b*d*(-15*a*d*f-15*b*c*f+14*b*d*e)*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/f^3+1/7*b^2*d^2*x^5*sqrt(b*x^2+a)*sqrt(d*x^2+c)/f^2+1/2*(-a*f+b*e)^2*(-c*f+d*e)^2*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/e/f^4/(f*x^2+e)-1/210*sqrt(a)*(30*a^3*d^3*e*f^3-a^2*b*d*f^2*(105*c^2*f^2-970*c*d*e*f+749*d^2*e^2)+2*a*b^2*d*e*f*(485*c^2*f^2-1358*c*d*e*f+840*d^2*e^2)-b^3*e*(-30*c^3*f^3+749*c^2*d*e*f^2-1680*c*d^2*e^2*f+945*d^3*e^3))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/sqrt(b)/d/e/f^5/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/210*a^(3/2)*(60*a^2*d^2*e*f^2*(-9*c*f+7*d*e)+b^2*e*(-225*c^3*f^3+1267*c^2*d*e*f^2-1995*c*d^2*e^2*f+945*d^3*e^3)-a*b*f*(-105*c^3*f^3+1235*c^2*d*e*f^2-2527*c*d^2*e^2*f+1365*d^3*e^3))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(b)/c/e/f^5/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/2*a^(3/2)*(-a*f+b*e)*(-c*f+d*e)^2*(b*e*(-4*c*f+9*d*e)-a*f*(c*f+4*d*e))*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e^2/f^5/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(b*x^2+a)^(5/2)*(d*x^2+c)^(3/2)/(f*x^2+e)^2,x,7,-1/30*b*(2*a*b*d*e*f*(-62*c*f+85*d*e)-a^2*d*f^2*(-15*c*f+61*d*e)-b^2*e*(6*c^2*f^2-95*c*d*e*f+105*d^2*e^2))*x*sqrt(d*x^2+c)/d/e/f^4/sqrt(b*x^2+a)-1/15*b*(-11*a*d*f-6*b*c*f+10*b*d*e)*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/f^3+1/5*b^2*d*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/f^2-1/2*(-a*f+b*e)^2*(-c*f+d*e)*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/e/f^3/(f*x^2+e)+1/30*sqrt(a)*sqrt(b)*(2*a*b*d*e*f*(-62*c*f+85*d*e)-a^2*d*f^2*(-15*c*f+61*d*e)-b^2*e*(6*c^2*f^2-95*c*d*e*f+105*d^2*e^2))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/d/e/f^4/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/30*a^(3/2)*(30*a^2*d^2*e*f^2-a*b*f*(15*c^2*f^2-128*c*d*e*f+135*d^2*e^2)+b^2*e*(33*c^2*f^2-130*c*d*e*f+105*d^2*e^2))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(b)/c/e/f^4/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/2*a^(3/2)*(-a*f+b*e)*(-c*f+d*e)*(b*e*(-4*c*f+7*d*e)-a*f*(c*f+2*d*e))*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e^2/f^4/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(b*x^2+a)^(5/2)*sqrt(d*x^2+c)/(f*x^2+e)^2,x,6,1/6*b*(20*a*b*d*e*f-3*a^2*d*f^2-b^2*e*(-2*c*f+15*d*e))*x*sqrt(d*x^2+c)/d/e/f^3/sqrt(b*x^2+a)+1/3*b^2*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/f^2+1/2*(-a*f+b*e)^2*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/e/f^2/(f*x^2+e)-1/6*sqrt(a)*sqrt(b)*(20*a*b*d*e*f-3*a^2*d*f^2-b^2*e*(-2*c*f+15*d*e))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/d/e/f^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/6*a^(3/2)*sqrt(b)*(b*e*(-7*c*f+15*d*e)-3*a*f*(-c*f+5*d*e))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/c/e/f^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/2*a^(3/2)*(-a*f+b*e)*(a*c*f^2-b*e*(-4*c*f+5*d*e))*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e^2/f^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(b*x^2+a)^(5/2)/sqrt(d*x^2+c)/(f*x^2+e)^2,x,7,-1/2*b*(2*a*b*d*e*f-a^2*d*f^2-b^2*e*(-2*c*f+3*d*e))*x*sqrt(d*x^2+c)/d/e/f^2/(-c*f+d*e)/sqrt(b*x^2+a)-1/2*b*(-a*f+b*e)*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/e/f/(-c*f+d*e)+1/2*b*x*(b*x^2+a)^(3/2)*sqrt(d*x^2+c)/e/(-c*f+d*e)-1/2*f*x*(b*x^2+a)^(5/2)*sqrt(d*x^2+c)/e/(-c*f+d*e)/(f*x^2+e)+1/2*sqrt(a)*sqrt(b)*(2*a*b*d*e*f-a^2*d*f^2-b^2*e*(-2*c*f+3*d*e))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/d/e/f^2/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/2*a^(3/2)*sqrt(b)*(-a*f+3*b*e)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/c/e/f^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/2*a^(3/2)*(-a*f+b*e)*(b*e*(-4*c*f+3*d*e)+a*f*(-c*f+2*d*e))*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e^2/f^2/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(b*x^2+a)^(5/2)/(d*x^2+c)^(3/2)/(f*x^2+e)^2,x,7,1/2*(-a*d+b*c)^2*(c*f+2*d*e)*x*sqrt(b*x^2+a)/c/d/e/(-c*f+d*e)^2/sqrt(d*x^2+c)+1/2*b*(6*a*b*c*d*e*f-a^2*d*f*(c*f+2*d*e)-b^2*c*e*(2*c*f+d*e))*x*sqrt(d*x^2+c)/c/d/e/f/(-c*f+d*e)^2/sqrt(b*x^2+a)+1/2*b^2*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/d/e/(-c*f+d*e)-1/2*f*x*(b*x^2+a)^(5/2)/e/(-c*f+d*e)/sqrt(d*x^2+c)/(f*x^2+e)-1/2*sqrt(a)*sqrt(b)*(6*a*b*c*d*e*f-a^2*d*f*(c*f+2*d*e)-b^2*c*e*(2*c*f+d*e))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/c/d/e/f/(-c*f+d*e)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/2*a^(3/2)*sqrt(b)*(-a*f+b*e)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/c/e/f/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/2*a^(3/2)*(-a*f+b*e)*(b*e*(-4*c*f+d*e)+a*f*(-c*f+4*d*e))*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e^2/f/(-c*f+d*e)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(b*x^2+a)^(5/2)/(d*x^2+c)^(5/2)/(f*x^2+e)^2,x,6,1/6*(-a*d+b*c)^2*(3*c*f+2*d*e)*x*sqrt(b*x^2+a)/c/d/e/(-c*f+d*e)^2/(d*x^2+c)^(3/2)+1/2*b^2*x*sqrt(b*x^2+a)/d/e/(-c*f+d*e)/sqrt(d*x^2+c)-1/2*f*x*(b*x^2+a)^(5/2)/e/(-c*f+d*e)/(d*x^2+c)^(3/2)/(f*x^2+e)-1/6*(b^2*c^2*e*(2*c*f+13*d*e)-6*a*b*c*d*e*(4*c*f+d*e)-a^2*d*(-3*c^2*f^2-16*c*d*e*f+4*d^2*e^2))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/c^(3/2)/sqrt(d)/e/(-c*f+d*e)^3/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+1/6*(3*a^3*c*d*f^2*(-c*f+6*d*e)-3*b^3*c^2*e^2*(4*c*f+d*e)+a*b^2*c*e*(14*c^2*f^2+23*c*d*e*f+8*d^2*e^2)-a^2*b*d*e*(23*c^2*f^2+20*c*d*e*f+2*d^2*e^2))*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a/sqrt(c)/sqrt(d)/e/(-c*f+d*e)^4/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-1/2*c^(3/2)*(-a*f+b*e)^2*(a*f*(-c*f+6*d*e)-b*e*(4*c*f+d*e))*sqrt(b*x^2+a)*EllipticPi(sin(arctan(sqrt(d)*x/sqrt(c))),1-c*f/d/e,sqrt(1-b*c/a/d))/a/sqrt(d)/e^2/(-c*f+d*e)^4/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[sqrt(-d*x^2+c)*sqrt(f*x^2+e)/(b*x^2+a)^2,x,11,1/2*x*sqrt(-d*x^2+c)*sqrt(f*x^2+e)/a/(b*x^2+a)+1/2*sqrt(c)*sqrt(d)*sqrt(1-d*x^2/c)*sqrt(f*x^2+e)*EllipticE(sin(arcsin(sqrt(d)*x/sqrt(c))),sqrt(-c*f/d/e))/a/b/sqrt(-d*x^2+c)/sqrt(1+f*x^2/e)-1/2*sqrt(c)*sqrt(d)*(a*f+b*e)*sqrt(1-d*x^2/c)*sqrt(1+f*x^2/e)*InverseJacobiAM(arcsin(sqrt(d)*x/sqrt(c)),sqrt(-c*f/d/e))/a/b^2/sqrt(-d*x^2+c)/sqrt(f*x^2+e)+1/2*sqrt(c)*(a^2*d*f+b^2*c*e)*sqrt(1-d*x^2/c)*sqrt(1+f*x^2/e)*EllipticPi(sin(arcsin(sqrt(d)*x/sqrt(c))),-b*c/a/d,sqrt(-c*f/d/e))/a^2/b^2/sqrt(d)/sqrt(-d*x^2+c)/sqrt(f*x^2+e),1],
[sqrt(d*x^2+c)*sqrt(f*x^2+e)/(b*x^2+a)^2,x,5,-1/2*d*x*sqrt(f*x^2+e)/a/b/sqrt(d*x^2+c)+1/2*x*sqrt(d*x^2+c)*sqrt(f*x^2+e)/a/(b*x^2+a)+1/2*sqrt(c)*sqrt(d)*sqrt(f*x^2+e)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-c*f/d/e))/a/b/sqrt(d*x^2+c)/sqrt(c*(f*x^2+e)/e/(d*x^2+c))-1/2*c^(3/2)*sqrt(d)*(-a*f+b*e)*sqrt(f*x^2+e)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-c*f/d/e))/a/b/(-a*d+b*c)/e/sqrt(d*x^2+c)/sqrt(c*(f*x^2+e)/e/(d*x^2+c))+1/2*c^(3/2)*(-a^2*d*f+b^2*c*e)*sqrt(f*x^2+e)*EllipticPi(sin(arctan(sqrt(d)*x/sqrt(c))),1-b*c/a/d,sqrt(1-c*f/d/e))/a^2/b/sqrt(d)/(-a*d+b*c)/e/sqrt(d*x^2+c)/sqrt(c*(f*x^2+e)/e/(d*x^2+c)),1],
[1/sqrt(b*x^2+a)/sqrt(d*x^2+c)/(f*x^2+e)^2,x,4,-1/2*f*x*sqrt(b*x^2+a)/e/(-a*f+b*e)/sqrt(d*x^2+c)/(f*x^2+e)+1/2*sqrt(c)*sqrt(d)*f*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/e/(-a*f+b*e)/(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+1/2*sqrt(c)*sqrt(d)*(-c*f+2*d*e)*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a/e/(-c*f+d*e)^2/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-1/2*c^(3/2)*f*(b*e*(-2*c*f+3*d*e)-a*f*(-c*f+2*d*e))*sqrt(b*x^2+a)*EllipticPi(sin(arctan(sqrt(d)*x/sqrt(c))),1-c*f/d/e,sqrt(1-b*c/a/d))/a/sqrt(d)/e^2/(-a*f+b*e)/(-c*f+d*e)^2/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[1/sqrt(b*x^2+a)/(d*x^2+c)^(3/2)/(f*x^2+e)^2,x,4,1/2*f^2*x*sqrt(b*x^2+a)/e/(-a*f+b*e)/(-c*f+d*e)/sqrt(d*x^2+c)/(f*x^2+e)+1/2*sqrt(d)*(a*d*f*(c*f+2*d*e)-b*(c^2*f^2+2*d^2*e^2))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/sqrt(c)/(-a*d+b*c)/e/(-a*f+b*e)/(-c*f+d*e)^2/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+1/2*sqrt(c)*sqrt(d)*(a*d*f*(-c*f+4*d*e)+b*(c^2*f^2-6*c*d*e*f+2*d^2*e^2))*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a/(-a*d+b*c)/e/(-c*f+d*e)^3/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+1/2*c^(3/2)*f^2*(b*e*(-2*c*f+5*d*e)-a*f*(-c*f+4*d*e))*sqrt(b*x^2+a)*EllipticPi(sin(arctan(sqrt(d)*x/sqrt(c))),1-c*f/d/e,sqrt(1-b*c/a/d))/a/sqrt(d)/e^2/(-a*f+b*e)/(-c*f+d*e)^3/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[1/sqrt(b*x^2+a)/(d*x^2+c)^(5/2)/(f*x^2+e)^2,x,5,1/6*d*(a*d*f*(3*c*f+2*d*e)-b*(3*c^2*f^2+2*d^2*e^2))*x*sqrt(b*x^2+a)/c/(-a*d+b*c)/e/(-a*f+b*e)/(-c*f+d*e)^2/(d*x^2+c)^(3/2)+1/2*f^2*x*sqrt(b*x^2+a)/e/(-a*f+b*e)/(-c*f+d*e)/(d*x^2+c)^(3/2)/(f*x^2+e)-1/6*sqrt(d)*(a^2*d^2*f*(-3*c^2*f^2-16*c*d*e*f+4*d^2*e^2)+b^2*c*(-3*c^3*f^3-20*c*d^2*e^2*f+8*d^3*e^3)-2*a*b*d*(-3*c^3*f^3-10*c^2*d*e*f^2-4*c*d^2*e^2*f+2*d^3*e^3))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/c^(3/2)/(-a*d+b*c)^2/e/(-a*f+b*e)/(-c*f+d*e)^3/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+1/6*sqrt(d)*(3*a^2*c*d^2*f^2*(-c*f+6*d*e)-2*a*b*d*(-3*c^3*f^3+25*c^2*d*e*f^2-8*c*d^2*e^2*f+d^3*e^3)+3*b^2*c*(-c^3*f^3+12*c^2*d*e*f^2-8*c*d^2*e^2*f+2*d^3*e^3))*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a/sqrt(c)/(-a*d+b*c)^2/e/(-c*f+d*e)^4/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-1/2*c^(3/2)*f^3*(b*e*(-2*c*f+7*d*e)-a*f*(-c*f+6*d*e))*sqrt(b*x^2+a)*EllipticPi(sin(arctan(sqrt(d)*x/sqrt(c))),1-c*f/d/e,sqrt(1-b*c/a/d))/a/sqrt(d)/e^2/(-a*f+b*e)/(-c*f+d*e)^4/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[1/(b*x^2+a)^(3/2)/sqrt(d*x^2+c)/(f*x^2+e)^2,x,4,1/2*f^2*x*sqrt(d*x^2+c)/e/(-a*f+b*e)/(-c*f+d*e)/sqrt(b*x^2+a)/(f*x^2+e)-1/2*sqrt(b)*(a*b*c*f^2-a^2*d*f^2-2*b^2*e*(-c*f+d*e))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/sqrt(a)/(-a*d+b*c)/e/(-a*f+b*e)^2/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/2*sqrt(a)*sqrt(b)*(a^2*d*f^2-a*b*f*(c*f+6*d*e)+2*b^2*e*(2*c*f+d*e))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/c/(-a*d+b*c)/e/(-a*f+b*e)^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/2*a^(3/2)*f^2*(b*e*(-4*c*f+5*d*e)-a*f*(-c*f+2*d*e))*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e^2/(-a*f+b*e)^3/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[1/(b*x^2+a)^(3/2)/(d*x^2+c)^(3/2)/(f*x^2+e)^2,x,5,-1/2*b*(a*b*c*f^2-a^2*d*f^2-2*b^2*e*(-c*f+d*e))*x/a/(-a*d+b*c)/e/(-a*f+b*e)^2/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(d*x^2+c)+1/2*f^2*x/e/(-a*f+b*e)/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(d*x^2+c)/(f*x^2+e)+1/2*sqrt(d)*(2*b^3*c*e*(-c*f+d*e)^2+a^3*d^2*f^2*(c*f+2*d*e)-2*a^2*b*d*f*(c^2*f^2+2*d^2*e^2)+a*b^2*(c^3*f^3+2*d^3*e^3))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/a/sqrt(c)/(-a*d+b*c)^2/e/(-a*f+b*e)^2/(-c*f+d*e)^2/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-1/2*sqrt(c)*sqrt(d)*(2*a*b*c*d*f^2*(-c*f+4*d*e)-a^2*d^2*f^2*(-c*f+4*d*e)+b^2*(c^3*f^3-8*c*d^2*e^2*f+4*d^3*e^3))*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a/(-a*d+b*c)^2/e/(-a*f+b*e)/(-c*f+d*e)^3/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-1/2*c^(3/2)*f^3*(b*e*(-4*c*f+7*d*e)-a*f*(-c*f+4*d*e))*sqrt(b*x^2+a)*EllipticPi(sin(arctan(sqrt(d)*x/sqrt(c))),1-c*f/d/e,sqrt(1-b*c/a/d))/a/sqrt(d)/e^2/(-a*f+b*e)^2/(-c*f+d*e)^3/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[1/(b*x^2+a)^(5/2)/sqrt(d*x^2+c)/(f*x^2+e)^2,x,5,-1/6*b*(3*a*b*c*f^2-3*a^2*d*f^2-2*b^2*e*(-c*f+d*e))*x*sqrt(d*x^2+c)/a/(-a*d+b*c)/e/(-a*f+b*e)^2/(-c*f+d*e)/(b*x^2+a)^(3/2)+1/2*f^2*x*sqrt(d*x^2+c)/e/(-a*f+b*e)/(-c*f+d*e)/(b*x^2+a)^(3/2)/(f*x^2+e)-1/6*sqrt(b)*(6*a^3*b*c*d*f^3-3*a^4*d^2*f^3-4*b^4*c*e^2*(-c*f+d*e)+8*a*b^3*e*(-2*c^2*f^2+c*d*e*f+d^2*e^2)-a^2*b^2*f*(3*c^2*f^2-20*c*d*e*f+20*d^2*e^2))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/a^(3/2)/(-a*d+b*c)^2/e/(-a*f+b*e)^3/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/6*sqrt(b)*(2*b^4*c*d*e^3+3*a^4*d^2*f^3-6*a^3*b*d*f^2*(c*f+6*d*e)+a^2*b^2*f*(3*c^2*f^2+50*c*d*e*f+24*d^2*e^2)-2*a*b^3*e*(9*c^2*f^2+8*c*d*e*f+3*d^2*e^2))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(a)/c/(-a*d+b*c)^2/e/(-a*f+b*e)^4/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/2*a^(3/2)*f^3*(b*e*(-6*c*f+7*d*e)-a*f*(-c*f+2*d*e))*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e^2/(-a*f+b*e)^4/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[1/(b*x^2+a)^(5/2)/(d*x^2+c)^(3/2)/(f*x^2+e)^2,x,6,-1/6*b*(3*a*b*c*f^2-3*a^2*d*f^2-2*b^2*e*(-c*f+d*e))*x/a/(-a*d+b*c)/e/(-a*f+b*e)^2/(-c*f+d*e)/(b*x^2+a)^(3/2)/sqrt(d*x^2+c)-1/6*b*(6*a^3*b*c*d*f^3-3*a^4*d^2*f^3-4*b^4*c*e^2*(-c*f+d*e)+4*a*b^3*e*(-4*c^2*f^2+c*d*e*f+3*d^2*e^2)-3*a^2*b^2*f*(c^2*f^2-8*c*d*e*f+8*d^2*e^2))*x/a^2/(-a*d+b*c)^2/e/(-a*f+b*e)^3/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(d*x^2+c)+1/2*f^2*x/e/(-a*f+b*e)/(-c*f+d*e)/(b*x^2+a)^(3/2)/sqrt(d*x^2+c)/(f*x^2+e)+1/6*sqrt(d)*(4*b^5*c^2*e^2*(-c*f+d*e)^2+3*a^5*d^3*f^3*(c*f+2*d*e)-2*a*b^4*c*e*(-c*f+d*e)^2*(8*c*f+7*d*e)-9*a^4*b*d^2*f^2*(c^2*f^2+2*d^2*e^2)+9*a^3*b^2*d*f*(c^3*f^3+2*d^3*e^3)-a^2*b^3*(3*c^4*f^4-26*c^3*d*e*f^3+52*c^2*d^2*e^2*f^2-26*c*d^3*e^3*f+6*d^4*e^4))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/a^2/sqrt(c)/(-a*d+b*c)^3/e/(-a*f+b*e)^3/(-c*f+d*e)^2/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-1/6*sqrt(c)*sqrt(d)*(2*b^4*c*e*(-c*f+d*e)^3-3*a^4*d^3*f^3*(-c*f+4*d*e)+3*a^3*b*d^2*f^2*(-3*c^2*f^2+10*c*d*e*f+2*d^2*e^2)+3*a^2*b^2*d*f*(3*c^3*f^3-20*c*d^2*e^2*f+8*d^3*e^3)-3*a*b^3*(c^4*f^4-10*c*d^3*e^3*f+6*d^4*e^4))*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a^2/(-a*d+b*c)^3/e/(-a*f+b*e)^2/(-c*f+d*e)^3/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+1/2*c^(3/2)*f^4*(3*b*e*(-2*c*f+3*d*e)-a*f*(-c*f+4*d*e))*sqrt(b*x^2+a)*EllipticPi(sin(arctan(sqrt(d)*x/sqrt(c))),1-c*f/d/e,sqrt(1-b*c/a/d))/a/sqrt(d)/e^2/(-a*f+b*e)^3/(-c*f+d*e)^3/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[1/(b*x^2+a)^2/sqrt(-d*x^2+c)/sqrt(f*x^2+e),x,11,1/2*b^2*x*sqrt(-d*x^2+c)*sqrt(f*x^2+e)/a/(a*d+b*c)/(-a*f+b*e)/(b*x^2+a)+1/2*b*sqrt(c)*sqrt(d)*sqrt(1-d*x^2/c)*sqrt(f*x^2+e)*EllipticE(sin(arcsin(sqrt(d)*x/sqrt(c))),sqrt(-c*f/d/e))/a/(a*d+b*c)/(-a*f+b*e)/sqrt(-d*x^2+c)/sqrt(1+f*x^2/e)-1/2*sqrt(c)*sqrt(d)*sqrt(1-d*x^2/c)*sqrt(1+f*x^2/e)*InverseJacobiAM(arcsin(sqrt(d)*x/sqrt(c)),sqrt(-c*f/d/e))/a/(a*d+b*c)/sqrt(-d*x^2+c)/sqrt(f*x^2+e)+1/2*sqrt(c)*(b^2*c*e-3*a^2*d*f+a*b*(-2*c*f+2*d*e))*sqrt(1-d*x^2/c)*sqrt(1+f*x^2/e)*EllipticPi(sin(arcsin(sqrt(d)*x/sqrt(c))),-b*c/a/d,sqrt(-c*f/d/e))/a^2/sqrt(d)/(a*d+b*c)/(-a*f+b*e)/sqrt(-d*x^2+c)/sqrt(f*x^2+e),1],
[1/(b*x^2+a)^2/sqrt(d*x^2+c)/sqrt(f*x^2+e),x,4,1/2*b*x*sqrt(d*x^2+c)/a/(-a*d+b*c)/(b*x^2+a)/sqrt(f*x^2+e)+1/2*b*sqrt(e)*sqrt(f)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(f)*x/sqrt(e))),sqrt(1-d*e/c/f))/a/(-a*d+b*c)/(-a*f+b*e)/sqrt(e*(d*x^2+c)/c/(f*x^2+e))/sqrt(f*x^2+e)-1/2*sqrt(e)*sqrt(f)*(-2*a*f+b*e)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(f)*x/sqrt(e)),sqrt(1-d*e/c/f))/a/c/(-a*f+b*e)^2/sqrt(e*(d*x^2+c)/c/(f*x^2+e))/sqrt(f*x^2+e)+1/2*b*e^(3/2)*(b^2*c*e+3*a^2*d*f-2*a*b*(c*f+d*e))*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(f)*x/sqrt(e))),1-b*e/a/f,sqrt(1-d*e/c/f))/a^2/c/(-a*d+b*c)/sqrt(f)/(-a*f+b*e)^2/sqrt(e*(d*x^2+c)/c/(f*x^2+e))/sqrt(f*x^2+e),1],
[sqrt(b*x^2+a)*(d*x^2+c)^(7/2)/(f*x^2+e)^3,x,7,-1/24*(8*a^2*d^3*e^2*f^2+b^2*e*(6*c^3*f^3+21*c^2*d*e*f^2-140*c*d^2*e^2*f+105*d^3*e^3)-a*b*f*(9*c^3*f^3+12*c^2*d*e*f^2-131*c*d^2*e^2*f+110*d^3*e^3))*x*sqrt(d*x^2+c)/e^2/f^4/(-a*f+b*e)/sqrt(b*x^2+a)+1/3*d^3*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/f^3-1/4*(-c*f+d*e)^3*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/e/f^3/(f*x^2+e)^2+1/8*(-c*f+d*e)^2*(b*e*(2*c*f+11*d*e)-a*f*(3*c*f+10*d*e))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/e^2/f^3/(-a*f+b*e)/(f*x^2+e)+1/24*sqrt(a)*(8*a^2*d^3*e^2*f^2+b^2*e*(6*c^3*f^3+21*c^2*d*e*f^2-140*c*d^2*e^2*f+105*d^3*e^3)-a*b*f*(9*c^3*f^3+12*c^2*d*e*f^2-131*c*d^2*e^2*f+110*d^3*e^3))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/sqrt(b)/e^2/f^4/(-a*f+b*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/24*a^(3/2)*(8*a^2*d^3*e^2*f^2*(-11*c*f+9*d*e)+b^2*e*(-12*c^4*f^4+3*c^3*d*e*f^3+63*c^2*d^2*e^2*f^2-175*c*d^3*e^3*f+105*d^4*e^4)-a*b*f*(-9*c^4*f^4-9*c^3*d*e*f^3+81*c^2*d^2*e^2*f^2-275*c*d^3*e^3*f+180*d^4*e^4))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(b)/c/e^2/f^4/(-a*f+b*e)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/8*a^(3/2)*(-c*f+d*e)^2*(35*b^2*d^2*e^4-2*a*b*e*f*(2*c^2*f^2+3*c*d*e*f+30*d^2*e^2)+a^2*f^2*(3*c^2*f^2+8*c*d*e*f+24*d^2*e^2))*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e^3/f^4/(-a*f+b*e)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[sqrt(b*x^2+a)*(d*x^2+c)^(5/2)/(f*x^2+e)^3,x,6,-1/8*b*(a*f*(-3*c^2*f^2-3*c*d*e*f+14*d^2*e^2)-b*e*(-2*c^2*f^2-5*c*d*e*f+15*d^2*e^2))*x*sqrt(d*x^2+c)/e^2/f^3/(-a*f+b*e)/sqrt(b*x^2+a)+1/4*(-c*f+d*e)^2*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/e/f^2/(f*x^2+e)^2+1/8*(-c*f+d*e)*(3*a*f*(c*f+2*d*e)-b*e*(2*c*f+7*d*e))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/e^2/f^2/(-a*f+b*e)/(f*x^2+e)+1/8*sqrt(a)*sqrt(b)*(a*f*(-3*c^2*f^2-3*c*d*e*f+14*d^2*e^2)-b*e*(-2*c^2*f^2-5*c*d*e*f+15*d^2*e^2))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/e^2/f^3/(-a*f+b*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/8*a^(3/2)*(8*a^2*d^3*e^2*f^2-a*b*f*(3*c^3*f^3+2*c^2*d*e*f^2-13*c*d^2*e^2*f+24*d^3*e^3)+b^2*e*(4*c^3*f^3-c^2*d*e*f^2-10*c*d^2*e^2*f+15*d^3*e^3))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(b)/c/e^2/f^3/(-a*f+b*e)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/8*a^(3/2)*(-c*f+d*e)*(15*b^2*d^2*e^4-2*a*b*e*f*(2*c^2*f^2+c*d*e*f+12*d^2*e^2)+a^2*f^2*(3*c^2*f^2+4*c*d*e*f+8*d^2*e^2))*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e^3/f^3/(-a*f+b*e)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[sqrt(b*x^2+a)*(d*x^2+c)^(3/2)/(f*x^2+e)^3,x,5,-1/4*(-c*f+d*e)*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/e/f/(f*x^2+e)^2-1/8*(-c*f+d*e)*(b*e*(2*c*f+3*d*e)-a*f*(3*c*f+2*d*e))*x*sqrt(b*x^2+a)/e^2/f^2/(-a*f+b*e)/sqrt(d*x^2+c)/(f*x^2+e)+1/8*sqrt(c)*sqrt(d)*(b*e*(2*c*f+3*d*e)-a*f*(3*c*f+2*d*e))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/e^2/f^2/(-a*f+b*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-3/8*c^(3/2)*sqrt(d)*(-a*c*f^2+b*d*e^2)*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a/e^2/f^2/(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+1/8*c^(3/2)*(3*b^2*d^2*e^4+3*a^2*c^2*f^4-2*a*b*e*f*(2*c^2*f^2-c*d*e*f+2*d^2*e^2))*sqrt(b*x^2+a)*EllipticPi(sin(arctan(sqrt(d)*x/sqrt(c))),1-c*f/d/e,sqrt(1-b*c/a/d))/a/sqrt(d)/e^3/f^2/(-a*f+b*e)/(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[sqrt(b*x^2+a)*sqrt(d*x^2+c)/(f*x^2+e)^3,x,5,1/4*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/e/(f*x^2+e)^2+1/8*(a*f*(-3*c*f+2*d*e)-b*e*(-2*c*f+d*e))*x*sqrt(b*x^2+a)/e^2/f/(-a*f+b*e)/sqrt(d*x^2+c)/(f*x^2+e)-1/8*sqrt(c)*sqrt(d)*(a*f*(-3*c*f+2*d*e)-b*e*(-2*c*f+d*e))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/e^2/f/(-a*f+b*e)/(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-1/8*c^(3/2)*sqrt(d)*(b*d*e^2-a*f*(-3*c*f+4*d*e))*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a/e^2/f/(-c*f+d*e)^2/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+1/8*c^(3/2)*(b^2*d^2*e^4+a^2*c*f^3*(-3*c*f+4*d*e)-2*a*b*c*e*f^2*(-2*c*f+3*d*e))*sqrt(b*x^2+a)*EllipticPi(sin(arctan(sqrt(d)*x/sqrt(c))),1-c*f/d/e,sqrt(1-b*c/a/d))/a/sqrt(d)/e^3/f/(-a*f+b*e)/(-c*f+d*e)^2/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[sqrt(b*x^2+a)/sqrt(d*x^2+c)/(f*x^2+e)^3,x,5,-1/4*f*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/e/(-c*f+d*e)/(f*x^2+e)^2+1/8*(b*e*(-2*c*f+5*d*e)-3*a*f*(-c*f+2*d*e))*x*sqrt(b*x^2+a)/e^2/(-a*f+b*e)/(-c*f+d*e)/sqrt(d*x^2+c)/(f*x^2+e)-1/8*sqrt(c)*sqrt(d)*(b*e*(-2*c*f+5*d*e)-3*a*f*(-c*f+2*d*e))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/e^2/(-a*f+b*e)/(-c*f+d*e)^2/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-1/8*sqrt(c)*sqrt(d)*(3*b*c*d*e^2-a*(3*c^2*f^2-8*c*d*e*f+8*d^2*e^2))*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a/e^2/(-c*f+d*e)^3/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+1/8*c^(3/2)*(3*b^2*d^2*e^4-2*a*b*e*f*(2*c^2*f^2-5*c*d*e*f+6*d^2*e^2)+a^2*f^2*(3*c^2*f^2-8*c*d*e*f+8*d^2*e^2))*sqrt(b*x^2+a)*EllipticPi(sin(arctan(sqrt(d)*x/sqrt(c))),1-c*f/d/e,sqrt(1-b*c/a/d))/a/sqrt(d)/e^3/(-a*f+b*e)/(-c*f+d*e)^3/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[sqrt(b*x^2+a)/(d*x^2+c)^(3/2)/(f*x^2+e)^3,x,5,-1/4*f*x*sqrt(b*x^2+a)/e/(-c*f+d*e)/sqrt(d*x^2+c)/(f*x^2+e)^2+1/8*f*(a*f*(-3*c*f+8*d*e)-b*e*(-2*c*f+7*d*e))*x*sqrt(b*x^2+a)/e^2/(-a*f+b*e)/(-c*f+d*e)^2/sqrt(d*x^2+c)/(f*x^2+e)-1/8*sqrt(d)*(a*f*(-3*c^2*f^2+10*c*d*e*f+8*d^2*e^2)-b*e*(-2*c^2*f^2+9*c*d*e*f+8*d^2*e^2))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/sqrt(c)/e^2/(-a*f+b*e)/(-c*f+d*e)^3/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+3/8*sqrt(c)*sqrt(d)*f*(5*b*c*d*e^2-a*(c^2*f^2-4*c*d*e*f+8*d^2*e^2))*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a/e^2/(-c*f+d*e)^4/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-1/8*c^(3/2)*f*(15*b^2*d^2*e^4+3*a^2*f^2*(c^2*f^2-4*c*d*e*f+8*d^2*e^2)-2*a*b*e*f*(2*c^2*f^2-7*c*d*e*f+20*d^2*e^2))*sqrt(b*x^2+a)*EllipticPi(sin(arctan(sqrt(d)*x/sqrt(c))),1-c*f/d/e,sqrt(1-b*c/a/d))/a/sqrt(d)/e^3/(-a*f+b*e)/(-c*f+d*e)^4/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[sqrt(b*x^2+a)/(d*x^2+c)^(5/2)/(f*x^2+e)^3,x,6,-1/24*d*(a*f*(-9*c^2*f^2+36*c*d*e*f+8*d^2*e^2)-b*e*(-6*c^2*f^2+33*c*d*e*f+8*d^2*e^2))*x*sqrt(b*x^2+a)/c/e^2/(-a*f+b*e)/(-c*f+d*e)^3/(d*x^2+c)^(3/2)-1/4*f*x*sqrt(b*x^2+a)/e/(-c*f+d*e)/(d*x^2+c)^(3/2)/(f*x^2+e)^2+1/8*f*(a*f*(-3*c*f+10*d*e)-b*e*(-2*c*f+9*d*e))*x*sqrt(b*x^2+a)/e^2/(-a*f+b*e)/(-c*f+d*e)^2/(d*x^2+c)^(3/2)/(f*x^2+e)+1/24*sqrt(d)*(b^2*c*e*(6*c^3*f^3-39*c^2*d*e*f^2-80*c*d^2*e^2*f+8*d^3*e^3)+a^2*d*f*(9*c^3*f^3-42*c^2*d*e*f^2-88*c*d^2*e^2*f+16*d^3*e^3)-a*b*(9*c^4*f^4-36*c^3*d*e*f^3-119*c^2*d^2*e^2*f^2-80*c*d^3*e^3*f+16*d^4*e^4))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/c^(3/2)/(-a*d+b*c)/e^2/(-a*f+b*e)/(-c*f+d*e)^4/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-1/24*sqrt(d)*(105*b^2*c^3*d*e^2*f^2+3*a^2*c*d*f^2*(3*c^2*f^2-16*c*d*e*f+48*d^2*e^2)-a*b*(9*c^4*f^4-48*c^3*d*e*f^3+257*c^2*d^2*e^2*f^2-16*c*d^3*e^3*f+8*d^4*e^4))*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a/sqrt(c)/(-a*d+b*c)/e^2/(-c*f+d*e)^5/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+1/8*c^(3/2)*f^2*(35*b^2*d^2*e^4-2*a*b*e*f*(2*c^2*f^2-9*c*d*e*f+42*d^2*e^2)+a^2*f^2*(3*c^2*f^2-16*c*d*e*f+48*d^2*e^2))*sqrt(b*x^2+a)*EllipticPi(sin(arctan(sqrt(d)*x/sqrt(c))),1-c*f/d/e,sqrt(1-b*c/a/d))/a/sqrt(d)/e^3/(-a*f+b*e)/(-c*f+d*e)^5/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[(b*x^2+a)^(3/2)*(d*x^2+c)^(5/2)/(f*x^2+e)^3,x,7,1/24*b*(a*f*(-9*c^2*f^2-9*c*d*e*f+50*d^2*e^2)-b*e*(6*c^2*f^2-95*c*d*e*f+105*d^2*e^2))*x*sqrt(d*x^2+c)/e^2/f^4/sqrt(b*x^2+a)+1/3*b*d^2*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/f^3-1/4*(-a*f+b*e)*(-c*f+d*e)^2*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/e/f^3/(f*x^2+e)^2+1/8*(-c*f+d*e)*(b*e*(-2*c*f+11*d*e)-3*a*f*(c*f+2*d*e))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/e^2/f^3/(f*x^2+e)-1/24*sqrt(a)*sqrt(b)*(a*f*(-9*c^2*f^2-9*c*d*e*f+50*d^2*e^2)-b*e*(6*c^2*f^2-95*c*d*e*f+105*d^2*e^2))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/e^2/f^4/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/24*a^(3/2)*(24*a^2*d^3*e^2*f^2+b^2*d*e^2*(33*c^2*f^2-130*c*d*e*f+105*d^2*e^2)-a*b*f*(9*c^3*f^3+6*c^2*d*e*f^2-103*c*d^2*e^2*f+120*d^3*e^3))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(b)/c/e^2/f^4/(-a*f+b*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/8*a^(3/2)*(-c*f+d*e)*(5*b^2*d*e^3*(-4*c*f+7*d*e)-10*a*b*d*e^2*f*(-c*f+4*d*e)+a^2*f^2*(3*c^2*f^2+4*c*d*e*f+8*d^2*e^2))*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e^3/f^4/(-a*f+b*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(b*x^2+a)^(3/2)*(d*x^2+c)^(3/2)/(f*x^2+e)^3,x,6,1/8*b*(b*e*(-2*c*f+15*d*e)-a*f*(3*c*f+2*d*e))*x*sqrt(d*x^2+c)/e^2/f^3/sqrt(b*x^2+a)+1/4*(-a*f+b*e)*(-c*f+d*e)*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/e/f^2/(f*x^2+e)^2-1/8*(b*e*(-2*c*f+7*d*e)-a*f*(3*c*f+2*d*e))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/e^2/f^2/(f*x^2+e)-1/8*sqrt(a)*sqrt(b)*(b*e*(-2*c*f+15*d*e)-a*f*(3*c*f+2*d*e))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/e^2/f^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/8*a^(3/2)*sqrt(b)*(b*d*e^2*(-7*c*f+15*d*e)-a*f*(-3*c^2*f^2-c*d*e*f+12*d^2*e^2))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/c/e^2/f^3/(-a*f+b*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-3/8*a^(3/2)*(a^2*c^2*f^4+b^2*d*e^3*(-4*c*f+5*d*e)-2*a*b*d*e^2*f*(-c*f+2*d*e))*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e^3/f^3/(-a*f+b*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(b*x^2+a)^(3/2)*sqrt(d*x^2+c)/(f*x^2+e)^3,x,5,-1/4*(-a*f+b*e)*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/e/f/(f*x^2+e)^2-1/8*(a*f*(-3*c*f+2*d*e)+b*e*(-2*c*f+3*d*e))*x*sqrt(b*x^2+a)/e^2/f^2/sqrt(d*x^2+c)/(f*x^2+e)+1/8*sqrt(c)*sqrt(d)*(a*f*(-3*c*f+2*d*e)+b*e*(-2*c*f+3*d*e))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/e^2/f^2/(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-1/8*c^(3/2)*sqrt(d)*(-a*f+b*e)*(b*e*(-4*c*f+3*d*e)+a*f*(-3*c*f+4*d*e))*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a/e^2/f^2/(-c*f+d*e)^2/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+1/8*c^(3/2)*(2*a*b*c*d*e^2*f^2+b^2*d*e^3*(-4*c*f+3*d*e)-a^2*c*f^3*(-3*c*f+4*d*e))*sqrt(b*x^2+a)*EllipticPi(sin(arctan(sqrt(d)*x/sqrt(c))),1-c*f/d/e,sqrt(1-b*c/a/d))/a/sqrt(d)/e^3/f^2/(-c*f+d*e)^2/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[(b*x^2+a)^(3/2)/sqrt(d*x^2+c)/(f*x^2+e)^3,x,7,1/8*b*(3*a*f*(-c*f+2*d*e)-b*e*(2*c*f+d*e))*x*sqrt(d*x^2+c)/e^2/f/(-c*f+d*e)^2/sqrt(b*x^2+a)+3/8*b*(b*d*e^2-a*f*(-c*f+2*d*e))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/e^2/(-a*f+b*e)/(-c*f+d*e)^2-1/4*f*x*(b*x^2+a)^(3/2)*sqrt(d*x^2+c)/e/(-c*f+d*e)/(f*x^2+e)^2-3/8*f*(b*d*e^2-a*f*(-c*f+2*d*e))*x*(b*x^2+a)^(3/2)*sqrt(d*x^2+c)/e^2/(-a*f+b*e)/(-c*f+d*e)^2/(f*x^2+e)-1/8*sqrt(a)*sqrt(b)*(3*a*f*(-c*f+2*d*e)-b*e*(2*c*f+d*e))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/e^2/f/(-c*f+d*e)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/8*a^(3/2)*sqrt(b)*(b*d*e^2-a*f*(-3*c*f+4*d*e))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/c/e^2/f/(-a*f+b*e)/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/8*a^(3/2)*(b^2*d*e^3*(-4*c*f+d*e)+2*a*b*d*e^2*f*(c*f+2*d*e)-a^2*f^2*(3*c^2*f^2-8*c*d*e*f+8*d^2*e^2))*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e^3/f/(-a*f+b*e)/(-c*f+d*e)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(b*x^2+a)^(3/2)/(d*x^2+c)^(3/2)/(f*x^2+e)^3,x,7,-1/8*(-a*d+b*c)*(b*d*e^2*(7*c*f+8*d*e)-a*f*(-3*c^2*f^2+10*c*d*e*f+8*d^2*e^2))*x*sqrt(b*x^2+a)/c/e^2/(-a*f+b*e)/(-c*f+d*e)^3/sqrt(d*x^2+c)+1/8*b*(b*c*e*(2*c*f+13*d*e)-a*(-3*c^2*f^2+10*c*d*e*f+8*d^2*e^2))*x*sqrt(d*x^2+c)/c/e^2/(-c*f+d*e)^3/sqrt(b*x^2+a)-1/4*f*x*(b*x^2+a)^(3/2)/e/(-c*f+d*e)/sqrt(d*x^2+c)/(f*x^2+e)^2-1/8*f*(5*b*d*e^2-a*f*(-3*c*f+8*d*e))*x*(b*x^2+a)^(3/2)/e^2/(-a*f+b*e)/(-c*f+d*e)^2/sqrt(d*x^2+c)/(f*x^2+e)-1/8*sqrt(a)*sqrt(b)*(b*c*e*(2*c*f+13*d*e)-a*(-3*c^2*f^2+10*c*d*e*f+8*d^2*e^2))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/c/e^2/(-c*f+d*e)^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/8*a^(3/2)*sqrt(b)*(5*b*d*e^2-a*f*(-3*c*f+8*d*e))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/c/e^2/(-a*f+b*e)/(-c*f+d*e)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-3/8*a^(3/2)*(2*a*b*d*e^2*f*(c*f+4*d*e)-b^2*d*e^3*(4*c*f+d*e)-a^2*f^2*(c^2*f^2-4*c*d*e*f+8*d^2*e^2))*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e^3/(-a*f+b*e)/(-c*f+d*e)^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(b*x^2+a)^(3/2)/(c*x^2+d)^(5/2)/(f*x^2+e)^3,x,6,1/24*(a*c-b*d)*(b*c*e^2*(8*c*e+27*d*f)-a*f*(8*c^2*e^2+36*c*d*e*f-9*d^2*f^2))*x*sqrt(b*x^2+a)/d/e^2/(-a*f+b*e)/(c*e-d*f)^3/(c*x^2+d)^(3/2)-1/4*f*x*(b*x^2+a)^(3/2)/e/(c*e-d*f)/(c*x^2+d)^(3/2)/(f*x^2+e)^2-1/8*f*(7*b*c*e^2-a*f*(10*c*e-3*d*f))*x*(b*x^2+a)^(3/2)/e^2/(-a*f+b*e)/(c*e-d*f)^2/(c*x^2+d)^(3/2)/(f*x^2+e)+1/24*sqrt(c)*(b*d*e*(16*c^2*e^2+83*c*d*e*f+6*d^2*f^2)+a*(16*c^3*e^3-88*c^2*d*e^2*f-42*c*d^2*e*f^2+9*d^3*f^3))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(c)*x/sqrt(d))),sqrt(1-b*d/a/c))/d^(3/2)/e^2/(c*e-d*f)^4/sqrt(d*(b*x^2+a)/a/(c*x^2+d))/sqrt(c*x^2+d)+1/24*sqrt(c)*(15*b^2*d^2*e^2*f*(3*c*e+4*d*f)+3*a^2*d*f^2*(48*c^2*e^2-16*c*d*e*f+3*d^2*f^2)-a*b*e*(8*c^3*e^3+56*c^2*d*e^2*f+149*c*d^2*e*f^2-3*d^3*f^3))*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(c)*x/sqrt(d)),sqrt(1-b*d/a/c))/a/sqrt(d)/e^2/(c*e-d*f)^5/sqrt(d*(b*x^2+a)/a/(c*x^2+d))/sqrt(c*x^2+d)+1/8*d^(3/2)*f*(10*a*b*c*e^2*f*(6*c*e+d*f)-5*b^2*c*e^3*(3*c*e+4*d*f)-a^2*f^2*(48*c^2*e^2-16*c*d*e*f+3*d^2*f^2))*sqrt(b*x^2+a)*EllipticPi(sin(arctan(sqrt(c)*x/sqrt(d))),1-d*f/c/e,sqrt(1-b*d/a/c))/a/sqrt(c)/e^3/(c*e-d*f)^5/sqrt(d*(b*x^2+a)/a/(c*x^2+d))/sqrt(c*x^2+d),1],
[(b*x^2+a)^(5/2)*(d*x^2+c)^(5/2)/(f*x^2+e)^3,x,8,1/120*b*(a^2*f^2*(-45*c^2*f^2-45*c*d*e*f+274*d^2*e^2)-a*b*e*f*(45*c^2*f^2-1016*c*d*e*f+1155*d^2*e^2)+b^2*e^2*(274*c^2*f^2-1155*c*d*e*f+945*d^2*e^2))*x*sqrt(d*x^2+c)/e^2/f^5/sqrt(b*x^2+a)-1/15*b*d*(-11*a*d*f-11*b*c*f+15*b*d*e)*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/f^4+1/5*b^2*d^2*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/f^3+1/4*(-a*f+b*e)^2*(-c*f+d*e)^2*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/e/f^4/(f*x^2+e)^2-3/8*(-a*f+b*e)*(-c*f+d*e)*(b*e*(-2*c*f+5*d*e)-a*f*(c*f+2*d*e))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/e^2/f^4/(f*x^2+e)-1/120*sqrt(a)*sqrt(b)*(a^2*f^2*(-45*c^2*f^2-45*c*d*e*f+274*d^2*e^2)-a*b*e*f*(45*c^2*f^2-1016*c*d*e*f+1155*d^2*e^2)+b^2*e^2*(274*c^2*f^2-1155*c*d*e*f+945*d^2*e^2))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/e^2/f^5/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/120*a^(3/2)*(120*a^2*d^3*e^2*f^2+b^2*e*(-60*c^3*f^3+617*c^2*d*e*f^2-1470*c*d^2*e^2*f+945*d^3*e^3)-a*b*f*(45*c^3*f^3+30*c^2*d*e*f^2-827*c*d^2*e^2*f+840*d^3*e^3))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(b)/c/e^2/f^5/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/8*a^(3/2)*(-c*f+d*e)*(2*a*b*e*f*(-2*c^2*f^2-11*c*d*e*f+28*d^2*e^2)-a^2*f^2*(3*c^2*f^2+4*c*d*e*f+8*d^2*e^2)-b^2*e^2*(8*c^2*f^2-56*c*d*e*f+63*d^2*e^2))*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e^3/f^5/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(b*x^2+a)^(5/2)*(d*x^2+c)^(3/2)/(f*x^2+e)^3,x,7,-1/24*b*(5*b^2*e^2*(-10*c*f+21*d*e)-a*b*e*f*(-9*c*f+95*d*e)+3*a^2*f^2*(3*c*f+2*d*e))*x*sqrt(d*x^2+c)/e^2/f^4/sqrt(b*x^2+a)+1/3*b^2*d*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/f^3-1/4*(-a*f+b*e)^2*(-c*f+d*e)*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/e/f^3/(f*x^2+e)^2+1/8*(-a*f+b*e)*(b*e*(-6*c*f+11*d*e)-a*f*(3*c*f+2*d*e))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/e^2/f^3/(f*x^2+e)+1/24*sqrt(a)*sqrt(b)*(5*b^2*e^2*(-10*c*f+21*d*e)-a*b*e*f*(-9*c*f+95*d*e)+3*a^2*f^2*(3*c*f+2*d*e))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/e^2/f^4/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/24*a^(3/2)*sqrt(b)*(3*a*f*(-3*c^2*f^2-c*d*e*f+20*d^2*e^2)-b*e*(12*c^2*f^2-85*c*d*e*f+105*d^2*e^2))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/c/e^2/f^4/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/8*a^(3/2)*(3*a^2*c^2*f^4-2*a*b*e*f*(-2*c^2*f^2-5*c*d*e*f+10*d^2*e^2)+b^2*e^2*(8*c^2*f^2-40*c*d*e*f+35*d^2*e^2))*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e^3/f^4/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(b*x^2+a)^(5/2)*sqrt(d*x^2+c)/(f*x^2+e)^3,x,6,1/8*b*(b^2*e^2*(-14*c*f+15*d*e)-a^2*f^2*(-3*c*f+2*d*e)-a*b*e*f*(-3*c*f+5*d*e))*x*sqrt(d*x^2+c)/e^2/f^3/(-c*f+d*e)/sqrt(b*x^2+a)+1/4*(-a*f+b*e)^2*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/e/f^2/(f*x^2+e)^2-1/8*(-a*f+b*e)*(b*e*(-6*c*f+7*d*e)+a*f*(-3*c*f+2*d*e))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/e^2/f^2/(-c*f+d*e)/(f*x^2+e)-1/8*sqrt(a)*sqrt(b)*(b^2*e^2*(-14*c*f+15*d*e)-a^2*f^2*(-3*c*f+2*d*e)-a*b*e*f*(-3*c*f+5*d*e))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/e^2/f^3/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/8*a^(3/2)*sqrt(b)*(3*a*c*f^2-b*e*(-4*c*f+15*d*e))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/c/e^2/f^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/8*a^(3/2)*(a^2*c*f^3*(-3*c*f+4*d*e)+2*a*b*c*e*f^2*(-2*c*f+d*e)-b^2*e^2*(8*c^2*f^2-24*c*d*e*f+15*d^2*e^2))*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e^3/f^3/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(b*x^2+a)^(5/2)/sqrt(d*x^2+c)/(f*x^2+e)^3,x,8,-3/8*b*(-a*f+b*e)*(b*e*(-2*c*f+d*e)+a*f*(-c*f+2*d*e))*x*sqrt(d*x^2+c)/e^2/f^2/(-c*f+d*e)^2/sqrt(b*x^2+a)+1/8*b*(b*e*(-4*c*f+d*e)+3*a*f*(-c*f+2*d*e))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/e^2/f/(-c*f+d*e)^2-1/8*b*(3*a*f*(-c*f+2*d*e)-b*e*(2*c*f+d*e))*x*(b*x^2+a)^(3/2)*sqrt(d*x^2+c)/e^2/(-a*f+b*e)/(-c*f+d*e)^2-1/4*f*x*(b*x^2+a)^(5/2)*sqrt(d*x^2+c)/e/(-c*f+d*e)/(f*x^2+e)^2+1/8*f*(3*a*f*(-c*f+2*d*e)-b*e*(2*c*f+d*e))*x*(b*x^2+a)^(5/2)*sqrt(d*x^2+c)/e^2/(-a*f+b*e)/(-c*f+d*e)^2/(f*x^2+e)+3/8*sqrt(a)*sqrt(b)*(-a*f+b*e)*(b*e*(-2*c*f+d*e)+a*f*(-c*f+2*d*e))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/e^2/f^2/(-c*f+d*e)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/8*a^(3/2)*sqrt(b)*(b*e*(-4*c*f+3*d*e)+a*f*(-3*c*f+4*d*e))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/c/e^2/f^2/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/8*a^(3/2)*(2*a*b*e*f*(2*c^2*f^2-7*c*d*e*f+2*d^2*e^2)+a^2*f^2*(3*c^2*f^2-8*c*d*e*f+8*d^2*e^2)+b^2*e^2*(8*c^2*f^2-8*c*d*e*f+3*d^2*e^2))*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e^3/f^2/(-c*f+d*e)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(b*x^2+a)^(5/2)/(d*x^2+c)^(3/2)/(f*x^2+e)^3,x,8,-1/8*(-a*d+b*c)^2*(a*f*(-3*c^2*f^2+10*c*d*e*f+8*d^2*e^2)-b*e*(2*c^2*f^2+5*c*d*e*f+8*d^2*e^2))*x*sqrt(b*x^2+a)/c/d/e^2/(-a*f+b*e)/(-c*f+d*e)^3/sqrt(d*x^2+c)+1/8*b*(3*a*b*c*e*f*(c*f+9*d*e)-b^2*c*e^2*(14*c*f+d*e)-a^2*f*(-3*c^2*f^2+10*c*d*e*f+8*d^2*e^2))*x*sqrt(d*x^2+c)/c/e^2/f/(-c*f+d*e)^3/sqrt(b*x^2+a)-1/8*b^2*(a*f*(-3*c*f+8*d*e)-b*e*(2*c*f+3*d*e))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/d/e^2/(-a*f+b*e)/(-c*f+d*e)^2-1/4*f*x*(b*x^2+a)^(5/2)/e/(-c*f+d*e)/sqrt(d*x^2+c)/(f*x^2+e)^2+1/8*f*(a*f*(-3*c*f+8*d*e)-b*e*(2*c*f+3*d*e))*x*(b*x^2+a)^(5/2)/e^2/(-a*f+b*e)/(-c*f+d*e)^2/sqrt(d*x^2+c)/(f*x^2+e)-1/8*sqrt(a)*sqrt(b)*(3*a*b*c*e*f*(c*f+9*d*e)-b^2*c*e^2*(14*c*f+d*e)-a^2*f*(-3*c^2*f^2+10*c*d*e*f+8*d^2*e^2))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/c/e^2/f/(-c*f+d*e)^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/8*a^(3/2)*sqrt(b)*(a*f*(-3*c*f+8*d*e)-b*e*(4*c*f+d*e))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/c/e^2/f/(-c*f+d*e)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/8*a^(3/2)*(b^2*e^2*(-8*c^2*f^2-8*c*d*e*f+d^2*e^2)+2*a*b*e*f*(-2*c^2*f^2+13*c*d*e*f+4*d^2*e^2)-3*a^2*f^2*(c^2*f^2-4*c*d*e*f+8*d^2*e^2))*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e^3/f/(-c*f+d*e)^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(b*x^2+a)^(5/2)/(d*x^2+c)^(5/2)/(f*x^2+e)^3,x,7,-1/24*(-a*d+b*c)^2*(a*f*(-9*c^2*f^2+36*c*d*e*f+8*d^2*e^2)-b*e*(6*c^2*f^2+21*c*d*e*f+8*d^2*e^2))*x*sqrt(b*x^2+a)/c/d/e^2/(-a*f+b*e)/(-c*f+d*e)^3/(d*x^2+c)^(3/2)-1/8*b^2*(a*f*(-3*c*f+10*d*e)-b*e*(2*c*f+5*d*e))*x*sqrt(b*x^2+a)/d/e^2/(-a*f+b*e)/(-c*f+d*e)^2/sqrt(d*x^2+c)-1/4*f*x*(b*x^2+a)^(5/2)/e/(-c*f+d*e)/(d*x^2+c)^(3/2)/(f*x^2+e)^2+1/8*f*(a*f*(-3*c*f+10*d*e)-b*e*(2*c*f+5*d*e))*x*(b*x^2+a)^(5/2)/e^2/(-a*f+b*e)/(-c*f+d*e)^2/(d*x^2+c)^(3/2)/(f*x^2+e)-1/24*sqrt(d)*(5*b^2*c^2*e^2*(10*c*f+11*d*e)-3*a*b*c*e*(3*c^2*f^2+59*c*d*e*f+8*d^2*e^2)-a^2*(9*c^3*f^3-42*c^2*d*e*f^2-88*c*d^2*e^2*f+16*d^3*e^3))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/c^(3/2)/e^2/(-c*f+d*e)^4/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+1/24*(3*a^3*c*d*f^2*(3*c^2*f^2-16*c*d*e*f+48*d^2*e^2)-3*b^3*c^2*e^2*(8*c^2*f^2+24*c*d*e*f+3*d^2*e^2)+a*b^2*c*d*e^2*(137*c^2*f^2+146*c*d*e*f+32*d^2*e^2)-a^2*b*d*e*(-6*c^3*f^3+185*c^2*d*e*f^2+128*c*d^2*e^2*f+8*d^3*e^3))*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a/sqrt(c)/sqrt(d)/e^2/(-c*f+d*e)^5/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-1/8*c^(3/2)*(-a*f+b*e)*(2*a*b*e*f*(-2*c^2*f^2+19*c*d*e*f+18*d^2*e^2)-a^2*f^2*(3*c^2*f^2-16*c*d*e*f+48*d^2*e^2)-b^2*e^2*(8*c^2*f^2+24*c*d*e*f+3*d^2*e^2))*sqrt(b*x^2+a)*EllipticPi(sin(arctan(sqrt(d)*x/sqrt(c))),1-c*f/d/e,sqrt(1-b*c/a/d))/a/sqrt(d)/e^3/(-c*f+d*e)^5/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[(b*x^2+a)^(7/2)/sqrt(d*x^2+c)/(f*x^2+e)^3,x,9,-1/8*b*(a*b^2*d*e^2*f*(-17*c*f+8*d*e)-3*a^3*d*f^3*(-c*f+2*d*e)+a^2*b*d*e*f^2*(4*c*f+5*d*e)-b^3*e^2*(8*c^2*f^2-26*c*d*e*f+15*d^2*e^2))*x*sqrt(d*x^2+c)/d/e^2/f^3/(-c*f+d*e)^2/sqrt(b*x^2+a)-1/8*b*(-a*f+b*e)*(b*e*(-8*c*f+5*d*e)+3*a*f*(-c*f+2*d*e))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/e^2/f^2/(-c*f+d*e)^2+3/8*b*(b*e*(-2*c*f+d*e)+a*f*(-c*f+2*d*e))*x*(b*x^2+a)^(3/2)*sqrt(d*x^2+c)/e^2/f/(-c*f+d*e)^2-1/8*b*(b*e*(-4*c*f+d*e)+3*a*f*(-c*f+2*d*e))*x*(b*x^2+a)^(5/2)*sqrt(d*x^2+c)/e^2/(-a*f+b*e)/(-c*f+d*e)^2-1/4*f*x*(b*x^2+a)^(7/2)*sqrt(d*x^2+c)/e/(-c*f+d*e)/(f*x^2+e)^2+1/8*f*(b*e*(-4*c*f+d*e)+3*a*f*(-c*f+2*d*e))*x*(b*x^2+a)^(7/2)*sqrt(d*x^2+c)/e^2/(-a*f+b*e)/(-c*f+d*e)^2/(f*x^2+e)+1/8*sqrt(a)*sqrt(b)*(a*b^2*d*e^2*f*(-17*c*f+8*d*e)-3*a^3*d*f^3*(-c*f+2*d*e)+a^2*b*d*e*f^2*(4*c*f+5*d*e)-b^3*e^2*(8*c^2*f^2-26*c*d*e*f+15*d^2*e^2))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/d/e^2/f^3/(-c*f+d*e)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/8*a^(3/2)*sqrt(b)*(b^2*e^2*(-16*c*f+15*d*e)-a*b*e*f*(-5*c*f+3*d*e)-a^2*f^2*(-3*c*f+4*d*e))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/c/e^2/f^3/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/8*a^(3/2)*(-a*f+b*e)*(a^2*f^2*(3*c^2*f^2-8*c*d*e*f+8*d^2*e^2)+2*a*b*e*f*(4*c^2*f^2-13*c*d*e*f+6*d^2*e^2)+3*b^2*e^2*(8*c^2*f^2-12*c*d*e*f+5*d^2*e^2))*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e^3/f^3/(-c*f+d*e)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(b*x^2+a)^(7/2)/(d*x^2+c)^(3/2)/(f*x^2+e)^3,x,9,1/8*(-a*d+b*c)^3*(a*f*(-3*c^2*f^2+10*c*d*e*f+8*d^2*e^2)-b*e*(4*c^2*f^2+3*c*d*e*f+8*d^2*e^2))*x*sqrt(b*x^2+a)/c/d^2/e^2/(-a*f+b*e)/(-c*f+d*e)^3/sqrt(d*x^2+c)+1/8*b*(a^2*b*c*d*e*f^2*(4*c*f+41*d*e)-a*b^2*c*d*e^2*f*(41*c*f+4*d*e)-b^3*c*e^2*(-8*c^2*f^2-10*c*d*e*f+3*d^2*e^2)-a^3*d*f^2*(-3*c^2*f^2+10*c*d*e*f+8*d^2*e^2))*x*sqrt(d*x^2+c)/c/d/e^2/f^2/(-c*f+d*e)^3/sqrt(b*x^2+a)-1/8*b^2*(3*a^2*d*f^2*(-3*c*f+8*d*e)-b^2*e*(-4*c^2*f^2-7*c*d*e*f+d^2*e^2)-a*b*f*(-3*c^2*f^2+19*c*d*e*f+9*d^2*e^2))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/d^2/e^2/f/(-a*f+b*e)/(-c*f+d*e)^2-1/8*b^3*(a*f*(-3*c*f+8*d*e)-b*e*(4*c*f+d*e))*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/d/e^2/(-a*f+b*e)/(-c*f+d*e)^2-1/4*f*x*(b*x^2+a)^(7/2)/e/(-c*f+d*e)/sqrt(d*x^2+c)/(f*x^2+e)^2+1/8*f*(a*f*(-3*c*f+8*d*e)-b*e*(4*c*f+d*e))*x*(b*x^2+a)^(7/2)/e^2/(-a*f+b*e)/(-c*f+d*e)^2/sqrt(d*x^2+c)/(f*x^2+e)-1/8*sqrt(a)*sqrt(b)*(a^2*b*c*d*e*f^2*(4*c*f+41*d*e)-a*b^2*c*d*e^2*f*(41*c*f+4*d*e)-b^3*c*e^2*(-8*c^2*f^2-10*c*d*e*f+3*d^2*e^2)-a^3*d*f^2*(-3*c^2*f^2+10*c*d*e*f+8*d^2*e^2))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/c/d/e^2/f^2/(-c*f+d*e)^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/8*a^(3/2)*sqrt(b)*(-a*f+b*e)*(b*e*(-8*c*f+3*d*e)+a*f*(-3*c*f+8*d*e))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/c/e^2/f^2/(-c*f+d*e)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/8*a^(3/2)*(-a*f+b*e)*(3*a^2*f^2*(c^2*f^2-4*c*d*e*f+8*d^2*e^2)+2*a*b*e*f*(4*c^2*f^2-23*c*d*e*f+4*d^2*e^2)+3*b^2*e^2*(8*c^2*f^2-4*c*d*e*f+d^2*e^2))*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e^3/f^2/(-c*f+d*e)^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(b*x^2+a)^(7/2)/(d*x^2+c)^(5/2)/(f*x^2+e)^3,x,8,1/24*(-a*d+b*c)^3*(a*f*(-9*c^2*f^2+36*c*d*e*f+8*d^2*e^2)-b*e*(12*c^2*f^2+15*c*d*e*f+8*d^2*e^2))*x*sqrt(b*x^2+a)/c/d^2/e^2/(-a*f+b*e)/(-c*f+d*e)^3/(d*x^2+c)^(3/2)-1/8*b^2*(3*a^2*d*f^2*(-3*c*f+10*d*e)-a*b*f*(-3*c^2*f^2+21*c*d*e*f+17*d^2*e^2)+b^2*e*(4*c^2*f^2+9*c*d*e*f+d^2*e^2))*x*sqrt(b*x^2+a)/d^2/e^2/f/(-a*f+b*e)/(-c*f+d*e)^2/sqrt(d*x^2+c)-1/8*b^3*(a*f*(-3*c*f+10*d*e)-b*e*(4*c*f+3*d*e))*x^3*sqrt(b*x^2+a)/d/e^2/(-a*f+b*e)/(-c*f+d*e)^2/sqrt(d*x^2+c)-1/4*f*x*(b*x^2+a)^(7/2)/e/(-c*f+d*e)/(d*x^2+c)^(3/2)/(f*x^2+e)^2+1/8*f*(a*f*(-3*c*f+10*d*e)-b*e*(4*c*f+3*d*e))*x*(b*x^2+a)^(7/2)/e^2/(-a*f+b*e)/(-c*f+d*e)^2/(d*x^2+c)^(3/2)/(f*x^2+e)-1/24*(5*a*b^2*c^2*d*e^2*f*(31*c*f+32*d*e)-b^3*c^2*e^2*(8*c^2*f^2+94*c*d*e*f+3*d^2*e^2)-a^2*b*c*d*e*f*(12*c^2*f^2+271*c*d*e*f+32*d^2*e^2)-a^3*d*f*(9*c^3*f^3-42*c^2*d*e*f^2-88*c*d^2*e^2*f+16*d^3*e^3))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/c^(3/2)/sqrt(d)/e^2/f/(-c*f+d*e)^4/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-1/24*(3*b^4*c^2*e^3*(-24*c^2*f^2-12*c*d*e*f+d^2*e^2)-3*a^4*c*d*f^3*(3*c^2*f^2-16*c*d*e*f+48*d^2*e^2)+5*a*b^3*c^2*e^2*f*(16*c^2*f^2+49*c*d*e*f+19*d^2*e^2)-a^2*b^2*c*d*e^2*f*(223*c^2*f^2+319*c*d*e*f+88*d^2*e^2)+a^3*b*d*e*f*(-9*c^3*f^3+221*c^2*d*e*f^2+200*c*d^2*e^2*f+8*d^3*e^3))*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a/sqrt(c)/sqrt(d)/e^2/f/(-c*f+d*e)^5/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+1/8*c^(3/2)*(-a*f+b*e)^2*(b^2*e^2*(-24*c^2*f^2-12*c*d*e*f+d^2*e^2)+2*a*b*e*f*(-4*c^2*f^2+33*c*d*e*f+6*d^2*e^2)-a^2*f^2*(3*c^2*f^2-16*c*d*e*f+48*d^2*e^2))*sqrt(b*x^2+a)*EllipticPi(sin(arctan(sqrt(d)*x/sqrt(c))),1-c*f/d/e,sqrt(1-b*c/a/d))/a/sqrt(d)/e^3/f/(-c*f+d*e)^5/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[1/sqrt(b*x^2+a)/sqrt(d*x^2+c)/(f*x^2+e)^3,x,5,1/4*f^2*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/e/(-a*f+b*e)/(-c*f+d*e)/(f*x^2+e)^2-3/8*f*(b*e*(-2*c*f+3*d*e)-a*f*(-c*f+2*d*e))*x*sqrt(b*x^2+a)/e^2/(-a*f+b*e)^2/(-c*f+d*e)/sqrt(d*x^2+c)/(f*x^2+e)+3/8*sqrt(c)*sqrt(d)*f*(b*e*(-2*c*f+3*d*e)-a*f*(-c*f+2*d*e))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/e^2/(-a*f+b*e)^2/(-c*f+d*e)^2/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-1/8*sqrt(c)*sqrt(d)*(a*f*(3*c^2*f^2-8*c*d*e*f+8*d^2*e^2)-b*e*(4*c^2*f^2-9*c*d*e*f+8*d^2*e^2))*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a/e^2/(-a*f+b*e)/(-c*f+d*e)^3/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-1/8*c^(3/2)*f*(a^2*f^2*(3*c^2*f^2-8*c*d*e*f+8*d^2*e^2)-2*a*b*e*f*(4*c^2*f^2-11*c*d*e*f+10*d^2*e^2)+b^2*e^2*(8*c^2*f^2-20*c*d*e*f+15*d^2*e^2))*sqrt(b*x^2+a)*EllipticPi(sin(arctan(sqrt(d)*x/sqrt(c))),1-c*f/d/e,sqrt(1-b*c/a/d))/a/sqrt(d)/e^3/(-a*f+b*e)^2/(-c*f+d*e)^3/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[1/sqrt(b*x^2+a)/(d*x^2+c)^(3/2)/(f*x^2+e)^3,x,5,1/4*f^2*x*sqrt(b*x^2+a)/e/(-a*f+b*e)/(-c*f+d*e)/sqrt(d*x^2+c)/(f*x^2+e)^2+1/8*f^2*(b*e*(-6*c*f+11*d*e)-a*f*(-3*c*f+8*d*e))*x*sqrt(b*x^2+a)/e^2/(-a*f+b*e)^2/(-c*f+d*e)^2/sqrt(d*x^2+c)/(f*x^2+e)-1/8*sqrt(d)*(a^2*d*f^2*(-3*c^2*f^2+10*c*d*e*f+8*d^2*e^2)+b^2*e*(-6*c^3*f^3+13*c^2*d*e*f^2+8*d^3*e^3)-a*b*f*(-3*c^3*f^3+4*c^2*d*e*f^2+13*c*d^2*e^2*f+16*d^3*e^3))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/sqrt(c)/(-a*d+b*c)/e^2/(-a*f+b*e)^2/(-c*f+d*e)^3/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-1/8*sqrt(c)*sqrt(d)*(3*a^2*d*f^2*(c^2*f^2-4*c*d*e*f+8*d^2*e^2)-b^2*e*(-4*c^3*f^3+13*c^2*d*e*f^2-32*c*d^2*e^2*f+8*d^3*e^3)-a*b*f*(3*c^3*f^3-8*c^2*d*e*f^2+19*c*d^2*e^2*f+16*d^3*e^3))*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a/(-a*d+b*c)/e^2/(-a*f+b*e)/(-c*f+d*e)^4/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+1/8*c^(3/2)*f^2*(3*a^2*f^2*(c^2*f^2-4*c*d*e*f+8*d^2*e^2)-2*a*b*e*f*(4*c^2*f^2-17*c*d*e*f+28*d^2*e^2)+b^2*e^2*(8*c^2*f^2-28*c*d*e*f+35*d^2*e^2))*sqrt(b*x^2+a)*EllipticPi(sin(arctan(sqrt(d)*x/sqrt(c))),1-c*f/d/e,sqrt(1-b*c/a/d))/a/sqrt(d)/e^3/(-a*f+b*e)^2/(-c*f+d*e)^4/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[1/(b*x^2+a)^(3/2)/sqrt(d*x^2+c)/(f*x^2+e)^3,x,5,1/4*f^2*x*sqrt(d*x^2+c)/e/(-a*f+b*e)/(-c*f+d*e)/sqrt(b*x^2+a)/(f*x^2+e)^2+1/8*f^2*(b*e*(-8*c*f+11*d*e)-3*a*f*(-c*f+2*d*e))*x*sqrt(d*x^2+c)/e^2/(-a*f+b*e)^2/(-c*f+d*e)^2/sqrt(b*x^2+a)/(f*x^2+e)-1/8*sqrt(b)*(a*b^2*c*e*f^2*(-10*c*f+13*d*e)-8*b^3*e^2*(-c*f+d*e)^2+3*a^3*d*f^3*(-c*f+2*d*e)-a^2*b*f^2*(-3*c^2*f^2-4*c*d*e*f+13*d^2*e^2))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/sqrt(a)/(-a*d+b*c)/e^2/(-a*f+b*e)^3/(-c*f+d*e)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/8*sqrt(a)*sqrt(b)*(a^3*d*f^3*(-3*c*f+4*d*e)+a*b^2*e*f*(-12*c^2*f^2-19*c*d*e*f+32*d^2*e^2)-a^2*b*f^2*(-3*c^2*f^2-8*c*d*e*f+13*d^2*e^2)-8*b^3*e^2*(-3*c^2*f^2+2*c*d*e*f+d^2*e^2))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/c/(-a*d+b*c)/e^2/(-a*f+b*e)^4/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/8*a^(3/2)*f^2*(a^2*f^2*(3*c^2*f^2-8*c*d*e*f+8*d^2*e^2)-2*a*b*e*f*(6*c^2*f^2-17*c*d*e*f+14*d^2*e^2)+b^2*e^2*(24*c^2*f^2-56*c*d*e*f+35*d^2*e^2))*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e^3/(-a*f+b*e)^4/(-c*f+d*e)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[1/(b*x^2+a)^(3/2)/(d*x^2+c)^(3/2)/(f*x^2+e)^3,x,6,-1/8*b*(a^3*d*f^3*(-3*c*f+8*d*e)+5*a*b^2*c*e*f^2*(-2*c*f+3*d*e)-8*b^3*e^2*(-c*f+d*e)^2-a^2*b*f^2*(-3*c^2*f^2-2*c*d*e*f+15*d^2*e^2))*x/a/(-a*d+b*c)/e^2/(-a*f+b*e)^3/(-c*f+d*e)^2/sqrt(b*x^2+a)/sqrt(d*x^2+c)+1/4*f^2*x/e/(-a*f+b*e)/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(d*x^2+c)/(f*x^2+e)^2+1/8*f^2*(b*e*(-8*c*f+13*d*e)-a*f*(-3*c*f+8*d*e))*x/e^2/(-a*f+b*e)^2/(-c*f+d*e)^2/sqrt(b*x^2+a)/sqrt(d*x^2+c)/(f*x^2+e)+1/8*sqrt(d)*(8*b^4*c*e^2*(-c*f+d*e)^3-a^4*d^2*f^3*(-3*c^2*f^2+10*c*d*e*f+8*d^2*e^2)+a^3*b*d*f^2*(-6*c^3*f^3+10*c^2*d*e*f^2+17*c*d^2*e^2*f+24*d^3*e^3)+a*b^3*e*(-10*c^4*f^4+17*c^3*d*e*f^3+8*d^4*e^4)-a^2*b^2*f*(-3*c^4*f^4-10*c^3*d*e*f^3+34*c^2*d^2*e^2*f^2+24*d^4*e^4))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/a/sqrt(c)/(-a*d+b*c)^2/e^2/(-a*f+b*e)^3/(-c*f+d*e)^3/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-1/8*sqrt(c)*sqrt(d)*(3*a^3*d^2*f^3*(c^2*f^2-4*c*d*e*f+8*d^2*e^2)-a^2*b*d*f^2*(6*c^3*f^3-16*c^2*d*e*f^2+23*c*d^2*e^2*f+32*d^3*e^3)+b^3*e*(-8*c^4*f^4+17*c^3*d*e*f^3-40*c*d^3*e^3*f+16*d^4*e^4)-a*b^2*f*(-3*c^4*f^4-4*c^3*d*e*f^3+34*c^2*d^2*e^2*f^2-80*c*d^3*e^3*f+8*d^4*e^4))*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a/(-a*d+b*c)^2/e^2/(-a*f+b*e)^2/(-c*f+d*e)^4/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-3/8*c^(3/2)*f^3*(a^2*f^2*(c^2*f^2-4*c*d*e*f+8*d^2*e^2)-2*a*b*e*f*(2*c^2*f^2-9*c*d*e*f+12*d^2*e^2)+b^2*e^2*(8*c^2*f^2-24*c*d*e*f+21*d^2*e^2))*sqrt(b*x^2+a)*EllipticPi(sin(arctan(sqrt(d)*x/sqrt(c))),1-c*f/d/e,sqrt(1-b*c/a/d))/a/sqrt(d)/e^3/(-a*f+b*e)^3/(-c*f+d*e)^4/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[1/(b*x^2+a)^(5/2)/sqrt(d*x^2+c)/(f*x^2+e)^3,x,6,-1/24*b*(9*a*b^2*c*e*f^2*(-4*c*f+5*d*e)-8*b^3*e^2*(-c*f+d*e)^2+9*a^3*d*f^3*(-c*f+2*d*e)-9*a^2*b*f^2*(-c^2*f^2-2*c*d*e*f+5*d^2*e^2))*x*sqrt(d*x^2+c)/a/(-a*d+b*c)/e^2/(-a*f+b*e)^3/(-c*f+d*e)^2/(b*x^2+a)^(3/2)+1/4*f^2*x*sqrt(d*x^2+c)/e/(-a*f+b*e)/(-c*f+d*e)/(b*x^2+a)^(3/2)/(f*x^2+e)^2+1/8*f^2*(b*e*(-10*c*f+13*d*e)-3*a*f*(-c*f+2*d*e))*x*sqrt(d*x^2+c)/e^2/(-a*f+b*e)^2/(-c*f+d*e)^2/(b*x^2+a)^(3/2)/(f*x^2+e)+1/24*sqrt(b)*(16*b^5*c*e^3*(-c*f+d*e)^2-9*a^5*d^2*f^4*(-c*f+2*d*e)-8*a*b^4*e^2*(-c*f+d*e)^2*(11*c*f+4*d*e)+3*a^4*b*d*f^3*(-6*c^2*f^2-2*c*d*e*f+17*d^2*e^2)-3*a^3*b^2*c*f^3*(-3*c^2*f^2-22*c*d*e*f+34*d^2*e^2)+a^2*b^3*e*f*(-42*c^3*f^3+155*c^2*d*e*f^2-208*c*d^2*e^2*f+104*d^3*e^3))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/a^(3/2)/(-a*d+b*c)^2/e^2/(-a*f+b*e)^4/(-c*f+d*e)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/24*sqrt(b)*(3*a^5*d^2*f^4*(-3*c*f+4*d*e)-8*b^5*c*d*e^4*(-c*f+d*e)-3*a^4*b*d*f^3*(-6*c^2*f^2-8*c*d*e*f+17*d^2*e^2)-a^2*b^3*e*f*(-48*c^3*f^3-317*c^2*d*e*f^2+248*c*d^2*e^2*f+120*d^3*e^3)+8*a*b^4*e^2*(-18*c^3*f^3+7*c^2*d*e*f^2+8*c*d^2*e^2*f+3*d^3*e^3)+3*a^3*b^2*f^2*(-3*c^3*f^3-28*c^2*d*e*f^2-46*c*d^2*e^2*f+80*d^3*e^3))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(a)/c/(-a*d+b*c)^2/e^2/(-a*f+b*e)^5/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/8*a^(3/2)*f^3*(a^2*f^2*(3*c^2*f^2-8*c*d*e*f+8*d^2*e^2)-2*a*b*e*f*(8*c^2*f^2-23*c*d*e*f+18*d^2*e^2)+3*b^2*e^2*(16*c^2*f^2-36*c*d*e*f+21*d^2*e^2))*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e^3/(-a*f+b*e)^5/(-c*f+d*e)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[1/(b*x^2+a)^(5/2)/(d*x^2+c)^(3/2)/(f*x^2+e)^3,x,7,-1/24*b*(3*a*b^2*c*e*f^2*(-12*c*f+17*d*e)+3*a^3*d*f^3*(-3*c*f+8*d*e)-8*b^3*e^2*(-c*f+d*e)^2-3*a^2*b*f^2*(-3*c^2*f^2-4*c*d*e*f+17*d^2*e^2))*x/a/(-a*d+b*c)/e^2/(-a*f+b*e)^3/(-c*f+d*e)^2/(b*x^2+a)^(3/2)/sqrt(d*x^2+c)-1/24*b*(3*a^5*d^2*f^4*(-3*c*f+8*d*e)-16*b^5*c*e^3*(-c*f+d*e)^2+8*a*b^4*e^2*(-c*f+d*e)^2*(11*c*f+6*d*e)-3*a^4*b*d*f^3*(-6*c^2*f^2+2*c*d*e*f+19*d^2*e^2)+3*a^3*b^2*c*f^3*(-3*c^2*f^2-20*c*d*e*f+38*d^2*e^2)-3*a^2*b^3*e*f*(-14*c^3*f^3+59*c^2*d*e*f^2-80*c*d^2*e^2*f+40*d^3*e^3))*x/a^2/(-a*d+b*c)^2/e^2/(-a*f+b*e)^4/(-c*f+d*e)^2/sqrt(b*x^2+a)/sqrt(d*x^2+c)+1/4*f^2*x/e/(-a*f+b*e)/(-c*f+d*e)/(b*x^2+a)^(3/2)/sqrt(d*x^2+c)/(f*x^2+e)^2-1/8*f^2*(a*f*(-3*c*f+8*d*e)-5*b*e*(-2*c*f+3*d*e))*x/e^2/(-a*f+b*e)^2/(-c*f+d*e)^2/(b*x^2+a)^(3/2)/sqrt(d*x^2+c)/(f*x^2+e)+1/24*sqrt(d)*(16*b^6*c^2*e^3*(-c*f+d*e)^3-8*a*b^5*c*e^2*(-c*f+d*e)^3*(11*c*f+7*d*e)-3*a^6*d^3*f^4*(-3*c^2*f^2+10*c*d*e*f+8*d^2*e^2)+3*a^5*b*d^2*f^3*(-9*c^3*f^3+16*c^2*d*e*f^2+21*c*d^2*e^2*f+32*d^3*e^3)-9*a^4*b^2*d*f^2*(-3*c^4*f^4-4*c^3*d*e*f^3+21*c^2*d^2*e^2*f^2+16*d^4*e^4)-a^2*b^4*e*(-42*c^5*f^5+191*c^4*d*e*f^4-384*c^3*d^2*e^2*f^3+384*c^2*d^3*e^3*f^2-128*c*d^4*e^4*f+24*d^5*e^5)+3*a^3*b^3*f*(-3*c^5*f^5-32*c^4*d*e*f^4+63*c^3*d^2*e^2*f^3+32*d^5*e^5))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/a^2/sqrt(c)/(-a*d+b*c)^3/e^2/(-a*f+b*e)^4/(-c*f+d*e)^3/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-1/24*sqrt(c)*sqrt(d)*(8*b^5*c*e^2*(-c*f+d*e)^4+9*a^5*d^3*f^4*(c^2*f^2-4*c*d*e*f+8*d^2*e^2)+27*a^3*b^2*c*d*f^3*(c^3*f^3-7*c*d^2*e^2*f+16*d^3*e^3)-9*a^4*b*d^2*f^3*(3*c^3*f^3-8*c^2*d*e*f^2+9*c*d^2*e^2*f+16*d^3*e^3)-9*a*b^4*e*(-4*c^5*f^5+7*c^4*d*e*f^4-16*c*d^4*e^4*f+8*d^5*e^5)+9*a^2*b^3*f*(-c^5*f^5-8*c^4*d*e*f^4+21*c^3*d^2*e^2*f^3-48*c*d^4*e^4*f+16*d^5*e^5))*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a^2/(-a*d+b*c)^3/e^2/(-a*f+b*e)^3/(-c*f+d*e)^4/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+1/8*c^(3/2)*f^4*(3*a^2*f^2*(c^2*f^2-4*c*d*e*f+8*d^2*e^2)-2*a*b*e*f*(8*c^2*f^2-37*c*d*e*f+44*d^2*e^2)+3*b^2*e^2*(16*c^2*f^2-44*c*d*e*f+33*d^2*e^2))*sqrt(b*x^2+a)*EllipticPi(sin(arctan(sqrt(d)*x/sqrt(c))),1-c*f/d/e,sqrt(1-b*c/a/d))/a/sqrt(d)/e^3/(-a*f+b*e)^4/(-c*f+d*e)^4/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[(b*x^2+a)*(d*x^2+c)*(f*x^2+e)^4,x,2,a*c*e^4*x+1/3*e^3*(4*a*c*f+a*d*e+b*c*e)*x^3+1/5*e^2*(2*a*f*(3*c*f+2*d*e)+b*e*(4*c*f+d*e))*x^5+2/7*e*f*(a*f*(2*c*f+3*d*e)+b*e*(3*c*f+2*d*e))*x^7+1/9*f^2*(a*f*(c*f+4*d*e)+2*b*e*(2*c*f+3*d*e))*x^9+1/11*f^3*(a*d*f+b*c*f+4*b*d*e)*x^11+1/13*b*d*f^4*x^13,1],
[(b*x^2+a)*(d*x^2+c)*(f*x^2+e)^3,x,2,a*c*e^3*x+1/3*e^2*(3*a*c*f+a*d*e+b*c*e)*x^3+1/5*e*(3*a*f*(c*f+d*e)+b*e*(3*c*f+d*e))*x^5+1/7*f*(3*b*e*(c*f+d*e)+a*f*(c*f+3*d*e))*x^7+1/9*f^2*(a*d*f+b*c*f+3*b*d*e)*x^9+1/11*b*d*f^3*x^11,1],
[(b*x^2+a)*(d*x^2+c)*(f*x^2+e)^2,x,2,a*c*e^2*x+1/3*e*(2*a*c*f+a*d*e+b*c*e)*x^3+1/5*(a*f*(c*f+2*d*e)+b*e*(2*c*f+d*e))*x^5+1/7*f*(a*d*f+b*c*f+2*b*d*e)*x^7+1/9*b*d*f^2*x^9,1],
[(b*x^2+a)*(d*x^2+c)*(f*x^2+e),x,2,a*c*e*x+1/3*(a*c*f+a*d*e+b*c*e)*x^3+1/5*(a*d*f+b*c*f+b*d*e)*x^5+1/7*b*d*f*x^7,1],
[(b*x^2+a)*(d*x^2+c)/(f*x^2+e),x,3,-(-a*d*f-b*c*f+b*d*e)*x/f^2+1/3*b*d*x^3/f+(-a*f+b*e)*(-c*f+d*e)*arctan(sqrt(f)*x/sqrt(e))/sqrt(e)/f^(5/2),1],
[(b*x^2+a)*(d*x^2+c)/(f*x^2+e)^2,x,4,b*d*x/f^2+1/2*(-a*f+b*e)*(-c*f+d*e)*x/e/f^2/(f*x^2+e)-1/2*(b*e*(-c*f+3*d*e)-a*f*(c*f+d*e))*arctan(sqrt(f)*x/sqrt(e))/e^(3/2)/f^(5/2),1],
[(b*x^2+a)*(d*x^2+c)/(f*x^2+e)^3,x,3,1/4*(-a*f+b*e)*(-c*f+d*e)*x/e/f^2/(f*x^2+e)^2-1/8*(b*e*(-c*f+5*d*e)-a*f*(3*c*f+d*e))*x/e^2/f^2/(f*x^2+e)+1/8*(b*e*(c*f+3*d*e)+a*f*(3*c*f+d*e))*arctan(sqrt(f)*x/sqrt(e))/e^(5/2)/f^(5/2),1],
[(b*x^2+a)*(d*x^2+c)/(f*x^2+e)^4,x,4,1/6*(-a*f+b*e)*(-c*f+d*e)*x/e/f^2/(f*x^2+e)^3-1/24*(b*e*(-c*f+7*d*e)-a*f*(5*c*f+d*e))*x/e^2/f^2/(f*x^2+e)^2+1/16*(b*e*(c*f+d*e)+a*f*(5*c*f+d*e))*x/e^3/f^2/(f*x^2+e)+1/16*(b*e*(c*f+d*e)+a*f*(5*c*f+d*e))*arctan(sqrt(f)*x/sqrt(e))/e^(7/2)/f^(5/2),1],
[(b*x^2+a)*(d*x^2+c)^2*(f*x^2+e)^3,x,2,a*c^2*e^3*x+1/3*c*e^2*(3*a*c*f+2*a*d*e+b*c*e)*x^3+1/5*e*(b*c*e*(3*c*f+2*d*e)+a*(3*c^2*f^2+6*c*d*e*f+d^2*e^2))*x^5+1/7*(a*f*(c^2*f^2+6*c*d*e*f+3*d^2*e^2)+b*e*(3*c^2*f^2+6*c*d*e*f+d^2*e^2))*x^7+1/9*f*(a*d*f*(2*c*f+3*d*e)+b*(c^2*f^2+6*c*d*e*f+3*d^2*e^2))*x^9+1/11*d*f^2*(a*d*f+2*b*c*f+3*b*d*e)*x^11+1/13*b*d^2*f^3*x^13,1],
[(b*x^2+a)*(d*x^2+c)^2*(f*x^2+e)^2,x,2,a*c^2*e^2*x+1/3*c*e*(b*c*e+2*a*(c*f+d*e))*x^3+1/5*(2*b*c*e*(c*f+d*e)+a*(c^2*f^2+4*c*d*e*f+d^2*e^2))*x^5+1/7*(2*a*d*f*(c*f+d*e)+b*(c^2*f^2+4*c*d*e*f+d^2*e^2))*x^7+1/9*d*f*(a*d*f+2*b*(c*f+d*e))*x^9+1/11*b*d^2*f^2*x^11,1],
[(b*x^2+a)*(d*x^2+c)^2/(f*x^2+e),x,3,-(a*d*f*(-2*c*f+d*e)-b*(-c*f+d*e)^2)*x/f^3-1/3*d*(-a*d*f-2*b*c*f+b*d*e)*x^3/f^2+1/5*b*d^2*x^5/f-(-a*f+b*e)*(-c*f+d*e)^2*arctan(sqrt(f)*x/sqrt(e))/sqrt(e)/f^(7/2),1],
[(b*x^2+a)*(d*x^2+c)^2/(f*x^2+e)^2,x,4,-d*(-a*d*f-2*b*c*f+2*b*d*e)*x/f^3+1/3*b*d^2*x^3/f^2-1/2*(-a*f+b*e)*(-c*f+d*e)^2*x/e/f^3/(f*x^2+e)+1/2*(-c*f+d*e)*(b*e*(-c*f+5*d*e)-a*f*(c*f+3*d*e))*arctan(sqrt(f)*x/sqrt(e))/e^(3/2)/f^(7/2),1],
[(b*x^2+a)*(d*x^2+c)^2/(f*x^2+e)^3,x,5,b*d^2*x/f^3-1/4*(-a*f+b*e)*(-c*f+d*e)^2*x/e/f^3/(f*x^2+e)^2+1/8*(-c*f+d*e)*(b*e*(-c*f+9*d*e)-a*f*(3*c*f+5*d*e))*x/e^2/f^3/(f*x^2+e)-1/8*(b*e*(-c^2*f^2-6*c*d*e*f+15*d^2*e^2)-a*f*(3*c^2*f^2+2*c*d*e*f+3*d^2*e^2))*arctan(sqrt(f)*x/sqrt(e))/e^(5/2)/f^(7/2),1],
[(b*x^2+a)*(d*x^2+c)^2/(f*x^2+e)^4,x,4,-1/6*(-a*f+b*e)*(-c*f+d*e)^2*x/e/f^3/(f*x^2+e)^3+1/24*(-c*f+d*e)*(b*e*(-c*f+13*d*e)-a*f*(5*c*f+7*d*e))*x/e^2/f^3/(f*x^2+e)^2-1/16*(b*e*(-c^2*f^2-2*c*d*e*f+11*d^2*e^2)-a*f*(5*c^2*f^2+2*c*d*e*f+d^2*e^2))*x/e^3/f^3/(f*x^2+e)+1/16*(b*e*(c^2*f^2+2*c*d*e*f+5*d^2*e^2)+a*f*(5*c^2*f^2+2*c*d*e*f+d^2*e^2))*arctan(sqrt(f)*x/sqrt(e))/e^(7/2)/f^(7/2),1],
[(b*x^2+a)*(d*x^2+c)^3*(f*x^2+e)^3,x,2,a*c^3*e^3*x+1/3*c^2*e^2*(b*c*e+3*a*(c*f+d*e))*x^3+3/5*c*e*(b*c*e*(c*f+d*e)+a*(c^2*f^2+3*c*d*e*f+d^2*e^2))*x^5+1/7*(3*b*c*e*(c^2*f^2+3*c*d*e*f+d^2*e^2)+a*(c^3*f^3+9*c^2*d*e*f^2+9*c*d^2*e^2*f+d^3*e^3))*x^7+1/9*(3*a*d*f*(c^2*f^2+3*c*d*e*f+d^2*e^2)+b*(c^3*f^3+9*c^2*d*e*f^2+9*c*d^2*e^2*f+d^3*e^3))*x^9+3/11*d*f*(a*d*f*(c*f+d*e)+b*(c^2*f^2+3*c*d*e*f+d^2*e^2))*x^11+1/13*d^2*f^2*(a*d*f+3*b*(c*f+d*e))*x^13+1/15*b*d^3*f^3*x^15,1],
[(b*x^2+a)*(d*x^2+c)^3/(f*x^2+e),x,3,-(b*(-c*f+d*e)^3-a*d*f*(3*c^2*f^2-3*c*d*e*f+d^2*e^2))*x/f^4-1/3*d*(a*d*f*(-3*c*f+d*e)-b*(3*c^2*f^2-3*c*d*e*f+d^2*e^2))*x^3/f^3-1/5*d^2*(-a*d*f-3*b*c*f+b*d*e)*x^5/f^2+1/7*b*d^3*x^7/f+(-a*f+b*e)*(-c*f+d*e)^3*arctan(sqrt(f)*x/sqrt(e))/sqrt(e)/f^(9/2),1],
[(b*x^2+a)*(d*x^2+c)^3/(f*x^2+e)^2,x,4,-d*(a*d*f*(-3*c*f+2*d*e)-3*b*(-c*f+d*e)^2)*x/f^4-1/3*d^2*(-a*d*f-3*b*c*f+2*b*d*e)*x^3/f^3+1/5*b*d^3*x^5/f^2+1/2*(-a*f+b*e)*(-c*f+d*e)^3*x/e/f^4/(f*x^2+e)-1/2*(-c*f+d*e)^2*(b*e*(-c*f+7*d*e)-a*f*(c*f+5*d*e))*arctan(sqrt(f)*x/sqrt(e))/e^(3/2)/f^(9/2),1],
[(b*x^2+a)*(d*x^2+c)^3/(f*x^2+e)^3,x,5,-d^2*(-a*d*f-3*b*c*f+3*b*d*e)*x/f^4+1/3*b*d^3*x^3/f^3+1/4*(-a*f+b*e)*(-c*f+d*e)^3*x/e/f^4/(f*x^2+e)^2-1/8*(-c*f+d*e)^2*(b*e*(-c*f+13*d*e)-3*a*f*(c*f+3*d*e))*x/e^2/f^4/(f*x^2+e)+1/8*(-c*f+d*e)*(b*e*(-c^2*f^2-10*c*d*e*f+35*d^2*e^2)-3*a*f*(c^2*f^2+2*c*d*e*f+5*d^2*e^2))*arctan(sqrt(f)*x/sqrt(e))/e^(5/2)/f^(9/2),1],
[(b*x^2+a)*(d*x^2+c)^3/(f*x^2+e)^4,x,6,b*d^3*x/f^4+1/6*(-a*f+b*e)*(-c*f+d*e)^3*x/e/f^4/(f*x^2+e)^3-1/24*(-c*f+d*e)^2*(b*e*(-c*f+19*d*e)-a*f*(5*c*f+13*d*e))*x/e^2/f^4/(f*x^2+e)^2+1/16*(-c*f+d*e)*(b*e*(-c^2*f^2-4*c*d*e*f+29*d^2*e^2)-a*f*(5*c^2*f^2+8*c*d*e*f+11*d^2*e^2))*x/e^3/f^4/(f*x^2+e)-1/16*(b*e*(-c^3*f^3-3*c^2*d*e*f^2-15*c*d^2*e^2*f+35*d^3*e^3)-a*f*(5*c^3*f^3+3*c^2*d*e*f^2+3*c*d^2*e^2*f+5*d^3*e^3))*arctan(sqrt(f)*x/sqrt(e))/e^(7/2)/f^(9/2),1],
[(b*x^2+a)/(d*x^2+c)/(f*x^2+e),x,3,-(-a*d+b*c)*arctan(sqrt(d)*x/sqrt(c))/sqrt(c)/sqrt(d)/(-c*f+d*e)+(-a*f+b*e)*arctan(sqrt(f)*x/sqrt(e))/sqrt(e)/sqrt(f)/(-c*f+d*e),1],
[(b*x^2+a)/(d*x^2+c)/(f*x^2+e)^2,x,4,1/2*(-a*f+b*e)*x/e/(-c*f+d*e)/(f*x^2+e)-sqrt(d)*(-a*d+b*c)*arctan(sqrt(d)*x/sqrt(c))/sqrt(c)/(-c*f+d*e)^2-1/2*(a*f*(-c*f+3*d*e)-b*e*(c*f+d*e))*arctan(sqrt(f)*x/sqrt(e))/e^(3/2)/sqrt(f)/(-c*f+d*e)^2,1],
[(b*x^2+a)/(d*x^2+c)/(f*x^2+e)^3,x,5,1/4*(-a*f+b*e)*x/e/(-c*f+d*e)/(f*x^2+e)^2-1/8*(a*f*(-3*c*f+7*d*e)-b*e*(c*f+3*d*e))*x/e^2/(-c*f+d*e)^2/(f*x^2+e)-d^(3/2)*(-a*d+b*c)*arctan(sqrt(d)*x/sqrt(c))/sqrt(c)/(-c*f+d*e)^3+1/8*(b*e*(-c^2*f^2+6*c*d*e*f+3*d^2*e^2)-a*f*(3*c^2*f^2-10*c*d*e*f+15*d^2*e^2))*arctan(sqrt(f)*x/sqrt(e))/e^(5/2)/sqrt(f)/(-c*f+d*e)^3,1],
[(b*x^2+a)/(d*x^2+c)^2/(f*x^2+e)^2,x,5,-1/2*f*(-a*c*f-a*d*e+2*b*c*e)*x/c/e/(-c*f+d*e)^2/(f*x^2+e)-1/2*(-a*d+b*c)*x/c/(-c*f+d*e)/(d*x^2+c)/(f*x^2+e)+1/2*sqrt(d)*(a*d*(-5*c*f+d*e)+b*c*(3*c*f+d*e))*arctan(sqrt(d)*x/sqrt(c))/c^(3/2)/(-c*f+d*e)^3+1/2*sqrt(f)*(a*f*(-c*f+5*d*e)-b*e*(c*f+3*d*e))*arctan(sqrt(f)*x/sqrt(e))/e^(3/2)/(-c*f+d*e)^3,1],
[(b*x^2+a)/(d*x^2+c)^2/(f*x^2+e)^3,x,6,-1/4*f*(-a*c*f-2*a*d*e+3*b*c*e)*x/c/e/(-c*f+d*e)^2/(f*x^2+e)^2-1/2*(-a*d+b*c)*x/c/(-c*f+d*e)/(d*x^2+c)/(f*x^2+e)^2-1/8*f*(b*c*e*(c*f+11*d*e)-a*(-3*c^2*f^2+11*c*d*e*f+4*d^2*e^2))*x/c/e^2/(-c*f+d*e)^3/(f*x^2+e)+1/2*d^(3/2)*(a*d*(-7*c*f+d*e)+b*c*(5*c*f+d*e))*arctan(sqrt(d)*x/sqrt(c))/c^(3/2)/(-c*f+d*e)^4-1/8*sqrt(f)*(b*e*(-c^2*f^2+10*c*d*e*f+15*d^2*e^2)-a*f*(3*c^2*f^2-14*c*d*e*f+35*d^2*e^2))*arctan(sqrt(f)*x/sqrt(e))/e^(5/2)/(-c*f+d*e)^4,1],
[(b*x^2+a)/(d*x^2+c)^3/(f*x^2+e)^3,x,7,1/8*f*(b*c*e*(11*c*f+d*e)+a*(-2*c^2*f^2-13*c*d*e*f+3*d^2*e^2))*x/c^2/e/(-c*f+d*e)^3/(f*x^2+e)^2-1/4*(-a*d+b*c)*x/c/(-c*f+d*e)/(d*x^2+c)^2/(f*x^2+e)^2+1/8*(a*d*(-11*c*f+3*d*e)+b*c*(7*c*f+d*e))*x/c^2/(-c*f+d*e)^2/(d*x^2+c)/(f*x^2+e)^2+1/8*f*(b*c*e*(c^2*f^2+22*c*d*e*f+d^2*e^2)+3*a*(c^3*f^3-5*c^2*d*e*f^2-5*c*d^2*e^2*f+d^3*e^3))*x/c^2/e^2/(-c*f+d*e)^4/(f*x^2+e)+1/8*d^(3/2)*(b*c*(-35*c^2*f^2-14*c*d*e*f+d^2*e^2)+3*a*d*(21*c^2*f^2-6*c*d*e*f+d^2*e^2))*arctan(sqrt(d)*x/sqrt(c))/c^(5/2)/(-c*f+d*e)^5+1/8*f^(3/2)*(b*e*(-c^2*f^2+14*c*d*e*f+35*d^2*e^2)-3*a*f*(c^2*f^2-6*c*d*e*f+21*d^2*e^2))*arctan(sqrt(f)*x/sqrt(e))/e^(5/2)/(-c*f+d*e)^5,1],
[(b*x^2+a)^2*(d*x^2+c)^2*(f*x^2+e)^3,x,2,a^2*c^2*e^3*x+1/3*a*c*e^2*(3*a*c*f+2*a*d*e+2*b*c*e)*x^3+1/5*e*(b^2*c^2*e^2+2*a*b*c*e*(3*c*f+2*d*e)+a^2*(3*c^2*f^2+6*c*d*e*f+d^2*e^2))*x^5+1/7*(b^2*c*e^2*(3*c*f+2*d*e)+a^2*f*(c^2*f^2+6*c*d*e*f+3*d^2*e^2)+2*a*b*e*(3*c^2*f^2+6*c*d*e*f+d^2*e^2))*x^7+1/9*(a^2*d*f^2*(2*c*f+3*d*e)+2*a*b*f*(c^2*f^2+6*c*d*e*f+3*d^2*e^2)+b^2*e*(3*c^2*f^2+6*c*d*e*f+d^2*e^2))*x^9+1/11*f*(a^2*d^2*f^2+2*a*b*d*f*(2*c*f+3*d*e)+b^2*(c^2*f^2+6*c*d*e*f+3*d^2*e^2))*x^11+1/13*b*d*f^2*(2*a*d*f+2*b*c*f+3*b*d*e)*x^13+1/15*b^2*d^2*f^3*x^15,1],
[(b*x^2+a)^2*(d*x^2+c)^2*(f*x^2+e)^2,x,2,a^2*c^2*e^2*x+2/3*a*c*e*(a*c*f+a*d*e+b*c*e)*x^3+1/5*(b^2*c^2*e^2+4*a*b*c*e*(c*f+d*e)+a^2*(c^2*f^2+4*c*d*e*f+d^2*e^2))*x^5+2/7*(b^2*c*e*(c*f+d*e)+a^2*d*f*(c*f+d*e)+a*b*(c^2*f^2+4*c*d*e*f+d^2*e^2))*x^7+1/9*(a^2*d^2*f^2+4*a*b*d*f*(c*f+d*e)+b^2*(c^2*f^2+4*c*d*e*f+d^2*e^2))*x^9+2/11*b*d*f*(a*d*f+b*c*f+b*d*e)*x^11+1/13*b^2*d^2*f^2*x^13,1],
[(b*x^2+a)^2*(d*x^2+c)^2/(f*x^2+e),x,3,(-a*d*f-b*c*f+b*d*e)*(a*f*(-2*c*f+d*e)-b*e*(-c*f+d*e))*x/f^4+1/3*(a^2*d^2*f^2-2*a*b*d*f*(-2*c*f+d*e)+b^2*(-c*f+d*e)^2)*x^3/f^3-1/5*b*d*(-2*a*d*f-2*b*c*f+b*d*e)*x^5/f^2+1/7*b^2*d^2*x^7/f+(-a*f+b*e)^2*(-c*f+d*e)^2*arctan(sqrt(f)*x/sqrt(e))/sqrt(e)/f^(9/2),1],
[(b*x^2+a)^2*(d*x^2+c)^2/(f*x^2+e)^2,x,4,(a^2*d^2*f^2-4*a*b*d*f*(-c*f+d*e)+b^2*(c^2*f^2-4*c*d*e*f+3*d^2*e^2))*x/f^4-2/3*b*d*(-a*d*f-b*c*f+b*d*e)*x^3/f^3+1/5*b^2*d^2*x^5/f^2+1/2*(-a*f+b*e)^2*(-c*f+d*e)^2*x/e/f^4/(f*x^2+e)-1/2*(-a*f+b*e)*(-c*f+d*e)*(b*e*(-3*c*f+7*d*e)-a*f*(c*f+3*d*e))*arctan(sqrt(f)*x/sqrt(e))/e^(3/2)/f^(9/2),1],
[(b*x^2+a)^2*(d*x^2+c)^2/(f*x^2+e)^3,x,5,-b*d*(-2*a*d*f-2*b*c*f+3*b*d*e)*x/f^4+1/3*b^2*d^2*x^3/f^3+1/4*(-a*f+b*e)^2*(-c*f+d*e)^2*x/e/f^4/(f*x^2+e)^2-1/8*(-a*f+b*e)*(-c*f+d*e)*(b*e*(-5*c*f+13*d*e)-a*f*(3*c*f+5*d*e))*x/e^2/f^4/(f*x^2+e)-1/8*(2*a*b*e*f*(-c^2*f^2-6*c*d*e*f+15*d^2*e^2)-b^2*e^2*(3*c^2*f^2-30*c*d*e*f+35*d^2*e^2)-a^2*f^2*(3*c^2*f^2+2*c*d*e*f+3*d^2*e^2))*arctan(sqrt(f)*x/sqrt(e))/e^(5/2)/f^(9/2),1],
[(b*x^2+a)^2*(d*x^2+c)^2/(f*x^2+e)^4,x,6,b^2*d^2*x/f^4+1/6*(-a*f+b*e)^2*(-c*f+d*e)^2*x/e/f^4/(f*x^2+e)^3-1/24*(-a*f+b*e)*(-c*f+d*e)*(b*e*(-7*c*f+19*d*e)-a*f*(5*c*f+7*d*e))*x/e^2/f^4/(f*x^2+e)^2-1/16*(2*a*b*e*f*(-c^2*f^2-2*c*d*e*f+11*d^2*e^2)-b^2*e^2*(c^2*f^2-22*c*d*e*f+29*d^2*e^2)-a^2*f^2*(5*c^2*f^2+2*c*d*e*f+d^2*e^2))*x/e^3/f^4/(f*x^2+e)-1/16*(b^2*e^2*(-c^2*f^2-10*c*d*e*f+35*d^2*e^2)-2*a*b*e*f*(c^2*f^2+2*c*d*e*f+5*d^2*e^2)-a^2*f^2*(5*c^2*f^2+2*c*d*e*f+d^2*e^2))*arctan(sqrt(f)*x/sqrt(e))/e^(7/2)/f^(9/2),1],
[(b*x^2+a)^2*(d*x^2+c)^3*(f*x^2+e)^3,x,2,a^2*c^3*e^3*x+1/3*a*c^2*e^2*(2*b*c*e+3*a*(c*f+d*e))*x^3+1/5*c*e*(b^2*c^2*e^2+6*a*b*c*e*(c*f+d*e)+3*a^2*(c^2*f^2+3*c*d*e*f+d^2*e^2))*x^5+1/7*(3*b^2*c^2*e^2*(c*f+d*e)+6*a*b*c*e*(c^2*f^2+3*c*d*e*f+d^2*e^2)+a^2*(c^3*f^3+9*c^2*d*e*f^2+9*c*d^2*e^2*f+d^3*e^3))*x^7+1/9*(3*b^2*c*e*(c^2*f^2+3*c*d*e*f+d^2*e^2)+3*a^2*d*f*(c^2*f^2+3*c*d*e*f+d^2*e^2)+2*a*b*(c^3*f^3+9*c^2*d*e*f^2+9*c*d^2*e^2*f+d^3*e^3))*x^9+1/11*(3*a^2*d^2*f^2*(c*f+d*e)+6*a*b*d*f*(c^2*f^2+3*c*d*e*f+d^2*e^2)+b^2*(c^3*f^3+9*c^2*d*e*f^2+9*c*d^2*e^2*f+d^3*e^3))*x^11+1/13*d*f*(a^2*d^2*f^2+6*a*b*d*f*(c*f+d*e)+3*b^2*(c^2*f^2+3*c*d*e*f+d^2*e^2))*x^13+1/15*b*d^2*f^2*(2*a*d*f+3*b*(c*f+d*e))*x^15+1/17*b^2*d^3*f^3*x^17,1],
[(b*x^2+a)^2*(d*x^2+c)^3/(f*x^2+e),x,3,(b^2*e*(-c*f+d*e)^3-2*a*b*f*(-c*f+d*e)^3+a^2*d*f^2*(3*c^2*f^2-3*c*d*e*f+d^2*e^2))*x/f^5-1/3*(a^2*d^2*f^2*(-3*c*f+d*e)+b^2*(-c*f+d*e)^3-2*a*b*d*f*(3*c^2*f^2-3*c*d*e*f+d^2*e^2))*x^3/f^4+1/5*d*(a^2*d^2*f^2-2*a*b*d*f*(-3*c*f+d*e)+b^2*(3*c^2*f^2-3*c*d*e*f+d^2*e^2))*x^5/f^3-1/7*b*d^2*(-2*a*d*f-3*b*c*f+b*d*e)*x^7/f^2+1/9*b^2*d^3*x^9/f-(-a*f+b*e)^2*(-c*f+d*e)^3*arctan(sqrt(f)*x/sqrt(e))/sqrt(e)/f^(11/2),1],
[(b*x^2+a)^2*(d*x^2+c)^3/(f*x^2+e)^2,x,4,-(a^2*d^2*f^2*(-3*c*f+2*d*e)-6*a*b*d*f*(-c*f+d*e)^2+b^2*(-c*f+d*e)^2*(-c*f+4*d*e))*x/f^5+1/3*d*(a^2*d^2*f^2-2*a*b*d*f*(-3*c*f+2*d*e)+3*b^2*(-c*f+d*e)^2)*x^3/f^4-1/5*b*d^2*(-2*a*d*f-3*b*c*f+2*b*d*e)*x^5/f^3+1/7*b^2*d^3*x^7/f^2-1/2*(-a*f+b*e)^2*(-c*f+d*e)^3*x/e/f^5/(f*x^2+e)+1/2*(-a*f+b*e)*(-c*f+d*e)^2*(3*b*e*(-c*f+3*d*e)-a*f*(c*f+5*d*e))*arctan(sqrt(f)*x/sqrt(e))/e^(3/2)/f^(11/2),1],
[(b*x^2+a)^2*(d*x^2+c)^3/(f*x^2+e)^3,x,5,d*(a^2*d^2*f^2-6*a*b*d*f*(-c*f+d*e)+3*b^2*(c^2*f^2-3*c*d*e*f+2*d^2*e^2))*x/f^5-1/3*b*d^2*(-2*a*d*f-3*b*c*f+3*b*d*e)*x^3/f^4+1/5*b^2*d^3*x^5/f^3-1/4*(-a*f+b*e)^2*(-c*f+d*e)^3*x/e/f^5/(f*x^2+e)^2+1/8*(-a*f+b*e)*(-c*f+d*e)^2*(b*e*(-5*c*f+17*d*e)-3*a*f*(c*f+3*d*e))*x/e^2/f^5/(f*x^2+e)+1/8*(-c*f+d*e)*(2*a*b*e*f*(-c^2*f^2-10*c*d*e*f+35*d^2*e^2)-3*b^2*e^2*(c^2*f^2-14*c*d*e*f+21*d^2*e^2)-3*a^2*f^2*(c^2*f^2+2*c*d*e*f+5*d^2*e^2))*arctan(sqrt(f)*x/sqrt(e))/e^(5/2)/f^(11/2),1],
[(b*x^2+a)^2*(d*x^2+c)^3/(f*x^2+e)^4,x,6,-b*d^2*(-2*a*d*f-3*b*c*f+4*b*d*e)*x/f^5+1/3*b^2*d^3*x^3/f^4-1/6*(-a*f+b*e)^2*(-c*f+d*e)^3*x/e/f^5/(f*x^2+e)^3+1/24*(-a*f+b*e)*(-c*f+d*e)^2*(b*e*(-7*c*f+25*d*e)-a*f*(5*c*f+13*d*e))*x/e^2/f^5/(f*x^2+e)^2+1/16*(-c*f+d*e)*(2*a*b*e*f*(-c^2*f^2-4*c*d*e*f+29*d^2*e^2)-b^2*e^2*(c^2*f^2-32*c*d*e*f+55*d^2*e^2)-a^2*f^2*(5*c^2*f^2+8*c*d*e*f+11*d^2*e^2))*x/e^3/f^5/(f*x^2+e)-1/16*(2*a*b*e*f*(-c^3*f^3-3*c^2*d*e*f^2-15*c*d^2*e^2*f+35*d^3*e^3)-b^2*e^2*(c^3*f^3+15*c^2*d*e*f^2-105*c*d^2*e^2*f+105*d^3*e^3)-a^2*f^2*(5*c^3*f^3+3*c^2*d*e*f^2+3*c*d^2*e^2*f+5*d^3*e^3))*arctan(sqrt(f)*x/sqrt(e))/e^(7/2)/f^(11/2),1],
[(b*x^2+a)^2/(d*x^2+c)/(f*x^2+e),x,5,b^2*x/d/f+(-a*d+b*c)^2*arctan(sqrt(d)*x/sqrt(c))/sqrt(c)/d^(3/2)/(-c*f+d*e)-(-a*f+b*e)^2*arctan(sqrt(f)*x/sqrt(e))/sqrt(e)/f^(3/2)/(-c*f+d*e),1],
[(b*x^2+a)^2/(d*x^2+c)/(f*x^2+e)^2,x,4,-1/2*(-a*f+b*e)^2*x/e/f/(-c*f+d*e)/(f*x^2+e)+(-a*d+b*c)^2*arctan(sqrt(d)*x/sqrt(c))/sqrt(c)/sqrt(d)/(-c*f+d*e)^2+1/2*(-a*f+b*e)*(b*e*(-3*c*f+d*e)+a*f*(-c*f+3*d*e))*arctan(sqrt(f)*x/sqrt(e))/e^(3/2)/f^(3/2)/(-c*f+d*e)^2,1],
[(b*x^2+a)^2/(d*x^2+c)/(f*x^2+e)^3,x,5,-1/4*(-a*f+b*e)^2*x/e/f/(-c*f+d*e)/(f*x^2+e)^2+1/8*(-a*f+b*e)*(b*e*(-5*c*f+d*e)+a*f*(-3*c*f+7*d*e))*x/e^2/f/(-c*f+d*e)^2/(f*x^2+e)+sqrt(d)*(-a*d+b*c)^2*arctan(sqrt(d)*x/sqrt(c))/sqrt(c)/(-c*f+d*e)^3+1/8*(b^2*e^2*(-3*c^2*f^2-6*c*d*e*f+d^2*e^2)+2*a*b*e*f*(-c^2*f^2+6*c*d*e*f+3*d^2*e^2)-a^2*f^2*(3*c^2*f^2-10*c*d*e*f+15*d^2*e^2))*arctan(sqrt(f)*x/sqrt(e))/e^(5/2)/f^(3/2)/(-c*f+d*e)^3,1],
[(b*x^2+a)^2/(d*x^2+c)^2/(f*x^2+e)^2,x,5,-1/2*(4*a*b*c*d*e*f-b^2*c*e*(c*f+d*e)-a^2*d*f*(c*f+d*e))*x/c/d/e/(-c*f+d*e)^2/(f*x^2+e)+1/2*(-a*d+b*c)^2*x/c/d/(-c*f+d*e)/(d*x^2+c)/(f*x^2+e)-1/2*(-a*d+b*c)*(a*d*(-5*c*f+d*e)+b*c*(c*f+3*d*e))*arctan(sqrt(d)*x/sqrt(c))/c^(3/2)/sqrt(d)/(-c*f+d*e)^3-1/2*(-a*f+b*e)*(a*f*(-c*f+5*d*e)-b*e*(3*c*f+d*e))*arctan(sqrt(f)*x/sqrt(e))/e^(3/2)/sqrt(f)/(-c*f+d*e)^3,1],
[(b*x^2+a)^2/(d*x^2+c)^2/(f*x^2+e)^3,x,6,-1/4*(6*a*b*c*d*e*f-a^2*d*f*(c*f+2*d*e)-b^2*c*e*(2*c*f+d*e))*x/c/d/e/(-c*f+d*e)^2/(f*x^2+e)^2+1/2*(-a*d+b*c)^2*x/c/d/(-c*f+d*e)/(d*x^2+c)/(f*x^2+e)^2-1/8*(2*a*b*c*e*f*(c*f+11*d*e)-3*b^2*c*e^2*(3*c*f+d*e)-a^2*f*(-3*c^2*f^2+11*c*d*e*f+4*d^2*e^2))*x/c/e^2/(-c*f+d*e)^3/(f*x^2+e)-1/2*sqrt(d)*(-a*d+b*c)*(a*d*(-7*c*f+d*e)+3*b*c*(c*f+d*e))*arctan(sqrt(d)*x/sqrt(c))/c^(3/2)/(-c*f+d*e)^4-1/8*(2*a*b*e*f*(-c^2*f^2+10*c*d*e*f+15*d^2*e^2)-3*b^2*e^2*(c^2*f^2+6*c*d*e*f+d^2*e^2)-a^2*f^2*(3*c^2*f^2-14*c*d*e*f+35*d^2*e^2))*arctan(sqrt(f)*x/sqrt(e))/e^(5/2)/sqrt(f)/(-c*f+d*e)^4,1],
[(b*x^2+a)^2/(d*x^2+c)^3/(f*x^2+e)^3,x,7,-1/8*f*(b^2*c^2*e*(5*c*f+7*d*e)-2*a*b*c*d*e*(11*c*f+d*e)-a^2*d*(-2*c^2*f^2-13*c*d*e*f+3*d^2*e^2))*x/c^2/d/e/(-c*f+d*e)^3/(f*x^2+e)^2+1/4*(-a*d+b*c)^2*x/c/d/(-c*f+d*e)/(d*x^2+c)^2/(f*x^2+e)^2-1/8*(-a*d+b*c)*(a*d*(-11*c*f+3*d*e)+b*c*(3*c*f+5*d*e))*x/c^2/d/(-c*f+d*e)^2/(d*x^2+c)/(f*x^2+e)^2-1/8*f*(12*b^2*c^2*e^2*(c*f+d*e)-2*a*b*c*e*(c^2*f^2+22*c*d*e*f+d^2*e^2)-3*a^2*(c^3*f^3-5*c^2*d*e*f^2-5*c*d^2*e^2*f+d^3*e^3))*x/c^2/e^2/(-c*f+d*e)^4/(f*x^2+e)+1/8*sqrt(d)*(2*a*b*c*d*(-35*c^2*f^2-14*c*d*e*f+d^2*e^2)+3*b^2*c^2*(5*c^2*f^2+10*c*d*e*f+d^2*e^2)+3*a^2*d^2*(21*c^2*f^2-6*c*d*e*f+d^2*e^2))*arctan(sqrt(d)*x/sqrt(c))/c^(5/2)/(-c*f+d*e)^5+1/8*sqrt(f)*(2*a*b*e*f*(-c^2*f^2+14*c*d*e*f+35*d^2*e^2)-3*a^2*f^2*(c^2*f^2-6*c*d*e*f+21*d^2*e^2)-3*b^2*e^2*(c^2*f^2+10*c*d*e*f+5*d^2*e^2))*arctan(sqrt(f)*x/sqrt(e))/e^(5/2)/(-c*f+d*e)^5,1],
[(b*x^2+a)^3*(d*x^2+c)^3*(f*x^2+e)^3,x,2,a^3*c^3*e^3*x+a^2*c^2*e^2*(a*c*f+a*d*e+b*c*e)*x^3+3/5*a*c*e*(b^2*c^2*e^2+3*a*b*c*e*(c*f+d*e)+a^2*(c^2*f^2+3*c*d*e*f+d^2*e^2))*x^5+1/7*(b^3*c^3*e^3+9*a*b^2*c^2*e^2*(c*f+d*e)+9*a^2*b*c*e*(c^2*f^2+3*c*d*e*f+d^2*e^2)+a^3*(c^3*f^3+9*c^2*d*e*f^2+9*c*d^2*e^2*f+d^3*e^3))*x^7+1/3*(b^3*c^2*e^2*(c*f+d*e)+3*a*b^2*c*e*(c^2*f^2+3*c*d*e*f+d^2*e^2)+a^3*d*f*(c^2*f^2+3*c*d*e*f+d^2*e^2)+a^2*b*(c^3*f^3+9*c^2*d*e*f^2+9*c*d^2*e^2*f+d^3*e^3))*x^9+3/11*(a^3*d^2*f^2*(c*f+d*e)+b^3*c*e*(c^2*f^2+3*c*d*e*f+d^2*e^2)+3*a^2*b*d*f*(c^2*f^2+3*c*d*e*f+d^2*e^2)+a*b^2*(c^3*f^3+9*c^2*d*e*f^2+9*c*d^2*e^2*f+d^3*e^3))*x^11+1/13*(a^3*d^3*f^3+9*a^2*b*d^2*f^2*(c*f+d*e)+9*a*b^2*d*f*(c^2*f^2+3*c*d*e*f+d^2*e^2)+b^3*(c^3*f^3+9*c^2*d*e*f^2+9*c*d^2*e^2*f+d^3*e^3))*x^13+1/5*b*d*f*(a^2*d^2*f^2+3*a*b*d*f*(c*f+d*e)+b^2*(c^2*f^2+3*c*d*e*f+d^2*e^2))*x^15+3/17*b^2*d^2*f^2*(a*d*f+b*c*f+b*d*e)*x^17+1/19*b^3*d^3*f^3*x^19,1],
[(b*x^2+a)^3*(d*x^2+c)^3/(f*x^2+e),x,3,-(b^3*e^2*(-c*f+d*e)^3-3*a*b^2*e*f*(-c*f+d*e)^3+3*a^2*b*f^2*(-c*f+d*e)^3-a^3*d*f^3*(3*c^2*f^2-3*c*d*e*f+d^2*e^2))*x/f^6-1/3*(a^3*d^2*f^3*(-3*c*f+d*e)-b^3*e*(-c*f+d*e)^3+3*a*b^2*f*(-c*f+d*e)^3-3*a^2*b*d*f^2*(3*c^2*f^2-3*c*d*e*f+d^2*e^2))*x^3/f^5+1/5*(a^3*d^3*f^3-3*a^2*b*d^2*f^2*(-3*c*f+d*e)-b^3*(-c*f+d*e)^3+3*a*b^2*d*f*(3*c^2*f^2-3*c*d*e*f+d^2*e^2))*x^5/f^4+1/7*b*d*(3*a^2*d^2*f^2-3*a*b*d*f*(-3*c*f+d*e)+b^2*(3*c^2*f^2-3*c*d*e*f+d^2*e^2))*x^7/f^3-1/9*b^2*d^2*(-3*a*d*f-3*b*c*f+b*d*e)*x^9/f^2+1/11*b^3*d^3*x^11/f+(-a*f+b*e)^3*(-c*f+d*e)^3*arctan(sqrt(f)*x/sqrt(e))/sqrt(e)/f^(13/2),1],
[(b*x^2+a)^3*(d*x^2+c)^3/(f*x^2+e)^2,x,4,-(a^3*d^2*f^3*(-3*c*f+2*d*e)-9*a^2*b*d*f^2*(-c*f+d*e)^2-b^3*e*(-2*c*f+5*d*e)*(-c*f+d*e)^2+3*a*b^2*f*(-c*f+d*e)^2*(-c*f+4*d*e))*x/f^6-1/3*(-a*d*f-b*c*f+b*d*e)*(a^2*d^2*f^2-a*b*d*f*(-8*c*f+5*d*e)+b^2*(c^2*f^2-5*c*d*e*f+4*d^2*e^2))*x^3/f^5+3/5*b*d*(a^2*d^2*f^2-a*b*d*f*(-3*c*f+2*d*e)+b^2*(-c*f+d*e)^2)*x^5/f^4-1/7*b^2*d^2*(-3*a*d*f-3*b*c*f+2*b*d*e)*x^7/f^3+1/9*b^3*d^3*x^9/f^2+1/2*(-a*f+b*e)^3*(-c*f+d*e)^3*x/e/f^6/(f*x^2+e)-1/2*(-a*f+b*e)^2*(-c*f+d*e)^2*(b*e*(-5*c*f+11*d*e)-a*f*(c*f+5*d*e))*arctan(sqrt(f)*x/sqrt(e))/e^(3/2)/f^(13/2),1],
[(b*x^2+a)^3*(d*x^2+c)^3/(f*x^2+e)^3,x,5,(a^3*d^3*f^3-9*a^2*b*d^2*f^2*(-c*f+d*e)+9*a*b^2*d*f*(c^2*f^2-3*c*d*e*f+2*d^2*e^2)-b^3*(-c^3*f^3+9*c^2*d*e*f^2-18*c*d^2*e^2*f+10*d^3*e^3))*x/f^6+b*d*(a^2*d^2*f^2-3*a*b*d*f*(-c*f+d*e)+b^2*(c^2*f^2-3*c*d*e*f+2*d^2*e^2))*x^3/f^5-3/5*b^2*d^2*(-a*d*f-b*c*f+b*d*e)*x^5/f^4+1/7*b^3*d^3*x^7/f^3+1/4*(-a*f+b*e)^3*(-c*f+d*e)^3*x/e/f^6/(f*x^2+e)^2-3/8*(-a*f+b*e)^2*(-c*f+d*e)^2*(b*e*(-3*c*f+7*d*e)-a*f*(c*f+3*d*e))*x/e^2/f^6/(f*x^2+e)-3/8*(-a*f+b*e)*(-c*f+d*e)*(2*a*b*e*f*(-c^2*f^2-6*c*d*e*f+15*d^2*e^2)-a^2*f^2*(c^2*f^2+2*c*d*e*f+5*d^2*e^2)-b^2*e^2*(5*c^2*f^2-30*c*d*e*f+33*d^2*e^2))*arctan(sqrt(f)*x/sqrt(e))/e^(5/2)/f^(13/2),1],
[(b*x^2+a)^3*(d*x^2+c)^3/(f*x^2+e)^4,x,6,b*d*(3*a^2*d^2*f^2-3*a*b*d*f*(-3*c*f+4*d*e)+b^2*(3*c^2*f^2-12*c*d*e*f+10*d^2*e^2))*x/f^6-1/3*b^2*d^2*(-3*a*d*f-3*b*c*f+4*b*d*e)*x^3/f^5+1/5*b^3*d^3*x^5/f^4+1/6*(-a*f+b*e)^3*(-c*f+d*e)^3*x/e/f^6/(f*x^2+e)^3-1/24*(-a*f+b*e)^2*(-c*f+d*e)^2*(b*e*(-13*c*f+31*d*e)-a*f*(5*c*f+13*d*e))*x/e^2/f^6/(f*x^2+e)^2-1/16*(-a*f+b*e)*(-c*f+d*e)*(4*a*b*e*f*(-2*c^2*f^2-5*c*d*e*f+19*d^2*e^2)-a^2*f^2*(5*c^2*f^2+8*c*d*e*f+11*d^2*e^2)-b^2*e^2*(11*c^2*f^2-76*c*d*e*f+89*d^2*e^2))*x/e^3/f^6/(f*x^2+e)-1/16*(b^3*e^3*(-5*c^3*f^3+105*c^2*d*e*f^2-315*c*d^2*e^2*f+231*d^3*e^3)+3*a^2*b*e*f^2*(-c^3*f^3-3*c^2*d*e*f^2-15*c*d^2*e^2*f+35*d^3*e^3)-3*a*b^2*e^2*f*(c^3*f^3+15*c^2*d*e*f^2-105*c*d^2*e^2*f+105*d^3*e^3)-a^3*f^3*(5*c^3*f^3+3*c^2*d*e*f^2+3*c*d^2*e^2*f+5*d^3*e^3))*arctan(sqrt(f)*x/sqrt(e))/e^(7/2)/f^(13/2),1],
[(b*x^2+a)^3/(d*x^2+c)/(f*x^2+e),x,5,-b^2*(-3*a*d*f+b*c*f+b*d*e)*x/d^2/f^2+1/3*b^3*x^3/d/f-(-a*d+b*c)^3*arctan(sqrt(d)*x/sqrt(c))/sqrt(c)/d^(5/2)/(-c*f+d*e)+(-a*f+b*e)^3*arctan(sqrt(f)*x/sqrt(e))/sqrt(e)/f^(5/2)/(-c*f+d*e),1],
[(b*x^2+a)^3/(d*x^2+c)/(f*x^2+e)^2,x,7,b^3*x/d/f^2+1/2*(-a*f+b*e)^3*x/e/f^2/(-c*f+d*e)/(f*x^2+e)-(-a*d+b*c)^3*arctan(sqrt(d)*x/sqrt(c))/sqrt(c)/d^(3/2)/(-c*f+d*e)^2-1/2*(-a*f+b*e)^2*(b*e*(-5*c*f+3*d*e)+a*f*(-c*f+3*d*e))*arctan(sqrt(f)*x/sqrt(e))/e^(3/2)/f^(5/2)/(-c*f+d*e)^2,1],
[(b*x^2+a)^3/(d*x^2+c)/(f*x^2+e)^3,x,6,1/4*(-a*f+b*e)^3*x/e/f^2/(-c*f+d*e)/(f*x^2+e)^2-1/8*(-a*f+b*e)^2*(b*e*(-9*c*f+5*d*e)+a*f*(-3*c*f+7*d*e))*x/e^2/f^2/(-c*f+d*e)^2/(f*x^2+e)-(-a*d+b*c)^3*arctan(sqrt(d)*x/sqrt(c))/sqrt(c)/sqrt(d)/(-c*f+d*e)^3+1/8*(-a*f+b*e)*(2*a*b*e*f*(3*c^2*f^2-14*c*d*e*f+3*d^2*e^2)+a^2*f^2*(3*c^2*f^2-10*c*d*e*f+15*d^2*e^2)+b^2*e^2*(15*c^2*f^2-10*c*d*e*f+3*d^2*e^2))*arctan(sqrt(f)*x/sqrt(e))/e^(5/2)/f^(5/2)/(-c*f+d*e)^3,1],
[(b*x^2+a)^3/(d*x^2+c)^2/(f*x^2+e)^2,x,6,-1/2*(6*a^2*b*c*d^2*e*f^2-3*a*b^2*c*d*e*f*(c*f+d*e)-a^3*d^2*f^2*(c*f+d*e)+b^3*(c^3*e*f^2+c*d^2*e^3))*x/c/d^2/e/f/(-c*f+d*e)^2/(f*x^2+e)-1/2*(-a*d+b*c)^3*x/c/d^2/(-c*f+d*e)/(d*x^2+c)/(f*x^2+e)+1/2*(-a*d+b*c)^2*(a*d*(-5*c*f+d*e)+b*c*(-c*f+5*d*e))*arctan(sqrt(d)*x/sqrt(c))/c^(3/2)/d^(3/2)/(-c*f+d*e)^3+1/2*(-a*f+b*e)^2*(b*e*(-5*c*f+d*e)+a*f*(-c*f+5*d*e))*arctan(sqrt(f)*x/sqrt(e))/e^(3/2)/f^(3/2)/(-c*f+d*e)^3,1],
[(b*x^2+a)^3/(d*x^2+c)^2/(f*x^2+e)^3,x,7,-1/4*(9*a^2*b*c*d^2*e*f^2-a^3*d^2*f^2*(c*f+2*d*e)-3*a*b^2*c*d*e*f*(2*c*f+d*e)+b^3*(2*c^3*e*f^2+c*d^2*e^3))*x/c/d^2/e/f/(-c*f+d*e)^2/(f*x^2+e)^2-1/2*(-a*d+b*c)^3*x/c/d^2/(-c*f+d*e)/(d*x^2+c)/(f*x^2+e)^2-1/8*(3*a^2*b*c*d*e*f^2*(c*f+11*d*e)-9*a*b^2*c*d*e^2*f*(3*c*f+d*e)-b^3*c*e^2*(-4*c^2*f^2-9*c*d*e*f+d^2*e^2)-a^3*d*f^2*(-3*c^2*f^2+11*c*d*e*f+4*d^2*e^2))*x/c/d/e^2/f/(-c*f+d*e)^3/(f*x^2+e)+1/2*(-a*d+b*c)^2*(a*d*(-7*c*f+d*e)+b*c*(c*f+5*d*e))*arctan(sqrt(d)*x/sqrt(c))/c^(3/2)/sqrt(d)/(-c*f+d*e)^4+1/8*(-a*f+b*e)*(b^2*e^2*(-15*c^2*f^2-10*c*d*e*f+d^2*e^2)+2*a*b*e*f*(-3*c^2*f^2+22*c*d*e*f+5*d^2*e^2)-a^2*f^2*(3*c^2*f^2-14*c*d*e*f+35*d^2*e^2))*arctan(sqrt(f)*x/sqrt(e))/e^(5/2)/f^(3/2)/(-c*f+d*e)^4,1],
[(b*x^2+a)^3/(d*x^2+c)^3/(f*x^2+e)^3,x,8,1/8*(-a*d+b*c)^2*(a*d*(-11*c*f+3*d*e)+b*c*(-c*f+9*d*e))*x/c^2/(-c*f+d*e)^4/(d*x^2+c)+1/4*(6*a^2*b*c*d^2*e*f^2-3*a*b^2*c*d*e*f*(c*f+d*e)-a^3*d^2*f^2*(c*f+d*e)+b^3*(c^3*e*f^2+c*d^2*e^3))*x/c/d^2/e/(-c*f+d*e)^3/(f*x^2+e)^2-1/4*(-a*d+b*c)^3*x/c/d^2/(-c*f+d*e)/(d*x^2+c)^2/(f*x^2+e)^2+1/8*(3*a^2*b*c*d*e*f^2*(c*f+15*d*e)-3*a*b^2*c*d*e^2*f*(9*c*f+7*d*e)-a^3*d*f^2*(-3*c^2*f^2+15*c*d*e*f+4*d^2*e^2)+b^3*c*e^2*(4*c^2*f^2+9*c*d*e*f+3*d^2*e^2))*x/c/d/e^2/(-c*f+d*e)^4/(f*x^2+e)-3/8*(-a*d+b*c)*(2*a*b*c*d*(-7*c^2*f^2-10*c*d*e*f+d^2*e^2)+b^2*c^2*(c^2*f^2+10*c*d*e*f+5*d^2*e^2)+a^2*d^2*(21*c^2*f^2-6*c*d*e*f+d^2*e^2))*arctan(sqrt(d)*x/sqrt(c))/c^(5/2)/sqrt(d)/(-c*f+d*e)^5-3/8*(-a*f+b*e)*(2*a*b*e*f*(-c^2*f^2+10*c*d*e*f+7*d^2*e^2)-a^2*f^2*(c^2*f^2-6*c*d*e*f+21*d^2*e^2)-b^2*e^2*(5*c^2*f^2+10*c*d*e*f+d^2*e^2))*arctan(sqrt(f)*x/sqrt(e))/e^(5/2)/sqrt(f)/(-c*f+d*e)^5,1],
[1/(b*x^2+a)/(d*x^2+c)/(f*x^2+e),x,5,b^(3/2)*arctan(sqrt(b)*x/sqrt(a))/sqrt(a)/(-a*d+b*c)/(-a*f+b*e)-d^(3/2)*arctan(sqrt(d)*x/sqrt(c))/sqrt(c)/(-a*d+b*c)/(-c*f+d*e)+f^(3/2)*arctan(sqrt(f)*x/sqrt(e))/sqrt(e)/(-a*f+b*e)/(-c*f+d*e),1],
[1/(b*x^2+a)/(d*x^2+c)/(f*x^2+e)^2,x,6,1/2*f^2*x/e/(-a*f+b*e)/(-c*f+d*e)/(f*x^2+e)+b^(5/2)*arctan(sqrt(b)*x/sqrt(a))/sqrt(a)/(-a*d+b*c)/(-a*f+b*e)^2-d^(5/2)*arctan(sqrt(d)*x/sqrt(c))/sqrt(c)/(-a*d+b*c)/(-c*f+d*e)^2+1/2*f^(3/2)*(b*e*(-3*c*f+5*d*e)-a*f*(-c*f+3*d*e))*arctan(sqrt(f)*x/sqrt(e))/e^(3/2)/(-a*f+b*e)^2/(-c*f+d*e)^2,1],
[1/(b*x^2+a)/(d*x^2+c)/(f*x^2+e)^3,x,7,1/4*f^2*x/e/(-a*f+b*e)/(-c*f+d*e)/(f*x^2+e)^2+1/8*f^2*(b*e*(-7*c*f+11*d*e)-a*f*(-3*c*f+7*d*e))*x/e^2/(-a*f+b*e)^2/(-c*f+d*e)^2/(f*x^2+e)+b^(7/2)*arctan(sqrt(b)*x/sqrt(a))/sqrt(a)/(-a*d+b*c)/(-a*f+b*e)^3-d^(7/2)*arctan(sqrt(d)*x/sqrt(c))/sqrt(c)/(-a*d+b*c)/(-c*f+d*e)^3+1/8*f^(3/2)*(a^2*f^2*(3*c^2*f^2-10*c*d*e*f+15*d^2*e^2)-2*a*b*e*f*(5*c^2*f^2-18*c*d*e*f+21*d^2*e^2)+b^2*e^2*(15*c^2*f^2-42*c*d*e*f+35*d^2*e^2))*arctan(sqrt(f)*x/sqrt(e))/e^(5/2)/(-a*f+b*e)^3/(-c*f+d*e)^3,1],
[1/(b*x^2+a)/(d*x^2+c)^2/(f*x^2+e)^2,x,7,-1/2*d^3*x/c/(-a*d+b*c)/(-c*f+d*e)^2/(d*x^2+c)-1/2*f^3*x/e/(-a*f+b*e)/(-c*f+d*e)^2/(f*x^2+e)+b^(7/2)*arctan(sqrt(b)*x/sqrt(a))/sqrt(a)/(-a*d+b*c)^2/(-a*f+b*e)^2-1/2*d^(5/2)*(b*c*(-7*c*f+3*d*e)-a*d*(-5*c*f+d*e))*arctan(sqrt(d)*x/sqrt(c))/c^(3/2)/(-a*d+b*c)^2/(-c*f+d*e)^3-1/2*f^(5/2)*(b*e*(-3*c*f+7*d*e)-a*f*(-c*f+5*d*e))*arctan(sqrt(f)*x/sqrt(e))/e^(3/2)/(-a*f+b*e)^2/(-c*f+d*e)^3,1],
[1/(b*x^2+a)/(d*x^2+c)^2/(f*x^2+e)^3,x,8,-1/2*d^4*x/c/(-a*d+b*c)/(-c*f+d*e)^3/(d*x^2+c)-1/4*f^3*x/e/(-a*f+b*e)/(-c*f+d*e)^2/(f*x^2+e)^2-1/8*f^3*(b*e*(-7*c*f+15*d*e)-a*f*(-3*c*f+11*d*e))*x/e^2/(-a*f+b*e)^2/(-c*f+d*e)^3/(f*x^2+e)+b^(9/2)*arctan(sqrt(b)*x/sqrt(a))/sqrt(a)/(-a*d+b*c)^2/(-a*f+b*e)^3+1/2*d^(7/2)*(a*d*(-7*c*f+d*e)-3*b*c*(-3*c*f+d*e))*arctan(sqrt(d)*x/sqrt(c))/c^(3/2)/(-a*d+b*c)^2/(-c*f+d*e)^4-1/8*f^(5/2)*(a^2*f^2*(3*c^2*f^2-14*c*d*e*f+35*d^2*e^2)-2*a*b*e*f*(5*c^2*f^2-26*c*d*e*f+45*d^2*e^2)+3*b^2*e^2*(5*c^2*f^2-18*c*d*e*f+21*d^2*e^2))*arctan(sqrt(f)*x/sqrt(e))/e^(5/2)/(-a*f+b*e)^3/(-c*f+d*e)^4,1],
[1/(b*x^2+a)/(d*x^2+c)^3/(f*x^2+e)^3,x,9,-1/4*d^4*x/c/(-a*d+b*c)/(-c*f+d*e)^3/(d*x^2+c)^2-1/8*d^4*(b*c*(-19*c*f+7*d*e)-3*a*d*(-5*c*f+d*e))*x/c^2/(-a*d+b*c)^2/(-c*f+d*e)^4/(d*x^2+c)+1/4*f^4*x/e/(-a*f+b*e)/(-c*f+d*e)^3/(f*x^2+e)^2+1/8*f^4*(b*e*(-7*c*f+19*d*e)-3*a*f*(-c*f+5*d*e))*x/e^2/(-a*f+b*e)^2/(-c*f+d*e)^4/(f*x^2+e)+b^(11/2)*arctan(sqrt(b)*x/sqrt(a))/sqrt(a)/(-a*d+b*c)^3/(-a*f+b*e)^3-1/8*d^(7/2)*(3*a^2*d^2*(21*c^2*f^2-6*c*d*e*f+d^2*e^2)+3*b^2*c^2*(33*c^2*f^2-22*c*d*e*f+5*d^2*e^2)-2*a*b*c*d*(77*c^2*f^2-34*c*d*e*f+5*d^2*e^2))*arctan(sqrt(d)*x/sqrt(c))/c^(5/2)/(-a*d+b*c)^3/(-c*f+d*e)^5+1/8*f^(7/2)*(3*a^2*f^2*(c^2*f^2-6*c*d*e*f+21*d^2*e^2)-2*a*b*e*f*(5*c^2*f^2-34*c*d*e*f+77*d^2*e^2)+3*b^2*e^2*(5*c^2*f^2-22*c*d*e*f+33*d^2*e^2))*arctan(sqrt(f)*x/sqrt(e))/e^(5/2)/(-a*f+b*e)^3/(-c*f+d*e)^5,1],
[1/(b*x^2+a)^2/(d*x^2+c)^2/(f*x^2+e)^2,x,8,1/2*b^4*x/a/(-a*d+b*c)^2/(-a*f+b*e)^2/(b*x^2+a)+1/2*d^4*x/c/(-a*d+b*c)^2/(-c*f+d*e)^2/(d*x^2+c)+1/2*f^4*x/e/(-a*f+b*e)^2/(-c*f+d*e)^2/(f*x^2+e)+1/2*b^(7/2)*(b^2*c*e+9*a^2*d*f-5*a*b*(c*f+d*e))*arctan(sqrt(b)*x/sqrt(a))/a^(3/2)/(-a*d+b*c)^3/(-a*f+b*e)^3+1/2*d^(7/2)*(b*c*(-9*c*f+5*d*e)-a*d*(-5*c*f+d*e))*arctan(sqrt(d)*x/sqrt(c))/c^(3/2)/(-a*d+b*c)^3/(-c*f+d*e)^3+1/2*f^(7/2)*(b*e*(-5*c*f+9*d*e)-a*f*(-c*f+5*d*e))*arctan(sqrt(f)*x/sqrt(e))/e^(3/2)/(-a*f+b*e)^3/(-c*f+d*e)^3,1],
[sqrt(b*x^2+a)*(d*x^2+c)*(f*x^2+e)^3,x,7,1/256*(128*b^4*c*e^3+7*a^4*d*f^3+48*a^2*b^2*e*f*(c*f+d*e)-10*a^3*b*f^2*(c*f+3*d*e)-32*a*b^3*e^2*(3*c*f+d*e))*x*sqrt(b*x^2+a)/b^4-1/128*(7*a^3*d*f^3+48*a*b^2*e*f*(c*f+d*e)-10*a^2*b*f^2*(c*f+3*d*e)-32*b^3*e^2*(3*c*f+d*e))*x*(b*x^2+a)^(3/2)/b^4+1/96*f*(7*a^2*d*f^2+48*b^2*e*(c*f+d*e)-10*a*b*f*(c*f+3*d*e))*x^3*(b*x^2+a)^(3/2)/b^3-1/80*f^2*(7*a*d*f-10*b*(c*f+3*d*e))*x^5*(b*x^2+a)^(3/2)/b^2+1/10*d*f^3*x^7*(b*x^2+a)^(3/2)/b+1/256*a*(128*b^4*c*e^3+7*a^4*d*f^3+48*a^2*b^2*e*f*(c*f+d*e)-10*a^3*b*f^2*(c*f+3*d*e)-32*a*b^3*e^2*(3*c*f+d*e))*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(9/2),1],
[sqrt(b*x^2+a)*(d*x^2+c)*(f*x^2+e)^2,x,6,1/128*(64*b^3*c*e^2-5*a^3*d*f^2+8*a^2*b*f*(c*f+2*d*e)-16*a*b^2*e*(2*c*f+d*e))*x*sqrt(b*x^2+a)/b^3+1/64*(5*a^2*d*f^2-8*a*b*f*(c*f+2*d*e)+16*b^2*e*(2*c*f+d*e))*x*(b*x^2+a)^(3/2)/b^3-1/48*f*(5*a*d*f-8*b*(c*f+2*d*e))*x^3*(b*x^2+a)^(3/2)/b^2+1/8*d*f^2*x^5*(b*x^2+a)^(3/2)/b+1/128*a*(64*b^3*c*e^2-5*a^3*d*f^2+8*a^2*b*f*(c*f+2*d*e)-16*a*b^2*e*(2*c*f+d*e))*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(7/2),1],
[sqrt(b*x^2+a)*(d*x^2+c)*(f*x^2+e),x,5,1/16*(8*b^2*c*e+a^2*d*f-2*a*b*(c*f+d*e))*x*sqrt(b*x^2+a)/b^2-1/8*(a*d*f-2*b*(c*f+d*e))*x*(b*x^2+a)^(3/2)/b^2+1/6*d*f*x^3*(b*x^2+a)^(3/2)/b+1/16*a*(8*b^2*c*e+a^2*d*f-2*a*b*(c*f+d*e))*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(5/2),1],
[sqrt(b*x^2+a)*(d*x^2+c)/(f*x^2+e),x,6,1/2*d*x*sqrt(b*x^2+a)/f-1/2*(-a*d*f-2*b*c*f+2*b*d*e)*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/sqrt(b)/f^2+sqrt(-a*f+b*e)*(-c*f+d*e)*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/sqrt(e)/f^2,1],
[sqrt(b*x^2+a)*(d*x^2+c)/(f*x^2+e)^2,x,6,-1/2*(-c*f+d*e)*x*sqrt(b*x^2+a)/e/f/(f*x^2+e)+sqrt(b)*d*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/f^2-1/2*(2*b*d*e^2-a*f*(c*f+d*e))*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/e^(3/2)/f^2/sqrt(-a*f+b*e),1],
[sqrt(b*x^2+a)*(d*x^2+c)/(f*x^2+e)^3,x,4,1/4*(-c*f+d*e)*x*(b*x^2+a)^(3/2)/e/(-a*f+b*e)/(f*x^2+e)^2+1/8*(-3*a*c*f-a*d*e+4*b*c*e)*x*sqrt(b*x^2+a)/e^2/(-a*f+b*e)/(f*x^2+e)+1/8*a*(-3*a*c*f-a*d*e+4*b*c*e)*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/e^(5/2)/(-a*f+b*e)^(3/2),1],
[sqrt(b*x^2+a)*(d*x^2+c)/(f*x^2+e)^4,x,5,-1/6*(-c*f+d*e)*x*sqrt(b*x^2+a)/e/f/(f*x^2+e)^3+1/24*(2*b*e*(2*c*f+d*e)-a*f*(5*c*f+d*e))*x*sqrt(b*x^2+a)/e^2/f/(-a*f+b*e)/(f*x^2+e)^2+1/48*(4*b^2*e^2*(2*c*f+d*e)+3*a^2*f^2*(5*c*f+d*e)-2*a*b*e*f*(13*c*f+2*d*e))*x*sqrt(b*x^2+a)/e^3/f/(-a*f+b*e)^2/(f*x^2+e)+1/16*a*(8*b^2*c*e^2+a^2*f*(5*c*f+d*e)-2*a*b*e*(6*c*f+d*e))*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/e^(7/2)/(-a*f+b*e)^(5/2),1],
[sqrt(b*x^2+a)*(d*x^2+c)^2*(f*x^2+e)^3,x,8,1/1024*(512*b^5*c^2*e^3-21*a^5*d^2*f^3+28*a^4*b*d*f^2*(2*c*f+3*d*e)-128*a*b^4*c*e^2*(3*c*f+2*d*e)-40*a^3*b^2*f*(c^2*f^2+6*c*d*e*f+3*d^2*e^2)+64*a^2*b^3*e*(3*c^2*f^2+6*c*d*e*f+d^2*e^2))*x*sqrt(b*x^2+a)/b^5+1/512*(21*a^4*d^2*f^3-28*a^3*b*d*f^2*(2*c*f+3*d*e)+128*b^4*c*e^2*(3*c*f+2*d*e)+40*a^2*b^2*f*(c^2*f^2+6*c*d*e*f+3*d^2*e^2)-64*a*b^3*e*(3*c^2*f^2+6*c*d*e*f+d^2*e^2))*x*(b*x^2+a)^(3/2)/b^5-1/384*(21*a^3*d^2*f^3-28*a^2*b*d*f^2*(2*c*f+3*d*e)+40*a*b^2*f*(c^2*f^2+6*c*d*e*f+3*d^2*e^2)-64*b^3*e*(3*c^2*f^2+6*c*d*e*f+d^2*e^2))*x^3*(b*x^2+a)^(3/2)/b^4+1/320*f*(21*a^2*d^2*f^2-28*a*b*d*f*(2*c*f+3*d*e)+40*b^2*(c^2*f^2+6*c*d*e*f+3*d^2*e^2))*x^5*(b*x^2+a)^(3/2)/b^3+1/40*d*f^2*(-3*a*d*f+8*b*c*f+12*b*d*e)*x^7*(b*x^2+a)^(3/2)/b^2+1/12*d^2*f^3*x^9*(b*x^2+a)^(3/2)/b+1/1024*a*(512*b^5*c^2*e^3-21*a^5*d^2*f^3+28*a^4*b*d*f^2*(2*c*f+3*d*e)-128*a*b^4*c*e^2*(3*c*f+2*d*e)-40*a^3*b^2*f*(c^2*f^2+6*c*d*e*f+3*d^2*e^2)+64*a^2*b^3*e*(3*c^2*f^2+6*c*d*e*f+d^2*e^2))*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(11/2),1],
[sqrt(b*x^2+a)*(d*x^2+c)^2*(f*x^2+e)^2,x,7,1/256*(128*b^4*c^2*e^2+7*a^4*d^2*f^2-64*a*b^3*c*e*(c*f+d*e)-20*a^3*b*d*f*(c*f+d*e)+16*a^2*b^2*(c^2*f^2+4*c*d*e*f+d^2*e^2))*x*sqrt(b*x^2+a)/b^4-1/128*(7*a^3*d^2*f^2-64*b^3*c*e*(c*f+d*e)-20*a^2*b*d*f*(c*f+d*e)+16*a*b^2*(c^2*f^2+4*c*d*e*f+d^2*e^2))*x*(b*x^2+a)^(3/2)/b^4+1/96*(7*a^2*d^2*f^2-20*a*b*d*f*(c*f+d*e)+16*b^2*(c^2*f^2+4*c*d*e*f+d^2*e^2))*x^3*(b*x^2+a)^(3/2)/b^3-1/80*d*f*(7*a*d*f-20*b*(c*f+d*e))*x^5*(b*x^2+a)^(3/2)/b^2+1/10*d^2*f^2*x^7*(b*x^2+a)^(3/2)/b+1/256*a*(128*b^4*c^2*e^2+7*a^4*d^2*f^2-64*a*b^3*c*e*(c*f+d*e)-20*a^3*b*d*f*(c*f+d*e)+16*a^2*b^2*(c^2*f^2+4*c*d*e*f+d^2*e^2))*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(9/2),1],
[sqrt(b*x^2+a)*(d*x^2+c)^2*(f*x^2+e),x,6,1/128*(64*b^3*c^2*e-5*a^3*d^2*f-16*a*b^2*c*(c*f+2*d*e)+8*a^2*b*d*(2*c*f+d*e))*x*sqrt(b*x^2+a)/b^3+1/64*(5*a^2*d^2*f+16*b^2*c*(c*f+2*d*e)-8*a*b*d*(2*c*f+d*e))*x*(b*x^2+a)^(3/2)/b^3-1/48*d*(5*a*d*f-8*b*(2*c*f+d*e))*x^3*(b*x^2+a)^(3/2)/b^2+1/8*d^2*f*x^5*(b*x^2+a)^(3/2)/b+1/128*a*(64*b^3*c^2*e-5*a^3*d^2*f-16*a*b^2*c*(c*f+2*d*e)+8*a^2*b*d*(2*c*f+d*e))*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(7/2),1],
[sqrt(b*x^2+a)*(d*x^2+c)^2/(f*x^2+e),x,8,-1/8*d*(-a*d*f-8*b*c*f+4*b*d*e)*x*sqrt(b*x^2+a)/b/f^2+1/4*d^2*x^3*sqrt(b*x^2+a)/f-1/8*(a^2*d^2*f^2+4*a*b*d*f*(-2*c*f+d*e)-8*b^2*(-c*f+d*e)^2)*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(3/2)/f^3-sqrt(-a*f+b*e)*(-c*f+d*e)^2*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/sqrt(e)/f^3,1],
[sqrt(b*x^2+a)*(d*x^2+c)^2/(f*x^2+e)^2,x,8,1/2*d^2*x*sqrt(b*x^2+a)/f^2+1/2*(-c*f+d*e)^2*x*sqrt(b*x^2+a)/e/f^2/(f*x^2+e)-1/2*d*(-a*d*f-4*b*c*f+4*b*d*e)*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/sqrt(b)/f^3+1/2*(-c*f+d*e)*(4*b*d*e^2-a*f*(c*f+3*d*e))*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/e^(3/2)/f^3/sqrt(-a*f+b*e),1],
[sqrt(b*x^2+a)*(d*x^2+c)^2/(f*x^2+e)^3,x,8,1/4*(-c*f+d*e)^2*x*sqrt(b*x^2+a)/e/f^2/(f*x^2+e)^2-1/8*(-c*f+d*e)*(2*b*e*(c*f+3*d*e)-a*f*(3*c*f+5*d*e))*x*sqrt(b*x^2+a)/e^2/f^2/(-a*f+b*e)/(f*x^2+e)+sqrt(b)*d^2*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/f^3-1/8*(8*b^2*d^2*e^4-4*a*b*e*f*(c^2*f^2+3*d^2*e^2)+a^2*f^2*(3*c^2*f^2+2*c*d*e*f+3*d^2*e^2))*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/e^(5/2)/f^3/(-a*f+b*e)^(3/2),1],
[sqrt(b*x^2+a)*(d*x^2+c)^2/(f*x^2+e)^4,x,5,1/6*(-c*f+d*e)^2*x*sqrt(b*x^2+a)/e/f^2/(f*x^2+e)^3-1/24*(-c*f+d*e)*(4*b*e*(c*f+2*d*e)-a*f*(5*c*f+7*d*e))*x*sqrt(b*x^2+a)/e^2/f^2/(-a*f+b*e)/(f*x^2+e)^2+1/48*(8*b^2*e^2*(c^2*f^2+c*d*e*f+d^2*e^2)+3*a^2*f^2*(5*c^2*f^2+2*c*d*e*f+d^2*e^2)-2*a*b*e*f*(13*c^2*f^2+4*c*d*e*f+7*d^2*e^2))*x*sqrt(b*x^2+a)/e^3/f^2/(-a*f+b*e)^2/(f*x^2+e)+1/16*a*(8*b^2*c^2*e^2-4*a*b*c*e*(3*c*f+d*e)+a^2*(5*c^2*f^2+2*c*d*e*f+d^2*e^2))*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/e^(7/2)/(-a*f+b*e)^(5/2),1],
[sqrt(b*x^2+a)*(d*x^2+c)^3*(f*x^2+e)^2,x,8,1/1024*(512*b^5*c^3*e^2-21*a^5*d^3*f^2-128*a*b^4*c^2*e*(2*c*f+3*d*e)+28*a^4*b*d^2*f*(3*c*f+2*d*e)+64*a^2*b^3*c*(c^2*f^2+6*c*d*e*f+3*d^2*e^2)-40*a^3*b^2*d*(3*c^2*f^2+6*c*d*e*f+d^2*e^2))*x*sqrt(b*x^2+a)/b^5+1/512*(21*a^4*d^3*f^2+128*b^4*c^2*e*(2*c*f+3*d*e)-28*a^3*b*d^2*f*(3*c*f+2*d*e)-64*a*b^3*c*(c^2*f^2+6*c*d*e*f+3*d^2*e^2)+40*a^2*b^2*d*(3*c^2*f^2+6*c*d*e*f+d^2*e^2))*x*(b*x^2+a)^(3/2)/b^5-1/384*(21*a^3*d^3*f^2-28*a^2*b*d^2*f*(3*c*f+2*d*e)-64*b^3*c*(c^2*f^2+6*c*d*e*f+3*d^2*e^2)+40*a*b^2*d*(3*c^2*f^2+6*c*d*e*f+d^2*e^2))*x^3*(b*x^2+a)^(3/2)/b^4+1/320*d*(21*a^2*d^2*f^2-28*a*b*d*f*(3*c*f+2*d*e)+40*b^2*(3*c^2*f^2+6*c*d*e*f+d^2*e^2))*x^5*(b*x^2+a)^(3/2)/b^3+1/40*d^2*f*(-3*a*d*f+12*b*c*f+8*b*d*e)*x^7*(b*x^2+a)^(3/2)/b^2+1/12*d^3*f^2*x^9*(b*x^2+a)^(3/2)/b+1/1024*a*(512*b^5*c^3*e^2-21*a^5*d^3*f^2-128*a*b^4*c^2*e*(2*c*f+3*d*e)+28*a^4*b*d^2*f*(3*c*f+2*d*e)+64*a^2*b^3*c*(c^2*f^2+6*c*d*e*f+3*d^2*e^2)-40*a^3*b^2*d*(3*c^2*f^2+6*c*d*e*f+d^2*e^2))*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(11/2),1],
[sqrt(b*x^2+a)*(d*x^2+c)^3*(f*x^2+e),x,7,1/256*(128*b^4*c^3*e+7*a^4*d^3*f+48*a^2*b^2*c*d*(c*f+d*e)-32*a*b^3*c^2*(c*f+3*d*e)-10*a^3*b*d^2*(3*c*f+d*e))*x*sqrt(b*x^2+a)/b^4-1/128*(7*a^3*d^3*f+48*a*b^2*c*d*(c*f+d*e)-32*b^3*c^2*(c*f+3*d*e)-10*a^2*b*d^2*(3*c*f+d*e))*x*(b*x^2+a)^(3/2)/b^4+1/96*d*(7*a^2*d^2*f+48*b^2*c*(c*f+d*e)-10*a*b*d*(3*c*f+d*e))*x^3*(b*x^2+a)^(3/2)/b^3-1/80*d^2*(7*a*d*f-10*b*(3*c*f+d*e))*x^5*(b*x^2+a)^(3/2)/b^2+1/10*d^3*f*x^7*(b*x^2+a)^(3/2)/b+1/256*a*(128*b^4*c^3*e+7*a^4*d^3*f+48*a^2*b^2*c*d*(c*f+d*e)-32*a*b^3*c^2*(c*f+3*d*e)-10*a^3*b*d^2*(3*c*f+d*e))*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(9/2),1],
[sqrt(b*x^2+a)*(d*x^2+c)^3/(f*x^2+e),x,9,-1/16*d*(a^2*d^2*f^2+2*a*b*d*f*(-3*c*f+d*e)-8*b^2*(3*c^2*f^2-3*c*d*e*f+d^2*e^2))*x*sqrt(b*x^2+a)/b^2/f^3-1/24*d^2*(-a*d*f-18*b*c*f+6*b*d*e)*x^3*sqrt(b*x^2+a)/b/f^2+1/6*d^3*x^5*sqrt(b*x^2+a)/f+1/16*(a^3*d^3*f^3+2*a^2*b*d^2*f^2*(-3*c*f+d*e)-16*b^3*(-c*f+d*e)^3+8*a*b^2*d*f*(3*c^2*f^2-3*c*d*e*f+d^2*e^2))*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(5/2)/f^4+sqrt(-a*f+b*e)*(-c*f+d*e)^3*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/sqrt(e)/f^4,1],
[sqrt(b*x^2+a)*(d*x^2+c)^3/(f*x^2+e)^2,x,9,-1/8*d^2*(-a*d*f-12*b*c*f+8*b*d*e)*x*sqrt(b*x^2+a)/b/f^3+1/4*d^3*x^3*sqrt(b*x^2+a)/f^2-1/2*(-c*f+d*e)^3*x*sqrt(b*x^2+a)/e/f^3/(f*x^2+e)-1/8*d*(a^2*d^2*f^2+4*a*b*d*f*(-3*c*f+2*d*e)-24*b^2*(-c*f+d*e)^2)*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(3/2)/f^4-1/2*(-c*f+d*e)^2*(6*b*d*e^2-a*f*(c*f+5*d*e))*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/e^(3/2)/f^4/sqrt(-a*f+b*e),1],
[sqrt(b*x^2+a)*(d*x^2+c)^3/(f*x^2+e)^3,x,9,1/2*d^3*x*sqrt(b*x^2+a)/f^3-1/4*(-c*f+d*e)^3*x*sqrt(b*x^2+a)/e/f^3/(f*x^2+e)^2-1/8*(-c*f+d*e)^2*(3*a*f*(c*f+3*d*e)-2*b*e*(c*f+5*d*e))*x*sqrt(b*x^2+a)/e^2/f^3/(-a*f+b*e)/(f*x^2+e)-1/2*d^2*(-a*d*f-6*b*c*f+6*b*d*e)*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/sqrt(b)/f^4+1/8*(-c*f+d*e)*(24*b^2*d^2*e^4-4*a*b*e*f*(c^2*f^2+c*d*e*f+10*d^2*e^2)+3*a^2*f^2*(c^2*f^2+2*c*d*e*f+5*d^2*e^2))*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/e^(5/2)/f^4/(-a*f+b*e)^(3/2),1],
[sqrt(b*x^2+a)*(d*x^2+c)^3/(f*x^2+e)^4,x,9,-1/6*(-c*f+d*e)^3*x*sqrt(b*x^2+a)/e/f^3/(f*x^2+e)^3+1/24*(-c*f+d*e)^2*(2*b*e*(2*c*f+7*d*e)-a*f*(5*c*f+13*d*e))*x*sqrt(b*x^2+a)/e^2/f^3/(-a*f+b*e)/(f*x^2+e)^2-1/48*(-c*f+d*e)*(4*b^2*e^2*(2*c^2*f^2+5*c*d*e*f+11*d^2*e^2)+3*a^2*f^2*(5*c^2*f^2+8*c*d*e*f+11*d^2*e^2)-2*a*b*e*f*(13*c^2*f^2+19*c*d*e*f+40*d^2*e^2))*x*sqrt(b*x^2+a)/e^3/f^3/(-a*f+b*e)^2/(f*x^2+e)+sqrt(b)*d^3*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/f^4-1/16*(16*b^3*d^3*e^6-8*a*b^2*e^2*f*(c^3*f^3+5*d^3*e^3)+6*a^2*b*e*f^2*(2*c^3*f^3+c^2*d*e*f^2+5*d^3*e^3)-a^3*f^3*(5*c^3*f^3+3*c^2*d*e*f^2+3*c*d^2*e^2*f+5*d^3*e^3))*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/e^(7/2)/f^4/(-a*f+b*e)^(5/2),1],
[sqrt(b*x^2+a)/(d*x^2+c)/(f*x^2+e),x,5,-sqrt(-a*d+b*c)*arctanh(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))/sqrt(c)/(-c*f+d*e)+sqrt(-a*f+b*e)*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/sqrt(e)/(-c*f+d*e),1],
[sqrt(b*x^2+a)/(d*x^2+c)/(f*x^2+e)^2,x,6,-1/2*f*x*sqrt(b*x^2+a)/e/(-c*f+d*e)/(f*x^2+e)-d*sqrt(-a*d+b*c)*arctanh(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))/sqrt(c)/(-c*f+d*e)^2+1/2*(2*b*d*e^2-a*f*(-c*f+3*d*e))*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/e^(3/2)/sqrt(-a*f+b*e)/(-c*f+d*e)^2,1],
[sqrt(b*x^2+a)/(d*x^2+c)/(f*x^2+e)^3,x,7,-1/4*f*x*sqrt(b*x^2+a)/e/(-c*f+d*e)/(f*x^2+e)^2+1/8*f*(a*f*(-3*c*f+7*d*e)-2*b*e*(-c*f+3*d*e))*x*sqrt(b*x^2+a)/e^2/(-a*f+b*e)/(-c*f+d*e)^2/(f*x^2+e)-d^2*sqrt(-a*d+b*c)*arctanh(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))/sqrt(c)/(-c*f+d*e)^3+1/8*(8*b^2*d^2*e^4-4*a*b*e*f*(c^2*f^2-3*c*d*e*f+6*d^2*e^2)+a^2*f^2*(3*c^2*f^2-10*c*d*e*f+15*d^2*e^2))*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/e^(5/2)/(-a*f+b*e)^(3/2)/(-c*f+d*e)^3,1],
[sqrt(b*x^2+a)/(d*x^2+c)/(f*x^2+e)^4,x,8,-1/6*f*x*sqrt(b*x^2+a)/e/(-c*f+d*e)/(f*x^2+e)^3+1/24*f*(a*f*(-5*c*f+11*d*e)-2*b*e*(-2*c*f+5*d*e))*x*sqrt(b*x^2+a)/e^2/(-a*f+b*e)/(-c*f+d*e)^2/(f*x^2+e)^2-1/48*f*(4*b^2*e^2*(2*c^2*f^2-7*c*d*e*f+11*d^2*e^2)+3*a^2*f^2*(5*c^2*f^2-16*c*d*e*f+19*d^2*e^2)-2*a*b*e*f*(13*c^2*f^2-41*c*d*e*f+52*d^2*e^2))*x*sqrt(b*x^2+a)/e^3/(-a*f+b*e)^2/(-c*f+d*e)^3/(f*x^2+e)-d^3*sqrt(-a*d+b*c)*arctanh(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))/sqrt(c)/(-c*f+d*e)^4+1/16*(16*b^3*d^3*e^6+2*a^2*b*e*f^2*(-6*c^3*f^3+25*c^2*d*e*f^2-40*c*d^2*e^2*f+45*d^3*e^3)-a^3*f^3*(-5*c^3*f^3+21*c^2*d*e*f^2-35*c*d^2*e^2*f+35*d^3*e^3)-8*a*b^2*e^2*f*(-c^3*f^3+4*c^2*d*e*f^2-6*c*d^2*e^2*f+9*d^3*e^3))*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/e^(7/2)/(-a*f+b*e)^(5/2)/(-c*f+d*e)^4,1],
[sqrt(b*x^2+a)/(d*x^2+c)^2/(f*x^2+e),x,6,1/2*d*x*sqrt(b*x^2+a)/c/(-c*f+d*e)/(d*x^2+c)+1/2*(2*b*c^2*f+a*d*(-3*c*f+d*e))*arctanh(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))/c^(3/2)/sqrt(-a*d+b*c)/(-c*f+d*e)^2-f*sqrt(-a*f+b*e)*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/sqrt(e)/(-c*f+d*e)^2,1],
[sqrt(b*x^2+a)/(d*x^2+c)^2/(f*x^2+e)^2,x,8,1/2*d^2*x*sqrt(b*x^2+a)/c/(-c*f+d*e)^2/(d*x^2+c)+1/2*f^2*x*sqrt(b*x^2+a)/e/(-c*f+d*e)^2/(f*x^2+e)+1/2*d*(4*b*c^2*f+a*d*(-5*c*f+d*e))*arctanh(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))/c^(3/2)/sqrt(-a*d+b*c)/(-c*f+d*e)^3-1/2*f*(4*b*d*e^2-a*f*(-c*f+5*d*e))*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/e^(3/2)/sqrt(-a*f+b*e)/(-c*f+d*e)^3,1],
[sqrt(b*x^2+a)/(d*x^2+c)^2/(f*x^2+e)^3,x,9,1/2*d^3*x*sqrt(b*x^2+a)/c/(-c*f+d*e)^3/(d*x^2+c)+1/4*f^2*x*sqrt(b*x^2+a)/e/(-c*f+d*e)^2/(f*x^2+e)^2-1/8*f^2*(a*f*(-3*c*f+11*d*e)-2*b*e*(-c*f+5*d*e))*x*sqrt(b*x^2+a)/e^2/(-a*f+b*e)/(-c*f+d*e)^3/(f*x^2+e)+1/2*d^2*(6*b*c^2*f+a*d*(-7*c*f+d*e))*arctanh(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))/c^(3/2)/sqrt(-a*d+b*c)/(-c*f+d*e)^4-1/8*f*(24*b^2*d^2*e^4-4*a*b*e*f*(c^2*f^2-4*c*d*e*f+15*d^2*e^2)+a^2*f^2*(3*c^2*f^2-14*c*d*e*f+35*d^2*e^2))*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/e^(5/2)/(-a*f+b*e)^(3/2)/(-c*f+d*e)^4,1],
[sqrt(b*x^2+a)/(d*x^2+c)^3/(f*x^2+e),x,7,1/4*d*x*sqrt(b*x^2+a)/c/(-c*f+d*e)/(d*x^2+c)^2-1/8*d*(a*d*(-7*c*f+3*d*e)-2*b*c*(-3*c*f+d*e))*x*sqrt(b*x^2+a)/c^2/(-a*d+b*c)/(-c*f+d*e)^2/(d*x^2+c)-1/8*(8*b^2*c^4*f^2-4*a*b*c*d*(6*c^2*f^2-3*c*d*e*f+d^2*e^2)+a^2*d^2*(15*c^2*f^2-10*c*d*e*f+3*d^2*e^2))*arctanh(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))/c^(5/2)/(-a*d+b*c)^(3/2)/(-c*f+d*e)^3+f^2*sqrt(-a*f+b*e)*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/sqrt(e)/(-c*f+d*e)^3,1],
[sqrt(b*x^2+a)/(d*x^2+c)^3/(f*x^2+e)^2,x,9,1/4*d^2*x*sqrt(b*x^2+a)/c/(-c*f+d*e)^2/(d*x^2+c)^2-1/8*d^2*(a*d*(-11*c*f+3*d*e)-2*b*c*(-5*c*f+d*e))*x*sqrt(b*x^2+a)/c^2/(-a*d+b*c)/(-c*f+d*e)^3/(d*x^2+c)-1/2*f^3*x*sqrt(b*x^2+a)/e/(-c*f+d*e)^3/(f*x^2+e)-1/8*d*(24*b^2*c^4*f^2-4*a*b*c*d*(15*c^2*f^2-4*c*d*e*f+d^2*e^2)+a^2*d^2*(35*c^2*f^2-14*c*d*e*f+3*d^2*e^2))*arctanh(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))/c^(5/2)/(-a*d+b*c)^(3/2)/(-c*f+d*e)^4+1/2*f^2*(6*b*d*e^2-a*f*(-c*f+7*d*e))*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/e^(3/2)/sqrt(-a*f+b*e)/(-c*f+d*e)^4,1],
[sqrt(b*x^2+a)/(d*x^2+c)^3/(f*x^2+e)^3,x,10,1/4*d^3*x*sqrt(b*x^2+a)/c/(-c*f+d*e)^3/(d*x^2+c)^2+1/8*d^3*(2*b*c*(-7*c*f+d*e)-3*a*d*(-5*c*f+d*e))*x*sqrt(b*x^2+a)/c^2/(-a*d+b*c)/(-c*f+d*e)^4/(d*x^2+c)-1/4*f^3*x*sqrt(b*x^2+a)/e/(-c*f+d*e)^3/(f*x^2+e)^2+1/8*f^3*(3*a*f*(-c*f+5*d*e)-2*b*e*(-c*f+7*d*e))*x*sqrt(b*x^2+a)/e^2/(-a*f+b*e)/(-c*f+d*e)^4/(f*x^2+e)-1/8*d^2*(48*b^2*c^4*f^2+3*a^2*d^2*(21*c^2*f^2-6*c*d*e*f+d^2*e^2)-4*a*b*c*d*(28*c^2*f^2-5*c*d*e*f+d^2*e^2))*arctanh(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))/c^(5/2)/(-a*d+b*c)^(3/2)/(-c*f+d*e)^5+1/8*f^2*(48*b^2*d^2*e^4+3*a^2*f^2*(c^2*f^2-6*c*d*e*f+21*d^2*e^2)-4*a*b*e*f*(c^2*f^2-5*c*d*e*f+28*d^2*e^2))*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/e^(5/2)/(-a*f+b*e)^(3/2)/(-c*f+d*e)^5,1],
[(b*x^2+a)^(3/2)*(d*x^2+c)*(f*x^2+e)^3,x,8,1/1024*a*(384*b^4*c*e^3+7*a^4*d*f^3+72*a^2*b^2*e*f*(c*f+d*e)-12*a^3*b*f^2*(c*f+3*d*e)-64*a*b^3*e^2*(3*c*f+d*e))*x*sqrt(b*x^2+a)/b^4+1/1536*(384*b^4*c*e^3+7*a^4*d*f^3+72*a^2*b^2*e*f*(c*f+d*e)-12*a^3*b*f^2*(c*f+3*d*e)-64*a*b^3*e^2*(3*c*f+d*e))*x*(b*x^2+a)^(3/2)/b^4-1/384*(7*a^3*d*f^3+72*a*b^2*e*f*(c*f+d*e)-12*a^2*b*f^2*(c*f+3*d*e)-64*b^3*e^2*(3*c*f+d*e))*x*(b*x^2+a)^(5/2)/b^4+1/192*f*(7*a^2*d*f^2+72*b^2*e*(c*f+d*e)-12*a*b*f*(c*f+3*d*e))*x^3*(b*x^2+a)^(5/2)/b^3-1/120*f^2*(7*a*d*f-12*b*(c*f+3*d*e))*x^5*(b*x^2+a)^(5/2)/b^2+1/12*d*f^3*x^7*(b*x^2+a)^(5/2)/b+1/1024*a^2*(384*b^4*c*e^3+7*a^4*d*f^3+72*a^2*b^2*e*f*(c*f+d*e)-12*a^3*b*f^2*(c*f+3*d*e)-64*a*b^3*e^2*(3*c*f+d*e))*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(9/2),1],
[(b*x^2+a)^(3/2)*(d*x^2+c)*(f*x^2+e)^2,x,7,1/256*a*(96*b^3*c*e^2-3*a^3*d*f^2+6*a^2*b*f*(c*f+2*d*e)-16*a*b^2*e*(2*c*f+d*e))*x*sqrt(b*x^2+a)/b^3+1/384*(96*b^3*c*e^2-3*a^3*d*f^2+6*a^2*b*f*(c*f+2*d*e)-16*a*b^2*e*(2*c*f+d*e))*x*(b*x^2+a)^(3/2)/b^3+1/96*(3*a^2*d*f^2-6*a*b*f*(c*f+2*d*e)+16*b^2*e*(2*c*f+d*e))*x*(b*x^2+a)^(5/2)/b^3+1/16*f*(-a*d*f+2*b*c*f+4*b*d*e)*x^3*(b*x^2+a)^(5/2)/b^2+1/10*d*f^2*x^5*(b*x^2+a)^(5/2)/b+1/256*a^2*(96*b^3*c*e^2-3*a^3*d*f^2+6*a^2*b*f*(c*f+2*d*e)-16*a*b^2*e*(2*c*f+d*e))*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(7/2),1],
[(b*x^2+a)^(3/2)*(d*x^2+c)*(f*x^2+e),x,6,1/128*a*(48*b^2*c*e+3*a^2*d*f-8*a*b*(c*f+d*e))*x*sqrt(b*x^2+a)/b^2+1/192*(48*b^2*c*e+3*a^2*d*f-8*a*b*(c*f+d*e))*x*(b*x^2+a)^(3/2)/b^2-1/48*(3*a*d*f-8*b*(c*f+d*e))*x*(b*x^2+a)^(5/2)/b^2+1/8*d*f*x^3*(b*x^2+a)^(5/2)/b+1/128*a^2*(48*b^2*c*e+3*a^2*d*f-8*a*b*(c*f+d*e))*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(5/2),1],
[(b*x^2+a)^(3/2)*(d*x^2+c)/(f*x^2+e),x,7,-1/8*(-3*a*d*f-4*b*c*f+4*b*d*e)*x*sqrt(b*x^2+a)/f^2+1/4*d*x*(b*x^2+a)^(3/2)/f+1/8*(3*a^2*d*f^2+8*b^2*e*(-c*f+d*e)-12*a*b*f*(-c*f+d*e))*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/sqrt(b)/f^3-(-a*f+b*e)^(3/2)*(-c*f+d*e)*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/sqrt(e)/f^3,1],
[(b*x^2+a)^(3/2)*(d*x^2+c)/(f*x^2+e)^2,x,7,1/2*b*(-c*f+2*d*e)*x*sqrt(b*x^2+a)/e/f^2-1/2*(-c*f+d*e)*x*(b*x^2+a)^(3/2)/e/f/(f*x^2+e)-1/2*sqrt(b)*(-3*a*d*f-2*b*c*f+4*b*d*e)*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/f^3+1/2*sqrt(-a*f+b*e)*(2*b*e*(-c*f+2*d*e)-a*f*(c*f+d*e))*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/e^(3/2)/f^3,1],
[(b*x^2+a)^(3/2)*(d*x^2+c)/(f*x^2+e)^3,x,7,-1/4*(-c*f+d*e)*x*(b*x^2+a)^(3/2)/e/f/(f*x^2+e)^2-1/8*(4*b*d*e^2-a*f*(3*c*f+d*e))*x*sqrt(b*x^2+a)/e^2/f^2/(f*x^2+e)+b^(3/2)*d*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/f^3-1/8*(8*b^2*d*e^3-a*f*(4*b*d*e^2+a*f*(3*c*f+d*e)))*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/e^(5/2)/f^3/sqrt(-a*f+b*e),1],
[(b*x^2+a)^(3/2)*(d*x^2+c)/(f*x^2+e)^4,x,5,1/6*(-c*f+d*e)*x*(b*x^2+a)^(5/2)/e/(-a*f+b*e)/(f*x^2+e)^3+1/24*(-5*a*c*f-a*d*e+6*b*c*e)*x*(b*x^2+a)^(3/2)/e^2/(-a*f+b*e)/(f*x^2+e)^2+1/16*a*(-5*a*c*f-a*d*e+6*b*c*e)*x*sqrt(b*x^2+a)/e^3/(-a*f+b*e)/(f*x^2+e)+1/16*a^2*(-5*a*c*f-a*d*e+6*b*c*e)*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/e^(7/2)/(-a*f+b*e)^(3/2),1],
[(b*x^2+a)^(3/2)*(d*x^2+c)/(f*x^2+e)^5,x,6,-1/8*(-c*f+d*e)*x*(b*x^2+a)^(3/2)/e/f/(f*x^2+e)^4-1/48*(4*b*e*(c*f+d*e)-a*f*(7*c*f+d*e))*x*sqrt(b*x^2+a)/e^2/f^2/(f*x^2+e)^3+1/192*(24*a*b*c*e*f^2+8*b^2*e^2*(c*f+d*e)-5*a^2*f^2*(7*c*f+d*e))*x*sqrt(b*x^2+a)/e^3/f^2/(-a*f+b*e)/(f*x^2+e)^2-1/384*(8*a*b^2*e^2*f*(-5*c*f+d*e)-16*b^3*e^3*(c*f+d*e)-15*a^3*f^3*(7*c*f+d*e)+2*a^2*b*e*f^2*(85*c*f+7*d*e))*x*sqrt(b*x^2+a)/e^4/f^2/(-a*f+b*e)^2/(f*x^2+e)+1/128*a^2*(48*b^2*c*e^2+5*a^2*f*(7*c*f+d*e)-8*a*b*e*(10*c*f+d*e))*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/e^(9/2)/(-a*f+b*e)^(5/2),1],
[(b*x^2+a)^(3/2)*(d*x^2+c)^2*(f*x^2+e)^3,x,9,1/2048*a*(768*b^5*c^2*e^3-9*a^5*d^2*f^3+14*a^4*b*d*f^2*(2*c*f+3*d*e)-128*a*b^4*c*e^2*(3*c*f+2*d*e)-24*a^3*b^2*f*(c^2*f^2+6*c*d*e*f+3*d^2*e^2)+48*a^2*b^3*e*(3*c^2*f^2+6*c*d*e*f+d^2*e^2))*x*sqrt(b*x^2+a)/b^5+1/3072*(768*b^5*c^2*e^3-9*a^5*d^2*f^3+14*a^4*b*d*f^2*(2*c*f+3*d*e)-128*a*b^4*c*e^2*(3*c*f+2*d*e)-24*a^3*b^2*f*(c^2*f^2+6*c*d*e*f+3*d^2*e^2)+48*a^2*b^3*e*(3*c^2*f^2+6*c*d*e*f+d^2*e^2))*x*(b*x^2+a)^(3/2)/b^5+1/768*(9*a^4*d^2*f^3-14*a^3*b*d*f^2*(2*c*f+3*d*e)+128*b^4*c*e^2*(3*c*f+2*d*e)+24*a^2*b^2*f*(c^2*f^2+6*c*d*e*f+3*d^2*e^2)-48*a*b^3*e*(3*c^2*f^2+6*c*d*e*f+d^2*e^2))*x*(b*x^2+a)^(5/2)/b^5-1/384*(9*a^3*d^2*f^3-14*a^2*b*d*f^2*(2*c*f+3*d*e)+24*a*b^2*f*(c^2*f^2+6*c*d*e*f+3*d^2*e^2)-48*b^3*e*(3*c^2*f^2+6*c*d*e*f+d^2*e^2))*x^3*(b*x^2+a)^(5/2)/b^4+1/240*f*(9*a^2*d^2*f^2-14*a*b*d*f*(2*c*f+3*d*e)+24*b^2*(c^2*f^2+6*c*d*e*f+3*d^2*e^2))*x^5*(b*x^2+a)^(5/2)/b^3+1/168*d*f^2*(-9*a*d*f+28*b*c*f+42*b*d*e)*x^7*(b*x^2+a)^(5/2)/b^2+1/14*d^2*f^3*x^9*(b*x^2+a)^(5/2)/b+1/2048*a^2*(768*b^5*c^2*e^3-9*a^5*d^2*f^3+14*a^4*b*d*f^2*(2*c*f+3*d*e)-128*a*b^4*c*e^2*(3*c*f+2*d*e)-24*a^3*b^2*f*(c^2*f^2+6*c*d*e*f+3*d^2*e^2)+48*a^2*b^3*e*(3*c^2*f^2+6*c*d*e*f+d^2*e^2))*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(11/2),1],
[(b*x^2+a)^(3/2)*(d*x^2+c)^2*(f*x^2+e)^2,x,8,1/1024*a*(384*b^4*c^2*e^2+7*a^4*d^2*f^2-128*a*b^3*c*e*(c*f+d*e)-24*a^3*b*d*f*(c*f+d*e)+24*a^2*b^2*(c^2*f^2+4*c*d*e*f+d^2*e^2))*x*sqrt(b*x^2+a)/b^4+1/1536*(384*b^4*c^2*e^2+7*a^4*d^2*f^2-128*a*b^3*c*e*(c*f+d*e)-24*a^3*b*d*f*(c*f+d*e)+24*a^2*b^2*(c^2*f^2+4*c*d*e*f+d^2*e^2))*x*(b*x^2+a)^(3/2)/b^4-1/384*(7*a^3*d^2*f^2-128*b^3*c*e*(c*f+d*e)-24*a^2*b*d*f*(c*f+d*e)+24*a*b^2*(c^2*f^2+4*c*d*e*f+d^2*e^2))*x*(b*x^2+a)^(5/2)/b^4+1/192*(7*a^2*d^2*f^2-24*a*b*d*f*(c*f+d*e)+24*b^2*(c^2*f^2+4*c*d*e*f+d^2*e^2))*x^3*(b*x^2+a)^(5/2)/b^3-1/120*d*f*(7*a*d*f-24*b*(c*f+d*e))*x^5*(b*x^2+a)^(5/2)/b^2+1/12*d^2*f^2*x^7*(b*x^2+a)^(5/2)/b+1/1024*a^2*(384*b^4*c^2*e^2+7*a^4*d^2*f^2-128*a*b^3*c*e*(c*f+d*e)-24*a^3*b*d*f*(c*f+d*e)+24*a^2*b^2*(c^2*f^2+4*c*d*e*f+d^2*e^2))*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(9/2),1],
[(b*x^2+a)^(3/2)*(d*x^2+c)^2/(f*x^2+e),x,9,1/16*(a^2*d^2*f^2-10*a*b*d*f*(-2*c*f+d*e)+8*b^2*(-c*f+d*e)^2)*x*sqrt(b*x^2+a)/b/f^3+1/24*d*(7*a*d*f-6*b*(-2*c*f+d*e))*x^3*sqrt(b*x^2+a)/f^2+1/6*b*d^2*x^5*sqrt(b*x^2+a)/f-1/16*(a^3*d^2*f^3+6*a^2*b*d*f^2*(-2*c*f+d*e)+16*b^3*e*(-c*f+d*e)^2-24*a*b^2*f*(-c*f+d*e)^2)*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(3/2)/f^4+(-a*f+b*e)^(3/2)*(-c*f+d*e)^2*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/sqrt(e)/f^4,1],
[(b*x^2+a)^(3/2)*(d*x^2+c)^2/(f*x^2+e)^2,x,9,-1/8*d*(-5*a*d*f-8*b*c*f+8*b*d*e)*x*sqrt(b*x^2+a)/f^3+1/4*b*d^2*x^3*sqrt(b*x^2+a)/f^2-1/2*(-a*f+b*e)*(-c*f+d*e)^2*x*sqrt(b*x^2+a)/e/f^3/(f*x^2+e)+1/8*(3*a^2*d^2*f^2-24*a*b*d*f*(-c*f+d*e)+8*b^2*(c^2*f^2-4*c*d*e*f+3*d^2*e^2))*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/sqrt(b)/f^4-1/2*sqrt(-a*f+b*e)*(-c*f+d*e)*(2*b*e*(-c*f+3*d*e)-a*f*(c*f+3*d*e))*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/e^(3/2)/f^4,1],
[(b*x^2+a)^(3/2)*(d*x^2+c)^2/(f*x^2+e)^3,x,9,1/2*b*d^2*x*sqrt(b*x^2+a)/f^3-1/4*(-a*f+b*e)*(-c*f+d*e)^2*x*sqrt(b*x^2+a)/e/f^3/(f*x^2+e)^2+1/8*(-c*f+d*e)*(2*b*e*(-c*f+5*d*e)-a*f*(3*c*f+5*d*e))*x*sqrt(b*x^2+a)/e^2/f^3/(f*x^2+e)-1/2*sqrt(b)*d*(-3*a*d*f-4*b*c*f+6*b*d*e)*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/f^4+1/8*(8*b^2*d*e^3*(-2*c*f+3*d*e)-8*a*b*d*e^2*f*(-c*f+3*d*e)+a^2*f^2*(3*c^2*f^2+2*c*d*e*f+3*d^2*e^2))*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/e^(5/2)/f^4/sqrt(-a*f+b*e),1],
[(b*x^2+a)^(3/2)*(d*x^2+c)^2/(f*x^2+e)^4,x,9,-1/6*(-a*f+b*e)*(-c*f+d*e)^2*x*sqrt(b*x^2+a)/e/f^3/(f*x^2+e)^3+1/24*(-c*f+d*e)*(2*b*e*(-c*f+7*d*e)-a*f*(5*c*f+7*d*e))*x*sqrt(b*x^2+a)/e^2/f^3/(f*x^2+e)^2-1/48*(4*b^2*e^2*(-c^2*f^2-4*c*d*e*f+11*d^2*e^2)-4*a*b*e*f*(2*c^2*f^2-c*d*e*f+11*d^2*e^2)+3*a^2*f^2*(5*c^2*f^2+2*c*d*e*f+d^2*e^2))*x*sqrt(b*x^2+a)/e^3/f^3/(-a*f+b*e)/(f*x^2+e)+b^(3/2)*d^2*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/f^4-1/16*(16*b^3*d^2*e^5-24*a*b^2*d^2*e^4*f+6*a^2*b*e*f^2*(-c^2*f^2+d^2*e^2)+a^3*f^3*(5*c^2*f^2+2*c*d*e*f+d^2*e^2))*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/e^(7/2)/f^4/(-a*f+b*e)^(3/2),1],
[(b*x^2+a)^(3/2)*(d*x^2+c)^3/(f*x^2+e),x,10,-1/128*(3*a^3*d^3*f^3+8*a^2*b*d^2*f^2*(-3*c*f+d*e)+64*b^3*(-c*f+d*e)^3-80*a*b^2*d*f*(3*c^2*f^2-3*c*d*e*f+d^2*e^2))*x*sqrt(b*x^2+a)/b^2/f^4+1/192*d*(3*a^2*d^2*f^2-56*a*b*d*f*(-3*c*f+d*e)+48*b^2*(3*c^2*f^2-3*c*d*e*f+d^2*e^2))*x^3*sqrt(b*x^2+a)/b/f^3-1/48*d^2*(-9*a*d*f-24*b*c*f+8*b*d*e)*x^5*sqrt(b*x^2+a)/f^2+1/8*b*d^3*x^7*sqrt(b*x^2+a)/f+1/128*(3*a^4*d^3*f^4+8*a^3*b*d^2*f^3*(-3*c*f+d*e)+128*b^4*e*(-c*f+d*e)^3-192*a*b^3*f*(-c*f+d*e)^3+48*a^2*b^2*d*f^2*(3*c^2*f^2-3*c*d*e*f+d^2*e^2))*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(5/2)/f^5-(-a*f+b*e)^(3/2)*(-c*f+d*e)^3*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/sqrt(e)/f^5,1],
[(b*x^2+a)^(3/2)*(d*x^2+c)^3/(f*x^2+e)^2,x,10,1/16*d*(a^2*d^2*f^2-10*a*b*d*f*(-3*c*f+2*d*e)+24*b^2*(-c*f+d*e)^2)*x*sqrt(b*x^2+a)/b/f^4-1/24*d^2*(-7*a*d*f-18*b*c*f+12*b*d*e)*x^3*sqrt(b*x^2+a)/f^3+1/6*b*d^3*x^5*sqrt(b*x^2+a)/f^2+1/2*(-a*f+b*e)*(-c*f+d*e)^3*x*sqrt(b*x^2+a)/e/f^4/(f*x^2+e)-1/16*(a^3*d^3*f^3+6*a^2*b*d^2*f^2*(-3*c*f+2*d*e)-72*a*b^2*d*f*(-c*f+d*e)^2+16*b^3*(-c*f+d*e)^2*(-c*f+4*d*e))*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(3/2)/f^5+1/2*sqrt(-a*f+b*e)*(-c*f+d*e)^2*(2*b*e*(-c*f+4*d*e)-a*f*(c*f+5*d*e))*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/e^(3/2)/f^5,1],
[(b*x^2+a)^(3/2)*(d*x^2+c)^3/(f*x^2+e)^3,x,10,1/8*d^2*(5*a*d*f-12*b*(-c*f+d*e))*x*sqrt(b*x^2+a)/f^4+1/4*b*d^3*x^3*sqrt(b*x^2+a)/f^3+1/4*(-a*f+b*e)*(-c*f+d*e)^3*x*sqrt(b*x^2+a)/e/f^4/(f*x^2+e)^2-1/8*(-c*f+d*e)^2*(2*b*e*(-c*f+7*d*e)-3*a*f*(c*f+3*d*e))*x*sqrt(b*x^2+a)/e^2/f^4/(f*x^2+e)+3/8*d*(a^2*d^2*f^2-12*a*b*d*f*(-c*f+d*e)+8*b^2*(c^2*f^2-3*c*d*e*f+2*d^2*e^2))*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/sqrt(b)/f^5-3/8*(-c*f+d*e)*(8*b^2*d*e^3*(-c*f+2*d*e)-4*a*b*d*e^2*f*(-c*f+5*d*e)+a^2*f^2*(c^2*f^2+2*c*d*e*f+5*d^2*e^2))*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/e^(5/2)/f^5/sqrt(-a*f+b*e),1],
[(b*x^2+a)^(3/2)*(d*x^2+c)^3/(f*x^2+e)^4,x,10,1/2*b*d^3*x*sqrt(b*x^2+a)/f^4+1/6*(-a*f+b*e)*(-c*f+d*e)^3*x*sqrt(b*x^2+a)/e/f^4/(f*x^2+e)^3-1/24*(-c*f+d*e)^2*(2*b*e*(-c*f+10*d*e)-a*f*(5*c*f+13*d*e))*x*sqrt(b*x^2+a)/e^2/f^4/(f*x^2+e)^2+1/48*(-c*f+d*e)*(4*b^2*e^2*(-c^2*f^2-7*c*d*e*f+26*d^2*e^2)-2*a*b*e*f*(4*c^2*f^2+c*d*e*f+67*d^2*e^2)+3*a^2*f^2*(5*c^2*f^2+8*c*d*e*f+11*d^2*e^2))*x*sqrt(b*x^2+a)/e^3/f^4/(-a*f+b*e)/(f*x^2+e)-1/2*sqrt(b)*d^2*(-3*a*d*f-6*b*c*f+8*b*d*e)*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/f^5+1/16*(16*b^3*d^2*e^5*(-3*c*f+4*d*e)-24*a*b^2*d^2*e^4*f*(-3*c*f+5*d*e)+6*a^2*b*e*f^2*(c^3*f^3-3*c*d^2*e^2*f+10*d^3*e^3)-a^3*f^3*(5*c^3*f^3+3*c^2*d*e*f^2+3*c*d^2*e^2*f+5*d^3*e^3))*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/e^(7/2)/f^5/(-a*f+b*e)^(3/2),1],
[(b*x^2+a)^(3/2)/(d*x^2+c)/(f*x^2+e),x,7,b^(3/2)*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/d/f+(-a*d+b*c)^(3/2)*arctanh(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))/sqrt(c)/d/(-c*f+d*e)-(-a*f+b*e)^(3/2)*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/sqrt(e)/f/(-c*f+d*e),1],
[(b*x^2+a)^(3/2)/(d*x^2+c)/(f*x^2+e)^2,x,6,1/2*(-a*f+b*e)*x*sqrt(b*x^2+a)/e/(-c*f+d*e)/(f*x^2+e)+(-a*d+b*c)^(3/2)*arctanh(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))/sqrt(c)/(-c*f+d*e)^2-1/2*sqrt(-a*f+b*e)*(a*c*f-3*a*d*e+2*b*c*e)*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/e^(3/2)/(-c*f+d*e)^2,1],
[(b*x^2+a)^(3/2)/(d*x^2+c)/(f*x^2+e)^3,x,7,1/4*(-a*f+b*e)*x*sqrt(b*x^2+a)/e/(-c*f+d*e)/(f*x^2+e)^2-1/8*(a*f*(-3*c*f+7*d*e)-2*b*e*(c*f+d*e))*x*sqrt(b*x^2+a)/e^2/(-c*f+d*e)^2/(f*x^2+e)+d*(-a*d+b*c)^(3/2)*arctanh(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))/sqrt(c)/(-c*f+d*e)^3-1/8*(8*b^2*c*d*e^3-4*a*b*d*e^2*(c*f+3*d*e)+a^2*f*(3*c^2*f^2-10*c*d*e*f+15*d^2*e^2))*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/e^(5/2)/sqrt(-a*f+b*e)/(-c*f+d*e)^3,1],
[(b*x^2+a)^(3/2)/(d*x^2+c)/(f*x^2+e)^4,x,8,1/6*(-a*f+b*e)*x*sqrt(b*x^2+a)/e/(-c*f+d*e)/(f*x^2+e)^3-1/24*(a*f*(-5*c*f+11*d*e)-2*b*e*(c*f+2*d*e))*x*sqrt(b*x^2+a)/e^2/(-c*f+d*e)^2/(f*x^2+e)^2+1/48*(4*b^2*e^2*(-c^2*f^2+5*c*d*e*f+2*d^2*e^2)-2*a*b*e*f*(4*c^2*f^2-11*c*d*e*f+31*d^2*e^2)+3*a^2*f^2*(5*c^2*f^2-16*c*d*e*f+19*d^2*e^2))*x*sqrt(b*x^2+a)/e^3/(-a*f+b*e)/(-c*f+d*e)^3/(f*x^2+e)+d^2*(-a*d+b*c)^(3/2)*arctanh(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))/sqrt(c)/(-c*f+d*e)^4-1/16*(16*b^3*c*d^2*e^5-24*a*b^2*d^2*e^4*(c*f+d*e)-a^3*f^2*(-5*c^3*f^3+21*c^2*d*e*f^2-35*c*d^2*e^2*f+35*d^3*e^3)+6*a^2*b*e*f*(-c^3*f^3+4*c^2*d*e*f^2-5*c*d^2*e^2*f+10*d^3*e^3))*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/e^(7/2)/(-a*f+b*e)^(3/2)/(-c*f+d*e)^4,1],
[(b*x^2+a)^(3/2)/(d*x^2+c)^2/(f*x^2+e)^2,x,8,-1/2*d*(-a*d+b*c)*x*sqrt(b*x^2+a)/c/(-c*f+d*e)^2/(d*x^2+c)-1/2*f*(-a*f+b*e)*x*sqrt(b*x^2+a)/e/(-c*f+d*e)^2/(f*x^2+e)-1/2*sqrt(-a*d+b*c)*(a*d*(-5*c*f+d*e)+2*b*c*(c*f+d*e))*arctanh(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))/c^(3/2)/(-c*f+d*e)^3-1/2*sqrt(-a*f+b*e)*(a*f*(-c*f+5*d*e)-2*b*e*(c*f+d*e))*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/e^(3/2)/(-c*f+d*e)^3,1],
[(b*x^2+a)^(3/2)/(d*x^2+c)^2/(f*x^2+e)^3,x,9,-1/2*d^2*(-a*d+b*c)*x*sqrt(b*x^2+a)/c/(-c*f+d*e)^3/(d*x^2+c)-1/4*f*(-a*f+b*e)*x*sqrt(b*x^2+a)/e/(-c*f+d*e)^2/(f*x^2+e)^2+1/8*f*(a*f*(-3*c*f+11*d*e)-2*b*e*(c*f+3*d*e))*x*sqrt(b*x^2+a)/e^2/(-c*f+d*e)^3/(f*x^2+e)-1/2*d*sqrt(-a*d+b*c)*(a*d*(-7*c*f+d*e)+2*b*c*(2*c*f+d*e))*arctanh(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))/c^(3/2)/(-c*f+d*e)^4-1/8*(8*a*b*d*e^2*f*(c*f+5*d*e)-8*b^2*d*e^3*(2*c*f+d*e)-a^2*f^2*(3*c^2*f^2-14*c*d*e*f+35*d^2*e^2))*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/e^(5/2)/sqrt(-a*f+b*e)/(-c*f+d*e)^4,1],
[(b*x^2+a)^(3/2)/(d*x^2+c)^3/(f*x^2+e)^3,x,10,-1/4*d^2*(-a*d+b*c)*x*sqrt(b*x^2+a)/c/(-c*f+d*e)^3/(d*x^2+c)^2+1/8*d^2*(3*a*d*(-5*c*f+d*e)+2*b*c*(5*c*f+d*e))*x*sqrt(b*x^2+a)/c^2/(-c*f+d*e)^4/(d*x^2+c)+1/4*f^2*(-a*f+b*e)*x*sqrt(b*x^2+a)/e/(-c*f+d*e)^3/(f*x^2+e)^2-1/8*f^2*(3*a*f*(-c*f+5*d*e)-2*b*e*(c*f+5*d*e))*x*sqrt(b*x^2+a)/e^2/(-c*f+d*e)^4/(f*x^2+e)+3/8*d*(8*b^2*c^3*f*(c*f+d*e)-4*a*b*c^2*d*f*(7*c*f+d*e)+a^2*d^2*(21*c^2*f^2-6*c*d*e*f+d^2*e^2))*arctanh(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))/c^(5/2)/sqrt(-a*d+b*c)/(-c*f+d*e)^5-3/8*f*(8*b^2*d*e^3*(c*f+d*e)-4*a*b*d*e^2*f*(c*f+7*d*e)+a^2*f^2*(c^2*f^2-6*c*d*e*f+21*d^2*e^2))*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/e^(5/2)/sqrt(-a*f+b*e)/(-c*f+d*e)^5,1],
[(b*x^2+a)^(5/2)/(d*x^2+c)/(f*x^2+e),x,9,1/2*b^2*x*sqrt(b*x^2+a)/d/f+1/2*b^(3/2)*(5*a*d*f-2*b*(c*f+d*e))*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/d^2/f^2-(-a*d+b*c)^(5/2)*arctanh(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))/sqrt(c)/d^2/(-c*f+d*e)+(-a*f+b*e)^(5/2)*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/sqrt(e)/f^2/(-c*f+d*e),1],
[(d*x^2+c)*(f*x^2+e)^3/sqrt(b*x^2+a),x,6,-1/128*(35*a^3*d*f^3+144*a*b^2*e*f*(c*f+d*e)-40*a^2*b*f^2*(c*f+3*d*e)-64*b^3*e^2*(3*c*f+d*e))*x*sqrt(b*x^2+a)/b^4+1/192*f*(35*a^2*d*f^2+144*b^2*e*(c*f+d*e)-40*a*b*f*(c*f+3*d*e))*x^3*sqrt(b*x^2+a)/b^3-1/48*f^2*(7*a*d*f-8*b*(c*f+3*d*e))*x^5*sqrt(b*x^2+a)/b^2+1/8*d*f^3*x^7*sqrt(b*x^2+a)/b+1/128*(128*b^4*c*e^3+35*a^4*d*f^3+144*a^2*b^2*e*f*(c*f+d*e)-40*a^3*b*f^2*(c*f+3*d*e)-64*a*b^3*e^2*(3*c*f+d*e))*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(9/2),1],
[(d*x^2+c)*(f*x^2+e)^2/sqrt(b*x^2+a),x,5,1/16*(5*a^2*d*f^2-6*a*b*f*(c*f+2*d*e)+8*b^2*e*(2*c*f+d*e))*x*sqrt(b*x^2+a)/b^3-1/24*f*(5*a*d*f-6*b*(c*f+2*d*e))*x^3*sqrt(b*x^2+a)/b^2+1/6*d*f^2*x^5*sqrt(b*x^2+a)/b+1/16*(16*b^3*c*e^2-5*a^3*d*f^2+6*a^2*b*f*(c*f+2*d*e)-8*a*b^2*e*(2*c*f+d*e))*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(7/2),1],
[(d*x^2+c)*(f*x^2+e)/sqrt(b*x^2+a),x,4,-1/8*(3*a*d*f-4*b*(c*f+d*e))*x*sqrt(b*x^2+a)/b^2+1/4*d*f*x^3*sqrt(b*x^2+a)/b+1/8*(8*b^2*c*e+3*a^2*d*f-4*a*b*(c*f+d*e))*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(5/2),1],
[(d*x^2+c)/sqrt(b*x^2+a)/(f*x^2+e),x,5,d*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/sqrt(b)/f-(-c*f+d*e)*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/sqrt(e)/f/sqrt(-a*f+b*e),1],
[(d*x^2+c)/sqrt(b*x^2+a)/(f*x^2+e)^2,x,3,1/2*(-c*f+d*e)*x*sqrt(b*x^2+a)/e/(-a*f+b*e)/(f*x^2+e)+1/2*(2*b*c*e-a*(c*f+d*e))*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/e^(3/2)/(-a*f+b*e)^(3/2),1],
[(d*x^2+c)/sqrt(b*x^2+a)/(f*x^2+e)^3,x,4,1/4*(-c*f+d*e)*x*sqrt(b*x^2+a)/e/(-a*f+b*e)/(f*x^2+e)^2+1/8*(2*b*e*(-3*c*f+d*e)+a*f*(3*c*f+d*e))*x*sqrt(b*x^2+a)/e^2/(-a*f+b*e)^2/(f*x^2+e)+1/8*(8*b^2*c*e^2-4*a*b*e*(2*c*f+d*e)+a^2*f*(3*c*f+d*e))*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/e^(5/2)/(-a*f+b*e)^(5/2),1],
[(d*x^2+c)/sqrt(b*x^2+a)/(f*x^2+e)^4,x,5,1/6*(-c*f+d*e)*x*sqrt(b*x^2+a)/e/(-a*f+b*e)/(f*x^2+e)^3+1/24*(2*b*e*(-5*c*f+2*d*e)+a*f*(5*c*f+d*e))*x*sqrt(b*x^2+a)/e^2/(-a*f+b*e)^2/(f*x^2+e)^2+1/48*(4*b^2*e^2*(-11*c*f+2*d*e)-3*a^2*f^2*(5*c*f+d*e)+2*a*b*e*f*(22*c*f+5*d*e))*x*sqrt(b*x^2+a)/e^3/(-a*f+b*e)^3/(f*x^2+e)+1/16*(16*b^3*c*e^3-8*a*b^2*e^2*(3*c*f+d*e)-a^3*f^2*(5*c*f+d*e)+2*a^2*b*e*f*(9*c*f+2*d*e))*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/e^(7/2)/(-a*f+b*e)^(7/2),1],
[(d*x^2+c)^2*(f*x^2+e)^3/sqrt(b*x^2+a),x,7,1/256*(63*a^4*d^2*f^3-70*a^3*b*d*f^2*(2*c*f+3*d*e)+128*b^4*c*e^2*(3*c*f+2*d*e)+80*a^2*b^2*f*(c^2*f^2+6*c*d*e*f+3*d^2*e^2)-96*a*b^3*e*(3*c^2*f^2+6*c*d*e*f+d^2*e^2))*x*sqrt(b*x^2+a)/b^5-1/384*(63*a^3*d^2*f^3-70*a^2*b*d*f^2*(2*c*f+3*d*e)+80*a*b^2*f*(c^2*f^2+6*c*d*e*f+3*d^2*e^2)-96*b^3*e*(3*c^2*f^2+6*c*d*e*f+d^2*e^2))*x^3*sqrt(b*x^2+a)/b^4+1/480*f*(63*a^2*d^2*f^2-70*a*b*d*f*(2*c*f+3*d*e)+80*b^2*(c^2*f^2+6*c*d*e*f+3*d^2*e^2))*x^5*sqrt(b*x^2+a)/b^3+1/80*d*f^2*(-9*a*d*f+20*b*c*f+30*b*d*e)*x^7*sqrt(b*x^2+a)/b^2+1/10*d^2*f^3*x^9*sqrt(b*x^2+a)/b+1/256*(256*b^5*c^2*e^3-63*a^5*d^2*f^3+70*a^4*b*d*f^2*(2*c*f+3*d*e)-128*a*b^4*c*e^2*(3*c*f+2*d*e)-80*a^3*b^2*f*(c^2*f^2+6*c*d*e*f+3*d^2*e^2)+96*a^2*b^3*e*(3*c^2*f^2+6*c*d*e*f+d^2*e^2))*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(11/2),1],
[(d*x^2+c)^2*(f*x^2+e)^2/sqrt(b*x^2+a),x,6,-1/128*(35*a^3*d^2*f^2-128*b^3*c*e*(c*f+d*e)-80*a^2*b*d*f*(c*f+d*e)+48*a*b^2*(c^2*f^2+4*c*d*e*f+d^2*e^2))*x*sqrt(b*x^2+a)/b^4+1/192*(35*a^2*d^2*f^2-80*a*b*d*f*(c*f+d*e)+48*b^2*(c^2*f^2+4*c*d*e*f+d^2*e^2))*x^3*sqrt(b*x^2+a)/b^3-1/48*d*f*(7*a*d*f-16*b*(c*f+d*e))*x^5*sqrt(b*x^2+a)/b^2+1/8*d^2*f^2*x^7*sqrt(b*x^2+a)/b+1/128*(128*b^4*c^2*e^2+35*a^4*d^2*f^2-128*a*b^3*c*e*(c*f+d*e)-80*a^3*b*d*f*(c*f+d*e)+48*a^2*b^2*(c^2*f^2+4*c*d*e*f+d^2*e^2))*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(9/2),1],
[(d*x^2+c)^2/sqrt(b*x^2+a)/(f*x^2+e),x,7,1/2*d^2*x*sqrt(b*x^2+a)/b/f-1/2*d*(a*d*f-4*b*c*f+2*b*d*e)*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(3/2)/f^2+(-c*f+d*e)^2*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/sqrt(e)/f^2/sqrt(-a*f+b*e),1],
[(d*x^2+c)^2/sqrt(b*x^2+a)/(f*x^2+e)^2,x,7,-1/2*(-c*f+d*e)^2*x*sqrt(b*x^2+a)/e/f/(-a*f+b*e)/(f*x^2+e)+d^2*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/sqrt(b)/f^2-1/2*(-c*f+d*e)*(2*b*e*(c*f+d*e)-a*f*(c*f+3*d*e))*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/e^(3/2)/f^2/(-a*f+b*e)^(3/2),1],
[(d*x^2+c)^2/sqrt(b*x^2+a)/(f*x^2+e)^3,x,7,1/4*d^2*x*sqrt(b*x^2+a)/e/f/(-a*f+b*e)-1/4*f*x*sqrt(b*x^2+a)*(d*x^2+c)^2/e/(-a*f+b*e)/(f*x^2+e)^2-1/8*(-c*f+d*e)*(2*b*e*(-3*c*f+d*e)+a*f*(3*c*f+d*e))*x*sqrt(b*x^2+a)/e^2/f/(-a*f+b*e)^2/(f*x^2+e)+1/8*(8*b^2*c^2*e^2-8*a*b*c*e*(c*f+d*e)+a^2*(3*c^2*f^2+2*c*d*e*f+3*d^2*e^2))*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/e^(5/2)/(-a*f+b*e)^(5/2),1],
[(d*x^2+c)^3/sqrt(b*x^2+a)/(f*x^2+e),x,8,-1/8*d^2*(3*a*d*f-12*b*c*f+4*b*d*e)*x*sqrt(b*x^2+a)/b^2/f^2+1/4*d^3*x^3*sqrt(b*x^2+a)/b/f+1/8*d*(3*a^2*d^2*f^2+4*a*b*d*f*(-3*c*f+d*e)+8*b^2*(3*c^2*f^2-3*c*d*e*f+d^2*e^2))*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(5/2)/f^3-(-c*f+d*e)^3*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/sqrt(e)/f^3/sqrt(-a*f+b*e),1],
[(d*x^2+c)^3/sqrt(b*x^2+a)/(f*x^2+e)^2,x,8,1/2*d^3*x*sqrt(b*x^2+a)/b/f^2+1/2*(-c*f+d*e)^3*x*sqrt(b*x^2+a)/e/f^2/(-a*f+b*e)/(f*x^2+e)-1/2*d^2*(a*d*f-6*b*c*f+4*b*d*e)*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(3/2)/f^3+1/2*(-c*f+d*e)^2*(2*b*e*(c*f+2*d*e)-a*f*(c*f+5*d*e))*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/e^(3/2)/f^3/(-a*f+b*e)^(3/2),1],
[(d*x^2+c)^3/sqrt(b*x^2+a)/(f*x^2+e)^3,x,8,1/4*(-c*f+d*e)^3*x*sqrt(b*x^2+a)/e/f^2/(-a*f+b*e)/(f*x^2+e)^2-3/8*(-c*f+d*e)^2*(2*b*e*(c*f+d*e)-a*f*(c*f+3*d*e))*x*sqrt(b*x^2+a)/e^2/f^2/(-a*f+b*e)^2/(f*x^2+e)+d^3*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/sqrt(b)/f^3-1/8*(-c*f+d*e)*(8*b^2*e^2*(c^2*f^2+c*d*e*f+d^2*e^2)+3*a^2*f^2*(c^2*f^2+2*c*d*e*f+5*d^2*e^2)-4*a*b*e*f*(2*c^2*f^2+5*c*d*e*f+5*d^2*e^2))*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/e^(5/2)/f^3/(-a*f+b*e)^(5/2),1],
[1/sqrt(b*x^2+a)/(d*x^2+c)/(f*x^2+e),x,5,d*arctanh(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))/sqrt(c)/sqrt(-a*d+b*c)/(-c*f+d*e)-f*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/sqrt(e)/sqrt(-a*f+b*e)/(-c*f+d*e),1],
[1/sqrt(b*x^2+a)/(d*x^2+c)/(f*x^2+e)^2,x,6,1/2*f^2*x*sqrt(b*x^2+a)/e/(-a*f+b*e)/(-c*f+d*e)/(f*x^2+e)+d^2*arctanh(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))/sqrt(c)/sqrt(-a*d+b*c)/(-c*f+d*e)^2-1/2*f*(2*b*e*(-c*f+2*d*e)-a*f*(-c*f+3*d*e))*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/e^(3/2)/(-a*f+b*e)^(3/2)/(-c*f+d*e)^2,1],
[1/sqrt(b*x^2+a)/(d*x^2+c)/(f*x^2+e)^3,x,7,1/4*f^2*x*sqrt(b*x^2+a)/e/(-a*f+b*e)/(-c*f+d*e)/(f*x^2+e)^2+1/8*f^2*(2*b*e*(-3*c*f+5*d*e)-a*f*(-3*c*f+7*d*e))*x*sqrt(b*x^2+a)/e^2/(-a*f+b*e)^2/(-c*f+d*e)^2/(f*x^2+e)+d^3*arctanh(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))/sqrt(c)/sqrt(-a*d+b*c)/(-c*f+d*e)^3-1/8*f*(8*b^2*e^2*(c^2*f^2-3*c*d*e*f+3*d^2*e^2)-4*a*b*e*f*(2*c^2*f^2-7*c*d*e*f+9*d^2*e^2)+a^2*f^2*(3*c^2*f^2-10*c*d*e*f+15*d^2*e^2))*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/e^(5/2)/(-a*f+b*e)^(5/2)/(-c*f+d*e)^3,1],
[1/sqrt(b*x^2+a)/(d*x^2+c)^2/(f*x^2+e)^2,x,7,-1/2*d^3*x*sqrt(b*x^2+a)/c/(-a*d+b*c)/(-c*f+d*e)^2/(d*x^2+c)-1/2*f^3*x*sqrt(b*x^2+a)/e/(-a*f+b*e)/(-c*f+d*e)^2/(f*x^2+e)-1/2*d^2*(a*d*(-5*c*f+d*e)-2*b*c*(-3*c*f+d*e))*arctanh(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))/c^(3/2)/(-a*d+b*c)^(3/2)/(-c*f+d*e)^3+1/2*f^2*(2*b*e*(-c*f+3*d*e)-a*f*(-c*f+5*d*e))*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/e^(3/2)/(-a*f+b*e)^(3/2)/(-c*f+d*e)^3,1],
[1/sqrt(b*x^2+a)/(d*x^2+c)^2/(f*x^2+e)^3,x,8,-1/2*d^4*x*sqrt(b*x^2+a)/c/(-a*d+b*c)/(-c*f+d*e)^3/(d*x^2+c)-1/4*f^3*x*sqrt(b*x^2+a)/e/(-a*f+b*e)/(-c*f+d*e)^2/(f*x^2+e)^2-1/8*f^3*(2*b*e*(-3*c*f+7*d*e)-a*f*(-3*c*f+11*d*e))*x*sqrt(b*x^2+a)/e^2/(-a*f+b*e)^2/(-c*f+d*e)^3/(f*x^2+e)-1/2*d^3*(a*d*(-7*c*f+d*e)-2*b*c*(-4*c*f+d*e))*arctanh(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))/c^(3/2)/(-a*d+b*c)^(3/2)/(-c*f+d*e)^4-1/8*f^2*(8*a*b*e*f*(c^2*f^2-5*c*d*e*f+10*d^2*e^2)-8*b^2*e^2*(c^2*f^2-4*c*d*e*f+6*d^2*e^2)-a^2*f^2*(3*c^2*f^2-14*c*d*e*f+35*d^2*e^2))*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/e^(5/2)/(-a*f+b*e)^(5/2)/(-c*f+d*e)^4,1],
[1/sqrt(b*x^2+a)/(d*x^2+c)^3/(f*x^2+e)^3,x,9,-1/4*d^4*x*sqrt(b*x^2+a)/c/(-a*d+b*c)/(-c*f+d*e)^3/(d*x^2+c)^2+3/8*d^4*(a*d*(-5*c*f+d*e)-2*b*c*(-3*c*f+d*e))*x*sqrt(b*x^2+a)/c^2/(-a*d+b*c)^2/(-c*f+d*e)^4/(d*x^2+c)+1/4*f^4*x*sqrt(b*x^2+a)/e/(-a*f+b*e)/(-c*f+d*e)^3/(f*x^2+e)^2+3/8*f^4*(2*b*e*(-c*f+3*d*e)-a*f*(-c*f+5*d*e))*x*sqrt(b*x^2+a)/e^2/(-a*f+b*e)^2/(-c*f+d*e)^4/(f*x^2+e)+1/8*d^3*(8*b^2*c^2*(10*c^2*f^2-5*c*d*e*f+d^2*e^2)+3*a^2*d^2*(21*c^2*f^2-6*c*d*e*f+d^2*e^2)-4*a*b*c*d*(35*c^2*f^2-13*c*d*e*f+2*d^2*e^2))*arctanh(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))/c^(5/2)/(-a*d+b*c)^(5/2)/(-c*f+d*e)^5-1/8*f^3*(3*a^2*f^2*(c^2*f^2-6*c*d*e*f+21*d^2*e^2)+8*b^2*e^2*(c^2*f^2-5*c*d*e*f+10*d^2*e^2)-4*a*b*e*f*(2*c^2*f^2-13*c*d*e*f+35*d^2*e^2))*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/e^(5/2)/(-a*f+b*e)^(5/2)/(-c*f+d*e)^5,1],
[(d*x^2+c)*(f*x^2+e)^3/(b*x^2+a)^(3/2),x,6,(-a*d+b*c)*(-a*f+b*e)^3*x/a/b^4/sqrt(b*x^2+a)+1/16*f*(19*a^2*d*f^2+24*b^2*e*(c*f+d*e)-14*a*b*f*(c*f+3*d*e))*x*sqrt(b*x^2+a)/b^4+1/24*f^2*(-11*a*d*f+6*b*c*f+18*b*d*e)*x^3*sqrt(b*x^2+a)/b^3+1/6*d*f^3*x^5*sqrt(b*x^2+a)/b^2-1/16*(35*a^3*d*f^3+72*a*b^2*e*f*(c*f+d*e)-30*a^2*b*f^2*(c*f+3*d*e)-16*b^3*e^2*(3*c*f+d*e))*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(9/2),1],
[(d*x^2+c)*(f*x^2+e)^2/(b*x^2+a)^(3/2),x,5,(-a*d+b*c)*(-a*f+b*e)^2*x/a/b^3/sqrt(b*x^2+a)+1/8*f*(-7*a*d*f+4*b*c*f+8*b*d*e)*x*sqrt(b*x^2+a)/b^3+1/4*d*f^2*x^3*sqrt(b*x^2+a)/b^2+1/8*(15*a^2*d*f^2-12*a*b*f*(c*f+2*d*e)+8*b^2*e*(2*c*f+d*e))*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(7/2),1],
[(d*x^2+c)*(f*x^2+e)/(b*x^2+a)^(3/2),x,4,(-a*d+b*c)*(-a*f+b*e)*x/a/b^2/sqrt(b*x^2+a)+1/2*d*f*x*sqrt(b*x^2+a)/b^2-1/2*(3*a*d*f-2*b*(c*f+d*e))*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(5/2),1],
[(d*x^2+c)/(b*x^2+a)^(3/2)/(f*x^2+e),x,3,(-a*d+b*c)*x/a/(-a*f+b*e)/sqrt(b*x^2+a)+(-c*f+d*e)*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/sqrt(e)/(-a*f+b*e)^(3/2),1],
[(d*x^2+c)/(b*x^2+a)^(3/2)/(f*x^2+e)^2,x,4,1/2*b*(a*c*f-3*a*d*e+2*b*c*e)*x/a/e/(-a*f+b*e)^2/sqrt(b*x^2+a)+1/2*(-c*f+d*e)*x/e/(-a*f+b*e)/sqrt(b*x^2+a)/(f*x^2+e)+1/2*(2*b*e*(-2*c*f+d*e)+a*f*(c*f+d*e))*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/e^(3/2)/(-a*f+b*e)^(5/2),1],
[(d*x^2+c)/(b*x^2+a)^(3/2)/(f*x^2+e)^3,x,5,1/8*b*(8*b^2*c*e^2-2*a*b*e*(-5*c*f+7*d*e)-a^2*f*(3*c*f+d*e))*x/a/e^2/(-a*f+b*e)^3/sqrt(b*x^2+a)+1/4*(-c*f+d*e)*x/e/(-a*f+b*e)/sqrt(b*x^2+a)/(f*x^2+e)^2+1/8*(4*b*e*(-2*c*f+d*e)+a*f*(3*c*f+d*e))*x/e^2/(-a*f+b*e)^2/sqrt(b*x^2+a)/(f*x^2+e)+1/8*(8*b^2*e^2*(-3*c*f+d*e)-a^2*f^2*(3*c*f+d*e)+4*a*b*e*f*(3*c*f+2*d*e))*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/e^(5/2)/(-a*f+b*e)^(7/2),1],
[(d*x^2+c)^2*(f*x^2+e)^3/(b*x^2+a)^(3/2),x,7,(-a*d+b*c)^2*(-a*f+b*e)^3*x/a/b^5/sqrt(b*x^2+a)-1/128*(187*a^3*d^2*f^3-152*a^2*b*d*f^2*(2*c*f+3*d*e)+112*a*b^2*f*(c^2*f^2+6*c*d*e*f+3*d^2*e^2)-64*b^3*e*(3*c^2*f^2+6*c*d*e*f+d^2*e^2))*x*sqrt(b*x^2+a)/b^5+1/192*f*(123*a^2*d^2*f^2-88*a*b*d*f*(2*c*f+3*d*e)+48*b^2*(c^2*f^2+6*c*d*e*f+3*d^2*e^2))*x^3*sqrt(b*x^2+a)/b^4+1/48*d*f^2*(-15*a*d*f+16*b*c*f+24*b*d*e)*x^5*sqrt(b*x^2+a)/b^3+1/8*d^2*f^3*x^7*sqrt(b*x^2+a)/b^2+1/128*(315*a^4*d^2*f^3-280*a^3*b*d*f^2*(2*c*f+3*d*e)+128*b^4*c*e^2*(3*c*f+2*d*e)+240*a^2*b^2*f*(c^2*f^2+6*c*d*e*f+3*d^2*e^2)-192*a*b^3*e*(3*c^2*f^2+6*c*d*e*f+d^2*e^2))*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(11/2),1],
[(d*x^2+c)^2*(f*x^2+e)^2/(b*x^2+a)^(3/2),x,6,(-a*d+b*c)^2*(-a*f+b*e)^2*x/a/b^4/sqrt(b*x^2+a)+1/16*(19*a^2*d^2*f^2-28*a*b*d*f*(c*f+d*e)+8*b^2*(c^2*f^2+4*c*d*e*f+d^2*e^2))*x*sqrt(b*x^2+a)/b^4-1/24*d*f*(11*a*d*f-12*b*(c*f+d*e))*x^3*sqrt(b*x^2+a)/b^3+1/6*d^2*f^2*x^5*sqrt(b*x^2+a)/b^2-1/16*(35*a^3*d^2*f^2-32*b^3*c*e*(c*f+d*e)-60*a^2*b*d*f*(c*f+d*e)+24*a*b^2*(c^2*f^2+4*c*d*e*f+d^2*e^2))*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(9/2),1],
[(d*x^2+c)^2/(b*x^2+a)^(3/2)/(f*x^2+e),x,6,(-a*d+b*c)^2*x/a/b/(-a*f+b*e)/sqrt(b*x^2+a)+d^2*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(3/2)/f-(-c*f+d*e)^2*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/sqrt(e)/f/(-a*f+b*e)^(3/2),1],
[(d*x^2+c)^2/(b*x^2+a)^(3/2)/(f*x^2+e)^2,x,7,d^2*x/a/f^2/sqrt(b*x^2+a)+1/2*b*(-c*f+d*e)*(a*f*(-c*f+5*d*e)-2*b*e*(c*f+d*e))*x/a/e/f^2/(-a*f+b*e)^2/sqrt(b*x^2+a)-1/2*(-c*f+d*e)^2*x/e/f/(-a*f+b*e)/sqrt(b*x^2+a)/(f*x^2+e)+1/2*(-c*f+d*e)*(-a*c*f-3*a*d*e+4*b*c*e)*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/e^(3/2)/(-a*f+b*e)^(5/2),1],
[(d*x^2+c)^2/(b*x^2+a)^(3/2)/(f*x^2+e)^3,x,8,1/4*d*(a*d*f-4*b*c*f+4*b*d*e)*x/a/e/f^2/(-a*f+b*e)/sqrt(b*x^2+a)+1/8*b*(a^2*f^2*(-3*c^2*f^2+6*c*d*e*f+5*d^2*e^2)-8*b^2*e^2*(-c^2*f^2-c*d*e*f+d^2*e^2)+2*a*b*e*f*(5*c^2*f^2-22*c*d*e*f+9*d^2*e^2))*x/a/e^2/f^2/(-a*f+b*e)^3/sqrt(b*x^2+a)-1/4*f*x*(d*x^2+c)^2/e/(-a*f+b*e)/sqrt(b*x^2+a)/(f*x^2+e)^2-1/8*(-c*f+d*e)*(4*b*e*(-2*c*f+d*e)+a*f*(3*c*f+d*e))*x/e^2/f/(-a*f+b*e)^2/sqrt(b*x^2+a)/(f*x^2+e)+1/8*(8*b^2*c*e^2*(-3*c*f+2*d*e)-4*a*b*e*(-3*c^2*f^2-4*c*d*e*f+3*d^2*e^2)-a^2*f*(3*c^2*f^2+2*c*d*e*f+3*d^2*e^2))*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/e^(5/2)/(-a*f+b*e)^(7/2),1],
[(d*x^2+c)^3*(f*x^2+e)^3/(b*x^2+a)^(3/2),x,8,(-a*d+b*c)^3*(-a*f+b*e)^3*x/a/b^6/sqrt(b*x^2+a)+1/256*(437*a^4*d^3*f^3-1122*a^3*b*d^2*f^2*(c*f+d*e)+384*b^4*c*e*(c^2*f^2+3*c*d*e*f+d^2*e^2)+912*a^2*b^2*d*f*(c^2*f^2+3*c*d*e*f+d^2*e^2)-224*a*b^3*(c^3*f^3+9*c^2*d*e*f^2+9*c*d^2*e^2*f+d^3*e^3))*x*sqrt(b*x^2+a)/b^6-1/128*(103*a^3*d^3*f^3-246*a^2*b*d^2*f^2*(c*f+d*e)+176*a*b^2*d*f*(c^2*f^2+3*c*d*e*f+d^2*e^2)-32*b^3*(c^3*f^3+9*c^2*d*e*f^2+9*c*d^2*e^2*f+d^3*e^3))*x^3*sqrt(b*x^2+a)/b^5+1/160*d*f*(71*a^2*d^2*f^2-150*a*b*d*f*(c*f+d*e)+80*b^2*(c^2*f^2+3*c*d*e*f+d^2*e^2))*x^5*sqrt(b*x^2+a)/b^4-1/80*d^2*f^2*(19*a*d*f-30*b*(c*f+d*e))*x^7*sqrt(b*x^2+a)/b^3+1/10*d^3*f^3*x^9*sqrt(b*x^2+a)/b^2-3/256*(231*a^5*d^3*f^3-256*b^5*c^2*e^2*(c*f+d*e)-630*a^4*b*d^2*f^2*(c*f+d*e)+384*a*b^4*c*e*(c^2*f^2+3*c*d*e*f+d^2*e^2)+560*a^3*b^2*d*f*(c^2*f^2+3*c*d*e*f+d^2*e^2)-160*a^2*b^3*(c^3*f^3+9*c^2*d*e*f^2+9*c*d^2*e^2*f+d^3*e^3))*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(13/2),1],
[(d*x^2+c)^3/(b*x^2+a)^(3/2)/(f*x^2+e),x,8,(-a*d+b*c)^3*x/a/b^2/(-a*f+b*e)/sqrt(b*x^2+a)+1/2*d^3*x*sqrt(b*x^2+a)/b^2/f-1/2*d^2*(3*a*d*f-6*b*c*f+2*b*d*e)*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(5/2)/f^2+(-c*f+d*e)^3*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/sqrt(e)/f^2/(-a*f+b*e)^(3/2),1],
[(d*x^2+c)^3/(b*x^2+a)^(3/2)/(f*x^2+e)^2,x,9,-d^2*(a*d*f-3*b*c*f+2*b*d*e)*x/a/b/f^3/sqrt(b*x^2+a)-1/2*b*(-c*f+d*e)^2*(a*f*(-c*f+7*d*e)-2*b*e*(c*f+2*d*e))*x/a/e/f^3/(-a*f+b*e)^2/sqrt(b*x^2+a)+1/2*(-c*f+d*e)^3*x/e/f^2/(-a*f+b*e)/sqrt(b*x^2+a)/(f*x^2+e)+d^3*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(3/2)/f^2+1/2*(-c*f+d*e)^2*(a*f*(c*f+5*d*e)-2*b*e*(2*c*f+d*e))*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/e^(3/2)/f^2/(-a*f+b*e)^(5/2),1],
[(d*x^2+c)^3/(b*x^2+a)^(3/2)/(f*x^2+e)^3,x,8,d^3*x/a/f^3/sqrt(b*x^2+a)+1/8*b*(-c*f+d*e)*(2*a*b*e*f*(-5*c^2*f^2+16*c*d*e*f+13*d^2*e^2)-3*a^2*f^2*(-c^2*f^2-2*c*d*e*f+11*d^2*e^2)-8*b^2*e^2*(c^2*f^2+c*d*e*f+d^2*e^2))*x/a/e^2/f^3/(-a*f+b*e)^3/sqrt(b*x^2+a)+1/4*(-c*f+d*e)^3*x/e/f^2/(-a*f+b*e)/sqrt(b*x^2+a)/(f*x^2+e)^2+1/8*(-c*f+d*e)^2*(3*a*f*(c*f+3*d*e)-4*b*e*(2*c*f+d*e))*x/e^2/f^2/(-a*f+b*e)^2/sqrt(b*x^2+a)/(f*x^2+e)+3/8*(-c*f+d*e)*(8*b^2*c^2*e^2-4*a*b*c*e*(c*f+3*d*e)+a^2*(c^2*f^2+2*c*d*e*f+5*d^2*e^2))*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/e^(5/2)/(-a*f+b*e)^(7/2),1],
[1/(b*x^2+a)^(3/2)/(d*x^2+c)/(f*x^2+e),x,6,b^2*x/a/(-a*d+b*c)/(-a*f+b*e)/sqrt(b*x^2+a)-d^2*arctanh(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))/sqrt(c)/(-a*d+b*c)^(3/2)/(-c*f+d*e)+f^2*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/sqrt(e)/(-a*f+b*e)^(3/2)/(-c*f+d*e),1],
[1/(b*x^2+a)^(3/2)/(d*x^2+c)/(f*x^2+e)^2,x,7,-1/2*b*(a*b*c*f^2-a^2*d*f^2-2*b^2*e*(-c*f+d*e))*x/a/(-a*d+b*c)/e/(-a*f+b*e)^2/(-c*f+d*e)/sqrt(b*x^2+a)+1/2*f^2*x/e/(-a*f+b*e)/(-c*f+d*e)/sqrt(b*x^2+a)/(f*x^2+e)-d^3*arctanh(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))/sqrt(c)/(-a*d+b*c)^(3/2)/(-c*f+d*e)^2+1/2*f^2*(2*b*e*(-2*c*f+3*d*e)-a*f*(-c*f+3*d*e))*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/e^(3/2)/(-a*f+b*e)^(5/2)/(-c*f+d*e)^2,1],
[1/(b*x^2+a)^(3/2)/(d*x^2+c)/(f*x^2+e)^3,x,8,-1/8*b*(2*a*b^2*c*e*f^2*(-5*c*f+7*d*e)+a^3*d*f^3*(-3*c*f+7*d*e)-8*b^3*e^2*(-c*f+d*e)^2-a^2*b*f^2*(-3*c^2*f^2-3*c*d*e*f+14*d^2*e^2))*x/a/(-a*d+b*c)/e^2/(-a*f+b*e)^3/(-c*f+d*e)^2/sqrt(b*x^2+a)+1/4*f^2*x/e/(-a*f+b*e)/(-c*f+d*e)/sqrt(b*x^2+a)/(f*x^2+e)^2-1/8*f^2*(a*f*(-3*c*f+7*d*e)-4*b*e*(-2*c*f+3*d*e))*x/e^2/(-a*f+b*e)^2/(-c*f+d*e)^2/sqrt(b*x^2+a)/(f*x^2+e)-d^4*arctanh(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))/sqrt(c)/(-a*d+b*c)^(3/2)/(-c*f+d*e)^3-1/8*f^2*(4*a*b*e*f*(3*c^2*f^2-11*c*d*e*f+12*d^2*e^2)-a^2*f^2*(3*c^2*f^2-10*c*d*e*f+15*d^2*e^2)-8*b^2*e^2*(3*c^2*f^2-8*c*d*e*f+6*d^2*e^2))*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/e^(5/2)/(-a*f+b*e)^(7/2)/(-c*f+d*e)^3,1],
[1/(b*x^2+a)^(3/2)/(d*x^2+c)^2/(f*x^2+e)^2,x,8,1/2*b*(2*b^3*c*e*(-c*f+d*e)^2+a^3*d^2*f^2*(c*f+d*e)-2*a^2*b*d*f*(c^2*f^2+d^2*e^2)+a*b^2*(c^3*f^3+d^3*e^3))*x/a/c/(-a*d+b*c)^2/e/(-a*f+b*e)^2/(-c*f+d*e)^2/sqrt(b*x^2+a)-1/2*d^3*x/c/(-a*d+b*c)/(-c*f+d*e)^2/sqrt(b*x^2+a)/(d*x^2+c)-1/2*f^3*x/e/(-a*f+b*e)/(-c*f+d*e)^2/sqrt(b*x^2+a)/(f*x^2+e)+1/2*d^3*(a*d*(-5*c*f+d*e)-4*b*c*(-2*c*f+d*e))*arctanh(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))/c^(3/2)/(-a*d+b*c)^(5/2)/(-c*f+d*e)^3-1/2*f^3*(4*b*e*(-c*f+2*d*e)-a*f*(-c*f+5*d*e))*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/e^(3/2)/(-a*f+b*e)^(5/2)/(-c*f+d*e)^3,1],
[1/(b*x^2+a)^(3/2)/(d*x^2+c)^2/(f*x^2+e)^3,x,9,1/8*b*(8*b^4*c*e^2*(-c*f+d*e)^3-a^4*d^2*f^3*(-3*c^2*f^2+11*c*d*e*f+4*d^2*e^2)+6*a^3*b*d*f^2*(-c^3*f^3+2*c^2*d*e*f^2+3*c*d^2*e^2*f+2*d^3*e^3)+2*a*b^3*e*(-5*c^4*f^4+9*c^3*d*e*f^3+2*d^4*e^4)-3*a^2*b^2*f*(-c^4*f^4-3*c^3*d*e*f^3+12*c^2*d^2*e^2*f^2+4*d^4*e^4))*x/a/c/(-a*d+b*c)^2/e^2/(-a*f+b*e)^3/(-c*f+d*e)^3/sqrt(b*x^2+a)-1/2*d^4*x/c/(-a*d+b*c)/(-c*f+d*e)^3/sqrt(b*x^2+a)/(d*x^2+c)-1/4*f^3*x/e/(-a*f+b*e)/(-c*f+d*e)^2/sqrt(b*x^2+a)/(f*x^2+e)^2+1/8*f^3*(a*f*(-3*c*f+11*d*e)-8*b*e*(-c*f+2*d*e))*x/e^2/(-a*f+b*e)^2/(-c*f+d*e)^3/sqrt(b*x^2+a)/(f*x^2+e)+1/2*d^4*(a*d*(-7*c*f+d*e)-2*b*c*(-5*c*f+2*d*e))*arctanh(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))/c^(3/2)/(-a*d+b*c)^(5/2)/(-c*f+d*e)^4+1/8*f^3*(4*a*b*e*f*(3*c^2*f^2-16*c*d*e*f+25*d^2*e^2)-a^2*f^2*(3*c^2*f^2-14*c*d*e*f+35*d^2*e^2)-8*b^2*e^2*(3*c^2*f^2-10*c*d*e*f+10*d^2*e^2))*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/e^(5/2)/(-a*f+b*e)^(7/2)/(-c*f+d*e)^4,1],
[1/(b*x^2+a)^(3/2)/(d*x^2+c)^3/(f*x^2+e)^3,x,10,1/8*b*(8*b^5*c^2*e^2*(-c*f+d*e)^4+3*a^5*d^3*f^3*(c^3*f^3-5*c^2*d*e*f^2-5*c*d^2*e^2*f+d^3*e^3)-a^4*b*d^2*f^2*(9*c^4*f^4-35*c^3*d*e*f^3-44*c^2*d^2*e^2*f^2-35*c*d^3*e^3*f+9*d^4*e^4)+3*a^3*b^2*d*f*(3*c^5*f^5-5*c^4*d*e*f^4-22*c^3*d^2*e^2*f^3-22*c^2*d^3*e^3*f^2-5*c*d^4*e^4*f+3*d^5*e^5)+2*a*b^4*c*e*(5*c^5*f^5-11*c^4*d*e*f^4-11*c*d^4*e^4*f+5*d^5*e^5)-3*a^2*b^3*(c^6*f^6+5*c^5*d*e*f^5-22*c^4*d^2*e^2*f^4-22*c^2*d^4*e^4*f^2+5*c*d^5*e^5*f+d^6*e^6))*x/a/c^2/(-a*d+b*c)^3/e^2/(-a*f+b*e)^3/(-c*f+d*e)^4/sqrt(b*x^2+a)-1/4*d^4*x/c/(-a*d+b*c)/(-c*f+d*e)^3/sqrt(b*x^2+a)/(d*x^2+c)^2+1/8*d^4*(3*a*d*(-5*c*f+d*e)-4*b*c*(-5*c*f+2*d*e))*x/c^2/(-a*d+b*c)^2/(-c*f+d*e)^4/sqrt(b*x^2+a)/(d*x^2+c)+1/4*f^4*x/e/(-a*f+b*e)/(-c*f+d*e)^3/sqrt(b*x^2+a)/(f*x^2+e)^2+1/8*f^4*(4*b*e*(-2*c*f+5*d*e)-3*a*f*(-c*f+5*d*e))*x/e^2/(-a*f+b*e)^2/(-c*f+d*e)^4/sqrt(b*x^2+a)/(f*x^2+e)-3/8*d^4*(8*b^2*c^2*(5*c^2*f^2-4*c*d*e*f+d^2*e^2)-4*a*b*c*d*(14*c^2*f^2-7*c*d*e*f+d^2*e^2)+a^2*d^2*(21*c^2*f^2-6*c*d*e*f+d^2*e^2))*arctanh(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))/c^(5/2)/(-a*d+b*c)^(7/2)/(-c*f+d*e)^5-3/8*f^4*(4*a*b*e*f*(c^2*f^2-7*c*d*e*f+14*d^2*e^2)-a^2*f^2*(c^2*f^2-6*c*d*e*f+21*d^2*e^2)-8*b^2*e^2*(c^2*f^2-4*c*d*e*f+5*d^2*e^2))*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/e^(5/2)/(-a*f+b*e)^(7/2)/(-c*f+d*e)^5,1],
[(d*x^2+c)*(f*x^2+e)^3/(b*x^2+a)^(5/2),x,6,1/3*(-a*d+b*c)*(-a*f+b*e)^3*x/a/b^4/(b*x^2+a)^(3/2)+1/3*(-a*f+b*e)^2*(2*b^2*c*e-10*a^2*d*f+a*b*(7*c*f+d*e))*x/a^2/b^4/sqrt(b*x^2+a)+1/8*f^2*(-11*a*d*f+4*b*c*f+12*b*d*e)*x*sqrt(b*x^2+a)/b^4+1/4*d*f^3*x^3*sqrt(b*x^2+a)/b^3+1/8*f*(35*a^2*d*f^2+24*b^2*e*(c*f+d*e)-20*a*b*f*(c*f+3*d*e))*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(9/2),1],
[(d*x^2+c)*(f*x^2+e)^2/(b*x^2+a)^(5/2),x,5,1/3*(-a*d+b*c)*(-a*f+b*e)^2*x/a/b^3/(b*x^2+a)^(3/2)+1/3*(-a*f+b*e)*(2*b^2*c*e-7*a^2*d*f+a*b*(4*c*f+d*e))*x/a^2/b^3/sqrt(b*x^2+a)+1/2*d*f^2*x*sqrt(b*x^2+a)/b^3+1/2*f*(-5*a*d*f+2*b*c*f+4*b*d*e)*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(7/2),1],
[(d*x^2+c)*(f*x^2+e)/(b*x^2+a)^(5/2),x,4,1/3*(-a*d+b*c)*(-a*f+b*e)*x/a/b^2/(b*x^2+a)^(3/2)+1/3*(2*b^2*c*e-4*a^2*d*f+a*b*(c*f+d*e))*x/a^2/b^2/sqrt(b*x^2+a)+d*f*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(5/2),1],
[(d*x^2+c)/(b*x^2+a)^(5/2)/(f*x^2+e),x,4,1/3*(-a*d+b*c)*x/a/(-a*f+b*e)/(b*x^2+a)^(3/2)+1/3*(2*b^2*c*e+2*a^2*d*f+a*b*(-5*c*f+d*e))*x/a^2/(-a*f+b*e)^2/sqrt(b*x^2+a)-f*(-c*f+d*e)*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/sqrt(e)/(-a*f+b*e)^(5/2),1],
[(d*x^2+c)/(b*x^2+a)^(5/2)/(f*x^2+e)^2,x,5,1/6*b*(3*a*c*f-5*a*d*e+2*b*c*e)*x/a/e/(-a*f+b*e)^2/(b*x^2+a)^(3/2)+1/6*b*(4*b^2*c*e^2+2*a*b*e*(-8*c*f+d*e)+a^2*f*(-3*c*f+13*d*e))*x/a^2/e/(-a*f+b*e)^3/sqrt(b*x^2+a)+1/2*(-c*f+d*e)*x/e/(-a*f+b*e)/(b*x^2+a)^(3/2)/(f*x^2+e)-1/2*f*(2*b*e*(-3*c*f+2*d*e)+a*f*(c*f+d*e))*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/e^(3/2)/(-a*f+b*e)^(7/2),1],
[(d*x^2+c)/(b*x^2+a)^(5/2)/(f*x^2+e)^3,x,6,1/24*b*(8*b^2*c*e^2-4*a*b*e*(-9*c*f+8*d*e)-3*a^2*f*(3*c*f+d*e))*x/a/e^2/(-a*f+b*e)^3/(b*x^2+a)^(3/2)+1/24*b*(16*b^3*c*e^3+2*a^2*b*e*f*(-21*c*f+47*d*e)+8*a*b^2*e^2*(-11*c*f+d*e)+3*a^3*f^2*(3*c*f+d*e))*x/a^2/e^2/(-a*f+b*e)^4/sqrt(b*x^2+a)+1/4*(-c*f+d*e)*x/e/(-a*f+b*e)/(b*x^2+a)^(3/2)/(f*x^2+e)^2+1/8*(2*b*e*(-5*c*f+3*d*e)+a*f*(3*c*f+d*e))*x/e^2/(-a*f+b*e)^2/(b*x^2+a)^(3/2)/(f*x^2+e)-1/8*f*(24*b^2*e^2*(-2*c*f+d*e)-a^2*f^2*(3*c*f+d*e)+4*a*b*e*f*(4*c*f+3*d*e))*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/e^(5/2)/(-a*f+b*e)^(9/2),1],
[(d*x^2+c)^2*(f*x^2+e)^3/(b*x^2+a)^(5/2),x,7,1/3*(-a*d+b*c)^2*(-a*f+b*e)^3*x/a/b^5/(b*x^2+a)^(3/2)+1/3*(-a*d+b*c)*(-a*f+b*e)^2*(2*b^2*c*e-13*a^2*d*f+a*b*(7*c*f+4*d*e))*x/a^2/b^5/sqrt(b*x^2+a)+1/16*f*(41*a^2*d^2*f^2-22*a*b*d*f*(2*c*f+3*d*e)+8*b^2*(c^2*f^2+6*c*d*e*f+3*d^2*e^2))*x*sqrt(b*x^2+a)/b^5+1/24*d*f^2*(-17*a*d*f+12*b*c*f+18*b*d*e)*x^3*sqrt(b*x^2+a)/b^4+1/6*d^2*f^3*x^5*sqrt(b*x^2+a)/b^3-1/16*(105*a^3*d^2*f^3-70*a^2*b*d*f^2*(2*c*f+3*d*e)+40*a*b^2*f*(c^2*f^2+6*c*d*e*f+3*d^2*e^2)-16*b^3*e*(3*c^2*f^2+6*c*d*e*f+d^2*e^2))*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(11/2),1],
[(d*x^2+c)^2*(f*x^2+e)^2/(b*x^2+a)^(5/2),x,6,1/3*(-a*d+b*c)^2*(-a*f+b*e)^2*x/a/b^4/(b*x^2+a)^(3/2)+2/3*(-a*d+b*c)*(-a*f+b*e)*(b^2*c*e-5*a^2*d*f+2*a*b*(c*f+d*e))*x/a^2/b^4/sqrt(b*x^2+a)-1/8*d*f*(11*a*d*f-8*b*(c*f+d*e))*x*sqrt(b*x^2+a)/b^4+1/4*d^2*f^2*x^3*sqrt(b*x^2+a)/b^3+1/8*(35*a^2*d^2*f^2-40*a*b*d*f*(c*f+d*e)+8*b^2*(c^2*f^2+4*c*d*e*f+d^2*e^2))*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(9/2),1],
[(d*x^2+c)^2*(f*x^2+e)/(b*x^2+a)^(5/2),x,5,1/3*(-a*d+b*c)^2*(-a*f+b*e)*x/a/b^3/(b*x^2+a)^(3/2)+1/3*(-a*d+b*c)*(2*b^2*c*e-7*a^2*d*f+a*b*(c*f+4*d*e))*x/a^2/b^3/sqrt(b*x^2+a)+1/2*d^2*f*x*sqrt(b*x^2+a)/b^3+1/2*d*(-5*a*d*f+4*b*c*f+2*b*d*e)*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(7/2),1],
[(d*x^2+c)^2/(b*x^2+a)^(5/2)/(f*x^2+e),x,4,1/3*(-a*d+b*c)^2*x/a/b/(-a*f+b*e)/(b*x^2+a)^(3/2)+1/3*(-a*d+b*c)*(2*b^2*c*e-a^2*d*f+a*b*(-5*c*f+4*d*e))*x/a^2/b/(-a*f+b*e)^2/sqrt(b*x^2+a)+(-c*f+d*e)^2*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/sqrt(e)/(-a*f+b*e)^(5/2),1],
[(d*x^2+c)^2/(b*x^2+a)^(5/2)/(f*x^2+e)^2,x,9,1/3*d^2*x/a/f^2/(b*x^2+a)^(3/2)+1/6*b*(-c*f+d*e)*(a*f*(-3*c*f+7*d*e)-2*b*e*(c*f+d*e))*x/a/e/f^2/(-a*f+b*e)^2/(b*x^2+a)^(3/2)+2/3*d^2*x/a^2/f^2/sqrt(b*x^2+a)-1/6*b*(-c*f+d*e)*(a^2*f^2*(-3*c*f+23*d*e)+4*b^2*e^2*(c*f+d*e)-4*a*b*e*f*(4*c*f+3*d*e))*x/a^2/e/f^2/(-a*f+b*e)^3/sqrt(b*x^2+a)-1/2*(-c*f+d*e)^2*x/e/f/(-a*f+b*e)/(b*x^2+a)^(3/2)/(f*x^2+e)+1/2*(-c*f+d*e)*(2*b*e*(-3*c*f+d*e)+a*f*(c*f+3*d*e))*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/e^(3/2)/(-a*f+b*e)^(7/2),1],
[(d*x^2+c)^2/(b*x^2+a)^(5/2)/(f*x^2+e)^3,x,10,1/12*d*(3*a*d*f-8*b*c*f+8*b*d*e)*x/a/e/f^2/(-a*f+b*e)/(b*x^2+a)^(3/2)+1/24*b*(a^2*f^2*(-9*c^2*f^2+10*c*d*e*f+7*d^2*e^2)-8*b^2*e^2*(-c^2*f^2-2*c*d*e*f+2*d^2*e^2)+4*a*b*e*f*(9*c^2*f^2-24*c*d*e*f+11*d^2*e^2))*x/a/e^2/f^2/(-a*f+b*e)^3/(b*x^2+a)^(3/2)+4/3*b*d*(-c*f+d*e)*x/a^2/e/f^2/(-a*f+b*e)/sqrt(b*x^2+a)+1/24*b*(8*a*b^2*e^2*f*(-11*c^2*f^2-10*c*d*e*f+12*d^2*e^2)-a^3*f^3*(-9*c^2*f^2+26*c*d*e*f+23*d^2*e^2)-16*b^3*e^3*(-c^2*f^2-2*c*d*e*f+2*d^2*e^2)-2*a^2*b*e*f^2*(21*c^2*f^2-142*c*d*e*f+73*d^2*e^2))*x/a^2/e^2/f^2/(-a*f+b*e)^4/sqrt(b*x^2+a)-1/4*f*x*(d*x^2+c)^2/e/(-a*f+b*e)/(b*x^2+a)^(3/2)/(f*x^2+e)^2-1/8*(-c*f+d*e)*(2*b*e*(-5*c*f+3*d*e)+a*f*(3*c*f+d*e))*x/e^2/f/(-a*f+b*e)^2/(b*x^2+a)^(3/2)/(f*x^2+e)+1/8*(8*a*b*e*f*(-2*c^2*f^2-3*c*d*e*f+3*d^2*e^2)+a^2*f^2*(3*c^2*f^2+2*c*d*e*f+3*d^2*e^2)+8*b^2*e^2*(6*c^2*f^2-6*c*d*e*f+d^2*e^2))*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/e^(5/2)/(-a*f+b*e)^(9/2),1],
[(d*x^2+c)^3*(f*x^2+e)^3/(b*x^2+a)^(5/2),x,8,1/3*(-a*d+b*c)^3*(-a*f+b*e)^3*x/a/b^6/(b*x^2+a)^(3/2)+1/3*(-a*d+b*c)^2*(-a*f+b*e)^2*(2*b^2*c*e-16*a^2*d*f+7*a*b*(c*f+d*e))*x/a^2/b^6/sqrt(b*x^2+a)-1/128*(515*a^3*d^3*f^3-984*a^2*b*d^2*f^2*(c*f+d*e)+528*a*b^2*d*f*(c^2*f^2+3*c*d*e*f+d^2*e^2)-64*b^3*(c^3*f^3+9*c^2*d*e*f^2+9*c*d^2*e^2*f+d^3*e^3))*x*sqrt(b*x^2+a)/b^6+1/192*d*f*(259*a^2*d^2*f^2-408*a*b*d*f*(c*f+d*e)+144*b^2*(c^2*f^2+3*c*d*e*f+d^2*e^2))*x^3*sqrt(b*x^2+a)/b^5-1/48*d^2*f^2*(23*a*d*f-24*b*(c*f+d*e))*x^5*sqrt(b*x^2+a)/b^4+1/8*d^3*f^3*x^7*sqrt(b*x^2+a)/b^3+1/128*(1155*a^4*d^3*f^3-2520*a^3*b*d^2*f^2*(c*f+d*e)+384*b^4*c*e*(c^2*f^2+3*c*d*e*f+d^2*e^2)+1680*a^2*b^2*d*f*(c^2*f^2+3*c*d*e*f+d^2*e^2)-320*a*b^3*(c^3*f^3+9*c^2*d*e*f^2+9*c*d^2*e^2*f+d^3*e^3))*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(13/2),1],
[(d*x^2+c)^3*(f*x^2+e)^2/(b*x^2+a)^(5/2),x,7,1/3*(-a*d+b*c)^3*(-a*f+b*e)^2*x/a/b^5/(b*x^2+a)^(3/2)+1/3*(-a*d+b*c)^2*(-a*f+b*e)*(2*b^2*c*e-13*a^2*d*f+a*b*(4*c*f+7*d*e))*x/a^2/b^5/sqrt(b*x^2+a)+1/16*d*(41*a^2*d^2*f^2-22*a*b*d*f*(3*c*f+2*d*e)+8*b^2*(3*c^2*f^2+6*c*d*e*f+d^2*e^2))*x*sqrt(b*x^2+a)/b^5+1/24*d^2*f*(-17*a*d*f+18*b*c*f+12*b*d*e)*x^3*sqrt(b*x^2+a)/b^4+1/6*d^3*f^2*x^5*sqrt(b*x^2+a)/b^3-1/16*(105*a^3*d^3*f^2-70*a^2*b*d^2*f*(3*c*f+2*d*e)-16*b^3*c*(c^2*f^2+6*c*d*e*f+3*d^2*e^2)+40*a*b^2*d*(3*c^2*f^2+6*c*d*e*f+d^2*e^2))*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(11/2),1],
[(d*x^2+c)^3*(f*x^2+e)/(b*x^2+a)^(5/2),x,6,1/3*(-a*d+b*c)^3*(-a*f+b*e)*x/a/b^4/(b*x^2+a)^(3/2)+1/3*(-a*d+b*c)^2*(2*b^2*c*e-10*a^2*d*f+a*b*(c*f+7*d*e))*x/a^2/b^4/sqrt(b*x^2+a)+1/8*d^2*(-11*a*d*f+12*b*c*f+4*b*d*e)*x*sqrt(b*x^2+a)/b^4+1/4*d^3*f*x^3*sqrt(b*x^2+a)/b^3+1/8*d*(35*a^2*d^2*f+24*b^2*c*(c*f+d*e)-20*a*b*d*(3*c*f+d*e))*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(9/2),1],
[(d*x^2+c)^3/(b*x^2+a)^(5/2)/(f*x^2+e),x,7,1/3*(-a*d+b*c)^3*x/a/b^2/(-a*f+b*e)/(b*x^2+a)^(3/2)+1/3*(-a*d+b*c)^2*(2*b^2*c*e-4*a^2*d*f+a*b*(-5*c*f+7*d*e))*x/a^2/b^2/(-a*f+b*e)^2/sqrt(b*x^2+a)+d^3*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(5/2)/f-(-c*f+d*e)^3*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/sqrt(e)/f/(-a*f+b*e)^(5/2),1],
[(d*x^2+c)^3/(b*x^2+a)^(5/2)/(f*x^2+e)^2,x,9,-1/3*d^2*(a*d*f-3*b*c*f+2*b*d*e)*x/a/b/f^3/(b*x^2+a)^(3/2)-1/6*b*(-c*f+d*e)^2*(3*a*f*(-c*f+3*d*e)-2*b*e*(c*f+2*d*e))*x/a/e/f^3/(-a*f+b*e)^2/(b*x^2+a)^(3/2)-1/3*d^2*(-a*d*f-6*b*c*f+4*b*d*e)*x/a^2/b/f^3/sqrt(b*x^2+a)+1/6*b*(-c*f+d*e)^2*(3*a^2*f^2*(-c*f+11*d*e)+4*b^2*e^2*(c*f+2*d*e)-2*a*b*e*f*(8*c*f+13*d*e))*x/a^2/e/f^3/(-a*f+b*e)^3/sqrt(b*x^2+a)+1/2*(-c*f+d*e)^3*x/e/f^2/(-a*f+b*e)/(b*x^2+a)^(3/2)/(f*x^2+e)+1/2*(-c*f+d*e)^2*(-a*c*f-5*a*d*e+6*b*c*e)*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/e^(3/2)/(-a*f+b*e)^(7/2),1],
[(d*x^2+c)^3/(b*x^2+a)^(5/2)/(f*x^2+e)^3,x,10,1/3*d^3*x/a/f^3/(b*x^2+a)^(3/2)-1/24*b*(-c*f+d*e)*(3*a^2*f^2*(-3*c^2*f^2-6*c*d*e*f+17*d^2*e^2)-12*a*b*e*f*(-3*c^2*f^2+5*c*d*e*f+2*d^2*e^2)+8*b^2*e^2*(c^2*f^2+c*d*e*f+d^2*e^2))*x/a/e^2/f^3/(-a*f+b*e)^3/(b*x^2+a)^(3/2)+2/3*d^3*x/a^2/f^3/sqrt(b*x^2+a)-1/24*b*(-c*f+d*e)*(6*a^2*b*e*f^2*(-7*c^2*f^2+40*c*d*e*f+15*d^2*e^2)-3*a^3*f^3*(-3*c^2*f^2-6*c*d*e*f+49*d^2*e^2)+16*b^3*e^3*(c^2*f^2+c*d*e*f+d^2*e^2)-8*a*b^2*e^2*f*(11*c^2*f^2+8*c*d*e*f+8*d^2*e^2))*x/a^2/e^2/f^3/(-a*f+b*e)^4/sqrt(b*x^2+a)+1/4*(-c*f+d*e)^3*x/e/f^2/(-a*f+b*e)/(b*x^2+a)^(3/2)/(f*x^2+e)^2+1/8*(-c*f+d*e)^2*(3*a*f*(c*f+3*d*e)-2*b*e*(5*c*f+d*e))*x/e^2/f^2/(-a*f+b*e)^2/(b*x^2+a)^(3/2)/(f*x^2+e)+1/8*(-c*f+d*e)*(24*b^2*c*e^2*(-2*c*f+d*e)-4*a*b*e*(-4*c^2*f^2-13*c*d*e*f+5*d^2*e^2)-3*a^2*f*(c^2*f^2+2*c*d*e*f+5*d^2*e^2))*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/e^(5/2)/(-a*f+b*e)^(9/2),1],
[1/(b*x^2+a)^(5/2)/(d*x^2+c)/(f*x^2+e),x,7,1/3*b^2*x/a/(-a*d+b*c)/(-a*f+b*e)/(b*x^2+a)^(3/2)+1/3*b^2*(2*b^2*c*e+8*a^2*d*f-5*a*b*(c*f+d*e))*x/a^2/(-a*d+b*c)^2/(-a*f+b*e)^2/sqrt(b*x^2+a)+d^3*arctanh(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))/sqrt(c)/(-a*d+b*c)^(5/2)/(-c*f+d*e)-f^3*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/sqrt(e)/(-a*f+b*e)^(5/2)/(-c*f+d*e),1],
[1/(b*x^2+a)^(5/2)/(d*x^2+c)/(f*x^2+e)^2,x,8,-1/6*b*(3*a*b*c*f^2-3*a^2*d*f^2-2*b^2*e*(-c*f+d*e))*x/a/(-a*d+b*c)/e/(-a*f+b*e)^2/(-c*f+d*e)/(b*x^2+a)^(3/2)-1/6*b*(6*a^3*b*c*d*f^3-3*a^4*d^2*f^3-4*b^4*c*e^2*(-c*f+d*e)+2*a*b^3*e*(-8*c^2*f^2+3*c*d*e*f+5*d^2*e^2)-a^2*b^2*f*(3*c^2*f^2-22*c*d*e*f+22*d^2*e^2))*x/a^2/(-a*d+b*c)^2/e/(-a*f+b*e)^3/(-c*f+d*e)/sqrt(b*x^2+a)+1/2*f^2*x/e/(-a*f+b*e)/(-c*f+d*e)/(b*x^2+a)^(3/2)/(f*x^2+e)+d^4*arctanh(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))/sqrt(c)/(-a*d+b*c)^(5/2)/(-c*f+d*e)^2-1/2*f^3*(2*b*e*(-3*c*f+4*d*e)-a*f*(-c*f+3*d*e))*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/e^(3/2)/(-a*f+b*e)^(7/2)/(-c*f+d*e)^2,1],
[1/(b*x^2+a)^(5/2)/(d*x^2+c)/(f*x^2+e)^3,x,9,-1/24*b*(12*a*b^2*c*e*f^2*(-3*c*f+4*d*e)+3*a^3*d*f^3*(-3*c*f+7*d*e)-8*b^3*e^2*(-c*f+d*e)^2-3*a^2*b*f^2*(-3*c^2*f^2-5*c*d*e*f+16*d^2*e^2))*x/a/(-a*d+b*c)/e^2/(-a*f+b*e)^3/(-c*f+d*e)^2/(b*x^2+a)^(3/2)-1/24*b*(3*a^5*d^2*f^4*(-3*c*f+7*d*e)-16*b^5*c*e^3*(-c*f+d*e)^2+8*a*b^4*e^2*(-c*f+d*e)^2*(11*c*f+5*d*e)-18*a^4*b*d*f^3*(-c^2*f^2+3*d^2*e^2)+9*a^3*b^2*c*f^3*(-c^2*f^2-7*c*d*e*f+12*d^2*e^2)-2*a^2*b^3*e*f*(-21*c^3*f^3+83*c^2*d*e*f^2-112*c*d^2*e^2*f+56*d^3*e^3))*x/a^2/(-a*d+b*c)^2/e^2/(-a*f+b*e)^4/(-c*f+d*e)^2/sqrt(b*x^2+a)+1/4*f^2*x/e/(-a*f+b*e)/(-c*f+d*e)/(b*x^2+a)^(3/2)/(f*x^2+e)^2+1/8*f^2*(2*b*e*(-5*c*f+7*d*e)-a*f*(-3*c*f+7*d*e))*x/e^2/(-a*f+b*e)^2/(-c*f+d*e)^2/(b*x^2+a)^(3/2)/(f*x^2+e)+d^5*arctanh(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))/sqrt(c)/(-a*d+b*c)^(5/2)/(-c*f+d*e)^3-1/8*f^3*(a^2*f^2*(3*c^2*f^2-10*c*d*e*f+15*d^2*e^2)-4*a*b*e*f*(4*c^2*f^2-15*c*d*e*f+15*d^2*e^2)+8*b^2*e^2*(6*c^2*f^2-15*c*d*e*f+10*d^2*e^2))*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/e^(5/2)/(-a*f+b*e)^(9/2)/(-c*f+d*e)^3,1],
[1/(b*x^2+a)^(5/2)/(d*x^2+c)^2/(f*x^2+e)^2,x,9,1/6*b*(2*b^3*c*e*(-c*f+d*e)^2+3*a^3*d^2*f^2*(c*f+d*e)-6*a^2*b*d*f*(c^2*f^2+d^2*e^2)+3*a*b^2*(c^3*f^3+d^3*e^3))*x/a/c/(-a*d+b*c)^2/e/(-a*f+b*e)^2/(-c*f+d*e)^2/(b*x^2+a)^(3/2)+1/6*b*(4*b^5*c^2*e^2*(-c*f+d*e)^2+3*a^5*d^3*f^3*(c*f+d*e)-16*a*b^4*c*e*(-c*f+d*e)^2*(c*f+d*e)-9*a^4*b*d^2*f^2*(c^2*f^2+d^2*e^2)+9*a^3*b^2*d*f*(c^3*f^3+d^3*e^3)-a^2*b^3*(3*c^4*f^4-28*c^3*d*e*f^3+56*c^2*d^2*e^2*f^2-28*c*d^3*e^3*f+3*d^4*e^4))*x/a^2/c/(-a*d+b*c)^3/e/(-a*f+b*e)^3/(-c*f+d*e)^2/sqrt(b*x^2+a)-1/2*d^3*x/c/(-a*d+b*c)/(-c*f+d*e)^2/(b*x^2+a)^(3/2)/(d*x^2+c)-1/2*f^3*x/e/(-a*f+b*e)/(-c*f+d*e)^2/(b*x^2+a)^(3/2)/(f*x^2+e)-1/2*d^4*(a*d*(-5*c*f+d*e)-2*b*c*(-5*c*f+3*d*e))*arctanh(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))/c^(3/2)/(-a*d+b*c)^(7/2)/(-c*f+d*e)^3+1/2*f^4*(2*b*e*(-3*c*f+5*d*e)-a*f*(-c*f+5*d*e))*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/e^(3/2)/(-a*f+b*e)^(7/2)/(-c*f+d*e)^3,1],
[1/(b*x^2+a)^(5/2)/(d*x^2+c)^2/(f*x^2+e)^3,x,10,1/24*b*(8*b^4*c*e^2*(-c*f+d*e)^3-3*a^4*d^2*f^3*(-3*c^2*f^2+11*c*d*e*f+4*d^2*e^2)+6*a^3*b*d*f^2*(-3*c^3*f^3+5*c^2*d*e*f^2+10*c*d^2*e^2*f+6*d^3*e^3)-3*a^2*b^2*f*(-3*c^4*f^4-13*c^3*d*e*f^3+40*c^2*d^2*e^2*f^2+12*d^4*e^4)+12*a*b^3*e*(-3*c^4*f^4+5*c^3*d*e*f^3+d^4*e^4))*x/a/c/(-a*d+b*c)^2/e^2/(-a*f+b*e)^3/(-c*f+d*e)^3/(b*x^2+a)^(3/2)+1/24*b*(16*b^6*c^2*e^3*(-c*f+d*e)^3-8*a*b^5*c*e^2*(-c*f+d*e)^3*(11*c*f+8*d*e)-3*a^6*d^3*f^4*(-3*c^2*f^2+11*c*d*e*f+4*d^2*e^2)+3*a^5*b*d^2*f^3*(-9*c^3*f^3+19*c^2*d*e*f^2+22*c*d^2*e^2*f+16*d^3*e^3)-9*a^4*b^2*d*f^2*(-3*c^4*f^4-3*c^3*d*e*f^3+22*c^2*d^2*e^2*f^2+8*d^4*e^4)-2*a^2*b^4*e*(-21*c^5*f^5+101*c^4*d*e*f^4-204*c^3*d^2*e^2*f^3+204*c^2*d^3*e^3*f^2-68*c*d^4*e^4*f+6*d^5*e^5)+3*a^3*b^3*f*(-3*c^5*f^5-31*c^4*d*e*f^4+66*c^3*d^2*e^2*f^3+16*d^5*e^5))*x/a^2/c/(-a*d+b*c)^3/e^2/(-a*f+b*e)^4/(-c*f+d*e)^3/sqrt(b*x^2+a)-1/2*d^4*x/c/(-a*d+b*c)/(-c*f+d*e)^3/(b*x^2+a)^(3/2)/(d*x^2+c)-1/4*f^3*x/e/(-a*f+b*e)/(-c*f+d*e)^2/(b*x^2+a)^(3/2)/(f*x^2+e)^2-1/8*f^3*(2*b*e*(-5*c*f+9*d*e)-a*f*(-3*c*f+11*d*e))*x/e^2/(-a*f+b*e)^2/(-c*f+d*e)^3/(b*x^2+a)^(3/2)/(f*x^2+e)-1/2*d^5*(a*d*(-7*c*f+d*e)-6*b*c*(-2*c*f+d*e))*arctanh(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))/c^(3/2)/(-a*d+b*c)^(7/2)/(-c*f+d*e)^4-1/8*f^4*(8*a*b*e*f*(2*c^2*f^2-11*c*d*e*f+15*d^2*e^2)-24*b^2*e^2*(2*c^2*f^2-6*c*d*e*f+5*d^2*e^2)-a^2*f^2*(3*c^2*f^2-14*c*d*e*f+35*d^2*e^2))*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/e^(5/2)/(-a*f+b*e)^(9/2)/(-c*f+d*e)^4,1],
[1/(b*x^2+a)^(5/2)/(d*x^2+c)^3/(f*x^2+e)^3,x,11,1/24*b*(8*b^5*c^2*e^2*(-c*f+d*e)^4+27*a^3*b^2*d*f*(c*f+d*e)^3*(c^2*f^2-4*c*d*e*f+d^2*e^2)+9*a^5*d^3*f^3*(c^3*f^3-5*c^2*d*e*f^2-5*c*d^2*e^2*f+d^3*e^3)-9*a^4*b*d^2*f^2*(3*c^4*f^4-11*c^3*d*e*f^3-16*c^2*d^2*e^2*f^2-11*c*d^3*e^3*f+3*d^4*e^4)+36*a*b^4*c*e*(c^5*f^5-2*c^4*d*e*f^4-2*c*d^4*e^4*f+d^5*e^5)-9*a^2*b^3*(c^6*f^6+7*c^5*d*e*f^5-24*c^4*d^2*e^2*f^4-24*c^2*d^4*e^4*f^2+7*c*d^5*e^5*f+d^6*e^6))*x/a/c^2/(-a*d+b*c)^3/e^2/(-a*f+b*e)^3/(-c*f+d*e)^4/(b*x^2+a)^(3/2)+1/24*b*(16*b^7*c^3*e^3*(-c*f+d*e)^4-88*a*b^6*c^2*e^2*(-c*f+d*e)^4*(c*f+d*e)+9*a^7*d^4*f^4*(c^3*f^3-5*c^2*d*e*f^2-5*c*d^2*e^2*f+d^3*e^3)-6*a^6*b*d^3*f^3*(6*c^4*f^4-23*c^3*d*e*f^3-26*c^2*d^2*e^2*f^2-23*c*d^3*e^3*f+6*d^4*e^4)+6*a^5*b^2*d^2*f^2*(9*c^5*f^5-17*c^4*d*e*f^4-52*c^3*d^2*e^2*f^3-52*c^2*d^3*e^3*f^2-17*c*d^4*e^4*f+9*d^5*e^5)-36*a^4*b^3*d*f*(c^6*f^6+2*c^5*d*e*f^5-13*c^4*d^2*e^2*f^4-13*c^2*d^4*e^4*f^2+2*c*d^5*e^5*f+d^6*e^6)-2*a^2*b^5*c*e*(21*c^6*f^6-119*c^5*d*e*f^5+320*c^4*d^2*e^2*f^4-480*c^3*d^3*e^3*f^3+320*c^2*d^4*e^4*f^2-119*c*d^5*e^5*f+21*d^6*e^6)+3*a^3*b^4*(3*c^7*f^7+41*c^6*d*e*f^6-104*c^5*d^2*e^2*f^5-104*c^2*d^5*e^5*f^2+41*c*d^6*e^6*f+3*d^7*e^7))*x/a^2/c^2/(-a*d+b*c)^4/e^2/(-a*f+b*e)^4/(-c*f+d*e)^4/sqrt(b*x^2+a)-1/4*d^4*x/c/(-a*d+b*c)/(-c*f+d*e)^3/(b*x^2+a)^(3/2)/(d*x^2+c)^2-1/8*d^4*(2*b*c*(-11*c*f+5*d*e)-3*a*d*(-5*c*f+d*e))*x/c^2/(-a*d+b*c)^2/(-c*f+d*e)^4/(b*x^2+a)^(3/2)/(d*x^2+c)+1/4*f^4*x/e/(-a*f+b*e)/(-c*f+d*e)^3/(b*x^2+a)^(3/2)/(f*x^2+e)^2+1/8*f^4*(2*b*e*(-5*c*f+11*d*e)-3*a*f*(-c*f+5*d*e))*x/e^2/(-a*f+b*e)^2/(-c*f+d*e)^4/(b*x^2+a)^(3/2)/(f*x^2+e)+1/8*d^5*(24*b^2*c^2*(7*c^2*f^2-7*c*d*e*f+2*d^2*e^2)+3*a^2*d^2*(21*c^2*f^2-6*c*d*e*f+d^2*e^2)-4*a*b*c*d*(49*c^2*f^2-29*c*d*e*f+4*d^2*e^2))*arctanh(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))/c^(5/2)/(-a*d+b*c)^(9/2)/(-c*f+d*e)^5-1/8*f^5*(3*a^2*f^2*(c^2*f^2-6*c*d*e*f+21*d^2*e^2)+24*b^2*e^2*(2*c^2*f^2-7*c*d*e*f+7*d^2*e^2)-4*a*b*e*f*(4*c^2*f^2-29*c*d*e*f+49*d^2*e^2))*arctanh(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))/e^(5/2)/(-a*f+b*e)^(9/2)/(-c*f+d*e)^5,1],
[sqrt(b*x^2+a)*(d*x^2+c)^(3/2)*sqrt(f*x^2+e),x,9,1/48*(8*a*c+3*b*c^2/d-3*a^2*d/b-3*b*d*e^2/f^2+8*b*c*e/f+2*a*d*e/f)*x*sqrt(d*x^2+c)*sqrt(f*x^2+e)/sqrt(b*x^2+a)+1/24*(a*d*f+7*b*c*f+b*d*e)*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)/b/f+1/6*d*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)+1/48*sqrt(-a*d+b*c)*e*(3*a^2*d^2*f^2-2*a*b*d*f*(4*c*f+d*e)+b^2*(-3*c^2*f^2-8*c*d*e*f+3*d^2*e^2))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticE(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^2/sqrt(c)/d/f^2/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)+1/48*a*sqrt(-a*d+b*c)*(3*a^2*d^2*f^2-6*a*b*d*f*(c*f+d*e)-b^2*(-3*c^2*f^2-22*c*d*e*f+d^2*e^2))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*InverseJacobiAM(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a)),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^3/sqrt(c)/d/f/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)+1/16*a*(a^3*d^3*f^3+b^3*(-c*f+d*e)^3-a^2*b*d^2*f^2*(3*c*f+d*e)-a*b^2*d*f*(-3*c^2*f^2-6*c*d*e*f+d^2*e^2))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticPi(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),b*c/(-a*d+b*c),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^3/sqrt(c)/d/sqrt(-a*d+b*c)/f^2/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e),1],
[sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e),x,8,1/8*(a*d*f+b*c*f+b*d*e)*x*sqrt(d*x^2+c)*sqrt(f*x^2+e)/d/f/sqrt(b*x^2+a)+1/4*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)-1/8*sqrt(-a*d+b*c)*e*(a*d*f+b*c*f+b*d*e)*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticE(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b/sqrt(c)/d/f/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)+1/8*a*sqrt(-a*d+b*c)*(-a*d*f+b*c*f+3*b*d*e)*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*InverseJacobiAM(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a)),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^2/sqrt(c)/d/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)-1/8*a*(a^2*d^2*f^2+b^2*(-c*f+d*e)^2-2*a*b*d*f*(c*f+d*e))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticPi(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),b*c/(-a*d+b*c),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^2/sqrt(c)/d/sqrt(-a*d+b*c)/f/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e),1],
[sqrt(b*x^2+a)*sqrt(f*x^2+e)/sqrt(d*x^2+c),x,7,1/2*b*x*sqrt(d*x^2+c)*sqrt(f*x^2+e)/d/sqrt(b*x^2+a)-1/2*sqrt(-a*d+b*c)*e*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticE(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/sqrt(c)/d/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)+1/2*a*sqrt(-a*d+b*c)*f*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*InverseJacobiAM(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a)),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b/sqrt(c)/d/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)+1/2*a*(a*d*f-b*c*f+b*d*e)*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticPi(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),b*c/(-a*d+b*c),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b/sqrt(c)/d/sqrt(-a*d+b*c)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e),1],
[sqrt(b*x^2+a)*sqrt(f*x^2+e)/(d*x^2+c)^(3/2),x,6,a*sqrt(-c*f+d*e)*sqrt(c*(b*x^2+a)/a/(d*x^2+c))*sqrt(f*x^2+e)*EllipticE(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c))),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/c/d/sqrt(e)/sqrt(b*x^2+a)/sqrt(c*(f*x^2+e)/e/(d*x^2+c))-(-a*d+b*c)*f*sqrt(c*(b*x^2+a)/a/(d*x^2+c))*sqrt(f*x^2+e)*InverseJacobiAM(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c)),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/d^2/sqrt(e)/sqrt(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(c*(f*x^2+e)/e/(d*x^2+c))+b*c*f*sqrt(c*(b*x^2+a)/a/(d*x^2+c))*sqrt(f*x^2+e)*EllipticPi(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c))),d*e/(-c*f+d*e),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/d^2/sqrt(e)/sqrt(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(c*(f*x^2+e)/e/(d*x^2+c)),1],
[sqrt(b*x^2+a)*sqrt(f*x^2+e)/(d*x^2+c)^(5/2),x,5,1/3*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/c/(d*x^2+c)^(3/2)+1/3*sqrt(e)*(a*c*f-2*a*d*e+b*c*e)*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*EllipticE(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c))),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/c^2/(-a*d+b*c)/sqrt(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e)+1/3*sqrt(e)*(-a*f+b*e)*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*InverseJacobiAM(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c)),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/c/(-a*d+b*c)/sqrt(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e),1],
[sqrt(b*x^2+a)*sqrt(f*x^2+e)/(d*x^2+c)^(7/2),x,6,1/5*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/c/(d*x^2+c)^(5/2)-1/15*(a*d*(-3*c*f+4*d*e)-b*c*(-2*c*f+3*d*e))*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/c^2/(-a*d+b*c)/(-c*f+d*e)/(d*x^2+c)^(3/2)+1/15*sqrt(e)*(b^2*c^2*e*(-5*c*f+3*d*e)+a^2*d*(3*c^2*f^2-13*c*d*e*f+8*d^2*e^2)-a*b*c*(5*c^2*f^2-22*c*d*e*f+13*d^2*e^2))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*EllipticE(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c))),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/c^3/(-a*d+b*c)^2/(-c*f+d*e)^(3/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e)+1/15*sqrt(e)*(-a*f+b*e)*(b*c*(-5*c*f+6*d*e)-a*d*(-3*c*f+4*d*e))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*InverseJacobiAM(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c)),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/c^2/(-a*d+b*c)^2/(-c*f+d*e)^(3/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e),1],
[sqrt(b*x^2+a)*sqrt(f*x^2+e)/(d*x^2+c)^(9/2),x,7,1/7*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/c/(d*x^2+c)^(7/2)-1/35*(a*d*(-5*c*f+6*d*e)-b*c*(-4*c*f+5*d*e))*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/c^2/(-a*d+b*c)/(-c*f+d*e)/(d*x^2+c)^(5/2)+1/105*(b^2*c^2*(8*c^2*f^2-27*c*d*e*f+15*d^2*e^2)+a^2*d^2*(15*c^2*f^2-43*c*d*e*f+24*d^2*e^2)-a*b*c*d*(27*c^2*f^2-78*c*d*e*f+43*d^2*e^2))*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/c^3/(-a*d+b*c)^2/(-c*f+d*e)^2/(d*x^2+c)^(3/2)+1/105*sqrt(e)*(b^3*c^3*e*(35*c^2*f^2-42*c*d*e*f+15*d^2*e^2)-a*b^2*c^2*(-35*c^3*f^3+238*c^2*d*e*f^2-282*c*d^2*e^2*f+103*d^3*e^3)+2*a^2*b*c*d*(-21*c^3*f^3+141*c^2*d*e*f^2-172*c*d^2*e^2*f+64*d^3*e^3)-a^3*d^2*(-15*c^3*f^3+103*c^2*d*e*f^2-128*c*d^2*e^2*f+48*d^3*e^3))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*EllipticE(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c))),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/c^4/(-a*d+b*c)^3/(-c*f+d*e)^(5/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e)+1/105*sqrt(e)*(-a*f+b*e)*(a^2*d^2*(15*c^2*f^2-43*c*d*e*f+24*d^2*e^2)+b^2*c^2*(35*c^2*f^2-84*c*d*e*f+45*d^2*e^2)-a*b*c*d*(42*c^2*f^2-111*c*d*e*f+61*d^2*e^2))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*InverseJacobiAM(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c)),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/c^3/(-a*d+b*c)^3/(-c*f+d*e)^(5/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e),1],
[(b*x^2+a)^(3/2)*sqrt(d*x^2+c)*sqrt(f*x^2+e),x,9,1/48*(3*a^2*d^2*f^2+8*a*b*d*f*(c*f+d*e)-b^2*(3*c^2*f^2-2*c*d*e*f+3*d^2*e^2))*x*sqrt(d*x^2+c)*sqrt(f*x^2+e)/d^2/f^2/sqrt(b*x^2+a)+1/24*(7*a*d*f+b*c*f+b*d*e)*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)/d/f+1/6*b*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)-1/48*sqrt(-a*d+b*c)*e*(3*a^2*d^2*f^2+8*a*b*d*f*(c*f+d*e)-b^2*(3*c^2*f^2-2*c*d*e*f+3*d^2*e^2))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticE(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b/sqrt(c)/d^2/f^2/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)-1/48*a*sqrt(-a*d+b*c)*(3*a^2*d^2*f^2-6*a*b*d*f*(c*f+2*d*e)+b^2*(3*c^2*f^2-4*c*d*e*f+d^2*e^2))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*InverseJacobiAM(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a)),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^2/sqrt(c)/d^2/f/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)-1/16*a*(a^3*d^3*f^3+3*a*b^2*d*f*(-c*f+d*e)^2-3*a^2*b*d^2*f^2*(c*f+d*e)-b^3*(-c*f+d*e)^2*(c*f+d*e))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticPi(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),b*c/(-a*d+b*c),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^2/sqrt(c)/d^2/sqrt(-a*d+b*c)/f^2/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e),1],
[(b*x^2+a)^(3/2)*sqrt(f*x^2+e)/sqrt(d*x^2+c),x,8,1/8*b*(5*a*d*f-3*b*c*f+b*d*e)*x*sqrt(d*x^2+c)*sqrt(f*x^2+e)/d^2/f/sqrt(b*x^2+a)+1/4*b*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)/d-1/8*sqrt(-a*d+b*c)*e*(5*a*d*f-3*b*c*f+b*d*e)*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticE(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/sqrt(c)/d^2/f/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)+3/8*a*sqrt(-a*d+b*c)*(a*d*f-b*c*f+b*d*e)*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*InverseJacobiAM(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a)),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b/sqrt(c)/d^2/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)+1/8*a*(3*a^2*d^2*f^2+6*a*b*d*f*(-c*f+d*e)-b^2*(-3*c^2*f^2+2*c*d*e*f+d^2*e^2))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticPi(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),b*c/(-a*d+b*c),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b/sqrt(c)/d^2/sqrt(-a*d+b*c)/f/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e),1],
[(b*x^2+a)^(3/2)*sqrt(f*x^2+e)/(d*x^2+c)^(3/2),x,7,1/2*b*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/d/sqrt(d*x^2+c)-1/2*(-2*a*d+3*b*c)*sqrt(e)*sqrt(-c*f+d*e)*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*EllipticE(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c))),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/c/d^2/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e)+1/2*sqrt(e)*(2*a^2*d^2*f-b^2*c*(-3*c*f+d*e)+2*a*b*d*(-3*c*f+d*e))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*InverseJacobiAM(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c)),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/a/d^3/sqrt(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e)+1/2*b*c*sqrt(e)*(3*a*d*f-3*b*c*f+b*d*e)*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*EllipticPi(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c))),d*e/(-c*f+d*e),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/a/d^3/sqrt(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e),1],
[(b*x^2+a)^(3/2)*sqrt(f*x^2+e)/(d*x^2+c)^(5/2),x,7,1/3*(a/c-b/d)*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/(d*x^2+c)^(3/2)+1/3*sqrt(e)*(b*c*(-3*c*f+2*d*e)+a*d*(-c*f+2*d*e))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*EllipticE(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c))),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/c^2/d^2/sqrt(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e)-1/3*sqrt(e)*(3*b^2*c^2*f-a^2*d^2*f+a*b*d*(-3*c*f+d*e))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*InverseJacobiAM(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c)),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/a/c/d^3/sqrt(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e)+b^2*c*sqrt(e)*f*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*EllipticPi(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c))),d*e/(-c*f+d*e),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/a/d^3/sqrt(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e),1],
[(b*x^2+a)^(3/2)*sqrt(f*x^2+e)/(d*x^2+c)^(7/2),x,6,1/5*(a/c-b/d)*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/(d*x^2+c)^(5/2)+1/15*(b*c*(-3*c*f+2*d*e)+a*d*(-3*c*f+4*d*e))*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/c^2/d/(-c*f+d*e)/(d*x^2+c)^(3/2)+1/15*sqrt(e)*(2*b^2*c^2*e^2+a*b*c*e*(-7*c*f+3*d*e)-a^2*(3*c^2*f^2-13*c*d*e*f+8*d^2*e^2))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*EllipticE(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c))),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/c^3/(-a*d+b*c)/(-c*f+d*e)^(3/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e)-1/15*sqrt(e)*(-a*f+b*e)*(3*a*c*f-4*a*d*e+b*c*e)*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*InverseJacobiAM(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c)),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/c^2/(-a*d+b*c)/(-c*f+d*e)^(3/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e),1],
[(b*x^2+a)^(3/2)*sqrt(f*x^2+e)/(d*x^2+c)^(9/2),x,7,1/7*(a/c-b/d)*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/(d*x^2+c)^(7/2)+1/35*(a*d*(-5*c*f+6*d*e)+b*c*(-3*c*f+2*d*e))*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/c^2/d/(-c*f+d*e)/(d*x^2+c)^(5/2)+1/105*(2*b^2*c^2*(3*c^2*f^2-4*c*d*e*f+3*d^2*e^2)+a*b*c*d*(6*c^2*f^2-29*c*d*e*f+15*d^2*e^2)-a^2*d^2*(15*c^2*f^2-43*c*d*e*f+24*d^2*e^2))*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/c^3/d/(-a*d+b*c)/(-c*f+d*e)^2/(d*x^2+c)^(3/2)+1/105*sqrt(e)*(2*b^3*c^3*e^2*(-7*c*f+3*d*e)+a*b^2*c^2*e*(49*c^2*f^2-37*c*d*e*f+12*d^2*e^2)-a^2*b*c*(-21*c^3*f^3+170*c^2*d*e*f^2-197*c*d^2*e^2*f+72*d^3*e^3)+a^3*d*(-15*c^3*f^3+103*c^2*d*e*f^2-128*c*d^2*e^2*f+48*d^3*e^3))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*EllipticE(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c))),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/c^4/(-a*d+b*c)^2/(-c*f+d*e)^(5/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e)-1/105*sqrt(e)*(-a*f+b*e)*(b^2*c^2*e*(-7*c*f+3*d*e)+a^2*d*(15*c^2*f^2-43*c*d*e*f+24*d^2*e^2)-a*b*c*(21*c^2*f^2-62*c*d*e*f+33*d^2*e^2))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*InverseJacobiAM(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c)),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/c^3/(-a*d+b*c)^2/(-c*f+d*e)^(5/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e),1],
[(b*x^2+a)^(5/2)*sqrt(d*x^2+c)*sqrt(f*x^2+e),x,10,1/384*(15*a^3*d^3*f^3+73*a^2*b*d^2*f^2*(c*f+d*e)-a*b^2*d*f*(55*c^2*f^2-38*c*d*e*f+55*d^2*e^2)+b^3*(15*c^3*f^3-7*c^2*d*e*f^2-7*c*d^2*e^2*f+15*d^3*e^3))*x*sqrt(d*x^2+c)*sqrt(f*x^2+e)/d^3/f^3/sqrt(b*x^2+a)+1/192*(59*a^2*d^2*f^2+18*a*b*d*f*(c*f+d*e)-b^2*(5*c^2*f^2-2*c*d*e*f+5*d^2*e^2))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)/d^2/f^2+1/48*b*(17*a*d*f+b*c*f+b*d*e)*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)/d/f+1/8*b^2*x^5*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)-1/384*sqrt(-a*d+b*c)*e*(15*a^3*d^3*f^3+73*a^2*b*d^2*f^2*(c*f+d*e)-a*b^2*d*f*(55*c^2*f^2-38*c*d*e*f+55*d^2*e^2)+b^3*(15*c^3*f^3-7*c^2*d*e*f^2-7*c*d^2*e^2*f+15*d^3*e^3))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticE(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b/sqrt(c)/d^3/f^3/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)-1/384*a*sqrt(-a*d+b*c)*(15*a^3*d^3*f^3-15*a^2*b*d^2*f^2*(3*c*f+5*d*e)+a*b^2*d*f*(45*c^2*f^2-62*c*d*e*f+17*d^2*e^2)-b^3*(15*c^3*f^3-17*c^2*d*e*f^2-3*c*d^2*e^2*f+5*d^3*e^3))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*InverseJacobiAM(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a)),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^2/sqrt(c)/d^3/f^2/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)-1/128*a*(5*a^4*d^4*f^4+30*a^2*b^2*d^2*f^2*(-c*f+d*e)^2-20*a^3*b*d^3*f^3*(c*f+d*e)-20*a*b^3*d*f*(-c*f+d*e)^2*(c*f+d*e)+b^4*(-c*f+d*e)^2*(5*c^2*f^2+6*c*d*e*f+5*d^2*e^2))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticPi(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),b*c/(-a*d+b*c),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^2/sqrt(c)/d^3/sqrt(-a*d+b*c)/f^3/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e),1],
[(b*x^2+a)^(5/2)*sqrt(f*x^2+e)/sqrt(d*x^2+c),x,9,1/48*b*(33*a^2*d^2*f^2+2*a*b*d*f*(-20*c*f+7*d*e)-b^2*(-15*c^2*f^2+4*c*d*e*f+3*d^2*e^2))*x*sqrt(d*x^2+c)*sqrt(f*x^2+e)/d^3/f^2/sqrt(b*x^2+a)+1/24*b*(13*a*d*f-5*b*c*f+b*d*e)*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)/d^2/f+1/6*b^2*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)/d-1/48*sqrt(-a*d+b*c)*e*(33*a^2*d^2*f^2+2*a*b*d*f*(-20*c*f+7*d*e)-b^2*(-15*c^2*f^2+4*c*d*e*f+3*d^2*e^2))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticE(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/sqrt(c)/d^3/f^2/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)+1/48*a*sqrt(-a*d+b*c)*(15*a^2*d^2*f^2+30*a*b*d*f*(-c*f+d*e)-b^2*(-15*c^2*f^2+14*c*d*e*f+d^2*e^2))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*InverseJacobiAM(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a)),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b/sqrt(c)/d^3/f/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)+1/16*a*(5*a^3*d^3*f^3+15*a^2*b*d^2*f^2*(-c*f+d*e)-5*a*b^2*d*f*(-3*c^2*f^2+2*c*d*e*f+d^2*e^2)+b^3*(-5*c^3*f^3+3*c^2*d*e*f^2+c*d^2*e^2*f+d^3*e^3))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticPi(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),b*c/(-a*d+b*c),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b/sqrt(c)/d^3/sqrt(-a*d+b*c)/f^2/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e),1],
[(b*x^2+a)^(5/2)*sqrt(f*x^2+e)/(d*x^2+c)^(3/2),x,8,1/8*b*(9*a*d*f-5*b*c*f+b*d*e)*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/d^2/f/sqrt(d*x^2+c)+1/4*b^2*x^3*sqrt(b*x^2+a)*sqrt(f*x^2+e)/d/sqrt(d*x^2+c)-1/8*sqrt(e)*sqrt(-c*f+d*e)*(25*a*b*c*d*f-8*a^2*d^2*f+b^2*c*(-15*c*f+d*e))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*EllipticE(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c))),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/c/d^3/f/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e)+1/8*sqrt(e)*(8*a^3*d^3*f^2-3*a*b^2*c*d*f*(-15*c*f+7*d*e)+8*a^2*b*d^2*f*(-5*c*f+2*d*e)+b^3*c*(-15*c^2*f^2+6*c*d*e*f+d^2*e^2))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*InverseJacobiAM(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c)),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/a/d^4/f/sqrt(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e)+1/8*b*c*sqrt(e)*(15*a^2*d^2*f^2+10*a*b*d*f*(-3*c*f+d*e)-b^2*(-15*c^2*f^2+6*c*d*e*f+d^2*e^2))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*EllipticPi(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c))),d*e/(-c*f+d*e),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/a/d^4/f/sqrt(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e),1],
[(b*x^2+a)^(5/2)*sqrt(f*x^2+e)/(d*x^2+c)^(5/2),x,8,1/3*(-a*d+b*c)^2*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/c/d^2/(d*x^2+c)^(3/2)+1/2*b^2*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/d^2/sqrt(d*x^2+c)-1/6*sqrt(e)*(b^2*c^2*(-15*c*f+13*d*e)-2*a*b*c*d*(-5*c*f+3*d*e)-2*a^2*d^2*(-c*f+2*d*e))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*EllipticE(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c))),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/c^2/d^3/sqrt(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e)+1/6*sqrt(e)*(2*a^3*d^3*f+2*a*b^2*c*d*(-15*c*f+4*d*e)-3*b^3*c^2*(-5*c*f+d*e)-2*a^2*b*d^2*(-5*c*f+d*e))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*InverseJacobiAM(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c)),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/a/c/d^4/sqrt(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e)+1/2*b^2*c*sqrt(e)*(5*a*d*f-5*b*c*f+b*d*e)*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*EllipticPi(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c))),d*e/(-c*f+d*e),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/a/d^4/sqrt(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e),1],
[(b*x^2+a)^(5/2)*sqrt(f*x^2+e)/(d*x^2+c)^(7/2),x,8,1/5*(-a*d+b*c)^2*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/c/d^2/(d*x^2+c)^(5/2)-1/15*(-a*d+b*c)*(b*c*(-8*c*f+7*d*e)+a*d*(-3*c*f+4*d*e))*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/c^2/d^2/(-c*f+d*e)/(d*x^2+c)^(3/2)+1/15*sqrt(e)*(a^2*d^2*(3*c^2*f^2-13*c*d*e*f+8*d^2*e^2)+a*b*c*d*(5*c^2*f^2-8*c*d*e*f+7*d^2*e^2)+b^2*c^2*(15*c^2*f^2-25*c*d*e*f+8*d^2*e^2))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*EllipticE(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c))),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/c^3/d^3/(-c*f+d*e)^(3/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e)+1/15*sqrt(e)*(a^3*d^3*f*(-3*c*f+4*d*e)-15*b^3*c^3*f*(-c*f+d*e)-a^2*b*d^2*(5*c^2*f^2-7*c*d*e*f+4*d^2*e^2)-a*b^2*c*d*(15*c^2*f^2-20*c*d*e*f+4*d^2*e^2))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*InverseJacobiAM(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c)),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/a/c^2/d^4/(-c*f+d*e)^(3/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e)+b^3*c*sqrt(e)*f*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*EllipticPi(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c))),d*e/(-c*f+d*e),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/a/d^4/sqrt(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e),1],
[(b*x^2+a)^(5/2)*sqrt(f*x^2+e)/(d*x^2+c)^(9/2),x,7,1/7*(-a*d+b*c)^2*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/c/d^2/(d*x^2+c)^(7/2)-1/35*(-a*d+b*c)*(b*c*(-10*c*f+9*d*e)+a*d*(-5*c*f+6*d*e))*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/c^2/d^2/(-c*f+d*e)/(d*x^2+c)^(5/2)+1/105*(a^2*d^2*(15*c^2*f^2-43*c*d*e*f+24*d^2*e^2)+b^2*c^2*(15*c^2*f^2-27*c*d*e*f+8*d^2*e^2)+a*b*c*d*(15*c^2*f^2-20*c*d*e*f+13*d^2*e^2))*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/c^3/d^2/(-c*f+d*e)^2/(d*x^2+c)^(3/2)+1/105*sqrt(e)*(8*b^3*c^3*e^3+3*a*b^2*c^2*e^2*(-11*c*f+3*d*e)+2*a^2*b*c*e*(29*c^2*f^2-25*c*d*e*f+8*d^2*e^2)-a^3*(-15*c^3*f^3+103*c^2*d*e*f^2-128*c*d^2*e^2*f+48*d^3*e^3))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*EllipticE(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c))),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/c^4/(-a*d+b*c)/(-c*f+d*e)^(5/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e)-1/105*sqrt(e)*(-a*f+b*e)*(4*b^2*c^2*e^2+a*b*c*e*(-13*c*f+5*d*e)-a^2*(15*c^2*f^2-43*c*d*e*f+24*d^2*e^2))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*InverseJacobiAM(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c)),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/c^3/(-a*d+b*c)/(-c*f+d*e)^(5/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e),1],
[(b*x^2+a)^(5/2)*sqrt(f*x^2+e)/(d*x^2+c)^(11/2),x,8,1/9*(-a*d+b*c)^2*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/c/d^2/(d*x^2+c)^(9/2)-1/63*(-a*d+b*c)*(b*c*(-12*c*f+11*d*e)+a*d*(-7*c*f+8*d*e))*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/c^2/d^2/(-c*f+d*e)/(d*x^2+c)^(7/2)+1/315*(b^2*c^2*(15*c^2*f^2-29*c*d*e*f+8*d^2*e^2)+a*b*c*d*(25*c^2*f^2-32*c*d*e*f+19*d^2*e^2)+a^2*d^2*(35*c^2*f^2-89*c*d*e*f+48*d^2*e^2))*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/c^3/d^2/(-c*f+d*e)^2/(d*x^2+c)^(5/2)-1/315*(a^3*d^3*(-35*c^3*f^3+159*c^2*d*e*f^2-180*c*d^2*e^2*f+64*d^3*e^3)-a*b^2*c^2*d*(-10*c^3*f^3+14*c^2*d*e*f^2-43*c*d^2*e^2*f+15*d^3*e^3)-2*b^3*c^3*(-5*c^3*f^3+13*c^2*d*e*f^2-8*c*d^2*e^2*f+4*d^3*e^3)-2*a^2*b*c*d^2*(-5*c^3*f^3+52*c^2*d*e*f^2-53*c*d^2*e^2*f+18*d^3*e^3))*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/c^4/d^2/(-a*d+b*c)/(-c*f+d*e)^3/(d*x^2+c)^(3/2)+1/315*sqrt(e)*(8*b^4*c^4*e^3*(-3*c*f+d*e)+a*b^3*c^3*e^2*(99*c^2*f^2-46*c*d*e*f+11*d^2*e^2)+3*a^2*b^2*c^2*e*(-58*c^3*f^3+53*c^2*d*e*f^2-36*c*d^2*e^2*f+9*d^3*e^3)+a^4*d*(35*c^4*f^4-334*c^3*d*e*f^3+627*c^2*d^2*e^2*f^2-472*c*d^3*e^3*f+128*d^4*e^4)-a^3*b*c*(45*c^4*f^4-548*c^3*d*e*f^3+945*c^2*d^2*e^2*f^2-690*c*d^3*e^3*f+184*d^4*e^4))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*EllipticE(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c))),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/c^5/(-a*d+b*c)^2/(-c*f+d*e)^(7/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e)-1/315*sqrt(e)*(-a*f+b*e)*(4*b^3*c^3*e^2*(-3*c*f+d*e)+3*a*b^2*c^2*e*(13*c^2*f^2-7*c*d*e*f+2*d^2*e^2)+a^3*d*(-35*c^3*f^3+159*c^2*d*e*f^2-180*c*d^2*e^2*f+64*d^3*e^3)-3*a^2*b*c*(-15*c^3*f^3+76*c^2*d*e*f^2-81*c*d^2*e^2*f+28*d^3*e^3))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*InverseJacobiAM(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c)),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/c^4/(-a*d+b*c)^2/(-c*f+d*e)^(7/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e),1],
[(d*x^2+c)^(3/2)*sqrt(f*x^2+e)/sqrt(b*x^2+a),x,8,1/8*(-3*a*d*f+5*b*c*f+b*d*e)*x*sqrt(d*x^2+c)*sqrt(f*x^2+e)/b/f/sqrt(b*x^2+a)+1/4*d*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)/b-1/8*sqrt(-a*d+b*c)*e*(-3*a*d*f+5*b*c*f+b*d*e)*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticE(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^2/sqrt(c)/f/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)+1/8*sqrt(-a*d+b*c)*(3*a^2*d*f-3*a*b*c*f-5*a*b*d*e+8*b^2*c*e)*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*InverseJacobiAM(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a)),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^3/sqrt(c)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)+1/8*a*(3*a^2*d^2*f^2-2*a*b*d*f*(3*c*f+d*e)-b^2*(-3*c^2*f^2-6*c*d*e*f+d^2*e^2))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticPi(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),b*c/(-a*d+b*c),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^3/sqrt(c)/sqrt(-a*d+b*c)/f/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e),1],
[sqrt(d*x^2+c)*sqrt(f*x^2+e)/sqrt(b*x^2+a),x,7,1/2*d*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/b/sqrt(d*x^2+c)-1/2*sqrt(e)*sqrt(-c*f+d*e)*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*EllipticE(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c))),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/b/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e)+1/2*c*sqrt(e)*sqrt(-c*f+d*e)*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*InverseJacobiAM(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c)),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/a/d/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e)+1/2*c*sqrt(e)*(-a*d*f+b*c*f+b*d*e)*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*EllipticPi(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c))),d*e/(-c*f+d*e),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/a/b/d/sqrt(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e),1],
[sqrt(f*x^2+e)/sqrt(b*x^2+a)/sqrt(d*x^2+c),x,2,e*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticPi(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),-a*f/(-a*f+b*e),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/sqrt(a*f-b*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[sqrt(f*x^2+e)/sqrt(b*x^2+a)/(d*x^2+c)^(3/2),x,2,sqrt(a)*sqrt(c*(b*x^2+a)/a/(d*x^2+c))*sqrt(f*x^2+e)*EllipticE(sin(arcsin(sqrt(a*d-b*c)*x/sqrt(a)/sqrt(d*x^2+c))),sqrt(-a*(-c*f+d*e)/(-a*d+b*c)/e))/c/sqrt(a*d-b*c)/sqrt(b*x^2+a)/sqrt(c*(f*x^2+e)/e/(d*x^2+c)),1],
[sqrt(f*x^2+e)/sqrt(b*x^2+a)/(d*x^2+c)^(5/2),x,5,-1/3*d*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/c/(-a*d+b*c)/(d*x^2+c)^(3/2)-1/3*sqrt(e)*(b*c*(-3*c*f+4*d*e)-a*d*(-c*f+2*d*e))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*EllipticE(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c))),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/c^2/(-a*d+b*c)^2/sqrt(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e)+1/3*(-a*d+3*b*c)*sqrt(e)*(-a*f+b*e)*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*InverseJacobiAM(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c)),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/a/c/(-a*d+b*c)^2/sqrt(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e),1],
[sqrt(f*x^2+e)/sqrt(b*x^2+a)/(d*x^2+c)^(7/2),x,6,-1/5*d*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/c/(-a*d+b*c)/(d*x^2+c)^(5/2)-1/15*d*(b*c*(-7*c*f+8*d*e)-a*d*(-3*c*f+4*d*e))*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/c^2/(-a*d+b*c)^2/(-c*f+d*e)/(d*x^2+c)^(3/2)-1/15*sqrt(e)*(a^2*d^2*(3*c^2*f^2-13*c*d*e*f+8*d^2*e^2)-a*b*c*d*(10*c^2*f^2-37*c*d*e*f+23*d^2*e^2)+b^2*c^2*(15*c^2*f^2-40*c*d*e*f+23*d^2*e^2))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*EllipticE(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c))),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/c^3/(-a*d+b*c)^3/(-c*f+d*e)^(3/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e)-1/15*sqrt(e)*(-a*f+b*e)*(a*b*c*d*(-10*c*f+11*d*e)-a^2*d^2*(-3*c*f+4*d*e)-15*b^2*c^2*(-c*f+d*e))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*InverseJacobiAM(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c)),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/a/c^2/(-a*d+b*c)^3/(-c*f+d*e)^(3/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e),1],
[(d*x^2+c)^(3/2)*sqrt(f*x^2+e)/(b*x^2+a)^(3/2),x,7,1/2*d*x*sqrt(d*x^2+c)*sqrt(f*x^2+e)/b/sqrt(b*x^2+a)+1/2*(-3*a*d+2*b*c)*sqrt(-a*d+b*c)*e*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticE(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/a/b^2/sqrt(c)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)+1/2*d*sqrt(-a*d+b*c)*(-3*a*f+4*b*e)*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*InverseJacobiAM(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a)),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^3/sqrt(c)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)+1/2*a*d*(-3*a*d*f+3*b*c*f+b*d*e)*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticPi(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),b*c/(-a*d+b*c),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^3/sqrt(c)/sqrt(-a*d+b*c)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e),1],
[sqrt(d*x^2+c)*sqrt(f*x^2+e)/(b*x^2+a)^(3/2),x,6,sqrt(c)*sqrt(-a*d+b*c)*sqrt(a*(d*x^2+c)/c/(b*x^2+a))*sqrt(f*x^2+e)*EllipticE(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/a/b/sqrt(d*x^2+c)/sqrt(a*(f*x^2+e)/e/(b*x^2+a))+sqrt(c)*d*(-a*f+b*e)*sqrt(a*(d*x^2+c)/c/(b*x^2+a))*sqrt(f*x^2+e)*InverseJacobiAM(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a)),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^2/sqrt(-a*d+b*c)/e/sqrt(d*x^2+c)/sqrt(a*(f*x^2+e)/e/(b*x^2+a))+a*sqrt(c)*d*f*sqrt(a*(d*x^2+c)/c/(b*x^2+a))*sqrt(f*x^2+e)*EllipticPi(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),b*c/(-a*d+b*c),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^2/sqrt(-a*d+b*c)/e/sqrt(d*x^2+c)/sqrt(a*(f*x^2+e)/e/(b*x^2+a)),1],
[sqrt(f*x^2+e)/(b*x^2+a)^(3/2)/sqrt(d*x^2+c),x,2,sqrt(c)*sqrt(a*(d*x^2+c)/c/(b*x^2+a))*sqrt(f*x^2+e)*EllipticE(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/a/sqrt(-a*d+b*c)/sqrt(d*x^2+c)/sqrt(a*(f*x^2+e)/e/(b*x^2+a)),1],
[sqrt(f*x^2+e)/(b*x^2+a)^(3/2)/(d*x^2+c)^(3/2),x,5,b*x*sqrt(f*x^2+e)/a/(-a*d+b*c)/sqrt(b*x^2+a)/sqrt(d*x^2+c)+(a*d+b*c)*sqrt(e)*sqrt(-c*f+d*e)*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*EllipticE(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c))),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/a/c/(-a*d+b*c)^2/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e)-sqrt(e)*(-a*d*f-b*c*f+2*b*d*e)*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*InverseJacobiAM(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c)),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/a/(-a*d+b*c)^2/sqrt(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e),1],
[sqrt(f*x^2+e)/(b*x^2+a)^(3/2)/(d*x^2+c)^(5/2),x,6,-1/3*d*x*sqrt(f*x^2+e)/c/(-a*d+b*c)/sqrt(b*x^2+a)/(d*x^2+c)^(3/2)+1/3*b*(a*d+3*b*c)*x*sqrt(f*x^2+e)/a/c/(-a*d+b*c)^2/sqrt(b*x^2+a)/sqrt(d*x^2+c)+1/3*sqrt(e)*(a*b*c*d*(-6*c*f+7*d*e)+3*b^2*c^2*(-c*f+d*e)-a^2*d^2*(-c*f+2*d*e))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*EllipticE(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c))),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/a/c^2/(-a*d+b*c)^3/sqrt(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e)-1/3*sqrt(e)*(a^2*d^2*f+3*b^2*c*(-c*f+3*d*e)-a*b*d*(6*c*f+d*e))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*InverseJacobiAM(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c)),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/a/c/(-a*d+b*c)^3/sqrt(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e),1],
[(d*x^2+c)^(5/2)*sqrt(f*x^2+e)/(b*x^2+a)^(5/2),x,8,1/3*(-a*d+b*c)^2*x*sqrt(d*x^2+c)*sqrt(f*x^2+e)/a/b^2/(b*x^2+a)^(3/2)+1/2*d^2*x*sqrt(d*x^2+c)*sqrt(f*x^2+e)/b^2/sqrt(b*x^2+a)+1/6*sqrt(-a*d+b*c)*e*(4*b^3*c^2*e+15*a^3*d^2*f+2*a*b^2*c*(-c*f+3*d*e)-a^2*b*d*(10*c*f+13*d*e))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticE(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/a^2/b^3/sqrt(c)/(-a*f+b*e)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)-1/6*sqrt(-a*d+b*c)*(33*a^2*b*d^2*e*f-15*a^3*d^2*f^2-2*b^3*c*e*(-c*f+d*e)-2*a*b^2*d*e*(c*f+8*d*e))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*InverseJacobiAM(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a)),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/a/b^4/sqrt(c)/(-a*f+b*e)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)+1/2*a*d^2*(-5*a*d*f+5*b*c*f+b*d*e)*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticPi(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),b*c/(-a*d+b*c),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^4/sqrt(c)/sqrt(-a*d+b*c)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e),1],
[(d*x^2+c)^(3/2)*sqrt(f*x^2+e)/(b*x^2+a)^(5/2),x,7,1/3*(-a*d+b*c)*x*sqrt(d*x^2+c)*sqrt(f*x^2+e)/a/b/(b*x^2+a)^(3/2)+1/3*sqrt(-a*d+b*c)*e*(-3*a^2*d*f-a*b*c*f+2*a*b*d*e+2*b^2*c*e)*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticE(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/a^2/b^2/sqrt(c)/(-a*f+b*e)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)-1/3*(6*a^2*b*d^2*e*f-3*a^3*d^2*f^2-b^3*c*e*(-c*f+d*e)-a*b^2*d*e*(c*f+2*d*e))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*InverseJacobiAM(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a)),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/a/b^3/sqrt(c)/sqrt(-a*d+b*c)/(-a*f+b*e)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)+a*d^2*f*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticPi(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),b*c/(-a*d+b*c),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^3/sqrt(c)/sqrt(-a*d+b*c)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e),1],
[sqrt(d*x^2+c)*sqrt(f*x^2+e)/(b*x^2+a)^(5/2),x,5,1/3*x*sqrt(d*x^2+c)*sqrt(f*x^2+e)/a/(b*x^2+a)^(3/2)+1/3*e*(2*b*c*e-a*(c*f+d*e))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticE(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/a^2/sqrt(c)/sqrt(-a*d+b*c)/(-a*f+b*e)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)+1/3*e*(-c*f+d*e)*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*InverseJacobiAM(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a)),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/a/sqrt(c)/sqrt(-a*d+b*c)/(-a*f+b*e)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e),1],
[sqrt(f*x^2+e)/(b*x^2+a)^(5/2)/sqrt(d*x^2+c),x,5,1/3*b*x*sqrt(d*x^2+c)*sqrt(f*x^2+e)/a/(-a*d+b*c)/(b*x^2+a)^(3/2)+1/3*e*(2*b^2*c*e+3*a^2*d*f-a*b*(c*f+4*d*e))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticE(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/a^2/sqrt(c)/(-a*d+b*c)^(3/2)/(-a*f+b*e)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)+1/3*b*e*(-c*f+d*e)*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*InverseJacobiAM(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a)),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/a/sqrt(c)/(-a*d+b*c)^(3/2)/(-a*f+b*e)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e),1],
[sqrt(f*x^2+e)/(b*x^2+a)^(5/2)/(d*x^2+c)^(3/2),x,6,1/3*b*x*sqrt(f*x^2+e)/a/(-a*d+b*c)/(b*x^2+a)^(3/2)/sqrt(d*x^2+c)+1/3*b*(2*b^2*c*e+5*a^2*d*f-a*b*(c*f+6*d*e))*x*sqrt(f*x^2+e)/a^2/(-a*d+b*c)^2/(-a*f+b*e)/sqrt(b*x^2+a)/sqrt(d*x^2+c)+1/3*sqrt(e)*sqrt(-c*f+d*e)*(2*b^3*c^2*e+3*a^3*d^2*f-3*a^2*b*d*(-2*c*f+d*e)-a*b^2*c*(c*f+7*d*e))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*EllipticE(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c))),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/a^2/c/(-a*d+b*c)^3/(-a*f+b*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e)-1/3*sqrt(e)*(3*a^2*d^2*f-3*a*b*d*(-2*c*f+3*d*e)+b^2*c*(-c*f+d*e))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*InverseJacobiAM(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c)),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/a^2/(-a*d+b*c)^3/sqrt(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e),1],
[sqrt(f*x^2+e)/(b*x^2+a)^(5/2)/(d*x^2+c)^(5/2),x,7,1/3*b*x*sqrt(f*x^2+e)/a/(-a*d+b*c)/(b*x^2+a)^(3/2)/(d*x^2+c)^(3/2)+1/3*b*(2*b^2*c*e+7*a^2*d*f-a*b*(c*f+8*d*e))*x*sqrt(f*x^2+e)/a^2/(-a*d+b*c)^2/(-a*f+b*e)/sqrt(b*x^2+a)/(d*x^2+c)^(3/2)+1/3*d*(2*b^3*c^2*e+a^3*d^2*f-a^2*b*d*(-8*c*f+d*e)-a*b^2*c*(c*f+9*d*e))*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/a^2/c/(-a*d+b*c)^3/(-a*f+b*e)/(d*x^2+c)^(3/2)+1/3*sqrt(e)*(2*b^4*c^3*e*(-c*f+d*e)-a^4*d^3*f*(-c*f+2*d*e)+a^3*b*d^2*(-9*c^2*f^2+9*c*d*e*f+2*d^2*e^2)-a*b^3*c^2*(-c^2*f^2-9*c*d*e*f+10*d^2*e^2)-a^2*b^2*c*d*(9*c^2*f^2-18*c*d*e*f+10*d^2*e^2))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*EllipticE(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c))),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/a^2/c^2/(-a*d+b*c)^4/(-a*f+b*e)/sqrt(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e)+1/3*sqrt(e)*(a^3*d^3*f-b^3*c^2*(-c*f+d*e)+9*a*b^2*c*d*(-c*f+2*d*e)-a^2*b*d^2*(9*c*f+d*e))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*InverseJacobiAM(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c)),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/a^2/c/(-a*d+b*c)^4/sqrt(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e),1],
[sqrt(b*x^2+a)*(d*x^2+c)^(3/2)*(f*x^2+e)^(3/2),x,10,1/384*(15*a^3*d^2*f^2/b-31*a^2*d*f*(c*f+d*e)+a*b*(9*c^2*f^2+86*c*d*e*f+9*d^2*e^2)+b^2*(33*c*d*e^2-9*d^2*e^3/f+33*c^2*e*f-9*c^3*f^2/d))*x*sqrt(d*x^2+c)*sqrt(f*x^2+e)/b/d/f/sqrt(b*x^2+a)+1/192*(66*c*e+3*d*e^2/f+3*c^2*f/d-5*a^2*d*f/b^2+10*a*(c*f+d*e)/b)*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)+1/48*(a*d*f+9*b*(c*f+d*e))*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)/b+1/8*d*f*x^5*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)-1/384*sqrt(-a*d+b*c)*e*(15*a^3*d^3*f^3-31*a^2*b*d^2*f^2*(c*f+d*e)+a*b^2*d*f*(9*c^2*f^2+86*c*d*e*f+9*d^2*e^2)-b^3*(9*c^3*f^3-33*c^2*d*e*f^2-33*c*d^2*e^2*f+9*d^3*e^3))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticE(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^3/sqrt(c)/d^2/f^2/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)-1/384*a*sqrt(-a*d+b*c)*(15*a^3*d^3*f^3-3*a^2*b*d^2*f^2*(7*c*f+17*d*e)+a*b^2*d*f*(-3*c^2*f^2+98*c*d*e*f+49*d^2*e^2)+3*b^3*(3*c^3*f^3-13*c^2*d*e*f^2-55*c*d^2*e^2*f+d^3*e^3))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*InverseJacobiAM(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a)),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^4/sqrt(c)/d^2/f/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)-1/128*a*(5*a^4*d^4*f^4-3*b^4*(-c*f+d*e)^4-12*a^3*b*d^3*f^3*(c*f+d*e)+6*a^2*b^2*d^2*f^2*(c^2*f^2+6*c*d*e*f+d^2*e^2)+4*a*b^3*d*f*(c^3*f^3-9*c^2*d*e*f^2-9*c*d^2*e^2*f+d^3*e^3))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticPi(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),b*c/(-a*d+b*c),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^4/sqrt(c)/d^2/sqrt(-a*d+b*c)/f^2/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e),1],
[sqrt(b*x^2+a)*sqrt(d*x^2+c)*(f*x^2+e)^(3/2),x,9,1/48*(8*a*e+8*b*c*e/d+3*b*e^2/f-3*a^2*f/b-3*b*c^2*f/d^2+2*a*c*f/d)*x*sqrt(d*x^2+c)*sqrt(f*x^2+e)/sqrt(b*x^2+a)+1/24*(a*d*f+b*c*f+7*b*d*e)*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)/b/d+1/6*f*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)+1/48*sqrt(-a*d+b*c)*e*(3*a^2*d^2*f^2-2*a*b*d*f*(c*f+4*d*e)-b^2*(-3*c^2*f^2+8*c*d*e*f+3*d^2*e^2))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticE(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^2/sqrt(c)/d^2/f/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)-1/48*a*sqrt(-a*d+b*c)*(12*a*b*d^2*e*f-3*a^2*d^2*f^2-b^2*(-3*c^2*f^2+10*c*d*e*f+17*d^2*e^2))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*InverseJacobiAM(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a)),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^3/sqrt(c)/d^2/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)+1/16*a*(a^3*d^3*f^3-b^3*(-c*f+d*e)^3-a^2*b*d^2*f^2*(c*f+3*d*e)+a*b^2*d*f*(-c^2*f^2+6*c*d*e*f+3*d^2*e^2))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticPi(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),b*c/(-a*d+b*c),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^3/sqrt(c)/d^2/sqrt(-a*d+b*c)/f/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e),1],
[sqrt(b*x^2+a)*(f*x^2+e)^(3/2)/sqrt(d*x^2+c),x,8,1/8*(a*d*f-3*b*c*f+5*b*d*e)*x*sqrt(d*x^2+c)*sqrt(f*x^2+e)/d^2/sqrt(b*x^2+a)+1/4*f*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)/d-1/8*sqrt(-a*d+b*c)*e*(a*d*f-3*b*c*f+5*b*d*e)*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticE(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b/sqrt(c)/d^2/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)+1/8*a*sqrt(-a*d+b*c)*f*(-a*d*f-3*b*c*f+7*b*d*e)*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*InverseJacobiAM(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a)),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^2/sqrt(c)/d^2/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)-1/8*a*(a^2*d^2*f^2-3*b^2*(-c*f+d*e)^2-2*a*b*d*f*(-c*f+3*d*e))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticPi(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),b*c/(-a*d+b*c),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^2/sqrt(c)/d^2/sqrt(-a*d+b*c)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e),1],
[sqrt(b*x^2+a)*(f*x^2+e)^(3/2)/(d*x^2+c)^(3/2),x,7,1/2*f*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/d/sqrt(d*x^2+c)+1/2*sqrt(e)*(-3*c*f+2*d*e)*sqrt(-c*f+d*e)*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*EllipticE(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c))),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/c/d^2/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e)-1/2*(-4*a*d+3*b*c)*sqrt(e)*f*sqrt(-c*f+d*e)*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*InverseJacobiAM(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c)),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/a/d^3/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e)+1/2*c*sqrt(e)*f*(a*d*f-3*b*c*f+3*b*d*e)*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*EllipticPi(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c))),d*e/(-c*f+d*e),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/a/d^3/sqrt(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e),1],
[sqrt(b*x^2+a)*(f*x^2+e)^(3/2)/(d*x^2+c)^(5/2),x,7,1/3*(-c*f+d*e)*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/c/d/(d*x^2+c)^(3/2)-1/3*sqrt(e)*sqrt(-c*f+d*e)*(2*a*d*(c*f+d*e)-b*c*(3*c*f+d*e))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*EllipticE(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c))),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/c^2/d^2/(-a*d+b*c)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e)-1/3*sqrt(e)*(3*b^2*c^3*f^2+a^2*d^2*f*(2*c*f+d*e)-a*b*d*(6*c^2*f^2-c*d*e*f+d^2*e^2))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*InverseJacobiAM(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c)),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/a/c/d^3/(-a*d+b*c)/sqrt(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e)+b*c*sqrt(e)*f^2*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*EllipticPi(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c))),d*e/(-c*f+d*e),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/a/d^3/sqrt(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e),1],
[sqrt(b*x^2+a)*(f*x^2+e)^(3/2)/(d*x^2+c)^(7/2),x,6,1/5*(-c*f+d*e)*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/c/d/(d*x^2+c)^(5/2)+1/15*(3*b*c*(c*f+d*e)-2*a*d*(c*f+2*d*e))*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/c^2/d/(-a*d+b*c)/(d*x^2+c)^(3/2)+1/15*sqrt(e)*(3*b^2*c^2*e^2-a*b*c*e*(-7*c*f+13*d*e)+a^2*(-2*c^2*f^2-3*c*d*e*f+8*d^2*e^2))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*EllipticE(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c))),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/c^3/(-a*d+b*c)^2/sqrt(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e)+2/15*sqrt(e)*(-a*f+b*e)*(-a*c*f-2*a*d*e+3*b*c*e)*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*InverseJacobiAM(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c)),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/c^2/(-a*d+b*c)^2/sqrt(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e),1],
[sqrt(b*x^2+a)*(f*x^2+e)^(3/2)/(d*x^2+c)^(9/2),x,7,1/7*(-c*f+d*e)*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/c/d/(d*x^2+c)^(7/2)-1/35*(2*a*d*(c*f+3*d*e)-b*c*(3*c*f+5*d*e))*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/c^2/d/(-a*d+b*c)/(d*x^2+c)^(5/2)-1/105*(a*b*c*d*(-8*c^2*f^2-29*c*d*e*f+43*d^2*e^2)-3*a^2*d^2*(-2*c^2*f^2-5*c*d*e*f+8*d^2*e^2)-3*b^2*c^2*(-2*c^2*f^2-2*c*d*e*f+5*d^2*e^2))*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/c^3/d/(-a*d+b*c)^2/(-c*f+d*e)/(d*x^2+c)^(3/2)+1/105*sqrt(e)*(3*b^3*c^3*e^2*(-7*c*f+5*d*e)-a*b^2*c^2*e*(49*c^2*f^2-170*c*d*e*f+103*d^2*e^2)-6*a^3*d*(c^3*f^3+2*c^2*d*e*f^2-12*c*d^2*e^2*f+8*d^3*e^3)+a^2*b*c*(14*c^3*f^3+37*c^2*d*e*f^2-197*c*d^2*e^2*f+128*d^3*e^3))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*EllipticE(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c))),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/c^4/(-a*d+b*c)^3/(-c*f+d*e)^(3/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e)+1/105*sqrt(e)*(-a*f+b*e)*(3*b^2*c^2*e*(-14*c*f+15*d*e)-a*b*c*(-14*c^2*f^2-41*c*d*e*f+61*d^2*e^2)+3*a^2*d*(-2*c^2*f^2-5*c*d*e*f+8*d^2*e^2))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*InverseJacobiAM(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c)),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/c^3/(-a*d+b*c)^3/(-c*f+d*e)^(3/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e),1],
[sqrt(b*x^2+a)*(f*x^2+e)^(3/2)/(d*x^2+c)^(11/2),x,8,1/9*(-c*f+d*e)*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/c/d/(d*x^2+c)^(9/2)-1/63*(2*a*d*(c*f+4*d*e)-b*c*(3*c*f+7*d*e))*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/c^2/d/(-a*d+b*c)/(d*x^2+c)^(7/2)-1/315*(a*b*c*d*(-16*c^2*f^2-67*c*d*e*f+89*d^2*e^2)-b^2*c^2*(-12*c^2*f^2-20*c*d*e*f+35*d^2*e^2)-a^2*d^2*(-10*c^2*f^2-35*c*d*e*f+48*d^2*e^2))*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/c^3/d/(-a*d+b*c)^2/(-c*f+d*e)/(d*x^2+c)^(5/2)-1/315*(2*a^3*d^3*(5*c^3*f^3+15*c^2*d*e*f^2-54*c*d^2*e^2*f+32*d^3*e^3)-b^3*c^3*(8*c^3*f^3+8*c^2*d*e*f^2-55*c*d^2*e^2*f+35*d^3*e^3)+a*b^2*c^2*d*(16*c^3*f^3+91*c^2*d*e*f^2-278*c*d^2*e^2*f+159*d^3*e^3)-a^2*b*c*d^2*(26*c^3*f^3+89*c^2*d*e*f^2-307*c*d^2*e^2*f+180*d^3*e^3))*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/c^4/d/(-a*d+b*c)^3/(-c*f+d*e)^2/(d*x^2+c)^(3/2)+1/315*sqrt(e)*(b^4*c^4*e^2*(63*c^2*f^2-90*c*d*e*f+35*d^2*e^2)-a*b^3*c^3*e*(-147*c^3*f^3+747*c^2*d*e*f^2-902*c*d^2*e^2*f+334*d^3*e^3)-a^3*b*c*d*(-36*c^4*f^4-101*c^3*d*e*f^3+915*c^2*d^2*e^2*f^2-1218*c*d^3*e^3*f+472*d^4*e^4)+3*a^2*b^2*c^2*(-14*c^4*f^4-53*c^3*d*e*f^3+420*c^2*d^2*e^2*f^2-546*c*d^3*e^3*f+209*d^4*e^4)+a^4*d^2*(-10*c^4*f^4-25*c^3*d*e*f^3+243*c^2*d^2*e^2*f^2-328*c*d^3*e^3*f+128*d^4*e^4))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*EllipticE(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c))),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/c^5/(-a*d+b*c)^4/(-c*f+d*e)^(5/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e)+2/315*sqrt(e)*(-a*f+b*e)*(b^3*c^3*e*(63*c^2*f^2-135*c*d*e*f+70*d^2*e^2)-a^3*d^2*(5*c^3*f^3+15*c^2*d*e*f^2-54*c*d^2*e^2*f+32*d^3*e^3)+3*a^2*b*c*d*(6*c^3*f^3+19*c^2*d*e*f^2-65*c*d^2*e^2*f+38*d^3*e^3)-3*a*b^2*c^2*(7*c^3*f^3+27*c^2*d*e*f^2-84*c*d^2*e^2*f+48*d^3*e^3))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*InverseJacobiAM(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c)),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/c^4/(-a*d+b*c)^4/(-c*f+d*e)^(5/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e),1],
[(b*x^2+a)^(3/2)*sqrt(d*x^2+c)*(f*x^2+e)^(3/2),x,10,-1/384*(9*a^3*d^3*f^3-3*a^2*b*d^2*f^2*(3*c*f+11*d*e)-a*b^2*d*f*(-31*c^2*f^2+86*c*d*e*f+33*d^2*e^2)+b^3*(-15*c^3*f^3+31*c^2*d*e*f^2-9*c*d^2*e^2*f+9*d^3*e^3))*x*sqrt(d*x^2+c)*sqrt(f*x^2+e)/b/d^3/f^2/sqrt(b*x^2+a)+1/192*(66*a*e+10*b*c*e/d+3*b*e^2/f+3*a^2*f/b-5*b*c^2*f/d^2+10*a*c*f/d)*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)+1/48*(9*a*d*f+b*c*f+9*b*d*e)*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)/d+1/8*b*f*x^5*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)+1/384*sqrt(-a*d+b*c)*e*(9*a^3*d^3*f^3-3*a^2*b*d^2*f^2*(3*c*f+11*d*e)-a*b^2*d*f*(-31*c^2*f^2+86*c*d*e*f+33*d^2*e^2)+b^3*(-15*c^3*f^3+31*c^2*d*e*f^2-9*c*d^2*e^2*f+9*d^3*e^3))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticE(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^2/sqrt(c)/d^3/f^2/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)+1/384*a*sqrt(-a*d+b*c)*(9*a^3*d^3*f^3-3*a^2*b*d^2*f^2*(c*f+15*d*e)+3*a*b^2*d*f*(-7*c^2*f^2+26*c*d*e*f+29*d^2*e^2)-b^3*(-15*c^3*f^3+41*c^2*d*e*f^2-29*c*d^2*e^2*f+3*d^3*e^3))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*InverseJacobiAM(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a)),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^3/sqrt(c)/d^3/f/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)+1/128*a*(3*a^4*d^4*f^4-12*a*b^3*d*f*(-c*f+d*e)^3-4*a^3*b*d^3*f^3*(c*f+3*d*e)+b^4*(-c*f+d*e)^3*(5*c*f+3*d*e)+6*a^2*b^2*d^2*f^2*(-c^2*f^2+6*c*d*e*f+3*d^2*e^2))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticPi(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),b*c/(-a*d+b*c),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^3/sqrt(c)/d^3/sqrt(-a*d+b*c)/f^2/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e),1],
[(b*x^2+a)^(3/2)*(f*x^2+e)^(3/2)/sqrt(d*x^2+c),x,9,1/48*(3*a^2*d^2*f^2+2*a*b*d*f*(-11*c*f+19*d*e)+b^2*(15*c^2*f^2-22*c*d*e*f+3*d^2*e^2))*x*sqrt(d*x^2+c)*sqrt(f*x^2+e)/d^3/f/sqrt(b*x^2+a)+1/24*(7*a*d*f-5*b*c*f+7*b*d*e)*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)/d^2+1/6*b*f*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)/d-1/48*sqrt(-a*d+b*c)*e*(3*a^2*d^2*f^2+2*a*b*d*f*(-11*c*f+19*d*e)+b^2*(15*c^2*f^2-22*c*d*e*f+3*d^2*e^2))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticE(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b/sqrt(c)/d^3/f/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)-1/48*a*sqrt(-a*d+b*c)*(3*a^2*d^2*f^2-6*a*b*d*f*(-2*c*f+5*d*e)-b^2*(15*c^2*f^2-32*c*d*e*f+17*d^2*e^2))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*InverseJacobiAM(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a)),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^2/sqrt(c)/d^3/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)-1/16*a*(a^3*d^3*f^3-9*a*b^2*d*f*(-c*f+d*e)^2-3*a^2*b*d^2*f^2*(-c*f+3*d*e)+b^3*(-c*f+d*e)^2*(5*c*f+d*e))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticPi(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),b*c/(-a*d+b*c),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^2/sqrt(c)/d^3/sqrt(-a*d+b*c)/f/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e),1],
[(b*x^2+a)^(3/2)*(f*x^2+e)^(3/2)/(d*x^2+c)^(3/2),x,8,5/8*(a*d*f-b*c*f+b*d*e)*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/d^2/sqrt(d*x^2+c)+1/4*b*f*x^3*sqrt(b*x^2+a)*sqrt(f*x^2+e)/d/sqrt(d*x^2+c)-1/8*sqrt(e)*sqrt(-c*f+d*e)*(b*c*(-15*c*f+13*d*e)-a*d*(-13*c*f+8*d*e))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*EllipticE(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c))),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/c/d^3/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e)+1/8*sqrt(e)*sqrt(-c*f+d*e)*(16*a^2*d^2*f+a*b*d*(-33*c*f+8*d*e)-3*b^2*c*(-5*c*f+d*e))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*InverseJacobiAM(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c)),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/a/d^4/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e)+3/8*c*sqrt(e)*(a^2*d^2*f^2+6*a*b*d*f*(-c*f+d*e)+b^2*(5*c^2*f^2-6*c*d*e*f+d^2*e^2))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*EllipticPi(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c))),d*e/(-c*f+d*e),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/a/d^4/sqrt(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e),1],
[(b*x^2+a)^(3/2)*(f*x^2+e)^(3/2)/(d*x^2+c)^(5/2),x,8,-1/3*(-a*d+b*c)*(-c*f+d*e)*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/c/d^2/(d*x^2+c)^(3/2)+1/2*b*f*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/d^2/sqrt(d*x^2+c)+1/6*sqrt(e)*sqrt(-c*f+d*e)*(b*c*(-15*c*f+4*d*e)+4*a*d*(c*f+d*e))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*EllipticE(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c))),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/c^2/d^3/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e)-1/6*sqrt(e)*(3*b^2*c^2*f*(-5*c*f+3*d*e)-2*a^2*d^2*f*(2*c*f+d*e)+2*a*b*d*(12*c^2*f^2-7*c*d*e*f+d^2*e^2))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*InverseJacobiAM(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c)),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/a/c/d^4/sqrt(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e)+1/2*b*c*sqrt(e)*f*(3*a*d*f-5*b*c*f+3*b*d*e)*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*EllipticPi(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c))),d*e/(-c*f+d*e),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/a/d^4/sqrt(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e),1],
[(b*x^2+a)^(3/2)*(f*x^2+e)^(3/2)/(d*x^2+c)^(7/2),x,8,-1/5*(-a*d+b*c)*(-c*f+d*e)*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/c/d^2/(d*x^2+c)^(5/2)+2/15*(b*c*(-4*c*f+d*e)+a*d*(c*f+2*d*e))*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/c^2/d^2/(d*x^2+c)^(3/2)+1/15*sqrt(e)*(b^2*c^2*(-15*c^2*f^2+10*c*d*e*f+2*d^2*e^2)-a^2*d^2*(-2*c^2*f^2-3*c*d*e*f+8*d^2*e^2)+a*b*c*d*(10*c^2*f^2-7*c*d*e*f+3*d^2*e^2))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*EllipticE(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c))),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/c^3/d^3/(-a*d+b*c)/sqrt(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e)-1/15*sqrt(e)*(15*b^3*c^4*f^2+2*a^3*d^3*f*(c*f+2*d*e)+a*b^2*c*d*(-30*c^2*f^2+5*c*d*e*f+d^2*e^2)-a^2*b*d^2*(-10*c^2*f^2+3*c*d*e*f+4*d^2*e^2))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*InverseJacobiAM(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c)),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/a/c^2/d^4/(-a*d+b*c)/sqrt(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e)+b^2*c*sqrt(e)*f^2*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*EllipticPi(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c))),d*e/(-c*f+d*e),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/a/d^4/sqrt(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e),1],
[(b*x^2+a)^(3/2)*(f*x^2+e)^(3/2)/(d*x^2+c)^(9/2),x,7,-1/7*(-a*d+b*c)*(-c*f+d*e)*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/c/d^2/(d*x^2+c)^(7/2)+2/35*(b*c*(-5*c*f+d*e)+a*d*(c*f+3*d*e))*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/c^2/d^2/(d*x^2+c)^(5/2)+1/35*(b^2*c^2*(-5*c^2*f^2+2*c*d*e*f+2*d^2*e^2)-a^2*d^2*(-2*c^2*f^2-5*c*d*e*f+8*d^2*e^2)+a*b*c*d*(2*c^2*f^2-5*c*d*e*f+5*d^2*e^2))*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/c^3/d^2/(-a*d+b*c)/(-c*f+d*e)/(d*x^2+c)^(3/2)+2/35*sqrt(e)*(a*c*f-2*a*d*e+b*c*e)*(b^2*c^2*e^2+2*a*b*c*e*(-3*c*f+2*d*e)-a^2*(-c^2*f^2-4*c*d*e*f+4*d^2*e^2))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*EllipticE(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c))),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/c^4/(-a*d+b*c)^2/(-c*f+d*e)^(3/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e)-1/35*sqrt(e)*(-a*f+b*e)*(b^2*c^2*e^2-a*b*c*e*(-9*c*f+11*d*e)+a^2*(-2*c^2*f^2-5*c*d*e*f+8*d^2*e^2))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*InverseJacobiAM(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c)),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/c^3/(-a*d+b*c)^2/(-c*f+d*e)^(3/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e),1],
[(b*x^2+a)^(3/2)*(f*x^2+e)^(3/2)/(d*x^2+c)^(11/2),x,8,-1/9*(-a*d+b*c)*(-c*f+d*e)*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/c/d^2/(d*x^2+c)^(9/2)+2/63*(b*c*(-6*c*f+d*e)+a*d*(c*f+4*d*e))*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/c^2/d^2/(d*x^2+c)^(7/2)+1/315*(b^2*c^2*(-15*c^2*f^2+2*c*d*e*f+10*d^2*e^2)-a^2*d^2*(-10*c^2*f^2-35*c*d*e*f+48*d^2*e^2)+a*b*c*d*(2*c^2*f^2-31*c*d*e*f+35*d^2*e^2))*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/c^3/d^2/(-a*d+b*c)/(-c*f+d*e)/(d*x^2+c)^(5/2)+2/315*(a*b^2*c^2*d*(-4*c^3*f^3+14*c^2*d*e*f^2-31*c*d^2*e^2*f+15*d^3*e^3)-a^2*b*c*d^2*(4*c^3*f^3+31*c^2*d*e*f^2-95*c*d^2*e^2*f+54*d^3*e^3)+b^3*c^3*(5*c^3*f^3-4*c^2*d*e*f^2-4*c*d^2*e^2*f+5*d^3*e^3)+a^3*d^3*(5*c^3*f^3+15*c^2*d*e*f^2-54*c*d^2*e^2*f+32*d^3*e^3))*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/c^4/d^2/(-a*d+b*c)^2/(-c*f+d*e)^2/(d*x^2+c)^(3/2)+1/315*sqrt(e)*(2*b^4*c^4*e^3*(-9*c*f+5*d*e)+a*b^3*c^3*e^2*(90*c^2*f^2-83*c*d*e*f+25*d^2*e^2)-3*a^2*b^2*c^2*e*(-30*c^3*f^3+186*c^2*d*e*f^2-221*c*d^2*e^2*f+81*d^3*e^3)+a^3*b*c*(-18*c^4*f^4-83*c^3*d*e*f^3+663*c^2*d^2*e^2*f^2-858*c*d^3*e^3*f+328*d^4*e^4)-a^4*d*(-10*c^4*f^4-25*c^3*d*e*f^3+243*c^2*d^2*e^2*f^2-328*c*d^3*e^3*f+128*d^4*e^4))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*EllipticE(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c))),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/c^5/(-a*d+b*c)^3/(-c*f+d*e)^(5/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e)-1/315*sqrt(e)*(-a*f+b*e)*(b^3*c^3*e^2*(-9*c*f+5*d*e)-3*a*b^2*c^2*e*(27*c^2*f^2-66*c*d*e*f+35*d^2*e^2)-2*a^3*d*(5*c^3*f^3+15*c^2*d*e*f^2-54*c*d^2*e^2*f+32*d^3*e^3)+3*a^2*b*c*(6*c^3*f^3+29*c^2*d*e*f^2-91*c*d^2*e^2*f+52*d^3*e^3))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*InverseJacobiAM(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c)),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/c^4/(-a*d+b*c)^3/(-c*f+d*e)^(5/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e),1],
[(b*x^2+a)^(5/2)*(f*x^2+e)^(3/2)/sqrt(d*x^2+c),x,10,1/384*(15*a^3*d^3*f^3+a^2*b*d^2*f^2*(-191*c*f+337*d*e)+a*b^2*d*f*(265*c^2*f^2-394*c*d*e*f+57*d^2*e^2)-b^3*(105*c^3*f^3-145*c^2*d*e*f^2+15*c*d^2*e^2*f+9*d^3*e^3))*x*sqrt(d*x^2+c)*sqrt(f*x^2+e)/d^4/f^2/sqrt(b*x^2+a)+1/192*(59*a^2*d^2*f^2+2*a*b*d*f*(-43*c*f+61*d*e)+b^2*(35*c^2*f^2-46*c*d*e*f+3*d^2*e^2))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)/d^3/f+1/48*b*(17*a*d*f-7*b*c*f+9*b*d*e)*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)/d^2+1/8*b^2*f*x^5*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)/d-1/384*sqrt(-a*d+b*c)*e*(15*a^3*d^3*f^3+a^2*b*d^2*f^2*(-191*c*f+337*d*e)+a*b^2*d*f*(265*c^2*f^2-394*c*d*e*f+57*d^2*e^2)-b^3*(105*c^3*f^3-145*c^2*d*e*f^2+15*c*d^2*e^2*f+9*d^3*e^3))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticE(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b/sqrt(c)/d^4/f^2/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)-1/384*a*sqrt(-a*d+b*c)*(15*a^3*d^3*f^3-15*a^2*b*d^2*f^2*(-5*c*f+13*d*e)-a*b^2*d*f*(195*c^2*f^2-418*c*d*e*f+223*d^2*e^2)+b^3*(105*c^3*f^3-215*c^2*d*e*f^2+107*c*d^2*e^2*f+3*d^3*e^3))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*InverseJacobiAM(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a)),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^2/sqrt(c)/d^4/f/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)-1/128*a*(5*a^4*d^4*f^4-90*a^2*b^2*d^2*f^2*(-c*f+d*e)^2-20*a^3*b*d^3*f^3*(-c*f+3*d*e)+20*a*b^3*d*f*(-c*f+d*e)^2*(5*c*f+d*e)-b^4*(-c*f+d*e)^2*(35*c^2*f^2+10*c*d*e*f+3*d^2*e^2))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticPi(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),b*c/(-a*d+b*c),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^2/sqrt(c)/d^4/sqrt(-a*d+b*c)/f^2/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e),1],
[(b*x^2+a)^(5/2)*(f*x^2+e)^(3/2)/(d*x^2+c)^(3/2),x,9,1/48*(33*a^2*d^2*f^2+68*a*b*d*f*(-c*f+d*e)+b^2*(35*c^2*f^2-38*c*d*e*f+3*d^2*e^2))*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/d^3/f/sqrt(d*x^2+c)+1/24*b*(13*a*d*f-7*b*c*f+7*b*d*e)*x^3*sqrt(b*x^2+a)*sqrt(f*x^2+e)/d^2/sqrt(d*x^2+c)+1/6*b^2*f*x^5*sqrt(b*x^2+a)*sqrt(f*x^2+e)/d/sqrt(d*x^2+c)-1/48*sqrt(e)*sqrt(-c*f+d*e)*(2*a*b*c*d*f*(-95*c*f+82*d*e)-3*a^2*d^2*f*(-27*c*f+16*d*e)+b^2*c*(105*c^2*f^2-100*c*d*e*f+3*d^2*e^2))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*EllipticE(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c))),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/c/d^4/f/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e)+1/48*sqrt(e)*sqrt(-c*f+d*e)*(96*a^3*d^3*f^2+a^2*b*d^2*f*(-325*c*f+96*d*e)-110*a*b^2*c*d*f*(-3*c*f+d*e)+3*b^3*c*(-35*c^2*f^2+10*c*d*e*f+d^2*e^2))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*InverseJacobiAM(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c)),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/a/d^5/f/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e)+1/16*c*sqrt(e)*(5*a^3*d^3*f^3+45*a^2*b*d^2*f^2*(-c*f+d*e)+15*a*b^2*d*f*(5*c^2*f^2-6*c*d*e*f+d^2*e^2)-b^3*(35*c^3*f^3-45*c^2*d*e*f^2+9*c*d^2*e^2*f+d^3*e^3))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*EllipticPi(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c))),d*e/(-c*f+d*e),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/a/d^5/f/sqrt(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e),1],
[(b*x^2+a)^(5/2)*(f*x^2+e)^(3/2)/(d*x^2+c)^(5/2),x,9,1/3*(-a*d+b*c)^2*(-c*f+d*e)*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/c/d^3/(d*x^2+c)^(3/2)+1/8*b*(9*a*d*f-9*b*c*f+5*b*d*e)*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/d^3/sqrt(d*x^2+c)+1/4*b^2*f*x^3*sqrt(b*x^2+a)*sqrt(f*x^2+e)/d^2/sqrt(d*x^2+c)+1/24*sqrt(e)*sqrt(-c*f+d*e)*(a*b*c*d*(-115*c*f+24*d*e)-5*b^2*c^2*(-21*c*f+11*d*e)+16*a^2*d^2*(c*f+d*e))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*EllipticE(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c))),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/c^2/d^4/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e)+1/24*sqrt(e)*(8*a^3*d^3*f*(2*c*f+d*e)-8*a^2*b*d^2*(20*c^2*f^2-12*c*d*e*f+d^2*e^2)-3*b^3*c^2*(35*c^2*f^2-30*c*d*e*f+3*d^2*e^2)+a*b^2*c*d*(255*c^2*f^2-215*c*d*e*f+32*d^2*e^2))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*InverseJacobiAM(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c)),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/a/c/d^5/sqrt(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e)+1/8*b*c*sqrt(e)*(15*a^2*d^2*f^2+10*a*b*d*f*(-5*c*f+3*d*e)+b^2*(35*c^2*f^2-30*c*d*e*f+3*d^2*e^2))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*EllipticPi(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c))),d*e/(-c*f+d*e),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/a/d^5/sqrt(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e),1],
[(b*x^2+a)^(5/2)*(f*x^2+e)^(3/2)/(d*x^2+c)^(7/2),x,9,1/5*(-a*d+b*c)^2*(-c*f+d*e)*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/c/d^3/(d*x^2+c)^(5/2)-1/15*(-a*d+b*c)*(b*c*(-13*c*f+7*d*e)+2*a*d*(c*f+2*d*e))*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/c^2/d^3/(d*x^2+c)^(3/2)+1/2*b^2*f*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/d^3/sqrt(d*x^2+c)+1/30*sqrt(e)*(2*a*b*c*d*(-20*c^2*f^2+7*c*d*e*f+7*d^2*e^2)+2*a^2*d^2*(-2*c^2*f^2-3*c*d*e*f+8*d^2*e^2)+b^2*c^2*(105*c^2*f^2-115*c*d*e*f+16*d^2*e^2))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*EllipticE(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c))),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/c^3/d^4/sqrt(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e)-1/30*sqrt(e)*(15*b^3*c^3*f*(-7*c*f+3*d*e)-4*a^3*d^3*f*(c*f+2*d*e)+4*a^2*b*d^2*(-10*c^2*f^2-c*d*e*f+2*d^2*e^2)+4*a*b^2*c*d*(45*c^2*f^2-20*c*d*e*f+2*d^2*e^2))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*InverseJacobiAM(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c)),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/a/c^2/d^5/sqrt(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e)+1/2*b^2*c*sqrt(e)*f*(5*a*d*f-7*b*c*f+3*b*d*e)*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*EllipticPi(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c))),d*e/(-c*f+d*e),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/a/d^5/sqrt(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e),1],
[(b*x^2+a)^(5/2)*(f*x^2+e)^(3/2)/(d*x^2+c)^(9/2),x,9,1/7*(-a*d+b*c)^2*(-c*f+d*e)*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/c/d^3/(d*x^2+c)^(7/2)-1/35*(-a*d+b*c)*(b*c*(-17*c*f+9*d*e)+2*a*d*(c*f+3*d*e))*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/c^2/d^3/(d*x^2+c)^(5/2)+1/105*(a*b*c*d*(-20*c^2*f^2+c*d*e*f+13*d^2*e^2)+3*a^2*d^2*(-2*c^2*f^2-5*c*d*e*f+8*d^2*e^2)+b^2*c^2*(71*c^2*f^2-76*c*d*e*f+8*d^2*e^2))*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/c^3/d^3/(-c*f+d*e)/(d*x^2+c)^(3/2)+1/105*sqrt(e)*(a*b^2*c^2*d*(-70*c^3*f^3+119*c^2*d*e*f^2-40*c*d^2*e^2*f+9*d^3*e^3)+a^2*b*c*d^2*(-14*c^3*f^3+23*c^2*d*e*f^2-43*c*d^2*e^2*f+16*d^3*e^3)-6*a^3*d^3*(c^3*f^3+2*c^2*d*e*f^2-12*c*d^2*e^2*f+8*d^3*e^3)+b^3*c^3*(105*c^3*f^3-175*c^2*d*e*f^2+56*c*d^2*e^2*f+8*d^3*e^3))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*EllipticE(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c))),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/c^4/d^4/(-a*d+b*c)/(-c*f+d*e)^(3/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e)-1/105*sqrt(e)*(105*b^4*c^5*f^2*(-c*f+d*e)+3*a^4*d^4*f*(-2*c^2*f^2-5*c*d*e*f+8*d^2*e^2)+a^2*b^2*c*d^2*(-70*c^3*f^3+91*c^2*d*e*f^2-17*c*d^2*e^2*f+5*d^3*e^3)-a^3*b*d^3*(14*c^3*f^3-19*c^2*d*e*f^2-10*c*d^2*e^2*f+24*d^3*e^3)+a*b^3*c^2*d*(210*c^3*f^3-245*c^2*d*e*f^2+28*c*d^2*e^2*f+4*d^3*e^3))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*InverseJacobiAM(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c)),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/a/c^3/d^5/(-a*d+b*c)/(-c*f+d*e)^(3/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e)+b^3*c*sqrt(e)*f^2*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*EllipticPi(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c))),d*e/(-c*f+d*e),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/a/d^5/sqrt(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e),1],
[(b*x^2+a)^(5/2)*(f*x^2+e)^(3/2)/(d*x^2+c)^(11/2),x,8,1/9*(-a*d+b*c)^2*(-c*f+d*e)*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/c/d^3/(d*x^2+c)^(9/2)-1/63*(-a*d+b*c)*(b*c*(-21*c*f+11*d*e)+2*a*d*(c*f+4*d*e))*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/c^2/d^3/(d*x^2+c)^(7/2)+1/315*(a*b*c*d*(-20*c^2*f^2-5*c*d*e*f+19*d^2*e^2)+a^2*d^2*(-10*c^2*f^2-35*c*d*e*f+48*d^2*e^2)+b^2*c^2*(105*c^2*f^2-110*c*d*e*f+8*d^2*e^2))*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/c^3/d^3/(-c*f+d*e)/(d*x^2+c)^(5/2)+1/315*(a^2*b*c*d^2*(-10*c^3*f^3+35*c^2*d*e*f^2-73*c*d^2*e^2*f+36*d^3*e^3)+a*b^2*c^2*d*(-10*c^3*f^3+35*c^2*d*e*f^2-28*c*d^2*e^2*f+15*d^3*e^3)-2*a^3*d^3*(5*c^3*f^3+15*c^2*d*e*f^2-54*c*d^2*e^2*f+32*d^3*e^3)+b^3*c^3*(35*c^3*f^3-55*c^2*d*e*f^2+8*c*d^2*e^2*f+8*d^3*e^3))*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/c^4/d^3/(-a*d+b*c)/(-c*f+d*e)^2/(d*x^2+c)^(3/2)+1/315*sqrt(e)*(8*b^4*c^4*e^4+a*b^3*c^3*e^3*(-43*c*f+11*d*e)+3*a^2*b^2*c^2*e^2*(36*c^2*f^2-29*c*d*e*f+9*d^2*e^2)-a^3*b*c*e*(-65*c^3*f^3+411*c^2*d*e*f^2-498*c*d^2*e^2*f+184*d^3*e^3)+a^4*(-10*c^4*f^4-25*c^3*d*e*f^3+243*c^2*d^2*e^2*f^2-328*c*d^3*e^3*f+128*d^4*e^4))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*EllipticE(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c))),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/c^5/(-a*d+b*c)^2/(-c*f+d*e)^(5/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e)-2/315*sqrt(e)*(-a*f+b*e)*(2*b^3*c^3*e^3+3*a*b^2*c^2*e^2*(-3*c*f+d*e)-6*a^2*b*c*e*(5*c^2*f^2-13*c*d*e*f+7*d^2*e^2)+a^3*(5*c^3*f^3+15*c^2*d*e*f^2-54*c*d^2*e^2*f+32*d^3*e^3))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*InverseJacobiAM(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c)),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/c^4/(-a*d+b*c)^2/(-c*f+d*e)^(5/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e),1],
[(d*x^2+c)^(3/2)*(f*x^2+e)^(3/2)/sqrt(b*x^2+a),x,9,1/48*(38*c*e-22*a*d*e/b+3*d*e^2/f-22*a*c*f/b+3*c^2*f/d+15*a^2*d*f/b^2)*x*sqrt(d*x^2+c)*sqrt(f*x^2+e)/sqrt(b*x^2+a)-1/24*(5*a*d*f-7*b*(c*f+d*e))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)/b^2+1/6*d*f*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)/b-1/48*sqrt(-a*d+b*c)*e*(15*a^2*d^2*f^2-22*a*b*d*f*(c*f+d*e)+b^2*(3*c^2*f^2+38*c*d*e*f+3*d^2*e^2))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticE(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^3/sqrt(c)/d/f/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)+1/48*sqrt(-a*d+b*c)*(48*b^3*c*d*e^2-15*a^3*d^2*f^2+6*a^2*b*d*f*(2*c*f+7*d*e)-a*b^2*(-3*c^2*f^2+44*c*d*e*f+31*d^2*e^2))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*InverseJacobiAM(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a)),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^4/sqrt(c)/d/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)+1/16*a*(-a*d*f+b*c*f+b*d*e)*(5*a^2*d^2*f^2-4*a*b*d*f*(c*f+d*e)-b^2*(c^2*f^2-10*c*d*e*f+d^2*e^2))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticPi(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),b*c/(-a*d+b*c),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^4/sqrt(c)/d/sqrt(-a*d+b*c)/f/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e),1],
[sqrt(d*x^2+c)*(f*x^2+e)^(3/2)/sqrt(b*x^2+a),x,8,1/8*(-3*a*d*f+b*c*f+5*b*d*e)*x*sqrt(d*x^2+c)*sqrt(f*x^2+e)/b/d/sqrt(b*x^2+a)+1/4*f*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)/b-1/8*sqrt(-a*d+b*c)*e*(-3*a*d*f+b*c*f+5*b*d*e)*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticE(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^2/sqrt(c)/d/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)+1/8*sqrt(-a*d+b*c)*(8*b^2*d*e^2+3*a^2*d*f^2-a*b*f*(-c*f+9*d*e))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*InverseJacobiAM(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a)),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^3/sqrt(c)/d/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)+1/8*a*(3*a^2*d^2*f^2-2*a*b*d*f*(c*f+3*d*e)+b^2*(-c^2*f^2+6*c*d*e*f+3*d^2*e^2))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticPi(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),b*c/(-a*d+b*c),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^3/sqrt(c)/d/sqrt(-a*d+b*c)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e),1],
[(f*x^2+e)^(3/2)/sqrt(b*x^2+a)/sqrt(d*x^2+c),x,7,1/2*f^2*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b/d/sqrt(f*x^2+e)-1/2*c*f*sqrt(a*f-b*e)*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/b/d/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))+1/2*e*sqrt(a*f-b*e)*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/b/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))+1/2*e*(-a*d*f-b*c*f+3*b*d*e)*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticPi(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),-a*f/(-a*f+b*e),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/b/d/sqrt(a*f-b*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[(f*x^2+e)^(3/2)/sqrt(b*x^2+a)/(d*x^2+c)^(3/2),x,6,-a*(-c*f+d*e)^(3/2)*sqrt(c*(b*x^2+a)/a/(d*x^2+c))*sqrt(f*x^2+e)*EllipticE(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c))),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/c/d/(-a*d+b*c)/sqrt(e)/sqrt(b*x^2+a)/sqrt(c*(f*x^2+e)/e/(d*x^2+c))+sqrt(-c*f+d*e)*(-2*a*d*f+b*c*f+b*d*e)*sqrt(c*(b*x^2+a)/a/(d*x^2+c))*sqrt(f*x^2+e)*InverseJacobiAM(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c)),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/d^2/(-a*d+b*c)/sqrt(e)/sqrt(b*x^2+a)/sqrt(c*(f*x^2+e)/e/(d*x^2+c))+c*f^2*sqrt(c*(b*x^2+a)/a/(d*x^2+c))*sqrt(f*x^2+e)*EllipticPi(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c))),d*e/(-c*f+d*e),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/d^2/sqrt(e)/sqrt(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(c*(f*x^2+e)/e/(d*x^2+c)),1],
[(f*x^2+e)^(3/2)/sqrt(b*x^2+a)/(d*x^2+c)^(5/2),x,5,-1/3*(-c*f+d*e)*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/c/(-a*d+b*c)/(d*x^2+c)^(3/2)-2/3*sqrt(e)*sqrt(-c*f+d*e)*(-a*c*f-a*d*e+2*b*c*e)*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*EllipticE(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c))),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/c^2/(-a*d+b*c)^2/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e)+1/3*sqrt(e)*(-a*f+b*e)*(-2*a*c*f-a*d*e+3*b*c*e)*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*InverseJacobiAM(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c)),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/a/c/(-a*d+b*c)^2/sqrt(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e),1],
[(f*x^2+e)^(3/2)/sqrt(b*x^2+a)/(d*x^2+c)^(7/2),x,6,-1/5*(-c*f+d*e)*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/c/(-a*d+b*c)/(d*x^2+c)^(5/2)-2/15*(b*c*(-c*f+4*d*e)-a*d*(c*f+2*d*e))*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/c^2/(-a*d+b*c)^2/(d*x^2+c)^(3/2)-1/15*sqrt(e)*(b^2*c^2*e*(-20*c*f+23*d*e)-a*b*c*(-10*c^2*f^2-7*c*d*e*f+23*d^2*e^2)+a^2*d*(-2*c^2*f^2-3*c*d*e*f+8*d^2*e^2))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*EllipticE(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c))),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/c^3/(-a*d+b*c)^3/sqrt(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e)+1/15*sqrt(e)*(-a*f+b*e)*(15*b^2*c^2*e+2*a^2*d*(c*f+2*d*e)-a*b*c*(10*c*f+11*d*e))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*InverseJacobiAM(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c)),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/a/c^2/(-a*d+b*c)^3/sqrt(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e),1],
[(f*x^2+e)^(3/2)/sqrt(b*x^2+a)/(d*x^2+c)^(9/2),x,7,-1/7*(-c*f+d*e)*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/c/(-a*d+b*c)/(d*x^2+c)^(7/2)-2/35*(2*b*c*(-c*f+3*d*e)-a*d*(c*f+3*d*e))*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/c^2/(-a*d+b*c)^2/(d*x^2+c)^(5/2)+1/105*(a*b*c*d*(-22*c^2*f^2-43*c*d*e*f+71*d^2*e^2)-3*a^2*d^2*(-2*c^2*f^2-5*c*d*e*f+8*d^2*e^2)-b^2*c^2*(8*c^2*f^2-76*c*d*e*f+71*d^2*e^2))*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/c^3/(-a*d+b*c)^3/(-c*f+d*e)/(d*x^2+c)^(3/2)-2/105*sqrt(e)*(b^3*c^3*e*(70*c^2*f^2-161*c*d*e*f+88*d^2*e^2)-3*a^3*d^2*(c^3*f^3+2*c^2*d*e*f^2-12*c*d^2*e^2*f+8*d^3*e^3)+a^2*b*c*d*(14*c^3*f^3+22*c^2*d*e*f^2-137*c*d^2*e^2*f+92*d^3*e^3)-a*b^2*c^2*(35*c^3*f^3+14*c^2*d*e*f^2-190*c*d^2*e^2*f+132*d^3*e^3))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*EllipticE(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c))),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/c^4/(-a*d+b*c)^4/(-c*f+d*e)^(3/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e)+1/105*sqrt(e)*(-a*f+b*e)*(105*b^3*c^3*e*(-c*f+d*e)-a*b^2*c^2*(-70*c^2*f^2-49*c*d*e*f+122*d^2*e^2)+a^2*b*c*d*(-28*c^2*f^2-55*c*d*e*f+89*d^2*e^2)-3*a^3*d^2*(-2*c^2*f^2-5*c*d*e*f+8*d^2*e^2))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*InverseJacobiAM(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c)),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/a/c^3/(-a*d+b*c)^4/(-c*f+d*e)^(3/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e),1],
[(d*x^2+c)^(3/2)*(f*x^2+e)^(3/2)/(b*x^2+a)^(3/2),x,8,-5/8*(a*d*f-b*(c*f+d*e))*x*sqrt(d*x^2+c)*sqrt(f*x^2+e)/b^2/sqrt(b*x^2+a)+1/4*d*f*x^3*sqrt(d*x^2+c)*sqrt(f*x^2+e)/b/sqrt(b*x^2+a)+1/8*sqrt(-a*d+b*c)*e*(8*b^2*c*e+15*a^2*d*f-13*a*b*(c*f+d*e))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticE(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/a/b^3/sqrt(c)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)+1/8*sqrt(-a*d+b*c)*(15*a^2*d*f^2+8*b^2*e*(c*f+2*d*e)-3*a*b*f*(c*f+11*d*e))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*InverseJacobiAM(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a)),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^4/sqrt(c)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)+3/8*a*(5*a^2*d^2*f^2-6*a*b*d*f*(c*f+d*e)+b^2*(c^2*f^2+6*c*d*e*f+d^2*e^2))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticPi(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),b*c/(-a*d+b*c),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^4/sqrt(c)/sqrt(-a*d+b*c)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e),1],
[sqrt(d*x^2+c)*(f*x^2+e)^(3/2)/(b*x^2+a)^(3/2),x,7,1/2*f*x*sqrt(d*x^2+c)*sqrt(f*x^2+e)/b/sqrt(b*x^2+a)+1/2*sqrt(-a*d+b*c)*e*(-3*a*f+2*b*e)*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticE(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/a/b^2/sqrt(c)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)+1/2*(3*a^2*d*f^2+2*b^2*e*(c*f+d*e)-a*b*f*(c*f+6*d*e))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*InverseJacobiAM(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a)),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^3/sqrt(c)/sqrt(-a*d+b*c)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)+1/2*a*f*(-3*a*d*f+b*c*f+3*b*d*e)*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticPi(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),b*c/(-a*d+b*c),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^3/sqrt(c)/sqrt(-a*d+b*c)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e),1],
[(f*x^2+e)^(3/2)/(b*x^2+a)^(3/2)/sqrt(d*x^2+c),x,6,sqrt(c)*(-a*f+b*e)*sqrt(a*(d*x^2+c)/c/(b*x^2+a))*sqrt(f*x^2+e)*EllipticE(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/a/b/sqrt(-a*d+b*c)/sqrt(d*x^2+c)/sqrt(a*(f*x^2+e)/e/(b*x^2+a))+sqrt(c)*f*(-a*f+b*e)*sqrt(a*(d*x^2+c)/c/(b*x^2+a))*sqrt(f*x^2+e)*InverseJacobiAM(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a)),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^2/sqrt(-a*d+b*c)/e/sqrt(d*x^2+c)/sqrt(a*(f*x^2+e)/e/(b*x^2+a))+a*sqrt(c)*f^2*sqrt(a*(d*x^2+c)/c/(b*x^2+a))*sqrt(f*x^2+e)*EllipticPi(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),b*c/(-a*d+b*c),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^2/sqrt(-a*d+b*c)/e/sqrt(d*x^2+c)/sqrt(a*(f*x^2+e)/e/(b*x^2+a)),1],
[(f*x^2+e)^(3/2)/(b*x^2+a)^(3/2)/(d*x^2+c)^(3/2),x,5,(-a*f+b*e)*x*sqrt(f*x^2+e)/a/(-a*d+b*c)/sqrt(b*x^2+a)/sqrt(d*x^2+c)+sqrt(e)*sqrt(-c*f+d*e)*(-2*a*c*f+a*d*e+b*c*e)*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*EllipticE(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c))),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/a/c/(-a*d+b*c)^2/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e)-2*sqrt(e)*(-a*f+b*e)*sqrt(-c*f+d*e)*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*InverseJacobiAM(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c)),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/a/(-a*d+b*c)^2/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e),1],
[(f*x^2+e)^(3/2)/(b*x^2+a)^(3/2)/(d*x^2+c)^(5/2),x,6,-1/3*(-c*f+d*e)*x*sqrt(f*x^2+e)/c/(-a*d+b*c)/sqrt(b*x^2+a)/(d*x^2+c)^(3/2)+1/3*b*(-4*a*c*f+a*d*e+3*b*c*e)*x*sqrt(f*x^2+e)/a/c/(-a*d+b*c)^2/sqrt(b*x^2+a)/sqrt(d*x^2+c)+1/3*sqrt(e)*sqrt(-c*f+d*e)*(3*b^2*c^2*e+a*b*c*(-6*c*f+7*d*e)-2*a^2*d*(c*f+d*e))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*EllipticE(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c))),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/a/c^2/(-a*d+b*c)^3/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e)-1/3*sqrt(e)*(-a*f+b*e)*(3*b*c*(-2*c*f+3*d*e)-a*d*(2*c*f+d*e))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*InverseJacobiAM(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c)),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/a/c/(-a*d+b*c)^3/sqrt(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e),1],
[(f*x^2+e)^(3/2)/(b*x^2+a)^(3/2)/(d*x^2+c)^(7/2),x,7,-1/5*(-c*f+d*e)*x*sqrt(f*x^2+e)/c/(-a*d+b*c)/sqrt(b*x^2+a)/(d*x^2+c)^(5/2)+1/5*b*(-6*a*c*f+a*d*e+5*b*c*e)*x*sqrt(f*x^2+e)/a/c/(-a*d+b*c)^2/sqrt(b*x^2+a)/(d*x^2+c)^(3/2)+1/15*d*(15*b^2*c^2*e+a*b*c*(-22*c*f+13*d*e)-2*a^2*d*(c*f+2*d*e))*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/a/c^2/(-a*d+b*c)^3/(d*x^2+c)^(3/2)+1/15*sqrt(e)*(15*b^3*c^3*e*(-c*f+d*e)-a^2*b*c*d*(-20*c^2*f^2-7*c*d*e*f+33*d^2*e^2)+a^3*d^2*(-2*c^2*f^2-3*c*d*e*f+8*d^2*e^2)+a*b^2*c^2*(30*c^2*f^2-85*c*d*e*f+58*d^2*e^2))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*EllipticE(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c))),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/a/c^3/(-a*d+b*c)^4/sqrt(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e)-2/15*sqrt(e)*(-a*f+b*e)*(15*b^2*c^2*(-c*f+2*d*e)+a^2*d^2*(c*f+2*d*e)-2*a*b*c*d*(5*c*f+4*d*e))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*InverseJacobiAM(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c)),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/a/c^2/(-a*d+b*c)^4/sqrt(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e),1],
[(d*x^2+c)^(3/2)*(f*x^2+e)^(3/2)/(b*x^2+a)^(5/2),x,8,1/3*(-a*d+b*c)*(-a*f+b*e)*x*sqrt(d*x^2+c)*sqrt(f*x^2+e)/a/b^2/(b*x^2+a)^(3/2)+1/2*d*f*x*sqrt(d*x^2+c)*sqrt(f*x^2+e)/b^2/sqrt(b*x^2+a)+1/6*sqrt(-a*d+b*c)*e*(4*b^2*c*e-15*a^2*d*f+4*a*b*(c*f+d*e))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticE(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/a^2/b^3/sqrt(c)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)+1/6*(15*a^3*d^2*f^2+2*b^3*c*e*(-c*f+d*e)-3*a^2*b*d*f*(3*c*f+8*d*e)+2*a*b^2*d*e*(7*c*f+2*d*e))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*InverseJacobiAM(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a)),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/a/b^4/sqrt(c)/sqrt(-a*d+b*c)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)-1/2*a*d*f*(5*a*d*f-3*b*(c*f+d*e))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticPi(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),b*c/(-a*d+b*c),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^4/sqrt(c)/sqrt(-a*d+b*c)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e),1],
[sqrt(d*x^2+c)*(f*x^2+e)^(3/2)/(b*x^2+a)^(5/2),x,7,1/3*(-a*f+b*e)*x*sqrt(d*x^2+c)*sqrt(f*x^2+e)/a/b/(b*x^2+a)^(3/2)+1/3*e*(2*b^2*c*e-3*a^2*d*f-a*b*(-2*c*f+d*e))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticE(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/a^2/b^2/sqrt(c)/sqrt(-a*d+b*c)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)+1/3*(3*a*b*d*e*f-3*a^2*d*f^2+b^2*e*(-c*f+d*e))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*InverseJacobiAM(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a)),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/a/b^3/sqrt(c)/sqrt(-a*d+b*c)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)+a*d*f^2*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticPi(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),b*c/(-a*d+b*c),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^3/sqrt(c)/sqrt(-a*d+b*c)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e),1],
[(f*x^2+e)^(3/2)/(b*x^2+a)^(5/2)/sqrt(d*x^2+c),x,5,1/3*(-a*f+b*e)*x*sqrt(d*x^2+c)*sqrt(f*x^2+e)/a/(-a*d+b*c)/(b*x^2+a)^(3/2)+2/3*e*(a*c*f-2*a*d*e+b*c*e)*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticE(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/a^2/sqrt(c)/(-a*d+b*c)^(3/2)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)+1/3*e*(-c*f+d*e)*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*InverseJacobiAM(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a)),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/a/sqrt(c)/(-a*d+b*c)^(3/2)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e),1],
[(f*x^2+e)^(3/2)/(b*x^2+a)^(5/2)/(d*x^2+c)^(3/2),x,6,1/3*(-a*f+b*e)*x*sqrt(f*x^2+e)/a/(-a*d+b*c)/(b*x^2+a)^(3/2)/sqrt(d*x^2+c)+2/3*(b^2*c*e+a^2*d*f-a*b*(-c*f+3*d*e))*x*sqrt(f*x^2+e)/a^2/(-a*d+b*c)^2/sqrt(b*x^2+a)/sqrt(d*x^2+c)+1/3*sqrt(e)*sqrt(-c*f+d*e)*(2*b^2*c^2*e-3*a^2*d*(-2*c*f+d*e)-a*b*c*(-2*c*f+7*d*e))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*EllipticE(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c))),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/a^2/c/(-a*d+b*c)^3/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e)-1/3*sqrt(e)*sqrt(-c*f+d*e)*(6*a^2*d*f+2*a*b*c*f-9*a*b*d*e+b^2*c*e)*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*InverseJacobiAM(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c)),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/a^2/(-a*d+b*c)^3/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e),1],
[(f*x^2+e)^(3/2)/(b*x^2+a)^(5/2)/(d*x^2+c)^(5/2),x,7,1/3*(-a*f+b*e)*x*sqrt(f*x^2+e)/a/(-a*d+b*c)/(b*x^2+a)^(3/2)/(d*x^2+c)^(3/2)+2/3*(b^2*c*e+2*a^2*d*f-a*b*(-c*f+4*d*e))*x*sqrt(f*x^2+e)/a^2/(-a*d+b*c)^2/sqrt(b*x^2+a)/(d*x^2+c)^(3/2)+1/3*d*(2*b^2*c^2*e-a^2*d*(-6*c*f+d*e)-a*b*c*(-2*c*f+9*d*e))*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/a^2/c/(-a*d+b*c)^3/(d*x^2+c)^(3/2)+2/3*sqrt(e)*sqrt(-c*f+d*e)*(b^3*c^3*e-a^2*b*c*d*(-6*c*f+5*d*e)-a*b^2*c^2*(-c*f+5*d*e)+a^3*d^2*(c*f+d*e))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*EllipticE(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c))),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/a^2/c^2/(-a*d+b*c)^4/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e)-1/3*sqrt(e)*(b^3*c^2*e*(-c*f+d*e)-a^3*d^2*f*(2*c*f+d*e)+a^2*b*d*(-12*c^2*f^2+17*c*d*e*f+d^2*e^2)-a*b^2*c*(2*c^2*f^2-17*c*d*e*f+18*d^2*e^2))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*InverseJacobiAM(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c)),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/a^2/c/(-a*d+b*c)^4/sqrt(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e),1],
[sqrt(b*x^2+a)*(d*x^2+c)^(3/2)/sqrt(f*x^2+e),x,8,-1/8*(-a*d*f-5*b*c*f+3*b*d*e)*x*sqrt(d*x^2+c)*sqrt(f*x^2+e)/f^2/sqrt(b*x^2+a)+1/4*d*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)/f+1/8*sqrt(-a*d+b*c)*e*(-a*d*f-5*b*c*f+3*b*d*e)*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticE(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b/sqrt(c)/f^2/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)-1/8*a*sqrt(-a*d+b*c)*(a*d*f-5*b*c*f+b*d*e)*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*InverseJacobiAM(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a)),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^2/sqrt(c)/f/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)-1/8*a*(a^2*d^2*f^2+2*a*b*d*f*(-3*c*f+d*e)-3*b^2*(-c*f+d*e)^2)*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticPi(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),b*c/(-a*d+b*c),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^2/sqrt(c)/sqrt(-a*d+b*c)/f^2/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e),1],
[sqrt(b*x^2+a)*sqrt(d*x^2+c)/sqrt(f*x^2+e),x,7,1/2*b*x*sqrt(d*x^2+c)*sqrt(f*x^2+e)/f/sqrt(b*x^2+a)-1/2*sqrt(-a*d+b*c)*e*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticE(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/sqrt(c)/f/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)+1/2*a*sqrt(-a*d+b*c)*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*InverseJacobiAM(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a)),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b/sqrt(c)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)-1/2*a*(-a*d*f-b*c*f+b*d*e)*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticPi(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),b*c/(-a*d+b*c),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b/sqrt(c)/sqrt(-a*d+b*c)/f/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e),1],
[sqrt(b*x^2+a)/sqrt(d*x^2+c)/sqrt(f*x^2+e),x,2,a*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticPi(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),b*c/(-a*d+b*c),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/sqrt(c)/sqrt(-a*d+b*c)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e),1],
[sqrt(b*x^2+a)/(d*x^2+c)^(3/2)/sqrt(f*x^2+e),x,2,sqrt(e)*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*EllipticE(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c))),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/c/sqrt(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e),1],
[sqrt(b*x^2+a)/(d*x^2+c)^(5/2)/sqrt(f*x^2+e),x,5,1/3*d*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/c/(-c*f+d*e)/(d*x^2+c)^(3/2)+1/3*sqrt(e)*(b*c*(-3*c*f+d*e)-2*a*d*(-2*c*f+d*e))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*EllipticE(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c))),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/c^2/(-a*d+b*c)/(-c*f+d*e)^(3/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e)+1/3*d*sqrt(e)*(-a*f+b*e)*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*InverseJacobiAM(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c)),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/c/(-a*d+b*c)/(-c*f+d*e)^(3/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e),1],
[sqrt(b*x^2+a)/(d*x^2+c)^(7/2)/sqrt(f*x^2+e),x,6,1/5*d*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/c/(-c*f+d*e)/(d*x^2+c)^(5/2)+1/15*d*(b*c*(-7*c*f+3*d*e)-4*a*d*(-2*c*f+d*e))*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/c^2/(-a*d+b*c)/(-c*f+d*e)^2/(d*x^2+c)^(3/2)+1/15*sqrt(e)*(b^2*c^2*(15*c^2*f^2-10*c*d*e*f+3*d^2*e^2)+a^2*d^2*(23*c^2*f^2-23*c*d*e*f+8*d^2*e^2)-a*b*c*d*(40*c^2*f^2-37*c*d*e*f+13*d^2*e^2))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*EllipticE(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c))),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/c^3/(-a*d+b*c)^2/(-c*f+d*e)^(5/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e)+2/15*d*sqrt(e)*(-a*f+b*e)*(b*c*(-5*c*f+3*d*e)-2*a*d*(-2*c*f+d*e))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*InverseJacobiAM(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c)),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/c^2/(-a*d+b*c)^2/(-c*f+d*e)^(5/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e),1],
[(b*x^2+a)^(3/2)*sqrt(d*x^2+c)/sqrt(f*x^2+e),x,8,-1/8*b*(-5*a*d*f-b*c*f+3*b*d*e)*x*sqrt(d*x^2+c)*sqrt(f*x^2+e)/d/f^2/sqrt(b*x^2+a)+1/4*b*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)/f+1/8*sqrt(-a*d+b*c)*e*(-5*a*d*f-b*c*f+3*b*d*e)*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticE(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/sqrt(c)/d/f^2/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)-1/8*a*sqrt(-a*d+b*c)*(-3*a*d*f-b*c*f+b*d*e)*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*InverseJacobiAM(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a)),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b/sqrt(c)/d/f/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)+1/8*a*(3*a^2*d^2*f^2-6*a*b*d*f*(-c*f+d*e)+b^2*(-c^2*f^2-2*c*d*e*f+3*d^2*e^2))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticPi(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),b*c/(-a*d+b*c),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b/sqrt(c)/d/sqrt(-a*d+b*c)/f^2/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e),1],
[(b*x^2+a)^(3/2)/sqrt(d*x^2+c)/sqrt(f*x^2+e),x,7,1/2*b^2*x*sqrt(d*x^2+c)*sqrt(f*x^2+e)/d/f/sqrt(b*x^2+a)-1/2*b*sqrt(-a*d+b*c)*e*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticE(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/sqrt(c)/d/f/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)+1/2*a*sqrt(-a*d+b*c)*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*InverseJacobiAM(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a)),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/sqrt(c)/d/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)-1/2*a*(-3*a*d*f+b*c*f+b*d*e)*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticPi(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),b*c/(-a*d+b*c),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/sqrt(c)/d/sqrt(-a*d+b*c)/f/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e),1],
[(b*x^2+a)^(3/2)/(d*x^2+c)^(3/2)/sqrt(f*x^2+e),x,6,-(-a*d+b*c)*sqrt(e)*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*EllipticE(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c))),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/c/d/sqrt(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e)-b*(-a*d+b*c)*sqrt(e)*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*InverseJacobiAM(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c)),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/a/d^2/sqrt(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e)+b^2*c*sqrt(e)*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*EllipticPi(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c))),d*e/(-c*f+d*e),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/a/d^2/sqrt(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e),1],
[(b*x^2+a)^(3/2)/(d*x^2+c)^(5/2)/sqrt(f*x^2+e),x,5,-1/3*(-a*d+b*c)*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/c/(-c*f+d*e)/(d*x^2+c)^(3/2)+2/3*sqrt(e)*(-2*a*c*f+a*d*e+b*c*e)*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*EllipticE(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c))),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/c^2/(-c*f+d*e)^(3/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e)-1/3*sqrt(e)*(-a*f+b*e)*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*InverseJacobiAM(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c)),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/c/(-c*f+d*e)^(3/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e),1],
[(b*x^2+a)^(3/2)/(d*x^2+c)^(7/2)/sqrt(f*x^2+e),x,6,-1/5*(-a*d+b*c)*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/c/(-c*f+d*e)/(d*x^2+c)^(5/2)+2/15*(2*a*d*(-2*c*f+d*e)+b*c*(c*f+d*e))*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/c^2/(-c*f+d*e)^2/(d*x^2+c)^(3/2)+1/15*sqrt(e)*(2*b^2*c^2*e*(-5*c*f+d*e)+a*b*c*(20*c^2*f^2-7*c*d*e*f+3*d^2*e^2)-a^2*d*(23*c^2*f^2-23*c*d*e*f+8*d^2*e^2))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*EllipticE(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c))),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/c^3/(-a*d+b*c)/(-c*f+d*e)^(5/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e)-1/15*sqrt(e)*(-a*f+b*e)*(b*c*(-5*c*f+d*e)-4*a*d*(-2*c*f+d*e))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*InverseJacobiAM(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c)),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/c^2/(-a*d+b*c)/(-c*f+d*e)^(5/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e),1],
[(b*x^2+a)^(3/2)/(d*x^2+c)^(9/2)/sqrt(f*x^2+e),x,7,-1/7*(-a*d+b*c)*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/c/(-c*f+d*e)/(d*x^2+c)^(7/2)+2/35*(3*a*d*(-2*c*f+d*e)+b*c*(2*c*f+d*e))*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/c^2/(-c*f+d*e)^2/(d*x^2+c)^(5/2)+1/105*(2*b^2*c^2*(-4*c^2*f^2-11*c*d*e*f+3*d^2*e^2)-a^2*d^2*(71*c^2*f^2-71*c*d*e*f+24*d^2*e^2)+a*b*c*d*(76*c^2*f^2-43*c*d*e*f+15*d^2*e^2))*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/c^3/(-a*d+b*c)/(-c*f+d*e)^3/(d*x^2+c)^(3/2)+2/105*sqrt(e)*(b^3*c^3*e*(35*c^2*f^2-14*c*d*e*f+3*d^2*e^2)-a^2*b*c*d*(-161*c^3*f^3+190*c^2*d*e*f^2-137*c*d^2*e^2*f+36*d^3*e^3)+2*a*b^2*c^2*(-35*c^3*f^3+7*c^2*d*e*f^2-11*c*d^2*e^2*f+3*d^3*e^3)+4*a^3*d^2*(-22*c^3*f^3+33*c^2*d*e*f^2-23*c*d^2*e^2*f+6*d^3*e^3))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*EllipticE(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c))),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/c^4/(-a*d+b*c)^2/(-c*f+d*e)^(7/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e)-1/105*sqrt(e)*(-a*f+b*e)*(b^2*c^2*(35*c^2*f^2-14*c*d*e*f+3*d^2*e^2)+a^2*d^2*(71*c^2*f^2-71*c*d*e*f+24*d^2*e^2)-a*b*c*d*(112*c^2*f^2-97*c*d*e*f+33*d^2*e^2))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*InverseJacobiAM(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c)),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/c^3/(-a*d+b*c)^2/(-c*f+d*e)^(7/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e),1],
[(b*x^2+a)^(5/2)*sqrt(d*x^2+c)/sqrt(f*x^2+e),x,9,1/48*b*(33*a^2*d^2*f^2-2*a*b*d*f*(-7*c*f+20*d*e)+b^2*(-3*c^2*f^2-4*c*d*e*f+15*d^2*e^2))*x*sqrt(d*x^2+c)*sqrt(f*x^2+e)/d^2/f^3/sqrt(b*x^2+a)-1/24*b*(-13*a*d*f-b*c*f+5*b*d*e)*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)/d/f^2+1/6*b^2*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)/f-1/48*sqrt(-a*d+b*c)*e*(33*a^2*d^2*f^2-2*a*b*d*f*(-7*c*f+20*d*e)+b^2*(-3*c^2*f^2-4*c*d*e*f+15*d^2*e^2))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticE(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/sqrt(c)/d^2/f^3/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)+1/48*a*sqrt(-a*d+b*c)*(15*a^2*d^2*f^2-12*a*b*d*f*(-c*f+d*e)+b^2*(-3*c^2*f^2-2*c*d*e*f+5*d^2*e^2))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*InverseJacobiAM(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a)),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b/sqrt(c)/d^2/f^2/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)+1/16*a*(5*a^3*d^3*f^3-15*a^2*b*d^2*f^2*(-c*f+d*e)+5*a*b^2*d*f*(-c^2*f^2-2*c*d*e*f+3*d^2*e^2)-b^3*(-c^3*f^3-c^2*d*e*f^2-3*c*d^2*e^2*f+5*d^3*e^3))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticPi(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),b*c/(-a*d+b*c),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b/sqrt(c)/d^2/sqrt(-a*d+b*c)/f^3/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e),1],
[(b*x^2+a)^(5/2)/sqrt(d*x^2+c)/sqrt(f*x^2+e),x,8,-3/8*b^2*(-3*a*d*f+b*c*f+b*d*e)*x*sqrt(d*x^2+c)*sqrt(f*x^2+e)/d^2/f^2/sqrt(b*x^2+a)+1/4*b^2*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)/d/f+3/8*b*sqrt(-a*d+b*c)*e*(-3*a*d*f+b*c*f+b*d*e)*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticE(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/sqrt(c)/d^2/f^2/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)-1/8*a*sqrt(-a*d+b*c)*(-7*a*d*f+3*b*c*f+b*d*e)*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*InverseJacobiAM(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a)),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/sqrt(c)/d^2/f/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)+1/8*a*(15*a^2*d^2*f^2-10*a*b*d*f*(c*f+d*e)+b^2*(3*c^2*f^2+2*c*d*e*f+3*d^2*e^2))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticPi(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),b*c/(-a*d+b*c),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/sqrt(c)/d^2/sqrt(-a*d+b*c)/f^2/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e),1],
[(b*x^2+a)^(5/2)/(d*x^2+c)^(3/2)/sqrt(f*x^2+e),x,7,1/2*b^2*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/d/f/sqrt(d*x^2+c)-1/2*sqrt(e)*(4*a*b*c*d*f-2*a^2*d^2*f+b^2*c*(-3*c*f+d*e))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*EllipticE(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c))),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/c/d^2/f/sqrt(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e)-1/2*b*sqrt(e)*(8*a*b*c*d*f-4*a^2*d^2*f-b^2*c*(3*c*f+d*e))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*InverseJacobiAM(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c)),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/a/d^3/f/sqrt(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e)-1/2*b^2*c*sqrt(e)*(-5*a*d*f+3*b*c*f+b*d*e)*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*EllipticPi(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c))),d*e/(-c*f+d*e),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/a/d^3/f/sqrt(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e),1],
[(b*x^2+a)^(5/2)/(d*x^2+c)^(5/2)/sqrt(f*x^2+e),x,7,1/3*(-a*d+b*c)^2*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/c/d/(-c*f+d*e)/(d*x^2+c)^(3/2)-1/3*(-a*d+b*c)*sqrt(e)*(b*c*(-3*c*f+5*d*e)+2*a*d*(-2*c*f+d*e))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*EllipticE(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c))),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/c^2/d^2/(-c*f+d*e)^(3/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e)+1/3*(-a*d+b*c)*sqrt(e)*(a*b*d^2*e-a^2*d^2*f-3*b^2*c*(-c*f+d*e))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*InverseJacobiAM(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c)),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/a/c/d^3/(-c*f+d*e)^(3/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e)+b^3*c*sqrt(e)*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*EllipticPi(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c))),d*e/(-c*f+d*e),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/a/d^3/sqrt(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e),1],
[(b*x^2+a)^(5/2)/(d*x^2+c)^(7/2)/sqrt(f*x^2+e),x,6,1/5*(-a*d+b*c)^2*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/c/d/(-c*f+d*e)/(d*x^2+c)^(5/2)-1/15*(-a*d+b*c)*(b*c*(-3*c*f+7*d*e)+4*a*d*(-2*c*f+d*e))*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/c^2/d/(-c*f+d*e)^2/(d*x^2+c)^(3/2)+1/15*sqrt(e)*(8*b^2*c^2*e^2+a*b*c*e*(-23*c*f+7*d*e)+a^2*(23*c^2*f^2-23*c*d*e*f+8*d^2*e^2))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*EllipticE(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c))),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/c^3/(-c*f+d*e)^(5/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e)-4/15*sqrt(e)*(-a*f+b*e)*(-2*a*c*f+a*d*e+b*c*e)*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*InverseJacobiAM(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c)),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/c^2/(-c*f+d*e)^(5/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e),1],
[(b*x^2+a)^(5/2)/(d*x^2+c)^(9/2)/sqrt(f*x^2+e),x,7,1/7*(-a*d+b*c)^2*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/c/d/(-c*f+d*e)/(d*x^2+c)^(7/2)-3/35*(-a*d+b*c)*(2*a*d*(-2*c*f+d*e)+b*c*(-c*f+3*d*e))*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/c^2/d/(-c*f+d*e)^2/(d*x^2+c)^(5/2)+1/105*(a*b*c*d*(-20*c^2*f^2-41*c*d*e*f+13*d^2*e^2)+2*b^2*c^2*(-3*c^2*f^2+11*c*d*e*f+4*d^2*e^2)+a^2*d^2*(71*c^2*f^2-71*c*d*e*f+24*d^2*e^2))*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/c^3/d/(-c*f+d*e)^3/(d*x^2+c)^(3/2)+1/105*sqrt(e)*(8*b^3*c^3*e^2*(-7*c*f+d*e)+a*b^2*c^2*e*(161*c^2*f^2-26*c*d*e*f+9*d^2*e^2)+a^2*b*c*(-161*c^3*f^3+58*c^2*d*e*f^2-57*c*d^2*e^2*f+16*d^3*e^3)-8*a^3*d*(-22*c^3*f^3+33*c^2*d*e*f^2-23*c*d^2*e^2*f+6*d^3*e^3))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*EllipticE(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c))),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/c^4/(-a*d+b*c)/(-c*f+d*e)^(7/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e)-1/105*sqrt(e)*(-a*f+b*e)*(4*b^2*c^2*e*(-7*c*f+d*e)+a*b*c*(56*c^2*f^2-13*c*d*e*f+5*d^2*e^2)-a^2*d*(71*c^2*f^2-71*c*d*e*f+24*d^2*e^2))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*InverseJacobiAM(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c)),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/c^3/(-a*d+b*c)/(-c*f+d*e)^(7/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e),1],
[1/sqrt(b*x^2+a)/sqrt(d*x^2+c)/sqrt(f*x^2+e),x,2,sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*InverseJacobiAM(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a)),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/sqrt(c)/sqrt(-a*d+b*c)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e),1],
[1/sqrt(b*x^2+a)/(d*x^2+c)^(3/2)/sqrt(f*x^2+e),x,4,-a*d*sqrt(c*(b*x^2+a)/a/(d*x^2+c))*sqrt(f*x^2+e)*EllipticE(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c))),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/c/(-a*d+b*c)/sqrt(e)/sqrt(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(c*(f*x^2+e)/e/(d*x^2+c))+b*sqrt(c*(b*x^2+a)/a/(d*x^2+c))*sqrt(f*x^2+e)*InverseJacobiAM(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c)),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/(-a*d+b*c)/sqrt(e)/sqrt(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(c*(f*x^2+e)/e/(d*x^2+c)),1],
[1/sqrt(b*x^2+a)/(d*x^2+c)^(5/2)/sqrt(f*x^2+e),x,5,-1/3*d^2*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/c/(-a*d+b*c)/(-c*f+d*e)/(d*x^2+c)^(3/2)-2/3*d*sqrt(e)*(b*c*(-3*c*f+2*d*e)-a*d*(-2*c*f+d*e))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*EllipticE(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c))),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/c^2/(-a*d+b*c)^2/(-c*f+d*e)^(3/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e)-1/3*sqrt(e)*(a*b*d^2*e-a^2*d^2*f-3*b^2*c*(-c*f+d*e))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*InverseJacobiAM(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c)),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/a/c/(-a*d+b*c)^2/(-c*f+d*e)^(3/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e),1],
[1/(b*x^2+a)^(3/2)/sqrt(d*x^2+c)/sqrt(f*x^2+e),x,4,b*sqrt(c)*sqrt(a*(d*x^2+c)/c/(b*x^2+a))*sqrt(f*x^2+e)*EllipticE(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/a/sqrt(-a*d+b*c)/(-a*f+b*e)/sqrt(d*x^2+c)/sqrt(a*(f*x^2+e)/e/(b*x^2+a))-sqrt(c)*f*sqrt(a*(d*x^2+c)/c/(b*x^2+a))*sqrt(f*x^2+e)*InverseJacobiAM(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a)),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/sqrt(-a*d+b*c)/e/(-a*f+b*e)/sqrt(d*x^2+c)/sqrt(a*(f*x^2+e)/e/(b*x^2+a)),1],
[1/(b*x^2+a)^(3/2)/(d*x^2+c)^(3/2)/sqrt(f*x^2+e),x,5,b^2*x*sqrt(f*x^2+e)/a/(-a*d+b*c)/(-a*f+b*e)/sqrt(b*x^2+a)/sqrt(d*x^2+c)+sqrt(e)*(a*b*d^2*e-a^2*d^2*f+b^2*c*(-c*f+d*e))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*EllipticE(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c))),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/a/c/(-a*d+b*c)^2/(-a*f+b*e)/sqrt(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e)-2*b*d*sqrt(e)*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*InverseJacobiAM(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c)),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/a/(-a*d+b*c)^2/sqrt(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e),1],
[1/(b*x^2+a)^(3/2)/(d*x^2+c)^(5/2)/sqrt(f*x^2+e),x,6,b^2*x*sqrt(f*x^2+e)/a/(-a*d+b*c)/(-a*f+b*e)/sqrt(b*x^2+a)/(d*x^2+c)^(3/2)+1/3*d*(a*b*d^2*e-a^2*d^2*f+3*b^2*c*(-c*f+d*e))*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/a/c/(-a*d+b*c)^2/(-a*f+b*e)/(-c*f+d*e)/(d*x^2+c)^(3/2)+1/3*sqrt(e)*(a*b^2*c*d^2*e*(-9*c*f+7*d*e)+2*a^3*d^3*f*(-2*c*f+d*e)+3*b^3*c^2*(-c*f+d*e)^2-a^2*b*d^2*(-9*c^2*f^2+3*c*d*e*f+2*d^2*e^2))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*EllipticE(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c))),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/a/c^2/(-a*d+b*c)^3/(-a*f+b*e)/(-c*f+d*e)^(3/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e)+1/3*d*sqrt(e)*(a*b*d^2*e-a^2*d^2*f-9*b^2*c*(-c*f+d*e))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*InverseJacobiAM(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c)),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/a/c/(-a*d+b*c)^3/(-c*f+d*e)^(3/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e),1],
[1/(b*x^2+a)^(5/2)/sqrt(d*x^2+c)/sqrt(f*x^2+e),x,5,1/3*b^2*x*sqrt(d*x^2+c)*sqrt(f*x^2+e)/a/(-a*d+b*c)/(-a*f+b*e)/(b*x^2+a)^(3/2)+2/3*b*e*(b^2*c*e+3*a^2*d*f-2*a*b*(c*f+d*e))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticE(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/a^2/sqrt(c)/(-a*d+b*c)^(3/2)/(-a*f+b*e)^2/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)+1/3*(3*a*b*c*f^2-3*a^2*d*f^2+b^2*e*(-c*f+d*e))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*InverseJacobiAM(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a)),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/a/sqrt(c)/(-a*d+b*c)^(3/2)/(-a*f+b*e)^2/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e),1],
[1/(b*x^2+a)^(5/2)/(d*x^2+c)^(3/2)/sqrt(f*x^2+e),x,6,1/3*b^2*x*sqrt(f*x^2+e)/a/(-a*d+b*c)/(-a*f+b*e)/(b*x^2+a)^(3/2)/sqrt(d*x^2+c)+2/3*b^2*(4*a^2*d*f-2*a*b*c*f-3*a*b*d*e+b^2*c*e)*x*sqrt(f*x^2+e)/a^2/(-a*d+b*c)^2/(-a*f+b*e)^2/sqrt(b*x^2+a)/sqrt(d*x^2+c)+1/3*sqrt(e)*(6*a^3*b*d^3*e*f-3*a^4*d^3*f^2+2*b^4*c^2*e*(-c*f+d*e)-a*b^3*c*(-4*c^2*f^2-3*c*d*e*f+7*d^2*e^2)-3*a^2*b^2*d*(3*c^2*f^2-3*c*d*e*f+d^2*e^2))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*EllipticE(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c))),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/a^2/c/(-a*d+b*c)^3/(-a*f+b*e)^2/sqrt(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e)+1/3*b*sqrt(e)*(9*a*b*d^2*e-9*a^2*d^2*f-b^2*c*(-c*f+d*e))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*InverseJacobiAM(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c)),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/a^2/(-a*d+b*c)^3/(-a*f+b*e)/sqrt(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e),1],
[1/(b*x^2+a)^(5/2)/(d*x^2+c)^(5/2)/sqrt(f*x^2+e),x,7,1/3*b^2*x*sqrt(f*x^2+e)/a/(-a*d+b*c)/(-a*f+b*e)/(b*x^2+a)^(3/2)/(d*x^2+c)^(3/2)+2/3*b^2*(b^2*c*e+5*a^2*d*f-2*a*b*(c*f+2*d*e))*x*sqrt(f*x^2+e)/a^2/(-a*d+b*c)^2/(-a*f+b*e)^2/sqrt(b*x^2+a)/(d*x^2+c)^(3/2)+1/3*d*(2*a^3*b*d^3*e*f-a^4*d^3*f^2+2*b^4*c^2*e*(-c*f+d*e)-a*b^3*c*(-4*c^2*f^2-5*c*d*e*f+9*d^2*e^2)-a^2*b^2*d*(11*c^2*f^2-11*c*d*e*f+d^2*e^2))*x*sqrt(b*x^2+a)*sqrt(f*x^2+e)/a^2/c/(-a*d+b*c)^3/(-a*f+b*e)^2/(-c*f+d*e)/(d*x^2+c)^(3/2)+2/3*sqrt(e)*(a^5*d^4*f^2*(-2*c*f+d*e)+b^5*c^3*e*(-c*f+d*e)^2-a*b^4*c^2*(-c*f+d*e)^2*(2*c*f+5*d*e)+a^3*b^2*d^3*e*(-12*c^2*f^2+8*c*d*e*f+d^2*e^2)-a^4*b*d^3*f*(-6*c^2*f^2+c*d*e*f+2*d^2*e^2)-a^2*b^3*c*d*(-6*c^3*f^3+12*c^2*d*e*f^2-12*c*d^2*e^2*f+5*d^3*e^3))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*EllipticE(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c))),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/a^2/c^2/(-a*d+b*c)^4/(-a*f+b*e)^2/(-c*f+d*e)^(3/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e)+1/3*sqrt(e)*(2*a^3*b*d^4*e*f-a^4*d^4*f^2+18*a*b^3*c*d^2*e*(-c*f+d*e)-b^4*c^2*(-c*f+d*e)^2-a^2*b^2*d^2*(-18*c^2*f^2+18*c*d*e*f+d^2*e^2))*sqrt(b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*InverseJacobiAM(arcsin(sqrt(-c*f+d*e)*x/sqrt(e)/sqrt(d*x^2+c)),sqrt(-(-a*d+b*c)*e/a/(-c*f+d*e)))/a^2/c/(-a*d+b*c)^4/(-a*f+b*e)/(-c*f+d*e)^(3/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e),1],
[1/sqrt(2*x^2+1)/sqrt(5*x^2+3)/sqrt(11*x^2+7),x,2,sqrt(5*x^2+3)*sqrt((11*x^2+7)/(2*x^2+1))*InverseJacobiAM(arcsin(x/sqrt(3)/sqrt(2*x^2+1)),sqrt(9/7))/sqrt(7)/sqrt((5*x^2+3)/(2*x^2+1))/sqrt(11*x^2+7),1],
[1/sqrt(-2*x^2+1)/sqrt(5*x^2+3)/sqrt(11*x^2+7),x,2,sqrt(-2*x^2+1)*sqrt((11*x^2+7)/(5*x^2+3))*InverseJacobiAM(arcsin(sqrt(11)*x/sqrt(5*x^2+3)),sqrt(2/77))/sqrt(77)/sqrt((-2*x^2+1)/(5*x^2+3))/sqrt(11*x^2+7),1],
[1/sqrt(-5*x^2+3)/sqrt(-2*x^2+1)/sqrt(11*x^2+7),x,2,sqrt(-2*x^2+1)*sqrt((11*x^2+7)/(-5*x^2+3))*InverseJacobiAM(arcsin(x/sqrt(-5*x^2+3)),sqrt(-68/7))/sqrt(7)/sqrt((-2*x^2+1)/(-5*x^2+3))/sqrt(11*x^2+7),1],
[1/sqrt(-5*x^2+3)/sqrt(2*x^2+1)/sqrt(11*x^2+7),x,2,sqrt(-5*x^2+3)*sqrt((11*x^2+7)/(2*x^2+1))*InverseJacobiAM(arcsin(sqrt(11/3)*x/sqrt(2*x^2+1)),sqrt(9/77))/sqrt(77)/sqrt((-5*x^2+3)/(2*x^2+1))/sqrt(11*x^2+7),1],
[1/sqrt(-11*x^2+7)/sqrt(-5*x^2+3)/sqrt(2*x^2+1),x,2,sqrt(-5*x^2+3)*sqrt((2*x^2+1)/(-11*x^2+7))*InverseJacobiAM(arcsin(sqrt(2/3)*x/sqrt(-11*x^2+7)),sqrt(-75/2))/sqrt(2)/sqrt((-5*x^2+3)/(-11*x^2+7))/sqrt(2*x^2+1),1],
[1/sqrt(-11*x^2+7)/sqrt(-5*x^2+3)/sqrt(-2*x^2+1),x,2,1/3*sqrt(-5*x^2+3)*sqrt((-2*x^2+1)/(-11*x^2+7))*InverseJacobiAM(arcsin(sqrt(3)*x/sqrt(-11*x^2+7)),sqrt(2/9))/sqrt((-5*x^2+3)/(-11*x^2+7))/sqrt(-2*x^2+1),1],
[1/sqrt(-11*x^2+7)/sqrt(-2*x^2+1)/sqrt(5*x^2+3),x,2,1/3*sqrt(-2*x^2+1)*sqrt((5*x^2+3)/(-11*x^2+7))*InverseJacobiAM(arcsin(sqrt(3)*x/sqrt(-11*x^2+7)),sqrt(-68/9))/sqrt((-2*x^2+1)/(-11*x^2+7))/sqrt(5*x^2+3),1],
[1/sqrt(-11*x^2+7)/sqrt(2*x^2+1)/sqrt(5*x^2+3),x,2,sqrt(-11*x^2+7)*sqrt((5*x^2+3)/(2*x^2+1))*InverseJacobiAM(arcsin(x/sqrt(3)/sqrt(2*x^2+1)),sqrt(75/7))/sqrt(7)/sqrt((-11*x^2+7)/(2*x^2+1))/sqrt(5*x^2+3),1],
[sqrt(2*x^2+1)/sqrt(5*x^2+3)/sqrt(11*x^2+7),x,2,sqrt(5*x^2+3)*sqrt((11*x^2+7)/(2*x^2+1))*EllipticPi(sin(arcsin(x/sqrt(3)/sqrt(2*x^2+1))),6,sqrt(9/7))/sqrt(7)/sqrt((5*x^2+3)/(2*x^2+1))/sqrt(11*x^2+7),1],
[sqrt(2*x^2+1)/sqrt(-5*x^2+3)/sqrt(11*x^2+7),x,2,sqrt(-5*x^2+3)*sqrt((11*x^2+7)/(2*x^2+1))*EllipticPi(sin(arcsin(sqrt(11/3)*x/sqrt(2*x^2+1))),6/11,sqrt(9/77))/sqrt(77)/sqrt((-5*x^2+3)/(2*x^2+1))/sqrt(11*x^2+7),1],
[sqrt(2*x^2+1)/sqrt(-11*x^2+7)/sqrt(5*x^2+3),x,2,sqrt(-11*x^2+7)*sqrt((5*x^2+3)/(2*x^2+1))*EllipticPi(sin(arcsin(x/sqrt(3)/sqrt(2*x^2+1))),6,sqrt(75/7))/sqrt(7)/sqrt((-11*x^2+7)/(2*x^2+1))/sqrt(5*x^2+3),1],
[sqrt(2*x^2+1)/sqrt(-11*x^2+7)/sqrt(-5*x^2+3),x,2,sqrt(-11*x^2+7)*sqrt((-5*x^2+3)/(2*x^2+1))*EllipticPi(sin(arcsin(sqrt(11/3)*x/sqrt(2*x^2+1))),6/11,sqrt(75/77))/sqrt(77)/sqrt(-5*x^2+3)/sqrt((-11*x^2+7)/(2*x^2+1)),1],
[sqrt(-2*x^2+1)/sqrt(5*x^2+3)/sqrt(11*x^2+7),x,4,5/11*sqrt(5*x^2+3)*sqrt((11*x^2+7)/(-2*x^2+1))*InverseJacobiAM(arctan(5*x/sqrt(7)/sqrt(-2*x^2+1)),sqrt(-2/75))/sqrt(3)/sqrt((5*x^2+3)/(-2*x^2+1))/sqrt(11*x^2+7)-14/55*sqrt(5*x^2+3)*sqrt((11*x^2+7)/(-2*x^2+1))*EllipticPi(sin(arctan(5*x/sqrt(7)/sqrt(-2*x^2+1))),11/25,sqrt(-2/75))/sqrt(3)/sqrt((5*x^2+3)/(-2*x^2+1))/sqrt(11*x^2+7),1],
[sqrt(-2*x^2+1)/sqrt(-5*x^2+3)/sqrt(11*x^2+7),x,4,-1/5*sqrt(-5*x^2+3)*sqrt((11*x^2+7)/(-2*x^2+1))*InverseJacobiAM(arctan(x/sqrt(3)/sqrt(-2*x^2+1)),sqrt(-68/7))/sqrt(7)/sqrt((-5*x^2+3)/(-2*x^2+1))/sqrt(11*x^2+7)+6/5*sqrt(-5*x^2+3)*sqrt((11*x^2+7)/(-2*x^2+1))*EllipticPi(sin(arctan(x/sqrt(3)/sqrt(-2*x^2+1))),-5,sqrt(-68/7))/sqrt(7)/sqrt((-5*x^2+3)/(-2*x^2+1))/sqrt(11*x^2+7),1],
[sqrt(-2*x^2+1)/sqrt(-11*x^2+7)/sqrt(5*x^2+3),x,4,-1/11*sqrt(-11*x^2+7)*sqrt((5*x^2+3)/(-2*x^2+1))*InverseJacobiAM(arctan(sqrt(3/7)*x/sqrt(-2*x^2+1)),sqrt(-68/9))/sqrt((-11*x^2+7)/(-2*x^2+1))/sqrt(5*x^2+3)+14/33*sqrt(-11*x^2+7)*sqrt((5*x^2+3)/(-2*x^2+1))*EllipticPi(sin(arctan(sqrt(3/7)*x/sqrt(-2*x^2+1))),-11/3,sqrt(-68/9))/sqrt((-11*x^2+7)/(-2*x^2+1))/sqrt(5*x^2+3),1],
[sqrt(-2*x^2+1)/sqrt(-11*x^2+7)/sqrt(-5*x^2+3),x,4,-1/5*sqrt(-11*x^2+7)*sqrt((-5*x^2+3)/(-2*x^2+1))*InverseJacobiAM(arctan(x/sqrt(3)/sqrt(-2*x^2+1)),sqrt(-2/7))/sqrt(7)/sqrt(-5*x^2+3)/sqrt((-11*x^2+7)/(-2*x^2+1))+6/5*sqrt(-11*x^2+7)*sqrt((-5*x^2+3)/(-2*x^2+1))*EllipticPi(sin(arctan(x/sqrt(3)/sqrt(-2*x^2+1))),-5,sqrt(-2/7))/sqrt(7)/sqrt(-5*x^2+3)/sqrt((-11*x^2+7)/(-2*x^2+1)),1],
[sqrt(2*x^2+1)*sqrt(5*x^2+3)/sqrt(11*x^2+7),x,7,1/11*x*sqrt(5*x^2+3)*sqrt(11*x^2+7)/sqrt(2*x^2+1)-1/22*sqrt(7)*sqrt(5*x^2+3)*sqrt((11*x^2+7)/(2*x^2+1))*EllipticE(sin(arcsin(x/sqrt(3)/sqrt(2*x^2+1))),sqrt(9/7))/sqrt((5*x^2+3)/(2*x^2+1))/sqrt(11*x^2+7)+1/4*sqrt(5*x^2+3)*sqrt((11*x^2+7)/(2*x^2+1))*InverseJacobiAM(arcsin(x/sqrt(3)/sqrt(2*x^2+1)),sqrt(9/7))/sqrt(7)/sqrt((5*x^2+3)/(2*x^2+1))/sqrt(11*x^2+7)+51/44*sqrt(5*x^2+3)*sqrt((11*x^2+7)/(2*x^2+1))*EllipticPi(sin(arcsin(x/sqrt(3)/sqrt(2*x^2+1))),6,sqrt(9/7))/sqrt(7)/sqrt((5*x^2+3)/(2*x^2+1))/sqrt(11*x^2+7),1],
[sqrt(-2*x^2+1)*sqrt(5*x^2+3)/sqrt(11*x^2+7),x,7,5/22*x*sqrt(-2*x^2+1)*sqrt(11*x^2+7)/sqrt(5*x^2+3)-1/2*sqrt(7/11)*sqrt(-2*x^2+1)*sqrt((11*x^2+7)/(5*x^2+3))*EllipticE(sin(arcsin(sqrt(11)*x/sqrt(5*x^2+3))),sqrt(2/77))/sqrt((-2*x^2+1)/(5*x^2+3))/sqrt(11*x^2+7)+3/10*sqrt(11/7)*sqrt(-2*x^2+1)*sqrt((11*x^2+7)/(5*x^2+3))*InverseJacobiAM(arcsin(sqrt(11)*x/sqrt(5*x^2+3)),sqrt(2/77))/sqrt((-2*x^2+1)/(5*x^2+3))/sqrt(11*x^2+7)+177/110*sqrt(-2*x^2+1)*sqrt((11*x^2+7)/(5*x^2+3))*EllipticPi(sin(arcsin(sqrt(11)*x/sqrt(5*x^2+3))),5/11,sqrt(2/77))/sqrt(77)/sqrt((-2*x^2+1)/(5*x^2+3))/sqrt(11*x^2+7),1],
[sqrt(-5*x^2+3)*sqrt(2*x^2+1)/sqrt(11*x^2+7),x,7,1/11*x*sqrt(-5*x^2+3)*sqrt(11*x^2+7)/sqrt(2*x^2+1)-1/2*sqrt(7/11)*sqrt(-5*x^2+3)*sqrt((11*x^2+7)/(2*x^2+1))*EllipticE(sin(arcsin(sqrt(11/3)*x/sqrt(2*x^2+1))),sqrt(9/77))/sqrt((-5*x^2+3)/(2*x^2+1))/sqrt(11*x^2+7)+1/4*sqrt(11/7)*sqrt(-5*x^2+3)*sqrt((11*x^2+7)/(2*x^2+1))*InverseJacobiAM(arcsin(sqrt(11/3)*x/sqrt(2*x^2+1)),sqrt(9/77))/sqrt((-5*x^2+3)/(2*x^2+1))/sqrt(11*x^2+7)+81/44*sqrt(-5*x^2+3)*sqrt((11*x^2+7)/(2*x^2+1))*EllipticPi(sin(arcsin(sqrt(11/3)*x/sqrt(2*x^2+1))),6/11,sqrt(9/77))/sqrt(77)/sqrt((-5*x^2+3)/(2*x^2+1))/sqrt(11*x^2+7),1],
[sqrt(-5*x^2+3)*sqrt(-2*x^2+1)/sqrt(11*x^2+7),x,7,-5/22*x*sqrt(-2*x^2+1)*sqrt(11*x^2+7)/sqrt(-5*x^2+3)-1/22*sqrt(7)*sqrt(-2*x^2+1)*sqrt((11*x^2+7)/(-5*x^2+3))*EllipticE(sin(arcsin(x/sqrt(-5*x^2+3))),sqrt(-68/7))/sqrt((-2*x^2+1)/(-5*x^2+3))/sqrt(11*x^2+7)-3/10*sqrt(-2*x^2+1)*sqrt((11*x^2+7)/(-5*x^2+3))*InverseJacobiAM(arcsin(x/sqrt(-5*x^2+3)),sqrt(-68/7))/sqrt(7)/sqrt((-2*x^2+1)/(-5*x^2+3))/sqrt(11*x^2+7)+573/110*sqrt(-2*x^2+1)*sqrt((11*x^2+7)/(-5*x^2+3))*EllipticPi(sin(arcsin(x/sqrt(-5*x^2+3))),-5,sqrt(-68/7))/sqrt(7)/sqrt((-2*x^2+1)/(-5*x^2+3))/sqrt(11*x^2+7),1],
[sqrt(2*x^2+1)*sqrt(5*x^2+3)/sqrt(-11*x^2+7),x,7,-1/11*x*sqrt(-11*x^2+7)*sqrt(5*x^2+3)/sqrt(2*x^2+1)+1/22*sqrt(7)*sqrt(-11*x^2+7)*sqrt((5*x^2+3)/(2*x^2+1))*EllipticE(sin(arcsin(x/sqrt(3)/sqrt(2*x^2+1))),sqrt(75/7))/sqrt((-11*x^2+7)/(2*x^2+1))/sqrt(5*x^2+3)+1/4*sqrt(-11*x^2+7)*sqrt((5*x^2+3)/(2*x^2+1))*InverseJacobiAM(arcsin(x/sqrt(3)/sqrt(2*x^2+1)),sqrt(75/7))/sqrt(7)/sqrt((-11*x^2+7)/(2*x^2+1))/sqrt(5*x^2+3)+191/44*sqrt(-11*x^2+7)*sqrt((5*x^2+3)/(2*x^2+1))*EllipticPi(sin(arcsin(x/sqrt(3)/sqrt(2*x^2+1))),6,sqrt(75/7))/sqrt(7)/sqrt((-11*x^2+7)/(2*x^2+1))/sqrt(5*x^2+3),1],
[sqrt(-2*x^2+1)*sqrt(5*x^2+3)/sqrt(-11*x^2+7),x,7,-5/22*x*sqrt(-11*x^2+7)*sqrt(-2*x^2+1)/sqrt(5*x^2+3)+1/2*sqrt(7/11)*sqrt(-11*x^2+7)*sqrt((-2*x^2+1)/(5*x^2+3))*EllipticE(sin(arcsin(sqrt(11)*x/sqrt(5*x^2+3))),sqrt(68/77))/sqrt(-2*x^2+1)/sqrt((-11*x^2+7)/(5*x^2+3))+3/10*sqrt(11/7)*sqrt(-11*x^2+7)*sqrt((-2*x^2+1)/(5*x^2+3))*InverseJacobiAM(arcsin(sqrt(11)*x/sqrt(5*x^2+3)),sqrt(68/77))/sqrt(-2*x^2+1)/sqrt((-11*x^2+7)/(5*x^2+3))-243/110*sqrt(-11*x^2+7)*sqrt((-2*x^2+1)/(5*x^2+3))*EllipticPi(sin(arcsin(sqrt(11)*x/sqrt(5*x^2+3))),5/11,sqrt(68/77))/sqrt(77)/sqrt(-2*x^2+1)/sqrt((-11*x^2+7)/(5*x^2+3)),1],
[sqrt(-5*x^2+3)*sqrt(2*x^2+1)/sqrt(-11*x^2+7),x,7,-1/11*x*sqrt(-11*x^2+7)*sqrt(-5*x^2+3)/sqrt(2*x^2+1)+1/2*sqrt(7/11)*sqrt(-11*x^2+7)*sqrt((-5*x^2+3)/(2*x^2+1))*EllipticE(sin(arcsin(sqrt(11/3)*x/sqrt(2*x^2+1))),sqrt(75/77))/sqrt(-5*x^2+3)/sqrt((-11*x^2+7)/(2*x^2+1))+1/4*sqrt(11/7)*sqrt(-11*x^2+7)*sqrt((-5*x^2+3)/(2*x^2+1))*InverseJacobiAM(arcsin(sqrt(11/3)*x/sqrt(2*x^2+1)),sqrt(75/77))/sqrt(-5*x^2+3)/sqrt((-11*x^2+7)/(2*x^2+1))-59/44*sqrt(-11*x^2+7)*sqrt((-5*x^2+3)/(2*x^2+1))*EllipticPi(sin(arcsin(sqrt(11/3)*x/sqrt(2*x^2+1))),6/11,sqrt(75/77))/sqrt(77)/sqrt(-5*x^2+3)/sqrt((-11*x^2+7)/(2*x^2+1)),1],
[sqrt(-5*x^2+3)*sqrt(-2*x^2+1)/sqrt(-11*x^2+7),x,7,5/22*x*sqrt(-11*x^2+7)*sqrt(-2*x^2+1)/sqrt(-5*x^2+3)+1/22*sqrt(7)*sqrt(-11*x^2+7)*sqrt((-2*x^2+1)/(-5*x^2+3))*EllipticE(sin(arcsin(x/sqrt(-5*x^2+3))),sqrt(-2/7))/sqrt((-11*x^2+7)/(-5*x^2+3))/sqrt(-2*x^2+1)-3/10*sqrt(-11*x^2+7)*sqrt((-2*x^2+1)/(-5*x^2+3))*InverseJacobiAM(arcsin(x/sqrt(-5*x^2+3)),sqrt(-2/7))/sqrt(7)/sqrt((-11*x^2+7)/(-5*x^2+3))/sqrt(-2*x^2+1)+153/110*sqrt(-11*x^2+7)*sqrt((-2*x^2+1)/(-5*x^2+3))*EllipticPi(sin(arcsin(x/sqrt(-5*x^2+3))),-5,sqrt(-2/7))/sqrt(7)/sqrt((-11*x^2+7)/(-5*x^2+3))/sqrt(-2*x^2+1),1],
[sqrt(b*x^2+a)*(d*x^2+c)^(3/2)/(f*x^2+e)^(3/2),x,7,1/2*d*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/f/sqrt(f*x^2+e)-1/2*c*sqrt(a*f-b*e)*(-2*c*f+3*d*e)*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/e/f^2/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))-1/2*(a*d*f*(-2*c*f+d*e)-b*(2*c^2*f^2-6*c*d*e*f+3*d^2*e^2))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/f^3/sqrt(a*f-b*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))-1/2*d*e*(-a*d*f-3*b*c*f+3*b*d*e)*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticPi(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),-a*f/(-a*f+b*e),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/f^3/sqrt(a*f-b*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[sqrt(b*x^2+a)*sqrt(d*x^2+c)/(f*x^2+e)^(3/2),x,6,sqrt(a)*sqrt(a*f-b*e)*sqrt(d*x^2+c)*sqrt(e*(b*x^2+a)/a/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/e/f/sqrt(b*x^2+a)/sqrt(e*(d*x^2+c)/c/(f*x^2+e))-sqrt(a)*b*(-c*f+d*e)*sqrt(d*x^2+c)*sqrt(e*(b*x^2+a)/a/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/c/f^2/sqrt(a*f-b*e)/sqrt(b*x^2+a)/sqrt(e*(d*x^2+c)/c/(f*x^2+e))+sqrt(a)*b*d*e*sqrt(d*x^2+c)*sqrt(e*(b*x^2+a)/a/(f*x^2+e))*EllipticPi(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),-a*f/(-a*f+b*e),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/c/f^2/sqrt(a*f-b*e)/sqrt(b*x^2+a)/sqrt(e*(d*x^2+c)/c/(f*x^2+e)),1],
[sqrt(b*x^2+a)/sqrt(d*x^2+c)/(f*x^2+e)^(3/2),x,2,sqrt(c)*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(c*f-d*e)*x/sqrt(c)/sqrt(f*x^2+e))),sqrt(c*(-a*f+b*e)/a/(-c*f+d*e)))/e/sqrt(c*f-d*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[sqrt(b*x^2+a)/(d*x^2+c)^(3/2)/(f*x^2+e)^(3/2),x,5,d*x*sqrt(b*x^2+a)/c/(-c*f+d*e)/sqrt(d*x^2+c)/sqrt(f*x^2+e)+a*(c*f+d*e)*sqrt(d*x^2+c)*sqrt(e*(b*x^2+a)/a/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(c*f-d*e)*x/sqrt(c)/sqrt(f*x^2+e))),sqrt(c*(-a*f+b*e)/a/(-c*f+d*e)))/c^(3/2)/e/(c*f-d*e)^(3/2)/sqrt(b*x^2+a)/sqrt(e*(d*x^2+c)/c/(f*x^2+e))-a*d*sqrt(d*x^2+c)*sqrt(e*(b*x^2+a)/a/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(c*f-d*e)*x/sqrt(c)/sqrt(f*x^2+e)),sqrt(c*(-a*f+b*e)/a/(-c*f+d*e)))/c^(3/2)/(c*f-d*e)^(3/2)/sqrt(b*x^2+a)/sqrt(e*(d*x^2+c)/c/(f*x^2+e)),1],
[sqrt(b*x^2+a)/(d*x^2+c)^(5/2)/(f*x^2+e)^(3/2),x,6,1/3*d*x*sqrt(b*x^2+a)/c/(-c*f+d*e)/(d*x^2+c)^(3/2)/sqrt(f*x^2+e)+1/3*d*(b*c*(-5*c*f+d*e)-2*a*d*(-3*c*f+d*e))*x*sqrt(b*x^2+a)/c^2/(-a*d+b*c)/(-c*f+d*e)^2/sqrt(d*x^2+c)/sqrt(f*x^2+e)-1/3*sqrt(a*f-b*e)*(a*d*(-3*c^2*f^2-7*c*d*e*f+2*d^2*e^2)-b*c*(-3*c^2*f^2-6*c*d*e*f+d^2*e^2))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/c/(-a*d+b*c)/e/(-c*f+d*e)^3/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))-1/3*(a*d*f*(-9*c*f+d*e)-b*(-3*c^2*f^2-6*c*d*e*f+d^2*e^2))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/c/sqrt(a*f-b*e)/(-c*f+d*e)^3/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[(b*x^2+a)^(3/2)*(d*x^2+c)^(3/2)/(f*x^2+e)^(3/2),x,8,-5/8*(-a*d*f-b*c*f+b*d*e)*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/f^2/sqrt(f*x^2+e)+1/4*b*d*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/f/sqrt(f*x^2+e)+1/8*c*sqrt(a*f-b*e)*(b*e*(-13*c*f+15*d*e)-a*f*(-8*c*f+13*d*e))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/e/f^3/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))-1/8*sqrt(a*f-b*e)*(a*d*f*(-8*c*f+3*d*e)-b*(16*c^2*f^2-33*c*d*e*f+15*d^2*e^2))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/f^4/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))+3/8*e*(a^2*d^2*f^2-6*a*b*d*f*(-c*f+d*e)+b^2*(c^2*f^2-6*c*d*e*f+5*d^2*e^2))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticPi(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),-a*f/(-a*f+b*e),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/f^4/sqrt(a*f-b*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[(b*x^2+a)^(3/2)*sqrt(d*x^2+c)/(f*x^2+e)^(3/2),x,7,1/2*b*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/f/sqrt(f*x^2+e)-1/2*c*(-2*a*f+3*b*e)*sqrt(a*f-b*e)*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/e/f^2/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))-1/2*b*sqrt(a*f-b*e)*(-4*c*f+3*d*e)*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/f^3/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))-1/2*b*e*(-3*a*d*f-b*c*f+3*b*d*e)*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticPi(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),-a*f/(-a*f+b*e),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/f^3/sqrt(a*f-b*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[(b*x^2+a)^(3/2)/sqrt(d*x^2+c)/(f*x^2+e)^(3/2),x,6,-c*(a*f-b*e)^(3/2)*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/e/f/(-c*f+d*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))+sqrt(a*f-b*e)*(a*d*f-2*b*c*f+b*d*e)*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/f^2/(-c*f+d*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))+b^2*e*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticPi(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),-a*f/(-a*f+b*e),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/f^2/sqrt(a*f-b*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[(b*x^2+a)^(3/2)/(d*x^2+c)^(3/2)/(f*x^2+e)^(3/2),x,5,-(-a*d+b*c)*x*sqrt(b*x^2+a)/c/(-c*f+d*e)/sqrt(d*x^2+c)/sqrt(f*x^2+e)-sqrt(a*f-b*e)*(2*b*c*e-a*(c*f+d*e))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/e/(-c*f+d*e)^2/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))+2*(-a*d+b*c)*sqrt(a*f-b*e)*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/(-c*f+d*e)^2/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[(b*x^2+a)^(3/2)/(d*x^2+c)^(5/2)/(f*x^2+e)^(3/2),x,6,-1/3*(-a*d+b*c)*x*sqrt(b*x^2+a)/c/(-c*f+d*e)/(d*x^2+c)^(3/2)/sqrt(f*x^2+e)+2/3*(a*d*(-3*c*f+d*e)+b*c*(c*f+d*e))*x*sqrt(b*x^2+a)/c^2/(-c*f+d*e)^2/sqrt(d*x^2+c)/sqrt(f*x^2+e)+1/3*sqrt(a*f-b*e)*(2*b*c*e*(3*c*f+d*e)+a*(-3*c^2*f^2-7*c*d*e*f+2*d^2*e^2))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/c/e/(-c*f+d*e)^3/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))-1/3*sqrt(a*f-b*e)*(a*d*(-9*c*f+d*e)+2*b*c*(3*c*f+d*e))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/c/(-c*f+d*e)^3/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[(b*x^2+a)^(3/2)/(d*x^2+c)^(7/2)/(f*x^2+e)^(3/2),x,7,-1/5*(-a*d+b*c)*x*sqrt(b*x^2+a)/c/(-c*f+d*e)/(d*x^2+c)^(5/2)/sqrt(f*x^2+e)+2/15*(a*d*(-5*c*f+2*d*e)+b*c*(2*c*f+d*e))*x*sqrt(b*x^2+a)/c^2/(-c*f+d*e)^2/(d*x^2+c)^(3/2)/sqrt(f*x^2+e)+1/15*(2*b^2*c^2*(-4*c^2*f^2-9*c*d*e*f+d^2*e^2)-a^2*d^2*(45*c^2*f^2-29*c*d*e*f+8*d^2*e^2)+a*b*c*d*(50*c^2*f^2-5*c*d*e*f+3*d^2*e^2))*x*sqrt(b*x^2+a)/c^3/(-a*d+b*c)/(-c*f+d*e)^3/sqrt(d*x^2+c)/sqrt(f*x^2+e)+1/15*sqrt(a*f-b*e)*(2*b^2*c^2*e*(-15*c^2*f^2-10*c*d*e*f+d^2*e^2)-a^2*d*(15*c^3*f^3+58*c^2*d*e*f^2-33*c*d^2*e^2*f+8*d^3*e^3)+a*b*c*(15*c^3*f^3+85*c^2*d*e*f^2-7*c*d^2*e^2*f+3*d^3*e^3))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/c^2/(-a*d+b*c)/e/(-c*f+d*e)^4/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))-2/15*sqrt(a*f-b*e)*(b*c*(-15*c^2*f^2-10*c*d*e*f+d^2*e^2)+2*a*d*(15*c^2*f^2-4*c*d*e*f+d^2*e^2))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/c^2/(-c*f+d*e)^4/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[(b*x^2+a)^(5/2)*(d*x^2+c)^(3/2)/(f*x^2+e)^(3/2),x,9,1/48*(33*a^2*d^2*f^2-68*a*b*d*f*(-c*f+d*e)+b^2*(3*c^2*f^2-38*c*d*e*f+35*d^2*e^2))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/d/f^3/sqrt(f*x^2+e)-1/24*b*(-13*a*d*f-7*b*c*f+7*b*d*e)*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/f^2/sqrt(f*x^2+e)+1/6*b^2*d*x^5*sqrt(b*x^2+a)*sqrt(d*x^2+c)/f/sqrt(f*x^2+e)+1/48*c*sqrt(a*f-b*e)*(2*a*b*d*e*f*(-82*c*f+95*d*e)-3*a^2*d*f^2*(-16*c*f+27*d*e)-b^2*e*(3*c^2*f^2-100*c*d*e*f+105*d^2*e^2))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/d/e/f^4/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))-1/48*sqrt(a*f-b*e)*(3*a^2*d*f^2*(-16*c*f+5*d*e)-2*a*b*f*(72*c^2*f^2-145*c*d*e*f+60*d^2*e^2)+b^2*e*(127*c^2*f^2-240*c*d*e*f+105*d^2*e^2))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/f^5/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))+1/16*e*(5*a^3*d^3*f^3-45*a^2*b*d^2*f^2*(-c*f+d*e)+15*a*b^2*d*f*(c^2*f^2-6*c*d*e*f+5*d^2*e^2)-b^3*(c^3*f^3+9*c^2*d*e*f^2-45*c*d^2*e^2*f+35*d^3*e^3))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticPi(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),-a*f/(-a*f+b*e),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/d/f^5/sqrt(a*f-b*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[(b*x^2+a)^(5/2)*sqrt(d*x^2+c)/(f*x^2+e)^(3/2),x,8,-1/8*b*(-9*a*d*f-b*c*f+5*b*d*e)*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/d/f^2/sqrt(f*x^2+e)+1/4*b^2*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/f/sqrt(f*x^2+e)-1/8*c*sqrt(a*f-b*e)*(25*a*b*d*e*f-8*a^2*d*f^2-b^2*e*(-c*f+15*d*e))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/d/e/f^3/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))-3/8*b*sqrt(a*f-b*e)*(a*f*(-8*c*f+5*d*e)-b*e*(-7*c*f+5*d*e))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/f^4/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))+1/8*b*e*(15*a^2*d^2*f^2-10*a*b*d*f*(-c*f+3*d*e)+b^2*(-c^2*f^2-6*c*d*e*f+15*d^2*e^2))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticPi(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),-a*f/(-a*f+b*e),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/d/f^4/sqrt(a*f-b*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[(b*x^2+a)^(5/2)/sqrt(d*x^2+c)/(f*x^2+e)^(3/2),x,7,1/2*b^2*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/d/f/sqrt(f*x^2+e)+1/2*c*sqrt(a*f-b*e)*(4*a*b*d*e*f-2*a^2*d*f^2-b^2*e*(-c*f+3*d*e))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/d/e/f^2/(-c*f+d*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))+1/2*sqrt(a*f-b*e)*(2*a^2*d*f^2-b^2*e*(-5*c*f+3*d*e)+2*a*b*f*(-3*c*f+d*e))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/f^3/(-c*f+d*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))-1/2*b^2*e*(-5*a*d*f+b*c*f+3*b*d*e)*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticPi(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),-a*f/(-a*f+b*e),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/d/f^3/sqrt(a*f-b*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[(b*x^2+a)^(5/2)/(d*x^2+c)^(3/2)/(f*x^2+e)^(3/2),x,7,(-a*d+b*c)^2*x*sqrt(b*x^2+a)/c/d/(-c*f+d*e)/sqrt(d*x^2+c)/sqrt(f*x^2+e)-sqrt(a*f-b*e)*(4*a*b*c*d*e*f-b^2*c*e*(c*f+d*e)-a^2*d*f*(c*f+d*e))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/d/e/f/(-c*f+d*e)^2/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))-(a*f-b*e)^(3/2)*(2*a*d*f-3*b*c*f+b*d*e)*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/f^2/(-c*f+d*e)^2/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))+b^3*e*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticPi(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),-a*f/(-a*f+b*e),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/d/f^2/sqrt(a*f-b*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[(b*x^2+a)^(5/2)/(d*x^2+c)^(5/2)/(f*x^2+e)^(3/2),x,6,1/3*(-a*d+b*c)^2*x*sqrt(b*x^2+a)/c/d/(-c*f+d*e)/(d*x^2+c)^(3/2)/sqrt(f*x^2+e)-1/3*(-a*d+b*c)*(2*a*d*(-3*c*f+d*e)+b*c*(-c*f+5*d*e))*x*sqrt(b*x^2+a)/c^2/d/(-c*f+d*e)^2/sqrt(d*x^2+c)/sqrt(f*x^2+e)-1/3*sqrt(a*f-b*e)*(8*b^2*c^2*e^2-a*b*c*e*(13*c*f+3*d*e)-a^2*(-3*c^2*f^2-7*c*d*e*f+2*d^2*e^2))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/c/e/(-c*f+d*e)^3/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))+1/3*(-a*d+b*c)*sqrt(a*f-b*e)*(-9*a*c*f+a*d*e+8*b*c*e)*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/c/(-c*f+d*e)^3/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[(b*x^2+a)^(5/2)/(d*x^2+c)^(7/2)/(f*x^2+e)^(3/2),x,7,1/5*(-a*d+b*c)^2*x*sqrt(b*x^2+a)/c/d/(-c*f+d*e)/(d*x^2+c)^(5/2)/sqrt(f*x^2+e)-1/15*(-a*d+b*c)*(2*a*d*(-5*c*f+2*d*e)+b*c*(-c*f+7*d*e))*x*sqrt(b*x^2+a)/c^2/d/(-c*f+d*e)^2/(d*x^2+c)^(3/2)/sqrt(f*x^2+e)+1/15*(a*b*c*d*(-20*c^2*f^2-35*c*d*e*f+7*d^2*e^2)+2*b^2*c^2*(-c^2*f^2+9*c*d*e*f+4*d^2*e^2)+a^2*d^2*(45*c^2*f^2-29*c*d*e*f+8*d^2*e^2))*x*sqrt(b*x^2+a)/c^3/d/(-c*f+d*e)^3/sqrt(d*x^2+c)/sqrt(f*x^2+e)+1/15*sqrt(a*f-b*e)*(8*b^2*c^2*e^2*(5*c*f+d*e)+a*b*c*e*(-65*c^2*f^2-38*c*d*e*f+7*d^2*e^2)+a^2*(15*c^3*f^3+58*c^2*d*e*f^2-33*c*d^2*e^2*f+8*d^3*e^3))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/c^2/e/(-c*f+d*e)^4/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))-1/15*sqrt(a*f-b*e)*(8*b^2*c^2*e*(5*c*f+d*e)+3*a*b*c*(-15*c^2*f^2-18*c*d*e*f+d^2*e^2)+4*a^2*d*(15*c^2*f^2-4*c*d*e*f+d^2*e^2))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/c^2/(-c*f+d*e)^4/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[(b*x^2+a)^(5/2)/(d*x^2+c)^(9/2)/(f*x^2+e)^(3/2),x,8,1/7*(-a*d+b*c)^2*x*sqrt(b*x^2+a)/c/d/(-c*f+d*e)/(d*x^2+c)^(7/2)/sqrt(f*x^2+e)-1/35*(-a*d+b*c)*(2*a*d*(-7*c*f+3*d*e)+b*c*(-c*f+9*d*e))*x*sqrt(b*x^2+a)/c^2/d/(-c*f+d*e)^2/(d*x^2+c)^(5/2)/sqrt(f*x^2+e)+1/105*(a*b*c*d*(-56*c^2*f^2-53*c*d*e*f+13*d^2*e^2)+4*b^2*c^2*(-c^2*f^2+11*c*d*e*f+2*d^2*e^2)+3*a^2*d^2*(35*c^2*f^2-27*c*d*e*f+8*d^2*e^2))*x*sqrt(b*x^2+a)/c^3/d/(-c*f+d*e)^3/(d*x^2+c)^(3/2)/sqrt(f*x^2+e)+1/105*(a^2*b*c*d^2*(-525*c^3*f^3-14*c^2*d*e*f^2-53*c*d^2*e^2*f+16*d^3*e^3)-12*a^3*d^3*(-35*c^3*f^3+33*c^2*d*e*f^2-18*c*d^2*e^2*f+4*d^3*e^3)+8*b^3*c^3*(c^3*f^3-13*c^2*d*e*f^2-13*c*d^2*e^2*f+d^3*e^3)+a*b^2*c^2*d*(112*c^3*f^3+469*c^2*d*e*f^2-14*c*d^2*e^2*f+9*d^3*e^3))*x*sqrt(b*x^2+a)/c^4/d/(-a*d+b*c)/(-c*f+d*e)^4/sqrt(d*x^2+c)/sqrt(f*x^2+e)+1/105*sqrt(a*f-b*e)*(8*b^3*c^3*e^2*(-35*c^2*f^2-14*c*d*e*f+d^2*e^2)+a*b^2*c^2*e*(455*c^3*f^3+707*c^2*d*e*f^2-19*c*d^2*e^2*f+9*d^3*e^3)+a^2*b*c*(-105*c^4*f^4-1022*c^3*d*e*f^3+23*c^2*d^2*e^2*f^2-64*c*d^3*e^3*f+16*d^4*e^4)-3*a^3*d*(-35*c^4*f^4-194*c^3*d*e*f^3+165*c^2*d^2*e^2*f^2-80*c*d^3*e^3*f+16*d^4*e^4))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/c^3/(-a*d+b*c)/e/(-c*f+d*e)^5/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))-1/105*sqrt(a*f-b*e)*(8*b^2*c^2*e*(-35*c^2*f^2-14*c*d*e*f+d^2*e^2)+3*a^2*d*(-175*c^3*f^3+78*c^2*d*e*f^2-39*c*d^2*e^2*f+8*d^3*e^3)+a*b*c*(315*c^3*f^3+511*c^2*d*e*f^2-71*c*d^2*e^2*f+13*d^3*e^3))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/c^3/(-c*f+d*e)^5/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[1/sqrt(b*x^2+a)/sqrt(d*x^2+c)/(f*x^2+e)^(3/2),x,4,-sqrt(a)*f*sqrt(d*x^2+c)*sqrt(e*(b*x^2+a)/a/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/e/sqrt(a*f-b*e)/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(e*(d*x^2+c)/c/(f*x^2+e))+sqrt(a)*d*sqrt(d*x^2+c)*sqrt(e*(b*x^2+a)/a/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/c/sqrt(a*f-b*e)/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(e*(d*x^2+c)/c/(f*x^2+e)),1],
[1/sqrt(b*x^2+a)/(d*x^2+c)^(3/2)/(f*x^2+e)^(3/2),x,5,-d^2*x*sqrt(b*x^2+a)/c/(-a*d+b*c)/(-c*f+d*e)/sqrt(d*x^2+c)/sqrt(f*x^2+e)-(a*d*f*(c*f+d*e)-b*(c^2*f^2+d^2*e^2))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/(-a*d+b*c)/e/sqrt(a*f-b*e)/(-c*f+d*e)^2/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))-2*d*f*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/sqrt(a*f-b*e)/(-c*f+d*e)^2/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[1/sqrt(b*x^2+a)/(d*x^2+c)^(5/2)/(f*x^2+e)^(3/2),x,6,-1/3*d^2*x*sqrt(b*x^2+a)/c/(-a*d+b*c)/(-c*f+d*e)/(d*x^2+c)^(3/2)/sqrt(f*x^2+e)+2/3*d^2*(a*d*(-3*c*f+d*e)-2*b*c*(-2*c*f+d*e))*x*sqrt(b*x^2+a)/c^2/(-a*d+b*c)^2/(-c*f+d*e)^2/sqrt(d*x^2+c)/sqrt(f*x^2+e)+1/3*(a^2*d^2*f*(-3*c^2*f^2-7*c*d*e*f+2*d^2*e^2)-a*b*d*(-6*c^3*f^3-9*c^2*d*e*f^2-3*c*d^2*e^2*f+2*d^3*e^3)+b^2*c*(-3*c^3*f^3-9*c*d^2*e^2*f+4*d^3*e^3))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/c/(-a*d+b*c)^2/e/sqrt(a*f-b*e)/(-c*f+d*e)^3/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))+1/3*d*(a*d*f*(-9*c*f+d*e)-b*(-9*c^2*f^2+d^2*e^2))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/c/(-a*d+b*c)/sqrt(a*f-b*e)/(-c*f+d*e)^3/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[1/(b*x^2+a)^(3/2)/sqrt(d*x^2+c)/(f*x^2+e)^(3/2),x,5,b^2*x*sqrt(d*x^2+c)/a/(-a*d+b*c)/(-a*f+b*e)/sqrt(b*x^2+a)/sqrt(f*x^2+e)-c*(a*b*c*f^2-a^2*d*f^2-b^2*e*(-c*f+d*e))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/a^(3/2)/(-a*d+b*c)/e/(a*f-b*e)^(3/2)/(-c*f+d*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))-(-a*d*f-b*c*f+b*d*e)*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/a^(3/2)/(a*f-b*e)^(3/2)/(-c*f+d*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[1/(b*x^2+a)^(3/2)/(d*x^2+c)^(3/2)/(f*x^2+e)^(3/2),x,6,b^2*x/a/(-a*d+b*c)/(-a*f+b*e)/sqrt(b*x^2+a)/sqrt(d*x^2+c)/sqrt(f*x^2+e)+d*(a*b*d^2*e-a^2*d^2*f+b^2*c*(-c*f+d*e))*x*sqrt(b*x^2+a)/a/c/(-a*d+b*c)^2/(-a*f+b*e)/(-c*f+d*e)/sqrt(d*x^2+c)/sqrt(f*x^2+e)+(b^3*c*e*(-c*f+d*e)^2+a^3*d^2*f^2*(c*f+d*e)-2*a^2*b*d*f*(c^2*f^2+d^2*e^2)+a*b^2*(c^3*f^3+d^3*e^3))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/a^(3/2)/(-a*d+b*c)^2/e/(a*f-b*e)^(3/2)/(-c*f+d*e)^2/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))+(2*a^2*d^2*f^2-b^2*(-c*f+d*e)^2-a*b*d*f*(c*f+d*e))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/a^(3/2)/(-a*d+b*c)/(a*f-b*e)^(3/2)/(-c*f+d*e)^2/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[1/(b*x^2+a)^(3/2)/(d*x^2+c)^(5/2)/(f*x^2+e)^(3/2),x,7,b^2*x/a/(-a*d+b*c)/(-a*f+b*e)/sqrt(b*x^2+a)/(d*x^2+c)^(3/2)/sqrt(f*x^2+e)+1/3*d*(a*b*d^2*e-a^2*d^2*f+3*b^2*c*(-c*f+d*e))*x*sqrt(b*x^2+a)/a/c/(-a*d+b*c)^2/(-a*f+b*e)/(-c*f+d*e)/(d*x^2+c)^(3/2)/sqrt(f*x^2+e)+1/3*d*(a*b^2*c*d^2*e*(-11*c*f+7*d*e)+2*a^3*d^3*f*(-3*c*f+d*e)+3*b^3*c^2*(-c*f+d*e)^2-a^2*b*d^2*(-11*c^2*f^2+c*d*e*f+2*d^2*e^2))*x*sqrt(b*x^2+a)/a/c^2/(-a*d+b*c)^3/(-a*f+b*e)/(-c*f+d*e)^2/sqrt(d*x^2+c)/sqrt(f*x^2+e)+1/3*(3*b^4*c^2*e*(-c*f+d*e)^3-a^4*d^3*f^2*(-3*c^2*f^2-7*c*d*e*f+2*d^2*e^2)+a^3*b*d^2*f*(-9*c^3*f^3-12*c^2*d*e*f^2-7*c*d^2*e^2*f+4*d^3*e^3)-a^2*b^2*d*(-9*c^4*f^4-24*c^2*d^2*e^2*f^2+7*c*d^3*e^3*f+2*d^4*e^4)+a*b^3*c*(-3*c^4*f^4-12*c*d^3*e^3*f+7*d^4*e^4))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/a^(3/2)/c/(-a*d+b*c)^3/e/(a*f-b*e)^(3/2)/(-c*f+d*e)^3/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))-1/3*(a^3*d^3*f^2*(-9*c*f+d*e)+3*b^3*c*(-c*f+d*e)^3-a^2*b*d^2*f*(-15*c^2*f^2-3*c*d*e*f+2*d^2*e^2)+a*b^2*d*(-3*c^3*f^3-9*c^2*d*e*f^2+3*c*d^2*e^2*f+d^3*e^3))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/a^(3/2)/c/(-a*d+b*c)^2/(a*f-b*e)^(3/2)/(-c*f+d*e)^3/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[1/(b*x^2+a)^(5/2)/sqrt(d*x^2+c)/(f*x^2+e)^(3/2),x,6,1/3*b^2*x*sqrt(d*x^2+c)/a/(-a*d+b*c)/(-a*f+b*e)/(b*x^2+a)^(3/2)/sqrt(f*x^2+e)+2/3*b^2*(4*a^2*d*f-3*a*b*c*f-2*a*b*d*e+b^2*c*e)*x*sqrt(d*x^2+c)/a^2/(-a*d+b*c)^2/(-a*f+b*e)^2/sqrt(b*x^2+a)/sqrt(f*x^2+e)+1/3*c*(6*a^3*b*c*d*f^3-3*a^4*d^2*f^3-2*b^4*c*e^2*(-c*f+d*e)+a*b^3*e*(-7*c^2*f^2+3*c*d*e*f+4*d^2*e^2)-3*a^2*b^2*f*(c^2*f^2-3*c*d*e*f+3*d^2*e^2))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/a^(5/2)/(-a*d+b*c)^2/e/(a*f-b*e)^(5/2)/(-c*f+d*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))-1/3*(3*a^3*d^2*f^2-2*b^3*c*e*(-c*f+d*e)-3*a^2*b*d*f*(-c*f+2*d*e)+3*a*b^2*(-2*c^2*f^2+c*d*e*f+d^2*e^2))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/a^(5/2)/(-a*d+b*c)/(a*f-b*e)^(5/2)/(-c*f+d*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[1/(b*x^2+a)^(5/2)/(d*x^2+c)^(3/2)/(f*x^2+e)^(3/2),x,7,1/3*b^2*x/a/(-a*d+b*c)/(-a*f+b*e)/(b*x^2+a)^(3/2)/sqrt(d*x^2+c)/sqrt(f*x^2+e)+2/3*b^2*(b^2*c*e+5*a^2*d*f-3*a*b*(c*f+d*e))*x/a^2/(-a*d+b*c)^2/(-a*f+b*e)^2/sqrt(b*x^2+a)/sqrt(d*x^2+c)/sqrt(f*x^2+e)+1/3*d*(6*a^3*b*d^3*e*f-3*a^4*d^3*f^2+2*b^4*c^2*e*(-c*f+d*e)-a*b^3*c*(-6*c^2*f^2-c*d*e*f+7*d^2*e^2)-a^2*b^2*d*(11*c^2*f^2-11*c*d*e*f+3*d^2*e^2))*x*sqrt(b*x^2+a)/a^2/c/(-a*d+b*c)^3/(-a*f+b*e)^2/(-c*f+d*e)/sqrt(d*x^2+c)/sqrt(f*x^2+e)-1/3*(2*b^5*c^2*e^2*(-c*f+d*e)^2+3*a^5*d^3*f^3*(c*f+d*e)-7*a*b^4*c*e*(-c*f+d*e)^2*(c*f+d*e)-9*a^4*b*d^2*f^2*(c^2*f^2+d^2*e^2)+9*a^3*b^2*d*f*(c^3*f^3+d^3*e^3)-3*a^2*b^3*(c^4*f^4-4*c^3*d*e*f^3+8*c^2*d^2*e^2*f^2-4*c*d^3*e^3*f+d^4*e^4))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/a^(5/2)/(-a*d+b*c)^3/e/(a*f-b*e)^(5/2)/(-c*f+d*e)^2/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))-2/3*(3*a^4*d^3*f^3-b^4*c*e*(-c*f+d*e)^2-3*a^3*b*d^2*f^2*(c*f+d*e)+3*a*b^3*(-c*f+d*e)^2*(c*f+d*e)-3*a^2*b^2*d*f*(c^2*f^2-3*c*d*e*f+d^2*e^2))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/a^(5/2)/(-a*d+b*c)^2/(a*f-b*e)^(5/2)/(-c*f+d*e)^2/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[sqrt(b*x^2+a)*(d*x^2+c)^(5/2)/(f*x^2+e)^(5/2),x,8,1/3*(-c*f+d*e)^2*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/e/f^2/(f*x^2+e)^(3/2)+1/2*d^2*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/f^2/sqrt(f*x^2+e)-1/6*c*(a*f*(-4*c^2*f^2-6*c*d*e*f+13*d^2*e^2)-b*e*(-2*c^2*f^2-10*c*d*e*f+15*d^2*e^2))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/e^2/f^3/sqrt(a*f-b*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))-1/6*(a*d*f*(2*c^2*f^2-8*c*d*e*f+3*d^2*e^2)-b*(2*c^3*f^3+10*c^2*d*e*f^2-30*c*d^2*e^2*f+15*d^3*e^3))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/e/f^4/sqrt(a*f-b*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))-1/2*d^2*e*(-a*d*f-5*b*c*f+5*b*d*e)*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticPi(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),-a*f/(-a*f+b*e),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/f^4/sqrt(a*f-b*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[sqrt(b*x^2+a)*(d*x^2+c)^(3/2)/(f*x^2+e)^(5/2),x,7,-1/3*(-c*f+d*e)*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/e/f/(f*x^2+e)^(3/2)+1/3*c*(2*a*f*(c*f+d*e)-b*e*(c*f+3*d*e))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/e^2/f^2/sqrt(a*f-b*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))-1/3*(a*c*d*f^2+b*(-c^2*f^2-3*c*d*e*f+3*d^2*e^2))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/e/f^3/sqrt(a*f-b*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))+b*d^2*e*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticPi(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),-a*f/(-a*f+b*e),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/f^3/sqrt(a*f-b*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[sqrt(b*x^2+a)*sqrt(d*x^2+c)/(f*x^2+e)^(5/2),x,5,1/3*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/e/(f*x^2+e)^(3/2)+1/3*c*(-2*a*c*f+a*d*e+b*c*e)*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/e^2/sqrt(a*f-b*e)/(-c*f+d*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))-1/3*c*(-a*d+b*c)*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/e/sqrt(a*f-b*e)/(-c*f+d*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[sqrt(b*x^2+a)/sqrt(d*x^2+c)/(f*x^2+e)^(5/2),x,5,-1/3*f*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/e/(-c*f+d*e)/(f*x^2+e)^(3/2)-1/3*c*(2*a*f*(-c*f+2*d*e)-b*e*(-c*f+3*d*e))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/e^2/sqrt(a*f-b*e)/(-c*f+d*e)^2/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))-1/3*(-a*d+b*c)*(-c*f+3*d*e)*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/e/sqrt(a*f-b*e)/(-c*f+d*e)^2/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[sqrt(b*x^2+a)/(d*x^2+c)^(3/2)/(f*x^2+e)^(5/2),x,6,-1/3*f*x*sqrt(b*x^2+a)/e/(-c*f+d*e)/sqrt(d*x^2+c)/(f*x^2+e)^(3/2)+1/3*d*(c*f+3*d*e)*x*sqrt(b*x^2+a)/c/e/(-c*f+d*e)^2/sqrt(d*x^2+c)/sqrt(f*x^2+e)+1/3*(a*f*(-2*c^2*f^2+7*c*d*e*f+3*d^2*e^2)-b*e*(-c^2*f^2+6*c*d*e*f+3*d^2*e^2))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/e^2/sqrt(a*f-b*e)/(-c*f+d*e)^3/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))-1/3*(a*d*f*(-c*f+9*d*e)-b*(-c^2*f^2+6*c*d*e*f+3*d^2*e^2))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/e/sqrt(a*f-b*e)/(-c*f+d*e)^3/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[sqrt(b*x^2+a)/(d*x^2+c)^(5/2)/(f*x^2+e)^(5/2),x,7,1/3*d*x*sqrt(b*x^2+a)/c/(-c*f+d*e)/(d*x^2+c)^(3/2)/(f*x^2+e)^(3/2)+1/3*d*(b*c*(-7*c*f+d*e)-2*a*d*(-4*c*f+d*e))*x*sqrt(b*x^2+a)/c^2/(-a*d+b*c)/(-c*f+d*e)^2/sqrt(d*x^2+c)/(f*x^2+e)^(3/2)-1/3*f*(a*d*(-c^2*f^2-9*c*d*e*f+2*d^2*e^2)-b*c*(-c^2*f^2-8*c*d*e*f+d^2*e^2))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/c^2/(-a*d+b*c)/e/(-c*f+d*e)^3/(f*x^2+e)^(3/2)-1/3*(b^2*c*e*(c^3*f^3-9*c^2*d*e*f^2-9*c*d^2*e^2*f+d^3*e^3)+2*a^2*d*f*(c^3*f^3-5*c^2*d*e*f^2-5*c*d^2*e^2*f+d^3*e^3)-a*b*(2*c^4*f^4-9*c^3*d*e*f^3-18*c^2*d^2*e^2*f^2-9*c*d^3*e^3*f+2*d^4*e^4))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/c/(-a*d+b*c)/e^2/sqrt(a*f-b*e)/(-c*f+d*e)^4/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))-1/3*(a*d*f*(c^2*f^2-18*c*d*e*f+d^2*e^2)-b*(c^3*f^3-9*c^2*d*e*f^2-9*c*d^2*e^2*f+d^3*e^3))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/c/e/sqrt(a*f-b*e)/(-c*f+d*e)^4/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[(b*x^2+a)^(3/2)*(d*x^2+c)^(3/2)/(f*x^2+e)^(5/2),x,8,1/3*(-a*f+b*e)*(-c*f+d*e)*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/e/f^2/(f*x^2+e)^(3/2)+1/2*b*d*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/f^2/sqrt(f*x^2+e)-1/6*c*sqrt(a*f-b*e)*(b*e*(-4*c*f+15*d*e)-4*a*f*(c*f+d*e))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/e^2/f^3/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))-1/6*(2*a^2*c*d*f^3+a*b*f*(-2*c^2*f^2-14*c*d*e*f+9*d^2*e^2)-b^2*e*(4*c^2*f^2-24*c*d*e*f+15*d^2*e^2))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/e/f^4/sqrt(a*f-b*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))-1/2*b*d*e*(-3*a*d*f-3*b*c*f+5*b*d*e)*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticPi(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),-a*f/(-a*f+b*e),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/f^4/sqrt(a*f-b*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[(b*x^2+a)^(3/2)*sqrt(d*x^2+c)/(f*x^2+e)^(5/2),x,7,-1/3*(-a*f+b*e)*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/e/f/(f*x^2+e)^(3/2)+1/3*c*sqrt(a*f-b*e)*(a*f*(-2*c*f+d*e)+b*e*(-2*c*f+3*d*e))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/e^2/f^2/(-c*f+d*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))+1/3*(a^2*c*d*f^3-a*b*c*f^2*(c*f+d*e)-b^2*e*(2*c^2*f^2-6*c*d*e*f+3*d^2*e^2))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/e/f^3/sqrt(a*f-b*e)/(-c*f+d*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))+b^2*d*e*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticPi(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),-a*f/(-a*f+b*e),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/f^3/sqrt(a*f-b*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[(b*x^2+a)^(3/2)/sqrt(d*x^2+c)/(f*x^2+e)^(5/2),x,5,1/3*(-a*f+b*e)*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/e/(-c*f+d*e)/(f*x^2+e)^(3/2)+2/3*c*sqrt(a*f-b*e)*(a*c*f-2*a*d*e+b*c*e)*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/e^2/(-c*f+d*e)^2/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))+1/3*(-a*d+b*c)*(a*c*f-3*a*d*e+2*b*c*e)*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/e/sqrt(a*f-b*e)/(-c*f+d*e)^2/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[(b*x^2+a)^(3/2)/(d*x^2+c)^(3/2)/(f*x^2+e)^(5/2),x,6,1/3*(-a*f+b*e)*x*sqrt(b*x^2+a)/e/(-c*f+d*e)/sqrt(d*x^2+c)/(f*x^2+e)^(3/2)-1/3*d*(-a*c*f-3*a*d*e+4*b*c*e)*x*sqrt(b*x^2+a)/c/e/(-c*f+d*e)^2/sqrt(d*x^2+c)/sqrt(f*x^2+e)-1/3*sqrt(a*f-b*e)*(2*b*c*e*(c*f+3*d*e)-a*(-2*c^2*f^2+7*c*d*e*f+3*d^2*e^2))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/e^2/(-c*f+d*e)^3/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))+1/3*(-a*d+b*c)*(a*f*(-c*f+9*d*e)-2*b*e*(c*f+3*d*e))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/e/sqrt(a*f-b*e)/(-c*f+d*e)^3/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[(b*x^2+a)^(3/2)/(d*x^2+c)^(5/2)/(f*x^2+e)^(5/2),x,7,-1/3*(-a*d+b*c)*x*sqrt(b*x^2+a)/c/(-c*f+d*e)/(d*x^2+c)^(3/2)/(f*x^2+e)^(3/2)+2/3*(a*d*(-4*c*f+d*e)+b*c*(2*c*f+d*e))*x*sqrt(b*x^2+a)/c^2/(-c*f+d*e)^2/sqrt(d*x^2+c)/(f*x^2+e)^(3/2)+1/3*f*(2*b*c*e*(3*c*f+d*e)+a*(-c^2*f^2-9*c*d*e*f+2*d^2*e^2))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/c^2/e/(-c*f+d*e)^3/(f*x^2+e)^(3/2)+2/3*sqrt(a*f-b*e)*(b*c*e*(c^2*f^2+6*c*d*e*f+d^2*e^2)+a*(c^3*f^3-5*c^2*d*e*f^2-5*c*d^2*e^2*f+d^3*e^3))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/c/e^2/(-c*f+d*e)^4/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))-1/3*(a^2*d*f*(c^2*f^2-18*c*d*e*f+d^2*e^2)-2*b^2*c*e*(c^2*f^2+6*c*d*e*f+d^2*e^2)-a*b*(c^3*f^3-17*c^2*d*e*f^2-17*c*d^2*e^2*f+d^3*e^3))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/c/e/sqrt(a*f-b*e)/(-c*f+d*e)^4/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[(b*x^2+a)^(5/2)*(d*x^2+c)^(3/2)/(f*x^2+e)^(5/2),x,9,-1/3*(-a*f+b*e)^2*(-c*f+d*e)*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/e/f^3/(f*x^2+e)^(3/2)-1/8*b*(-9*a*d*f-5*b*c*f+9*b*d*e)*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/f^3/sqrt(f*x^2+e)+1/4*b^2*d*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/f^2/sqrt(f*x^2+e)-1/24*c*sqrt(a*f-b*e)*(a*b*e*f*(-24*c*f+115*d*e)-5*b^2*e^2*(-11*c*f+21*d*e)-16*a^2*f^2*(c*f+d*e))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/e^2/f^4/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))-1/24*sqrt(a*f-b*e)*(8*a^2*c*d*f^3+a*b*f*(-8*c^2*f^2-80*c*d*e*f+45*d^2*e^2)-b^2*e*(64*c^2*f^2-195*c*d*e*f+105*d^2*e^2))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/e/f^5/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))+1/8*b*e*(15*a^2*d^2*f^2-10*a*b*d*f*(-3*c*f+5*d*e)+b^2*(3*c^2*f^2-30*c*d*e*f+35*d^2*e^2))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticPi(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),-a*f/(-a*f+b*e),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/f^5/sqrt(a*f-b*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[(b*x^2+a)^(5/2)*sqrt(d*x^2+c)/(f*x^2+e)^(5/2),x,8,1/3*(-a*f+b*e)^2*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/e/f^2/(f*x^2+e)^(3/2)+1/2*b^2*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/f^2/sqrt(f*x^2+e)-1/6*c*sqrt(a*f-b*e)*(b^2*e^2*(-13*c*f+15*d*e)-2*a*b*e*f*(-3*c*f+5*d*e)-2*a^2*f^2*(-2*c*f+d*e))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/e^2/f^3/(-c*f+d*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))+1/6*sqrt(a*f-b*e)*(2*a^2*c*d*f^3-2*a*b*c*f^2*(c*f+d*e)-b^2*e*(16*c^2*f^2-33*c*d*e*f+15*d^2*e^2))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/e/f^4/(-c*f+d*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))-1/2*b^2*e*(-5*a*d*f-b*c*f+5*b*d*e)*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticPi(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),-a*f/(-a*f+b*e),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/f^4/sqrt(a*f-b*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[(b*x^2+a)^(5/2)/sqrt(d*x^2+c)/(f*x^2+e)^(5/2),x,7,-1/3*(-a*f+b*e)^2*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/e/f/(-c*f+d*e)/(f*x^2+e)^(3/2)-1/3*c*(a*f-b*e)^(3/2)*(b*e*(-5*c*f+3*d*e)+2*a*f*(-c*f+2*d*e))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/e^2/f^2/(-c*f+d*e)^2/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))+1/3*sqrt(a*f-b*e)*(a^2*d*f^2*(-c*f+3*d*e)+a*b*f*(c^2*f^2-8*c*d*e*f+3*d^2*e^2)+b^2*e*(8*c^2*f^2-9*c*d*e*f+3*d^2*e^2))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/e/f^3/(-c*f+d*e)^2/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))+b^3*e*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticPi(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),-a*f/(-a*f+b*e),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/f^3/sqrt(a*f-b*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[(b*x^2+a)^(5/2)/(d*x^2+c)^(3/2)/(f*x^2+e)^(5/2),x,6,-1/3*(-a*f+b*e)^2*x*sqrt(b*x^2+a)/e/f/(-c*f+d*e)/sqrt(d*x^2+c)/(f*x^2+e)^(3/2)-1/3*(8*a*b*c*d*e*f-a^2*d*f*(c*f+3*d*e)-b^2*c*e*(3*c*f+d*e))*x*sqrt(b*x^2+a)/c/e/f/(-c*f+d*e)^2/sqrt(d*x^2+c)/sqrt(f*x^2+e)+1/3*sqrt(a*f-b*e)*(8*b^2*c^2*e^2-a*b*c*e*(3*c*f+13*d*e)+a^2*(-2*c^2*f^2+7*c*d*e*f+3*d^2*e^2))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/e^2/(-c*f+d*e)^3/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))-1/3*(-a*d+b*c)*sqrt(a*f-b*e)*(a*c*f-9*a*d*e+8*b*c*e)*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/e/(-c*f+d*e)^3/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[(b*x^2+a)^(5/2)/(d*x^2+c)^(5/2)/(f*x^2+e)^(5/2),x,7,1/3*(-a*d+b*c)^2*x*sqrt(b*x^2+a)/c/d/(-c*f+d*e)/(d*x^2+c)^(3/2)/(f*x^2+e)^(3/2)-1/3*(-a*d+b*c)*(2*a*d*(-4*c*f+d*e)+b*c*(c*f+5*d*e))*x*sqrt(b*x^2+a)/c^2/d/(-c*f+d*e)^2/sqrt(d*x^2+c)/(f*x^2+e)^(3/2)-1/3*f*(2*b^2*c^2*e*(c*f+3*d*e)-a*b*c*d*e*(13*c*f+3*d*e)-a^2*d*(-c^2*f^2-9*c*d*e*f+2*d^2*e^2))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/c^2/d/e/(-c*f+d*e)^3/(f*x^2+e)^(3/2)-1/3*sqrt(a*f-b*e)*(8*b^2*c^2*e^2*(c*f+d*e)-a*b*c*e*(3*c^2*f^2+26*c*d*e*f+3*d^2*e^2)-2*a^2*(c^3*f^3-5*c^2*d*e*f^2-5*c*d^2*e^2*f+d^3*e^3))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/c/e^2/(-c*f+d*e)^4/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))+1/3*(-a*d+b*c)*sqrt(a*f-b*e)*(8*b*c*e*(c*f+d*e)+a*(c^2*f^2-18*c*d*e*f+d^2*e^2))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/c/e/(-c*f+d*e)^4/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[(b*x^2+a)^(5/2)/(d*x^2+c)^(7/2)/(f*x^2+e)^(5/2),x,8,1/5*(-a*d+b*c)^2*x*sqrt(b*x^2+a)/c/d/(-c*f+d*e)/(d*x^2+c)^(5/2)/(f*x^2+e)^(3/2)-1/15*(-a*d+b*c)*(4*a*d*(-3*c*f+d*e)+b*c*(c*f+7*d*e))*x*sqrt(b*x^2+a)/c^2/d/(-c*f+d*e)^2/(d*x^2+c)^(3/2)/(f*x^2+e)^(3/2)+1/15*(a*b*c*d*(-56*c^2*f^2-47*c*d*e*f+7*d^2*e^2)+4*b^2*c^2*(c^2*f^2+9*c*d*e*f+2*d^2*e^2)+a^2*d^2*(75*c^2*f^2-35*c*d*e*f+8*d^2*e^2))*x*sqrt(b*x^2+a)/c^3/d/(-c*f+d*e)^3/sqrt(d*x^2+c)/(f*x^2+e)^(3/2)+1/15*f*(a*b*c*d*e*(-85*c^2*f^2-50*c*d*e*f+7*d^2*e^2)+8*b^2*c^2*e*(c^2*f^2+6*c*d*e*f+d^2*e^2)+a^2*d*(5*c^3*f^3+90*c^2*d*e*f^2-39*c*d^2*e^2*f+8*d^3*e^3))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/c^3/d/e/(-c*f+d*e)^4/(f*x^2+e)^(3/2)+1/15*sqrt(a*f-b*e)*(8*b^2*c^2*e^2*(5*c^2*f^2+10*c*d*e*f+d^2*e^2)+a*b*c*e*(-15*c^3*f^3-195*c^2*d*e*f^2-53*c*d^2*e^2*f+7*d^3*e^3)+a^2*(-10*c^4*f^4+65*c^3*d*e*f^3+108*c^2*d^2*e^2*f^2-43*c*d^3*e^3*f+8*d^4*e^4))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/c^2/e^2/(-c*f+d*e)^5/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))-1/15*sqrt(a*f-b*e)*(8*b^2*c^2*e*(5*c^2*f^2+10*c*d*e*f+d^2*e^2)+a^2*d*(-5*c^3*f^3+150*c^2*d*e*f^2-21*c*d^2*e^2*f+4*d^3*e^3)+a*b*c*(5*c^3*f^3-175*c^2*d*e*f^2-89*c*d^2*e^2*f+3*d^3*e^3))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/c^2/e/(-c*f+d*e)^5/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[1/sqrt(b*x^2+a)/sqrt(d*x^2+c)/(f*x^2+e)^(5/2),x,5,1/3*f^2*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/e/(-a*f+b*e)/(-c*f+d*e)/(f*x^2+e)^(3/2)+2/3*c*f*(b*e*(-2*c*f+3*d*e)-a*f*(-c*f+2*d*e))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/e^2/(a*f-b*e)^(3/2)/(-c*f+d*e)^2/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))+1/3*(a*d*f*(-c*f+3*d*e)-b*(-c^2*f^2+3*d^2*e^2))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/e/(a*f-b*e)^(3/2)/(-c*f+d*e)^2/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[1/sqrt(b*x^2+a)/(d*x^2+c)^(3/2)/(f*x^2+e)^(5/2),x,6,-d^2*x*sqrt(b*x^2+a)/c/(-a*d+b*c)/(-c*f+d*e)/sqrt(d*x^2+c)/(f*x^2+e)^(3/2)+1/3*f*(a*d*f*(c*f+3*d*e)-b*(c^2*f^2+3*d^2*e^2))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/c/(-a*d+b*c)/e/(-a*f+b*e)/(-c*f+d*e)^2/(f*x^2+e)^(3/2)-1/3*(a^2*d*f^2*(-2*c^2*f^2+7*c*d*e*f+3*d^2*e^2)+b^2*e*(-4*c^3*f^3+9*c^2*d*e*f^2+3*d^3*e^3)-a*b*f*(-2*c^3*f^3+3*c^2*d*e*f^2+9*c*d^2*e^2*f+6*d^3*e^3))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/(-a*d+b*c)/e^2/(a*f-b*e)^(3/2)/(-c*f+d*e)^3/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))-1/3*f*(a*d*f*(-c*f+9*d*e)-b*(-c^2*f^2+9*d^2*e^2))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/e/(a*f-b*e)^(3/2)/(-c*f+d*e)^3/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[1/sqrt(b*x^2+a)/(d*x^2+c)^(5/2)/(f*x^2+e)^(5/2),x,7,-1/3*d^2*x*sqrt(b*x^2+a)/c/(-a*d+b*c)/(-c*f+d*e)/(d*x^2+c)^(3/2)/(f*x^2+e)^(3/2)-2/3*d^2*(b*c*(-5*c*f+2*d*e)-a*d*(-4*c*f+d*e))*x*sqrt(b*x^2+a)/c^2/(-a*d+b*c)^2/(-c*f+d*e)^2/sqrt(d*x^2+c)/(f*x^2+e)^(3/2)-1/3*f*(a^2*d^2*f*(-c^2*f^2-9*c*d*e*f+2*d^2*e^2)-a*b*d*(-2*c^3*f^3-11*c^2*d*e*f^2-5*c*d^2*e^2*f+2*d^3*e^3)+b^2*c*(-c^3*f^3-11*c*d^2*e^2*f+4*d^3*e^3))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/c^2/(-a*d+b*c)^2/e/(-a*f+b*e)/(-c*f+d*e)^3/(f*x^2+e)^(3/2)+2/3*(a^3*d^2*f^2*(c^3*f^3-5*c^2*d*e*f^2-5*c*d^2*e^2*f+d^3*e^3)-2*a^2*b*d*f*(c^4*f^4-4*c^3*d*e*f^3-6*c^2*d^2*e^2*f^2-4*c*d^3*e^3*f+d^4*e^4)-2*b^3*c*e*(c^4*f^4-3*c^3*d*e*f^3-3*c*d^3*e^3*f+d^4*e^4)+a*b^2*(c^5*f^5-c^4*d*e*f^4-12*c^3*d^2*e^2*f^3-12*c^2*d^3*e^3*f^2-c*d^4*e^4*f+d^5*e^5))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/c/(-a*d+b*c)^2/e^2/(a*f-b*e)^(3/2)/(-c*f+d*e)^4/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))+1/3*(a^2*d^2*f^2*(c^2*f^2-18*c*d*e*f+d^2*e^2)-2*a*b*d*f*(c^3*f^3-9*c^2*d*e*f^2-9*c*d^2*e^2*f+d^3*e^3)+b^2*(c^4*f^4-18*c^2*d^2*e^2*f^2+d^4*e^4))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/c/(-a*d+b*c)/e/(a*f-b*e)^(3/2)/(-c*f+d*e)^4/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[1/(b*x^2+a)^(3/2)/sqrt(d*x^2+c)/(f*x^2+e)^(5/2),x,6,b^2*x*sqrt(d*x^2+c)/a/(-a*d+b*c)/(-a*f+b*e)/sqrt(b*x^2+a)/(f*x^2+e)^(3/2)-1/3*f*(a*b*c*f^2-a^2*d*f^2-3*b^2*e*(-c*f+d*e))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a/(-a*d+b*c)/e/(-a*f+b*e)^2/(-c*f+d*e)/(f*x^2+e)^(3/2)+1/3*c*(a*b^2*c*e*f^2*(-7*c*f+9*d*e)-3*b^3*e^2*(-c*f+d*e)^2+2*a^3*d*f^3*(-c*f+2*d*e)-a^2*b*f^2*(-2*c^2*f^2-3*c*d*e*f+9*d^2*e^2))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/a^(3/2)/(-a*d+b*c)/e^2/(a*f-b*e)^(5/2)/(-c*f+d*e)^2/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))+1/3*(3*b^2*e*(-c*f+d*e)^2+a^2*d*f^2*(-c*f+3*d*e)-a*b*f*(-c^2*f^2-3*c*d*e*f+6*d^2*e^2))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/a^(3/2)/e/(a*f-b*e)^(5/2)/(-c*f+d*e)^2/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[1/(b*x^2+a)^(3/2)/(d*x^2+c)^(3/2)/(f*x^2+e)^(5/2),x,7,b^2*x/a/(-a*d+b*c)/(-a*f+b*e)/sqrt(b*x^2+a)/sqrt(d*x^2+c)/(f*x^2+e)^(3/2)+d*(a*b*d^2*e-a^2*d^2*f+b^2*c*(-c*f+d*e))*x*sqrt(b*x^2+a)/a/c/(-a*d+b*c)^2/(-a*f+b*e)/(-c*f+d*e)/sqrt(d*x^2+c)/(f*x^2+e)^(3/2)+1/3*f*(3*b^3*c*e*(-c*f+d*e)^2+a^3*d^2*f^2*(c*f+3*d*e)-2*a^2*b*d*f*(c^2*f^2+3*d^2*e^2)+a*b^2*(c^3*f^3+3*d^3*e^3))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a/c/(-a*d+b*c)^2/e/(-a*f+b*e)^2/(-c*f+d*e)^2/(f*x^2+e)^(3/2)-1/3*(3*b^4*c*e^2*(-c*f+d*e)^3-a^4*d^2*f^3*(-2*c^2*f^2+7*c*d*e*f+3*d^2*e^2)+a^3*b*d*f^2*(-4*c^3*f^3+7*c^2*d*e*f^2+12*c*d^2*e^2*f+9*d^3*e^3)+a*b^3*e*(-7*c^4*f^4+12*c^3*d*e*f^3+3*d^4*e^4)-a^2*b^2*f*(-2*c^4*f^4-7*c^3*d*e*f^3+24*c^2*d^2*e^2*f^2+9*d^4*e^4))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/a^(3/2)/(-a*d+b*c)^2/e^2/(a*f-b*e)^(5/2)/(-c*f+d*e)^3/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))+1/3*(3*b^3*e*(-c*f+d*e)^3+a^3*d^2*f^3*(-c*f+9*d*e)-a^2*b*d*f^2*(-2*c^2*f^2+3*c*d*e*f+15*d^2*e^2)+a*b^2*f*(-c^3*f^3-3*c^2*d*e*f^2+9*c*d^2*e^2*f+3*d^3*e^3))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/a^(3/2)/(-a*d+b*c)/e/(a*f-b*e)^(5/2)/(-c*f+d*e)^3/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[1/(b*x^2+a)^(5/2)/sqrt(d*x^2+c)/(f*x^2+e)^(5/2),x,7,1/3*b^2*x*sqrt(d*x^2+c)/a/(-a*d+b*c)/(-a*f+b*e)/(b*x^2+a)^(3/2)/(f*x^2+e)^(3/2)+2/3*b^2*(b^2*c*e+5*a^2*d*f-2*a*b*(2*c*f+d*e))*x*sqrt(d*x^2+c)/a^2/(-a*d+b*c)^2/(-a*f+b*e)^2/sqrt(b*x^2+a)/(f*x^2+e)^(3/2)-1/3*f*(2*a^3*b*c*d*f^3-a^4*d^2*f^3-2*b^4*c*e^2*(-c*f+d*e)+a*b^3*e*(-9*c^2*f^2+5*c*d*e*f+4*d^2*e^2)-a^2*b^2*f*(c^2*f^2-11*c*d*e*f+11*d^2*e^2))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a^2/(-a*d+b*c)^2/e/(-a*f+b*e)^3/(-c*f+d*e)/(f*x^2+e)^(3/2)+2/3*c*(b^5*c*e^3*(-c*f+d*e)^2-a^5*d^2*f^4*(-c*f+2*d*e)-a*b^4*e^2*(-c*f+d*e)^2*(5*c*f+2*d*e)+a^4*b*d*f^3*(-2*c^2*f^2-c*d*e*f+6*d^2*e^2)-a^3*b^2*c*f^3*(-c^2*f^2-8*c*d*e*f+12*d^2*e^2)+a^2*b^3*e*f*(-5*c^3*f^3+12*c^2*d*e*f^2-12*c*d^2*e^2*f+6*d^3*e^3))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/a^(5/2)/(-a*d+b*c)^2/e^2/(a*f-b*e)^(7/2)/(-c*f+d*e)^2/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))-1/3*(2*b^4*c*e^2*(-c*f+d*e)^2+a^4*d^2*f^3*(-c*f+3*d*e)-3*a*b^3*e*(-c*f+d*e)^2*(3*c*f+d*e)-a^3*b*d*f^2*(-2*c^2*f^2-3*c*d*e*f+9*d^2*e^2)+a^2*b^2*f*(-c^3*f^3+3*c^2*d*e*f^2-9*c*d^2*e^2*f+9*d^3*e^3))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/a^(5/2)/(-a*d+b*c)/e/(a*f-b*e)^(7/2)/(-c*f+d*e)^2/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[1/(b*x^2+a)^(5/2)/(d*x^2+c)^(3/2)/(f*x^2+e)^(5/2),x,8,1/3*b^2*x/a/(-a*d+b*c)/(-a*f+b*e)/(b*x^2+a)^(3/2)/sqrt(d*x^2+c)/(f*x^2+e)^(3/2)+2/3*b^2*(6*a^2*d*f-4*a*b*c*f-3*a*b*d*e+b^2*c*e)*x/a^2/(-a*d+b*c)^2/(-a*f+b*e)^2/sqrt(b*x^2+a)/sqrt(d*x^2+c)/(f*x^2+e)^(3/2)+1/3*d*(6*a^3*b*d^3*e*f-3*a^4*d^3*f^2+2*b^4*c^2*e*(-c*f+d*e)-a*b^3*c*(-8*c^2*f^2+c*d*e*f+7*d^2*e^2)-a^2*b^2*d*(13*c^2*f^2-13*c*d*e*f+3*d^2*e^2))*x*sqrt(b*x^2+a)/a^2/c/(-a*d+b*c)^3/(-a*f+b*e)^2/(-c*f+d*e)/sqrt(d*x^2+c)/(f*x^2+e)^(3/2)+1/3*f*(2*b^5*c^2*e^2*(-c*f+d*e)^2+a^5*d^3*f^3*(c*f+3*d*e)-a*b^4*c*e*(-c*f+d*e)^2*(9*c*f+7*d*e)-3*a^4*b*d^2*f^2*(c^2*f^2+3*d^2*e^2)+3*a^3*b^2*d*f*(c^3*f^3+3*d^3*e^3)-a^2*b^3*(c^4*f^4-14*c^3*d*e*f^3+28*c^2*d^2*e^2*f^2-14*c*d^3*e^3*f+3*d^4*e^4))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a^2/c/(-a*d+b*c)^3/e/(-a*f+b*e)^3/(-c*f+d*e)^2/(f*x^2+e)^(3/2)+1/3*(2*b^6*c^2*e^3*(-c*f+d*e)^3-a*b^5*c*e^2*(-c*f+d*e)^3*(10*c*f+7*d*e)-a^6*d^3*f^4*(-2*c^2*f^2+7*c*d*e*f+3*d^2*e^2)+a^5*b*d^2*f^3*(-6*c^3*f^3+11*c^2*d*e*f^2+15*c*d^2*e^2*f+12*d^3*e^3)-3*a^4*b^2*d*f^2*(-2*c^4*f^4-3*c^3*d*e*f^3+15*c^2*d^2*e^2*f^2+6*d^4*e^4)-a^2*b^4*e*(-10*c^5*f^5+30*c^4*d*e*f^4-45*c^3*d^2*e^2*f^3+45*c^2*d^3*e^3*f^2-15*c*d^4*e^4*f+3*d^5*e^5)+a^3*b^3*f*(-2*c^5*f^5-23*c^4*d*e*f^4+45*c^3*d^2*e^2*f^3+12*d^5*e^5))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/a^(5/2)/(-a*d+b*c)^3/e^2/(a*f-b*e)^(7/2)/(-c*f+d*e)^3/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))-1/3*(2*b^5*c*e^2*(-c*f+d*e)^3+a^5*d^3*f^4*(-c*f+9*d*e)-3*a*b^4*e*(-c*f+d*e)^3*(3*c*f+2*d*e)-3*a^4*b*d^2*f^3*(-c^2*f^2+2*c*d*e*f+7*d^2*e^2)+3*a^3*b^2*d*f^2*(-c^3*f^3-2*c^2*d*e*f^2+8*c*d^2*e^2*f+3*d^3*e^3)+a^2*b^3*f*(c^4*f^4-6*c^3*d*e*f^3+24*c^2*d^2*e^2*f^2-36*c*d^3*e^3*f+9*d^4*e^4))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/a^(5/2)/(-a*d+b*c)^2/e/(a*f-b*e)^(7/2)/(-c*f+d*e)^3/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[(d*x^2+c)^2*(f*x^2+e)/(b*x^2+a)^(5/4),x,6,2*(-a*d+b*c)^2*(-a*f+b*e)*x/a/b^3/(b*x^2+a)^(1/4)-2/15*(15*b^3*c^2*e-40*a^3*d^2*f-30*a*b^2*c*(c*f+2*d*e)+36*a^2*b*d*(2*c*f+d*e))*x/a/b^3/(b*x^2+a)^(1/4)+2/15*d*(-5*a*d*f+6*b*c*f+3*b*d*e)*x*(b*x^2+a)^(3/4)/b^3+2/9*d^2*f*x^3*(b*x^2+a)^(3/4)/b^2+2/15*(15*b^3*c^2*e-40*a^3*d^2*f-30*a*b^2*c*(c*f+2*d*e)+36*a^2*b*d*(2*c*f+d*e))*(1+b*x^2/a)^(1/4)*EllipticE(sin(1/2*arctan(sqrt(b)*x/sqrt(a))),sqrt(2))/sqrt(a)/b^(7/2)/(b*x^2+a)^(1/4),1],
[(d*x^2+c)*(f*x^2+e)/(b*x^2+a)^(5/4),x,5,2*(-a*d+b*c)*(-a*f+b*e)*x/a/b^2/(b*x^2+a)^(1/4)-2/5*(5*b^2*c*e+12*a^2*d*f-10*a*b*(c*f+d*e))*x/a/b^2/(b*x^2+a)^(1/4)+2/5*d*f*x*(b*x^2+a)^(3/4)/b^2+2/5*(5*b^2*c*e+12*a^2*d*f-10*a*b*(c*f+d*e))*(1+b*x^2/a)^(1/4)*EllipticE(sin(1/2*arctan(sqrt(b)*x/sqrt(a))),sqrt(2))/sqrt(a)/b^(5/2)/(b*x^2+a)^(1/4),1],
[(f*x^2+e)/(b*x^2+a)^(5/4),x,3,2*f*x/b/(b*x^2+a)^(1/4)+2*(-2*a*f+b*e)*(1+b*x^2/a)^(1/4)*EllipticE(sin(1/2*arctan(sqrt(b)*x/sqrt(a))),sqrt(2))/sqrt(a)/b^(3/2)/(b*x^2+a)^(1/4),1],
[(f*x^2+e)/(b*x^2+a)^(5/4)/(d*x^2+c),x,7,2*(-a*f+b*e)*(1+b*x^2/a)^(1/4)*EllipticE(sin(1/2*arctan(sqrt(b)*x/sqrt(a))),sqrt(2))/sqrt(a)/sqrt(b)/(-a*d+b*c)/(b*x^2+a)^(1/4)+a^(1/4)*(-c*f+d*e)*sqrt(-b*x^2/a)*EllipticPi(sin(arcsin((b*x^2+a)^(1/4)/a^(1/4))),-sqrt(a)*sqrt(d)/sqrt(a*d-b*c),sqrt(-1))/sqrt(d)/(a*d-b*c)^(3/2)/x-a^(1/4)*(-c*f+d*e)*sqrt(-b*x^2/a)*EllipticPi(sin(arcsin((b*x^2+a)^(1/4)/a^(1/4))),sqrt(a)*sqrt(d)/sqrt(a*d-b*c),sqrt(-1))/sqrt(d)/(a*d-b*c)^(3/2)/x,1],
[(f*x^2+e)/(b*x^2+a)^(5/4)/(d*x^2+c)^2,x,8,-1/2*(-c*f+d*e)*x/c/(-a*d+b*c)/(b*x^2+a)^(1/4)/(d*x^2+c)+1/2*sqrt(b)*(-5*a*c*f+a*d*e+4*b*c*e)*(1+b*x^2/a)^(1/4)*EllipticE(sin(1/2*arctan(sqrt(b)*x/sqrt(a))),sqrt(2))/sqrt(a)/c/(-a*d+b*c)^2/(b*x^2+a)^(1/4)-1/4*a^(1/4)*(b*c*(-3*c*f+7*d*e)-2*a*d*(c*f+d*e))*sqrt(-b*x^2/a)*EllipticPi(sin(arcsin((b*x^2+a)^(1/4)/a^(1/4))),-sqrt(a)*sqrt(d)/sqrt(a*d-b*c),sqrt(-1))/c/sqrt(d)/(a*d-b*c)^(5/2)/x+1/4*a^(1/4)*(b*c*(-3*c*f+7*d*e)-2*a*d*(c*f+d*e))*sqrt(-b*x^2/a)*EllipticPi(sin(arcsin((b*x^2+a)^(1/4)/a^(1/4))),sqrt(a)*sqrt(d)/sqrt(a*d-b*c),sqrt(-1))/c/sqrt(d)/(a*d-b*c)^(5/2)/x,1],
[(f*x^2+e)/(b*x^2+a)^(5/4)/(d*x^2+c)^3,x,9,-1/4*(-c*f+d*e)*x/c/(-a*d+b*c)/(b*x^2+a)^(1/4)/(d*x^2+c)^2-1/16*(b*c*(-7*c*f+15*d*e)-2*a*d*(c*f+3*d*e))*x/c^2/(-a*d+b*c)^2/(b*x^2+a)^(1/4)/(d*x^2+c)+1/16*sqrt(b)*(32*b^2*c^2*e+a*b*c*(-43*c*f+19*d*e)-2*a^2*d*(c*f+3*d*e))*(1+b*x^2/a)^(1/4)*EllipticE(sin(1/2*arctan(sqrt(b)*x/sqrt(a))),sqrt(2))/sqrt(a)/c^2/(-a*d+b*c)^3/(b*x^2+a)^(1/4)+1/32*a^(1/4)*(7*b^2*c^2*(-3*c*f+11*d*e)+4*a^2*d^2*(c*f+3*d*e)-4*a*b*c*d*(7*c*f+11*d*e))*sqrt(-b*x^2/a)*EllipticPi(sin(arcsin((b*x^2+a)^(1/4)/a^(1/4))),-sqrt(a)*sqrt(d)/sqrt(a*d-b*c),sqrt(-1))/c^2/sqrt(d)/(a*d-b*c)^(7/2)/x-1/32*a^(1/4)*(7*b^2*c^2*(-3*c*f+11*d*e)+4*a^2*d^2*(c*f+3*d*e)-4*a*b*c*d*(7*c*f+11*d*e))*sqrt(-b*x^2/a)*EllipticPi(sin(arcsin((b*x^2+a)^(1/4)/a^(1/4))),sqrt(a)*sqrt(d)/sqrt(a*d-b*c),sqrt(-1))/c^2/sqrt(d)/(a*d-b*c)^(7/2)/x,1],
[(f*x^2+e)/(b*x^2+a)^(5/4)/(d*x^2+c)^(5/4),x,2,2*(-a*f+b*e)*x/a/(-a*d+b*c)/(b*x^2+a)^(1/4)/(d*x^2+c)^(1/4)-(-2*a*c*f+a*d*e+b*c*e)*x*(c*(b*x^2+a)/a/(d*x^2+c))^(1/4)*hypergeom([1/4, 1/2],[3/2],-(-a*d+b*c)*x^2/a/(d*x^2+c))/a/c/(-a*d+b*c)/(b*x^2+a)^(1/4)/(d*x^2+c)^(1/4),1],
[(f*x^2+e)/(b*x^2+a)^(9/4)/(d*x^2+c)^(1/4),x,2,2/5*(-a*f+b*e)*x*(d*x^2+c)^(3/4)/a/(-a*d+b*c)/(b*x^2+a)^(5/4)+1/5*(2*a*c*f-5*a*d*e+3*b*c*e)*x*(c*(b*x^2+a)/a/(d*x^2+c))^(5/4)*(d*x^2+c)^(3/4)*hypergeom([1/2, 5/4],[3/2],-(-a*d+b*c)*x^2/a/(d*x^2+c))/a/c/(-a*d+b*c)/(b*x^2+a)^(5/4),1],
[(d*x^2+c)^(3/4)*(f*x^2+e)/(b*x^2+a)^(13/4),x,2,2/9*(-a*f+b*e)*x*(d*x^2+c)^(7/4)/a/(-a*d+b*c)/(b*x^2+a)^(9/4)+1/9*(2*a*c*f-9*a*d*e+7*b*c*e)*x*(c*(b*x^2+a)/a/(d*x^2+c))^(9/4)*(d*x^2+c)^(7/4)*hypergeom([1/2, 9/4],[3/2],-(-a*d+b*c)*x^2/a/(d*x^2+c))/a/c/(-a*d+b*c)/(b*x^2+a)^(9/4),1],
[(d*x^2+c)^(7/4)*(f*x^2+e)/(b*x^2+a)^(17/4),x,2,2/13*(-a*f+b*e)*x*(d*x^2+c)^(11/4)/a/(-a*d+b*c)/(b*x^2+a)^(13/4)+1/13*(2*a*c*f-13*a*d*e+11*b*c*e)*x*(c*(b*x^2+a)/a/(d*x^2+c))^(13/4)*(d*x^2+c)^(11/4)*hypergeom([1/2, 13/4],[3/2],-(-a*d+b*c)*x^2/a/(d*x^2+c))/a/c/(-a*d+b*c)/(b*x^2+a)^(13/4),1],
[(d*x^2+c)^(11/4)*(f*x^2+e)/(b*x^2+a)^(21/4),x,2,2/17*(-a*f+b*e)*x*(d*x^2+c)^(15/4)/a/(-a*d+b*c)/(b*x^2+a)^(17/4)+1/17*(2*a*c*f-17*a*d*e+15*b*c*e)*x*(c*(b*x^2+a)/a/(d*x^2+c))^(17/4)*(d*x^2+c)^(15/4)*hypergeom([1/2, 17/4],[3/2],-(-a*d+b*c)*x^2/a/(d*x^2+c))/a/c/(-a*d+b*c)/(b*x^2+a)^(17/4),1],
[(b*x^2+a)^p*(d*x^2+c)^q*(f*x^2+e),x,10,e*x*(b*x^2+a)^p*(d*x^2+c)^q*AppellF1(1/2,-p,-q,3/2,-b*x^2/a,-d*x^2/c)/((1+b*x^2/a)^p)/((1+d*x^2/c)^q)+1/3*f*x^3*(b*x^2+a)^p*(d*x^2+c)^q*AppellF1(3/2,-p,-q,5/2,-b*x^2/a,-d*x^2/c)/((1+b*x^2/a)^p)/((1+d*x^2/c)^q),1],
[(b*x^2+a)^p*(d*x^2+c)^(-5/2-p)*(f*x^2+e),x,2,-1/2*(-a*f+b*e)*x*(b*x^2+a)^(p+1)*(d*x^2+c)^(-3/2-p)/a/(-a*d+b*c)/(p+1)-1/2*(a*c*f+2*a*d*e*(p+1)-b*c*e*(3+2*p))*x*(b*x^2+a)^(p+1)*(c*(b*x^2+a)/a/(d*x^2+c))^(-1-p)*(d*x^2+c)^(-3/2-p)*hypergeom([1/2, -1-p],[3/2],-(-a*d+b*c)*x^2/a/(d*x^2+c))/a/c/(-a*d+b*c)/(p+1),1]]: