lst:=[[(f*x^3+e*x^2+d*x+c)*(b*x^4+a),x,3,a*c*x+1/2*a*d*x^2+1/3*a*e*x^3+1/5*b*c*x^5+1/6*b*d*x^6+1/7*b*e*x^7+1/8*f*(b*x^4+a)^2/b,1],
[x^3*(f*x^3+e*x^2+d*x+c)*(b*x^4+a),x,2,1/4*a*c*x^4+1/5*a*d*x^5+1/6*a*e*x^6+1/7*a*f*x^7+1/8*b*c*x^8+1/9*b*d*x^9+1/10*b*e*x^10+1/11*b*f*x^11,1],
[(f*x^3+e*x^2+d*x+c)*(b*x^4+a)^2,x,3,a^2*c*x+1/2*a^2*d*x^2+1/3*a^2*e*x^3+2/5*a*b*c*x^5+1/3*a*b*d*x^6+2/7*a*b*e*x^7+1/9*b^2*c*x^9+1/10*b^2*d*x^10+1/11*b^2*e*x^11+1/12*f*(b*x^4+a)^3/b,1],
[x^3*(f*x^3+e*x^2+d*x+c)*(b*x^4+a)^2,x,4,1/5*a^2*d*x^5+1/6*a^2*e*x^6+1/7*a^2*f*x^7+2/9*a*b*d*x^9+1/5*a*b*e*x^10+2/11*a*b*f*x^11+1/13*b^2*d*x^13+1/14*b^2*e*x^14+1/15*b^2*f*x^15+1/12*c*(b*x^4+a)^3/b,1],
[(f*x^3+e*x^2+d*x+c)*(b*x^4+a)^3,x,3,a^3*c*x+1/2*a^3*d*x^2+1/3*a^3*e*x^3+3/5*a^2*b*c*x^5+1/2*a^2*b*d*x^6+3/7*a^2*b*e*x^7+1/3*a*b^2*c*x^9+3/10*a*b^2*d*x^10+3/11*a*b^2*e*x^11+1/13*b^3*c*x^13+1/14*b^3*d*x^14+1/15*b^3*e*x^15+1/16*f*(b*x^4+a)^4/b,1],
[x^3*(f*x^3+e*x^2+d*x+c)*(b*x^4+a)^3,x,4,1/5*a^3*d*x^5+1/6*a^3*e*x^6+1/7*a^3*f*x^7+1/3*a^2*b*d*x^9+3/10*a^2*b*e*x^10+3/11*a^2*b*f*x^11+3/13*a*b^2*d*x^13+3/14*a*b^2*e*x^14+1/5*a*b^2*f*x^15+1/17*b^3*d*x^17+1/18*b^3*e*x^18+1/19*b^3*f*x^19+1/16*c*(b*x^4+a)^4/b,1],
[(f*x^3+e*x^2+d*x+c)*(b*x^4+a)^4,x,3,a^4*c*x+1/2*a^4*d*x^2+1/3*a^4*e*x^3+4/5*a^3*b*c*x^5+2/3*a^3*b*d*x^6+4/7*a^3*b*e*x^7+2/3*a^2*b^2*c*x^9+3/5*a^2*b^2*d*x^10+6/11*a^2*b^2*e*x^11+4/13*a*b^3*c*x^13+2/7*a*b^3*d*x^14+4/15*a*b^3*e*x^15+1/17*b^4*c*x^17+1/18*b^4*d*x^18+1/19*b^4*e*x^19+1/20*f*(b*x^4+a)^5/b,1],
[x^3*(f*x^3+e*x^2+d*x+c)*(b*x^4+a)^4,x,4,1/5*a^4*d*x^5+1/6*a^4*e*x^6+1/7*a^4*f*x^7+4/9*a^3*b*d*x^9+2/5*a^3*b*e*x^10+4/11*a^3*b*f*x^11+6/13*a^2*b^2*d*x^13+3/7*a^2*b^2*e*x^14+2/5*a^2*b^2*f*x^15+4/17*a*b^3*d*x^17+2/9*a*b^3*e*x^18+4/19*a*b^3*f*x^19+1/21*b^4*d*x^21+1/22*b^4*e*x^22+1/23*b^4*f*x^23+1/20*c*(b*x^4+a)^5/b,1],
[(f*x^3+e*x^2+d*x+c)/(-b*x^4+a),x,9,1/2*(c-sqrt(a)*e/sqrt(b))*arctan(b^(1/4)*x/a^(1/4))/a^(3/4)/b^(1/4)+1/2*(sqrt(b)*c+sqrt(a)*e)*arctanh(b^(1/4)*x/a^(1/4))/a^(3/4)/b^(3/4)+1/2*d*arctanh(sqrt(b)*x^2/sqrt(a))/sqrt(a)/sqrt(b)-1/4*f*ln(-b*x^4+a)/b,1],
[x^3*(f*x^3+e*x^2+d*x+c)/(-b*x^4+a),x,11,-d*x/b-1/2*e*x^2/b-1/3*f*x^3/b+1/2*a^(1/4)*(d-sqrt(a)*f/sqrt(b))*arctan(b^(1/4)*x/a^(1/4))/b^(5/4)+1/2*a^(1/4)*(sqrt(b)*d+sqrt(a)*f)*arctanh(b^(1/4)*x/a^(1/4))/b^(7/4)+1/2*sqrt(a)*e*arctanh(sqrt(b)*x^2/sqrt(a))/b^(3/2)-1/4*c*ln(-b*x^4+a)/b,1],
[(f*x^3+e*x^2+d*x+c)/(b*x^4+a),x,14,1/2*d*arctan(sqrt(b)*x^2/sqrt(a))/sqrt(a)/sqrt(b)-1/2*(sqrt(b)*c+sqrt(a)*e)*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)*e)*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)*e)*arctanh(sqrt(2)*a^(1/4)*b^(1/4)*x/(sqrt(a)+sqrt(b)*x^2))/sqrt(2)/a^(3/4)/b^(3/4)+1/4*f*ln(b*x^4+a)/b,1],
[x^3*(f*x^3+e*x^2+d*x+c)/(b*x^4+a),x,16,d*x/b+1/2*e*x^2/b+1/3*f*x^3/b-1/2*sqrt(a)*e*arctan(sqrt(b)*x^2/sqrt(a))/b^(3/2)+1/2*a^(1/4)*(sqrt(b)*d+sqrt(a)*f)*arctan(1-sqrt(2)*b^(1/4)*x/a^(1/4))/sqrt(2)/b^(7/4)-1/2*a^(1/4)*(sqrt(b)*d+sqrt(a)*f)*arctan(1+sqrt(2)*b^(1/4)*x/a^(1/4))/sqrt(2)/b^(7/4)-1/2*a^(1/4)*(sqrt(b)*d-sqrt(a)*f)*arctanh(sqrt(2)*a^(1/4)*b^(1/4)*x/(sqrt(a)+sqrt(b)*x^2))/sqrt(2)/b^(7/4)+1/4*c*ln(b*x^4+a)/b,1],
[(f*x^3+e*x^2+d*x+c)/(b*x^4+a)^2,x,14,-1/4*f/b/(b*x^4+a)+1/4*x*(e*x^2+d*x+c)/a/(b*x^4+a)+1/4*d*arctan(sqrt(b)*x^2/sqrt(a))/a^(3/2)/sqrt(b)-1/8*(3*sqrt(b)*c+sqrt(a)*e)*arctan(1-sqrt(2)*b^(1/4)*x/a^(1/4))/sqrt(2)/a^(7/4)/b^(3/4)+1/8*(3*sqrt(b)*c+sqrt(a)*e)*arctan(1+sqrt(2)*b^(1/4)*x/a^(1/4))/sqrt(2)/a^(7/4)/b^(3/4)+1/8*(3*sqrt(b)*c-sqrt(a)*e)*arctanh(sqrt(2)*a^(1/4)*b^(1/4)*x/(sqrt(a)+sqrt(b)*x^2))/sqrt(2)/a^(7/4)/b^(3/4),1],
[x^3*(f*x^3+e*x^2+d*x+c)/(b*x^4+a)^2,x,13,-1/4*(e*x^2+c)/b/(b*x^4+a)-1/4*x*(f*x^2+d)/b/(b*x^4+a)+1/4*e*arctan(sqrt(b)*x^2/sqrt(a))/sqrt(a)/b^(3/2)-1/8*(sqrt(b)*d+3*sqrt(a)*f)*arctan(1-sqrt(2)*b^(1/4)*x/a^(1/4))/sqrt(2)/a^(3/4)/b^(7/4)+1/8*(sqrt(b)*d+3*sqrt(a)*f)*arctan(1+sqrt(2)*b^(1/4)*x/a^(1/4))/sqrt(2)/a^(3/4)/b^(7/4)+1/8*(d-3*sqrt(a)*f/sqrt(b))*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],
[(f*x^3+e*x^2+d*x+c)/(b*x^4+a)^3,x,15,-1/8*f/b/(b*x^4+a)^2+1/8*x*(e*x^2+d*x+c)/a/(b*x^4+a)^2+1/32*x*(5*e*x^2+6*d*x+7*c)/a^2/(b*x^4+a)+3/16*d*arctan(sqrt(b)*x^2/sqrt(a))/a^(5/2)/sqrt(b)-1/64*(21*sqrt(b)*c+5*sqrt(a)*e)*arctan(1-sqrt(2)*b^(1/4)*x/a^(1/4))/sqrt(2)/a^(11/4)/b^(3/4)+1/64*(21*sqrt(b)*c+5*sqrt(a)*e)*arctan(1+sqrt(2)*b^(1/4)*x/a^(1/4))/sqrt(2)/a^(11/4)/b^(3/4)+1/64*(21*sqrt(b)*c-5*sqrt(a)*e)*arctanh(sqrt(2)*a^(1/4)*b^(1/4)*x/(sqrt(a)+sqrt(b)*x^2))/sqrt(2)/a^(11/4)/b^(3/4),1],
[x^3*(f*x^3+e*x^2+d*x+c)/(b*x^4+a)^3,x,15,-1/8*(e*x^2+c)/b/(b*x^4+a)^2-1/8*x*(f*x^2+d)/b/(b*x^4+a)^2+1/16*e*x^2/a/b/(b*x^4+a)+1/32*x*(3*f*x^2+d)/a/b/(b*x^4+a)+1/16*e*arctan(sqrt(b)*x^2/sqrt(a))/a^(3/2)/b^(3/2)-3/64*(sqrt(b)*d+sqrt(a)*f)*arctan(1-sqrt(2)*b^(1/4)*x/a^(1/4))/sqrt(2)/a^(7/4)/b^(7/4)+3/64*(sqrt(b)*d+sqrt(a)*f)*arctan(1+sqrt(2)*b^(1/4)*x/a^(1/4))/sqrt(2)/a^(7/4)/b^(7/4)+3/64*(sqrt(b)*d-sqrt(a)*f)*arctanh(sqrt(2)*a^(1/4)*b^(1/4)*x/(sqrt(a)+sqrt(b)*x^2))/sqrt(2)/a^(7/4)/b^(7/4),1],
[(f*x^3+e*x^2+d*x+c)/(b*x^4+a)^4,x,16,-1/12*f/b/(b*x^4+a)^3+1/12*x*(e*x^2+d*x+c)/a/(b*x^4+a)^3+1/96*x*(9*e*x^2+10*d*x+11*c)/a^2/(b*x^4+a)^2+1/384*x*(45*e*x^2+60*d*x+77*c)/a^3/(b*x^4+a)+5/32*d*arctan(sqrt(b)*x^2/sqrt(a))/a^(7/2)/sqrt(b)-1/256*(77*sqrt(b)*c+15*sqrt(a)*e)*arctan(1-sqrt(2)*b^(1/4)*x/a^(1/4))/sqrt(2)/a^(15/4)/b^(3/4)+1/256*(77*sqrt(b)*c+15*sqrt(a)*e)*arctan(1+sqrt(2)*b^(1/4)*x/a^(1/4))/sqrt(2)/a^(15/4)/b^(3/4)+1/256*(77*sqrt(b)*c-15*sqrt(a)*e)*arctanh(sqrt(2)*a^(1/4)*b^(1/4)*x/(sqrt(a)+sqrt(b)*x^2))/sqrt(2)/a^(15/4)/b^(3/4),1],
[x^3*(f*x^3+e*x^2+d*x+c)/(b*x^4+a)^4,x,17,-1/12*(e*x^2+c)/b/(b*x^4+a)^3-1/12*x*(f*x^2+d)/b/(b*x^4+a)^3+1/48*e*x^2/a/b/(b*x^4+a)^2+1/96*x*(3*f*x^2+d)/a/b/(b*x^4+a)^2+1/32*e*x^2/a^2/b/(b*x^4+a)+1/384*x*(15*f*x^2+7*d)/a^2/b/(b*x^4+a)+1/32*e*arctan(sqrt(b)*x^2/sqrt(a))/a^(5/2)/b^(3/2)-1/256*(7*sqrt(b)*d+5*sqrt(a)*f)*arctan(1-sqrt(2)*b^(1/4)*x/a^(1/4))/sqrt(2)/a^(11/4)/b^(7/4)+1/256*(7*sqrt(b)*d+5*sqrt(a)*f)*arctan(1+sqrt(2)*b^(1/4)*x/a^(1/4))/sqrt(2)/a^(11/4)/b^(7/4)+1/256*(7*sqrt(b)*d-5*sqrt(a)*f)*arctanh(sqrt(2)*a^(1/4)*b^(1/4)*x/(sqrt(a)+sqrt(b)*x^2))/sqrt(2)/a^(11/4)/b^(7/4),1],
[x^4*sqrt(-b*x^4+a)*(C*x^4+B*x^2+A),x,11,1/1155*a*x*(77*B*b*x^2+55*A*b+25*C*a)*sqrt(-b*x^4+a)/b^2-1/77*(11*A*b+5*C*a)*x*(-b*x^4+a)^(3/2)/b^2-1/9*B*x^3*(-b*x^4+a)^(3/2)/b-1/11*C*x^5*(-b*x^4+a)^(3/2)/b+2/15*a^(11/4)*B*sqrt(1-b*x^4/a)*EllipticE(sin(arcsin(b^(1/4)*x/a^(1/4))),sqrt(-1))/b^(7/4)/sqrt(-b*x^4+a)+2/1155*a^(9/4)*(55*A*b-77*sqrt(a)*sqrt(b)*B+25*a*C)*sqrt(1-b*x^4/a)*InverseJacobiAM(arcsin(b^(1/4)*x/a^(1/4)),sqrt(-1))/b^(9/4)/sqrt(-b*x^4+a),1],
[x^2*sqrt(-b*x^4+a)*(C*x^4+B*x^2+A),x,9,1/105*x*(5*a*B+7*(3*A*b+C*a)*x^2)*sqrt(-b*x^4+a)/b-1/7*B*x*(-b*x^4+a)^(3/2)/b-1/9*C*x^3*(-b*x^4+a)^(3/2)/b+2/15*a^(7/4)*(3*A*b+C*a)*sqrt(1-b*x^4/a)*EllipticE(sin(arcsin(b^(1/4)*x/a^(1/4))),sqrt(-1))/b^(7/4)/sqrt(-b*x^4+a)-2/105*a^(7/4)*(21*A*b-5*sqrt(a)*sqrt(b)*B+7*a*C)*sqrt(1-b*x^4/a)*InverseJacobiAM(arcsin(b^(1/4)*x/a^(1/4)),sqrt(-1))/b^(7/4)/sqrt(-b*x^4+a),1],
[sqrt(-b*x^4+a)*(C*x^4+B*x^2+A),x,7,1/105*x*(21*B*b*x^2+35*A*b+5*C*a)*sqrt(-b*x^4+a)/b-1/7*C*x*(-b*x^4+a)^(3/2)/b+2/5*a^(7/4)*B*sqrt(1-b*x^4/a)*EllipticE(sin(arcsin(b^(1/4)*x/a^(1/4))),sqrt(-1))/b^(3/4)/sqrt(-b*x^4+a)+2/105*a^(5/4)*(35*A*b-21*sqrt(a)*sqrt(b)*B+5*a*C)*sqrt(1-b*x^4/a)*InverseJacobiAM(arcsin(b^(1/4)*x/a^(1/4)),sqrt(-1))/b^(5/4)/sqrt(-b*x^4+a),1],
[sqrt(-b*x^4+a)*(C*x^4+B*x^2+A)/x^2,x,8,1/15*x*(5*a*B-3*(5*A*b-C*a)*x^2)*sqrt(-b*x^4+a)/a-A*(-b*x^4+a)^(3/2)/a/x-2/5*a^(3/4)*(5*A*b-C*a)*sqrt(1-b*x^4/a)*EllipticE(sin(arcsin(b^(1/4)*x/a^(1/4))),sqrt(-1))/b^(3/4)/sqrt(-b*x^4+a)+2/15*a^(3/4)*(15*A*b+5*sqrt(a)*sqrt(b)*B-3*a*C)*sqrt(1-b*x^4/a)*InverseJacobiAM(arcsin(b^(1/4)*x/a^(1/4)),sqrt(-1))/b^(3/4)/sqrt(-b*x^4+a),1],
[sqrt(-b*x^4+a)*(C*x^4+B*x^2+A)/x^4,x,8,-1/3*(3*a*B+(A*b-C*a)*x^2)*sqrt(-b*x^4+a)/a/x-1/3*A*(-b*x^4+a)^(3/2)/a/x^3-2*a^(3/4)*b^(1/4)*B*sqrt(1-b*x^4/a)*EllipticE(sin(arcsin(b^(1/4)*x/a^(1/4))),sqrt(-1))/sqrt(-b*x^4+a)-2/3*a^(1/4)*(A*b-3*sqrt(a)*sqrt(b)*B-a*C)*sqrt(1-b*x^4/a)*InverseJacobiAM(arcsin(b^(1/4)*x/a^(1/4)),sqrt(-1))/b^(1/4)/sqrt(-b*x^4+a),1],
[sqrt(-b*x^4+a)*(C*x^4+B*x^2+A)/x^6,x,7,-1/15*(3*A/x^5+5*B/x^3+15*C/x)*sqrt(-b*x^4+a)+2/5*A*b*sqrt(-b*x^4+a)/a/x+2/5*b^(1/4)*(A*b-5*C*a)*sqrt(1-b*x^4/a)*EllipticE(sin(arcsin(b^(1/4)*x/a^(1/4))),sqrt(-1))/a^(1/4)/sqrt(-b*x^4+a)-2/15*b^(1/4)*(3*A*b+5*sqrt(a)*sqrt(b)*B-15*a*C)*sqrt(1-b*x^4/a)*InverseJacobiAM(arcsin(b^(1/4)*x/a^(1/4)),sqrt(-1))/a^(1/4)/sqrt(-b*x^4+a),1],
[sqrt(-b*x^4+a)*(C*x^4+B*x^2+A)/x^8,x,8,-1/105*(15*A/x^7+21*B/x^5+35*C/x^3)*sqrt(-b*x^4+a)+2/21*A*b*sqrt(-b*x^4+a)/a/x^3+2/5*b*B*sqrt(-b*x^4+a)/a/x+2/5*b^(5/4)*B*sqrt(1-b*x^4/a)*EllipticE(sin(arcsin(b^(1/4)*x/a^(1/4))),sqrt(-1))/a^(1/4)/sqrt(-b*x^4+a)-2/105*b^(3/4)*(5*A*b+21*sqrt(a)*sqrt(b)*B+35*a*C)*sqrt(1-b*x^4/a)*InverseJacobiAM(arcsin(b^(1/4)*x/a^(1/4)),sqrt(-1))/a^(3/4)/sqrt(-b*x^4+a),1],
[sqrt(-b*x^4+a)*(C*x^4+B*x^2+A)/x^10,x,9,-1/315*(35*A/x^9+45*B/x^7+63*C/x^5)*sqrt(-b*x^4+a)+2/45*A*b*sqrt(-b*x^4+a)/a/x^5+2/21*b*B*sqrt(-b*x^4+a)/a/x^3+2/15*b*(A*b+3*C*a)*sqrt(-b*x^4+a)/a^2/x+2/15*b^(5/4)*(A*b+3*C*a)*sqrt(1-b*x^4/a)*EllipticE(sin(arcsin(b^(1/4)*x/a^(1/4))),sqrt(-1))/a^(5/4)/sqrt(-b*x^4+a)-2/105*b^(5/4)*(7*A*b+5*sqrt(a)*sqrt(b)*B+21*a*C)*sqrt(1-b*x^4/a)*InverseJacobiAM(arcsin(b^(1/4)*x/a^(1/4)),sqrt(-1))/a^(5/4)/sqrt(-b*x^4+a),1],
[x^4*(C*x^4+B*x^2+A)/sqrt(-b*x^4+a),x,9,-1/21*(7*A*b+5*C*a)*x*sqrt(-b*x^4+a)/b^2-1/5*B*x^3*sqrt(-b*x^4+a)/b-1/7*C*x^5*sqrt(-b*x^4+a)/b+3/5*a^(7/4)*B*sqrt(1-b*x^4/a)*EllipticE(sin(arcsin(b^(1/4)*x/a^(1/4))),sqrt(-1))/b^(7/4)/sqrt(-b*x^4+a)+1/105*a^(5/4)*(35*A*b-63*sqrt(a)*sqrt(b)*B+25*a*C)*sqrt(1-b*x^4/a)*InverseJacobiAM(arcsin(b^(1/4)*x/a^(1/4)),sqrt(-1))/b^(9/4)/sqrt(-b*x^4+a),1],
[x^2*(C*x^4+B*x^2+A)/sqrt(-b*x^4+a),x,8,-1/3*B*x*sqrt(-b*x^4+a)/b-1/5*C*x^3*sqrt(-b*x^4+a)/b+1/5*a^(3/4)*(5*A*b+3*C*a)*sqrt(1-b*x^4/a)*EllipticE(sin(arcsin(b^(1/4)*x/a^(1/4))),sqrt(-1))/b^(7/4)/sqrt(-b*x^4+a)-1/15*a^(3/4)*(15*A*b-5*sqrt(a)*sqrt(b)*B+9*a*C)*sqrt(1-b*x^4/a)*InverseJacobiAM(arcsin(b^(1/4)*x/a^(1/4)),sqrt(-1))/b^(7/4)/sqrt(-b*x^4+a),1],
[(C*x^4+B*x^2+A)/sqrt(-b*x^4+a),x,6,-1/3*C*x*sqrt(-b*x^4+a)/b+a^(3/4)*B*sqrt(1-b*x^4/a)*EllipticE(sin(arcsin(b^(1/4)*x/a^(1/4))),sqrt(-1))/b^(3/4)/sqrt(-b*x^4+a)+1/3*a^(1/4)*(3*A*b-3*sqrt(a)*sqrt(b)*B+a*C)*sqrt(1-b*x^4/a)*InverseJacobiAM(arcsin(b^(1/4)*x/a^(1/4)),sqrt(-1))/b^(5/4)/sqrt(-b*x^4+a),1],
[(C*x^4+B*x^2+A)/x^2/sqrt(-b*x^4+a),x,6,-A*sqrt(-b*x^4+a)/a/x-(A*b-C*a)*sqrt(1-b*x^4/a)*EllipticE(sin(arcsin(b^(1/4)*x/a^(1/4))),sqrt(-1))/a^(1/4)/b^(3/4)/sqrt(-b*x^4+a)+(A*b+sqrt(a)*sqrt(b)*B-a*C)*sqrt(1-b*x^4/a)*InverseJacobiAM(arcsin(b^(1/4)*x/a^(1/4)),sqrt(-1))/a^(1/4)/b^(3/4)/sqrt(-b*x^4+a),1],
[(C*x^4+B*x^2+A)/x^4/sqrt(-b*x^4+a),x,7,-1/3*A*sqrt(-b*x^4+a)/a/x^3-B*sqrt(-b*x^4+a)/a/x-b^(1/4)*B*sqrt(1-b*x^4/a)*EllipticE(sin(arcsin(b^(1/4)*x/a^(1/4))),sqrt(-1))/a^(1/4)/sqrt(-b*x^4+a)+1/3*(A*b+3*sqrt(a)*sqrt(b)*B+3*a*C)*sqrt(1-b*x^4/a)*InverseJacobiAM(arcsin(b^(1/4)*x/a^(1/4)),sqrt(-1))/a^(3/4)/b^(1/4)/sqrt(-b*x^4+a),1],
[(C*x^4+B*x^2+A)/x^6/sqrt(-b*x^4+a),x,8,-1/5*A*sqrt(-b*x^4+a)/a/x^5-1/3*B*sqrt(-b*x^4+a)/a/x^3-1/5*(3*A*b+5*C*a)*sqrt(-b*x^4+a)/a^2/x-1/5*b^(1/4)*(3*A*b+5*C*a)*sqrt(1-b*x^4/a)*EllipticE(sin(arcsin(b^(1/4)*x/a^(1/4))),sqrt(-1))/a^(5/4)/sqrt(-b*x^4+a)+1/15*b^(1/4)*(9*A*b+5*sqrt(a)*sqrt(b)*B+15*a*C)*sqrt(1-b*x^4/a)*InverseJacobiAM(arcsin(b^(1/4)*x/a^(1/4)),sqrt(-1))/a^(5/4)/sqrt(-b*x^4+a),1],
[x^6*(C*x^4+B*x^2+A)/(-b*x^4+a)^(3/2),x,8,1/2*x*(a*B+(A*b+C*a)*x^2)/b^2/sqrt(-b*x^4+a)+1/3*B*x*sqrt(-b*x^4+a)/b^2+1/5*C*x^3*sqrt(-b*x^4+a)/b^2-3/10*a^(3/4)*(5*A*b+7*C*a)*sqrt(1-b*x^4/a)*EllipticE(sin(arcsin(b^(1/4)*x/a^(1/4))),sqrt(-1))/b^(11/4)/sqrt(-b*x^4+a)+1/30*a^(3/4)*(45*A*b-25*sqrt(a)*sqrt(b)*B+63*a*C)*sqrt(1-b*x^4/a)*InverseJacobiAM(arcsin(b^(1/4)*x/a^(1/4)),sqrt(-1))/b^(11/4)/sqrt(-b*x^4+a),1],
[x^4*(C*x^4+B*x^2+A)/(-b*x^4+a)^(3/2),x,7,1/2*x*(B*b*x^2+A*b+C*a)/b^2/sqrt(-b*x^4+a)+1/3*C*x*sqrt(-b*x^4+a)/b^2-3/2*a^(3/4)*B*sqrt(1-b*x^4/a)*EllipticE(sin(arcsin(b^(1/4)*x/a^(1/4))),sqrt(-1))/b^(7/4)/sqrt(-b*x^4+a)-1/6*a^(1/4)*(3*A*b-9*sqrt(a)*sqrt(b)*B+5*a*C)*sqrt(1-b*x^4/a)*InverseJacobiAM(arcsin(b^(1/4)*x/a^(1/4)),sqrt(-1))/b^(9/4)/sqrt(-b*x^4+a),1],
[x^2*(C*x^4+B*x^2+A)/(-b*x^4+a)^(3/2),x,6,1/2*x*(a*B+(A*b+C*a)*x^2)/a/b/sqrt(-b*x^4+a)-1/2*(A*b+3*C*a)*sqrt(1-b*x^4/a)*EllipticE(sin(arcsin(b^(1/4)*x/a^(1/4))),sqrt(-1))/a^(1/4)/b^(7/4)/sqrt(-b*x^4+a)+1/2*(A*b-sqrt(a)*sqrt(b)*B+3*a*C)*sqrt(1-b*x^4/a)*InverseJacobiAM(arcsin(b^(1/4)*x/a^(1/4)),sqrt(-1))/a^(1/4)/b^(7/4)/sqrt(-b*x^4+a),1],
[(C*x^4+B*x^2+A)/(-b*x^4+a)^(3/2),x,6,1/2*x*(A+a*C/b+B*x^2)/a/sqrt(-b*x^4+a)-1/2*B*sqrt(1-b*x^4/a)*EllipticE(sin(arcsin(b^(1/4)*x/a^(1/4))),sqrt(-1))/a^(1/4)/b^(3/4)/sqrt(-b*x^4+a)+1/2*(A*b+sqrt(a)*sqrt(b)*B-a*C)*sqrt(1-b*x^4/a)*InverseJacobiAM(arcsin(b^(1/4)*x/a^(1/4)),sqrt(-1))/a^(3/4)/b^(5/4)/sqrt(-b*x^4+a),1],
[(C*x^4+B*x^2+A)/x^2/(-b*x^4+a)^(3/2),x,7,1/2*x*(a*B+(A*b+C*a)*x^2)/a^2/sqrt(-b*x^4+a)-A*sqrt(-b*x^4+a)/a^2/x-1/2*(3*A*b+C*a)*sqrt(1-b*x^4/a)*EllipticE(sin(arcsin(b^(1/4)*x/a^(1/4))),sqrt(-1))/a^(5/4)/b^(3/4)/sqrt(-b*x^4+a)+1/2*(3*A*b+sqrt(a)*sqrt(b)*B+a*C)*sqrt(1-b*x^4/a)*InverseJacobiAM(arcsin(b^(1/4)*x/a^(1/4)),sqrt(-1))/a^(5/4)/b^(3/4)/sqrt(-b*x^4+a),1],
[(C*x^4+B*x^2+A)/x^4/(-b*x^4+a)^(3/2),x,8,1/2*x*(a*(A*b/a+C)+b*B*x^2)/a^2/sqrt(-b*x^4+a)-1/3*A*sqrt(-b*x^4+a)/a^2/x^3-B*sqrt(-b*x^4+a)/a^2/x-3/2*b^(1/4)*B*sqrt(1-b*x^4/a)*EllipticE(sin(arcsin(b^(1/4)*x/a^(1/4))),sqrt(-1))/a^(5/4)/sqrt(-b*x^4+a)+1/6*(5*A*b+9*sqrt(a)*sqrt(b)*B+3*a*C)*sqrt(1-b*x^4/a)*InverseJacobiAM(arcsin(b^(1/4)*x/a^(1/4)),sqrt(-1))/a^(7/4)/b^(1/4)/sqrt(-b*x^4+a),1],
[(C*x^4+B*x^2+A)/x^2/sqrt(b*x^4+a),x,5,-A*sqrt(b*x^4+a)/a/x+(A*b+C*a)*x*sqrt(b*x^4+a)/a/sqrt(b)/(sqrt(a)+sqrt(b)*x^2)-(A*b+C*a)*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*EllipticE(sin(2*arctan(b^(1/4)*x/a^(1/4))),sqrt(1/2))/a^(3/4)/b^(3/4)/sqrt(b*x^4+a)+1/2*(A*b+sqrt(a)*sqrt(b)*B+a*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^(3/4)/b^(3/4)/sqrt(b*x^4+a),1],
[(C*x^4+B*x^2+A)/x^2/(b*x^4+a)^(3/2),x,6,1/2*x*(a*B-(A*b-C*a)*x^2)/a^2/sqrt(b*x^4+a)-A*sqrt(b*x^4+a)/a^2/x+1/2*(3*A*b-C*a)*x*sqrt(b*x^4+a)/a^2/sqrt(b)/(sqrt(a)+sqrt(b)*x^2)-1/2*(3*A*b-C*a)*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*EllipticE(sin(2*arctan(b^(1/4)*x/a^(1/4))),sqrt(1/2))/a^(7/4)/b^(3/4)/sqrt(b*x^4+a)+1/4*(3*A*b+sqrt(a)*sqrt(b)*B-a*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^(7/4)/b^(3/4)/sqrt(b*x^4+a),1],
[x^3*(f*x^3+e*x^2+d*x+c)*sqrt(b*x^4+a),x,16,1/16*a*e*x^2*sqrt(b*x^4+a)/b+1/8*e*x^6*sqrt(b*x^4+a)-2/15*a^2*f*x*sqrt(b*x^4+a)/b^(3/2)/(sqrt(a)+sqrt(b)*x^2)-1/105*a*x*(7*f*x^2+5*d)*sqrt(b*x^4+a)/b+1/6*c*(b*x^4+a)^(3/2)/b+1/7*d*x*(b*x^4+a)^(3/2)/b+1/9*f*x^3*(b*x^4+a)^(3/2)/b-1/16*a^2*e*arctanh(sqrt(b)*x^2/sqrt(b*x^4+a))/b^(3/2)+2/15*a^(9/4)*f*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*EllipticE(sin(2*arctan(b^(1/4)*x/a^(1/4))),sqrt(1/2))/b^(7/4)/sqrt(b*x^4+a)-1/105*a^(7/4)*(5*sqrt(b)*d+7*sqrt(a)*f)*(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^(7/4)/sqrt(b*x^4+a),1],
[x^2*(f*x^3+e*x^2+d*x+c)*sqrt(b*x^4+a),x,14,1/16*a*f*x^2*sqrt(b*x^4+a)/b+1/8*f*x^6*sqrt(b*x^4+a)+2/5*a*c*x*sqrt(b*x^4+a)/sqrt(b)/(sqrt(a)+sqrt(b)*x^2)-1/105*x*(-21*b*c*x^2+5*a*e)*sqrt(b*x^4+a)/b+1/6*d*(b*x^4+a)^(3/2)/b+1/7*e*x*(b*x^4+a)^(3/2)/b-1/16*a^2*f*arctanh(sqrt(b)*x^2/sqrt(b*x^4+a))/b^(3/2)-2/5*a^(5/4)*c*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*EllipticE(sin(2*arctan(b^(1/4)*x/a^(1/4))),sqrt(1/2))/b^(3/4)/sqrt(b*x^4+a)+1/105*a^(5/4)*(21*sqrt(b)*c-5*sqrt(a)*e)*(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],
[x*(f*x^3+e*x^2+d*x+c)*sqrt(b*x^4+a),x,12,1/4*c*x^2*sqrt(b*x^4+a)+2/5*a*d*x*sqrt(b*x^4+a)/sqrt(b)/(sqrt(a)+sqrt(b)*x^2)-1/105*x*(-21*b*d*x^2+5*a*f)*sqrt(b*x^4+a)/b+1/6*e*(b*x^4+a)^(3/2)/b+1/7*f*x*(b*x^4+a)^(3/2)/b+1/4*a*c*arctanh(sqrt(b)*x^2/sqrt(b*x^4+a))/sqrt(b)-2/5*a^(5/4)*d*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*EllipticE(sin(2*arctan(b^(1/4)*x/a^(1/4))),sqrt(1/2))/b^(3/4)/sqrt(b*x^4+a)+1/105*a^(5/4)*(21*sqrt(b)*d-5*sqrt(a)*f)*(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],
[(f*x^3+e*x^2+d*x+c)*sqrt(b*x^4+a),x,11,1/4*d*x^2*sqrt(b*x^4+a)+2/5*a*e*x*sqrt(b*x^4+a)/sqrt(b)/(sqrt(a)+sqrt(b)*x^2)+1/15*x*(3*e*x^2+5*c)*sqrt(b*x^4+a)+1/6*f*(b*x^4+a)^(3/2)/b+1/4*a*d*arctanh(sqrt(b)*x^2/sqrt(b*x^4+a))/sqrt(b)-2/5*a^(5/4)*e*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*EllipticE(sin(2*arctan(b^(1/4)*x/a^(1/4))),sqrt(1/2))/b^(3/4)/sqrt(b*x^4+a)+1/15*a^(3/4)*(5*sqrt(b)*c+3*sqrt(a)*e)*(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^(3/4)/sqrt(b*x^4+a),1],
[(f*x^3+e*x^2+d*x+c)*sqrt(b*x^4+a)/x,x,13,2/5*a*f*x*sqrt(b*x^4+a)/sqrt(b)/(sqrt(a)+sqrt(b)*x^2)+1/4*(e*x^2+2*c)*sqrt(b*x^4+a)+1/15*x*(3*f*x^2+5*d)*sqrt(b*x^4+a)+1/4*a*e*arctanh(sqrt(b)*x^2/sqrt(b*x^4+a))/sqrt(b)-1/2*sqrt(a)*c*arctanh(sqrt(b*x^4+a)/sqrt(a))-2/5*a^(5/4)*f*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*EllipticE(sin(2*arctan(b^(1/4)*x/a^(1/4))),sqrt(1/2))/b^(3/4)/sqrt(b*x^4+a)+1/15*a^(3/4)*(5*sqrt(b)*d+3*sqrt(a)*f)*(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^(3/4)/sqrt(b*x^4+a),1],
[(f*x^3+e*x^2+d*x+c)*sqrt(b*x^4+a)/x^2,x,13,2*sqrt(b)*c*x*sqrt(b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)-1/3*(-e*x^2+3*c)*sqrt(b*x^4+a)/x+1/4*(f*x^2+2*d)*sqrt(b*x^4+a)+1/4*a*f*arctanh(sqrt(b)*x^2/sqrt(b*x^4+a))/sqrt(b)-1/2*sqrt(a)*d*arctanh(sqrt(b*x^4+a)/sqrt(a))-2*a^(1/4)*b^(1/4)*c*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*EllipticE(sin(2*arctan(b^(1/4)*x/a^(1/4))),sqrt(1/2))/sqrt(b*x^4+a)+1/3*a^(1/4)*(3*sqrt(b)*c+sqrt(a)*e)*(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^(1/4)/sqrt(b*x^4+a),1],
[(f*x^3+e*x^2+d*x+c)*sqrt(b*x^4+a)/x^3,x,13,2*sqrt(b)*d*x*sqrt(b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)-1/2*(-e*x^2+c)*sqrt(b*x^4+a)/x^2-1/3*(-f*x^2+3*d)*sqrt(b*x^4+a)/x+1/2*sqrt(b)*c*arctanh(sqrt(b)*x^2/sqrt(b*x^4+a))-1/2*sqrt(a)*e*arctanh(sqrt(b*x^4+a)/sqrt(a))-2*a^(1/4)*b^(1/4)*d*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*EllipticE(sin(2*arctan(b^(1/4)*x/a^(1/4))),sqrt(1/2))/sqrt(b*x^4+a)+1/3*a^(1/4)*(3*sqrt(b)*d+sqrt(a)*f)*(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^(1/4)/sqrt(b*x^4+a),1],
[(f*x^3+e*x^2+d*x+c)*sqrt(b*x^4+a)/x^4,x,13,-2*sqrt(a)*e*sqrt(b*x^4+a)/x/(sqrt(a)+sqrt(b)*x^2)-1/3*(-3*e*x^2+c)*sqrt(b*x^4+a)/x^3-1/2*(-f*x^2+d)*sqrt(b*x^4+a)/x^2+1/2*sqrt(b)*d*arctanh(sqrt(b)*x^2/sqrt(b*x^4+a))-1/2*sqrt(a)*f*arctanh(sqrt(b*x^4+a)/sqrt(a))-2*a^(1/4)*b^(1/4)*e*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*EllipticE(sin(2*arctan(b^(1/4)*x/a^(1/4))),sqrt(1/2))/sqrt(b*x^4+a)+1/3*b^(1/4)*(sqrt(b)*c+3*sqrt(a)*e)*(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)/sqrt(b*x^4+a),1],
[(f*x^3+e*x^2+d*x+c)*sqrt(b*x^4+a)/x^5,x,13,-2*sqrt(a)*f*sqrt(b*x^4+a)/x/(sqrt(a)+sqrt(b)*x^2)-1/4*(2*e*x^2+c)*sqrt(b*x^4+a)/x^4-1/3*(-3*f*x^2+d)*sqrt(b*x^4+a)/x^3+1/2*sqrt(b)*e*arctanh(sqrt(b)*x^2/sqrt(b*x^4+a))-1/4*b*c*arctanh(sqrt(b*x^4+a)/sqrt(a))/sqrt(a)-2*a^(1/4)*b^(1/4)*f*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*EllipticE(sin(2*arctan(b^(1/4)*x/a^(1/4))),sqrt(1/2))/sqrt(b*x^4+a)+1/3*b^(1/4)*(sqrt(b)*d+3*sqrt(a)*f)*(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)/sqrt(b*x^4+a),1],
[(f*x^3+e*x^2+d*x+c)*sqrt(b*x^4+a)/x^6,x,14,2/3*e*sqrt(b*x^4+a)/x^3-2/5*b*c*sqrt(b*x^4+a)/sqrt(a)/x/(sqrt(a)+sqrt(b)*x^2)-1/5*(5*e*x^2+c)*sqrt(b*x^4+a)/x^5-1/4*(2*f*x^2+d)*sqrt(b*x^4+a)/x^4+1/2*sqrt(b)*f*arctanh(sqrt(b)*x^2/sqrt(b*x^4+a))-1/4*b*d*arctanh(sqrt(b*x^4+a)/sqrt(a))/sqrt(a)-2/5*b^(5/4)*c*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*EllipticE(sin(2*arctan(b^(1/4)*x/a^(1/4))),sqrt(1/2))/a^(3/4)/sqrt(b*x^4+a)+1/15*b^(3/4)*(3*sqrt(b)*c+5*sqrt(a)*e)*(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^(3/4)/sqrt(b*x^4+a),1],
[(f*x^3+e*x^2+d*x+c)*sqrt(b*x^4+a)/x^7,x,14,-1/4*e*sqrt(b*x^4+a)/x^4+2/3*f*sqrt(b*x^4+a)/x^3-2/5*b*d*sqrt(b*x^4+a)/sqrt(a)/x/(sqrt(a)+sqrt(b)*x^2)-1/5*(5*f*x^2+d)*sqrt(b*x^4+a)/x^5-1/6*c*(b*x^4+a)^(3/2)/a/x^6-1/4*b*e*arctanh(sqrt(b*x^4+a)/sqrt(a))/sqrt(a)-2/5*b^(5/4)*d*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*EllipticE(sin(2*arctan(b^(1/4)*x/a^(1/4))),sqrt(1/2))/a^(3/4)/sqrt(b*x^4+a)+1/15*b^(3/4)*(3*sqrt(b)*d+5*sqrt(a)*f)*(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^(3/4)/sqrt(b*x^4+a),1],
[(f*x^3+e*x^2+d*x+c)*sqrt(b*x^4+a)/x^8,x,15,2/15*e*sqrt(b*x^4+a)/x^5-1/4*f*sqrt(b*x^4+a)/x^4-2/21*b*c*sqrt(b*x^4+a)/a/x^3-2/5*b*e*sqrt(b*x^4+a)/sqrt(a)/x/(sqrt(a)+sqrt(b)*x^2)-1/21*(7*e*x^2+3*c)*sqrt(b*x^4+a)/x^7-1/6*d*(b*x^4+a)^(3/2)/a/x^6-1/4*b*f*arctanh(sqrt(b*x^4+a)/sqrt(a))/sqrt(a)-2/5*b^(5/4)*e*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*EllipticE(sin(2*arctan(b^(1/4)*x/a^(1/4))),sqrt(1/2))/a^(3/4)/sqrt(b*x^4+a)-1/105*b^(5/4)*(5*sqrt(b)*c-21*sqrt(a)*e)*(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)/sqrt(b*x^4+a),1],
[(f*x^3+e*x^2+d*x+c)*sqrt(b*x^4+a)/x^9,x,16,-1/8*c*sqrt(b*x^4+a)/x^8+2/15*f*sqrt(b*x^4+a)/x^5-1/16*b*c*sqrt(b*x^4+a)/a/x^4-2/21*b*d*sqrt(b*x^4+a)/a/x^3-2/5*b*f*sqrt(b*x^4+a)/sqrt(a)/x/(sqrt(a)+sqrt(b)*x^2)-1/21*(7*f*x^2+3*d)*sqrt(b*x^4+a)/x^7-1/6*e*(b*x^4+a)^(3/2)/a/x^6+1/16*b^2*c*arctanh(sqrt(b*x^4+a)/sqrt(a))/a^(3/2)-2/5*b^(5/4)*f*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*EllipticE(sin(2*arctan(b^(1/4)*x/a^(1/4))),sqrt(1/2))/a^(3/4)/sqrt(b*x^4+a)-1/105*b^(5/4)*(5*sqrt(b)*d-21*sqrt(a)*f)*(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)/sqrt(b*x^4+a),1],
[x^3*(f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(3/2),x,18,1/32*a^2*e*x^2*sqrt(b*x^4+a)/b+1/16*a*e*x^6*sqrt(b*x^4+a)-4/65*a^3*f*x*sqrt(b*x^4+a)/b^(3/2)/(sqrt(a)+sqrt(b)*x^2)-2/5005*a^2*x*(77*f*x^2+65*d)*sqrt(b*x^4+a)/b+1/12*e*x^6*(b*x^4+a)^(3/2)-1/3003*a*x*(77*f*x^2+39*d)*(b*x^4+a)^(3/2)/b+1/10*c*(b*x^4+a)^(5/2)/b+1/11*d*x*(b*x^4+a)^(5/2)/b+1/13*f*x^3*(b*x^4+a)^(5/2)/b-1/32*a^3*e*arctanh(sqrt(b)*x^2/sqrt(b*x^4+a))/b^(3/2)+4/65*a^(13/4)*f*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*EllipticE(sin(2*arctan(b^(1/4)*x/a^(1/4))),sqrt(1/2))/b^(7/4)/sqrt(b*x^4+a)-2/5005*a^(11/4)*(65*sqrt(b)*d+77*sqrt(a)*f)*(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^(7/4)/sqrt(b*x^4+a),1],
[x^2*(f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(3/2),x,16,1/32*a^2*f*x^2*sqrt(b*x^4+a)/b+1/16*a*f*x^6*sqrt(b*x^4+a)+4/15*a^2*c*x*sqrt(b*x^4+a)/sqrt(b)/(sqrt(a)+sqrt(b)*x^2)-2/1155*a*x*(-77*b*c*x^2+15*a*e)*sqrt(b*x^4+a)/b+1/12*f*x^6*(b*x^4+a)^(3/2)-1/693*x*(-77*b*c*x^2+9*a*e)*(b*x^4+a)^(3/2)/b+1/10*d*(b*x^4+a)^(5/2)/b+1/11*e*x*(b*x^4+a)^(5/2)/b-1/32*a^3*f*arctanh(sqrt(b)*x^2/sqrt(b*x^4+a))/b^(3/2)-4/15*a^(9/4)*c*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*EllipticE(sin(2*arctan(b^(1/4)*x/a^(1/4))),sqrt(1/2))/b^(3/4)/sqrt(b*x^4+a)+2/1155*a^(9/4)*(77*sqrt(b)*c-15*sqrt(a)*e)*(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],
[x*(f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(3/2),x,14,3/16*a*c*x^2*sqrt(b*x^4+a)+4/15*a^2*d*x*sqrt(b*x^4+a)/sqrt(b)/(sqrt(a)+sqrt(b)*x^2)-2/1155*a*x*(-77*b*d*x^2+15*a*f)*sqrt(b*x^4+a)/b+1/8*c*x^2*(b*x^4+a)^(3/2)-1/693*x*(-77*b*d*x^2+9*a*f)*(b*x^4+a)^(3/2)/b+1/10*e*(b*x^4+a)^(5/2)/b+1/11*f*x*(b*x^4+a)^(5/2)/b+3/16*a^2*c*arctanh(sqrt(b)*x^2/sqrt(b*x^4+a))/sqrt(b)-4/15*a^(9/4)*d*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*EllipticE(sin(2*arctan(b^(1/4)*x/a^(1/4))),sqrt(1/2))/b^(3/4)/sqrt(b*x^4+a)+2/1155*a^(9/4)*(77*sqrt(b)*d-15*sqrt(a)*f)*(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],
[(f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(3/2),x,13,3/16*a*d*x^2*sqrt(b*x^4+a)+4/15*a^2*e*x*sqrt(b*x^4+a)/sqrt(b)/(sqrt(a)+sqrt(b)*x^2)+2/105*a*x*(7*e*x^2+15*c)*sqrt(b*x^4+a)+1/8*d*x^2*(b*x^4+a)^(3/2)+1/63*x*(7*e*x^2+9*c)*(b*x^4+a)^(3/2)+1/10*f*(b*x^4+a)^(5/2)/b+3/16*a^2*d*arctanh(sqrt(b)*x^2/sqrt(b*x^4+a))/sqrt(b)-4/15*a^(9/4)*e*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*EllipticE(sin(2*arctan(b^(1/4)*x/a^(1/4))),sqrt(1/2))/b^(3/4)/sqrt(b*x^4+a)+2/105*a^(7/4)*(15*sqrt(b)*c+7*sqrt(a)*e)*(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^(3/4)/sqrt(b*x^4+a),1],
[(f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(3/2)/x,x,15,4/15*a^2*f*x*sqrt(b*x^4+a)/sqrt(b)/(sqrt(a)+sqrt(b)*x^2)+1/16*a*(3*e*x^2+8*c)*sqrt(b*x^4+a)+2/105*a*x*(7*f*x^2+15*d)*sqrt(b*x^4+a)+1/24*(3*e*x^2+4*c)*(b*x^4+a)^(3/2)+1/63*x*(7*f*x^2+9*d)*(b*x^4+a)^(3/2)+3/16*a^2*e*arctanh(sqrt(b)*x^2/sqrt(b*x^4+a))/sqrt(b)-1/2*a^(3/2)*c*arctanh(sqrt(b*x^4+a)/sqrt(a))-4/15*a^(9/4)*f*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*EllipticE(sin(2*arctan(b^(1/4)*x/a^(1/4))),sqrt(1/2))/b^(3/4)/sqrt(b*x^4+a)+2/105*a^(7/4)*(15*sqrt(b)*d+7*sqrt(a)*f)*(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^(3/4)/sqrt(b*x^4+a),1],
[(f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(3/2)/x^2,x,15,12*a*sqrt(b)*c*x*sqrt(b*x^4+a)/(5*sqrt(a)+5*sqrt(b)*x^2)+2/35*x*(21*b*c*x^2+5*a*e)*sqrt(b*x^4+a)+1/16*a*(3*f*x^2+8*d)*sqrt(b*x^4+a)-1/7*(-e*x^2+7*c)*(b*x^4+a)^(3/2)/x+1/24*(3*f*x^2+4*d)*(b*x^4+a)^(3/2)+3/16*a^2*f*arctanh(sqrt(b)*x^2/sqrt(b*x^4+a))/sqrt(b)-1/2*a^(3/2)*d*arctanh(sqrt(b*x^4+a)/sqrt(a))-12/5*a^(5/4)*b^(1/4)*c*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*EllipticE(sin(2*arctan(b^(1/4)*x/a^(1/4))),sqrt(1/2))/sqrt(b*x^4+a)+2/35*a^(5/4)*(21*sqrt(b)*c+5*sqrt(a)*e)*(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^(1/4)/sqrt(b*x^4+a),1],
[(f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(3/2)/x^3,x,15,12*a*sqrt(b)*d*x*sqrt(b*x^4+a)/(5*sqrt(a)+5*sqrt(b)*x^2)+1/4*(3*b*c*x^2+2*a*e)*sqrt(b*x^4+a)+2/35*x*(21*b*d*x^2+5*a*f)*sqrt(b*x^4+a)-1/6*(-e*x^2+3*c)*(b*x^4+a)^(3/2)/x^2-1/7*(-f*x^2+7*d)*(b*x^4+a)^(3/2)/x+3/4*a*sqrt(b)*c*arctanh(sqrt(b)*x^2/sqrt(b*x^4+a))-1/2*a^(3/2)*e*arctanh(sqrt(b*x^4+a)/sqrt(a))-12/5*a^(5/4)*b^(1/4)*d*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*EllipticE(sin(2*arctan(b^(1/4)*x/a^(1/4))),sqrt(1/2))/sqrt(b*x^4+a)+2/35*a^(5/4)*(21*sqrt(b)*d+5*sqrt(a)*f)*(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^(1/4)/sqrt(b*x^4+a),1],
[(f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(3/2)/x^4,x,15,12*a*sqrt(b)*e*x*sqrt(b*x^4+a)/(5*sqrt(a)+5*sqrt(b)*x^2)-2/15*(-5*b*c*x^2+9*a*e)*sqrt(b*x^4+a)/x+1/4*(3*b*d*x^2+2*a*f)*sqrt(b*x^4+a)-1/15*(-3*e*x^2+5*c)*(b*x^4+a)^(3/2)/x^3-1/6*(-f*x^2+3*d)*(b*x^4+a)^(3/2)/x^2+3/4*a*sqrt(b)*d*arctanh(sqrt(b)*x^2/sqrt(b*x^4+a))-1/2*a^(3/2)*f*arctanh(sqrt(b*x^4+a)/sqrt(a))-12/5*a^(5/4)*b^(1/4)*e*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*EllipticE(sin(2*arctan(b^(1/4)*x/a^(1/4))),sqrt(1/2))/sqrt(b*x^4+a)+2/15*a^(3/4)*b^(1/4)*(5*sqrt(b)*c+9*sqrt(a)*e)*(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))/sqrt(b*x^4+a),1],
[(f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(3/2)/x^5,x,15,12*a*sqrt(b)*f*x*sqrt(b*x^4+a)/(5*sqrt(a)+5*sqrt(b)*x^2)-2/15*(-5*b*d*x^2+9*a*f)*sqrt(b*x^4+a)/x+3/4*b*(e*x^2+c)*sqrt(b*x^4+a)-1/4*(2*e*x^2+c)*(b*x^4+a)^(3/2)/x^4-1/15*(-3*f*x^2+5*d)*(b*x^4+a)^(3/2)/x^3+3/4*a*sqrt(b)*e*arctanh(sqrt(b)*x^2/sqrt(b*x^4+a))-3/4*sqrt(a)*b*c*arctanh(sqrt(b*x^4+a)/sqrt(a))-12/5*a^(5/4)*b^(1/4)*f*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*EllipticE(sin(2*arctan(b^(1/4)*x/a^(1/4))),sqrt(1/2))/sqrt(b*x^4+a)+2/15*a^(3/4)*b^(1/4)*(5*sqrt(b)*d+9*sqrt(a)*f)*(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))/sqrt(b*x^4+a),1],
[(f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(3/2)/x^6,x,15,-12/5*sqrt(a)*b*c*sqrt(b*x^4+a)/x/(sqrt(a)+sqrt(b)*x^2)-2/15*(-9*b*c*x^2+5*a*e)*sqrt(b*x^4+a)/x^3+3/4*b*(f*x^2+d)*sqrt(b*x^4+a)-1/15*(-5*e*x^2+3*c)*(b*x^4+a)^(3/2)/x^5-1/4*(2*f*x^2+d)*(b*x^4+a)^(3/2)/x^4+3/4*a*sqrt(b)*f*arctanh(sqrt(b)*x^2/sqrt(b*x^4+a))-3/4*sqrt(a)*b*d*arctanh(sqrt(b*x^4+a)/sqrt(a))-12/5*a^(1/4)*b^(5/4)*c*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*EllipticE(sin(2*arctan(b^(1/4)*x/a^(1/4))),sqrt(1/2))/sqrt(b*x^4+a)+2/15*a^(1/4)*b^(3/4)*(9*sqrt(b)*c+5*sqrt(a)*e)*(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))/sqrt(b*x^4+a),1],
[(f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(3/2)/x^7,x,15,-12/5*sqrt(a)*b*d*sqrt(b*x^4+a)/x/(sqrt(a)+sqrt(b)*x^2)-2/15*(-9*b*d*x^2+5*a*f)*sqrt(b*x^4+a)/x^3-1/4*b*(-3*e*x^2+2*c)*sqrt(b*x^4+a)/x^2-1/12*(3*e*x^2+2*c)*(b*x^4+a)^(3/2)/x^6-1/15*(-5*f*x^2+3*d)*(b*x^4+a)^(3/2)/x^5+1/2*b^(3/2)*c*arctanh(sqrt(b)*x^2/sqrt(b*x^4+a))-3/4*sqrt(a)*b*e*arctanh(sqrt(b*x^4+a)/sqrt(a))-12/5*a^(1/4)*b^(5/4)*d*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*EllipticE(sin(2*arctan(b^(1/4)*x/a^(1/4))),sqrt(1/2))/sqrt(b*x^4+a)+2/15*a^(1/4)*b^(3/4)*(9*sqrt(b)*d+5*sqrt(a)*f)*(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))/sqrt(b*x^4+a),1],
[(f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(3/2)/x^8,x,16,4/7*b*c*sqrt(b*x^4+a)/x^3-12/5*sqrt(a)*b*e*sqrt(b*x^4+a)/x/(sqrt(a)+sqrt(b)*x^2)-6/35*(5*b*c*x^2+7*a*e)*sqrt(b*x^4+a)/x^5-1/4*b*(-3*f*x^2+2*d)*sqrt(b*x^4+a)/x^2-1/7*(-7*e*x^2+c)*(b*x^4+a)^(3/2)/x^7-1/12*(3*f*x^2+2*d)*(b*x^4+a)^(3/2)/x^6+1/2*b^(3/2)*d*arctanh(sqrt(b)*x^2/sqrt(b*x^4+a))-3/4*sqrt(a)*b*f*arctanh(sqrt(b*x^4+a)/sqrt(a))-12/5*a^(1/4)*b^(5/4)*e*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*EllipticE(sin(2*arctan(b^(1/4)*x/a^(1/4))),sqrt(1/2))/sqrt(b*x^4+a)+2/35*b^(5/4)*(5*sqrt(b)*c+21*sqrt(a)*e)*(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)/sqrt(b*x^4+a),1],
[(f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(3/2)/x^9,x,16,4/7*b*d*sqrt(b*x^4+a)/x^3-12/5*sqrt(a)*b*f*sqrt(b*x^4+a)/x/(sqrt(a)+sqrt(b)*x^2)-6/35*(5*b*d*x^2+7*a*f)*sqrt(b*x^4+a)/x^5-1/16*b*(8*e*x^2+3*c)*sqrt(b*x^4+a)/x^4-1/24*(4*e*x^2+3*c)*(b*x^4+a)^(3/2)/x^8-1/7*(-7*f*x^2+d)*(b*x^4+a)^(3/2)/x^7+1/2*b^(3/2)*e*arctanh(sqrt(b)*x^2/sqrt(b*x^4+a))-3/16*b^2*c*arctanh(sqrt(b*x^4+a)/sqrt(a))/sqrt(a)-12/5*a^(1/4)*b^(5/4)*f*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*EllipticE(sin(2*arctan(b^(1/4)*x/a^(1/4))),sqrt(1/2))/sqrt(b*x^4+a)+2/35*b^(5/4)*(5*sqrt(b)*d+21*sqrt(a)*f)*(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)/sqrt(b*x^4+a),1],
[(f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(3/2)/x^10,x,17,4/45*b*c*sqrt(b*x^4+a)/x^5+4/7*b*e*sqrt(b*x^4+a)/x^3-4/15*b^2*c*sqrt(b*x^4+a)/sqrt(a)/x/(sqrt(a)+sqrt(b)*x^2)+2/63*(-7*b*c*x^2+27*a*e)*sqrt(b*x^4+a)/x^7-1/16*b*(8*f*x^2+3*d)*sqrt(b*x^4+a)/x^4-1/9*(9*e*x^2+c)*(b*x^4+a)^(3/2)/x^9-1/24*(4*f*x^2+3*d)*(b*x^4+a)^(3/2)/x^8+1/2*b^(3/2)*f*arctanh(sqrt(b)*x^2/sqrt(b*x^4+a))-3/16*b^2*d*arctanh(sqrt(b*x^4+a)/sqrt(a))/sqrt(a)-4/15*b^(9/4)*c*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*EllipticE(sin(2*arctan(b^(1/4)*x/a^(1/4))),sqrt(1/2))/a^(3/4)/sqrt(b*x^4+a)+2/105*b^(7/4)*(7*sqrt(b)*c+15*sqrt(a)*e)*(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^(3/4)/sqrt(b*x^4+a),1],
[(f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(3/2)/x^11,x,17,-1/8*a*e*sqrt(b*x^4+a)/x^8+4/45*b*d*sqrt(b*x^4+a)/x^5-5/16*b*e*sqrt(b*x^4+a)/x^4+4/7*b*f*sqrt(b*x^4+a)/x^3-4/15*b^2*d*sqrt(b*x^4+a)/sqrt(a)/x/(sqrt(a)+sqrt(b)*x^2)+2/63*(-7*b*d*x^2+27*a*f)*sqrt(b*x^4+a)/x^7-1/9*(9*f*x^2+d)*(b*x^4+a)^(3/2)/x^9-1/10*c*(b*x^4+a)^(5/2)/a/x^10-3/16*b^2*e*arctanh(sqrt(b*x^4+a)/sqrt(a))/sqrt(a)-4/15*b^(9/4)*d*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*EllipticE(sin(2*arctan(b^(1/4)*x/a^(1/4))),sqrt(1/2))/a^(3/4)/sqrt(b*x^4+a)+2/105*b^(7/4)*(7*sqrt(b)*d+15*sqrt(a)*f)*(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^(3/4)/sqrt(b*x^4+a),1],
[(f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(3/2)/x^12,x,18,-1/8*a*f*sqrt(b*x^4+a)/x^8+12/385*b*c*sqrt(b*x^4+a)/x^7+4/45*b*e*sqrt(b*x^4+a)/x^5-5/16*b*f*sqrt(b*x^4+a)/x^4-4/77*b^2*c*sqrt(b*x^4+a)/a/x^3-4/15*b^2*e*sqrt(b*x^4+a)/sqrt(a)/x/(sqrt(a)+sqrt(b)*x^2)+2/495*(-27*b*c*x^2+55*a*e)*sqrt(b*x^4+a)/x^9-1/33*(11*e*x^2+3*c)*(b*x^4+a)^(3/2)/x^11-1/10*d*(b*x^4+a)^(5/2)/a/x^10-3/16*b^2*f*arctanh(sqrt(b*x^4+a)/sqrt(a))/sqrt(a)-4/15*b^(9/4)*e*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*EllipticE(sin(2*arctan(b^(1/4)*x/a^(1/4))),sqrt(1/2))/a^(3/4)/sqrt(b*x^4+a)-2/1155*b^(9/4)*(15*sqrt(b)*c-77*sqrt(a)*e)*(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)/sqrt(b*x^4+a),1],
[(f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(3/2)/x^13,x,19,-1/12*a*c*sqrt(b*x^4+a)/x^12-7/48*b*c*sqrt(b*x^4+a)/x^8+12/385*b*d*sqrt(b*x^4+a)/x^7+4/45*b*f*sqrt(b*x^4+a)/x^5-1/32*b^2*c*sqrt(b*x^4+a)/a/x^4-4/77*b^2*d*sqrt(b*x^4+a)/a/x^3-4/15*b^2*f*sqrt(b*x^4+a)/sqrt(a)/x/(sqrt(a)+sqrt(b)*x^2)+2/495*(-27*b*d*x^2+55*a*f)*sqrt(b*x^4+a)/x^9-1/33*(11*f*x^2+3*d)*(b*x^4+a)^(3/2)/x^11-1/10*e*(b*x^4+a)^(5/2)/a/x^10+1/32*b^3*c*arctanh(sqrt(b*x^4+a)/sqrt(a))/a^(3/2)-4/15*b^(9/4)*f*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*EllipticE(sin(2*arctan(b^(1/4)*x/a^(1/4))),sqrt(1/2))/a^(3/4)/sqrt(b*x^4+a)-2/1155*b^(9/4)*(15*sqrt(b)*d-77*sqrt(a)*f)*(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)/sqrt(b*x^4+a),1],
[(f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(3/2)/x^14,x,20,-1/12*a*d*sqrt(b*x^4+a)/x^12+4/273*b*c*sqrt(b*x^4+a)/x^9-7/48*b*d*sqrt(b*x^4+a)/x^8+12/385*b*e*sqrt(b*x^4+a)/x^7-4/195*b^2*c*sqrt(b*x^4+a)/a/x^5-1/32*b^2*d*sqrt(b*x^4+a)/a/x^4-4/77*b^2*e*sqrt(b*x^4+a)/a/x^3+4/65*b^3*c*sqrt(b*x^4+a)/a^(3/2)/x/(sqrt(a)+sqrt(b)*x^2)+6/5005*(-55*b*c*x^2+91*a*e)*sqrt(b*x^4+a)/x^11-1/65*(13*e*x^2+5*c)*(b*x^4+a)^(3/2)/x^13-1/10*f*(b*x^4+a)^(5/2)/a/x^10+1/32*b^3*d*arctanh(sqrt(b*x^4+a)/sqrt(a))/a^(3/2)+4/65*b^(13/4)*c*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*EllipticE(sin(2*arctan(b^(1/4)*x/a^(1/4))),sqrt(1/2))/a^(7/4)/sqrt(b*x^4+a)-2/5005*b^(11/4)*(77*sqrt(b)*c+65*sqrt(a)*e)*(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^(7/4)/sqrt(b*x^4+a),1],
[x^4*(f*x^3+e*x^2+d*x+c)/sqrt(b*x^4+a),x,15,-1/2*a*f*sqrt(b*x^4+a)/b^2+1/3*c*x*sqrt(b*x^4+a)/b+1/4*d*x^2*sqrt(b*x^4+a)/b+1/5*e*x^3*sqrt(b*x^4+a)/b-3/5*a*e*x*sqrt(b*x^4+a)/b^(3/2)/(sqrt(a)+sqrt(b)*x^2)+1/6*f*(b*x^4+a)^(3/2)/b^2-1/4*a*d*arctanh(sqrt(b)*x^2/sqrt(b*x^4+a))/b^(3/2)+3/5*a^(5/4)*e*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*EllipticE(sin(2*arctan(b^(1/4)*x/a^(1/4))),sqrt(1/2))/b^(7/4)/sqrt(b*x^4+a)-1/30*a^(3/4)*(5*sqrt(b)*c+9*sqrt(a)*e)*(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^(7/4)/sqrt(b*x^4+a),1],
[x^3*(f*x^3+e*x^2+d*x+c)/sqrt(b*x^4+a),x,13,1/2*c*sqrt(b*x^4+a)/b+1/3*d*x*sqrt(b*x^4+a)/b+1/4*e*x^2*sqrt(b*x^4+a)/b+1/5*f*x^3*sqrt(b*x^4+a)/b-3/5*a*f*x*sqrt(b*x^4+a)/b^(3/2)/(sqrt(a)+sqrt(b)*x^2)-1/4*a*e*arctanh(sqrt(b)*x^2/sqrt(b*x^4+a))/b^(3/2)+3/5*a^(5/4)*f*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*EllipticE(sin(2*arctan(b^(1/4)*x/a^(1/4))),sqrt(1/2))/b^(7/4)/sqrt(b*x^4+a)-1/30*a^(3/4)*(5*sqrt(b)*d+9*sqrt(a)*f)*(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^(7/4)/sqrt(b*x^4+a),1],
[x^2*(f*x^3+e*x^2+d*x+c)/sqrt(b*x^4+a),x,12,1/2*d*sqrt(b*x^4+a)/b+1/3*e*x*sqrt(b*x^4+a)/b+1/4*f*x^2*sqrt(b*x^4+a)/b+c*x*sqrt(b*x^4+a)/sqrt(b)/(sqrt(a)+sqrt(b)*x^2)-1/4*a*f*arctanh(sqrt(b)*x^2/sqrt(b*x^4+a))/b^(3/2)-a^(1/4)*c*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*EllipticE(sin(2*arctan(b^(1/4)*x/a^(1/4))),sqrt(1/2))/b^(3/4)/sqrt(b*x^4+a)+1/6*a^(1/4)*(3*sqrt(b)*c-sqrt(a)*e)*(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],
[x*(f*x^3+e*x^2+d*x+c)/sqrt(b*x^4+a),x,10,1/2*e*sqrt(b*x^4+a)/b+1/3*f*x*sqrt(b*x^4+a)/b+d*x*sqrt(b*x^4+a)/sqrt(b)/(sqrt(a)+sqrt(b)*x^2)+1/2*c*arctanh(sqrt(b)*x^2/sqrt(b*x^4+a))/sqrt(b)-a^(1/4)*d*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*EllipticE(sin(2*arctan(b^(1/4)*x/a^(1/4))),sqrt(1/2))/b^(3/4)/sqrt(b*x^4+a)+1/6*a^(1/4)*(3*sqrt(b)*d-sqrt(a)*f)*(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],
[(f*x^3+e*x^2+d*x+c)/sqrt(b*x^4+a),x,9,1/2*f*sqrt(b*x^4+a)/b+e*x*sqrt(b*x^4+a)/sqrt(b)/(sqrt(a)+sqrt(b)*x^2)+1/2*d*arctanh(sqrt(b)*x^2/sqrt(b*x^4+a))/sqrt(b)-a^(1/4)*e*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*EllipticE(sin(2*arctan(b^(1/4)*x/a^(1/4))),sqrt(1/2))/b^(3/4)/sqrt(b*x^4+a)+1/2*(sqrt(b)*c+sqrt(a)*e)*(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^(3/4)/sqrt(b*x^4+a),1],
[(f*x^3+e*x^2+d*x+c)/x/sqrt(b*x^4+a),x,11,f*x*sqrt(b*x^4+a)/sqrt(b)/(sqrt(a)+sqrt(b)*x^2)+1/2*e*arctanh(sqrt(b)*x^2/sqrt(b*x^4+a))/sqrt(b)-1/2*c*arctanh(sqrt(b*x^4+a)/sqrt(a))/sqrt(a)-a^(1/4)*f*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*EllipticE(sin(2*arctan(b^(1/4)*x/a^(1/4))),sqrt(1/2))/b^(3/4)/sqrt(b*x^4+a)+1/2*(sqrt(b)*d+sqrt(a)*f)*(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^(3/4)/sqrt(b*x^4+a),1],
[(f*x^3+e*x^2+d*x+c)/x^2/sqrt(b*x^4+a),x,11,-c*sqrt(b*x^4+a)/sqrt(a)/x/(sqrt(a)+sqrt(b)*x^2)+1/2*f*arctanh(sqrt(b)*x^2/sqrt(b*x^4+a))/sqrt(b)-1/2*d*arctanh(sqrt(b*x^4+a)/sqrt(a))/sqrt(a)-b^(1/4)*c*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*EllipticE(sin(2*arctan(b^(1/4)*x/a^(1/4))),sqrt(1/2))/a^(3/4)/sqrt(b*x^4+a)+1/2*(sqrt(b)*c+sqrt(a)*e)*(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^(3/4)/b^(1/4)/sqrt(b*x^4+a),1],
[(f*x^3+e*x^2+d*x+c)/x^3/sqrt(b*x^4+a),x,9,-1/2*c*sqrt(b*x^4+a)/a/x^2-d*sqrt(b*x^4+a)/sqrt(a)/x/(sqrt(a)+sqrt(b)*x^2)-1/2*e*arctanh(sqrt(b*x^4+a)/sqrt(a))/sqrt(a)-b^(1/4)*d*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*EllipticE(sin(2*arctan(b^(1/4)*x/a^(1/4))),sqrt(1/2))/a^(3/4)/sqrt(b*x^4+a)+1/2*(sqrt(b)*d+sqrt(a)*f)*(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^(3/4)/b^(1/4)/sqrt(b*x^4+a),1],
[(f*x^3+e*x^2+d*x+c)/x^4/sqrt(b*x^4+a),x,10,-1/3*c*sqrt(b*x^4+a)/a/x^3-1/2*d*sqrt(b*x^4+a)/a/x^2-e*sqrt(b*x^4+a)/sqrt(a)/x/(sqrt(a)+sqrt(b)*x^2)-1/2*f*arctanh(sqrt(b*x^4+a)/sqrt(a))/sqrt(a)-b^(1/4)*e*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*EllipticE(sin(2*arctan(b^(1/4)*x/a^(1/4))),sqrt(1/2))/a^(3/4)/sqrt(b*x^4+a)-1/6*b^(1/4)*(sqrt(b)*c-3*sqrt(a)*e)*(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)/sqrt(b*x^4+a),1],
[(f*x^3+e*x^2+d*x+c)/x^5/sqrt(b*x^4+a),x,11,-1/4*c*sqrt(b*x^4+a)/a/x^4-1/3*d*sqrt(b*x^4+a)/a/x^3-1/2*e*sqrt(b*x^4+a)/a/x^2-f*sqrt(b*x^4+a)/sqrt(a)/x/(sqrt(a)+sqrt(b)*x^2)+1/4*b*c*arctanh(sqrt(b*x^4+a)/sqrt(a))/a^(3/2)-b^(1/4)*f*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*EllipticE(sin(2*arctan(b^(1/4)*x/a^(1/4))),sqrt(1/2))/a^(3/4)/sqrt(b*x^4+a)-1/6*b^(1/4)*(sqrt(b)*d-3*sqrt(a)*f)*(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)/sqrt(b*x^4+a),1],
[(f*x^3+e*x^2+d*x+c)/x^6/sqrt(b*x^4+a),x,12,-1/5*c*sqrt(b*x^4+a)/a/x^5-1/4*d*sqrt(b*x^4+a)/a/x^4-1/3*e*sqrt(b*x^4+a)/a/x^3-1/2*f*sqrt(b*x^4+a)/a/x^2+3/5*b*c*sqrt(b*x^4+a)/a^(3/2)/x/(sqrt(a)+sqrt(b)*x^2)+1/4*b*d*arctanh(sqrt(b*x^4+a)/sqrt(a))/a^(3/2)+3/5*b^(5/4)*c*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*EllipticE(sin(2*arctan(b^(1/4)*x/a^(1/4))),sqrt(1/2))/a^(7/4)/sqrt(b*x^4+a)-1/30*b^(3/4)*(9*sqrt(b)*c+5*sqrt(a)*e)*(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^(7/4)/sqrt(b*x^4+a),1],
[x^6*(f*x^3+e*x^2+d*x+c)/(b*x^4+a)^(3/2),x,13,1/2*x*(-b*c*x^2+a*e)/b^2/sqrt(b*x^4+a)+1/2*a*(f*x^2+d)/b^2/sqrt(b*x^4+a)+1/2*d*sqrt(b*x^4+a)/b^2+1/3*e*x*sqrt(b*x^4+a)/b^2+1/4*f*x^2*sqrt(b*x^4+a)/b^2+3/2*c*x*sqrt(b*x^4+a)/b^(3/2)/(sqrt(a)+sqrt(b)*x^2)-3/4*a*f*arctanh(sqrt(b)*x^2/sqrt(b*x^4+a))/b^(5/2)-3/2*a^(1/4)*c*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*EllipticE(sin(2*arctan(b^(1/4)*x/a^(1/4))),sqrt(1/2))/b^(7/4)/sqrt(b*x^4+a)+1/12*a^(1/4)*(9*sqrt(b)*c-5*sqrt(a)*e)*(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],
[x^5*(f*x^3+e*x^2+d*x+c)/(b*x^4+a)^(3/2),x,12,1/2*(-b*c*x^2+a*e)/b^2/sqrt(b*x^4+a)+1/2*x*(-b*d*x^2+a*f)/b^2/sqrt(b*x^4+a)+1/2*e*sqrt(b*x^4+a)/b^2+1/3*f*x*sqrt(b*x^4+a)/b^2+3/2*d*x*sqrt(b*x^4+a)/b^(3/2)/(sqrt(a)+sqrt(b)*x^2)+1/2*c*arctanh(sqrt(b)*x^2/sqrt(b*x^4+a))/b^(3/2)-3/2*a^(1/4)*d*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*EllipticE(sin(2*arctan(b^(1/4)*x/a^(1/4))),sqrt(1/2))/b^(7/4)/sqrt(b*x^4+a)+1/12*a^(1/4)*(9*sqrt(b)*d-5*sqrt(a)*f)*(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],
[x^4*(f*x^3+e*x^2+d*x+c)/(b*x^4+a)^(3/2),x,11,1/2*(-b*d*x^2+a*f)/b^2/sqrt(b*x^4+a)-1/2*x*(e*x^2+c)/b/sqrt(b*x^4+a)+1/2*f*sqrt(b*x^4+a)/b^2+3/2*e*x*sqrt(b*x^4+a)/b^(3/2)/(sqrt(a)+sqrt(b)*x^2)+1/2*d*arctanh(sqrt(b)*x^2/sqrt(b*x^4+a))/b^(3/2)-3/2*a^(1/4)*e*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*EllipticE(sin(2*arctan(b^(1/4)*x/a^(1/4))),sqrt(1/2))/b^(7/4)/sqrt(b*x^4+a)+1/4*(sqrt(b)*c+3*sqrt(a)*e)*(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^(7/4)/sqrt(b*x^4+a),1],
[x^3*(f*x^3+e*x^2+d*x+c)/(b*x^4+a)^(3/2),x,13,-1/2*c/b/sqrt(b*x^4+a)-1/2*e*x^2/b/sqrt(b*x^4+a)-1/2*x*(f*x^2+d)/b/sqrt(b*x^4+a)+3/2*f*x*sqrt(b*x^4+a)/b^(3/2)/(sqrt(a)+sqrt(b)*x^2)+1/2*e*arctanh(sqrt(b)*x^2/sqrt(b*x^4+a))/b^(3/2)-3/2*a^(1/4)*f*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*EllipticE(sin(2*arctan(b^(1/4)*x/a^(1/4))),sqrt(1/2))/b^(7/4)/sqrt(b*x^4+a)+1/4*(sqrt(b)*d+3*sqrt(a)*f)*(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^(7/4)/sqrt(b*x^4+a),1],
[x^2*(f*x^3+e*x^2+d*x+c)/(b*x^4+a)^(3/2),x,12,-1/2*d/b/sqrt(b*x^4+a)-1/2*f*x^2/b/sqrt(b*x^4+a)-1/2*x*(-b*c*x^2+a*e)/a/b/sqrt(b*x^4+a)-1/2*c*x*sqrt(b*x^4+a)/a/sqrt(b)/(sqrt(a)+sqrt(b)*x^2)+1/2*f*arctanh(sqrt(b)*x^2/sqrt(b*x^4+a))/b^(3/2)+1/2*c*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*EllipticE(sin(2*arctan(b^(1/4)*x/a^(1/4))),sqrt(1/2))/a^(3/4)/b^(3/4)/sqrt(b*x^4+a)-1/4*(c-sqrt(a)*e/sqrt(b))*(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^(3/4)/b^(3/4)/sqrt(b*x^4+a),1],
[x*(f*x^3+e*x^2+d*x+c)/(b*x^4+a)^(3/2),x,10,-1/2*e/b/sqrt(b*x^4+a)+1/2*c*x^2/a/sqrt(b*x^4+a)-1/2*x*(-b*d*x^2+a*f)/a/b/sqrt(b*x^4+a)-1/2*d*x*sqrt(b*x^4+a)/a/sqrt(b)/(sqrt(a)+sqrt(b)*x^2)+1/2*d*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*EllipticE(sin(2*arctan(b^(1/4)*x/a^(1/4))),sqrt(1/2))/a^(3/4)/b^(3/4)/sqrt(b*x^4+a)-1/4*(d-sqrt(a)*f/sqrt(b))*(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^(3/4)/b^(3/4)/sqrt(b*x^4+a),1],
[(f*x^3+e*x^2+d*x+c)/(b*x^4+a)^(3/2),x,6,-1/2*f/b/sqrt(b*x^4+a)+1/2*x*(e*x^2+d*x+c)/a/sqrt(b*x^4+a)-1/2*e*x*sqrt(b*x^4+a)/a/sqrt(b)/(sqrt(a)+sqrt(b)*x^2)+1/2*e*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*EllipticE(sin(2*arctan(b^(1/4)*x/a^(1/4))),sqrt(1/2))/a^(3/4)/b^(3/4)/sqrt(b*x^4+a)+1/4*(sqrt(b)*c-sqrt(a)*e)*(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^(3/4)/sqrt(b*x^4+a),1],
[(f*x^3+e*x^2+d*x+c)/x/(b*x^4+a)^(3/2),x,11,1/2*(e*x^2+c)/a/sqrt(b*x^4+a)+1/2*x*(f*x^2+d)/a/sqrt(b*x^4+a)-1/2*f*x*sqrt(b*x^4+a)/a/sqrt(b)/(sqrt(a)+sqrt(b)*x^2)-1/2*c*arctanh(sqrt(b*x^4+a)/sqrt(a))/a^(3/2)+1/2*f*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*EllipticE(sin(2*arctan(b^(1/4)*x/a^(1/4))),sqrt(1/2))/a^(3/4)/b^(3/4)/sqrt(b*x^4+a)+1/4*(sqrt(b)*d-sqrt(a)*f)*(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^(3/4)/sqrt(b*x^4+a),1],
[(f*x^3+e*x^2+d*x+c)/x^2/(b*x^4+a)^(3/2),x,11,1/2*(e*x^2+c)/a/x/sqrt(b*x^4+a)+1/2*(f*x^2+d)/a/sqrt(b*x^4+a)-3/2*c*sqrt(b*x^4+a)/a^(3/2)/x/(sqrt(a)+sqrt(b)*x^2)-1/2*d*arctanh(sqrt(b*x^4+a)/sqrt(a))/a^(3/2)-3/2*b^(1/4)*c*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*EllipticE(sin(2*arctan(b^(1/4)*x/a^(1/4))),sqrt(1/2))/a^(7/4)/sqrt(b*x^4+a)+1/4*(3*sqrt(b)*c+sqrt(a)*e)*(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^(7/4)/b^(1/4)/sqrt(b*x^4+a),1],
[(f*x^3+e*x^2+d*x+c)/x^3/(b*x^4+a)^(3/2),x,11,1/2*(-b*c*x^2+a*e)/a^2/sqrt(b*x^4+a)+1/2*(f*x^2+d)/a/x/sqrt(b*x^4+a)-1/2*c*sqrt(b*x^4+a)/a^2/x^2-3/2*d*sqrt(b*x^4+a)/a^(3/2)/x/(sqrt(a)+sqrt(b)*x^2)-1/2*e*arctanh(sqrt(b*x^4+a)/sqrt(a))/a^(3/2)-3/2*b^(1/4)*d*(sqrt(a)+sqrt(b)*x^2)*sqrt((b*x^4+a)/(sqrt(a)+sqrt(b)*x^2)^2)*EllipticE(sin(2*arctan(b^(1/4)*x/a^(1/4))),sqrt(1/2))/a^(7/4)/sqrt(b*x^4+a)+1/4*(3*sqrt(b)*d+sqrt(a)*f)*(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^(7/4)/b^(1/4)/sqrt(b*x^4+a),1],
[x^4*(b*x^4+a)^(1/3)*(C*x^4+B*x^2+A),x,8,3/31*C*x^5*(b*x^4+a)^(4/3)/b+1/155*(31*A*b-15*C*a)*x^5*(b*x^4+a)^(1/3)*hypergeom([-1/3, 5/4],[9/4],-b*x^4/a)/b/(1+b*x^4/a)^(1/3)+1/7*B*x^7*(b*x^4+a)^(1/3)*hypergeom([-1/3, 7/4],[11/4],-b*x^4/a)/(1+b*x^4/a)^(1/3),1],
[x^2*(b*x^4+a)^(1/3)*(C*x^4+B*x^2+A),x,8,3/25*C*x^3*(b*x^4+a)^(4/3)/b+1/75*(25*A*b-9*C*a)*x^3*(b*x^4+a)^(1/3)*hypergeom([-1/3, 3/4],[7/4],-b*x^4/a)/b/(1+b*x^4/a)^(1/3)+1/5*B*x^5*(b*x^4+a)^(1/3)*hypergeom([-1/3, 5/4],[9/4],-b*x^4/a)/(1+b*x^4/a)^(1/3),1],
[(b*x^4+a)^(1/3)*(C*x^4+B*x^2+A),x,6,3/19*C*x*(b*x^4+a)^(4/3)/b+1/19*(19*A*b-3*C*a)*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)+1/3*B*x^3*(b*x^4+a)^(1/3)*hypergeom([-1/3, 3/4],[7/4],-b*x^4/a)/(1+b*x^4/a)^(1/3),1],
[(b*x^4+a)^(1/3)*(C*x^4+B*x^2+A)/x^2,x,7,-A*(b*x^4+a)^(4/3)/a/x+B*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)+1/9*(13*A*b+3*C*a)*x^3*(b*x^4+a)^(1/3)*hypergeom([-1/3, 3/4],[7/4],-b*x^4/a)/a/(1+b*x^4/a)^(1/3),1],
[(b*x^4+a)^(1/3)*(C*x^4+B*x^2+A)/x^4,x,7,-1/3*A*(b*x^4+a)^(4/3)/a/x^3-B*(b*x^4+a)^(1/3)*hypergeom([-1/3, -1/4],[3/4],-b*x^4/a)/x/(1+b*x^4/a)^(1/3)+1/9*(7*A*b+9*C*a)*x*(b*x^4+a)^(1/3)*hypergeom([-1/3, 1/4],[5/4],-b*x^4/a)/a/(1+b*x^4/a)^(1/3),1],
[(b*x^4+a)^(1/3)*(C*x^4+B*x^2+A)/x^6,x,7,-1/5*A*(b*x^4+a)^(4/3)/a/x^5-1/3*B*(b*x^4+a)^(1/3)*hypergeom([-3/4, -1/3],[1/4],-b*x^4/a)/x^3/(1+b*x^4/a)^(1/3)-1/15*(A*b+15*C*a)*(b*x^4+a)^(1/3)*hypergeom([-1/3, -1/4],[3/4],-b*x^4/a)/a/x/(1+b*x^4/a)^(1/3),1],
[x^2*(C*x^4+B*x^2+A)/(b*x^4+a)^(1/3),x,8,3/17*C*x^3*(b*x^4+a)^(2/3)/b+1/51*(17*A*b-9*C*a)*x^3*(1+b*x^4/a)^(1/3)*hypergeom([1/3, 3/4],[7/4],-b*x^4/a)/b/(b*x^4+a)^(1/3)+1/5*B*x^5*(1+b*x^4/a)^(1/3)*hypergeom([1/3, 5/4],[9/4],-b*x^4/a)/(b*x^4+a)^(1/3),1],
[(C*x^4+B*x^2+A)/(b*x^4+a)^(1/3),x,6,3/11*C*x*(b*x^4+a)^(2/3)/b+1/11*(11*A*b-3*C*a)*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)+1/3*B*x^3*(1+b*x^4/a)^(1/3)*hypergeom([1/3, 3/4],[7/4],-b*x^4/a)/(b*x^4+a)^(1/3),1],
[(C*x^4+B*x^2+A)/x^2/(b*x^4+a)^(1/3),x,6,-A*(b*x^4+a)^(2/3)/a/x+B*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)+1/9*(5*A*b+3*C*a)*x^3*(1+b*x^4/a)^(1/3)*hypergeom([1/3, 3/4],[7/4],-b*x^4/a)/a/(b*x^4+a)^(1/3),1],
[(C*x^4+B*x^2+A)/x^4/(b*x^4+a)^(1/3),x,6,-1/3*A*(b*x^4+a)^(2/3)/a/x^3-B*(1+b*x^4/a)^(1/3)*hypergeom([-1/4, 1/3],[3/4],-b*x^4/a)/x/(b*x^4+a)^(1/3)-1/9*(A*b-9*C*a)*x*(1+b*x^4/a)^(1/3)*hypergeom([1/4, 1/3],[5/4],-b*x^4/a)/a/(b*x^4+a)^(1/3),1],
[(C*x^4+B*x^2+A)/x^6/(b*x^4+a)^(1/3),x,6,-1/5*A*(b*x^4+a)^(2/3)/a/x^5-1/3*B*(1+b*x^4/a)^(1/3)*hypergeom([-3/4, 1/3],[1/4],-b*x^4/a)/x^3/(b*x^4+a)^(1/3)+1/15*(7*A*b-15*C*a)*(1+b*x^4/a)^(1/3)*hypergeom([-1/4, 1/3],[3/4],-b*x^4/a)/a/x/(b*x^4+a)^(1/3),1],
[x^4*(C*x^4+B*x^2+A)/(b*x^4+a)^(4/3),x,8,3/11*C*x^5/b/(b*x^4+a)^(1/3)+1/55*(11*A*b-15*C*a)*x^5*(1+b*x^4/a)^(1/3)*hypergeom([5/4, 4/3],[9/4],-b*x^4/a)/a/b/(b*x^4+a)^(1/3)+1/7*B*x^7*(1+b*x^4/a)^(1/3)*hypergeom([4/3, 7/4],[11/4],-b*x^4/a)/a/(b*x^4+a)^(1/3),1],
[x^2*(C*x^4+B*x^2+A)/(b*x^4+a)^(4/3),x,8,3/5*C*x^3/b/(b*x^4+a)^(1/3)+1/15*(5*A*b-9*C*a)*x^3*(1+b*x^4/a)^(1/3)*hypergeom([3/4, 4/3],[7/4],-b*x^4/a)/a/b/(b*x^4+a)^(1/3)+1/5*B*x^5*(1+b*x^4/a)^(1/3)*hypergeom([5/4, 4/3],[9/4],-b*x^4/a)/a/(b*x^4+a)^(1/3),1],
[(C*x^4+B*x^2+A)/(b*x^4+a)^(4/3),x,6,-3*C*x/b/(b*x^4+a)^(1/3)+(A*b+3*C*a)*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)+1/3*B*x^3*(1+b*x^4/a)^(1/3)*hypergeom([3/4, 4/3],[7/4],-b*x^4/a)/a/(b*x^4+a)^(1/3),1],
[(C*x^4+B*x^2+A)/x^2/(b*x^4+a)^(4/3),x,7,-A/a/x/(b*x^4+a)^(1/3)+B*x*(1+b*x^4/a)^(1/3)*hypergeom([1/4, 4/3],[5/4],-b*x^4/a)/a/(b*x^4+a)^(1/3)-1/9*(7*A*b-3*C*a)*x^3*(1+b*x^4/a)^(1/3)*hypergeom([3/4, 4/3],[7/4],-b*x^4/a)/a^2/(b*x^4+a)^(1/3),1],
[(C*x^4+B*x^2+A)/x^4/(b*x^4+a)^(4/3),x,7,-1/3*A/a/x^3/(b*x^4+a)^(1/3)-B*(1+b*x^4/a)^(1/3)*hypergeom([-1/4, 4/3],[3/4],-b*x^4/a)/a/x/(b*x^4+a)^(1/3)-1/9*(13*A*b-9*C*a)*x*(1+b*x^4/a)^(1/3)*hypergeom([1/4, 4/3],[5/4],-b*x^4/a)/a^2/(b*x^4+a)^(1/3),1],
[(g*x)^m*(f*x^3+e*x^2+d*x+c)*(b*x^4+a)^p,x,11,c*(g*x)^(1+m)*(b*x^4+a)^p*hypergeom([1/4+1/4*m, -p],[5/4+1/4*m],-b*x^4/a)/g/(1+m)/((1+b*x^4/a)^p)+d*(g*x)^(2+m)*(b*x^4+a)^p*hypergeom([1/2+1/4*m, -p],[3/2+1/4*m],-b*x^4/a)/g^2/(2+m)/((1+b*x^4/a)^p)+e*(g*x)^(3+m)*(b*x^4+a)^p*hypergeom([3/4+1/4*m, -p],[7/4+1/4*m],-b*x^4/a)/g^3/(3+m)/((1+b*x^4/a)^p)+f*(g*x)^(4+m)*(b*x^4+a)^p*hypergeom([1+1/4*m, -p],[2+1/4*m],-b*x^4/a)/g^4/(4+m)/((1+b*x^4/a)^p),1],
[(c*x)^m*(b*x^4+a)^p*(C*x^4+B*x^2+A),x,7,C*(c*x)^(1+m)*(b*x^4+a)^(p+1)/b/c/(5+m+4*p)+(A/(1+m)-a*C/b/(5+m+4*p))*(c*x)^(1+m)*(b*x^4+a)^p*hypergeom([1/4+1/4*m, -p],[5/4+1/4*m],-b*x^4/a)/c/((1+b*x^4/a)^p)+B*(c*x)^(3+m)*(b*x^4+a)^p*hypergeom([3/4+1/4*m, -p],[7/4+1/4*m],-b*x^4/a)/c^3/(3+m)/((1+b*x^4/a)^p),1],
[(c*x)^m*(b*x^4+a)^p*(D*x^6+C*x^4+B*x^2+A),x,8,C*(c*x)^(1+m)*(b*x^4+a)^(p+1)/b/c/(5+m+4*p)+D*(c*x)^(3+m)*(b*x^4+a)^(p+1)/b/c^3/(7+m+4*p)+(A/(1+m)-a*C/b/(5+m+4*p))*(c*x)^(1+m)*(b*x^4+a)^p*hypergeom([1/4+1/4*m, -p],[5/4+1/4*m],-b*x^4/a)/c/((1+b*x^4/a)^p)+(B/(3+m)-a*D/b/(7+m+4*p))*(c*x)^(3+m)*(b*x^4+a)^p*hypergeom([3/4+1/4*m, -p],[7/4+1/4*m],-b*x^4/a)/c^3/((1+b*x^4/a)^p),1],
[(f*x^3+e*x^2+d*x+c)*(b*x^4+a)^p,x,10,1/4*f*(b*x^4+a)^(p+1)/b/(p+1)+c*x*(b*x^4+a)^(p+1)*hypergeom([1, 5/4+p],[5/4],-b*x^4/a)/a+1/2*d*x^2*(b*x^4+a)^(p+1)*hypergeom([1, 3/2+p],[3/2],-b*x^4/a)/a+1/3*e*x^3*(b*x^4+a)^(p+1)*hypergeom([1, 7/4+p],[7/4],-b*x^4/a)/a,1],
[x^3*(f*x^3+e*x^2+d*x+c)*(b*x^4+a)^p,x,11,1/4*c*(b*x^4+a)^(p+1)/b/(p+1)+1/5*d*x^5*(b*x^4+a)^p*hypergeom([5/4, -p],[9/4],-b*x^4/a)/((1+b*x^4/a)^p)+1/6*e*x^6*(b*x^4+a)^p*hypergeom([3/2, -p],[5/2],-b*x^4/a)/((1+b*x^4/a)^p)+1/7*f*x^7*(b*x^4+a)^p*hypergeom([7/4, -p],[11/4],-b*x^4/a)/((1+b*x^4/a)^p),1]]: