lst:=[[(x^3+3*x^2+x+9)/(x^2+1)/(x^2+3),x,4,3*arctan(x)+1/2*ln(x^2+3),1],
[(x^3+x^2+x+3)/(x^2+1)/(x^2+3),x,4,arctan(x)+1/2*ln(x^2+3),1],
[(3*x^3-x^2+6*x-4)/(x^2+1)/(x^2+2),x,6,-3*arctan(x)+sqrt(2)*arctan(x/sqrt(2))+3/2*ln(x^2+1),1],
[sqrt(b*x^2+a)*(f*x^2+c)^2*(C*x^4+B*x^2+A),x,7,1/256*(128*A*c^2+a*(7*a^3*C*f^2-32*b^3*c*(2*A*f+B*c)-10*a^2*b*f*(B*f+2*C*c)+16*a*b^2*(A*f^2+2*B*c*f+C*c^2))/b^4)*x*sqrt(b*x^2+a)-1/128*(7*a^3*C*f^2-32*b^3*c*(2*A*f+B*c)-10*a^2*b*f*(B*f+2*C*c)+16*a*b^2*(A*f^2+2*B*c*f+C*c^2))*x*(b*x^2+a)^(3/2)/b^4+1/96*(7*a^2*C*f^2-10*a*b*f*(B*f+2*C*c)+16*b^2*(A*f^2+2*B*c*f+C*c^2))*x^3*(b*x^2+a)^(3/2)/b^3-1/80*f*(7*a*C*f-10*b*(B*f+2*C*c))*x^5*(b*x^2+a)^(3/2)/b^2+1/10*C*f^2*x^7*(b*x^2+a)^(3/2)/b+1/256*a*(128*A*b^4*c^2+a*(7*a^3*C*f^2-32*b^3*c*(2*A*f+B*c)-10*a^2*b*f*(B*f+2*C*c)+16*a*b^2*(A*f^2+2*B*c*f+C*c^2)))*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(9/2),1],
[sqrt(b*x^2+a)*(C*x^4+B*x^2+A),x,5,1/16*(8*A-a*(2*B*b-C*a)/b^2)*x*sqrt(b*x^2+a)+1/8*(2*B*b-C*a)*x*(b*x^2+a)^(3/2)/b^2+1/6*C*x^3*(b*x^2+a)^(3/2)/b+1/16*a*(8*A*b^2-a*(2*B*b-C*a))*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(5/2),1],
[sqrt(b*x^2+a)*(C*x^4+B*x^2+A)/(f*x^2+c),x,8,-1/8*(-4*B*b*f-C*a*f+4*C*b*c)*x*sqrt(b*x^2+a)/b/f^2+1/4*C*x^3*sqrt(b*x^2+a)/f-1/8*(a^2*C*f^2+4*a*b*f*(-B*f+C*c)-8*b^2*(A*f^2-B*c*f+C*c^2))*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(3/2)/f^3-sqrt(-a*f+b*c)*(A*f^2-B*c*f+C*c^2)*arctanh(sqrt(-a*f+b*c)*x/sqrt(c)/sqrt(b*x^2+a))/sqrt(c)/f^3,1],
[sqrt(b*x^2+a)*(C*x^4+B*x^2+A)/(f*x^2+c)^2,x,8,1/2*C*x*sqrt(b*x^2+a)/f^2+1/2*(A*f^2-B*c*f+C*c^2)*x*sqrt(b*x^2+a)/c/f^2/(f*x^2+c)-1/2*(-2*B*b*f-C*a*f+4*C*b*c)*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/sqrt(b)/f^3+1/2*(2*b*c^2*(-B*f+2*C*c)-a*f*(-A*f^2-B*c*f+3*C*c^2))*arctanh(sqrt(-a*f+b*c)*x/sqrt(c)/sqrt(b*x^2+a))/c^(3/2)/f^3/sqrt(-a*f+b*c),1],
[sqrt(b*x^2+a)*(C*x^4+B*x^2+A)/(f*x^2+c)^3,x,8,1/4*(A*f^2-B*c*f+C*c^2)*x*sqrt(b*x^2+a)/c/f^2/(f*x^2+c)^2+1/8*(a*f*(-3*A*f^2-B*c*f+5*C*c^2)-2*b*c*(-A*f^2-B*c*f+3*C*c^2))*x*sqrt(b*x^2+a)/c^2/f^2/(-a*f+b*c)/(f*x^2+c)+sqrt(b)*C*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/f^3-1/8*(8*b^2*c^4*C-4*a*b*c*f*(A*f^2+3*C*c^2)+a^2*f^2*(3*A*f^2+B*c*f+3*C*c^2))*arctanh(sqrt(-a*f+b*c)*x/sqrt(c)/sqrt(b*x^2+a))/c^(5/2)/f^3/(-a*f+b*c)^(3/2),1],
[(D*x^6+C*x^4+B*x^2+A)/(b*x^2+a)^(1/4)/(f*x^2+e),x,11,2/15*(4*a^2*D*f^2+6*a*b*f*(-C*f+D*e)+15*b^2*(D*e^2-f*(-B*f+C*e)))*x/b^2/f^3/(b*x^2+a)^(1/4)-2/15*(-3*C*b*f+2*D*a*f+3*D*b*e)*x*(b*x^2+a)^(3/4)/b^2/f^2+2/9*D*x^3*(b*x^2+a)^(3/4)/b/f-2/15*sqrt(a)*(4*a^2*D*f^2+6*a*b*f*(-C*f+D*e)+15*b^2*(D*e^2-f*(-B*f+C*e)))*(1+b*x^2/a)^(1/4)*EllipticE(sin(1/2*arctan(sqrt(b)*x/sqrt(a))),sqrt(2))/b^(5/2)/f^3/(b*x^2+a)^(1/4)-a^(1/4)*(D*e^3-f*(C*e^2-f*(-A*f+B*e)))*sqrt(-b*x^2/a)*EllipticPi(sin(arcsin((b*x^2+a)^(1/4)/a^(1/4))),-sqrt(a)*sqrt(f)/sqrt(a*f-b*e),sqrt(-1))/f^(7/2)/sqrt(a*f-b*e)/x+a^(1/4)*(D*e^3-f*(C*e^2-f*(-A*f+B*e)))*sqrt(-b*x^2/a)*EllipticPi(sin(arcsin((b*x^2+a)^(1/4)/a^(1/4))),sqrt(a)*sqrt(f)/sqrt(a*f-b*e),sqrt(-1))/f^(7/2)/sqrt(a*f-b*e)/x,1],
[(d*x^2+c)^(3/2)*(C*x^4+B*x^2+A)/sqrt(b*x^2+a),x,7,-1/105*(48*a^3*C*d^3-8*a^2*b*d^2*(7*B*d+9*C*c)+b^3*c*(-140*A*d^2-21*B*c*d+6*C*c^2)+a*b^2*d*(70*A*d^2+91*B*c*d+12*C*c^2))*x*sqrt(d*x^2+c)/b^3/d^2/sqrt(b*x^2+a)+1/105*(24*a^2*C*d^2-a*b*d*(28*B*d+33*C*c)+b^2*(35*A*d^2+42*B*c*d+3*C*c^2))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b^3/d+1/35*(7*B*b*d-6*C*a*d+8*C*b*c)*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b^2+1/7*C*d*x^5*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b+1/105*sqrt(a)*(48*a^3*C*d^3-8*a^2*b*d^2*(7*B*d+9*C*c)+b^3*c*(-140*A*d^2-21*B*c*d+6*C*c^2)+a*b^2*d*(70*A*d^2+91*B*c*d+12*C*c^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*A*b^3*c*d-24*a^3*C*d^2+a^2*b*d*(28*B*d+33*C*c)-a*b^2*(35*A*d^2+42*B*c*d+3*C*c^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)*(C*x^4+B*x^2+A)/sqrt(b*x^2+a),x,6,1/15*(5*b*B*c-3*a*c*C-2*b*c^2*C/d+15*A*b*d-10*a*B*d+8*a^2*C*d/b)*x*sqrt(d*x^2+c)/b/d/sqrt(b*x^2+a)+1/15*(5*B*b*d-4*C*a*d+C*b*c)*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b^2/d+1/5*C*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b-1/15*sqrt(a)*(8*a^2*C*d^2-a*b*d*(10*B*d+3*C*c)-b^2*(-15*A*d^2-5*B*c*d+2*C*c^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*A*b^2*d+4*a^2*C*d-a*b*(5*B*d+C*c))*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],
[(C*x^4+B*x^2+A)/sqrt(b*x^2+a)/sqrt(d*x^2+c),x,5,-1/3*(-3*B*b*d+2*C*a*d+2*C*b*c)*x*sqrt(d*x^2+c)/b/d^2/sqrt(b*x^2+a)+1/3*C*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b/d+1/3*sqrt(a)*(-3*B*b*d+2*C*a*d+2*C*b*c)*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)*(-3*A*b*d+C*a*c)*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],
[(C*x^4+B*x^2+A)/sqrt(b*x^2+a)/(d*x^2+c)^(3/2),x,2,C*x*sqrt(b*x^2+a)/b/d/sqrt(d*x^2+c)+(a*c*C*d-b*(A*d^2-B*c*d+2*C*c^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)*(A*b*d-B*a*d+C*a*c)*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],
[(C*x^4+B*x^2+A)/sqrt(b*x^2+a)/(d*x^2+c)^(5/2),x,2,-1/3*(A*d^2-B*c*d+C*c^2)*x*sqrt(b*x^2+a)/c/d/(-a*d+b*c)/(d*x^2+c)^(3/2)+1/3*(b*c*(-4*A*d^2+B*c*d+2*C*c^2)-a*d*(-2*A*d^2-B*c*d+4*C*c^2))*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*A*b^2*c*d+3*a^2*c*C*d-a*b*(A*d^2+2*B*c*d+C*c^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],
[(C*x^4+B*x^2+A)/sqrt(b*x^2+a)/(d*x^2+c)^(7/2),x,3,-1/5*(A*d^2-B*c*d+C*c^2)*x*sqrt(b*x^2+a)/c/d/(-a*d+b*c)/(d*x^2+c)^(5/2)+1/15*(b*c*(-8*A*d^2+3*B*c*d+2*C*c^2)-a*d*(-4*A*d^2-B*c*d+6*C*c^2))*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*(-23*A*d^2-7*B*c*d+7*C*c^2)-b^2*c^2*(-23*A*d^2+3*B*c*d+2*C*c^2)+a^2*d^2*(8*A*d^2+2*B*c*d+3*C*c^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*A*b^2*c^2*d+a^2*d*(4*A*d^2+B*c*d+9*C*c^2)-a*b*c*(11*A*d^2+9*B*c*d+C*c^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)^(3/2)*(C*x^4+B*x^2+A)/(b*x^2+a)^(3/2),x,4,1/15*(24*a^2*C*d^2-a*b*d*(20*B*d+27*C*c)+b^2*(15*A*d^2+20*B*c*d+3*C*c^2))*x*sqrt(d*x^2+c)/b^3/d/sqrt(b*x^2+a)+1/15*(5*B*b*d-6*C*a*d+6*C*b*c)*x^3*sqrt(d*x^2+c)/b^2/sqrt(b*x^2+a)+1/5*C*d*x^5*sqrt(d*x^2+c)/b/sqrt(b*x^2+a)+1/15*(15*A*b^3*c*d-48*a^3*C*d^2+8*a^2*b*d*(5*B*d+6*C*c)-a*b^2*(30*A*d^2+35*B*c*d+3*C*c^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*C*d+15*b^2*(A*d+B*c)-a*b*(20*B*d+21*C*c))*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)*(C*x^4+B*x^2+A)/(b*x^2+a)^(3/2),x,3,1/3*(3*B*b*d-4*C*a*d+C*b*c)*x*sqrt(d*x^2+c)/b^2/d/sqrt(b*x^2+a)+1/3*C*x^3*sqrt(d*x^2+c)/b/sqrt(b*x^2+a)+1/3*(3*A*b^2*d+8*a^2*C*d-a*b*(6*B*d+C*c))*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))+1/3*sqrt(a)*(3*B*b-4*C*a)*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],
[(C*x^4+B*x^2+A)/(b*x^2+a)^(3/2)/sqrt(d*x^2+c),x,2,C*x*sqrt(d*x^2+c)/b/d/sqrt(b*x^2+a)+(A*b^2*d+2*a^2*C*d-a*b*(B*d+C*c))*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*b*d+B*b*c-C*a*c)*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],
[(C*x^4+B*x^2+A)/(b*x^2+a)^(3/2)/(d*x^2+c)^(3/2),x,2,(A*b^2-a*(B*b-C*a))*x/a/b/(-a*d+b*c)/sqrt(b*x^2+a)/sqrt(d*x^2+c)+(A*b^2*c*d+a^2*c*C*d+a*b*(A*d^2-2*B*c*d+C*c^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)+sqrt(c)*(-2*A*b*d+B*a*d+B*b*c-2*C*a*c)*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],
[(C*x^4+B*x^2+A)/(b*x^2+a)^(3/2)/(d*x^2+c)^(5/2),x,3,(A*b^2-a*(B*b-C*a))*x/a/b/(-a*d+b*c)/sqrt(b*x^2+a)/(d*x^2+c)^(3/2)+1/3*(3*A*b^2*c*d+3*a^2*c*C*d+a*b*(A*d^2-4*B*c*d+C*c^2))*x*sqrt(b*x^2+a)/a/b/c/(-a*d+b*c)^2/(d*x^2+c)^(3/2)+1/3*(3*A*b^2*c^2*d+a^2*d*(-2*A*d^2-B*c*d+7*C*c^2)+a*b*c*(7*A*d^2-7*B*c*d+C*c^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*C*d-3*b^2*c*(-3*A*d+B*c)+a*b*(-A*d^2-5*B*c*d+5*C*c^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],
[(b*d*x^4+2*b*c*x^2+a*c)/sqrt(b*x^2+a)/(d*x^2+c)^(3/2),x,1,x*sqrt(b*x^2+a)/sqrt(d*x^2+c),1],
[(b*d*x^4+2*b*c*x^2+a*c)/(b*x^2+a)^(3/2)/(d*x^2+c)^(3/2),x,3,-x/sqrt(b*x^2+a)/sqrt(d*x^2+c)-2*sqrt(c)*sqrt(d)*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/(-a*d+b*c)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+2*b*c^(3/2)*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],
[(C*x^4+B*x^2+A)/sqrt(b*x^2+a)/(-d*x^2+c)^(3/2),x,8,(A*d^2+B*c*d+C*c^2)*x*sqrt(b*x^2+a)/c/d/(a*d+b*c)/sqrt(-d*x^2+c)-(a*c*C*d+b*(A*d^2+B*c*d+2*C*c^2))*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(c)/d^(3/2)/(a*d+b*c)/sqrt(1+b*x^2/a)/sqrt(-d*x^2+c)+(A*b*d+C*a*c)*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(c)/d^(3/2)/sqrt(b*x^2+a)/sqrt(-d*x^2+c),1],
[sqrt(b*x^2+a)*(d*x^2+c)^(3/2)*(D*x^6+C*x^4+B*x^2+A),x,9,1/3465*(128*a^5*d^5*D-8*a^4*b*d^4*(22*C*d+29*D*c)+a^3*b^2*d^3*(264*B*d^2+352*C*c*d+51*D*c^2)+b^5*c^2*(693*A*d^3-198*B*c*d^2+88*C*c^2*d-48*D*c^3)-a*b^4*c*d*(-1617*A*d^3-297*B*c*d^2+77*C*c^2*d-32*D*c^3)-a^2*b^3*d^2*(462*A*d^3+627*B*c*d^2+99*C*c^2*d-29*D*c^3))*x*sqrt(d*x^2+c)/b^4/d^4/sqrt(b*x^2+a)-1/3465*(64*a^4*d^4*D-4*a^3*b*d^3*(22*C*d+27*D*c)+3*a^2*b^2*d^2*(44*B*d^2+55*C*c*d+5*D*c^2)+b^4*c*(-1386*A*d^3-99*B*c*d^2+44*C*c^2*d-24*D*c^3)-a*b^3*d*(231*A*d^3+297*B*c*d^2+33*C*c^2*d-13*D*c^3))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b^4/d^3+1/3465*(48*a^3*d^3*D-a^2*b*d^2*(66*C*d+79*D*c)+a*b^2*d*(99*B*d^2+121*C*c*d+9*D*c^2)+b^3*(693*A*d^3+792*B*c*d^2+33*C*c^2*d-18*D*c^3))*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b^3/d^2-1/693*(8*a^2*d^2*D-a*b*d*(11*C*d+13*D*c)-b^2*(99*B*d^2+110*C*c*d+3*D*c^2))*x^5*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b^2/d+1/99*(11*C*b*d+D*a*d+12*D*b*c)*x^7*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b+1/11*d*D*x^9*sqrt(b*x^2+a)*sqrt(d*x^2+c)-1/3465*sqrt(a)*(128*a^5*d^5*D-8*a^4*b*d^4*(22*C*d+29*D*c)+a^3*b^2*d^3*(264*B*d^2+352*C*c*d+51*D*c^2)+b^5*c^2*(693*A*d^3-198*B*c*d^2+88*C*c^2*d-48*D*c^3)-a*b^4*c*d*(-1617*A*d^3-297*B*c*d^2+77*C*c^2*d-32*D*c^3)-a^2*b^3*d^2*(462*A*d^3+627*B*c*d^2+99*C*c^2*d-29*D*c^3))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/b^(9/2)/d^4/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/3465*a^(3/2)*(64*a^4*d^4*D-4*a^3*b*d^3*(22*C*d+27*D*c)+3*a^2*b^2*d^2*(44*B*d^2+55*C*c*d+5*D*c^2)+b^4*c*(2079*A*d^3-99*B*c*d^2+44*C*c^2*d-24*D*c^3)-a*b^3*d*(231*A*d^3+297*B*c*d^2+33*C*c^2*d-13*D*c^3))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(9/2)/d^3/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)*(D*x^6+C*x^4+B*x^2+A),x,8,-1/315*(16*a^4*d^4*D-8*a^3*b*d^3*(3*C*d+D*c)+3*a^2*b^2*d^2*(14*B*d^2+5*C*c*d-2*D*c^2)-b^4*c*(105*A*d^3-42*B*c*d^2+24*C*c^2*d-16*D*c^3)+a*b^3*d*(-105*A*d^3-42*B*c*d^2+15*C*c^2*d-8*D*c^3))*x*sqrt(d*x^2+c)/b^3/d^4/sqrt(b*x^2+a)+1/315*(8*a^3*d^3*D-3*a^2*b*d^2*(4*C*d+D*c)+3*a*b^2*d*(7*B*d^2+2*C*c*d-D*c^2)-b^3*(-105*A*d^3-21*B*c*d^2+12*C*c^2*d-8*D*c^3))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b^3/d^3+1/315*(9*b*c*C+63*b*B*d+9*a*C*d+2*a*c*D-6*b*c^2*D/d-6*a^2*d*D/b)*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b/d+1/63*(9*C*b*d+D*a*d+D*b*c)*x^5*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b/d+1/9*D*x^7*sqrt(b*x^2+a)*sqrt(d*x^2+c)+1/315*sqrt(a)*(16*a^4*d^4*D-8*a^3*b*d^3*(3*C*d+D*c)+3*a^2*b^2*d^2*(14*B*d^2+5*C*c*d-2*D*c^2)-b^4*c*(105*A*d^3-42*B*c*d^2+24*C*c^2*d-16*D*c^3)+a*b^3*d*(-105*A*d^3-42*B*c*d^2+15*C*c^2*d-8*D*c^3))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/b^(7/2)/d^4/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*D-3*a^2*b*d^2*(4*C*d+D*c)+3*a*b^2*d*(7*B*d^2+2*C*c*d-D*c^2)-b^3*(210*A*d^3-21*B*c*d^2+12*C*c^2*d-8*D*c^3))*sqrt(d*x^2+c)*InverseJacobiAM(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],
[sqrt(b*x^2+a)*(D*x^6+C*x^4+B*x^2+A)/sqrt(d*x^2+c),x,7,1/105*(8*a^3*d^3*D-a^2*b*d^2*(14*C*d-9*D*c)-a*b^2*d*(-35*B*d^2+21*C*c*d-16*D*c^2)+b^3*(105*A*d^3-70*B*c*d^2+56*C*c^2*d-48*D*c^3))*x*sqrt(d*x^2+c)/b^2/d^4/sqrt(b*x^2+a)-1/105*(4*a^2*d^2*D-a*b*d*(7*C*d-5*D*c)+b^2*(-35*B*d^2+28*C*c*d-24*D*c^2))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b^2/d^3+1/35*(7*C*b*d+D*a*d-6*D*b*c)*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b/d^2+1/7*D*x^5*sqrt(b*x^2+a)*sqrt(d*x^2+c)/d-1/105*sqrt(a)*(8*a^3*d^3*D-a^2*b*d^2*(14*C*d-9*D*c)-a*b^2*d*(-35*B*d^2+21*C*c*d-16*D*c^2)+b^3*(105*A*d^3-70*B*c*d^2+56*C*c^2*d-48*D*c^3))*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))+1/105*a^(3/2)*(4*a^2*c*d^2*D-a*b*c*d*(7*C*d-5*D*c)+b^2*(105*A*d^3-35*B*c*d^2+28*C*c^2*d-24*D*c^3))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(5/2)/c/d^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^6+C*x^4+B*x^2+A)/(d*x^2+c)^(3/2),x,4,-1/15*(2*a^2*d^2*D-a*b*d*(5*C*d-7*D*c)+b^2*(-15*B*d^2+20*C*c*d-24*D*c^2))*x*sqrt(b*x^2+a)/b^2/d^3/sqrt(d*x^2+c)+1/15*(5*C*b*d+D*a*d-6*D*b*c)*x^3*sqrt(b*x^2+a)/b/d^2/sqrt(d*x^2+c)+1/5*D*x^5*sqrt(b*x^2+a)/d/sqrt(d*x^2+c)+1/15*(2*a^2*c*d^2*D-a*b*c*d*(5*C*d-8*D*c)+b^2*(15*A*d^3-30*B*c*d^2+40*C*c^2*d-48*D*c^3))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/b^2/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)*(a*c*d*D+b*(-15*B*d^2+20*C*c*d-24*D*c^2))*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/b/d^(7/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[sqrt(b*x^2+a)*(D*x^6+C*x^4+B*x^2+A)/(d*x^2+c)^(5/2),x,4,1/3*(A*d^3-B*c*d^2+C*c^2*d-2*D*c^3)*x*sqrt(b*x^2+a)/c/d^3/(d*x^2+c)^(3/2)+1/3*D*x^5*sqrt(b*x^2+a)/d/(d*x^2+c)^(3/2)+1/3*(3*C*b*d+D*a*d-6*D*b*c)*x*sqrt(b*x^2+a)/b/d^3/sqrt(d*x^2+c)+1/3*(a^2*c^2*d^2*D+a*b*d*(-2*A*d^3-B*c*d^2+7*C*c^2*d-16*D*c^3)-b^2*c*(-A*d^3-2*B*c*d^2+8*C*c^2*d-16*D*c^3))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/b/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)-1/3*(a*c*d*(3*C*d-7*D*c)-b*(A*d^3-B*c*d^2+4*C*c^2*d-8*D*c^3))*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/sqrt(c)/d^(7/2)/(-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)*(D*x^6+C*x^4+B*x^2+A)/(d*x^2+c)^(7/2),x,4,1/5*(A*d^3-B*c*d^2+C*c^2*d-6*D*c^3)*x*sqrt(b*x^2+a)/c/d^3/(d*x^2+c)^(5/2)+D*x^5*sqrt(b*x^2+a)/d/(d*x^2+c)^(5/2)-1/15*(b*c*(-3*A*d^3-2*B*c*d^2+7*C*c^2*d-42*D*c^3)-a*d*(-4*A*d^3-B*c*d^2+6*C*c^2*d-41*D*c^3))*x*sqrt(b*x^2+a)/c^2/d^3/(-a*d+b*c)/(d*x^2+c)^(3/2)-1/15*(a*b*c*d*(13*A*d^3+2*B*c*d^2+13*C*c^2*d-88*D*c^3)-b^2*c^2*(3*A*d^3+2*B*c*d^2+8*C*c^2*d-48*D*c^3)-a^2*d^2*(8*A*d^3+2*B*c*d^2+3*C*c^2*d-38*D*c^3))*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)^2/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+1/15*(15*a^2*c^2*d^2*D+a*b*d*(-4*A*d^3-B*c*d^2+6*C*c^2*d-41*D*c^3)-b^2*c*(-6*A*d^3+B*c*d^2+4*C*c^2*d-24*D*c^3))*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)^2/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[sqrt(b*x^2+a)*(D*x^6+C*x^4+B*x^2+A)/(d*x^2+c)^(9/2),x,5,1/7*(A*d^3-B*c*d^2+C*c^2*d+6*D*c^3)*x*sqrt(b*x^2+a)/c/d^3/(d*x^2+c)^(7/2)-D*x^5*sqrt(b*x^2+a)/d/(d*x^2+c)^(7/2)-1/35*(b*c*(-5*A*d^3-2*B*c*d^2+9*C*c^2*d+54*D*c^3)-a*d*(-6*A*d^3-B*c*d^2+8*C*c^2*d+55*D*c^3))*x*sqrt(b*x^2+a)/c^2/d^3/(-a*d+b*c)/(d*x^2+c)^(5/2)+1/105*(b^2*c^2*(15*A*d^3+6*B*c*d^2+8*C*c^2*d+48*D*c^3)+a^2*d^2*(24*A*d^3+4*B*c*d^2+3*C*c^2*d+60*D*c^3)-a*b*c*d*(43*A*d^3+6*B*c*d^2+15*C*c^2*d+104*D*c^3))*x*sqrt(b*x^2+a)/c^3/d^3/(-a*d+b*c)^2/(d*x^2+c)^(3/2)-1/105*(a^3*d^3*(48*A*d^3+8*B*c*d^2+6*C*c^2*d+15*D*c^3)-b^3*c^3*(15*A*d^3+6*B*c*d^2+8*C*c^2*d+48*D*c^3)-a^2*b*c*d^2*(128*A*d^3+19*B*c*d^2+9*C*c^2*d+103*D*c^3)+a*b^2*c^2*d*(103*A*d^3+9*B*c*d^2+19*C*c^2*d+128*D*c^3))*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)^3/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+1/105*b*(a^2*d^2*(24*A*d^3+4*B*c*d^2+3*C*c^2*d-45*D*c^3)-b^2*c^2*(-45*A*d^3+3*B*c*d^2+4*C*c^2*d+24*D*c^3)+a*b*c*d*(-61*A*d^3-9*B*c*d^2+9*C*c^2*d+61*D*c^3))*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)^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)*(D*x^6+C*x^4+B*x^2+A),x,9,-1/3465*(48*a^5*d^5*D-8*a^4*b*d^4*(11*C*d+4*D*c)+a^3*b^2*d^3*(198*B*d^2+77*C*c*d-29*D*c^2)-a*b^4*c*d*(1617*A*d^3-627*B*c*d^2+352*C*c^2*d-232*D*c^3)+2*b^5*c^2*(231*A*d^3-132*B*c*d^2+88*C*c^2*d-64*D*c^3)+3*a^2*b^3*d^2*(-231*A*d^3-99*B*c*d^2+33*C*c^2*d-17*D*c^3))*x*sqrt(d*x^2+c)/b^3/d^5/sqrt(b*x^2+a)+1/3465*(24*a^4*d^4*D-a^3*b*d^3*(44*C*d+13*D*c)+3*a^2*b^2*d^2*(33*B*d^2+11*C*c*d-5*D*c^2)+b^4*c*(231*A*d^3-132*B*c*d^2+88*C*c^2*d-64*D*c^3)-3*a*b^3*d*(-462*A*d^3-99*B*c*d^2+55*C*c^2*d-36*D*c^3))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b^3/d^4-1/3465*(18*a^3*d^3*D-3*a^2*b*d^2*(11*C*d+3*D*c)-a*b^2*d*(792*B*d^2+121*C*c*d-79*D*c^2)+b^3*(-693*A*d^3-99*B*c*d^2+66*C*c^2*d-48*D*c^3))*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b^2/d^3+1/693*(3*a^2*d^2*D+a*b*d*(110*C*d+13*D*c)+b^2*(99*B*d^2+11*C*c*d-8*D*c^2))*x^5*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b/d^2+1/99*(11*C*b*d+12*D*a*d+D*b*c)*x^7*sqrt(b*x^2+a)*sqrt(d*x^2+c)/d+1/11*b*D*x^9*sqrt(b*x^2+a)*sqrt(d*x^2+c)+1/3465*sqrt(a)*(48*a^5*d^5*D-8*a^4*b*d^4*(11*C*d+4*D*c)+a^3*b^2*d^3*(198*B*d^2+77*C*c*d-29*D*c^2)-a*b^4*c*d*(1617*A*d^3-627*B*c*d^2+352*C*c^2*d-232*D*c^3)+2*b^5*c^2*(231*A*d^3-132*B*c*d^2+88*C*c^2*d-64*D*c^3)+3*a^2*b^3*d^2*(-231*A*d^3-99*B*c*d^2+33*C*c^2*d-17*D*c^3))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/b^(7/2)/d^5/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/3465*a^(3/2)*(24*a^4*d^4*D-a^3*b*d^3*(44*C*d+13*D*c)+3*a^2*b^2*d^2*(33*B*d^2+11*C*c*d-5*D*c^2)+b^4*c*(231*A*d^3-132*B*c*d^2+88*C*c^2*d-64*D*c^3)-3*a*b^3*d*(693*A*d^3-99*B*c*d^2+55*C*c^2*d-36*D*c^3))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(7/2)/d^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^6+C*x^4+B*x^2+A)/sqrt(d*x^2+c),x,8,1/315*(8*a^4*d^4*D-a^3*b*d^3*(18*C*d-11*D*c)-9*a^2*b^2*d^2*(-7*B*d^2+4*C*c*d-3*D*c^2)+a*b^3*d*(420*A*d^3-273*B*c*d^2+216*C*c^2*d-184*D*c^3)-2*b^4*c*(105*A*d^3-84*B*c*d^2+72*C*c^2*d-64*D*c^3))*x*sqrt(d*x^2+c)/b^2/d^5/sqrt(b*x^2+a)-1/315*(4*a^3*d^3*D-3*a^2*b*d^2*(3*C*d-2*D*c)+3*a*b^2*d*(-42*B*d^2+33*C*c*d-28*D*c^2)-b^3*(105*A*d^3-84*B*c*d^2+72*C*c^2*d-64*D*c^3))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b^2/d^4+1/315*(3*a^2*d^2*D+a*b*d*(72*C*d-61*D*c)-b^2*(-63*B*d^2+54*C*c*d-48*D*c^2))*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b/d^3+1/63*(9*C*b*d+10*D*a*d-8*D*b*c)*x^5*sqrt(b*x^2+a)*sqrt(d*x^2+c)/d^2+1/9*b*D*x^7*sqrt(b*x^2+a)*sqrt(d*x^2+c)/d-1/315*sqrt(a)*(8*a^4*d^4*D-a^3*b*d^3*(18*C*d-11*D*c)-9*a^2*b^2*d^2*(-7*B*d^2+4*C*c*d-3*D*c^2)+a*b^3*d*(420*A*d^3-273*B*c*d^2+216*C*c^2*d-184*D*c^3)-2*b^4*c*(105*A*d^3-84*B*c*d^2+72*C*c^2*d-64*D*c^3))*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))+1/315*a^(3/2)*(4*a^3*c*d^3*D-3*a^2*b*c*d^2*(3*C*d-2*D*c)-b^3*c*(105*A*d^3-84*B*c*d^2+72*C*c^2*d-64*D*c^3)+3*a*b^2*d*(105*A*d^3-42*B*c*d^2+33*C*c^2*d-28*D*c^3))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(5/2)/c/d^4/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(b*x^2+a)^(3/2)*(D*x^6+C*x^4+B*x^2+A)/(d*x^2+c)^(3/2),x,5,-1/105*(6*a^3*d^3*D-3*a^2*b*d^2*(7*C*d-10*D*c)+a*b^2*d*(-140*B*d^2+189*C*c*d-228*D*c^2)-b^3*(105*A*d^3-140*B*c*d^2+168*C*c^2*d-192*D*c^3))*x*sqrt(b*x^2+a)/b^2/d^4/sqrt(d*x^2+c)+1/105*(3*a^2*d^2*D+3*a*b*d*(14*C*d-17*D*c)-b^2*(-35*B*d^2+42*C*c*d-48*D*c^2))*x^3*sqrt(b*x^2+a)/b/d^3/sqrt(d*x^2+c)+1/35*(7*C*b*d+8*D*a*d-8*D*b*c)*x^5*sqrt(b*x^2+a)/d^2/sqrt(d*x^2+c)+1/7*b*D*x^7*sqrt(b*x^2+a)/d/sqrt(d*x^2+c)+1/105*(6*a^3*c*d^3*D-3*a^2*b*c*d^2*(7*C*d-11*D*c)+a*b^2*d*(105*A*d^3-245*B*c*d^2+336*C*c^2*d-408*D*c^3)-2*b^3*c*(105*A*d^3-140*B*c*d^2+168*C*c^2*d-192*D*c^3))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/b^2/sqrt(c)/d^(9/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-1/105*sqrt(c)*(3*a^2*c*d^2*D+3*a*b*d*(-35*B*d^2+49*C*c*d-60*D*c^2)-b^2*(105*A*d^3-140*B*c*d^2+168*C*c^2*d-192*D*c^3))*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/b/d^(9/2)/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^6+C*x^4+B*x^2+A)/(d*x^2+c)^(5/2),x,5,-1/15*(b*c*(5*A*d^3-5*B*c*d^2+5*C*c^2*d-8*D*c^3)-5*a*d*(A*d^3-B*c*d^2+C*c^2*d-D*c^3))*x*sqrt(b*x^2+a)/c/d^4/(d*x^2+c)^(3/2)+1/5*b*D*x^7*sqrt(b*x^2+a)/d/(d*x^2+c)^(3/2)+1/15*(3*a^2*d^2*D+a*b*d*(20*C*d-47*D*c)-b^2*(-15*B*d^2+35*C*c*d-56*D*c^2))*x*sqrt(b*x^2+a)/b/d^4/sqrt(d*x^2+c)+1/15*(5*C*b*d+6*D*a*d-8*D*b*c)*x^3*sqrt(b*x^2+a)/d^3/sqrt(d*x^2+c)-1/15*(3*a^2*c^2*d^2*D+a*b*d*(-10*A*d^3-5*B*c*d^2+40*C*c^2*d-88*D*c^3)-2*b^2*c*(5*A*d^3-20*B*c*d^2+40*C*c^2*d-64*D*c^3))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/b/c^(3/2)/d^(9/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+1/15*(3*a*c*d*(5*C*d-12*D*c)-b*(5*A*d^3-20*B*c*d^2+40*C*c^2*d-64*D*c^3))*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)^(3/2)*(D*x^6+C*x^4+B*x^2+A)/(d*x^2+c)^(7/2),x,5,-1/15*(b*c*(3*A*d^3-3*B*c*d^2+3*C*c^2*d-8*D*c^3)-3*a*d*(A*d^3-B*c*d^2+C*c^2*d-D*c^3))*x*sqrt(b*x^2+a)/c/d^4/(d*x^2+c)^(5/2)+1/3*b*D*x^7*sqrt(b*x^2+a)/d/(d*x^2+c)^(5/2)+1/15*(b*c*(2*A*d^3-7*B*c*d^2+12*C*c^2*d-32*D*c^3)-a*d*(-4*A*d^3-B*c*d^2+6*C*c^2*d-11*D*c^3))*x*sqrt(b*x^2+a)/c^2/d^4/(d*x^2+c)^(3/2)+1/3*(3*C*b*d+4*D*a*d-8*D*b*c)*x*sqrt(b*x^2+a)/d^4/sqrt(d*x^2+c)-1/15*(2*b^2*c^2*(-A*d^3-4*B*c*d^2+24*C*c^2*d-64*D*c^3)-3*a*b*c*d*(A*d^3-B*c*d^2+16*C*c^2*d-56*D*c^3)+a^2*d^2*(8*A*d^3+2*B*c*d^2+3*C*c^2*d-43*D*c^3))*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)/(-a*d+b*c)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-1/15*(15*a^2*c^2*d^2*D+a*b*d*(-4*A*d^3-B*c*d^2+21*C*c^2*d-76*D*c^3)-b^2*c*(-A*d^3-4*B*c*d^2+24*C*c^2*d-64*D*c^3))*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/c^(3/2)/d^(9/2)/(-a*d+b*c)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[(b*x^2+a)^(3/2)*(D*x^6+C*x^4+B*x^2+A)/(d*x^2+c)^(9/2),x,5,-1/7*(b*c*(A*d^3-B*c*d^2+C*c^2*d-8*D*c^3)-a*d*(A*d^3-B*c*d^2+C*c^2*d-D*c^3))*x*sqrt(b*x^2+a)/c/d^4/(d*x^2+c)^(7/2)+b*D*x^7*sqrt(b*x^2+a)/d/(d*x^2+c)^(7/2)+1/35*(b*c*(2*A*d^3-9*B*c*d^2+16*C*c^2*d-128*D*c^3)-a*d*(-6*A*d^3-B*c*d^2+8*C*c^2*d-15*D*c^3))*x*sqrt(b*x^2+a)/c^2/d^4/(d*x^2+c)^(5/2)+1/105*(a*b*c*d*(15*A*d^3-B*c*d^2+57*C*c^2*d-498*D*c^3)-b^2*c^2*(-6*A*d^3-8*B*c*d^2+57*C*c^2*d-456*D*c^3)-a^2*d^2*(24*A*d^3+4*B*c*d^2+3*C*c^2*d-45*D*c^3))*x*sqrt(b*x^2+a)/c^3/d^4/(-a*d+b*c)/(d*x^2+c)^(3/2)-1/105*(a*b^2*c^2*d*(-12*A*d^3+5*B*c*d^2+72*C*c^2*d-744*D*c^3)-a^2*b*c*d^2*(-72*A*d^3-5*B*c*d^2+12*C*c^2*d-369*D*c^3)-2*b^3*c^3*(3*A*d^3+4*B*c*d^2+24*C*c^2*d-192*D*c^3)-a^3*d^3*(48*A*d^3+8*B*c*d^2+6*C*c^2*d+15*D*c^3))*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)^2/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+1/105*b*(a*b*c*d*(33*A*d^3+2*B*c*d^2+33*C*c^2*d-348*D*c^3)-b^2*c^2*(3*A*d^3+4*B*c*d^2+24*C*c^2*d-192*D*c^3)-a^2*d^2*(24*A*d^3+4*B*c*d^2+3*C*c^2*d-150*D*c^3))*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)^2/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[(d*x^2+c)^(3/2)*(D*x^6+C*x^4+B*x^2+A)/sqrt(b*x^2+a),x,8,1/315*(128*a^4*d^4*D-8*a^3*b*d^3*(18*C*d+23*D*c)+3*a^2*b^2*d^2*(56*B*d^2+72*C*c*d+9*D*c^2)-a*b^3*d*(210*A*d^3+273*B*c*d^2+36*C*c^2*d-11*D*c^3)-b^4*c*(-420*A*d^3-63*B*c*d^2+18*C*c^2*d-8*D*c^3))*x*sqrt(d*x^2+c)/b^4/d^3/sqrt(b*x^2+a)-1/315*(64*a^3*d^3*D-12*a^2*b*d^2*(6*C*d+7*D*c)+3*a*b^2*d*(28*B*d^2+33*C*c*d+2*D*c^2)-b^3*(105*A*d^3+126*B*c*d^2+9*C*c^2*d-4*D*c^3))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b^4/d^2+1/315*(48*a^2*d^2*D-a*b*d*(54*C*d+61*D*c)+3*b^2*(21*B*d^2+24*C*c*d+D*c^2))*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b^3/d+1/63*(9*C*b*d-8*D*a*d+10*D*b*c)*x^5*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b^2+1/9*d*D*x^7*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b-1/315*sqrt(a)*(128*a^4*d^4*D-8*a^3*b*d^3*(18*C*d+23*D*c)+3*a^2*b^2*d^2*(56*B*d^2+72*C*c*d+9*D*c^2)-a*b^3*d*(210*A*d^3+273*B*c*d^2+36*C*c^2*d-11*D*c^3)-b^4*c*(-420*A*d^3-63*B*c*d^2+18*C*c^2*d-8*D*c^3))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/b^(9/2)/d^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/315*sqrt(a)*(315*A*b^4*c*d^2+64*a^4*d^3*D-12*a^3*b*d^2*(6*C*d+7*D*c)+3*a^2*b^2*d*(28*B*d^2+33*C*c*d+2*D*c^2)-a*b^3*(105*A*d^3+126*B*c*d^2+9*C*c^2*d-4*D*c^3))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(9/2)/d^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[sqrt(d*x^2+c)*(D*x^6+C*x^4+B*x^2+A)/sqrt(b*x^2+a),x,7,-1/105*(48*a^3*d^3*D-8*a^2*b*d^2*(7*C*d+2*D*c)+a*b^2*d*(70*B*d^2+21*C*c*d-9*D*c^2)+b^3*(-105*A*d^3-35*B*c*d^2+14*C*c^2*d-8*D*c^3))*x*sqrt(d*x^2+c)/b^3/d^3/sqrt(b*x^2+a)+1/105*(24*a^2*d^2*D-a*b*d*(28*C*d+5*D*c)+b^2*(35*B*d^2+7*C*c*d-4*D*c^2))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b^3/d^2+1/35*(7*C*b*d-6*D*a*d+D*b*c)*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b^2/d+1/7*D*x^5*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b+1/105*sqrt(a)*(48*a^3*d^3*D-8*a^2*b*d^2*(7*C*d+2*D*c)+a*b^2*d*(70*B*d^2+21*C*c*d-9*D*c^2)+b^3*(-105*A*d^3-35*B*c*d^2+14*C*c^2*d-8*D*c^3))*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))+1/105*sqrt(a)*(105*A*b^3*d^2-24*a^3*d^2*D+a^2*b*d*(28*C*d+5*D*c)-a*b^2*(35*B*d^2+7*C*c*d-4*D*c^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],
[(D*x^6+C*x^4+B*x^2+A)/sqrt(b*x^2+a)/sqrt(d*x^2+c),x,6,1/15*(8*a^2*d^2*D-a*b*d*(10*C*d-7*D*c)-b^2*(-15*B*d^2+10*C*c*d-8*D*c^2))*x*sqrt(d*x^2+c)/b^2/d^3/sqrt(b*x^2+a)+1/15*(5*C*b*d-4*D*a*d-4*D*b*c)*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b^2/d^2+1/5*D*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b/d-1/15*sqrt(a)*(8*a^2*d^2*D-a*b*d*(10*C*d-7*D*c)-b^2*(-15*B*d^2+10*C*c*d-8*D*c^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))+1/15*sqrt(a)*(15*A*b^2*d^2+4*a^2*c*d*D-a*b*c*(5*C*d-4*D*c))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(5/2)/c/d^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(D*x^6+C*x^4+B*x^2+A)/sqrt(b*x^2+a)/(d*x^2+c)^(3/2),x,3,1/3*(3*C*b*d-2*D*a*d-4*D*b*c)*x*sqrt(b*x^2+a)/b^2/d^2/sqrt(d*x^2+c)+1/3*D*x^3*sqrt(b*x^2+a)/b/d/sqrt(d*x^2+c)-1/3*(2*a^2*c*d^2*D-3*a*b*c*d*(C*d-D*c)+b^2*(3*A*d^3-3*B*c*d^2+6*C*c^2*d-8*D*c^3))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/b^2/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)+1/3*sqrt(c)*(3*A*b^2*d^2+a^2*c*d*D+a*b*(-3*B*d^2+3*C*c*d-4*D*c^2))*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a/b/d^(5/2)/(-a*d+b*c)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[(D*x^6+C*x^4+B*x^2+A)/sqrt(b*x^2+a)/(d*x^2+c)^(5/2),x,3,-1/3*(A*d^3-B*c*d^2+C*c^2*d-D*c^3)*x*sqrt(b*x^2+a)/c/d^2/(-a*d+b*c)/(d*x^2+c)^(3/2)+D*x*sqrt(b*x^2+a)/b/d^2/sqrt(d*x^2+c)-1/3*(3*a^2*c^2*d^2*D+a*b*d*(-2*A*d^3-B*c*d^2+4*C*c^2*d-13*D*c^3)-b^2*c*(-4*A*d^3+B*c*d^2+2*C*c^2*d-8*D*c^3))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/b/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)+1/3*(3*A*b^2*c*d^2+3*a^2*c*d*(C*d-2*D*c)-a*b*(A*d^3+2*B*c*d^2+C*c^2*d-4*D*c^3))*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a/sqrt(c)/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],
[(D*x^6+C*x^4+B*x^2+A)/sqrt(b*x^2+a)/(d*x^2+c)^(7/2),x,3,-1/5*(A*d^3-B*c*d^2+C*c^2*d-D*c^3)*x*sqrt(b*x^2+a)/c/d^2/(-a*d+b*c)/(d*x^2+c)^(5/2)-1/15*(a*d*(-4*A*d^3-B*c*d^2+6*C*c^2*d-11*D*c^3)-b*c*(-8*A*d^3+3*B*c*d^2+2*C*c^2*d-7*D*c^3))*x*sqrt(b*x^2+a)/c^2/d^2/(-a*d+b*c)^2/(d*x^2+c)^(3/2)-1/15*(a^2*d^2*(8*A*d^3+2*B*c*d^2+3*C*c^2*d-23*D*c^3)-b^2*c^2*(-23*A*d^3+3*B*c*d^2+2*C*c^2*d+8*D*c^3)+a*b*c*d*(-23*A*d^3-7*B*c*d^2+7*C*c^2*d+23*D*c^3))*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)^3/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+1/15*(15*A*b^3*c^2*d^2-15*a^3*c^2*d^2*D-a*b^2*c*(11*A*d^3+9*B*c*d^2+C*c^2*d+4*D*c^3)+a^2*b*d*(4*A*d^3+B*c*d^2+9*C*c^2*d+11*D*c^3))*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a/c^(3/2)/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],
[(d*x^2+c)^(3/2)*(D*x^6+C*x^4+B*x^2+A)/(b*x^2+a)^(3/2),x,5,-1/105*(192*a^3*d^3*D-12*a^2*b*d^2*(14*C*d+19*D*c)+a*b^2*d*(140*B*d^2+189*C*c*d+30*D*c^2)-b^3*(105*A*d^3+140*B*c*d^2+21*C*c^2*d-6*D*c^3))*x*sqrt(d*x^2+c)/b^4/d^2/sqrt(b*x^2+a)+1/105*(48*a^2*d^2*D-3*a*b*d*(14*C*d+17*D*c)+b^2*(35*B*d^2+42*C*c*d+3*D*c^2))*x^3*sqrt(d*x^2+c)/b^3/d/sqrt(b*x^2+a)+1/35*(7*C*b*d-8*D*a*d+8*D*b*c)*x^5*sqrt(d*x^2+c)/b^2/sqrt(b*x^2+a)+1/7*d*D*x^7*sqrt(d*x^2+c)/b/sqrt(b*x^2+a)+1/105*(105*A*b^4*c*d^2+384*a^4*d^3*D-24*a^3*b*d^2*(14*C*d+17*D*c)+a^2*b^2*d*(280*B*d^2+336*C*c*d+33*D*c^2)-a*b^3*(210*A*d^3+245*B*c*d^2+21*C*c^2*d-6*D*c^3))*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^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/105*sqrt(a)*(105*b^3*d*(A*d+B*c)-192*a^3*d^2*D+12*a^2*b*d*(14*C*d+15*D*c)-a*b^2*(140*B*d^2+147*C*c*d+3*D*c^2))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(9/2)/d/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[sqrt(d*x^2+c)*(D*x^6+C*x^4+B*x^2+A)/(b*x^2+a)^(3/2),x,4,1/15*(24*a^2*d^2*D-a*b*d*(20*C*d+7*D*c)+b^2*(15*B*d^2+5*C*c*d-2*D*c^2))*x*sqrt(d*x^2+c)/b^3/d^2/sqrt(b*x^2+a)+1/15*(5*C*b*d-6*D*a*d+D*b*c)*x^3*sqrt(d*x^2+c)/b^2/d/sqrt(b*x^2+a)+1/5*D*x^5*sqrt(d*x^2+c)/b/sqrt(b*x^2+a)+1/15*(15*A*b^3*d^2-48*a^3*d^2*D+8*a^2*b*d*(5*C*d+D*c)-a*b^2*(30*B*d^2+5*C*c*d-2*D*c^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^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/15*sqrt(a)*(15*b^2*B*d+24*a^2*d*D-a*b*(20*C*d+D*c))*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],
[(D*x^6+C*x^4+B*x^2+A)/(b*x^2+a)^(3/2)/sqrt(d*x^2+c),x,3,1/3*(3*C*b*d-4*D*a*d-2*D*b*c)*x*sqrt(d*x^2+c)/b^2/d^2/sqrt(b*x^2+a)+1/3*D*x^3*sqrt(d*x^2+c)/b/d/sqrt(b*x^2+a)+1/3*(3*A*b^3*d^2-8*a^3*d^2*D+3*a^2*b*d*(2*C*d+D*c)-a*b^2*(3*B*d^2+3*C*c*d-2*D*c^2))*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^2/(-a*d+b*c)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/3*sqrt(a)*(3*b^2*d*(-A*d+B*c)+4*a^2*c*d*D-a*b*c*(3*C*d+D*c))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(5/2)/c/d/(-a*d+b*c)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(D*x^6+C*x^4+B*x^2+A)/(b*x^2+a)^(3/2)/(d*x^2+c)^(3/2),x,3,(A*b^3-a*(B*b^2-C*a*b+D*a^2))*x/a/b^2/(-a*d+b*c)/sqrt(b*x^2+a)/sqrt(d*x^2+c)+D*x*sqrt(b*x^2+a)/b^2/d/sqrt(d*x^2+c)+(A*b^3*c*d^2-2*a^3*c*d^2*D+a^2*b*c*d*(C*d+2*D*c)+a*b^2*(A*d^3-2*B*c*d^2+C*c^2*d-2*D*c^3))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/a/b^2/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)+sqrt(c)*(b^2*d*(-2*A*d+B*c)+a^2*c*d*D-a*b*(-B*d^2+2*C*c*d-D*c^2))*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a/b/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],
[(D*x^6+C*x^4+B*x^2+A)/(b*x^2+a)^(3/2)/(d*x^2+c)^(5/2),x,3,(A*b^3-a*(B*b^2-C*a*b+D*a^2))*x/a/b^2/(-a*d+b*c)/sqrt(b*x^2+a)/(d*x^2+c)^(3/2)+1/3*(3*A*b^3*c*d^2+3*a^2*b*c*C*d^2-3*a^3*c*d^2*D+a*b^2*(A*d^3-4*B*c*d^2+C*c^2*d-D*c^3))*x*sqrt(b*x^2+a)/a/b^2/c/d/(-a*d+b*c)^2/(d*x^2+c)^(3/2)+1/3*(3*A*b^3*c^2*d^2-3*a^3*c^2*d^2*D+a^2*b*d*(-2*A*d^3-B*c*d^2+7*C*c^2*d-7*D*c^3)+a*b^2*c*(7*A*d^3-7*B*c*d^2+C*c^2*d+2*D*c^3))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/a/b/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)+1/3*(3*b^2*c*d*(-3*A*d+B*c)-3*a^2*c*d*(C*d-3*D*c)-a*b*(-A*d^3-5*B*c*d^2+5*C*c^2*d+D*c^3))*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)^3/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[(d*x^2+c)^(3/2)*(D*x^6+C*x^4+B*x^2+A)/(b*x^2+a)^(5/2),x,5,1/15*(5*A*b*c/a-5*A*d-5*B*c+5*a*(B*d+C*c)/b+8*a^3*d*D/b^3-5*a^2*(C*d+D*c)/b^2)*x*sqrt(d*x^2+c)/b/(b*x^2+a)^(3/2)+1/5*d*D*x^7*sqrt(d*x^2+c)/b/(b*x^2+a)^(3/2)+1/15*(56*a^2*d^2*D-a*b*d*(35*C*d+47*D*c)+b^2*(15*B*d^2+20*C*c*d+3*D*c^2))*x*sqrt(d*x^2+c)/b^4/d/sqrt(b*x^2+a)+1/15*(5*C*b*d-8*D*a*d+6*D*b*c)*x^3*sqrt(d*x^2+c)/b^3/sqrt(b*x^2+a)+1/15*(10*A*b^3*d*(a*d+b*c)+a*(5*b^3*B*c*d-128*a^3*d^2*D+8*a^2*b*d*(10*C*d+11*D*c)-a*b^2*(40*B*d^2+40*C*c*d+3*D*c^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)/d/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/15*(5*A*b^3*d-5*a*b^2*(4*B*d+3*C*c)-64*a^3*d*D+4*a^2*b*(10*C*d+9*D*c))*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],
[sqrt(d*x^2+c)*(D*x^6+C*x^4+B*x^2+A)/(b*x^2+a)^(5/2),x,4,1/3*(A/a-(B*b^2-C*a*b+2*D*a^2)/b^3)*x*sqrt(d*x^2+c)/(b*x^2+a)^(3/2)+1/3*D*x^5*sqrt(d*x^2+c)/b/(b*x^2+a)^(3/2)+1/3*(3*C*b*d-6*D*a*d+D*b*c)*x*sqrt(d*x^2+c)/b^3/d/sqrt(b*x^2+a)+1/3*(A*b^3*d*(-a*d+2*b*c)+a*(b^3*B*c*d-16*a^3*d^2*D+8*a^2*b*d*(C*d+2*D*c)-a*b^2*(2*B*d^2+7*C*c*d+D*c^2)))*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)/d/(-a*d+b*c)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/3*(A*b^3*d-a*b^2*(B*d+3*C*c)-8*a^3*d*D+a^2*b*(4*C*d+7*D*c))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(a)/b^(7/2)/(-a*d+b*c)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(D*x^6+C*x^4+B*x^2+A)/(b*x^2+a)^(5/2)/sqrt(d*x^2+c),x,3,1/3*(A*b^3-a*(B*b^2-C*a*b+D*a^2))*x*sqrt(d*x^2+c)/a/b^2/(-a*d+b*c)/(b*x^2+a)^(3/2)+D*x*sqrt(d*x^2+c)/b^2/d/sqrt(b*x^2+a)+1/3*(2*A*b^3*d*(-2*a*d+b*c)+a*(b^3*B*c*d-8*a^3*d^2*D+a^2*b*d*(2*C*d+13*D*c)-a*b^2*(-B*d^2+4*C*c*d+3*D*c^2)))*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)/d/(-a*d+b*c)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/3*(A*b^3*c*d-a*b^2*(3*A*d^2-2*B*c*d+3*C*c^2)-4*a^3*c*d*D+a^2*b*c*(C*d+6*D*c))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(a)/b^(5/2)/c/(-a*d+b*c)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(D*x^6+C*x^4+B*x^2+A)/(b*x^2+a)^(5/2)/(d*x^2+c)^(3/2),x,3,1/3*(A*b^3-a*(B*b^2-C*a*b+D*a^2))*x/a/b^2/(-a*d+b*c)/(b*x^2+a)^(3/2)/sqrt(d*x^2+c)+1/3*(2*A*b^3*(-3*a*d+b*c)+a*(b^3*B*c-a*b^2*(-3*B*d+4*C*c)+7*a^2*b*c*D-3*a^3*d*D))*x/a^2/b^2/(-a*d+b*c)^2/sqrt(b*x^2+a)/sqrt(d*x^2+c)+1/3*(A*b^2*d*(-3*a^2*d^2-7*a*b*c*d+2*b^2*c^2)+a*c*(b^3*B*c*d-2*a^3*d^2*D-a^2*b*d*(C*d-7*D*c)-a*b^2*(-7*B*d^2+7*C*c*d-3*D*c^2)))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/a^2/b^2/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)-1/3*sqrt(c)*(A*b^3*c*d-a*b^2*(9*A*d^2-5*B*c*d+3*C*c^2)-a^3*c*d*D-a^2*b*(-3*B*d^2+5*C*c*d-9*D*c^2))*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a^2/b/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^6+C*x^4+B*x^2+A)/(b*x^2+a)^(5/2)/(d*x^2+c)^(5/2),x,4,1/3*(A*b^3-a*(B*b^2-C*a*b+D*a^2))*x/a/b^2/(-a*d+b*c)/(b*x^2+a)^(3/2)/(d*x^2+c)^(3/2)+1/3*(2*A*b^3*(-4*a*d+b*c)+a*(b^3*B*c-a*b^2*(-5*B*d+4*C*c)-a^3*d*D-a^2*b*(2*C*d-7*D*c)))*x/a^2/b^2/(-a*d+b*c)^2/sqrt(b*x^2+a)/(d*x^2+c)^(3/2)+1/3*(A*b*d*(-a^2*d^2-9*a*b*c*d+2*b^2*c^2)+a*c*(b^2*B*c*d-a^2*d*(3*C*d-7*D*c)-a*b*(-7*B*d^2+5*C*c*d-D*c^2)))*x*sqrt(b*x^2+a)/a^2/b/c/(-a*d+b*c)^3/(d*x^2+c)^(3/2)+1/3*(2*A*b*d*(a^3*d^3-5*a^2*b*c*d^2-5*a*b^2*c^2*d+b^3*c^3)+a*c*(b^3*B*c^2*d+a^3*c*d^2*D-a^2*b*d*(-B*d^2+8*C*c*d-14*D*c^2)-a*b^2*c*(-14*B*d^2+8*C*c*d-D*c^2)))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/a^2/b/c^(3/2)/sqrt(d)/(-a*d+b*c)^4/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-1/3*(A*b^3*c^2*d-a*b^2*c*(18*A*d^2-8*B*c*d+3*C*c^2)-a^3*c*d*(3*C*d-8*D*c)-a^2*b*(-A*d^3-8*B*c*d^2+10*C*c^2*d-8*D*c^3))*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],
[(b*x^2+a)^p*(C*x^4+B*x^2+A)/(d*x^2+c),x,8,C*x*(b*x^2+a)^(p+1)/b/d/(3+2*p)+(A*d^2-B*c*d+C*c^2)*x*(b*x^2+a)^p*AppellF1(1/2,-p,1,3/2,-b*x^2/a,-d*x^2/c)/c/d^2/((1+b*x^2/a)^p)-(c*C-B*d+a*C*d/(2*b*p+3*b))*x*(b*x^2+a)^p*hypergeom([1/2, -p],[3/2],-b*x^2/a)/d^2/((1+b*x^2/a)^p),1],
[(B*x+A)*(b*x^2+a)^p*(d*x^2+c)^q,x,7,A*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)+1/2*B*(b*x^2+a)^(p+1)*(d*x^2+c)^(1+q)*hypergeom([1, 2+p+q],[2+p],-d*(b*x^2+a)/(-a*d+b*c))/(-a*d+b*c)/(p+1),1],
[(b*x^2+a)^p*(C*x^2+A)*(d*x^2+c)^q,x,10,A*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*C*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*(C*x^2+B*x+A)*(d*x^2+c)^q,x,14,A*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*C*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)+1/2*B*(b*x^2+a)^(p+1)*(d*x^2+c)^(1+q)*hypergeom([1, 2+p+q],[2+p],-d*(b*x^2+a)/(-a*d+b*c))/(-a*d+b*c)/(p+1),1],
[(b*x^2+a)^p*(d*x^2+c)^q*(a*A*c+A*(b*c*(3+2*p)+a*d*(3+2*q))*x^2+A*b*d*(5+2*p+2*q)*x^4),x,1,A*x*(b*x^2+a)^(p+1)*(d*x^2+c)^(1+q),1]]: