lst:=[[(b*x^4+a)*(d*x^4+c)^4,x,2,a*c^4*x+1/5*c^3*(4*a*d+b*c)*x^5+2/9*c^2*d*(3*a*d+2*b*c)*x^9+2/13*c*d^2*(2*a*d+3*b*c)*x^13+1/17*d^3*(a*d+4*b*c)*x^17+1/21*b*d^4*x^21,1],
[(b*x^4+a)*(d*x^4+c)^3,x,2,a*c^3*x+1/5*c^2*(3*a*d+b*c)*x^5+1/3*c*d*(a*d+b*c)*x^9+1/13*d^2*(a*d+3*b*c)*x^13+1/17*b*d^3*x^17,1],
[(b*x^4+a)*(d*x^4+c)^2,x,2,a*c^2*x+1/5*c*(2*a*d+b*c)*x^5+1/9*d*(a*d+2*b*c)*x^9+1/13*b*d^2*x^13,1],
[(b*x^4+a)*(d*x^4+c),x,2,a*c*x+1/5*(a*d+b*c)*x^5+1/9*b*d*x^9,1],
[(b*x^4+a)/(d*x^4+c),x,9,b*x/d+1/2*(-a*d+b*c)*arctan(1-sqrt(2)*d^(1/4)*x/c^(1/4))/sqrt(2)/c^(3/4)/d^(5/4)-1/2*(-a*d+b*c)*arctan(1+sqrt(2)*d^(1/4)*x/c^(1/4))/sqrt(2)/c^(3/4)/d^(5/4)-1/2*(-a*d+b*c)*arctanh(sqrt(2)*c^(1/4)*d^(1/4)*x/(sqrt(c)+sqrt(d)*x^2))/sqrt(2)/c^(3/4)/d^(5/4),1],
[(b*x^4+a)/(d*x^4+c)^2,x,9,-1/4*(-a*d+b*c)*x/c/d/(d*x^4+c)-1/8*(3*a*d+b*c)*arctan(1-sqrt(2)*d^(1/4)*x/c^(1/4))/sqrt(2)/c^(7/4)/d^(5/4)+1/8*(3*a*d+b*c)*arctan(1+sqrt(2)*d^(1/4)*x/c^(1/4))/sqrt(2)/c^(7/4)/d^(5/4)+1/8*(3*a*d+b*c)*arctanh(sqrt(2)*c^(1/4)*d^(1/4)*x/(sqrt(c)+sqrt(d)*x^2))/sqrt(2)/c^(7/4)/d^(5/4),1],
[(b*x^4+a)/(d*x^4+c)^3,x,10,-1/8*(-a*d+b*c)*x/c/d/(d*x^4+c)^2+1/32*(7*a*d+b*c)*x/c^2/d/(d*x^4+c)-3/64*(7*a*d+b*c)*arctan(1-sqrt(2)*d^(1/4)*x/c^(1/4))/sqrt(2)/c^(11/4)/d^(5/4)+3/64*(7*a*d+b*c)*arctan(1+sqrt(2)*d^(1/4)*x/c^(1/4))/sqrt(2)/c^(11/4)/d^(5/4)+3/64*(7*a*d+b*c)*arctanh(sqrt(2)*c^(1/4)*d^(1/4)*x/(sqrt(c)+sqrt(d)*x^2))/sqrt(2)/c^(11/4)/d^(5/4),1],
[(b*x^4+a)^2*(d*x^4+c)^4,x,2,a^2*c^4*x+2/5*a*c^3*(2*a*d+b*c)*x^5+1/9*c^2*(6*a^2*d^2+8*a*b*c*d+b^2*c^2)*x^9+4/13*c*d*(a^2*d^2+3*a*b*c*d+b^2*c^2)*x^13+1/17*d^2*(a^2*d^2+8*a*b*c*d+6*b^2*c^2)*x^17+2/21*b*d^3*(a*d+2*b*c)*x^21+1/25*b^2*d^4*x^25,1],
[(b*x^4+a)^2*(d*x^4+c)^3,x,2,a^2*c^3*x+1/5*a*c^2*(3*a*d+2*b*c)*x^5+1/9*c*(3*a^2*d^2+6*a*b*c*d+b^2*c^2)*x^9+1/13*d*(a^2*d^2+6*a*b*c*d+3*b^2*c^2)*x^13+1/17*b*d^2*(2*a*d+3*b*c)*x^17+1/21*b^2*d^3*x^21,1],
[(b*x^4+a)^2*(d*x^4+c)^2,x,2,a^2*c^2*x+2/5*a*c*(a*d+b*c)*x^5+1/9*(a^2*d^2+4*a*b*c*d+b^2*c^2)*x^9+2/13*b*d*(a*d+b*c)*x^13+1/17*b^2*d^2*x^17,1],
[(b*x^4+a)^2*(d*x^4+c),x,2,a^2*c*x+1/5*a*(a*d+2*b*c)*x^5+1/9*b*(2*a*d+b*c)*x^9+1/13*b^2*d*x^13,1],
[(b*x^4+a)^2/(d*x^4+c),x,10,-b*(-2*a*d+b*c)*x/d^2+1/5*b^2*x^5/d-1/2*(-a*d+b*c)^2*arctan(1-sqrt(2)*d^(1/4)*x/c^(1/4))/sqrt(2)/c^(3/4)/d^(9/4)+1/2*(-a*d+b*c)^2*arctan(1+sqrt(2)*d^(1/4)*x/c^(1/4))/sqrt(2)/c^(3/4)/d^(9/4)+1/2*(-a*d+b*c)^2*arctanh(sqrt(2)*c^(1/4)*d^(1/4)*x/(sqrt(c)+sqrt(d)*x^2))/sqrt(2)/c^(3/4)/d^(9/4),1],
[(b*x^4+a)^2/(d*x^4+c)^2,x,10,b^2*x/d^2+1/4*(-a*d+b*c)^2*x/c/d^2/(d*x^4+c)+1/8*(-a*d+b*c)*(3*a*d+5*b*c)*arctan(1-sqrt(2)*d^(1/4)*x/c^(1/4))/sqrt(2)/c^(7/4)/d^(9/4)-1/8*(-a*d+b*c)*(3*a*d+5*b*c)*arctan(1+sqrt(2)*d^(1/4)*x/c^(1/4))/sqrt(2)/c^(7/4)/d^(9/4)-1/8*(-a*d+b*c)*(3*a*d+5*b*c)*arctanh(sqrt(2)*c^(1/4)*d^(1/4)*x/(sqrt(c)+sqrt(d)*x^2))/sqrt(2)/c^(7/4)/d^(9/4),1],
[(b*x^4+a)^2/(d*x^4+c)^3,x,10,1/8*(-a*d+b*c)^2*x/c/d^2/(d*x^4+c)^2-1/32*(-a*d+b*c)*(7*a*d+9*b*c)*x/c^2/d^2/(d*x^4+c)-1/64*(21*a^2*d^2+6*a*b*c*d+5*b^2*c^2)*arctan(1-sqrt(2)*d^(1/4)*x/c^(1/4))/sqrt(2)/c^(11/4)/d^(9/4)+1/64*(21*a^2*d^2+6*a*b*c*d+5*b^2*c^2)*arctan(1+sqrt(2)*d^(1/4)*x/c^(1/4))/sqrt(2)/c^(11/4)/d^(9/4)+1/64*(21*a^2*d^2+6*a*b*c*d+5*b^2*c^2)*arctanh(sqrt(2)*c^(1/4)*d^(1/4)*x/(sqrt(c)+sqrt(d)*x^2))/sqrt(2)/c^(11/4)/d^(9/4),1],
[(d*x^4+c)^4/(b*x^4+a),x,10,d*(-a*d+2*b*c)*(a^2*d^2-2*a*b*c*d+2*b^2*c^2)*x/b^4+1/5*d^2*(a^2*d^2-4*a*b*c*d+6*b^2*c^2)*x^5/b^3+1/9*d^3*(-a*d+4*b*c)*x^9/b^2+1/13*d^4*x^13/b-1/2*(-a*d+b*c)^4*arctan(1-sqrt(2)*b^(1/4)*x/a^(1/4))/sqrt(2)/a^(3/4)/b^(17/4)+1/2*(-a*d+b*c)^4*arctan(1+sqrt(2)*b^(1/4)*x/a^(1/4))/sqrt(2)/a^(3/4)/b^(17/4)+1/2*(-a*d+b*c)^4*arctanh(sqrt(2)*a^(1/4)*b^(1/4)*x/(sqrt(a)+sqrt(b)*x^2))/sqrt(2)/a^(3/4)/b^(17/4),1],
[(d*x^4+c)^3/(b*x^4+a),x,10,d*(a^2*d^2-3*a*b*c*d+3*b^2*c^2)*x/b^3+1/5*d^2*(-a*d+3*b*c)*x^5/b^2+1/9*d^3*x^9/b-1/2*(-a*d+b*c)^3*arctan(1-sqrt(2)*b^(1/4)*x/a^(1/4))/sqrt(2)/a^(3/4)/b^(13/4)+1/2*(-a*d+b*c)^3*arctan(1+sqrt(2)*b^(1/4)*x/a^(1/4))/sqrt(2)/a^(3/4)/b^(13/4)+1/2*(-a*d+b*c)^3*arctanh(sqrt(2)*a^(1/4)*b^(1/4)*x/(sqrt(a)+sqrt(b)*x^2))/sqrt(2)/a^(3/4)/b^(13/4),1],
[(d*x^4+c)^2/(b*x^4+a),x,10,d*(-a*d+2*b*c)*x/b^2+1/5*d^2*x^5/b-1/2*(-a*d+b*c)^2*arctan(1-sqrt(2)*b^(1/4)*x/a^(1/4))/sqrt(2)/a^(3/4)/b^(9/4)+1/2*(-a*d+b*c)^2*arctan(1+sqrt(2)*b^(1/4)*x/a^(1/4))/sqrt(2)/a^(3/4)/b^(9/4)+1/2*(-a*d+b*c)^2*arctanh(sqrt(2)*a^(1/4)*b^(1/4)*x/(sqrt(a)+sqrt(b)*x^2))/sqrt(2)/a^(3/4)/b^(9/4),1],
[(d*x^4+c)/(b*x^4+a),x,9,d*x/b-1/2*(-a*d+b*c)*arctan(1-sqrt(2)*b^(1/4)*x/a^(1/4))/sqrt(2)/a^(3/4)/b^(5/4)+1/2*(-a*d+b*c)*arctan(1+sqrt(2)*b^(1/4)*x/a^(1/4))/sqrt(2)/a^(3/4)/b^(5/4)+1/2*(-a*d+b*c)*arctanh(sqrt(2)*a^(1/4)*b^(1/4)*x/(sqrt(a)+sqrt(b)*x^2))/sqrt(2)/a^(3/4)/b^(5/4),1],
[1/(b*x^4+a)/(d*x^4+c),x,17,-1/2*b^(3/4)*arctan(1-sqrt(2)*b^(1/4)*x/a^(1/4))/sqrt(2)/a^(3/4)/(-a*d+b*c)+1/2*b^(3/4)*arctan(1+sqrt(2)*b^(1/4)*x/a^(1/4))/sqrt(2)/a^(3/4)/(-a*d+b*c)+1/2*d^(3/4)*arctan(1-sqrt(2)*d^(1/4)*x/c^(1/4))/sqrt(2)/c^(3/4)/(-a*d+b*c)-1/2*d^(3/4)*arctan(1+sqrt(2)*d^(1/4)*x/c^(1/4))/sqrt(2)/c^(3/4)/(-a*d+b*c)+1/2*b^(3/4)*arctanh(sqrt(2)*a^(1/4)*b^(1/4)*x/(sqrt(a)+sqrt(b)*x^2))/sqrt(2)/a^(3/4)/(-a*d+b*c)-1/2*d^(3/4)*arctanh(sqrt(2)*c^(1/4)*d^(1/4)*x/(sqrt(c)+sqrt(d)*x^2))/sqrt(2)/c^(3/4)/(-a*d+b*c),1],
[1/(b*x^4+a)/(d*x^4+c)^2,x,18,-1/4*d*x/c/(-a*d+b*c)/(d*x^4+c)-1/2*b^(7/4)*arctan(1-sqrt(2)*b^(1/4)*x/a^(1/4))/sqrt(2)/a^(3/4)/(-a*d+b*c)^2+1/2*b^(7/4)*arctan(1+sqrt(2)*b^(1/4)*x/a^(1/4))/sqrt(2)/a^(3/4)/(-a*d+b*c)^2+1/8*d^(3/4)*(-3*a*d+7*b*c)*arctan(1-sqrt(2)*d^(1/4)*x/c^(1/4))/sqrt(2)/c^(7/4)/(-a*d+b*c)^2-1/8*d^(3/4)*(-3*a*d+7*b*c)*arctan(1+sqrt(2)*d^(1/4)*x/c^(1/4))/sqrt(2)/c^(7/4)/(-a*d+b*c)^2+1/2*b^(7/4)*arctanh(sqrt(2)*a^(1/4)*b^(1/4)*x/(sqrt(a)+sqrt(b)*x^2))/sqrt(2)/a^(3/4)/(-a*d+b*c)^2-1/8*d^(3/4)*(-3*a*d+7*b*c)*arctanh(sqrt(2)*c^(1/4)*d^(1/4)*x/(sqrt(c)+sqrt(d)*x^2))/sqrt(2)/c^(7/4)/(-a*d+b*c)^2,1],
[(d*x^4+c)^5/(b*x^4+a)^2,x,11,d^2*(-4*a^3*d^3+15*a^2*b*c*d^2-20*a*b^2*c^2*d+10*b^3*c^3)*x/b^5+1/5*d^3*(3*a^2*d^2-10*a*b*c*d+10*b^2*c^2)*x^5/b^4+1/9*d^4*(-2*a*d+5*b*c)*x^9/b^3+1/13*d^5*x^13/b^2+1/4*(-a*d+b*c)^5*x/a/b^5/(b*x^4+a)-1/8*(-a*d+b*c)^4*(17*a*d+3*b*c)*arctan(1-sqrt(2)*b^(1/4)*x/a^(1/4))/sqrt(2)/a^(7/4)/b^(21/4)+1/8*(-a*d+b*c)^4*(17*a*d+3*b*c)*arctan(1+sqrt(2)*b^(1/4)*x/a^(1/4))/sqrt(2)/a^(7/4)/b^(21/4)+1/8*(-a*d+b*c)^4*(17*a*d+3*b*c)*arctanh(sqrt(2)*a^(1/4)*b^(1/4)*x/(sqrt(a)+sqrt(b)*x^2))/sqrt(2)/a^(7/4)/b^(21/4),1],
[(d*x^4+c)^4/(b*x^4+a)^2,x,11,d^2*(3*a^2*d^2-8*a*b*c*d+6*b^2*c^2)*x/b^4+2/5*d^3*(-a*d+2*b*c)*x^5/b^3+1/9*d^4*x^9/b^2+1/4*(-a*d+b*c)^4*x/a/b^4/(b*x^4+a)-1/8*(-a*d+b*c)^3*(13*a*d+3*b*c)*arctan(1-sqrt(2)*b^(1/4)*x/a^(1/4))/sqrt(2)/a^(7/4)/b^(17/4)+1/8*(-a*d+b*c)^3*(13*a*d+3*b*c)*arctan(1+sqrt(2)*b^(1/4)*x/a^(1/4))/sqrt(2)/a^(7/4)/b^(17/4)+1/8*(-a*d+b*c)^3*(13*a*d+3*b*c)*arctanh(sqrt(2)*a^(1/4)*b^(1/4)*x/(sqrt(a)+sqrt(b)*x^2))/sqrt(2)/a^(7/4)/b^(17/4),1],
[(d*x^4+c)^3/(b*x^4+a)^2,x,11,d^2*(-2*a*d+3*b*c)*x/b^3+1/5*d^3*x^5/b^2+1/4*(-a*d+b*c)^3*x/a/b^3/(b*x^4+a)-3/8*(-a*d+b*c)^2*(3*a*d+b*c)*arctan(1-sqrt(2)*b^(1/4)*x/a^(1/4))/sqrt(2)/a^(7/4)/b^(13/4)+3/8*(-a*d+b*c)^2*(3*a*d+b*c)*arctan(1+sqrt(2)*b^(1/4)*x/a^(1/4))/sqrt(2)/a^(7/4)/b^(13/4)+3/8*(-a*d+b*c)^2*(3*a*d+b*c)*arctanh(sqrt(2)*a^(1/4)*b^(1/4)*x/(sqrt(a)+sqrt(b)*x^2))/sqrt(2)/a^(7/4)/b^(13/4),1],
[(d*x^4+c)^2/(b*x^4+a)^2,x,10,d^2*x/b^2+1/4*(-a*d+b*c)^2*x/a/b^2/(b*x^4+a)-1/8*(-a*d+b*c)*(5*a*d+3*b*c)*arctan(1-sqrt(2)*b^(1/4)*x/a^(1/4))/sqrt(2)/a^(7/4)/b^(9/4)+1/8*(-a*d+b*c)*(5*a*d+3*b*c)*arctan(1+sqrt(2)*b^(1/4)*x/a^(1/4))/sqrt(2)/a^(7/4)/b^(9/4)+1/8*(-a*d+b*c)*(5*a*d+3*b*c)*arctanh(sqrt(2)*a^(1/4)*b^(1/4)*x/(sqrt(a)+sqrt(b)*x^2))/sqrt(2)/a^(7/4)/b^(9/4),1],
[(d*x^4+c)/(b*x^4+a)^2,x,9,1/4*(-a*d+b*c)*x/a/b/(b*x^4+a)-1/8*(a*d+3*b*c)*arctan(1-sqrt(2)*b^(1/4)*x/a^(1/4))/sqrt(2)/a^(7/4)/b^(5/4)+1/8*(a*d+3*b*c)*arctan(1+sqrt(2)*b^(1/4)*x/a^(1/4))/sqrt(2)/a^(7/4)/b^(5/4)+1/8*(a*d+3*b*c)*arctanh(sqrt(2)*a^(1/4)*b^(1/4)*x/(sqrt(a)+sqrt(b)*x^2))/sqrt(2)/a^(7/4)/b^(5/4),1],
[1/(b*x^4+a)^2/(d*x^4+c),x,18,1/4*b*x/a/(-a*d+b*c)/(b*x^4+a)-1/8*b^(3/4)*(-7*a*d+3*b*c)*arctan(1-sqrt(2)*b^(1/4)*x/a^(1/4))/sqrt(2)/a^(7/4)/(-a*d+b*c)^2+1/8*b^(3/4)*(-7*a*d+3*b*c)*arctan(1+sqrt(2)*b^(1/4)*x/a^(1/4))/sqrt(2)/a^(7/4)/(-a*d+b*c)^2-1/2*d^(7/4)*arctan(1-sqrt(2)*d^(1/4)*x/c^(1/4))/sqrt(2)/c^(3/4)/(-a*d+b*c)^2+1/2*d^(7/4)*arctan(1+sqrt(2)*d^(1/4)*x/c^(1/4))/sqrt(2)/c^(3/4)/(-a*d+b*c)^2+1/8*b^(3/4)*(-7*a*d+3*b*c)*arctanh(sqrt(2)*a^(1/4)*b^(1/4)*x/(sqrt(a)+sqrt(b)*x^2))/sqrt(2)/a^(7/4)/(-a*d+b*c)^2+1/2*d^(7/4)*arctanh(sqrt(2)*c^(1/4)*d^(1/4)*x/(sqrt(c)+sqrt(d)*x^2))/sqrt(2)/c^(3/4)/(-a*d+b*c)^2,1],
[1/(b*x^4+a)^2/(d*x^4+c)^2,x,19,1/4*d*(a*d+b*c)*x/a/c/(-a*d+b*c)^2/(d*x^4+c)+1/4*b*x/a/(-a*d+b*c)/(b*x^4+a)/(d*x^4+c)-1/8*b^(7/4)*(-11*a*d+3*b*c)*arctan(1-sqrt(2)*b^(1/4)*x/a^(1/4))/sqrt(2)/a^(7/4)/(-a*d+b*c)^3+1/8*b^(7/4)*(-11*a*d+3*b*c)*arctan(1+sqrt(2)*b^(1/4)*x/a^(1/4))/sqrt(2)/a^(7/4)/(-a*d+b*c)^3-1/8*d^(7/4)*(-3*a*d+11*b*c)*arctan(1-sqrt(2)*d^(1/4)*x/c^(1/4))/sqrt(2)/c^(7/4)/(-a*d+b*c)^3+1/8*d^(7/4)*(-3*a*d+11*b*c)*arctan(1+sqrt(2)*d^(1/4)*x/c^(1/4))/sqrt(2)/c^(7/4)/(-a*d+b*c)^3+1/8*b^(7/4)*(-11*a*d+3*b*c)*arctanh(sqrt(2)*a^(1/4)*b^(1/4)*x/(sqrt(a)+sqrt(b)*x^2))/sqrt(2)/a^(7/4)/(-a*d+b*c)^3+1/8*d^(7/4)*(-3*a*d+11*b*c)*arctanh(sqrt(2)*c^(1/4)*d^(1/4)*x/(sqrt(c)+sqrt(d)*x^2))/sqrt(2)/c^(7/4)/(-a*d+b*c)^3,1],
[sqrt(b*x^4+a)*(d*x^4+c)^2,x,4,1/231*(77*c^2-a*d*(-5*a*d+22*b*c)/b^2)*x*sqrt(b*x^4+a)+1/77*d*(-5*a*d+22*b*c)*x*(b*x^4+a)^(3/2)/b^2+1/11*d^2*x^5*(b*x^4+a)^(3/2)/b+1/231*a^(3/4)*(5*a^2*d^2-22*a*b*c*d+77*b^2*c^2)*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*InverseJacobiAM(2*arctan(b^(1/4)*x/a^(1/4)),sqrt(1/2))/b^(9/4)/sqrt(b*x^4+a),1],
[sqrt(b*x^4+a)*(d*x^4+c),x,3,1/21*(-a*d+7*b*c)*x*sqrt(b*x^4+a)/b+1/7*d*x*(b*x^4+a)^(3/2)/b+1/21*a^(3/4)*(-a*d+7*b*c)*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*InverseJacobiAM(2*arctan(b^(1/4)*x/a^(1/4)),sqrt(1/2))/b^(5/4)/sqrt(b*x^4+a),1],
[sqrt(b*x^4+a)/(d*x^4+c),x,5,1/4*sqrt(-a*d+b*c)*arctan(sqrt(-a*d+b*c)*x/(-c)^(1/4)/d^(1/4)/sqrt(b*x^4+a))/(-c)^(3/4)/d^(3/4)+1/4*sqrt(-a*d+b*c)*arctanh(sqrt(-a*d+b*c)*x/(-c)^(1/4)/d^(1/4)/sqrt(b*x^4+a))/(-c)^(3/4)/d^(3/4)+1/2*b^(3/4)*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*InverseJacobiAM(2*arctan(b^(1/4)*x/a^(1/4)),sqrt(1/2))/a^(1/4)/d/sqrt(b*x^4+a)-1/2*b^(3/4)*(-a*d+b*c)*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*InverseJacobiAM(2*arctan(b^(1/4)*x/a^(1/4)),sqrt(1/2))/a^(1/4)/d/(a*d+b*c)/sqrt(b*x^4+a)+1/8*(sqrt(b)*sqrt(-c)+sqrt(a)*sqrt(d))*(-a*d+b*c)*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*EllipticPi(sin(2*arctan(b^(1/4)*x/a^(1/4))),-1/4*(sqrt(b)*sqrt(-c)-sqrt(a)*sqrt(d))^2/sqrt(a)/sqrt(b)/sqrt(-c)/sqrt(d),sqrt(1/2))/a^(1/4)/b^(1/4)/c/(sqrt(b)*sqrt(-c)-sqrt(a)*sqrt(d))/d/sqrt(b*x^4+a)+1/8*(sqrt(b)*sqrt(-c)-sqrt(a)*sqrt(d))*(-a*d+b*c)*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*EllipticPi(sin(2*arctan(b^(1/4)*x/a^(1/4))),1/4*(sqrt(b)*sqrt(-c)+sqrt(a)*sqrt(d))^2/sqrt(a)/sqrt(b)/sqrt(-c)/sqrt(d),sqrt(1/2))/a^(1/4)/b^(1/4)/c/(sqrt(b)*sqrt(-c)+sqrt(a)*sqrt(d))/d/sqrt(b*x^4+a),1],
[sqrt(b*x^4+a)/(d*x^4+c)^2,x,4,1/4*x*sqrt(b*x^4+a)/c/(d*x^4+c)-1/16*(-3*a*d+b*c)*arctan(sqrt(-a*d+b*c)*x/(-c)^(1/4)/d^(1/4)/sqrt(b*x^4+a))/(-c)^(7/4)/d^(3/4)/sqrt(-a*d+b*c)-1/16*(-3*a*d+b*c)*arctanh(sqrt(-a*d+b*c)*x/(-c)^(1/4)/d^(1/4)/sqrt(b*x^4+a))/(-c)^(7/4)/d^(3/4)/sqrt(-a*d+b*c)+1/2*a^(3/4)*b^(3/4)*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*InverseJacobiAM(2*arctan(b^(1/4)*x/a^(1/4)),sqrt(1/2))/c/(a*d+b*c)/sqrt(b*x^4+a)+1/32*(sqrt(b)*sqrt(-c)+sqrt(a)*sqrt(d))*(-3*a*d+b*c)*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*EllipticPi(sin(2*arctan(b^(1/4)*x/a^(1/4))),-1/4*(sqrt(b)*sqrt(-c)-sqrt(a)*sqrt(d))^2/sqrt(a)/sqrt(b)/sqrt(-c)/sqrt(d),sqrt(1/2))/a^(1/4)/b^(1/4)/c^2/(sqrt(b)*sqrt(-c)-sqrt(a)*sqrt(d))/d/sqrt(b*x^4+a)+1/32*(sqrt(b)*sqrt(-c)-sqrt(a)*sqrt(d))*(-3*a*d+b*c)*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*EllipticPi(sin(2*arctan(b^(1/4)*x/a^(1/4))),1/4*(sqrt(b)*sqrt(-c)+sqrt(a)*sqrt(d))^2/sqrt(a)/sqrt(b)/sqrt(-c)/sqrt(d),sqrt(1/2))/a^(1/4)/b^(1/4)/c^2/(sqrt(b)*sqrt(-c)+sqrt(a)*sqrt(d))/d/sqrt(b*x^4+a),1],
[(d*x^4+c)^2/sqrt(b*x^4+a),x,3,1/21*d*(-5*a*d+14*b*c)*x*sqrt(b*x^4+a)/b^2+1/7*d^2*x^5*sqrt(b*x^4+a)/b+1/42*(5*a^2*d^2-14*a*b*c*d+21*b^2*c^2)*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*InverseJacobiAM(2*arctan(b^(1/4)*x/a^(1/4)),sqrt(1/2))/a^(1/4)/b^(9/4)/sqrt(b*x^4+a),1],
[(d*x^4+c)/sqrt(b*x^4+a),x,2,1/3*d*x*sqrt(b*x^4+a)/b+1/6*(-a*d+3*b*c)*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*InverseJacobiAM(2*arctan(b^(1/4)*x/a^(1/4)),sqrt(1/2))/a^(1/4)/b^(5/4)/sqrt(b*x^4+a),1],
[1/sqrt(b*x^4+a)/(d*x^4+c),x,3,-1/4*d^(1/4)*arctan(sqrt(-a*d+b*c)*x/(-c)^(1/4)/d^(1/4)/sqrt(b*x^4+a))/(-c)^(3/4)/sqrt(-a*d+b*c)-1/4*d^(1/4)*arctanh(sqrt(-a*d+b*c)*x/(-c)^(1/4)/d^(1/4)/sqrt(b*x^4+a))/(-c)^(3/4)/sqrt(-a*d+b*c)+1/2*b^(3/4)*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*InverseJacobiAM(2*arctan(b^(1/4)*x/a^(1/4)),sqrt(1/2))/a^(1/4)/(a*d+b*c)/sqrt(b*x^4+a)-1/8*(sqrt(b)*sqrt(-c)+sqrt(a)*sqrt(d))*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*EllipticPi(sin(2*arctan(b^(1/4)*x/a^(1/4))),-1/4*(sqrt(b)*sqrt(-c)-sqrt(a)*sqrt(d))^2/sqrt(a)/sqrt(b)/sqrt(-c)/sqrt(d),sqrt(1/2))/a^(1/4)/b^(1/4)/c/(sqrt(b)*sqrt(-c)-sqrt(a)*sqrt(d))/sqrt(b*x^4+a)-1/8*(sqrt(b)*sqrt(-c)-sqrt(a)*sqrt(d))*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*EllipticPi(sin(2*arctan(b^(1/4)*x/a^(1/4))),1/4*(sqrt(b)*sqrt(-c)+sqrt(a)*sqrt(d))^2/sqrt(a)/sqrt(b)/sqrt(-c)/sqrt(d),sqrt(1/2))/a^(1/4)/b^(1/4)/c/(sqrt(b)*sqrt(-c)+sqrt(a)*sqrt(d))/sqrt(b*x^4+a),1],
[1/sqrt(b*x^4+a)/(d*x^4+c)^2,x,4,-1/4*d*x*sqrt(b*x^4+a)/c/(-a*d+b*c)/(d*x^4+c)+1/16*d^(1/4)*(-3*a*d+5*b*c)*arctan(sqrt(-a*d+b*c)*x/(-c)^(1/4)/d^(1/4)/sqrt(b*x^4+a))/(-c)^(7/4)/(-a*d+b*c)^(3/2)+1/16*d^(1/4)*(-3*a*d+5*b*c)*arctanh(sqrt(-a*d+b*c)*x/(-c)^(1/4)/d^(1/4)/sqrt(b*x^4+a))/(-c)^(7/4)/(-a*d+b*c)^(3/2)+1/2*b^(3/4)*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*InverseJacobiAM(2*arctan(b^(1/4)*x/a^(1/4)),sqrt(1/2))/a^(1/4)/c/(a*d+b*c)/sqrt(b*x^4+a)-1/32*(sqrt(b)*sqrt(-c)+sqrt(a)*sqrt(d))*(-3*a*d+5*b*c)*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*EllipticPi(sin(2*arctan(b^(1/4)*x/a^(1/4))),-1/4*(sqrt(b)*sqrt(-c)-sqrt(a)*sqrt(d))^2/sqrt(a)/sqrt(b)/sqrt(-c)/sqrt(d),sqrt(1/2))/a^(1/4)/b^(1/4)/c^2/(sqrt(b)*sqrt(-c)-sqrt(a)*sqrt(d))/(-a*d+b*c)/sqrt(b*x^4+a)-1/32*(sqrt(b)*sqrt(-c)-sqrt(a)*sqrt(d))*(-3*a*d+5*b*c)*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*EllipticPi(sin(2*arctan(b^(1/4)*x/a^(1/4))),1/4*(sqrt(b)*sqrt(-c)+sqrt(a)*sqrt(d))^2/sqrt(a)/sqrt(b)/sqrt(-c)/sqrt(d),sqrt(1/2))/a^(1/4)/b^(1/4)/c^2/(sqrt(b)*sqrt(-c)+sqrt(a)*sqrt(d))/(-a*d+b*c)/sqrt(b*x^4+a),1],
[(d*x^4+c)^3/(b*x^4+a)^(3/2),x,4,1/2*(-a*d+b*c)^3*x/a/b^3/sqrt(b*x^4+a)+1/7*d^2*(-4*a*d+7*b*c)*x*sqrt(b*x^4+a)/b^3+1/7*d^3*x^5*sqrt(b*x^4+a)/b^2+1/28*(15*a^3*d^3-35*a^2*b*c*d^2+21*a*b^2*c^2*d+7*b^3*c^3)*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*InverseJacobiAM(2*arctan(b^(1/4)*x/a^(1/4)),sqrt(1/2))/a^(5/4)/b^(13/4)/sqrt(b*x^4+a),1],
[(d*x^4+c)^2/(b*x^4+a)^(3/2),x,3,1/2*(-a*d+b*c)^2*x/a/b^2/sqrt(b*x^4+a)+1/3*d^2*x*sqrt(b*x^4+a)/b^2+1/12*(-5*a^2*d^2+6*a*b*c*d+3*b^2*c^2)*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*InverseJacobiAM(2*arctan(b^(1/4)*x/a^(1/4)),sqrt(1/2))/a^(5/4)/b^(9/4)/sqrt(b*x^4+a),1],
[(d*x^4+c)/(b*x^4+a)^(3/2),x,2,1/2*(-a*d+b*c)*x/a/b/sqrt(b*x^4+a)+1/4*(a*d+b*c)*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*InverseJacobiAM(2*arctan(b^(1/4)*x/a^(1/4)),sqrt(1/2))/a^(5/4)/b^(5/4)/sqrt(b*x^4+a),1],
[1/(b*x^4+a)^(3/2)/(d*x^4+c),x,4,1/2*b*x/a/(-a*d+b*c)/sqrt(b*x^4+a)+1/4*d^(5/4)*arctan(sqrt(-a*d+b*c)*x/(-c)^(1/4)/d^(1/4)/sqrt(b*x^4+a))/(-c)^(3/4)/(-a*d+b*c)^(3/2)+1/4*d^(5/4)*arctanh(sqrt(-a*d+b*c)*x/(-c)^(1/4)/d^(1/4)/sqrt(b*x^4+a))/(-c)^(3/4)/(-a*d+b*c)^(3/2)+1/4*b^(3/4)*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*InverseJacobiAM(2*arctan(b^(1/4)*x/a^(1/4)),sqrt(1/2))/a^(5/4)/(a*d+b*c)/sqrt(b*x^4+a)+1/8*(sqrt(b)*sqrt(-c)+sqrt(a)*sqrt(d))*d*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*EllipticPi(sin(2*arctan(b^(1/4)*x/a^(1/4))),-1/4*(sqrt(b)*sqrt(-c)-sqrt(a)*sqrt(d))^2/sqrt(a)/sqrt(b)/sqrt(-c)/sqrt(d),sqrt(1/2))/a^(1/4)/b^(1/4)/c/(sqrt(b)*sqrt(-c)-sqrt(a)*sqrt(d))/(-a*d+b*c)/sqrt(b*x^4+a)+1/8*(sqrt(b)*sqrt(-c)-sqrt(a)*sqrt(d))*d*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*EllipticPi(sin(2*arctan(b^(1/4)*x/a^(1/4))),1/4*(sqrt(b)*sqrt(-c)+sqrt(a)*sqrt(d))^2/sqrt(a)/sqrt(b)/sqrt(-c)/sqrt(d),sqrt(1/2))/a^(1/4)/b^(1/4)/c/(sqrt(b)*sqrt(-c)+sqrt(a)*sqrt(d))/(-a*d+b*c)/sqrt(b*x^4+a),1],
[1/(b*x^4+a)^(3/2)/(d*x^4+c)^2,x,5,1/4*b*(a*d+2*b*c)*x/a/c/(-a*d+b*c)^2/sqrt(b*x^4+a)-1/4*d*x/c/(-a*d+b*c)/sqrt(b*x^4+a)/(d*x^4+c)-3/16*d^(5/4)*(-a*d+3*b*c)*arctan(sqrt(-a*d+b*c)*x/(-c)^(1/4)/d^(1/4)/sqrt(b*x^4+a))/(-c)^(7/4)/(-a*d+b*c)^(5/2)-3/16*d^(5/4)*(-a*d+3*b*c)*arctanh(sqrt(-a*d+b*c)*x/(-c)^(1/4)/d^(1/4)/sqrt(b*x^4+a))/(-c)^(7/4)/(-a*d+b*c)^(5/2)+1/4*b^(3/4)*(-2*a*d+b*c)*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*InverseJacobiAM(2*arctan(b^(1/4)*x/a^(1/4)),sqrt(1/2))/a^(5/4)/c/(-a*d+b*c)/(a*d+b*c)/sqrt(b*x^4+a)+3/32*(sqrt(b)*sqrt(-c)+sqrt(a)*sqrt(d))*d*(-a*d+3*b*c)*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*EllipticPi(sin(2*arctan(b^(1/4)*x/a^(1/4))),-1/4*(sqrt(b)*sqrt(-c)-sqrt(a)*sqrt(d))^2/sqrt(a)/sqrt(b)/sqrt(-c)/sqrt(d),sqrt(1/2))/a^(1/4)/b^(1/4)/c^2/(sqrt(b)*sqrt(-c)-sqrt(a)*sqrt(d))/(-a*d+b*c)^2/sqrt(b*x^4+a)+3/32*(sqrt(b)*sqrt(-c)-sqrt(a)*sqrt(d))*d*(-a*d+3*b*c)*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*EllipticPi(sin(2*arctan(b^(1/4)*x/a^(1/4))),1/4*(sqrt(b)*sqrt(-c)+sqrt(a)*sqrt(d))^2/sqrt(a)/sqrt(b)/sqrt(-c)/sqrt(d),sqrt(1/2))/a^(1/4)/b^(1/4)/c^2/(sqrt(b)*sqrt(-c)+sqrt(a)*sqrt(d))/(-a*d+b*c)^2/sqrt(b*x^4+a),1],
[(x^4-1)/(x^4+1)^(3/2),x,1,-x/sqrt(x^4+1),1],
[(-b*x^4+a)^(5/2)/(-d*x^4+c),x,10,-1/21*b*(-13*a*d+7*b*c)*x*sqrt(-b*x^4+a)/d^2+1/7*b*x*(-b*x^4+a)^(3/2)/d+1/21*a^(1/4)*b^(3/4)*(47*a^2*d^2-56*a*b*c*d+21*b^2*c^2)*sqrt(1-b*x^4/a)*InverseJacobiAM(arcsin(b^(1/4)*x/a^(1/4)),sqrt(-1))/d^3/sqrt(-b*x^4+a)-1/2*a^(1/4)*(-a*d+b*c)^3*sqrt(1-b*x^4/a)*EllipticPi(sin(arcsin(b^(1/4)*x/a^(1/4))),-sqrt(a)*sqrt(d)/sqrt(b)/sqrt(c),sqrt(-1))/b^(1/4)/c/d^3/sqrt(-b*x^4+a)-1/2*a^(1/4)*(-a*d+b*c)^3*sqrt(1-b*x^4/a)*EllipticPi(sin(arcsin(b^(1/4)*x/a^(1/4))),sqrt(a)*sqrt(d)/sqrt(b)/sqrt(c),sqrt(-1))/b^(1/4)/c/d^3/sqrt(-b*x^4+a),1],
[(-b*x^4+a)^(3/2)/(-d*x^4+c),x,9,1/3*b*x*sqrt(-b*x^4+a)/d-1/3*a^(1/4)*b^(3/4)*(-5*a*d+3*b*c)*sqrt(1-b*x^4/a)*InverseJacobiAM(arcsin(b^(1/4)*x/a^(1/4)),sqrt(-1))/d^2/sqrt(-b*x^4+a)+1/2*a^(1/4)*(-a*d+b*c)^2*sqrt(1-b*x^4/a)*EllipticPi(sin(arcsin(b^(1/4)*x/a^(1/4))),-sqrt(a)*sqrt(d)/sqrt(b)/sqrt(c),sqrt(-1))/b^(1/4)/c/d^2/sqrt(-b*x^4+a)+1/2*a^(1/4)*(-a*d+b*c)^2*sqrt(1-b*x^4/a)*EllipticPi(sin(arcsin(b^(1/4)*x/a^(1/4))),sqrt(a)*sqrt(d)/sqrt(b)/sqrt(c),sqrt(-1))/b^(1/4)/c/d^2/sqrt(-b*x^4+a),1],
[sqrt(-b*x^4+a)/(-d*x^4+c),x,8,a^(1/4)*b^(3/4)*sqrt(1-b*x^4/a)*InverseJacobiAM(arcsin(b^(1/4)*x/a^(1/4)),sqrt(-1))/d/sqrt(-b*x^4+a)-1/2*a^(1/4)*(-a*d+b*c)*sqrt(1-b*x^4/a)*EllipticPi(sin(arcsin(b^(1/4)*x/a^(1/4))),-sqrt(a)*sqrt(d)/sqrt(b)/sqrt(c),sqrt(-1))/b^(1/4)/c/d/sqrt(-b*x^4+a)-1/2*a^(1/4)*(-a*d+b*c)*sqrt(1-b*x^4/a)*EllipticPi(sin(arcsin(b^(1/4)*x/a^(1/4))),sqrt(a)*sqrt(d)/sqrt(b)/sqrt(c),sqrt(-1))/b^(1/4)/c/d/sqrt(-b*x^4+a),1],
[1/sqrt(-b*x^4+a)/(-d*x^4+c),x,5,1/2*a^(1/4)*sqrt(1-b*x^4/a)*EllipticPi(sin(arcsin(b^(1/4)*x/a^(1/4))),-sqrt(a)*sqrt(d)/sqrt(b)/sqrt(c),sqrt(-1))/b^(1/4)/c/sqrt(-b*x^4+a)+1/2*a^(1/4)*sqrt(1-b*x^4/a)*EllipticPi(sin(arcsin(b^(1/4)*x/a^(1/4))),sqrt(a)*sqrt(d)/sqrt(b)/sqrt(c),sqrt(-1))/b^(1/4)/c/sqrt(-b*x^4+a),1],
[1/(-b*x^4+a)^(3/2)/(-d*x^4+c),x,9,1/2*b*x/a/(-a*d+b*c)/sqrt(-b*x^4+a)+1/2*b^(3/4)*sqrt(1-b*x^4/a)*InverseJacobiAM(arcsin(b^(1/4)*x/a^(1/4)),sqrt(-1))/a^(3/4)/(-a*d+b*c)/sqrt(-b*x^4+a)-1/2*a^(1/4)*d*sqrt(1-b*x^4/a)*EllipticPi(sin(arcsin(b^(1/4)*x/a^(1/4))),-sqrt(a)*sqrt(d)/sqrt(b)/sqrt(c),sqrt(-1))/b^(1/4)/c/(-a*d+b*c)/sqrt(-b*x^4+a)-1/2*a^(1/4)*d*sqrt(1-b*x^4/a)*EllipticPi(sin(arcsin(b^(1/4)*x/a^(1/4))),sqrt(a)*sqrt(d)/sqrt(b)/sqrt(c),sqrt(-1))/b^(1/4)/c/(-a*d+b*c)/sqrt(-b*x^4+a),1],
[1/(-b*x^4+a)^(5/2)/(-d*x^4+c),x,10,1/6*b*x/a/(-a*d+b*c)/(-b*x^4+a)^(3/2)+1/12*b*(-11*a*d+5*b*c)*x/a^2/(-a*d+b*c)^2/sqrt(-b*x^4+a)+1/12*b^(3/4)*(-11*a*d+5*b*c)*sqrt(1-b*x^4/a)*InverseJacobiAM(arcsin(b^(1/4)*x/a^(1/4)),sqrt(-1))/a^(7/4)/(-a*d+b*c)^2/sqrt(-b*x^4+a)+1/2*a^(1/4)*d^2*sqrt(1-b*x^4/a)*EllipticPi(sin(arcsin(b^(1/4)*x/a^(1/4))),-sqrt(a)*sqrt(d)/sqrt(b)/sqrt(c),sqrt(-1))/b^(1/4)/c/(-a*d+b*c)^2/sqrt(-b*x^4+a)+1/2*a^(1/4)*d^2*sqrt(1-b*x^4/a)*EllipticPi(sin(arcsin(b^(1/4)*x/a^(1/4))),sqrt(a)*sqrt(d)/sqrt(b)/sqrt(c),sqrt(-1))/b^(1/4)/c/(-a*d+b*c)^2/sqrt(-b*x^4+a),1],
[(b*x^4+a)^(3/2)/(-d*x^4+c),x,4,-1/3*b*x*sqrt(b*x^4+a)/d+1/4*(a*d+b*c)^(3/2)*arctan(sqrt(a*d+b*c)*x/c^(1/4)/d^(1/4)/sqrt(b*x^4+a))/c^(3/4)/d^(7/4)+1/4*(a*d+b*c)^(3/2)*arctanh(sqrt(a*d+b*c)*x/c^(1/4)/d^(1/4)/sqrt(b*x^4+a))/c^(3/4)/d^(7/4)+2/3*a^(3/4)*b^(3/4)*(2*a*d+b*c)*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*InverseJacobiAM(2*arctan(b^(1/4)*x/a^(1/4)),sqrt(1/2))/d/(-a*d+b*c)/sqrt(b*x^4+a)-1/8*(sqrt(b)*sqrt(c)+sqrt(a)*sqrt(d))*(a*d+b*c)^2*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*EllipticPi(sin(2*arctan(b^(1/4)*x/a^(1/4))),-1/4*(sqrt(b)*sqrt(c)-sqrt(a)*sqrt(d))^2/sqrt(a)/sqrt(b)/sqrt(c)/sqrt(d),sqrt(1/2))/a^(1/4)/b^(1/4)/c/(sqrt(b)*sqrt(c)-sqrt(a)*sqrt(d))/d^2/sqrt(b*x^4+a)-1/8*(sqrt(b)*sqrt(c)-sqrt(a)*sqrt(d))*(a*d+b*c)^2*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*EllipticPi(sin(2*arctan(b^(1/4)*x/a^(1/4))),1/4*(sqrt(b)*sqrt(c)+sqrt(a)*sqrt(d))^2/sqrt(a)/sqrt(b)/sqrt(c)/sqrt(d),sqrt(1/2))/a^(1/4)/b^(1/4)/c/(sqrt(b)*sqrt(c)+sqrt(a)*sqrt(d))/d^2/sqrt(b*x^4+a),1],
[sqrt(b*x^4+a)/(-d*x^4+c),x,5,1/4*sqrt(a*d+b*c)*arctan(sqrt(a*d+b*c)*x/c^(1/4)/d^(1/4)/sqrt(b*x^4+a))/c^(3/4)/d^(3/4)+1/4*sqrt(a*d+b*c)*arctanh(sqrt(a*d+b*c)*x/c^(1/4)/d^(1/4)/sqrt(b*x^4+a))/c^(3/4)/d^(3/4)-1/2*b^(3/4)*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*InverseJacobiAM(2*arctan(b^(1/4)*x/a^(1/4)),sqrt(1/2))/a^(1/4)/d/sqrt(b*x^4+a)+1/2*b^(3/4)*(a*d+b*c)*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*InverseJacobiAM(2*arctan(b^(1/4)*x/a^(1/4)),sqrt(1/2))/a^(1/4)/d/(-a*d+b*c)/sqrt(b*x^4+a)-1/8*(sqrt(b)*sqrt(c)+sqrt(a)*sqrt(d))^2*(a*d+b*c)*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*EllipticPi(sin(2*arctan(b^(1/4)*x/a^(1/4))),-1/4*(sqrt(b)*sqrt(c)-sqrt(a)*sqrt(d))^2/sqrt(a)/sqrt(b)/sqrt(c)/sqrt(d),sqrt(1/2))/a^(1/4)/b^(1/4)/c/d/(-a*d+b*c)/sqrt(b*x^4+a)-1/8*(sqrt(b)*sqrt(c)-sqrt(a)*sqrt(d))^2*(a*d+b*c)*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*EllipticPi(sin(2*arctan(b^(1/4)*x/a^(1/4))),1/4*(sqrt(b)*sqrt(c)+sqrt(a)*sqrt(d))^2/sqrt(a)/sqrt(b)/sqrt(c)/sqrt(d),sqrt(1/2))/a^(1/4)/b^(1/4)/c/d/(-a*d+b*c)/sqrt(b*x^4+a),1],
[1/sqrt(b*x^4+a)/(-d*x^4+c),x,3,1/4*d^(1/4)*arctan(sqrt(a*d+b*c)*x/c^(1/4)/d^(1/4)/sqrt(b*x^4+a))/c^(3/4)/sqrt(a*d+b*c)+1/4*d^(1/4)*arctanh(sqrt(a*d+b*c)*x/c^(1/4)/d^(1/4)/sqrt(b*x^4+a))/c^(3/4)/sqrt(a*d+b*c)+1/2*b^(3/4)*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*InverseJacobiAM(2*arctan(b^(1/4)*x/a^(1/4)),sqrt(1/2))/a^(1/4)/(-a*d+b*c)/sqrt(b*x^4+a)-1/8*(sqrt(b)*sqrt(c)+sqrt(a)*sqrt(d))^2*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*EllipticPi(sin(2*arctan(b^(1/4)*x/a^(1/4))),-1/4*(sqrt(b)*sqrt(c)-sqrt(a)*sqrt(d))^2/sqrt(a)/sqrt(b)/sqrt(c)/sqrt(d),sqrt(1/2))/a^(1/4)/b^(1/4)/c/(-a*d+b*c)/sqrt(b*x^4+a)-1/8*(sqrt(b)*sqrt(c)-sqrt(a)*sqrt(d))^2*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*EllipticPi(sin(2*arctan(b^(1/4)*x/a^(1/4))),1/4*(sqrt(b)*sqrt(c)+sqrt(a)*sqrt(d))^2/sqrt(a)/sqrt(b)/sqrt(c)/sqrt(d),sqrt(1/2))/a^(1/4)/b^(1/4)/c/(-a*d+b*c)/sqrt(b*x^4+a),1],
[1/(b*x^4+a)^(3/2)/(-d*x^4+c),x,4,1/2*b*x/a/(a*d+b*c)/sqrt(b*x^4+a)+1/4*d^(5/4)*arctan(sqrt(a*d+b*c)*x/c^(1/4)/d^(1/4)/sqrt(b*x^4+a))/c^(3/4)/(a*d+b*c)^(3/2)+1/4*d^(5/4)*arctanh(sqrt(a*d+b*c)*x/c^(1/4)/d^(1/4)/sqrt(b*x^4+a))/c^(3/4)/(a*d+b*c)^(3/2)+1/4*b^(3/4)*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*InverseJacobiAM(2*arctan(b^(1/4)*x/a^(1/4)),sqrt(1/2))/a^(5/4)/(-a*d+b*c)/sqrt(b*x^4+a)-1/8*(sqrt(b)*sqrt(c)+sqrt(a)*sqrt(d))^2*d*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*EllipticPi(sin(2*arctan(b^(1/4)*x/a^(1/4))),-1/4*(sqrt(b)*sqrt(c)-sqrt(a)*sqrt(d))^2/sqrt(a)/sqrt(b)/sqrt(c)/sqrt(d),sqrt(1/2))/a^(1/4)/b^(1/4)/c/(-a*d+b*c)/(a*d+b*c)/sqrt(b*x^4+a)-1/8*(sqrt(b)*sqrt(c)-sqrt(a)*sqrt(d))^2*d*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*EllipticPi(sin(2*arctan(b^(1/4)*x/a^(1/4))),1/4*(sqrt(b)*sqrt(c)+sqrt(a)*sqrt(d))^2/sqrt(a)/sqrt(b)/sqrt(c)/sqrt(d),sqrt(1/2))/a^(1/4)/b^(1/4)/c/(-a*d+b*c)/(a*d+b*c)/sqrt(b*x^4+a),1],
[1/(b*x^4+a)^(5/2)/(-d*x^4+c),x,5,1/6*b*x/a/(a*d+b*c)/(b*x^4+a)^(3/2)+1/12*b*(11*a*d+5*b*c)*x/a^2/(a*d+b*c)^2/sqrt(b*x^4+a)+1/4*d^(9/4)*arctan(sqrt(a*d+b*c)*x/c^(1/4)/d^(1/4)/sqrt(b*x^4+a))/c^(3/4)/(a*d+b*c)^(5/2)+1/4*d^(9/4)*arctanh(sqrt(a*d+b*c)*x/c^(1/4)/d^(1/4)/sqrt(b*x^4+a))/c^(3/4)/(a*d+b*c)^(5/2)+1/24*b^(3/4)*(a*d+5*b*c)*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*InverseJacobiAM(2*arctan(b^(1/4)*x/a^(1/4)),sqrt(1/2))/a^(9/4)/(-a*d+b*c)/(a*d+b*c)/sqrt(b*x^4+a)-1/8*(sqrt(b)*sqrt(c)+sqrt(a)*sqrt(d))*d^2*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*EllipticPi(sin(2*arctan(b^(1/4)*x/a^(1/4))),-1/4*(sqrt(b)*sqrt(c)-sqrt(a)*sqrt(d))^2/sqrt(a)/sqrt(b)/sqrt(c)/sqrt(d),sqrt(1/2))/a^(1/4)/b^(1/4)/c/(sqrt(b)*sqrt(c)-sqrt(a)*sqrt(d))/(a*d+b*c)^2/sqrt(b*x^4+a)-1/8*(sqrt(b)*sqrt(c)-sqrt(a)*sqrt(d))*d^2*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*EllipticPi(sin(2*arctan(b^(1/4)*x/a^(1/4))),1/4*(sqrt(b)*sqrt(c)+sqrt(a)*sqrt(d))^2/sqrt(a)/sqrt(b)/sqrt(c)/sqrt(d),sqrt(1/2))/a^(1/4)/b^(1/4)/c/(sqrt(b)*sqrt(c)+sqrt(a)*sqrt(d))/(a*d+b*c)^2/sqrt(b*x^4+a),1],
[(-b*x^4+a)^(7/2)/(-d*x^4+c)^2,x,11,-1/84*b*(21*a^2*d^2-122*a*b*c*d+77*b^2*c^2)*x*sqrt(-b*x^4+a)/c/d^3+1/28*b*(-7*a*d+11*b*c)*x*(-b*x^4+a)^(3/2)/c/d^2-1/4*(-a*d+b*c)*x*(-b*x^4+a)^(5/2)/c/d/(-d*x^4+c)+1/84*a^(1/4)*b^(3/4)*(21*a^3*d^3+349*a^2*b*c*d^2-553*a*b^2*c^2*d+231*b^3*c^3)*sqrt(1-b*x^4/a)*InverseJacobiAM(arcsin(b^(1/4)*x/a^(1/4)),sqrt(-1))/c/d^4/sqrt(-b*x^4+a)-1/8*a^(1/4)*(-a*d+b*c)^3*(3*a*d+11*b*c)*sqrt(1-b*x^4/a)*EllipticPi(sin(arcsin(b^(1/4)*x/a^(1/4))),-sqrt(a)*sqrt(d)/sqrt(b)/sqrt(c),sqrt(-1))/b^(1/4)/c^2/d^4/sqrt(-b*x^4+a)-1/8*a^(1/4)*(-a*d+b*c)^3*(3*a*d+11*b*c)*sqrt(1-b*x^4/a)*EllipticPi(sin(arcsin(b^(1/4)*x/a^(1/4))),sqrt(a)*sqrt(d)/sqrt(b)/sqrt(c),sqrt(-1))/b^(1/4)/c^2/d^4/sqrt(-b*x^4+a),1],
[(-b*x^4+a)^(5/2)/(-d*x^4+c)^2,x,10,1/12*b*(-3*a*d+7*b*c)*x*sqrt(-b*x^4+a)/c/d^2-1/4*(-a*d+b*c)*x*(-b*x^4+a)^(3/2)/c/d/(-d*x^4+c)-1/12*a^(1/4)*b^(3/4)*(-3*a^2*d^2-26*a*b*c*d+21*b^2*c^2)*sqrt(1-b*x^4/a)*InverseJacobiAM(arcsin(b^(1/4)*x/a^(1/4)),sqrt(-1))/c/d^3/sqrt(-b*x^4+a)+1/8*a^(1/4)*(-a*d+b*c)^2*(3*a*d+7*b*c)*sqrt(1-b*x^4/a)*EllipticPi(sin(arcsin(b^(1/4)*x/a^(1/4))),-sqrt(a)*sqrt(d)/sqrt(b)/sqrt(c),sqrt(-1))/b^(1/4)/c^2/d^3/sqrt(-b*x^4+a)+1/8*a^(1/4)*(-a*d+b*c)^2*(3*a*d+7*b*c)*sqrt(1-b*x^4/a)*EllipticPi(sin(arcsin(b^(1/4)*x/a^(1/4))),sqrt(a)*sqrt(d)/sqrt(b)/sqrt(c),sqrt(-1))/b^(1/4)/c^2/d^3/sqrt(-b*x^4+a),1],
[(-b*x^4+a)^(3/2)/(-d*x^4+c)^2,x,9,-1/4*(-a*d+b*c)*x*sqrt(-b*x^4+a)/c/d/(-d*x^4+c)+1/4*a^(1/4)*b^(3/4)*(a*d+3*b*c)*sqrt(1-b*x^4/a)*InverseJacobiAM(arcsin(b^(1/4)*x/a^(1/4)),sqrt(-1))/c/d^2/sqrt(-b*x^4+a)-3/8*a^(1/4)*(-a*d+b*c)*(a*d+b*c)*sqrt(1-b*x^4/a)*EllipticPi(sin(arcsin(b^(1/4)*x/a^(1/4))),-sqrt(a)*sqrt(d)/sqrt(b)/sqrt(c),sqrt(-1))/b^(1/4)/c^2/d^2/sqrt(-b*x^4+a)-3/8*a^(1/4)*(-a*d+b*c)*(a*d+b*c)*sqrt(1-b*x^4/a)*EllipticPi(sin(arcsin(b^(1/4)*x/a^(1/4))),sqrt(a)*sqrt(d)/sqrt(b)/sqrt(c),sqrt(-1))/b^(1/4)/c^2/d^2/sqrt(-b*x^4+a),1],
[sqrt(-b*x^4+a)/(-d*x^4+c)^2,x,9,1/4*x*sqrt(-b*x^4+a)/c/(-d*x^4+c)+1/4*a^(1/4)*b^(3/4)*sqrt(1-b*x^4/a)*InverseJacobiAM(arcsin(b^(1/4)*x/a^(1/4)),sqrt(-1))/c/d/sqrt(-b*x^4+a)-1/8*a^(1/4)*(-3*a*d+b*c)*sqrt(1-b*x^4/a)*EllipticPi(sin(arcsin(b^(1/4)*x/a^(1/4))),-sqrt(a)*sqrt(d)/sqrt(b)/sqrt(c),sqrt(-1))/b^(1/4)/c^2/d/sqrt(-b*x^4+a)-1/8*a^(1/4)*(-3*a*d+b*c)*sqrt(1-b*x^4/a)*EllipticPi(sin(arcsin(b^(1/4)*x/a^(1/4))),sqrt(a)*sqrt(d)/sqrt(b)/sqrt(c),sqrt(-1))/b^(1/4)/c^2/d/sqrt(-b*x^4+a),1],
[1/sqrt(-b*x^4+a)/(-d*x^4+c)^2,x,9,-1/4*d*x*sqrt(-b*x^4+a)/c/(-a*d+b*c)/(-d*x^4+c)-1/4*a^(1/4)*b^(3/4)*sqrt(1-b*x^4/a)*InverseJacobiAM(arcsin(b^(1/4)*x/a^(1/4)),sqrt(-1))/c/(-a*d+b*c)/sqrt(-b*x^4+a)+1/8*a^(1/4)*(-3*a*d+5*b*c)*sqrt(1-b*x^4/a)*EllipticPi(sin(arcsin(b^(1/4)*x/a^(1/4))),-sqrt(a)*sqrt(d)/sqrt(b)/sqrt(c),sqrt(-1))/b^(1/4)/c^2/(-a*d+b*c)/sqrt(-b*x^4+a)+1/8*a^(1/4)*(-3*a*d+5*b*c)*sqrt(1-b*x^4/a)*EllipticPi(sin(arcsin(b^(1/4)*x/a^(1/4))),sqrt(a)*sqrt(d)/sqrt(b)/sqrt(c),sqrt(-1))/b^(1/4)/c^2/(-a*d+b*c)/sqrt(-b*x^4+a),1],
[1/(-b*x^4+a)^(3/2)/(-d*x^4+c)^2,x,10,1/4*b*(a*d+2*b*c)*x/a/c/(-a*d+b*c)^2/sqrt(-b*x^4+a)-1/4*d*x/c/(-a*d+b*c)/sqrt(-b*x^4+a)/(-d*x^4+c)+1/4*b^(3/4)*(a*d+2*b*c)*sqrt(1-b*x^4/a)*InverseJacobiAM(arcsin(b^(1/4)*x/a^(1/4)),sqrt(-1))/a^(3/4)/c/(-a*d+b*c)^2/sqrt(-b*x^4+a)-3/8*a^(1/4)*d*(-a*d+3*b*c)*sqrt(1-b*x^4/a)*EllipticPi(sin(arcsin(b^(1/4)*x/a^(1/4))),-sqrt(a)*sqrt(d)/sqrt(b)/sqrt(c),sqrt(-1))/b^(1/4)/c^2/(-a*d+b*c)^2/sqrt(-b*x^4+a)-3/8*a^(1/4)*d*(-a*d+3*b*c)*sqrt(1-b*x^4/a)*EllipticPi(sin(arcsin(b^(1/4)*x/a^(1/4))),sqrt(a)*sqrt(d)/sqrt(b)/sqrt(c),sqrt(-1))/b^(1/4)/c^2/(-a*d+b*c)^2/sqrt(-b*x^4+a),1],
[1/(-b*x^4+a)^(5/2)/(-d*x^4+c)^2,x,11,1/12*b*(3*a*d+2*b*c)*x/a/c/(-a*d+b*c)^2/(-b*x^4+a)^(3/2)+1/12*b*(-3*a^2*d^2-17*a*b*c*d+5*b^2*c^2)*x/a^2/c/(-a*d+b*c)^3/sqrt(-b*x^4+a)-1/4*d*x/c/(-a*d+b*c)/(-b*x^4+a)^(3/2)/(-d*x^4+c)+1/12*b^(3/4)*(-3*a^2*d^2-17*a*b*c*d+5*b^2*c^2)*sqrt(1-b*x^4/a)*InverseJacobiAM(arcsin(b^(1/4)*x/a^(1/4)),sqrt(-1))/a^(7/4)/c/(-a*d+b*c)^3/sqrt(-b*x^4+a)+1/8*a^(1/4)*d^2*(-3*a*d+13*b*c)*sqrt(1-b*x^4/a)*EllipticPi(sin(arcsin(b^(1/4)*x/a^(1/4))),-sqrt(a)*sqrt(d)/sqrt(b)/sqrt(c),sqrt(-1))/b^(1/4)/c^2/(-a*d+b*c)^3/sqrt(-b*x^4+a)+1/8*a^(1/4)*d^2*(-3*a*d+13*b*c)*sqrt(1-b*x^4/a)*EllipticPi(sin(arcsin(b^(1/4)*x/a^(1/4))),sqrt(a)*sqrt(d)/sqrt(b)/sqrt(c),sqrt(-1))/b^(1/4)/c^2/(-a*d+b*c)^3/sqrt(-b*x^4+a),1],
[sqrt(b*x^4+a)/(-b*c*x^4+a*c),x,4,1/2*arctan(sqrt(2)*a^(1/4)*b^(1/4)*x/sqrt(b*x^4+a))/sqrt(2)/a^(1/4)/b^(1/4)/c+1/2*arctanh(sqrt(2)*a^(1/4)*b^(1/4)*x/sqrt(b*x^4+a))/sqrt(2)/a^(1/4)/b^(1/4)/c,1],
[sqrt(-b*x^4+a)/(b*c*x^4+a*c),x,1,1/2*arctan(b^(1/4)*x*(sqrt(a)+sqrt(b)*x^2)/a^(1/4)/sqrt(-b*x^4+a))/a^(1/4)/b^(1/4)/c+1/2*arctanh(b^(1/4)*x*(sqrt(a)-sqrt(b)*x^2)/a^(1/4)/sqrt(-b*x^4+a))/a^(1/4)/b^(1/4)/c,1],
[sqrt(d*x^4+c)/sqrt(-d*x^4+c),x,6,c*x*sqrt(1-d^2*x^8/c^2)*hypergeom([1/8, 1/2],[9/8],d^2*x^8/c^2)/sqrt(-d*x^4+c)/sqrt(d*x^4+c)+1/5*d*x^5*sqrt(1-d^2*x^8/c^2)*hypergeom([1/2, 5/8],[13/8],d^2*x^8/c^2)/sqrt(-d*x^4+c)/sqrt(d*x^4+c),1],
[(b*x^4+a)^(1/3)*(d*x^4+c)^2,x,4,3/589*d*(-15*a*d+62*b*c)*x*(b*x^4+a)^(4/3)/b^2+3/31*d^2*x^5*(b*x^4+a)^(4/3)/b+1/589*(589*c^2-3*a*d*(-15*a*d+62*b*c)/b^2)*x*(b*x^4+a)^(1/3)*hypergeom([-1/3, 1/4],[5/4],-b*x^4/a)/(1+b*x^4/a)^(1/3),1],
[(b*x^4+a)^(1/3)*(d*x^4+c),x,3,3/19*d*x*(b*x^4+a)^(4/3)/b+1/19*(-3*a*d+19*b*c)*x*(b*x^4+a)^(1/3)*hypergeom([-1/3, 1/4],[5/4],-b*x^4/a)/b/(1+b*x^4/a)^(1/3),1],
[(b*x^4+a)^(1/3)/(d*x^4+c),x,3,x*(b*x^4+a)^(1/3)*AppellF1(1/4,-1/3,1,5/4,-b*x^4/a,-d*x^4/c)/c/(1+b*x^4/a)^(1/3),1],
[(b*x^4+a)^(1/3)/(d*x^4+c)^2,x,3,x*(b*x^4+a)^(1/3)*AppellF1(1/4,-1/3,2,5/4,-b*x^4/a,-d*x^4/c)/c^2/(1+b*x^4/a)^(1/3),1],
[(d*x^4+c)^2/(b*x^4+a)^(1/3),x,4,3/253*d*(-15*a*d+46*b*c)*x*(b*x^4+a)^(2/3)/b^2+3/23*d^2*x^5*(b*x^4+a)^(2/3)/b+1/253*(253*c^2-3*a*d*(-15*a*d+46*b*c)/b^2)*x*(1+b*x^4/a)^(1/3)*hypergeom([1/4, 1/3],[5/4],-b*x^4/a)/(b*x^4+a)^(1/3),1],
