lst:=[[(e*x)^m*(b*x^2+a)^3*(B*x^2+A)*(d*x^2+c),x,3,a^3*A*c*(e*x)^(1+m)/e/(1+m)+a^2*(A*a*d+3*A*b*c+B*a*c)*(e*x)^(3+m)/e^3/(3+m)+a*(3*A*b*(a*d+b*c)+a*B*(a*d+3*b*c))*(e*x)^(5+m)/e^5/(5+m)+b*(3*a*B*(a*d+b*c)+A*b*(3*a*d+b*c))*(e*x)^(7+m)/e^7/(7+m)+b^2*(A*b*d+3*B*a*d+B*b*c)*(e*x)^(9+m)/e^9/(9+m)+b^3*B*d*(e*x)^(11+m)/e^11/(11+m),1],
[(e*x)^m*(b*x^2+a)^2*(B*x^2+A)*(d*x^2+c),x,3,a^2*A*c*(e*x)^(1+m)/e/(1+m)+a*(A*a*d+2*A*b*c+B*a*c)*(e*x)^(3+m)/e^3/(3+m)+(a*B*(a*d+2*b*c)+A*b*(2*a*d+b*c))*(e*x)^(5+m)/e^5/(5+m)+b*(A*b*d+2*B*a*d+B*b*c)*(e*x)^(7+m)/e^7/(7+m)+b^2*B*d*(e*x)^(9+m)/e^9/(9+m),1],
[(e*x)^m*(b*x^2+a)*(B*x^2+A)*(d*x^2+c),x,3,a*A*c*(e*x)^(1+m)/e/(1+m)+(A*a*d+A*b*c+B*a*c)*(e*x)^(3+m)/e^3/(3+m)+(A*b*d+B*a*d+B*b*c)*(e*x)^(5+m)/e^5/(5+m)+b*B*d*(e*x)^(7+m)/e^7/(7+m),1],
[(e*x)^m*(B*x^2+A)*(d*x^2+c),x,3,A*c*(e*x)^(1+m)/e/(1+m)+(A*d+B*c)*(e*x)^(3+m)/e^3/(3+m)+B*d*(e*x)^(5+m)/e^5/(5+m),1],
[(e*x)^m*(B*x^2+A)*(d*x^2+c)/(b*x^2+a),x,4,(A*b*d-B*a*d+B*b*c)*(e*x)^(1+m)/b^2/e/(1+m)+B*d*(e*x)^(3+m)/b/e^3/(3+m)+(A*b-B*a)*(-a*d+b*c)*(e*x)^(1+m)*hypergeom([1, 1/2+1/2*m],[3/2+1/2*m],-b*x^2/a)/a/b^2/e/(1+m),1],
[(e*x)^m*(B*x^2+A)*(d*x^2+c)/(b*x^2+a)^2,x,4,B*d*(e*x)^(1+m)/b^2/e/(1+m)+1/2*(A*b-B*a)*(-a*d+b*c)*(e*x)^(1+m)/a/b^2/e/(b*x^2+a)+1/2*(a*B*(b*c*(1+m)-a*d*(3+m))+A*b*(a*d*(1+m)+b*(-c*m+c)))*(e*x)^(1+m)*hypergeom([1, 1/2+1/2*m],[3/2+1/2*m],-b*x^2/a)/a^2/b^2/e/(1+m),1],
[(e*x)^m*(B*x^2+A)*(d*x^2+c)/(b*x^2+a)^3,x,4,1/4*(A*b-B*a)*(-a*d+b*c)*(e*x)^(1+m)/a/b^2/e/(b*x^2+a)^2+1/8*(A*b*(b*c*(3-m)+a*d*(1+m))+a*B*(b*c*(1+m)-a*d*(5+m)))*(e*x)^(1+m)/a^2/b^2/e/(b*x^2+a)+1/8*(A*b*(1-m)*(b*c*(3-m)+a*d*(1+m))+a*B*(1+m)*(a*d*(3+m)+b*(-c*m+c)))*(e*x)^(1+m)*hypergeom([1, 1/2+1/2*m],[3/2+1/2*m],-b*x^2/a)/a^3/b^2/e/(1+m),1],
[(e*x)^m*(b*x^2+a)^3*(B*x^2+A)*(d*x^2+c)^2,x,3,a^3*A*c^2*(e*x)^(1+m)/e/(1+m)+a^2*c*(2*A*a*d+3*A*b*c+B*a*c)*(e*x)^(3+m)/e^3/(3+m)+a*(a*B*c*(2*a*d+3*b*c)+A*(a^2*d^2+6*a*b*c*d+3*b^2*c^2))*(e*x)^(5+m)/e^5/(5+m)+(a*B*(a^2*d^2+6*a*b*c*d+3*b^2*c^2)+A*b*(3*a^2*d^2+6*a*b*c*d+b^2*c^2))*(e*x)^(7+m)/e^7/(7+m)+b*(3*a^2*B*d^2+3*a*b*d*(A*d+2*B*c)+b^2*c*(2*A*d+B*c))*(e*x)^(9+m)/e^9/(9+m)+b^2*d*(A*b*d+3*B*a*d+2*B*b*c)*(e*x)^(11+m)/e^11/(11+m)+b^3*B*d^2*(e*x)^(13+m)/e^13/(13+m),1],
[(e*x)^m*(b*x^2+a)^2*(B*x^2+A)*(d*x^2+c)^2,x,3,a^2*A*c^2*(e*x)^(1+m)/e/(1+m)+a*c*(a*B*c+2*A*(a*d+b*c))*(e*x)^(3+m)/e^3/(3+m)+(2*a*B*c*(a*d+b*c)+A*(a^2*d^2+4*a*b*c*d+b^2*c^2))*(e*x)^(5+m)/e^5/(5+m)+(a^2*B*d^2+2*a*b*d*(A*d+2*B*c)+b^2*c*(2*A*d+B*c))*(e*x)^(7+m)/e^7/(7+m)+b*d*(A*b*d+2*B*a*d+2*B*b*c)*(e*x)^(9+m)/e^9/(9+m)+b^2*B*d^2*(e*x)^(11+m)/e^11/(11+m),1],
[(e*x)^m*(b*x^2+a)*(B*x^2+A)*(d*x^2+c)^2,x,3,a*A*c^2*(e*x)^(1+m)/e/(1+m)+c*(2*A*a*d+A*b*c+B*a*c)*(e*x)^(3+m)/e^3/(3+m)+(a*d*(A*d+2*B*c)+b*c*(2*A*d+B*c))*(e*x)^(5+m)/e^5/(5+m)+d*(A*b*d+B*a*d+2*B*b*c)*(e*x)^(7+m)/e^7/(7+m)+b*B*d^2*(e*x)^(9+m)/e^9/(9+m),1],
[(e*x)^m*(B*x^2+A)*(d*x^2+c)^2,x,3,A*c^2*(e*x)^(1+m)/e/(1+m)+c*(2*A*d+B*c)*(e*x)^(3+m)/e^3/(3+m)+d*(A*d+2*B*c)*(e*x)^(5+m)/e^5/(5+m)+B*d^2*(e*x)^(7+m)/e^7/(7+m),1],
[(e*x)^m*(B*x^2+A)*(d*x^2+c)^2/(b*x^2+a),x,4,(a^2*B*d^2-a*b*d*(A*d+2*B*c)+b^2*c*(2*A*d+B*c))*(e*x)^(1+m)/b^3/e/(1+m)+d*(A*b*d-B*a*d+2*B*b*c)*(e*x)^(3+m)/b^2/e^3/(3+m)+B*d^2*(e*x)^(5+m)/b/e^5/(5+m)+(A*b-B*a)*(-a*d+b*c)^2*(e*x)^(1+m)*hypergeom([1, 1/2+1/2*m],[3/2+1/2*m],-b*x^2/a)/a/b^3/e/(1+m),1],
[(e*x)^m*(B*x^2+A)*(d*x^2+c)^2/(b*x^2+a)^2,x,5,d*(A*b*d-2*B*a*d+2*B*b*c)*(e*x)^(1+m)/b^3/e/(1+m)+B*d^2*(e*x)^(3+m)/b^2/e^3/(3+m)+1/2*(A*b-B*a)*(-a*d+b*c)^2*(e*x)^(1+m)/a/b^3/e/(b*x^2+a)+1/2*(-a*d+b*c)*(a*B*(b*c*(1+m)-a*d*(5+m))+A*b*(a*d*(3+m)+b*(-c*m+c)))*(e*x)^(1+m)*hypergeom([1, 1/2+1/2*m],[3/2+1/2*m],-b*x^2/a)/a^2/b^3/e/(1+m),1],
[(e*x)^m*(B*x^2+A)*(d*x^2+c)^2/(b*x^2+a)^3,x,5,B*d^2*(e*x)^(1+m)/b^3/e/(1+m)+1/4*(A*b-B*a)*(-a*d+b*c)^2*(e*x)^(1+m)/a/b^3/e/(b*x^2+a)^2+1/8*(-a*d+b*c)*(A*b*(b*c*(3-m)+a*d*(5+m))+a*B*(b*c*(1+m)-a*d*(9+m)))*(e*x)^(1+m)/a^2/b^3/e/(b*x^2+a)+1/8*(A*b*(2*a*b*c*d*(-m^2+1)+b^2*c^2*(m^2-4*m+3)+a^2*d^2*(m^2+4*m+3))+a*B*(b^2*c^2*(-m^2+1)+2*a*b*c*d*(m^2+4*m+3)-a^2*d^2*(m^2+8*m+15)))*(e*x)^(1+m)*hypergeom([1, 1/2+1/2*m],[3/2+1/2*m],-b*x^2/a)/a^3/b^3/e/(1+m),1],
[(e*x)^m*(b*x^2+a)^3*(B*x^2+A)*(d*x^2+c)^3,x,3,a^3*A*c^3*(e*x)^(1+m)/e/(1+m)+a^2*c^2*(a*B*c+3*A*(a*d+b*c))*(e*x)^(3+m)/e^3/(3+m)+3*a*c*(a*B*c*(a*d+b*c)+A*(a^2*d^2+3*a*b*c*d+b^2*c^2))*(e*x)^(5+m)/e^5/(5+m)+(3*a*B*c*(a^2*d^2+3*a*b*c*d+b^2*c^2)+A*(a^3*d^3+9*a^2*b*c*d^2+9*a*b^2*c^2*d+b^3*c^3))*(e*x)^(7+m)/e^7/(7+m)+(a^3*B*d^3+9*a*b^2*c*d*(A*d+B*c)+3*a^2*b*d^2*(A*d+3*B*c)+b^3*c^2*(3*A*d+B*c))*(e*x)^(9+m)/e^9/(9+m)+3*b*d*(a^2*B*d^2+b^2*c*(A*d+B*c)+a*b*d*(A*d+3*B*c))*(e*x)^(11+m)/e^11/(11+m)+b^2*d^2*(A*b*d+3*B*a*d+3*B*b*c)*(e*x)^(13+m)/e^13/(13+m)+b^3*B*d^3*(e*x)^(15+m)/e^15/(15+m),1],
[(e*x)^m*(b*x^2+a)^2*(B*x^2+A)*(d*x^2+c)^3,x,3,a^2*A*c^3*(e*x)^(1+m)/e/(1+m)+a*c^2*(3*A*a*d+2*A*b*c+B*a*c)*(e*x)^(3+m)/e^3/(3+m)+c*(a*B*c*(3*a*d+2*b*c)+A*(3*a^2*d^2+6*a*b*c*d+b^2*c^2))*(e*x)^(5+m)/e^5/(5+m)+(6*a*b*c*d*(A*d+B*c)+a^2*d^2*(A*d+3*B*c)+b^2*c^2*(3*A*d+B*c))*(e*x)^(7+m)/e^7/(7+m)+d*(a^2*B*d^2+3*b^2*c*(A*d+B*c)+2*a*b*d*(A*d+3*B*c))*(e*x)^(9+m)/e^9/(9+m)+b*d^2*(A*b*d+2*B*a*d+3*B*b*c)*(e*x)^(11+m)/e^11/(11+m)+b^2*B*d^3*(e*x)^(13+m)/e^13/(13+m),1],
[(e*x)^m*(b*x^2+a)*(B*x^2+A)*(d*x^2+c)^3,x,3,a*A*c^3*(e*x)^(1+m)/e/(1+m)+c^2*(3*A*a*d+A*b*c+B*a*c)*(e*x)^(3+m)/e^3/(3+m)+c*(3*a*d*(A*d+B*c)+b*c*(3*A*d+B*c))*(e*x)^(5+m)/e^5/(5+m)+d*(3*b*c*(A*d+B*c)+a*d*(A*d+3*B*c))*(e*x)^(7+m)/e^7/(7+m)+d^2*(A*b*d+B*a*d+3*B*b*c)*(e*x)^(9+m)/e^9/(9+m)+b*B*d^3*(e*x)^(11+m)/e^11/(11+m),1],
[(e*x)^m*(B*x^2+A)*(d*x^2+c)^3,x,3,A*c^3*(e*x)^(1+m)/e/(1+m)+c^2*(3*A*d+B*c)*(e*x)^(3+m)/e^3/(3+m)+3*c*d*(A*d+B*c)*(e*x)^(5+m)/e^5/(5+m)+d^2*(A*d+3*B*c)*(e*x)^(7+m)/e^7/(7+m)+B*d^3*(e*x)^(9+m)/e^9/(9+m),1],
[(e*x)^m*(B*x^2+A)*(d*x^2+c)^3/(b*x^2+a),x,4,-(a^3*B*d^3+3*a*b^2*c*d*(A*d+B*c)-a^2*b*d^2*(A*d+3*B*c)-b^3*c^2*(3*A*d+B*c))*(e*x)^(1+m)/b^4/e/(1+m)+d*(a^2*B*d^2+3*b^2*c*(A*d+B*c)-a*b*d*(A*d+3*B*c))*(e*x)^(3+m)/b^3/e^3/(3+m)+d^2*(A*b*d-B*a*d+3*B*b*c)*(e*x)^(5+m)/b^2/e^5/(5+m)+B*d^3*(e*x)^(7+m)/b/e^7/(7+m)+(A*b-B*a)*(-a*d+b*c)^3*(e*x)^(1+m)*hypergeom([1, 1/2+1/2*m],[3/2+1/2*m],-b*x^2/a)/a/b^4/e/(1+m),1],
[(e*x)^m*(B*x^2+A)*(d*x^2+c)^3/(b*x^2+a)^2,x,6,d*(3*a^2*B*d^2+3*b^2*c*(A*d+B*c)-2*a*b*d*(A*d+3*B*c))*(e*x)^(1+m)/b^4/e/(1+m)+d^2*(A*b*d-2*B*a*d+3*B*b*c)*(e*x)^(3+m)/b^3/e^3/(3+m)+B*d^3*(e*x)^(5+m)/b^2/e^5/(5+m)+1/2*(A*b-B*a)*(-a*d+b*c)^3*(e*x)^(1+m)/a/b^4/e/(b*x^2+a)+1/2*(-a*d+b*c)^2*(a*B*(b*c*(1+m)-a*d*(7+m))+A*b*(a*d*(5+m)+b*(-c*m+c)))*(e*x)^(1+m)*hypergeom([1, 1/2+1/2*m],[3/2+1/2*m],-b*x^2/a)/a^2/b^4/e/(1+m),1],
[(e*x)^m*(B*x^2+A)*(d*x^2+c)^3/(b*x^2+a)^3,x,6,d^2*(A*b*d-3*B*a*d+3*B*b*c)*(e*x)^(1+m)/b^4/e/(1+m)+B*d^3*(e*x)^(3+m)/b^3/e^3/(3+m)+1/4*(A*b-B*a)*(-a*d+b*c)^3*(e*x)^(1+m)/a/b^4/e/(b*x^2+a)^2+1/8*(-a*d+b*c)^2*(A*b*(b*c*(3-m)+a*d*(9+m))+a*B*(b*c*(1+m)-a*d*(13+m)))*(e*x)^(1+m)/a^2/b^4/e/(b*x^2+a)+1/8*(-a*d+b*c)*(A*b*(2*a*b*c*d*(-m^2-2*m+3)+b^2*c^2*(m^2-4*m+3)+a^2*d^2*(m^2+8*m+15))+a*B*(b^2*c^2*(-m^2+1)+2*a*b*c*d*(m^2+6*m+5)-a^2*d^2*(m^2+12*m+35)))*(e*x)^(1+m)*hypergeom([1, 1/2+1/2*m],[3/2+1/2*m],-b*x^2/a)/a^3/b^4/e/(1+m),1],
[(e*x)^m*(b*x^2+a)^4*(B*x^2+A)/(d*x^2+c),x,4,(a^4*B*d^4+b^4*c^3*(-A*d+B*c)-4*a*b^3*c^2*d*(-A*d+B*c)+6*a^2*b^2*c*d^2*(-A*d+B*c)-4*a^3*b*d^3*(-A*d+B*c))*(e*x)^(1+m)/d^5/e/(1+m)+b*(4*a^3*B*d^3-b^3*c^2*(-A*d+B*c)+4*a*b^2*c*d*(-A*d+B*c)-6*a^2*b*d^2*(-A*d+B*c))*(e*x)^(3+m)/d^4/e^3/(3+m)+b^2*(6*a^2*B*d^2+b^2*c*(-A*d+B*c)-4*a*b*d*(-A*d+B*c))*(e*x)^(5+m)/d^3/e^5/(5+m)-b^3*(-A*b*d-4*B*a*d+B*b*c)*(e*x)^(7+m)/d^2/e^7/(7+m)+b^4*B*(e*x)^(9+m)/d/e^9/(9+m)-(-a*d+b*c)^4*(-A*d+B*c)*(e*x)^(1+m)*hypergeom([1, 1/2+1/2*m],[3/2+1/2*m],-d*x^2/c)/c/d^5/e/(1+m),1],
[(e*x)^m*(b*x^2+a)^3*(B*x^2+A)/(d*x^2+c),x,4,(a^3*B*d^3-b^3*c^2*(-A*d+B*c)+3*a*b^2*c*d*(-A*d+B*c)-3*a^2*b*d^2*(-A*d+B*c))*(e*x)^(1+m)/d^4/e/(1+m)+b*(3*a^2*B*d^2+b^2*c*(-A*d+B*c)-3*a*b*d*(-A*d+B*c))*(e*x)^(3+m)/d^3/e^3/(3+m)-b^2*(-A*b*d-3*B*a*d+B*b*c)*(e*x)^(5+m)/d^2/e^5/(5+m)+b^3*B*(e*x)^(7+m)/d/e^7/(7+m)+(-a*d+b*c)^3*(-A*d+B*c)*(e*x)^(1+m)*hypergeom([1, 1/2+1/2*m],[3/2+1/2*m],-d*x^2/c)/c/d^4/e/(1+m),1],
[(e*x)^m*(b*x^2+a)^2*(B*x^2+A)/(d*x^2+c),x,4,(a^2*B*d^2+b^2*c*(-A*d+B*c)-2*a*b*d*(-A*d+B*c))*(e*x)^(1+m)/d^3/e/(1+m)-b*(-A*b*d-2*B*a*d+B*b*c)*(e*x)^(3+m)/d^2/e^3/(3+m)+b^2*B*(e*x)^(5+m)/d/e^5/(5+m)-(-a*d+b*c)^2*(-A*d+B*c)*(e*x)^(1+m)*hypergeom([1, 1/2+1/2*m],[3/2+1/2*m],-d*x^2/c)/c/d^3/e/(1+m),1],
[(e*x)^m*(b*x^2+a)*(B*x^2+A)/(d*x^2+c),x,4,-(-A*b*d-B*a*d+B*b*c)*(e*x)^(1+m)/d^2/e/(1+m)+b*B*(e*x)^(3+m)/d/e^3/(3+m)+(-a*d+b*c)*(-A*d+B*c)*(e*x)^(1+m)*hypergeom([1, 1/2+1/2*m],[3/2+1/2*m],-d*x^2/c)/c/d^2/e/(1+m),1],
[(e*x)^m*(B*x^2+A)/(d*x^2+c),x,3,B*(e*x)^(1+m)/d/e/(1+m)-(-A*d+B*c)*(e*x)^(1+m)*hypergeom([1, 1/2+1/2*m],[3/2+1/2*m],-d*x^2/c)/c/d/e/(1+m),1],
[(e*x)^m*(B*x^2+A)/(b*x^2+a)/(d*x^2+c),x,5,(A*b-B*a)*(e*x)^(1+m)*hypergeom([1, 1/2+1/2*m],[3/2+1/2*m],-b*x^2/a)/a/(-a*d+b*c)/e/(1+m)+(-A*d+B*c)*(e*x)^(1+m)*hypergeom([1, 1/2+1/2*m],[3/2+1/2*m],-d*x^2/c)/c/(-a*d+b*c)/e/(1+m),1],
[(e*x)^m*(B*x^2+A)/(b*x^2+a)^2/(d*x^2+c),x,6,1/2*(A*b-B*a)*(e*x)^(1+m)/a/(-a*d+b*c)/e/(b*x^2+a)+1/2*(A*b*(b*c*(1-m)-a*d*(3-m))+a*B*(a*d*(1-m)+b*c*(1+m)))*(e*x)^(1+m)*hypergeom([1, 1/2+1/2*m],[3/2+1/2*m],-b*x^2/a)/a^2/(-a*d+b*c)^2/e/(1+m)-d*(-A*d+B*c)*(e*x)^(1+m)*hypergeom([1, 1/2+1/2*m],[3/2+1/2*m],-d*x^2/c)/c/(-a*d+b*c)^2/e/(1+m),1],
[(e*x)^m*(B*x^2+A)/(b*x^2+a)^3/(d*x^2+c),x,7,1/4*(A*b-B*a)*(e*x)^(1+m)/a/(-a*d+b*c)/e/(b*x^2+a)^2+1/8*(A*b*(b*c*(3-m)-a*d*(7-m))+a*B*(a*d*(3-m)+b*c*(1+m)))*(e*x)^(1+m)/a^2/(-a*d+b*c)^2/e/(b*x^2+a)+1/8*(A*b*(a^2*d^2*(m^2-8*m+15)-2*a*b*c*d*(m^2-6*m+5)+b^2*c^2*(m^2-4*m+3))+a*B*(b^2*c^2*(-m^2+1)-2*a*b*c*d*(-m^2+2*m+3)-a^2*d^2*(m^2-4*m+3)))*(e*x)^(1+m)*hypergeom([1, 1/2+1/2*m],[3/2+1/2*m],-b*x^2/a)/a^3/(-a*d+b*c)^3/e/(1+m)+d^2*(-A*d+B*c)*(e*x)^(1+m)*hypergeom([1, 1/2+1/2*m],[3/2+1/2*m],-d*x^2/c)/c/(-a*d+b*c)^3/e/(1+m),1],
[(e*x)^m*(b*x^2+a)^3*(B*x^2+A)/(d*x^2+c)^2,x,6,b*(3*a^2*B*d^2+b^2*c*(-2*A*d+3*B*c)-3*a*b*d*(-A*d+2*B*c))*(e*x)^(1+m)/d^4/e/(1+m)-b^2*(-A*b*d-3*B*a*d+2*B*b*c)*(e*x)^(3+m)/d^3/e^3/(3+m)+b^3*B*(e*x)^(5+m)/d^2/e^5/(5+m)+1/2*(-a*d+b*c)^3*(-A*d+B*c)*(e*x)^(1+m)/c/d^4/e/(d*x^2+c)+1/2*(-a*d+b*c)^2*(a*d*(A*d*(1-m)+B*c*(1+m))+b*c*(A*d*(5+m)-B*c*(7+m)))*(e*x)^(1+m)*hypergeom([1, 1/2+1/2*m],[3/2+1/2*m],-d*x^2/c)/c^2/d^4/e/(1+m),1],
[(e*x)^m*(b*x^2+a)^2*(B*x^2+A)/(d*x^2+c)^2,x,5,-b*(-A*b*d-2*B*a*d+2*B*b*c)*(e*x)^(1+m)/d^3/e/(1+m)+b^2*B*(e*x)^(3+m)/d^2/e^3/(3+m)-1/2*(-a*d+b*c)^2*(-A*d+B*c)*(e*x)^(1+m)/c/d^3/e/(d*x^2+c)-1/2*(-a*d+b*c)*(a*d*(A*d*(1-m)+B*c*(1+m))+b*c*(A*d*(3+m)-B*c*(5+m)))*(e*x)^(1+m)*hypergeom([1, 1/2+1/2*m],[3/2+1/2*m],-d*x^2/c)/c^2/d^3/e/(1+m),1],
[(e*x)^m*(b*x^2+a)*(B*x^2+A)/(d*x^2+c)^2,x,4,b*B*(e*x)^(1+m)/d^2/e/(1+m)+1/2*(-a*d+b*c)*(-A*d+B*c)*(e*x)^(1+m)/c/d^2/e/(d*x^2+c)+1/2*(a*d*(A*d*(1-m)+B*c*(1+m))+b*c*(A*d*(1+m)-B*c*(3+m)))*(e*x)^(1+m)*hypergeom([1, 1/2+1/2*m],[3/2+1/2*m],-d*x^2/c)/c^2/d^2/e/(1+m),1],
[(e*x)^m*(B*x^2+A)/(d*x^2+c)^2,x,3,-1/2*(-A*d+B*c)*(e*x)^(1+m)/c/d/e/(d*x^2+c)+1/2*(A*d*(1-m)+B*c*(1+m))*(e*x)^(1+m)*hypergeom([1, 1/2+1/2*m],[3/2+1/2*m],-d*x^2/c)/c^2/d/e/(1+m),1],
[(e*x)^m*(B*x^2+A)/(b*x^2+a)/(d*x^2+c)^2,x,6,1/2*(-A*d+B*c)*(e*x)^(1+m)/c/(-a*d+b*c)/e/(d*x^2+c)+b*(A*b-B*a)*(e*x)^(1+m)*hypergeom([1, 1/2+1/2*m],[3/2+1/2*m],-b*x^2/a)/a/(-a*d+b*c)^2/e/(1+m)+1/2*(b*c*(B*c*(1-m)-A*d*(3-m))+a*d*(A*d*(1-m)+B*c*(1+m)))*(e*x)^(1+m)*hypergeom([1, 1/2+1/2*m],[3/2+1/2*m],-d*x^2/c)/c^2/(-a*d+b*c)^2/e/(1+m),1],
[(e*x)^m*(B*x^2+A)/(b*x^2+a)^2/(d*x^2+c)^2,x,7,1/2*d*(A*a*d+A*b*c-2*B*a*c)*(e*x)^(1+m)/a/c/(-a*d+b*c)^2/e/(d*x^2+c)+1/2*(A*b-B*a)*(e*x)^(1+m)/a/(-a*d+b*c)/e/(b*x^2+a)/(d*x^2+c)+1/2*b*(A*b*(b*c*(1-m)-a*d*(5-m))+a*B*(a*d*(3-m)+b*c*(1+m)))*(e*x)^(1+m)*hypergeom([1, 1/2+1/2*m],[3/2+1/2*m],-b*x^2/a)/a^2/(-a*d+b*c)^3/e/(1+m)-1/2*d*(b*c*(B*c*(3-m)-A*d*(5-m))+a*d*(A*d*(1-m)+B*c*(1+m)))*(e*x)^(1+m)*hypergeom([1, 1/2+1/2*m],[3/2+1/2*m],-d*x^2/c)/c^2/(-a*d+b*c)^3/e/(1+m),1],
[(e*x)^m*(B*x^2+A)/(b*x^2+a)^3/(d*x^2+c)^2,x,8,-1/8*d*(A*(4*a^2*d^2-b^2*c^2*(3-m)+a*b*c*d*(11-m))-a*B*c*(a*d*(11-m)+b*c*(1+m)))*(e*x)^(1+m)/a^2/c/(-a*d+b*c)^3/e/(d*x^2+c)+1/4*(A*b-B*a)*(e*x)^(1+m)/a/(-a*d+b*c)/e/(b*x^2+a)^2/(d*x^2+c)+1/8*(A*b*(b*c*(3-m)-a*d*(9-m))+a*B*(a*d*(5-m)+b*c*(1+m)))*(e*x)^(1+m)/a^2/(-a*d+b*c)^2/e/(b*x^2+a)/(d*x^2+c)+1/8*b*(a*B*(b^2*c^2*(-m^2+1)-2*a*b*c*d*(-m^2+4*m+5)-a^2*d^2*(m^2-8*m+15))+A*b*(a^2*d^2*(m^2-12*m+35)-2*a*b*c*d*(m^2-8*m+7)+b^2*c^2*(m^2-4*m+3)))*(e*x)^(1+m)*hypergeom([1, 1/2+1/2*m],[3/2+1/2*m],-b*x^2/a)/a^3/(-a*d+b*c)^4/e/(1+m)+1/2*d^2*(b*c*(B*c*(5-m)-A*d*(7-m))+a*d*(A*d*(1-m)+B*c*(1+m)))*(e*x)^(1+m)*hypergeom([1, 1/2+1/2*m],[3/2+1/2*m],-d*x^2/c)/c^2/(-a*d+b*c)^4/e/(1+m),1],
[(e*x)^m*(b*x^2+a)^3*(B*x^2+A)/(d*x^2+c)^3,x,6,-b^2*(-A*b*d-3*B*a*d+3*B*b*c)*(e*x)^(1+m)/d^4/e/(1+m)+b^3*B*(e*x)^(3+m)/d^3/e^3/(3+m)+1/4*(-a*d+b*c)^3*(-A*d+B*c)*(e*x)^(1+m)/c/d^4/e/(d*x^2+c)^2+1/8*(-a*d+b*c)^2*(a*d*(A*d*(3-m)+B*c*(1+m))+b*c*(A*d*(9+m)-B*c*(13+m)))*(e*x)^(1+m)/c^2/d^4/e/(d*x^2+c)-1/8*(-a*d+b*c)*(a^2*d^2*(1-m)*(A*d*(3-m)+B*c*(1+m))+b^2*c^2*(5+m)*(A*d*(3+m)-B*c*(7+m))+2*a*b*c*d*(A*d*(-m^2-2*m+3)+B*c*(m^2+6*m+5)))*(e*x)^(1+m)*hypergeom([1, 1/2+1/2*m],[3/2+1/2*m],-d*x^2/c)/c^3/d^4/e/(1+m),1],
[(e*x)^m*(b*x^2+a)^2*(B*x^2+A)/(d*x^2+c)^3,x,5,b^2*B*(e*x)^(1+m)/d^3/e/(1+m)-1/4*(-a*d+b*c)^2*(-A*d+B*c)*(e*x)^(1+m)/c/d^3/e/(d*x^2+c)^2-1/8*(-a*d+b*c)*(a*d*(A*d*(3-m)+B*c*(1+m))+b*c*(A*d*(5+m)-B*c*(9+m)))*(e*x)^(1+m)/c^2/d^3/e/(d*x^2+c)+1/8*(a^2*d^2*(1-m)*(A*d*(3-m)+B*c*(1+m))+2*a*b*c*d*(1+m)*(A*d*(1-m)+B*c*(3+m))+b^2*c^2*(3+m)*(A*d*(1+m)-B*c*(5+m)))*(e*x)^(1+m)*hypergeom([1, 1/2+1/2*m],[3/2+1/2*m],-d*x^2/c)/c^3/d^3/e/(1+m),1],
[(e*x)^m*(b*x^2+a)*(B*x^2+A)/(d*x^2+c)^3,x,4,1/4*(-a*d+b*c)*(-A*d+B*c)*(e*x)^(1+m)/c/d^2/e/(d*x^2+c)^2+1/8*(a*d*(A*d*(3-m)+B*c*(1+m))+b*c*(A*d*(1+m)-B*c*(5+m)))*(e*x)^(1+m)/c^2/d^2/e/(d*x^2+c)+1/8*(a*d*(1-m)*(A*d*(3-m)+B*c*(1+m))+b*c*(1+m)*(A*d*(1-m)+B*c*(3+m)))*(e*x)^(1+m)*hypergeom([1, 1/2+1/2*m],[3/2+1/2*m],-d*x^2/c)/c^3/d^2/e/(1+m),1],
[(e*x)^m*(B*x^2+A)/(d*x^2+c)^3,x,3,-1/4*(-A*d+B*c)*(e*x)^(1+m)/c/d/e/(d*x^2+c)^2+1/4*(A*d*(3-m)+B*c*(1+m))*(e*x)^(1+m)*hypergeom([2, 1/2+1/2*m],[3/2+1/2*m],-d*x^2/c)/c^3/d/e/(1+m),1],
[(e*x)^m*(B*x^2+A)/(b*x^2+a)/(d*x^2+c)^3,x,7,1/4*(-A*d+B*c)*(e*x)^(1+m)/c/(-a*d+b*c)/e/(d*x^2+c)^2+1/8*(b*c*(B*c*(3-m)-A*d*(7-m))+a*d*(A*d*(3-m)+B*c*(1+m)))*(e*x)^(1+m)/c^2/(-a*d+b*c)^2/e/(d*x^2+c)+b^2*(A*b-B*a)*(e*x)^(1+m)*hypergeom([1, 1/2+1/2*m],[3/2+1/2*m],-b*x^2/a)/a/(-a*d+b*c)^3/e/(1+m)+1/8*(b^2*c^2*(B*c*(1-m)-A*d*(5-m))*(3-m)-a^2*d^2*(1-m)*(A*d*(3-m)+B*c*(1+m))+2*a*b*c*d*(B*c*(-m^2+2*m+3)+A*d*(m^2-6*m+5)))*(e*x)^(1+m)*hypergeom([1, 1/2+1/2*m],[3/2+1/2*m],-d*x^2/c)/c^3/(-a*d+b*c)^3/e/(1+m),1],
[(e*x)^m*(B*x^2+A)/(b*x^2+a)^2/(d*x^2+c)^3,x,8,1/4*d*(A*a*d+2*A*b*c-3*B*a*c)*(e*x)^(1+m)/a/c/(-a*d+b*c)^2/e/(d*x^2+c)^2+1/2*(A*b-B*a)*(e*x)^(1+m)/a/(-a*d+b*c)/e/(b*x^2+a)/(d*x^2+c)^2+1/8*d*(A*(4*b^2*c^2-a^2*d^2*(3-m)+a*b*c*d*(11-m))-a*B*c*(b*c*(11-m)+a*d*(1+m)))*(e*x)^(1+m)/a/c^2/(-a*d+b*c)^3/e/(d*x^2+c)+1/2*b^2*(A*b*(b*c*(1-m)-a*d*(7-m))+a*B*(a*d*(5-m)+b*c*(1+m)))*(e*x)^(1+m)*hypergeom([1, 1/2+1/2*m],[3/2+1/2*m],-b*x^2/a)/a^2/(-a*d+b*c)^4/e/(1+m)-1/8*d*(b^2*c^2*(B*c*(3-m)-A*d*(7-m))*(5-m)-a^2*d^2*(1-m)*(A*d*(3-m)+B*c*(1+m))+2*a*b*c*d*(B*c*(-m^2+4*m+5)+A*d*(m^2-8*m+7)))*(e*x)^(1+m)*hypergeom([1, 1/2+1/2*m],[3/2+1/2*m],-d*x^2/c)/c^3/(-a*d+b*c)^4/e/(1+m),1],
[(e*x)^m*(B*x^2+A)/(b*x^2+a)^3/(d*x^2+c)^3,x,9,-1/8*d*(A*(2*a^2*d^2-b^2*c^2*(3-m)+a*b*c*d*(13-m))-a*B*c*(a*d*(11-m)+b*c*(1+m)))*(e*x)^(1+m)/a^2/c/(-a*d+b*c)^3/e/(d*x^2+c)^2+1/4*(A*b-B*a)*(e*x)^(1+m)/a/(-a*d+b*c)/e/(b*x^2+a)^2/(d*x^2+c)^2+1/8*(A*b*(b*c*(3-m)-a*d*(11-m))+a*B*(a*d*(7-m)+b*c*(1+m)))*(e*x)^(1+m)/a^2/(-a*d+b*c)^2/e/(b*x^2+a)/(d*x^2+c)^2+1/8*d*(A*(a*d+b*c)*(b^2*c^2*(3-m)+a^2*d^2*(3-m)-2*a*b*c*d*(9-m))+a*B*c*(2*a*b*c*d*(11-m)+b^2*c^2*(1+m)+a^2*d^2*(1+m)))*(e*x)^(1+m)/a^2/c^2/(-a*d+b*c)^4/e/(d*x^2+c)+1/8*b^2*(a*B*(b^2*c^2*(-m^2+1)-2*a*b*c*d*(-m^2+6*m+7)-a^2*d^2*(m^2-12*m+35))+A*b*(a^2*d^2*(m^2-16*m+63)-2*a*b*c*d*(m^2-10*m+9)+b^2*c^2*(m^2-4*m+3)))*(e*x)^(1+m)*hypergeom([1, 1/2+1/2*m],[3/2+1/2*m],-b*x^2/a)/a^3/(-a*d+b*c)^5/e/(1+m)+1/8*d^2*(b^2*c^2*(B*c*(5-m)-A*d*(9-m))*(7-m)-a^2*d^2*(1-m)*(A*d*(3-m)+B*c*(1+m))+2*a*b*c*d*(B*c*(-m^2+6*m+7)+A*d*(m^2-10*m+9)))*(e*x)^(1+m)*hypergeom([1, 1/2+1/2*m],[3/2+1/2*m],-d*x^2/c)/c^3/(-a*d+b*c)^5/e/(1+m),1],
[(e*x)^m*(b*x^2+a)^p*(B*x^2+A)*(d*x^2+c)^3,x,7,-(a^3*B*d^3*(m^3+15*m^2+71*m+105)-a^2*b*d^2*(A*d+3*B*c)*(m^2+8*m+15)*(9+m+2*p)+3*a*b^2*c*d*(A*d+B*c)*(3+m)*(63+m^2+32*p+4*p^2+4*m*(4+p))-b^3*c^2*(3*A*d+B*c)*(315+m^3+286*p+84*p^2+8*p^3+3*m^2*(7+2*p)+m*(12*p^2+84*p+143)))*(e*x)^(1+m)*(b*x^2+a)^(p+1)/b^4/e/(3+m+2*p)/(5+m+2*p)/(7+m+2*p)/(9+m+2*p)+d*(a^2*B*d^2*(m^2+12*m+35)-a*b*d*(A*d+3*B*c)*(5+m)*(9+m+2*p)+3*b^2*c*(A*d+B*c)*(63+m^2+32*p+4*p^2+4*m*(4+p)))*(e*x)^(3+m)*(b*x^2+a)^(p+1)/b^3/e^3/(5+m+2*p)/(7+m+2*p)/(9+m+2*p)-d^2*(a*B*d*(7+m)-b*(A*d+3*B*c)*(9+m+2*p))*(e*x)^(5+m)*(b*x^2+a)^(p+1)/b^2/e^5/(7+m+2*p)/(9+m+2*p)+B*d^3*(e*x)^(7+m)*(b*x^2+a)^(p+1)/b/e^7/(9+m+2*p)+(A*c^3/(1+m)+a*(a^3*B*d^3*(m^3+15*m^2+71*m+105)-a^2*b*d^2*(A*d+3*B*c)*(m^2+8*m+15)*(9+m+2*p)+3*a*b^2*c*d*(A*d+B*c)*(3+m)*(63+m^2+32*p+4*p^2+4*m*(4+p))-b^3*c^2*(3*A*d+B*c)*(315+m^3+286*p+84*p^2+8*p^3+3*m^2*(7+2*p)+m*(12*p^2+84*p+143)))/b^4/(3+m+2*p)/(5+m+2*p)/(7+m+2*p)/(9+m+2*p))*(e*x)^(1+m)*(b*x^2+a)^p*hypergeom([1/2+1/2*m, -p],[3/2+1/2*m],-b*x^2/a)/e/((1+b*x^2/a)^p),1],
[(e*x)^m*(b*x^2+a)^p*(B*x^2+A)*(d*x^2+c)^2,x,6,(a^2*B*d^2*(m^2+8*m+15)-a*b*d*(A*d+2*B*c)*(3+m)*(7+m+2*p)+b^2*c*(2*A*d+B*c)*(35+m^2+24*p+4*p^2+4*m*(3+p)))*(e*x)^(1+m)*(b*x^2+a)^(p+1)/b^3/e/(3+m+2*p)/(5+m+2*p)/(7+m+2*p)-d*(a*B*d*(5+m)-b*(A*d+2*B*c)*(7+m+2*p))*(e*x)^(3+m)*(b*x^2+a)^(p+1)/b^2/e^3/(5+m+2*p)/(7+m+2*p)+B*d^2*(e*x)^(5+m)*(b*x^2+a)^(p+1)/b/e^5/(7+m+2*p)+(A*c^2/(1+m)-a*(a^2*B*d^2*(m^2+8*m+15)-a*b*d*(A*d+2*B*c)*(3+m)*(7+m+2*p)+b^2*c*(2*A*d+B*c)*(35+m^2+24*p+4*p^2+4*m*(3+p)))/b^3/(3+m+2*p)/(5+m+2*p)/(7+m+2*p))*(e*x)^(1+m)*(b*x^2+a)^p*hypergeom([1/2+1/2*m, -p],[3/2+1/2*m],-b*x^2/a)/e/((1+b*x^2/a)^p),1],
[(e*x)^m*(b*x^2+a)^p*(B*x^2+A)*(d*x^2+c),x,5,-(a*B*d*(3+m)-b*(A*d+B*c)*(5+m+2*p))*(e*x)^(1+m)*(b*x^2+a)^(p+1)/b^2/e/(3+m+2*p)/(5+m+2*p)+B*d*(e*x)^(3+m)*(b*x^2+a)^(p+1)/b/e^3/(5+m+2*p)+(A*c/(1+m)+a*(a*B*d*(3+m)-b*(A*d+B*c)*(5+m+2*p))/b^2/(3+m+2*p)/(5+m+2*p))*(e*x)^(1+m)*(b*x^2+a)^p*hypergeom([1/2+1/2*m, -p],[3/2+1/2*m],-b*x^2/a)/e/((1+b*x^2/a)^p),1],
[(e*x)^m*(b*x^2+a)^p*(B*x^2+A)/(d*x^2+c),x,8,-(-A*d+B*c)*(e*x)^(1+m)*(b*x^2+a)^p*AppellF1(1/2+1/2*m,-p,1,3/2+1/2*m,-b*x^2/a,-d*x^2/c)/c/d/e/(1+m)/((1+b*x^2/a)^p)+B*(e*x)^(1+m)*(b*x^2+a)^p*hypergeom([1/2+1/2*m, -p],[3/2+1/2*m],-b*x^2/a)/d/e/(1+m)/((1+b*x^2/a)^p),1],
[(e*x)^m*(b*x^2+a)^p*(B*x^2+A)/(d*x^2+c)^2,x,9,1/2*(-A*d+B*c)*(e*x)^(1+m)*(b*x^2+a)^(p+1)/c/(-a*d+b*c)/e/(d*x^2+c)-1/2*(a*d*(A*d*(1-m)+B*c*(1+m))-b*c*(A*d*(1-m-2*p)+B*c*(1+m+2*p)))*(e*x)^(1+m)*(b*x^2+a)^p*AppellF1(1/2+1/2*m,-p,1,3/2+1/2*m,-b*x^2/a,-d*x^2/c)/c^2/d/(-a*d+b*c)/e/(1+m)/((1+b*x^2/a)^p)-1/2*b*(-A*d+B*c)*(1+m+2*p)*(e*x)^(1+m)*(b*x^2+a)^p*hypergeom([1/2+1/2*m, -p],[3/2+1/2*m],-b*x^2/a)/c/d/(-a*d+b*c)/e/(1+m)/((1+b*x^2/a)^p),1],
[(e*x)^m*(b*x^2+a)^p*(B*x^2+A)/(d*x^2+c)^3,x,10,1/4*(-A*d+B*c)*(e*x)^(1+m)*(b*x^2+a)^(p+1)/c/(-a*d+b*c)/e/(d*x^2+c)^2+1/8*(a*d*(A*d*(3-m)+B*c*(1+m))+b*c*(B*c*(1-m-2*p)-A*d*(5-m-2*p)))*(e*x)^(1+m)*(b*x^2+a)^(p+1)/c^2/(-a*d+b*c)^2/e/(d*x^2+c)+1/8*(a^2*d^2*(1-m)*(A*d*(3-m)+B*c*(1+m))-2*a*b*c*d*(B*c*(1+m)*(1-m-2*p)+A*d*(1-m)*(3-m-2*p))+b^2*c^2*(1-m-2*p)*(A*d*(3-m-2*p)+B*c*(1+m+2*p)))*(e*x)^(1+m)*(b*x^2+a)^p*AppellF1(1/2+1/2*m,-p,1,3/2+1/2*m,-b*x^2/a,-d*x^2/c)/c^3/d/(-a*d+b*c)^2/e/(1+m)/((1+b*x^2/a)^p)-1/8*b*(a*d*(A*d*(3-m)+B*c*(1+m))+b*c*(B*c*(1-m-2*p)-A*d*(5-m-2*p)))*(1+m+2*p)*(e*x)^(1+m)*(b*x^2+a)^p*hypergeom([1/2+1/2*m, -p],[3/2+1/2*m],-b*x^2/a)/c^2/d/(-a*d+b*c)^2/e/(1+m)/((1+b*x^2/a)^p),1],
[sqrt(b*x^2+a)*(B*x^2+A)*(d*x^2+c)/x,x,6,A*c*sqrt(b*x^2+a)+1/3*(A*b*d-B*a*d+B*b*c)*(b*x^2+a)^(3/2)/b^2+1/5*B*d*(b*x^2+a)^(5/2)/b^2-sqrt(a)*A*c*arctanh(sqrt(b*x^2+a)/sqrt(a)),1],
[(b*x^2+a)*(B*x^2+A)*sqrt(d*x^2+c)/x,x,6,a*A*sqrt(d*x^2+c)-1/3*(-A*b*d-B*a*d+B*b*c)*(d*x^2+c)^(3/2)/d^2+1/5*b*B*(d*x^2+c)^(5/2)/d^2-a*A*sqrt(c)*arctanh(sqrt(d*x^2+c)/sqrt(c)),1],
[x^6*sqrt(b*x^2+a)*sqrt(d*x^2+c)*(f*x^2+e)^2,x,10,-2/45045*(640*a^6*d^6*f^2-128*a^5*b*d^5*f*(2*c*f+13*d*e)+a^4*b^2*d^4*(-157*c^2*f^2+728*c*d*e*f+1144*d^2*e^2)-4*a*b^5*c^3*d*(64*c^2*f^2-182*c*d*e*f+143*d^2*e^2)+8*b^6*c^4*(80*c^2*f^2-208*c*d*e*f+143*d^2*e^2)-a^3*b^3*c*d^3*(139*c^2*f^2-481*c*d*e*f+572*d^2*e^2)-a^2*b^4*c^2*d^2*(157*c^2*f^2-481*c*d*e*f+429*d^2*e^2))*x*sqrt(d*x^2+c)/b^5/d^6/sqrt(b*x^2+a)+1/45045*(640*a^5*d^5*f^3-16*a^4*b*d^4*f^2*(11*c*f+104*d*e)+a^2*b^3*c*d^2*f*(-149*c^2*f^2+468*c*d*e*f+2721*d^2*e^2)+a^3*b^2*d^3*f*(-149*c^2*f^2+520*c*d*e*f+1144*d^2*e^2)+8*b^5*c^3*f*(80*c^2*f^2-208*c*d*e*f+143*d^2*e^2)-a*b^4*c*d*(176*c^3*f^3-520*c^2*d*e*f^2-2721*c*d^2*e^2*f+1260*d^3*e^3))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b^5/d^5/f-1/45045*(480*a^4*d^4*f^3-16*a^3*b*d^3*f^2*(7*c*f+78*d*e)-2*a^2*b^2*d^2*f*(53*c^2*f^2+2981*c*d*e*f+1146*d^2*e^2)+a*b^3*d*(-112*c^3*f^3-5962*c^2*d*e*f^2-601*c*d^2*e^2*f+1260*d^3*e^3)+12*b^4*c*(40*c^3*f^3-104*c^2*d*e*f^2-191*c*d^2*e^2*f+105*d^3*e^3))*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b^4/d^4/f+1/9009*(80*a^3*d^3*f^3+a^2*b*d^2*f^2*(613*c*f+1052*d*e)-a*b^2*d*f*(-613*c^2*f^2-934*c*d*e*f+424*d^2*e^2)-4*b^3*(-20*c^3*f^3-263*c^2*d*e*f^2+106*c*d^2*e^2*f+63*d^3*e^3))*x^5*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b^3/d^3/f+1/1287*(80*a^2*d^2*f^2-a*b*d*f*(-83*c*f+28*d*e)-4*b^2*(-20*c^2*f^2+7*c*d*e*f+7*d^2*e^2))*x^7*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b^2/d^2-2/143*(5*a/b+5*c/d-2*e/f)*x*(b*x^2+a)^(3/2)*(d*x^2+c)^(3/2)*(f*x^2+e)^2/b/d+1/13*x^3*(b*x^2+a)^(3/2)*(d*x^2+c)^(3/2)*(f*x^2+e)^2/b/d+2/45045*sqrt(a)*(640*a^6*d^6*f^2-128*a^5*b*d^5*f*(2*c*f+13*d*e)+a^4*b^2*d^4*(-157*c^2*f^2+728*c*d*e*f+1144*d^2*e^2)-4*a*b^5*c^3*d*(64*c^2*f^2-182*c*d*e*f+143*d^2*e^2)+8*b^6*c^4*(80*c^2*f^2-208*c*d*e*f+143*d^2*e^2)-a^3*b^3*c*d^3*(139*c^2*f^2-481*c*d*e*f+572*d^2*e^2)-a^2*b^4*c^2*d^2*(157*c^2*f^2-481*c*d*e*f+429*d^2*e^2))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/b^(11/2)/d^6/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/45045*a^(3/2)*(640*a^5*d^5*f^2-16*a^4*b*d^4*f*(11*c*f+104*d*e)+a^3*b^2*d^3*(-149*c^2*f^2+520*c*d*e*f+1144*d^2*e^2)+8*b^5*c^3*(80*c^2*f^2-208*c*d*e*f+143*d^2*e^2)-a^2*b^3*c*d^2*(149*c^2*f^2-468*c*d*e*f+429*d^2*e^2)-a*b^4*c^2*d*(176*c^2*f^2-520*c*d*e*f+429*d^2*e^2))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(11/2)/d^5/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[x^4*sqrt(b*x^2+a)*sqrt(d*x^2+c)*(f*x^2+e)^2,x,9,1/3465*(128*a^5*d^5*f^2-8*a^4*b*d^4*f*(7*c*f+44*d*e)+a^3*b^2*d^3*(-37*c^2*f^2+176*c*d*e*f+264*d^2*e^2)+8*b^5*c^3*(16*c^2*f^2-44*c*d*e*f+33*d^2*e^2)-a^2*b^3*c*d^2*(37*c^2*f^2-132*c*d*e*f+165*d^2*e^2)-a*b^4*c^2*d*(56*c^2*f^2-176*c*d*e*f+165*d^2*e^2))*x*sqrt(d*x^2+c)/b^4/d^5/sqrt(b*x^2+a)-1/3465*(64*a^4*d^4*f^2-4*a^3*b*d^3*f*(5*c*f+44*d*e)+a*b^3*c*d*(-20*c^2*f^2+66*c*d*e*f+249*d^2*e^2)+6*a^2*b^2*d^2*(-3*c^2*f^2+11*c*d*e*f+22*d^2*e^2)+4*b^4*c^2*(16*c^2*f^2-44*c*d*e*f+33*d^2*e^2))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b^4/d^4+1/3465*(48*a^3*d^3*f^2-a^2*b*d^2*f*(13*c*f+132*d*e)-12*b^3*c*(-4*c^2*f^2+11*c*d*e*f+18*d^2*e^2)-a*b^2*d*(13*c^2*f^2+586*c*d*e*f+216*d^2*e^2))*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b^3/d^3-1/693*(8*a^2*d*f^2/b+a*f*(61*c*f+104*d*e)-b*(36*d*e^2-104*c*e*f-8*c^2*f^2/d))*x^5*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b/d+4/99*f*(-2*a*d*f-2*b*c*f+b*d*e)*x^7*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b/d+1/11*x*(b*x^2+a)^(3/2)*(d*x^2+c)^(3/2)*(f*x^2+e)^2/b/d-1/3465*sqrt(a)*(128*a^5*d^5*f^2-8*a^4*b*d^4*f*(7*c*f+44*d*e)+a^3*b^2*d^3*(-37*c^2*f^2+176*c*d*e*f+264*d^2*e^2)+8*b^5*c^3*(16*c^2*f^2-44*c*d*e*f+33*d^2*e^2)-a^2*b^3*c*d^2*(37*c^2*f^2-132*c*d*e*f+165*d^2*e^2)-a*b^4*c^2*d*(56*c^2*f^2-176*c*d*e*f+165*d^2*e^2))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/b^(9/2)/d^5/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+2/3465*a^(3/2)*(32*a^4*d^4*f^2-2*a^3*b*d^3*f*(5*c*f+44*d*e)+3*a^2*b^2*d^2*(-3*c^2*f^2+11*c*d*e*f+22*d^2*e^2)-a*b^3*c*d*(10*c^2*f^2-33*c*d*e*f+33*d^2*e^2)+2*b^4*c^2*(16*c^2*f^2-44*c*d*e*f+33*d^2*e^2))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(9/2)/d^4/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[x^2*sqrt(b*x^2+a)*sqrt(d*x^2+c)*(f*x^2+e)^2,x,9,-2/315*(8*a^4*d^4*f^2-4*a^3*b*d^3*f*(c*f+6*d*e)+3*a^2*b^2*d^2*(-c^2*f^2+5*c*d*e*f+7*d^2*e^2)-a*b^3*c*d*(4*c^2*f^2-15*c*d*e*f+21*d^2*e^2)+b^4*c^2*(8*c^2*f^2-24*c*d*e*f+21*d^2*e^2))*x*sqrt(d*x^2+c)/b^3/d^4/sqrt(b*x^2+a)+1/315*(8*a^3*d^3*f^2-3*a^2*b*d^2*f*(c*f+8*d*e)+3*a*b^2*d*(-c^2*f^2+4*c*d*e*f+7*d^2*e^2)+b^3*c*(8*c^2*f^2-24*c*d*e*f+21*d^2*e^2))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b^3/d^3-1/315*(6*a^2*d*f^2/b-2*a*f*(c*f+9*d*e)-b*(63*d*e^2+18*c*e*f-6*c^2*f^2/d))*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b/d+1/63*f*(a*d*f+b*c*f+18*b*d*e)*x^5*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b/d+1/9*f^2*x^7*sqrt(b*x^2+a)*sqrt(d*x^2+c)+2/315*sqrt(a)*(8*a^4*d^4*f^2-4*a^3*b*d^3*f*(c*f+6*d*e)+3*a^2*b^2*d^2*(-c^2*f^2+5*c*d*e*f+7*d^2*e^2)-a*b^3*c*d*(4*c^2*f^2-15*c*d*e*f+21*d^2*e^2)+b^4*c^2*(8*c^2*f^2-24*c*d*e*f+21*d^2*e^2))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/b^(7/2)/d^4/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/315*a^(3/2)*(8*a^3*d^3*f^2-3*a^2*b*d^2*f*(c*f+8*d*e)+3*a*b^2*d*(-c^2*f^2+4*c*d*e*f+7*d^2*e^2)+b^3*c*(8*c^2*f^2-24*c*d*e*f+21*d^2*e^2))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(7/2)/d^3/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)*(f*x^2+e)^2,x,7,1/105*(8*a^3*d^3*f^2-a^2*b*d^2*f*(5*c*f+28*d*e)+a*b^2*d*(-5*c^2*f^2+28*c*d*e*f+35*d^2*e^2)+b^3*c*(8*c^2*f^2-28*c*d*e*f+35*d^2*e^2))*x*sqrt(d*x^2+c)/b^2/d^3/sqrt(b*x^2+a)-1/105*(4*a^2*d*f^2/b-2*a*f*(c*f+7*d*e)-b*(35*d*e^2+14*c*e*f-4*c^2*f^2/d))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b/d+1/35*f*(a*d*f+b*c*f+14*b*d*e)*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b/d+1/7*f^2*x^5*sqrt(b*x^2+a)*sqrt(d*x^2+c)-1/105*sqrt(a)*(8*a^3*d^3*f^2-a^2*b*d^2*f*(5*c*f+28*d*e)+a*b^2*d*(-5*c^2*f^2+28*c*d*e*f+35*d^2*e^2)+b^3*c*(8*c^2*f^2-28*c*d*e*f+35*d^2*e^2))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/b^(5/2)/d^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+2/105*a^(3/2)*(2*a^2*d^2*f^2-a*b*d*f*(c*f+7*d*e)+b^2*(2*c^2*f^2-7*c*d*e*f+35*d^2*e^2))*sqrt(d*x^2+c)*InverseJacobiAM(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],
[sqrt(b*x^2+a)*sqrt(d*x^2+c)*(f*x^2+e)^2/x^2,x,10,-2/15*(a^2*d^2*f^2-a*b*d*f*(c*f+5*d*e)-b^2*(-c^2*f^2+5*c*d*e*f+15*d^2*e^2))*x*sqrt(d*x^2+c)/b/d^2/sqrt(b*x^2+a)+1/15*(15*b*e^2/a+15*d*e^2/c+55*e*f+a*f^2/b+c*f^2/d)*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)+1/5*(5*b*e*(3*c*f+d*e)+a*f*(16*c*f+15*d*e))*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a/c+f*(3*b*e*(c*f+d*e)+a*f*(c*f+3*d*e))*x^5*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a/c/e+f^2*(a*d*f+b*c*f+3*b*d*e)*x^7*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a/c/e+b*d*f^3*x^9*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a/c/e-(b*x^2+a)^(3/2)*(d*x^2+c)^(3/2)*(f*x^2+e)^3/a/c/e/x+2/15*sqrt(a)*(a^2*d^2*f^2-a*b*d*f*(c*f+5*d*e)-b^2*(-c^2*f^2+5*c*d*e*f+15*d^2*e^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))+1/15*sqrt(a)*(15*b^2*c*d*e^2-a^2*c*d*f^2+a*b*(-c^2*f^2+20*c*d*e*f+15*d^2*e^2))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(3/2)/c/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)*(f*x^2+e)^2/x^4,x,11,1/3*(b^2*e^2/a+a*f^2+b*(d*e^2/c+12*e*f+c*f^2/d))*x*sqrt(d*x^2+c)/sqrt(b*x^2+a)+1/3*(b*e*(6*c*f+d*e)+a*f*(13*c*f+6*d*e))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a/c+2/3*f*(3*b*e*(2*c*f+d*e)+a*f*(5*c*f+6*d*e))*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a/c/e+1/3*f^2*(a*f*(3*c*f+10*d*e)+2*b*e*(5*c*f+6*d*e))*x^5*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a/c/e^2+1/3*f^3*(3*a*d*f+3*b*c*f+10*b*d*e)*x^7*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a/c/e^2+b*d*f^4*x^9*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a/c/e^2-1/3*(b*x^2+a)^(3/2)*(d*x^2+c)^(3/2)*(f*x^2+e)^3/a/c/e/x^3-f*(b*x^2+a)^(3/2)*(d*x^2+c)^(3/2)*(f*x^2+e)^3/a/c/e^2/x-1/3*(b^2*c*d*e^2+a^2*c*d*f^2+a*b*(c^2*f^2+12*c*d*e*f+d^2*e^2))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/sqrt(a)/sqrt(b)/c/d/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+2/3*sqrt(a)*(a*f*(c*f+3*d*e)+b*e*(3*c*f+d*e))*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],
[sqrt(b*x^2+a)*sqrt(d*x^2+c)*(f*x^2+e)^2/x^6,x,12,-2/15*b*(b^2*c^2*e^2-a*b*c*e*(5*c*f+d*e)+a^2*(-15*c^2*f^2-5*c*d*e*f+d^2*e^2))*x*sqrt(d*x^2+c)/a^2/c^2/sqrt(b*x^2+a)+1/15*(b^2*c*d*e^3+3*a^2*c*f^2*(5*c*f+9*d*e)+a*b*e*(27*c^2*f^2+19*c*d*e*f+d^2*e^2))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a^2/c^2/e+1/15*(3*b^2*e^2*(4*c^2*f^2+3*c*d*e*f+d^2*e^2)+a^2*f^2*(10*c^2*f^2+31*c*d*e*f+12*d^2*e^2)+a*b*e*f*(31*c^2*f^2+48*c*d*e*f+9*d^2*e^2))*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a^2/c^2/e^2+1/15*f*(a^2*f^2*(3*c^2*f^2+16*c*d*e*f+16*d^2*e^2)+b^2*e^2*(16*c^2*f^2+21*c*d*e*f+9*d^2*e^2)+a*b*e*f*(16*c^2*f^2+50*c*d*e*f+21*d^2*e^2))*x^5*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a^2/c^2/e^3+1/15*f^2*(3*a^2*d*f^2*(c*f+2*d*e)+a*b*f*(3*c^2*f^2+22*c*d*e*f+19*d^2*e^2)+b^2*e*(6*c^2*f^2+19*c*d*e*f+9*d^2*e^2))*x^7*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a^2/c^2/e^3+1/5*b*d*f^3*(a*f*(c*f+2*d*e)+b*e*(2*c*f+d*e))*x^9*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a^2/c^2/e^3-1/5*(b*x^2+a)^(3/2)*(d*x^2+c)^(3/2)*(f*x^2+e)^3/a/c/e/x^5+1/15*(-a*c*f+2*a*d*e+2*b*c*e)*(b*x^2+a)^(3/2)*(d*x^2+c)^(3/2)*(f*x^2+e)^3/a^2/c^2/e^2/x^3-1/5*(a*f*(c*f+2*d*e)+b*e*(2*c*f+d*e))*(b*x^2+a)^(3/2)*(d*x^2+c)^(3/2)*(f*x^2+e)^3/a^2/c^2/e^3/x+2/15*sqrt(b)*(b^2*c^2*e^2-a*b*c*e*(5*c*f+d*e)+a^2*(-15*c^2*f^2-5*c*d*e*f+d^2*e^2))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/a^(3/2)/c^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/15*(b^2*c*d*e^2-15*a^2*c*d*f^2+a*b*(-15*c^2*f^2-20*c*d*e*f+d^2*e^2))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(a)/sqrt(b)/c^2/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)*(f*x^2+e)^2/x^8,x,13,1/105*b*(8*b^3*c^3*e^2-a*b^2*c^2*e*(28*c*f+5*d*e)-a^2*b*c*(-35*c^2*f^2-28*c*d*e*f+5*d^2*e^2)+a^3*d*(35*c^2*f^2-28*c*d*e*f+8*d^2*e^2))*x*sqrt(d*x^2+c)/a^3/c^3/sqrt(b*x^2+a)-1/105*(4*b^3*c^2*d*e^4+3*a^3*c*f^2*(5*c^2*f^2-16*c*d*e*f+16*d^2*e^2)+a*b^2*c*e^2*(48*c^2*f^2+22*c*d*e*f+13*d^2*e^2)+a^2*b*e*(-48*c^3*f^3-95*c^2*d*e*f^2+22*c*d^2*e^2*f+4*d^3*e^3))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a^3/c^3/e^2-1/105*(12*b^3*c*e^3*(4*c^2*f^2+3*c*d*e*f+d^2*e^2)+a^2*b*e*f*(-29*c^3*f^3-134*c^2*d*e*f^2+24*c*d^2*e^2*f+36*d^3*e^3)+2*a*b^2*e^2*(8*c^3*f^3+12*c^2*d*e*f^2+15*c*d^2*e^2*f+6*d^3*e^3)+a^3*f^2*(10*c^3*f^3-29*c^2*d*e*f^2+16*c*d^2*e^2*f+48*d^3*e^3))*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a^3/c^3/e^3-1/105*f*(4*b^3*c*e^3*(16*c^2*f^2+21*c*d*e*f+9*d^2*e^2)+2*a*b^2*e^2*(-10*c^3*f^3-5*c^2*d*e*f^2+6*c*d^2*e^2*f+18*d^3*e^3)+2*a^2*b*e*f*(-c^3*f^3-41*c^2*d*e*f^2-5*c*d^2*e^2*f+42*d^3*e^3)+a^3*f^2*(3*c^3*f^3-2*c^2*d*e*f^2-20*c*d^2*e^2*f+64*d^3*e^3))*x^5*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a^3/c^3/e^4-1/105*f^2*(3*a^3*d*f^2*(c^2*f^2-4*c*d*e*f+8*d^2*e^2)+4*b^3*c*e^2*(6*c^2*f^2+19*c*d*e*f+9*d^2*e^2)+a*b^2*e*(-12*c^3*f^3-29*c^2*d*e*f^2-14*c*d^2*e^2*f+36*d^3*e^3)+a^2*b*f*(3*c^3*f^3-14*c^2*d*e*f^2-29*c*d^2*e^2*f+76*d^3*e^3))*x^7*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a^3/c^3/e^4-1/35*b*d*f^3*(4*b^2*c*e^2*(2*c*f+d*e)+a*b*e*(-4*c^2*f^2-3*c*d*e*f+4*d^2*e^2)+a^2*f*(c^2*f^2-4*c*d*e*f+8*d^2*e^2))*x^9*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a^3/c^3/e^4-1/7*(b*x^2+a)^(3/2)*(d*x^2+c)^(3/2)*(f*x^2+e)^3/a/c/e/x^7+1/35*(a*c*f+4*a*d*e+4*b*c*e)*(b*x^2+a)^(3/2)*(d*x^2+c)^(3/2)*(f*x^2+e)^3/a^2/c^2/e^2/x^5-1/105*(8*b^2*c*e/a+11*b*d*e+8*a*d^2*e/c+8*b*c*f+8*a*d*f-a*c*f^2/e)*(b*x^2+a)^(3/2)*(d*x^2+c)^(3/2)*(f*x^2+e)^3/a^2/c^2/e^2/x^3+1/35*(4*b^2*c*e^2*(2*c*f+d*e)+a*b*e*(-4*c^2*f^2-3*c*d*e*f+4*d^2*e^2)+a^2*f*(c^2*f^2-4*c*d*e*f+8*d^2*e^2))*(b*x^2+a)^(3/2)*(d*x^2+c)^(3/2)*(f*x^2+e)^3/a^3/c^3/e^4/x-1/105*sqrt(b)*(8*b^3*c^3*e^2-a*b^2*c^2*e*(28*c*f+5*d*e)-a^2*b*c*(-35*c^2*f^2-28*c*d*e*f+5*d^2*e^2)+a^3*d*(35*c^2*f^2-28*c*d*e*f+8*d^2*e^2))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/a^(5/2)/c^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+2/105*sqrt(b)*d*(2*b^2*c^2*e^2-a*b*c*e*(7*c*f+d*e)+a^2*(35*c^2*f^2-7*c*d*e*f+2*d^2*e^2))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/a^(3/2)/c^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[x^4*sqrt(b*x^2+a)*sqrt(d*x^2+c)*(f*x^2+e),x,8,-1/315*(16*a^4*d^4*f+a*b^3*c^2*d*(-8*c*f+15*d*e)-8*b^4*c^3*(-2*c*f+3*d*e)+3*a^2*b^2*c*d^2*(-2*c*f+5*d*e)-8*a^3*b*d^3*(c*f+3*d*e))*x*sqrt(d*x^2+c)/b^3/d^4/sqrt(b*x^2+a)+1/315*(8*a^3*d^3*f-4*b^3*c^2*(-2*c*f+3*d*e)+3*a*b^2*c*d*(-c*f+2*d*e)-3*a^2*b*d^2*(c*f+4*d*e))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b^3/d^3+1/315*(9*b*c*e+9*a*d*e+2*a*c*f-6*b*c^2*f/d-6*a^2*d*f/b)*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b/d+1/63*(-6*a*d*f+b*c*f+9*b*d*e)*x^5*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b/d+1/9*f*x^5*(b*x^2+a)^(3/2)*sqrt(d*x^2+c)/b+1/315*sqrt(a)*(16*a^4*d^4*f+a*b^3*c^2*d*(-8*c*f+15*d*e)-8*b^4*c^3*(-2*c*f+3*d*e)+3*a^2*b^2*c*d^2*(-2*c*f+5*d*e)-8*a^3*b*d^3*(c*f+3*d*e))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/b^(7/2)/d^4/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/315*a^(3/2)*(8*a^3*d^3*f-4*b^3*c^2*(-2*c*f+3*d*e)+3*a*b^2*c*d*(-c*f+2*d*e)-3*a^2*b*d^2*(c*f+4*d*e))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(7/2)/d^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[x^2*sqrt(b*x^2+a)*sqrt(d*x^2+c)*(f*x^2+e),x,7,1/105*(8*a^3*d^3*f+a*b^2*c*d*(-5*c*f+14*d*e)-2*b^3*c^2*(-4*c*f+7*d*e)-a^2*b*d^2*(5*c*f+14*d*e))*x*sqrt(d*x^2+c)/b^2/d^3/sqrt(b*x^2+a)-1/105*(4*a^2*d^2*f-b^2*c*(-4*c*f+7*d*e)-a*b*d*(2*c*f+7*d*e))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b^2/d^2+1/35*(-4*a*d*f+b*c*f+7*b*d*e)*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b/d+1/7*f*x^3*(b*x^2+a)^(3/2)*sqrt(d*x^2+c)/b-1/105*sqrt(a)*(8*a^3*d^3*f+a*b^2*c*d*(-5*c*f+14*d*e)-2*b^3*c^2*(-4*c*f+7*d*e)-a^2*b*d^2*(5*c*f+14*d*e))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/b^(5/2)/d^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/105*a^(3/2)*(4*a^2*d^2*f-b^2*c*(-4*c*f+7*d*e)-a*b*d*(2*c*f+7*d*e))*sqrt(d*x^2+c)*InverseJacobiAM(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],
[sqrt(b*x^2+a)*sqrt(d*x^2+c)*(f*x^2+e),x,6,1/15*(5*b*c*e+5*a*d*e+2*a*c*f-2*b*c^2*f/d-2*a^2*d*f/b)*x*sqrt(d*x^2+c)/d/sqrt(b*x^2+a)+1/15*(a*d*f-2*b*c*f+5*b*d*e)*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b/d+1/5*f*x*sqrt(b*x^2+a)*(d*x^2+c)^(3/2)/d+1/15*sqrt(a)*(2*a^2*d^2*f-b^2*c*(-2*c*f+5*d*e)-a*b*d*(2*c*f+5*d*e))*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))+1/15*a^(3/2)*(-a*d*f-b*c*f+10*b*d*e)*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)*sqrt(d*x^2+c)*(f*x^2+e)/x^2,x,6,1/3*(a*d*f+b*c*f+6*b*d*e)*x*sqrt(d*x^2+c)/d/sqrt(b*x^2+a)+1/3*(a*f+3*b*e)*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a-e*(b*x^2+a)^(3/2)*sqrt(d*x^2+c)/a/x-1/3*sqrt(a)*(a*d*f+b*c*f+6*b*d*e)*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))+1/3*sqrt(a)*(2*a*c*f+3*a*d*e+3*b*c*e)*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],
[sqrt(b*x^2+a)*sqrt(d*x^2+c)*(f*x^2+e)/x^4,x,6,1/3*b*(6*a*c*f+a*d*e+b*c*e)*x*sqrt(d*x^2+c)/a/c/sqrt(b*x^2+a)-1/3*(3*c*f+d*e)*sqrt(b*x^2+a)*sqrt(d*x^2+c)/c/x-1/3*e*(b*x^2+a)^(3/2)*sqrt(d*x^2+c)/a/x^3-1/3*sqrt(b)*(6*a*c*f+a*d*e+b*c*e)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/sqrt(a)/c/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/3*sqrt(a)*(3*a*d*f+3*b*c*f+2*b*d*e)*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],
[sqrt(b*x^2+a)*sqrt(d*x^2+c)*(f*x^2+e)/x^6,x,4,1/15*(2*b^2*c^2*e+a^2*d*(-5*c*f+2*d*e)-a*b*c*(5*c*f+2*d*e))*sqrt(d*x^2+c)/a/c^2/x/sqrt(b*x^2+a)+1/15*(-5*a*c*f-a*d*e+2*b*c*e)*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a/c/x^3-1/5*e*(b*x^2+a)^(3/2)*sqrt(d*x^2+c)/a/x^5+1/15*sqrt(b)*(2*b^2*c^2*e+a^2*d*(-5*c*f+2*d*e)-a*b*c*(5*c*f+2*d*e))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/a^(3/2)/c^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/15*sqrt(b)*d*(-10*a*c*f+a*d*e+b*c*e)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(a)/c^2/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)*(f*x^2+e)/x^8,x,5,-1/105*(8*b^3*c^3*e-a^2*b*c*d*(-14*c*f+5*d*e)+2*a^3*d^2*(-7*c*f+4*d*e)-a*b^2*c^2*(14*c*f+5*d*e))*sqrt(d*x^2+c)/a^2/c^3/x/sqrt(b*x^2+a)+1/35*(-7*a*c*f-a*d*e+4*b*c*e)*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a/c/x^5+1/105*(4*b^2*c^2*e+a^2*d*(-7*c*f+4*d*e)-a*b*c*(7*c*f+2*d*e))*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a^2/c^2/x^3-1/7*e*(b*x^2+a)^(3/2)*sqrt(d*x^2+c)/a/x^7-1/105*sqrt(b)*(8*b^3*c^3*e-a^2*b*c*d*(-14*c*f+5*d*e)+2*a^3*d^2*(-7*c*f+4*d*e)-a*b^2*c^2*(14*c*f+5*d*e))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/a^(5/2)/c^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/105*sqrt(b)*d*(4*b^2*c^2*e+a^2*d*(-7*c*f+4*d*e)-a*b*c*(7*c*f+2*d*e))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/a^(3/2)/c^3/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)*(f*x^2+e)/x^10,x,6,1/315*(16*b^4*c^4*e-a^3*b*c*d^2*(-15*c*f+8*d*e)-3*a^2*b^2*c^2*d*(-5*c*f+2*d*e)+8*a^4*d^3*(-3*c*f+2*d*e)-8*a*b^3*c^3*(3*c*f+d*e))*sqrt(d*x^2+c)/a^3/c^4/x/sqrt(b*x^2+a)+1/63*(-9*a*c*f-a*d*e+6*b*c*e)*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a/c/x^7+1/315*(6*b^2*c*e/a-2*b*d*e+6*a*d^2*e/c-9*b*c*f-9*a*d*f)*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a/c/x^5-1/315*(8*b^3*c^3*e+4*a^3*d^2*(-3*c*f+2*d*e)-3*a^2*b*c*d*(-2*c*f+d*e)-3*a*b^2*c^2*(4*c*f+d*e))*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a^3/c^3/x^3-1/9*e*(b*x^2+a)^(3/2)*sqrt(d*x^2+c)/a/x^9+1/315*sqrt(b)*(16*b^4*c^4*e-a^3*b*c*d^2*(-15*c*f+8*d*e)-3*a^2*b^2*c^2*d*(-5*c*f+2*d*e)+8*a^4*d^3*(-3*c*f+2*d*e)-8*a*b^3*c^3*(3*c*f+d*e))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/a^(7/2)/c^4/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/315*sqrt(b)*d*(8*b^3*c^3*e+4*a^3*d^2*(-3*c*f+2*d*e)-3*a^2*b*c*d*(-2*c*f+d*e)-3*a*b^2*c^2*(4*c*f+d*e))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/a^(5/2)/c^4/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[x^8*sqrt(b*x^2+a)*sqrt(d*x^2+c)/(f*x^2+e),x,10,-1/63*(-a*d*f+6*b*c*f+9*b*d*e)*x^5*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b/d/f^2+1/9*x^5*sqrt(b*x^2+a)*(d*x^2+c)^(3/2)/d/f-1/315*((16*a^4*d^4*f^4+8*a^3*b*d^3*f^3*(-c*f+3*d*e)+3*a^2*b^2*d^2*f^2*(-2*c^2*f^2-5*c*d*e*f+14*d^2*e^2)+a*b^3*d*f*(-8*c^3*f^3-15*c^2*d*e*f^2-42*c*d^2*e^2*f+105*d^3*e^3)-b^4*(-16*c^4*f^4-24*c^3*d*e*f^3-42*c^2*d^2*e^2*f^2-105*c*d^3*e^3*f+315*d^4*e^4))*x*sqrt(d*x^2+c)/b^2/d^3/f^3/sqrt(b*x^2+a)-(8*a^3*d^3*f^3+3*a^2*b*d^2*f^2*(-c*f+4*d*e)+3*a*b^2*d*f*(-c^2*f^2-2*c*d*e*f+7*d^2*e^2)-b^3*(-8*c^3*f^3-12*c^2*d*e*f^2-21*c*d^2*e^2*f+105*d^3*e^3))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b^2/d^2/f^2+(9*b*c*e+9*a*d*e-63*b*d*e^2/f-2*a*c*f+6*b*c^2*f/d+6*a^2*d*f/b)*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)-sqrt(a)*(16*a^4*d^4*f^4+8*a^3*b*d^3*f^3*(-c*f+3*d*e)+3*a^2*b^2*d^2*f^2*(-2*c^2*f^2-5*c*d*e*f+14*d^2*e^2)+a*b^3*d*f*(-8*c^3*f^3-15*c^2*d*e*f^2-42*c*d^2*e^2*f+105*d^3*e^3)-b^4*(-16*c^4*f^4-24*c^3*d*e*f^3-42*c^2*d^2*e^2*f^2-105*c*d^3*e^3*f+315*d^4*e^4))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/b^(5/2)/d^3/f^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+a^(3/2)*(8*a^3*c*d^3*f^4+3*a^2*b*c*d^2*f^3*(-c*f+4*d*e)+3*a*b^2*c*d*f^2*(-c^2*f^2-2*c*d*e*f+7*d^2*e^2)-b^3*(-8*c^4*f^4-12*c^3*d*e*f^3-21*c^2*d^2*e^2*f^2-210*c*d^3*e^3*f+315*d^4*e^4))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(5/2)/c/d^2/f^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+315*a^(3/2)*sqrt(b)*d*e^3*(-c*f+d*e)*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/c/f^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)))/b/d/f^2,1],
[x^6*sqrt(b*x^2+a)*sqrt(d*x^2+c)/(f*x^2+e),x,8,-1/35*(-a*d*f+4*b*c*f+7*b*d*e)*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b/d/f^2+1/7*x^3*sqrt(b*x^2+a)*(d*x^2+c)^(3/2)/d/f+1/105*((8*a^3*d^3*f^3+a^2*b*d^2*f^2*(-5*c*f+14*d*e)+a*b^2*d*f*(-5*c^2*f^2-14*c*d*e*f+35*d^2*e^2)-b^3*(-8*c^3*f^3-14*c^2*d*e*f^2-35*c*d^2*e^2*f+105*d^3*e^3))*x*sqrt(d*x^2+c)/b/d^2/f^2/sqrt(b*x^2+a)-(7*b*c*e+7*a*d*e-35*b*d*e^2/f-2*a*c*f+4*b*c^2*f/d+4*a^2*d*f/b)*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)-sqrt(a)*(8*a^3*d^3*f^3+a^2*b*d^2*f^2*(-5*c*f+14*d*e)+a*b^2*d*f*(-5*c^2*f^2-14*c*d*e*f+35*d^2*e^2)-b^3*(-8*c^3*f^3-14*c^2*d*e*f^2-35*c*d^2*e^2*f+105*d^3*e^3))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/b^(3/2)/d^2/f^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+a^(3/2)*(4*a^2*c*d^2*f^3+a*b*c*d*f^2*(-2*c*f+7*d*e)-b^2*(-4*c^3*f^3-7*c^2*d*e*f^2-70*c*d^2*e^2*f+105*d^3*e^3))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(3/2)/c/d/f^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+105*a^(3/2)*sqrt(b)*d*e^2*(-c*f+d*e)*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/c/f^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)))/b/d/f^2,1],
[x^4*sqrt(b*x^2+a)*sqrt(d*x^2+c)/(f*x^2+e),x,6,-1/15*(2*a^2*d*f+a*b*(-2*c*f+5*d*e)+b^2*(5*c*e-15*d*e^2/f+2*c^2*f/d))*x*sqrt(d*x^2+c)/b/d/f^2/sqrt(b*x^2+a)-1/15*(-a*d*f+2*b*c*f+5*b*d*e)*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b/d/f^2+1/5*x*sqrt(b*x^2+a)*(d*x^2+c)^(3/2)/d/f+1/15*sqrt(a)*(2*a^2*d^2*f^2+a*b*d*f*(-2*c*f+5*d*e)-b^2*(-2*c^2*f^2-5*c*d*e*f+15*d^2*e^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/f^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/15*a^(3/2)*(a*c*d*f^2-b*(-c^2*f^2-10*c*d*e*f+15*d^2*e^2))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(3/2)/c/d/f^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-a^(3/2)*e*(-c*f+d*e)*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/f^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[x^2*sqrt(b*x^2+a)*sqrt(d*x^2+c)/(f*x^2+e),x,5,-1/3*(-a*d*f-b*c*f+3*b*d*e)*x*sqrt(d*x^2+c)/d/f^2/sqrt(b*x^2+a)+1/3*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/f+1/3*sqrt(a)*(-a*d*f-b*c*f+3*b*d*e)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/sqrt(b)/d/f^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/3*a^(3/2)*(-2*c*f+3*d*e)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(b)/c/f^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+a^(3/2)*(-c*f+d*e)*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/f^2/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)/(f*x^2+e),x,5,b*x*sqrt(d*x^2+c)/f/sqrt(b*x^2+a)-sqrt(a)*sqrt(b)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/f/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+a^(3/2)*d*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(b)/c/f/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-a^(3/2)*(-c*f+d*e)*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e/f/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^2/(f*x^2+e),x,8,b*x*sqrt(d*x^2+c)/e/sqrt(b*x^2+a)+d*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/c/e+b*x*sqrt(b*x^2+a)*(d*x^2+c)^(3/2)/a/c/e-(b*x^2+a)^(3/2)*(d*x^2+c)^(3/2)/a/c/e/x-sqrt(a)*sqrt(b)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/e/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+sqrt(a)*sqrt(b)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/e/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+a^(3/2)*(-c*f+d*e)*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e^2/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^4/(f*x^2+e),x,8,1/3*b*(-3*a*c*f+a*d*e+b*c*e)*x*sqrt(d*x^2+c)/a/c/e^2/sqrt(b*x^2+a)+1/3*d*(-3*a*f+b*e)*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a/c/e^2-b*f*x*sqrt(b*x^2+a)*(d*x^2+c)^(3/2)/a/c/e^2-1/3*(b*x^2+a)^(3/2)*(d*x^2+c)^(3/2)/a/c/e/x^3+f*(b*x^2+a)^(3/2)*(d*x^2+c)^(3/2)/a/c/e^2/x-1/3*sqrt(b)*(-3*a*c*f+a*d*e+b*c*e)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/sqrt(a)/c/e^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/3*sqrt(a)*sqrt(b)*(-3*c*f+2*d*e)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/c/e^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-a^(3/2)*f*(-c*f+d*e)*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e^3/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^6/(f*x^2+e),x,9,-1/15*b*(2*b^2*c^2*e^2-a*b*c*e*(-5*c*f+2*d*e)+a^2*(-15*c^2*f^2+5*c*d*e*f+2*d^2*e^2))*x*sqrt(d*x^2+c)/a^2/c^2/e^3/sqrt(b*x^2+a)-1/15*d*(2*b^2*c*e^2-15*a^2*c*f^2-a*b*e*(-5*c*f+d*e))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a^2/c^2/e^3+1/5*b*(5*a*c*f^2+b*d*e^2)*x*sqrt(b*x^2+a)*(d*x^2+c)^(3/2)/a^2/c^2/e^3-1/5*(b*x^2+a)^(3/2)*(d*x^2+c)^(3/2)/a/c/e/x^5+1/15*(5*a*c*f+2*a*d*e+2*b*c*e)*(b*x^2+a)^(3/2)*(d*x^2+c)^(3/2)/a^2/c^2/e^2/x^3-1/5*(5*a*c*f^2+b*d*e^2)*(b*x^2+a)^(3/2)*(d*x^2+c)^(3/2)/a^2/c^2/e^3/x+1/15*sqrt(b)*(2*b^2*c^2*e^2-a*b*c*e*(-5*c*f+2*d*e)+a^2*(-15*c^2*f^2+5*c*d*e*f+2*d^2*e^2))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/a^(3/2)/c^2/e^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/15*sqrt(b)*(b*c*d*e^2+a*(-15*c^2*f^2+10*c*d*e*f+d^2*e^2))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(a)/c^2/e^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+a^(3/2)*f^2*(-c*f+d*e)*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e^4/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[x^6*sqrt(b*x^2+a)*sqrt(d*x^2+c)/(f*x^2+e)^2,x,7,-1/30*(4*a^2*d^2*f^2+4*a*b*d*f*(-c*f+5*d*e)-b^2*(-4*c^2*f^2-20*c*d*e*f+105*d^2*e^2))*x*sqrt(d*x^2+c)/b/d^2/f^4/sqrt(b*x^2+a)+1/30*(2*a*f/b-(-4*c^2*f^2-16*c*d*e*f+35*d^2*e^2)/d/(-c*f+d*e))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/f^3+1/10*(b*e*(-2*c*f+7*d*e)-2*a*f*(-c*f+d*e))*x*sqrt(b*x^2+a)*(d*x^2+c)^(3/2)/d/f^2/(-a*f+b*e)/(-c*f+d*e)-1/2*e^2*x*(b*x^2+a)^(3/2)*(d*x^2+c)^(3/2)/f/(-a*f+b*e)/(-c*f+d*e)/(f*x^2+e)+1/30*sqrt(a)*(4*a^2*d^2*f^2+4*a*b*d*f*(-c*f+5*d*e)-b^2*(-4*c^2*f^2-20*c*d*e*f+105*d^2*e^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/f^4/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/30*a^(3/2)*(2*a^2*c*d*f^3+b^2*e*(-2*c^2*f^2-55*c*d*e*f+105*d^2*e^2)-2*a*b*f*(-c^2*f^2-19*c*d*e*f+45*d^2*e^2))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(3/2)/c/d/f^4/(-a*f+b*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/2*a^(3/2)*e*(b*e*(-6*c*f+7*d*e)-a*f*(-5*c*f+6*d*e))*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/f^4/(-a*f+b*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[x^4*sqrt(b*x^2+a)*sqrt(d*x^2+c)/(f*x^2+e)^2,x,7,-1/6*(-2*a*d*f-2*b*c*f+15*b*d*e)*x*sqrt(d*x^2+c)/d/f^3/sqrt(b*x^2+a)+1/6*(-2*c*f+5*d*e)*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/f^2/(-c*f+d*e)-1/2*b*e*x*sqrt(b*x^2+a)*(d*x^2+c)^(3/2)/f/(-a*f+b*e)/(-c*f+d*e)+1/2*e*x*(b*x^2+a)^(3/2)*(d*x^2+c)^(3/2)/(-a*f+b*e)/(-c*f+d*e)/(f*x^2+e)+1/6*sqrt(a)*(-2*a*d*f-2*b*c*f+15*b*d*e)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/sqrt(b)/d/f^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/6*a^(3/2)*(b*e*(-7*c*f+15*d*e)-4*a*f*(-c*f+3*d*e))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(b)/c/f^3/(-a*f+b*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/2*a^(3/2)*(b*e*(-4*c*f+5*d*e)-a*f*(-3*c*f+4*d*e))*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/f^3/(-a*f+b*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[x^2*sqrt(b*x^2+a)*sqrt(d*x^2+c)/(f*x^2+e)^2,x,7,3/2*b*x*sqrt(d*x^2+c)/f^2/sqrt(b*x^2+a)-1/2*d*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/f/(-c*f+d*e)+1/2*b*x*sqrt(b*x^2+a)*(d*x^2+c)^(3/2)/(-a*f+b*e)/(-c*f+d*e)-1/2*f*x*(b*x^2+a)^(3/2)*(d*x^2+c)^(3/2)/(-a*f+b*e)/(-c*f+d*e)/(f*x^2+e)-3/2*sqrt(a)*sqrt(b)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/f^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/2*a^(3/2)*(-2*a*d*f-b*c*f+3*b*d*e)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(b)/c/f^2/(-a*f+b*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/2*a^(3/2)*(b*e*(-2*c*f+3*d*e)-a*f*(-c*f+2*d*e))*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e/f^2/(-a*f+b*e)/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)/(f*x^2+e)^2,x,5,-1/2*b*x*sqrt(d*x^2+c)/e/f/sqrt(b*x^2+a)+1/2*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/e/(f*x^2+e)+1/2*sqrt(a)*sqrt(b)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/e/f/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/2*a^(3/2)*sqrt(b)*(-c*f+d*e)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/c/e/f/(-a*f+b*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/2*a^(3/2)*(-a*c*f^2+b*d*e^2)*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e^2/f/(-a*f+b*e)/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^2/(f*x^2+e)^2,x,8,3/2*b*x*sqrt(d*x^2+c)/e^2/sqrt(b*x^2+a)+1/2*d*(-3*c*f+2*d*e)*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/c/e^2/(-c*f+d*e)-1/2*b*(a*f*(-3*c*f+2*d*e)-2*b*e*(-c*f+d*e))*x*sqrt(b*x^2+a)*(d*x^2+c)^(3/2)/a/c/e^2/(-a*f+b*e)/(-c*f+d*e)-(b*x^2+a)^(3/2)*(d*x^2+c)^(3/2)/a/c/e/x/(f*x^2+e)+1/2*f*(a*f*(-3*c*f+2*d*e)-2*b*e*(-c*f+d*e))*x*(b*x^2+a)^(3/2)*(d*x^2+c)^(3/2)/a/c/e^2/(-a*f+b*e)/(-c*f+d*e)/(f*x^2+e)-3/2*sqrt(a)*sqrt(b)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/e^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/2*sqrt(a)*sqrt(b)*(-3*a*c*f+a*d*e+2*b*c*e)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/c/e^2/(-a*f+b*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/2*a^(3/2)*(a*f*(-3*c*f+2*d*e)-b*e*(-2*c*f+d*e))*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e^3/(-a*f+b*e)/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^4/(f*x^2+e)^2,x,9,1/6*b*(-15*a*c*f+2*a*d*e+2*b*c*e)*x*sqrt(d*x^2+c)/a/c/e^3/sqrt(b*x^2+a)+1/6*d*(2*b-3*a*f*(-5*c*f+4*d*e)/e/(-c*f+d*e))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a/c/e^2+1/2*b*f*(a*f*(-5*c*f+4*d*e)-4*b*e*(-c*f+d*e))*x*sqrt(b*x^2+a)*(d*x^2+c)^(3/2)/a/c/e^3/(-a*f+b*e)/(-c*f+d*e)-1/3*(b*x^2+a)^(3/2)*(d*x^2+c)^(3/2)/a/c/e/x^3/(f*x^2+e)+5/3*f*(b*x^2+a)^(3/2)*(d*x^2+c)^(3/2)/a/c/e^2/x/(f*x^2+e)-1/2*f^2*(a*f*(-5*c*f+4*d*e)-4*b*e*(-c*f+d*e))*x*(b*x^2+a)^(3/2)*(d*x^2+c)^(3/2)/a/c/e^3/(-a*f+b*e)/(-c*f+d*e)/(f*x^2+e)-1/6*sqrt(b)*(-15*a*c*f+2*a*d*e+2*b*c*e)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/sqrt(a)/c/e^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/6*sqrt(a)*sqrt(b)*(a*f*(-15*c*f+7*d*e)-4*b*e*(-3*c*f+d*e))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/c/e^3/(-a*f+b*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/2*a^(3/2)*f*(a*f*(-5*c*f+4*d*e)-b*e*(-4*c*f+3*d*e))*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e^4/(-a*f+b*e)/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^6/(f*x^2+e)^2,x,10,-1/30*b*(4*b^2*c^2*e^2-4*a*b*c*e*(-5*c*f+d*e)+a^2*(-105*c^2*f^2+20*c*d*e*f+4*d^2*e^2))*x*sqrt(d*x^2+c)/a^2/c^2/e^4/sqrt(b*x^2+a)+1/30*d*(15*a^2*c*f^2*(-7*c*f+6*d*e)-4*b^2*c*e^2*(-c*f+d*e)+2*a*b*e*(10*c^2*f^2-11*c*d*e*f+d^2*e^2))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a^2/c^2/e^4/(-c*f+d*e)-1/10*b*(5*a^2*c*f^3*(-7*c*f+6*d*e)-2*b^2*d*e^3*(-c*f+d*e)+2*a*b*e*f*(15*c^2*f^2-16*c*d*e*f+d^2*e^2))*x*sqrt(b*x^2+a)*(d*x^2+c)^(3/2)/a^2/c^2/e^4/(-a*f+b*e)/(-c*f+d*e)-1/5*(b*x^2+a)^(3/2)*(d*x^2+c)^(3/2)/a/c/e/x^5/(f*x^2+e)+1/15*(7*a*c*f+2*a*d*e+2*b*c*e)*(b*x^2+a)^(3/2)*(d*x^2+c)^(3/2)/a^2/c^2/e^2/x^3/(f*x^2+e)+1/15*(a*f*(-35*c*f+2*d*e)-b*e*(-2*c*f+3*d*e))*(b*x^2+a)^(3/2)*(d*x^2+c)^(3/2)/a^2/c^2/e^3/x/(f*x^2+e)+1/10*f*(5*a^2*c*f^3*(-7*c*f+6*d*e)-2*b^2*d*e^3*(-c*f+d*e)+2*a*b*e*f*(15*c^2*f^2-16*c*d*e*f+d^2*e^2))*x*(b*x^2+a)^(3/2)*(d*x^2+c)^(3/2)/a^2/c^2/e^4/(-a*f+b*e)/(-c*f+d*e)/(f*x^2+e)+1/30*sqrt(b)*(4*b^2*c^2*e^2-4*a*b*c*e*(-5*c*f+d*e)+a^2*(-105*c^2*f^2+20*c*d*e*f+4*d^2*e^2))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/a^(3/2)/c^2/e^4/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/30*sqrt(b)*(2*b^2*c*d*e^3-a^2*f*(-105*c^2*f^2+55*c*d*e*f+2*d^2*e^2)+2*a*b*e*(-45*c^2*f^2+19*c*d*e*f+d^2*e^2))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(a)/c^2/e^4/(-a*f+b*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/2*a^(3/2)*f^2*(a*f*(-7*c*f+6*d*e)-b*e*(-6*c*f+5*d*e))*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e^5/(-a*f+b*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[x^6*sqrt(b*x^2+a)*(d*x^2+c)^(3/2)*(f*x^2+e)^2,x,11,1/45045*(1024*a^7*d^7*f^2-128*a^6*b*d^6*f*(13*c*f+20*d*e)-a^4*b^3*c*d^4*(-129*c^2*f^2+828*c*d*e*f+3016*d^2*e^2)+16*a*b^6*c^4*d*(8*c^2*f^2-27*c*d*e*f+26*d^2*e^2)+32*a^5*b^2*d^5*(9*c^2*f^2+136*c*d*e*f+52*d^2*e^2)-16*b^7*c^5*(16*c^2*f^2-48*c*d*e*f+39*d^2*e^2)+a^2*b^5*c^3*d^2*(90*c^2*f^2-334*c*d*e*f+377*d^2*e^2)+a^3*b^4*c^2*d^3*(93*c^2*f^2-406*c*d*e*f+663*d^2*e^2))*x*sqrt(d*x^2+c)/b^6/d^6/sqrt(b*x^2+a)-1/45045*(512*a^6*d^6*f^3-256*a^5*b*d^5*f^2*(3*c*f+5*d*e)-a^2*b^4*c^2*d^2*f*(-45*c^2*f^2+170*c*d*e*f+2577*d^2*e^2)-3*a^3*b^3*c*d^3*f*(-17*c^2*f^2+74*c*d*e*f+468*d^2*e^2)+8*a^4*b^2*d^4*f*(9*c^2*f^2+252*c*d*e*f+104*d^2*e^2)-8*b^6*c^4*f*(16*c^2*f^2-48*c*d*e*f+39*d^2*e^2)+a*b^5*c^2*d*(48*c^3*f^3-168*c^2*d*e*f^2-2141*c*d^2*e^2*f+924*d^3*e^3))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b^6/d^5/f+1/45045*(384*a^5*d^5*f^3-80*a^4*b*d^4*f^2*(7*c*f+12*d*e)+a^2*b^3*c*d^2*f*(33*c^2*f^2+5418*c*d*e*f+4517*d^2*e^2)+a^3*b^2*d^3*f*(39*c^2*f^2+1472*c*d*e*f+624*d^2*e^2)-2*a*b^4*c*d*(-16*c^3*f^3-2253*c^2*d*e*f^2-1329*c*d^2*e^2*f+924*d^3*e^3)-12*b^5*c^2*(8*c^3*f^3-24*c^2*d*e*f^2-173*c*d^2*e^2*f+77*d^3*e^3))*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b^5/d^4/f-1/45045*(320*a^4*d^4*f^3-20*a^3*b*d^3*f^2*(23*c*f+40*d*e)-a^2*b^2*d^2*f*(2745*c^2*f^2+9878*c*d*e*f+2252*d^2*e^2)+a*b^3*d*(-2285*c^3*f^3-7944*c^2*d*e*f^2+1003*c*d^2*e^2*f+924*d^3*e^3)+4*b^4*c*(-20*c^3*f^3-1095*c^2*d*e*f^2+9*c*d^2*e^2*f+462*d^3*e^3))*x^5*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b^4/d^3/f+1/6435*(40*a^3*d^3*f^3+a^2*b*d^2*f^2*(735*c*f+692*d*e)-2*a*b^2*d*f*(-315*c^2*f^2-207*c*d*e*f+116*d^2*e^2)-4*b^3*(-80*c^3*f^3-90*c^2*d*e*f^2+69*c*d^2*e^2*f+33*d^3*e^3))*x^7*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b^3/d^2/f+1/2145*(120*a^2*d^2*f^2-3*a*b*d*f*(-35*c*f+12*d*e)-4*b^2*(-20*c^2*f^2+5*c*d*e*f+9*d^2*e^2))*x^9*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b^2/d-2/195*(6*a/b+5*c/d-2*e/f)*x*(b*x^2+a)^(3/2)*(d*x^2+c)^(5/2)*(f*x^2+e)^2/b/d+1/15*x^3*(b*x^2+a)^(3/2)*(d*x^2+c)^(5/2)*(f*x^2+e)^2/b/d-1/45045*sqrt(a)*(1024*a^7*d^7*f^2-128*a^6*b*d^6*f*(13*c*f+20*d*e)-a^4*b^3*c*d^4*(-129*c^2*f^2+828*c*d*e*f+3016*d^2*e^2)+16*a*b^6*c^4*d*(8*c^2*f^2-27*c*d*e*f+26*d^2*e^2)+32*a^5*b^2*d^5*(9*c^2*f^2+136*c*d*e*f+52*d^2*e^2)-16*b^7*c^5*(16*c^2*f^2-48*c*d*e*f+39*d^2*e^2)+a^2*b^5*c^3*d^2*(90*c^2*f^2-334*c*d*e*f+377*d^2*e^2)+a^3*b^4*c^2*d^3*(93*c^2*f^2-406*c*d*e*f+663*d^2*e^2))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/b^(13/2)/d^6/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/45045*a^(3/2)*(512*a^6*d^6*f^2-256*a^5*b*d^5*f*(3*c*f+5*d*e)-3*a^3*b^3*c*d^3*(-17*c^2*f^2+74*c*d*e*f+468*d^2*e^2)+5*a^2*b^4*c^2*d^2*(9*c^2*f^2-34*c*d*e*f+39*d^2*e^2)+8*a^4*b^2*d^4*(9*c^2*f^2+252*c*d*e*f+104*d^2*e^2)-8*b^6*c^4*(16*c^2*f^2-48*c*d*e*f+39*d^2*e^2)+a*b^5*c^3*d*(48*c^2*f^2-168*c*d*e*f+169*d^2*e^2))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(13/2)/d^5/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[x^4*sqrt(b*x^2+a)*(d*x^2+c)^(3/2)*(f*x^2+e)^2,x,10,-1/45045*(1280*a^6*d^6*f^2-128*a^5*b*d^5*f*(17*c*f+26*d*e)-a^3*b^3*c*d^3*(-203*c^2*f^2+1326*c*d*e*f+4576*d^2*e^2)-8*b^6*c^4*(48*c^2*f^2-156*c*d*e*f+143*d^2*e^2)+a^2*b^4*c^2*d^2*(167*c^2*f^2-754*c*d*e*f+1287*d^2*e^2)+2*a^4*b^2*d^4*(207*c^2*f^2+3016*c*d*e*f+1144*d^2*e^2)+a*b^5*c^3*d*(216*c^2*f^2-832*c*d*e*f+1001*d^2*e^2))*x*sqrt(d*x^2+c)/b^5/d^5/sqrt(b*x^2+a)+1/45045*(640*a^5*d^5*f^2-16*a^4*b*d^4*f*(63*c*f+104*d*e)-2*a*b^4*c^2*d*(-42*c^2*f^2+169*c*d*e*f+1518*d^2*e^2)-5*a^2*b^3*c*d^2*(-17*c^2*f^2+78*c*d*e*f+429*d^2*e^2)-4*b^5*c^3*(48*c^2*f^2-156*c*d*e*f+143*d^2*e^2)+a^3*b^2*d^3*(111*c^2*f^2+2808*c*d*e*f+1144*d^2*e^2))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b^5/d^4-1/45045*(480*a^4*d^4*f^2-32*a^3*b*d^3*f*(23*c*f+39*d*e)+12*b^4*c^2*(-12*c^2*f^2+39*c*d*e*f+253*d^2*e^2)+a*b^3*c*d*(57*c^2*f^2+6696*c*d*e*f+5357*d^2*e^2)+a^2*b^2*d^2*(63*c^2*f^2+2054*c*d*e*f+858*d^2*e^2))*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b^4/d^3+1/9009*(80*a^3*d^3*f^2-a^2*b*d^2*f*(121*c*f+208*d*e)+4*b^3*c*(-6*c^2*f^2-327*c*d*e*f+11*d^2*e^2)-2*a*b^2*d*(342*c^2*f^2+1217*c*d*e*f+275*d^2*e^2))*x^5*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b^3/d^2-1/1287*(10*a^2*d^2*f^2+a*b*d*f*(183*c*f+172*d*e)-b^2*(-96*c^2*f^2-84*c*d*e*f+44*d^2*e^2))*x^7*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b^2/d+2/143*f*(-5*a*d*f-4*b*c*f+2*b*d*e)*x^9*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b+1/13*x*(b*x^2+a)^(3/2)*(d*x^2+c)^(5/2)*(f*x^2+e)^2/b/d+1/45045*sqrt(a)*(1280*a^6*d^6*f^2-128*a^5*b*d^5*f*(17*c*f+26*d*e)-a^3*b^3*c*d^3*(-203*c^2*f^2+1326*c*d*e*f+4576*d^2*e^2)-8*b^6*c^4*(48*c^2*f^2-156*c*d*e*f+143*d^2*e^2)+a^2*b^4*c^2*d^2*(167*c^2*f^2-754*c*d*e*f+1287*d^2*e^2)+2*a^4*b^2*d^4*(207*c^2*f^2+3016*c*d*e*f+1144*d^2*e^2)+a*b^5*c^3*d*(216*c^2*f^2-832*c*d*e*f+1001*d^2*e^2))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/b^(11/2)/d^5/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/45045*a^(3/2)*(640*a^5*d^5*f^2-16*a^4*b*d^4*f*(63*c*f+104*d*e)-5*a^2*b^3*c*d^2*(-17*c^2*f^2+78*c*d*e*f+429*d^2*e^2)-4*b^5*c^3*(48*c^2*f^2-156*c*d*e*f+143*d^2*e^2)+a*b^4*c^2*d*(84*c^2*f^2-338*c*d*e*f+429*d^2*e^2)+a^3*b^2*d^3*(111*c^2*f^2+2808*c*d*e*f+1144*d^2*e^2))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(11/2)/d^4/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[x^2*sqrt(b*x^2+a)*(d*x^2+c)^(3/2)*(f*x^2+e)^2,x,10,1/3465*(128*a^5*d^5*f^2-8*a^4*b*d^4*f*(29*c*f+44*d*e)-a^2*b^3*c*d^2*(-29*c^2*f^2+198*c*d*e*f+627*d^2*e^2)-2*b^5*c^3*(24*c^2*f^2-88*c*d*e*f+99*d^2*e^2)+a*b^4*c^2*d*(32*c^2*f^2-154*c*d*e*f+297*d^2*e^2)+a^3*b^2*d^3*(51*c^2*f^2+704*c*d*e*f+264*d^2*e^2))*x*sqrt(d*x^2+c)/b^4/d^4/sqrt(b*x^2+a)-1/3465*(64*a^4*d^4*f^2-4*a^3*b*d^3*f*(27*c*f+44*d*e)-a*b^3*c*d*(-13*c^2*f^2+66*c*d*e*f+297*d^2*e^2)+3*a^2*b^2*d^2*(5*c^2*f^2+110*c*d*e*f+44*d^2*e^2)-b^4*c^2*(24*c^2*f^2-88*c*d*e*f+99*d^2*e^2))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b^4/d^3+1/3465*(48*a^3*d^3*f^2-a^2*b*d^2*f*(79*c*f+132*d*e)+6*b^3*c*(-3*c^2*f^2+11*c*d*e*f+132*d^2*e^2)+a*b^2*d*(9*c^2*f^2+242*c*d*e*f+99*d^2*e^2))*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b^3/d^2-1/693*(8*a^2*d^2*f^2-a*b*d*f*(13*c*f+22*d*e)-b^2*(3*c^2*f^2+220*c*d*e*f+99*d^2*e^2))*x^5*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b^2/d+1/99*f*(a*d*f+12*b*c*f+22*b*d*e)*x^7*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b+1/11*d*f^2*x^9*sqrt(b*x^2+a)*sqrt(d*x^2+c)-1/3465*sqrt(a)*(128*a^5*d^5*f^2-8*a^4*b*d^4*f*(29*c*f+44*d*e)-a^2*b^3*c*d^2*(-29*c^2*f^2+198*c*d*e*f+627*d^2*e^2)-2*b^5*c^3*(24*c^2*f^2-88*c*d*e*f+99*d^2*e^2)+a*b^4*c^2*d*(32*c^2*f^2-154*c*d*e*f+297*d^2*e^2)+a^3*b^2*d^3*(51*c^2*f^2+704*c*d*e*f+264*d^2*e^2))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/b^(9/2)/d^4/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/3465*a^(3/2)*(64*a^4*d^4*f^2-4*a^3*b*d^3*f*(27*c*f+44*d*e)-a*b^3*c*d*(-13*c^2*f^2+66*c*d*e*f+297*d^2*e^2)+3*a^2*b^2*d^2*(5*c^2*f^2+110*c*d*e*f+44*d^2*e^2)-b^4*c^2*(24*c^2*f^2-88*c*d*e*f+99*d^2*e^2))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(9/2)/d^3/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)*(f*x^2+e)^2,x,8,-1/315*(16*a^4*d^4*f^2-16*a^3*b*d^3*f*(2*c*f+3*d*e)-a*b^3*c*d*(-7*c^2*f^2+54*c*d*e*f+147*d^2*e^2)+3*a^2*b^2*d^2*(3*c^2*f^2+38*c*d*e*f+14*d^2*e^2)-b^4*c^2*(8*c^2*f^2-36*c*d*e*f+63*d^2*e^2))*x*sqrt(d*x^2+c)/b^3/d^3/sqrt(b*x^2+a)+1/315*(8*a^3*d^3*f^2-3*a^2*b*d^2*f*(5*c*f+8*d*e)+2*b^3*c*(-2*c^2*f^2+9*c*d*e*f+63*d^2*e^2)+3*a*b^2*d*(c^2*f^2+18*c*d*e*f+7*d^2*e^2))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b^3/d^2-1/315*(6*a^2*d^2*f^2-a*b*d*f*(11*c*f+18*d*e)-3*b^2*(c^2*f^2+48*c*d*e*f+21*d^2*e^2))*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b^2/d+1/63*f*(a*d*f+10*b*c*f+18*b*d*e)*x^5*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b+1/9*d*f^2*x^7*sqrt(b*x^2+a)*sqrt(d*x^2+c)+1/315*sqrt(a)*(16*a^4*d^4*f^2-16*a^3*b*d^3*f*(2*c*f+3*d*e)-a*b^3*c*d*(-7*c^2*f^2+54*c*d*e*f+147*d^2*e^2)+3*a^2*b^2*d^2*(3*c^2*f^2+38*c*d*e*f+14*d^2*e^2)-b^4*c^2*(8*c^2*f^2-36*c*d*e*f+63*d^2*e^2))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/b^(7/2)/d^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/315*a^(3/2)*(8*a^3*d^3*f^2-3*a^2*b*d^2*f*(5*c*f+8*d*e)+3*a*b^2*d*(c^2*f^2+18*c*d*e*f+7*d^2*e^2)-b^3*c*(4*c^2*f^2-18*c*d*e*f+189*d^2*e^2))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(7/2)/d^2/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)*(f*x^2+e)^2/x^2,x,11,1/105*(8*a^3*d^3*f^2-a^2*b*d^2*f*(19*c*f+28*d*e)+b^3*c*(-6*c^2*f^2+42*c*d*e*f+245*d^2*e^2)+a*b^2*d*(9*c^2*f^2+98*c*d*e*f+35*d^2*e^2))*x*sqrt(d*x^2+c)/b^2/d^2/sqrt(b*x^2+a)+1/105*(105*b*c*e^2/a+245*d*e^2+399*c*e*f+3*c^2*f^2/d-4*a^2*d*f^2/b^2+a*f*(9*c*f+14*d*e)/b)*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)+1/35*(35*d^2*e^2/c+224*d*e*f+113*c*f^2+a*d*f^2/b+35*b*e*(3*c*f+2*d*e)/a)*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)+1/7*(7*b*e*(3*c^2*f^2+6*c*d*e*f+d^2*e^2)+a*f*(7*c^2*f^2+43*c*d*e*f+21*d^2*e^2))*x^5*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a/c/e+f*(a*d*f*(2*c*f+3*d*e)+b*(c^2*f^2+6*c*d*e*f+3*d^2*e^2))*x^7*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a/c/e+d*f^2*(a*d*f+2*b*c*f+3*b*d*e)*x^9*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a/c/e+b*d^2*f^3*x^11*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a/c/e-(b*x^2+a)^(3/2)*(d*x^2+c)^(5/2)*(f*x^2+e)^3/a/c/e/x-1/105*sqrt(a)*(8*a^3*d^3*f^2-a^2*b*d^2*f*(19*c*f+28*d*e)+b^3*c*(-6*c^2*f^2+42*c*d*e*f+245*d^2*e^2)+a*b^2*d*(9*c^2*f^2+98*c*d*e*f+35*d^2*e^2))*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))+1/105*sqrt(a)*(105*b^3*c*d*e^2+4*a^3*d^2*f^2-a^2*b*d*f*(9*c*f+14*d*e)+a*b^2*(-3*c^2*f^2+126*c*d*e*f+175*d^2*e^2))*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)^(3/2)*(f*x^2+e)^2/x^4,x,12,1/15*(5*b^2*c*e^2/a-2*a^2*d*f^2/b+a*f*(7*c*f+10*d*e)+b*(35*d*e^2+70*c*e*f+3*c^2*f^2/d))*x*sqrt(d*x^2+c)/sqrt(b*x^2+a)+1/15*(25*d^2*e^2/c+100*d*e*f+66*c*f^2+a*d*f^2/b+10*b*e*(3*c*f+2*d*e)/a)*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)+1/15*(5*b*c*e*(12*c^2*f^2+18*c*d*e*f+5*d^2*e^2)+a*(50*c^3*f^3+153*c^2*d*e*f^2+90*c*d^2*e^2*f+10*d^3*e^3))*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a/c^2/e+1/3*(a*f*(3*c^3*f^3+22*c^2*d*e*f^2+24*c*d^2*e^2*f+6*d^3*e^3)+2*b*e*(5*c^3*f^3+15*c^2*d*e*f^2+9*c*d^2*e^2*f+d^3*e^3))*x^5*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a/c^2/e^2+1/3*f*(2*a*d*f*(3*c^2*f^2+7*c*d*e*f+3*d^2*e^2)+b*(3*c^3*f^3+22*c^2*d*e*f^2+24*c*d^2*e^2*f+6*d^3*e^3))*x^7*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a/c^2/e^2+1/3*d*f^2*(a*d*f*(3*c*f+2*d*e)+2*b*(3*c^2*f^2+7*c*d*e*f+3*d^2*e^2))*x^9*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a/c^2/e^2+1/3*b*d^2*f^3*(3*c*f+2*d*e)*x^11*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a/c^2/e^2-1/3*(b*x^2+a)^(3/2)*(d*x^2+c)^(5/2)*(f*x^2+e)^3/a/c/e/x^3-1/3*(3*c*f+2*d*e)*(b*x^2+a)^(3/2)*(d*x^2+c)^(5/2)*(f*x^2+e)^3/a/c^2/e^2/x-1/15*(5*b^3*c*d*e^2-2*a^3*d^2*f^2+a^2*b*d*f*(7*c*f+10*d*e)+a*b^2*(3*c^2*f^2+70*c*d*e*f+35*d^2*e^2))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/sqrt(a)/b^(3/2)/d/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/15*sqrt(a)*(a^2*c*d*f^2-5*b^2*c*e*(6*c*f+5*d*e)-a*b*(9*c^2*f^2+50*c*d*e*f+15*d^2*e^2))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(3/2)/c/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)*(f*x^2+e)^2/x^6,x,13,-1/15*(2*b^3*c^2*e^2-5*a^3*c*d*f^2-a*b^2*c*e*(10*c*f+7*d*e)-a^2*b*(35*c^2*f^2+70*c*d*e*f+3*d^2*e^2))*x*sqrt(d*x^2+c)/a^2/c/sqrt(b*x^2+a)+1/15*(b^2*c*d*e^3+5*a^2*f*(3*c^2*f^2+19*c*d*e*f+10*d^2*e^2)+a*b*e*(27*c^2*f^2+55*c*d*e*f+11*d^2*e^2))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a^2/c/e+1/15*(b^2*c*e^2*(12*c^2*f^2+15*c*d*e*f+8*d^2*e^2)+5*a^2*f*(2*c^3*f^3+18*c^2*d*e*f^2+27*c*d^2*e^2*f+4*d^3*e^3)+a*b*e*(31*c^3*f^3+129*c^2*d*e*f^2+80*c*d^2*e^2*f+5*d^3*e^3))*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a^2/c^2/e^2+1/15*(a^2*f^2*(3*c^3*f^3+40*c^2*d*e*f^2+135*c*d^2*e^2*f+60*d^3*e^3)+b^2*e^2*(16*c^3*f^3+39*c^2*d*e*f^2+30*c*d^2*e^2*f+5*d^3*e^3)+a*b*e*f*(16*c^3*f^3+127*c^2*d*e*f^2+177*c*d^2*e^2*f+35*d^3*e^3))*x^5*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a^2/c^2/e^3+1/15*f*(2*a^2*d*f^2*(3*c^2*f^2+25*c*d*e*f+30*d^2*e^2)+a*b*f*(3*c^3*f^3+52*c^2*d*e*f^2+161*c*d^2*e^2*f+75*d^3*e^3)+b^2*e*(6*c^3*f^3+37*c^2*d*e*f^2+42*c*d^2*e^2*f+15*d^3*e^3))*x^7*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a^2/c^2/e^3+1/15*d*f^2*(a^2*d*f^2*(3*c*f+20*d*e)+a*b*f*(6*c^2*f^2+56*c*d*e*f+65*d^2*e^2)+b^2*e*(12*c^2*f^2+26*c*d*e*f+15*d^2*e^2))*x^9*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a^2/c^2/e^3+1/15*b*d^2*f^3*(a*f*(3*c*f+20*d*e)+b*e*(6*c*f+5*d*e))*x^11*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a^2/c^2/e^3-1/5*(b*x^2+a)^(3/2)*(d*x^2+c)^(5/2)*(f*x^2+e)^3/a/c/e/x^5+1/15*(-a*f+2*b*e)*(b*x^2+a)^(3/2)*(d*x^2+c)^(5/2)*(f*x^2+e)^3/a^2/c/e^2/x^3-1/15*(a*f*(3*c*f+20*d*e)+b*e*(6*c*f+5*d*e))*(b*x^2+a)^(3/2)*(d*x^2+c)^(5/2)*(f*x^2+e)^3/a^2/c^2/e^3/x+1/15*(2*b^3*c^2*e^2-5*a^3*c*d*f^2-a*b^2*c*e*(10*c*f+7*d*e)-a^2*b*(35*c^2*f^2+70*c*d*e*f+3*d^2*e^2))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/a^(3/2)/sqrt(b)/c/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/15*(b^2*c*d*e^2-5*a^2*d*f*(5*c*f+6*d*e)-a*b*(15*c^2*f^2+50*c*d*e*f+9*d^2*e^2))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(a)/sqrt(b)/c/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[x^2*sqrt(b*x^2+a)*(d*x^2+c)^(3/2)*(f*x^2+e),x,8,-1/315*(16*a^4*d^4*f-a*b^3*c^2*d*(-7*c*f+27*d*e)+2*b^4*c^3*(-4*c*f+9*d*e)+3*a^2*b^2*c*d^2*(3*c*f+19*d*e)-8*a^3*b*d^3*(4*c*f+3*d*e))*x*sqrt(d*x^2+c)/b^3/d^3/sqrt(b*x^2+a)+1/315*(8*a^3*d^3*f+b^3*c^2*(-4*c*f+9*d*e)+3*a*b^2*c*d*(c*f+9*d*e)-3*a^2*b*d^2*(5*c*f+4*d*e))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b^3/d^2+1/105*(24*b*c*e-12*a*d*e-13*a*c*f+b*c^2*f/d+8*a^2*d*f/b)*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b+1/21*(-2*a*d*f+b*c*f+3*b*d*e)*x^3*(b*x^2+a)^(3/2)*sqrt(d*x^2+c)/b^2+1/9*f*x^3*(b*x^2+a)^(3/2)*(d*x^2+c)^(3/2)/b+1/315*sqrt(a)*(16*a^4*d^4*f-a*b^3*c^2*d*(-7*c*f+27*d*e)+2*b^4*c^3*(-4*c*f+9*d*e)+3*a^2*b^2*c*d^2*(3*c*f+19*d*e)-8*a^3*b*d^3*(4*c*f+3*d*e))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/b^(7/2)/d^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/315*a^(3/2)*(8*a^3*d^3*f+b^3*c^2*(-4*c*f+9*d*e)+3*a*b^2*c*d*(c*f+9*d*e)-3*a^2*b*d^2*(5*c*f+4*d*e))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(7/2)/d^2/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)*(f*x^2+e),x,7,1/105*(8*a^3*d^3*f+3*b^3*c^2*(-2*c*f+7*d*e)+a*b^2*c*d*(9*c*f+49*d*e)-a^2*b*d^2*(19*c*f+14*d*e))*x*sqrt(d*x^2+c)/b^2/d^2/sqrt(b*x^2+a)-1/105*(4*a^2*d^2*f-3*b^2*c*(-2*c*f+7*d*e)-a*b*d*(6*c*f+7*d*e))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b^2/d+1/35*(a*d*f-2*b*c*f+7*b*d*e)*x*sqrt(b*x^2+a)*(d*x^2+c)^(3/2)/b/d+1/7*f*x*sqrt(b*x^2+a)*(d*x^2+c)^(5/2)/d-1/105*sqrt(a)*(8*a^3*d^3*f+3*b^3*c^2*(-2*c*f+7*d*e)+a*b^2*c*d*(9*c*f+49*d*e)-a^2*b*d^2*(19*c*f+14*d*e))*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))+1/105*a^(3/2)*(4*a^2*d^2*f+3*b^2*c*(-c*f+21*d*e)-a*b*d*(9*c*f+7*d*e))*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)^(3/2)*(f*x^2+e)/x^2,x,7,-1/15*(2*a^2*d^2*f-b^2*c*(3*c*f+35*d*e)-a*b*d*(7*c*f+5*d*e))*x*sqrt(d*x^2+c)/b/d/sqrt(b*x^2+a)+1/15*(a*d*f+3*b*c*f+20*b*d*e)*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b+1/5*(a*f+5*b*e)*x*sqrt(b*x^2+a)*(d*x^2+c)^(3/2)/a-e*(b*x^2+a)^(3/2)*(d*x^2+c)^(3/2)/a/x+1/15*sqrt(a)*(2*a^2*d^2*f-b^2*c*(3*c*f+35*d*e)-a*b*d*(7*c*f+5*d*e))*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*sqrt(a)*(15*b^2*c*e-a^2*d*f+a*b*(9*c*f+25*d*e))*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],
[sqrt(b*x^2+a)*(d*x^2+c)^(3/2)*(f*x^2+e)/x^4,x,7,1/3*(b^2*c*e+a^2*d*f+7*a*b*(c*f+d*e))*x*sqrt(d*x^2+c)/a/sqrt(b*x^2+a)+1/3*(a*d*f+3*b*c*f+4*b*d*e)*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a-(c*f+d*e)*(b*x^2+a)^(3/2)*sqrt(d*x^2+c)/a/x-1/3*e*(b*x^2+a)^(3/2)*(d*x^2+c)^(3/2)/a/x^3-1/3*(b^2*c*e+a^2*d*f+7*a*b*(c*f+d*e))*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))+1/3*sqrt(a)*(b*c*(3*c*f+5*d*e)+a*d*(5*c*f+3*d*e))*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],
[sqrt(b*x^2+a)*(d*x^2+c)^(3/2)*(f*x^2+e)/x^6,x,7,-1/15*b*(2*b^2*c^2*e-a*b*c*(5*c*f+7*d*e)-a^2*d*(35*c*f+3*d*e))*x*sqrt(d*x^2+c)/a^2/c/sqrt(b*x^2+a)-1/15*d*(20*a*c*f+3*a*d*e+b*c*e)*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a/c/x+1/15*(-5*a*c*f-3*a*d*e+2*b*c*e)*(b*x^2+a)^(3/2)*sqrt(d*x^2+c)/a^2/x^3-1/5*e*(b*x^2+a)^(3/2)*(d*x^2+c)^(3/2)/a/x^5+1/15*sqrt(b)*(2*b^2*c^2*e-a*b*c*(5*c*f+7*d*e)-a^2*d*(35*c*f+3*d*e))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/a^(3/2)/c/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/15*d*(b^2*c*e-15*a^2*d*f-a*b*(25*c*f+9*d*e))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(a)/sqrt(b)/c/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)*(f*x^2+e)/x^8,x,5,-1/105*(8*b^3*c^3*e-3*a^3*d^2*(-7*c*f+2*d*e)-a*b^2*c^2*(14*c*f+19*d*e)+a^2*b*c*d*(49*c*f+9*d*e))*sqrt(d*x^2+c)/a^2/c^2/x/sqrt(b*x^2+a)-1/105*(8*b^2*c*e/a-15*b*d*e+3*a*d^2*e/c-14*b*c*f+42*a*d*f)*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a/x^3+1/35*(-7*a*c*f-3*a*d*e+4*b*c*e)*(b*x^2+a)^(3/2)*sqrt(d*x^2+c)/a^2/x^5-1/7*e*(b*x^2+a)^(3/2)*(d*x^2+c)^(3/2)/a/x^7-1/105*sqrt(b)*(8*b^3*c^3*e-3*a^3*d^2*(-7*c*f+2*d*e)-a*b^2*c^2*(14*c*f+19*d*e)+a^2*b*c*d*(49*c*f+9*d*e))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/a^(5/2)/c^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/105*sqrt(b)*d*(4*b^2*c^2*e-3*a^2*d*(-21*c*f+d*e)-a*b*c*(7*c*f+9*d*e))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/a^(3/2)/c^2/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)*(f*x^2+e)/x^10,x,6,1/315*(16*b^4*c^4*e+a^3*b*c*d^2*(-27*c*f+7*d*e)-2*a^4*d^3*(-9*c*f+4*d*e)-8*a*b^3*c^3*(3*c*f+4*d*e)+3*a^2*b^2*c^2*d*(19*c*f+3*d*e))*sqrt(d*x^2+c)/a^3/c^3/x/sqrt(b*x^2+a)-1/105*(8*b^2*c*e/a-13*b*d*e+a*d^2*e/c-12*b*c*f+24*a*d*f)*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a/x^5-1/315*(8*b^3*c^3*e-a^3*d^2*(-9*c*f+4*d*e)-3*a*b^2*c^2*(4*c*f+5*d*e)+3*a^2*b*c*d*(9*c*f+d*e))*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a^3/c^2/x^3+1/21*(-3*a*c*f-a*d*e+2*b*c*e)*(b*x^2+a)^(3/2)*sqrt(d*x^2+c)/a^2/x^7-1/9*e*(b*x^2+a)^(3/2)*(d*x^2+c)^(3/2)/a/x^9+1/315*sqrt(b)*(16*b^4*c^4*e+a^3*b*c*d^2*(-27*c*f+7*d*e)-2*a^4*d^3*(-9*c*f+4*d*e)-8*a*b^3*c^3*(3*c*f+4*d*e)+3*a^2*b^2*c^2*d*(19*c*f+3*d*e))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/a^(7/2)/c^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/315*sqrt(b)*d*(8*b^3*c^3*e-a^3*d^2*(-9*c*f+4*d*e)-3*a*b^2*c^2*(4*c*f+5*d*e)+3*a^2*b*c*d*(9*c*f+d*e))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/a^(5/2)/c^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[x^4*sqrt(b*x^2+a)*(d*x^2+c)^(3/2)/(f*x^2+e),x,7,1/105*(8*a^3*d^3*f^3+a^2*b*d^2*f^2*(-19*c*f+14*d*e)+a*b^2*d*f*(9*c^2*f^2-49*c*d*e*f+35*d^2*e^2)-b^3*(6*c^3*f^3+21*c^2*d*e*f^2-140*c*d^2*e^2*f+105*d^3*e^3))*x*sqrt(d*x^2+c)/b^2/d^2/f^4/sqrt(b*x^2+a)-1/105*(4*a^2*d^2*f/b+a*d*(-6*c*f+7*d*e)+b*(21*c*d*e-35*d^2*e^2/f+6*c^2*f))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b/d/f^2-1/35*(-a*d*f+2*b*c*f+7*b*d*e)*x*sqrt(b*x^2+a)*(d*x^2+c)^(3/2)/b/d/f^2+1/7*x*sqrt(b*x^2+a)*(d*x^2+c)^(5/2)/d/f-1/105*sqrt(a)*(8*a^3*d^3*f^3+a^2*b*d^2*f^2*(-19*c*f+14*d*e)+a*b^2*d*f*(9*c^2*f^2-49*c*d*e*f+35*d^2*e^2)-b^3*(6*c^3*f^3+21*c^2*d*e*f^2-140*c*d^2*e^2*f+105*d^3*e^3))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/b^(5/2)/d^2/f^4/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/105*a^(3/2)*(4*a^2*c*d^2*f^3+a*b*c*d*f^2*(-9*c*f+7*d*e)-b^2*(3*c^3*f^3+63*c^2*d*e*f^2-175*c*d^2*e^2*f+105*d^3*e^3))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(5/2)/c/d/f^4/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+a^(3/2)*e*(-c*f+d*e)^2*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/f^4/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[x^2*sqrt(b*x^2+a)*(d*x^2+c)^(3/2)/(f*x^2+e),x,6,-1/15*(2*a^2*d*f+a*b*(-7*c*f+5*d*e)+b^2*(20*c*e-15*d*e^2/f-3*c^2*f/d))*x*sqrt(d*x^2+c)/b/f^2/sqrt(b*x^2+a)-1/15*(-a*d*f-3*b*c*f+5*b*d*e)*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b/f^2+1/5*x*sqrt(b*x^2+a)*(d*x^2+c)^(3/2)/f+1/15*sqrt(a)*(2*a^2*d^2*f^2+a*b*d*f*(-7*c*f+5*d*e)-b^2*(3*c^2*f^2-20*c*d*e*f+15*d^2*e^2))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/b^(3/2)/d/f^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/15*a^(3/2)*(a*c*d*f^2-b*(9*c^2*f^2-25*c*d*e*f+15*d^2*e^2))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(3/2)/c/f^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-a^(3/2)*(-c*f+d*e)^2*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/f^3/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)/(f*x^2+e),x,5,-1/3*(-a*d*f-4*b*c*f+3*b*d*e)*x*sqrt(d*x^2+c)/f^2/sqrt(b*x^2+a)+1/3*d*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/f+1/3*sqrt(a)*(-a*d*f-4*b*c*f+3*b*d*e)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/sqrt(b)/f^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/3*a^(3/2)*d*(-5*c*f+3*d*e)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(b)/c/f^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+a^(3/2)*(-c*f+d*e)^2*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e/f^2/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^2/(f*x^2+e),x,8,b*(c*f+d*e)*x*sqrt(d*x^2+c)/e/f/sqrt(b*x^2+a)+(2*a*d+b*c)*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a/e+d*(a*d+2*b*c)*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a/c/e+b*d^2*x^5*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a/c/e-(b*x^2+a)^(3/2)*(d*x^2+c)^(5/2)/a/c/e/x-sqrt(a)*sqrt(b)*(c*f+d*e)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/e/f/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+sqrt(a)*(a*d^2*e+b*c^2*f)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(b)/c/e/f/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-a^(3/2)*(-c*f+d*e)^2*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e^2/f/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^4/(f*x^2+e),x,9,1/3*b*(-3*a*c*f+4*a*d*e+b*c*e)*x*sqrt(d*x^2+c)/a/e^2/sqrt(b*x^2+a)+1/3*(a*d*(-6*c*f+5*d*e)+b*c*(-3*c*f+4*d*e))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a/c/e^2+1/3*d*(b*c*(-6*c*f+5*d*e)+a*d*(-3*c*f+2*d*e))*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a/c^2/e^2+1/3*b*d^2*(-3*c*f+2*d*e)*x^5*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a/c^2/e^2-1/3*(b*x^2+a)^(3/2)*(d*x^2+c)^(5/2)/a/c/e/x^3-1/3*(-3*c*f+2*d*e)*(b*x^2+a)^(3/2)*(d*x^2+c)^(5/2)/a/c^2/e^2/x-1/3*sqrt(b)*(-3*a*c*f+4*a*d*e+b*c*e)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/sqrt(a)/e^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/3*sqrt(a)*sqrt(b)*(-3*c*f+5*d*e)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/e^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+a^(3/2)*(-c*f+d*e)^2*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e^3/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/(f*x^2+e),x,10,-1/15*b*(2*b^2*c^2*e^2-a*b*c*e*(-5*c*f+7*d*e)-a^2*(15*c^2*f^2-20*c*d*e*f+3*d^2*e^2))*x*sqrt(d*x^2+c)/a^2/c/e^3/sqrt(b*x^2+a)+1/15*(b^2*c*d*e^2-5*a^2*d*f*(-6*c*f+5*d*e)+a*b*(15*c^2*f^2-20*c*d*e*f+11*d^2*e^2))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a^2/c/e^3+1/15*d*(8*b^2*c*d*e^2-5*a^2*d*f*(-3*c*f+2*d*e)+5*a*b*(6*c^2*f^2-5*c*d*e*f+d^2*e^2))*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a^2/c^2/e^3+1/3*b*d^2*(b*d*e^2-a*f*(-3*c*f+2*d*e))*x^5*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a^2/c^2/e^3-1/5*(b*x^2+a)^(3/2)*(d*x^2+c)^(5/2)/a/c/e/x^5+1/15*(5*a*f+2*b*e)*(b*x^2+a)^(3/2)*(d*x^2+c)^(5/2)/a^2/c/e^2/x^3-1/3*(b*d*e^2-a*f*(-3*c*f+2*d*e))*(b*x^2+a)^(3/2)*(d*x^2+c)^(5/2)/a^2/c^2/e^3/x+1/15*sqrt(b)*(2*b^2*c^2*e^2-a*b*c*e*(-5*c*f+7*d*e)-a^2*(15*c^2*f^2-20*c*d*e*f+3*d^2*e^2))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/a^(3/2)/c/e^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/15*sqrt(b)*(b*c*d*e^2-a*(15*c^2*f^2-25*c*d*e*f+9*d^2*e^2))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(a)/c/e^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-a^(3/2)*f*(-c*f+d*e)^2*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e^4/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[x^4*sqrt(b*x^2+a)*(d*x^2+c)^(3/2)/(f*x^2+e)^2,x,8,-1/30*(4*a^2*d^2*f^2+2*a*b*d*f*(-7*c*f+10*d*e)-b^2*(6*c^2*f^2-95*c*d*e*f+105*d^2*e^2))*x*sqrt(d*x^2+c)/b/d/f^4/sqrt(b*x^2+a)-1/30*(2*a^2*d*f^2*(-c*f+d*e)-a*b*f*(12*c^2*f^2-64*c*d*e*f+37*d^2*e^2)+b^2*e*(27*c^2*f^2-62*c*d*e*f+35*d^2*e^2))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b/f^3/(-a*f+b*e)/(-c*f+d*e)+1/10*d*(b*e*(-12*c*f+7*d*e)-a*f*(-2*c*f+7*d*e))*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/f^2/(-a*f+b*e)/(-c*f+d*e)-1/2*b*d^2*e*x^5*sqrt(b*x^2+a)*sqrt(d*x^2+c)/f/(-a*f+b*e)/(-c*f+d*e)+1/2*e*x*(b*x^2+a)^(3/2)*(d*x^2+c)^(5/2)/(-a*f+b*e)/(-c*f+d*e)/(f*x^2+e)+1/30*sqrt(a)*(4*a^2*d^2*f^2+2*a*b*d*f*(-7*c*f+10*d*e)-b^2*(6*c^2*f^2-95*c*d*e*f+105*d^2*e^2))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/b^(3/2)/d/f^4/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/30*a^(3/2)*(2*a^2*c*d*f^3-2*a*b*f*(9*c^2*f^2-49*c*d*e*f+45*d^2*e^2)+b^2*e*(33*c^2*f^2-130*c*d*e*f+105*d^2*e^2))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(3/2)/c/f^4/(-a*f+b*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/2*a^(3/2)*(-c*f+d*e)*(b*e*(-4*c*f+7*d*e)-3*a*f*(-c*f+2*d*e))*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/f^4/(-a*f+b*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[x^2*sqrt(b*x^2+a)*(d*x^2+c)^(3/2)/(f*x^2+e)^2,x,8,-1/6*(-2*a*d*f-11*b*c*f+15*b*d*e)*x*sqrt(d*x^2+c)/f^3/sqrt(b*x^2+a)-1/6*(a*d*f*(-8*c*f+5*d*e)-b*(3*c^2*f^2-8*c*d*e*f+5*d^2*e^2))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/f^2/(-a*f+b*e)/(-c*f+d*e)-1/2*d*(-a*d*f-2*b*c*f+b*d*e)*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/f/(-a*f+b*e)/(-c*f+d*e)+1/2*b*d^2*x^5*sqrt(b*x^2+a)*sqrt(d*x^2+c)/(-a*f+b*e)/(-c*f+d*e)-1/2*f*x*(b*x^2+a)^(3/2)*(d*x^2+c)^(5/2)/(-a*f+b*e)/(-c*f+d*e)/(f*x^2+e)+1/6*sqrt(a)*(-2*a*d*f-11*b*c*f+15*b*d*e)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/sqrt(b)/f^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/6*a^(3/2)*(2*a*d*f*(-5*c*f+6*d*e)-b*(3*c^2*f^2-16*c*d*e*f+15*d^2*e^2))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(b)/c/f^3/(-a*f+b*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/2*a^(3/2)*(-c*f+d*e)*(b*e*(-2*c*f+5*d*e)-a*f*(-c*f+4*d*e))*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e/f^3/(-a*f+b*e)/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)/(f*x^2+e)^2,x,5,1/2*b*(-c*f+3*d*e)*x*sqrt(d*x^2+c)/e/f^2/sqrt(b*x^2+a)-1/2*(-c*f+d*e)*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/e/f/(f*x^2+e)-1/2*sqrt(a)*sqrt(b)*(-c*f+3*d*e)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/e/f^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/2*a^(3/2)*(2*a*d^2*e*f-b*(c^2*f^2-2*c*d*e*f+3*d^2*e^2))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(b)/c/e/f^2/(-a*f+b*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/2*a^(3/2)*(-c*f+d*e)*(3*b*d*e^2-a*f*(c*f+2*d*e))*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e^2/f^2/(-a*f+b*e)/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^2/(f*x^2+e)^2,x,9,-1/2*b*(-3*c*f+d*e)*x*sqrt(d*x^2+c)/e^2/f/sqrt(b*x^2+a)-1/2*(a^2*d*f*(-6*c*f+5*d*e)-2*b^2*c*e*(-c*f+d*e)-a*b*(3*c^2*f^2-8*c*d*e*f+5*d^2*e^2))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a/e^2/(-a*f+b*e)/(-c*f+d*e)-1/2*d*(a^2*d*f*(-3*c*f+2*d*e)-4*b^2*c*e*(-c*f+d*e)-a*b*(6*c^2*f^2-7*c*d*e*f+2*d^2*e^2))*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a/c/e^2/(-a*f+b*e)/(-c*f+d*e)-1/2*b*d^2*(a*f*(-3*c*f+2*d*e)-2*b*e*(-c*f+d*e))*x^5*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a/c/e^2/(-a*f+b*e)/(-c*f+d*e)-(b*x^2+a)^(3/2)*(d*x^2+c)^(5/2)/a/c/e/x/(f*x^2+e)+1/2*f*(a*f*(-3*c*f+2*d*e)-2*b*e*(-c*f+d*e))*x*(b*x^2+a)^(3/2)*(d*x^2+c)^(5/2)/a/c/e^2/(-a*f+b*e)/(-c*f+d*e)/(f*x^2+e)+1/2*sqrt(a)*sqrt(b)*(-3*c*f+d*e)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/e^2/f/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/2*sqrt(a)*sqrt(b)*(2*b*c^2*e*f-a*(3*c^2*f^2-2*c*d*e*f+d^2*e^2))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/c/e^2/f/(-a*f+b*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/2*a^(3/2)*(-c*f+d*e)*(3*a*c*f^2-b*e*(2*c*f+d*e))*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e^3/f/(-a*f+b*e)/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^4/(f*x^2+e)^2,x,10,1/6*b*(-15*a*c*f+11*a*d*e+2*b*c*e)*x*sqrt(d*x^2+c)/a/e^3/sqrt(b*x^2+a)+1/6*(4*b^2*c*e*(3*c^2*f^2-5*c*d*e*f+2*d^2*e^2)-a^2*d*f*(30*c^2*f^2-37*c*d*e*f+10*d^2*e^2)+5*a*b*(-3*c^3*f^3+10*c^2*d*e*f^2-9*c*d^2*e^2*f+2*d^3*e^3))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a/c/e^3/(-a*f+b*e)/(-c*f+d*e)+1/6*d*(2*b^2*c*e*(12*c^2*f^2-17*c*d*e*f+5*d^2*e^2)-a^2*d*f*(15*c^2*f^2-16*c*d*e*f+4*d^2*e^2)+a*b*(-30*c^3*f^3+49*c^2*d*e*f^2-26*c*d^2*e^2*f+4*d^3*e^3))*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a/c^2/e^3/(-a*f+b*e)/(-c*f+d*e)+1/6*b*d^2*(4*b*e*(3*c^2*f^2-4*c*d*e*f+d^2*e^2)-a*f*(15*c^2*f^2-16*c*d*e*f+4*d^2*e^2))*x^5*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a/c^2/e^3/(-a*f+b*e)/(-c*f+d*e)-1/3*(b*x^2+a)^(3/2)*(d*x^2+c)^(5/2)/a/c/e/x^3/(f*x^2+e)-1/3*(-5*c*f+2*d*e)*(b*x^2+a)^(3/2)*(d*x^2+c)^(5/2)/a/c^2/e^2/x/(f*x^2+e)-1/6*f*(4*b*e*(3*c^2*f^2-4*c*d*e*f+d^2*e^2)-a*f*(15*c^2*f^2-16*c*d*e*f+4*d^2*e^2))*x*(b*x^2+a)^(3/2)*(d*x^2+c)^(5/2)/a/c^2/e^3/(-a*f+b*e)/(-c*f+d*e)/(f*x^2+e)-1/6*sqrt(b)*(-15*a*c*f+11*a*d*e+2*b*c*e)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/sqrt(a)/e^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/6*sqrt(a)*sqrt(b)*(2*b*c*e*(-6*c*f+5*d*e)+a*(15*c^2*f^2-16*c*d*e*f+3*d^2*e^2))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/c/e^3/(-a*f+b*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/2*a^(3/2)*(-c*f+d*e)*(a*f*(-5*c*f+2*d*e)-b*e*(-4*c*f+d*e))*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e^4/(-a*f+b*e)/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/(f*x^2+e)^2,x,11,-1/30*b*(4*b^2*c^2*e^2-2*a*b*c*e*(-10*c*f+7*d*e)-a^2*(105*c^2*f^2-95*c*d*e*f+6*d^2*e^2))*x*sqrt(d*x^2+c)/a^2/c/e^4/sqrt(b*x^2+a)+1/30*(2*b^3*c*d*e^3*(-c*f+d*e)+5*a^3*d*f^2*(42*c^2*f^2-59*c*d*e*f+20*d^2*e^2)-a^2*b*f*(-105*c^3*f^3+380*c^2*d*e*f^2-397*c*d^2*e^2*f+122*d^3*e^3)+2*a*b^2*e*(-45*c^3*f^3+86*c^2*d*e*f^2-52*c*d^2*e^2*f+11*d^3*e^3))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a^2/c/e^4/(-a*f+b*e)/(-c*f+d*e)+1/30*d*(16*b^3*c*d*e^3*(-c*f+d*e)+5*a^3*d*f^2*(21*c^2*f^2-26*c*d*e*f+8*d^2*e^2)+2*a*b^2*e*(-90*c^3*f^3+148*c^2*d*e*f^2-63*c*d^2*e^2*f+5*d^3*e^3)-5*a^2*b*f*(-42*c^3*f^3+77*c^2*d*e*f^2-48*c*d^2*e^2*f+10*d^3*e^3))*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a^2/c^2/e^4/(-a*f+b*e)/(-c*f+d*e)+1/6*b*d^2*(2*b^2*d*e^3*(-c*f+d*e)-2*a*b*e*f*(9*c^2*f^2-14*c*d*e*f+5*d^2*e^2)+a^2*f^2*(21*c^2*f^2-26*c*d*e*f+8*d^2*e^2))*x^5*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a^2/c^2/e^4/(-a*f+b*e)/(-c*f+d*e)-1/5*(b*x^2+a)^(3/2)*(d*x^2+c)^(5/2)/a/c/e/x^5/(f*x^2+e)+1/15*(7*a*f+2*b*e)*(b*x^2+a)^(3/2)*(d*x^2+c)^(5/2)/a^2/c/e^2/x^3/(f*x^2+e)+1/15*(5*a*f*(-7*c*f+4*d*e)-b*e*(-2*c*f+5*d*e))*(b*x^2+a)^(3/2)*(d*x^2+c)^(5/2)/a^2/c^2/e^3/x/(f*x^2+e)-1/6*f*(2*b^2*d*e^3*(-c*f+d*e)-2*a*b*e*f*(9*c^2*f^2-14*c*d*e*f+5*d^2*e^2)+a^2*f^2*(21*c^2*f^2-26*c*d*e*f+8*d^2*e^2))*x*(b*x^2+a)^(3/2)*(d*x^2+c)^(5/2)/a^2/c^2/e^4/(-a*f+b*e)/(-c*f+d*e)/(f*x^2+e)+1/30*sqrt(b)*(4*b^2*c^2*e^2-2*a*b*c*e*(-10*c*f+7*d*e)-a^2*(105*c^2*f^2-95*c*d*e*f+6*d^2*e^2))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/a^(3/2)/c/e^4/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/30*sqrt(b)*(2*b^2*c*d*e^3-2*a*b*e*(45*c^2*f^2-49*c*d*e*f+9*d^2*e^2)+a^2*f*(105*c^2*f^2-130*c*d*e*f+33*d^2*e^2))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(a)/c/e^4/(-a*f+b*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/2*a^(3/2)*f*(-c*f+d*e)*(a*f*(-7*c*f+4*d*e)-3*b*e*(-2*c*f+d*e))*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e^5/(-a*f+b*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[x^2*sqrt(-b*x^2+a)*(d*x^2+c)^(3/2)/(f*x^2+e),x,12,-1/15*(a*d*f-3*b*c*f+5*b*d*e)*x*sqrt(-b*x^2+a)*sqrt(d*x^2+c)/b/f^2+1/5*x*sqrt(-b*x^2+a)*(d*x^2+c)^(3/2)/f+1/15*sqrt(a)*(2*a^2*d^2*f^2-a*b*d*f*(-7*c*f+5*d*e)-b^2*(3*c^2*f^2-20*c*d*e*f+15*d^2*e^2))*sqrt(1-b*x^2/a)*sqrt(d*x^2+c)*EllipticE(sin(arcsin(sqrt(b)*x/sqrt(a))),sqrt(-a*d/b/c))/b^(3/2)/d/f^3/sqrt(-b*x^2+a)/sqrt(1+d*x^2/c)-1/15*sqrt(a)*(a^2*c*d^2*f^3-a*b*d*f*(2*c^2*f^2-20*c*d*e*f+15*d^2*e^2)-b^2*(3*c^3*f^3-5*c^2*d*e*f^2-15*c*d^2*e^2*f+15*d^3*e^3))*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*InverseJacobiAM(arcsin(sqrt(b)*x/sqrt(a)),sqrt(-a*d/b/c))/b^(3/2)/d/f^4/sqrt(-b*x^2+a)/sqrt(d*x^2+c)-sqrt(a)*(a*f+b*e)*(-c*f+d*e)^2*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*EllipticPi(sin(arcsin(sqrt(b)*x/sqrt(a))),-a*f/b/e,sqrt(-a*d/b/c))/sqrt(b)/f^4/sqrt(-b*x^2+a)/sqrt(d*x^2+c),1],
[x^6*sqrt(b*x^2+a)*(f*x^2+e)^2/sqrt(d*x^2+c),x,9,1/3465*(128*a^5*d^5*f^2-8*a^4*b*d^4*f*(-15*c*f+44*d*e)+16*a*b^4*c^2*d*(24*c^2*f^2-55*c*d*e*f+33*d^2*e^2)-16*b^5*c^3*(80*c^2*f^2-176*c*d*e*f+99*d^2*e^2)+a^3*b^2*d^3*(139*c^2*f^2-352*c*d*e*f+264*d^2*e^2)+a^2*b^3*c*d^2*(194*c^2*f^2-462*c*d*e*f+297*d^2*e^2))*x*sqrt(d*x^2+c)/b^4/d^6/sqrt(b*x^2+a)-1/3465*(64*a^4*d^4*f^3-4*a^3*b*d^3*f^2*(-17*c*f+44*d*e)-a^2*b^2*d^2*f*(-81*c^2*f^2+198*c*d*e*f+148*d^2*e^2)-8*b^4*c^2*f*(80*c^2*f^2-176*c*d*e*f+99*d^2*e^2)+a*b^3*d*(112*c^3*f^3-264*c^2*d*e*f^2-185*c*d^2*e^2*f+140*d^3*e^3))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b^4/d^5/f+1/3465*(48*a^3*d^3*f^3+a^2*b*d^2*f^2*(53*c*f+428*d*e)-2*a*b^2*d*f*(-32*c^2*f^2-273*c*d*e*f+108*d^2*e^2)-4*b^3*(120*c^3*f^3-264*c^2*d*e*f^2+61*c*d^2*e^2*f+35*d^3*e^3))*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b^3/d^4/f+1/693*(48*a^2*d^2*f^2-a*b*d*f*(-61*c*f+20*d*e)-4*b^2*(-20*c^2*f^2+9*c*d*e*f+5*d^2*e^2))*x^5*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b^2/d^3-2/99*(4*a/b+5*c/d-2*e/f)*x*(b*x^2+a)^(3/2)*sqrt(d*x^2+c)*(f*x^2+e)^2/b/d+1/11*x^3*(b*x^2+a)^(3/2)*sqrt(d*x^2+c)*(f*x^2+e)^2/b/d-1/3465*sqrt(a)*(128*a^5*d^5*f^2-8*a^4*b*d^4*f*(-15*c*f+44*d*e)+16*a*b^4*c^2*d*(24*c^2*f^2-55*c*d*e*f+33*d^2*e^2)-16*b^5*c^3*(80*c^2*f^2-176*c*d*e*f+99*d^2*e^2)+a^3*b^2*d^3*(139*c^2*f^2-352*c*d*e*f+264*d^2*e^2)+a^2*b^3*c*d^2*(194*c^2*f^2-462*c*d*e*f+297*d^2*e^2))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/b^(9/2)/d^6/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/3465*a^(3/2)*(64*a^4*d^4*f^2-4*a^3*b*d^3*f*(-17*c*f+44*d*e)+3*a^2*b^2*d^2*(27*c^2*f^2-66*c*d*e*f+44*d^2*e^2)-8*b^4*c^2*(80*c^2*f^2-176*c*d*e*f+99*d^2*e^2)+a*b^3*c*d*(112*c^2*f^2-264*c*d*e*f+165*d^2*e^2))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(9/2)/d^5/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[x^4*sqrt(b*x^2+a)*(f*x^2+e)^2/sqrt(d*x^2+c),x,8,-1/315*(16*a^4*d^4*f^2-16*a^3*b*d^3*f*(-c*f+3*d*e)+3*a^2*b^2*d^2*(7*c^2*f^2-18*c*d*e*f+14*d^2*e^2)-8*b^4*c^2*(16*c^2*f^2-36*c*d*e*f+21*d^2*e^2)+a*b^3*c*d*(40*c^2*f^2-96*c*d*e*f+63*d^2*e^2))*x*sqrt(d*x^2+c)/b^3/d^5/sqrt(b*x^2+a)+1/315*(8*a^3*d^3*f^2-3*a^2*b*d^2*f*(-3*c*f+8*d*e)-2*a*b^2*d*(-6*c^2*f^2+15*c*d*e*f+7*d^2*e^2)-4*b^3*c*(16*c^2*f^2-36*c*d*e*f+21*d^2*e^2))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b^3/d^4-1/315*(6*a^2*d^2*f^2+a*b*d*f*(7*c*f+52*d*e)-4*b^2*(12*c^2*f^2-27*c*d*e*f+7*d^2*e^2))*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b^2/d^3+2/63*f*(-3*a*d*f-4*b*c*f+2*b*d*e)*x^5*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b/d^2+1/9*x*(b*x^2+a)^(3/2)*sqrt(d*x^2+c)*(f*x^2+e)^2/b/d+1/315*sqrt(a)*(16*a^4*d^4*f^2-16*a^3*b*d^3*f*(-c*f+3*d*e)+3*a^2*b^2*d^2*(7*c^2*f^2-18*c*d*e*f+14*d^2*e^2)-8*b^4*c^2*(16*c^2*f^2-36*c*d*e*f+21*d^2*e^2)+a*b^3*c*d*(40*c^2*f^2-96*c*d*e*f+63*d^2*e^2))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/b^(7/2)/d^5/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/315*a^(3/2)*(8*a^3*d^3*f^2-3*a^2*b*d^2*f*(-3*c*f+8*d*e)+3*a*b^2*d*(4*c^2*f^2-10*c*d*e*f+7*d^2*e^2)-4*b^3*c*(16*c^2*f^2-36*c*d*e*f+21*d^2*e^2))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(7/2)/d^4/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[x^2*sqrt(b*x^2+a)*(f*x^2+e)^2/sqrt(d*x^2+c),x,8,1/105*(8*a^3*d^3*f^2-a^2*b*d^2*f*(-9*c*f+28*d*e)+a*b^2*d*(16*c^2*f^2-42*c*d*e*f+35*d^2*e^2)-2*b^3*c*(24*c^2*f^2-56*c*d*e*f+35*d^2*e^2))*x*sqrt(d*x^2+c)/b^2/d^4/sqrt(b*x^2+a)-1/105*(4*a^2*d^2*f^2-a*b*d*f*(-5*c*f+14*d*e)-b^2*(24*c^2*f^2-56*c*d*e*f+35*d^2*e^2))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b^2/d^3+1/35*f*(a*d*f-6*b*c*f+14*b*d*e)*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b/d^2+1/7*f^2*x^5*sqrt(b*x^2+a)*sqrt(d*x^2+c)/d-1/105*sqrt(a)*(8*a^3*d^3*f^2-a^2*b*d^2*f*(-9*c*f+28*d*e)+a*b^2*d*(16*c^2*f^2-42*c*d*e*f+35*d^2*e^2)-2*b^3*c*(24*c^2*f^2-56*c*d*e*f+35*d^2*e^2))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/b^(5/2)/d^4/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/105*a^(3/2)*(4*a^2*d^2*f^2-a*b*d*f*(-5*c*f+14*d*e)-b^2*(24*c^2*f^2-56*c*d*e*f+35*d^2*e^2))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(5/2)/d^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[sqrt(b*x^2+a)*(f*x^2+e)^2/sqrt(d*x^2+c),x,6,-1/15*(2*a^2*d^2*f^2-a*b*d*f*(-3*c*f+10*d*e)-b^2*(8*c^2*f^2-20*c*d*e*f+15*d^2*e^2))*x*sqrt(d*x^2+c)/b/d^3/sqrt(b*x^2+a)+1/15*f*(a*d*f-4*b*c*f+10*b*d*e)*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b/d^2+1/5*f^2*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/d+1/15*sqrt(a)*(2*a^2*d^2*f^2-a*b*d*f*(-3*c*f+10*d*e)-b^2*(8*c^2*f^2-20*c*d*e*f+15*d^2*e^2))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/b^(3/2)/d^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/15*a^(3/2)*(a*c*d*f^2-b*(4*c^2*f^2-10*c*d*e*f+15*d^2*e^2))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(3/2)/c/d^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[sqrt(b*x^2+a)*(f*x^2+e)^2/x^2/sqrt(d*x^2+c),x,9,1/3*(a*c*d*f^2+b*(-2*c^2*f^2+6*c*d*e*f+3*d^2*e^2))*x*sqrt(d*x^2+c)/c/d^2/sqrt(b*x^2+a)+1/3*(3*b*d*e^2+a*f*(c*f+9*d*e))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a/c/d+3*f*(a*f+b*e)*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a/c+f^2*(a*f+3*b*e)*x^5*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a/c/e+b*f^3*x^7*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a/c/e-(b*x^2+a)^(3/2)*sqrt(d*x^2+c)*(f*x^2+e)^3/a/c/e/x-1/3*sqrt(a)*(a*c*d*f^2+b*(-2*c^2*f^2+6*c*d*e*f+3*d^2*e^2))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/sqrt(b)/c/d^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/3*sqrt(a)*(3*b*d*e^2+a*f*(-c*f+6*d*e))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(b)/c/d/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[sqrt(b*x^2+a)*(f*x^2+e)^2/x^4/sqrt(d*x^2+c),x,10,1/3*b*(b*c*d*e^2-a*(-3*c^2*f^2-6*c*d*e*f+2*d^2*e^2))*x*sqrt(d*x^2+c)/a/c^2/d/sqrt(b*x^2+a)-2/3*(b*e*(-3*c*f+d*e)+3*a*f*(-2*c*f+d*e))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a/c^2-2/3*f*(a*f*(-5*c*f+3*d*e)+3*b*e*(-2*c*f+d*e))*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a/c^2/e-1/3*f^2*(2*b*e*(-5*c*f+3*d*e)+a*f*(-3*c*f+2*d*e))*x^5*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a/c^2/e^2-1/3*b*f^3*(-3*c*f+2*d*e)*x^7*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a/c^2/e^2-1/3*(b*x^2+a)^(3/2)*sqrt(d*x^2+c)*(f*x^2+e)^3/a/c/e/x^3+1/3*(-3*c*f+2*d*e)*(b*x^2+a)^(3/2)*sqrt(d*x^2+c)*(f*x^2+e)^3/a/c^2/e^2/x-1/3*sqrt(b)*(b*c*d*e^2-a*(-3*c^2*f^2-6*c*d*e*f+2*d^2*e^2))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/sqrt(a)/c^2/d/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/3*sqrt(a)*(3*a*c*f^2-b*e*(-6*c*f+d*e))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(b)/c^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[x^4*sqrt(b*x^2+a)*(f*x^2+e)/sqrt(d*x^2+c),x,7,1/105*(8*a^3*d^3*f-a*b^2*c*d*(-16*c*f+21*d*e)-a^2*b*d^2*(-9*c*f+14*d*e)+8*b^3*c^2*(-6*c*f+7*d*e))*x*sqrt(d*x^2+c)/b^2/d^4/sqrt(b*x^2+a)-1/105*(4*a^2*d^2*f+4*b^2*c*(-6*c*f+7*d*e)-a*b*d*(-5*c*f+7*d*e))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b^2/d^3+1/35*(a*d*f-6*b*c*f+7*b*d*e)*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b/d^2+1/7*f*x^5*sqrt(b*x^2+a)*sqrt(d*x^2+c)/d-1/105*sqrt(a)*(8*a^3*d^3*f-a*b^2*c*d*(-16*c*f+21*d*e)-a^2*b*d^2*(-9*c*f+14*d*e)+8*b^3*c^2*(-6*c*f+7*d*e))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/b^(5/2)/d^4/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/105*a^(3/2)*(4*a^2*d^2*f+4*b^2*c*(-6*c*f+7*d*e)-a*b*d*(-5*c*f+7*d*e))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(5/2)/d^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[x^2*sqrt(b*x^2+a)*(f*x^2+e)/sqrt(d*x^2+c),x,6,-1/15*(2*a^2*d^2*f+2*b^2*c*(-4*c*f+5*d*e)-a*b*d*(-3*c*f+5*d*e))*x*sqrt(d*x^2+c)/b/d^3/sqrt(b*x^2+a)+1/15*(a*d*f-4*b*c*f+5*b*d*e)*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b/d^2+1/5*f*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/d+1/15*sqrt(a)*(2*a^2*d^2*f+2*b^2*c*(-4*c*f+5*d*e)-a*b*d*(-3*c*f+5*d*e))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/b^(3/2)/d^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/15*a^(3/2)*(a*d*f-4*b*c*f+5*b*d*e)*sqrt(d*x^2+c)*InverseJacobiAM(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],
[sqrt(b*x^2+a)*(f*x^2+e)/sqrt(d*x^2+c),x,5,1/3*(a*d*f-2*b*c*f+3*b*d*e)*x*sqrt(d*x^2+c)/d^2/sqrt(b*x^2+a)+1/3*f*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/d-1/3*sqrt(a)*(a*d*f-2*b*c*f+3*b*d*e)*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))+1/3*a^(3/2)*(-c*f+3*d*e)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(b)/c/d/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[sqrt(b*x^2+a)*(f*x^2+e)/x^2/sqrt(d*x^2+c),x,5,b*(c*f+d*e)*x*sqrt(d*x^2+c)/c/d/sqrt(b*x^2+a)-e*sqrt(b*x^2+a)*sqrt(d*x^2+c)/c/x-sqrt(a)*sqrt(b)*(c*f+d*e)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/c/d/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+sqrt(a)*(a*f+b*e)*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],
[sqrt(b*x^2+a)*(f*x^2+e)/x^4/sqrt(d*x^2+c),x,3,-1/3*(3*a*c*f-2*a*d*e+b*c*e)*sqrt(d*x^2+c)/c^2/x/sqrt(b*x^2+a)-1/3*e*sqrt(b*x^2+a)*sqrt(d*x^2+c)/c/x^3-1/3*sqrt(b)*(3*a*c*f-2*a*d*e+b*c*e)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/sqrt(a)/c^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/3*sqrt(a)*sqrt(b)*(-3*c*f+d*e)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/c^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[sqrt(b*x^2+a)*(f*x^2+e)/x^6/sqrt(d*x^2+c),x,4,1/15*(2*b^2*c^2*e+a*b*c*(-5*c*f+3*d*e)-2*a^2*d*(-5*c*f+4*d*e))*sqrt(d*x^2+c)/a/c^3/x/sqrt(b*x^2+a)-1/5*e*sqrt(b*x^2+a)*sqrt(d*x^2+c)/c/x^5-1/15*(5*a*c*f-4*a*d*e+b*c*e)*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a/c^2/x^3+1/15*sqrt(b)*(2*b^2*c^2*e+a*b*c*(-5*c*f+3*d*e)-2*a^2*d*(-5*c*f+4*d*e))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/a^(3/2)/c^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/15*sqrt(b)*d*(5*a*c*f-4*a*d*e+b*c*e)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(a)/c^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[sqrt(b*x^2+a)*(f*x^2+e)/x^8/sqrt(d*x^2+c),x,5,-1/105*(8*b^3*c^3*e+a^2*b*c*d*(-21*c*f+16*d*e)+a*b^2*c^2*(-14*c*f+9*d*e)-8*a^3*d^2*(-7*c*f+6*d*e))*sqrt(d*x^2+c)/a^2/c^4/x/sqrt(b*x^2+a)-1/7*e*sqrt(b*x^2+a)*sqrt(d*x^2+c)/c/x^7-1/35*(7*a*c*f-6*a*d*e+b*c*e)*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a/c^2/x^5+1/105*(4*b^2*c^2*e+a*b*c*(-7*c*f+5*d*e)-4*a^2*d*(-7*c*f+6*d*e))*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a^2/c^3/x^3-1/105*sqrt(b)*(8*b^3*c^3*e+a^2*b*c*d*(-21*c*f+16*d*e)+a*b^2*c^2*(-14*c*f+9*d*e)-8*a^3*d^2*(-7*c*f+6*d*e))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/a^(5/2)/c^4/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/105*sqrt(b)*d*(4*b^2*c^2*e+a*b*c*(-7*c*f+5*d*e)-4*a^2*d*(-7*c*f+6*d*e))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/a^(3/2)/c^4/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[x^6*sqrt(b*x^2+a)/sqrt(d*x^2+c)/(f*x^2+e),x,6,-1/15*(2*a^2*d*f+a*b*(3*c*f+5*d*e)-b^2*(10*c*e+15*d*e^2/f+8*c^2*f/d))*x*sqrt(d*x^2+c)/b/d^2/f^2/sqrt(b*x^2+a)-1/15*(-a*d*f+4*b*c*f+5*b*d*e)*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b/d^2/f^2+1/5*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/d/f+1/15*sqrt(a)*(2*a^2*d^2*f^2+a*b*d*f*(3*c*f+5*d*e)-b^2*(8*c^2*f^2+10*c*d*e*f+15*d^2*e^2))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/b^(3/2)/d^3/f^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/15*a^(3/2)*(a*c*d*f^2-b*(4*c^2*f^2+5*c*d*e*f+15*d^2*e^2))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(3/2)/c/d^2/f^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-a^(3/2)*e^2*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/f^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[x^4*sqrt(b*x^2+a)/sqrt(d*x^2+c)/(f*x^2+e),x,5,-1/3*(-a*d*f+2*b*c*f+3*b*d*e)*x*sqrt(d*x^2+c)/d^2/f^2/sqrt(b*x^2+a)+1/3*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/d/f+1/3*sqrt(a)*(-a*d*f+2*b*c*f+3*b*d*e)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/sqrt(b)/d^2/f^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/3*a^(3/2)*(c*f+3*d*e)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(b)/c/d/f^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+a^(3/2)*e*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/f^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[x^2*sqrt(b*x^2+a)/sqrt(d*x^2+c)/(f*x^2+e),x,5,b*x*sqrt(d*x^2+c)/d/f/sqrt(b*x^2+a)-sqrt(a)*sqrt(b)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/d/f/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+a^(3/2)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(b)/c/f/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-a^(3/2)*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/f/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)/(f*x^2+e),x,1,a^(3/2)*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[sqrt(b*x^2+a)/x^2/sqrt(d*x^2+c)/(f*x^2+e),x,7,b*x*sqrt(d*x^2+c)/c/e/sqrt(b*x^2+a)+b*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a/c/e-(b*x^2+a)^(3/2)*sqrt(d*x^2+c)/a/c/e/x-sqrt(a)*sqrt(b)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/c/e/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+sqrt(a)*sqrt(b)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/c/e/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-a^(3/2)*f*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[sqrt(b*x^2+a)/x^4/sqrt(d*x^2+c)/(f*x^2+e),x,7,1/3*b*(-3*a*c*f-2*a*d*e+b*c*e)*x*sqrt(d*x^2+c)/a/c^2/e^2/sqrt(b*x^2+a)-1/3*b*(3*c*f+2*d*e)*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a/c^2/e^2-1/3*(b*x^2+a)^(3/2)*sqrt(d*x^2+c)/a/c/e/x^3+1/3*(3*c*f+2*d*e)*(b*x^2+a)^(3/2)*sqrt(d*x^2+c)/a/c^2/e^2/x-1/3*sqrt(b)*(-3*a*c*f-2*a*d*e+b*c*e)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/sqrt(a)/c^2/e^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/3*sqrt(a)*sqrt(b)*(3*c*f+d*e)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/c^2/e^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+a^(3/2)*f^2*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[sqrt(b*x^2+a)/x^6/sqrt(d*x^2+c)/(f*x^2+e),x,8,-1/15*b*(2*b^2*c^2*e^2+a*b*c*e*(5*c*f+3*d*e)-a^2*(15*c^2*f^2+10*c*d*e*f+8*d^2*e^2))*x*sqrt(d*x^2+c)/a^2/c^3/e^3/sqrt(b*x^2+a)+1/15*b*(b*c*d*e^2+a*(15*c^2*f^2+10*c*d*e*f+8*d^2*e^2))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a^2/c^3/e^3-1/5*(b*x^2+a)^(3/2)*sqrt(d*x^2+c)/a/c/e/x^5+1/15*(5*a*c*f+4*a*d*e+2*b*c*e)*(b*x^2+a)^(3/2)*sqrt(d*x^2+c)/a^2/c^2/e^2/x^3-1/15*(b*d*e+a*(8*d^2*e/c+10*d*f+15*c*f^2/e))*(b*x^2+a)^(3/2)*sqrt(d*x^2+c)/a^2/c^2/e^2/x+1/15*sqrt(b)*(2*b^2*c^2*e^2+a*b*c*e*(5*c*f+3*d*e)-a^2*(15*c^2*f^2+10*c*d*e*f+8*d^2*e^2))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/a^(3/2)/c^3/e^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/15*sqrt(b)*(b*c*d*e^2-a*(15*c^2*f^2+5*c*d*e*f+4*d^2*e^2))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(a)/c^3/e^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-a^(3/2)*f^3*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e^4/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[x^6*sqrt(b*x^2+a)/sqrt(d*x^2+c)/(f*x^2+e)^2,x,6,1/6*(2*a*d*f-b*(-4*c^2*f^2-8*c*d*e*f+15*d^2*e^2)/(-c*f+d*e))*x*sqrt(d*x^2+c)/d^2/f^3/sqrt(b*x^2+a)+1/6*(b*e*(-2*c*f+5*d*e)-2*a*f*(-c*f+d*e))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/d/f^2/(-a*f+b*e)/(-c*f+d*e)-1/2*e^2*x*(b*x^2+a)^(3/2)*sqrt(d*x^2+c)/f/(-a*f+b*e)/(-c*f+d*e)/(f*x^2+e)-1/6*sqrt(a)*(2*a*d*f*(-c*f+d*e)-b*(-4*c^2*f^2-8*c*d*e*f+15*d^2*e^2))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/sqrt(b)/d^2/f^3/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/6*a^(3/2)*(2*a*f*(c*f+6*d*e)-b*e*(2*c*f+15*d*e))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(b)/c/d/f^3/(-a*f+b*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/2*a^(3/2)*e*(b*e*(-6*c*f+5*d*e)-a*f*(-5*c*f+4*d*e))*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/f^3/(-a*f+b*e)/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[x^4*sqrt(b*x^2+a)/sqrt(d*x^2+c)/(f*x^2+e)^2,x,6,1/2*b*(-2*c*f+3*d*e)*x*sqrt(d*x^2+c)/d/f^2/(-c*f+d*e)/sqrt(b*x^2+a)-1/2*b*e*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/f/(-a*f+b*e)/(-c*f+d*e)+1/2*e*x*(b*x^2+a)^(3/2)*sqrt(d*x^2+c)/(-a*f+b*e)/(-c*f+d*e)/(f*x^2+e)-1/2*sqrt(a)*sqrt(b)*(-2*c*f+3*d*e)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/d/f^2/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/2*a^(3/2)*(-2*a*f+3*b*e)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(b)/c/f^2/(-a*f+b*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/2*a^(3/2)*(b*e*(-4*c*f+3*d*e)-a*f*(-3*c*f+2*d*e))*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/f^2/(-a*f+b*e)/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[x^2*sqrt(b*x^2+a)/sqrt(d*x^2+c)/(f*x^2+e)^2,x,6,-1/2*b*x*sqrt(d*x^2+c)/f/(-c*f+d*e)/sqrt(b*x^2+a)+1/2*b*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/(-a*f+b*e)/(-c*f+d*e)-1/2*f*x*(b*x^2+a)^(3/2)*sqrt(d*x^2+c)/(-a*f+b*e)/(-c*f+d*e)/(f*x^2+e)+1/2*sqrt(a)*sqrt(b)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/f/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/2*a^(3/2)*sqrt(b)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/c/f/(-a*f+b*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/2*a^(3/2)*(a*c*f^2+b*e*(-2*c*f+d*e))*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e/f/(-a*f+b*e)/(-c*f+d*e)/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)/(f*x^2+e)^2,x,5,1/2*b*x*sqrt(d*x^2+c)/e/(-c*f+d*e)/sqrt(b*x^2+a)-1/2*f*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/e/(-c*f+d*e)/(f*x^2+e)-1/2*sqrt(a)*sqrt(b)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/e/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/2*a^(3/2)*sqrt(b)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/c/e/(-a*f+b*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/2*a^(3/2)*(b*d*e^2-a*f*(-c*f+2*d*e))*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e^2/(-a*f+b*e)/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[sqrt(b*x^2+a)/x^2/sqrt(d*x^2+c)/(f*x^2+e)^2,x,7,1/2*b*(-3*c*f+2*d*e)*x*sqrt(d*x^2+c)/c/e^2/(-c*f+d*e)/sqrt(b*x^2+a)-1/2*b*(a*f*(-3*c*f+2*d*e)-2*b*e*(-c*f+d*e))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a/c/e^2/(-a*f+b*e)/(-c*f+d*e)-(b*x^2+a)^(3/2)*sqrt(d*x^2+c)/a/c/e/x/(f*x^2+e)+1/2*f*(a*f*(-3*c*f+2*d*e)-2*b*e*(-c*f+d*e))*x*(b*x^2+a)^(3/2)*sqrt(d*x^2+c)/a/c/e^2/(-a*f+b*e)/(-c*f+d*e)/(f*x^2+e)-1/2*sqrt(a)*sqrt(b)*(-3*c*f+2*d*e)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/c/e^2/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/2*sqrt(a)*sqrt(b)*(-3*a*f+2*b*e)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/c/e^2/(-a*f+b*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/2*a^(3/2)*f*(a*f*(-3*c*f+4*d*e)-b*e*(-2*c*f+3*d*e))*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e^3/(-a*f+b*e)/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[sqrt(b*x^2+a)/x^4/sqrt(d*x^2+c)/(f*x^2+e)^2,x,8,1/6*b*(2*b*c-a*(-15*c^2*f^2+8*c*d*e*f+4*d^2*e^2)/e/(-c*f+d*e))*x*sqrt(d*x^2+c)/a/c^2/e^2/sqrt(b*x^2+a)+1/6*b*(a*f*(-15*c^2*f^2+8*c*d*e*f+4*d^2*e^2)-4*b*e*(-3*c^2*f^2+2*c*d*e*f+d^2*e^2))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a/c^2/e^3/(-a*f+b*e)/(-c*f+d*e)-1/3*(b*x^2+a)^(3/2)*sqrt(d*x^2+c)/a/c/e/x^3/(f*x^2+e)+1/3*(5*c*f+2*d*e)*(b*x^2+a)^(3/2)*sqrt(d*x^2+c)/a/c^2/e^2/x/(f*x^2+e)-1/6*f*(a*f*(-15*c^2*f^2+8*c*d*e*f+4*d^2*e^2)-4*b*e*(-3*c^2*f^2+2*c*d*e*f+d^2*e^2))*x*(b*x^2+a)^(3/2)*sqrt(d*x^2+c)/a/c^2/e^3/(-a*f+b*e)/(-c*f+d*e)/(f*x^2+e)-1/6*sqrt(b)*(2*b*c*e*(-c*f+d*e)-a*(-15*c^2*f^2+8*c*d*e*f+4*d^2*e^2))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/sqrt(a)/c^2/e^3/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/6*sqrt(a)*sqrt(b)*(2*b*e*(6*c*f+d*e)-a*f*(15*c*f+2*d*e))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/c^2/e^3/(-a*f+b*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/2*a^(3/2)*f^2*(a*f*(-5*c*f+6*d*e)-b*e*(-4*c*f+5*d*e))*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e^4/(-a*f+b*e)/(-c*f+d*e)/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^6/(f*x^2+e)^2,x,10,-1/30*b*(4*b^2*c^2*e^2-4*a*b*c*e*(-5*c*f+d*e)+a^2*(-105*c^2*f^2+20*c*d*e*f+4*d^2*e^2))*x*sqrt(d*x^2+c)/a^2/c^2/e^4/sqrt(b*x^2+a)+1/30*d*(15*a^2*c*f^2*(-7*c*f+6*d*e)-4*b^2*c*e^2*(-c*f+d*e)+2*a*b*e*(10*c^2*f^2-11*c*d*e*f+d^2*e^2))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a^2/c^2/e^4/(-c*f+d*e)-1/10*b*(5*a^2*c*f^3*(-7*c*f+6*d*e)-2*b^2*d*e^3*(-c*f+d*e)+2*a*b*e*f*(15*c^2*f^2-16*c*d*e*f+d^2*e^2))*x*sqrt(b*x^2+a)*(d*x^2+c)^(3/2)/a^2/c^2/e^4/(-a*f+b*e)/(-c*f+d*e)-1/5*(b*x^2+a)^(3/2)*(d*x^2+c)^(3/2)/a/c/e/x^5/(f*x^2+e)+1/15*(7*a*c*f+2*a*d*e+2*b*c*e)*(b*x^2+a)^(3/2)*(d*x^2+c)^(3/2)/a^2/c^2/e^2/x^3/(f*x^2+e)+1/15*(a*f*(-35*c*f+2*d*e)-b*e*(-2*c*f+3*d*e))*(b*x^2+a)^(3/2)*(d*x^2+c)^(3/2)/a^2/c^2/e^3/x/(f*x^2+e)+1/10*f*(5*a^2*c*f^3*(-7*c*f+6*d*e)-2*b^2*d*e^3*(-c*f+d*e)+2*a*b*e*f*(15*c^2*f^2-16*c*d*e*f+d^2*e^2))*x*(b*x^2+a)^(3/2)*(d*x^2+c)^(3/2)/a^2/c^2/e^4/(-a*f+b*e)/(-c*f+d*e)/(f*x^2+e)+1/30*sqrt(b)*(4*b^2*c^2*e^2-4*a*b*c*e*(-5*c*f+d*e)+a^2*(-105*c^2*f^2+20*c*d*e*f+4*d^2*e^2))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/a^(3/2)/c^2/e^4/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/30*sqrt(b)*(2*b^2*c*d*e^3-a^2*f*(-105*c^2*f^2+55*c*d*e*f+2*d^2*e^2)+2*a*b*e*(-45*c^2*f^2+19*c*d*e*f+d^2*e^2))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(a)/c^2/e^4/(-a*f+b*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/2*a^(3/2)*f^2*(a*f*(-7*c*f+6*d*e)-b*e*(-6*c*f+5*d*e))*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e^5/(-a*f+b*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[x^4*sqrt(b*x^2+a)*(f*x^2+e)^2/(d*x^2+c)^(3/2),x,5,1/105*(8*a^3*d^3*f^2-a^2*b*d^2*f*(-19*c*f+28*d*e)+2*a*b^2*d*(30*c^2*f^2-49*c*d*e*f+10*d^2*e^2)-4*b^3*c*(48*c^2*f^2-84*c*d*e*f+35*d^2*e^2))*x*sqrt(b*x^2+a)/b^3/d^4/sqrt(d*x^2+c)-1/105*(4*a^2*d^2*f^2+a*b*d*f*(9*c*f+16*d*e)-4*b^2*(12*c^2*f^2-21*c*d*e*f+5*d^2*e^2))*x^3*sqrt(b*x^2+a)/b^2/d^3/sqrt(d*x^2+c)+4/35*f*(-a*d*f-2*b*c*f+b*d*e)*x^5*sqrt(b*x^2+a)/b/d^2/sqrt(d*x^2+c)+1/7*x*(b*x^2+a)^(3/2)*(f*x^2+e)^2/b/d/sqrt(d*x^2+c)-1/105*sqrt(c)*(8*a^3*d^3*f^2-a^2*b*d^2*f*(-23*c*f+28*d*e)-8*b^3*c*(48*c^2*f^2-84*c*d*e*f+35*d^2*e^2)+a*b^2*d*(72*c^2*f^2-112*c*d*e*f+35*d^2*e^2))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/b^3/d^(9/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+2/105*c^(3/2)*(2*a^2*d^2*f^2-a*b*d*f*(-6*c*f+7*d*e)-2*b^2*(48*c^2*f^2-84*c*d*e*f+35*d^2*e^2))*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/b^2/d^(9/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[x^2*sqrt(b*x^2+a)*(f*x^2+e)^2/(d*x^2+c)^(3/2),x,5,-1/15*(2*a^2*d^2*f^2-a*b*d*f*(-7*c*f+10*d*e)-b^2*(24*c^2*f^2-40*c*d*e*f+15*d^2*e^2))*x*sqrt(b*x^2+a)/b^2/d^3/sqrt(d*x^2+c)+1/15*f*(a*d*f-6*b*c*f+10*b*d*e)*x^3*sqrt(b*x^2+a)/b/d^2/sqrt(d*x^2+c)+1/5*f^2*x^5*sqrt(b*x^2+a)/d/sqrt(d*x^2+c)+2/15*sqrt(c)*(a^2*d^2*f^2-a*b*d*f*(-4*c*f+5*d*e)-b^2*(24*c^2*f^2-40*c*d*e*f+15*d^2*e^2))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/b^2/d^(7/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-1/15*sqrt(c)*(a*c*d*f^2-b*(24*c^2*f^2-40*c*d*e*f+15*d^2*e^2))*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/b/d^(7/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[sqrt(b*x^2+a)*(f*x^2+e)^2/(d*x^2+c)^(3/2),x,3,1/3*f*(a*d*f-4*b*c*f+6*b*d*e)*x*sqrt(b*x^2+a)/b/d^2/sqrt(d*x^2+c)+1/3*f^2*x^3*sqrt(b*x^2+a)/d/sqrt(d*x^2+c)-1/3*(a*c*d*f^2-b*(8*c^2*f^2-12*c*d*e*f+3*d^2*e^2))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/b/sqrt(c)/d^(5/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+2/3*sqrt(c)*f*(-2*c*f+3*d*e)*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/d^(5/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[sqrt(b*x^2+a)*(f*x^2+e)^2/x^2/(d*x^2+c)^(3/2),x,6,(b*d*e^2+a*f*(c*f+3*d*e))*x*sqrt(b*x^2+a)/a/c/d/sqrt(d*x^2+c)+3*f*(a*f+b*e)*x^3*sqrt(b*x^2+a)/a/c/sqrt(d*x^2+c)+f^2*(a*f+3*b*e)*x^5*sqrt(b*x^2+a)/a/c/e/sqrt(d*x^2+c)+b*f^3*x^7*sqrt(b*x^2+a)/a/c/e/sqrt(d*x^2+c)-(b*x^2+a)^(3/2)*(f*x^2+e)^3/a/c/e/x/sqrt(d*x^2+c)-2*(c^2*f^2-c*d*e*f+d^2*e^2)*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/c^(3/2)/d^(3/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+(a*c*f^2+b*d*e^2)*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a/sqrt(c)/d^(3/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[sqrt(b*x^2+a)*(f*x^2+e)^2/x^4/(d*x^2+c)^(3/2),x,7,-2/3*(b*e*(-3*c*f+2*d*e)+6*a*f*(-c*f+d*e))*x*sqrt(b*x^2+a)/a/c^2/sqrt(d*x^2+c)-2/3*f*(a*f*(-5*c*f+6*d*e)+6*b*e*(-c*f+d*e))*x^3*sqrt(b*x^2+a)/a/c^2/e/sqrt(d*x^2+c)-1/3*f^2*(2*b*e*(-5*c*f+6*d*e)+a*f*(-3*c*f+4*d*e))*x^5*sqrt(b*x^2+a)/a/c^2/e^2/sqrt(d*x^2+c)-1/3*b*f^3*(-3*c*f+4*d*e)*x^7*sqrt(b*x^2+a)/a/c^2/e^2/sqrt(d*x^2+c)-1/3*(b*x^2+a)^(3/2)*(f*x^2+e)^3/a/c/e/x^3/sqrt(d*x^2+c)+1/3*(-3*c*f+4*d*e)*(b*x^2+a)^(3/2)*(f*x^2+e)^3/a/c^2/e^2/x/sqrt(d*x^2+c)-1/3*(b*c*d*e^2-a*(3*c^2*f^2-12*c*d*e*f+8*d^2*e^2))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/a/c^(5/2)/sqrt(d)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-2/3*b*e*(-3*c*f+2*d*e)*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a/c^(3/2)/sqrt(d)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[sqrt(b*x^2+a)*(f*x^2+e)^2/x^6/(d*x^2+c)^(3/2),x,8,-1/15*(b^2*c*d*e^3-3*a^2*f*(5*c^2*f^2-28*c*d*e*f+24*d^2*e^2)-a*b*e*(27*c^2*f^2-43*c*d*e*f+24*d^2*e^2))*x*sqrt(b*x^2+a)/a^2/c^3/e/sqrt(d*x^2+c)-1/15*f*(3*b^2*c*e^2*(-4*c*f+d*e)-2*a^2*f*(5*c^2*f^2-36*c*d*e*f+36*d^2*e^2)-a*b*e*(31*c^2*f^2-87*c*d*e*f+72*d^2*e^2))*x^3*sqrt(b*x^2+a)/a^2/c^3/e^2/sqrt(d*x^2+c)-1/15*f^2*(b^2*c*e^2*(-16*c*f+3*d*e)-a^2*f*(3*c^2*f^2-22*c*d*e*f+24*d^2*e^2)-a*b*e*(16*c^2*f^2-73*c*d*e*f+72*d^2*e^2))*x^5*sqrt(b*x^2+a)/a^2/c^3/e^3/sqrt(d*x^2+c)-1/15*b*f^3*(b*c*e*(-6*c*f+d*e)-a*(3*c^2*f^2-22*c*d*e*f+24*d^2*e^2))*x^7*sqrt(b*x^2+a)/a^2/c^3/e^3/sqrt(d*x^2+c)-1/5*(b*x^2+a)^(3/2)*(f*x^2+e)^3/a/c/e/x^5/sqrt(d*x^2+c)+1/15*(-a*c*f+6*a*d*e+2*b*c*e)*(b*x^2+a)^(3/2)*(f*x^2+e)^3/a^2/c^2/e^2/x^3/sqrt(d*x^2+c)+1/15*(b*c*e*(-6*c*f+d*e)-a*(3*c^2*f^2-22*c*d*e*f+24*d^2*e^2))*(b*x^2+a)^(3/2)*(f*x^2+e)^3/a^2/c^3/e^3/x/sqrt(d*x^2+c)+2/15*sqrt(d)*(b^2*c^2*e^2+a*b*c*e*(-5*c*f+4*d*e)-a^2*(15*c^2*f^2-40*c*d*e*f+24*d^2*e^2))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/a^2/c^(7/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-1/15*b*(b*c*d*e^2-a*(15*c^2*f^2-40*c*d*e*f+24*d^2*e^2))*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a^2/c^(5/2)/sqrt(d)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[x^4*sqrt(b*x^2+a)*(f*x^2+e)/(d*x^2+c)^(3/2),x,4,-1/15*(2*a^2*d^2*f-a*b*d*(-7*c*f+5*d*e)+4*b^2*c*(-6*c*f+5*d*e))*x*sqrt(b*x^2+a)/b^2/d^3/sqrt(d*x^2+c)+1/15*(a*d*f-6*b*c*f+5*b*d*e)*x^3*sqrt(b*x^2+a)/b/d^2/sqrt(d*x^2+c)+1/5*f*x^5*sqrt(b*x^2+a)/d/sqrt(d*x^2+c)+1/15*sqrt(c)*(2*a^2*d^2*f-a*b*d*(-8*c*f+5*d*e)+8*b^2*c*(-6*c*f+5*d*e))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/b^2/d^(7/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-1/15*c^(3/2)*(a*d*f+4*b*(-6*c*f+5*d*e))*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/b/d^(7/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[x^2*sqrt(b*x^2+a)*(f*x^2+e)/(d*x^2+c)^(3/2),x,3,1/3*(a*d*f-4*b*c*f+3*b*d*e)*x*sqrt(b*x^2+a)/b/d^2/sqrt(d*x^2+c)+1/3*f*x^3*sqrt(b*x^2+a)/d/sqrt(d*x^2+c)-1/3*sqrt(c)*(a*d*f-8*b*c*f+6*b*d*e)*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/b/d^(5/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+1/3*sqrt(c)*(-4*c*f+3*d*e)*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/d^(5/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[sqrt(b*x^2+a)*(f*x^2+e)/(d*x^2+c)^(3/2),x,2,f*x*sqrt(b*x^2+a)/d/sqrt(d*x^2+c)+(-2*c*f+d*e)*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/sqrt(c)/d^(3/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+sqrt(c)*f*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/d^(3/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[sqrt(b*x^2+a)*(f*x^2+e)/x^2/(d*x^2+c)^(3/2),x,2,-e*sqrt(b*x^2+a)/c/x/sqrt(d*x^2+c)-(-c*f+2*d*e)*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/c^(3/2)/sqrt(d)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+b*e*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a/sqrt(c)/sqrt(d)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[sqrt(b*x^2+a)*(f*x^2+e)/x^4/(d*x^2+c)^(3/2),x,3,-1/3*e*sqrt(b*x^2+a)/c/x^3/sqrt(d*x^2+c)-1/3*(3*a*c*f-4*a*d*e+b*c*e)*sqrt(b*x^2+a)/a/c^2/x/sqrt(d*x^2+c)-1/3*sqrt(d)*(6*a*c*f-8*a*d*e+b*c*e)*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/a/c^(5/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-1/3*b*(-3*c*f+4*d*e)*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a/c^(3/2)/sqrt(d)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[sqrt(b*x^2+a)*(f*x^2+e)/x^6/(d*x^2+c)^(3/2),x,4,-1/5*e*sqrt(b*x^2+a)/c/x^5/sqrt(d*x^2+c)-1/15*(5*a*c*f-6*a*d*e+b*c*e)*sqrt(b*x^2+a)/a/c^2/x^3/sqrt(d*x^2+c)+1/15*(2*b^2*c^2*e-4*a^2*d*(-5*c*f+6*d*e)+a*b*c*(-5*c*f+7*d*e))*sqrt(b*x^2+a)/a^2/c^3/x/sqrt(d*x^2+c)+1/15*sqrt(d)*(2*b^2*c^2*e-8*a^2*d*(-5*c*f+6*d*e)+a*b*c*(-5*c*f+8*d*e))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/a^2/c^(7/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-1/15*b*sqrt(d)*(20*a*c*f-24*a*d*e+b*c*e)*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a^2/c^(5/2)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[x^4*sqrt(b*x^2+a)/(d*x^2+c)^(3/2)/(f*x^2+e),x,4,x*sqrt(b*x^2+a)/d/f/sqrt(d*x^2+c)-sqrt(c)*(-2*c*f+d*e)*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/d^(3/2)/f/(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+c^(3/2)*(b*d*e^2-a*f*(-c*f+2*d*e))*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a/d^(3/2)/f/(-c*f+d*e)^2/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-c^(3/2)*e*(-a*f+b*e)*sqrt(b*x^2+a)*EllipticPi(sin(arctan(sqrt(d)*x/sqrt(c))),1-c*f/d/e,sqrt(1-b*c/a/d))/a/sqrt(d)/f/(-c*f+d*e)^2/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[x^2*sqrt(b*x^2+a)/(d*x^2+c)^(3/2)/(f*x^2+e),x,5,(-a*d+b*c)*x/d/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(d*x^2+c)-sqrt(a)*sqrt(b)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/d/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+a^(3/2)*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/(-c*f+d*e)/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)/(f*x^2+e),x,3,sqrt(d)*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/sqrt(c)/(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-a^(3/2)*f*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[sqrt(b*x^2+a)/x^2/(d*x^2+c)^(3/2)/(f*x^2+e),x,6,(b-a*d*(-c*f+2*d*e)/c/(-c*f+d*e))*x*sqrt(b*x^2+a)/a/c/e/sqrt(d*x^2+c)-(b*x^2+a)^(3/2)/a/c/e/x/sqrt(d*x^2+c)+b*(-c*f+2*d*e)*x*sqrt(d*x^2+c)/c^2/e/(-c*f+d*e)/sqrt(b*x^2+a)-sqrt(a)*sqrt(b)*(-c*f+2*d*e)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/c^2/e/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+sqrt(a)*sqrt(b)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/c^2/e/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+a^(3/2)*f^2*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e^2/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[sqrt(b*x^2+a)/x^4/(d*x^2+c)^(3/2)/(f*x^2+e),x,7,-1/3*(b*c*(-3*c^2*f^2-2*c*d*e*f+5*d^2*e^2)-a*d*(-3*c^2*f^2-2*c*d*e*f+8*d^2*e^2))*x*sqrt(b*x^2+a)/a/c^3/e^2/(-c*f+d*e)/sqrt(d*x^2+c)-1/3*(b*x^2+a)^(3/2)/a/c/e/x^3/sqrt(d*x^2+c)+1/3*(3*c*f+4*d*e)*(b*x^2+a)^(3/2)/a/c^2/e^2/x/sqrt(d*x^2+c)+1/3*b*(b*c-a*(-3*c^2*f^2-2*c*d*e*f+8*d^2*e^2)/e/(-c*f+d*e))*x*sqrt(d*x^2+c)/a/c^3/e/sqrt(b*x^2+a)-1/3*sqrt(b)*(b*c*e*(-c*f+d*e)-a*(-3*c^2*f^2-2*c*d*e*f+8*d^2*e^2))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/sqrt(a)/c^3/e^2/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/3*sqrt(a)*sqrt(b)*(3*c*f+4*d*e)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/c^3/e^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-a^(3/2)*f^3*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e^3/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[sqrt(b*x^2+a)/x^6/(d*x^2+c)^(3/2)/(f*x^2+e),x,8,1/15*(b^2*c^2*d*e^2*(-c*f+d*e)-a^2*d*(-15*c^3*f^3-10*c^2*d*e*f^2-8*c*d^2*e^2*f+48*d^3*e^3)+a*b*c*(-15*c^3*f^3-10*c^2*d*e*f^2-7*c*d^2*e^2*f+32*d^3*e^3))*x*sqrt(b*x^2+a)/a^2/c^4/e^3/(-c*f+d*e)/sqrt(d*x^2+c)-1/5*(b*x^2+a)^(3/2)/a/c/e/x^5/sqrt(d*x^2+c)+1/15*(5*a*c*f+6*a*d*e+2*b*c*e)*(b*x^2+a)^(3/2)/a^2/c^2/e^2/x^3/sqrt(d*x^2+c)+1/15*(b*c*d*e^2-a*(15*c^2*f^2+20*c*d*e*f+24*d^2*e^2))*(b*x^2+a)^(3/2)/a^2/c^3/e^3/x/sqrt(d*x^2+c)-1/15*b*(2*b^2*c^2*e^2*(-c*f+d*e)+a*b*c*e*(-5*c^2*f^2-3*c*d*e*f+8*d^2*e^2)-a^2*(-15*c^3*f^3-10*c^2*d*e*f^2-8*c*d^2*e^2*f+48*d^3*e^3))*x*sqrt(d*x^2+c)/a^2/c^4/e^3/(-c*f+d*e)/sqrt(b*x^2+a)+1/15*sqrt(b)*(2*b^2*c^2*e^2*(-c*f+d*e)+a*b*c*e*(-5*c^2*f^2-3*c*d*e*f+8*d^2*e^2)-a^2*(-15*c^3*f^3-10*c^2*d*e*f^2-8*c*d^2*e^2*f+48*d^3*e^3))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/a^(3/2)/c^4/e^3/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/15*sqrt(b)*(b*c*d*e^2-a*(15*c^2*f^2+20*c*d*e*f+24*d^2*e^2))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(a)/c^4/e^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+a^(3/2)*f^4*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e^4/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[x^4*sqrt(b*x^2+a)/(d*x^2+c)^(3/2)/(f*x^2+e)^2,x,6,1/2*(-2*a*c*f-a*d*e+3*b*c*e)*x*sqrt(b*x^2+a)/(-a*f+b*e)/(-c*f+d*e)^2/sqrt(d*x^2+c)-1/2*b*(2*c*f+d*e)*x*sqrt(d*x^2+c)/d/f/(-c*f+d*e)^2/sqrt(b*x^2+a)+1/2*e*x*(b*x^2+a)^(3/2)/(-a*f+b*e)/(-c*f+d*e)/sqrt(d*x^2+c)/(f*x^2+e)+1/2*sqrt(a)*sqrt(b)*(2*c*f+d*e)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/d/f/(-c*f+d*e)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/2*a^(3/2)*sqrt(b)*e*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/c/f/(-a*f+b*e)/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/2*a^(3/2)*(3*a*c*f^2+b*e*(-4*c*f+d*e))*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/f/(-a*f+b*e)/(-c*f+d*e)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[x^2*sqrt(b*x^2+a)/(d*x^2+c)^(3/2)/(f*x^2+e)^2,x,6,-1/2*(-3*a*d*f+b*c*f+2*b*d*e)*x*sqrt(b*x^2+a)/(-a*f+b*e)/(-c*f+d*e)^2/sqrt(d*x^2+c)+3/2*b*x*sqrt(d*x^2+c)/(-c*f+d*e)^2/sqrt(b*x^2+a)-1/2*f*x*(b*x^2+a)^(3/2)/(-a*f+b*e)/(-c*f+d*e)/sqrt(d*x^2+c)/(f*x^2+e)-3/2*sqrt(a)*sqrt(b)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/(-c*f+d*e)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/2*a^(3/2)*sqrt(b)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/c/(-a*f+b*e)/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/2*a^(3/2)*(a*f*(c*f+2*d*e)-b*e*(2*c*f+d*e))*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e/(-a*f+b*e)/(-c*f+d*e)^2/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)/(f*x^2+e)^2,x,4,-1/2*f*x*sqrt(b*x^2+a)/e/(-c*f+d*e)/sqrt(d*x^2+c)/(f*x^2+e)+1/2*sqrt(d)*(c*f+2*d*e)*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/sqrt(c)/e/(-c*f+d*e)^2/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+1/2*sqrt(c)*sqrt(d)*f*(a*c*f-4*a*d*e+3*b*c*e)*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a/e/(-c*f+d*e)^3/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-1/2*c^(3/2)*f*(3*b*d*e^2-a*f*(-c*f+4*d*e))*sqrt(b*x^2+a)*EllipticPi(sin(arctan(sqrt(d)*x/sqrt(c))),1-c*f/d/e,sqrt(1-b*c/a/d))/a/sqrt(d)/e^2/(-c*f+d*e)^3/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[sqrt(b*x^2+a)/x^2/(d*x^2+c)^(3/2)/(f*x^2+e)^2,x,7,1/2*(2*b^2*c*e*(-c*f+d*e)^2+a^2*d*f*(3*c^2*f^2-4*c*d*e*f+4*d^2*e^2)-a*b*(3*c^3*f^3-2*c^2*d*e*f^2-2*c*d^2*e^2*f+4*d^3*e^3))*x*sqrt(b*x^2+a)/a/c^2/e^2/(-a*f+b*e)/(-c*f+d*e)^2/sqrt(d*x^2+c)+1/2*b*(3*c^2*f^2-4*c*d*e*f+4*d^2*e^2)*x*sqrt(d*x^2+c)/c^2/e^2/(-c*f+d*e)^2/sqrt(b*x^2+a)-(b*x^2+a)^(3/2)/a/c/e/x/sqrt(d*x^2+c)/(f*x^2+e)+1/2*f*(a*f*(-3*c*f+2*d*e)-2*b*e*(-c*f+d*e))*x*(b*x^2+a)^(3/2)/a/c/e^2/(-a*f+b*e)/(-c*f+d*e)/sqrt(d*x^2+c)/(f*x^2+e)-1/2*sqrt(a)*sqrt(b)*(3*c^2*f^2-4*c*d*e*f+4*d^2*e^2)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/c^2/e^2/(-c*f+d*e)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/2*sqrt(a)*sqrt(b)*(a*f*(-3*c*f+2*d*e)-2*b*e*(-c*f+d*e))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/c^2/e^2/(-a*f+b*e)/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/2*a^(3/2)*f^2*(b*e*(-2*c*f+5*d*e)-3*a*f*(-c*f+2*d*e))*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e^3/(-a*f+b*e)/(-c*f+d*e)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[sqrt(b*x^2+a)/x^4/(d*x^2+c)^(3/2)/(f*x^2+e)^2,x,8,-1/6*(2*b^2*c*e*(-c*f+d*e)^2*(6*c*f+5*d*e)+a^2*d*f*(15*c^3*f^3-14*c^2*d*e*f^2-8*c*d^2*e^2*f+16*d^3*e^3)-a*b*(15*c^4*f^4-2*c^3*d*e*f^3-22*c^2*d^2*e^2*f^2+2*c*d^3*e^3*f+16*d^4*e^4))*x*sqrt(b*x^2+a)/a/c^3/e^3/(-a*f+b*e)/(-c*f+d*e)^2/sqrt(d*x^2+c)+1/6*b*(2*b-a*(15*c^3*f^3-14*c^2*d*e*f^2-8*c*d^2*e^2*f+16*d^3*e^3)/c/e/(-c*f+d*e)^2)*x*sqrt(d*x^2+c)/a/c^2/e^2/sqrt(b*x^2+a)-1/3*(b*x^2+a)^(3/2)/a/c/e/x^3/sqrt(d*x^2+c)/(f*x^2+e)+1/3*(5*c*f+4*d*e)*(b*x^2+a)^(3/2)/a/c^2/e^2/x/sqrt(d*x^2+c)/(f*x^2+e)-1/6*f*(a*f*(-15*c^2*f^2+4*c*d*e*f+8*d^2*e^2)-4*b*e*(-3*c^2*f^2+c*d*e*f+2*d^2*e^2))*x*(b*x^2+a)^(3/2)/a/c^2/e^3/(-a*f+b*e)/(-c*f+d*e)/sqrt(d*x^2+c)/(f*x^2+e)-1/6*sqrt(b)*(2*b-a*(15*c^3*f^3-14*c^2*d*e*f^2-8*c*d^2*e^2*f+16*d^3*e^3)/c/e/(-c*f+d*e)^2)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/sqrt(a)/c^2/e^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/6*sqrt(a)*sqrt(b)*(a*f*(-15*c^2*f^2+4*c*d*e*f+8*d^2*e^2)-4*b*e*(-3*c^2*f^2+c*d*e*f+2*d^2*e^2))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/c^3/e^3/(-a*f+b*e)/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/2*a^(3/2)*f^3*(a*f*(-5*c*f+8*d*e)-b*e*(-4*c*f+7*d*e))*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e^4/(-a*f+b*e)/(-c*f+d*e)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[sqrt(b*x^2+a)/x^6/(d*x^2+c)^(3/2)/(f*x^2+e)^2,x,9,1/30*(2*b^3*c^2*d*e^3*(-c*f+d*e)^2+2*a*b^2*c*e*(-c*f+d*e)^2*(45*c^2*f^2+49*c*d*e*f+32*d^2*e^2)+a^3*d*f*(105*c^4*f^4-80*c^3*d*e*f^3-44*c^2*d^2*e^2*f^2-32*c*d^3*e^3*f+96*d^4*e^4)-a^2*b*(105*c^5*f^5+10*c^4*d*e*f^4-126*c^3*d^2*e^2*f^3-72*c^2*d^3*e^3*f^2+32*c*d^4*e^4*f+96*d^5*e^5))*x*sqrt(b*x^2+a)/a^2/c^4/e^4/(-a*f+b*e)/(-c*f+d*e)^2/sqrt(d*x^2+c)-1/30*b*(4*b^2*c*e+4*a*b*(5*c*f+4*d*e)-a^2*(105*c^4*f^4-80*c^3*d*e*f^3-44*c^2*d^2*e^2*f^2-32*c*d^3*e^3*f+96*d^4*e^4)/c/e/(-c*f+d*e)^2)*x*sqrt(d*x^2+c)/a^2/c^3/e^3/sqrt(b*x^2+a)-1/5*(b*x^2+a)^(3/2)/a/c/e/x^5/sqrt(d*x^2+c)/(f*x^2+e)+1/15*(7*a*c*f+6*a*d*e+2*b*c*e)*(b*x^2+a)^(3/2)/a^2/c^2/e^2/x^3/sqrt(d*x^2+c)/(f*x^2+e)+1/15*(b*c*e*(2*c*f+d*e)-a*(35*c^2*f^2+34*c*d*e*f+24*d^2*e^2))*(b*x^2+a)^(3/2)/a^2/c^3/e^3/x/sqrt(d*x^2+c)/(f*x^2+e)+1/30*f*(2*b^2*c*d*e^3*(-c*f+d*e)+a^2*f*(-105*c^3*f^3+10*c^2*d*e*f^2+32*c*d^2*e^2*f+48*d^3*e^3)-2*a*b*e*(-45*c^3*f^3+4*c^2*d*e*f^2+17*c*d^2*e^2*f+24*d^3*e^3))*x*(b*x^2+a)^(3/2)/a^2/c^3/e^4/(-a*f+b*e)/(-c*f+d*e)/sqrt(d*x^2+c)/(f*x^2+e)+1/30*sqrt(b)*(4*b^2*c*e+4*a*b*(5*c*f+4*d*e)-a^2*(105*c^4*f^4-80*c^3*d*e*f^3-44*c^2*d^2*e^2*f^2-32*c*d^3*e^3*f+96*d^4*e^4)/c/e/(-c*f+d*e)^2)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/a^(3/2)/c^3/e^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/30*sqrt(b)*(2*b^2*c*d*e^3*(-c*f+d*e)+a^2*f*(-105*c^3*f^3+10*c^2*d*e*f^2+32*c*d^2*e^2*f+48*d^3*e^3)-2*a*b*e*(-45*c^3*f^3+4*c^2*d*e*f^2+17*c*d^2*e^2*f+24*d^3*e^3))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(a)/c^4/e^4/(-a*f+b*e)/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/2*a^(3/2)*f^4*(a*f*(-7*c*f+10*d*e)-3*b*e*(-2*c*f+3*d*e))*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e^5/(-a*f+b*e)/(-c*f+d*e)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[x^2*sqrt(b*x^2+a)/(d*x^2+c)^(3/2)/(f*x^2+e),x,5,(-a*d+b*c)*x/d/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(d*x^2+c)-sqrt(a)*sqrt(b)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/d/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+a^(3/2)*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[x^2*sqrt(b*x^2+a)/(-d*x^2+c)^(3/2)/(f*x^2+e),x,11,x*sqrt(b*x^2+a)/(c*f+d*e)/sqrt(-d*x^2+c)-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)/(c*f+d*e)/sqrt(1+b*x^2/a)/sqrt(-d*x^2+c)-sqrt(c)*(-a*f+b*e)*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)/f/(c*f+d*e)/sqrt(b*x^2+a)/sqrt(-d*x^2+c)+sqrt(c)*(-a*f+b*e)*sqrt(1+b*x^2/a)*sqrt(1-d*x^2/c)*EllipticPi(sin(arcsin(sqrt(d)*x/sqrt(c))),-c*f/d/e,sqrt(-b*c/a/d))/sqrt(d)/f/(c*f+d*e)/sqrt(b*x^2+a)/sqrt(-d*x^2+c),1],
[(f*x^2+e)/x^2/sqrt(b*x^2+a)/sqrt(d*x^2+c),x,2,-e*sqrt(d*x^2+c)/c/x/sqrt(b*x^2+a)-sqrt(b)*e*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/sqrt(a)/c/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+sqrt(a)*f*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],
[(f*x^2+e)/x^2/sqrt(-b*x^2+a)/sqrt(d*x^2+c),x,8,-e*sqrt(-b*x^2+a)*sqrt(d*x^2+c)/a/c/x-sqrt(b)*e*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)/c/sqrt(-b*x^2+a)/sqrt(1+d*x^2/c)+(a*f+b*e)*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],
[(f*x^2+e)/x^2/sqrt(b*x^2+a)/sqrt(-d*x^2+c),x,8,-e*sqrt(b*x^2+a)*sqrt(-d*x^2+c)/a/c/x-sqrt(d)*e*sqrt(b*x^2+a)*sqrt(1-d*x^2/c)*EllipticE(sin(arcsin(sqrt(d)*x/sqrt(c))),sqrt(-b*c/a/d))/a/sqrt(c)/sqrt(1+b*x^2/a)/sqrt(-d*x^2+c)+(c*f+d*e)*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(c)/sqrt(d)/sqrt(b*x^2+a)/sqrt(-d*x^2+c),1],
[(f*x^2+e)/x^2/sqrt(-b*x^2+a)/sqrt(-d*x^2+c),x,8,-e*sqrt(-b*x^2+a)*sqrt(-d*x^2+c)/a/c/x-sqrt(b)*e*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)/c/sqrt(-b*x^2+a)/sqrt(1-d*x^2/c)+(a*f+b*e)*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],
[x^4*(f*x^2+e)^2/sqrt(b*x^2+a)/sqrt(d*x^2+c),x,7,-2/105*(9*a*b*c*d*f*(-3*a*d*f-3*b*c*f+7*b*d*e)-(a*d+b*c)*(8*(a*d+b*c)*f*(-3*a*d*f-3*b*c*f+7*b*d*e)-5*b*d*(-5*a*c*f^2+7*b*d*e^2)))*x*sqrt(d*x^2+c)/b^3/d^4/sqrt(b*x^2+a)-1/105*(8*(a*d+b*c)*f*(-3*a*d*f-3*b*c*f+7*b*d*e)-5*b*d*(-5*a*c*f^2+7*b*d*e^2))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b^3/d^3+2/35*f*(-3*a*d*f-3*b*c*f+7*b*d*e)*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b^2/d^2+1/7*f^2*x^5*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b/d+2/105*sqrt(a)*(9*a*b*c*d*f*(-3*a*d*f-3*b*c*f+7*b*d*e)-(a*d+b*c)*(8*(a*d+b*c)*f*(-3*a*d*f-3*b*c*f+7*b*d*e)-5*b*d*(-5*a*c*f^2+7*b*d*e^2)))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/b^(7/2)/d^4/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/105*a^(3/2)*(8*(a*d+b*c)*f*(-3*a*d*f-3*b*c*f+7*b*d*e)-5*b*d*(-5*a*c*f^2+7*b*d*e^2))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(7/2)/d^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[x^2*(f*x^2+e)^2/sqrt(b*x^2+a)/sqrt(d*x^2+c),x,6,-1/15*(4*(a*d+b*c)*f*(-2*a*d*f-2*b*c*f+5*b*d*e)-3*b*d*(-3*a*c*f^2+5*b*d*e^2))*x*sqrt(d*x^2+c)/b^2/d^3/sqrt(b*x^2+a)+2/15*f*(-2*a*d*f-2*b*c*f+5*b*d*e)*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b^2/d^2+1/5*f^2*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b/d+1/15*sqrt(a)*(4*(a*d+b*c)*f*(-2*a*d*f-2*b*c*f+5*b*d*e)-3*b*d*(-3*a*c*f^2+5*b*d*e^2))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/b^(5/2)/d^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-2/15*a^(3/2)*f*(-2*a*d*f-2*b*c*f+5*b*d*e)*sqrt(d*x^2+c)*InverseJacobiAM(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],
[(f*x^2+e)^2/sqrt(b*x^2+a)/sqrt(d*x^2+c),x,5,2/3*f*(-a*d*f-b*c*f+3*b*d*e)*x*sqrt(d*x^2+c)/b/d^2/sqrt(b*x^2+a)+1/3*f^2*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b/d-2/3*sqrt(a)*f*(-a*d*f-b*c*f+3*b*d*e)*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))+1/3*sqrt(a)*(-a*c*f^2+3*b*d*e^2)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(3/2)/c/d/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(f*x^2+e)^2/x^2/sqrt(b*x^2+a)/sqrt(d*x^2+c),x,5,(b*e^2/a/c+f^2/d)*x*sqrt(d*x^2+c)/sqrt(b*x^2+a)-e^2*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a/c/x-(a*c*f^2+b*d*e^2)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/sqrt(a)/sqrt(b)/c/d/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+2*sqrt(a)*e*f*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],
[(f*x^2+e)^2/x^4/sqrt(b*x^2+a)/sqrt(d*x^2+c),x,3,2/3*e*(-3*a*c*f+a*d*e+b*c*e)*sqrt(d*x^2+c)/a/c^2/x/sqrt(b*x^2+a)-1/3*e^2*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a/c/x^3+2/3*sqrt(b)*e*(-3*a*c*f+a*d*e+b*c*e)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/a^(3/2)/c^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/3*(-3*a*c*f^2+b*d*e^2)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(a)/sqrt(b)/c^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(f*x^2+e)^2/x^6/sqrt(b*x^2+a)/sqrt(d*x^2+c),x,4,-1/15*(4*(a*d+b*c)*e*(-5*a*c*f+2*a*d*e+2*b*c*e)-3*a*c*(-5*a*c*f^2+3*b*d*e^2))*sqrt(d*x^2+c)/a^2/c^3/x/sqrt(b*x^2+a)-1/5*e^2*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a/c/x^5+2/15*e*(-5*a*c*f+2*a*d*e+2*b*c*e)*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a^2/c^2/x^3-1/15*sqrt(b)*(8*b^2*c^2*e^2+a*b*c*e*(-20*c*f+7*d*e)+a^2*(15*c^2*f^2-20*c*d*e*f+8*d^2*e^2))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/a^(5/2)/c^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+2/15*sqrt(b)*d*e*(-5*a*c*f+2*a*d*e+2*b*c*e)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/a^(3/2)/c^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(f*x^2+e)^2/x^8/sqrt(b*x^2+a)/sqrt(d*x^2+c),x,5,-2/105*(9*a*b*c*d*e*(-7*a*c*f+3*a*d*e+3*b*c*e)-(a*d+b*c)*(8*(a*d+b*c)*e*(-7*a*c*f+3*a*d*e+3*b*c*e)-5*a*c*(-7*a*c*f^2+5*b*d*e^2)))*sqrt(d*x^2+c)/a^3/c^4/x/sqrt(b*x^2+a)-1/7*e^2*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a/c/x^7+2/35*e*(-7*a*c*f+3*a*d*e+3*b*c*e)*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a^2/c^2/x^5-1/105*(8*(a*d+b*c)*e*(-7*a*c*f+3*a*d*e+3*b*c*e)-5*a*c*(-7*a*c*f^2+5*b*d*e^2))*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a^3/c^3/x^3+2/105*sqrt(b)*(24*b^3*c^3*e^2+4*a*b^2*c^2*e*(-14*c*f+5*d*e)+a^3*d*(35*c^2*f^2-56*c*d*e*f+24*d^2*e^2)+a^2*b*c*(35*c^2*f^2-49*c*d*e*f+20*d^2*e^2))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/a^(7/2)/c^4/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/105*sqrt(b)*d*(24*b^2*c^2*e^2+a*b*c*e*(-56*c*f+23*d*e)+a^2*(35*c^2*f^2-56*c*d*e*f+24*d^2*e^2))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/a^(5/2)/c^4/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[x^6*(f*x^2+e)/sqrt(b*x^2+a)/sqrt(d*x^2+c),x,7,-1/105*(48*a^3*d^3*f-a*b^2*c*d*(-40*c*f+49*d*e)-8*b^3*c^2*(-6*c*f+7*d*e)-8*a^2*b*d^2*(-5*c*f+7*d*e))*x*sqrt(d*x^2+c)/b^3/d^4/sqrt(b*x^2+a)-1/105*(25*a*b*c*d*f+4*(a*d+b*c)*(-6*a*d*f-6*b*c*f+7*b*d*e))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b^3/d^3+1/35*(-6*a*d*f-6*b*c*f+7*b*d*e)*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b^2/d^2+1/7*f*x^5*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b/d+1/105*sqrt(a)*(48*a^3*d^3*f-a*b^2*c*d*(-40*c*f+49*d*e)-8*b^3*c^2*(-6*c*f+7*d*e)-8*a^2*b*d^2*(-5*c*f+7*d*e))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/b^(7/2)/d^4/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/105*a^(3/2)*(25*a*b*c*d*f+4*(a*d+b*c)*(-6*a*d*f-6*b*c*f+7*b*d*e))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(7/2)/d^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[x^4*(f*x^2+e)/sqrt(b*x^2+a)/sqrt(d*x^2+c),x,6,-1/15*(9*a*b*c*d*f+2*(a*d+b*c)*(-4*a*d*f-4*b*c*f+5*b*d*e))*x*sqrt(d*x^2+c)/b^2/d^3/sqrt(b*x^2+a)+1/15*(-4*a*d*f-4*b*c*f+5*b*d*e)*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b^2/d^2+1/5*f*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b/d+1/15*sqrt(a)*(9*a*b*c*d*f+2*(a*d+b*c)*(-4*a*d*f-4*b*c*f+5*b*d*e))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/b^(5/2)/d^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/15*a^(3/2)*(-4*a*d*f-4*b*c*f+5*b*d*e)*sqrt(d*x^2+c)*InverseJacobiAM(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],
[x^2*(f*x^2+e)/sqrt(b*x^2+a)/sqrt(d*x^2+c),x,5,1/3*(-2*a*d*f-2*b*c*f+3*b*d*e)*x*sqrt(d*x^2+c)/b/d^2/sqrt(b*x^2+a)+1/3*f*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b/d-1/3*sqrt(a)*(-2*a*d*f-2*b*c*f+3*b*d*e)*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))-1/3*a^(3/2)*f*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],
[(f*x^2+e)/sqrt(b*x^2+a)/sqrt(d*x^2+c),x,4,f*x*sqrt(d*x^2+c)/d/sqrt(b*x^2+a)-sqrt(a)*f*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))+sqrt(a)*e*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],
[(f*x^2+e)/x^2/sqrt(b*x^2+a)/sqrt(d*x^2+c),x,2,-e*sqrt(d*x^2+c)/c/x/sqrt(b*x^2+a)-sqrt(b)*e*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/sqrt(a)/c/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+sqrt(a)*f*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],
[(f*x^2+e)/x^4/sqrt(b*x^2+a)/sqrt(d*x^2+c),x,3,1/3*(-3*a*c*f+2*a*d*e+2*b*c*e)*sqrt(d*x^2+c)/a/c^2/x/sqrt(b*x^2+a)-1/3*e*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a/c/x^3+1/3*sqrt(b)*(-3*a*c*f+2*a*d*e+2*b*c*e)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/a^(3/2)/c^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/3*sqrt(b)*d*e*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(a)/c^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(f*x^2+e)/x^6/sqrt(b*x^2+a)/sqrt(d*x^2+c),x,4,1/15*(9*a*b*c*d*e-2*(a*d+b*c)*(-5*a*c*f+4*a*d*e+4*b*c*e))*sqrt(d*x^2+c)/a^2/c^3/x/sqrt(b*x^2+a)-1/5*e*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a/c/x^5+1/15*(-5*a*c*f+4*a*d*e+4*b*c*e)*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a^2/c^2/x^3-1/15*sqrt(b)*(8*b^2*c^2*e+a*b*c*(-10*c*f+7*d*e)+2*a^2*d*(-5*c*f+4*d*e))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/a^(5/2)/c^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/15*sqrt(b)*d*(-5*a*c*f+4*a*d*e+4*b*c*e)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/a^(3/2)/c^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[x^8/sqrt(b*x^2+a)/sqrt(d*x^2+c)/(f*x^2+e),x,6,1/15*(8*a^2*d*f+a*b*(7*c*f+10*d*e)+b^2*(10*c*e+15*d*e^2/f+8*c^2*f/d))*x*sqrt(d*x^2+c)/b^2/d^2/f^2/sqrt(b*x^2+a)-1/15*(4*a*d*f+4*b*c*f+5*b*d*e)*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b^2/d^2/f^2+1/5*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b/d/f-1/15*sqrt(a)*(8*a^2*d^2*f^2+a*b*d*f*(7*c*f+10*d*e)+b^2*(8*c^2*f^2+10*c*d*e*f+15*d^2*e^2))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/b^(5/2)/d^3/f^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/15*a^(3/2)*(4*a^2*c*d*f^3+a*b*c*f^2*(4*c*f+d*e)-b^2*e*(4*c^2*f^2+5*c*d*e*f+15*d^2*e^2))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(5/2)/c/d^2/f^3/(-a*f+b*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-a^(3/2)*e^3*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/f^3/(-a*f+b*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[x^6/sqrt(b*x^2+a)/sqrt(d*x^2+c)/(f*x^2+e),x,5,-1/3*(2*a*d*f+2*b*c*f+3*b*d*e)*x*sqrt(d*x^2+c)/b/d^2/f^2/sqrt(b*x^2+a)+1/3*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b/d/f+1/3*sqrt(a)*(2*a*d*f+2*b*c*f+3*b*d*e)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/b^(3/2)/d^2/f^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/3*a^(3/2)*(a*c*f^2-b*e*(c*f+3*d*e))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(3/2)/c/d/f^2/(-a*f+b*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+a^(3/2)*e^2*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/f^2/(-a*f+b*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[x^4/sqrt(b*x^2+a)/sqrt(d*x^2+c)/(f*x^2+e),x,6,x*sqrt(d*x^2+c)/d/f/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)/d/f/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+sqrt(a)*e*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(b)/f/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-c^(3/2)*e*sqrt(b*x^2+a)*EllipticPi(sin(arctan(sqrt(d)*x/sqrt(c))),1-c*f/d/e,sqrt(1-b*c/a/d))/a/sqrt(d)/f/(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[x^2/sqrt(b*x^2+a)/sqrt(d*x^2+c)/(f*x^2+e),x,3,-sqrt(a)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(b)/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+c^(3/2)*sqrt(b*x^2+a)*EllipticPi(sin(arctan(sqrt(d)*x/sqrt(c))),1-c*f/d/e,sqrt(1-b*c/a/d))/a/sqrt(d)/(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[1/sqrt(b*x^2+a)/sqrt(d*x^2+c)/(f*x^2+e),x,3,sqrt(a)*sqrt(b)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/c/(-a*f+b*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-a^(3/2)*f*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e/(-a*f+b*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[1/x^2/sqrt(b*x^2+a)/sqrt(d*x^2+c)/(f*x^2+e),x,5,b*x*sqrt(d*x^2+c)/a/c/e/sqrt(b*x^2+a)-sqrt(b*x^2+a)*sqrt(d*x^2+c)/a/c/e/x-sqrt(b)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/sqrt(a)/c/e/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-sqrt(a)*sqrt(b)*f*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/c/e/(-a*f+b*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+a^(3/2)*f^2*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e^2/(-a*f+b*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[1/x^4/sqrt(b*x^2+a)/sqrt(d*x^2+c)/(f*x^2+e),x,5,1/3*(3*a*c*f+2*a*d*e+2*b*c*e)*sqrt(b*x^2+a)/a^2/c/e^2/x/sqrt(d*x^2+c)-1/3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a/c/e/x^3+1/3*sqrt(d)*(3*a*c*f+2*a*d*e+2*b*c*e)*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/a^2/c^(3/2)/e^2/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+1/3*sqrt(d)*(3*a*c*f^2-b*e*(-c*f+d*e))*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a^2/sqrt(c)/e^2/(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-c^(3/2)*f^3*sqrt(b*x^2+a)*EllipticPi(sin(arctan(sqrt(d)*x/sqrt(c))),1-c*f/d/e,sqrt(1-b*c/a/d))/a/sqrt(d)/e^3/(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[1/x^6/sqrt(b*x^2+a)/sqrt(d*x^2+c)/(f*x^2+e),x,6,-1/15*(8*b^2*c^2*e/a+b*c*(10*c*f+7*d*e)+a*(8*d^2*e+10*c*d*f+15*c^2*f^2/e))*sqrt(b*x^2+a)/a^2/c^2/e^2/x/sqrt(d*x^2+c)-1/5*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a/c/e/x^5+1/15*(5*a*c*f+4*a*d*e+4*b*c*e)*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a^2/c^2/e^2/x^3-1/15*sqrt(d)*(8*b^2*c^2*e^2+a*b*c*e*(10*c*f+7*d*e)+a^2*(15*c^2*f^2+10*c*d*e*f+8*d^2*e^2))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/a^3/c^(5/2)/e^3/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-1/15*sqrt(d)*(15*a^2*c^2*f^3-4*b^2*c*e^2*(-c*f+d*e)-a*b*e*(-5*c^2*f^2+c*d*e*f+4*d^2*e^2))*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a^3/c^(3/2)/e^3/(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+c^(3/2)*f^4*sqrt(b*x^2+a)*EllipticPi(sin(arctan(sqrt(d)*x/sqrt(c))),1-c*f/d/e,sqrt(1-b*c/a/d))/a/sqrt(d)/e^4/(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[x^8/sqrt(b*x^2+a)/sqrt(d*x^2+c)/(f*x^2+e)^2,x,6,1/6*(4*a^2*d*f^2*(-c*f+d*e)-b^2*e*(-4*c^2*f^2-8*c*d*e*f+15*d^2*e^2)+4*a*b*f*(-c^2*f^2-c*d*e*f+2*d^2*e^2))*x*sqrt(d*x^2+c)/b/d^2/f^3/(-a*f+b*e)/(-c*f+d*e)/sqrt(b*x^2+a)+1/3*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b/d/f^2+1/2*e^3*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/f^2/(-a*f+b*e)/(-c*f+d*e)/(f*x^2+e)-1/6*sqrt(a)*(4*a^2*d*f^2*(-c*f+d*e)-b^2*e*(-4*c^2*f^2-8*c*d*e*f+15*d^2*e^2)+4*a*b*f*(-c^2*f^2-c*d*e*f+2*d^2*e^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/f^3/(-a*f+b*e)/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/6*a^(3/2)*(2*a^2*c*f^3-2*a*b*e*f*(2*c*f+9*d*e)+b^2*e^2*(2*c*f+15*d*e))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(3/2)/c/d/f^3/(-a*f+b*e)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/2*a^(3/2)*e^2*(a*f*(-7*c*f+6*d*e)-b*e*(-6*c*f+5*d*e))*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/f^3/(-a*f+b*e)^2/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[x^6/sqrt(b*x^2+a)/sqrt(d*x^2+c)/(f*x^2+e)^2,x,5,1/2*(b*e*(-2*c*f+3*d*e)-2*a*f*(-c*f+d*e))*x*sqrt(d*x^2+c)/d/f^2/(-a*f+b*e)/(-c*f+d*e)/sqrt(b*x^2+a)-1/2*e^2*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/f/(-a*f+b*e)/(-c*f+d*e)/(f*x^2+e)-1/2*sqrt(a)*(b*e*(-2*c*f+3*d*e)-2*a*f*(-c*f+d*e))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/sqrt(b)/d/f^2/(-a*f+b*e)/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/2*a^(3/2)*e*(-4*a*f+3*b*e)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(b)/c/f^2/(-a*f+b*e)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/2*a^(3/2)*e*(a*f*(-5*c*f+4*d*e)-b*e*(-4*c*f+3*d*e))*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/f^2/(-a*f+b*e)^2/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[x^4/sqrt(b*x^2+a)/sqrt(d*x^2+c)/(f*x^2+e)^2,x,5,-1/2*b*e*x*sqrt(d*x^2+c)/f/(-a*f+b*e)/(-c*f+d*e)/sqrt(b*x^2+a)+1/2*e*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/(-a*f+b*e)/(-c*f+d*e)/(f*x^2+e)+1/2*sqrt(a)*sqrt(b)*e*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/f/(-a*f+b*e)/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/2*a^(3/2)*(-2*a*f+b*e)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(b)/c/f/(-a*f+b*e)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/2*a^(3/2)*(a*f*(-3*c*f+2*d*e)-b*e*(-2*c*f+d*e))*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/f/(-a*f+b*e)^2/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[x^2/sqrt(b*x^2+a)/sqrt(d*x^2+c)/(f*x^2+e)^2,x,5,1/2*b*x*sqrt(d*x^2+c)/(-a*f+b*e)/(-c*f+d*e)/sqrt(b*x^2+a)-1/2*f*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/(-a*f+b*e)/(-c*f+d*e)/(f*x^2+e)-1/2*sqrt(a)*sqrt(b)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/(-a*f+b*e)/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/2*a^(3/2)*sqrt(b)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/c/(-a*f+b*e)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/2*a^(3/2)*(-a*c*f^2+b*d*e^2)*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e/(-a*f+b*e)^2/(-c*f+d*e)/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)/(f*x^2+e)^2,x,4,-1/2*f*x*sqrt(b*x^2+a)/e/(-a*f+b*e)/sqrt(d*x^2+c)/(f*x^2+e)+1/2*sqrt(c)*sqrt(d)*f*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/e/(-a*f+b*e)/(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+1/2*sqrt(c)*sqrt(d)*(-c*f+2*d*e)*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a/e/(-c*f+d*e)^2/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-1/2*c^(3/2)*f*(b*e*(-2*c*f+3*d*e)-a*f*(-c*f+2*d*e))*sqrt(b*x^2+a)*EllipticPi(sin(arctan(sqrt(d)*x/sqrt(c))),1-c*f/d/e,sqrt(1-b*c/a/d))/a/sqrt(d)/e^2/(-a*f+b*e)/(-c*f+d*e)^2/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[1/x^2/sqrt(b*x^2+a)/sqrt(d*x^2+c)/(f*x^2+e)^2,x,5,-1/2*(a*f*(-3*c*f+2*d*e)-2*b*e*(-c*f+d*e))*x*sqrt(b*x^2+a)/a/c/e^2/(-a*f+b*e)/sqrt(d*x^2+c)/(f*x^2+e)-sqrt(b*x^2+a)*sqrt(d*x^2+c)/a/c/e/x/(f*x^2+e)+1/2*sqrt(d)*(a*f*(-3*c*f+2*d*e)-2*b*e*(-c*f+d*e))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/a/sqrt(c)/e^2/(-a*f+b*e)/(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-1/2*sqrt(c)*sqrt(d)*f*(-3*c*f+4*d*e)*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a/e^2/(-c*f+d*e)^2/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+1/2*c^(3/2)*f^2*(b*e*(-4*c*f+5*d*e)-a*f*(-3*c*f+4*d*e))*sqrt(b*x^2+a)*EllipticPi(sin(arctan(sqrt(d)*x/sqrt(c))),1-c*f/d/e,sqrt(1-b*c/a/d))/a/sqrt(d)/e^3/(-a*f+b*e)/(-c*f+d*e)^2/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[1/x^4/sqrt(b*x^2+a)/sqrt(d*x^2+c)/(f*x^2+e)^2,x,6,-1/6*(4*b^2*c*e^2*(-c*f+d*e)-a^2*f*(-15*c^2*f^2+8*c*d*e*f+4*d^2*e^2)+4*a*b*e*(-2*c^2*f^2+c*d*e*f+d^2*e^2))*x*sqrt(b*x^2+a)/a^2/c^2/e^3/(-a*f+b*e)/sqrt(d*x^2+c)/(f*x^2+e)-1/3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a/c/e/x^3/(f*x^2+e)+1/3*(5*a*c*f+2*a*d*e+2*b*c*e)*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a^2/c^2/e^2/x/(f*x^2+e)+1/6*sqrt(d)*(4*b^2*c*e^2*(-c*f+d*e)-a^2*f*(-15*c^2*f^2+8*c*d*e*f+4*d^2*e^2)+4*a*b*e*(-2*c^2*f^2+c*d*e*f+d^2*e^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)/e^3/(-a*f+b*e)/(-c*f+d*e)/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-1/6*sqrt(d)*(2*b-3*a*c*f^2*(-5*c*f+6*d*e)/e/(-c*f+d*e)^2)*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a^2/sqrt(c)/e^2/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-1/2*c^(3/2)*f^3*(b*e*(-6*c*f+7*d*e)-a*f*(-5*c*f+6*d*e))*sqrt(b*x^2+a)*EllipticPi(sin(arctan(sqrt(d)*x/sqrt(c))),1-c*f/d/e,sqrt(1-b*c/a/d))/a/sqrt(d)/e^4/(-a*f+b*e)/(-c*f+d*e)^2/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[x^10/sqrt(b*x^2+a)/sqrt(d*x^2+c)/(f*x^2+e)^3,x,7,-1/24*(16*a^3*d*f^3*(-c*f+d*e)^2+8*a^2*b*f^2*(-c*f+d*e)^2*(2*c*f+5*d*e)+b^3*e^2*(16*c^3*f^3+40*c^2*d*e*f^2-170*c*d^2*e^2*f+105*d^3*e^3)-a*b^2*e*f*(32*c^3*f^3+64*c^2*d*e*f^2-275*c*d^2*e^2*f+170*d^3*e^3))*x*sqrt(d*x^2+c)/b/d^2/f^4/(-a*f+b*e)^2/(-c*f+d*e)^2/sqrt(b*x^2+a)+1/3*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b/d/f^3-1/4*e^4*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/f^3/(-a*f+b*e)/(-c*f+d*e)/(f*x^2+e)^2-1/8*e^3*(a*f*(-17*c*f+14*d*e)-b*e*(-14*c*f+11*d*e))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/f^3/(-a*f+b*e)^2/(-c*f+d*e)^2/(f*x^2+e)+1/24*sqrt(a)*(16*a^3*d*f^3*(-c*f+d*e)^2+8*a^2*b*f^2*(-c*f+d*e)^2*(2*c*f+5*d*e)+b^3*e^2*(16*c^3*f^3+40*c^2*d*e*f^2-170*c*d^2*e^2*f+105*d^3*e^3)-a*b^2*e*f*(32*c^3*f^3+64*c^2*d*e*f^2-275*c*d^2*e^2*f+170*d^3*e^3))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/b^(3/2)/d^2/f^4/(-a*f+b*e)^2/(-c*f+d*e)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/24*a^(3/2)*(8*a^3*c*f^4*(-c*f+d*e)-b^3*e^3*(-8*c^2*f^2-100*c*d*e*f+105*d^2*e^2)+3*a*b^2*e^2*f*(-8*c^2*f^2-73*c*d*e*f+80*d^2*e^2)-24*a^2*b*e*f^2*(-c^2*f^2-5*c*d*e*f+6*d^2*e^2))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(3/2)/c/d/f^4/(-a*f+b*e)^3/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/8*a^(3/2)*e^2*(3*a^2*f^2*(21*c^2*f^2-36*c*d*e*f+16*d^2*e^2)+b^2*e^2*(48*c^2*f^2-80*c*d*e*f+35*d^2*e^2)-2*a*b*e*f*(54*c^2*f^2-91*c*d*e*f+40*d^2*e^2))*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/f^4/(-a*f+b*e)^3/(-c*f+d*e)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[x^8/sqrt(b*x^2+a)/sqrt(d*x^2+c)/(f*x^2+e)^3,x,6,1/8*(8*a^2*f^2*(-c*f+d*e)^2+b^2*e^2*(8*c^2*f^2-26*c*d*e*f+15*d^2*e^2)-a*b*e*f*(16*c^2*f^2-45*c*d*e*f+26*d^2*e^2))*x*sqrt(d*x^2+c)/d/f^3/(-a*f+b*e)^2/(-c*f+d*e)^2/sqrt(b*x^2+a)+1/4*e^3*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/f^2/(-a*f+b*e)/(-c*f+d*e)/(f*x^2+e)^2+1/8*e^2*(a*f*(-13*c*f+10*d*e)-b*e*(-10*c*f+7*d*e))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/f^2/(-a*f+b*e)^2/(-c*f+d*e)^2/(f*x^2+e)-1/8*sqrt(a)*(8*a^2*f^2*(-c*f+d*e)^2+b^2*e^2*(8*c^2*f^2-26*c*d*e*f+15*d^2*e^2)-a*b*e*f*(16*c^2*f^2-45*c*d*e*f+26*d^2*e^2))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/sqrt(b)/d/f^3/(-a*f+b*e)^2/(-c*f+d*e)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/8*a^(3/2)*e*(a*b*e*f*(-37*c*f+36*d*e)-b^2*e^2*(-16*c*f+15*d*e)-24*a^2*f^2*(-c*f+d*e))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/sqrt(b)/c/f^3/(-a*f+b*e)^3/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/8*a^(3/2)*e*(3*b^2*e^2*(8*c^2*f^2-12*c*d*e*f+5*d^2*e^2)-2*a*b*e*f*(28*c^2*f^2-43*c*d*e*f+18*d^2*e^2)+a^2*f^2*(35*c^2*f^2-56*c*d*e*f+24*d^2*e^2))*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/f^3/(-a*f+b*e)^3/(-c*f+d*e)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[x^6/sqrt(b*x^2+a)/sqrt(d*x^2+c)/(f*x^2+e)^3,x,5,-1/4*e^2*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/f/(-a*f+b*e)/(-c*f+d*e)/(f*x^2+e)^2+3/8*e*(a*f*(-3*c*f+2*d*e)-b*e*(-2*c*f+d*e))*x*sqrt(b*x^2+a)/f^2/(-a*f+b*e)^2/(-c*f+d*e)/sqrt(d*x^2+c)/(f*x^2+e)-3/8*sqrt(c)*sqrt(d)*e*(a*f*(-3*c*f+2*d*e)-b*e*(-2*c*f+d*e))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/f^2/(-a*f+b*e)^2/(-c*f+d*e)^2/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+1/8*c^(3/2)*(a*f*(8*c^2*f^2-9*c*d*e*f+4*d^2*e^2)-b*e*(8*c^2*f^2-8*c*d*e*f+3*d^2*e^2))*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a/sqrt(d)/f^2/(-a*f+b*e)/(-c*f+d*e)^3/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+1/8*c^(3/2)*(b^2*e^2*(8*c^2*f^2-8*c*d*e*f+3*d^2*e^2)-2*a*b*e*f*(10*c^2*f^2-11*c*d*e*f+4*d^2*e^2)+a^2*f^2*(15*c^2*f^2-20*c*d*e*f+8*d^2*e^2))*sqrt(b*x^2+a)*EllipticPi(sin(arctan(sqrt(d)*x/sqrt(c))),1-c*f/d/e,sqrt(1-b*c/a/d))/a/sqrt(d)/f^2/(-a*f+b*e)^2/(-c*f+d*e)^3/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[x^4/sqrt(b*x^2+a)/sqrt(d*x^2+c)/(f*x^2+e)^3,x,5,1/4*e*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/(-a*f+b*e)/(-c*f+d*e)/(f*x^2+e)^2-1/8*(a*f*(-5*c*f+2*d*e)+b*e*(2*c*f+d*e))*x*sqrt(b*x^2+a)/f/(-a*f+b*e)^2/(-c*f+d*e)/sqrt(d*x^2+c)/(f*x^2+e)+1/8*sqrt(c)*sqrt(d)*(a*f*(-5*c*f+2*d*e)+b*e*(2*c*f+d*e))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/f/(-a*f+b*e)^2/(-c*f+d*e)^2/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-1/8*c^(3/2)*sqrt(d)*(3*a*c*f^2+b*e*(-4*c*f+d*e))*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a/f/(-a*f+b*e)/(-c*f+d*e)^3/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-1/8*c^(3/2)*(3*a^2*c^2*f^4+2*a*b*d*e^2*f*(-5*c*f+2*d*e)-b^2*d*e^3*(-4*c*f+d*e))*sqrt(b*x^2+a)*EllipticPi(sin(arctan(sqrt(d)*x/sqrt(c))),1-c*f/d/e,sqrt(1-b*c/a/d))/a/sqrt(d)/e/f/(-a*f+b*e)^2/(-c*f+d*e)^3/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[x^2/sqrt(b*x^2+a)/sqrt(d*x^2+c)/(f*x^2+e)^3,x,5,-1/4*f*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/(-a*f+b*e)/(-c*f+d*e)/(f*x^2+e)^2+1/8*(b*e*(-2*c*f+5*d*e)-a*f*(c*f+2*d*e))*x*sqrt(b*x^2+a)/e/(-a*f+b*e)^2/(-c*f+d*e)/sqrt(d*x^2+c)/(f*x^2+e)-1/8*sqrt(c)*sqrt(d)*(b*e*(-2*c*f+5*d*e)-a*f*(c*f+2*d*e))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/e/(-a*f+b*e)^2/(-c*f+d*e)^2/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-1/8*c^(3/2)*sqrt(d)*(3*b*d*e^2-a*f*(-c*f+4*d*e))*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a/e/(-a*f+b*e)/(-c*f+d*e)^3/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+1/8*c^(3/2)*(3*b^2*d^2*e^4-2*a*b*c*e*f^2*(-2*c*f+5*d*e)+a^2*c*f^3*(-c*f+4*d*e))*sqrt(b*x^2+a)*EllipticPi(sin(arctan(sqrt(d)*x/sqrt(c))),1-c*f/d/e,sqrt(1-b*c/a/d))/a/sqrt(d)/e^2/(-a*f+b*e)^2/(-c*f+d*e)^3/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[1/sqrt(b*x^2+a)/sqrt(d*x^2+c)/(f*x^2+e)^3,x,5,1/4*f^2*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/e/(-a*f+b*e)/(-c*f+d*e)/(f*x^2+e)^2-3/8*f*(b*e*(-2*c*f+3*d*e)-a*f*(-c*f+2*d*e))*x*sqrt(b*x^2+a)/e^2/(-a*f+b*e)^2/(-c*f+d*e)/sqrt(d*x^2+c)/(f*x^2+e)+3/8*sqrt(c)*sqrt(d)*f*(b*e*(-2*c*f+3*d*e)-a*f*(-c*f+2*d*e))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/e^2/(-a*f+b*e)^2/(-c*f+d*e)^2/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-1/8*sqrt(c)*sqrt(d)*(a*f*(3*c^2*f^2-8*c*d*e*f+8*d^2*e^2)-b*e*(4*c^2*f^2-9*c*d*e*f+8*d^2*e^2))*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a/e^2/(-a*f+b*e)/(-c*f+d*e)^3/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-1/8*c^(3/2)*f*(a^2*f^2*(3*c^2*f^2-8*c*d*e*f+8*d^2*e^2)-2*a*b*e*f*(4*c^2*f^2-11*c*d*e*f+10*d^2*e^2)+b^2*e^2*(8*c^2*f^2-20*c*d*e*f+15*d^2*e^2))*sqrt(b*x^2+a)*EllipticPi(sin(arctan(sqrt(d)*x/sqrt(c))),1-c*f/d/e,sqrt(1-b*c/a/d))/a/sqrt(d)/e^3/(-a*f+b*e)^2/(-c*f+d*e)^3/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[1/x^2/sqrt(b*x^2+a)/sqrt(d*x^2+c)/(f*x^2+e)^3,x,6,-sqrt(b*x^2+a)*sqrt(d*x^2+c)/a/c/e/x/(f*x^2+e)^2+1/4*f*(a*f*(-5*c*f+4*d*e)-4*b*e*(-c*f+d*e))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a/c/e^2/(-a*f+b*e)/(-c*f+d*e)/(f*x^2+e)^2+1/8*(8*b^2*e^2*(-c*f+d*e)^2+a^2*f^2*(15*c^2*f^2-26*c*d*e*f+8*d^2*e^2)-a*b*e*f*(26*c^2*f^2-45*c*d*e*f+16*d^2*e^2))*x*sqrt(b*x^2+a)/a/c/e^3/(-a*f+b*e)^2/(-c*f+d*e)/sqrt(d*x^2+c)/(f*x^2+e)-1/8*sqrt(d)*(8*b^2*e^2*(-c*f+d*e)^2+a^2*f^2*(15*c^2*f^2-26*c*d*e*f+8*d^2*e^2)-a*b*e*f*(26*c^2*f^2-45*c*d*e*f+16*d^2*e^2))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/a/sqrt(c)/e^3/(-a*f+b*e)^2/(-c*f+d*e)^2/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+1/8*sqrt(c)*sqrt(d)*f*(3*a*f*(5*c^2*f^2-12*c*d*e*f+8*d^2*e^2)-b*e*(16*c^2*f^2-37*c*d*e*f+24*d^2*e^2))*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a/e^3/(-a*f+b*e)/(-c*f+d*e)^3/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)+1/8*c^(3/2)*f^2*(3*a^2*f^2*(5*c^2*f^2-12*c*d*e*f+8*d^2*e^2)-2*a*b*e*f*(18*c^2*f^2-43*c*d*e*f+28*d^2*e^2)+b^2*e^2*(24*c^2*f^2-56*c*d*e*f+35*d^2*e^2))*sqrt(b*x^2+a)*EllipticPi(sin(arctan(sqrt(d)*x/sqrt(c))),1-c*f/d/e,sqrt(1-b*c/a/d))/a/sqrt(d)/e^4/(-a*f+b*e)^2/(-c*f+d*e)^3/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[1/x^4/sqrt(b*x^2+a)/sqrt(d*x^2+c)/(f*x^2+e)^3,x,7,-1/3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a/c/e/x^3/(f*x^2+e)^2+1/3*(7*a*c*f+2*a*d*e+2*b*c*e)*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a^2/c^2/e^2/x/(f*x^2+e)^2+1/12*f*(8*b^2*c*e^2*(-c*f+d*e)-a^2*f*(-35*c^2*f^2+24*c*d*e*f+8*d^2*e^2)+8*a*b*e*(-3*c^2*f^2+2*c*d*e*f+d^2*e^2))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a^2/c^2/e^3/(-a*f+b*e)/(-c*f+d*e)/(f*x^2+e)^2-1/24*(16*b^3*c*e^3*(-c*f+d*e)^2+8*a*b^2*e^2*(-c*f+d*e)^2*(5*c*f+2*d*e)+a^3*f^2*(105*c^3*f^3-170*c^2*d*e*f^2+40*c*d^2*e^2*f+16*d^3*e^3)-a^2*b*e*f*(170*c^3*f^3-275*c^2*d*e*f^2+64*c*d^2*e^2*f+32*d^3*e^3))*x*sqrt(b*x^2+a)/a^2/c^2/e^4/(-a*f+b*e)^2/(-c*f+d*e)/sqrt(d*x^2+c)/(f*x^2+e)+1/24*sqrt(d)*(16*b^3*c*e^3*(-c*f+d*e)^2+8*a*b^2*e^2*(-c*f+d*e)^2*(5*c*f+2*d*e)+a^3*f^2*(105*c^3*f^3-170*c^2*d*e*f^2+40*c*d^2*e^2*f+16*d^3*e^3)-a^2*b*e*f*(170*c^3*f^3-275*c^2*d*e*f^2+64*c*d^2*e^2*f+32*d^3*e^3))*sqrt(b*x^2+a)*EllipticE(sin(arctan(sqrt(d)*x/sqrt(c))),sqrt(1-b*c/a/d))/a^2/c^(3/2)/e^4/(-a*f+b*e)^2/(-c*f+d*e)^2/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-1/24*sqrt(d)*(8*b^2*e^2*(-c*f+d*e)^3+3*a^2*c*f^3*(35*c^2*f^2-80*c*d*e*f+48*d^2*e^2)-a*b*e*f*(100*c^3*f^3-219*c^2*d*e*f^2+120*c*d^2*e^2*f+8*d^3*e^3))*sqrt(b*x^2+a)*InverseJacobiAM(arctan(sqrt(d)*x/sqrt(c)),sqrt(1-b*c/a/d))/a^2/sqrt(c)/e^4/(-a*f+b*e)/(-c*f+d*e)^3/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c)-1/8*c^(3/2)*f^3*(3*b^2*e^2*(16*c^2*f^2-36*c*d*e*f+21*d^2*e^2)+a^2*f^2*(35*c^2*f^2-80*c*d*e*f+48*d^2*e^2)-2*a*b*e*f*(40*c^2*f^2-91*c*d*e*f+54*d^2*e^2))*sqrt(b*x^2+a)*EllipticPi(sin(arctan(sqrt(d)*x/sqrt(c))),1-c*f/d/e,sqrt(1-b*c/a/d))/a/sqrt(d)/e^5/(-a*f+b*e)^2/(-c*f+d*e)^3/sqrt(c*(b*x^2+a)/a/(d*x^2+c))/sqrt(d*x^2+c),1],
[x^4*(f*x^2+e)^2/sqrt(-b*x^2+a)/sqrt(d*x^2+c),x,10,1/105*(8*(-a*d+b*c)*f*(3*a*d*f-3*b*c*f+7*b*d*e)-5*b*d*(5*a*c*f^2+7*b*d*e^2))*x*sqrt(-b*x^2+a)*sqrt(d*x^2+c)/b^3/d^3-2/35*f*(3*a*d*f-3*b*c*f+7*b*d*e)*x^3*sqrt(-b*x^2+a)*sqrt(d*x^2+c)/b^2/d^2-1/7*f^2*x^5*sqrt(-b*x^2+a)*sqrt(d*x^2+c)/b/d+2/105*sqrt(a)*(9*a*b*c*d*f*(3*a*d*f-3*b*c*f+7*b*d*e)+(-a*d+b*c)*(8*(-a*d+b*c)*f*(3*a*d*f-3*b*c*f+7*b*d*e)-5*b*d*(5*a*c*f^2+7*b*d*e^2)))*sqrt(1-b*x^2/a)*sqrt(d*x^2+c)*EllipticE(sin(arcsin(sqrt(b)*x/sqrt(a))),sqrt(-a*d/b/c))/b^(7/2)/d^4/sqrt(-b*x^2+a)/sqrt(1+d*x^2/c)-1/105*sqrt(a)*c*(24*a^3*d^3*f^2+a^2*b*d^2*f*(-17*c*f+56*d*e)+a*b^2*d*(16*c^2*f^2-42*c*d*e*f+35*d^2*e^2)-2*b^3*c*(24*c^2*f^2-56*c*d*e*f+35*d^2*e^2))*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*InverseJacobiAM(arcsin(sqrt(b)*x/sqrt(a)),sqrt(-a*d/b/c))/b^(7/2)/d^4/sqrt(-b*x^2+a)/sqrt(d*x^2+c),1],
[x^2*(f*x^2+e)^2/sqrt(-b*x^2+a)/sqrt(d*x^2+c),x,9,-2/15*f*(2*a*d*f-2*b*c*f+5*b*d*e)*x*sqrt(-b*x^2+a)*sqrt(d*x^2+c)/b^2/d^2-1/5*f^2*x^3*sqrt(-b*x^2+a)*sqrt(d*x^2+c)/b/d-1/15*sqrt(a)*(4*(-a*d+b*c)*f*(2*a*d*f-2*b*c*f+5*b*d*e)-3*b*d*(3*a*c*f^2+5*b*d*e^2))*sqrt(1-b*x^2/a)*sqrt(d*x^2+c)*EllipticE(sin(arcsin(sqrt(b)*x/sqrt(a))),sqrt(-a*d/b/c))/b^(5/2)/d^3/sqrt(-b*x^2+a)/sqrt(1+d*x^2/c)-1/15*sqrt(a)*c*(4*a^2*d^2*f^2+a*b*d*f*(-3*c*f+10*d*e)+b^2*(8*c^2*f^2-20*c*d*e*f+15*d^2*e^2))*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*InverseJacobiAM(arcsin(sqrt(b)*x/sqrt(a)),sqrt(-a*d/b/c))/b^(5/2)/d^3/sqrt(-b*x^2+a)/sqrt(d*x^2+c),1],
[(f*x^2+e)^2/sqrt(-b*x^2+a)/sqrt(d*x^2+c),x,8,-1/3*f^2*x*sqrt(-b*x^2+a)*sqrt(d*x^2+c)/b/d+2/3*sqrt(a)*f*(a*d*f-b*c*f+3*b*d*e)*sqrt(1-b*x^2/a)*sqrt(d*x^2+c)*EllipticE(sin(arcsin(sqrt(b)*x/sqrt(a))),sqrt(-a*d/b/c))/b^(3/2)/d^2/sqrt(-b*x^2+a)/sqrt(1+d*x^2/c)-1/3*sqrt(a)*(a*c*d*f^2-b*(2*c^2*f^2-6*c*d*e*f+3*d^2*e^2))*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*InverseJacobiAM(arcsin(sqrt(b)*x/sqrt(a)),sqrt(-a*d/b/c))/b^(3/2)/d^2/sqrt(-b*x^2+a)/sqrt(d*x^2+c),1],
[(f*x^2+e)^2/x^2/sqrt(-b*x^2+a)/sqrt(d*x^2+c),x,8,-e^2*sqrt(-b*x^2+a)*sqrt(d*x^2+c)/a/c/x-(-a*c*f^2+b*d*e^2)*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)/c/d/sqrt(-b*x^2+a)/sqrt(1+d*x^2/c)+(b*d*e^2+a*f*(-c*f+2*d*e))*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)/d/sqrt(-b*x^2+a)/sqrt(d*x^2+c),1],
[(f*x^2+e)^2/x^4/sqrt(-b*x^2+a)/sqrt(d*x^2+c),x,9,-1/3*e^2*sqrt(-b*x^2+a)*sqrt(d*x^2+c)/a/c/x^3-2/3*e*(3*a*c*f-a*d*e+b*c*e)*sqrt(-b*x^2+a)*sqrt(d*x^2+c)/a^2/c^2/x-2/3*sqrt(b)*e*(3*a*c*f-a*d*e+b*c*e)*sqrt(1-b*x^2/a)*sqrt(d*x^2+c)*EllipticE(sin(arcsin(sqrt(b)*x/sqrt(a))),sqrt(-a*d/b/c))/a^(3/2)/c^2/sqrt(-b*x^2+a)/sqrt(1+d*x^2/c)+1/3*(2*b^2*c*e^2+3*a^2*c*f^2-a*b*e*(-6*c*f+d*e))*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*InverseJacobiAM(arcsin(sqrt(b)*x/sqrt(a)),sqrt(-a*d/b/c))/a^(3/2)/sqrt(b)/c/sqrt(-b*x^2+a)/sqrt(d*x^2+c),1],
[(f*x^2+e)^2/x^6/sqrt(-b*x^2+a)/sqrt(d*x^2+c),x,10,-1/5*e^2*sqrt(-b*x^2+a)*sqrt(d*x^2+c)/a/c/x^5-2/15*e*(5*a*c*f-2*a*d*e+2*b*c*e)*sqrt(-b*x^2+a)*sqrt(d*x^2+c)/a^2/c^2/x^3-1/15*(4*(-a*d+b*c)*e*(5*a*c*f-2*a*d*e+2*b*c*e)+3*a*c*(5*a*c*f^2+3*b*d*e^2))*sqrt(-b*x^2+a)*sqrt(d*x^2+c)/a^3/c^3/x-1/15*sqrt(b)*(4*(-a*d+b*c)*e*(5*a*c*f-2*a*d*e+2*b*c*e)+3*a*c*(5*a*c*f^2+3*b*d*e^2))*sqrt(1-b*x^2/a)*sqrt(d*x^2+c)*EllipticE(sin(arcsin(sqrt(b)*x/sqrt(a))),sqrt(-a*d/b/c))/a^(5/2)/c^3/sqrt(-b*x^2+a)/sqrt(1+d*x^2/c)+1/15*sqrt(b)*(8*b^2*c^2*e^2-a*b*c*e*(-20*c*f+3*d*e)+a^2*(15*c^2*f^2-10*c*d*e*f+4*d^2*e^2))*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*InverseJacobiAM(arcsin(sqrt(b)*x/sqrt(a)),sqrt(-a*d/b/c))/a^(5/2)/c^2/sqrt(-b*x^2+a)/sqrt(d*x^2+c),1],
[(f*x^2+e)^2/x^8/sqrt(-b*x^2+a)/sqrt(d*x^2+c),x,11,-1/7*e^2*sqrt(-b*x^2+a)*sqrt(d*x^2+c)/a/c/x^7-2/35*e*(7*a*c*f-3*a*d*e+3*b*c*e)*sqrt(-b*x^2+a)*sqrt(d*x^2+c)/a^2/c^2/x^5-1/105*(8*(-a*d+b*c)*e*(7*a*c*f-3*a*d*e+3*b*c*e)+5*a*c*(7*a*c*f^2+5*b*d*e^2))*sqrt(-b*x^2+a)*sqrt(d*x^2+c)/a^3/c^3/x^3-2/105*(9*a*b*c*d*e*(7*a*c*f-3*a*d*e+3*b*c*e)+(-a*d+b*c)*(8*(-a*d+b*c)*e*(7*a*c*f-3*a*d*e+3*b*c*e)+5*a*c*(7*a*c*f^2+5*b*d*e^2)))*sqrt(-b*x^2+a)*sqrt(d*x^2+c)/a^4/c^4/x-2/105*sqrt(b)*(9*a*b*c*d*e*(7*a*c*f-3*a*d*e+3*b*c*e)+(-a*d+b*c)*(8*(-a*d+b*c)*e*(7*a*c*f-3*a*d*e+3*b*c*e)+5*a*c*(7*a*c*f^2+5*b*d*e^2)))*sqrt(1-b*x^2/a)*sqrt(d*x^2+c)*EllipticE(sin(arcsin(sqrt(b)*x/sqrt(a))),sqrt(-a*d/b/c))/a^(7/2)/c^4/sqrt(-b*x^2+a)/sqrt(1+d*x^2/c)+1/105*sqrt(b)*(48*b^3*c^3*e^2-16*a*b^2*c^2*e*(-7*c*f+d*e)-a^3*d*(35*c^2*f^2-56*c*d*e*f+24*d^2*e^2)+a^2*b*c*(70*c^2*f^2-42*c*d*e*f+17*d^2*e^2))*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*InverseJacobiAM(arcsin(sqrt(b)*x/sqrt(a)),sqrt(-a*d/b/c))/a^(7/2)/c^3/sqrt(-b*x^2+a)/sqrt(d*x^2+c),1],
[x^6*(f*x^2+e)/sqrt(-b*x^2+a)/sqrt(d*x^2+c),x,10,-1/105*(25*a*b*c*d*f-4*(-a*d+b*c)*(6*a*d*f-6*b*c*f+7*b*d*e))*x*sqrt(-b*x^2+a)*sqrt(d*x^2+c)/b^3/d^3-1/35*(6*a*d*f-6*b*c*f+7*b*d*e)*x^3*sqrt(-b*x^2+a)*sqrt(d*x^2+c)/b^2/d^2-1/7*f*x^5*sqrt(-b*x^2+a)*sqrt(d*x^2+c)/b/d+1/105*sqrt(a)*(48*a^3*d^3*f-a*b^2*c*d*(-40*c*f+49*d*e)+8*b^3*c^2*(-6*c*f+7*d*e)+8*a^2*b*d^2*(-5*c*f+7*d*e))*sqrt(1-b*x^2/a)*sqrt(d*x^2+c)*EllipticE(sin(arcsin(sqrt(b)*x/sqrt(a))),sqrt(-a*d/b/c))/b^(7/2)/d^4/sqrt(-b*x^2+a)/sqrt(1+d*x^2/c)-1/105*sqrt(a)*c*(24*a^3*d^3*f+a^2*b*d^2*(-17*c*f+28*d*e)-a*b^2*c*d*(-16*c*f+21*d*e)+8*b^3*c^2*(-6*c*f+7*d*e))*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*InverseJacobiAM(arcsin(sqrt(b)*x/sqrt(a)),sqrt(-a*d/b/c))/b^(7/2)/d^4/sqrt(-b*x^2+a)/sqrt(d*x^2+c),1],
[x^4*(f*x^2+e)/sqrt(-b*x^2+a)/sqrt(d*x^2+c),x,9,-1/15*(4*a*d*f-4*b*c*f+5*b*d*e)*x*sqrt(-b*x^2+a)*sqrt(d*x^2+c)/b^2/d^2-1/5*f*x^3*sqrt(-b*x^2+a)*sqrt(d*x^2+c)/b/d+1/15*sqrt(a)*(9*a*b*c*d*f-2*(-a*d+b*c)*(4*a*d*f-4*b*c*f+5*b*d*e))*sqrt(1-b*x^2/a)*sqrt(d*x^2+c)*EllipticE(sin(arcsin(sqrt(b)*x/sqrt(a))),sqrt(-a*d/b/c))/b^(5/2)/d^3/sqrt(-b*x^2+a)/sqrt(1+d*x^2/c)-1/15*sqrt(a)*c*(4*a^2*d^2*f-2*b^2*c*(-4*c*f+5*d*e)+a*b*d*(-3*c*f+5*d*e))*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*InverseJacobiAM(arcsin(sqrt(b)*x/sqrt(a)),sqrt(-a*d/b/c))/b^(5/2)/d^3/sqrt(-b*x^2+a)/sqrt(d*x^2+c),1],
[x^2*(f*x^2+e)/sqrt(-b*x^2+a)/sqrt(d*x^2+c),x,8,-1/3*f*x*sqrt(-b*x^2+a)*sqrt(d*x^2+c)/b/d+1/3*sqrt(a)*(2*a*d*f-2*b*c*f+3*b*d*e)*sqrt(1-b*x^2/a)*sqrt(d*x^2+c)*EllipticE(sin(arcsin(sqrt(b)*x/sqrt(a))),sqrt(-a*d/b/c))/b^(3/2)/d^2/sqrt(-b*x^2+a)/sqrt(1+d*x^2/c)-1/3*sqrt(a)*c*(a*d*f-2*b*c*f+3*b*d*e)*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*InverseJacobiAM(arcsin(sqrt(b)*x/sqrt(a)),sqrt(-a*d/b/c))/b^(3/2)/d^2/sqrt(-b*x^2+a)/sqrt(d*x^2+c),1],
[(f*x^2+e)/sqrt(-b*x^2+a)/sqrt(d*x^2+c),x,7,sqrt(a)*f*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)/d/sqrt(-b*x^2+a)/sqrt(1+d*x^2/c)+sqrt(a)*(-c*f+d*e)*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)/d/sqrt(-b*x^2+a)/sqrt(d*x^2+c),1],
[(f*x^2+e)/x^2/sqrt(-b*x^2+a)/sqrt(d*x^2+c),x,8,-e*sqrt(-b*x^2+a)*sqrt(d*x^2+c)/a/c/x-sqrt(b)*e*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)/c/sqrt(-b*x^2+a)/sqrt(1+d*x^2/c)+(a*f+b*e)*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],
[(f*x^2+e)/x^4/sqrt(-b*x^2+a)/sqrt(d*x^2+c),x,9,-1/3*e*sqrt(-b*x^2+a)*sqrt(d*x^2+c)/a/c/x^3-1/3*(3*a*c*f-2*a*d*e+2*b*c*e)*sqrt(-b*x^2+a)*sqrt(d*x^2+c)/a^2/c^2/x-1/3*sqrt(b)*(3*a*c*f-2*a*d*e+2*b*c*e)*sqrt(1-b*x^2/a)*sqrt(d*x^2+c)*EllipticE(sin(arcsin(sqrt(b)*x/sqrt(a))),sqrt(-a*d/b/c))/a^(3/2)/c^2/sqrt(-b*x^2+a)/sqrt(1+d*x^2/c)+1/3*sqrt(b)*(3*a*c*f-a*d*e+2*b*c*e)*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*InverseJacobiAM(arcsin(sqrt(b)*x/sqrt(a)),sqrt(-a*d/b/c))/a^(3/2)/c/sqrt(-b*x^2+a)/sqrt(d*x^2+c),1],
[(f*x^2+e)/x^6/sqrt(-b*x^2+a)/sqrt(d*x^2+c),x,10,-1/5*e*sqrt(-b*x^2+a)*sqrt(d*x^2+c)/a/c/x^5-1/15*(5*a*c*f-4*a*d*e+4*b*c*e)*sqrt(-b*x^2+a)*sqrt(d*x^2+c)/a^2/c^2/x^3-1/15*(9*a*b*c*d*e+2*(-a*d+b*c)*(5*a*c*f-4*a*d*e+4*b*c*e))*sqrt(-b*x^2+a)*sqrt(d*x^2+c)/a^3/c^3/x-1/15*sqrt(b)*(9*a*b*c*d*e+2*(-a*d+b*c)*(5*a*c*f-4*a*d*e+4*b*c*e))*sqrt(1-b*x^2/a)*sqrt(d*x^2+c)*EllipticE(sin(arcsin(sqrt(b)*x/sqrt(a))),sqrt(-a*d/b/c))/a^(5/2)/c^3/sqrt(-b*x^2+a)/sqrt(1+d*x^2/c)+1/15*sqrt(b)*(8*b^2*c^2*e-a*b*c*(-10*c*f+3*d*e)+a^2*d*(-5*c*f+4*d*e))*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*InverseJacobiAM(arcsin(sqrt(b)*x/sqrt(a)),sqrt(-a*d/b/c))/a^(5/2)/c^2/sqrt(-b*x^2+a)/sqrt(d*x^2+c),1],
[x^8/sqrt(-b*x^2+a)/sqrt(d*x^2+c)/(f*x^2+e),x,12,1/15*(-4*a*d*f+4*b*c*f+5*b*d*e)*x*sqrt(-b*x^2+a)*sqrt(d*x^2+c)/b^2/d^2/f^2-1/5*x^3*sqrt(-b*x^2+a)*sqrt(d*x^2+c)/b/d/f+1/15*sqrt(a)*(8*a^2*d^2*f^2-a*b*d*f*(7*c*f+10*d*e)+b^2*(8*c^2*f^2+10*c*d*e*f+15*d^2*e^2))*sqrt(1-b*x^2/a)*sqrt(d*x^2+c)*EllipticE(sin(arcsin(sqrt(b)*x/sqrt(a))),sqrt(-a*d/b/c))/b^(5/2)/d^3/f^3/sqrt(-b*x^2+a)/sqrt(1+d*x^2/c)-1/15*sqrt(a)*(4*a^2*c*d^2*f^3-a*b*c*d*f^2*(3*c*f+5*d*e)+b^2*(8*c^3*f^3+10*c^2*d*e*f^2+15*c*d^2*e^2*f+15*d^3*e^3))*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*InverseJacobiAM(arcsin(sqrt(b)*x/sqrt(a)),sqrt(-a*d/b/c))/b^(5/2)/d^3/f^4/sqrt(-b*x^2+a)/sqrt(d*x^2+c)+sqrt(a)*e^3*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*EllipticPi(sin(arcsin(sqrt(b)*x/sqrt(a))),-a*f/b/e,sqrt(-a*d/b/c))/sqrt(b)/f^4/sqrt(-b*x^2+a)/sqrt(d*x^2+c),1],
[x^6/sqrt(-b*x^2+a)/sqrt(d*x^2+c)/(f*x^2+e),x,11,-1/3*x*sqrt(-b*x^2+a)*sqrt(d*x^2+c)/b/d/f-1/3*sqrt(a)*(-2*a*d*f+2*b*c*f+3*b*d*e)*sqrt(1-b*x^2/a)*sqrt(d*x^2+c)*EllipticE(sin(arcsin(sqrt(b)*x/sqrt(a))),sqrt(-a*d/b/c))/b^(3/2)/d^2/f^2/sqrt(-b*x^2+a)/sqrt(1+d*x^2/c)+1/3*sqrt(a)*(-a*c*d*f^2+2*b*c^2*f^2+3*b*c*d*e*f+3*b*d^2*e^2)*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*InverseJacobiAM(arcsin(sqrt(b)*x/sqrt(a)),sqrt(-a*d/b/c))/b^(3/2)/d^2/f^3/sqrt(-b*x^2+a)/sqrt(d*x^2+c)-sqrt(a)*e^2*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*EllipticPi(sin(arcsin(sqrt(b)*x/sqrt(a))),-a*f/b/e,sqrt(-a*d/b/c))/sqrt(b)/f^3/sqrt(-b*x^2+a)/sqrt(d*x^2+c),1],
[x^4/sqrt(-b*x^2+a)/sqrt(d*x^2+c)/(f*x^2+e),x,10,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)/d/f/sqrt(-b*x^2+a)/sqrt(1+d*x^2/c)-sqrt(a)*(c*f+d*e)*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)/d/f^2/sqrt(-b*x^2+a)/sqrt(d*x^2+c)+sqrt(a)*e*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*EllipticPi(sin(arcsin(sqrt(b)*x/sqrt(a))),-a*f/b/e,sqrt(-a*d/b/c))/sqrt(b)/f^2/sqrt(-b*x^2+a)/sqrt(d*x^2+c),1],
[x^2/sqrt(-b*x^2+a)/sqrt(d*x^2+c)/(f*x^2+e),x,6,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)/f/sqrt(-b*x^2+a)/sqrt(d*x^2+c)-sqrt(a)*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*EllipticPi(sin(arcsin(sqrt(b)*x/sqrt(a))),-a*f/b/e,sqrt(-a*d/b/c))/sqrt(b)/f/sqrt(-b*x^2+a)/sqrt(d*x^2+c),1],
[1/sqrt(-b*x^2+a)/sqrt(d*x^2+c)/(f*x^2+e),x,2,sqrt(a)*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*EllipticPi(sin(arcsin(sqrt(b)*x/sqrt(a))),-a*f/b/e,sqrt(-a*d/b/c))/sqrt(b)/e/sqrt(-b*x^2+a)/sqrt(d*x^2+c),1],
[1/x^2/sqrt(-b*x^2+a)/sqrt(d*x^2+c)/(f*x^2+e),x,12,-sqrt(-b*x^2+a)*sqrt(d*x^2+c)/a/c/e/x-sqrt(b)*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)/c/e/sqrt(-b*x^2+a)/sqrt(1+d*x^2/c)+sqrt(b)*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)/e/sqrt(-b*x^2+a)/sqrt(d*x^2+c)-sqrt(a)*f*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*EllipticPi(sin(arcsin(sqrt(b)*x/sqrt(a))),-a*f/b/e,sqrt(-a*d/b/c))/sqrt(b)/e^2/sqrt(-b*x^2+a)/sqrt(d*x^2+c),1],
[1/x^4/sqrt(-b*x^2+a)/sqrt(d*x^2+c)/(f*x^2+e),x,12,-1/3*sqrt(-b*x^2+a)*sqrt(d*x^2+c)/a/c/e/x^3-1/3*(-3*a*c*f-2*a*d*e+2*b*c*e)*sqrt(-b*x^2+a)*sqrt(d*x^2+c)/a^2/c^2/e^2/x-1/3*sqrt(b)*(-3*a*c*f-2*a*d*e+2*b*c*e)*sqrt(1-b*x^2/a)*sqrt(d*x^2+c)*EllipticE(sin(arcsin(sqrt(b)*x/sqrt(a))),sqrt(-a*d/b/c))/a^(3/2)/c^2/e^2/sqrt(-b*x^2+a)/sqrt(1+d*x^2/c)+1/3*sqrt(b)*(-3*a*c*f-a*d*e+2*b*c*e)*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*InverseJacobiAM(arcsin(sqrt(b)*x/sqrt(a)),sqrt(-a*d/b/c))/a^(3/2)/c/e^2/sqrt(-b*x^2+a)/sqrt(d*x^2+c)+sqrt(a)*f^2*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*EllipticPi(sin(arcsin(sqrt(b)*x/sqrt(a))),-a*f/b/e,sqrt(-a*d/b/c))/sqrt(b)/e^3/sqrt(-b*x^2+a)/sqrt(d*x^2+c),1],
[1/x^6/sqrt(-b*x^2+a)/sqrt(d*x^2+c)/(f*x^2+e),x,13,-1/5*sqrt(-b*x^2+a)*sqrt(d*x^2+c)/a/c/e/x^5-1/15*(-5*a*c*f-4*a*d*e+4*b*c*e)*sqrt(-b*x^2+a)*sqrt(d*x^2+c)/a^2/c^2/e^2/x^3-1/15*(8*b^2*c*e/a-7*b*d*e+8*a*d^2*e/c-10*b*c*f+10*a*d*f+15*a*c*f^2/e)*sqrt(-b*x^2+a)*sqrt(d*x^2+c)/a^2/c^2/e^2/x-1/15*sqrt(b)*(8*b^2*c^2*e^2-a*b*c*e*(10*c*f+7*d*e)+a^2*(15*c^2*f^2+10*c*d*e*f+8*d^2*e^2))*sqrt(1-b*x^2/a)*sqrt(d*x^2+c)*EllipticE(sin(arcsin(sqrt(b)*x/sqrt(a))),sqrt(-a*d/b/c))/a^(5/2)/c^3/e^3/sqrt(-b*x^2+a)/sqrt(1+d*x^2/c)+1/15*sqrt(b)*(8*b^2*c^2*e^2-a*b*c*e*(10*c*f+3*d*e)+a^2*(15*c^2*f^2+5*c*d*e*f+4*d^2*e^2))*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*InverseJacobiAM(arcsin(sqrt(b)*x/sqrt(a)),sqrt(-a*d/b/c))/a^(5/2)/c^2/e^3/sqrt(-b*x^2+a)/sqrt(d*x^2+c)-sqrt(a)*f^3*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*EllipticPi(sin(arcsin(sqrt(b)*x/sqrt(a))),-a*f/b/e,sqrt(-a*d/b/c))/sqrt(b)/e^4/sqrt(-b*x^2+a)/sqrt(d*x^2+c),1],
[x^8/sqrt(-b*x^2+a)/sqrt(d*x^2+c)/(f*x^2+e)^2,x,12,-1/3*x*sqrt(-b*x^2+a)*sqrt(d*x^2+c)/b/d/f^2-1/2*e^3*x*sqrt(-b*x^2+a)*sqrt(d*x^2+c)/f^2/(a*f+b*e)/(-c*f+d*e)/(f*x^2+e)+1/6*sqrt(a)*(4*a^2*d*f^2*(-c*f+d*e)-b^2*e*(-4*c^2*f^2-8*c*d*e*f+15*d^2*e^2)-4*a*b*f*(-c^2*f^2-c*d*e*f+2*d^2*e^2))*sqrt(1-b*x^2/a)*sqrt(d*x^2+c)*EllipticE(sin(arcsin(sqrt(b)*x/sqrt(a))),sqrt(-a*d/b/c))/b^(3/2)/d^2/f^3/(a*f+b*e)/(-c*f+d*e)/sqrt(-b*x^2+a)/sqrt(1+d*x^2/c)-1/6*sqrt(a)*(2*a^2*c*d*f^3-2*a*b*f*(2*c^2*f^2+5*c*d*e*f+9*d^2*e^2)-b^2*e*(4*c^2*f^2+12*c*d*e*f+15*d^2*e^2))*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*InverseJacobiAM(arcsin(sqrt(b)*x/sqrt(a)),sqrt(-a*d/b/c))/b^(3/2)/d^2/f^4/(a*f+b*e)/sqrt(-b*x^2+a)/sqrt(d*x^2+c)-1/2*sqrt(a)*e^2*(a*f*(-7*c*f+6*d*e)+b*e*(-6*c*f+5*d*e))*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*EllipticPi(sin(arcsin(sqrt(b)*x/sqrt(a))),-a*f/b/e,sqrt(-a*d/b/c))/sqrt(b)/f^4/(a*f+b*e)/(-c*f+d*e)/sqrt(-b*x^2+a)/sqrt(d*x^2+c),1],
[x^6/sqrt(-b*x^2+a)/sqrt(d*x^2+c)/(f*x^2+e)^2,x,11,1/2*e^2*x*sqrt(-b*x^2+a)*sqrt(d*x^2+c)/f/(a*f+b*e)/(-c*f+d*e)/(f*x^2+e)+1/2*sqrt(a)*(b*e*(-2*c*f+3*d*e)+2*a*f*(-c*f+d*e))*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)/d/f^2/(a*f+b*e)/(-c*f+d*e)/sqrt(-b*x^2+a)/sqrt(1+d*x^2/c)-1/2*sqrt(a)*(2*a*f*(c*f+2*d*e)+b*e*(2*c*f+3*d*e))*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)/d/f^3/(a*f+b*e)/sqrt(-b*x^2+a)/sqrt(d*x^2+c)+1/2*sqrt(a)*e*(a*f*(-5*c*f+4*d*e)+b*e*(-4*c*f+3*d*e))*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*EllipticPi(sin(arcsin(sqrt(b)*x/sqrt(a))),-a*f/b/e,sqrt(-a*d/b/c))/sqrt(b)/f^3/(a*f+b*e)/(-c*f+d*e)/sqrt(-b*x^2+a)/sqrt(d*x^2+c),1],
[x^4/sqrt(-b*x^2+a)/sqrt(d*x^2+c)/(f*x^2+e)^2,x,11,-1/2*e*x*sqrt(-b*x^2+a)*sqrt(d*x^2+c)/(a*f+b*e)/(-c*f+d*e)/(f*x^2+e)-1/2*sqrt(a)*sqrt(b)*e*sqrt(1-b*x^2/a)*sqrt(d*x^2+c)*EllipticE(sin(arcsin(sqrt(b)*x/sqrt(a))),sqrt(-a*d/b/c))/f/(a*f+b*e)/(-c*f+d*e)/sqrt(-b*x^2+a)/sqrt(1+d*x^2/c)+1/2*sqrt(a)*(2*a*f+b*e)*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)/f^2/(a*f+b*e)/sqrt(-b*x^2+a)/sqrt(d*x^2+c)-1/2*sqrt(a)*(a*f*(-3*c*f+2*d*e)+b*e*(-2*c*f+d*e))*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*EllipticPi(sin(arcsin(sqrt(b)*x/sqrt(a))),-a*f/b/e,sqrt(-a*d/b/c))/sqrt(b)/f^2/(a*f+b*e)/(-c*f+d*e)/sqrt(-b*x^2+a)/sqrt(d*x^2+c),1],
[x^2/sqrt(-b*x^2+a)/sqrt(d*x^2+c)/(f*x^2+e)^2,x,11,1/2*f*x*sqrt(-b*x^2+a)*sqrt(d*x^2+c)/(a*f+b*e)/(-c*f+d*e)/(f*x^2+e)+1/2*sqrt(a)*sqrt(b)*sqrt(1-b*x^2/a)*sqrt(d*x^2+c)*EllipticE(sin(arcsin(sqrt(b)*x/sqrt(a))),sqrt(-a*d/b/c))/(a*f+b*e)/(-c*f+d*e)/sqrt(-b*x^2+a)/sqrt(1+d*x^2/c)+1/2*sqrt(a)*sqrt(b)*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*InverseJacobiAM(arcsin(sqrt(b)*x/sqrt(a)),sqrt(-a*d/b/c))/f/(a*f+b*e)/sqrt(-b*x^2+a)/sqrt(d*x^2+c)-1/2*sqrt(a)*(a*c*f^2+b*d*e^2)*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*EllipticPi(sin(arcsin(sqrt(b)*x/sqrt(a))),-a*f/b/e,sqrt(-a*d/b/c))/sqrt(b)/e/f/(a*f+b*e)/(-c*f+d*e)/sqrt(-b*x^2+a)/sqrt(d*x^2+c),1],
[1/sqrt(-b*x^2+a)/sqrt(d*x^2+c)/(f*x^2+e)^2,x,11,-1/2*f^2*x*sqrt(-b*x^2+a)*sqrt(d*x^2+c)/e/(a*f+b*e)/(-c*f+d*e)/(f*x^2+e)-1/2*sqrt(a)*sqrt(b)*f*sqrt(1-b*x^2/a)*sqrt(d*x^2+c)*EllipticE(sin(arcsin(sqrt(b)*x/sqrt(a))),sqrt(-a*d/b/c))/e/(a*f+b*e)/(-c*f+d*e)/sqrt(-b*x^2+a)/sqrt(1+d*x^2/c)-1/2*sqrt(a)*sqrt(b)*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*InverseJacobiAM(arcsin(sqrt(b)*x/sqrt(a)),sqrt(-a*d/b/c))/e/(a*f+b*e)/sqrt(-b*x^2+a)/sqrt(d*x^2+c)+1/2*sqrt(a)*(b*e*(-2*c*f+3*d*e)+a*f*(-c*f+2*d*e))*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*EllipticPi(sin(arcsin(sqrt(b)*x/sqrt(a))),-a*f/b/e,sqrt(-a*d/b/c))/sqrt(b)/e^2/(a*f+b*e)/(-c*f+d*e)/sqrt(-b*x^2+a)/sqrt(d*x^2+c),1],
[1/x^2/sqrt(-b*x^2+a)/sqrt(d*x^2+c)/(f*x^2+e)^2,x,12,-sqrt(-b*x^2+a)*sqrt(d*x^2+c)/a/c/e/x/(f*x^2+e)-1/2*f*(a*f*(-3*c*f+2*d*e)+2*b*e*(-c*f+d*e))*x*sqrt(-b*x^2+a)*sqrt(d*x^2+c)/a/c/e^2/(a*f+b*e)/(-c*f+d*e)/(f*x^2+e)-1/2*sqrt(b)*(a*f*(-3*c*f+2*d*e)+2*b*e*(-c*f+d*e))*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)/c/e^2/(a*f+b*e)/(-c*f+d*e)/sqrt(-b*x^2+a)/sqrt(1+d*x^2/c)+1/2*sqrt(b)*(3*a*f+2*b*e)*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)/e^2/(a*f+b*e)/sqrt(-b*x^2+a)/sqrt(d*x^2+c)-1/2*sqrt(a)*f*(b*e*(-4*c*f+5*d*e)+a*f*(-3*c*f+4*d*e))*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*EllipticPi(sin(arcsin(sqrt(b)*x/sqrt(a))),-a*f/b/e,sqrt(-a*d/b/c))/sqrt(b)/e^3/(a*f+b*e)/(-c*f+d*e)/sqrt(-b*x^2+a)/sqrt(d*x^2+c),1],
[1/x^4/sqrt(-b*x^2+a)/sqrt(d*x^2+c)/(f*x^2+e)^2,x,13,-1/3*sqrt(-b*x^2+a)*sqrt(d*x^2+c)/a/c/e/x^3/(f*x^2+e)-1/3*(-5*a*c*f-2*a*d*e+2*b*c*e)*sqrt(-b*x^2+a)*sqrt(d*x^2+c)/a^2/c^2/e^2/x/(f*x^2+e)-1/6*f*(4*b^2*c*e^2*(-c*f+d*e)-a^2*f*(-15*c^2*f^2+8*c*d*e*f+4*d^2*e^2)-4*a*b*e*(-2*c^2*f^2+c*d*e*f+d^2*e^2))*x*sqrt(-b*x^2+a)*sqrt(d*x^2+c)/a^2/c^2/e^3/(a*f+b*e)/(-c*f+d*e)/(f*x^2+e)-1/6*sqrt(b)*(4*b^2*c*e^2*(-c*f+d*e)-a^2*f*(-15*c^2*f^2+8*c*d*e*f+4*d^2*e^2)-4*a*b*e*(-2*c^2*f^2+c*d*e*f+d^2*e^2))*sqrt(1-b*x^2/a)*sqrt(d*x^2+c)*EllipticE(sin(arcsin(sqrt(b)*x/sqrt(a))),sqrt(-a*d/b/c))/a^(3/2)/c^2/e^3/(a*f+b*e)/(-c*f+d*e)/sqrt(-b*x^2+a)/sqrt(1+d*x^2/c)+1/6*sqrt(b)*(4*b^2*c*e^2-2*a*b*e*(4*c*f+d*e)-a^2*f*(15*c*f+2*d*e))*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*InverseJacobiAM(arcsin(sqrt(b)*x/sqrt(a)),sqrt(-a*d/b/c))/a^(3/2)/c/e^3/(a*f+b*e)/sqrt(-b*x^2+a)/sqrt(d*x^2+c)+1/2*sqrt(a)*f^2*(b*e*(-6*c*f+7*d*e)+a*f*(-5*c*f+6*d*e))*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*EllipticPi(sin(arcsin(sqrt(b)*x/sqrt(a))),-a*f/b/e,sqrt(-a*d/b/c))/sqrt(b)/e^4/(a*f+b*e)/(-c*f+d*e)/sqrt(-b*x^2+a)/sqrt(d*x^2+c),1],
[x^6*(f*x^2+e)^2/(b*x^2+a)^(3/2)/sqrt(d*x^2+c),x,5,-2/105*(96*a^3*d^3*f^2-6*a^2*b*d^2*f*(-9*c*f+28*d*e)+b^3*c*(24*c^2*f^2-56*c*d*e*f+35*d^2*e^2)+a*b^2*d*(36*c^2*f^2-91*c*d*e*f+70*d^2*e^2))*x*sqrt(d*x^2+c)/b^4/d^4/sqrt(b*x^2+a)+1/105*(48*a^2*d^2*f^2-3*a*b*d*f*(-11*c*f+28*d*e)+b^2*(24*c^2*f^2-56*c*d*e*f+35*d^2*e^2))*x^3*sqrt(d*x^2+c)/b^3/d^3/sqrt(b*x^2+a)+2/35*f*(-4*a*d*f-3*b*c*f+7*b*d*e)*x^5*sqrt(d*x^2+c)/b^2/d^2/sqrt(b*x^2+a)+1/7*f^2*x^7*sqrt(d*x^2+c)/b/d/sqrt(b*x^2+a)-1/105*sqrt(a)*(384*a^4*d^4*f^2-24*a^3*b*d^3*f*(5*c*f+28*d*e)+7*a^2*b^2*d^2*(-9*c^2*f^2+32*c*d*e*f+40*d^2*e^2)-3*a*b^3*c*d*(16*c^2*f^2-42*c*d*e*f+35*d^2*e^2)-2*b^4*c^2*(24*c^2*f^2-56*c*d*e*f+35*d^2*e^2))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/b^(9/2)/d^4/(-a*d+b*c)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/105*a^(3/2)*(192*a^3*d^3*f^2-12*a^2*b*d^2*f*(3*c*f+28*d*e)+a*b^2*d*(-27*c^2*f^2+70*c*d*e*f+140*d^2*e^2)-b^3*c*(24*c^2*f^2-56*c*d*e*f+35*d^2*e^2))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(9/2)/d^3/(-a*d+b*c)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[x^4*(f*x^2+e)^2/(b*x^2+a)^(3/2)/sqrt(d*x^2+c),x,4,1/15*(24*a^2*d^2*f^2-a*b*d*f*(-13*c*f+40*d*e)+b^2*(8*c^2*f^2-20*c*d*e*f+15*d^2*e^2))*x*sqrt(d*x^2+c)/b^3/d^3/sqrt(b*x^2+a)+2/15*f*(-3*a*d*f-2*b*c*f+5*b*d*e)*x^3*sqrt(d*x^2+c)/b^2/d^2/sqrt(b*x^2+a)+1/5*f^2*x^5*sqrt(d*x^2+c)/b/d/sqrt(b*x^2+a)+1/15*sqrt(a)*(48*a^3*d^3*f^2-16*a^2*b*d^2*f*(c*f+5*d*e)+3*a*b^2*d*(-3*c^2*f^2+10*c*d*e*f+10*d^2*e^2)-b^3*c*(8*c^2*f^2-20*c*d*e*f+15*d^2*e^2))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/b^(7/2)/d^3/(-a*d+b*c)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/15*a^(3/2)*(24*a^2*d^2*f^2-5*a*b*d*f*(c*f+8*d*e)+b^2*(-4*c^2*f^2+10*c*d*e*f+15*d^2*e^2))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(7/2)/d^2/(-a*d+b*c)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[x^2*(f*x^2+e)^2/(b*x^2+a)^(3/2)/sqrt(d*x^2+c),x,3,2/3*f*(-2*a*d*f-b*c*f+3*b*d*e)*x*sqrt(d*x^2+c)/b^2/d^2/sqrt(b*x^2+a)+1/3*f^2*x^3*sqrt(d*x^2+c)/b/d/sqrt(b*x^2+a)-1/3*sqrt(a)*(8*a^2*d^2*f^2-3*a*b*d*f*(c*f+4*d*e)+b^2*(-2*c^2*f^2+6*c*d*e*f+3*d^2*e^2))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/b^(5/2)/d^2/(-a*d+b*c)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/3*sqrt(a)*(3*b^2*d*e^2+4*a^2*d*f^2-a*b*f*(c*f+6*d*e))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(5/2)/d/(-a*d+b*c)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(f*x^2+e)^2/(b*x^2+a)^(3/2)/sqrt(d*x^2+c),x,2,f^2*x*sqrt(d*x^2+c)/b/d/sqrt(b*x^2+a)+(b^2*d*e^2+2*a^2*d*f^2-a*b*f*(c*f+2*d*e))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/sqrt(a)/b^(3/2)/d/(-a*d+b*c)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-sqrt(a)*(a*c*f^2+b*e*(-2*c*f+d*e))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(3/2)/c/(-a*d+b*c)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(f*x^2+e)^2/x^2/(b*x^2+a)^(3/2)/sqrt(d*x^2+c),x,2,-e^2*sqrt(d*x^2+c)/a/c/x/sqrt(b*x^2+a)-(2*b^2*c*e^2+a^2*c*f^2-a*b*e*(2*c*f+d*e))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/a^(3/2)/sqrt(b)/c/(-a*d+b*c)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+(b*d*e^2-a*f*(-c*f+2*d*e))*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)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(f*x^2+e)^2/x^4/(b*x^2+a)^(3/2)/sqrt(d*x^2+c),x,3,-1/3*e^2*sqrt(d*x^2+c)/a/c/x^3/sqrt(b*x^2+a)+2/3*e*(-3*a*c*f+a*d*e+2*b*c*e)*sqrt(d*x^2+c)/a^2/c^2/x/sqrt(b*x^2+a)+1/3*sqrt(b)*(8*b^2*c^2*e^2-3*a*b*c*e*(4*c*f+d*e)-a^2*(-3*c^2*f^2-6*c*d*e*f+2*d^2*e^2))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/a^(5/2)/c^2/(-a*d+b*c)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/3*d*(4*b^2*c*e^2+3*a^2*c*f^2-a*b*e*(6*c*f+d*e))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/a^(3/2)/sqrt(b)/c^2/(-a*d+b*c)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(f*x^2+e)^2/x^6/(b*x^2+a)^(3/2)/sqrt(d*x^2+c),x,4,-1/5*e^2*sqrt(d*x^2+c)/a/c/x^5/sqrt(b*x^2+a)+2/15*e*(-5*a*c*f+2*a*d*e+3*b*c*e)*sqrt(d*x^2+c)/a^2/c^2/x^3/sqrt(b*x^2+a)-1/15*(4*(a*d+2*b*c)*e*(-5*a*c*f+2*a*d*e+3*b*c*e)-15*a*c*(-a*c*f^2+b*d*e^2))*sqrt(d*x^2+c)/a^3/c^3/x/sqrt(b*x^2+a)-1/15*sqrt(b)*(48*b^3*c^3*e^2-16*a*b^2*c^2*e*(5*c*f+d*e)-3*a^2*b*c*(-10*c^2*f^2-10*c*d*e*f+3*d^2*e^2)-a^3*d*(15*c^2*f^2-20*c*d*e*f+8*d^2*e^2))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/a^(7/2)/c^3/(-a*d+b*c)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/15*sqrt(b)*d*(24*b^2*c^2*e^2-5*a*b*c*e*(8*c*f+d*e)-a^2*(-15*c^2*f^2-10*c*d*e*f+4*d^2*e^2))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/a^(5/2)/c^3/(-a*d+b*c)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[x^6*(f*x^2+e)/(b*x^2+a)^(3/2)/sqrt(d*x^2+c),x,4,1/15*(24*a^2*d^2*f-a*b*d*(-13*c*f+20*d*e)-2*b^2*c*(-4*c*f+5*d*e))*x*sqrt(d*x^2+c)/b^3/d^3/sqrt(b*x^2+a)+1/15*(-6*a*d*f-4*b*c*f+5*b*d*e)*x^3*sqrt(d*x^2+c)/b^2/d^2/sqrt(b*x^2+a)+1/5*f*x^5*sqrt(d*x^2+c)/b/d/sqrt(b*x^2+a)+1/15*sqrt(a)*(48*a^3*d^3*f+2*b^3*c^2*(-4*c*f+5*d*e)+3*a*b^2*c*d*(-3*c*f+5*d*e)-8*a^2*b*d^2*(2*c*f+5*d*e))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/b^(7/2)/d^3/(-a*d+b*c)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/15*a^(3/2)*(24*a^2*d^2*f+b^2*c*(-4*c*f+5*d*e)-5*a*b*d*(c*f+4*d*e))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(7/2)/d^2/(-a*d+b*c)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[x^4*(f*x^2+e)/(b*x^2+a)^(3/2)/sqrt(d*x^2+c),x,3,1/3*(-4*a*d*f-2*b*c*f+3*b*d*e)*x*sqrt(d*x^2+c)/b^2/d^2/sqrt(b*x^2+a)+1/3*f*x^3*sqrt(d*x^2+c)/b/d/sqrt(b*x^2+a)-1/3*sqrt(a)*(8*a^2*d^2*f+b^2*c*(-2*c*f+3*d*e)-3*a*b*d*(c*f+2*d*e))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/b^(5/2)/d^2/(-a*d+b*c)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/3*a^(3/2)*(-4*a*d*f+b*c*f+3*b*d*e)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(5/2)/d/(-a*d+b*c)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[x^2*(f*x^2+e)/(b*x^2+a)^(3/2)/sqrt(d*x^2+c),x,2,f*x*sqrt(d*x^2+c)/b/d/sqrt(b*x^2+a)-sqrt(a)*(-2*a*d*f+b*c*f+b*d*e)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/b^(3/2)/d/(-a*d+b*c)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+sqrt(a)*(-a*f+b*e)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(3/2)/(-a*d+b*c)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(f*x^2+e)/(b*x^2+a)^(3/2)/sqrt(d*x^2+c),x,1,(-a*f+b*e)*sqrt(d*x^2+c)*EllipticE(sin(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))-sqrt(a)*(-c*f+d*e)*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],
[(f*x^2+e)/x^2/(b*x^2+a)^(3/2)/sqrt(d*x^2+c),x,2,-e*sqrt(d*x^2+c)/a/c/x/sqrt(b*x^2+a)-sqrt(b)*(-a*c*f-a*d*e+2*b*c*e)*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)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+d*(-a*f+b*e)*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)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(f*x^2+e)/x^4/(b*x^2+a)^(3/2)/sqrt(d*x^2+c),x,3,-1/3*e*sqrt(d*x^2+c)/a/c/x^3/sqrt(b*x^2+a)+1/3*(-3*a*c*f+2*a*d*e+4*b*c*e)*sqrt(d*x^2+c)/a^2/c^2/x/sqrt(b*x^2+a)+1/3*sqrt(b)*(8*b^2*c^2*e-a^2*d*(-3*c*f+2*d*e)-3*a*b*c*(2*c*f+d*e))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/a^(5/2)/c^2/(-a*d+b*c)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/3*sqrt(b)*d*(-3*a*c*f-a*d*e+4*b*c*e)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/a^(3/2)/c^2/(-a*d+b*c)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[(f*x^2+e)/x^6/(b*x^2+a)^(3/2)/sqrt(d*x^2+c),x,4,-1/5*e*sqrt(d*x^2+c)/a/c/x^5/sqrt(b*x^2+a)+1/15*(-5*a*c*f+4*a*d*e+6*b*c*e)*sqrt(d*x^2+c)/a^2/c^2/x^3/sqrt(b*x^2+a)+1/15*(15*a*b*c*d*e-2*(a*d+2*b*c)*(-5*a*c*f+4*a*d*e+6*b*c*e))*sqrt(d*x^2+c)/a^3/c^3/x/sqrt(b*x^2+a)-1/15*sqrt(b)*(48*b^3*c^3*e-3*a^2*b*c*d*(-5*c*f+3*d*e)-2*a^3*d^2*(-5*c*f+4*d*e)-8*a*b^2*c^2*(5*c*f+2*d*e))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/a^(7/2)/c^3/(-a*d+b*c)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/15*sqrt(b)*d*(24*b^2*c^2*e-a^2*d*(-5*c*f+4*d*e)-5*a*b*c*(4*c*f+d*e))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/a^(5/2)/c^3/(-a*d+b*c)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[x^10/(b*x^2+a)^(3/2)/sqrt(d*x^2+c)/(f*x^2+e),x,7,1/15*(10*b*c*e+20*a*d*e+15*b*d*e^2/f+13*a*c*f+8*b*c^2*f/d+24*a^2*d*f/b)*x*sqrt(d*x^2+c)/b^2/d^2/f^2/sqrt(b*x^2+a)-1/15*(6*a*d*f+4*b*c*f+5*b*d*e)*x^3*sqrt(d*x^2+c)/b^2/d^2/f^2/sqrt(b*x^2+a)+1/5*x^5*sqrt(d*x^2+c)/b/d/f/sqrt(b*x^2+a)-1/15*sqrt(a)*(48*a^4*d^3*f^3-8*a^3*b*d^2*f^2*(2*c*f+d*e)+b^4*c*e*(8*c^2*f^2+10*c*d*e*f+15*d^2*e^2)-a^2*b^2*d*f*(9*c^2*f^2-c*d*e*f+10*d^2*e^2)-a*b^3*(8*c^3*f^3+c^2*d*e*f^2+15*d^3*e^3))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/b^(7/2)/d^3/(-a*d+b*c)/f^3/(-a*f+b*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/15*a^(3/2)*(24*a^4*c*d^2*f^4-a^3*b*c*d*f^3*(5*c*f+28*d*e)-a^2*b^2*c*f^2*(4*c^2*f^2-5*c*d*e*f+d^2*e^2)-b^4*c*e^2*(4*c^2*f^2+5*c*d*e*f+15*d^2*e^2)+a*b^3*e*(8*c^3*f^3+5*c^2*d*e*f^2+5*c*d^2*e^2*f+15*d^3*e^3))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(7/2)/c/d^2/(-a*d+b*c)/f^3/(-a*f+b*e)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-a^(3/2)*e^4*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/f^3/(-a*f+b*e)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[x^8/(b*x^2+a)^(3/2)/sqrt(d*x^2+c)/(f*x^2+e),x,5,-1/3*(4*a*d*f+2*b*c*f+3*b*d*e)*x*sqrt(d*x^2+c)/b^2/d^2/f^2/sqrt(b*x^2+a)+1/3*x^3*sqrt(d*x^2+c)/b/d/f/sqrt(b*x^2+a)+1/3*sqrt(a)*(8*a^3*d^2*f^2+b^3*c*e*(2*c*f+3*d*e)-a^2*b*d*f*(3*c*f+2*d*e)-a*b^2*(2*c^2*f^2+3*d^2*e^2))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/b^(5/2)/d^2/(-a*d+b*c)/f^2/(-a*f+b*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/3*a^(3/2)*(4*a^3*c*d*f^3-b^3*c*e^2*(c*f+3*d*e)-a^2*b*c*f^2*(c*f+5*d*e)+a*b^2*e*(2*c^2*f^2+c*d*e*f+3*d^2*e^2))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(5/2)/c/d/(-a*d+b*c)/f^2/(-a*f+b*e)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+a^(3/2)*e^3*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/f^2/(-a*f+b*e)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[x^6/(b*x^2+a)^(3/2)/sqrt(d*x^2+c)/(f*x^2+e),x,4,x*sqrt(d*x^2+c)/b/d/f/sqrt(b*x^2+a)-sqrt(a)*(b^2*c*e+2*a^2*d*f-a*b*(c*f+d*e))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/b^(3/2)/d/(-a*d+b*c)/f/(-a*f+b*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+a^(3/2)*(b^2*c*e^2-a^2*c*f^2-a*b*e*(-c*f+d*e))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(3/2)/c/(-a*d+b*c)/f/(-a*f+b*e)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-a^(3/2)*e^2*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/f/(-a*f+b*e)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[x^4/(b*x^2+a)^(3/2)/sqrt(d*x^2+c)/(f*x^2+e),x,3,a^(3/2)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/sqrt(b)/(-a*d+b*c)/(-a*f+b*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-a^(3/2)*(-a*c*f-a*d*e+2*b*c*e)*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)/(-a*f+b*e)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+a^(3/2)*e*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/(-a*f+b*e)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[x^2/(b*x^2+a)^(3/2)/sqrt(d*x^2+c)/(f*x^2+e),x,3,-sqrt(a)*sqrt(b)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/(-a*d+b*c)/(-a*f+b*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+sqrt(a)*(-a^2*d*f+b^2*c*e)*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)/(-a*f+b*e)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-a^(3/2)*f*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/(-a*f+b*e)^2/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)/(f*x^2+e),x,3,b^(3/2)*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)/(-a*f+b*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-sqrt(a)*sqrt(b)*(-2*a*d*f+b*c*f+b*d*e)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/c/(-a*d+b*c)/(-a*f+b*e)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+a^(3/2)*f^2*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e/(-a*f+b*e)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[1/x^2/(b*x^2+a)^(3/2)/sqrt(d*x^2+c)/(f*x^2+e),x,4,-sqrt(d*x^2+c)/a/c/e/x/sqrt(b*x^2+a)-sqrt(b)*(2*b^2*c*e+a^2*d*f-a*b*(c*f+d*e))*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)/e/(-a*f+b*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+sqrt(b)*(b^2*d*e^2-a^2*d*f^2-a*b*f*(-c*f+d*e))*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)/e/(-a*f+b*e)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-a^(3/2)*f^3*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e^2/(-a*f+b*e)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[1/x^4/(b*x^2+a)^(3/2)/sqrt(d*x^2+c)/(f*x^2+e),x,5,-1/3*sqrt(d*x^2+c)/a/c/e/x^3/sqrt(b*x^2+a)+1/3*(3*a*c*f+2*a*d*e+4*b*c*e)*sqrt(d*x^2+c)/a^2/c^2/e^2/x/sqrt(b*x^2+a)+1/3*sqrt(b)*(8*b^3*c^2*e^2-a*b^2*c*e*(2*c*f+3*d*e)+a^3*d*f*(3*c*f+2*d*e)-a^2*b*(3*c^2*f^2+2*d^2*e^2))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/a^(5/2)/c^2/(-a*d+b*c)/e^2/(-a*f+b*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/3*sqrt(b)*(4*b^3*c*d*e^3-a^3*d*f^2*(3*c*f+d*e)-a*b^2*d*e^2*(5*c*f+d*e)+a^2*b*f*(3*c^2*f^2+c*d*e*f+2*d^2*e^2))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/a^(3/2)/c^2/(-a*d+b*c)/e^2/(-a*f+b*e)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+a^(3/2)*f^4*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e^3/(-a*f+b*e)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[1/x^6/(b*x^2+a)^(3/2)/sqrt(d*x^2+c)/(f*x^2+e),x,6,-1/5*sqrt(d*x^2+c)/a/c/e/x^5/sqrt(b*x^2+a)+1/15*(5*a*c*f+4*a*d*e+6*b*c*e)*sqrt(d*x^2+c)/a^2/c^2/e^2/x^3/sqrt(b*x^2+a)-1/15*(24*b^2*c*e/a+13*b*d*e+8*a*d^2*e/c+20*b*c*f+10*a*d*f+15*a*c*f^2/e)*sqrt(d*x^2+c)/a^2/c^2/e^2/x/sqrt(b*x^2+a)-1/15*sqrt(b)*(48*b^4*c^3*e^3-8*a*b^3*c^2*e^2*(c*f+2*d*e)-a^2*b^2*c*e*(10*c^2*f^2-c*d*e*f+9*d^2*e^2)+a^4*d*f*(15*c^2*f^2+10*c*d*e*f+8*d^2*e^2)-a^3*b*(15*c^3*f^3+c*d^2*e^2*f+8*d^3*e^3))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/a^(7/2)/c^3/(-a*d+b*c)/e^3/(-a*f+b*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/15*sqrt(b)*(24*b^4*c^2*d*e^4-a*b^3*c*d*e^3*(28*c*f+5*d*e)-a^2*b^2*d*e^2*(c^2*f^2-5*c*d*e*f+4*d^2*e^2)-a^4*d*f^2*(15*c^2*f^2+5*c*d*e*f+4*d^2*e^2)+a^3*b*f*(15*c^3*f^3+5*c^2*d*e*f^2+5*c*d^2*e^2*f+8*d^3*e^3))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/a^(5/2)/c^3/(-a*d+b*c)/e^3/(-a*f+b*e)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-a^(3/2)*f^5*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e^4/(-a*f+b*e)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[x^8/(b*x^2+a)^(3/2)/sqrt(d*x^2+c)/(f*x^2+e)^2,x,5,x*sqrt(d*x^2+c)/b/d/f^2/sqrt(b*x^2+a)+1/2*e^3*x*sqrt(d*x^2+c)/f^2/(-a*f+b*e)/(-c*f+d*e)/sqrt(b*x^2+a)/(f*x^2+e)-1/2*sqrt(a)*(b^3*c*e^2*(-2*c*f+3*d*e)-4*a^3*d*f^2*(-c*f+d*e)-a*b^2*e*(-4*c^2*f^2+2*c*d*e*f+3*d^2*e^2)+2*a^2*b*f*(-c^2*f^2-c*d*e*f+2*d^2*e^2))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/b^(3/2)/d/(-a*d+b*c)/f^2/(-a*f+b*e)^2/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/2*a^(3/2)*(3*b^3*c*e^3+2*a^3*c*f^3+2*a^2*b*e*f*(-c*f+3*d*e)-3*a*b^2*e^2*(2*c*f+d*e))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(3/2)/c/(-a*d+b*c)/f^2/(-a*f+b*e)^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/2*a^(3/2)*e^2*(a*f*(-7*c*f+6*d*e)-b*e*(-4*c*f+3*d*e))*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/f^2/(-a*f+b*e)^3/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[x^6/(b*x^2+a)^(3/2)/sqrt(d*x^2+c)/(f*x^2+e)^2,x,4,-1/2*e^2*x*sqrt(d*x^2+c)/f/(-a*f+b*e)/(-c*f+d*e)/sqrt(b*x^2+a)/(f*x^2+e)+1/2*sqrt(a)*(b^2*c*e^2-a*b*d*e^2-2*a^2*f*(-c*f+d*e))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/sqrt(b)/(-a*d+b*c)/f/(-a*f+b*e)^2/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/2*a^(3/2)*(b^2*c*e^2+2*a^2*f*(c*f+2*d*e)-a*b*e*(6*c*f+d*e))*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)/f/(-a*f+b*e)^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/2*a^(3/2)*e*(a*f*(-5*c*f+4*d*e)-b*e*(-2*c*f+d*e))*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/f/(-a*f+b*e)^3/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[x^4/(b*x^2+a)^(3/2)/sqrt(d*x^2+c)/(f*x^2+e)^2,x,4,1/2*e*x*sqrt(d*x^2+c)/(-a*f+b*e)/(-c*f+d*e)/sqrt(b*x^2+a)/(f*x^2+e)-1/2*sqrt(a)*sqrt(b)*(2*a*c*f-3*a*d*e+b*c*e)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/(-a*d+b*c)/(-a*f+b*e)^2/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/2*a^(3/2)*(-2*a^2*d*f-a*b*d*e+3*b^2*c*e)*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)/(-a*f+b*e)^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/2*a^(3/2)*(b*d*e^2+a*f*(-3*c*f+2*d*e))*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/(-a*f+b*e)^3/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[x^2/(b*x^2+a)^(3/2)/sqrt(d*x^2+c)/(f*x^2+e)^2,x,4,-1/2*f*x*sqrt(d*x^2+c)/(-a*f+b*e)/(-c*f+d*e)/sqrt(b*x^2+a)/(f*x^2+e)-1/2*sqrt(a)*sqrt(b)*(a*d*f-3*b*c*f+2*b*d*e)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/(-a*d+b*c)/(-a*f+b*e)^2/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/2*sqrt(a)*sqrt(b)*(-3*a^2*d*f+a*b*c*f+2*b^2*c*e)*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/c/(-a*d+b*c)/(-a*f+b*e)^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/2*a^(3/2)*f*(a*c*f^2-b*e*(-2*c*f+3*d*e))*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e/(-a*f+b*e)^3/(-c*f+d*e)/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)/(f*x^2+e)^2,x,4,1/2*f^2*x*sqrt(d*x^2+c)/e/(-a*f+b*e)/(-c*f+d*e)/sqrt(b*x^2+a)/(f*x^2+e)-1/2*sqrt(b)*(a*b*c*f^2-a^2*d*f^2-2*b^2*e*(-c*f+d*e))*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)/e/(-a*f+b*e)^2/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/2*sqrt(a)*sqrt(b)*(a^2*d*f^2-a*b*f*(c*f+6*d*e)+2*b^2*e*(2*c*f+d*e))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/c/(-a*d+b*c)/e/(-a*f+b*e)^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/2*a^(3/2)*f^2*(b*e*(-4*c*f+5*d*e)-a*f*(-c*f+2*d*e))*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e^2/(-a*f+b*e)^3/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[1/x^2/(b*x^2+a)^(3/2)/sqrt(d*x^2+c)/(f*x^2+e)^2,x,5,-sqrt(d*x^2+c)/a/c/e/x/sqrt(b*x^2+a)/(f*x^2+e)+1/2*f*(a*f*(-3*c*f+2*d*e)-2*b*e*(-c*f+d*e))*x*sqrt(d*x^2+c)/a/c/e^2/(-a*f+b*e)/(-c*f+d*e)/sqrt(b*x^2+a)/(f*x^2+e)+1/2*sqrt(b)*(a^3*d*f^2*(-3*c*f+2*d*e)-4*b^3*c*e^2*(-c*f+d*e)-a^2*b*f*(-3*c^2*f^2-2*c*d*e*f+4*d^2*e^2)+2*a*b^2*e*(-2*c^2*f^2+c*d*e*f+d^2*e^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)/e^2/(-a*f+b*e)^2/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/2*sqrt(b)*(2*b^3*d*e^3+3*a^3*d*f^3-2*a*b^2*e*f*(-3*c*f+d*e)-3*a^2*b*f^2*(c*f+2*d*e))*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)/e^2/(-a*f+b*e)^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/2*a^(3/2)*f^3*(b*e*(-6*c*f+7*d*e)-a*f*(-3*c*f+4*d*e))*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e^3/(-a*f+b*e)^3/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[1/x^4/(b*x^2+a)^(3/2)/sqrt(d*x^2+c)/(f*x^2+e)^2,x,6,-1/3*sqrt(d*x^2+c)/a/c/e/x^3/sqrt(b*x^2+a)/(f*x^2+e)+1/3*(5*a*c*f+2*a*d*e+4*b*c*e)*sqrt(d*x^2+c)/a^2/c^2/e^2/x/sqrt(b*x^2+a)/(f*x^2+e)+1/6*f*(8*b^2*c*e^2*(-c*f+d*e)-a^2*f*(-15*c^2*f^2+8*c*d*e*f+4*d^2*e^2)+4*a*b*e*(-c^2*f^2+d^2*e^2))*x*sqrt(d*x^2+c)/a^2/c^2/e^3/(-a*f+b*e)/(-c*f+d*e)/sqrt(b*x^2+a)/(f*x^2+e)+1/6*sqrt(b)*(16*b^4*c^2*e^3*(-c*f+d*e)-a^4*d*f^2*(-15*c^2*f^2+8*c*d*e*f+4*d^2*e^2)-2*a*b^3*c*e^2*(-4*c^2*f^2+c*d*e*f+3*d^2*e^2)+a^3*b*f*(-15*c^3*f^3-6*c^2*d*e*f^2+10*c*d^2*e^2*f+8*d^3*e^3)-2*a^2*b^2*e*(-7*c^3*f^3+7*c^2*d*e*f^2-2*c*d^2*e^2*f+2*d^3*e^3))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/a^(5/2)/c^2/(-a*d+b*c)/e^3/(-a*f+b*e)^2/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/6*sqrt(b)*(8*b^4*c*d*e^4-2*a*b^3*d*e^3*(6*c*f+d*e)+a^4*d*f^3*(15*c*f+2*d*e)+6*a^2*b^2*e*f*(4*c^2*f^2+c*d*e*f+d^2*e^2)-a^3*b*f^2*(15*c^2*f^2+26*c*d*e*f+6*d^2*e^2))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/a^(3/2)/c^2/(-a*d+b*c)/e^3/(-a*f+b*e)^3/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/2*a^(3/2)*f^4*(b*e*(-8*c*f+9*d*e)-a*f*(-5*c*f+6*d*e))*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e^4/(-a*f+b*e)^3/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[x^10/(b*x^2+a)^(3/2)/sqrt(d*x^2+c)/(f*x^2+e)^3,x,6,x*sqrt(d*x^2+c)/b/d/f^3/sqrt(b*x^2+a)-1/4*e^4*x*sqrt(d*x^2+c)/f^3/(-a*f+b*e)/(-c*f+d*e)/sqrt(b*x^2+a)/(f*x^2+e)^2-1/8*e^3*(a*f*(-17*c*f+14*d*e)-3*b*e*(-4*c*f+3*d*e))*x*sqrt(d*x^2+c)/f^3/(-a*f+b*e)^2/(-c*f+d*e)^2/sqrt(b*x^2+a)/(f*x^2+e)-1/8*sqrt(a)*(16*a^4*d*f^3*(-c*f+d*e)^2-8*a^3*b*f^2*(-c*f+d*e)^2*(c*f+3*d*e)+b^4*c*e^3*(8*c^2*f^2-26*c*d*e*f+15*d^2*e^2)-3*a*b^3*e^2*(8*c^3*f^3-19*c^2*d*e*f^2+4*c*d^2*e^2*f+5*d^3*e^3)+a^2*b^2*e*f*(24*c^3*f^3-24*c^2*d*e*f^2-41*c*d^2*e^2*f+38*d^3*e^3))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/b^(3/2)/d/(-a*d+b*c)/f^3/(-a*f+b*e)^3/(-c*f+d*e)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/8*a^(3/2)*(b^4*c*e^4*(-16*c*f+15*d*e)-8*a^4*c*f^4*(-c*f+d*e)-a*b^3*e^3*(-49*c^2*f^2+32*c*d*e*f+15*d^2*e^2)+a^2*b^2*e^2*f*(-48*c^2*f^2-c*d*e*f+48*d^2*e^2)-8*a^3*b*e*f^2*(c^2*f^2-7*c*d*e*f+6*d^2*e^2))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/b^(3/2)/c/(-a*d+b*c)/f^3/(-a*f+b*e)^4/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-3/8*a^(3/2)*e^2*(b^2*e^2*(8*c^2*f^2-12*c*d*e*f+5*d^2*e^2)-2*a*b*e*f*(12*c^2*f^2-19*c*d*e*f+8*d^2*e^2)+a^2*f^2*(21*c^2*f^2-36*c*d*e*f+16*d^2*e^2))*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/f^3/(-a*f+b*e)^4/(-c*f+d*e)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[x^8/(b*x^2+a)^(3/2)/sqrt(d*x^2+c)/(f*x^2+e)^3,x,5,1/4*e^3*x*sqrt(d*x^2+c)/f^2/(-a*f+b*e)/(-c*f+d*e)/sqrt(b*x^2+a)/(f*x^2+e)^2+1/8*e^2*(a*f*(-13*c*f+10*d*e)-b*e*(-8*c*f+5*d*e))*x*sqrt(d*x^2+c)/f^2/(-a*f+b*e)^2/(-c*f+d*e)^2/sqrt(b*x^2+a)/(f*x^2+e)+1/8*sqrt(a)*(a^2*b*d*e^2*f*(-13*c*f+10*d*e)+3*b^3*c*e^3*(-2*c*f+d*e)+8*a^3*f^2*(-c*f+d*e)^2-a*b^2*e^2*(-13*c^2*f^2+4*c*d*e*f+3*d^2*e^2))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/sqrt(b)/(-a*d+b*c)/f^2/(-a*f+b*e)^3/(-c*f+d*e)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/8*a^(3/2)*(b^3*c*e^3*(-4*c*f+3*d*e)+a^2*b*e*f*(-32*c^2*f^2+19*c*d*e*f+12*d^2*e^2)-a*b^2*e^2*(-13*c^2*f^2+8*c*d*e*f+3*d^2*e^2)-8*a^3*f^2*(-c^2*f^2-2*c*d*e*f+3*d^2*e^2))*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)/f^2/(-a*f+b*e)^4/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/8*a^(3/2)*e*(b^2*e^2*(8*c^2*f^2-8*c*d*e*f+3*d^2*e^2)-2*a*b*e*f*(14*c^2*f^2-17*c*d*e*f+6*d^2*e^2)+a^2*f^2*(35*c^2*f^2-56*c*d*e*f+24*d^2*e^2))*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/f^2/(-a*f+b*e)^4/(-c*f+d*e)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[x^6/(b*x^2+a)^(3/2)/sqrt(d*x^2+c)/(f*x^2+e)^3,x,5,-1/4*e^2*x*sqrt(d*x^2+c)/f/(-a*f+b*e)/(-c*f+d*e)/sqrt(b*x^2+a)/(f*x^2+e)^2+1/8*e*(b*e*(-4*c*f+d*e)-3*a*f*(-3*c*f+2*d*e))*x*sqrt(d*x^2+c)/f/(-a*f+b*e)^2/(-c*f+d*e)^2/sqrt(b*x^2+a)/(f*x^2+e)+1/8*sqrt(a)*sqrt(b)*(b^2*c*e^2*(2*c*f+d*e)-a^2*f*(8*c^2*f^2-25*c*d*e*f+14*d^2*e^2)-a*b*e*(9*c^2*f^2-4*c*d*e*f+d^2*e^2))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/(-a*d+b*c)/f/(-a*f+b*e)^3/(-c*f+d*e)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/8*a^(3/2)*(b^3*c*d*e^3+a^2*b*d*e*f*(-7*c*f+8*d*e)+8*a^3*d*f^2*(-c*f+d*e)-a*b^2*e*(-15*c^2*f^2+16*c*d*e*f+d^2*e^2))*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)/f/(-a*f+b*e)^4/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/8*a^(3/2)*(2*a*b*d*e^2*f*(-7*c*f+4*d*e)-b^2*d*e^3*(-4*c*f+d*e)+a^2*f^2*(15*c^2*f^2-20*c*d*e*f+8*d^2*e^2))*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/f/(-a*f+b*e)^4/(-c*f+d*e)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[x^4/(b*x^2+a)^(3/2)/sqrt(d*x^2+c)/(f*x^2+e)^3,x,5,1/4*e*x*sqrt(d*x^2+c)/(-a*f+b*e)/(-c*f+d*e)/sqrt(b*x^2+a)/(f*x^2+e)^2+1/8*(3*b*d*e^2+a*f*(-5*c*f+2*d*e))*x*sqrt(d*x^2+c)/(-a*f+b*e)^2/(-c*f+d*e)^2/sqrt(b*x^2+a)/(f*x^2+e)+1/8*sqrt(a)*sqrt(b)*(a^2*d*f*(-5*c*f+2*d*e)-b^2*c*e*(-2*c*f+5*d*e)+a*b*(13*c^2*f^2-20*c*d*e*f+13*d^2*e^2))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/(-a*d+b*c)/(-a*f+b*e)^3/(-c*f+d*e)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/8*a^(3/2)*sqrt(b)*(b^2*c*e*(-12*c*f+11*d*e)-a^2*d*f*(-11*c*f+12*d*e)-a*b*(3*c^2*f^2-8*c*d*e*f+3*d^2*e^2))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/c/(-a*d+b*c)/(-a*f+b*e)^4/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+3/8*a^(3/2)*(b^2*d^2*e^4+a^2*c^2*f^4+2*a*b*e*f*(2*c^2*f^2-5*c*d*e*f+2*d^2*e^2))*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e/(-a*f+b*e)^4/(-c*f+d*e)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[x^2/(b*x^2+a)^(3/2)/sqrt(d*x^2+c)/(f*x^2+e)^3,x,5,-1/4*f*x*sqrt(d*x^2+c)/(-a*f+b*e)/(-c*f+d*e)/sqrt(b*x^2+a)/(f*x^2+e)^2-1/8*f*(b*e*(-4*c*f+7*d*e)-a*f*(c*f+2*d*e))*x*sqrt(d*x^2+c)/e/(-a*f+b*e)^2/(-c*f+d*e)^2/sqrt(b*x^2+a)/(f*x^2+e)+1/8*sqrt(a)*sqrt(b)*(a^2*d*f^2*(c*f+2*d*e)-a*b*f*(c^2*f^2-4*c*d*e*f+9*d^2*e^2)-b^2*e*(14*c^2*f^2-25*c*d*e*f+8*d^2*e^2))*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(b)*x/sqrt(a))),sqrt(1-a*d/b/c))/(-a*d+b*c)/e/(-a*f+b*e)^3/(-c*f+d*e)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/8*sqrt(a)*sqrt(b)*(a^3*c*d*f^3-a*b^2*c*e*f*(-8*c*f+7*d*e)-8*b^3*c*e^2*(-c*f+d*e)+a^2*b*f*(-c^2*f^2-16*c*d*e*f+15*d^2*e^2))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/c/(-a*d+b*c)/e/(-a*f+b*e)^4/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/8*a^(3/2)*f*(2*a*b*c*e*f^2*(-4*c*f+7*d*e)-a^2*c*f^3*(-c*f+4*d*e)-b^2*e^2*(8*c^2*f^2-20*c*d*e*f+15*d^2*e^2))*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e^2/(-a*f+b*e)^4/(-c*f+d*e)^2/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)/(f*x^2+e)^3,x,5,1/4*f^2*x*sqrt(d*x^2+c)/e/(-a*f+b*e)/(-c*f+d*e)/sqrt(b*x^2+a)/(f*x^2+e)^2+1/8*f^2*(b*e*(-8*c*f+11*d*e)-3*a*f*(-c*f+2*d*e))*x*sqrt(d*x^2+c)/e^2/(-a*f+b*e)^2/(-c*f+d*e)^2/sqrt(b*x^2+a)/(f*x^2+e)-1/8*sqrt(b)*(a*b^2*c*e*f^2*(-10*c*f+13*d*e)-8*b^3*e^2*(-c*f+d*e)^2+3*a^3*d*f^3*(-c*f+2*d*e)-a^2*b*f^2*(-3*c^2*f^2-4*c*d*e*f+13*d^2*e^2))*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)/e^2/(-a*f+b*e)^3/(-c*f+d*e)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/8*sqrt(a)*sqrt(b)*(a^3*d*f^3*(-3*c*f+4*d*e)+a*b^2*e*f*(-12*c^2*f^2-19*c*d*e*f+32*d^2*e^2)-a^2*b*f^2*(-3*c^2*f^2-8*c*d*e*f+13*d^2*e^2)-8*b^3*e^2*(-3*c^2*f^2+2*c*d*e*f+d^2*e^2))*sqrt(d*x^2+c)*InverseJacobiAM(arctan(sqrt(b)*x/sqrt(a)),sqrt(1-a*d/b/c))/c/(-a*d+b*c)/e^2/(-a*f+b*e)^4/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))+1/8*a^(3/2)*f^2*(a^2*f^2*(3*c^2*f^2-8*c*d*e*f+8*d^2*e^2)-2*a*b*e*f*(6*c^2*f^2-17*c*d*e*f+14*d^2*e^2)+b^2*e^2*(24*c^2*f^2-56*c*d*e*f+35*d^2*e^2))*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e^3/(-a*f+b*e)^4/(-c*f+d*e)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[1/x^2/(b*x^2+a)^(3/2)/sqrt(d*x^2+c)/(f*x^2+e)^3,x,6,-sqrt(d*x^2+c)/a/c/e/x/sqrt(b*x^2+a)/(f*x^2+e)^2+1/4*f*(a*f*(-5*c*f+4*d*e)-4*b*e*(-c*f+d*e))*x*sqrt(d*x^2+c)/a/c/e^2/(-a*f+b*e)/(-c*f+d*e)/sqrt(b*x^2+a)/(f*x^2+e)^2-1/8*f*(8*b^2*e^2*(-c*f+d*e)^2+a^2*f^2*(15*c^2*f^2-26*c*d*e*f+8*d^2*e^2)-a*b*e*f*(28*c^2*f^2-47*c*d*e*f+16*d^2*e^2))*x*sqrt(d*x^2+c)/a/c/e^3/(-a*f+b*e)^2/(-c*f+d*e)^2/sqrt(b*x^2+a)/(f*x^2+e)-1/8*sqrt(b)*(16*b^4*c*e^3*(-c*f+d*e)^2-8*a*b^3*e^2*(-c*f+d*e)^2*(3*c*f+d*e)+a^4*d*f^3*(15*c^2*f^2-26*c*d*e*f+8*d^2*e^2)-3*a^3*b*f^2*(5*c^3*f^3+4*c^2*d*e*f^2-19*c*d^2*e^2*f+8*d^3*e^3)+a^2*b^2*e*f*(38*c^3*f^3-41*c^2*d*e*f^2-24*c*d^2*e^2*f+24*d^3*e^3))*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)/e^3/(-a*f+b*e)^3/(-c*f+d*e)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-1/8*sqrt(b)*(a^4*d*f^4*(-15*c*f+16*d*e)-8*b^4*d*e^4*(-c*f+d*e)+a^2*b^2*e*f^2*(-48*c^2*f^2+c*d*e*f+48*d^2*e^2)-a^3*b*f^3*(-15*c^2*f^2-32*c*d*e*f+49*d^2*e^2)+8*a*b^3*e^2*f*(6*c^2*f^2-7*c*d*e*f+d^2*e^2))*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)/e^3/(-a*f+b*e)^4/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))-3/8*a^(3/2)*f^3*(a^2*f^2*(5*c^2*f^2-12*c*d*e*f+8*d^2*e^2)-2*a*b*e*f*(8*c^2*f^2-19*c*d*e*f+12*d^2*e^2)+b^2*e^2*(16*c^2*f^2-36*c*d*e*f+21*d^2*e^2))*sqrt(d*x^2+c)*EllipticPi(sin(arctan(sqrt(b)*x/sqrt(a))),1-a*f/b/e,sqrt(1-a*d/b/c))/sqrt(b)/c/e^4/(-a*f+b*e)^4/(-c*f+d*e)^2/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[x^4*(f*x^2+e)^2/(-b*x^2+a)^(3/2)/sqrt(d*x^2+c),x,10,1/5*(5*b^2*d*e^2+6*a^2*d*f^2+a*b*f*(c*f+10*d*e))*x^3*sqrt(d*x^2+c)/b^2/d/(a*d+b*c)/sqrt(-b*x^2+a)-1/5*f^2*x^5*sqrt(d*x^2+c)/b/d/sqrt(-b*x^2+a)+1/15*(24*a^2*d*f^2/b+5*a*f*(c*f+8*d*e)+b*(15*d*e^2+10*c*e*f-4*c^2*f^2/d))*x*sqrt(-b*x^2+a)*sqrt(d*x^2+c)/b^2/d/(a*d+b*c)-1/15*sqrt(a)*(48*a^3*d^3*f^2+16*a^2*b*d^2*f*(c*f+5*d*e)+3*a*b^2*d*(-3*c^2*f^2+10*c*d*e*f+10*d^2*e^2)+b^3*c*(8*c^2*f^2-20*c*d*e*f+15*d^2*e^2))*sqrt(1-b*x^2/a)*sqrt(d*x^2+c)*EllipticE(sin(arcsin(sqrt(b)*x/sqrt(a))),sqrt(-a*d/b/c))/b^(7/2)/d^3/(a*d+b*c)/sqrt(-b*x^2+a)/sqrt(1+d*x^2/c)+1/15*sqrt(a)*c*(24*a^2*d^2*f^2+a*b*d*f*(-13*c*f+40*d*e)+b^2*(8*c^2*f^2-20*c*d*e*f+15*d^2*e^2))*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*InverseJacobiAM(arcsin(sqrt(b)*x/sqrt(a)),sqrt(-a*d/b/c))/b^(7/2)/d^3/sqrt(-b*x^2+a)/sqrt(d*x^2+c),1],
[x^2*(f*x^2+e)^2/(-b*x^2+a)^(3/2)/sqrt(d*x^2+c),x,9,1/3*(3*b^2*d*e^2+4*a^2*d*f^2+a*b*f*(c*f+6*d*e))*x*sqrt(d*x^2+c)/b^2/d/(a*d+b*c)/sqrt(-b*x^2+a)-1/3*f^2*x^3*sqrt(d*x^2+c)/b/d/sqrt(-b*x^2+a)-1/3*sqrt(a)*(8*a^2*d^2*f^2+3*a*b*d*f*(c*f+4*d*e)+b^2*(-2*c^2*f^2+6*c*d*e*f+3*d^2*e^2))*sqrt(1-b*x^2/a)*sqrt(d*x^2+c)*EllipticE(sin(arcsin(sqrt(b)*x/sqrt(a))),sqrt(-a*d/b/c))/b^(5/2)/d^2/(a*d+b*c)/sqrt(-b*x^2+a)/sqrt(1+d*x^2/c)+2/3*sqrt(a)*c*f*(2*a*d*f-b*c*f+3*b*d*e)*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*InverseJacobiAM(arcsin(sqrt(b)*x/sqrt(a)),sqrt(-a*d/b/c))/b^(5/2)/d^2/sqrt(-b*x^2+a)/sqrt(d*x^2+c),1],
[(f*x^2+e)^2/(-b*x^2+a)^(3/2)/sqrt(d*x^2+c),x,8,(a*f+b*e)^2*x*sqrt(d*x^2+c)/a/b/(a*d+b*c)/sqrt(-b*x^2+a)-(b^2*d*e^2+2*a^2*d*f^2+a*b*f*(c*f+2*d*e))*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)/b^(3/2)/d/(a*d+b*c)/sqrt(-b*x^2+a)/sqrt(1+d*x^2/c)+(a*c*f^2+b*d*e^2)*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)/b^(3/2)/d/sqrt(-b*x^2+a)/sqrt(d*x^2+c),1],
[(f*x^2+e)^2/x^2/(-b*x^2+a)^(3/2)/sqrt(d*x^2+c),x,9,-e^2*sqrt(d*x^2+c)/a/c/x/sqrt(-b*x^2+a)+(2*b^2*c*e^2+a^2*c*f^2+a*b*e*(2*c*f+d*e))*x*sqrt(d*x^2+c)/a^2/c/(a*d+b*c)/sqrt(-b*x^2+a)-(2*b^2*c*e^2+a^2*c*f^2+a*b*e*(2*c*f+d*e))*sqrt(1-b*x^2/a)*sqrt(d*x^2+c)*EllipticE(sin(arcsin(sqrt(b)*x/sqrt(a))),sqrt(-a*d/b/c))/a^(3/2)/sqrt(b)/c/(a*d+b*c)/sqrt(-b*x^2+a)/sqrt(1+d*x^2/c)+2*e*(a*f+b*e)*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*InverseJacobiAM(arcsin(sqrt(b)*x/sqrt(a)),sqrt(-a*d/b/c))/a^(3/2)/sqrt(b)/sqrt(-b*x^2+a)/sqrt(d*x^2+c),1],
[(f*x^2+e)^2/x^4/(-b*x^2+a)^(3/2)/sqrt(d*x^2+c),x,10,-1/3*e^2*sqrt(d*x^2+c)/a/c/x^3/sqrt(-b*x^2+a)-2/3*e*(3*a*c*f-a*d*e+2*b*c*e)*sqrt(d*x^2+c)/a^2/c^2/x/sqrt(-b*x^2+a)+1/3*b*(8*b^2*c^2*e^2+3*a*b*c*e*(4*c*f+d*e)-a^2*(-3*c^2*f^2-6*c*d*e*f+2*d^2*e^2))*x*sqrt(d*x^2+c)/a^3/c^2/(a*d+b*c)/sqrt(-b*x^2+a)-1/3*sqrt(b)*(8*b^2*c^2*e^2+3*a*b*c*e*(4*c*f+d*e)-a^2*(-3*c^2*f^2-6*c*d*e*f+2*d^2*e^2))*sqrt(1-b*x^2/a)*sqrt(d*x^2+c)*EllipticE(sin(arcsin(sqrt(b)*x/sqrt(a))),sqrt(-a*d/b/c))/a^(5/2)/c^2/(a*d+b*c)/sqrt(-b*x^2+a)/sqrt(1+d*x^2/c)+1/3*(8*b^2*c*e^2+3*a^2*c*f^2-a*b*e*(-12*c*f+d*e))*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*InverseJacobiAM(arcsin(sqrt(b)*x/sqrt(a)),sqrt(-a*d/b/c))/a^(5/2)/sqrt(b)/c/sqrt(-b*x^2+a)/sqrt(d*x^2+c),1],
[x^6*(f*x^2+e)/(-b*x^2+a)^(3/2)/sqrt(d*x^2+c),x,10,(a*f+b*e)*x^5*sqrt(d*x^2+c)/b/(a*d+b*c)/sqrt(-b*x^2+a)+1/15*(24*a^2*d^2*f+b^2*c*(-4*c*f+5*d*e)+5*a*b*d*(c*f+4*d*e))*x*sqrt(-b*x^2+a)*sqrt(d*x^2+c)/b^3/d^2/(a*d+b*c)+1/5*(6*a*d*f+b*c*f+5*b*d*e)*x^3*sqrt(-b*x^2+a)*sqrt(d*x^2+c)/b^2/d/(a*d+b*c)-1/15*sqrt(a)*(48*a^3*d^3*f-2*b^3*c^2*(-4*c*f+5*d*e)+3*a*b^2*c*d*(-3*c*f+5*d*e)+8*a^2*b*d^2*(2*c*f+5*d*e))*sqrt(1-b*x^2/a)*sqrt(d*x^2+c)*EllipticE(sin(arcsin(sqrt(b)*x/sqrt(a))),sqrt(-a*d/b/c))/b^(7/2)/d^3/(a*d+b*c)/sqrt(-b*x^2+a)/sqrt(1+d*x^2/c)+1/15*sqrt(a)*c*(24*a^2*d^2*f+a*b*d*(-13*c*f+20*d*e)-2*b^2*c*(-4*c*f+5*d*e))*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*InverseJacobiAM(arcsin(sqrt(b)*x/sqrt(a)),sqrt(-a*d/b/c))/b^(7/2)/d^3/sqrt(-b*x^2+a)/sqrt(d*x^2+c),1],
[x^4*(f*x^2+e)/(-b*x^2+a)^(3/2)/sqrt(d*x^2+c),x,9,(a*f+b*e)*x^3*sqrt(d*x^2+c)/b/(a*d+b*c)/sqrt(-b*x^2+a)+1/3*(4*a*d*f+b*c*f+3*b*d*e)*x*sqrt(-b*x^2+a)*sqrt(d*x^2+c)/b^2/d/(a*d+b*c)-1/3*sqrt(a)*(8*a^2*d^2*f+b^2*c*(-2*c*f+3*d*e)+3*a*b*d*(c*f+2*d*e))*sqrt(1-b*x^2/a)*sqrt(d*x^2+c)*EllipticE(sin(arcsin(sqrt(b)*x/sqrt(a))),sqrt(-a*d/b/c))/b^(5/2)/d^2/(a*d+b*c)/sqrt(-b*x^2+a)/sqrt(1+d*x^2/c)+1/3*sqrt(a)*c*(4*a*d*f-2*b*c*f+3*b*d*e)*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*InverseJacobiAM(arcsin(sqrt(b)*x/sqrt(a)),sqrt(-a*d/b/c))/b^(5/2)/d^2/sqrt(-b*x^2+a)/sqrt(d*x^2+c),1],
[x^2*(f*x^2+e)/(-b*x^2+a)^(3/2)/sqrt(d*x^2+c),x,8,(a*f+b*e)*x*sqrt(d*x^2+c)/b/(a*d+b*c)/sqrt(-b*x^2+a)-sqrt(a)*(2*a*d*f+b*c*f+b*d*e)*sqrt(1-b*x^2/a)*sqrt(d*x^2+c)*EllipticE(sin(arcsin(sqrt(b)*x/sqrt(a))),sqrt(-a*d/b/c))/b^(3/2)/d/(a*d+b*c)/sqrt(-b*x^2+a)/sqrt(1+d*x^2/c)+sqrt(a)*c*f*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*InverseJacobiAM(arcsin(sqrt(b)*x/sqrt(a)),sqrt(-a*d/b/c))/b^(3/2)/d/sqrt(-b*x^2+a)/sqrt(d*x^2+c),1],
[(f*x^2+e)/(-b*x^2+a)^(3/2)/sqrt(d*x^2+c),x,8,(a*f+b*e)*x*sqrt(d*x^2+c)/a/(a*d+b*c)/sqrt(-b*x^2+a)-(a*f+b*e)*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)/(a*d+b*c)/sqrt(-b*x^2+a)/sqrt(1+d*x^2/c)+e*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],
[(f*x^2+e)/x^2/(-b*x^2+a)^(3/2)/sqrt(d*x^2+c),x,9,-e*sqrt(d*x^2+c)/a/c/x/sqrt(-b*x^2+a)+b*(a*c*f+a*d*e+2*b*c*e)*x*sqrt(d*x^2+c)/a^2/c/(a*d+b*c)/sqrt(-b*x^2+a)-sqrt(b)*(a*c*f+a*d*e+2*b*c*e)*sqrt(1-b*x^2/a)*sqrt(d*x^2+c)*EllipticE(sin(arcsin(sqrt(b)*x/sqrt(a))),sqrt(-a*d/b/c))/a^(3/2)/c/(a*d+b*c)/sqrt(-b*x^2+a)/sqrt(1+d*x^2/c)+(a*f+2*b*e)*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*InverseJacobiAM(arcsin(sqrt(b)*x/sqrt(a)),sqrt(-a*d/b/c))/a^(3/2)/sqrt(b)/sqrt(-b*x^2+a)/sqrt(d*x^2+c),1],
[(f*x^2+e)/x^4/(-b*x^2+a)^(3/2)/sqrt(d*x^2+c),x,10,-1/3*e*sqrt(d*x^2+c)/a/c/x^3/sqrt(-b*x^2+a)-1/3*(3*a*c*f-2*a*d*e+4*b*c*e)*sqrt(d*x^2+c)/a^2/c^2/x/sqrt(-b*x^2+a)+1/3*b*(8*b^2*c^2*e-a^2*d*(-3*c*f+2*d*e)+3*a*b*c*(2*c*f+d*e))*x*sqrt(d*x^2+c)/a^3/c^2/(a*d+b*c)/sqrt(-b*x^2+a)-1/3*sqrt(b)*(8*b^2*c^2*e-a^2*d*(-3*c*f+2*d*e)+3*a*b*c*(2*c*f+d*e))*sqrt(1-b*x^2/a)*sqrt(d*x^2+c)*EllipticE(sin(arcsin(sqrt(b)*x/sqrt(a))),sqrt(-a*d/b/c))/a^(5/2)/c^2/(a*d+b*c)/sqrt(-b*x^2+a)/sqrt(1+d*x^2/c)+1/3*sqrt(b)*(6*a*c*f-a*d*e+8*b*c*e)*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*InverseJacobiAM(arcsin(sqrt(b)*x/sqrt(a)),sqrt(-a*d/b/c))/a^(5/2)/c/sqrt(-b*x^2+a)/sqrt(d*x^2+c),1],
[x^6/(-b*x^2+a)^(3/2)/sqrt(d*x^2+c),x,9,a*x^3*sqrt(d*x^2+c)/b/(a*d+b*c)/sqrt(-b*x^2+a)+1/3*(4*a*d+b*c)*x*sqrt(-b*x^2+a)*sqrt(d*x^2+c)/b^2/d/(a*d+b*c)+1/3*sqrt(a)*(-8*a^2*d^2-3*a*b*c*d+2*b^2*c^2)*sqrt(1-b*x^2/a)*sqrt(d*x^2+c)*EllipticE(sin(arcsin(sqrt(b)*x/sqrt(a))),sqrt(-a*d/b/c))/b^(5/2)/d^2/(a*d+b*c)/sqrt(-b*x^2+a)/sqrt(1+d*x^2/c)-2/3*sqrt(a)*c*(-2*a*d+b*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))/b^(5/2)/d^2/sqrt(-b*x^2+a)/sqrt(d*x^2+c),1],
[x^4/(-b*x^2+a)^(3/2)/sqrt(d*x^2+c),x,8,a*x*sqrt(d*x^2+c)/b/(a*d+b*c)/sqrt(-b*x^2+a)-sqrt(a)*(2*a*d+b*c)*sqrt(1-b*x^2/a)*sqrt(d*x^2+c)*EllipticE(sin(arcsin(sqrt(b)*x/sqrt(a))),sqrt(-a*d/b/c))/b^(3/2)/d/(a*d+b*c)/sqrt(-b*x^2+a)/sqrt(1+d*x^2/c)+sqrt(a)*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))/b^(3/2)/d/sqrt(-b*x^2+a)/sqrt(d*x^2+c),1],
[x^2/(-b*x^2+a)^(3/2)/sqrt(d*x^2+c),x,4,x*sqrt(d*x^2+c)/(a*d+b*c)/sqrt(-b*x^2+a)-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)/(a*d+b*c)/sqrt(-b*x^2+a)/sqrt(1+d*x^2/c),1],
[1/(-b*x^2+a)^(3/2)/sqrt(d*x^2+c),x,6,b*x*sqrt(d*x^2+c)/a/(a*d+b*c)/sqrt(-b*x^2+a)-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))/a^(3/2)/(a*d+b*c)/sqrt(1-b*x^2/a)/sqrt(d*x^2+c)+sqrt(-b*x^2+a)*sqrt(1+d*x^2/c)*InverseJacobiAM(arcsin(sqrt(b)*x/sqrt(a)),sqrt(-a*d/b/c))/a^(3/2)/sqrt(b)/sqrt(1-b*x^2/a)/sqrt(d*x^2+c),1],
[1/x^2/(-b*x^2+a)^(3/2)/sqrt(d*x^2+c),x,9,-sqrt(d*x^2+c)/a/c/x/sqrt(-b*x^2+a)+b*(a*d+2*b*c)*x*sqrt(d*x^2+c)/a^2/c/(a*d+b*c)/sqrt(-b*x^2+a)-sqrt(b)*(a*d+2*b*c)*sqrt(1-b*x^2/a)*sqrt(d*x^2+c)*EllipticE(sin(arcsin(sqrt(b)*x/sqrt(a))),sqrt(-a*d/b/c))/a^(3/2)/c/(a*d+b*c)/sqrt(-b*x^2+a)/sqrt(1+d*x^2/c)+2*sqrt(b)*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*InverseJacobiAM(arcsin(sqrt(b)*x/sqrt(a)),sqrt(-a*d/b/c))/a^(3/2)/sqrt(-b*x^2+a)/sqrt(d*x^2+c),1],
[1/x^4/(-b*x^2+a)^(3/2)/sqrt(d*x^2+c),x,10,-1/3*sqrt(d*x^2+c)/a/c/x^3/sqrt(-b*x^2+a)-2/3*(-a*d+2*b*c)*sqrt(d*x^2+c)/a^2/c^2/x/sqrt(-b*x^2+a)+1/3*b*(-2*a^2*d^2+3*a*b*c*d+8*b^2*c^2)*x*sqrt(d*x^2+c)/a^3/c^2/(a*d+b*c)/sqrt(-b*x^2+a)-1/3*sqrt(b)*(-2*a^2*d^2+3*a*b*c*d+8*b^2*c^2)*sqrt(1-b*x^2/a)*sqrt(d*x^2+c)*EllipticE(sin(arcsin(sqrt(b)*x/sqrt(a))),sqrt(-a*d/b/c))/a^(5/2)/c^2/(a*d+b*c)/sqrt(-b*x^2+a)/sqrt(1+d*x^2/c)+1/3*sqrt(b)*(-a*d+8*b*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))/a^(5/2)/c/sqrt(-b*x^2+a)/sqrt(d*x^2+c),1],
[x^8/(-b*x^2+a)^(3/2)/sqrt(d*x^2+c)/(f*x^2+e),x,12,a^3*x*sqrt(d*x^2+c)/b^2/(a*d+b*c)/(a*f+b*e)/sqrt(-b*x^2+a)+1/3*x*sqrt(-b*x^2+a)*sqrt(d*x^2+c)/b^2/d/f-1/3*sqrt(a)*(8*a^3*d^2*f^2-b^3*c*e*(2*c*f+3*d*e)+a^2*b*d*f*(3*c*f+2*d*e)-a*b^2*(2*c^2*f^2+3*d^2*e^2))*sqrt(1-b*x^2/a)*sqrt(d*x^2+c)*EllipticE(sin(arcsin(sqrt(b)*x/sqrt(a))),sqrt(-a*d/b/c))/b^(5/2)/d^2/(a*d+b*c)/f^2/(a*f+b*e)/sqrt(-b*x^2+a)/sqrt(1+d*x^2/c)+1/3*sqrt(a)*(4*a^2*c*d*f^3+a*b*c*f^2*(-2*c*f+d*e)-b^2*e*(2*c^2*f^2+3*c*d*e*f+3*d^2*e^2))*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*InverseJacobiAM(arcsin(sqrt(b)*x/sqrt(a)),sqrt(-a*d/b/c))/b^(5/2)/d^2/f^3/(a*f+b*e)/sqrt(-b*x^2+a)/sqrt(d*x^2+c)+sqrt(a)*e^3*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*EllipticPi(sin(arcsin(sqrt(b)*x/sqrt(a))),-a*f/b/e,sqrt(-a*d/b/c))/sqrt(b)/f^3/(a*f+b*e)/sqrt(-b*x^2+a)/sqrt(d*x^2+c),1],
[x^6/(-b*x^2+a)^(3/2)/sqrt(d*x^2+c)/(f*x^2+e),x,11,a^2*x*sqrt(d*x^2+c)/b/(a*d+b*c)/(a*f+b*e)/sqrt(-b*x^2+a)-sqrt(a)*(b^2*c*e+2*a^2*d*f+a*b*(c*f+d*e))*sqrt(1-b*x^2/a)*sqrt(d*x^2+c)*EllipticE(sin(arcsin(sqrt(b)*x/sqrt(a))),sqrt(-a*d/b/c))/b^(3/2)/d/(a*d+b*c)/f/(a*f+b*e)/sqrt(-b*x^2+a)/sqrt(1+d*x^2/c)+sqrt(a)*(a*c*f^2+b*e*(c*f+d*e))*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*InverseJacobiAM(arcsin(sqrt(b)*x/sqrt(a)),sqrt(-a*d/b/c))/b^(3/2)/d/f^2/(a*f+b*e)/sqrt(-b*x^2+a)/sqrt(d*x^2+c)-sqrt(a)*e^2*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*EllipticPi(sin(arcsin(sqrt(b)*x/sqrt(a))),-a*f/b/e,sqrt(-a*d/b/c))/sqrt(b)/f^2/(a*f+b*e)/sqrt(-b*x^2+a)/sqrt(d*x^2+c),1],
[x^4/(-b*x^2+a)^(3/2)/sqrt(d*x^2+c)/(f*x^2+e),x,11,a*x*sqrt(d*x^2+c)/(a*d+b*c)/(a*f+b*e)/sqrt(-b*x^2+a)-a^(3/2)*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)/(a*d+b*c)/(a*f+b*e)/sqrt(-b*x^2+a)/sqrt(1+d*x^2/c)-sqrt(a)*e*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)/f/(a*f+b*e)/sqrt(-b*x^2+a)/sqrt(d*x^2+c)+sqrt(a)*e*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*EllipticPi(sin(arcsin(sqrt(b)*x/sqrt(a))),-a*f/b/e,sqrt(-a*d/b/c))/sqrt(b)/f/(a*f+b*e)/sqrt(-b*x^2+a)/sqrt(d*x^2+c),1],
[x^2/(-b*x^2+a)^(3/2)/sqrt(d*x^2+c)/(f*x^2+e),x,10,b*x*sqrt(d*x^2+c)/(a*d+b*c)/(a*f+b*e)/sqrt(-b*x^2+a)-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)/(a*d+b*c)/(a*f+b*e)/sqrt(1-b*x^2/a)/sqrt(d*x^2+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)/(a*f+b*e)/sqrt(1-b*x^2/a)/sqrt(d*x^2+c)-sqrt(a)*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*EllipticPi(sin(arcsin(sqrt(b)*x/sqrt(a))),-a*f/b/e,sqrt(-a*d/b/c))/sqrt(b)/(a*f+b*e)/sqrt(-b*x^2+a)/sqrt(d*x^2+c),1],
[1/(-b*x^2+a)^(3/2)/sqrt(d*x^2+c)/(f*x^2+e),x,10,b^2*x*sqrt(d*x^2+c)/a/(a*d+b*c)/(a*f+b*e)/sqrt(-b*x^2+a)-b^(3/2)*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))/a^(3/2)/(a*d+b*c)/(a*f+b*e)/sqrt(1-b*x^2/a)/sqrt(d*x^2+c)+sqrt(b)*sqrt(-b*x^2+a)*sqrt(1+d*x^2/c)*InverseJacobiAM(arcsin(sqrt(b)*x/sqrt(a)),sqrt(-a*d/b/c))/a^(3/2)/(a*f+b*e)/sqrt(1-b*x^2/a)/sqrt(d*x^2+c)+sqrt(a)*f*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*EllipticPi(sin(arcsin(sqrt(b)*x/sqrt(a))),-a*f/b/e,sqrt(-a*d/b/c))/sqrt(b)/e/(a*f+b*e)/sqrt(-b*x^2+a)/sqrt(d*x^2+c),1],
[1/x^2/(-b*x^2+a)^(3/2)/sqrt(d*x^2+c)/(f*x^2+e),x,12,-sqrt(d*x^2+c)/a/c/e/x/sqrt(-b*x^2+a)+b*(2*b^2*c*e+a^2*d*f+a*b*(c*f+d*e))*x*sqrt(d*x^2+c)/a^2/c/(a*d+b*c)/e/(a*f+b*e)/sqrt(-b*x^2+a)-sqrt(b)*(2*b^2*c*e+a^2*d*f+a*b*(c*f+d*e))*sqrt(1-b*x^2/a)*sqrt(d*x^2+c)*EllipticE(sin(arcsin(sqrt(b)*x/sqrt(a))),sqrt(-a*d/b/c))/a^(3/2)/c/(a*d+b*c)/e/(a*f+b*e)/sqrt(-b*x^2+a)/sqrt(1+d*x^2/c)+sqrt(b)*(a*f+2*b*e)*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*InverseJacobiAM(arcsin(sqrt(b)*x/sqrt(a)),sqrt(-a*d/b/c))/a^(3/2)/e/(a*f+b*e)/sqrt(-b*x^2+a)/sqrt(d*x^2+c)-sqrt(a)*f^2*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*EllipticPi(sin(arcsin(sqrt(b)*x/sqrt(a))),-a*f/b/e,sqrt(-a*d/b/c))/sqrt(b)/e^2/(a*f+b*e)/sqrt(-b*x^2+a)/sqrt(d*x^2+c),1],
[1/x^4/(-b*x^2+a)^(3/2)/sqrt(d*x^2+c)/(f*x^2+e),x,13,-1/3*sqrt(d*x^2+c)/a/c/e/x^3/sqrt(-b*x^2+a)-1/3*(-3*a*c*f-2*a*d*e+4*b*c*e)*sqrt(d*x^2+c)/a^2/c^2/e^2/x/sqrt(-b*x^2+a)+1/3*b*(8*b^3*c^2*e^2+a*b^2*c*e*(2*c*f+3*d*e)-a^3*d*f*(3*c*f+2*d*e)-a^2*b*(3*c^2*f^2+2*d^2*e^2))*x*sqrt(d*x^2+c)/a^3/c^2/(a*d+b*c)/e^2/(a*f+b*e)/sqrt(-b*x^2+a)-1/3*sqrt(b)*(8*b^3*c^2*e^2+a*b^2*c*e*(2*c*f+3*d*e)-a^3*d*f*(3*c*f+2*d*e)-a^2*b*(3*c^2*f^2+2*d^2*e^2))*sqrt(1-b*x^2/a)*sqrt(d*x^2+c)*EllipticE(sin(arcsin(sqrt(b)*x/sqrt(a))),sqrt(-a*d/b/c))/a^(5/2)/c^2/(a*d+b*c)/e^2/(a*f+b*e)/sqrt(-b*x^2+a)/sqrt(1+d*x^2/c)+1/3*sqrt(b)*(8*b^2*c*e^2-a*b*e*(-2*c*f+d*e)-a^2*f*(3*c*f+d*e))*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*InverseJacobiAM(arcsin(sqrt(b)*x/sqrt(a)),sqrt(-a*d/b/c))/a^(5/2)/c/e^2/(a*f+b*e)/sqrt(-b*x^2+a)/sqrt(d*x^2+c)+sqrt(a)*f^3*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*EllipticPi(sin(arcsin(sqrt(b)*x/sqrt(a))),-a*f/b/e,sqrt(-a*d/b/c))/sqrt(b)/e^3/(a*f+b*e)/sqrt(-b*x^2+a)/sqrt(d*x^2+c),1],
[1/x^6/(-b*x^2+a)^(3/2)/sqrt(d*x^2+c)/(f*x^2+e),x,14,-1/5*sqrt(d*x^2+c)/a/c/e/x^5/sqrt(-b*x^2+a)-1/15*(-5*a*c*f-4*a*d*e+6*b*c*e)*sqrt(d*x^2+c)/a^2/c^2/e^2/x^3/sqrt(-b*x^2+a)-1/15*(24*b^2*c*e/a-13*b*d*e+8*a*d^2*e/c-20*b*c*f+10*a*d*f+15*a*c*f^2/e)*sqrt(d*x^2+c)/a^2/c^2/e^2/x/sqrt(-b*x^2+a)+1/15*b*(48*b^4*c^3*e^3+8*a*b^3*c^2*e^2*(c*f+2*d*e)-a^2*b^2*c*e*(10*c^2*f^2-c*d*e*f+9*d^2*e^2)+a^4*d*f*(15*c^2*f^2+10*c*d*e*f+8*d^2*e^2)+a^3*b*(15*c^3*f^3+c*d^2*e^2*f+8*d^3*e^3))*x*sqrt(d*x^2+c)/a^4/c^3/(a*d+b*c)/e^3/(a*f+b*e)/sqrt(-b*x^2+a)-1/15*sqrt(b)*(48*b^4*c^3*e^3+8*a*b^3*c^2*e^2*(c*f+2*d*e)-a^2*b^2*c*e*(10*c^2*f^2-c*d*e*f+9*d^2*e^2)+a^4*d*f*(15*c^2*f^2+10*c*d*e*f+8*d^2*e^2)+a^3*b*(15*c^3*f^3+c*d^2*e^2*f+8*d^3*e^3))*sqrt(1-b*x^2/a)*sqrt(d*x^2+c)*EllipticE(sin(arcsin(sqrt(b)*x/sqrt(a))),sqrt(-a*d/b/c))/a^(7/2)/c^3/(a*d+b*c)/e^3/(a*f+b*e)/sqrt(-b*x^2+a)/sqrt(1+d*x^2/c)+1/15*sqrt(b)*(48*b^3*c^2*e^3-8*a*b^2*c*e^2*(-c*f+d*e)+a^2*b*e*(-10*c^2*f^2-3*c*d*e*f+4*d^2*e^2)+a^3*f*(15*c^2*f^2+5*c*d*e*f+4*d^2*e^2))*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*InverseJacobiAM(arcsin(sqrt(b)*x/sqrt(a)),sqrt(-a*d/b/c))/a^(7/2)/c^2/e^3/(a*f+b*e)/sqrt(-b*x^2+a)/sqrt(d*x^2+c)-sqrt(a)*f^4*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*EllipticPi(sin(arcsin(sqrt(b)*x/sqrt(a))),-a*f/b/e,sqrt(-a*d/b/c))/sqrt(b)/e^4/(a*f+b*e)/sqrt(-b*x^2+a)/sqrt(d*x^2+c),1],
[x^8/(-b*x^2+a)^(3/2)/sqrt(d*x^2+c)/(f*x^2+e)^2,x,13,-x*sqrt(d*x^2+c)/b/d/f^2/sqrt(-b*x^2+a)+1/2*(b^3*c*e^2*(-2*c*f+3*d*e)+4*a^3*d*f^2*(-c*f+d*e)+a*b^2*e*(-4*c^2*f^2+2*c*d*e*f+3*d^2*e^2)+2*a^2*b*f*(-c^2*f^2-c*d*e*f+2*d^2*e^2))*x*sqrt(d*x^2+c)/b/d/(a*d+b*c)/f^2/(a*f+b*e)^2/(-c*f+d*e)/sqrt(-b*x^2+a)-1/2*e^3*x*sqrt(d*x^2+c)/f^2/(a*f+b*e)/(-c*f+d*e)/sqrt(-b*x^2+a)/(f*x^2+e)-1/2*sqrt(a)*(b^3*c*e^2*(-2*c*f+3*d*e)+4*a^3*d*f^2*(-c*f+d*e)+a*b^2*e*(-4*c^2*f^2+2*c*d*e*f+3*d^2*e^2)+2*a^2*b*f*(-c^2*f^2-c*d*e*f+2*d^2*e^2))*sqrt(1-b*x^2/a)*sqrt(d*x^2+c)*EllipticE(sin(arcsin(sqrt(b)*x/sqrt(a))),sqrt(-a*d/b/c))/b^(3/2)/d/(a*d+b*c)/f^2/(a*f+b*e)^2/(-c*f+d*e)/sqrt(-b*x^2+a)/sqrt(1+d*x^2/c)+1/2*sqrt(a)*(2*a^2*c*f^3+b^2*e^2*(2*c*f+3*d*e)+2*a*b*e*f*(2*c*f+3*d*e))*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*InverseJacobiAM(arcsin(sqrt(b)*x/sqrt(a)),sqrt(-a*d/b/c))/b^(3/2)/d/f^3/(a*f+b*e)^2/sqrt(-b*x^2+a)/sqrt(d*x^2+c)-1/2*sqrt(a)*e^2*(a*f*(-7*c*f+6*d*e)+b*e*(-4*c*f+3*d*e))*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*EllipticPi(sin(arcsin(sqrt(b)*x/sqrt(a))),-a*f/b/e,sqrt(-a*d/b/c))/sqrt(b)/f^3/(a*f+b*e)^2/(-c*f+d*e)/sqrt(-b*x^2+a)/sqrt(d*x^2+c),1],
[x^6/(-b*x^2+a)^(3/2)/sqrt(d*x^2+c)/(f*x^2+e)^2,x,12,-1/2*(b^2*c*e^2+a*b*d*e^2-2*a^2*f*(-c*f+d*e))*x*sqrt(d*x^2+c)/(a*d+b*c)/f/(a*f+b*e)^2/(-c*f+d*e)/sqrt(-b*x^2+a)+1/2*e^2*x*sqrt(d*x^2+c)/f/(a*f+b*e)/(-c*f+d*e)/sqrt(-b*x^2+a)/(f*x^2+e)+1/2*sqrt(a)*(b^2*c*e^2+a*b*d*e^2-2*a^2*f*(-c*f+d*e))*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)/(a*d+b*c)/f/(a*f+b*e)^2/(-c*f+d*e)/sqrt(-b*x^2+a)/sqrt(1+d*x^2/c)-1/2*sqrt(a)*e*(4*a*f+b*e)*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)/f^2/(a*f+b*e)^2/sqrt(-b*x^2+a)/sqrt(d*x^2+c)+1/2*sqrt(a)*e*(a*f*(-5*c*f+4*d*e)+b*e*(-2*c*f+d*e))*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*EllipticPi(sin(arcsin(sqrt(b)*x/sqrt(a))),-a*f/b/e,sqrt(-a*d/b/c))/sqrt(b)/f^2/(a*f+b*e)^2/(-c*f+d*e)/sqrt(-b*x^2+a)/sqrt(d*x^2+c),1],
[x^4/(-b*x^2+a)^(3/2)/sqrt(d*x^2+c)/(f*x^2+e)^2,x,12,1/2*b*(-2*a*c*f+3*a*d*e+b*c*e)*x*sqrt(d*x^2+c)/(a*d+b*c)/(a*f+b*e)^2/(-c*f+d*e)/sqrt(-b*x^2+a)-1/2*e*x*sqrt(d*x^2+c)/(a*f+b*e)/(-c*f+d*e)/sqrt(-b*x^2+a)/(f*x^2+e)-1/2*sqrt(a)*sqrt(b)*(-2*a*c*f+3*a*d*e+b*c*e)*sqrt(1-b*x^2/a)*sqrt(d*x^2+c)*EllipticE(sin(arcsin(sqrt(b)*x/sqrt(a))),sqrt(-a*d/b/c))/(a*d+b*c)/(a*f+b*e)^2/(-c*f+d*e)/sqrt(-b*x^2+a)/sqrt(1+d*x^2/c)-1/2*sqrt(a)*(-2*a*f+b*e)*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)/f/(a*f+b*e)^2/sqrt(-b*x^2+a)/sqrt(d*x^2+c)+1/2*sqrt(a)*(b*d*e^2-a*f*(-3*c*f+2*d*e))*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*EllipticPi(sin(arcsin(sqrt(b)*x/sqrt(a))),-a*f/b/e,sqrt(-a*d/b/c))/sqrt(b)/f/(a*f+b*e)^2/(-c*f+d*e)/sqrt(-b*x^2+a)/sqrt(d*x^2+c),1],
[x^2/(-b*x^2+a)^(3/2)/sqrt(d*x^2+c)/(f*x^2+e)^2,x,12,1/2*b*(-a*d*f-3*b*c*f+2*b*d*e)*x*sqrt(d*x^2+c)/(a*d+b*c)/(a*f+b*e)^2/(-c*f+d*e)/sqrt(-b*x^2+a)+1/2*f*x*sqrt(d*x^2+c)/(a*f+b*e)/(-c*f+d*e)/sqrt(-b*x^2+a)/(f*x^2+e)-1/2*sqrt(a)*sqrt(b)*(-a*d*f-3*b*c*f+2*b*d*e)*sqrt(1-b*x^2/a)*sqrt(d*x^2+c)*EllipticE(sin(arcsin(sqrt(b)*x/sqrt(a))),sqrt(-a*d/b/c))/(a*d+b*c)/(a*f+b*e)^2/(-c*f+d*e)/sqrt(-b*x^2+a)/sqrt(1+d*x^2/c)+3/2*sqrt(a)*sqrt(b)*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*InverseJacobiAM(arcsin(sqrt(b)*x/sqrt(a)),sqrt(-a*d/b/c))/(a*f+b*e)^2/sqrt(-b*x^2+a)/sqrt(d*x^2+c)-1/2*sqrt(a)*(a*c*f^2+b*e*(-2*c*f+3*d*e))*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*EllipticPi(sin(arcsin(sqrt(b)*x/sqrt(a))),-a*f/b/e,sqrt(-a*d/b/c))/sqrt(b)/e/(a*f+b*e)^2/(-c*f+d*e)/sqrt(-b*x^2+a)/sqrt(d*x^2+c),1],
[1/(-b*x^2+a)^(3/2)/sqrt(d*x^2+c)/(f*x^2+e)^2,x,12,1/2*b*(a*b*c*f^2+a^2*d*f^2+2*b^2*e*(-c*f+d*e))*x*sqrt(d*x^2+c)/a/(a*d+b*c)/e/(a*f+b*e)^2/(-c*f+d*e)/sqrt(-b*x^2+a)-1/2*f^2*x*sqrt(d*x^2+c)/e/(a*f+b*e)/(-c*f+d*e)/sqrt(-b*x^2+a)/(f*x^2+e)-1/2*sqrt(b)*(a*b*c*f^2+a^2*d*f^2+2*b^2*e*(-c*f+d*e))*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)/(a*d+b*c)/e/(a*f+b*e)^2/(-c*f+d*e)/sqrt(-b*x^2+a)/sqrt(1+d*x^2/c)+1/2*sqrt(b)*(-a*f+2*b*e)*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)/e/(a*f+b*e)^2/sqrt(-b*x^2+a)/sqrt(d*x^2+c)+1/2*sqrt(a)*f*(b*e*(-4*c*f+5*d*e)+a*f*(-c*f+2*d*e))*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*EllipticPi(sin(arcsin(sqrt(b)*x/sqrt(a))),-a*f/b/e,sqrt(-a*d/b/c))/sqrt(b)/e^2/(a*f+b*e)^2/(-c*f+d*e)/sqrt(-b*x^2+a)/sqrt(d*x^2+c),1],
[1/x^2/(-b*x^2+a)^(3/2)/sqrt(d*x^2+c)/(f*x^2+e)^2,x,13,1/2*b*(a^3*d*f^2*(-3*c*f+2*d*e)+4*b^3*c*e^2*(-c*f+d*e)+a^2*b*f*(-3*c^2*f^2-2*c*d*e*f+4*d^2*e^2)+2*a*b^2*e*(-2*c^2*f^2+c*d*e*f+d^2*e^2))*x*sqrt(d*x^2+c)/a^2/c/(a*d+b*c)/e^2/(a*f+b*e)^2/(-c*f+d*e)/sqrt(-b*x^2+a)-sqrt(d*x^2+c)/a/c/e/x/sqrt(-b*x^2+a)/(f*x^2+e)-1/2*f*(a*f*(-3*c*f+2*d*e)+2*b*e*(-c*f+d*e))*x*sqrt(d*x^2+c)/a/c/e^2/(a*f+b*e)/(-c*f+d*e)/sqrt(-b*x^2+a)/(f*x^2+e)-1/2*sqrt(b)*(a^3*d*f^2*(-3*c*f+2*d*e)+4*b^3*c*e^2*(-c*f+d*e)+a^2*b*f*(-3*c^2*f^2-2*c*d*e*f+4*d^2*e^2)+2*a*b^2*e*(-2*c^2*f^2+c*d*e*f+d^2*e^2))*sqrt(1-b*x^2/a)*sqrt(d*x^2+c)*EllipticE(sin(arcsin(sqrt(b)*x/sqrt(a))),sqrt(-a*d/b/c))/a^(3/2)/c/(a*d+b*c)/e^2/(a*f+b*e)^2/(-c*f+d*e)/sqrt(-b*x^2+a)/sqrt(1+d*x^2/c)+1/2*sqrt(b)*(3*a^2*f^2+4*a*b*e*f+4*b^2*e^2)*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*InverseJacobiAM(arcsin(sqrt(b)*x/sqrt(a)),sqrt(-a*d/b/c))/a^(3/2)/e^2/(a*f+b*e)^2/sqrt(-b*x^2+a)/sqrt(d*x^2+c)-1/2*sqrt(a)*f^2*(b*e*(-6*c*f+7*d*e)+a*f*(-3*c*f+4*d*e))*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*EllipticPi(sin(arcsin(sqrt(b)*x/sqrt(a))),-a*f/b/e,sqrt(-a*d/b/c))/sqrt(b)/e^3/(a*f+b*e)^2/(-c*f+d*e)/sqrt(-b*x^2+a)/sqrt(d*x^2+c),1],
[1/x^4/(-b*x^2+a)^(3/2)/sqrt(d*x^2+c)/(f*x^2+e)^2,x,14,1/6*b*(16*b^4*c^2*e^3*(-c*f+d*e)-a^4*d*f^2*(-15*c^2*f^2+8*c*d*e*f+4*d^2*e^2)+2*a*b^3*c*e^2*(-4*c^2*f^2+c*d*e*f+3*d^2*e^2)-a^3*b*f*(-15*c^3*f^3-6*c^2*d*e*f^2+10*c*d^2*e^2*f+8*d^3*e^3)-2*a^2*b^2*e*(-7*c^3*f^3+7*c^2*d*e*f^2-2*c*d^2*e^2*f+2*d^3*e^3))*x*sqrt(d*x^2+c)/a^3/c^2/(a*d+b*c)/e^3/(a*f+b*e)^2/(-c*f+d*e)/sqrt(-b*x^2+a)-1/3*sqrt(d*x^2+c)/a/c/e/x^3/sqrt(-b*x^2+a)/(f*x^2+e)-1/3*(-5*a*c*f-2*a*d*e+4*b*c*e)*sqrt(d*x^2+c)/a^2/c^2/e^2/x/sqrt(-b*x^2+a)/(f*x^2+e)-1/6*f*(8*b^2*c*e^2*(-c*f+d*e)-a^2*f*(-15*c^2*f^2+8*c*d*e*f+4*d^2*e^2)-a*b*(-4*c^2*e*f^2+4*d^2*e^3))*x*sqrt(d*x^2+c)/a^2/c^2/e^3/(a*f+b*e)/(-c*f+d*e)/sqrt(-b*x^2+a)/(f*x^2+e)-1/6*sqrt(b)*(16*b^4*c^2*e^3*(-c*f+d*e)-a^4*d*f^2*(-15*c^2*f^2+8*c*d*e*f+4*d^2*e^2)+2*a*b^3*c*e^2*(-4*c^2*f^2+c*d*e*f+3*d^2*e^2)-a^3*b*f*(-15*c^3*f^3-6*c^2*d*e*f^2+10*c*d^2*e^2*f+8*d^3*e^3)-2*a^2*b^2*e*(-7*c^3*f^3+7*c^2*d*e*f^2-2*c*d^2*e^2*f+2*d^3*e^3))*sqrt(1-b*x^2/a)*sqrt(d*x^2+c)*EllipticE(sin(arcsin(sqrt(b)*x/sqrt(a))),sqrt(-a*d/b/c))/a^(5/2)/c^2/(a*d+b*c)/e^3/(a*f+b*e)^2/(-c*f+d*e)/sqrt(-b*x^2+a)/sqrt(1+d*x^2/c)+1/6*sqrt(b)*(16*b^3*c*e^3-2*a*b^2*e^2*(-4*c*f+d*e)-2*a^2*b*e*f*(7*c*f+2*d*e)-a^3*f^2*(15*c*f+2*d*e))*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*InverseJacobiAM(arcsin(sqrt(b)*x/sqrt(a)),sqrt(-a*d/b/c))/a^(5/2)/c/e^3/(a*f+b*e)^2/sqrt(-b*x^2+a)/sqrt(d*x^2+c)+1/2*sqrt(a)*f^3*(b*e*(-8*c*f+9*d*e)+a*f*(-5*c*f+6*d*e))*sqrt(1-b*x^2/a)*sqrt(1+d*x^2/c)*EllipticPi(sin(arcsin(sqrt(b)*x/sqrt(a))),-a*f/b/e,sqrt(-a*d/b/c))/sqrt(b)/e^4/(a*f+b*e)^2/(-c*f+d*e)/sqrt(-b*x^2+a)/sqrt(d*x^2+c),1],
[x^4*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e),x,11,1/384*(15*a^3*d^3*f^3-7*a^2*b*d^2*f^2*(c*f+d*e)-a*b^2*d*f*(7*c^2*f^2-6*c*d*e*f+7*d^2*e^2)+b^3*(15*c^3*f^3-7*c^2*d*e*f^2-7*c*d^2*e^2*f+15*d^3*e^3))*x*sqrt(d*x^2+c)*sqrt(f*x^2+e)/b^2/d^3/f^3/sqrt(b*x^2+a)-1/192*(5*a^2*d*f/b-2*a*(c*f+d*e)-b*(2*c*e-5*d*e^2/f-5*c^2*f/d))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)/b/d/f+1/48*(a/b+c/d+e/f)*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)+1/8*x^5*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)-1/384*sqrt(-a*d+b*c)*e*(15*a^3*d^3*f^3-7*a^2*b*d^2*f^2*(c*f+d*e)-a*b^2*d*f*(7*c^2*f^2-6*c*d*e*f+7*d^2*e^2)+b^3*(15*c^3*f^3-7*c^2*d*e*f^2-7*c*d^2*e^2*f+15*d^3*e^3))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticE(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^3/sqrt(c)/d^3/f^3/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)-1/384*a*sqrt(-a*d+b*c)*(15*a^3*d^3*f^3-3*a^2*b*d^2*f^2*(-c*f+9*d*e)+a*b^2*d*f*(-3*c^2*f^2+2*c*d*e*f+d^2*e^2)-b^3*(15*c^3*f^3-17*c^2*d*e*f^2-3*c*d^2*e^2*f+5*d^3*e^3))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*InverseJacobiAM(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a)),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^4/sqrt(c)/d^3/f^2/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)-1/128*a*(5*a^4*d^4*f^4-2*a^2*b^2*d^2*f^2*(-c*f+d*e)^2-4*a^3*b*d^3*f^3*(c*f+d*e)-4*a*b^3*d*f*(-c*f+d*e)^2*(c*f+d*e)+b^4*(-c*f+d*e)^2*(5*c^2*f^2+6*c*d*e*f+5*d^2*e^2))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticPi(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),b*c/(-a*d+b*c),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^4/sqrt(c)/d^3/sqrt(-a*d+b*c)/f^3/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e),1],
[x^2*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e),x,9,-1/48*(3*a^2*d*f-2*a*b*(c*f+d*e)-b^2*(2*c*e-3*d*e^2/f-3*c^2*f/d))*x*sqrt(d*x^2+c)*sqrt(f*x^2+e)/b/d/f/sqrt(b*x^2+a)+1/24*(a/b+c/d+e/f)*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)+1/6*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)+1/48*sqrt(-a*d+b*c)*e*(3*a^2*d^2*f^2-2*a*b*d*f*(c*f+d*e)+b^2*(3*c^2*f^2-2*c*d*e*f+3*d^2*e^2))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticE(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^2/sqrt(c)/d^2/f^2/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)-1/48*a*sqrt(-a*d+b*c)*(6*a*b*d^2*e*f-3*a^2*d^2*f^2+b^2*(3*c^2*f^2-4*c*d*e*f+d^2*e^2))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*InverseJacobiAM(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a)),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^3/sqrt(c)/d^2/f/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)-1/16*a*(-a*d*f-b*c*f+b*d*e)*(a*d*f-b*c*f+b*d*e)*(a*d*f-b*(c*f+d*e))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticPi(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),b*c/(-a*d+b*c),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^3/sqrt(c)/d^2/sqrt(-a*d+b*c)/f^2/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e),1],
[sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e),x,8,1/8*(a*d*f+b*c*f+b*d*e)*x*sqrt(d*x^2+c)*sqrt(f*x^2+e)/d/f/sqrt(b*x^2+a)+1/4*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)-1/8*sqrt(-a*d+b*c)*e*(a*d*f+b*c*f+b*d*e)*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticE(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b/sqrt(c)/d/f/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)+1/8*a*sqrt(-a*d+b*c)*(-a*d*f+b*c*f+3*b*d*e)*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*InverseJacobiAM(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a)),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^2/sqrt(c)/d/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)-1/8*a*(a^2*d^2*f^2+b^2*(-c*f+d*e)^2-2*a*b*d*f*(c*f+d*e))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticPi(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),b*c/(-a*d+b*c),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^2/sqrt(c)/d/sqrt(-a*d+b*c)/f/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e),1],
[sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)/x^2,x,8,-a*sqrt(d*x^2+c)*sqrt(f*x^2+e)/x/sqrt(b*x^2+a)+1/2*b*x*sqrt(d*x^2+c)*sqrt(f*x^2+e)/sqrt(b*x^2+a)-3/2*sqrt(-a*d+b*c)*e*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticE(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/sqrt(c)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)+1/2*sqrt(-a*d+b*c)*(a*f+2*b*e)*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*InverseJacobiAM(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a)),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b/sqrt(c)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)+1/2*a*(a*d*f+b*c*f+b*d*e)*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticPi(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),b*c/(-a*d+b*c),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b/sqrt(c)/sqrt(-a*d+b*c)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e),1],
[sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)/x^4,x,8,-1/3*a*sqrt(d*x^2+c)*sqrt(f*x^2+e)/x^3/sqrt(b*x^2+a)-1/3*(a*c*f+a*d*e+2*b*c*e)*sqrt(d*x^2+c)*sqrt(f*x^2+e)/c/e/x/sqrt(b*x^2+a)-1/3*sqrt(-a*d+b*c)*(a*c*f+a*d*e+b*c*e)*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticE(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/a/c^(3/2)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)+1/3*sqrt(-a*d+b*c)*(2*c*f+d*e)*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*InverseJacobiAM(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a)),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/c^(3/2)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)+a*d*f*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticPi(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),b*c/(-a*d+b*c),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/sqrt(c)/sqrt(-a*d+b*c)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e),1],
[sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)/x^6,x,7,-1/5*a*sqrt(d*x^2+c)*sqrt(f*x^2+e)/x^5/sqrt(b*x^2+a)-1/15*(a*c*f+a*d*e+4*b*c*e)*sqrt(d*x^2+c)*sqrt(f*x^2+e)/c/e/x^3/sqrt(b*x^2+a)+1/15*(b^2*c*e-3*a*b*(c*f+d*e)+2*a^2*(d^2*e/c-d*f+c*f^2/e))*sqrt(d*x^2+c)*sqrt(f*x^2+e)/a/c/e/x/sqrt(b*x^2+a)+2/15*sqrt(-a*d+b*c)*(b^2*c^2*e^2-a*b*c*e*(c*f+d*e)+a^2*(c^2*f^2-c*d*e*f+d^2*e^2))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticE(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/a^2/c^(5/2)/e/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)+1/15*sqrt(-a*d+b*c)*(-c*f+d*e)*(a*c*f-2*a*d*e+b*c*e)*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*InverseJacobiAM(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a)),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/a/c^(5/2)/e/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e),1],
[sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)/x^8,x,8,-1/7*a*sqrt(d*x^2+c)*sqrt(f*x^2+e)/x^7/sqrt(b*x^2+a)-1/35*(a*c*f+a*d*e+6*b*c*e)*sqrt(d*x^2+c)*sqrt(f*x^2+e)/c/e/x^5/sqrt(b*x^2+a)+1/105*(b^2*c*e-5*a*b*(c*f+d*e)+2*a^2*(2*d^2*e/c-d*f+2*c*f^2/e))*sqrt(d*x^2+c)*sqrt(f*x^2+e)/a/c/e/x^3/sqrt(b*x^2+a)-1/105*(4*b^3*c^3*e^3-3*a*b^2*c^2*e^2*(c*f+d*e)-a^2*b*c*e*(9*c^2*f^2-8*c*d*e*f+9*d^2*e^2)+a^3*(8*c^3*f^3-5*c^2*d*e*f^2-5*c*d^2*e^2*f+8*d^3*e^3))*sqrt(d*x^2+c)*sqrt(f*x^2+e)/a^2/c^3/e^3/x/sqrt(b*x^2+a)-1/105*sqrt(-a*d+b*c)*(8*b^3*c^3*e^3-5*a*b^2*c^2*e^2*(c*f+d*e)-a^2*b*c*e*(5*c^2*f^2-6*c*d*e*f+5*d^2*e^2)+a^3*(8*c^3*f^3-5*c^2*d*e*f^2-5*c*d^2*e^2*f+8*d^3*e^3))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticE(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/a^3/c^(7/2)/e^2/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)-1/105*sqrt(-a*d+b*c)*(-c*f+d*e)*(4*b^2*c^2*e^2+a*b*c*e*(-2*c*f+d*e)-a^2*(-4*c^2*f^2-c*d*e*f+8*d^2*e^2))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*InverseJacobiAM(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a)),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/a^2/c^(7/2)/e^2/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e),1],
[sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)/x^10,x,9,-1/9*a*sqrt(d*x^2+c)*sqrt(f*x^2+e)/x^9/sqrt(b*x^2+a)-1/63*(a*c*f+a*d*e+8*b*c*e)*sqrt(d*x^2+c)*sqrt(f*x^2+e)/c/e/x^7/sqrt(b*x^2+a)+1/315*(b^2*c*e-7*a*b*(c*f+d*e)+2*a^2*(3*d^2*e/c-d*f+3*c*f^2/e))*sqrt(d*x^2+c)*sqrt(f*x^2+e)/a/c/e/x^5/sqrt(b*x^2+a)-1/315*(2*b^3*c^3*e^3-a*b^2*c^2*e^2*(c*f+d*e)-a^2*b*c*e*(9*c^2*f^2-4*c*d*e*f+9*d^2*e^2)+a^3*(8*c^3*f^3-3*c^2*d*e*f^2-3*c*d^2*e^2*f+8*d^3*e^3))*sqrt(d*x^2+c)*sqrt(f*x^2+e)/a^2/c^3/e^3/x^3/sqrt(b*x^2+a)+1/315*(8*b^4*c^4*e^4-5*a*b^3*c^3*e^3*(c*f+d*e)-a^2*b^2*c^2*e^2*(3*c^2*f^2-4*c*d*e*f+3*d^2*e^2)-a^3*b*c*e*(16*c^3*f^3-9*c^2*d*e*f^2-9*c*d^2*e^2*f+16*d^3*e^3)+2*a^4*(8*c^4*f^4-4*c^3*d*e*f^3-3*c^2*d^2*e^2*f^2-4*c*d^3*e^3*f+8*d^4*e^4))*sqrt(d*x^2+c)*sqrt(f*x^2+e)/a^3/c^4/e^4/x/sqrt(b*x^2+a)+2/315*sqrt(-a*d+b*c)*(8*b^4*c^4*e^4-4*a*b^3*c^3*e^3*(c*f+d*e)-3*a^2*b^2*c^2*e^2*(c^2*f^2-c*d*e*f+d^2*e^2)-a^3*b*c*e*(4*c^3*f^3-3*c^2*d*e*f^2-3*c*d^2*e^2*f+4*d^3*e^3)+a^4*(8*c^4*f^4-4*c^3*d*e*f^3-3*c^2*d^2*e^2*f^2-4*c*d^3*e^3*f+8*d^4*e^4))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticE(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/a^4/c^(9/2)/e^3/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)+1/315*sqrt(-a*d+b*c)*(-c*f+d*e)*(8*b^3*c^3*e^3-3*a^2*b*c^3*e*f^2+3*a*b^2*c^2*e^2*(-c*f+d*e)-a^3*(-8*c^3*f^3-3*c^2*d*e*f^2+16*d^3*e^3))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*InverseJacobiAM(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a)),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/a^3/c^(9/2)/e^3/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e),1],
[x^4*sqrt(b*x^2+a)*sqrt(d*x^2+c)*(f*x^2+e)^(3/2),x,13,-1/3840*(105*a^4*d^4*f^4-10*a^3*b*d^3*f^3*(4*c*f+19*d*e)+2*a^2*b^2*d^2*f^2*(-17*c^2*f^2+47*c*d*e*f+18*d^2*e^2)+2*a*b^3*d*f*(-20*c^3*f^3+47*c^2*d*e*f^2-18*c*d^2*e^2*f+15*d^3*e^3)-b^4*(-105*c^4*f^4+190*c^3*d*e*f^3-36*c^2*d^2*e^2*f^2-30*c*d^3*e^3*f+45*d^4*e^4))*x*sqrt(d*x^2+c)*sqrt(f*x^2+e)/b^3/d^4/f^3/sqrt(b*x^2+a)+1/1920*(35*a^3*d^3*f^3-a^2*b*d^2*f^2*(11*c*f+61*d*e)+a*b^2*d*f*(-11*c^2*f^2+26*c*d*e*f+9*d^2*e^2)-b^3*(-35*c^3*f^3+61*c^2*d*e*f^2-9*c*d^2*e^2*f+15*d^3*e^3))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)/b^3/d^3/f^2-1/480*(7*a^2*d*f^2/b-2*a*f*(c*f+6*d*e)-b*(3*d*e^2+12*c*e*f-7*c^2*f^2/d))*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)/b/d/f+1/80*(a*d*f+b*c*f+11*b*d*e)*x^5*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)/b/d+1/10*f*x^7*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)+1/3840*sqrt(-a*d+b*c)*e*(105*a^4*d^4*f^4-10*a^3*b*d^3*f^3*(4*c*f+19*d*e)+2*a^2*b^2*d^2*f^2*(-17*c^2*f^2+47*c*d*e*f+18*d^2*e^2)+2*a*b^3*d*f*(-20*c^3*f^3+47*c^2*d*e*f^2-18*c*d^2*e^2*f+15*d^3*e^3)-b^4*(-105*c^4*f^4+190*c^3*d*e*f^3-36*c^2*d^2*e^2*f^2-30*c*d^3*e^3*f+45*d^4*e^4))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticE(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^4/sqrt(c)/d^4/f^3/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)+1/3840*a*sqrt(-a*d+b*c)*(105*a^4*d^4*f^4+40*a^2*b^2*d^3*e*f^2*(-c*f+7*d*e)-30*a^3*b*d^3*f^3*(-c*f+11*d*e)-2*a*b^3*d*f*(15*c^3*f^3-31*c^2*d*e*f^2+13*c*d^2*e^2*f+3*d^3*e^3)+b^4*(-105*c^4*f^4+260*c^3*d*e*f^3-158*c^2*d^2*e^2*f^2-12*c*d^3*e^3*f+15*d^4*e^4))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*InverseJacobiAM(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a)),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^5/sqrt(c)/d^4/f^2/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)+1/256*a*(7*a^5*d^5*f^5+2*a^2*b^3*d^2*f^2*(-c*f+d*e)^3-5*a^4*b*d^4*f^4*(c*f+3*d*e)+a*b^4*d*f*(-c*f+d*e)^3*(5*c*f+3*d*e)+2*a^3*b^2*d^3*f^3*(-c^2*f^2+6*c*d*e*f+3*d^2*e^2)-b^5*(-c*f+d*e)^3*(7*c^2*f^2+6*c*d*e*f+3*d^2*e^2))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticPi(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),b*c/(-a*d+b*c),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^5/sqrt(c)/d^4/sqrt(-a*d+b*c)/f^3/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e),1],
[x^2*sqrt(b*x^2+a)*sqrt(d*x^2+c)*(f*x^2+e)^(3/2),x,11,1/384*(15*a^3*d^3*f^3-a^2*b*d^2*f^2*(7*c*f+31*d*e)+a*b^2*d*f*(-7*c^2*f^2+22*c*d*e*f+9*d^2*e^2)-b^3*(-15*c^3*f^3+31*c^2*d*e*f^2-9*c*d^2*e^2*f+9*d^3*e^3))*x*sqrt(d*x^2+c)*sqrt(f*x^2+e)/b^2/d^3/f^2/sqrt(b*x^2+a)-1/192*(5*a^2*d*f^2/b-2*a*f*(c*f+5*d*e)-b*(3*d*e^2+10*c*e*f-5*c^2*f^2/d))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)/b/d/f+1/48*(a*d*f+b*c*f+9*b*d*e)*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)/b/d+1/8*f*x^5*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)-1/384*sqrt(-a*d+b*c)*e*(15*a^3*d^3*f^3-a^2*b*d^2*f^2*(7*c*f+31*d*e)+a*b^2*d*f*(-7*c^2*f^2+22*c*d*e*f+9*d^2*e^2)-b^3*(-15*c^3*f^3+31*c^2*d*e*f^2-9*c*d^2*e^2*f+9*d^3*e^3))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticE(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^3/sqrt(c)/d^3/f^2/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)-1/384*a*sqrt(-a*d+b*c)*(15*a^3*d^3*f^3-3*a^2*b*d^2*f^2*(-c*f+17*d*e)+a*b^2*d*f*(-3*c^2*f^2+2*c*d*e*f+49*d^2*e^2)+b^3*(-15*c^3*f^3+41*c^2*d*e*f^2-29*c*d^2*e^2*f+3*d^3*e^3))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*InverseJacobiAM(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a)),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^4/sqrt(c)/d^3/f/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)-1/128*a*(5*a^4*d^4*f^4+4*a*b^3*d*f*(-c*f+d*e)^3-4*a^3*b*d^3*f^3*(c*f+3*d*e)-b^4*(-c*f+d*e)^3*(5*c*f+3*d*e)+2*a^2*b^2*d^2*f^2*(-c^2*f^2+6*c*d*e*f+3*d^2*e^2))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticPi(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),b*c/(-a*d+b*c),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^4/sqrt(c)/d^3/sqrt(-a*d+b*c)/f^2/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e),1],
[sqrt(b*x^2+a)*sqrt(d*x^2+c)*(f*x^2+e)^(3/2),x,9,1/48*(8*a*e+8*b*c*e/d+3*b*e^2/f-3*a^2*f/b-3*b*c^2*f/d^2+2*a*c*f/d)*x*sqrt(d*x^2+c)*sqrt(f*x^2+e)/sqrt(b*x^2+a)+1/24*(a*d*f+b*c*f+7*b*d*e)*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)/b/d+1/6*f*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)+1/48*sqrt(-a*d+b*c)*e*(3*a^2*d^2*f^2-2*a*b*d*f*(c*f+4*d*e)-b^2*(-3*c^2*f^2+8*c*d*e*f+3*d^2*e^2))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticE(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^2/sqrt(c)/d^2/f/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)-1/48*a*sqrt(-a*d+b*c)*(12*a*b*d^2*e*f-3*a^2*d^2*f^2-b^2*(-3*c^2*f^2+10*c*d*e*f+17*d^2*e^2))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*InverseJacobiAM(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a)),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^3/sqrt(c)/d^2/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)+1/16*a*(a^3*d^3*f^3-b^3*(-c*f+d*e)^3-a^2*b*d^2*f^2*(c*f+3*d*e)+a*b^2*d*f*(-c^2*f^2+6*c*d*e*f+3*d^2*e^2))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticPi(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),b*c/(-a*d+b*c),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^3/sqrt(c)/d^2/sqrt(-a*d+b*c)/f/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e),1],
[sqrt(b*x^2+a)*sqrt(d*x^2+c)*(f*x^2+e)^(3/2)/x^2,x,9,1/8*(a*d*f+b*c*f+13*b*d*e)*x*sqrt(d*x^2+c)*sqrt(f*x^2+e)/d/sqrt(b*x^2+a)-e*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)/x+1/4*f*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)-1/8*sqrt(-a*d+b*c)*e*(a*d*f+b*c*f+13*b*d*e)*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticE(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b/sqrt(c)/d/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)+1/8*sqrt(-a*d+b*c)*(8*b^2*d*e^2-a^2*d*f^2+a*b*f*(c*f+7*d*e))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*InverseJacobiAM(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a)),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^2/sqrt(c)/d/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)-1/8*a*(a^2*d^2*f^2-2*a*b*d*f*(c*f+3*d*e)-b^2*(-c^2*f^2+6*c*d*e*f+3*d^2*e^2))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticPi(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),b*c/(-a*d+b*c),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^2/sqrt(c)/d/sqrt(-a*d+b*c)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e),1],
[sqrt(b*x^2+a)*sqrt(d*x^2+c)*(f*x^2+e)^(3/2)/x^4,x,9,-1/6*e*(11*a*c*f+2*a*d*e+2*b*c*e)*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a/c/x/sqrt(f*x^2+e)-1/3*e*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)/x^3+1/2*f*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)/x-1/6*sqrt(a*f-b*e)*(11*a*c*f+2*a*d*e+2*b*c*e)*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/a^(3/2)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))+1/6*sqrt(a*f-b*e)*(6*a*c*f+7*a*d*e+2*b*c*e)*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/a^(3/2)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))+1/2*e*(a*d*f+b*c*f+3*b*d*e)*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticPi(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),-a*f/(-a*f+b*e),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/sqrt(a*f-b*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[sqrt(b*x^2+a)*sqrt(d*x^2+c)*(f*x^2+e)^(3/2)/x^6,x,9,1/15*(2*b^2*c^2*e^2-a*b*c*e*(7*c*f+2*d*e)+a^2*(-3*c^2*f^2-7*c*d*e*f+2*d^2*e^2))*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a^2/c^2/x/sqrt(f*x^2+e)-1/5*e*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)/x^5-1/15*(6*a*c*f+a*d*e+b*c*e)*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)/a/c/x^3+1/15*sqrt(a*f-b*e)*(2*b^2*c^2*e^2-a*b*c*e*(7*c*f+2*d*e)+a^2*(-3*c^2*f^2-7*c*d*e*f+2*d^2*e^2))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/a^(5/2)/c/e/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))-1/15*sqrt(a*f-b*e)*(2*b^2*c^2*e+a^2*d*(-9*c*f+d*e)-3*a*b*c*(2*c*f+d*e))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/a^(5/2)/c/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))+b*d*e*f*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticPi(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),-a*f/(-a*f+b*e),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/sqrt(a*f-b*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[sqrt(b*x^2+a)*sqrt(d*x^2+c)*(f*x^2+e)^(3/2)/x^8,x,9,-1/105*(-2*a*c*f+a*d*e+b*c*e)*(8*b^2*c^2*e^2-a*b*c*e*(3*c*f+13*d*e)+a^2*(3*c^2*f^2-3*c*d*e*f+8*d^2*e^2))*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a^3/c^3/e/x/sqrt(f*x^2+e)-1/7*e*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)/x^7-1/2*f*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)/x^5-1/70*(-19*a*c*f+2*a*d*e+2*b*c*e)*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)/a/c/x^5+1/105*(4*b^2*c^2*e^2-a*b*c*e*(9*c*f+2*d*e)+a^2*(-3*c^2*f^2-9*c*d*e*f+4*d^2*e^2))*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)/a^2/c^2/e/x^3-1/105*sqrt(a*f-b*e)*(-2*a*c*f+a*d*e+b*c*e)*(8*b^2*c^2*e^2-a*b*c*e*(3*c*f+13*d*e)+a^2*(3*c^2*f^2-3*c*d*e*f+8*d^2*e^2))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/a^(7/2)/c^2/e^2/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))+1/105*(-a*d+b*c)*sqrt(a*f-b*e)*(8*b^2*c^2*e^2-a*b*c*e*(15*c*f+d*e)-a^2*(-3*c^2*f^2-9*c*d*e*f+4*d^2*e^2))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/a^(7/2)/c^2/e/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[x^4*sqrt(b*x^2+a)*sqrt(d*x^2+c)/sqrt(f*x^2+e),x,9,1/48*(2*a*c-3*b*c^2/d-3*a^2*d/b+15*b*d*e^2/f^2-4*b*c*e/f-4*a*d*e/f)*x*sqrt(d*x^2+c)*sqrt(f*x^2+e)/d/f/sqrt(b*x^2+a)-1/24*(-a*d*f+3*b*c*f+5*b*d*e)*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)/b/d/f^2+1/6*x*sqrt(b*x^2+a)*(d*x^2+c)^(3/2)*sqrt(f*x^2+e)/d/f+1/48*sqrt(-a*d+b*c)*e*(3*a^2*d^2*f^2+2*a*b*d*f*(-c*f+2*d*e)-b^2*(-3*c^2*f^2-4*c*d*e*f+15*d^2*e^2))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticE(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^2/sqrt(c)/d^2/f^3/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)+1/48*a*sqrt(-a*d+b*c)*(3*a^2*d^2*f^2+b^2*(-3*c^2*f^2-2*c*d*e*f+5*d^2*e^2))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*InverseJacobiAM(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a)),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^3/sqrt(c)/d^2/f^2/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)+1/16*a*(a^3*d^3*f^3+a^2*b*d^2*f^2*(-c*f+d*e)+a*b^2*d*f*(-c^2*f^2-2*c*d*e*f+3*d^2*e^2)-b^3*(-c^3*f^3-c^2*d*e*f^2-3*c*d^2*e^2*f+5*d^3*e^3))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticPi(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),b*c/(-a*d+b*c),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^3/sqrt(c)/d^2/sqrt(-a*d+b*c)/f^3/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e),1],
[x^2*sqrt(b*x^2+a)*sqrt(d*x^2+c)/sqrt(f*x^2+e),x,8,-1/8*(-a*d*f-b*c*f+3*b*d*e)*x*sqrt(d*x^2+c)*sqrt(f*x^2+e)/d/f^2/sqrt(b*x^2+a)+1/4*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)/f+1/8*sqrt(-a*d+b*c)*e*(-a*d*f-b*c*f+3*b*d*e)*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticE(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b/sqrt(c)/d/f^2/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)-1/8*a*sqrt(-a*d+b*c)*(a*d*f-b*c*f+b*d*e)*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*InverseJacobiAM(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a)),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^2/sqrt(c)/d/f/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)-1/8*a*(a^2*d^2*f^2+2*a*b*d*f*(-c*f+d*e)-b^2*(-c^2*f^2-2*c*d*e*f+3*d^2*e^2))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticPi(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),b*c/(-a*d+b*c),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^2/sqrt(c)/d/sqrt(-a*d+b*c)/f^2/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e),1],
[sqrt(b*x^2+a)*sqrt(d*x^2+c)/sqrt(f*x^2+e),x,7,1/2*b*x*sqrt(d*x^2+c)*sqrt(f*x^2+e)/f/sqrt(b*x^2+a)-1/2*sqrt(-a*d+b*c)*e*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticE(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/sqrt(c)/f/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)+1/2*a*sqrt(-a*d+b*c)*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*InverseJacobiAM(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a)),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b/sqrt(c)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)-1/2*a*(-a*d*f-b*c*f+b*d*e)*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticPi(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),b*c/(-a*d+b*c),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b/sqrt(c)/sqrt(-a*d+b*c)/f/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e),1],
[sqrt(b*x^2+a)*sqrt(d*x^2+c)/x^2/sqrt(f*x^2+e),x,7,-sqrt(b*x^2+a)*sqrt(d*x^2+c)/x/sqrt(f*x^2+e)-c*sqrt(a*f-b*e)*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/e/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))+d*sqrt(a*f-b*e)*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/f/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))+b*d*e*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticPi(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),-a*f/(-a*f+b*e),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/f/sqrt(a*f-b*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[sqrt(b*x^2+a)*sqrt(d*x^2+c)/x^4/sqrt(f*x^2+e),x,6,-1/3*(b/a+d/c-2*f/e)*sqrt(b*x^2+a)*sqrt(d*x^2+c)/x/sqrt(f*x^2+e)-1/3*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)/e/x^3-1/3*sqrt(a*f-b*e)*(-2*a*c*f+a*d*e+b*c*e)*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/a^(3/2)/e^2/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))+1/3*(-a*d+b*c)*sqrt(a*f-b*e)*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/a^(3/2)/e/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[sqrt(b*x^2+a)*sqrt(d*x^2+c)/x^6/sqrt(f*x^2+e),x,7,1/15*(2*b^2*c^2*e^2-a*b*c*e*(-3*c*f+2*d*e)+a^2*(-8*c^2*f^2+3*c*d*e*f+2*d^2*e^2))*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a^2/c^2/e^2/x/sqrt(f*x^2+e)-1/5*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)/e/x^5-1/15*(b/a+d/c-4*f/e)*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)/e/x^3+1/15*sqrt(a*f-b*e)*(2*b^2*c^2*e^2-a*b*c*e*(-3*c*f+2*d*e)+a^2*(-8*c^2*f^2+3*c*d*e*f+2*d^2*e^2))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/a^(5/2)/c/e^3/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))-1/15*(-a*d+b*c)*sqrt(a*f-b*e)*(4*a*c*f-a*d*e+2*b*c*e)*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/a^(5/2)/c/e^2/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[sqrt(b*x^2+a)*sqrt(d*x^2+c)/x^8/sqrt(f*x^2+e),x,8,-1/105*(8*b^3*c^3*e^3-a*b^2*c^2*e^2*(-9*c*f+5*d*e)-a^2*b*c*e*(-16*c^2*f^2+8*c*d*e*f+5*d^2*e^2)+a^3*(-48*c^3*f^3+16*c^2*d*e*f^2+9*c*d^2*e^2*f+8*d^3*e^3))*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a^3/c^3/e^3/x/sqrt(f*x^2+e)-1/7*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)/e/x^7-1/35*(b/a+d/c-6*f/e)*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)/e/x^5+1/105*(4*b^2*c*e/a-2*b*d*e+4*a*d^2*e/c+5*b*c*f+5*a*d*f-24*a*c*f^2/e)*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)/a/c/e^2/x^3-1/105*sqrt(a*f-b*e)*(8*b^3*c^3*e^3-a*b^2*c^2*e^2*(-9*c*f+5*d*e)-a^2*b*c*e*(-16*c^2*f^2+8*c*d*e*f+5*d^2*e^2)+a^3*(-48*c^3*f^3+16*c^2*d*e*f^2+9*c*d^2*e^2*f+8*d^3*e^3))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/a^(7/2)/c^2/e^4/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))+1/105*(-a*d+b*c)*sqrt(a*f-b*e)*(8*b^2*c^2*e^2-a*b*c*e*(-13*c*f+d*e)-a^2*(-24*c^2*f^2+5*c*d*e*f+4*d^2*e^2))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/a^(7/2)/c^2/e^3/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[x^4*sqrt(b*x^2+a)*sqrt(d*x^2+c)/(f*x^2+e)^(3/2),x,9,5/4*e*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/f^2/sqrt(f*x^2+e)+1/4*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/f/sqrt(f*x^2+e)-1/8*(-a*d*f-b*c*f+15*b*d*e)*x*sqrt(d*x^2+c)*sqrt(f*x^2+e)/d/f^3/sqrt(b*x^2+a)+1/8*sqrt(-a*d+b*c)*e*(-a*d*f-b*c*f+15*b*d*e)*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticE(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b/sqrt(c)/d/f^3/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)-1/8*a*sqrt(-a*d+b*c)*(a*d*f-b*c*f+5*b*d*e)*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*InverseJacobiAM(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a)),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^2/sqrt(c)/d/f^2/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)-1/8*a*(a^2*d^2*f^2+2*a*b*d*f*(-c*f+3*d*e)-b^2*(-c^2*f^2-6*c*d*e*f+15*d^2*e^2))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticPi(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),b*c/(-a*d+b*c),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^2/sqrt(c)/d/sqrt(-a*d+b*c)/f^3/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e),1],
[x^2*sqrt(b*x^2+a)*sqrt(d*x^2+c)/(f*x^2+e)^(3/2),x,8,-x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/f/sqrt(f*x^2+e)+3/2*b*x*sqrt(d*x^2+c)*sqrt(f*x^2+e)/f^2/sqrt(b*x^2+a)-3/2*sqrt(-a*d+b*c)*e*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticE(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/sqrt(c)/f^2/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)+1/2*a*sqrt(-a*d+b*c)*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*InverseJacobiAM(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a)),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b/sqrt(c)/f/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)-1/2*a*(-a*d*f-b*c*f+3*b*d*e)*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticPi(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),b*c/(-a*d+b*c),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b/sqrt(c)/sqrt(-a*d+b*c)/f^2/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e),1],
[sqrt(b*x^2+a)*sqrt(d*x^2+c)/(f*x^2+e)^(3/2),x,6,sqrt(a)*sqrt(a*f-b*e)*sqrt(d*x^2+c)*sqrt(e*(b*x^2+a)/a/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/e/f/sqrt(b*x^2+a)/sqrt(e*(d*x^2+c)/c/(f*x^2+e))-sqrt(a)*b*(-c*f+d*e)*sqrt(d*x^2+c)*sqrt(e*(b*x^2+a)/a/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/c/f^2/sqrt(a*f-b*e)/sqrt(b*x^2+a)/sqrt(e*(d*x^2+c)/c/(f*x^2+e))+sqrt(a)*b*d*e*sqrt(d*x^2+c)*sqrt(e*(b*x^2+a)/a/(f*x^2+e))*EllipticPi(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),-a*f/(-a*f+b*e),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/c/f^2/sqrt(a*f-b*e)/sqrt(b*x^2+a)/sqrt(e*(d*x^2+c)/c/(f*x^2+e)),1],
[sqrt(b*x^2+a)*sqrt(d*x^2+c)/x^2/(f*x^2+e)^(3/2),x,5,-sqrt(b*x^2+a)*sqrt(d*x^2+c)/e/x/sqrt(f*x^2+e)-2*c*sqrt(a*f-b*e)*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/e^2/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))-(-a*d+b*c)*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/e/sqrt(a*f-b*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[sqrt(b*x^2+a)*sqrt(d*x^2+c)/x^4/(f*x^2+e)^(3/2),x,6,-1/3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/e/x^3/sqrt(f*x^2+e)-1/3*(b/a+d/c-4*f/e)*sqrt(b*x^2+a)*sqrt(d*x^2+c)/e/x/sqrt(f*x^2+e)-1/3*sqrt(a*f-b*e)*(-8*a*c*f+a*d*e+b*c*e)*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/a^(3/2)/e^3/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))-1/3*(-a*d+b*c)*(-4*a*f+b*e)*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/a^(3/2)/e^2/sqrt(a*f-b*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[sqrt(b*x^2+a)*sqrt(d*x^2+c)/x^6/(f*x^2+e)^(3/2),x,7,-1/5*sqrt(b*x^2+a)*sqrt(d*x^2+c)/e/x^5/sqrt(f*x^2+e)-1/15*(b/a+d/c-6*f/e)*sqrt(b*x^2+a)*sqrt(d*x^2+c)/e/x^3/sqrt(f*x^2+e)+1/15*(2*b^2*c*e/a-2*b*d*e+2*a*d^2*e/c+7*b*c*f+7*a*d*f-24*a*c*f^2/e)*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a/c/e^2/x/sqrt(f*x^2+e)+2/15*sqrt(a*f-b*e)*(b^2*c^2*e^2-a*b*c*e*(-4*c*f+d*e)+a^2*(-24*c^2*f^2+4*c*d*e*f+d^2*e^2))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/a^(5/2)/c/e^4/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))+1/15*(-a*d+b*c)*(2*b^2*c*e^2+a^2*f*(-24*c*f+d*e)-a*b*e*(-7*c*f+d*e))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/a^(5/2)/c/e^3/sqrt(a*f-b*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[sqrt(b*x^2+a)*sqrt(d*x^2+c)/x^8/(f*x^2+e)^(3/2),x,8,-1/7*sqrt(b*x^2+a)*sqrt(d*x^2+c)/e/x^7/sqrt(f*x^2+e)-1/35*(b/a+d/c-8*f/e)*sqrt(b*x^2+a)*sqrt(d*x^2+c)/e/x^5/sqrt(f*x^2+e)+1/105*(4*b^2*c*e/a-2*b*d*e+4*a*d^2*e/c+9*b*c*f+9*a*d*f-48*a*c*f^2/e)*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a/c/e^2/x^3/sqrt(f*x^2+e)-1/105*(8*b^3*c^2*e^2/a-b^2*c*e*(-19*c*f+5*d*e)-5*a*b*(-12*c^2*f^2+4*c*d*e*f+d^2*e^2)+a^2*(8*d^3*e^2/c+19*d^2*e*f+60*c*d*f^2-192*c^2*f^3/e))*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a^2/c^2/e^3/x/sqrt(f*x^2+e)-1/105*sqrt(a*f-b*e)*(8*b^3*c^3*e^3-a*b^2*c^2*e^2*(-23*c*f+5*d*e)-a^2*b*c*e*(-72*c^2*f^2+22*c*d*e*f+5*d^2*e^2)+a^3*(-384*c^3*f^3+72*c^2*d*e*f^2+23*c*d^2*e^2*f+8*d^3*e^3))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/a^(7/2)/c^2/e^5/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))-1/105*(-a*d+b*c)*(8*b^3*c^2*e^3-a*b^2*c*e^2*(-19*c*f+d*e)-a^2*b*e*(-60*c^2*f^2+11*c*d*e*f+4*d^2*e^2)+4*a^3*f*(-48*c^2*f^2+3*c*d*e*f+d^2*e^2))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/a^(7/2)/c^2/e^4/sqrt(a*f-b*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[x^6*sqrt(b*x^2+a)*sqrt(d*x^2+c)/(f*x^2+e)^(5/2),x,9,-1/3*e^2*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/f^3/(f*x^2+e)^(3/2)-1/8*(-a*d*f-b*c*f+9*b*d*e)*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b/d/f^3/sqrt(f*x^2+e)+1/4*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/f^2/sqrt(f*x^2+e)-1/24*c*(3*a^2*d*f^2*(-c*f+d*e)+b^2*e*(3*c^2*f^2-100*c*d*e*f+105*d^2*e^2)-a*b*f*(3*c^2*f^2-95*c*d*e*f+100*d^2*e^2))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/b/d/f^4/sqrt(a*f-b*e)/(-c*f+d*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))+1/24*e*(3*a^2*d*f^2*(-c*f+d*e)+a*b*f*(63*c^2*f^2-101*c*d*e*f+30*d^2*e^2)-b^2*e*(127*c^2*f^2-240*c*d*e*f+105*d^2*e^2))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/b/f^5/sqrt(a*f-b*e)/(-c*f+d*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))-1/8*e*(a^2*d^2*f^2+2*a*b*d*f*(-c*f+5*d*e)-b^2*(-c^2*f^2-10*c*d*e*f+35*d^2*e^2))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticPi(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),-a*f/(-a*f+b*e),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/b/d/f^5/sqrt(a*f-b*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[x^4*sqrt(b*x^2+a)*sqrt(d*x^2+c)/(f*x^2+e)^(5/2),x,8,1/3*e*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/f^2/(f*x^2+e)^(3/2)+1/2*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/f^2/sqrt(f*x^2+e)+1/6*c*(b*e*(-13*c*f+15*d*e)-a*f*(-11*c*f+13*d*e))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/f^3/sqrt(a*f-b*e)/(-c*f+d*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))-1/6*(a*f*(6*c^2*f^2-11*c*d*e*f+3*d^2*e^2)-b*e*(16*c^2*f^2-33*c*d*e*f+15*d^2*e^2))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/f^4/sqrt(a*f-b*e)/(-c*f+d*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))-1/2*e*(-a*d*f-b*c*f+5*b*d*e)*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticPi(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),-a*f/(-a*f+b*e),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/f^4/sqrt(a*f-b*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[x^2*sqrt(b*x^2+a)*sqrt(d*x^2+c)/(f*x^2+e)^(5/2),x,7,-1/3*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/f/(f*x^2+e)^(3/2)-1/3*c*(b*e*(-2*c*f+3*d*e)-a*f*(-c*f+2*d*e))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/e/f^2/sqrt(a*f-b*e)/(-c*f+d*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))-1/3*(a*c*d*f^2+b*(2*c^2*f^2-6*c*d*e*f+3*d^2*e^2))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/f^3/sqrt(a*f-b*e)/(-c*f+d*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))+b*d*e*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticPi(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),-a*f/(-a*f+b*e),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/f^3/sqrt(a*f-b*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[sqrt(b*x^2+a)*sqrt(d*x^2+c)/(f*x^2+e)^(5/2),x,5,1/3*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/e/(f*x^2+e)^(3/2)+1/3*c*(-2*a*c*f+a*d*e+b*c*e)*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/e^2/sqrt(a*f-b*e)/(-c*f+d*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))-1/3*c*(-a*d+b*c)*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/e/sqrt(a*f-b*e)/(-c*f+d*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[sqrt(b*x^2+a)*sqrt(d*x^2+c)/x^2/(f*x^2+e)^(5/2),x,6,-sqrt(b*x^2+a)*sqrt(d*x^2+c)/e/x/(f*x^2+e)^(3/2)-4/3*f*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/e^2/(f*x^2+e)^(3/2)-1/3*c*(a*f*(-8*c*f+7*d*e)-b*e*(-7*c*f+6*d*e))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/e^3/sqrt(a*f-b*e)/(-c*f+d*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))-1/3*(-a*d+b*c)*(-4*c*f+3*d*e)*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/e^2/sqrt(a*f-b*e)/(-c*f+d*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[sqrt(b*x^2+a)*sqrt(d*x^2+c)/x^4/(f*x^2+e)^(5/2),x,7,-1/3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/e/x^3/(f*x^2+e)^(3/2)-1/3*(b/a+d/c-6*f/e)*sqrt(b*x^2+a)*sqrt(d*x^2+c)/e/x/(f*x^2+e)^(3/2)-1/3*f*(-8*a*c*f+a*d*e+b*c*e)*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a/c/e^3/(f*x^2+e)^(3/2)+1/3*(b^2*c*e^2*(-c*f+d*e)+a*b*e*(16*c^2*f^2-16*c*d*e*f+d^2*e^2)-a^2*f*(16*c^2*f^2-16*c*d*e*f+d^2*e^2))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/a^(3/2)/e^4/sqrt(a*f-b*e)/(-c*f+d*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))+1/3*(-a*d+b*c)*(a*f*(-8*c*f+7*d*e)-b*e*(-c*f+d*e))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/a^(3/2)/e^3/sqrt(a*f-b*e)/(-c*f+d*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[sqrt(b*x^2+a)*sqrt(d*x^2+c)/x^6/(f*x^2+e)^(5/2),x,8,-1/5*sqrt(b*x^2+a)*sqrt(d*x^2+c)/e/x^5/(f*x^2+e)^(3/2)-1/15*(b/a+d/c-8*f/e)*sqrt(b*x^2+a)*sqrt(d*x^2+c)/e/x^3/(f*x^2+e)^(3/2)+1/15*(2*b^2*c*e/a-2*b*d*e+2*a*d^2*e/c+11*b*c*f+11*a*d*f-48*a*c*f^2/e)*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a/c/e^2/x/(f*x^2+e)^(3/2)+2/15*f*(b^2*c^2*e^2-a*b*c*e*(-6*c*f+d*e)+a^2*(-32*c^2*f^2+6*c*d*e*f+d^2*e^2))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a^2/c^2/e^4/(f*x^2+e)^(3/2)-1/15*(2*b^3*c^2*e^3*(-c*f+d*e)-a*b^2*c*e^2*(11*c^2*f^2-13*c*d*e*f+2*d^2*e^2)-a^3*f*(128*c^3*f^3-136*c^2*d*e*f^2+11*c*d^2*e^2*f+2*d^3*e^3)+a^2*b*e*(136*c^3*f^3-146*c^2*d*e*f^2+13*c*d^2*e^2*f+2*d^3*e^3))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/a^(5/2)/c/e^5/sqrt(a*f-b*e)/(-c*f+d*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))+1/15*(-a*d+b*c)*(2*b^2*c*e^2*(-c*f+d*e)-a*b*e*(12*c^2*f^2-13*c*d*e*f+d^2*e^2)+a^2*f*(64*c^2*f^2-60*c*d*e*f+d^2*e^2))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/a^(5/2)/c/e^4/sqrt(a*f-b*e)/(-c*f+d*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[x^4*sqrt(f*x^2+e)/sqrt(b*x^2+a)/sqrt(d*x^2+c),x,8,1/8*(-3*a*d*f-3*b*c*f+b*d*e)*x*sqrt(d*x^2+c)*sqrt(f*x^2+e)/b/d^2/f/sqrt(b*x^2+a)+1/4*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)/b/d-1/8*sqrt(-a*d+b*c)*e*(-3*a*d*f-3*b*c*f+b*d*e)*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticE(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^2/sqrt(c)/d^2/f/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)-1/8*a*(3*a^2*d^2*f-a*b*d*(-2*c*f+5*d*e)-3*b^2*c*(-c*f+d*e))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*InverseJacobiAM(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a)),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^3/sqrt(c)/d^2/sqrt(-a*d+b*c)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)+1/8*a*(3*a^2*d^2*f^2-2*a*b*d*f*(-c*f+d*e)-b^2*(-3*c^2*f^2+2*c*d*e*f+d^2*e^2))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticPi(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),b*c/(-a*d+b*c),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^3/sqrt(c)/d^2/sqrt(-a*d+b*c)/f/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e),1],
[x^2*sqrt(f*x^2+e)/sqrt(b*x^2+a)/sqrt(d*x^2+c),x,7,1/2*f*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b/d/sqrt(f*x^2+e)-1/2*c*sqrt(a*f-b*e)*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/b/d/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))+1/2*e*sqrt(a*f-b*e)*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/b/f/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))+1/2*e*(-a*d*f-b*c*f+b*d*e)*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticPi(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),-a*f/(-a*f+b*e),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/b/d/f/sqrt(a*f-b*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[sqrt(f*x^2+e)/sqrt(b*x^2+a)/sqrt(d*x^2+c),x,2,e*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticPi(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),-a*f/(-a*f+b*e),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/sqrt(a*f-b*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[sqrt(f*x^2+e)/x^2/sqrt(b*x^2+a)/sqrt(d*x^2+c),x,3,-sqrt(-b*x^2+a)*sqrt(f*x^2+e)/a/x/sqrt(d*x^2+c)-sqrt(a*d+b*c)*sqrt(f*x^2+e)*EllipticE(sin(arctan(sqrt(a*d+b*c)*x/sqrt(c)/sqrt(-b*x^2+a))),sqrt(a*(-c*f+d*e)/(a*d+b*c)/e))/a/sqrt(c)/sqrt(d*x^2+c)/sqrt(c*(f*x^2+e)/e/(d*x^2+c))+sqrt(c)*(a*f+b*e)*sqrt(f*x^2+e)*InverseJacobiAM(arctan(sqrt(a*d+b*c)*x/sqrt(c)/sqrt(-b*x^2+a)),sqrt(a*(-c*f+d*e)/(a*d+b*c)/e))/a/sqrt(a*d+b*c)/e/sqrt(d*x^2+c)/sqrt(c*(f*x^2+e)/e/(d*x^2+c)),1],
[sqrt(f*x^2+e)/x^4/sqrt(b*x^2+a)/sqrt(d*x^2+c),x,6,1/3*(-a*c*f+2*a*d*e+2*b*c*e)*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a^2/c^2/x/sqrt(f*x^2+e)-1/3*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)/a/c/x^3+1/3*sqrt(a*f-b*e)*(-a*c*f+2*a*d*e+2*b*c*e)*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/a^(5/2)/c/e/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))-1/3*(a*d+2*b*c)*sqrt(a*f-b*e)*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/a^(5/2)/c/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[sqrt(f*x^2+e)/x^6/sqrt(b*x^2+a)/sqrt(d*x^2+c),x,7,-1/15*(8*b^2*c*e^2/a+b*e*(-3*c*f+7*d*e)+a*(8*d^2*e^2/c-3*d*e*f-2*c*f^2))*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a^2/c^2/e/x/sqrt(f*x^2+e)-1/5*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)/a/c/x^5+1/15*(-a*c*f+4*a*d*e+4*b*c*e)*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)/a^2/c^2/e/x^3-1/15*sqrt(a*f-b*e)*(8*b^2*c^2*e^2+a*b*c*e*(-3*c*f+7*d*e)+a^2*(-2*c^2*f^2-3*c*d*e*f+8*d^2*e^2))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/a^(7/2)/c^2/e^2/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))+1/15*sqrt(a*f-b*e)*(8*b^2*c^2*e+a^2*d*(-c*f+4*d*e)+a*b*c*(c*f+3*d*e))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/a^(7/2)/c^2/e/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[x^4*(f*x^2+e)^(3/2)/sqrt(b*x^2+a)/sqrt(d*x^2+c),x,10,1/48*(15*a^2*d^2*f^2-2*a*b*d*f*(-7*c*f+11*d*e)+b^2*(15*c^2*f^2-22*c*d*e*f+3*d^2*e^2))*x*sqrt(d*x^2+c)*sqrt(f*x^2+e)/b^2/d^3/f/sqrt(b*x^2+a)+1/24*(-5*a*d*f-5*b*c*f+7*b*d*e)*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)/b^2/d^2+1/6*f*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)/b/d-1/48*sqrt(-a*d+b*c)*e*(15*a^2*d^2*f^2-2*a*b*d*f*(-7*c*f+11*d*e)+b^2*(15*c^2*f^2-22*c*d*e*f+3*d^2*e^2))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticE(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^3/sqrt(c)/d^3/f/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)+1/48*a*(15*a^3*d^3*f^2-3*a^2*b*d^2*f*(-3*c*f+14*d*e)+a*b^2*d*(9*c^2*f^2-22*c*d*e*f+31*d^2*e^2)+b^3*c*(15*c^2*f^2-32*c*d*e*f+17*d^2*e^2))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*InverseJacobiAM(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a)),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^4/sqrt(c)/d^3/sqrt(-a*d+b*c)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)-1/16*a*(5*a^3*d^3*f^3+3*a*b^2*d*f*(-c*f+d*e)^2-3*a^2*b*d^2*f^2*(-c*f+3*d*e)+b^3*(-c*f+d*e)^2*(5*c*f+d*e))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticPi(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),b*c/(-a*d+b*c),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^4/sqrt(c)/d^3/sqrt(-a*d+b*c)/f/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e),1],
[x^2*(f*x^2+e)^(3/2)/sqrt(b*x^2+a)/sqrt(d*x^2+c),x,8,1/8*(-3*a*d*f-3*b*c*f+5*b*d*e)*x*sqrt(d*x^2+c)*sqrt(f*x^2+e)/b/d^2/sqrt(b*x^2+a)+1/4*f*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)/b/d-1/8*sqrt(-a*d+b*c)*e*(-3*a*d*f-3*b*c*f+5*b*d*e)*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticE(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^2/sqrt(c)/d^2/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)-1/8*a*(3*a^2*d^2*f^2-a*b*d*f*(-2*c*f+9*d*e)+b^2*(3*c^2*f^2-7*c*d*e*f+8*d^2*e^2))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*InverseJacobiAM(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a)),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^3/sqrt(c)/d^2/sqrt(-a*d+b*c)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)+1/8*a*(3*a^2*d^2*f^2+3*b^2*(-c*f+d*e)^2-2*a*b*d*f*(-c*f+3*d*e))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticPi(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),b*c/(-a*d+b*c),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^3/sqrt(c)/d^2/sqrt(-a*d+b*c)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e),1],
[(f*x^2+e)^(3/2)/sqrt(b*x^2+a)/sqrt(d*x^2+c),x,7,1/2*f^2*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b/d/sqrt(f*x^2+e)-1/2*c*f*sqrt(a*f-b*e)*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/b/d/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))+1/2*e*sqrt(a*f-b*e)*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/b/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))+1/2*e*(-a*d*f-b*c*f+3*b*d*e)*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticPi(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),-a*f/(-a*f+b*e),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/b/d/sqrt(a*f-b*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[(f*x^2+e)^(3/2)/x^2/sqrt(b*x^2+a)/sqrt(d*x^2+c),x,7,-e*sqrt(d*x^2+c)*sqrt(f*x^2+e)/c/x/sqrt(b*x^2+a)-sqrt(-a*d+b*c)*e^2*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticE(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/a/c^(3/2)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)-(a*c*f^2+b*e*(-2*c*f+d*e))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*InverseJacobiAM(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a)),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b/c^(3/2)/sqrt(-a*d+b*c)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)+a*f^2*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticPi(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),b*c/(-a*d+b*c),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b/sqrt(c)/sqrt(-a*d+b*c)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e),1],
[(f*x^2+e)^(3/2)/x^4/sqrt(b*x^2+a)/sqrt(d*x^2+c),x,6,2/3*e*(-2*a*c*f+a*d*e+b*c*e)*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a^2/c^2/x/sqrt(f*x^2+e)-1/3*e*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)/a/c/x^3+2/3*sqrt(a*f-b*e)*(-2*a*c*f+a*d*e+b*c*e)*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/a^(5/2)/c/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))-1/3*sqrt(a*f-b*e)*(-3*a*c*f+a*d*e+2*b*c*e)*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/a^(5/2)/c/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[(f*x^2+e)^(3/2)/x^6/sqrt(b*x^2+a)/sqrt(d*x^2+c),x,7,-1/15*(8*b^2*c^2*e^2+a*b*c*e*(-13*c*f+7*d*e)+a^2*(3*c^2*f^2-13*c*d*e*f+8*d^2*e^2))*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a^3/c^3/x/sqrt(f*x^2+e)-1/5*e*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)/a/c/x^5+2/15*(-3*a*c*f+2*a*d*e+2*b*c*e)*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)/a^2/c^2/x^3-1/15*sqrt(a*f-b*e)*(8*b^2*c^2*e^2+a*b*c*e*(-13*c*f+7*d*e)+a^2*(3*c^2*f^2-13*c*d*e*f+8*d^2*e^2))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/a^(7/2)/c^2/e/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))+1/15*sqrt(a*f-b*e)*(8*b^2*c^2*e+3*a*b*c*(-3*c*f+d*e)+2*a^2*d*(-3*c*f+2*d*e))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/a^(7/2)/c^2/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[(f*x^2+e)^(3/2)/x^8/sqrt(b*x^2+a)/sqrt(d*x^2+c),x,8,2/105*(24*b^3*c^3*e^3+4*a*b^2*c^2*e^2*(-9*c*f+5*d*e)+a^2*b*c*e*(6*c^2*f^2-31*c*d*e*f+20*d^2*e^2)+3*a^3*(c^3*f^3+2*c^2*d*e*f^2-12*c*d^2*e^2*f+8*d^3*e^3))*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a^4/c^4/e/x/sqrt(f*x^2+e)-1/7*e*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)/a/c/x^7+2/35*(-4*a*c*f+3*a*d*e+3*b*c*e)*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)/a^2/c^2/x^5-1/105*(24*b^2*c*e^2/a+b*e*(-33*c*f+23*d*e)+a*(24*d^2*e^2/c-33*d*e*f+3*c*f^2))*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)/a^2/c^2/e/x^3+2/105*sqrt(a*f-b*e)*(24*b^3*c^3*e^3+4*a*b^2*c^2*e^2*(-9*c*f+5*d*e)+a^2*b*c*e*(6*c^2*f^2-31*c*d*e*f+20*d^2*e^2)+3*a^3*(c^3*f^3+2*c^2*d*e*f^2-12*c*d^2*e^2*f+8*d^3*e^3))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/a^(9/2)/c^3/e^2/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))-1/105*sqrt(a*f-b*e)*(48*b^3*c^3*e^2+16*a*b^2*c^2*e*(-3*c*f+d*e)+a^2*b*c*(-3*c^2*f^2-24*c*d*e*f+17*d^2*e^2)+3*a^3*d*(c^2*f^2-11*c*d*e*f+8*d^2*e^2))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/a^(9/2)/c^3/e/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[sqrt(f*x^2+e)/x^2/sqrt(b*x^2+a)/sqrt(d*x^2+c),x,3,-sqrt(d*x^2+c)*sqrt(f*x^2+e)/c/x/sqrt(b*x^2+a)-sqrt(e)*sqrt(-a*f+b*e)*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticE(sin(arcsin(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))),sqrt((-a*d+b*c)*e/c/(-a*f+b*e)))/a/c/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e),1],
[sqrt(f*x^2+e)/x^2/sqrt(-b*x^2+a)/sqrt(d*x^2+c),x,3,-sqrt(-b*x^2+a)*sqrt(f*x^2+e)/a/x/sqrt(d*x^2+c)-sqrt(a*d+b*c)*sqrt(f*x^2+e)*EllipticE(sin(arctan(sqrt(a*d+b*c)*x/sqrt(c)/sqrt(-b*x^2+a))),sqrt(a*(-c*f+d*e)/(a*d+b*c)/e))/a/sqrt(c)/sqrt(d*x^2+c)/sqrt(c*(f*x^2+e)/e/(d*x^2+c))+sqrt(c)*(a*f+b*e)*sqrt(f*x^2+e)*InverseJacobiAM(arctan(sqrt(a*d+b*c)*x/sqrt(c)/sqrt(-b*x^2+a)),sqrt(a*(-c*f+d*e)/(a*d+b*c)/e))/a/sqrt(a*d+b*c)/e/sqrt(d*x^2+c)/sqrt(c*(f*x^2+e)/e/(d*x^2+c)),1],
[sqrt(f*x^2+e)/x^2/sqrt(b*x^2+a)/sqrt(-d*x^2+c),x,3,-sqrt(-d*x^2+c)*sqrt(f*x^2+e)/c/x/sqrt(b*x^2+a)-sqrt(e)*sqrt(-a*f+b*e)*sqrt(-d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticE(sin(arcsin(sqrt(-a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))),sqrt((a*d+b*c)*e/c/(-a*f+b*e)))/a/c/sqrt(a*(-d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e),1],
[sqrt(f*x^2+e)/x^2/sqrt(-b*x^2+a)/sqrt(-d*x^2+c),x,3,-sqrt(-d*x^2+c)*sqrt(f*x^2+e)/c/x/sqrt(-b*x^2+a)-sqrt(a*d-b*c)*e*sqrt(-d*x^2+c)*sqrt(a*(f*x^2+e)/e/(-b*x^2+a))*EllipticE(sin(arcsin(sqrt(a*d-b*c)*x/sqrt(c)/sqrt(-b*x^2+a))),sqrt(c*(a*f+b*e)/(-a*d+b*c)/e))/a/c^(3/2)/sqrt(a*(-d*x^2+c)/c/(-b*x^2+a))/sqrt(f*x^2+e)+(c*f+d*e)*sqrt(-d*x^2+c)*sqrt(a*(f*x^2+e)/e/(-b*x^2+a))*InverseJacobiAM(arcsin(sqrt(a*d-b*c)*x/sqrt(c)/sqrt(-b*x^2+a)),sqrt(c*(a*f+b*e)/(-a*d+b*c)/e))/c^(3/2)/sqrt(a*d-b*c)/sqrt(a*(-d*x^2+c)/c/(-b*x^2+a))/sqrt(f*x^2+e),1],
[sqrt(-f*x^2+e)/x^2/sqrt(b*x^2+a)/sqrt(d*x^2+c),x,3,-sqrt(d*x^2+c)*sqrt(-f*x^2+e)/c/x/sqrt(b*x^2+a)-sqrt(e)*sqrt(a*f+b*e)*sqrt(d*x^2+c)*sqrt(a*(-f*x^2+e)/e/(b*x^2+a))*EllipticE(sin(arcsin(sqrt(a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))),sqrt((-a*d+b*c)*e/c/(a*f+b*e)))/a/c/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(-f*x^2+e),1],
[sqrt(-f*x^2+e)/x^2/sqrt(-b*x^2+a)/sqrt(d*x^2+c),x,3,-sqrt(d*x^2+c)*sqrt(-f*x^2+e)/c/x/sqrt(-b*x^2+a)-sqrt(e)*sqrt(a*f-b*e)*sqrt(d*x^2+c)*sqrt(a*(-f*x^2+e)/e/(-b*x^2+a))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(e)/sqrt(-b*x^2+a))),sqrt((a*d+b*c)*e/c/(-a*f+b*e)))/a/c/sqrt(a*(d*x^2+c)/c/(-b*x^2+a))/sqrt(-f*x^2+e),1],
[sqrt(-f*x^2+e)/x^2/sqrt(b*x^2+a)/sqrt(-d*x^2+c),x,3,-sqrt(-d*x^2+c)*sqrt(-f*x^2+e)/c/x/sqrt(b*x^2+a)-sqrt(e)*sqrt(a*f+b*e)*sqrt(-d*x^2+c)*sqrt(a*(-f*x^2+e)/e/(b*x^2+a))*EllipticE(sin(arcsin(sqrt(a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))),sqrt((a*d+b*c)*e/c/(a*f+b*e)))/a/c/sqrt(a*(-d*x^2+c)/c/(b*x^2+a))/sqrt(-f*x^2+e),1],
[sqrt(-f*x^2+e)/x^2/sqrt(-b*x^2+a)/sqrt(-d*x^2+c),x,3,-sqrt(-d*x^2+c)*sqrt(-f*x^2+e)/c/x/sqrt(-b*x^2+a)-sqrt(e)*sqrt(a*f-b*e)*sqrt(-d*x^2+c)*sqrt(a*(-f*x^2+e)/e/(-b*x^2+a))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(e)/sqrt(-b*x^2+a))),sqrt((-a*d+b*c)*e/c/(-a*f+b*e)))/a/c/sqrt(a*(-d*x^2+c)/c/(-b*x^2+a))/sqrt(-f*x^2+e),1],
[x^6/sqrt(b*x^2+a)/sqrt(d*x^2+c)/sqrt(f*x^2+e),x,8,-3/8*(a*d*f+b*c*f+b*d*e)*x*sqrt(d*x^2+c)*sqrt(f*x^2+e)/b/d^2/f^2/sqrt(b*x^2+a)+1/4*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)/b/d/f+3/8*sqrt(-a*d+b*c)*e*(a*d*f+b*c*f+b*d*e)*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticE(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^2/sqrt(c)/d^2/f^2/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)-1/8*a*(3*a^2*d^2*f-a*b*d*(-2*c*f+d*e)+b^2*c*(3*c*f+d*e))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*InverseJacobiAM(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a)),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^3/sqrt(c)/d^2/sqrt(-a*d+b*c)/f/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)+1/8*a*(3*a^2*d^2*f^2+2*a*b*d*f*(c*f+d*e)+b^2*(3*c^2*f^2+2*c*d*e*f+3*d^2*e^2))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticPi(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),b*c/(-a*d+b*c),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^3/sqrt(c)/d^2/sqrt(-a*d+b*c)/f^2/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e),1],
[x^4/sqrt(b*x^2+a)/sqrt(d*x^2+c)/sqrt(f*x^2+e),x,7,1/2*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b/d/sqrt(f*x^2+e)-1/2*c*sqrt(a*f-b*e)*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/b/d/f/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))+1/2*e*(a*f+b*e)*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/b/f^2/sqrt(a*f-b*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))-1/2*e*(a*d*f+b*c*f+b*d*e)*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticPi(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),-a*f/(-a*f+b*e),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/b/d/f^2/sqrt(a*f-b*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[x^2/sqrt(b*x^2+a)/sqrt(d*x^2+c)/sqrt(f*x^2+e),x,5,-a*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*InverseJacobiAM(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a)),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b/sqrt(c)/sqrt(-a*d+b*c)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)+a*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticPi(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),b*c/(-a*d+b*c),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b/sqrt(c)/sqrt(-a*d+b*c)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e),1],
[1/sqrt(b*x^2+a)/sqrt(d*x^2+c)/sqrt(f*x^2+e),x,2,sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*InverseJacobiAM(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a)),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/sqrt(c)/sqrt(-a*d+b*c)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e),1],
[1/x^2/sqrt(b*x^2+a)/sqrt(d*x^2+c)/sqrt(f*x^2+e),x,5,-sqrt(d*x^2+c)*sqrt(f*x^2+e)/c/e/x/sqrt(b*x^2+a)-sqrt(-a*d+b*c)*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticE(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/a/c^(3/2)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)-d*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*InverseJacobiAM(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a)),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/c^(3/2)/sqrt(-a*d+b*c)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e),1],
[1/x^4/sqrt(b*x^2+a)/sqrt(d*x^2+c)/sqrt(f*x^2+e),x,6,2/3*(a*c*f+a*d*e+b*c*e)*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a^2/c^2/e/x/sqrt(f*x^2+e)-1/3*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)/a/c/e/x^3+2/3*sqrt(a*f-b*e)*(a*c*f+a*d*e+b*c*e)*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/a^(5/2)/c/e^2/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))+1/3*(2*b^2*c*e-a^2*d*f+a*b*(c*f+d*e))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/a^(5/2)/c/e/sqrt(a*f-b*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[1/x^6/sqrt(b*x^2+a)/sqrt(d*x^2+c)/sqrt(f*x^2+e),x,7,-1/15*(8*b^2*c*e^2/a+7*b*e*(c*f+d*e)+a*(8*d^2*e^2/c+7*d*e*f+8*c*f^2))*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a^2/c^2/e^2/x/sqrt(f*x^2+e)-1/5*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)/a/c/e/x^5+4/15*(a*c*f+a*d*e+b*c*e)*sqrt(b*x^2+a)*sqrt(d*x^2+c)*sqrt(f*x^2+e)/a^2/c^2/e^2/x^3-1/15*sqrt(a*f-b*e)*(8*b^2*c^2*e^2+7*a*b*c*e*(c*f+d*e)+a^2*(8*c^2*f^2+7*c*d*e*f+8*d^2*e^2))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/a^(7/2)/c^2/e^3/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))-1/15*(8*b^3*c^2*e^2+3*a*b^2*c*e*(c*f+d*e)-4*a^3*d*f*(c*f+d*e)+a^2*b*(4*c^2*f^2+c*d*e*f+4*d^2*e^2))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/a^(7/2)/c^2/e^2/sqrt(a*f-b*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[x^8/sqrt(b*x^2+a)/sqrt(d*x^2+c)/(f*x^2+e)^(3/2),x,9,-1/4*e*(a*f*(-c*f+d*e)-b*e*(-c*f+5*d*e))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b/d/f^2/(-a*f+b*e)/(-c*f+d*e)/sqrt(f*x^2+e)+1/4*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b/d/f/sqrt(f*x^2+e)+1/8*(3*a^2*d*f^2*(-c*f+d*e)-b^2*e*(-3*c^2*f^2-4*c*d*e*f+15*d^2*e^2)+a*b*f*(-3*c^2*f^2-c*d*e*f+4*d^2*e^2))*x*sqrt(d*x^2+c)*sqrt(f*x^2+e)/b/d^2/f^3/(-a*f+b*e)/(-c*f+d*e)/sqrt(b*x^2+a)-1/8*sqrt(-a*d+b*c)*e*(3*a^2*d*f^2*(-c*f+d*e)-b^2*e*(-3*c^2*f^2-4*c*d*e*f+15*d^2*e^2)+a*b*f*(-3*c^2*f^2-c*d*e*f+4*d^2*e^2))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticE(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^2/sqrt(c)/d^2/f^3/(-a*f+b*e)/(-c*f+d*e)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)+1/8*a*(2*a^2*b*c*d*f^2+3*a^3*d^2*f^2-b^3*c*e*(3*c*f+5*d*e)+a*b^2*(3*c^2*f^2+3*c*d*e*f+5*d^2*e^2))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*InverseJacobiAM(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a)),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^3/sqrt(c)/d^2/sqrt(-a*d+b*c)/f^2/(-a*f+b*e)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)+1/8*a*(3*a^2*d^2*f^2+2*a*b*d*f*(c*f+3*d*e)+3*b^2*(c^2*f^2+2*c*d*e*f+5*d^2*e^2))*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticPi(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),b*c/(-a*d+b*c),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b^3/sqrt(c)/d^2/sqrt(-a*d+b*c)/f^3/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e),1],
[x^6/sqrt(b*x^2+a)/sqrt(d*x^2+c)/(f*x^2+e)^(3/2),x,7,1/2*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b/d/f/sqrt(f*x^2+e)-1/2*c*(a*f*(-c*f+d*e)-b*e*(-c*f+3*d*e))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/b/d/f^2/sqrt(a*f-b*e)/(-c*f+d*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))+1/2*e*(b*e*(-5*c*f+3*d*e)+a*f*(-c*f+d*e))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/b/f^3/sqrt(a*f-b*e)/(-c*f+d*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))-1/2*e*(a*d*f+b*c*f+3*b*d*e)*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticPi(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),-a*f/(-a*f+b*e),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/b/d/f^3/sqrt(a*f-b*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[x^4/sqrt(b*x^2+a)/sqrt(d*x^2+c)/(f*x^2+e)^(3/2),x,6,-c*e*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/f/sqrt(a*f-b*e)/(-c*f+d*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))-e*(-2*c*f+d*e)*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/f^2/sqrt(a*f-b*e)/(-c*f+d*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))+e*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticPi(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),-a*f/(-a*f+b*e),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/f^2/sqrt(a*f-b*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[x^2/sqrt(b*x^2+a)/sqrt(d*x^2+c)/(f*x^2+e)^(3/2),x,4,c*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/sqrt(a*f-b*e)/(-c*f+d*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))-c*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/sqrt(a*f-b*e)/(-c*f+d*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[1/sqrt(b*x^2+a)/sqrt(d*x^2+c)/(f*x^2+e)^(3/2),x,4,-sqrt(a)*f*sqrt(d*x^2+c)*sqrt(e*(b*x^2+a)/a/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/e/sqrt(a*f-b*e)/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(e*(d*x^2+c)/c/(f*x^2+e))+sqrt(a)*d*sqrt(d*x^2+c)*sqrt(e*(b*x^2+a)/a/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/c/sqrt(a*f-b*e)/(-c*f+d*e)/sqrt(b*x^2+a)/sqrt(e*(d*x^2+c)/c/(f*x^2+e)),1],
[1/x^2/sqrt(b*x^2+a)/sqrt(d*x^2+c)/(f*x^2+e)^(3/2),x,5,-sqrt(b*x^2+a)*sqrt(d*x^2+c)/a/c/e/x/sqrt(f*x^2+e)-(a*f*(-2*c*f+d*e)-b*e*(-c*f+d*e))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/a^(3/2)/e^2/sqrt(a*f-b*e)/(-c*f+d*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))-(a*d*f-b*c*f+b*d*e)*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/a^(3/2)/e/sqrt(a*f-b*e)/(-c*f+d*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[1/x^4/sqrt(b*x^2+a)/sqrt(d*x^2+c)/(f*x^2+e)^(3/2),x,6,-1/3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a/c/e/x^3/sqrt(f*x^2+e)+2/3*(2*a*c*f+a*d*e+b*c*e)*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a^2/c^2/e^2/x/sqrt(f*x^2+e)-1/3*(2*b^2*c*e^2*(-c*f+d*e)-a^2*f*(-8*c^2*f^2+3*c*d*e*f+2*d^2*e^2)+a*b*e*(-3*c^2*f^2+c*d*e*f+2*d^2*e^2))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/a^(5/2)/c/e^3/sqrt(a*f-b*e)/(-c*f+d*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))-1/3*(a^2*d*f*(-4*c*f+d*e)-2*b^2*c*e*(-c*f+d*e)-a*b*(-4*c^2*f^2+3*c*d*e*f+d^2*e^2))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/a^(5/2)/c/e^2/sqrt(a*f-b*e)/(-c*f+d*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[x^10/sqrt(b*x^2+a)/sqrt(d*x^2+c)/(f*x^2+e)^(5/2),x,9,-1/12*e^2*(b*e*(-3*c*f+7*d*e)-3*a*f*(-c*f+d*e))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b/d/f^3/(-a*f+b*e)/(-c*f+d*e)/(f*x^2+e)^(3/2)+1/4*x^5*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b/d/f/(f*x^2+e)^(3/2)-1/8*(3*a*d*f+3*b*c*f+7*b*d*e)*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b^2/d^2/f^3/sqrt(f*x^2+e)+1/24*c*(9*a^3*d*f^3*(-c*f+d*e)^2+3*a^2*b*f^2*(-c*f+d*e)^2*(3*c*f+5*d*e)+b^3*e^2*(9*c^3*f^3+15*c^2*d*e*f^2-145*c*d^2*e^2*f+105*d^3*e^3)-a*b^2*e*f*(18*c^3*f^3+21*c^2*d*e*f^2-200*c*d^2*e^2*f+145*d^3*e^3))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/b^2/d^2/f^4/(a*f-b*e)^(3/2)/(-c*f+d*e)^2/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))-1/24*e*(9*a^3*d*f^3*(-c*f+d*e)^2+3*a^2*b*f^2*(-c*f+d*e)^2*(c*f+7*d*e)+a*b^2*e*f*(-6*c^3*f^3+183*c^2*d*e*f^2-236*c*d^2*e^2*f+75*d^3*e^3)-b^3*e^2*(-3*c^3*f^3+199*c^2*d*e*f^2-285*c*d^2*e^2*f+105*d^3*e^3))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/b^2/d/f^5/(a*f-b*e)^(3/2)/(-c*f+d*e)^2/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))+1/8*e*(3*a^2*d^2*f^2+2*a*b*d*f*(c*f+5*d*e)+b^2*(3*c^2*f^2+10*c*d*e*f+35*d^2*e^2))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticPi(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),-a*f/(-a*f+b*e),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/b^2/d^2/f^5/sqrt(a*f-b*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[x^8/sqrt(b*x^2+a)/sqrt(d*x^2+c)/(f*x^2+e)^(5/2),x,8,1/6*e*(b*e*(-3*c*f+5*d*e)-3*a*f*(-c*f+d*e))*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b/d/f^2/(-a*f+b*e)/(-c*f+d*e)/(f*x^2+e)^(3/2)+1/2*x^3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/b/d/f/(f*x^2+e)^(3/2)-1/6*c*(3*a^2*f^2*(-c*f+d*e)^2+b^2*e^2*(3*c^2*f^2-22*c*d*e*f+15*d^2*e^2)-2*a*b*e*f*(3*c^2*f^2-16*c*d*e*f+11*d^2*e^2))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/b/d/f^3/(a*f-b*e)^(3/2)/(-c*f+d*e)^2/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))+1/6*e*(3*a^2*f^2*(-c*f+d*e)^2+2*a*b*e*f*(15*c^2*f^2-19*c*d*e*f+6*d^2*e^2)-b^2*e^2*(31*c^2*f^2-42*c*d*e*f+15*d^2*e^2))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/b/f^4/(a*f-b*e)^(3/2)/(-c*f+d*e)^2/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))-1/2*e*(a*d*f+b*c*f+5*b*d*e)*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticPi(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),-a*f/(-a*f+b*e),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/b/d/f^4/sqrt(a*f-b*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[x^6/sqrt(b*x^2+a)/sqrt(d*x^2+c)/(f*x^2+e)^(5/2),x,7,-1/3*e^2*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/f/(-a*f+b*e)/(-c*f+d*e)/(f*x^2+e)^(3/2)-1/3*c*e*(a*f*(-7*c*f+5*d*e)-b*e*(-5*c*f+3*d*e))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/f^2/(a*f-b*e)^(3/2)/(-c*f+d*e)^2/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))+1/3*e*(b*e*(8*c^2*f^2-9*c*d*e*f+3*d^2*e^2)-a*f*(9*c^2*f^2-10*c*d*e*f+3*d^2*e^2))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/f^3/(a*f-b*e)^(3/2)/(-c*f+d*e)^2/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))+e*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticPi(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),-a*f/(-a*f+b*e),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/f^3/sqrt(a*f-b*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[x^4/sqrt(b*x^2+a)/sqrt(d*x^2+c)/(f*x^2+e)^(5/2),x,5,1/3*e*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/(-a*f+b*e)/(-c*f+d*e)/(f*x^2+e)^(3/2)+2/3*c*(-2*a*c*f+a*d*e+b*c*e)*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/(a*f-b*e)^(3/2)/(-c*f+d*e)^2/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))-1/3*c*(-3*a*c*f+a*d*e+2*b*c*e)*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/(a*f-b*e)^(3/2)/(-c*f+d*e)^2/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[x^2/sqrt(b*x^2+a)/sqrt(d*x^2+c)/(f*x^2+e)^(5/2),x,5,-1/3*f*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/(-a*f+b*e)/(-c*f+d*e)/(f*x^2+e)^(3/2)-1/3*c*(b*e*(-c*f+3*d*e)-a*f*(c*f+d*e))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/e/(a*f-b*e)^(3/2)/(-c*f+d*e)^2/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))+1/3*c*(-2*a*d*f-b*c*f+3*b*d*e)*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/(a*f-b*e)^(3/2)/(-c*f+d*e)^2/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[1/sqrt(b*x^2+a)/sqrt(d*x^2+c)/(f*x^2+e)^(5/2),x,5,1/3*f^2*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/e/(-a*f+b*e)/(-c*f+d*e)/(f*x^2+e)^(3/2)+2/3*c*f*(b*e*(-2*c*f+3*d*e)-a*f*(-c*f+2*d*e))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/e^2/(a*f-b*e)^(3/2)/(-c*f+d*e)^2/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))+1/3*(a*d*f*(-c*f+3*d*e)-b*(-c^2*f^2+3*d^2*e^2))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/e/(a*f-b*e)^(3/2)/(-c*f+d*e)^2/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[1/x^2/sqrt(b*x^2+a)/sqrt(d*x^2+c)/(f*x^2+e)^(5/2),x,6,-1/3*f^3*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/e^2/(-a*f+b*e)/(-c*f+d*e)/(f*x^2+e)^(3/2)-sqrt(b*x^2+a)*sqrt(d*x^2+c)/a/c/e^2/x/sqrt(f*x^2+e)-1/3*(3*b^2*e^2*(-c*f+d*e)^2+a^2*f^2*(8*c^2*f^2-13*c*d*e*f+3*d^2*e^2)-a*b*e*f*(13*c^2*f^2-21*c*d*e*f+6*d^2*e^2))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/a^(3/2)/e^3/(a*f-b*e)^(3/2)/(-c*f+d*e)^2/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))-1/3*(2*a^2*d*f^2*(-2*c*f+3*d*e)-3*b^2*e*(-c*f+d*e)^2-a*b*f*(-4*c^2*f^2+3*c*d*e*f+3*d^2*e^2))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/a^(3/2)/e^2/(a*f-b*e)^(3/2)/(-c*f+d*e)^2/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[1/x^4/sqrt(b*x^2+a)/sqrt(d*x^2+c)/(f*x^2+e)^(5/2),x,7,1/3*f^4*x*sqrt(b*x^2+a)*sqrt(d*x^2+c)/e^3/(-a*f+b*e)/(-c*f+d*e)/(f*x^2+e)^(3/2)-1/3*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a/c/e^2/x^3/sqrt(f*x^2+e)+1/3*(7*a*c*f+2*a*d*e+2*b*c*e)*sqrt(b*x^2+a)*sqrt(d*x^2+c)/a^2/c^2/e^3/x/sqrt(f*x^2+e)+2/3*(b^3*c*e^3*(-c*f+d*e)^2+a*b^2*e^2*(-c*f+d*e)^2*(2*c*f+d*e)+a^3*f^2*(8*c^3*f^3-12*c^2*d*e*f^2+2*c*d^2*e^2*f+d^3*e^3)-a^2*b*e*f*(12*c^3*f^3-18*c^2*d*e*f^2+3*c*d^2*e^2*f+2*d^3*e^3))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/a^(5/2)/c/e^4/(a*f-b*e)^(3/2)/(-c*f+d*e)^2/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))-1/3*(2*b^3*c*e^2*(-c*f+d*e)^2+a*b^2*e*(-c*f+d*e)^2*(5*c*f+d*e)+a^3*d*f^2*(8*c^2*f^2-11*c*d*e*f+d^2*e^2)-2*a^2*b*f*(4*c^3*f^3-3*c^2*d*e*f^2-3*c*d^2*e^2*f+d^3*e^3))*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/a^(5/2)/c/e^3/(a*f-b*e)^(3/2)/(-c*f+d*e)^2/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[x^2/sqrt(b*x^2+a)/sqrt(d*x^2+c)/sqrt(f*x^2+e),x,5,-a*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*InverseJacobiAM(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a)),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b/sqrt(c)/sqrt(-a*d+b*c)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)+a*sqrt(d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticPi(sin(arcsin(sqrt(-a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),b*c/(-a*d+b*c),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b/sqrt(c)/sqrt(-a*d+b*c)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e),1],
[x^2/sqrt(-b*x^2+a)/sqrt(d*x^2+c)/sqrt(f*x^2+e),x,7,sqrt(a)*sqrt(-b*x^2+a)*sqrt(c*(f*x^2+e)/e/(d*x^2+c))*InverseJacobiAM(arcsin(sqrt(a*d+b*c)*x/sqrt(a)/sqrt(d*x^2+c)),sqrt(a*(-c*f+d*e)/(a*d+b*c)/e))/b/sqrt(a*d+b*c)/sqrt(c*(-b*x^2+a)/a/(d*x^2+c))/sqrt(f*x^2+e)-sqrt(c)*sqrt(a*d+b*c)*sqrt(f*x^2+e)*InverseJacobiAM(arctan(sqrt(a*d+b*c)*x/sqrt(c)/sqrt(-b*x^2+a)),sqrt(a*(-c*f+d*e)/(a*d+b*c)/e))/b/d/e/sqrt(d*x^2+c)/sqrt(c*(f*x^2+e)/e/(d*x^2+c))+c^(3/2)*sqrt(f*x^2+e)*EllipticPi(sin(arctan(sqrt(a*d+b*c)*x/sqrt(c)/sqrt(-b*x^2+a))),a*d/(a*d+b*c),sqrt(a*(-c*f+d*e)/(a*d+b*c)/e))/d/sqrt(a*d+b*c)/e/sqrt(d*x^2+c)/sqrt(c*(f*x^2+e)/e/(d*x^2+c)),1],
[x^2/sqrt(b*x^2+a)/sqrt(-d*x^2+c)/sqrt(f*x^2+e),x,5,-a*sqrt(-d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*InverseJacobiAM(arcsin(sqrt(a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a)),sqrt(c*(-a*f+b*e)/(a*d+b*c)/e))/b/sqrt(c)/sqrt(a*d+b*c)/sqrt(a*(-d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e)+a*sqrt(-d*x^2+c)*sqrt(a*(f*x^2+e)/e/(b*x^2+a))*EllipticPi(sin(arcsin(sqrt(a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),b*c/(a*d+b*c),sqrt(c*(-a*f+b*e)/(a*d+b*c)/e))/b/sqrt(c)/sqrt(a*d+b*c)/sqrt(a*(-d*x^2+c)/c/(b*x^2+a))/sqrt(f*x^2+e),1],
[x^2/sqrt(-b*x^2+a)/sqrt(-d*x^2+c)/sqrt(f*x^2+e),x,5,a*sqrt(-d*x^2+c)*sqrt(a*(f*x^2+e)/e/(-b*x^2+a))*InverseJacobiAM(arcsin(sqrt(a*d-b*c)*x/sqrt(c)/sqrt(-b*x^2+a)),sqrt(c*(a*f+b*e)/(-a*d+b*c)/e))/b/sqrt(c)/sqrt(a*d-b*c)/sqrt(a*(-d*x^2+c)/c/(-b*x^2+a))/sqrt(f*x^2+e)-a*sqrt(-d*x^2+c)*sqrt(a*(f*x^2+e)/e/(-b*x^2+a))*EllipticPi(sin(arcsin(sqrt(a*d-b*c)*x/sqrt(c)/sqrt(-b*x^2+a))),b*c/(-a*d+b*c),sqrt(c*(a*f+b*e)/(-a*d+b*c)/e))/b/sqrt(c)/sqrt(a*d-b*c)/sqrt(a*(-d*x^2+c)/c/(-b*x^2+a))/sqrt(f*x^2+e),1],
[x^2/sqrt(b*x^2+a)/sqrt(d*x^2+c)/sqrt(-f*x^2+e),x,5,-a*sqrt(e)*sqrt(d*x^2+c)*sqrt(a*(-f*x^2+e)/e/(b*x^2+a))*InverseJacobiAM(arcsin(sqrt(a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a)),sqrt((-a*d+b*c)*e/c/(a*f+b*e)))/b/c/sqrt(a*f+b*e)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(-f*x^2+e)+a*sqrt(e)*sqrt(d*x^2+c)*sqrt(a*(-f*x^2+e)/e/(b*x^2+a))*EllipticPi(sin(arcsin(sqrt(a*f+b*e)*x/sqrt(e)/sqrt(b*x^2+a))),b*e/(a*f+b*e),sqrt((-a*d+b*c)*e/c/(a*f+b*e)))/b/c/sqrt(a*f+b*e)/sqrt(a*(d*x^2+c)/c/(b*x^2+a))/sqrt(-f*x^2+e),1],
[x^2/sqrt(-b*x^2+a)/sqrt(d*x^2+c)/sqrt(-f*x^2+e),x,5,a*sqrt(a*(d*x^2+c)/c/(-b*x^2+a))*sqrt(-f*x^2+e)*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(e)/sqrt(-b*x^2+a)),sqrt((a*d+b*c)*e/c/(-a*f+b*e)))/b/sqrt(e)/sqrt(a*f-b*e)/sqrt(d*x^2+c)/sqrt(a*(-f*x^2+e)/e/(-b*x^2+a))-a*sqrt(e)*sqrt(d*x^2+c)*sqrt(a*(-f*x^2+e)/e/(-b*x^2+a))*EllipticPi(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(e)/sqrt(-b*x^2+a))),b*e/(-a*f+b*e),sqrt((a*d+b*c)*e/c/(-a*f+b*e)))/b/c/sqrt(a*f-b*e)/sqrt(a*(d*x^2+c)/c/(-b*x^2+a))/sqrt(-f*x^2+e),1],
[x^2/sqrt(b*x^2+a)/sqrt(-d*x^2+c)/sqrt(-f*x^2+e),x,5,-a*sqrt(-d*x^2+c)*sqrt(a*(-f*x^2+e)/e/(b*x^2+a))*InverseJacobiAM(arcsin(sqrt(a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a)),sqrt(c*(a*f+b*e)/(a*d+b*c)/e))/b/sqrt(c)/sqrt(a*d+b*c)/sqrt(a*(-d*x^2+c)/c/(b*x^2+a))/sqrt(-f*x^2+e)+a*sqrt(-d*x^2+c)*sqrt(a*(-f*x^2+e)/e/(b*x^2+a))*EllipticPi(sin(arcsin(sqrt(a*d+b*c)*x/sqrt(c)/sqrt(b*x^2+a))),b*c/(a*d+b*c),sqrt(c*(a*f+b*e)/(a*d+b*c)/e))/b/sqrt(c)/sqrt(a*d+b*c)/sqrt(a*(-d*x^2+c)/c/(b*x^2+a))/sqrt(-f*x^2+e),1],
[x^2/sqrt(-b*x^2+a)/sqrt(-d*x^2+c)/sqrt(-f*x^2+e),x,5,a*sqrt(-d*x^2+c)*sqrt(a*(-f*x^2+e)/e/(-b*x^2+a))*InverseJacobiAM(arcsin(sqrt(a*d-b*c)*x/sqrt(c)/sqrt(-b*x^2+a)),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b/sqrt(c)/sqrt(a*d-b*c)/sqrt(a*(-d*x^2+c)/c/(-b*x^2+a))/sqrt(-f*x^2+e)-a*sqrt(-d*x^2+c)*sqrt(a*(-f*x^2+e)/e/(-b*x^2+a))*EllipticPi(sin(arcsin(sqrt(a*d-b*c)*x/sqrt(c)/sqrt(-b*x^2+a))),b*c/(-a*d+b*c),sqrt(c*(-a*f+b*e)/(-a*d+b*c)/e))/b/sqrt(c)/sqrt(a*d-b*c)/sqrt(a*(-d*x^2+c)/c/(-b*x^2+a))/sqrt(-f*x^2+e),1],
[x^2/sqrt(b*x^2+a)/sqrt(d*x^2+c)/(f*x^2+e)^(3/2),x,4,c*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/sqrt(a*f-b*e)/(-c*f+d*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))-c*sqrt(b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f-b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/sqrt(a*f-b*e)/(-c*f+d*e)/sqrt(d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[x^2/sqrt(-b*x^2+a)/sqrt(d*x^2+c)/(f*x^2+e)^(3/2),x,4,c*sqrt(-b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f+b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(-a*(-c*f+d*e)/c/(a*f+b*e)))/sqrt(a)/sqrt(a*f+b*e)/(-c*f+d*e)/sqrt(d*x^2+c)/sqrt(e*(-b*x^2+a)/a/(f*x^2+e))-c*sqrt(-b*x^2+a)*sqrt(e*(d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f+b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(-a*(-c*f+d*e)/c/(a*f+b*e)))/sqrt(a)/sqrt(a*f+b*e)/(-c*f+d*e)/sqrt(d*x^2+c)/sqrt(e*(-b*x^2+a)/a/(f*x^2+e)),1],
[x^2/sqrt(b*x^2+a)/sqrt(-d*x^2+c)/(f*x^2+e)^(3/2),x,4,sqrt(c)*sqrt(b*x^2+a)*sqrt(e*(-d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(c*f+d*e)*x/sqrt(c)/sqrt(f*x^2+e))),sqrt(-c*(-a*f+b*e)/a/(c*f+d*e)))/(-a*f+b*e)/sqrt(c*f+d*e)/sqrt(-d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e))-sqrt(c)*sqrt(b*x^2+a)*sqrt(e*(-d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(c*f+d*e)*x/sqrt(c)/sqrt(f*x^2+e)),sqrt(-c*(-a*f+b*e)/a/(c*f+d*e)))/(-a*f+b*e)/sqrt(c*f+d*e)/sqrt(-d*x^2+c)/sqrt(e*(b*x^2+a)/a/(f*x^2+e)),1],
[x^2/sqrt(-b*x^2+a)/sqrt(-d*x^2+c)/(f*x^2+e)^(3/2),x,4,-c*sqrt(-b*x^2+a)*sqrt(e*(-d*x^2+c)/c/(f*x^2+e))*EllipticE(sin(arcsin(sqrt(a*f+b*e)*x/sqrt(a)/sqrt(f*x^2+e))),sqrt(a*(c*f+d*e)/c/(a*f+b*e)))/sqrt(a)/sqrt(a*f+b*e)/(c*f+d*e)/sqrt(-d*x^2+c)/sqrt(e*(-b*x^2+a)/a/(f*x^2+e))+c*sqrt(-b*x^2+a)*sqrt(e*(-d*x^2+c)/c/(f*x^2+e))*InverseJacobiAM(arcsin(sqrt(a*f+b*e)*x/sqrt(a)/sqrt(f*x^2+e)),sqrt(a*(c*f+d*e)/c/(a*f+b*e)))/sqrt(a)/sqrt(a*f+b*e)/(c*f+d*e)/sqrt(-d*x^2+c)/sqrt(e*(-b*x^2+a)/a/(f*x^2+e)),1],
[x^2/sqrt(b*x^2+a)/sqrt(d*x^2+c)/(-f*x^2+e)^(3/2),x,3,x*sqrt(d*x^2+c)/(c*f+d*e)/sqrt(b*x^2+a)/sqrt(-f*x^2+e)-sqrt(a)*sqrt(d*x^2+c)*EllipticE(sin(arctan(sqrt(a*f+b*e)*x/sqrt(a)/sqrt(-f*x^2+e))),sqrt((-a*d+b*c)*e/c/(a*f+b*e)))/sqrt(a*f+b*e)/(c*f+d*e)/sqrt(b*x^2+a)/sqrt(a*(d*x^2+c)/c/(b*x^2+a)),1],
[x^2/sqrt(-b*x^2+a)/sqrt(d*x^2+c)/(-f*x^2+e)^(3/2),x,4,c*sqrt(-b*x^2+a)*sqrt(e*(d*x^2+c)/c/(-f*x^2+e))*EllipticE(sin(arcsin(sqrt(-a*f+b*e)*x/sqrt(a)/sqrt(-f*x^2+e))),sqrt(-a*(c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/sqrt(-a*f+b*e)/(c*f+d*e)/sqrt(d*x^2+c)/sqrt(e*(-b*x^2+a)/a/(-f*x^2+e))-c*sqrt(-b*x^2+a)*sqrt(e*(d*x^2+c)/c/(-f*x^2+e))*InverseJacobiAM(arcsin(sqrt(-a*f+b*e)*x/sqrt(a)/sqrt(-f*x^2+e)),sqrt(-a*(c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/sqrt(-a*f+b*e)/(c*f+d*e)/sqrt(d*x^2+c)/sqrt(e*(-b*x^2+a)/a/(-f*x^2+e)),1],
[x^2/sqrt(b*x^2+a)/sqrt(-d*x^2+c)/(-f*x^2+e)^(3/2),x,4,sqrt(c)*sqrt(b*x^2+a)*sqrt(e*(-d*x^2+c)/c/(-f*x^2+e))*EllipticE(sin(arcsin(sqrt(-c*f+d*e)*x/sqrt(c)/sqrt(-f*x^2+e))),sqrt(-c*(a*f+b*e)/a/(-c*f+d*e)))/(a*f+b*e)/sqrt(-c*f+d*e)/sqrt(-d*x^2+c)/sqrt(e*(b*x^2+a)/a/(-f*x^2+e))-sqrt(c)*sqrt(b*x^2+a)*sqrt(e*(-d*x^2+c)/c/(-f*x^2+e))*InverseJacobiAM(arcsin(sqrt(-c*f+d*e)*x/sqrt(c)/sqrt(-f*x^2+e)),sqrt(-c*(a*f+b*e)/a/(-c*f+d*e)))/(a*f+b*e)/sqrt(-c*f+d*e)/sqrt(-d*x^2+c)/sqrt(e*(b*x^2+a)/a/(-f*x^2+e)),1],
[x^2/sqrt(-b*x^2+a)/sqrt(-d*x^2+c)/(-f*x^2+e)^(3/2),x,4,-c*sqrt(-b*x^2+a)*sqrt(e*(-d*x^2+c)/c/(-f*x^2+e))*EllipticE(sin(arcsin(sqrt(-a*f+b*e)*x/sqrt(a)/sqrt(-f*x^2+e))),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/sqrt(-a*f+b*e)/(-c*f+d*e)/sqrt(-d*x^2+c)/sqrt(e*(-b*x^2+a)/a/(-f*x^2+e))+c*sqrt(-b*x^2+a)*sqrt(e*(-d*x^2+c)/c/(-f*x^2+e))*InverseJacobiAM(arcsin(sqrt(-a*f+b*e)*x/sqrt(a)/sqrt(-f*x^2+e)),sqrt(a*(-c*f+d*e)/c/(-a*f+b*e)))/sqrt(a)/sqrt(-a*f+b*e)/(-c*f+d*e)/sqrt(-d*x^2+c)/sqrt(e*(-b*x^2+a)/a/(-f*x^2+e)),1]]: