lst:=[[(b*x^2+a)*(d*x^2+c)^4,x,2,a*c^4*x+1/3*c^3*(4*a*d+b*c)*x^3+2/5*c^2*d*(3*a*d+2*b*c)*x^5+2/7*c*d^2*(2*a*d+3*b*c)*x^7+1/9*d^3*(a*d+4*b*c)*x^9+1/11*b*d^4*x^11,1],
[(b*x^2+a)*(d*x^2+c)^3,x,2,a*c^3*x+1/3*c^2*(3*a*d+b*c)*x^3+3/5*c*d*(a*d+b*c)*x^5+1/7*d^2*(a*d+3*b*c)*x^7+1/9*b*d^3*x^9,1],
[(b*x^2+a)*(d*x^2+c)^2,x,2,a*c^2*x+1/3*c*(2*a*d+b*c)*x^3+1/5*d*(a*d+2*b*c)*x^5+1/7*b*d^2*x^7,1],
[(b*x^2+a)*(d*x^2+c),x,2,a*c*x+1/3*(a*d+b*c)*x^3+1/5*b*d*x^5,1],
[(b*x^2+a)/(d*x^2+c),x,2,b*x/d-(-a*d+b*c)*arctan(sqrt(d)*x/sqrt(c))/sqrt(c)/d^(3/2),1],
[(b*x^2+a)/(d*x^2+c)^2,x,2,-1/2*(-a*d+b*c)*x/c/d/(d*x^2+c)+1/2*(a*d+b*c)*arctan(sqrt(d)*x/sqrt(c))/c^(3/2)/d^(3/2),1],
[(b*x^2+a)/(d*x^2+c)^3,x,3,-1/4*(-a*d+b*c)*x/c/d/(d*x^2+c)^2+1/8*(3*a*d+b*c)*x/c^2/d/(d*x^2+c)+1/8*(3*a*d+b*c)*arctan(sqrt(d)*x/sqrt(c))/c^(5/2)/d^(3/2),1],
[(b*x^2+a)^2*(d*x^2+c)^3,x,2,a^2*c^3*x+1/3*a*c^2*(3*a*d+2*b*c)*x^3+1/5*c*(3*a^2*d^2+6*a*b*c*d+b^2*c^2)*x^5+1/7*d*(a^2*d^2+6*a*b*c*d+3*b^2*c^2)*x^7+1/9*b*d^2*(2*a*d+3*b*c)*x^9+1/11*b^2*d^3*x^11,1],
[(b*x^2+a)^2*(d*x^2+c)^2,x,2,a^2*c^2*x+2/3*a*c*(a*d+b*c)*x^3+1/5*(a^2*d^2+4*a*b*c*d+b^2*c^2)*x^5+2/7*b*d*(a*d+b*c)*x^7+1/9*b^2*d^2*x^9,1],
[(b*x^2+a)^2*(d*x^2+c),x,2,a^2*c*x+1/3*a*(a*d+2*b*c)*x^3+1/5*b*(2*a*d+b*c)*x^5+1/7*b^2*d*x^7,1],
[(b*x^2+a)^2/(d*x^2+c),x,3,-b*(-2*a*d+b*c)*x/d^2+1/3*b^2*x^3/d+(-a*d+b*c)^2*arctan(sqrt(d)*x/sqrt(c))/sqrt(c)/d^(5/2),1],
[(b*x^2+a)^2/(d*x^2+c)^2,x,3,b^2*x/d^2+1/2*(-a*d+b*c)^2*x/c/d^2/(d*x^2+c)-1/2*(-a*d+b*c)*(a*d+3*b*c)*arctan(sqrt(d)*x/sqrt(c))/c^(3/2)/d^(5/2),1],
[(b*x^2+a)^2/(d*x^2+c)^3,x,3,1/4*(-a*d+b*c)^2*x/c/d^2/(d*x^2+c)^2-1/8*(-a*d+b*c)*(3*a*d+5*b*c)*x/c^2/d^2/(d*x^2+c)+1/8*(3*a^2*d^2+2*a*b*c*d+3*b^2*c^2)*arctan(sqrt(d)*x/sqrt(c))/c^(5/2)/d^(5/2),1],
[(b*x^2+a)^3*(d*x^2+c)^3,x,2,a^3*c^3*x+a^2*c^2*(a*d+b*c)*x^3+3/5*a*c*(a^2*d^2+3*a*b*c*d+b^2*c^2)*x^5+1/7*(a*d+b*c)*(a^2*d^2+8*a*b*c*d+b^2*c^2)*x^7+1/3*b*d*(a^2*d^2+3*a*b*c*d+b^2*c^2)*x^9+3/11*b^2*d^2*(a*d+b*c)*x^11+1/13*b^3*d^3*x^13,1],
[(b*x^2+a)^3*(d*x^2+c)^2,x,2,a^3*c^2*x+1/3*a^2*c*(2*a*d+3*b*c)*x^3+1/5*a*(a^2*d^2+6*a*b*c*d+3*b^2*c^2)*x^5+1/7*b*(3*a^2*d^2+6*a*b*c*d+b^2*c^2)*x^7+1/9*b^2*d*(3*a*d+2*b*c)*x^9+1/11*b^3*d^2*x^11,1],
[(b*x^2+a)^3*(d*x^2+c),x,2,a^3*c*x+1/3*a^2*(a*d+3*b*c)*x^3+3/5*a*b*(a*d+b*c)*x^5+1/7*b^2*(3*a*d+b*c)*x^7+1/9*b^3*d*x^9,1],
[(b*x^2+a)^3/(d*x^2+c),x,3,b*(3*a^2*d^2-3*a*b*c*d+b^2*c^2)*x/d^3-1/3*b^2*(-3*a*d+b*c)*x^3/d^2+1/5*b^3*x^5/d-(-a*d+b*c)^3*arctan(sqrt(d)*x/sqrt(c))/sqrt(c)/d^(7/2),1],
[(b*x^2+a)^3/(d*x^2+c)^2,x,4,-b^2*(-3*a*d+2*b*c)*x/d^3+1/3*b^3*x^3/d^2-1/2*(-a*d+b*c)^3*x/c/d^3/(d*x^2+c)+1/2*(-a*d+b*c)^2*(a*d+5*b*c)*arctan(sqrt(d)*x/sqrt(c))/c^(3/2)/d^(7/2),1],
[(b*x^2+a)^3/(d*x^2+c)^3,x,4,b^3*x/d^3-1/4*(-a*d+b*c)^3*x/c/d^3/(d*x^2+c)^2+3/8*(-a*d+b*c)^2*(a*d+3*b*c)*x/c^2/d^3/(d*x^2+c)-3/8*(-a*d+b*c)*(4*b^2*c^2+(a*d+b*c)^2)*arctan(sqrt(d)*x/sqrt(c))/c^(5/2)/d^(7/2),1],
[(d*x^2+c)^4/(b*x^2+a),x,3,d*(-a*d+2*b*c)*(a^2*d^2-2*a*b*c*d+2*b^2*c^2)*x/b^4+1/3*d^2*(a^2*d^2-4*a*b*c*d+6*b^2*c^2)*x^3/b^3+1/5*d^3*(-a*d+4*b*c)*x^5/b^2+1/7*d^4*x^7/b+(-a*d+b*c)^4*arctan(sqrt(b)*x/sqrt(a))/sqrt(a)/b^(9/2),1],
[(d*x^2+c)^3/(b*x^2+a),x,3,d*(a^2*d^2-3*a*b*c*d+3*b^2*c^2)*x/b^3+1/3*d^2*(-a*d+3*b*c)*x^3/b^2+1/5*d^3*x^5/b+(-a*d+b*c)^3*arctan(sqrt(b)*x/sqrt(a))/sqrt(a)/b^(7/2),1],
[(d*x^2+c)^2/(b*x^2+a),x,3,d*(-a*d+2*b*c)*x/b^2+1/3*d^2*x^3/b+(-a*d+b*c)^2*arctan(sqrt(b)*x/sqrt(a))/sqrt(a)/b^(5/2),1],
[(d*x^2+c)/(b*x^2+a),x,2,d*x/b+(-a*d+b*c)*arctan(sqrt(b)*x/sqrt(a))/sqrt(a)/b^(3/2),1],
[1/(b*x^2+a)/(d*x^2+c),x,3,sqrt(b)*arctan(sqrt(b)*x/sqrt(a))/sqrt(a)/(-a*d+b*c)-sqrt(d)*arctan(sqrt(d)*x/sqrt(c))/sqrt(c)/(-a*d+b*c),1],
[1/(b*x^2+a)/(d*x^2+c)^2,x,4,-1/2*d*x/c/(-a*d+b*c)/(d*x^2+c)+b^(3/2)*arctan(sqrt(b)*x/sqrt(a))/sqrt(a)/(-a*d+b*c)^2-1/2*sqrt(d)*(-a*d+3*b*c)*arctan(sqrt(d)*x/sqrt(c))/c^(3/2)/(-a*d+b*c)^2,1],
[1/(b*x^2+a)/(d*x^2+c)^3,x,5,-1/4*d*x/c/(-a*d+b*c)/(d*x^2+c)^2-1/8*d*(-3*a*d+7*b*c)*x/c^2/(-a*d+b*c)^2/(d*x^2+c)+b^(5/2)*arctan(sqrt(b)*x/sqrt(a))/sqrt(a)/(-a*d+b*c)^3-1/8*sqrt(d)*(3*a^2*d^2-10*a*b*c*d+15*b^2*c^2)*arctan(sqrt(d)*x/sqrt(c))/c^(5/2)/(-a*d+b*c)^3,1],
[(d*x^2+c)^5/(b*x^2+a)^2,x,4,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+1/3*d^3*(3*a^2*d^2-10*a*b*c*d+10*b^2*c^2)*x^3/b^4+1/5*d^4*(-2*a*d+5*b*c)*x^5/b^3+1/7*d^5*x^7/b^2+1/2*(-a*d+b*c)^5*x/a/b^5/(b*x^2+a)+1/2*(-a*d+b*c)^4*(9*a*d+b*c)*arctan(sqrt(b)*x/sqrt(a))/a^(3/2)/b^(11/2),1],
[(d*x^2+c)^4/(b*x^2+a)^2,x,4,d^2*(3*a^2*d^2-8*a*b*c*d+6*b^2*c^2)*x/b^4+2/3*d^3*(-a*d+2*b*c)*x^3/b^3+1/5*d^4*x^5/b^2+1/2*(-a*d+b*c)^4*x/a/b^4/(b*x^2+a)+1/2*(-a*d+b*c)^3*(7*a*d+b*c)*arctan(sqrt(b)*x/sqrt(a))/a^(3/2)/b^(9/2),1],
[(d*x^2+c)^3/(b*x^2+a)^2,x,4,d^2*(-2*a*d+3*b*c)*x/b^3+1/3*d^3*x^3/b^2+1/2*(-a*d+b*c)^3*x/a/b^3/(b*x^2+a)+1/2*(-a*d+b*c)^2*(5*a*d+b*c)*arctan(sqrt(b)*x/sqrt(a))/a^(3/2)/b^(7/2),1],
[(d*x^2+c)^2/(b*x^2+a)^2,x,3,d^2*x/b^2+1/2*(-a*d+b*c)^2*x/a/b^2/(b*x^2+a)+1/2*(-a*d+b*c)*(3*a*d+b*c)*arctan(sqrt(b)*x/sqrt(a))/a^(3/2)/b^(5/2),1],
[(d*x^2+c)/(b*x^2+a)^2,x,2,1/2*(-a*d+b*c)*x/a/b/(b*x^2+a)+1/2*(a*d+b*c)*arctan(sqrt(b)*x/sqrt(a))/a^(3/2)/b^(3/2),1],
[1/(b*x^2+a)^2/(d*x^2+c),x,4,1/2*b*x/a/(-a*d+b*c)/(b*x^2+a)+1/2*sqrt(b)*(-3*a*d+b*c)*arctan(sqrt(b)*x/sqrt(a))/a^(3/2)/(-a*d+b*c)^2+d^(3/2)*arctan(sqrt(d)*x/sqrt(c))/sqrt(c)/(-a*d+b*c)^2,1],
[1/(b*x^2+a)^2/(d*x^2+c)^2,x,5,1/2*d*(a*d+b*c)*x/a/c/(-a*d+b*c)^2/(d*x^2+c)+1/2*b*x/a/(-a*d+b*c)/(b*x^2+a)/(d*x^2+c)+1/2*b^(3/2)*(-5*a*d+b*c)*arctan(sqrt(b)*x/sqrt(a))/a^(3/2)/(-a*d+b*c)^3+1/2*d^(3/2)*(-a*d+5*b*c)*arctan(sqrt(d)*x/sqrt(c))/c^(3/2)/(-a*d+b*c)^3,1],
[1/(b*x^2+a)^2/(d*x^2+c)^3,x,6,1/4*d*(a*d+2*b*c)*x/a/c/(-a*d+b*c)^2/(d*x^2+c)^2+1/2*b*x/a/(-a*d+b*c)/(b*x^2+a)/(d*x^2+c)^2+1/8*d*(-a*d+4*b*c)*(3*a*d+b*c)*x/a/c^2/(-a*d+b*c)^3/(d*x^2+c)+1/2*b^(5/2)*(-7*a*d+b*c)*arctan(sqrt(b)*x/sqrt(a))/a^(3/2)/(-a*d+b*c)^4+1/8*d^(3/2)*(3*a^2*d^2-14*a*b*c*d+35*b^2*c^2)*arctan(sqrt(d)*x/sqrt(c))/c^(5/2)/(-a*d+b*c)^4,1],
[(d*x^2+c)^5/(b*x^2+a)^3,x,5,d^3*(6*a^2*d^2-15*a*b*c*d+10*b^2*c^2)*x/b^5+1/3*d^4*(-3*a*d+5*b*c)*x^3/b^4+1/5*d^5*x^5/b^3+1/4*(-a*d+b*c)^5*x/a/b^5/(b*x^2+a)^2+1/8*(-a*d+b*c)^4*(17*a*d+3*b*c)*x/a^2/b^5/(b*x^2+a)+1/8*(-a*d+b*c)^3*(63*a^2*d^2+14*a*b*c*d+3*b^2*c^2)*arctan(sqrt(b)*x/sqrt(a))/a^(5/2)/b^(11/2),1],
[(d*x^2+c)^4/(b*x^2+a)^3,x,5,d^3*(-3*a*d+4*b*c)*x/b^4+1/3*d^4*x^3/b^3+1/4*(-a*d+b*c)^4*x/a/b^4/(b*x^2+a)^2+1/8*(-a*d+b*c)^3*(13*a*d+3*b*c)*x/a^2/b^4/(b*x^2+a)+1/8*(-a*d+b*c)^2*(35*a^2*d^2+10*a*b*c*d+3*b^2*c^2)*arctan(sqrt(b)*x/sqrt(a))/a^(5/2)/b^(9/2),1],
[(d*x^2+c)^3/(b*x^2+a)^3,x,4,d^3*x/b^3+1/4*(-a*d+b*c)^3*x/a/b^3/(b*x^2+a)^2+3/8*(-a*d+b*c)^2*(3*a*d+b*c)*x/a^2/b^3/(b*x^2+a)+3/8*(-a*d+b*c)*(4*a^2*d^2+(a*d+b*c)^2)*arctan(sqrt(b)*x/sqrt(a))/a^(5/2)/b^(7/2),1],
[(d*x^2+c)^2/(b*x^2+a)^3,x,3,1/4*(-a*d+b*c)^2*x/a/b^2/(b*x^2+a)^2+1/8*(-a*d+b*c)*(5*a*d+3*b*c)*x/a^2/b^2/(b*x^2+a)+1/8*(3*a^2*d^2+2*a*b*c*d+3*b^2*c^2)*arctan(sqrt(b)*x/sqrt(a))/a^(5/2)/b^(5/2),1],
[(d*x^2+c)/(b*x^2+a)^3,x,3,1/4*(-a*d+b*c)*x/a/b/(b*x^2+a)^2+1/8*(a*d+3*b*c)*x/a^2/b/(b*x^2+a)+1/8*(a*d+3*b*c)*arctan(sqrt(b)*x/sqrt(a))/a^(5/2)/b^(3/2),1],
[1/(b*x^2+a)^3/(d*x^2+c),x,5,1/4*b*x/a/(-a*d+b*c)/(b*x^2+a)^2+1/8*b*(-7*a*d+3*b*c)*x/a^2/(-a*d+b*c)^2/(b*x^2+a)+1/8*sqrt(b)*(15*a^2*d^2-10*a*b*c*d+3*b^2*c^2)*arctan(sqrt(b)*x/sqrt(a))/a^(5/2)/(-a*d+b*c)^3-d^(5/2)*arctan(sqrt(d)*x/sqrt(c))/sqrt(c)/(-a*d+b*c)^3,1],
[1/(b*x^2+a)^3/(d*x^2+c)^2,x,6,1/8*d*(-4*a*d+b*c)*(a*d+3*b*c)*x/a^2/c/(-a*d+b*c)^3/(d*x^2+c)+1/4*b*x/a/(-a*d+b*c)/(b*x^2+a)^2/(d*x^2+c)+3/8*b*(-3*a*d+b*c)*x/a^2/(-a*d+b*c)^2/(b*x^2+a)/(d*x^2+c)+1/8*b^(3/2)*(35*a^2*d^2-14*a*b*c*d+3*b^2*c^2)*arctan(sqrt(b)*x/sqrt(a))/a^(5/2)/(-a*d+b*c)^4-1/2*d^(5/2)*(-a*d+7*b*c)*arctan(sqrt(d)*x/sqrt(c))/c^(3/2)/(-a*d+b*c)^4,1],
[1/(b*x^2+a)^3/(d*x^2+c)^3,x,7,1/8*d*(-2*a^2*d^2-13*a*b*c*d+3*b^2*c^2)*x/a^2/c/(-a*d+b*c)^3/(d*x^2+c)^2+1/4*b*x/a/(-a*d+b*c)/(b*x^2+a)^2/(d*x^2+c)^2+1/8*b*(-11*a*d+3*b*c)*x/a^2/(-a*d+b*c)^2/(b*x^2+a)/(d*x^2+c)^2+3/8*d*(a*d+b*c)*(a^2*d^2-6*a*b*c*d+b^2*c^2)*x/a^2/c^2/(-a*d+b*c)^4/(d*x^2+c)+3/8*b^(5/2)*(21*a^2*d^2-6*a*b*c*d+b^2*c^2)*arctan(sqrt(b)*x/sqrt(a))/a^(5/2)/(-a*d+b*c)^5-3/8*d^(5/2)*(a^2*d^2-6*a*b*c*d+21*b^2*c^2)*arctan(sqrt(d)*x/sqrt(c))/c^(5/2)/(-a*d+b*c)^5,1],
[(x^2+3)/(x^2-3),x,2,x-2*sqrt(3)*arctanh(x/sqrt(3)),1],
[(x^2-1)/(x^2+1),x,2,x-2*arctan(x),1],
[(x^2-1)^3/(x^2+1)^4,x,3,-4/3*x/(x^2+1)^3+4/3*x/(x^2+1)^2-x/(x^2+1),1],
[(x^2-1)^4/(x^2+1)^5,x,5,2*x/(x^2+1)^4-3*x/(x^2+1)^3+9/4*x/(x^2+1)^2-5*x/(8*x^2+8)+3/8*arctan(x),1],
[(b*x^2+a)/(x^2+1),x,2,b*x+(a-b)*arctan(x),1],
[(b*x^2+a)/(-x^2+1),x,2,-b*x+(a+b)*arctanh(x),1],
[(x^2+1)/(x^2-1)^2,x,1,x/(-x^2+1),1],
[(-x^2+1)/(x^2+1)^2,x,1,x/(x^2+1),1],
[(2*x^2+3)/(x^2+1)^2,x,2,x/(2*x^2+2)+5/2*arctan(x),1],
[(x^2-2)/(x^2+1)^2,x,2,-3*x/(2*x^2+2)-1/2*arctan(x),1],
[(x^2+3)/(x^2+1)^2,x,2,x/(x^2+1)+2*arctan(x),1],
[(b*x^2+a)/(b*x^2-a)^2,x,1,x/(-b*x^2+a),1],
[(b*x^2+a)/(-b*x^2+a)^2,x,1,x/(-b*x^2+a),1],
[(B*x^2+A)/(-b*x^2+a),x,2,-B*x/b+(A*b+B*a)*arctanh(sqrt(b)*x/sqrt(a))/sqrt(a)/b^(3/2),1],
[(x^2+1)/(x^2+16)^3,x,3,-15/64*x/(x^2+16)^2+19*x/(2048*x^2+32768)+19/8192*arctan(1/4*x),1],
[(-x^2+1)^2/(x^2-1)^2,x,2,x,1],
[sqrt(b*x^2+a)*(d*x^2+c)^3,x,6,1/128*(64*c^3-a*d*(5*a^2*d^2-24*a*b*c*d+48*b^2*c^2)/b^3)*x*sqrt(b*x^2+a)+1/64*d*(5*a^2*d^2-24*a*b*c*d+48*b^2*c^2)*x*(b*x^2+a)^(3/2)/b^3+1/48*d^2*(-5*a*d+24*b*c)*x^3*(b*x^2+a)^(3/2)/b^2+1/8*d^3*x^5*(b*x^2+a)^(3/2)/b+1/128*a*(64*b^3*c^3-a*d*(5*a^2*d^2-24*a*b*c*d+48*b^2*c^2))*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(7/2),1],
[sqrt(b*x^2+a)*(d*x^2+c)^2,x,5,1/16*(a^2*d^2-4*a*b*c*d+8*b^2*c^2)*x*sqrt(b*x^2+a)/b^2+1/8*d*(-a*d+4*b*c)*x*(b*x^2+a)^(3/2)/b^2+1/6*d^2*x^3*(b*x^2+a)^(3/2)/b+1/16*a*(a^2*d^2-4*a*b*c*d+8*b^2*c^2)*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(5/2),1],
[sqrt(b*x^2+a)*(d*x^2+c),x,4,1/8*(-a*d+4*b*c)*x*sqrt(b*x^2+a)/b+1/4*d*x*(b*x^2+a)^(3/2)/b+1/8*a*(-a*d+4*b*c)*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(3/2),1],
[sqrt(b*x^2+a),x,3,1/2*x*sqrt(b*x^2+a)+1/2*a*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/sqrt(b),1],
[sqrt(b*x^2+a)/(d*x^2+c),x,5,sqrt(b)*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/d-sqrt(-a*d+b*c)*arctanh(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))/sqrt(c)/d,1],
[sqrt(b*x^2+a)/(d*x^2+c)^2,x,3,1/2*x*sqrt(b*x^2+a)/c/(d*x^2+c)+1/2*a*arctanh(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))/c^(3/2)/sqrt(-a*d+b*c),1],
[sqrt(b*x^2+a)/(d*x^2+c)^3,x,4,1/4*x*sqrt(b*x^2+a)/c/(d*x^2+c)^2+1/8*(-3*a*d+2*b*c)*x*sqrt(b*x^2+a)/c^2/(-a*d+b*c)/(d*x^2+c)+1/8*a*(-3*a*d+4*b*c)*arctanh(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))/c^(5/2)/(-a*d+b*c)^(3/2),1],
[sqrt(b*x^2+a)/(d*x^2+c)^4,x,5,1/6*x*sqrt(b*x^2+a)/c/(d*x^2+c)^3+1/24*(-5*a*d+4*b*c)*x*sqrt(b*x^2+a)/c^2/(-a*d+b*c)/(d*x^2+c)^2+1/48*(-5*a*d+2*b*c)*(-3*a*d+4*b*c)*x*sqrt(b*x^2+a)/c^3/(-a*d+b*c)^2/(d*x^2+c)+1/16*a*(5*a^2*d^2-12*a*b*c*d+8*b^2*c^2)*arctanh(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))/c^(7/2)/(-a*d+b*c)^(5/2),1],
[(b*x^2+a)^(3/2)*(d*x^2+c)^3,x,7,3/256*a*(-a*d+4*b*c)*(a^2*d^2-2*a*b*c*d+8*b^2*c^2)*x*sqrt(b*x^2+a)/b^3+1/128*(-a*d+4*b*c)*(a^2*d^2-2*a*b*c*d+8*b^2*c^2)*x*(b*x^2+a)^(3/2)/b^3+1/32*d*(a^2*d^2-6*a*b*c*d+16*b^2*c^2)*x*(b*x^2+a)^(5/2)/b^3+1/16*d^2*(-a*d+6*b*c)*x^3*(b*x^2+a)^(5/2)/b^2+1/10*d^3*x^5*(b*x^2+a)^(5/2)/b+3/256*a^2*(-a*d+4*b*c)*(a^2*d^2-2*a*b*c*d+8*b^2*c^2)*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(7/2),1],
[(b*x^2+a)^(3/2)*(d*x^2+c)^2,x,6,1/128*a*(3*a^2*d^2-16*a*b*c*d+48*b^2*c^2)*x*sqrt(b*x^2+a)/b^2+1/192*(48*c^2-a*d*(-3*a*d+16*b*c)/b^2)*x*(b*x^2+a)^(3/2)+1/48*d*(-3*a*d+16*b*c)*x*(b*x^2+a)^(5/2)/b^2+1/8*d^2*x^3*(b*x^2+a)^(5/2)/b+1/128*a^2*(3*a^2*d^2-16*a*b*c*d+48*b^2*c^2)*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(5/2),1],
[(b*x^2+a)^(3/2)*(d*x^2+c),x,5,1/16*a*(-a*d+6*b*c)*x*sqrt(b*x^2+a)/b+1/24*(-a*d+6*b*c)*x*(b*x^2+a)^(3/2)/b+1/6*d*x*(b*x^2+a)^(5/2)/b+1/16*a^2*(-a*d+6*b*c)*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(3/2),1],
[(b*x^2+a)^(3/2),x,4,3/8*a*x*sqrt(b*x^2+a)+1/4*x*(b*x^2+a)^(3/2)+3/8*a^2*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/sqrt(b),1],
[(b*x^2+a)^(3/2)/(d*x^2+c),x,6,1/2*b*x*sqrt(b*x^2+a)/d-1/2*sqrt(b)*(-3*a*d+2*b*c)*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/d^2+(-a*d+b*c)^(3/2)*arctanh(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))/sqrt(c)/d^2,1],
[(b*x^2+a)^(3/2)/(d*x^2+c)^2,x,6,-1/2*(-a*d+b*c)*x*sqrt(b*x^2+a)/c/d/(d*x^2+c)+b^(3/2)*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/d^2-1/2*sqrt(-a*d+b*c)*(a*d+2*b*c)*arctanh(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))/c^(3/2)/d^2,1],
[(b*x^2+a)^(3/2)/(d*x^2+c)^3,x,4,1/4*x*(b*x^2+a)^(3/2)/c/(d*x^2+c)^2+3/8*a*x*sqrt(b*x^2+a)/c^2/(d*x^2+c)+3/8*a^2*arctanh(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))/c^(5/2)/sqrt(-a*d+b*c),1],
[(b*x^2+a)^(3/2)/(d*x^2+c)^4,x,5,-1/6*d*x*(b*x^2+a)^(5/2)/c/(-a*d+b*c)/(d*x^2+c)^3+1/24*(-5*a*d+6*b*c)*x*(b*x^2+a)^(3/2)/c^2/(-a*d+b*c)/(d*x^2+c)^2+1/16*a*(-5*a*d+6*b*c)*x*sqrt(b*x^2+a)/c^3/(-a*d+b*c)/(d*x^2+c)+1/16*a^2*(-5*a*d+6*b*c)*arctanh(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))/c^(7/2)/(-a*d+b*c)^(3/2),1],
[(b*x^2+a)^(3/2)/(d*x^2+c)^5,x,6,-1/8*(-a*d+b*c)*x*sqrt(b*x^2+a)/c/d/(d*x^2+c)^4+1/48*(7*a*d+2*b*c)*x*sqrt(b*x^2+a)/c^2/d/(d*x^2+c)^3+1/192*(-35*a^2*d^2+24*a*b*c*d+8*b^2*c^2)*x*sqrt(b*x^2+a)/c^3/d/(-a*d+b*c)/(d*x^2+c)^2+1/384*(105*a^3*d^3-170*a^2*b*c*d^2+40*a*b^2*c^2*d+16*b^3*c^3)*x*sqrt(b*x^2+a)/c^4/d/(-a*d+b*c)^2/(d*x^2+c)+1/128*a^2*(35*a^2*d^2-80*a*b*c*d+48*b^2*c^2)*arctanh(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))/c^(9/2)/(-a*d+b*c)^(5/2),1],
[(b*x^2+a)^(5/2)*(d*x^2+c)^3,x,8,1/1024*a^2*(320*b^3*c^3-a*d*(5*a^2*d^2-36*a*b*c*d+120*b^2*c^2))*x*sqrt(b*x^2+a)/b^3+1/1536*a*(320*b^3*c^3-a*d*(5*a^2*d^2-36*a*b*c*d+120*b^2*c^2))*x*(b*x^2+a)^(3/2)/b^3+1/1920*(320*c^3-a*d*(5*a^2*d^2-36*a*b*c*d+120*b^2*c^2)/b^3)*x*(b*x^2+a)^(5/2)+1/320*d*(5*a^2*d^2-36*a*b*c*d+120*b^2*c^2)*x*(b*x^2+a)^(7/2)/b^3+1/120*d^2*(-5*a*d+36*b*c)*x^3*(b*x^2+a)^(7/2)/b^2+1/12*d^3*x^5*(b*x^2+a)^(7/2)/b+1/1024*a^3*(320*b^3*c^3-a*d*(5*a^2*d^2-36*a*b*c*d+120*b^2*c^2))*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(7/2),1],
[(b*x^2+a)^(5/2)*(d*x^2+c)^2,x,7,1/256*a^2*(3*a^2*d^2-20*a*b*c*d+80*b^2*c^2)*x*sqrt(b*x^2+a)/b^2+1/384*a*(3*a^2*d^2-20*a*b*c*d+80*b^2*c^2)*x*(b*x^2+a)^(3/2)/b^2+1/480*(80*c^2-a*d*(-3*a*d+20*b*c)/b^2)*x*(b*x^2+a)^(5/2)+1/80*d*(-3*a*d+20*b*c)*x*(b*x^2+a)^(7/2)/b^2+1/10*d^2*x^3*(b*x^2+a)^(7/2)/b+1/256*a^3*(3*a^2*d^2-20*a*b*c*d+80*b^2*c^2)*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(5/2),1],
[(b*x^2+a)^(5/2)*(d*x^2+c),x,6,5/128*a^2*(-a*d+8*b*c)*x*sqrt(b*x^2+a)/b+5/192*a*(-a*d+8*b*c)*x*(b*x^2+a)^(3/2)/b+1/48*(-a*d+8*b*c)*x*(b*x^2+a)^(5/2)/b+1/8*d*x*(b*x^2+a)^(7/2)/b+5/128*a^3*(-a*d+8*b*c)*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(3/2),1],
[(b*x^2+a)^(5/2),x,5,5/16*a^2*x*sqrt(b*x^2+a)+5/24*a*x*(b*x^2+a)^(3/2)+1/6*x*(b*x^2+a)^(5/2)+5/16*a^3*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/sqrt(b),1],
[(b*x^2+a)^(5/2)/(d*x^2+c),x,7,-1/8*b*(-7*a*d+4*b*c)*x*sqrt(b*x^2+a)/d^2+1/4*b*x*(b*x^2+a)^(3/2)/d+1/8*sqrt(b)*(15*a^2*d^2-20*a*b*c*d+8*b^2*c^2)*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/d^3-(-a*d+b*c)^(5/2)*arctanh(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))/sqrt(c)/d^3,1],
[(b*x^2+a)^(5/2)/(d*x^2+c)^2,x,7,1/2*b*(-a*d+2*b*c)*x*sqrt(b*x^2+a)/c/d^2-1/2*(-a*d+b*c)*x*(b*x^2+a)^(3/2)/c/d/(d*x^2+c)-1/2*b^(3/2)*(-5*a*d+4*b*c)*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/d^3+1/2*(-a*d+b*c)^(3/2)*(a*d+4*b*c)*arctanh(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))/c^(3/2)/d^3,1],
[(b*x^2+a)^(5/2)/(d*x^2+c)^3,x,7,-1/4*(-a*d+b*c)*x*(b*x^2+a)^(3/2)/c/d/(d*x^2+c)^2-1/8*(-a*d+b*c)*(3*a*d+4*b*c)*x*sqrt(b*x^2+a)/c^2/d^2/(d*x^2+c)+b^(5/2)*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/d^3-1/8*sqrt(-a*d+b*c)*(3*a^2*d^2+4*a*b*c*d+8*b^2*c^2)*arctanh(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))/c^(5/2)/d^3,1],
[(b*x^2+a)^(5/2)/(d*x^2+c)^4,x,5,1/6*x*(b*x^2+a)^(5/2)/c/(d*x^2+c)^3+5/24*a*x*(b*x^2+a)^(3/2)/c^2/(d*x^2+c)^2+5/16*a^2*x*sqrt(b*x^2+a)/c^3/(d*x^2+c)+5/16*a^3*arctanh(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))/c^(7/2)/sqrt(-a*d+b*c),1],
[(b*x^2+a)^(5/2)/(d*x^2+c)^5,x,6,-1/8*d*x*(b*x^2+a)^(7/2)/c/(-a*d+b*c)/(d*x^2+c)^4+1/48*(-7*a*d+8*b*c)*x*(b*x^2+a)^(5/2)/c^2/(-a*d+b*c)/(d*x^2+c)^3+5/192*a*(-7*a*d+8*b*c)*x*(b*x^2+a)^(3/2)/c^3/(-a*d+b*c)/(d*x^2+c)^2+5/128*a^2*(-7*a*d+8*b*c)*x*sqrt(b*x^2+a)/c^4/(-a*d+b*c)/(d*x^2+c)+5/128*a^3*(-7*a*d+8*b*c)*arctanh(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))/c^(9/2)/(-a*d+b*c)^(3/2),1],
[sqrt(-x^2+1)/(x^2+1),x,4,-arcsin(x)+sqrt(2)*arctan(sqrt(2)*x/sqrt(-x^2+1)),1],
[sqrt(x^2+1)/(x^2-1),x,4,arcsinh(x)-sqrt(2)*arctanh(sqrt(2)*x/sqrt(x^2+1)),1],
[sqrt(-x^2+1)/(2*x^2-1),x,4,-1/2*arcsin(x)-1/2*arctanh(x/sqrt(-x^2+1)),1],
[(d*x^2+c)^3/sqrt(b*x^2+a),x,5,1/16*d*(5*a^2*d^2-18*a*b*c*d+24*b^2*c^2)*x*sqrt(b*x^2+a)/b^3+1/24*d^2*(-5*a*d+18*b*c)*x^3*sqrt(b*x^2+a)/b^2+1/6*d^3*x^5*sqrt(b*x^2+a)/b+1/16*(-a*d+2*b*c)*(5*a^2*d^2-8*a*b*c*d+8*b^2*c^2)*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(7/2),1],
[(d*x^2+c)^2/sqrt(b*x^2+a),x,4,1/8*d*(-3*a*d+8*b*c)*x*sqrt(b*x^2+a)/b^2+1/4*d^2*x^3*sqrt(b*x^2+a)/b+1/8*(3*a^2*d^2-8*a*b*c*d+8*b^2*c^2)*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(5/2),1],
[(d*x^2+c)/sqrt(b*x^2+a),x,3,1/2*d*x*sqrt(b*x^2+a)/b+1/2*(-a*d+2*b*c)*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(3/2),1],
[1/sqrt(b*x^2+a),x,2,arctanh(sqrt(b)*x/sqrt(b*x^2+a))/sqrt(b),1],
[1/sqrt(b*x^2+a)/(d*x^2+c),x,2,arctanh(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))/sqrt(c)/sqrt(-a*d+b*c),1],
[1/sqrt(b*x^2+a)/(d*x^2+c)^2,x,3,-1/2*d*x*sqrt(b*x^2+a)/c/(-a*d+b*c)/(d*x^2+c)+1/2*(-a*d+2*b*c)*arctanh(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))/c^(3/2)/(-a*d+b*c)^(3/2),1],
[1/sqrt(b*x^2+a)/(d*x^2+c)^3,x,4,-1/4*d*x*sqrt(b*x^2+a)/c/(-a*d+b*c)/(d*x^2+c)^2-3/8*d*(-a*d+2*b*c)*x*sqrt(b*x^2+a)/c^2/(-a*d+b*c)^2/(d*x^2+c)+1/8*(3*a^2*d^2-8*a*b*c*d+8*b^2*c^2)*arctanh(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))/c^(5/2)/(-a*d+b*c)^(5/2),1],
[(d*x^2+c)^4/(b*x^2+a)^(3/2),x,6,(-a*d+b*c)^4*x/a/b^4/sqrt(b*x^2+a)+1/16*d^2*(19*a^2*d^2-56*a*b*c*d+48*b^2*c^2)*x*sqrt(b*x^2+a)/b^4+1/24*d^3*(-11*a*d+24*b*c)*x^3*sqrt(b*x^2+a)/b^3+1/6*d^4*x^5*sqrt(b*x^2+a)/b^2+1/16*d*(-35*a^3*d^3+120*a^2*b*c*d^2-144*a*b^2*c^2*d+64*b^3*c^3)*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(9/2),1],
[(d*x^2+c)^3/(b*x^2+a)^(3/2),x,5,(-a*d+b*c)^3*x/a/b^3/sqrt(b*x^2+a)+1/8*d^2*(-7*a*d+12*b*c)*x*sqrt(b*x^2+a)/b^3+1/4*d^3*x^3*sqrt(b*x^2+a)/b^2+3/8*d*(5*a^2*d^2-12*a*b*c*d+8*b^2*c^2)*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(7/2),1],
[(d*x^2+c)^2/(b*x^2+a)^(3/2),x,4,(-a*d+b*c)^2*x/a/b^2/sqrt(b*x^2+a)+1/2*d^2*x*sqrt(b*x^2+a)/b^2+1/2*d*(-3*a*d+4*b*c)*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(5/2),1],
[(d*x^2+c)/(b*x^2+a)^(3/2),x,3,(-a*d+b*c)*x/a/b/sqrt(b*x^2+a)+d*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(3/2),1],
[1/(b*x^2+a)^(3/2),x,1,x/a/sqrt(b*x^2+a),1],
[1/(b*x^2+a)^(3/2)/(d*x^2+c),x,3,b*x/a/(-a*d+b*c)/sqrt(b*x^2+a)-d*arctanh(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))/sqrt(c)/(-a*d+b*c)^(3/2),1],
[1/(b*x^2+a)^(3/2)/(d*x^2+c)^2,x,4,1/2*b*(a*d+2*b*c)*x/a/c/(-a*d+b*c)^2/sqrt(b*x^2+a)-1/2*d*x/c/(-a*d+b*c)/sqrt(b*x^2+a)/(d*x^2+c)-1/2*d*(-a*d+4*b*c)*arctanh(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))/c^(3/2)/(-a*d+b*c)^(5/2),1],
[1/(b*x^2+a)^(3/2)/(d*x^2+c)^3,x,5,1/8*b*(-a*d+4*b*c)*(3*a*d+2*b*c)*x/a/c^2/(-a*d+b*c)^3/sqrt(b*x^2+a)-1/4*d*x/c/(-a*d+b*c)/sqrt(b*x^2+a)/(d*x^2+c)^2-1/8*d*(-3*a*d+8*b*c)*x/c^2/(-a*d+b*c)^2/sqrt(b*x^2+a)/(d*x^2+c)-3/8*d*(a^2*d^2-4*a*b*c*d+8*b^2*c^2)*arctanh(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))/c^(5/2)/(-a*d+b*c)^(7/2),1],
[(d*x^2+c)^4/(b*x^2+a)^(5/2),x,6,1/3*(-a*d+b*c)^4*x/a/b^4/(b*x^2+a)^(3/2)+2/3*(-a*d+b*c)^3*(5*a*d+b*c)*x/a^2/b^4/sqrt(b*x^2+a)+1/8*d^3*(-11*a*d+16*b*c)*x*sqrt(b*x^2+a)/b^4+1/4*d^4*x^3*sqrt(b*x^2+a)/b^3+1/8*d^2*(35*a^2*d^2-80*a*b*c*d+48*b^2*c^2)*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(9/2),1],
[(d*x^2+c)^3/(b*x^2+a)^(5/2),x,5,1/3*(-a*d+b*c)^3*x/a/b^3/(b*x^2+a)^(3/2)+1/3*(-a*d+b*c)^2*(7*a*d+2*b*c)*x/a^2/b^3/sqrt(b*x^2+a)+1/2*d^3*x*sqrt(b*x^2+a)/b^3+1/2*d^2*(-5*a*d+6*b*c)*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(7/2),1],
[(d*x^2+c)^2/(b*x^2+a)^(5/2),x,4,1/3*(-a*d+b*c)^2*x/a/b^2/(b*x^2+a)^(3/2)+2/3*(-a*d+b*c)*(2*a*d+b*c)*x/a^2/b^2/sqrt(b*x^2+a)+d^2*arctanh(sqrt(b)*x/sqrt(b*x^2+a))/b^(5/2),1],
[(d*x^2+c)/(b*x^2+a)^(5/2),x,2,1/3*(-a*d+b*c)*x/a/b/(b*x^2+a)^(3/2)+1/3*(a*d+2*b*c)*x/a^2/b/sqrt(b*x^2+a),1],
[1/(b*x^2+a)^(5/2),x,2,1/3*x/a/(b*x^2+a)^(3/2)+2/3*x/a^2/sqrt(b*x^2+a),1],
[1/(b*x^2+a)^(5/2)/(d*x^2+c),x,4,1/3*b*x/a/(-a*d+b*c)/(b*x^2+a)^(3/2)+1/3*b*(-5*a*d+2*b*c)*x/a^2/(-a*d+b*c)^2/sqrt(b*x^2+a)+d^2*arctanh(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))/sqrt(c)/(-a*d+b*c)^(5/2),1],
[1/(b*x^2+a)^(5/2)/(d*x^2+c)^2,x,5,1/6*b*(3*a*d+2*b*c)*x/a/c/(-a*d+b*c)^2/(b*x^2+a)^(3/2)+1/6*b*(-3*a^2*d^2-16*a*b*c*d+4*b^2*c^2)*x/a^2/c/(-a*d+b*c)^3/sqrt(b*x^2+a)-1/2*d*x/c/(-a*d+b*c)/(b*x^2+a)^(3/2)/(d*x^2+c)+1/2*d^2*(-a*d+6*b*c)*arctanh(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))/c^(3/2)/(-a*d+b*c)^(7/2),1],
[1/(b*x^2+a)^(5/2)/(d*x^2+c)^3,x,6,1/24*b*(-9*a^2*d^2+36*a*b*c*d+8*b^2*c^2)*x/a/c^2/(-a*d+b*c)^3/(b*x^2+a)^(3/2)+1/24*b*(9*a^3*d^3-42*a^2*b*c*d^2-88*a*b^2*c^2*d+16*b^3*c^3)*x/a^2/c^2/(-a*d+b*c)^4/sqrt(b*x^2+a)-1/4*d*x/c/(-a*d+b*c)/(b*x^2+a)^(3/2)/(d*x^2+c)^2-1/8*d*(-3*a*d+10*b*c)*x/c^2/(-a*d+b*c)^2/(b*x^2+a)^(3/2)/(d*x^2+c)+1/8*d^2*(3*a^2*d^2-16*a*b*c*d+48*b^2*c^2)*arctanh(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))/c^(5/2)/(-a*d+b*c)^(9/2),1],
[(b*x^2+a)^3/(d*x^2+c)^(11/2),x,5,-1/9*(-a*d+b*c)^3*x/c/d^3/(d*x^2+c)^(9/2)+1/63*(-a*d+b*c)^2*(8*a*d+19*b*c)*x/c^2/d^3/(d*x^2+c)^(7/2)-1/105*(-a*d+b*c)*(16*a^2*d^2+22*a*b*c*d+25*b^2*c^2)*x/c^3/d^3/(d*x^2+c)^(5/2)+1/315*(64*a^3*d^3+24*a^2*b*c*d^2+12*a*b^2*c^2*d+5*b^3*c^3)*x/c^4/d^3/(d*x^2+c)^(3/2)+2/315*(64*a^3*d^3+24*a^2*b*c*d^2+12*a*b^2*c^2*d+5*b^3*c^3)*x/c^5/d^3/sqrt(d*x^2+c),1],
[(b*x^2+a)^2/(d*x^2+c)^(9/2),x,4,1/7*(-a*d+b*c)^2*x/c/d^2/(d*x^2+c)^(7/2)-2/35*(-a*d+b*c)*(3*a*d+4*b*c)*x/c^2/d^2/(d*x^2+c)^(5/2)+1/105*(24*a^2*d^2+8*a*b*c*d+3*b^2*c^2)*x/c^3/d^2/(d*x^2+c)^(3/2)+2/105*(24*a^2*d^2+8*a*b*c*d+3*b^2*c^2)*x/c^4/d^2/sqrt(d*x^2+c),1],
[(b*x^2+a)/(d*x^2+c)^(7/2),x,3,-1/5*(-a*d+b*c)*x/c/d/(d*x^2+c)^(5/2)+1/15*(4*a*d+b*c)*x/c^2/d/(d*x^2+c)^(3/2)+2/15*(4*a*d+b*c)*x/c^3/d/sqrt(d*x^2+c),1],
[1/(d*x^2+c)^(5/2),x,2,1/3*x/c/(d*x^2+c)^(3/2)+2/3*x/c^2/sqrt(d*x^2+c),1],
[1/(b*x^2+a)/(d*x^2+c)^(3/2),x,3,-d*x/c/(-a*d+b*c)/sqrt(d*x^2+c)+b*arctan(sqrt(-a*d+b*c)*x/sqrt(a)/sqrt(d*x^2+c))/sqrt(a)/(-a*d+b*c)^(3/2),1],
[1/(b*x^2+a)^2/sqrt(d*x^2+c),x,3,1/2*b*x*sqrt(d*x^2+c)/a/(-a*d+b*c)/(b*x^2+a)+1/2*(-2*a*d+b*c)*arctan(sqrt(-a*d+b*c)*x/sqrt(a)/sqrt(d*x^2+c))/a^(3/2)/(-a*d+b*c)^(3/2),1],
[sqrt(d*x^2+c)/(b*x^2+a)^3,x,4,1/4*x*sqrt(d*x^2+c)/a/(b*x^2+a)^2+1/8*(-2*a*d+3*b*c)*x*sqrt(d*x^2+c)/a^2/(-a*d+b*c)/(b*x^2+a)+1/8*c*(-4*a*d+3*b*c)*arctan(sqrt(-a*d+b*c)*x/sqrt(a)/sqrt(d*x^2+c))/a^(5/2)/(-a*d+b*c)^(3/2),1],
[(d*x^2+c)^(3/2)/(b*x^2+a)^4,x,5,1/16*c*(-6*a*d+5*b*c)*x*sqrt(d*x^2+c)/a^3/(-a*d+b*c)/(b*x^2+a)+1/24*(-6*a*d+5*b*c)*x*(d*x^2+c)^(3/2)/a^2/(-a*d+b*c)/(b*x^2+a)^2+1/6*b*x*(d*x^2+c)^(5/2)/a/(-a*d+b*c)/(b*x^2+a)^3+1/16*c^2*(-6*a*d+5*b*c)*arctan(sqrt(-a*d+b*c)*x/sqrt(a)/sqrt(d*x^2+c))/a^(7/2)/(-a*d+b*c)^(3/2),1],
[1/(b*c/d+b*x^2)/sqrt(d*x^2+c),x,2,d*x/b/c/sqrt(d*x^2+c),1],
[1/sqrt(-x^2+1)/(x^2+1),x,2,arctan(sqrt(2)*x/sqrt(-x^2+1))/sqrt(2),1],
[1/(b*x^2+a)/sqrt(d*x^2+c),x,2,arctan(sqrt(-a*d+b*c)*x/sqrt(a)/sqrt(d*x^2+c))/sqrt(a)/sqrt(-a*d+b*c),1],
[(x^2-1)/(x^2+1)^(3/2),x,2,-2*x/sqrt(x^2+1)+arcsinh(x),1],
[sqrt(c^2*x^2-1)/(-c^2*d*x^2+d)^(5/2),x,3,1/2*x*sqrt(c^2*x^2-1)/d/(-c^2*d*x^2+d)^(3/2)+1/2*sqrt(c^2*x^2-1)*arctanh(c*x)/c/d^2/sqrt(-c^2*d*x^2+d),1],
[1/(c^2*x^2-1)^(3/2)/sqrt(-c^2*d*x^2+d),x,3,1/2*d*x*sqrt(c^2*x^2-1)/(-c^2*d*x^2+d)^(3/2)+1/2*sqrt(c^2*x^2-1)*arctanh(c*x)/c/sqrt(-c^2*d*x^2+d),1],
[1/sqrt(c^2*x^2-1)/(-c^2*d*x^2+d)^(3/2),x,3,-1/2*x*sqrt(c^2*x^2-1)/(-c^2*d*x^2+d)^(3/2)-1/2*sqrt(c^2*x^2-1)*arctanh(c*x)/c/d/sqrt(-c^2*d*x^2+d),1],
[sqrt(b*x^2+a)/sqrt(-b*x^2+a),x,2,a^(3/2)*sqrt(1-b^2*x^4/a^2)*EllipticE(sin(arcsin(sqrt(b)*x/sqrt(a))),sqrt(-1))/sqrt(b)/sqrt(-b*x^2+a)/sqrt(b*x^2+a),1],
[sqrt(-b*x^2+a)/sqrt(b*x^2+a),x,5,-a^(3/2)*sqrt(1-b^2*x^4/a^2)*EllipticE(sin(arcsin(sqrt(b)*x/sqrt(a))),sqrt(-1))/sqrt(b)/sqrt(-b*x^2+a)/sqrt(b*x^2+a)+2*a^(3/2)*sqrt(1-b^2*x^4/a^2)*InverseJacobiAM(arcsin(sqrt(b)*x/sqrt(a)),sqrt(-1))/sqrt(b)/sqrt(-b*x^2+a)/sqrt(b*x^2+a),1],
[(b*x^2+2)^(3/2)*(3*b*x^2-6)^(3/2),x,3,-24/7*sqrt(3)*x*sqrt(b*x^2-2)*sqrt(b*x^2+2)+3/7*sqrt(3)*x*(b*x^2-2)^(3/2)*(b*x^2+2)^(3/2)+96/7*sqrt(3)*InverseJacobiAM(arcsin(sqrt(2)*sqrt(b)*x/sqrt(b*x^2-2)),sqrt(1/2))/sqrt(b),1],
[sqrt(b*x^2+2)*sqrt(3*b*x^2-6),x,2,x*sqrt(b*x^2-2)*sqrt(b*x^2+2)/sqrt(3)-4*InverseJacobiAM(arcsin(sqrt(2)*sqrt(b)*x/sqrt(b*x^2-2)),sqrt(1/2))/sqrt(3)/sqrt(b),1],
[1/sqrt(b*x^2+2)/sqrt(3*b*x^2-6),x,1,1/2*InverseJacobiAM(arcsin(sqrt(2)*sqrt(b)*x/sqrt(b*x^2-2)),sqrt(1/2))/sqrt(3)/sqrt(b),1],
[1/(b*x^2+2)^(3/2)/(3*b*x^2-6)^(3/2),x,2,-1/24*x/sqrt(3)/sqrt(b*x^2-2)/sqrt(b*x^2+2)-1/48*InverseJacobiAM(arcsin(sqrt(2)*sqrt(b)*x/sqrt(b*x^2-2)),sqrt(1/2))/sqrt(3)/sqrt(b),1],
[1/(b*x^2+2)^(5/2)/(3*b*x^2-6)^(5/2),x,3,-1/216*x/sqrt(3)/(b*x^2-2)^(3/2)/(b*x^2+2)^(3/2)+5/1728*x/sqrt(3)/sqrt(b*x^2-2)/sqrt(b*x^2+2)+5/3456*InverseJacobiAM(arcsin(sqrt(2)*sqrt(b)*x/sqrt(b*x^2-2)),sqrt(1/2))/sqrt(3)/sqrt(b),1],
[1/sqrt(x^2-1)/sqrt(x^2+1),x,1,InverseJacobiAM(arcsin(sqrt(2)*x/sqrt(x^2-1)),sqrt(1/2))/sqrt(2),1],
[1/sqrt(a^2*x^2-1)/sqrt(a^2*x^2+1),x,1,InverseJacobiAM(arcsin(sqrt(2)*a*x/sqrt(a^2*x^2-1)),sqrt(1/2))/sqrt(2)/a,1],
[(b*x^2+a)^(3/2)*sqrt(d*x^2+c),x,6,-1/15*(-3*a^2*d^2-7*a*b*c*d+2*b^2*c^2)*x*sqrt(d*x^2+c)/d^2/sqrt(b*x^2+a)+1/15*(3*a*d+b*c)*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/d+1/5*x*(b*x^2+a)^(3/2)*sqrt(d*x^2+c)+1/15*sqrt(a)*(-3*a^2*d^2-7*a*b*c*d+2*b^2*c^2)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/sqrt(b)/d^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/15*a^(3/2)*(-9*a*d+b*c)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(b)/d/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[sqrt(b*x^2+a)*sqrt(d*x^2+c),x,5,1/3*(a*d+b*c)*x*sqrt(d*x^2+c)/d/sqrt(b*x^2+a)+1/3*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)-1/3*sqrt(a)*(a*d+b*c)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/sqrt(b)/d/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+2/3*a^(3/2)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(b)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[sqrt(d*x^2+c)/sqrt(b*x^2+a),x,2,x*sqrt(d*x^2+c)/sqrt(b*x^2+a)-sqrt(a)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/sqrt(b)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+sqrt(a)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(b)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[sqrt(d*x^2+c)/(b*x^2+a)^(3/2),x,1,sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/sqrt(a)/sqrt(b)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[sqrt(d*x^2+c)/(b*x^2+a)^(5/2),x,2,1/3*x*sqrt(d*x^2+c)/a/(b*x^2+a)^(3/2)+1/3*(-a*d+2*b*c)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/a^(3/2)/sqrt(b)/(-a*d+b*c)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/3*d*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(a)/sqrt(b)/(-a*d+b*c)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[sqrt(d*x^2+c)/(b*x^2+a)^(7/2),x,3,1/5*x*sqrt(d*x^2+c)/a/(b*x^2+a)^(5/2)+1/15*(-3*a*d+4*b*c)*x*sqrt(d*x^2+c)/a^2/(-a*d+b*c)/(b*x^2+a)^(3/2)+1/15*(3*a^2*d^2-13*a*b*c*d+8*b^2*c^2)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/a^(5/2)/sqrt(b)/(-a*d+b*c)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-2/15*d*(-3*a*d+2*b*c)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/a^(3/2)/sqrt(b)/(-a*d+b*c)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(b*x^2+a)^(3/2)*(d*x^2+c)^(3/2),x,7,-2/35*(a*d+b*c)*(a^2*d^2-6*a*b*c*d+b^2*c^2)*x*sqrt(d*x^2+c)/b/d^2/sqrt(b*x^2+a)+1/35*(9*a*c-2*b*c^2/d+a^2*d/b)*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)+3/35*(a*d+b*c)*x*sqrt(b*x^2+a)*(d*x^2+c)^(3/2)/d+1/7*x*(b*x^2+a)^(3/2)*(d*x^2+c)^(3/2)+2/35*sqrt(a)*(a*d+b*c)*(a^2*d^2-6*a*b*c*d+b^2*c^2)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/b^(3/2)/d^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/35*a^(3/2)*(a^2*d^2-18*a*b*c*d+b^2*c^2)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(3/2)/d/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[sqrt(b*x^2+a)*(d*x^2+c)^(3/2),x,6,1/15*(7*a*c+3*b*c^2/d-2*a^2*d/b)*x*sqrt(d*x^2+c)/sqrt(b*x^2+a)+1/15*(a*d+3*b*c)*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b+1/5*x*sqrt(b*x^2+a)*(d*x^2+c)^(3/2)-1/15*sqrt(a)*(-2*a^2*d^2+7*a*b*c*d+3*b^2*c^2)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/b^(3/2)/d/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/15*a^(3/2)*(-a*d+9*b*c)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(3/2)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(d*x^2+c)^(3/2)/sqrt(b*x^2+a),x,5,2/3*(-a*d+2*b*c)*x*sqrt(d*x^2+c)/b/sqrt(b*x^2+a)+1/3*d*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b-2/3*sqrt(a)*(-a*d+2*b*c)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/b^(3/2)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/3*sqrt(a)*(-a*d+3*b*c)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(3/2)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(d*x^2+c)^(3/2)/(b*x^2+a)^(3/2),x,2,d*x*sqrt(d*x^2+c)/b/sqrt(b*x^2+a)+(-2*a*d+b*c)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/sqrt(a)/b^(3/2)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+sqrt(a)*d*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(3/2)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(d*x^2+c)^(3/2)/(b*x^2+a)^(5/2),x,2,1/3*(-a*d+b*c)*x*sqrt(d*x^2+c)/a/b/(b*x^2+a)^(3/2)+2/3*(a*d+b*c)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/a^(3/2)/b^(3/2)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/3*d*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(a)/b^(3/2)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(d*x^2+c)^(3/2)/(b*x^2+a)^(7/2),x,3,1/5*(-a*d+b*c)*x*sqrt(d*x^2+c)/a/b/(b*x^2+a)^(5/2)+2/15*(a*d+2*b*c)*x*sqrt(d*x^2+c)/a^2/b/(b*x^2+a)^(3/2)+1/15*(-2*a^2*d^2-3*a*b*c*d+8*b^2*c^2)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/a^(5/2)/b^(3/2)/(-a*d+b*c)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/15*d*(-a*d+4*b*c)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/a^(3/2)/b^(3/2)/(-a*d+b*c)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(d*x^2+c)^(3/2)/(b*x^2+a)^(9/2),x,4,1/7*(-a*d+b*c)*x*sqrt(d*x^2+c)/a/b/(b*x^2+a)^(7/2)+2/35*(a*d+3*b*c)*x*sqrt(d*x^2+c)/a^2/b/(b*x^2+a)^(5/2)+1/35*(-2*a^2*d^2-5*a*b*c*d+8*b^2*c^2)*x*sqrt(d*x^2+c)/a^3/b/(-a*d+b*c)/(b*x^2+a)^(3/2)+2/35*(-a*d+2*b*c)*(-a^2*d^2-4*a*b*c*d+4*b^2*c^2)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/a^(7/2)/b^(3/2)/(-a*d+b*c)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/35*d*(a^2*d^2-11*a*b*c*d+8*b^2*c^2)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/a^(5/2)/b^(3/2)/(-a*d+b*c)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(b*x^2+a)^(3/2)*(d*x^2+c)^(5/2),x,8,-1/315*(-8*a^4*d^4+43*a^3*b*c*d^3-108*a^2*b^2*c^2*d^2-65*a*b^3*c^3*d+10*b^4*c^4)*x*sqrt(d*x^2+c)/b^2/d^2/sqrt(b*x^2+a)-2/315*(2*a^3*d^3-9*a^2*b*c*d^2-30*a*b^2*c^2*d+5*b^3*c^3)*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b^2/d+1/315*(55*a*c-10*b*c^2/d+3*a^2*d/b)*x*sqrt(b*x^2+a)*(d*x^2+c)^(3/2)+1/63*(3*a*d+5*b*c)*x*sqrt(b*x^2+a)*(d*x^2+c)^(5/2)/d+1/9*x*(b*x^2+a)^(3/2)*(d*x^2+c)^(5/2)+1/315*sqrt(a)*(-8*a^4*d^4+43*a^3*b*c*d^3-108*a^2*b^2*c^2*d^2-65*a*b^3*c^3*d+10*b^4*c^4)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/b^(5/2)/d^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/315*a^(3/2)*(-4*a^3*d^3+21*a^2*b*c*d^2-150*a*b^2*c^2*d+5*b^3*c^3)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(5/2)/d/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[sqrt(b*x^2+a)*(d*x^2+c)^(5/2),x,7,1/105*(8*a^3*d^3-33*a^2*b*c*d^2+58*a*b^2*c^2*d+15*b^3*c^3)*x*sqrt(d*x^2+c)/b^2/d/sqrt(b*x^2+a)+1/105*(-4*a^2*d^2+13*a*b*c*d+15*b^2*c^2)*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b^2+1/35*(a*d+5*b*c)*x*sqrt(b*x^2+a)*(d*x^2+c)^(3/2)/b+1/7*x*sqrt(b*x^2+a)*(d*x^2+c)^(5/2)-1/105*sqrt(a)*(8*a^3*d^3-33*a^2*b*c*d^2+58*a*b^2*c^2*d+15*b^3*c^3)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/b^(5/2)/d/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+4/105*a^(3/2)*(a^2*d^2-4*a*b*c*d+15*b^2*c^2)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(5/2)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(d*x^2+c)^(5/2)/sqrt(b*x^2+a),x,6,1/15*(8*a^2*d^2-23*a*b*c*d+23*b^2*c^2)*x*sqrt(d*x^2+c)/b^2/sqrt(b*x^2+a)+4/15*d*(-a*d+2*b*c)*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b^2+1/5*d*x*sqrt(b*x^2+a)*(d*x^2+c)^(3/2)/b-1/15*sqrt(a)*(8*a^2*d^2-23*a*b*c*d+23*b^2*c^2)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/b^(5/2)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/15*sqrt(a)*(4*a^2*d^2-11*a*b*c*d+15*b^2*c^2)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(5/2)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(d*x^2+c)^(5/2)/(b*x^2+a)^(3/2),x,3,2/3*d*(-2*a*d+3*b*c)*x*sqrt(d*x^2+c)/b^2/sqrt(b*x^2+a)+1/3*d*x*(d*x^2+c)^(3/2)/b/sqrt(b*x^2+a)+1/3*(8*a^2*d^2-13*a*b*c*d+3*b^2*c^2)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/sqrt(a)/b^(5/2)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+2/3*sqrt(a)*d*(-2*a*d+3*b*c)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(5/2)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(d*x^2+c)^(5/2)/(b*x^2+a)^(5/2),x,3,-1/3*d*(-4*a*d+b*c)*x*sqrt(d*x^2+c)/a/b^2/sqrt(b*x^2+a)+1/3*(-a*d+b*c)*x*(d*x^2+c)^(3/2)/a/b/(b*x^2+a)^(3/2)+1/3*(-8*a^2*d^2+3*a*b*c*d+2*b^2*c^2)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/a^(3/2)/b^(5/2)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/3*d*(-4*a*d+b*c)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(a)/b^(5/2)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(d*x^2+c)^(5/2)/(b*x^2+a)^(7/2),x,3,4/15*(c^2/a^2-d^2/b^2)*x*sqrt(d*x^2+c)/(b*x^2+a)^(3/2)+1/5*(-a*d+b*c)*x*(d*x^2+c)^(3/2)/a/b/(b*x^2+a)^(5/2)+1/15*(8*a^2*d^2+7*a*b*c*d+8*b^2*c^2)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/a^(5/2)/b^(5/2)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-4/15*d*(a*d+b*c)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/a^(3/2)/b^(5/2)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(d*x^2+c)^(5/2)/(b*x^2+a)^(9/2),x,4,2/35*(-a*d+b*c)*(2*a*d+3*b*c)*x*sqrt(d*x^2+c)/a^2/b^2/(b*x^2+a)^(5/2)+1/105*(8*a^2*d^2+13*a*b*c*d+24*b^2*c^2)*x*sqrt(d*x^2+c)/a^3/b^2/(b*x^2+a)^(3/2)+1/7*(-a*d+b*c)*x*(d*x^2+c)^(3/2)/a/b/(b*x^2+a)^(7/2)+1/105*(-8*a^3*d^3-9*a^2*b*c*d^2-16*a*b^2*c^2*d+48*b^3*c^3)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/a^(7/2)/b^(5/2)/(-a*d+b*c)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/105*d*(-4*a^2*d^2-5*a*b*c*d+24*b^2*c^2)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/a^(5/2)/b^(5/2)/(-a*d+b*c)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(d*x^2+c)^(5/2)/(b*x^2+a)^(11/2),x,5,4/63*(-a*d+b*c)*(a*d+2*b*c)*x*sqrt(d*x^2+c)/a^2/b^2/(b*x^2+a)^(7/2)+1/315*(8*a^2*d^2+19*a*b*c*d+48*b^2*c^2)*x*sqrt(d*x^2+c)/a^3/b^2/(b*x^2+a)^(5/2)+1/315*(-8*a^3*d^3-15*a^2*b*c*d^2-36*a*b^2*c^2*d+64*b^3*c^3)*x*sqrt(d*x^2+c)/a^4/b^2/(-a*d+b*c)/(b*x^2+a)^(3/2)+1/9*(-a*d+b*c)*x*(d*x^2+c)^(3/2)/a/b/(b*x^2+a)^(9/2)+1/315*(8*a^4*d^4+11*a^3*b*c*d^3+27*a^2*b^2*c^2*d^2-184*a*b^3*c^3*d+128*b^4*c^4)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/a^(9/2)/b^(5/2)/(-a*d+b*c)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-2/315*d*(2*a^3*d^3+3*a^2*b*c*d^2-42*a*b^2*c^2*d+32*b^3*c^3)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/a^(7/2)/b^(5/2)/(-a*d+b*c)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(d*x^2+c)^(5/2)/(b*x^2+a)^(13/2),x,6,2/99*(-a*d+b*c)*(2*a*d+5*b*c)*x*sqrt(d*x^2+c)/a^2/b^2/(b*x^2+a)^(9/2)+1/693*(8*a^2*d^2+25*a*b*c*d+80*b^2*c^2)*x*sqrt(d*x^2+c)/a^3/b^2/(b*x^2+a)^(7/2)+1/693*(-8*a^3*d^3-21*a^2*b*c*d^2-64*a*b^2*c^2*d+96*b^3*c^3)*x*sqrt(d*x^2+c)/a^4/b^2/(-a*d+b*c)/(b*x^2+a)^(5/2)+1/693*(8*a^4*d^4+17*a^3*b*c*d^3+51*a^2*b^2*c^2*d^2-208*a*b^3*c^3*d+128*b^4*c^4)*x*sqrt(d*x^2+c)/a^5/b^2/(-a*d+b*c)^2/(b*x^2+a)^(3/2)+1/11*(-a*d+b*c)*x*(d*x^2+c)^(3/2)/a/b/(b*x^2+a)^(11/2)+1/693*(-a*d+2*b*c)*(8*a^4*d^4+29*a^3*b*c*d^3+99*a^2*b^2*c^2*d^2-256*a*b^3*c^3*d+128*b^4*c^4)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/a^(11/2)/b^(5/2)/(-a*d+b*c)^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/693*d*(-4*a^4*d^4-7*a^3*b*c*d^3+195*a^2*b^2*c^2*d^2-304*a*b^3*c^3*d+128*b^4*c^4)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/a^(9/2)/b^(5/2)/(-a*d+b*c)^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[sqrt(d*x^2+c)/(-b*x^2+a)^(3/2),x,8,x*sqrt(d*x^2+c)/a/sqrt(-b*x^2+a)-sqrt(1-b*x^2/a)*sqrt(d*x^2+c)*EllipticE(sin(arcsin(sqrt(b)*x/sqrt(a))),sqrt(-a*d/b/c))/sqrt(a)/sqrt(b)/sqrt(-b*x^2+a)/sqrt(1+d*x^2/c)+c*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*InverseJacobiAM(arcsin(sqrt(b)*x/sqrt(a)),sqrt(-a*d/b/c))/sqrt(a)/sqrt(b)/sqrt(-b*x^2+a)/sqrt(d*x^2+c),1],
[1/sqrt(b*x^2+a)/sqrt(d*x^2+c),x,1,sqrt(a)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(b)/c/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[1/(b*x^2+a)^(3/2)/sqrt(d*x^2+c),x,1,sqrt(b)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/sqrt(a)/(-a*d+b*c)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-sqrt(a)*d*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(b)/c/(-a*d+b*c)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[1/(b*x^2+a)^(5/2)/sqrt(d*x^2+c),x,2,1/3*b*x*sqrt(d*x^2+c)/a/(-a*d+b*c)/(b*x^2+a)^(3/2)+2/3*sqrt(b)*(-2*a*d+b*c)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/a^(3/2)/(-a*d+b*c)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/3*d*(-3*a*d+b*c)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(a)/sqrt(b)/c/(-a*d+b*c)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[1/(b*x^2+a)^(7/2)/sqrt(d*x^2+c),x,3,1/5*b*x*sqrt(d*x^2+c)/a/(-a*d+b*c)/(b*x^2+a)^(5/2)+4/15*b*(-2*a*d+b*c)*x*sqrt(d*x^2+c)/a^2/(-a*d+b*c)^2/(b*x^2+a)^(3/2)+1/15*sqrt(b)*(23*a^2*d^2-23*a*b*c*d+8*b^2*c^2)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/a^(5/2)/(-a*d+b*c)^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/15*d*(15*a^2*d^2-11*a*b*c*d+4*b^2*c^2)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/a^(3/2)/sqrt(b)/c/(-a*d+b*c)^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[1/sqrt(b*x^2+a)/(d*x^2+c)^(3/2),x,1,-sqrt(d)*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/sqrt(c)/(-a*d+b*c)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+b*sqrt(c)*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a/sqrt(d)/(-a*d+b*c)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[1/(b*x^2+a)^(3/2)/(d*x^2+c)^(3/2),x,2,b*x/a/(-a*d+b*c)/sqrt(b*x^2+a)/sqrt(d*x^2+c)+sqrt(d)*(a*d+b*c)*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/a/sqrt(c)/(-a*d+b*c)^2/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-2*b*sqrt(c)*sqrt(d)*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a/(-a*d+b*c)^2/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[1/(b*x^2+a)^(5/2)/(d*x^2+c)^(3/2),x,3,-d*x/c/(-a*d+b*c)/(b*x^2+a)^(3/2)/sqrt(d*x^2+c)+1/3*b*(3*a*d+b*c)*x*sqrt(d*x^2+c)/a/c/(-a*d+b*c)^2/(b*x^2+a)^(3/2)+1/3*sqrt(b)*(-3*a^2*d^2-7*a*b*c*d+2*b^2*c^2)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/a^(3/2)/c/(-a*d+b*c)^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/3*sqrt(b)*d*(-9*a*d+b*c)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(a)/c/(-a*d+b*c)^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[1/sqrt(b*x^2+a)/(d*x^2+c)^(5/2),x,2,-1/3*d*x*sqrt(b*x^2+a)/c/(-a*d+b*c)/(d*x^2+c)^(3/2)-2/3*sqrt(d)*(-a*d+2*b*c)*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/c^(3/2)/(-a*d+b*c)^2/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+1/3*b*(-a*d+3*b*c)*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a/sqrt(c)/sqrt(d)/(-a*d+b*c)^2/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[1/(b*x^2+a)^(3/2)/(d*x^2+c)^(5/2),x,3,b*x/a/(-a*d+b*c)/sqrt(b*x^2+a)/(d*x^2+c)^(3/2)+1/3*d*(a*d+3*b*c)*x*sqrt(b*x^2+a)/a/c/(-a*d+b*c)^2/(d*x^2+c)^(3/2)+1/3*sqrt(d)*(-2*a^2*d^2+7*a*b*c*d+3*b^2*c^2)*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/a/c^(3/2)/(-a*d+b*c)^3/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-1/3*b*sqrt(d)*(-a*d+9*b*c)*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a/sqrt(c)/(-a*d+b*c)^3/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[1/(b*x^2+a)^(5/2)/(d*x^2+c)^(5/2),x,4,1/3*b*x/a/(-a*d+b*c)/(b*x^2+a)^(3/2)/(d*x^2+c)^(3/2)+2/3*b*(-4*a*d+b*c)*x/a^2/(-a*d+b*c)^2/sqrt(b*x^2+a)/(d*x^2+c)^(3/2)+1/3*d*(-a^2*d^2-9*a*b*c*d+2*b^2*c^2)*x*sqrt(b*x^2+a)/a^2/c/(-a*d+b*c)^3/(d*x^2+c)^(3/2)+2/3*sqrt(d)*(a*d+b*c)*(a^2*d^2-6*a*b*c*d+b^2*c^2)*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/a^2/c^(3/2)/(-a*d+b*c)^4/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-1/3*b*sqrt(d)*(a^2*d^2-18*a*b*c*d+b^2*c^2)*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a^2/sqrt(c)/(-a*d+b*c)^4/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[sqrt(b*x^2+2)*sqrt(d*x^2+3),x,5,1/3*(3*b+2*d)*x*sqrt(d*x^2+3)/d/sqrt(b*x^2+2)+1/3*x*sqrt(b*x^2+2)*sqrt(d*x^2+3)-(3*b+2*d)*sqrt(d*x^2+3)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(2))),sqrt(1-2/3*d/b))/sqrt(3)/sqrt(b)/d/sqrt(b*x^2+2)/sqrt((d*x^2+3)/(b*x^2+2))+4*sqrt(d*x^2+3)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(2)),sqrt(1-2/3*d/b))/sqrt(3)/sqrt(b)/sqrt(b*x^2+2)/sqrt((d*x^2+3)/(b*x^2+2)),1],
[sqrt(-6*x^2+3)*sqrt(4*x^2+2),x,3,sqrt(2/3)*x*sqrt(-4*x^4+1)+2*InverseJacobiAM(arcsin(sqrt(2)*x),sqrt(-1))/sqrt(3),1],
[sqrt(4*x^2+2)*sqrt(6*x^2+3),x,2,sqrt(6)*x+2*sqrt(2/3)*x^3,1],
[sqrt(b*x^2+a)/sqrt(-d*x^2+c),x,3,sqrt(c)*sqrt(b*x^2+a)*sqrt(1-d*x^2/c)*EllipticE(sin(arcsin(sqrt(d)*x/sqrt(c))),sqrt(-b*c/a/d))/sqrt(d)/sqrt(1+b*x^2/a)/sqrt(-d*x^2+c),1],
[sqrt(-b*x^2-a)/sqrt(-d*x^2+c),x,3,sqrt(c)*sqrt(-b*x^2-a)*sqrt(1-d*x^2/c)*EllipticE(sin(arcsin(sqrt(d)*x/sqrt(c))),sqrt(-b*c/a/d))/sqrt(d)/sqrt(1+b*x^2/a)/sqrt(-d*x^2+c),1],
[sqrt(b*x^2+a)/sqrt(d*x^2-c),x,3,sqrt(c)*sqrt(b*x^2+a)*sqrt(1-d*x^2/c)*EllipticE(sin(arcsin(sqrt(d)*x/sqrt(c))),sqrt(-b*c/a/d))/sqrt(d)/sqrt(1+b*x^2/a)/sqrt(d*x^2-c),1],
[sqrt(-b*x^2-a)/sqrt(d*x^2-c),x,3,sqrt(c)*sqrt(-b*x^2-a)*sqrt(1-d*x^2/c)*EllipticE(sin(arcsin(sqrt(d)*x/sqrt(c))),sqrt(-b*c/a/d))/sqrt(d)/sqrt(1+b*x^2/a)/sqrt(d*x^2-c),1],
[sqrt(-b*x^2+a)/sqrt(-d*x^2+c),x,3,sqrt(c)*sqrt(-b*x^2+a)*sqrt(1-d*x^2/c)*EllipticE(sin(arcsin(sqrt(d)*x/sqrt(c))),sqrt(b*c/a/d))/sqrt(d)/sqrt(1-b*x^2/a)/sqrt(-d*x^2+c),1],
[sqrt(b*x^2-a)/sqrt(-d*x^2+c),x,3,sqrt(c)*sqrt(b*x^2-a)*sqrt(1-d*x^2/c)*EllipticE(sin(arcsin(sqrt(d)*x/sqrt(c))),sqrt(b*c/a/d))/sqrt(d)/sqrt(1-b*x^2/a)/sqrt(-d*x^2+c),1],
[sqrt(-b*x^2+a)/sqrt(d*x^2-c),x,3,sqrt(c)*sqrt(-b*x^2+a)*sqrt(1-d*x^2/c)*EllipticE(sin(arcsin(sqrt(d)*x/sqrt(c))),sqrt(b*c/a/d))/sqrt(d)/sqrt(1-b*x^2/a)/sqrt(d*x^2-c),1],
[sqrt(b*x^2-a)/sqrt(d*x^2-c),x,3,sqrt(c)*sqrt(b*x^2-a)*sqrt(1-d*x^2/c)*EllipticE(sin(arcsin(sqrt(d)*x/sqrt(c))),sqrt(b*c/a/d))/sqrt(d)/sqrt(1-b*x^2/a)/sqrt(d*x^2-c),1],
[sqrt(b*x^2+a)/sqrt(d*x^2+c),x,2,x*sqrt(b*x^2+a)/sqrt(d*x^2+c)-sqrt(c)*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/sqrt(d)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+sqrt(c)*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/sqrt(d)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[sqrt(-b*x^2-a)/sqrt(d*x^2+c),x,2,x*sqrt(-b*x^2-a)/sqrt(d*x^2+c)-sqrt(c)*sqrt(-b*x^2-a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/sqrt(d)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+sqrt(c)*sqrt(-b*x^2-a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/sqrt(d)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[sqrt(b*x^2+a)/sqrt(-d*x^2-c),x,2,x*sqrt(b*x^2+a)/sqrt(-d*x^2-c)-sqrt(c)*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/sqrt(d)/sqrt(-d*x^2-c)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))+sqrt(c)*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/sqrt(d)/sqrt(-d*x^2-c)/sqrt(c*(b*x^2+a)/a/(d*x^2+c)),1],
[sqrt(-b*x^2-a)/sqrt(-d*x^2-c),x,2,x*sqrt(-b*x^2-a)/sqrt(-d*x^2-c)-sqrt(c)*sqrt(-b*x^2-a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/sqrt(d)/sqrt(-d*x^2-c)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))+sqrt(c)*sqrt(-b*x^2-a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/sqrt(d)/sqrt(-d*x^2-c)/sqrt(c*(b*x^2+a)/a/(d*x^2+c)),1],
[sqrt(-b*x^2+a)/sqrt(d*x^2+c),x,5,-sqrt(b)*c*sqrt(-b*x^2+a)*sqrt(1+d*x^2/c)*EllipticE(sin(arcsin(sqrt(b)*x/sqrt(a))),sqrt(-a*d/b/c))/sqrt(a)/d/sqrt(1-b*x^2/a)/sqrt(d*x^2+c)+(a*d+b*c)*sqrt(-b*x^2+a)*sqrt(1+d*x^2/c)*InverseJacobiAM(arcsin(sqrt(b)*x/sqrt(a)),sqrt(-a*d/b/c))/sqrt(a)/sqrt(b)/d/sqrt(1-b*x^2/a)/sqrt(d*x^2+c),1],
[sqrt(b*x^2-a)/sqrt(d*x^2+c),x,5,-sqrt(b)*c*sqrt(b*x^2-a)*sqrt(1+d*x^2/c)*EllipticE(sin(arcsin(sqrt(b)*x/sqrt(a))),sqrt(-a*d/b/c))/sqrt(a)/d/sqrt(1-b*x^2/a)/sqrt(d*x^2+c)+(a*d+b*c)*sqrt(b*x^2-a)*sqrt(1+d*x^2/c)*InverseJacobiAM(arcsin(sqrt(b)*x/sqrt(a)),sqrt(-a*d/b/c))/sqrt(a)/sqrt(b)/d/sqrt(1-b*x^2/a)/sqrt(d*x^2+c),1],
[sqrt(-b*x^2+a)/sqrt(-d*x^2-c),x,5,-sqrt(b)*c*sqrt(-b*x^2+a)*sqrt(1+d*x^2/c)*EllipticE(sin(arcsin(sqrt(b)*x/sqrt(a))),sqrt(-a*d/b/c))/sqrt(a)/d/sqrt(1-b*x^2/a)/sqrt(-d*x^2-c)+(a*d+b*c)*sqrt(-b*x^2+a)*sqrt(1+d*x^2/c)*InverseJacobiAM(arcsin(sqrt(b)*x/sqrt(a)),sqrt(-a*d/b/c))/sqrt(a)/sqrt(b)/d/sqrt(1-b*x^2/a)/sqrt(-d*x^2-c),1],
[sqrt(b*x^2-a)/sqrt(-d*x^2-c),x,5,-sqrt(b)*c*sqrt(b*x^2-a)*sqrt(1+d*x^2/c)*EllipticE(sin(arcsin(sqrt(b)*x/sqrt(a))),sqrt(-a*d/b/c))/sqrt(a)/d/sqrt(1-b*x^2/a)/sqrt(-d*x^2-c)+(a*d+b*c)*sqrt(b*x^2-a)*sqrt(1+d*x^2/c)*InverseJacobiAM(arcsin(sqrt(b)*x/sqrt(a)),sqrt(-a*d/b/c))/sqrt(a)/sqrt(b)/d/sqrt(1-b*x^2/a)/sqrt(-d*x^2-c),1],
[sqrt(d*x^2+c)/sqrt(-b*x^2+a),x,3,sqrt(a)*sqrt(1-b*x^2/a)*sqrt(d*x^2+c)*EllipticE(sin(arcsin(sqrt(b)*x/sqrt(a))),sqrt(-a*d/b/c))/sqrt(b)/sqrt(-b*x^2+a)/sqrt(1+d*x^2/c),1],
[sqrt(-d*x^2-c)/sqrt(-b*x^2+a),x,3,sqrt(a)*sqrt(1-b*x^2/a)*sqrt(-d*x^2-c)*EllipticE(sin(arcsin(sqrt(b)*x/sqrt(a))),sqrt(-a*d/b/c))/sqrt(b)/sqrt(-b*x^2+a)/sqrt(1+d*x^2/c),1],
[sqrt(d*x^2+c)/sqrt(b*x^2-a),x,3,sqrt(a)*sqrt(1-b*x^2/a)*sqrt(d*x^2+c)*EllipticE(sin(arcsin(sqrt(b)*x/sqrt(a))),sqrt(-a*d/b/c))/sqrt(b)/sqrt(b*x^2-a)/sqrt(1+d*x^2/c),1],
[sqrt(-d*x^2-c)/sqrt(b*x^2-a),x,3,sqrt(a)*sqrt(1-b*x^2/a)*sqrt(-d*x^2-c)*EllipticE(sin(arcsin(sqrt(b)*x/sqrt(a))),sqrt(-a*d/b/c))/sqrt(b)/sqrt(b*x^2-a)/sqrt(1+d*x^2/c),1],
[sqrt(-d*x^2+c)/sqrt(-b*x^2+a),x,3,sqrt(a)*sqrt(1-b*x^2/a)*sqrt(-d*x^2+c)*EllipticE(sin(arcsin(sqrt(b)*x/sqrt(a))),sqrt(a*d/b/c))/sqrt(b)/sqrt(-b*x^2+a)/sqrt(1-d*x^2/c),1],
[sqrt(d*x^2-c)/sqrt(-b*x^2+a),x,3,sqrt(a)*sqrt(1-b*x^2/a)*sqrt(d*x^2-c)*EllipticE(sin(arcsin(sqrt(b)*x/sqrt(a))),sqrt(a*d/b/c))/sqrt(b)/sqrt(-b*x^2+a)/sqrt(1-d*x^2/c),1],
[sqrt(-d*x^2+c)/sqrt(b*x^2-a),x,3,sqrt(a)*sqrt(1-b*x^2/a)*sqrt(-d*x^2+c)*EllipticE(sin(arcsin(sqrt(b)*x/sqrt(a))),sqrt(a*d/b/c))/sqrt(b)/sqrt(b*x^2-a)/sqrt(1-d*x^2/c),1],
[sqrt(d*x^2-c)/sqrt(b*x^2-a),x,3,sqrt(a)*sqrt(1-b*x^2/a)*sqrt(d*x^2-c)*EllipticE(sin(arcsin(sqrt(b)*x/sqrt(a))),sqrt(a*d/b/c))/sqrt(b)/sqrt(b*x^2-a)/sqrt(1-d*x^2/c),1],
[sqrt(d*x^2+c)/sqrt(b*x^2+a),x,2,x*sqrt(d*x^2+c)/sqrt(b*x^2+a)-sqrt(a)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/sqrt(b)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+sqrt(a)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(b)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[sqrt(-d*x^2-c)/sqrt(b*x^2+a),x,2,x*sqrt(-d*x^2-c)/sqrt(b*x^2+a)-sqrt(a)*sqrt(-d*x^2-c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/sqrt(b)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+sqrt(a)*sqrt(-d*x^2-c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(b)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[sqrt(d*x^2+c)/sqrt(-b*x^2-a),x,2,x*sqrt(d*x^2+c)/sqrt(-b*x^2-a)-sqrt(a)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/sqrt(b)/sqrt(-b*x^2-a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+sqrt(a)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(b)/sqrt(-b*x^2-a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[sqrt(-d*x^2-c)/sqrt(-b*x^2-a),x,2,x*sqrt(-d*x^2-c)/sqrt(-b*x^2-a)-sqrt(a)*sqrt(-d*x^2-c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/sqrt(b)/sqrt(-b*x^2-a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+sqrt(a)*sqrt(-d*x^2-c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(b)/sqrt(-b*x^2-a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[sqrt(-d*x^2+c)/sqrt(b*x^2+a),x,5,-a*sqrt(d)*sqrt(1+b*x^2/a)*sqrt(-d*x^2+c)*EllipticE(sin(arcsin(sqrt(d)*x/sqrt(c))),sqrt(-b*c/a/d))/b/sqrt(c)/sqrt(b*x^2+a)/sqrt(1-d*x^2/c)+(a*d+b*c)*sqrt(1+b*x^2/a)*sqrt(-d*x^2+c)*InverseJacobiAM(arcsin(sqrt(d)*x/sqrt(c)),sqrt(-b*c/a/d))/b/sqrt(c)/sqrt(d)/sqrt(b*x^2+a)/sqrt(1-d*x^2/c),1],
[sqrt(d*x^2-c)/sqrt(b*x^2+a),x,5,-a*sqrt(d)*sqrt(1+b*x^2/a)*sqrt(d*x^2-c)*EllipticE(sin(arcsin(sqrt(d)*x/sqrt(c))),sqrt(-b*c/a/d))/b/sqrt(c)/sqrt(b*x^2+a)/sqrt(1-d*x^2/c)+(a*d+b*c)*sqrt(1+b*x^2/a)*sqrt(d*x^2-c)*InverseJacobiAM(arcsin(sqrt(d)*x/sqrt(c)),sqrt(-b*c/a/d))/b/sqrt(c)/sqrt(d)/sqrt(b*x^2+a)/sqrt(1-d*x^2/c),1],
[sqrt(-d*x^2+c)/sqrt(-b*x^2-a),x,5,-a*sqrt(d)*sqrt(1+b*x^2/a)*sqrt(-d*x^2+c)*EllipticE(sin(arcsin(sqrt(d)*x/sqrt(c))),sqrt(-b*c/a/d))/b/sqrt(c)/sqrt(-b*x^2-a)/sqrt(1-d*x^2/c)+(a*d+b*c)*sqrt(1+b*x^2/a)*sqrt(-d*x^2+c)*InverseJacobiAM(arcsin(sqrt(d)*x/sqrt(c)),sqrt(-b*c/a/d))/b/sqrt(c)/sqrt(d)/sqrt(-b*x^2-a)/sqrt(1-d*x^2/c),1],
[sqrt(d*x^2-c)/sqrt(-b*x^2-a),x,5,-a*sqrt(d)*sqrt(1+b*x^2/a)*sqrt(d*x^2-c)*EllipticE(sin(arcsin(sqrt(d)*x/sqrt(c))),sqrt(-b*c/a/d))/b/sqrt(c)/sqrt(-b*x^2-a)/sqrt(1-d*x^2/c)+(a*d+b*c)*sqrt(1+b*x^2/a)*sqrt(d*x^2-c)*InverseJacobiAM(arcsin(sqrt(d)*x/sqrt(c)),sqrt(-b*c/a/d))/b/sqrt(c)/sqrt(d)/sqrt(-b*x^2-a)/sqrt(1-d*x^2/c),1],
[sqrt(-x^2-1)/sqrt(x^2+1),x,2,x*sqrt(-x^2-1)/sqrt(x^2+1),1],
[sqrt(x^2-1)/sqrt(-x^2+1),x,2,x*sqrt(x^2-1)/sqrt(-x^2+1),1],
[sqrt(-x^2+1)/sqrt(x^2-1),x,2,x*sqrt(-x^2+1)/sqrt(x^2-1),1],
[sqrt(x^2+1)/sqrt(-x^2-1),x,2,x*sqrt(x^2+1)/sqrt(-x^2-1),1],
[sqrt(x^2+1)/sqrt(-x^2+1),x,1,EllipticE(sin(arcsin(x)),sqrt(-1)),1],
[sqrt(-x^2-1)/sqrt(-x^2+1),x,2,sqrt(-x^2-1)*EllipticE(sin(arcsin(x)),sqrt(-1))/sqrt(x^2+1),1],
[sqrt(x^2+1)/sqrt(x^2-1),x,2,sqrt(-x^2+1)*EllipticE(sin(arcsin(x)),sqrt(-1))/sqrt(x^2-1),1],
[sqrt(-x^2-1)/sqrt(x^2-1),x,2,-sqrt(-x^4+1)*EllipticE(sin(arcsin(x)),sqrt(-1))/sqrt(-x^2-1)/sqrt(x^2-1),1],
[sqrt(-x^2+1)/sqrt(x^2+1),x,4,-EllipticE(sin(arcsin(x)),sqrt(-1))+2*InverseJacobiAM(arcsin(x),sqrt(-1)),1],
[sqrt(-x^2+1)/sqrt(-x^2-1),x,5,-sqrt(x^2+1)*EllipticE(sin(arcsin(x)),sqrt(-1))/sqrt(-x^2-1)+2*sqrt(x^2+1)*InverseJacobiAM(arcsin(x),sqrt(-1))/sqrt(-x^2-1),1],
[sqrt(x^2-1)/sqrt(-x^2-1),x,5,sqrt(-x^4+1)*EllipticE(sin(arcsin(x)),sqrt(-1))/sqrt(-x^2-1)/sqrt(x^2-1)-2*sqrt(-x^4+1)*InverseJacobiAM(arcsin(x),sqrt(-1))/sqrt(-x^2-1)/sqrt(x^2-1),1],
[sqrt(x^2-1)/sqrt(x^2+1),x,5,-sqrt(x^2-1)*EllipticE(sin(arcsin(x)),sqrt(-1))/sqrt(-x^2+1)+2*sqrt(x^2-1)*InverseJacobiAM(arcsin(x),sqrt(-1))/sqrt(-x^2+1),1],
[sqrt(b*x^2+2)/sqrt(d*x^2+3),x,2,x*sqrt(b*x^2+2)/sqrt(d*x^2+3)-sqrt(2)*sqrt(b*x^2+2)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(3))),sqrt(1-3/2*b/d))/sqrt(d)/sqrt((b*x^2+2)/(d*x^2+3))/sqrt(d*x^2+3)+sqrt(2)*sqrt(b*x^2+2)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(3)),sqrt(1-3/2*b/d))/sqrt(d)/sqrt((b*x^2+2)/(d*x^2+3))/sqrt(d*x^2+3),1],
[sqrt(-x^2+4)/sqrt(d*x^2+c),x,4,-c*sqrt(1+d*x^2/c)*EllipticE(sin(arcsin(1/2*x)),sqrt(-4*d/c))/d/sqrt(d*x^2+c)+(c+4*d)*sqrt(1+d*x^2/c)*InverseJacobiAM(arcsin(1/2*x),sqrt(-4*d/c))/d/sqrt(d*x^2+c),1],
[sqrt(x^2+4)/sqrt(d*x^2+c),x,2,x*sqrt(d*x^2+c)/d/sqrt(x^2+4)-sqrt(d*x^2+c)*EllipticE(sin(arctan(1/2*x)),sqrt(1-4*d/c))/d/sqrt(x^2+4)/sqrt((d*x^2+c)/c/(x^2+4))+4*sqrt(d*x^2+c)*InverseJacobiAM(arctan(1/2*x),sqrt(1-4*d/c))/c/sqrt(x^2+4)/sqrt((d*x^2+c)/c/(x^2+4)),1],
[sqrt(-x^2+1)/sqrt(-3*x^2+2),x,1,EllipticE(sin(arcsin(sqrt(3/2)*x)),sqrt(2/3))/sqrt(3),1],
[sqrt(-x^2+4)/sqrt(-3*x^2+2),x,1,2*EllipticE(sin(arcsin(sqrt(3/2)*x)),sqrt(1/6))/sqrt(3),1],
[sqrt(-4*x^2+1)/sqrt(-3*x^2+2),x,1,EllipticE(sin(arcsin(sqrt(3/2)*x)),sqrt(8/3))/sqrt(3),1],
[sqrt(x^2+1)/sqrt(-3*x^2+2),x,1,EllipticE(sin(arcsin(sqrt(3/2)*x)),sqrt(-2/3))/sqrt(3),1],
[sqrt(x^2+4)/sqrt(-3*x^2+2),x,1,2*EllipticE(sin(arcsin(sqrt(3/2)*x)),sqrt(-1/6))/sqrt(3),1],
[sqrt(4*x^2+1)/sqrt(-3*x^2+2),x,1,EllipticE(sin(arcsin(sqrt(3/2)*x)),sqrt(-8/3))/sqrt(3),1],
[sqrt(-x^2+1)/sqrt(3*x^2+2),x,3,-1/3*sqrt(2)*EllipticE(sin(arcsin(x)),sqrt(-3/2))+5/3*InverseJacobiAM(arcsin(x),sqrt(-3/2))/sqrt(2),1],
[sqrt(-x^2+4)/sqrt(3*x^2+2),x,3,-1/3*sqrt(2)*EllipticE(sin(arcsin(1/2*x)),sqrt(-6))+7/3*sqrt(2)*InverseJacobiAM(arcsin(1/2*x),sqrt(-6)),1],
[sqrt(-4*x^2+1)/sqrt(3*x^2+2),x,3,-2/3*sqrt(2)*EllipticE(sin(arcsin(2*x)),sqrt(-3/8))+11/6*InverseJacobiAM(arcsin(2*x),sqrt(-3/8))/sqrt(2),1],
[sqrt(x^2+1)/sqrt(3*x^2+2),x,2,x*sqrt(x^2+1)/sqrt(3*x^2+2)-sqrt(x^2+1)*EllipticE(sin(arctan(sqrt(3/2)*x)),sqrt(1/3))/sqrt(3)/sqrt((x^2+1)/(3*x^2+2))/sqrt(3*x^2+2)+sqrt(x^2+1)*InverseJacobiAM(arctan(sqrt(3/2)*x),sqrt(1/3))/sqrt(3)/sqrt((x^2+1)/(3*x^2+2))/sqrt(3*x^2+2),1],
[sqrt(x^2+4)/sqrt(3*x^2+2),x,2,x*sqrt(x^2+4)/sqrt(3*x^2+2)-2*sqrt(x^2+4)*EllipticE(sin(arctan(sqrt(3/2)*x)),sqrt(5/6))/sqrt(3)/sqrt((x^2+4)/(3*x^2+2))/sqrt(3*x^2+2)+2*sqrt(x^2+4)*InverseJacobiAM(arctan(sqrt(3/2)*x),sqrt(5/6))/sqrt(3)/sqrt((x^2+4)/(3*x^2+2))/sqrt(3*x^2+2),1],
[sqrt(4*x^2+1)/sqrt(3*x^2+2),x,4,x*sqrt(4*x^2+1)/sqrt(3*x^2+2)-EllipticE(sin(arctan(sqrt(3/2)*x)),sqrt(-5/3))/sqrt(3)+InverseJacobiAM(arctan(sqrt(3/2)*x),sqrt(-5/3))/sqrt(3),1],
[sqrt(-x^2+1)/sqrt(2*x^2-1),x,3,1/2*EllipticE(sin(arccos(x)),sqrt(2))-1/2*InverseJacobiAM(arccos(x),sqrt(2)),1],
[sqrt(-c^2*x^2+1)/sqrt(c^2*x^2+1),x,4,-EllipticE(sin(arcsin(c*x)),sqrt(-1))/c+2*InverseJacobiAM(arcsin(c*x),sqrt(-1))/c,1],
[sqrt(b*x^2+2)/sqrt(d*x^2+3),x,2,x*sqrt(b*x^2+2)/sqrt(d*x^2+3)-sqrt(2)*sqrt(b*x^2+2)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(3))),sqrt(1-3/2*b/d))/sqrt(d)/sqrt((b*x^2+2)/(d*x^2+3))/sqrt(d*x^2+3)+sqrt(2)*sqrt(b*x^2+2)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(3)),sqrt(1-3/2*b/d))/sqrt(d)/sqrt((b*x^2+2)/(d*x^2+3))/sqrt(d*x^2+3),1],
[sqrt(3*x^2-1)/sqrt(-3*x^2+2),x,1,-EllipticE(sin(arccos(sqrt(3/2)*x)),sqrt(2))/sqrt(3),1],
[sqrt(1+2*c*x^2/(b-sqrt(-4*a*c+b^2)))/sqrt(1-2*c*x^2/(b+sqrt(-4*a*c+b^2))),x,1,sqrt(b+sqrt(-4*a*c+b^2))*EllipticE(sin(arcsin(sqrt(2)*sqrt(c)*x/sqrt(b+sqrt(-4*a*c+b^2)))),sqrt(-(b+sqrt(-4*a*c+b^2))/(b-sqrt(-4*a*c+b^2))))/sqrt(2)/sqrt(c),1],
[sqrt(1-2*c*x^2/(b-sqrt(-4*a*c+b^2)))/sqrt(1-2*c*x^2/(b+sqrt(-4*a*c+b^2))),x,1,sqrt(b+sqrt(-4*a*c+b^2))*EllipticE(sin(arcsin(sqrt(2)*sqrt(c)*x/sqrt(b+sqrt(-4*a*c+b^2)))),sqrt((b+sqrt(-4*a*c+b^2))/(b-sqrt(-4*a*c+b^2))))/sqrt(2)/sqrt(c),1],
[sqrt(1+2*c*x^2/(b-sqrt(-4*a*c+b^2)))/sqrt(1+2*c*x^2/(b+sqrt(-4*a*c+b^2))),x,3,-(b+sqrt(-4*a*c+b^2))*EllipticE(sin(arcsin(sqrt(2)*sqrt(c)*x/sqrt(-b+sqrt(-4*a*c+b^2)))),sqrt((b-sqrt(-4*a*c+b^2))/(b+sqrt(-4*a*c+b^2))))/sqrt(2)/sqrt(c)/sqrt(-b+sqrt(-4*a*c+b^2))+sqrt(2)*sqrt(-4*a*c+b^2)*InverseJacobiAM(arcsin(sqrt(2)*sqrt(c)*x/sqrt(-b+sqrt(-4*a*c+b^2))),sqrt((b-sqrt(-4*a*c+b^2))/(b+sqrt(-4*a*c+b^2))))/sqrt(c)/sqrt(-b+sqrt(-4*a*c+b^2)),1],
[sqrt(1-2*c*x^2/(b-sqrt(-4*a*c+b^2)))/sqrt(1+2*c*x^2/(b+sqrt(-4*a*c+b^2))),x,3,-(b+sqrt(-4*a*c+b^2))*EllipticE(sin(arcsin(sqrt(2)*sqrt(c)*x/sqrt(b-sqrt(-4*a*c+b^2)))),sqrt(-(b-sqrt(-4*a*c+b^2))/(b+sqrt(-4*a*c+b^2))))/sqrt(2)/sqrt(c)/sqrt(b-sqrt(-4*a*c+b^2))+sqrt(2)*b*InverseJacobiAM(arcsin(sqrt(2)*sqrt(c)*x/sqrt(b-sqrt(-4*a*c+b^2))),sqrt(-(b-sqrt(-4*a*c+b^2))/(b+sqrt(-4*a*c+b^2))))/sqrt(c)/sqrt(b-sqrt(-4*a*c+b^2)),1],
[1/sqrt(b*x^2+a)/sqrt(d*x^2+c),x,1,sqrt(a)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(b)/c/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[1/sqrt(-b*x^2+a)/sqrt(d*x^2+c),x,3,sqrt(a)*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*InverseJacobiAM(arcsin(sqrt(b)*x/sqrt(a)),sqrt(-a*d/b/c))/sqrt(b)/sqrt(-b*x^2+a)/sqrt(d*x^2+c),1],
[1/sqrt(b*x^2+a)/sqrt(-d*x^2+c),x,3,sqrt(c)*sqrt(1+b*x^2/a)*sqrt(1-d*x^2/c)*InverseJacobiAM(arcsin(sqrt(d)*x/sqrt(c)),sqrt(-b*c/a/d))/sqrt(d)/sqrt(b*x^2+a)/sqrt(-d*x^2+c),1],
[1/sqrt(-b*x^2+a)/sqrt(-d*x^2+c),x,3,sqrt(a)*sqrt(1-b*x^2/a)*sqrt(1-d*x^2/c)*InverseJacobiAM(arcsin(sqrt(b)*x/sqrt(a)),sqrt(a*d/b/c))/sqrt(b)/sqrt(-b*x^2+a)/sqrt(-d*x^2+c),1],
[1/sqrt(-x^2+1)/sqrt(5*x^2+2),x,1,InverseJacobiAM(arcsin(x),sqrt(-5/2))/sqrt(2),1],
[1/sqrt(-x^2+1)/sqrt(4*x^2+2),x,1,InverseJacobiAM(arcsin(x),sqrt(-2))/sqrt(2),1],
[1/sqrt(-x^2+1)/sqrt(3*x^2+2),x,1,InverseJacobiAM(arcsin(x),sqrt(-3/2))/sqrt(2),1],
[1/sqrt(-x^2+1)/sqrt(2*x^2+2),x,2,InverseJacobiAM(arcsin(x),sqrt(-1))/sqrt(2),1],
[1/sqrt(-x^2+1)/sqrt(x^2+2),x,1,InverseJacobiAM(arcsin(x),sqrt(-1/2))/sqrt(2),1],
[1/sqrt(-x^2+1)/sqrt(-x^2+2),x,1,InverseJacobiAM(arcsin(x),sqrt(1/2))/sqrt(2),1],
[1/sqrt(-2*x^2+2)/sqrt(-x^2+1),x,2,arctanh(x)/sqrt(2),1],
[1/sqrt(-3*x^2+2)/sqrt(-x^2+1),x,1,InverseJacobiAM(arcsin(x),sqrt(3/2))/sqrt(2),1],
[1/sqrt(-4*x^2+2)/sqrt(-x^2+1),x,1,InverseJacobiAM(arcsin(x),sqrt(2))/sqrt(2),1],
[1/sqrt(-5*x^2+2)/sqrt(-x^2+1),x,1,InverseJacobiAM(arcsin(x),sqrt(5/2))/sqrt(2),1],
[1/sqrt(x^2+1)/sqrt(5*x^2+2),x,1,InverseJacobiAM(arctan(x),sqrt(-3/2))/sqrt(2),1],
[1/sqrt(x^2+1)/sqrt(4*x^2+2),x,1,InverseJacobiAM(arctan(x),sqrt(-1))/sqrt(2),1],
[1/sqrt(x^2+1)/sqrt(3*x^2+2),x,1,InverseJacobiAM(arctan(x),sqrt(-1/2))/sqrt(2),1],
[1/sqrt(x^2+1)/sqrt(2*x^2+2),x,2,arctan(x)/sqrt(2),1],
[1/sqrt(x^2+1)/sqrt(x^2+2),x,1,InverseJacobiAM(arctan(x/sqrt(2)),sqrt(-1)),1],
[1/sqrt(-x^2+2)/sqrt(x^2+1),x,1,InverseJacobiAM(arcsin(x/sqrt(2)),sqrt(-2)),1],
[1/sqrt(-2*x^2+2)/sqrt(x^2+1),x,2,InverseJacobiAM(arcsin(x),sqrt(-1))/sqrt(2),1],
[1/sqrt(-3*x^2+2)/sqrt(x^2+1),x,1,InverseJacobiAM(arcsin(sqrt(3/2)*x),sqrt(-2/3))/sqrt(3),1],
[1/sqrt(-4*x^2+2)/sqrt(x^2+1),x,1,1/2*InverseJacobiAM(arcsin(sqrt(2)*x),sqrt(-1/2)),1],
[1/sqrt(-5*x^2+2)/sqrt(x^2+1),x,1,InverseJacobiAM(arcsin(sqrt(5/2)*x),sqrt(-2/5))/sqrt(5),1],
[1/sqrt(x^2-1)/sqrt(5*x^2+2),x,2,sqrt(-x^2+1)*InverseJacobiAM(arcsin(x),sqrt(-5/2))/sqrt(2)/sqrt(x^2-1),1],
[1/sqrt(x^2-1)/sqrt(4*x^2+2),x,2,sqrt(-x^2+1)*InverseJacobiAM(arcsin(x),sqrt(-2))/sqrt(2)/sqrt(x^2-1),1],
[1/sqrt(x^2-1)/sqrt(3*x^2+2),x,2,sqrt(-x^2+1)*InverseJacobiAM(arcsin(x),sqrt(-3/2))/sqrt(2)/sqrt(x^2-1),1],
[1/sqrt(x^2-1)/sqrt(2*x^2+2),x,1,1/2*InverseJacobiAM(arcsin(sqrt(2)*x/sqrt(x^2-1)),sqrt(1/2)),1],
[1/sqrt(x^2-1)/sqrt(x^2+2),x,2,sqrt(-x^2+1)*InverseJacobiAM(arcsin(x),sqrt(-1/2))/sqrt(2)/sqrt(x^2-1),1],
[1/sqrt(-x^2+2)/sqrt(x^2-1),x,1,-InverseJacobiAM(arccos(x/sqrt(2)),sqrt(2)),1],
[1/sqrt(-2*x^2+2)/sqrt(x^2-1),x,2,-sqrt(x^2-1)*arctanh(x)/sqrt(2)/sqrt(-x^2+1),1],
[1/sqrt(-3*x^2+2)/sqrt(x^2-1),x,2,sqrt(-x^2+1)*InverseJacobiAM(arcsin(x),sqrt(3/2))/sqrt(2)/sqrt(x^2-1),1],
[1/sqrt(-4*x^2+2)/sqrt(x^2-1),x,2,sqrt(-x^2+1)*InverseJacobiAM(arcsin(x),sqrt(2))/sqrt(2)/sqrt(x^2-1),1],
[1/sqrt(-5*x^2+2)/sqrt(x^2-1),x,2,sqrt(-x^2+1)*InverseJacobiAM(arcsin(x),sqrt(5/2))/sqrt(2)/sqrt(x^2-1),1],
[1/sqrt(-x^2-1)/sqrt(5*x^2+2),x,2,sqrt(x^2+1)*InverseJacobiAM(arctan(x),sqrt(-3/2))/sqrt(2)/sqrt(-x^2-1),1],
[1/sqrt(-x^2-1)/sqrt(4*x^2+2),x,2,sqrt(x^2+1)*InverseJacobiAM(arctan(x),sqrt(-1))/sqrt(2)/sqrt(-x^2-1),1],
[1/sqrt(-x^2-1)/sqrt(3*x^2+2),x,2,sqrt(x^2+1)*InverseJacobiAM(arctan(x),sqrt(-1/2))/sqrt(2)/sqrt(-x^2-1),1],
[1/sqrt(-x^2-1)/sqrt(2*x^2+2),x,2,-sqrt(-x^2-1)*arctan(x)/sqrt(2)/sqrt(x^2+1),1],
[1/sqrt(-x^2-1)/sqrt(x^2+2),x,2,sqrt(x^2+1)*InverseJacobiAM(arctan(x/sqrt(2)),sqrt(-1))/sqrt(-x^2-1),1],
[1/sqrt(-x^2-1)/sqrt(-x^2+2),x,2,sqrt(x^2+1)*InverseJacobiAM(arcsin(x/sqrt(2)),sqrt(-2))/sqrt(-x^2-1),1],
[1/sqrt(-2*x^2+2)/sqrt(-x^2-1),x,2,sqrt(x^2+1)*InverseJacobiAM(arcsin(x),sqrt(-1))/sqrt(2)/sqrt(-x^2-1),1],
[1/sqrt(-3*x^2+2)/sqrt(-x^2-1),x,2,sqrt(x^2+1)*InverseJacobiAM(arcsin(sqrt(3/2)*x),sqrt(-2/3))/sqrt(3)/sqrt(-x^2-1),1],
[1/sqrt(-4*x^2+2)/sqrt(-x^2-1),x,2,1/2*sqrt(x^2+1)*InverseJacobiAM(arcsin(sqrt(2)*x),sqrt(-1/2))/sqrt(-x^2-1),1],
[1/sqrt(-5*x^2+2)/sqrt(-x^2-1),x,2,sqrt(x^2+1)*InverseJacobiAM(arcsin(sqrt(5/2)*x),sqrt(-2/5))/sqrt(5)/sqrt(-x^2-1),1],
[1/sqrt(b*x^2+2)/sqrt(d*x^2+3),x,1,sqrt(d*x^2+3)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(2)),sqrt(1-2/3*d/b))/sqrt(3)/sqrt(b)/sqrt(b*x^2+2)/sqrt((d*x^2+3)/(b*x^2+2)),1],
[1/sqrt(-x^2+4)/sqrt(d*x^2+c),x,2,sqrt(1+d*x^2/c)*InverseJacobiAM(arcsin(1/2*x),sqrt(-4*d/c))/sqrt(d*x^2+c),1],
[1/sqrt(x^2+4)/sqrt(d*x^2+c),x,1,sqrt(d*x^2+c)*InverseJacobiAM(arctan(1/2*x),sqrt(1-4*d/c))/c/sqrt(x^2+4)/sqrt((d*x^2+c)/c/(x^2+4)),1],
[1/sqrt(-x^2+1)/sqrt(2*x^2-1),x,1,-InverseJacobiAM(arccos(x),sqrt(2)),1],
[1/sqrt(x^2-1)/sqrt(7-4*sqrt(3)+x^2),x,2,sqrt(-x^2+1)*InverseJacobiAM(arcsin(x),sqrt(-7-4*sqrt(3)))/sqrt(7-4*sqrt(3))/sqrt(x^2-1),1],
[1/sqrt(3-3*sqrt(3)+2*sqrt(3)*x^2)/sqrt(3+(-3+sqrt(3))*x^2),x,1,-1/6*sqrt(3+sqrt(3))*InverseJacobiAM(arccos(sqrt(1-1/3*sqrt(3))*x),sqrt(1/2+1/2*sqrt(3))),1],
[1/sqrt(x^2+1)/sqrt(3*x^2+2),x,1,InverseJacobiAM(arctan(x),sqrt(-1/2))/sqrt(2),1],
[1/(x^2+1)/sqrt((3*x^2+2)/(x^2+1)),x,2,InverseJacobiAM(arctan(x),sqrt(-1/2))/sqrt(2),1],
[1/sqrt(-3*x^2-2)/sqrt(x^2+1),x,2,sqrt(3*x^2+2)*InverseJacobiAM(arctan(x),sqrt(-1/2))/sqrt(2)/sqrt(-3*x^2-2),1],
[1/sqrt(3*x^2+2)/(7*x^2+5)^(3/2),x,3,-1/5*sqrt(14)*EllipticE(sin(arctan(sqrt(7/5)*x)),sqrt(-1/14))+3*InverseJacobiAM(arctan(sqrt(7/5)*x),sqrt(-1/14))/sqrt(14),1],
[1/sqrt((3*x^2+2)/(7*x^2+5))/(7*x^2+5)^2,x,4,-1/5*sqrt(14)*EllipticE(sin(arctan(sqrt(7/5)*x)),sqrt(-1/14))+3*InverseJacobiAM(arctan(sqrt(7/5)*x),sqrt(-1/14))/sqrt(14),1],
[-7*sqrt(3*x^2+2)/(7*x^2+5)^(3/2)+3/sqrt(3*x^2+2)/sqrt(7*x^2+5),x,3,-1/5*sqrt(14)*EllipticE(sin(arctan(sqrt(7/5)*x)),sqrt(-1/14))+3*InverseJacobiAM(arctan(sqrt(7/5)*x),sqrt(-1/14))/sqrt(14),1],
[1/sqrt(1-1/2*(b-sqrt(4*a*c+b^2))*x^2/a)/sqrt(1-1/2*(b+sqrt(4*a*c+b^2))*x^2/a),x,1,sqrt(2)*sqrt(a)*InverseJacobiAM(arcsin(sqrt(b+sqrt(4*a*c+b^2))*x/sqrt(2)/sqrt(a)),sqrt((b-sqrt(4*a*c+b^2))/(b+sqrt(4*a*c+b^2))))/sqrt(b+sqrt(4*a*c+b^2)),1],
[1/sqrt(1+2*c*x^2/(b-sqrt(4*a*c+b^2)))/sqrt(1+2*c*x^2/(b+sqrt(4*a*c+b^2))),x,1,sqrt(-b+sqrt(4*a*c+b^2))*InverseJacobiAM(arcsin(sqrt(2)*sqrt(c)*x/sqrt(-b+sqrt(4*a*c+b^2))),sqrt((b-sqrt(4*a*c+b^2))/(b+sqrt(4*a*c+b^2))))/sqrt(2)/sqrt(c),1],
[sqrt(-3*x^2+2)/(-x^2+1)^(3/2),x,4,x*sqrt(-3*x^2+2)/sqrt(-x^2+1)-sqrt(2)*EllipticE(sin(arcsin(x)),sqrt(3/2))+sqrt(2)*InverseJacobiAM(arcsin(x),sqrt(3/2)),1],
[sqrt(-3*x^2-2)/(x^2+1)^(3/2),x,2,sqrt(2)*sqrt(-3*x^2-2)*EllipticE(sin(arctan(x)),sqrt(-1/2))/sqrt(3*x^2+2),1],
[sqrt(-x^2-1)/(3*x^2+2)^(3/2),x,2,1/2*sqrt(-3*x^2-2)*EllipticE(sin(arctan(sqrt(3/2)*x)),sqrt(1/3))/sqrt(3)/sqrt(3*x^2+2),1],
[1/(x^2+1),x,1,arctan(x),1],
[sqrt(-x^2+1)/(x^2+1)^(3/2),x,1,sqrt(1/(x^2+1))*sqrt(x^2+1)*EllipticE(sin(arctan(x)),sqrt(2)),1],
[sqrt(x^2+1)/(-x^2+1)^(3/2),x,5,x*sqrt(x^2+1)/sqrt(-x^2+1)-EllipticE(sin(arcsin(x)),sqrt(-1))+InverseJacobiAM(arcsin(x),sqrt(-1)),1],
[1/(-x^2+1),x,1,arctanh(x),1],
[1/(x^2-1),x,1,-arctanh(x),1],
[sqrt(-x^2-1)/(x^2-1)^(3/2),x,5,-x*sqrt(-x^2-1)/sqrt(x^2-1)-sqrt(-x^4+1)*EllipticE(sin(arcsin(x)),sqrt(-1))/sqrt(-x^2-1)/sqrt(x^2-1)+sqrt(-x^4+1)*InverseJacobiAM(arcsin(x),sqrt(-1))/sqrt(-x^2-1)/sqrt(x^2-1),1],
[sqrt(x^2-1)/(-x^2-1)^(3/2),x,1,-sqrt(x^2-1)*EllipticE(sin(arctan(x)),sqrt(2))/sqrt(-x^2-1)/sqrt((-x^2+1)/(x^2+1)),1],
[1/(-x^2-1),x,1,-arctan(x),1],
[sqrt(x^2+1)/(x^2-1)^(3/2),x,5,-x*sqrt(x^2+1)/sqrt(x^2-1)+sqrt(-x^2+1)*EllipticE(sin(arcsin(x)),sqrt(-1))/sqrt(x^2-1)-sqrt(-x^2+1)*InverseJacobiAM(arcsin(x),sqrt(-1))/sqrt(x^2-1),1],
[sqrt(-x^2+1)/(x^2-1)^(3/2),x,2,-sqrt(-x^2+1)*arctanh(x)/sqrt(x^2-1),1],
[sqrt(x^2+1)/(-x^2-1)^(3/2),x,2,-sqrt(x^2+1)*arctan(x)/sqrt(-x^2-1),1],
[sqrt(-x^2+1)/(-x^2-1)^(3/2),x,1,sqrt(-x^2-1)*sqrt(1/(x^2+1))*EllipticE(sin(arctan(x)),sqrt(2)),1],
[sqrt(x^2-1)/(x^2+1)^(3/2),x,1,sqrt(x^2-1)*EllipticE(sin(arctan(x)),sqrt(2))/sqrt((-x^2+1)/(x^2+1))/sqrt(x^2+1),1],
[sqrt(-x^2-1)/(x^2+1)^(3/2),x,2,sqrt(-x^2-1)*arctan(x)/sqrt(x^2+1),1],
[sqrt(x^2-1)/(-x^2+1)^(3/2),x,2,sqrt(x^2-1)*arctanh(x)/sqrt(-x^2+1),1],
[sqrt(-x^2-1)/(-x^2+1)^(3/2),x,5,x*sqrt(-x^2-1)/sqrt(-x^2+1)+sqrt(x^2+1)*EllipticE(sin(arcsin(x)),sqrt(-1))/sqrt(-x^2-1)-sqrt(x^2+1)*InverseJacobiAM(arcsin(x),sqrt(-1))/sqrt(-x^2-1),1],
[1/(5*x^2-2)^(3/2)/sqrt(15*x^2+6),x,6,-1/4*EllipticE(sin(arcsin(sqrt(10)*x/sqrt(5*x^2-2))),sqrt(1/2))/sqrt(15),1],
[1/sqrt(b*x^2+1)/(d*x^2+1)^(3/2),x,1,-sqrt(d)*sqrt(b*x^2+1)*EllipticE(sin(arctan(sqrt(d)*x)),sqrt(1-b/d))/(b-d)/sqrt((b*x^2+1)/(d*x^2+1))/sqrt(d*x^2+1)+b*sqrt(b*x^2+1)*InverseJacobiAM(arctan(sqrt(d)*x),sqrt(1-b/d))/(b-d)/sqrt(d)/sqrt((b*x^2+1)/(d*x^2+1))/sqrt(d*x^2+1),1],
[1/(b*x^2+1)^(3/2)/sqrt(d*x^2+1),x,1,sqrt(b)*sqrt(d*x^2+1)*EllipticE(sin(arctan(sqrt(b)*x)),sqrt(1-d/b))/(b-d)/sqrt(b*x^2+1)/sqrt((d*x^2+1)/(b*x^2+1))-d*sqrt(d*x^2+1)*InverseJacobiAM(arctan(sqrt(b)*x),sqrt(1-d/b))/sqrt(b)/(b-d)/sqrt(b*x^2+1)/sqrt((d*x^2+1)/(b*x^2+1)),1],
[1/sqrt(b*x^2+a)/(d*x^2+c)^(3/2),x,1,-sqrt(d)*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/sqrt(c)/(-a*d+b*c)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+b*sqrt(c)*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a/sqrt(d)/(-a*d+b*c)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[1/(b*x^2+a)^(3/2)/sqrt(d*x^2+c),x,1,sqrt(b)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/sqrt(a)/(-a*d+b*c)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-sqrt(a)*d*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(b)/c/(-a*d+b*c)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(-b*x^2+a)^(2/3)*(b*x^2+3*a)^3,x,8,18144/1235*a^3*x*(-b*x^2+a)^(2/3)-8991/1235*a^2*x*(-b*x^2+a)^(5/3)-144/95*a*b*x^3*(-b*x^2+a)^(5/3)-3/25*b^2*x^5*(-b*x^2+a)^(5/3)-72576*a^4*x/(1235*(1-sqrt(3))*a^(1/3)-1235*(-b*x^2+a)^(1/3))-36288/1235*3^(1/4)*sqrt(2+sqrt(3))*a^(13/3)*(a^(1/3)-(-b*x^2+a)^(1/3))*sqrt((a^(2/3)+a^(1/3)*(-b*x^2+a)^(1/3)+(-b*x^2+a)^(2/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)*EllipticE(sin(arcsin(((1+sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3)))),sqrt(-7+4*sqrt(3)))/b/x/sqrt(-a^(1/3)*(a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)+24192/1235*sqrt(2)*3^(3/4)*a^(13/3)*(a^(1/3)-(-b*x^2+a)^(1/3))*sqrt((a^(2/3)+a^(1/3)*(-b*x^2+a)^(1/3)+(-b*x^2+a)^(2/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)*InverseJacobiAM(arcsin(((1+sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))),sqrt(-7+4*sqrt(3)))/b/x/sqrt(-a^(1/3)*(a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2),1],
[(-b*x^2+a)^(2/3)*(b*x^2+3*a)^2,x,7,7776/1729*a^2*x*(-b*x^2+a)^(2/3)-369/247*a*x*(-b*x^2+a)^(5/3)-3/19*b*x^3*(-b*x^2+a)^(5/3)-31104*a^3*x/(1729*(1-sqrt(3))*a^(1/3)-1729*(-b*x^2+a)^(1/3))-15552/1729*3^(1/4)*sqrt(2+sqrt(3))*a^(10/3)*(a^(1/3)-(-b*x^2+a)^(1/3))*sqrt((a^(2/3)+a^(1/3)*(-b*x^2+a)^(1/3)+(-b*x^2+a)^(2/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)*EllipticE(sin(arcsin(((1+sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3)))),sqrt(-7+4*sqrt(3)))/b/x/sqrt(-a^(1/3)*(a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)+10368/1729*sqrt(2)*3^(3/4)*a^(10/3)*(a^(1/3)-(-b*x^2+a)^(1/3))*sqrt((a^(2/3)+a^(1/3)*(-b*x^2+a)^(1/3)+(-b*x^2+a)^(2/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)*InverseJacobiAM(arcsin(((1+sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))),sqrt(-7+4*sqrt(3)))/b/x/sqrt(-a^(1/3)*(a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2),1],
[(-b*x^2+a)^(2/3)*(b*x^2+3*a),x,6,18/13*a*x*(-b*x^2+a)^(2/3)-3/13*x*(-b*x^2+a)^(5/3)-72*a^2*x/(13*(1-sqrt(3))*a^(1/3)-13*(-b*x^2+a)^(1/3))-36/13*3^(1/4)*sqrt(2+sqrt(3))*a^(7/3)*(a^(1/3)-(-b*x^2+a)^(1/3))*sqrt((a^(2/3)+a^(1/3)*(-b*x^2+a)^(1/3)+(-b*x^2+a)^(2/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)*EllipticE(sin(arcsin(((1+sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3)))),sqrt(-7+4*sqrt(3)))/b/x/sqrt(-a^(1/3)*(a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)+24/13*sqrt(2)*3^(3/4)*a^(7/3)*(a^(1/3)-(-b*x^2+a)^(1/3))*sqrt((a^(2/3)+a^(1/3)*(-b*x^2+a)^(1/3)+(-b*x^2+a)^(2/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)*InverseJacobiAM(arcsin(((1+sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))),sqrt(-7+4*sqrt(3)))/b/x/sqrt(-a^(1/3)*(a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2),1],
[(-b*x^2+a)^(2/3)/(b*x^2+3*a),x,6,3*x/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))+2^(1/3)*a^(1/6)*arctan(sqrt(3)*sqrt(a)/sqrt(b)/x)/sqrt(3)/sqrt(b)+2^(1/3)*a^(1/6)*arctan(sqrt(3)*a^(1/6)*(a^(1/3)-2^(1/3)*(-b*x^2+a)^(1/3))/sqrt(b)/x)/sqrt(3)/sqrt(b)-1/3*2^(1/3)*a^(1/6)*arctanh(sqrt(b)*x/sqrt(a))/sqrt(b)+2^(1/3)*a^(1/6)*arctanh(sqrt(b)*x/a^(1/6)/(a^(1/3)+2^(1/3)*(-b*x^2+a)^(1/3)))/sqrt(b)+3/2*3^(1/4)*sqrt(2+sqrt(3))*a^(1/3)*(a^(1/3)-(-b*x^2+a)^(1/3))*sqrt((a^(2/3)+a^(1/3)*(-b*x^2+a)^(1/3)+(-b*x^2+a)^(2/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)*EllipticE(sin(arcsin(((1+sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3)))),sqrt(-7+4*sqrt(3)))/b/x/sqrt(-a^(1/3)*(a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)-sqrt(2)*3^(3/4)*a^(1/3)*(a^(1/3)-(-b*x^2+a)^(1/3))*sqrt((a^(2/3)+a^(1/3)*(-b*x^2+a)^(1/3)+(-b*x^2+a)^(2/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)*InverseJacobiAM(arcsin(((1+sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))),sqrt(-7+4*sqrt(3)))/b/x/sqrt(-a^(1/3)*(a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2),1],
[(-b*x^2+a)^(2/3)/(b*x^2+3*a)^2,x,6,1/6*x*(-b*x^2+a)^(2/3)/a/(b*x^2+3*a)-1/6*x/a/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))-1/12*sqrt(2+sqrt(3))*(a^(1/3)-(-b*x^2+a)^(1/3))*sqrt((a^(2/3)+a^(1/3)*(-b*x^2+a)^(1/3)+(-b*x^2+a)^(2/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)*EllipticE(sin(arcsin(((1+sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3)))),sqrt(-7+4*sqrt(3)))*3^(1/4)/a^(2/3)/b/x/sqrt(-a^(1/3)*(a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)+1/9*(a^(1/3)-(-b*x^2+a)^(1/3))*sqrt((a^(2/3)+a^(1/3)*(-b*x^2+a)^(1/3)+(-b*x^2+a)^(2/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)*InverseJacobiAM(arcsin(((1+sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))),sqrt(-7+4*sqrt(3)))/sqrt(2)*3^(3/4)/a^(2/3)/b/x/sqrt(-a^(1/3)*(a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2),1],
[(-b*x^2+a)^(2/3)/(b*x^2+3*a)^3,x,8,1/12*x*(-b*x^2+a)^(2/3)/a/(b*x^2+3*a)^2+1/36*x*(-b*x^2+a)^(2/3)/a^2/(b*x^2+3*a)-1/36*x/a^2/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))+1/144*arctan(sqrt(3)*sqrt(a)/sqrt(b)/x)*2^(1/3)/sqrt(3)/a^(11/6)/sqrt(b)+1/144*arctan(sqrt(3)*a^(1/6)*(a^(1/3)-2^(1/3)*(-b*x^2+a)^(1/3))/sqrt(b)/x)*2^(1/3)/sqrt(3)/a^(11/6)/sqrt(b)-1/432*arctanh(sqrt(b)*x/sqrt(a))*2^(1/3)/a^(11/6)/sqrt(b)+1/144*arctanh(sqrt(b)*x/a^(1/6)/(a^(1/3)+2^(1/3)*(-b*x^2+a)^(1/3)))*2^(1/3)/a^(11/6)/sqrt(b)-1/72*sqrt(2+sqrt(3))*(a^(1/3)-(-b*x^2+a)^(1/3))*sqrt((a^(2/3)+a^(1/3)*(-b*x^2+a)^(1/3)+(-b*x^2+a)^(2/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)*EllipticE(sin(arcsin(((1+sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3)))),sqrt(-7+4*sqrt(3)))*3^(1/4)/a^(5/3)/b/x/sqrt(-a^(1/3)*(a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)+1/54*(a^(1/3)-(-b*x^2+a)^(1/3))*sqrt((a^(2/3)+a^(1/3)*(-b*x^2+a)^(1/3)+(-b*x^2+a)^(2/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)*InverseJacobiAM(arcsin(((1+sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))),sqrt(-7+4*sqrt(3)))/sqrt(2)*3^(3/4)/a^(5/3)/b/x/sqrt(-a^(1/3)*(a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2),1],
[(-b*x^2+a)^(2/3)/(b*x^2+3*a)^4,x,9,1/18*x*(-b*x^2+a)^(2/3)/a/(b*x^2+3*a)^3+1/54*x*(-b*x^2+a)^(2/3)/a^2/(b*x^2+3*a)^2+1/144*x*(-b*x^2+a)^(2/3)/a^3/(b*x^2+3*a)-1/144*x/a^3/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))+7/2592*arctan(sqrt(3)*sqrt(a)/sqrt(b)/x)*2^(1/3)/sqrt(3)/a^(17/6)/sqrt(b)+7/2592*arctan(sqrt(3)*a^(1/6)*(a^(1/3)-2^(1/3)*(-b*x^2+a)^(1/3))/sqrt(b)/x)*2^(1/3)/sqrt(3)/a^(17/6)/sqrt(b)-7/7776*arctanh(sqrt(b)*x/sqrt(a))*2^(1/3)/a^(17/6)/sqrt(b)+7/2592*arctanh(sqrt(b)*x/a^(1/6)/(a^(1/3)+2^(1/3)*(-b*x^2+a)^(1/3)))*2^(1/3)/a^(17/6)/sqrt(b)-1/288*sqrt(2+sqrt(3))*(a^(1/3)-(-b*x^2+a)^(1/3))*sqrt((a^(2/3)+a^(1/3)*(-b*x^2+a)^(1/3)+(-b*x^2+a)^(2/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)*EllipticE(sin(arcsin(((1+sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3)))),sqrt(-7+4*sqrt(3)))*3^(1/4)/a^(8/3)/b/x/sqrt(-a^(1/3)*(a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)+1/216*(a^(1/3)-(-b*x^2+a)^(1/3))*sqrt((a^(2/3)+a^(1/3)*(-b*x^2+a)^(1/3)+(-b*x^2+a)^(2/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)*InverseJacobiAM(arcsin(((1+sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))),sqrt(-7+4*sqrt(3)))/sqrt(2)*3^(3/4)/a^(8/3)/b/x/sqrt(-a^(1/3)*(a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2),1],
[(-b*x^2+a)^(5/3)*(b*x^2+3*a)^3,x,9,2809728/267995*a^4*x*(-b*x^2+a)^(2/3)+1404864/191425*a^3*x*(-b*x^2+a)^(5/3)-70713/14725*a^2*x*(-b*x^2+a)^(8/3)-882/775*a*b*x^3*(-b*x^2+a)^(8/3)-3/31*b^2*x^5*(-b*x^2+a)^(8/3)-11238912*a^5*x/(267995*(1-sqrt(3))*a^(1/3)-267995*(-b*x^2+a)^(1/3))-5619456/267995*3^(1/4)*sqrt(2+sqrt(3))*a^(16/3)*(a^(1/3)-(-b*x^2+a)^(1/3))*sqrt((a^(2/3)+a^(1/3)*(-b*x^2+a)^(1/3)+(-b*x^2+a)^(2/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)*EllipticE(sin(arcsin(((1+sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3)))),sqrt(-7+4*sqrt(3)))/b/x/sqrt(-a^(1/3)*(a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)+3746304/267995*sqrt(2)*3^(3/4)*a^(16/3)*(a^(1/3)-(-b*x^2+a)^(1/3))*sqrt((a^(2/3)+a^(1/3)*(-b*x^2+a)^(1/3)+(-b*x^2+a)^(2/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)*InverseJacobiAM(arcsin(((1+sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))),sqrt(-7+4*sqrt(3)))/b/x/sqrt(-a^(1/3)*(a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2),1],
[(-b*x^2+a)^(5/3)*(b*x^2+3*a)^2,x,8,28512/8645*a^3*x*(-b*x^2+a)^(2/3)+14256/6175*a^2*x*(-b*x^2+a)^(5/3)-477/475*a*x*(-b*x^2+a)^(8/3)-3/25*b*x^3*(-b*x^2+a)^(8/3)-114048*a^4*x/(8645*(1-sqrt(3))*a^(1/3)-8645*(-b*x^2+a)^(1/3))-57024/8645*3^(1/4)*sqrt(2+sqrt(3))*a^(13/3)*(a^(1/3)-(-b*x^2+a)^(1/3))*sqrt((a^(2/3)+a^(1/3)*(-b*x^2+a)^(1/3)+(-b*x^2+a)^(2/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)*EllipticE(sin(arcsin(((1+sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3)))),sqrt(-7+4*sqrt(3)))/b/x/sqrt(-a^(1/3)*(a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)+38016/8645*sqrt(2)*3^(3/4)*a^(13/3)*(a^(1/3)-(-b*x^2+a)^(1/3))*sqrt((a^(2/3)+a^(1/3)*(-b*x^2+a)^(1/3)+(-b*x^2+a)^(2/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)*InverseJacobiAM(arcsin(((1+sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))),sqrt(-7+4*sqrt(3)))/b/x/sqrt(-a^(1/3)*(a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2),1],
[(-b*x^2+a)^(5/3)*(b*x^2+3*a),x,7,1800/1729*a^2*x*(-b*x^2+a)^(2/3)+180/247*a*x*(-b*x^2+a)^(5/3)-3/19*x*(-b*x^2+a)^(8/3)-7200*a^3*x/(1729*(1-sqrt(3))*a^(1/3)-1729*(-b*x^2+a)^(1/3))-3600/1729*3^(1/4)*sqrt(2+sqrt(3))*a^(10/3)*(a^(1/3)-(-b*x^2+a)^(1/3))*sqrt((a^(2/3)+a^(1/3)*(-b*x^2+a)^(1/3)+(-b*x^2+a)^(2/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)*EllipticE(sin(arcsin(((1+sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3)))),sqrt(-7+4*sqrt(3)))/b/x/sqrt(-a^(1/3)*(a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)+2400/1729*sqrt(2)*3^(3/4)*a^(10/3)*(a^(1/3)-(-b*x^2+a)^(1/3))*sqrt((a^(2/3)+a^(1/3)*(-b*x^2+a)^(1/3)+(-b*x^2+a)^(2/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)*InverseJacobiAM(arcsin(((1+sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))),sqrt(-7+4*sqrt(3)))/b/x/sqrt(-a^(1/3)*(a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2),1],
[(-b*x^2+a)^(5/3)/(b*x^2+3*a),x,7,-3/7*x*(-b*x^2+a)^(2/3)+96*a*x/(7*(1-sqrt(3))*a^(1/3)-7*(-b*x^2+a)^(1/3))+4*2^(1/3)*a^(7/6)*arctan(sqrt(3)*sqrt(a)/sqrt(b)/x)/sqrt(3)/sqrt(b)+4*2^(1/3)*a^(7/6)*arctan(sqrt(3)*a^(1/6)*(a^(1/3)-2^(1/3)*(-b*x^2+a)^(1/3))/sqrt(b)/x)/sqrt(3)/sqrt(b)-4/3*2^(1/3)*a^(7/6)*arctanh(sqrt(b)*x/sqrt(a))/sqrt(b)+4*2^(1/3)*a^(7/6)*arctanh(sqrt(b)*x/a^(1/6)/(a^(1/3)+2^(1/3)*(-b*x^2+a)^(1/3)))/sqrt(b)+48/7*3^(1/4)*sqrt(2+sqrt(3))*a^(4/3)*(a^(1/3)-(-b*x^2+a)^(1/3))*sqrt((a^(2/3)+a^(1/3)*(-b*x^2+a)^(1/3)+(-b*x^2+a)^(2/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)*EllipticE(sin(arcsin(((1+sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3)))),sqrt(-7+4*sqrt(3)))/b/x/sqrt(-a^(1/3)*(a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)-32/7*sqrt(2)*3^(3/4)*a^(4/3)*(a^(1/3)-(-b*x^2+a)^(1/3))*sqrt((a^(2/3)+a^(1/3)*(-b*x^2+a)^(1/3)+(-b*x^2+a)^(2/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)*InverseJacobiAM(arcsin(((1+sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))),sqrt(-7+4*sqrt(3)))/b/x/sqrt(-a^(1/3)*(a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2),1],
[(-b*x^2+a)^(5/3)/(b*x^2+3*a)^2,x,7,2*x*(-b*x^2+a)^(2/3)/(3*b*x^2+9*a)-11*x/(3*(1-sqrt(3))*a^(1/3)-3*(-b*x^2+a)^(1/3))-2^(1/3)*a^(1/6)*arctan(sqrt(3)*sqrt(a)/sqrt(b)/x)/sqrt(3)/sqrt(b)-2^(1/3)*a^(1/6)*arctan(sqrt(3)*a^(1/6)*(a^(1/3)-2^(1/3)*(-b*x^2+a)^(1/3))/sqrt(b)/x)/sqrt(3)/sqrt(b)+1/3*2^(1/3)*a^(1/6)*arctanh(sqrt(b)*x/sqrt(a))/sqrt(b)-2^(1/3)*a^(1/6)*arctanh(sqrt(b)*x/a^(1/6)/(a^(1/3)+2^(1/3)*(-b*x^2+a)^(1/3)))/sqrt(b)-11/6*sqrt(2+sqrt(3))*a^(1/3)*(a^(1/3)-(-b*x^2+a)^(1/3))*sqrt((a^(2/3)+a^(1/3)*(-b*x^2+a)^(1/3)+(-b*x^2+a)^(2/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)*EllipticE(sin(arcsin(((1+sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3)))),sqrt(-7+4*sqrt(3)))*3^(1/4)/b/x/sqrt(-a^(1/3)*(a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)+11/9*sqrt(2)*a^(1/3)*(a^(1/3)-(-b*x^2+a)^(1/3))*sqrt((a^(2/3)+a^(1/3)*(-b*x^2+a)^(1/3)+(-b*x^2+a)^(2/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)*InverseJacobiAM(arcsin(((1+sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))),sqrt(-7+4*sqrt(3)))*3^(3/4)/b/x/sqrt(-a^(1/3)*(a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2),1],
[(-b*x^2+a)^(5/3)/(b*x^2+3*a)^3,x,9,1/3*x*(-b*x^2+a)^(2/3)/(b*x^2+3*a)^2-1/18*x*(-b*x^2+a)^(2/3)/a/(b*x^2+3*a)+1/18*x/a/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))+1/36*arctan(sqrt(3)*sqrt(a)/sqrt(b)/x)*2^(1/3)/sqrt(3)/a^(5/6)/sqrt(b)+1/36*arctan(sqrt(3)*a^(1/6)*(a^(1/3)-2^(1/3)*(-b*x^2+a)^(1/3))/sqrt(b)/x)*2^(1/3)/sqrt(3)/a^(5/6)/sqrt(b)-1/108*arctanh(sqrt(b)*x/sqrt(a))*2^(1/3)/a^(5/6)/sqrt(b)+1/36*arctanh(sqrt(b)*x/a^(1/6)/(a^(1/3)+2^(1/3)*(-b*x^2+a)^(1/3)))*2^(1/3)/a^(5/6)/sqrt(b)+1/36*sqrt(2+sqrt(3))*(a^(1/3)-(-b*x^2+a)^(1/3))*sqrt((a^(2/3)+a^(1/3)*(-b*x^2+a)^(1/3)+(-b*x^2+a)^(2/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)*EllipticE(sin(arcsin(((1+sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3)))),sqrt(-7+4*sqrt(3)))*3^(1/4)/a^(2/3)/b/x/sqrt(-a^(1/3)*(a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)-1/27*(a^(1/3)-(-b*x^2+a)^(1/3))*sqrt((a^(2/3)+a^(1/3)*(-b*x^2+a)^(1/3)+(-b*x^2+a)^(2/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)*InverseJacobiAM(arcsin(((1+sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))),sqrt(-7+4*sqrt(3)))/sqrt(2)*3^(3/4)/a^(2/3)/b/x/sqrt(-a^(1/3)*(a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2),1],
[(b*x^2+3*a)^3/(-b*x^2+a)^(1/3),x,7,-25029/1729*a^2*x*(-b*x^2+a)^(2/3)-558/247*a*b*x^3*(-b*x^2+a)^(2/3)-3/19*b^2*x^5*(-b*x^2+a)^(2/3)-215136*a^3*x/(1729*(1-sqrt(3))*a^(1/3)-1729*(-b*x^2+a)^(1/3))-107568/1729*3^(1/4)*sqrt(2+sqrt(3))*a^(10/3)*(a^(1/3)-(-b*x^2+a)^(1/3))*sqrt((a^(2/3)+a^(1/3)*(-b*x^2+a)^(1/3)+(-b*x^2+a)^(2/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)*EllipticE(sin(arcsin(((1+sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3)))),sqrt(-7+4*sqrt(3)))/b/x/sqrt(-a^(1/3)*(a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)+71712/1729*sqrt(2)*3^(3/4)*a^(10/3)*(a^(1/3)-(-b*x^2+a)^(1/3))*sqrt((a^(2/3)+a^(1/3)*(-b*x^2+a)^(1/3)+(-b*x^2+a)^(2/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)*InverseJacobiAM(arcsin(((1+sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))),sqrt(-7+4*sqrt(3)))/b/x/sqrt(-a^(1/3)*(a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2),1],
[(b*x^2+3*a)^2/(-b*x^2+a)^(1/3),x,6,-261/91*a*x*(-b*x^2+a)^(2/3)-3/13*b*x^3*(-b*x^2+a)^(2/3)-3240*a^2*x/(91*(1-sqrt(3))*a^(1/3)-91*(-b*x^2+a)^(1/3))-1620/91*3^(1/4)*sqrt(2+sqrt(3))*a^(7/3)*(a^(1/3)-(-b*x^2+a)^(1/3))*sqrt((a^(2/3)+a^(1/3)*(-b*x^2+a)^(1/3)+(-b*x^2+a)^(2/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)*EllipticE(sin(arcsin(((1+sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3)))),sqrt(-7+4*sqrt(3)))/b/x/sqrt(-a^(1/3)*(a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)+1080/91*sqrt(2)*3^(3/4)*a^(7/3)*(a^(1/3)-(-b*x^2+a)^(1/3))*sqrt((a^(2/3)+a^(1/3)*(-b*x^2+a)^(1/3)+(-b*x^2+a)^(2/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)*InverseJacobiAM(arcsin(((1+sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))),sqrt(-7+4*sqrt(3)))/b/x/sqrt(-a^(1/3)*(a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2),1],
[(b*x^2+3*a)/(-b*x^2+a)^(1/3),x,5,-3/7*x*(-b*x^2+a)^(2/3)-72*a*x/(7*(1-sqrt(3))*a^(1/3)-7*(-b*x^2+a)^(1/3))-36/7*3^(1/4)*sqrt(2+sqrt(3))*a^(4/3)*(a^(1/3)-(-b*x^2+a)^(1/3))*sqrt((a^(2/3)+a^(1/3)*(-b*x^2+a)^(1/3)+(-b*x^2+a)^(2/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)*EllipticE(sin(arcsin(((1+sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3)))),sqrt(-7+4*sqrt(3)))/b/x/sqrt(-a^(1/3)*(a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)+24/7*sqrt(2)*3^(3/4)*a^(4/3)*(a^(1/3)-(-b*x^2+a)^(1/3))*sqrt((a^(2/3)+a^(1/3)*(-b*x^2+a)^(1/3)+(-b*x^2+a)^(2/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)*InverseJacobiAM(arcsin(((1+sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))),sqrt(-7+4*sqrt(3)))/b/x/sqrt(-a^(1/3)*(a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2),1],
[1/(-b*x^2+a)^(1/3)/(b*x^2+3*a),x,1,1/4*arctan(sqrt(3)*sqrt(a)/sqrt(b)/x)*2^(1/3)/sqrt(3)/a^(5/6)/sqrt(b)+1/4*arctan(sqrt(3)*a^(1/6)*(a^(1/3)-2^(1/3)*(-b*x^2+a)^(1/3))/sqrt(b)/x)*2^(1/3)/sqrt(3)/a^(5/6)/sqrt(b)-1/12*arctanh(sqrt(b)*x/sqrt(a))*2^(1/3)/a^(5/6)/sqrt(b)+1/4*arctanh(sqrt(b)*x/a^(1/6)/(a^(1/3)+2^(1/3)*(-b*x^2+a)^(1/3)))*2^(1/3)/a^(5/6)/sqrt(b),1],
[1/(-b*x^2+a)^(1/3)/(b*x^2+3*a)^2,x,7,1/24*x*(-b*x^2+a)^(2/3)/a^2/(b*x^2+3*a)-1/24*x/a^2/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))+1/16*arctan(sqrt(3)*sqrt(a)/sqrt(b)/x)*2^(1/3)/sqrt(3)/a^(11/6)/sqrt(b)+1/16*arctan(sqrt(3)*a^(1/6)*(a^(1/3)-2^(1/3)*(-b*x^2+a)^(1/3))/sqrt(b)/x)*2^(1/3)/sqrt(3)/a^(11/6)/sqrt(b)-1/48*arctanh(sqrt(b)*x/sqrt(a))*2^(1/3)/a^(11/6)/sqrt(b)+1/16*arctanh(sqrt(b)*x/a^(1/6)/(a^(1/3)+2^(1/3)*(-b*x^2+a)^(1/3)))*2^(1/3)/a^(11/6)/sqrt(b)-1/48*sqrt(2+sqrt(3))*(a^(1/3)-(-b*x^2+a)^(1/3))*sqrt((a^(2/3)+a^(1/3)*(-b*x^2+a)^(1/3)+(-b*x^2+a)^(2/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)*EllipticE(sin(arcsin(((1+sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3)))),sqrt(-7+4*sqrt(3)))*3^(1/4)/a^(5/3)/b/x/sqrt(-a^(1/3)*(a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)+1/36*(a^(1/3)-(-b*x^2+a)^(1/3))*sqrt((a^(2/3)+a^(1/3)*(-b*x^2+a)^(1/3)+(-b*x^2+a)^(2/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)*InverseJacobiAM(arcsin(((1+sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))),sqrt(-7+4*sqrt(3)))/sqrt(2)*3^(3/4)/a^(5/3)/b/x/sqrt(-a^(1/3)*(a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2),1],
[1/(-b*x^2+a)^(1/3)/(b*x^2+3*a)^3,x,8,1/48*x*(-b*x^2+a)^(2/3)/a^2/(b*x^2+3*a)^2+5/288*x*(-b*x^2+a)^(2/3)/a^3/(b*x^2+3*a)-5/288*x/a^3/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))+5/288*arctan(sqrt(3)*sqrt(a)/sqrt(b)/x)*2^(1/3)/sqrt(3)/a^(17/6)/sqrt(b)+5/288*arctan(sqrt(3)*a^(1/6)*(a^(1/3)-2^(1/3)*(-b*x^2+a)^(1/3))/sqrt(b)/x)*2^(1/3)/sqrt(3)/a^(17/6)/sqrt(b)-5/864*arctanh(sqrt(b)*x/sqrt(a))*2^(1/3)/a^(17/6)/sqrt(b)+5/288*arctanh(sqrt(b)*x/a^(1/6)/(a^(1/3)+2^(1/3)*(-b*x^2+a)^(1/3)))*2^(1/3)/a^(17/6)/sqrt(b)-5/576*sqrt(2+sqrt(3))*(a^(1/3)-(-b*x^2+a)^(1/3))*sqrt((a^(2/3)+a^(1/3)*(-b*x^2+a)^(1/3)+(-b*x^2+a)^(2/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)*EllipticE(sin(arcsin(((1+sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3)))),sqrt(-7+4*sqrt(3)))*3^(1/4)/a^(8/3)/b/x/sqrt(-a^(1/3)*(a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)+5/432*(a^(1/3)-(-b*x^2+a)^(1/3))*sqrt((a^(2/3)+a^(1/3)*(-b*x^2+a)^(1/3)+(-b*x^2+a)^(2/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)*InverseJacobiAM(arcsin(((1+sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))),sqrt(-7+4*sqrt(3)))/sqrt(2)*3^(3/4)/a^(8/3)/b/x/sqrt(-a^(1/3)*(a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2),1],
[(b*x^2+3*a)^4/(-b*x^2+a)^(4/3),x,8,384*a^3*x/(-b*x^2+a)^(1/3)+8103/247*a^2*x*(-b*x^2+a)^(2/3)+786/247*a*b*x^3*(-b*x^2+a)^(2/3)+3/19*b^2*x^5*(-b*x^2+a)^(2/3)+248832*a^3*x/(247*(1-sqrt(3))*a^(1/3)-247*(-b*x^2+a)^(1/3))+124416/247*3^(1/4)*sqrt(2+sqrt(3))*a^(10/3)*(a^(1/3)-(-b*x^2+a)^(1/3))*sqrt((a^(2/3)+a^(1/3)*(-b*x^2+a)^(1/3)+(-b*x^2+a)^(2/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)*EllipticE(sin(arcsin(((1+sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3)))),sqrt(-7+4*sqrt(3)))/b/x/sqrt(-a^(1/3)*(a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)-82944/247*sqrt(2)*3^(3/4)*a^(10/3)*(a^(1/3)-(-b*x^2+a)^(1/3))*sqrt((a^(2/3)+a^(1/3)*(-b*x^2+a)^(1/3)+(-b*x^2+a)^(2/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)*InverseJacobiAM(arcsin(((1+sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))),sqrt(-7+4*sqrt(3)))/b/x/sqrt(-a^(1/3)*(a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2),1],
[(b*x^2+3*a)^3/(-b*x^2+a)^(4/3),x,7,96*a^2*x/(-b*x^2+a)^(1/3)+417/91*a*x*(-b*x^2+a)^(2/3)+3/13*b*x^3*(-b*x^2+a)^(2/3)+20088*a^2*x/(91*(1-sqrt(3))*a^(1/3)-91*(-b*x^2+a)^(1/3))+10044/91*3^(1/4)*sqrt(2+sqrt(3))*a^(7/3)*(a^(1/3)-(-b*x^2+a)^(1/3))*sqrt((a^(2/3)+a^(1/3)*(-b*x^2+a)^(1/3)+(-b*x^2+a)^(2/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)*EllipticE(sin(arcsin(((1+sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3)))),sqrt(-7+4*sqrt(3)))/b/x/sqrt(-a^(1/3)*(a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)-6696/91*sqrt(2)*3^(3/4)*a^(7/3)*(a^(1/3)-(-b*x^2+a)^(1/3))*sqrt((a^(2/3)+a^(1/3)*(-b*x^2+a)^(1/3)+(-b*x^2+a)^(2/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)*InverseJacobiAM(arcsin(((1+sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))),sqrt(-7+4*sqrt(3)))/b/x/sqrt(-a^(1/3)*(a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2),1],
[(b*x^2+3*a)^2/(-b*x^2+a)^(4/3),x,6,24*a*x/(-b*x^2+a)^(1/3)+3/7*x*(-b*x^2+a)^(2/3)+324*a*x/(7*(1-sqrt(3))*a^(1/3)-7*(-b*x^2+a)^(1/3))+162/7*3^(1/4)*sqrt(2+sqrt(3))*a^(4/3)*(a^(1/3)-(-b*x^2+a)^(1/3))*sqrt((a^(2/3)+a^(1/3)*(-b*x^2+a)^(1/3)+(-b*x^2+a)^(2/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)*EllipticE(sin(arcsin(((1+sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3)))),sqrt(-7+4*sqrt(3)))/b/x/sqrt(-a^(1/3)*(a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)-108/7*sqrt(2)*3^(3/4)*a^(4/3)*(a^(1/3)-(-b*x^2+a)^(1/3))*sqrt((a^(2/3)+a^(1/3)*(-b*x^2+a)^(1/3)+(-b*x^2+a)^(2/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)*InverseJacobiAM(arcsin(((1+sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))),sqrt(-7+4*sqrt(3)))/b/x/sqrt(-a^(1/3)*(a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2),1],
[(b*x^2+3*a)/(-b*x^2+a)^(4/3),x,5,6*x/(-b*x^2+a)^(1/3)+9*x/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))+9/2*3^(1/4)*sqrt(2+sqrt(3))*a^(1/3)*(a^(1/3)-(-b*x^2+a)^(1/3))*sqrt((a^(2/3)+a^(1/3)*(-b*x^2+a)^(1/3)+(-b*x^2+a)^(2/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)*EllipticE(sin(arcsin(((1+sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3)))),sqrt(-7+4*sqrt(3)))/b/x/sqrt(-a^(1/3)*(a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)-3*sqrt(2)*3^(3/4)*a^(1/3)*(a^(1/3)-(-b*x^2+a)^(1/3))*sqrt((a^(2/3)+a^(1/3)*(-b*x^2+a)^(1/3)+(-b*x^2+a)^(2/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)*InverseJacobiAM(arcsin(((1+sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))),sqrt(-7+4*sqrt(3)))/b/x/sqrt(-a^(1/3)*(a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2),1],
[1/(-b*x^2+a)^(4/3)/(b*x^2+3*a),x,7,3/8*x/a^2/(-b*x^2+a)^(1/3)+3/8*x/a^2/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))+1/16*arctan(sqrt(3)*sqrt(a)/sqrt(b)/x)*2^(1/3)/sqrt(3)/a^(11/6)/sqrt(b)+1/16*arctan(sqrt(3)*a^(1/6)*(a^(1/3)-2^(1/3)*(-b*x^2+a)^(1/3))/sqrt(b)/x)*2^(1/3)/sqrt(3)/a^(11/6)/sqrt(b)-1/48*arctanh(sqrt(b)*x/sqrt(a))*2^(1/3)/a^(11/6)/sqrt(b)+1/16*arctanh(sqrt(b)*x/a^(1/6)/(a^(1/3)+2^(1/3)*(-b*x^2+a)^(1/3)))*2^(1/3)/a^(11/6)/sqrt(b)+3/16*sqrt(2+sqrt(3))*(a^(1/3)-(-b*x^2+a)^(1/3))*sqrt((a^(2/3)+a^(1/3)*(-b*x^2+a)^(1/3)+(-b*x^2+a)^(2/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)*EllipticE(sin(arcsin(((1+sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3)))),sqrt(-7+4*sqrt(3)))*3^(1/4)/a^(5/3)/b/x/sqrt(-a^(1/3)*(a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)-1/4*(a^(1/3)-(-b*x^2+a)^(1/3))*sqrt((a^(2/3)+a^(1/3)*(-b*x^2+a)^(1/3)+(-b*x^2+a)^(2/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)*InverseJacobiAM(arcsin(((1+sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))),sqrt(-7+4*sqrt(3)))/sqrt(2)*3^(3/4)/a^(5/3)/b/x/sqrt(-a^(1/3)*(a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2),1],
[1/(-b*x^2+a)^(4/3)/(b*x^2+3*a)^2,x,8,1/12*x/a^3/(-b*x^2+a)^(1/3)+1/24*x/a^2/(-b*x^2+a)^(1/3)/(b*x^2+3*a)+1/12*x/a^3/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))+1/32*arctan(sqrt(3)*sqrt(a)/sqrt(b)/x)*2^(1/3)/sqrt(3)/a^(17/6)/sqrt(b)+1/32*arctan(sqrt(3)*a^(1/6)*(a^(1/3)-2^(1/3)*(-b*x^2+a)^(1/3))/sqrt(b)/x)*2^(1/3)/sqrt(3)/a^(17/6)/sqrt(b)-1/96*arctanh(sqrt(b)*x/sqrt(a))*2^(1/3)/a^(17/6)/sqrt(b)+1/32*arctanh(sqrt(b)*x/a^(1/6)/(a^(1/3)+2^(1/3)*(-b*x^2+a)^(1/3)))*2^(1/3)/a^(17/6)/sqrt(b)+1/24*sqrt(2+sqrt(3))*(a^(1/3)-(-b*x^2+a)^(1/3))*sqrt((a^(2/3)+a^(1/3)*(-b*x^2+a)^(1/3)+(-b*x^2+a)^(2/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)*EllipticE(sin(arcsin(((1+sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3)))),sqrt(-7+4*sqrt(3)))*3^(1/4)/a^(8/3)/b/x/sqrt(-a^(1/3)*(a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)-1/18*(a^(1/3)-(-b*x^2+a)^(1/3))*sqrt((a^(2/3)+a^(1/3)*(-b*x^2+a)^(1/3)+(-b*x^2+a)^(2/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)*InverseJacobiAM(arcsin(((1+sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))),sqrt(-7+4*sqrt(3)))/sqrt(2)*3^(3/4)/a^(8/3)/b/x/sqrt(-a^(1/3)*(a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2),1],
[(b*x^2+3*a)^4/(-b*x^2+a)^(7/3),x,8,96*a^3*x/(-b*x^2+a)^(4/3)-144*a^2*x/(-b*x^2+a)^(1/3)-573/91*a*x*(-b*x^2+a)^(2/3)-3/13*b*x^3*(-b*x^2+a)^(2/3)-36936*a^2*x/(91*(1-sqrt(3))*a^(1/3)-91*(-b*x^2+a)^(1/3))-18468/91*3^(1/4)*sqrt(2+sqrt(3))*a^(7/3)*(a^(1/3)-(-b*x^2+a)^(1/3))*sqrt((a^(2/3)+a^(1/3)*(-b*x^2+a)^(1/3)+(-b*x^2+a)^(2/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)*EllipticE(sin(arcsin(((1+sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3)))),sqrt(-7+4*sqrt(3)))/b/x/sqrt(-a^(1/3)*(a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)+12312/91*sqrt(2)*3^(3/4)*a^(7/3)*(a^(1/3)-(-b*x^2+a)^(1/3))*sqrt((a^(2/3)+a^(1/3)*(-b*x^2+a)^(1/3)+(-b*x^2+a)^(2/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)*InverseJacobiAM(arcsin(((1+sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))),sqrt(-7+4*sqrt(3)))/b/x/sqrt(-a^(1/3)*(a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2),1],
[(b*x^2+3*a)^3/(-b*x^2+a)^(7/3),x,7,24*a^2*x/(-b*x^2+a)^(4/3)-12*a*x/(-b*x^2+a)^(1/3)-3/7*x*(-b*x^2+a)^(2/3)-324*a*x/(7*(1-sqrt(3))*a^(1/3)-7*(-b*x^2+a)^(1/3))-162/7*3^(1/4)*sqrt(2+sqrt(3))*a^(4/3)*(a^(1/3)-(-b*x^2+a)^(1/3))*sqrt((a^(2/3)+a^(1/3)*(-b*x^2+a)^(1/3)+(-b*x^2+a)^(2/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)*EllipticE(sin(arcsin(((1+sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3)))),sqrt(-7+4*sqrt(3)))/b/x/sqrt(-a^(1/3)*(a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)+108/7*sqrt(2)*3^(3/4)*a^(4/3)*(a^(1/3)-(-b*x^2+a)^(1/3))*sqrt((a^(2/3)+a^(1/3)*(-b*x^2+a)^(1/3)+(-b*x^2+a)^(2/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)*InverseJacobiAM(arcsin(((1+sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))),sqrt(-7+4*sqrt(3)))/b/x/sqrt(-a^(1/3)*(a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2),1],
[(b*x^2+3*a)^2/(-b*x^2+a)^(7/3),x,2,6*a*x/(-b*x^2+a)^(4/3)+3*x/(-b*x^2+a)^(1/3),1],
[(b*x^2+3*a)/(-b*x^2+a)^(7/3),x,6,3/2*x/(-b*x^2+a)^(4/3)+9/4*x/a/(-b*x^2+a)^(1/3)+9/4*x/a/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))+9/8*3^(1/4)*sqrt(2+sqrt(3))*(a^(1/3)-(-b*x^2+a)^(1/3))*sqrt((a^(2/3)+a^(1/3)*(-b*x^2+a)^(1/3)+(-b*x^2+a)^(2/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)*EllipticE(sin(arcsin(((1+sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3)))),sqrt(-7+4*sqrt(3)))/a^(2/3)/b/x/sqrt(-a^(1/3)*(a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)-3/2*3^(3/4)*(a^(1/3)-(-b*x^2+a)^(1/3))*sqrt((a^(2/3)+a^(1/3)*(-b*x^2+a)^(1/3)+(-b*x^2+a)^(2/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)*InverseJacobiAM(arcsin(((1+sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))),sqrt(-7+4*sqrt(3)))/sqrt(2)/a^(2/3)/b/x/sqrt(-a^(1/3)*(a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2),1],
[1/(-b*x^2+a)^(7/3)/(b*x^2+3*a),x,8,3/32*x/a^2/(-b*x^2+a)^(4/3)+21/64*x/a^3/(-b*x^2+a)^(1/3)+21/64*x/a^3/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))+1/64*arctan(sqrt(3)*sqrt(a)/sqrt(b)/x)*2^(1/3)/sqrt(3)/a^(17/6)/sqrt(b)+1/64*arctan(sqrt(3)*a^(1/6)*(a^(1/3)-2^(1/3)*(-b*x^2+a)^(1/3))/sqrt(b)/x)*2^(1/3)/sqrt(3)/a^(17/6)/sqrt(b)-1/192*arctanh(sqrt(b)*x/sqrt(a))*2^(1/3)/a^(17/6)/sqrt(b)+1/64*arctanh(sqrt(b)*x/a^(1/6)/(a^(1/3)+2^(1/3)*(-b*x^2+a)^(1/3)))*2^(1/3)/a^(17/6)/sqrt(b)+21/128*3^(1/4)*sqrt(2+sqrt(3))*(a^(1/3)-(-b*x^2+a)^(1/3))*sqrt((a^(2/3)+a^(1/3)*(-b*x^2+a)^(1/3)+(-b*x^2+a)^(2/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)*EllipticE(sin(arcsin(((1+sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3)))),sqrt(-7+4*sqrt(3)))/a^(8/3)/b/x/sqrt(-a^(1/3)*(a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)-7/32*3^(3/4)*(a^(1/3)-(-b*x^2+a)^(1/3))*sqrt((a^(2/3)+a^(1/3)*(-b*x^2+a)^(1/3)+(-b*x^2+a)^(2/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)*InverseJacobiAM(arcsin(((1+sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))),sqrt(-7+4*sqrt(3)))/sqrt(2)/a^(8/3)/b/x/sqrt(-a^(1/3)*(a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2),1],
[1/(-b*x^2+a)^(7/3)/(b*x^2+3*a)^2,x,9,5/384*x/a^3/(-b*x^2+a)^(4/3)+79/768*x/a^4/(-b*x^2+a)^(1/3)+1/24*x/a^2/(-b*x^2+a)^(4/3)/(b*x^2+3*a)+79/768*x/a^4/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))+1/256*sqrt(3)*arctan(sqrt(3)*sqrt(a)/sqrt(b)/x)*2^(1/3)/a^(23/6)/sqrt(b)+1/256*sqrt(3)*arctan(sqrt(3)*a^(1/6)*(a^(1/3)-2^(1/3)*(-b*x^2+a)^(1/3))/sqrt(b)/x)*2^(1/3)/a^(23/6)/sqrt(b)-1/256*arctanh(sqrt(b)*x/sqrt(a))*2^(1/3)/a^(23/6)/sqrt(b)+3/256*arctanh(sqrt(b)*x/a^(1/6)/(a^(1/3)+2^(1/3)*(-b*x^2+a)^(1/3)))*2^(1/3)/a^(23/6)/sqrt(b)+79/1536*sqrt(2+sqrt(3))*(a^(1/3)-(-b*x^2+a)^(1/3))*sqrt((a^(2/3)+a^(1/3)*(-b*x^2+a)^(1/3)+(-b*x^2+a)^(2/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)*EllipticE(sin(arcsin(((1+sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3)))),sqrt(-7+4*sqrt(3)))*3^(1/4)/a^(11/3)/b/x/sqrt(-a^(1/3)*(a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)-79/1152*(a^(1/3)-(-b*x^2+a)^(1/3))*sqrt((a^(2/3)+a^(1/3)*(-b*x^2+a)^(1/3)+(-b*x^2+a)^(2/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2)*InverseJacobiAM(arcsin(((1+sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))),sqrt(-7+4*sqrt(3)))/sqrt(2)*3^(3/4)/a^(11/3)/b/x/sqrt(-a^(1/3)*(a^(1/3)-(-b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(-b*x^2+a)^(1/3))^2),1],
[1/(-b*x^2-3*a)/(b*x^2-a)^(1/3),x,1,-1/4*arctan(sqrt(3)*sqrt(a)/sqrt(b)/x)*2^(1/3)/sqrt(3)/(-a)^(1/3)/sqrt(a)/sqrt(b)-1/4*arctan(sqrt(3)*sqrt(a)*((-a)^(1/3)-2^(1/3)*(b*x^2-a)^(1/3))/(-a)^(1/3)/sqrt(b)/x)*2^(1/3)/sqrt(3)/(-a)^(1/3)/sqrt(a)/sqrt(b)+1/12*arctanh(sqrt(b)*x/sqrt(a))*2^(1/3)/(-a)^(1/3)/sqrt(a)/sqrt(b)-1/4*arctanh((-a)^(1/3)*sqrt(b)*x/sqrt(a)/((-a)^(1/3)+2^(1/3)*(b*x^2-a)^(1/3)))*2^(1/3)/(-a)^(1/3)/sqrt(a)/sqrt(b),1],
[1/(-b*x^2+3*a)/(b*x^2+a)^(1/3),x,1,-1/12*arctan(sqrt(b)*x/sqrt(a))*2^(1/3)/a^(5/6)/sqrt(b)+1/4*arctan(sqrt(b)*x/a^(1/6)/(a^(1/3)+2^(1/3)*(b*x^2+a)^(1/3)))*2^(1/3)/a^(5/6)/sqrt(b)-1/4*arctanh(sqrt(3)*sqrt(a)/sqrt(b)/x)*2^(1/3)/sqrt(3)/a^(5/6)/sqrt(b)-1/4*arctanh(sqrt(3)*a^(1/6)*(a^(1/3)-2^(1/3)*(b*x^2+a)^(1/3))/sqrt(b)/x)*2^(1/3)/sqrt(3)/a^(5/6)/sqrt(b),1],
[1/(-d*x^2+c)/(3*d*x^2+c)^(1/3),x,1,-1/4*arctan(sqrt(3)*sqrt(d)*x/sqrt(c))*2^(1/3)/sqrt(3)/c^(5/6)/sqrt(d)+1/4*sqrt(3)*arctan(sqrt(3)*sqrt(d)*x/c^(1/6)/(c^(1/3)+2^(1/3)*(3*d*x^2+c)^(1/3)))*2^(1/3)/c^(5/6)/sqrt(d)-1/4*arctanh(sqrt(c)/sqrt(d)/x)*2^(1/3)/c^(5/6)/sqrt(d)-1/4*arctanh(c^(1/6)*(c^(1/3)-2^(1/3)*(3*d*x^2+c)^(1/3))/sqrt(d)/x)*2^(1/3)/c^(5/6)/sqrt(d),1],
[1/(-b*x^2+a)^(1/3)/(b*x^2+3*a),x,1,1/4*arctan(sqrt(3)*sqrt(a)/sqrt(b)/x)*2^(1/3)/sqrt(3)/a^(5/6)/sqrt(b)+1/4*arctan(sqrt(3)*a^(1/6)*(a^(1/3)-2^(1/3)*(-b*x^2+a)^(1/3))/sqrt(b)/x)*2^(1/3)/sqrt(3)/a^(5/6)/sqrt(b)-1/12*arctanh(sqrt(b)*x/sqrt(a))*2^(1/3)/a^(5/6)/sqrt(b)+1/4*arctanh(sqrt(b)*x/a^(1/6)/(a^(1/3)+2^(1/3)*(-b*x^2+a)^(1/3)))*2^(1/3)/a^(5/6)/sqrt(b),1],
[1/(-3*d*x^2+c)^(1/3)/(d*x^2+c),x,1,1/4*arctan(sqrt(c)/sqrt(d)/x)*2^(1/3)/c^(5/6)/sqrt(d)+1/4*arctan(c^(1/6)*(c^(1/3)-2^(1/3)*(-3*d*x^2+c)^(1/3))/sqrt(d)/x)*2^(1/3)/c^(5/6)/sqrt(d)-1/4*arctanh(sqrt(3)*sqrt(d)*x/sqrt(c))*2^(1/3)/sqrt(3)/c^(5/6)/sqrt(d)+1/4*sqrt(3)*arctanh(sqrt(3)*sqrt(d)*x/c^(1/6)/(c^(1/3)+2^(1/3)*(-3*d*x^2+c)^(1/3)))*2^(1/3)/c^(5/6)/sqrt(d),1],
[1/(-x^2+1)^(1/3)/(x^2+3),x,1,1/4*arctan(sqrt(3)/x)*2^(1/3)/sqrt(3)+1/4*arctan(sqrt(3)*(1-2^(1/3)*(-x^2+1)^(1/3))/x)*2^(1/3)/sqrt(3)-1/12*arctanh(x)*2^(1/3)+1/4*arctanh(x/(1+2^(1/3)*(-x^2+1)^(1/3)))*2^(1/3),1],
[1/(-x^2+3)/(x^2+1)^(1/3),x,1,-1/12*arctan(x)*2^(1/3)+1/4*arctan(x/(1+2^(1/3)*(x^2+1)^(1/3)))*2^(1/3)-1/4*arctanh(sqrt(3)/x)*2^(1/3)/sqrt(3)-1/4*arctanh(sqrt(3)*(1-2^(1/3)*(x^2+1)^(1/3))/x)*2^(1/3)/sqrt(3),1],
[(3-x)/(-x^2+1)^(1/3)/(x^2+3),x,1,-1/2*sqrt(3)*arctan(1/sqrt(3)-2^(2/3)*(1+x)^(2/3)/sqrt(3)/(1-x)^(1/3))*2^(1/3)-1/4*ln(x^2+3)*2^(1/3)+3/4*ln(2^(1/3)*(1-x)^(1/3)+(1+x)^(2/3))*2^(1/3),1],
[(3+x)/(-x^2+1)^(1/3)/(x^2+3),x,1,1/2*sqrt(3)*arctan(1/sqrt(3)-2^(2/3)*(1-x)^(2/3)/sqrt(3)/(1+x)^(1/3))*2^(1/3)+1/4*ln(x^2+3)*2^(1/3)-3/4*ln((1-x)^(2/3)+2^(1/3)*(1+x)^(1/3))*2^(1/3),1],
[1/(b*x^2+a)^(1/3)/(9*a*d/b+d*x^2),x,1,1/12*sqrt(b)*arctan(1/3*sqrt(b)*x/sqrt(a))/a^(5/6)/d+1/12*sqrt(b)*arctan(1/3*(a^(1/3)-(b*x^2+a)^(1/3))^2/a^(1/6)/sqrt(b)/x)/a^(5/6)/d-1/4*sqrt(b)*arctanh(sqrt(3)*a^(1/6)*(a^(1/3)-(b*x^2+a)^(1/3))/sqrt(b)/x)/sqrt(3)/a^(5/6)/d,1],
[1/(-b*x^2+a)^(1/3)/(-9*a*d/b+d*x^2),x,1,-1/4*sqrt(b)*arctan(sqrt(3)*a^(1/6)*(a^(1/3)-(-b*x^2+a)^(1/3))/sqrt(b)/x)/sqrt(3)/a^(5/6)/d-1/12*sqrt(b)*arctanh(1/3*sqrt(b)*x/sqrt(a))/a^(5/6)/d+1/12*sqrt(b)*arctanh(1/3*(a^(1/3)-(-b*x^2+a)^(1/3))^2/a^(1/6)/sqrt(b)/x)/a^(5/6)/d,1],
[1/(b*x^2-a)^(1/3)/(-9*a*d/b+d*x^2),x,1,1/4*sqrt(b)*arctan(sqrt(3)*a^(1/6)*(a^(1/3)+(b*x^2-a)^(1/3))/sqrt(b)/x)/sqrt(3)/a^(5/6)/d+1/12*sqrt(b)*arctanh(1/3*sqrt(b)*x/sqrt(a))/a^(5/6)/d-1/12*sqrt(b)*arctanh(1/3*(a^(1/3)+(b*x^2-a)^(1/3))^2/a^(1/6)/sqrt(b)/x)/a^(5/6)/d,1],
[1/(-b*x^2-a)^(1/3)/(9*a*d/b+d*x^2),x,1,-1/12*sqrt(b)*arctan(1/3*sqrt(b)*x/sqrt(a))/a^(5/6)/d-1/12*sqrt(b)*arctan(1/3*(a^(1/3)+(-b*x^2-a)^(1/3))^2/a^(1/6)/sqrt(b)/x)/a^(5/6)/d+1/4*sqrt(b)*arctanh(sqrt(3)*a^(1/6)*(a^(1/3)+(-b*x^2-a)^(1/3))/sqrt(b)/x)/sqrt(3)/a^(5/6)/d,1],
[1/(b*x^2+2)^(1/3)/(18*d/b+d*x^2),x,1,1/24*sqrt(b)*arctan(1/3*sqrt(b)*x/sqrt(2))*2^(1/6)/d+1/24*sqrt(b)*arctan(1/6*(2^(1/3)-(b*x^2+2)^(1/3))^2*2^(5/6)/sqrt(b)/x)*2^(1/6)/d-1/8*sqrt(b)*arctanh(2^(1/6)*sqrt(3)*(2^(1/3)-(b*x^2+2)^(1/3))/sqrt(b)/x)*2^(1/6)/sqrt(3)/d,1],
[1/(b*x^2-2)^(1/3)/(-18*d/b+d*x^2),x,1,1/8*sqrt(b)*arctan(2^(1/6)*sqrt(3)*(2^(1/3)+(b*x^2-2)^(1/3))/sqrt(b)/x)*2^(1/6)/sqrt(3)/d+1/24*sqrt(b)*arctanh(1/3*sqrt(b)*x/sqrt(2))*2^(1/6)/d-1/24*sqrt(b)*arctanh(1/6*(2^(1/3)+(b*x^2-2)^(1/3))^2*2^(5/6)/sqrt(b)/x)*2^(1/6)/d,1],
[1/(3*x^2+2)^(1/3)/(d*x^2+6*d),x,1,1/8*arctan(x/sqrt(6))*2^(1/6)/sqrt(3)/d+1/8*arctan(1/6*(2^(1/3)-(3*x^2+2)^(1/3))^2*2^(5/6)/sqrt(3)/x)*2^(1/6)/sqrt(3)/d-1/8*arctanh(2^(1/6)*(2^(1/3)-(3*x^2+2)^(1/3))/x)*2^(1/6)/d,1],
[1/(-3*x^2+2)^(1/3)/(d*x^2-6*d),x,1,-1/8*arctan(2^(1/6)*(2^(1/3)-(-3*x^2+2)^(1/3))/x)*2^(1/6)/d-1/8*arctanh(x/sqrt(6))*2^(1/6)/sqrt(3)/d+1/8*arctanh(1/6*(2^(1/3)-(-3*x^2+2)^(1/3))^2*2^(5/6)/sqrt(3)/x)*2^(1/6)/sqrt(3)/d,1],
[1/(3*x^2-2)^(1/3)/(d*x^2-6*d),x,1,1/8*arctan(2^(1/6)*(2^(1/3)+(3*x^2-2)^(1/3))/x)*2^(1/6)/d+1/8*arctanh(x/sqrt(6))*2^(1/6)/sqrt(3)/d-1/8*arctanh(1/6*(2^(1/3)+(3*x^2-2)^(1/3))^2*2^(5/6)/sqrt(3)/x)*2^(1/6)/sqrt(3)/d,1],
[1/(-3*x^2-2)^(1/3)/(d*x^2+6*d),x,1,-1/8*arctan(x/sqrt(6))*2^(1/6)/sqrt(3)/d-1/8*arctan(1/6*(2^(1/3)+(-3*x^2-2)^(1/3))^2*2^(5/6)/sqrt(3)/x)*2^(1/6)/sqrt(3)/d+1/8*arctanh(2^(1/6)*(2^(1/3)+(-3*x^2-2)^(1/3))/x)*2^(1/6)/d,1],
[1/(x^2+1)^(1/3)/(x^2+9),x,1,1/12*arctan(1/3*x)+1/12*arctan(1/3*(1-(x^2+1)^(1/3))^2/x)-1/4*arctanh(sqrt(3)*(1-(x^2+1)^(1/3))/x)/sqrt(3),1],
[1/(b*x^2+1)^(1/3)/(b*x^2+9),x,1,1/12*arctan(1/3*sqrt(b)*x)/sqrt(b)+1/12*arctan(1/3*(1-(b*x^2+1)^(1/3))^2/sqrt(b)/x)/sqrt(b)-1/4*arctanh(sqrt(3)*(1-(b*x^2+1)^(1/3))/sqrt(b)/x)/sqrt(3)/sqrt(b),1],
[1/(-x^2+1)^(1/3)/(-x^2+9),x,1,1/4*arctan(sqrt(3)*(1-(-x^2+1)^(1/3))/x)/sqrt(3)+1/12*arctanh(1/3*x)-1/12*arctanh(1/3*(1-(-x^2+1)^(1/3))^2/x),1],
[(b*x^2+a)^(1/3)*(d*x^2+c)^2,x,5,3/935*(187*c^2-3*a*d*(-9*a*d+34*b*c)/b^2)*x*(b*x^2+a)^(1/3)+3/187*d*(-9*a*d+34*b*c)*x*(b*x^2+a)^(4/3)/b^2+3/17*d^2*x^3*(b*x^2+a)^(4/3)/b-2/935*3^(3/4)*sqrt(2-sqrt(3))*a*(187*b^2*c^2-3*a*d*(-9*a*d+34*b*c))*(a^(1/3)-(b*x^2+a)^(1/3))*sqrt((a^(2/3)+a^(1/3)*(b*x^2+a)^(1/3)+(b*x^2+a)^(2/3))/((1-sqrt(3))*a^(1/3)-(b*x^2+a)^(1/3))^2)*InverseJacobiAM(arcsin(((1+sqrt(3))*a^(1/3)-(b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(b*x^2+a)^(1/3))),sqrt(-7+4*sqrt(3)))/b^3/x/sqrt(-a^(1/3)*(a^(1/3)-(b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(b*x^2+a)^(1/3))^2),1],
[(b*x^2+a)^(1/3)*(d*x^2+c),x,4,3/55*(-3*a*d+11*b*c)*x*(b*x^2+a)^(1/3)/b+3/11*d*x*(b*x^2+a)^(4/3)/b-2/55*3^(3/4)*sqrt(2-sqrt(3))*a*(-3*a*d+11*b*c)*(a^(1/3)-(b*x^2+a)^(1/3))*sqrt((a^(2/3)+a^(1/3)*(b*x^2+a)^(1/3)+(b*x^2+a)^(2/3))/((1-sqrt(3))*a^(1/3)-(b*x^2+a)^(1/3))^2)*InverseJacobiAM(arcsin(((1+sqrt(3))*a^(1/3)-(b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(b*x^2+a)^(1/3))),sqrt(-7+4*sqrt(3)))/b^2/x/sqrt(-a^(1/3)*(a^(1/3)-(b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(b*x^2+a)^(1/3))^2),1],
[(b*x^2+a)^(1/3)/(d*x^2+c),x,2,x*(b*x^2+a)^(1/3)*AppellF1(1/2,-1/3,1,3/2,-b*x^2/a,-d*x^2/c)/c/(1+b*x^2/a)^(1/3),1],
[(b*x^2+a)^(1/3)/(d*x^2+c)^2,x,2,x*(b*x^2+a)^(1/3)*AppellF1(1/2,-1/3,2,3/2,-b*x^2/a,-d*x^2/c)/c^2/(1+b*x^2/a)^(1/3),1],
[(d*x^2+c)^2/(b*x^2+a)^(1/3),x,6,3/91*d*(-9*a*d+26*b*c)*x*(b*x^2+a)^(2/3)/b^2+3/13*d^2*x^3*(b*x^2+a)^(2/3)/b-3*(91*c^2-3*a*d*(-9*a*d+26*b*c)/b^2)*x/(91*(1-sqrt(3))*a^(1/3)-91*(b*x^2+a)^(1/3))+3/182*3^(1/4)*sqrt(2+sqrt(3))*a^(1/3)*(91*b^2*c^2-3*a*d*(-9*a*d+26*b*c))*(a^(1/3)-(b*x^2+a)^(1/3))*sqrt((a^(2/3)+a^(1/3)*(b*x^2+a)^(1/3)+(b*x^2+a)^(2/3))/((1-sqrt(3))*a^(1/3)-(b*x^2+a)^(1/3))^2)*EllipticE(sin(arcsin(((1+sqrt(3))*a^(1/3)-(b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(b*x^2+a)^(1/3)))),sqrt(-7+4*sqrt(3)))/b^3/x/sqrt(-a^(1/3)*(a^(1/3)-(b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(b*x^2+a)^(1/3))^2)-1/91*sqrt(2)*3^(3/4)*a^(1/3)*(91*b^2*c^2-3*a*d*(-9*a*d+26*b*c))*(a^(1/3)-(b*x^2+a)^(1/3))*sqrt((a^(2/3)+a^(1/3)*(b*x^2+a)^(1/3)+(b*x^2+a)^(2/3))/((1-sqrt(3))*a^(1/3)-(b*x^2+a)^(1/3))^2)*InverseJacobiAM(arcsin(((1+sqrt(3))*a^(1/3)-(b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(b*x^2+a)^(1/3))),sqrt(-7+4*sqrt(3)))/b^3/x/sqrt(-a^(1/3)*(a^(1/3)-(b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(b*x^2+a)^(1/3))^2),1],
[(d*x^2+c)/(b*x^2+a)^(1/3),x,5,3/7*d*x*(b*x^2+a)^(2/3)/b-3/7*(-3*a*d+7*b*c)*x/b/((1-sqrt(3))*a^(1/3)-(b*x^2+a)^(1/3))+3/14*3^(1/4)*sqrt(2+sqrt(3))*a^(1/3)*(-3*a*d+7*b*c)*(a^(1/3)-(b*x^2+a)^(1/3))*sqrt((a^(2/3)+a^(1/3)*(b*x^2+a)^(1/3)+(b*x^2+a)^(2/3))/((1-sqrt(3))*a^(1/3)-(b*x^2+a)^(1/3))^2)*EllipticE(sin(arcsin(((1+sqrt(3))*a^(1/3)-(b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(b*x^2+a)^(1/3)))),sqrt(-7+4*sqrt(3)))/b^2/x/sqrt(-a^(1/3)*(a^(1/3)-(b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(b*x^2+a)^(1/3))^2)-1/7*sqrt(2)*3^(3/4)*a^(1/3)*(-3*a*d+7*b*c)*(a^(1/3)-(b*x^2+a)^(1/3))*sqrt((a^(2/3)+a^(1/3)*(b*x^2+a)^(1/3)+(b*x^2+a)^(2/3))/((1-sqrt(3))*a^(1/3)-(b*x^2+a)^(1/3))^2)*InverseJacobiAM(arcsin(((1+sqrt(3))*a^(1/3)-(b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(b*x^2+a)^(1/3))),sqrt(-7+4*sqrt(3)))/b^2/x/sqrt(-a^(1/3)*(a^(1/3)-(b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(b*x^2+a)^(1/3))^2),1],
[1/(b*x^2+a)^(1/3)/(d*x^2+c),x,2,x*(1+b*x^2/a)^(1/3)*AppellF1(1/2,1/3,1,3/2,-b*x^2/a,-d*x^2/c)/c/(b*x^2+a)^(1/3),1],
[1/(b*x^2+a)^(1/3)/(d*x^2+c)^2,x,2,x*(1+b*x^2/a)^(1/3)*AppellF1(1/2,1/3,2,3/2,-b*x^2/a,-d*x^2/c)/c^2/(b*x^2+a)^(1/3),1],
[(d*x^2+c)^2/(b*x^2+a)^(4/3),x,6,3/2*(-a*d+b*c)^2*x/a/b^2/(b*x^2+a)^(1/3)+3/7*d^2*x*(b*x^2+a)^(2/3)/b^2+3/14*(27*a^2*d^2-42*a*b*c*d+7*b^2*c^2)*x/a/b^2/((1-sqrt(3))*a^(1/3)-(b*x^2+a)^(1/3))-3/28*3^(1/4)*sqrt(2+sqrt(3))*(27*a^2*d^2-42*a*b*c*d+7*b^2*c^2)*(a^(1/3)-(b*x^2+a)^(1/3))*sqrt((a^(2/3)+a^(1/3)*(b*x^2+a)^(1/3)+(b*x^2+a)^(2/3))/((1-sqrt(3))*a^(1/3)-(b*x^2+a)^(1/3))^2)*EllipticE(sin(arcsin(((1+sqrt(3))*a^(1/3)-(b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(b*x^2+a)^(1/3)))),sqrt(-7+4*sqrt(3)))/a^(2/3)/b^3/x/sqrt(-a^(1/3)*(a^(1/3)-(b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(b*x^2+a)^(1/3))^2)+1/7*3^(3/4)*(27*a^2*d^2-42*a*b*c*d+7*b^2*c^2)*(a^(1/3)-(b*x^2+a)^(1/3))*sqrt((a^(2/3)+a^(1/3)*(b*x^2+a)^(1/3)+(b*x^2+a)^(2/3))/((1-sqrt(3))*a^(1/3)-(b*x^2+a)^(1/3))^2)*InverseJacobiAM(arcsin(((1+sqrt(3))*a^(1/3)-(b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(b*x^2+a)^(1/3))),sqrt(-7+4*sqrt(3)))/sqrt(2)/a^(2/3)/b^3/x/sqrt(-a^(1/3)*(a^(1/3)-(b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(b*x^2+a)^(1/3))^2),1],
[(d*x^2+c)/(b*x^2+a)^(4/3),x,5,3/2*(-a*d+b*c)*x/a/b/(b*x^2+a)^(1/3)+3/2*(-3*a*d+b*c)*x/a/b/((1-sqrt(3))*a^(1/3)-(b*x^2+a)^(1/3))-3/4*3^(1/4)*sqrt(2+sqrt(3))*(-3*a*d+b*c)*(a^(1/3)-(b*x^2+a)^(1/3))*sqrt((a^(2/3)+a^(1/3)*(b*x^2+a)^(1/3)+(b*x^2+a)^(2/3))/((1-sqrt(3))*a^(1/3)-(b*x^2+a)^(1/3))^2)*EllipticE(sin(arcsin(((1+sqrt(3))*a^(1/3)-(b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(b*x^2+a)^(1/3)))),sqrt(-7+4*sqrt(3)))/a^(2/3)/b^2/x/sqrt(-a^(1/3)*(a^(1/3)-(b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(b*x^2+a)^(1/3))^2)+3^(3/4)*(-3*a*d+b*c)*(a^(1/3)-(b*x^2+a)^(1/3))*sqrt((a^(2/3)+a^(1/3)*(b*x^2+a)^(1/3)+(b*x^2+a)^(2/3))/((1-sqrt(3))*a^(1/3)-(b*x^2+a)^(1/3))^2)*InverseJacobiAM(arcsin(((1+sqrt(3))*a^(1/3)-(b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(b*x^2+a)^(1/3))),sqrt(-7+4*sqrt(3)))/sqrt(2)/a^(2/3)/b^2/x/sqrt(-a^(1/3)*(a^(1/3)-(b*x^2+a)^(1/3))/((1-sqrt(3))*a^(1/3)-(b*x^2+a)^(1/3))^2),1],
[1/(b*x^2+a)^(4/3)/(d*x^2+c),x,2,x*(1+b*x^2/a)^(1/3)*AppellF1(1/2,4/3,1,3/2,-b*x^2/a,-d*x^2/c)/a/c/(b*x^2+a)^(1/3),1],
[1/(b*x^2+a)^(4/3)/(d*x^2+c)^2,x,2,x*(1+b*x^2/a)^(1/3)*AppellF1(1/2,4/3,2,3/2,-b*x^2/a,-d*x^2/c)/a/c^2/(b*x^2+a)^(1/3),1],
[1/(x^2+1)^(1/4)/(x^2+2),x,1,1/2*arctan(x*(x^2+1)^(1/4)/(1+sqrt(x^2+1)))-1/2*arctanh((1-sqrt(x^2+1))/x/(x^2+1)^(1/4)),1],
[1/(-x^2+1)^(1/4)/(-x^2+2),x,1,1/2*arctan((1-sqrt(-x^2+1))/x/(-x^2+1)^(1/4))+1/2*arctanh(x*(-x^2+1)^(1/4)/(1+sqrt(-x^2+1))),1],
[1/(3*x^2+2)^(1/4)/(3*x^2+4),x,1,1/4*arctan(2^(1/4)*sqrt(3)*x*(3*x^2+2)^(1/4)/(2+sqrt(2)*sqrt(3*x^2+2)))*2^(1/4)/sqrt(3)-1/4*arctanh(1/2*(2*2^(3/4)-2*2^(1/4)*sqrt(3*x^2+2))/sqrt(3)/x/(3*x^2+2)^(1/4))*2^(1/4)/sqrt(3),1],
[1/(-3*x^2+2)^(1/4)/(-3*x^2+4),x,1,1/4*arctan(1/2*(2-sqrt(2)*sqrt(-3*x^2+2))*2^(3/4)/sqrt(3)/x/(-3*x^2+2)^(1/4))*2^(1/4)/sqrt(3)+1/4*arctanh(2^(1/4)*sqrt(3)*x*(-3*x^2+2)^(1/4)/(2+sqrt(2)*sqrt(-3*x^2+2)))*2^(1/4)/sqrt(3),1],
[1/(b*x^2+2)^(1/4)/(b*x^2+4),x,1,1/4*arctan(2^(1/4)*b^(3/2)*x*(b*x^2+2)^(1/4)/(2*b+sqrt(2)*b*sqrt(b*x^2+2)))*2^(1/4)/sqrt(b)-1/4*arctanh(1/2*(2*2^(3/4)-2*2^(1/4)*sqrt(b*x^2+2))/sqrt(b)/x/(b*x^2+2)^(1/4))*2^(1/4)/sqrt(b),1],
[1/(-b*x^2+2)^(1/4)/(-b*x^2+4),x,1,1/4*arctan(1/2*(2-sqrt(2)*sqrt(-b*x^2+2))*2^(3/4)/sqrt(b)/x/(-b*x^2+2)^(1/4))*2^(1/4)/sqrt(b)+1/4*arctanh(2^(1/4)*b^(3/2)*x*(-b*x^2+2)^(1/4)/(2*b+sqrt(2)*b*sqrt(-b*x^2+2)))*2^(1/4)/sqrt(b),1],
[1/(3*x^2+a)^(1/4)/(3*x^2+2*a),x,1,1/2*arctan(sqrt(3)*x*(3*x^2+a)^(1/4)/a^(3/4)/(1+sqrt(3*x^2+a)/sqrt(a)))/sqrt(3)/a^(3/4)-1/2*arctanh(a^(3/4)*(1-sqrt(3*x^2+a)/sqrt(a))/sqrt(3)/x/(3*x^2+a)^(1/4))/sqrt(3)/a^(3/4),1],
[1/(-3*x^2+a)^(1/4)/(-3*x^2+2*a),x,1,1/2*arctan(a^(3/4)*(1-sqrt(-3*x^2+a)/sqrt(a))/sqrt(3)/x/(-3*x^2+a)^(1/4))/sqrt(3)/a^(3/4)+1/2*arctanh(sqrt(3)*x*(-3*x^2+a)^(1/4)/a^(3/4)/(1+sqrt(-3*x^2+a)/sqrt(a)))/sqrt(3)/a^(3/4),1],
[1/(b*x^2+a)^(1/4)/(b*x^2+2*a),x,1,1/2*arctan(b^(3/2)*x*(b*x^2+a)^(1/4)/a^(3/4)/(b+b*sqrt(b*x^2+a)/sqrt(a)))/a^(3/4)/sqrt(b)-1/2*arctanh(a^(3/4)*(1-sqrt(b*x^2+a)/sqrt(a))/sqrt(b)/x/(b*x^2+a)^(1/4))/a^(3/4)/sqrt(b),1],
[1/(-b*x^2+a)^(1/4)/(-b*x^2+2*a),x,1,1/2*arctan(a^(3/4)*(1-sqrt(-b*x^2+a)/sqrt(a))/sqrt(b)/x/(-b*x^2+a)^(1/4))/a^(3/4)/sqrt(b)+1/2*arctanh(b^(3/2)*x*(-b*x^2+a)^(1/4)/a^(3/4)/(b+b*sqrt(-b*x^2+a)/sqrt(a)))/a^(3/4)/sqrt(b),1],
[1/(-x^2+2)/(x^2-1)^(1/4),x,1,1/2*arctan(x/sqrt(2)/(x^2-1)^(1/4))/sqrt(2)+1/2*arctanh(sqrt(2)*(x^2-1)^(1/4)/x)/sqrt(2),1],
[1/(-x^2-1)^(1/4)/(x^2+2),x,1,1/2*arctan(x/sqrt(2)/(-x^2-1)^(1/4))/sqrt(2)+1/2*arctanh(x/sqrt(2)/(-x^2-1)^(1/4))/sqrt(2),1],
[1/(3*x^2-2)/(3*x^2-1)^(1/4),x,1,-1/2*arctan(sqrt(3/2)*x/(3*x^2-1)^(1/4))/sqrt(6)-1/2*arctanh(sqrt(2/3)*(3*x^2-1)^(1/4)/x)/sqrt(6),1],
[1/(-3*x^2-2)/(-3*x^2-1)^(1/4),x,1,-1/2*arctan(sqrt(3/2)*x/(-3*x^2-1)^(1/4))/sqrt(6)-1/2*arctanh(sqrt(3/2)*x/(-3*x^2-1)^(1/4))/sqrt(6),1],
[1/(b*x^2-2)/(b*x^2-1)^(1/4),x,1,-1/2*arctan(sqrt(b)*x/sqrt(2)/(b*x^2-1)^(1/4))/sqrt(2)/sqrt(b)-1/2*arctanh(sqrt(2)*(b*x^2-1)^(1/4)/sqrt(b)/x)/sqrt(2)/sqrt(b),1],
[1/(-b*x^2-2)/(-b*x^2-1)^(1/4),x,1,-1/2*arctan(sqrt(b)*x/sqrt(2)/(-b*x^2-1)^(1/4))/sqrt(2)/sqrt(b)-1/2*arctanh(sqrt(b)*x/sqrt(2)/(-b*x^2-1)^(1/4))/sqrt(2)/sqrt(b),1],
[1/(3*x^2-2*a)/(3*x^2-a)^(1/4),x,1,-1/2*arctan(sqrt(3/2)*x/a^(1/4)/(3*x^2-a)^(1/4))/sqrt(6)/a^(3/4)-1/2*arctanh(sqrt(2/3)*a^(1/4)*(3*x^2-a)^(1/4)/x)/sqrt(6)/a^(3/4),1],
[1/(-3*x^2-2*a)/(-3*x^2-a)^(1/4),x,1,-1/2*arctan(sqrt(3/2)*x/a^(1/4)/(-3*x^2-a)^(1/4))/sqrt(6)/a^(3/4)-1/2*arctanh(sqrt(3/2)*x/a^(1/4)/(-3*x^2-a)^(1/4))/sqrt(6)/a^(3/4),1],
[1/(b*x^2-2*a)/(b*x^2-a)^(1/4),x,1,-1/2*arctan(sqrt(b)*x/sqrt(2)/a^(1/4)/(b*x^2-a)^(1/4))/sqrt(2)/a^(3/4)/sqrt(b)-1/2*arctanh(sqrt(2)*a^(1/4)*(b*x^2-a)^(1/4)/sqrt(b)/x)/sqrt(2)/a^(3/4)/sqrt(b),1],
[1/(-b*x^2-2*a)/(-b*x^2-a)^(1/4),x,1,-1/2*arctan(sqrt(b)*x/sqrt(2)/a^(1/4)/(-b*x^2-a)^(1/4))/sqrt(2)/a^(3/4)/sqrt(b)-1/2*arctanh(sqrt(b)*x/sqrt(2)/a^(1/4)/(-b*x^2-a)^(1/4))/sqrt(2)/a^(3/4)/sqrt(b),1],
[(b*x^2+a)^(1/4)*(d*x^2+c)^3,x,6,2/231*(77*c^3-2*a*d*(4*a^2*d^2-18*a*b*c*d+33*b^2*c^2)/b^3)*x*(b*x^2+a)^(1/4)+2/77*d*(4*a^2*d^2-18*a*b*c*d+33*b^2*c^2)*x*(b*x^2+a)^(5/4)/b^3+2/33*d^2*(-2*a*d+9*b*c)*x^3*(b*x^2+a)^(5/4)/b^2+2/15*d^3*x^5*(b*x^2+a)^(5/4)/b+2/231*a^(3/2)*(77*b^3*c^3-2*a*d*(4*a^2*d^2-18*a*b*c*d+33*b^2*c^2))*(1+b*x^2/a)^(3/4)*InverseJacobiAM(1/2*arctan(sqrt(b)*x/sqrt(a)),sqrt(2))/b^(7/2)/(b*x^2+a)^(3/4),1],
[(b*x^2+a)^(1/4)*(d*x^2+c)^2,x,5,2/231*(77*c^2-4*a*d*(-3*a*d+11*b*c)/b^2)*x*(b*x^2+a)^(1/4)+4/77*d*(-3*a*d+11*b*c)*x*(b*x^2+a)^(5/4)/b^2+2/11*d^2*x^3*(b*x^2+a)^(5/4)/b+2/231*a^(3/2)*(77*b^2*c^2-4*a*d*(-3*a*d+11*b*c))*(1+b*x^2/a)^(3/4)*InverseJacobiAM(1/2*arctan(sqrt(b)*x/sqrt(a)),sqrt(2))/b^(5/2)/(b*x^2+a)^(3/4),1],
[(b*x^2+a)^(1/4)*(d*x^2+c),x,4,2/21*(-2*a*d+7*b*c)*x*(b*x^2+a)^(1/4)/b+2/7*d*x*(b*x^2+a)^(5/4)/b+2/21*a^(3/2)*(-2*a*d+7*b*c)*(1+b*x^2/a)^(3/4)*InverseJacobiAM(1/2*arctan(sqrt(b)*x/sqrt(a)),sqrt(2))/b^(3/2)/(b*x^2+a)^(3/4),1],
[(b*x^2+a)^(1/4)/(d*x^2+c),x,8,2*sqrt(a)*sqrt(b)*(1+b*x^2/a)^(3/4)*InverseJacobiAM(1/2*arctan(sqrt(b)*x/sqrt(a)),sqrt(2))/d/(b*x^2+a)^(3/4)-a^(1/4)*sqrt(-b*x^2/a)*EllipticPi(sin(arcsin((b*x^2+a)^(1/4)/a^(1/4))),-sqrt(a)*sqrt(d)/sqrt(a*d-b*c),sqrt(-1))/d/x-a^(1/4)*sqrt(-b*x^2/a)*EllipticPi(sin(arcsin((b*x^2+a)^(1/4)/a^(1/4))),sqrt(a)*sqrt(d)/sqrt(a*d-b*c),sqrt(-1))/d/x,1],
[(b*x^2+a)^(1/4)/(d*x^2+c)^2,x,9,1/2*x*(b*x^2+a)^(1/4)/c/(d*x^2+c)+1/2*sqrt(a)*sqrt(b)*(1+b*x^2/a)^(3/4)*InverseJacobiAM(1/2*arctan(sqrt(b)*x/sqrt(a)),sqrt(2))/c/d/(b*x^2+a)^(3/4)-1/4*a^(1/4)*(-2*a*d+b*c)*sqrt(-b*x^2/a)*EllipticPi(sin(arcsin((b*x^2+a)^(1/4)/a^(1/4))),-sqrt(a)*sqrt(d)/sqrt(a*d-b*c),sqrt(-1))/c/d/(-a*d+b*c)/x-1/4*a^(1/4)*(-2*a*d+b*c)*sqrt(-b*x^2/a)*EllipticPi(sin(arcsin((b*x^2+a)^(1/4)/a^(1/4))),sqrt(a)*sqrt(d)/sqrt(a*d-b*c),sqrt(-1))/c/d/(-a*d+b*c)/x,1],
[(b*x^2+a)^(3/4)*(d*x^2+c)^3,x,7,2/1105*a*(663*b^3*c^3-2*a*d*(20*a^2*d^2-102*a*b*c*d+221*b^2*c^2))*x/b^3/(b*x^2+a)^(1/4)+2/3315*(663*c^3-2*a*d*(20*a^2*d^2-102*a*b*c*d+221*b^2*c^2)/b^3)*x*(b*x^2+a)^(3/4)+2/663*d*(20*a^2*d^2-102*a*b*c*d+221*b^2*c^2)*x*(b*x^2+a)^(7/4)/b^3+2/221*d^2*(-10*a*d+51*b*c)*x^3*(b*x^2+a)^(7/4)/b^2+2/17*d^3*x^5*(b*x^2+a)^(7/4)/b-2/1105*a^(3/2)*(663*b^3*c^3-2*a*d*(20*a^2*d^2-102*a*b*c*d+221*b^2*c^2))*(1+b*x^2/a)^(1/4)*EllipticE(sin(1/2*arctan(sqrt(b)*x/sqrt(a))),sqrt(2))/b^(7/2)/(b*x^2+a)^(1/4),1],
[(b*x^2+a)^(3/4)*(d*x^2+c)^2,x,6,2/195*a*(117*b^2*c^2-4*a*d*(-3*a*d+13*b*c))*x/b^2/(b*x^2+a)^(1/4)+2/585*(117*c^2-4*a*d*(-3*a*d+13*b*c)/b^2)*x*(b*x^2+a)^(3/4)+4/117*d*(-3*a*d+13*b*c)*x*(b*x^2+a)^(7/4)/b^2+2/13*d^2*x^3*(b*x^2+a)^(7/4)/b-2/195*a^(3/2)*(117*b^2*c^2-4*a*d*(-3*a*d+13*b*c))*(1+b*x^2/a)^(1/4)*EllipticE(sin(1/2*arctan(sqrt(b)*x/sqrt(a))),sqrt(2))/b^(5/2)/(b*x^2+a)^(1/4),1],
[(b*x^2+a)^(3/4)*(d*x^2+c),x,5,2/15*a*(-2*a*d+9*b*c)*x/b/(b*x^2+a)^(1/4)+2/45*(-2*a*d+9*b*c)*x*(b*x^2+a)^(3/4)/b+2/9*d*x*(b*x^2+a)^(7/4)/b-2/15*a^(3/2)*(-2*a*d+9*b*c)*(1+b*x^2/a)^(1/4)*EllipticE(sin(1/2*arctan(sqrt(b)*x/sqrt(a))),sqrt(2))/b^(3/2)/(b*x^2+a)^(1/4),1],
[(b*x^2+a)^(3/4)/(d*x^2+c),x,8,2*b*x/d/(b*x^2+a)^(1/4)-2*sqrt(a)*sqrt(b)*(1+b*x^2/a)^(1/4)*EllipticE(sin(1/2*arctan(sqrt(b)*x/sqrt(a))),sqrt(2))/d/(b*x^2+a)^(1/4)+a^(1/4)*sqrt(a*d-b*c)*sqrt(-b*x^2/a)*EllipticPi(sin(arcsin((b*x^2+a)^(1/4)/a^(1/4))),-sqrt(a)*sqrt(d)/sqrt(a*d-b*c),sqrt(-1))/d^(3/2)/x-a^(1/4)*sqrt(a*d-b*c)*sqrt(-b*x^2/a)*EllipticPi(sin(arcsin((b*x^2+a)^(1/4)/a^(1/4))),sqrt(a)*sqrt(d)/sqrt(a*d-b*c),sqrt(-1))/d^(3/2)/x,1],
[(b*x^2+a)^(3/4)/(d*x^2+c)^2,x,9,-1/2*b*x/c/d/(b*x^2+a)^(1/4)+1/2*x*(b*x^2+a)^(3/4)/c/(d*x^2+c)+1/2*sqrt(a)*sqrt(b)*(1+b*x^2/a)^(1/4)*EllipticE(sin(1/2*arctan(sqrt(b)*x/sqrt(a))),sqrt(2))/c/d/(b*x^2+a)^(1/4)+1/4*a^(1/4)*(2*a*d+b*c)*sqrt(-b*x^2/a)*EllipticPi(sin(arcsin((b*x^2+a)^(1/4)/a^(1/4))),-sqrt(a)*sqrt(d)/sqrt(a*d-b*c),sqrt(-1))/c/d^(3/2)/sqrt(a*d-b*c)/x-1/4*a^(1/4)*(2*a*d+b*c)*sqrt(-b*x^2/a)*EllipticPi(sin(arcsin((b*x^2+a)^(1/4)/a^(1/4))),sqrt(a)*sqrt(d)/sqrt(a*d-b*c),sqrt(-1))/c/d^(3/2)/sqrt(a*d-b*c)/x,1],
[(b*x^2+a)^(5/4)*(d*x^2+c)^3,x,7,2/4389*a*(1045*b^3*c^3-2*a*d*(20*a^2*d^2-114*a*b*c*d+285*b^2*c^2))*x*(b*x^2+a)^(1/4)/b^3+2/7315*(1045*c^3-2*a*d*(20*a^2*d^2-114*a*b*c*d+285*b^2*c^2)/b^3)*x*(b*x^2+a)^(5/4)+2/1045*d*(20*a^2*d^2-114*a*b*c*d+285*b^2*c^2)*x*(b*x^2+a)^(9/4)/b^3+2/285*d^2*(-10*a*d+57*b*c)*x^3*(b*x^2+a)^(9/4)/b^2+2/19*d^3*x^5*(b*x^2+a)^(9/4)/b+2/4389*a^(5/2)*(1045*b^3*c^3-2*a*d*(20*a^2*d^2-114*a*b*c*d+285*b^2*c^2))*(1+b*x^2/a)^(3/4)*InverseJacobiAM(1/2*arctan(sqrt(b)*x/sqrt(a)),sqrt(2))/b^(7/2)/(b*x^2+a)^(3/4),1],
[(b*x^2+a)^(5/4)*(d*x^2+c)^2,x,6,2/231*a*(55*b^2*c^2-4*a*d*(-a*d+5*b*c))*x*(b*x^2+a)^(1/4)/b^2+2/385*(55*c^2-4*a*d*(-a*d+5*b*c)/b^2)*x*(b*x^2+a)^(5/4)+4/55*d*(-a*d+5*b*c)*x*(b*x^2+a)^(9/4)/b^2+2/15*d^2*x^3*(b*x^2+a)^(9/4)/b+2/231*a^(5/2)*(55*b^2*c^2-4*a*d*(-a*d+5*b*c))*(1+b*x^2/a)^(3/4)*InverseJacobiAM(1/2*arctan(sqrt(b)*x/sqrt(a)),sqrt(2))/b^(5/2)/(b*x^2+a)^(3/4),1],
[(b*x^2+a)^(5/4)*(d*x^2+c),x,5,10/231*a*(-2*a*d+11*b*c)*x*(b*x^2+a)^(1/4)/b+2/77*(-2*a*d+11*b*c)*x*(b*x^2+a)^(5/4)/b+2/11*d*x*(b*x^2+a)^(9/4)/b+10/231*a^(5/2)*(-2*a*d+11*b*c)*(1+b*x^2/a)^(3/4)*InverseJacobiAM(1/2*arctan(sqrt(b)*x/sqrt(a)),sqrt(2))/b^(3/2)/(b*x^2+a)^(3/4),1],
[(b*x^2+a)^(5/4)/(d*x^2+c),x,9,2/3*b*x*(b*x^2+a)^(1/4)/d-2/3*sqrt(a)*sqrt(b)*(-4*a*d+3*b*c)*(1+b*x^2/a)^(3/4)*InverseJacobiAM(1/2*arctan(sqrt(b)*x/sqrt(a)),sqrt(2))/d^2/(b*x^2+a)^(3/4)+a^(1/4)*(-a*d+b*c)*sqrt(-b*x^2/a)*EllipticPi(sin(arcsin((b*x^2+a)^(1/4)/a^(1/4))),-sqrt(a)*sqrt(d)/sqrt(a*d-b*c),sqrt(-1))/d^2/x+a^(1/4)*(-a*d+b*c)*sqrt(-b*x^2/a)*EllipticPi(sin(arcsin((b*x^2+a)^(1/4)/a^(1/4))),sqrt(a)*sqrt(d)/sqrt(a*d-b*c),sqrt(-1))/d^2/x,1],
[(b*x^2+a)^(5/4)/(d*x^2+c)^2,x,9,-1/2*(-a*d+b*c)*x*(b*x^2+a)^(1/4)/c/d/(d*x^2+c)+1/2*sqrt(a)*sqrt(b)*(a*d+3*b*c)*(1+b*x^2/a)^(3/4)*InverseJacobiAM(1/2*arctan(sqrt(b)*x/sqrt(a)),sqrt(2))/c/d^2/(b*x^2+a)^(3/4)-1/4*a^(1/4)*(2*a*d+3*b*c)*sqrt(-b*x^2/a)*EllipticPi(sin(arcsin((b*x^2+a)^(1/4)/a^(1/4))),-sqrt(a)*sqrt(d)/sqrt(a*d-b*c),sqrt(-1))/c/d^2/x-1/4*a^(1/4)*(2*a*d+3*b*c)*sqrt(-b*x^2/a)*EllipticPi(sin(arcsin((b*x^2+a)^(1/4)/a^(1/4))),sqrt(a)*sqrt(d)/sqrt(a*d-b*c),sqrt(-1))/c/d^2/x,1],
[(b*x^2+a)^(7/4)*(d*x^2+c)^3,x,8,2/3315*a^2*(1547*b^3*c^3-2*a*d*(20*a^2*d^2-126*a*b*c*d+357*b^2*c^2))*x/b^3/(b*x^2+a)^(1/4)+2/9945*a*(1547*b^3*c^3-2*a*d*(20*a^2*d^2-126*a*b*c*d+357*b^2*c^2))*x*(b*x^2+a)^(3/4)/b^3+2/13923*(1547*c^3-2*a*d*(20*a^2*d^2-126*a*b*c*d+357*b^2*c^2)/b^3)*x*(b*x^2+a)^(7/4)+2/1547*d*(20*a^2*d^2-126*a*b*c*d+357*b^2*c^2)*x*(b*x^2+a)^(11/4)/b^3+2/357*d^2*(-10*a*d+63*b*c)*x^3*(b*x^2+a)^(11/4)/b^2+2/21*d^3*x^5*(b*x^2+a)^(11/4)/b-2/3315*a^(5/2)*(1547*b^3*c^3-2*a*d*(20*a^2*d^2-126*a*b*c*d+357*b^2*c^2))*(1+b*x^2/a)^(1/4)*EllipticE(sin(1/2*arctan(sqrt(b)*x/sqrt(a))),sqrt(2))/b^(7/2)/(b*x^2+a)^(1/4),1],
[(b*x^2+a)^(7/4)*(d*x^2+c)^2,x,7,14/3315*a^2*(221*b^2*c^2-4*a*d*(-3*a*d+17*b*c))*x/b^2/(b*x^2+a)^(1/4)+14/9945*a*(221*b^2*c^2-4*a*d*(-3*a*d+17*b*c))*x*(b*x^2+a)^(3/4)/b^2+2/1989*(221*c^2-4*a*d*(-3*a*d+17*b*c)/b^2)*x*(b*x^2+a)^(7/4)+4/221*d*(-3*a*d+17*b*c)*x*(b*x^2+a)^(11/4)/b^2+2/17*d^2*x^3*(b*x^2+a)^(11/4)/b-14/3315*a^(5/2)*(221*b^2*c^2-4*a*d*(-3*a*d+17*b*c))*(1+b*x^2/a)^(1/4)*EllipticE(sin(1/2*arctan(sqrt(b)*x/sqrt(a))),sqrt(2))/b^(5/2)/(b*x^2+a)^(1/4),1],
[(b*x^2+a)^(7/4)*(d*x^2+c),x,6,14/195*a^2*(-2*a*d+13*b*c)*x/b/(b*x^2+a)^(1/4)+14/585*a*(-2*a*d+13*b*c)*x*(b*x^2+a)^(3/4)/b+2/117*(-2*a*d+13*b*c)*x*(b*x^2+a)^(7/4)/b+2/13*d*x*(b*x^2+a)^(11/4)/b-14/195*a^(5/2)*(-2*a*d+13*b*c)*(1+b*x^2/a)^(1/4)*EllipticE(sin(1/2*arctan(sqrt(b)*x/sqrt(a))),sqrt(2))/b^(3/2)/(b*x^2+a)^(1/4),1],
[(b*x^2+a)^(7/4)/(d*x^2+c),x,9,-2/5*b*(-8*a*d+5*b*c)*x/d^2/(b*x^2+a)^(1/4)+2/5*b*x*(b*x^2+a)^(3/4)/d+2/5*sqrt(a)*sqrt(b)*(-8*a*d+5*b*c)*(1+b*x^2/a)^(1/4)*EllipticE(sin(1/2*arctan(sqrt(b)*x/sqrt(a))),sqrt(2))/d^2/(b*x^2+a)^(1/4)+a^(1/4)*(a*d-b*c)^(3/2)*sqrt(-b*x^2/a)*EllipticPi(sin(arcsin((b*x^2+a)^(1/4)/a^(1/4))),-sqrt(a)*sqrt(d)/sqrt(a*d-b*c),sqrt(-1))/d^(5/2)/x-a^(1/4)*(a*d-b*c)^(3/2)*sqrt(-b*x^2/a)*EllipticPi(sin(arcsin((b*x^2+a)^(1/4)/a^(1/4))),sqrt(a)*sqrt(d)/sqrt(a*d-b*c),sqrt(-1))/d^(5/2)/x,1],
[(b*x^2+a)^(7/4)/(d*x^2+c)^2,x,9,1/2*b*(-a*d+5*b*c)*x/c/d^2/(b*x^2+a)^(1/4)-1/2*(-a*d+b*c)*x*(b*x^2+a)^(3/4)/c/d/(d*x^2+c)-1/2*sqrt(a)*sqrt(b)*(-a*d+5*b*c)*(1+b*x^2/a)^(1/4)*EllipticE(sin(1/2*arctan(sqrt(b)*x/sqrt(a))),sqrt(2))/c/d^2/(b*x^2+a)^(1/4)+1/4*a^(1/4)*sqrt(a*d-b*c)*(2*a*d+5*b*c)*sqrt(-b*x^2/a)*EllipticPi(sin(arcsin((b*x^2+a)^(1/4)/a^(1/4))),-sqrt(a)*sqrt(d)/sqrt(a*d-b*c),sqrt(-1))/c/d^(5/2)/x-1/4*a^(1/4)*sqrt(a*d-b*c)*(2*a*d+5*b*c)*sqrt(-b*x^2/a)*EllipticPi(sin(arcsin((b*x^2+a)^(1/4)/a^(1/4))),sqrt(a)*sqrt(d)/sqrt(a*d-b*c),sqrt(-1))/c/d^(5/2)/x,1],
[(d*x^2+c)^3/(b*x^2+a)^(1/4),x,6,2/195*(195*c^3-2*a*d*(20*a^2*d^2-78*a*b*c*d+117*b^2*c^2)/b^3)*x/(b*x^2+a)^(1/4)+2/195*d*(20*a^2*d^2-78*a*b*c*d+117*b^2*c^2)*x*(b*x^2+a)^(3/4)/b^3+2/117*d^2*(-10*a*d+39*b*c)*x^3*(b*x^2+a)^(3/4)/b^2+2/13*d^3*x^5*(b*x^2+a)^(3/4)/b-2/195*sqrt(a)*(195*b^3*c^3-2*a*d*(20*a^2*d^2-78*a*b*c*d+117*b^2*c^2))*(1+b*x^2/a)^(1/4)*EllipticE(sin(1/2*arctan(sqrt(b)*x/sqrt(a))),sqrt(2))/b^(7/2)/(b*x^2+a)^(1/4),1],
[(d*x^2+c)^2/(b*x^2+a)^(1/4),x,5,2/15*(15*c^2-4*a*d*(-a*d+3*b*c)/b^2)*x/(b*x^2+a)^(1/4)+4/15*d*(-a*d+3*b*c)*x*(b*x^2+a)^(3/4)/b^2+2/9*d^2*x^3*(b*x^2+a)^(3/4)/b-2/15*sqrt(a)*(15*b^2*c^2-4*a*d*(-a*d+3*b*c))*(1+b*x^2/a)^(1/4)*EllipticE(sin(1/2*arctan(sqrt(b)*x/sqrt(a))),sqrt(2))/b^(5/2)/(b*x^2+a)^(1/4),1],
[(d*x^2+c)/(b*x^2+a)^(1/4),x,4,2/5*(-2*a*d+5*b*c)*x/b/(b*x^2+a)^(1/4)+2/5*d*x*(b*x^2+a)^(3/4)/b-2/5*sqrt(a)*(-2*a*d+5*b*c)*(1+b*x^2/a)^(1/4)*EllipticE(sin(1/2*arctan(sqrt(b)*x/sqrt(a))),sqrt(2))/b^(3/2)/(b*x^2+a)^(1/4),1],
[1/(b*x^2+a)^(1/4)/(d*x^2+c),x,4,a^(1/4)*sqrt(-b*x^2/a)*EllipticPi(sin(arcsin((b*x^2+a)^(1/4)/a^(1/4))),-sqrt(a)*sqrt(d)/sqrt(a*d-b*c),sqrt(-1))/sqrt(d)/sqrt(a*d-b*c)/x-a^(1/4)*sqrt(-b*x^2/a)*EllipticPi(sin(arcsin((b*x^2+a)^(1/4)/a^(1/4))),sqrt(a)*sqrt(d)/sqrt(a*d-b*c),sqrt(-1))/sqrt(d)/sqrt(a*d-b*c)/x,1],
[1/(b*x^2+a)^(1/4)/(d*x^2+c)^2,x,9,1/2*b*x/c/(-a*d+b*c)/(b*x^2+a)^(1/4)-1/2*d*x*(b*x^2+a)^(3/4)/c/(-a*d+b*c)/(d*x^2+c)-1/2*sqrt(a)*sqrt(b)*(1+b*x^2/a)^(1/4)*EllipticE(sin(1/2*arctan(sqrt(b)*x/sqrt(a))),sqrt(2))/c/(-a*d+b*c)/(b*x^2+a)^(1/4)-1/4*a^(1/4)*(-2*a*d+3*b*c)*sqrt(-b*x^2/a)*EllipticPi(sin(arcsin((b*x^2+a)^(1/4)/a^(1/4))),-sqrt(a)*sqrt(d)/sqrt(a*d-b*c),sqrt(-1))/c/sqrt(d)/(a*d-b*c)^(3/2)/x+1/4*a^(1/4)*(-2*a*d+3*b*c)*sqrt(-b*x^2/a)*EllipticPi(sin(arcsin((b*x^2+a)^(1/4)/a^(1/4))),sqrt(a)*sqrt(d)/sqrt(a*d-b*c),sqrt(-1))/c/sqrt(d)/(a*d-b*c)^(3/2)/x,1],
[(d*x^2+c)^3/(b*x^2+a)^(3/4),x,5,2/77*d*(20*a^2*d^2-66*a*b*c*d+77*b^2*c^2)*x*(b*x^2+a)^(1/4)/b^3+2/77*d^2*(-10*a*d+33*b*c)*x^3*(b*x^2+a)^(1/4)/b^2+2/11*d^3*x^5*(b*x^2+a)^(1/4)/b+2/77*sqrt(a)*(77*b^3*c^3-2*a*d*(20*a^2*d^2-66*a*b*c*d+77*b^2*c^2))*(1+b*x^2/a)^(3/4)*InverseJacobiAM(1/2*arctan(sqrt(b)*x/sqrt(a)),sqrt(2))/b^(7/2)/(b*x^2+a)^(3/4),1],
[(d*x^2+c)^2/(b*x^2+a)^(3/4),x,4,4/21*d*(-3*a*d+7*b*c)*x*(b*x^2+a)^(1/4)/b^2+2/7*d^2*x^3*(b*x^2+a)^(1/4)/b+2/21*sqrt(a)*(21*b^2*c^2-4*a*d*(-3*a*d+7*b*c))*(1+b*x^2/a)^(3/4)*InverseJacobiAM(1/2*arctan(sqrt(b)*x/sqrt(a)),sqrt(2))/b^(5/2)/(b*x^2+a)^(3/4),1],
[(d*x^2+c)/(b*x^2+a)^(3/4),x,3,2/3*d*x*(b*x^2+a)^(1/4)/b+2/3*sqrt(a)*(-2*a*d+3*b*c)*(1+b*x^2/a)^(3/4)*InverseJacobiAM(1/2*arctan(sqrt(b)*x/sqrt(a)),sqrt(2))/b^(3/2)/(b*x^2+a)^(3/4),1],
[1/(b*x^2+a)^(3/4)/(d*x^2+c),x,5,a^(1/4)*sqrt(-b*x^2/a)*EllipticPi(sin(arcsin((b*x^2+a)^(1/4)/a^(1/4))),-sqrt(a)*sqrt(d)/sqrt(a*d-b*c),sqrt(-1))/(-a*d+b*c)/x+a^(1/4)*sqrt(-b*x^2/a)*EllipticPi(sin(arcsin((b*x^2+a)^(1/4)/a^(1/4))),sqrt(a)*sqrt(d)/sqrt(a*d-b*c),sqrt(-1))/(-a*d+b*c)/x,1],
[1/(b*x^2+a)^(3/4)/(d*x^2+c)^2,x,9,-1/2*d*x*(b*x^2+a)^(1/4)/c/(-a*d+b*c)/(d*x^2+c)-1/2*sqrt(a)*sqrt(b)*(1+b*x^2/a)^(3/4)*InverseJacobiAM(1/2*arctan(sqrt(b)*x/sqrt(a)),sqrt(2))/c/(-a*d+b*c)/(b*x^2+a)^(3/4)+1/4*a^(1/4)*(-2*a*d+5*b*c)*sqrt(-b*x^2/a)*EllipticPi(sin(arcsin((b*x^2+a)^(1/4)/a^(1/4))),-sqrt(a)*sqrt(d)/sqrt(a*d-b*c),sqrt(-1))/c/(-a*d+b*c)^2/x+1/4*a^(1/4)*(-2*a*d+5*b*c)*sqrt(-b*x^2/a)*EllipticPi(sin(arcsin((b*x^2+a)^(1/4)/a^(1/4))),sqrt(a)*sqrt(d)/sqrt(a*d-b*c),sqrt(-1))/c/(-a*d+b*c)^2/x,1],
[(d*x^2+c)^3/(b*x^2+a)^(5/4),x,5,2/15*d*(25*a^2*d^2-63*a*b*c*d+45*b^2*c^2)*x/b^3/(b*x^2+a)^(1/4)+2/15*d^2*(-5*a*d+9*b*c)*x*(b*x^2+a)^(3/4)/b^3+2/9*d^3*x^3*(b*x^2+a)^(3/4)/b^2+2/15*(-40*a^3*d^3+108*a^2*b*c*d^2-90*a*b^2*c^2*d+15*b^3*c^3)*(1+b*x^2/a)^(1/4)*EllipticE(sin(1/2*arctan(sqrt(b)*x/sqrt(a))),sqrt(2))/sqrt(a)/b^(7/2)/(b*x^2+a)^(1/4),1],
[(d*x^2+c)^2/(b*x^2+a)^(5/4),x,4,2/5*d*(-7*a*d+10*b*c)*x/b^2/(b*x^2+a)^(1/4)+2/5*d^2*x*(b*x^2+a)^(3/4)/b^2+2/5*(12*a^2*d^2-20*a*b*c*d+5*b^2*c^2)*(1+b*x^2/a)^(1/4)*EllipticE(sin(1/2*arctan(sqrt(b)*x/sqrt(a))),sqrt(2))/sqrt(a)/b^(5/2)/(b*x^2+a)^(1/4),1],
[(d*x^2+c)/(b*x^2+a)^(5/4),x,3,2*d*x/b/(b*x^2+a)^(1/4)+2*(-2*a*d+b*c)*(1+b*x^2/a)^(1/4)*EllipticE(sin(1/2*arctan(sqrt(b)*x/sqrt(a))),sqrt(2))/sqrt(a)/b^(3/2)/(b*x^2+a)^(1/4),1],
[1/(b*x^2+a)^(5/4)/(d*x^2+c),x,7,2*sqrt(b)*(1+b*x^2/a)^(1/4)*EllipticE(sin(1/2*arctan(sqrt(b)*x/sqrt(a))),sqrt(2))/sqrt(a)/(-a*d+b*c)/(b*x^2+a)^(1/4)+a^(1/4)*sqrt(d)*sqrt(-b*x^2/a)*EllipticPi(sin(arcsin((b*x^2+a)^(1/4)/a^(1/4))),-sqrt(a)*sqrt(d)/sqrt(a*d-b*c),sqrt(-1))/(a*d-b*c)^(3/2)/x-a^(1/4)*sqrt(d)*sqrt(-b*x^2/a)*EllipticPi(sin(arcsin((b*x^2+a)^(1/4)/a^(1/4))),sqrt(a)*sqrt(d)/sqrt(a*d-b*c),sqrt(-1))/(a*d-b*c)^(3/2)/x,1],
[1/(b*x^2+a)^(5/4)/(d*x^2+c)^2,x,8,-1/2*d*x/c/(-a*d+b*c)/(b*x^2+a)^(1/4)/(d*x^2+c)+1/2*sqrt(b)*(a*d+4*b*c)*(1+b*x^2/a)^(1/4)*EllipticE(sin(1/2*arctan(sqrt(b)*x/sqrt(a))),sqrt(2))/sqrt(a)/c/(-a*d+b*c)^2/(b*x^2+a)^(1/4)-1/4*a^(1/4)*sqrt(d)*(-2*a*d+7*b*c)*sqrt(-b*x^2/a)*EllipticPi(sin(arcsin((b*x^2+a)^(1/4)/a^(1/4))),-sqrt(a)*sqrt(d)/sqrt(a*d-b*c),sqrt(-1))/c/(a*d-b*c)^(5/2)/x+1/4*a^(1/4)*sqrt(d)*(-2*a*d+7*b*c)*sqrt(-b*x^2/a)*EllipticPi(sin(arcsin((b*x^2+a)^(1/4)/a^(1/4))),sqrt(a)*sqrt(d)/sqrt(a*d-b*c),sqrt(-1))/c/(a*d-b*c)^(5/2)/x,1],
[(d*x^2+c)^3/(b*x^2+a)^(7/4),x,5,2/3*(-a*d+b*c)^3*x/a/b^3/(b*x^2+a)^(3/4)+2/21*d^2*(-13*a*d+21*b*c)*x*(b*x^2+a)^(1/4)/b^3+2/7*d^3*x^3*(b*x^2+a)^(1/4)/b^2+2/21*(40*a^3*d^3-84*a^2*b*c*d^2+42*a*b^2*c^2*d+7*b^3*c^3)*(1+b*x^2/a)^(3/4)*InverseJacobiAM(1/2*arctan(sqrt(b)*x/sqrt(a)),sqrt(2))/sqrt(a)/b^(7/2)/(b*x^2+a)^(3/4),1],
[(d*x^2+c)^2/(b*x^2+a)^(7/4),x,4,2/3*(-a*d+b*c)^2*x/a/b^2/(b*x^2+a)^(3/4)+2/3*d^2*x*(b*x^2+a)^(1/4)/b^2+2/3*(-4*a^2*d^2+4*a*b*c*d+b^2*c^2)*(1+b*x^2/a)^(3/4)*InverseJacobiAM(1/2*arctan(sqrt(b)*x/sqrt(a)),sqrt(2))/sqrt(a)/b^(5/2)/(b*x^2+a)^(3/4),1],
[(d*x^2+c)/(b*x^2+a)^(7/4),x,3,2/3*(-a*d+b*c)*x/a/b/(b*x^2+a)^(3/4)+2/3*(2*a*d+b*c)*(1+b*x^2/a)^(3/4)*InverseJacobiAM(1/2*arctan(sqrt(b)*x/sqrt(a)),sqrt(2))/sqrt(a)/b^(3/2)/(b*x^2+a)^(3/4),1],
[1/(b*x^2+a)^(7/4)/(d*x^2+c),x,9,2/3*b*x/a/(-a*d+b*c)/(b*x^2+a)^(3/4)+2/3*sqrt(b)*(1+b*x^2/a)^(3/4)*InverseJacobiAM(1/2*arctan(sqrt(b)*x/sqrt(a)),sqrt(2))/sqrt(a)/(-a*d+b*c)/(b*x^2+a)^(3/4)-a^(1/4)*d*sqrt(-b*x^2/a)*EllipticPi(sin(arcsin((b*x^2+a)^(1/4)/a^(1/4))),-sqrt(a)*sqrt(d)/sqrt(a*d-b*c),sqrt(-1))/(-a*d+b*c)^2/x-a^(1/4)*d*sqrt(-b*x^2/a)*EllipticPi(sin(arcsin((b*x^2+a)^(1/4)/a^(1/4))),sqrt(a)*sqrt(d)/sqrt(a*d-b*c),sqrt(-1))/(-a*d+b*c)^2/x,1],
[1/(b*x^2+a)^(7/4)/(d*x^2+c)^2,x,10,1/6*b*(3*a*d+4*b*c)*x/a/c/(-a*d+b*c)^2/(b*x^2+a)^(3/4)-1/2*d*x/c/(-a*d+b*c)/(b*x^2+a)^(3/4)/(d*x^2+c)+1/6*sqrt(b)*(3*a*d+4*b*c)*(1+b*x^2/a)^(3/4)*InverseJacobiAM(1/2*arctan(sqrt(b)*x/sqrt(a)),sqrt(2))/sqrt(a)/c/(-a*d+b*c)^2/(b*x^2+a)^(3/4)-1/4*a^(1/4)*d*(-2*a*d+9*b*c)*sqrt(-b*x^2/a)*EllipticPi(sin(arcsin((b*x^2+a)^(1/4)/a^(1/4))),-sqrt(a)*sqrt(d)/sqrt(a*d-b*c),sqrt(-1))/c/(-a*d+b*c)^3/x-1/4*a^(1/4)*d*(-2*a*d+9*b*c)*sqrt(-b*x^2/a)*EllipticPi(sin(arcsin((b*x^2+a)^(1/4)/a^(1/4))),sqrt(a)*sqrt(d)/sqrt(a*d-b*c),sqrt(-1))/c/(-a*d+b*c)^3/x,1],
[(d*x^2+c)^3/(b*x^2+a)^(9/4),x,5,2/5*(-a*d+b*c)^3*x/a/b^3/(b*x^2+a)^(5/4)+6/5*d^2*(-4*a*d+5*b*c)*x/b^3/(b*x^2+a)^(1/4)+2/5*d^3*x*(b*x^2+a)^(3/4)/b^3+6/5*(-2*a*d+b*c)*(-4*a^2*d^2+4*a*b*c*d+b^2*c^2)*(1+b*x^2/a)^(1/4)*EllipticE(sin(1/2*arctan(sqrt(b)*x/sqrt(a))),sqrt(2))/a^(3/2)/b^(7/2)/(b*x^2+a)^(1/4),1],
[(d*x^2+c)^2/(b*x^2+a)^(9/4),x,4,2/5*(-a*d+b*c)^2*x/a/b^2/(b*x^2+a)^(5/4)+2*d^2*x/b^2/(b*x^2+a)^(1/4)+2/5*(-12*a^2*d^2+4*a*b*c*d+3*b^2*c^2)*(1+b*x^2/a)^(1/4)*EllipticE(sin(1/2*arctan(sqrt(b)*x/sqrt(a))),sqrt(2))/a^(3/2)/b^(5/2)/(b*x^2+a)^(1/4),1],
[(d*x^2+c)/(b*x^2+a)^(9/4),x,3,2/5*(-a*d+b*c)*x/a/b/(b*x^2+a)^(5/4)+2/5*(2*a*d+3*b*c)*(1+b*x^2/a)^(1/4)*EllipticE(sin(1/2*arctan(sqrt(b)*x/sqrt(a))),sqrt(2))/a^(3/2)/b^(3/2)/(b*x^2+a)^(1/4),1],
[1/(b*x^2+a)^(9/4)/(d*x^2+c),x,8,2/5*b*x/a/(-a*d+b*c)/(b*x^2+a)^(5/4)+2/5*sqrt(b)*(-8*a*d+3*b*c)*(1+b*x^2/a)^(1/4)*EllipticE(sin(1/2*arctan(sqrt(b)*x/sqrt(a))),sqrt(2))/a^(3/2)/(-a*d+b*c)^2/(b*x^2+a)^(1/4)+a^(1/4)*d^(3/2)*sqrt(-b*x^2/a)*EllipticPi(sin(arcsin((b*x^2+a)^(1/4)/a^(1/4))),-sqrt(a)*sqrt(d)/sqrt(a*d-b*c),sqrt(-1))/(a*d-b*c)^(5/2)/x-a^(1/4)*d^(3/2)*sqrt(-b*x^2/a)*EllipticPi(sin(arcsin((b*x^2+a)^(1/4)/a^(1/4))),sqrt(a)*sqrt(d)/sqrt(a*d-b*c),sqrt(-1))/(a*d-b*c)^(5/2)/x,1],
[1/(b*x^2+a)^(9/4)/(d*x^2+c)^2,x,9,1/10*b*(5*a*d+4*b*c)*x/a/c/(-a*d+b*c)^2/(b*x^2+a)^(5/4)-1/2*d*x/c/(-a*d+b*c)/(b*x^2+a)^(5/4)/(d*x^2+c)+1/10*sqrt(b)*(-5*a^2*d^2-52*a*b*c*d+12*b^2*c^2)*(1+b*x^2/a)^(1/4)*EllipticE(sin(1/2*arctan(sqrt(b)*x/sqrt(a))),sqrt(2))/a^(3/2)/c/(-a*d+b*c)^3/(b*x^2+a)^(1/4)-1/4*a^(1/4)*d^(3/2)*(-2*a*d+11*b*c)*sqrt(-b*x^2/a)*EllipticPi(sin(arcsin((b*x^2+a)^(1/4)/a^(1/4))),-sqrt(a)*sqrt(d)/sqrt(a*d-b*c),sqrt(-1))/c/(a*d-b*c)^(7/2)/x+1/4*a^(1/4)*d^(3/2)*(-2*a*d+11*b*c)*sqrt(-b*x^2/a)*EllipticPi(sin(arcsin((b*x^2+a)^(1/4)/a^(1/4))),sqrt(a)*sqrt(d)/sqrt(a*d-b*c),sqrt(-1))/c/(a*d-b*c)^(7/2)/x,1],
[(-b*x^2+a)^(1/4)*(d*x^2+c)^3,x,6,2/231*(77*c^3+2*a*d*(4*a^2*d^2+18*a*b*c*d+33*b^2*c^2)/b^3)*x*(-b*x^2+a)^(1/4)-2/77*d*(4*a^2*d^2+18*a*b*c*d+33*b^2*c^2)*x*(-b*x^2+a)^(5/4)/b^3-2/33*d^2*(2*a*d+9*b*c)*x^3*(-b*x^2+a)^(5/4)/b^2-2/15*d^3*x^5*(-b*x^2+a)^(5/4)/b+2/231*a^(3/2)*(77*b^3*c^3+2*a*d*(4*a^2*d^2+18*a*b*c*d+33*b^2*c^2))*(1-b*x^2/a)^(3/4)*InverseJacobiAM(1/2*arcsin(sqrt(b)*x/sqrt(a)),sqrt(2))/b^(7/2)/(-b*x^2+a)^(3/4),1],
[(-b*x^2+a)^(1/4)*(d*x^2+c)^2,x,5,2/231*(77*c^2+4*a*d*(3*a*d+11*b*c)/b^2)*x*(-b*x^2+a)^(1/4)-4/77*d*(3*a*d+11*b*c)*x*(-b*x^2+a)^(5/4)/b^2-2/11*d^2*x^3*(-b*x^2+a)^(5/4)/b+2/231*a^(3/2)*(77*b^2*c^2+4*a*d*(3*a*d+11*b*c))*(1-b*x^2/a)^(3/4)*InverseJacobiAM(1/2*arcsin(sqrt(b)*x/sqrt(a)),sqrt(2))/b^(5/2)/(-b*x^2+a)^(3/4),1],
[(-b*x^2+a)^(1/4)*(d*x^2+c),x,4,2/21*(2*a*d+7*b*c)*x*(-b*x^2+a)^(1/4)/b-2/7*d*x*(-b*x^2+a)^(5/4)/b+2/21*a^(3/2)*(2*a*d+7*b*c)*(1-b*x^2/a)^(3/4)*InverseJacobiAM(1/2*arcsin(sqrt(b)*x/sqrt(a)),sqrt(2))/b^(3/2)/(-b*x^2+a)^(3/4),1],
[(-b*x^2+a)^(1/4)/(d*x^2+c),x,8,-2*sqrt(a)*sqrt(b)*(1-b*x^2/a)^(3/4)*InverseJacobiAM(1/2*arcsin(sqrt(b)*x/sqrt(a)),sqrt(2))/d/(-b*x^2+a)^(3/4)-a^(1/4)*sqrt(b*x^2/a)*EllipticPi(sin(arcsin((-b*x^2+a)^(1/4)/a^(1/4))),-sqrt(a)*sqrt(d)/sqrt(a*d+b*c),sqrt(-1))/d/x-a^(1/4)*sqrt(b*x^2/a)*EllipticPi(sin(arcsin((-b*x^2+a)^(1/4)/a^(1/4))),sqrt(a)*sqrt(d)/sqrt(a*d+b*c),sqrt(-1))/d/x,1],
[(-b*x^2+a)^(1/4)/(d*x^2+c)^2,x,9,1/2*x*(-b*x^2+a)^(1/4)/c/(d*x^2+c)-1/2*sqrt(a)*sqrt(b)*(1-b*x^2/a)^(3/4)*InverseJacobiAM(1/2*arcsin(sqrt(b)*x/sqrt(a)),sqrt(2))/c/d/(-b*x^2+a)^(3/4)-1/4*a^(1/4)*(2*a*d+b*c)*sqrt(b*x^2/a)*EllipticPi(sin(arcsin((-b*x^2+a)^(1/4)/a^(1/4))),-sqrt(a)*sqrt(d)/sqrt(a*d+b*c),sqrt(-1))/c/d/(a*d+b*c)/x-1/4*a^(1/4)*(2*a*d+b*c)*sqrt(b*x^2/a)*EllipticPi(sin(arcsin((-b*x^2+a)^(1/4)/a^(1/4))),sqrt(a)*sqrt(d)/sqrt(a*d+b*c),sqrt(-1))/c/d/(a*d+b*c)/x,1],
[(-b*x^2+a)^(3/4)*(d*x^2+c)^3,x,6,2/3315*(663*c^3+2*a*d*(20*a^2*d^2+102*a*b*c*d+221*b^2*c^2)/b^3)*x*(-b*x^2+a)^(3/4)-2/663*d*(20*a^2*d^2+102*a*b*c*d+221*b^2*c^2)*x*(-b*x^2+a)^(7/4)/b^3-2/221*d^2*(10*a*d+51*b*c)*x^3*(-b*x^2+a)^(7/4)/b^2-2/17*d^3*x^5*(-b*x^2+a)^(7/4)/b+2/1105*a^(3/2)*(663*b^3*c^3+2*a*d*(20*a^2*d^2+102*a*b*c*d+221*b^2*c^2))*(1-b*x^2/a)^(1/4)*EllipticE(sin(1/2*arcsin(sqrt(b)*x/sqrt(a))),sqrt(2))/b^(7/2)/(-b*x^2+a)^(1/4),1],
[(-b*x^2+a)^(3/4)*(d*x^2+c)^2,x,5,2/585*(117*c^2+4*a*d*(3*a*d+13*b*c)/b^2)*x*(-b*x^2+a)^(3/4)-4/117*d*(3*a*d+13*b*c)*x*(-b*x^2+a)^(7/4)/b^2-2/13*d^2*x^3*(-b*x^2+a)^(7/4)/b+2/195*a^(3/2)*(117*b^2*c^2+4*a*d*(3*a*d+13*b*c))*(1-b*x^2/a)^(1/4)*EllipticE(sin(1/2*arcsin(sqrt(b)*x/sqrt(a))),sqrt(2))/b^(5/2)/(-b*x^2+a)^(1/4),1],
[(-b*x^2+a)^(3/4)*(d*x^2+c),x,4,2/45*(2*a*d+9*b*c)*x*(-b*x^2+a)^(3/4)/b-2/9*d*x*(-b*x^2+a)^(7/4)/b+2/15*a^(3/2)*(2*a*d+9*b*c)*(1-b*x^2/a)^(1/4)*EllipticE(sin(1/2*arcsin(sqrt(b)*x/sqrt(a))),sqrt(2))/b^(3/2)/(-b*x^2+a)^(1/4),1],
[(-b*x^2+a)^(3/4)/(d*x^2+c),x,7,-2*sqrt(a)*sqrt(b)*(1-b*x^2/a)^(1/4)*EllipticE(sin(1/2*arcsin(sqrt(b)*x/sqrt(a))),sqrt(2))/d/(-b*x^2+a)^(1/4)+a^(1/4)*sqrt(a*d+b*c)*sqrt(b*x^2/a)*EllipticPi(sin(arcsin((-b*x^2+a)^(1/4)/a^(1/4))),-sqrt(a)*sqrt(d)/sqrt(a*d+b*c),sqrt(-1))/d^(3/2)/x-a^(1/4)*sqrt(a*d+b*c)*sqrt(b*x^2/a)*EllipticPi(sin(arcsin((-b*x^2+a)^(1/4)/a^(1/4))),sqrt(a)*sqrt(d)/sqrt(a*d+b*c),sqrt(-1))/d^(3/2)/x,1],
[(-b*x^2+a)^(3/4)/(d*x^2+c)^2,x,8,1/2*x*(-b*x^2+a)^(3/4)/c/(d*x^2+c)+1/2*sqrt(a)*sqrt(b)*(1-b*x^2/a)^(1/4)*EllipticE(sin(1/2*arcsin(sqrt(b)*x/sqrt(a))),sqrt(2))/c/d/(-b*x^2+a)^(1/4)-1/4*a^(1/4)*(-2*a*d+b*c)*sqrt(b*x^2/a)*EllipticPi(sin(arcsin((-b*x^2+a)^(1/4)/a^(1/4))),-sqrt(a)*sqrt(d)/sqrt(a*d+b*c),sqrt(-1))/c/d^(3/2)/sqrt(a*d+b*c)/x+1/4*a^(1/4)*(-2*a*d+b*c)*sqrt(b*x^2/a)*EllipticPi(sin(arcsin((-b*x^2+a)^(1/4)/a^(1/4))),sqrt(a)*sqrt(d)/sqrt(a*d+b*c),sqrt(-1))/c/d^(3/2)/sqrt(a*d+b*c)/x,1],
[(-b*x^2+a)^(5/4)*(d*x^2+c)^3,x,7,2/4389*a*(1045*b^3*c^3+2*a*d*(20*a^2*d^2+114*a*b*c*d+285*b^2*c^2))*x*(-b*x^2+a)^(1/4)/b^3+2/7315*(1045*c^3+2*a*d*(20*a^2*d^2+114*a*b*c*d+285*b^2*c^2)/b^3)*x*(-b*x^2+a)^(5/4)-2/1045*d*(20*a^2*d^2+114*a*b*c*d+285*b^2*c^2)*x*(-b*x^2+a)^(9/4)/b^3-2/285*d^2*(10*a*d+57*b*c)*x^3*(-b*x^2+a)^(9/4)/b^2-2/19*d^3*x^5*(-b*x^2+a)^(9/4)/b+2/4389*a^(5/2)*(1045*b^3*c^3+2*a*d*(20*a^2*d^2+114*a*b*c*d+285*b^2*c^2))*(1-b*x^2/a)^(3/4)*InverseJacobiAM(1/2*arcsin(sqrt(b)*x/sqrt(a)),sqrt(2))/b^(7/2)/(-b*x^2+a)^(3/4),1],
[(-b*x^2+a)^(5/4)*(d*x^2+c)^2,x,6,2/231*a*(55*b^2*c^2+4*a*d*(a*d+5*b*c))*x*(-b*x^2+a)^(1/4)/b^2+2/385*(55*c^2+4*a*d*(a*d+5*b*c)/b^2)*x*(-b*x^2+a)^(5/4)-4/55*d*(a*d+5*b*c)*x*(-b*x^2+a)^(9/4)/b^2-2/15*d^2*x^3*(-b*x^2+a)^(9/4)/b+2/231*a^(5/2)*(55*b^2*c^2+4*a*d*(a*d+5*b*c))*(1-b*x^2/a)^(3/4)*InverseJacobiAM(1/2*arcsin(sqrt(b)*x/sqrt(a)),sqrt(2))/b^(5/2)/(-b*x^2+a)^(3/4),1],
[(-b*x^2+a)^(5/4)*(d*x^2+c),x,5,10/231*a*(2*a*d+11*b*c)*x*(-b*x^2+a)^(1/4)/b+2/77*(2*a*d+11*b*c)*x*(-b*x^2+a)^(5/4)/b-2/11*d*x*(-b*x^2+a)^(9/4)/b+10/231*a^(5/2)*(2*a*d+11*b*c)*(1-b*x^2/a)^(3/4)*InverseJacobiAM(1/2*arcsin(sqrt(b)*x/sqrt(a)),sqrt(2))/b^(3/2)/(-b*x^2+a)^(3/4),1],
[(-b*x^2+a)^(5/4)/(d*x^2+c),x,9,-2/3*b*x*(-b*x^2+a)^(1/4)/d-2/3*sqrt(a)*sqrt(b)*(4*a*d+3*b*c)*(1-b*x^2/a)^(3/4)*InverseJacobiAM(1/2*arcsin(sqrt(b)*x/sqrt(a)),sqrt(2))/d^2/(-b*x^2+a)^(3/4)-a^(1/4)*(a*d+b*c)*sqrt(b*x^2/a)*EllipticPi(sin(arcsin((-b*x^2+a)^(1/4)/a^(1/4))),-sqrt(a)*sqrt(d)/sqrt(a*d+b*c),sqrt(-1))/d^2/x-a^(1/4)*(a*d+b*c)*sqrt(b*x^2/a)*EllipticPi(sin(arcsin((-b*x^2+a)^(1/4)/a^(1/4))),sqrt(a)*sqrt(d)/sqrt(a*d+b*c),sqrt(-1))/d^2/x,1],
[(-b*x^2+a)^(5/4)/(d*x^2+c)^2,x,9,1/2*(a*d+b*c)*x*(-b*x^2+a)^(1/4)/c/d/(d*x^2+c)+1/2*sqrt(a)*sqrt(b)*(-a*d+3*b*c)*(1-b*x^2/a)^(3/4)*InverseJacobiAM(1/2*arcsin(sqrt(b)*x/sqrt(a)),sqrt(2))/c/d^2/(-b*x^2+a)^(3/4)+1/4*a^(1/4)*(-2*a*d+3*b*c)*sqrt(b*x^2/a)*EllipticPi(sin(arcsin((-b*x^2+a)^(1/4)/a^(1/4))),-sqrt(a)*sqrt(d)/sqrt(a*d+b*c),sqrt(-1))/c/d^2/x+1/4*a^(1/4)*(-2*a*d+3*b*c)*sqrt(b*x^2/a)*EllipticPi(sin(arcsin((-b*x^2+a)^(1/4)/a^(1/4))),sqrt(a)*sqrt(d)/sqrt(a*d+b*c),sqrt(-1))/c/d^2/x,1],
[(-b*x^2+a)^(7/4)*(d*x^2+c)^3,x,7,2/9945*a*(1547*b^3*c^3+2*a*d*(20*a^2*d^2+126*a*b*c*d+357*b^2*c^2))*x*(-b*x^2+a)^(3/4)/b^3+2/13923*(1547*c^3+2*a*d*(20*a^2*d^2+126*a*b*c*d+357*b^2*c^2)/b^3)*x*(-b*x^2+a)^(7/4)-2/1547*d*(20*a^2*d^2+126*a*b*c*d+357*b^2*c^2)*x*(-b*x^2+a)^(11/4)/b^3-2/357*d^2*(10*a*d+63*b*c)*x^3*(-b*x^2+a)^(11/4)/b^2-2/21*d^3*x^5*(-b*x^2+a)^(11/4)/b+2/3315*a^(5/2)*(1547*b^3*c^3+2*a*d*(20*a^2*d^2+126*a*b*c*d+357*b^2*c^2))*(1-b*x^2/a)^(1/4)*EllipticE(sin(1/2*arcsin(sqrt(b)*x/sqrt(a))),sqrt(2))/b^(7/2)/(-b*x^2+a)^(1/4),1],
[(-b*x^2+a)^(7/4)*(d*x^2+c)^2,x,6,14/9945*a*(221*b^2*c^2+4*a*d*(3*a*d+17*b*c))*x*(-b*x^2+a)^(3/4)/b^2+2/1989*(221*c^2+4*a*d*(3*a*d+17*b*c)/b^2)*x*(-b*x^2+a)^(7/4)-4/221*d*(3*a*d+17*b*c)*x*(-b*x^2+a)^(11/4)/b^2-2/17*d^2*x^3*(-b*x^2+a)^(11/4)/b+14/3315*a^(5/2)*(221*b^2*c^2+4*a*d*(3*a*d+17*b*c))*(1-b*x^2/a)^(1/4)*EllipticE(sin(1/2*arcsin(sqrt(b)*x/sqrt(a))),sqrt(2))/b^(5/2)/(-b*x^2+a)^(1/4),1],
[(-b*x^2+a)^(7/4)*(d*x^2+c),x,5,14/585*a*(2*a*d+13*b*c)*x*(-b*x^2+a)^(3/4)/b+2/117*(2*a*d+13*b*c)*x*(-b*x^2+a)^(7/4)/b-2/13*d*x*(-b*x^2+a)^(11/4)/b+14/195*a^(5/2)*(2*a*d+13*b*c)*(1-b*x^2/a)^(1/4)*EllipticE(sin(1/2*arcsin(sqrt(b)*x/sqrt(a))),sqrt(2))/b^(3/2)/(-b*x^2+a)^(1/4),1],
[(-b*x^2+a)^(7/4)/(d*x^2+c),x,8,-2/5*b*x*(-b*x^2+a)^(3/4)/d-2/5*sqrt(a)*sqrt(b)*(8*a*d+5*b*c)*(1-b*x^2/a)^(1/4)*EllipticE(sin(1/2*arcsin(sqrt(b)*x/sqrt(a))),sqrt(2))/d^2/(-b*x^2+a)^(1/4)+a^(1/4)*(a*d+b*c)^(3/2)*sqrt(b*x^2/a)*EllipticPi(sin(arcsin((-b*x^2+a)^(1/4)/a^(1/4))),-sqrt(a)*sqrt(d)/sqrt(a*d+b*c),sqrt(-1))/d^(5/2)/x-a^(1/4)*(a*d+b*c)^(3/2)*sqrt(b*x^2/a)*EllipticPi(sin(arcsin((-b*x^2+a)^(1/4)/a^(1/4))),sqrt(a)*sqrt(d)/sqrt(a*d+b*c),sqrt(-1))/d^(5/2)/x,1],
[(-b*x^2+a)^(7/4)/(d*x^2+c)^2,x,8,1/2*(a*d+b*c)*x*(-b*x^2+a)^(3/4)/c/d/(d*x^2+c)+1/2*sqrt(a)*sqrt(b)*(a*d+5*b*c)*(1-b*x^2/a)^(1/4)*EllipticE(sin(1/2*arcsin(sqrt(b)*x/sqrt(a))),sqrt(2))/c/d^2/(-b*x^2+a)^(1/4)-1/4*a^(1/4)*(-2*a*d+5*b*c)*sqrt(a*d+b*c)*sqrt(b*x^2/a)*EllipticPi(sin(arcsin((-b*x^2+a)^(1/4)/a^(1/4))),-sqrt(a)*sqrt(d)/sqrt(a*d+b*c),sqrt(-1))/c/d^(5/2)/x+1/4*a^(1/4)*(-2*a*d+5*b*c)*sqrt(a*d+b*c)*sqrt(b*x^2/a)*EllipticPi(sin(arcsin((-b*x^2+a)^(1/4)/a^(1/4))),sqrt(a)*sqrt(d)/sqrt(a*d+b*c),sqrt(-1))/c/d^(5/2)/x,1],
[(d*x^2+c)^3/(-b*x^2+a)^(1/4),x,5,-2/195*d*(20*a^2*d^2+78*a*b*c*d+117*b^2*c^2)*x*(-b*x^2+a)^(3/4)/b^3-2/117*d^2*(10*a*d+39*b*c)*x^3*(-b*x^2+a)^(3/4)/b^2-2/13*d^3*x^5*(-b*x^2+a)^(3/4)/b+2/195*sqrt(a)*(195*b^3*c^3+2*a*d*(20*a^2*d^2+78*a*b*c*d+117*b^2*c^2))*(1-b*x^2/a)^(1/4)*EllipticE(sin(1/2*arcsin(sqrt(b)*x/sqrt(a))),sqrt(2))/b^(7/2)/(-b*x^2+a)^(1/4),1],
[(d*x^2+c)^2/(-b*x^2+a)^(1/4),x,4,-4/15*d*(a*d+3*b*c)*x*(-b*x^2+a)^(3/4)/b^2-2/9*d^2*x^3*(-b*x^2+a)^(3/4)/b+2/15*sqrt(a)*(15*b^2*c^2+4*a*d*(a*d+3*b*c))*(1-b*x^2/a)^(1/4)*EllipticE(sin(1/2*arcsin(sqrt(b)*x/sqrt(a))),sqrt(2))/b^(5/2)/(-b*x^2+a)^(1/4),1],
[(d*x^2+c)/(-b*x^2+a)^(1/4),x,3,-2/5*d*x*(-b*x^2+a)^(3/4)/b+2/5*sqrt(a)*(2*a*d+5*b*c)*(1-b*x^2/a)^(1/4)*EllipticE(sin(1/2*arcsin(sqrt(b)*x/sqrt(a))),sqrt(2))/b^(3/2)/(-b*x^2+a)^(1/4),1],
[1/(-b*x^2+a)^(1/4)/(d*x^2+c),x,4,a^(1/4)*sqrt(b*x^2/a)*EllipticPi(sin(arcsin((-b*x^2+a)^(1/4)/a^(1/4))),-sqrt(a)*sqrt(d)/sqrt(a*d+b*c),sqrt(-1))/sqrt(d)/sqrt(a*d+b*c)/x-a^(1/4)*sqrt(b*x^2/a)*EllipticPi(sin(arcsin((-b*x^2+a)^(1/4)/a^(1/4))),sqrt(a)*sqrt(d)/sqrt(a*d+b*c),sqrt(-1))/sqrt(d)/sqrt(a*d+b*c)/x,1],
[1/(-b*x^2+a)^(1/4)/(d*x^2+c)^2,x,8,1/2*d*x*(-b*x^2+a)^(3/4)/c/(a*d+b*c)/(d*x^2+c)+1/2*sqrt(a)*sqrt(b)*(1-b*x^2/a)^(1/4)*EllipticE(sin(1/2*arcsin(sqrt(b)*x/sqrt(a))),sqrt(2))/c/(a*d+b*c)/(-b*x^2+a)^(1/4)+1/4*a^(1/4)*(2*a*d+3*b*c)*sqrt(b*x^2/a)*EllipticPi(sin(arcsin((-b*x^2+a)^(1/4)/a^(1/4))),-sqrt(a)*sqrt(d)/sqrt(a*d+b*c),sqrt(-1))/c/sqrt(d)/(a*d+b*c)^(3/2)/x-1/4*a^(1/4)*(2*a*d+3*b*c)*sqrt(b*x^2/a)*EllipticPi(sin(arcsin((-b*x^2+a)^(1/4)/a^(1/4))),sqrt(a)*sqrt(d)/sqrt(a*d+b*c),sqrt(-1))/c/sqrt(d)/(a*d+b*c)^(3/2)/x,1],
[(d*x^2+c)^3/(-b*x^2+a)^(3/4),x,5,-2/77*d*(20*a^2*d^2+66*a*b*c*d+77*b^2*c^2)*x*(-b*x^2+a)^(1/4)/b^3-2/77*d^2*(10*a*d+33*b*c)*x^3*(-b*x^2+a)^(1/4)/b^2-2/11*d^3*x^5*(-b*x^2+a)^(1/4)/b+2/77*sqrt(a)*(77*b^3*c^3+2*a*d*(20*a^2*d^2+66*a*b*c*d+77*b^2*c^2))*(1-b*x^2/a)^(3/4)*InverseJacobiAM(1/2*arcsin(sqrt(b)*x/sqrt(a)),sqrt(2))/b^(7/2)/(-b*x^2+a)^(3/4),1],
[(d*x^2+c)^2/(-b*x^2+a)^(3/4),x,4,-4/21*d*(3*a*d+7*b*c)*x*(-b*x^2+a)^(1/4)/b^2-2/7*d^2*x^3*(-b*x^2+a)^(1/4)/b+2/21*sqrt(a)*(21*b^2*c^2+4*a*d*(3*a*d+7*b*c))*(1-b*x^2/a)^(3/4)*InverseJacobiAM(1/2*arcsin(sqrt(b)*x/sqrt(a)),sqrt(2))/b^(5/2)/(-b*x^2+a)^(3/4),1],
[(d*x^2+c)/(-b*x^2+a)^(3/4),x,3,-2/3*d*x*(-b*x^2+a)^(1/4)/b+2/3*sqrt(a)*(2*a*d+3*b*c)*(1-b*x^2/a)^(3/4)*InverseJacobiAM(1/2*arcsin(sqrt(b)*x/sqrt(a)),sqrt(2))/b^(3/2)/(-b*x^2+a)^(3/4),1],
[1/(-b*x^2+a)^(3/4)/(d*x^2+c),x,5,-a^(1/4)*sqrt(b*x^2/a)*EllipticPi(sin(arcsin((-b*x^2+a)^(1/4)/a^(1/4))),-sqrt(a)*sqrt(d)/sqrt(a*d+b*c),sqrt(-1))/(a*d+b*c)/x-a^(1/4)*sqrt(b*x^2/a)*EllipticPi(sin(arcsin((-b*x^2+a)^(1/4)/a^(1/4))),sqrt(a)*sqrt(d)/sqrt(a*d+b*c),sqrt(-1))/(a*d+b*c)/x,1],
[1/(-b*x^2+a)^(3/4)/(d*x^2+c)^2,x,9,1/2*d*x*(-b*x^2+a)^(1/4)/c/(a*d+b*c)/(d*x^2+c)-1/2*sqrt(a)*sqrt(b)*(1-b*x^2/a)^(3/4)*InverseJacobiAM(1/2*arcsin(sqrt(b)*x/sqrt(a)),sqrt(2))/c/(a*d+b*c)/(-b*x^2+a)^(3/4)-1/4*a^(1/4)*(2*a*d+5*b*c)*sqrt(b*x^2/a)*EllipticPi(sin(arcsin((-b*x^2+a)^(1/4)/a^(1/4))),-sqrt(a)*sqrt(d)/sqrt(a*d+b*c),sqrt(-1))/c/(a*d+b*c)^2/x-1/4*a^(1/4)*(2*a*d+5*b*c)*sqrt(b*x^2/a)*EllipticPi(sin(arcsin((-b*x^2+a)^(1/4)/a^(1/4))),sqrt(a)*sqrt(d)/sqrt(a*d+b*c),sqrt(-1))/c/(a*d+b*c)^2/x,1],
[(d*x^2+c)^3/(-b*x^2+a)^(5/4),x,5,2*(a*d+b*c)^3*x/a/b^3/(-b*x^2+a)^(1/4)+2/15*d^2*(5*a*d+9*b*c)*x*(-b*x^2+a)^(3/4)/b^3+2/9*d^3*x^3*(-b*x^2+a)^(3/4)/b^2-2/15*(40*a^3*d^3+108*a^2*b*c*d^2+90*a*b^2*c^2*d+15*b^3*c^3)*(1-b*x^2/a)^(1/4)*EllipticE(sin(1/2*arcsin(sqrt(b)*x/sqrt(a))),sqrt(2))/sqrt(a)/b^(7/2)/(-b*x^2+a)^(1/4),1],
[(d*x^2+c)^2/(-b*x^2+a)^(5/4),x,4,2*(a*d+b*c)^2*x/a/b^2/(-b*x^2+a)^(1/4)+2/5*d^2*x*(-b*x^2+a)^(3/4)/b^2-2/5*(12*a^2*d^2+20*a*b*c*d+5*b^2*c^2)*(1-b*x^2/a)^(1/4)*EllipticE(sin(1/2*arcsin(sqrt(b)*x/sqrt(a))),sqrt(2))/sqrt(a)/b^(5/2)/(-b*x^2+a)^(1/4),1],
[(d*x^2+c)/(-b*x^2+a)^(5/4),x,3,2*(a*d+b*c)*x/a/b/(-b*x^2+a)^(1/4)-2*(2*a*d+b*c)*(1-b*x^2/a)^(1/4)*EllipticE(sin(1/2*arcsin(sqrt(b)*x/sqrt(a))),sqrt(2))/sqrt(a)/b^(3/2)/(-b*x^2+a)^(1/4),1],
[1/(-b*x^2+a)^(5/4)/(d*x^2+c),x,8,2*b*x/a/(a*d+b*c)/(-b*x^2+a)^(1/4)-2*sqrt(b)*(1-b*x^2/a)^(1/4)*EllipticE(sin(1/2*arcsin(sqrt(b)*x/sqrt(a))),sqrt(2))/sqrt(a)/(a*d+b*c)/(-b*x^2+a)^(1/4)+a^(1/4)*sqrt(d)*sqrt(b*x^2/a)*EllipticPi(sin(arcsin((-b*x^2+a)^(1/4)/a^(1/4))),-sqrt(a)*sqrt(d)/sqrt(a*d+b*c),sqrt(-1))/(a*d+b*c)^(3/2)/x-a^(1/4)*sqrt(d)*sqrt(b*x^2/a)*EllipticPi(sin(arcsin((-b*x^2+a)^(1/4)/a^(1/4))),sqrt(a)*sqrt(d)/sqrt(a*d+b*c),sqrt(-1))/(a*d+b*c)^(3/2)/x,1],
[1/(-b*x^2+a)^(5/4)/(d*x^2+c)^2,x,9,1/2*b*(-a*d+4*b*c)*x/a/c/(a*d+b*c)^2/(-b*x^2+a)^(1/4)+1/2*d*x/c/(a*d+b*c)/(-b*x^2+a)^(1/4)/(d*x^2+c)-1/2*sqrt(b)*(-a*d+4*b*c)*(1-b*x^2/a)^(1/4)*EllipticE(sin(1/2*arcsin(sqrt(b)*x/sqrt(a))),sqrt(2))/sqrt(a)/c/(a*d+b*c)^2/(-b*x^2+a)^(1/4)+1/4*a^(1/4)*sqrt(d)*(2*a*d+7*b*c)*sqrt(b*x^2/a)*EllipticPi(sin(arcsin((-b*x^2+a)^(1/4)/a^(1/4))),-sqrt(a)*sqrt(d)/sqrt(a*d+b*c),sqrt(-1))/c/(a*d+b*c)^(5/2)/x-1/4*a^(1/4)*sqrt(d)*(2*a*d+7*b*c)*sqrt(b*x^2/a)*EllipticPi(sin(arcsin((-b*x^2+a)^(1/4)/a^(1/4))),sqrt(a)*sqrt(d)/sqrt(a*d+b*c),sqrt(-1))/c/(a*d+b*c)^(5/2)/x,1],
[(d*x^2+c)^3/(-b*x^2+a)^(7/4),x,5,2/3*(a*d+b*c)^3*x/a/b^3/(-b*x^2+a)^(3/4)+2/21*d^2*(13*a*d+21*b*c)*x*(-b*x^2+a)^(1/4)/b^3+2/7*d^3*x^3*(-b*x^2+a)^(1/4)/b^2+2/21*(-40*a^3*d^3-84*a^2*b*c*d^2-42*a*b^2*c^2*d+7*b^3*c^3)*(1-b*x^2/a)^(3/4)*InverseJacobiAM(1/2*arcsin(sqrt(b)*x/sqrt(a)),sqrt(2))/sqrt(a)/b^(7/2)/(-b*x^2+a)^(3/4),1],
[(d*x^2+c)^2/(-b*x^2+a)^(7/4),x,4,2/3*(a*d+b*c)^2*x/a/b^2/(-b*x^2+a)^(3/4)+2/3*d^2*x*(-b*x^2+a)^(1/4)/b^2+2/3*(-4*a^2*d^2-4*a*b*c*d+b^2*c^2)*(1-b*x^2/a)^(3/4)*InverseJacobiAM(1/2*arcsin(sqrt(b)*x/sqrt(a)),sqrt(2))/sqrt(a)/b^(5/2)/(-b*x^2+a)^(3/4),1],
[(d*x^2+c)/(-b*x^2+a)^(7/4),x,3,2/3*(a*d+b*c)*x/a/b/(-b*x^2+a)^(3/4)+2/3*(-2*a*d+b*c)*(1-b*x^2/a)^(3/4)*InverseJacobiAM(1/2*arcsin(sqrt(b)*x/sqrt(a)),sqrt(2))/sqrt(a)/b^(3/2)/(-b*x^2+a)^(3/4),1],
[1/(-b*x^2+a)^(7/4)/(d*x^2+c),x,9,2/3*b*x/a/(a*d+b*c)/(-b*x^2+a)^(3/4)+2/3*sqrt(b)*(1-b*x^2/a)^(3/4)*InverseJacobiAM(1/2*arcsin(sqrt(b)*x/sqrt(a)),sqrt(2))/sqrt(a)/(a*d+b*c)/(-b*x^2+a)^(3/4)-a^(1/4)*d*sqrt(b*x^2/a)*EllipticPi(sin(arcsin((-b*x^2+a)^(1/4)/a^(1/4))),-sqrt(a)*sqrt(d)/sqrt(a*d+b*c),sqrt(-1))/(a*d+b*c)^2/x-a^(1/4)*d*sqrt(b*x^2/a)*EllipticPi(sin(arcsin((-b*x^2+a)^(1/4)/a^(1/4))),sqrt(a)*sqrt(d)/sqrt(a*d+b*c),sqrt(-1))/(a*d+b*c)^2/x,1],
[1/(-b*x^2+a)^(7/4)/(d*x^2+c)^2,x,10,1/6*b*(-3*a*d+4*b*c)*x/a/c/(a*d+b*c)^2/(-b*x^2+a)^(3/4)+1/2*d*x/c/(a*d+b*c)/(-b*x^2+a)^(3/4)/(d*x^2+c)+1/6*sqrt(b)*(-3*a*d+4*b*c)*(1-b*x^2/a)^(3/4)*InverseJacobiAM(1/2*arcsin(sqrt(b)*x/sqrt(a)),sqrt(2))/sqrt(a)/c/(a*d+b*c)^2/(-b*x^2+a)^(3/4)-1/4*a^(1/4)*d*(2*a*d+9*b*c)*sqrt(b*x^2/a)*EllipticPi(sin(arcsin((-b*x^2+a)^(1/4)/a^(1/4))),-sqrt(a)*sqrt(d)/sqrt(a*d+b*c),sqrt(-1))/c/(a*d+b*c)^3/x-1/4*a^(1/4)*d*(2*a*d+9*b*c)*sqrt(b*x^2/a)*EllipticPi(sin(arcsin((-b*x^2+a)^(1/4)/a^(1/4))),sqrt(a)*sqrt(d)/sqrt(a*d+b*c),sqrt(-1))/c/(a*d+b*c)^3/x,1],
[(d*x^2+c)^3/(-b*x^2+a)^(9/4),x,5,2/5*(a*d+b*c)^3*x/a/b^3/(-b*x^2+a)^(5/4)+6/5*(-4*a*d+b*c)*(a*d+b*c)^2*x/a^2/b^3/(-b*x^2+a)^(1/4)-2/5*d^3*x*(-b*x^2+a)^(3/4)/b^3-6/5*(2*a*d+b*c)*(-4*a^2*d^2-4*a*b*c*d+b^2*c^2)*(1-b*x^2/a)^(1/4)*EllipticE(sin(1/2*arcsin(sqrt(b)*x/sqrt(a))),sqrt(2))/a^(3/2)/b^(7/2)/(-b*x^2+a)^(1/4),1],
[(d*x^2+c)^2/(-b*x^2+a)^(9/4),x,4,2/5*(a*d+b*c)^2*x/a/b^2/(-b*x^2+a)^(5/4)+2/5*(-7*a*d+3*b*c)*(a*d+b*c)*x/a^2/b^2/(-b*x^2+a)^(1/4)-2/5*(-12*a^2*d^2-4*a*b*c*d+3*b^2*c^2)*(1-b*x^2/a)^(1/4)*EllipticE(sin(1/2*arcsin(sqrt(b)*x/sqrt(a))),sqrt(2))/a^(3/2)/b^(5/2)/(-b*x^2+a)^(1/4),1],
[(d*x^2+c)/(-b*x^2+a)^(9/4),x,4,2/5*(a*d+b*c)*x/a/b/(-b*x^2+a)^(5/4)+2/5*(-2*a*d+3*b*c)*x/a^2/b/(-b*x^2+a)^(1/4)-2/5*(-2*a*d+3*b*c)*(1-b*x^2/a)^(1/4)*EllipticE(sin(1/2*arcsin(sqrt(b)*x/sqrt(a))),sqrt(2))/a^(3/2)/b^(3/2)/(-b*x^2+a)^(1/4),1],
[1/(-b*x^2+a)^(9/4)/(d*x^2+c),x,9,2/5*b*x/a/(a*d+b*c)/(-b*x^2+a)^(5/4)+2/5*b*(8*a*d+3*b*c)*x/a^2/(a*d+b*c)^2/(-b*x^2+a)^(1/4)-2/5*sqrt(b)*(8*a*d+3*b*c)*(1-b*x^2/a)^(1/4)*EllipticE(sin(1/2*arcsin(sqrt(b)*x/sqrt(a))),sqrt(2))/a^(3/2)/(a*d+b*c)^2/(-b*x^2+a)^(1/4)+a^(1/4)*d^(3/2)*sqrt(b*x^2/a)*EllipticPi(sin(arcsin((-b*x^2+a)^(1/4)/a^(1/4))),-sqrt(a)*sqrt(d)/sqrt(a*d+b*c),sqrt(-1))/(a*d+b*c)^(5/2)/x-a^(1/4)*d^(3/2)*sqrt(b*x^2/a)*EllipticPi(sin(arcsin((-b*x^2+a)^(1/4)/a^(1/4))),sqrt(a)*sqrt(d)/sqrt(a*d+b*c),sqrt(-1))/(a*d+b*c)^(5/2)/x,1],
[1/(-b*x^2+a)^(9/4)/(d*x^2+c)^2,x,10,1/10*b*(-5*a*d+4*b*c)*x/a/c/(a*d+b*c)^2/(-b*x^2+a)^(5/4)+1/10*b*(-5*a^2*d^2+52*a*b*c*d+12*b^2*c^2)*x/a^2/c/(a*d+b*c)^3/(-b*x^2+a)^(1/4)+1/2*d*x/c/(a*d+b*c)/(-b*x^2+a)^(5/4)/(d*x^2+c)-1/10*sqrt(b)*(-5*a^2*d^2+52*a*b*c*d+12*b^2*c^2)*(1-b*x^2/a)^(1/4)*EllipticE(sin(1/2*arcsin(sqrt(b)*x/sqrt(a))),sqrt(2))/a^(3/2)/c/(a*d+b*c)^3/(-b*x^2+a)^(1/4)+1/4*a^(1/4)*d^(3/2)*(2*a*d+11*b*c)*sqrt(b*x^2/a)*EllipticPi(sin(arcsin((-b*x^2+a)^(1/4)/a^(1/4))),-sqrt(a)*sqrt(d)/sqrt(a*d+b*c),sqrt(-1))/c/(a*d+b*c)^(7/2)/x-1/4*a^(1/4)*d^(3/2)*(2*a*d+11*b*c)*sqrt(b*x^2/a)*EllipticPi(sin(arcsin((-b*x^2+a)^(1/4)/a^(1/4))),sqrt(a)*sqrt(d)/sqrt(a*d+b*c),sqrt(-1))/c/(a*d+b*c)^(7/2)/x,1],
[(b*x^2+a)^(1/4)*(d*x^2+c)^(5/4),x,3,c*x*(b*x^2+a)^(1/4)*(d*x^2+c)^(1/4)*AppellF1(1/2,-1/4,-5/4,3/2,-b*x^2/a,-d*x^2/c)/(1+b*x^2/a)^(1/4)/(1+d*x^2/c)^(1/4),1],
[(b*x^2+a)^(1/4)*(d*x^2+c)^(1/4),x,3,x*(b*x^2+a)^(1/4)*(d*x^2+c)^(1/4)*AppellF1(1/2,-1/4,-1/4,3/2,-b*x^2/a,-d*x^2/c)/(1+b*x^2/a)^(1/4)/(1+d*x^2/c)^(1/4),1],
[(b*x^2+a)^(1/4)/(d*x^2+c)^(3/4),x,3,x*(b*x^2+a)^(1/4)*(1+d*x^2/c)^(3/4)*AppellF1(1/2,-1/4,3/4,3/2,-b*x^2/a,-d*x^2/c)/(1+b*x^2/a)^(1/4)/(d*x^2+c)^(3/4),1],
[(b*x^2+a)^(1/4)/(d*x^2+c)^(7/4),x,1,x*(b*x^2+a)^(1/4)*hypergeom([-1/4, 1/2],[3/2],-(-a*d+b*c)*x^2/a/(d*x^2+c))/c/(c*(b*x^2+a)/a/(d*x^2+c))^(1/4)/(d*x^2+c)^(3/4),1],
[(b*x^2+a)^(1/4)/(d*x^2+c)^(11/4),x,2,-2/7*d*x*(b*x^2+a)^(5/4)/c/(-a*d+b*c)/(d*x^2+c)^(7/4)+1/7*(-5*a*d+7*b*c)*x*(b*x^2+a)^(1/4)*hypergeom([-1/4, 1/2],[3/2],-(-a*d+b*c)*x^2/a/(d*x^2+c))/c^2/(-a*d+b*c)/(c*(b*x^2+a)/a/(d*x^2+c))^(1/4)/(d*x^2+c)^(3/4),1],
[(b*x^2+a)^(1/4)/(d*x^2+c)^(15/4),x,3,-2/11*d*x*(b*x^2+a)^(5/4)/c/(-a*d+b*c)/(d*x^2+c)^(11/4)-2/55*b*(-5*a*d+11*b*c)*x*(b*x^2+a)^(5/4)/a/c/(-a*d+b*c)^2/(d*x^2+c)^(7/4)+1/55*(45*a^2*d^2-110*a*b*c*d+77*b^2*c^2)*x*(b*x^2+a)^(5/4)*hypergeom([-5/4, 1/2],[3/2],-(-a*d+b*c)*x^2/a/(d*x^2+c))/a/c^2/(-a*d+b*c)^2/(c*(b*x^2+a)/a/(d*x^2+c))^(5/4)/(d*x^2+c)^(7/4),1],
[(b*x^2+a)^(3/4)*(d*x^2+c)^(7/4),x,3,c*x*(b*x^2+a)^(3/4)*(d*x^2+c)^(3/4)*AppellF1(1/2,-3/4,-7/4,3/2,-b*x^2/a,-d*x^2/c)/(1+b*x^2/a)^(3/4)/(1+d*x^2/c)^(3/4),1],
[(b*x^2+a)^(3/4)*(d*x^2+c)^(3/4),x,3,x*(b*x^2+a)^(3/4)*(d*x^2+c)^(3/4)*AppellF1(1/2,-3/4,-3/4,3/2,-b*x^2/a,-d*x^2/c)/(1+b*x^2/a)^(3/4)/(1+d*x^2/c)^(3/4),1],
[(b*x^2+a)^(3/4)/(d*x^2+c)^(1/4),x,3,x*(b*x^2+a)^(3/4)*(1+d*x^2/c)^(1/4)*AppellF1(1/2,-3/4,1/4,3/2,-b*x^2/a,-d*x^2/c)/(1+b*x^2/a)^(3/4)/(d*x^2+c)^(1/4),1],
[(b*x^2+a)^(3/4)/(d*x^2+c)^(5/4),x,3,x*(b*x^2+a)^(3/4)*(1+d*x^2/c)^(1/4)*AppellF1(1/2,-3/4,5/4,3/2,-b*x^2/a,-d*x^2/c)/c/(1+b*x^2/a)^(3/4)/(d*x^2+c)^(1/4),1],
[(b*x^2+a)^(3/4)/(d*x^2+c)^(9/4),x,1,x*(b*x^2+a)^(3/4)*hypergeom([-3/4, 1/2],[3/2],-(-a*d+b*c)*x^2/a/(d*x^2+c))/c/(c*(b*x^2+a)/a/(d*x^2+c))^(3/4)/(d*x^2+c)^(5/4),1],
[(b*x^2+a)^(3/4)/(d*x^2+c)^(13/4),x,2,-2/9*d*x*(b*x^2+a)^(7/4)/c/(-a*d+b*c)/(d*x^2+c)^(9/4)+1/9*(-7*a*d+9*b*c)*x*(b*x^2+a)^(3/4)*hypergeom([-3/4, 1/2],[3/2],-(-a*d+b*c)*x^2/a/(d*x^2+c))/c^2/(-a*d+b*c)/(c*(b*x^2+a)/a/(d*x^2+c))^(3/4)/(d*x^2+c)^(5/4),1],
[(b*x^2+a)^(3/4)/(d*x^2+c)^(17/4),x,4,2/13*x*(b*x^2+a)^(3/4)/c/(d*x^2+c)^(13/4)-2/117*d*x*(b*x^2+a)^(3/4)*(8*b*x^2+11*a)/c^2/(-a*d+b*c)/(d*x^2+c)^(9/4)-2/39*b*(-a*d+3*b*c)*x*(b*x^2+a)^(3/4)/c^2/(-a*d+b*c)^2/(d*x^2+c)^(5/4)+1/117*(77*a^2*d^2-182*a*b*c*d+117*b^2*c^2)*x*(b*x^2+a)^(3/4)*hypergeom([-3/4, 1/2],[3/2],-(-a*d+b*c)*x^2/a/(d*x^2+c))/c^3/(-a*d+b*c)^2/(c*(b*x^2+a)/a/(d*x^2+c))^(3/4)/(d*x^2+c)^(5/4),1],
[(d*x^2+c)^(7/4)/(b*x^2+a)^(13/4),x,1,x*(d*x^2+c)^(7/4)*hypergeom([-7/4, 1/2],[3/2],(-a*d+b*c)*x^2/c/(b*x^2+a))/a/(b*x^2+a)^(9/4)/(a*(d*x^2+c)/c/(b*x^2+a))^(7/4),1],
[(b*x^2+a)^(7/4)/(d*x^2+c)^(13/4),x,1,x*(b*x^2+a)^(7/4)*hypergeom([-7/4, 1/2],[3/2],-(-a*d+b*c)*x^2/a/(d*x^2+c))/c/(c*(b*x^2+a)/a/(d*x^2+c))^(7/4)/(d*x^2+c)^(9/4),1],
[(d*x^2+c)^(7/4)/(b*x^2+a)^(1/4),x,3,c*x*(1+b*x^2/a)^(1/4)*(d*x^2+c)^(3/4)*AppellF1(1/2,1/4,-7/4,3/2,-b*x^2/a,-d*x^2/c)/(b*x^2+a)^(1/4)/(1+d*x^2/c)^(3/4),1],
[(d*x^2+c)^(3/4)/(b*x^2+a)^(1/4),x,3,x*(1+b*x^2/a)^(1/4)*(d*x^2+c)^(3/4)*AppellF1(1/2,1/4,-3/4,3/2,-b*x^2/a,-d*x^2/c)/(b*x^2+a)^(1/4)/(1+d*x^2/c)^(3/4),1],
[1/(b*x^2+a)^(1/4)/(d*x^2+c)^(1/4),x,3,x*(1+b*x^2/a)^(1/4)*(1+d*x^2/c)^(1/4)*AppellF1(1/2,1/4,1/4,3/2,-b*x^2/a,-d*x^2/c)/(b*x^2+a)^(1/4)/(d*x^2+c)^(1/4),1],
[1/(b*x^2+a)^(1/4)/(d*x^2+c)^(5/4),x,1,x*(c*(b*x^2+a)/a/(d*x^2+c))^(1/4)*hypergeom([1/4, 1/2],[3/2],-(-a*d+b*c)*x^2/a/(d*x^2+c))/c/(b*x^2+a)^(1/4)/(d*x^2+c)^(1/4),1],
[1/(b*x^2+a)^(1/4)/(d*x^2+c)^(9/4),x,2,-2/5*d*x*(b*x^2+a)^(3/4)/c/(-a*d+b*c)/(d*x^2+c)^(5/4)+1/5*(-3*a*d+5*b*c)*x*(c*(b*x^2+a)/a/(d*x^2+c))^(1/4)*hypergeom([1/4, 1/2],[3/2],-(-a*d+b*c)*x^2/a/(d*x^2+c))/c^2/(-a*d+b*c)/(b*x^2+a)^(1/4)/(d*x^2+c)^(1/4),1],
[1/(b*x^2+a)^(1/4)/(d*x^2+c)^(13/4),x,3,-2/9*d*x*(b*x^2+a)^(3/4)/c/(-a*d+b*c)/(d*x^2+c)^(9/4)-2/9*b*(-a*d+3*b*c)*x*(b*x^2+a)^(3/4)/a/c/(-a*d+b*c)^2/(d*x^2+c)^(5/4)+1/9*(7*a^2*d^2-18*a*b*c*d+15*b^2*c^2)*x*(b*x^2+a)^(3/4)*hypergeom([-3/4, 1/2],[3/2],-(-a*d+b*c)*x^2/a/(d*x^2+c))/a/c^2/(-a*d+b*c)^2/(c*(b*x^2+a)/a/(d*x^2+c))^(3/4)/(d*x^2+c)^(5/4),1],
[1/(b*x^2+a)^(1/4)/(d*x^2+c)^(17/4),x,4,-2/13*d*x*(b*x^2+a)^(3/4)/c/(-a*d+b*c)/(d*x^2+c)^(13/4)-2/117*b*(-3*a*d+13*b*c)*(-a*d+3*b*c)*x*(b*x^2+a)^(3/4)/a/c^2/(-a*d+b*c)^3/(d*x^2+c)^(5/4)-2/117*d*x*(b*x^2+a)^(3/4)*(-8*b*d*x^2-11*a*d+13*b*c)/c^2/(-a*d+b*c)^2/(d*x^2+c)^(9/4)+1/117*(-77*a^3*d^3+273*a^2*b*c*d^2-351*a*b^2*c^2*d+195*b^3*c^3)*x*(b*x^2+a)^(3/4)*hypergeom([-3/4, 1/2],[3/2],-(-a*d+b*c)*x^2/a/(d*x^2+c))/a/c^3/(-a*d+b*c)^3/(c*(b*x^2+a)/a/(d*x^2+c))^(3/4)/(d*x^2+c)^(5/4),1],
[1/(b*x^2+a)^(1/4)/(d*x^2+c)^(21/4),x,5,0,1],
[(d*x^2+c)^(9/4)/(b*x^2+a)^(3/4),x,3,c^2*x*(1+b*x^2/a)^(3/4)*(d*x^2+c)^(1/4)*AppellF1(1/2,3/4,-9/4,3/2,-b*x^2/a,-d*x^2/c)/(b*x^2+a)^(3/4)/(1+d*x^2/c)^(1/4),1],
[(d*x^2+c)^(5/4)/(b*x^2+a)^(3/4),x,3,c*x*(1+b*x^2/a)^(3/4)*(d*x^2+c)^(1/4)*AppellF1(1/2,3/4,-5/4,3/2,-b*x^2/a,-d*x^2/c)/(b*x^2+a)^(3/4)/(1+d*x^2/c)^(1/4),1],
[(d*x^2+c)^(1/4)/(b*x^2+a)^(3/4),x,3,x*(1+b*x^2/a)^(3/4)*(d*x^2+c)^(1/4)*AppellF1(1/2,3/4,-1/4,3/2,-b*x^2/a,-d*x^2/c)/(b*x^2+a)^(3/4)/(1+d*x^2/c)^(1/4),1],
[1/(b*x^2+a)^(3/4)/(d*x^2+c)^(3/4),x,1,x*(c*(b*x^2+a)/a/(d*x^2+c))^(3/4)*(d*x^2+c)^(1/4)*hypergeom([1/2, 3/4],[3/2],-(-a*d+b*c)*x^2/a/(d*x^2+c))/c/(b*x^2+a)^(3/4),1],
[1/(b*x^2+a)^(3/4)/(d*x^2+c)^(7/4),x,2,-2/3*d*x*(b*x^2+a)^(1/4)/c/(-a*d+b*c)/(d*x^2+c)^(3/4)+1/3*(-a*d+3*b*c)*x*(c*(b*x^2+a)/a/(d*x^2+c))^(3/4)*(d*x^2+c)^(1/4)*hypergeom([1/2, 3/4],[3/2],-(-a*d+b*c)*x^2/a/(d*x^2+c))/c^2/(-a*d+b*c)/(b*x^2+a)^(3/4),1],
[1/(b*x^2+a)^(3/4)/(d*x^2+c)^(11/4),x,3,-2/7*d*x*(b*x^2+a)^(1/4)/c/(-a*d+b*c)/(d*x^2+c)^(7/4)-2/7*b*(-a*d+7*b*c)*x*(b*x^2+a)^(1/4)/a/c/(-a*d+b*c)^2/(d*x^2+c)^(3/4)+1/7*(5*a^2*d^2-14*a*b*c*d+21*b^2*c^2)*x*(b*x^2+a)^(1/4)*hypergeom([-1/4, 1/2],[3/2],-(-a*d+b*c)*x^2/a/(d*x^2+c))/a/c^2/(-a*d+b*c)^2/(c*(b*x^2+a)/a/(d*x^2+c))^(1/4)/(d*x^2+c)^(3/4),1],
[1/(b*x^2+a)^(3/4)/(d*x^2+c)^(15/4),x,4,-2/11*d*x*(b*x^2+a)^(1/4)/c/(-a*d+b*c)/(d*x^2+c)^(11/4)-2/77*b*(-a*d+7*b*c)*(-a*d+11*b*c)*x*(b*x^2+a)^(1/4)/a/c^2/(-a*d+b*c)^3/(d*x^2+c)^(3/4)-2/77*d*x*(b*x^2+a)^(1/4)*(-8*b*d*x^2-9*a*d+11*b*c)/c^2/(-a*d+b*c)^2/(d*x^2+c)^(7/4)+3/77*(-15*a^3*d^3+55*a^2*b*c*d^2-77*a*b^2*c^2*d+77*b^3*c^3)*x*(b*x^2+a)^(1/4)*hypergeom([-1/4, 1/2],[3/2],-(-a*d+b*c)*x^2/a/(d*x^2+c))/a/c^3/(-a*d+b*c)^3/(c*(b*x^2+a)/a/(d*x^2+c))^(1/4)/(d*x^2+c)^(3/4),1],
[1/(b*x^2+a)^(3/4)/(d*x^2+c)^(19/4),x,5,0,1],
[(d*x^2+c)^(11/4)/(b*x^2+a)^(5/4),x,3,c^2*x*(1+b*x^2/a)^(1/4)*(d*x^2+c)^(3/4)*AppellF1(1/2,5/4,-11/4,3/2,-b*x^2/a,-d*x^2/c)/a/(b*x^2+a)^(1/4)/(1+d*x^2/c)^(3/4),1],
[(d*x^2+c)^(7/4)/(b*x^2+a)^(5/4),x,3,c*x*(1+b*x^2/a)^(1/4)*(d*x^2+c)^(3/4)*AppellF1(1/2,5/4,-7/4,3/2,-b*x^2/a,-d*x^2/c)/a/(b*x^2+a)^(1/4)/(1+d*x^2/c)^(3/4),1],
[(d*x^2+c)^(3/4)/(b*x^2+a)^(5/4),x,3,x*(1+b*x^2/a)^(1/4)*(d*x^2+c)^(3/4)*AppellF1(1/2,5/4,-3/4,3/2,-b*x^2/a,-d*x^2/c)/a/(b*x^2+a)^(1/4)/(1+d*x^2/c)^(3/4),1],
[1/(b*x^2+a)^(5/4)/(d*x^2+c)^(1/4),x,1,x*(a*(d*x^2+c)/c/(b*x^2+a))^(1/4)*hypergeom([1/4, 1/2],[3/2],(-a*d+b*c)*x^2/c/(b*x^2+a))/a/(b*x^2+a)^(1/4)/(d*x^2+c)^(1/4),1],
[1/(b*x^2+a)^(5/4)/(d*x^2+c)^(5/4),x,2,-2*d*x/c/(-a*d+b*c)/(b*x^2+a)^(1/4)/(d*x^2+c)^(1/4)+(a*d+b*c)*x*(a*(d*x^2+c)/c/(b*x^2+a))^(1/4)*hypergeom([1/4, 1/2],[3/2],(-a*d+b*c)*x^2/c/(b*x^2+a))/a/c/(-a*d+b*c)/(b*x^2+a)^(1/4)/(d*x^2+c)^(1/4),1],
[1/(b*x^2+a)^(5/4)/(d*x^2+c)^(9/4),x,3,2*b*x/a/(-a*d+b*c)/(b*x^2+a)^(1/4)/(d*x^2+c)^(5/4)+2/3*b*(5*a*d+b*c)*x*(b*x^2+a)^(3/4)/a^2/(-a*d+b*c)^2/(d*x^2+c)^(5/4)-1/3*(-3*a^2*d^2+10*a*b*c*d+5*b^2*c^2)*x*(b*x^2+a)^(3/4)*hypergeom([-3/4, 1/2],[3/2],-(-a*d+b*c)*x^2/a/(d*x^2+c))/a^2/c/(-a*d+b*c)^2/(c*(b*x^2+a)/a/(d*x^2+c))^(3/4)/(d*x^2+c)^(5/4),1],
[1/(b*x^2+a)^(5/4)/(d*x^2+c)^(13/4),x,4,2*b*x/a/(-a*d+b*c)/(b*x^2+a)^(1/4)/(d*x^2+c)^(9/4)+2/9*b*(-a*d+3*b*c)*(9*a*d+b*c)*x*(b*x^2+a)^(3/4)/a^2/c/(-a*d+b*c)^3/(d*x^2+c)^(5/4)+2/9*d*x*(b*x^2+a)^(3/4)*(-8*b*d*x^2+a*d+b*c)/a/c/(-a*d+b*c)^2/(d*x^2+c)^(9/4)-1/9*(7*a^3*d^3-27*a^2*b*c*d^2+45*a*b^2*c^2*d+15*b^3*c^3)*x*(b*x^2+a)^(3/4)*hypergeom([-3/4, 1/2],[3/2],-(-a*d+b*c)*x^2/a/(d*x^2+c))/a^2/c^2/(-a*d+b*c)^3/(c*(b*x^2+a)/a/(d*x^2+c))^(3/4)/(d*x^2+c)^(5/4),1],
[(d*x^2+c)^(13/4)/(b*x^2+a)^(7/4),x,3,c^3*x*(1+b*x^2/a)^(3/4)*(d*x^2+c)^(1/4)*AppellF1(1/2,7/4,-13/4,3/2,-b*x^2/a,-d*x^2/c)/a/(b*x^2+a)^(3/4)/(1+d*x^2/c)^(1/4),1],
[(d*x^2+c)^(9/4)/(b*x^2+a)^(7/4),x,3,c^2*x*(1+b*x^2/a)^(3/4)*(d*x^2+c)^(1/4)*AppellF1(1/2,7/4,-9/4,3/2,-b*x^2/a,-d*x^2/c)/a/(b*x^2+a)^(3/4)/(1+d*x^2/c)^(1/4),1],
[(d*x^2+c)^(5/4)/(b*x^2+a)^(7/4),x,3,c*x*(1+b*x^2/a)^(3/4)*(d*x^2+c)^(1/4)*AppellF1(1/2,7/4,-5/4,3/2,-b*x^2/a,-d*x^2/c)/a/(b*x^2+a)^(3/4)/(1+d*x^2/c)^(1/4),1],
[(d*x^2+c)^(1/4)/(b*x^2+a)^(7/4),x,1,x*(d*x^2+c)^(1/4)*hypergeom([-1/4, 1/2],[3/2],(-a*d+b*c)*x^2/c/(b*x^2+a))/a/(b*x^2+a)^(3/4)/(a*(d*x^2+c)/c/(b*x^2+a))^(1/4),1],
[1/(b*x^2+a)^(7/4)/(d*x^2+c)^(3/4),x,2,2/3*b*x*(d*x^2+c)^(1/4)/a/(-a*d+b*c)/(b*x^2+a)^(3/4)+1/3*(-3*a*d+b*c)*x*(c*(b*x^2+a)/a/(d*x^2+c))^(3/4)*(d*x^2+c)^(1/4)*hypergeom([1/2, 3/4],[3/2],-(-a*d+b*c)*x^2/a/(d*x^2+c))/a/c/(-a*d+b*c)/(b*x^2+a)^(3/4),1],
[1/(b*x^2+a)^(7/4)/(d*x^2+c)^(7/4),x,3,2/3*b*x/a/(-a*d+b*c)/(b*x^2+a)^(3/4)/(d*x^2+c)^(3/4)-2/3*b*(-7*a*d+b*c)*x*(b*x^2+a)^(1/4)/a^2/(-a*d+b*c)^2/(d*x^2+c)^(3/4)+(a^2*d^2-6*a*b*c*d+b^2*c^2)*x*(b*x^2+a)^(1/4)*hypergeom([-1/4, 1/2],[3/2],-(-a*d+b*c)*x^2/a/(d*x^2+c))/a^2/c/(-a*d+b*c)^2/(c*(b*x^2+a)/a/(d*x^2+c))^(1/4)/(d*x^2+c)^(3/4),1],
[1/(b*x^2+a)^(7/4)/(d*x^2+c)^(11/4),x,4,2/3*b*x/a/(-a*d+b*c)/(b*x^2+a)^(3/4)/(d*x^2+c)^(7/4)-2/21*b*(-11*a*d+b*c)*(-a*d+7*b*c)*x*(b*x^2+a)^(1/4)/a^2/c/(-a*d+b*c)^3/(d*x^2+c)^(3/4)-2/21*d*x*(b*x^2+a)^(1/4)*(8*b*d*x^2-3*a*d+b*c)/a/c/(-a*d+b*c)^2/(d*x^2+c)^(7/4)+1/7*(-5*a^3*d^3+21*a^2*b*c*d^2-63*a*b^2*c^2*d+7*b^3*c^3)*x*(b*x^2+a)^(1/4)*hypergeom([-1/4, 1/2],[3/2],-(-a*d+b*c)*x^2/a/(d*x^2+c))/a^2/c^2/(-a*d+b*c)^3/(c*(b*x^2+a)/a/(d*x^2+c))^(1/4)/(d*x^2+c)^(3/4),1],
[(d*x^2+c)^(15/4)/(b*x^2+a)^(9/4),x,3,c^3*x*(1+b*x^2/a)^(1/4)*(d*x^2+c)^(3/4)*AppellF1(1/2,9/4,-15/4,3/2,-b*x^2/a,-d*x^2/c)/a^2/(b*x^2+a)^(1/4)/(1+d*x^2/c)^(3/4),1],
[(d*x^2+c)^(11/4)/(b*x^2+a)^(9/4),x,3,c^2*x*(1+b*x^2/a)^(1/4)*(d*x^2+c)^(3/4)*AppellF1(1/2,9/4,-11/4,3/2,-b*x^2/a,-d*x^2/c)/a^2/(b*x^2+a)^(1/4)/(1+d*x^2/c)^(3/4),1],
[(d*x^2+c)^(7/4)/(b*x^2+a)^(9/4),x,3,c*x*(1+b*x^2/a)^(1/4)*(d*x^2+c)^(3/4)*AppellF1(1/2,9/4,-7/4,3/2,-b*x^2/a,-d*x^2/c)/a^2/(b*x^2+a)^(1/4)/(1+d*x^2/c)^(3/4),1],
[(d*x^2+c)^(3/4)/(b*x^2+a)^(9/4),x,1,x*(d*x^2+c)^(3/4)*hypergeom([-3/4, 1/2],[3/2],(-a*d+b*c)*x^2/c/(b*x^2+a))/a/(b*x^2+a)^(5/4)/(a*(d*x^2+c)/c/(b*x^2+a))^(3/4),1],
[1/(b*x^2+a)^(9/4)/(d*x^2+c)^(1/4),x,2,2/5*b*x*(d*x^2+c)^(3/4)/a/(-a*d+b*c)/(b*x^2+a)^(5/4)+1/5*(-5*a*d+3*b*c)*x*(a*(d*x^2+c)/c/(b*x^2+a))^(1/4)*hypergeom([1/4, 1/2],[3/2],(-a*d+b*c)*x^2/c/(b*x^2+a))/a^2/(-a*d+b*c)/(b*x^2+a)^(1/4)/(d*x^2+c)^(1/4),1],
[1/(b*x^2+a)^(9/4)/(d*x^2+c)^(5/4),x,3,2/5*b*x/a/(-a*d+b*c)/(b*x^2+a)^(5/4)/(d*x^2+c)^(1/4)+6/5*b*(-3*a*d+b*c)*x/a^2/(-a*d+b*c)^2/(b*x^2+a)^(1/4)/(d*x^2+c)^(1/4)-1/5*(-5*a^2*d^2-10*a*b*c*d+3*b^2*c^2)*x*(c*(b*x^2+a)/a/(d*x^2+c))^(1/4)*hypergeom([1/4, 1/2],[3/2],-(-a*d+b*c)*x^2/a/(d*x^2+c))/a^2/c/(-a*d+b*c)^2/(b*x^2+a)^(1/4)/(d*x^2+c)^(1/4),1],
[1/(b*x^2+a)^(9/4)/(d*x^2+c)^(9/4),x,4,2/5*b*x/a/(-a*d+b*c)/(b*x^2+a)^(5/4)/(d*x^2+c)^(5/4)+2/5*b*(-11*a*d+b*c)*(a*d+b*c)*x*(b*x^2+a)^(3/4)/a^3/(-a*d+b*c)^3/(d*x^2+c)^(5/4)+2/5*b*x*(8*b*d*x^2-5*a*d+3*b*c)/a^2/(-a*d+b*c)^2/(b*x^2+a)^(1/4)/(d*x^2+c)^(5/4)-(a*d+b*c)*(a^2*d^2-6*a*b*c*d+b^2*c^2)*x*(b*x^2+a)^(3/4)*hypergeom([-3/4, 1/2],[3/2],-(-a*d+b*c)*x^2/a/(d*x^2+c))/a^3/c/(-a*d+b*c)^3/(c*(b*x^2+a)/a/(d*x^2+c))^(3/4)/(d*x^2+c)^(5/4),1],
[(b*x^2+2)^p*(3*b*x^2-6)^p,x,2,12^p*x*(3*b*x^2-6)^p*hypergeom([1/4, -p],[5/4],1/4*b^2*x^4)/((-3*b*x^2+6)^p),1],
[(b*x^2+a)^p*(-b*c*x^2+a*c)^p,x,2,x*(b*x^2+a)^p*(-b*c*x^2+a*c)^p*hypergeom([1/4, -p],[5/4],b^2*x^4/a^2)/((1-b^2*x^4/a^2)^p),1],
[(b*x^2+a)^p*(d*x^2+c)^q,x,3,x*(b*x^2+a)^p*(d*x^2+c)^q*AppellF1(1/2,-p,-q,3/2,-b*x^2/a,-d*x^2/c)/((1+b*x^2/a)^p)/((1+d*x^2/c)^q),1],
[(b*x^2+a)^p*(d*x^2+c)^3,x,5,3*d*(5*a^2*d^2-3*a*b*c*d*(7+2*p)+b^2*c^2*(4*p^2+24*p+35))*x*(b*x^2+a)^(p+1)/b^3/(3+2*p)/(5+2*p)/(7+2*p)-d^2*(5*a*d-3*b*c*(7+2*p))*x^3*(b*x^2+a)^(p+1)/b^2/(5+2*p)/(7+2*p)+d^3*x^5*(b*x^2+a)^(p+1)/b/(7+2*p)+(b^3*c^3*(4*p^2+24*p+35)-3*a*d*(5*a^2*d^2-3*a*b*c*d*(7+2*p)+b^2*c^2*(4*p^2+24*p+35))/(3+2*p))*x*(b*x^2+a)^p*hypergeom([1/2, -p],[3/2],-b*x^2/a)/b^3/(5+2*p)/(7+2*p)/((1+b*x^2/a)^p),1],
[(b*x^2+a)^p*(d*x^2+c)^2,x,4,-d*(3*a*d-2*b*c*(5+2*p))*x*(b*x^2+a)^(p+1)/b^2/(3+2*p)/(5+2*p)+d^2*x^3*(b*x^2+a)^(p+1)/b/(5+2*p)+(3*a^2*d^2-2*a*b*c*d*(5+2*p)+b^2*c^2*(4*p^2+16*p+15))*x*(b*x^2+a)^p*hypergeom([1/2, -p],[3/2],-b*x^2/a)/b^2/(3+2*p)/(5+2*p)/((1+b*x^2/a)^p),1],
[(b*x^2+a)^p*(d*x^2+c),x,3,d*x*(b*x^2+a)^(p+1)/b/(3+2*p)+(c-a*d/(2*b*p+3*b))*x*(b*x^2+a)^p*hypergeom([1/2, -p],[3/2],-b*x^2/a)/((1+b*x^2/a)^p),1],
[(b*x^2+a)^p,x,2,x*(b*x^2+a)^p*hypergeom([1/2, -p],[3/2],-b*x^2/a)/((1+b*x^2/a)^p),1],
[(b*x^2+a)^p/(d*x^2+c),x,2,x*(b*x^2+a)^p*AppellF1(1/2,-p,1,3/2,-b*x^2/a,-d*x^2/c)/c/((1+b*x^2/a)^p),1],
[(b*x^2+a)^p/(d*x^2+c)^2,x,2,x*(b*x^2+a)^p*AppellF1(1/2,-p,2,3/2,-b*x^2/a,-d*x^2/c)/c^2/((1+b*x^2/a)^p),1],
[(b*x^2+a)^(-1-b*c/(-2*a*d+2*b*c))*(d*x^2+c)^(-1+a*d/(-2*a*d+2*b*c)),x,1,x*(d*x^2+c)^(a*d/(-2*a*d+2*b*c))/a/c/((b*x^2+a)^(b*c/(-2*a*d+2*b*c))),1],
[(3*x^2+2)^p/((7*x^2+5)^p),x,1,(2/5)^p*x*AppellF1(1/2,-p,p,3/2,-3/2*x^2,-7/5*x^2),1],
[(3*x^2+2)^p/((-7*x^2+5)^p),x,1,(2/5)^p*x*AppellF1(1/2,p,-p,3/2,7/5*x^2,-3/2*x^2),1],
[(3*x^2-2)^p/((7*x^2+5)^p),x,2,x*(3*x^2-2)^p*AppellF1(1/2,-p,p,3/2,3/2*x^2,-7/5*x^2)/(5^p)/((1-3/2*x^2)^p),1],
[(3*x^2-2)^p/((-7*x^2+5)^p),x,2,x*(3*x^2-2)^p*AppellF1(1/2,p,-p,3/2,7/5*x^2,3/2*x^2)/(5^p)/((1-3/2*x^2)^p),1],
[(-6*x^2+2)^p/sqrt(-3*x^2+2),x,3,-2^(-1+p)*x*(-3*x^2+1)^(p+1)*hypergeom([1/2, 1/2*p+1/2],[3/2+1/2*p],(-3*x^2+1)^2)/sqrt(3)/(p+1)/sqrt(x^2),1],
[sqrt(x^2)*(-6*x^2+2)^p/sqrt(-3*x^4+2*x^2),x,5,-2^(-1+p)*sqrt(x^2)*(-3*x^2+1)^(p+1)*hypergeom([1/2, 1/2*p+1/2],[3/2+1/2*p],(-3*x^2+1)^2)/sqrt(3)/(p+1)/x,1],
[(-6*x^2+2)^(1/3)/sqrt(-3*x^2+2),x,7,-3*x*sqrt(x^2*(-3*x^2+2))/sqrt(x^2)/(2^(2/3)*(1+sqrt(3))-2^(2/3)*(-3*x^2+1)^(2/3))+1/2*3^(1/4)*sqrt(2-sqrt(3))*x*(1-(-3*x^2+1)^(2/3))*sqrt((2^(1/3)+2^(1/3)*(-3*x^2+1)^(2/3)+2^(1/3)*(-3*x^2+1)^(4/3))/(2^(2/3)*(1+sqrt(3))-2^(2/3)*(-3*x^2+1)^(2/3))^2)*EllipticE(sin(arcsin((2^(2/3)*(1-sqrt(3))-2^(2/3)*(-3*x^2+1)^(2/3))/(2^(2/3)*(1+sqrt(3))-2^(2/3)*(-3*x^2+1)^(2/3)))),sqrt(-7-4*sqrt(3)))/sqrt(2)/sqrt(x^2)/sqrt(x^2*(-3*x^2+2))/sqrt((2^(2/3)-2^(2/3)*(-3*x^2+1)^(2/3))/(2^(2/3)*(1+sqrt(3))-2^(2/3)*(-3*x^2+1)^(2/3))^2)-1/3*x*(1-(-3*x^2+1)^(2/3))*sqrt((2^(1/3)+2^(1/3)*(-3*x^2+1)^(2/3)+2^(1/3)*(-3*x^2+1)^(4/3))/(2^(2/3)*(1+sqrt(3))-2^(2/3)*(-3*x^2+1)^(2/3))^2)*InverseJacobiAM(arcsin((2^(2/3)*(1-sqrt(3))-2^(2/3)*(-3*x^2+1)^(2/3))/(2^(2/3)*(1+sqrt(3))-2^(2/3)*(-3*x^2+1)^(2/3))),sqrt(-7-4*sqrt(3)))*3^(3/4)/sqrt(x^2)/sqrt(x^2*(-3*x^2+2))/sqrt((2^(2/3)-2^(2/3)*(-3*x^2+1)^(2/3))/(2^(2/3)*(1+sqrt(3))-2^(2/3)*(-3*x^2+1)^(2/3))^2),1],
[sqrt(x^2)*(-6*x^2+2)^(1/3)/sqrt(-3*x^4+2*x^2),x,9,-3*sqrt(x^2)*sqrt(x^2*(-3*x^2+2))/x/(2^(2/3)*(1+sqrt(3))-2^(2/3)*(-3*x^2+1)^(2/3))+1/2*3^(1/4)*sqrt(2-sqrt(3))*sqrt(x^2)*(1-(-3*x^2+1)^(2/3))*sqrt((2^(1/3)+2^(1/3)*(-3*x^2+1)^(2/3)+2^(1/3)*(-3*x^2+1)^(4/3))/(2^(2/3)*(1+sqrt(3))-2^(2/3)*(-3*x^2+1)^(2/3))^2)*EllipticE(sin(arcsin((2^(2/3)*(1-sqrt(3))-2^(2/3)*(-3*x^2+1)^(2/3))/(2^(2/3)*(1+sqrt(3))-2^(2/3)*(-3*x^2+1)^(2/3)))),sqrt(-7-4*sqrt(3)))/sqrt(2)/x/sqrt(x^2*(-3*x^2+2))/sqrt((2^(2/3)-2^(2/3)*(-3*x^2+1)^(2/3))/(2^(2/3)*(1+sqrt(3))-2^(2/3)*(-3*x^2+1)^(2/3))^2)-1/3*sqrt(x^2)*(1-(-3*x^2+1)^(2/3))*sqrt((2^(1/3)+2^(1/3)*(-3*x^2+1)^(2/3)+2^(1/3)*(-3*x^2+1)^(4/3))/(2^(2/3)*(1+sqrt(3))-2^(2/3)*(-3*x^2+1)^(2/3))^2)*InverseJacobiAM(arcsin((2^(2/3)*(1-sqrt(3))-2^(2/3)*(-3*x^2+1)^(2/3))/(2^(2/3)*(1+sqrt(3))-2^(2/3)*(-3*x^2+1)^(2/3))),sqrt(-7-4*sqrt(3)))*3^(3/4)/x/sqrt(x^2*(-3*x^2+2))/sqrt((2^(2/3)-2^(2/3)*(-3*x^2+1)^(2/3))/(2^(2/3)*(1+sqrt(3))-2^(2/3)*(-3*x^2+1)^(2/3))^2),1]]: