1,1,8125,646,0.077000," ","int((b*x+a)^2*(B*x+A)/(d*x+c)^(1/2)/(f*x+e)^(1/2)/(h*x+g)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
2,1,3224,359,0.036000," ","int((b*x+a)*(B*x+A)/(d*x+c)^(1/2)/(f*x+e)^(1/2)/(h*x+g)^(1/2),x)","\text{output too large to display}"," ",0,"2/3*(2*B*((d*x+c)/(c*f-d*e)*f)^(1/2)*(-(h*x+g)/(c*h-d*g)*d)^(1/2)*(-(f*x+e)/(c*f-d*e)*d)^(1/2)*EllipticE(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*b*c^3*f^2*h^2+B*x^3*b*d^3*f^2*h^2+3*B*((d*x+c)/(c*f-d*e)*f)^(1/2)*(-(h*x+g)/(c*h-d*g)*d)^(1/2)*(-(f*x+e)/(c*f-d*e)*d)^(1/2)*EllipticE(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*a*c*d^2*f^2*g*h-3*B*((d*x+c)/(c*f-d*e)*f)^(1/2)*(-(h*x+g)/(c*h-d*g)*d)^(1/2)*(-(f*x+e)/(c*f-d*e)*d)^(1/2)*EllipticE(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*a*d^3*e*f*g*h-3*A*((d*x+c)/(c*f-d*e)*f)^(1/2)*(-(h*x+g)/(c*h-d*g)*d)^(1/2)*(-(f*x+e)/(c*f-d*e)*d)^(1/2)*EllipticF(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*a*d^3*e*f*h^2-3*A*((d*x+c)/(c*f-d*e)*f)^(1/2)*(-(h*x+g)/(c*h-d*g)*d)^(1/2)*(-(f*x+e)/(c*f-d*e)*d)^(1/2)*EllipticE(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*b*c^2*d*f^2*h^2+B*((d*x+c)/(c*f-d*e)*f)^(1/2)*(-(h*x+g)/(c*h-d*g)*d)^(1/2)*(-(f*x+e)/(c*f-d*e)*d)^(1/2)*EllipticF(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*b*c*d^2*e^2*h^2+2*B*((d*x+c)/(c*f-d*e)*f)^(1/2)*(-(h*x+g)/(c*h-d*g)*d)^(1/2)*(-(f*x+e)/(c*f-d*e)*d)^(1/2)*EllipticF(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*b*c*d^2*f^2*g^2-B*((d*x+c)/(c*f-d*e)*f)^(1/2)*(-(h*x+g)/(c*h-d*g)*d)^(1/2)*(-(f*x+e)/(c*f-d*e)*d)^(1/2)*EllipticF(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*b*d^3*e^2*g*h-2*B*((d*x+c)/(c*f-d*e)*f)^(1/2)*(-(h*x+g)/(c*h-d*g)*d)^(1/2)*(-(f*x+e)/(c*f-d*e)*d)^(1/2)*EllipticF(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*b*d^3*e*f*g^2-3*B*((d*x+c)/(c*f-d*e)*f)^(1/2)*(-(h*x+g)/(c*h-d*g)*d)^(1/2)*(-(f*x+e)/(c*f-d*e)*d)^(1/2)*EllipticE(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*a*c^2*d*f^2*h^2-2*B*((d*x+c)/(c*f-d*e)*f)^(1/2)*(-(h*x+g)/(c*h-d*g)*d)^(1/2)*(-(f*x+e)/(c*f-d*e)*d)^(1/2)*EllipticE(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*b*c*d^2*e^2*h^2-2*B*((d*x+c)/(c*f-d*e)*f)^(1/2)*(-(h*x+g)/(c*h-d*g)*d)^(1/2)*(-(f*x+e)/(c*f-d*e)*d)^(1/2)*EllipticE(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*b*c*d^2*e*f*g*h+3*A*((d*x+c)/(c*f-d*e)*f)^(1/2)*(-(h*x+g)/(c*h-d*g)*d)^(1/2)*(-(f*x+e)/(c*f-d*e)*d)^(1/2)*EllipticE(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*b*c*d^2*e*f*h^2+3*A*((d*x+c)/(c*f-d*e)*f)^(1/2)*(-(h*x+g)/(c*h-d*g)*d)^(1/2)*(-(f*x+e)/(c*f-d*e)*d)^(1/2)*EllipticE(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*b*c*d^2*f^2*g*h-3*A*((d*x+c)/(c*f-d*e)*f)^(1/2)*(-(h*x+g)/(c*h-d*g)*d)^(1/2)*(-(f*x+e)/(c*f-d*e)*d)^(1/2)*EllipticE(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*b*d^3*e*f*g*h-3*B*((d*x+c)/(c*f-d*e)*f)^(1/2)*(-(h*x+g)/(c*h-d*g)*d)^(1/2)*(-(f*x+e)/(c*f-d*e)*d)^(1/2)*EllipticF(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*a*c*d^2*f^2*g*h+3*B*((d*x+c)/(c*f-d*e)*f)^(1/2)*(-(h*x+g)/(c*h-d*g)*d)^(1/2)*(-(f*x+e)/(c*f-d*e)*d)^(1/2)*EllipticF(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*a*d^3*e*f*g*h-B*((d*x+c)/(c*f-d*e)*f)^(1/2)*(-(h*x+g)/(c*h-d*g)*d)^(1/2)*(-(f*x+e)/(c*f-d*e)*d)^(1/2)*EllipticF(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*b*c^2*d*e*f*h^2+B*((d*x+c)/(c*f-d*e)*f)^(1/2)*(-(h*x+g)/(c*h-d*g)*d)^(1/2)*(-(f*x+e)/(c*f-d*e)*d)^(1/2)*EllipticF(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*b*c^2*d*f^2*g*h-3*A*((d*x+c)/(c*f-d*e)*f)^(1/2)*(-(h*x+g)/(c*h-d*g)*d)^(1/2)*(-(f*x+e)/(c*f-d*e)*d)^(1/2)*EllipticF(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*b*c*d^2*f^2*g*h+3*A*((d*x+c)/(c*f-d*e)*f)^(1/2)*(-(h*x+g)/(c*h-d*g)*d)^(1/2)*(-(f*x+e)/(c*f-d*e)*d)^(1/2)*EllipticF(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*b*d^3*e*f*g*h-2*B*((d*x+c)/(c*f-d*e)*f)^(1/2)*(-(h*x+g)/(c*h-d*g)*d)^(1/2)*(-(f*x+e)/(c*f-d*e)*d)^(1/2)*EllipticE(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*b*c*d^2*f^2*g^2+2*B*((d*x+c)/(c*f-d*e)*f)^(1/2)*(-(h*x+g)/(c*h-d*g)*d)^(1/2)*(-(f*x+e)/(c*f-d*e)*d)^(1/2)*EllipticE(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*b*d^3*e^2*g*h+2*B*((d*x+c)/(c*f-d*e)*f)^(1/2)*(-(h*x+g)/(c*h-d*g)*d)^(1/2)*(-(f*x+e)/(c*f-d*e)*d)^(1/2)*EllipticE(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*b*d^3*e*f*g^2+3*A*((d*x+c)/(c*f-d*e)*f)^(1/2)*(-(h*x+g)/(c*h-d*g)*d)^(1/2)*(-(f*x+e)/(c*f-d*e)*d)^(1/2)*EllipticF(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*a*c*d^2*f^2*h^2+B*x^2*b*c*d^2*f^2*h^2+B*x^2*b*d^3*e*f*h^2+B*x^2*b*d^3*f^2*g*h+B*x*b*c*d^2*f^2*g*h+B*x*b*d^3*e*f*g*h+3*B*((d*x+c)/(c*f-d*e)*f)^(1/2)*(-(h*x+g)/(c*h-d*g)*d)^(1/2)*(-(f*x+e)/(c*f-d*e)*d)^(1/2)*EllipticE(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*a*c*d^2*e*f*h^2+B*b*c*d^2*e*f*g*h+B*x*b*c*d^2*e*f*h^2)*(d*x+c)^(1/2)*(f*x+e)^(1/2)*(h*x+g)^(1/2)/h^2/f^2/d^3/(d*f*h*x^3+c*f*h*x^2+d*e*h*x^2+d*f*g*x^2+c*e*h*x+c*f*g*x+d*e*g*x+c*e*g)","B"
3,1,559,250,0.028000," ","int((B*x+A)/(d*x+c)^(1/2)/(f*x+e)^(1/2)/(h*x+g)^(1/2),x)","\frac{2 \left(A c d f h \EllipticF \left(\sqrt{\frac{\left(d x +c \right) f}{c f -d e}}, \sqrt{\frac{\left(c f -d e \right) h}{\left(c h -d g \right) f}}\right)-A \,d^{2} e h \EllipticF \left(\sqrt{\frac{\left(d x +c \right) f}{c f -d e}}, \sqrt{\frac{\left(c f -d e \right) h}{\left(c h -d g \right) f}}\right)-B \,c^{2} f h \EllipticE \left(\sqrt{\frac{\left(d x +c \right) f}{c f -d e}}, \sqrt{\frac{\left(c f -d e \right) h}{\left(c h -d g \right) f}}\right)+B c d e h \EllipticE \left(\sqrt{\frac{\left(d x +c \right) f}{c f -d e}}, \sqrt{\frac{\left(c f -d e \right) h}{\left(c h -d g \right) f}}\right)+B c d f g \EllipticE \left(\sqrt{\frac{\left(d x +c \right) f}{c f -d e}}, \sqrt{\frac{\left(c f -d e \right) h}{\left(c h -d g \right) f}}\right)-B c d f g \EllipticF \left(\sqrt{\frac{\left(d x +c \right) f}{c f -d e}}, \sqrt{\frac{\left(c f -d e \right) h}{\left(c h -d g \right) f}}\right)-B \,d^{2} e g \EllipticE \left(\sqrt{\frac{\left(d x +c \right) f}{c f -d e}}, \sqrt{\frac{\left(c f -d e \right) h}{\left(c h -d g \right) f}}\right)+B \,d^{2} e g \EllipticF \left(\sqrt{\frac{\left(d x +c \right) f}{c f -d e}}, \sqrt{\frac{\left(c f -d e \right) h}{\left(c h -d g \right) f}}\right)\right) \sqrt{-\frac{\left(f x +e \right) d}{c f -d e}}\, \sqrt{-\frac{\left(h x +g \right) d}{c h -d g}}\, \sqrt{\frac{\left(d x +c \right) f}{c f -d e}}\, \sqrt{d x +c}\, \sqrt{f x +e}\, \sqrt{h x +g}}{\left(d f h \,x^{3}+c f h \,x^{2}+d e h \,x^{2}+d f g \,x^{2}+c e h x +c f g x +d e g x +c e g \right) d^{2} f h}"," ",0,"2*(A*EllipticF(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*c*d*f*h-A*EllipticF(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*d^2*e*h-B*EllipticF(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*c*d*f*g+B*EllipticF(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*d^2*e*g-B*EllipticE(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*c^2*f*h+B*EllipticE(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*c*d*e*h+B*EllipticE(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*c*d*f*g-B*EllipticE(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*d^2*e*g)*(-(f*x+e)/(c*f-d*e)*d)^(1/2)*(-(h*x+g)/(c*h-d*g)*d)^(1/2)*((d*x+c)/(c*f-d*e)*f)^(1/2)/h/f/d^2*(d*x+c)^(1/2)*(f*x+e)^(1/2)*(h*x+g)^(1/2)/(d*f*h*x^3+c*f*h*x^2+d*e*h*x^2+d*f*g*x^2+c*e*h*x+c*f*g*x+d*e*g*x+c*e*g)","B"
4,1,665,279,0.041000," ","int((B*x+A)/(b*x+a)/(d*x+c)^(1/2)/(f*x+e)^(1/2)/(h*x+g)^(1/2),x)","\frac{2 \sqrt{d x +c}\, \sqrt{f x +e}\, \sqrt{h x +g}\, \sqrt{\frac{\left(d x +c \right) f}{c f -d e}}\, \sqrt{-\frac{\left(h x +g \right) d}{c h -d g}}\, \sqrt{-\frac{\left(f x +e \right) d}{c f -d e}}\, \left(A b c d f \EllipticPi \left(\sqrt{\frac{\left(d x +c \right) f}{c f -d e}}, -\frac{\left(c f -d e \right) b}{\left(a d -b c \right) f}, \sqrt{\frac{\left(c f -d e \right) h}{\left(c h -d g \right) f}}\right)-A b \,d^{2} e \EllipticPi \left(\sqrt{\frac{\left(d x +c \right) f}{c f -d e}}, -\frac{\left(c f -d e \right) b}{\left(a d -b c \right) f}, \sqrt{\frac{\left(c f -d e \right) h}{\left(c h -d g \right) f}}\right)+B a c d f \EllipticF \left(\sqrt{\frac{\left(d x +c \right) f}{c f -d e}}, \sqrt{\frac{\left(c f -d e \right) h}{\left(c h -d g \right) f}}\right)-B a c d f \EllipticPi \left(\sqrt{\frac{\left(d x +c \right) f}{c f -d e}}, -\frac{\left(c f -d e \right) b}{\left(a d -b c \right) f}, \sqrt{\frac{\left(c f -d e \right) h}{\left(c h -d g \right) f}}\right)-B a \,d^{2} e \EllipticF \left(\sqrt{\frac{\left(d x +c \right) f}{c f -d e}}, \sqrt{\frac{\left(c f -d e \right) h}{\left(c h -d g \right) f}}\right)+B a \,d^{2} e \EllipticPi \left(\sqrt{\frac{\left(d x +c \right) f}{c f -d e}}, -\frac{\left(c f -d e \right) b}{\left(a d -b c \right) f}, \sqrt{\frac{\left(c f -d e \right) h}{\left(c h -d g \right) f}}\right)-B b \,c^{2} f \EllipticF \left(\sqrt{\frac{\left(d x +c \right) f}{c f -d e}}, \sqrt{\frac{\left(c f -d e \right) h}{\left(c h -d g \right) f}}\right)+B b c d e \EllipticF \left(\sqrt{\frac{\left(d x +c \right) f}{c f -d e}}, \sqrt{\frac{\left(c f -d e \right) h}{\left(c h -d g \right) f}}\right)\right)}{\left(a d -b c \right) \left(d f h \,x^{3}+c f h \,x^{2}+d e h \,x^{2}+d f g \,x^{2}+c e h x +c f g x +d e g x +c e g \right) b d f}"," ",0,"2*(d*x+c)^(1/2)*(f*x+e)^(1/2)*(h*x+g)^(1/2)/d/f/b*((d*x+c)/(c*f-d*e)*f)^(1/2)*(-(h*x+g)/(c*h-d*g)*d)^(1/2)*(-(f*x+e)/(c*f-d*e)*d)^(1/2)*(A*EllipticPi(((d*x+c)/(c*f-d*e)*f)^(1/2),-(c*f-d*e)/(a*d-b*c)*b/f,((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*b*c*d*f-A*EllipticPi(((d*x+c)/(c*f-d*e)*f)^(1/2),-(c*f-d*e)/(a*d-b*c)*b/f,((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*b*d^2*e+B*EllipticF(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*a*c*d*f-B*EllipticF(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*a*d^2*e-B*EllipticF(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*b*c^2*f+B*EllipticF(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*b*c*d*e-B*EllipticPi(((d*x+c)/(c*f-d*e)*f)^(1/2),-(c*f-d*e)/(a*d-b*c)*b/f,((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*a*c*d*f+B*EllipticPi(((d*x+c)/(c*f-d*e)*f)^(1/2),-(c*f-d*e)/(a*d-b*c)*b/f,((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*a*d^2*e)/(a*d-b*c)/(d*f*h*x^3+c*f*h*x^2+d*e*h*x^2+d*f*g*x^2+c*e*h*x+c*f*g*x+d*e*g*x+c*e*g)","B"
5,1,13380,621,0.115000," ","int((B*x+A)/(b*x+a)^2/(d*x+c)^(1/2)/(f*x+e)^(1/2)/(h*x+g)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
6,1,54623,898,0.156000," ","int((b*x+a)^(3/2)*(B*x+A)/(d*x+c)^(1/2)/(f*x+e)^(1/2)/(h*x+g)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
7,1,20733,671,0.087000," ","int((b*x+a)^(1/2)*(B*x+A)/(d*x+c)^(1/2)/(f*x+e)^(1/2)/(h*x+g)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
8,1,2453,404,0.092000," ","int((B*x+A)/(b*x+a)^(1/2)/(d*x+c)^(1/2)/(f*x+e)^(1/2)/(h*x+g)^(1/2),x)","\frac{2 \sqrt{\frac{\left(a f -b e \right) \left(h x +g \right)}{\left(a h -b g \right) \left(f x +e \right)}}\, \sqrt{\frac{\left(e h -f g \right) \left(d x +c \right)}{\left(c h -d g \right) \left(f x +e \right)}}\, \sqrt{\frac{\left(e h -f g \right) \left(b x +a \right)}{\left(a h -b g \right) \left(f x +e \right)}}\, \left(A a \,f^{3} h^{2} x^{2} \EllipticF \left(\sqrt{\frac{\left(a f -b e \right) \left(h x +g \right)}{\left(a h -b g \right) \left(f x +e \right)}}, \sqrt{\frac{\left(c f -d e \right) \left(a h -b g \right)}{\left(c h -d g \right) \left(a f -b e \right)}}\right)-A b \,f^{3} g h \,x^{2} \EllipticF \left(\sqrt{\frac{\left(a f -b e \right) \left(h x +g \right)}{\left(a h -b g \right) \left(f x +e \right)}}, \sqrt{\frac{\left(c f -d e \right) \left(a h -b g \right)}{\left(c h -d g \right) \left(a f -b e \right)}}\right)-B a e \,f^{2} h^{2} x^{2} \EllipticF \left(\sqrt{\frac{\left(a f -b e \right) \left(h x +g \right)}{\left(a h -b g \right) \left(f x +e \right)}}, \sqrt{\frac{\left(c f -d e \right) \left(a h -b g \right)}{\left(c h -d g \right) \left(a f -b e \right)}}\right)+B a e \,f^{2} h^{2} x^{2} \EllipticPi \left(\sqrt{\frac{\left(a f -b e \right) \left(h x +g \right)}{\left(a h -b g \right) \left(f x +e \right)}}, \frac{\left(a h -b g \right) f}{\left(a f -b e \right) h}, \sqrt{\frac{\left(c f -d e \right) \left(a h -b g \right)}{\left(c h -d g \right) \left(a f -b e \right)}}\right)-B a \,f^{3} g h \,x^{2} \EllipticPi \left(\sqrt{\frac{\left(a f -b e \right) \left(h x +g \right)}{\left(a h -b g \right) \left(f x +e \right)}}, \frac{\left(a h -b g \right) f}{\left(a f -b e \right) h}, \sqrt{\frac{\left(c f -d e \right) \left(a h -b g \right)}{\left(c h -d g \right) \left(a f -b e \right)}}\right)+B b e \,f^{2} g h \,x^{2} \EllipticF \left(\sqrt{\frac{\left(a f -b e \right) \left(h x +g \right)}{\left(a h -b g \right) \left(f x +e \right)}}, \sqrt{\frac{\left(c f -d e \right) \left(a h -b g \right)}{\left(c h -d g \right) \left(a f -b e \right)}}\right)-B b e \,f^{2} g h \,x^{2} \EllipticPi \left(\sqrt{\frac{\left(a f -b e \right) \left(h x +g \right)}{\left(a h -b g \right) \left(f x +e \right)}}, \frac{\left(a h -b g \right) f}{\left(a f -b e \right) h}, \sqrt{\frac{\left(c f -d e \right) \left(a h -b g \right)}{\left(c h -d g \right) \left(a f -b e \right)}}\right)+B b \,f^{3} g^{2} x^{2} \EllipticPi \left(\sqrt{\frac{\left(a f -b e \right) \left(h x +g \right)}{\left(a h -b g \right) \left(f x +e \right)}}, \frac{\left(a h -b g \right) f}{\left(a f -b e \right) h}, \sqrt{\frac{\left(c f -d e \right) \left(a h -b g \right)}{\left(c h -d g \right) \left(a f -b e \right)}}\right)+2 A a e \,f^{2} h^{2} x \EllipticF \left(\sqrt{\frac{\left(a f -b e \right) \left(h x +g \right)}{\left(a h -b g \right) \left(f x +e \right)}}, \sqrt{\frac{\left(c f -d e \right) \left(a h -b g \right)}{\left(c h -d g \right) \left(a f -b e \right)}}\right)-2 A b e \,f^{2} g h x \EllipticF \left(\sqrt{\frac{\left(a f -b e \right) \left(h x +g \right)}{\left(a h -b g \right) \left(f x +e \right)}}, \sqrt{\frac{\left(c f -d e \right) \left(a h -b g \right)}{\left(c h -d g \right) \left(a f -b e \right)}}\right)-2 B a \,e^{2} f \,h^{2} x \EllipticF \left(\sqrt{\frac{\left(a f -b e \right) \left(h x +g \right)}{\left(a h -b g \right) \left(f x +e \right)}}, \sqrt{\frac{\left(c f -d e \right) \left(a h -b g \right)}{\left(c h -d g \right) \left(a f -b e \right)}}\right)+2 B a \,e^{2} f \,h^{2} x \EllipticPi \left(\sqrt{\frac{\left(a f -b e \right) \left(h x +g \right)}{\left(a h -b g \right) \left(f x +e \right)}}, \frac{\left(a h -b g \right) f}{\left(a f -b e \right) h}, \sqrt{\frac{\left(c f -d e \right) \left(a h -b g \right)}{\left(c h -d g \right) \left(a f -b e \right)}}\right)-2 B a e \,f^{2} g h x \EllipticPi \left(\sqrt{\frac{\left(a f -b e \right) \left(h x +g \right)}{\left(a h -b g \right) \left(f x +e \right)}}, \frac{\left(a h -b g \right) f}{\left(a f -b e \right) h}, \sqrt{\frac{\left(c f -d e \right) \left(a h -b g \right)}{\left(c h -d g \right) \left(a f -b e \right)}}\right)+2 B b \,e^{2} f g h x \EllipticF \left(\sqrt{\frac{\left(a f -b e \right) \left(h x +g \right)}{\left(a h -b g \right) \left(f x +e \right)}}, \sqrt{\frac{\left(c f -d e \right) \left(a h -b g \right)}{\left(c h -d g \right) \left(a f -b e \right)}}\right)-2 B b \,e^{2} f g h x \EllipticPi \left(\sqrt{\frac{\left(a f -b e \right) \left(h x +g \right)}{\left(a h -b g \right) \left(f x +e \right)}}, \frac{\left(a h -b g \right) f}{\left(a f -b e \right) h}, \sqrt{\frac{\left(c f -d e \right) \left(a h -b g \right)}{\left(c h -d g \right) \left(a f -b e \right)}}\right)+2 B b e \,f^{2} g^{2} x \EllipticPi \left(\sqrt{\frac{\left(a f -b e \right) \left(h x +g \right)}{\left(a h -b g \right) \left(f x +e \right)}}, \frac{\left(a h -b g \right) f}{\left(a f -b e \right) h}, \sqrt{\frac{\left(c f -d e \right) \left(a h -b g \right)}{\left(c h -d g \right) \left(a f -b e \right)}}\right)+A a \,e^{2} f \,h^{2} \EllipticF \left(\sqrt{\frac{\left(a f -b e \right) \left(h x +g \right)}{\left(a h -b g \right) \left(f x +e \right)}}, \sqrt{\frac{\left(c f -d e \right) \left(a h -b g \right)}{\left(c h -d g \right) \left(a f -b e \right)}}\right)-A b \,e^{2} f g h \EllipticF \left(\sqrt{\frac{\left(a f -b e \right) \left(h x +g \right)}{\left(a h -b g \right) \left(f x +e \right)}}, \sqrt{\frac{\left(c f -d e \right) \left(a h -b g \right)}{\left(c h -d g \right) \left(a f -b e \right)}}\right)-B a \,e^{3} h^{2} \EllipticF \left(\sqrt{\frac{\left(a f -b e \right) \left(h x +g \right)}{\left(a h -b g \right) \left(f x +e \right)}}, \sqrt{\frac{\left(c f -d e \right) \left(a h -b g \right)}{\left(c h -d g \right) \left(a f -b e \right)}}\right)+B a \,e^{3} h^{2} \EllipticPi \left(\sqrt{\frac{\left(a f -b e \right) \left(h x +g \right)}{\left(a h -b g \right) \left(f x +e \right)}}, \frac{\left(a h -b g \right) f}{\left(a f -b e \right) h}, \sqrt{\frac{\left(c f -d e \right) \left(a h -b g \right)}{\left(c h -d g \right) \left(a f -b e \right)}}\right)-B a \,e^{2} f g h \EllipticPi \left(\sqrt{\frac{\left(a f -b e \right) \left(h x +g \right)}{\left(a h -b g \right) \left(f x +e \right)}}, \frac{\left(a h -b g \right) f}{\left(a f -b e \right) h}, \sqrt{\frac{\left(c f -d e \right) \left(a h -b g \right)}{\left(c h -d g \right) \left(a f -b e \right)}}\right)+B b \,e^{3} g h \EllipticF \left(\sqrt{\frac{\left(a f -b e \right) \left(h x +g \right)}{\left(a h -b g \right) \left(f x +e \right)}}, \sqrt{\frac{\left(c f -d e \right) \left(a h -b g \right)}{\left(c h -d g \right) \left(a f -b e \right)}}\right)-B b \,e^{3} g h \EllipticPi \left(\sqrt{\frac{\left(a f -b e \right) \left(h x +g \right)}{\left(a h -b g \right) \left(f x +e \right)}}, \frac{\left(a h -b g \right) f}{\left(a f -b e \right) h}, \sqrt{\frac{\left(c f -d e \right) \left(a h -b g \right)}{\left(c h -d g \right) \left(a f -b e \right)}}\right)+B b \,e^{2} f \,g^{2} \EllipticPi \left(\sqrt{\frac{\left(a f -b e \right) \left(h x +g \right)}{\left(a h -b g \right) \left(f x +e \right)}}, \frac{\left(a h -b g \right) f}{\left(a f -b e \right) h}, \sqrt{\frac{\left(c f -d e \right) \left(a h -b g \right)}{\left(c h -d g \right) \left(a f -b e \right)}}\right)\right)}{\sqrt{h x +g}\, \sqrt{f x +e}\, \sqrt{d x +c}\, \sqrt{b x +a}\, \left(e h -f g \right) \left(a f -b e \right) f h}"," ",0,"2/(h*x+g)^(1/2)/(f*x+e)^(1/2)/(d*x+c)^(1/2)/(b*x+a)^(1/2)/f/h*((a*f-b*e)*(h*x+g)/(a*h-b*g)/(f*x+e))^(1/2)*((e*h-f*g)*(d*x+c)/(c*h-d*g)/(f*x+e))^(1/2)*((e*h-f*g)*(b*x+a)/(a*h-b*g)/(f*x+e))^(1/2)*(A*EllipticF(((a*f-b*e)*(h*x+g)/(a*h-b*g)/(f*x+e))^(1/2),((c*f-d*e)*(a*h-b*g)/(c*h-d*g)/(a*f-b*e))^(1/2))*x^2*a*f^3*h^2-A*EllipticF(((a*f-b*e)*(h*x+g)/(a*h-b*g)/(f*x+e))^(1/2),((c*f-d*e)*(a*h-b*g)/(c*h-d*g)/(a*f-b*e))^(1/2))*x^2*b*f^3*g*h-B*EllipticF(((a*f-b*e)*(h*x+g)/(a*h-b*g)/(f*x+e))^(1/2),((c*f-d*e)*(a*h-b*g)/(c*h-d*g)/(a*f-b*e))^(1/2))*x^2*a*e*f^2*h^2+B*EllipticF(((a*f-b*e)*(h*x+g)/(a*h-b*g)/(f*x+e))^(1/2),((c*f-d*e)*(a*h-b*g)/(c*h-d*g)/(a*f-b*e))^(1/2))*x^2*b*e*f^2*g*h+B*EllipticPi(((a*f-b*e)*(h*x+g)/(a*h-b*g)/(f*x+e))^(1/2),(a*h-b*g)/(a*f-b*e)*f/h,((c*f-d*e)*(a*h-b*g)/(c*h-d*g)/(a*f-b*e))^(1/2))*x^2*a*e*f^2*h^2-B*EllipticPi(((a*f-b*e)*(h*x+g)/(a*h-b*g)/(f*x+e))^(1/2),(a*h-b*g)/(a*f-b*e)*f/h,((c*f-d*e)*(a*h-b*g)/(c*h-d*g)/(a*f-b*e))^(1/2))*x^2*a*f^3*g*h-B*EllipticPi(((a*f-b*e)*(h*x+g)/(a*h-b*g)/(f*x+e))^(1/2),(a*h-b*g)/(a*f-b*e)*f/h,((c*f-d*e)*(a*h-b*g)/(c*h-d*g)/(a*f-b*e))^(1/2))*x^2*b*e*f^2*g*h+B*EllipticPi(((a*f-b*e)*(h*x+g)/(a*h-b*g)/(f*x+e))^(1/2),(a*h-b*g)/(a*f-b*e)*f/h,((c*f-d*e)*(a*h-b*g)/(c*h-d*g)/(a*f-b*e))^(1/2))*x^2*b*f^3*g^2+2*A*EllipticF(((a*f-b*e)*(h*x+g)/(a*h-b*g)/(f*x+e))^(1/2),((c*f-d*e)*(a*h-b*g)/(c*h-d*g)/(a*f-b*e))^(1/2))*x*a*e*f^2*h^2-2*A*EllipticF(((a*f-b*e)*(h*x+g)/(a*h-b*g)/(f*x+e))^(1/2),((c*f-d*e)*(a*h-b*g)/(c*h-d*g)/(a*f-b*e))^(1/2))*x*b*e*f^2*g*h-2*B*EllipticF(((a*f-b*e)*(h*x+g)/(a*h-b*g)/(f*x+e))^(1/2),((c*f-d*e)*(a*h-b*g)/(c*h-d*g)/(a*f-b*e))^(1/2))*x*a*e^2*f*h^2+2*B*EllipticF(((a*f-b*e)*(h*x+g)/(a*h-b*g)/(f*x+e))^(1/2),((c*f-d*e)*(a*h-b*g)/(c*h-d*g)/(a*f-b*e))^(1/2))*x*b*e^2*f*g*h+2*B*EllipticPi(((a*f-b*e)*(h*x+g)/(a*h-b*g)/(f*x+e))^(1/2),(a*h-b*g)/(a*f-b*e)*f/h,((c*f-d*e)*(a*h-b*g)/(c*h-d*g)/(a*f-b*e))^(1/2))*x*a*e^2*f*h^2-2*B*EllipticPi(((a*f-b*e)*(h*x+g)/(a*h-b*g)/(f*x+e))^(1/2),(a*h-b*g)/(a*f-b*e)*f/h,((c*f-d*e)*(a*h-b*g)/(c*h-d*g)/(a*f-b*e))^(1/2))*x*a*e*f^2*g*h-2*B*EllipticPi(((a*f-b*e)*(h*x+g)/(a*h-b*g)/(f*x+e))^(1/2),(a*h-b*g)/(a*f-b*e)*f/h,((c*f-d*e)*(a*h-b*g)/(c*h-d*g)/(a*f-b*e))^(1/2))*x*b*e^2*f*g*h+2*B*EllipticPi(((a*f-b*e)*(h*x+g)/(a*h-b*g)/(f*x+e))^(1/2),(a*h-b*g)/(a*f-b*e)*f/h,((c*f-d*e)*(a*h-b*g)/(c*h-d*g)/(a*f-b*e))^(1/2))*x*b*e*f^2*g^2+A*EllipticF(((a*f-b*e)*(h*x+g)/(a*h-b*g)/(f*x+e))^(1/2),((c*f-d*e)*(a*h-b*g)/(c*h-d*g)/(a*f-b*e))^(1/2))*a*e^2*f*h^2-A*EllipticF(((a*f-b*e)*(h*x+g)/(a*h-b*g)/(f*x+e))^(1/2),((c*f-d*e)*(a*h-b*g)/(c*h-d*g)/(a*f-b*e))^(1/2))*b*e^2*f*g*h-B*EllipticF(((a*f-b*e)*(h*x+g)/(a*h-b*g)/(f*x+e))^(1/2),((c*f-d*e)*(a*h-b*g)/(c*h-d*g)/(a*f-b*e))^(1/2))*a*e^3*h^2+B*EllipticF(((a*f-b*e)*(h*x+g)/(a*h-b*g)/(f*x+e))^(1/2),((c*f-d*e)*(a*h-b*g)/(c*h-d*g)/(a*f-b*e))^(1/2))*b*e^3*g*h+B*EllipticPi(((a*f-b*e)*(h*x+g)/(a*h-b*g)/(f*x+e))^(1/2),(a*h-b*g)/(a*f-b*e)*f/h,((c*f-d*e)*(a*h-b*g)/(c*h-d*g)/(a*f-b*e))^(1/2))*a*e^3*h^2-B*EllipticPi(((a*f-b*e)*(h*x+g)/(a*h-b*g)/(f*x+e))^(1/2),(a*h-b*g)/(a*f-b*e)*f/h,((c*f-d*e)*(a*h-b*g)/(c*h-d*g)/(a*f-b*e))^(1/2))*a*e^2*f*g*h-B*EllipticPi(((a*f-b*e)*(h*x+g)/(a*h-b*g)/(f*x+e))^(1/2),(a*h-b*g)/(a*f-b*e)*f/h,((c*f-d*e)*(a*h-b*g)/(c*h-d*g)/(a*f-b*e))^(1/2))*b*e^3*g*h+B*EllipticPi(((a*f-b*e)*(h*x+g)/(a*h-b*g)/(f*x+e))^(1/2),(a*h-b*g)/(a*f-b*e)*f/h,((c*f-d*e)*(a*h-b*g)/(c*h-d*g)/(a*f-b*e))^(1/2))*b*e^2*f*g^2)/(e*h-f*g)/(a*f-b*e)","B"
9,1,9328,552,0.180000," ","int((B*x+A)/(b*x+a)^(3/2)/(d*x+c)^(1/2)/(f*x+e)^(1/2)/(h*x+g)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
10,1,71656,1009,1.783000," ","int((B*x+A)/(b*x+a)^(5/2)/(d*x+c)^(1/2)/(f*x+e)^(1/2)/(h*x+g)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
11,1,35476,817,0.121000," ","int((b*x+a)^(3/2)*(2*d*f*x+c*f+d*e)/(d*x+c)^(1/2)/(f*x+e)^(1/2)/(h*x+g)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
12,1,13177,426,0.073000," ","int((b*x+a)^(1/2)*(2*d*f*x+c*f+d*e)/(d*x+c)^(1/2)/(f*x+e)^(1/2)/(h*x+g)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
13,1,2454,411,0.075000," ","int((2*d*f*x+c*f+d*e)/(b*x+a)^(1/2)/(d*x+c)^(1/2)/(f*x+e)^(1/2)/(h*x+g)^(1/2),x)","\frac{2 \left(a c \,f^{3} h^{2} x^{2} \EllipticF \left(\sqrt{\frac{\left(a f -b e \right) \left(h x +g \right)}{\left(a h -b g \right) \left(f x +e \right)}}, \sqrt{\frac{\left(c f -d e \right) \left(a h -b g \right)}{\left(c h -d g \right) \left(a f -b e \right)}}\right)-a d e \,f^{2} h^{2} x^{2} \EllipticF \left(\sqrt{\frac{\left(a f -b e \right) \left(h x +g \right)}{\left(a h -b g \right) \left(f x +e \right)}}, \sqrt{\frac{\left(c f -d e \right) \left(a h -b g \right)}{\left(c h -d g \right) \left(a f -b e \right)}}\right)+2 a d e \,f^{2} h^{2} x^{2} \EllipticPi \left(\sqrt{\frac{\left(a f -b e \right) \left(h x +g \right)}{\left(a h -b g \right) \left(f x +e \right)}}, \frac{\left(a h -b g \right) f}{\left(a f -b e \right) h}, \sqrt{\frac{\left(c f -d e \right) \left(a h -b g \right)}{\left(c h -d g \right) \left(a f -b e \right)}}\right)-2 a d \,f^{3} g h \,x^{2} \EllipticPi \left(\sqrt{\frac{\left(a f -b e \right) \left(h x +g \right)}{\left(a h -b g \right) \left(f x +e \right)}}, \frac{\left(a h -b g \right) f}{\left(a f -b e \right) h}, \sqrt{\frac{\left(c f -d e \right) \left(a h -b g \right)}{\left(c h -d g \right) \left(a f -b e \right)}}\right)-b c \,f^{3} g h \,x^{2} \EllipticF \left(\sqrt{\frac{\left(a f -b e \right) \left(h x +g \right)}{\left(a h -b g \right) \left(f x +e \right)}}, \sqrt{\frac{\left(c f -d e \right) \left(a h -b g \right)}{\left(c h -d g \right) \left(a f -b e \right)}}\right)+b d e \,f^{2} g h \,x^{2} \EllipticF \left(\sqrt{\frac{\left(a f -b e \right) \left(h x +g \right)}{\left(a h -b g \right) \left(f x +e \right)}}, \sqrt{\frac{\left(c f -d e \right) \left(a h -b g \right)}{\left(c h -d g \right) \left(a f -b e \right)}}\right)-2 b d e \,f^{2} g h \,x^{2} \EllipticPi \left(\sqrt{\frac{\left(a f -b e \right) \left(h x +g \right)}{\left(a h -b g \right) \left(f x +e \right)}}, \frac{\left(a h -b g \right) f}{\left(a f -b e \right) h}, \sqrt{\frac{\left(c f -d e \right) \left(a h -b g \right)}{\left(c h -d g \right) \left(a f -b e \right)}}\right)+2 b d \,f^{3} g^{2} x^{2} \EllipticPi \left(\sqrt{\frac{\left(a f -b e \right) \left(h x +g \right)}{\left(a h -b g \right) \left(f x +e \right)}}, \frac{\left(a h -b g \right) f}{\left(a f -b e \right) h}, \sqrt{\frac{\left(c f -d e \right) \left(a h -b g \right)}{\left(c h -d g \right) \left(a f -b e \right)}}\right)+2 a c e \,f^{2} h^{2} x \EllipticF \left(\sqrt{\frac{\left(a f -b e \right) \left(h x +g \right)}{\left(a h -b g \right) \left(f x +e \right)}}, \sqrt{\frac{\left(c f -d e \right) \left(a h -b g \right)}{\left(c h -d g \right) \left(a f -b e \right)}}\right)-2 a d \,e^{2} f \,h^{2} x \EllipticF \left(\sqrt{\frac{\left(a f -b e \right) \left(h x +g \right)}{\left(a h -b g \right) \left(f x +e \right)}}, \sqrt{\frac{\left(c f -d e \right) \left(a h -b g \right)}{\left(c h -d g \right) \left(a f -b e \right)}}\right)+4 a d \,e^{2} f \,h^{2} x \EllipticPi \left(\sqrt{\frac{\left(a f -b e \right) \left(h x +g \right)}{\left(a h -b g \right) \left(f x +e \right)}}, \frac{\left(a h -b g \right) f}{\left(a f -b e \right) h}, \sqrt{\frac{\left(c f -d e \right) \left(a h -b g \right)}{\left(c h -d g \right) \left(a f -b e \right)}}\right)-4 a d e \,f^{2} g h x \EllipticPi \left(\sqrt{\frac{\left(a f -b e \right) \left(h x +g \right)}{\left(a h -b g \right) \left(f x +e \right)}}, \frac{\left(a h -b g \right) f}{\left(a f -b e \right) h}, \sqrt{\frac{\left(c f -d e \right) \left(a h -b g \right)}{\left(c h -d g \right) \left(a f -b e \right)}}\right)-2 b c e \,f^{2} g h x \EllipticF \left(\sqrt{\frac{\left(a f -b e \right) \left(h x +g \right)}{\left(a h -b g \right) \left(f x +e \right)}}, \sqrt{\frac{\left(c f -d e \right) \left(a h -b g \right)}{\left(c h -d g \right) \left(a f -b e \right)}}\right)+2 b d \,e^{2} f g h x \EllipticF \left(\sqrt{\frac{\left(a f -b e \right) \left(h x +g \right)}{\left(a h -b g \right) \left(f x +e \right)}}, \sqrt{\frac{\left(c f -d e \right) \left(a h -b g \right)}{\left(c h -d g \right) \left(a f -b e \right)}}\right)-4 b d \,e^{2} f g h x \EllipticPi \left(\sqrt{\frac{\left(a f -b e \right) \left(h x +g \right)}{\left(a h -b g \right) \left(f x +e \right)}}, \frac{\left(a h -b g \right) f}{\left(a f -b e \right) h}, \sqrt{\frac{\left(c f -d e \right) \left(a h -b g \right)}{\left(c h -d g \right) \left(a f -b e \right)}}\right)+4 b d e \,f^{2} g^{2} x \EllipticPi \left(\sqrt{\frac{\left(a f -b e \right) \left(h x +g \right)}{\left(a h -b g \right) \left(f x +e \right)}}, \frac{\left(a h -b g \right) f}{\left(a f -b e \right) h}, \sqrt{\frac{\left(c f -d e \right) \left(a h -b g \right)}{\left(c h -d g \right) \left(a f -b e \right)}}\right)+a c \,e^{2} f \,h^{2} \EllipticF \left(\sqrt{\frac{\left(a f -b e \right) \left(h x +g \right)}{\left(a h -b g \right) \left(f x +e \right)}}, \sqrt{\frac{\left(c f -d e \right) \left(a h -b g \right)}{\left(c h -d g \right) \left(a f -b e \right)}}\right)-a d \,e^{3} h^{2} \EllipticF \left(\sqrt{\frac{\left(a f -b e \right) \left(h x +g \right)}{\left(a h -b g \right) \left(f x +e \right)}}, \sqrt{\frac{\left(c f -d e \right) \left(a h -b g \right)}{\left(c h -d g \right) \left(a f -b e \right)}}\right)+2 a d \,e^{3} h^{2} \EllipticPi \left(\sqrt{\frac{\left(a f -b e \right) \left(h x +g \right)}{\left(a h -b g \right) \left(f x +e \right)}}, \frac{\left(a h -b g \right) f}{\left(a f -b e \right) h}, \sqrt{\frac{\left(c f -d e \right) \left(a h -b g \right)}{\left(c h -d g \right) \left(a f -b e \right)}}\right)-2 a d \,e^{2} f g h \EllipticPi \left(\sqrt{\frac{\left(a f -b e \right) \left(h x +g \right)}{\left(a h -b g \right) \left(f x +e \right)}}, \frac{\left(a h -b g \right) f}{\left(a f -b e \right) h}, \sqrt{\frac{\left(c f -d e \right) \left(a h -b g \right)}{\left(c h -d g \right) \left(a f -b e \right)}}\right)-b c \,e^{2} f g h \EllipticF \left(\sqrt{\frac{\left(a f -b e \right) \left(h x +g \right)}{\left(a h -b g \right) \left(f x +e \right)}}, \sqrt{\frac{\left(c f -d e \right) \left(a h -b g \right)}{\left(c h -d g \right) \left(a f -b e \right)}}\right)+b d \,e^{3} g h \EllipticF \left(\sqrt{\frac{\left(a f -b e \right) \left(h x +g \right)}{\left(a h -b g \right) \left(f x +e \right)}}, \sqrt{\frac{\left(c f -d e \right) \left(a h -b g \right)}{\left(c h -d g \right) \left(a f -b e \right)}}\right)-2 b d \,e^{3} g h \EllipticPi \left(\sqrt{\frac{\left(a f -b e \right) \left(h x +g \right)}{\left(a h -b g \right) \left(f x +e \right)}}, \frac{\left(a h -b g \right) f}{\left(a f -b e \right) h}, \sqrt{\frac{\left(c f -d e \right) \left(a h -b g \right)}{\left(c h -d g \right) \left(a f -b e \right)}}\right)+2 b d \,e^{2} f \,g^{2} \EllipticPi \left(\sqrt{\frac{\left(a f -b e \right) \left(h x +g \right)}{\left(a h -b g \right) \left(f x +e \right)}}, \frac{\left(a h -b g \right) f}{\left(a f -b e \right) h}, \sqrt{\frac{\left(c f -d e \right) \left(a h -b g \right)}{\left(c h -d g \right) \left(a f -b e \right)}}\right)\right) \sqrt{\frac{\left(e h -f g \right) \left(b x +a \right)}{\left(a h -b g \right) \left(f x +e \right)}}\, \sqrt{\frac{\left(e h -f g \right) \left(d x +c \right)}{\left(c h -d g \right) \left(f x +e \right)}}\, \sqrt{\frac{\left(a f -b e \right) \left(h x +g \right)}{\left(a h -b g \right) \left(f x +e \right)}}}{\sqrt{b x +a}\, \sqrt{d x +c}\, \sqrt{f x +e}\, \sqrt{h x +g}\, \left(e h -f g \right) \left(a f -b e \right) h}"," ",0,"2*(EllipticF(((a*f-b*e)*(h*x+g)/(a*h-b*g)/(f*x+e))^(1/2),((c*f-d*e)*(a*h-b*g)/(c*h-d*g)/(a*f-b*e))^(1/2))*x^2*a*c*f^3*h^2-EllipticF(((a*f-b*e)*(h*x+g)/(a*h-b*g)/(f*x+e))^(1/2),((c*f-d*e)*(a*h-b*g)/(c*h-d*g)/(a*f-b*e))^(1/2))*x^2*a*d*e*f^2*h^2-EllipticF(((a*f-b*e)*(h*x+g)/(a*h-b*g)/(f*x+e))^(1/2),((c*f-d*e)*(a*h-b*g)/(c*h-d*g)/(a*f-b*e))^(1/2))*x^2*b*c*f^3*g*h+EllipticF(((a*f-b*e)*(h*x+g)/(a*h-b*g)/(f*x+e))^(1/2),((c*f-d*e)*(a*h-b*g)/(c*h-d*g)/(a*f-b*e))^(1/2))*x^2*b*d*e*f^2*g*h+2*EllipticPi(((a*f-b*e)*(h*x+g)/(a*h-b*g)/(f*x+e))^(1/2),(a*h-b*g)/(a*f-b*e)*f/h,((c*f-d*e)*(a*h-b*g)/(c*h-d*g)/(a*f-b*e))^(1/2))*x^2*a*d*e*f^2*h^2-2*EllipticPi(((a*f-b*e)*(h*x+g)/(a*h-b*g)/(f*x+e))^(1/2),(a*h-b*g)/(a*f-b*e)*f/h,((c*f-d*e)*(a*h-b*g)/(c*h-d*g)/(a*f-b*e))^(1/2))*x^2*a*d*f^3*g*h-2*EllipticPi(((a*f-b*e)*(h*x+g)/(a*h-b*g)/(f*x+e))^(1/2),(a*h-b*g)/(a*f-b*e)*f/h,((c*f-d*e)*(a*h-b*g)/(c*h-d*g)/(a*f-b*e))^(1/2))*x^2*b*d*e*f^2*g*h+2*EllipticPi(((a*f-b*e)*(h*x+g)/(a*h-b*g)/(f*x+e))^(1/2),(a*h-b*g)/(a*f-b*e)*f/h,((c*f-d*e)*(a*h-b*g)/(c*h-d*g)/(a*f-b*e))^(1/2))*x^2*b*d*f^3*g^2+2*EllipticF(((a*f-b*e)*(h*x+g)/(a*h-b*g)/(f*x+e))^(1/2),((c*f-d*e)*(a*h-b*g)/(c*h-d*g)/(a*f-b*e))^(1/2))*x*a*c*e*f^2*h^2-2*EllipticF(((a*f-b*e)*(h*x+g)/(a*h-b*g)/(f*x+e))^(1/2),((c*f-d*e)*(a*h-b*g)/(c*h-d*g)/(a*f-b*e))^(1/2))*x*a*d*e^2*f*h^2-2*EllipticF(((a*f-b*e)*(h*x+g)/(a*h-b*g)/(f*x+e))^(1/2),((c*f-d*e)*(a*h-b*g)/(c*h-d*g)/(a*f-b*e))^(1/2))*x*b*c*e*f^2*g*h+2*EllipticF(((a*f-b*e)*(h*x+g)/(a*h-b*g)/(f*x+e))^(1/2),((c*f-d*e)*(a*h-b*g)/(c*h-d*g)/(a*f-b*e))^(1/2))*x*b*d*e^2*f*g*h+4*EllipticPi(((a*f-b*e)*(h*x+g)/(a*h-b*g)/(f*x+e))^(1/2),(a*h-b*g)/(a*f-b*e)*f/h,((c*f-d*e)*(a*h-b*g)/(c*h-d*g)/(a*f-b*e))^(1/2))*x*a*d*e^2*f*h^2-4*EllipticPi(((a*f-b*e)*(h*x+g)/(a*h-b*g)/(f*x+e))^(1/2),(a*h-b*g)/(a*f-b*e)*f/h,((c*f-d*e)*(a*h-b*g)/(c*h-d*g)/(a*f-b*e))^(1/2))*x*a*d*e*f^2*g*h-4*EllipticPi(((a*f-b*e)*(h*x+g)/(a*h-b*g)/(f*x+e))^(1/2),(a*h-b*g)/(a*f-b*e)*f/h,((c*f-d*e)*(a*h-b*g)/(c*h-d*g)/(a*f-b*e))^(1/2))*x*b*d*e^2*f*g*h+4*EllipticPi(((a*f-b*e)*(h*x+g)/(a*h-b*g)/(f*x+e))^(1/2),(a*h-b*g)/(a*f-b*e)*f/h,((c*f-d*e)*(a*h-b*g)/(c*h-d*g)/(a*f-b*e))^(1/2))*x*b*d*e*f^2*g^2+EllipticF(((a*f-b*e)*(h*x+g)/(a*h-b*g)/(f*x+e))^(1/2),((c*f-d*e)*(a*h-b*g)/(c*h-d*g)/(a*f-b*e))^(1/2))*a*c*e^2*f*h^2-EllipticF(((a*f-b*e)*(h*x+g)/(a*h-b*g)/(f*x+e))^(1/2),((c*f-d*e)*(a*h-b*g)/(c*h-d*g)/(a*f-b*e))^(1/2))*a*d*e^3*h^2-EllipticF(((a*f-b*e)*(h*x+g)/(a*h-b*g)/(f*x+e))^(1/2),((c*f-d*e)*(a*h-b*g)/(c*h-d*g)/(a*f-b*e))^(1/2))*b*c*e^2*f*g*h+EllipticF(((a*f-b*e)*(h*x+g)/(a*h-b*g)/(f*x+e))^(1/2),((c*f-d*e)*(a*h-b*g)/(c*h-d*g)/(a*f-b*e))^(1/2))*b*d*e^3*g*h+2*EllipticPi(((a*f-b*e)*(h*x+g)/(a*h-b*g)/(f*x+e))^(1/2),(a*h-b*g)/(a*f-b*e)*f/h,((c*f-d*e)*(a*h-b*g)/(c*h-d*g)/(a*f-b*e))^(1/2))*a*d*e^3*h^2-2*EllipticPi(((a*f-b*e)*(h*x+g)/(a*h-b*g)/(f*x+e))^(1/2),(a*h-b*g)/(a*f-b*e)*f/h,((c*f-d*e)*(a*h-b*g)/(c*h-d*g)/(a*f-b*e))^(1/2))*a*d*e^2*f*g*h-2*EllipticPi(((a*f-b*e)*(h*x+g)/(a*h-b*g)/(f*x+e))^(1/2),(a*h-b*g)/(a*f-b*e)*f/h,((c*f-d*e)*(a*h-b*g)/(c*h-d*g)/(a*f-b*e))^(1/2))*b*d*e^3*g*h+2*EllipticPi(((a*f-b*e)*(h*x+g)/(a*h-b*g)/(f*x+e))^(1/2),(a*h-b*g)/(a*f-b*e)*f/h,((c*f-d*e)*(a*h-b*g)/(c*h-d*g)/(a*f-b*e))^(1/2))*b*d*e^2*f*g^2)*((e*h-f*g)*(b*x+a)/(a*h-b*g)/(f*x+e))^(1/2)*((e*h-f*g)*(d*x+c)/(c*h-d*g)/(f*x+e))^(1/2)*((a*f-b*e)*(h*x+g)/(a*h-b*g)/(f*x+e))^(1/2)/h/(b*x+a)^(1/2)/(d*x+c)^(1/2)/(f*x+e)^(1/2)/(h*x+g)^(1/2)/(e*h-f*g)/(a*f-b*e)","B"
14,1,12900,571,0.136000," ","int((2*d*f*x+c*f+d*e)/(b*x+a)^(3/2)/(d*x+c)^(1/2)/(f*x+e)^(1/2)/(h*x+g)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
15,1,65243,1018,0.866000," ","int((2*d*f*x+c*f+d*e)/(b*x+a)^(5/2)/(d*x+c)^(1/2)/(f*x+e)^(1/2)/(h*x+g)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
16,1,8421,667,0.059000," ","int((b*x+a)*(C*b^2*x^2+B*b^2*x+B*a*b-C*a^2)/(d*x+c)^(1/2)/(f*x+e)^(1/2)/(h*x+g)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
17,1,2825,364,0.040000," ","int((C*b^2*x^2+B*b^2*x+B*a*b-C*a^2)/(d*x+c)^(1/2)/(f*x+e)^(1/2)/(h*x+g)^(1/2),x)","\text{output too large to display}"," ",0,"-2/3*(-C*x^3*b^2*d^3*f^2*h^2-C*x*b^2*c*d^2*f^2*g*h+3*C*(-(f*x+e)/(c*f-d*e)*d)^(1/2)*EllipticF(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*((d*x+c)/(c*f-d*e)*f)^(1/2)*(-(h*x+g)/(c*h-d*g)*d)^(1/2)*a^2*c*d^2*f^2*h^2-3*C*(-(f*x+e)/(c*f-d*e)*d)^(1/2)*EllipticF(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*((d*x+c)/(c*f-d*e)*f)^(1/2)*(-(h*x+g)/(c*h-d*g)*d)^(1/2)*a^2*d^3*e*f*h^2-C*(-(f*x+e)/(c*f-d*e)*d)^(1/2)*EllipticF(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*((d*x+c)/(c*f-d*e)*f)^(1/2)*(-(h*x+g)/(c*h-d*g)*d)^(1/2)*b^2*c*d^2*e^2*h^2-2*C*(-(f*x+e)/(c*f-d*e)*d)^(1/2)*EllipticF(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*((d*x+c)/(c*f-d*e)*f)^(1/2)*(-(h*x+g)/(c*h-d*g)*d)^(1/2)*b^2*c*d^2*f^2*g^2+C*(-(f*x+e)/(c*f-d*e)*d)^(1/2)*EllipticF(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*((d*x+c)/(c*f-d*e)*f)^(1/2)*(-(h*x+g)/(c*h-d*g)*d)^(1/2)*b^2*d^3*e^2*g*h+2*C*(-(f*x+e)/(c*f-d*e)*d)^(1/2)*EllipticF(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*((d*x+c)/(c*f-d*e)*f)^(1/2)*(-(h*x+g)/(c*h-d*g)*d)^(1/2)*b^2*d^3*e*f*g^2+2*C*(-(f*x+e)/(c*f-d*e)*d)^(1/2)*EllipticE(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*((d*x+c)/(c*f-d*e)*f)^(1/2)*(-(h*x+g)/(c*h-d*g)*d)^(1/2)*b^2*c*d^2*e^2*h^2+3*B*(-(f*x+e)/(c*f-d*e)*d)^(1/2)*EllipticE(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*((d*x+c)/(c*f-d*e)*f)^(1/2)*(-(h*x+g)/(c*h-d*g)*d)^(1/2)*b^2*c^2*d*f^2*h^2+2*C*(-(f*x+e)/(c*f-d*e)*d)^(1/2)*EllipticE(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*((d*x+c)/(c*f-d*e)*f)^(1/2)*(-(h*x+g)/(c*h-d*g)*d)^(1/2)*b^2*c*d^2*f^2*g^2-2*C*(-(f*x+e)/(c*f-d*e)*d)^(1/2)*EllipticE(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*((d*x+c)/(c*f-d*e)*f)^(1/2)*(-(h*x+g)/(c*h-d*g)*d)^(1/2)*b^2*d^3*e^2*g*h-2*C*(-(f*x+e)/(c*f-d*e)*d)^(1/2)*EllipticE(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*((d*x+c)/(c*f-d*e)*f)^(1/2)*(-(h*x+g)/(c*h-d*g)*d)^(1/2)*b^2*d^3*e*f*g^2+3*B*(-(f*x+e)/(c*f-d*e)*d)^(1/2)*EllipticF(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*((d*x+c)/(c*f-d*e)*f)^(1/2)*(-(h*x+g)/(c*h-d*g)*d)^(1/2)*a*b*d^3*e*f*h^2+3*B*(-(f*x+e)/(c*f-d*e)*d)^(1/2)*EllipticF(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*((d*x+c)/(c*f-d*e)*f)^(1/2)*(-(h*x+g)/(c*h-d*g)*d)^(1/2)*b^2*c*d^2*f^2*g*h-3*B*(-(f*x+e)/(c*f-d*e)*d)^(1/2)*EllipticF(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*((d*x+c)/(c*f-d*e)*f)^(1/2)*(-(h*x+g)/(c*h-d*g)*d)^(1/2)*b^2*d^3*e*f*g*h-3*B*(-(f*x+e)/(c*f-d*e)*d)^(1/2)*EllipticE(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*((d*x+c)/(c*f-d*e)*f)^(1/2)*(-(h*x+g)/(c*h-d*g)*d)^(1/2)*b^2*c*d^2*e*f*h^2-3*B*(-(f*x+e)/(c*f-d*e)*d)^(1/2)*EllipticE(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*((d*x+c)/(c*f-d*e)*f)^(1/2)*(-(h*x+g)/(c*h-d*g)*d)^(1/2)*b^2*c*d^2*f^2*g*h+3*B*(-(f*x+e)/(c*f-d*e)*d)^(1/2)*EllipticE(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*((d*x+c)/(c*f-d*e)*f)^(1/2)*(-(h*x+g)/(c*h-d*g)*d)^(1/2)*b^2*d^3*e*f*g*h+C*(-(f*x+e)/(c*f-d*e)*d)^(1/2)*EllipticF(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*((d*x+c)/(c*f-d*e)*f)^(1/2)*(-(h*x+g)/(c*h-d*g)*d)^(1/2)*b^2*c^2*d*e*f*h^2-C*(-(f*x+e)/(c*f-d*e)*d)^(1/2)*EllipticF(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*((d*x+c)/(c*f-d*e)*f)^(1/2)*(-(h*x+g)/(c*h-d*g)*d)^(1/2)*b^2*c^2*d*f^2*g*h-3*B*(-(f*x+e)/(c*f-d*e)*d)^(1/2)*EllipticF(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*((d*x+c)/(c*f-d*e)*f)^(1/2)*(-(h*x+g)/(c*h-d*g)*d)^(1/2)*a*b*c*d^2*f^2*h^2+2*C*(-(f*x+e)/(c*f-d*e)*d)^(1/2)*EllipticE(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*((d*x+c)/(c*f-d*e)*f)^(1/2)*(-(h*x+g)/(c*h-d*g)*d)^(1/2)*b^2*c*d^2*e*f*g*h-2*C*(-(f*x+e)/(c*f-d*e)*d)^(1/2)*EllipticE(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*((d*x+c)/(c*f-d*e)*f)^(1/2)*(-(h*x+g)/(c*h-d*g)*d)^(1/2)*b^2*c^3*f^2*h^2-C*x*b^2*c*d^2*e*f*h^2-C*x*b^2*d^3*e*f*g*h-C*x^2*b^2*c*d^2*f^2*h^2-C*x^2*b^2*d^3*e*f*h^2-C*x^2*b^2*d^3*f^2*g*h-C*b^2*c*d^2*e*f*g*h)*(d*x+c)^(1/2)*(f*x+e)^(1/2)*(h*x+g)^(1/2)/h^2/f^2/d^3/(d*f*h*x^3+c*f*h*x^2+d*e*h*x^2+d*f*g*x^2+c*e*h*x+c*f*g*x+d*e*g*x+c*e*g)","B"
18,1,673,257,0.029000," ","int((C*b^2*x^2+B*b^2*x+B*a*b-C*a^2)/(b*x+a)/(d*x+c)^(1/2)/(f*x+e)^(1/2)/(h*x+g)^(1/2),x)","\frac{2 \left(B b c d f h \EllipticF \left(\sqrt{\frac{\left(d x +c \right) f}{c f -d e}}, \sqrt{\frac{\left(c f -d e \right) h}{\left(c h -d g \right) f}}\right)-B b \,d^{2} e h \EllipticF \left(\sqrt{\frac{\left(d x +c \right) f}{c f -d e}}, \sqrt{\frac{\left(c f -d e \right) h}{\left(c h -d g \right) f}}\right)-C a c d f h \EllipticF \left(\sqrt{\frac{\left(d x +c \right) f}{c f -d e}}, \sqrt{\frac{\left(c f -d e \right) h}{\left(c h -d g \right) f}}\right)+C a \,d^{2} e h \EllipticF \left(\sqrt{\frac{\left(d x +c \right) f}{c f -d e}}, \sqrt{\frac{\left(c f -d e \right) h}{\left(c h -d g \right) f}}\right)-C b \,c^{2} f h \EllipticE \left(\sqrt{\frac{\left(d x +c \right) f}{c f -d e}}, \sqrt{\frac{\left(c f -d e \right) h}{\left(c h -d g \right) f}}\right)+C b c d e h \EllipticE \left(\sqrt{\frac{\left(d x +c \right) f}{c f -d e}}, \sqrt{\frac{\left(c f -d e \right) h}{\left(c h -d g \right) f}}\right)+C b c d f g \EllipticE \left(\sqrt{\frac{\left(d x +c \right) f}{c f -d e}}, \sqrt{\frac{\left(c f -d e \right) h}{\left(c h -d g \right) f}}\right)-C b c d f g \EllipticF \left(\sqrt{\frac{\left(d x +c \right) f}{c f -d e}}, \sqrt{\frac{\left(c f -d e \right) h}{\left(c h -d g \right) f}}\right)-C b \,d^{2} e g \EllipticE \left(\sqrt{\frac{\left(d x +c \right) f}{c f -d e}}, \sqrt{\frac{\left(c f -d e \right) h}{\left(c h -d g \right) f}}\right)+C b \,d^{2} e g \EllipticF \left(\sqrt{\frac{\left(d x +c \right) f}{c f -d e}}, \sqrt{\frac{\left(c f -d e \right) h}{\left(c h -d g \right) f}}\right)\right) \sqrt{-\frac{\left(f x +e \right) d}{c f -d e}}\, \sqrt{-\frac{\left(h x +g \right) d}{c h -d g}}\, \sqrt{\frac{\left(d x +c \right) f}{c f -d e}}\, \sqrt{h x +g}\, \sqrt{f x +e}\, \sqrt{d x +c}}{\left(d f h \,x^{3}+c f h \,x^{2}+d e h \,x^{2}+d f g \,x^{2}+c e h x +c f g x +d e g x +c e g \right) d^{2} f h}"," ",0,"2*(B*EllipticF(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*b*c*d*f*h-B*EllipticF(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*b*d^2*e*h-C*EllipticF(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*a*c*d*f*h+C*EllipticF(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*a*d^2*e*h-C*EllipticF(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*b*c*d*f*g+C*EllipticF(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*b*d^2*e*g-C*EllipticE(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*b*c^2*f*h+C*EllipticE(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*b*c*d*e*h+C*EllipticE(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*b*c*d*f*g-C*EllipticE(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*b*d^2*e*g)*(-(f*x+e)/(c*f-d*e)*d)^(1/2)*(-(h*x+g)/(c*h-d*g)*d)^(1/2)*((d*x+c)/(c*f-d*e)*f)^(1/2)/h/f/d^2*(h*x+g)^(1/2)*(f*x+e)^(1/2)*(d*x+c)^(1/2)/(d*f*h*x^3+c*f*h*x^2+d*e*h*x^2+d*f*g*x^2+c*e*h*x+c*f*g*x+d*e*g*x+c*e*g)","B"
19,1,663,275,0.043000," ","int((C*b^2*x^2+B*b^2*x+B*a*b-C*a^2)/(b*x+a)^2/(d*x+c)^(1/2)/(f*x+e)^(1/2)/(h*x+g)^(1/2),x)","\frac{2 \sqrt{h x +g}\, \sqrt{f x +e}\, \sqrt{d x +c}\, \sqrt{\frac{\left(d x +c \right) f}{c f -d e}}\, \sqrt{-\frac{\left(h x +g \right) d}{c h -d g}}\, \sqrt{-\frac{\left(f x +e \right) d}{c f -d e}}\, \left(B b c d f \EllipticPi \left(\sqrt{\frac{\left(d x +c \right) f}{c f -d e}}, -\frac{\left(c f -d e \right) b}{\left(a d -b c \right) f}, \sqrt{\frac{\left(c f -d e \right) h}{\left(c h -d g \right) f}}\right)-B b \,d^{2} e \EllipticPi \left(\sqrt{\frac{\left(d x +c \right) f}{c f -d e}}, -\frac{\left(c f -d e \right) b}{\left(a d -b c \right) f}, \sqrt{\frac{\left(c f -d e \right) h}{\left(c h -d g \right) f}}\right)+C a c d f \EllipticF \left(\sqrt{\frac{\left(d x +c \right) f}{c f -d e}}, \sqrt{\frac{\left(c f -d e \right) h}{\left(c h -d g \right) f}}\right)-2 C a c d f \EllipticPi \left(\sqrt{\frac{\left(d x +c \right) f}{c f -d e}}, -\frac{\left(c f -d e \right) b}{\left(a d -b c \right) f}, \sqrt{\frac{\left(c f -d e \right) h}{\left(c h -d g \right) f}}\right)-C a \,d^{2} e \EllipticF \left(\sqrt{\frac{\left(d x +c \right) f}{c f -d e}}, \sqrt{\frac{\left(c f -d e \right) h}{\left(c h -d g \right) f}}\right)+2 C a \,d^{2} e \EllipticPi \left(\sqrt{\frac{\left(d x +c \right) f}{c f -d e}}, -\frac{\left(c f -d e \right) b}{\left(a d -b c \right) f}, \sqrt{\frac{\left(c f -d e \right) h}{\left(c h -d g \right) f}}\right)-C b \,c^{2} f \EllipticF \left(\sqrt{\frac{\left(d x +c \right) f}{c f -d e}}, \sqrt{\frac{\left(c f -d e \right) h}{\left(c h -d g \right) f}}\right)+C b c d e \EllipticF \left(\sqrt{\frac{\left(d x +c \right) f}{c f -d e}}, \sqrt{\frac{\left(c f -d e \right) h}{\left(c h -d g \right) f}}\right)\right)}{\left(a d -b c \right) \left(d f h \,x^{3}+c f h \,x^{2}+d e h \,x^{2}+d f g \,x^{2}+c e h x +c f g x +d e g x +c e g \right) d f}"," ",0,"2*(h*x+g)^(1/2)*(f*x+e)^(1/2)*(d*x+c)^(1/2)/d/f*((d*x+c)/(c*f-d*e)*f)^(1/2)*(-(h*x+g)/(c*h-d*g)*d)^(1/2)*(-(f*x+e)/(c*f-d*e)*d)^(1/2)*(B*EllipticPi(((d*x+c)/(c*f-d*e)*f)^(1/2),-(c*f-d*e)/(a*d-b*c)*b/f,((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*b*c*d*f-B*EllipticPi(((d*x+c)/(c*f-d*e)*f)^(1/2),-(c*f-d*e)/(a*d-b*c)*b/f,((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*b*d^2*e+C*EllipticF(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*a*c*d*f-C*EllipticF(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*a*d^2*e-C*EllipticF(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*b*c^2*f+C*EllipticF(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*b*c*d*e-2*C*EllipticPi(((d*x+c)/(c*f-d*e)*f)^(1/2),-(c*f-d*e)/(a*d-b*c)*b/f,((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*a*c*d*f+2*C*EllipticPi(((d*x+c)/(c*f-d*e)*f)^(1/2),-(c*f-d*e)/(a*d-b*c)*b/f,((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*a*d^2*e)/(a*d-b*c)/(d*f*h*x^3+c*f*h*x^2+d*e*h*x^2+d*f*g*x^2+c*e*h*x+c*f*g*x+d*e*g*x+c*e*g)","B"
20,1,13405,623,0.092000," ","int((C*b^2*x^2+B*b^2*x+B*a*b-C*a^2)/(b*x+a)^3/(d*x+c)^(1/2)/(f*x+e)^(1/2)/(h*x+g)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
21,1,55327,897,0.155000," ","int((b*x+a)^(1/2)*(C*b^2*x^2+B*b^2*x+B*a*b-C*a^2)/(d*x+c)^(1/2)/(f*x+e)^(1/2)/(h*x+g)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
22,1,20235,669,0.086000," ","int((C*b^2*x^2+B*b^2*x+B*a*b-C*a^2)/(b*x+a)^(1/2)/(d*x+c)^(1/2)/(f*x+e)^(1/2)/(h*x+g)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
23,1,3003,398,0.097000," ","int((C*b^2*x^2+B*b^2*x+B*a*b-C*a^2)/(b*x+a)^(3/2)/(d*x+c)^(1/2)/(f*x+e)^(1/2)/(h*x+g)^(1/2),x)","\text{output too large to display}"," ",0,"2/(b*x+a)^(1/2)/(d*x+c)^(1/2)/(f*x+e)^(1/2)/(h*x+g)^(1/2)/f/h*((a*f-b*e)*(h*x+g)/(a*h-b*g)/(f*x+e))^(1/2)*((e*h-f*g)*(d*x+c)/(c*h-d*g)/(f*x+e))^(1/2)*((e*h-f*g)*(b*x+a)/(a*h-b*g)/(f*x+e))^(1/2)*(2*C*EllipticF(((a*f-b*e)*(h*x+g)/(a*h-b*g)/(f*x+e))^(1/2),((c*f-d*e)*(a*h-b*g)/(c*h-d*g)/(a*f-b*e))^(1/2))*x*a*b*e*f^2*g*h+B*EllipticF(((a*f-b*e)*(h*x+g)/(a*h-b*g)/(f*x+e))^(1/2),((c*f-d*e)*(a*h-b*g)/(c*h-d*g)/(a*f-b*e))^(1/2))*x^2*a*b*f^3*h^2-B*EllipticF(((a*f-b*e)*(h*x+g)/(a*h-b*g)/(f*x+e))^(1/2),((c*f-d*e)*(a*h-b*g)/(c*h-d*g)/(a*f-b*e))^(1/2))*x^2*b^2*f^3*g*h-2*C*EllipticF(((a*f-b*e)*(h*x+g)/(a*h-b*g)/(f*x+e))^(1/2),((c*f-d*e)*(a*h-b*g)/(c*h-d*g)/(a*f-b*e))^(1/2))*x*a^2*e*f^2*h^2+2*C*EllipticPi(((a*f-b*e)*(h*x+g)/(a*h-b*g)/(f*x+e))^(1/2),(a*h-b*g)/(a*f-b*e)*f/h,((c*f-d*e)*(a*h-b*g)/(c*h-d*g)/(a*f-b*e))^(1/2))*x*b^2*e*f^2*g^2+B*EllipticF(((a*f-b*e)*(h*x+g)/(a*h-b*g)/(f*x+e))^(1/2),((c*f-d*e)*(a*h-b*g)/(c*h-d*g)/(a*f-b*e))^(1/2))*a*b*e^2*f*h^2-B*EllipticF(((a*f-b*e)*(h*x+g)/(a*h-b*g)/(f*x+e))^(1/2),((c*f-d*e)*(a*h-b*g)/(c*h-d*g)/(a*f-b*e))^(1/2))*b^2*e^2*f*g*h-C*EllipticF(((a*f-b*e)*(h*x+g)/(a*h-b*g)/(f*x+e))^(1/2),((c*f-d*e)*(a*h-b*g)/(c*h-d*g)/(a*f-b*e))^(1/2))*x^2*a^2*f^3*h^2-2*C*EllipticPi(((a*f-b*e)*(h*x+g)/(a*h-b*g)/(f*x+e))^(1/2),(a*h-b*g)/(a*f-b*e)*f/h,((c*f-d*e)*(a*h-b*g)/(c*h-d*g)/(a*f-b*e))^(1/2))*x*a*b*e*f^2*g*h-C*EllipticF(((a*f-b*e)*(h*x+g)/(a*h-b*g)/(f*x+e))^(1/2),((c*f-d*e)*(a*h-b*g)/(c*h-d*g)/(a*f-b*e))^(1/2))*x^2*a*b*e*f^2*h^2+C*EllipticF(((a*f-b*e)*(h*x+g)/(a*h-b*g)/(f*x+e))^(1/2),((c*f-d*e)*(a*h-b*g)/(c*h-d*g)/(a*f-b*e))^(1/2))*x^2*a*b*f^3*g*h+C*EllipticF(((a*f-b*e)*(h*x+g)/(a*h-b*g)/(f*x+e))^(1/2),((c*f-d*e)*(a*h-b*g)/(c*h-d*g)/(a*f-b*e))^(1/2))*x^2*b^2*e*f^2*g*h+C*EllipticPi(((a*f-b*e)*(h*x+g)/(a*h-b*g)/(f*x+e))^(1/2),(a*h-b*g)/(a*f-b*e)*f/h,((c*f-d*e)*(a*h-b*g)/(c*h-d*g)/(a*f-b*e))^(1/2))*x^2*a*b*e*f^2*h^2-C*EllipticPi(((a*f-b*e)*(h*x+g)/(a*h-b*g)/(f*x+e))^(1/2),(a*h-b*g)/(a*f-b*e)*f/h,((c*f-d*e)*(a*h-b*g)/(c*h-d*g)/(a*f-b*e))^(1/2))*x^2*a*b*f^3*g*h-C*EllipticPi(((a*f-b*e)*(h*x+g)/(a*h-b*g)/(f*x+e))^(1/2),(a*h-b*g)/(a*f-b*e)*f/h,((c*f-d*e)*(a*h-b*g)/(c*h-d*g)/(a*f-b*e))^(1/2))*x^2*b^2*e*f^2*g*h+2*B*EllipticF(((a*f-b*e)*(h*x+g)/(a*h-b*g)/(f*x+e))^(1/2),((c*f-d*e)*(a*h-b*g)/(c*h-d*g)/(a*f-b*e))^(1/2))*x*a*b*e*f^2*h^2-2*B*EllipticF(((a*f-b*e)*(h*x+g)/(a*h-b*g)/(f*x+e))^(1/2),((c*f-d*e)*(a*h-b*g)/(c*h-d*g)/(a*f-b*e))^(1/2))*x*b^2*e*f^2*g*h-2*C*EllipticF(((a*f-b*e)*(h*x+g)/(a*h-b*g)/(f*x+e))^(1/2),((c*f-d*e)*(a*h-b*g)/(c*h-d*g)/(a*f-b*e))^(1/2))*x*a*b*e^2*f*h^2+2*C*EllipticF(((a*f-b*e)*(h*x+g)/(a*h-b*g)/(f*x+e))^(1/2),((c*f-d*e)*(a*h-b*g)/(c*h-d*g)/(a*f-b*e))^(1/2))*x*b^2*e^2*f*g*h+2*C*EllipticPi(((a*f-b*e)*(h*x+g)/(a*h-b*g)/(f*x+e))^(1/2),(a*h-b*g)/(a*f-b*e)*f/h,((c*f-d*e)*(a*h-b*g)/(c*h-d*g)/(a*f-b*e))^(1/2))*x*a*b*e^2*f*h^2-2*C*EllipticPi(((a*f-b*e)*(h*x+g)/(a*h-b*g)/(f*x+e))^(1/2),(a*h-b*g)/(a*f-b*e)*f/h,((c*f-d*e)*(a*h-b*g)/(c*h-d*g)/(a*f-b*e))^(1/2))*x*b^2*e^2*f*g*h+C*EllipticF(((a*f-b*e)*(h*x+g)/(a*h-b*g)/(f*x+e))^(1/2),((c*f-d*e)*(a*h-b*g)/(c*h-d*g)/(a*f-b*e))^(1/2))*a*b*e^2*f*g*h-C*EllipticPi(((a*f-b*e)*(h*x+g)/(a*h-b*g)/(f*x+e))^(1/2),(a*h-b*g)/(a*f-b*e)*f/h,((c*f-d*e)*(a*h-b*g)/(c*h-d*g)/(a*f-b*e))^(1/2))*a*b*e^2*f*g*h+C*EllipticPi(((a*f-b*e)*(h*x+g)/(a*h-b*g)/(f*x+e))^(1/2),(a*h-b*g)/(a*f-b*e)*f/h,((c*f-d*e)*(a*h-b*g)/(c*h-d*g)/(a*f-b*e))^(1/2))*x^2*b^2*f^3*g^2-C*EllipticF(((a*f-b*e)*(h*x+g)/(a*h-b*g)/(f*x+e))^(1/2),((c*f-d*e)*(a*h-b*g)/(c*h-d*g)/(a*f-b*e))^(1/2))*a^2*e^2*f*h^2-C*EllipticF(((a*f-b*e)*(h*x+g)/(a*h-b*g)/(f*x+e))^(1/2),((c*f-d*e)*(a*h-b*g)/(c*h-d*g)/(a*f-b*e))^(1/2))*a*b*e^3*h^2+C*EllipticF(((a*f-b*e)*(h*x+g)/(a*h-b*g)/(f*x+e))^(1/2),((c*f-d*e)*(a*h-b*g)/(c*h-d*g)/(a*f-b*e))^(1/2))*b^2*e^3*g*h+C*EllipticPi(((a*f-b*e)*(h*x+g)/(a*h-b*g)/(f*x+e))^(1/2),(a*h-b*g)/(a*f-b*e)*f/h,((c*f-d*e)*(a*h-b*g)/(c*h-d*g)/(a*f-b*e))^(1/2))*a*b*e^3*h^2-C*EllipticPi(((a*f-b*e)*(h*x+g)/(a*h-b*g)/(f*x+e))^(1/2),(a*h-b*g)/(a*f-b*e)*f/h,((c*f-d*e)*(a*h-b*g)/(c*h-d*g)/(a*f-b*e))^(1/2))*b^2*e^3*g*h+C*EllipticPi(((a*f-b*e)*(h*x+g)/(a*h-b*g)/(f*x+e))^(1/2),(a*h-b*g)/(a*f-b*e)*f/h,((c*f-d*e)*(a*h-b*g)/(c*h-d*g)/(a*f-b*e))^(1/2))*b^2*e^2*f*g^2)/(e*h-f*g)/(a*f-b*e)","B"
24,1,9443,562,0.202000," ","int((C*b^2*x^2+B*b^2*x+B*a*b-C*a^2)/(b*x+a)^(5/2)/(d*x+c)^(1/2)/(f*x+e)^(1/2)/(h*x+g)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
25,1,75992,1056,1.881000," ","int((C*b^2*x^2+B*b^2*x+B*a*b-C*a^2)/(b*x+a)^(7/2)/(d*x+c)^(1/2)/(f*x+e)^(1/2)/(h*x+g)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
26,1,12279,1035,0.092000," ","int((b*x+a)^2*(C*x^2+A)/(d*x+c)^(1/2)/(f*x+e)^(1/2)/(h*x+g)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
27,1,5679,557,0.045000," ","int((b*x+a)*(C*x^2+A)/(d*x+c)^(1/2)/(f*x+e)^(1/2)/(h*x+g)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
28,1,1804,322,0.031000," ","int((C*x^2+A)/(d*x+c)^(1/2)/(f*x+e)^(1/2)/(h*x+g)^(1/2),x)","\frac{2 \left(C \,d^{3} f^{2} h^{2} x^{3}+C c \,d^{2} f^{2} h^{2} x^{2}+C \,d^{3} e f \,h^{2} x^{2}+C \,d^{3} f^{2} g h \,x^{2}+3 \sqrt{\frac{\left(d x +c \right) f}{c f -d e}}\, \sqrt{-\frac{\left(h x +g \right) d}{c h -d g}}\, \sqrt{-\frac{\left(f x +e \right) d}{c f -d e}}\, A c \,d^{2} f^{2} h^{2} \EllipticF \left(\sqrt{\frac{\left(d x +c \right) f}{c f -d e}}, \sqrt{\frac{\left(c f -d e \right) h}{\left(c h -d g \right) f}}\right)-3 \sqrt{\frac{\left(d x +c \right) f}{c f -d e}}\, \sqrt{-\frac{\left(h x +g \right) d}{c h -d g}}\, \sqrt{-\frac{\left(f x +e \right) d}{c f -d e}}\, A \,d^{3} e f \,h^{2} \EllipticF \left(\sqrt{\frac{\left(d x +c \right) f}{c f -d e}}, \sqrt{\frac{\left(c f -d e \right) h}{\left(c h -d g \right) f}}\right)+2 \sqrt{\frac{\left(d x +c \right) f}{c f -d e}}\, \sqrt{-\frac{\left(h x +g \right) d}{c h -d g}}\, \sqrt{-\frac{\left(f x +e \right) d}{c f -d e}}\, C \,c^{3} f^{2} h^{2} \EllipticE \left(\sqrt{\frac{\left(d x +c \right) f}{c f -d e}}, \sqrt{\frac{\left(c f -d e \right) h}{\left(c h -d g \right) f}}\right)-\sqrt{\frac{\left(d x +c \right) f}{c f -d e}}\, \sqrt{-\frac{\left(h x +g \right) d}{c h -d g}}\, \sqrt{-\frac{\left(f x +e \right) d}{c f -d e}}\, C \,c^{2} d e f \,h^{2} \EllipticF \left(\sqrt{\frac{\left(d x +c \right) f}{c f -d e}}, \sqrt{\frac{\left(c f -d e \right) h}{\left(c h -d g \right) f}}\right)+\sqrt{\frac{\left(d x +c \right) f}{c f -d e}}\, \sqrt{-\frac{\left(h x +g \right) d}{c h -d g}}\, \sqrt{-\frac{\left(f x +e \right) d}{c f -d e}}\, C \,c^{2} d \,f^{2} g h \EllipticF \left(\sqrt{\frac{\left(d x +c \right) f}{c f -d e}}, \sqrt{\frac{\left(c f -d e \right) h}{\left(c h -d g \right) f}}\right)-2 \sqrt{\frac{\left(d x +c \right) f}{c f -d e}}\, \sqrt{-\frac{\left(h x +g \right) d}{c h -d g}}\, \sqrt{-\frac{\left(f x +e \right) d}{c f -d e}}\, C c \,d^{2} e^{2} h^{2} \EllipticE \left(\sqrt{\frac{\left(d x +c \right) f}{c f -d e}}, \sqrt{\frac{\left(c f -d e \right) h}{\left(c h -d g \right) f}}\right)+\sqrt{\frac{\left(d x +c \right) f}{c f -d e}}\, \sqrt{-\frac{\left(h x +g \right) d}{c h -d g}}\, \sqrt{-\frac{\left(f x +e \right) d}{c f -d e}}\, C c \,d^{2} e^{2} h^{2} \EllipticF \left(\sqrt{\frac{\left(d x +c \right) f}{c f -d e}}, \sqrt{\frac{\left(c f -d e \right) h}{\left(c h -d g \right) f}}\right)-2 \sqrt{\frac{\left(d x +c \right) f}{c f -d e}}\, \sqrt{-\frac{\left(h x +g \right) d}{c h -d g}}\, \sqrt{-\frac{\left(f x +e \right) d}{c f -d e}}\, C c \,d^{2} e f g h \EllipticE \left(\sqrt{\frac{\left(d x +c \right) f}{c f -d e}}, \sqrt{\frac{\left(c f -d e \right) h}{\left(c h -d g \right) f}}\right)+C c \,d^{2} e f \,h^{2} x -2 \sqrt{\frac{\left(d x +c \right) f}{c f -d e}}\, \sqrt{-\frac{\left(h x +g \right) d}{c h -d g}}\, \sqrt{-\frac{\left(f x +e \right) d}{c f -d e}}\, C c \,d^{2} f^{2} g^{2} \EllipticE \left(\sqrt{\frac{\left(d x +c \right) f}{c f -d e}}, \sqrt{\frac{\left(c f -d e \right) h}{\left(c h -d g \right) f}}\right)+2 \sqrt{\frac{\left(d x +c \right) f}{c f -d e}}\, \sqrt{-\frac{\left(h x +g \right) d}{c h -d g}}\, \sqrt{-\frac{\left(f x +e \right) d}{c f -d e}}\, C c \,d^{2} f^{2} g^{2} \EllipticF \left(\sqrt{\frac{\left(d x +c \right) f}{c f -d e}}, \sqrt{\frac{\left(c f -d e \right) h}{\left(c h -d g \right) f}}\right)+C c \,d^{2} f^{2} g h x +2 \sqrt{\frac{\left(d x +c \right) f}{c f -d e}}\, \sqrt{-\frac{\left(h x +g \right) d}{c h -d g}}\, \sqrt{-\frac{\left(f x +e \right) d}{c f -d e}}\, C \,d^{3} e^{2} g h \EllipticE \left(\sqrt{\frac{\left(d x +c \right) f}{c f -d e}}, \sqrt{\frac{\left(c f -d e \right) h}{\left(c h -d g \right) f}}\right)-\sqrt{\frac{\left(d x +c \right) f}{c f -d e}}\, \sqrt{-\frac{\left(h x +g \right) d}{c h -d g}}\, \sqrt{-\frac{\left(f x +e \right) d}{c f -d e}}\, C \,d^{3} e^{2} g h \EllipticF \left(\sqrt{\frac{\left(d x +c \right) f}{c f -d e}}, \sqrt{\frac{\left(c f -d e \right) h}{\left(c h -d g \right) f}}\right)+2 \sqrt{\frac{\left(d x +c \right) f}{c f -d e}}\, \sqrt{-\frac{\left(h x +g \right) d}{c h -d g}}\, \sqrt{-\frac{\left(f x +e \right) d}{c f -d e}}\, C \,d^{3} e f \,g^{2} \EllipticE \left(\sqrt{\frac{\left(d x +c \right) f}{c f -d e}}, \sqrt{\frac{\left(c f -d e \right) h}{\left(c h -d g \right) f}}\right)-2 \sqrt{\frac{\left(d x +c \right) f}{c f -d e}}\, \sqrt{-\frac{\left(h x +g \right) d}{c h -d g}}\, \sqrt{-\frac{\left(f x +e \right) d}{c f -d e}}\, C \,d^{3} e f \,g^{2} \EllipticF \left(\sqrt{\frac{\left(d x +c \right) f}{c f -d e}}, \sqrt{\frac{\left(c f -d e \right) h}{\left(c h -d g \right) f}}\right)+C \,d^{3} e f g h x +C c \,d^{2} e f g h \right) \sqrt{d x +c}\, \sqrt{f x +e}\, \sqrt{h x +g}}{3 \left(d f h \,x^{3}+c f h \,x^{2}+d e h \,x^{2}+d f g \,x^{2}+c e h x +c f g x +d e g x +c e g \right) d^{3} f^{2} h^{2}}"," ",0,"2/3*(3*A*((d*x+c)/(c*f-d*e)*f)^(1/2)*(-(h*x+g)/(c*h-d*g)*d)^(1/2)*(-(f*x+e)/(c*f-d*e)*d)^(1/2)*EllipticF(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*c*d^2*f^2*h^2-3*A*((d*x+c)/(c*f-d*e)*f)^(1/2)*(-(h*x+g)/(c*h-d*g)*d)^(1/2)*(-(f*x+e)/(c*f-d*e)*d)^(1/2)*EllipticF(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*d^3*e*f*h^2-C*((d*x+c)/(c*f-d*e)*f)^(1/2)*(-(h*x+g)/(c*h-d*g)*d)^(1/2)*(-(f*x+e)/(c*f-d*e)*d)^(1/2)*EllipticF(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*c^2*d*e*f*h^2+C*((d*x+c)/(c*f-d*e)*f)^(1/2)*(-(h*x+g)/(c*h-d*g)*d)^(1/2)*(-(f*x+e)/(c*f-d*e)*d)^(1/2)*EllipticF(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*c^2*d*f^2*g*h+C*((d*x+c)/(c*f-d*e)*f)^(1/2)*(-(h*x+g)/(c*h-d*g)*d)^(1/2)*(-(f*x+e)/(c*f-d*e)*d)^(1/2)*EllipticF(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*c*d^2*e^2*h^2+2*C*((d*x+c)/(c*f-d*e)*f)^(1/2)*(-(h*x+g)/(c*h-d*g)*d)^(1/2)*(-(f*x+e)/(c*f-d*e)*d)^(1/2)*EllipticF(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*c*d^2*f^2*g^2-C*((d*x+c)/(c*f-d*e)*f)^(1/2)*(-(h*x+g)/(c*h-d*g)*d)^(1/2)*(-(f*x+e)/(c*f-d*e)*d)^(1/2)*EllipticF(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*d^3*e^2*g*h-2*C*((d*x+c)/(c*f-d*e)*f)^(1/2)*(-(h*x+g)/(c*h-d*g)*d)^(1/2)*(-(f*x+e)/(c*f-d*e)*d)^(1/2)*EllipticF(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*d^3*e*f*g^2+2*C*((d*x+c)/(c*f-d*e)*f)^(1/2)*(-(h*x+g)/(c*h-d*g)*d)^(1/2)*(-(f*x+e)/(c*f-d*e)*d)^(1/2)*EllipticE(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*c^3*f^2*h^2-2*C*((d*x+c)/(c*f-d*e)*f)^(1/2)*(-(h*x+g)/(c*h-d*g)*d)^(1/2)*(-(f*x+e)/(c*f-d*e)*d)^(1/2)*EllipticE(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*c*d^2*e^2*h^2-2*C*((d*x+c)/(c*f-d*e)*f)^(1/2)*(-(h*x+g)/(c*h-d*g)*d)^(1/2)*(-(f*x+e)/(c*f-d*e)*d)^(1/2)*EllipticE(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*c*d^2*e*f*g*h-2*C*((d*x+c)/(c*f-d*e)*f)^(1/2)*(-(h*x+g)/(c*h-d*g)*d)^(1/2)*(-(f*x+e)/(c*f-d*e)*d)^(1/2)*EllipticE(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*c*d^2*f^2*g^2+2*C*((d*x+c)/(c*f-d*e)*f)^(1/2)*(-(h*x+g)/(c*h-d*g)*d)^(1/2)*(-(f*x+e)/(c*f-d*e)*d)^(1/2)*EllipticE(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*d^3*e^2*g*h+2*C*((d*x+c)/(c*f-d*e)*f)^(1/2)*(-(h*x+g)/(c*h-d*g)*d)^(1/2)*(-(f*x+e)/(c*f-d*e)*d)^(1/2)*EllipticE(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*d^3*e*f*g^2+C*x^3*d^3*f^2*h^2+C*x^2*c*d^2*f^2*h^2+C*x^2*d^3*e*f*h^2+C*x^2*d^3*f^2*g*h+C*x*c*d^2*e*f*h^2+C*x*c*d^2*f^2*g*h+C*x*d^3*e*f*g*h+C*c*d^2*e*f*g*h)*(d*x+c)^(1/2)*(f*x+e)^(1/2)*(h*x+g)^(1/2)/h^2/f^2/d^3/(d*f*h*x^3+c*f*h*x^2+d*e*h*x^2+d*f*g*x^2+c*e*h*x+c*f*g*x+d*e*g*x+c*e*g)","B"
29,1,1368,414,0.039000," ","int((C*x^2+A)/(b*x+a)/(d*x+c)^(1/2)/(f*x+e)^(1/2)/(h*x+g)^(1/2),x)","\frac{2 \sqrt{d x +c}\, \sqrt{f x +e}\, \sqrt{h x +g}\, \sqrt{\frac{\left(d x +c \right) f}{c f -d e}}\, \sqrt{-\frac{\left(h x +g \right) d}{c h -d g}}\, \sqrt{-\frac{\left(f x +e \right) d}{c f -d e}}\, \left(A \,b^{2} c \,d^{2} f h \EllipticPi \left(\sqrt{\frac{\left(d x +c \right) f}{c f -d e}}, -\frac{\left(c f -d e \right) b}{\left(a d -b c \right) f}, \sqrt{\frac{\left(c f -d e \right) h}{\left(c h -d g \right) f}}\right)-A \,b^{2} d^{3} e h \EllipticPi \left(\sqrt{\frac{\left(d x +c \right) f}{c f -d e}}, -\frac{\left(c f -d e \right) b}{\left(a d -b c \right) f}, \sqrt{\frac{\left(c f -d e \right) h}{\left(c h -d g \right) f}}\right)-C \,a^{2} c \,d^{2} f h \EllipticF \left(\sqrt{\frac{\left(d x +c \right) f}{c f -d e}}, \sqrt{\frac{\left(c f -d e \right) h}{\left(c h -d g \right) f}}\right)+C \,a^{2} c \,d^{2} f h \EllipticPi \left(\sqrt{\frac{\left(d x +c \right) f}{c f -d e}}, -\frac{\left(c f -d e \right) b}{\left(a d -b c \right) f}, \sqrt{\frac{\left(c f -d e \right) h}{\left(c h -d g \right) f}}\right)+C \,a^{2} d^{3} e h \EllipticF \left(\sqrt{\frac{\left(d x +c \right) f}{c f -d e}}, \sqrt{\frac{\left(c f -d e \right) h}{\left(c h -d g \right) f}}\right)-C \,a^{2} d^{3} e h \EllipticPi \left(\sqrt{\frac{\left(d x +c \right) f}{c f -d e}}, -\frac{\left(c f -d e \right) b}{\left(a d -b c \right) f}, \sqrt{\frac{\left(c f -d e \right) h}{\left(c h -d g \right) f}}\right)-C a b \,c^{2} d f h \EllipticE \left(\sqrt{\frac{\left(d x +c \right) f}{c f -d e}}, \sqrt{\frac{\left(c f -d e \right) h}{\left(c h -d g \right) f}}\right)+C a b \,c^{2} d f h \EllipticF \left(\sqrt{\frac{\left(d x +c \right) f}{c f -d e}}, \sqrt{\frac{\left(c f -d e \right) h}{\left(c h -d g \right) f}}\right)+C a b c \,d^{2} e h \EllipticE \left(\sqrt{\frac{\left(d x +c \right) f}{c f -d e}}, \sqrt{\frac{\left(c f -d e \right) h}{\left(c h -d g \right) f}}\right)-C a b c \,d^{2} e h \EllipticF \left(\sqrt{\frac{\left(d x +c \right) f}{c f -d e}}, \sqrt{\frac{\left(c f -d e \right) h}{\left(c h -d g \right) f}}\right)+C a b c \,d^{2} f g \EllipticE \left(\sqrt{\frac{\left(d x +c \right) f}{c f -d e}}, \sqrt{\frac{\left(c f -d e \right) h}{\left(c h -d g \right) f}}\right)-C a b c \,d^{2} f g \EllipticF \left(\sqrt{\frac{\left(d x +c \right) f}{c f -d e}}, \sqrt{\frac{\left(c f -d e \right) h}{\left(c h -d g \right) f}}\right)-C a b \,d^{3} e g \EllipticE \left(\sqrt{\frac{\left(d x +c \right) f}{c f -d e}}, \sqrt{\frac{\left(c f -d e \right) h}{\left(c h -d g \right) f}}\right)+C a b \,d^{3} e g \EllipticF \left(\sqrt{\frac{\left(d x +c \right) f}{c f -d e}}, \sqrt{\frac{\left(c f -d e \right) h}{\left(c h -d g \right) f}}\right)+C \,b^{2} c^{3} f h \EllipticE \left(\sqrt{\frac{\left(d x +c \right) f}{c f -d e}}, \sqrt{\frac{\left(c f -d e \right) h}{\left(c h -d g \right) f}}\right)-C \,b^{2} c^{2} d e h \EllipticE \left(\sqrt{\frac{\left(d x +c \right) f}{c f -d e}}, \sqrt{\frac{\left(c f -d e \right) h}{\left(c h -d g \right) f}}\right)-C \,b^{2} c^{2} d f g \EllipticE \left(\sqrt{\frac{\left(d x +c \right) f}{c f -d e}}, \sqrt{\frac{\left(c f -d e \right) h}{\left(c h -d g \right) f}}\right)+C \,b^{2} c^{2} d f g \EllipticF \left(\sqrt{\frac{\left(d x +c \right) f}{c f -d e}}, \sqrt{\frac{\left(c f -d e \right) h}{\left(c h -d g \right) f}}\right)+C \,b^{2} c \,d^{2} e g \EllipticE \left(\sqrt{\frac{\left(d x +c \right) f}{c f -d e}}, \sqrt{\frac{\left(c f -d e \right) h}{\left(c h -d g \right) f}}\right)-C \,b^{2} c \,d^{2} e g \EllipticF \left(\sqrt{\frac{\left(d x +c \right) f}{c f -d e}}, \sqrt{\frac{\left(c f -d e \right) h}{\left(c h -d g \right) f}}\right)\right)}{\left(a d -b c \right) \left(d f h \,x^{3}+c f h \,x^{2}+d e h \,x^{2}+d f g \,x^{2}+c e h x +c f g x +d e g x +c e g \right) b^{2} d^{2} f h}"," ",0,"2*(d*x+c)^(1/2)*(f*x+e)^(1/2)*(h*x+g)^(1/2)/d^2/f/h/b^2*((d*x+c)/(c*f-d*e)*f)^(1/2)*(-(h*x+g)/(c*h-d*g)*d)^(1/2)*(-(f*x+e)/(c*f-d*e)*d)^(1/2)*(A*EllipticPi(((d*x+c)/(c*f-d*e)*f)^(1/2),-(c*f-d*e)/(a*d-b*c)*b/f,((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*b^2*c*d^2*f*h-A*EllipticPi(((d*x+c)/(c*f-d*e)*f)^(1/2),-(c*f-d*e)/(a*d-b*c)*b/f,((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*b^2*d^3*e*h-C*EllipticF(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*a^2*c*d^2*f*h+C*EllipticF(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*a^2*d^3*e*h+C*EllipticF(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*a*b*c^2*d*f*h-C*EllipticF(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*a*b*c*d^2*e*h-C*EllipticF(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*a*b*c*d^2*f*g+C*EllipticF(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*a*b*d^3*e*g+C*EllipticF(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*b^2*c^2*d*f*g-C*EllipticF(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*b^2*c*d^2*e*g-C*EllipticE(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*a*b*c^2*d*f*h+C*EllipticE(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*a*b*c*d^2*e*h+C*EllipticE(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*a*b*c*d^2*f*g-C*EllipticE(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*a*b*d^3*e*g+C*EllipticE(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*b^2*c^3*f*h-C*EllipticE(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*b^2*c^2*d*e*h-C*EllipticE(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*b^2*c^2*d*f*g+C*EllipticE(((d*x+c)/(c*f-d*e)*f)^(1/2),((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*b^2*c*d^2*e*g+C*EllipticPi(((d*x+c)/(c*f-d*e)*f)^(1/2),-(c*f-d*e)/(a*d-b*c)*b/f,((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*a^2*c*d^2*f*h-C*EllipticPi(((d*x+c)/(c*f-d*e)*f)^(1/2),-(c*f-d*e)/(a*d-b*c)*b/f,((c*f-d*e)/(c*h-d*g)/f*h)^(1/2))*a^2*d^3*e*h)/(a*d-b*c)/(d*f*h*x^3+c*f*h*x^2+d*e*h*x^2+d*f*g*x^2+c*e*h*x+c*f*g*x+d*e*g*x+c*e*g)","B"
30,1,17460,681,0.115000," ","int((C*x^2+A)/(b*x+a)^2/(d*x+c)^(1/2)/(f*x+e)^(1/2)/(h*x+g)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
31,1,89496,1302,0.260000," ","int((b*x+a)^(3/2)*(C*x^2+A)/(d*x+c)^(1/2)/(f*x+e)^(1/2)/(h*x+g)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
32,1,42545,854,0.128000," ","int((b*x+a)^(1/2)*(C*x^2+A)/(d*x+c)^(1/2)/(f*x+e)^(1/2)/(h*x+g)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
33,1,15875,692,0.108000," ","int((C*x^2+A)/(b*x+a)^(1/2)/(d*x+c)^(1/2)/(f*x+e)^(1/2)/(h*x+g)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
34,1,20597,794,0.199000," ","int((C*x^2+A)/(b*x+a)^(3/2)/(d*x+c)^(1/2)/(f*x+e)^(1/2)/(h*x+g)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
35,1,72702,998,1.548000," ","int((C*x^2+A)/(b*x+a)^(5/2)/(d*x+c)^(1/2)/(f*x+e)^(1/2)/(h*x+g)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"