lst:=[[(x^2+1)/sqrt(-x^4+1),x,1,EllipticE(sin(arcsin(x)),sqrt(-1)),1],
[sqrt(-x^4+1)/(-x^2+1),x,2,EllipticE(sin(arcsin(x)),sqrt(-1)),1],
[sqrt(x^2+1)/sqrt(-x^2+1),x,1,EllipticE(sin(arcsin(x)),sqrt(-1)),1],
[(e^2*x^2+1)/sqrt(-e^4*x^4+1),x,1,EllipticE(sin(arcsin(e*x)),sqrt(-1))/e,1],
[sqrt(-e^4*x^4+1)/(-e^2*x^2+1),x,2,EllipticE(sin(arcsin(e*x)),sqrt(-1))/e,1],
[sqrt(e^2*x^2+1)/sqrt(-e^2*x^2+1),x,1,EllipticE(sin(arcsin(e*x)),sqrt(-1))/e,1],
[(e*x^2+d)/sqrt(-e^2*x^4+d^2),x,2,d^(3/2)*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[sqrt(-e^2*x^4+d^2)/(-e*x^2+d),x,3,d^(3/2)*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[1/(e*x^2+d)/sqrt(-e^2*x^4+d^2),x,3,1/2*x*sqrt(-e^2*x^4+d^2)/d^2/(e*x^2+d)+1/2*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/sqrt(d)/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[(-e*x^2+d)/(-e^2*x^4+d^2)^(3/2),x,3,1/2*x*(-e*x^2+d)/d^2/sqrt(-e^2*x^4+d^2)+1/2*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/sqrt(d)/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[(-x^2+1)/sqrt(-x^4+1),x,3,-EllipticE(sin(arcsin(x)),sqrt(-1))+2*InverseJacobiAM(arcsin(x),sqrt(-1)),1],
[sqrt(-x^4+1)/(x^2+1),x,5,-EllipticE(sin(arcsin(x)),sqrt(-1))+2*InverseJacobiAM(arcsin(x),sqrt(-1)),1],
[sqrt(-x^2+1)/sqrt(x^2+1),x,4,-EllipticE(sin(arcsin(x)),sqrt(-1))+2*InverseJacobiAM(arcsin(x),sqrt(-1)),1],
[(-e^2*x^2+1)/sqrt(-e^4*x^4+1),x,3,-EllipticE(sin(arcsin(e*x)),sqrt(-1))/e+2*InverseJacobiAM(arcsin(e*x),sqrt(-1))/e,1],
[sqrt(-e^4*x^4+1)/(e^2*x^2+1),x,5,-EllipticE(sin(arcsin(e*x)),sqrt(-1))/e+2*InverseJacobiAM(arcsin(e*x),sqrt(-1))/e,1],
[sqrt(-e^2*x^2+1)/sqrt(e^2*x^2+1),x,4,-EllipticE(sin(arcsin(e*x)),sqrt(-1))/e+2*InverseJacobiAM(arcsin(e*x),sqrt(-1))/e,1],
[(-e*x^2+d)/sqrt(-e^2*x^4+d^2),x,5,-d^(3/2)*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/sqrt(e)/sqrt(-e^2*x^4+d^2)+2*d^(3/2)*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[sqrt(-e^2*x^4+d^2)/(e*x^2+d),x,6,-d^(3/2)*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/sqrt(e)/sqrt(-e^2*x^4+d^2)+2*d^(3/2)*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[1/(-e*x^2+d)/sqrt(-e^2*x^4+d^2),x,6,1/2*x*sqrt(-e^2*x^4+d^2)/d^2/(-e*x^2+d)-1/2*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/sqrt(d)/sqrt(e)/sqrt(-e^2*x^4+d^2)+sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/sqrt(d)/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[(e*x^2+d)/(-e^2*x^4+d^2)^(3/2),x,6,1/2*x*(e*x^2+d)/d^2/sqrt(-e^2*x^4+d^2)-1/2*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/sqrt(d)/sqrt(e)/sqrt(-e^2*x^4+d^2)+sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/sqrt(d)/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[(e*x^2+d)^4/(-e^2*x^4+d^2),x,4,-7*d^2*x-4/3*d*e*x^3-1/5*e^2*x^5+8*d^(5/2)*arctanh(sqrt(e)*x/sqrt(d))/sqrt(e),1],
[(e*x^2+d)^3/(-e^2*x^4+d^2),x,4,-3*d*x-1/3*e*x^3+4*d^(3/2)*arctanh(sqrt(e)*x/sqrt(d))/sqrt(e),1],
[(e*x^2+d)^2/(-e^2*x^4+d^2),x,3,-x+2*sqrt(d)*arctanh(sqrt(e)*x/sqrt(d))/sqrt(e),1],
[(e*x^2+d)/(-e^2*x^4+d^2),x,2,arctanh(sqrt(e)*x/sqrt(d))/sqrt(d)/sqrt(e),1],
[1/(e*x^2+d)/(-e^2*x^4+d^2),x,6,1/4*x/d^2/(e*x^2+d)+1/2*arctan(sqrt(e)*x/sqrt(d))/d^(5/2)/sqrt(e)+1/4*arctanh(sqrt(e)*x/sqrt(d))/d^(5/2)/sqrt(e),1],
[1/(e*x^2+d)^2/(-e^2*x^4+d^2),x,7,1/8*x/d^2/(e*x^2+d)^2+5/16*x/d^3/(e*x^2+d)+7/16*arctan(sqrt(e)*x/sqrt(d))/d^(7/2)/sqrt(e)+1/8*arctanh(sqrt(e)*x/sqrt(d))/d^(7/2)/sqrt(e),1],
[(e*x^2+d)^(3/2)/(-e^2*x^4+d^2),x,6,-arctanh(sqrt(e)*x/sqrt(e*x^2+d))/sqrt(e)+sqrt(2)*arctanh(sqrt(2)*sqrt(e)*x/sqrt(e*x^2+d))/sqrt(e),1],
[sqrt(e*x^2+d)/(-e^2*x^4+d^2),x,3,arctanh(sqrt(2)*sqrt(e)*x/sqrt(e*x^2+d))/sqrt(2)/d/sqrt(e),1],
[1/sqrt(e*x^2+d)/(-e^2*x^4+d^2),x,4,1/2*x/d^2/sqrt(e*x^2+d)+1/2*arctanh(sqrt(2)*sqrt(e)*x/sqrt(e*x^2+d))/sqrt(2)/d^2/sqrt(e),1],
[1/(e*x^2+d)^(3/2)/(-e^2*x^4+d^2),x,5,1/6*x/d^2/(e*x^2+d)^(3/2)+7/12*x/d^3/sqrt(e*x^2+d)+1/4*arctanh(sqrt(2)*sqrt(e)*x/sqrt(e*x^2+d))/sqrt(2)/d^3/sqrt(e),1],
[(e*x^2+d)^2/(-e^2*x^4+d^2)^(3/2),x,7,x*(e*x^2+d)/d/sqrt(-e^2*x^4+d^2)-sqrt(d)*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/sqrt(e)/sqrt(-e^2*x^4+d^2)+sqrt(d)*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[sqrt(-e^2*x^4+d^2)/(-e*x^2+d)^2,x,7,x*sqrt(-e^2*x^4+d^2)/d/(-e*x^2+d)-sqrt(d)*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/sqrt(e)/sqrt(-e^2*x^4+d^2)+sqrt(d)*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[(e*x^2+d)/(-e*x^2+d)/sqrt(-e^2*x^4+d^2),x,8,x*sqrt(-e^2*x^4+d^2)/d/(-e*x^2+d)-sqrt(d)*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/sqrt(e)/sqrt(-e^2*x^4+d^2)+sqrt(d)*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[(e*x^2+d)^3*sqrt(-e^2*x^4+d^2),x,8,2/21*d^2*x*(7*e*x^2+5*d)*sqrt(-e^2*x^4+d^2)-3/7*d*x*(-e^2*x^4+d^2)^(3/2)-1/9*e*x^3*(-e^2*x^4+d^2)^(3/2)+4/3*d^(11/2)*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/sqrt(e)/sqrt(-e^2*x^4+d^2)-8/21*d^(11/2)*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[(e*x^2+d)^2*sqrt(-e^2*x^4+d^2),x,7,2/105*d*x*(21*e*x^2+20*d)*sqrt(-e^2*x^4+d^2)-1/7*x*(-e^2*x^4+d^2)^(3/2)+4/5*d^(9/2)*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/sqrt(e)/sqrt(-e^2*x^4+d^2)-4/105*d^(9/2)*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[(e*x^2+d)*sqrt(-e^2*x^4+d^2),x,6,1/15*x*(3*e*x^2+5*d)*sqrt(-e^2*x^4+d^2)+2/5*d^(7/2)*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/sqrt(e)/sqrt(-e^2*x^4+d^2)+4/15*d^(7/2)*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[sqrt(-e^2*x^4+d^2),x,3,1/3*x*sqrt(-e^2*x^4+d^2)+2/3*d^(5/2)*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[sqrt(-e^2*x^4+d^2)/(e*x^2+d),x,6,-d^(3/2)*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/sqrt(e)/sqrt(-e^2*x^4+d^2)+2*d^(3/2)*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[sqrt(-e^2*x^4+d^2)/(e*x^2+d)^2,x,1,sqrt((-e*x^2+d)/(e*x^2+d))*(e*x^2+d)*EllipticE(sin(arctan(sqrt(e)*x/sqrt(d))),sqrt(2))/sqrt(d)/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[sqrt(-e^2*x^4+d^2)/(e*x^2+d)^3,x,7,1/3*x*sqrt(-e^2*x^4+d^2)/d/(e*x^2+d)^2+1/2*x*sqrt(-e^2*x^4+d^2)/d^2/(e*x^2+d)+1/2*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/sqrt(d)/sqrt(e)/sqrt(-e^2*x^4+d^2)-1/3*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/sqrt(d)/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[sqrt(-e^2*x^4+d^2)/(e*x^2+d)^4,x,8,1/5*x*sqrt(-e^2*x^4+d^2)/d/(e*x^2+d)^3+7/30*x*sqrt(-e^2*x^4+d^2)/d^2/(e*x^2+d)^2+2/5*x*sqrt(-e^2*x^4+d^2)/d^3/(e*x^2+d)+2/5*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/d^(3/2)/sqrt(e)/sqrt(-e^2*x^4+d^2)-7/30*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/d^(3/2)/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[sqrt(-e^2*x^4+d^2)/(e*x^2+d)^5,x,9,1/7*x*sqrt(-e^2*x^4+d^2)/d/(e*x^2+d)^4+11/70*x*sqrt(-e^2*x^4+d^2)/d^2/(e*x^2+d)^3+41/210*x*sqrt(-e^2*x^4+d^2)/d^3/(e*x^2+d)^2+7/20*x*sqrt(-e^2*x^4+d^2)/d^4/(e*x^2+d)+7/20*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/d^(5/2)/sqrt(e)/sqrt(-e^2*x^4+d^2)-41/210*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/d^(5/2)/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[(e*x^2+d)^3*(-e^2*x^4+d^2)^(3/2),x,9,4/715*d^4*x*(77*e*x^2+65*d)*sqrt(-e^2*x^4+d^2)+2/429*d^2*x*(77*e*x^2+39*d)*(-e^2*x^4+d^2)^(3/2)-3/11*d*x*(-e^2*x^4+d^2)^(5/2)-1/13*e*x^3*(-e^2*x^4+d^2)^(5/2)+56/65*d^(15/2)*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/sqrt(e)/sqrt(-e^2*x^4+d^2)-96/715*d^(15/2)*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[(e*x^2+d)^2*(-e^2*x^4+d^2)^(3/2),x,8,4/1155*d^3*x*(77*e*x^2+90*d)*sqrt(-e^2*x^4+d^2)+2/693*d*x*(77*e*x^2+54*d)*(-e^2*x^4+d^2)^(3/2)-1/11*x*(-e^2*x^4+d^2)^(5/2)+8/15*d^(13/2)*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/sqrt(e)/sqrt(-e^2*x^4+d^2)+104/1155*d^(13/2)*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[(e*x^2+d)*(-e^2*x^4+d^2)^(3/2),x,7,2/105*d^2*x*(7*e*x^2+15*d)*sqrt(-e^2*x^4+d^2)+1/63*x*(7*e*x^2+9*d)*(-e^2*x^4+d^2)^(3/2)+4/15*d^(11/2)*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/sqrt(e)/sqrt(-e^2*x^4+d^2)+32/105*d^(11/2)*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[(-e^2*x^4+d^2)^(3/2),x,4,2/7*d^2*x*sqrt(-e^2*x^4+d^2)+1/7*x*(-e^2*x^4+d^2)^(3/2)+4/7*d^(9/2)*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[(-e^2*x^4+d^2)^(3/2)/(e*x^2+d),x,7,1/15*x*(-3*e*x^2+5*d)*sqrt(-e^2*x^4+d^2)-2/5*d^(7/2)*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/sqrt(e)/sqrt(-e^2*x^4+d^2)+16/15*d^(7/2)*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[(-e^2*x^4+d^2)^(3/2)/(e*x^2+d)^2,x,7,-1/3*x*sqrt(-e^2*x^4+d^2)-2*d^(5/2)*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/sqrt(e)/sqrt(-e^2*x^4+d^2)+10/3*d^(5/2)*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[(-e^2*x^4+d^2)^(3/2)/(e*x^2+d)^3,x,6,2*x*sqrt(-e^2*x^4+d^2)/(e*x^2+d)+3*d^(3/2)*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/sqrt(e)/sqrt(-e^2*x^4+d^2)-4*d^(3/2)*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[(-e^2*x^4+d^2)^(3/2)/(e*x^2+d)^4,x,4,2/3*x*sqrt(-e^2*x^4+d^2)/(e*x^2+d)^2+1/3*sqrt(d)*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[(-e^2*x^4+d^2)^(3/2)/(e*x^2+d)^5,x,8,2/5*x*sqrt(-e^2*x^4+d^2)/(e*x^2+d)^3+2/15*x*sqrt(-e^2*x^4+d^2)/d/(e*x^2+d)^2+3/10*x*sqrt(-e^2*x^4+d^2)/d^2/(e*x^2+d)+3/10*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/sqrt(d)/sqrt(e)/sqrt(-e^2*x^4+d^2)-2/15*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/sqrt(d)/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[(-e^2*x^4+d^2)^(3/2)/(e*x^2+d)^6,x,9,2/7*x*sqrt(-e^2*x^4+d^2)/(e*x^2+d)^4+4/35*x*sqrt(-e^2*x^4+d^2)/d/(e*x^2+d)^3+11/70*x*sqrt(-e^2*x^4+d^2)/d^2/(e*x^2+d)^2+3/10*x*sqrt(-e^2*x^4+d^2)/d^3/(e*x^2+d)+3/10*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/d^(3/2)/sqrt(e)/sqrt(-e^2*x^4+d^2)-11/70*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/d^(3/2)/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[(-e^2*x^4+d^2)^(3/2)/(e*x^2+d)^7,x,10,2/9*x*sqrt(-e^2*x^4+d^2)/(e*x^2+d)^5+2/21*x*sqrt(-e^2*x^4+d^2)/d/(e*x^2+d)^4+73/630*x*sqrt(-e^2*x^4+d^2)/d^2/(e*x^2+d)^3+16/105*x*sqrt(-e^2*x^4+d^2)/d^3/(e*x^2+d)^2+17/60*x*sqrt(-e^2*x^4+d^2)/d^4/(e*x^2+d)+17/60*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/d^(5/2)/sqrt(e)/sqrt(-e^2*x^4+d^2)-16/105*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/d^(5/2)/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[(e*x^2+d)^3/sqrt(-e^2*x^4+d^2),x,7,-d*x*sqrt(-e^2*x^4+d^2)-1/5*e*x^3*sqrt(-e^2*x^4+d^2)+18/5*d^(7/2)*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/sqrt(e)/sqrt(-e^2*x^4+d^2)-8/5*d^(7/2)*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[(e*x^2+d)^2/sqrt(-e^2*x^4+d^2),x,6,-1/3*x*sqrt(-e^2*x^4+d^2)+2*d^(5/2)*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/sqrt(e)/sqrt(-e^2*x^4+d^2)-2/3*d^(5/2)*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[(e*x^2+d)/sqrt(-e^2*x^4+d^2),x,2,d^(3/2)*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[1/sqrt(-e^2*x^4+d^2),x,2,sqrt(d)*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[1/(e*x^2+d)/sqrt(-e^2*x^4+d^2),x,3,1/2*x*sqrt(-e^2*x^4+d^2)/d^2/(e*x^2+d)+1/2*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/sqrt(d)/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[1/(e*x^2+d)^2/sqrt(-e^2*x^4+d^2),x,7,1/6*x*sqrt(-e^2*x^4+d^2)/d^2/(e*x^2+d)^2+1/2*x*sqrt(-e^2*x^4+d^2)/d^3/(e*x^2+d)+1/2*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/d^(3/2)/sqrt(e)/sqrt(-e^2*x^4+d^2)-1/6*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/d^(3/2)/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[1/(e*x^2+d)^3/sqrt(-e^2*x^4+d^2),x,8,1/10*x*sqrt(-e^2*x^4+d^2)/d^2/(e*x^2+d)^3+1/5*x*sqrt(-e^2*x^4+d^2)/d^3/(e*x^2+d)^2+9/20*x*sqrt(-e^2*x^4+d^2)/d^4/(e*x^2+d)+9/20*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/d^(5/2)/sqrt(e)/sqrt(-e^2*x^4+d^2)-1/5*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/d^(5/2)/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[(e*x^2+d)^3/(-e^2*x^4+d^2)^(3/2),x,6,2*x*(e*x^2+d)/sqrt(-e^2*x^4+d^2)-3*d^(3/2)*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/sqrt(e)/sqrt(-e^2*x^4+d^2)+2*d^(3/2)*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[(e*x^2+d)^2/(-e^2*x^4+d^2)^(3/2),x,6,x*(e*x^2+d)/d/sqrt(-e^2*x^4+d^2)-sqrt(d)*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/sqrt(e)/sqrt(-e^2*x^4+d^2)+sqrt(d)*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[(e*x^2+d)/(-e^2*x^4+d^2)^(3/2),x,6,1/2*x*(e*x^2+d)/d^2/sqrt(-e^2*x^4+d^2)-1/2*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/sqrt(d)/sqrt(e)/sqrt(-e^2*x^4+d^2)+sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/sqrt(d)/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[1/(-e^2*x^4+d^2)^(3/2),x,3,1/2*x/d^2/sqrt(-e^2*x^4+d^2)+1/2*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/d^(3/2)/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[1/(e*x^2+d)/(-e^2*x^4+d^2)^(3/2),x,7,1/12*x*(-3*e*x^2+5*d)/d^4/sqrt(-e^2*x^4+d^2)+1/6*x/d^2/(e*x^2+d)/sqrt(-e^2*x^4+d^2)+1/4*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/d^(5/2)/sqrt(e)/sqrt(-e^2*x^4+d^2)+1/6*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/d^(5/2)/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[1/(e*x^2+d)^2/(-e^2*x^4+d^2)^(3/2),x,8,1/60*x*(-21*e*x^2+20*d)/d^5/sqrt(-e^2*x^4+d^2)+1/10*x/d^2/(e*x^2+d)^2/sqrt(-e^2*x^4+d^2)+7/30*x/d^3/(e*x^2+d)/sqrt(-e^2*x^4+d^2)+7/20*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/d^(7/2)/sqrt(e)/sqrt(-e^2*x^4+d^2)-1/60*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/d^(7/2)/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[1/(e*x^2+d)^3/(-e^2*x^4+d^2)^(3/2),x,9,3/56*x*(-7*e*x^2+5*d)/d^6/sqrt(-e^2*x^4+d^2)+1/14*x/d^2/(e*x^2+d)^3/sqrt(-e^2*x^4+d^2)+1/7*x/d^3/(e*x^2+d)^2/sqrt(-e^2*x^4+d^2)+1/4*x/d^4/(e*x^2+d)/sqrt(-e^2*x^4+d^2)+3/8*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/d^(9/2)/sqrt(e)/sqrt(-e^2*x^4+d^2)-3/28*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/d^(9/2)/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[(e*x^2+d)^3/(-e^2*x^4+d^2)^(5/2),x,7,2/3*x*(e*x^2+d)/(-e^2*x^4+d^2)^(3/2)+1/6*x*(3*e*x^2+d)/d^2/sqrt(-e^2*x^4+d^2)-1/2*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/sqrt(d)/sqrt(e)/sqrt(-e^2*x^4+d^2)+2/3*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/sqrt(d)/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[(e*x^2+d)^2/(-e^2*x^4+d^2)^(5/2),x,7,1/3*x*(e*x^2+d)/d/(-e^2*x^4+d^2)^(3/2)+1/6*x*(3*e*x^2+2*d)/d^3/sqrt(-e^2*x^4+d^2)-1/2*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/d^(3/2)/sqrt(e)/sqrt(-e^2*x^4+d^2)+5/6*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/d^(3/2)/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[(e*x^2+d)/(-e^2*x^4+d^2)^(5/2),x,7,1/6*x*(e*x^2+d)/d^2/(-e^2*x^4+d^2)^(3/2)+1/12*x*(3*e*x^2+5*d)/d^4/sqrt(-e^2*x^4+d^2)-1/4*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/d^(5/2)/sqrt(e)/sqrt(-e^2*x^4+d^2)+2/3*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/d^(5/2)/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[1/(-e^2*x^4+d^2)^(5/2),x,4,1/6*x/d^2/(-e^2*x^4+d^2)^(3/2)+5/12*x/d^4/sqrt(-e^2*x^4+d^2)+5/12*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/d^(7/2)/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[1/(e*x^2+d)/(-e^2*x^4+d^2)^(5/2),x,8,1/60*x*(-7*e*x^2+9*d)/d^4/(-e^2*x^4+d^2)^(3/2)+1/10*x/d^2/(e*x^2+d)/(-e^2*x^4+d^2)^(3/2)+1/40*x*(-7*e*x^2+15*d)/d^6/sqrt(-e^2*x^4+d^2)+7/40*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/d^(9/2)/sqrt(e)/sqrt(-e^2*x^4+d^2)+1/5*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/d^(9/2)/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[1/(e*x^2+d)^2/(-e^2*x^4+d^2)^(5/2),x,9,1/420*x*(-77*e*x^2+54*d)/d^5/(-e^2*x^4+d^2)^(3/2)+1/14*x/d^2/(e*x^2+d)^2/(-e^2*x^4+d^2)^(3/2)+11/70*x/d^3/(e*x^2+d)/(-e^2*x^4+d^2)^(3/2)+1/280*x*(-77*e*x^2+90*d)/d^7/sqrt(-e^2*x^4+d^2)+11/40*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/d^(11/2)/sqrt(e)/sqrt(-e^2*x^4+d^2)+13/280*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/d^(11/2)/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[1/(e*x^2+d)^3/(-e^2*x^4+d^2)^(5/2),x,10,1/360*x*(-77*e*x^2+39*d)/d^6/(-e^2*x^4+d^2)^(3/2)+1/18*x/d^2/(e*x^2+d)^3/(-e^2*x^4+d^2)^(3/2)+1/9*x/d^3/(e*x^2+d)^2/(-e^2*x^4+d^2)^(3/2)+11/60*x/d^4/(e*x^2+d)/(-e^2*x^4+d^2)^(3/2)+1/240*x*(-77*e*x^2+65*d)/d^8/sqrt(-e^2*x^4+d^2)+77/240*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/d^(13/2)/sqrt(e)/sqrt(-e^2*x^4+d^2)-1/20*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/d^(13/2)/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[(x^2+1)/sqrt(-x^4+1),x,1,EllipticE(sin(arcsin(x)),sqrt(-1)),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+1)/sqrt(x^4-1),x,2,sqrt(-x^4+1)*EllipticE(sin(arcsin(x)),sqrt(-1))/sqrt(x^4-1),1],
[1/(x^2+1)/sqrt(x^4-1),x,3,-1/2*x*sqrt(x^4-1)/(x^2+1)+1/2*sqrt(-x^4+1)*EllipticE(sin(arcsin(x)),sqrt(-1))/sqrt(x^4-1),1],
[(sqrt(a)+sqrt(c)*x^2)/sqrt(c*x^4-a),x,2,a^(3/4)*sqrt(1-c*x^4/a)*EllipticE(sin(arcsin(c^(1/4)*x/a^(1/4))),sqrt(-1))/c^(1/4)/sqrt(c*x^4-a),1],
[(1+sqrt(c/a)*x^2)/sqrt(c*x^4-a),x,2,sqrt(1-c*x^4/a)*EllipticE(sin(arcsin((c/a)^(1/4)*x)),sqrt(-1))/(c/a)^(1/4)/sqrt(c*x^4-a),1],
[(-e*x^2+d)^2/(-e^2*x^4+d^2)^(3/2),x,2,(-e*x^2+d)*EllipticE(sin(arctan(sqrt(e)*x/sqrt(d))),sqrt(2))/sqrt(d)/sqrt(e)/sqrt((-e*x^2+d)/(e*x^2+d))/sqrt(-e^2*x^4+d^2),1],
[sqrt(-e^2*x^4+d^2)/(e*x^2+d)^2,x,2,sqrt(-e^2*x^4+d^2)*EllipticE(sin(arctan(sqrt(e)*x/sqrt(d))),sqrt(2))/sqrt(d)/sqrt(e)/sqrt((-e*x^2+d)/(e*x^2+d))/(e*x^2+d),1],
[(-e*x^2+d)/(e*x^2+d)/sqrt(-e^2*x^4+d^2),x,3,(-e*x^2+d)*EllipticE(sin(arctan(sqrt(e)*x/sqrt(d))),sqrt(2))/sqrt(d)/sqrt(e)/sqrt((-e*x^2+d)/(e*x^2+d))/sqrt(-e^2*x^4+d^2),1],
[(-e*x^2+d)^3*sqrt(-e^2*x^4+d^2),x,8,2/21*d^2*x*(-7*e*x^2+5*d)*sqrt(-e^2*x^4+d^2)-3/7*d*x*(-e^2*x^4+d^2)^(3/2)+1/9*e*x^3*(-e^2*x^4+d^2)^(3/2)-4/3*d^(11/2)*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/sqrt(e)/sqrt(-e^2*x^4+d^2)+16/7*d^(11/2)*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[(-e*x^2+d)^2*sqrt(-e^2*x^4+d^2),x,7,2/105*d*x*(-21*e*x^2+20*d)*sqrt(-e^2*x^4+d^2)-1/7*x*(-e^2*x^4+d^2)^(3/2)-4/5*d^(9/2)*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/sqrt(e)/sqrt(-e^2*x^4+d^2)+164/105*d^(9/2)*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[(-e*x^2+d)*sqrt(-e^2*x^4+d^2),x,6,1/15*x*(-3*e*x^2+5*d)*sqrt(-e^2*x^4+d^2)-2/5*d^(7/2)*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/sqrt(e)/sqrt(-e^2*x^4+d^2)+16/15*d^(7/2)*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[sqrt(-e^2*x^4+d^2),x,3,1/3*x*sqrt(-e^2*x^4+d^2)+2/3*d^(5/2)*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[sqrt(-e^2*x^4+d^2)/(-e*x^2+d),x,3,d^(3/2)*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[sqrt(-e^2*x^4+d^2)/(-e*x^2+d)^2,x,7,x*(e*x^2+d)/d/sqrt(-e^2*x^4+d^2)-sqrt(d)*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/sqrt(e)/sqrt(-e^2*x^4+d^2)+sqrt(d)*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[sqrt(-e^2*x^4+d^2)/(-e*x^2+d)^3,x,7,1/3*x*sqrt(-e^2*x^4+d^2)/d/(-e*x^2+d)^2+1/2*x*sqrt(-e^2*x^4+d^2)/d^2/(-e*x^2+d)-1/2*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/sqrt(d)/sqrt(e)/sqrt(-e^2*x^4+d^2)+2/3*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/sqrt(d)/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[sqrt(-e^2*x^4+d^2)/(-e*x^2+d)^4,x,8,1/5*x*sqrt(-e^2*x^4+d^2)/d/(-e*x^2+d)^3+7/30*x*sqrt(-e^2*x^4+d^2)/d^2/(-e*x^2+d)^2+2/5*x*sqrt(-e^2*x^4+d^2)/d^3/(-e*x^2+d)-2/5*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/d^(3/2)/sqrt(e)/sqrt(-e^2*x^4+d^2)+17/30*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/d^(3/2)/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[sqrt(-e^2*x^4+d^2)/(-e*x^2+d)^5,x,9,1/7*x*sqrt(-e^2*x^4+d^2)/d/(-e*x^2+d)^4+11/70*x*sqrt(-e^2*x^4+d^2)/d^2/(-e*x^2+d)^3+41/210*x*sqrt(-e^2*x^4+d^2)/d^3/(-e*x^2+d)^2+7/20*x*sqrt(-e^2*x^4+d^2)/d^4/(-e*x^2+d)-7/20*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/d^(5/2)/sqrt(e)/sqrt(-e^2*x^4+d^2)+53/105*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/d^(5/2)/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[(-e*x^2+d)^3*(-e^2*x^4+d^2)^(3/2),x,9,4/715*d^4*x*(-77*e*x^2+65*d)*sqrt(-e^2*x^4+d^2)+2/429*d^2*x*(-77*e*x^2+39*d)*(-e^2*x^4+d^2)^(3/2)-3/11*d*x*(-e^2*x^4+d^2)^(5/2)+1/13*e*x^3*(-e^2*x^4+d^2)^(5/2)-56/65*d^(15/2)*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/sqrt(e)/sqrt(-e^2*x^4+d^2)+1136/715*d^(15/2)*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[(-e*x^2+d)^2*(-e^2*x^4+d^2)^(3/2),x,8,4/1155*d^3*x*(-77*e*x^2+90*d)*sqrt(-e^2*x^4+d^2)+2/693*d*x*(-77*e*x^2+54*d)*(-e^2*x^4+d^2)^(3/2)-1/11*x*(-e^2*x^4+d^2)^(5/2)-8/15*d^(13/2)*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/sqrt(e)/sqrt(-e^2*x^4+d^2)+1336/1155*d^(13/2)*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[(-e*x^2+d)*(-e^2*x^4+d^2)^(3/2),x,7,2/105*d^2*x*(-7*e*x^2+15*d)*sqrt(-e^2*x^4+d^2)+1/63*x*(-7*e*x^2+9*d)*(-e^2*x^4+d^2)^(3/2)-4/15*d^(11/2)*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/sqrt(e)/sqrt(-e^2*x^4+d^2)+88/105*d^(11/2)*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[(-e^2*x^4+d^2)^(3/2),x,4,2/7*d^2*x*sqrt(-e^2*x^4+d^2)+1/7*x*(-e^2*x^4+d^2)^(3/2)+4/7*d^(9/2)*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[(-e^2*x^4+d^2)^(3/2)/(-e*x^2+d),x,7,1/15*x*(3*e*x^2+5*d)*sqrt(-e^2*x^4+d^2)+2/5*d^(7/2)*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/sqrt(e)/sqrt(-e^2*x^4+d^2)+4/15*d^(7/2)*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[(-e^2*x^4+d^2)^(3/2)/(-e*x^2+d)^2,x,7,-1/3*x*sqrt(-e^2*x^4+d^2)+2*d^(5/2)*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/sqrt(e)/sqrt(-e^2*x^4+d^2)-2/3*d^(5/2)*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[(-e^2*x^4+d^2)^(3/2)/(-e*x^2+d)^3,x,7,2*x*sqrt(-e^2*x^4+d^2)/(-e*x^2+d)-3*d^(3/2)*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/sqrt(e)/sqrt(-e^2*x^4+d^2)+2*d^(3/2)*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[(-e^2*x^4+d^2)^(3/2)/(-e*x^2+d)^4,x,4,2/3*x*sqrt(-e^2*x^4+d^2)/(-e*x^2+d)^2+1/3*sqrt(d)*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[(-e^2*x^4+d^2)^(3/2)/(-e*x^2+d)^5,x,8,2/5*x*sqrt(-e^2*x^4+d^2)/(-e*x^2+d)^3+2/15*x*sqrt(-e^2*x^4+d^2)/d/(-e*x^2+d)^2+3/10*x*sqrt(-e^2*x^4+d^2)/d^2/(-e*x^2+d)-3/10*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/sqrt(d)/sqrt(e)/sqrt(-e^2*x^4+d^2)+7/15*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/sqrt(d)/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[(-e^2*x^4+d^2)^(3/2)/(-e*x^2+d)^6,x,9,2/7*x*sqrt(-e^2*x^4+d^2)/(-e*x^2+d)^4+4/35*x*sqrt(-e^2*x^4+d^2)/d/(-e*x^2+d)^3+11/70*x*sqrt(-e^2*x^4+d^2)/d^2/(-e*x^2+d)^2+3/10*x*sqrt(-e^2*x^4+d^2)/d^3/(-e*x^2+d)-3/10*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/d^(3/2)/sqrt(e)/sqrt(-e^2*x^4+d^2)+31/70*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/d^(3/2)/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[(-e^2*x^4+d^2)^(3/2)/(-e*x^2+d)^7,x,10,2/9*x*sqrt(-e^2*x^4+d^2)/(-e*x^2+d)^5+2/21*x*sqrt(-e^2*x^4+d^2)/d/(-e*x^2+d)^4+73/630*x*sqrt(-e^2*x^4+d^2)/d^2/(-e*x^2+d)^3+16/105*x*sqrt(-e^2*x^4+d^2)/d^3/(-e*x^2+d)^2+17/60*x*sqrt(-e^2*x^4+d^2)/d^4/(-e*x^2+d)-17/60*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/d^(5/2)/sqrt(e)/sqrt(-e^2*x^4+d^2)+29/70*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/d^(5/2)/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[(-e*x^2+d)^3/sqrt(-e^2*x^4+d^2),x,7,-d*x*sqrt(-e^2*x^4+d^2)+1/5*e*x^3*sqrt(-e^2*x^4+d^2)-18/5*d^(7/2)*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/sqrt(e)/sqrt(-e^2*x^4+d^2)+28/5*d^(7/2)*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[(-e*x^2+d)^2/sqrt(-e^2*x^4+d^2),x,6,-1/3*x*sqrt(-e^2*x^4+d^2)-2*d^(5/2)*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/sqrt(e)/sqrt(-e^2*x^4+d^2)+10/3*d^(5/2)*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[(-e*x^2+d)/sqrt(-e^2*x^4+d^2),x,5,-d^(3/2)*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/sqrt(e)/sqrt(-e^2*x^4+d^2)+2*d^(3/2)*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[1/sqrt(-e^2*x^4+d^2),x,2,sqrt(d)*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[1/(-e*x^2+d)/sqrt(-e^2*x^4+d^2),x,6,1/2*x*sqrt(-e^2*x^4+d^2)/d^2/(-e*x^2+d)-1/2*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/sqrt(d)/sqrt(e)/sqrt(-e^2*x^4+d^2)+sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/sqrt(d)/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[1/(-e*x^2+d)^2/sqrt(-e^2*x^4+d^2),x,7,1/6*x*sqrt(-e^2*x^4+d^2)/d^2/(-e*x^2+d)^2+1/2*x*sqrt(-e^2*x^4+d^2)/d^3/(-e*x^2+d)-1/2*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/d^(3/2)/sqrt(e)/sqrt(-e^2*x^4+d^2)+5/6*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/d^(3/2)/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[1/(-e*x^2+d)^3/sqrt(-e^2*x^4+d^2),x,8,1/10*x*sqrt(-e^2*x^4+d^2)/d^2/(-e*x^2+d)^3+1/5*x*sqrt(-e^2*x^4+d^2)/d^3/(-e*x^2+d)^2+9/20*x*sqrt(-e^2*x^4+d^2)/d^4/(-e*x^2+d)-9/20*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/d^(5/2)/sqrt(e)/sqrt(-e^2*x^4+d^2)+7/10*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/d^(5/2)/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[(-e*x^2+d)^4/(-e^2*x^4+d^2)^(3/2),x,7,4*d*x*(-e*x^2+d)/sqrt(-e^2*x^4+d^2)+1/3*x*sqrt(-e^2*x^4+d^2)+8*d^(5/2)*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/sqrt(e)/sqrt(-e^2*x^4+d^2)-34/3*d^(5/2)*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[(-e*x^2+d)^3/(-e^2*x^4+d^2)^(3/2),x,6,2*x*(-e*x^2+d)/sqrt(-e^2*x^4+d^2)+3*d^(3/2)*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/sqrt(e)/sqrt(-e^2*x^4+d^2)-4*d^(3/2)*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[(-e*x^2+d)^2/(-e^2*x^4+d^2)^(3/2),x,1,sqrt((-e*x^2+d)/(e*x^2+d))*(e*x^2+d)*EllipticE(sin(arctan(sqrt(e)*x/sqrt(d))),sqrt(2))/sqrt(d)/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[(-e*x^2+d)/(-e^2*x^4+d^2)^(3/2),x,3,1/2*x*(-e*x^2+d)/d^2/sqrt(-e^2*x^4+d^2)+1/2*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/sqrt(d)/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[1/(-e^2*x^4+d^2)^(3/2),x,3,1/2*x/d^2/sqrt(-e^2*x^4+d^2)+1/2*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/d^(3/2)/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[1/(-e*x^2+d)/(-e^2*x^4+d^2)^(3/2),x,7,1/6*x/d^2/(-e*x^2+d)/sqrt(-e^2*x^4+d^2)+1/12*x*(3*e*x^2+5*d)/d^4/sqrt(-e^2*x^4+d^2)-1/4*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/d^(5/2)/sqrt(e)/sqrt(-e^2*x^4+d^2)+2/3*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/d^(5/2)/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[1/(-e*x^2+d)^2/(-e^2*x^4+d^2)^(3/2),x,8,1/10*x/d^2/(-e*x^2+d)^2/sqrt(-e^2*x^4+d^2)+7/30*x/d^3/(-e*x^2+d)/sqrt(-e^2*x^4+d^2)+1/60*x*(21*e*x^2+20*d)/d^5/sqrt(-e^2*x^4+d^2)-7/20*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/d^(7/2)/sqrt(e)/sqrt(-e^2*x^4+d^2)+41/60*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/d^(7/2)/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[1/(-e*x^2+d)^3/(-e^2*x^4+d^2)^(3/2),x,9,1/14*x/d^2/(-e*x^2+d)^3/sqrt(-e^2*x^4+d^2)+1/7*x/d^3/(-e*x^2+d)^2/sqrt(-e^2*x^4+d^2)+1/4*x/d^4/(-e*x^2+d)/sqrt(-e^2*x^4+d^2)+3/56*x*(7*e*x^2+5*d)/d^6/sqrt(-e^2*x^4+d^2)-3/8*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/d^(9/2)/sqrt(e)/sqrt(-e^2*x^4+d^2)+9/14*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/d^(9/2)/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[(-e*x^2+d)^3/(-e^2*x^4+d^2)^(5/2),x,7,2/3*x*(-e*x^2+d)/(-e^2*x^4+d^2)^(3/2)+1/6*x*(-3*e*x^2+d)/d^2/sqrt(-e^2*x^4+d^2)+1/2*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/sqrt(d)/sqrt(e)/sqrt(-e^2*x^4+d^2)-1/3*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/sqrt(d)/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[(-e*x^2+d)^2/(-e^2*x^4+d^2)^(5/2),x,7,1/3*x*(-e*x^2+d)/d/(-e^2*x^4+d^2)^(3/2)+1/6*x*(-3*e*x^2+2*d)/d^3/sqrt(-e^2*x^4+d^2)+1/2*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/d^(3/2)/sqrt(e)/sqrt(-e^2*x^4+d^2)-1/6*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/d^(3/2)/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[(-e*x^2+d)/(-e^2*x^4+d^2)^(5/2),x,7,1/6*x*(-e*x^2+d)/d^2/(-e^2*x^4+d^2)^(3/2)+1/12*x*(-3*e*x^2+5*d)/d^4/sqrt(-e^2*x^4+d^2)+1/4*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/d^(5/2)/sqrt(e)/sqrt(-e^2*x^4+d^2)+1/6*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/d^(5/2)/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[1/(-e^2*x^4+d^2)^(5/2),x,4,1/6*x/d^2/(-e^2*x^4+d^2)^(3/2)+5/12*x/d^4/sqrt(-e^2*x^4+d^2)+5/12*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/d^(7/2)/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[1/(-e*x^2+d)/(-e^2*x^4+d^2)^(5/2),x,8,1/10*x/d^2/(-e*x^2+d)/(-e^2*x^4+d^2)^(3/2)+1/60*x*(7*e*x^2+9*d)/d^4/(-e^2*x^4+d^2)^(3/2)+1/40*x*(7*e*x^2+15*d)/d^6/sqrt(-e^2*x^4+d^2)-7/40*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/d^(9/2)/sqrt(e)/sqrt(-e^2*x^4+d^2)+11/20*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/d^(9/2)/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[1/(-e*x^2+d)^2/(-e^2*x^4+d^2)^(5/2),x,9,1/14*x/d^2/(-e*x^2+d)^2/(-e^2*x^4+d^2)^(3/2)+11/70*x/d^3/(-e*x^2+d)/(-e^2*x^4+d^2)^(3/2)+1/420*x*(77*e*x^2+54*d)/d^5/(-e^2*x^4+d^2)^(3/2)+1/280*x*(77*e*x^2+90*d)/d^7/sqrt(-e^2*x^4+d^2)-11/40*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/d^(11/2)/sqrt(e)/sqrt(-e^2*x^4+d^2)+167/280*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/d^(11/2)/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[1/(-e*x^2+d)^3/(-e^2*x^4+d^2)^(5/2),x,10,1/18*x/d^2/(-e*x^2+d)^3/(-e^2*x^4+d^2)^(3/2)+1/9*x/d^3/(-e*x^2+d)^2/(-e^2*x^4+d^2)^(3/2)+11/60*x/d^4/(-e*x^2+d)/(-e^2*x^4+d^2)^(3/2)+1/360*x*(77*e*x^2+39*d)/d^6/(-e^2*x^4+d^2)^(3/2)+1/240*x*(77*e*x^2+65*d)/d^8/sqrt(-e^2*x^4+d^2)-77/240*sqrt(1-e^2*x^4/d^2)*EllipticE(sin(arcsin(sqrt(e)*x/sqrt(d))),sqrt(-1))/d^(13/2)/sqrt(e)/sqrt(-e^2*x^4+d^2)+71/120*sqrt(1-e^2*x^4/d^2)*InverseJacobiAM(arcsin(sqrt(e)*x/sqrt(d)),sqrt(-1))/d^(13/2)/sqrt(e)/sqrt(-e^2*x^4+d^2),1],
[(-x^2+1)/sqrt(-x^4+1),x,3,-EllipticE(sin(arcsin(x)),sqrt(-1))+2*InverseJacobiAM(arcsin(x),sqrt(-1)),1],
[1/(-x^2+1)/sqrt(-x^4+1),x,4,x*sqrt(-x^4+1)/(-2*x^2+2)-1/2*EllipticE(sin(arcsin(x)),sqrt(-1))+InverseJacobiAM(arcsin(x),sqrt(-1)),1],
[(-x^2+1)/sqrt(x^4-1),x,5,-sqrt(-x^4+1)*EllipticE(sin(arcsin(x)),sqrt(-1))/sqrt(x^4-1)+2*sqrt(-x^4+1)*InverseJacobiAM(arcsin(x),sqrt(-1))/sqrt(x^4-1),1],
[1/(-x^2+1)/sqrt(x^4-1),x,6,-1/2*x*sqrt(x^4-1)/(-x^2+1)-1/2*sqrt(-x^4+1)*EllipticE(sin(arcsin(x)),sqrt(-1))/sqrt(x^4-1)+sqrt(-x^4+1)*InverseJacobiAM(arcsin(x),sqrt(-1))/sqrt(x^4-1),1],
[(e*x^2+d)^(5/2)*sqrt(-e^2*x^4+d^2),x,6,-13/128*d^3*x*sqrt(-e^2*x^4+d^2)/sqrt(e*x^2+d)+115/192*d^2*e*x^3*sqrt(-e^2*x^4+d^2)/sqrt(e*x^2+d)+23/48*d*e^2*x^5*sqrt(-e^2*x^4+d^2)/sqrt(e*x^2+d)+1/8*e^3*x^7*sqrt(-e^2*x^4+d^2)/sqrt(e*x^2+d)+141/128*d^4*arctan(sqrt(e)*x*sqrt(e*x^2+d)/sqrt(-e^2*x^4+d^2))/sqrt(e),1],
[(e*x^2+d)^(3/2)*sqrt(-e^2*x^4+d^2),x,5,3/16*d^2*x*sqrt(-e^2*x^4+d^2)/sqrt(e*x^2+d)+11/24*d*e*x^3*sqrt(-e^2*x^4+d^2)/sqrt(e*x^2+d)+1/6*e^2*x^5*sqrt(-e^2*x^4+d^2)/sqrt(e*x^2+d)+13/16*d^3*arctan(sqrt(e)*x*sqrt(e*x^2+d)/sqrt(-e^2*x^4+d^2))/sqrt(e),1],
[sqrt(e*x^2+d)*sqrt(-e^2*x^4+d^2),x,4,3/8*d*x*sqrt(-e^2*x^4+d^2)/sqrt(e*x^2+d)+1/4*e*x^3*sqrt(-e^2*x^4+d^2)/sqrt(e*x^2+d)+5/8*d^2*arctan(sqrt(e)*x*sqrt(e*x^2+d)/sqrt(-e^2*x^4+d^2))/sqrt(e),1],
[sqrt(-e^2*x^4+d^2)/sqrt(e*x^2+d),x,3,1/2*x*sqrt(-e^2*x^4+d^2)/sqrt(e*x^2+d)+1/2*d*arctan(sqrt(e)*x*sqrt(e*x^2+d)/sqrt(-e^2*x^4+d^2))/sqrt(e),1],
[sqrt(-e^2*x^4+d^2)/(e*x^2+d)^(3/2),x,5,-arctan(sqrt(e)*x*sqrt(e*x^2+d)/sqrt(-e^2*x^4+d^2))/sqrt(e)+sqrt(2)*arctan(sqrt(2)*sqrt(e)*x*sqrt(e*x^2+d)/sqrt(-e^2*x^4+d^2))/sqrt(e),1],
[sqrt(-e^2*x^4+d^2)/(e*x^2+d)^(5/2),x,4,1/2*x*sqrt(-e^2*x^4+d^2)/d/(e*x^2+d)^(3/2)+1/2*arctan(sqrt(2)*sqrt(e)*x*sqrt(e*x^2+d)/sqrt(-e^2*x^4+d^2))/sqrt(2)/d/sqrt(e),1],
[sqrt(-e^2*x^4+d^2)/(e*x^2+d)^(7/2),x,5,1/4*x*sqrt(-e^2*x^4+d^2)/d/(e*x^2+d)^(5/2)+5/16*x*sqrt(-e^2*x^4+d^2)/d^2/(e*x^2+d)^(3/2)+7/16*arctan(sqrt(2)*sqrt(e)*x*sqrt(e*x^2+d)/sqrt(-e^2*x^4+d^2))/sqrt(2)/d^2/sqrt(e),1],
[(e*x^2+d)^(5/2)*(-e^2*x^4+d^2)^(3/2),x,8,185/1024*d^5*x*sqrt(-e^2*x^4+d^2)/sqrt(e*x^2+d)+403/512*d^4*e*x^3*sqrt(-e^2*x^4+d^2)/sqrt(e*x^2+d)+55/128*d^3*e^2*x^5*sqrt(-e^2*x^4+d^2)/sqrt(e*x^2+d)-13/64*d^2*e^3*x^7*sqrt(-e^2*x^4+d^2)/sqrt(e*x^2+d)-7/24*d*e^4*x^9*sqrt(-e^2*x^4+d^2)/sqrt(e*x^2+d)-1/12*e^5*x^11*sqrt(-e^2*x^4+d^2)/sqrt(e*x^2+d)+839/1024*d^6*arctan(sqrt(e)*x*sqrt(e*x^2+d)/sqrt(-e^2*x^4+d^2))/sqrt(e),1],
[(e*x^2+d)^(3/2)*(-e^2*x^4+d^2)^(3/2),x,7,91/256*d^4*x*sqrt(-e^2*x^4+d^2)/sqrt(e*x^2+d)+73/128*d^3*e*x^3*sqrt(-e^2*x^4+d^2)/sqrt(e*x^2+d)+9/160*d^2*e^2*x^5*sqrt(-e^2*x^4+d^2)/sqrt(e*x^2+d)-19/80*d*e^3*x^7*sqrt(-e^2*x^4+d^2)/sqrt(e*x^2+d)-1/10*e^4*x^9*sqrt(-e^2*x^4+d^2)/sqrt(e*x^2+d)+165/256*d^5*arctan(sqrt(e)*x*sqrt(e*x^2+d)/sqrt(-e^2*x^4+d^2))/sqrt(e),1],
[sqrt(e*x^2+d)*(-e^2*x^4+d^2)^(3/2),x,6,61/128*d^3*x*sqrt(-e^2*x^4+d^2)/sqrt(e*x^2+d)+61/192*d^2*e*x^3*sqrt(-e^2*x^4+d^2)/sqrt(e*x^2+d)-7/48*d*e^2*x^5*sqrt(-e^2*x^4+d^2)/sqrt(e*x^2+d)-1/8*e^3*x^7*sqrt(-e^2*x^4+d^2)/sqrt(e*x^2+d)+67/128*d^4*arctan(sqrt(e)*x*sqrt(e*x^2+d)/sqrt(-e^2*x^4+d^2))/sqrt(e),1],
[(-e^2*x^4+d^2)^(3/2)/sqrt(e*x^2+d),x,5,9/16*d^2*x*sqrt(-e^2*x^4+d^2)/sqrt(e*x^2+d)+1/24*d*e*x^3*sqrt(-e^2*x^4+d^2)/sqrt(e*x^2+d)-1/6*e^2*x^5*sqrt(-e^2*x^4+d^2)/sqrt(e*x^2+d)+7/16*d^3*arctan(sqrt(e)*x*sqrt(e*x^2+d)/sqrt(-e^2*x^4+d^2))/sqrt(e),1],
[(-e^2*x^4+d^2)^(3/2)/(e*x^2+d)^(3/2),x,4,3/8*d*x*sqrt(-e^2*x^4+d^2)/sqrt(e*x^2+d)+1/4*x*(-e^2*x^4+d^2)^(3/2)/(e*x^2+d)^(3/2)+3/8*d^2*arctan(sqrt(e)*x*sqrt(e*x^2+d)/sqrt(-e^2*x^4+d^2))/sqrt(e),1],
[(-e^2*x^4+d^2)^(3/2)/(e*x^2+d)^(5/2),x,6,-1/2*x*sqrt(-e^2*x^4+d^2)/sqrt(e*x^2+d)-5/2*d*arctan(sqrt(e)*x*sqrt(e*x^2+d)/sqrt(-e^2*x^4+d^2))/sqrt(e)+2*sqrt(2)*d*arctan(sqrt(2)*sqrt(e)*x*sqrt(e*x^2+d)/sqrt(-e^2*x^4+d^2))/sqrt(e),1],
[(-e^2*x^4+d^2)^(3/2)/(e*x^2+d)^(7/2),x,7,x*sqrt(-e^2*x^4+d^2)/(e*x^2+d)^(3/2)+arctan(sqrt(e)*x*sqrt(e*x^2+d)/sqrt(-e^2*x^4+d^2))/sqrt(e)-arctan(sqrt(2)*sqrt(e)*x*sqrt(e*x^2+d)/sqrt(-e^2*x^4+d^2))/sqrt(2)/sqrt(e),1],
[(-e^2*x^4+d^2)^(3/2)/(e*x^2+d)^(9/2),x,6,1/2*x*sqrt(-e^2*x^4+d^2)/(e*x^2+d)^(5/2)+1/8*x*sqrt(-e^2*x^4+d^2)/d/(e*x^2+d)^(3/2)+3/8*arctan(sqrt(2)*sqrt(e)*x*sqrt(e*x^2+d)/sqrt(-e^2*x^4+d^2))/sqrt(2)/d/sqrt(e),1],
[(-e^2*x^4+d^2)^(3/2)/(e*x^2+d)^(11/2),x,6,1/3*x*sqrt(-e^2*x^4+d^2)/(e*x^2+d)^(7/2)+1/8*x*sqrt(-e^2*x^4+d^2)/d/(e*x^2+d)^(5/2)+19/96*x*sqrt(-e^2*x^4+d^2)/d^2/(e*x^2+d)^(3/2)+11/32*arctan(sqrt(2)*sqrt(e)*x*sqrt(e*x^2+d)/sqrt(-e^2*x^4+d^2))/sqrt(2)/d^2/sqrt(e),1],
[(-e^2*x^4+d^2)^(3/2)/(e*x^2+d)^(13/2),x,7,1/4*x*sqrt(-e^2*x^4+d^2)/(e*x^2+d)^(9/2)+5/48*x*sqrt(-e^2*x^4+d^2)/d/(e*x^2+d)^(7/2)+17/128*x*sqrt(-e^2*x^4+d^2)/d^2/(e*x^2+d)^(5/2)+299/1536*x*sqrt(-e^2*x^4+d^2)/d^3/(e*x^2+d)^(3/2)+163/512*arctan(sqrt(2)*sqrt(e)*x*sqrt(e*x^2+d)/sqrt(-e^2*x^4+d^2))/sqrt(2)/d^3/sqrt(e),1],
[(-e^2*x^4+d^2)^(3/2)/(e*x^2+d)^(15/2),x,8,1/5*x*sqrt(-e^2*x^4+d^2)/(e*x^2+d)^(11/2)+7/80*x*sqrt(-e^2*x^4+d^2)/d/(e*x^2+d)^(9/2)+33/320*x*sqrt(-e^2*x^4+d^2)/d^2/(e*x^2+d)^(7/2)+327/2560*x*sqrt(-e^2*x^4+d^2)/d^3/(e*x^2+d)^(5/2)+1887/10240*x*sqrt(-e^2*x^4+d^2)/d^4/(e*x^2+d)^(3/2)+609/2048*arctan(sqrt(2)*sqrt(e)*x*sqrt(e*x^2+d)/sqrt(-e^2*x^4+d^2))/sqrt(2)/d^4/sqrt(e),1],
[sqrt(x^2+1),x,2,1/2*x*sqrt(x^2+1)+1/2*arcsinh(x),1],
[sqrt(-x^4+1)/sqrt(-x^2+1),x,3,1/2*x*sqrt(x^2+1)+1/2*arcsinh(x),1],
[(e*x^2+d)^(7/2)/sqrt(-e^2*x^4+d^2),x,5,-47/16*d^2*x*sqrt(-e^2*x^4+d^2)/sqrt(e*x^2+d)-23/24*d*e*x^3*sqrt(-e^2*x^4+d^2)/sqrt(e*x^2+d)-1/6*e^2*x^5*sqrt(-e^2*x^4+d^2)/sqrt(e*x^2+d)+63/16*d^3*arctan(sqrt(e)*x*sqrt(e*x^2+d)/sqrt(-e^2*x^4+d^2))/sqrt(e),1],
[(e*x^2+d)^(5/2)/sqrt(-e^2*x^4+d^2),x,4,-11/8*d*x*sqrt(-e^2*x^4+d^2)/sqrt(e*x^2+d)-1/4*e*x^3*sqrt(-e^2*x^4+d^2)/sqrt(e*x^2+d)+19/8*d^2*arctan(sqrt(e)*x*sqrt(e*x^2+d)/sqrt(-e^2*x^4+d^2))/sqrt(e),1],
[(e*x^2+d)^(3/2)/sqrt(-e^2*x^4+d^2),x,4,-1/2*x*sqrt(-e^2*x^4+d^2)/sqrt(e*x^2+d)+3/2*d*arctan(sqrt(e)*x*sqrt(e*x^2+d)/sqrt(-e^2*x^4+d^2))/sqrt(e),1],
[sqrt(e*x^2+d)/sqrt(-e^2*x^4+d^2),x,2,arctan(sqrt(e)*x*sqrt(e*x^2+d)/sqrt(-e^2*x^4+d^2))/sqrt(e),1],
[1/sqrt(e*x^2+d)/sqrt(-e^2*x^4+d^2),x,2,arctan(sqrt(2)*sqrt(e)*x*sqrt(e*x^2+d)/sqrt(-e^2*x^4+d^2))/sqrt(2)/d/sqrt(e),1],
[1/(e*x^2+d)^(3/2)/sqrt(-e^2*x^4+d^2),x,4,1/4*x*sqrt(-e^2*x^4+d^2)/d^2/(e*x^2+d)^(3/2)+3/4*arctan(sqrt(2)*sqrt(e)*x*sqrt(e*x^2+d)/sqrt(-e^2*x^4+d^2))/sqrt(2)/d^2/sqrt(e),1],
[1/(e*x^2+d)^(5/2)/sqrt(-e^2*x^4+d^2),x,5,1/8*x*sqrt(-e^2*x^4+d^2)/d^2/(e*x^2+d)^(5/2)+9/32*x*sqrt(-e^2*x^4+d^2)/d^3/(e*x^2+d)^(3/2)+19/32*arctan(sqrt(2)*sqrt(e)*x*sqrt(e*x^2+d)/sqrt(-e^2*x^4+d^2))/sqrt(2)/d^3/sqrt(e),1],
[(-e*x^2+d)^(9/2)/(-e^2*x^4+d^2)^(3/2),x,6,8*d^2*x*sqrt(-e*x^2+d)/sqrt(-e^2*x^4+d^2)+19/8*d*x*sqrt(-e^2*x^4+d^2)/sqrt(-e*x^2+d)-1/4*e*x^3*sqrt(-e^2*x^4+d^2)/sqrt(-e*x^2+d)-75/8*d^2*arctanh(sqrt(e)*x*sqrt(-e*x^2+d)/sqrt(-e^2*x^4+d^2))/sqrt(e),1],
[(-e*x^2+d)^(7/2)/(-e^2*x^4+d^2)^(3/2),x,5,4*d*x*sqrt(-e*x^2+d)/sqrt(-e^2*x^4+d^2)+1/2*x*sqrt(-e^2*x^4+d^2)/sqrt(-e*x^2+d)-7/2*d*arctanh(sqrt(e)*x*sqrt(-e*x^2+d)/sqrt(-e^2*x^4+d^2))/sqrt(e),1],
[(-e*x^2+d)^(5/2)/(-e^2*x^4+d^2)^(3/2),x,4,2*x*sqrt(-e*x^2+d)/sqrt(-e^2*x^4+d^2)-arctanh(sqrt(e)*x*sqrt(-e*x^2+d)/sqrt(-e^2*x^4+d^2))/sqrt(e),1],
[(-e*x^2+d)^(3/2)/(-e^2*x^4+d^2)^(3/2),x,2,x*sqrt(-e*x^2+d)/d/sqrt(-e^2*x^4+d^2),1],
[sqrt(-e*x^2+d)/(-e^2*x^4+d^2)^(3/2),x,4,1/2*x*sqrt(-e*x^2+d)/d^2/sqrt(-e^2*x^4+d^2)+1/2*arctanh(sqrt(2)*sqrt(e)*x*sqrt(-e*x^2+d)/sqrt(-e^2*x^4+d^2))/sqrt(2)/d^2/sqrt(e),1],
[1/sqrt(-e*x^2+d)/(-e^2*x^4+d^2)^(3/2),x,5,1/4*x/d^2/sqrt(-e*x^2+d)/sqrt(-e^2*x^4+d^2)+1/8*x*sqrt(-e*x^2+d)/d^3/sqrt(-e^2*x^4+d^2)+5/8*arctanh(sqrt(2)*sqrt(e)*x*sqrt(-e*x^2+d)/sqrt(-e^2*x^4+d^2))/sqrt(2)/d^3/sqrt(e),1],
[1/(-e*x^2+d)^(3/2)/(-e^2*x^4+d^2)^(3/2),x,6,1/8*x/d^2/(-e*x^2+d)^(3/2)/sqrt(-e^2*x^4+d^2)+11/32*x/d^3/sqrt(-e*x^2+d)/sqrt(-e^2*x^4+d^2)-5/64*x*sqrt(-e*x^2+d)/d^4/sqrt(-e^2*x^4+d^2)+39/64*arctanh(sqrt(2)*sqrt(e)*x*sqrt(-e*x^2+d)/sqrt(-e^2*x^4+d^2))/sqrt(2)/d^4/sqrt(e),1],
[(-e*x^2+d)^(13/2)/(-e^2*x^4+d^2)^(5/2),x,7,16/3*d^3*x*(-e*x^2+d)^(3/2)/(-e^2*x^4+d^2)^(3/2)-64/3*d^2*x*sqrt(-e*x^2+d)/sqrt(-e^2*x^4+d^2)-27/8*d*x*sqrt(-e^2*x^4+d^2)/sqrt(-e*x^2+d)+1/4*e*x^3*sqrt(-e^2*x^4+d^2)/sqrt(-e*x^2+d)+163/8*d^2*arctanh(sqrt(e)*x*sqrt(-e*x^2+d)/sqrt(-e^2*x^4+d^2))/sqrt(e),1],
[(-e*x^2+d)^(11/2)/(-e^2*x^4+d^2)^(5/2),x,6,8/3*d^2*x*(-e*x^2+d)^(3/2)/(-e^2*x^4+d^2)^(3/2)-20/3*d*x*sqrt(-e*x^2+d)/sqrt(-e^2*x^4+d^2)-1/2*x*sqrt(-e^2*x^4+d^2)/sqrt(-e*x^2+d)+11/2*d*arctanh(sqrt(e)*x*sqrt(-e*x^2+d)/sqrt(-e^2*x^4+d^2))/sqrt(e),1],
[(-e*x^2+d)^(9/2)/(-e^2*x^4+d^2)^(5/2),x,5,4/3*d*x*(-e*x^2+d)^(3/2)/(-e^2*x^4+d^2)^(3/2)-4/3*x*sqrt(-e*x^2+d)/sqrt(-e^2*x^4+d^2)+arctanh(sqrt(e)*x*sqrt(-e*x^2+d)/sqrt(-e^2*x^4+d^2))/sqrt(e),1],
[(-e*x^2+d)^(7/2)/(-e^2*x^4+d^2)^(5/2),x,3,2/3*x*(-e*x^2+d)^(3/2)/(-e^2*x^4+d^2)^(3/2)+1/3*x*sqrt(-e*x^2+d)/d/sqrt(-e^2*x^4+d^2),1],
[(-e*x^2+d)^(5/2)/(-e^2*x^4+d^2)^(5/2),x,3,1/3*x*(-e*x^2+d)^(3/2)/d/(-e^2*x^4+d^2)^(3/2)+2/3*x*sqrt(-e*x^2+d)/d^2/sqrt(-e^2*x^4+d^2),1],
[(-e*x^2+d)^(3/2)/(-e^2*x^4+d^2)^(5/2),x,5,1/6*x*(-e*x^2+d)^(3/2)/d^2/(-e^2*x^4+d^2)^(3/2)+7/12*x*sqrt(-e*x^2+d)/d^3/sqrt(-e^2*x^4+d^2)+1/4*arctanh(sqrt(2)*sqrt(e)*x*sqrt(-e*x^2+d)/sqrt(-e^2*x^4+d^2))/sqrt(2)/d^3/sqrt(e),1],
[sqrt(-e*x^2+d)/(-e^2*x^4+d^2)^(5/2),x,6,1/4*x*sqrt(-e*x^2+d)/d^2/(-e^2*x^4+d^2)^(3/2)-1/24*x*(-e*x^2+d)^(3/2)/d^3/(-e^2*x^4+d^2)^(3/2)+17/48*x*sqrt(-e*x^2+d)/d^4/sqrt(-e^2*x^4+d^2)+7/16*arctanh(sqrt(2)*sqrt(e)*x*sqrt(-e*x^2+d)/sqrt(-e^2*x^4+d^2))/sqrt(2)/d^4/sqrt(e),1],
[1/sqrt(-e*x^2+d)/(-e^2*x^4+d^2)^(5/2),x,7,1/8*x/d^2/sqrt(-e*x^2+d)/(-e^2*x^4+d^2)^(3/2)+13/32*x*sqrt(-e*x^2+d)/d^3/(-e^2*x^4+d^2)^(3/2)-37/192*x*(-e*x^2+d)^(3/2)/d^4/(-e^2*x^4+d^2)^(3/2)+53/384*x*sqrt(-e*x^2+d)/d^5/sqrt(-e^2*x^4+d^2)+67/128*arctanh(sqrt(2)*sqrt(e)*x*sqrt(-e*x^2+d)/sqrt(-e^2*x^4+d^2))/sqrt(2)/d^5/sqrt(e),1],
[1/(-e*x^2+d)^(3/2)/(-e^2*x^4+d^2)^(5/2),x,8,1/12*x/d^2/(-e*x^2+d)^(3/2)/(-e^2*x^4+d^2)^(3/2)+19/96*x/d^3/sqrt(-e*x^2+d)/(-e^2*x^4+d^2)^(3/2)+61/128*x*sqrt(-e*x^2+d)/d^4/(-e^2*x^4+d^2)^(3/2)-71/256*x*(-e*x^2+d)^(3/2)/d^5/(-e^2*x^4+d^2)^(3/2)-9/512*x*sqrt(-e*x^2+d)/d^6/sqrt(-e^2*x^4+d^2)+275/512*arctanh(sqrt(2)*sqrt(e)*x*sqrt(-e*x^2+d)/sqrt(-e^2*x^4+d^2))/sqrt(2)/d^6/sqrt(e),1],
[sqrt(x^2+1)/sqrt(-x^4+1),x,2,arcsin(x),1],
[sqrt(-x^2+1)/sqrt(-x^4+1),x,2,arcsinh(x),1],
[sqrt(x^2-1)/sqrt(-x^4+1),x,2,arctan(x*sqrt(x^2-1)/sqrt(-x^4+1)),1],
[sqrt(-x^2-1)/sqrt(-x^4+1),x,2,arctanh(x*sqrt(-x^2-1)/sqrt(-x^4+1)),1],
[sqrt(x^2+1)/sqrt(x^4-1),x,2,arctanh(x*sqrt(x^2+1)/sqrt(x^4-1)),1],
[sqrt(-x^2+1)/sqrt(x^4-1),x,2,arctan(x*sqrt(-x^2+1)/sqrt(x^4-1)),1],
[sqrt(x^2-1)/sqrt(x^4-1),x,2,arctanh(x*sqrt(x^2-1)/sqrt(x^4-1)),1],
[sqrt(-x^2-1)/sqrt(x^4-1),x,2,arctan(x*sqrt(-x^2-1)/sqrt(x^4-1)),1],
[(-sqrt(x^2-1)+sqrt(x^2+1))/sqrt(x^4-1),x,6,-arctanh(x*sqrt(x^2-1)/sqrt(x^4-1))+arctanh(x*sqrt(x^2+1)/sqrt(x^4-1)),1],
[(3/2-3*x^2)^p,x,1,(3/2)^p*x*hypergeom([1/2, -p],[3/2],2*x^2),1],
[(-12*x^4+3)^p/((4*x^2+2)^p),x,2,(3/2)^p*x*hypergeom([1/2, -p],[3/2],2*x^2),1],
[(-e*x^2+2)^p*(e*x^2+2)^(p+q),x,2,2^(2*p+q)*x*AppellF1(1/2,-p,-p-q,3/2,1/2*e*x^2,-1/2*e*x^2),1],
[(e*x^2+2)^q*(-e^2*x^4+4)^p,x,3,2^(2*p+q)*x*AppellF1(1/2,-p,-p-q,3/2,1/2*e*x^2,-1/2*e*x^2),1],
[(-x^2+1)/sqrt(x^4+1),x,2,-x*sqrt(x^4+1)/(x^2+1)+(x^2+1)*sqrt((x^4+1)/(x^2+1)^2)*EllipticE(sin(2*arctan(x)),sqrt(1/2))/sqrt(x^4+1),1],
[(-e^2*x^2+1)/sqrt(e^4*x^4+1),x,2,-x*sqrt(e^4*x^4+1)/(e^2*x^2+1)+(e^2*x^2+1)*sqrt((e^4*x^4+1)/(e^2*x^2+1)^2)*EllipticE(sin(2*arctan(e*x)),sqrt(1/2))/e/sqrt(e^4*x^4+1),1],
[(-e*x^2+d)/sqrt(e^2*x^4+d^2),x,2,-x*sqrt(e^2*x^4+d^2)/(e*x^2+d)+sqrt(d)*(e*x^2+d)*sqrt((e^2*x^4+d^2)/(e*x^2+d)^2)*EllipticE(sin(2*arctan(sqrt(e)*x/sqrt(d))),sqrt(1/2))/sqrt(e)/sqrt(e^2*x^4+d^2),1],
[(-x^2+1)/sqrt(x^4+1),x,2,-x*sqrt(x^4+1)/(x^2+1)+(x^2+1)*sqrt((x^4+1)/(x^2+1)^2)*EllipticE(sin(2*arctan(x)),sqrt(1/2))/sqrt(x^4+1),1],
[1/(-x^2+1)/sqrt(x^4+1),x,4,1/2*arctanh(sqrt(2)*x/sqrt(x^4+1))/sqrt(2)+1/4*(x^2+1)*sqrt((x^4+1)/(x^2+1)^2)*InverseJacobiAM(2*arctan(x),sqrt(1/2))/sqrt(x^4+1),1],
[(-x^2+1)/sqrt(-x^4-1),x,2,x*sqrt(-x^4-1)/(x^2+1)+(x^2+1)*sqrt((x^4+1)/(x^2+1)^2)*EllipticE(sin(2*arctan(x)),sqrt(1/2))/sqrt(-x^4-1),1],
[1/(-x^2+1)/sqrt(-x^4-1),x,4,1/2*arctan(sqrt(2)*x/sqrt(-x^4-1))/sqrt(2)+1/4*(x^2+1)*sqrt((x^4+1)/(x^2+1)^2)*InverseJacobiAM(2*arctan(x),sqrt(1/2))/sqrt(-x^4-1),1],
[(x^2+1)/sqrt(x^4+1),x,4,x*sqrt(x^4+1)/(x^2+1)-(x^2+1)*sqrt((x^4+1)/(x^2+1)^2)*EllipticE(sin(2*arctan(x)),sqrt(1/2))/sqrt(x^4+1)+(x^2+1)*sqrt((x^4+1)/(x^2+1)^2)*InverseJacobiAM(2*arctan(x),sqrt(1/2))/sqrt(x^4+1),1],
[(e^2*x^2+1)/sqrt(e^4*x^4+1),x,4,x*sqrt(e^4*x^4+1)/(e^2*x^2+1)-(e^2*x^2+1)*sqrt((e^4*x^4+1)/(e^2*x^2+1)^2)*EllipticE(sin(2*arctan(e*x)),sqrt(1/2))/e/sqrt(e^4*x^4+1)+(e^2*x^2+1)*sqrt((e^4*x^4+1)/(e^2*x^2+1)^2)*InverseJacobiAM(2*arctan(e*x),sqrt(1/2))/e/sqrt(e^4*x^4+1),1],
[(e*x^2+d)/sqrt(e^2*x^4+d^2),x,4,x*sqrt(e^2*x^4+d^2)/(e*x^2+d)-sqrt(d)*(e*x^2+d)*sqrt((e^2*x^4+d^2)/(e*x^2+d)^2)*EllipticE(sin(2*arctan(sqrt(e)*x/sqrt(d))),sqrt(1/2))/sqrt(e)/sqrt(e^2*x^4+d^2)+sqrt(d)*(e*x^2+d)*sqrt((e^2*x^4+d^2)/(e*x^2+d)^2)*InverseJacobiAM(2*arctan(sqrt(e)*x/sqrt(d)),sqrt(1/2))/sqrt(e)/sqrt(e^2*x^4+d^2),1],
[(x^2+1)/sqrt(x^4+1),x,4,x*sqrt(x^4+1)/(x^2+1)-(x^2+1)*sqrt((x^4+1)/(x^2+1)^2)*EllipticE(sin(2*arctan(x)),sqrt(1/2))/sqrt(x^4+1)+(x^2+1)*sqrt((x^4+1)/(x^2+1)^2)*InverseJacobiAM(2*arctan(x),sqrt(1/2))/sqrt(x^4+1),1],
[1/(x^2+1)/sqrt(x^4+1),x,4,1/2*arctan(sqrt(2)*x/sqrt(x^4+1))/sqrt(2)+1/4*(x^2+1)*sqrt((x^4+1)/(x^2+1)^2)*InverseJacobiAM(2*arctan(x),sqrt(1/2))/sqrt(x^4+1),1],
[(x^2+1)/sqrt(-x^4-1),x,4,-x*sqrt(-x^4-1)/(x^2+1)-(x^2+1)*sqrt((x^4+1)/(x^2+1)^2)*EllipticE(sin(2*arctan(x)),sqrt(1/2))/sqrt(-x^4-1)+(x^2+1)*sqrt((x^4+1)/(x^2+1)^2)*InverseJacobiAM(2*arctan(x),sqrt(1/2))/sqrt(-x^4-1),1],
[1/(x^2+1)/sqrt(-x^4-1),x,4,1/2*arctanh(sqrt(2)*x/sqrt(-x^4-1))/sqrt(2)+1/4*(x^2+1)*sqrt((x^4+1)/(x^2+1)^2)*InverseJacobiAM(2*arctan(x),sqrt(1/2))/sqrt(-x^4-1),1],
[(C*x^4+A)/(b*x^2+a)^(5/4),x,4,-14/5*a*C*x/b^2/(b*x^2+a)^(1/4)+2/5*C*x*(b*x^2+a)^(3/4)/b^2+2/5*(5*A*b^2+12*C*a^2)*(1+b*x^2/a)^(1/4)*EllipticE(sin(1/2*arctan(sqrt(b)*x/sqrt(a))),sqrt(2))/sqrt(a)/b^(5/2)/(b*x^2+a)^(1/4),1],
[(d*x^2+c)/(b*x^4+a),x,8,-1/2*(sqrt(b)*c+sqrt(a)*d)*arctan(1-sqrt(2)*b^(1/4)*x/a^(1/4))/sqrt(2)/a^(3/4)/b^(3/4)+1/2*(sqrt(b)*c+sqrt(a)*d)*arctan(1+sqrt(2)*b^(1/4)*x/a^(1/4))/sqrt(2)/a^(3/4)/b^(3/4)+1/2*(sqrt(b)*c-sqrt(a)*d)*arctanh(sqrt(2)*a^(1/4)*b^(1/4)*x/(sqrt(a)+sqrt(b)*x^2))/sqrt(2)/a^(3/4)/b^(3/4),1],
[(-d*x^2+c)/(b*x^4+a),x,8,-1/2*(sqrt(b)*c-sqrt(a)*d)*arctan(1-sqrt(2)*b^(1/4)*x/a^(1/4))/sqrt(2)/a^(3/4)/b^(3/4)+1/2*(sqrt(b)*c-sqrt(a)*d)*arctan(1+sqrt(2)*b^(1/4)*x/a^(1/4))/sqrt(2)/a^(3/4)/b^(3/4)+1/2*(sqrt(b)*c+sqrt(a)*d)*arctanh(sqrt(2)*a^(1/4)*b^(1/4)*x/(sqrt(a)+sqrt(b)*x^2))/sqrt(2)/a^(3/4)/b^(3/4),1],
[(d*x^2+c)/(-b*x^4+a),x,3,1/2*(c-sqrt(a)*d/sqrt(b))*arctan(b^(1/4)*x/a^(1/4))/a^(3/4)/b^(1/4)+1/2*(sqrt(b)*c+sqrt(a)*d)*arctanh(b^(1/4)*x/a^(1/4))/a^(3/4)/b^(3/4),1],
[(-d*x^2+c)/(-b*x^4+a),x,3,1/2*(sqrt(b)*c+sqrt(a)*d)*arctan(b^(1/4)*x/a^(1/4))/a^(3/4)/b^(3/4)+1/2*(c-sqrt(a)*d/sqrt(b))*arctanh(b^(1/4)*x/a^(1/4))/a^(3/4)/b^(1/4),1],
[(3*x^2+2)/(9*x^4+4),x,5,-1/2*arctan(1-sqrt(3)*x)/sqrt(3)+1/2*arctan(1+sqrt(3)*x)/sqrt(3),1],
[(-3*x^2+2)/(9*x^4+4),x,2,1/2*arctanh(2*sqrt(3)*x/(3*x^2+2))/sqrt(3),1],
[(3*x^2+2)/(-9*x^4+4),x,2,arctanh(sqrt(3/2)*x)/sqrt(6),1],
[(-3*x^2+2)/(-9*x^4+4),x,2,arctan(sqrt(3/2)*x)/sqrt(6),1],
[(sqrt(a)*sqrt(b)+b*x^2)/(b*x^4+a),x,5,-b^(1/4)*arctan(1-sqrt(2)*b^(1/4)*x/a^(1/4))/sqrt(2)/a^(1/4)+b^(1/4)*arctan(1+sqrt(2)*b^(1/4)*x/a^(1/4))/sqrt(2)/a^(1/4),1],
[(sqrt(a)*sqrt(b)-b*x^2)/(b*x^4+a),x,2,b^(1/4)*arctanh(sqrt(2)*a^(1/4)*b^(1/4)*x/(sqrt(a)+sqrt(b)*x^2))/sqrt(2)/a^(1/4),1],
[(e*x^2+d)/(e^2*x^4+d^2),x,5,-arctan(1-sqrt(2)*sqrt(e)*x/sqrt(d))/sqrt(2)/sqrt(d)/sqrt(e)+arctan(1+sqrt(2)*sqrt(e)*x/sqrt(d))/sqrt(2)/sqrt(d)/sqrt(e),1],
[(-e*x^2+d)/(e^2*x^4+d^2),x,2,arctanh(sqrt(2)*sqrt(d)*sqrt(e)*x/(e*x^2+d))/sqrt(2)/sqrt(d)/sqrt(e),1],
[(2*x^2+5)/(x^4-1),x,3,-3/2*arctan(x)-7/2*arctanh(x),1],
[(e*x^2+d)*(-c*x^4+a)^(5/2),x,8,4/3003*a^2*x*(77*e*x^2+195*d)*sqrt(-c*x^4+a)+10/9009*a*x*(77*e*x^2+117*d)*(-c*x^4+a)^(3/2)+1/143*x*(11*e*x^2+13*d)*(-c*x^4+a)^(5/2)+8/39*a^(15/4)*e*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)+8/3003*a^(13/4)*(195*d-77*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)/sqrt(-c*x^4+a),1],
[(e*x^2+d)*(-c*x^4+a)^(3/2),x,7,2/105*a*x*(7*e*x^2+15*d)*sqrt(-c*x^4+a)+1/63*x*(7*e*x^2+9*d)*(-c*x^4+a)^(3/2)+4/15*a^(11/4)*e*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)+4/105*a^(9/4)*(15*d-7*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)/sqrt(-c*x^4+a),1],
[(e*x^2+d)*sqrt(-c*x^4+a),x,6,1/15*x*(3*e*x^2+5*d)*sqrt(-c*x^4+a)+2/5*a^(7/4)*e*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)+2/15*a^(5/4)*(5*d-3*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)/sqrt(-c*x^4+a),1],
[(e*x^2+d)/sqrt(-c*x^4+a),x,5,a^(3/4)*e*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)+a^(1/4)*(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)/sqrt(-c*x^4+a),1],
[(e*x^2+d)/(-c*x^4+a)^(3/2),x,6,1/2*x*(e*x^2+d)/a/sqrt(-c*x^4+a)-1/2*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)/sqrt(-c*x^4+a)+1/2*(sqrt(c)*d+sqrt(a)*e)*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],
[(e*x^2+d)/(-c*x^4+a)^(5/2),x,7,1/6*x*(e*x^2+d)/a/(-c*x^4+a)^(3/2)+1/12*x*(3*e*x^2+5*d)/a^2/sqrt(-c*x^4+a)-1/4*e*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*(5*sqrt(c)*d+3*sqrt(a)*e)*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],
[(e*x^2+d)*(-x^4+9)^(5/2),x,6,108/1001*x*(77*e*x^2+195*d)*sqrt(-x^4+9)+10/1001*x*(77*e*x^2+117*d)*(-x^4+9)^(3/2)+1/143*x*(11*e*x^2+13*d)*(-x^4+9)^(5/2)+1944/13*sqrt(3)*e*EllipticE(sin(arcsin(x/sqrt(3))),sqrt(-1))+1944/1001*sqrt(3)*(65*d-77*e)*InverseJacobiAM(arcsin(x/sqrt(3)),sqrt(-1)),1],
[(e*x^2+d)*(-x^4+9)^(3/2),x,5,6/35*x*(7*e*x^2+15*d)*sqrt(-x^4+9)+1/63*x*(7*e*x^2+9*d)*(-x^4+9)^(3/2)+108/5*sqrt(3)*e*EllipticE(sin(arcsin(x/sqrt(3))),sqrt(-1))+108/35*sqrt(3)*(5*d-7*e)*InverseJacobiAM(arcsin(x/sqrt(3)),sqrt(-1)),1],
[(e*x^2+d)*sqrt(-x^4+9),x,4,1/15*x*(3*e*x^2+5*d)*sqrt(-x^4+9)+18/5*sqrt(3)*e*EllipticE(sin(arcsin(x/sqrt(3))),sqrt(-1))+2/5*sqrt(3)*(5*d-9*e)*InverseJacobiAM(arcsin(x/sqrt(3)),sqrt(-1)),1],
[(e*x^2+d)/sqrt(-x^4+9),x,3,sqrt(3)*e*EllipticE(sin(arcsin(x/sqrt(3))),sqrt(-1))+(d-3*e)*InverseJacobiAM(arcsin(x/sqrt(3)),sqrt(-1))/sqrt(3),1],
[(e*x^2+d)/(-x^4+9)^(3/2),x,4,1/18*x*(e*x^2+d)/sqrt(-x^4+9)-1/6*e*EllipticE(sin(arcsin(x/sqrt(3))),sqrt(-1))/sqrt(3)+1/18*(d+3*e)*InverseJacobiAM(arcsin(x/sqrt(3)),sqrt(-1))/sqrt(3),1],
[(e*x^2+d)/(-x^4+9)^(5/2),x,5,1/54*x*(e*x^2+d)/(-x^4+9)^(3/2)+1/972*x*(3*e*x^2+5*d)/sqrt(-x^4+9)-1/108*e*EllipticE(sin(arcsin(x/sqrt(3))),sqrt(-1))/sqrt(3)+1/972*(5*d+9*e)*InverseJacobiAM(arcsin(x/sqrt(3)),sqrt(-1))/sqrt(3),1],
[(b*x^2+1)*(-b^2*x^4+1)^(5/2),x,6,4/3003*x*(77*b*x^2+195)*sqrt(-b^2*x^4+1)+10/9009*x*(77*b*x^2+117)*(-b^2*x^4+1)^(3/2)+1/143*x*(11*b*x^2+13)*(-b^2*x^4+1)^(5/2)+8/39*EllipticE(sin(arcsin(sqrt(b)*x)),sqrt(-1))/sqrt(b)+944/3003*InverseJacobiAM(arcsin(sqrt(b)*x),sqrt(-1))/sqrt(b),1],
[(b*x^2+1)*(-b^2*x^4+1)^(3/2),x,5,2/105*x*(7*b*x^2+15)*sqrt(-b^2*x^4+1)+1/63*x*(7*b*x^2+9)*(-b^2*x^4+1)^(3/2)+4/15*EllipticE(sin(arcsin(sqrt(b)*x)),sqrt(-1))/sqrt(b)+32/105*InverseJacobiAM(arcsin(sqrt(b)*x),sqrt(-1))/sqrt(b),1],
[(b*x^2+1)*sqrt(-b^2*x^4+1),x,4,1/15*x*(3*b*x^2+5)*sqrt(-b^2*x^4+1)+2/5*EllipticE(sin(arcsin(sqrt(b)*x)),sqrt(-1))/sqrt(b)+4/15*InverseJacobiAM(arcsin(sqrt(b)*x),sqrt(-1))/sqrt(b),1],
[(b*x^2+1)/sqrt(-b^2*x^4+1),x,1,EllipticE(sin(arcsin(sqrt(b)*x)),sqrt(-1))/sqrt(b),1],
[(b*x^2+1)/(-b^2*x^4+1)^(3/2),x,4,1/2*x*(b*x^2+1)/sqrt(-b^2*x^4+1)-1/2*EllipticE(sin(arcsin(sqrt(b)*x)),sqrt(-1))/sqrt(b)+InverseJacobiAM(arcsin(sqrt(b)*x),sqrt(-1))/sqrt(b),1],
[(b*x^2+1)/(-b^2*x^4+1)^(5/2),x,5,1/6*x*(b*x^2+1)/(-b^2*x^4+1)^(3/2)+1/12*x*(3*b*x^2+5)/sqrt(-b^2*x^4+1)-1/4*EllipticE(sin(arcsin(sqrt(b)*x)),sqrt(-1))/sqrt(b)+2/3*InverseJacobiAM(arcsin(sqrt(b)*x),sqrt(-1))/sqrt(b),1],
[(b*x^2+1)/(-b^2*x^4+1)^(7/2),x,6,1/10*x*(b*x^2+1)/(-b^2*x^4+1)^(5/2)+1/60*x*(7*b*x^2+9)/(-b^2*x^4+1)^(3/2)+1/40*x*(7*b*x^2+15)/sqrt(-b^2*x^4+1)-7/40*EllipticE(sin(arcsin(sqrt(b)*x)),sqrt(-1))/sqrt(b)+11/20*InverseJacobiAM(arcsin(sqrt(b)*x),sqrt(-1))/sqrt(b),1],
[(-b*x^2+1)*(-b^2*x^4+1)^(5/2),x,6,4/3003*x*(-77*b*x^2+195)*sqrt(-b^2*x^4+1)+10/9009*x*(-77*b*x^2+117)*(-b^2*x^4+1)^(3/2)+1/143*x*(-11*b*x^2+13)*(-b^2*x^4+1)^(5/2)-8/39*EllipticE(sin(arcsin(sqrt(b)*x)),sqrt(-1))/sqrt(b)+2176/3003*InverseJacobiAM(arcsin(sqrt(b)*x),sqrt(-1))/sqrt(b),1],
[(-b*x^2+1)*(-b^2*x^4+1)^(3/2),x,5,2/105*x*(-7*b*x^2+15)*sqrt(-b^2*x^4+1)+1/63*x*(-7*b*x^2+9)*(-b^2*x^4+1)^(3/2)-4/15*EllipticE(sin(arcsin(sqrt(b)*x)),sqrt(-1))/sqrt(b)+88/105*InverseJacobiAM(arcsin(sqrt(b)*x),sqrt(-1))/sqrt(b),1],
[(-b*x^2+1)*sqrt(-b^2*x^4+1),x,4,1/15*x*(-3*b*x^2+5)*sqrt(-b^2*x^4+1)-2/5*EllipticE(sin(arcsin(sqrt(b)*x)),sqrt(-1))/sqrt(b)+16/15*InverseJacobiAM(arcsin(sqrt(b)*x),sqrt(-1))/sqrt(b),1],
[(-b*x^2+1)/sqrt(-b^2*x^4+1),x,3,-EllipticE(sin(arcsin(sqrt(b)*x)),sqrt(-1))/sqrt(b)+2*InverseJacobiAM(arcsin(sqrt(b)*x),sqrt(-1))/sqrt(b),1],
[(-b*x^2+1)/(-b^2*x^4+1)^(3/2),x,2,1/2*x*(-b*x^2+1)/sqrt(-b^2*x^4+1)+1/2*EllipticE(sin(arcsin(sqrt(b)*x)),sqrt(-1))/sqrt(b),1],
[(-b*x^2+1)/(-b^2*x^4+1)^(5/2),x,5,1/6*x*(-b*x^2+1)/(-b^2*x^4+1)^(3/2)+1/12*x*(-3*b*x^2+5)/sqrt(-b^2*x^4+1)+1/4*EllipticE(sin(arcsin(sqrt(b)*x)),sqrt(-1))/sqrt(b)+1/6*InverseJacobiAM(arcsin(sqrt(b)*x),sqrt(-1))/sqrt(b),1],
[(-b*x^2+1)/(-b^2*x^4+1)^(7/2),x,6,1/10*x*(-b*x^2+1)/(-b^2*x^4+1)^(5/2)+1/60*x*(-7*b*x^2+9)/(-b^2*x^4+1)^(3/2)+1/40*x*(-7*b*x^2+15)/sqrt(-b^2*x^4+1)+7/40*EllipticE(sin(arcsin(sqrt(b)*x)),sqrt(-1))/sqrt(b)+1/5*InverseJacobiAM(arcsin(sqrt(b)*x),sqrt(-1))/sqrt(b),1],
[(-b*x^2+1)/(-b^2*x^4+1)^(9/2),x,7,1/14*x*(-b*x^2+1)/(-b^2*x^4+1)^(7/2)+1/140*x*(-11*b*x^2+13)/(-b^2*x^4+1)^(5/2)+1/840*x*(-77*b*x^2+117)/(-b^2*x^4+1)^(3/2)+1/560*x*(-77*b*x^2+195)/sqrt(-b^2*x^4+1)+11/80*EllipticE(sin(arcsin(sqrt(b)*x)),sqrt(-1))/sqrt(b)+59/280*InverseJacobiAM(arcsin(sqrt(b)*x),sqrt(-1))/sqrt(b),1],
[(e*x^2+d)*(c*x^4+a)^(5/2),x,7,8/39*a^3*e*x*sqrt(c*x^4+a)/sqrt(c)/(sqrt(a)+sqrt(c)*x^2)+4/3003*a^2*x*(77*e*x^2+195*d)*sqrt(c*x^4+a)+10/9009*a*x*(77*e*x^2+117*d)*(c*x^4+a)^(3/2)+1/143*x*(11*e*x^2+13*d)*(c*x^4+a)^(5/2)-8/39*a^(13/4)*e*(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)+4/3003*a^(11/4)*(195*sqrt(c)*d+77*sqrt(a)*e)*(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^(3/4)/sqrt(c*x^4+a),1],
[(e*x^2+d)*(c*x^4+a)^(3/2),x,6,4/15*a^2*e*x*sqrt(c*x^4+a)/sqrt(c)/(sqrt(a)+sqrt(c)*x^2)+2/105*a*x*(7*e*x^2+15*d)*sqrt(c*x^4+a)+1/63*x*(7*e*x^2+9*d)*(c*x^4+a)^(3/2)-4/15*a^(9/4)*e*(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)+2/105*a^(7/4)*(15*sqrt(c)*d+7*sqrt(a)*e)*(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^(3/4)/sqrt(c*x^4+a),1],
[(e*x^2+d)*sqrt(c*x^4+a),x,5,2/5*a*e*x*sqrt(c*x^4+a)/sqrt(c)/(sqrt(a)+sqrt(c)*x^2)+1/15*x*(3*e*x^2+5*d)*sqrt(c*x^4+a)-2/5*a^(5/4)*e*(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)+1/15*a^(3/4)*(5*sqrt(c)*d+3*sqrt(a)*e)*(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^(3/4)/sqrt(c*x^4+a),1],
[(e*x^2+d)/sqrt(c*x^4+a),x,4,e*x*sqrt(c*x^4+a)/sqrt(c)/(sqrt(a)+sqrt(c)*x^2)-a^(1/4)*e*(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(c)*d+sqrt(a)*e)*(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],
[(e*x^2+d)/(c*x^4+a)^(3/2),x,5,1/2*x*(e*x^2+d)/a/sqrt(c*x^4+a)-1/2*e*x*sqrt(c*x^4+a)/a/sqrt(c)/(sqrt(a)+sqrt(c)*x^2)+1/2*e*(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(c)*d-sqrt(a)*e)*(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],
[(e*x^2+d)/(c*x^4+a)^(5/2),x,6,1/6*x*(e*x^2+d)/a/(c*x^4+a)^(3/2)+1/12*x*(3*e*x^2+5*d)/a^2/sqrt(c*x^4+a)-1/4*e*x*sqrt(c*x^4+a)/a^2/sqrt(c)/(sqrt(a)+sqrt(c)*x^2)+1/4*e*(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^(7/4)/c^(3/4)/sqrt(c*x^4+a)+1/24*(5*sqrt(c)*d-3*sqrt(a)*e)*(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^(9/4)/c^(3/4)/sqrt(c*x^4+a),1],
[(e*x^2+d)*(x^4+9)^(5/2),x,7,1944*e*x*sqrt(x^4+9)/(13*x^2+39)+108/1001*x*(77*e*x^2+195*d)*sqrt(x^4+9)+10/1001*x*(77*e*x^2+117*d)*(x^4+9)^(3/2)+1/143*x*(11*e*x^2+13*d)*(x^4+9)^(5/2)-1944/13*sqrt(3)*e*(x^2+3)*sqrt((x^4+9)/(x^2+3)^2)*EllipticE(sin(2*arctan(x/sqrt(3))),sqrt(1/2))/sqrt(x^4+9)+972/1001*sqrt(3)*(65*d+77*e)*(x^2+3)*sqrt((x^4+9)/(x^2+3)^2)*InverseJacobiAM(2*arctan(x/sqrt(3)),sqrt(1/2))/sqrt(x^4+9),1],
[(e*x^2+d)*(x^4+9)^(3/2),x,6,108*e*x*sqrt(x^4+9)/(5*x^2+15)+6/35*x*(7*e*x^2+15*d)*sqrt(x^4+9)+1/63*x*(7*e*x^2+9*d)*(x^4+9)^(3/2)-108/5*sqrt(3)*e*(x^2+3)*sqrt((x^4+9)/(x^2+3)^2)*EllipticE(sin(2*arctan(x/sqrt(3))),sqrt(1/2))/sqrt(x^4+9)+54/35*sqrt(3)*(5*d+7*e)*(x^2+3)*sqrt((x^4+9)/(x^2+3)^2)*InverseJacobiAM(2*arctan(x/sqrt(3)),sqrt(1/2))/sqrt(x^4+9),1],
[(e*x^2+d)*sqrt(x^4+9),x,5,18*e*x*sqrt(x^4+9)/(5*x^2+15)+1/15*x*(3*e*x^2+5*d)*sqrt(x^4+9)-18/5*sqrt(3)*e*(x^2+3)*sqrt((x^4+9)/(x^2+3)^2)*EllipticE(sin(2*arctan(x/sqrt(3))),sqrt(1/2))/sqrt(x^4+9)+1/5*sqrt(3)*(5*d+9*e)*(x^2+3)*sqrt((x^4+9)/(x^2+3)^2)*InverseJacobiAM(2*arctan(x/sqrt(3)),sqrt(1/2))/sqrt(x^4+9),1],
[(e*x^2+d)/sqrt(x^4+9),x,4,e*x*sqrt(x^4+9)/(x^2+3)-sqrt(3)*e*(x^2+3)*sqrt((x^4+9)/(x^2+3)^2)*EllipticE(sin(2*arctan(x/sqrt(3))),sqrt(1/2))/sqrt(x^4+9)+1/2*(d+3*e)*(x^2+3)*sqrt((x^4+9)/(x^2+3)^2)*InverseJacobiAM(2*arctan(x/sqrt(3)),sqrt(1/2))/sqrt(3)/sqrt(x^4+9),1],
[(e*x^2+d)/(x^4+9)^(3/2),x,5,1/18*x*(e*x^2+d)/sqrt(x^4+9)-e*x*sqrt(x^4+9)/(18*x^2+54)+1/6*e*(x^2+3)*sqrt((x^4+9)/(x^2+3)^2)*EllipticE(sin(2*arctan(x/sqrt(3))),sqrt(1/2))/sqrt(3)/sqrt(x^4+9)+1/36*(d-3*e)*(x^2+3)*sqrt((x^4+9)/(x^2+3)^2)*InverseJacobiAM(2*arctan(x/sqrt(3)),sqrt(1/2))/sqrt(3)/sqrt(x^4+9),1],
[(e*x^2+d)/(x^4+9)^(5/2),x,6,1/54*x*(e*x^2+d)/(x^4+9)^(3/2)+1/972*x*(3*e*x^2+5*d)/sqrt(x^4+9)-e*x*sqrt(x^4+9)/(324*x^2+972)+1/108*e*(x^2+3)*sqrt((x^4+9)/(x^2+3)^2)*EllipticE(sin(2*arctan(x/sqrt(3))),sqrt(1/2))/sqrt(3)/sqrt(x^4+9)+1/1944*(5*d-9*e)*(x^2+3)*sqrt((x^4+9)/(x^2+3)^2)*InverseJacobiAM(2*arctan(x/sqrt(3)),sqrt(1/2))/sqrt(3)/sqrt(x^4+9),1],
[(-b*x^2+1)*(b^2*x^4+1)^(5/2),x,7,4/3003*x*(-77*b*x^2+195)*sqrt(b^2*x^4+1)-8*x*sqrt(b^2*x^4+1)/(39*b*x^2+39)+10/9009*x*(-77*b*x^2+117)*(b^2*x^4+1)^(3/2)+1/143*x*(-11*b*x^2+13)*(b^2*x^4+1)^(5/2)+8/39*(b*x^2+1)*sqrt((b^2*x^4+1)/(b*x^2+1)^2)*EllipticE(sin(2*arctan(sqrt(b)*x)),sqrt(1/2))/sqrt(b)/sqrt(b^2*x^4+1)+472/3003*(b*x^2+1)*sqrt((b^2*x^4+1)/(b*x^2+1)^2)*InverseJacobiAM(2*arctan(sqrt(b)*x),sqrt(1/2))/sqrt(b)/sqrt(b^2*x^4+1),1],
[(-b*x^2+1)*(b^2*x^4+1)^(3/2),x,6,2/105*x*(-7*b*x^2+15)*sqrt(b^2*x^4+1)-4*x*sqrt(b^2*x^4+1)/(15*b*x^2+15)+1/63*x*(-7*b*x^2+9)*(b^2*x^4+1)^(3/2)+4/15*(b*x^2+1)*sqrt((b^2*x^4+1)/(b*x^2+1)^2)*EllipticE(sin(2*arctan(sqrt(b)*x)),sqrt(1/2))/sqrt(b)/sqrt(b^2*x^4+1)+16/105*(b*x^2+1)*sqrt((b^2*x^4+1)/(b*x^2+1)^2)*InverseJacobiAM(2*arctan(sqrt(b)*x),sqrt(1/2))/sqrt(b)/sqrt(b^2*x^4+1),1],
[(-b*x^2+1)*sqrt(b^2*x^4+1),x,5,1/15*x*(-3*b*x^2+5)*sqrt(b^2*x^4+1)-2*x*sqrt(b^2*x^4+1)/(5*b*x^2+5)+2/5*(b*x^2+1)*sqrt((b^2*x^4+1)/(b*x^2+1)^2)*EllipticE(sin(2*arctan(sqrt(b)*x)),sqrt(1/2))/sqrt(b)/sqrt(b^2*x^4+1)+2/15*(b*x^2+1)*sqrt((b^2*x^4+1)/(b*x^2+1)^2)*InverseJacobiAM(2*arctan(sqrt(b)*x),sqrt(1/2))/sqrt(b)/sqrt(b^2*x^4+1),1],
[(-b*x^2+1)/sqrt(b^2*x^4+1),x,2,-x*sqrt(b^2*x^4+1)/(b*x^2+1)+(b*x^2+1)*sqrt((b^2*x^4+1)/(b*x^2+1)^2)*EllipticE(sin(2*arctan(sqrt(b)*x)),sqrt(1/2))/sqrt(b)/sqrt(b^2*x^4+1),1],
[(-b*x^2+1)/(b^2*x^4+1)^(3/2),x,5,1/2*x*(-b*x^2+1)/sqrt(b^2*x^4+1)+x*sqrt(b^2*x^4+1)/(2*b*x^2+2)-1/2*(b*x^2+1)*sqrt((b^2*x^4+1)/(b*x^2+1)^2)*EllipticE(sin(2*arctan(sqrt(b)*x)),sqrt(1/2))/sqrt(b)/sqrt(b^2*x^4+1)+1/2*(b*x^2+1)*sqrt((b^2*x^4+1)/(b*x^2+1)^2)*InverseJacobiAM(2*arctan(sqrt(b)*x),sqrt(1/2))/sqrt(b)/sqrt(b^2*x^4+1),1],
[(-b*x^2+1)/(b^2*x^4+1)^(5/2),x,6,1/6*x*(-b*x^2+1)/(b^2*x^4+1)^(3/2)+1/12*x*(-3*b*x^2+5)/sqrt(b^2*x^4+1)+x*sqrt(b^2*x^4+1)/(4*b*x^2+4)-1/4*(b*x^2+1)*sqrt((b^2*x^4+1)/(b*x^2+1)^2)*EllipticE(sin(2*arctan(sqrt(b)*x)),sqrt(1/2))/sqrt(b)/sqrt(b^2*x^4+1)+1/3*(b*x^2+1)*sqrt((b^2*x^4+1)/(b*x^2+1)^2)*InverseJacobiAM(2*arctan(sqrt(b)*x),sqrt(1/2))/sqrt(b)/sqrt(b^2*x^4+1),1],
[(-b*x^2+1)/(b^2*x^4+1)^(7/2),x,7,1/10*x*(-b*x^2+1)/(b^2*x^4+1)^(5/2)+1/60*x*(-7*b*x^2+9)/(b^2*x^4+1)^(3/2)+1/40*x*(-7*b*x^2+15)/sqrt(b^2*x^4+1)+7*x*sqrt(b^2*x^4+1)/(40*b*x^2+40)-7/40*(b*x^2+1)*sqrt((b^2*x^4+1)/(b*x^2+1)^2)*EllipticE(sin(2*arctan(sqrt(b)*x)),sqrt(1/2))/sqrt(b)/sqrt(b^2*x^4+1)+11/40*(b*x^2+1)*sqrt((b^2*x^4+1)/(b*x^2+1)^2)*InverseJacobiAM(2*arctan(sqrt(b)*x),sqrt(1/2))/sqrt(b)/sqrt(b^2*x^4+1),1],
[(b*x^2+1)*(b^2*x^4+1)^(3/2),x,6,4*x*sqrt(b^2*x^4+1)/(15*b*x^2+15)+2/105*x*(7*b*x^2+15)*sqrt(b^2*x^4+1)+1/63*x*(7*b*x^2+9)*(b^2*x^4+1)^(3/2)-4/15*(b*x^2+1)*sqrt((b^2*x^4+1)/(b*x^2+1)^2)*EllipticE(sin(2*arctan(sqrt(b)*x)),sqrt(1/2))/sqrt(b)/sqrt(b^2*x^4+1)+44/105*(b*x^2+1)*sqrt((b^2*x^4+1)/(b*x^2+1)^2)*InverseJacobiAM(2*arctan(sqrt(b)*x),sqrt(1/2))/sqrt(b)/sqrt(b^2*x^4+1),1],
[(b*x^2+1)*sqrt(b^2*x^4+1),x,5,2*x*sqrt(b^2*x^4+1)/(5*b*x^2+5)+1/15*x*(3*b*x^2+5)*sqrt(b^2*x^4+1)-2/5*(b*x^2+1)*sqrt((b^2*x^4+1)/(b*x^2+1)^2)*EllipticE(sin(2*arctan(sqrt(b)*x)),sqrt(1/2))/sqrt(b)/sqrt(b^2*x^4+1)+8/15*(b*x^2+1)*sqrt((b^2*x^4+1)/(b*x^2+1)^2)*InverseJacobiAM(2*arctan(sqrt(b)*x),sqrt(1/2))/sqrt(b)/sqrt(b^2*x^4+1),1],
[(b*x^2+1)/sqrt(b^2*x^4+1),x,4,x*sqrt(b^2*x^4+1)/(b*x^2+1)-(b*x^2+1)*sqrt((b^2*x^4+1)/(b*x^2+1)^2)*EllipticE(sin(2*arctan(sqrt(b)*x)),sqrt(1/2))/sqrt(b)/sqrt(b^2*x^4+1)+(b*x^2+1)*sqrt((b^2*x^4+1)/(b*x^2+1)^2)*InverseJacobiAM(2*arctan(sqrt(b)*x),sqrt(1/2))/sqrt(b)/sqrt(b^2*x^4+1),1],
[(b*x^2+1)/(b^2*x^4+1)^(3/2),x,3,1/2*x*(b*x^2+1)/sqrt(b^2*x^4+1)-x*sqrt(b^2*x^4+1)/(2*b*x^2+2)+1/2*(b*x^2+1)*sqrt((b^2*x^4+1)/(b*x^2+1)^2)*EllipticE(sin(2*arctan(sqrt(b)*x)),sqrt(1/2))/sqrt(b)/sqrt(b^2*x^4+1),1],
[(b*x^2+1)/(b^2*x^4+1)^(5/2),x,6,1/6*x*(b*x^2+1)/(b^2*x^4+1)^(3/2)+1/12*x*(3*b*x^2+5)/sqrt(b^2*x^4+1)-x*sqrt(b^2*x^4+1)/(4*b*x^2+4)+1/4*(b*x^2+1)*sqrt((b^2*x^4+1)/(b*x^2+1)^2)*EllipticE(sin(2*arctan(sqrt(b)*x)),sqrt(1/2))/sqrt(b)/sqrt(b^2*x^4+1)+1/12*(b*x^2+1)*sqrt((b^2*x^4+1)/(b*x^2+1)^2)*InverseJacobiAM(2*arctan(sqrt(b)*x),sqrt(1/2))/sqrt(b)/sqrt(b^2*x^4+1),1],
[(b*x^2+1)/(b^2*x^4+1)^(7/2),x,7,1/10*x*(b*x^2+1)/(b^2*x^4+1)^(5/2)+1/60*x*(7*b*x^2+9)/(b^2*x^4+1)^(3/2)+1/40*x*(7*b*x^2+15)/sqrt(b^2*x^4+1)-7*x*sqrt(b^2*x^4+1)/(40*b*x^2+40)+7/40*(b*x^2+1)*sqrt((b^2*x^4+1)/(b*x^2+1)^2)*EllipticE(sin(2*arctan(sqrt(b)*x)),sqrt(1/2))/sqrt(b)/sqrt(b^2*x^4+1)+1/10*(b*x^2+1)*sqrt((b^2*x^4+1)/(b*x^2+1)^2)*InverseJacobiAM(2*arctan(sqrt(b)*x),sqrt(1/2))/sqrt(b)/sqrt(b^2*x^4+1),1],
[(b*x^2+1)*(b^2*x^4-1)^(5/2),x,8,4/3003*x*(77*b*x^2+195)*sqrt(b^2*x^4-1)-10/9009*x*(77*b*x^2+117)*(b^2*x^4-1)^(3/2)+1/143*x*(11*b*x^2+13)*(b^2*x^4-1)^(5/2)-8/39*sqrt(-b^2*x^4+1)*EllipticE(sin(arcsin(sqrt(b)*x)),sqrt(-1))/sqrt(b)/sqrt(b^2*x^4-1)-944/3003*sqrt(-b^2*x^4+1)*InverseJacobiAM(arcsin(sqrt(b)*x),sqrt(-1))/sqrt(b)/sqrt(b^2*x^4-1),1],
[(b*x^2+1)*(b^2*x^4-1)^(3/2),x,7,-2/105*x*(7*b*x^2+15)*sqrt(b^2*x^4-1)+1/63*x*(7*b*x^2+9)*(b^2*x^4-1)^(3/2)+4/15*sqrt(-b^2*x^4+1)*EllipticE(sin(arcsin(sqrt(b)*x)),sqrt(-1))/sqrt(b)/sqrt(b^2*x^4-1)+32/105*sqrt(-b^2*x^4+1)*InverseJacobiAM(arcsin(sqrt(b)*x),sqrt(-1))/sqrt(b)/sqrt(b^2*x^4-1),1],
[(b*x^2+1)*sqrt(b^2*x^4-1),x,6,1/15*x*(3*b*x^2+5)*sqrt(b^2*x^4-1)-2/5*sqrt(-b^2*x^4+1)*EllipticE(sin(arcsin(sqrt(b)*x)),sqrt(-1))/sqrt(b)/sqrt(b^2*x^4-1)-4/15*sqrt(-b^2*x^4+1)*InverseJacobiAM(arcsin(sqrt(b)*x),sqrt(-1))/sqrt(b)/sqrt(b^2*x^4-1),1],
[(b*x^2+1)/sqrt(b^2*x^4-1),x,2,sqrt(-b^2*x^4+1)*EllipticE(sin(arcsin(sqrt(b)*x)),sqrt(-1))/sqrt(b)/sqrt(b^2*x^4-1),1],
[(b*x^2+1)/(b^2*x^4-1)^(3/2),x,6,-1/2*x*(b*x^2+1)/sqrt(b^2*x^4-1)+1/2*sqrt(-b^2*x^4+1)*EllipticE(sin(arcsin(sqrt(b)*x)),sqrt(-1))/sqrt(b)/sqrt(b^2*x^4-1)-sqrt(-b^2*x^4+1)*InverseJacobiAM(arcsin(sqrt(b)*x),sqrt(-1))/sqrt(b)/sqrt(b^2*x^4-1),1],
[(b*x^2+1)/(b^2*x^4-1)^(5/2),x,7,-1/6*x*(b*x^2+1)/(b^2*x^4-1)^(3/2)+1/12*x*(3*b*x^2+5)/sqrt(b^2*x^4-1)-1/4*sqrt(-b^2*x^4+1)*EllipticE(sin(arcsin(sqrt(b)*x)),sqrt(-1))/sqrt(b)/sqrt(b^2*x^4-1)+2/3*sqrt(-b^2*x^4+1)*InverseJacobiAM(arcsin(sqrt(b)*x),sqrt(-1))/sqrt(b)/sqrt(b^2*x^4-1),1],
[(b*x^2+1)/(b^2*x^4-1)^(7/2),x,8,-1/10*x*(b*x^2+1)/(b^2*x^4-1)^(5/2)+1/60*x*(7*b*x^2+9)/(b^2*x^4-1)^(3/2)-1/40*x*(7*b*x^2+15)/sqrt(b^2*x^4-1)+7/40*sqrt(-b^2*x^4+1)*EllipticE(sin(arcsin(sqrt(b)*x)),sqrt(-1))/sqrt(b)/sqrt(b^2*x^4-1)-11/20*sqrt(-b^2*x^4+1)*InverseJacobiAM(arcsin(sqrt(b)*x),sqrt(-1))/sqrt(b)/sqrt(b^2*x^4-1),1],
[(-b*x^2+1)*(b^2*x^4-1)^(3/2),x,7,-2/105*x*(-7*b*x^2+15)*sqrt(b^2*x^4-1)+1/63*x*(-7*b*x^2+9)*(b^2*x^4-1)^(3/2)-4/15*sqrt(-b^2*x^4+1)*EllipticE(sin(arcsin(sqrt(b)*x)),sqrt(-1))/sqrt(b)/sqrt(b^2*x^4-1)+88/105*sqrt(-b^2*x^4+1)*InverseJacobiAM(arcsin(sqrt(b)*x),sqrt(-1))/sqrt(b)/sqrt(b^2*x^4-1),1],
[(-b*x^2+1)*sqrt(b^2*x^4-1),x,6,1/15*x*(-3*b*x^2+5)*sqrt(b^2*x^4-1)+2/5*sqrt(-b^2*x^4+1)*EllipticE(sin(arcsin(sqrt(b)*x)),sqrt(-1))/sqrt(b)/sqrt(b^2*x^4-1)-16/15*sqrt(-b^2*x^4+1)*InverseJacobiAM(arcsin(sqrt(b)*x),sqrt(-1))/sqrt(b)/sqrt(b^2*x^4-1),1],
[(-b*x^2+1)/sqrt(b^2*x^4-1),x,5,-sqrt(-b^2*x^4+1)*EllipticE(sin(arcsin(sqrt(b)*x)),sqrt(-1))/sqrt(b)/sqrt(b^2*x^4-1)+2*sqrt(-b^2*x^4+1)*InverseJacobiAM(arcsin(sqrt(b)*x),sqrt(-1))/sqrt(b)/sqrt(b^2*x^4-1),1],
[(-b*x^2+1)/(b^2*x^4-1)^(3/2),x,3,-1/2*x*(-b*x^2+1)/sqrt(b^2*x^4-1)-1/2*sqrt(-b^2*x^4+1)*EllipticE(sin(arcsin(sqrt(b)*x)),sqrt(-1))/sqrt(b)/sqrt(b^2*x^4-1),1],
[(-b*x^2+1)/(b^2*x^4-1)^(5/2),x,7,-1/6*x*(-b*x^2+1)/(b^2*x^4-1)^(3/2)+1/12*x*(-3*b*x^2+5)/sqrt(b^2*x^4-1)+1/4*sqrt(-b^2*x^4+1)*EllipticE(sin(arcsin(sqrt(b)*x)),sqrt(-1))/sqrt(b)/sqrt(b^2*x^4-1)+1/6*sqrt(-b^2*x^4+1)*InverseJacobiAM(arcsin(sqrt(b)*x),sqrt(-1))/sqrt(b)/sqrt(b^2*x^4-1),1],
[(-b*x^2+1)/(b^2*x^4-1)^(7/2),x,8,-1/10*x*(-b*x^2+1)/(b^2*x^4-1)^(5/2)+1/60*x*(-7*b*x^2+9)/(b^2*x^4-1)^(3/2)-1/40*x*(-7*b*x^2+15)/sqrt(b^2*x^4-1)-7/40*sqrt(-b^2*x^4+1)*EllipticE(sin(arcsin(sqrt(b)*x)),sqrt(-1))/sqrt(b)/sqrt(b^2*x^4-1)-1/5*sqrt(-b^2*x^4+1)*InverseJacobiAM(arcsin(sqrt(b)*x),sqrt(-1))/sqrt(b)/sqrt(b^2*x^4-1),1],
[(-b*x^2+1)/(b^2*x^4-1)^(9/2),x,9,-1/14*x*(-b*x^2+1)/(b^2*x^4-1)^(7/2)+1/140*x*(-11*b*x^2+13)/(b^2*x^4-1)^(5/2)-1/840*x*(-77*b*x^2+117)/(b^2*x^4-1)^(3/2)+1/560*x*(-77*b*x^2+195)/sqrt(b^2*x^4-1)+11/80*sqrt(-b^2*x^4+1)*EllipticE(sin(arcsin(sqrt(b)*x)),sqrt(-1))/sqrt(b)/sqrt(b^2*x^4-1)+59/280*sqrt(-b^2*x^4+1)*InverseJacobiAM(arcsin(sqrt(b)*x),sqrt(-1))/sqrt(b)/sqrt(b^2*x^4-1),1],
[(-b*x^2+1)*(-b^2*x^4-1)^(5/2),x,7,4/3003*x*(-77*b*x^2+195)*sqrt(-b^2*x^4-1)-8*x*sqrt(-b^2*x^4-1)/(39*b*x^2+39)-10/9009*x*(-77*b*x^2+117)*(-b^2*x^4-1)^(3/2)+1/143*x*(-11*b*x^2+13)*(-b^2*x^4-1)^(5/2)-8/39*(b*x^2+1)*sqrt((b^2*x^4+1)/(b*x^2+1)^2)*EllipticE(sin(2*arctan(sqrt(b)*x)),sqrt(1/2))/sqrt(b)/sqrt(-b^2*x^4-1)-472/3003*(b*x^2+1)*sqrt((b^2*x^4+1)/(b*x^2+1)^2)*InverseJacobiAM(2*arctan(sqrt(b)*x),sqrt(1/2))/sqrt(b)/sqrt(-b^2*x^4-1),1],
[(-b*x^2+1)*(-b^2*x^4-1)^(3/2),x,6,-2/105*x*(-7*b*x^2+15)*sqrt(-b^2*x^4-1)+4*x*sqrt(-b^2*x^4-1)/(15*b*x^2+15)+1/63*x*(-7*b*x^2+9)*(-b^2*x^4-1)^(3/2)+4/15*(b*x^2+1)*sqrt((b^2*x^4+1)/(b*x^2+1)^2)*EllipticE(sin(2*arctan(sqrt(b)*x)),sqrt(1/2))/sqrt(b)/sqrt(-b^2*x^4-1)+16/105*(b*x^2+1)*sqrt((b^2*x^4+1)/(b*x^2+1)^2)*InverseJacobiAM(2*arctan(sqrt(b)*x),sqrt(1/2))/sqrt(b)/sqrt(-b^2*x^4-1),1],
[(-b*x^2+1)*sqrt(-b^2*x^4-1),x,5,1/15*x*(-3*b*x^2+5)*sqrt(-b^2*x^4-1)-2*x*sqrt(-b^2*x^4-1)/(5*b*x^2+5)-2/5*(b*x^2+1)*sqrt((b^2*x^4+1)/(b*x^2+1)^2)*EllipticE(sin(2*arctan(sqrt(b)*x)),sqrt(1/2))/sqrt(b)/sqrt(-b^2*x^4-1)-2/15*(b*x^2+1)*sqrt((b^2*x^4+1)/(b*x^2+1)^2)*InverseJacobiAM(2*arctan(sqrt(b)*x),sqrt(1/2))/sqrt(b)/sqrt(-b^2*x^4-1),1],
[(-b*x^2+1)/sqrt(-b^2*x^4-1),x,2,x*sqrt(-b^2*x^4-1)/(b*x^2+1)+(b*x^2+1)*sqrt((b^2*x^4+1)/(b*x^2+1)^2)*EllipticE(sin(2*arctan(sqrt(b)*x)),sqrt(1/2))/sqrt(b)/sqrt(-b^2*x^4-1),1],
[(-b*x^2+1)/(-b^2*x^4-1)^(3/2),x,5,-1/2*x*(-b*x^2+1)/sqrt(-b^2*x^4-1)+x*sqrt(-b^2*x^4-1)/(2*b*x^2+2)+1/2*(b*x^2+1)*sqrt((b^2*x^4+1)/(b*x^2+1)^2)*EllipticE(sin(2*arctan(sqrt(b)*x)),sqrt(1/2))/sqrt(b)/sqrt(-b^2*x^4-1)-1/2*(b*x^2+1)*sqrt((b^2*x^4+1)/(b*x^2+1)^2)*InverseJacobiAM(2*arctan(sqrt(b)*x),sqrt(1/2))/sqrt(b)/sqrt(-b^2*x^4-1),1],
[(-b*x^2+1)/(-b^2*x^4-1)^(5/2),x,6,-1/6*x*(-b*x^2+1)/(-b^2*x^4-1)^(3/2)+1/12*x*(-3*b*x^2+5)/sqrt(-b^2*x^4-1)-x*sqrt(-b^2*x^4-1)/(4*b*x^2+4)-1/4*(b*x^2+1)*sqrt((b^2*x^4+1)/(b*x^2+1)^2)*EllipticE(sin(2*arctan(sqrt(b)*x)),sqrt(1/2))/sqrt(b)/sqrt(-b^2*x^4-1)+1/3*(b*x^2+1)*sqrt((b^2*x^4+1)/(b*x^2+1)^2)*InverseJacobiAM(2*arctan(sqrt(b)*x),sqrt(1/2))/sqrt(b)/sqrt(-b^2*x^4-1),1],
[(-b*x^2+1)/(-b^2*x^4-1)^(7/2),x,7,-1/10*x*(-b*x^2+1)/(-b^2*x^4-1)^(5/2)+1/60*x*(-7*b*x^2+9)/(-b^2*x^4-1)^(3/2)-1/40*x*(-7*b*x^2+15)/sqrt(-b^2*x^4-1)+7*x*sqrt(-b^2*x^4-1)/(40*b*x^2+40)+7/40*(b*x^2+1)*sqrt((b^2*x^4+1)/(b*x^2+1)^2)*EllipticE(sin(2*arctan(sqrt(b)*x)),sqrt(1/2))/sqrt(b)/sqrt(-b^2*x^4-1)-11/40*(b*x^2+1)*sqrt((b^2*x^4+1)/(b*x^2+1)^2)*InverseJacobiAM(2*arctan(sqrt(b)*x),sqrt(1/2))/sqrt(b)/sqrt(-b^2*x^4-1),1],
[(b*x^2+1)*(-b^2*x^4-1)^(3/2),x,6,-4*x*sqrt(-b^2*x^4-1)/(15*b*x^2+15)-2/105*x*(7*b*x^2+15)*sqrt(-b^2*x^4-1)+1/63*x*(7*b*x^2+9)*(-b^2*x^4-1)^(3/2)-4/15*(b*x^2+1)*sqrt((b^2*x^4+1)/(b*x^2+1)^2)*EllipticE(sin(2*arctan(sqrt(b)*x)),sqrt(1/2))/sqrt(b)/sqrt(-b^2*x^4-1)+44/105*(b*x^2+1)*sqrt((b^2*x^4+1)/(b*x^2+1)^2)*InverseJacobiAM(2*arctan(sqrt(b)*x),sqrt(1/2))/sqrt(b)/sqrt(-b^2*x^4-1),1],
[(b*x^2+1)*sqrt(-b^2*x^4-1),x,5,2*x*sqrt(-b^2*x^4-1)/(5*b*x^2+5)+1/15*x*(3*b*x^2+5)*sqrt(-b^2*x^4-1)+2/5*(b*x^2+1)*sqrt((b^2*x^4+1)/(b*x^2+1)^2)*EllipticE(sin(2*arctan(sqrt(b)*x)),sqrt(1/2))/sqrt(b)/sqrt(-b^2*x^4-1)-8/15*(b*x^2+1)*sqrt((b^2*x^4+1)/(b*x^2+1)^2)*InverseJacobiAM(2*arctan(sqrt(b)*x),sqrt(1/2))/sqrt(b)/sqrt(-b^2*x^4-1),1],
[(b*x^2+1)/sqrt(-b^2*x^4-1),x,4,-x*sqrt(-b^2*x^4-1)/(b*x^2+1)-(b*x^2+1)*sqrt((b^2*x^4+1)/(b*x^2+1)^2)*EllipticE(sin(2*arctan(sqrt(b)*x)),sqrt(1/2))/sqrt(b)/sqrt(-b^2*x^4-1)+(b*x^2+1)*sqrt((b^2*x^4+1)/(b*x^2+1)^2)*InverseJacobiAM(2*arctan(sqrt(b)*x),sqrt(1/2))/sqrt(b)/sqrt(-b^2*x^4-1),1],
[(b*x^2+1)/(-b^2*x^4-1)^(3/2),x,3,-1/2*x*(b*x^2+1)/sqrt(-b^2*x^4-1)-x*sqrt(-b^2*x^4-1)/(2*b*x^2+2)-1/2*(b*x^2+1)*sqrt((b^2*x^4+1)/(b*x^2+1)^2)*EllipticE(sin(2*arctan(sqrt(b)*x)),sqrt(1/2))/sqrt(b)/sqrt(-b^2*x^4-1),1],
[(b*x^2+1)/(-b^2*x^4-1)^(5/2),x,6,-1/6*x*(b*x^2+1)/(-b^2*x^4-1)^(3/2)+1/12*x*(3*b*x^2+5)/sqrt(-b^2*x^4-1)+x*sqrt(-b^2*x^4-1)/(4*b*x^2+4)+1/4*(b*x^2+1)*sqrt((b^2*x^4+1)/(b*x^2+1)^2)*EllipticE(sin(2*arctan(sqrt(b)*x)),sqrt(1/2))/sqrt(b)/sqrt(-b^2*x^4-1)+1/12*(b*x^2+1)*sqrt((b^2*x^4+1)/(b*x^2+1)^2)*InverseJacobiAM(2*arctan(sqrt(b)*x),sqrt(1/2))/sqrt(b)/sqrt(-b^2*x^4-1),1],
[(b*x^2+1)/(-b^2*x^4-1)^(7/2),x,7,-1/10*x*(b*x^2+1)/(-b^2*x^4-1)^(5/2)+1/60*x*(7*b*x^2+9)/(-b^2*x^4-1)^(3/2)-1/40*x*(7*b*x^2+15)/sqrt(-b^2*x^4-1)-7*x*sqrt(-b^2*x^4-1)/(40*b*x^2+40)-7/40*(b*x^2+1)*sqrt((b^2*x^4+1)/(b*x^2+1)^2)*EllipticE(sin(2*arctan(sqrt(b)*x)),sqrt(1/2))/sqrt(b)/sqrt(-b^2*x^4-1)-1/10*(b*x^2+1)*sqrt((b^2*x^4+1)/(b*x^2+1)^2)*InverseJacobiAM(2*arctan(sqrt(b)*x),sqrt(1/2))/sqrt(b)/sqrt(-b^2*x^4-1),1],
[(b*x^2+1)/(-b^2*x^4-1)^(9/2),x,8,-1/14*x*(b*x^2+1)/(-b^2*x^4-1)^(7/2)+1/140*x*(11*b*x^2+13)/(-b^2*x^4-1)^(5/2)-1/840*x*(77*b*x^2+117)/(-b^2*x^4-1)^(3/2)+1/560*x*(77*b*x^2+195)/sqrt(-b^2*x^4-1)+11*x*sqrt(-b^2*x^4-1)/(80*b*x^2+80)+11/80*(b*x^2+1)*sqrt((b^2*x^4+1)/(b*x^2+1)^2)*EllipticE(sin(2*arctan(sqrt(b)*x)),sqrt(1/2))/sqrt(b)/sqrt(-b^2*x^4-1)+59/560*(b*x^2+1)*sqrt((b^2*x^4+1)/(b*x^2+1)^2)*InverseJacobiAM(2*arctan(sqrt(b)*x),sqrt(1/2))/sqrt(b)/sqrt(-b^2*x^4-1),1],
[(e*x^2+d)^4*(c*x^4+a),x,2,a*d^4*x+4/3*a*d^3*e*x^3+1/5*d^2*(6*a*e^2+c*d^2)*x^5+4/7*d*e*(a*e^2+c*d^2)*x^7+1/9*e^2*(a*e^2+6*c*d^2)*x^9+4/11*c*d*e^3*x^11+1/13*c*e^4*x^13,1],
[(e*x^2+d)^3*(c*x^4+a),x,2,a*d^3*x+a*d^2*e*x^3+1/5*d*(3*a*e^2+c*d^2)*x^5+1/7*e*(a*e^2+3*c*d^2)*x^7+1/3*c*d*e^2*x^9+1/11*c*e^3*x^11,1],
[(e*x^2+d)^2*(c*x^4+a),x,2,a*d^2*x+2/3*a*d*e*x^3+1/5*(a*e^2+c*d^2)*x^5+2/7*c*d*e*x^7+1/9*c*e^2*x^9,1],
[(e*x^2+d)*(c*x^4+a),x,2,a*d*x+1/3*a*e*x^3+1/5*c*d*x^5+1/7*c*e*x^7,1],
[(c*x^4+a)/(e*x^2+d),x,3,-c*d*x/e^2+1/3*c*x^3/e+(a*e^2+c*d^2)*arctan(sqrt(e)*x/sqrt(d))/sqrt(d)/e^(5/2),1],
[(c*x^4+a)/(e*x^2+d)^2,x,3,c*x/e^2+1/2*(a+c*d^2/e^2)*x/d/(e*x^2+d)-1/2*(-a*e^2+3*c*d^2)*arctan(sqrt(e)*x/sqrt(d))/d^(3/2)/e^(5/2),1],
[(c*x^4+a)/(e*x^2+d)^3,x,3,1/4*(a+c*d^2/e^2)*x/d/(e*x^2+d)^2+(3*a/d^2-5*c/e^2)*x/(8*e*x^2+8*d)+3/8*(a*e^2+c*d^2)*arctan(sqrt(e)*x/sqrt(d))/d^(5/2)/e^(5/2),1],
[(c*x^4+a)/(e*x^2+d)^4,x,4,1/6*(a+c*d^2/e^2)*x/d/(e*x^2+d)^3+1/24*(5*a/d^2-7*c/e^2)*x/(e*x^2+d)^2+1/16*(5*a/d^2+c/e^2)*x/d/(e*x^2+d)+1/16*(5*a*e^2+c*d^2)*arctan(sqrt(e)*x/sqrt(d))/d^(7/2)/e^(5/2),1],
[(e*x^2+d)^3*(c*x^4+a)^2,x,2,a^2*d^3*x+a^2*d^2*e*x^3+1/5*a*d*(3*a*e^2+2*c*d^2)*x^5+1/7*a*e*(a*e^2+6*c*d^2)*x^7+1/9*c*d*(6*a*e^2+c*d^2)*x^9+1/11*c*e*(2*a*e^2+3*c*d^2)*x^11+3/13*c^2*d*e^2*x^13+1/15*c^2*e^3*x^15,1],
[(e*x^2+d)^2*(c*x^4+a)^2,x,2,a^2*d^2*x+2/3*a^2*d*e*x^3+1/5*a*(a*e^2+2*c*d^2)*x^5+4/7*a*c*d*e*x^7+1/9*c*(2*a*e^2+c*d^2)*x^9+2/11*c^2*d*e*x^11+1/13*c^2*e^2*x^13,1],
[(e*x^2+d)*(c*x^4+a)^2,x,2,a^2*d*x+1/3*a^2*e*x^3+2/5*a*c*d*x^5+2/7*a*c*e*x^7+1/9*c^2*d*x^9+1/11*c^2*e*x^11,1],
[(c*x^4+a)^2,x,2,a^2*x+2/5*a*c*x^5+1/9*c^2*x^9,1],
[(c*x^4+a)^2/(e*x^2+d),x,3,-c*d*(2*a*e^2+c*d^2)*x/e^4+1/3*c*(2*a*e^2+c*d^2)*x^3/e^3-1/5*c^2*d*x^5/e^2+1/7*c^2*x^7/e+(a*e^2+c*d^2)^2*arctan(sqrt(e)*x/sqrt(d))/sqrt(d)/e^(9/2),1],
[(c*x^4+a)^2/(e*x^2+d)^2,x,4,c*(2*a*e^2+3*c*d^2)*x/e^4-2/3*c^2*d*x^3/e^3+1/5*c^2*x^5/e^2+1/2*(a*e^2+c*d^2)^2*x/d/e^4/(e*x^2+d)-1/2*(-a*e^2+7*c*d^2)*(a*e^2+c*d^2)*arctan(sqrt(e)*x/sqrt(d))/d^(3/2)/e^(9/2),1],
[(c*x^4+a)^2/(e*x^2+d)^3,x,5,-3*c^2*d*x/e^4+1/3*c^2*x^3/e^3+1/4*(a*e^2+c*d^2)^2*x/d/e^4/(e*x^2+d)^2-1/8*(-3*a*e^2+13*c*d^2)*(a*e^2+c*d^2)*x/d^2/e^4/(e*x^2+d)+1/8*(3*a^2*e^4+6*a*c*d^2*e^2+35*c^2*d^4)*arctan(sqrt(e)*x/sqrt(d))/d^(5/2)/e^(9/2),1],
[(c*x^4+a)^2/(e*x^2+d)^4,x,5,c^2*x/e^4+1/6*(a*e^2+c*d^2)^2*x/d/e^4/(e*x^2+d)^3-1/24*(-5*a*e^2+19*c*d^2)*(a*e^2+c*d^2)*x/d^2/e^4/(e*x^2+d)^2+1/16*(5*a^2*e^4+2*a*c*d^2*e^2+29*c^2*d^4)*x/d^3/e^4/(e*x^2+d)-1/16*(-5*a^2*e^4-2*a*c*d^2*e^2+35*c^2*d^4)*arctan(sqrt(e)*x/sqrt(d))/d^(7/2)/e^(9/2),1],
[(c*x^4+a)^2/(e*x^2+d)^5,x,5,1/8*(a*e^2+c*d^2)^2*x/d/e^4/(e*x^2+d)^4-1/48*(-7*a*e^2+25*c*d^2)*(a*e^2+c*d^2)*x/d^2/e^4/(e*x^2+d)^3+1/192*(35*a^2*e^4+6*a*c*d^2*e^2+163*c^2*d^4)*x/d^3/e^4/(e*x^2+d)^2-1/128*(-35*a^2*e^4-6*a*c*d^2*e^2+93*c^2*d^4)*x/d^4/e^4/(e*x^2+d)+1/128*(35*a^2*e^4+6*a*c*d^2*e^2+35*c^2*d^4)*arctan(sqrt(e)*x/sqrt(d))/d^(9/2)/e^(9/2),1],
[(e*x^2+d)^4/(c*x^4+a),x,10,e^2*(-a*e^2+6*c*d^2)*x/c^2+4/3*d*e^3*x^3/c+1/5*e^4*x^5/c-1/2*(c^2*d^4+4*sqrt(a)*c^(3/2)*d^3*e-6*a*c*d^2*e^2-4*a^(3/2)*sqrt(c)*d*e^3+a^2*e^4)*arctan(1-sqrt(2)*c^(1/4)*x/a^(1/4))/sqrt(2)/a^(3/4)/c^(9/4)+1/2*(c^2*d^4+4*sqrt(a)*c^(3/2)*d^3*e-6*a*c*d^2*e^2-4*a^(3/2)*sqrt(c)*d*e^3+a^2*e^4)*arctan(1+sqrt(2)*c^(1/4)*x/a^(1/4))/sqrt(2)/a^(3/4)/c^(9/4)+1/2*(c^2*d^4-4*sqrt(a)*c^(3/2)*d^3*e-6*a*c*d^2*e^2+4*a^(3/2)*sqrt(c)*d*e^3+a^2*e^4)*arctanh(sqrt(2)*a^(1/4)*c^(1/4)*x/(sqrt(a)+sqrt(c)*x^2))/sqrt(2)/a^(3/4)/c^(9/4),1],
[(e*x^2+d)^3/(c*x^4+a),x,10,3*d*e^2*x/c+1/3*e^3*x^3/c-1/2*(sqrt(c)*d*(-3*a*e^2+c*d^2)+sqrt(a)*e*(-a*e^2+3*c*d^2))*arctan(1-sqrt(2)*c^(1/4)*x/a^(1/4))/sqrt(2)/a^(3/4)/c^(7/4)+1/2*(sqrt(c)*d*(-3*a*e^2+c*d^2)+sqrt(a)*e*(-a*e^2+3*c*d^2))*arctan(1+sqrt(2)*c^(1/4)*x/a^(1/4))/sqrt(2)/a^(3/4)/c^(7/4)+1/2*(sqrt(c)*d*(-3*a*e^2+c*d^2)-sqrt(a)*e*(-a*e^2+3*c*d^2))*arctanh(sqrt(2)*a^(1/4)*c^(1/4)*x/(sqrt(a)+sqrt(c)*x^2))/sqrt(2)/a^(3/4)/c^(7/4),1],
[(e*x^2+d)^2/(c*x^4+a),x,9,e^2*x/c-1/2*(c*d^2+2*sqrt(a)*sqrt(c)*d*e-a*e^2)*arctan(1-sqrt(2)*c^(1/4)*x/a^(1/4))/sqrt(2)/a^(3/4)/c^(5/4)+1/2*(c*d^2+2*sqrt(a)*sqrt(c)*d*e-a*e^2)*arctan(1+sqrt(2)*c^(1/4)*x/a^(1/4))/sqrt(2)/a^(3/4)/c^(5/4)+1/2*(c*d^2-2*sqrt(a)*sqrt(c)*d*e-a*e^2)*arctanh(sqrt(2)*a^(1/4)*c^(1/4)*x/(sqrt(a)+sqrt(c)*x^2))/sqrt(2)/a^(3/4)/c^(5/4),1],
[(e*x^2+d)/(c*x^4+a),x,8,-1/2*(sqrt(c)*d+sqrt(a)*e)*arctan(1-sqrt(2)*c^(1/4)*x/a^(1/4))/sqrt(2)/a^(3/4)/c^(3/4)+1/2*(sqrt(c)*d+sqrt(a)*e)*arctan(1+sqrt(2)*c^(1/4)*x/a^(1/4))/sqrt(2)/a^(3/4)/c^(3/4)+1/2*(sqrt(c)*d-sqrt(a)*e)*arctanh(sqrt(2)*a^(1/4)*c^(1/4)*x/(sqrt(a)+sqrt(c)*x^2))/sqrt(2)/a^(3/4)/c^(3/4),1],
[1/(c*x^4+a),x,8,-1/2*arctan(1-sqrt(2)*c^(1/4)*x/a^(1/4))/sqrt(2)/a^(3/4)/c^(1/4)+1/2*arctan(1+sqrt(2)*c^(1/4)*x/a^(1/4))/sqrt(2)/a^(3/4)/c^(1/4)+1/2*arctanh(sqrt(2)*a^(1/4)*c^(1/4)*x/(sqrt(a)+sqrt(c)*x^2))/sqrt(2)/a^(3/4)/c^(1/4),1],
[1/(e*x^2+d)/(c*x^4+a),x,10,e^(3/2)*arctan(sqrt(e)*x/sqrt(d))/sqrt(d)/(a*e^2+c*d^2)-1/2*c^(1/4)*(sqrt(c)*d-sqrt(a)*e)*arctan(1-sqrt(2)*c^(1/4)*x/a^(1/4))/sqrt(2)/a^(3/4)/(a*e^2+c*d^2)+1/2*c^(1/4)*(sqrt(c)*d-sqrt(a)*e)*arctan(1+sqrt(2)*c^(1/4)*x/a^(1/4))/sqrt(2)/a^(3/4)/(a*e^2+c*d^2)+1/2*c^(1/4)*(sqrt(c)*d+sqrt(a)*e)*arctanh(sqrt(2)*a^(1/4)*c^(1/4)*x/(sqrt(a)+sqrt(c)*x^2))/sqrt(2)/a^(3/4)/(a*e^2+c*d^2),1],
[1/(e*x^2+d)^2/(c*x^4+a),x,12,1/2*e^2*x/d/(a*e^2+c*d^2)/(e*x^2+d)+1/2*e^(3/2)*(a*e^2+5*c*d^2)*arctan(sqrt(e)*x/sqrt(d))/d^(3/2)/(a*e^2+c*d^2)^2-1/2*c^(3/4)*(c*d^2-2*sqrt(a)*sqrt(c)*d*e-a*e^2)*arctan(1-sqrt(2)*c^(1/4)*x/a^(1/4))/sqrt(2)/a^(3/4)/(a*e^2+c*d^2)^2+1/2*c^(3/4)*(c*d^2-2*sqrt(a)*sqrt(c)*d*e-a*e^2)*arctan(1+sqrt(2)*c^(1/4)*x/a^(1/4))/sqrt(2)/a^(3/4)/(a*e^2+c*d^2)^2+1/2*c^(3/4)*(c*d^2+2*sqrt(a)*sqrt(c)*d*e-a*e^2)*arctanh(sqrt(2)*a^(1/4)*c^(1/4)*x/(sqrt(a)+sqrt(c)*x^2))/sqrt(2)/a^(3/4)/(a*e^2+c*d^2)^2,1],
[(e*x^2+d)^3/(c*x^4+a)^2,x,9,1/4*x*(c*d*(d^2-3*a*e^2/c)+e*(-a*e^2+3*c*d^2)*x^2)/a/c/(c*x^4+a)-3/8*(sqrt(c)*d+sqrt(a)*e)*(a*e^2+c*d^2)*arctan(1-sqrt(2)*c^(1/4)*x/a^(1/4))/sqrt(2)/a^(7/4)/c^(7/4)+3/8*(sqrt(c)*d+sqrt(a)*e)*(a*e^2+c*d^2)*arctan(1+sqrt(2)*c^(1/4)*x/a^(1/4))/sqrt(2)/a^(7/4)/c^(7/4)+3/8*(sqrt(c)*d-sqrt(a)*e)*(a*e^2+c*d^2)*arctanh(sqrt(2)*a^(1/4)*c^(1/4)*x/(sqrt(a)+sqrt(c)*x^2))/sqrt(2)/a^(7/4)/c^(7/4),1],
[(e*x^2+d)^2/(c*x^4+a)^2,x,9,1/4*x*(d^2-a*e^2/c+2*d*e*x^2)/a/(c*x^4+a)-1/8*(3*c*d^2+2*sqrt(a)*sqrt(c)*d*e+a*e^2)*arctan(1-sqrt(2)*c^(1/4)*x/a^(1/4))/sqrt(2)/a^(7/4)/c^(5/4)+1/8*(3*c*d^2+2*sqrt(a)*sqrt(c)*d*e+a*e^2)*arctan(1+sqrt(2)*c^(1/4)*x/a^(1/4))/sqrt(2)/a^(7/4)/c^(5/4)+1/8*(3*c*d^2-2*sqrt(a)*sqrt(c)*d*e+a*e^2)*arctanh(sqrt(2)*a^(1/4)*c^(1/4)*x/(sqrt(a)+sqrt(c)*x^2))/sqrt(2)/a^(7/4)/c^(5/4),1],
[(e*x^2+d)/(c*x^4+a)^2,x,9,1/4*x*(e*x^2+d)/a/(c*x^4+a)-1/8*(3*sqrt(c)*d+sqrt(a)*e)*arctan(1-sqrt(2)*c^(1/4)*x/a^(1/4))/sqrt(2)/a^(7/4)/c^(3/4)+1/8*(3*sqrt(c)*d+sqrt(a)*e)*arctan(1+sqrt(2)*c^(1/4)*x/a^(1/4))/sqrt(2)/a^(7/4)/c^(3/4)+1/8*(3*sqrt(c)*d-sqrt(a)*e)*arctanh(sqrt(2)*a^(1/4)*c^(1/4)*x/(sqrt(a)+sqrt(c)*x^2))/sqrt(2)/a^(7/4)/c^(3/4),1],
[1/(c*x^4+a)^2,x,9,1/4*x/a/(c*x^4+a)-3/8*arctan(1-sqrt(2)*c^(1/4)*x/a^(1/4))/sqrt(2)/a^(7/4)/c^(1/4)+3/8*arctan(1+sqrt(2)*c^(1/4)*x/a^(1/4))/sqrt(2)/a^(7/4)/c^(1/4)+3/8*arctanh(sqrt(2)*a^(1/4)*c^(1/4)*x/(sqrt(a)+sqrt(c)*x^2))/sqrt(2)/a^(7/4)/c^(1/4),1],
[1/(e*x^2+d)/(c*x^4+a)^2,x,12,1/4*c*x*(-e*x^2+d)/a/(a*e^2+c*d^2)/(c*x^4+a)+e^(7/2)*arctan(sqrt(e)*x/sqrt(d))/sqrt(d)/(a*e^2+c*d^2)^2+1/8*c^(1/4)*(sqrt(a)*e*(5*a*e^2+c*d^2)-sqrt(c)*d*(7*a*e^2+3*c*d^2))*arctan(1-sqrt(2)*c^(1/4)*x/a^(1/4))/sqrt(2)/a^(7/4)/(a*e^2+c*d^2)^2-1/8*c^(1/4)*(sqrt(a)*e*(5*a*e^2+c*d^2)-sqrt(c)*d*(7*a*e^2+3*c*d^2))*arctan(1+sqrt(2)*c^(1/4)*x/a^(1/4))/sqrt(2)/a^(7/4)/(a*e^2+c*d^2)^2+1/8*c^(1/4)*(sqrt(a)*e*(5*a*e^2+c*d^2)+sqrt(c)*d*(7*a*e^2+3*c*d^2))*arctanh(sqrt(2)*a^(1/4)*c^(1/4)*x/(sqrt(a)+sqrt(c)*x^2))/sqrt(2)/a^(7/4)/(a*e^2+c*d^2)^2,1],
[1/(e*x^2+d)^2/(c*x^4+a)^2,x,13,-1/2*e^2*(-a*e^2+c*d^2)*x/a/d/(a*e^2+c*d^2)^2/(e*x^2+d)+1/4*c*x*(-e*x^2+d)/a/(a*e^2+c*d^2)/(e*x^2+d)/(c*x^4+a)+1/2*e^(7/2)*(a*e^2+9*c*d^2)*arctan(sqrt(e)*x/sqrt(d))/d^(3/2)/(a*e^2+c*d^2)^3-1/8*c^(3/4)*(3*c^2*d^4-2*sqrt(a)*c^(3/2)*d^3*e+12*a*c*d^2*e^2-18*a^(3/2)*sqrt(c)*d*e^3-7*a^2*e^4)*arctan(1-sqrt(2)*c^(1/4)*x/a^(1/4))/sqrt(2)/a^(7/4)/(a*e^2+c*d^2)^3+1/8*c^(3/4)*(3*c^2*d^4-2*sqrt(a)*c^(3/2)*d^3*e+12*a*c*d^2*e^2-18*a^(3/2)*sqrt(c)*d*e^3-7*a^2*e^4)*arctan(1+sqrt(2)*c^(1/4)*x/a^(1/4))/sqrt(2)/a^(7/4)/(a*e^2+c*d^2)^3+1/8*c^(3/4)*(3*c^2*d^4+12*a*c*d^2*e^2-7*a^2*e^4+2*sqrt(a)*sqrt(c)*d*e*(9*a*e^2+c*d^2))*arctanh(sqrt(2)*a^(1/4)*c^(1/4)*x/(sqrt(a)+sqrt(c)*x^2))/sqrt(2)/a^(7/4)/(a*e^2+c*d^2)^3,1],
[(e*x^2+d)^(3/2)*(-c*x^4+a),x,6,3/128*d*(16*a-c*d^2/e^2)*x*sqrt(e*x^2+d)+1/64*(16*a-c*d^2/e^2)*x*(e*x^2+d)^(3/2)+1/16*c*d*x*(e*x^2+d)^(5/2)/e^2-1/8*c*x^3*(e*x^2+d)^(5/2)/e-3/128*d^2*(-16*a*e^2+c*d^2)*arctanh(sqrt(e)*x/sqrt(e*x^2+d))/e^(5/2),1],
[sqrt(e*x^2+d)*(-c*x^4+a),x,5,1/16*(8*a-c*d^2/e^2)*x*sqrt(e*x^2+d)+1/8*c*d*x*(e*x^2+d)^(3/2)/e^2-1/6*c*x^3*(e*x^2+d)^(3/2)/e-1/16*d*(-8*a*e^2+c*d^2)*arctanh(sqrt(e)*x/sqrt(e*x^2+d))/e^(5/2),1],
[(-c*x^4+a)/sqrt(e*x^2+d),x,4,3/8*c*d*x*sqrt(e*x^2+d)/e^2-1/4*c*x^3*sqrt(e*x^2+d)/e-1/8*(-8*a*e^2+3*c*d^2)*arctanh(sqrt(e)*x/sqrt(e*x^2+d))/e^(5/2),1],
[(-c*x^4+a)/(e*x^2+d)^(3/2),x,4,(a-c*d^2/e^2)*x/d/sqrt(e*x^2+d)-1/2*c*x*sqrt(e*x^2+d)/e^2+3/2*c*d*arctanh(sqrt(e)*x/sqrt(e*x^2+d))/e^(5/2),1],
[(-c*x^4+a)/(e*x^2+d)^(5/2),x,4,1/3*(a-c*d^2/e^2)*x/d/(e*x^2+d)^(3/2)+2/3*(a/d^2+2*c/e^2)*x/sqrt(e*x^2+d)-c*arctanh(sqrt(e)*x/sqrt(e*x^2+d))/e^(5/2),1],
[(-c*x^4+a)/(e*x^2+d)^(7/2),x,3,1/5*(a-c*d^2/e^2)*x/d/(e*x^2+d)^(5/2)+2/15*(2*a/d^2+3*c/e^2)*x/(e*x^2+d)^(3/2)+1/15*(8*a/d^2-3*c/e^2)*x/d/sqrt(e*x^2+d),1],
[(-c*x^4+a)/(e*x^2+d)^(9/2),x,4,1/7*(a-c*d^2/e^2)*x/d/(e*x^2+d)^(7/2)+2/35*(3*a/d^2+4*c/e^2)*x/(e*x^2+d)^(5/2)+1/35*(8*a/d^2-c/e^2)*x/d/(e*x^2+d)^(3/2)-2/35*(-8*a*e^2+c*d^2)*x/d^4/e^2/sqrt(e*x^2+d),1],
[(-c*x^4+a)/(e*x^2+d)^(11/2),x,5,1/9*(a-c*d^2/e^2)*x/d/(e*x^2+d)^(9/2)+2/63*(4*a/d^2+5*c/e^2)*x/(e*x^2+d)^(7/2)+1/105*(16*a/d^2-c/e^2)*x/d/(e*x^2+d)^(5/2)-4/315*(-16*a*e^2+c*d^2)*x/d^4/e^2/(e*x^2+d)^(3/2)-8/315*(-16*a*e^2+c*d^2)*x/d^5/e^2/sqrt(e*x^2+d),1],
[(e*x^2+d)^(3/2)*(-c*x^4+a)^2,x,8,1/1024*d*(384*a^2*e^4-48*a*c*d^2*e^2+7*c^2*d^4)*x*sqrt(e*x^2+d)/e^4+1/1536*(384*a^2*e^4-48*a*c*d^2*e^2+7*c^2*d^4)*x*(e*x^2+d)^(3/2)/e^4-1/384*c*d*(-48*a*e^2+7*c*d^2)*x*(e*x^2+d)^(5/2)/e^4+1/192*c*(-48*a*e^2+7*c*d^2)*x^3*(e*x^2+d)^(5/2)/e^3-7/120*c^2*d*x^5*(e*x^2+d)^(5/2)/e^2+1/12*c^2*x^7*(e*x^2+d)^(5/2)/e+1/1024*d^2*(384*a^2*e^4-48*a*c*d^2*e^2+7*c^2*d^4)*arctanh(sqrt(e)*x/sqrt(e*x^2+d))/e^(9/2),1],
[sqrt(e*x^2+d)*(-c*x^4+a)^2,x,7,1/256*(128*a^2*e^4-32*a*c*d^2*e^2+7*c^2*d^4)*x*sqrt(e*x^2+d)/e^4-1/128*c*d*(-32*a*e^2+7*c*d^2)*x*(e*x^2+d)^(3/2)/e^4+1/96*c*(-32*a*e^2+7*c*d^2)*x^3*(e*x^2+d)^(3/2)/e^3-7/80*c^2*d*x^5*(e*x^2+d)^(3/2)/e^2+1/10*c^2*x^7*(e*x^2+d)^(3/2)/e+1/256*d*(128*a^2*e^4-32*a*c*d^2*e^2+7*c^2*d^4)*arctanh(sqrt(e)*x/sqrt(e*x^2+d))/e^(9/2),1],
[(-c*x^4+a)^2/sqrt(e*x^2+d),x,6,-1/128*c*d*(-96*a*e^2+35*c*d^2)*x*sqrt(e*x^2+d)/e^4+1/192*c*(-96*a*e^2+35*c*d^2)*x^3*sqrt(e*x^2+d)/e^3-7/48*c^2*d*x^5*sqrt(e*x^2+d)/e^2+1/8*c^2*x^7*sqrt(e*x^2+d)/e+1/128*(128*a^2*e^4-96*a*c*d^2*e^2+35*c^2*d^4)*arctanh(sqrt(e)*x/sqrt(e*x^2+d))/e^(9/2),1],
[(-c*x^4+a)^2/(e*x^2+d)^(3/2),x,6,(-a*e^2+c*d^2)^2*x/d/e^4/sqrt(e*x^2+d)+1/16*c*(-16*a*e^2+19*c*d^2)*x*sqrt(e*x^2+d)/e^4-11/24*c^2*d*x^3*sqrt(e*x^2+d)/e^3+1/6*c^2*x^5*sqrt(e*x^2+d)/e^2-1/16*c*d*(-48*a*e^2+35*c*d^2)*arctanh(sqrt(e)*x/sqrt(e*x^2+d))/e^(9/2),1],
[(-c*x^4+a)^2/(e*x^2+d)^(5/2),x,6,1/3*(-a*e^2+c*d^2)^2*x/d/e^4/(e*x^2+d)^(3/2)-2/3*(-a*e^2+c*d^2)*(a*e^2+5*c*d^2)*x/d^2/e^4/sqrt(e*x^2+d)-11/8*c^2*d*x*sqrt(e*x^2+d)/e^4+1/4*c^2*x^3*sqrt(e*x^2+d)/e^3+1/8*c*(-16*a*e^2+35*c*d^2)*arctanh(sqrt(e)*x/sqrt(e*x^2+d))/e^(9/2),1],
[(-c*x^4+a)^2/(e*x^2+d)^(7/2),x,6,1/5*(-a*e^2+c*d^2)^2*x/d/e^4/(e*x^2+d)^(5/2)-4/15*(-a*e^2+c*d^2)*(a*e^2+4*c*d^2)*x/d^2/e^4/(e*x^2+d)^(3/2)+2/15*(4*a^2*e^4-3*a*c*d^2*e^2+29*c^2*d^4)*x/d^3/e^4/sqrt(e*x^2+d)+1/2*c^2*x*sqrt(e*x^2+d)/e^4-7/2*c^2*d*arctanh(sqrt(e)*x/sqrt(e*x^2+d))/e^(9/2),1],
[(-c*x^4+a)^2/(e*x^2+d)^(9/2),x,6,1/7*(-a*e^2+c*d^2)^2*x/d/e^4/(e*x^2+d)^(7/2)-2/35*(-a*e^2+c*d^2)*(3*a*e^2+11*c*d^2)*x/d^2/e^4/(e*x^2+d)^(5/2)+2/105*(12*a^2*e^4-3*a*c*d^2*e^2+61*c^2*d^4)*x/d^3/e^4/(e*x^2+d)^(3/2)-4/105*(-12*a^2*e^4+3*a*c*d^2*e^2+44*c^2*d^4)*x/d^4/e^4/sqrt(e*x^2+d)+c^2*arctanh(sqrt(e)*x/sqrt(e*x^2+d))/e^(9/2),1],
[(-c*x^4+a)^2/(e*x^2+d)^(11/2),x,5,1/9*(-a*e^2+c*d^2)^2*x/d/e^4/(e*x^2+d)^(9/2)-4/63*(-a*e^2+c*d^2)*(2*a*e^2+7*c*d^2)*x/d^2/e^4/(e*x^2+d)^(7/2)+2/105*(8*a^2*e^4-a*c*d^2*e^2+35*c^2*d^4)*x/d^3/e^4/(e*x^2+d)^(5/2)-4/315*(-16*a^2*e^4+2*a*c*d^2*e^2+35*c^2*d^4)*x/d^4/e^4/(e*x^2+d)^(3/2)+1/315*(128*a^2*e^4-16*a*c*d^2*e^2+35*c^2*d^4)*x/d^5/e^4/sqrt(e*x^2+d),1],
[(-c*x^4+a)^2/(e*x^2+d)^(13/2),x,6,1/11*(-a*e^2+c*d^2)^2*x/d/e^4/(e*x^2+d)^(11/2)-2/99*(-a*e^2+c*d^2)*(5*a*e^2+17*c*d^2)*x/d^2/e^4/(e*x^2+d)^(9/2)+2/693*(40*a^2*e^4-3*a*c*d^2*e^2+161*c^2*d^4)*x/d^3/e^4/(e*x^2+d)^(7/2)-4/1155*(-40*a^2*e^4+3*a*c*d^2*e^2+70*c^2*d^4)*x/d^4/e^4/(e*x^2+d)^(5/2)+1/3465*(640*a^2*e^4-48*a*c*d^2*e^2+35*c^2*d^4)*x/d^5/e^4/(e*x^2+d)^(3/2)+2/3465*(640*a^2*e^4-48*a*c*d^2*e^2+35*c^2*d^4)*x/d^6/e^4/sqrt(e*x^2+d),1],
[(e*x^2+d)^(7/2)/(-c*x^4+a),x,9,-13/8*d*e^2*x*sqrt(e*x^2+d)/c-1/4*e^3*x^3*sqrt(e*x^2+d)/c+1/2*(sqrt(c)*d-sqrt(a)*e)^(7/2)*arctan(sqrt(sqrt(c)*d-sqrt(a)*e)*x/a^(1/4)/sqrt(e*x^2+d))/a^(3/4)/c^2-1/8*e^(3/2)*(8*a*e^2+35*c*d^2)*arctanh(sqrt(e)*x/sqrt(e*x^2+d))/c^2+1/2*(sqrt(c)*d+sqrt(a)*e)^(7/2)*arctanh(sqrt(sqrt(c)*d+sqrt(a)*e)*x/a^(1/4)/sqrt(e*x^2+d))/a^(3/4)/c^2,1],
[(e*x^2+d)^(5/2)/(-c*x^4+a),x,8,-1/2*e^2*x*sqrt(e*x^2+d)/c+1/2*(sqrt(c)*d-sqrt(a)*e)^(5/2)*arctan(sqrt(sqrt(c)*d-sqrt(a)*e)*x/a^(1/4)/sqrt(e*x^2+d))/a^(3/4)/c^(3/2)-5/2*d*e^(3/2)*arctanh(sqrt(e)*x/sqrt(e*x^2+d))/c+1/2*(sqrt(c)*d+sqrt(a)*e)^(5/2)*arctanh(sqrt(sqrt(c)*d+sqrt(a)*e)*x/a^(1/4)/sqrt(e*x^2+d))/a^(3/4)/c^(3/2),1],
[(e*x^2+d)^(3/2)/(-c*x^4+a),x,7,1/2*(sqrt(c)*d-sqrt(a)*e)^(3/2)*arctan(sqrt(sqrt(c)*d-sqrt(a)*e)*x/a^(1/4)/sqrt(e*x^2+d))/a^(3/4)/c-e^(3/2)*arctanh(sqrt(e)*x/sqrt(e*x^2+d))/c+1/2*(sqrt(c)*d+sqrt(a)*e)^(3/2)*arctanh(sqrt(sqrt(c)*d+sqrt(a)*e)*x/a^(1/4)/sqrt(e*x^2+d))/a^(3/4)/c,1],
[sqrt(e*x^2+d)/(-c*x^4+a),x,5,1/2*sqrt(sqrt(c)*d-sqrt(a)*e)*arctan(sqrt(sqrt(c)*d-sqrt(a)*e)*x/a^(1/4)/sqrt(e*x^2+d))/a^(3/4)/sqrt(c)+1/2*sqrt(sqrt(c)*d+sqrt(a)*e)*arctanh(sqrt(sqrt(c)*d+sqrt(a)*e)*x/a^(1/4)/sqrt(e*x^2+d))/a^(3/4)/sqrt(c),1],
[1/sqrt(e*x^2+d)/(-c*x^4+a),x,4,1/2*arctan(sqrt(sqrt(c)*d-sqrt(a)*e)*x/a^(1/4)/sqrt(e*x^2+d))/a^(3/4)/sqrt(sqrt(c)*d-sqrt(a)*e)+1/2*arctanh(sqrt(sqrt(c)*d+sqrt(a)*e)*x/a^(1/4)/sqrt(e*x^2+d))/a^(3/4)/sqrt(sqrt(c)*d+sqrt(a)*e),1],
[1/(e*x^2+d)^(3/2)/(-c*x^4+a),x,5,-e^2*x/d/(-a*e^2+c*d^2)/sqrt(e*x^2+d)+1/2*sqrt(c)*arctan(sqrt(sqrt(c)*d-sqrt(a)*e)*x/a^(1/4)/sqrt(e*x^2+d))/a^(3/4)/(sqrt(c)*d-sqrt(a)*e)^(3/2)+1/2*sqrt(c)*arctanh(sqrt(sqrt(c)*d+sqrt(a)*e)*x/a^(1/4)/sqrt(e*x^2+d))/a^(3/4)/(sqrt(c)*d+sqrt(a)*e)^(3/2),1],
[1/(e*x^2+d)^(5/2)/(-c*x^4+a),x,6,-1/3*e^2*x/d/(-a*e^2+c*d^2)/(e*x^2+d)^(3/2)-2/3*e^2*(-a*e^2+4*c*d^2)*x/d^2/(-a*e^2+c*d^2)^2/sqrt(e*x^2+d)+1/2*c*arctan(sqrt(sqrt(c)*d-sqrt(a)*e)*x/a^(1/4)/sqrt(e*x^2+d))/a^(3/4)/(sqrt(c)*d-sqrt(a)*e)^(5/2)+1/2*c*arctanh(sqrt(sqrt(c)*d+sqrt(a)*e)*x/a^(1/4)/sqrt(e*x^2+d))/a^(3/4)/(sqrt(c)*d+sqrt(a)*e)^(5/2),1],
[1/(e*x^2+d)^(7/2)/(-c*x^4+a),x,7,-1/5*e^2*x/d/(-a*e^2+c*d^2)/(e*x^2+d)^(5/2)-2/15*e^2*(-2*a*e^2+7*c*d^2)*x/d^2/(-a*e^2+c*d^2)^2/(e*x^2+d)^(3/2)-1/15*e^2*(8*a^2*e^4-21*a*c*d^2*e^2+73*c^2*d^4)*x/d^3/(-a*e^2+c*d^2)^3/sqrt(e*x^2+d)+1/2*c^(3/2)*arctan(sqrt(sqrt(c)*d-sqrt(a)*e)*x/a^(1/4)/sqrt(e*x^2+d))/a^(3/4)/(sqrt(c)*d-sqrt(a)*e)^(7/2)+1/2*c^(3/2)*arctanh(sqrt(sqrt(c)*d+sqrt(a)*e)*x/a^(1/4)/sqrt(e*x^2+d))/a^(3/4)/(sqrt(c)*d+sqrt(a)*e)^(7/2),1],
[(e*x^2+d)^(9/2)/(-c*x^4+a)^2,x,11,3/4*e^2*(a*e^2+2*c*d^2)*x*sqrt(e*x^2+d)/a/c^2+d*e^3*x^3*sqrt(e*x^2+d)/a/c+1/4*e^4*x^5*sqrt(e*x^2+d)/a/c+1/4*x*(e*x^2+d)^(9/2)/a/(-c*x^4+a)+3/8*(sqrt(c)*d-sqrt(a)*e)^(7/2)*(sqrt(c)*d+2*sqrt(a)*e)*arctan(sqrt(sqrt(c)*d-sqrt(a)*e)*x/a^(1/4)/sqrt(e*x^2+d))/a^(7/4)/c^(5/2)+9/2*d*e^(7/2)*arctanh(sqrt(e)*x/sqrt(e*x^2+d))/c^2+3/8*(sqrt(c)*d-2*sqrt(a)*e)*(sqrt(c)*d+sqrt(a)*e)^(7/2)*arctanh(sqrt(sqrt(c)*d+sqrt(a)*e)*x/a^(1/4)/sqrt(e*x^2+d))/a^(7/4)/c^(5/2),1],
[(e*x^2+d)^(7/2)/(-c*x^4+a)^2,x,10,3/4*d*e^2*x*sqrt(e*x^2+d)/a/c+1/4*e^3*x^3*sqrt(e*x^2+d)/a/c+1/4*x*(e*x^2+d)^(7/2)/a/(-c*x^4+a)+1/8*(sqrt(c)*d-sqrt(a)*e)^(5/2)*(3*sqrt(c)*d+4*sqrt(a)*e)*arctan(sqrt(sqrt(c)*d-sqrt(a)*e)*x/a^(1/4)/sqrt(e*x^2+d))/a^(7/4)/c^2+e^(7/2)*arctanh(sqrt(e)*x/sqrt(e*x^2+d))/c^2+1/8*(3*sqrt(c)*d-4*sqrt(a)*e)*(sqrt(c)*d+sqrt(a)*e)^(5/2)*arctanh(sqrt(sqrt(c)*d+sqrt(a)*e)*x/a^(1/4)/sqrt(e*x^2+d))/a^(7/4)/c^2,1],
[(e*x^2+d)^(5/2)/(-c*x^4+a)^2,x,6,1/4*e^2*x*sqrt(e*x^2+d)/a/c+1/4*x*(e*x^2+d)^(5/2)/a/(-c*x^4+a)+1/8*(sqrt(c)*d-sqrt(a)*e)^(3/2)*(3*sqrt(c)*d+2*sqrt(a)*e)*arctan(sqrt(sqrt(c)*d-sqrt(a)*e)*x/a^(1/4)/sqrt(e*x^2+d))/a^(7/4)/c^(3/2)+1/8*(3*sqrt(c)*d-2*sqrt(a)*e)*(sqrt(c)*d+sqrt(a)*e)^(3/2)*arctanh(sqrt(sqrt(c)*d+sqrt(a)*e)*x/a^(1/4)/sqrt(e*x^2+d))/a^(7/4)/c^(3/2),1],
[(e*x^2+d)^(3/2)/(-c*x^4+a)^2,x,7,1/4*x*(e*x^2+d)^(3/2)/a/(-c*x^4+a)+3/8*d*sqrt(sqrt(c)*d-sqrt(a)*e)*arctan(sqrt(sqrt(c)*d-sqrt(a)*e)*x/a^(1/4)/sqrt(e*x^2+d))/a^(7/4)/sqrt(c)+3/8*d*sqrt(sqrt(c)*d+sqrt(a)*e)*arctanh(sqrt(sqrt(c)*d+sqrt(a)*e)*x/a^(1/4)/sqrt(e*x^2+d))/a^(7/4)/sqrt(c),1],
[sqrt(e*x^2+d)/(-c*x^4+a)^2,x,5,1/4*x*sqrt(e*x^2+d)/a/(-c*x^4+a)+1/8*(3*sqrt(c)*d-2*sqrt(a)*e)*arctan(sqrt(sqrt(c)*d-sqrt(a)*e)*x/a^(1/4)/sqrt(e*x^2+d))/a^(7/4)/sqrt(c)/sqrt(sqrt(c)*d-sqrt(a)*e)+1/8*(3*sqrt(c)*d+2*sqrt(a)*e)*arctanh(sqrt(sqrt(c)*d+sqrt(a)*e)*x/a^(1/4)/sqrt(e*x^2+d))/a^(7/4)/sqrt(c)/sqrt(sqrt(c)*d+sqrt(a)*e),1],
[1/sqrt(e*x^2+d)/(-c*x^4+a)^2,x,5,1/4*c*x*(-e*x^2+d)*sqrt(e*x^2+d)/a/(-a*e^2+c*d^2)/(-c*x^4+a)+1/8*(3*sqrt(c)*d-4*sqrt(a)*e)*arctan(sqrt(sqrt(c)*d-sqrt(a)*e)*x/a^(1/4)/sqrt(e*x^2+d))/a^(7/4)/(sqrt(c)*d-sqrt(a)*e)^(3/2)+1/8*(3*sqrt(c)*d+4*sqrt(a)*e)*arctanh(sqrt(sqrt(c)*d+sqrt(a)*e)*x/a^(1/4)/sqrt(e*x^2+d))/a^(7/4)/(sqrt(c)*d+sqrt(a)*e)^(3/2),1],
[1/(e*x^2+d)^(3/2)/(-c*x^4+a)^2,x,6,1/2*e^2*(2*a*e^2+c*d^2)*x/a/d/(-a*e^2+c*d^2)^2/sqrt(e*x^2+d)+1/4*c*x*(-e*x^2+d)/a/(-a*e^2+c*d^2)/sqrt(e*x^2+d)/(-c*x^4+a)+3/8*sqrt(c)*(sqrt(c)*d-2*sqrt(a)*e)*arctan(sqrt(sqrt(c)*d-sqrt(a)*e)*x/a^(1/4)/sqrt(e*x^2+d))/a^(7/4)/(sqrt(c)*d-sqrt(a)*e)^(5/2)+3/8*sqrt(c)*(sqrt(c)*d+2*sqrt(a)*e)*arctanh(sqrt(sqrt(c)*d+sqrt(a)*e)*x/a^(1/4)/sqrt(e*x^2+d))/a^(7/4)/(sqrt(c)*d+sqrt(a)*e)^(5/2),1],
[1/(e*x^2+d)^(5/2)/(-c*x^4+a)^2,x,7,1/6*e^2*(2*a*e^2+3*c*d^2)*x/a/d/(-a*e^2+c*d^2)^2/(e*x^2+d)^(3/2)+1/12*e^2*(-8*a^2*e^4+59*a*c*d^2*e^2+9*c^2*d^4)*x/a/d^2/(-a*e^2+c*d^2)^3/sqrt(e*x^2+d)+1/4*c*x*(-e*x^2+d)/a/(-a*e^2+c*d^2)/(e*x^2+d)^(3/2)/(-c*x^4+a)+1/8*c*(3*sqrt(c)*d-8*sqrt(a)*e)*arctan(sqrt(sqrt(c)*d-sqrt(a)*e)*x/a^(1/4)/sqrt(e*x^2+d))/a^(7/4)/(sqrt(c)*d-sqrt(a)*e)^(7/2)+1/8*c*(3*sqrt(c)*d+8*sqrt(a)*e)*arctanh(sqrt(sqrt(c)*d+sqrt(a)*e)*x/a^(1/4)/sqrt(e*x^2+d))/a^(7/4)/(sqrt(c)*d+sqrt(a)*e)^(7/2),1],
[(e*x^2+d)^(11/2)/(-c*x^4+a)^3,x,13,1/32*d*e^2*(-21*a*e^2+17*c*d^2)*x*sqrt(e*x^2+d)/a^2/c^2+1/16*e^2*(-4*a*e^2+5*c*d^2)*x*(e*x^2+d)^(3/2)/a^2/c^2+3/32*d*e^2*x*(e*x^2+d)^(5/2)/a^2/c-1/8*e^2*x*(e*x^2+d)^(7/2)/a^2/c+1/8*x*(e*x^2+d)^(11/2)/a/(-c*x^4+a)^2+1/32*x*(-4*e*x^2+7*d)*(e*x^2+d)^(9/2)/a^2/(-c*x^4+a)+1/64*(sqrt(c)*d-sqrt(a)*e)^(7/2)*(21*c*d^2+46*sqrt(a)*sqrt(c)*d*e+32*a*e^2)*arctan(sqrt(sqrt(c)*d-sqrt(a)*e)*x/a^(1/4)/sqrt(e*x^2+d))/a^(11/4)/c^3-e^(11/2)*arctanh(sqrt(e)*x/sqrt(e*x^2+d))/c^3+1/64*(sqrt(c)*d+sqrt(a)*e)^(7/2)*(21*c*d^2-46*sqrt(a)*sqrt(c)*d*e+32*a*e^2)*arctanh(sqrt(sqrt(c)*d+sqrt(a)*e)*x/a^(1/4)/sqrt(e*x^2+d))/a^(11/4)/c^3,1],
[(e*x^2+d)^(9/2)/(-c*x^4+a)^3,x,9,3/16*e^2*(-a*e^2+2*c*d^2)*x*sqrt(e*x^2+d)/a^2/c^2+5/32*d*e^2*x*(e*x^2+d)^(3/2)/a^2/c-1/16*e^2*x*(e*x^2+d)^(5/2)/a^2/c+1/8*x*(e*x^2+d)^(9/2)/a/(-c*x^4+a)^2+1/32*x*(-2*e*x^2+7*d)*(e*x^2+d)^(7/2)/a^2/(-c*x^4+a)+3/64*(sqrt(c)*d-sqrt(a)*e)^(5/2)*(7*c*d^2+10*sqrt(a)*sqrt(c)*d*e+4*a*e^2)*arctan(sqrt(sqrt(c)*d-sqrt(a)*e)*x/a^(1/4)/sqrt(e*x^2+d))/a^(11/4)/c^(5/2)+3/64*(sqrt(c)*d+sqrt(a)*e)^(5/2)*(7*c*d^2-10*sqrt(a)*sqrt(c)*d*e+4*a*e^2)*arctanh(sqrt(sqrt(c)*d+sqrt(a)*e)*x/a^(1/4)/sqrt(e*x^2+d))/a^(11/4)/c^(5/2),1],
[(e*x^2+d)^(7/2)/(-c*x^4+a)^3,x,8,7/32*d*e^2*x*sqrt(e*x^2+d)/a^2/c+1/8*x*(e*x^2+d)^(7/2)/a/(-c*x^4+a)^2+7/32*d*x*(e*x^2+d)^(5/2)/a^2/(-c*x^4+a)+7/64*d*(sqrt(c)*d-sqrt(a)*e)^(3/2)*(3*sqrt(c)*d+2*sqrt(a)*e)*arctan(sqrt(sqrt(c)*d-sqrt(a)*e)*x/a^(1/4)/sqrt(e*x^2+d))/a^(11/4)/c^(3/2)+7/64*d*(3*sqrt(c)*d-2*sqrt(a)*e)*(sqrt(c)*d+sqrt(a)*e)^(3/2)*arctanh(sqrt(sqrt(c)*d+sqrt(a)*e)*x/a^(1/4)/sqrt(e*x^2+d))/a^(11/4)/c^(3/2),1],
[(e*x^2+d)^(5/2)/(-c*x^4+a)^3,x,7,1/16*e^2*x*sqrt(e*x^2+d)/a^2/c+1/8*x*(e*x^2+d)^(5/2)/a/(-c*x^4+a)^2+1/32*x*(e*x^2+d)^(3/2)*(2*e*x^2+7*d)/a^2/(-c*x^4+a)+1/64*sqrt(sqrt(c)*d-sqrt(a)*e)*(21*c*d^2-2*sqrt(a)*sqrt(c)*d*e-4*a*e^2)*arctan(sqrt(sqrt(c)*d-sqrt(a)*e)*x/a^(1/4)/sqrt(e*x^2+d))/a^(11/4)/c^(3/2)+1/64*sqrt(sqrt(c)*d+sqrt(a)*e)*(21*c*d^2+2*sqrt(a)*sqrt(c)*d*e-4*a*e^2)*arctanh(sqrt(sqrt(c)*d+sqrt(a)*e)*x/a^(1/4)/sqrt(e*x^2+d))/a^(11/4)/c^(3/2),1],
[(e*x^2+d)^(3/2)/(-c*x^4+a)^3,x,6,1/8*x*(e*x^2+d)^(3/2)/a/(-c*x^4+a)^2+1/32*x*sqrt(e*x^2+d)*(4*e*x^2+7*d)/a^2/(-c*x^4+a)+3/64*d*(7*sqrt(c)*d-6*sqrt(a)*e)*arctan(sqrt(sqrt(c)*d-sqrt(a)*e)*x/a^(1/4)/sqrt(e*x^2+d))/a^(11/4)/sqrt(c)/sqrt(sqrt(c)*d-sqrt(a)*e)+3/64*d*(7*sqrt(c)*d+6*sqrt(a)*e)*arctanh(sqrt(sqrt(c)*d+sqrt(a)*e)*x/a^(1/4)/sqrt(e*x^2+d))/a^(11/4)/sqrt(c)/sqrt(sqrt(c)*d+sqrt(a)*e),1],
[sqrt(e*x^2+d)/(-c*x^4+a)^3,x,6,1/8*x*sqrt(e*x^2+d)/a/(-c*x^4+a)^2+1/32*x*sqrt(e*x^2+d)*(-c*d*e*x^2-6*a*e^2+7*c*d^2)/a^2/(-a*e^2+c*d^2)/(-c*x^4+a)+1/64*(21*c*d^2-34*sqrt(a)*sqrt(c)*d*e+12*a*e^2)*arctan(sqrt(sqrt(c)*d-sqrt(a)*e)*x/a^(1/4)/sqrt(e*x^2+d))/a^(11/4)/sqrt(c)/(sqrt(c)*d-sqrt(a)*e)^(3/2)+1/64*(21*c*d^2+34*sqrt(a)*sqrt(c)*d*e+12*a*e^2)*arctanh(sqrt(sqrt(c)*d+sqrt(a)*e)*x/a^(1/4)/sqrt(e*x^2+d))/a^(11/4)/sqrt(c)/(sqrt(c)*d+sqrt(a)*e)^(3/2),1],
[1/sqrt(e*x^2+d)/(-c*x^4+a)^3,x,6,1/8*c*x*(-e*x^2+d)*sqrt(e*x^2+d)/a/(-a*e^2+c*d^2)/(-c*x^4+a)^2+1/32*c*x*sqrt(e*x^2+d)*(d*(-13*a*e^2+7*c*d^2)-6*e*(-2*a*e^2+c*d^2)*x^2)/a^2/(-a*e^2+c*d^2)^2/(-c*x^4+a)+1/64*(21*c*d^2-50*sqrt(a)*sqrt(c)*d*e+32*a*e^2)*arctan(sqrt(sqrt(c)*d-sqrt(a)*e)*x/a^(1/4)/sqrt(e*x^2+d))/a^(11/4)/(sqrt(c)*d-sqrt(a)*e)^(5/2)+1/64*(21*c*d^2+50*sqrt(a)*sqrt(c)*d*e+32*a*e^2)*arctanh(sqrt(sqrt(c)*d+sqrt(a)*e)*x/a^(1/4)/sqrt(e*x^2+d))/a^(11/4)/(sqrt(c)*d+sqrt(a)*e)^(5/2),1],
[1/(e*x^2+d)^(3/2)/(-c*x^4+a)^3,x,7,1/32*e^2*(-32*a^2*e^4-39*a*c*d^2*e^2+11*c^2*d^4)*x/a^2/d/(-a*e^2+c*d^2)^3/sqrt(e*x^2+d)+1/8*c*x*(-e*x^2+d)/a/(-a*e^2+c*d^2)/sqrt(e*x^2+d)/(-c*x^4+a)^2+1/32*c*x*(d*(-17*a*e^2+7*c*d^2)-2*e*(-7*a*e^2+2*c*d^2)*x^2)/a^2/(-a*e^2+c*d^2)^2/sqrt(e*x^2+d)/(-c*x^4+a)+3/64*sqrt(c)*(7*c*d^2-22*sqrt(a)*sqrt(c)*d*e+20*a*e^2)*arctan(sqrt(sqrt(c)*d-sqrt(a)*e)*x/a^(1/4)/sqrt(e*x^2+d))/a^(11/4)/(sqrt(c)*d-sqrt(a)*e)^(7/2)+3/64*sqrt(c)*(7*c*d^2+22*sqrt(a)*sqrt(c)*d*e+20*a*e^2)*arctanh(sqrt(sqrt(c)*d+sqrt(a)*e)*x/a^(1/4)/sqrt(e*x^2+d))/a^(11/4)/(sqrt(c)*d+sqrt(a)*e)^(7/2),1],
[(e*x^2+d)^(3/2)*(c*x^4+a),x,6,3/128*d*(16*a+c*d^2/e^2)*x*sqrt(e*x^2+d)+1/64*(16*a+c*d^2/e^2)*x*(e*x^2+d)^(3/2)-1/16*c*d*x*(e*x^2+d)^(5/2)/e^2+1/8*c*x^3*(e*x^2+d)^(5/2)/e+3/128*d^2*(16*a*e^2+c*d^2)*arctanh(sqrt(e)*x/sqrt(e*x^2+d))/e^(5/2),1],
[sqrt(e*x^2+d)*(c*x^4+a),x,5,1/16*(8*a+c*d^2/e^2)*x*sqrt(e*x^2+d)-1/8*c*d*x*(e*x^2+d)^(3/2)/e^2+1/6*c*x^3*(e*x^2+d)^(3/2)/e+1/16*d*(8*a*e^2+c*d^2)*arctanh(sqrt(e)*x/sqrt(e*x^2+d))/e^(5/2),1],
[(c*x^4+a)/sqrt(e*x^2+d),x,4,-3/8*c*d*x*sqrt(e*x^2+d)/e^2+1/4*c*x^3*sqrt(e*x^2+d)/e+1/8*(8*a*e^2+3*c*d^2)*arctanh(sqrt(e)*x/sqrt(e*x^2+d))/e^(5/2),1],
[(c*x^4+a)/(e*x^2+d)^(3/2),x,4,(a+c*d^2/e^2)*x/d/sqrt(e*x^2+d)+1/2*c*x*sqrt(e*x^2+d)/e^2-3/2*c*d*arctanh(sqrt(e)*x/sqrt(e*x^2+d))/e^(5/2),1],
[(c*x^4+a)/(e*x^2+d)^(5/2),x,4,1/3*(a+c*d^2/e^2)*x/d/(e*x^2+d)^(3/2)+2/3*(a/d^2-2*c/e^2)*x/sqrt(e*x^2+d)+c*arctanh(sqrt(e)*x/sqrt(e*x^2+d))/e^(5/2),1],
[(c*x^4+a)/(e*x^2+d)^(7/2),x,3,1/5*(a+c*d^2/e^2)*x/d/(e*x^2+d)^(5/2)+2/15*(2*a/d^2-3*c/e^2)*x/(e*x^2+d)^(3/2)+1/15*(8*a/d^2+3*c/e^2)*x/d/sqrt(e*x^2+d),1],
[(c*x^4+a)/(e*x^2+d)^(9/2),x,4,1/7*(a+c*d^2/e^2)*x/d/(e*x^2+d)^(7/2)+2/35*(3*a/d^2-4*c/e^2)*x/(e*x^2+d)^(5/2)+1/35*(8*a/d^2+c/e^2)*x/d/(e*x^2+d)^(3/2)+2/35*(8*a*e^2+c*d^2)*x/d^4/e^2/sqrt(e*x^2+d),1],
[(c*x^4+a)/(e*x^2+d)^(11/2),x,5,1/9*(a+c*d^2/e^2)*x/d/(e*x^2+d)^(9/2)+2/63*(4*a/d^2-5*c/e^2)*x/(e*x^2+d)^(7/2)+1/105*(16*a/d^2+c/e^2)*x/d/(e*x^2+d)^(5/2)+4/315*(16*a*e^2+c*d^2)*x/d^4/e^2/(e*x^2+d)^(3/2)+8/315*(16*a*e^2+c*d^2)*x/d^5/e^2/sqrt(e*x^2+d),1],
[(e*x^2+d)^(3/2)*(c*x^4+a)^2,x,8,1/1024*d*(384*a^2*e^4+48*a*c*d^2*e^2+7*c^2*d^4)*x*sqrt(e*x^2+d)/e^4+1/1536*(384*a^2*e^4+48*a*c*d^2*e^2+7*c^2*d^4)*x*(e*x^2+d)^(3/2)/e^4-1/384*c*d*(48*a*e^2+7*c*d^2)*x*(e*x^2+d)^(5/2)/e^4+1/192*c*(48*a*e^2+7*c*d^2)*x^3*(e*x^2+d)^(5/2)/e^3-7/120*c^2*d*x^5*(e*x^2+d)^(5/2)/e^2+1/12*c^2*x^7*(e*x^2+d)^(5/2)/e+1/1024*d^2*(384*a^2*e^4+48*a*c*d^2*e^2+7*c^2*d^4)*arctanh(sqrt(e)*x/sqrt(e*x^2+d))/e^(9/2),1],
[sqrt(e*x^2+d)*(c*x^4+a)^2,x,7,1/256*(128*a^2*e^4+32*a*c*d^2*e^2+7*c^2*d^4)*x*sqrt(e*x^2+d)/e^4-1/128*c*d*(32*a*e^2+7*c*d^2)*x*(e*x^2+d)^(3/2)/e^4+1/96*c*(32*a*e^2+7*c*d^2)*x^3*(e*x^2+d)^(3/2)/e^3-7/80*c^2*d*x^5*(e*x^2+d)^(3/2)/e^2+1/10*c^2*x^7*(e*x^2+d)^(3/2)/e+1/256*d*(128*a^2*e^4+32*a*c*d^2*e^2+7*c^2*d^4)*arctanh(sqrt(e)*x/sqrt(e*x^2+d))/e^(9/2),1],
[(c*x^4+a)^2/sqrt(e*x^2+d),x,6,-1/128*c*d*(96*a*e^2+35*c*d^2)*x*sqrt(e*x^2+d)/e^4+1/192*c*(96*a*e^2+35*c*d^2)*x^3*sqrt(e*x^2+d)/e^3-7/48*c^2*d*x^5*sqrt(e*x^2+d)/e^2+1/8*c^2*x^7*sqrt(e*x^2+d)/e+1/128*(128*a^2*e^4+96*a*c*d^2*e^2+35*c^2*d^4)*arctanh(sqrt(e)*x/sqrt(e*x^2+d))/e^(9/2),1],
[(c*x^4+a)^2/(e*x^2+d)^(3/2),x,6,(a*e^2+c*d^2)^2*x/d/e^4/sqrt(e*x^2+d)+1/16*c*(16*a*e^2+19*c*d^2)*x*sqrt(e*x^2+d)/e^4-11/24*c^2*d*x^3*sqrt(e*x^2+d)/e^3+1/6*c^2*x^5*sqrt(e*x^2+d)/e^2-1/16*c*d*(48*a*e^2+35*c*d^2)*arctanh(sqrt(e)*x/sqrt(e*x^2+d))/e^(9/2),1],
[(c*x^4+a)^2/(e*x^2+d)^(5/2),x,6,1/3*(a*e^2+c*d^2)^2*x/d/e^4/(e*x^2+d)^(3/2)-2/3*(-a*e^2+5*c*d^2)*(a*e^2+c*d^2)*x/d^2/e^4/sqrt(e*x^2+d)-11/8*c^2*d*x*sqrt(e*x^2+d)/e^4+1/4*c^2*x^3*sqrt(e*x^2+d)/e^3+1/8*c*(16*a*e^2+35*c*d^2)*arctanh(sqrt(e)*x/sqrt(e*x^2+d))/e^(9/2),1],
[(c*x^4+a)^2/(e*x^2+d)^(7/2),x,6,1/5*(a*e^2+c*d^2)^2*x/d/e^4/(e*x^2+d)^(5/2)-4/15*(-a*e^2+4*c*d^2)*(a*e^2+c*d^2)*x/d^2/e^4/(e*x^2+d)^(3/2)+2/15*(4*a^2*e^4+3*a*c*d^2*e^2+29*c^2*d^4)*x/d^3/e^4/sqrt(e*x^2+d)+1/2*c^2*x*sqrt(e*x^2+d)/e^4-7/2*c^2*d*arctanh(sqrt(e)*x/sqrt(e*x^2+d))/e^(9/2),1],
[(c*x^4+a)^2/(e*x^2+d)^(9/2),x,6,1/7*(a*e^2+c*d^2)^2*x/d/e^4/(e*x^2+d)^(7/2)-2/35*(-3*a*e^2+11*c*d^2)*(a*e^2+c*d^2)*x/d^2/e^4/(e*x^2+d)^(5/2)+2/105*(12*a^2*e^4+3*a*c*d^2*e^2+61*c^2*d^4)*x/d^3/e^4/(e*x^2+d)^(3/2)-4/105*(-12*a^2*e^4-3*a*c*d^2*e^2+44*c^2*d^4)*x/d^4/e^4/sqrt(e*x^2+d)+c^2*arctanh(sqrt(e)*x/sqrt(e*x^2+d))/e^(9/2),1],
[(c*x^4+a)^2/(e*x^2+d)^(11/2),x,5,1/9*(a*e^2+c*d^2)^2*x/d/e^4/(e*x^2+d)^(9/2)-4/63*(-2*a*e^2+7*c*d^2)*(a*e^2+c*d^2)*x/d^2/e^4/(e*x^2+d)^(7/2)+2/105*(8*a^2*e^4+a*c*d^2*e^2+35*c^2*d^4)*x/d^3/e^4/(e*x^2+d)^(5/2)-4/315*(-16*a^2*e^4-2*a*c*d^2*e^2+35*c^2*d^4)*x/d^4/e^4/(e*x^2+d)^(3/2)+1/315*(128*a^2*e^4+16*a*c*d^2*e^2+35*c^2*d^4)*x/d^5/e^4/sqrt(e*x^2+d),1],
[(c*x^4+a)^2/(e*x^2+d)^(13/2),x,6,1/11*(a*e^2+c*d^2)^2*x/d/e^4/(e*x^2+d)^(11/2)-2/99*(-5*a*e^2+17*c*d^2)*(a*e^2+c*d^2)*x/d^2/e^4/(e*x^2+d)^(9/2)+2/693*(40*a^2*e^4+3*a*c*d^2*e^2+161*c^2*d^4)*x/d^3/e^4/(e*x^2+d)^(7/2)-4/1155*(-40*a^2*e^4-3*a*c*d^2*e^2+70*c^2*d^4)*x/d^4/e^4/(e*x^2+d)^(5/2)+1/3465*(640*a^2*e^4+48*a*c*d^2*e^2+35*c^2*d^4)*x/d^5/e^4/(e*x^2+d)^(3/2)+2/3465*(640*a^2*e^4+48*a*c*d^2*e^2+35*c^2*d^4)*x/d^6/e^4/sqrt(e*x^2+d),1],
[(e*x^2+d)^(7/2)/(c*x^4+a),x,10,13/8*d*e^2*x*sqrt(e*x^2+d)/c+1/4*e^3*x^3*sqrt(e*x^2+d)/c+1/2*sqrt(sqrt(a)*e+sqrt(a*e^2+c*d^2))*(4*c*d^2*e*(-a*e^2+c*d^2)-(a^2*e^4-6*a*c*d^2*e^2+c^2*d^4)*(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^(5/2)/d/sqrt(a*e^2+c*d^2)+1/8*e^(3/2)*(-8*a*e^2+35*c*d^2)*arctanh(sqrt(e)*x/sqrt(e*x^2+d))/c^2+1/2*sqrt(-sqrt(a)*e+sqrt(a*e^2+c*d^2))*(4*c*d^2*e*(-a*e^2+c*d^2)-(a^2*e^4-6*a*c*d^2*e^2+c^2*d^4)*(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^(5/2)/d/sqrt(a*e^2+c*d^2),1],
[(e*x^2+d)^(5/2)/(c*x^4+a),x,9,1/2*e^2*x*sqrt(e*x^2+d)/c+1/2*sqrt(sqrt(a)*e+sqrt(a*e^2+c*d^2))*(2*sqrt(a)*c*d^2*e+2*a^(3/2)*e^3+(-3*a*e^2+c*d^2)*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^(3/4)/c^(3/2)/sqrt(a*e^2+c*d^2)+5/2*d*e^(3/2)*arctanh(sqrt(e)*x/sqrt(e*x^2+d))/c+1/2*sqrt(-sqrt(a)*e+sqrt(a*e^2+c*d^2))*(2*sqrt(a)*c*d^2*e+2*a^(3/2)*e^3-(-3*a*e^2+c*d^2)*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^(3/4)/c^(3/2)/sqrt(a*e^2+c*d^2),1],
[(e*x^2+d)^(3/2)/(c*x^4+a),x,8,1/2*sqrt(sqrt(a)*e+sqrt(a*e^2+c*d^2))*(2*c*d^2*e-(-a*e^2+c*d^2)*(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)+e^(3/2)*arctanh(sqrt(e)*x/sqrt(e*x^2+d))/c+1/2*sqrt(-sqrt(a)*e+sqrt(a*e^2+c*d^2))*(2*c*d^2*e-(-a*e^2+c*d^2)*(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],
[sqrt(e*x^2+d)/(c*x^4+a),x,5,1/2*sqrt(sqrt(a)*e+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^(3/4)/sqrt(c)-1/2*sqrt(-sqrt(a)*e+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^(3/4)/sqrt(c),1],
[1/sqrt(e*x^2+d)/(c*x^4+a),x,5,-1/2*sqrt(sqrt(a)*e+sqrt(a*e^2+c*d^2))*(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/sqrt(a*e^2+c*d^2)-1/2*sqrt(-sqrt(a)*e+sqrt(a*e^2+c*d^2))*(sqrt(a)*e+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^(3/4)/sqrt(c)/d/sqrt(a*e^2+c*d^2),1],
[1/(e*x^2+d)^(3/2)/(c*x^4+a),x,6,e^2*x/d/(a*e^2+c*d^2)/sqrt(e*x^2+d)-1/2*sqrt(c)*(2*sqrt(a)*e-sqrt(a*e^2+c*d^2))*sqrt(sqrt(a)*e+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^(3/4)/(a*e^2+c*d^2)^(3/2)-1/2*sqrt(c)*sqrt(-sqrt(a)*e+sqrt(a*e^2+c*d^2))*(2*sqrt(a)*e+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^(3/4)/(a*e^2+c*d^2)^(3/2),1],
[1/(e*x^2+d)^(5/2)/(c*x^4+a),x,7,1/3*e^2*x/d/(a*e^2+c*d^2)/(e*x^2+d)^(3/2)+2/3*e^2*(a*e^2+4*c*d^2)*x/d^2/(a*e^2+c*d^2)^2/sqrt(e*x^2+d)-1/2*sqrt(c)*sqrt(sqrt(a)*e+sqrt(a*e^2+c*d^2))*(2*c*d^2*e+(-a*e^2+c*d^2)*(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)/d/(a*e^2+c*d^2)^(5/2)-1/2*sqrt(c)*sqrt(-sqrt(a)*e+sqrt(a*e^2+c*d^2))*(2*c*d^2*e+(-a*e^2+c*d^2)*(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)/d/(a*e^2+c*d^2)^(5/2),1],
[(e*x^2+d)^(9/2)/(c*x^4+a)^2,x,12,-3/4*e^2*(-a*e^2+2*c*d^2)*x*sqrt(e*x^2+d)/a/c^2-d*e^3*x^3*sqrt(e*x^2+d)/a/c-1/4*e^4*x^5*sqrt(e*x^2+d)/a/c+1/4*x*(e*x^2+d)^(9/2)/a/(c*x^4+a)+3/8*sqrt(sqrt(a)*e+sqrt(a*e^2+c*d^2))*(2*c^2*d^4*e+8*a*c*d^2*e^3-2*a^2*e^5-(-7*a^2*e^4+2*a*c*d^2*e^2+c^2*d^4)*(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)/sqrt(a*e^2+c*d^2)+9/2*d*e^(7/2)*arctanh(sqrt(e)*x/sqrt(e*x^2+d))/c^2+3/8*sqrt(-sqrt(a)*e+sqrt(a*e^2+c*d^2))*(2*c^2*d^4*e+8*a*c*d^2*e^3-2*a^2*e^5-(-7*a^2*e^4+2*a*c*d^2*e^2+c^2*d^4)*(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)/sqrt(a*e^2+c*d^2),1],
[(e*x^2+d)^(7/2)/(c*x^4+a)^2,x,11,-3/4*d*e^2*x*sqrt(e*x^2+d)/a/c-1/4*e^3*x^3*sqrt(e*x^2+d)/a/c+1/4*x*(e*x^2+d)^(7/2)/a/(c*x^4+a)+1/8*sqrt(sqrt(a)*e+sqrt(a*e^2+c*d^2))*(c*d^2*e*(9*a*e^2+5*c*d^2)+(e-sqrt(a*e^2+c*d^2)/sqrt(a))*(4*a^2*e^4-3*c*d^2*(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)/c^(5/2)/d/sqrt(a*e^2+c*d^2)+e^(7/2)*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^2*e*(9*a*e^2+5*c*d^2)+(e+sqrt(a*e^2+c*d^2)/sqrt(a))*(4*a^2*e^4-3*c*d^2*(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)/c^(5/2)/d/sqrt(a*e^2+c*d^2),1],
[(e*x^2+d)^(5/2)/(c*x^4+a)^2,x,7,-1/4*e^2*x*sqrt(e*x^2+d)/a/c+1/4*x*(e*x^2+d)^(5/2)/a/(c*x^4+a)+1/8*sqrt(sqrt(a)*e+sqrt(a*e^2+c*d^2))*(4*c*d^2*e+2*a*e^3-(a*e^2+3*c*d^2)*(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^(3/2)/sqrt(a*e^2+c*d^2)+1/8*sqrt(-sqrt(a)*e+sqrt(a*e^2+c*d^2))*(4*c*d^2*e+2*a*e^3-(a*e^2+3*c*d^2)*(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^(3/2)/sqrt(a*e^2+c*d^2),1],
[(e*x^2+d)^(3/2)/(c*x^4+a)^2,x,7,1/4*x*(e*x^2+d)^(3/2)/a/(c*x^4+a)+3/8*d*sqrt(sqrt(a)*e+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)/sqrt(c)-3/8*d*sqrt(-sqrt(a)*e+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)/sqrt(c),1],
[sqrt(e*x^2+d)/(c*x^4+a)^2,x,6,1/4*x*sqrt(e*x^2+d)/a/(c*x^4+a)-1/8*(sqrt(a)*e-3*sqrt(a*e^2+c*d^2))*sqrt(sqrt(a)*e+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)/sqrt(c)/sqrt(a*e^2+c*d^2)-1/8*sqrt(-sqrt(a)*e+sqrt(a*e^2+c*d^2))*(sqrt(a)*e+3*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)/sqrt(c)/sqrt(a*e^2+c*d^2),1],
[1/sqrt(e*x^2+d)/(c*x^4+a)^2,x,6,1/4*c*x*(-e*x^2+d)*sqrt(e*x^2+d)/a/(a*e^2+c*d^2)/(c*x^4+a)+1/8*sqrt(sqrt(a)*e+sqrt(a*e^2+c*d^2))*(c*d^2*e-(4*a*e^2+3*c*d^2)*(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)/sqrt(c)/d/(a*e^2+c*d^2)^(3/2)+1/8*sqrt(-sqrt(a)*e+sqrt(a*e^2+c*d^2))*(c*d^2*e-(4*a*e^2+3*c*d^2)*(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)/sqrt(c)/d/(a*e^2+c*d^2)^(3/2),1],
[1/(e*x^2+d)^(3/2)/(c*x^4+a)^2,x,7,-1/2*e^2*(-2*a*e^2+c*d^2)*x/a/d/(a*e^2+c*d^2)^2/sqrt(e*x^2+d)+1/4*c*x*(-e*x^2+d)/a/(a*e^2+c*d^2)/sqrt(e*x^2+d)/(c*x^4+a)-3/8*sqrt(c)*sqrt(sqrt(a)*e+sqrt(a*e^2+c*d^2))*(2*a*e^3+(3*a*e^2+c*d^2)*(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)/(a*e^2+c*d^2)^(5/2)-3/8*sqrt(c)*sqrt(-sqrt(a)*e+sqrt(a*e^2+c*d^2))*(2*a*e^3+(3*a*e^2+c*d^2)*(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)/(a*e^2+c*d^2)^(5/2),1],
[1/(e*x^2+d)^(5/2)/(c*x^4+a)^2,x,8,-1/6*e^2*(-2*a*e^2+3*c*d^2)*x/a/d/(a*e^2+c*d^2)^2/(e*x^2+d)^(3/2)-1/12*e^2*(-8*a^2*e^4-59*a*c*d^2*e^2+9*c^2*d^4)*x/a/d^2/(a*e^2+c*d^2)^3/sqrt(e*x^2+d)+1/4*c*x*(-e*x^2+d)/a/(a*e^2+c*d^2)/(e*x^2+d)^(3/2)/(c*x^4+a)-1/8*sqrt(c)*sqrt(sqrt(a)*e+sqrt(a*e^2+c*d^2))*(c*d^2*e*(21*a*e^2+c*d^2)+(-8*a^2*e^4+15*a*c*d^2*e^2+3*c^2*d^4)*(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)/d/(a*e^2+c*d^2)^(7/2)-1/8*sqrt(c)*sqrt(-sqrt(a)*e+sqrt(a*e^2+c*d^2))*(c*d^2*e*(21*a*e^2+c*d^2)+(-8*a^2*e^4+15*a*c*d^2*e^2+3*c^2*d^4)*(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)/d/(a*e^2+c*d^2)^(7/2),1],
[(e*x^2+d)^(11/2)/(c*x^4+a)^3,x,14,-1/32*d*e^2*(21*a*e^2+17*c*d^2)*x*sqrt(e*x^2+d)/a^2/c^2-1/16*e^2*(4*a*e^2+5*c*d^2)*x*(e*x^2+d)^(3/2)/a^2/c^2-3/32*d*e^2*x*(e*x^2+d)^(5/2)/a^2/c+1/8*e^2*x*(e*x^2+d)^(7/2)/a^2/c+1/8*x*(e*x^2+d)^(11/2)/a/(c*x^4+a)^2+1/32*x*(-4*e*x^2+7*d)*(e*x^2+d)^(9/2)/a^2/(c*x^4+a)+1/64*sqrt(sqrt(a)*e+sqrt(a*e^2+c*d^2))*(2*c*d^2*e*(41*a^2*e^4+32*a*c*d^2*e^2+19*c^2*d^4)-(-32*a^3*e^6+29*a^2*c*d^2*e^4+26*a*c^2*d^4*e^2+21*c^3*d^6)*(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^(9/4)/c^(7/2)/d/sqrt(a*e^2+c*d^2)+e^(11/2)*arctanh(sqrt(e)*x/sqrt(e*x^2+d))/c^3+1/64*sqrt(-sqrt(a)*e+sqrt(a*e^2+c*d^2))*(2*c*d^2*e*(41*a^2*e^4+32*a*c*d^2*e^2+19*c^2*d^4)-(-32*a^3*e^6+29*a^2*c*d^2*e^4+26*a*c^2*d^4*e^2+21*c^3*d^6)*(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^(9/4)/c^(7/2)/d/sqrt(a*e^2+c*d^2),1],
[(e*x^2+d)^(9/2)/(c*x^4+a)^3,x,10,-3/16*e^2*(a*e^2+2*c*d^2)*x*sqrt(e*x^2+d)/a^2/c^2-5/32*d*e^2*x*(e*x^2+d)^(3/2)/a^2/c+1/16*e^2*x*(e*x^2+d)^(5/2)/a^2/c+1/8*x*(e*x^2+d)^(9/2)/a/(c*x^4+a)^2+1/32*x*(-2*e*x^2+7*d)*(e*x^2+d)^(7/2)/a^2/(c*x^4+a)+3/64*sqrt(sqrt(a)*e+sqrt(a*e^2+c*d^2))*(11*c^2*d^4*e+11*a*c*d^2*e^3+4*a^2*e^5-(2*a^2*e^4+5*a*c*d^2*e^2+7*c^2*d^4)*(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^(9/4)/c^(5/2)/sqrt(a*e^2+c*d^2)+3/64*sqrt(-sqrt(a)*e+sqrt(a*e^2+c*d^2))*(11*c^2*d^4*e+11*a*c*d^2*e^3+4*a^2*e^5-(2*a^2*e^4+5*a*c*d^2*e^2+7*c^2*d^4)*(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^(9/4)/c^(5/2)/sqrt(a*e^2+c*d^2),1],
[(e*x^2+d)^(7/2)/(c*x^4+a)^3,x,9,-7/32*d*e^2*x*sqrt(e*x^2+d)/a^2/c+1/8*x*(e*x^2+d)^(7/2)/a/(c*x^4+a)^2+7/32*d*x*(e*x^2+d)^(5/2)/a^2/(c*x^4+a)+7/64*d*sqrt(sqrt(a)*e+sqrt(a*e^2+c*d^2))*(4*c*d^2*e+2*a*e^3-(a*e^2+3*c*d^2)*(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^(9/4)/c^(3/2)/sqrt(a*e^2+c*d^2)+7/64*d*sqrt(-sqrt(a)*e+sqrt(a*e^2+c*d^2))*(4*c*d^2*e+2*a*e^3-(a*e^2+3*c*d^2)*(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^(9/4)/c^(3/2)/sqrt(a*e^2+c*d^2),1],
[(e*x^2+d)^(5/2)/(c*x^4+a)^3,x,8,-1/16*e^2*x*sqrt(e*x^2+d)/a^2/c+1/8*x*(e*x^2+d)^(5/2)/a/(c*x^4+a)^2+1/32*x*(e*x^2+d)^(3/2)*(2*e*x^2+7*d)/a^2/(c*x^4+a)+1/64*sqrt(sqrt(a)*e+sqrt(a*e^2+c*d^2))*(2*sqrt(a)*c*d^2*e+2*a^(3/2)*e^3+sqrt(a*e^2+c*d^2)*(2*a*e^2+21*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^(11/4)/c^(3/2)/sqrt(a*e^2+c*d^2)+1/64*sqrt(-sqrt(a)*e+sqrt(a*e^2+c*d^2))*(23*c*d^2*e+4*a*e^3-(2*a*e^2+21*c*d^2)*(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^(9/4)/c^(3/2)/sqrt(a*e^2+c*d^2),1],
[(e*x^2+d)^(3/2)/(c*x^4+a)^3,x,7,1/8*x*(e*x^2+d)^(3/2)/a/(c*x^4+a)^2+1/32*x*sqrt(e*x^2+d)*(4*e*x^2+7*d)/a^2/(c*x^4+a)-3/64*d*(sqrt(a)*e-7*sqrt(a*e^2+c*d^2))*sqrt(sqrt(a)*e+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^(11/4)/sqrt(c)/sqrt(a*e^2+c*d^2)-3/64*d*sqrt(-sqrt(a)*e+sqrt(a*e^2+c*d^2))*(sqrt(a)*e+7*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^(11/4)/sqrt(c)/sqrt(a*e^2+c*d^2),1],
[sqrt(e*x^2+d)/(c*x^4+a)^3,x,7,1/8*x*sqrt(e*x^2+d)/a/(c*x^4+a)^2+1/32*x*sqrt(e*x^2+d)*(-c*d*e*x^2+6*a*e^2+7*c*d^2)/a^2/(a*e^2+c*d^2)/(c*x^4+a)+1/64*sqrt(sqrt(a)*e+sqrt(a*e^2+c*d^2))*(13*c*d^2*e+12*a*e^3-(22*a*e^2+21*c*d^2)*(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^(9/4)/sqrt(c)/(a*e^2+c*d^2)^(3/2)+1/64*sqrt(-sqrt(a)*e+sqrt(a*e^2+c*d^2))*(13*c*d^2*e+12*a*e^3-(22*a*e^2+21*c*d^2)*(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^(9/4)/sqrt(c)/(a*e^2+c*d^2)^(3/2),1],
[1/sqrt(e*x^2+d)/(c*x^4+a)^3,x,7,1/8*c*x*(-e*x^2+d)*sqrt(e*x^2+d)/a/(a*e^2+c*d^2)/(c*x^4+a)^2+1/32*c*x*sqrt(e*x^2+d)*(d*(13*a*e^2+7*c*d^2)-6*e*(2*a*e^2+c*d^2)*x^2)/a^2/(a*e^2+c*d^2)^2/(c*x^4+a)+1/64*sqrt(sqrt(a)*e+sqrt(a*e^2+c*d^2))*(2*c*d^2*e*(7*a*e^2+4*c*d^2)-(32*a^2*e^4+47*a*c*d^2*e^2+21*c^2*d^4)*(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^(9/4)/sqrt(c)/d/(a*e^2+c*d^2)^(5/2)+1/64*sqrt(-sqrt(a)*e+sqrt(a*e^2+c*d^2))*(2*c*d^2*e*(7*a*e^2+4*c*d^2)-(32*a^2*e^4+47*a*c*d^2*e^2+21*c^2*d^4)*(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^(9/4)/sqrt(c)/d/(a*e^2+c*d^2)^(5/2),1],
[1/(e*x^2+d)^(3/2)/(c*x^4+a)^3,x,8,-1/32*e^2*(-32*a^2*e^4+39*a*c*d^2*e^2+11*c^2*d^4)*x/a^2/d/(a*e^2+c*d^2)^3/sqrt(e*x^2+d)+1/8*c*x*(-e*x^2+d)/a/(a*e^2+c*d^2)/sqrt(e*x^2+d)/(c*x^4+a)^2+1/32*c*x*(d*(17*a*e^2+7*c*d^2)-2*e*(7*a*e^2+2*c*d^2)*x^2)/a^2/(a*e^2+c*d^2)^2/sqrt(e*x^2+d)/(c*x^4+a)+3/64*sqrt(c)*sqrt(sqrt(a)*e+sqrt(a*e^2+c*d^2))*(e*(-4*a*e^2+c*d^2)*(5*a*e^2+c*d^2)-(38*a^2*e^4+25*a*c*d^2*e^2+7*c^2*d^4)*(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^(9/4)/(a*e^2+c*d^2)^(7/2)+3/64*sqrt(c)*sqrt(-sqrt(a)*e+sqrt(a*e^2+c*d^2))*(e*(-4*a*e^2+c*d^2)*(5*a*e^2+c*d^2)-(38*a^2*e^4+25*a*c*d^2*e^2+7*c^2*d^4)*(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^(9/4)/(a*e^2+c*d^2)^(7/2),1],
[(e*x^2+d)^3/sqrt(-c*x^4+a),x,7,-d*e^2*x*sqrt(-c*x^4+a)/c-1/5*e^3*x^3*sqrt(-c*x^4+a)/c+3/5*a^(3/4)*e*(a*e^2+5*c*d^2)*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)+1/5*a^(1/4)*(5*sqrt(c)*d*(a*e^2+c*d^2)-3*sqrt(a)*e*(a*e^2+5*c*d^2))*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],
[(e*x^2+d)^2/sqrt(-c*x^4+a),x,6,-1/3*e^2*x*sqrt(-c*x^4+a)/c+2*a^(3/4)*d*e*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*c*d^2-6*sqrt(a)*sqrt(c)*d*e+a*e^2)*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],
[(e*x^2+d)/sqrt(-c*x^4+a),x,5,a^(3/4)*e*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)+a^(1/4)*(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)/sqrt(-c*x^4+a),1],
[1/sqrt(-c*x^4+a),x,2,a^(1/4)*sqrt(1-c*x^4/a)*InverseJacobiAM(arcsin(c^(1/4)*x/a^(1/4)),sqrt(-1))/c^(1/4)/sqrt(-c*x^4+a),1],
[1/(e*x^2+d)/sqrt(-c*x^4+a),x,2,a^(1/4)*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/sqrt(-c*x^4+a),1],
[1/(e*x^2+d)^2/sqrt(-c*x^4+a),x,9,-1/2*e^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)*e*sqrt(1-c*x^4/a)*EllipticE(sin(arcsin(c^(1/4)*x/a^(1/4))),sqrt(-1))/d/(-a*e^2+c*d^2)/sqrt(-c*x^4+a)-1/2*a^(1/4)*c^(1/4)*sqrt(1-c*x^4/a)*InverseJacobiAM(arcsin(c^(1/4)*x/a^(1/4)),sqrt(-1))/d/(sqrt(c)*d+sqrt(a)*e)/sqrt(-c*x^4+a)+1/2*a^(1/4)*(-a*e^2+3*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^2/(-a*e^2+c*d^2)/sqrt(-c*x^4+a),1],
[1/(e*x^2+d)^3/sqrt(-c*x^4+a),x,10,-1/4*e^2*x*sqrt(-c*x^4+a)/d/(-a*e^2+c*d^2)/(e*x^2+d)^2-3/8*e^2*(-a*e^2+3*c*d^2)*x*sqrt(-c*x^4+a)/d^2/(-a*e^2+c*d^2)^2/(e*x^2+d)-3/8*a^(3/4)*c^(1/4)*e*(-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))/d^2/(-a*e^2+c*d^2)^2/sqrt(-c*x^4+a)-1/8*a^(1/4)*c^(1/4)*(7*c*d^2-2*sqrt(a)*sqrt(c)*d*e-3*a*e^2)*sqrt(1-c*x^4/a)*InverseJacobiAM(arcsin(c^(1/4)*x/a^(1/4)),sqrt(-1))/d^2/(sqrt(c)*d+sqrt(a)*e)/(-a*e^2+c*d^2)/sqrt(-c*x^4+a)+3/8*a^(1/4)*(a^2*e^4-2*a*c*d^2*e^2+5*c^2*d^4)*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/(-a*e^2+c*d^2)^2/sqrt(-c*x^4+a),1],
[1/(e*x^2+d)^4/sqrt(-c*x^4+a),x,11,-1/6*e^2*x*sqrt(-c*x^4+a)/d/(-a*e^2+c*d^2)/(e*x^2+d)^3-5/24*e^2*(-a*e^2+3*c*d^2)*x*sqrt(-c*x^4+a)/d^2/(-a*e^2+c*d^2)^2/(e*x^2+d)^2-1/16*e^2*(5*a^2*e^4-14*a*c*d^2*e^2+29*c^2*d^4)*x*sqrt(-c*x^4+a)/d^3/(-a*e^2+c*d^2)^3/(e*x^2+d)-1/16*a^(3/4)*c^(1/4)*e*(5*a^2*e^4-14*a*c*d^2*e^2+29*c^2*d^4)*sqrt(1-c*x^4/a)*EllipticE(sin(arcsin(c^(1/4)*x/a^(1/4))),sqrt(-1))/d^3/(-a*e^2+c*d^2)^3/sqrt(-c*x^4+a)-1/48*a^(1/4)*c^(1/4)*(57*c^2*d^4-30*sqrt(a)*c^(3/2)*d^3*e-32*a*c*d^2*e^2+10*a^(3/2)*sqrt(c)*d*e^3+15*a^2*e^4)*sqrt(1-c*x^4/a)*InverseJacobiAM(arcsin(c^(1/4)*x/a^(1/4)),sqrt(-1))/d^3/(sqrt(c)*d-sqrt(a)*e)^2/(sqrt(c)*d+sqrt(a)*e)^3/sqrt(-c*x^4+a)+1/16*a^(1/4)*(-5*a^3*e^6+17*a^2*c*d^2*e^4-7*a*c^2*d^4*e^2+35*c^3*d^6)*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^4/(-a*e^2+c*d^2)^3/sqrt(-c*x^4+a),1],
[(e*x^2+d)^3/(-c*x^4+a)^(3/2),x,6,1/2*x*(c*d*(d^2+3*a*e^2/c)+e*(a*e^2+3*c*d^2)*x^2)/a/c/sqrt(-c*x^4+a)-3/2*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^(1/4)/c^(7/4)/sqrt(-c*x^4+a)+1/2*(c^(3/2)*d^3+3*sqrt(a)*c*d^2*e-3*a*sqrt(c)*d*e^2+3*a^(3/2)*e^3)*sqrt(1-c*x^4/a)*InverseJacobiAM(arcsin(c^(1/4)*x/a^(1/4)),sqrt(-1))/a^(3/4)/c^(7/4)/sqrt(-c*x^4+a),1],
[(e*x^2+d)^2/(-c*x^4+a)^(3/2),x,6,1/2*x*(d^2+a*e^2/c+2*d*e*x^2)/a/sqrt(-c*x^4+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^(3/4)/sqrt(-c*x^4+a)+1/2*(c*d^2+2*sqrt(a)*sqrt(c)*d*e-a*e^2)*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+a)^(3/2),x,6,1/2*x*(e*x^2+d)/a/sqrt(-c*x^4+a)-1/2*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)/sqrt(-c*x^4+a)+1/2*(sqrt(c)*d+sqrt(a)*e)*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],
[1/(-c*x^4+a)^(3/2),x,3,1/2*x/a/sqrt(-c*x^4+a)+1/2*sqrt(1-c*x^4/a)*InverseJacobiAM(arcsin(c^(1/4)*x/a^(1/4)),sqrt(-1))/a^(3/4)/c^(1/4)/sqrt(-c*x^4+a),1],
[1/(e*x^2+d)/(-c*x^4+a)^(3/2),x,9,1/2*c*x*(-e*x^2+d)/a/(-a*e^2+c*d^2)/sqrt(-c*x^4+a)+1/2*c^(1/4)*e*sqrt(1-c*x^4/a)*EllipticE(sin(arcsin(c^(1/4)*x/a^(1/4))),sqrt(-1))/a^(1/4)/(-a*e^2+c*d^2)/sqrt(-c*x^4+a)+1/2*c^(1/4)*sqrt(1-c*x^4/a)*InverseJacobiAM(arcsin(c^(1/4)*x/a^(1/4)),sqrt(-1))/a^(3/4)/(sqrt(c)*d+sqrt(a)*e)/sqrt(-c*x^4+a)-a^(1/4)*e^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],
[1/(e*x^2+d)^2/(-c*x^4+a)^(3/2),x,10,1/2*c*x*(-e*x^2+d)/a/(-a*e^2+c*d^2)/(e*x^2+d)/sqrt(-c*x^4+a)+1/2*e^2*(a*e^2+2*c*d^2)*x*sqrt(-c*x^4+a)/a/d/(-a*e^2+c*d^2)^2/(e*x^2+d)+1/2*c^(1/4)*e*(a*e^2+2*c*d^2)*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*c^(1/4)*(c*d^2-sqrt(a)*sqrt(c)*d*e+a*e^2)*sqrt(1-c*x^4/a)*InverseJacobiAM(arcsin(c^(1/4)*x/a^(1/4)),sqrt(-1))/a^(3/4)/d/(sqrt(c)*d+sqrt(a)*e)/(-a*e^2+c*d^2)/sqrt(-c*x^4+a)-1/2*a^(1/4)*e^2*(-a*e^2+7*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^2/(-a*e^2+c*d^2)^2/sqrt(-c*x^4+a),1],
[1/(e*x^2+d)^3/(-c*x^4+a)^(3/2),x,11,1/2*c*x*(-e*x^2+d)/a/(-a*e^2+c*d^2)/(e*x^2+d)^2/sqrt(-c*x^4+a)+1/4*e^2*(a*e^2+4*c*d^2)*x*sqrt(-c*x^4+a)/a/d/(-a*e^2+c*d^2)^2/(e*x^2+d)^2+3/8*e^2*(-a^2*e^4+7*a*c*d^2*e^2+4*c^2*d^4)*x*sqrt(-c*x^4+a)/a/d^2/(-a*e^2+c*d^2)^3/(e*x^2+d)+3/8*c^(1/4)*e*(-a^2*e^4+7*a*c*d^2*e^2+4*c^2*d^4)*sqrt(1-c*x^4/a)*EllipticE(sin(arcsin(c^(1/4)*x/a^(1/4))),sqrt(-1))/a^(1/4)/d^2/(-a*e^2+c*d^2)^3/sqrt(-c*x^4+a)+1/8*c^(1/4)*(4*c^2*d^4-8*sqrt(a)*c^(3/2)*d^3*e+19*a*c*d^2*e^2-2*a^(3/2)*sqrt(c)*d*e^3-3*a^2*e^4)*sqrt(1-c*x^4/a)*InverseJacobiAM(arcsin(c^(1/4)*x/a^(1/4)),sqrt(-1))/a^(3/4)/d^2/(sqrt(c)*d-sqrt(a)*e)^2/(sqrt(c)*d+sqrt(a)*e)^3/sqrt(-c*x^4+a)-3/8*a^(1/4)*e^2*(a^2*e^4-2*a*c*d^2*e^2+21*c^2*d^4)*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/(-a*e^2+c*d^2)^3/sqrt(-c*x^4+a),1],
[1/(e*x^2+d)^4/(-c*x^4+a)^(3/2),x,12,1/2*c*x*(-e*x^2+d)/a/(-a*e^2+c*d^2)/(e*x^2+d)^3/sqrt(-c*x^4+a)+1/6*e^2*(a*e^2+6*c*d^2)*x*sqrt(-c*x^4+a)/a/d/(-a*e^2+c*d^2)^2/(e*x^2+d)^3+1/24*e^2*(-5*a^2*e^4+39*a*c*d^2*e^2+36*c^2*d^4)*x*sqrt(-c*x^4+a)/a/d^2/(-a*e^2+c*d^2)^3/(e*x^2+d)^2+1/16*e^2*(5*a^3*e^6-18*a^2*c*d^2*e^4+121*a*c^2*d^4*e^2+32*c^3*d^6)*x*sqrt(-c*x^4+a)/a/d^3/(-a*e^2+c*d^2)^4/(e*x^2+d)+1/16*c^(1/4)*e*(5*a^3*e^6-18*a^2*c*d^2*e^4+121*a*c^2*d^4*e^2+32*c^3*d^6)*sqrt(1-c*x^4/a)*EllipticE(sin(arcsin(c^(1/4)*x/a^(1/4))),sqrt(-1))/a^(1/4)/d^3/(-a*e^2+c*d^2)^4/sqrt(-c*x^4+a)+1/48*c^(1/4)*(24*c^3*d^6-72*sqrt(a)*c^(5/2)*d^5*e+285*a*c^2*d^4*e^2-78*a^(3/2)*c^(3/2)*d^3*e^3-44*a^2*c*d^2*e^4+10*a^(5/2)*sqrt(c)*d*e^5+15*a^3*e^6)*sqrt(1-c*x^4/a)*InverseJacobiAM(arcsin(c^(1/4)*x/a^(1/4)),sqrt(-1))/a^(3/4)/d^3/(sqrt(c)*d-sqrt(a)*e)^3/(sqrt(c)*d+sqrt(a)*e)^4/sqrt(-c*x^4+a)-1/16*a^(1/4)*e^2*(-5*a^3*e^6+21*a^2*c*d^2*e^4+33*a*c^2*d^4*e^2+231*c^3*d^6)*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^4/(-a*e^2+c*d^2)^4/sqrt(-c*x^4+a),1],
[(e*x^2+d)^4/sqrt(c*x^4+a),x,7,1/21*e^2*(-5*a*e^2+42*c*d^2)*x*sqrt(c*x^4+a)/c^2+4/5*d*e^3*x^3*sqrt(c*x^4+a)/c+1/7*e^4*x^5*sqrt(c*x^4+a)/c+4/5*d*e*(-3*a*e^2+5*c*d^2)*x*sqrt(c*x^4+a)/c^(3/2)/(sqrt(a)+sqrt(c)*x^2)-4/5*a^(1/4)*d*e*(-3*a*e^2+5*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)+1/210*(84*sqrt(a)*sqrt(c)*d*e*(-3*a*e^2+5*c*d^2)+25*a^2*e^4-210*a*c*d^2*e^2+105*c^2*d^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)/c^(9/4)/sqrt(c*x^4+a),1],
[(e*x^2+d)^3/sqrt(c*x^4+a),x,6,d*e^2*x*sqrt(c*x^4+a)/c+1/5*e^3*x^3*sqrt(c*x^4+a)/c+3/5*e*(-a*e^2+5*c*d^2)*x*sqrt(c*x^4+a)/c^(3/2)/(sqrt(a)+sqrt(c)*x^2)-3/5*a^(1/4)*e*(-a*e^2+5*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)+1/10*(5*sqrt(c)*d*(-a*e^2+c*d^2)+3*sqrt(a)*e*(-a*e^2+5*c*d^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))/a^(1/4)/c^(7/4)/sqrt(c*x^4+a),1],
[(e*x^2+d)^2/sqrt(c*x^4+a),x,5,1/3*e^2*x*sqrt(c*x^4+a)/c+2*d*e*x*sqrt(c*x^4+a)/sqrt(c)/(sqrt(a)+sqrt(c)*x^2)-2*a^(1/4)*d*e*(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*c*d^2+6*sqrt(a)*sqrt(c)*d*e-a*e^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))/a^(1/4)/c^(5/4)/sqrt(c*x^4+a),1],
[(e*x^2+d)/sqrt(c*x^4+a),x,4,e*x*sqrt(c*x^4+a)/sqrt(c)/(sqrt(a)+sqrt(c)*x^2)-a^(1/4)*e*(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(c)*d+sqrt(a)*e)*(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],
[1/(e*x^2+d)/sqrt(c*x^4+a),x,4,1/2*sqrt(e)*arctan(sqrt(a*e^2+c*d^2)*x/sqrt(d)/sqrt(e)/sqrt(c*x^4+a))/sqrt(d)/sqrt(a*e^2+c*d^2)+1/2*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)*(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^(3/4)/d/(d-sqrt(a)*e/sqrt(c))/sqrt(c*x^4+a),1],
[1/(e*x^2+d)^2/sqrt(c*x^4+a),x,8,-1/2*sqrt(c)*e*x*sqrt(c*x^4+a)/d/(a*e^2+c*d^2)/(sqrt(a)+sqrt(c)*x^2)+1/2*e^2*x*sqrt(c*x^4+a)/d/(a*e^2+c*d^2)/(e*x^2+d)+1/4*sqrt(e)*(a*e^2+3*c*d^2)*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)^(3/2)+1/2*a^(1/4)*c^(1/4)*e*(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*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*e^2+3*c*d^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^(1/4)/c^(1/4)/d^2/(sqrt(c)*d-sqrt(a)*e)/(a*e^2+c*d^2)/sqrt(c*x^4+a),1],
[1/(e*x^2+d)^3/sqrt(c*x^4+a),x,9,-3/8*sqrt(c)*e*(a*e^2+3*c*d^2)*x*sqrt(c*x^4+a)/d^2/(a*e^2+c*d^2)^2/(sqrt(a)+sqrt(c)*x^2)+1/4*e^2*x*sqrt(c*x^4+a)/d/(a*e^2+c*d^2)/(e*x^2+d)^2+3/8*e^2*(a*e^2+3*c*d^2)*x*sqrt(c*x^4+a)/d^2/(a*e^2+c*d^2)^2/(e*x^2+d)+3/16*sqrt(e)*(a^2*e^4+2*a*c*d^2*e^2+5*c^2*d^4)*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)^(5/2)+3/8*a^(1/4)*c^(1/4)*e*(a*e^2+3*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))/d^2/(a*e^2+c*d^2)^2/sqrt(c*x^4+a)+1/8*c^(1/4)*(4*c*d^2-sqrt(a)*sqrt(c)*d*e+3*a*e^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))/a^(1/4)/d^2/(sqrt(c)*d-sqrt(a)*e)/(a*e^2+c*d^2)/sqrt(c*x^4+a)-3/32*(sqrt(c)*d+sqrt(a)*e)*(a^2*e^4+2*a*c*d^2*e^2+5*c^2*d^4)*(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)^2/sqrt(c*x^4+a),1],
[(e*x^2+d)/sqrt(c*x^4-a),x,5,a^(3/4)*e*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)+a^(1/4)*(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)/sqrt(c*x^4-a),1],
[1/(e*x^2+d)/sqrt(c*x^4-a),x,2,a^(1/4)*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/sqrt(c*x^4-a),1],
[(e*x^2+d)/sqrt(-c*x^4-a),x,4,-e*x*sqrt(-c*x^4-a)/sqrt(c)/(sqrt(a)+sqrt(c)*x^2)-a^(1/4)*e*(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(c)*d+sqrt(a)*e)*(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],
[1/(e*x^2+d)/sqrt(-c*x^4-a),x,4,1/2*sqrt(e)*arctanh(sqrt(a*e^2+c*d^2)*x/sqrt(d)/sqrt(e)/sqrt(-c*x^4-a))/sqrt(d)/sqrt(a*e^2+c*d^2)+1/2*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)*(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^(3/4)/d/(d-sqrt(a)*e/sqrt(c))/sqrt(-c*x^4-a),1],
[1/(b*x^2+a)/sqrt(-5*x^4+4),x,1,1/5*EllipticPi(sin(arcsin(5^(1/4)*x/sqrt(2))),-2*b/sqrt(5)/a,sqrt(-1))/sqrt(2)*5^(3/4)/a,1],
[1/(b*x^2+a)/sqrt(5*x^4+4),x,4,1/2*sqrt(b)*arctan(sqrt(5*a^2+4*b^2)*x/sqrt(a)/sqrt(b)/sqrt(5*x^4+4))/sqrt(a)/sqrt(5*a^2+4*b^2)+1/2*5^(3/4)*(2+sqrt(5)*x^2)*sqrt((5*x^4+4)/(2+sqrt(5)*x^2)^2)*InverseJacobiAM(2*arctan(5^(1/4)*x/sqrt(2)),sqrt(1/2))/sqrt(2)/(5*a-2*sqrt(5)*b)/sqrt(5*x^4+4)-1/4*5^(1/4)*(sqrt(5)*a+2*b)*(2+sqrt(5)*x^2)*sqrt((5*x^4+4)/(2+sqrt(5)*x^2)^2)*EllipticPi(sin(2*arctan(5^(1/4)*x/sqrt(2))),-1/8*(sqrt(5)*a-2*b)^2/sqrt(5)/a/b,sqrt(1/2))/sqrt(2)/a/(5*a-2*sqrt(5)*b)/sqrt(5*x^4+4),1],
[1/(b*x^2+a)/sqrt(-d*x^4+4),x,1,EllipticPi(sin(arcsin(d^(1/4)*x/sqrt(2))),-2*b/a/sqrt(d),sqrt(-1))/sqrt(2)/a/d^(1/4),1],
[1/(b*x^2+a)/sqrt(d*x^4+4),x,4,1/2*sqrt(b)*arctan(sqrt(a^2*d+4*b^2)*x/sqrt(a)/sqrt(b)/sqrt(d*x^4+4))/sqrt(a)/sqrt(a^2*d+4*b^2)-1/2*d^(1/4)*(2+sqrt(d)*x^2)*sqrt((d*x^4+4)/(2+sqrt(d)*x^2)^2)*InverseJacobiAM(2*arctan(d^(1/4)*x/sqrt(2)),sqrt(1/2))/sqrt(2)/(2*b-a*sqrt(d))/sqrt(d*x^4+4)+1/4*(2*b+a*sqrt(d))*(2+sqrt(d)*x^2)*sqrt((d*x^4+4)/(2+sqrt(d)*x^2)^2)*EllipticPi(sin(2*arctan(d^(1/4)*x/sqrt(2))),-1/8*(2*b-a*sqrt(d))^2/a/b/sqrt(d),sqrt(1/2))/sqrt(2)/a/(2*b-a*sqrt(d))/d^(1/4)/sqrt(d*x^4+4),1],
[(e*x^2+d)^(3/2)*sqrt(-c*x^4+a),x,11,1/48*(3*d^2/e-8*a*e/c)*sqrt(e*x^2+d)*sqrt(-c*x^4+a)/x+7/24*d*x*sqrt(e*x^2+d)*sqrt(-c*x^4+a)+1/6*e*x^3*sqrt(e*x^2+d)*sqrt(-c*x^4+a)+1/48*(d+sqrt(a)*e/sqrt(c))*(-8*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)*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)+1/48*sqrt(a)*(8*a*e^2+31*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)/sqrt(e*x^2+d)/sqrt(-c*x^4+a)+1/16*d*(12*a*e^2+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/sqrt(e*x^2+d)/sqrt(-c*x^4+a),1],
[sqrt(e*x^2+d)*sqrt(-c*x^4+a),x,10,1/8*d*sqrt(e*x^2+d)*sqrt(-c*x^4+a)/e/x+1/4*x*sqrt(e*x^2+d)*sqrt(-c*x^4+a)+1/8*c*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/sqrt(e*x^2+d)/sqrt(-c*x^4+a)+5/8*sqrt(a)*sqrt(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)*InverseJacobiAM(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*e^2+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/sqrt(e*x^2+d)/sqrt(-c*x^4+a),1],
[sqrt(-c*x^4+a)/sqrt(e*x^2+d),x,9,1/2*sqrt(e*x^2+d)*sqrt(-c*x^4+a)/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*sqrt(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(e*x^2+d)/sqrt(-c*x^4+a)+1/2*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],
[sqrt(-c*x^4+a)/(e*x^2+d)^(3/2),x,12,x*sqrt(-c*x^4+a)/d/sqrt(e*x^2+d)-sqrt(e*x^2+d)*sqrt(-c*x^4+a)/d/e/x-sqrt(c)*(sqrt(c)*d+sqrt(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)*EllipticE(sin(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)+sqrt(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))))/d/sqrt(e*x^2+d)/sqrt(-c*x^4+a)-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/sqrt(e*x^2+d)/sqrt(-c*x^4+a),1],
[sqrt(-c*x^4+a)/(e*x^2+d)^(5/2),x,8,1/3*x*sqrt(-c*x^4+a)/d/(e*x^2+d)^(3/2)+2/3*a*e*sqrt(-c*x^4+a)/d/(-a*e^2+c*d^2)/x/sqrt(e*x^2+d)+2/3*a*sqrt(c)*e*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)/sqrt(e*x^2+d)/sqrt(-c*x^4+a)+2/3*sqrt(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))))/d^2/sqrt(e*x^2+d)/sqrt(-c*x^4+a),1],
[sqrt(-c*x^4+a)/(e*x^2+d)^(7/2),x,8,1/5*x*sqrt(-c*x^4+a)/d/(e*x^2+d)^(5/2)+2/15*(-2*a*e^2+c*d^2)*x*sqrt(-c*x^4+a)/d^2/(-a*e^2+c*d^2)/(e*x^2+d)^(3/2)+8/15*a*e*(-a*e^2+2*c*d^2)*sqrt(-c*x^4+a)/d^2/(-a*e^2+c*d^2)^2/x/sqrt(e*x^2+d)+8/15*a*sqrt(c)*e*(-a*e^2+2*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))))/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*e^2+5*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))))/d^3/(-a*e^2+c*d^2)/sqrt(e*x^2+d)/sqrt(-c*x^4+a),1],
[sqrt(-c*x^4+a)/(e*x^2+d)^(9/2),x,9,1/7*x*sqrt(-c*x^4+a)/d/(e*x^2+d)^(7/2)+2/35*(-3*a*e^2+2*c*d^2)*x*sqrt(-c*x^4+a)/d^2/(-a*e^2+c*d^2)/(e*x^2+d)^(5/2)+8/105*(3*a^2*e^4-6*a*c*d^2*e^2+c^2*d^4)*x*sqrt(-c*x^4+a)/d^3/(-a*e^2+c*d^2)^2/(e*x^2+d)^(3/2)+2/105*a*e*(24*a^2*e^4-69*a*c*d^2*e^2+77*c^2*d^4)*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)*e*(24*a^2*e^4-69*a*c*d^2*e^2+77*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))))/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)*(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],
[(e*x^2+d)^(3/2)*(-c*x^4+a)^(3/2),x,13,-1/1280*(-32*a*e^2+5*c*d^2)*(-4*a*e^2+3*c*d^2)*sqrt(e*x^2+d)*sqrt(-c*x^4+a)/c/e^3/x+1/640*d*(236*a+5*c*d^2/e^2)*x*sqrt(e*x^2+d)*sqrt(-c*x^4+a)-1/160*(-32*a*e^2+c*d^2)*x^3*sqrt(e*x^2+d)*sqrt(-c*x^4+a)/e-11/80*c*d*x^5*sqrt(e*x^2+d)*sqrt(-c*x^4+a)-1/10*c*e*x^7*sqrt(e*x^2+d)*sqrt(-c*x^4+a)-1/1280*(d+sqrt(a)*e/sqrt(c))*(-32*a*e^2+5*c*d^2)*(-4*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)*EllipticE(sin(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)+1/1280*sqrt(a)*(128*a^2*e^4+692*a*c*d^2*e^2+5*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^2/sqrt(e*x^2+d)/sqrt(-c*x^4+a)-3/256*d*(-12*a*e^2+c*d^2)*(4*a*e^2+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^3/sqrt(e*x^2+d)/sqrt(-c*x^4+a),1],
[sqrt(e*x^2+d)*(-c*x^4+a)^(3/2),x,12,-1/384*d*(-68*a*e^2+15*c*d^2)*sqrt(e*x^2+d)*sqrt(-c*x^4+a)/e^3/x+5/192*(12*a+c*d^2/e^2)*x*sqrt(e*x^2+d)*sqrt(-c*x^4+a)-1/48*c*d*x^3*sqrt(e*x^2+d)*sqrt(-c*x^4+a)/e-1/8*c*x^5*sqrt(e*x^2+d)*sqrt(-c*x^4+a)-1/384*c*d*(d+sqrt(a)*e/sqrt(c))*(-68*a*e^2+15*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^3/sqrt(e*x^2+d)/sqrt(-c*x^4+a)+1/384*sqrt(a)*sqrt(c)*d*(196*a*e^2+5*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))))/e^2/sqrt(e*x^2+d)/sqrt(-c*x^4+a)-1/128*(-48*a^2*e^4-24*a*c*d^2*e^2+5*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^3/sqrt(e*x^2+d)/sqrt(-c*x^4+a),1],
[(-c*x^4+a)^(3/2)/sqrt(e*x^2+d),x,11,-1/48*(-32*a*e^2+15*c*d^2)*sqrt(e*x^2+d)*sqrt(-c*x^4+a)/e^3/x+5/24*c*d*x*sqrt(e*x^2+d)*sqrt(-c*x^4+a)/e^2-1/6*c*x^3*sqrt(e*x^2+d)*sqrt(-c*x^4+a)/e-1/48*c*(d+sqrt(a)*e/sqrt(c))*(-32*a*e^2+15*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^3/sqrt(e*x^2+d)/sqrt(-c*x^4+a)+1/48*sqrt(a)*sqrt(c)*(16*a*e^2+5*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))))/e^2/sqrt(e*x^2+d)/sqrt(-c*x^4+a)-1/16*c*d*(-12*a*e^2+5*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^3/sqrt(e*x^2+d)/sqrt(-c*x^4+a),1],
[(-c*x^4+a)^(3/2)/(e*x^2+d)^(3/2),x,11,(a-c*d^2/e^2)*x*sqrt(-c*x^4+a)/d/sqrt(e*x^2+d)+1/8*(-8*a*e^2+15*c*d^2)*sqrt(e*x^2+d)*sqrt(-c*x^4+a)/d/e^3/x-1/4*c*x*sqrt(e*x^2+d)*sqrt(-c*x^4+a)/e^2+1/8*sqrt(c)*(sqrt(c)*d+sqrt(a)*e)*(-8*a*e^2+15*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))))/d/e^3/sqrt(e*x^2+d)/sqrt(-c*x^4+a)-1/8*sqrt(a)*sqrt(c)*(-8*a*e^2+5*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))))/d/e^2/sqrt(e*x^2+d)/sqrt(-c*x^4+a)+3/8*c*(-4*a*e^2+5*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^3/sqrt(e*x^2+d)/sqrt(-c*x^4+a),1],
[(-c*x^4+a)^(3/2)/(e*x^2+d)^(5/2),x,11,1/3*(a-c*d^2/e^2)*x*sqrt(-c*x^4+a)/d/(e*x^2+d)^(3/2)+2/3*(a/d^2+3*c/e^2)*x*sqrt(-c*x^4+a)/sqrt(e*x^2+d)-1/6*(4*a*e^2+15*c*d^2)*sqrt(e*x^2+d)*sqrt(-c*x^4+a)/d^2/e^3/x-1/6*sqrt(c)*(sqrt(c)*d+sqrt(a)*e)*(4*a*e^2+15*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))))/d^2/e^3/sqrt(e*x^2+d)/sqrt(-c*x^4+a)+1/6*sqrt(a)*sqrt(c)*(4*a*e^2+5*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))))/d^2/e^2/sqrt(e*x^2+d)/sqrt(-c*x^4+a)-5/2*c^2*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^3/sqrt(e*x^2+d)/sqrt(-c*x^4+a),1],
[(-c*x^4+a)^(3/2)/(e*x^2+d)^(7/2),x,11,1/5*(a-c*d^2/e^2)*x*sqrt(-c*x^4+a)/d/(e*x^2+d)^(5/2)+4/15*(a/d^2+2*c/e^2)*x*sqrt(-c*x^4+a)/(e*x^2+d)^(3/2)+1/15*(8*a^2*e^4-11*a*c*d^2*e^2+15*c^2*d^4)*sqrt(-c*x^4+a)/d^2/e^3/(-a*e^2+c*d^2)/x/sqrt(e*x^2+d)+1/15*sqrt(c)*(8*a^2*e^4-11*a*c*d^2*e^2+15*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))))/d^3/e^3/(sqrt(c)*d-sqrt(a)*e)/sqrt(e*x^2+d)/sqrt(-c*x^4+a)-1/15*sqrt(a)*sqrt(c)*(-8*a*e^2+5*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))))/d^3/e^2/sqrt(e*x^2+d)/sqrt(-c*x^4+a)+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^3/sqrt(e*x^2+d)/sqrt(-c*x^4+a),1],
[(-c*x^4+a)^(3/2)/(e*x^2+d)^(9/2),x,9,1/7*(a-c*d^2/e^2)*x*sqrt(-c*x^4+a)/d/(e*x^2+d)^(7/2)+2/35*(3*a/d^2+5*c/e^2)*x*sqrt(-c*x^4+a)/(e*x^2+d)^(5/2)-1/35*(8*a^2*e^4-9*a*c*d^2*e^2+5*c^2*d^4)*x*sqrt(-c*x^4+a)/d^3/e^2/(-a*e^2+c*d^2)/(e*x^2+d)^(3/2)+16/35*a^2*e*(-a*e^2+2*c*d^2)*sqrt(-c*x^4+a)/d^3/(-a*e^2+c*d^2)^2/x/sqrt(e*x^2+d)+16/35*a^2*sqrt(c)*e*(-a*e^2+2*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))))/d^4/(sqrt(c)*d-sqrt(a)*e)/(-a*e^2+c*d^2)/sqrt(e*x^2+d)/sqrt(-c*x^4+a)+4/35*a^(3/2)*sqrt(c)*(-4*a*e^2+5*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))))/d^4/(-a*e^2+c*d^2)/sqrt(e*x^2+d)/sqrt(-c*x^4+a),1],
[(-c*x^4+a)^(3/2)/(e*x^2+d)^(11/2),x,10,1/9*(a-c*d^2/e^2)*x*sqrt(-c*x^4+a)/d/(e*x^2+d)^(9/2)+4/63*(2*a/d^2+3*c/e^2)*x*sqrt(-c*x^4+a)/(e*x^2+d)^(7/2)-1/105*(16*a^2*e^4-17*a*c*d^2*e^2+5*c^2*d^4)*x*sqrt(-c*x^4+a)/d^3/e^2/(-a*e^2+c*d^2)/(e*x^2+d)^(5/2)-2/315*(-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)*x*sqrt(-c*x^4+a)/d^4/e^2/(-a*e^2+c*d^2)^2/(e*x^2+d)^(3/2)+4/315*a^2*e*(32*a^2*e^4-93*a*c*d^2*e^2+93*c^2*d^4)*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)*e*(32*a^2*e^4-93*a*c*d^2*e^2+93*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))))/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)*(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],
[(e*x^2+d)^(5/2)/sqrt(-c*x^4+a),x,10,-9/8*d*e*sqrt(e*x^2+d)*sqrt(-c*x^4+a)/c/x-1/4*e^2*x*sqrt(e*x^2+d)*sqrt(-c*x^4+a)/c-9/8*d*e*(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*d*(11*a*e^2+8*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(a)/sqrt(c)/sqrt(e*x^2+d)/sqrt(-c*x^4+a)+1/8*e*(4*a*e^2+15*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],
[(e*x^2+d)^(3/2)/sqrt(-c*x^4+a),x,9,-1/2*e*sqrt(e*x^2+d)*sqrt(-c*x^4+a)/c/x-1/2*e*(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*(a*e^2+2*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(a)/sqrt(c)/sqrt(e*x^2+d)/sqrt(-c*x^4+a)+3/2*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)*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],
[sqrt(e*x^2+d)/sqrt(-c*x^4+a),x,5,sqrt(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)*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)+e*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],
[1/sqrt(e*x^2+d)/sqrt(-c*x^4+a),x,2,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),1],
[1/(e*x^2+d)^(3/2)/sqrt(-c*x^4+a),x,6,e*sqrt(-c*x^4+a)/(-a*e^2+c*d^2)/x/sqrt(e*x^2+d)+sqrt(c)*e*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)+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],
[1/(e*x^2+d)^(5/2)/sqrt(-c*x^4+a),x,7,-1/3*e^2*x*sqrt(-c*x^4+a)/d/(-a*e^2+c*d^2)/(e*x^2+d)^(3/2)+2/3*e*(-a*e^2+3*c*d^2)*sqrt(-c*x^4+a)/d/(-a*e^2+c*d^2)^2/x/sqrt(e*x^2+d)+2/3*sqrt(c)*e*(-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)*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*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))))/sqrt(a)/d^2/(-a*e^2+c*d^2)/sqrt(e*x^2+d)/sqrt(-c*x^4+a),1],
[1/(e*x^2+d)^(7/2)/sqrt(-c*x^4+a),x,8,-1/5*e^2*x*sqrt(-c*x^4+a)/d/(-a*e^2+c*d^2)/(e*x^2+d)^(5/2)-4/15*e^2*(-a*e^2+3*c*d^2)*x*sqrt(-c*x^4+a)/d^2/(-a*e^2+c*d^2)^2/(e*x^2+d)^(3/2)+1/15*e*(8*a^2*e^4-21*a*c*d^2*e^2+45*c^2*d^4)*sqrt(-c*x^4+a)/d^2/(-a*e^2+c*d^2)^3/x/sqrt(e*x^2+d)+1/15*sqrt(c)*e*(8*a^2*e^4-21*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)*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)^3/(sqrt(c)*d+sqrt(a)*e)^2/sqrt(e*x^2+d)/sqrt(-c*x^4+a)+1/15*sqrt(c)*(8*a^2*e^4-15*a*c*d^2*e^2+15*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(a)/d^3/(-a*e^2+c*d^2)^2/sqrt(e*x^2+d)/sqrt(-c*x^4+a),1],
[(e*x^2+d)^(7/2)/(-c*x^4+a)^(3/2),x,12,1/2*x*(e*x^2+d)^(7/2)/a/sqrt(-c*x^4+a)+1/2*e*(2*a*e^2+3*c*d^2)*sqrt(e*x^2+d)*sqrt(-c*x^4+a)/a/c^2/x+3/2*d*e^2*x*sqrt(e*x^2+d)*sqrt(-c*x^4+a)/a/c+1/2*e^3*x^3*sqrt(e*x^2+d)*sqrt(-c*x^4+a)/a/c+1/2*e*(d+sqrt(a)*e/sqrt(c))*(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)*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*(-2*a^2*e^4-6*a*c*d^2*e^2+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))))/a^(3/2)/c^(3/2)/sqrt(e*x^2+d)/sqrt(-c*x^4+a)-7/2*d*e^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))))/c/sqrt(e*x^2+d)/sqrt(-c*x^4+a),1],
[(e*x^2+d)^(5/2)/(-c*x^4+a)^(3/2),x,11,1/2*x*(e*x^2+d)^(5/2)/a/sqrt(-c*x^4+a)+d*e*sqrt(e*x^2+d)*sqrt(-c*x^4+a)/a/c/x+1/2*e^2*x*sqrt(e*x^2+d)*sqrt(-c*x^4+a)/a/c+d*e*(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*d*(-3*a*e^2+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)/sqrt(c)/sqrt(e*x^2+d)/sqrt(-c*x^4+a)-e^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))))/c/sqrt(e*x^2+d)/sqrt(-c*x^4+a),1],
[(e*x^2+d)^(3/2)/(-c*x^4+a)^(3/2),x,7,1/2*x*(e*x^2+d)^(3/2)/a/sqrt(-c*x^4+a)+1/2*e*sqrt(e*x^2+d)*sqrt(-c*x^4+a)/a/c/x+1/2*e*(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*e^2+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)/sqrt(c)/sqrt(e*x^2+d)/sqrt(-c*x^4+a),1],
[sqrt(e*x^2+d)/(-c*x^4+a)^(3/2),x,4,1/2*x*sqrt(e*x^2+d)/a/sqrt(-c*x^4+a)+1/2*sqrt(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)*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],
[1/sqrt(e*x^2+d)/(-c*x^4+a)^(3/2),x,7,-1/2*e*sqrt(e*x^2+d)/(-a*e^2+c*d^2)/x/sqrt(-c*x^4+a)+1/2*c*d*x*sqrt(e*x^2+d)/a/(-a*e^2+c*d^2)/sqrt(-c*x^4+a)-1/2*sqrt(c)*e*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*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],
[1/(e*x^2+d)^(3/2)/(-c*x^4+a)^(3/2),x,7,1/2*c*x*(-e*x^2+d)/a/(-a*e^2+c*d^2)/sqrt(e*x^2+d)/sqrt(-c*x^4+a)-e*(a*e^2+c*d^2)*sqrt(-c*x^4+a)/a/(-a*e^2+c*d^2)^2/x/sqrt(e*x^2+d)-sqrt(c)*e*(a*e^2+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/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*e^2+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)/d/(-a*e^2+c*d^2)/sqrt(e*x^2+d)/sqrt(-c*x^4+a),1],
[1/(e*x^2+d)^(5/2)/(-c*x^4+a)^(3/2),x,8,1/2*c*x*(-e*x^2+d)/a/(-a*e^2+c*d^2)/(e*x^2+d)^(3/2)/sqrt(-c*x^4+a)+1/3*e^2*(a*e^2+3*c*d^2)*x*sqrt(-c*x^4+a)/a/d/(-a*e^2+c*d^2)^2/(e*x^2+d)^(3/2)-1/6*e*(-4*a^2*e^4+27*a*c*d^2*e^2+9*c^2*d^4)*sqrt(-c*x^4+a)/a/d/(-a*e^2+c*d^2)^3/x/sqrt(e*x^2+d)-1/6*sqrt(c)*e*(-4*a^2*e^4+27*a*c*d^2*e^2+9*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))))/a/d^2/(sqrt(c)*d-sqrt(a)*e)^3/(sqrt(c)*d+sqrt(a)*e)^2/sqrt(e*x^2+d)/sqrt(-c*x^4+a)+1/6*sqrt(c)*(4*a^2*e^4-15*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)*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^2/(-a*e^2+c*d^2)^2/sqrt(e*x^2+d)/sqrt(-c*x^4+a),1],
[(e*x^2+d)^(9/2)/(-c*x^4+a)^(5/2),x,14,1/6*x*(e*x^2+d)^(9/2)/a/(-c*x^4+a)^(3/2)+1/12*x*(-4*e*x^2+5*d)*(e*x^2+d)^(7/2)/a^2/sqrt(-c*x^4+a)+1/12*d*e*(-15*a*e^2+11*c*d^2)*sqrt(e*x^2+d)*sqrt(-c*x^4+a)/a^2/c^2/x+1/4*e^2*(-2*a*e^2+c*d^2)*x*sqrt(e*x^2+d)*sqrt(-c*x^4+a)/a^2/c^2-7/12*d*e^3*x^3*sqrt(e*x^2+d)*sqrt(-c*x^4+a)/a^2/c-1/3*e^4*x^5*sqrt(e*x^2+d)*sqrt(-c*x^4+a)/a^2/c+1/12*d*e*(d+sqrt(a)*e/sqrt(c))*(-15*a*e^2+11*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^2/c/sqrt(e*x^2+d)/sqrt(-c*x^4+a)+1/12*d*(21*a^2*e^4-14*a*c*d^2*e^2+5*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))))/a^(5/2)/c^(3/2)/sqrt(e*x^2+d)/sqrt(-c*x^4+a)+e^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))))/c^2/sqrt(e*x^2+d)/sqrt(-c*x^4+a),1],
[(e*x^2+d)^(7/2)/(-c*x^4+a)^(5/2),x,10,1/6*x*(e*x^2+d)^(7/2)/a/(-c*x^4+a)^(3/2)+1/12*x*(-2*e*x^2+5*d)*(e*x^2+d)^(5/2)/a^2/sqrt(-c*x^4+a)+1/3*e*(-a*e^2+2*c*d^2)*sqrt(e*x^2+d)*sqrt(-c*x^4+a)/a^2/c^2/x+1/12*d*e^2*x*sqrt(e*x^2+d)*sqrt(-c*x^4+a)/a^2/c-1/6*e^3*x^3*sqrt(e*x^2+d)*sqrt(-c*x^4+a)/a^2/c+1/3*e*(d+sqrt(a)*e/sqrt(c))*(-a*e^2+2*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^2/c/sqrt(e*x^2+d)/sqrt(-c*x^4+a)+1/12*(4*a^2*e^4-9*a*c*d^2*e^2+5*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))))/a^(5/2)/c^(3/2)/sqrt(e*x^2+d)/sqrt(-c*x^4+a),1],
[(e*x^2+d)^(5/2)/(-c*x^4+a)^(5/2),x,9,1/6*x*(e*x^2+d)^(5/2)/a/(-c*x^4+a)^(3/2)+5/12*d*x*(e*x^2+d)^(3/2)/a^2/sqrt(-c*x^4+a)+5/12*d*e*sqrt(e*x^2+d)*sqrt(-c*x^4+a)/a^2/c/x+5/12*d*e*(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^2/sqrt(e*x^2+d)/sqrt(-c*x^4+a)+5/12*d*(-a*e^2+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^(5/2)/sqrt(c)/sqrt(e*x^2+d)/sqrt(-c*x^4+a),1],
[(e*x^2+d)^(3/2)/(-c*x^4+a)^(5/2),x,8,1/6*x*(e*x^2+d)^(3/2)/a/(-c*x^4+a)^(3/2)+1/12*x*sqrt(e*x^2+d)*(2*e*x^2+5*d)/a^2/sqrt(-c*x^4+a)+1/6*e*sqrt(e*x^2+d)*sqrt(-c*x^4+a)/a^2/c/x+1/6*e*(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^2/sqrt(e*x^2+d)/sqrt(-c*x^4+a)+1/12*(-2*a*e^2+5*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^(5/2)/sqrt(c)/sqrt(e*x^2+d)/sqrt(-c*x^4+a),1],
[sqrt(e*x^2+d)/(-c*x^4+a)^(5/2),x,8,1/6*x*sqrt(e*x^2+d)/a/(-c*x^4+a)^(3/2)-1/12*d*e*sqrt(e*x^2+d)/a/(-a*e^2+c*d^2)/x/sqrt(-c*x^4+a)+1/12*(-4*a*e^2+5*c*d^2)*x*sqrt(e*x^2+d)/a^2/(-a*e^2+c*d^2)/sqrt(-c*x^4+a)-1/12*sqrt(c)*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)*EllipticE(sin(arcsin(sqrt(1-sqrt(a)/sqrt(c)/x^2)/sqrt(2))),sqrt(2*d/(d+sqrt(a)*e/sqrt(c))))/a^2/(sqrt(c)*d-sqrt(a)*e)/sqrt(e*x^2+d)/sqrt(-c*x^4+a)+5/12*sqrt(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)*InverseJacobiAM(arcsin(sqrt(1-sqrt(a)/sqrt(c)/x^2)/sqrt(2)),sqrt(2*d/(d+sqrt(a)*e/sqrt(c))))/a^(5/2)/sqrt(e*x^2+d)/sqrt(-c*x^4+a),1],
[1/sqrt(e*x^2+d)/(-c*x^4+a)^(5/2),x,8,1/6*c*x*(-e*x^2+d)*sqrt(e*x^2+d)/a/(-a*e^2+c*d^2)/(-c*x^4+a)^(3/2)-1/3*e*(-2*a*e^2+c*d^2)*sqrt(e*x^2+d)/a/(-a*e^2+c*d^2)^2/x/sqrt(-c*x^4+a)+1/12*c*d*(-9*a*e^2+5*c*d^2)*x*sqrt(e*x^2+d)/a^2/(-a*e^2+c*d^2)^2/sqrt(-c*x^4+a)-1/3*sqrt(c)*e*(-2*a*e^2+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^2/(sqrt(c)*d-sqrt(a)*e)/(-a*e^2+c*d^2)/sqrt(e*x^2+d)/sqrt(-c*x^4+a)+1/12*sqrt(c)*(-4*a*e^2+5*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^(5/2)/(-a*e^2+c*d^2)/sqrt(e*x^2+d)/sqrt(-c*x^4+a),1],
[1/(e*x^2+d)^(3/2)/(-c*x^4+a)^(5/2),x,9,1/6*c*x*(-e*x^2+d)/a/(-a*e^2+c*d^2)/sqrt(e*x^2+d)/(-c*x^4+a)^(3/2)+1/3*e^2*(3*a*e^2+c*d^2)*x/a/d/(-a*e^2+c*d^2)^2/sqrt(e*x^2+d)/sqrt(-c*x^4+a)-1/12*e*(-12*a^2*e^4-27*a*c*d^2*e^2+7*c^2*d^4)*sqrt(e*x^2+d)/a/d/(-a*e^2+c*d^2)^3/x/sqrt(-c*x^4+a)+1/12*c*(-22*a^2*e^4-15*a*c*d^2*e^2+5*c^2*d^4)*x*sqrt(e*x^2+d)/a^2/(-a*e^2+c*d^2)^3/sqrt(-c*x^4+a)-1/12*sqrt(c)*e*(-12*a^2*e^4-27*a*c*d^2*e^2+7*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))))/a^2/d/(sqrt(c)*d-sqrt(a)*e)^3/(sqrt(c)*d+sqrt(a)*e)^2/sqrt(e*x^2+d)/sqrt(-c*x^4+a)+1/12*sqrt(c)*(12*a^2*e^4-9*a*c*d^2*e^2+5*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))))/a^(5/2)/d/(-a*e^2+c*d^2)^2/sqrt(e*x^2+d)/sqrt(-c*x^4+a),1],
[1/(e*x^2+d)^(5/2)/(-c*x^4+a)^(5/2),x,10,1/6*c*x*(-e*x^2+d)/a/(-a*e^2+c*d^2)/(e*x^2+d)^(3/2)/(-c*x^4+a)^(3/2)+1/3*e^2*(a*e^2+c*d^2)*x/a/d/(-a*e^2+c*d^2)^2/(e*x^2+d)^(3/2)/sqrt(-c*x^4+a)+1/6*e^2*(-4*a^2*e^4+33*a*c*d^2*e^2+3*c^2*d^4)*x/a/d^2/(-a*e^2+c*d^2)^3/sqrt(e*x^2+d)/sqrt(-c*x^4+a)-1/6*e*(4*a^3*e^6-43*a^2*c*d^2*e^4-30*a*c^2*d^4*e^2+5*c^3*d^6)*sqrt(e*x^2+d)/a/d^2/(-a*e^2+c*d^2)^4/x/sqrt(-c*x^4+a)+1/12*c*(4*a^3*e^6-115*a^2*c*d^2*e^4-22*a*c^2*d^4*e^2+5*c^3*d^6)*x*sqrt(e*x^2+d)/a^2/d/(-a*e^2+c*d^2)^4/sqrt(-c*x^4+a)-1/6*sqrt(c)*e*(4*a^3*e^6-43*a^2*c*d^2*e^4-30*a*c^2*d^4*e^2+5*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)*EllipticE(sin(arcsin(sqrt(1-sqrt(a)/sqrt(c)/x^2)/sqrt(2))),sqrt(2*d/(d+sqrt(a)*e/sqrt(c))))/a^2/d^2/(sqrt(c)*d-sqrt(a)*e)^4/(sqrt(c)*d+sqrt(a)*e)^3/sqrt(e*x^2+d)/sqrt(-c*x^4+a)+1/12*sqrt(c)*(-8*a^3*e^6+50*a^2*c*d^2*e^4-15*a*c^2*d^4*e^2+5*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))))/a^(5/2)/d^2/(-a*e^2+c*d^2)^3/sqrt(e*x^2+d)/sqrt(-c*x^4+a),1],
[sqrt(b*x^2+a)/sqrt(-x^4+1),x,5,a*sqrt(1-1/x^4)*x^3*sqrt((b*x^2+a)/(a+b)/x^2)*InverseJacobiAM(arcsin(sqrt(1-1/x^2)/sqrt(2)),sqrt(2*a/(a+b)))/sqrt(b*x^2+a)/sqrt(-x^4+1)+b*sqrt(1-1/x^4)*x^3*sqrt((b*x^2+a)/(a+b)/x^2)*EllipticPi(sin(arcsin(sqrt(1-1/x^2)/sqrt(2))),2,sqrt(2*a/(a+b)))/sqrt(b*x^2+a)/sqrt(-x^4+1),1],
[(e*x^2+d)^q*(c*x^4+a)^2,x,6,-3*c*d*(35*c*d^2+2*a*e^2*(4*q^2+32*q+63))*x*(e*x^2+d)^(1+q)/e^4/(3+2*q)/(5+2*q)/(7+2*q)/(9+2*q)+c*(35*c*d^2+2*a*e^2*(4*q^2+32*q+63))*x^3*(e*x^2+d)^(1+q)/e^3/(5+2*q)/(7+2*q)/(9+2*q)-7*c^2*d*x^5*(e*x^2+d)^(1+q)/e^2/(7+2*q)/(9+2*q)+c^2*x^7*(e*x^2+d)^(1+q)/e/(9+2*q)+(a^2*e^4*(4*q^2+32*q+63)+3*c*d^2*(35*c*d^2+2*a*e^2*(4*q^2+32*q+63))/(3+2*q)/(5+2*q))*x*(e*x^2+d)^q*hypergeom([1/2, -q],[3/2],-e*x^2/d)/e^4/(7+2*q)/(9+2*q)/((1+e*x^2/d)^q),1],
[(e*x^2+d)^q*(c*x^4+a),x,4,-3*c*d*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+a*e^2*(4*q^2+16*q+15))*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,x,2,x*(e*x^2+d)^q*hypergeom([1/2, -q],[3/2],-e*x^2/d)/((1+e*x^2/d)^q),1],
[(e*x^2+d)^q/(c*x^4+a),x,7,1/2*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*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],
[(e*x^2+d)^q/(c*x^4+a)^2,x,13,1/4*c*x*(-e*x^2+d)*(e*x^2+d)^(1+q)/a/(a*e^2+c*d^2)/(c*x^4+a)+1/8*(3*c*d^2+a*e^2*(3-2*q)+2*sqrt(-a)*sqrt(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/(a*e^2+c*d^2)/((1+e*x^2/d)^q)+1/8*(3*c*d^2+a*e^2*(3-2*q)-2*sqrt(-a)*sqrt(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/(a*e^2+c*d^2)/((1+e*x^2/d)^q)+1/4*e^2*(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)^3,x,14,1/8*c*x*(-e*x^2+d)*(e*x^2+d)^(1+q)/a/(a*e^2+c*d^2)/(c*x^4+a)^2+1/32*c*x*(e*x^2+d)^(1+q)*(d*(7*c*d^2+a*e^2*(11-4*q))-e*(a*e^2*(11-2*q)+c*d^2*(7+2*q))*x^2)/a^2/(a*e^2+c*d^2)^2/(c*x^4+a)+1/64*(21*c^2*d^4+8*sqrt(-a)*sqrt(c)*d*e*(2*c*d^2+a*e^2*(3-q))*q+2*a*c*d^2*e^2*(-2*q^2-6*q+21)+a^2*e^4*(4*q^2-20*q+21))*x*(e*x^2+d)^q*AppellF1(1/2,-q,1,3/2,-e*x^2/d,-sqrt(c)*x^2/sqrt(-a))/a^3/(a*e^2+c*d^2)^2/((1+e*x^2/d)^q)+1/64*(21*c^2*d^4-8*sqrt(-a)*sqrt(c)*d*e*(2*c*d^2+a*e^2*(3-q))*q+2*a*c*d^2*e^2*(-2*q^2-6*q+21)+a^2*e^4*(4*q^2-20*q+21))*x*(e*x^2+d)^q*AppellF1(1/2,-q,1,3/2,-e*x^2/d,sqrt(c)*x^2/sqrt(-a))/a^3/(a*e^2+c*d^2)^2/((1+e*x^2/d)^q)+1/32*e^2*(1+2*q)*(a*e^2*(11-2*q)+c*d^2*(7+2*q))*x*(e*x^2+d)^q*hypergeom([1/2, -q],[3/2],-e*x^2/d)/a^2/(a*e^2+c*d^2)^2/((1+e*x^2/d)^q),1],
[(e*x^2+c)^q*(b*x^4+a)^p,x,0,Defer(Int)((e*x^2+c)^q*(b*x^4+a)^p,x),0],
[(d*x^2+c)^3*(b*x^4+a)^p,x,7,3*c*d^2*x*(b*x^4+a)^(p+1)/b/(5+4*p)+d^3*x^3*(b*x^4+a)^(p+1)/b/(7+4*p)+c*(c^2-3*a*d^2/(4*b*p+5*b))*x*(b*x^4+a)^p*hypergeom([1/4, -p],[5/4],-b*x^4/a)/((1+b*x^4/a)^p)+d*(c^2-a*d^2/(4*b*p+7*b))*x^3*(b*x^4+a)^p*hypergeom([3/4, -p],[7/4],-b*x^4/a)/((1+b*x^4/a)^p),1],
[(d*x^2+c)^2*(b*x^4+a)^p,x,6,d^2*x*(b*x^4+a)^(p+1)/b/(5+4*p)+(c^2-a*d^2/(4*b*p+5*b))*x*(b*x^4+a)^p*hypergeom([1/4, -p],[5/4],-b*x^4/a)/((1+b*x^4/a)^p)+2/3*c*d*x^3*(b*x^4+a)^p*hypergeom([3/4, -p],[7/4],-b*x^4/a)/((1+b*x^4/a)^p),1],
[(d*x^2+c)*(b*x^4+a)^p,x,5,c*x*(b*x^4+a)^p*hypergeom([1/4, -p],[5/4],-b*x^4/a)/((1+b*x^4/a)^p)+1/3*d*x^3*(b*x^4+a)^p*hypergeom([3/4, -p],[7/4],-b*x^4/a)/((1+b*x^4/a)^p),1],
[(b*x^4+a)^p,x,2,x*(b*x^4+a)^p*hypergeom([1/4, -p],[5/4],-b*x^4/a)/((1+b*x^4/a)^p),1],
[(b*x^4+a)^p/(d*x^2+c),x,8,x*(b*x^4+a)^p*AppellF1(1/4,-p,1,5/4,-b*x^4/a,d^2*x^4/c^2)/c/((1+b*x^4/a)^p)-1/3*d*x^3*(b*x^4+a)^p*AppellF1(3/4,-p,1,7/4,-b*x^4/a,d^2*x^4/c^2)/c^2/((1+b*x^4/a)^p),1],
[(b*x^4+a)^p/(d*x^2+c)^2,x,11,x*(b*x^4+a)^p*AppellF1(1/4,-p,2,5/4,-b*x^4/a,d^2*x^4/c^2)/c^2/((1+b*x^4/a)^p)-2/3*d*x^3*(b*x^4+a)^p*AppellF1(3/4,-p,2,7/4,-b*x^4/a,d^2*x^4/c^2)/c^3/((1+b*x^4/a)^p)+1/5*d^2*x^5*(b*x^4+a)^p*AppellF1(5/4,-p,2,9/4,-b*x^4/a,d^2*x^4/c^2)/c^4/((1+b*x^4/a)^p),1],
[(-x^2+1)^3*(b*x^4+1)^p,x,5,3*x*(b*x^4+1)^(p+1)/b/(5+4*p)-x^3*(b*x^4+1)^(p+1)/b/(7+4*p)+(1-3/(4*b*p+5*b))*x*hypergeom([1/4, -p],[5/4],-b*x^4)-(1-1/(4*b*p+7*b))*x^3*hypergeom([3/4, -p],[7/4],-b*x^4),1],
[(-x^2+1)^2*(b*x^4+1)^p,x,4,x*(b*x^4+1)^(p+1)/b/(5+4*p)+(1-1/(4*b*p+5*b))*x*hypergeom([1/4, -p],[5/4],-b*x^4)-2/3*x^3*hypergeom([3/4, -p],[7/4],-b*x^4),1],
[(-x^2+1)*(b*x^4+1)^p,x,3,x*hypergeom([1/4, -p],[5/4],-b*x^4)-1/3*x^3*hypergeom([3/4, -p],[7/4],-b*x^4),1],
[(b*x^4+1)^p,x,1,x*hypergeom([1/4, -p],[5/4],-b*x^4),1],
[(b*x^4+1)^p/(-x^2+1),x,6,x*AppellF1(1/4,1,-p,5/4,x^4,-b*x^4)+1/3*x^3*AppellF1(3/4,-p,1,7/4,-b*x^4,x^4),1],
[(b*x^4+1)^p/(-x^2+1)^2,x,8,x*AppellF1(1/4,-p,2,5/4,-b*x^4,x^4)+2/3*x^3*AppellF1(3/4,-p,2,7/4,-b*x^4,x^4)+1/5*x^5*AppellF1(5/4,-p,2,9/4,-b*x^4,x^4),1],
[(b*x^4+1)^p/(-x^2+1)^3,x,10,x*AppellF1(1/4,-p,3,5/4,-b*x^4,x^4)+x^3*AppellF1(3/4,-p,3,7/4,-b*x^4,x^4)+3/5*x^5*AppellF1(5/4,-p,3,9/4,-b*x^4,x^4)+1/7*x^7*AppellF1(7/4,-p,3,11/4,-b*x^4,x^4),1]]: