lst:=[[(b*x^2+1)*(B*x^2+A)/sqrt(-b^2*x^4+1),x,4,-1/3*B*x*sqrt(-b^2*x^4+1)/b+(A*b+B)*EllipticE(sin(arcsin(sqrt(b)*x)),sqrt(-1))/b^(3/2)-2/3*B*InverseJacobiAM(arcsin(sqrt(b)*x),sqrt(-1))/b^(3/2),1],
[sqrt(b*x^2+1)*(B*x^2+A)/sqrt(-b*x^2+1),x,5,-1/3*B*x*sqrt(-b^2*x^4+1)/b+(A*b+B)*EllipticE(sin(arcsin(sqrt(b)*x)),sqrt(-1))/b^(3/2)-2/3*B*InverseJacobiAM(arcsin(sqrt(b)*x),sqrt(-1))/b^(3/2),1],
[(B*x^2+A)/(e*x^2+d)/sqrt(-a*e^2*x^4+a*d^2),x,6,-1/2*(-A*e+B*d)*x*sqrt(-a*e^2*x^4+a*d^2)/a/d^2/e/(e*x^2+d)-1/2*(-A*e+B*d)*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/sqrt(d)/e^(3/2)/sqrt(-a*e^2*x^4+a*d^2)+B*sqrt(d)*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/e^(3/2)/sqrt(-a*e^2*x^4+a*d^2),1],
[(B*x^2+A)/(-e*x^2+d)/sqrt(-a*e^2*x^4+a*d^2),x,6,1/2*(A*e+B*d)*x*sqrt(-a*e^2*x^4+a*d^2)/a/d^2/e/(-e*x^2+d)-1/2*(A*e+B*d)*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/sqrt(d)/e^(3/2)/sqrt(-a*e^2*x^4+a*d^2)+A*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/sqrt(d)/sqrt(e)/sqrt(-a*e^2*x^4+a*d^2),1],
[(B*x^2+A)/sqrt(e*x^2+d)/sqrt(-e^2*x^4+d^2),x,5,B*arctan(sqrt(e)*x*sqrt(e*x^2+d)/sqrt(-e^2*x^4+d^2))/e^(3/2)-(-A*e+B*d)*arctan(sqrt(2)*sqrt(e)*x*sqrt(e*x^2+d)/sqrt(-e^2*x^4+d^2))/sqrt(2)/d/e^(3/2),1],
[(B*x^2+A)/sqrt(-e*x^2+d)/sqrt(-e^2*x^4+d^2),x,5,-B*arctanh(sqrt(e)*x*sqrt(-e*x^2+d)/sqrt(-e^2*x^4+d^2))/e^(3/2)+(A*e+B*d)*arctanh(sqrt(2)*sqrt(e)*x*sqrt(-e*x^2+d)/sqrt(-e^2*x^4+d^2))/sqrt(2)/d/e^(3/2),1],
[(B*x^2+A)/sqrt(e*x^2-d)/sqrt(-e^2*x^4+d^2),x,5,B*arctan(sqrt(e)*x*sqrt(e*x^2-d)/sqrt(-e^2*x^4+d^2))/e^(3/2)-(A*e+B*d)*arctan(sqrt(2)*sqrt(e)*x*sqrt(e*x^2-d)/sqrt(-e^2*x^4+d^2))/sqrt(2)/d/e^(3/2),1],
[(B*x^2+A)/sqrt(-e*x^2-d)/sqrt(-e^2*x^4+d^2),x,5,-B*arctanh(sqrt(e)*x*sqrt(-e*x^2-d)/sqrt(-e^2*x^4+d^2))/e^(3/2)+(-A*e+B*d)*arctanh(sqrt(2)*sqrt(e)*x*sqrt(-e*x^2-d)/sqrt(-e^2*x^4+d^2))/sqrt(2)/d/e^(3/2),1],
[(B*x^2+A)/sqrt(e*x^2+d)/sqrt(e^2*x^4-d^2),x,5,B*arctanh(sqrt(e)*x*sqrt(e*x^2+d)/sqrt(e^2*x^4-d^2))/e^(3/2)-(-A*e+B*d)*arctanh(sqrt(2)*sqrt(e)*x*sqrt(e*x^2+d)/sqrt(e^2*x^4-d^2))/sqrt(2)/d/e^(3/2),1],
[(B*x^2+A)/sqrt(-e*x^2+d)/sqrt(e^2*x^4-d^2),x,5,-B*arctan(sqrt(e)*x*sqrt(-e*x^2+d)/sqrt(e^2*x^4-d^2))/e^(3/2)+(A*e+B*d)*arctan(sqrt(2)*sqrt(e)*x*sqrt(-e*x^2+d)/sqrt(e^2*x^4-d^2))/sqrt(2)/d/e^(3/2),1],
[(B*x^2+A)/sqrt(e*x^2-d)/sqrt(e^2*x^4-d^2),x,5,B*arctanh(sqrt(e)*x*sqrt(e*x^2-d)/sqrt(e^2*x^4-d^2))/e^(3/2)-(A*e+B*d)*arctanh(sqrt(2)*sqrt(e)*x*sqrt(e*x^2-d)/sqrt(e^2*x^4-d^2))/sqrt(2)/d/e^(3/2),1],
[(B*x^2+A)/sqrt(-e*x^2-d)/sqrt(e^2*x^4-d^2),x,5,-B*arctan(sqrt(e)*x*sqrt(-e*x^2-d)/sqrt(e^2*x^4-d^2))/e^(3/2)+(-A*e+B*d)*arctan(sqrt(2)*sqrt(e)*x*sqrt(-e*x^2-d)/sqrt(e^2*x^4-d^2))/sqrt(2)/d/e^(3/2),1],
[(e*x^2+d)^(5/2)*(C*x^4+B*x^2+A)/(c*x^4+a),x,11,1/16*(8*A*c*e^2+14*B*c*d*e-8*C*a*e^2+5*C*c*d^2)*x*sqrt(e*x^2+d)/c^2+1/24*(6*B*e+5*C*d)*x*(e*x^2+d)^(3/2)/c+1/6*C*x*(e*x^2+d)^(5/2)/c+1/2*sqrt(sqrt(a)*e+sqrt(a*e^2+c*d^2))*(d*(B*c*d*(-3*a*e^2+c*d^2)+(A*c-C*a)*e*(-a*e^2+3*c*d^2))-(e-sqrt(a*e^2+c*d^2)/sqrt(a))*(A*c*d*(-3*a*e^2+c*d^2)+a*(a*e^2*(B*e+3*C*d)-c*d^2*(3*B*e+C*d))))*arctan(sqrt(2)*a^(1/4)*sqrt(c)*sqrt(sqrt(a)*e+sqrt(a*e^2+c*d^2))*x*sqrt(e*x^2+d)/(sqrt(a)*(sqrt(a)*e+sqrt(a*e^2+c*d^2))-c*d*x^2))/sqrt(2)/a^(1/4)/c^(5/2)/d/sqrt(a*e^2+c*d^2)-1/16*(8*a*e^2*(2*B*e+5*C*d)-5*c*d*(8*A*e^2+6*B*d*e+C*d^2))*arctanh(sqrt(e)*x/sqrt(e*x^2+d))/c^2/sqrt(e)+1/2*sqrt(-sqrt(a)*e+sqrt(a*e^2+c*d^2))*(d*(B*c*d*(-3*a*e^2+c*d^2)+(A*c-C*a)*e*(-a*e^2+3*c*d^2))-(e+sqrt(a*e^2+c*d^2)/sqrt(a))*(A*c*d*(-3*a*e^2+c*d^2)+a*(a*e^2*(B*e+3*C*d)-c*d^2*(3*B*e+C*d))))*arctanh(sqrt(2)*a^(1/4)*sqrt(c)*sqrt(-sqrt(a)*e+sqrt(a*e^2+c*d^2))*x*sqrt(e*x^2+d)/(sqrt(a)*(sqrt(a)*e-sqrt(a*e^2+c*d^2))-c*d*x^2))/sqrt(2)/a^(1/4)/c^(5/2)/d/sqrt(a*e^2+c*d^2),1],
[(e*x^2+d)^(3/2)*(C*x^4+B*x^2+A)/(c*x^4+a),x,10,1/8*(4*B*e+3*C*d)*x*sqrt(e*x^2+d)/c+1/4*C*x*(e*x^2+d)^(3/2)/c+1/2*sqrt(sqrt(a)*e+sqrt(a*e^2+c*d^2))*(c*d*(2*A*c*d*e-B*a*e^2+B*c*d^2-2*C*a*d*e)-(e-sqrt(a*e^2+c*d^2)/sqrt(a))*(A*c*(-a*e^2+c*d^2)+a*(a*C*e^2-c*d*(2*B*e+C*d))))*arctan(sqrt(2)*a^(1/4)*sqrt(c)*sqrt(sqrt(a)*e+sqrt(a*e^2+c*d^2))*x*sqrt(e*x^2+d)/(sqrt(a)*(sqrt(a)*e+sqrt(a*e^2+c*d^2))-c*d*x^2))/sqrt(2)/a^(1/4)/c^(5/2)/d/sqrt(a*e^2+c*d^2)+1/8*(8*A*c*e^2+12*B*c*d*e-8*C*a*e^2+3*C*c*d^2)*arctanh(sqrt(e)*x/sqrt(e*x^2+d))/c^2/sqrt(e)+1/2*sqrt(-sqrt(a)*e+sqrt(a*e^2+c*d^2))*(c*d*(2*A*c*d*e-B*a*e^2+B*c*d^2-2*C*a*d*e)-(e+sqrt(a*e^2+c*d^2)/sqrt(a))*(A*c*(-a*e^2+c*d^2)+a*(a*C*e^2-c*d*(2*B*e+C*d))))*arctanh(sqrt(2)*a^(1/4)*sqrt(c)*sqrt(-sqrt(a)*e+sqrt(a*e^2+c*d^2))*x*sqrt(e*x^2+d)/(sqrt(a)*(sqrt(a)*e-sqrt(a*e^2+c*d^2))-c*d*x^2))/sqrt(2)/a^(1/4)/c^(5/2)/d/sqrt(a*e^2+c*d^2),1],
[sqrt(e*x^2+d)*(C*x^4+B*x^2+A)/(c*x^4+a),x,9,1/2*C*x*sqrt(e*x^2+d)/c+1/2*sqrt(sqrt(a)*e+sqrt(a*e^2+c*d^2))*(d*(A*c*e+B*c*d-C*a*e)-(A*c*d-a*(B*e+C*d))*(e-sqrt(a*e^2+c*d^2)/sqrt(a)))*arctan(sqrt(2)*a^(1/4)*sqrt(c)*sqrt(sqrt(a)*e+sqrt(a*e^2+c*d^2))*x*sqrt(e*x^2+d)/(sqrt(a)*(sqrt(a)*e+sqrt(a*e^2+c*d^2))-c*d*x^2))/sqrt(2)/a^(1/4)/c^(3/2)/d/sqrt(a*e^2+c*d^2)+1/2*(2*B*e+C*d)*arctanh(sqrt(e)*x/sqrt(e*x^2+d))/c/sqrt(e)+1/2*sqrt(-sqrt(a)*e+sqrt(a*e^2+c*d^2))*(d*(A*c*e+B*c*d-C*a*e)-(A*c*d-a*(B*e+C*d))*(e+sqrt(a*e^2+c*d^2)/sqrt(a)))*arctanh(sqrt(2)*a^(1/4)*sqrt(c)*sqrt(-sqrt(a)*e+sqrt(a*e^2+c*d^2))*x*sqrt(e*x^2+d)/(sqrt(a)*(sqrt(a)*e-sqrt(a*e^2+c*d^2))-c*d*x^2))/sqrt(2)/a^(1/4)/c^(3/2)/d/sqrt(a*e^2+c*d^2),1],
[(C*x^4+B*x^2+A)/sqrt(e*x^2+d)/(c*x^4+a),x,8,1/2*sqrt(sqrt(a)*e+sqrt(a*e^2+c*d^2))*(B*c*d-(A*c-C*a)*(e-sqrt(a*e^2+c*d^2)/sqrt(a)))*arctan(sqrt(2)*a^(1/4)*sqrt(c)*sqrt(sqrt(a)*e+sqrt(a*e^2+c*d^2))*x*sqrt(e*x^2+d)/(sqrt(a)*(sqrt(a)*e+sqrt(a*e^2+c*d^2))-c*d*x^2))/sqrt(2)/a^(1/4)/c^(3/2)/d/sqrt(a*e^2+c*d^2)+C*arctanh(sqrt(e)*x/sqrt(e*x^2+d))/c/sqrt(e)+1/2*sqrt(-sqrt(a)*e+sqrt(a*e^2+c*d^2))*(B*c*d-(A*c-C*a)*(e+sqrt(a*e^2+c*d^2)/sqrt(a)))*arctanh(sqrt(2)*a^(1/4)*sqrt(c)*sqrt(-sqrt(a)*e+sqrt(a*e^2+c*d^2))*x*sqrt(e*x^2+d)/(sqrt(a)*(sqrt(a)*e-sqrt(a*e^2+c*d^2))-c*d*x^2))/sqrt(2)/a^(1/4)/c^(3/2)/d/sqrt(a*e^2+c*d^2),1],
[(C*x^4+B*x^2+A)/(e*x^2+d)^(3/2)/(c*x^4+a),x,6,(A*e^2-B*d*e+C*d^2)*x/d/(a*e^2+c*d^2)/sqrt(e*x^2+d)+1/2*sqrt(sqrt(a)*e+sqrt(a*e^2+c*d^2))*(d*(-A*c*e+B*c*d+C*a*e)-(A*c*d+B*a*e-C*a*d)*(e-sqrt(a*e^2+c*d^2)/sqrt(a)))*arctan(sqrt(2)*a^(1/4)*sqrt(c)*sqrt(sqrt(a)*e+sqrt(a*e^2+c*d^2))*x*sqrt(e*x^2+d)/(sqrt(a)*(sqrt(a)*e+sqrt(a*e^2+c*d^2))-c*d*x^2))/sqrt(2)/a^(1/4)/sqrt(c)/d/(a*e^2+c*d^2)^(3/2)+1/2*sqrt(-sqrt(a)*e+sqrt(a*e^2+c*d^2))*(d*(-A*c*e+B*c*d+C*a*e)-(A*c*d+B*a*e-C*a*d)*(e+sqrt(a*e^2+c*d^2)/sqrt(a)))*arctanh(sqrt(2)*a^(1/4)*sqrt(c)*sqrt(-sqrt(a)*e+sqrt(a*e^2+c*d^2))*x*sqrt(e*x^2+d)/(sqrt(a)*(sqrt(a)*e-sqrt(a*e^2+c*d^2))-c*d*x^2))/sqrt(2)/a^(1/4)/sqrt(c)/d/(a*e^2+c*d^2)^(3/2),1],
[(C*x^4+B*x^2+A)/(e*x^2+d)^(5/2)/(c*x^4+a),x,7,1/3*(A*e^2-B*d*e+C*d^2)*x/d/(a*e^2+c*d^2)/(e*x^2+d)^(3/2)+1/3*(c*d^2*(2*C*d^2-e*(-8*A*e+5*B*d))-a*e^2*(4*C*d^2-e*(2*A*e+B*d)))*x/d^2/(a*e^2+c*d^2)^2/sqrt(e*x^2+d)+1/2*sqrt(sqrt(a)*e+sqrt(a*e^2+c*d^2))*(c*d*(-2*A*c*d*e-B*a*e^2+B*c*d^2+2*C*a*d*e)-(e-sqrt(a*e^2+c*d^2)/sqrt(a))*(A*c*(-a*e^2+c*d^2)+a*(a*C*e^2-c*d*(-2*B*e+C*d))))*arctan(sqrt(2)*a^(1/4)*sqrt(c)*sqrt(sqrt(a)*e+sqrt(a*e^2+c*d^2))*x*sqrt(e*x^2+d)/(sqrt(a)*(sqrt(a)*e+sqrt(a*e^2+c*d^2))-c*d*x^2))/sqrt(2)/a^(1/4)/sqrt(c)/d/(a*e^2+c*d^2)^(5/2)+1/2*sqrt(-sqrt(a)*e+sqrt(a*e^2+c*d^2))*(c*d*(-2*A*c*d*e-B*a*e^2+B*c*d^2+2*C*a*d*e)-(e+sqrt(a*e^2+c*d^2)/sqrt(a))*(A*c*(-a*e^2+c*d^2)+a*(a*C*e^2-c*d*(-2*B*e+C*d))))*arctanh(sqrt(2)*a^(1/4)*sqrt(c)*sqrt(-sqrt(a)*e+sqrt(a*e^2+c*d^2))*x*sqrt(e*x^2+d)/(sqrt(a)*(sqrt(a)*e-sqrt(a*e^2+c*d^2))-c*d*x^2))/sqrt(2)/a^(1/4)/sqrt(c)/d/(a*e^2+c*d^2)^(5/2),1],
[(e*x^2+d)^(5/2)*(C*x^4+B*x^2+A)/(c*x^4+a)^2,x,11,-1/4*e*(A*c*e+B*c*d-3*C*a*e)*x*sqrt(e*x^2+d)/a/c^2-1/4*B*e*x*(e*x^2+d)^(3/2)/a/c+1/4*x*(B*c*x^2+A*c-C*a)*(e*x^2+d)^(5/2)/a/c/(c*x^4+a)+1/8*sqrt(sqrt(a)*e+sqrt(a*e^2+c*d^2))*(sqrt(a)*c^2*d^3*(A*e+B*d)+a^(5/2)*e^3*(4*B*e+7*C*d)+3*A*c^2*d^3*sqrt(a*e^2+c*d^2)-a^2*e^2*(4*B*e+13*C*d)*sqrt(a*e^2+c*d^2)+a*c*d*sqrt(a*e^2+c*d^2)*(C*d^2+e*(A*e+2*B*d))+a^(3/2)*c*d*e*(7*C*d^2+e*(A*e+5*B*d)))*arctan(sqrt(2)*a^(1/4)*sqrt(c)*sqrt(sqrt(a)*e+sqrt(a*e^2+c*d^2))*x*sqrt(e*x^2+d)/(sqrt(a)*(sqrt(a)*e+sqrt(a*e^2+c*d^2))-c*d*x^2))/sqrt(2)/a^(7/4)/c^(5/2)/d/sqrt(a*e^2+c*d^2)+1/2*e^(3/2)*(2*B*e+5*C*d)*arctanh(sqrt(e)*x/sqrt(e*x^2+d))/c^2-1/8*sqrt(-sqrt(a)*e+sqrt(a*e^2+c*d^2))*((e+sqrt(a*e^2+c*d^2)/sqrt(a))*(A*c*d*(a*e^2+3*c*d^2)+a*(c*d^2*(2*B*e+C*d)-a*e^2*(4*B*e+13*C*d)))-d*(B*c*d*(7*a*e^2+c*d^2)+2*e*(a*C*(-3*a*e^2+4*c*d^2)+A*c*(a*e^2+2*c*d^2))))*arctanh(sqrt(2)*a^(1/4)*sqrt(c)*sqrt(-sqrt(a)*e+sqrt(a*e^2+c*d^2))*x*sqrt(e*x^2+d)/(sqrt(a)*(sqrt(a)*e-sqrt(a*e^2+c*d^2))-c*d*x^2))/sqrt(2)/a^(5/4)/c^(5/2)/d/sqrt(a*e^2+c*d^2),1],
[(e*x^2+d)^(3/2)*(C*x^4+B*x^2+A)/(c*x^4+a)^2,x,10,-1/4*B*e*x*sqrt(e*x^2+d)/a/c+1/4*x*(B*c*x^2+A*c-C*a)*(e*x^2+d)^(3/2)/a/c/(c*x^4+a)+1/8*sqrt(sqrt(a)*e+sqrt(a*e^2+c*d^2))*(c*d*(3*A*c*d*e+2*B*a*e^2+B*c*d^2+5*C*a*d*e)+(4*a^2*C*e^2-c*d*(3*A*c*d+B*a*e+C*a*d))*(e-sqrt(a*e^2+c*d^2)/sqrt(a)))*arctan(sqrt(2)*a^(1/4)*sqrt(c)*sqrt(sqrt(a)*e+sqrt(a*e^2+c*d^2))*x*sqrt(e*x^2+d)/(sqrt(a)*(sqrt(a)*e+sqrt(a*e^2+c*d^2))-c*d*x^2))/sqrt(2)/a^(5/4)/c^(5/2)/d/sqrt(a*e^2+c*d^2)+C*e^(3/2)*arctanh(sqrt(e)*x/sqrt(e*x^2+d))/c^2+1/8*sqrt(-sqrt(a)*e+sqrt(a*e^2+c*d^2))*(c*d*(3*A*c*d*e+2*B*a*e^2+B*c*d^2+5*C*a*d*e)+(4*a^2*C*e^2-c*d*(3*A*c*d+B*a*e+C*a*d))*(e+sqrt(a*e^2+c*d^2)/sqrt(a)))*arctanh(sqrt(2)*a^(1/4)*sqrt(c)*sqrt(-sqrt(a)*e+sqrt(a*e^2+c*d^2))*x*sqrt(e*x^2+d)/(sqrt(a)*(sqrt(a)*e-sqrt(a*e^2+c*d^2))-c*d*x^2))/sqrt(2)/a^(5/4)/c^(5/2)/d/sqrt(a*e^2+c*d^2),1],
[sqrt(e*x^2+d)*(C*x^4+B*x^2+A)/(c*x^4+a)^2,x,6,1/4*x*(B*c*x^2+A*c-C*a)*sqrt(e*x^2+d)/a/c/(c*x^4+a)+1/8*sqrt(sqrt(a)*e+sqrt(a*e^2+c*d^2))*(a^(3/2)*C*e+sqrt(a)*c*(-A*e+B*d)+(3*A*c+C*a)*sqrt(a*e^2+c*d^2))*arctan(sqrt(2)*a^(1/4)*sqrt(c)*sqrt(sqrt(a)*e+sqrt(a*e^2+c*d^2))*x*sqrt(e*x^2+d)/(sqrt(a)*(sqrt(a)*e+sqrt(a*e^2+c*d^2))-c*d*x^2))/sqrt(2)/a^(7/4)/c^(3/2)/sqrt(a*e^2+c*d^2)+1/8*sqrt(-sqrt(a)*e+sqrt(a*e^2+c*d^2))*(a^(3/2)*C*e+sqrt(a)*c*(-A*e+B*d)-(3*A*c+C*a)*sqrt(a*e^2+c*d^2))*arctanh(sqrt(2)*a^(1/4)*sqrt(c)*sqrt(-sqrt(a)*e+sqrt(a*e^2+c*d^2))*x*sqrt(e*x^2+d)/(sqrt(a)*(sqrt(a)*e-sqrt(a*e^2+c*d^2))-c*d*x^2))/sqrt(2)/a^(7/4)/c^(3/2)/sqrt(a*e^2+c*d^2),1],
[(C*x^4+B*x^2+A)/sqrt(e*x^2+d)/(c*x^4+a)^2,x,6,1/4*x*sqrt(e*x^2+d)*(A*c*d-a*C*d+a*B*e+(-A*c*e+B*c*d+C*a*e)*x^2)/a/(a*e^2+c*d^2)/(c*x^4+a)+1/8*sqrt(sqrt(a)*e+sqrt(a*e^2+c*d^2))*(d*(A*c*d*e+2*B*a*e^2+B*c*d^2-C*a*d*e)-(e-sqrt(a*e^2+c*d^2)/sqrt(a))*(a*d*(-B*e+C*d)+A*(4*a*e^2+3*c*d^2)))*arctan(sqrt(2)*a^(1/4)*sqrt(c)*sqrt(sqrt(a)*e+sqrt(a*e^2+c*d^2))*x*sqrt(e*x^2+d)/(sqrt(a)*(sqrt(a)*e+sqrt(a*e^2+c*d^2))-c*d*x^2))/sqrt(2)/a^(5/4)/sqrt(c)/d/(a*e^2+c*d^2)^(3/2)+1/8*sqrt(-sqrt(a)*e+sqrt(a*e^2+c*d^2))*(d*(A*c*d*e+2*B*a*e^2+B*c*d^2-C*a*d*e)-(e+sqrt(a*e^2+c*d^2)/sqrt(a))*(a*d*(-B*e+C*d)+A*(4*a*e^2+3*c*d^2)))*arctanh(sqrt(2)*a^(1/4)*sqrt(c)*sqrt(-sqrt(a)*e+sqrt(a*e^2+c*d^2))*x*sqrt(e*x^2+d)/(sqrt(a)*(sqrt(a)*e-sqrt(a*e^2+c*d^2))-c*d*x^2))/sqrt(2)/a^(5/4)/sqrt(c)/d/(a*e^2+c*d^2)^(3/2),1],
[(C*x^4+B*x^2+A)/(e*x^2+d)^(3/2)/(c*x^4+a)^2,x,7,1/4*e*(4*A*a*e^3-2*A*c*d^2*e-5*B*a*d*e^2+B*c*d^3+6*C*a*d^2*e)*x/a/d/(a*e^2+c*d^2)^2/sqrt(e*x^2+d)+1/4*x*(A*c*d-a*C*d+a*B*e+(-A*c*e+B*c*d+C*a*e)*x^2)/a/(a*e^2+c*d^2)/sqrt(e*x^2+d)/(c*x^4+a)+1/8*sqrt(sqrt(a)*e+sqrt(a*e^2+c*d^2))*(d*(B*c*d*(7*a*e^2+c*d^2)-2*a*e*(3*A*c*e^2-C*a*e^2+2*C*c*d^2))-(sqrt(a)*e-sqrt(a*e^2+c*d^2))*(3*A*c*d*(3*a*e^2+c*d^2)-a*(a*e^2*(-4*B*e+5*C*d)-c*d^2*(-2*B*e+C*d)))/sqrt(a))*arctan(sqrt(2)*a^(1/4)*sqrt(c)*sqrt(sqrt(a)*e+sqrt(a*e^2+c*d^2))*x*sqrt(e*x^2+d)/(sqrt(a)*(sqrt(a)*e+sqrt(a*e^2+c*d^2))-c*d*x^2))/sqrt(2)/a^(5/4)/sqrt(c)/d/(a*e^2+c*d^2)^(5/2)+1/8*sqrt(-sqrt(a)*e+sqrt(a*e^2+c*d^2))*(d*(B*c*d*(7*a*e^2+c*d^2)-2*a*e*(3*A*c*e^2-C*a*e^2+2*C*c*d^2))-(e+sqrt(a*e^2+c*d^2)/sqrt(a))*(3*A*c*d*(3*a*e^2+c*d^2)-a*(a*e^2*(-4*B*e+5*C*d)-c*d^2*(-2*B*e+C*d))))*arctanh(sqrt(2)*a^(1/4)*sqrt(c)*sqrt(-sqrt(a)*e+sqrt(a*e^2+c*d^2))*x*sqrt(e*x^2+d)/(sqrt(a)*(sqrt(a)*e-sqrt(a*e^2+c*d^2))-c*d*x^2))/sqrt(2)/a^(5/4)/sqrt(c)/d/(a*e^2+c*d^2)^(5/2),1],
[(C*x^4+B*x^2+A)/(e*x^2+d)^(5/2)/(c*x^4+a)^2,x,8,1/12*e*(4*A*a*e^3-6*A*c*d^2*e-7*B*a*d*e^2+3*B*c*d^3+10*C*a*d^2*e)*x/a/d/(a*e^2+c*d^2)^2/(e*x^2+d)^(3/2)+1/12*e*(a*C*d^2*e*(-19*a*e^2+41*c*d^2)+B*(4*a^2*d*e^4-53*a*c*d^3*e^2+3*c^2*d^5)-A*(-8*a^2*e^5-59*a*c*d^2*e^3+9*c^2*d^4*e))*x/a/d^2/(a*e^2+c*d^2)^3/sqrt(e*x^2+d)+1/4*x*(A*c*d-a*C*d+a*B*e+(-A*c*e+B*c*d+C*a*e)*x^2)/a/(a*e^2+c*d^2)/(e*x^2+d)^(3/2)/(c*x^4+a)-1/8*sqrt(sqrt(a)*e+sqrt(a*e^2+c*d^2))*((e-sqrt(a*e^2+c*d^2)/sqrt(a))*(A*c*(-8*a^2*e^4+15*a*c*d^2*e^2+3*c^2*d^4)+a*(4*a^2*C*e^4-a*c*d*e^2*(-17*B*e+15*C*d)+c^2*d^3*(-3*B*e+C*d)))-c*d*(B*(-6*a^2*e^4+15*a*c*d^2*e^2+c^2*d^4)-d*e*(a*C*(-13*a*e^2+7*c*d^2)+A*c*(21*a*e^2+c*d^2))))*arctan(sqrt(2)*a^(1/4)*sqrt(c)*sqrt(sqrt(a)*e+sqrt(a*e^2+c*d^2))*x*sqrt(e*x^2+d)/(sqrt(a)*(sqrt(a)*e+sqrt(a*e^2+c*d^2))-c*d*x^2))/sqrt(2)/a^(5/4)/sqrt(c)/d/(a*e^2+c*d^2)^(7/2)-1/8*sqrt(-sqrt(a)*e+sqrt(a*e^2+c*d^2))*((e+sqrt(a*e^2+c*d^2)/sqrt(a))*(A*c*(-8*a^2*e^4+15*a*c*d^2*e^2+3*c^2*d^4)+a*(4*a^2*C*e^4-a*c*d*e^2*(-17*B*e+15*C*d)+c^2*d^3*(-3*B*e+C*d)))-c*d*(B*(-6*a^2*e^4+15*a*c*d^2*e^2+c^2*d^4)-d*e*(a*C*(-13*a*e^2+7*c*d^2)+A*c*(21*a*e^2+c*d^2))))*arctanh(sqrt(2)*a^(1/4)*sqrt(c)*sqrt(-sqrt(a)*e+sqrt(a*e^2+c*d^2))*x*sqrt(e*x^2+d)/(sqrt(a)*(sqrt(a)*e-sqrt(a*e^2+c*d^2))-c*d*x^2))/sqrt(2)/a^(5/4)/sqrt(c)/d/(a*e^2+c*d^2)^(7/2),1],
[(B*x^2+A)*(e*x^2+d)^(1/3)/(c*x^4+a),x,10,1/2*(sqrt(c)*(A*e+B*d)-(A*c*d-B*a*e)/sqrt(-a))*x*(1+e*x^2/d)^(2/3)*AppellF1(1/2,2/3,1,3/2,-e*x^2/d,-sqrt(c)*x^2/sqrt(-a))/sqrt(-a)/c/(e*x^2+d)^(2/3)-1/2*(sqrt(c)*(A*e+B*d)+(A*c*d-B*a*e)/sqrt(-a))*x*(1+e*x^2/d)^(2/3)*AppellF1(1/2,2/3,1,3/2,-e*x^2/d,sqrt(c)*x^2/sqrt(-a))/sqrt(-a)/c/(e*x^2+d)^(2/3)-3^(3/4)*sqrt(2-sqrt(3))*B*(d^(1/3)-(e*x^2+d)^(1/3))*sqrt((d^(2/3)+d^(1/3)*(e*x^2+d)^(1/3)+(e*x^2+d)^(2/3))/((1-sqrt(3))*d^(1/3)-(e*x^2+d)^(1/3))^2)*InverseJacobiAM(arcsin(((1+sqrt(3))*d^(1/3)-(e*x^2+d)^(1/3))/((1-sqrt(3))*d^(1/3)-(e*x^2+d)^(1/3))),sqrt(-7+4*sqrt(3)))/c/x/sqrt(-d^(1/3)*(d^(1/3)-(e*x^2+d)^(1/3))/((1-sqrt(3))*d^(1/3)-(e*x^2+d)^(1/3))^2),1],
[(e*x^2+d)^3*sqrt(-c*x^4+a)*(C*x^4+B*x^2+A),x,10,1/15015*x*(715*A*c*d*(3*a*e^2+7*c*d^2)+65*a*(5*a*e^2*(B*e+3*C*d)+11*c*d^2*(3*B*e+C*d))+77*(39*B*c*d*(a*e^2+c*d^2)+e*(13*A*c*(a*e^2+9*c*d^2)+a*C*(7*a*e^2+39*c*d^2)))*x^2)*sqrt(-c*x^4+a)/c^2-1/77*(5*a*e^2*(B*e+3*C*d)+11*c*d*(C*d^2+3*e*(A*e+B*d)))*x*(-c*x^4+a)^(3/2)/c^2-1/117*e*(7*a*C*e^2+13*c*(3*C*d^2+e*(A*e+3*B*d)))*x^3*(-c*x^4+a)^(3/2)/c^2-1/11*e^2*(B*e+3*C*d)*x^5*(-c*x^4+a)^(3/2)/c-1/13*C*e^3*x^7*(-c*x^4+a)^(3/2)/c+2/195*a^(7/4)*(39*B*c*d*(a*e^2+c*d^2)+e*(13*A*c*(a*e^2+9*c*d^2)+a*C*(7*a*e^2+39*c*d^2)))*sqrt(1-c*x^4/a)*EllipticE(sin(arcsin(c^(1/4)*x/a^(1/4))),sqrt(-1))/c^(11/4)/sqrt(-c*x^4+a)+2/15015*a^(5/4)*(65*sqrt(c)*(11*A*c*d*(3*a*e^2+7*c*d^2)+a*(5*a*e^2*(B*e+3*C*d)+11*c*d^2*(3*B*e+C*d)))-77*sqrt(a)*(39*B*c*d*(a*e^2+c*d^2)+e*(13*A*c*(a*e^2+9*c*d^2)+a*C*(7*a*e^2+39*c*d^2))))*sqrt(1-c*x^4/a)*InverseJacobiAM(arcsin(c^(1/4)*x/a^(1/4)),sqrt(-1))/c^(11/4)/sqrt(-c*x^4+a),1],
[(e*x^2+d)^2*sqrt(-c*x^4+a)*(C*x^4+B*x^2+A),x,9,1/1155*x*(55*A*c*(a*e^2+7*c*d^2)+5*a*(5*a*C*e^2+11*c*d*(2*B*e+C*d))+77*c*(6*A*c*d*e+B*a*e^2+3*B*c*d^2+2*C*a*d*e)*x^2)*sqrt(-c*x^4+a)/c^2-1/77*(5*a*C*e^2+11*c*(C*d^2+e*(A*e+2*B*d)))*x*(-c*x^4+a)^(3/2)/c^2-1/9*e*(B*e+2*C*d)*x^3*(-c*x^4+a)^(3/2)/c-1/11*C*e^2*x^5*(-c*x^4+a)^(3/2)/c+2/15*a^(7/4)*(6*A*c*d*e+B*a*e^2+3*B*c*d^2+2*C*a*d*e)*sqrt(1-c*x^4/a)*EllipticE(sin(arcsin(c^(1/4)*x/a^(1/4))),sqrt(-1))/c^(7/4)/sqrt(-c*x^4+a)-2/1155*a^(5/4)*(77*sqrt(a)*sqrt(c)*(6*A*c*d*e+B*a*e^2+3*B*c*d^2+2*C*a*d*e)-55*A*c*(a*e^2+7*c*d^2)-5*a*(5*a*C*e^2+11*c*d*(2*B*e+C*d)))*sqrt(1-c*x^4/a)*InverseJacobiAM(arcsin(c^(1/4)*x/a^(1/4)),sqrt(-1))/c^(9/4)/sqrt(-c*x^4+a),1],
[(e*x^2+d)*sqrt(-c*x^4+a)*(C*x^4+B*x^2+A),x,8,1/105*x*(35*A*c*d+5*a*B*e+5*a*C*d+7*(3*A*c*e+3*B*c*d+C*a*e)*x^2)*sqrt(-c*x^4+a)/c-1/7*(B*e+C*d)*x*(-c*x^4+a)^(3/2)/c-1/9*C*e*x^3*(-c*x^4+a)^(3/2)/c+2/15*a^(7/4)*(3*A*c*e+3*B*c*d+C*a*e)*sqrt(1-c*x^4/a)*EllipticE(sin(arcsin(c^(1/4)*x/a^(1/4))),sqrt(-1))/c^(7/4)/sqrt(-c*x^4+a)+2/105*a^(5/4)*(5*sqrt(c)*(7*A*c*d+B*a*e+C*a*d)-7*sqrt(a)*(3*A*c*e+3*B*c*d+C*a*e))*sqrt(1-c*x^4/a)*InverseJacobiAM(arcsin(c^(1/4)*x/a^(1/4)),sqrt(-1))/c^(7/4)/sqrt(-c*x^4+a),1],
[sqrt(-c*x^4+a)*(C*x^4+B*x^2+A),x,7,1/105*x*(21*B*c*x^2+35*A*c+5*C*a)*sqrt(-c*x^4+a)/c-1/7*C*x*(-c*x^4+a)^(3/2)/c+2/5*a^(7/4)*B*sqrt(1-c*x^4/a)*EllipticE(sin(arcsin(c^(1/4)*x/a^(1/4))),sqrt(-1))/c^(3/4)/sqrt(-c*x^4+a)-2/105*a^(5/4)*(21*sqrt(a)*B*sqrt(c)-35*A*c-5*a*C)*sqrt(1-c*x^4/a)*InverseJacobiAM(arcsin(c^(1/4)*x/a^(1/4)),sqrt(-1))/c^(5/4)/sqrt(-c*x^4+a),1],
[sqrt(-c*x^4+a)*(C*x^4+B*x^2+A)/(e*x^2+d),x,10,-1/3*(-B*e+C*d)*x*sqrt(-c*x^4+a)/e^2+1/5*C*x^3*sqrt(-c*x^4+a)/e+1/5*a^(3/4)*(2*a*C*e^2-5*c*(C*d^2-e*(-A*e+B*d)))*sqrt(1-c*x^4/a)*EllipticE(sin(arcsin(c^(1/4)*x/a^(1/4))),sqrt(-1))/c^(3/4)/e^3/sqrt(-c*x^4+a)-1/15*a^(1/4)*(3*sqrt(a)*e*(2*a*C*e^2-5*c*(C*d^2-e*(-A*e+B*d)))+5*sqrt(c)*(2*a*e^2*(-B*e+C*d)-3*c*d*(C*d^2-e*(-A*e+B*d))))*sqrt(1-c*x^4/a)*InverseJacobiAM(arcsin(c^(1/4)*x/a^(1/4)),sqrt(-1))/c^(3/4)/e^4/sqrt(-c*x^4+a)-a^(1/4)*(-a*e^2+c*d^2)*(A*e^2-B*d*e+C*d^2)*sqrt(1-c*x^4/a)*EllipticPi(sin(arcsin(c^(1/4)*x/a^(1/4))),-sqrt(a)*e/sqrt(c)/d,sqrt(-1))/c^(1/4)/d/e^4/sqrt(-c*x^4+a),1],
[sqrt(-c*x^4+a)*(C*x^4+B*x^2+A)/(e*x^2+d)^2,x,10,1/3*C*x*sqrt(-c*x^4+a)/e^2+1/2*(A*e^2-B*d*e+C*d^2)*x*sqrt(-c*x^4+a)/d/e^2/(e*x^2+d)+1/2*a^(3/4)*c^(1/4)*(5*C*d^2-e*(-A*e+3*B*d))*sqrt(1-c*x^4/a)*EllipticE(sin(arcsin(c^(1/4)*x/a^(1/4))),sqrt(-1))/d/e^3/sqrt(-c*x^4+a)+1/6*a^(1/4)*(4*a*C*d*e^2-3*c*d*(5*C*d^2-e*(-A*e+3*B*d))-3*sqrt(a)*sqrt(c)*e*(5*C*d^2-e*(-A*e+3*B*d)))*sqrt(1-c*x^4/a)*InverseJacobiAM(arcsin(c^(1/4)*x/a^(1/4)),sqrt(-1))/c^(1/4)/d/e^4/sqrt(-c*x^4+a)+1/2*a^(1/4)*(c*d^2*(5*C*d^2-e*(-A*e+3*B*d))-a*e^2*(3*C*d^2-e*(A*e+B*d)))*sqrt(1-c*x^4/a)*EllipticPi(sin(arcsin(c^(1/4)*x/a^(1/4))),-sqrt(a)*e/sqrt(c)/d,sqrt(-1))/c^(1/4)/d^2/e^4/sqrt(-c*x^4+a),1],
[sqrt(-c*x^4+a)*(C*x^4+B*x^2+A)/(e*x^2+d)^3,x,10,1/4*(A*e^2-B*d*e+C*d^2)*x*sqrt(-c*x^4+a)/d/e^2/(e*x^2+d)^2-1/8*(c*d^2*(7*C*d^2-e*(A*e+3*B*d))-a*e^2*(5*C*d^2-e*(3*A*e+B*d)))*x*sqrt(-c*x^4+a)/d^2/e^2/(-a*e^2+c*d^2)/(e*x^2+d)-1/8*a^(3/4)*c^(1/4)*(c*d^2*(15*C*d^2-e*(A*e+3*B*d))-a*e^2*(13*C*d^2-e*(3*A*e+B*d)))*sqrt(1-c*x^4/a)*EllipticE(sin(arcsin(c^(1/4)*x/a^(1/4))),sqrt(-1))/d^2/e^3/(-a*e^2+c*d^2)/sqrt(-c*x^4+a)+1/8*a^(1/4)*c^(1/4)*(c*d^2*(15*C*d^2-e*(A*e+3*B*d))+2*sqrt(a)*sqrt(c)*d*e*(15*C*d^2-e*(A*e+3*B*d))+a*e^2*(13*C*d^2-e*(3*A*e+B*d)))*sqrt(1-c*x^4/a)*InverseJacobiAM(arcsin(c^(1/4)*x/a^(1/4)),sqrt(-1))/d^2/e^4/(sqrt(c)*d+sqrt(a)*e)/sqrt(-c*x^4+a)+1/8*a^(1/4)*(2*a*c*d^2*e^2*(11*C*d^2-3*e*(-A*e+B*d))-c^2*d^4*(15*C*d^2-e*(A*e+3*B*d))-a^2*e^4*(3*C*d^2+e*(3*A*e+B*d)))*sqrt(1-c*x^4/a)*EllipticPi(sin(arcsin(c^(1/4)*x/a^(1/4))),-sqrt(a)*e/sqrt(c)/d,sqrt(-1))/c^(1/4)/d^3/e^4/(-a*e^2+c*d^2)/sqrt(-c*x^4+a),1],
[(e*x^2+d)^3*(-c*x^4+a)^(3/2)*(C*x^4+B*x^2+A),x,11,2/255255*a*x*(3315*A*c*d*(3*a*e^2+11*c*d^2)+1105*a*(a*e^2*(B*e+3*C*d)+3*c*d^2*(3*B*e+C*d))+77*(17*B*c*d*(9*a*e^2+13*c*d^2)+3*e*(17*A*c*(a*e^2+13*c*d^2)+a*C*(7*a*e^2+51*c*d^2)))*x^2)*sqrt(-c*x^4+a)/c^2+1/153153*x*(1989*A*c*d*(3*a*e^2+11*c*d^2)+663*a*(a*e^2*(B*e+3*C*d)+3*c*d^2*(3*B*e+C*d))+77*(17*B*c*d*(9*a*e^2+13*c*d^2)+3*e*(17*A*c*(a*e^2+13*c*d^2)+a*C*(7*a*e^2+51*c*d^2)))*x^2)*(-c*x^4+a)^(3/2)/c^2-1/33*(a*e^2*(B*e+3*C*d)+3*c*d*(C*d^2+3*e*(A*e+B*d)))*x*(-c*x^4+a)^(5/2)/c^2-1/221*e*(7*a*C*e^2+17*c*(3*C*d^2+e*(A*e+3*B*d)))*x^3*(-c*x^4+a)^(5/2)/c^2-1/15*e^2*(B*e+3*C*d)*x^5*(-c*x^4+a)^(5/2)/c-1/17*C*e^3*x^7*(-c*x^4+a)^(5/2)/c+4/3315*a^(11/4)*(17*B*c*d*(9*a*e^2+13*c*d^2)+3*e*(17*A*c*(a*e^2+13*c*d^2)+a*C*(7*a*e^2+51*c*d^2)))*sqrt(1-c*x^4/a)*EllipticE(sin(arcsin(c^(1/4)*x/a^(1/4))),sqrt(-1))/c^(11/4)/sqrt(-c*x^4+a)+4/255255*a^(9/4)*(1105*sqrt(c)*(3*A*c*d*(3*a*e^2+11*c*d^2)+a*(a*e^2*(B*e+3*C*d)+3*c*d^2*(3*B*e+C*d)))-77*sqrt(a)*(17*B*c*d*(9*a*e^2+13*c*d^2)+3*e*(17*A*c*(a*e^2+13*c*d^2)+a*C*(7*a*e^2+51*c*d^2))))*sqrt(1-c*x^4/a)*InverseJacobiAM(arcsin(c^(1/4)*x/a^(1/4)),sqrt(-1))/c^(11/4)/sqrt(-c*x^4+a),1],
[(e*x^2+d)^2*(-c*x^4+a)^(3/2)*(C*x^4+B*x^2+A),x,10,2/15015*a*x*(195*A*c*(a*e^2+11*c*d^2)+65*a*(a*C*e^2+3*c*d*(2*B*e+C*d))+77*c*(26*A*c*d*e+3*B*a*e^2+13*B*c*d^2+6*C*a*d*e)*x^2)*sqrt(-c*x^4+a)/c^2+1/9009*x*(117*A*c*(a*e^2+11*c*d^2)+39*a*(a*C*e^2+3*c*d*(2*B*e+C*d))+77*c*(26*A*c*d*e+3*B*a*e^2+13*B*c*d^2+6*C*a*d*e)*x^2)*(-c*x^4+a)^(3/2)/c^2-1/33*(a*C*e^2+3*c*(C*d^2+e*(A*e+2*B*d)))*x*(-c*x^4+a)^(5/2)/c^2-1/13*e*(B*e+2*C*d)*x^3*(-c*x^4+a)^(5/2)/c-1/15*C*e^2*x^5*(-c*x^4+a)^(5/2)/c+4/195*a^(11/4)*(26*A*c*d*e+3*B*a*e^2+13*B*c*d^2+6*C*a*d*e)*sqrt(1-c*x^4/a)*EllipticE(sin(arcsin(c^(1/4)*x/a^(1/4))),sqrt(-1))/c^(7/4)/sqrt(-c*x^4+a)-4/15015*a^(9/4)*(77*sqrt(a)*sqrt(c)*(26*A*c*d*e+3*B*a*e^2+13*B*c*d^2+6*C*a*d*e)-195*A*c*(a*e^2+11*c*d^2)-65*a*(a*C*e^2+3*c*d*(2*B*e+C*d)))*sqrt(1-c*x^4/a)*InverseJacobiAM(arcsin(c^(1/4)*x/a^(1/4)),sqrt(-1))/c^(9/4)/sqrt(-c*x^4+a),1],
[(e*x^2+d)*(-c*x^4+a)^(3/2)*(C*x^4+B*x^2+A),x,9,2/15015*a*x*(2145*A*c*d+195*a*B*e+195*a*C*d+77*(13*A*c*e+13*B*c*d+3*C*a*e)*x^2)*sqrt(-c*x^4+a)/c+1/9009*x*(1287*A*c*d+117*a*B*e+117*a*C*d+77*(13*A*c*e+13*B*c*d+3*C*a*e)*x^2)*(-c*x^4+a)^(3/2)/c-1/11*(B*e+C*d)*x*(-c*x^4+a)^(5/2)/c-1/13*C*e*x^3*(-c*x^4+a)^(5/2)/c+4/195*a^(11/4)*(13*A*c*e+13*B*c*d+3*C*a*e)*sqrt(1-c*x^4/a)*EllipticE(sin(arcsin(c^(1/4)*x/a^(1/4))),sqrt(-1))/c^(7/4)/sqrt(-c*x^4+a)+4/15015*a^(9/4)*(195*sqrt(c)*(11*A*c*d+B*a*e+C*a*d)-77*sqrt(a)*(13*A*c*e+13*B*c*d+3*C*a*e))*sqrt(1-c*x^4/a)*InverseJacobiAM(arcsin(c^(1/4)*x/a^(1/4)),sqrt(-1))/c^(7/4)/sqrt(-c*x^4+a),1],
[(-c*x^4+a)^(3/2)*(C*x^4+B*x^2+A),x,8,2/1155*a*x*(77*B*c*x^2+165*A*c+15*C*a)*sqrt(-c*x^4+a)/c+1/693*x*(77*B*c*x^2+99*A*c+9*C*a)*(-c*x^4+a)^(3/2)/c-1/11*C*x*(-c*x^4+a)^(5/2)/c+4/15*a^(11/4)*B*sqrt(1-c*x^4/a)*EllipticE(sin(arcsin(c^(1/4)*x/a^(1/4))),sqrt(-1))/c^(3/4)/sqrt(-c*x^4+a)-4/1155*a^(9/4)*(77*sqrt(a)*B*sqrt(c)-165*A*c-15*a*C)*sqrt(1-c*x^4/a)*InverseJacobiAM(arcsin(c^(1/4)*x/a^(1/4)),sqrt(-1))/c^(5/4)/sqrt(-c*x^4+a),1],
[(-c*x^4+a)^(3/2)*(C*x^4+B*x^2+A)/(e*x^2+d),x,12,-1/21*(9*a*e^2*(-B*e+C*d)-7*c*d*(C*d^2-e*(-A*e+B*d)))*x*sqrt(-c*x^4+a)/e^4+1/45*(11*a*C*e^2-9*c*(C*d^2-e*(-A*e+B*d)))*x^3*sqrt(-c*x^4+a)/e^3+1/7*c*(-B*e+C*d)*x^5*sqrt(-c*x^4+a)/e^2-1/9*c*C*x^7*sqrt(-c*x^4+a)/e+1/15*a^(3/4)*(4*a^2*C*e^4+15*c^2*d^2*(C*d^2-e*(-A*e+B*d))-21*a*c*e^2*(C*d^2-e*(-A*e+B*d)))*sqrt(1-c*x^4/a)*EllipticE(sin(arcsin(c^(1/4)*x/a^(1/4))),sqrt(-1))/c^(3/4)/e^5/sqrt(-c*x^4+a)-1/105*a^(1/4)*(7*sqrt(a)*e*(4*a^2*C*e^4+15*c^2*d^2*(C*d^2-e*(-A*e+B*d))-21*a*c*e^2*(C*d^2-e*(-A*e+B*d)))+5*sqrt(c)*(12*a^2*e^4*(-B*e+C*d)+21*c^2*d^3*(C*d^2-e*(-A*e+B*d))-35*a*c*d*e^2*(C*d^2-e*(-A*e+B*d))))*sqrt(1-c*x^4/a)*InverseJacobiAM(arcsin(c^(1/4)*x/a^(1/4)),sqrt(-1))/c^(3/4)/e^6/sqrt(-c*x^4+a)+a^(1/4)*(-a*e^2+c*d^2)^2*(A*e^2-B*d*e+C*d^2)*sqrt(1-c*x^4/a)*EllipticPi(sin(arcsin(c^(1/4)*x/a^(1/4))),-sqrt(a)*e/sqrt(c)/d,sqrt(-1))/c^(1/4)/d/e^6/sqrt(-c*x^4+a),1],
[(-c*x^4+a)^(3/2)*(C*x^4+B*x^2+A)/(e*x^2+d)^2,x,12,1/21*(9*a*C*e^2-7*c*(3*C*d^2-e*(-A*e+2*B*d)))*x*sqrt(-c*x^4+a)/e^4+1/5*c*(-B*e+2*C*d)*x^3*sqrt(-c*x^4+a)/e^3-1/7*c*C*x^5*sqrt(-c*x^4+a)/e^2-1/2*(-a*e^2+c*d^2)*(A*e^2-B*d*e+C*d^2)*x*sqrt(-c*x^4+a)/d/e^4/(e*x^2+d)-1/10*a^(3/4)*c^(1/4)*(5*c*d^2*(9*C*d^2-e*(-5*A*e+7*B*d))-a*e^2*(33*C*d^2-e*(-5*A*e+19*B*d)))*sqrt(1-c*x^4/a)*EllipticE(sin(arcsin(c^(1/4)*x/a^(1/4))),sqrt(-1))/d/e^5/sqrt(-c*x^4+a)+1/210*a^(1/4)*(120*a^2*C*d*e^4-35*a*c*d*e^2*(27*C*d^2-e*(-7*A*e+17*B*d))+105*c^2*d^3*(9*C*d^2-e*(-5*A*e+7*B*d))+105*sqrt(a)*c^(3/2)*d^2*e*(9*C*d^2-e*(-5*A*e+7*B*d))-21*a^(3/2)*sqrt(c)*e^3*(33*C*d^2-e*(-5*A*e+19*B*d)))*sqrt(1-c*x^4/a)*InverseJacobiAM(arcsin(c^(1/4)*x/a^(1/4)),sqrt(-1))/c^(1/4)/d/e^6/sqrt(-c*x^4+a)-1/2*a^(1/4)*(-a*e^2+c*d^2)*(c*d^2*(9*C*d^2-e*(-5*A*e+7*B*d))-a*e^2*(3*C*d^2-e*(A*e+B*d)))*sqrt(1-c*x^4/a)*EllipticPi(sin(arcsin(c^(1/4)*x/a^(1/4))),-sqrt(a)*e/sqrt(c)/d,sqrt(-1))/c^(1/4)/d^2/e^6/sqrt(-c*x^4+a),1],
[(-c*x^4+a)^(3/2)*(C*x^4+B*x^2+A)/(e*x^2+d)^3,x,12,1/3*c*(-B*e+3*C*d)*x*sqrt(-c*x^4+a)/e^4-1/5*c*C*x^3*sqrt(-c*x^4+a)/e^3-1/4*(-a*e^2+c*d^2)*(A*e^2-B*d*e+C*d^2)*x*sqrt(-c*x^4+a)/d/e^4/(e*x^2+d)^2+1/8*(c*d^2*(15*C*d^2-e*(-7*A*e+11*B*d))-a*e^2*(5*C*d^2-e*(3*A*e+B*d)))*x*sqrt(-c*x^4+a)/d^2/e^4/(e*x^2+d)+1/40*a^(3/4)*c^(1/4)*(5*c*d^2*(63*C*d^2-5*e*(-3*A*e+7*B*d))-a*e^2*(81*C*d^2-5*e*(3*A*e+B*d)))*sqrt(1-c*x^4/a)*EllipticE(sin(arcsin(c^(1/4)*x/a^(1/4))),sqrt(-1))/d^2/e^5/sqrt(-c*x^4+a)-1/120*a^(1/4)*c^(1/4)*(15*c^(3/2)*d^3*(63*C*d^2-5*e*(-3*A*e+7*B*d))+15*sqrt(a)*c*d^2*e*(63*C*d^2-5*e*(-3*A*e+7*B*d))-5*a*sqrt(c)*d*e^2*(99*C*d^2-e*(-3*A*e+31*B*d))-3*a^(3/2)*e^3*(81*C*d^2-5*e*(3*A*e+B*d)))*sqrt(1-c*x^4/a)*InverseJacobiAM(arcsin(c^(1/4)*x/a^(1/4)),sqrt(-1))/d^2/e^6/sqrt(-c*x^4+a)+1/8*a^(1/4)*(c^2*d^4*(63*C*d^2-5*e*(-3*A*e+7*B*d))-2*a*c*d^2*e^2*(27*C*d^2-e*(-3*A*e+11*B*d))+a^2*e^4*(3*C*d^2+e*(3*A*e+B*d)))*sqrt(1-c*x^4/a)*EllipticPi(sin(arcsin(c^(1/4)*x/a^(1/4))),-sqrt(a)*e/sqrt(c)/d,sqrt(-1))/c^(1/4)/d^3/e^6/sqrt(-c*x^4+a),1],
[(e*x^2+d)^3*(C*x^4+B*x^2+A)/sqrt(-c*x^4+a),x,9,-1/21*(5*a*e^2*(B*e+3*C*d)+7*c*d*(C*d^2+3*e*(A*e+B*d)))*x*sqrt(-c*x^4+a)/c^2-1/45*e*(7*a*C*e^2+9*c*(3*C*d^2+e*(A*e+3*B*d)))*x^3*sqrt(-c*x^4+a)/c^2-1/7*e^2*(B*e+3*C*d)*x^5*sqrt(-c*x^4+a)/c-1/9*C*e^3*x^7*sqrt(-c*x^4+a)/c+1/15*a^(3/4)*(3*B*c*d*(9*a*e^2+5*c*d^2)+e*(9*A*c*(a*e^2+5*c*d^2)+a*C*(7*a*e^2+27*c*d^2)))*sqrt(1-c*x^4/a)*EllipticE(sin(arcsin(c^(1/4)*x/a^(1/4))),sqrt(-1))/c^(11/4)/sqrt(-c*x^4+a)+1/105*a^(1/4)*(5*sqrt(c)*(21*A*c*d*(a*e^2+c*d^2)+a*(5*a*e^2*(B*e+3*C*d)+7*c*d^2*(3*B*e+C*d)))-7*sqrt(a)*(3*B*c*d*(9*a*e^2+5*c*d^2)+e*(9*A*c*(a*e^2+5*c*d^2)+a*C*(7*a*e^2+27*c*d^2))))*sqrt(1-c*x^4/a)*InverseJacobiAM(arcsin(c^(1/4)*x/a^(1/4)),sqrt(-1))/c^(11/4)/sqrt(-c*x^4+a),1],
[(e*x^2+d)^2*(C*x^4+B*x^2+A)/sqrt(-c*x^4+a),x,8,-1/21*(5*a*C*e^2+7*c*(C*d^2+e*(A*e+2*B*d)))*x*sqrt(-c*x^4+a)/c^2-1/5*e*(B*e+2*C*d)*x^3*sqrt(-c*x^4+a)/c-1/7*C*e^2*x^5*sqrt(-c*x^4+a)/c+1/5*a^(3/4)*(10*A*c*d*e+3*B*a*e^2+5*B*c*d^2+6*C*a*d*e)*sqrt(1-c*x^4/a)*EllipticE(sin(arcsin(c^(1/4)*x/a^(1/4))),sqrt(-1))/c^(7/4)/sqrt(-c*x^4+a)-1/105*a^(1/4)*(21*sqrt(a)*sqrt(c)*(10*A*c*d*e+3*B*a*e^2+5*B*c*d^2+6*C*a*d*e)-35*A*c*(a*e^2+3*c*d^2)-5*a*(5*a*C*e^2+7*c*d*(2*B*e+C*d)))*sqrt(1-c*x^4/a)*InverseJacobiAM(arcsin(c^(1/4)*x/a^(1/4)),sqrt(-1))/c^(9/4)/sqrt(-c*x^4+a),1],
[(e*x^2+d)*(C*x^4+B*x^2+A)/sqrt(-c*x^4+a),x,7,-1/3*(B*e+C*d)*x*sqrt(-c*x^4+a)/c-1/5*C*e*x^3*sqrt(-c*x^4+a)/c+1/5*a^(3/4)*(5*A*c*e+5*B*c*d+3*C*a*e)*sqrt(1-c*x^4/a)*EllipticE(sin(arcsin(c^(1/4)*x/a^(1/4))),sqrt(-1))/c^(7/4)/sqrt(-c*x^4+a)+1/15*a^(1/4)*(5*sqrt(c)*(3*A*c*d+B*a*e+C*a*d)-3*sqrt(a)*(5*A*c*e+5*B*c*d+3*C*a*e))*sqrt(1-c*x^4/a)*InverseJacobiAM(arcsin(c^(1/4)*x/a^(1/4)),sqrt(-1))/c^(7/4)/sqrt(-c*x^4+a),1],
[(C*x^4+B*x^2+A)/sqrt(-c*x^4+a),x,6,-1/3*C*x*sqrt(-c*x^4+a)/c+a^(3/4)*B*sqrt(1-c*x^4/a)*EllipticE(sin(arcsin(c^(1/4)*x/a^(1/4))),sqrt(-1))/c^(3/4)/sqrt(-c*x^4+a)-1/3*a^(1/4)*(3*sqrt(a)*B*sqrt(c)-3*A*c-a*C)*sqrt(1-c*x^4/a)*InverseJacobiAM(arcsin(c^(1/4)*x/a^(1/4)),sqrt(-1))/c^(5/4)/sqrt(-c*x^4+a),1],
[(C*x^4+B*x^2+A)/(e*x^2+d)/sqrt(-c*x^4+a),x,8,a^(3/4)*C*sqrt(1-c*x^4/a)*EllipticE(sin(arcsin(c^(1/4)*x/a^(1/4))),sqrt(-1))/c^(3/4)/e/sqrt(-c*x^4+a)+a^(1/4)*(B*e-C*(d+sqrt(a)*e/sqrt(c)))*sqrt(1-c*x^4/a)*InverseJacobiAM(arcsin(c^(1/4)*x/a^(1/4)),sqrt(-1))/c^(1/4)/e^2/sqrt(-c*x^4+a)+a^(1/4)*(A*e^2-B*d*e+C*d^2)*sqrt(1-c*x^4/a)*EllipticPi(sin(arcsin(c^(1/4)*x/a^(1/4))),-sqrt(a)*e/sqrt(c)/d,sqrt(-1))/c^(1/4)/d/e^2/sqrt(-c*x^4+a),1],
[(C*x^4+B*x^2+A)/(e*x^2+d)^2/sqrt(-c*x^4+a),x,9,-1/2*(A*e^2-B*d*e+C*d^2)*x*sqrt(-c*x^4+a)/d/(-a*e^2+c*d^2)/(e*x^2+d)-1/2*a^(3/4)*c^(1/4)*(A*e^2-B*d*e+C*d^2)*sqrt(1-c*x^4/a)*EllipticE(sin(arcsin(c^(1/4)*x/a^(1/4))),sqrt(-1))/d/e/(-a*e^2+c*d^2)/sqrt(-c*x^4+a)+1/2*a^(1/4)*(2*sqrt(a)*C*d*e+sqrt(c)*(C*d^2+e*(-A*e+B*d)))*sqrt(1-c*x^4/a)*InverseJacobiAM(arcsin(c^(1/4)*x/a^(1/4)),sqrt(-1))/c^(1/4)/d/e^2/(sqrt(c)*d+sqrt(a)*e)/sqrt(-c*x^4+a)-1/2*a^(1/4)*(c*d^2*(C*d^2+e*(-3*A*e+B*d))-a*e^2*(3*C*d^2-e*(A*e+B*d)))*sqrt(1-c*x^4/a)*EllipticPi(sin(arcsin(c^(1/4)*x/a^(1/4))),-sqrt(a)*e/sqrt(c)/d,sqrt(-1))/c^(1/4)/d^2/e^2/(-a*e^2+c*d^2)/sqrt(-c*x^4+a),1],
[(C*x^4+B*x^2+A)/(e*x^2+d)^3/sqrt(-c*x^4+a),x,10,-1/4*(A*e^2-B*d*e+C*d^2)*x*sqrt(-c*x^4+a)/d/(-a*e^2+c*d^2)/(e*x^2+d)^2-1/8*(c*d^2*(C*d^2-e*(-9*A*e+5*B*d))+a*e^2*(5*C*d^2-e*(3*A*e+B*d)))*x*sqrt(-c*x^4+a)/d^2/(-a*e^2+c*d^2)^2/(e*x^2+d)-1/8*a^(3/4)*c^(1/4)*(c*d^2*(C*d^2-e*(-9*A*e+5*B*d))+a*e^2*(5*C*d^2-e*(3*A*e+B*d)))*sqrt(1-c*x^4/a)*EllipticE(sin(arcsin(c^(1/4)*x/a^(1/4))),sqrt(-1))/d^2/e/(-a*e^2+c*d^2)^2/sqrt(-c*x^4+a)+1/8*a^(1/4)*c^(1/4)*(c*d^2*(C*d^2+e*(-7*A*e+3*B*d))+2*sqrt(a)*sqrt(c)*d*e*(C*d^2-e*(-A*e+B*d))-a*e^2*(5*C*d^2-e*(3*A*e+B*d)))*sqrt(1-c*x^4/a)*InverseJacobiAM(arcsin(c^(1/4)*x/a^(1/4)),sqrt(-1))/d^2/e^2/(sqrt(c)*d+sqrt(a)*e)/(-a*e^2+c*d^2)/sqrt(-c*x^4+a)-1/8*a^(1/4)*(c^2*d^4*(C*d^2+3*e*(-5*A*e+B*d))-a^2*e^4*(3*C*d^2+e*(3*A*e+B*d))-2*a*c*d^2*e^2*(5*C*d^2-e*(3*A*e+5*B*d)))*sqrt(1-c*x^4/a)*EllipticPi(sin(arcsin(c^(1/4)*x/a^(1/4))),-sqrt(a)*e/sqrt(c)/d,sqrt(-1))/c^(1/4)/d^3/e^2/(-a*e^2+c*d^2)^2/sqrt(-c*x^4+a),1],
[(e*x^2+d)^3*(C*x^4+B*x^2+A)/(-c*x^4+a)^(3/2),x,8,1/2*x*(A*c*d*(3*a*e^2+c*d^2)+a*(a*e^2*(B*e+3*C*d)+c*d^2*(3*B*e+C*d))+((A*c+C*a)*e*(a*e^2+3*c*d^2)+B*c*d*(3*a*e^2+c*d^2))*x^2)/a/c^2/sqrt(-c*x^4+a)+1/3*e^2*(B*e+3*C*d)*x*sqrt(-c*x^4+a)/c^2+1/5*C*e^3*x^3*sqrt(-c*x^4+a)/c^2-1/10*(5*B*c*d*(9*a*e^2+c*d^2)+3*e*(5*A*c*(a*e^2+c*d^2)+a*C*(7*a*e^2+15*c*d^2)))*sqrt(1-c*x^4/a)*EllipticE(sin(arcsin(c^(1/4)*x/a^(1/4))),sqrt(-1))/a^(1/4)/c^(11/4)/sqrt(-c*x^4+a)+1/30*(15*A*c*d*(-3*a*e^2+c*d^2)-5*a*(5*a*e^2*(B*e+3*C*d)+3*c*d^2*(3*B*e+C*d))+3*sqrt(a)*(5*B*c*d*(9*a*e^2+c*d^2)+3*e*(5*A*c*(a*e^2+c*d^2)+a*C*(7*a*e^2+15*c*d^2)))/sqrt(c))*sqrt(1-c*x^4/a)*InverseJacobiAM(arcsin(c^(1/4)*x/a^(1/4)),sqrt(-1))/a^(3/4)/c^(9/4)/sqrt(-c*x^4+a),1],
[(e*x^2+d)^2*(C*x^4+B*x^2+A)/(-c*x^4+a)^(3/2),x,7,1/2*x*(A*c*(a*e^2+c*d^2)+a*(a*C*e^2+c*d*(2*B*e+C*d))+c*(2*(A*c+C*a)*d*e+B*(a*e^2+c*d^2))*x^2)/a/c^2/sqrt(-c*x^4+a)+1/3*C*e^2*x*sqrt(-c*x^4+a)/c^2-1/2*(2*A*c*d*e+3*B*a*e^2+B*c*d^2+6*C*a*d*e)*sqrt(1-c*x^4/a)*EllipticE(sin(arcsin(c^(1/4)*x/a^(1/4))),sqrt(-1))/a^(1/4)/c^(7/4)/sqrt(-c*x^4+a)+1/6*(3*A*(-a*e^2+c*d^2)+3*sqrt(a)*(2*A*c*d*e+3*B*a*e^2+B*c*d^2+6*C*a*d*e)/sqrt(c)-a*(5*a*C*e^2+3*c*d*(2*B*e+C*d))/c)*sqrt(1-c*x^4/a)*InverseJacobiAM(arcsin(c^(1/4)*x/a^(1/4)),sqrt(-1))/a^(3/4)/c^(5/4)/sqrt(-c*x^4+a),1],
[(e*x^2+d)*(C*x^4+B*x^2+A)/(-c*x^4+a)^(3/2),x,6,1/2*x*(A*c*d+a*C*d+a*B*e+(A*c*e+B*c*d+C*a*e)*x^2)/a/c/sqrt(-c*x^4+a)-1/2*(A*c*e+B*c*d+3*C*a*e)*sqrt(1-c*x^4/a)*EllipticE(sin(arcsin(c^(1/4)*x/a^(1/4))),sqrt(-1))/a^(1/4)/c^(7/4)/sqrt(-c*x^4+a)+1/2*(sqrt(a)*(B*d+(A+3*a*C/c)*e)+(A*c*d-a*(B*e+C*d))/sqrt(c))*sqrt(1-c*x^4/a)*InverseJacobiAM(arcsin(c^(1/4)*x/a^(1/4)),sqrt(-1))/a^(3/4)/c^(3/4)/sqrt(-c*x^4+a),1],
[(C*x^4+B*x^2+A)/(-c*x^4+a)^(3/2),x,6,1/2*x*(A+a*C/c+B*x^2)/a/sqrt(-c*x^4+a)-1/2*B*sqrt(1-c*x^4/a)*EllipticE(sin(arcsin(c^(1/4)*x/a^(1/4))),sqrt(-1))/a^(1/4)/c^(3/4)/sqrt(-c*x^4+a)+1/2*(sqrt(a)*B*sqrt(c)+A*c-a*C)*sqrt(1-c*x^4/a)*InverseJacobiAM(arcsin(c^(1/4)*x/a^(1/4)),sqrt(-1))/a^(3/4)/c^(5/4)/sqrt(-c*x^4+a),1],
[(C*x^4+B*x^2+A)/(e*x^2+d)/(-c*x^4+a)^(3/2),x,9,1/2*x*((A*c+C*a)*d-a*B*e+(B*c*d-(A*c+C*a)*e)*x^2)/a/(-a*e^2+c*d^2)/sqrt(-c*x^4+a)-1/2*(B*c*d-(A*c+C*a)*e)*sqrt(1-c*x^4/a)*EllipticE(sin(arcsin(c^(1/4)*x/a^(1/4))),sqrt(-1))/a^(1/4)/c^(3/4)/(-a*e^2+c*d^2)/sqrt(-c*x^4+a)+1/2*(sqrt(a)*B*sqrt(c)+A*c+a*C)*sqrt(1-c*x^4/a)*InverseJacobiAM(arcsin(c^(1/4)*x/a^(1/4)),sqrt(-1))/a^(3/4)/c^(3/4)/(sqrt(c)*d+sqrt(a)*e)/sqrt(-c*x^4+a)-a^(1/4)*(A*e^2-B*d*e+C*d^2)*sqrt(1-c*x^4/a)*EllipticPi(sin(arcsin(c^(1/4)*x/a^(1/4))),-sqrt(a)*e/sqrt(c)/d,sqrt(-1))/c^(1/4)/d/(-a*e^2+c*d^2)/sqrt(-c*x^4+a),1],
[(C*x^4+B*x^2+A)/(e*x^2+d)^2/(-c*x^4+a)^(3/2),x,10,-1/2*(A*e^2-B*d*e+C*d^2)*x/d/(-a*e^2+c*d^2)/(e*x^2+d)/sqrt(-c*x^4+a)+1/2*x*(d*(A*c*(2*a*e^2+c*d^2)+a*(a*C*e^2+c*d*(-3*B*e+2*C*d)))+c*(-A*a*e^3-2*A*c*d^2*e+2*B*a*d*e^2+B*c*d^3-3*C*a*d^2*e)*x^2)/a/d/(-a*e^2+c*d^2)^2/sqrt(-c*x^4+a)+1/2*c^(1/4)*(e*(A*a*e^2+2*A*c*d^2+3*C*a*d^2)-B*(2*a*d*e^2+c*d^3))*sqrt(1-c*x^4/a)*EllipticE(sin(arcsin(c^(1/4)*x/a^(1/4))),sqrt(-1))/a^(1/4)/d/(-a*e^2+c*d^2)^2/sqrt(-c*x^4+a)+1/2*(A*c^(3/2)*d^2-a^(3/2)*C*d*e+sqrt(a)*c*d*(-A*e+B*d)+a*sqrt(c)*(2*C*d^2-e*(-A*e+2*B*d)))*sqrt(1-c*x^4/a)*InverseJacobiAM(arcsin(c^(1/4)*x/a^(1/4)),sqrt(-1))/a^(3/4)/c^(1/4)/d/(sqrt(c)*d+sqrt(a)*e)/(-a*e^2+c*d^2)/sqrt(-c*x^4+a)-1/2*a^(1/4)*(c*d^2*(3*C*d^2-e*(-7*A*e+5*B*d))+a*e^2*(3*C*d^2-e*(A*e+B*d)))*sqrt(1-c*x^4/a)*EllipticPi(sin(arcsin(c^(1/4)*x/a^(1/4))),-sqrt(a)*e/sqrt(c)/d,sqrt(-1))/c^(1/4)/d^2/(-a*e^2+c*d^2)^2/sqrt(-c*x^4+a),1],
[(e*x^2+d)^3*(C*x^4+B*x^2+A)/(-c*x^4+a)^(5/2),x,7,1/6*x*(A*c*d*(3*a*e^2+c*d^2)+a*(a*e^2*(B*e+3*C*d)+c*d^2*(3*B*e+C*d))+((A*c+C*a)*e*(a*e^2+3*c*d^2)+B*c*d*(3*a*e^2+c*d^2))*x^2)/a/c^2/(-c*x^4+a)^(3/2)+1/12*x*(A*c*d*(-3*a*e^2+5*c*d^2)-a*(7*a*e^2*(B*e+3*C*d)+c*d^2*(3*B*e+C*d))+3*(B*c*d*(-3*a*e^2+c*d^2)+A*c*e*(-a*e^2+3*c*d^2)-3*a*C*e*(a*e^2+c*d^2))*x^2)/a^2/c^2/sqrt(-c*x^4+a)-1/4*(B*c*d*(-3*a*e^2+c*d^2)+A*c*e*(-a*e^2+3*c*d^2)-a*C*e*(7*a*e^2+3*c*d^2))*sqrt(1-c*x^4/a)*EllipticE(sin(arcsin(c^(1/4)*x/a^(1/4))),sqrt(-1))/a^(5/4)/c^(11/4)/sqrt(-c*x^4+a)+1/12*(5*A*c^(5/2)*d^3-21*a^(5/2)*C*e^3+3*sqrt(a)*c^2*d^2*(3*A*e+B*d)+5*a^2*sqrt(c)*e^2*(B*e+3*C*d)-a*c^(3/2)*d*(C*d^2+3*e*(A*e+B*d))-3*a^(3/2)*c*e*(3*C*d^2+e*(A*e+3*B*d)))*sqrt(1-c*x^4/a)*InverseJacobiAM(arcsin(c^(1/4)*x/a^(1/4)),sqrt(-1))/a^(7/4)/c^(11/4)/sqrt(-c*x^4+a),1],
[(e*x^2+d)^2*(C*x^4+B*x^2+A)/(-c*x^4+a)^(5/2),x,7,1/6*x*(A*c*(a*e^2+c*d^2)+a*(a*C*e^2+c*d*(2*B*e+C*d))+c*(2*(A*c+C*a)*d*e+B*(a*e^2+c*d^2))*x^2)/a/c^2/(-c*x^4+a)^(3/2)+1/12*x*(A*c*(-a*e^2+5*c*d^2)-a*(7*a*C*e^2+c*d*(2*B*e+C*d))+3*c*(2*A*c*d*e-B*a*e^2+B*c*d^2-2*C*a*d*e)*x^2)/a^2/c^2/sqrt(-c*x^4+a)-1/4*(2*A*c*d*e-B*a*e^2+B*c*d^2-2*C*a*d*e)*sqrt(1-c*x^4/a)*EllipticE(sin(arcsin(c^(1/4)*x/a^(1/4))),sqrt(-1))/a^(5/4)/c^(7/4)/sqrt(-c*x^4+a)+1/12*(5*A*c^2*d^2+5*a^2*C*e^2+3*sqrt(a)*c^(3/2)*d*(2*A*e+B*d)-3*a^(3/2)*sqrt(c)*e*(B*e+2*C*d)-a*c*(C*d^2+e*(A*e+2*B*d)))*sqrt(1-c*x^4/a)*InverseJacobiAM(arcsin(c^(1/4)*x/a^(1/4)),sqrt(-1))/a^(7/4)/c^(9/4)/sqrt(-c*x^4+a),1],
[(e*x^2+d)*(C*x^4+B*x^2+A)/(-c*x^4+a)^(5/2),x,7,1/6*x*(A*c*d+a*C*d+a*B*e+(A*c*e+B*c*d+C*a*e)*x^2)/a/c/(-c*x^4+a)^(3/2)+1/12*x*(5*A*c*d-a*(B*e+C*d)+3*(A*c*e+B*c*d-C*a*e)*x^2)/a^2/c/sqrt(-c*x^4+a)-1/4*(A*c*e+B*c*d-C*a*e)*sqrt(1-c*x^4/a)*EllipticE(sin(arcsin(c^(1/4)*x/a^(1/4))),sqrt(-1))/a^(5/4)/c^(7/4)/sqrt(-c*x^4+a)+1/12*(3*sqrt(a)*(B*d+(A-a*C/c)*e)+(5*A*c*d-a*(B*e+C*d))/sqrt(c))*sqrt(1-c*x^4/a)*InverseJacobiAM(arcsin(c^(1/4)*x/a^(1/4)),sqrt(-1))/a^(7/4)/c^(3/4)/sqrt(-c*x^4+a),1],
[(C*x^4+B*x^2+A)/(-c*x^4+a)^(5/2),x,7,1/6*x*(A+a*C/c+B*x^2)/a/(-c*x^4+a)^(3/2)+1/12*x*(5*A-a*C/c+3*B*x^2)/a^2/sqrt(-c*x^4+a)-1/4*B*sqrt(1-c*x^4/a)*EllipticE(sin(arcsin(c^(1/4)*x/a^(1/4))),sqrt(-1))/a^(5/4)/c^(3/4)/sqrt(-c*x^4+a)+1/12*(3*sqrt(a)*B*sqrt(c)+5*A*c-a*C)*sqrt(1-c*x^4/a)*InverseJacobiAM(arcsin(c^(1/4)*x/a^(1/4)),sqrt(-1))/a^(7/4)/c^(5/4)/sqrt(-c*x^4+a),1],
[(C*x^4+B*x^2+A)/(e*x^2+d)/(-c*x^4+a)^(5/2),x,10,1/6*x*((A*c+C*a)*d-a*B*e+(B*c*d-(A*c+C*a)*e)*x^2)/a/(-a*e^2+c*d^2)/(-c*x^4+a)^(3/2)+1/12*x*(A*c*d*(-11*a*e^2+5*c*d^2)-a*(-B*e+C*d)*(5*a*e^2+c*d^2)+3*(B*c*d*(-3*a*e^2+c*d^2)-A*c*e*(-3*a*e^2+c*d^2)+a*C*e*(a*e^2+c*d^2))*x^2)/a^2/(-a*e^2+c*d^2)^2/sqrt(-c*x^4+a)-1/4*(B*c*d*(-3*a*e^2+c*d^2)-A*c*e*(-3*a*e^2+c*d^2)+a*C*e*(a*e^2+c*d^2))*sqrt(1-c*x^4/a)*EllipticE(sin(arcsin(c^(1/4)*x/a^(1/4))),sqrt(-1))/a^(5/4)/c^(3/4)/(-a*e^2+c*d^2)^2/sqrt(-c*x^4+a)+1/12*(5*A*c^2*d^2-3*a^2*C*e^2+sqrt(a)*c^(3/2)*d*(2*A*e+3*B*d)+a^(3/2)*sqrt(c)*e*(-5*B*e+2*C*d)-a*c*(C*d^2-e*(-9*A*e+4*B*d)))*sqrt(1-c*x^4/a)*InverseJacobiAM(arcsin(c^(1/4)*x/a^(1/4)),sqrt(-1))/a^(7/4)/c^(3/4)/(sqrt(c)*d+sqrt(a)*e)/(-a*e^2+c*d^2)/sqrt(-c*x^4+a)+a^(1/4)*e^2*(A*e^2-B*d*e+C*d^2)*sqrt(1-c*x^4/a)*EllipticPi(sin(arcsin(c^(1/4)*x/a^(1/4))),-sqrt(a)*e/sqrt(c)/d,sqrt(-1))/c^(1/4)/d/(-a*e^2+c*d^2)^2/sqrt(-c*x^4+a),1],
[(C*x^4+B*x^2+A)/(e*x^2+d)^2/(-c*x^4+a)^(5/2),x,11,1/6*x*((A*c+C*a)*d-a*B*e+(B*c*d-(A*c+C*a)*e)*x^2)/a/(-a*e^2+c*d^2)/(e*x^2+d)/(-c*x^4+a)^(3/2)-1/6*e*(-3*A*a*e^3-2*A*c*d^2*e+4*B*a*d*e^2+B*c*d^3-5*C*a*d^2*e)*x/a/d/(-a*e^2+c*d^2)^2/(e*x^2+d)/sqrt(-c*x^4+a)+1/12*x*(d*(A*c*(-17*a^2*e^4-18*a*c*d^2*e^2+5*c^2*d^4)-a*(5*a^2*C*e^4+4*a*c*d*e^2*(-7*B*e+6*C*d)+c^2*d^3*(-2*B*e+C*d)))+3*c*(B*(-5*a^2*d*e^4-6*a*c*d^3*e^2+c^2*d^5)+2*a*C*d^2*e*(4*a*e^2+c*d^2)-2*A*(-a^2*e^5-5*a*c*d^2*e^3+c^2*d^4*e))*x^2)/a^2/d/(-a*e^2+c*d^2)^3/sqrt(-c*x^4+a)-1/4*c^(1/4)*(B*(-5*a^2*d*e^4-6*a*c*d^3*e^2+c^2*d^5)+2*a*C*d^2*e*(4*a*e^2+c*d^2)-2*A*(-a^2*e^5-5*a*c*d^2*e^3+c^2*d^4*e))*sqrt(1-c*x^4/a)*EllipticE(sin(arcsin(c^(1/4)*x/a^(1/4))),sqrt(-1))/a^(5/4)/d/(-a*e^2+c*d^2)^3/sqrt(-c*x^4+a)+1/12*(5*A*c^(5/2)*d^4+5*a^(5/2)*C*d*e^3+sqrt(a)*c^2*d^3*(-A*e+3*B*d)-a*c^(3/2)*d^2*(C*d^2-e*(-19*A*e+5*B*d))+a^(3/2)*c*d*e*(5*C*d^2-e*(-11*A*e+13*B*d))-a^2*sqrt(c)*e^2*(19*C*d^2-3*e*(-2*A*e+5*B*d)))*sqrt(1-c*x^4/a)*InverseJacobiAM(arcsin(c^(1/4)*x/a^(1/4)),sqrt(-1))/a^(7/4)/c^(1/4)/d/(sqrt(c)*d-sqrt(a)*e)^2/(sqrt(c)*d+sqrt(a)*e)^3/sqrt(-c*x^4+a)+1/2*a^(1/4)*e^2*(c*d^2*(7*C*d^2-e*(-11*A*e+9*B*d))+a*e^2*(3*C*d^2-e*(A*e+B*d)))*sqrt(1-c*x^4/a)*EllipticPi(sin(arcsin(c^(1/4)*x/a^(1/4))),-sqrt(a)*e/sqrt(c)/d,sqrt(-1))/c^(1/4)/d^2/(-a*e^2+c*d^2)^3/sqrt(-c*x^4+a),1],
[(1+sqrt(c)*x^2/sqrt(a))/(e*x^2+d)/sqrt(-c*x^4+a),x,2,(sqrt(a)-sqrt(c)*x^2)*EllipticPi(sin(arctan(c^(1/4)*x/a^(1/4))),1-sqrt(a)*e/sqrt(c)/d,sqrt(2))/a^(1/4)/c^(1/4)/d/sqrt((sqrt(a)-sqrt(c)*x^2)/(sqrt(a)+sqrt(c)*x^2))/sqrt(-c*x^4+a),1],
[(1+sqrt(c/a)*x^2)/(e*x^2+d)/sqrt(-c*x^4+a),x,2,a*(c/a)^(3/4)*(1-sqrt(c/a)*x^2)*EllipticPi(sin(arctan((c/a)^(1/4)*x)),1-e/sqrt(c/a)/d,sqrt(2))/c/d/sqrt((1-sqrt(c/a)*x^2)/(1+sqrt(c/a)*x^2))/sqrt(-c*x^4+a),1],
[(1-sqrt(c)*x^2/sqrt(a))/(e*x^2+d)/sqrt(-c*x^4+a),x,7,-c^(1/4)*sqrt(1-c*x^4/a)*InverseJacobiAM(arcsin(c^(1/4)*x/a^(1/4)),sqrt(-1))/a^(1/4)/e/sqrt(-c*x^4+a)+(sqrt(c)*d+sqrt(a)*e)*sqrt(1-sqrt(c)*x^2/sqrt(a))*sqrt(1+sqrt(c)*x^2/sqrt(a))*EllipticPi(sin(arcsin(c^(1/4)*x/a^(1/4))),-sqrt(a)*e/sqrt(c)/d,sqrt(-1))/a^(1/4)/c^(1/4)/d/e/sqrt(-c*x^4+a),1],
[(1-sqrt(c/a)*x^2)/(e*x^2+d)/sqrt(-c*x^4+a),x,7,-a^(1/4)*sqrt(c/a)*sqrt(1-c*x^4/a)*InverseJacobiAM(arcsin(c^(1/4)*x/a^(1/4)),sqrt(-1))/c^(1/4)/e/sqrt(-c*x^4+a)+a^(1/4)*(sqrt(c/a)*d+e)*sqrt(1-sqrt(c/a)*x^2)*sqrt(1+sqrt(c/a)*x^2)*EllipticPi(sin(arcsin(c^(1/4)*x/a^(1/4))),-sqrt(a)*e/sqrt(c)/d,sqrt(-1))/c^(1/4)/d/e/sqrt(-c*x^4+a),1],
[1/(x^2+1)/sqrt(-x^4+1),x,2,x*sqrt(-x^4+1)/(2*x^2+2)+1/2*EllipticE(sin(arcsin(x)),sqrt(-1)),1],
[x^2/(x^2+1)/sqrt(-x^4+1),x,4,-1/2*x*sqrt(-x^4+1)/(x^2+1)-1/2*EllipticE(sin(arcsin(x)),sqrt(-1))+InverseJacobiAM(arcsin(x),sqrt(-1)),1],
[(B*x^2+A)/(x^2+1)/sqrt(-x^4+1),x,4,(A-B)*x*sqrt(-x^4+1)/(2*x^2+2)+1/2*(A-B)*EllipticE(sin(arcsin(x)),sqrt(-1))+B*InverseJacobiAM(arcsin(x),sqrt(-1)),1],
[(C*x^4+B*x^2+A)/(x^2+1)/sqrt(-x^4+1),x,4,(A-B+C)*x*sqrt(-x^4+1)/(2*x^2+2)+1/2*(A-B+3*C)*EllipticE(sin(arcsin(x)),sqrt(-1))+(B-2*C)*InverseJacobiAM(arcsin(x),sqrt(-1)),1],
[(B*x^2+A)*(e*x^2+d)^3/sqrt(c*x^4+a),x,7,1/21*e*(21*A*c*d*e-5*B*a*e^2+21*B*c*d^2)*x*sqrt(c*x^4+a)/c^2+1/5*e^2*(A*e+3*B*d)*x^3*sqrt(c*x^4+a)/c+1/7*B*e^3*x^5*sqrt(c*x^4+a)/c+1/5*(-3*A*a*e^3+15*A*c*d^2*e-9*B*a*d*e^2+5*B*c*d^3)*x*sqrt(c*x^4+a)/c^(3/2)/(sqrt(a)+sqrt(c)*x^2)-1/5*a^(1/4)*(-3*A*a*e^3+15*A*c*d^2*e-9*B*a*d*e^2+5*B*c*d^3)*(sqrt(a)+sqrt(c)*x^2)*sqrt((c*x^4+a)/(sqrt(a)+sqrt(c)*x^2)^2)*EllipticE(sin(2*arctan(c^(1/4)*x/a^(1/4))),sqrt(1/2))/c^(7/4)/sqrt(c*x^4+a)+1/210*(105*A*c^2*d^3+25*a^2*B*e^3-105*a*c*d*e*(A*e+B*d)-63*a^(3/2)*sqrt(c)*e^2*(A*e+3*B*d)+105*sqrt(a)*c^(3/2)*d^2*(3*A*e+B*d))*(sqrt(a)+sqrt(c)*x^2)*sqrt((c*x^4+a)/(sqrt(a)+sqrt(c)*x^2)^2)*InverseJacobiAM(2*arctan(c^(1/4)*x/a^(1/4)),sqrt(1/2))/a^(1/4)/c^(9/4)/sqrt(c*x^4+a),1],
[(B*x^2+A)*(e*x^2+d)^2/sqrt(c*x^4+a),x,6,1/3*e*(A*e+2*B*d)*x*sqrt(c*x^4+a)/c+1/5*B*e^2*x^3*sqrt(c*x^4+a)/c+1/5*(10*A*c*d*e-3*B*a*e^2+5*B*c*d^2)*x*sqrt(c*x^4+a)/c^(3/2)/(sqrt(a)+sqrt(c)*x^2)-1/5*a^(1/4)*(10*A*c*d*e-3*B*a*e^2+5*B*c*d^2)*(sqrt(a)+sqrt(c)*x^2)*sqrt((c*x^4+a)/(sqrt(a)+sqrt(c)*x^2)^2)*EllipticE(sin(2*arctan(c^(1/4)*x/a^(1/4))),sqrt(1/2))/c^(7/4)/sqrt(c*x^4+a)+1/30*(15*A*c^(3/2)*d^2-9*a^(3/2)*B*e^2-5*a*sqrt(c)*e*(A*e+2*B*d)+15*sqrt(a)*c*d*(2*A*e+B*d))*(sqrt(a)+sqrt(c)*x^2)*sqrt((c*x^4+a)/(sqrt(a)+sqrt(c)*x^2)^2)*InverseJacobiAM(2*arctan(c^(1/4)*x/a^(1/4)),sqrt(1/2))/a^(1/4)/c^(7/4)/sqrt(c*x^4+a),1],
[(B*x^2+A)*(e*x^2+d)/sqrt(c*x^4+a),x,5,1/3*B*e*x*sqrt(c*x^4+a)/c+(A*e+B*d)*x*sqrt(c*x^4+a)/sqrt(c)/(sqrt(a)+sqrt(c)*x^2)-a^(1/4)*(A*e+B*d)*(sqrt(a)+sqrt(c)*x^2)*sqrt((c*x^4+a)/(sqrt(a)+sqrt(c)*x^2)^2)*EllipticE(sin(2*arctan(c^(1/4)*x/a^(1/4))),sqrt(1/2))/c^(3/4)/sqrt(c*x^4+a)+1/6*(3*A*c*d-a*B*e+3*sqrt(a)*sqrt(c)*(A*e+B*d))*(sqrt(a)+sqrt(c)*x^2)*sqrt((c*x^4+a)/(sqrt(a)+sqrt(c)*x^2)^2)*InverseJacobiAM(2*arctan(c^(1/4)*x/a^(1/4)),sqrt(1/2))/a^(1/4)/c^(5/4)/sqrt(c*x^4+a),1],
[(B*x^2+A)/sqrt(c*x^4+a),x,4,B*x*sqrt(c*x^4+a)/sqrt(c)/(sqrt(a)+sqrt(c)*x^2)-a^(1/4)*B*(sqrt(a)+sqrt(c)*x^2)*sqrt((c*x^4+a)/(sqrt(a)+sqrt(c)*x^2)^2)*EllipticE(sin(2*arctan(c^(1/4)*x/a^(1/4))),sqrt(1/2))/c^(3/4)/sqrt(c*x^4+a)+1/2*(sqrt(a)*B+A*sqrt(c))*(sqrt(a)+sqrt(c)*x^2)*sqrt((c*x^4+a)/(sqrt(a)+sqrt(c)*x^2)^2)*InverseJacobiAM(2*arctan(c^(1/4)*x/a^(1/4)),sqrt(1/2))/a^(1/4)/c^(3/4)/sqrt(c*x^4+a),1],
[(B*x^2+A)/(e*x^2+d)/sqrt(c*x^4+a),x,4,-1/2*(-A*e+B*d)*arctan(sqrt(a*e^2+c*d^2)*x/sqrt(d)/sqrt(e)/sqrt(c*x^4+a))/sqrt(d)/sqrt(e)/sqrt(a*e^2+c*d^2)-1/2*(sqrt(a)*B-A*sqrt(c))*(sqrt(a)+sqrt(c)*x^2)*sqrt((c*x^4+a)/(sqrt(a)+sqrt(c)*x^2)^2)*InverseJacobiAM(2*arctan(c^(1/4)*x/a^(1/4)),sqrt(1/2))/a^(1/4)/c^(1/4)/(sqrt(c)*d-sqrt(a)*e)/sqrt(c*x^4+a)+1/4*(sqrt(c)*d+sqrt(a)*e)*(-A*e+B*d)*(sqrt(a)+sqrt(c)*x^2)*sqrt((c*x^4+a)/(sqrt(a)+sqrt(c)*x^2)^2)*EllipticPi(sin(2*arctan(c^(1/4)*x/a^(1/4))),-1/4*(sqrt(c)*d-sqrt(a)*e)^2/sqrt(a)/sqrt(c)/d/e,sqrt(1/2))/a^(1/4)/c^(1/4)/d/e/(sqrt(c)*d-sqrt(a)*e)/sqrt(c*x^4+a),1],
[(B*x^2+A)/(e*x^2+d)^2/sqrt(c*x^4+a),x,8,1/2*sqrt(c)*(-A*e+B*d)*x*sqrt(c*x^4+a)/d/(a*e^2+c*d^2)/(sqrt(a)+sqrt(c)*x^2)-1/2*e*(-A*e+B*d)*x*sqrt(c*x^4+a)/d/(a*e^2+c*d^2)/(e*x^2+d)-1/4*(-A*a*e^3-3*A*c*d^2*e-B*a*d*e^2+B*c*d^3)*arctan(sqrt(a*e^2+c*d^2)*x/sqrt(d)/sqrt(e)/sqrt(c*x^4+a))/d^(3/2)/sqrt(e)/(a*e^2+c*d^2)^(3/2)-1/2*a^(1/4)*c^(1/4)*(-A*e+B*d)*(sqrt(a)+sqrt(c)*x^2)*sqrt((c*x^4+a)/(sqrt(a)+sqrt(c)*x^2)^2)*EllipticE(sin(2*arctan(c^(1/4)*x/a^(1/4))),sqrt(1/2))/d/(a*e^2+c*d^2)/sqrt(c*x^4+a)+1/2*A*c^(1/4)*(sqrt(a)+sqrt(c)*x^2)*sqrt((c*x^4+a)/(sqrt(a)+sqrt(c)*x^2)^2)*InverseJacobiAM(2*arctan(c^(1/4)*x/a^(1/4)),sqrt(1/2))/a^(1/4)/d/(sqrt(c)*d-sqrt(a)*e)/sqrt(c*x^4+a)+1/8*(sqrt(c)*d+sqrt(a)*e)*(-A*a*e^3-3*A*c*d^2*e-B*a*d*e^2+B*c*d^3)*(sqrt(a)+sqrt(c)*x^2)*sqrt((c*x^4+a)/(sqrt(a)+sqrt(c)*x^2)^2)*EllipticPi(sin(2*arctan(c^(1/4)*x/a^(1/4))),-1/4*(sqrt(c)*d-sqrt(a)*e)^2/sqrt(a)/sqrt(c)/d/e,sqrt(1/2))/a^(1/4)/c^(1/4)/d^2/e/(sqrt(c)*d-sqrt(a)*e)/(a*e^2+c*d^2)/sqrt(c*x^4+a),1],
[(B*x^2+A)/(e*x^2+d)^3/sqrt(c*x^4+a),x,9,1/8*sqrt(c)*(-3*A*a*e^3-9*A*c*d^2*e-B*a*d*e^2+5*B*c*d^3)*x*sqrt(c*x^4+a)/d^2/(a*e^2+c*d^2)^2/(sqrt(a)+sqrt(c)*x^2)-1/4*e*(-A*e+B*d)*x*sqrt(c*x^4+a)/d/(a*e^2+c*d^2)/(e*x^2+d)^2-1/8*e*(-3*A*a*e^3-9*A*c*d^2*e-B*a*d*e^2+5*B*c*d^3)*x*sqrt(c*x^4+a)/d^2/(a*e^2+c*d^2)^2/(e*x^2+d)+1/16*(3*A*e*(a^2*e^4+2*a*c*d^2*e^2+5*c^2*d^4)-B*(-a^2*d*e^4-10*a*c*d^3*e^2+3*c^2*d^5))*arctan(sqrt(a*e^2+c*d^2)*x/sqrt(d)/sqrt(e)/sqrt(c*x^4+a))/d^(5/2)/sqrt(e)/(a*e^2+c*d^2)^(5/2)-1/8*a^(1/4)*c^(1/4)*(-3*A*a*e^3-9*A*c*d^2*e-B*a*d*e^2+5*B*c*d^3)*(sqrt(a)+sqrt(c)*x^2)*sqrt((c*x^4+a)/(sqrt(a)+sqrt(c)*x^2)^2)*EllipticE(sin(2*arctan(c^(1/4)*x/a^(1/4))),sqrt(1/2))/d^2/(a*e^2+c*d^2)^2/sqrt(c*x^4+a)+1/8*c^(1/4)*(4*A*c*d^2+sqrt(a)*sqrt(c)*d*(-A*e+B*d)+a*e*(3*A*e+B*d))*(sqrt(a)+sqrt(c)*x^2)*sqrt((c*x^4+a)/(sqrt(a)+sqrt(c)*x^2)^2)*InverseJacobiAM(2*arctan(c^(1/4)*x/a^(1/4)),sqrt(1/2))/a^(1/4)/d^2/(sqrt(c)*d-sqrt(a)*e)/(a*e^2+c*d^2)/sqrt(c*x^4+a)-1/32*(sqrt(c)*d+sqrt(a)*e)*(3*A*e*(a^2*e^4+2*a*c*d^2*e^2+5*c^2*d^4)-B*(-a^2*d*e^4-10*a*c*d^3*e^2+3*c^2*d^5))*(sqrt(a)+sqrt(c)*x^2)*sqrt((c*x^4+a)/(sqrt(a)+sqrt(c)*x^2)^2)*EllipticPi(sin(2*arctan(c^(1/4)*x/a^(1/4))),-1/4*(sqrt(c)*d-sqrt(a)*e)^2/sqrt(a)/sqrt(c)/d/e,sqrt(1/2))/a^(1/4)/c^(1/4)/d^3/e/(sqrt(c)*d-sqrt(a)*e)/(a*e^2+c*d^2)^2/sqrt(c*x^4+a),1],
[(B*x^2+A)*(e*x^2+d)^3/(c*x^4+a)^(3/2),x,6,1/2*x*(A*c*d*(-3*a*e^2+c*d^2)-a*B*e*(-a*e^2+3*c*d^2)+c*(-A*a*e^3+3*A*c*d^2*e-3*B*a*d*e^2+B*c*d^3)*x^2)/a/c^2/sqrt(c*x^4+a)+1/3*B*e^3*x*sqrt(c*x^4+a)/c^2-1/2*(-3*A*a*e^3+3*A*c*d^2*e-9*B*a*d*e^2+B*c*d^3)*x*sqrt(c*x^4+a)/a/c^(3/2)/(sqrt(a)+sqrt(c)*x^2)+1/2*(-3*A*a*e^3+3*A*c*d^2*e-9*B*a*d*e^2+B*c*d^3)*(sqrt(a)+sqrt(c)*x^2)*sqrt((c*x^4+a)/(sqrt(a)+sqrt(c)*x^2)^2)*EllipticE(sin(2*arctan(c^(1/4)*x/a^(1/4))),sqrt(1/2))/a^(3/4)/c^(7/4)/sqrt(c*x^4+a)+1/12*(3*A*c^2*d^3-5*a^2*B*e^3+9*a*c*d*e*(A*e+B*d)+9*a^(3/2)*sqrt(c)*e^2*(A*e+3*B*d)-3*sqrt(a)*c^(3/2)*d^2*(3*A*e+B*d))*(sqrt(a)+sqrt(c)*x^2)*sqrt((c*x^4+a)/(sqrt(a)+sqrt(c)*x^2)^2)*InverseJacobiAM(2*arctan(c^(1/4)*x/a^(1/4)),sqrt(1/2))/a^(5/4)/c^(9/4)/sqrt(c*x^4+a),1],
[(B*x^2+A)*(e*x^2+d)^2/(c*x^4+a)^(3/2),x,5,1/2*x*(A*c*d^2-2*a*B*d*e-a*A*e^2+(2*A*c*d*e-B*a*e^2+B*c*d^2)*x^2)/a/c/sqrt(c*x^4+a)-1/2*(2*A*c*d*e-3*B*a*e^2+B*c*d^2)*x*sqrt(c*x^4+a)/a/c^(3/2)/(sqrt(a)+sqrt(c)*x^2)+1/2*(2*A*c*d*e-3*B*a*e^2+B*c*d^2)*(sqrt(a)+sqrt(c)*x^2)*sqrt((c*x^4+a)/(sqrt(a)+sqrt(c)*x^2)^2)*EllipticE(sin(2*arctan(c^(1/4)*x/a^(1/4))),sqrt(1/2))/a^(3/4)/c^(7/4)/sqrt(c*x^4+a)+1/4*(A*c^(3/2)*d^2+3*a^(3/2)*B*e^2+a*sqrt(c)*e*(A*e+2*B*d)-sqrt(a)*c*d*(2*A*e+B*d))*(sqrt(a)+sqrt(c)*x^2)*sqrt((c*x^4+a)/(sqrt(a)+sqrt(c)*x^2)^2)*InverseJacobiAM(2*arctan(c^(1/4)*x/a^(1/4)),sqrt(1/2))/a^(5/4)/c^(7/4)/sqrt(c*x^4+a),1],
[(B*x^2+A)*(e*x^2+d)/(c*x^4+a)^(3/2),x,5,1/2*x*(A*d-a*B*e/c+(A*e+B*d)*x^2)/a/sqrt(c*x^4+a)-1/2*(A*e+B*d)*x*sqrt(c*x^4+a)/a/sqrt(c)/(sqrt(a)+sqrt(c)*x^2)+1/2*(A*e+B*d)*(sqrt(a)+sqrt(c)*x^2)*sqrt((c*x^4+a)/(sqrt(a)+sqrt(c)*x^2)^2)*EllipticE(sin(2*arctan(c^(1/4)*x/a^(1/4))),sqrt(1/2))/a^(3/4)/c^(3/4)/sqrt(c*x^4+a)-1/4*(sqrt(a)*(A*e+B*d)-(A*c*d+B*a*e)/sqrt(c))*(sqrt(a)+sqrt(c)*x^2)*sqrt((c*x^4+a)/(sqrt(a)+sqrt(c)*x^2)^2)*InverseJacobiAM(2*arctan(c^(1/4)*x/a^(1/4)),sqrt(1/2))/a^(5/4)/c^(3/4)/sqrt(c*x^4+a),1],
[(B*x^2+A)/(c*x^4+a)^(3/2),x,5,1/2*x*(B*x^2+A)/a/sqrt(c*x^4+a)-1/2*B*x*sqrt(c*x^4+a)/a/sqrt(c)/(sqrt(a)+sqrt(c)*x^2)+1/2*B*(sqrt(a)+sqrt(c)*x^2)*sqrt((c*x^4+a)/(sqrt(a)+sqrt(c)*x^2)^2)*EllipticE(sin(2*arctan(c^(1/4)*x/a^(1/4))),sqrt(1/2))/a^(3/4)/c^(3/4)/sqrt(c*x^4+a)-1/4*(sqrt(a)*B-A*sqrt(c))*(sqrt(a)+sqrt(c)*x^2)*sqrt((c*x^4+a)/(sqrt(a)+sqrt(c)*x^2)^2)*InverseJacobiAM(2*arctan(c^(1/4)*x/a^(1/4)),sqrt(1/2))/a^(5/4)/c^(3/4)/sqrt(c*x^4+a),1],
[(B*x^2+A)/(e*x^2+d)/(c*x^4+a)^(3/2),x,8,1/2*x*(A*c*d+a*B*e+c*(-A*e+B*d)*x^2)/a/(a*e^2+c*d^2)/sqrt(c*x^4+a)-1/2*sqrt(c)*(-A*e+B*d)*x*sqrt(c*x^4+a)/a/(a*e^2+c*d^2)/(sqrt(a)+sqrt(c)*x^2)-1/2*e^(3/2)*(-A*e+B*d)*arctan(sqrt(a*e^2+c*d^2)*x/sqrt(d)/sqrt(e)/sqrt(c*x^4+a))/sqrt(d)/(a*e^2+c*d^2)^(3/2)+1/2*c^(1/4)*(-A*e+B*d)*(sqrt(a)+sqrt(c)*x^2)*sqrt((c*x^4+a)/(sqrt(a)+sqrt(c)*x^2)^2)*EllipticE(sin(2*arctan(c^(1/4)*x/a^(1/4))),sqrt(1/2))/a^(3/4)/(a*e^2+c*d^2)/sqrt(c*x^4+a)-1/4*(sqrt(a)*B-A*sqrt(c))*(sqrt(a)+sqrt(c)*x^2)*sqrt((c*x^4+a)/(sqrt(a)+sqrt(c)*x^2)^2)*InverseJacobiAM(2*arctan(c^(1/4)*x/a^(1/4)),sqrt(1/2))/a^(5/4)/c^(1/4)/(sqrt(c)*d-sqrt(a)*e)/sqrt(c*x^4+a)+1/4*e*(sqrt(c)*d+sqrt(a)*e)*(-A*e+B*d)*(sqrt(a)+sqrt(c)*x^2)*sqrt((c*x^4+a)/(sqrt(a)+sqrt(c)*x^2)^2)*EllipticPi(sin(2*arctan(c^(1/4)*x/a^(1/4))),-1/4*(sqrt(c)*d-sqrt(a)*e)^2/sqrt(a)/sqrt(c)/d/e,sqrt(1/2))/a^(1/4)/c^(1/4)/d/(sqrt(c)*d-sqrt(a)*e)/(a*e^2+c*d^2)/sqrt(c*x^4+a),1],
[(B*x^2+A)/(e*x^2+d)^2/(c*x^4+a)^(3/2),x,9,-1/2*e*(-A*e+B*d)*x/d/(a*e^2+c*d^2)/(e*x^2+d)/sqrt(c*x^4+a)+1/2*c*x*(d*(-2*A*a*e^2+A*c*d^2+3*B*a*d*e)+(A*a*e^3-2*A*c*d^2*e-2*B*a*d*e^2+B*c*d^3)*x^2)/a/d/(a*e^2+c*d^2)^2/sqrt(c*x^4+a)-1/2*sqrt(c)*(A*a*e^3-2*A*c*d^2*e-2*B*a*d*e^2+B*c*d^3)*x*sqrt(c*x^4+a)/a/d/(a*e^2+c*d^2)^2/(sqrt(a)+sqrt(c)*x^2)-1/4*e^(3/2)*(-A*a*e^3-7*A*c*d^2*e-B*a*d*e^2+5*B*c*d^3)*arctan(sqrt(a*e^2+c*d^2)*x/sqrt(d)/sqrt(e)/sqrt(c*x^4+a))/d^(3/2)/(a*e^2+c*d^2)^(5/2)+1/2*c^(1/4)*(A*a*e^3-2*A*c*d^2*e-2*B*a*d*e^2+B*c*d^3)*(sqrt(a)+sqrt(c)*x^2)*sqrt((c*x^4+a)/(sqrt(a)+sqrt(c)*x^2)^2)*EllipticE(sin(2*arctan(c^(1/4)*x/a^(1/4))),sqrt(1/2))/a^(3/4)/d/(a*e^2+c*d^2)^2/sqrt(c*x^4+a)+1/4*c^(1/4)*(A*c*d^2-a*e*(-2*A*e+B*d)-sqrt(a)*sqrt(c)*d*(-A*e+B*d))*(sqrt(a)+sqrt(c)*x^2)*sqrt((c*x^4+a)/(sqrt(a)+sqrt(c)*x^2)^2)*InverseJacobiAM(2*arctan(c^(1/4)*x/a^(1/4)),sqrt(1/2))/a^(5/4)/d/(sqrt(c)*d-sqrt(a)*e)/(a*e^2+c*d^2)/sqrt(c*x^4+a)+1/8*e*(sqrt(c)*d+sqrt(a)*e)*(-A*a*e^3-7*A*c*d^2*e-B*a*d*e^2+5*B*c*d^3)*(sqrt(a)+sqrt(c)*x^2)*sqrt((c*x^4+a)/(sqrt(a)+sqrt(c)*x^2)^2)*EllipticPi(sin(2*arctan(c^(1/4)*x/a^(1/4))),-1/4*(sqrt(c)*d-sqrt(a)*e)^2/sqrt(a)/sqrt(c)/d/e,sqrt(1/2))/a^(1/4)/c^(1/4)/d^2/(sqrt(c)*d-sqrt(a)*e)/(a*e^2+c*d^2)^2/sqrt(c*x^4+a),1],
[(B*x^2+A)/(e*x^2+d)^3/(c*x^4+a)^(3/2),x,10,-1/4*e*(-A*e+B*d)*x/d/(a*e^2+c*d^2)/(e*x^2+d)^2/sqrt(c*x^4+a)-1/8*e*(-3*A*a*e^3-13*A*c*d^2*e-B*a*d*e^2+9*B*c*d^3)*x/d^2/(a*e^2+c*d^2)^2/(e*x^2+d)/sqrt(c*x^4+a)+1/8*c*x*(d*(a*B*d*e*(-7*a*e^2+23*c*d^2)+A*(-a^2*e^4-27*a*c*d^2*e^2+4*c^2*d^4))-(3*A*e*(-a^2*e^4-7*a*c*d^2*e^2+4*c^2*d^4)-B*(a^2*d*e^4-25*a*c*d^3*e^2+4*c^2*d^5))*x^2)/a/d^2/(a*e^2+c*d^2)^3/sqrt(c*x^4+a)+1/8*sqrt(c)*(3*A*e*(-a^2*e^4-7*a*c*d^2*e^2+4*c^2*d^4)-B*(a^2*d*e^4-25*a*c*d^3*e^2+4*c^2*d^5))*x*sqrt(c*x^4+a)/a/d^2/(a*e^2+c*d^2)^3/(sqrt(a)+sqrt(c)*x^2)+1/16*e^(3/2)*(3*A*e*(a^2*e^4+2*a*c*d^2*e^2+21*c^2*d^4)-B*(-a^2*d*e^4-26*a*c*d^3*e^2+35*c^2*d^5))*arctan(sqrt(a*e^2+c*d^2)*x/sqrt(d)/sqrt(e)/sqrt(c*x^4+a))/d^(5/2)/(a*e^2+c*d^2)^(7/2)-1/8*c^(1/4)*(3*A*e*(-a^2*e^4-7*a*c*d^2*e^2+4*c^2*d^4)-B*(a^2*d*e^4-25*a*c*d^3*e^2+4*c^2*d^5))*(sqrt(a)+sqrt(c)*x^2)*sqrt((c*x^4+a)/(sqrt(a)+sqrt(c)*x^2)^2)*EllipticE(sin(2*arctan(c^(1/4)*x/a^(1/4))),sqrt(1/2))/a^(3/4)/d^2/(a*e^2+c*d^2)^3/sqrt(c*x^4+a)+1/8*c^(1/4)*(2*A*c^2*d^4-2*a*c*d^2*e*(-5*A*e+2*B*d)-2*sqrt(a)*c^(3/2)*d^3*(-2*A*e+B*d)+a^(3/2)*sqrt(c)*d*e^2*(-A*e+3*B*d)+a^2*e^3*(3*A*e+B*d))*(sqrt(a)+sqrt(c)*x^2)*sqrt((c*x^4+a)/(sqrt(a)+sqrt(c)*x^2)^2)*InverseJacobiAM(2*arctan(c^(1/4)*x/a^(1/4)),sqrt(1/2))/a^(5/4)/d^2/(sqrt(c)*d-sqrt(a)*e)/(a*e^2+c*d^2)^2/sqrt(c*x^4+a)-1/32*e*(sqrt(c)*d+sqrt(a)*e)*(3*A*e*(a^2*e^4+2*a*c*d^2*e^2+21*c^2*d^4)-B*(-a^2*d*e^4-26*a*c*d^3*e^2+35*c^2*d^5))*(sqrt(a)+sqrt(c)*x^2)*sqrt((c*x^4+a)/(sqrt(a)+sqrt(c)*x^2)^2)*EllipticPi(sin(2*arctan(c^(1/4)*x/a^(1/4))),-1/4*(sqrt(c)*d-sqrt(a)*e)^2/sqrt(a)/sqrt(c)/d/e,sqrt(1/2))/a^(1/4)/c^(1/4)/d^3/(sqrt(c)*d-sqrt(a)*e)/(a*e^2+c*d^2)^3/sqrt(c*x^4+a),1],
[(1+sqrt(c)*x^2/sqrt(a))/(e*x^2+d)/sqrt(c*x^4+a),x,2,-1/2*(sqrt(c)*d/sqrt(a)-e)*arctan(sqrt(a*e^2+c*d^2)*x/sqrt(d)/sqrt(e)/sqrt(c*x^4+a))/sqrt(d)/sqrt(e)/sqrt(a*e^2+c*d^2)+1/4*(sqrt(c)*d+sqrt(a)*e)*(sqrt(a)+sqrt(c)*x^2)*sqrt((c*x^4+a)/(sqrt(a)+sqrt(c)*x^2)^2)*EllipticPi(sin(2*arctan(c^(1/4)*x/a^(1/4))),-1/4*sqrt(a)*(sqrt(c)*d/sqrt(a)-e)^2/sqrt(c)/d/e,sqrt(1/2))/a^(3/4)/c^(1/4)/d/e/sqrt(c*x^4+a),1],
[(1+sqrt(c/a)*x^2)/(e*x^2+d)/sqrt(c*x^4+a),x,2,-1/2*(sqrt(c/a)*d-e)*arctan(sqrt(a*e^2+c*d^2)*x/sqrt(d)/sqrt(e)/sqrt(c*x^4+a))/sqrt(d)/sqrt(e)/sqrt(a*e^2+c*d^2)+1/4*(sqrt(c/a)*d+e)*(1+sqrt(c/a)*x^2)*sqrt(sqrt(c/a)*(c*x^4+a)/c/(1/(c/a)^(1/4)+(c/a)^(1/4)*x^2)^2)*EllipticPi(sin(2*arctan((c/a)^(1/4)*x)),-1/4*(sqrt(c/a)*d-e)^2/sqrt(c/a)/d/e,sqrt(1/2))/(c/a)^(1/4)/d/e/sqrt(c*x^4+a),1],
[(1-sqrt(c)*x^2/sqrt(a))/(e*x^2+d)/sqrt(c*x^4+a),x,4,1/2*(sqrt(c)*d+sqrt(a)*e)*arctan(sqrt(a*e^2+c*d^2)*x/sqrt(d)/sqrt(e)/sqrt(c*x^4+a))/sqrt(a)/sqrt(d)/sqrt(e)/sqrt(a*e^2+c*d^2)+c^(1/4)*(sqrt(a)+sqrt(c)*x^2)*sqrt((c*x^4+a)/(sqrt(a)+sqrt(c)*x^2)^2)*InverseJacobiAM(2*arctan(c^(1/4)*x/a^(1/4)),sqrt(1/2))/a^(1/4)/(sqrt(c)*d-sqrt(a)*e)/sqrt(c*x^4+a)-1/4*(sqrt(c)*d+sqrt(a)*e)^2*(sqrt(a)+sqrt(c)*x^2)*sqrt((c*x^4+a)/(sqrt(a)+sqrt(c)*x^2)^2)*EllipticPi(sin(2*arctan(c^(1/4)*x/a^(1/4))),-1/4*(sqrt(c)*d-sqrt(a)*e)^2/sqrt(a)/sqrt(c)/d/e,sqrt(1/2))/a^(3/4)/c^(1/4)/d/e/(sqrt(c)*d-sqrt(a)*e)/sqrt(c*x^4+a),1],
[(1-sqrt(c/a)*x^2)/(e*x^2+d)/sqrt(c*x^4+a),x,4,1/2*(sqrt(c/a)*d+e)*arctan(sqrt(a*e^2+c*d^2)*x/sqrt(d)/sqrt(e)/sqrt(c*x^4+a))/sqrt(d)/sqrt(e)/sqrt(a*e^2+c*d^2)+a^(3/4)*(c/a)^(3/2)*(sqrt(a)+sqrt(c)*x^2)*sqrt((c*x^4+a)/(sqrt(a)+sqrt(c)*x^2)^2)*InverseJacobiAM(2*arctan(c^(1/4)*x/a^(1/4)),sqrt(1/2))/c^(5/4)/(sqrt(c/a)*d-e)/sqrt(c*x^4+a)-1/4*(sqrt(c/a)*d+e)^2*(1+sqrt(c/a)*x^2)*sqrt(sqrt(c/a)*(c*x^4+a)/c/(1/(c/a)^(1/4)+(c/a)^(1/4)*x^2)^2)*EllipticPi(sin(2*arctan((c/a)^(1/4)*x)),-1/4*(sqrt(c/a)*d-e)^2/sqrt(c/a)/d/e,sqrt(1/2))/(c/a)^(1/4)/d/(sqrt(c/a)*d-e)/e/sqrt(c*x^4+a),1],
[(1+sqrt(b)*x^2/sqrt(a+b))/(-x^2+1)/sqrt(b*x^4+a+b),x,2,1/2*(1+sqrt(b)/sqrt(a+b))*arctanh(sqrt(a+2*b)*x/sqrt(b*x^4+a+b))/sqrt(a+2*b)+1/4*(1-sqrt(b)/sqrt(a+b))*(sqrt(a+b)+sqrt(b)*x^2)*sqrt((b*x^4+a+b)/(sqrt(a+b)+sqrt(b)*x^2)^2)*EllipticPi(sin(2*arctan(b^(1/4)*x/(a+b)^(1/4))),1/4*(sqrt(b)+sqrt(a+b))^2/sqrt(b)/sqrt(a+b),sqrt(1/2))/b^(1/4)/(a+b)^(1/4)/sqrt(b*x^4+a+b),1],
[(1+sqrt(b)*(a+b-sqrt(b)*sqrt(a+b))*x^2/(a+b)/(-sqrt(b)+sqrt(a+b)))/(-x^2+1)/sqrt(b*x^4+a+b),x,2,1/2*(1+sqrt(b)/sqrt(a+b))*arctanh(sqrt(a+2*b)*x/sqrt(b*x^4+a+b))/sqrt(a+2*b)+1/4*(1-sqrt(b)/sqrt(a+b))*((a+b)^(1/4)+sqrt(b)*x^2/(a+b)^(1/4))*sqrt((b*x^4+a+b)/(sqrt(a+b)+sqrt(b)*x^2)^2)*EllipticPi(sin(2*arctan(b^(1/4)*x/(a+b)^(1/4))),1/4*(sqrt(b)+sqrt(a+b))^2/sqrt(b)/sqrt(a+b),sqrt(1/2))/b^(1/4)/sqrt(b*x^4+a+b),1],
[(-sqrt(a+b)-sqrt(b)*x^2)/sqrt(a+b)/(x^2-1)/sqrt(b*x^4+a+b),x,3,1/2*(sqrt(b)+sqrt(a+b))*arctanh(sqrt(a+2*b)*x/sqrt(b*x^4+a+b))/sqrt(a+b)/sqrt(a+2*b)-1/4*(sqrt(b)-sqrt(a+b))*(sqrt(a+b)+sqrt(b)*x^2)*sqrt((b*x^4+a+b)/(sqrt(a+b)+sqrt(b)*x^2)^2)*EllipticPi(sin(2*arctan(b^(1/4)*x/(a+b)^(1/4))),1/4*(sqrt(b)+sqrt(a+b))^2/sqrt(b)/sqrt(a+b),sqrt(1/2))/b^(1/4)/(a+b)^(3/4)/sqrt(b*x^4+a+b),1],
[((a+b)*(-sqrt(b)+sqrt(a+b))+sqrt(b)*(a+b-sqrt(b)*sqrt(a+b))*x^2)/(-x^2+1)/sqrt(b*x^4+a+b),x,2,1/2*a*sqrt(a+b)*arctanh(sqrt(a+2*b)*x/sqrt(b*x^4+a+b))/sqrt(a+2*b)+1/4*(a+b)^(1/4)*(sqrt(b)-sqrt(a+b))^2*(sqrt(a+b)+sqrt(b)*x^2)*sqrt((b*x^4+a+b)/(sqrt(a+b)+sqrt(b)*x^2)^2)*EllipticPi(sin(2*arctan(b^(1/4)*x/(a+b)^(1/4))),1/4*(sqrt(b)+sqrt(a+b))^2/sqrt(b)/sqrt(a+b),sqrt(1/2))/b^(1/4)/sqrt(b*x^4+a+b),1],
[(a*sqrt(a+b)+b*sqrt(a+b)+sqrt(b)*(a+b))*(1-sqrt(b)*x^2/sqrt(a+b))/(-x^2+1)/sqrt(b*x^4+a+b),x,5,1/2*a*sqrt(a+b)*arctanh(sqrt(a+2*b)*x/sqrt(b*x^4+a+b))/sqrt(a+2*b)+b^(1/4)*(a+b)^(5/4)*(1+sqrt(b)*x^2/sqrt(a+b))*sqrt((b*x^4+a+b)/(a+b)/(1+sqrt(b)*x^2/sqrt(a+b))^2)*InverseJacobiAM(2*arctan(b^(1/4)*x/(a+b)^(1/4)),sqrt(1/2))/sqrt(b*x^4+a+b)+1/4*(a+b)^(3/4)*(sqrt(b)-sqrt(a+b))^2*(1+sqrt(b)*x^2/sqrt(a+b))*sqrt((b*x^4+a+b)/(a+b)/(1+sqrt(b)*x^2/sqrt(a+b))^2)*EllipticPi(sin(2*arctan(b^(1/4)*x/(a+b)^(1/4))),1/4*(sqrt(b)+sqrt(a+b))^2/sqrt(b)/sqrt(a+b),sqrt(1/2))/b^(1/4)/sqrt(b*x^4+a+b),1],
[(a*sqrt(a+b)+b*sqrt(a+b)+sqrt(b)*(a+b)-sqrt(b)*(a+b+sqrt(b)*sqrt(a+b))*x^2)/(-x^2+1)/sqrt(b*x^4+a+b),x,4,1/2*a*sqrt(a+b)*arctanh(sqrt(a+2*b)*x/sqrt(b*x^4+a+b))/sqrt(a+2*b)+b^(1/4)*(a+b)^(5/4)*(1+sqrt(b)*x^2/sqrt(a+b))*sqrt((b*x^4+a+b)/(a+b)/(1+sqrt(b)*x^2/sqrt(a+b))^2)*InverseJacobiAM(2*arctan(b^(1/4)*x/(a+b)^(1/4)),sqrt(1/2))/sqrt(b*x^4+a+b)+1/4*(a+b)^(3/4)*(sqrt(b)-sqrt(a+b))^2*(1+sqrt(b)*x^2/sqrt(a+b))*sqrt((b*x^4+a+b)/(a+b)/(1+sqrt(b)*x^2/sqrt(a+b))^2)*EllipticPi(sin(2*arctan(b^(1/4)*x/(a+b)^(1/4))),1/4*(sqrt(b)+sqrt(a+b))^2/sqrt(b)/sqrt(a+b),sqrt(1/2))/b^(1/4)/sqrt(b*x^4+a+b),1],
[(B*x^2+A)*(e*x^2+d)^(3/2)*sqrt(-c*x^4+a),x,12,-1/384*(64*A*a*e^3-24*A*c*d^2*e+84*B*a*d*e^2+9*B*c*d^3)*sqrt(e*x^2+d)*sqrt(-c*x^4+a)/c/e^2/x+1/192*(56*A*c*d*e-12*B*a*e^2+3*B*c*d^2)*x*sqrt(e*x^2+d)*sqrt(-c*x^4+a)/c/e+1/48*(8*A*e+9*B*d)*x^3*sqrt(e*x^2+d)*sqrt(-c*x^4+a)+1/8*B*e*x^5*sqrt(e*x^2+d)*sqrt(-c*x^4+a)-1/384*(d+sqrt(a)*e/sqrt(c))*(64*A*a*e^3-24*A*c*d^2*e+84*B*a*d*e^2+9*B*c*d^3)*sqrt(1-a/c/x^4)*x^3*sqrt(sqrt(a)*(e*x^2+d)/(sqrt(c)*d+sqrt(a)*e)/x^2)*EllipticE(sin(arcsin(sqrt(1-sqrt(a)/sqrt(c)/x^2)/sqrt(2))),sqrt(2*d/(d+sqrt(a)*e/sqrt(c))))/e^2/sqrt(e*x^2+d)/sqrt(-c*x^4+a)+1/384*sqrt(a)*(64*A*a*e^3+248*A*c*d^2*e+108*B*a*d*e^2+3*B*c*d^3)*sqrt(1-a/c/x^4)*x^3*sqrt(sqrt(a)*(e*x^2+d)/(sqrt(c)*d+sqrt(a)*e)/x^2)*InverseJacobiAM(arcsin(sqrt(1-sqrt(a)/sqrt(c)/x^2)/sqrt(2)),sqrt(2*d/(d+sqrt(a)*e/sqrt(c))))/sqrt(c)/e/sqrt(e*x^2+d)/sqrt(-c*x^4+a)+1/128*(8*A*c*d*e*(12*a*e^2+c*d^2)-B*(-16*a^2*e^4-24*a*c*d^2*e^2+3*c^2*d^4))*sqrt(1-a/c/x^4)*x^3*sqrt(sqrt(a)*(e*x^2+d)/(sqrt(c)*d+sqrt(a)*e)/x^2)*EllipticPi(sin(arcsin(sqrt(1-sqrt(a)/sqrt(c)/x^2)/sqrt(2))),2,sqrt(2*d/(d+sqrt(a)*e/sqrt(c))))/c/e^2/sqrt(e*x^2+d)/sqrt(-c*x^4+a),1],
[(B*x^2+A)*sqrt(e*x^2+d)*sqrt(-c*x^4+a),x,11,-1/48*(-6*A*c*d*e+8*B*a*e^2+3*B*c*d^2)*sqrt(e*x^2+d)*sqrt(-c*x^4+a)/c/e^2/x+1/24*(6*A*e+B*d)*x*sqrt(e*x^2+d)*sqrt(-c*x^4+a)/e+1/6*B*x^3*sqrt(e*x^2+d)*sqrt(-c*x^4+a)-1/48*(d+sqrt(a)*e/sqrt(c))*(-6*A*c*d*e+8*B*a*e^2+3*B*c*d^2)*sqrt(1-a/c/x^4)*x^3*sqrt(sqrt(a)*(e*x^2+d)/(sqrt(c)*d+sqrt(a)*e)/x^2)*EllipticE(sin(arcsin(sqrt(1-sqrt(a)/sqrt(c)/x^2)/sqrt(2))),sqrt(2*d/(d+sqrt(a)*e/sqrt(c))))/e^2/sqrt(e*x^2+d)/sqrt(-c*x^4+a)+1/48*sqrt(a)*(30*A*c*d*e+8*B*a*e^2+B*c*d^2)*sqrt(1-a/c/x^4)*x^3*sqrt(sqrt(a)*(e*x^2+d)/(sqrt(c)*d+sqrt(a)*e)/x^2)*InverseJacobiAM(arcsin(sqrt(1-sqrt(a)/sqrt(c)/x^2)/sqrt(2)),sqrt(2*d/(d+sqrt(a)*e/sqrt(c))))/sqrt(c)/e/sqrt(e*x^2+d)/sqrt(-c*x^4+a)-1/16*(-8*A*a*e^3-2*A*c*d^2*e-4*B*a*d*e^2+B*c*d^3)*sqrt(1-a/c/x^4)*x^3*sqrt(sqrt(a)*(e*x^2+d)/(sqrt(c)*d+sqrt(a)*e)/x^2)*EllipticPi(sin(arcsin(sqrt(1-sqrt(a)/sqrt(c)/x^2)/sqrt(2))),2,sqrt(2*d/(d+sqrt(a)*e/sqrt(c))))/e^2/sqrt(e*x^2+d)/sqrt(-c*x^4+a),1],
[(B*x^2+A)*sqrt(-c*x^4+a)/sqrt(e*x^2+d),x,10,-1/8*(-4*A*e+3*B*d)*sqrt(e*x^2+d)*sqrt(-c*x^4+a)/e^2/x+1/4*B*x*sqrt(e*x^2+d)*sqrt(-c*x^4+a)/e-1/8*c*(-4*A*e+3*B*d)*(d+sqrt(a)*e/sqrt(c))*sqrt(1-a/c/x^4)*x^3*sqrt(sqrt(a)*(e*x^2+d)/(sqrt(c)*d+sqrt(a)*e)/x^2)*EllipticE(sin(arcsin(sqrt(1-sqrt(a)/sqrt(c)/x^2)/sqrt(2))),sqrt(2*d/(d+sqrt(a)*e/sqrt(c))))/e^2/sqrt(e*x^2+d)/sqrt(-c*x^4+a)+1/8*sqrt(a)*sqrt(c)*(4*A*e+B*d)*sqrt(1-a/c/x^4)*x^3*sqrt(sqrt(a)*(e*x^2+d)/(sqrt(c)*d+sqrt(a)*e)/x^2)*InverseJacobiAM(arcsin(sqrt(1-sqrt(a)/sqrt(c)/x^2)/sqrt(2)),sqrt(2*d/(d+sqrt(a)*e/sqrt(c))))/e/sqrt(e*x^2+d)/sqrt(-c*x^4+a)-1/8*(-4*A*c*d*e-4*B*a*e^2+3*B*c*d^2)*sqrt(1-a/c/x^4)*x^3*sqrt(sqrt(a)*(e*x^2+d)/(sqrt(c)*d+sqrt(a)*e)/x^2)*EllipticPi(sin(arcsin(sqrt(1-sqrt(a)/sqrt(c)/x^2)/sqrt(2))),2,sqrt(2*d/(d+sqrt(a)*e/sqrt(c))))/e^2/sqrt(e*x^2+d)/sqrt(-c*x^4+a),1],
[(B*x^2+A)*sqrt(-c*x^4+a)/(e*x^2+d)^(3/2),x,10,(A/d-B/e)*x*sqrt(-c*x^4+a)/sqrt(e*x^2+d)+1/2*(-2*A*e+3*B*d)*sqrt(e*x^2+d)*sqrt(-c*x^4+a)/d/e^2/x+1/2*sqrt(c)*(sqrt(c)*d+sqrt(a)*e)*(-2*A*e+3*B*d)*sqrt(1-a/c/x^4)*x^3*sqrt(sqrt(a)*(e*x^2+d)/(sqrt(c)*d+sqrt(a)*e)/x^2)*EllipticE(sin(arcsin(sqrt(1-sqrt(a)/sqrt(c)/x^2)/sqrt(2))),sqrt(2*d/(d+sqrt(a)*e/sqrt(c))))/d/e^2/sqrt(e*x^2+d)/sqrt(-c*x^4+a)-1/2*sqrt(a)*sqrt(c)*(-2*A*e+B*d)*sqrt(1-a/c/x^4)*x^3*sqrt(sqrt(a)*(e*x^2+d)/(sqrt(c)*d+sqrt(a)*e)/x^2)*InverseJacobiAM(arcsin(sqrt(1-sqrt(a)/sqrt(c)/x^2)/sqrt(2)),sqrt(2*d/(d+sqrt(a)*e/sqrt(c))))/d/e/sqrt(e*x^2+d)/sqrt(-c*x^4+a)+1/2*c*(-2*A*e+3*B*d)*sqrt(1-a/c/x^4)*x^3*sqrt(sqrt(a)*(e*x^2+d)/(sqrt(c)*d+sqrt(a)*e)/x^2)*EllipticPi(sin(arcsin(sqrt(1-sqrt(a)/sqrt(c)/x^2)/sqrt(2))),2,sqrt(2*d/(d+sqrt(a)*e/sqrt(c))))/e^2/sqrt(e*x^2+d)/sqrt(-c*x^4+a),1],
[(B*x^2+A)*sqrt(-c*x^4+a)/(e*x^2+d)^(5/2),x,10,1/3*(A/d-B/e)*x*sqrt(-c*x^4+a)/(e*x^2+d)^(3/2)-1/3*(-2*A*a*e^3-B*a*d*e^2+3*B*c*d^3)*sqrt(-c*x^4+a)/d/e^2/(-a*e^2+c*d^2)/x/sqrt(e*x^2+d)-1/3*sqrt(c)*(-2*A*a*e^3-B*a*d*e^2+3*B*c*d^3)*sqrt(1-a/c/x^4)*x^3*sqrt(sqrt(a)*(e*x^2+d)/(sqrt(c)*d+sqrt(a)*e)/x^2)*EllipticE(sin(arcsin(sqrt(1-sqrt(a)/sqrt(c)/x^2)/sqrt(2))),sqrt(2*d/(d+sqrt(a)*e/sqrt(c))))/d^2/e^2/(sqrt(c)*d-sqrt(a)*e)/sqrt(e*x^2+d)/sqrt(-c*x^4+a)+1/3*sqrt(a)*sqrt(c)*(2*A*e+B*d)*sqrt(1-a/c/x^4)*x^3*sqrt(sqrt(a)*(e*x^2+d)/(sqrt(c)*d+sqrt(a)*e)/x^2)*InverseJacobiAM(arcsin(sqrt(1-sqrt(a)/sqrt(c)/x^2)/sqrt(2)),sqrt(2*d/(d+sqrt(a)*e/sqrt(c))))/d^2/e/sqrt(e*x^2+d)/sqrt(-c*x^4+a)-B*c*sqrt(1-a/c/x^4)*x^3*sqrt(sqrt(a)*(e*x^2+d)/(sqrt(c)*d+sqrt(a)*e)/x^2)*EllipticPi(sin(arcsin(sqrt(1-sqrt(a)/sqrt(c)/x^2)/sqrt(2))),2,sqrt(2*d/(d+sqrt(a)*e/sqrt(c))))/e^2/sqrt(e*x^2+d)/sqrt(-c*x^4+a),1],
[(B*x^2+A)*sqrt(-c*x^4+a)/(e*x^2+d)^(7/2),x,8,1/5*(A/d-B/e)*x*sqrt(-c*x^4+a)/(e*x^2+d)^(5/2)+1/15*(-4*A*a*e^3+2*A*c*d^2*e-B*a*d*e^2+3*B*c*d^3)*x*sqrt(-c*x^4+a)/d^2/e/(-a*e^2+c*d^2)/(e*x^2+d)^(3/2)-2/15*a*(4*A*a*e^3-8*A*c*d^2*e+B*a*d*e^2+3*B*c*d^3)*sqrt(-c*x^4+a)/d^2/(-a*e^2+c*d^2)^2/x/sqrt(e*x^2+d)-2/15*a*sqrt(c)*(4*A*a*e^3-8*A*c*d^2*e+B*a*d*e^2+3*B*c*d^3)*sqrt(1-a/c/x^4)*x^3*sqrt(sqrt(a)*(e*x^2+d)/(sqrt(c)*d+sqrt(a)*e)/x^2)*EllipticE(sin(arcsin(sqrt(1-sqrt(a)/sqrt(c)/x^2)/sqrt(2))),sqrt(2*d/(d+sqrt(a)*e/sqrt(c))))/d^3/(sqrt(c)*d-sqrt(a)*e)/(-a*e^2+c*d^2)/sqrt(e*x^2+d)/sqrt(-c*x^4+a)+2/15*sqrt(a)*sqrt(c)*(-4*A*a*e^2+5*A*c*d^2-B*a*d*e)*sqrt(1-a/c/x^4)*x^3*sqrt(sqrt(a)*(e*x^2+d)/(sqrt(c)*d+sqrt(a)*e)/x^2)*InverseJacobiAM(arcsin(sqrt(1-sqrt(a)/sqrt(c)/x^2)/sqrt(2)),sqrt(2*d/(d+sqrt(a)*e/sqrt(c))))/d^3/(-a*e^2+c*d^2)/sqrt(e*x^2+d)/sqrt(-c*x^4+a),1],
[(B*x^2+A)*sqrt(-c*x^4+a)/(e*x^2+d)^(9/2),x,9,1/7*(A/d-B/e)*x*sqrt(-c*x^4+a)/(e*x^2+d)^(7/2)+1/35*(-6*A*a*e^3+4*A*c*d^2*e-B*a*d*e^2+3*B*c*d^3)*x*sqrt(-c*x^4+a)/d^2/e/(-a*e^2+c*d^2)/(e*x^2+d)^(5/2)+2/105*(4*A*e*(3*a^2*e^4-6*a*c*d^2*e^2+c^2*d^4)+B*(2*a^2*d*e^4+3*a*c*d^3*e^2+3*c^2*d^5))*x*sqrt(-c*x^4+a)/d^3/e/(-a*e^2+c*d^2)^2/(e*x^2+d)^(3/2)+2/105*a*(A*e*(24*a^2*e^4-69*a*c*d^2*e^2+77*c^2*d^4)-B*(-4*a^2*d*e^4+15*a*c*d^3*e^2+21*c^2*d^5))*sqrt(-c*x^4+a)/d^3/(-a*e^2+c*d^2)^3/x/sqrt(e*x^2+d)-2/105*a*sqrt(c)*(-24*A*a^2*e^5+69*A*a*c*d^2*e^3-77*A*c^2*d^4*e-4*B*a^2*d*e^4+15*B*a*c*d^3*e^2+21*B*c^2*d^5)*sqrt(1-a/c/x^4)*x^3*sqrt(sqrt(a)*(e*x^2+d)/(sqrt(c)*d+sqrt(a)*e)/x^2)*EllipticE(sin(arcsin(sqrt(1-sqrt(a)/sqrt(c)/x^2)/sqrt(2))),sqrt(2*d/(d+sqrt(a)*e/sqrt(c))))/d^4/(sqrt(c)*d-sqrt(a)*e)^3/(sqrt(c)*d+sqrt(a)*e)^2/sqrt(e*x^2+d)/sqrt(-c*x^4+a)-2/105*sqrt(a)*sqrt(c)*(4*a*B*d*e*(-a*e^2+3*c*d^2)-A*(24*a^2*e^4-51*a*c*d^2*e^2+35*c^2*d^4))*sqrt(1-a/c/x^4)*x^3*sqrt(sqrt(a)*(e*x^2+d)/(sqrt(c)*d+sqrt(a)*e)/x^2)*InverseJacobiAM(arcsin(sqrt(1-sqrt(a)/sqrt(c)/x^2)/sqrt(2)),sqrt(2*d/(d+sqrt(a)*e/sqrt(c))))/d^4/(-a*e^2+c*d^2)^2/sqrt(e*x^2+d)/sqrt(-c*x^4+a),1],
[(B*x^2+A)*sqrt(-c*x^4+a)/(e*x^2+d)^(11/2),x,10,1/9*(A/d-B/e)*x*sqrt(-c*x^4+a)/(e*x^2+d)^(9/2)+1/63*(-8*A*a*e^3+6*A*c*d^2*e-B*a*d*e^2+3*B*c*d^3)*x*sqrt(-c*x^4+a)/d^2/e/(-a*e^2+c*d^2)/(e*x^2+d)^(7/2)+2/105*(4*A*e*(2*a^2*e^4-4*a*c*d^2*e^2+c^2*d^4)+B*(a^2*d*e^4+a*c*d^3*e^2+2*c^2*d^5))*x*sqrt(-c*x^4+a)/d^3/e/(-a*e^2+c*d^2)^2/(e*x^2+d)^(5/2)+2/315*(A*e*(-32*a^3*e^6+95*a^2*c*d^2*e^4-103*a*c^2*d^4*e^2+8*c^3*d^6)+B*(-4*a^3*d*e^6+13*a^2*c*d^3*e^4+19*a*c^2*d^5*e^2+4*c^3*d^7))*x*sqrt(-c*x^4+a)/d^4/e/(-a*e^2+c*d^2)^3/(e*x^2+d)^(3/2)+2/315*a*(2*A*e*(-32*a^3*e^6+123*a^2*c*d^2*e^4-174*a*c^2*d^4*e^2+147*c^3*d^6)-B*(8*a^3*d*e^6-33*a^2*c*d^3*e^4+90*a*c^2*d^5*e^2+63*c^3*d^7))*sqrt(-c*x^4+a)/d^4/(-a*e^2+c*d^2)^4/x/sqrt(e*x^2+d)+2/315*a*sqrt(c)*(2*A*e*(-32*a^3*e^6+123*a^2*c*d^2*e^4-174*a*c^2*d^4*e^2+147*c^3*d^6)-B*(8*a^3*d*e^6-33*a^2*c*d^3*e^4+90*a*c^2*d^5*e^2+63*c^3*d^7))*sqrt(1-a/c/x^4)*x^3*sqrt(sqrt(a)*(e*x^2+d)/(sqrt(c)*d+sqrt(a)*e)/x^2)*EllipticE(sin(arcsin(sqrt(1-sqrt(a)/sqrt(c)/x^2)/sqrt(2))),sqrt(2*d/(d+sqrt(a)*e/sqrt(c))))/d^5/(sqrt(c)*d-sqrt(a)*e)^4/(sqrt(c)*d+sqrt(a)*e)^3/sqrt(e*x^2+d)/sqrt(-c*x^4+a)-2/315*sqrt(a)*sqrt(c)*(a*B*d*e*(8*a^2*e^4-27*a*c*d^2*e^2+51*c^2*d^4)-A*(-64*a^3*e^6+198*a^2*c*d^2*e^4-207*a*c^2*d^4*e^2+105*c^3*d^6))*sqrt(1-a/c/x^4)*x^3*sqrt(sqrt(a)*(e*x^2+d)/(sqrt(c)*d+sqrt(a)*e)/x^2)*InverseJacobiAM(arcsin(sqrt(1-sqrt(a)/sqrt(c)/x^2)/sqrt(2)),sqrt(2*d/(d+sqrt(a)*e/sqrt(c))))/d^5/(-a*e^2+c*d^2)^3/sqrt(e*x^2+d)/sqrt(-c*x^4+a),1],
[(B*x^2+A)*(e*x^2+d)^(3/2)*(-c*x^4+a)^(3/2),x,14,-1/15360*(12*A*e*(128*a^2*e^4-116*a*c*d^2*e^2+15*c^2*d^4)-B*(-2064*a^2*d*e^4-512*a*c*d^3*e^2+105*c^2*d^5))*sqrt(e*x^2+d)*sqrt(-c*x^4+a)/c/e^4/x+1/7680*(12*A*c*d*e*(236*a*e^2+5*c*d^2)-B*(240*a^2*e^4-168*a*c*d^2*e^2+35*c^2*d^4))*x*sqrt(e*x^2+d)*sqrt(-c*x^4+a)/c/e^3+1/1920*(384*A*a*e^3-12*A*c*d^2*e+436*B*a*d*e^2+7*B*c*d^3)*x^3*sqrt(e*x^2+d)*sqrt(-c*x^4+a)/e^2-1/960*(132*A*c*d*e-140*B*a*e^2+3*B*c*d^2)*x^5*sqrt(e*x^2+d)*sqrt(-c*x^4+a)/e-1/120*c*(12*A*e+13*B*d)*x^7*sqrt(e*x^2+d)*sqrt(-c*x^4+a)-1/12*B*c*e*x^9*sqrt(e*x^2+d)*sqrt(-c*x^4+a)+1/15360*(sqrt(c)*d+sqrt(a)*e)*(-1536*A*a^2*e^5+1392*A*a*c*d^2*e^3-180*A*c^2*d^4*e-2064*B*a^2*d*e^4-512*B*a*c*d^3*e^2+105*B*c^2*d^5)*sqrt(1-a/c/x^4)*x^3*sqrt(sqrt(a)*(e*x^2+d)/(sqrt(c)*d+sqrt(a)*e)/x^2)*EllipticE(sin(arcsin(sqrt(1-sqrt(a)/sqrt(c)/x^2)/sqrt(2))),sqrt(2*d/(d+sqrt(a)*e/sqrt(c))))/sqrt(c)/e^4/sqrt(e*x^2+d)/sqrt(-c*x^4+a)-1/15360*sqrt(a)*(-1536*A*a^2*e^5-8304*A*a*c*d^2*e^3-60*A*c^2*d^4*e-2544*B*a^2*d*e^4-176*B*a*c*d^3*e^2+35*B*c^2*d^5)*sqrt(1-a/c/x^4)*x^3*sqrt(sqrt(a)*(e*x^2+d)/(sqrt(c)*d+sqrt(a)*e)/x^2)*InverseJacobiAM(arcsin(sqrt(1-sqrt(a)/sqrt(c)/x^2)/sqrt(2)),sqrt(2*d/(d+sqrt(a)*e/sqrt(c))))/sqrt(c)/e^3/sqrt(e*x^2+d)/sqrt(-c*x^4+a)-1/1024*(12*A*c*d*e*(-48*a^2*e^4-8*a*c*d^2*e^2+c^2*d^4)-B*(64*a^3*e^6+144*a^2*c*d^2*e^4-36*a*c^2*d^4*e^2+7*c^3*d^6))*sqrt(1-a/c/x^4)*x^3*sqrt(sqrt(a)*(e*x^2+d)/(sqrt(c)*d+sqrt(a)*e)/x^2)*EllipticPi(sin(arcsin(sqrt(1-sqrt(a)/sqrt(c)/x^2)/sqrt(2))),2,sqrt(2*d/(d+sqrt(a)*e/sqrt(c))))/c/e^4/sqrt(e*x^2+d)/sqrt(-c*x^4+a),1],
[(B*x^2+A)*sqrt(e*x^2+d)*(-c*x^4+a)^(3/2),x,13,-1/3840*(10*A*c*d*e*(-68*a*e^2+15*c*d^2)-B*(-384*a^2*e^4-332*a*c*d^2*e^2+105*c^2*d^4))*sqrt(e*x^2+d)*sqrt(-c*x^4+a)/c/e^4/x-1/1920*(-600*A*a*e^3-50*A*c*d^2*e-108*B*a*d*e^2+35*B*c*d^3)*x*sqrt(e*x^2+d)*sqrt(-c*x^4+a)/e^3+1/480*(-10*A*c*d*e+96*B*a*e^2+7*B*c*d^2)*x^3*sqrt(e*x^2+d)*sqrt(-c*x^4+a)/e^2-1/80*c*(10*A*e+B*d)*x^5*sqrt(e*x^2+d)*sqrt(-c*x^4+a)/e-1/10*B*c*x^7*sqrt(e*x^2+d)*sqrt(-c*x^4+a)-1/3840*(sqrt(c)*d+sqrt(a)*e)*(10*A*c*d*e*(-68*a*e^2+15*c*d^2)-B*(-384*a^2*e^4-332*a*c*d^2*e^2+105*c^2*d^4))*sqrt(1-a/c/x^4)*x^3*sqrt(sqrt(a)*(e*x^2+d)/(sqrt(c)*d+sqrt(a)*e)/x^2)*EllipticE(sin(arcsin(sqrt(1-sqrt(a)/sqrt(c)/x^2)/sqrt(2))),sqrt(2*d/(d+sqrt(a)*e/sqrt(c))))/sqrt(c)/e^4/sqrt(e*x^2+d)/sqrt(-c*x^4+a)+1/3840*sqrt(a)*(10*A*c*d*e*(196*a*e^2+5*c*d^2)-B*(-384*a^2*e^4-116*a*c*d^2*e^2+35*c^2*d^4))*sqrt(1-a/c/x^4)*x^3*sqrt(sqrt(a)*(e*x^2+d)/(sqrt(c)*d+sqrt(a)*e)/x^2)*InverseJacobiAM(arcsin(sqrt(1-sqrt(a)/sqrt(c)/x^2)/sqrt(2)),sqrt(2*d/(d+sqrt(a)*e/sqrt(c))))/sqrt(c)/e^3/sqrt(e*x^2+d)/sqrt(-c*x^4+a)+1/256*(96*A*a^2*e^5+48*A*a*c*d^2*e^3-10*A*c^2*d^4*e+48*B*a^2*d*e^4-24*B*a*c*d^3*e^2+7*B*c^2*d^5)*sqrt(1-a/c/x^4)*x^3*sqrt(sqrt(a)*(e*x^2+d)/(sqrt(c)*d+sqrt(a)*e)/x^2)*EllipticPi(sin(arcsin(sqrt(1-sqrt(a)/sqrt(c)/x^2)/sqrt(2))),2,sqrt(2*d/(d+sqrt(a)*e/sqrt(c))))/e^4/sqrt(e*x^2+d)/sqrt(-c*x^4+a),1],
[(B*x^2+A)*(-c*x^4+a)^(3/2)/sqrt(e*x^2+d),x,12,1/384*(256*A*a*e^3-120*A*c*d^2*e-188*B*a*d*e^2+105*B*c*d^3)*sqrt(e*x^2+d)*sqrt(-c*x^4+a)/e^4/x-5/192*(-8*A*c*d*e-12*B*a*e^2+7*B*c*d^2)*x*sqrt(e*x^2+d)*sqrt(-c*x^4+a)/e^3+1/48*c*(-8*A*e+7*B*d)*x^3*sqrt(e*x^2+d)*sqrt(-c*x^4+a)/e^2-1/8*B*c*x^5*sqrt(e*x^2+d)*sqrt(-c*x^4+a)/e+1/384*c*(d+sqrt(a)*e/sqrt(c))*(256*A*a*e^3-120*A*c*d^2*e-188*B*a*d*e^2+105*B*c*d^3)*sqrt(1-a/c/x^4)*x^3*sqrt(sqrt(a)*(e*x^2+d)/(sqrt(c)*d+sqrt(a)*e)/x^2)*EllipticE(sin(arcsin(sqrt(1-sqrt(a)/sqrt(c)/x^2)/sqrt(2))),sqrt(2*d/(d+sqrt(a)*e/sqrt(c))))/e^4/sqrt(e*x^2+d)/sqrt(-c*x^4+a)-1/384*sqrt(a)*sqrt(c)*(-128*A*a*e^3-40*A*c*d^2*e-68*B*a*d*e^2+35*B*c*d^3)*sqrt(1-a/c/x^4)*x^3*sqrt(sqrt(a)*(e*x^2+d)/(sqrt(c)*d+sqrt(a)*e)/x^2)*InverseJacobiAM(arcsin(sqrt(1-sqrt(a)/sqrt(c)/x^2)/sqrt(2)),sqrt(2*d/(d+sqrt(a)*e/sqrt(c))))/e^3/sqrt(e*x^2+d)/sqrt(-c*x^4+a)-1/128*(8*A*c*d*e*(-12*a*e^2+5*c*d^2)-B*(48*a^2*e^4-72*a*c*d^2*e^2+35*c^2*d^4))*sqrt(1-a/c/x^4)*x^3*sqrt(sqrt(a)*(e*x^2+d)/(sqrt(c)*d+sqrt(a)*e)/x^2)*EllipticPi(sin(arcsin(sqrt(1-sqrt(a)/sqrt(c)/x^2)/sqrt(2))),2,sqrt(2*d/(d+sqrt(a)*e/sqrt(c))))/e^4/sqrt(e*x^2+d)/sqrt(-c*x^4+a),1],
[(B*x^2+A)*(-c*x^4+a)^(3/2)/(e*x^2+d)^(3/2),x,12,(-A*e+B*d)*(-a*e^2+c*d^2)*x*sqrt(-c*x^4+a)/d/e^3/sqrt(e*x^2+d)-1/48*(48*A*a*e^3-90*A*c*d^2*e-80*B*a*d*e^2+105*B*c*d^3)*sqrt(e*x^2+d)*sqrt(-c*x^4+a)/d/e^4/x+1/24*c*(-6*A*e+11*B*d)*x*sqrt(e*x^2+d)*sqrt(-c*x^4+a)/e^3-1/6*B*c*x^3*sqrt(e*x^2+d)*sqrt(-c*x^4+a)/e^2-1/48*sqrt(c)*(sqrt(c)*d+sqrt(a)*e)*(48*A*a*e^3-90*A*c*d^2*e-80*B*a*d*e^2+105*B*c*d^3)*sqrt(1-a/c/x^4)*x^3*sqrt(sqrt(a)*(e*x^2+d)/(sqrt(c)*d+sqrt(a)*e)/x^2)*EllipticE(sin(arcsin(sqrt(1-sqrt(a)/sqrt(c)/x^2)/sqrt(2))),sqrt(2*d/(d+sqrt(a)*e/sqrt(c))))/d/e^4/sqrt(e*x^2+d)/sqrt(-c*x^4+a)+1/48*sqrt(a)*sqrt(c)*(48*A*a*e^3-30*A*c*d^2*e-32*B*a*d*e^2+35*B*c*d^3)*sqrt(1-a/c/x^4)*x^3*sqrt(sqrt(a)*(e*x^2+d)/(sqrt(c)*d+sqrt(a)*e)/x^2)*InverseJacobiAM(arcsin(sqrt(1-sqrt(a)/sqrt(c)/x^2)/sqrt(2)),sqrt(2*d/(d+sqrt(a)*e/sqrt(c))))/d/e^3/sqrt(e*x^2+d)/sqrt(-c*x^4+a)-1/16*c*(24*A*a*e^3-30*A*c*d^2*e-36*B*a*d*e^2+35*B*c*d^3)*sqrt(1-a/c/x^4)*x^3*sqrt(sqrt(a)*(e*x^2+d)/(sqrt(c)*d+sqrt(a)*e)/x^2)*EllipticPi(sin(arcsin(sqrt(1-sqrt(a)/sqrt(c)/x^2)/sqrt(2))),2,sqrt(2*d/(d+sqrt(a)*e/sqrt(c))))/e^4/sqrt(e*x^2+d)/sqrt(-c*x^4+a),1],
[(B*x^2+A)*(-c*x^4+a)^(3/2)/(e*x^2+d)^(5/2),x,12,1/3*(-A*e+B*d)*(-a*e^2+c*d^2)*x*sqrt(-c*x^4+a)/d/e^3/(e*x^2+d)^(3/2)-1/3*(-2*A*a*e^3-6*A*c*d^2*e-B*a*d*e^2+9*B*c*d^3)*x*sqrt(-c*x^4+a)/d^2/e^3/sqrt(e*x^2+d)+1/24*(-16*A*a*e^3-60*A*c*d^2*e-8*B*a*d*e^2+105*B*c*d^3)*sqrt(e*x^2+d)*sqrt(-c*x^4+a)/d^2/e^4/x-1/4*B*c*x*sqrt(e*x^2+d)*sqrt(-c*x^4+a)/e^3+1/24*sqrt(c)*(sqrt(c)*d+sqrt(a)*e)*(-16*A*a*e^3-60*A*c*d^2*e-8*B*a*d*e^2+105*B*c*d^3)*sqrt(1-a/c/x^4)*x^3*sqrt(sqrt(a)*(e*x^2+d)/(sqrt(c)*d+sqrt(a)*e)/x^2)*EllipticE(sin(arcsin(sqrt(1-sqrt(a)/sqrt(c)/x^2)/sqrt(2))),sqrt(2*d/(d+sqrt(a)*e/sqrt(c))))/d^2/e^4/sqrt(e*x^2+d)/sqrt(-c*x^4+a)-1/24*sqrt(a)*sqrt(c)*(-16*A*a*e^3-20*A*c*d^2*e-8*B*a*d*e^2+35*B*c*d^3)*sqrt(1-a/c/x^4)*x^3*sqrt(sqrt(a)*(e*x^2+d)/(sqrt(c)*d+sqrt(a)*e)/x^2)*InverseJacobiAM(arcsin(sqrt(1-sqrt(a)/sqrt(c)/x^2)/sqrt(2)),sqrt(2*d/(d+sqrt(a)*e/sqrt(c))))/d^2/e^3/sqrt(e*x^2+d)/sqrt(-c*x^4+a)+1/8*c*(-20*A*c*d*e-12*B*a*e^2+35*B*c*d^2)*sqrt(1-a/c/x^4)*x^3*sqrt(sqrt(a)*(e*x^2+d)/(sqrt(c)*d+sqrt(a)*e)/x^2)*EllipticPi(sin(arcsin(sqrt(1-sqrt(a)/sqrt(c)/x^2)/sqrt(2))),2,sqrt(2*d/(d+sqrt(a)*e/sqrt(c))))/e^4/sqrt(e*x^2+d)/sqrt(-c*x^4+a),1],
[(B*x^2+A)*(-c*x^4+a)^(3/2)/(e*x^2+d)^(7/2),x,12,1/5*(-A*e+B*d)*(-a*e^2+c*d^2)*x*sqrt(-c*x^4+a)/d/e^3/(e*x^2+d)^(5/2)-1/15*(-4*A*a*e^3-8*A*c*d^2*e-B*a*d*e^2+13*B*c*d^3)*x*sqrt(-c*x^4+a)/d^2/e^3/(e*x^2+d)^(3/2)+1/15*(-8*A*a^2*e^5+11*A*a*c*d^2*e^3-15*A*c^2*d^4*e-2*B*a^2*d*e^4-31*B*a*c*d^3*e^2+45*B*c^2*d^5)*x*sqrt(-c*x^4+a)/d^3/e^3/(-a*e^2+c*d^2)/sqrt(e*x^2+d)-1/30*(-16*A*a^2*e^5+22*A*a*c*d^2*e^3-30*A*c^2*d^4*e-4*B*a^2*d*e^4-77*B*a*c*d^3*e^2+105*B*c^2*d^5)*sqrt(e*x^2+d)*sqrt(-c*x^4+a)/d^3/e^4/(-a*e^2+c*d^2)/x+1/30*sqrt(c)*(2*A*e*(8*a^2*e^4-11*a*c*d^2*e^2+15*c^2*d^4)-B*(-4*a^2*d*e^4-77*a*c*d^3*e^2+105*c^2*d^5))*sqrt(1-a/c/x^4)*x^3*sqrt(sqrt(a)*(e*x^2+d)/(sqrt(c)*d+sqrt(a)*e)/x^2)*EllipticE(sin(arcsin(sqrt(1-sqrt(a)/sqrt(c)/x^2)/sqrt(2))),sqrt(2*d/(d+sqrt(a)*e/sqrt(c))))/d^3/e^4/(sqrt(c)*d-sqrt(a)*e)/sqrt(e*x^2+d)/sqrt(-c*x^4+a)+1/30*sqrt(a)*sqrt(c)*(16*A*a*e^3-10*A*c*d^2*e+4*B*a*d*e^2+35*B*c*d^3)*sqrt(1-a/c/x^4)*x^3*sqrt(sqrt(a)*(e*x^2+d)/(sqrt(c)*d+sqrt(a)*e)/x^2)*InverseJacobiAM(arcsin(sqrt(1-sqrt(a)/sqrt(c)/x^2)/sqrt(2)),sqrt(2*d/(d+sqrt(a)*e/sqrt(c))))/d^3/e^3/sqrt(e*x^2+d)/sqrt(-c*x^4+a)-1/2*c^2*(-2*A*e+7*B*d)*sqrt(1-a/c/x^4)*x^3*sqrt(sqrt(a)*(e*x^2+d)/(sqrt(c)*d+sqrt(a)*e)/x^2)*EllipticPi(sin(arcsin(sqrt(1-sqrt(a)/sqrt(c)/x^2)/sqrt(2))),2,sqrt(2*d/(d+sqrt(a)*e/sqrt(c))))/e^4/sqrt(e*x^2+d)/sqrt(-c*x^4+a),1],
[(B*x^2+A)*(-c*x^4+a)^(3/2)/(e*x^2+d)^(9/2),x,12,1/7*(-A*e+B*d)*(-a*e^2+c*d^2)*x*sqrt(-c*x^4+a)/d/e^3/(e*x^2+d)^(7/2)-1/35*(-6*A*a*e^3-10*A*c*d^2*e-B*a*d*e^2+17*B*c*d^3)*x*sqrt(-c*x^4+a)/d^2/e^3/(e*x^2+d)^(5/2)+1/105*(-24*A*a^2*e^5+27*A*a*c*d^2*e^3-15*A*c^2*d^4*e-4*B*a^2*d*e^4-55*B*a*c*d^3*e^2+71*B*c^2*d^5)*x*sqrt(-c*x^4+a)/d^3/e^3/(-a*e^2+c*d^2)/(e*x^2+d)^(3/2)+1/105*(48*a^2*A*e^5*(-a*e^2+2*c*d^2)+B*(-8*a^3*d*e^6+37*a^2*c*d^3*e^4-182*a*c^2*d^5*e^2+105*c^3*d^7))*sqrt(-c*x^4+a)/d^3/e^4/(-a*e^2+c*d^2)^2/x/sqrt(e*x^2+d)+1/105*sqrt(c)*(48*a^2*A*e^5*(-a*e^2+2*c*d^2)+B*(-8*a^3*d*e^6+37*a^2*c*d^3*e^4-182*a*c^2*d^5*e^2+105*c^3*d^7))*sqrt(1-a/c/x^4)*x^3*sqrt(sqrt(a)*(e*x^2+d)/(sqrt(c)*d+sqrt(a)*e)/x^2)*EllipticE(sin(arcsin(sqrt(1-sqrt(a)/sqrt(c)/x^2)/sqrt(2))),sqrt(2*d/(d+sqrt(a)*e/sqrt(c))))/d^4/e^4/(sqrt(c)*d-sqrt(a)*e)/(-a*e^2+c*d^2)/sqrt(e*x^2+d)/sqrt(-c*x^4+a)+1/105*sqrt(a)*sqrt(c)*(12*a*A*e^3*(-4*a*e^2+5*c*d^2)-B*(8*a^2*d*e^4-31*a*c*d^3*e^2+35*c^2*d^5))*sqrt(1-a/c/x^4)*x^3*sqrt(sqrt(a)*(e*x^2+d)/(sqrt(c)*d+sqrt(a)*e)/x^2)*InverseJacobiAM(arcsin(sqrt(1-sqrt(a)/sqrt(c)/x^2)/sqrt(2)),sqrt(2*d/(d+sqrt(a)*e/sqrt(c))))/d^4/e^3/(-a*e^2+c*d^2)/sqrt(e*x^2+d)/sqrt(-c*x^4+a)+B*c^2*sqrt(1-a/c/x^4)*x^3*sqrt(sqrt(a)*(e*x^2+d)/(sqrt(c)*d+sqrt(a)*e)/x^2)*EllipticPi(sin(arcsin(sqrt(1-sqrt(a)/sqrt(c)/x^2)/sqrt(2))),2,sqrt(2*d/(d+sqrt(a)*e/sqrt(c))))/e^4/sqrt(e*x^2+d)/sqrt(-c*x^4+a),1],
[(B*x^2+A)*(-c*x^4+a)^(3/2)/(e*x^2+d)^(11/2),x,10,1/9*(-A*e+B*d)*(-a*e^2+c*d^2)*x*sqrt(-c*x^4+a)/d/e^3/(e*x^2+d)^(9/2)-1/63*(-8*A*a*e^3-12*A*c*d^2*e-B*a*d*e^2+21*B*c*d^3)*x*sqrt(-c*x^4+a)/d^2/e^3/(e*x^2+d)^(7/2)+1/105*(-16*A*a^2*e^5+17*A*a*c*d^2*e^3-5*A*c^2*d^4*e-2*B*a^2*d*e^4-29*B*a*c*d^3*e^2+35*B*c^2*d^5)*x*sqrt(-c*x^4+a)/d^3/e^3/(-a*e^2+c*d^2)/(e*x^2+d)^(5/2)-1/315*(2*A*e*(-32*a^3*e^6+65*a^2*c*d^2*e^4-22*a*c^2*d^4*e^2+5*c^3*d^6)+B*(-8*a^3*d*e^6+23*a^2*c*d^3*e^4-82*a*c^2*d^5*e^2+35*c^3*d^7))*x*sqrt(-c*x^4+a)/d^4/e^3/(-a*e^2+c*d^2)^2/(e*x^2+d)^(3/2)-4/315*a^2*(-32*A*a^2*e^5+93*A*a*c*d^2*e^3-93*A*c^2*d^4*e-4*B*a^2*d*e^4+15*B*a*c*d^3*e^2+21*B*c^2*d^5)*sqrt(-c*x^4+a)/d^4/(-a*e^2+c*d^2)^3/x/sqrt(e*x^2+d)-4/315*a^2*sqrt(c)*(-32*A*a^2*e^5+93*A*a*c*d^2*e^3-93*A*c^2*d^4*e-4*B*a^2*d*e^4+15*B*a*c*d^3*e^2+21*B*c^2*d^5)*sqrt(1-a/c/x^4)*x^3*sqrt(sqrt(a)*(e*x^2+d)/(sqrt(c)*d+sqrt(a)*e)/x^2)*EllipticE(sin(arcsin(sqrt(1-sqrt(a)/sqrt(c)/x^2)/sqrt(2))),sqrt(2*d/(d+sqrt(a)*e/sqrt(c))))/d^5/(sqrt(c)*d-sqrt(a)*e)^3/(sqrt(c)*d+sqrt(a)*e)^2/sqrt(e*x^2+d)/sqrt(-c*x^4+a)-4/315*a^(3/2)*sqrt(c)*(4*a*B*d*e*(-a*e^2+3*c*d^2)-A*(32*a^2*e^4-69*a*c*d^2*e^2+45*c^2*d^4))*sqrt(1-a/c/x^4)*x^3*sqrt(sqrt(a)*(e*x^2+d)/(sqrt(c)*d+sqrt(a)*e)/x^2)*InverseJacobiAM(arcsin(sqrt(1-sqrt(a)/sqrt(c)/x^2)/sqrt(2)),sqrt(2*d/(d+sqrt(a)*e/sqrt(c))))/d^5/(-a*e^2+c*d^2)^2/sqrt(e*x^2+d)/sqrt(-c*x^4+a),1],
[(B*x^2+A)*(e*x^2+d)^(3/2)/sqrt(-c*x^4+a),x,10,-1/8*(4*A*e+5*B*d)*sqrt(e*x^2+d)*sqrt(-c*x^4+a)/c/x-1/4*B*e*x*sqrt(e*x^2+d)*sqrt(-c*x^4+a)/c-1/8*(4*A*e+5*B*d)*(d+sqrt(a)*e/sqrt(c))*sqrt(1-a/c/x^4)*x^3*sqrt(sqrt(a)*(e*x^2+d)/(sqrt(c)*d+sqrt(a)*e)/x^2)*EllipticE(sin(arcsin(sqrt(1-sqrt(a)/sqrt(c)/x^2)/sqrt(2))),sqrt(2*d/(d+sqrt(a)*e/sqrt(c))))/sqrt(e*x^2+d)/sqrt(-c*x^4+a)+1/8*(4*A*a*e^2+8*A*c*d^2+7*B*a*d*e)*sqrt(1-a/c/x^4)*x^3*sqrt(sqrt(a)*(e*x^2+d)/(sqrt(c)*d+sqrt(a)*e)/x^2)*InverseJacobiAM(arcsin(sqrt(1-sqrt(a)/sqrt(c)/x^2)/sqrt(2)),sqrt(2*d/(d+sqrt(a)*e/sqrt(c))))/sqrt(a)/sqrt(c)/sqrt(e*x^2+d)/sqrt(-c*x^4+a)+1/8*(12*A*c*d*e+4*B*a*e^2+3*B*c*d^2)*sqrt(1-a/c/x^4)*x^3*sqrt(sqrt(a)*(e*x^2+d)/(sqrt(c)*d+sqrt(a)*e)/x^2)*EllipticPi(sin(arcsin(sqrt(1-sqrt(a)/sqrt(c)/x^2)/sqrt(2))),2,sqrt(2*d/(d+sqrt(a)*e/sqrt(c))))/c/sqrt(e*x^2+d)/sqrt(-c*x^4+a),1],
[(B*x^2+A)*sqrt(e*x^2+d)/sqrt(-c*x^4+a),x,9,-1/2*B*sqrt(e*x^2+d)*sqrt(-c*x^4+a)/c/x-1/2*B*(d+sqrt(a)*e/sqrt(c))*sqrt(1-a/c/x^4)*x^3*sqrt(sqrt(a)*(e*x^2+d)/(sqrt(c)*d+sqrt(a)*e)/x^2)*EllipticE(sin(arcsin(sqrt(1-sqrt(a)/sqrt(c)/x^2)/sqrt(2))),sqrt(2*d/(d+sqrt(a)*e/sqrt(c))))/sqrt(e*x^2+d)/sqrt(-c*x^4+a)+1/2*(2*A*c*d+B*a*e)*sqrt(1-a/c/x^4)*x^3*sqrt(sqrt(a)*(e*x^2+d)/(sqrt(c)*d+sqrt(a)*e)/x^2)*InverseJacobiAM(arcsin(sqrt(1-sqrt(a)/sqrt(c)/x^2)/sqrt(2)),sqrt(2*d/(d+sqrt(a)*e/sqrt(c))))/sqrt(a)/sqrt(c)/sqrt(e*x^2+d)/sqrt(-c*x^4+a)+1/2*(2*A*e+B*d)*sqrt(1-a/c/x^4)*x^3*sqrt(sqrt(a)*(e*x^2+d)/(sqrt(c)*d+sqrt(a)*e)/x^2)*EllipticPi(sin(arcsin(sqrt(1-sqrt(a)/sqrt(c)/x^2)/sqrt(2))),2,sqrt(2*d/(d+sqrt(a)*e/sqrt(c))))/sqrt(e*x^2+d)/sqrt(-c*x^4+a),1],
[(B*x^2+A)/sqrt(e*x^2+d)/sqrt(-c*x^4+a),x,5,A*sqrt(c)*sqrt(1-a/c/x^4)*x^3*sqrt(sqrt(a)*(e*x^2+d)/(sqrt(c)*d+sqrt(a)*e)/x^2)*InverseJacobiAM(arcsin(sqrt(1-sqrt(a)/sqrt(c)/x^2)/sqrt(2)),sqrt(2*d/(d+sqrt(a)*e/sqrt(c))))/sqrt(a)/sqrt(e*x^2+d)/sqrt(-c*x^4+a)+B*sqrt(1-a/c/x^4)*x^3*sqrt(sqrt(a)*(e*x^2+d)/(sqrt(c)*d+sqrt(a)*e)/x^2)*EllipticPi(sin(arcsin(sqrt(1-sqrt(a)/sqrt(c)/x^2)/sqrt(2))),2,sqrt(2*d/(d+sqrt(a)*e/sqrt(c))))/sqrt(e*x^2+d)/sqrt(-c*x^4+a),1],
[(B*x^2+A)/(e*x^2+d)^(3/2)/sqrt(-c*x^4+a),x,6,-(-A*e+B*d)*sqrt(-c*x^4+a)/(-a*e^2+c*d^2)/x/sqrt(e*x^2+d)-sqrt(c)*(-A*e+B*d)*sqrt(1-a/c/x^4)*x^3*sqrt(sqrt(a)*(e*x^2+d)/(sqrt(c)*d+sqrt(a)*e)/x^2)*EllipticE(sin(arcsin(sqrt(1-sqrt(a)/sqrt(c)/x^2)/sqrt(2))),sqrt(2*d/(d+sqrt(a)*e/sqrt(c))))/d/(sqrt(c)*d-sqrt(a)*e)/sqrt(e*x^2+d)/sqrt(-c*x^4+a)+A*sqrt(c)*sqrt(1-a/c/x^4)*x^3*sqrt(sqrt(a)*(e*x^2+d)/(sqrt(c)*d+sqrt(a)*e)/x^2)*InverseJacobiAM(arcsin(sqrt(1-sqrt(a)/sqrt(c)/x^2)/sqrt(2)),sqrt(2*d/(d+sqrt(a)*e/sqrt(c))))/sqrt(a)/d/sqrt(e*x^2+d)/sqrt(-c*x^4+a),1],
[(B*x^2+A)/(e*x^2+d)^(5/2)/sqrt(-c*x^4+a),x,7,1/3*e*(-A*e+B*d)*x*sqrt(-c*x^4+a)/d/(-a*e^2+c*d^2)/(e*x^2+d)^(3/2)-1/3*(2*A*a*e^3-6*A*c*d^2*e+B*a*d*e^2+3*B*c*d^3)*sqrt(-c*x^4+a)/d/(-a*e^2+c*d^2)^2/x/sqrt(e*x^2+d)-1/3*sqrt(c)*(2*A*a*e^3-6*A*c*d^2*e+B*a*d*e^2+3*B*c*d^3)*sqrt(1-a/c/x^4)*x^3*sqrt(sqrt(a)*(e*x^2+d)/(sqrt(c)*d+sqrt(a)*e)/x^2)*EllipticE(sin(arcsin(sqrt(1-sqrt(a)/sqrt(c)/x^2)/sqrt(2))),sqrt(2*d/(d+sqrt(a)*e/sqrt(c))))/d^2/(sqrt(c)*d-sqrt(a)*e)/(-a*e^2+c*d^2)/sqrt(e*x^2+d)/sqrt(-c*x^4+a)+1/3*sqrt(c)*(-2*A*a*e^2+3*A*c*d^2-B*a*d*e)*sqrt(1-a/c/x^4)*x^3*sqrt(sqrt(a)*(e*x^2+d)/(sqrt(c)*d+sqrt(a)*e)/x^2)*InverseJacobiAM(arcsin(sqrt(1-sqrt(a)/sqrt(c)/x^2)/sqrt(2)),sqrt(2*d/(d+sqrt(a)*e/sqrt(c))))/sqrt(a)/d^2/(-a*e^2+c*d^2)/sqrt(e*x^2+d)/sqrt(-c*x^4+a),1],
[(B*x^2+A)*(e*x^2+d)^(5/2)/(-c*x^4+a)^(3/2),x,12,1/2*x*(B*x^2+A)*(e*x^2+d)^(5/2)/a/sqrt(-c*x^4+a)+1/2*(2*A*c*d*e+2*B*a*e^2+B*c*d^2)*sqrt(e*x^2+d)*sqrt(-c*x^4+a)/a/c^2/x+1/2*e*(A*e+2*B*d)*x*sqrt(e*x^2+d)*sqrt(-c*x^4+a)/a/c+1/2*B*e^2*x^3*sqrt(e*x^2+d)*sqrt(-c*x^4+a)/a/c+1/2*(d+sqrt(a)*e/sqrt(c))*(2*A*c*d*e+2*B*a*e^2+B*c*d^2)*sqrt(1-a/c/x^4)*x^3*sqrt(sqrt(a)*(e*x^2+d)/(sqrt(c)*d+sqrt(a)*e)/x^2)*EllipticE(sin(arcsin(sqrt(1-sqrt(a)/sqrt(c)/x^2)/sqrt(2))),sqrt(2*d/(d+sqrt(a)*e/sqrt(c))))/a/c/sqrt(e*x^2+d)/sqrt(-c*x^4+a)+1/2*(A*c*d*(-3*a*e^2+c*d^2)-a*B*e*(2*a*e^2+3*c*d^2))*sqrt(1-a/c/x^4)*x^3*sqrt(sqrt(a)*(e*x^2+d)/(sqrt(c)*d+sqrt(a)*e)/x^2)*InverseJacobiAM(arcsin(sqrt(1-sqrt(a)/sqrt(c)/x^2)/sqrt(2)),sqrt(2*d/(d+sqrt(a)*e/sqrt(c))))/a^(3/2)/c^(3/2)/sqrt(e*x^2+d)/sqrt(-c*x^4+a)-1/2*e^2*(2*A*e+5*B*d)*sqrt(1-a/c/x^4)*x^3*sqrt(sqrt(a)*(e*x^2+d)/(sqrt(c)*d+sqrt(a)*e)/x^2)*EllipticPi(sin(arcsin(sqrt(1-sqrt(a)/sqrt(c)/x^2)/sqrt(2))),2,sqrt(2*d/(d+sqrt(a)*e/sqrt(c))))/c/sqrt(e*x^2+d)/sqrt(-c*x^4+a),1],
[(B*x^2+A)*(e*x^2+d)^(3/2)/(-c*x^4+a)^(3/2),x,11,1/2*x*(B*x^2+A)*(e*x^2+d)^(3/2)/a/sqrt(-c*x^4+a)+1/2*(A*e+B*d)*sqrt(e*x^2+d)*sqrt(-c*x^4+a)/a/c/x+1/2*B*e*x*sqrt(e*x^2+d)*sqrt(-c*x^4+a)/a/c+1/2*(A*e+B*d)*(d+sqrt(a)*e/sqrt(c))*sqrt(1-a/c/x^4)*x^3*sqrt(sqrt(a)*(e*x^2+d)/(sqrt(c)*d+sqrt(a)*e)/x^2)*EllipticE(sin(arcsin(sqrt(1-sqrt(a)/sqrt(c)/x^2)/sqrt(2))),sqrt(2*d/(d+sqrt(a)*e/sqrt(c))))/a/sqrt(e*x^2+d)/sqrt(-c*x^4+a)+1/2*(-A*a*e^2+A*c*d^2-2*B*a*d*e)*sqrt(1-a/c/x^4)*x^3*sqrt(sqrt(a)*(e*x^2+d)/(sqrt(c)*d+sqrt(a)*e)/x^2)*InverseJacobiAM(arcsin(sqrt(1-sqrt(a)/sqrt(c)/x^2)/sqrt(2)),sqrt(2*d/(d+sqrt(a)*e/sqrt(c))))/a^(3/2)/sqrt(c)/sqrt(e*x^2+d)/sqrt(-c*x^4+a)-B*e^2*sqrt(1-a/c/x^4)*x^3*sqrt(sqrt(a)*(e*x^2+d)/(sqrt(c)*d+sqrt(a)*e)/x^2)*EllipticPi(sin(arcsin(sqrt(1-sqrt(a)/sqrt(c)/x^2)/sqrt(2))),2,sqrt(2*d/(d+sqrt(a)*e/sqrt(c))))/c/sqrt(e*x^2+d)/sqrt(-c*x^4+a),1],
[(B*x^2+A)*sqrt(e*x^2+d)/(-c*x^4+a)^(3/2),x,7,1/2*x*(B*x^2+A)*sqrt(e*x^2+d)/a/sqrt(-c*x^4+a)+1/2*B*sqrt(e*x^2+d)*sqrt(-c*x^4+a)/a/c/x+1/2*B*(d+sqrt(a)*e/sqrt(c))*sqrt(1-a/c/x^4)*x^3*sqrt(sqrt(a)*(e*x^2+d)/(sqrt(c)*d+sqrt(a)*e)/x^2)*EllipticE(sin(arcsin(sqrt(1-sqrt(a)/sqrt(c)/x^2)/sqrt(2))),sqrt(2*d/(d+sqrt(a)*e/sqrt(c))))/a/sqrt(e*x^2+d)/sqrt(-c*x^4+a)+1/2*(A*c*d-B*a*e)*sqrt(1-a/c/x^4)*x^3*sqrt(sqrt(a)*(e*x^2+d)/(sqrt(c)*d+sqrt(a)*e)/x^2)*InverseJacobiAM(arcsin(sqrt(1-sqrt(a)/sqrt(c)/x^2)/sqrt(2)),sqrt(2*d/(d+sqrt(a)*e/sqrt(c))))/a^(3/2)/sqrt(c)/sqrt(e*x^2+d)/sqrt(-c*x^4+a),1],
[(B*x^2+A)/sqrt(e*x^2+d)/(-c*x^4+a)^(3/2),x,7,1/2*(-A*e+B*d)*sqrt(e*x^2+d)/(-a*e^2+c*d^2)/x/sqrt(-c*x^4+a)+1/2*(A*c*d-B*a*e)*x*sqrt(e*x^2+d)/a/(-a*e^2+c*d^2)/sqrt(-c*x^4+a)+1/2*sqrt(c)*(-A*e+B*d)*sqrt(1-a/c/x^4)*x^3*sqrt(sqrt(a)*(e*x^2+d)/(sqrt(c)*d+sqrt(a)*e)/x^2)*EllipticE(sin(arcsin(sqrt(1-sqrt(a)/sqrt(c)/x^2)/sqrt(2))),sqrt(2*d/(d+sqrt(a)*e/sqrt(c))))/a/(sqrt(c)*d-sqrt(a)*e)/sqrt(e*x^2+d)/sqrt(-c*x^4+a)+1/2*A*sqrt(c)*sqrt(1-a/c/x^4)*x^3*sqrt(sqrt(a)*(e*x^2+d)/(sqrt(c)*d+sqrt(a)*e)/x^2)*InverseJacobiAM(arcsin(sqrt(1-sqrt(a)/sqrt(c)/x^2)/sqrt(2)),sqrt(2*d/(d+sqrt(a)*e/sqrt(c))))/a^(3/2)/sqrt(e*x^2+d)/sqrt(-c*x^4+a),1],
[(B*x^2+A)/(e*x^2+d)^(3/2)/(-c*x^4+a)^(3/2),x,8,e*(-A*e+B*d)*x/d/(-a*e^2+c*d^2)/sqrt(e*x^2+d)/sqrt(-c*x^4+a)+1/2*(-2*A*a*e^3-2*A*c*d^2*e+3*B*a*d*e^2+B*c*d^3)*sqrt(e*x^2+d)/d/(-a*e^2+c*d^2)^2/x/sqrt(-c*x^4+a)+1/2*c*(3*A*a*e^2+A*c*d^2-4*B*a*d*e)*x*sqrt(e*x^2+d)/a/(-a*e^2+c*d^2)^2/sqrt(-c*x^4+a)-1/2*sqrt(c)*(2*A*e*(a*e^2+c*d^2)-B*(3*a*d*e^2+c*d^3))*sqrt(1-a/c/x^4)*x^3*sqrt(sqrt(a)*(e*x^2+d)/(sqrt(c)*d+sqrt(a)*e)/x^2)*EllipticE(sin(arcsin(sqrt(1-sqrt(a)/sqrt(c)/x^2)/sqrt(2))),sqrt(2*d/(d+sqrt(a)*e/sqrt(c))))/a/d/(sqrt(c)*d-sqrt(a)*e)/(-a*e^2+c*d^2)/sqrt(e*x^2+d)/sqrt(-c*x^4+a)+1/2*sqrt(c)*(-2*A*a*e^2+A*c*d^2+B*a*d*e)*sqrt(1-a/c/x^4)*x^3*sqrt(sqrt(a)*(e*x^2+d)/(sqrt(c)*d+sqrt(a)*e)/x^2)*InverseJacobiAM(arcsin(sqrt(1-sqrt(a)/sqrt(c)/x^2)/sqrt(2)),sqrt(2*d/(d+sqrt(a)*e/sqrt(c))))/a^(3/2)/d/(-a*e^2+c*d^2)/sqrt(e*x^2+d)/sqrt(-c*x^4+a),1],
[(C*x^4+B*x^2+A)/sqrt(e*x^2+d)/sqrt(-c*x^4+a),x,9,-1/2*C*sqrt(e*x^2+d)*sqrt(-c*x^4+a)/c/e/x-1/2*C*(d+sqrt(a)*e/sqrt(c))*sqrt(1-a/c/x^4)*x^3*sqrt(sqrt(a)*(e*x^2+d)/(sqrt(c)*d+sqrt(a)*e)/x^2)*EllipticE(sin(arcsin(sqrt(1-sqrt(a)/sqrt(c)/x^2)/sqrt(2))),sqrt(2*d/(d+sqrt(a)*e/sqrt(c))))/e/sqrt(e*x^2+d)/sqrt(-c*x^4+a)+1/2*(2*A*c+C*a)*sqrt(1-a/c/x^4)*x^3*sqrt(sqrt(a)*(e*x^2+d)/(sqrt(c)*d+sqrt(a)*e)/x^2)*InverseJacobiAM(arcsin(sqrt(1-sqrt(a)/sqrt(c)/x^2)/sqrt(2)),sqrt(2*d/(d+sqrt(a)*e/sqrt(c))))/sqrt(a)/sqrt(c)/sqrt(e*x^2+d)/sqrt(-c*x^4+a)-1/2*(-2*B*e+C*d)*sqrt(1-a/c/x^4)*x^3*sqrt(sqrt(a)*(e*x^2+d)/(sqrt(c)*d+sqrt(a)*e)/x^2)*EllipticPi(sin(arcsin(sqrt(1-sqrt(a)/sqrt(c)/x^2)/sqrt(2))),2,sqrt(2*d/(d+sqrt(a)*e/sqrt(c))))/e/sqrt(e*x^2+d)/sqrt(-c*x^4+a),1],
[(2*C*e*x^4+C*d*x^2+2*A*e)/sqrt(e*x^2+d)/sqrt(-c*x^4+a),x,6,-C*sqrt(e*x^2+d)*sqrt(-c*x^4+a)/c/x-C*(d+sqrt(a)*e/sqrt(c))*sqrt(1-a/c/x^4)*x^3*sqrt(sqrt(a)*(e*x^2+d)/(sqrt(c)*d+sqrt(a)*e)/x^2)*EllipticE(sin(arcsin(sqrt(1-sqrt(a)/sqrt(c)/x^2)/sqrt(2))),sqrt(2*d/(d+sqrt(a)*e/sqrt(c))))/sqrt(e*x^2+d)/sqrt(-c*x^4+a)+(2*A*c+C*a)*e*sqrt(1-a/c/x^4)*x^3*sqrt(sqrt(a)*(e*x^2+d)/(sqrt(c)*d+sqrt(a)*e)/x^2)*InverseJacobiAM(arcsin(sqrt(1-sqrt(a)/sqrt(c)/x^2)/sqrt(2)),sqrt(2*d/(d+sqrt(a)*e/sqrt(c))))/sqrt(a)/sqrt(c)/sqrt(e*x^2+d)/sqrt(-c*x^4+a),1],
[(B*x^2+A)*sqrt(c*x^4+a)/sqrt(e*x^2+d),x,10,1/8*sqrt(a)*d*(-4*A*e+3*B*d)*(c+a/x^4)*(e+d/x^2)*x^3/e^2/sqrt(a*e^2+c*d^2)/(1+sqrt(a)*(e+d/x^2)/sqrt(a*e^2+c*d^2))/sqrt(e*x^2+d)/sqrt(c*x^4+a)-1/8*(-4*A*e+3*B*d)*sqrt(e*x^2+d)*sqrt(c*x^4+a)/e^2/x+1/4*B*x*sqrt(e*x^2+d)*sqrt(c*x^4+a)/e+1/16*(-4*A*c*d*e+4*B*a*e^2+3*B*c*d^2)*sqrt(c+a/x^4)*sqrt(e+d/x^2)*x^3*arctanh(sqrt(c)*sqrt(e+d/x^2)/sqrt(e)/sqrt(c+a/x^4))/sqrt(c)/e^(5/2)/sqrt(e*x^2+d)/sqrt(c*x^4+a)-1/8*a^(1/4)*(-4*A*e+3*B*d)*(a*e^2+c*d^2)^(3/4)*(1+sqrt(a)*(e+d/x^2)/sqrt(a*e^2+c*d^2))*sqrt(d^2*(c+a/x^4)/(a*e^2+c*d^2)/(1+sqrt(a)*(e+d/x^2)/sqrt(a*e^2+c*d^2))^2)*sqrt(e+d/x^2)*x^3*EllipticE(sin(2*arctan(a^(1/4)*sqrt(e+d/x^2)/(a*e^2+c*d^2)^(1/4))),sqrt(1/2+1/2*sqrt(a)*e/sqrt(a*e^2+c*d^2)))/d/e^2/sqrt(e*x^2+d)/sqrt(c*x^4+a)-1/8*a^(1/4)*(a*e^2+c*d^2)^(3/4)*(4*A*c*d*e-B*(3*c*d^2+2*a*e^2-2*sqrt(a)*e*sqrt(a*e^2+c*d^2)))*(1+sqrt(a)*(e+d/x^2)/sqrt(a*e^2+c*d^2))*sqrt((c+a/x^4)/(c+a*e^2/d^2)/(1+sqrt(a)*(e+d/x^2)/sqrt(a*e^2+c*d^2))^2)*sqrt(e+d/x^2)*x^3*InverseJacobiAM(2*arctan(a^(1/4)*sqrt(e+d/x^2)/(a*e^2+c*d^2)^(1/4)),sqrt(1/2+1/2*sqrt(a)*e/sqrt(a*e^2+c*d^2)))/c/d^2/e^2/sqrt(e*x^2+d)/sqrt(c*x^4+a)+1/32*(a*e^2+c*d^2)^(1/4)*(-4*A*c*d*e+4*B*a*e^2+3*B*c*d^2)*(sqrt(a)*e-sqrt(a*e^2+c*d^2))^2*(1+sqrt(a)*(e+d/x^2)/sqrt(a*e^2+c*d^2))*sqrt((c+a/x^4)/(c+a*e^2/d^2)/(1+sqrt(a)*(e+d/x^2)/sqrt(a*e^2+c*d^2))^2)*sqrt(e+d/x^2)*x^3*EllipticPi(sin(2*arctan(a^(1/4)*sqrt(e+d/x^2)/(a*e^2+c*d^2)^(1/4))),1/4*(sqrt(a)*e+sqrt(a*e^2+c*d^2))^2/sqrt(a)/e/sqrt(a*e^2+c*d^2),sqrt(1/2+1/2*sqrt(a)*e/sqrt(a*e^2+c*d^2)))/a^(1/4)/c/d^2/e^3/sqrt(e*x^2+d)/sqrt(c*x^4+a),1],
[(B*x^2+A)/sqrt(e*x^2+d)/sqrt(c*x^4+a),x,5,1/2*B*sqrt(c+a/x^4)*sqrt(e+d/x^2)*x^3*arctanh(sqrt(c)*sqrt(e+d/x^2)/sqrt(e)/sqrt(c+a/x^4))/sqrt(c)/sqrt(e)/sqrt(e*x^2+d)/sqrt(c*x^4+a)+1/2*(sqrt(a)*B*c*d^2+a^(3/2)*B*e^2-(A*c*d+B*a*e)*sqrt(a*e^2+c*d^2))*(1+sqrt(a)*(e+d/x^2)/sqrt(a*e^2+c*d^2))*sqrt((c+a/x^4)/(c+a*e^2/d^2)/(1+sqrt(a)*(e+d/x^2)/sqrt(a*e^2+c*d^2))^2)*sqrt(e+d/x^2)*x^3*InverseJacobiAM(2*arctan(a^(1/4)*sqrt(e+d/x^2)/(a*e^2+c*d^2)^(1/4)),sqrt(1/2+1/2*sqrt(a)*e/sqrt(a*e^2+c*d^2)))/a^(1/4)/c/d^2/(a*e^2+c*d^2)^(1/4)/sqrt(e*x^2+d)/sqrt(c*x^4+a)+1/4*B*(a*e^2+c*d^2)^(1/4)*(sqrt(a)*e-sqrt(a*e^2+c*d^2))^2*(1+sqrt(a)*(e+d/x^2)/sqrt(a*e^2+c*d^2))*sqrt((c+a/x^4)/(c+a*e^2/d^2)/(1+sqrt(a)*(e+d/x^2)/sqrt(a*e^2+c*d^2))^2)*sqrt(e+d/x^2)*x^3*EllipticPi(sin(2*arctan(a^(1/4)*sqrt(e+d/x^2)/(a*e^2+c*d^2)^(1/4))),1/4*(sqrt(a)*e+sqrt(a*e^2+c*d^2))^2/sqrt(a)/e/sqrt(a*e^2+c*d^2),sqrt(1/2+1/2*sqrt(a)*e/sqrt(a*e^2+c*d^2)))/a^(1/4)/c/d^2/e/sqrt(e*x^2+d)/sqrt(c*x^4+a),1],
[(C*x^4+B*x^2+A)/sqrt(e*x^2+d)/sqrt(c*x^4+a),x,9,-1/2*sqrt(a)*C*d*(c+a/x^4)*(e+d/x^2)*x^3/c/e/sqrt(a*e^2+c*d^2)/(1+sqrt(a)*(e+d/x^2)/sqrt(a*e^2+c*d^2))/sqrt(e*x^2+d)/sqrt(c*x^4+a)+1/2*C*sqrt(e*x^2+d)*sqrt(c*x^4+a)/c/e/x-1/4*(-2*B*e+C*d)*sqrt(c+a/x^4)*sqrt(e+d/x^2)*x^3*arctanh(sqrt(c)*sqrt(e+d/x^2)/sqrt(e)/sqrt(c+a/x^4))/sqrt(c)/e^(3/2)/sqrt(e*x^2+d)/sqrt(c*x^4+a)+1/2*a^(1/4)*C*(a*e^2+c*d^2)^(3/4)*(1+sqrt(a)*(e+d/x^2)/sqrt(a*e^2+c*d^2))*sqrt(d^2*(c+a/x^4)/(a*e^2+c*d^2)/(1+sqrt(a)*(e+d/x^2)/sqrt(a*e^2+c*d^2))^2)*sqrt(e+d/x^2)*x^3*EllipticE(sin(2*arctan(a^(1/4)*sqrt(e+d/x^2)/(a*e^2+c*d^2)^(1/4))),sqrt(1/2+1/2*sqrt(a)*e/sqrt(a*e^2+c*d^2)))/c/d/e/sqrt(e*x^2+d)/sqrt(c*x^4+a)-1/2*(sqrt(a)*c*d^2*(-B*e+C*d)+a^(3/2)*e^2*(-B*e+C*d)+e*(A*c*d+B*a*e-C*a*d)*sqrt(a*e^2+c*d^2))*(1+sqrt(a)*(e+d/x^2)/sqrt(a*e^2+c*d^2))*sqrt((c+a/x^4)/(c+a*e^2/d^2)/(1+sqrt(a)*(e+d/x^2)/sqrt(a*e^2+c*d^2))^2)*sqrt(e+d/x^2)*x^3*InverseJacobiAM(2*arctan(a^(1/4)*sqrt(e+d/x^2)/(a*e^2+c*d^2)^(1/4)),sqrt(1/2+1/2*sqrt(a)*e/sqrt(a*e^2+c*d^2)))/a^(1/4)/c/d^2/e/(a*e^2+c*d^2)^(1/4)/sqrt(e*x^2+d)/sqrt(c*x^4+a)-1/8*(-2*B*e+C*d)*(a*e^2+c*d^2)^(1/4)*(sqrt(a)*e-sqrt(a*e^2+c*d^2))^2*(1+sqrt(a)*(e+d/x^2)/sqrt(a*e^2+c*d^2))*sqrt((c+a/x^4)/(c+a*e^2/d^2)/(1+sqrt(a)*(e+d/x^2)/sqrt(a*e^2+c*d^2))^2)*sqrt(e+d/x^2)*x^3*EllipticPi(sin(2*arctan(a^(1/4)*sqrt(e+d/x^2)/(a*e^2+c*d^2)^(1/4))),1/4*(sqrt(a)*e+sqrt(a*e^2+c*d^2))^2/sqrt(a)/e/sqrt(a*e^2+c*d^2),sqrt(1/2+1/2*sqrt(a)*e/sqrt(a*e^2+c*d^2)))/a^(1/4)/c/d^2/e^2/sqrt(e*x^2+d)/sqrt(c*x^4+a),1],
[(2*C*e*x^4+C*d*x^2+2*A*e)/sqrt(e*x^2+d)/sqrt(c*x^4+a),x,6,-sqrt(a)*C*d*(c+a/x^4)*(e+d/x^2)*x^3/c/(sqrt(a*e^2+c*d^2)+sqrt(a)*(e+d/x^2))/sqrt(e*x^2+d)/sqrt(c*x^4+a)+C*sqrt(e*x^2+d)*sqrt(c*x^4+a)/c/x+a^(1/4)*C*(a*e^2+c*d^2)^(1/4)*(sqrt(a*e^2+c*d^2)+sqrt(a)*(e+d/x^2))*sqrt(d^2*(c+a/x^4)/(sqrt(a*e^2+c*d^2)+sqrt(a)*(e+d/x^2))^2)*sqrt(e+d/x^2)*x^3*EllipticE(sin(2*arctan(a^(1/4)*sqrt(e+d/x^2)/(a*e^2+c*d^2)^(1/4))),sqrt(1/2+1/2*sqrt(a)*e/sqrt(a*e^2+c*d^2)))/c/d/sqrt(e*x^2+d)/sqrt(c*x^4+a)-1/2*(a*e^2+c*d^2)^(1/4)*(2*A*c*e-a*C*e+sqrt(a)*C*sqrt(a*e^2+c*d^2))*(1+sqrt(a)*(e+d/x^2)/sqrt(a*e^2+c*d^2))*sqrt(d^2*(c+a/x^4)/(a*e^2+c*d^2)/(1+sqrt(a)*(e+d/x^2)/sqrt(a*e^2+c*d^2))^2)*sqrt(e+d/x^2)*x^3*InverseJacobiAM(2*arctan(a^(1/4)*sqrt(e+d/x^2)/(a*e^2+c*d^2)^(1/4)),sqrt(1/2+1/2*sqrt(a)*e/sqrt(a*e^2+c*d^2)))/a^(1/4)/c/d/sqrt(e*x^2+d)/sqrt(c*x^4+a),1],
[(B*x^2+A)*(e*x^2+d)^q*(c*x^4+a),x,5,-(3*A*c*d*e*(7+2*q)-B*(15*c*d^2+a*e^2*(4*q^2+24*q+35)))*x*(e*x^2+d)^(1+q)/e^3/(3+2*q)/(5+2*q)/(7+2*q)-c*(5*B*d-A*e*(7+2*q))*x^3*(e*x^2+d)^(1+q)/e^2/(5+2*q)/(7+2*q)+B*c*x^5*(e*x^2+d)^(1+q)/e/(7+2*q)+(A*e*(7+2*q)*(3*c*d^2+a*e^2*(4*q^2+16*q+15))-B*d*(15*c*d^2+a*e^2*(4*q^2+24*q+35)))*x*(e*x^2+d)^q*hypergeom([1/2, -q],[3/2],-e*x^2/d)/e^3/(3+2*q)/(5+2*q)/(7+2*q)/((1+e*x^2/d)^q),1],
[(B*x^2+A)*(e*x^2+d)^q,x,3,B*x*(e*x^2+d)^(1+q)/e/(3+2*q)-(B*d-A*e*(3+2*q))*x*(e*x^2+d)^q*hypergeom([1/2, -q],[3/2],-e*x^2/d)/e/(3+2*q)/((1+e*x^2/d)^q),1],
[(B*x^2+A)*(e*x^2+d)^q/(c*x^4+a),x,8,1/2*(A-sqrt(-a)*B/sqrt(c))*x*(e*x^2+d)^q*AppellF1(1/2,-q,1,3/2,-e*x^2/d,-sqrt(c)*x^2/sqrt(-a))/a/((1+e*x^2/d)^q)+1/2*(A+sqrt(-a)*B/sqrt(c))*x*(e*x^2+d)^q*AppellF1(1/2,-q,1,3/2,-e*x^2/d,sqrt(c)*x^2/sqrt(-a))/a/((1+e*x^2/d)^q),1],
[(B*x^2+A)*(e*x^2+d)^q/(c*x^4+a)^2,x,13,1/4*x*(e*x^2+d)^(1+q)*(A*c*d+a*B*e+c*(-A*e+B*d)*x^2)/a/(a*e^2+c*d^2)/(c*x^4+a)+1/8*(sqrt(c)*(A*(3*c*d^2+a*e^2*(3-2*q))+2*a*B*d*e*q)-sqrt(-a)*(B*(c*d^2+a*e^2*(1-2*q))-2*A*c*d*e*q))*x*(e*x^2+d)^q*AppellF1(1/2,-q,1,3/2,-e*x^2/d,-sqrt(c)*x^2/sqrt(-a))/a^2/sqrt(c)/(a*e^2+c*d^2)/((1+e*x^2/d)^q)+1/8*(sqrt(c)*(A*(3*c*d^2+a*e^2*(3-2*q))+2*a*B*d*e*q)+sqrt(-a)*(B*(c*d^2+a*e^2*(1-2*q))-2*A*c*d*e*q))*x*(e*x^2+d)^q*AppellF1(1/2,-q,1,3/2,-e*x^2/d,sqrt(c)*x^2/sqrt(-a))/a^2/sqrt(c)/(a*e^2+c*d^2)/((1+e*x^2/d)^q)-1/4*e*(-A*e+B*d)*(1+2*q)*x*(e*x^2+d)^q*hypergeom([1/2, -q],[3/2],-e*x^2/d)/a/(a*e^2+c*d^2)/((1+e*x^2/d)^q),1],
[(e*x^2+d)^q*(c*x^4+a)*(C*x^4+B*x^2+A),x,6,-(a*e^2*(4*q^2+32*q+63)*(3*C*d-B*e*(5+2*q))+3*c*d*(35*C*d^2-e*(9+2*q)*(5*B*d-A*e*(7+2*q))))*x*(e*x^2+d)^(1+q)/e^4/(3+2*q)/(5+2*q)/(7+2*q)/(9+2*q)+(a*C*e^2*(4*q^2+32*q+63)+c*(35*C*d^2-e*(9+2*q)*(5*B*d-A*e*(7+2*q))))*x^3*(e*x^2+d)^(1+q)/e^3/(5+2*q)/(7+2*q)/(9+2*q)-c*(7*C*d-B*e*(9+2*q))*x^5*(e*x^2+d)^(1+q)/e^2/(7+2*q)/(9+2*q)+c*C*x^7*(e*x^2+d)^(1+q)/e/(9+2*q)+(a*e^2*(4*q^2+32*q+63)*(3*C*d^2-e*(5+2*q)*(B*d-A*e*(3+2*q)))+3*c*d^2*(35*C*d^2-e*(9+2*q)*(5*B*d-A*e*(7+2*q))))*x*(e*x^2+d)^q*hypergeom([1/2, -q],[3/2],-e*x^2/d)/e^4/(3+2*q)/(5+2*q)/(7+2*q)/(9+2*q)/((1+e*x^2/d)^q),1],
[(e*x^2+d)^q*(C*x^4+B*x^2+A),x,4,-(3*C*d-B*e*(5+2*q))*x*(e*x^2+d)^(1+q)/e^2/(3+2*q)/(5+2*q)+C*x^3*(e*x^2+d)^(1+q)/e/(5+2*q)+(3*C*d^2-e*(5+2*q)*(B*d-A*e*(3+2*q)))*x*(e*x^2+d)^q*hypergeom([1/2, -q],[3/2],-e*x^2/d)/e^2/(3+2*q)/(5+2*q)/((1+e*x^2/d)^q),1],
[(e*x^2+d)^q*(C*x^4+B*x^2+A)/(c*x^4+a),x,12,-1/2*(sqrt(-a)*B*sqrt(c)-A*c+a*C)*x*(e*x^2+d)^q*AppellF1(1/2,-q,1,3/2,-e*x^2/d,-sqrt(c)*x^2/sqrt(-a))/a/c/((1+e*x^2/d)^q)+1/2*(sqrt(-a)*B*sqrt(c)+A*c-a*C)*x*(e*x^2+d)^q*AppellF1(1/2,-q,1,3/2,-e*x^2/d,sqrt(c)*x^2/sqrt(-a))/a/c/((1+e*x^2/d)^q)+C*x*(e*x^2+d)^q*hypergeom([1/2, -q],[3/2],-e*x^2/d)/c/((1+e*x^2/d)^q),1],
[(e*x^2+d)^q*(C*x^4+B*x^2+A)/(c*x^4+a)^2,x,13,1/4*x*(e*x^2+d)^(1+q)*(A*c*d-a*C*d+a*B*e+(-A*c*e+B*c*d+C*a*e)*x^2)/a/(a*e^2+c*d^2)/(c*x^4+a)+1/8*(A*c*(3*c*d^2+a*e^2*(3-2*q))-sqrt(-a)*sqrt(c)*(B*(c*d^2+a*e^2*(1-2*q))-2*(A*c-C*a)*d*e*q)+a*(a*C*e^2*(1+2*q)+c*d*(2*B*e*q+C*d)))*x*(e*x^2+d)^q*AppellF1(1/2,-q,1,3/2,-e*x^2/d,-sqrt(c)*x^2/sqrt(-a))/a^2/c/(a*e^2+c*d^2)/((1+e*x^2/d)^q)+1/8*(A*c*(3*c*d^2+a*e^2*(3-2*q))+sqrt(-a)*sqrt(c)*(B*(c*d^2+a*e^2*(1-2*q))-2*(A*c-C*a)*d*e*q)+a*(a*C*e^2*(1+2*q)+c*d*(2*B*e*q+C*d)))*x*(e*x^2+d)^q*AppellF1(1/2,-q,1,3/2,-e*x^2/d,sqrt(c)*x^2/sqrt(-a))/a^2/c/(a*e^2+c*d^2)/((1+e*x^2/d)^q)-1/4*e*(-A*c*e+B*c*d+C*a*e)*(1+2*q)*x*(e*x^2+d)^q*hypergeom([1/2, -q],[3/2],-e*x^2/d)/a/c/(a*e^2+c*d^2)/((1+e*x^2/d)^q),1],
[(B*x^2+A)/(e*x^2+d)/sqrt(a*d^2+b*d^2*x^2+(-a*e^2+b*d*e)*x^4),x,1,a*(-A*e+B*d)*(e*x^2+d)*sqrt((a*d+(-a*e+b*d)*x^2)/a/(e*x^2+d))*EllipticE(sin(arctan(sqrt(e)*x/sqrt(d))),sqrt(2-b*d/a/e))/d^(3/2)/sqrt(e)/(-2*a*e+b*d)/sqrt(a*d^2+b*d^2*x^2+e*(-a*e+b*d)*x^4)+(-A*a*e+A*b*d-B*a*d)*(e*x^2+d)*sqrt((a*d+(-a*e+b*d)*x^2)/a/(e*x^2+d))*InverseJacobiAM(arctan(sqrt(e)*x/sqrt(d)),sqrt(2-b*d/a/e))/d^(3/2)/sqrt(e)/(-2*a*e+b*d)/sqrt(a*d^2+b*d^2*x^2+e*(-a*e+b*d)*x^4),1],
[(B*x^2+A)/(-e*x^2+d)/sqrt(a*d^2+b*d^2*x^2+(-a*e^2+b*d*e)*x^4),x,5,-sqrt(a)*B*sqrt(d)*sqrt(1+e*x^2/d)*sqrt(1+(-a*e+b*d)*x^2/a/d)*InverseJacobiAM(arcsin(sqrt(a*e-b*d)*x/sqrt(a)/sqrt(d)),sqrt(a*e/(-a*e+b*d)))/e/sqrt(a*e-b*d)/sqrt(a*d^2+b*d^2*x^2+e*(-a*e+b*d)*x^4)+sqrt(a)*(A*e+B*d)*sqrt(1+e*x^2/d)*sqrt(1+(-a*e+b*d)*x^2/a/d)*EllipticPi(sin(arcsin(sqrt(a*e-b*d)*x/sqrt(a)/sqrt(d))),-a*e/(-a*e+b*d),sqrt(a*e/(-a*e+b*d)))/sqrt(d)/e/sqrt(a*e-b*d)/sqrt(a*d^2+b*d^2*x^2+e*(-a*e+b*d)*x^4),1],
[sqrt(x^4+3*x^2+2)/(x^2+1)^2,x,1,sqrt(2)*(x^2+1)*sqrt((x^2+2)/(x^2+1))*EllipticE(sin(arctan(x)),sqrt(1/2))/sqrt(x^4+3*x^2+2),1],
[(x^2+2)^2/(x^4+3*x^2+2)^(3/2),x,1,sqrt(2)*(x^2+1)*sqrt((x^2+2)/(x^2+1))*EllipticE(sin(arctan(x)),sqrt(1/2))/sqrt(x^4+3*x^2+2),1],
[(x^2+2)/(x^2+1)/sqrt(x^4+3*x^2+2),x,2,sqrt(2)*(x^2+1)*sqrt((x^2+2)/(x^2+1))*EllipticE(sin(arctan(x)),sqrt(1/2))/sqrt(x^4+3*x^2+2),1],
[(-2*x^4+x^2+4)/(x^2+1)^2/sqrt(x^4+x^2+1),x,4,3*arctan(x/sqrt(x^4+x^2+1))+1/2*(x^2+1)*sqrt((x^4+x^2+1)/(x^2+1)^2)*EllipticE(sin(2*arctan(x)),sqrt(1/4))/sqrt(x^4+x^2+1),1],
[(B*x^2+A)*sqrt(e*x^2+d)/sqrt(a*d+(a*e+b*d)*x^2+b*e*x^4),x,3,1/2*B*x*sqrt(a*d+(a*e+b*d)*x^2+b*e*x^4)/b/sqrt(e*x^2+d)+1/2*(2*A*b-B*a)*arctanh(sqrt(b)*x*sqrt(e*x^2+d)/sqrt(a*d+(a*e+b*d)*x^2+b*e*x^4))/b^(3/2),1],
[(B*x^2+A)/sqrt(e*x^2+d)/sqrt(d*e+(d^2+e^2)*x^2+d*e*x^4),x,5,B*arctanh(sqrt(d)*x*sqrt(e*x^2+d)/sqrt(d*e+(d^2+e^2)*x^2+d*e*x^4))/sqrt(d)/e-(-A*e+B*d)*arctanh(sqrt(d^2-e^2)*x*sqrt(e*x^2+d)/sqrt(d)/sqrt(d*e+(d^2+e^2)*x^2+d*e*x^4))/sqrt(d)/e/sqrt(d^2-e^2),1],
[(B*x^2+A)/sqrt(-e*x^2+d)/sqrt(-d*e+(d^2+e^2)*x^2-d*e*x^4),x,5,-B*arctanh(sqrt(d)*x*sqrt(-e*x^2+d)/sqrt(-d*e+(d^2+e^2)*x^2-d*e*x^4))/sqrt(d)/e+(A*e+B*d)*arctanh(sqrt(d^2-e^2)*x*sqrt(-e*x^2+d)/sqrt(d)/sqrt(-d*e+(d^2+e^2)*x^2-d*e*x^4))/sqrt(d)/e/sqrt(d^2-e^2),1],
[(B*x^2+A)/sqrt(e*x^2-d)/sqrt(-d*e+(d^2+e^2)*x^2-d*e*x^4),x,5,B*arctan(sqrt(d)*x*sqrt(e*x^2-d)/sqrt(-d*e+(d^2+e^2)*x^2-d*e*x^4))/sqrt(d)/e-(A*e+B*d)*arctan(sqrt(d^2-e^2)*x*sqrt(e*x^2-d)/sqrt(d)/sqrt(-d*e+(d^2+e^2)*x^2-d*e*x^4))/sqrt(d)/e/sqrt(d^2-e^2),1],
[(B*x^2+A)/sqrt(-e*x^2-d)/sqrt(d*e+(d^2+e^2)*x^2+d*e*x^4),x,5,-B*arctan(sqrt(d)*x*sqrt(-e*x^2-d)/sqrt(d*e+(d^2+e^2)*x^2+d*e*x^4))/sqrt(d)/e+(-A*e+B*d)*arctan(sqrt(d^2-e^2)*x*sqrt(-e*x^2-d)/sqrt(d)/sqrt(d*e+(d^2+e^2)*x^2+d*e*x^4))/sqrt(d)/e/sqrt(d^2-e^2),1],
[(B*x^2+A)/sqrt(e*x^2+d)/sqrt(-d*e+(d^2-e^2)*x^2+d*e*x^4),x,5,B*arctanh(sqrt(d)*x*sqrt(e*x^2+d)/sqrt(-d*e+(d^2-e^2)*x^2+d*e*x^4))/sqrt(d)/e-(-A*e+B*d)*arctanh(sqrt(d^2+e^2)*x*sqrt(e*x^2+d)/sqrt(d)/sqrt(-d*e+(d^2-e^2)*x^2+d*e*x^4))/sqrt(d)/e/sqrt(d^2+e^2),1],
[(B*x^2+A)/sqrt(-e*x^2+d)/sqrt(d*e+(d^2-e^2)*x^2-d*e*x^4),x,5,-B*arctanh(sqrt(d)*x*sqrt(-e*x^2+d)/sqrt(d*e+(d^2-e^2)*x^2-d*e*x^4))/sqrt(d)/e+(A*e+B*d)*arctanh(sqrt(d^2+e^2)*x*sqrt(-e*x^2+d)/sqrt(d)/sqrt(d*e+(d^2-e^2)*x^2-d*e*x^4))/sqrt(d)/e/sqrt(d^2+e^2),1],
[(B*x^2+A)/sqrt(e*x^2-d)/sqrt(d*e+(d^2-e^2)*x^2-d*e*x^4),x,5,B*arctan(sqrt(d)*x*sqrt(e*x^2-d)/sqrt(d*e+(d^2-e^2)*x^2-d*e*x^4))/sqrt(d)/e-(A*e+B*d)*arctan(sqrt(d^2+e^2)*x*sqrt(e*x^2-d)/sqrt(d)/sqrt(d*e+(d^2-e^2)*x^2-d*e*x^4))/sqrt(d)/e/sqrt(d^2+e^2),1],
[(B*x^2+A)/sqrt(-e*x^2-d)/sqrt(-d*e+(d^2-e^2)*x^2+d*e*x^4),x,5,-B*arctan(sqrt(d)*x*sqrt(-e*x^2-d)/sqrt(-d*e+(d^2-e^2)*x^2+d*e*x^4))/sqrt(d)/e+(-A*e+B*d)*arctan(sqrt(d^2+e^2)*x*sqrt(-e*x^2-d)/sqrt(d)/sqrt(-d*e+(d^2-e^2)*x^2+d*e*x^4))/sqrt(d)/e/sqrt(d^2+e^2),1],
[(e*x^2+d)^(5/2)*(C*x^4+B*x^2+A)/sqrt(a*d+(a*e+b*d)*x^2+b*e*x^4),x,6,-1/128*(35*a^3*C*e^2-64*b^3*d*(2*A*e+B*d)-40*a^2*b*e*(B*e+2*C*d)+48*a*b^2*(C*d^2+e*(A*e+2*B*d)))*x*sqrt(a*d+(a*e+b*d)*x^2+b*e*x^4)/b^4/sqrt(e*x^2+d)+1/192*(35*a^2*C*e^2-40*a*b*e*(B*e+2*C*d)+48*b^2*(C*d^2+e*(A*e+2*B*d)))*x^3*sqrt(a*d+(a*e+b*d)*x^2+b*e*x^4)/b^3/sqrt(e*x^2+d)-1/48*e*(7*a*C*e-8*b*(B*e+2*C*d))*x^5*sqrt(a*d+(a*e+b*d)*x^2+b*e*x^4)/b^2/sqrt(e*x^2+d)+1/8*C*e^2*x^7*sqrt(a*d+(a*e+b*d)*x^2+b*e*x^4)/b/sqrt(e*x^2+d)+1/128*(16*A*b^2*(3*a^2*e^2-8*a*b*d*e+8*b^2*d^2)-a*(64*b^3*B*d^2-35*a^3*C*e^2+40*a^2*b*e*(B*e+2*C*d)-48*a*b^2*d*(2*B*e+C*d)))*arctanh(sqrt(b)*x*sqrt(e*x^2+d)/sqrt(a*d+(a*e+b*d)*x^2+b*e*x^4))/b^(9/2),1],
[(e*x^2+d)^(3/2)*(C*x^4+B*x^2+A)/sqrt(a*d+(a*e+b*d)*x^2+b*e*x^4),x,5,1/16*(5*a^2*C*e+8*b^2*(A*e+B*d)-6*a*b*(B*e+C*d))*x*sqrt(a*d+(a*e+b*d)*x^2+b*e*x^4)/b^3/sqrt(e*x^2+d)-1/24*(5*a*C*e-6*b*(B*e+C*d))*x^3*sqrt(a*d+(a*e+b*d)*x^2+b*e*x^4)/b^2/sqrt(e*x^2+d)+1/6*C*e*x^5*sqrt(a*d+(a*e+b*d)*x^2+b*e*x^4)/b/sqrt(e*x^2+d)+1/16*(8*A*b^2*(-a*e+2*b*d)-a*(8*b^2*B*d+5*a^2*C*e-6*a*b*(B*e+C*d)))*arctanh(sqrt(b)*x*sqrt(e*x^2+d)/sqrt(a*d+(a*e+b*d)*x^2+b*e*x^4))/b^(7/2),1],
[sqrt(e*x^2+d)*(C*x^4+B*x^2+A)/sqrt(a*d+(a*e+b*d)*x^2+b*e*x^4),x,4,1/8*(4*B*b-3*C*a)*x*sqrt(a*d+(a*e+b*d)*x^2+b*e*x^4)/b^2/sqrt(e*x^2+d)+1/4*C*x^3*sqrt(a*d+(a*e+b*d)*x^2+b*e*x^4)/b/sqrt(e*x^2+d)+1/8*(8*A*b^2-a*(4*B*b-3*C*a))*arctanh(sqrt(b)*x*sqrt(e*x^2+d)/sqrt(a*d+(a*e+b*d)*x^2+b*e*x^4))/b^(5/2),1],
[(C*x^4+B*x^2+A)/sqrt(e*x^2+d)/sqrt(a*d+(a*e+b*d)*x^2+b*e*x^4),x,6,1/2*C*x*sqrt(a*d+(a*e+b*d)*x^2+b*e*x^4)/b/e/sqrt(e*x^2+d)-1/2*(-2*B*b*e+C*a*e+2*C*b*d)*arctanh(sqrt(b)*x*sqrt(e*x^2+d)/sqrt(a*d+(a*e+b*d)*x^2+b*e*x^4))/b^(3/2)/e^2+(A*e^2-B*d*e+C*d^2)*arctanh(sqrt(-a*e+b*d)*x*sqrt(e*x^2+d)/sqrt(d)/sqrt(a*d+(a*e+b*d)*x^2+b*e*x^4))/sqrt(d)/e^2/sqrt(-a*e+b*d),1],
[(C*x^4+B*x^2+A)/(e*x^2+d)^(3/2)/sqrt(a*d+(a*e+b*d)*x^2+b*e*x^4),x,6,-1/2*(A*e^2-B*d*e+C*d^2)*x*sqrt(a*d+(a*e+b*d)*x^2+b*e*x^4)/d/e/(-a*e+b*d)/(e*x^2+d)^(3/2)+C*arctanh(sqrt(b)*x*sqrt(e*x^2+d)/sqrt(a*d+(a*e+b*d)*x^2+b*e*x^4))/sqrt(b)/e^2-1/2*(2*b*(-A*d*e^2+C*d^3)-a*e*(3*C*d^2-e*(A*e+B*d)))*arctanh(sqrt(-a*e+b*d)*x*sqrt(e*x^2+d)/sqrt(d)/sqrt(a*d+(a*e+b*d)*x^2+b*e*x^4))/d^(3/2)/e^2/(-a*e+b*d)^(3/2),1],
[(C*x^4+B*x^2+A)/(e*x^2+d)^(5/2)/sqrt(a*d+(a*e+b*d)*x^2+b*e*x^4),x,5,-1/4*(A*e^2-B*d*e+C*d^2)*x*sqrt(a*d+(a*e+b*d)*x^2+b*e*x^4)/d/e/(-a*e+b*d)/(e*x^2+d)^(5/2)+1/8*(2*b*d*(C*d^2+e*(-3*A*e+B*d))-a*e*(5*C*d^2-e*(3*A*e+B*d)))*x*sqrt(a*d+(a*e+b*d)*x^2+b*e*x^4)/d^2/e/(-a*e+b*d)^2/(e*x^2+d)^(3/2)-1/8*(a*d*(-B*a*e+4*B*b*d-3*C*a*d)-A*(3*a^2*e^2-8*a*b*d*e+8*b^2*d^2))*arctanh(sqrt(-a*e+b*d)*x*sqrt(e*x^2+d)/sqrt(d)/sqrt(a*d+(a*e+b*d)*x^2+b*e*x^4))/d^(5/2)/(-a*e+b*d)^(5/2),1],
[(C*x^4+B*x^2+A)/(e*x^2+d)^(7/2)/sqrt(a*d+(a*e+b*d)*x^2+b*e*x^4),x,6,-1/6*(A*e^2-B*d*e+C*d^2)*x*sqrt(a*d+(a*e+b*d)*x^2+b*e*x^4)/d/e/(-a*e+b*d)/(e*x^2+d)^(7/2)+1/24*(2*b*d*(C*d^2+e*(-5*A*e+2*B*d))-a*e*(7*C*d^2-e*(5*A*e+B*d)))*x*sqrt(a*d+(a*e+b*d)*x^2+b*e*x^4)/d^2/e/(-a*e+b*d)^2/(e*x^2+d)^(5/2)+1/48*(4*b^2*d^2*(C*d^2+e*(-11*A*e+2*B*d))-3*a^2*e^2*(C*d^2+e*(5*A*e+B*d))-2*a*b*d*e*(8*C*d^2-e*(22*A*e+5*B*d)))*x*sqrt(a*d+(a*e+b*d)*x^2+b*e*x^4)/d^3/e/(-a*e+b*d)^3/(e*x^2+d)^(3/2)+1/16*(A*(-5*a^3*e^3+18*a^2*b*d*e^2-24*a*b^2*d^2*e+16*b^3*d^3)-a*d*(8*b^2*B*d^2+a^2*e*(B*e+C*d)-2*a*b*d*(2*B*e+3*C*d)))*arctanh(sqrt(-a*e+b*d)*x*sqrt(e*x^2+d)/sqrt(d)/sqrt(a*d+(a*e+b*d)*x^2+b*e*x^4))/d^(7/2)/(-a*e+b*d)^(7/2),1],
[(1-sqrt(3)-2*x^2)/sqrt(x^2+1)/(x^4-x^2+1),x,2,-1/3*sqrt(2)*arctan(sqrt(-3+2*sqrt(3))*x*sqrt(x^2+1)/(1+(1-sqrt(3))*x^2))*3^(3/4),1],
[(e*x^2+d)^(5/2)*(C*x^4+B*x^2+A)/(c*x^4+b*x^2+a),x,11,1/16*(8*b^2*C*e^2-2*c*e*(4*B*b*e+4*C*a*e+7*C*b*d)+c^2*(5*C*d^2+2*e*(4*A*e+7*B*d)))*x*sqrt(e*x^2+d)/c^3+1/24*(6*B*c*e-6*C*b*e+5*C*c*d)*x*(e*x^2+d)^(3/2)/c^2+1/6*C*x*(e*x^2+d)^(5/2)/c-(3*b^3*c*C*d*e^2-b^4*C*e^3-c^2*(A*c-C*a)*e*(-a*e^2+3*c*d^2)+b*c^2*d*(3*A*c*e^2-6*C*a*e^2+C*c*d^2)-b^2*c*e*(A*c*e^2-3*C*a*e^2+3*C*c*d^2)-B*c*(c^3*d^3-b^3*e^3-3*c^2*d*e*(a*e+b*d)+b*c*e^2*(2*a*e+3*b*d))+(b^5*C*e^3-b^4*c*e^2*(B*e+3*C*d)+b^2*c^2*(4*a*e^2*(B*e+3*C*d)-c*d*(C*d^2+3*e*(A*e+B*d)))-b^3*c*e*(5*a*C*e^2-c*(3*C*d^2+e*(A*e+3*B*d)))-2*c^3*(A*c*d*(-3*a*e^2+c*d^2)+a*(a*e^2*(B*e+3*C*d)-c*d^2*(3*B*e+C*d)))+b*c^2*(B*c*d*(-9*a*e^2+c*d^2)-e*(a*C*(-5*a*e^2+9*c*d^2)-3*A*c*(-a*e^2+c*d^2))))/sqrt(-4*a*c+b^2))*arctan(sqrt(2*c*d-(b-sqrt(-4*a*c+b^2))*e)*x/sqrt(b-sqrt(-4*a*c+b^2))/sqrt(e*x^2+d))/c^4/sqrt(b-sqrt(-4*a*c+b^2))/sqrt(2*c*d-(b-sqrt(-4*a*c+b^2))*e)-(3*b^3*c*C*d*e^2-b^4*C*e^3-c^2*(A*c-C*a)*e*(-a*e^2+3*c*d^2)+b*c^2*d*(3*A*c*e^2-6*C*a*e^2+C*c*d^2)-b^2*c*e*(A*c*e^2-3*C*a*e^2+3*C*c*d^2)-B*c*(c^3*d^3-b^3*e^3-3*c^2*d*e*(a*e+b*d)+b*c*e^2*(2*a*e+3*b*d))-(b^5*C*e^3-b^4*c*e^2*(B*e+3*C*d)+b*c^2*(B*c*d*(-9*a*e^2+c*d^2)-a*C*e*(-5*a*e^2+9*c*d^2)+3*A*c*e*(-a*e^2+c*d^2))+b^2*c^2*(4*a*e^2*(B*e+3*C*d)-c*d*(C*d^2+3*e*(A*e+B*d)))-b^3*c*e*(5*a*C*e^2-c*(3*C*d^2+e*(A*e+3*B*d)))-2*c^3*(A*c*d*(-3*a*e^2+c*d^2)+a*(a*e^2*(B*e+3*C*d)-c*d^2*(3*B*e+C*d))))/sqrt(-4*a*c+b^2))*arctan(sqrt(2*c*d-(b+sqrt(-4*a*c+b^2))*e)*x/sqrt(b+sqrt(-4*a*c+b^2))/sqrt(e*x^2+d))/c^4/sqrt(b+sqrt(-4*a*c+b^2))/sqrt(2*c*d-(b+sqrt(-4*a*c+b^2))*e)-1/16*(16*b^3*C*e^3-8*b*c*e^2*(2*B*b*e+4*C*a*e+5*C*b*d)-5*c^3*d*(8*A*e^2+6*B*d*e+C*d^2)+2*c^2*e*(4*a*e*(2*B*e+5*C*d)+b*(8*A*e^2+20*B*d*e+15*C*d^2)))*arctanh(sqrt(e)*x/sqrt(e*x^2+d))/c^4/sqrt(e),1],
[(e*x^2+d)^(3/2)*(C*x^4+B*x^2+A)/(c*x^4+b*x^2+a),x,10,1/8*(4*B*c*e-4*C*b*e+3*C*c*d)*x*sqrt(e*x^2+d)/c^2+1/4*C*x*(e*x^2+d)^(3/2)/c+(2*b^2*c*C*d*e+2*c^2*(A*c-C*a)*d*e-b^3*C*e^2-b*c*(A*c*e^2-2*C*a*e^2+C*c*d^2)+B*c*(c^2*d^2+b^2*e^2-c*e*(a*e+2*b*d))+(b^4*C*e^2-b^3*c*e*(B*e+2*C*d)-b*c^2*(2*A*c*d*e-3*B*a*e^2+B*c*d^2-6*C*a*d*e)-b^2*c*(4*a*C*e^2-c*(A*e^2+2*B*d*e+C*d^2))+2*c^2*(A*c*(-a*e^2+c*d^2)+a*(a*C*e^2-c*d*(2*B*e+C*d))))/sqrt(-4*a*c+b^2))*arctan(sqrt(2*c*d-(b-sqrt(-4*a*c+b^2))*e)*x/sqrt(b-sqrt(-4*a*c+b^2))/sqrt(e*x^2+d))/c^3/sqrt(b-sqrt(-4*a*c+b^2))/sqrt(2*c*d-(b-sqrt(-4*a*c+b^2))*e)+(2*b^2*c*C*d*e+2*c^2*(A*c-C*a)*d*e-b^3*C*e^2-b*c*(A*c*e^2-2*C*a*e^2+C*c*d^2)+B*c*(c^2*d^2+b^2*e^2-c*e*(a*e+2*b*d))-(b^4*C*e^2-b^3*c*e*(B*e+2*C*d)-b*c^2*(2*A*c*d*e-3*B*a*e^2+B*c*d^2-6*C*a*d*e)-b^2*c*(4*a*C*e^2-c*(A*e^2+2*B*d*e+C*d^2))+2*c^2*(A*c*(-a*e^2+c*d^2)+a*(a*C*e^2-c*d*(2*B*e+C*d))))/sqrt(-4*a*c+b^2))*arctan(sqrt(2*c*d-(b+sqrt(-4*a*c+b^2))*e)*x/sqrt(b+sqrt(-4*a*c+b^2))/sqrt(e*x^2+d))/c^3/sqrt(b+sqrt(-4*a*c+b^2))/sqrt(2*c*d-(b+sqrt(-4*a*c+b^2))*e)+1/8*(8*b^2*C*e^2-4*c*e*(2*B*b*e+2*C*a*e+3*C*b*d)+c^2*(3*C*d^2+4*e*(2*A*e+3*B*d)))*arctanh(sqrt(e)*x/sqrt(e*x^2+d))/c^3/sqrt(e),1],
[sqrt(e*x^2+d)*(C*x^4+B*x^2+A)/(c*x^4+b*x^2+a),x,9,1/2*C*x*sqrt(e*x^2+d)/c-(b*c*C*d-b^2*C*e-c*(A*c-C*a)*e-B*c*(-b*e+c*d)+(b^3*C*e-b^2*c*(B*e+C*d)-2*c^2*(A*c*d-B*a*e-C*a*d)+b*c*(A*c*e+B*c*d-3*C*a*e))/sqrt(-4*a*c+b^2))*arctan(sqrt(2*c*d-(b-sqrt(-4*a*c+b^2))*e)*x/sqrt(b-sqrt(-4*a*c+b^2))/sqrt(e*x^2+d))/c^2/sqrt(b-sqrt(-4*a*c+b^2))/sqrt(2*c*d-(b-sqrt(-4*a*c+b^2))*e)-(b*c*C*d-b^2*C*e-c*(A*c-C*a)*e-B*c*(-b*e+c*d)-(b^3*C*e-b^2*c*(B*e+C*d)+b*c*(A*c*e+B*c*d-3*C*a*e)-2*c^2*(A*c*d-a*(B*e+C*d)))/sqrt(-4*a*c+b^2))*arctan(sqrt(2*c*d-(b+sqrt(-4*a*c+b^2))*e)*x/sqrt(b+sqrt(-4*a*c+b^2))/sqrt(e*x^2+d))/c^2/sqrt(b+sqrt(-4*a*c+b^2))/sqrt(2*c*d-(b+sqrt(-4*a*c+b^2))*e)+1/2*(2*B*c*e-2*C*b*e+C*c*d)*arctanh(sqrt(e)*x/sqrt(e*x^2+d))/c^2/sqrt(e),1],
[(C*x^4+B*x^2+A)/sqrt(e*x^2+d)/(c*x^4+b*x^2+a),x,8,(B*c-b*C-(b*B*c-b^2*C-2*c*(A*c-C*a))/sqrt(-4*a*c+b^2))*arctan(sqrt(2*c*d-(b-sqrt(-4*a*c+b^2))*e)*x/sqrt(b-sqrt(-4*a*c+b^2))/sqrt(e*x^2+d))/c/sqrt(b-sqrt(-4*a*c+b^2))/sqrt(2*c*d-(b-sqrt(-4*a*c+b^2))*e)+(B*c-b*C+(b*B*c-b^2*C-2*c*(A*c-C*a))/sqrt(-4*a*c+b^2))*arctan(sqrt(2*c*d-(b+sqrt(-4*a*c+b^2))*e)*x/sqrt(b+sqrt(-4*a*c+b^2))/sqrt(e*x^2+d))/c/sqrt(b+sqrt(-4*a*c+b^2))/sqrt(2*c*d-(b+sqrt(-4*a*c+b^2))*e)+C*arctanh(sqrt(e)*x/sqrt(e*x^2+d))/c/sqrt(e),1],
[(C*x^4+B*x^2+A)/(e*x^2+d)^(3/2)/(c*x^4+b*x^2+a),x,6,(C*d^2-e*(-A*e+B*d))*x/d/(a*e^2-b*d*e+c*d^2)/sqrt(e*x^2+d)+(B*c*d-b*C*d-A*c*e+a*C*e+(b^2*C*d+2*c*(A*c*d+B*a*e-C*a*d)-b*(A*c*e+B*c*d+C*a*e))/sqrt(-4*a*c+b^2))*arctan(sqrt(2*c*d-(b-sqrt(-4*a*c+b^2))*e)*x/sqrt(b-sqrt(-4*a*c+b^2))/sqrt(e*x^2+d))/sqrt(b-sqrt(-4*a*c+b^2))/sqrt(2*c*d-(b-sqrt(-4*a*c+b^2))*e)/(c*d^2-e*(-a*e+b*d))+(B*c*d-b*C*d-A*c*e+a*C*e-(b^2*C*d+2*c*(A*c*d+B*a*e-C*a*d)-b*(A*c*e+B*c*d+C*a*e))/sqrt(-4*a*c+b^2))*arctan(sqrt(2*c*d-(b+sqrt(-4*a*c+b^2))*e)*x/sqrt(b+sqrt(-4*a*c+b^2))/sqrt(e*x^2+d))/sqrt(b+sqrt(-4*a*c+b^2))/sqrt(2*c*d-(b+sqrt(-4*a*c+b^2))*e)/(c*d^2-e*(-a*e+b*d)),1],
[(C*x^4+B*x^2+A)/(e*x^2+d)^(5/2)/(c*x^4+b*x^2+a),x,7,1/3*(C*d^2-e*(-A*e+B*d))*x/d/(a*e^2-b*d*e+c*d^2)/(e*x^2+d)^(3/2)+1/3*(c*d^2*(2*C*d^2-e*(-8*A*e+5*B*d))+e*(b*d*(-5*A*e^2+2*B*d*e+C*d^2)-a*e*(-2*A*e^2-B*d*e+4*C*d^2)))*x/d^2/(a*e^2-b*d*e+c*d^2)^2/sqrt(e*x^2+d)+c*(B*c*d^2-b*C*d^2-2*A*c*d*e+2*a*C*d*e+A*b*e^2-a*B*e^2+(b^2*(A*e^2+C*d^2)-b*(2*(A*c+C*a)*d*e+B*(a*e^2+c*d^2))+2*A*c*(-a*e^2+c*d^2)+2*a*(a*C*e^2-c*d*(-2*B*e+C*d)))/sqrt(-4*a*c+b^2))*arctan(sqrt(2*c*d-(b-sqrt(-4*a*c+b^2))*e)*x/sqrt(b-sqrt(-4*a*c+b^2))/sqrt(e*x^2+d))/sqrt(b-sqrt(-4*a*c+b^2))/sqrt(2*c*d-(b-sqrt(-4*a*c+b^2))*e)/(c*d^2-e*(-a*e+b*d))^2+c*(B*c*d^2-b*C*d^2-2*A*c*d*e+2*a*C*d*e+A*b*e^2-a*B*e^2-(b^2*(A*e^2+C*d^2)-b*(2*(A*c+C*a)*d*e+B*(a*e^2+c*d^2))+2*A*c*(-a*e^2+c*d^2)+2*a*(a*C*e^2-c*d*(-2*B*e+C*d)))/sqrt(-4*a*c+b^2))*arctan(sqrt(2*c*d-(b+sqrt(-4*a*c+b^2))*e)*x/sqrt(b+sqrt(-4*a*c+b^2))/sqrt(e*x^2+d))/sqrt(b+sqrt(-4*a*c+b^2))/sqrt(2*c*d-(b+sqrt(-4*a*c+b^2))*e)/(c*d^2-e*(-a*e+b*d))^2,1],
[(e*x^2+d)^(5/2)*(C*x^4+B*x^2+A)/(c*x^4+b*x^2+a)^2,x,11,-1/2*e*(A*c^2*(-2*a*e+b*d)-a*(B*c*(-b*e+2*c*d)-C*(6*a*c*e-2*b^2*e+b*c*d)))*x*sqrt(e*x^2+d)/a/c^2/(-4*a*c+b^2)-1/2*(A*b*c-2*B*a*c+C*a*b)*e*x*(e*x^2+d)^(3/2)/a/c/(-4*a*c+b^2)+1/2*x*(A*(-2*a*c+b^2)-a*(B*b-2*C*a)+(A*b*c-2*B*a*c+C*a*b)*x^2)*(e*x^2+d)^(5/2)/a/(-4*a*c+b^2)/(c*x^4+b*x^2+a)-1/2*(A*c^3*(4*a*e*(a*e^2+2*c*d^2)-b*(5*a*d*e^2+c*d^3))+a*(B*c*(2*c^3*d^3+2*b^3*e^3-2*c^2*d*e*(-7*a*e+2*b*d)-b*c*e^2*(10*a*e+b*d))+C*(7*b^3*c*d*e^2-4*b^4*e^3-2*b^2*c*e*(-10*a*e^2+c*d^2)+4*a*c^2*e*(-3*a*e^2+4*c*d^2)-b*c^2*d*(33*a*e^2+c*d^2)))+(A*c^3*(4*a*c*d*(a*e^2+3*c*d^2)-4*a*b*e*(a*e^2+3*c*d^2)-b^2*(-5*a*d*e^2+c*d^3))+a*(4*b^5*C*e^3-b^4*c*e^2*(2*B*e+7*C*d)-b^3*c*e*(28*a*C*e^2-c*d*(B*e+2*C*d))+4*a*c^3*(c*d^2*(2*B*e+C*d)-a*e^2*(4*B*e+13*C*d))+b^2*c^2*(c*d^2*(4*B*e+C*d)+a*e^2*(14*B*e+47*C*d))-4*b*c^2*(a*C*e*(-11*a*e^2+5*c*d^2)+B*c*d*(4*a*e^2+c*d^2))))/sqrt(-4*a*c+b^2))*arctan(sqrt(2*c*d-(b-sqrt(-4*a*c+b^2))*e)*x/sqrt(b-sqrt(-4*a*c+b^2))/sqrt(e*x^2+d))/a/c^3/(-4*a*c+b^2)/sqrt(b-sqrt(-4*a*c+b^2))/sqrt(2*c*d-(b-sqrt(-4*a*c+b^2))*e)-1/2*(A*c^3*(4*a*e*(a*e^2+2*c*d^2)-b*(5*a*d*e^2+c*d^3))+a*(B*c*(2*c^3*d^3+2*b^3*e^3-2*c^2*d*e*(-7*a*e+2*b*d)-b*c*e^2*(10*a*e+b*d))+C*(7*b^3*c*d*e^2-4*b^4*e^3-2*b^2*c*e*(-10*a*e^2+c*d^2)+4*a*c^2*e*(-3*a*e^2+4*c*d^2)-b*c^2*d*(33*a*e^2+c*d^2)))-(A*c^3*(4*a*c*d*(a*e^2+3*c*d^2)-4*a*b*e*(a*e^2+3*c*d^2)-b^2*(-5*a*d*e^2+c*d^3))+a*(4*b^5*C*e^3-b^4*c*e^2*(2*B*e+7*C*d)-b^3*c*e*(28*a*C*e^2-c*d*(B*e+2*C*d))+4*a*c^3*(c*d^2*(2*B*e+C*d)-a*e^2*(4*B*e+13*C*d))+b^2*c^2*(c*d^2*(4*B*e+C*d)+a*e^2*(14*B*e+47*C*d))-4*b*c^2*(a*C*e*(-11*a*e^2+5*c*d^2)+B*c*d*(4*a*e^2+c*d^2))))/sqrt(-4*a*c+b^2))*arctan(sqrt(2*c*d-(b+sqrt(-4*a*c+b^2))*e)*x/sqrt(b+sqrt(-4*a*c+b^2))/sqrt(e*x^2+d))/a/c^3/(-4*a*c+b^2)/sqrt(b+sqrt(-4*a*c+b^2))/sqrt(2*c*d-(b+sqrt(-4*a*c+b^2))*e)+1/2*e^(3/2)*(2*B*c*e-4*C*b*e+5*C*c*d)*arctanh(sqrt(e)*x/sqrt(e*x^2+d))/c^3,1],
[(e*x^2+d)^(3/2)*(C*x^4+B*x^2+A)/(c*x^4+b*x^2+a)^2,x,10,-1/2*(A*b*c-2*B*a*c+C*a*b)*e*x*sqrt(e*x^2+d)/a/c/(-4*a*c+b^2)+1/2*x*(A*(-2*a*c+b^2)-a*(B*b-2*C*a)+(A*b*c-2*B*a*c+C*a*b)*x^2)*(e*x^2+d)^(3/2)/a/(-4*a*c+b^2)/(c*x^4+b*x^2+a)+1/2*(A*c^2*(2*a*b*e^2-6*a*c*d*e+b*c*d^2)+a*(C*(-b*e+c*d)*(-10*a*c*e+2*b^2*e+b*c*d)-B*c^2*(2*c*d^2-e*(-4*a*e+3*b*d)))-(A*c^2*(12*a*c^2*d^2-8*a*b*c*d*e-b^2*(-2*a*e^2+c*d^2))+a*(b^3*c*C*d*e-2*b^4*C*e^2-4*b*c^2*(B*a*e^2+B*c*d^2+3*C*a*d*e)-4*a*c^2*(4*a*C*e^2-c*d*(B*e+C*d))+b^2*c*(14*a*C*e^2+c*d*(3*B*e+C*d))))/sqrt(-4*a*c+b^2))*arctan(sqrt(2*c*d-(b-sqrt(-4*a*c+b^2))*e)*x/sqrt(b-sqrt(-4*a*c+b^2))/sqrt(e*x^2+d))/a/c^2/(-4*a*c+b^2)/sqrt(b-sqrt(-4*a*c+b^2))/sqrt(2*c*d-(b-sqrt(-4*a*c+b^2))*e)+1/2*(A*c^2*(2*a*b*e^2-6*a*c*d*e+b*c*d^2)+a*(C*(-b*e+c*d)*(-10*a*c*e+2*b^2*e+b*c*d)-B*c^2*(2*c*d^2-e*(-4*a*e+3*b*d)))+(A*c^2*(12*a*c^2*d^2-8*a*b*c*d*e-b^2*(-2*a*e^2+c*d^2))+a*(b^3*c*C*d*e-2*b^4*C*e^2-4*b*c^2*(B*a*e^2+B*c*d^2+3*C*a*d*e)-4*a*c^2*(4*a*C*e^2-c*d*(B*e+C*d))+b^2*c*(14*a*C*e^2+c*d*(3*B*e+C*d))))/sqrt(-4*a*c+b^2))*arctan(sqrt(2*c*d-(b+sqrt(-4*a*c+b^2))*e)*x/sqrt(b+sqrt(-4*a*c+b^2))/sqrt(e*x^2+d))/a/c^2/(-4*a*c+b^2)/sqrt(b+sqrt(-4*a*c+b^2))/sqrt(2*c*d-(b+sqrt(-4*a*c+b^2))*e)+C*e^(3/2)*arctanh(sqrt(e)*x/sqrt(e*x^2+d))/c^2,1],
[sqrt(e*x^2+d)*(C*x^4+B*x^2+A)/(c*x^4+b*x^2+a)^2,x,6,1/2*x*(A*(-2*a*c+b^2)-a*(B*b-2*C*a)+(A*b*c-2*B*a*c+C*a*b)*x^2)*sqrt(e*x^2+d)/a/(-4*a*c+b^2)/(c*x^4+b*x^2+a)+1/2*(A*c*(-4*a*e+b*d)-a*(-2*B*b*e+2*B*c*d+4*C*a*e-C*b*d)+(A*c*(4*a*b*e-12*a*c*d+b^2*d)-a*(4*a*c*C*d+b^2*(2*B*e+C*d)-4*b*(B*c*d+C*a*e)))/sqrt(-4*a*c+b^2))*arctan(sqrt(2*c*d-(b-sqrt(-4*a*c+b^2))*e)*x/sqrt(b-sqrt(-4*a*c+b^2))/sqrt(e*x^2+d))/a/(-4*a*c+b^2)/sqrt(b-sqrt(-4*a*c+b^2))/sqrt(2*c*d-(b-sqrt(-4*a*c+b^2))*e)-1/2*(A*c*(b^2*d-12*a*c*d-b*sqrt(-4*a*c+b^2)*d+4*a*b*e+4*a*sqrt(-4*a*c+b^2)*e)+a*(2*B*c*sqrt(-4*a*c+b^2)*d-4*a*c*C*d+4*a*sqrt(-4*a*c+b^2)*C*e-b^2*(2*B*e+C*d)+b*(4*B*c*d-sqrt(-4*a*c+b^2)*C*d-2*B*sqrt(-4*a*c+b^2)*e+4*a*C*e)))*arctan(sqrt(2*c*d-(b+sqrt(-4*a*c+b^2))*e)*x/sqrt(b+sqrt(-4*a*c+b^2))/sqrt(e*x^2+d))/a/(-4*a*c+b^2)^(3/2)/sqrt(b+sqrt(-4*a*c+b^2))/sqrt(2*c*d-(b+sqrt(-4*a*c+b^2))*e),1],
[(C*x^4+B*x^2+A)/sqrt(e*x^2+d)/(c*x^4+b*x^2+a)^2,x,6,1/2*x*sqrt(e*x^2+d)*(A*(3*a*b*c*e-2*a*c^2*d-b^3*e+b^2*c*d)-a*(2*B*a*c*e-B*b^2*e+B*b*c*d+C*a*b*e-2*C*a*c*d)+c*(A*(2*a*c*e-b^2*e+b*c*d)-a*(-B*b*e+2*B*c*d+2*C*a*e-C*b*d))*x^2)/a/(-4*a*c+b^2)/(a*e^2-b*d*e+c*d^2)/(c*x^4+b*x^2+a)+1/2*((A*c-C*a)*(-2*a*e+b*d)*(-b*e+c*d)-a*(B*c-C*b)*(2*c*d^2-e*(-4*a*e+3*b*d))-(A*c*(b^3*d*e-12*a*b*c*d*e-b^2*(2*a*e^2+c*d^2)+4*a*c*(4*a*e^2+3*c*d^2))-a*(2*b^3*C*d*e-4*a*c^2*d*(-B*e+C*d)+4*b*B*c*(a*e^2+c*d^2)-b^2*(2*a*C*e^2+c*d*(5*B*e+C*d))))/sqrt(-4*a*c+b^2))*arctan(sqrt(2*c*d-(b-sqrt(-4*a*c+b^2))*e)*x/sqrt(b-sqrt(-4*a*c+b^2))/sqrt(e*x^2+d))/a/(-4*a*c+b^2)/sqrt(b-sqrt(-4*a*c+b^2))/sqrt(2*c*d-(b-sqrt(-4*a*c+b^2))*e)/(c*d^2-e*(-a*e+b*d))+1/2*((A*c-C*a)*(-2*a*e+b*d)*(-b*e+c*d)-a*(B*c-C*b)*(2*c*d^2-e*(-4*a*e+3*b*d))+(A*c*(b^3*d*e-12*a*b*c*d*e-b^2*(2*a*e^2+c*d^2)+4*a*c*(4*a*e^2+3*c*d^2))-a*(2*b^3*C*d*e-4*a*c^2*d*(-B*e+C*d)+4*b*B*c*(a*e^2+c*d^2)-b^2*(2*a*C*e^2+c*d*(5*B*e+C*d))))/sqrt(-4*a*c+b^2))*arctan(sqrt(2*c*d-(b+sqrt(-4*a*c+b^2))*e)*x/sqrt(b+sqrt(-4*a*c+b^2))/sqrt(e*x^2+d))/a/(-4*a*c+b^2)/sqrt(b+sqrt(-4*a*c+b^2))/sqrt(2*c*d-(b+sqrt(-4*a*c+b^2))*e)/(c*d^2-e*(-a*e+b*d)),1],
[(C*x^4+B*x^2+A)/(e*x^2+d)^(3/2)/(c*x^4+b*x^2+a)^2,x,7,1/2*e*(A*(b^3*d*e^2+b*c*d*(-3*a*e^2+c*d^2)+4*a*c*e*(-2*a*e^2+c*d^2)-b^2*(-2*a*e^3+2*c*d^2*e))+a*d*(C*(a*b*e^2-12*a*c*d*e+2*b^2*d*e+b*c*d^2)-B*(2*c^2*d^2+3*b^2*e^2-2*c*e*(5*a*e+b*d))))*x/a/(-4*a*c+b^2)/d/(a*e^2-b*d*e+c*d^2)^2/sqrt(e*x^2+d)+1/2*x*(A*(3*a*b*c*e-2*a*c^2*d-b^3*e+b^2*c*d)-a*(2*B*a*c*e-B*b^2*e+B*b*c*d+C*a*b*e-2*C*a*c*d)+c*(A*(2*a*c*e-b^2*e+b*c*d)-a*(-B*b*e+2*B*c*d+2*C*a*e-C*b*d))*x^2)/a/(-4*a*c+b^2)/(a*e^2-b*d*e+c*d^2)/sqrt(e*x^2+d)/(c*x^4+b*x^2+a)+1/2*c*(A*(b^3*d*e^2+12*a^2*c*e^3+b*c*d*(a*e^2+c*d^2)-2*b^2*(2*a*e^3+c*d^2*e))+a*(C*(-4*a^2*e^3+5*a*b*d*e^2+8*a*c*d^2*e-4*b^2*d^2*e+b*c*d^3)-B*(2*c^2*d^3-2*c*d*e*(-7*a*e+2*b*d)-b*e^2*(2*a*e+b*d)))+(A*(b^4*d*e^2+b^2*c*d*(-a*e^2+c*d^2)+20*a*b*c*e*(a*e^2+c*d^2)-12*a*c^2*d*(3*a*e^2+c*d^2)-2*b^3*(2*a*e^3+c*d^2*e))+a*(b^3*d*e*(B*e+4*C*d)+4*a*c*(a*e^2*(-4*B*e+5*C*d)-c*d^2*(-2*B*e+C*d))-b^2*(a*e^2*(-2*B*e+11*C*d)+c*d^2*(8*B*e+C*d))-4*b*(a*C*e*(-a*e^2+c*d^2)-B*c*d*(2*a*e^2+c*d^2))))/sqrt(-4*a*c+b^2))*arctan(sqrt(2*c*d-(b-sqrt(-4*a*c+b^2))*e)*x/sqrt(b-sqrt(-4*a*c+b^2))/sqrt(e*x^2+d))/a/(-4*a*c+b^2)/sqrt(b-sqrt(-4*a*c+b^2))/sqrt(2*c*d-(b-sqrt(-4*a*c+b^2))*e)/(a*e^2-b*d*e+c*d^2)^2+1/2*c*(A*(b^3*d*e^2+12*a^2*c*e^3+b*c*d*(a*e^2+c*d^2)-2*b^2*(2*a*e^3+c*d^2*e))+a*(C*(-4*a^2*e^3+5*a*b*d*e^2+8*a*c*d^2*e-4*b^2*d^2*e+b*c*d^3)-B*(2*c^2*d^3-2*c*d*e*(-7*a*e+2*b*d)-b*e^2*(2*a*e+b*d)))-(A*(b^4*d*e^2+b^2*c*d*(-a*e^2+c*d^2)+20*a*b*c*e*(a*e^2+c*d^2)-12*a*c^2*d*(3*a*e^2+c*d^2)-2*b^3*(2*a*e^3+c*d^2*e))+a*(b^3*d*e*(B*e+4*C*d)+4*a*c*(a*e^2*(-4*B*e+5*C*d)-c*d^2*(-2*B*e+C*d))-b^2*(a*e^2*(-2*B*e+11*C*d)+c*d^2*(8*B*e+C*d))-4*b*(a*C*e*(-a*e^2+c*d^2)-B*c*d*(2*a*e^2+c*d^2))))/sqrt(-4*a*c+b^2))*arctan(sqrt(2*c*d-(b+sqrt(-4*a*c+b^2))*e)*x/sqrt(b+sqrt(-4*a*c+b^2))/sqrt(e*x^2+d))/a/(-4*a*c+b^2)/sqrt(b+sqrt(-4*a*c+b^2))/sqrt(2*c*d-(b+sqrt(-4*a*c+b^2))*e)/(a*e^2-b*d*e+c*d^2)^2,1],
[(C*x^4+B*x^2+A)/(e*x^2+d)^(5/2)/(c*x^4+b*x^2+a)^2,x,8,1/6*e*(A*(3*b^3*d*e^2+3*b*c*d*(-3*a*e^2+c*d^2)+4*a*c*e*(-2*a*e^2+3*c*d^2)-b^2*(-2*a*e^3+6*c*d^2*e))-a*d*(B*(6*c^2*d^2+5*b^2*e^2-2*c*e*(7*a*e+3*b*d))-C*(2*b^2*d*e-20*a*c*d*e+3*b*(a*e^2+c*d^2))))*x/a/(-4*a*c+b^2)/d/(a*e^2-b*d*e+c*d^2)^2/(e*x^2+d)^(3/2)-1/6*e*(A*(3*b^4*d^2*e^3-2*a*c*e*(-8*a^2*e^4-59*a*c*d^2*e^2+9*c^2*d^4)-b*c*d*(64*a^2*e^4-27*a*c*d^2*e^2+3*c^2*d^4)-b^3*(-16*a*d*e^4+9*c*d^3*e^2)+b^2*(-4*a^2*e^5-40*a*c*d^2*e^3+9*c^2*d^4*e))+a*d*(B*(6*c^3*d^4-b^2*e^3*(2*a*e+13*b*d)-c^2*d^2*e*(106*a*e+9*b*d)+c*e^2*(8*a^2*e^2+49*a*b*d*e+31*b^2*d^2))+C*d*(4*b^3*d*e^2+2*a*c*e*(-19*a*e^2+41*c*d^2)-b*c*d*(25*a*e^2+3*c*d^2)-b^2*(-11*a*e^3+16*c*d^2*e))))*x/a/(-4*a*c+b^2)/d^2/(a*e^2-b*d*e+c*d^2)^3/sqrt(e*x^2+d)+1/2*x*(A*(3*a*b*c*e-2*a*c^2*d-b^3*e+b^2*c*d)-a*(2*B*a*c*e-B*b^2*e+B*b*c*d+C*a*b*e-2*C*a*c*d)+c*(A*(2*a*c*e-b^2*e+b*c*d)-a*(-B*b*e+2*B*c*d+2*C*a*e-C*b*d))*x^2)/a/(-4*a*c+b^2)/(a*e^2-b*d*e+c*d^2)/(e*x^2+d)^(3/2)/(c*x^4+b*x^2+a)-1/2*c*(A*(b^5*d*e^3+b^3*e*(3*c^2*d^3-6*a*sqrt(-4*a*c+b^2)*e^3-c*d*e*(3*sqrt(-4*a*c+b^2)*d-8*a*e))-b^4*e^2*(3*c*d^2-e*(sqrt(-4*a*c+b^2)*d-6*a*e))+2*a*c^2*(6*c^2*d^4-c*d^2*e*(sqrt(-4*a*c+b^2)*d-30*a*e)-a*e^3*(21*sqrt(-4*a*c+b^2)*d+16*a*e))-b^2*c*(c^2*d^4-3*c*d^2*e*(sqrt(-4*a*c+b^2)*d+3*a*e)-2*a*e^3*(5*sqrt(-4*a*c+b^2)*d+17*a*e))+b*c*(22*a^2*sqrt(-4*a*c+b^2)*e^4+a*c*d*e^2*(3*sqrt(-4*a*c+b^2)*d-64*a*e)-c^2*d^3*(sqrt(-4*a*c+b^2)*d+28*a*e)))+a*(b^4*B*d*e^3-b^3*e*(3*c*d^2*(B*e+2*C*d)-e^2*(B*sqrt(-4*a*c+b^2)*d-3*a*C*d+4*a*B*e))+b^2*(c^2*d^3*(11*B*e+C*d)-a*e^3*(3*sqrt(-4*a*c+b^2)*C*d-4*B*sqrt(-4*a*c+b^2)*e+2*a*C*e)+c*d*e*(3*C*d*(2*sqrt(-4*a*c+b^2)*d+9*a*e)-B*e*(3*sqrt(-4*a*c+b^2)*d+13*a*e)))-b*(C*(2*a^2*sqrt(-4*a*c+b^2)*e^4+c^2*d^3*(sqrt(-4*a*c+b^2)*d-8*a*e)+a*c*d*e^2*(9*sqrt(-4*a*c+b^2)*d+4*a*e))+B*c*(4*c^2*d^4+c*d^2*e*(5*sqrt(-4*a*c+b^2)*d+12*a*e)+a*e^3*(11*sqrt(-4*a*c+b^2)*d+20*a*e)))+2*c*(a*C*(2*c^2*d^4+a*e^3*(13*sqrt(-4*a*c+b^2)*d+8*a*e)-c*d^2*e*(7*sqrt(-4*a*c+b^2)*d+30*a*e))-B*(6*a^2*sqrt(-4*a*c+b^2)*e^4-c^2*d^3*(sqrt(-4*a*c+b^2)*d-6*a*e)-a*c*d*e^2*(15*sqrt(-4*a*c+b^2)*d+34*a*e)))))*arctan(sqrt(2*c*d-(b-sqrt(-4*a*c+b^2))*e)*x/sqrt(b-sqrt(-4*a*c+b^2))/sqrt(e*x^2+d))/a/(-4*a*c+b^2)^(3/2)/sqrt(b-sqrt(-4*a*c+b^2))/sqrt(2*c*d-(b-sqrt(-4*a*c+b^2))*e)/(a*e^2-b*d*e+c*d^2)^3+1/2*c*(A*(b^5*d*e^3-b^2*c*(c^2*d^4+2*a*e^3*(5*sqrt(-4*a*c+b^2)*d-17*a*e)+3*c*d^2*e*(sqrt(-4*a*c+b^2)*d-3*a*e))-b^4*e^2*(3*c*d^2+e*(sqrt(-4*a*c+b^2)*d+6*a*e))+b^3*e*(3*c^2*d^3+6*a*sqrt(-4*a*c+b^2)*e^3+c*d*e*(3*sqrt(-4*a*c+b^2)*d+8*a*e))+2*a*c^2*(6*c^2*d^4+a*e^3*(21*sqrt(-4*a*c+b^2)*d-16*a*e)+c*d^2*e*(sqrt(-4*a*c+b^2)*d+30*a*e))-b*c*(22*a^2*sqrt(-4*a*c+b^2)*e^4-c^2*d^3*(sqrt(-4*a*c+b^2)*d-28*a*e)+a*c*d*e^2*(3*sqrt(-4*a*c+b^2)*d+64*a*e)))+a*(b^4*B*d*e^3-b^3*e*(3*c*d^2*(B*e+2*C*d)+e^2*(B*sqrt(-4*a*c+b^2)*d+3*a*C*d-4*a*B*e))+b^2*(c^2*d^3*(11*B*e+C*d)+a*e^3*(3*sqrt(-4*a*c+b^2)*C*d-4*B*sqrt(-4*a*c+b^2)*e-2*a*C*e)+c*d*e*(B*e*(3*sqrt(-4*a*c+b^2)*d-13*a*e)-3*C*d*(2*sqrt(-4*a*c+b^2)*d-9*a*e)))+2*c*(a*C*(2*c^2*d^4+c*d^2*e*(7*sqrt(-4*a*c+b^2)*d-30*a*e)-a*e^3*(13*sqrt(-4*a*c+b^2)*d-8*a*e))+B*(6*a^2*sqrt(-4*a*c+b^2)*e^4-a*c*d*e^2*(15*sqrt(-4*a*c+b^2)*d-34*a*e)-c^2*d^3*(sqrt(-4*a*c+b^2)*d+6*a*e)))-b*(B*c*(4*c^2*d^4-a*e^3*(11*sqrt(-4*a*c+b^2)*d-20*a*e)-c*d^2*e*(5*sqrt(-4*a*c+b^2)*d-12*a*e))-C*(2*a^2*sqrt(-4*a*c+b^2)*e^4+a*c*d*e^2*(9*sqrt(-4*a*c+b^2)*d-4*a*e)+c^2*d^3*(sqrt(-4*a*c+b^2)*d+8*a*e)))))*arctan(sqrt(2*c*d-(b+sqrt(-4*a*c+b^2))*e)*x/sqrt(b+sqrt(-4*a*c+b^2))/sqrt(e*x^2+d))/a/(-4*a*c+b^2)^(3/2)/sqrt(b+sqrt(-4*a*c+b^2))/sqrt(2*c*d-(b+sqrt(-4*a*c+b^2))*e)/(a*e^2-b*d*e+c*d^2)^3,1],
[(B*x^2+A)*(e*x^2+d)^(1/3)/(c*x^4+b*x^2+a),x,10,(A*c*e+B*(-b*e+c*d)+(b^2*B*e-b*c*(A*e+B*d)+2*c*(A*c*d-B*a*e))/sqrt(-4*a*c+b^2))*x*(1+e*x^2/d)^(2/3)*AppellF1(1/2,2/3,1,3/2,-e*x^2/d,-2*c*x^2/(b-sqrt(-4*a*c+b^2)))/c/(b-sqrt(-4*a*c+b^2))/(e*x^2+d)^(2/3)+(A*c*e+B*(-b*e+c*d)-(b^2*B*e-b*c*(A*e+B*d)+2*c*(A*c*d-B*a*e))/sqrt(-4*a*c+b^2))*x*(1+e*x^2/d)^(2/3)*AppellF1(1/2,2/3,1,3/2,-e*x^2/d,-2*c*x^2/(b+sqrt(-4*a*c+b^2)))/c/(b+sqrt(-4*a*c+b^2))/(e*x^2+d)^(2/3)-3^(3/4)*sqrt(2-sqrt(3))*B*(d^(1/3)-(e*x^2+d)^(1/3))*sqrt((d^(2/3)+d^(1/3)*(e*x^2+d)^(1/3)+(e*x^2+d)^(2/3))/((1-sqrt(3))*d^(1/3)-(e*x^2+d)^(1/3))^2)*InverseJacobiAM(arcsin(((1+sqrt(3))*d^(1/3)-(e*x^2+d)^(1/3))/((1-sqrt(3))*d^(1/3)-(e*x^2+d)^(1/3))),sqrt(-7+4*sqrt(3)))/c/x/sqrt(-d^(1/3)*(d^(1/3)-(e*x^2+d)^(1/3))/((1-sqrt(3))*d^(1/3)-(e*x^2+d)^(1/3))^2),1],
[(B*x^2+A)*(e*x^2+d)^3/sqrt(c*x^4+b*x^2+a),x,7,1/105*e*(7*A*c*e*(-4*b*e+15*c*d)+B*(105*c^2*d^2+24*b^2*e^2-c*e*(25*a*e+84*b*d)))*x*sqrt(c*x^4+b*x^2+a)/c^3+1/35*e^2*(7*A*c*e-6*B*b*e+21*B*c*d)*x^3*sqrt(c*x^4+b*x^2+a)/c^2+1/7*B*e^3*x^5*sqrt(c*x^4+b*x^2+a)/c+1/105*(7*A*c*e*(45*c^2*d^2+8*b^2*e^2-3*c*e*(3*a*e+10*b*d))+B*(105*c^3*d^3-48*b^3*e^3-21*c^2*d*e*(9*a*e+10*b*d)+8*b*c*e^2*(13*a*e+21*b*d)))*x*sqrt(c*x^4+b*x^2+a)/c^(7/2)/(sqrt(a)+sqrt(c)*x^2)-1/105*a^(1/4)*(7*A*c*e*(45*c^2*d^2+8*b^2*e^2-3*c*e*(3*a*e+10*b*d))+B*(105*c^3*d^3-48*b^3*e^3-21*c^2*d*e*(9*a*e+10*b*d)+8*b*c*e^2*(13*a*e+21*b*d)))*(sqrt(a)+sqrt(c)*x^2)*sqrt((c*x^4+b*x^2+a)/(sqrt(a)+sqrt(c)*x^2)^2)*EllipticE(sin(2*arctan(c^(1/4)*x/a^(1/4))),sqrt(1/2-1/4*b/sqrt(a)/sqrt(c)))/c^(15/4)/sqrt(c*x^4+b*x^2+a)+1/210*(7*A*c*(4*a*b*e^3-15*a*c*d*e^2+15*c^2*d^3)-a*B*e*(105*c^2*d^2+24*b^2*e^2-c*e*(25*a*e+84*b*d))+sqrt(a)*(7*A*c*e*(45*c^2*d^2+8*b^2*e^2-3*c*e*(3*a*e+10*b*d))+B*(105*c^3*d^3-48*b^3*e^3-21*c^2*d*e*(9*a*e+10*b*d)+8*b*c*e^2*(13*a*e+21*b*d)))/sqrt(c))*(sqrt(a)+sqrt(c)*x^2)*sqrt((c*x^4+b*x^2+a)/(sqrt(a)+sqrt(c)*x^2)^2)*InverseJacobiAM(2*arctan(c^(1/4)*x/a^(1/4)),sqrt(1/2-1/4*b/sqrt(a)/sqrt(c)))/a^(1/4)/c^(13/4)/sqrt(c*x^4+b*x^2+a),1],
[(B*x^2+A)*(e*x^2+d)^2/sqrt(c*x^4+b*x^2+a),x,6,1/15*e*(5*A*c*e-4*B*b*e+10*B*c*d)*x*sqrt(c*x^4+b*x^2+a)/c^2+1/5*B*e^2*x^3*sqrt(c*x^4+b*x^2+a)/c+1/15*(10*A*c*e*(-b*e+3*c*d)+B*(15*c^2*d^2+8*b^2*e^2-c*e*(9*a*e+20*b*d)))*x*sqrt(c*x^4+b*x^2+a)/c^(5/2)/(sqrt(a)+sqrt(c)*x^2)-1/15*a^(1/4)*(10*A*c*e*(-b*e+3*c*d)+B*(15*c^2*d^2+8*b^2*e^2-c*e*(9*a*e+20*b*d)))*(sqrt(a)+sqrt(c)*x^2)*sqrt((c*x^4+b*x^2+a)/(sqrt(a)+sqrt(c)*x^2)^2)*EllipticE(sin(2*arctan(c^(1/4)*x/a^(1/4))),sqrt(1/2-1/4*b/sqrt(a)/sqrt(c)))/c^(11/4)/sqrt(c*x^4+b*x^2+a)-1/30*(2*a*B*e*(-2*b*e+5*c*d)-5*A*c*(-a*e^2+3*c*d^2)-sqrt(a)*(10*A*c*e*(-b*e+3*c*d)+B*(15*c^2*d^2+8*b^2*e^2-c*e*(9*a*e+20*b*d)))/sqrt(c))*(sqrt(a)+sqrt(c)*x^2)*sqrt((c*x^4+b*x^2+a)/(sqrt(a)+sqrt(c)*x^2)^2)*InverseJacobiAM(2*arctan(c^(1/4)*x/a^(1/4)),sqrt(1/2-1/4*b/sqrt(a)/sqrt(c)))/a^(1/4)/c^(9/4)/sqrt(c*x^4+b*x^2+a),1],
[(B*x^2+A)*(e*x^2+d)/sqrt(c*x^4+b*x^2+a),x,5,1/3*B*e*x*sqrt(c*x^4+b*x^2+a)/c+1/3*(3*A*c*e-2*B*b*e+3*B*c*d)*x*sqrt(c*x^4+b*x^2+a)/c^(3/2)/(sqrt(a)+sqrt(c)*x^2)-1/3*a^(1/4)*(3*A*c*e-2*B*b*e+3*B*c*d)*(sqrt(a)+sqrt(c)*x^2)*sqrt((c*x^4+b*x^2+a)/(sqrt(a)+sqrt(c)*x^2)^2)*EllipticE(sin(2*arctan(c^(1/4)*x/a^(1/4))),sqrt(1/2-1/4*b/sqrt(a)/sqrt(c)))/c^(7/4)/sqrt(c*x^4+b*x^2+a)+1/6*(3*A*c*d-a*B*e+sqrt(a)*(3*A*c*e-2*B*b*e+3*B*c*d)/sqrt(c))*(sqrt(a)+sqrt(c)*x^2)*sqrt((c*x^4+b*x^2+a)/(sqrt(a)+sqrt(c)*x^2)^2)*InverseJacobiAM(2*arctan(c^(1/4)*x/a^(1/4)),sqrt(1/2-1/4*b/sqrt(a)/sqrt(c)))/a^(1/4)/c^(5/4)/sqrt(c*x^4+b*x^2+a),1],
[(B*x^2+A)/sqrt(c*x^4+b*x^2+a),x,4,B*x*sqrt(c*x^4+b*x^2+a)/sqrt(c)/(sqrt(a)+sqrt(c)*x^2)-a^(1/4)*B*(sqrt(a)+sqrt(c)*x^2)*sqrt((c*x^4+b*x^2+a)/(sqrt(a)+sqrt(c)*x^2)^2)*EllipticE(sin(2*arctan(c^(1/4)*x/a^(1/4))),sqrt(1/2-1/4*b/sqrt(a)/sqrt(c)))/c^(3/4)/sqrt(c*x^4+b*x^2+a)+1/2*(sqrt(a)*B+A*sqrt(c))*(sqrt(a)+sqrt(c)*x^2)*sqrt((c*x^4+b*x^2+a)/(sqrt(a)+sqrt(c)*x^2)^2)*InverseJacobiAM(2*arctan(c^(1/4)*x/a^(1/4)),sqrt(1/2-1/4*b/sqrt(a)/sqrt(c)))/a^(1/4)/c^(3/4)/sqrt(c*x^4+b*x^2+a),1],
[(B*x^2+A)/(e*x^2+d)/sqrt(c*x^4+b*x^2+a),x,4,-1/2*(-A*e+B*d)*arctan(sqrt(a*e^2-b*d*e+c*d^2)*x/sqrt(d)/sqrt(e)/sqrt(c*x^4+b*x^2+a))/sqrt(d)/sqrt(e)/sqrt(a*e^2-b*d*e+c*d^2)-1/2*(sqrt(a)*B-A*sqrt(c))*(sqrt(a)+sqrt(c)*x^2)*sqrt((c*x^4+b*x^2+a)/(sqrt(a)+sqrt(c)*x^2)^2)*InverseJacobiAM(2*arctan(c^(1/4)*x/a^(1/4)),sqrt(1/2-1/4*b/sqrt(a)/sqrt(c)))/a^(1/4)/c^(1/4)/(sqrt(c)*d-sqrt(a)*e)/sqrt(c*x^4+b*x^2+a)+1/4*(sqrt(c)*d+sqrt(a)*e)*(-A*e+B*d)*(sqrt(a)+sqrt(c)*x^2)*sqrt((c*x^4+b*x^2+a)/(sqrt(a)+sqrt(c)*x^2)^2)*EllipticPi(sin(2*arctan(c^(1/4)*x/a^(1/4))),-1/4*(sqrt(c)*d-sqrt(a)*e)^2/sqrt(a)/sqrt(c)/d/e,sqrt(1/2-1/4*b/sqrt(a)/sqrt(c)))/a^(1/4)/c^(1/4)/d/e/(sqrt(c)*d-sqrt(a)*e)/sqrt(c*x^4+b*x^2+a),1],
[(B*x^2+A)/(e*x^2+d)^2/sqrt(c*x^4+b*x^2+a),x,8,1/2*sqrt(c)*(-A*e+B*d)*x*sqrt(c*x^4+b*x^2+a)/d/(a*e^2-b*d*e+c*d^2)/(sqrt(a)+sqrt(c)*x^2)-1/2*e*(-A*e+B*d)*x*sqrt(c*x^4+b*x^2+a)/d/(a*e^2-b*d*e+c*d^2)/(e*x^2+d)-1/4*(B*(-a*d*e^2+c*d^3)-A*e*(3*c*d^2-e*(-a*e+2*b*d)))*arctan(sqrt(a*e^2-b*d*e+c*d^2)*x/sqrt(d)/sqrt(e)/sqrt(c*x^4+b*x^2+a))/d^(3/2)/sqrt(e)/(a*e^2-b*d*e+c*d^2)^(3/2)-1/2*a^(1/4)*c^(1/4)*(-A*e+B*d)*(sqrt(a)+sqrt(c)*x^2)*sqrt((c*x^4+b*x^2+a)/(sqrt(a)+sqrt(c)*x^2)^2)*EllipticE(sin(2*arctan(c^(1/4)*x/a^(1/4))),sqrt(1/2-1/4*b/sqrt(a)/sqrt(c)))/d/(a*e^2-b*d*e+c*d^2)/sqrt(c*x^4+b*x^2+a)+1/2*A*c^(1/4)*(sqrt(a)+sqrt(c)*x^2)*sqrt((c*x^4+b*x^2+a)/(sqrt(a)+sqrt(c)*x^2)^2)*InverseJacobiAM(2*arctan(c^(1/4)*x/a^(1/4)),sqrt(1/2-1/4*b/sqrt(a)/sqrt(c)))/a^(1/4)/d/(sqrt(c)*d-sqrt(a)*e)/sqrt(c*x^4+b*x^2+a)+1/8*(sqrt(c)*d+sqrt(a)*e)*(B*(-a*d*e^2+c*d^3)-A*e*(3*c*d^2-e*(-a*e+2*b*d)))*(sqrt(a)+sqrt(c)*x^2)*sqrt((c*x^4+b*x^2+a)/(sqrt(a)+sqrt(c)*x^2)^2)*EllipticPi(sin(2*arctan(c^(1/4)*x/a^(1/4))),-1/4*(sqrt(c)*d-sqrt(a)*e)^2/sqrt(a)/sqrt(c)/d/e,sqrt(1/2-1/4*b/sqrt(a)/sqrt(c)))/a^(1/4)/c^(1/4)/d^2/e/(sqrt(c)*d-sqrt(a)*e)/(a*e^2-b*d*e+c*d^2)/sqrt(c*x^4+b*x^2+a),1],
[(B*x^2+A)/(e*x^2+d)^3/sqrt(c*x^4+b*x^2+a),x,9,-1/8*sqrt(c)*(3*A*e*(3*c*d^2-e*(-a*e+2*b*d))-B*d*(5*c*d^2-e*(a*e+2*b*d)))*x*sqrt(c*x^4+b*x^2+a)/d^2/(a*e^2-b*d*e+c*d^2)^2/(sqrt(a)+sqrt(c)*x^2)-1/4*e*(-A*e+B*d)*x*sqrt(c*x^4+b*x^2+a)/d/(a*e^2-b*d*e+c*d^2)/(e*x^2+d)^2+1/8*e*(3*A*e*(3*c*d^2-e*(-a*e+2*b*d))-B*d*(5*c*d^2-e*(a*e+2*b*d)))*x*sqrt(c*x^4+b*x^2+a)/d^2/(a*e^2-b*d*e+c*d^2)^2/(e*x^2+d)-1/16*(B*d*(3*c^2*d^4-10*a*c*d^2*e^2+a*e^3*(-a*e+4*b*d))-A*e*(15*c^2*d^4-2*c*d^2*e*(-3*a*e+10*b*d)+e^2*(3*a^2*e^2-8*a*b*d*e+8*b^2*d^2)))*arctan(sqrt(a*e^2-b*d*e+c*d^2)*x/sqrt(d)/sqrt(e)/sqrt(c*x^4+b*x^2+a))/d^(5/2)/sqrt(e)/(a*e^2-b*d*e+c*d^2)^(5/2)+1/8*a^(1/4)*c^(1/4)*(3*A*e*(3*c*d^2-e*(-a*e+2*b*d))-B*d*(5*c*d^2-e*(a*e+2*b*d)))*(sqrt(a)+sqrt(c)*x^2)*sqrt((c*x^4+b*x^2+a)/(sqrt(a)+sqrt(c)*x^2)^2)*EllipticE(sin(2*arctan(c^(1/4)*x/a^(1/4))),sqrt(1/2-1/4*b/sqrt(a)/sqrt(c)))/d^2/(a*e^2-b*d*e+c*d^2)^2/sqrt(c*x^4+b*x^2+a)+1/8*c^(1/4)*(sqrt(a)*sqrt(c)*d*(-A*e+B*d)+a*e*(3*A*e+B*d)+4*A*d*(-b*e+c*d))*(sqrt(a)+sqrt(c)*x^2)*sqrt((c*x^4+b*x^2+a)/(sqrt(a)+sqrt(c)*x^2)^2)*InverseJacobiAM(2*arctan(c^(1/4)*x/a^(1/4)),sqrt(1/2-1/4*b/sqrt(a)/sqrt(c)))/a^(1/4)/d^2/(sqrt(c)*d-sqrt(a)*e)/(a*e^2-b*d*e+c*d^2)/sqrt(c*x^4+b*x^2+a)+1/32*(sqrt(c)*d+sqrt(a)*e)*(B*d*(3*c^2*d^4-10*a*c*d^2*e^2+a*e^3*(-a*e+4*b*d))-A*e*(15*c^2*d^4-2*c*d^2*e*(-3*a*e+10*b*d)+e^2*(3*a^2*e^2-8*a*b*d*e+8*b^2*d^2)))*(sqrt(a)+sqrt(c)*x^2)*sqrt((c*x^4+b*x^2+a)/(sqrt(a)+sqrt(c)*x^2)^2)*EllipticPi(sin(2*arctan(c^(1/4)*x/a^(1/4))),-1/4*(sqrt(c)*d-sqrt(a)*e)^2/sqrt(a)/sqrt(c)/d/e,sqrt(1/2-1/4*b/sqrt(a)/sqrt(c)))/a^(1/4)/c^(1/4)/d^3/e/(sqrt(c)*d-sqrt(a)*e)/(a*e^2-b*d*e+c*d^2)^2/sqrt(c*x^4+b*x^2+a),1],
[(B*x^2+A)*(e*x^2+d)^3/(c*x^4+b*x^2+a)^(3/2),x,6,x*(A*c*(b^2*c*d^3-2*a*c*d*(-3*a*e^2+c*d^2)-a*b*e*(a*e^2+3*c*d^2))+a*B*(a*b^2*e^3+2*a*c*e*(-a*e^2+3*c*d^2)-b*c*d*(3*a*e^2+c*d^2))-(a*B*(-b*e+2*c*d)*(c^2*d^2+b^2*e^2-c*e*(3*a*e+b*d))+A*c*(a*b^2*e^3+2*a*c*e*(-a*e^2+3*c*d^2)-b*c*d*(3*a*e^2+c*d^2)))*x^2)/a/c^2/(-4*a*c+b^2)/sqrt(c*x^4+b*x^2+a)+1/3*B*e^3*x*sqrt(c*x^4+b*x^2+a)/c^2+1/3*(a*B*(6*c^3*d^3-8*b^3*e^3-9*c^2*d*e*(6*a*e+b*d)+b*c*e^2*(29*a*e+18*b*d))+3*A*c*(2*a*b^2*e^3+6*a*c*e*(-a*e^2+c*d^2)-b*c*d*(3*a*e^2+c*d^2)))*x*sqrt(c*x^4+b*x^2+a)/a/c^(5/2)/(-4*a*c+b^2)/(sqrt(a)+sqrt(c)*x^2)-1/3*(a*B*(6*c^3*d^3-8*b^3*e^3-9*c^2*d*e*(6*a*e+b*d)+b*c*e^2*(29*a*e+18*b*d))+3*A*c*(2*a*b^2*e^3+6*a*c*e*(-a*e^2+c*d^2)-b*c*d*(3*a*e^2+c*d^2)))*(sqrt(a)+sqrt(c)*x^2)*sqrt((c*x^4+b*x^2+a)/(sqrt(a)+sqrt(c)*x^2)^2)*EllipticE(sin(2*arctan(c^(1/4)*x/a^(1/4))),sqrt(1/2-1/4*b/sqrt(a)/sqrt(c)))/a^(3/4)/c^(11/4)/(-4*a*c+b^2)/sqrt(c*x^4+b*x^2+a)-1/6*(3*A*c^3*d^3-5*a^2*B*c*e^3-3*sqrt(a)*c^(5/2)*d^2*(3*A*e+B*d)+a*e*(-2*b*e+3*c*d)*(3*A*c*e-4*B*b*e+3*B*c*d)+3*a^(3/2)*sqrt(c)*e^2*(3*A*c*e-4*B*b*e+9*B*c*d))*(sqrt(a)+sqrt(c)*x^2)*sqrt((c*x^4+b*x^2+a)/(sqrt(a)+sqrt(c)*x^2)^2)*InverseJacobiAM(2*arctan(c^(1/4)*x/a^(1/4)),sqrt(1/2-1/4*b/sqrt(a)/sqrt(c)))/a^(3/4)/(b-2*sqrt(a)*sqrt(c))/c^(11/4)/sqrt(c*x^4+b*x^2+a),1],
[(B*x^2+A)*(e*x^2+d)^2/(c*x^4+b*x^2+a)^(3/2),x,5,-x*(c*(a*B*(a*b*e^2-4*a*c*d*e+b*c*d^2)/c-A*(b^2*d^2-2*a*b*d*e-2*a*(-a*e^2+c*d^2)))-(A*c*(a*b*e^2-4*a*c*d*e+b*c*d^2)-a*B*(2*c^2*d^2+b^2*e^2-2*c*e*(a*e+b*d)))*x^2)/a/c/(-4*a*c+b^2)/sqrt(c*x^4+b*x^2+a)-(A*c*(a*b*e^2-4*a*c*d*e+b*c*d^2)-2*a*B*(c^2*d^2+b^2*e^2-c*e*(3*a*e+b*d)))*x*sqrt(c*x^4+b*x^2+a)/a/c^(3/2)/(-4*a*c+b^2)/(sqrt(a)+sqrt(c)*x^2)+(A*c*(a*b*e^2-4*a*c*d*e+b*c*d^2)-2*a*B*(c^2*d^2+b^2*e^2-c*e*(3*a*e+b*d)))*(sqrt(a)+sqrt(c)*x^2)*sqrt((c*x^4+b*x^2+a)/(sqrt(a)+sqrt(c)*x^2)^2)*EllipticE(sin(2*arctan(c^(1/4)*x/a^(1/4))),sqrt(1/2-1/4*b/sqrt(a)/sqrt(c)))/a^(3/4)/c^(7/4)/(-4*a*c+b^2)/sqrt(c*x^4+b*x^2+a)-1/2*(A*c^2*d^2+3*a^(3/2)*B*sqrt(c)*e^2-sqrt(a)*c^(3/2)*d*(2*A*e+B*d)+a*e*(A*c*e-2*B*b*e+2*B*c*d))*(sqrt(a)+sqrt(c)*x^2)*sqrt((c*x^4+b*x^2+a)/(sqrt(a)+sqrt(c)*x^2)^2)*InverseJacobiAM(2*arctan(c^(1/4)*x/a^(1/4)),sqrt(1/2-1/4*b/sqrt(a)/sqrt(c)))/a^(3/4)/(b-2*sqrt(a)*sqrt(c))/c^(7/4)/sqrt(c*x^4+b*x^2+a),1],
[(B*x^2+A)*(e*x^2+d)/(c*x^4+b*x^2+a)^(3/2),x,5,-x*(a*B*(-2*a*e+b*d)-A*(-a*b*e-2*a*c*d+b^2*d)-(A*c*(-2*a*e+b*d)-a*B*(-b*e+2*c*d))*x^2)/a/(-4*a*c+b^2)/sqrt(c*x^4+b*x^2+a)-(A*c*(-2*a*e+b*d)-a*B*(-b*e+2*c*d))*x*sqrt(c*x^4+b*x^2+a)/a/sqrt(c)/(-4*a*c+b^2)/(sqrt(a)+sqrt(c)*x^2)+(A*c*(-2*a*e+b*d)-a*B*(-b*e+2*c*d))*(sqrt(a)+sqrt(c)*x^2)*sqrt((c*x^4+b*x^2+a)/(sqrt(a)+sqrt(c)*x^2)^2)*EllipticE(sin(2*arctan(c^(1/4)*x/a^(1/4))),sqrt(1/2-1/4*b/sqrt(a)/sqrt(c)))/a^(3/4)/c^(3/4)/(-4*a*c+b^2)/sqrt(c*x^4+b*x^2+a)+1/2*(sqrt(a)*B-A*sqrt(c))*(sqrt(c)*d-sqrt(a)*e)*(sqrt(a)+sqrt(c)*x^2)*sqrt((c*x^4+b*x^2+a)/(sqrt(a)+sqrt(c)*x^2)^2)*InverseJacobiAM(2*arctan(c^(1/4)*x/a^(1/4)),sqrt(1/2-1/4*b/sqrt(a)/sqrt(c)))/a^(3/4)/(b-2*sqrt(a)*sqrt(c))/c^(3/4)/sqrt(c*x^4+b*x^2+a),1],
[(B*x^2+A)/(c*x^4+b*x^2+a)^(3/2),x,5,x*(A*b^2-a*b*B-2*a*A*c+(A*b-2*B*a)*c*x^2)/a/(-4*a*c+b^2)/sqrt(c*x^4+b*x^2+a)-(A*b-2*B*a)*sqrt(c)*x*sqrt(c*x^4+b*x^2+a)/a/(-4*a*c+b^2)/(sqrt(a)+sqrt(c)*x^2)+(A*b-2*B*a)*c^(1/4)*(sqrt(a)+sqrt(c)*x^2)*sqrt((c*x^4+b*x^2+a)/(sqrt(a)+sqrt(c)*x^2)^2)*EllipticE(sin(2*arctan(c^(1/4)*x/a^(1/4))),sqrt(1/2-1/4*b/sqrt(a)/sqrt(c)))/a^(3/4)/(-4*a*c+b^2)/sqrt(c*x^4+b*x^2+a)+1/2*(sqrt(a)*B-A*sqrt(c))*(sqrt(a)+sqrt(c)*x^2)*sqrt((c*x^4+b*x^2+a)/(sqrt(a)+sqrt(c)*x^2)^2)*InverseJacobiAM(2*arctan(c^(1/4)*x/a^(1/4)),sqrt(1/2-1/4*b/sqrt(a)/sqrt(c)))/a^(3/4)/(b-2*sqrt(a)*sqrt(c))/c^(1/4)/sqrt(c*x^4+b*x^2+a),1],
[(B*x^2+A)/(e*x^2+d)/(c*x^4+b*x^2+a)^(3/2),x,8,-x*(a*B*(2*a*c*e-b^2*e+b*c*d)-A*(3*a*b*c*e-2*a*c^2*d-b^3*e+b^2*c*d)+c*(a*B*(-b*e+2*c*d)-A*(2*a*c*e-b^2*e+b*c*d))*x^2)/a/(-4*a*c+b^2)/(a*e^2-b*d*e+c*d^2)/sqrt(c*x^4+b*x^2+a)+sqrt(c)*(a*B*(-b*e+2*c*d)-A*(2*a*c*e-b^2*e+b*c*d))*x*sqrt(c*x^4+b*x^2+a)/a/(-4*a*c+b^2)/(a*e^2-b*d*e+c*d^2)/(sqrt(a)+sqrt(c)*x^2)-1/2*e^(3/2)*(-A*e+B*d)*arctan(sqrt(a*e^2-b*d*e+c*d^2)*x/sqrt(d)/sqrt(e)/sqrt(c*x^4+b*x^2+a))/sqrt(d)/(a*e^2-b*d*e+c*d^2)^(3/2)-c^(1/4)*(a*B*(-b*e+2*c*d)-A*(2*a*c*e-b^2*e+b*c*d))*(sqrt(a)+sqrt(c)*x^2)*sqrt((c*x^4+b*x^2+a)/(sqrt(a)+sqrt(c)*x^2)^2)*EllipticE(sin(2*arctan(c^(1/4)*x/a^(1/4))),sqrt(1/2-1/4*b/sqrt(a)/sqrt(c)))/a^(3/4)/(-4*a*c+b^2)/(a*e^2-b*d*e+c*d^2)/sqrt(c*x^4+b*x^2+a)+1/2*(sqrt(a)*B-A*sqrt(c))*c^(1/4)*(sqrt(a)+sqrt(c)*x^2)*sqrt((c*x^4+b*x^2+a)/(sqrt(a)+sqrt(c)*x^2)^2)*InverseJacobiAM(2*arctan(c^(1/4)*x/a^(1/4)),sqrt(1/2-1/4*b/sqrt(a)/sqrt(c)))/a^(3/4)/(b-2*sqrt(a)*sqrt(c))/(sqrt(c)*d-sqrt(a)*e)/sqrt(c*x^4+b*x^2+a)+1/4*e*(sqrt(c)*d+sqrt(a)*e)*(-A*e+B*d)*(sqrt(a)+sqrt(c)*x^2)*sqrt((c*x^4+b*x^2+a)/(sqrt(a)+sqrt(c)*x^2)^2)*EllipticPi(sin(2*arctan(c^(1/4)*x/a^(1/4))),-1/4*(sqrt(c)*d-sqrt(a)*e)^2/sqrt(a)/sqrt(c)/d/e,sqrt(1/2-1/4*b/sqrt(a)/sqrt(c)))/a^(1/4)/c^(1/4)/d/(sqrt(c)*d-sqrt(a)*e)/(a*e^2-b*d*e+c*d^2)/sqrt(c*x^4+b*x^2+a),1],
[(B*x^2+A)/(e*x^2+d)^2/(c*x^4+b*x^2+a)^(3/2),x,9,-1/2*e*(-A*e+B*d)*x/d/(a*e^2-b*d*e+c*d^2)/(e*x^2+d)/sqrt(c*x^4+b*x^2+a)-1/2*x*(a*(-A*e+B*d)*(b*e+2*c*d)*(2*a*c*e-b^2*e+b*c*d)-2*(c*(-2*a*c+b^2)*d-b*(-3*a*c+b^2)*e)*(2*a*B*d*e+A*(c*d^2-e*(a*e+b*d)))+c*(a*(-A*e+B*d)*(-b*e+2*c*d)*(b*e+2*c*d)-2*(2*a*c*e-b^2*e+b*c*d)*(2*a*B*d*e+A*(c*d^2-e*(a*e+b*d))))*x^2)/a/(-4*a*c+b^2)/d/(a*e^2-b*d*e+c*d^2)^2/sqrt(c*x^4+b*x^2+a)+1/2*sqrt(c)*(a*(-A*e+B*d)*(-b*e+2*c*d)*(b*e+2*c*d)-2*(2*a*c*e-b^2*e+b*c*d)*(2*a*B*d*e+A*(c*d^2-e*(a*e+b*d))))*x*sqrt(c*x^4+b*x^2+a)/a/(-4*a*c+b^2)/d/(a*e^2-b*d*e+c*d^2)^2/(sqrt(a)+sqrt(c)*x^2)+1/4*e^(3/2)*(A*e*(7*c*d^2-e*(-a*e+4*b*d))-B*d*(5*c*d^2-e*(a*e+2*b*d)))*arctan(sqrt(a*e^2-b*d*e+c*d^2)*x/sqrt(d)/sqrt(e)/sqrt(c*x^4+b*x^2+a))/d^(3/2)/(a*e^2-b*d*e+c*d^2)^(5/2)-1/2*c^(1/4)*(a*(-A*e+B*d)*(-b*e+2*c*d)*(b*e+2*c*d)-2*(2*a*c*e-b^2*e+b*c*d)*(2*a*B*d*e+A*(c*d^2-e*(a*e+b*d))))*(sqrt(a)+sqrt(c)*x^2)*sqrt((c*x^4+b*x^2+a)/(sqrt(a)+sqrt(c)*x^2)^2)*EllipticE(sin(2*arctan(c^(1/4)*x/a^(1/4))),sqrt(1/2-1/4*b/sqrt(a)/sqrt(c)))/a^(3/4)/(-4*a*c+b^2)/d/(a*e^2-b*d*e+c*d^2)^2/sqrt(c*x^4+b*x^2+a)+1/2*c^(1/4)*(a*sqrt(c)*e*(-2*A*e+B*d)-A*sqrt(c)*d*(-b*e+c*d)+sqrt(a)*(-A*e+B*d)*(-b*e+c*d))*(sqrt(a)+sqrt(c)*x^2)*sqrt((c*x^4+b*x^2+a)/(sqrt(a)+sqrt(c)*x^2)^2)*InverseJacobiAM(2*arctan(c^(1/4)*x/a^(1/4)),sqrt(1/2-1/4*b/sqrt(a)/sqrt(c)))/a^(3/4)/(b-2*sqrt(a)*sqrt(c))/d/(sqrt(c)*d-sqrt(a)*e)/(a*e^2-b*d*e+c*d^2)/sqrt(c*x^4+b*x^2+a)-1/8*e*(sqrt(c)*d+sqrt(a)*e)*(A*e*(7*c*d^2-e*(-a*e+4*b*d))-B*d*(5*c*d^2-e*(a*e+2*b*d)))*(sqrt(a)+sqrt(c)*x^2)*sqrt((c*x^4+b*x^2+a)/(sqrt(a)+sqrt(c)*x^2)^2)*EllipticPi(sin(2*arctan(c^(1/4)*x/a^(1/4))),-1/4*(sqrt(c)*d-sqrt(a)*e)^2/sqrt(a)/sqrt(c)/d/e,sqrt(1/2-1/4*b/sqrt(a)/sqrt(c)))/a^(1/4)/c^(1/4)/d^2/(sqrt(c)*d-sqrt(a)*e)/(a*e^2-b*d*e+c*d^2)^2/sqrt(c*x^4+b*x^2+a),1],
[(1+sqrt(c)*x^2/sqrt(a))/(e*x^2+d)/sqrt(c*x^4+b*x^2+a),x,2,-1/2*(sqrt(c)*d/sqrt(a)-e)*arctan(sqrt(a*e^2-b*d*e+c*d^2)*x/sqrt(d)/sqrt(e)/sqrt(c*x^4+b*x^2+a))/sqrt(d)/sqrt(e)/sqrt(a*e^2-b*d*e+c*d^2)+1/4*(sqrt(c)*d+sqrt(a)*e)*(sqrt(a)+sqrt(c)*x^2)*sqrt((c*x^4+b*x^2+a)/(sqrt(a)+sqrt(c)*x^2)^2)*EllipticPi(sin(2*arctan(c^(1/4)*x/a^(1/4))),-1/4*sqrt(a)*(sqrt(c)*d/sqrt(a)-e)^2/sqrt(c)/d/e,sqrt(1/2-1/4*b/sqrt(a)/sqrt(c)))/a^(3/4)/c^(1/4)/d/e/sqrt(c*x^4+b*x^2+a),1],
[(1+sqrt(c/a)*x^2)/(e*x^2+d)/sqrt(c*x^4+b*x^2+a),x,2,-1/2*(sqrt(c/a)*d-e)*arctan(sqrt(a*e^2-b*d*e+c*d^2)*x/sqrt(d)/sqrt(e)/sqrt(c*x^4+b*x^2+a))/sqrt(d)/sqrt(e)/sqrt(a*e^2-b*d*e+c*d^2)+1/4*(sqrt(c/a)*d+e)*(1+sqrt(c/a)*x^2)*sqrt(sqrt(c/a)*(c*x^4+b*x^2+a)/c/(1/(c/a)^(1/4)+(c/a)^(1/4)*x^2)^2)*EllipticPi(sin(2*arctan((c/a)^(1/4)*x)),-1/4*(sqrt(c/a)*d-e)^2/sqrt(c/a)/d/e,sqrt(1/2-1/4*b*sqrt(c/a)/c))/(c/a)^(1/4)/d/e/sqrt(c*x^4+b*x^2+a),1],
[(1-sqrt(c)*x^2/sqrt(a))/(e*x^2+d)/sqrt(c*x^4+b*x^2+a),x,4,1/2*(sqrt(c)*d+sqrt(a)*e)*arctan(sqrt(a*e^2-b*d*e+c*d^2)*x/sqrt(d)/sqrt(e)/sqrt(c*x^4+b*x^2+a))/sqrt(a)/sqrt(d)/sqrt(e)/sqrt(a*e^2-b*d*e+c*d^2)+c^(1/4)*(sqrt(a)+sqrt(c)*x^2)*sqrt((c*x^4+b*x^2+a)/(sqrt(a)+sqrt(c)*x^2)^2)*InverseJacobiAM(2*arctan(c^(1/4)*x/a^(1/4)),sqrt(1/2-1/4*b/sqrt(a)/sqrt(c)))/a^(1/4)/(sqrt(c)*d-sqrt(a)*e)/sqrt(c*x^4+b*x^2+a)-1/4*(sqrt(c)*d+sqrt(a)*e)^2*(sqrt(a)+sqrt(c)*x^2)*sqrt((c*x^4+b*x^2+a)/(sqrt(a)+sqrt(c)*x^2)^2)*EllipticPi(sin(2*arctan(c^(1/4)*x/a^(1/4))),-1/4*(sqrt(c)*d-sqrt(a)*e)^2/sqrt(a)/sqrt(c)/d/e,sqrt(1/2-1/4*b/sqrt(a)/sqrt(c)))/a^(3/4)/c^(1/4)/d/e/(sqrt(c)*d-sqrt(a)*e)/sqrt(c*x^4+b*x^2+a),1],
[(1-sqrt(c/a)*x^2)/(e*x^2+d)/sqrt(c*x^4+b*x^2+a),x,4,1/2*(sqrt(c/a)*d+e)*arctan(sqrt(a*e^2-b*d*e+c*d^2)*x/sqrt(d)/sqrt(e)/sqrt(c*x^4+b*x^2+a))/sqrt(d)/sqrt(e)/sqrt(a*e^2-b*d*e+c*d^2)+a^(3/4)*(c/a)^(3/2)*(sqrt(a)+sqrt(c)*x^2)*sqrt((c*x^4+b*x^2+a)/(sqrt(a)+sqrt(c)*x^2)^2)*InverseJacobiAM(2*arctan(c^(1/4)*x/a^(1/4)),sqrt(1/2-1/4*b/sqrt(a)/sqrt(c)))/c^(5/4)/(sqrt(c/a)*d-e)/sqrt(c*x^4+b*x^2+a)-1/4*(sqrt(c/a)*d+e)^2*(1+sqrt(c/a)*x^2)*sqrt(sqrt(c/a)*(c*x^4+b*x^2+a)/c/(1/(c/a)^(1/4)+(c/a)^(1/4)*x^2)^2)*EllipticPi(sin(2*arctan((c/a)^(1/4)*x)),-1/4*(sqrt(c/a)*d-e)^2/sqrt(c/a)/d/e,sqrt(1/2-1/4*b*sqrt(c/a)/c))/(c/a)^(1/4)/d/(sqrt(c/a)*d-e)/e/sqrt(c*x^4+b*x^2+a),1],
[(B*x^2+A)/(e*x^2+d)/sqrt(b*x^2+c*(a/c+x^4)),x,5,-1/2*(-A*e+B*d)*arctan(sqrt(a*e^2-b*d*e+c*d^2)*x/sqrt(d)/sqrt(e)/sqrt(c*x^4+b*x^2+a))/sqrt(d)/sqrt(e)/sqrt(a*e^2-b*d*e+c*d^2)-1/2*(sqrt(a)*B-A*sqrt(c))*(sqrt(a)+sqrt(c)*x^2)*sqrt((c*x^4+b*x^2+a)/(sqrt(a)+sqrt(c)*x^2)^2)*InverseJacobiAM(2*arctan(c^(1/4)*x/a^(1/4)),sqrt(1/2-1/4*b/sqrt(a)/sqrt(c)))/a^(1/4)/c^(1/4)/(sqrt(c)*d-sqrt(a)*e)/sqrt(c*x^4+b*x^2+a)+1/4*(sqrt(c)*d+sqrt(a)*e)*(-A*e+B*d)*(sqrt(a)+sqrt(c)*x^2)*sqrt((c*x^4+b*x^2+a)/(sqrt(a)+sqrt(c)*x^2)^2)*EllipticPi(sin(2*arctan(c^(1/4)*x/a^(1/4))),-1/4*(sqrt(c)*d-sqrt(a)*e)^2/sqrt(a)/sqrt(c)/d/e,sqrt(1/2-1/4*b/sqrt(a)/sqrt(c)))/a^(1/4)/c^(1/4)/d/e/(sqrt(c)*d-sqrt(a)*e)/sqrt(c*x^4+b*x^2+a),1],
[(315*x^2+946)/(5*x^2+7)/sqrt(x^4+3*x^2+2),x,4,631/2*(x^2+1)*sqrt((x^2+2)/(x^2+1))*InverseJacobiAM(arctan(x),sqrt(1/2))/sqrt(2)/sqrt(x^4+3*x^2+2)-2525/14*(x^2+2)*EllipticPi(sin(arctan(x)),2/7,sqrt(1/2))/sqrt(2)/sqrt((x^2+2)/(x^2+1))/sqrt(x^4+3*x^2+2),1],
[(sqrt(a)+sqrt(c)*x^2)/(e*x^2+d)/sqrt(c*x^4+b*x^2+a),x,2,-1/2*(sqrt(c)*d-sqrt(a)*e)*arctan(sqrt(a*e^2-b*d*e+c*d^2)*x/sqrt(d)/sqrt(e)/sqrt(c*x^4+b*x^2+a))/sqrt(d)/sqrt(e)/sqrt(a*e^2-b*d*e+c*d^2)+1/4*(sqrt(c)*d+sqrt(a)*e)*(sqrt(a)+sqrt(c)*x^2)*sqrt((c*x^4+b*x^2+a)/(sqrt(a)+sqrt(c)*x^2)^2)*EllipticPi(sin(2*arctan(c^(1/4)*x/a^(1/4))),-1/4*sqrt(a)*(sqrt(c)*d/sqrt(a)-e)^2/sqrt(c)/d/e,sqrt(1/2-1/4*b/sqrt(a)/sqrt(c)))/a^(1/4)/c^(1/4)/d/e/sqrt(c*x^4+b*x^2+a),1],
[(1+sqrt(c/a)*x^2)/(e*x^2+d)/sqrt(c*x^4+b*x^2+a),x,2,-1/2*(sqrt(c/a)*d-e)*arctan(sqrt(a*e^2-b*d*e+c*d^2)*x/sqrt(d)/sqrt(e)/sqrt(c*x^4+b*x^2+a))/sqrt(d)/sqrt(e)/sqrt(a*e^2-b*d*e+c*d^2)+1/4*(sqrt(c/a)*d+e)*(1+sqrt(c/a)*x^2)*sqrt(sqrt(c/a)*(c*x^4+b*x^2+a)/c/(1/(c/a)^(1/4)+(c/a)^(1/4)*x^2)^2)*EllipticPi(sin(2*arctan((c/a)^(1/4)*x)),-1/4*(sqrt(c/a)*d-e)^2/sqrt(c/a)/d/e,sqrt(1/2-1/4*b*sqrt(c/a)/c))/(c/a)^(1/4)/d/e/sqrt(c*x^4+b*x^2+a),1],
[(2+3*sqrt(2)+2*(3+sqrt(2))*x^2)/(2*x^2+3)/sqrt(2*x^4+2*x^2+1),x,2,-7/2*arctan(sqrt(5/3)*x/sqrt(2*x^4+2*x^2+1))/sqrt(15)+1/24*(3+sqrt(2))^2*(1+sqrt(2)*x^2)*sqrt((2*x^4+2*x^2+1)/(1+sqrt(2)*x^2)^2)*EllipticPi(sin(2*arctan(2^(1/4)*x)),1/2-11/24*sqrt(2),sqrt(1/2-1/4*sqrt(2)))*2^(3/4)/sqrt(2*x^4+2*x^2+1),1],
[(a+b+sqrt(b)*sqrt(a+b)-(b+sqrt(b)*sqrt(a+b))*x^2)/(-x^2+1)/sqrt(b*x^4-2*b*x^2+a+b),x,4,1/2*sqrt(a)*arctanh(sqrt(a)*x/sqrt(b*x^4-2*b*x^2+a+b))+b^(1/4)*(a+b)^(1/4)*(sqrt(b)+sqrt(a+b))*(a+b+sqrt(b)*sqrt(a+b))*(1+sqrt(b)*x^2/sqrt(a+b))*sqrt((b*x^4-2*b*x^2+a+b)/(a+b)/(1+sqrt(b)*x^2/sqrt(a+b))^2)*InverseJacobiAM(2*arctan(b^(1/4)*x/(a+b)^(1/4)),sqrt(1/2+1/2*sqrt(b)/sqrt(a+b)))/(a+2*b+2*sqrt(b)*sqrt(a+b))/sqrt(b*x^4-2*b*x^2+a+b)+1/4*a^2*(sqrt(a+b)+sqrt(b)*x^2)*sqrt((b*x^4-2*b*x^2+a+b)/(sqrt(a+b)+sqrt(b)*x^2)^2)*EllipticPi(sin(2*arctan(b^(1/4)*x/(a+b)^(1/4))),1/4*(sqrt(b)+sqrt(a+b))^2/sqrt(b)/sqrt(a+b),sqrt(1/2+1/2*sqrt(b)/sqrt(a+b)))/b^(1/4)/(a+b)^(1/4)/(a+2*b+2*sqrt(b)*sqrt(a+b))/sqrt(b*x^4-2*b*x^2+a+b),1],
[(2*x^2+1)^3*(x^4-7*x^2+4)*sqrt(3*x^4+5*x^2+2),x,9,34898492/32837805*x*(3*x^2+2)/sqrt(3*x^4+5*x^2+2)+1/10945935*x*(19259523*x^2+23671285)*sqrt(3*x^4+5*x^2+2)+54101/243243*x*(3*x^4+5*x^2+2)^(3/2)+21742/34749*x^3*(3*x^4+5*x^2+2)^(3/2)-2116/1287*x^5*(3*x^4+5*x^2+2)^(3/2)+8/39*x^7*(3*x^4+5*x^2+2)^(3/2)-34898492/32837805*sqrt(2)*(x^2+1)*sqrt((3*x^2+2)/(x^2+1))*EllipticE(sin(arctan(x)),sqrt(-1/2))/sqrt(3*x^4+5*x^2+2)+3048673/2189187*sqrt(2)*(x^2+1)*sqrt((3*x^2+2)/(x^2+1))*InverseJacobiAM(arctan(x),sqrt(-1/2))/sqrt(3*x^4+5*x^2+2),1],
[(2*x^2+1)^2*(x^4-7*x^2+4)*sqrt(3*x^4+5*x^2+2),x,8,1291552/841995*x*(3*x^2+2)/sqrt(3*x^4+5*x^2+2)+1/280665*x*(-195687*x^2+88715)*sqrt(3*x^4+5*x^2+2)+5893/6237*x*(3*x^4+5*x^2+2)^(3/2)-952/891*x^3*(3*x^4+5*x^2+2)^(3/2)+4/33*x^5*(3*x^4+5*x^2+2)^(3/2)-1291552/841995*sqrt(2)*(x^2+1)*sqrt((3*x^2+2)/(x^2+1))*EllipticE(sin(arctan(x)),sqrt(-1/2))/sqrt(3*x^4+5*x^2+2)+100715/56133*sqrt(2)*(x^2+1)*sqrt((3*x^2+2)/(x^2+1))*InverseJacobiAM(arctan(x),sqrt(-1/2))/sqrt(3*x^4+5*x^2+2),1],
[(2*x^2+1)*(x^4-7*x^2+4)*sqrt(3*x^4+5*x^2+2),x,7,7484/5103*x*(3*x^2+2)/sqrt(3*x^4+5*x^2+2)+1/1701*x*(5121*x^2+5935)*sqrt(3*x^4+5*x^2+2)-137/189*x*(3*x^4+5*x^2+2)^(3/2)+2/27*x^3*(3*x^4+5*x^2+2)^(3/2)-7484/5103*sqrt(2)*(x^2+1)*sqrt((3*x^2+2)/(x^2+1))*EllipticE(sin(arctan(x)),sqrt(-1/2))/sqrt(3*x^4+5*x^2+2)+3335/1701*sqrt(2)*(x^2+1)*sqrt((3*x^2+2)/(x^2+1))*InverseJacobiAM(arctan(x),sqrt(-1/2))/sqrt(3*x^4+5*x^2+2),1],
[(x^4-7*x^2+4)*sqrt(3*x^4+5*x^2+2),x,6,8488/2835*x*(3*x^2+2)/sqrt(3*x^4+5*x^2+2)+1/945*x*(-1503*x^2+395)*sqrt(3*x^4+5*x^2+2)+1/21*x*(3*x^4+5*x^2+2)^(3/2)-8488/2835*sqrt(2)*(x^2+1)*sqrt((3*x^2+2)/(x^2+1))*EllipticE(sin(arctan(x)),sqrt(-1/2))/sqrt(3*x^4+5*x^2+2)+659/189*sqrt(2)*(x^2+1)*sqrt((3*x^2+2)/(x^2+1))*InverseJacobiAM(arctan(x),sqrt(-1/2))/sqrt(3*x^4+5*x^2+2),1],
[(x^4-7*x^2+4)*sqrt(3*x^4+5*x^2+2)/(2*x^2+1),x,11,1879/1080*x*(3*x^2+2)/sqrt(3*x^4+5*x^2+2)-43/36*x*sqrt(3*x^4+5*x^2+2)+1/10*x^3*sqrt(3*x^4+5*x^2+2)-1879/540*(x^2+1)*sqrt((3*x^2+2)/(x^2+1))*EllipticE(sin(arctan(x)),sqrt(-1/2))/sqrt(2)/sqrt(3*x^4+5*x^2+2)+95/36*(x^2+1)*sqrt((3*x^2+2)/(x^2+1))*InverseJacobiAM(arctan(x),sqrt(-1/2))/sqrt(2)/sqrt(3*x^4+5*x^2+2)+31/4*(x^2+1)*EllipticPi(sin(arctan(sqrt(3/2)*x)),-1/3,sqrt(1/3))/sqrt(3)/sqrt((x^2+1)/(3*x^2+2))/sqrt(3*x^4+5*x^2+2),1],
[(x^4-7*x^2+4)*sqrt(3*x^4+5*x^2+2)/(2*x^2+1)^2,x,11,-547/144*x*(3*x^2+2)/sqrt(3*x^4+5*x^2+2)+1/12*x*sqrt(3*x^4+5*x^2+2)+31*x*sqrt(3*x^4+5*x^2+2)/(16*x^2+8)+547/72*(x^2+1)*sqrt((3*x^2+2)/(x^2+1))*EllipticE(sin(arctan(x)),sqrt(-1/2))/sqrt(2)/sqrt(3*x^4+5*x^2+2)-367/24*(x^2+1)*sqrt((3*x^2+2)/(x^2+1))*InverseJacobiAM(arctan(x),sqrt(-1/2))/sqrt(2)/sqrt(3*x^4+5*x^2+2)+41/8*sqrt(3)*(x^2+1)*EllipticPi(sin(arctan(sqrt(3/2)*x)),-1/3,sqrt(1/3))/sqrt((x^2+1)/(3*x^2+2))/sqrt(3*x^4+5*x^2+2),1],
[(x^4-7*x^2+4)*sqrt(3*x^4+5*x^2+2)/(2*x^2+1)^3,x,11,-145/64*x*(3*x^2+2)/sqrt(3*x^4+5*x^2+2)+31/16*x*sqrt(3*x^4+5*x^2+2)/(2*x^2+1)^2+153*x*sqrt(3*x^4+5*x^2+2)/(64*x^2+32)+145/32*(x^2+1)*sqrt((3*x^2+2)/(x^2+1))*EllipticE(sin(arctan(x)),sqrt(-1/2))/sqrt(2)/sqrt(3*x^4+5*x^2+2)-79/32*(x^2+1)*sqrt((3*x^2+2)/(x^2+1))*InverseJacobiAM(arctan(x),sqrt(-1/2))/sqrt(2)/sqrt(3*x^4+5*x^2+2)-95/32*(x^2+1)*EllipticPi(sin(arctan(sqrt(3/2)*x)),-1/3,sqrt(1/3))/sqrt(3)/sqrt((x^2+1)/(3*x^2+2))/sqrt(3*x^4+5*x^2+2),1],
[(2*x^2+1)^3*(x^4-7*x^2+4)*(3*x^4+5*x^2+2)^(3/2),x,10,1152397882/558242685*x*(3*x^2+2)/sqrt(3*x^4+5*x^2+2)+2/186080895*x*(101236329*x^2+202977940)*sqrt(3*x^4+5*x^2+2)+1/4135131*x*(3917921*x^2+4895329)*(3*x^4+5*x^2+2)^(3/2)+2609/11583*x*(3*x^4+5*x^2+2)^(5/2)+1706/5967*x^3*(3*x^4+5*x^2+2)^(5/2)-908/765*x^5*(3*x^4+5*x^2+2)^(5/2)+8/51*x^7*(3*x^4+5*x^2+2)^(5/2)-1152397882/558242685*sqrt(2)*(x^2+1)*sqrt((3*x^2+2)/(x^2+1))*EllipticE(sin(arctan(x)),sqrt(-1/2))/sqrt(3*x^4+5*x^2+2)+94891466/37216179*sqrt(2)*(x^2+1)*sqrt((3*x^2+2)/(x^2+1))*InverseJacobiAM(arctan(x),sqrt(-1/2))/sqrt(3*x^4+5*x^2+2),1],
[(2*x^2+1)^2*(x^4-7*x^2+4)*(3*x^4+5*x^2+2)^(3/2),x,9,15107402/6567561*x*(3*x^2+2)/sqrt(3*x^4+5*x^2+2)+2/2189187*x*(1514979*x^2+2823722)*sqrt(3*x^4+5*x^2+2)+1/243243*x*(-63175*x^2+57469)*(3*x^4+5*x^2+2)^(3/2)+6067/11583*x*(3*x^4+5*x^2+2)^(5/2)-256/351*x^3*(3*x^4+5*x^2+2)^(5/2)+4/45*x^5*(3*x^4+5*x^2+2)^(5/2)-15107402/6567561*sqrt(2)*(x^2+1)*sqrt((3*x^2+2)/(x^2+1))*EllipticE(sin(arctan(x)),sqrt(-1/2))/sqrt(3*x^4+5*x^2+2)+6244958/2189187*sqrt(2)*(x^2+1)*sqrt((3*x^2+2)/(x^2+1))*InverseJacobiAM(arctan(x),sqrt(-1/2))/sqrt(3*x^4+5*x^2+2),1],
[(2*x^2+1)*(x^4-7*x^2+4)*(3*x^4+5*x^2+2)^(3/2),x,8,9842698/3648645*x*(3*x^2+2)/sqrt(3*x^4+5*x^2+2)+2/1216215*x*(836181*x^2+1708960)*sqrt(3*x^4+5*x^2+2)+1/27027*x*(43169*x^2+49801)*(3*x^4+5*x^2+2)^(3/2)-587/1287*x*(3*x^4+5*x^2+2)^(5/2)+2/39*x^3*(3*x^4+5*x^2+2)^(5/2)-9842698/3648645*sqrt(2)*(x^2+1)*sqrt((3*x^2+2)/(x^2+1))*EllipticE(sin(arctan(x)),sqrt(-1/2))/sqrt(3*x^4+5*x^2+2)+809714/243243*sqrt(2)*(x^2+1)*sqrt((3*x^2+2)/(x^2+1))*InverseJacobiAM(arctan(x),sqrt(-1/2))/sqrt(3*x^4+5*x^2+2),1],
[(x^4-7*x^2+4)*(3*x^4+5*x^2+2)^(3/2),x,7,104954/31185*x*(3*x^2+2)/sqrt(3*x^4+5*x^2+2)+2/10395*x*(10863*x^2+19910)*sqrt(3*x^4+5*x^2+2)-1/231*x*(203*x^2+15)*(3*x^4+5*x^2+2)^(3/2)+1/33*x*(3*x^4+5*x^2+2)^(5/2)-104954/31185*sqrt(2)*(x^2+1)*sqrt((3*x^2+2)/(x^2+1))*EllipticE(sin(arctan(x)),sqrt(-1/2))/sqrt(3*x^4+5*x^2+2)+8686/2079*sqrt(2)*(x^2+1)*sqrt((3*x^2+2)/(x^2+1))*InverseJacobiAM(arctan(x),sqrt(-1/2))/sqrt(3*x^4+5*x^2+2),1],
[(x^4-7*x^2+4)*(3*x^4+5*x^2+2)^(3/2)/(2*x^2+1),x,13,246517/54432*x*(3*x^2+2)/sqrt(3*x^4+5*x^2+2)+15823/9072*x*sqrt(3*x^4+5*x^2+2)-845/504*x^3*sqrt(3*x^4+5*x^2+2)-305/252*x^5*sqrt(3*x^4+5*x^2+2)+1/6*x^7*sqrt(3*x^4+5*x^2+2)-246517/27216*(x^2+1)*sqrt((3*x^2+2)/(x^2+1))*EllipticE(sin(arctan(x)),sqrt(-1/2))/sqrt(2)/sqrt(3*x^4+5*x^2+2)+95929/9072*(x^2+1)*sqrt((3*x^2+2)/(x^2+1))*InverseJacobiAM(arctan(x),sqrt(-1/2))/sqrt(2)/sqrt(3*x^4+5*x^2+2)+31/16*(x^2+1)*EllipticPi(sin(arctan(sqrt(3/2)*x)),-1/3,sqrt(1/3))/sqrt(3)/sqrt((x^2+1)/(3*x^2+2))/sqrt(3*x^4+5*x^2+2),1],
[(x^4-7*x^2+4)*(3*x^4+5*x^2+2)^(3/2)/(2*x^2+1)^2,x,13,61199/20160*x*(3*x^2+2)/sqrt(3*x^4+5*x^2+2)-265/336*x*sqrt(3*x^4+5*x^2+2)-32/35*x^3*sqrt(3*x^4+5*x^2+2)+3/28*x^5*sqrt(3*x^4+5*x^2+2)+31*x*sqrt(3*x^4+5*x^2+2)/(64*x^2+32)-61199/10080*(x^2+1)*sqrt((3*x^2+2)/(x^2+1))*EllipticE(sin(arctan(x)),sqrt(-1/2))/sqrt(2)/sqrt(3*x^4+5*x^2+2)+2719/672*(x^2+1)*sqrt((3*x^2+2)/(x^2+1))*InverseJacobiAM(arctan(x),sqrt(-1/2))/sqrt(2)/sqrt(3*x^4+5*x^2+2)+371/32*(x^2+1)*EllipticPi(sin(arctan(sqrt(3/2)*x)),-1/3,sqrt(1/3))/sqrt(3)/sqrt((x^2+1)/(3*x^2+2))/sqrt(3*x^4+5*x^2+2),1],
[(x^4-7*x^2+4)*(3*x^4+5*x^2+2)^(3/2)/(2*x^2+1)^3,x,13,-3917/1280*x*(3*x^2+2)/sqrt(3*x^4+5*x^2+2)-13/16*x*sqrt(3*x^4+5*x^2+2)+3/40*x^3*sqrt(3*x^4+5*x^2+2)+31/64*x*sqrt(3*x^4+5*x^2+2)/(2*x^2+1)^2+649*x*sqrt(3*x^4+5*x^2+2)/(256*x^2+128)+3917/640*(x^2+1)*sqrt((3*x^2+2)/(x^2+1))*EllipticE(sin(arctan(x)),sqrt(-1/2))/sqrt(2)/sqrt(3*x^4+5*x^2+2)-1783/128*(x^2+1)*sqrt((3*x^2+2)/(x^2+1))*InverseJacobiAM(arctan(x),sqrt(-1/2))/sqrt(2)/sqrt(3*x^4+5*x^2+2)+2617/128*(x^2+1)*EllipticPi(sin(arctan(sqrt(3/2)*x)),-1/3,sqrt(1/3))/sqrt(3)/sqrt((x^2+1)/(3*x^2+2))/sqrt(3*x^4+5*x^2+2),1],
[(2*x^2+1)^3*(x^4-7*x^2+4)/sqrt(3*x^4+5*x^2+2),x,8,299197/76545*x*(3*x^2+2)/sqrt(3*x^4+5*x^2+2)-3359/5103*x*sqrt(3*x^4+5*x^2+2)+5602/2835*x^3*sqrt(3*x^4+5*x^2+2)-1508/567*x^5*sqrt(3*x^4+5*x^2+2)+8/27*x^7*sqrt(3*x^4+5*x^2+2)-299197/76545*sqrt(2)*(x^2+1)*sqrt((3*x^2+2)/(x^2+1))*EllipticE(sin(arctan(x)),sqrt(-1/2))/sqrt(3*x^4+5*x^2+2)+13565/5103*sqrt(2)*(x^2+1)*sqrt((3*x^2+2)/(x^2+1))*InverseJacobiAM(arctan(x),sqrt(-1/2))/sqrt(3*x^4+5*x^2+2),1],
[(2*x^2+1)^2*(x^4-7*x^2+4)/sqrt(3*x^4+5*x^2+2),x,7,-2771/945*x*(3*x^2+2)/sqrt(3*x^4+5*x^2+2)+187/63*x*sqrt(3*x^4+5*x^2+2)-208/105*x^3*sqrt(3*x^4+5*x^2+2)+4/21*x^5*sqrt(3*x^4+5*x^2+2)+2771/945*sqrt(2)*(x^2+1)*sqrt((3*x^2+2)/(x^2+1))*EllipticE(sin(arctan(x)),sqrt(-1/2))/sqrt(3*x^4+5*x^2+2)-61/63*sqrt(2)*(x^2+1)*sqrt((3*x^2+2)/(x^2+1))*InverseJacobiAM(arctan(x),sqrt(-1/2))/sqrt(3*x^4+5*x^2+2),1],
[(2*x^2+1)*(x^4-7*x^2+4)/sqrt(3*x^4+5*x^2+2),x,6,2377/405*x*(3*x^2+2)/sqrt(3*x^4+5*x^2+2)-47/27*x*sqrt(3*x^4+5*x^2+2)+2/15*x^3*sqrt(3*x^4+5*x^2+2)-2377/405*sqrt(2)*(x^2+1)*sqrt((3*x^2+2)/(x^2+1))*EllipticE(sin(arctan(x)),sqrt(-1/2))/sqrt(3*x^4+5*x^2+2)+101/27*sqrt(2)*(x^2+1)*sqrt((3*x^2+2)/(x^2+1))*InverseJacobiAM(arctan(x),sqrt(-1/2))/sqrt(3*x^4+5*x^2+2),1],
[(x^4-7*x^2+4)/sqrt(3*x^4+5*x^2+2),x,5,-73/27*x*(3*x^2+2)/sqrt(3*x^4+5*x^2+2)+1/9*x*sqrt(3*x^4+5*x^2+2)+73/27*sqrt(2)*(x^2+1)*sqrt((3*x^2+2)/(x^2+1))*EllipticE(sin(arctan(x)),sqrt(-1/2))/sqrt(3*x^4+5*x^2+2)+17/9*sqrt(2)*(x^2+1)*sqrt((3*x^2+2)/(x^2+1))*InverseJacobiAM(arctan(x),sqrt(-1/2))/sqrt(3*x^4+5*x^2+2),1],
[(x^4-7*x^2+4)/(2*x^2+1)/sqrt(3*x^4+5*x^2+2),x,9,1/6*x*(3*x^2+2)/sqrt(3*x^4+5*x^2+2)-1/3*(x^2+1)*sqrt((3*x^2+2)/(x^2+1))*EllipticE(sin(arctan(x)),sqrt(-1/2))/sqrt(2)/sqrt(3*x^4+5*x^2+2)-27*(x^2+1)*sqrt((3*x^2+2)/(x^2+1))*InverseJacobiAM(arctan(x),sqrt(-1/2))/sqrt(2)/sqrt(3*x^4+5*x^2+2)+31*(x^2+1)*EllipticPi(sin(arctan(sqrt(3/2)*x)),-1/3,sqrt(1/3))/sqrt(3)/sqrt((x^2+1)/(3*x^2+2))/sqrt(3*x^4+5*x^2+2),1],
[(x^4-7*x^2+4)/(2*x^2+1)^2/sqrt(3*x^4+5*x^2+2),x,10,-31/4*x*(3*x^2+2)/sqrt(3*x^4+5*x^2+2)+31*x*sqrt(3*x^4+5*x^2+2)/(4*x^2+2)+31/2*(x^2+1)*sqrt((3*x^2+2)/(x^2+1))*EllipticE(sin(arctan(x)),sqrt(-1/2))/sqrt(2)/sqrt(3*x^4+5*x^2+2)+71/2*(x^2+1)*sqrt((3*x^2+2)/(x^2+1))*InverseJacobiAM(arctan(x),sqrt(-1/2))/sqrt(2)/sqrt(3*x^4+5*x^2+2)-125/2*(x^2+1)*EllipticPi(sin(arctan(sqrt(3/2)*x)),-1/3,sqrt(1/3))/sqrt(3)/sqrt((x^2+1)/(3*x^2+2))/sqrt(3*x^4+5*x^2+2),1],
[(x^4-7*x^2+4)/(2*x^2+1)^3/sqrt(3*x^4+5*x^2+2),x,11,343/16*x*(3*x^2+2)/sqrt(3*x^4+5*x^2+2)+31/4*x*sqrt(3*x^4+5*x^2+2)/(2*x^2+1)^2-343*x*sqrt(3*x^4+5*x^2+2)/(16*x^2+8)-343/8*(x^2+1)*sqrt((3*x^2+2)/(x^2+1))*EllipticE(sin(arctan(x)),sqrt(-1/2))/sqrt(2)/sqrt(3*x^4+5*x^2+2)-567/8*(x^2+1)*sqrt((3*x^2+2)/(x^2+1))*InverseJacobiAM(arctan(x),sqrt(-1/2))/sqrt(2)/sqrt(3*x^4+5*x^2+2)+387/8*sqrt(3)*(x^2+1)*EllipticPi(sin(arctan(sqrt(3/2)*x)),-1/3,sqrt(1/3))/sqrt((x^2+1)/(3*x^2+2))/sqrt(3*x^4+5*x^2+2),1],
[(2*x^2+1)^3*(x^4-7*x^2+4)/(3*x^4+5*x^2+2)^(3/2),x,7,3437/135*x*(3*x^2+2)/sqrt(3*x^4+5*x^2+2)-1/27*x*(1013*x^2+689)/sqrt(3*x^4+5*x^2+2)-68/27*x*sqrt(3*x^4+5*x^2+2)+8/45*x^3*sqrt(3*x^4+5*x^2+2)-3437/135*sqrt(2)*(x^2+1)*sqrt((3*x^2+2)/(x^2+1))*EllipticE(sin(arctan(x)),sqrt(-1/2))/sqrt(3*x^4+5*x^2+2)+293/9*(x^2+1)*sqrt((3*x^2+2)/(x^2+1))*InverseJacobiAM(arctan(x),sqrt(-1/2))/sqrt(2)/sqrt(3*x^4+5*x^2+2),1],
[(2*x^2+1)^2*(x^4-7*x^2+4)/(3*x^4+5*x^2+2)^(3/2),x,6,-1411/81*x*(3*x^2+2)/sqrt(3*x^4+5*x^2+2)+1/9*x*(365*x^2+257)/sqrt(3*x^4+5*x^2+2)+4/27*x*sqrt(3*x^4+5*x^2+2)+1411/81*sqrt(2)*(x^2+1)*sqrt((3*x^2+2)/(x^2+1))*EllipticE(sin(arctan(x)),sqrt(-1/2))/sqrt(3*x^4+5*x^2+2)-725/27*(x^2+1)*sqrt((3*x^2+2)/(x^2+1))*InverseJacobiAM(arctan(x),sqrt(-1/2))/sqrt(2)/sqrt(3*x^4+5*x^2+2),1],
[(2*x^2+1)*(x^4-7*x^2+4)/(3*x^4+5*x^2+2)^(3/2),x,5,151/9*x*(3*x^2+2)/sqrt(3*x^4+5*x^2+2)-1/3*x*(149*x^2+113)/sqrt(3*x^4+5*x^2+2)-151/9*sqrt(2)*(x^2+1)*sqrt((3*x^2+2)/(x^2+1))*EllipticE(sin(arctan(x)),sqrt(-1/2))/sqrt(3*x^4+5*x^2+2)+119/3*(x^2+1)*sqrt((3*x^2+2)/(x^2+1))*InverseJacobiAM(arctan(x),sqrt(-1/2))/sqrt(2)/sqrt(3*x^4+5*x^2+2),1],
[(x^4-7*x^2+4)/(3*x^4+5*x^2+2)^(3/2),x,4,41/3*x/sqrt(3*x^4+5*x^2+2)+77/3*sqrt(2)*(x^2+1)*sqrt((3*x^2+2)/(x^2+1))*EllipticE(sin(arctan(x)),sqrt(-1/2))/sqrt(3*x^4+5*x^2+2)-63*(x^2+1)*sqrt((3*x^2+2)/(x^2+1))*InverseJacobiAM(arctan(x),sqrt(-1/2))/sqrt(2)/sqrt(3*x^4+5*x^2+2),1],
[(x^4-7*x^2+4)/(2*x^2+1)/(3*x^4+5*x^2+2)^(3/2),x,10,53*x*(3*x^2+2)/sqrt(3*x^4+5*x^2+2)-3*x*(53*x^2+49)/sqrt(3*x^4+5*x^2+2)-53*sqrt(2)*(x^2+1)*sqrt((3*x^2+2)/(x^2+1))*EllipticE(sin(arctan(x)),sqrt(-1/2))/sqrt(3*x^4+5*x^2+2)+25*(x^2+1)*sqrt((3*x^2+2)/(x^2+1))*InverseJacobiAM(arctan(x),sqrt(-1/2))/sqrt(2)/sqrt(3*x^4+5*x^2+2)+124*(x^2+1)*EllipticPi(sin(arctan(sqrt(3/2)*x)),-1/3,sqrt(1/3))/sqrt(3)/sqrt((x^2+1)/(3*x^2+2))/sqrt(3*x^4+5*x^2+2),1],
[(x^4-7*x^2+4)/(2*x^2+1)^2/(3*x^4+5*x^2+2)^(3/2),x,11,31/2*x/(2*x^2+1)/sqrt(3*x^4+5*x^2+2)-166*x*(3*x^2+2)/sqrt(3*x^4+5*x^2+2)+1/2*x*(996*x^2+1003)/sqrt(3*x^4+5*x^2+2)+166*sqrt(2)*(x^2+1)*sqrt((3*x^2+2)/(x^2+1))*EllipticE(sin(arctan(x)),sqrt(-1/2))/sqrt(3*x^4+5*x^2+2)+231*(x^2+1)*sqrt((3*x^2+2)/(x^2+1))*InverseJacobiAM(arctan(x),sqrt(-1/2))/sqrt(2)/sqrt(3*x^4+5*x^2+2)-746*(x^2+1)*EllipticPi(sin(arctan(sqrt(3/2)*x)),-1/3,sqrt(1/3))/sqrt(3)/sqrt((x^2+1)/(3*x^2+2))/sqrt(3*x^4+5*x^2+2),1],
[(x^4-7*x^2+4)/(2*x^2+1)^3/(3*x^4+5*x^2+2)^(3/2),x,12,31/4*x/(2*x^2+1)^2/sqrt(3*x^4+5*x^2+2)-591/8*x/(2*x^2+1)/sqrt(3*x^4+5*x^2+2)+2363/4*x*(3*x^2+2)/sqrt(3*x^4+5*x^2+2)-1/8*x*(14178*x^2+14735)/sqrt(3*x^4+5*x^2+2)-2363/2*(x^2+1)*sqrt((3*x^2+2)/(x^2+1))*EllipticE(sin(arctan(x)),sqrt(-1/2))/sqrt(2)/sqrt(3*x^4+5*x^2+2)-2565/2*(x^2+1)*sqrt((3*x^2+2)/(x^2+1))*InverseJacobiAM(arctan(x),sqrt(-1/2))/sqrt(2)/sqrt(3*x^4+5*x^2+2)+6385/2*(x^2+1)*EllipticPi(sin(arctan(sqrt(3/2)*x)),-1/3,sqrt(1/3))/sqrt(3)/sqrt((x^2+1)/(3*x^2+2))/sqrt(3*x^4+5*x^2+2),1],
[(2*x^2+1)^3*(x^4-7*x^2+4)/(3*x^4+5*x^2+2)^(5/2),x,6,-1/81*x*(1013*x^2+689)/(3*x^4+5*x^2+2)^(3/2)-5803/162*x*(3*x^2+2)/sqrt(3*x^4+5*x^2+2)+1/162*x*(17553*x^2+15689)/sqrt(3*x^4+5*x^2+2)+5803/81*(x^2+1)*sqrt((3*x^2+2)/(x^2+1))*EllipticE(sin(arctan(x)),sqrt(-1/2))/sqrt(2)/sqrt(3*x^4+5*x^2+2)-2473/27*(x^2+1)*sqrt((3*x^2+2)/(x^2+1))*InverseJacobiAM(arctan(x),sqrt(-1/2))/sqrt(2)/sqrt(3*x^4+5*x^2+2),1],
[(2*x^2+1)^2*(x^4-7*x^2+4)/(3*x^4+5*x^2+2)^(5/2),x,5,1/27*x*(365*x^2+257)/(3*x^4+5*x^2+2)^(3/2)-733/18*x/sqrt(3*x^4+5*x^2+2)-4171/27*(x^2+1)*sqrt((3*x^2+2)/(x^2+1))*EllipticE(sin(arctan(x)),sqrt(-1/2))/sqrt(2)/sqrt(3*x^4+5*x^2+2)+1723/9*(x^2+1)*sqrt((3*x^2+2)/(x^2+1))*InverseJacobiAM(arctan(x),sqrt(-1/2))/sqrt(2)/sqrt(3*x^4+5*x^2+2),1],
[(2*x^2+1)*(x^4-7*x^2+4)/(3*x^4+5*x^2+2)^(5/2),x,5,-1/9*x*(149*x^2+113)/(3*x^4+5*x^2+2)^(3/2)+425/6*x/sqrt(3*x^4+5*x^2+2)+2419/9*(x^2+1)*sqrt((3*x^2+2)/(x^2+1))*EllipticE(sin(arctan(x)),sqrt(-1/2))/sqrt(2)/sqrt(3*x^4+5*x^2+2)-997/3*(x^2+1)*sqrt((3*x^2+2)/(x^2+1))*InverseJacobiAM(arctan(x),sqrt(-1/2))/sqrt(2)/sqrt(3*x^4+5*x^2+2),1],
[(x^4-7*x^2+4)/(3*x^4+5*x^2+2)^(5/2),x,5,1/3*x*(77*x^2+65)/(3*x^4+5*x^2+2)^(3/2)-213/2*x/sqrt(3*x^4+5*x^2+2)-1219/3*(x^2+1)*sqrt((3*x^2+2)/(x^2+1))*EllipticE(sin(arctan(x)),sqrt(-1/2))/sqrt(2)/sqrt(3*x^4+5*x^2+2)+503*(x^2+1)*sqrt((3*x^2+2)/(x^2+1))*InverseJacobiAM(arctan(x),sqrt(-1/2))/sqrt(2)/sqrt(3*x^4+5*x^2+2),1],
[(x^4-7*x^2+4)/(2*x^2+1)/(3*x^4+5*x^2+2)^(5/2),x,11,-x*(53*x^2+49)/(3*x^4+5*x^2+2)^(3/2)-395/2*x*(3*x^2+2)/sqrt(3*x^4+5*x^2+2)+1/2*x*(1185*x^2+889)/sqrt(3*x^4+5*x^2+2)+395*(x^2+1)*sqrt((3*x^2+2)/(x^2+1))*EllipticE(sin(arctan(x)),sqrt(-1/2))/sqrt(2)/sqrt(3*x^4+5*x^2+2)-915*(x^2+1)*sqrt((3*x^2+2)/(x^2+1))*InverseJacobiAM(arctan(x),sqrt(-1/2))/sqrt(2)/sqrt(3*x^4+5*x^2+2)+496*(x^2+1)*EllipticPi(sin(arctan(sqrt(3/2)*x)),-1/3,sqrt(1/3))/sqrt(3)/sqrt((x^2+1)/(3*x^2+2))/sqrt(3*x^4+5*x^2+2),1],
[(x^4-7*x^2+4)/(2*x^2+1)^2/(3*x^4+5*x^2+2)^(5/2),x,12,-x*(53*x^2+49)/(2*x^2+1)/(3*x^4+5*x^2+2)^(3/2)+152*x/(2*x^2+1)/sqrt(3*x^4+5*x^2+2)-967/2*x*(3*x^2+2)/sqrt(3*x^4+5*x^2+2)+1/2*x*(2901*x^2+3533)/sqrt(3*x^4+5*x^2+2)+967*(x^2+1)*sqrt((3*x^2+2)/(x^2+1))*EllipticE(sin(arctan(x)),sqrt(-1/2))/sqrt(2)/sqrt(3*x^4+5*x^2+2)+3075*(x^2+1)*sqrt((3*x^2+2)/(x^2+1))*InverseJacobiAM(arctan(x),sqrt(-1/2))/sqrt(2)/sqrt(3*x^4+5*x^2+2)-1656*sqrt(3)*(x^2+1)*EllipticPi(sin(arctan(sqrt(3/2)*x)),-1/3,sqrt(1/3))/sqrt((x^2+1)/(3*x^2+2))/sqrt(3*x^4+5*x^2+2),1],
[(B*x^2+A)*(e*x^2+d)^(3/2)*sqrt(c*x^4+b*x^2+a),x,12,1/384*(8*A*c*e*(3*c^2*d^2-3*b^2*e^2+8*c*e*(a*e+b*d))-B*(9*c^3*d^3-15*b^3*e^3-3*c^2*d*e*(28*a*e+3*b*d)+b*c*e^2*(52*a*e+31*b*d)))*sqrt(e*x^2+d)*sqrt(c*x^4+b*x^2+a)/c^3/e^2/x+1/192*(8*A*c*e*(b*e+7*c*d)+B*(3*c^2*d^2-5*b^2*e^2+2*c*e*(6*a*e+5*b*d)))*x*sqrt(e*x^2+d)*sqrt(c*x^4+b*x^2+a)/c^2/e+1/48*(8*A*c*e+B*b*e+9*B*c*d)*x^3*sqrt(e*x^2+d)*sqrt(c*x^4+b*x^2+a)/c+1/8*B*e*x^5*sqrt(e*x^2+d)*sqrt(c*x^4+b*x^2+a)-1/384*sqrt(-4*a*c+b^2)*(8*A*c*e*(3*c^2*d^2-3*b^2*e^2+8*c*e*(a*e+b*d))-B*(9*c^3*d^3-15*b^3*e^3-3*c^2*d*e*(28*a*e+3*b*d)+b*c*e^2*(52*a*e+31*b*d)))*sqrt(-a*(c+a/x^4+b/x^2)/(-4*a*c+b^2))*x*sqrt(e*x^2+d)*EllipticE(sin(arcsin(sqrt(1+(b+2*a/x^2)/sqrt(-4*a*c+b^2))/sqrt(2))),sqrt(2*sqrt(-4*a*c+b^2)*d/(b*d+sqrt(-4*a*c+b^2)*d-2*a*e)))/sqrt(2)/c^3/e^2/sqrt(-a*(e+d/x^2)/((b+sqrt(-4*a*c+b^2))*d-2*a*e))/sqrt(c*x^4+b*x^2+a)-1/192*sqrt(-4*a*c+b^2)*(8*A*c*e*(31*c^2*d^2+3*b^2*e^2-2*c*e*(4*a*e+5*b*d))+B*(3*c^3*d^3-15*b^3*e^3+b*c*e^2*(52*a*e+41*b*d)-c^2*d*e*(108*a*e+29*b*d)))*sqrt(-a*(c+a/x^4+b/x^2)/(-4*a*c+b^2))*sqrt(-a*(e+d/x^2)/((b+sqrt(-4*a*c+b^2))*d-2*a*e))*x^3*InverseJacobiAM(arcsin(sqrt(1+(b+2*a/x^2)/sqrt(-4*a*c+b^2))/sqrt(2)),sqrt(2*sqrt(-4*a*c+b^2)*d/(b*d+sqrt(-4*a*c+b^2)*d-2*a*e)))/sqrt(2)/c^3/e/sqrt(e*x^2+d)/sqrt(c*x^4+b*x^2+a)-1/32*sqrt(-4*a*c+b^2)*(8*A*c*e*(c^3*d^3-b^3*e^3-3*c^2*d*e*(4*a*e+b*d)+b*c*e^2*(4*a*e+3*b*d))-B*(3*c^4*d^4-5*b^4*e^4-4*c^3*d^2*e*(-6*a*e+b*d)+12*b^2*c*e^3*(2*a*e+b*d)-2*c^2*e^2*(8*a^2*e^2+24*a*b*d*e+3*b^2*d^2)))*sqrt(-a*(c+a/x^4+b/x^2)/(-4*a*c+b^2))*sqrt(-a*(e+d/x^2)/((b+sqrt(-4*a*c+b^2))*d-2*a*e))*x^3*EllipticPi(sin(arcsin(sqrt(1+(b+2*a/x^2)/sqrt(-4*a*c+b^2))/sqrt(2))),2*sqrt(-4*a*c+b^2)/(b+sqrt(-4*a*c+b^2)),sqrt(2*sqrt(-4*a*c+b^2)*d/(b*d+sqrt(-4*a*c+b^2)*d-2*a*e)))/sqrt(2)/c^3/(b+sqrt(-4*a*c+b^2))/e^2/sqrt(e*x^2+d)/sqrt(c*x^4+b*x^2+a),1],
[(B*x^2+A)*sqrt(e*x^2+d)*sqrt(c*x^4+b*x^2+a),x,11,1/48*(6*A*c*e*(b*e+c*d)-B*(3*c^2*d^2+3*b^2*e^2-2*c*e*(4*a*e+b*d)))*sqrt(e*x^2+d)*sqrt(c*x^4+b*x^2+a)/c^2/e^2/x+1/24*(6*A*c*e+B*b*e+B*c*d)*x*sqrt(e*x^2+d)*sqrt(c*x^4+b*x^2+a)/c/e+1/6*B*x^3*sqrt(e*x^2+d)*sqrt(c*x^4+b*x^2+a)-1/48*sqrt(-4*a*c+b^2)*(6*A*c*e*(b*e+c*d)-B*(3*c^2*d^2+3*b^2*e^2-2*c*e*(4*a*e+b*d)))*sqrt(-a*(c+a/x^4+b/x^2)/(-4*a*c+b^2))*x*sqrt(e*x^2+d)*EllipticE(sin(arcsin(sqrt(1+(b+2*a/x^2)/sqrt(-4*a*c+b^2))/sqrt(2))),sqrt(2*sqrt(-4*a*c+b^2)*d/(b*d+sqrt(-4*a*c+b^2)*d-2*a*e)))/sqrt(2)/c^2/e^2/sqrt(-a*(e+d/x^2)/((b+sqrt(-4*a*c+b^2))*d-2*a*e))/sqrt(c*x^4+b*x^2+a)-1/24*sqrt(-4*a*c+b^2)*(6*A*c*e*(-b*e+5*c*d)+B*(c^2*d^2+3*b^2*e^2-4*c*e*(2*a*e+b*d)))*sqrt(-a*(c+a/x^4+b/x^2)/(-4*a*c+b^2))*sqrt(-a*(e+d/x^2)/((b+sqrt(-4*a*c+b^2))*d-2*a*e))*x^3*InverseJacobiAM(arcsin(sqrt(1+(b+2*a/x^2)/sqrt(-4*a*c+b^2))/sqrt(2)),sqrt(2*sqrt(-4*a*c+b^2)*d/(b*d+sqrt(-4*a*c+b^2)*d-2*a*e)))/sqrt(2)/c^2/e/sqrt(e*x^2+d)/sqrt(c*x^4+b*x^2+a)+1/4*sqrt(-4*a*c+b^2)*(B*(-b*e+c*d)*(4*a*c*e^2-b^2*e^2+c^2*d^2)-2*A*c*e*(c^2*d^2+b^2*e^2-2*c*e*(2*a*e+b*d)))*sqrt(-a*(c+a/x^4+b/x^2)/(-4*a*c+b^2))*sqrt(-a*(e+d/x^2)/((b+sqrt(-4*a*c+b^2))*d-2*a*e))*x^3*EllipticPi(sin(arcsin(sqrt(1+(b+2*a/x^2)/sqrt(-4*a*c+b^2))/sqrt(2))),2*sqrt(-4*a*c+b^2)/(b+sqrt(-4*a*c+b^2)),sqrt(2*sqrt(-4*a*c+b^2)*d/(b*d+sqrt(-4*a*c+b^2)*d-2*a*e)))/sqrt(2)/c^2/(b+sqrt(-4*a*c+b^2))/e^2/sqrt(e*x^2+d)/sqrt(c*x^4+b*x^2+a),1],
[(B*x^2+A)*sqrt(c*x^4+b*x^2+a)/sqrt(e*x^2+d),x,10,-1/8*(-4*A*c*e-B*b*e+3*B*c*d)*sqrt(e*x^2+d)*sqrt(c*x^4+b*x^2+a)/c/e^2/x+1/4*B*x*sqrt(e*x^2+d)*sqrt(c*x^4+b*x^2+a)/e+1/8*sqrt(-4*a*c+b^2)*(-4*A*c*e-B*b*e+3*B*c*d)*sqrt(-a*(c+a/x^4+b/x^2)/(-4*a*c+b^2))*x*sqrt(e*x^2+d)*EllipticE(sin(arcsin(sqrt(1+(b+2*a/x^2)/sqrt(-4*a*c+b^2))/sqrt(2))),sqrt(2*sqrt(-4*a*c+b^2)*d/(b*d+sqrt(-4*a*c+b^2)*d-2*a*e)))/sqrt(2)/c/e^2/sqrt(-a*(e+d/x^2)/((b+sqrt(-4*a*c+b^2))*d-2*a*e))/sqrt(c*x^4+b*x^2+a)-1/4*sqrt(-4*a*c+b^2)*(4*A*c*e-B*b*e+B*c*d)*sqrt(-a*(c+a/x^4+b/x^2)/(-4*a*c+b^2))*sqrt(-a*(e+d/x^2)/((b+sqrt(-4*a*c+b^2))*d-2*a*e))*x^3*InverseJacobiAM(arcsin(sqrt(1+(b+2*a/x^2)/sqrt(-4*a*c+b^2))/sqrt(2)),sqrt(2*sqrt(-4*a*c+b^2)*d/(b*d+sqrt(-4*a*c+b^2)*d-2*a*e)))/sqrt(2)/c/e/sqrt(e*x^2+d)/sqrt(c*x^4+b*x^2+a)-1/2*sqrt(-4*a*c+b^2)*(4*A*c*e*(-b*e+c*d)-B*(3*c^2*d^2-b^2*e^2-2*c*e*(-2*a*e+b*d)))*sqrt(-a*(c+a/x^4+b/x^2)/(-4*a*c+b^2))*sqrt(-a*(e+d/x^2)/((b+sqrt(-4*a*c+b^2))*d-2*a*e))*x^3*EllipticPi(sin(arcsin(sqrt(1+(b+2*a/x^2)/sqrt(-4*a*c+b^2))/sqrt(2))),2*sqrt(-4*a*c+b^2)/(b+sqrt(-4*a*c+b^2)),sqrt(2*sqrt(-4*a*c+b^2)*d/(b*d+sqrt(-4*a*c+b^2)*d-2*a*e)))/sqrt(2)/c/(b+sqrt(-4*a*c+b^2))/e^2/sqrt(e*x^2+d)/sqrt(c*x^4+b*x^2+a),1],
[(B*x^2+A)*sqrt(c*x^4+b*x^2+a)/(e*x^2+d)^(3/2),x,10,-(-A*e+B*d)*x*sqrt(c*x^4+b*x^2+a)/d/e/sqrt(e*x^2+d)+1/2*(-2*A*e+3*B*d)*sqrt(e*x^2+d)*sqrt(c*x^4+b*x^2+a)/d/e^2/x-1/2*sqrt(-4*a*c+b^2)*(-2*A*e+3*B*d)*sqrt(-a*(c+a/x^4+b/x^2)/(-4*a*c+b^2))*x*sqrt(e*x^2+d)*EllipticE(sin(arcsin(sqrt(1+(b+2*a/x^2)/sqrt(-4*a*c+b^2))/sqrt(2))),sqrt(2*sqrt(-4*a*c+b^2)*d/(b*d+sqrt(-4*a*c+b^2)*d-2*a*e)))/sqrt(2)/d/e^2/sqrt(-a*(e+d/x^2)/((b+sqrt(-4*a*c+b^2))*d-2*a*e))/sqrt(c*x^4+b*x^2+a)+sqrt(-4*a*c+b^2)*(-2*A*e+B*d)*sqrt(-a*(c+a/x^4+b/x^2)/(-4*a*c+b^2))*sqrt(-a*(e+d/x^2)/((b+sqrt(-4*a*c+b^2))*d-2*a*e))*x^3*InverseJacobiAM(arcsin(sqrt(1+(b+2*a/x^2)/sqrt(-4*a*c+b^2))/sqrt(2)),sqrt(2*sqrt(-4*a*c+b^2)*d/(b*d+sqrt(-4*a*c+b^2)*d-2*a*e)))/sqrt(2)/d/e/sqrt(e*x^2+d)/sqrt(c*x^4+b*x^2+a)-sqrt(2)*sqrt(-4*a*c+b^2)*(-2*A*c*e-B*b*e+3*B*c*d)*sqrt(-a*(c+a/x^4+b/x^2)/(-4*a*c+b^2))*sqrt(-a*(e+d/x^2)/((b+sqrt(-4*a*c+b^2))*d-2*a*e))*x^3*EllipticPi(sin(arcsin(sqrt(1+(b+2*a/x^2)/sqrt(-4*a*c+b^2))/sqrt(2))),2*sqrt(-4*a*c+b^2)/(b+sqrt(-4*a*c+b^2)),sqrt(2*sqrt(-4*a*c+b^2)*d/(b*d+sqrt(-4*a*c+b^2)*d-2*a*e)))/(b+sqrt(-4*a*c+b^2))/e^2/sqrt(e*x^2+d)/sqrt(c*x^4+b*x^2+a),1],
[(B*x^2+A)*sqrt(c*x^4+b*x^2+a)/(e*x^2+d)^(5/2),x,10,-1/3*(-A*e+B*d)*x*sqrt(c*x^4+b*x^2+a)/d/e/(e*x^2+d)^(3/2)+1/3*(A*e^2*(-2*a*e+b*d)-B*d*(3*c*d^2-e*(-a*e+2*b*d)))*sqrt(c*x^4+b*x^2+a)/d/e^2/(a*e^2-b*d*e+c*d^2)/x/sqrt(e*x^2+d)-1/3*sqrt(-4*a*c+b^2)*(A*e^2*(-2*a*e+b*d)-B*d*(3*c*d^2-e*(-a*e+2*b*d)))*sqrt(-a*(c+a/x^4+b/x^2)/(-4*a*c+b^2))*x*sqrt(e*x^2+d)*EllipticE(sin(arcsin(sqrt(1+(b+2*a/x^2)/sqrt(-4*a*c+b^2))/sqrt(2))),sqrt(2*sqrt(-4*a*c+b^2)*d/(b*d+sqrt(-4*a*c+b^2)*d-2*a*e)))/sqrt(2)/d^2/e^2/(a*e^2-b*d*e+c*d^2)/sqrt(-a*(e+d/x^2)/((b+sqrt(-4*a*c+b^2))*d-2*a*e))/sqrt(c*x^4+b*x^2+a)-1/3*sqrt(2)*sqrt(-4*a*c+b^2)*(2*A*e+B*d)*sqrt(-a*(c+a/x^4+b/x^2)/(-4*a*c+b^2))*sqrt(-a*(e+d/x^2)/((b+sqrt(-4*a*c+b^2))*d-2*a*e))*x^3*InverseJacobiAM(arcsin(sqrt(1+(b+2*a/x^2)/sqrt(-4*a*c+b^2))/sqrt(2)),sqrt(2*sqrt(-4*a*c+b^2)*d/(b*d+sqrt(-4*a*c+b^2)*d-2*a*e)))/d^2/e/sqrt(e*x^2+d)/sqrt(c*x^4+b*x^2+a)+2*sqrt(2)*B*c*sqrt(-4*a*c+b^2)*sqrt(-a*(c+a/x^4+b/x^2)/(-4*a*c+b^2))*sqrt(-a*(e+d/x^2)/((b+sqrt(-4*a*c+b^2))*d-2*a*e))*x^3*EllipticPi(sin(arcsin(sqrt(1+(b+2*a/x^2)/sqrt(-4*a*c+b^2))/sqrt(2))),2*sqrt(-4*a*c+b^2)/(b+sqrt(-4*a*c+b^2)),sqrt(2*sqrt(-4*a*c+b^2)*d/(b*d+sqrt(-4*a*c+b^2)*d-2*a*e)))/(b+sqrt(-4*a*c+b^2))/e^2/sqrt(e*x^2+d)/sqrt(c*x^4+b*x^2+a),1],
[(B*x^2+A)*sqrt(c*x^4+b*x^2+a)/(e*x^2+d)^(7/2),x,8,-1/5*(-A*e+B*d)*x*sqrt(c*x^4+b*x^2+a)/d/e/(e*x^2+d)^(5/2)+1/15*(A*e*(2*c*d^2-e*(-4*a*e+3*b*d))+B*d*(3*c*d^2-e*(-a*e+2*b*d)))*x*sqrt(c*x^4+b*x^2+a)/d^2/e/(a*e^2-b*d*e+c*d^2)/(e*x^2+d)^(3/2)-1/15*(b^2*d^2*(3*A*e+2*B*d)-b*d*(13*A*a*e^2+5*A*c*d^2+2*B*a*d*e)-2*a*(-4*A*a*e^3-8*A*c*d^2*e-B*a*d*e^2+3*B*c*d^3))*sqrt(c*x^4+b*x^2+a)/d^2/(a*e^2-b*d*e+c*d^2)^2/x/sqrt(e*x^2+d)+1/15*sqrt(-4*a*c+b^2)*(b^2*d^2*(3*A*e+2*B*d)-b*d*(13*A*a*e^2+5*A*c*d^2+2*B*a*d*e)-2*a*(-4*A*a*e^3-8*A*c*d^2*e-B*a*d*e^2+3*B*c*d^3))*sqrt(-a*(c+a/x^4+b/x^2)/(-4*a*c+b^2))*x*sqrt(e*x^2+d)*EllipticE(sin(arcsin(sqrt(1+(b+2*a/x^2)/sqrt(-4*a*c+b^2))/sqrt(2))),sqrt(2*sqrt(-4*a*c+b^2)*d/(b*d+sqrt(-4*a*c+b^2)*d-2*a*e)))/sqrt(2)/d^3/(a*e^2-b*d*e+c*d^2)^2/sqrt(-a*(e+d/x^2)/((b+sqrt(-4*a*c+b^2))*d-2*a*e))/sqrt(c*x^4+b*x^2+a)+1/15*sqrt(2)*sqrt(-4*a*c+b^2)*(-8*A*a*e^2+9*A*b*d*e-10*A*c*d^2-2*B*a*d*e+B*b*d^2)*sqrt(-a*(c+a/x^4+b/x^2)/(-4*a*c+b^2))*sqrt(-a*(e+d/x^2)/((b+sqrt(-4*a*c+b^2))*d-2*a*e))*x^3*InverseJacobiAM(arcsin(sqrt(1+(b+2*a/x^2)/sqrt(-4*a*c+b^2))/sqrt(2)),sqrt(2*sqrt(-4*a*c+b^2)*d/(b*d+sqrt(-4*a*c+b^2)*d-2*a*e)))/d^3/(a*e^2-b*d*e+c*d^2)/sqrt(e*x^2+d)/sqrt(c*x^4+b*x^2+a),1],
[(B*x^2+A)*sqrt(c*x^4+b*x^2+a)/(e*x^2+d)^(9/2),x,9,-1/7*(-A*e+B*d)*x*sqrt(c*x^4+b*x^2+a)/d/e/(e*x^2+d)^(7/2)+1/35*(A*e*(4*c*d^2-e*(-6*a*e+5*b*d))+B*d*(3*c*d^2-e*(-a*e+2*b*d)))*x*sqrt(c*x^4+b*x^2+a)/d^2/e/(a*e^2-b*d*e+c*d^2)/(e*x^2+d)^(5/2)+1/105*(2*B*d*(3*c^2*d^4-c*d^2*e*(3*a*e+4*b*d)+e^2*(2*a^2*e^2-3*a*b*d*e+3*b^2*d^2))+A*e*(8*c^2*d^4-3*c*d^2*e*(-16*a*e+9*b*d)+e^2*(24*a^2*e^2-43*a*b*d*e+15*b^2*d^2)))*x*sqrt(c*x^4+b*x^2+a)/d^3/e/(a*e^2-b*d*e+c*d^2)^2/(e*x^2+d)^(3/2)+1/105*(3*b^3*d^3*e*(5*A*e+2*B*d)-b^2*d^2*(103*A*a*e^3+42*A*c*d^2*e+9*B*a*d*e^2+14*B*c*d^3)+b*d*(a*B*d*e*(19*a*e^2+c*d^2)+A*(128*a^2*e^4+237*a*c*d^2*e^2+35*c^2*d^4))-2*a*(A*e*(24*a^2*e^4+69*a*c*d^2*e^2+77*c^2*d^4)-B*(-4*a^2*d*e^4-15*a*c*d^3*e^2+21*c^2*d^5)))*sqrt(c*x^4+b*x^2+a)/d^3/(a*e^2-b*d*e+c*d^2)^3/x/sqrt(e*x^2+d)-1/105*sqrt(-4*a*c+b^2)*(3*b^3*d^3*e*(5*A*e+2*B*d)-b^2*d^2*(103*A*a*e^3+42*A*c*d^2*e+9*B*a*d*e^2+14*B*c*d^3)+b*d*(a*B*d*e*(19*a*e^2+c*d^2)+A*(128*a^2*e^4+237*a*c*d^2*e^2+35*c^2*d^4))-2*a*(A*e*(24*a^2*e^4+69*a*c*d^2*e^2+77*c^2*d^4)-B*(-4*a^2*d*e^4-15*a*c*d^3*e^2+21*c^2*d^5)))*sqrt(-a*(c+a/x^4+b/x^2)/(-4*a*c+b^2))*x*sqrt(e*x^2+d)*EllipticE(sin(arcsin(sqrt(1+(b+2*a/x^2)/sqrt(-4*a*c+b^2))/sqrt(2))),sqrt(2*sqrt(-4*a*c+b^2)*d/(b*d+sqrt(-4*a*c+b^2)*d-2*a*e)))/sqrt(2)/d^4/(a*e^2-b*d*e+c*d^2)^3/sqrt(-a*(e+d/x^2)/((b+sqrt(-4*a*c+b^2))*d-2*a*e))/sqrt(c*x^4+b*x^2+a)-1/105*sqrt(2)*sqrt(-4*a*c+b^2)*(3*b^2*d^2*e*(20*A*e+B*d)+8*a*B*d*e*(a*e^2+3*c*d^2)-b*d*(104*A*a*e^3+126*A*c*d^2*e+15*B*a*d*e^2+7*B*c*d^3)+2*A*(24*a^2*e^4+51*a*c*d^2*e^2+35*c^2*d^4))*sqrt(-a*(c+a/x^4+b/x^2)/(-4*a*c+b^2))*sqrt(-a*(e+d/x^2)/((b+sqrt(-4*a*c+b^2))*d-2*a*e))*x^3*InverseJacobiAM(arcsin(sqrt(1+(b+2*a/x^2)/sqrt(-4*a*c+b^2))/sqrt(2)),sqrt(2*sqrt(-4*a*c+b^2)*d/(b*d+sqrt(-4*a*c+b^2)*d-2*a*e)))/d^4/(a*e^2-b*d*e+c*d^2)^2/sqrt(e*x^2+d)/sqrt(c*x^4+b*x^2+a),1],
[(B*x^2+A)*sqrt(e*x^2+d)*(c*x^4+b*x^2+a)^(3/2),x,13,1/3840*(10*A*c*e*(15*c^3*d^3-9*b^3*e^3-c^2*d*e*(-68*a*e+31*b*d)+3*b*c*e^2*(20*a*e+3*b*d))-B*(105*c^4*d^4-45*b^4*e^4-2*c^3*d^2*e*(-166*a*e+95*b*d)+30*b^2*c*e^3*(10*a*e+b*d)+12*c^2*e^2*(-32*a^2*e^2-18*a*b*d*e+3*b^2*d^2)))*sqrt(e*x^2+d)*sqrt(c*x^4+b*x^2+a)/c^3/e^4/x-1/1920*(10*A*c*e*(5*c^2*d^2-3*b^2*e^2-10*c*e*(6*a*e+b*d))-B*(35*c^3*d^3-15*b^3*e^3-c^2*d*e*(-108*a*e+61*b*d)+3*b*c*e^2*(28*a*e+3*b*d)))*x*sqrt(e*x^2+d)*sqrt(c*x^4+b*x^2+a)/c^2/e^3+1/480*(10*A*c*e*(9*b*e+c*d)-B*(7*c^2*d^2-3*b^2*e^2-12*c*e*(8*a*e+b*d)))*x^3*sqrt(e*x^2+d)*sqrt(c*x^4+b*x^2+a)/c/e^2+1/80*(10*A*c*e+11*B*b*e+B*c*d)*x^5*sqrt(e*x^2+d)*sqrt(c*x^4+b*x^2+a)/e+1/10*B*c*x^7*sqrt(e*x^2+d)*sqrt(c*x^4+b*x^2+a)-1/3840*sqrt(-4*a*c+b^2)*(10*A*c*e*(15*c^3*d^3-9*b^3*e^3-c^2*d*e*(-68*a*e+31*b*d)+3*b*c*e^2*(20*a*e+3*b*d))-B*(105*c^4*d^4-45*b^4*e^4-2*c^3*d^2*e*(-166*a*e+95*b*d)+30*b^2*c*e^3*(10*a*e+b*d)+12*c^2*e^2*(-32*a^2*e^2-18*a*b*d*e+3*b^2*d^2)))*sqrt(-a*(c+a/x^4+b/x^2)/(-4*a*c+b^2))*x*sqrt(e*x^2+d)*EllipticE(sin(arcsin(sqrt(1+(b+2*a/x^2)/sqrt(-4*a*c+b^2))/sqrt(2))),sqrt(2*sqrt(-4*a*c+b^2)*d/(b*d+sqrt(-4*a*c+b^2)*d-2*a*e)))/sqrt(2)/c^3/e^4/sqrt(-a*(e+d/x^2)/((b+sqrt(-4*a*c+b^2))*d-2*a*e))/sqrt(c*x^4+b*x^2+a)+1/1920*sqrt(-4*a*c+b^2)*(10*A*c*e*(5*c^3*d^3-9*b^3*e^3+15*b*c*e^2*(4*a*e+b*d)-c^2*d*e*(196*a*e+11*b*d))-B*(35*c^4*d^4-45*b^4*e^4-4*c^3*d^2*e*(-29*a*e+17*b*d)+60*b^2*c*e^3*(5*a*e+b*d)+6*c^2*e^2*(-64*a^2*e^2-64*a*b*d*e+3*b^2*d^2)))*sqrt(-a*(c+a/x^4+b/x^2)/(-4*a*c+b^2))*sqrt(-a*(e+d/x^2)/((b+sqrt(-4*a*c+b^2))*d-2*a*e))*x^3*InverseJacobiAM(arcsin(sqrt(1+(b+2*a/x^2)/sqrt(-4*a*c+b^2))/sqrt(2)),sqrt(2*sqrt(-4*a*c+b^2)*d/(b*d+sqrt(-4*a*c+b^2)*d-2*a*e)))/sqrt(2)/c^3/e^3/sqrt(e*x^2+d)/sqrt(c*x^4+b*x^2+a)-1/64*sqrt(-4*a*c+b^2)*(2*A*c*e*(5*c^4*d^4-3*b^4*e^4-12*c^3*d^2*e*(-2*a*e+b*d)+4*b^2*c*e^3*(6*a*e+b*d)+6*c^2*e^2*(-8*a^2*e^2-8*a*b*d*e+b^2*d^2))-B*(-b*e+c*d)*(7*c^4*d^4+3*b^4*e^4-24*a*b^2*c*e^4-8*c^3*d^2*e*(-3*a*e+b*d)-c^2*(-48*a^2*e^4+2*b^2*d^2*e^2)))*sqrt(-a*(c+a/x^4+b/x^2)/(-4*a*c+b^2))*sqrt(-a*(e+d/x^2)/((b+sqrt(-4*a*c+b^2))*d-2*a*e))*x^3*EllipticPi(sin(arcsin(sqrt(1+(b+2*a/x^2)/sqrt(-4*a*c+b^2))/sqrt(2))),2*sqrt(-4*a*c+b^2)/(b+sqrt(-4*a*c+b^2)),sqrt(2*sqrt(-4*a*c+b^2)*d/(b*d+sqrt(-4*a*c+b^2)*d-2*a*e)))/sqrt(2)/c^3/(b+sqrt(-4*a*c+b^2))/e^4/sqrt(e*x^2+d)/sqrt(c*x^4+b*x^2+a),1],
[(B*x^2+A)*(c*x^4+b*x^2+a)^(3/2)/sqrt(e*x^2+d),x,12,1/384*(8*A*c*e*(32*a*c*e^2+3*b^2*e^2-22*b*c*d*e+15*c^2*d^2)-B*(105*c^3*d^3+9*b^3*e^3-c^2*d*e*(-188*a*e+145*b*d)+15*b*c*e^2*(-4*a*e+b*d)))*sqrt(e*x^2+d)*sqrt(c*x^4+b*x^2+a)/c^2/e^4/x-1/192*(8*A*c*e*(-7*b*e+5*c*d)-B*(60*a*c*e^2+3*b^2*e^2-46*b*c*d*e+35*c^2*d^2))*x*sqrt(e*x^2+d)*sqrt(c*x^4+b*x^2+a)/c/e^3-1/48*(-8*A*c*e-9*B*b*e+7*B*c*d)*x^3*sqrt(e*x^2+d)*sqrt(c*x^4+b*x^2+a)/e^2+1/8*B*c*x^5*sqrt(e*x^2+d)*sqrt(c*x^4+b*x^2+a)/e-1/384*sqrt(-4*a*c+b^2)*(8*A*c*e*(32*a*c*e^2+3*b^2*e^2-22*b*c*d*e+15*c^2*d^2)-B*(105*c^3*d^3+9*b^3*e^3-c^2*d*e*(-188*a*e+145*b*d)+15*b*c*e^2*(-4*a*e+b*d)))*sqrt(-a*(c+a/x^4+b/x^2)/(-4*a*c+b^2))*x*sqrt(e*x^2+d)*EllipticE(sin(arcsin(sqrt(1+(b+2*a/x^2)/sqrt(-4*a*c+b^2))/sqrt(2))),sqrt(2*sqrt(-4*a*c+b^2)*d/(b*d+sqrt(-4*a*c+b^2)*d-2*a*e)))/sqrt(2)/c^2/e^4/sqrt(-a*(e+d/x^2)/((b+sqrt(-4*a*c+b^2))*d-2*a*e))/sqrt(c*x^4+b*x^2+a)-1/192*sqrt(-4*a*c+b^2)*(B*(35*c^3*d^3+9*b^3*e^3-c^2*d*e*(-68*a*e+53*b*d)+3*b*c*e^2*(-20*a*e+3*b*d))-8*A*c*e*(5*c^2*d^2+3*b^2*e^2-8*c*e*(2*a*e+b*d)))*sqrt(-a*(c+a/x^4+b/x^2)/(-4*a*c+b^2))*sqrt(-a*(e+d/x^2)/((b+sqrt(-4*a*c+b^2))*d-2*a*e))*x^3*InverseJacobiAM(arcsin(sqrt(1+(b+2*a/x^2)/sqrt(-4*a*c+b^2))/sqrt(2)),sqrt(2*sqrt(-4*a*c+b^2)*d/(b*d+sqrt(-4*a*c+b^2)*d-2*a*e)))/sqrt(2)/c^2/e^3/sqrt(e*x^2+d)/sqrt(c*x^4+b*x^2+a)-1/32*sqrt(-4*a*c+b^2)*(8*A*c*e*(-b*e+c*d)*(5*c^2*d^2-b^2*e^2-4*c*e*(-3*a*e+b*d))-B*(35*c^4*d^4+3*b^4*e^4+4*b^2*c*e^3*(-6*a*e+b*d)-12*c^3*d^2*e*(-6*a*e+5*b*d)+6*c^2*e^2*(8*a^2*e^2-8*a*b*d*e+3*b^2*d^2)))*sqrt(-a*(c+a/x^4+b/x^2)/(-4*a*c+b^2))*sqrt(-a*(e+d/x^2)/((b+sqrt(-4*a*c+b^2))*d-2*a*e))*x^3*EllipticPi(sin(arcsin(sqrt(1+(b+2*a/x^2)/sqrt(-4*a*c+b^2))/sqrt(2))),2*sqrt(-4*a*c+b^2)/(b+sqrt(-4*a*c+b^2)),sqrt(2*sqrt(-4*a*c+b^2)*d/(b*d+sqrt(-4*a*c+b^2)*d-2*a*e)))/sqrt(2)/c^2/(b+sqrt(-4*a*c+b^2))/e^4/sqrt(e*x^2+d)/sqrt(c*x^4+b*x^2+a),1],
[(B*x^2+A)*(c*x^4+b*x^2+a)^(3/2)/(e*x^2+d)^(3/2),x,12,-(-A*e+B*d)*(a*e^2-b*d*e+c*d^2)*x*sqrt(c*x^4+b*x^2+a)/d/e^3/sqrt(e*x^2+d)-1/48*(6*A*c*e*(15*c*d^2-e*(-8*a*e+13*b*d))-B*d*(105*c^2*d^2+3*b^2*e^2-20*c*e*(-4*a*e+5*b*d)))*sqrt(e*x^2+d)*sqrt(c*x^4+b*x^2+a)/c/d/e^4/x-1/24*(-6*A*c*e-7*B*b*e+11*B*c*d)*x*sqrt(e*x^2+d)*sqrt(c*x^4+b*x^2+a)/e^3+1/6*B*c*x^3*sqrt(e*x^2+d)*sqrt(c*x^4+b*x^2+a)/e^2+1/48*sqrt(-4*a*c+b^2)*(6*A*c*e*(15*c*d^2-e*(-8*a*e+13*b*d))-B*d*(105*c^2*d^2+3*b^2*e^2-20*c*e*(-4*a*e+5*b*d)))*sqrt(-a*(c+a/x^4+b/x^2)/(-4*a*c+b^2))*x*sqrt(e*x^2+d)*EllipticE(sin(arcsin(sqrt(1+(b+2*a/x^2)/sqrt(-4*a*c+b^2))/sqrt(2))),sqrt(2*sqrt(-4*a*c+b^2)*d/(b*d+sqrt(-4*a*c+b^2)*d-2*a*e)))/sqrt(2)/c/d/e^4/sqrt(-a*(e+d/x^2)/((b+sqrt(-4*a*c+b^2))*d-2*a*e))/sqrt(c*x^4+b*x^2+a)+1/24*sqrt(-4*a*c+b^2)*(B*d*(32*a*c*e^2+3*b^2*e^2-38*b*c*d*e+35*c^2*d^2)-6*A*c*e*(5*c*d^2-e*(-8*a*e+5*b*d)))*sqrt(-a*(c+a/x^4+b/x^2)/(-4*a*c+b^2))*sqrt(-a*(e+d/x^2)/((b+sqrt(-4*a*c+b^2))*d-2*a*e))*x^3*InverseJacobiAM(arcsin(sqrt(1+(b+2*a/x^2)/sqrt(-4*a*c+b^2))/sqrt(2)),sqrt(2*sqrt(-4*a*c+b^2)*d/(b*d+sqrt(-4*a*c+b^2)*d-2*a*e)))/sqrt(2)/c/d/e^3/sqrt(e*x^2+d)/sqrt(c*x^4+b*x^2+a)+1/4*sqrt(-4*a*c+b^2)*(6*A*c*e*(4*a*c*e^2+b^2*e^2-6*b*c*d*e+5*c^2*d^2)-B*(35*c^3*d^3+b^3*e^3+3*b*c*e^2*(-4*a*e+3*b*d)-9*c^2*d*e*(-4*a*e+5*b*d)))*sqrt(-a*(c+a/x^4+b/x^2)/(-4*a*c+b^2))*sqrt(-a*(e+d/x^2)/((b+sqrt(-4*a*c+b^2))*d-2*a*e))*x^3*EllipticPi(sin(arcsin(sqrt(1+(b+2*a/x^2)/sqrt(-4*a*c+b^2))/sqrt(2))),2*sqrt(-4*a*c+b^2)/(b+sqrt(-4*a*c+b^2)),sqrt(2*sqrt(-4*a*c+b^2)*d/(b*d+sqrt(-4*a*c+b^2)*d-2*a*e)))/sqrt(2)/c/(b+sqrt(-4*a*c+b^2))/e^4/sqrt(e*x^2+d)/sqrt(c*x^4+b*x^2+a),1],
[(B*x^2+A)*(c*x^4+b*x^2+a)^(3/2)/(e*x^2+d)^(5/2),x,12,-1/3*(-A*e+B*d)*(a*e^2-b*d*e+c*d^2)*x*sqrt(c*x^4+b*x^2+a)/d/e^3/(e*x^2+d)^(3/2)+1/3*(B*d*(9*c*d^2-e*(-a*e+5*b*d))-2*A*e*(3*c*d^2-e*(a*e+b*d)))*x*sqrt(c*x^4+b*x^2+a)/d^2/e^3/sqrt(e*x^2+d)-1/24*(B*d*(105*c*d^2-e*(-8*a*e+55*b*d))-4*A*e*(15*c*d^2-4*e*(a*e+b*d)))*sqrt(e*x^2+d)*sqrt(c*x^4+b*x^2+a)/d^2/e^4/x+1/4*B*c*x*sqrt(e*x^2+d)*sqrt(c*x^4+b*x^2+a)/e^3+1/24*sqrt(-4*a*c+b^2)*(B*d*(105*c*d^2-e*(-8*a*e+55*b*d))-4*A*e*(15*c*d^2-4*e*(a*e+b*d)))*sqrt(-a*(c+a/x^4+b/x^2)/(-4*a*c+b^2))*x*sqrt(e*x^2+d)*EllipticE(sin(arcsin(sqrt(1+(b+2*a/x^2)/sqrt(-4*a*c+b^2))/sqrt(2))),sqrt(2*sqrt(-4*a*c+b^2)*d/(b*d+sqrt(-4*a*c+b^2)*d-2*a*e)))/sqrt(2)/d^2/e^4/sqrt(-a*(e+d/x^2)/((b+sqrt(-4*a*c+b^2))*d-2*a*e))/sqrt(c*x^4+b*x^2+a)-1/12*sqrt(-4*a*c+b^2)*(B*d*(35*c*d^2-e*(-8*a*e+23*b*d))-4*A*e*(5*c*d^2-2*e*(2*a*e+b*d)))*sqrt(-a*(c+a/x^4+b/x^2)/(-4*a*c+b^2))*sqrt(-a*(e+d/x^2)/((b+sqrt(-4*a*c+b^2))*d-2*a*e))*x^3*InverseJacobiAM(arcsin(sqrt(1+(b+2*a/x^2)/sqrt(-4*a*c+b^2))/sqrt(2)),sqrt(2*sqrt(-4*a*c+b^2)*d/(b*d+sqrt(-4*a*c+b^2)*d-2*a*e)))/sqrt(2)/d^2/e^3/sqrt(e*x^2+d)/sqrt(c*x^4+b*x^2+a)-1/2*sqrt(-4*a*c+b^2)*(4*A*c*e*(-3*b*e+5*c*d)-B*(35*c^2*d^2+3*b^2*e^2-6*c*e*(-2*a*e+5*b*d)))*sqrt(-a*(c+a/x^4+b/x^2)/(-4*a*c+b^2))*sqrt(-a*(e+d/x^2)/((b+sqrt(-4*a*c+b^2))*d-2*a*e))*x^3*EllipticPi(sin(arcsin(sqrt(1+(b+2*a/x^2)/sqrt(-4*a*c+b^2))/sqrt(2))),2*sqrt(-4*a*c+b^2)/(b+sqrt(-4*a*c+b^2)),sqrt(2*sqrt(-4*a*c+b^2)*d/(b*d+sqrt(-4*a*c+b^2)*d-2*a*e)))/sqrt(2)/(b+sqrt(-4*a*c+b^2))/e^4/sqrt(e*x^2+d)/sqrt(c*x^4+b*x^2+a),1],
[(B*x^2+A)*(c*x^4+b*x^2+a)^(3/2)/(e*x^2+d)^(7/2),x,12,-1/5*(-A*e+B*d)*(a*e^2-b*d*e+c*d^2)*x*sqrt(c*x^4+b*x^2+a)/d/e^3/(e*x^2+d)^(5/2)+1/15*(B*d*(13*c*d^2-e*(-a*e+7*b*d))-2*A*e*(4*c*d^2-e*(2*a*e+b*d)))*x*sqrt(c*x^4+b*x^2+a)/d^2/e^3/(e*x^2+d)^(3/2)+1/15*(A*e*(15*c^2*d^4-c*d^2*e*(-11*a*e+10*b*d)-e^2*(-8*a^2*e^2+3*a*b*d*e+2*b^2*d^2))-B*d*(45*c^2*d^4-c*d^2*e*(-31*a*e+50*b*d)+e^2*(-2*a^2*e^2-3*a*b*d*e+8*b^2*d^2)))*x*sqrt(c*x^4+b*x^2+a)/d^3/e^3/(a*e^2-b*d*e+c*d^2)/sqrt(e*x^2+d)-1/30*(2*A*e*(15*c^2*d^4-c*d^2*e*(-11*a*e+10*b*d)-e^2*(-8*a^2*e^2+3*a*b*d*e+2*b^2*d^2))-B*d*(105*c^2*d^4-c*d^2*e*(-77*a*e+115*b*d)+2*e^2*(-2*a^2*e^2-3*a*b*d*e+8*b^2*d^2)))*sqrt(e*x^2+d)*sqrt(c*x^4+b*x^2+a)/d^3/e^4/(a*e^2-b*d*e+c*d^2)/x+1/30*sqrt(-4*a*c+b^2)*(2*A*e*(15*c^2*d^4-c*d^2*e*(-11*a*e+10*b*d)-e^2*(-8*a^2*e^2+3*a*b*d*e+2*b^2*d^2))-B*d*(105*c^2*d^4-c*d^2*e*(-77*a*e+115*b*d)+2*e^2*(-2*a^2*e^2-3*a*b*d*e+8*b^2*d^2)))*sqrt(-a*(c+a/x^4+b/x^2)/(-4*a*c+b^2))*x*sqrt(e*x^2+d)*EllipticE(sin(arcsin(sqrt(1+(b+2*a/x^2)/sqrt(-4*a*c+b^2))/sqrt(2))),sqrt(2*sqrt(-4*a*c+b^2)*d/(b*d+sqrt(-4*a*c+b^2)*d-2*a*e)))/sqrt(2)/d^3/e^4/(a*e^2-b*d*e+c*d^2)/sqrt(-a*(e+d/x^2)/((b+sqrt(-4*a*c+b^2))*d-2*a*e))/sqrt(c*x^4+b*x^2+a)+1/15*sqrt(-4*a*c+b^2)*(B*d*(35*c*d^2-4*e*(a*e+2*b*d))-2*A*e*(5*c*d^2+e*(8*a*e+b*d)))*sqrt(-a*(c+a/x^4+b/x^2)/(-4*a*c+b^2))*sqrt(-a*(e+d/x^2)/((b+sqrt(-4*a*c+b^2))*d-2*a*e))*x^3*InverseJacobiAM(arcsin(sqrt(1+(b+2*a/x^2)/sqrt(-4*a*c+b^2))/sqrt(2)),sqrt(2*sqrt(-4*a*c+b^2)*d/(b*d+sqrt(-4*a*c+b^2)*d-2*a*e)))/sqrt(2)/d^3/e^3/sqrt(e*x^2+d)/sqrt(c*x^4+b*x^2+a)-sqrt(2)*c*sqrt(-4*a*c+b^2)*(-2*A*c*e-3*B*b*e+7*B*c*d)*sqrt(-a*(c+a/x^4+b/x^2)/(-4*a*c+b^2))*sqrt(-a*(e+d/x^2)/((b+sqrt(-4*a*c+b^2))*d-2*a*e))*x^3*EllipticPi(sin(arcsin(sqrt(1+(b+2*a/x^2)/sqrt(-4*a*c+b^2))/sqrt(2))),2*sqrt(-4*a*c+b^2)/(b+sqrt(-4*a*c+b^2)),sqrt(2*sqrt(-4*a*c+b^2)*d/(b*d+sqrt(-4*a*c+b^2)*d-2*a*e)))/(b+sqrt(-4*a*c+b^2))/e^4/sqrt(e*x^2+d)/sqrt(c*x^4+b*x^2+a),1],
[(B*x^2+A)*(c*x^4+b*x^2+a)^(3/2)/(e*x^2+d)^(9/2),x,12,-1/7*(-A*e+B*d)*(a*e^2-b*d*e+c*d^2)*x*sqrt(c*x^4+b*x^2+a)/d/e^3/(e*x^2+d)^(7/2)+1/35*(B*d*(17*c*d^2-e*(-a*e+9*b*d))-2*A*e*(5*c*d^2-e*(3*a*e+b*d)))*x*sqrt(c*x^4+b*x^2+a)/d^2/e^3/(e*x^2+d)^(5/2)+1/105*(3*A*e*(5*c^2*d^4-c*d^2*e*(-9*a*e+2*b*d)-e^2*(-8*a^2*e^2+5*a*b*d*e+2*b^2*d^2))-B*d*(71*c^2*d^4-c*d^2*e*(-55*a*e+76*b*d)+e^2*(-4*a^2*e^2-a*b*d*e+8*b^2*d^2)))*x*sqrt(c*x^4+b*x^2+a)/d^3/e^3/(a*e^2-b*d*e+c*d^2)/(e*x^2+d)^(3/2)-1/105*(6*A*e^4*(-2*a*e+b*d)*(b^2*d^2+4*a*b*d*e-4*a*(a*e^2+2*c*d^2))+B*d*(105*c^3*d^6-7*c^2*d^4*e*(-26*a*e+25*b*d)+c*d^2*e^2*(37*a^2*e^2-120*a*b*d*e+56*b^2*d^2)+e^3*(8*a^3*e^3-5*a^2*b*d*e^2-5*a*b^2*d^2*e+8*b^3*d^3)))*sqrt(c*x^4+b*x^2+a)/d^3/e^4/(a*e^2-b*d*e+c*d^2)^2/x/sqrt(e*x^2+d)+1/105*sqrt(-4*a*c+b^2)*(6*A*e^4*(-2*a*e+b*d)*(b^2*d^2+4*a*b*d*e-4*a*(a*e^2+2*c*d^2))+B*d*(105*c^3*d^6-7*c^2*d^4*e*(-26*a*e+25*b*d)+c*d^2*e^2*(37*a^2*e^2-120*a*b*d*e+56*b^2*d^2)+e^3*(8*a^3*e^3-5*a^2*b*d*e^2-5*a*b^2*d^2*e+8*b^3*d^3)))*sqrt(-a*(c+a/x^4+b/x^2)/(-4*a*c+b^2))*x*sqrt(e*x^2+d)*EllipticE(sin(arcsin(sqrt(1+(b+2*a/x^2)/sqrt(-4*a*c+b^2))/sqrt(2))),sqrt(2*sqrt(-4*a*c+b^2)*d/(b*d+sqrt(-4*a*c+b^2)*d-2*a*e)))/sqrt(2)/d^4/e^4/(a*e^2-b*d*e+c*d^2)^2/sqrt(-a*(e+d/x^2)/((b+sqrt(-4*a*c+b^2))*d-2*a*e))/sqrt(c*x^4+b*x^2+a)+1/105*sqrt(2)*sqrt(-4*a*c+b^2)*(3*A*e^3*(b^2*d^2+16*a*b*d*e-4*a*(4*a*e^2+5*c*d^2))-B*d*(35*c^2*d^4-c*d^2*e*(-31*a*e+28*b*d)-e^2*(-8*a^2*e^2+a*b*d*e+4*b^2*d^2)))*sqrt(-a*(c+a/x^4+b/x^2)/(-4*a*c+b^2))*sqrt(-a*(e+d/x^2)/((b+sqrt(-4*a*c+b^2))*d-2*a*e))*x^3*InverseJacobiAM(arcsin(sqrt(1+(b+2*a/x^2)/sqrt(-4*a*c+b^2))/sqrt(2)),sqrt(2*sqrt(-4*a*c+b^2)*d/(b*d+sqrt(-4*a*c+b^2)*d-2*a*e)))/d^4/e^3/(a*e^2-b*d*e+c*d^2)/sqrt(e*x^2+d)/sqrt(c*x^4+b*x^2+a)+2*sqrt(2)*B*c^2*sqrt(-4*a*c+b^2)*sqrt(-a*(c+a/x^4+b/x^2)/(-4*a*c+b^2))*sqrt(-a*(e+d/x^2)/((b+sqrt(-4*a*c+b^2))*d-2*a*e))*x^3*EllipticPi(sin(arcsin(sqrt(1+(b+2*a/x^2)/sqrt(-4*a*c+b^2))/sqrt(2))),2*sqrt(-4*a*c+b^2)/(b+sqrt(-4*a*c+b^2)),sqrt(2*sqrt(-4*a*c+b^2)*d/(b*d+sqrt(-4*a*c+b^2)*d-2*a*e)))/(b+sqrt(-4*a*c+b^2))/e^4/sqrt(e*x^2+d)/sqrt(c*x^4+b*x^2+a),1],
[(B*x^2+A)*(c*x^4+b*x^2+a)^(3/2)/(e*x^2+d)^(11/2),x,10,-1/9*(-A*e+B*d)*(a*e^2-b*d*e+c*d^2)*x*sqrt(c*x^4+b*x^2+a)/d/e^3/(e*x^2+d)^(9/2)+1/63*(B*d*(21*c*d^2-e*(-a*e+11*b*d))-2*A*e*(6*c*d^2-e*(4*a*e+b*d)))*x*sqrt(c*x^4+b*x^2+a)/d^2/e^3/(e*x^2+d)^(7/2)+1/315*(A*e*(15*c^2*d^4-c*d^2*e*(-51*a*e+2*b*d)-e^2*(-48*a^2*e^2+35*a*b*d*e+10*b^2*d^2))-B*d*(105*c^2*d^4-c*d^2*e*(-87*a*e+110*b*d)+e^2*(-6*a^2*e^2+a*b*d*e+8*b^2*d^2)))*x*sqrt(c*x^4+b*x^2+a)/d^3/e^3/(a*e^2-b*d*e+c*d^2)/(e*x^2+d)^(5/2)+1/315*(B*d*(35*c^3*d^6-c^2*d^4*e*(-82*a*e+55*b*d)+c*d^2*e^2*(23*a^2*e^2-52*a*b*d*e+8*b^2*d^2)+e^3*(8*a^3*e^3-9*a^2*b*d*e^2-3*a*b^2*d^2*e+8*b^3*d^3))+2*A*e*(5*c^3*d^6-2*c^2*d^4*e*(-11*a*e+2*b*d)-c*d^2*e^2*(-65*a^2*e^2+46*a*b*d*e+4*b^2*d^2)+e^3*(32*a^3*e^3-54*a^2*b*d*e^2+15*a*b^2*d^2*e+5*b^3*d^3)))*x*sqrt(c*x^4+b*x^2+a)/d^4/e^3/(a*e^2-b*d*e+c*d^2)^2/(e*x^2+d)^(3/2)+1/315*(2*b^4*d^4*(5*A*e+4*B*d)-b^3*d^3*(-25*A*a*e^2+18*A*c*d^2+7*B*a*d*e)-3*a*b^2*d^2*(81*A*a*e^3+41*A*c*d^2*e+3*B*a*d*e^2+19*B*c*d^3)+4*a*b*d*(a*B*d*e*(8*a*e^2+15*c*d^2)+A*(82*a^2*e^4+147*a*c*d^2*e^2+36*c^2*d^4))-4*a^2*(A*e*(32*a^2*e^4+93*a*c*d^2*e^2+93*c^2*d^4)-B*(-4*a^2*d*e^4-15*a*c*d^3*e^2+21*c^2*d^5)))*sqrt(c*x^4+b*x^2+a)/d^4/(a*e^2-b*d*e+c*d^2)^3/x/sqrt(e*x^2+d)-1/315*sqrt(-4*a*c+b^2)*(2*b^4*d^4*(5*A*e+4*B*d)-b^3*d^3*(-25*A*a*e^2+18*A*c*d^2+7*B*a*d*e)-3*a*b^2*d^2*(81*A*a*e^3+41*A*c*d^2*e+3*B*a*d*e^2+19*B*c*d^3)+4*a*b*d*(a*B*d*e*(8*a*e^2+15*c*d^2)+A*(82*a^2*e^4+147*a*c*d^2*e^2+36*c^2*d^4))-4*a^2*(A*e*(32*a^2*e^4+93*a*c*d^2*e^2+93*c^2*d^4)-B*(-4*a^2*d*e^4-15*a*c*d^3*e^2+21*c^2*d^5)))*sqrt(-a*(c+a/x^4+b/x^2)/(-4*a*c+b^2))*x*sqrt(e*x^2+d)*EllipticE(sin(arcsin(sqrt(1+(b+2*a/x^2)/sqrt(-4*a*c+b^2))/sqrt(2))),sqrt(2*sqrt(-4*a*c+b^2)*d/(b*d+sqrt(-4*a*c+b^2)*d-2*a*e)))/sqrt(2)/d^5/(a*e^2-b*d*e+c*d^2)^3/sqrt(-a*(e+d/x^2)/((b+sqrt(-4*a*c+b^2))*d-2*a*e))/sqrt(c*x^4+b*x^2+a)-1/315*sqrt(2)*sqrt(-4*a*c+b^2)*(b^3*d^3*(5*A*e+4*B*d)-9*A*b^2*d^2*(-15*a*e^2+c*d^2)-12*a*b*d*(22*A*a*e^3+25*A*c*d^2*e+2*B*a*d*e^2+2*B*c*d^3)+4*a*(4*a*B*d*e*(a*e^2+3*c*d^2)+A*(32*a^2*e^4+69*a*c*d^2*e^2+45*c^2*d^4)))*sqrt(-a*(c+a/x^4+b/x^2)/(-4*a*c+b^2))*sqrt(-a*(e+d/x^2)/((b+sqrt(-4*a*c+b^2))*d-2*a*e))*x^3*InverseJacobiAM(arcsin(sqrt(1+(b+2*a/x^2)/sqrt(-4*a*c+b^2))/sqrt(2)),sqrt(2*sqrt(-4*a*c+b^2)*d/(b*d+sqrt(-4*a*c+b^2)*d-2*a*e)))/d^5/(a*e^2-b*d*e+c*d^2)^2/sqrt(e*x^2+d)/sqrt(c*x^4+b*x^2+a),1],
[(B*x^2+A)*(e*x^2+d)^(3/2)/sqrt(c*x^4+b*x^2+a),x,10,1/8*(4*A*c*e-3*B*b*e+5*B*c*d)*sqrt(e*x^2+d)*sqrt(c*x^4+b*x^2+a)/c^2/x+1/4*B*e*x*sqrt(e*x^2+d)*sqrt(c*x^4+b*x^2+a)/c-1/8*sqrt(-4*a*c+b^2)*(4*A*c*e-3*B*b*e+5*B*c*d)*sqrt(-a*(c+a/x^4+b/x^2)/(-4*a*c+b^2))*x*sqrt(e*x^2+d)*EllipticE(sin(arcsin(sqrt(1+(b+2*a/x^2)/sqrt(-4*a*c+b^2))/sqrt(2))),sqrt(2*sqrt(-4*a*c+b^2)*d/(b*d+sqrt(-4*a*c+b^2)*d-2*a*e)))/sqrt(2)/c^2/sqrt(-a*(e+d/x^2)/((b+sqrt(-4*a*c+b^2))*d-2*a*e))/sqrt(c*x^4+b*x^2+a)+1/4*sqrt(-4*a*c+b^2)*(a*B*e*(-3*b*e+7*c*d)-4*A*c*(-a*e^2+2*c*d^2))*sqrt(-a*(c+a/x^4+b/x^2)/(-4*a*c+b^2))*sqrt(-a*(e+d/x^2)/((b+sqrt(-4*a*c+b^2))*d-2*a*e))*x^3*InverseJacobiAM(arcsin(sqrt(1+(b+2*a/x^2)/sqrt(-4*a*c+b^2))/sqrt(2)),sqrt(2*sqrt(-4*a*c+b^2)*d/(b*d+sqrt(-4*a*c+b^2)*d-2*a*e)))/sqrt(2)/a/c^2/sqrt(e*x^2+d)/sqrt(c*x^4+b*x^2+a)+1/2*sqrt(-4*a*c+b^2)*(4*A*c*e*(-b*e+3*c*d)+B*(3*c^2*d^2+3*b^2*e^2-2*c*e*(2*a*e+3*b*d)))*sqrt(-a*(c+a/x^4+b/x^2)/(-4*a*c+b^2))*sqrt(-a*(e+d/x^2)/((b+sqrt(-4*a*c+b^2))*d-2*a*e))*x^3*EllipticPi(sin(arcsin(sqrt(1+(b+2*a/x^2)/sqrt(-4*a*c+b^2))/sqrt(2))),2*sqrt(-4*a*c+b^2)/(b+sqrt(-4*a*c+b^2)),sqrt(2*sqrt(-4*a*c+b^2)*d/(b*d+sqrt(-4*a*c+b^2)*d-2*a*e)))/sqrt(2)/c^2/(b+sqrt(-4*a*c+b^2))/sqrt(e*x^2+d)/sqrt(c*x^4+b*x^2+a),1],
[(B*x^2+A)*sqrt(e*x^2+d)/sqrt(c*x^4+b*x^2+a),x,9,1/2*B*sqrt(e*x^2+d)*sqrt(c*x^4+b*x^2+a)/c/x-1/2*B*sqrt(-4*a*c+b^2)*sqrt(-a*(c+a/x^4+b/x^2)/(-4*a*c+b^2))*x*sqrt(e*x^2+d)*EllipticE(sin(arcsin(sqrt(1+(b+2*a/x^2)/sqrt(-4*a*c+b^2))/sqrt(2))),sqrt(2*sqrt(-4*a*c+b^2)*d/(b*d+sqrt(-4*a*c+b^2)*d-2*a*e)))/sqrt(2)/c/sqrt(-a*(e+d/x^2)/((b+sqrt(-4*a*c+b^2))*d-2*a*e))/sqrt(c*x^4+b*x^2+a)-sqrt(-4*a*c+b^2)*(2*A*c*d-B*a*e)*sqrt(-a*(c+a/x^4+b/x^2)/(-4*a*c+b^2))*sqrt(-a*(e+d/x^2)/((b+sqrt(-4*a*c+b^2))*d-2*a*e))*x^3*InverseJacobiAM(arcsin(sqrt(1+(b+2*a/x^2)/sqrt(-4*a*c+b^2))/sqrt(2)),sqrt(2*sqrt(-4*a*c+b^2)*d/(b*d+sqrt(-4*a*c+b^2)*d-2*a*e)))/sqrt(2)/a/c/sqrt(e*x^2+d)/sqrt(c*x^4+b*x^2+a)+sqrt(2)*sqrt(-4*a*c+b^2)*(2*A*c*e-B*b*e+B*c*d)*sqrt(-a*(c+a/x^4+b/x^2)/(-4*a*c+b^2))*sqrt(-a*(e+d/x^2)/((b+sqrt(-4*a*c+b^2))*d-2*a*e))*x^3*EllipticPi(sin(arcsin(sqrt(1+(b+2*a/x^2)/sqrt(-4*a*c+b^2))/sqrt(2))),2*sqrt(-4*a*c+b^2)/(b+sqrt(-4*a*c+b^2)),sqrt(2*sqrt(-4*a*c+b^2)*d/(b*d+sqrt(-4*a*c+b^2)*d-2*a*e)))/c/(b+sqrt(-4*a*c+b^2))/sqrt(e*x^2+d)/sqrt(c*x^4+b*x^2+a),1],
[(B*x^2+A)/sqrt(e*x^2+d)/sqrt(c*x^4+b*x^2+a),x,5,-sqrt(2)*A*sqrt(-4*a*c+b^2)*sqrt(-a*(c+a/x^4+b/x^2)/(-4*a*c+b^2))*sqrt(-a*(e+d/x^2)/((b+sqrt(-4*a*c+b^2))*d-2*a*e))*x^3*InverseJacobiAM(arcsin(sqrt(1+(b+2*a/x^2)/sqrt(-4*a*c+b^2))/sqrt(2)),sqrt(2*sqrt(-4*a*c+b^2)*d/(b*d+sqrt(-4*a*c+b^2)*d-2*a*e)))/a/sqrt(e*x^2+d)/sqrt(c*x^4+b*x^2+a)+2*sqrt(2)*B*sqrt(-4*a*c+b^2)*sqrt(-a*(c+a/x^4+b/x^2)/(-4*a*c+b^2))*sqrt(-a*(e+d/x^2)/((b+sqrt(-4*a*c+b^2))*d-2*a*e))*x^3*EllipticPi(sin(arcsin(sqrt(1+(b+2*a/x^2)/sqrt(-4*a*c+b^2))/sqrt(2))),2*sqrt(-4*a*c+b^2)/(b+sqrt(-4*a*c+b^2)),sqrt(2*sqrt(-4*a*c+b^2)*d/(b*d+sqrt(-4*a*c+b^2)*d-2*a*e)))/(b+sqrt(-4*a*c+b^2))/sqrt(e*x^2+d)/sqrt(c*x^4+b*x^2+a),1],
[(B*x^2+A)/(e*x^2+d)^(3/2)/sqrt(c*x^4+b*x^2+a),x,6,(-A*e+B*d)*sqrt(c*x^4+b*x^2+a)/(a*e^2-b*d*e+c*d^2)/x/sqrt(e*x^2+d)-sqrt(-4*a*c+b^2)*(-A*e+B*d)*sqrt(-a*(c+a/x^4+b/x^2)/(-4*a*c+b^2))*x*sqrt(e*x^2+d)*EllipticE(sin(arcsin(sqrt(1+(b+2*a/x^2)/sqrt(-4*a*c+b^2))/sqrt(2))),sqrt(2*sqrt(-4*a*c+b^2)*d/(b*d+sqrt(-4*a*c+b^2)*d-2*a*e)))/sqrt(2)/d/(a*e^2-b*d*e+c*d^2)/sqrt(-a*(e+d/x^2)/((b+sqrt(-4*a*c+b^2))*d-2*a*e))/sqrt(c*x^4+b*x^2+a)-sqrt(2)*A*sqrt(-4*a*c+b^2)*sqrt(-a*(c+a/x^4+b/x^2)/(-4*a*c+b^2))*sqrt(-a*(e+d/x^2)/((b+sqrt(-4*a*c+b^2))*d-2*a*e))*x^3*InverseJacobiAM(arcsin(sqrt(1+(b+2*a/x^2)/sqrt(-4*a*c+b^2))/sqrt(2)),sqrt(2*sqrt(-4*a*c+b^2)*d/(b*d+sqrt(-4*a*c+b^2)*d-2*a*e)))/a/d/sqrt(e*x^2+d)/sqrt(c*x^4+b*x^2+a),1],
[(B*x^2+A)/(e*x^2+d)^(5/2)/sqrt(c*x^4+b*x^2+a),x,7,-1/3*e*(-A*e+B*d)*x*sqrt(c*x^4+b*x^2+a)/d/(a*e^2-b*d*e+c*d^2)/(e*x^2+d)^(3/2)-1/3*(2*A*e*(3*c*d^2-e*(-a*e+2*b*d))-B*d*(3*c*d^2-e*(a*e+b*d)))*sqrt(c*x^4+b*x^2+a)/d/(a*e^2-b*d*e+c*d^2)^2/x/sqrt(e*x^2+d)+1/3*sqrt(-4*a*c+b^2)*(2*A*e*(3*c*d^2-e*(-a*e+2*b*d))-B*d*(3*c*d^2-e*(a*e+b*d)))*sqrt(-a*(c+a/x^4+b/x^2)/(-4*a*c+b^2))*x*sqrt(e*x^2+d)*EllipticE(sin(arcsin(sqrt(1+(b+2*a/x^2)/sqrt(-4*a*c+b^2))/sqrt(2))),sqrt(2*sqrt(-4*a*c+b^2)*d/(b*d+sqrt(-4*a*c+b^2)*d-2*a*e)))/sqrt(2)/d^2/(a*e^2-b*d*e+c*d^2)^2/sqrt(-a*(e+d/x^2)/((b+sqrt(-4*a*c+b^2))*d-2*a*e))/sqrt(c*x^4+b*x^2+a)-1/3*sqrt(2)*sqrt(-4*a*c+b^2)*(a*B*d*e+A*(3*c*d^2-e*(-2*a*e+3*b*d)))*sqrt(-a*(c+a/x^4+b/x^2)/(-4*a*c+b^2))*sqrt(-a*(e+d/x^2)/((b+sqrt(-4*a*c+b^2))*d-2*a*e))*x^3*InverseJacobiAM(arcsin(sqrt(1+(b+2*a/x^2)/sqrt(-4*a*c+b^2))/sqrt(2)),sqrt(2*sqrt(-4*a*c+b^2)*d/(b*d+sqrt(-4*a*c+b^2)*d-2*a*e)))/a/d^2/(a*e^2-b*d*e+c*d^2)/sqrt(e*x^2+d)/sqrt(c*x^4+b*x^2+a),1],
[(B*x^2+A)*(e*x^2+d)^(5/2)/(c*x^4+b*x^2+a)^(3/2),x,12,x*(A*b^2-a*b*B-2*a*A*c+(A*b-2*B*a)*c*x^2)*(e*x^2+d)^(5/2)/a/(-4*a*c+b^2)/sqrt(c*x^4+b*x^2+a)-1/2*(2*A*c*(a*b*e^2-4*a*c*d*e+b*c*d^2)-a*B*(4*c^2*d^2+3*b^2*e^2-4*c*e*(2*a*e+b*d)))*sqrt(e*x^2+d)*sqrt(c*x^4+b*x^2+a)/a/c^2/(-4*a*c+b^2)/x-e*(2*A*c*(-a*e+b*d)-a*B*(-b*e+4*c*d))*x*sqrt(e*x^2+d)*sqrt(c*x^4+b*x^2+a)/a/c/(-4*a*c+b^2)-(A*b-2*B*a)*e^2*x^3*sqrt(e*x^2+d)*sqrt(c*x^4+b*x^2+a)/a/(-4*a*c+b^2)+1/2*(2*A*c*(a*b*e^2-4*a*c*d*e+b*c*d^2)-a*B*(4*c^2*d^2+3*b^2*e^2-4*c*e*(2*a*e+b*d)))*sqrt(-a*(c+a/x^4+b/x^2)/(-4*a*c+b^2))*x*sqrt(e*x^2+d)*EllipticE(sin(arcsin(sqrt(1+(b+2*a/x^2)/sqrt(-4*a*c+b^2))/sqrt(2))),sqrt(2*sqrt(-4*a*c+b^2)*d/(b*d+sqrt(-4*a*c+b^2)*d-2*a*e)))/sqrt(2)/a/c^2/sqrt(-4*a*c+b^2)/sqrt(-a*(e+d/x^2)/((b+sqrt(-4*a*c+b^2))*d-2*a*e))/sqrt(c*x^4+b*x^2+a)+(3*a*b^2*B*e^3-2*b*c*(A*a*e^3+3*A*c*d^2*e+3*B*a*d*e^2+B*c*d^3)+4*c*(a*B*e*(-2*a*e^2+3*c*d^2)+A*c*d*(3*a*e^2+c*d^2)))*sqrt(-a*(c+a/x^4+b/x^2)/(-4*a*c+b^2))*sqrt(-a*(e+d/x^2)/((b+sqrt(-4*a*c+b^2))*d-2*a*e))*x^3*InverseJacobiAM(arcsin(sqrt(1+(b+2*a/x^2)/sqrt(-4*a*c+b^2))/sqrt(2)),sqrt(2*sqrt(-4*a*c+b^2)*d/(b*d+sqrt(-4*a*c+b^2)*d-2*a*e)))/sqrt(2)/a/c^2/sqrt(-4*a*c+b^2)/sqrt(e*x^2+d)/sqrt(c*x^4+b*x^2+a)+sqrt(2)*sqrt(-4*a*c+b^2)*e^2*(2*A*c*e-3*B*b*e+5*B*c*d)*sqrt(-a*(c+a/x^4+b/x^2)/(-4*a*c+b^2))*sqrt(-a*(e+d/x^2)/((b+sqrt(-4*a*c+b^2))*d-2*a*e))*x^3*EllipticPi(sin(arcsin(sqrt(1+(b+2*a/x^2)/sqrt(-4*a*c+b^2))/sqrt(2))),2*sqrt(-4*a*c+b^2)/(b+sqrt(-4*a*c+b^2)),sqrt(2*sqrt(-4*a*c+b^2)*d/(b*d+sqrt(-4*a*c+b^2)*d-2*a*e)))/c^2/(b+sqrt(-4*a*c+b^2))/sqrt(e*x^2+d)/sqrt(c*x^4+b*x^2+a),1],
[(B*x^2+A)*(e*x^2+d)^(3/2)/(c*x^4+b*x^2+a)^(3/2),x,11,x*(A*b^2-a*b*B-2*a*A*c+(A*b-2*B*a)*c*x^2)*(e*x^2+d)^(3/2)/a/(-4*a*c+b^2)/sqrt(c*x^4+b*x^2+a)-(A*c*(-2*a*e+b*d)-a*B*(-b*e+2*c*d))*sqrt(e*x^2+d)*sqrt(c*x^4+b*x^2+a)/a/c/(-4*a*c+b^2)/x-(A*b-2*B*a)*e*x*sqrt(e*x^2+d)*sqrt(c*x^4+b*x^2+a)/a/(-4*a*c+b^2)+(A*c*(-2*a*e+b*d)-a*B*(-b*e+2*c*d))*sqrt(-a*(c+a/x^4+b/x^2)/(-4*a*c+b^2))*x*sqrt(e*x^2+d)*EllipticE(sin(arcsin(sqrt(1+(b+2*a/x^2)/sqrt(-4*a*c+b^2))/sqrt(2))),sqrt(2*sqrt(-4*a*c+b^2)*d/(b*d+sqrt(-4*a*c+b^2)*d-2*a*e)))/sqrt(2)/a/c/sqrt(-4*a*c+b^2)/sqrt(-a*(e+d/x^2)/((b+sqrt(-4*a*c+b^2))*d-2*a*e))/sqrt(c*x^4+b*x^2+a)+sqrt(2)*(2*c*(A*a*e^2+A*c*d^2+2*B*a*d*e)-b*(2*A*c*d*e+B*a*e^2+B*c*d^2))*sqrt(-a*(c+a/x^4+b/x^2)/(-4*a*c+b^2))*sqrt(-a*(e+d/x^2)/((b+sqrt(-4*a*c+b^2))*d-2*a*e))*x^3*InverseJacobiAM(arcsin(sqrt(1+(b+2*a/x^2)/sqrt(-4*a*c+b^2))/sqrt(2)),sqrt(2*sqrt(-4*a*c+b^2)*d/(b*d+sqrt(-4*a*c+b^2)*d-2*a*e)))/a/c/sqrt(-4*a*c+b^2)/sqrt(e*x^2+d)/sqrt(c*x^4+b*x^2+a)+2*sqrt(2)*B*sqrt(-4*a*c+b^2)*e^2*sqrt(-a*(c+a/x^4+b/x^2)/(-4*a*c+b^2))*sqrt(-a*(e+d/x^2)/((b+sqrt(-4*a*c+b^2))*d-2*a*e))*x^3*EllipticPi(sin(arcsin(sqrt(1+(b+2*a/x^2)/sqrt(-4*a*c+b^2))/sqrt(2))),2*sqrt(-4*a*c+b^2)/(b+sqrt(-4*a*c+b^2)),sqrt(2*sqrt(-4*a*c+b^2)*d/(b*d+sqrt(-4*a*c+b^2)*d-2*a*e)))/c/(b+sqrt(-4*a*c+b^2))/sqrt(e*x^2+d)/sqrt(c*x^4+b*x^2+a),1],
[(B*x^2+A)*sqrt(e*x^2+d)/(c*x^4+b*x^2+a)^(3/2),x,7,x*(A*b^2-a*b*B-2*a*A*c+(A*b-2*B*a)*c*x^2)*sqrt(e*x^2+d)/a/(-4*a*c+b^2)/sqrt(c*x^4+b*x^2+a)-(A*b-2*B*a)*sqrt(e*x^2+d)*sqrt(c*x^4+b*x^2+a)/a/(-4*a*c+b^2)/x+(A*b-2*B*a)*sqrt(-a*(c+a/x^4+b/x^2)/(-4*a*c+b^2))*x*sqrt(e*x^2+d)*EllipticE(sin(arcsin(sqrt(1+(b+2*a/x^2)/sqrt(-4*a*c+b^2))/sqrt(2))),sqrt(2*sqrt(-4*a*c+b^2)*d/(b*d+sqrt(-4*a*c+b^2)*d-2*a*e)))/sqrt(2)/a/sqrt(-4*a*c+b^2)/sqrt(-a*(e+d/x^2)/((b+sqrt(-4*a*c+b^2))*d-2*a*e))/sqrt(c*x^4+b*x^2+a)-sqrt(2)*(A*b*e-2*A*c*d-2*B*a*e+B*b*d)*sqrt(-a*(c+a/x^4+b/x^2)/(-4*a*c+b^2))*sqrt(-a*(e+d/x^2)/((b+sqrt(-4*a*c+b^2))*d-2*a*e))*x^3*InverseJacobiAM(arcsin(sqrt(1+(b+2*a/x^2)/sqrt(-4*a*c+b^2))/sqrt(2)),sqrt(2*sqrt(-4*a*c+b^2)*d/(b*d+sqrt(-4*a*c+b^2)*d-2*a*e)))/a/sqrt(-4*a*c+b^2)/sqrt(e*x^2+d)/sqrt(c*x^4+b*x^2+a),1],
[(B*x^2+A)/sqrt(e*x^2+d)/(c*x^4+b*x^2+a)^(3/2),x,7,(a*B*(-b*e+2*c*d)-A*(2*a*c*e-b^2*e+b*c*d))*sqrt(e*x^2+d)/(-4*a*c+b^2)/(a*e^2-b*d*e+c*d^2)/x/sqrt(c*x^4+b*x^2+a)+c*(b*(A*e+B*d)-2*A*c*d-2*a*B*e)*x*sqrt(e*x^2+d)/(-4*a*c+b^2)/(a*e^2-b*d*e+c*d^2)/sqrt(c*x^4+b*x^2+a)-(a*B*(-b*e+2*c*d)-A*(2*a*c*e-b^2*e+b*c*d))*sqrt(-a*(c+a/x^4+b/x^2)/(-4*a*c+b^2))*x*sqrt(e*x^2+d)*EllipticE(sin(arcsin(sqrt(1+(b+2*a/x^2)/sqrt(-4*a*c+b^2))/sqrt(2))),sqrt(2*sqrt(-4*a*c+b^2)*d/(b*d+sqrt(-4*a*c+b^2)*d-2*a*e)))/sqrt(2)/a/sqrt(-4*a*c+b^2)/(a*e^2-b*d*e+c*d^2)/sqrt(-a*(e+d/x^2)/((b+sqrt(-4*a*c+b^2))*d-2*a*e))/sqrt(c*x^4+b*x^2+a)-sqrt(2)*(-2*A*c+B*b)*sqrt(-a*(c+a/x^4+b/x^2)/(-4*a*c+b^2))*sqrt(-a*(e+d/x^2)/((b+sqrt(-4*a*c+b^2))*d-2*a*e))*x^3*InverseJacobiAM(arcsin(sqrt(1+(b+2*a/x^2)/sqrt(-4*a*c+b^2))/sqrt(2)),sqrt(2*sqrt(-4*a*c+b^2)*d/(b*d+sqrt(-4*a*c+b^2)*d-2*a*e)))/a/sqrt(-4*a*c+b^2)/sqrt(e*x^2+d)/sqrt(c*x^4+b*x^2+a),1],
[(B*x^2+A)/(e*x^2+d)^(3/2)/(c*x^4+b*x^2+a)^(3/2),x,8,-e*(-A*e+B*d)*x/d/(a*e^2-b*d*e+c*d^2)/sqrt(e*x^2+d)/sqrt(c*x^4+b*x^2+a)+(2*a*B*d*(c^2*d^2+b^2*e^2-c*e*(3*a*e+b*d))-A*(b^3*d*e^2+b*c*d*(-3*a*e^2+c*d^2)+4*a*c*e*(-a*e^2+c*d^2)-b^2*(-a*e^3+2*c*d^2*e)))*sqrt(e*x^2+d)/(-4*a*c+b^2)/d/(a*e^2-b*d*e+c*d^2)^2/x/sqrt(c*x^4+b*x^2+a)+c*(b^2*e*(-2*A*e+B*d)-2*c*(-3*A*a*e^2+A*c*d^2+4*B*a*d*e)+b*(2*A*c*d*e+B*a*e^2+B*c*d^2))*x*sqrt(e*x^2+d)/(-4*a*c+b^2)/(a*e^2-b*d*e+c*d^2)^2/sqrt(c*x^4+b*x^2+a)-(2*a*B*d*(c^2*d^2+b^2*e^2-c*e*(3*a*e+b*d))-A*(b^3*d*e^2+b*c*d*(-3*a*e^2+c*d^2)+4*a*c*e*(-a*e^2+c*d^2)-b^2*(-a*e^3+2*c*d^2*e)))*sqrt(-a*(c+a/x^4+b/x^2)/(-4*a*c+b^2))*x*sqrt(e*x^2+d)*EllipticE(sin(arcsin(sqrt(1+(b+2*a/x^2)/sqrt(-4*a*c+b^2))/sqrt(2))),sqrt(2*sqrt(-4*a*c+b^2)*d/(b*d+sqrt(-4*a*c+b^2)*d-2*a*e)))/sqrt(2)/a/sqrt(-4*a*c+b^2)/d/(a*e^2-b*d*e+c*d^2)^2/sqrt(-a*(e+d/x^2)/((b+sqrt(-4*a*c+b^2))*d-2*a*e))/sqrt(c*x^4+b*x^2+a)+sqrt(2)*(b^2*e*(-A*e+B*d)-b*c*d*(A*e+B*d)+2*c*(2*A*a*e^2+A*c*d^2-B*a*d*e))*sqrt(-a*(c+a/x^4+b/x^2)/(-4*a*c+b^2))*sqrt(-a*(e+d/x^2)/((b+sqrt(-4*a*c+b^2))*d-2*a*e))*x^3*InverseJacobiAM(arcsin(sqrt(1+(b+2*a/x^2)/sqrt(-4*a*c+b^2))/sqrt(2)),sqrt(2*sqrt(-4*a*c+b^2)*d/(b*d+sqrt(-4*a*c+b^2)*d-2*a*e)))/a/sqrt(-4*a*c+b^2)/d/(a*e^2-b*d*e+c*d^2)/sqrt(e*x^2+d)/sqrt(c*x^4+b*x^2+a),1],
[(B*x^2+A)*(e*x^2+d)^(7/2)/(c*x^4+b*x^2+a)^(5/2),x,13,1/3*x*(A*b^2-a*b*B-2*a*A*c+(A*b-2*B*a)*c*x^2)*(e*x^2+d)^(7/2)/a/(-4*a*c+b^2)/(c*x^4+b*x^2+a)^(3/2)+1/3*x*(e*x^2+d)^(5/2)*(a*B*(16*a^2*c*e-8*a*b^2*e+4*a*b*c*d+b^3*d)+A*(-12*a^2*b*c*e+20*a^2*c^2*d+5*a*b^3*e-17*a*b^2*c*d+2*b^4*d)+c*(a*B*(-8*a*b*e+12*a*c*d+b^2*d)+2*A*(-4*a^2*c*e+3*a*b^2*e-8*a*b*c*d+b^3*d))*x^2)/a^2/(-4*a*c+b^2)^2/sqrt(c*x^4+b*x^2+a)-1/3*(2*A*c^2*(-2*a*e+b*d)*(b^2*d^2+4*a*b*d*e-4*a*(a*e^2+2*c*d^2))+a*B*(3*a*b^3*e^3+b^2*c*d*(a*e^2+c*d^2)-4*a*b*c*e*(5*a*e^2+6*c*d^2)+4*a*c^2*d*(11*a*e^2+3*c*d^2)))*sqrt(e*x^2+d)*sqrt(c*x^4+b*x^2+a)/a^2/c^2/(-4*a*c+b^2)^2/x+1/3*e*(2*a*B*(12*a*b*c*d*e-b^2*(-a*e^2+c*d^2)-12*a*c*(a*e^2+c*d^2))-A*c*(4*b^3*d^2+11*a*b^2*d*e+4*a^2*c*d*e-8*a*b*(a*e^2+4*c*d^2)))*x*sqrt(e*x^2+d)*sqrt(c*x^4+b*x^2+a)/a^2/c/(-4*a*c+b^2)^2-1/3*e^2*(a*B*(-8*a*b*e+12*a*c*d+b^2*d)+2*A*(-4*a^2*c*e+3*a*b^2*e-8*a*b*c*d+b^3*d))*x^3*sqrt(e*x^2+d)*sqrt(c*x^4+b*x^2+a)/a^2/(-4*a*c+b^2)^2+1/3*(2*A*c^2*(-2*a*e+b*d)*(b^2*d^2+4*a*b*d*e-4*a*(a*e^2+2*c*d^2))+a*B*(3*a*b^3*e^3+b^2*c*d*(a*e^2+c*d^2)-4*a*b*c*e*(5*a*e^2+6*c*d^2)+4*a*c^2*d*(11*a*e^2+3*c*d^2)))*sqrt(-a*(c+a/x^4+b/x^2)/(-4*a*c+b^2))*x*sqrt(e*x^2+d)*EllipticE(sin(arcsin(sqrt(1+(b+2*a/x^2)/sqrt(-4*a*c+b^2))/sqrt(2))),sqrt(2*sqrt(-4*a*c+b^2)*d/(b*d+sqrt(-4*a*c+b^2)*d-2*a*e)))/sqrt(2)/a^2/c^2/(-4*a*c+b^2)^(3/2)/sqrt(-a*(e+d/x^2)/((b+sqrt(-4*a*c+b^2))*d-2*a*e))/sqrt(c*x^4+b*x^2+a)-1/3*sqrt(2)*(A*c^2*(b^3*d^3*e-4*a*b*d*e*(8*a*e^2+9*c*d^2)-b^2*(-15*a*d^2*e^2+c*d^4)+4*a*(4*a^2*e^4+9*a*c*d^2*e^2+5*c^2*d^4))+a*B*(3*a*b^3*e^4+b^2*c*d*e*(-a*e^2+11*c*d^2)+4*a*c^2*d*e*(17*a*e^2+5*c*d^2)-4*b*c*(5*a^2*e^4+12*a*c*d^2*e^2+2*c^2*d^4)))*sqrt(-a*(c+a/x^4+b/x^2)/(-4*a*c+b^2))*sqrt(-a*(e+d/x^2)/((b+sqrt(-4*a*c+b^2))*d-2*a*e))*x^3*InverseJacobiAM(arcsin(sqrt(1+(b+2*a/x^2)/sqrt(-4*a*c+b^2))/sqrt(2)),sqrt(2*sqrt(-4*a*c+b^2)*d/(b*d+sqrt(-4*a*c+b^2)*d-2*a*e)))/a^2/c^2/(-4*a*c+b^2)^(3/2)/sqrt(e*x^2+d)/sqrt(c*x^4+b*x^2+a)+2*sqrt(2)*B*sqrt(-4*a*c+b^2)*e^4*sqrt(-a*(c+a/x^4+b/x^2)/(-4*a*c+b^2))*sqrt(-a*(e+d/x^2)/((b+sqrt(-4*a*c+b^2))*d-2*a*e))*x^3*EllipticPi(sin(arcsin(sqrt(1+(b+2*a/x^2)/sqrt(-4*a*c+b^2))/sqrt(2))),2*sqrt(-4*a*c+b^2)/(b+sqrt(-4*a*c+b^2)),sqrt(2*sqrt(-4*a*c+b^2)*d/(b*d+sqrt(-4*a*c+b^2)*d-2*a*e)))/c^2/(b+sqrt(-4*a*c+b^2))/sqrt(e*x^2+d)/sqrt(c*x^4+b*x^2+a),1],
[(B*x^2+A)*(e*x^2+d)^(5/2)/(c*x^4+b*x^2+a)^(5/2),x,9,1/3*x*(A*b^2-a*b*B-2*a*A*c+(A*b-2*B*a)*c*x^2)*(e*x^2+d)^(5/2)/a/(-4*a*c+b^2)/(c*x^4+b*x^2+a)^(3/2)+1/3*x*(e*x^2+d)^(3/2)*(a*B*(8*a^2*c*e-6*a*b^2*e+4*a*b*c*d+b^3*d)+A*(-4*a^2*b*c*e+20*a^2*c^2*d+3*a*b^3*e-17*a*b^2*c*d+2*b^4*d)+c*(a*B*(-8*a*b*e+12*a*c*d+b^2*d)+2*A*b*(2*a*b*e-8*a*c*d+b^2*d))*x^2)/a^2/(-4*a*c+b^2)^2/sqrt(c*x^4+b*x^2+a)-1/3*(A*(2*b^3*d^2+3*a*b^2*d*e+20*a^2*c*d*e-8*a*b*(a*e^2+2*c*d^2))+a*B*(b^2*d^2-16*a*b*d*e+4*a*(4*a*e^2+3*c*d^2)))*sqrt(e*x^2+d)*sqrt(c*x^4+b*x^2+a)/a^2/(-4*a*c+b^2)^2/x-1/3*e*(a*B*(-8*a*b*e+12*a*c*d+b^2*d)+2*A*b*(2*a*b*e-8*a*c*d+b^2*d))*x*sqrt(e*x^2+d)*sqrt(c*x^4+b*x^2+a)/a^2/(-4*a*c+b^2)^2+1/3*(A*(2*b^3*d^2+3*a*b^2*d*e+20*a^2*c*d*e-8*a*b*(a*e^2+2*c*d^2))+a*B*(b^2*d^2-16*a*b*d*e+4*a*(4*a*e^2+3*c*d^2)))*sqrt(-a*(c+a/x^4+b/x^2)/(-4*a*c+b^2))*x*sqrt(e*x^2+d)*EllipticE(sin(arcsin(sqrt(1+(b+2*a/x^2)/sqrt(-4*a*c+b^2))/sqrt(2))),sqrt(2*sqrt(-4*a*c+b^2)*d/(b*d+sqrt(-4*a*c+b^2)*d-2*a*e)))/sqrt(2)/a^2/(-4*a*c+b^2)^(3/2)/sqrt(-a*(e+d/x^2)/((b+sqrt(-4*a*c+b^2))*d-2*a*e))/sqrt(c*x^4+b*x^2+a)+1/3*sqrt(2)*(a*e^2-b*d*e+c*d^2)*(8*a*B*(-2*a*e+b*d)+A*(8*a*b*e-20*a*c*d+b^2*d))*sqrt(-a*(c+a/x^4+b/x^2)/(-4*a*c+b^2))*sqrt(-a*(e+d/x^2)/((b+sqrt(-4*a*c+b^2))*d-2*a*e))*x^3*InverseJacobiAM(arcsin(sqrt(1+(b+2*a/x^2)/sqrt(-4*a*c+b^2))/sqrt(2)),sqrt(2*sqrt(-4*a*c+b^2)*d/(b*d+sqrt(-4*a*c+b^2)*d-2*a*e)))/a^2/(-4*a*c+b^2)^(3/2)/sqrt(e*x^2+d)/sqrt(c*x^4+b*x^2+a),1],
[(B*x^2+A)*(e*x^2+d)^(3/2)/(c*x^4+b*x^2+a)^(5/2),x,8,1/3*x*(A*b^2-a*b*B-2*a*A*c+(A*b-2*B*a)*c*x^2)*(e*x^2+d)^(3/2)/a/(-4*a*c+b^2)/(c*x^4+b*x^2+a)^(3/2)+1/3*x*sqrt(e*x^2+d)*(a*b*B*(-4*a*b*e+4*a*c*d+b^2*d)+A*(4*a^2*b*c*e+20*a^2*c^2*d+a*b^3*e-17*a*b^2*c*d+2*b^4*d)+c*(a*B*(-8*a*b*e+12*a*c*d+b^2*d)+2*A*(4*a^2*c*e+a*b^2*e-8*a*b*c*d+b^3*d))*x^2)/a^2/(-4*a*c+b^2)^2/sqrt(c*x^4+b*x^2+a)-1/3*(a*B*(-8*a*b*e+12*a*c*d+b^2*d)+2*A*(4*a^2*c*e+a*b^2*e-8*a*b*c*d+b^3*d))*sqrt(e*x^2+d)*sqrt(c*x^4+b*x^2+a)/a^2/(-4*a*c+b^2)^2/x+1/3*(a*B*(-8*a*b*e+12*a*c*d+b^2*d)+2*A*(4*a^2*c*e+a*b^2*e-8*a*b*c*d+b^3*d))*sqrt(-a*(c+a/x^4+b/x^2)/(-4*a*c+b^2))*x*sqrt(e*x^2+d)*EllipticE(sin(arcsin(sqrt(1+(b+2*a/x^2)/sqrt(-4*a*c+b^2))/sqrt(2))),sqrt(2*sqrt(-4*a*c+b^2)*d/(b*d+sqrt(-4*a*c+b^2)*d-2*a*e)))/sqrt(2)/a^2/(-4*a*c+b^2)^(3/2)/sqrt(-a*(e+d/x^2)/((b+sqrt(-4*a*c+b^2))*d-2*a*e))/sqrt(c*x^4+b*x^2+a)-1/3*sqrt(2)*(a*B*(5*b^2*d*e+12*a*c*d*e-8*b*(a*e^2+c*d^2))+A*(b^3*d*e-20*a*b*c*d*e-b^2*(-2*a*e^2+c*d^2)+4*a*c*(2*a*e^2+5*c*d^2)))*sqrt(-a*(c+a/x^4+b/x^2)/(-4*a*c+b^2))*sqrt(-a*(e+d/x^2)/((b+sqrt(-4*a*c+b^2))*d-2*a*e))*x^3*InverseJacobiAM(arcsin(sqrt(1+(b+2*a/x^2)/sqrt(-4*a*c+b^2))/sqrt(2)),sqrt(2*sqrt(-4*a*c+b^2)*d/(b*d+sqrt(-4*a*c+b^2)*d-2*a*e)))/a^2/(-4*a*c+b^2)^(3/2)/sqrt(e*x^2+d)/sqrt(c*x^4+b*x^2+a),1],
[(B*x^2+A)*sqrt(e*x^2+d)/(c*x^4+b*x^2+a)^(5/2),x,8,1/3*x*(A*b^2-a*b*B-2*a*A*c+(A*b-2*B*a)*c*x^2)*sqrt(e*x^2+d)/a/(-4*a*c+b^2)/(c*x^4+b*x^2+a)^(3/2)+1/3*(a*B*(b^3*d*e+12*a*b*c*d*e-b^2*(2*a*e^2+c*d^2)-4*a*c*(2*a*e^2+3*c*d^2))+A*(2*b^4*d*e-17*a*b^2*c*d*e+4*a^2*c^2*d*e-b^3*(a*e^2+2*c*d^2)+4*a*b*c*(3*a*e^2+4*c*d^2)))*sqrt(e*x^2+d)/a/(-4*a*c+b^2)^2/(a*e^2-b*d*e+c*d^2)/x/sqrt(c*x^4+b*x^2+a)+1/3*c*(a*B*(7*b^2*d*e+4*a*c*d*e-8*b*(a*e^2+c*d^2))-A*(b^2*c*d^2-b^3*d*e+20*a*b*c*d*e-4*a*c*(4*a*e^2+5*c*d^2)))*x*sqrt(e*x^2+d)/a/(-4*a*c+b^2)^2/(a*e^2-b*d*e+c*d^2)/sqrt(c*x^4+b*x^2+a)-1/3*(a*B*(b^3*d*e+12*a*b*c*d*e-b^2*(2*a*e^2+c*d^2)-4*a*c*(2*a*e^2+3*c*d^2))+A*(2*b^4*d*e-17*a*b^2*c*d*e+4*a^2*c^2*d*e-b^3*(a*e^2+2*c*d^2)+4*a*b*c*(3*a*e^2+4*c*d^2)))*sqrt(-a*(c+a/x^4+b/x^2)/(-4*a*c+b^2))*x*sqrt(e*x^2+d)*EllipticE(sin(arcsin(sqrt(1+(b+2*a/x^2)/sqrt(-4*a*c+b^2))/sqrt(2))),sqrt(2*sqrt(-4*a*c+b^2)*d/(b*d+sqrt(-4*a*c+b^2)*d-2*a*e)))/sqrt(2)/a^2/(-4*a*c+b^2)^(3/2)/(a*e^2-b*d*e+c*d^2)/sqrt(-a*(e+d/x^2)/((b+sqrt(-4*a*c+b^2))*d-2*a*e))/sqrt(c*x^4+b*x^2+a)+1/3*sqrt(2)*(2*a*B*(-4*a*c*e-b^2*e+4*b*c*d)+A*(12*a*b*c*e-20*a*c^2*d-b^3*e+b^2*c*d))*sqrt(-a*(c+a/x^4+b/x^2)/(-4*a*c+b^2))*sqrt(-a*(e+d/x^2)/((b+sqrt(-4*a*c+b^2))*d-2*a*e))*x^3*InverseJacobiAM(arcsin(sqrt(1+(b+2*a/x^2)/sqrt(-4*a*c+b^2))/sqrt(2)),sqrt(2*sqrt(-4*a*c+b^2)*d/(b*d+sqrt(-4*a*c+b^2)*d-2*a*e)))/a^2/(-4*a*c+b^2)^(3/2)/sqrt(e*x^2+d)/sqrt(c*x^4+b*x^2+a),1],
[(B*x^2+A)/sqrt(e*x^2+d)/(c*x^4+b*x^2+a)^(5/2),x,8,-1/3*x*sqrt(e*x^2+d)*(a*B*(2*a*c*e-b^2*e+b*c*d)-A*(3*a*b*c*e-2*a*c^2*d-b^3*e+b^2*c*d)+c*(a*B*(-b*e+2*c*d)-A*(2*a*c*e-b^2*e+b*c*d))*x^2)/a/(-4*a*c+b^2)/(a*e^2-b*d*e+c*d^2)/(c*x^4+b*x^2+a)^(3/2)-1/3*(a*B*(b^4*d*e^2+b^2*c*d*(a*e^2+c*d^2)-4*a*b*c*e*(3*a*e^2+4*c*d^2)+4*a*c^2*d*(7*a*e^2+3*c*d^2)-b^3*(-a*e^3+2*c*d^2*e))+2*A*(b^5*d*e^2+b^3*c*d*(-6*a*e^2+c*d^2)-4*a*b*c^2*d*(a*e^2+2*c*d^2)-8*a^2*c^2*e*(2*a*e^2+c*d^2)+2*a*b^2*c*e*(7*a*e^2+8*c*d^2)-2*b^4*(a*e^3+c*d^2*e)))*sqrt(e*x^2+d)/a/(-4*a*c+b^2)^2/(a*e^2-b*d*e+c*d^2)^2/x/sqrt(c*x^4+b*x^2+a)+1/3*c*(2*a*B*(6*b^2*c*d^2*e-b^3*d*e^2+8*a^2*c*e^3-4*b*c*d*(2*a*e^2+c*d^2))-A*(b^4*d*e^2+b^2*c*d*(-7*a*e^2+c*d^2)+4*a*b*c*e*(5*a*e^2+8*c*d^2)-4*a*c^2*d*(9*a*e^2+5*c*d^2)-b^3*(3*a*e^3+2*c*d^2*e)))*x*sqrt(e*x^2+d)/a/(-4*a*c+b^2)^2/(a*e^2-b*d*e+c*d^2)^2/sqrt(c*x^4+b*x^2+a)+1/3*(a*B*(b^4*d*e^2+b^2*c*d*(a*e^2+c*d^2)-4*a*b*c*e*(3*a*e^2+4*c*d^2)+4*a*c^2*d*(7*a*e^2+3*c*d^2)-b^3*(-a*e^3+2*c*d^2*e))+2*A*(b^5*d*e^2+b^3*c*d*(-6*a*e^2+c*d^2)-4*a*b*c^2*d*(a*e^2+2*c*d^2)-8*a^2*c^2*e*(2*a*e^2+c*d^2)+2*a*b^2*c*e*(7*a*e^2+8*c*d^2)-2*b^4*(a*e^3+c*d^2*e)))*sqrt(-a*(c+a/x^4+b/x^2)/(-4*a*c+b^2))*x*sqrt(e*x^2+d)*EllipticE(sin(arcsin(sqrt(1+(b+2*a/x^2)/sqrt(-4*a*c+b^2))/sqrt(2))),sqrt(2*sqrt(-4*a*c+b^2)*d/(b*d+sqrt(-4*a*c+b^2)*d-2*a*e)))/sqrt(2)/a^2/(-4*a*c+b^2)^(3/2)/(a*e^2-b*d*e+c*d^2)^2/sqrt(-a*(e+d/x^2)/((b+sqrt(-4*a*c+b^2))*d-2*a*e))/sqrt(c*x^4+b*x^2+a)-1/3*sqrt(2)*(a*B*(7*b^2*c*d*e+4*a*c^2*d*e+b^3*e^2-4*b*c*(3*a*e^2+2*c*d^2))+A*(2*b^3*c*d*e-24*a*b*c^2*d*e-b^4*e^2-b^2*c*(-4*a*e^2+c*d^2)+4*a*c^2*(4*a*e^2+5*c*d^2)))*sqrt(-a*(c+a/x^4+b/x^2)/(-4*a*c+b^2))*sqrt(-a*(e+d/x^2)/((b+sqrt(-4*a*c+b^2))*d-2*a*e))*x^3*InverseJacobiAM(arcsin(sqrt(1+(b+2*a/x^2)/sqrt(-4*a*c+b^2))/sqrt(2)),sqrt(2*sqrt(-4*a*c+b^2)*d/(b*d+sqrt(-4*a*c+b^2)*d-2*a*e)))/a^2/(-4*a*c+b^2)^(3/2)/(a*e^2-b*d*e+c*d^2)/sqrt(e*x^2+d)/sqrt(c*x^4+b*x^2+a),1],
[(B*x^2+A)/(e*x^2+d)^(3/2)/(c*x^4+b*x^2+a)^(5/2),x,9,-1/3*x*(a*B*(2*a*c*e-b^2*e+b*c*d)-A*(3*a*b*c*e-2*a*c^2*d-b^3*e+b^2*c*d)+c*(a*B*(-b*e+2*c*d)-A*(2*a*c*e-b^2*e+b*c*d))*x^2)/a/(-4*a*c+b^2)/(a*e^2-b*d*e+c*d^2)/sqrt(e*x^2+d)/(c*x^4+b*x^2+a)^(3/2)-1/3*e*(2*a*B*d*(c^2*d^2+2*b^2*e^2-c*e*(7*a*e+b*d))-A*(b^3*d*e^2+b*c*d*(-3*a*e^2+c*d^2)+4*a*c*e*(-3*a*e^2+c*d^2)-b^2*(-3*a*e^3+2*c*d^2*e)))*x/a/(-4*a*c+b^2)/d/(a*e^2-b*d*e+c*d^2)^2/sqrt(e*x^2+d)/sqrt(c*x^4+b*x^2+a)+1/3*(a*B*d*(b^5*d*e^3+b^3*c*d*e*(-10*a*e^2+3*c*d^2)+4*a*b*c^2*d*e*(14*a*e^2+5*c*d^2)-b^4*(-7*a*e^4+3*c*d^2*e^2)-4*a*c^2*(-20*a^2*e^4+15*a*c*d^2*e^2+3*c^2*d^4)-b^2*c*(52*a^2*e^4-3*a*c*d^2*e^2+c^2*d^4))+A*(2*b^6*d^2*e^3-b^3*c*d*(-50*a^2*e^4-39*a*c*d^2*e^2+2*c^2*d^4)-a*b^2*c*e*(-24*a^2*e^4+71*a*c*d^2*e^2+47*c^2*d^4)+4*a*b*c^2*d*(-20*a^2*e^4-3*a*c*d^2*e^2+4*c^2*d^4)+4*a^2*c^2*e*(-12*a^2*e^4+27*a*c*d^2*e^2+7*c^2*d^4)-b^5*(7*a*d*e^4+6*c*d^3*e^2)+b^4*(-3*a^2*e^5-a*c*d^2*e^3+6*c^2*d^4*e)))*sqrt(e*x^2+d)/a/(-4*a*c+b^2)^2/d/(a*e^2-b*d*e+c*d^2)^3/x/sqrt(c*x^4+b*x^2+a)+1/3*c*(A*(b^5*d*e^3+b^3*c*d*e*(4*a*e^2+3*c*d^2)-4*a*b*c^2*d*e*(16*a*e^2+11*c*d^2)-3*b^4*(3*a*e^4+c*d^2*e^2)-b^2*c*(-62*a^2*e^4-21*a*c*d^2*e^2+c^2*d^4)+4*a*c^2*(-22*a^2*e^4+15*a*c*d^2*e^2+5*c^2*d^4))+a*B*(5*b^4*d*e^3+b^2*c*d*e*(-35*a*e^2+17*c*d^2)-4*a*c^2*d*e*(-31*a*e^2+c*d^2)-b^3*(-3*a*e^4+6*c*d^2*e^2)-4*b*c*(5*a^2*e^4+6*a*c*d^2*e^2+2*c^2*d^4)))*x*sqrt(e*x^2+d)/a/(-4*a*c+b^2)^2/(a*e^2-b*d*e+c*d^2)^3/sqrt(c*x^4+b*x^2+a)-1/3*(a*B*d*(b^5*d*e^3+b^3*c*d*e*(-10*a*e^2+3*c*d^2)+4*a*b*c^2*d*e*(14*a*e^2+5*c*d^2)-b^4*(-7*a*e^4+3*c*d^2*e^2)-4*a*c^2*(-20*a^2*e^4+15*a*c*d^2*e^2+3*c^2*d^4)-b^2*c*(52*a^2*e^4-3*a*c*d^2*e^2+c^2*d^4))+A*(2*b^6*d^2*e^3-b^3*c*d*(-50*a^2*e^4-39*a*c*d^2*e^2+2*c^2*d^4)-a*b^2*c*e*(-24*a^2*e^4+71*a*c*d^2*e^2+47*c^2*d^4)+4*a*b*c^2*d*(-20*a^2*e^4-3*a*c*d^2*e^2+4*c^2*d^4)+4*a^2*c^2*e*(-12*a^2*e^4+27*a*c*d^2*e^2+7*c^2*d^4)-b^5*(7*a*d*e^4+6*c*d^3*e^2)+b^4*(-3*a^2*e^5-a*c*d^2*e^3+6*c^2*d^4*e)))*sqrt(-a*(c+a/x^4+b/x^2)/(-4*a*c+b^2))*x*sqrt(e*x^2+d)*EllipticE(sin(arcsin(sqrt(1+(b+2*a/x^2)/sqrt(-4*a*c+b^2))/sqrt(2))),sqrt(2*sqrt(-4*a*c+b^2)*d/(b*d+sqrt(-4*a*c+b^2)*d-2*a*e)))/sqrt(2)/a^2/(-4*a*c+b^2)^(3/2)/d/(a*e^2-b*d*e+c*d^2)^3/sqrt(-a*(e+d/x^2)/((b+sqrt(-4*a*c+b^2))*d-2*a*e))/sqrt(c*x^4+b*x^2+a)+1/3*sqrt(2)*(4*a*B*d*(b^4*e^3+8*a^2*c^2*e^3+2*b*c^2*d*(3*a*e^2+c*d^2)-b^2*c*e*(7*a*e^2+3*c*d^2))-A*(b^5*d*e^3+b^3*c*d*e*(-2*a*e^2+3*c*d^2)-4*a*b*c^2*d*e*(4*a*e^2+9*c*d^2)-b^4*(-3*a*e^4+3*c*d^2*e^2)+4*a*c^2*(12*a^2*e^4+9*a*c*d^2*e^2+5*c^2*d^4)-b^2*c*(24*a^2*e^4-15*a*c*d^2*e^2+c^2*d^4)))*sqrt(-a*(c+a/x^4+b/x^2)/(-4*a*c+b^2))*sqrt(-a*(e+d/x^2)/((b+sqrt(-4*a*c+b^2))*d-2*a*e))*x^3*InverseJacobiAM(arcsin(sqrt(1+(b+2*a/x^2)/sqrt(-4*a*c+b^2))/sqrt(2)),sqrt(2*sqrt(-4*a*c+b^2)*d/(b*d+sqrt(-4*a*c+b^2)*d-2*a*e)))/a^2/(-4*a*c+b^2)^(3/2)/d/(a*e^2-b*d*e+c*d^2)^2/sqrt(e*x^2+d)/sqrt(c*x^4+b*x^2+a),1],
[(C*x^4+B*x^2+A)/sqrt(e*x^2+d)/sqrt(c*x^4+b*x^2+a),x,9,1/2*C*sqrt(e*x^2+d)*sqrt(c*x^4+b*x^2+a)/c/e/x-1/2*sqrt(-4*a*c+b^2)*C*sqrt(-a*(c+a/x^4+b/x^2)/(-4*a*c+b^2))*x*sqrt(e*x^2+d)*EllipticE(sin(arcsin(sqrt(1+(b+2*a/x^2)/sqrt(-4*a*c+b^2))/sqrt(2))),sqrt(2*sqrt(-4*a*c+b^2)*d/(b*d+sqrt(-4*a*c+b^2)*d-2*a*e)))/sqrt(2)/c/e/sqrt(-a*(e+d/x^2)/((b+sqrt(-4*a*c+b^2))*d-2*a*e))/sqrt(c*x^4+b*x^2+a)-sqrt(-4*a*c+b^2)*(2*A*c-C*a)*sqrt(-a*(c+a/x^4+b/x^2)/(-4*a*c+b^2))*sqrt(-a*(e+d/x^2)/((b+sqrt(-4*a*c+b^2))*d-2*a*e))*x^3*InverseJacobiAM(arcsin(sqrt(1+(b+2*a/x^2)/sqrt(-4*a*c+b^2))/sqrt(2)),sqrt(2*sqrt(-4*a*c+b^2)*d/(b*d+sqrt(-4*a*c+b^2)*d-2*a*e)))/sqrt(2)/a/c/sqrt(e*x^2+d)/sqrt(c*x^4+b*x^2+a)-sqrt(2)*sqrt(-4*a*c+b^2)*(-2*B*c*e+C*b*e+C*c*d)*sqrt(-a*(c+a/x^4+b/x^2)/(-4*a*c+b^2))*sqrt(-a*(e+d/x^2)/((b+sqrt(-4*a*c+b^2))*d-2*a*e))*x^3*EllipticPi(sin(arcsin(sqrt(1+(b+2*a/x^2)/sqrt(-4*a*c+b^2))/sqrt(2))),2*sqrt(-4*a*c+b^2)/(b+sqrt(-4*a*c+b^2)),sqrt(2*sqrt(-4*a*c+b^2)*d/(b*d+sqrt(-4*a*c+b^2)*d-2*a*e)))/c/(b+sqrt(-4*a*c+b^2))/e/sqrt(e*x^2+d)/sqrt(c*x^4+b*x^2+a),1],
[(B*x^2+A)*(e*x^2+d)^q*(c*x^4+b*x^2+a),x,5,-(A*e*(7+2*q)*(3*c*d-b*e*(5+2*q))-B*(15*c*d^2-e*(7+2*q)*(3*b*d-a*e*(5+2*q))))*x*(e*x^2+d)^(1+q)/e^3/(3+2*q)/(5+2*q)/(7+2*q)+(A*c*e*(7+2*q)-B*(5*c*d-b*e*(7+2*q)))*x^3*(e*x^2+d)^(1+q)/e^2/(5+2*q)/(7+2*q)+B*c*x^5*(e*x^2+d)^(1+q)/e/(7+2*q)+(A*e*(7+2*q)*(3*c*d^2-e*(5+2*q)*(b*d-a*e*(3+2*q)))-B*d*(15*c*d^2-e*(7+2*q)*(3*b*d-a*e*(5+2*q))))*x*(e*x^2+d)^q*hypergeom([1/2, -q],[3/2],-e*x^2/d)/e^3/(3+2*q)/(5+2*q)/(7+2*q)/((1+e*x^2/d)^q),1],
[(B*x^2+A)*(e*x^2+d)^q,x,3,B*x*(e*x^2+d)^(1+q)/e/(3+2*q)-(B*d-A*e*(3+2*q))*x*(e*x^2+d)^q*hypergeom([1/2, -q],[3/2],-e*x^2/d)/e/(3+2*q)/((1+e*x^2/d)^q),1],
[(B*x^2+A)*(e*x^2+d)^q/(c*x^4+b*x^2+a),x,8,(B-(-2*A*c+B*b)/sqrt(-4*a*c+b^2))*x*(e*x^2+d)^q*AppellF1(1/2,-q,1,3/2,-e*x^2/d,-2*c*x^2/(b-sqrt(-4*a*c+b^2)))/(b-sqrt(-4*a*c+b^2))/((1+e*x^2/d)^q)+(B+(-2*A*c+B*b)/sqrt(-4*a*c+b^2))*x*(e*x^2+d)^q*AppellF1(1/2,-q,1,3/2,-e*x^2/d,-2*c*x^2/(b+sqrt(-4*a*c+b^2)))/(b+sqrt(-4*a*c+b^2))/((1+e*x^2/d)^q),1],
[(B*x^2+A)*(e*x^2+d)^q/(c*x^4+b*x^2+a)^2,x,13,-1/2*x*(e*x^2+d)^(1+q)*(a*B*(2*a*c*e-b^2*e+b*c*d)-A*(3*a*b*c*e-2*a*c^2*d-b^3*e+b^2*c*d)+c*(a*B*(-b*e+2*c*d)-A*(2*a*c*e-b^2*e+b*c*d))*x^2)/a/(-4*a*c+b^2)/(a*e^2-b*d*e+c*d^2)/(c*x^4+b*x^2+a)-1/2*c*(2*a*B*(c*d^2+e*(a*e*(1-2*q)-b*d*(1-q)))+A*(b^2*d*e-b*(c*d^2+a*e^2*(1-2*q))-4*a*c*d*e*q)+(A*(b^3*d*e-12*a*b*c*d*e-b^2*(c*d^2+a*e^2*(1-2*q))+4*a*c*(3*c*d^2+a*e^2*(3-2*q)))-2*a*B*(2*b*(a*e^2+c*d^2)-b^2*d*e*(2-q)-4*a*c*d*e*q))/sqrt(-4*a*c+b^2))*x*(e*x^2+d)^q*AppellF1(1/2,-q,1,3/2,-e*x^2/d,-2*c*x^2/(b-sqrt(-4*a*c+b^2)))/a/(-4*a*c+b^2)/(b-sqrt(-4*a*c+b^2))/(a*e^2-b*d*e+c*d^2)/((1+e*x^2/d)^q)-1/2*c*(2*a*B*(c*d^2+e*(a*e*(1-2*q)-b*d*(1-q)))+A*(b^2*d*e-b*(c*d^2+a*e^2*(1-2*q))-4*a*c*d*e*q)-(A*(b^3*d*e-12*a*b*c*d*e-b^2*(c*d^2+a*e^2*(1-2*q))+4*a*c*(3*c*d^2+a*e^2*(3-2*q)))-2*a*B*(2*b*(a*e^2+c*d^2)-b^2*d*e*(2-q)-4*a*c*d*e*q))/sqrt(-4*a*c+b^2))*x*(e*x^2+d)^q*AppellF1(1/2,-q,1,3/2,-e*x^2/d,-2*c*x^2/(b+sqrt(-4*a*c+b^2)))/a/(-4*a*c+b^2)/(b+sqrt(-4*a*c+b^2))/(a*e^2-b*d*e+c*d^2)/((1+e*x^2/d)^q)+1/2*e*(a*B*(-b*e+2*c*d)-A*(2*a*c*e-b^2*e+b*c*d))*(1+2*q)*x*(e*x^2+d)^q*hypergeom([1/2, -q],[3/2],-e*x^2/d)/a/(-4*a*c+b^2)/(a*e^2-b*d*e+c*d^2)/((1+e*x^2/d)^q),1],
[(e*x^2+d)^q*(c*x^4+b*x^2+a)*(C*x^4+B*x^2+A),x,6,-(3*c*(35*C*d^3-d*e*(9+2*q)*(5*B*d-A*e*(7+2*q)))+e*(9+2*q)*(a*e*(7+2*q)*(3*C*d-B*e*(5+2*q))-b*(15*C*d^2-e*(7+2*q)*(3*B*d-A*e*(5+2*q)))))*x*(e*x^2+d)^(1+q)/e^4/(3+2*q)/(5+2*q)/(7+2*q)/(9+2*q)-(e*(9+2*q)*(5*b*C*d-b*B*e*(7+2*q)-a*C*e*(7+2*q))-c*(35*C*d^2-e*(9+2*q)*(5*B*d-A*e*(7+2*q))))*x^3*(e*x^2+d)^(1+q)/e^3/(5+2*q)/(7+2*q)/(9+2*q)-(7*c*C*d-B*c*e*(9+2*q)-b*C*e*(9+2*q))*x^5*(e*x^2+d)^(1+q)/e^2/(7+2*q)/(9+2*q)+c*C*x^7*(e*x^2+d)^(1+q)/e/(9+2*q)+(a*A*e^4*(8*q^3+84*q^2+286*q+315)-d*(e*(9+2*q)*(15*b*C*d^2-b*e*(7+2*q)*(3*B*d-A*e*(5+2*q))-a*e*(7+2*q)*(3*C*d-B*e*(5+2*q)))-3*c*d*(35*C*d^2-e*(9+2*q)*(5*B*d-A*e*(7+2*q))))/(3+2*q))*x*(e*x^2+d)^q*hypergeom([1/2, -q],[3/2],-e*x^2/d)/e^4/(5+2*q)/(7+2*q)/(9+2*q)/((1+e*x^2/d)^q),1],
[(e*x^2+d)^q*(C*x^4+B*x^2+A),x,4,-(3*C*d-B*e*(5+2*q))*x*(e*x^2+d)^(1+q)/e^2/(3+2*q)/(5+2*q)+C*x^3*(e*x^2+d)^(1+q)/e/(5+2*q)+(3*C*d^2-e*(5+2*q)*(B*d-A*e*(3+2*q)))*x*(e*x^2+d)^q*hypergeom([1/2, -q],[3/2],-e*x^2/d)/e^2/(3+2*q)/(5+2*q)/((1+e*x^2/d)^q),1],
[(e*x^2+d)^q*(C*x^4+B*x^2+A)/(c*x^4+b*x^2+a),x,12,(B*c-b*C-(b*B*c-b^2*C-2*c*(A*c-C*a))/sqrt(-4*a*c+b^2))*x*(e*x^2+d)^q*AppellF1(1/2,-q,1,3/2,-e*x^2/d,-2*c*x^2/(b-sqrt(-4*a*c+b^2)))/c/(b-sqrt(-4*a*c+b^2))/((1+e*x^2/d)^q)+(B*c-b*C+(b*B*c-b^2*C-2*c*(A*c-C*a))/sqrt(-4*a*c+b^2))*x*(e*x^2+d)^q*AppellF1(1/2,-q,1,3/2,-e*x^2/d,-2*c*x^2/(b+sqrt(-4*a*c+b^2)))/c/(b+sqrt(-4*a*c+b^2))/((1+e*x^2/d)^q)+C*x*(e*x^2+d)^q*hypergeom([1/2, -q],[3/2],-e*x^2/d)/c/((1+e*x^2/d)^q),1],
[(e*x^2+d)^q*(C*x^4+B*x^2+A)/(c*x^4+b*x^2+a)^2,x,13,1/2*x*(e*x^2+d)^(1+q)*(A*(3*a*b*c*e-2*a*c^2*d-b^3*e+b^2*c*d)-a*(2*B*a*c*e-B*b^2*e+B*b*c*d+C*a*b*e-2*C*a*c*d)+c*(A*(2*a*c*e-b^2*e+b*c*d)-a*(-B*b*e+2*B*c*d+2*C*a*e-C*b*d))*x^2)/a/(-4*a*c+b^2)/(a*e^2-b*d*e+c*d^2)/(c*x^4+b*x^2+a)-1/2*(A*c*(b^2*d*e-b*(c*d^2+a*e^2*(1-2*q))-4*a*c*d*e*q)+a*(2*B*c*(c*d^2+e*(a*e*(1-2*q)-b*d*(1-q)))-C*(b*(c*d^2+a*e^2*(1-2*q))-b^2*d*e*(1-2*q)-4*a*c*d*e*q))+(A*c*(b^3*d*e-12*a*b*c*d*e-b^2*(c*d^2+a*e^2*(1-2*q))+4*a*c*(3*c*d^2+a*e^2*(3-2*q)))+a*(b^2*(c*d*(C*d+2*B*e*(2-q))+a*C*e^2*(1-2*q))-b^3*C*d*e*(1-2*q)-4*b*c*(B*(a*e^2+c*d^2)+a*C*d*e*(1+2*q))+4*a*c*(a*C*e^2*(1+2*q)+c*d*(2*B*e*q+C*d))))/sqrt(-4*a*c+b^2))*x*(e*x^2+d)^q*AppellF1(1/2,-q,1,3/2,-e*x^2/d,-2*c*x^2/(b-sqrt(-4*a*c+b^2)))/a/(-4*a*c+b^2)/(b-sqrt(-4*a*c+b^2))/(a*e^2-b*d*e+c*d^2)/((1+e*x^2/d)^q)-1/2*(A*c*(b^2*d*e-b*(c*d^2+a*e^2*(1-2*q))-4*a*c*d*e*q)+a*(2*B*c*(c*d^2+e*(a*e*(1-2*q)-b*d*(1-q)))-C*(b*(c*d^2+a*e^2*(1-2*q))-b^2*d*e*(1-2*q)-4*a*c*d*e*q))-(A*c*(b^3*d*e-12*a*b*c*d*e-b^2*(c*d^2+a*e^2*(1-2*q))+4*a*c*(3*c*d^2+a*e^2*(3-2*q)))+a*(b^2*(c*d*(C*d+2*B*e*(2-q))+a*C*e^2*(1-2*q))-b^3*C*d*e*(1-2*q)-4*b*c*(B*(a*e^2+c*d^2)+a*C*d*e*(1+2*q))+4*a*c*(a*C*e^2*(1+2*q)+c*d*(2*B*e*q+C*d))))/sqrt(-4*a*c+b^2))*x*(e*x^2+d)^q*AppellF1(1/2,-q,1,3/2,-e*x^2/d,-2*c*x^2/(b+sqrt(-4*a*c+b^2)))/a/(-4*a*c+b^2)/(b+sqrt(-4*a*c+b^2))/(a*e^2-b*d*e+c*d^2)/((1+e*x^2/d)^q)-1/2*e*(A*(2*a*c*e-b^2*e+b*c*d)-a*(-B*b*e+2*B*c*d+2*C*a*e-C*b*d))*(1+2*q)*x*(e*x^2+d)^q*hypergeom([1/2, -q],[3/2],-e*x^2/d)/a/(-4*a*c+b^2)/(a*e^2-b*d*e+c*d^2)/((1+e*x^2/d)^q),1]]: