1,1,176,160,0.000000," ","int((b*x^2+a)*(d*x^2+c)*(f*x^2+e)^4,x)","\frac{b d \,f^{4} x^{13}}{13}+\frac{\left(4 b d e \,f^{3}+\left(a d +b c \right) f^{4}\right) x^{11}}{11}+\frac{\left(a c \,f^{4}+6 b d \,e^{2} f^{2}+4 \left(a d +b c \right) e \,f^{3}\right) x^{9}}{9}+a c \,e^{4} x +\frac{\left(4 a c e \,f^{3}+4 b d \,e^{3} f +6 \left(a d +b c \right) e^{2} f^{2}\right) x^{7}}{7}+\frac{\left(6 a c \,e^{2} f^{2}+b d \,e^{4}+4 \left(a d +b c \right) e^{3} f \right) x^{5}}{5}+\frac{\left(4 a c \,e^{3} f +\left(a d +b c \right) e^{4}\right) x^{3}}{3}"," ",0,"1/13*b*d*f^4*x^13+1/11*((a*d+b*c)*f^4+4*b*d*e*f^3)*x^11+1/9*(a*c*f^4+4*(a*d+b*c)*e*f^3+6*b*d*e^2*f^2)*x^9+1/7*(4*a*c*e*f^3+6*(a*d+b*c)*e^2*f^2+4*b*d*e^3*f)*x^7+1/5*(6*a*c*e^2*f^2+4*(a*d+b*c)*e^3*f+b*d*e^4)*x^5+1/3*(4*a*c*e^3*f+(a*d+b*c)*e^4)*x^3+a*c*e^4*x","A"
2,1,135,120,0.001000," ","int((b*x^2+a)*(d*x^2+c)*(f*x^2+e)^3,x)","\frac{b d \,f^{3} x^{11}}{11}+\frac{\left(3 b d e \,f^{2}+\left(a d +b c \right) f^{3}\right) x^{9}}{9}+\frac{\left(a c \,f^{3}+3 b d \,e^{2} f +3 \left(a d +b c \right) e \,f^{2}\right) x^{7}}{7}+a c \,e^{3} x +\frac{\left(3 a c e \,f^{2}+b d \,e^{3}+3 \left(a d +b c \right) e^{2} f \right) x^{5}}{5}+\frac{\left(3 a c \,e^{2} f +\left(a d +b c \right) e^{3}\right) x^{3}}{3}"," ",0,"1/11*b*d*f^3*x^11+1/9*((a*d+b*c)*f^3+3*b*d*e*f^2)*x^9+1/7*(a*c*f^3+3*(a*d+b*c)*e*f^2+3*b*d*e^2*f)*x^7+1/5*(3*a*c*e*f^2+3*(a*d+b*c)*e^2*f+b*d*e^3)*x^5+1/3*(3*a*c*e^2*f+(a*d+b*c)*e^3)*x^3+a*c*e^3*x","A"
3,1,94,86,0.001000," ","int((b*x^2+a)*(d*x^2+c)*(f*x^2+e)^2,x)","\frac{b d \,f^{2} x^{9}}{9}+\frac{\left(2 b d e f +\left(a d +b c \right) f^{2}\right) x^{7}}{7}+a c \,e^{2} x +\frac{\left(a c \,f^{2}+b d \,e^{2}+2 \left(a d +b c \right) e f \right) x^{5}}{5}+\frac{\left(2 a c e f +\left(a d +b c \right) e^{2}\right) x^{3}}{3}"," ",0,"1/9*b*d*f^2*x^9+1/7*((a*d+b*c)*f^2+2*b*d*e*f)*x^7+1/5*(a*c*f^2+2*(a*d+b*c)*e*f+b*d*e^2)*x^5+1/3*(2*a*c*e*f+(a*d+b*c)*e^2)*x^3+a*c*e^2*x","A"
4,1,53,50,0.002000," ","int((b*x^2+a)*(d*x^2+c)*(f*x^2+e),x)","\frac{b d f \,x^{7}}{7}+\frac{\left(b d e +\left(a d +b c \right) f \right) x^{5}}{5}+a c e x +\frac{\left(a c f +\left(a d +b c \right) e \right) x^{3}}{3}"," ",0,"1/7*b*d*f*x^7+1/5*((a*d+b*c)*f+b*d*e)*x^5+1/3*(a*c*f+(a*d+b*c)*e)*x^3+a*c*e*x","A"
5,1,119,69,0.006000," ","int((b*x^2+a)*(d*x^2+c)/(f*x^2+e),x)","\frac{b d \,x^{3}}{3 f}+\frac{a c \arctan \left(\frac{f x}{\sqrt{e f}}\right)}{\sqrt{e f}}-\frac{a d e \arctan \left(\frac{f x}{\sqrt{e f}}\right)}{\sqrt{e f}\, f}-\frac{b c e \arctan \left(\frac{f x}{\sqrt{e f}}\right)}{\sqrt{e f}\, f}+\frac{b d \,e^{2} \arctan \left(\frac{f x}{\sqrt{e f}}\right)}{\sqrt{e f}\, f^{2}}+\frac{a d x}{f}+\frac{b c x}{f}-\frac{b d e x}{f^{2}}"," ",0,"1/3/f*x^3*b*d+1/f*a*d*x+1/f*b*c*x-1/f^2*b*d*e*x+1/(e*f)^(1/2)*arctan(f*x/(e*f)^(1/2))*a*c-1/f/(e*f)^(1/2)*arctan(f*x/(e*f)^(1/2))*a*d*e-1/f/(e*f)^(1/2)*arctan(f*x/(e*f)^(1/2))*b*c*e+1/f^2/(e*f)^(1/2)*arctan(f*x/(e*f)^(1/2))*b*d*e^2","A"
6,1,163,94,0.012000," ","int((b*x^2+a)*(d*x^2+c)/(f*x^2+e)^2,x)","\frac{a c x}{2 \left(f \,x^{2}+e \right) e}+\frac{a c \arctan \left(\frac{f x}{\sqrt{e f}}\right)}{2 \sqrt{e f}\, e}-\frac{a d x}{2 \left(f \,x^{2}+e \right) f}+\frac{a d \arctan \left(\frac{f x}{\sqrt{e f}}\right)}{2 \sqrt{e f}\, f}-\frac{b c x}{2 \left(f \,x^{2}+e \right) f}+\frac{b c \arctan \left(\frac{f x}{\sqrt{e f}}\right)}{2 \sqrt{e f}\, f}+\frac{b d e x}{2 \left(f \,x^{2}+e \right) f^{2}}-\frac{3 b d e \arctan \left(\frac{f x}{\sqrt{e f}}\right)}{2 \sqrt{e f}\, f^{2}}+\frac{b d x}{f^{2}}"," ",0,"b*d/f^2*x+1/2/e*x/(f*x^2+e)*a*c-1/2/f*x/(f*x^2+e)*a*d-1/2/f*x/(f*x^2+e)*b*c+1/2/f^2*e*x/(f*x^2+e)*b*d+1/2/e/(e*f)^(1/2)*arctan(1/(e*f)^(1/2)*f*x)*a*c+1/2/f/(e*f)^(1/2)*arctan(1/(e*f)^(1/2)*f*x)*a*d+1/2/f/(e*f)^(1/2)*arctan(1/(e*f)^(1/2)*f*x)*b*c-3/2/f^2*e/(e*f)^(1/2)*arctan(1/(e*f)^(1/2)*f*x)*b*d","A"
7,1,175,116,0.010000," ","int((b*x^2+a)*(d*x^2+c)/(f*x^2+e)^3,x)","\frac{3 a c \arctan \left(\frac{f x}{\sqrt{e f}}\right)}{8 \sqrt{e f}\, e^{2}}+\frac{a d \arctan \left(\frac{f x}{\sqrt{e f}}\right)}{8 \sqrt{e f}\, e f}+\frac{b c \arctan \left(\frac{f x}{\sqrt{e f}}\right)}{8 \sqrt{e f}\, e f}+\frac{3 b d \arctan \left(\frac{f x}{\sqrt{e f}}\right)}{8 \sqrt{e f}\, f^{2}}+\frac{\frac{\left(3 a c \,f^{2}+a d e f +b c e f -5 b d \,e^{2}\right) x^{3}}{8 e^{2} f}+\frac{\left(5 a c \,f^{2}-a d e f -b c e f -3 b d \,e^{2}\right) x}{8 e \,f^{2}}}{\left(f \,x^{2}+e \right)^{2}}"," ",0,"(1/8*(3*a*c*f^2+a*d*e*f+b*c*e*f-5*b*d*e^2)/e^2/f*x^3+1/8*(5*a*c*f^2-a*d*e*f-b*c*e*f-3*b*d*e^2)/f^2/e*x)/(f*x^2+e)^2+3/8/e^2/(e*f)^(1/2)*arctan(1/(e*f)^(1/2)*f*x)*a*c+1/8/e/f/(e*f)^(1/2)*arctan(1/(e*f)^(1/2)*f*x)*a*d+1/8/e/f/(e*f)^(1/2)*arctan(1/(e*f)^(1/2)*f*x)*b*c+3/8/f^2/(e*f)^(1/2)*arctan(1/(e*f)^(1/2)*f*x)*b*d","A"
8,1,210,155,0.010000," ","int((b*x^2+a)*(d*x^2+c)/(f*x^2+e)^4,x)","\frac{5 a c \arctan \left(\frac{f x}{\sqrt{e f}}\right)}{16 \sqrt{e f}\, e^{3}}+\frac{a d \arctan \left(\frac{f x}{\sqrt{e f}}\right)}{16 \sqrt{e f}\, e^{2} f}+\frac{b c \arctan \left(\frac{f x}{\sqrt{e f}}\right)}{16 \sqrt{e f}\, e^{2} f}+\frac{b d \arctan \left(\frac{f x}{\sqrt{e f}}\right)}{16 \sqrt{e f}\, e \,f^{2}}+\frac{\frac{\left(5 a c \,f^{2}+a d e f +b c e f +b d \,e^{2}\right) x^{5}}{16 e^{3}}+\frac{\left(5 a c \,f^{2}+a d e f +b c e f -b d \,e^{2}\right) x^{3}}{6 e^{2} f}+\frac{\left(11 a c \,f^{2}-a d e f -b c e f -b d \,e^{2}\right) x}{16 e \,f^{2}}}{\left(f \,x^{2}+e \right)^{3}}"," ",0,"(1/16*(5*a*c*f^2+a*d*e*f+b*c*e*f+b*d*e^2)/e^3*x^5+1/6*(5*a*c*f^2+a*d*e*f+b*c*e*f-b*d*e^2)/e^2/f*x^3+1/16*(11*a*c*f^2-a*d*e*f-b*c*e*f-b*d*e^2)/e/f^2*x)/(f*x^2+e)^3+5/16/e^3/(e*f)^(1/2)*arctan(1/(e*f)^(1/2)*f*x)*a*c+1/16/e^2/f/(e*f)^(1/2)*arctan(1/(e*f)^(1/2)*f*x)*a*d+1/16/e^2/f/(e*f)^(1/2)*arctan(1/(e*f)^(1/2)*f*x)*b*c+1/16/e/f^2/(e*f)^(1/2)*arctan(1/(e*f)^(1/2)*f*x)*b*d","A"
9,1,237,214,0.001000," ","int((b*x^2+a)*(d*x^2+c)^2*(f*x^2+e)^3,x)","\frac{b \,d^{2} f^{3} x^{13}}{13}+\frac{\left(3 b \,d^{2} e \,f^{2}+\left(a \,d^{2}+2 b c d \right) f^{3}\right) x^{11}}{11}+\frac{\left(3 b \,d^{2} e^{2} f +3 \left(a \,d^{2}+2 b c d \right) e \,f^{2}+\left(2 a c d +b \,c^{2}\right) f^{3}\right) x^{9}}{9}+a \,c^{2} e^{3} x +\frac{\left(a \,c^{2} f^{3}+b \,d^{2} e^{3}+3 \left(a \,d^{2}+2 b c d \right) e^{2} f +3 \left(2 a c d +b \,c^{2}\right) e \,f^{2}\right) x^{7}}{7}+\frac{\left(3 a \,c^{2} e \,f^{2}+\left(a \,d^{2}+2 b c d \right) e^{3}+3 \left(2 a c d +b \,c^{2}\right) e^{2} f \right) x^{5}}{5}+\frac{\left(3 a \,c^{2} e^{2} f +\left(2 a c d +b \,c^{2}\right) e^{3}\right) x^{3}}{3}"," ",0,"1/13*b*d^2*f^3*x^13+1/11*((a*d^2+2*b*c*d)*f^3+3*b*d^2*e*f^2)*x^11+1/9*((2*a*c*d+b*c^2)*f^3+3*(a*d^2+2*b*c*d)*e*f^2+3*b*d^2*e^2*f)*x^9+1/7*(a*c^2*f^3+3*(2*a*c*d+b*c^2)*e*f^2+3*(a*d^2+2*b*c*d)*e^2*f+b*d^2*e^3)*x^7+1/5*(3*a*c^2*e*f^2+3*(2*a*c*d+b*c^2)*e^2*f+(a*d^2+2*b*c*d)*e^3)*x^5+1/3*(3*a*c^2*e^2*f+(2*a*c*d+b*c^2)*e^3)*x^3+a*c^2*e^3*x","A"
10,1,169,148,0.001000," ","int((b*x^2+a)*(d*x^2+c)^2*(f*x^2+e)^2,x)","\frac{b \,d^{2} f^{2} x^{11}}{11}+\frac{\left(2 b \,d^{2} e f +\left(a \,d^{2}+2 b c d \right) f^{2}\right) x^{9}}{9}+\frac{\left(b \,d^{2} e^{2}+2 \left(a \,d^{2}+2 b c d \right) e f +\left(2 a c d +b \,c^{2}\right) f^{2}\right) x^{7}}{7}+a \,c^{2} e^{2} x +\frac{\left(a \,c^{2} f^{2}+\left(a \,d^{2}+2 b c d \right) e^{2}+2 \left(2 a c d +b \,c^{2}\right) e f \right) x^{5}}{5}+\frac{\left(2 a \,c^{2} e f +\left(2 a c d +b \,c^{2}\right) e^{2}\right) x^{3}}{3}"," ",0,"1/11*b*d^2*f^2*x^11+1/9*((a*d^2+2*b*c*d)*f^2+2*b*d^2*e*f)*x^9+1/7*((2*a*c*d+b*c^2)*f^2+2*(a*d^2+2*b*c*d)*e*f+b*d^2*e^2)*x^7+1/5*(a*c^2*f^2+2*(2*a*c*d+b*c^2)*e*f+(a*d^2+2*b*c*d)*e^2)*x^5+1/3*(2*a*c^2*e*f+(2*a*c*d+b*c^2)*e^2)*x^3+a*c^2*e^2*x","A"
11,1,101,86,0.000000," ","int((b*x^2+a)*(d*x^2+c)^2*(f*x^2+e),x)","\frac{b \,d^{2} f \,x^{9}}{9}+\frac{\left(b \,d^{2} e +\left(a \,d^{2}+2 b c d \right) f \right) x^{7}}{7}+a \,c^{2} e x +\frac{\left(\left(a \,d^{2}+2 b c d \right) e +\left(2 a c d +b \,c^{2}\right) f \right) x^{5}}{5}+\frac{\left(a \,c^{2} f +\left(2 a c d +b \,c^{2}\right) e \right) x^{3}}{3}"," ",0,"1/9*b*d^2*f*x^9+1/7*((a*d^2+2*b*c*d)*f+b*d^2*e)*x^7+1/5*((2*a*c*d+b*c^2)*f+(a*d^2+2*b*c*d)*e)*x^5+1/3*(a*c^2*f+(2*a*c*d+b*c^2)*e)*x^3+a*c^2*e*x","A"
12,1,243,128,0.006000," ","int((b*x^2+a)*(d*x^2+c)^2/(f*x^2+e),x)","\frac{b \,d^{2} x^{5}}{5 f}+\frac{a \,d^{2} x^{3}}{3 f}+\frac{2 b c d \,x^{3}}{3 f}-\frac{b \,d^{2} e \,x^{3}}{3 f^{2}}+\frac{a \,c^{2} \arctan \left(\frac{f x}{\sqrt{e f}}\right)}{\sqrt{e f}}-\frac{2 a c d e \arctan \left(\frac{f x}{\sqrt{e f}}\right)}{\sqrt{e f}\, f}+\frac{a \,d^{2} e^{2} \arctan \left(\frac{f x}{\sqrt{e f}}\right)}{\sqrt{e f}\, f^{2}}-\frac{b \,c^{2} e \arctan \left(\frac{f x}{\sqrt{e f}}\right)}{\sqrt{e f}\, f}+\frac{2 b c d \,e^{2} \arctan \left(\frac{f x}{\sqrt{e f}}\right)}{\sqrt{e f}\, f^{2}}-\frac{b \,d^{2} e^{3} \arctan \left(\frac{f x}{\sqrt{e f}}\right)}{\sqrt{e f}\, f^{3}}+\frac{2 a c d x}{f}-\frac{a \,d^{2} e x}{f^{2}}+\frac{b \,c^{2} x}{f}-\frac{2 b c d e x}{f^{2}}+\frac{b \,d^{2} e^{2} x}{f^{3}}"," ",0,"1/5/f*b*d^2*x^5+1/3/f*x^3*a*d^2+2/3/f*x^3*b*c*d-1/3/f^2*x^3*b*d^2*e+2/f*a*c*d*x-1/f^2*a*d^2*e*x+1/f*b*c^2*x-2/f^2*b*c*d*e*x+1/f^3*b*d^2*e^2*x+1/(e*f)^(1/2)*arctan(1/(e*f)^(1/2)*f*x)*a*c^2-2/f/(e*f)^(1/2)*arctan(1/(e*f)^(1/2)*f*x)*a*c*d*e+1/f^2/(e*f)^(1/2)*arctan(1/(e*f)^(1/2)*f*x)*a*d^2*e^2-1/f/(e*f)^(1/2)*arctan(1/(e*f)^(1/2)*f*x)*b*c^2*e+2/f^2/(e*f)^(1/2)*arctan(1/(e*f)^(1/2)*f*x)*b*c*d*e^2-1/f^3/(e*f)^(1/2)*arctan(1/(e*f)^(1/2)*f*x)*b*d^2*e^3","A"
13,1,299,148,0.013000," ","int((b*x^2+a)*(d*x^2+c)^2/(f*x^2+e)^2,x)","\frac{b \,d^{2} x^{3}}{3 f^{2}}+\frac{a \,c^{2} x}{2 \left(f \,x^{2}+e \right) e}+\frac{a \,c^{2} \arctan \left(\frac{f x}{\sqrt{e f}}\right)}{2 \sqrt{e f}\, e}-\frac{a c d x}{\left(f \,x^{2}+e \right) f}+\frac{a c d \arctan \left(\frac{f x}{\sqrt{e f}}\right)}{\sqrt{e f}\, f}+\frac{a \,d^{2} e x}{2 \left(f \,x^{2}+e \right) f^{2}}-\frac{3 a \,d^{2} e \arctan \left(\frac{f x}{\sqrt{e f}}\right)}{2 \sqrt{e f}\, f^{2}}-\frac{b \,c^{2} x}{2 \left(f \,x^{2}+e \right) f}+\frac{b \,c^{2} \arctan \left(\frac{f x}{\sqrt{e f}}\right)}{2 \sqrt{e f}\, f}+\frac{b c d e x}{\left(f \,x^{2}+e \right) f^{2}}-\frac{3 b c d e \arctan \left(\frac{f x}{\sqrt{e f}}\right)}{\sqrt{e f}\, f^{2}}-\frac{b \,d^{2} e^{2} x}{2 \left(f \,x^{2}+e \right) f^{3}}+\frac{5 b \,d^{2} e^{2} \arctan \left(\frac{f x}{\sqrt{e f}}\right)}{2 \sqrt{e f}\, f^{3}}+\frac{a \,d^{2} x}{f^{2}}+\frac{2 b c d x}{f^{2}}-\frac{2 b \,d^{2} e x}{f^{3}}"," ",0,"1/3*d^2/f^2*x^3*b+d^2/f^2*a*x+2*d/f^2*b*c*x-2*d^2/f^3*b*e*x+1/2/e*x/(f*x^2+e)*a*c^2-1/f*x/(f*x^2+e)*a*c*d+1/2/f^2*e*x/(f*x^2+e)*a*d^2-1/2/f*x/(f*x^2+e)*b*c^2+1/f^2*e*x/(f*x^2+e)*b*c*d-1/2/f^3*e^2*x/(f*x^2+e)*b*d^2+1/2/e/(e*f)^(1/2)*arctan(1/(e*f)^(1/2)*f*x)*a*c^2+1/f/(e*f)^(1/2)*arctan(1/(e*f)^(1/2)*f*x)*a*c*d-3/2/f^2*e/(e*f)^(1/2)*arctan(1/(e*f)^(1/2)*f*x)*a*d^2+1/2/f/(e*f)^(1/2)*arctan(1/(e*f)^(1/2)*f*x)*b*c^2-3/f^2*e/(e*f)^(1/2)*arctan(1/(e*f)^(1/2)*f*x)*b*c*d+5/2/f^3*e^2/(e*f)^(1/2)*arctan(1/(e*f)^(1/2)*f*x)*b*d^2","B"
14,1,397,191,0.013000," ","int((b*x^2+a)*(d*x^2+c)^2/(f*x^2+e)^3,x)","\frac{3 a \,c^{2} f \,x^{3}}{8 \left(f \,x^{2}+e \right)^{2} e^{2}}+\frac{a c d \,x^{3}}{4 \left(f \,x^{2}+e \right)^{2} e}-\frac{5 a \,d^{2} x^{3}}{8 \left(f \,x^{2}+e \right)^{2} f}+\frac{b \,c^{2} x^{3}}{8 \left(f \,x^{2}+e \right)^{2} e}-\frac{5 b c d \,x^{3}}{4 \left(f \,x^{2}+e \right)^{2} f}+\frac{9 b \,d^{2} e \,x^{3}}{8 \left(f \,x^{2}+e \right)^{2} f^{2}}+\frac{5 a \,c^{2} x}{8 \left(f \,x^{2}+e \right)^{2} e}-\frac{a c d x}{4 \left(f \,x^{2}+e \right)^{2} f}-\frac{3 a \,d^{2} e x}{8 \left(f \,x^{2}+e \right)^{2} f^{2}}-\frac{b \,c^{2} x}{8 \left(f \,x^{2}+e \right)^{2} f}-\frac{3 b c d e x}{4 \left(f \,x^{2}+e \right)^{2} f^{2}}+\frac{7 b \,d^{2} e^{2} x}{8 \left(f \,x^{2}+e \right)^{2} f^{3}}+\frac{3 a \,c^{2} \arctan \left(\frac{f x}{\sqrt{e f}}\right)}{8 \sqrt{e f}\, e^{2}}+\frac{a c d \arctan \left(\frac{f x}{\sqrt{e f}}\right)}{4 \sqrt{e f}\, e f}+\frac{3 a \,d^{2} \arctan \left(\frac{f x}{\sqrt{e f}}\right)}{8 \sqrt{e f}\, f^{2}}+\frac{b \,c^{2} \arctan \left(\frac{f x}{\sqrt{e f}}\right)}{8 \sqrt{e f}\, e f}+\frac{3 b c d \arctan \left(\frac{f x}{\sqrt{e f}}\right)}{4 \sqrt{e f}\, f^{2}}-\frac{15 b \,d^{2} e \arctan \left(\frac{f x}{\sqrt{e f}}\right)}{8 \sqrt{e f}\, f^{3}}+\frac{b \,d^{2} x}{f^{3}}"," ",0,"b*d^2/f^3*x+3/8*f/(f*x^2+e)^2/e^2*x^3*a*c^2+1/4/(f*x^2+e)^2/e*x^3*a*c*d-5/8/f/(f*x^2+e)^2*x^3*a*d^2+1/8/(f*x^2+e)^2/e*x^3*b*c^2-5/4/f/(f*x^2+e)^2*x^3*b*c*d+9/8/f^2/(f*x^2+e)^2*x^3*b*d^2*e+5/8/(f*x^2+e)^2/e*x*a*c^2-1/4/f/(f*x^2+e)^2*a*c*d*x-3/8/f^2/(f*x^2+e)^2*a*d^2*e*x-1/8/f/(f*x^2+e)^2*b*c^2*x-3/4/f^2/(f*x^2+e)^2*b*c*d*e*x+7/8/f^3/(f*x^2+e)^2*b*d^2*e^2*x+3/8/e^2/(e*f)^(1/2)*arctan(1/(e*f)^(1/2)*f*x)*a*c^2+1/4/f/e/(e*f)^(1/2)*arctan(1/(e*f)^(1/2)*f*x)*a*c*d+3/8/f^2/(e*f)^(1/2)*arctan(1/(e*f)^(1/2)*f*x)*a*d^2+1/8/f/e/(e*f)^(1/2)*arctan(1/(e*f)^(1/2)*f*x)*b*c^2+3/4/f^2/(e*f)^(1/2)*arctan(1/(e*f)^(1/2)*f*x)*b*c*d-15/8/f^3*e/(e*f)^(1/2)*arctan(1/(e*f)^(1/2)*f*x)*b*d^2","B"
15,1,360,224,0.013000," ","int((b*x^2+a)*(d*x^2+c)^2/(f*x^2+e)^4,x)","\frac{5 a \,c^{2} \arctan \left(\frac{f x}{\sqrt{e f}}\right)}{16 \sqrt{e f}\, e^{3}}+\frac{a c d \arctan \left(\frac{f x}{\sqrt{e f}}\right)}{8 \sqrt{e f}\, e^{2} f}+\frac{a \,d^{2} \arctan \left(\frac{f x}{\sqrt{e f}}\right)}{16 \sqrt{e f}\, e \,f^{2}}+\frac{b \,c^{2} \arctan \left(\frac{f x}{\sqrt{e f}}\right)}{16 \sqrt{e f}\, e^{2} f}+\frac{b c d \arctan \left(\frac{f x}{\sqrt{e f}}\right)}{8 \sqrt{e f}\, e \,f^{2}}+\frac{5 b \,d^{2} \arctan \left(\frac{f x}{\sqrt{e f}}\right)}{16 \sqrt{e f}\, f^{3}}+\frac{\frac{\left(5 a \,c^{2} f^{3}+2 a c d e \,f^{2}+a \,d^{2} e^{2} f +b \,c^{2} e \,f^{2}+2 b c d \,e^{2} f -11 b \,d^{2} e^{3}\right) x^{5}}{16 e^{3} f}+\frac{\left(5 a \,c^{2} f^{3}+2 a c d e \,f^{2}-a \,d^{2} e^{2} f +b \,c^{2} e \,f^{2}-2 b c d \,e^{2} f -5 b \,d^{2} e^{3}\right) x^{3}}{6 e^{2} f^{2}}+\frac{\left(11 a \,c^{2} f^{3}-2 a c d e \,f^{2}-a \,d^{2} e^{2} f -b \,c^{2} e \,f^{2}-2 b c d \,e^{2} f -5 b \,d^{2} e^{3}\right) x}{16 e \,f^{3}}}{\left(f \,x^{2}+e \right)^{3}}"," ",0,"(1/16*(5*a*c^2*f^3+2*a*c*d*e*f^2+a*d^2*e^2*f+b*c^2*e*f^2+2*b*c*d*e^2*f-11*b*d^2*e^3)/e^3/f*x^5+1/6*(5*a*c^2*f^3+2*a*c*d*e*f^2-a*d^2*e^2*f+b*c^2*e*f^2-2*b*c*d*e^2*f-5*b*d^2*e^3)/e^2/f^2*x^3+1/16*(11*a*c^2*f^3-2*a*c*d*e*f^2-a*d^2*e^2*f-b*c^2*e*f^2-2*b*c*d*e^2*f-5*b*d^2*e^3)/f^3/e*x)/(f*x^2+e)^3+5/16/e^3/(e*f)^(1/2)*arctan(1/(e*f)^(1/2)*f*x)*a*c^2+1/8/e^2/f/(e*f)^(1/2)*arctan(1/(e*f)^(1/2)*f*x)*a*c*d+1/16/e/f^2/(e*f)^(1/2)*arctan(1/(e*f)^(1/2)*f*x)*a*d^2+1/16/e^2/f/(e*f)^(1/2)*arctan(1/(e*f)^(1/2)*f*x)*b*c^2+1/8/e/f^2/(e*f)^(1/2)*arctan(1/(e*f)^(1/2)*f*x)*b*c*d+5/16/f^3/(e*f)^(1/2)*arctan(1/(e*f)^(1/2)*f*x)*b*d^2","A"
16,1,339,296,0.003000," ","int((b*x^2+a)*(d*x^2+c)^3*(f*x^2+e)^3,x)","\frac{b \,d^{3} f^{3} x^{15}}{15}+\frac{\left(3 b \,d^{3} e \,f^{2}+\left(a \,d^{3}+3 b c \,d^{2}\right) f^{3}\right) x^{13}}{13}+\frac{\left(3 b \,d^{3} e^{2} f +3 \left(a \,d^{3}+3 b c \,d^{2}\right) e \,f^{2}+\left(3 a c \,d^{2}+3 b \,c^{2} d \right) f^{3}\right) x^{11}}{11}+\frac{\left(b \,d^{3} e^{3}+3 \left(a \,d^{3}+3 b c \,d^{2}\right) e^{2} f +3 \left(3 a c \,d^{2}+3 b \,c^{2} d \right) e \,f^{2}+\left(3 a \,c^{2} d +b \,c^{3}\right) f^{3}\right) x^{9}}{9}+a \,c^{3} e^{3} x +\frac{\left(a \,c^{3} f^{3}+\left(a \,d^{3}+3 b c \,d^{2}\right) e^{3}+3 \left(3 a c \,d^{2}+3 b \,c^{2} d \right) e^{2} f +3 \left(3 a \,c^{2} d +b \,c^{3}\right) e \,f^{2}\right) x^{7}}{7}+\frac{\left(3 a \,c^{3} e \,f^{2}+\left(3 a c \,d^{2}+3 b \,c^{2} d \right) e^{3}+3 \left(3 a \,c^{2} d +b \,c^{3}\right) e^{2} f \right) x^{5}}{5}+\frac{\left(3 a \,c^{3} e^{2} f +\left(3 a \,c^{2} d +b \,c^{3}\right) e^{3}\right) x^{3}}{3}"," ",0,"1/15*b*d^3*f^3*x^15+1/13*((a*d^3+3*b*c*d^2)*f^3+3*b*d^3*e*f^2)*x^13+1/11*((3*a*c*d^2+3*b*c^2*d)*f^3+3*(a*d^3+3*b*c*d^2)*e*f^2+3*b*d^3*e^2*f)*x^11+1/9*((3*a*c^2*d+b*c^3)*f^3+3*(3*a*c*d^2+3*b*c^2*d)*e*f^2+3*(a*d^3+3*b*c*d^2)*e^2*f+b*d^3*e^3)*x^9+1/7*(a*c^3*f^3+3*(3*a*c^2*d+b*c^3)*e*f^2+3*(3*a*c*d^2+3*b*c^2*d)*e^2*f+(a*d^3+3*b*c*d^2)*e^3)*x^7+1/5*(3*a*c^3*e*f^2+3*(3*a*c^2*d+b*c^3)*e^2*f+(3*a*c*d^2+3*b*c^2*d)*e^3)*x^5+1/3*(3*a*c^3*e^2*f+(3*a*c^2*d+b*c^3)*e^3)*x^3+a*c^3*e^3*x","A"
17,1,244,214,0.001000," ","int((b*x^2+a)*(d*x^2+c)^3*(f*x^2+e)^2,x)","\frac{b \,d^{3} f^{2} x^{13}}{13}+\frac{\left(2 b \,d^{3} e f +\left(a \,d^{3}+3 b c \,d^{2}\right) f^{2}\right) x^{11}}{11}+\frac{\left(b \,d^{3} e^{2}+2 \left(a \,d^{3}+3 b c \,d^{2}\right) e f +\left(3 a c \,d^{2}+3 b \,c^{2} d \right) f^{2}\right) x^{9}}{9}+a \,c^{3} e^{2} x +\frac{\left(\left(a \,d^{3}+3 b c \,d^{2}\right) e^{2}+2 \left(3 a c \,d^{2}+3 b \,c^{2} d \right) e f +\left(3 a \,c^{2} d +b \,c^{3}\right) f^{2}\right) x^{7}}{7}+\frac{\left(a \,c^{3} f^{2}+\left(3 a c \,d^{2}+3 b \,c^{2} d \right) e^{2}+2 \left(3 a \,c^{2} d +b \,c^{3}\right) e f \right) x^{5}}{5}+\frac{\left(2 a \,c^{3} e f +\left(3 a \,c^{2} d +b \,c^{3}\right) e^{2}\right) x^{3}}{3}"," ",0,"1/13*b*d^3*f^2*x^13+1/11*((a*d^3+3*b*c*d^2)*f^2+2*b*d^3*e*f)*x^11+1/9*((3*a*c*d^2+3*b*c^2*d)*f^2+2*(a*d^3+3*b*c*d^2)*e*f+b*d^3*e^2)*x^9+1/7*((3*a*c^2*d+b*c^3)*f^2+2*(3*a*c*d^2+3*b*c^2*d)*e*f+(a*d^3+3*b*c*d^2)*e^2)*x^7+1/5*(a*c^3*f^2+2*(3*a*c^2*d+b*c^3)*e*f+(3*a*c*d^2+3*b*c^2*d)*e^2)*x^5+1/3*(2*a*c^3*e*f+(3*a*c^2*d+b*c^3)*e^2)*x^3+a*c^3*e^2*x","A"
18,1,149,120,0.001000," ","int((b*x^2+a)*(d*x^2+c)^3*(f*x^2+e),x)","\frac{b \,d^{3} f \,x^{11}}{11}+\frac{\left(b \,d^{3} e +\left(a \,d^{3}+3 b c \,d^{2}\right) f \right) x^{9}}{9}+\frac{\left(\left(a \,d^{3}+3 b c \,d^{2}\right) e +\left(3 a c \,d^{2}+3 b \,c^{2} d \right) f \right) x^{7}}{7}+a \,c^{3} e x +\frac{\left(\left(3 a c \,d^{2}+3 b \,c^{2} d \right) e +\left(3 a \,c^{2} d +b \,c^{3}\right) f \right) x^{5}}{5}+\frac{\left(a \,c^{3} f +\left(3 a \,c^{2} d +b \,c^{3}\right) e \right) x^{3}}{3}"," ",0,"1/11*b*d^3*f*x^11+1/9*((a*d^3+3*b*c*d^2)*f+b*d^3*e)*x^9+1/7*((3*a*c*d^2+3*b*c^2*d)*f+(a*d^3+3*b*c*d^2)*e)*x^7+1/5*((3*a*c^2*d+b*c^3)*f+(3*a*c*d^2+3*b*c^2*d)*e)*x^5+1/3*(a*c^3*f+(3*a*c^2*d+b*c^3)*e)*x^3+a*c^3*e*x","A"
19,1,401,211,0.007000," ","int((b*x^2+a)*(d*x^2+c)^3/(f*x^2+e),x)","\frac{b \,d^{3} x^{7}}{7 f}+\frac{a \,d^{3} x^{5}}{5 f}+\frac{3 b c \,d^{2} x^{5}}{5 f}-\frac{b \,d^{3} e \,x^{5}}{5 f^{2}}+\frac{a c \,d^{2} x^{3}}{f}-\frac{a \,d^{3} e \,x^{3}}{3 f^{2}}+\frac{b \,c^{2} d \,x^{3}}{f}-\frac{b c \,d^{2} e \,x^{3}}{f^{2}}+\frac{b \,d^{3} e^{2} x^{3}}{3 f^{3}}+\frac{a \,c^{3} \arctan \left(\frac{f x}{\sqrt{e f}}\right)}{\sqrt{e f}}-\frac{3 a \,c^{2} d e \arctan \left(\frac{f x}{\sqrt{e f}}\right)}{\sqrt{e f}\, f}+\frac{3 a c \,d^{2} e^{2} \arctan \left(\frac{f x}{\sqrt{e f}}\right)}{\sqrt{e f}\, f^{2}}-\frac{a \,d^{3} e^{3} \arctan \left(\frac{f x}{\sqrt{e f}}\right)}{\sqrt{e f}\, f^{3}}-\frac{b \,c^{3} e \arctan \left(\frac{f x}{\sqrt{e f}}\right)}{\sqrt{e f}\, f}+\frac{3 b \,c^{2} d \,e^{2} \arctan \left(\frac{f x}{\sqrt{e f}}\right)}{\sqrt{e f}\, f^{2}}-\frac{3 b c \,d^{2} e^{3} \arctan \left(\frac{f x}{\sqrt{e f}}\right)}{\sqrt{e f}\, f^{3}}+\frac{b \,d^{3} e^{4} \arctan \left(\frac{f x}{\sqrt{e f}}\right)}{\sqrt{e f}\, f^{4}}+\frac{3 a \,c^{2} d x}{f}-\frac{3 a c \,d^{2} e x}{f^{2}}+\frac{a \,d^{3} e^{2} x}{f^{3}}+\frac{b \,c^{3} x}{f}-\frac{3 b \,c^{2} d e x}{f^{2}}+\frac{3 b c \,d^{2} e^{2} x}{f^{3}}-\frac{b \,d^{3} e^{3} x}{f^{4}}"," ",0,"1/7/f*b*d^3*x^7+1/5/f*x^5*a*d^3+3/5/f*x^5*b*c*d^2-1/5/f^2*x^5*b*d^3*e+1/f*x^3*a*c*d^2-1/3/f^2*x^3*a*d^3*e+1/f*x^3*b*c^2*d-1/f^2*x^3*b*c*d^2*e+1/3/f^3*x^3*b*d^3*e^2+3/f*a*c^2*d*x-3/f^2*a*c*d^2*e*x+1/f^3*a*d^3*e^2*x+1/f*b*c^3*x-3/f^2*b*c^2*d*e*x+3/f^3*b*c*d^2*e^2*x-1/f^4*b*d^3*e^3*x+1/(e*f)^(1/2)*arctan(1/(e*f)^(1/2)*f*x)*a*c^3-3/f/(e*f)^(1/2)*arctan(1/(e*f)^(1/2)*f*x)*a*c^2*d*e+3/f^2/(e*f)^(1/2)*arctan(1/(e*f)^(1/2)*f*x)*a*c*d^2*e^2-1/f^3/(e*f)^(1/2)*arctan(1/(e*f)^(1/2)*f*x)*a*d^3*e^3-1/f/(e*f)^(1/2)*arctan(1/(e*f)^(1/2)*f*x)*b*c^3*e+3/f^2/(e*f)^(1/2)*arctan(1/(e*f)^(1/2)*f*x)*b*c^2*d*e^2-3/f^3/(e*f)^(1/2)*arctan(1/(e*f)^(1/2)*f*x)*b*c*d^2*e^3+1/f^4/(e*f)^(1/2)*arctan(1/(e*f)^(1/2)*f*x)*b*d^3*e^4","A"
20,1,475,224,0.015000," ","int((b*x^2+a)*(d*x^2+c)^3/(f*x^2+e)^2,x)","\frac{b \,d^{3} x^{5}}{5 f^{2}}+\frac{a \,d^{3} x^{3}}{3 f^{2}}+\frac{b c \,d^{2} x^{3}}{f^{2}}-\frac{2 b \,d^{3} e \,x^{3}}{3 f^{3}}+\frac{a \,c^{3} x}{2 \left(f \,x^{2}+e \right) e}+\frac{a \,c^{3} \arctan \left(\frac{f x}{\sqrt{e f}}\right)}{2 \sqrt{e f}\, e}-\frac{3 a \,c^{2} d x}{2 \left(f \,x^{2}+e \right) f}+\frac{3 a \,c^{2} d \arctan \left(\frac{f x}{\sqrt{e f}}\right)}{2 \sqrt{e f}\, f}+\frac{3 a c \,d^{2} e x}{2 \left(f \,x^{2}+e \right) f^{2}}-\frac{9 a c \,d^{2} e \arctan \left(\frac{f x}{\sqrt{e f}}\right)}{2 \sqrt{e f}\, f^{2}}-\frac{a \,d^{3} e^{2} x}{2 \left(f \,x^{2}+e \right) f^{3}}+\frac{5 a \,d^{3} e^{2} \arctan \left(\frac{f x}{\sqrt{e f}}\right)}{2 \sqrt{e f}\, f^{3}}-\frac{b \,c^{3} x}{2 \left(f \,x^{2}+e \right) f}+\frac{b \,c^{3} \arctan \left(\frac{f x}{\sqrt{e f}}\right)}{2 \sqrt{e f}\, f}+\frac{3 b \,c^{2} d e x}{2 \left(f \,x^{2}+e \right) f^{2}}-\frac{9 b \,c^{2} d e \arctan \left(\frac{f x}{\sqrt{e f}}\right)}{2 \sqrt{e f}\, f^{2}}-\frac{3 b c \,d^{2} e^{2} x}{2 \left(f \,x^{2}+e \right) f^{3}}+\frac{15 b c \,d^{2} e^{2} \arctan \left(\frac{f x}{\sqrt{e f}}\right)}{2 \sqrt{e f}\, f^{3}}+\frac{b \,d^{3} e^{3} x}{2 \left(f \,x^{2}+e \right) f^{4}}-\frac{7 b \,d^{3} e^{3} \arctan \left(\frac{f x}{\sqrt{e f}}\right)}{2 \sqrt{e f}\, f^{4}}+\frac{3 a c \,d^{2} x}{f^{2}}-\frac{2 a \,d^{3} e x}{f^{3}}+\frac{3 b \,c^{2} d x}{f^{2}}-\frac{6 b c \,d^{2} e x}{f^{3}}+\frac{3 b \,d^{3} e^{2} x}{f^{4}}"," ",0,"3*d^2/f^2*a*c*x+d^2/f^2*x^3*b*c+3/2/f^2*e*x/(f*x^2+e)*b*c^2*d-3/2/f^3*e^2*x/(f*x^2+e)*b*c*d^2-9/2/f^2*e/(e*f)^(1/2)*arctan(1/(e*f)^(1/2)*f*x)*a*c*d^2-9/2/f^2*e/(e*f)^(1/2)*arctan(1/(e*f)^(1/2)*f*x)*b*c^2*d+15/2/f^3*e^2/(e*f)^(1/2)*arctan(1/(e*f)^(1/2)*f*x)*b*c*d^2+3/2/f^2*e*x/(f*x^2+e)*a*c*d^2-1/2/f^3*e^2*x/(f*x^2+e)*a*d^3+1/2/f^4*e^3*x/(f*x^2+e)*b*d^3+3/2/f/(e*f)^(1/2)*arctan(1/(e*f)^(1/2)*f*x)*a*c^2*d+5/2/f^3*e^2/(e*f)^(1/2)*arctan(1/(e*f)^(1/2)*f*x)*a*d^3-7/2/f^4*e^3/(e*f)^(1/2)*arctan(1/(e*f)^(1/2)*f*x)*b*d^3-6*d^2/f^3*b*c*e*x-3/2/f*x/(f*x^2+e)*a*c^2*d+1/5*d^3/f^2*b*x^5+1/3*d^3/f^2*x^3*a-2/3*d^3/f^3*x^3*b*e+1/2/e*x/(f*x^2+e)*a*c^3+1/2/e/(e*f)^(1/2)*arctan(1/(e*f)^(1/2)*f*x)*a*c^3+1/2/f/(e*f)^(1/2)*arctan(1/(e*f)^(1/2)*f*x)*b*c^3+3*d/f^2*b*c^2*x+3*d^3/f^4*b*e^2*x-1/2/f*x/(f*x^2+e)*b*c^3-2*d^3/f^3*a*e*x","B"
21,1,589,273,0.015000," ","int((b*x^2+a)*(d*x^2+c)^3/(f*x^2+e)^3,x)","\frac{3 a \,c^{3} f \,x^{3}}{8 \left(f \,x^{2}+e \right)^{2} e^{2}}+\frac{3 a \,c^{2} d \,x^{3}}{8 \left(f \,x^{2}+e \right)^{2} e}-\frac{15 a c \,d^{2} x^{3}}{8 \left(f \,x^{2}+e \right)^{2} f}+\frac{9 a \,d^{3} e \,x^{3}}{8 \left(f \,x^{2}+e \right)^{2} f^{2}}+\frac{b \,c^{3} x^{3}}{8 \left(f \,x^{2}+e \right)^{2} e}-\frac{15 b \,c^{2} d \,x^{3}}{8 \left(f \,x^{2}+e \right)^{2} f}+\frac{27 b c \,d^{2} e \,x^{3}}{8 \left(f \,x^{2}+e \right)^{2} f^{2}}-\frac{13 b \,d^{3} e^{2} x^{3}}{8 \left(f \,x^{2}+e \right)^{2} f^{3}}+\frac{5 a \,c^{3} x}{8 \left(f \,x^{2}+e \right)^{2} e}-\frac{3 a \,c^{2} d x}{8 \left(f \,x^{2}+e \right)^{2} f}-\frac{9 a c \,d^{2} e x}{8 \left(f \,x^{2}+e \right)^{2} f^{2}}+\frac{7 a \,d^{3} e^{2} x}{8 \left(f \,x^{2}+e \right)^{2} f^{3}}-\frac{b \,c^{3} x}{8 \left(f \,x^{2}+e \right)^{2} f}-\frac{9 b \,c^{2} d e x}{8 \left(f \,x^{2}+e \right)^{2} f^{2}}+\frac{21 b c \,d^{2} e^{2} x}{8 \left(f \,x^{2}+e \right)^{2} f^{3}}-\frac{11 b \,d^{3} e^{3} x}{8 \left(f \,x^{2}+e \right)^{2} f^{4}}+\frac{b \,d^{3} x^{3}}{3 f^{3}}+\frac{3 a \,c^{3} \arctan \left(\frac{f x}{\sqrt{e f}}\right)}{8 \sqrt{e f}\, e^{2}}+\frac{3 a \,c^{2} d \arctan \left(\frac{f x}{\sqrt{e f}}\right)}{8 \sqrt{e f}\, e f}+\frac{9 a c \,d^{2} \arctan \left(\frac{f x}{\sqrt{e f}}\right)}{8 \sqrt{e f}\, f^{2}}-\frac{15 a \,d^{3} e \arctan \left(\frac{f x}{\sqrt{e f}}\right)}{8 \sqrt{e f}\, f^{3}}+\frac{b \,c^{3} \arctan \left(\frac{f x}{\sqrt{e f}}\right)}{8 \sqrt{e f}\, e f}+\frac{9 b \,c^{2} d \arctan \left(\frac{f x}{\sqrt{e f}}\right)}{8 \sqrt{e f}\, f^{2}}-\frac{45 b c \,d^{2} e \arctan \left(\frac{f x}{\sqrt{e f}}\right)}{8 \sqrt{e f}\, f^{3}}+\frac{35 b \,d^{3} e^{2} \arctan \left(\frac{f x}{\sqrt{e f}}\right)}{8 \sqrt{e f}\, f^{4}}+\frac{a \,d^{3} x}{f^{3}}+\frac{3 b c \,d^{2} x}{f^{3}}-\frac{3 b \,d^{3} e x}{f^{4}}"," ",0,"-45/8/f^3*e/(e*f)^(1/2)*arctan(1/(e*f)^(1/2)*f*x)*b*c*d^2+27/8/f^2/(f*x^2+e)^2*x^3*b*c*d^2*e-9/8/f^2/(f*x^2+e)^2*a*c*d^2*e*x-9/8/f^2/(f*x^2+e)^2*b*c^2*d*e*x+21/8/f^3/(f*x^2+e)^2*b*c*d^2*e^2*x+3/8/f/e/(e*f)^(1/2)*arctan(1/(e*f)^(1/2)*f*x)*a*c^2*d+3/8/(f*x^2+e)^2/e*x^3*a*c^2*d-15/8/f/(f*x^2+e)^2*x^3*b*c^2*d-13/8/f^3/(f*x^2+e)^2*x^3*b*d^3*e^2-3/8/f/(f*x^2+e)^2*a*c^2*d*x+7/8/f^3/(f*x^2+e)^2*a*d^3*e^2*x-11/8/f^4/(f*x^2+e)^2*b*d^3*e^3*x+9/8/f^2/(e*f)^(1/2)*arctan(1/(e*f)^(1/2)*f*x)*a*c*d^2-15/8/f^3*e/(e*f)^(1/2)*arctan(1/(e*f)^(1/2)*f*x)*a*d^3+1/8/f/e/(e*f)^(1/2)*arctan(1/(e*f)^(1/2)*f*x)*b*c^3+9/8/f^2/(e*f)^(1/2)*arctan(1/(e*f)^(1/2)*f*x)*b*c^2*d+35/8/f^4*e^2/(e*f)^(1/2)*arctan(1/(e*f)^(1/2)*f*x)*b*d^3+3/8*f/(f*x^2+e)^2/e^2*x^3*a*c^3-15/8/f/(f*x^2+e)^2*x^3*a*c*d^2+9/8/f^2/(f*x^2+e)^2*x^3*a*d^3*e+d^3/f^3*a*x+1/3*d^3/f^3*x^3*b-3*d^3/f^4*b*e*x-1/8/f/(f*x^2+e)^2*b*c^3*x+3/8/e^2/(e*f)^(1/2)*arctan(1/(e*f)^(1/2)*f*x)*a*c^3+3*d^2/f^3*b*c*x+1/8/(f*x^2+e)^2/e*x^3*b*c^3+5/8/(f*x^2+e)^2/e*x*a*c^3","B"
22,1,735,330,0.014000," ","int((b*x^2+a)*(d*x^2+c)^3/(f*x^2+e)^4,x)","\frac{5 a \,c^{3} f^{2} x^{5}}{16 \left(f \,x^{2}+e \right)^{3} e^{3}}+\frac{3 a \,c^{2} d f \,x^{5}}{16 \left(f \,x^{2}+e \right)^{3} e^{2}}+\frac{3 a c \,d^{2} x^{5}}{16 \left(f \,x^{2}+e \right)^{3} e}-\frac{11 a \,d^{3} x^{5}}{16 \left(f \,x^{2}+e \right)^{3} f}+\frac{b \,c^{3} f \,x^{5}}{16 \left(f \,x^{2}+e \right)^{3} e^{2}}+\frac{3 b \,c^{2} d \,x^{5}}{16 \left(f \,x^{2}+e \right)^{3} e}-\frac{33 b c \,d^{2} x^{5}}{16 \left(f \,x^{2}+e \right)^{3} f}+\frac{29 b \,d^{3} e \,x^{5}}{16 \left(f \,x^{2}+e \right)^{3} f^{2}}+\frac{5 a \,c^{3} f \,x^{3}}{6 \left(f \,x^{2}+e \right)^{3} e^{2}}+\frac{a \,c^{2} d \,x^{3}}{2 \left(f \,x^{2}+e \right)^{3} e}-\frac{a c \,d^{2} x^{3}}{2 \left(f \,x^{2}+e \right)^{3} f}-\frac{5 a \,d^{3} e \,x^{3}}{6 \left(f \,x^{2}+e \right)^{3} f^{2}}+\frac{b \,c^{3} x^{3}}{6 \left(f \,x^{2}+e \right)^{3} e}-\frac{b \,c^{2} d \,x^{3}}{2 \left(f \,x^{2}+e \right)^{3} f}-\frac{5 b c \,d^{2} e \,x^{3}}{2 \left(f \,x^{2}+e \right)^{3} f^{2}}+\frac{17 b \,d^{3} e^{2} x^{3}}{6 \left(f \,x^{2}+e \right)^{3} f^{3}}+\frac{11 a \,c^{3} x}{16 \left(f \,x^{2}+e \right)^{3} e}-\frac{3 a \,c^{2} d x}{16 \left(f \,x^{2}+e \right)^{3} f}-\frac{3 a c \,d^{2} e x}{16 \left(f \,x^{2}+e \right)^{3} f^{2}}-\frac{5 a \,d^{3} e^{2} x}{16 \left(f \,x^{2}+e \right)^{3} f^{3}}-\frac{b \,c^{3} x}{16 \left(f \,x^{2}+e \right)^{3} f}-\frac{3 b \,c^{2} d e x}{16 \left(f \,x^{2}+e \right)^{3} f^{2}}-\frac{15 b c \,d^{2} e^{2} x}{16 \left(f \,x^{2}+e \right)^{3} f^{3}}+\frac{19 b \,d^{3} e^{3} x}{16 \left(f \,x^{2}+e \right)^{3} f^{4}}+\frac{5 a \,c^{3} \arctan \left(\frac{f x}{\sqrt{e f}}\right)}{16 \sqrt{e f}\, e^{3}}+\frac{3 a \,c^{2} d \arctan \left(\frac{f x}{\sqrt{e f}}\right)}{16 \sqrt{e f}\, e^{2} f}+\frac{3 a c \,d^{2} \arctan \left(\frac{f x}{\sqrt{e f}}\right)}{16 \sqrt{e f}\, e \,f^{2}}+\frac{5 a \,d^{3} \arctan \left(\frac{f x}{\sqrt{e f}}\right)}{16 \sqrt{e f}\, f^{3}}+\frac{b \,c^{3} \arctan \left(\frac{f x}{\sqrt{e f}}\right)}{16 \sqrt{e f}\, e^{2} f}+\frac{3 b \,c^{2} d \arctan \left(\frac{f x}{\sqrt{e f}}\right)}{16 \sqrt{e f}\, e \,f^{2}}+\frac{15 b c \,d^{2} \arctan \left(\frac{f x}{\sqrt{e f}}\right)}{16 \sqrt{e f}\, f^{3}}-\frac{35 b \,d^{3} e \arctan \left(\frac{f x}{\sqrt{e f}}\right)}{16 \sqrt{e f}\, f^{4}}+\frac{b \,d^{3} x}{f^{4}}"," ",0,"-15/16/f^3/(f*x^2+e)^3*b*c*d^2*e^2*x+3/16/f/e^2/(e*f)^(1/2)*arctan(1/(e*f)^(1/2)*f*x)*a*c^2*d+3/16/f^2/e/(e*f)^(1/2)*arctan(1/(e*f)^(1/2)*f*x)*a*c*d^2+3/16/f^2/e/(e*f)^(1/2)*arctan(1/(e*f)^(1/2)*f*x)*b*c^2*d-5/2/f^2/(f*x^2+e)^3*x^3*b*c*d^2*e-3/16/f^2/(f*x^2+e)^3*a*c*d^2*e*x-3/16/f^2/(f*x^2+e)^3*b*c^2*d*e*x+3/16*f/(f*x^2+e)^3/e^2*x^5*a*c^2*d+29/16/f^2/(f*x^2+e)^3*x^5*b*d^3*e+5/6*f/(f*x^2+e)^3/e^2*x^3*a*c^3-1/2/f/(f*x^2+e)^3*x^3*a*c*d^2-5/6/f^2/(f*x^2+e)^3*x^3*a*d^3*e+3/16/(f*x^2+e)^3/e*x^5*b*c^2*d+1/2/(f*x^2+e)^3/e*x^3*a*c^2*d+3/16/(f*x^2+e)^3/e*x^5*a*c*d^2+19/16/f^4/(f*x^2+e)^3*b*d^3*e^3*x+15/16/f^3/(e*f)^(1/2)*arctan(1/(e*f)^(1/2)*f*x)*b*c*d^2-35/16/f^4*e/(e*f)^(1/2)*arctan(1/(e*f)^(1/2)*f*x)*b*d^3+1/16/f/e^2/(e*f)^(1/2)*arctan(1/(e*f)^(1/2)*f*x)*b*c^3-1/2/f/(f*x^2+e)^3*x^3*b*c^2*d+17/6/f^3/(f*x^2+e)^3*x^3*b*d^3*e^2-3/16/f/(f*x^2+e)^3*a*c^2*d*x-5/16/f^3/(f*x^2+e)^3*a*d^3*e^2*x+5/16*f^2/(f*x^2+e)^3/e^3*x^5*a*c^3+1/16*f/(f*x^2+e)^3/e^2*x^5*b*c^3-33/16/f/(f*x^2+e)^3*x^5*b*c*d^2+b*d^3/f^4*x+5/16/e^3/(e*f)^(1/2)*arctan(1/(e*f)^(1/2)*f*x)*a*c^3+5/16/f^3/(e*f)^(1/2)*arctan(1/(e*f)^(1/2)*f*x)*a*d^3-11/16/f/(f*x^2+e)^3*x^5*a*d^3-1/16/f/(f*x^2+e)^3*b*c^3*x+1/6/(f*x^2+e)^3/e*x^3*b*c^3+11/16/(f*x^2+e)^3/e*x*a*c^3","B"
23,1,1332,566,0.049000," ","int((b*x^2+a)*(d*x^2+c)^(3/2)*(f*x^2+e)^(1/2),x)","\frac{\sqrt{d \,x^{2}+c}\, \sqrt{f \,x^{2}+e}\, \left(15 \sqrt{-\frac{d}{c}}\, b \,d^{3} f^{4} x^{9}+21 \sqrt{-\frac{d}{c}}\, a \,d^{3} f^{4} x^{7}+39 \sqrt{-\frac{d}{c}}\, b c \,d^{2} f^{4} x^{7}+18 \sqrt{-\frac{d}{c}}\, b \,d^{3} e \,f^{3} x^{7}+63 \sqrt{-\frac{d}{c}}\, a c \,d^{2} f^{4} x^{5}+28 \sqrt{-\frac{d}{c}}\, a \,d^{3} e \,f^{3} x^{5}+27 \sqrt{-\frac{d}{c}}\, b \,c^{2} d \,f^{4} x^{5}+51 \sqrt{-\frac{d}{c}}\, b c \,d^{2} e \,f^{3} x^{5}-\sqrt{-\frac{d}{c}}\, b \,d^{3} e^{2} f^{2} x^{5}+42 \sqrt{-\frac{d}{c}}\, a \,c^{2} d \,f^{4} x^{3}+70 \sqrt{-\frac{d}{c}}\, a c \,d^{2} e \,f^{3} x^{3}+7 \sqrt{-\frac{d}{c}}\, a \,d^{3} e^{2} f^{2} x^{3}+3 \sqrt{-\frac{d}{c}}\, b \,c^{3} f^{4} x^{3}+36 \sqrt{-\frac{d}{c}}\, b \,c^{2} d e \,f^{3} x^{3}+8 \sqrt{-\frac{d}{c}}\, b c \,d^{2} e^{2} f^{2} x^{3}-4 \sqrt{-\frac{d}{c}}\, b \,d^{3} e^{3} f \,x^{3}+42 \sqrt{-\frac{d}{c}}\, a \,c^{2} d e \,f^{3} x +21 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,c^{2} d e \,f^{3} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+42 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,c^{2} d e \,f^{3} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+7 \sqrt{-\frac{d}{c}}\, a c \,d^{2} e^{2} f^{2} x +49 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a c \,d^{2} e^{2} f^{2} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-56 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a c \,d^{2} e^{2} f^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-14 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,d^{3} e^{3} f \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+14 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,d^{3} e^{3} f \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+3 \sqrt{-\frac{d}{c}}\, b \,c^{3} e \,f^{3} x -6 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b \,c^{3} e \,f^{3} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+3 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b \,c^{3} e \,f^{3} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+9 \sqrt{-\frac{d}{c}}\, b \,c^{2} d \,e^{2} f^{2} x +9 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b \,c^{2} d \,e^{2} f^{2} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-18 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b \,c^{2} d \,e^{2} f^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-4 \sqrt{-\frac{d}{c}}\, b c \,d^{2} e^{3} f x -19 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b c \,d^{2} e^{3} f \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+23 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b c \,d^{2} e^{3} f \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+8 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b \,d^{3} e^{4} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-8 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b \,d^{3} e^{4} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)\right)}{105 \left(d f \,x^{4}+c f \,x^{2}+d e \,x^{2}+c e \right) \sqrt{-\frac{d}{c}}\, d \,f^{3}}"," ",0,"1/105*(d*x^2+c)^(1/2)*(f*x^2+e)^(1/2)*(-4*(-1/c*d)^(1/2)*x^3*b*d^3*e^3*f+15*(-1/c*d)^(1/2)*x^9*b*d^3*f^4+3*(-1/c*d)^(1/2)*x*b*c^3*e*f^3+39*(-1/c*d)^(1/2)*x^7*b*c*d^2*f^4+18*(-1/c*d)^(1/2)*x^7*b*d^3*e*f^3+63*(-1/c*d)^(1/2)*x^5*a*c*d^2*f^4+28*(-1/c*d)^(1/2)*x^5*a*d^3*e*f^3+27*(-1/c*d)^(1/2)*x^5*b*c^2*d*f^4-(-1/c*d)^(1/2)*x^5*b*d^3*e^2*f^2+42*(-1/c*d)^(1/2)*x^3*a*c^2*d*f^4+7*(-1/c*d)^(1/2)*x^3*a*d^3*e^2*f^2-8*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c*f/d/e)^(1/2))*b*d^3*e^4+8*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c*f/d/e)^(1/2))*b*d^3*e^4+21*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c*f/d/e)^(1/2))*a*c^2*d*e*f^3+42*(-1/c*d)^(1/2)*x*a*c^2*d*e*f^3+7*(-1/c*d)^(1/2)*x*a*c*d^2*e^2*f^2+9*(-1/c*d)^(1/2)*x*b*c^2*d*e^2*f^2-4*(-1/c*d)^(1/2)*x*b*c*d^2*e^3*f+14*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c*f/d/e)^(1/2))*a*d^3*e^3*f+3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c*f/d/e)^(1/2))*b*c^3*e*f^3-14*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c*f/d/e)^(1/2))*a*d^3*e^3*f-6*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c*f/d/e)^(1/2))*b*c^3*e*f^3+49*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c*f/d/e)^(1/2))*a*c*d^2*e^2*f^2+9*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c*f/d/e)^(1/2))*b*c^2*d*e^2*f^2-19*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c*f/d/e)^(1/2))*b*c*d^2*e^3*f+42*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c*f/d/e)^(1/2))*a*c^2*d*e*f^3-56*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c*f/d/e)^(1/2))*a*c*d^2*e^2*f^2-18*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c*f/d/e)^(1/2))*b*c^2*d*e^2*f^2+23*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c*f/d/e)^(1/2))*b*c*d^2*e^3*f+21*(-1/c*d)^(1/2)*x^7*a*d^3*f^4+3*(-1/c*d)^(1/2)*x^3*b*c^3*f^4+51*(-1/c*d)^(1/2)*x^5*b*c*d^2*e*f^3+70*(-1/c*d)^(1/2)*x^3*a*c*d^2*e*f^3+36*(-1/c*d)^(1/2)*x^3*b*c^2*d*e*f^3+8*(-1/c*d)^(1/2)*x^3*b*c*d^2*e^2*f^2)/d/(d*f*x^4+c*f*x^2+d*e*x^2+c*e)/f^3/(-1/c*d)^(1/2)","B"
24,1,865,409,0.017000," ","int((b*x^2+a)*(d*x^2+c)^(1/2)*(f*x^2+e)^(1/2),x)","\frac{\sqrt{d \,x^{2}+c}\, \sqrt{f \,x^{2}+e}\, \left(3 \sqrt{-\frac{d}{c}}\, b \,d^{2} f^{3} x^{7}+5 \sqrt{-\frac{d}{c}}\, a \,d^{2} f^{3} x^{5}+4 \sqrt{-\frac{d}{c}}\, b c d \,f^{3} x^{5}+4 \sqrt{-\frac{d}{c}}\, b \,d^{2} e \,f^{2} x^{5}+5 \sqrt{-\frac{d}{c}}\, a c d \,f^{3} x^{3}+5 \sqrt{-\frac{d}{c}}\, a \,d^{2} e \,f^{2} x^{3}+\sqrt{-\frac{d}{c}}\, b \,c^{2} f^{3} x^{3}+5 \sqrt{-\frac{d}{c}}\, b c d e \,f^{2} x^{3}+\sqrt{-\frac{d}{c}}\, b \,d^{2} e^{2} f \,x^{3}+5 \sqrt{-\frac{d}{c}}\, a c d e \,f^{2} x +5 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a c d e \,f^{2} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+5 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a c d e \,f^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+5 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,d^{2} e^{2} f \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-5 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,d^{2} e^{2} f \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+\sqrt{-\frac{d}{c}}\, b \,c^{2} e \,f^{2} x -2 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b \,c^{2} e \,f^{2} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b \,c^{2} e \,f^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+\sqrt{-\frac{d}{c}}\, b c d \,e^{2} f x +2 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b c d \,e^{2} f \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-3 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b c d \,e^{2} f \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-2 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b \,d^{2} e^{3} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+2 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b \,d^{2} e^{3} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)\right)}{15 \left(d f \,x^{4}+c f \,x^{2}+d e \,x^{2}+c e \right) \sqrt{-\frac{d}{c}}\, d \,f^{2}}"," ",0,"1/15*(d*x^2+c)^(1/2)*(f*x^2+e)^(1/2)*(3*(-1/c*d)^(1/2)*x^7*b*d^2*f^3+5*(-1/c*d)^(1/2)*x^5*a*d^2*f^3+4*(-1/c*d)^(1/2)*x^5*b*c*d*f^3+4*(-1/c*d)^(1/2)*x^5*b*d^2*e*f^2+5*(-1/c*d)^(1/2)*x^3*a*c*d*f^3+5*(-1/c*d)^(1/2)*x^3*a*d^2*e*f^2+(-1/c*d)^(1/2)*x^3*b*c^2*f^3+5*(-1/c*d)^(1/2)*x^3*b*c*d*e*f^2+(-1/c*d)^(1/2)*x^3*b*d^2*e^2*f+5*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*c*d*e*f^2-5*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*d^2*e^2*f+((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c^2*e*f^2-3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c*d*e^2*f+2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*d^2*e^3+5*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*c*d*e*f^2+5*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*d^2*e^2*f-2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c^2*e*f^2+2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c*d*e^2*f-2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*d^2*e^3+5*(-1/c*d)^(1/2)*x*a*c*d*e*f^2+(-1/c*d)^(1/2)*x*b*c^2*e*f^2+(-1/c*d)^(1/2)*x*b*c*d*e^2*f)/(d*f*x^4+c*f*x^2+d*e*x^2+c*e)/d/f^2/(-1/c*d)^(1/2)","B"
25,1,394,317,0.023000," ","int((b*x^2+a)*(f*x^2+e)^(1/2)/(d*x^2+c)^(1/2),x)","\frac{\sqrt{f \,x^{2}+e}\, \sqrt{d \,x^{2}+c}\, \left(\sqrt{-\frac{d}{c}}\, b d \,f^{2} x^{5}+\sqrt{-\frac{d}{c}}\, b c \,f^{2} x^{3}+\sqrt{-\frac{d}{c}}\, b d e f \,x^{3}+3 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a d e f \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+\sqrt{-\frac{d}{c}}\, b c e f x -2 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b c e f \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b c e f \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b d \,e^{2} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b d \,e^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)\right)}{3 \left(d f \,x^{4}+c f \,x^{2}+d e \,x^{2}+c e \right) \sqrt{-\frac{d}{c}}\, d f}"," ",0,"1/3*(f*x^2+e)^(1/2)*(d*x^2+c)^(1/2)*((-1/c*d)^(1/2)*x^5*b*d*f^2+(-1/c*d)^(1/2)*x^3*b*c*f^2+(-1/c*d)^(1/2)*x^3*b*d*e*f+((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c*e*f-((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*d*e^2+3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*d*e*f-2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c*e*f+((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*d*e^2+(-1/c*d)^(1/2)*x*b*c*e*f)/(d*f*x^4+c*f*x^2+d*e*x^2+c*e)/d/(-1/c*d)^(1/2)/f","A"
26,1,328,313,0.043000," ","int((b*x^2+a)*(f*x^2+e)^(1/2)/(d*x^2+c)^(3/2),x)","\frac{\sqrt{f \,x^{2}+e}\, \sqrt{d \,x^{2}+c}\, \left(\sqrt{-\frac{d}{c}}\, a d f \,x^{3}-\sqrt{-\frac{d}{c}}\, b c f \,x^{3}+\sqrt{-\frac{d}{c}}\, a d e x -\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a d e \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a d e \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-\sqrt{-\frac{d}{c}}\, b c e x +2 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b c e \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b c e \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)\right)}{\left(d f \,x^{4}+c f \,x^{2}+d e \,x^{2}+c e \right) \sqrt{-\frac{d}{c}}\, c d}"," ",0,"(f*x^2+e)^(1/2)*(d*x^2+c)^(1/2)*(x^3*a*d*f*(-1/c*d)^(1/2)-x^3*b*c*f*(-1/c*d)^(1/2)+EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*d*e*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c*e*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*d*e*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+2*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c*e*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+x*a*d*e*(-1/c*d)^(1/2)-x*b*c*e*(-1/c*d)^(1/2))/d/(d*f*x^4+c*f*x^2+d*e*x^2+c*e)/c/(-1/c*d)^(1/2)","A"
27,1,1236,314,0.059000," ","int((b*x^2+a)*(f*x^2+e)^(1/2)/(d*x^2+c)^(5/2),x)","\frac{\sqrt{-\frac{d}{c}}\, a c \,d^{2} f^{2} x^{5}-2 \sqrt{-\frac{d}{c}}\, a \,d^{3} e f \,x^{5}+2 \sqrt{-\frac{d}{c}}\, b \,c^{2} d \,f^{2} x^{5}-\sqrt{-\frac{d}{c}}\, b c \,d^{2} e f \,x^{5}+2 \sqrt{-\frac{d}{c}}\, a \,c^{2} d \,f^{2} x^{3}-2 \sqrt{-\frac{d}{c}}\, a c \,d^{2} e f \,x^{3}-\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a c \,d^{2} e f \,x^{2} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+2 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a c \,d^{2} e f \,x^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-2 \sqrt{-\frac{d}{c}}\, a \,d^{3} e^{2} x^{3}+2 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,d^{3} e^{2} x^{2} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-2 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,d^{3} e^{2} x^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+\sqrt{-\frac{d}{c}}\, b \,c^{3} f^{2} x^{3}+2 \sqrt{-\frac{d}{c}}\, b \,c^{2} d e f \,x^{3}-2 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b \,c^{2} d e f \,x^{2} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b \,c^{2} d e f \,x^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-\sqrt{-\frac{d}{c}}\, b c \,d^{2} e^{2} x^{3}+\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b c \,d^{2} e^{2} x^{2} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b c \,d^{2} e^{2} x^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+2 \sqrt{-\frac{d}{c}}\, a \,c^{2} d e f x -\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,c^{2} d e f \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+2 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,c^{2} d e f \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-3 \sqrt{-\frac{d}{c}}\, a c \,d^{2} e^{2} x +2 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a c \,d^{2} e^{2} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-2 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a c \,d^{2} e^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+\sqrt{-\frac{d}{c}}\, b \,c^{3} e f x -2 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b \,c^{3} e f \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b \,c^{3} e f \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b \,c^{2} d \,e^{2} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b \,c^{2} d \,e^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)}{3 \sqrt{f \,x^{2}+e}\, \sqrt{-\frac{d}{c}}\, \left(c f -d e \right) \left(d \,x^{2}+c \right)^{\frac{3}{2}} c^{2} d}"," ",0,"1/3*(-3*x*a*c*d^2*e^2*(-1/c*d)^(1/2)-EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*b*c*d^2*e^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-2*x^3*a*d^3*e^2*(-1/c*d)^(1/2)+x*b*c^3*e*f*(-1/c*d)^(1/2)+x^5*a*c*d^2*f^2*(-1/c*d)^(1/2)-2*x^5*a*d^3*e*f*(-1/c*d)^(1/2)+2*x^5*b*c^2*d*f^2*(-1/c*d)^(1/2)+2*x^3*a*c^2*d*f^2*(-1/c*d)^(1/2)-x^3*b*c*d^2*e^2*(-1/c*d)^(1/2)+x^3*b*c^3*f^2*(-1/c*d)^(1/2)+EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*b*c*d^2*e^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-x^5*b*c*d^2*e*f*(-1/c*d)^(1/2)-2*x^3*a*c*d^2*e*f*(-1/c*d)^(1/2)+2*x^3*b*c^2*d*e*f*(-1/c*d)^(1/2)+2*x*a*c^2*d*e*f*(-1/c*d)^(1/2)-2*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a*d^3*e^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+2*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a*d^3*e^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-2*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*c*d^2*e^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c^3*e*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c^2*d*e^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+2*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*c*d^2*e^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-2*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c^3*e*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c^2*d*e^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+2*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*c^2*d*e*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*c^2*d*e*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+2*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a*c*d^2*e*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*b*c^2*d*e*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a*c*d^2*e*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-2*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*b*c^2*d*e*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2))/(f*x^2+e)^(1/2)/(-1/c*d)^(1/2)/(c*f-d*e)/c^2/d/(d*x^2+c)^(3/2)","B"
28,1,2856,419,0.067000," ","int((b*x^2+a)*(f*x^2+e)^(1/2)/(d*x^2+c)^(7/2),x)","\text{output too large to display}"," ",0,"1/15*(x^3*b*c^5*f^3*(-1/c*d)^(1/2)+9*x^3*a*c^4*d*f^3*(-1/c*d)^(1/2)+8*x^5*a*d^5*e^3*(-1/c*d)^(1/2)+20*x^3*a*c*d^4*e^3*(-1/c*d)^(1/2)+5*x^3*b*c^2*d^3*e^3*(-1/c*d)^(1/2)+15*x*a*c^2*d^3*e^3*(-1/c*d)^(1/2)+x*b*c^5*e*f^2*(-1/c*d)^(1/2)+3*x^7*a*c^2*d^3*f^3*(-1/c*d)^(1/2)+8*x^7*a*d^5*e^2*f*(-1/c*d)^(1/2)+2*x^7*b*c^3*d^2*f^3*(-1/c*d)^(1/2)+9*x^5*a*c^3*d^2*f^3*(-1/c*d)^(1/2)+6*x^5*b*c^4*d*f^3*(-1/c*d)^(1/2)+2*x^5*b*c*d^4*e^3*(-1/c*d)^(1/2)+13*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^4*a*c*d^4*e^2*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-2*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^4*b*c^3*d^2*e*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+2*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^4*b*c^2*d^3*e^2*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+18*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a*c^3*d^2*e*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-34*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a*c^2*d^3*e^2*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-8*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^4*a*d^5*e^3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+8*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*c^2*d^3*e^3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c^5*e*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+2*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c^3*d^2*e^3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-8*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*c^2*d^3*e^3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-2*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c^5*e*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+2*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*b*c^4*d*e*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-6*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*b*c^3*d^2*e^2*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-2*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c^3*d^2*e^3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-13*x^7*a*c*d^4*e*f^2*(-1/c*d)^(1/2)-2*x^7*b*c^2*d^3*e*f^2*(-1/c*d)^(1/2)+2*x^7*b*c*d^4*e^2*f*(-1/c*d)^(1/2)-30*x^5*a*c^2*d^3*e*f^2*(-1/c*d)^(1/2)+7*x^5*a*c*d^4*e^2*f*(-1/c*d)^(1/2)-5*x^5*b*c^3*d^2*e*f^2*(-1/c*d)^(1/2)+3*x^5*b*c^2*d^3*e^2*f*(-1/c*d)^(1/2)-17*x^3*a*c^3*d^2*e*f^2*(-1/c*d)^(1/2)-18*x^3*a*c^2*d^3*e^2*f*(-1/c*d)^(1/2)+7*x^3*b*c^4*d*e*f^2*(-1/c*d)^(1/2)-7*x^3*b*c^3*d^2*e^2*f*(-1/c*d)^(1/2)+9*x*a*c^4*d*e*f^2*(-1/c*d)^(1/2)-26*x*a*c^3*d^2*e^2*f*(-1/c*d)^(1/2)+x*b*c^4*d*e^2*f*(-1/c*d)^(1/2)+8*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^4*a*d^5*e^3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-6*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a*c^3*d^2*e*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+26*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a*c^2*d^3*e^2*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-4*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*b*c^4*d*e*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+4*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*b*c^3*d^2*e^2*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+9*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^4*a*c^2*d^3*e*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-17*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^4*a*c*d^4*e^2*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^4*b*c^3*d^2*e*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-3*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^4*b*c^2*d^3*e^2*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-3*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^4*a*c^2*d^3*e*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-16*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a*c*d^4*e^3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-2*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^4*b*c*d^4*e^3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+16*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a*c*d^4*e^3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+4*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*b*c^2*d^3*e^3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-4*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*b*c^2*d^3*e^3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+9*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*c^4*d*e*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-17*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*c^3*d^2*e^2*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-3*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c^4*d*e^2*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-3*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*c^4*d*e*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+13*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*c^3*d^2*e^2*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+2*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c^4*d*e^2*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+2*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^4*b*c*d^4*e^3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2))/(f*x^2+e)^(1/2)/(-1/c*d)^(1/2)/(c*f-d*e)^2/c^3/d/(d*x^2+c)^(5/2)","B"
29,1,1331,565,0.025000," ","int((b*x^2+a)*(d*x^2+c)^(1/2)*(f*x^2+e)^(3/2),x)","-\frac{\sqrt{d \,x^{2}+c}\, \sqrt{f \,x^{2}+e}\, \left(-15 \sqrt{-\frac{d}{c}}\, b \,d^{3} f^{4} x^{9}-21 \sqrt{-\frac{d}{c}}\, a \,d^{3} f^{4} x^{7}-18 \sqrt{-\frac{d}{c}}\, b c \,d^{2} f^{4} x^{7}-39 \sqrt{-\frac{d}{c}}\, b \,d^{3} e \,f^{3} x^{7}-28 \sqrt{-\frac{d}{c}}\, a c \,d^{2} f^{4} x^{5}-63 \sqrt{-\frac{d}{c}}\, a \,d^{3} e \,f^{3} x^{5}+\sqrt{-\frac{d}{c}}\, b \,c^{2} d \,f^{4} x^{5}-51 \sqrt{-\frac{d}{c}}\, b c \,d^{2} e \,f^{3} x^{5}-27 \sqrt{-\frac{d}{c}}\, b \,d^{3} e^{2} f^{2} x^{5}-7 \sqrt{-\frac{d}{c}}\, a \,c^{2} d \,f^{4} x^{3}-70 \sqrt{-\frac{d}{c}}\, a c \,d^{2} e \,f^{3} x^{3}-42 \sqrt{-\frac{d}{c}}\, a \,d^{3} e^{2} f^{2} x^{3}+4 \sqrt{-\frac{d}{c}}\, b \,c^{3} f^{4} x^{3}-8 \sqrt{-\frac{d}{c}}\, b \,c^{2} d e \,f^{3} x^{3}-36 \sqrt{-\frac{d}{c}}\, b c \,d^{2} e^{2} f^{2} x^{3}-3 \sqrt{-\frac{d}{c}}\, b \,d^{3} e^{3} f \,x^{3}-7 \sqrt{-\frac{d}{c}}\, a \,c^{2} d e \,f^{3} x +14 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,c^{2} d e \,f^{3} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-7 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,c^{2} d e \,f^{3} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-42 \sqrt{-\frac{d}{c}}\, a c \,d^{2} e^{2} f^{2} x -49 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a c \,d^{2} e^{2} f^{2} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-14 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a c \,d^{2} e^{2} f^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-21 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,d^{3} e^{3} f \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+21 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,d^{3} e^{3} f \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+4 \sqrt{-\frac{d}{c}}\, b \,c^{3} e \,f^{3} x -8 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b \,c^{3} e \,f^{3} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+4 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b \,c^{3} e \,f^{3} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-9 \sqrt{-\frac{d}{c}}\, b \,c^{2} d \,e^{2} f^{2} x +19 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b \,c^{2} d \,e^{2} f^{2} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-10 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b \,c^{2} d \,e^{2} f^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-3 \sqrt{-\frac{d}{c}}\, b c \,d^{2} e^{3} f x -9 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b c \,d^{2} e^{3} f \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+12 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b c \,d^{2} e^{3} f \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+6 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b \,d^{3} e^{4} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-6 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b \,d^{3} e^{4} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)\right)}{105 \left(d f \,x^{4}+c f \,x^{2}+d e \,x^{2}+c e \right) \sqrt{-\frac{d}{c}}\, d^{2} f^{2}}"," ",0,"-1/105*(d*x^2+c)^(1/2)*(f*x^2+e)^(1/2)*(-3*(-1/c*d)^(1/2)*b*d^3*e^3*f*x^3-15*(-1/c*d)^(1/2)*b*d^3*f^4*x^9+4*(-1/c*d)^(1/2)*b*c^3*e*f^3*x-18*(-1/c*d)^(1/2)*b*c*d^2*f^4*x^7-39*(-1/c*d)^(1/2)*b*d^3*e*f^3*x^7-28*(-1/c*d)^(1/2)*a*c*d^2*f^4*x^5-63*(-1/c*d)^(1/2)*a*d^3*e*f^3*x^5+(-1/c*d)^(1/2)*b*c^2*d*f^4*x^5-27*(-1/c*d)^(1/2)*b*d^3*e^2*f^2*x^5-7*(-1/c*d)^(1/2)*a*c^2*d*f^4*x^3-42*(-1/c*d)^(1/2)*a*d^3*e^2*f^2*x^3-6*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*d^3*e^4+6*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*d^3*e^4+14*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*c^2*d*e*f^3-7*(-1/c*d)^(1/2)*a*c^2*d*e*f^3*x-42*(-1/c*d)^(1/2)*a*c*d^2*e^2*f^2*x-9*(-1/c*d)^(1/2)*b*c^2*d*e^2*f^2*x-3*(-1/c*d)^(1/2)*b*c*d^2*e^3*f*x+21*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*d^3*e^3*f+4*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c^3*e*f^3-21*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*d^3*e^3*f-8*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c^3*e*f^3-49*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*c*d^2*e^2*f^2+19*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c^2*d*e^2*f^2-9*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c*d^2*e^3*f-7*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*c^2*d*e*f^3-14*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*c*d^2*e^2*f^2-10*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c^2*d*e^2*f^2+12*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c*d^2*e^3*f-21*(-1/c*d)^(1/2)*a*d^3*f^4*x^7+4*(-1/c*d)^(1/2)*b*c^3*f^4*x^3-51*(-1/c*d)^(1/2)*b*c*d^2*e*f^3*x^5-70*(-1/c*d)^(1/2)*a*c*d^2*e*f^3*x^3-8*(-1/c*d)^(1/2)*b*c^2*d*e*f^3*x^3-36*(-1/c*d)^(1/2)*b*c*d^2*e^2*f^2*x^3)/f^2/(d*f*x^4+c*f*x^2+d*e*x^2+c*e)/d^2/(-1/c*d)^(1/2)","B"
30,1,870,428,0.024000," ","int((b*x^2+a)*(f*x^2+e)^(3/2)/(d*x^2+c)^(1/2),x)","\frac{\sqrt{f \,x^{2}+e}\, \sqrt{d \,x^{2}+c}\, \left(3 \sqrt{-\frac{d}{c}}\, b \,d^{2} f^{3} x^{7}+5 \sqrt{-\frac{d}{c}}\, a \,d^{2} f^{3} x^{5}-\sqrt{-\frac{d}{c}}\, b c d \,f^{3} x^{5}+9 \sqrt{-\frac{d}{c}}\, b \,d^{2} e \,f^{2} x^{5}+5 \sqrt{-\frac{d}{c}}\, a c d \,f^{3} x^{3}+5 \sqrt{-\frac{d}{c}}\, a \,d^{2} e \,f^{2} x^{3}-4 \sqrt{-\frac{d}{c}}\, b \,c^{2} f^{3} x^{3}+5 \sqrt{-\frac{d}{c}}\, b c d e \,f^{2} x^{3}+6 \sqrt{-\frac{d}{c}}\, b \,d^{2} e^{2} f \,x^{3}+5 \sqrt{-\frac{d}{c}}\, a c d e \,f^{2} x -10 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a c d e \,f^{2} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+5 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a c d e \,f^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+20 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,d^{2} e^{2} f \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-5 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,d^{2} e^{2} f \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-4 \sqrt{-\frac{d}{c}}\, b \,c^{2} e \,f^{2} x +8 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b \,c^{2} e \,f^{2} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-4 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b \,c^{2} e \,f^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+6 \sqrt{-\frac{d}{c}}\, b c d \,e^{2} f x -13 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b c d \,e^{2} f \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+7 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b c d \,e^{2} f \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+3 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b \,d^{2} e^{3} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-3 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b \,d^{2} e^{3} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)\right)}{15 \left(d f \,x^{4}+c f \,x^{2}+d e \,x^{2}+c e \right) \sqrt{-\frac{d}{c}}\, d^{2} f}"," ",0,"1/15*(f*x^2+e)^(1/2)*(d*x^2+c)^(1/2)*(3*(-1/c*d)^(1/2)*b*d^2*f^3*x^7+5*(-1/c*d)^(1/2)*a*d^2*f^3*x^5-(-1/c*d)^(1/2)*b*c*d*f^3*x^5+9*(-1/c*d)^(1/2)*b*d^2*e*f^2*x^5+5*(-1/c*d)^(1/2)*a*c*d*f^3*x^3+5*(-1/c*d)^(1/2)*a*d^2*e*f^2*x^3-4*(-1/c*d)^(1/2)*b*c^2*f^3*x^3+5*(-1/c*d)^(1/2)*b*c*d*e*f^2*x^3+6*(-1/c*d)^(1/2)*b*d^2*e^2*f*x^3+5*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*c*d*e*f^2-5*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*d^2*e^2*f-4*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c^2*e*f^2+7*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c*d*e^2*f-3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*d^2*e^3-10*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*c*d*e*f^2+20*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*d^2*e^2*f+8*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c^2*e*f^2-13*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c*d*e^2*f+3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*d^2*e^3+5*(-1/c*d)^(1/2)*a*c*d*e*f^2*x-4*(-1/c*d)^(1/2)*b*c^2*e*f^2*x+6*(-1/c*d)^(1/2)*b*c*d*e^2*f*x)/d^2/f/(d*f*x^4+c*f*x^2+d*e*x^2+c*e)/(-1/c*d)^(1/2)","B"
31,1,671,399,0.031000," ","int((b*x^2+a)*(f*x^2+e)^(3/2)/(d*x^2+c)^(3/2),x)","-\frac{\sqrt{f \,x^{2}+e}\, \sqrt{d \,x^{2}+c}\, \left(-\sqrt{-\frac{d}{c}}\, b c d \,f^{2} x^{5}+3 \sqrt{-\frac{d}{c}}\, a c d \,f^{2} x^{3}-3 \sqrt{-\frac{d}{c}}\, a \,d^{2} e f \,x^{3}-4 \sqrt{-\frac{d}{c}}\, b \,c^{2} f^{2} x^{3}+2 \sqrt{-\frac{d}{c}}\, b c d e f \,x^{3}+3 \sqrt{-\frac{d}{c}}\, a c d e f x -6 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a c d e f \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+3 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a c d e f \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-3 \sqrt{-\frac{d}{c}}\, a \,d^{2} e^{2} x +3 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,d^{2} e^{2} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-3 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,d^{2} e^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-4 \sqrt{-\frac{d}{c}}\, b \,c^{2} e f x +8 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b \,c^{2} e f \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-4 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b \,c^{2} e f \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+3 \sqrt{-\frac{d}{c}}\, b c d \,e^{2} x -7 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b c d \,e^{2} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+4 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b c d \,e^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)\right)}{3 \left(d f \,x^{4}+c f \,x^{2}+d e \,x^{2}+c e \right) \sqrt{-\frac{d}{c}}\, c \,d^{2}}"," ",0,"-1/3*(f*x^2+e)^(1/2)*(d*x^2+c)^(1/2)*(-x^5*b*c*d*f^2*(-1/c*d)^(1/2)+3*x^3*a*c*d*f^2*(-1/c*d)^(1/2)-3*x^3*a*d^2*e*f*(-1/c*d)^(1/2)-4*x^3*b*c^2*f^2*(-1/c*d)^(1/2)+2*x^3*b*c*d*e*f*(-1/c*d)^(1/2)+3*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*c*d*e*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-3*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*d^2*e^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-4*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c^2*e*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+4*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c*d*e^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-6*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*c*d*e*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+3*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*d^2*e^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+8*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c^2*e*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-7*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c*d*e^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+3*x*a*c*d*e*f*(-1/c*d)^(1/2)-3*x*a*d^2*e^2*(-1/c*d)^(1/2)-4*x*b*c^2*e*f*(-1/c*d)^(1/2)+3*x*b*c*d*e^2*(-1/c*d)^(1/2))/d^2/(d*f*x^4+c*f*x^2+d*e*x^2+c*e)/(-1/c*d)^(1/2)/c","A"
32,1,1231,401,0.034000," ","int((b*x^2+a)*(f*x^2+e)^(3/2)/(d*x^2+c)^(5/2),x)","-\frac{-2 \sqrt{-\frac{d}{c}}\, a c \,d^{2} f^{2} x^{5}-2 \sqrt{-\frac{d}{c}}\, a \,d^{3} e f \,x^{5}+5 \sqrt{-\frac{d}{c}}\, b \,c^{2} d \,f^{2} x^{5}-\sqrt{-\frac{d}{c}}\, b c \,d^{2} e f \,x^{5}-\sqrt{-\frac{d}{c}}\, a \,c^{2} d \,f^{2} x^{3}-5 \sqrt{-\frac{d}{c}}\, a c \,d^{2} e f \,x^{3}+2 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a c \,d^{2} e f \,x^{2} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a c \,d^{2} e f \,x^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-2 \sqrt{-\frac{d}{c}}\, a \,d^{3} e^{2} x^{3}+2 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,d^{3} e^{2} x^{2} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-2 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,d^{3} e^{2} x^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+4 \sqrt{-\frac{d}{c}}\, b \,c^{3} f^{2} x^{3}+5 \sqrt{-\frac{d}{c}}\, b \,c^{2} d e f \,x^{3}-8 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b \,c^{2} d e f \,x^{2} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+4 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b \,c^{2} d e f \,x^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-\sqrt{-\frac{d}{c}}\, b c \,d^{2} e^{2} x^{3}+\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b c \,d^{2} e^{2} x^{2} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b c \,d^{2} e^{2} x^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-\sqrt{-\frac{d}{c}}\, a \,c^{2} d e f x +2 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,c^{2} d e f \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,c^{2} d e f \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-3 \sqrt{-\frac{d}{c}}\, a c \,d^{2} e^{2} x +2 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a c \,d^{2} e^{2} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-2 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a c \,d^{2} e^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+4 \sqrt{-\frac{d}{c}}\, b \,c^{3} e f x -8 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b \,c^{3} e f \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+4 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b \,c^{3} e f \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b \,c^{2} d \,e^{2} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b \,c^{2} d \,e^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)}{3 \sqrt{f \,x^{2}+e}\, \sqrt{-\frac{d}{c}}\, \left(d \,x^{2}+c \right)^{\frac{3}{2}} c^{2} d^{2}}"," ",0,"-1/3*(-3*(-1/c*d)^(1/2)*a*c*d^2*e^2*x-EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*b*c*d^2*e^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-2*(-1/c*d)^(1/2)*a*d^3*e^2*x^3+4*(-1/c*d)^(1/2)*b*c^3*e*f*x-2*(-1/c*d)^(1/2)*a*c*d^2*f^2*x^5-2*(-1/c*d)^(1/2)*a*d^3*e*f*x^5+5*(-1/c*d)^(1/2)*b*c^2*d*f^2*x^5-(-1/c*d)^(1/2)*a*c^2*d*f^2*x^3-(-1/c*d)^(1/2)*b*c*d^2*e^2*x^3+4*(-1/c*d)^(1/2)*b*c^3*f^2*x^3+EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*b*c*d^2*e^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-(-1/c*d)^(1/2)*b*c*d^2*e*f*x^5-5*(-1/c*d)^(1/2)*a*c*d^2*e*f*x^3+5*(-1/c*d)^(1/2)*b*c^2*d*e*f*x^3-(-1/c*d)^(1/2)*a*c^2*d*e*f*x-2*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a*d^3*e^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+2*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a*d^3*e^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-2*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*c*d^2*e^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+4*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c^3*e*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c^2*d*e^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+2*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*c*d^2*e^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-8*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c^3*e*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c^2*d*e^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*c^2*d*e*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+2*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*c^2*d*e*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a*c*d^2*e*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+4*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*b*c^2*d*e*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+2*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a*c*d^2*e*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-8*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*b*c^2*d*e*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2))/(f*x^2+e)^(1/2)/c^2/(-1/c*d)^(1/2)/(d*x^2+c)^(3/2)/d^2","B"
33,1,2860,410,0.042000," ","int((b*x^2+a)*(f*x^2+e)^(3/2)/(d*x^2+c)^(7/2),x)","\text{output too large to display}"," ",0,"-1/15*(-4*x^3*b*c^5*f^3*(-1/c*d)^(1/2)-x^3*a*c^4*d*f^3*(-1/c*d)^(1/2)+8*x^5*a*d^5*e^3*(-1/c*d)^(1/2)+20*x^3*a*c*d^4*e^3*(-1/c*d)^(1/2)+5*x^3*b*c^2*d^3*e^3*(-1/c*d)^(1/2)+15*x*a*c^2*d^3*e^3*(-1/c*d)^(1/2)-4*x*b*c^5*e*f^2*(-1/c*d)^(1/2)-2*x^7*a*c^2*d^3*f^3*(-1/c*d)^(1/2)+8*x^7*a*d^5*e^2*f*(-1/c*d)^(1/2)-8*x^7*b*c^3*d^2*f^3*(-1/c*d)^(1/2)-6*x^5*a*c^3*d^2*f^3*(-1/c*d)^(1/2)-9*x^5*b*c^4*d*f^3*(-1/c*d)^(1/2)+2*x^5*b*c*d^4*e^3*(-1/c*d)^(1/2)+3*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^4*a*c*d^4*e^2*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+8*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^4*b*c^3*d^2*e*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-3*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^4*b*c^2*d^3*e^2*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-2*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a*c^3*d^2*e*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-14*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a*c^2*d^3*e^2*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-8*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^4*a*d^5*e^3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+8*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*c^2*d^3*e^3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-4*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c^5*e*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+2*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c^3*d^2*e^3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-8*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*c^2*d^3*e^3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+8*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c^5*e*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-8*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*b*c^4*d*e*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+4*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*b*c^3*d^2*e^2*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-2*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c^3*d^2*e^3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-3*x^7*a*c*d^4*e*f^2*(-1/c*d)^(1/2)+3*x^7*b*c^2*d^3*e*f^2*(-1/c*d)^(1/2)+2*x^7*b*c*d^4*e^2*f*(-1/c*d)^(1/2)-10*x^5*a*c^2*d^3*e*f^2*(-1/c*d)^(1/2)+17*x^5*a*c*d^4*e^2*f*(-1/c*d)^(1/2)-10*x^5*b*c^3*d^2*e*f^2*(-1/c*d)^(1/2)+8*x^5*b*c^2*d^3*e^2*f*(-1/c*d)^(1/2)-17*x^3*a*c^3*d^2*e*f^2*(-1/c*d)^(1/2)+7*x^3*a*c^2*d^3*e^2*f*(-1/c*d)^(1/2)-8*x^3*b*c^4*d*e*f^2*(-1/c*d)^(1/2)-2*x^3*b*c^3*d^2*e^2*f*(-1/c*d)^(1/2)-x*a*c^4*d*e*f^2*(-1/c*d)^(1/2)-11*x*a*c^3*d^2*e^2*f*(-1/c*d)^(1/2)+x*b*c^4*d*e^2*f*(-1/c*d)^(1/2)+8*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^4*a*d^5*e^3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+4*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a*c^3*d^2*e*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+6*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a*c^2*d^3*e^2*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+16*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*b*c^4*d*e*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-6*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*b*c^3*d^2*e^2*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^4*a*c^2*d^3*e*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-7*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^4*a*c*d^4*e^2*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-4*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^4*b*c^3*d^2*e*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+2*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^4*b*c^2*d^3*e^2*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+2*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^4*a*c^2*d^3*e*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-16*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a*c*d^4*e^3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-2*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^4*b*c*d^4*e^3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+16*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a*c*d^4*e^3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+4*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*b*c^2*d^3*e^3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-4*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*b*c^2*d^3*e^3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*c^4*d*e*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-7*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*c^3*d^2*e^2*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+2*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c^4*d*e^2*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+2*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*c^4*d*e*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+3*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*c^3*d^2*e^2*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-3*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c^4*d*e^2*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+2*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^4*b*c*d^4*e^3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2))/(f*x^2+e)^(1/2)/c^3/(c*f-d*e)/(-1/c*d)^(1/2)/(d*x^2+c)^(5/2)/d^2","B"
34,1,5113,559,0.078000," ","int((b*x^2+a)*(f*x^2+e)^(3/2)/(d*x^2+c)^(9/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
35,1,1386,573,0.028000," ","int((b*x^2+a)*(d*x^2+c)^(5/2)/(f*x^2+e)^(1/2),x)","\frac{\sqrt{d \,x^{2}+c}\, \sqrt{f \,x^{2}+e}\, \left(15 \sqrt{-\frac{d}{c}}\, b \,d^{3} f^{4} x^{9}+21 \sqrt{-\frac{d}{c}}\, a \,d^{3} f^{4} x^{7}+60 \sqrt{-\frac{d}{c}}\, b c \,d^{2} f^{4} x^{7}-3 \sqrt{-\frac{d}{c}}\, b \,d^{3} e \,f^{3} x^{7}+98 \sqrt{-\frac{d}{c}}\, a c \,d^{2} f^{4} x^{5}-7 \sqrt{-\frac{d}{c}}\, a \,d^{3} e \,f^{3} x^{5}+90 \sqrt{-\frac{d}{c}}\, b \,c^{2} d \,f^{4} x^{5}-19 \sqrt{-\frac{d}{c}}\, b c \,d^{2} e \,f^{3} x^{5}+6 \sqrt{-\frac{d}{c}}\, b \,d^{3} e^{2} f^{2} x^{5}+77 \sqrt{-\frac{d}{c}}\, a \,c^{2} d \,f^{4} x^{3}+70 \sqrt{-\frac{d}{c}}\, a c \,d^{2} e \,f^{3} x^{3}-28 \sqrt{-\frac{d}{c}}\, a \,d^{3} e^{2} f^{2} x^{3}+45 \sqrt{-\frac{d}{c}}\, b \,c^{3} f^{4} x^{3}+29 \sqrt{-\frac{d}{c}}\, b \,c^{2} d e \,f^{3} x^{3}-55 \sqrt{-\frac{d}{c}}\, b c \,d^{2} e^{2} f^{2} x^{3}+24 \sqrt{-\frac{d}{c}}\, b \,d^{3} e^{3} f \,x^{3}+105 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,c^{3} f^{4} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+77 \sqrt{-\frac{d}{c}}\, a \,c^{2} d e \,f^{3} x +161 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,c^{2} d e \,f^{3} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-238 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,c^{2} d e \,f^{3} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-28 \sqrt{-\frac{d}{c}}\, a c \,d^{2} e^{2} f^{2} x -161 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a c \,d^{2} e^{2} f^{2} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+189 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a c \,d^{2} e^{2} f^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+56 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,d^{3} e^{3} f \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-56 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,d^{3} e^{3} f \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+45 \sqrt{-\frac{d}{c}}\, b \,c^{3} e \,f^{3} x +15 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b \,c^{3} e \,f^{3} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-60 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b \,c^{3} e \,f^{3} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-61 \sqrt{-\frac{d}{c}}\, b \,c^{2} d \,e^{2} f^{2} x -103 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b \,c^{2} d \,e^{2} f^{2} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+164 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b \,c^{2} d \,e^{2} f^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+24 \sqrt{-\frac{d}{c}}\, b c \,d^{2} e^{3} f x +128 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b c \,d^{2} e^{3} f \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-152 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b c \,d^{2} e^{3} f \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-48 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b \,d^{3} e^{4} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+48 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b \,d^{3} e^{4} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)\right)}{105 \left(d f \,x^{4}+c f \,x^{2}+d e \,x^{2}+c e \right) \sqrt{-\frac{d}{c}}\, f^{4}}"," ",0,"1/105*(d*x^2+c)^(1/2)*(f*x^2+e)^(1/2)*(24*(-1/c*d)^(1/2)*b*d^3*e^3*f*x^3+15*(-1/c*d)^(1/2)*b*d^3*f^4*x^9+105*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*c^3*f^4+45*(-1/c*d)^(1/2)*b*c^3*e*f^3*x+60*(-1/c*d)^(1/2)*b*c*d^2*f^4*x^7-3*(-1/c*d)^(1/2)*b*d^3*e*f^3*x^7+98*(-1/c*d)^(1/2)*a*c*d^2*f^4*x^5-7*(-1/c*d)^(1/2)*a*d^3*e*f^3*x^5+90*(-1/c*d)^(1/2)*b*c^2*d*f^4*x^5+6*(-1/c*d)^(1/2)*b*d^3*e^2*f^2*x^5+77*(-1/c*d)^(1/2)*a*c^2*d*f^4*x^3-28*(-1/c*d)^(1/2)*a*d^3*e^2*f^2*x^3+48*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*d^3*e^4-48*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*d^3*e^4+161*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*c^2*d*e*f^3+77*(-1/c*d)^(1/2)*a*c^2*d*e*f^3*x-28*(-1/c*d)^(1/2)*a*c*d^2*e^2*f^2*x-61*(-1/c*d)^(1/2)*b*c^2*d*e^2*f^2*x+24*(-1/c*d)^(1/2)*b*c*d^2*e^3*f*x-56*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*d^3*e^3*f-60*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c^3*e*f^3+56*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*d^3*e^3*f+15*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c^3*e*f^3-161*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*c*d^2*e^2*f^2-103*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c^2*d*e^2*f^2+128*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c*d^2*e^3*f-238*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*c^2*d*e*f^3+189*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*c*d^2*e^2*f^2+164*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c^2*d*e^2*f^2-152*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c*d^2*e^3*f+21*(-1/c*d)^(1/2)*a*d^3*f^4*x^7+45*(-1/c*d)^(1/2)*b*c^3*f^4*x^3-19*(-1/c*d)^(1/2)*b*c*d^2*e*f^3*x^5+70*(-1/c*d)^(1/2)*a*c*d^2*e*f^3*x^3+29*(-1/c*d)^(1/2)*b*c^2*d*e*f^3*x^3-55*(-1/c*d)^(1/2)*b*c*d^2*e^2*f^2*x^3)/f^4/(d*f*x^4+c*f*x^2+d*e*x^2+c*e)/(-1/c*d)^(1/2)","B"
36,1,924,424,0.023000," ","int((b*x^2+a)*(d*x^2+c)^(3/2)/(f*x^2+e)^(1/2),x)","\frac{\sqrt{d \,x^{2}+c}\, \sqrt{f \,x^{2}+e}\, \left(3 \sqrt{-\frac{d}{c}}\, b \,d^{2} f^{3} x^{7}+5 \sqrt{-\frac{d}{c}}\, a \,d^{2} f^{3} x^{5}+9 \sqrt{-\frac{d}{c}}\, b c d \,f^{3} x^{5}-\sqrt{-\frac{d}{c}}\, b \,d^{2} e \,f^{2} x^{5}+5 \sqrt{-\frac{d}{c}}\, a c d \,f^{3} x^{3}+5 \sqrt{-\frac{d}{c}}\, a \,d^{2} e \,f^{2} x^{3}+6 \sqrt{-\frac{d}{c}}\, b \,c^{2} f^{3} x^{3}+5 \sqrt{-\frac{d}{c}}\, b c d e \,f^{2} x^{3}-4 \sqrt{-\frac{d}{c}}\, b \,d^{2} e^{2} f \,x^{3}+15 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,c^{2} f^{3} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+5 \sqrt{-\frac{d}{c}}\, a c d e \,f^{2} x +20 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a c d e \,f^{2} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-25 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a c d e \,f^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-10 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,d^{2} e^{2} f \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+10 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,d^{2} e^{2} f \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+6 \sqrt{-\frac{d}{c}}\, b \,c^{2} e \,f^{2} x +3 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b \,c^{2} e \,f^{2} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-9 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b \,c^{2} e \,f^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-4 \sqrt{-\frac{d}{c}}\, b c d \,e^{2} f x -13 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b c d \,e^{2} f \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+17 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b c d \,e^{2} f \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+8 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b \,d^{2} e^{3} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-8 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b \,d^{2} e^{3} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)\right)}{15 \left(d f \,x^{4}+c f \,x^{2}+d e \,x^{2}+c e \right) \sqrt{-\frac{d}{c}}\, f^{3}}"," ",0,"1/15*(d*x^2+c)^(1/2)*(f*x^2+e)^(1/2)*(3*(-1/c*d)^(1/2)*b*d^2*f^3*x^7+5*(-1/c*d)^(1/2)*a*d^2*f^3*x^5+9*(-1/c*d)^(1/2)*b*c*d*f^3*x^5-(-1/c*d)^(1/2)*b*d^2*e*f^2*x^5+5*(-1/c*d)^(1/2)*a*c*d*f^3*x^3+5*(-1/c*d)^(1/2)*a*d^2*e*f^2*x^3+6*(-1/c*d)^(1/2)*b*c^2*f^3*x^3+5*(-1/c*d)^(1/2)*b*c*d*e*f^2*x^3-4*(-1/c*d)^(1/2)*b*d^2*e^2*f*x^3+15*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*c^2*f^3-25*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*c*d*e*f^2+10*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*d^2*e^2*f-9*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c^2*e*f^2+17*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c*d*e^2*f-8*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*d^2*e^3+20*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*c*d*e*f^2-10*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*d^2*e^2*f+3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c^2*e*f^2-13*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c*d*e^2*f+8*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*d^2*e^3+5*(-1/c*d)^(1/2)*a*c*d*e*f^2*x+6*(-1/c*d)^(1/2)*b*c^2*e*f^2*x-4*(-1/c*d)^(1/2)*b*c*d*e^2*f*x)/f^3/(d*f*x^4+c*f*x^2+d*e*x^2+c*e)/(-1/c*d)^(1/2)","B"
37,1,501,316,0.017000," ","int((b*x^2+a)*(d*x^2+c)^(1/2)/(f*x^2+e)^(1/2),x)","\frac{\sqrt{d \,x^{2}+c}\, \sqrt{f \,x^{2}+e}\, \left(\sqrt{-\frac{d}{c}}\, b d \,f^{2} x^{5}+\sqrt{-\frac{d}{c}}\, b c \,f^{2} x^{3}+\sqrt{-\frac{d}{c}}\, b d e f \,x^{3}+3 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a c \,f^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+3 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a d e f \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-3 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a d e f \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+\sqrt{-\frac{d}{c}}\, b c e f x +\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b c e f \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-2 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b c e f \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-2 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b d \,e^{2} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+2 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b d \,e^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)\right)}{3 \left(d f \,x^{4}+c f \,x^{2}+d e \,x^{2}+c e \right) \sqrt{-\frac{d}{c}}\, f^{2}}"," ",0,"1/3*(d*x^2+c)^(1/2)*(f*x^2+e)^(1/2)*((-1/c*d)^(1/2)*b*d*f^2*x^5+(-1/c*d)^(1/2)*b*c*f^2*x^3+(-1/c*d)^(1/2)*b*d*e*f*x^3+3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*c*f^2-3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*d*e*f-2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c*e*f+2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*d*e^2+3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*d*e*f+((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c*e*f-2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*d*e^2+(-1/c*d)^(1/2)*b*c*e*f*x)/(d*f*x^4+c*f*x^2+d*e*x^2+c*e)/f^2/(-1/c*d)^(1/2)","A"
38,1,158,252,0.020000," ","int((b*x^2+a)/(d*x^2+c)^(1/2)/(f*x^2+e)^(1/2),x)","\frac{\left(a f \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+b e \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-b e \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)\right) \sqrt{\frac{f \,x^{2}+e}{e}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{d \,x^{2}+c}\, \sqrt{f \,x^{2}+e}}{\sqrt{-\frac{d}{c}}\, \left(d f \,x^{4}+c f \,x^{2}+d e \,x^{2}+c e \right) f}"," ",0,"(EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*f-EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*e+EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*e)*((f*x^2+e)/e)^(1/2)*((d*x^2+c)/c)^(1/2)*(d*x^2+c)^(1/2)*(f*x^2+e)^(1/2)/f/(-1/c*d)^(1/2)/(d*f*x^4+c*f*x^2+d*e*x^2+c*e)","A"
39,1,334,259,0.035000," ","int((b*x^2+a)/(d*x^2+c)^(3/2)/(f*x^2+e)^(1/2),x)","\frac{\left(-\sqrt{-\frac{d}{c}}\, a d f \,x^{3}+\sqrt{-\frac{d}{c}}\, b c f \,x^{3}+\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a c f \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-\sqrt{-\frac{d}{c}}\, a d e x +\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a d e \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a d e \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+\sqrt{-\frac{d}{c}}\, b c e x -\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b c e \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)\right) \sqrt{f \,x^{2}+e}\, \sqrt{d \,x^{2}+c}}{\sqrt{-\frac{d}{c}}\, \left(c f -d e \right) \left(d f \,x^{4}+c f \,x^{2}+d e \,x^{2}+c e \right) c}"," ",0,"(-(-1/c*d)^(1/2)*a*d*f*x^3+(-1/c*d)^(1/2)*b*c*f*x^3+EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*c*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*d*e*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*d*e*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c*e*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-(-1/c*d)^(1/2)*a*d*e*x+(-1/c*d)^(1/2)*b*c*e*x)*(f*x^2+e)^(1/2)*(d*x^2+c)^(1/2)/c/(-1/c*d)^(1/2)/(c*f-d*e)/(d*f*x^4+c*f*x^2+d*e*x^2+c*e)","A"
40,1,1352,324,0.039000," ","int((b*x^2+a)/(d*x^2+c)^(5/2)/(f*x^2+e)^(1/2),x)","\frac{-4 \sqrt{-\frac{d}{c}}\, a c \,d^{2} f^{2} x^{5}+2 \sqrt{-\frac{d}{c}}\, a \,d^{3} e f \,x^{5}+\sqrt{-\frac{d}{c}}\, b \,c^{2} d \,f^{2} x^{5}+\sqrt{-\frac{d}{c}}\, b c \,d^{2} e f \,x^{5}-5 \sqrt{-\frac{d}{c}}\, a \,c^{2} d \,f^{2} x^{3}+3 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,c^{2} d \,f^{2} x^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-\sqrt{-\frac{d}{c}}\, a c \,d^{2} e f \,x^{3}+4 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a c \,d^{2} e f \,x^{2} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-5 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a c \,d^{2} e f \,x^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+2 \sqrt{-\frac{d}{c}}\, a \,d^{3} e^{2} x^{3}-2 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,d^{3} e^{2} x^{2} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+2 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,d^{3} e^{2} x^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+2 \sqrt{-\frac{d}{c}}\, b \,c^{3} f^{2} x^{3}+\sqrt{-\frac{d}{c}}\, b \,c^{2} d e f \,x^{3}-\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b \,c^{2} d e f \,x^{2} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b \,c^{2} d e f \,x^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+\sqrt{-\frac{d}{c}}\, b c \,d^{2} e^{2} x^{3}-\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b c \,d^{2} e^{2} x^{2} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b c \,d^{2} e^{2} x^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+3 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,c^{3} f^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-5 \sqrt{-\frac{d}{c}}\, a \,c^{2} d e f x +4 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,c^{2} d e f \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-5 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,c^{2} d e f \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+3 \sqrt{-\frac{d}{c}}\, a c \,d^{2} e^{2} x -2 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a c \,d^{2} e^{2} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+2 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a c \,d^{2} e^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+2 \sqrt{-\frac{d}{c}}\, b \,c^{3} e f x -\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b \,c^{3} e f \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b \,c^{3} e f \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b \,c^{2} d \,e^{2} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b \,c^{2} d \,e^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)}{3 \sqrt{f \,x^{2}+e}\, \left(c f -d e \right)^{2} \sqrt{-\frac{d}{c}}\, \left(d \,x^{2}+c \right)^{\frac{3}{2}} c^{2}}"," ",0,"1/3*(3*(-1/c*d)^(1/2)*a*c*d^2*e^2*x+EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*b*c*d^2*e^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+2*(-1/c*d)^(1/2)*a*d^3*e^2*x^3+2*(-1/c*d)^(1/2)*b*c^3*e*f*x-4*(-1/c*d)^(1/2)*a*c*d^2*f^2*x^5+2*(-1/c*d)^(1/2)*a*d^3*e*f*x^5+(-1/c*d)^(1/2)*b*c^2*d*f^2*x^5-5*(-1/c*d)^(1/2)*a*c^2*d*f^2*x^3+(-1/c*d)^(1/2)*b*c*d^2*e^2*x^3+3*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*c^3*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+2*(-1/c*d)^(1/2)*b*c^3*f^2*x^3+3*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a*c^2*d*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*b*c*d^2*e^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+(-1/c*d)^(1/2)*b*c*d^2*e*f*x^5-(-1/c*d)^(1/2)*a*c*d^2*e*f*x^3+(-1/c*d)^(1/2)*b*c^2*d*e*f*x^3-5*(-1/c*d)^(1/2)*a*c^2*d*e*f*x+2*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a*d^3*e^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-2*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a*d^3*e^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+2*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*c*d^2*e^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c^3*e*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c^2*d*e^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-2*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*c*d^2*e^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c^3*e*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c^2*d*e^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-5*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*c^2*d*e*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+4*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*c^2*d*e*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-5*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a*c*d^2*e*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*b*c^2*d*e*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+4*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a*c*d^2*e*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*b*c^2*d*e*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2))/(f*x^2+e)^(1/2)/(c*f-d*e)^2/c^2/(-1/c*d)^(1/2)/(d*x^2+c)^(3/2)","B"
41,1,3039,435,0.052000," ","int((b*x^2+a)/(d*x^2+c)^(7/2)/(f*x^2+e)^(1/2),x)","\text{output too large to display}"," ",0,"1/15*(9*x^3*b*c^5*f^3*(-1/c*d)^(1/2)-34*x^3*a*c^4*d*f^3*(-1/c*d)^(1/2)-8*x^5*a*d^5*e^3*(-1/c*d)^(1/2)-20*x^3*a*c*d^4*e^3*(-1/c*d)^(1/2)-5*x^3*b*c^2*d^3*e^3*(-1/c*d)^(1/2)-15*x*a*c^2*d^3*e^3*(-1/c*d)^(1/2)+9*x*b*c^5*e*f^2*(-1/c*d)^(1/2)-23*x^7*a*c^2*d^3*f^3*(-1/c*d)^(1/2)-8*x^7*a*d^5*e^2*f*(-1/c*d)^(1/2)+3*x^7*b*c^3*d^2*f^3*(-1/c*d)^(1/2)-54*x^5*a*c^3*d^2*f^3*(-1/c*d)^(1/2)+9*x^5*b*c^4*d*f^3*(-1/c*d)^(1/2)-2*x^5*b*c*d^4*e^3*(-1/c*d)^(1/2)+15*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*c^5*f^3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-23*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^4*a*c*d^4*e^2*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-3*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^4*b*c^3*d^2*e*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-7*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^4*b*c^2*d^3*e^2*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-68*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a*c^3*d^2*e*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+54*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a*c^2*d^3*e^2*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+8*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^4*a*d^5*e^3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-8*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*c^2*d^3*e^3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-6*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c^5*e*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-2*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c^3*d^2*e^3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+8*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*c^2*d^3*e^3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-3*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c^5*e*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-12*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*b*c^4*d*e*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+16*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*b*c^3*d^2*e^2*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+2*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c^3*d^2*e^3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+23*x^7*a*c*d^4*e*f^2*(-1/c*d)^(1/2)+7*x^7*b*c^2*d^3*e*f^2*(-1/c*d)^(1/2)-2*x^7*b*c*d^4*e^2*f*(-1/c*d)^(1/2)+35*x^5*a*c^2*d^3*e*f^2*(-1/c*d)^(1/2)+3*x^5*a*c*d^4*e^2*f*(-1/c*d)^(1/2)+15*x^5*b*c^3*d^2*e*f^2*(-1/c*d)^(1/2)+2*x^5*b*c^2*d^3*e^2*f*(-1/c*d)^(1/2)-13*x^3*a*c^3*d^2*e*f^2*(-1/c*d)^(1/2)+43*x^3*a*c^2*d^3*e^2*f*(-1/c*d)^(1/2)+8*x^3*b*c^4*d*e*f^2*(-1/c*d)^(1/2)+12*x^3*b*c^3*d^2*e^2*f*(-1/c*d)^(1/2)-34*x*a*c^4*d*e*f^2*(-1/c*d)^(1/2)+41*x*a*c^3*d^2*e^2*f*(-1/c*d)^(1/2)-x*b*c^4*d*e^2*f*(-1/c*d)^(1/2)-8*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^4*a*d^5*e^3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+46*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a*c^3*d^2*e*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-46*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a*c^2*d^3*e^2*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-6*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*b*c^4*d*e*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-14*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*b*c^3*d^2*e^2*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-34*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^4*a*c^2*d^3*e*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+27*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^4*a*c*d^4*e^2*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-6*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^4*b*c^3*d^2*e*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+8*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^4*b*c^2*d^3*e^2*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+23*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^4*a*c^2*d^3*e*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+16*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a*c*d^4*e^3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+30*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a*c^4*d*f^3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+2*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^4*b*c*d^4*e^3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-16*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a*c*d^4*e^3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-4*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*b*c^2*d^3*e^3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+4*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*b*c^2*d^3*e^3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-34*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*c^4*d*e*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+27*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*c^3*d^2*e^2*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+8*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c^4*d*e^2*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+23*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*c^4*d*e*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-23*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*c^3*d^2*e^2*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-7*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c^4*d*e^2*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-2*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^4*b*c*d^4*e^3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+15*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^4*a*c^3*d^2*f^3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2))/(f*x^2+e)^(1/2)/(c*f-d*e)^3/c^3/(-1/c*d)^(1/2)/(d*x^2+c)^(5/2)","B"
42,1,1169,525,0.055000," ","int((b*x^2+a)*(d*x^2+c)^(5/2)/(f*x^2+e)^(3/2),x)","\frac{\sqrt{d \,x^{2}+c}\, \sqrt{f \,x^{2}+e}\, \left(3 \sqrt{-\frac{d}{c}}\, b \,d^{3} e \,f^{3} x^{7}+5 \sqrt{-\frac{d}{c}}\, a \,d^{3} e \,f^{3} x^{5}+14 \sqrt{-\frac{d}{c}}\, b c \,d^{2} e \,f^{3} x^{5}-6 \sqrt{-\frac{d}{c}}\, b \,d^{3} e^{2} f^{2} x^{5}+15 \sqrt{-\frac{d}{c}}\, a \,c^{2} d \,f^{4} x^{3}-25 \sqrt{-\frac{d}{c}}\, a c \,d^{2} e \,f^{3} x^{3}+20 \sqrt{-\frac{d}{c}}\, a \,d^{3} e^{2} f^{2} x^{3}-4 \sqrt{-\frac{d}{c}}\, b \,c^{2} d e \,f^{3} x^{3}+35 \sqrt{-\frac{d}{c}}\, b c \,d^{2} e^{2} f^{2} x^{3}-24 \sqrt{-\frac{d}{c}}\, b \,d^{3} e^{3} f \,x^{3}+15 \sqrt{-\frac{d}{c}}\, a \,c^{3} f^{4} x -30 \sqrt{-\frac{d}{c}}\, a \,c^{2} d e \,f^{3} x -15 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,c^{2} d e \,f^{3} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+45 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,c^{2} d e \,f^{3} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+20 \sqrt{-\frac{d}{c}}\, a c \,d^{2} e^{2} f^{2} x +65 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a c \,d^{2} e^{2} f^{2} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-85 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a c \,d^{2} e^{2} f^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-40 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,d^{3} e^{3} f \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+40 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,d^{3} e^{3} f \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-15 \sqrt{-\frac{d}{c}}\, b \,c^{3} e \,f^{3} x +15 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b \,c^{3} e \,f^{3} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+41 \sqrt{-\frac{d}{c}}\, b \,c^{2} d \,e^{2} f^{2} x +38 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b \,c^{2} d \,e^{2} f^{2} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-79 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b \,c^{2} d \,e^{2} f^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-24 \sqrt{-\frac{d}{c}}\, b c \,d^{2} e^{3} f x -88 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b c \,d^{2} e^{3} f \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+112 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b c \,d^{2} e^{3} f \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+48 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b \,d^{3} e^{4} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-48 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b \,d^{3} e^{4} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)\right)}{15 \left(d f \,x^{4}+c f \,x^{2}+d e \,x^{2}+c e \right) \sqrt{-\frac{d}{c}}\, e \,f^{4}}"," ",0,"1/15*(d*x^2+c)^(1/2)*(f*x^2+e)^(1/2)*(-24*(-1/c*d)^(1/2)*b*d^3*e^3*f*x^3+15*x*a*c^3*f^4*(-1/c*d)^(1/2)-15*(-1/c*d)^(1/2)*b*c^3*e*f^3*x+3*(-1/c*d)^(1/2)*b*d^3*e*f^3*x^7+5*(-1/c*d)^(1/2)*a*d^3*e*f^3*x^5-6*(-1/c*d)^(1/2)*b*d^3*e^2*f^2*x^5+15*(-1/c*d)^(1/2)*a*c^2*d*f^4*x^3+20*(-1/c*d)^(1/2)*a*d^3*e^2*f^2*x^3-48*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*d^3*e^4+48*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*d^3*e^4-15*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*c^2*d*e*f^3-30*(-1/c*d)^(1/2)*a*c^2*d*e*f^3*x+20*(-1/c*d)^(1/2)*a*c*d^2*e^2*f^2*x+41*(-1/c*d)^(1/2)*b*c^2*d*e^2*f^2*x-24*(-1/c*d)^(1/2)*b*c*d^2*e^3*f*x+40*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*d^3*e^3*f+15*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c^3*e*f^3-40*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*d^3*e^3*f+65*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*c*d^2*e^2*f^2+38*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c^2*d*e^2*f^2-88*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c*d^2*e^3*f+45*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*c^2*d*e*f^3-85*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*c*d^2*e^2*f^2-79*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c^2*d*e^2*f^2+112*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c*d^2*e^3*f+14*(-1/c*d)^(1/2)*b*c*d^2*e*f^3*x^5-25*(-1/c*d)^(1/2)*a*c*d^2*e*f^3*x^3-4*(-1/c*d)^(1/2)*b*c^2*d*e*f^3*x^3+35*(-1/c*d)^(1/2)*b*c*d^2*e^2*f^2*x^3)/f^4/(d*f*x^4+c*f*x^2+d*e*x^2+c*e)/(-1/c*d)^(1/2)/e","B"
43,1,750,388,0.030000," ","int((b*x^2+a)*(d*x^2+c)^(3/2)/(f*x^2+e)^(3/2),x)","\frac{\sqrt{d \,x^{2}+c}\, \sqrt{f \,x^{2}+e}\, \left(\sqrt{-\frac{d}{c}}\, b \,d^{2} e \,f^{2} x^{5}+3 \sqrt{-\frac{d}{c}}\, a c d \,f^{3} x^{3}-3 \sqrt{-\frac{d}{c}}\, a \,d^{2} e \,f^{2} x^{3}-2 \sqrt{-\frac{d}{c}}\, b c d e \,f^{2} x^{3}+4 \sqrt{-\frac{d}{c}}\, b \,d^{2} e^{2} f \,x^{3}+3 \sqrt{-\frac{d}{c}}\, a \,c^{2} f^{3} x -3 \sqrt{-\frac{d}{c}}\, a c d e \,f^{2} x -3 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a c d e \,f^{2} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+6 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a c d e \,f^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+6 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,d^{2} e^{2} f \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-6 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,d^{2} e^{2} f \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-3 \sqrt{-\frac{d}{c}}\, b \,c^{2} e \,f^{2} x +3 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b \,c^{2} e \,f^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+4 \sqrt{-\frac{d}{c}}\, b c d \,e^{2} f x +7 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b c d \,e^{2} f \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-11 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b c d \,e^{2} f \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-8 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b \,d^{2} e^{3} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+8 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b \,d^{2} e^{3} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)\right)}{3 \left(d f \,x^{4}+c f \,x^{2}+d e \,x^{2}+c e \right) \sqrt{-\frac{d}{c}}\, e \,f^{3}}"," ",0,"1/3*(d*x^2+c)^(1/2)*(f*x^2+e)^(1/2)*((-1/c*d)^(1/2)*b*d^2*e*f^2*x^5+3*(-1/c*d)^(1/2)*a*c*d*f^3*x^3-3*(-1/c*d)^(1/2)*a*d^2*e*f^2*x^3-2*(-1/c*d)^(1/2)*b*c*d*e*f^2*x^3+4*(-1/c*d)^(1/2)*b*d^2*e^2*f*x^3+6*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*c*d*e*f^2-6*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*d^2*e^2*f+3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c^2*e*f^2-11*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c*d*e^2*f+8*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*d^2*e^3-3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*c*d*e*f^2+6*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*d^2*e^2*f+7*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c*d*e^2*f-8*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*d^2*e^3+3*x*a*c^2*f^3*(-1/c*d)^(1/2)-3*(-1/c*d)^(1/2)*a*c*d*e*f^2*x-3*(-1/c*d)^(1/2)*b*c^2*e*f^2*x+4*(-1/c*d)^(1/2)*b*c*d*e^2*f*x)/(d*f*x^4+c*f*x^2+d*e*x^2+c*e)/f^3/e/(-1/c*d)^(1/2)","A"
44,1,393,300,0.029000," ","int((b*x^2+a)*(d*x^2+c)^(1/2)/(f*x^2+e)^(3/2),x)","\frac{\sqrt{d \,x^{2}+c}\, \sqrt{f \,x^{2}+e}\, \left(\sqrt{-\frac{d}{c}}\, a d \,f^{2} x^{3}-\sqrt{-\frac{d}{c}}\, b d e f \,x^{3}+\sqrt{-\frac{d}{c}}\, a c \,f^{2} x -\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a d e f \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a d e f \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-\sqrt{-\frac{d}{c}}\, b c e f x +\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b c e f \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+2 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b d \,e^{2} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-2 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b d \,e^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)\right)}{\left(d f \,x^{4}+c f \,x^{2}+d e \,x^{2}+c e \right) \sqrt{-\frac{d}{c}}\, e \,f^{2}}"," ",0,"(d*x^2+c)^(1/2)*(f*x^2+e)^(1/2)*(x^3*a*d*f^2*(-1/c*d)^(1/2)-(-1/c*d)^(1/2)*b*d*e*f*x^3+((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*d*e*f+((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c*e*f-2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*d*e^2-((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*d*e*f+2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*d*e^2+x*a*c*f^2*(-1/c*d)^(1/2)-(-1/c*d)^(1/2)*b*c*e*f*x)/(d*f*x^4+c*f*x^2+d*e*x^2+c*e)/f^2/e/(-1/c*d)^(1/2)","A"
45,1,349,259,0.031000," ","int((b*x^2+a)/(d*x^2+c)^(1/2)/(f*x^2+e)^(3/2),x)","\frac{\left(\sqrt{-\frac{d}{c}}\, a d \,f^{2} x^{3}-\sqrt{-\frac{d}{c}}\, b d e f \,x^{3}+\sqrt{-\frac{d}{c}}\, a c \,f^{2} x -\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a d e f \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-\sqrt{-\frac{d}{c}}\, b c e f x +\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b c e f \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b d \,e^{2} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b d \,e^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)\right) \sqrt{f \,x^{2}+e}\, \sqrt{d \,x^{2}+c}}{\sqrt{-\frac{d}{c}}\, \left(c f -d e \right) \left(d f \,x^{4}+c f \,x^{2}+d e \,x^{2}+c e \right) e f}"," ",0,"((-1/c*d)^(1/2)*a*d*f^2*x^3-(-1/c*d)^(1/2)*b*d*e*f*x^3+((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c*e*f-((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*d*e^2-((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*d*e*f+((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*d*e^2+(-1/c*d)^(1/2)*a*c*f^2*x-(-1/c*d)^(1/2)*b*c*e*f*x)*(f*x^2+e)^(1/2)*(d*x^2+c)^(1/2)/(-1/c*d)^(1/2)/e/f/(c*f-d*e)/(d*f*x^4+c*f*x^2+d*e*x^2+c*e)","A"
46,1,581,318,0.036000," ","int((b*x^2+a)/(d*x^2+c)^(3/2)/(f*x^2+e)^(3/2),x)","\frac{\left(\sqrt{-\frac{d}{c}}\, a c d \,f^{2} x^{3}+\sqrt{-\frac{d}{c}}\, a \,d^{2} e f \,x^{3}-2 \sqrt{-\frac{d}{c}}\, b c d e f \,x^{3}+\sqrt{-\frac{d}{c}}\, a \,c^{2} f^{2} x -\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a c d e f \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a c d e f \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+\sqrt{-\frac{d}{c}}\, a \,d^{2} e^{2} x -\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,d^{2} e^{2} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,d^{2} e^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-\sqrt{-\frac{d}{c}}\, b \,c^{2} e f x +\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b \,c^{2} e f \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-\sqrt{-\frac{d}{c}}\, b c d \,e^{2} x +2 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b c d \,e^{2} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b c d \,e^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)\right) \sqrt{f \,x^{2}+e}\, \sqrt{d \,x^{2}+c}}{\sqrt{-\frac{d}{c}}\, \left(c f -d e \right)^{2} \left(d f \,x^{4}+c f \,x^{2}+d e \,x^{2}+c e \right) c e}"," ",0,"((-1/c*d)^(1/2)*a*c*d*f^2*x^3+(-1/c*d)^(1/2)*a*d^2*e*f*x^3-2*(-1/c*d)^(1/2)*b*c*d*e*f*x^3-EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*c*d*e*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*d^2*e^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c^2*e*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c*d*e^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*c*d*e*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*d^2*e^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+2*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c*d*e^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+x*a*c^2*f^2*(-1/c*d)^(1/2)+(-1/c*d)^(1/2)*a*d^2*e^2*x-(-1/c*d)^(1/2)*b*c^2*e*f*x-(-1/c*d)^(1/2)*b*c*d*e^2*x)*(f*x^2+e)^(1/2)*(d*x^2+c)^(1/2)/c/(-1/c*d)^(1/2)/e/(c*f-d*e)^2/(d*f*x^4+c*f*x^2+d*e*x^2+c*e)","A"
47,1,1742,409,0.042000," ","int((b*x^2+a)/(d*x^2+c)^(5/2)/(f*x^2+e)^(3/2),x)","-\frac{-3 \sqrt{-\frac{d}{c}}\, a \,c^{2} d^{2} f^{3} x^{5}-7 \sqrt{-\frac{d}{c}}\, a c \,d^{3} e \,f^{2} x^{5}+2 \sqrt{-\frac{d}{c}}\, a \,d^{4} e^{2} f \,x^{5}+7 \sqrt{-\frac{d}{c}}\, b \,c^{2} d^{2} e \,f^{2} x^{5}+\sqrt{-\frac{d}{c}}\, b c \,d^{3} e^{2} f \,x^{5}-6 \sqrt{-\frac{d}{c}}\, a \,c^{3} d \,f^{3} x^{3}-8 \sqrt{-\frac{d}{c}}\, a \,c^{2} d^{2} e \,f^{2} x^{3}+3 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,c^{2} d^{2} e \,f^{2} x^{2} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+6 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,c^{2} d^{2} e \,f^{2} x^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-4 \sqrt{-\frac{d}{c}}\, a c \,d^{3} e^{2} f \,x^{3}+7 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a c \,d^{3} e^{2} f \,x^{2} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-8 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a c \,d^{3} e^{2} f \,x^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+2 \sqrt{-\frac{d}{c}}\, a \,d^{4} e^{3} x^{3}-2 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,d^{4} e^{3} x^{2} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+2 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,d^{4} e^{3} x^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+11 \sqrt{-\frac{d}{c}}\, b \,c^{3} d e \,f^{2} x^{3}-3 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b \,c^{3} d e \,f^{2} x^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+4 \sqrt{-\frac{d}{c}}\, b \,c^{2} d^{2} e^{2} f \,x^{3}-7 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b \,c^{2} d^{2} e^{2} f \,x^{2} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+2 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b \,c^{2} d^{2} e^{2} f \,x^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+\sqrt{-\frac{d}{c}}\, b c \,d^{3} e^{3} x^{3}-\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b c \,d^{3} e^{3} x^{2} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b c \,d^{3} e^{3} x^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-3 \sqrt{-\frac{d}{c}}\, a \,c^{4} f^{3} x +3 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,c^{3} d e \,f^{2} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+6 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,c^{3} d e \,f^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-8 \sqrt{-\frac{d}{c}}\, a \,c^{2} d^{2} e^{2} f x +7 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,c^{2} d^{2} e^{2} f \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-8 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,c^{2} d^{2} e^{2} f \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+3 \sqrt{-\frac{d}{c}}\, a c \,d^{3} e^{3} x -2 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a c \,d^{3} e^{3} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+2 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a c \,d^{3} e^{3} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+3 \sqrt{-\frac{d}{c}}\, b \,c^{4} e \,f^{2} x -3 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b \,c^{4} e \,f^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+5 \sqrt{-\frac{d}{c}}\, b \,c^{3} d \,e^{2} f x -7 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b \,c^{3} d \,e^{2} f \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+2 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b \,c^{3} d \,e^{2} f \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b \,c^{2} d^{2} e^{3} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b \,c^{2} d^{2} e^{3} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)}{3 \sqrt{f \,x^{2}+e}\, \left(c f -d e \right)^{3} \sqrt{-\frac{d}{c}}\, \left(d \,x^{2}+c \right)^{\frac{3}{2}} c^{2} e}"," ",0,"-1/3*(-3*x*a*c^4*f^3*(-1/c*d)^(1/2)+6*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a*c^2*d^2*e*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-8*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a*c*d^3*e^2*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-3*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*b*c^3*d*e*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+2*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*b*c^2*d^2*e^2*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+3*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a*c^2*d^2*e*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+7*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a*c*d^3*e^2*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-7*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*b*c^2*d^2*e^2*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+3*x*b*c^4*e*f^2*(-1/c*d)^(1/2)-3*x^5*a*c^2*d^2*f^3*(-1/c*d)^(1/2)+2*x^5*a*d^4*e^2*f*(-1/c*d)^(1/2)+3*x*a*c*d^3*e^3*(-1/c*d)^(1/2)+x^3*b*c*d^3*e^3*(-1/c*d)^(1/2)-6*x^3*a*c^3*d*f^3*(-1/c*d)^(1/2)+2*x^3*a*d^4*e^3*(-1/c*d)^(1/2)-8*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*c^2*d^2*e^2*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+2*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*c*d^3*e^3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-3*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c^4*e*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-7*x^5*a*c*d^3*e*f^2*(-1/c*d)^(1/2)+7*x^5*b*c^2*d^2*e*f^2*(-1/c*d)^(1/2)+x^5*b*c*d^3*e^2*f*(-1/c*d)^(1/2)-8*x^3*a*c^2*d^2*e*f^2*(-1/c*d)^(1/2)-4*x^3*a*c*d^3*e^2*f*(-1/c*d)^(1/2)+EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c^2*d^2*e^3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-2*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*c*d^3*e^3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c^2*d^2*e^3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+11*x^3*b*c^3*d*e*f^2*(-1/c*d)^(1/2)+4*x^3*b*c^2*d^2*e^2*f*(-1/c*d)^(1/2)-8*x*a*c^2*d^2*e^2*f*(-1/c*d)^(1/2)+5*x*b*c^3*d*e^2*f*(-1/c*d)^(1/2)+2*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a*d^4*e^3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-2*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a*d^4*e^3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+2*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c^3*d*e^2*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+3*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*c^3*d*e*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+7*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*c^2*d^2*e^2*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-7*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*b*c^3*d*e^2*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*b*c*d^3*e^3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*b*c*d^3*e^3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+6*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*c^3*d*e*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2))/(f*x^2+e)^(1/2)/(c*f-d*e)^3/e/(-1/c*d)^(1/2)/c^2/(d*x^2+c)^(3/2)","B"
48,1,349,259,0.059000," ","int((f*x^2+e)/(d*x^2+c)^(3/2)/(b*x^2+a)^(1/2),x)","\frac{\left(-\sqrt{-\frac{b}{a}}\, b c d f \,x^{3}+\sqrt{-\frac{b}{a}}\, b \,d^{2} e \,x^{3}-\sqrt{-\frac{b}{a}}\, a c d f x +\sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a c d f \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+\sqrt{-\frac{b}{a}}\, a \,d^{2} e x +\sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b \,c^{2} f \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-\sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b \,c^{2} f \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-\sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b c d e \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)\right) \sqrt{b \,x^{2}+a}\, \sqrt{d \,x^{2}+c}}{\sqrt{-\frac{b}{a}}\, \left(a d -b c \right) \left(b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c \right) c d}"," ",0,"(-x^3*b*c*d*f*(-1/a*b)^(1/2)+x^3*b*d^2*e*(-1/a*b)^(1/2)+EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a*c*d*f*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)-EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*b*c^2*f*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)+EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*b*c^2*f*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)-EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*b*c*d*e*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)-x*a*c*d*f*(-1/a*b)^(1/2)+x*a*d^2*e*(-1/a*b)^(1/2))*(b*x^2+a)^(1/2)*(d*x^2+c)^(1/2)/c/d/(-1/a*b)^(1/2)/(a*d-b*c)/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)","A"
49,1,359,213,0.062000," ","int((f*x^2+e)/(d*x^2+c)^(3/2)/(-b*x^2+a)^(1/2),x)","\frac{\left(-\sqrt{\frac{b}{a}}\, b c d f \,x^{3}+\sqrt{\frac{b}{a}}\, b \,d^{2} e \,x^{3}+\sqrt{\frac{b}{a}}\, a c d f x -\sqrt{-\frac{b \,x^{2}-a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a c d f \EllipticF \left(\sqrt{\frac{b}{a}}\, x , \sqrt{-\frac{a d}{b c}}\right)-\sqrt{\frac{b}{a}}\, a \,d^{2} e x +\sqrt{-\frac{b \,x^{2}-a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b \,c^{2} f \EllipticE \left(\sqrt{\frac{b}{a}}\, x , \sqrt{-\frac{a d}{b c}}\right)-\sqrt{-\frac{b \,x^{2}-a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b \,c^{2} f \EllipticF \left(\sqrt{\frac{b}{a}}\, x , \sqrt{-\frac{a d}{b c}}\right)-\sqrt{-\frac{b \,x^{2}-a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b c d e \EllipticE \left(\sqrt{\frac{b}{a}}\, x , \sqrt{-\frac{a d}{b c}}\right)\right) \sqrt{-b \,x^{2}+a}\, \sqrt{d \,x^{2}+c}}{\sqrt{\frac{b}{a}}\, \left(a d +b c \right) \left(b d \,x^{4}-a d \,x^{2}+b c \,x^{2}-a c \right) c d}"," ",0,"(-x^3*b*c*d*f*(1/a*b)^(1/2)+x^3*b*d^2*e*(1/a*b)^(1/2)-EllipticF(x*(1/a*b)^(1/2),(-a/b/c*d)^(1/2))*a*c*d*f*(-(b*x^2-a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)-EllipticF(x*(1/a*b)^(1/2),(-a/b/c*d)^(1/2))*b*c^2*f*(-(b*x^2-a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)+EllipticE(x*(1/a*b)^(1/2),(-a/b/c*d)^(1/2))*b*c^2*f*(-(b*x^2-a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)-EllipticE(x*(1/a*b)^(1/2),(-a/b/c*d)^(1/2))*b*c*d*e*(-(b*x^2-a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)+x*a*c*d*f*(1/a*b)^(1/2)-x*a*d^2*e*(1/a*b)^(1/2))*(-b*x^2+a)^(1/2)*(d*x^2+c)^(1/2)/c/d/(1/a*b)^(1/2)/(a*d+b*c)/(b*d*x^4-a*d*x^2+b*c*x^2-a*c)","A"
50,1,345,203,0.056000," ","int((f*x^2+e)/(-d*x^2+c)^(3/2)/(b*x^2+a)^(1/2),x)","\frac{\left(-\sqrt{\frac{d}{c}}\, b c f \,x^{3}-\sqrt{\frac{d}{c}}\, b d e \,x^{3}-\sqrt{\frac{d}{c}}\, a c f x +\sqrt{-\frac{d \,x^{2}-c}{c}}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, a c f \EllipticE \left(\sqrt{\frac{d}{c}}\, x , \sqrt{-\frac{b c}{a d}}\right)-\sqrt{\frac{d}{c}}\, a d e x +\sqrt{-\frac{d \,x^{2}-c}{c}}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, a d e \EllipticE \left(\sqrt{\frac{d}{c}}\, x , \sqrt{-\frac{b c}{a d}}\right)-\sqrt{-\frac{d \,x^{2}-c}{c}}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, a d e \EllipticF \left(\sqrt{\frac{d}{c}}\, x , \sqrt{-\frac{b c}{a d}}\right)-\sqrt{-\frac{d \,x^{2}-c}{c}}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, b c e \EllipticF \left(\sqrt{\frac{d}{c}}\, x , \sqrt{-\frac{b c}{a d}}\right)\right) \sqrt{b \,x^{2}+a}\, \sqrt{-d \,x^{2}+c}}{\sqrt{\frac{d}{c}}\, \left(a d +b c \right) \left(b d \,x^{4}+a d \,x^{2}-b c \,x^{2}-a c \right) c}"," ",0,"(-x^3*b*c*f*(1/c*d)^(1/2)-x^3*b*d*e*(1/c*d)^(1/2)-EllipticF(x*(1/c*d)^(1/2),(-b*c/a/d)^(1/2))*a*d*e*(-(d*x^2-c)/c)^(1/2)*((b*x^2+a)/a)^(1/2)-EllipticF(x*(1/c*d)^(1/2),(-b*c/a/d)^(1/2))*b*c*e*(-(d*x^2-c)/c)^(1/2)*((b*x^2+a)/a)^(1/2)+EllipticE(x*(1/c*d)^(1/2),(-b*c/a/d)^(1/2))*a*c*f*(-(d*x^2-c)/c)^(1/2)*((b*x^2+a)/a)^(1/2)+EllipticE(x*(1/c*d)^(1/2),(-b*c/a/d)^(1/2))*a*d*e*(-(d*x^2-c)/c)^(1/2)*((b*x^2+a)/a)^(1/2)-x*a*c*f*(1/c*d)^(1/2)-x*a*d*e*(1/c*d)^(1/2))*(b*x^2+a)^(1/2)*(-d*x^2+c)^(1/2)/c/(1/c*d)^(1/2)/(a*d+b*c)/(b*d*x^4+a*d*x^2-b*c*x^2-a*c)","A"
51,1,354,208,0.060000," ","int((f*x^2+e)/(-d*x^2+c)^(3/2)/(-b*x^2+a)^(1/2),x)","\frac{\left(-\sqrt{\frac{d}{c}}\, b c f \,x^{3}-\sqrt{\frac{d}{c}}\, b d e \,x^{3}+\sqrt{\frac{d}{c}}\, a c f x -\sqrt{-\frac{d \,x^{2}-c}{c}}\, \sqrt{-\frac{b \,x^{2}-a}{a}}\, a c f \EllipticE \left(\sqrt{\frac{d}{c}}\, x , \sqrt{\frac{b c}{a d}}\right)+\sqrt{\frac{d}{c}}\, a d e x -\sqrt{-\frac{d \,x^{2}-c}{c}}\, \sqrt{-\frac{b \,x^{2}-a}{a}}\, a d e \EllipticE \left(\sqrt{\frac{d}{c}}\, x , \sqrt{\frac{b c}{a d}}\right)+\sqrt{-\frac{d \,x^{2}-c}{c}}\, \sqrt{-\frac{b \,x^{2}-a}{a}}\, a d e \EllipticF \left(\sqrt{\frac{d}{c}}\, x , \sqrt{\frac{b c}{a d}}\right)-\sqrt{-\frac{d \,x^{2}-c}{c}}\, \sqrt{-\frac{b \,x^{2}-a}{a}}\, b c e \EllipticF \left(\sqrt{\frac{d}{c}}\, x , \sqrt{\frac{b c}{a d}}\right)\right) \sqrt{-b \,x^{2}+a}\, \sqrt{-d \,x^{2}+c}}{\sqrt{\frac{d}{c}}\, \left(a d -b c \right) \left(b d \,x^{4}-a d \,x^{2}-b c \,x^{2}+a c \right) c}"," ",0,"(-(1/c*d)^(1/2)*b*c*f*x^3-(1/c*d)^(1/2)*b*d*e*x^3+EllipticF((1/c*d)^(1/2)*x,(1/a*b*c/d)^(1/2))*a*d*e*(-(d*x^2-c)/c)^(1/2)*(-(b*x^2-a)/a)^(1/2)-EllipticF((1/c*d)^(1/2)*x,(1/a*b*c/d)^(1/2))*b*c*e*(-(d*x^2-c)/c)^(1/2)*(-(b*x^2-a)/a)^(1/2)-EllipticE((1/c*d)^(1/2)*x,(1/a*b*c/d)^(1/2))*a*c*f*(-(d*x^2-c)/c)^(1/2)*(-(b*x^2-a)/a)^(1/2)-EllipticE((1/c*d)^(1/2)*x,(1/a*b*c/d)^(1/2))*a*d*e*(-(d*x^2-c)/c)^(1/2)*(-(b*x^2-a)/a)^(1/2)+(1/c*d)^(1/2)*a*c*f*x+(1/c*d)^(1/2)*a*d*e*x)*(-b*x^2+a)^(1/2)*(-d*x^2+c)^(1/2)/(1/c*d)^(1/2)/c/(a*d-b*c)/(b*d*x^4-a*d*x^2-b*c*x^2+a*c)","A"
52,1,105,226,0.042000," ","int((b*x^2+a)/(d*x^2+2)^(1/2)/(f*x^2+3)^(1/2),x)","\frac{\sqrt{2}\, \left(a d \EllipticF \left(\frac{\sqrt{3}\, \sqrt{-f}\, x}{3}, \frac{\sqrt{3}\, \sqrt{2}\, \sqrt{\frac{d}{f}}}{2}\right)+2 b \EllipticE \left(\frac{\sqrt{3}\, \sqrt{-f}\, x}{3}, \frac{\sqrt{3}\, \sqrt{2}\, \sqrt{\frac{d}{f}}}{2}\right)-2 b \EllipticF \left(\frac{\sqrt{3}\, \sqrt{-f}\, x}{3}, \frac{\sqrt{3}\, \sqrt{2}\, \sqrt{\frac{d}{f}}}{2}\right)\right)}{2 \sqrt{-f}\, d}"," ",0,"1/2*2^(1/2)*(EllipticF(1/3*x*3^(1/2)*(-f)^(1/2),1/2*3^(1/2)*2^(1/2)*(d/f)^(1/2))*a*d-2*EllipticF(1/3*x*3^(1/2)*(-f)^(1/2),1/2*3^(1/2)*2^(1/2)*(d/f)^(1/2))*b+2*EllipticE(1/3*x*3^(1/2)*(-f)^(1/2),1/2*3^(1/2)*2^(1/2)*(d/f)^(1/2))*b)/(-f)^(1/2)/d","A"
53,1,367,286,0.025000," ","int((b*x^2+a)*(d*x^2+2)^(1/2)/(f*x^2+3)^(1/2),x)","\frac{\sqrt{d \,x^{2}+2}\, \sqrt{f \,x^{2}+3}\, \left(\sqrt{-f}\, b \,d^{2} f \,x^{5}+3 \sqrt{-f}\, b \,d^{2} x^{3}+2 \sqrt{-f}\, b d f \,x^{3}+3 \sqrt{2}\, \sqrt{d \,x^{2}+2}\, \sqrt{f \,x^{2}+3}\, a d f \EllipticE \left(\frac{\sqrt{3}\, \sqrt{-f}\, x}{3}, \frac{\sqrt{3}\, \sqrt{2}\, \sqrt{\frac{d}{f}}}{2}\right)+6 \sqrt{-f}\, b d x -6 \sqrt{2}\, \sqrt{d \,x^{2}+2}\, \sqrt{f \,x^{2}+3}\, b d \EllipticE \left(\frac{\sqrt{3}\, \sqrt{-f}\, x}{3}, \frac{\sqrt{3}\, \sqrt{2}\, \sqrt{\frac{d}{f}}}{2}\right)+3 \sqrt{2}\, \sqrt{d \,x^{2}+2}\, \sqrt{f \,x^{2}+3}\, b d \EllipticF \left(\frac{\sqrt{3}\, \sqrt{-f}\, x}{3}, \frac{\sqrt{3}\, \sqrt{2}\, \sqrt{\frac{d}{f}}}{2}\right)+2 \sqrt{2}\, \sqrt{d \,x^{2}+2}\, \sqrt{f \,x^{2}+3}\, b f \EllipticE \left(\frac{\sqrt{3}\, \sqrt{-f}\, x}{3}, \frac{\sqrt{3}\, \sqrt{2}\, \sqrt{\frac{d}{f}}}{2}\right)-2 \sqrt{2}\, \sqrt{d \,x^{2}+2}\, \sqrt{f \,x^{2}+3}\, b f \EllipticF \left(\frac{\sqrt{3}\, \sqrt{-f}\, x}{3}, \frac{\sqrt{3}\, \sqrt{2}\, \sqrt{\frac{d}{f}}}{2}\right)\right)}{3 \left(d f \,x^{4}+3 d \,x^{2}+2 f \,x^{2}+6\right) \sqrt{-f}\, d f}"," ",0,"1/3*(d*x^2+2)^(1/2)*(f*x^2+3)^(1/2)*(x^5*b*d^2*f*(-f)^(1/2)+3*2^(1/2)*EllipticE(1/3*3^(1/2)*(-f)^(1/2)*x,1/2*3^(1/2)*2^(1/2)*(d/f)^(1/2))*a*d*f*(d*x^2+2)^(1/2)*(f*x^2+3)^(1/2)+3*x^3*b*d^2*(-f)^(1/2)+2*x^3*b*d*f*(-f)^(1/2)-6*2^(1/2)*EllipticE(1/3*3^(1/2)*(-f)^(1/2)*x,1/2*3^(1/2)*2^(1/2)*(d/f)^(1/2))*b*d*(d*x^2+2)^(1/2)*(f*x^2+3)^(1/2)+2*2^(1/2)*EllipticE(1/3*3^(1/2)*(-f)^(1/2)*x,1/2*3^(1/2)*2^(1/2)*(d/f)^(1/2))*b*f*(d*x^2+2)^(1/2)*(f*x^2+3)^(1/2)+3*2^(1/2)*EllipticF(1/3*3^(1/2)*(-f)^(1/2)*x,1/2*3^(1/2)*2^(1/2)*(d/f)^(1/2))*b*d*(d*x^2+2)^(1/2)*(f*x^2+3)^(1/2)-2*2^(1/2)*EllipticF(1/3*3^(1/2)*(-f)^(1/2)*x,1/2*3^(1/2)*2^(1/2)*(d/f)^(1/2))*b*f*(d*x^2+2)^(1/2)*(f*x^2+3)^(1/2)+6*x*b*d*(-f)^(1/2))/(d*f*x^4+3*d*x^2+2*f*x^2+6)/f/(-f)^(1/2)/d","A"
54,1,775,372,0.026000," ","int((b*x^2+a)*(d*x^2+2)^(1/2)*(f*x^2+3)^(1/2),x)","\frac{\sqrt{d \,x^{2}+2}\, \sqrt{f \,x^{2}+3}\, \left(3 \sqrt{-f}\, b \,d^{3} f^{2} x^{7}+5 \sqrt{-f}\, a \,d^{3} f^{2} x^{5}+12 \sqrt{-f}\, b \,d^{3} f \,x^{5}+8 \sqrt{-f}\, b \,d^{2} f^{2} x^{5}+15 \sqrt{-f}\, a \,d^{3} f \,x^{3}+10 \sqrt{-f}\, a \,d^{2} f^{2} x^{3}+9 \sqrt{-f}\, b \,d^{3} x^{3}+30 \sqrt{-f}\, b \,d^{2} f \,x^{3}+4 \sqrt{-f}\, b d \,f^{2} x^{3}+30 \sqrt{-f}\, a \,d^{2} f x +15 \sqrt{2}\, \sqrt{d \,x^{2}+2}\, \sqrt{f \,x^{2}+3}\, a \,d^{2} f \EllipticE \left(\frac{\sqrt{3}\, \sqrt{-f}\, x}{3}, \frac{\sqrt{3}\, \sqrt{2}\, \sqrt{\frac{d}{f}}}{2}\right)+15 \sqrt{2}\, \sqrt{d \,x^{2}+2}\, \sqrt{f \,x^{2}+3}\, a \,d^{2} f \EllipticF \left(\frac{\sqrt{3}\, \sqrt{-f}\, x}{3}, \frac{\sqrt{3}\, \sqrt{2}\, \sqrt{\frac{d}{f}}}{2}\right)+10 \sqrt{2}\, \sqrt{d \,x^{2}+2}\, \sqrt{f \,x^{2}+3}\, a d \,f^{2} \EllipticE \left(\frac{\sqrt{3}\, \sqrt{-f}\, x}{3}, \frac{\sqrt{3}\, \sqrt{2}\, \sqrt{\frac{d}{f}}}{2}\right)-10 \sqrt{2}\, \sqrt{d \,x^{2}+2}\, \sqrt{f \,x^{2}+3}\, a d \,f^{2} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{-f}\, x}{3}, \frac{\sqrt{3}\, \sqrt{2}\, \sqrt{\frac{d}{f}}}{2}\right)+18 \sqrt{-f}\, b \,d^{2} x -18 \sqrt{2}\, \sqrt{d \,x^{2}+2}\, \sqrt{f \,x^{2}+3}\, b \,d^{2} \EllipticE \left(\frac{\sqrt{3}\, \sqrt{-f}\, x}{3}, \frac{\sqrt{3}\, \sqrt{2}\, \sqrt{\frac{d}{f}}}{2}\right)+9 \sqrt{2}\, \sqrt{d \,x^{2}+2}\, \sqrt{f \,x^{2}+3}\, b \,d^{2} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{-f}\, x}{3}, \frac{\sqrt{3}\, \sqrt{2}\, \sqrt{\frac{d}{f}}}{2}\right)+12 \sqrt{-f}\, b d f x +12 \sqrt{2}\, \sqrt{d \,x^{2}+2}\, \sqrt{f \,x^{2}+3}\, b d f \EllipticE \left(\frac{\sqrt{3}\, \sqrt{-f}\, x}{3}, \frac{\sqrt{3}\, \sqrt{2}\, \sqrt{\frac{d}{f}}}{2}\right)-18 \sqrt{2}\, \sqrt{d \,x^{2}+2}\, \sqrt{f \,x^{2}+3}\, b d f \EllipticF \left(\frac{\sqrt{3}\, \sqrt{-f}\, x}{3}, \frac{\sqrt{3}\, \sqrt{2}\, \sqrt{\frac{d}{f}}}{2}\right)-8 \sqrt{2}\, \sqrt{d \,x^{2}+2}\, \sqrt{f \,x^{2}+3}\, b \,f^{2} \EllipticE \left(\frac{\sqrt{3}\, \sqrt{-f}\, x}{3}, \frac{\sqrt{3}\, \sqrt{2}\, \sqrt{\frac{d}{f}}}{2}\right)+8 \sqrt{2}\, \sqrt{d \,x^{2}+2}\, \sqrt{f \,x^{2}+3}\, b \,f^{2} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{-f}\, x}{3}, \frac{\sqrt{3}\, \sqrt{2}\, \sqrt{\frac{d}{f}}}{2}\right)\right)}{15 \left(d f \,x^{4}+3 d \,x^{2}+2 f \,x^{2}+6\right) \sqrt{-f}\, d^{2} f}"," ",0,"1/15*(d*x^2+2)^(1/2)*(f*x^2+3)^(1/2)*(3*x^7*b*d^3*f^2*(-f)^(1/2)+5*x^5*a*d^3*f^2*(-f)^(1/2)+12*x^5*b*d^3*f*(-f)^(1/2)+8*x^5*b*d^2*f^2*(-f)^(1/2)+15*x^3*a*d^3*f*(-f)^(1/2)+10*x^3*a*d^2*f^2*(-f)^(1/2)+15*2^(1/2)*EllipticF(1/3*3^(1/2)*(-f)^(1/2)*x,1/2*3^(1/2)*2^(1/2)*(d/f)^(1/2))*a*d^2*f*(d*x^2+2)^(1/2)*(f*x^2+3)^(1/2)-10*2^(1/2)*EllipticF(1/3*3^(1/2)*(-f)^(1/2)*x,1/2*3^(1/2)*2^(1/2)*(d/f)^(1/2))*a*d*f^2*(d*x^2+2)^(1/2)*(f*x^2+3)^(1/2)+15*2^(1/2)*EllipticE(1/3*3^(1/2)*(-f)^(1/2)*x,1/2*3^(1/2)*2^(1/2)*(d/f)^(1/2))*a*d^2*f*(d*x^2+2)^(1/2)*(f*x^2+3)^(1/2)+10*2^(1/2)*EllipticE(1/3*3^(1/2)*(-f)^(1/2)*x,1/2*3^(1/2)*2^(1/2)*(d/f)^(1/2))*a*d*f^2*(d*x^2+2)^(1/2)*(f*x^2+3)^(1/2)+9*x^3*b*d^3*(-f)^(1/2)+30*x^3*b*d^2*f*(-f)^(1/2)+4*x^3*b*d*f^2*(-f)^(1/2)+9*2^(1/2)*EllipticF(1/3*3^(1/2)*(-f)^(1/2)*x,1/2*3^(1/2)*2^(1/2)*(d/f)^(1/2))*b*d^2*(d*x^2+2)^(1/2)*(f*x^2+3)^(1/2)-18*2^(1/2)*EllipticF(1/3*3^(1/2)*(-f)^(1/2)*x,1/2*3^(1/2)*2^(1/2)*(d/f)^(1/2))*b*d*f*(d*x^2+2)^(1/2)*(f*x^2+3)^(1/2)+8*2^(1/2)*EllipticF(1/3*3^(1/2)*(-f)^(1/2)*x,1/2*3^(1/2)*2^(1/2)*(d/f)^(1/2))*b*f^2*(d*x^2+2)^(1/2)*(f*x^2+3)^(1/2)-18*2^(1/2)*EllipticE(1/3*3^(1/2)*(-f)^(1/2)*x,1/2*3^(1/2)*2^(1/2)*(d/f)^(1/2))*b*d^2*(d*x^2+2)^(1/2)*(f*x^2+3)^(1/2)+12*2^(1/2)*EllipticE(1/3*3^(1/2)*(-f)^(1/2)*x,1/2*3^(1/2)*2^(1/2)*(d/f)^(1/2))*b*d*f*(d*x^2+2)^(1/2)*(f*x^2+3)^(1/2)-8*2^(1/2)*EllipticE(1/3*3^(1/2)*(-f)^(1/2)*x,1/2*3^(1/2)*2^(1/2)*(d/f)^(1/2))*b*f^2*(d*x^2+2)^(1/2)*(f*x^2+3)^(1/2)+30*x*a*d^2*f*(-f)^(1/2)+18*x*b*d^2*(-f)^(1/2)+12*x*b*d*f*(-f)^(1/2))/(d*f*x^4+3*d*x^2+2*f*x^2+6)/d^2/f/(-f)^(1/2)","B"
55,0,0,92,0.273000," ","int((-b+2*c*x^2-(-4*a*c+b^2)^(1/2))/(1+2*c*x^2/(-b-(-4*a*c+b^2)^(1/2)))^(1/2)/(1+2*c*x^2/(-b+(-4*a*c+b^2)^(1/2)))^(1/2),x)","\int \frac{2 c \,x^{2}-b -\sqrt{-4 a c +b^{2}}}{\sqrt{\frac{2 c \,x^{2}}{-b -\sqrt{-4 a c +b^{2}}}+1}\, \sqrt{\frac{2 c \,x^{2}}{-b +\sqrt{-4 a c +b^{2}}}+1}}\, dx"," ",0,"int((-b+2*c*x^2-(-4*a*c+b^2)^(1/2))/(1+2*c*x^2/(-b-(-4*a*c+b^2)^(1/2)))^(1/2)/(1+2*c*x^2/(-b+(-4*a*c+b^2)^(1/2)))^(1/2),x)","F"
56,0,0,499,0.217000," ","int((b+2*c*x^2-(-4*a*c+b^2)^(1/2))/(1+2*c*x^2/(b-(-4*a*c+b^2)^(1/2)))^(1/2)/(1+2*c*x^2/(b+(-4*a*c+b^2)^(1/2)))^(1/2),x)","\int \frac{2 c \,x^{2}+b -\sqrt{-4 a c +b^{2}}}{\sqrt{\frac{2 c \,x^{2}}{b -\sqrt{-4 a c +b^{2}}}+1}\, \sqrt{\frac{2 c \,x^{2}}{b +\sqrt{-4 a c +b^{2}}}+1}}\, dx"," ",0,"int((b+2*c*x^2-(-4*a*c+b^2)^(1/2))/(1+2*c*x^2/(b-(-4*a*c+b^2)^(1/2)))^(1/2)/(1+2*c*x^2/(b+(-4*a*c+b^2)^(1/2)))^(1/2),x)","F"
57,1,1942,106,0.033000," ","int((b*x^2+a)*(d*x^2+c)^(1/2)/(f*x^2+e),x)","-\frac{a c \ln \left(\frac{\frac{2 \sqrt{-e f}\, \left(x -\frac{\sqrt{-e f}}{f}\right) d}{f}+\frac{2 c f -2 d e}{f}+2 \sqrt{\frac{c f -d e}{f}}\, \sqrt{\left(x -\frac{\sqrt{-e f}}{f}\right)^{2} d +\frac{2 \sqrt{-e f}\, \left(x -\frac{\sqrt{-e f}}{f}\right) d}{f}+\frac{c f -d e}{f}}}{x -\frac{\sqrt{-e f}}{f}}\right)}{2 \sqrt{-e f}\, \sqrt{\frac{c f -d e}{f}}}+\frac{a c \ln \left(\frac{-\frac{2 \sqrt{-e f}\, \left(x +\frac{\sqrt{-e f}}{f}\right) d}{f}+\frac{2 c f -2 d e}{f}+2 \sqrt{\frac{c f -d e}{f}}\, \sqrt{\left(x +\frac{\sqrt{-e f}}{f}\right)^{2} d -\frac{2 \sqrt{-e f}\, \left(x +\frac{\sqrt{-e f}}{f}\right) d}{f}+\frac{c f -d e}{f}}}{x +\frac{\sqrt{-e f}}{f}}\right)}{2 \sqrt{-e f}\, \sqrt{\frac{c f -d e}{f}}}+\frac{a d e \ln \left(\frac{\frac{2 \sqrt{-e f}\, \left(x -\frac{\sqrt{-e f}}{f}\right) d}{f}+\frac{2 c f -2 d e}{f}+2 \sqrt{\frac{c f -d e}{f}}\, \sqrt{\left(x -\frac{\sqrt{-e f}}{f}\right)^{2} d +\frac{2 \sqrt{-e f}\, \left(x -\frac{\sqrt{-e f}}{f}\right) d}{f}+\frac{c f -d e}{f}}}{x -\frac{\sqrt{-e f}}{f}}\right)}{2 \sqrt{-e f}\, \sqrt{\frac{c f -d e}{f}}\, f}-\frac{a d e \ln \left(\frac{-\frac{2 \sqrt{-e f}\, \left(x +\frac{\sqrt{-e f}}{f}\right) d}{f}+\frac{2 c f -2 d e}{f}+2 \sqrt{\frac{c f -d e}{f}}\, \sqrt{\left(x +\frac{\sqrt{-e f}}{f}\right)^{2} d -\frac{2 \sqrt{-e f}\, \left(x +\frac{\sqrt{-e f}}{f}\right) d}{f}+\frac{c f -d e}{f}}}{x +\frac{\sqrt{-e f}}{f}}\right)}{2 \sqrt{-e f}\, \sqrt{\frac{c f -d e}{f}}\, f}+\frac{b c e \ln \left(\frac{\frac{2 \sqrt{-e f}\, \left(x -\frac{\sqrt{-e f}}{f}\right) d}{f}+\frac{2 c f -2 d e}{f}+2 \sqrt{\frac{c f -d e}{f}}\, \sqrt{\left(x -\frac{\sqrt{-e f}}{f}\right)^{2} d +\frac{2 \sqrt{-e f}\, \left(x -\frac{\sqrt{-e f}}{f}\right) d}{f}+\frac{c f -d e}{f}}}{x -\frac{\sqrt{-e f}}{f}}\right)}{2 \sqrt{-e f}\, \sqrt{\frac{c f -d e}{f}}\, f}-\frac{b c e \ln \left(\frac{-\frac{2 \sqrt{-e f}\, \left(x +\frac{\sqrt{-e f}}{f}\right) d}{f}+\frac{2 c f -2 d e}{f}+2 \sqrt{\frac{c f -d e}{f}}\, \sqrt{\left(x +\frac{\sqrt{-e f}}{f}\right)^{2} d -\frac{2 \sqrt{-e f}\, \left(x +\frac{\sqrt{-e f}}{f}\right) d}{f}+\frac{c f -d e}{f}}}{x +\frac{\sqrt{-e f}}{f}}\right)}{2 \sqrt{-e f}\, \sqrt{\frac{c f -d e}{f}}\, f}-\frac{b d \,e^{2} \ln \left(\frac{\frac{2 \sqrt{-e f}\, \left(x -\frac{\sqrt{-e f}}{f}\right) d}{f}+\frac{2 c f -2 d e}{f}+2 \sqrt{\frac{c f -d e}{f}}\, \sqrt{\left(x -\frac{\sqrt{-e f}}{f}\right)^{2} d +\frac{2 \sqrt{-e f}\, \left(x -\frac{\sqrt{-e f}}{f}\right) d}{f}+\frac{c f -d e}{f}}}{x -\frac{\sqrt{-e f}}{f}}\right)}{2 \sqrt{-e f}\, \sqrt{\frac{c f -d e}{f}}\, f^{2}}+\frac{b d \,e^{2} \ln \left(\frac{-\frac{2 \sqrt{-e f}\, \left(x +\frac{\sqrt{-e f}}{f}\right) d}{f}+\frac{2 c f -2 d e}{f}+2 \sqrt{\frac{c f -d e}{f}}\, \sqrt{\left(x +\frac{\sqrt{-e f}}{f}\right)^{2} d -\frac{2 \sqrt{-e f}\, \left(x +\frac{\sqrt{-e f}}{f}\right) d}{f}+\frac{c f -d e}{f}}}{x +\frac{\sqrt{-e f}}{f}}\right)}{2 \sqrt{-e f}\, \sqrt{\frac{c f -d e}{f}}\, f^{2}}+\frac{a \sqrt{d}\, \ln \left(\frac{\left(x +\frac{\sqrt{-e f}}{f}\right) d -\frac{\sqrt{-e f}\, d}{f}}{\sqrt{d}}+\sqrt{\left(x +\frac{\sqrt{-e f}}{f}\right)^{2} d -\frac{2 \sqrt{-e f}\, \left(x +\frac{\sqrt{-e f}}{f}\right) d}{f}+\frac{c f -d e}{f}}\right)}{2 f}+\frac{a \sqrt{d}\, \ln \left(\frac{\left(x -\frac{\sqrt{-e f}}{f}\right) d +\frac{\sqrt{-e f}\, d}{f}}{\sqrt{d}}+\sqrt{\left(x -\frac{\sqrt{-e f}}{f}\right)^{2} d +\frac{2 \sqrt{-e f}\, \left(x -\frac{\sqrt{-e f}}{f}\right) d}{f}+\frac{c f -d e}{f}}\right)}{2 f}+\frac{b c \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)}{2 \sqrt{d}\, f}-\frac{b \sqrt{d}\, e \ln \left(\frac{\left(x +\frac{\sqrt{-e f}}{f}\right) d -\frac{\sqrt{-e f}\, d}{f}}{\sqrt{d}}+\sqrt{\left(x +\frac{\sqrt{-e f}}{f}\right)^{2} d -\frac{2 \sqrt{-e f}\, \left(x +\frac{\sqrt{-e f}}{f}\right) d}{f}+\frac{c f -d e}{f}}\right)}{2 f^{2}}-\frac{b \sqrt{d}\, e \ln \left(\frac{\left(x -\frac{\sqrt{-e f}}{f}\right) d +\frac{\sqrt{-e f}\, d}{f}}{\sqrt{d}}+\sqrt{\left(x -\frac{\sqrt{-e f}}{f}\right)^{2} d +\frac{2 \sqrt{-e f}\, \left(x -\frac{\sqrt{-e f}}{f}\right) d}{f}+\frac{c f -d e}{f}}\right)}{2 f^{2}}+\frac{\sqrt{\left(x -\frac{\sqrt{-e f}}{f}\right)^{2} d +\frac{2 \sqrt{-e f}\, \left(x -\frac{\sqrt{-e f}}{f}\right) d}{f}+\frac{c f -d e}{f}}\, a}{2 \sqrt{-e f}}-\frac{\sqrt{\left(x +\frac{\sqrt{-e f}}{f}\right)^{2} d -\frac{2 \sqrt{-e f}\, \left(x +\frac{\sqrt{-e f}}{f}\right) d}{f}+\frac{c f -d e}{f}}\, a}{2 \sqrt{-e f}}-\frac{\sqrt{\left(x -\frac{\sqrt{-e f}}{f}\right)^{2} d +\frac{2 \sqrt{-e f}\, \left(x -\frac{\sqrt{-e f}}{f}\right) d}{f}+\frac{c f -d e}{f}}\, b e}{2 \sqrt{-e f}\, f}+\frac{\sqrt{\left(x +\frac{\sqrt{-e f}}{f}\right)^{2} d -\frac{2 \sqrt{-e f}\, \left(x +\frac{\sqrt{-e f}}{f}\right) d}{f}+\frac{c f -d e}{f}}\, b e}{2 \sqrt{-e f}\, f}+\frac{\sqrt{d \,x^{2}+c}\, b x}{2 f}"," ",0,"1/2*b*x*(d*x^2+c)^(1/2)/f+1/2*b/f*c/d^(1/2)*ln(d^(1/2)*x+(d*x^2+c)^(1/2))+1/2/(-e*f)^(1/2)*((x-(-e*f)^(1/2)/f)^2*d+2*d*(-e*f)^(1/2)/f*(x-(-e*f)^(1/2)/f)+(c*f-d*e)/f)^(1/2)*a-1/2/(-e*f)^(1/2)/f*((x-(-e*f)^(1/2)/f)^2*d+2*d*(-e*f)^(1/2)/f*(x-(-e*f)^(1/2)/f)+(c*f-d*e)/f)^(1/2)*b*e+1/2/f*d^(1/2)*ln((d*(-e*f)^(1/2)/f+d*(x-(-e*f)^(1/2)/f))/d^(1/2)+((x-(-e*f)^(1/2)/f)^2*d+2*d*(-e*f)^(1/2)/f*(x-(-e*f)^(1/2)/f)+(c*f-d*e)/f)^(1/2))*a-1/2/f^2*d^(1/2)*ln((d*(-e*f)^(1/2)/f+d*(x-(-e*f)^(1/2)/f))/d^(1/2)+((x-(-e*f)^(1/2)/f)^2*d+2*d*(-e*f)^(1/2)/f*(x-(-e*f)^(1/2)/f)+(c*f-d*e)/f)^(1/2))*b*e-1/2/(-e*f)^(1/2)/((c*f-d*e)/f)^(1/2)*ln((2*(c*f-d*e)/f+2*d*(-e*f)^(1/2)/f*(x-(-e*f)^(1/2)/f)+2*((c*f-d*e)/f)^(1/2)*((x-(-e*f)^(1/2)/f)^2*d+2*d*(-e*f)^(1/2)/f*(x-(-e*f)^(1/2)/f)+(c*f-d*e)/f)^(1/2))/(x-(-e*f)^(1/2)/f))*c*a+1/2/(-e*f)^(1/2)/f/((c*f-d*e)/f)^(1/2)*ln((2*(c*f-d*e)/f+2*d*(-e*f)^(1/2)/f*(x-(-e*f)^(1/2)/f)+2*((c*f-d*e)/f)^(1/2)*((x-(-e*f)^(1/2)/f)^2*d+2*d*(-e*f)^(1/2)/f*(x-(-e*f)^(1/2)/f)+(c*f-d*e)/f)^(1/2))/(x-(-e*f)^(1/2)/f))*c*b*e+1/2/(-e*f)^(1/2)/f/((c*f-d*e)/f)^(1/2)*ln((2*(c*f-d*e)/f+2*d*(-e*f)^(1/2)/f*(x-(-e*f)^(1/2)/f)+2*((c*f-d*e)/f)^(1/2)*((x-(-e*f)^(1/2)/f)^2*d+2*d*(-e*f)^(1/2)/f*(x-(-e*f)^(1/2)/f)+(c*f-d*e)/f)^(1/2))/(x-(-e*f)^(1/2)/f))*d*e*a-1/2/(-e*f)^(1/2)/f^2/((c*f-d*e)/f)^(1/2)*ln((2*(c*f-d*e)/f+2*d*(-e*f)^(1/2)/f*(x-(-e*f)^(1/2)/f)+2*((c*f-d*e)/f)^(1/2)*((x-(-e*f)^(1/2)/f)^2*d+2*d*(-e*f)^(1/2)/f*(x-(-e*f)^(1/2)/f)+(c*f-d*e)/f)^(1/2))/(x-(-e*f)^(1/2)/f))*d*e^2*b-1/2/(-e*f)^(1/2)*((x+(-e*f)^(1/2)/f)^2*d-2*d*(-e*f)^(1/2)/f*(x+(-e*f)^(1/2)/f)+(c*f-d*e)/f)^(1/2)*a+1/2/(-e*f)^(1/2)/f*((x+(-e*f)^(1/2)/f)^2*d-2*d*(-e*f)^(1/2)/f*(x+(-e*f)^(1/2)/f)+(c*f-d*e)/f)^(1/2)*b*e+1/2/f*d^(1/2)*ln((-d*(-e*f)^(1/2)/f+d*(x+(-e*f)^(1/2)/f))/d^(1/2)+((x+(-e*f)^(1/2)/f)^2*d-2*d*(-e*f)^(1/2)/f*(x+(-e*f)^(1/2)/f)+(c*f-d*e)/f)^(1/2))*a-1/2/f^2*d^(1/2)*ln((-d*(-e*f)^(1/2)/f+d*(x+(-e*f)^(1/2)/f))/d^(1/2)+((x+(-e*f)^(1/2)/f)^2*d-2*d*(-e*f)^(1/2)/f*(x+(-e*f)^(1/2)/f)+(c*f-d*e)/f)^(1/2))*b*e+1/2/(-e*f)^(1/2)/((c*f-d*e)/f)^(1/2)*ln((2*(c*f-d*e)/f-2*d*(-e*f)^(1/2)/f*(x+(-e*f)^(1/2)/f)+2*((c*f-d*e)/f)^(1/2)*((x+(-e*f)^(1/2)/f)^2*d-2*d*(-e*f)^(1/2)/f*(x+(-e*f)^(1/2)/f)+(c*f-d*e)/f)^(1/2))/(x+(-e*f)^(1/2)/f))*c*a-1/2/(-e*f)^(1/2)/f/((c*f-d*e)/f)^(1/2)*ln((2*(c*f-d*e)/f-2*d*(-e*f)^(1/2)/f*(x+(-e*f)^(1/2)/f)+2*((c*f-d*e)/f)^(1/2)*((x+(-e*f)^(1/2)/f)^2*d-2*d*(-e*f)^(1/2)/f*(x+(-e*f)^(1/2)/f)+(c*f-d*e)/f)^(1/2))/(x+(-e*f)^(1/2)/f))*c*b*e-1/2/(-e*f)^(1/2)/f/((c*f-d*e)/f)^(1/2)*ln((2*(c*f-d*e)/f-2*d*(-e*f)^(1/2)/f*(x+(-e*f)^(1/2)/f)+2*((c*f-d*e)/f)^(1/2)*((x+(-e*f)^(1/2)/f)^2*d-2*d*(-e*f)^(1/2)/f*(x+(-e*f)^(1/2)/f)+(c*f-d*e)/f)^(1/2))/(x+(-e*f)^(1/2)/f))*d*e*a+1/2/(-e*f)^(1/2)/f^2/((c*f-d*e)/f)^(1/2)*ln((2*(c*f-d*e)/f-2*d*(-e*f)^(1/2)/f*(x+(-e*f)^(1/2)/f)+2*((c*f-d*e)/f)^(1/2)*((x+(-e*f)^(1/2)/f)^2*d-2*d*(-e*f)^(1/2)/f*(x+(-e*f)^(1/2)/f)+(c*f-d*e)/f)^(1/2))/(x+(-e*f)^(1/2)/f))*d*e^2*b","B"
58,1,1541,260,0.038000," ","int((b*x^2+a)^3/(d*x^2+c)/(f*x^2+e)^(1/2),x)","-\frac{a^{3} \ln \left(\frac{\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) f}{d}-\frac{2 \left(c f -d e \right)}{d}+2 \sqrt{-\frac{c f -d e}{d}}\, \sqrt{\left(x -\frac{\sqrt{-c d}}{d}\right)^{2} f +\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) f}{d}-\frac{c f -d e}{d}}}{x -\frac{\sqrt{-c d}}{d}}\right)}{2 \sqrt{-c d}\, \sqrt{-\frac{c f -d e}{d}}}+\frac{a^{3} \ln \left(\frac{-\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) f}{d}-\frac{2 \left(c f -d e \right)}{d}+2 \sqrt{-\frac{c f -d e}{d}}\, \sqrt{\left(x +\frac{\sqrt{-c d}}{d}\right)^{2} f -\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) f}{d}-\frac{c f -d e}{d}}}{x +\frac{\sqrt{-c d}}{d}}\right)}{2 \sqrt{-c d}\, \sqrt{-\frac{c f -d e}{d}}}+\frac{3 a^{2} b c \ln \left(\frac{\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) f}{d}-\frac{2 \left(c f -d e \right)}{d}+2 \sqrt{-\frac{c f -d e}{d}}\, \sqrt{\left(x -\frac{\sqrt{-c d}}{d}\right)^{2} f +\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) f}{d}-\frac{c f -d e}{d}}}{x -\frac{\sqrt{-c d}}{d}}\right)}{2 \sqrt{-c d}\, \sqrt{-\frac{c f -d e}{d}}\, d}-\frac{3 a^{2} b c \ln \left(\frac{-\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) f}{d}-\frac{2 \left(c f -d e \right)}{d}+2 \sqrt{-\frac{c f -d e}{d}}\, \sqrt{\left(x +\frac{\sqrt{-c d}}{d}\right)^{2} f -\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) f}{d}-\frac{c f -d e}{d}}}{x +\frac{\sqrt{-c d}}{d}}\right)}{2 \sqrt{-c d}\, \sqrt{-\frac{c f -d e}{d}}\, d}-\frac{3 a \,b^{2} c^{2} \ln \left(\frac{\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) f}{d}-\frac{2 \left(c f -d e \right)}{d}+2 \sqrt{-\frac{c f -d e}{d}}\, \sqrt{\left(x -\frac{\sqrt{-c d}}{d}\right)^{2} f +\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) f}{d}-\frac{c f -d e}{d}}}{x -\frac{\sqrt{-c d}}{d}}\right)}{2 \sqrt{-c d}\, \sqrt{-\frac{c f -d e}{d}}\, d^{2}}+\frac{3 a \,b^{2} c^{2} \ln \left(\frac{-\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) f}{d}-\frac{2 \left(c f -d e \right)}{d}+2 \sqrt{-\frac{c f -d e}{d}}\, \sqrt{\left(x +\frac{\sqrt{-c d}}{d}\right)^{2} f -\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) f}{d}-\frac{c f -d e}{d}}}{x +\frac{\sqrt{-c d}}{d}}\right)}{2 \sqrt{-c d}\, \sqrt{-\frac{c f -d e}{d}}\, d^{2}}+\frac{b^{3} c^{3} \ln \left(\frac{\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) f}{d}-\frac{2 \left(c f -d e \right)}{d}+2 \sqrt{-\frac{c f -d e}{d}}\, \sqrt{\left(x -\frac{\sqrt{-c d}}{d}\right)^{2} f +\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) f}{d}-\frac{c f -d e}{d}}}{x -\frac{\sqrt{-c d}}{d}}\right)}{2 \sqrt{-c d}\, \sqrt{-\frac{c f -d e}{d}}\, d^{3}}-\frac{b^{3} c^{3} \ln \left(\frac{-\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) f}{d}-\frac{2 \left(c f -d e \right)}{d}+2 \sqrt{-\frac{c f -d e}{d}}\, \sqrt{\left(x +\frac{\sqrt{-c d}}{d}\right)^{2} f -\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) f}{d}-\frac{c f -d e}{d}}}{x +\frac{\sqrt{-c d}}{d}}\right)}{2 \sqrt{-c d}\, \sqrt{-\frac{c f -d e}{d}}\, d^{3}}+\frac{\sqrt{f \,x^{2}+e}\, b^{3} x^{3}}{4 d f}+\frac{3 a^{2} b \ln \left(\sqrt{f}\, x +\sqrt{f \,x^{2}+e}\right)}{d \sqrt{f}}-\frac{3 a \,b^{2} c \ln \left(\sqrt{f}\, x +\sqrt{f \,x^{2}+e}\right)}{d^{2} \sqrt{f}}-\frac{3 a \,b^{2} e \ln \left(\sqrt{f}\, x +\sqrt{f \,x^{2}+e}\right)}{2 d \,f^{\frac{3}{2}}}+\frac{b^{3} c^{2} \ln \left(\sqrt{f}\, x +\sqrt{f \,x^{2}+e}\right)}{d^{3} \sqrt{f}}+\frac{b^{3} c e \ln \left(\sqrt{f}\, x +\sqrt{f \,x^{2}+e}\right)}{2 d^{2} f^{\frac{3}{2}}}+\frac{3 b^{3} e^{2} \ln \left(\sqrt{f}\, x +\sqrt{f \,x^{2}+e}\right)}{8 d \,f^{\frac{5}{2}}}+\frac{3 \sqrt{f \,x^{2}+e}\, a \,b^{2} x}{2 d f}-\frac{\sqrt{f \,x^{2}+e}\, b^{3} c x}{2 d^{2} f}-\frac{3 \sqrt{f \,x^{2}+e}\, b^{3} e x}{8 d \,f^{2}}"," ",0,"1/4*b^3/d*x^3/f*(f*x^2+e)^(1/2)-3/8*b^3/d*e/f^2*x*(f*x^2+e)^(1/2)+3/8*b^3/d*e^2/f^(5/2)*ln(x*f^(1/2)+(f*x^2+e)^(1/2))+3/2*b^2/d*x/f*(f*x^2+e)^(1/2)*a-1/2*b^3/d^2*x/f*(f*x^2+e)^(1/2)*c-3/2*b^2/d*e/f^(3/2)*ln(x*f^(1/2)+(f*x^2+e)^(1/2))*a+1/2*b^3/d^2*e/f^(3/2)*ln(x*f^(1/2)+(f*x^2+e)^(1/2))*c+3*b/d*a^2*ln(x*f^(1/2)+(f*x^2+e)^(1/2))/f^(1/2)-3*b^2/d^2*a*c*ln(x*f^(1/2)+(f*x^2+e)^(1/2))/f^(1/2)+b^3/d^3*c^2*ln(x*f^(1/2)+(f*x^2+e)^(1/2))/f^(1/2)-1/2/(-c*d)^(1/2)/(-(c*f-d*e)/d)^(1/2)*ln((-2*(c*f-d*e)/d+2*f*(-c*d)^(1/2)/d*(x-1/d*(-c*d)^(1/2))+2*(-(c*f-d*e)/d)^(1/2)*((x-1/d*(-c*d)^(1/2))^2*f+2*f*(-c*d)^(1/2)/d*(x-1/d*(-c*d)^(1/2))-(c*f-d*e)/d)^(1/2))/(x-1/d*(-c*d)^(1/2)))*a^3+3/2/d/(-c*d)^(1/2)/(-(c*f-d*e)/d)^(1/2)*ln((-2*(c*f-d*e)/d+2*f*(-c*d)^(1/2)/d*(x-1/d*(-c*d)^(1/2))+2*(-(c*f-d*e)/d)^(1/2)*((x-1/d*(-c*d)^(1/2))^2*f+2*f*(-c*d)^(1/2)/d*(x-1/d*(-c*d)^(1/2))-(c*f-d*e)/d)^(1/2))/(x-1/d*(-c*d)^(1/2)))*a^2*c*b-3/2/d^2/(-c*d)^(1/2)/(-(c*f-d*e)/d)^(1/2)*ln((-2*(c*f-d*e)/d+2*f*(-c*d)^(1/2)/d*(x-1/d*(-c*d)^(1/2))+2*(-(c*f-d*e)/d)^(1/2)*((x-1/d*(-c*d)^(1/2))^2*f+2*f*(-c*d)^(1/2)/d*(x-1/d*(-c*d)^(1/2))-(c*f-d*e)/d)^(1/2))/(x-1/d*(-c*d)^(1/2)))*a*b^2*c^2+1/2/d^3/(-c*d)^(1/2)/(-(c*f-d*e)/d)^(1/2)*ln((-2*(c*f-d*e)/d+2*f*(-c*d)^(1/2)/d*(x-1/d*(-c*d)^(1/2))+2*(-(c*f-d*e)/d)^(1/2)*((x-1/d*(-c*d)^(1/2))^2*f+2*f*(-c*d)^(1/2)/d*(x-1/d*(-c*d)^(1/2))-(c*f-d*e)/d)^(1/2))/(x-1/d*(-c*d)^(1/2)))*b^3*c^3+1/2/(-c*d)^(1/2)/(-(c*f-d*e)/d)^(1/2)*ln((-2*(c*f-d*e)/d-2*f*(-c*d)^(1/2)/d*(x+1/d*(-c*d)^(1/2))+2*(-(c*f-d*e)/d)^(1/2)*((x+1/d*(-c*d)^(1/2))^2*f-2*f*(-c*d)^(1/2)/d*(x+1/d*(-c*d)^(1/2))-(c*f-d*e)/d)^(1/2))/(x+1/d*(-c*d)^(1/2)))*a^3-3/2/d/(-c*d)^(1/2)/(-(c*f-d*e)/d)^(1/2)*ln((-2*(c*f-d*e)/d-2*f*(-c*d)^(1/2)/d*(x+1/d*(-c*d)^(1/2))+2*(-(c*f-d*e)/d)^(1/2)*((x+1/d*(-c*d)^(1/2))^2*f-2*f*(-c*d)^(1/2)/d*(x+1/d*(-c*d)^(1/2))-(c*f-d*e)/d)^(1/2))/(x+1/d*(-c*d)^(1/2)))*a^2*c*b+3/2/d^2/(-c*d)^(1/2)/(-(c*f-d*e)/d)^(1/2)*ln((-2*(c*f-d*e)/d-2*f*(-c*d)^(1/2)/d*(x+1/d*(-c*d)^(1/2))+2*(-(c*f-d*e)/d)^(1/2)*((x+1/d*(-c*d)^(1/2))^2*f-2*f*(-c*d)^(1/2)/d*(x+1/d*(-c*d)^(1/2))-(c*f-d*e)/d)^(1/2))/(x+1/d*(-c*d)^(1/2)))*a*b^2*c^2-1/2/d^3/(-c*d)^(1/2)/(-(c*f-d*e)/d)^(1/2)*ln((-2*(c*f-d*e)/d-2*f*(-c*d)^(1/2)/d*(x+1/d*(-c*d)^(1/2))+2*(-(c*f-d*e)/d)^(1/2)*((x+1/d*(-c*d)^(1/2))^2*f-2*f*(-c*d)^(1/2)/d*(x+1/d*(-c*d)^(1/2))-(c*f-d*e)/d)^(1/2))/(x+1/d*(-c*d)^(1/2)))*b^3*c^3","B"
59,1,1052,138,0.016000," ","int((b*x^2+a)^2/(d*x^2+c)/(f*x^2+e)^(1/2),x)","-\frac{a^{2} \ln \left(\frac{\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) f}{d}-\frac{2 \left(c f -d e \right)}{d}+2 \sqrt{-\frac{c f -d e}{d}}\, \sqrt{\left(x -\frac{\sqrt{-c d}}{d}\right)^{2} f +\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) f}{d}-\frac{c f -d e}{d}}}{x -\frac{\sqrt{-c d}}{d}}\right)}{2 \sqrt{-c d}\, \sqrt{-\frac{c f -d e}{d}}}+\frac{a^{2} \ln \left(\frac{-\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) f}{d}-\frac{2 \left(c f -d e \right)}{d}+2 \sqrt{-\frac{c f -d e}{d}}\, \sqrt{\left(x +\frac{\sqrt{-c d}}{d}\right)^{2} f -\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) f}{d}-\frac{c f -d e}{d}}}{x +\frac{\sqrt{-c d}}{d}}\right)}{2 \sqrt{-c d}\, \sqrt{-\frac{c f -d e}{d}}}+\frac{a b c \ln \left(\frac{\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) f}{d}-\frac{2 \left(c f -d e \right)}{d}+2 \sqrt{-\frac{c f -d e}{d}}\, \sqrt{\left(x -\frac{\sqrt{-c d}}{d}\right)^{2} f +\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) f}{d}-\frac{c f -d e}{d}}}{x -\frac{\sqrt{-c d}}{d}}\right)}{\sqrt{-c d}\, \sqrt{-\frac{c f -d e}{d}}\, d}-\frac{a b c \ln \left(\frac{-\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) f}{d}-\frac{2 \left(c f -d e \right)}{d}+2 \sqrt{-\frac{c f -d e}{d}}\, \sqrt{\left(x +\frac{\sqrt{-c d}}{d}\right)^{2} f -\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) f}{d}-\frac{c f -d e}{d}}}{x +\frac{\sqrt{-c d}}{d}}\right)}{\sqrt{-c d}\, \sqrt{-\frac{c f -d e}{d}}\, d}-\frac{b^{2} c^{2} \ln \left(\frac{\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) f}{d}-\frac{2 \left(c f -d e \right)}{d}+2 \sqrt{-\frac{c f -d e}{d}}\, \sqrt{\left(x -\frac{\sqrt{-c d}}{d}\right)^{2} f +\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) f}{d}-\frac{c f -d e}{d}}}{x -\frac{\sqrt{-c d}}{d}}\right)}{2 \sqrt{-c d}\, \sqrt{-\frac{c f -d e}{d}}\, d^{2}}+\frac{b^{2} c^{2} \ln \left(\frac{-\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) f}{d}-\frac{2 \left(c f -d e \right)}{d}+2 \sqrt{-\frac{c f -d e}{d}}\, \sqrt{\left(x +\frac{\sqrt{-c d}}{d}\right)^{2} f -\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) f}{d}-\frac{c f -d e}{d}}}{x +\frac{\sqrt{-c d}}{d}}\right)}{2 \sqrt{-c d}\, \sqrt{-\frac{c f -d e}{d}}\, d^{2}}+\frac{2 a b \ln \left(\sqrt{f}\, x +\sqrt{f \,x^{2}+e}\right)}{d \sqrt{f}}-\frac{b^{2} c \ln \left(\sqrt{f}\, x +\sqrt{f \,x^{2}+e}\right)}{d^{2} \sqrt{f}}-\frac{b^{2} e \ln \left(\sqrt{f}\, x +\sqrt{f \,x^{2}+e}\right)}{2 d \,f^{\frac{3}{2}}}+\frac{\sqrt{f \,x^{2}+e}\, b^{2} x}{2 d f}"," ",0,"1/2*b^2*x*(f*x^2+e)^(1/2)/d/f-1/2*b^2/d*e/f^(3/2)*ln(f^(1/2)*x+(f*x^2+e)^(1/2))+2*b/d*a*ln(f^(1/2)*x+(f*x^2+e)^(1/2))/f^(1/2)-b^2/d^2*c*ln(f^(1/2)*x+(f*x^2+e)^(1/2))/f^(1/2)-1/2/(-c*d)^(1/2)/(-(c*f-d*e)/d)^(1/2)*ln((2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)/d*f-2*(c*f-d*e)/d+2*(-(c*f-d*e)/d)^(1/2)*((x-(-c*d)^(1/2)/d)^2*f+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)/d*f-(c*f-d*e)/d)^(1/2))/(x-(-c*d)^(1/2)/d))*a^2+1/d/(-c*d)^(1/2)/(-(c*f-d*e)/d)^(1/2)*ln((2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)/d*f-2*(c*f-d*e)/d+2*(-(c*f-d*e)/d)^(1/2)*((x-(-c*d)^(1/2)/d)^2*f+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)/d*f-(c*f-d*e)/d)^(1/2))/(x-(-c*d)^(1/2)/d))*a*b*c-1/2/d^2/(-c*d)^(1/2)/(-(c*f-d*e)/d)^(1/2)*ln((2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)/d*f-2*(c*f-d*e)/d+2*(-(c*f-d*e)/d)^(1/2)*((x-(-c*d)^(1/2)/d)^2*f+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)/d*f-(c*f-d*e)/d)^(1/2))/(x-(-c*d)^(1/2)/d))*b^2*c^2+1/2/(-c*d)^(1/2)/(-(c*f-d*e)/d)^(1/2)*ln((-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)/d*f-2*(c*f-d*e)/d+2*(-(c*f-d*e)/d)^(1/2)*((x+(-c*d)^(1/2)/d)^2*f-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)/d*f-(c*f-d*e)/d)^(1/2))/(x+(-c*d)^(1/2)/d))*a^2-1/d/(-c*d)^(1/2)/(-(c*f-d*e)/d)^(1/2)*ln((-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)/d*f-2*(c*f-d*e)/d+2*(-(c*f-d*e)/d)^(1/2)*((x+(-c*d)^(1/2)/d)^2*f-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)/d*f-(c*f-d*e)/d)^(1/2))/(x+(-c*d)^(1/2)/d))*a*b*c+1/2/d^2/(-c*d)^(1/2)/(-(c*f-d*e)/d)^(1/2)*ln((-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)/d*f-2*(c*f-d*e)/d+2*(-(c*f-d*e)/d)^(1/2)*((x+(-c*d)^(1/2)/d)^2*f-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)/d*f-(c*f-d*e)/d)^(1/2))/(x+(-c*d)^(1/2)/d))*b^2*c^2","B"
60,1,646,75,0.011000," ","int((b*x^2+a)/(d*x^2+c)/(f*x^2+e)^(1/2),x)","-\frac{a \ln \left(\frac{\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) f}{d}-\frac{2 \left(c f -d e \right)}{d}+2 \sqrt{-\frac{c f -d e}{d}}\, \sqrt{\left(x -\frac{\sqrt{-c d}}{d}\right)^{2} f +\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) f}{d}-\frac{c f -d e}{d}}}{x -\frac{\sqrt{-c d}}{d}}\right)}{2 \sqrt{-c d}\, \sqrt{-\frac{c f -d e}{d}}}+\frac{a \ln \left(\frac{-\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) f}{d}-\frac{2 \left(c f -d e \right)}{d}+2 \sqrt{-\frac{c f -d e}{d}}\, \sqrt{\left(x +\frac{\sqrt{-c d}}{d}\right)^{2} f -\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) f}{d}-\frac{c f -d e}{d}}}{x +\frac{\sqrt{-c d}}{d}}\right)}{2 \sqrt{-c d}\, \sqrt{-\frac{c f -d e}{d}}}+\frac{b c \ln \left(\frac{\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) f}{d}-\frac{2 \left(c f -d e \right)}{d}+2 \sqrt{-\frac{c f -d e}{d}}\, \sqrt{\left(x -\frac{\sqrt{-c d}}{d}\right)^{2} f +\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) f}{d}-\frac{c f -d e}{d}}}{x -\frac{\sqrt{-c d}}{d}}\right)}{2 \sqrt{-c d}\, \sqrt{-\frac{c f -d e}{d}}\, d}-\frac{b c \ln \left(\frac{-\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) f}{d}-\frac{2 \left(c f -d e \right)}{d}+2 \sqrt{-\frac{c f -d e}{d}}\, \sqrt{\left(x +\frac{\sqrt{-c d}}{d}\right)^{2} f -\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) f}{d}-\frac{c f -d e}{d}}}{x +\frac{\sqrt{-c d}}{d}}\right)}{2 \sqrt{-c d}\, \sqrt{-\frac{c f -d e}{d}}\, d}+\frac{b \ln \left(\sqrt{f}\, x +\sqrt{f \,x^{2}+e}\right)}{d \sqrt{f}}"," ",0,"b/d*ln(f^(1/2)*x+(f*x^2+e)^(1/2))/f^(1/2)-1/2/(-c*d)^(1/2)/(-(c*f-d*e)/d)^(1/2)*ln((2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)/d*f-2*(c*f-d*e)/d+2*(-(c*f-d*e)/d)^(1/2)*((x-(-c*d)^(1/2)/d)^2*f+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)/d*f-(c*f-d*e)/d)^(1/2))/(x-(-c*d)^(1/2)/d))*a+1/2/(-c*d)^(1/2)/d/(-(c*f-d*e)/d)^(1/2)*ln((2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)/d*f-2*(c*f-d*e)/d+2*(-(c*f-d*e)/d)^(1/2)*((x-(-c*d)^(1/2)/d)^2*f+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)/d*f-(c*f-d*e)/d)^(1/2))/(x-(-c*d)^(1/2)/d))*b*c+1/2/(-c*d)^(1/2)/(-(c*f-d*e)/d)^(1/2)*ln((-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)/d*f-2*(c*f-d*e)/d+2*(-(c*f-d*e)/d)^(1/2)*((x+(-c*d)^(1/2)/d)^2*f-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)/d*f-(c*f-d*e)/d)^(1/2))/(x+(-c*d)^(1/2)/d))*a-1/2/(-c*d)^(1/2)/d/(-(c*f-d*e)/d)^(1/2)*ln((-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)/d*f-2*(c*f-d*e)/d+2*(-(c*f-d*e)/d)^(1/2)*((x+(-c*d)^(1/2)/d)^2*f-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)/d*f-(c*f-d*e)/d)^(1/2))/(x+(-c*d)^(1/2)/d))*b*c","B"
61,1,306,39,0.011000," ","int(1/(d*x^2+c)/(f*x^2+e)^(1/2),x)","-\frac{\ln \left(\frac{\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) f}{d}-\frac{2 \left(c f -d e \right)}{d}+2 \sqrt{-\frac{c f -d e}{d}}\, \sqrt{\left(x -\frac{\sqrt{-c d}}{d}\right)^{2} f +\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) f}{d}-\frac{c f -d e}{d}}}{x -\frac{\sqrt{-c d}}{d}}\right)}{2 \sqrt{-c d}\, \sqrt{-\frac{c f -d e}{d}}}+\frac{\ln \left(\frac{-\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) f}{d}-\frac{2 \left(c f -d e \right)}{d}+2 \sqrt{-\frac{c f -d e}{d}}\, \sqrt{\left(x +\frac{\sqrt{-c d}}{d}\right)^{2} f -\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) f}{d}-\frac{c f -d e}{d}}}{x +\frac{\sqrt{-c d}}{d}}\right)}{2 \sqrt{-c d}\, \sqrt{-\frac{c f -d e}{d}}}"," ",0,"-1/2/(-c*d)^(1/2)/(-(c*f-d*e)/d)^(1/2)*ln((2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)/d*f-2*(c*f-d*e)/d+2*(-(c*f-d*e)/d)^(1/2)*((x-(-c*d)^(1/2)/d)^2*f+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)/d*f-(c*f-d*e)/d)^(1/2))/(x-(-c*d)^(1/2)/d))+1/2/(-c*d)^(1/2)/(-(c*f-d*e)/d)^(1/2)*ln((-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)/d*f-2*(c*f-d*e)/d+2*(-(c*f-d*e)/d)^(1/2)*((x+(-c*d)^(1/2)/d)^2*f-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)/d*f-(c*f-d*e)/d)^(1/2))/(x+(-c*d)^(1/2)/d))","B"
62,1,782,102,0.031000," ","int(1/(b*x^2+a)/(d*x^2+c)/(f*x^2+e)^(1/2),x)","-\frac{b^{2} d \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) f}{b}-\frac{2 \left(a f -b e \right)}{b}+2 \sqrt{-\frac{a f -b e}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} f +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) f}{b}-\frac{a f -b e}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-a b}\, \left(\sqrt{-c d}\, b +\sqrt{-a b}\, d \right) \left(-\sqrt{-c d}\, b +\sqrt{-a b}\, d \right) \sqrt{-\frac{a f -b e}{b}}}+\frac{b^{2} d \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) f}{b}-\frac{2 \left(a f -b e \right)}{b}+2 \sqrt{-\frac{a f -b e}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} f -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) f}{b}-\frac{a f -b e}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-a b}\, \left(\sqrt{-c d}\, b +\sqrt{-a b}\, d \right) \left(-\sqrt{-c d}\, b +\sqrt{-a b}\, d \right) \sqrt{-\frac{a f -b e}{b}}}+\frac{b \,d^{2} \ln \left(\frac{\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) f}{d}-\frac{2 \left(c f -d e \right)}{d}+2 \sqrt{-\frac{c f -d e}{d}}\, \sqrt{\left(x -\frac{\sqrt{-c d}}{d}\right)^{2} f +\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) f}{d}-\frac{c f -d e}{d}}}{x -\frac{\sqrt{-c d}}{d}}\right)}{2 \left(\sqrt{-c d}\, b +\sqrt{-a b}\, d \right) \left(-\sqrt{-c d}\, b +\sqrt{-a b}\, d \right) \sqrt{-c d}\, \sqrt{-\frac{c f -d e}{d}}}-\frac{b \,d^{2} \ln \left(\frac{-\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) f}{d}-\frac{2 \left(c f -d e \right)}{d}+2 \sqrt{-\frac{c f -d e}{d}}\, \sqrt{\left(x +\frac{\sqrt{-c d}}{d}\right)^{2} f -\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) f}{d}-\frac{c f -d e}{d}}}{x +\frac{\sqrt{-c d}}{d}}\right)}{2 \left(\sqrt{-c d}\, b +\sqrt{-a b}\, d \right) \left(-\sqrt{-c d}\, b +\sqrt{-a b}\, d \right) \sqrt{-c d}\, \sqrt{-\frac{c f -d e}{d}}}"," ",0,"1/2*b*d^2/((-a*b)^(1/2)*d+(-c*d)^(1/2)*b)/((-a*b)^(1/2)*d-(-c*d)^(1/2)*b)/(-c*d)^(1/2)/(-(c*f-d*e)/d)^(1/2)*ln((2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)/d*f-2*(c*f-d*e)/d+2*(-(c*f-d*e)/d)^(1/2)*((x-(-c*d)^(1/2)/d)^2*f+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)/d*f-(c*f-d*e)/d)^(1/2))/(x-(-c*d)^(1/2)/d))+1/2*b^2*d/(-a*b)^(1/2)/((-a*b)^(1/2)*d+(-c*d)^(1/2)*b)/((-a*b)^(1/2)*d-(-c*d)^(1/2)*b)/(-(a*f-b*e)/b)^(1/2)*ln((-2*(a*f-b*e)/b-2*f*(-a*b)^(1/2)/b*(x+(-a*b)^(1/2)/b)+2*(-(a*f-b*e)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*f-2*f*(-a*b)^(1/2)/b*(x+(-a*b)^(1/2)/b)-(a*f-b*e)/b)^(1/2))/(x+(-a*b)^(1/2)/b))-1/2*b*d^2/((-a*b)^(1/2)*d+(-c*d)^(1/2)*b)/((-a*b)^(1/2)*d-(-c*d)^(1/2)*b)/(-c*d)^(1/2)/(-(c*f-d*e)/d)^(1/2)*ln((-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)/d*f-2*(c*f-d*e)/d+2*(-(c*f-d*e)/d)^(1/2)*((x+(-c*d)^(1/2)/d)^2*f-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)/d*f-(c*f-d*e)/d)^(1/2))/(x+(-c*d)^(1/2)/d))-1/2*b^2*d/(-a*b)^(1/2)/((-a*b)^(1/2)*d+(-c*d)^(1/2)*b)/((-a*b)^(1/2)*d-(-c*d)^(1/2)*b)/(-(a*f-b*e)/b)^(1/2)*ln((-2*(a*f-b*e)/b+2*f*(-a*b)^(1/2)/b*(x-(-a*b)^(1/2)/b)+2*(-(a*f-b*e)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*f+2*f*(-a*b)^(1/2)/b*(x-(-a*b)^(1/2)/b)-(a*f-b*e)/b)^(1/2))/(x-(-a*b)^(1/2)/b))","B"
63,1,1865,177,0.036000," ","int(1/(b*x^2+a)^2/(d*x^2+c)/(f*x^2+e)^(1/2),x)","-\frac{b^{4} c \,d^{2} \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) f}{b}-\frac{2 \left(a f -b e \right)}{b}+2 \sqrt{-\frac{a f -b e}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} f +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) f}{b}-\frac{a f -b e}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-a b}\, \left(\sqrt{-c d}\, b +\sqrt{-a b}\, d \right)^{2} \left(-\sqrt{-c d}\, b +\sqrt{-a b}\, d \right)^{2} \sqrt{-\frac{a f -b e}{b}}\, a}+\frac{b^{4} c \,d^{2} \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) f}{b}-\frac{2 \left(a f -b e \right)}{b}+2 \sqrt{-\frac{a f -b e}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} f -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) f}{b}-\frac{a f -b e}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-a b}\, \left(\sqrt{-c d}\, b +\sqrt{-a b}\, d \right)^{2} \left(-\sqrt{-c d}\, b +\sqrt{-a b}\, d \right)^{2} \sqrt{-\frac{a f -b e}{b}}\, a}+\frac{3 b^{3} d^{3} \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) f}{b}-\frac{2 \left(a f -b e \right)}{b}+2 \sqrt{-\frac{a f -b e}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} f +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) f}{b}-\frac{a f -b e}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-a b}\, \left(\sqrt{-c d}\, b +\sqrt{-a b}\, d \right)^{2} \left(-\sqrt{-c d}\, b +\sqrt{-a b}\, d \right)^{2} \sqrt{-\frac{a f -b e}{b}}}-\frac{3 b^{3} d^{3} \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) f}{b}-\frac{2 \left(a f -b e \right)}{b}+2 \sqrt{-\frac{a f -b e}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} f -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) f}{b}-\frac{a f -b e}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-a b}\, \left(\sqrt{-c d}\, b +\sqrt{-a b}\, d \right)^{2} \left(-\sqrt{-c d}\, b +\sqrt{-a b}\, d \right)^{2} \sqrt{-\frac{a f -b e}{b}}}-\frac{b^{2} d^{4} \ln \left(\frac{\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) f}{d}-\frac{2 \left(c f -d e \right)}{d}+2 \sqrt{-\frac{c f -d e}{d}}\, \sqrt{\left(x -\frac{\sqrt{-c d}}{d}\right)^{2} f +\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) f}{d}-\frac{c f -d e}{d}}}{x -\frac{\sqrt{-c d}}{d}}\right)}{2 \left(\sqrt{-c d}\, b +\sqrt{-a b}\, d \right)^{2} \left(-\sqrt{-c d}\, b +\sqrt{-a b}\, d \right)^{2} \sqrt{-c d}\, \sqrt{-\frac{c f -d e}{d}}}+\frac{b^{2} d^{4} \ln \left(\frac{-\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) f}{d}-\frac{2 \left(c f -d e \right)}{d}+2 \sqrt{-\frac{c f -d e}{d}}\, \sqrt{\left(x +\frac{\sqrt{-c d}}{d}\right)^{2} f -\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) f}{d}-\frac{c f -d e}{d}}}{x +\frac{\sqrt{-c d}}{d}}\right)}{2 \left(\sqrt{-c d}\, b +\sqrt{-a b}\, d \right)^{2} \left(-\sqrt{-c d}\, b +\sqrt{-a b}\, d \right)^{2} \sqrt{-c d}\, \sqrt{-\frac{c f -d e}{d}}}+\frac{\sqrt{-a b}\, b d f \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) f}{b}-\frac{2 \left(a f -b e \right)}{b}+2 \sqrt{-\frac{a f -b e}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} f +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) f}{b}-\frac{a f -b e}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{4 \left(\sqrt{-c d}\, b +\sqrt{-a b}\, d \right) \left(-\sqrt{-c d}\, b +\sqrt{-a b}\, d \right) \left(a f -b e \right) \sqrt{-\frac{a f -b e}{b}}\, a}-\frac{\sqrt{-a b}\, b d f \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) f}{b}-\frac{2 \left(a f -b e \right)}{b}+2 \sqrt{-\frac{a f -b e}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} f -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) f}{b}-\frac{a f -b e}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{4 \left(\sqrt{-c d}\, b +\sqrt{-a b}\, d \right) \left(-\sqrt{-c d}\, b +\sqrt{-a b}\, d \right) \left(a f -b e \right) \sqrt{-\frac{a f -b e}{b}}\, a}-\frac{\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} f +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) f}{b}-\frac{a f -b e}{b}}\, b^{2} d}{4 \left(\sqrt{-c d}\, b +\sqrt{-a b}\, d \right) \left(-\sqrt{-c d}\, b +\sqrt{-a b}\, d \right) \left(a f -b e \right) \left(x -\frac{\sqrt{-a b}}{b}\right) a}-\frac{\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} f -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) f}{b}-\frac{a f -b e}{b}}\, b^{2} d}{4 \left(\sqrt{-c d}\, b +\sqrt{-a b}\, d \right) \left(-\sqrt{-c d}\, b +\sqrt{-a b}\, d \right) \left(a f -b e \right) \left(x +\frac{\sqrt{-a b}}{b}\right) a}"," ",0,"-1/2*b^2*d^4/((-c*d)^(1/2)*b+(-a*b)^(1/2)*d)^2/(-(-c*d)^(1/2)*b+(-a*b)^(1/2)*d)^2/(-c*d)^(1/2)/(-(c*f-d*e)/d)^(1/2)*ln((2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)/d*f-2*(c*f-d*e)/d+2*(-(c*f-d*e)/d)^(1/2)*((x-(-c*d)^(1/2)/d)^2*f+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)/d*f-(c*f-d*e)/d)^(1/2))/(x-(-c*d)^(1/2)/d))-3/4*b^3*d^3/(-a*b)^(1/2)/((-c*d)^(1/2)*b+(-a*b)^(1/2)*d)^2/(-(-c*d)^(1/2)*b+(-a*b)^(1/2)*d)^2/(-(a*f-b*e)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*f-2*(a*f-b*e)/b+2*(-(a*f-b*e)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*f-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*f-(a*f-b*e)/b)^(1/2))/(x+(-a*b)^(1/2)/b))+1/4*b^4*d^2/(-a*b)^(1/2)/a/((-c*d)^(1/2)*b+(-a*b)^(1/2)*d)^2/(-(-c*d)^(1/2)*b+(-a*b)^(1/2)*d)^2/(-(a*f-b*e)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*f-2*(a*f-b*e)/b+2*(-(a*f-b*e)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*f-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*f-(a*f-b*e)/b)^(1/2))/(x+(-a*b)^(1/2)/b))*c-1/4*b^2*d/a/((-c*d)^(1/2)*b+(-a*b)^(1/2)*d)/(-(-c*d)^(1/2)*b+(-a*b)^(1/2)*d)/(a*f-b*e)/(x-(-a*b)^(1/2)/b)*((x-(-a*b)^(1/2)/b)^2*f+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*f-(a*f-b*e)/b)^(1/2)+1/4*b*d/a/((-c*d)^(1/2)*b+(-a*b)^(1/2)*d)/(-(-c*d)^(1/2)*b+(-a*b)^(1/2)*d)*f*(-a*b)^(1/2)/(a*f-b*e)/(-(a*f-b*e)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*f-2*(a*f-b*e)/b+2*(-(a*f-b*e)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*f+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*f-(a*f-b*e)/b)^(1/2))/(x-(-a*b)^(1/2)/b))+1/2*b^2*d^4/((-c*d)^(1/2)*b+(-a*b)^(1/2)*d)^2/(-(-c*d)^(1/2)*b+(-a*b)^(1/2)*d)^2/(-c*d)^(1/2)/(-(c*f-d*e)/d)^(1/2)*ln((-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)/d*f-2*(c*f-d*e)/d+2*(-(c*f-d*e)/d)^(1/2)*((x+(-c*d)^(1/2)/d)^2*f-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)/d*f-(c*f-d*e)/d)^(1/2))/(x+(-c*d)^(1/2)/d))-1/4*b^2*d/a/((-c*d)^(1/2)*b+(-a*b)^(1/2)*d)/(-(-c*d)^(1/2)*b+(-a*b)^(1/2)*d)/(a*f-b*e)/(x+(-a*b)^(1/2)/b)*((x+(-a*b)^(1/2)/b)^2*f-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*f-(a*f-b*e)/b)^(1/2)-1/4*b*d/a/((-c*d)^(1/2)*b+(-a*b)^(1/2)*d)/(-(-c*d)^(1/2)*b+(-a*b)^(1/2)*d)*f*(-a*b)^(1/2)/(a*f-b*e)/(-(a*f-b*e)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*f-2*(a*f-b*e)/b+2*(-(a*f-b*e)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*f-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*f-(a*f-b*e)/b)^(1/2))/(x+(-a*b)^(1/2)/b))+3/4*b^3*d^3/(-a*b)^(1/2)/((-c*d)^(1/2)*b+(-a*b)^(1/2)*d)^2/(-(-c*d)^(1/2)*b+(-a*b)^(1/2)*d)^2/(-(a*f-b*e)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*f-2*(a*f-b*e)/b+2*(-(a*f-b*e)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*f+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*f-(a*f-b*e)/b)^(1/2))/(x-(-a*b)^(1/2)/b))-1/4*b^4*d^2/(-a*b)^(1/2)/a/((-c*d)^(1/2)*b+(-a*b)^(1/2)*d)^2/(-(-c*d)^(1/2)*b+(-a*b)^(1/2)*d)^2/(-(a*f-b*e)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*f-2*(a*f-b*e)/b+2*(-(a*f-b*e)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*f+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*f-(a*f-b*e)/b)^(1/2))/(x-(-a*b)^(1/2)/b))*c","B"
64,1,1891,649,0.062000," ","int((d*x^2+c)^(5/2)*(f*x^2+e)^(1/2)/(b*x^2+a),x)","-\frac{\sqrt{d \,x^{2}+c}\, \sqrt{f \,x^{2}+e}\, \left(-3 \sqrt{-\frac{d}{c}}\, a \,b^{3} d^{3} f^{3} x^{7}+5 \sqrt{-\frac{d}{c}}\, a^{2} b^{2} d^{3} f^{3} x^{5}-14 \sqrt{-\frac{d}{c}}\, a \,b^{3} c \,d^{2} f^{3} x^{5}-4 \sqrt{-\frac{d}{c}}\, a \,b^{3} d^{3} e \,f^{2} x^{5}+5 \sqrt{-\frac{d}{c}}\, a^{2} b^{2} c \,d^{2} f^{3} x^{3}+5 \sqrt{-\frac{d}{c}}\, a^{2} b^{2} d^{3} e \,f^{2} x^{3}-11 \sqrt{-\frac{d}{c}}\, a \,b^{3} c^{2} d \,f^{3} x^{3}-15 \sqrt{-\frac{d}{c}}\, a \,b^{3} c \,d^{2} e \,f^{2} x^{3}-\sqrt{-\frac{d}{c}}\, a \,b^{3} d^{3} e^{2} f \,x^{3}+15 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{4} d^{3} f^{3} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-15 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{4} d^{3} f^{3} \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)-45 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{3} b c \,d^{2} f^{3} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+45 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{3} b c \,d^{2} f^{3} \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)-15 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{3} b \,d^{3} e \,f^{2} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+15 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{3} b \,d^{3} e \,f^{2} \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)+45 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} b^{2} c^{2} d \,f^{3} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-45 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} b^{2} c^{2} d \,f^{3} \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)+5 \sqrt{-\frac{d}{c}}\, a^{2} b^{2} c \,d^{2} e \,f^{2} x +35 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} b^{2} c \,d^{2} e \,f^{2} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+5 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} b^{2} c \,d^{2} e \,f^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-45 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} b^{2} c \,d^{2} e \,f^{2} \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)+5 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} b^{2} d^{3} e^{2} f \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-5 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} b^{2} d^{3} e^{2} f \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-15 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,b^{3} c^{3} f^{3} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+15 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,b^{3} c^{3} f^{3} \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)-11 \sqrt{-\frac{d}{c}}\, a \,b^{3} c^{2} d e \,f^{2} x -23 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,b^{3} c^{2} d e \,f^{2} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-11 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,b^{3} c^{2} d e \,f^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+45 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,b^{3} c^{2} d e \,f^{2} \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)-\sqrt{-\frac{d}{c}}\, a \,b^{3} c \,d^{2} e^{2} f x -12 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,b^{3} c \,d^{2} e^{2} f \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+13 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,b^{3} c \,d^{2} e^{2} f \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+2 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,b^{3} d^{3} e^{3} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-2 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,b^{3} d^{3} e^{3} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-15 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b^{4} c^{3} e \,f^{2} \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)\right)}{15 \left(d f \,x^{4}+c f \,x^{2}+d e \,x^{2}+c e \right) \sqrt{-\frac{d}{c}}\, a \,b^{4} f^{2}}"," ",0,"-1/15*(d*x^2+c)^(1/2)*(f*x^2+e)^(1/2)*(-3*(-1/c*d)^(1/2)*x^7*a*b^3*d^3*f^3+15*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a^4*d^3*f^3-15*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-f/e)^(1/2)/(-1/c*d)^(1/2))*a^4*d^3*f^3+5*(-1/c*d)^(1/2)*x^5*a^2*b^2*d^3*f^3-23*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*b^3*c^2*d*e*f^2-12*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*b^3*c*d^2*e^2*f-45*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-f/e)^(1/2)/(-1/c*d)^(1/2))*a^2*b^2*c*d^2*e*f^2+45*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-f/e)^(1/2)/(-1/c*d)^(1/2))*a*b^3*c^2*d*e*f^2+5*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a^2*b^2*c*d^2*e*f^2-11*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*b^3*c^2*d*e*f^2+13*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*b^3*c*d^2*e^2*f-14*(-1/c*d)^(1/2)*x^5*a*b^3*c*d^2*f^3-4*(-1/c*d)^(1/2)*x^5*a*b^3*d^3*e*f^2+5*(-1/c*d)^(1/2)*x^3*a^2*b^2*c*d^2*f^3+5*(-1/c*d)^(1/2)*x^3*a^2*b^2*d^3*e*f^2-11*(-1/c*d)^(1/2)*x^3*a*b^3*c^2*d*f^3-(-1/c*d)^(1/2)*x^3*a*b^3*d^3*e^2*f-15*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*b^3*c^3*f^3-2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*b^3*d^3*e^3+2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*b^3*d^3*e^3+15*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-f/e)^(1/2)/(-1/c*d)^(1/2))*a*b^3*c^3*f^3-15*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-f/e)^(1/2)/(-1/c*d)^(1/2))*b^4*c^3*e*f^2+45*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-f/e)^(1/2)/(-1/c*d)^(1/2))*a^3*b*c*d^2*f^3+15*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-f/e)^(1/2)/(-1/c*d)^(1/2))*a^3*b*d^3*e*f^2-45*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-f/e)^(1/2)/(-1/c*d)^(1/2))*a^2*b^2*c^2*d*f^3+35*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a^2*b^2*c*d^2*e*f^2-15*(-1/c*d)^(1/2)*x^3*a*b^3*c*d^2*e*f^2-45*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a^3*b*c*d^2*f^3+45*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a^2*b^2*c^2*d*f^3-5*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a^2*b^2*d^3*e^2*f-15*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a^3*b*d^3*e*f^2+5*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a^2*b^2*d^3*e^2*f+5*(-1/c*d)^(1/2)*x*a^2*b^2*c*d^2*e*f^2-11*(-1/c*d)^(1/2)*x*a*b^3*c^2*d*e*f^2-(-1/c*d)^(1/2)*x*a*b^3*c*d^2*e^2*f)/(d*f*x^4+c*f*x^2+d*e*x^2+c*e)/b^4/f^2/(-1/c*d)^(1/2)/a","B"
65,1,1059,459,0.020000," ","int((d*x^2+c)^(3/2)*(f*x^2+e)^(1/2)/(b*x^2+a),x)","\frac{\sqrt{d \,x^{2}+c}\, \sqrt{f \,x^{2}+e}\, \left(\sqrt{-\frac{d}{c}}\, a \,b^{2} d^{2} f^{2} x^{5}+\sqrt{-\frac{d}{c}}\, a \,b^{2} c d \,f^{2} x^{3}+\sqrt{-\frac{d}{c}}\, a \,b^{2} d^{2} e f \,x^{3}+3 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{3} d^{2} f^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-3 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{3} d^{2} f^{2} \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)-6 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} b c d \,f^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+6 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} b c d \,f^{2} \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)-3 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} b \,d^{2} e f \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+3 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} b \,d^{2} e f \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)+3 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,b^{2} c^{2} f^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-3 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,b^{2} c^{2} f^{2} \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)+\sqrt{-\frac{d}{c}}\, a \,b^{2} c d e f x +4 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,b^{2} c d e f \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,b^{2} c d e f \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-6 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,b^{2} c d e f \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)+\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,b^{2} d^{2} e^{2} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,b^{2} d^{2} e^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+3 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b^{3} c^{2} e f \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)\right)}{3 \left(d f \,x^{4}+c f \,x^{2}+d e \,x^{2}+c e \right) \sqrt{-\frac{d}{c}}\, a \,b^{3} f}"," ",0,"1/3*(d*x^2+c)^(1/2)*(f*x^2+e)^(1/2)*((-1/c*d)^(1/2)*x^5*a*b^2*d^2*f^2+(-1/c*d)^(1/2)*x^3*a*b^2*c*d*f^2+(-1/c*d)^(1/2)*x^3*a*b^2*d^2*e*f+3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a^3*d^2*f^2-6*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a^2*b*c*d*f^2+3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*b^2*c^2*f^2+((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*b^2*c*d*e*f-((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*b^2*d^2*e^2-3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a^2*b*d^2*e*f+4*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*b^2*c*d*e*f+((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*b^2*d^2*e^2-3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*a^3*d^2*f^2+6*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*a^2*b*c*d*f^2+3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*a^2*b*d^2*e*f-3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*a*b^2*c^2*f^2-6*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*a*b^2*c*d*e*f+3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*b^3*c^2*e*f+(-1/c*d)^(1/2)*x*a*b^2*c*d*e*f)/(d*f*x^4+c*f*x^2+d*e*x^2+c*e)/b^3/(-1/c*d)^(1/2)/f/a","B"
66,1,340,392,0.016000," ","int((d*x^2+c)^(1/2)*(f*x^2+e)^(1/2)/(b*x^2+a),x)","\frac{\left(-a^{2} d f \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+a^{2} d f \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)+a b c f \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-a b c f \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)+a b d e \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-a b d e \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)+b^{2} c e \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)\right) \sqrt{d \,x^{2}+c}\, \sqrt{f \,x^{2}+e}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}}{\left(d f \,x^{4}+c f \,x^{2}+d e \,x^{2}+c e \right) \sqrt{-\frac{d}{c}}\, a \,b^{2}}"," ",0,"(-EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a^2*d*f+EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*b*c*f+EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*b*d*e+EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*a^2*d*f-EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*a*b*c*f-EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*a*b*d*e+EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*b^2*c*e)*(d*x^2+c)^(1/2)*(f*x^2+e)^(1/2)*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)/(d*f*x^4+c*f*x^2+d*e*x^2+c*e)/b^2/(-1/c*d)^(1/2)/a","A"
67,1,191,127,0.023000," ","int((f*x^2+e)^(1/2)/(b*x^2+a)/(d*x^2+c)^(1/2),x)","\frac{\left(a f \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-a f \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)+b e \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)\right) \sqrt{\frac{f \,x^{2}+e}{e}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{d \,x^{2}+c}\, \sqrt{f \,x^{2}+e}}{\sqrt{-\frac{d}{c}}\, \left(d f \,x^{4}+c f \,x^{2}+d e \,x^{2}+c e \right) a b}"," ",0,"(EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*f-EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*a*f+EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*b*e)*((f*x^2+e)/e)^(1/2)*((d*x^2+c)/c)^(1/2)/b*(d*x^2+c)^(1/2)*(f*x^2+e)^(1/2)/a/(-1/c*d)^(1/2)/(d*f*x^4+c*f*x^2+d*e*x^2+c*e)","A"
68,1,390,259,0.029000," ","int((f*x^2+e)^(1/2)/(b*x^2+a)/(d*x^2+c)^(3/2),x)","\frac{\left(\sqrt{-\frac{d}{c}}\, a d f \,x^{3}-\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a c f \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a c f \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)+\sqrt{-\frac{d}{c}}\, a d e x -\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a d e \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a d e \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b c e \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)\right) \sqrt{d \,x^{2}+c}\, \sqrt{f \,x^{2}+e}}{\sqrt{-\frac{d}{c}}\, \left(a d -b c \right) \left(d f \,x^{4}+c f \,x^{2}+d e \,x^{2}+c e \right) a c}"," ",0,"((-1/c*d)^(1/2)*a*d*f*x^3-EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*c*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*d*e*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*d*e*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*a*c*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*b*c*e*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+(-1/c*d)^(1/2)*a*d*e*x)*(d*x^2+c)^(1/2)*(f*x^2+e)^(1/2)/c/a/(-1/c*d)^(1/2)/(a*d-b*c)/(d*f*x^4+c*f*x^2+d*e*x^2+c*e)","A"
69,1,2068,466,0.043000," ","int((f*x^2+e)^(1/2)/(b*x^2+a)/(d*x^2+c)^(5/2),x)","\frac{\sqrt{-\frac{d}{c}}\, a^{2} c \,d^{3} f^{2} x^{5}-2 \sqrt{-\frac{d}{c}}\, a^{2} d^{4} e f \,x^{5}-4 \sqrt{-\frac{d}{c}}\, a b \,c^{2} d^{2} f^{2} x^{5}+5 \sqrt{-\frac{d}{c}}\, a b c \,d^{3} e f \,x^{5}+2 \sqrt{-\frac{d}{c}}\, a^{2} c^{2} d^{2} f^{2} x^{3}-2 \sqrt{-\frac{d}{c}}\, a^{2} c \,d^{3} e f \,x^{3}-\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} c \,d^{3} e f \,x^{2} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+2 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} c \,d^{3} e f \,x^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-2 \sqrt{-\frac{d}{c}}\, a^{2} d^{4} e^{2} x^{3}+2 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} d^{4} e^{2} x^{2} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-2 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} d^{4} e^{2} x^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-5 \sqrt{-\frac{d}{c}}\, a b \,c^{3} d \,f^{2} x^{3}+3 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a b \,c^{3} d \,f^{2} x^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-3 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a b \,c^{3} d \,f^{2} x^{2} \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)+2 \sqrt{-\frac{d}{c}}\, a b \,c^{2} d^{2} e f \,x^{3}+4 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a b \,c^{2} d^{2} e f \,x^{2} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-8 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a b \,c^{2} d^{2} e f \,x^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+3 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a b \,c^{2} d^{2} e f \,x^{2} \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)+5 \sqrt{-\frac{d}{c}}\, a b c \,d^{3} e^{2} x^{3}-5 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a b c \,d^{3} e^{2} x^{2} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+5 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a b c \,d^{3} e^{2} x^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+3 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b^{2} c^{3} d e f \,x^{2} \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)-3 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b^{2} c^{2} d^{2} e^{2} x^{2} \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)+2 \sqrt{-\frac{d}{c}}\, a^{2} c^{2} d^{2} e f x -\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} c^{2} d^{2} e f \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+2 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} c^{2} d^{2} e f \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-3 \sqrt{-\frac{d}{c}}\, a^{2} c \,d^{3} e^{2} x +2 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} c \,d^{3} e^{2} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-2 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} c \,d^{3} e^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+3 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a b \,c^{4} f^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-3 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a b \,c^{4} f^{2} \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)-5 \sqrt{-\frac{d}{c}}\, a b \,c^{3} d e f x +4 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a b \,c^{3} d e f \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-8 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a b \,c^{3} d e f \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+3 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a b \,c^{3} d e f \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)+6 \sqrt{-\frac{d}{c}}\, a b \,c^{2} d^{2} e^{2} x -5 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a b \,c^{2} d^{2} e^{2} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+5 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a b \,c^{2} d^{2} e^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+3 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b^{2} c^{4} e f \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)-3 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b^{2} c^{3} d \,e^{2} \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)}{3 \sqrt{f \,x^{2}+e}\, \left(a d -b c \right)^{2} \sqrt{-\frac{d}{c}}\, \left(c f -d e \right) \left(d \,x^{2}+c \right)^{\frac{3}{2}} a \,c^{2}}"," ",0,"1/3*(2*x^3*a^2*c^2*d^2*f^2*(-1/c*d)^(1/2)-3*x*a^2*c*d^3*e^2*(-1/c*d)^(1/2)-2*x^5*a^2*d^4*e*f*(-1/c*d)^(1/2)+x^5*a^2*c*d^3*f^2*(-1/c*d)^(1/2)+6*x*a*b*c^2*d^2*e^2*(-1/c*d)^(1/2)-2*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a^2*d^4*e^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+2*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a^2*d^4*e^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-2*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a^2*c*d^3*e^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+3*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*b*c^4*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+2*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a^2*c*d^3*e^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-3*EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*a*b*c^4*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+3*EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*b^2*c^4*e*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-3*EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*b^2*c^3*d*e^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+2*x*a^2*c^2*d^2*e*f*(-1/c*d)^(1/2)-4*x^5*a*b*c^2*d^2*f^2*(-1/c*d)^(1/2)-2*x^3*a^2*c*d^3*e*f*(-1/c*d)^(1/2)-5*x^3*a*b*c^3*d*f^2*(-1/c*d)^(1/2)+5*x^3*a*b*c*d^3*e^2*(-1/c*d)^(1/2)-2*x^3*a^2*d^4*e^2*(-1/c*d)^(1/2)-8*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a*b*c^2*d^2*e*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+4*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a*b*c^2*d^2*e*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+3*EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*x^2*a*b*c^2*d^2*e*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+2*x^3*a*b*c^2*d^2*e*f*(-1/c*d)^(1/2)-5*x*a*b*c^3*d*e*f*(-1/c*d)^(1/2)-3*EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*x^2*b^2*c^2*d^2*e^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+2*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a^2*c^2*d^2*e*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+5*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*b*c^2*d^2*e^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a^2*c^2*d^2*e*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-5*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*b*c^2*d^2*e^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+2*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a^2*c*d^3*e*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+3*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a*b*c^3*d*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+5*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a*b*c*d^3*e^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a^2*c*d^3*e*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-5*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a*b*c*d^3*e^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-3*EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*x^2*a*b*c^3*d*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+3*EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*x^2*b^2*c^3*d*e*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-8*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*b*c^3*d*e*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+4*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*b*c^3*d*e*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+3*EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*a*b*c^3*d*e*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+5*x^5*a*b*c*d^3*e*f*(-1/c*d)^(1/2))/(f*x^2+e)^(1/2)/(a*d-b*c)^2/(-1/c*d)^(1/2)/a/c^2/(c*f-d*e)/(d*x^2+c)^(3/2)","B"
70,1,6245,714,0.068000," ","int((f*x^2+e)^(1/2)/(b*x^2+a)/(d*x^2+c)^(7/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
71,1,1939,696,0.026000," ","int((d*x^2+c)^(3/2)*(f*x^2+e)^(3/2)/(b*x^2+a),x)","-\frac{\sqrt{d \,x^{2}+c}\, \sqrt{f \,x^{2}+e}\, \left(-3 \sqrt{-\frac{d}{c}}\, a \,b^{3} d^{2} f^{3} x^{7}+5 \sqrt{-\frac{d}{c}}\, a^{2} b^{2} d^{2} f^{3} x^{5}-9 \sqrt{-\frac{d}{c}}\, a \,b^{3} c d \,f^{3} x^{5}-9 \sqrt{-\frac{d}{c}}\, a \,b^{3} d^{2} e \,f^{2} x^{5}+5 \sqrt{-\frac{d}{c}}\, a^{2} b^{2} c d \,f^{3} x^{3}+5 \sqrt{-\frac{d}{c}}\, a^{2} b^{2} d^{2} e \,f^{2} x^{3}-6 \sqrt{-\frac{d}{c}}\, a \,b^{3} c^{2} f^{3} x^{3}-15 \sqrt{-\frac{d}{c}}\, a \,b^{3} c d e \,f^{2} x^{3}-6 \sqrt{-\frac{d}{c}}\, a \,b^{3} d^{2} e^{2} f \,x^{3}+15 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{4} d^{2} f^{3} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-15 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{4} d^{2} f^{3} \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)-30 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{3} b c d \,f^{3} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+30 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{3} b c d \,f^{3} \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)-15 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{3} b \,d^{2} e \,f^{2} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-15 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{3} b \,d^{2} e \,f^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+30 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{3} b \,d^{2} e \,f^{2} \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)+15 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} b^{2} c^{2} f^{3} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-15 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} b^{2} c^{2} f^{3} \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)+5 \sqrt{-\frac{d}{c}}\, a^{2} b^{2} c d e \,f^{2} x +20 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} b^{2} c d e \,f^{2} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+35 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} b^{2} c d e \,f^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-60 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} b^{2} c d e \,f^{2} \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)+20 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} b^{2} d^{2} e^{2} f \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-5 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} b^{2} d^{2} e^{2} f \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-15 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} b^{2} d^{2} e^{2} f \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)-6 \sqrt{-\frac{d}{c}}\, a \,b^{3} c^{2} e \,f^{2} x -3 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,b^{3} c^{2} e \,f^{2} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-21 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,b^{3} c^{2} e \,f^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+30 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,b^{3} c^{2} e \,f^{2} \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)-6 \sqrt{-\frac{d}{c}}\, a \,b^{3} c d \,e^{2} f x -27 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,b^{3} c d \,e^{2} f \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+3 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,b^{3} c d \,e^{2} f \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+30 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,b^{3} c d \,e^{2} f \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)-3 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,b^{3} d^{2} e^{3} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+3 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,b^{3} d^{2} e^{3} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-15 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b^{4} c^{2} e^{2} f \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)\right)}{15 \left(d f \,x^{4}+c f \,x^{2}+d e \,x^{2}+c e \right) \sqrt{-\frac{d}{c}}\, a \,b^{4} f}"," ",0,"-1/15*(d*x^2+c)^(1/2)*(f*x^2+e)^(1/2)*(-6*(-1/c*d)^(1/2)*x^3*a*b^3*c^2*f^3-3*(-1/c*d)^(1/2)*x^7*a*b^3*d^2*f^3-15*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*a^4*d^2*f^3+15*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a^4*d^2*f^3+5*(-1/c*d)^(1/2)*x^5*a^2*b^2*d^2*f^3+30*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*a*b^3*c*d*e^2*f+35*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a^2*b^2*c*d*e*f^2+3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*b^3*c*d*e^2*f+20*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a^2*b^2*c*d*e*f^2-27*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*b^3*c*d*e^2*f-60*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*a^2*b^2*c*d*e*f^2+15*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a^2*b^2*c^2*f^3+3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*b^3*d^2*e^3-3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*b^3*d^2*e^3-15*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*a^2*b^2*c^2*f^3-15*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*b^4*c^2*e^2*f-9*(-1/c*d)^(1/2)*x^5*a*b^3*c*d*f^3-9*(-1/c*d)^(1/2)*x^5*a*b^3*d^2*e*f^2+5*(-1/c*d)^(1/2)*x^3*a^2*b^2*c*d*f^3+5*(-1/c*d)^(1/2)*x^3*a^2*b^2*d^2*e*f^2-6*(-1/c*d)^(1/2)*x^3*a*b^3*d^2*e^2*f-6*(-1/c*d)^(1/2)*x*a*b^3*c^2*e*f^2+5*(-1/c*d)^(1/2)*x*a^2*b^2*c*d*e*f^2-6*(-1/c*d)^(1/2)*x*a*b^3*c*d*e^2*f-15*(-1/c*d)^(1/2)*x^3*a*b^3*c*d*e*f^2-30*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a^3*b*c*d*f^3-15*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a^3*b*d^2*e*f^2-5*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a^2*b^2*d^2*e^2*f-21*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*b^3*c^2*e*f^2-15*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a^3*b*d^2*e*f^2+20*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a^2*b^2*d^2*e^2*f-3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*b^3*c^2*e*f^2+30*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*a^3*b*c*d*f^3+30*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*a^3*b*d^2*e*f^2-15*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*a^2*b^2*d^2*e^2*f+30*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*a*b^3*c^2*e*f^2)/f/(d*f*x^4+c*f*x^2+d*e*x^2+c*e)/b^4/(-1/c*d)^(1/2)/a","B"
72,1,1028,462,0.022000," ","int((d*x^2+c)^(1/2)*(f*x^2+e)^(3/2)/(b*x^2+a),x)","\frac{\sqrt{d \,x^{2}+c}\, \sqrt{f \,x^{2}+e}\, \left(\sqrt{-\frac{d}{c}}\, a \,b^{2} d \,f^{2} x^{5}+\sqrt{-\frac{d}{c}}\, a \,b^{2} c \,f^{2} x^{3}+\sqrt{-\frac{d}{c}}\, a \,b^{2} d e f \,x^{3}+3 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{3} d \,f^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-3 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{3} d \,f^{2} \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)-3 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} b c \,f^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+3 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} b c \,f^{2} \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)-3 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} b d e f \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-3 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} b d e f \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+6 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} b d e f \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)+\sqrt{-\frac{d}{c}}\, a \,b^{2} c e f x +\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,b^{2} c e f \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+4 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,b^{2} c e f \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-6 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,b^{2} c e f \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)+4 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,b^{2} d \,e^{2} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,b^{2} d \,e^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-3 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,b^{2} d \,e^{2} \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)+3 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b^{3} c \,e^{2} \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)\right)}{3 \left(d f \,x^{4}+c f \,x^{2}+d e \,x^{2}+c e \right) \sqrt{-\frac{d}{c}}\, a \,b^{3}}"," ",0,"1/3*(d*x^2+c)^(1/2)*(f*x^2+e)^(1/2)*((-1/c*d)^(1/2)*x^5*a*b^2*d*f^2+(-1/c*d)^(1/2)*x^3*a*b^2*c*f^2+(-1/c*d)^(1/2)*x^3*a*b^2*d*e*f+3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a^3*d*f^2-3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a^2*b*c*f^2-3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a^2*b*d*e*f+4*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*b^2*c*e*f-((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*b^2*d*e^2-3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a^2*b*d*e*f+((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*b^2*c*e*f+4*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*b^2*d*e^2-3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*a^3*d*f^2+3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*a^2*b*c*f^2+6*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*a^2*b*d*e*f-6*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*a*b^2*c*e*f-3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*a*b^2*d*e^2+3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*b^3*c*e^2+(-1/c*d)^(1/2)*x*a*b^2*c*e*f)/(d*f*x^4+c*f*x^2+d*e*x^2+c*e)/b^3/(-1/c*d)^(1/2)/a","B"
73,1,300,399,0.023000," ","int((f*x^2+e)^(3/2)/(b*x^2+a)/(d*x^2+c)^(1/2),x)","\frac{\left(-a^{2} f^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+a^{2} f^{2} \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)+a b e f \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+a b e f \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-2 a b e f \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)+b^{2} e^{2} \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)\right) \sqrt{\frac{f \,x^{2}+e}{e}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{d \,x^{2}+c}\, \sqrt{f \,x^{2}+e}}{\sqrt{-\frac{d}{c}}\, \left(d f \,x^{4}+c f \,x^{2}+d e \,x^{2}+c e \right) a \,b^{2}}"," ",0,"(-EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a^2*f^2+EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*b*e*f+EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*b*e*f+EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*a^2*f^2-2*EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*a*b*e*f+EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*b^2*e^2)*((f*x^2+e)/e)^(1/2)*((d*x^2+c)/c)^(1/2)*(d*x^2+c)^(1/2)*(f*x^2+e)^(1/2)/a/(-1/c*d)^(1/2)/b^2/(d*f*x^4+c*f*x^2+d*e*x^2+c*e)","A"
74,1,630,274,0.031000," ","int((f*x^2+e)^(3/2)/(b*x^2+a)/(d*x^2+c)^(3/2),x)","\frac{\left(-\sqrt{-\frac{d}{c}}\, a b c \,f^{2} x^{3}+\sqrt{-\frac{d}{c}}\, a b d e f \,x^{3}+\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} c \,f^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} c \,f^{2} \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)-\sqrt{-\frac{d}{c}}\, a b c e f x +\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a b c e f \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-2 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a b c e f \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+2 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a b c e f \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)+\sqrt{-\frac{d}{c}}\, a b d \,e^{2} x -\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a b d \,e^{2} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a b d \,e^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b^{2} c \,e^{2} \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)\right) \sqrt{d \,x^{2}+c}\, \sqrt{f \,x^{2}+e}}{\sqrt{-\frac{d}{c}}\, \left(a d -b c \right) \left(d f \,x^{4}+c f \,x^{2}+d e \,x^{2}+c e \right) a b c}"," ",0,"(-x^3*a*b*c*f^2*(-1/c*d)^(1/2)+x^3*a*b*d*e*f*(-1/c*d)^(1/2)+EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a^2*c*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-2*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*b*c*e*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*b*d*e^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*b*c*e*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*b*d*e^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*a^2*c*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+2*EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*a*b*c*e*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*b^2*c*e^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-x*a*b*c*e*f*(-1/c*d)^(1/2)+x*a*b*d*e^2*(-1/c*d)^(1/2))*(d*x^2+c)^(1/2)*(f*x^2+e)^(1/2)/b/c/a/(-1/c*d)^(1/2)/(a*d-b*c)/(d*f*x^4+c*f*x^2+d*e*x^2+c*e)","B"
75,1,1879,456,0.043000," ","int((f*x^2+e)^(3/2)/(b*x^2+a)/(d*x^2+c)^(5/2),x)","-\frac{-2 \sqrt{-\frac{d}{c}}\, a^{2} c \,d^{2} f^{2} x^{5}-2 \sqrt{-\frac{d}{c}}\, a^{2} d^{3} e f \,x^{5}-\sqrt{-\frac{d}{c}}\, a b \,c^{2} d \,f^{2} x^{5}+5 \sqrt{-\frac{d}{c}}\, a b c \,d^{2} e f \,x^{5}-\sqrt{-\frac{d}{c}}\, a^{2} c^{2} d \,f^{2} x^{3}+3 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} c^{2} d \,f^{2} x^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-3 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} c^{2} d \,f^{2} x^{2} \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)-5 \sqrt{-\frac{d}{c}}\, a^{2} c \,d^{2} e f \,x^{3}+2 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} c \,d^{2} e f \,x^{2} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} c \,d^{2} e f \,x^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-2 \sqrt{-\frac{d}{c}}\, a^{2} d^{3} e^{2} x^{3}+2 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} d^{3} e^{2} x^{2} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-2 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} d^{3} e^{2} x^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-2 \sqrt{-\frac{d}{c}}\, a b \,c^{3} f^{2} x^{3}+5 \sqrt{-\frac{d}{c}}\, a b \,c^{2} d e f \,x^{3}+\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a b \,c^{2} d e f \,x^{2} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-5 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a b \,c^{2} d e f \,x^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+6 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a b \,c^{2} d e f \,x^{2} \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)+5 \sqrt{-\frac{d}{c}}\, a b c \,d^{2} e^{2} x^{3}-5 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a b c \,d^{2} e^{2} x^{2} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+5 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a b c \,d^{2} e^{2} x^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-3 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b^{2} c^{2} d \,e^{2} x^{2} \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)+3 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} c^{3} f^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-3 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} c^{3} f^{2} \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)-\sqrt{-\frac{d}{c}}\, a^{2} c^{2} d e f x +2 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} c^{2} d e f \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} c^{2} d e f \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-3 \sqrt{-\frac{d}{c}}\, a^{2} c \,d^{2} e^{2} x +2 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} c \,d^{2} e^{2} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-2 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} c \,d^{2} e^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-2 \sqrt{-\frac{d}{c}}\, a b \,c^{3} e f x +\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a b \,c^{3} e f \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-5 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a b \,c^{3} e f \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+6 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a b \,c^{3} e f \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)+6 \sqrt{-\frac{d}{c}}\, a b \,c^{2} d \,e^{2} x -5 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a b \,c^{2} d \,e^{2} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+5 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a b \,c^{2} d \,e^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-3 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b^{2} c^{3} e^{2} \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)}{3 \sqrt{f \,x^{2}+e}\, \left(a d -b c \right)^{2} \sqrt{-\frac{d}{c}}\, \left(d \,x^{2}+c \right)^{\frac{3}{2}} a \,c^{2}}"," ",0,"-1/3*(-2*x^5*a^2*c*d^2*f^2*(-1/c*d)^(1/2)-2*x^3*a^2*d^3*e^2*(-1/c*d)^(1/2)-3*EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*b^2*c^3*e^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-2*x^5*a^2*d^3*e*f*(-1/c*d)^(1/2)-x^3*a^2*c^2*d*f^2*(-1/c*d)^(1/2)-2*x^3*a*b*c^3*f^2*(-1/c*d)^(1/2)-3*x*a^2*c*d^2*e^2*(-1/c*d)^(1/2)+3*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a^2*c^3*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-3*EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*a^2*c^3*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-5*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*b*c^2*d*e^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+5*x^5*a*b*c*d^2*e*f*(-1/c*d)^(1/2)+5*x^3*a*b*c^2*d*e*f*(-1/c*d)^(1/2)+3*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a^2*c^2*d*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-3*EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*x^2*a^2*c^2*d*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-3*EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*x^2*b^2*c^2*d*e^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a^2*c^2*d*e*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-5*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*b*c^3*e*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+5*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*b*c^2*d*e^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+6*EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*a*b*c^3*e*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+2*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a^2*c^2*d*e*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+6*EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*x^2*a*b*c^2*d*e*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a*b*c^2*d*e*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-5*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a*b*c^2*d*e*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*b*c^3*e*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a^2*c*d^2*e*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+5*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a*b*c*d^2*e^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+2*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a^2*c*d^2*e*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-5*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a*b*c*d^2*e^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-2*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a^2*d^3*e^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+2*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a^2*d^3*e^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-2*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a^2*c*d^2*e^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+2*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a^2*c*d^2*e^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-x^5*a*b*c^2*d*f^2*(-1/c*d)^(1/2)-5*x^3*a^2*c*d^2*e*f*(-1/c*d)^(1/2)+5*x^3*a*b*c*d^2*e^2*(-1/c*d)^(1/2)-x*a^2*c^2*d*e*f*(-1/c*d)^(1/2)-2*x*a*b*c^3*e*f*(-1/c*d)^(1/2)+6*x*a*b*c^2*d*e^2*(-1/c*d)^(1/2))/(f*x^2+e)^(1/2)/(a*d-b*c)^2/(-1/c*d)^(1/2)/a/c^2/(d*x^2+c)^(3/2)","B"
76,1,6215,723,0.068000," ","int((f*x^2+e)^(3/2)/(b*x^2+a)/(d*x^2+c)^(7/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
77,1,992,726,0.028000," ","int((d*x^2+c)^(5/2)/(b*x^2+a)/(f*x^2+e)^(1/2),x)","-\frac{\left(-\sqrt{-\frac{d}{c}}\, a \,b^{2} d^{3} f^{2} x^{5}-\sqrt{-\frac{d}{c}}\, a \,b^{2} c \,d^{2} f^{2} x^{3}-\sqrt{-\frac{d}{c}}\, a \,b^{2} d^{3} e f \,x^{3}-3 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{3} d^{3} f^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+3 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{3} d^{3} f^{2} \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)+9 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} b c \,d^{2} f^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-9 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} b c \,d^{2} f^{2} \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)+3 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} b \,d^{3} e f \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-3 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} b \,d^{3} e f \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-9 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,b^{2} c^{2} d \,f^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+9 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,b^{2} c^{2} d \,f^{2} \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)-\sqrt{-\frac{d}{c}}\, a \,b^{2} c \,d^{2} e f x -7 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,b^{2} c \,d^{2} e f \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+8 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,b^{2} c \,d^{2} e f \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+2 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,b^{2} d^{3} e^{2} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-2 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,b^{2} d^{3} e^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-3 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b^{3} c^{3} f^{2} \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)\right) \sqrt{f \,x^{2}+e}\, \sqrt{d \,x^{2}+c}}{3 \sqrt{-\frac{d}{c}}\, \left(d f \,x^{4}+c f \,x^{2}+d e \,x^{2}+c e \right) a \,b^{3} f^{2}}"," ",0,"-1/3*(-(-1/c*d)^(1/2)*x^5*a*b^2*d^3*f^2-(-1/c*d)^(1/2)*x^3*a*b^2*c*d^2*f^2-(-1/c*d)^(1/2)*x^3*a*b^2*d^3*e*f+3*EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*a^3*d^3*f^2-9*EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*a^2*b*c*d^2*f^2+9*EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*a*b^2*c^2*d*f^2-3*EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*b^3*c^3*f^2-3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a^3*d^3*f^2+9*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a^2*b*c*d^2*f^2-3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a^2*b*d^3*e*f-9*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*b^2*c^2*d*f^2+8*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*b^2*c*d^2*e*f-2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*b^2*d^3*e^2+3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a^2*b*d^3*e*f-7*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*b^2*c*d^2*e*f+2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*b^2*d^3*e^2-(-1/c*d)^(1/2)*x*a*b^2*c*d^2*e*f)*(f*x^2+e)^(1/2)*(d*x^2+c)^(1/2)/a/(-1/c*d)^(1/2)/f^2/b^3/(d*f*x^4+c*f*x^2+d*e*x^2+c*e)","A"
78,1,341,390,0.025000," ","int((d*x^2+c)^(3/2)/(b*x^2+a)/(f*x^2+e)^(1/2),x)","\frac{\left(-a^{2} d^{2} f \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+a^{2} d^{2} f \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)+2 a b c d f \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-2 a b c d f \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)+a b \,d^{2} e \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-a b \,d^{2} e \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+b^{2} c^{2} f \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)\right) \sqrt{\frac{f \,x^{2}+e}{e}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{f \,x^{2}+e}\, \sqrt{d \,x^{2}+c}}{\sqrt{-\frac{d}{c}}\, \left(d f \,x^{4}+c f \,x^{2}+d e \,x^{2}+c e \right) a \,b^{2} f}"," ",0,"(-EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a^2*d^2*f+2*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*b*c*d*f-EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*b*d^2*e+EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*b*d^2*e+EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*a^2*d^2*f-2*EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*a*b*c*d*f+EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*b^2*c^2*f)*((f*x^2+e)/e)^(1/2)*((d*x^2+c)/c)^(1/2)*(f*x^2+e)^(1/2)*(d*x^2+c)^(1/2)/f/a/(-1/c*d)^(1/2)/b^2/(d*f*x^4+c*f*x^2+d*e*x^2+c*e)","A"
79,1,191,127,0.023000," ","int((d*x^2+c)^(1/2)/(b*x^2+a)/(f*x^2+e)^(1/2),x)","\frac{\left(a d \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-a d \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)+b c \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)\right) \sqrt{\frac{f \,x^{2}+e}{e}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{f \,x^{2}+e}\, \sqrt{d \,x^{2}+c}}{\sqrt{-\frac{d}{c}}\, \left(d f \,x^{4}+c f \,x^{2}+d e \,x^{2}+c e \right) a b}"," ",0,"(EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*d-EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*a*d+EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*b*c)*((f*x^2+e)/e)^(1/2)*((d*x^2+c)/c)^(1/2)/b*(f*x^2+e)^(1/2)*(d*x^2+c)^(1/2)/a/(-1/c*d)^(1/2)/(d*f*x^4+c*f*x^2+d*e*x^2+c*e)","A"
80,1,118,85,0.023000," ","int(1/(b*x^2+a)/(d*x^2+c)^(1/2)/(f*x^2+e)^(1/2),x)","\frac{\sqrt{\frac{f \,x^{2}+e}{e}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{f \,x^{2}+e}\, \sqrt{d \,x^{2}+c}\, \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)}{\sqrt{-\frac{d}{c}}\, \left(d f \,x^{4}+c f \,x^{2}+d e \,x^{2}+c e \right) a}"," ",0,"EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*((f*x^2+e)/e)^(1/2)*((d*x^2+c)/c)^(1/2)*(f*x^2+e)^(1/2)*(d*x^2+c)^(1/2)/a/(-1/c*d)^(1/2)/(d*f*x^4+c*f*x^2+d*e*x^2+c*e)","A"
81,1,413,419,0.033000," ","int(1/(b*x^2+a)/(d*x^2+c)^(3/2)/(f*x^2+e)^(1/2),x)","\frac{\left(-\sqrt{-\frac{d}{c}}\, a \,d^{2} f \,x^{3}+\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a c d f \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-\sqrt{-\frac{d}{c}}\, a \,d^{2} e x +\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,d^{2} e \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,d^{2} e \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b \,c^{2} f \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)+\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b c d e \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)\right) \sqrt{f \,x^{2}+e}\, \sqrt{d \,x^{2}+c}}{\left(c f -d e \right) \sqrt{-\frac{d}{c}}\, \left(a d -b c \right) \left(d f \,x^{4}+c f \,x^{2}+d e \,x^{2}+c e \right) a c}"," ",0,"(-x^3*a*d^2*f*(-1/c*d)^(1/2)+EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*c*d*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*d^2*e*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*d^2*e*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*b*c^2*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*b*c*d*e*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-x*a*d^2*e*(-1/c*d)^(1/2))*(f*x^2+e)^(1/2)*(d*x^2+c)^(1/2)/c/(c*f-d*e)/a/(-1/c*d)^(1/2)/(a*d-b*c)/(d*f*x^4+c*f*x^2+d*e*x^2+c*e)","A"
82,1,2062,460,0.051000," ","int(1/(b*x^2+a)/(d*x^2+c)^(5/2)/(f*x^2+e)^(1/2),x)","\frac{-4 \sqrt{-\frac{d}{c}}\, a^{2} c \,d^{4} f^{2} x^{5}+2 \sqrt{-\frac{d}{c}}\, a^{2} d^{5} e f \,x^{5}+7 \sqrt{-\frac{d}{c}}\, a b \,c^{2} d^{3} f^{2} x^{5}-5 \sqrt{-\frac{d}{c}}\, a b c \,d^{4} e f \,x^{5}-5 \sqrt{-\frac{d}{c}}\, a^{2} c^{2} d^{3} f^{2} x^{3}+3 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} c^{2} d^{3} f^{2} x^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-\sqrt{-\frac{d}{c}}\, a^{2} c \,d^{4} e f \,x^{3}+4 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} c \,d^{4} e f \,x^{2} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-5 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} c \,d^{4} e f \,x^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+2 \sqrt{-\frac{d}{c}}\, a^{2} d^{5} e^{2} x^{3}-2 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} d^{5} e^{2} x^{2} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+2 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} d^{5} e^{2} x^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+8 \sqrt{-\frac{d}{c}}\, a b \,c^{3} d^{2} f^{2} x^{3}-6 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a b \,c^{3} d^{2} f^{2} x^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+\sqrt{-\frac{d}{c}}\, a b \,c^{2} d^{3} e f \,x^{3}-7 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a b \,c^{2} d^{3} e f \,x^{2} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+11 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a b \,c^{2} d^{3} e f \,x^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-5 \sqrt{-\frac{d}{c}}\, a b c \,d^{4} e^{2} x^{3}+5 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a b c \,d^{4} e^{2} x^{2} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-5 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a b c \,d^{4} e^{2} x^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+3 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b^{2} c^{4} d \,f^{2} x^{2} \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)-6 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b^{2} c^{3} d^{2} e f \,x^{2} \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)+3 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b^{2} c^{2} d^{3} e^{2} x^{2} \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)+3 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} c^{3} d^{2} f^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-5 \sqrt{-\frac{d}{c}}\, a^{2} c^{2} d^{3} e f x +4 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} c^{2} d^{3} e f \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-5 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} c^{2} d^{3} e f \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+3 \sqrt{-\frac{d}{c}}\, a^{2} c \,d^{4} e^{2} x -2 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} c \,d^{4} e^{2} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+2 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} c \,d^{4} e^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-6 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a b \,c^{4} d \,f^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+8 \sqrt{-\frac{d}{c}}\, a b \,c^{3} d^{2} e f x -7 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a b \,c^{3} d^{2} e f \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+11 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a b \,c^{3} d^{2} e f \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-6 \sqrt{-\frac{d}{c}}\, a b \,c^{2} d^{3} e^{2} x +5 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a b \,c^{2} d^{3} e^{2} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-5 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a b \,c^{2} d^{3} e^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+3 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b^{2} c^{5} f^{2} \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)-6 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b^{2} c^{4} d e f \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)+3 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b^{2} c^{3} d^{2} e^{2} \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)}{3 \sqrt{f \,x^{2}+e}\, \left(a d -b c \right)^{2} \sqrt{-\frac{d}{c}}\, \left(c f -d e \right)^{2} \left(d \,x^{2}+c \right)^{\frac{3}{2}} a \,c^{2}}"," ",0,"1/3*(3*x*a^2*c*d^4*e^2*(-1/c*d)^(1/2)+3*EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*b^2*c^5*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-4*x^5*a^2*c*d^4*f^2*(-1/c*d)^(1/2)+2*x^5*a^2*d^5*e*f*(-1/c*d)^(1/2)-5*x^3*a^2*c^2*d^3*f^2*(-1/c*d)^(1/2)-5*x^5*a*b*c*d^4*e*f*(-1/c*d)^(1/2)+2*x^3*a^2*d^5*e^2*(-1/c*d)^(1/2)+11*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a*b*c^2*d^3*e*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-7*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a*b*c^2*d^3*e*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-5*x*a^2*c^2*d^3*e*f*(-1/c*d)^(1/2)-6*x*a*b*c^2*d^3*e^2*(-1/c*d)^(1/2)+2*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a^2*d^5*e^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-2*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a^2*d^5*e^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+3*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a^2*c^3*d^2*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+2*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a^2*c*d^4*e^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-2*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a^2*c*d^4*e^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+3*EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*b^2*c^3*d^2*e^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+7*x^5*a*b*c^2*d^3*f^2*(-1/c*d)^(1/2)-x^3*a^2*c*d^4*e*f*(-1/c*d)^(1/2)+8*x^3*a*b*c^3*d^2*f^2*(-1/c*d)^(1/2)-5*x^3*a*b*c*d^4*e^2*(-1/c*d)^(1/2)-5*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a^2*c*d^4*e*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-6*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a*b*c^3*d^2*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-5*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a*b*c*d^4*e^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+4*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a^2*c*d^4*e*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+5*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a*b*c*d^4*e^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-6*EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*x^2*b^2*c^3*d^2*e*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+11*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*b*c^3*d^2*e*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-7*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*b*c^3*d^2*e*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+x^3*a*b*c^2*d^3*e*f*(-1/c*d)^(1/2)+8*x*a*b*c^3*d^2*e*f*(-1/c*d)^(1/2)+3*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a^2*c^2*d^3*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+3*EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*x^2*b^2*c^4*d*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+3*EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*x^2*b^2*c^2*d^3*e^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-5*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a^2*c^2*d^3*e*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-6*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*b*c^4*d*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-5*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*b*c^2*d^3*e^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+4*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a^2*c^2*d^3*e*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+5*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*b*c^2*d^3*e^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-6*EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*b^2*c^4*d*e*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2))/(f*x^2+e)^(1/2)/(a*d-b*c)^2/(-1/c*d)^(1/2)/a/(c*f-d*e)^2/c^2/(d*x^2+c)^(3/2)","B"
83,1,1063,1069,0.033000," ","int((d*x^2+c)^(5/2)/(b*x^2+a)/(f*x^2+e)^(3/2),x)","\frac{\left(\sqrt{-\frac{d}{c}}\, a \,b^{2} c^{2} d \,f^{3} x^{3}-2 \sqrt{-\frac{d}{c}}\, a \,b^{2} c \,d^{2} e \,f^{2} x^{3}+\sqrt{-\frac{d}{c}}\, a \,b^{2} d^{3} e^{2} f \,x^{3}-\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{3} d^{3} e \,f^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{3} d^{3} e \,f^{2} \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)+3 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} b c \,d^{2} e \,f^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-3 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} b c \,d^{2} e \,f^{2} \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)+\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} b \,d^{3} e^{2} f \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} b \,d^{3} e^{2} f \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+\sqrt{-\frac{d}{c}}\, a \,b^{2} c^{3} f^{3} x -2 \sqrt{-\frac{d}{c}}\, a \,b^{2} c^{2} d e \,f^{2} x -\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,b^{2} c^{2} d e \,f^{2} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+3 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,b^{2} c^{2} d e \,f^{2} \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)+\sqrt{-\frac{d}{c}}\, a \,b^{2} c \,d^{2} e^{2} f x +2 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,b^{2} c \,d^{2} e^{2} f \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-3 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,b^{2} c \,d^{2} e^{2} f \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-2 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,b^{2} d^{3} e^{3} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+2 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,b^{2} d^{3} e^{3} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b^{3} c^{3} e \,f^{2} \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)\right) \sqrt{f \,x^{2}+e}\, \sqrt{d \,x^{2}+c}}{\sqrt{-\frac{d}{c}}\, \left(a f -b e \right) \left(d f \,x^{4}+c f \,x^{2}+d e \,x^{2}+c e \right) a \,b^{2} e \,f^{2}}"," ",0,"(x^3*a*b^2*c^2*d*f^3*(-1/c*d)^(1/2)-2*x^3*a*b^2*c*d^2*e*f^2*(-1/c*d)^(1/2)+x^3*a*b^2*d^3*e^2*f*(-1/c*d)^(1/2)-EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a^3*d^3*e*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+3*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a^2*b*c*d^2*e*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a^2*b*d^3*e^2*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-3*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*b^2*c*d^2*e^2*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+2*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*b^2*d^3*e^3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a^2*b*d^3*e^2*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*b^2*c^2*d*e*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+2*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*b^2*c*d^2*e^2*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-2*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*b^2*d^3*e^3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*a^3*d^3*e*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-3*EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*a^2*b*c*d^2*e*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+3*EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*a*b^2*c^2*d*e*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*b^3*c^3*e*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+x*a*b^2*c^3*f^3*(-1/c*d)^(1/2)-2*x*a*b^2*c^2*d*e*f^2*(-1/c*d)^(1/2)+x*a*b^2*c*d^2*e^2*f*(-1/c*d)^(1/2))*(f*x^2+e)^(1/2)*(d*x^2+c)^(1/2)/e/f^2/a/(-1/c*d)^(1/2)/b^2/(a*f-b*e)/(d*f*x^4+c*f*x^2+d*e*x^2+c*e)","A"
84,1,594,273,0.031000," ","int((d*x^2+c)^(3/2)/(b*x^2+a)/(f*x^2+e)^(3/2),x)","\frac{\left(\sqrt{-\frac{d}{c}}\, a b c d \,f^{2} x^{3}-\sqrt{-\frac{d}{c}}\, a b \,d^{2} e f \,x^{3}+\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} d^{2} e f \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} d^{2} e f \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)+\sqrt{-\frac{d}{c}}\, a b \,c^{2} f^{2} x -\sqrt{-\frac{d}{c}}\, a b c d e f x -\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a b c d e f \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+2 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a b c d e f \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)+\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a b \,d^{2} e^{2} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a b \,d^{2} e^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b^{2} c^{2} e f \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)\right) \sqrt{f \,x^{2}+e}\, \sqrt{d \,x^{2}+c}}{\sqrt{-\frac{d}{c}}\, \left(a f -b e \right) \left(d f \,x^{4}+c f \,x^{2}+d e \,x^{2}+c e \right) a b e f}"," ",0,"(x^3*a*b*c*d*f^2*(-1/c*d)^(1/2)-x^3*a*b*d^2*e*f*(-1/c*d)^(1/2)+EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a^2*d^2*e*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*b*d^2*e^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*b*c*d*e*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*b*d^2*e^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*a^2*d^2*e*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+2*EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*a*b*c*d*e*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*b^2*c^2*e*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+x*a*b*c^2*f^2*(-1/c*d)^(1/2)-x*a*b*c*d*e*f*(-1/c*d)^(1/2))*(f*x^2+e)^(1/2)*(d*x^2+c)^(1/2)/b/e/f/a/(-1/c*d)^(1/2)/(a*f-b*e)/(d*f*x^4+c*f*x^2+d*e*x^2+c*e)","B"
85,1,285,259,0.032000," ","int((d*x^2+c)^(1/2)/(b*x^2+a)/(f*x^2+e)^(3/2),x)","\frac{\left(\sqrt{-\frac{d}{c}}\, a d f \,x^{3}+\sqrt{-\frac{d}{c}}\, a c f x -\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a d e \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a d e \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)-\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b c e \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)\right) \sqrt{f \,x^{2}+e}\, \sqrt{d \,x^{2}+c}}{\sqrt{-\frac{d}{c}}\, \left(a f -b e \right) \left(d f \,x^{4}+c f \,x^{2}+d e \,x^{2}+c e \right) a e}"," ",0,"((-1/c*d)^(1/2)*a*d*f*x^3-EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*d*e*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*a*d*e*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*b*c*e*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+x*a*c*f*(-1/c*d)^(1/2))*(f*x^2+e)^(1/2)*(d*x^2+c)^(1/2)/e/a/(-1/c*d)^(1/2)/(a*f-b*e)/(d*f*x^4+c*f*x^2+d*e*x^2+c*e)","A"
86,1,303,419,0.031000," ","int(1/(b*x^2+a)/(d*x^2+c)^(1/2)/(f*x^2+e)^(3/2),x)","\frac{\left(\sqrt{-\frac{d}{c}}\, a d \,f^{2} x^{3}+\sqrt{-\frac{d}{c}}\, a c \,f^{2} x -\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a d e f \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b c e f \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)+\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b d \,e^{2} \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)\right) \sqrt{f \,x^{2}+e}\, \sqrt{d \,x^{2}+c}}{\left(c f -d e \right) \sqrt{-\frac{d}{c}}\, \left(a f -b e \right) \left(d f \,x^{4}+c f \,x^{2}+d e \,x^{2}+c e \right) a e}"," ",0,"((-1/c*d)^(1/2)*a*d*f^2*x^3-((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*d*e*f-EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*b*c*e*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*b*d*e^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+(-1/c*d)^(1/2)*a*c*f^2*x)*(f*x^2+e)^(1/2)*(d*x^2+c)^(1/2)/e/(c*f-d*e)/a/(-1/c*d)^(1/2)/(a*f-b*e)/(d*f*x^4+c*f*x^2+d*e*x^2+c*e)","A"
87,1,956,635,0.040000," ","int(1/(b*x^2+a)/(d*x^2+c)^(3/2)/(f*x^2+e)^(3/2),x)","\frac{\left(\sqrt{-\frac{d}{c}}\, a^{2} c \,d^{2} f^{3} x^{3}+\sqrt{-\frac{d}{c}}\, a^{2} d^{3} e \,f^{2} x^{3}-\sqrt{-\frac{d}{c}}\, a b \,c^{2} d \,f^{3} x^{3}-\sqrt{-\frac{d}{c}}\, a b \,d^{3} e^{2} f \,x^{3}+\sqrt{-\frac{d}{c}}\, a^{2} c^{2} d \,f^{3} x -\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} c \,d^{2} e \,f^{2} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} c \,d^{2} e \,f^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+\sqrt{-\frac{d}{c}}\, a^{2} d^{3} e^{2} f x -\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} d^{3} e^{2} f \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} d^{3} e^{2} f \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-\sqrt{-\frac{d}{c}}\, a b \,c^{3} f^{3} x +\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a b \,c^{2} d e \,f^{2} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a b c \,d^{2} e^{2} f \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-\sqrt{-\frac{d}{c}}\, a b \,d^{3} e^{3} x +\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a b \,d^{3} e^{3} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a b \,d^{3} e^{3} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b^{2} c^{3} e \,f^{2} \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)-2 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b^{2} c^{2} d \,e^{2} f \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)+\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b^{2} c \,d^{2} e^{3} \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)\right) \sqrt{f \,x^{2}+e}\, \sqrt{d \,x^{2}+c}}{\left(c f -d e \right)^{2} \sqrt{-\frac{d}{c}}\, \left(a f -b e \right) \left(a d -b c \right) \left(d f \,x^{4}+c f \,x^{2}+d e \,x^{2}+c e \right) a c e}"," ",0,"(x^3*a^2*c*d^2*f^3*(-1/c*d)^(1/2)+x^3*a^2*d^3*e*f^2*(-1/c*d)^(1/2)-x^3*a*b*c^2*d*f^3*(-1/c*d)^(1/2)-x^3*a*b*d^3*e^2*f*(-1/c*d)^(1/2)-EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a^2*c*d^2*e*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a^2*d^3*e^2*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*b*c*d^2*e^2*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*b*d^3*e^3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a^2*c*d^2*e*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a^2*d^3*e^2*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*b*c^2*d*e*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*b*d^3*e^3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*b^2*c^3*e*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-2*EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*b^2*c^2*d*e^2*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*b^2*c*d^2*e^3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+x*a^2*c^2*d*f^3*(-1/c*d)^(1/2)+x*a^2*d^3*e^2*f*(-1/c*d)^(1/2)-x*a*b*c^3*f^3*(-1/c*d)^(1/2)-x*a*b*d^3*e^3*(-1/c*d)^(1/2))*(f*x^2+e)^(1/2)*(d*x^2+c)^(1/2)/c/e/(c*f-d*e)^2/a/(-1/c*d)^(1/2)/(a*f-b*e)/(a*d-b*c)/(d*f*x^4+c*f*x^2+d*e*x^2+c*e)","A"
88,1,4115,923,0.066000," ","int(1/(b*x^2+a)/(d*x^2+c)^(5/2)/(f*x^2+e)^(3/2),x)","\text{output too large to display}"," ",0,"-1/3*(-6*x^3*a^3*c^3*d^3*f^4*(-1/c*d)^(1/2)+2*x^3*a^3*d^6*e^3*f*(-1/c*d)^(1/2)-2*x^3*a^2*b*d^6*e^4*(-1/c*d)^(1/2)-3*x*a^3*c^4*d^2*f^4*(-1/c*d)^(1/2)-3*x*a*b^2*c^6*f^4*(-1/c*d)^(1/2)-3*x^5*a^3*c^2*d^4*f^4*(-1/c*d)^(1/2)+2*x^5*a^3*d^6*e^2*f^2*(-1/c*d)^(1/2)+2*x^5*a^2*b*c*d^5*e^2*f^2*(-1/c*d)^(1/2)+5*x^5*a*b^2*c*d^5*e^3*f*(-1/c*d)^(1/2)+11*x^3*a^2*b*c^3*d^3*e*f^3*(-1/c*d)^(1/2)+12*x^3*a^2*b*c^2*d^4*e^2*f^2*(-1/c*d)^(1/2)-x^3*a^2*b*c*d^5*e^3*f*(-1/c*d)^(1/2)-11*x^3*a*b^2*c^3*d^3*e^2*f^2*(-1/c*d)^(1/2)-4*x^3*a*b^2*c^2*d^4*e^3*f*(-1/c*d)^(1/2)+11*x*a^2*b*c^3*d^3*e^2*f^2*(-1/c*d)^(1/2)+2*x*a^2*b*c^2*d^4*e^3*f*(-1/c*d)^(1/2)+10*x^5*a^2*b*c^2*d^4*e*f^3*(-1/c*d)^(1/2)-11*x*a*b^2*c^3*d^3*e^3*f*(-1/c*d)^(1/2)+2*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a^3*d^6*e^3*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-2*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a^2*b*d^6*e^4*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-2*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a^3*d^6*e^3*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+2*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a^2*b*d^6*e^4*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-3*EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*x^2*b^3*c^2*d^4*e^4*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+6*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a^3*c^3*d^3*e*f^3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-8*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a^3*c^2*d^4*e^2*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+2*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a^3*c*d^5*e^3*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-2*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a^2*b*c*d^5*e^4*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+5*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*b^2*c^2*d^4*e^4*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+3*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a^3*c^3*d^3*e*f^3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+7*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a^3*c^2*d^4*e^2*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-2*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a^3*c*d^5*e^3*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+2*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a^2*b*c*d^5*e^4*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-5*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*b^2*c^2*d^4*e^4*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-9*EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*b^3*c^5*d*e^2*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+9*EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*b^3*c^4*d^2*e^3*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-3*x^5*a*b^2*c^4*d^2*f^4*(-1/c*d)^(1/2)-8*x^3*a^3*c^2*d^4*e*f^3*(-1/c*d)^(1/2)-4*x^3*a^3*c*d^5*e^2*f^2*(-1/c*d)^(1/2)+12*x^3*a^2*b*c^4*d^2*f^4*(-1/c*d)^(1/2)-6*x^3*a*b^2*c^5*d*f^4*(-1/c*d)^(1/2)+5*x^3*a*b^2*c*d^5*e^4*(-1/c*d)^(1/2)-8*x*a^3*c^2*d^4*e^2*f^2*(-1/c*d)^(1/2)+3*x*a^3*c*d^5*e^3*f*(-1/c*d)^(1/2)+6*x*a^2*b*c^5*d*f^4*(-1/c*d)^(1/2)-3*x*a^2*b*c*d^5*e^4*(-1/c*d)^(1/2)+6*x*a*b^2*c^2*d^4*e^4*(-1/c*d)^(1/2)+3*EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*b^3*c^6*e*f^3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-3*EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*b^3*c^3*d^3*e^4*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-7*x^5*a^3*c*d^5*e*f^3*(-1/c*d)^(1/2)+6*x^5*a^2*b*c^3*d^3*f^4*(-1/c*d)^(1/2)-2*x^5*a^2*b*d^6*e^3*f*(-1/c*d)^(1/2)-10*x^5*a*b^2*c^2*d^4*e^2*f^2*(-1/c*d)^(1/2)-5*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a*b^2*c*d^5*e^4*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+3*EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*x^2*b^3*c^5*d*e*f^3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-9*EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*x^2*b^3*c^4*d^2*e^2*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+9*EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*x^2*b^3*c^3*d^3*e^3*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-9*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a^2*b*c^4*d^2*e*f^3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+8*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a^2*b*c^3*d^3*e^2*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+3*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a^2*b*c^2*d^4*e^3*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+9*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*b^2*c^4*d^2*e^2*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-14*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*b^2*c^3*d^3*e^3*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-6*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a^2*b*c^4*d^2*e*f^3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-10*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a^2*b*c^3*d^3*e^2*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-2*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a^2*b*c^2*d^4*e^3*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+3*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*b^2*c^5*d*e*f^3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+10*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a*b^2*c^3*d^3*e^3*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+6*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a^3*c^2*d^4*e*f^3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-8*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a^3*c*d^5*e^2*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+5*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a*b^2*c*d^5*e^4*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+3*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a^3*c^2*d^4*e*f^3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+7*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a^3*c*d^5*e^2*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-14*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a*b^2*c^2*d^4*e^3*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-6*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a^2*b*c^3*d^3*e*f^3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-10*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a^2*b*c^2*d^4*e^2*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-2*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a^2*b*c*d^5*e^3*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+3*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a*b^2*c^4*d^2*e*f^3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+10*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a*b^2*c^2*d^4*e^3*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)-9*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a^2*b*c^3*d^3*e*f^3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+8*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a^2*b*c^2*d^4*e^2*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+3*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a^2*b*c*d^5*e^3*f*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)+9*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a*b^2*c^3*d^3*e^2*f^2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2))/(f*x^2+e)^(1/2)/(a*d-b*c)^2/(a*f-b*e)/(-1/c*d)^(1/2)/a/(c*f-d*e)^3/e/c^2/(d*x^2+c)^(3/2)","B"
89,1,370,240,0.066000," ","int((x^2+1)^(3/2)*(x^2+2)^(1/2)/(b*x^2+a),x)","-\frac{\sqrt{x^{2}+1}\, \sqrt{x^{2}+2}\, \left(-a \,b^{2} x^{5}-3 a \,b^{2} x^{3}+3 i \sqrt{x^{2}+2}\, \sqrt{x^{2}+1}\, a^{3} \EllipticF \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)-3 i \sqrt{x^{2}+2}\, \sqrt{x^{2}+1}\, a^{3} \EllipticPi \left(\frac{i \sqrt{2}\, x}{2}, \frac{2 b}{a}, \sqrt{2}\right)-3 i \sqrt{x^{2}+2}\, \sqrt{x^{2}+1}\, a^{2} b \EllipticE \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)-9 i \sqrt{x^{2}+2}\, \sqrt{x^{2}+1}\, a^{2} b \EllipticF \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)+12 i \sqrt{x^{2}+2}\, \sqrt{x^{2}+1}\, a^{2} b \EllipticPi \left(\frac{i \sqrt{2}\, x}{2}, \frac{2 b}{a}, \sqrt{2}\right)-2 a \,b^{2} x +6 i \sqrt{x^{2}+2}\, \sqrt{x^{2}+1}\, a \,b^{2} \EllipticE \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)+7 i \sqrt{x^{2}+2}\, \sqrt{x^{2}+1}\, a \,b^{2} \EllipticF \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)-15 i \sqrt{x^{2}+2}\, \sqrt{x^{2}+1}\, a \,b^{2} \EllipticPi \left(\frac{i \sqrt{2}\, x}{2}, \frac{2 b}{a}, \sqrt{2}\right)+6 i \sqrt{x^{2}+2}\, \sqrt{x^{2}+1}\, b^{3} \EllipticPi \left(\frac{i \sqrt{2}\, x}{2}, \frac{2 b}{a}, \sqrt{2}\right)\right)}{3 \left(x^{4}+3 x^{2}+2\right) a \,b^{3}}"," ",0,"-1/3*(x^2+1)^(1/2)*(x^2+2)^(1/2)*(-x^5*a*b^2+3*I*(x^2+2)^(1/2)*EllipticF(1/2*I*x*2^(1/2),2^(1/2))*(x^2+1)^(1/2)*a^3-9*I*(x^2+2)^(1/2)*EllipticF(1/2*I*x*2^(1/2),2^(1/2))*(x^2+1)^(1/2)*a^2*b+7*I*(x^2+2)^(1/2)*EllipticF(1/2*I*x*2^(1/2),2^(1/2))*(x^2+1)^(1/2)*a*b^2-3*I*(x^2+2)^(1/2)*EllipticE(1/2*I*x*2^(1/2),2^(1/2))*(x^2+1)^(1/2)*a^2*b+6*I*(x^2+2)^(1/2)*EllipticE(1/2*I*x*2^(1/2),2^(1/2))*(x^2+1)^(1/2)*a*b^2-3*I*(x^2+2)^(1/2)*EllipticPi(1/2*I*x*2^(1/2),2/a*b,2^(1/2))*(x^2+1)^(1/2)*a^3+12*I*(x^2+2)^(1/2)*EllipticPi(1/2*I*x*2^(1/2),2/a*b,2^(1/2))*(x^2+1)^(1/2)*a^2*b-15*I*(x^2+2)^(1/2)*EllipticPi(1/2*I*x*2^(1/2),2/a*b,2^(1/2))*(x^2+1)^(1/2)*a*b^2+6*I*(x^2+2)^(1/2)*EllipticPi(1/2*I*x*2^(1/2),2/a*b,2^(1/2))*(x^2+1)^(1/2)*b^3-3*x^3*a*b^2-2*x*a*b^2)/(x^4+3*x^2+2)/b^3/a","C"
90,1,120,198,0.012000," ","int((x^2+1)^(1/2)*(x^2+2)^(1/2)/(b*x^2+a),x)","-\frac{i \left(-a^{2} \EllipticF \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)+a^{2} \EllipticPi \left(\frac{i \sqrt{2}\, x}{2}, \frac{2 b}{a}, \sqrt{2}\right)+a b \EllipticE \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)+2 a b \EllipticF \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)-3 a b \EllipticPi \left(\frac{i \sqrt{2}\, x}{2}, \frac{2 b}{a}, \sqrt{2}\right)+2 b^{2} \EllipticPi \left(\frac{i \sqrt{2}\, x}{2}, \frac{2 b}{a}, \sqrt{2}\right)\right)}{a \,b^{2}}"," ",0,"-I*(a^2*EllipticPi(1/2*I*2^(1/2)*x,2/a*b,2^(1/2))-3*EllipticPi(1/2*I*2^(1/2)*x,2/a*b,2^(1/2))*b*a+2*EllipticPi(1/2*I*2^(1/2)*x,2/a*b,2^(1/2))*b^2-EllipticF(1/2*I*2^(1/2)*x,2^(1/2))*a^2+2*EllipticF(1/2*I*2^(1/2)*x,2^(1/2))*b*a+EllipticE(1/2*I*2^(1/2)*x,2^(1/2))*b*a)/a/b^2","C"
91,1,64,79,0.021000," ","int((x^2+2)^(1/2)/(x^2+1)^(1/2)/(b*x^2+a),x)","-\frac{i \left(a \EllipticF \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)-a \EllipticPi \left(\frac{i \sqrt{2}\, x}{2}, \frac{2 b}{a}, \sqrt{2}\right)+2 b \EllipticPi \left(\frac{i \sqrt{2}\, x}{2}, \frac{2 b}{a}, \sqrt{2}\right)\right)}{a b}"," ",0,"-I*(a*EllipticF(1/2*I*2^(1/2)*x,2^(1/2))-a*EllipticPi(1/2*I*2^(1/2)*x,2/a*b,2^(1/2))+2*b*EllipticPi(1/2*I*2^(1/2)*x,2/a*b,2^(1/2)))/a/b","A"
92,1,147,145,0.038000," ","int((x^2+2)^(1/2)/(x^2+1)^(3/2)/(b*x^2+a),x)","\frac{\left(a \,x^{3}+2 a x +i \sqrt{x^{2}+2}\, \sqrt{x^{2}+1}\, a \EllipticE \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)-i \sqrt{x^{2}+2}\, \sqrt{x^{2}+1}\, a \EllipticPi \left(\frac{i \sqrt{2}\, x}{2}, \frac{2 b}{a}, \sqrt{2}\right)+2 i \sqrt{x^{2}+2}\, \sqrt{x^{2}+1}\, b \EllipticPi \left(\frac{i \sqrt{2}\, x}{2}, \frac{2 b}{a}, \sqrt{2}\right)\right) \sqrt{x^{2}+1}\, \sqrt{x^{2}+2}}{\left(x^{4}+3 x^{2}+2\right) \left(a -b \right) a}"," ",0,"(I*EllipticE(1/2*I*2^(1/2)*x,2^(1/2))*a*(x^2+2)^(1/2)*(x^2+1)^(1/2)-I*EllipticPi(1/2*I*2^(1/2)*x,2/a*b,2^(1/2))*a*(x^2+2)^(1/2)*(x^2+1)^(1/2)+2*I*EllipticPi(1/2*I*2^(1/2)*x,2/a*b,2^(1/2))*b*(x^2+2)^(1/2)*(x^2+1)^(1/2)+a*x^3+2*a*x)*(x^2+1)^(1/2)*(x^2+2)^(1/2)/(x^4+3*x^2+2)/a/(a-b)","A"
93,1,477,234,0.040000," ","int((x^2+2)^(1/2)/(x^2+1)^(5/2)/(b*x^2+a),x)","\frac{3 a^{2} x^{5}-6 a b \,x^{5}+10 a^{2} x^{3}+3 i \sqrt{x^{2}+1}\, \sqrt{x^{2}+2}\, a^{2} x^{2} \EllipticE \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)-i \sqrt{x^{2}+1}\, \sqrt{x^{2}+2}\, a^{2} x^{2} \EllipticF \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)-19 a b \,x^{3}-6 i \sqrt{x^{2}+1}\, \sqrt{x^{2}+2}\, a b \,x^{2} \EllipticE \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)+i \sqrt{x^{2}+1}\, \sqrt{x^{2}+2}\, a b \,x^{2} \EllipticF \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)+3 i \sqrt{x^{2}+1}\, \sqrt{x^{2}+2}\, a b \,x^{2} \EllipticPi \left(\frac{i \sqrt{2}\, x}{2}, \frac{2 b}{a}, \sqrt{2}\right)-6 i \sqrt{x^{2}+1}\, \sqrt{x^{2}+2}\, b^{2} x^{2} \EllipticPi \left(\frac{i \sqrt{2}\, x}{2}, \frac{2 b}{a}, \sqrt{2}\right)+8 a^{2} x +3 i \sqrt{x^{2}+1}\, \sqrt{x^{2}+2}\, a^{2} \EllipticE \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)-i \sqrt{x^{2}+1}\, \sqrt{x^{2}+2}\, a^{2} \EllipticF \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)-14 a b x -6 i \sqrt{x^{2}+1}\, \sqrt{x^{2}+2}\, a b \EllipticE \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)+i \sqrt{x^{2}+1}\, \sqrt{x^{2}+2}\, a b \EllipticF \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)+3 i \sqrt{x^{2}+1}\, \sqrt{x^{2}+2}\, a b \EllipticPi \left(\frac{i \sqrt{2}\, x}{2}, \frac{2 b}{a}, \sqrt{2}\right)-6 i \sqrt{x^{2}+1}\, \sqrt{x^{2}+2}\, b^{2} \EllipticPi \left(\frac{i \sqrt{2}\, x}{2}, \frac{2 b}{a}, \sqrt{2}\right)}{3 \sqrt{x^{2}+2}\, \left(a -b \right)^{2} \left(x^{2}+1\right)^{\frac{3}{2}} a}"," ",0,"1/3*(-I*EllipticF(1/2*I*2^(1/2)*x,2^(1/2))*a^2*(x^2+1)^(1/2)*(x^2+2)^(1/2)+I*EllipticF(1/2*I*2^(1/2)*x,2^(1/2))*x^2*a*b*(x^2+1)^(1/2)*(x^2+2)^(1/2)-6*I*EllipticPi(1/2*I*2^(1/2)*x,2/a*b,2^(1/2))*x^2*b^2*(x^2+1)^(1/2)*(x^2+2)^(1/2)+3*I*EllipticE(1/2*I*2^(1/2)*x,2^(1/2))*a^2*(x^2+1)^(1/2)*(x^2+2)^(1/2)-6*I*EllipticE(1/2*I*2^(1/2)*x,2^(1/2))*a*b*(x^2+1)^(1/2)*(x^2+2)^(1/2)-6*I*EllipticE(1/2*I*2^(1/2)*x,2^(1/2))*x^2*a*b*(x^2+1)^(1/2)*(x^2+2)^(1/2)+3*x^5*a^2-6*x^5*a*b+3*I*EllipticPi(1/2*I*2^(1/2)*x,2/a*b,2^(1/2))*x^2*a*b*(x^2+1)^(1/2)*(x^2+2)^(1/2)-I*EllipticF(1/2*I*2^(1/2)*x,2^(1/2))*x^2*a^2*(x^2+1)^(1/2)*(x^2+2)^(1/2)-6*I*EllipticPi(1/2*I*2^(1/2)*x,2/a*b,2^(1/2))*b^2*(x^2+1)^(1/2)*(x^2+2)^(1/2)+3*I*EllipticPi(1/2*I*2^(1/2)*x,2/a*b,2^(1/2))*a*b*(x^2+1)^(1/2)*(x^2+2)^(1/2)+I*EllipticF(1/2*I*2^(1/2)*x,2^(1/2))*a*b*(x^2+1)^(1/2)*(x^2+2)^(1/2)+3*I*EllipticE(1/2*I*2^(1/2)*x,2^(1/2))*x^2*a^2*(x^2+1)^(1/2)*(x^2+2)^(1/2)+10*x^3*a^2-19*x^3*a*b+8*x*a^2-14*x*a*b)/(x^2+2)^(1/2)/(a-b)^2/a/(x^2+1)^(3/2)","B"
94,1,293,351,0.045000," ","int((d*x^2+2)^(1/2)*(f*x^2+3)^(1/2)/(b*x^2+a),x)","-\frac{\left(a^{2} d f \EllipticF \left(\frac{\sqrt{3}\, \sqrt{-f}\, x}{3}, \frac{\sqrt{3}\, \sqrt{2}\, \sqrt{\frac{d}{f}}}{2}\right)-a^{2} d f \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{-f}\, x}{3}, \frac{3 b}{a f}, \frac{\sqrt{2}\, \sqrt{-d}\, \sqrt{3}}{2 \sqrt{-f}}\right)-3 a b d \EllipticF \left(\frac{\sqrt{3}\, \sqrt{-f}\, x}{3}, \frac{\sqrt{3}\, \sqrt{2}\, \sqrt{\frac{d}{f}}}{2}\right)+3 a b d \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{-f}\, x}{3}, \frac{3 b}{a f}, \frac{\sqrt{2}\, \sqrt{-d}\, \sqrt{3}}{2 \sqrt{-f}}\right)-2 a b f \EllipticE \left(\frac{\sqrt{3}\, \sqrt{-f}\, x}{3}, \frac{\sqrt{3}\, \sqrt{2}\, \sqrt{\frac{d}{f}}}{2}\right)+2 a b f \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{-f}\, x}{3}, \frac{3 b}{a f}, \frac{\sqrt{2}\, \sqrt{-d}\, \sqrt{3}}{2 \sqrt{-f}}\right)-6 b^{2} \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{-f}\, x}{3}, \frac{3 b}{a f}, \frac{\sqrt{2}\, \sqrt{-d}\, \sqrt{3}}{2 \sqrt{-f}}\right)\right) \sqrt{2}}{2 \sqrt{-f}\, a \,b^{2}}"," ",0,"-1/2*(EllipticF(1/3*3^(1/2)*(-f)^(1/2)*x,1/2*3^(1/2)*2^(1/2)*(d/f)^(1/2))*a^2*d*f-a^2*EllipticPi(1/3*3^(1/2)*(-f)^(1/2)*x,3*b/a/f,1/2*2^(1/2)*(-d)^(1/2)*3^(1/2)/(-f)^(1/2))*d*f-3*EllipticF(1/3*3^(1/2)*(-f)^(1/2)*x,1/2*3^(1/2)*2^(1/2)*(d/f)^(1/2))*d*b*a-2*f*EllipticE(1/3*3^(1/2)*(-f)^(1/2)*x,1/2*3^(1/2)*2^(1/2)*(d/f)^(1/2))*b*a+3*EllipticPi(1/3*3^(1/2)*(-f)^(1/2)*x,3*b/a/f,1/2*2^(1/2)*(-d)^(1/2)*3^(1/2)/(-f)^(1/2))*d*b*a+2*EllipticPi(1/3*3^(1/2)*(-f)^(1/2)*x,3*b/a/f,1/2*2^(1/2)*(-d)^(1/2)*3^(1/2)/(-f)^(1/2))*f*b*a-6*EllipticPi(1/3*3^(1/2)*(-f)^(1/2)*x,3*b/a/f,1/2*2^(1/2)*(-d)^(1/2)*3^(1/2)/(-f)^(1/2))*b^2)*2^(1/2)/a/(-f)^(1/2)/b^2","A"
95,1,133,112,0.024000," ","int((d*x^2+2)^(1/2)/(b*x^2+a)/(f*x^2+3)^(1/2),x)","\frac{\sqrt{2}\, \left(a d \EllipticF \left(\frac{\sqrt{3}\, \sqrt{-f}\, x}{3}, \frac{\sqrt{3}\, \sqrt{2}\, \sqrt{\frac{d}{f}}}{2}\right)-a d \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{-f}\, x}{3}, \frac{3 b}{a f}, \frac{\sqrt{2}\, \sqrt{-d}\, \sqrt{3}}{2 \sqrt{-f}}\right)+2 b \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{-f}\, x}{3}, \frac{3 b}{a f}, \frac{\sqrt{2}\, \sqrt{-d}\, \sqrt{3}}{2 \sqrt{-f}}\right)\right)}{2 \sqrt{-f}\, a b}"," ",0,"1/2*2^(1/2)*(EllipticF(1/3*3^(1/2)*(-f)^(1/2)*x,1/2*3^(1/2)*2^(1/2)*(d/f)^(1/2))*a*d-EllipticPi(1/3*3^(1/2)*(-f)^(1/2)*x,3/a*b/f,1/2*2^(1/2)*(-d)^(1/2)*3^(1/2)/(-f)^(1/2))*a*d+2*EllipticPi(1/3*3^(1/2)*(-f)^(1/2)*x,3/a*b/f,1/2*2^(1/2)*(-d)^(1/2)*3^(1/2)/(-f)^(1/2))*b)/(-f)^(1/2)/a/b","A"
96,1,53,46,0.025000," ","int(1/(b*x^2+a)/(d*x^2+2)^(1/2)/(f*x^2+3)^(1/2),x)","\frac{\sqrt{2}\, \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{-f}\, x}{3}, \frac{3 b}{a f}, \frac{\sqrt{2}\, \sqrt{-d}\, \sqrt{3}}{2 \sqrt{-f}}\right)}{2 \sqrt{-f}\, a}"," ",0,"1/2*2^(1/2)*EllipticPi(1/3*3^(1/2)*(-f)^(1/2)*x,3/a*b/f,1/2*2^(1/2)*(-d)^(1/2)*3^(1/2)/(-f)^(1/2))/(-f)^(1/2)/a","A"
97,1,35,33,0.033000," ","int((-x^2+1)^(1/2)/(x^2-1)/(b*x^2+a)^(1/2),x)","-\frac{\sqrt{\frac{b \,x^{2}+a}{a}}\, \EllipticF \left(x , \sqrt{-\frac{b}{a}}\right)}{\sqrt{b \,x^{2}+a}}"," ",0,"-1/(b*x^2+a)^(1/2)*((b*x^2+a)/a)^(1/2)*EllipticF(x,(-1/a*b)^(1/2))","A"
98,1,1622,97,0.029000," ","int((b*x^2+a)/(f*x^2+e)^2/(d*x^2+c)^(1/2),x)","-\frac{\sqrt{-e f}\, a d \ln \left(\frac{\frac{2 \sqrt{-e f}\, \left(x -\frac{\sqrt{-e f}}{f}\right) d}{f}+\frac{2 c f -2 d e}{f}+2 \sqrt{\frac{c f -d e}{f}}\, \sqrt{\left(x -\frac{\sqrt{-e f}}{f}\right)^{2} d +\frac{2 \sqrt{-e f}\, \left(x -\frac{\sqrt{-e f}}{f}\right) d}{f}+\frac{c f -d e}{f}}}{x -\frac{\sqrt{-e f}}{f}}\right)}{4 \left(c f -d e \right) \sqrt{\frac{c f -d e}{f}}\, e f}+\frac{\sqrt{-e f}\, a d \ln \left(\frac{-\frac{2 \sqrt{-e f}\, \left(x +\frac{\sqrt{-e f}}{f}\right) d}{f}+\frac{2 c f -2 d e}{f}+2 \sqrt{\frac{c f -d e}{f}}\, \sqrt{\left(x +\frac{\sqrt{-e f}}{f}\right)^{2} d -\frac{2 \sqrt{-e f}\, \left(x +\frac{\sqrt{-e f}}{f}\right) d}{f}+\frac{c f -d e}{f}}}{x +\frac{\sqrt{-e f}}{f}}\right)}{4 \left(c f -d e \right) \sqrt{\frac{c f -d e}{f}}\, e f}-\frac{a \ln \left(\frac{\frac{2 \sqrt{-e f}\, \left(x -\frac{\sqrt{-e f}}{f}\right) d}{f}+\frac{2 c f -2 d e}{f}+2 \sqrt{\frac{c f -d e}{f}}\, \sqrt{\left(x -\frac{\sqrt{-e f}}{f}\right)^{2} d +\frac{2 \sqrt{-e f}\, \left(x -\frac{\sqrt{-e f}}{f}\right) d}{f}+\frac{c f -d e}{f}}}{x -\frac{\sqrt{-e f}}{f}}\right)}{4 \sqrt{-e f}\, \sqrt{\frac{c f -d e}{f}}\, e}+\frac{a \ln \left(\frac{-\frac{2 \sqrt{-e f}\, \left(x +\frac{\sqrt{-e f}}{f}\right) d}{f}+\frac{2 c f -2 d e}{f}+2 \sqrt{\frac{c f -d e}{f}}\, \sqrt{\left(x +\frac{\sqrt{-e f}}{f}\right)^{2} d -\frac{2 \sqrt{-e f}\, \left(x +\frac{\sqrt{-e f}}{f}\right) d}{f}+\frac{c f -d e}{f}}}{x +\frac{\sqrt{-e f}}{f}}\right)}{4 \sqrt{-e f}\, \sqrt{\frac{c f -d e}{f}}\, e}+\frac{\sqrt{-e f}\, b d \ln \left(\frac{\frac{2 \sqrt{-e f}\, \left(x -\frac{\sqrt{-e f}}{f}\right) d}{f}+\frac{2 c f -2 d e}{f}+2 \sqrt{\frac{c f -d e}{f}}\, \sqrt{\left(x -\frac{\sqrt{-e f}}{f}\right)^{2} d +\frac{2 \sqrt{-e f}\, \left(x -\frac{\sqrt{-e f}}{f}\right) d}{f}+\frac{c f -d e}{f}}}{x -\frac{\sqrt{-e f}}{f}}\right)}{4 \left(c f -d e \right) \sqrt{\frac{c f -d e}{f}}\, f^{2}}-\frac{\sqrt{-e f}\, b d \ln \left(\frac{-\frac{2 \sqrt{-e f}\, \left(x +\frac{\sqrt{-e f}}{f}\right) d}{f}+\frac{2 c f -2 d e}{f}+2 \sqrt{\frac{c f -d e}{f}}\, \sqrt{\left(x +\frac{\sqrt{-e f}}{f}\right)^{2} d -\frac{2 \sqrt{-e f}\, \left(x +\frac{\sqrt{-e f}}{f}\right) d}{f}+\frac{c f -d e}{f}}}{x +\frac{\sqrt{-e f}}{f}}\right)}{4 \left(c f -d e \right) \sqrt{\frac{c f -d e}{f}}\, f^{2}}-\frac{b \ln \left(\frac{\frac{2 \sqrt{-e f}\, \left(x -\frac{\sqrt{-e f}}{f}\right) d}{f}+\frac{2 c f -2 d e}{f}+2 \sqrt{\frac{c f -d e}{f}}\, \sqrt{\left(x -\frac{\sqrt{-e f}}{f}\right)^{2} d +\frac{2 \sqrt{-e f}\, \left(x -\frac{\sqrt{-e f}}{f}\right) d}{f}+\frac{c f -d e}{f}}}{x -\frac{\sqrt{-e f}}{f}}\right)}{4 \sqrt{-e f}\, \sqrt{\frac{c f -d e}{f}}\, f}+\frac{b \ln \left(\frac{-\frac{2 \sqrt{-e f}\, \left(x +\frac{\sqrt{-e f}}{f}\right) d}{f}+\frac{2 c f -2 d e}{f}+2 \sqrt{\frac{c f -d e}{f}}\, \sqrt{\left(x +\frac{\sqrt{-e f}}{f}\right)^{2} d -\frac{2 \sqrt{-e f}\, \left(x +\frac{\sqrt{-e f}}{f}\right) d}{f}+\frac{c f -d e}{f}}}{x +\frac{\sqrt{-e f}}{f}}\right)}{4 \sqrt{-e f}\, \sqrt{\frac{c f -d e}{f}}\, f}+\frac{\sqrt{\left(x -\frac{\sqrt{-e f}}{f}\right)^{2} d +\frac{2 \sqrt{-e f}\, \left(x -\frac{\sqrt{-e f}}{f}\right) d}{f}+\frac{c f -d e}{f}}\, a}{4 \left(c f -d e \right) \left(x -\frac{\sqrt{-e f}}{f}\right) e}+\frac{\sqrt{\left(x +\frac{\sqrt{-e f}}{f}\right)^{2} d -\frac{2 \sqrt{-e f}\, \left(x +\frac{\sqrt{-e f}}{f}\right) d}{f}+\frac{c f -d e}{f}}\, a}{4 \left(c f -d e \right) \left(x +\frac{\sqrt{-e f}}{f}\right) e}-\frac{\sqrt{\left(x -\frac{\sqrt{-e f}}{f}\right)^{2} d +\frac{2 \sqrt{-e f}\, \left(x -\frac{\sqrt{-e f}}{f}\right) d}{f}+\frac{c f -d e}{f}}\, b}{4 \left(c f -d e \right) \left(x -\frac{\sqrt{-e f}}{f}\right) f}-\frac{\sqrt{\left(x +\frac{\sqrt{-e f}}{f}\right)^{2} d -\frac{2 \sqrt{-e f}\, \left(x +\frac{\sqrt{-e f}}{f}\right) d}{f}+\frac{c f -d e}{f}}\, b}{4 \left(c f -d e \right) \left(x +\frac{\sqrt{-e f}}{f}\right) f}"," ",0,"1/4/e/(c*f-d*e)/(x-(-e*f)^(1/2)/f)*((x-(-e*f)^(1/2)/f)^2*d+2*(-e*f)^(1/2)*(x-(-e*f)^(1/2)/f)*d/f+(c*f-d*e)/f)^(1/2)*a-1/4/f/(c*f-d*e)/(x-(-e*f)^(1/2)/f)*((x-(-e*f)^(1/2)/f)^2*d+2*(-e*f)^(1/2)*(x-(-e*f)^(1/2)/f)*d/f+(c*f-d*e)/f)^(1/2)*b-1/4/e/f*(-e*f)^(1/2)*d/(c*f-d*e)/((c*f-d*e)/f)^(1/2)*ln((2*(-e*f)^(1/2)*(x-(-e*f)^(1/2)/f)*d/f+2*(c*f-d*e)/f+2*((c*f-d*e)/f)^(1/2)*((x-(-e*f)^(1/2)/f)^2*d+2*(-e*f)^(1/2)*(x-(-e*f)^(1/2)/f)*d/f+(c*f-d*e)/f)^(1/2))/(x-(-e*f)^(1/2)/f))*a+1/4/f^2*(-e*f)^(1/2)*d/(c*f-d*e)/((c*f-d*e)/f)^(1/2)*ln((2*(-e*f)^(1/2)*(x-(-e*f)^(1/2)/f)*d/f+2*(c*f-d*e)/f+2*((c*f-d*e)/f)^(1/2)*((x-(-e*f)^(1/2)/f)^2*d+2*(-e*f)^(1/2)*(x-(-e*f)^(1/2)/f)*d/f+(c*f-d*e)/f)^(1/2))/(x-(-e*f)^(1/2)/f))*b-1/4/e/(-e*f)^(1/2)/((c*f-d*e)/f)^(1/2)*ln((2*(-e*f)^(1/2)*(x-(-e*f)^(1/2)/f)*d/f+2*(c*f-d*e)/f+2*((c*f-d*e)/f)^(1/2)*((x-(-e*f)^(1/2)/f)^2*d+2*(-e*f)^(1/2)*(x-(-e*f)^(1/2)/f)*d/f+(c*f-d*e)/f)^(1/2))/(x-(-e*f)^(1/2)/f))*a-1/4/(-e*f)^(1/2)/f/((c*f-d*e)/f)^(1/2)*ln((2*(-e*f)^(1/2)*(x-(-e*f)^(1/2)/f)*d/f+2*(c*f-d*e)/f+2*((c*f-d*e)/f)^(1/2)*((x-(-e*f)^(1/2)/f)^2*d+2*(-e*f)^(1/2)*(x-(-e*f)^(1/2)/f)*d/f+(c*f-d*e)/f)^(1/2))/(x-(-e*f)^(1/2)/f))*b+1/4/e/(c*f-d*e)/(x+(-e*f)^(1/2)/f)*((x+(-e*f)^(1/2)/f)^2*d-2*(-e*f)^(1/2)*(x+(-e*f)^(1/2)/f)*d/f+(c*f-d*e)/f)^(1/2)*a-1/4/f/(c*f-d*e)/(x+(-e*f)^(1/2)/f)*((x+(-e*f)^(1/2)/f)^2*d-2*(-e*f)^(1/2)*(x+(-e*f)^(1/2)/f)*d/f+(c*f-d*e)/f)^(1/2)*b+1/4/e/f*(-e*f)^(1/2)*d/(c*f-d*e)/((c*f-d*e)/f)^(1/2)*ln((-2*(-e*f)^(1/2)*(x+(-e*f)^(1/2)/f)*d/f+2*(c*f-d*e)/f+2*((c*f-d*e)/f)^(1/2)*((x+(-e*f)^(1/2)/f)^2*d-2*(-e*f)^(1/2)*(x+(-e*f)^(1/2)/f)*d/f+(c*f-d*e)/f)^(1/2))/(x+(-e*f)^(1/2)/f))*a-1/4/f^2*(-e*f)^(1/2)*d/(c*f-d*e)/((c*f-d*e)/f)^(1/2)*ln((-2*(-e*f)^(1/2)*(x+(-e*f)^(1/2)/f)*d/f+2*(c*f-d*e)/f+2*((c*f-d*e)/f)^(1/2)*((x+(-e*f)^(1/2)/f)^2*d-2*(-e*f)^(1/2)*(x+(-e*f)^(1/2)/f)*d/f+(c*f-d*e)/f)^(1/2))/(x+(-e*f)^(1/2)/f))*b+1/4/e/(-e*f)^(1/2)/((c*f-d*e)/f)^(1/2)*ln((-2*(-e*f)^(1/2)*(x+(-e*f)^(1/2)/f)*d/f+2*(c*f-d*e)/f+2*((c*f-d*e)/f)^(1/2)*((x+(-e*f)^(1/2)/f)^2*d-2*(-e*f)^(1/2)*(x+(-e*f)^(1/2)/f)*d/f+(c*f-d*e)/f)^(1/2))/(x+(-e*f)^(1/2)/f))*a+1/4/(-e*f)^(1/2)/f/((c*f-d*e)/f)^(1/2)*ln((-2*(-e*f)^(1/2)*(x+(-e*f)^(1/2)/f)*d/f+2*(c*f-d*e)/f+2*((c*f-d*e)/f)^(1/2)*((x+(-e*f)^(1/2)/f)^2*d-2*(-e*f)^(1/2)*(x+(-e*f)^(1/2)/f)*d/f+(c*f-d*e)/f)^(1/2))/(x+(-e*f)^(1/2)/f))*b","B"
99,1,793,302,0.066000," ","int((-d*x^2+c)^(1/2)*(f*x^2+e)^(1/2)/(b*x^2+a)^2,x)","\frac{\sqrt{-d \,x^{2}+c}\, \sqrt{f \,x^{2}+e}\, \left(\sqrt{\frac{d}{c}}\, a \,b^{2} d f \,x^{5}+\sqrt{-\frac{d \,x^{2}-c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} b d f \,x^{2} \EllipticF \left(\sqrt{\frac{d}{c}}\, x , \sqrt{-\frac{c f}{d e}}\right)-\sqrt{-\frac{d \,x^{2}-c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} b d f \,x^{2} \EllipticPi \left(\sqrt{\frac{d}{c}}\, x , -\frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{\frac{d}{c}}}\right)-\sqrt{\frac{d}{c}}\, a \,b^{2} c f \,x^{3}+\sqrt{\frac{d}{c}}\, a \,b^{2} d e \,x^{3}-\sqrt{-\frac{d \,x^{2}-c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,b^{2} d e \,x^{2} \EllipticE \left(\sqrt{\frac{d}{c}}\, x , \sqrt{-\frac{c f}{d e}}\right)+\sqrt{-\frac{d \,x^{2}-c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,b^{2} d e \,x^{2} \EllipticF \left(\sqrt{\frac{d}{c}}\, x , \sqrt{-\frac{c f}{d e}}\right)-\sqrt{-\frac{d \,x^{2}-c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b^{3} c e \,x^{2} \EllipticPi \left(\sqrt{\frac{d}{c}}\, x , -\frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{\frac{d}{c}}}\right)+\sqrt{-\frac{d \,x^{2}-c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{3} d f \EllipticF \left(\sqrt{\frac{d}{c}}\, x , \sqrt{-\frac{c f}{d e}}\right)-\sqrt{-\frac{d \,x^{2}-c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{3} d f \EllipticPi \left(\sqrt{\frac{d}{c}}\, x , -\frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{\frac{d}{c}}}\right)-\sqrt{-\frac{d \,x^{2}-c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} b d e \EllipticE \left(\sqrt{\frac{d}{c}}\, x , \sqrt{-\frac{c f}{d e}}\right)+\sqrt{-\frac{d \,x^{2}-c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} b d e \EllipticF \left(\sqrt{\frac{d}{c}}\, x , \sqrt{-\frac{c f}{d e}}\right)-\sqrt{\frac{d}{c}}\, a \,b^{2} c e x -\sqrt{-\frac{d \,x^{2}-c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,b^{2} c e \EllipticPi \left(\sqrt{\frac{d}{c}}\, x , -\frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{\frac{d}{c}}}\right)\right)}{2 \left(d f \,x^{4}-c f \,x^{2}+d e \,x^{2}-c e \right) \left(b \,x^{2}+a \right) \sqrt{\frac{d}{c}}\, a^{2} b^{2}}"," ",0,"1/2*(-d*x^2+c)^(1/2)*(f*x^2+e)^(1/2)*((1/c*d)^(1/2)*x^5*a*b^2*d*f+(-(d*x^2-c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((1/c*d)^(1/2)*x,(-c/d/e*f)^(1/2))*x^2*a^2*b*d*f+(-(d*x^2-c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((1/c*d)^(1/2)*x,(-c/d/e*f)^(1/2))*x^2*a*b^2*d*e-(-(d*x^2-c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((1/c*d)^(1/2)*x,(-c/d/e*f)^(1/2))*x^2*a*b^2*d*e-(-(d*x^2-c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticPi((1/c*d)^(1/2)*x,-1/a*b*c/d,(-1/e*f)^(1/2)/(1/c*d)^(1/2))*x^2*a^2*b*d*f-(-(d*x^2-c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticPi((1/c*d)^(1/2)*x,-1/a*b*c/d,(-1/e*f)^(1/2)/(1/c*d)^(1/2))*x^2*b^3*c*e-(1/c*d)^(1/2)*x^3*a*b^2*c*f+(1/c*d)^(1/2)*x^3*a*b^2*d*e+(-(d*x^2-c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((1/c*d)^(1/2)*x,(-c/d/e*f)^(1/2))*a^3*d*f+(-(d*x^2-c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((1/c*d)^(1/2)*x,(-c/d/e*f)^(1/2))*a^2*b*d*e-(-(d*x^2-c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((1/c*d)^(1/2)*x,(-c/d/e*f)^(1/2))*a^2*b*d*e-(-(d*x^2-c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticPi((1/c*d)^(1/2)*x,-1/a*b*c/d,(-1/e*f)^(1/2)/(1/c*d)^(1/2))*a^3*d*f-(-(d*x^2-c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticPi((1/c*d)^(1/2)*x,-1/a*b*c/d,(-1/e*f)^(1/2)/(1/c*d)^(1/2))*a*b^2*c*e-(1/c*d)^(1/2)*x*a*b^2*c*e)/(d*f*x^4-c*f*x^2+d*e*x^2-c*e)/a^2/(b*x^2+a)/b^2/(1/c*d)^(1/2)","B"
100,1,765,398,0.054000," ","int((d*x^2+c)^(1/2)*(f*x^2+e)^(1/2)/(b*x^2+a)^2,x)","\frac{\sqrt{d \,x^{2}+c}\, \sqrt{f \,x^{2}+e}\, \left(\sqrt{-\frac{d}{c}}\, a \,b^{2} d f \,x^{5}+\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} b d f \,x^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} b d f \,x^{2} \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)+\sqrt{-\frac{d}{c}}\, a \,b^{2} c f \,x^{3}+\sqrt{-\frac{d}{c}}\, a \,b^{2} d e \,x^{3}-\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,b^{2} d e \,x^{2} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,b^{2} d e \,x^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b^{3} c e \,x^{2} \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)+\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{3} d f \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{3} d f \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)-\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} b d e \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} b d e \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+\sqrt{-\frac{d}{c}}\, a \,b^{2} c e x +\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,b^{2} c e \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)\right)}{2 \left(d f \,x^{4}+c f \,x^{2}+d e \,x^{2}+c e \right) \left(b \,x^{2}+a \right) \sqrt{-\frac{d}{c}}\, a^{2} b^{2}}"," ",0,"1/2*(d*x^2+c)^(1/2)*(f*x^2+e)^(1/2)*((-1/c*d)^(1/2)*x^5*a*b^2*d*f+((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a^2*b*d*f+((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a*b^2*d*e-((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a*b^2*d*e-((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*x^2*a^2*b*d*f+((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*x^2*b^3*c*e+(-1/c*d)^(1/2)*x^3*a*b^2*c*f+(-1/c*d)^(1/2)*x^3*a*b^2*d*e+((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a^3*d*f+((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a^2*b*d*e-((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a^2*b*d*e-((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*a^3*d*f+((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*a*b^2*c*e+(-1/c*d)^(1/2)*x*a*b^2*c*e)/(d*f*x^4+c*f*x^2+d*e*x^2+c*e)/a^2/(b*x^2+a)/b^2/(-1/c*d)^(1/2)","A"
101,1,1105,369,0.056000," ","int(1/(b*x^2+a)^2/(-d*x^2+c)^(1/2)/(f*x^2+e)^(1/2),x)","\frac{\left(-\sqrt{\frac{d}{c}}\, a \,b^{2} d f \,x^{5}+\sqrt{-\frac{d \,x^{2}-c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} b d f \,x^{2} \EllipticF \left(\sqrt{\frac{d}{c}}\, x , \sqrt{-\frac{c f}{d e}}\right)-3 \sqrt{-\frac{d \,x^{2}-c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} b d f \,x^{2} \EllipticPi \left(\sqrt{\frac{d}{c}}\, x , -\frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{\frac{d}{c}}}\right)+\sqrt{\frac{d}{c}}\, a \,b^{2} c f \,x^{3}-2 \sqrt{-\frac{d \,x^{2}-c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,b^{2} c f \,x^{2} \EllipticPi \left(\sqrt{\frac{d}{c}}\, x , -\frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{\frac{d}{c}}}\right)-\sqrt{\frac{d}{c}}\, a \,b^{2} d e \,x^{3}+\sqrt{-\frac{d \,x^{2}-c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,b^{2} d e \,x^{2} \EllipticE \left(\sqrt{\frac{d}{c}}\, x , \sqrt{-\frac{c f}{d e}}\right)-\sqrt{-\frac{d \,x^{2}-c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,b^{2} d e \,x^{2} \EllipticF \left(\sqrt{\frac{d}{c}}\, x , \sqrt{-\frac{c f}{d e}}\right)+2 \sqrt{-\frac{d \,x^{2}-c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,b^{2} d e \,x^{2} \EllipticPi \left(\sqrt{\frac{d}{c}}\, x , -\frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{\frac{d}{c}}}\right)+\sqrt{-\frac{d \,x^{2}-c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b^{3} c e \,x^{2} \EllipticPi \left(\sqrt{\frac{d}{c}}\, x , -\frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{\frac{d}{c}}}\right)+\sqrt{-\frac{d \,x^{2}-c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{3} d f \EllipticF \left(\sqrt{\frac{d}{c}}\, x , \sqrt{-\frac{c f}{d e}}\right)-3 \sqrt{-\frac{d \,x^{2}-c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{3} d f \EllipticPi \left(\sqrt{\frac{d}{c}}\, x , -\frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{\frac{d}{c}}}\right)-2 \sqrt{-\frac{d \,x^{2}-c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} b c f \EllipticPi \left(\sqrt{\frac{d}{c}}\, x , -\frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{\frac{d}{c}}}\right)+\sqrt{-\frac{d \,x^{2}-c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} b d e \EllipticE \left(\sqrt{\frac{d}{c}}\, x , \sqrt{-\frac{c f}{d e}}\right)-\sqrt{-\frac{d \,x^{2}-c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} b d e \EllipticF \left(\sqrt{\frac{d}{c}}\, x , \sqrt{-\frac{c f}{d e}}\right)+2 \sqrt{-\frac{d \,x^{2}-c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} b d e \EllipticPi \left(\sqrt{\frac{d}{c}}\, x , -\frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{\frac{d}{c}}}\right)+\sqrt{\frac{d}{c}}\, a \,b^{2} c e x +\sqrt{-\frac{d \,x^{2}-c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,b^{2} c e \EllipticPi \left(\sqrt{\frac{d}{c}}\, x , -\frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{\frac{d}{c}}}\right)\right) \sqrt{f \,x^{2}+e}\, \sqrt{-d \,x^{2}+c}}{2 \left(b \,x^{2}+a \right) \sqrt{\frac{d}{c}}\, \left(a f -b e \right) \left(a d +b c \right) \left(d f \,x^{4}-c f \,x^{2}+d e \,x^{2}-c e \right) a^{2}}"," ",0,"1/2*(-(1/c*d)^(1/2)*a*b^2*d*f*x^5+(-(d*x^2-c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((1/c*d)^(1/2)*x,(-c/d/e*f)^(1/2))*x^2*a^2*b*d*f-(-(d*x^2-c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((1/c*d)^(1/2)*x,(-c/d/e*f)^(1/2))*x^2*a*b^2*d*e+(-(d*x^2-c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((1/c*d)^(1/2)*x,(-c/d/e*f)^(1/2))*x^2*a*b^2*d*e-3*(-(d*x^2-c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticPi((1/c*d)^(1/2)*x,-1/a*b*c/d,(-1/e*f)^(1/2)/(1/c*d)^(1/2))*x^2*a^2*b*d*f-2*(-(d*x^2-c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticPi((1/c*d)^(1/2)*x,-1/a*b*c/d,(-1/e*f)^(1/2)/(1/c*d)^(1/2))*x^2*a*b^2*c*f+2*(-(d*x^2-c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticPi((1/c*d)^(1/2)*x,-1/a*b*c/d,(-1/e*f)^(1/2)/(1/c*d)^(1/2))*x^2*a*b^2*d*e+(-(d*x^2-c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticPi((1/c*d)^(1/2)*x,-1/a*b*c/d,(-1/e*f)^(1/2)/(1/c*d)^(1/2))*x^2*b^3*c*e+(1/c*d)^(1/2)*a*b^2*c*f*x^3-(1/c*d)^(1/2)*a*b^2*d*e*x^3+(-(d*x^2-c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((1/c*d)^(1/2)*x,(-c/d/e*f)^(1/2))*a^3*d*f-(-(d*x^2-c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((1/c*d)^(1/2)*x,(-c/d/e*f)^(1/2))*a^2*b*d*e+(-(d*x^2-c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((1/c*d)^(1/2)*x,(-c/d/e*f)^(1/2))*a^2*b*d*e-3*(-(d*x^2-c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticPi((1/c*d)^(1/2)*x,-1/a*b*c/d,(-1/e*f)^(1/2)/(1/c*d)^(1/2))*a^3*d*f-2*(-(d*x^2-c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticPi((1/c*d)^(1/2)*x,-1/a*b*c/d,(-1/e*f)^(1/2)/(1/c*d)^(1/2))*a^2*b*c*f+2*(-(d*x^2-c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticPi((1/c*d)^(1/2)*x,-1/a*b*c/d,(-1/e*f)^(1/2)/(1/c*d)^(1/2))*a^2*b*d*e+(-(d*x^2-c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticPi((1/c*d)^(1/2)*x,-1/a*b*c/d,(-1/e*f)^(1/2)/(1/c*d)^(1/2))*a*b^2*c*e+(1/c*d)^(1/2)*a*b^2*c*e*x)*(f*x^2+e)^(1/2)*(-d*x^2+c)^(1/2)/(b*x^2+a)/a^2/(1/c*d)^(1/2)/(a*f-b*e)/(a*d+b*c)/(d*f*x^4-c*f*x^2+d*e*x^2-c*e)","B"
102,1,1078,502,0.032000," ","int(1/(b*x^2+a)^2/(d*x^2+c)^(1/2)/(f*x^2+e)^(1/2),x)","-\frac{\left(-\sqrt{-\frac{d}{c}}\, a \,b^{2} d f \,x^{5}+\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} b d f \,x^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-3 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} b d f \,x^{2} \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)-\sqrt{-\frac{d}{c}}\, a \,b^{2} c f \,x^{3}+2 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,b^{2} c f \,x^{2} \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)-\sqrt{-\frac{d}{c}}\, a \,b^{2} d e \,x^{3}+\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,b^{2} d e \,x^{2} \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,b^{2} d e \,x^{2} \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+2 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,b^{2} d e \,x^{2} \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)-\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, b^{3} c e \,x^{2} \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)+\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{3} d f \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-3 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{3} d f \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)+2 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} b c f \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)+\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} b d e \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)-\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} b d e \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{c f}{d e}}\right)+2 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a^{2} b d e \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)-\sqrt{-\frac{d}{c}}\, a \,b^{2} c e x -\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, a \,b^{2} c e \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , \frac{b c}{a d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)\right) \sqrt{f \,x^{2}+e}\, \sqrt{d \,x^{2}+c}}{2 \left(b \,x^{2}+a \right) \sqrt{-\frac{d}{c}}\, \left(a f -b e \right) \left(a d -b c \right) \left(d f \,x^{4}+c f \,x^{2}+d e \,x^{2}+c e \right) a^{2}}"," ",0,"-1/2*(-(-1/c*d)^(1/2)*a*b^2*d*f*x^5+((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a*b^2*d*e-3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*x^2*a^2*b*d*f+2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*x^2*a*b^2*c*f+2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*x^2*a*b^2*d*e-((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*x^2*b^3*c*e+((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a^2*b*d*f-((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*x^2*a*b^2*d*e-(-1/c*d)^(1/2)*a*b^2*c*f*x^3-(-1/c*d)^(1/2)*a*b^2*d*e*x^3+((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a^2*b*d*e-3*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*a^3*d*f+2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*a^2*b*c*f+2*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*a^2*b*d*e-((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticPi((-1/c*d)^(1/2)*x,1/a*b*c/d,(-1/e*f)^(1/2)/(-1/c*d)^(1/2))*a*b^2*c*e+((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a^3*d*f-((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,(c/d/e*f)^(1/2))*a^2*b*d*e-(-1/c*d)^(1/2)*a*b^2*c*e*x)*(f*x^2+e)^(1/2)*(d*x^2+c)^(1/2)/(b*x^2+a)/a^2/(-1/c*d)^(1/2)/(a*f-b*e)/(a*d-b*c)/(d*f*x^4+c*f*x^2+d*e*x^2+c*e)","B"
103,0,0,30,0.132000," ","int((b*x^2+a)^(3/2)*(d*x^2+c)^(1/2)/(f*x^2+e)^(1/2),x)","\int \frac{\left(b \,x^{2}+a \right)^{\frac{3}{2}} \sqrt{d \,x^{2}+c}}{\sqrt{f \,x^{2}+e}}\, dx"," ",0,"int((b*x^2+a)^(3/2)*(d*x^2+c)^(1/2)/(f*x^2+e)^(1/2),x)","F"
104,0,0,480,0.083000," ","int((b*x^2+a)^(1/2)*(d*x^2+c)^(1/2)/(f*x^2+e)^(1/2),x)","\int \frac{\sqrt{b \,x^{2}+a}\, \sqrt{d \,x^{2}+c}}{\sqrt{f \,x^{2}+e}}\, dx"," ",0,"int((b*x^2+a)^(1/2)*(d*x^2+c)^(1/2)/(f*x^2+e)^(1/2),x)","F"
105,0,0,146,0.073000," ","int((d*x^2+c)^(1/2)/(b*x^2+a)^(1/2)/(f*x^2+e)^(1/2),x)","\int \frac{\sqrt{d \,x^{2}+c}}{\sqrt{b \,x^{2}+a}\, \sqrt{f \,x^{2}+e}}\, dx"," ",0,"int((d*x^2+c)^(1/2)/(b*x^2+a)^(1/2)/(f*x^2+e)^(1/2),x)","F"
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