[(d*x^4+c)/(b*x^4+a)^(1/3),x,3,3/11*d*x*(b*x^4+a)^(2/3)/b+1/11*(-3*a*d+11*b*c)*x*(1+b*x^4/a)^(1/3)*hypergeom([1/4, 1/3],[5/4],-b*x^4/a)/b/(b*x^4+a)^(1/3),1],
[1/(b*x^4+a)^(1/3)/(d*x^4+c),x,3,x*(1+b*x^4/a)^(1/3)*AppellF1(1/4,1/3,1,5/4,-b*x^4/a,-d*x^4/c)/c/(b*x^4+a)^(1/3),1],
[1/(b*x^4+a)^(1/3)/(d*x^4+c)^2,x,3,x*(1+b*x^4/a)^(1/3)*AppellF1(1/4,1/3,2,5/4,-b*x^4/a,-d*x^4/c)/c^2/(b*x^4+a)^(1/3),1],
[(d*x^4+c)^2/(b*x^4+a)^(4/3),x,4,3/4*(-a*d+b*c)^2*x/a/b^2/(b*x^4+a)^(1/3)+3/11*d^2*x*(b*x^4+a)^(2/3)/b^2+1/44*(-45*a^2*d^2+66*a*b*c*d+11*b^2*c^2)*x*(1+b*x^4/a)^(1/3)*hypergeom([1/4, 1/3],[5/4],-b*x^4/a)/a/b^2/(b*x^4+a)^(1/3),1],
[(d*x^4+c)/(b*x^4+a)^(4/3),x,3,-3*d*x/b/(b*x^4+a)^(1/3)+(3*a*d+b*c)*x*(1+b*x^4/a)^(1/3)*hypergeom([1/4, 4/3],[5/4],-b*x^4/a)/a/b/(b*x^4+a)^(1/3),1],
[1/(b*x^4+a)^(4/3)/(d*x^4+c),x,3,x*(1+b*x^4/a)^(1/3)*AppellF1(1/4,4/3,1,5/4,-b*x^4/a,-d*x^4/c)/a/c/(b*x^4+a)^(1/3),1],
[1/(b*x^4+a)^(4/3)/(d*x^4+c)^2,x,3,x*(1+b*x^4/a)^(1/3)*AppellF1(1/4,4/3,2,5/4,-b*x^4/a,-d*x^4/c)/a/c^2/(b*x^4+a)^(1/3),1],
[(d*x^4+c)^2/(b*x^4+a)^(5/3),x,4,3/8*(-a*d+b*c)^2*x/a/b^2/(b*x^4+a)^(2/3)+3/7*d^2*x*(b*x^4+a)^(1/3)/b^2+1/56*(-45*a^2*d^2+42*a*b*c*d+35*b^2*c^2)*x*(1+b*x^4/a)^(2/3)*hypergeom([1/4, 2/3],[5/4],-b*x^4/a)/a/b^2/(b*x^4+a)^(2/3),1],
[(d*x^4+c)/(b*x^4+a)^(5/3),x,3,-3/5*d*x/b/(b*x^4+a)^(2/3)+1/5*(3*a*d+5*b*c)*x*(1+b*x^4/a)^(2/3)*hypergeom([1/4, 5/3],[5/4],-b*x^4/a)/a/b/(b*x^4+a)^(2/3),1],
[1/(b*x^4+a)^(5/3)/(d*x^4+c),x,3,x*(1+b*x^4/a)^(2/3)*AppellF1(1/4,5/3,1,5/4,-b*x^4/a,-d*x^4/c)/a/c/(b*x^4+a)^(2/3),1],
[1/(b*x^4+a)^(5/3)/(d*x^4+c)^2,x,3,x*(1+b*x^4/a)^(2/3)*AppellF1(1/4,5/3,2,5/4,-b*x^4/a,-d*x^4/c)/a/c^2/(b*x^4+a)^(2/3),1],
[(b*x^4+a)^(3/4)*(d*x^4+c),x,6,1/32*(-a*d+8*b*c)*x*(b*x^4+a)^(3/4)/b+1/8*d*x*(b*x^4+a)^(7/4)/b+3/64*a*(-a*d+8*b*c)*arctan(b^(1/4)*x/(b*x^4+a)^(1/4))/b^(5/4)+3/64*a*(-a*d+8*b*c)*arctanh(b^(1/4)*x/(b*x^4+a)^(1/4))/b^(5/4),1],
[(d*x^4+c)/(b*x^4+a)^(1/4),x,5,1/4*d*x*(b*x^4+a)^(3/4)/b+1/8*(-a*d+4*b*c)*arctan(b^(1/4)*x/(b*x^4+a)^(1/4))/b^(5/4)+1/8*(-a*d+4*b*c)*arctanh(b^(1/4)*x/(b*x^4+a)^(1/4))/b^(5/4),1],
[(d*x^4+c)/(b*x^4+a)^(5/4),x,5,(-a*d+b*c)*x/a/b/(b*x^4+a)^(1/4)+1/2*d*arctan(b^(1/4)*x/(b*x^4+a)^(1/4))/b^(5/4)+1/2*d*arctanh(b^(1/4)*x/(b*x^4+a)^(1/4))/b^(5/4),1],
[(d*x^4+c)/(b*x^4+a)^(9/4),x,2,1/5*(-a*d+b*c)*x/a/b/(b*x^4+a)^(5/4)+1/5*(a*d+4*b*c)*x/a^2/b/(b*x^4+a)^(1/4),1],
[(d*x^4+c)/(b*x^4+a)^(13/4),x,3,1/9*(-a*d+b*c)*x/a/b/(b*x^4+a)^(9/4)+1/45*(a*d+8*b*c)*x/a^2/b/(b*x^4+a)^(5/4)+4/45*(a*d+8*b*c)*x/a^3/b/(b*x^4+a)^(1/4),1],
[(d*x^4+c)/(b*x^4+a)^(17/4),x,4,1/13*(-a*d+b*c)*x/a/b/(b*x^4+a)^(13/4)+1/117*(a*d+12*b*c)*x/a^2/b/(b*x^4+a)^(9/4)+8/585*(a*d+12*b*c)*x/a^3/b/(b*x^4+a)^(5/4)+32/585*(a*d+12*b*c)*x/a^4/b/(b*x^4+a)^(1/4),1],
[(b*x^4+a)^(5/4)*(d*x^4+c),x,5,1/24*a*(-a*d+10*b*c)*x*(b*x^4+a)^(1/4)/b+1/60*(-a*d+10*b*c)*x*(b*x^4+a)^(5/4)/b+1/10*d*x*(b*x^4+a)^(9/4)/b-1/24*a^(3/2)*(-a*d+10*b*c)*(1+a/b/x^4)^(3/4)*x^3*InverseJacobiAM(1/2*arccot(sqrt(b)*x^2/sqrt(a)),sqrt(2))/sqrt(b)/(b*x^4+a)^(3/4),1],
[(b*x^4+a)^(1/4)*(d*x^4+c),x,4,1/12*(-a*d+6*b*c)*x*(b*x^4+a)^(1/4)/b+1/6*d*x*(b*x^4+a)^(5/4)/b-1/12*sqrt(a)*(-a*d+6*b*c)*(1+a/b/x^4)^(3/4)*x^3*InverseJacobiAM(1/2*arccot(sqrt(b)*x^2/sqrt(a)),sqrt(2))/sqrt(b)/(b*x^4+a)^(3/4),1],
[(d*x^4+c)/(b*x^4+a)^(3/4),x,3,1/2*d*x*(b*x^4+a)^(1/4)/b-1/2*(-a*d+2*b*c)*(1+a/b/x^4)^(3/4)*x^3*InverseJacobiAM(1/2*arccot(sqrt(b)*x^2/sqrt(a)),sqrt(2))/sqrt(a)/sqrt(b)/(b*x^4+a)^(3/4),1],
[(d*x^4+c)/(b*x^4+a)^(7/4),x,3,1/3*(-a*d+b*c)*x/a/b/(b*x^4+a)^(3/4)-1/3*(a*d+2*b*c)*(1+a/b/x^4)^(3/4)*x^3*InverseJacobiAM(1/2*arccot(sqrt(b)*x^2/sqrt(a)),sqrt(2))/a^(3/2)/sqrt(b)/(b*x^4+a)^(3/4),1],
[(d*x^4+c)/(b*x^4+a)^(11/4),x,4,1/7*(-a*d+b*c)*x/a/b/(b*x^4+a)^(7/4)+1/21*(a*d+6*b*c)*x/a^2/b/(b*x^4+a)^(3/4)-2/21*(a*d+6*b*c)*(1+a/b/x^4)^(3/4)*x^3*InverseJacobiAM(1/2*arccot(sqrt(b)*x^2/sqrt(a)),sqrt(2))/a^(5/2)/sqrt(b)/(b*x^4+a)^(3/4),1],
[(d*x^4+c)/(b*x^4+a)^(15/4),x,5,1/11*(-a*d+b*c)*x/a/b/(b*x^4+a)^(11/4)+1/77*(a*d+10*b*c)*x/a^2/b/(b*x^4+a)^(7/4)+2/77*(a*d+10*b*c)*x/a^3/b/(b*x^4+a)^(3/4)-4/77*(a*d+10*b*c)*(1+a/b/x^4)^(3/4)*x^3*InverseJacobiAM(1/2*arccot(sqrt(b)*x^2/sqrt(a)),sqrt(2))/a^(7/2)/sqrt(b)/(b*x^4+a)^(3/4),1],
[(b*x^4+a)^(3/4)*(d*x^4+c)^2,x,7,1/384*(96*c^2-a*d*(-5*a*d+24*b*c)/b^2)*x*(b*x^4+a)^(3/4)+1/96*d*(-5*a*d+24*b*c)*x*(b*x^4+a)^(7/4)/b^2+1/12*d^2*x^5*(b*x^4+a)^(7/4)/b+1/256*a*(5*a^2*d^2-24*a*b*c*d+96*b^2*c^2)*arctan(b^(1/4)*x/(b*x^4+a)^(1/4))/b^(9/4)+1/256*a*(5*a^2*d^2-24*a*b*c*d+96*b^2*c^2)*arctanh(b^(1/4)*x/(b*x^4+a)^(1/4))/b^(9/4),1],
[(d*x^4+c)^2/(b*x^4+a)^(1/4),x,6,1/32*d*(-5*a*d+16*b*c)*x*(b*x^4+a)^(3/4)/b^2+1/8*d^2*x^5*(b*x^4+a)^(3/4)/b+1/64*(5*a^2*d^2-16*a*b*c*d+32*b^2*c^2)*arctan(b^(1/4)*x/(b*x^4+a)^(1/4))/b^(9/4)+1/64*(5*a^2*d^2-16*a*b*c*d+32*b^2*c^2)*arctanh(b^(1/4)*x/(b*x^4+a)^(1/4))/b^(9/4),1],
[(d*x^4+c)^2/(b*x^4+a)^(5/4),x,6,(-a*d+b*c)^2*x/a/b^2/(b*x^4+a)^(1/4)+1/4*d^2*x*(b*x^4+a)^(3/4)/b^2+1/8*d*(-5*a*d+8*b*c)*arctan(b^(1/4)*x/(b*x^4+a)^(1/4))/b^(9/4)+1/8*d*(-5*a*d+8*b*c)*arctanh(b^(1/4)*x/(b*x^4+a)^(1/4))/b^(9/4),1],
[(d*x^4+c)^2/(b*x^4+a)^(9/4),x,6,1/5*(-a*d+b*c)^2*x/a/b^2/(b*x^4+a)^(5/4)+2/5*(-a*d+b*c)*(3*a*d+2*b*c)*x/a^2/b^2/(b*x^4+a)^(1/4)+1/2*d^2*arctan(b^(1/4)*x/(b*x^4+a)^(1/4))/b^(9/4)+1/2*d^2*arctanh(b^(1/4)*x/(b*x^4+a)^(1/4))/b^(9/4),1],
[(d*x^4+c)^2/(b*x^4+a)^(13/4),x,3,1/9*(-a*d+b*c)^2*x/a/b^2/(b*x^4+a)^(9/4)+2/45*(-a*d+b*c)*(5*a*d+4*b*c)*x/a^2/b^2/(b*x^4+a)^(5/4)+1/45*(5*a^2*d^2+8*a*b*c*d+32*b^2*c^2)*x/a^3/b^2/(b*x^4+a)^(1/4),1],
[(d*x^4+c)^2/(b*x^4+a)^(17/4),x,4,1/13*(-a*d+b*c)^2*x/a/b^2/(b*x^4+a)^(13/4)+2/117*(-a*d+b*c)*(7*a*d+6*b*c)*x/a^2/b^2/(b*x^4+a)^(9/4)+1/585*(5*a^2*d^2+16*a*b*c*d+96*b^2*c^2)*x/a^3/b^2/(b*x^4+a)^(5/4)+4/585*(5*a^2*d^2+16*a*b*c*d+96*b^2*c^2)*x/a^4/b^2/(b*x^4+a)^(1/4),1],
[(b*x^4+a)^(5/4)*(d*x^4+c)^2,x,6,1/336*a*(5*a^2*d^2-28*a*b*c*d+140*b^2*c^2)*x*(b*x^4+a)^(1/4)/b^2+1/840*(140*c^2-a*d*(-5*a*d+28*b*c)/b^2)*x*(b*x^4+a)^(5/4)+1/140*d*(-5*a*d+28*b*c)*x*(b*x^4+a)^(9/4)/b^2+1/14*d^2*x^5*(b*x^4+a)^(9/4)/b-1/336*a^(3/2)*(5*a^2*d^2-28*a*b*c*d+140*b^2*c^2)*(1+a/b/x^4)^(3/4)*x^3*InverseJacobiAM(1/2*arccot(sqrt(b)*x^2/sqrt(a)),sqrt(2))/b^(3/2)/(b*x^4+a)^(3/4),1],
[(b*x^4+a)^(1/4)*(d*x^4+c)^2,x,5,1/24*(a^2*d^2-4*a*b*c*d+12*b^2*c^2)*x*(b*x^4+a)^(1/4)/b^2+1/12*d*(-a*d+4*b*c)*x*(b*x^4+a)^(5/4)/b^2+1/10*d^2*x^5*(b*x^4+a)^(5/4)/b-1/24*sqrt(a)*(a^2*d^2-4*a*b*c*d+12*b^2*c^2)*(1+a/b/x^4)^(3/4)*x^3*InverseJacobiAM(1/2*arccot(sqrt(b)*x^2/sqrt(a)),sqrt(2))/b^(3/2)/(b*x^4+a)^(3/4),1],
[(d*x^4+c)^2/(b*x^4+a)^(3/4),x,4,1/12*d*(-5*a*d+12*b*c)*x*(b*x^4+a)^(1/4)/b^2+1/6*d^2*x^5*(b*x^4+a)^(1/4)/b-1/12*(5*a^2*d^2-12*a*b*c*d+12*b^2*c^2)*(1+a/b/x^4)^(3/4)*x^3*InverseJacobiAM(1/2*arccot(sqrt(b)*x^2/sqrt(a)),sqrt(2))/sqrt(a)/b^(3/2)/(b*x^4+a)^(3/4),1],
[(d*x^4+c)^2/(b*x^4+a)^(7/4),x,4,1/3*(-a*d+b*c)^2*x/a/b^2/(b*x^4+a)^(3/4)+1/2*d^2*x*(b*x^4+a)^(1/4)/b^2-1/6*(-5*a^2*d^2+4*a*b*c*d+4*b^2*c^2)*(1+a/b/x^4)^(3/4)*x^3*InverseJacobiAM(1/2*arccot(sqrt(b)*x^2/sqrt(a)),sqrt(2))/a^(3/2)/b^(3/2)/(b*x^4+a)^(3/4),1],
[(d*x^4+c)^2/(b*x^4+a)^(11/4),x,4,1/7*(-a*d+b*c)^2*x/a/b^2/(b*x^4+a)^(7/4)+2/21*(-a*d+b*c)*(4*a*d+3*b*c)*x/a^2/b^2/(b*x^4+a)^(3/4)-1/21*(5*a^2*d^2+4*a*b*c*d+12*b^2*c^2)*(1+a/b/x^4)^(3/4)*x^3*InverseJacobiAM(1/2*arccot(sqrt(b)*x^2/sqrt(a)),sqrt(2))/a^(5/2)/b^(3/2)/(b*x^4+a)^(3/4),1],
[(d*x^4+c)^2/(b*x^4+a)^(15/4),x,5,1/11*(-a*d+b*c)^2*x/a/b^2/(b*x^4+a)^(11/4)+2/77*(-a*d+b*c)*(6*a*d+5*b*c)*x/a^2/b^2/(b*x^4+a)^(7/4)+1/231*(5*a^2*d^2+12*a*b*c*d+60*b^2*c^2)*x/a^3/b^2/(b*x^4+a)^(3/4)-2/231*(5*a^2*d^2+12*a*b*c*d+60*b^2*c^2)*(1+a/b/x^4)^(3/4)*x^3*InverseJacobiAM(1/2*arccot(sqrt(b)*x^2/sqrt(a)),sqrt(2))/a^(7/2)/b^(3/2)/(b*x^4+a)^(3/4),1],
[(b*x^4+a)^(7/4)/(d*x^4+c),x,10,1/4*b*x*(b*x^4+a)^(3/4)/d-1/8*b^(3/4)*(-7*a*d+4*b*c)*arctan(b^(1/4)*x/(b*x^4+a)^(1/4))/d^2+1/2*(-a*d+b*c)^(7/4)*arctan((-a*d+b*c)^(1/4)*x/c^(1/4)/(b*x^4+a)^(1/4))/c^(3/4)/d^2-1/8*b^(3/4)*(-7*a*d+4*b*c)*arctanh(b^(1/4)*x/(b*x^4+a)^(1/4))/d^2+1/2*(-a*d+b*c)^(7/4)*arctanh((-a*d+b*c)^(1/4)*x/c^(1/4)/(b*x^4+a)^(1/4))/c^(3/4)/d^2,1],
[(b*x^4+a)^(3/4)/(d*x^4+c),x,9,1/2*b^(3/4)*arctan(b^(1/4)*x/(b*x^4+a)^(1/4))/d-1/2*(-a*d+b*c)^(3/4)*arctan((-a*d+b*c)^(1/4)*x/c^(1/4)/(b*x^4+a)^(1/4))/c^(3/4)/d+1/2*b^(3/4)*arctanh(b^(1/4)*x/(b*x^4+a)^(1/4))/d-1/2*(-a*d+b*c)^(3/4)*arctanh((-a*d+b*c)^(1/4)*x/c^(1/4)/(b*x^4+a)^(1/4))/c^(3/4)/d,1],
[1/(b*x^4+a)^(1/4)/(d*x^4+c),x,4,1/2*arctan((-a*d+b*c)^(1/4)*x/c^(1/4)/(b*x^4+a)^(1/4))/c^(3/4)/(-a*d+b*c)^(1/4)+1/2*arctanh((-a*d+b*c)^(1/4)*x/c^(1/4)/(b*x^4+a)^(1/4))/c^(3/4)/(-a*d+b*c)^(1/4),1],
[1/(b*x^4+a)^(5/4)/(d*x^4+c),x,5,b*x/a/(-a*d+b*c)/(b*x^4+a)^(1/4)-1/2*d*arctan((-a*d+b*c)^(1/4)*x/c^(1/4)/(b*x^4+a)^(1/4))/c^(3/4)/(-a*d+b*c)^(5/4)-1/2*d*arctanh((-a*d+b*c)^(1/4)*x/c^(1/4)/(b*x^4+a)^(1/4))/c^(3/4)/(-a*d+b*c)^(5/4),1],
[1/(b*x^4+a)^(9/4)/(d*x^4+c),x,6,1/5*b*x/a/(-a*d+b*c)/(b*x^4+a)^(5/4)+1/5*b*(-9*a*d+4*b*c)*x/a^2/(-a*d+b*c)^2/(b*x^4+a)^(1/4)+1/2*d^2*arctan((-a*d+b*c)^(1/4)*x/c^(1/4)/(b*x^4+a)^(1/4))/c^(3/4)/(-a*d+b*c)^(9/4)+1/2*d^2*arctanh((-a*d+b*c)^(1/4)*x/c^(1/4)/(b*x^4+a)^(1/4))/c^(3/4)/(-a*d+b*c)^(9/4),1],
[1/(b*x^4+a)^(13/4)/(d*x^4+c),x,7,1/9*b*x/a/(-a*d+b*c)/(b*x^4+a)^(9/4)+1/45*b*(-17*a*d+8*b*c)*x/a^2/(-a*d+b*c)^2/(b*x^4+a)^(5/4)+1/45*b*(113*a^2*d^2-100*a*b*c*d+32*b^2*c^2)*x/a^3/(-a*d+b*c)^3/(b*x^4+a)^(1/4)-1/2*d^3*arctan((-a*d+b*c)^(1/4)*x/c^(1/4)/(b*x^4+a)^(1/4))/c^(3/4)/(-a*d+b*c)^(13/4)-1/2*d^3*arctanh((-a*d+b*c)^(1/4)*x/c^(1/4)/(b*x^4+a)^(1/4))/c^(3/4)/(-a*d+b*c)^(13/4),1],
[(b*x^4+a)^(9/4)/(d*x^4+c),x,9,-1/12*b*(-11*a*d+6*b*c)*x*(b*x^4+a)^(1/4)/d^2+1/6*b*x*(b*x^4+a)^(5/4)/d+1/12*sqrt(a)*b^(3/2)*(-11*a*d+6*b*c)*(1+a/b/x^4)^(3/4)*x^3*InverseJacobiAM(1/2*arccot(sqrt(b)*x^2/sqrt(a)),sqrt(2))/d^2/(b*x^4+a)^(3/4)+1/2*(-a*d+b*c)^2*sqrt(a/(b*x^4+a))*sqrt(b*x^4+a)*EllipticPi(sin(arcsin(b^(1/4)*x/(b*x^4+a)^(1/4))),-sqrt(-a*d+b*c)/sqrt(b)/sqrt(c),sqrt(-1))/b^(1/4)/c/d^2+1/2*(-a*d+b*c)^2*sqrt(a/(b*x^4+a))*sqrt(b*x^4+a)*EllipticPi(sin(arcsin(b^(1/4)*x/(b*x^4+a)^(1/4))),sqrt(-a*d+b*c)/sqrt(b)/sqrt(c),sqrt(-1))/b^(1/4)/c/d^2,1],
[(b*x^4+a)^(5/4)/(d*x^4+c),x,8,1/2*b*x*(b*x^4+a)^(1/4)/d-1/2*sqrt(a)*b^(3/2)*(1+a/b/x^4)^(3/4)*x^3*InverseJacobiAM(1/2*arccot(sqrt(b)*x^2/sqrt(a)),sqrt(2))/d/(b*x^4+a)^(3/4)-1/2*(-a*d+b*c)*sqrt(a/(b*x^4+a))*sqrt(b*x^4+a)*EllipticPi(sin(arcsin(b^(1/4)*x/(b*x^4+a)^(1/4))),-sqrt(-a*d+b*c)/sqrt(b)/sqrt(c),sqrt(-1))/b^(1/4)/c/d-1/2*(-a*d+b*c)*sqrt(a/(b*x^4+a))*sqrt(b*x^4+a)*EllipticPi(sin(arcsin(b^(1/4)*x/(b*x^4+a)^(1/4))),sqrt(-a*d+b*c)/sqrt(b)/sqrt(c),sqrt(-1))/b^(1/4)/c/d,1],
[(b*x^4+a)^(1/4)/(d*x^4+c),x,4,1/2*sqrt(a/(b*x^4+a))*sqrt(b*x^4+a)*EllipticPi(sin(arcsin(b^(1/4)*x/(b*x^4+a)^(1/4))),-sqrt(-a*d+b*c)/sqrt(b)/sqrt(c),sqrt(-1))/b^(1/4)/c+1/2*sqrt(a/(b*x^4+a))*sqrt(b*x^4+a)*EllipticPi(sin(arcsin(b^(1/4)*x/(b*x^4+a)^(1/4))),sqrt(-a*d+b*c)/sqrt(b)/sqrt(c),sqrt(-1))/b^(1/4)/c,1],
[1/(b*x^4+a)^(3/4)/(d*x^4+c),x,7,-b^(3/2)*(1+a/b/x^4)^(3/4)*x^3*InverseJacobiAM(1/2*arccot(sqrt(b)*x^2/sqrt(a)),sqrt(2))/sqrt(a)/(-a*d+b*c)/(b*x^4+a)^(3/4)-1/2*d*sqrt(a/(b*x^4+a))*sqrt(b*x^4+a)*EllipticPi(sin(arcsin(b^(1/4)*x/(b*x^4+a)^(1/4))),-sqrt(-a*d+b*c)/sqrt(b)/sqrt(c),sqrt(-1))/b^(1/4)/c/(-a*d+b*c)-1/2*d*sqrt(a/(b*x^4+a))*sqrt(b*x^4+a)*EllipticPi(sin(arcsin(b^(1/4)*x/(b*x^4+a)^(1/4))),sqrt(-a*d+b*c)/sqrt(b)/sqrt(c),sqrt(-1))/b^(1/4)/c/(-a*d+b*c),1],
[1/(b*x^4+a)^(7/4)/(d*x^4+c),x,8,1/3*b*x/a/(-a*d+b*c)/(b*x^4+a)^(3/4)-1/3*b^(3/2)*(-5*a*d+2*b*c)*(1+a/b/x^4)^(3/4)*x^3*InverseJacobiAM(1/2*arccot(sqrt(b)*x^2/sqrt(a)),sqrt(2))/a^(3/2)/(-a*d+b*c)^2/(b*x^4+a)^(3/4)+1/2*d^2*sqrt(a/(b*x^4+a))*sqrt(b*x^4+a)*EllipticPi(sin(arcsin(b^(1/4)*x/(b*x^4+a)^(1/4))),-sqrt(-a*d+b*c)/sqrt(b)/sqrt(c),sqrt(-1))/b^(1/4)/c/(-a*d+b*c)^2+1/2*d^2*sqrt(a/(b*x^4+a))*sqrt(b*x^4+a)*EllipticPi(sin(arcsin(b^(1/4)*x/(b*x^4+a)^(1/4))),sqrt(-a*d+b*c)/sqrt(b)/sqrt(c),sqrt(-1))/b^(1/4)/c/(-a*d+b*c)^2,1],
[1/(b*x^4+a)^(11/4)/(d*x^4+c),x,9,1/7*b*x/a/(-a*d+b*c)/(b*x^4+a)^(7/4)+1/21*b*(-13*a*d+6*b*c)*x/a^2/(-a*d+b*c)^2/(b*x^4+a)^(3/4)-1/21*b^(3/2)*(47*a^2*d^2-38*a*b*c*d+12*b^2*c^2)*(1+a/b/x^4)^(3/4)*x^3*InverseJacobiAM(1/2*arccot(sqrt(b)*x^2/sqrt(a)),sqrt(2))/a^(5/2)/(-a*d+b*c)^3/(b*x^4+a)^(3/4)-1/2*d^3*sqrt(a/(b*x^4+a))*sqrt(b*x^4+a)*EllipticPi(sin(arcsin(b^(1/4)*x/(b*x^4+a)^(1/4))),-sqrt(-a*d+b*c)/sqrt(b)/sqrt(c),sqrt(-1))/b^(1/4)/c/(-a*d+b*c)^3-1/2*d^3*sqrt(a/(b*x^4+a))*sqrt(b*x^4+a)*EllipticPi(sin(arcsin(b^(1/4)*x/(b*x^4+a)^(1/4))),sqrt(-a*d+b*c)/sqrt(b)/sqrt(c),sqrt(-1))/b^(1/4)/c/(-a*d+b*c)^3,1],
[(b*x^4+a)^(11/4)/(d*x^4+c)^2,x,11,1/4*b*(-a*d+2*b*c)*x*(b*x^4+a)^(3/4)/c/d^2-1/4*(-a*d+b*c)*x*(b*x^4+a)^(7/4)/c/d/(d*x^4+c)-1/8*b^(7/4)*(-11*a*d+8*b*c)*arctan(b^(1/4)*x/(b*x^4+a)^(1/4))/d^3+1/8*(-a*d+b*c)^(7/4)*(3*a*d+8*b*c)*arctan((-a*d+b*c)^(1/4)*x/c^(1/4)/(b*x^4+a)^(1/4))/c^(7/4)/d^3-1/8*b^(7/4)*(-11*a*d+8*b*c)*arctanh(b^(1/4)*x/(b*x^4+a)^(1/4))/d^3+1/8*(-a*d+b*c)^(7/4)*(3*a*d+8*b*c)*arctanh((-a*d+b*c)^(1/4)*x/c^(1/4)/(b*x^4+a)^(1/4))/c^(7/4)/d^3,1],
[(b*x^4+a)^(7/4)/(d*x^4+c)^2,x,10,-1/4*(-a*d+b*c)*x*(b*x^4+a)^(3/4)/c/d/(d*x^4+c)+1/2*b^(7/4)*arctan(b^(1/4)*x/(b*x^4+a)^(1/4))/d^2-1/8*(-a*d+b*c)^(3/4)*(3*a*d+4*b*c)*arctan((-a*d+b*c)^(1/4)*x/c^(1/4)/(b*x^4+a)^(1/4))/c^(7/4)/d^2+1/2*b^(7/4)*arctanh(b^(1/4)*x/(b*x^4+a)^(1/4))/d^2-1/8*(-a*d+b*c)^(3/4)*(3*a*d+4*b*c)*arctanh((-a*d+b*c)^(1/4)*x/c^(1/4)/(b*x^4+a)^(1/4))/c^(7/4)/d^2,1],
[(b*x^4+a)^(3/4)/(d*x^4+c)^2,x,5,1/4*x*(b*x^4+a)^(3/4)/c/(d*x^4+c)+3/8*a*arctan((-a*d+b*c)^(1/4)*x/c^(1/4)/(b*x^4+a)^(1/4))/c^(7/4)/(-a*d+b*c)^(1/4)+3/8*a*arctanh((-a*d+b*c)^(1/4)*x/c^(1/4)/(b*x^4+a)^(1/4))/c^(7/4)/(-a*d+b*c)^(1/4),1],
[1/(b*x^4+a)^(1/4)/(d*x^4+c)^2,x,5,-1/4*d*x*(b*x^4+a)^(3/4)/c/(-a*d+b*c)/(d*x^4+c)+1/8*(-3*a*d+4*b*c)*arctan((-a*d+b*c)^(1/4)*x/c^(1/4)/(b*x^4+a)^(1/4))/c^(7/4)/(-a*d+b*c)^(5/4)+1/8*(-3*a*d+4*b*c)*arctanh((-a*d+b*c)^(1/4)*x/c^(1/4)/(b*x^4+a)^(1/4))/c^(7/4)/(-a*d+b*c)^(5/4),1],
[1/(b*x^4+a)^(5/4)/(d*x^4+c)^2,x,6,1/4*b*(a*d+4*b*c)*x/a/c/(-a*d+b*c)^2/(b*x^4+a)^(1/4)-1/4*d*x/c/(-a*d+b*c)/(b*x^4+a)^(1/4)/(d*x^4+c)-1/8*d*(-3*a*d+8*b*c)*arctan((-a*d+b*c)^(1/4)*x/c^(1/4)/(b*x^4+a)^(1/4))/c^(7/4)/(-a*d+b*c)^(9/4)-1/8*d*(-3*a*d+8*b*c)*arctanh((-a*d+b*c)^(1/4)*x/c^(1/4)/(b*x^4+a)^(1/4))/c^(7/4)/(-a*d+b*c)^(9/4),1],
[1/(b*x^4+a)^(9/4)/(d*x^4+c)^2,x,7,1/20*b*(5*a*d+4*b*c)*x/a/c/(-a*d+b*c)^2/(b*x^4+a)^(5/4)+1/20*b*(-5*a^2*d^2-56*a*b*c*d+16*b^2*c^2)*x/a^2/c/(-a*d+b*c)^3/(b*x^4+a)^(1/4)-1/4*d*x/c/(-a*d+b*c)/(b*x^4+a)^(5/4)/(d*x^4+c)+3/8*d^2*(-a*d+4*b*c)*arctan((-a*d+b*c)^(1/4)*x/c^(1/4)/(b*x^4+a)^(1/4))/c^(7/4)/(-a*d+b*c)^(13/4)+3/8*d^2*(-a*d+4*b*c)*arctanh((-a*d+b*c)^(1/4)*x/c^(1/4)/(b*x^4+a)^(1/4))/c^(7/4)/(-a*d+b*c)^(13/4),1],
[(b*x^4+a)^(9/4)/(d*x^4+c)^2,x,9,1/4*b*(-a*d+3*b*c)*x*(b*x^4+a)^(1/4)/c/d^2-1/4*(-a*d+b*c)*x*(b*x^4+a)^(5/4)/c/d/(d*x^4+c)-1/4*sqrt(a)*b^(3/2)*(-a*d+3*b*c)*(1+a/b/x^4)^(3/4)*x^3*InverseJacobiAM(1/2*arccot(sqrt(b)*x^2/sqrt(a)),sqrt(2))/c/d^2/(b*x^4+a)^(3/4)-3/8*(-a*d+b*c)*(a*d+2*b*c)*sqrt(a/(b*x^4+a))*sqrt(b*x^4+a)*EllipticPi(sin(arcsin(b^(1/4)*x/(b*x^4+a)^(1/4))),-sqrt(-a*d+b*c)/sqrt(b)/sqrt(c),sqrt(-1))/b^(1/4)/c^2/d^2-3/8*(-a*d+b*c)*(a*d+2*b*c)*sqrt(a/(b*x^4+a))*sqrt(b*x^4+a)*EllipticPi(sin(arcsin(b^(1/4)*x/(b*x^4+a)^(1/4))),sqrt(-a*d+b*c)/sqrt(b)/sqrt(c),sqrt(-1))/b^(1/4)/c^2/d^2,1],
[(b*x^4+a)^(5/4)/(d*x^4+c)^2,x,8,-1/4*(-a*d+b*c)*x*(b*x^4+a)^(1/4)/c/d/(d*x^4+c)+1/4*sqrt(a)*b^(3/2)*(1+a/b/x^4)^(3/4)*x^3*InverseJacobiAM(1/2*arccot(sqrt(b)*x^2/sqrt(a)),sqrt(2))/c/d/(b*x^4+a)^(3/4)+1/8*(3*a*d+2*b*c)*sqrt(a/(b*x^4+a))*sqrt(b*x^4+a)*EllipticPi(sin(arcsin(b^(1/4)*x/(b*x^4+a)^(1/4))),-sqrt(-a*d+b*c)/sqrt(b)/sqrt(c),sqrt(-1))/b^(1/4)/c^2/d+1/8*(3*a*d+2*b*c)*sqrt(a/(b*x^4+a))*sqrt(b*x^4+a)*EllipticPi(sin(arcsin(b^(1/4)*x/(b*x^4+a)^(1/4))),sqrt(-a*d+b*c)/sqrt(b)/sqrt(c),sqrt(-1))/b^(1/4)/c^2/d,1],
[(b*x^4+a)^(1/4)/(d*x^4+c)^2,x,8,1/4*x*(b*x^4+a)^(1/4)/c/(d*x^4+c)-1/4*sqrt(a)*b^(3/2)*(1+a/b/x^4)^(3/4)*x^3*InverseJacobiAM(1/2*arccot(sqrt(b)*x^2/sqrt(a)),sqrt(2))/c/(-a*d+b*c)/(b*x^4+a)^(3/4)+1/8*(-3*a*d+2*b*c)*sqrt(a/(b*x^4+a))*sqrt(b*x^4+a)*EllipticPi(sin(arcsin(b^(1/4)*x/(b*x^4+a)^(1/4))),-sqrt(-a*d+b*c)/sqrt(b)/sqrt(c),sqrt(-1))/b^(1/4)/c^2/(-a*d+b*c)+1/8*(-3*a*d+2*b*c)*sqrt(a/(b*x^4+a))*sqrt(b*x^4+a)*EllipticPi(sin(arcsin(b^(1/4)*x/(b*x^4+a)^(1/4))),sqrt(-a*d+b*c)/sqrt(b)/sqrt(c),sqrt(-1))/b^(1/4)/c^2/(-a*d+b*c),1],
[1/(b*x^4+a)^(3/4)/(d*x^4+c)^2,x,8,-1/4*d*x*(b*x^4+a)^(1/4)/c/(-a*d+b*c)/(d*x^4+c)-1/4*b^(3/2)*(-a*d+4*b*c)*(1+a/b/x^4)^(3/4)*x^3*InverseJacobiAM(1/2*arccot(sqrt(b)*x^2/sqrt(a)),sqrt(2))/sqrt(a)/c/(-a*d+b*c)^2/(b*x^4+a)^(3/4)-3/8*d*(-a*d+2*b*c)*sqrt(a/(b*x^4+a))*sqrt(b*x^4+a)*EllipticPi(sin(arcsin(b^(1/4)*x/(b*x^4+a)^(1/4))),-sqrt(-a*d+b*c)/sqrt(b)/sqrt(c),sqrt(-1))/b^(1/4)/c^2/(-a*d+b*c)^2-3/8*d*(-a*d+2*b*c)*sqrt(a/(b*x^4+a))*sqrt(b*x^4+a)*EllipticPi(sin(arcsin(b^(1/4)*x/(b*x^4+a)^(1/4))),sqrt(-a*d+b*c)/sqrt(b)/sqrt(c),sqrt(-1))/b^(1/4)/c^2/(-a*d+b*c)^2,1],
[1/(b*x^4+a)^(7/4)/(d*x^4+c)^2,x,9,1/12*b*(3*a*d+4*b*c)*x/a/c/(-a*d+b*c)^2/(b*x^4+a)^(3/4)-1/4*d*x/c/(-a*d+b*c)/(b*x^4+a)^(3/4)/(d*x^4+c)-1/12*b^(3/2)*(3*a^2*d^2-32*a*b*c*d+8*b^2*c^2)*(1+a/b/x^4)^(3/4)*x^3*InverseJacobiAM(1/2*arccot(sqrt(b)*x^2/sqrt(a)),sqrt(2))/a^(3/2)/c/(-a*d+b*c)^3/(b*x^4+a)^(3/4)+1/8*d^2*(-3*a*d+10*b*c)*sqrt(a/(b*x^4+a))*sqrt(b*x^4+a)*EllipticPi(sin(arcsin(b^(1/4)*x/(b*x^4+a)^(1/4))),-sqrt(-a*d+b*c)/sqrt(b)/sqrt(c),sqrt(-1))/b^(1/4)/c^2/(-a*d+b*c)^3+1/8*d^2*(-3*a*d+10*b*c)*sqrt(a/(b*x^4+a))*sqrt(b*x^4+a)*EllipticPi(sin(arcsin(b^(1/4)*x/(b*x^4+a)^(1/4))),sqrt(-a*d+b*c)/sqrt(b)/sqrt(c),sqrt(-1))/b^(1/4)/c^2/(-a*d+b*c)^3,1],
[1/(x^4+1)^(1/4)/(x^4+2),x,4,1/4*arctan(1/2*x*2^(3/4)/(x^4+1)^(1/4))*2^(1/4)+1/4*arctanh(1/2*x*2^(3/4)/(x^4+1)^(1/4))*2^(1/4),1],
[1/(a-(a-b)*x^4)/(b*x^4+a)^(1/4),x,4,1/2*arctan(a^(1/4)*x/(b*x^4+a)^(1/4))/a^(5/4)+1/2*arctanh(a^(1/4)*x/(b*x^4+a)^(1/4))/a^(5/4),1],
[(b*x^4+a)^p*(d*x^4+c)^q,x,4,x*(b*x^4+a)^p*(d*x^4+c)^q*AppellF1(1/4,-p,-q,5/4,-b*x^4/a,-d*x^4/c)/((1+b*x^4/a)^p)/((1+d*x^4/c)^q),1],
[(b*x^4+a)^p*(d*x^4+c)^3,x,5,3*d*(15*a^2*d^2-5*a*b*c*d*(13+4*p)+b^2*c^2*(16*p^2+88*p+117))*x*(b*x^4+a)^(p+1)/b^3/(5+4*p)/(9+4*p)/(13+4*p)-3*d^2*(3*a*d-b*c*(13+4*p))*x^5*(b*x^4+a)^(p+1)/b^2/(9+4*p)/(13+4*p)+d^3*x^9*(b*x^4+a)^(p+1)/b/(13+4*p)+(b^3*c^3*(16*p^2+88*p+117)-3*a*d*(15*a^2*d^2-5*a*b*c*d*(13+4*p)+b^2*c^2*(16*p^2+88*p+117))/(5+4*p))*x*(b*x^4+a)^p*hypergeom([1/4, -p],[5/4],-b*x^4/a)/b^3/(9+4*p)/(13+4*p)/((1+b*x^4/a)^p),1],
[(b*x^4+a)^p*(d*x^4+c)^2,x,4,-d*(5*a*d-2*b*c*(9+4*p))*x*(b*x^4+a)^(p+1)/b^2/(5+4*p)/(9+4*p)+d^2*x^5*(b*x^4+a)^(p+1)/b/(9+4*p)+(5*a^2*d^2-2*a*b*c*d*(9+4*p)+b^2*c^2*(16*p^2+56*p+45))*x*(b*x^4+a)^p*hypergeom([1/4, -p],[5/4],-b*x^4/a)/b^2/(5+4*p)/(9+4*p)/((1+b*x^4/a)^p),1],
[(b*x^4+a)^p*(d*x^4+c),x,3,d*x*(b*x^4+a)^(p+1)/b/(5+4*p)+(c-a*d/(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),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^4+c),x,3,x*(b*x^4+a)^p*AppellF1(1/4,-p,1,5/4,-b*x^4/a,-d*x^4/c)/c/((1+b*x^4/a)^p),1],
[(b*x^4+a)^p/(d*x^4+c)^2,x,3,x*(b*x^4+a)^p*AppellF1(1/4,-p,2,5/4,-b*x^4/a,-d*x^4/c)/c^2/((1+b*x^4/a)^p),1]]: