1,1,699,0,2.3321076,"\int \frac{(a+b x)^2 (A+B x)}{\sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","Int[((a + b*x)^2*(A + B*x))/(Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","-\frac{2 \sqrt{c f-d e} \sqrt{\frac{d (e+f x)}{d e-c f}} \sqrt{\frac{d (g+h x)}{d g-c h}} F\left(\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right) \left(15 a^2 d^2 f^2 h^2 (B g-A h)+10 a b d f h (3 A d f g h-B c h (f g-e h)-B d g (e h+2 f g))+b^2 \left(-\left(5 A d f h (c h (f g-e h)+d g (e h+2 f g))-B \left(4 c^2 f h^2 (f g-e h)+c d h \left(-4 e^2 h^2+e f g h+3 f^2 g^2\right)+d^2 g \left(4 e^2 h^2+3 e f g h+8 f^2 g^2\right)\right)\right)\right)\right)}{15 d^3 f^{5/2} h^3 \sqrt{e+f x} \sqrt{g+h x}}+\frac{2 \sqrt{g+h x} \sqrt{c f-d e} \sqrt{\frac{d (e+f x)}{d e-c f}} E\left(\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right) \left(15 a^2 B d^2 f^2 h^2+10 a b d f h (3 A d f h-2 B (c f h+d e h+d f g))+b^2 \left(-\left(10 A d f h (c f h+d e h+d f g)-B \left(8 c^2 f^2 h^2+7 c d f h (e h+f g)+d^2 \left(8 e^2 h^2+7 e f g h+8 f^2 g^2\right)\right)\right)\right)\right)}{15 d^3 f^{5/2} h^3 \sqrt{e+f x} \sqrt{\frac{d (g+h x)}{d g-c h}}}+\frac{2 b \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x} (7 a B d f h+5 A b d f h-4 b B (c f h+d e h+d f g))}{15 d^2 f^2 h^2}+\frac{2 b B (a+b x) \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}}{5 d f h}","-\frac{2 \sqrt{c f-d e} \sqrt{\frac{d (e+f x)}{d e-c f}} \sqrt{\frac{d (g+h x)}{d g-c h}} F\left(\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right) \left(15 a^2 d^2 f^2 h^2 (B g-A h)+10 a b d f h (3 A d f g h-B (c h (f g-e h)+d g (e h+2 f g)))+b^2 \left(-\left(5 A d f h (c h (f g-e h)+d g (e h+2 f g))-B \left(4 c^2 f h^2 (f g-e h)+c d h \left(-4 e^2 h^2+e f g h+3 f^2 g^2\right)+d^2 g \left(4 e^2 h^2+3 e f g h+8 f^2 g^2\right)\right)\right)\right)\right)}{15 d^3 f^{5/2} h^3 \sqrt{e+f x} \sqrt{g+h x}}+\frac{2 \sqrt{g+h x} \sqrt{c f-d e} \sqrt{\frac{d (e+f x)}{d e-c f}} E\left(\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right) \left(15 a^2 B d^2 f^2 h^2+10 a b d f h (3 A d f h-2 B (c f h+d e h+d f g))+b^2 \left(-\left(10 A d f h (c f h+d e h+d f g)-B \left(8 c^2 f^2 h^2+7 c d f h (e h+f g)+d^2 \left(8 e^2 h^2+7 e f g h+8 f^2 g^2\right)\right)\right)\right)\right)}{15 d^3 f^{5/2} h^3 \sqrt{e+f x} \sqrt{\frac{d (g+h x)}{d g-c h}}}+\frac{2 b \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x} (7 a B d f h+b (5 A d f h-4 B (c f h+d e h+d f g)))}{15 d^2 f^2 h^2}+\frac{2 b B (a+b x) \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}}{5 d f h}",1,"(2*b*(5*A*b*d*f*h + 7*a*B*d*f*h - 4*b*B*(d*f*g + d*e*h + c*f*h))*Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x])/(15*d^2*f^2*h^2) + (2*b*B*(a + b*x)*Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x])/(5*d*f*h) + (2*Sqrt[-(d*e) + c*f]*(15*a^2*B*d^2*f^2*h^2 + 10*a*b*d*f*h*(3*A*d*f*h - 2*B*(d*f*g + d*e*h + c*f*h)) - b^2*(10*A*d*f*h*(d*f*g + d*e*h + c*f*h) - B*(8*c^2*f^2*h^2 + 7*c*d*f*h*(f*g + e*h) + d^2*(8*f^2*g^2 + 7*e*f*g*h + 8*e^2*h^2))))*Sqrt[(d*(e + f*x))/(d*e - c*f)]*Sqrt[g + h*x]*EllipticE[ArcSin[(Sqrt[f]*Sqrt[c + d*x])/Sqrt[-(d*e) + c*f]], ((d*e - c*f)*h)/(f*(d*g - c*h))])/(15*d^3*f^(5/2)*h^3*Sqrt[e + f*x]*Sqrt[(d*(g + h*x))/(d*g - c*h)]) - (2*Sqrt[-(d*e) + c*f]*(15*a^2*d^2*f^2*h^2*(B*g - A*h) + 10*a*b*d*f*h*(3*A*d*f*g*h - B*c*h*(f*g - e*h) - B*d*g*(2*f*g + e*h)) - b^2*(5*A*d*f*h*(c*h*(f*g - e*h) + d*g*(2*f*g + e*h)) - B*(4*c^2*f*h^2*(f*g - e*h) + c*d*h*(3*f^2*g^2 + e*f*g*h - 4*e^2*h^2) + d^2*g*(8*f^2*g^2 + 3*e*f*g*h + 4*e^2*h^2))))*Sqrt[(d*(e + f*x))/(d*e - c*f)]*Sqrt[(d*(g + h*x))/(d*g - c*h)]*EllipticF[ArcSin[(Sqrt[f]*Sqrt[c + d*x])/Sqrt[-(d*e) + c*f]], ((d*e - c*f)*h)/(f*(d*g - c*h))])/(15*d^3*f^(5/2)*h^3*Sqrt[e + f*x]*Sqrt[g + h*x])","A",9,8,40,0.2000,1,"{1597, 1600, 1615, 158, 114, 113, 121, 120}"
2,1,404,0,0.8575027,"\int \frac{(a+b x) (A+B x)}{\sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","Int[((a + b*x)*(A + B*x))/(Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","-\frac{2 \sqrt{c f-d e} \sqrt{\frac{d (e+f x)}{d e-c f}} \sqrt{\frac{d (g+h x)}{d g-c h}} F\left(\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right) (3 a d f h (B g-A h)+b (3 A d f g h-B c h (f g-e h)-B d g (e h+2 f g)))}{3 d^2 f^{3/2} h^2 \sqrt{e+f x} \sqrt{g+h x}}+\frac{2 \sqrt{g+h x} \sqrt{c f-d e} \sqrt{\frac{d (e+f x)}{d e-c f}} E\left(\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right) (3 a B d f h+3 A b d f h-2 b B (c f h+d e h+d f g))}{3 d^2 f^{3/2} h^2 \sqrt{e+f x} \sqrt{\frac{d (g+h x)}{d g-c h}}}+\frac{2 b B \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}}{3 d f h}","-\frac{2 \sqrt{c f-d e} \sqrt{\frac{d (e+f x)}{d e-c f}} \sqrt{\frac{d (g+h x)}{d g-c h}} F\left(\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right) (3 a d f h (B g-A h)+b (3 A d f g h-B (c h (f g-e h)+d g (e h+2 f g))))}{3 d^2 f^{3/2} h^2 \sqrt{e+f x} \sqrt{g+h x}}+\frac{2 \sqrt{g+h x} \sqrt{c f-d e} \sqrt{\frac{d (e+f x)}{d e-c f}} E\left(\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right) (3 a B d f h+b (3 A d f h-2 B (c f h+d e h+d f g)))}{3 d^2 f^{3/2} h^2 \sqrt{e+f x} \sqrt{\frac{d (g+h x)}{d g-c h}}}+\frac{2 b B \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}}{3 d f h}",1,"(2*b*B*Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x])/(3*d*f*h) + (2*Sqrt[-(d*e) + c*f]*(3*A*b*d*f*h + 3*a*B*d*f*h - 2*b*B*(d*f*g + d*e*h + c*f*h))*Sqrt[(d*(e + f*x))/(d*e - c*f)]*Sqrt[g + h*x]*EllipticE[ArcSin[(Sqrt[f]*Sqrt[c + d*x])/Sqrt[-(d*e) + c*f]], ((d*e - c*f)*h)/(f*(d*g - c*h))])/(3*d^2*f^(3/2)*h^2*Sqrt[e + f*x]*Sqrt[(d*(g + h*x))/(d*g - c*h)]) - (2*Sqrt[-(d*e) + c*f]*(3*a*d*f*h*(B*g - A*h) + b*(3*A*d*f*g*h - B*c*h*(f*g - e*h) - B*d*g*(2*f*g + e*h)))*Sqrt[(d*(e + f*x))/(d*e - c*f)]*Sqrt[(d*(g + h*x))/(d*g - c*h)]*EllipticF[ArcSin[(Sqrt[f]*Sqrt[c + d*x])/Sqrt[-(d*e) + c*f]], ((d*e - c*f)*h)/(f*(d*g - c*h))])/(3*d^2*f^(3/2)*h^2*Sqrt[e + f*x]*Sqrt[g + h*x])","A",8,7,38,0.1842,1,"{1597, 1615, 158, 114, 113, 121, 120}"
3,1,284,0,0.1716116,"\int \frac{A+B x}{\sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","Int[(A + B*x)/(Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","\frac{2 B \sqrt{g+h x} \sqrt{c f-d e} \sqrt{\frac{d (e+f x)}{d e-c f}} E\left(\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right)}{d \sqrt{f} h \sqrt{e+f x} \sqrt{\frac{d (g+h x)}{d g-c h}}}-\frac{2 (B g-A h) \sqrt{c f-d e} \sqrt{\frac{d (e+f x)}{d e-c f}} \sqrt{\frac{d (g+h x)}{d g-c h}} F\left(\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right)}{d \sqrt{f} h \sqrt{e+f x} \sqrt{g+h x}}","\frac{2 B \sqrt{g+h x} \sqrt{c f-d e} \sqrt{\frac{d (e+f x)}{d e-c f}} E\left(\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right)}{d \sqrt{f} h \sqrt{e+f x} \sqrt{\frac{d (g+h x)}{d g-c h}}}-\frac{2 (B g-A h) \sqrt{c f-d e} \sqrt{\frac{d (e+f x)}{d e-c f}} \sqrt{\frac{d (g+h x)}{d g-c h}} F\left(\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right)}{d \sqrt{f} h \sqrt{e+f x} \sqrt{g+h x}}",1,"(2*B*Sqrt[-(d*e) + c*f]*Sqrt[(d*(e + f*x))/(d*e - c*f)]*Sqrt[g + h*x]*EllipticE[ArcSin[(Sqrt[f]*Sqrt[c + d*x])/Sqrt[-(d*e) + c*f]], ((d*e - c*f)*h)/(f*(d*g - c*h))])/(d*Sqrt[f]*h*Sqrt[e + f*x]*Sqrt[(d*(g + h*x))/(d*g - c*h)]) - (2*Sqrt[-(d*e) + c*f]*(B*g - A*h)*Sqrt[(d*(e + f*x))/(d*e - c*f)]*Sqrt[(d*(g + h*x))/(d*g - c*h)]*EllipticF[ArcSin[(Sqrt[f]*Sqrt[c + d*x])/Sqrt[-(d*e) + c*f]], ((d*e - c*f)*h)/(f*(d*g - c*h))])/(d*Sqrt[f]*h*Sqrt[e + f*x]*Sqrt[g + h*x])","A",6,5,33,0.1515,1,"{158, 114, 113, 121, 120}"
4,1,313,0,0.7465931,"\int \frac{A+B x}{(a+b x) \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","Int[(A + B*x)/((a + b*x)*Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","\frac{2 B \sqrt{c f-d e} \sqrt{\frac{d (e+f x)}{d e-c f}} \sqrt{\frac{d (g+h x)}{d g-c h}} F\left(\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right)}{b d \sqrt{f} \sqrt{e+f x} \sqrt{g+h x}}-\frac{2 \left(A-\frac{a B}{b}\right) \sqrt{c f-d e} \sqrt{\frac{d (e+f x)}{d e-c f}} \sqrt{\frac{d (g+h x)}{d g-c h}} \Pi \left(-\frac{b (d e-c f)}{(b c-a d) f};\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right)}{\sqrt{f} \sqrt{e+f x} \sqrt{g+h x} (b c-a d)}","\frac{2 B \sqrt{c f-d e} \sqrt{\frac{d (e+f x)}{d e-c f}} \sqrt{\frac{d (g+h x)}{d g-c h}} F\left(\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right)}{b d \sqrt{f} \sqrt{e+f x} \sqrt{g+h x}}-\frac{2 \left(A-\frac{a B}{b}\right) \sqrt{c f-d e} \sqrt{\frac{d (e+f x)}{d e-c f}} \sqrt{\frac{d (g+h x)}{d g-c h}} \Pi \left(-\frac{b (d e-c f)}{(b c-a d) f};\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right)}{\sqrt{f} \sqrt{e+f x} \sqrt{g+h x} (b c-a d)}",1,"(2*B*Sqrt[-(d*e) + c*f]*Sqrt[(d*(e + f*x))/(d*e - c*f)]*Sqrt[(d*(g + h*x))/(d*g - c*h)]*EllipticF[ArcSin[(Sqrt[f]*Sqrt[c + d*x])/Sqrt[-(d*e) + c*f]], ((d*e - c*f)*h)/(f*(d*g - c*h))])/(b*d*Sqrt[f]*Sqrt[e + f*x]*Sqrt[g + h*x]) - (2*(A - (a*B)/b)*Sqrt[-(d*e) + c*f]*Sqrt[(d*(e + f*x))/(d*e - c*f)]*Sqrt[(d*(g + h*x))/(d*g - c*h)]*EllipticPi[-((b*(d*e - c*f))/((b*c - a*d)*f)), ArcSin[(Sqrt[f]*Sqrt[c + d*x])/Sqrt[-(d*e) + c*f]], ((d*e - c*f)*h)/(f*(d*g - c*h))])/((b*c - a*d)*Sqrt[f]*Sqrt[e + f*x]*Sqrt[g + h*x])","A",9,7,40,0.1750,1,"{1607, 169, 538, 537, 12, 121, 120}"
5,1,678,0,1.5353757,"\int \frac{A+B x}{(a+b x)^2 \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","Int[(A + B*x)/((a + b*x)^2*Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","\frac{\sqrt{c f-d e} \sqrt{\frac{d (e+f x)}{d e-c f}} \sqrt{\frac{d (g+h x)}{d g-c h}} \left(3 a^2 A b d f h+a^3 (-B) d f h+a b^2 (B (c e h+c f g+d e g)-2 A (c f h+d e h+d f g))-b^3 (2 B c e g-A (c e h+c f g+d e g))\right) \Pi \left(-\frac{b (d e-c f)}{(b c-a d) f};\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right)}{b \sqrt{f} \sqrt{e+f x} \sqrt{g+h x} (b c-a d)^2 (b e-a f) (b g-a h)}-\frac{b \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x} (A b-a B)}{(a+b x) (b c-a d) (b e-a f) (b g-a h)}-\frac{\sqrt{f} (A b-a B) \sqrt{c f-d e} \sqrt{\frac{d (e+f x)}{d e-c f}} \sqrt{\frac{d (g+h x)}{d g-c h}} F\left(\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right)}{b \sqrt{e+f x} \sqrt{g+h x} (b c-a d) (b e-a f)}+\frac{\sqrt{f} \sqrt{g+h x} (A b-a B) \sqrt{c f-d e} \sqrt{\frac{d (e+f x)}{d e-c f}} E\left(\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right)}{\sqrt{e+f x} (b c-a d) (b e-a f) (b g-a h) \sqrt{\frac{d (g+h x)}{d g-c h}}}","\frac{\sqrt{c f-d e} \sqrt{\frac{d (e+f x)}{d e-c f}} \sqrt{\frac{d (g+h x)}{d g-c h}} \left(3 a^2 A b d f h+a^3 (-B) d f h+a b^2 (B (c e h+c f g+d e g)-2 A (c f h+d e h+d f g))-b^3 (2 B c e g-A (c e h+c f g+d e g))\right) \Pi \left(-\frac{b (d e-c f)}{(b c-a d) f};\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right)}{b \sqrt{f} \sqrt{e+f x} \sqrt{g+h x} (b c-a d)^2 (b e-a f) (b g-a h)}-\frac{b \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x} (A b-a B)}{(a+b x) (b c-a d) (b e-a f) (b g-a h)}-\frac{\sqrt{f} (A b-a B) \sqrt{c f-d e} \sqrt{\frac{d (e+f x)}{d e-c f}} \sqrt{\frac{d (g+h x)}{d g-c h}} F\left(\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right)}{b \sqrt{e+f x} \sqrt{g+h x} (b c-a d) (b e-a f)}+\frac{\sqrt{f} \sqrt{g+h x} (A b-a B) \sqrt{c f-d e} \sqrt{\frac{d (e+f x)}{d e-c f}} E\left(\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right)}{\sqrt{e+f x} (b c-a d) (b e-a f) (b g-a h) \sqrt{\frac{d (g+h x)}{d g-c h}}}",1,"-((b*(A*b - a*B)*Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x])/((b*c - a*d)*(b*e - a*f)*(b*g - a*h)*(a + b*x))) + ((A*b - a*B)*Sqrt[f]*Sqrt[-(d*e) + c*f]*Sqrt[(d*(e + f*x))/(d*e - c*f)]*Sqrt[g + h*x]*EllipticE[ArcSin[(Sqrt[f]*Sqrt[c + d*x])/Sqrt[-(d*e) + c*f]], ((d*e - c*f)*h)/(f*(d*g - c*h))])/((b*c - a*d)*(b*e - a*f)*(b*g - a*h)*Sqrt[e + f*x]*Sqrt[(d*(g + h*x))/(d*g - c*h)]) - ((A*b - a*B)*Sqrt[f]*Sqrt[-(d*e) + c*f]*Sqrt[(d*(e + f*x))/(d*e - c*f)]*Sqrt[(d*(g + h*x))/(d*g - c*h)]*EllipticF[ArcSin[(Sqrt[f]*Sqrt[c + d*x])/Sqrt[-(d*e) + c*f]], ((d*e - c*f)*h)/(f*(d*g - c*h))])/(b*(b*c - a*d)*(b*e - a*f)*Sqrt[e + f*x]*Sqrt[g + h*x]) + (Sqrt[-(d*e) + c*f]*(3*a^2*A*b*d*f*h - a^3*B*d*f*h - b^3*(2*B*c*e*g - A*(d*e*g + c*f*g + c*e*h)) + a*b^2*(B*(d*e*g + c*f*g + c*e*h) - 2*A*(d*f*g + d*e*h + c*f*h)))*Sqrt[(d*(e + f*x))/(d*e - c*f)]*Sqrt[(d*(g + h*x))/(d*g - c*h)]*EllipticPi[-((b*(d*e - c*f))/((b*c - a*d)*f)), ArcSin[(Sqrt[f]*Sqrt[c + d*x])/Sqrt[-(d*e) + c*f]], ((d*e - c*f)*h)/(f*(d*g - c*h))])/(b*(b*c - a*d)^2*Sqrt[f]*(b*e - a*f)*(b*g - a*h)*Sqrt[e + f*x]*Sqrt[g + h*x])","A",12,10,40,0.2500,1,"{1599, 1607, 169, 538, 537, 158, 114, 113, 121, 120}"
6,1,976,0,3.4119988,"\int \frac{(a+b x)^{3/2} (A+B x)}{\sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","Int[((a + b*x)^(3/2)*(A + B*x))/(Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","\frac{b \sqrt{a+b x} \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x} B}{2 d f h}-\frac{\sqrt{d g-c h} \sqrt{f g-e h} (4 A b d f h+5 a B d f h-3 b B (d f g+d e h+c f h)) \sqrt{a+b x} \sqrt{-\frac{(d e-c f) (g+h x)}{(f g-e h) (c+d x)}} E\left(\sin ^{-1}\left(\frac{\sqrt{d g-c h} \sqrt{e+f x}}{\sqrt{f g-e h} \sqrt{c+d x}}\right)|\frac{(b c-a d) (f g-e h)}{(b e-a f) (d g-c h)}\right)}{4 d^2 f^2 h^2 \sqrt{\frac{(d e-c f) (a+b x)}{(b e-a f) (c+d x)}} \sqrt{g+h x}}-\frac{(b e-a f) \sqrt{b g-a h} (4 A b d f h+3 a B d f h-b B (c f h+3 d (f g+e h))) \sqrt{\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}} \sqrt{g+h x} F\left(\sin ^{-1}\left(\frac{\sqrt{b g-a h} \sqrt{e+f x}}{\sqrt{f g-e h} \sqrt{a+b x}}\right)|-\frac{(b c-a d) (f g-e h)}{(d e-c f) (b g-a h)}\right)}{4 b d f^2 h^2 \sqrt{f g-e h} \sqrt{c+d x} \sqrt{-\frac{(b e-a f) (g+h x)}{(f g-e h) (a+b x)}}}-\frac{\sqrt{c h-d g} ((a d f h+b (d f g+d e h+c f h)) (4 A b d f h+5 a B d f h-3 b B (d f g+d e h+c f h))-4 d f h (2 a (2 A b+a B) d f h-b B (b (d e g+c f g+c e h)+a (d f g+d e h+c f h)))) (a+b x) \sqrt{\frac{(b g-a h) (c+d x)}{(d g-c h) (a+b x)}} \sqrt{\frac{(b g-a h) (e+f x)}{(f g-e h) (a+b x)}} \Pi \left(-\frac{b (d g-c h)}{(b c-a d) h};\sin ^{-1}\left(\frac{\sqrt{b c-a d} \sqrt{g+h x}}{\sqrt{c h-d g} \sqrt{a+b x}}\right)|\frac{(b e-a f) (d g-c h)}{(b c-a d) (f g-e h)}\right)}{4 b d^2 \sqrt{b c-a d} f^2 h^3 \sqrt{c+d x} \sqrt{e+f x}}+\frac{(4 A b d f h+5 a B d f h-3 b B (d f g+d e h+c f h)) \sqrt{a+b x} \sqrt{e+f x} \sqrt{g+h x}}{4 d f^2 h^2 \sqrt{c+d x}}","\frac{b \sqrt{a+b x} \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x} B}{2 d f h}-\frac{\sqrt{d g-c h} \sqrt{f g-e h} (5 a B d f h+b (4 A d f h-3 B (d f g+d e h+c f h))) \sqrt{a+b x} \sqrt{-\frac{(d e-c f) (g+h x)}{(f g-e h) (c+d x)}} E\left(\sin ^{-1}\left(\frac{\sqrt{d g-c h} \sqrt{e+f x}}{\sqrt{f g-e h} \sqrt{c+d x}}\right)|\frac{(b c-a d) (f g-e h)}{(b e-a f) (d g-c h)}\right)}{4 d^2 f^2 h^2 \sqrt{\frac{(d e-c f) (a+b x)}{(b e-a f) (c+d x)}} \sqrt{g+h x}}-\frac{(b e-a f) \sqrt{b g-a h} (3 a B d f h+b (4 A d f h-B (c f h+3 d (f g+e h)))) \sqrt{\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}} \sqrt{g+h x} F\left(\sin ^{-1}\left(\frac{\sqrt{b g-a h} \sqrt{e+f x}}{\sqrt{f g-e h} \sqrt{a+b x}}\right)|-\frac{(b c-a d) (f g-e h)}{(d e-c f) (b g-a h)}\right)}{4 b d f^2 h^2 \sqrt{f g-e h} \sqrt{c+d x} \sqrt{-\frac{(b e-a f) (g+h x)}{(f g-e h) (a+b x)}}}+\frac{\sqrt{c h-d g} (4 d f h (2 a (2 A b+a B) d f h-b B (b (d e g+c f g+c e h)+a (d f g+d e h+c f h)))-(a d f h+b (d f g+d e h+c f h)) (5 a B d f h+b (4 A d f h-3 B (d f g+d e h+c f h)))) (a+b x) \sqrt{\frac{(b g-a h) (c+d x)}{(d g-c h) (a+b x)}} \sqrt{\frac{(b g-a h) (e+f x)}{(f g-e h) (a+b x)}} \Pi \left(-\frac{b (d g-c h)}{(b c-a d) h};\sin ^{-1}\left(\frac{\sqrt{b c-a d} \sqrt{g+h x}}{\sqrt{c h-d g} \sqrt{a+b x}}\right)|\frac{(b e-a f) (d g-c h)}{(b c-a d) (f g-e h)}\right)}{4 b d^2 \sqrt{b c-a d} f^2 h^3 \sqrt{c+d x} \sqrt{e+f x}}+\frac{(5 a B d f h+b (4 A d f h-3 B (d f g+d e h+c f h))) \sqrt{a+b x} \sqrt{e+f x} \sqrt{g+h x}}{4 d f^2 h^2 \sqrt{c+d x}}",1,"((4*A*b*d*f*h + 5*a*B*d*f*h - 3*b*B*(d*f*g + d*e*h + c*f*h))*Sqrt[a + b*x]*Sqrt[e + f*x]*Sqrt[g + h*x])/(4*d*f^2*h^2*Sqrt[c + d*x]) + (b*B*Sqrt[a + b*x]*Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x])/(2*d*f*h) - (Sqrt[d*g - c*h]*Sqrt[f*g - e*h]*(4*A*b*d*f*h + 5*a*B*d*f*h - 3*b*B*(d*f*g + d*e*h + c*f*h))*Sqrt[a + b*x]*Sqrt[-(((d*e - c*f)*(g + h*x))/((f*g - e*h)*(c + d*x)))]*EllipticE[ArcSin[(Sqrt[d*g - c*h]*Sqrt[e + f*x])/(Sqrt[f*g - e*h]*Sqrt[c + d*x])], ((b*c - a*d)*(f*g - e*h))/((b*e - a*f)*(d*g - c*h))])/(4*d^2*f^2*h^2*Sqrt[((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x))]*Sqrt[g + h*x]) - ((b*e - a*f)*Sqrt[b*g - a*h]*(4*A*b*d*f*h + 3*a*B*d*f*h - b*B*(c*f*h + 3*d*(f*g + e*h)))*Sqrt[((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))]*Sqrt[g + h*x]*EllipticF[ArcSin[(Sqrt[b*g - a*h]*Sqrt[e + f*x])/(Sqrt[f*g - e*h]*Sqrt[a + b*x])], -(((b*c - a*d)*(f*g - e*h))/((d*e - c*f)*(b*g - a*h)))])/(4*b*d*f^2*h^2*Sqrt[f*g - e*h]*Sqrt[c + d*x]*Sqrt[-(((b*e - a*f)*(g + h*x))/((f*g - e*h)*(a + b*x)))]) - (Sqrt[-(d*g) + c*h]*((a*d*f*h + b*(d*f*g + d*e*h + c*f*h))*(4*A*b*d*f*h + 5*a*B*d*f*h - 3*b*B*(d*f*g + d*e*h + c*f*h)) - 4*d*f*h*(2*a*(2*A*b + a*B)*d*f*h - b*B*(b*(d*e*g + c*f*g + c*e*h) + a*(d*f*g + d*e*h + c*f*h))))*(a + b*x)*Sqrt[((b*g - a*h)*(c + d*x))/((d*g - c*h)*(a + b*x))]*Sqrt[((b*g - a*h)*(e + f*x))/((f*g - e*h)*(a + b*x))]*EllipticPi[-((b*(d*g - c*h))/((b*c - a*d)*h)), ArcSin[(Sqrt[b*c - a*d]*Sqrt[g + h*x])/(Sqrt[-(d*g) + c*h]*Sqrt[a + b*x])], ((b*e - a*f)*(d*g - c*h))/((b*c - a*d)*(f*g - e*h))])/(4*b*d^2*Sqrt[b*c - a*d]*f^2*h^3*Sqrt[c + d*x]*Sqrt[e + f*x])","A",10,10,42,0.2381,1,"{1597, 1600, 1602, 1598, 170, 419, 165, 537, 176, 424}"
7,1,735,0,0.6600597,"\int \frac{\sqrt{a+b x} (A+B x)}{\sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","Int[(Sqrt[a + b*x]*(A + B*x))/(Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","\frac{(a+b x) \sqrt{c h-d g} \sqrt{\frac{(c+d x) (b g-a h)}{(a+b x) (d g-c h)}} \sqrt{\frac{(e+f x) (b g-a h)}{(a+b x) (f g-e h)}} (a B d f h+2 A b d f h-b B (c f h+d e h+d f g)) \Pi \left(-\frac{b (d g-c h)}{(b c-a d) h};\sin ^{-1}\left(\frac{\sqrt{b c-a d} \sqrt{g+h x}}{\sqrt{c h-d g} \sqrt{a+b x}}\right)|\frac{(b e-a f) (d g-c h)}{(b c-a d) (f g-e h)}\right)}{b d f h^2 \sqrt{c+d x} \sqrt{e+f x} \sqrt{b c-a d}}+\frac{B \sqrt{a+b x} \sqrt{e+f x} \sqrt{g+h x}}{f h \sqrt{c+d x}}-\frac{B \sqrt{g+h x} (b e-a f) \sqrt{b g-a h} \sqrt{\frac{(c+d x) (b e-a f)}{(a+b x) (d e-c f)}} F\left(\sin ^{-1}\left(\frac{\sqrt{b g-a h} \sqrt{e+f x}}{\sqrt{f g-e h} \sqrt{a+b x}}\right)|-\frac{(b c-a d) (f g-e h)}{(d e-c f) (b g-a h)}\right)}{b f h \sqrt{c+d x} \sqrt{f g-e h} \sqrt{-\frac{(g+h x) (b e-a f)}{(a+b x) (f g-e h)}}}-\frac{B \sqrt{a+b x} \sqrt{d g-c h} \sqrt{f g-e h} \sqrt{-\frac{(g+h x) (d e-c f)}{(c+d x) (f g-e h)}} E\left(\sin ^{-1}\left(\frac{\sqrt{d g-c h} \sqrt{e+f x}}{\sqrt{f g-e h} \sqrt{c+d x}}\right)|\frac{(b c-a d) (f g-e h)}{(b e-a f) (d g-c h)}\right)}{d f h \sqrt{g+h x} \sqrt{\frac{(a+b x) (d e-c f)}{(c+d x) (b e-a f)}}}","\frac{(a+b x) \sqrt{c h-d g} \sqrt{\frac{(c+d x) (b g-a h)}{(a+b x) (d g-c h)}} \sqrt{\frac{(e+f x) (b g-a h)}{(a+b x) (f g-e h)}} (B (a d f h-b (c f h+d e h+d f g))+2 A b d f h) \Pi \left(-\frac{b (d g-c h)}{(b c-a d) h};\sin ^{-1}\left(\frac{\sqrt{b c-a d} \sqrt{g+h x}}{\sqrt{c h-d g} \sqrt{a+b x}}\right)|\frac{(b e-a f) (d g-c h)}{(b c-a d) (f g-e h)}\right)}{b d f h^2 \sqrt{c+d x} \sqrt{e+f x} \sqrt{b c-a d}}+\frac{B \sqrt{a+b x} \sqrt{e+f x} \sqrt{g+h x}}{f h \sqrt{c+d x}}-\frac{B \sqrt{g+h x} (b e-a f) \sqrt{b g-a h} \sqrt{\frac{(c+d x) (b e-a f)}{(a+b x) (d e-c f)}} F\left(\sin ^{-1}\left(\frac{\sqrt{b g-a h} \sqrt{e+f x}}{\sqrt{f g-e h} \sqrt{a+b x}}\right)|-\frac{(b c-a d) (f g-e h)}{(d e-c f) (b g-a h)}\right)}{b f h \sqrt{c+d x} \sqrt{f g-e h} \sqrt{-\frac{(g+h x) (b e-a f)}{(a+b x) (f g-e h)}}}-\frac{B \sqrt{a+b x} \sqrt{d g-c h} \sqrt{f g-e h} \sqrt{-\frac{(g+h x) (d e-c f)}{(c+d x) (f g-e h)}} E\left(\sin ^{-1}\left(\frac{\sqrt{d g-c h} \sqrt{e+f x}}{\sqrt{f g-e h} \sqrt{c+d x}}\right)|\frac{(b c-a d) (f g-e h)}{(b e-a f) (d g-c h)}\right)}{d f h \sqrt{g+h x} \sqrt{\frac{(a+b x) (d e-c f)}{(c+d x) (b e-a f)}}}",1,"(B*Sqrt[a + b*x]*Sqrt[e + f*x]*Sqrt[g + h*x])/(f*h*Sqrt[c + d*x]) - (B*Sqrt[d*g - c*h]*Sqrt[f*g - e*h]*Sqrt[a + b*x]*Sqrt[-(((d*e - c*f)*(g + h*x))/((f*g - e*h)*(c + d*x)))]*EllipticE[ArcSin[(Sqrt[d*g - c*h]*Sqrt[e + f*x])/(Sqrt[f*g - e*h]*Sqrt[c + d*x])], ((b*c - a*d)*(f*g - e*h))/((b*e - a*f)*(d*g - c*h))])/(d*f*h*Sqrt[((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x))]*Sqrt[g + h*x]) - (B*(b*e - a*f)*Sqrt[b*g - a*h]*Sqrt[((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))]*Sqrt[g + h*x]*EllipticF[ArcSin[(Sqrt[b*g - a*h]*Sqrt[e + f*x])/(Sqrt[f*g - e*h]*Sqrt[a + b*x])], -(((b*c - a*d)*(f*g - e*h))/((d*e - c*f)*(b*g - a*h)))])/(b*f*h*Sqrt[f*g - e*h]*Sqrt[c + d*x]*Sqrt[-(((b*e - a*f)*(g + h*x))/((f*g - e*h)*(a + b*x)))]) + (Sqrt[-(d*g) + c*h]*(2*A*b*d*f*h + a*B*d*f*h - b*B*(d*f*g + d*e*h + c*f*h))*(a + b*x)*Sqrt[((b*g - a*h)*(c + d*x))/((d*g - c*h)*(a + b*x))]*Sqrt[((b*g - a*h)*(e + f*x))/((f*g - e*h)*(a + b*x))]*EllipticPi[-((b*(d*g - c*h))/((b*c - a*d)*h)), ArcSin[(Sqrt[b*c - a*d]*Sqrt[g + h*x])/(Sqrt[-(d*g) + c*h]*Sqrt[a + b*x])], ((b*e - a*f)*(d*g - c*h))/((b*c - a*d)*(f*g - e*h))])/(b*d*Sqrt[b*c - a*d]*f*h^2*Sqrt[c + d*x]*Sqrt[e + f*x])","A",7,7,42,0.1667,1,"{1596, 170, 419, 176, 424, 165, 537}"
8,1,442,0,0.4613439,"\int \frac{A+B x}{\sqrt{a+b x} \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","Int[(A + B*x)/(Sqrt[a + b*x]*Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","\frac{2 \sqrt{g+h x} (A b-a B) \sqrt{\frac{(c+d x) (b e-a f)}{(a+b x) (d e-c f)}} F\left(\sin ^{-1}\left(\frac{\sqrt{b g-a h} \sqrt{e+f x}}{\sqrt{f g-e h} \sqrt{a+b x}}\right)|-\frac{(b c-a d) (f g-e h)}{(d e-c f) (b g-a h)}\right)}{b \sqrt{c+d x} \sqrt{b g-a h} \sqrt{f g-e h} \sqrt{-\frac{(g+h x) (b e-a f)}{(a+b x) (f g-e h)}}}+\frac{2 B (a+b x) \sqrt{c h-d g} \sqrt{\frac{(c+d x) (b g-a h)}{(a+b x) (d g-c h)}} \sqrt{\frac{(e+f x) (b g-a h)}{(a+b x) (f g-e h)}} \Pi \left(-\frac{b (d g-c h)}{(b c-a d) h};\sin ^{-1}\left(\frac{\sqrt{b c-a d} \sqrt{g+h x}}{\sqrt{c h-d g} \sqrt{a+b x}}\right)|\frac{(b e-a f) (d g-c h)}{(b c-a d) (f g-e h)}\right)}{b h \sqrt{c+d x} \sqrt{e+f x} \sqrt{b c-a d}}","\frac{2 \sqrt{g+h x} (A b-a B) \sqrt{\frac{(c+d x) (b e-a f)}{(a+b x) (d e-c f)}} F\left(\sin ^{-1}\left(\frac{\sqrt{b g-a h} \sqrt{e+f x}}{\sqrt{f g-e h} \sqrt{a+b x}}\right)|-\frac{(b c-a d) (f g-e h)}{(d e-c f) (b g-a h)}\right)}{b \sqrt{c+d x} \sqrt{b g-a h} \sqrt{f g-e h} \sqrt{-\frac{(g+h x) (b e-a f)}{(a+b x) (f g-e h)}}}+\frac{2 B (a+b x) \sqrt{c h-d g} \sqrt{\frac{(c+d x) (b g-a h)}{(a+b x) (d g-c h)}} \sqrt{\frac{(e+f x) (b g-a h)}{(a+b x) (f g-e h)}} \Pi \left(-\frac{b (d g-c h)}{(b c-a d) h};\sin ^{-1}\left(\frac{\sqrt{b c-a d} \sqrt{g+h x}}{\sqrt{c h-d g} \sqrt{a+b x}}\right)|\frac{(b e-a f) (d g-c h)}{(b c-a d) (f g-e h)}\right)}{b h \sqrt{c+d x} \sqrt{e+f x} \sqrt{b c-a d}}",1,"(2*(A*b - a*B)*Sqrt[((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))]*Sqrt[g + h*x]*EllipticF[ArcSin[(Sqrt[b*g - a*h]*Sqrt[e + f*x])/(Sqrt[f*g - e*h]*Sqrt[a + b*x])], -(((b*c - a*d)*(f*g - e*h))/((d*e - c*f)*(b*g - a*h)))])/(b*Sqrt[b*g - a*h]*Sqrt[f*g - e*h]*Sqrt[c + d*x]*Sqrt[-(((b*e - a*f)*(g + h*x))/((f*g - e*h)*(a + b*x)))]) + (2*B*Sqrt[-(d*g) + c*h]*(a + b*x)*Sqrt[((b*g - a*h)*(c + d*x))/((d*g - c*h)*(a + b*x))]*Sqrt[((b*g - a*h)*(e + f*x))/((f*g - e*h)*(a + b*x))]*EllipticPi[-((b*(d*g - c*h))/((b*c - a*d)*h)), ArcSin[(Sqrt[b*c - a*d]*Sqrt[g + h*x])/(Sqrt[-(d*g) + c*h]*Sqrt[a + b*x])], ((b*e - a*f)*(d*g - c*h))/((b*c - a*d)*(f*g - e*h))])/(b*Sqrt[b*c - a*d]*h*Sqrt[c + d*x]*Sqrt[e + f*x])","A",5,5,42,0.1190,1,"{1598, 170, 419, 165, 537}"
9,1,606,0,0.9855312,"\int \frac{A+B x}{(a+b x)^{3/2} \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","Int[(A + B*x)/((a + b*x)^(3/2)*Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","-\frac{2 b \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x} (A b-a B)}{\sqrt{a+b x} (b c-a d) (b e-a f) (b g-a h)}+\frac{2 d \sqrt{a+b x} \sqrt{e+f x} \sqrt{g+h x} (A b-a B)}{\sqrt{c+d x} (b c-a d) (b e-a f) (b g-a h)}+\frac{2 \sqrt{g+h x} (B c-A d) \sqrt{\frac{(c+d x) (b e-a f)}{(a+b x) (d e-c f)}} F\left(\sin ^{-1}\left(\frac{\sqrt{b g-a h} \sqrt{e+f x}}{\sqrt{f g-e h} \sqrt{a+b x}}\right)|-\frac{(b c-a d) (f g-e h)}{(d e-c f) (b g-a h)}\right)}{\sqrt{c+d x} (b c-a d) \sqrt{b g-a h} \sqrt{f g-e h} \sqrt{-\frac{(g+h x) (b e-a f)}{(a+b x) (f g-e h)}}}-\frac{2 \sqrt{a+b x} (A b-a B) \sqrt{d g-c h} \sqrt{f g-e h} \sqrt{-\frac{(g+h x) (d e-c f)}{(c+d x) (f g-e h)}} E\left(\sin ^{-1}\left(\frac{\sqrt{d g-c h} \sqrt{e+f x}}{\sqrt{f g-e h} \sqrt{c+d x}}\right)|\frac{(b c-a d) (f g-e h)}{(b e-a f) (d g-c h)}\right)}{\sqrt{g+h x} (b c-a d) (b e-a f) (b g-a h) \sqrt{\frac{(a+b x) (d e-c f)}{(c+d x) (b e-a f)}}}","-\frac{2 b \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x} (A b-a B)}{\sqrt{a+b x} (b c-a d) (b e-a f) (b g-a h)}+\frac{2 d \sqrt{a+b x} \sqrt{e+f x} \sqrt{g+h x} (A b-a B)}{\sqrt{c+d x} (b c-a d) (b e-a f) (b g-a h)}+\frac{2 \sqrt{g+h x} (B c-A d) \sqrt{\frac{(c+d x) (b e-a f)}{(a+b x) (d e-c f)}} F\left(\sin ^{-1}\left(\frac{\sqrt{b g-a h} \sqrt{e+f x}}{\sqrt{f g-e h} \sqrt{a+b x}}\right)|-\frac{(b c-a d) (f g-e h)}{(d e-c f) (b g-a h)}\right)}{\sqrt{c+d x} (b c-a d) \sqrt{b g-a h} \sqrt{f g-e h} \sqrt{-\frac{(g+h x) (b e-a f)}{(a+b x) (f g-e h)}}}-\frac{2 \sqrt{a+b x} (A b-a B) \sqrt{d g-c h} \sqrt{f g-e h} \sqrt{-\frac{(g+h x) (d e-c f)}{(c+d x) (f g-e h)}} E\left(\sin ^{-1}\left(\frac{\sqrt{d g-c h} \sqrt{e+f x}}{\sqrt{f g-e h} \sqrt{c+d x}}\right)|\frac{(b c-a d) (f g-e h)}{(b e-a f) (d g-c h)}\right)}{\sqrt{g+h x} (b c-a d) (b e-a f) (b g-a h) \sqrt{\frac{(a+b x) (d e-c f)}{(c+d x) (b e-a f)}}}",1,"(2*(A*b - a*B)*d*Sqrt[a + b*x]*Sqrt[e + f*x]*Sqrt[g + h*x])/((b*c - a*d)*(b*e - a*f)*(b*g - a*h)*Sqrt[c + d*x]) - (2*b*(A*b - a*B)*Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x])/((b*c - a*d)*(b*e - a*f)*(b*g - a*h)*Sqrt[a + b*x]) - (2*(A*b - a*B)*Sqrt[d*g - c*h]*Sqrt[f*g - e*h]*Sqrt[a + b*x]*Sqrt[-(((d*e - c*f)*(g + h*x))/((f*g - e*h)*(c + d*x)))]*EllipticE[ArcSin[(Sqrt[d*g - c*h]*Sqrt[e + f*x])/(Sqrt[f*g - e*h]*Sqrt[c + d*x])], ((b*c - a*d)*(f*g - e*h))/((b*e - a*f)*(d*g - c*h))])/((b*c - a*d)*(b*e - a*f)*(b*g - a*h)*Sqrt[((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x))]*Sqrt[g + h*x]) + (2*(B*c - A*d)*Sqrt[((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))]*Sqrt[g + h*x]*EllipticF[ArcSin[(Sqrt[b*g - a*h]*Sqrt[e + f*x])/(Sqrt[f*g - e*h]*Sqrt[a + b*x])], -(((b*c - a*d)*(f*g - e*h))/((d*e - c*f)*(b*g - a*h)))])/((b*c - a*d)*Sqrt[b*g - a*h]*Sqrt[f*g - e*h]*Sqrt[c + d*x]*Sqrt[-(((b*e - a*f)*(g + h*x))/((f*g - e*h)*(a + b*x)))])","A",7,7,42,0.1667,1,"{1599, 1602, 12, 170, 419, 176, 424}"
10,1,1080,0,3.3720967,"\int \frac{A+B x}{(a+b x)^{5/2} \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","Int[(A + B*x)/((a + b*x)^(5/2)*Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","-\frac{2 b \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x} (A b-a B)}{3 (b c-a d) (b e-a f) (b g-a h) (a+b x)^{3/2}}-\frac{2 \sqrt{d g-c h} \sqrt{f g-e h} \left(3 B d f h a^3-b (6 A d f h+B (d f g+d e h+c f h)) a^2-b^2 (B (d e g+c f g+c e h)-4 A (d f g+d e h+c f h)) a+b^3 (3 B c e g-2 A (d e g+c f g+c e h))\right) \sqrt{a+b x} \sqrt{-\frac{(d e-c f) (g+h x)}{(f g-e h) (c+d x)}} E\left(\sin ^{-1}\left(\frac{\sqrt{d g-c h} \sqrt{e+f x}}{\sqrt{f g-e h} \sqrt{c+d x}}\right)|\frac{(b c-a d) (f g-e h)}{(b e-a f) (d g-c h)}\right)}{3 (b c-a d)^2 (b e-a f)^2 (b g-a h)^2 \sqrt{\frac{(d e-c f) (a+b x)}{(b e-a f) (c+d x)}} \sqrt{g+h x}}-\frac{2 \left(3 d (B c-A d) f h a^2+b \left(3 A d^2 (f g+e h)-B \left(f h c^2+2 d (f g+e h) c+d^2 e g\right)\right) a+b^2 \left(A f h c^2+3 B d e g c-A d (f g+e h) c-2 A d^2 e g\right)\right) \sqrt{\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}} \sqrt{g+h x} F\left(\sin ^{-1}\left(\frac{\sqrt{b g-a h} \sqrt{e+f x}}{\sqrt{f g-e h} \sqrt{a+b x}}\right)|-\frac{(b c-a d) (f g-e h)}{(d e-c f) (b g-a h)}\right)}{3 (b c-a d)^2 (b e-a f) (b g-a h)^{3/2} \sqrt{f g-e h} \sqrt{c+d x} \sqrt{-\frac{(b e-a f) (g+h x)}{(f g-e h) (a+b x)}}}-\frac{2 b \left(3 B d f h a^3-b (6 A d f h+B (d f g+d e h+c f h)) a^2-b^2 (B (d e g+c f g+c e h)-4 A (d f g+d e h+c f h)) a+b^3 (3 B c e g-2 A (d e g+c f g+c e h))\right) \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}}{3 (b c-a d)^2 (b e-a f)^2 (b g-a h)^2 \sqrt{a+b x}}+\frac{2 d \left(3 B d f h a^3-b (6 A d f h+B (d f g+d e h+c f h)) a^2-b^2 (B (d e g+c f g+c e h)-4 A (d f g+d e h+c f h)) a+b^3 (3 B c e g-2 A (d e g+c f g+c e h))\right) \sqrt{a+b x} \sqrt{e+f x} \sqrt{g+h x}}{3 (b c-a d)^2 (b e-a f)^2 (b g-a h)^2 \sqrt{c+d x}}","-\frac{2 b \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x} (A b-a B)}{3 (b c-a d) (b e-a f) (b g-a h) (a+b x)^{3/2}}-\frac{2 \sqrt{d g-c h} \sqrt{f g-e h} \left(3 B d f h a^3-b (6 A d f h+B (d f g+d e h+c f h)) a^2-b^2 (B (d e g+c f g+c e h)-4 A (d f g+d e h+c f h)) a+b^3 (3 B c e g-2 A (d e g+c f g+c e h))\right) \sqrt{a+b x} \sqrt{-\frac{(d e-c f) (g+h x)}{(f g-e h) (c+d x)}} E\left(\sin ^{-1}\left(\frac{\sqrt{d g-c h} \sqrt{e+f x}}{\sqrt{f g-e h} \sqrt{c+d x}}\right)|\frac{(b c-a d) (f g-e h)}{(b e-a f) (d g-c h)}\right)}{3 (b c-a d)^2 (b e-a f)^2 (b g-a h)^2 \sqrt{\frac{(d e-c f) (a+b x)}{(b e-a f) (c+d x)}} \sqrt{g+h x}}-\frac{2 \left(3 d (B c-A d) f h a^2+b \left(3 A d^2 (f g+e h)-B \left(f h c^2+2 d (f g+e h) c+d^2 e g\right)\right) a+b^2 \left(3 B c d e g-A \left(-f h c^2+d (f g+e h) c+2 d^2 e g\right)\right)\right) \sqrt{\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}} \sqrt{g+h x} F\left(\sin ^{-1}\left(\frac{\sqrt{b g-a h} \sqrt{e+f x}}{\sqrt{f g-e h} \sqrt{a+b x}}\right)|-\frac{(b c-a d) (f g-e h)}{(d e-c f) (b g-a h)}\right)}{3 (b c-a d)^2 (b e-a f) (b g-a h)^{3/2} \sqrt{f g-e h} \sqrt{c+d x} \sqrt{-\frac{(b e-a f) (g+h x)}{(f g-e h) (a+b x)}}}-\frac{2 b \left(3 B d f h a^3-b (6 A d f h+B (d f g+d e h+c f h)) a^2-b^2 (B (d e g+c f g+c e h)-4 A (d f g+d e h+c f h)) a+b^3 (3 B c e g-2 A (d e g+c f g+c e h))\right) \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}}{3 (b c-a d)^2 (b e-a f)^2 (b g-a h)^2 \sqrt{a+b x}}+\frac{2 d \left(3 B d f h a^3-b (6 A d f h+B (d f g+d e h+c f h)) a^2-b^2 (B (d e g+c f g+c e h)-4 A (d f g+d e h+c f h)) a+b^3 (3 B c e g-2 A (d e g+c f g+c e h))\right) \sqrt{a+b x} \sqrt{e+f x} \sqrt{g+h x}}{3 (b c-a d)^2 (b e-a f)^2 (b g-a h)^2 \sqrt{c+d x}}",1,"(2*d*(3*a^3*B*d*f*h + b^3*(3*B*c*e*g - 2*A*(d*e*g + c*f*g + c*e*h)) - a*b^2*(B*(d*e*g + c*f*g + c*e*h) - 4*A*(d*f*g + d*e*h + c*f*h)) - a^2*b*(6*A*d*f*h + B*(d*f*g + d*e*h + c*f*h)))*Sqrt[a + b*x]*Sqrt[e + f*x]*Sqrt[g + h*x])/(3*(b*c - a*d)^2*(b*e - a*f)^2*(b*g - a*h)^2*Sqrt[c + d*x]) - (2*b*(A*b - a*B)*Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x])/(3*(b*c - a*d)*(b*e - a*f)*(b*g - a*h)*(a + b*x)^(3/2)) - (2*b*(3*a^3*B*d*f*h + b^3*(3*B*c*e*g - 2*A*(d*e*g + c*f*g + c*e*h)) - a*b^2*(B*(d*e*g + c*f*g + c*e*h) - 4*A*(d*f*g + d*e*h + c*f*h)) - a^2*b*(6*A*d*f*h + B*(d*f*g + d*e*h + c*f*h)))*Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x])/(3*(b*c - a*d)^2*(b*e - a*f)^2*(b*g - a*h)^2*Sqrt[a + b*x]) - (2*Sqrt[d*g - c*h]*Sqrt[f*g - e*h]*(3*a^3*B*d*f*h + b^3*(3*B*c*e*g - 2*A*(d*e*g + c*f*g + c*e*h)) - a*b^2*(B*(d*e*g + c*f*g + c*e*h) - 4*A*(d*f*g + d*e*h + c*f*h)) - a^2*b*(6*A*d*f*h + B*(d*f*g + d*e*h + c*f*h)))*Sqrt[a + b*x]*Sqrt[-(((d*e - c*f)*(g + h*x))/((f*g - e*h)*(c + d*x)))]*EllipticE[ArcSin[(Sqrt[d*g - c*h]*Sqrt[e + f*x])/(Sqrt[f*g - e*h]*Sqrt[c + d*x])], ((b*c - a*d)*(f*g - e*h))/((b*e - a*f)*(d*g - c*h))])/(3*(b*c - a*d)^2*(b*e - a*f)^2*(b*g - a*h)^2*Sqrt[((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x))]*Sqrt[g + h*x]) - (2*(3*a^2*d*(B*c - A*d)*f*h + b^2*(3*B*c*d*e*g - 2*A*d^2*e*g + A*c^2*f*h - A*c*d*(f*g + e*h)) + a*b*(3*A*d^2*(f*g + e*h) - B*(d^2*e*g + c^2*f*h + 2*c*d*(f*g + e*h))))*Sqrt[((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))]*Sqrt[g + h*x]*EllipticF[ArcSin[(Sqrt[b*g - a*h]*Sqrt[e + f*x])/(Sqrt[f*g - e*h]*Sqrt[a + b*x])], -(((b*c - a*d)*(f*g - e*h))/((d*e - c*f)*(b*g - a*h)))])/(3*(b*c - a*d)^2*(b*e - a*f)*(b*g - a*h)^(3/2)*Sqrt[f*g - e*h]*Sqrt[c + d*x]*Sqrt[-(((b*e - a*f)*(g + h*x))/((f*g - e*h)*(a + b*x)))])","A",8,7,42,0.1667,1,"{1599, 1602, 12, 170, 419, 176, 424}"
11,1,897,0,2.5184368,"\int \frac{(a+b x)^{3/2} (d e+c f+2 d f x)}{\sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","Int[((a + b*x)^(3/2)*(d*e + c*f + 2*d*f*x))/(Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","\frac{\sqrt{a+b x} \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x} b}{h}-\frac{\sqrt{d g-c h} \sqrt{f g-e h} (5 a d f h-b (3 d f g+d e h+c f h)) \sqrt{a+b x} \sqrt{-\frac{(d e-c f) (g+h x)}{(f g-e h) (c+d x)}} E\left(\sin ^{-1}\left(\frac{\sqrt{d g-c h} \sqrt{e+f x}}{\sqrt{f g-e h} \sqrt{c+d x}}\right)|\frac{(b c-a d) (f g-e h)}{(b e-a f) (d g-c h)}\right)}{2 d f h^2 \sqrt{\frac{(d e-c f) (a+b x)}{(b e-a f) (c+d x)}} \sqrt{g+h x}}+\frac{(5 a d f h-b (3 d f g+d e h+c f h)) \sqrt{a+b x} \sqrt{e+f x} \sqrt{g+h x}}{2 f h^2 \sqrt{c+d x}}-\frac{(b e-a f) \sqrt{b g-a h} (b c f h+3 a d f h-b d (3 f g+e h)) \sqrt{\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}} \sqrt{g+h x} F\left(\sin ^{-1}\left(\frac{\sqrt{b g-a h} \sqrt{e+f x}}{\sqrt{f g-e h} \sqrt{a+b x}}\right)|-\frac{(b c-a d) (f g-e h)}{(d e-c f) (b g-a h)}\right)}{2 f h^2 \sqrt{f g-e h} \sqrt{c+d x} \sqrt{-\frac{(b e-a f) (g+h x)}{(f g-e h) (a+b x)}} b}-\frac{\sqrt{c h-d g} \left(\left(-\left(3 f^2 g^2+e^2 h^2\right) d^2+2 c e f h^2 d-c^2 f^2 h^2\right) b^2+6 a d^2 f^2 g h b-3 a^2 d^2 f^2 h^2\right) (a+b x) \sqrt{\frac{(b g-a h) (c+d x)}{(d g-c h) (a+b x)}} \sqrt{\frac{(b g-a h) (e+f x)}{(f g-e h) (a+b x)}} \Pi \left(-\frac{b (d g-c h)}{(b c-a d) h};\sin ^{-1}\left(\frac{\sqrt{b c-a d} \sqrt{g+h x}}{\sqrt{c h-d g} \sqrt{a+b x}}\right)|\frac{(b e-a f) (d g-c h)}{(b c-a d) (f g-e h)}\right)}{2 d \sqrt{b c-a d} f h^3 \sqrt{c+d x} \sqrt{e+f x} b}","\frac{\sqrt{a+b x} \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x} b}{h}-\frac{\sqrt{d g-c h} \sqrt{f g-e h} (5 a d f h-b (3 d f g+d e h+c f h)) \sqrt{a+b x} \sqrt{-\frac{(d e-c f) (g+h x)}{(f g-e h) (c+d x)}} E\left(\sin ^{-1}\left(\frac{\sqrt{d g-c h} \sqrt{e+f x}}{\sqrt{f g-e h} \sqrt{c+d x}}\right)|\frac{(b c-a d) (f g-e h)}{(b e-a f) (d g-c h)}\right)}{2 d f h^2 \sqrt{\frac{(d e-c f) (a+b x)}{(b e-a f) (c+d x)}} \sqrt{g+h x}}+\frac{(5 a d f h-b (3 d f g+d e h+c f h)) \sqrt{a+b x} \sqrt{e+f x} \sqrt{g+h x}}{2 f h^2 \sqrt{c+d x}}-\frac{(b e-a f) \sqrt{b g-a h} (3 a d f h+b (c f h-d (3 f g+e h))) \sqrt{\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}} \sqrt{g+h x} F\left(\sin ^{-1}\left(\frac{\sqrt{b g-a h} \sqrt{e+f x}}{\sqrt{f g-e h} \sqrt{a+b x}}\right)|-\frac{(b c-a d) (f g-e h)}{(d e-c f) (b g-a h)}\right)}{2 f h^2 \sqrt{f g-e h} \sqrt{c+d x} \sqrt{-\frac{(b e-a f) (g+h x)}{(f g-e h) (a+b x)}} b}-\frac{\sqrt{c h-d g} \left(\left(-\left(3 f^2 g^2+e^2 h^2\right) d^2+2 c e f h^2 d-c^2 f^2 h^2\right) b^2+6 a d^2 f^2 g h b-3 a^2 d^2 f^2 h^2\right) (a+b x) \sqrt{\frac{(b g-a h) (c+d x)}{(d g-c h) (a+b x)}} \sqrt{\frac{(b g-a h) (e+f x)}{(f g-e h) (a+b x)}} \Pi \left(-\frac{b (d g-c h)}{(b c-a d) h};\sin ^{-1}\left(\frac{\sqrt{b c-a d} \sqrt{g+h x}}{\sqrt{c h-d g} \sqrt{a+b x}}\right)|\frac{(b e-a f) (d g-c h)}{(b c-a d) (f g-e h)}\right)}{2 d \sqrt{b c-a d} f h^3 \sqrt{c+d x} \sqrt{e+f x} b}",1,"((5*a*d*f*h - b*(3*d*f*g + d*e*h + c*f*h))*Sqrt[a + b*x]*Sqrt[e + f*x]*Sqrt[g + h*x])/(2*f*h^2*Sqrt[c + d*x]) + (b*Sqrt[a + b*x]*Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x])/h - (Sqrt[d*g - c*h]*Sqrt[f*g - e*h]*(5*a*d*f*h - b*(3*d*f*g + d*e*h + c*f*h))*Sqrt[a + b*x]*Sqrt[-(((d*e - c*f)*(g + h*x))/((f*g - e*h)*(c + d*x)))]*EllipticE[ArcSin[(Sqrt[d*g - c*h]*Sqrt[e + f*x])/(Sqrt[f*g - e*h]*Sqrt[c + d*x])], ((b*c - a*d)*(f*g - e*h))/((b*e - a*f)*(d*g - c*h))])/(2*d*f*h^2*Sqrt[((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x))]*Sqrt[g + h*x]) - ((b*e - a*f)*Sqrt[b*g - a*h]*(b*c*f*h + 3*a*d*f*h - b*d*(3*f*g + e*h))*Sqrt[((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))]*Sqrt[g + h*x]*EllipticF[ArcSin[(Sqrt[b*g - a*h]*Sqrt[e + f*x])/(Sqrt[f*g - e*h]*Sqrt[a + b*x])], -(((b*c - a*d)*(f*g - e*h))/((d*e - c*f)*(b*g - a*h)))])/(2*b*f*h^2*Sqrt[f*g - e*h]*Sqrt[c + d*x]*Sqrt[-(((b*e - a*f)*(g + h*x))/((f*g - e*h)*(a + b*x)))]) - (Sqrt[-(d*g) + c*h]*(6*a*b*d^2*f^2*g*h - 3*a^2*d^2*f^2*h^2 + b^2*(2*c*d*e*f*h^2 - c^2*f^2*h^2 - d^2*(3*f^2*g^2 + e^2*h^2)))*(a + b*x)*Sqrt[((b*g - a*h)*(c + d*x))/((d*g - c*h)*(a + b*x))]*Sqrt[((b*g - a*h)*(e + f*x))/((f*g - e*h)*(a + b*x))]*EllipticPi[-((b*(d*g - c*h))/((b*c - a*d)*h)), ArcSin[(Sqrt[b*c - a*d]*Sqrt[g + h*x])/(Sqrt[-(d*g) + c*h]*Sqrt[a + b*x])], ((b*e - a*f)*(d*g - c*h))/((b*c - a*d)*(f*g - e*h))])/(2*b*d*Sqrt[b*c - a*d]*f*h^3*Sqrt[c + d*x]*Sqrt[e + f*x])","A",10,10,49,0.2041,1,"{1597, 1600, 1602, 1598, 170, 419, 165, 537, 176, 424}"
12,1,472,0,0.519671,"\int \frac{\sqrt{a+b x} (d e+c f+2 d f x)}{\sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","Int[(Sqrt[a + b*x]*(d*e + c*f + 2*d*f*x))/(Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","-\frac{2 d (e+f x) (b g-a h)^{3/2} \sqrt{\frac{(a+b x) (f g-e h)}{(e+f x) (b g-a h)}} \sqrt{\frac{(c+d x) (f g-e h)}{(e+f x) (d g-c h)}} \Pi \left(\frac{f (b g-a h)}{(b e-a f) h};\sin ^{-1}\left(\frac{\sqrt{b e-a f} \sqrt{g+h x}}{\sqrt{b g-a h} \sqrt{e+f x}}\right)|\frac{(d e-c f) (b g-a h)}{(b e-a f) (d g-c h)}\right)}{h^2 \sqrt{a+b x} \sqrt{c+d x} \sqrt{b e-a f}}+\frac{2 b \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}}{h \sqrt{a+b x}}-\frac{2 \sqrt{c+d x} \sqrt{b g-a h} \sqrt{f g-e h} \sqrt{-\frac{(g+h x) (b e-a f)}{(a+b x) (f g-e h)}} E\left(\sin ^{-1}\left(\frac{\sqrt{b g-a h} \sqrt{e+f x}}{\sqrt{f g-e h} \sqrt{a+b x}}\right)|-\frac{(b c-a d) (f g-e h)}{(d e-c f) (b g-a h)}\right)}{h \sqrt{g+h x} \sqrt{\frac{(c+d x) (b e-a f)}{(a+b x) (d e-c f)}}}","-\frac{2 d (e+f x) (b g-a h)^{3/2} \sqrt{\frac{(a+b x) (f g-e h)}{(e+f x) (b g-a h)}} \sqrt{\frac{(c+d x) (f g-e h)}{(e+f x) (d g-c h)}} \Pi \left(\frac{f (b g-a h)}{(b e-a f) h};\sin ^{-1}\left(\frac{\sqrt{b e-a f} \sqrt{g+h x}}{\sqrt{b g-a h} \sqrt{e+f x}}\right)|\frac{(d e-c f) (b g-a h)}{(b e-a f) (d g-c h)}\right)}{h^2 \sqrt{a+b x} \sqrt{c+d x} \sqrt{b e-a f}}+\frac{2 b \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}}{h \sqrt{a+b x}}-\frac{2 \sqrt{c+d x} \sqrt{b g-a h} \sqrt{f g-e h} \sqrt{-\frac{(g+h x) (b e-a f)}{(a+b x) (f g-e h)}} E\left(\sin ^{-1}\left(\frac{\sqrt{b g-a h} \sqrt{e+f x}}{\sqrt{f g-e h} \sqrt{a+b x}}\right)|-\frac{(b c-a d) (f g-e h)}{(d e-c f) (b g-a h)}\right)}{h \sqrt{g+h x} \sqrt{\frac{(c+d x) (b e-a f)}{(a+b x) (d e-c f)}}}",1,"(2*b*Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x])/(h*Sqrt[a + b*x]) - (2*Sqrt[b*g - a*h]*Sqrt[f*g - e*h]*Sqrt[c + d*x]*Sqrt[-(((b*e - a*f)*(g + h*x))/((f*g - e*h)*(a + b*x)))]*EllipticE[ArcSin[(Sqrt[b*g - a*h]*Sqrt[e + f*x])/(Sqrt[f*g - e*h]*Sqrt[a + b*x])], -(((b*c - a*d)*(f*g - e*h))/((d*e - c*f)*(b*g - a*h)))])/(h*Sqrt[((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))]*Sqrt[g + h*x]) - (2*d*(b*g - a*h)^(3/2)*Sqrt[((f*g - e*h)*(a + b*x))/((b*g - a*h)*(e + f*x))]*Sqrt[((f*g - e*h)*(c + d*x))/((d*g - c*h)*(e + f*x))]*(e + f*x)*EllipticPi[(f*(b*g - a*h))/((b*e - a*f)*h), ArcSin[(Sqrt[b*e - a*f]*Sqrt[g + h*x])/(Sqrt[b*g - a*h]*Sqrt[e + f*x])], ((d*e - c*f)*(b*g - a*h))/((b*e - a*f)*(d*g - c*h))])/(Sqrt[b*e - a*f]*h^2*Sqrt[a + b*x]*Sqrt[c + d*x])","A",5,5,49,0.1020,1,"{1595, 165, 537, 176, 424}"
13,1,449,0,0.4638857,"\int \frac{d e+c f+2 d f x}{\sqrt{a+b x} \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","Int[(d*e + c*f + 2*d*f*x)/(Sqrt[a + b*x]*Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","\frac{2 \sqrt{g+h x} (-2 a d f+b c f+b d e) \sqrt{\frac{(c+d x) (b e-a f)}{(a+b x) (d e-c f)}} F\left(\sin ^{-1}\left(\frac{\sqrt{b g-a h} \sqrt{e+f x}}{\sqrt{f g-e h} \sqrt{a+b x}}\right)|-\frac{(b c-a d) (f g-e h)}{(d e-c f) (b g-a h)}\right)}{b \sqrt{c+d x} \sqrt{b g-a h} \sqrt{f g-e h} \sqrt{-\frac{(g+h x) (b e-a f)}{(a+b x) (f g-e h)}}}+\frac{4 d f (a+b x) \sqrt{c h-d g} \sqrt{\frac{(c+d x) (b g-a h)}{(a+b x) (d g-c h)}} \sqrt{\frac{(e+f x) (b g-a h)}{(a+b x) (f g-e h)}} \Pi \left(-\frac{b (d g-c h)}{(b c-a d) h};\sin ^{-1}\left(\frac{\sqrt{b c-a d} \sqrt{g+h x}}{\sqrt{c h-d g} \sqrt{a+b x}}\right)|\frac{(b e-a f) (d g-c h)}{(b c-a d) (f g-e h)}\right)}{b h \sqrt{c+d x} \sqrt{e+f x} \sqrt{b c-a d}}","\frac{2 \sqrt{g+h x} (-2 a d f+b c f+b d e) \sqrt{\frac{(c+d x) (b e-a f)}{(a+b x) (d e-c f)}} F\left(\sin ^{-1}\left(\frac{\sqrt{b g-a h} \sqrt{e+f x}}{\sqrt{f g-e h} \sqrt{a+b x}}\right)|-\frac{(b c-a d) (f g-e h)}{(d e-c f) (b g-a h)}\right)}{b \sqrt{c+d x} \sqrt{b g-a h} \sqrt{f g-e h} \sqrt{-\frac{(g+h x) (b e-a f)}{(a+b x) (f g-e h)}}}+\frac{4 d f (a+b x) \sqrt{c h-d g} \sqrt{\frac{(c+d x) (b g-a h)}{(a+b x) (d g-c h)}} \sqrt{\frac{(e+f x) (b g-a h)}{(a+b x) (f g-e h)}} \Pi \left(-\frac{b (d g-c h)}{(b c-a d) h};\sin ^{-1}\left(\frac{\sqrt{b c-a d} \sqrt{g+h x}}{\sqrt{c h-d g} \sqrt{a+b x}}\right)|\frac{(b e-a f) (d g-c h)}{(b c-a d) (f g-e h)}\right)}{b h \sqrt{c+d x} \sqrt{e+f x} \sqrt{b c-a d}}",1,"(2*(b*d*e + b*c*f - 2*a*d*f)*Sqrt[((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))]*Sqrt[g + h*x]*EllipticF[ArcSin[(Sqrt[b*g - a*h]*Sqrt[e + f*x])/(Sqrt[f*g - e*h]*Sqrt[a + b*x])], -(((b*c - a*d)*(f*g - e*h))/((d*e - c*f)*(b*g - a*h)))])/(b*Sqrt[b*g - a*h]*Sqrt[f*g - e*h]*Sqrt[c + d*x]*Sqrt[-(((b*e - a*f)*(g + h*x))/((f*g - e*h)*(a + b*x)))]) + (4*d*f*Sqrt[-(d*g) + c*h]*(a + b*x)*Sqrt[((b*g - a*h)*(c + d*x))/((d*g - c*h)*(a + b*x))]*Sqrt[((b*g - a*h)*(e + f*x))/((f*g - e*h)*(a + b*x))]*EllipticPi[-((b*(d*g - c*h))/((b*c - a*d)*h)), ArcSin[(Sqrt[b*c - a*d]*Sqrt[g + h*x])/(Sqrt[-(d*g) + c*h]*Sqrt[a + b*x])], ((b*e - a*f)*(d*g - c*h))/((b*c - a*d)*(f*g - e*h))])/(b*Sqrt[b*c - a*d]*h*Sqrt[c + d*x]*Sqrt[e + f*x])","A",5,5,49,0.1020,1,"{1598, 170, 419, 165, 537}"
14,1,625,0,1.0629718,"\int \frac{d e+c f+2 d f x}{(a+b x)^{3/2} \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","Int[(d*e + c*f + 2*d*f*x)/((a + b*x)^(3/2)*Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","-\frac{2 b \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x} (-2 a d f+b c f+b d e)}{\sqrt{a+b x} (b c-a d) (b e-a f) (b g-a h)}+\frac{2 d \sqrt{a+b x} \sqrt{e+f x} \sqrt{g+h x} (-2 a d f+b c f+b d e)}{\sqrt{c+d x} (b c-a d) (b e-a f) (b g-a h)}-\frac{2 d \sqrt{g+h x} (d e-c f) \sqrt{\frac{(c+d x) (b e-a f)}{(a+b x) (d e-c f)}} F\left(\sin ^{-1}\left(\frac{\sqrt{b g-a h} \sqrt{e+f x}}{\sqrt{f g-e h} \sqrt{a+b x}}\right)|-\frac{(b c-a d) (f g-e h)}{(d e-c f) (b g-a h)}\right)}{\sqrt{c+d x} (b c-a d) \sqrt{b g-a h} \sqrt{f g-e h} \sqrt{-\frac{(g+h x) (b e-a f)}{(a+b x) (f g-e h)}}}-\frac{2 \sqrt{a+b x} \sqrt{d g-c h} \sqrt{f g-e h} (-2 a d f+b c f+b d e) \sqrt{-\frac{(g+h x) (d e-c f)}{(c+d x) (f g-e h)}} E\left(\sin ^{-1}\left(\frac{\sqrt{d g-c h} \sqrt{e+f x}}{\sqrt{f g-e h} \sqrt{c+d x}}\right)|\frac{(b c-a d) (f g-e h)}{(b e-a f) (d g-c h)}\right)}{\sqrt{g+h x} (b c-a d) (b e-a f) (b g-a h) \sqrt{\frac{(a+b x) (d e-c f)}{(c+d x) (b e-a f)}}}","-\frac{2 b \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x} (-2 a d f+b c f+b d e)}{\sqrt{a+b x} (b c-a d) (b e-a f) (b g-a h)}+\frac{2 d \sqrt{a+b x} \sqrt{e+f x} \sqrt{g+h x} (-2 a d f+b c f+b d e)}{\sqrt{c+d x} (b c-a d) (b e-a f) (b g-a h)}-\frac{2 d \sqrt{g+h x} (d e-c f) \sqrt{\frac{(c+d x) (b e-a f)}{(a+b x) (d e-c f)}} F\left(\sin ^{-1}\left(\frac{\sqrt{b g-a h} \sqrt{e+f x}}{\sqrt{f g-e h} \sqrt{a+b x}}\right)|-\frac{(b c-a d) (f g-e h)}{(d e-c f) (b g-a h)}\right)}{\sqrt{c+d x} (b c-a d) \sqrt{b g-a h} \sqrt{f g-e h} \sqrt{-\frac{(g+h x) (b e-a f)}{(a+b x) (f g-e h)}}}-\frac{2 \sqrt{a+b x} \sqrt{d g-c h} \sqrt{f g-e h} (-2 a d f+b c f+b d e) \sqrt{-\frac{(g+h x) (d e-c f)}{(c+d x) (f g-e h)}} E\left(\sin ^{-1}\left(\frac{\sqrt{d g-c h} \sqrt{e+f x}}{\sqrt{f g-e h} \sqrt{c+d x}}\right)|\frac{(b c-a d) (f g-e h)}{(b e-a f) (d g-c h)}\right)}{\sqrt{g+h x} (b c-a d) (b e-a f) (b g-a h) \sqrt{\frac{(a+b x) (d e-c f)}{(c+d x) (b e-a f)}}}",1,"(2*d*(b*d*e + b*c*f - 2*a*d*f)*Sqrt[a + b*x]*Sqrt[e + f*x]*Sqrt[g + h*x])/((b*c - a*d)*(b*e - a*f)*(b*g - a*h)*Sqrt[c + d*x]) - (2*b*(b*d*e + b*c*f - 2*a*d*f)*Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x])/((b*c - a*d)*(b*e - a*f)*(b*g - a*h)*Sqrt[a + b*x]) - (2*(b*d*e + b*c*f - 2*a*d*f)*Sqrt[d*g - c*h]*Sqrt[f*g - e*h]*Sqrt[a + b*x]*Sqrt[-(((d*e - c*f)*(g + h*x))/((f*g - e*h)*(c + d*x)))]*EllipticE[ArcSin[(Sqrt[d*g - c*h]*Sqrt[e + f*x])/(Sqrt[f*g - e*h]*Sqrt[c + d*x])], ((b*c - a*d)*(f*g - e*h))/((b*e - a*f)*(d*g - c*h))])/((b*c - a*d)*(b*e - a*f)*(b*g - a*h)*Sqrt[((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x))]*Sqrt[g + h*x]) - (2*d*(d*e - c*f)*Sqrt[((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))]*Sqrt[g + h*x]*EllipticF[ArcSin[(Sqrt[b*g - a*h]*Sqrt[e + f*x])/(Sqrt[f*g - e*h]*Sqrt[a + b*x])], -(((b*c - a*d)*(f*g - e*h))/((d*e - c*f)*(b*g - a*h)))])/((b*c - a*d)*Sqrt[b*g - a*h]*Sqrt[f*g - e*h]*Sqrt[c + d*x]*Sqrt[-(((b*e - a*f)*(g + h*x))/((f*g - e*h)*(a + b*x)))])","A",7,7,49,0.1429,1,"{1599, 1602, 12, 170, 419, 176, 424}"
15,1,1090,0,3.01601,"\int \frac{d e+c f+2 d f x}{(a+b x)^{5/2} \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","Int[(d*e + c*f + 2*d*f*x)/((a + b*x)^(5/2)*Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","-\frac{2 b \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x} (b d e+b c f-2 a d f)}{3 (b c-a d) (b e-a f) (b g-a h) (a+b x)^{3/2}}-\frac{4 \sqrt{d g-c h} \sqrt{f g-e h} \left(3 d^2 f^2 h a^3-b d f (d f g+4 d e h+4 c f h) a^2+b^2 \left(e (f g+2 e h) d^2+c f (f g+3 e h) d+2 c^2 f^2 h\right) a-b^3 \left(f (f g+e h) c^2-d e (f g-e h) c+d^2 e^2 g\right)\right) \sqrt{a+b x} \sqrt{-\frac{(d e-c f) (g+h x)}{(f g-e h) (c+d x)}} E\left(\sin ^{-1}\left(\frac{\sqrt{d g-c h} \sqrt{e+f x}}{\sqrt{f g-e h} \sqrt{c+d x}}\right)|\frac{(b c-a d) (f g-e h)}{(b e-a f) (d g-c h)}\right)}{3 (b c-a d)^2 (b e-a f)^2 (b g-a h)^2 \sqrt{\frac{(d e-c f) (a+b x)}{(b e-a f) (c+d x)}} \sqrt{g+h x}}+\frac{2 (d e-c f) \left(\left(f h c^2-d f g c+d e h c+2 d^2 e g\right) b^2-a d (d f g+3 d e h+2 c f h) b+3 a^2 d^2 f h\right) \sqrt{\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}} \sqrt{g+h x} F\left(\sin ^{-1}\left(\frac{\sqrt{b g-a h} \sqrt{e+f x}}{\sqrt{f g-e h} \sqrt{a+b x}}\right)|-\frac{(b c-a d) (f g-e h)}{(d e-c f) (b g-a h)}\right)}{3 (b c-a d)^2 (b e-a f) (b g-a h)^{3/2} \sqrt{f g-e h} \sqrt{c+d x} \sqrt{-\frac{(b e-a f) (g+h x)}{(f g-e h) (a+b x)}}}-\frac{4 b \left(3 d^2 f^2 h a^3-b d f (d f g+4 d e h+4 c f h) a^2+b^2 \left(e (f g+2 e h) d^2+c f (f g+3 e h) d+2 c^2 f^2 h\right) a-b^3 \left(f (f g+e h) c^2-d e (f g-e h) c+d^2 e^2 g\right)\right) \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}}{3 (b c-a d)^2 (b e-a f)^2 (b g-a h)^2 \sqrt{a+b x}}+\frac{4 d \left(3 d^2 f^2 h a^3-b d f (d f g+4 d e h+4 c f h) a^2+b^2 \left(e (f g+2 e h) d^2+c f (f g+3 e h) d+2 c^2 f^2 h\right) a-b^3 \left(f (f g+e h) c^2-d e (f g-e h) c+d^2 e^2 g\right)\right) \sqrt{a+b x} \sqrt{e+f x} \sqrt{g+h x}}{3 (b c-a d)^2 (b e-a f)^2 (b g-a h)^2 \sqrt{c+d x}}","-\frac{2 b \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x} (b d e+b c f-2 a d f)}{3 (b c-a d) (b e-a f) (b g-a h) (a+b x)^{3/2}}-\frac{4 \sqrt{d g-c h} \sqrt{f g-e h} \left(3 d^2 f^2 h a^3-b d f (d f g+4 d e h+4 c f h) a^2+b^2 \left(e (f g+2 e h) d^2+c f (f g+3 e h) d+2 c^2 f^2 h\right) a-b^3 \left(f (f g+e h) c^2-d e (f g-e h) c+d^2 e^2 g\right)\right) \sqrt{a+b x} \sqrt{-\frac{(d e-c f) (g+h x)}{(f g-e h) (c+d x)}} E\left(\sin ^{-1}\left(\frac{\sqrt{d g-c h} \sqrt{e+f x}}{\sqrt{f g-e h} \sqrt{c+d x}}\right)|\frac{(b c-a d) (f g-e h)}{(b e-a f) (d g-c h)}\right)}{3 (b c-a d)^2 (b e-a f)^2 (b g-a h)^2 \sqrt{\frac{(d e-c f) (a+b x)}{(b e-a f) (c+d x)}} \sqrt{g+h x}}+\frac{2 (d e-c f) \left(\left(f h c^2-d f g c+d e h c+2 d^2 e g\right) b^2-a d (d f g+3 d e h+2 c f h) b+3 a^2 d^2 f h\right) \sqrt{\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}} \sqrt{g+h x} F\left(\sin ^{-1}\left(\frac{\sqrt{b g-a h} \sqrt{e+f x}}{\sqrt{f g-e h} \sqrt{a+b x}}\right)|-\frac{(b c-a d) (f g-e h)}{(d e-c f) (b g-a h)}\right)}{3 (b c-a d)^2 (b e-a f) (b g-a h)^{3/2} \sqrt{f g-e h} \sqrt{c+d x} \sqrt{-\frac{(b e-a f) (g+h x)}{(f g-e h) (a+b x)}}}-\frac{4 b \left(3 d^2 f^2 h a^3-b d f (d f g+4 d e h+4 c f h) a^2+b^2 \left(e (f g+2 e h) d^2+c f (f g+3 e h) d+2 c^2 f^2 h\right) a-b^3 \left(f (f g+e h) c^2-d e (f g-e h) c+d^2 e^2 g\right)\right) \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}}{3 (b c-a d)^2 (b e-a f)^2 (b g-a h)^2 \sqrt{a+b x}}+\frac{4 d \left(3 d^2 f^2 h a^3-b d f (d f g+4 d e h+4 c f h) a^2+b^2 \left(e (f g+2 e h) d^2+c f (f g+3 e h) d+2 c^2 f^2 h\right) a-b^3 \left(f (f g+e h) c^2-d e (f g-e h) c+d^2 e^2 g\right)\right) \sqrt{a+b x} \sqrt{e+f x} \sqrt{g+h x}}{3 (b c-a d)^2 (b e-a f)^2 (b g-a h)^2 \sqrt{c+d x}}",1,"(4*d*(3*a^3*d^2*f^2*h - a^2*b*d*f*(d*f*g + 4*d*e*h + 4*c*f*h) - b^3*(d^2*e^2*g - c*d*e*(f*g - e*h) + c^2*f*(f*g + e*h)) + a*b^2*(2*c^2*f^2*h + d^2*e*(f*g + 2*e*h) + c*d*f*(f*g + 3*e*h)))*Sqrt[a + b*x]*Sqrt[e + f*x]*Sqrt[g + h*x])/(3*(b*c - a*d)^2*(b*e - a*f)^2*(b*g - a*h)^2*Sqrt[c + d*x]) - (2*b*(b*d*e + b*c*f - 2*a*d*f)*Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x])/(3*(b*c - a*d)*(b*e - a*f)*(b*g - a*h)*(a + b*x)^(3/2)) - (4*b*(3*a^3*d^2*f^2*h - a^2*b*d*f*(d*f*g + 4*d*e*h + 4*c*f*h) - b^3*(d^2*e^2*g - c*d*e*(f*g - e*h) + c^2*f*(f*g + e*h)) + a*b^2*(2*c^2*f^2*h + d^2*e*(f*g + 2*e*h) + c*d*f*(f*g + 3*e*h)))*Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x])/(3*(b*c - a*d)^2*(b*e - a*f)^2*(b*g - a*h)^2*Sqrt[a + b*x]) - (4*Sqrt[d*g - c*h]*Sqrt[f*g - e*h]*(3*a^3*d^2*f^2*h - a^2*b*d*f*(d*f*g + 4*d*e*h + 4*c*f*h) - b^3*(d^2*e^2*g - c*d*e*(f*g - e*h) + c^2*f*(f*g + e*h)) + a*b^2*(2*c^2*f^2*h + d^2*e*(f*g + 2*e*h) + c*d*f*(f*g + 3*e*h)))*Sqrt[a + b*x]*Sqrt[-(((d*e - c*f)*(g + h*x))/((f*g - e*h)*(c + d*x)))]*EllipticE[ArcSin[(Sqrt[d*g - c*h]*Sqrt[e + f*x])/(Sqrt[f*g - e*h]*Sqrt[c + d*x])], ((b*c - a*d)*(f*g - e*h))/((b*e - a*f)*(d*g - c*h))])/(3*(b*c - a*d)^2*(b*e - a*f)^2*(b*g - a*h)^2*Sqrt[((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x))]*Sqrt[g + h*x]) + (2*(d*e - c*f)*(3*a^2*d^2*f*h - a*b*d*(d*f*g + 3*d*e*h + 2*c*f*h) + b^2*(2*d^2*e*g - c*d*f*g + c*d*e*h + c^2*f*h))*Sqrt[((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))]*Sqrt[g + h*x]*EllipticF[ArcSin[(Sqrt[b*g - a*h]*Sqrt[e + f*x])/(Sqrt[f*g - e*h]*Sqrt[a + b*x])], -(((b*c - a*d)*(f*g - e*h))/((d*e - c*f)*(b*g - a*h)))])/(3*(b*c - a*d)^2*(b*e - a*f)*(b*g - a*h)^(3/2)*Sqrt[f*g - e*h]*Sqrt[c + d*x]*Sqrt[-(((b*e - a*f)*(g + h*x))/((f*g - e*h)*(a + b*x)))])","A",8,7,49,0.1429,1,"{1599, 1602, 12, 170, 419, 176, 424}"
16,1,720,0,1.922444,"\int \frac{(a+b x) \left(a b B-a^2 C+b^2 B x+b^2 C x^2\right)}{\sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","Int[((a + b*x)*(a*b*B - a^2*C + b^2*B*x + b^2*C*x^2))/(Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","-\frac{2 \sqrt{c f-d e} \sqrt{\frac{d (e+f x)}{d e-c f}} \sqrt{\frac{d (g+h x)}{d g-c h}} F\left(\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right) \left(-15 a^2 b d^2 f^2 h^2 (B h+C g)+15 a^3 C d^2 f^2 h^3+5 a b^2 d f h (6 B d f g h-c C h (f g-e h)-C d g (e h+2 f g))+b^3 \left(-\left(5 B d f h (c h (f g-e h)+d g (e h+2 f g))-C \left(4 c^2 f h^2 (f g-e h)+c d h \left(-4 e^2 h^2+e f g h+3 f^2 g^2\right)+d^2 g \left(4 e^2 h^2+3 e f g h+8 f^2 g^2\right)\right)\right)\right)\right)}{15 d^3 f^{5/2} h^3 \sqrt{e+f x} \sqrt{g+h x}}-\frac{2 b \sqrt{g+h x} \sqrt{c f-d e} \sqrt{\frac{d (e+f x)}{d e-c f}} E\left(\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right) \left(15 a^2 C d^2 f^2 h^2-10 a b d f h (3 B d f h-C (c f h+d e h+d f g))+b^2 \left(10 B d f h (c f h+d e h+d f g)-C \left(8 c^2 f^2 h^2+7 c d f h (e h+f g)+d^2 \left(8 e^2 h^2+7 e f g h+8 f^2 g^2\right)\right)\right)\right)}{15 d^3 f^{5/2} h^3 \sqrt{e+f x} \sqrt{\frac{d (g+h x)}{d g-c h}}}+\frac{2 b^2 \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x} (2 a C d f h+5 b B d f h-4 b C (c f h+d e h+d f g))}{15 d^2 f^2 h^2}+\frac{2 b^2 C (a+b x) \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}}{5 d f h}","-\frac{2 \sqrt{c f-d e} \sqrt{\frac{d (e+f x)}{d e-c f}} \sqrt{\frac{d (g+h x)}{d g-c h}} F\left(\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right) \left(-15 a^2 b d^2 f^2 h^2 (B h+C g)+15 a^3 C d^2 f^2 h^3+5 a b^2 d f h (6 B d f g h-C (c h (f g-e h)+d g (e h+2 f g)))+b^3 \left(-\left(5 B d f h (c h (f g-e h)+d g (e h+2 f g))-C \left(4 c^2 f h^2 (f g-e h)+c d h \left(-4 e^2 h^2+e f g h+3 f^2 g^2\right)+d^2 g \left(4 e^2 h^2+3 e f g h+8 f^2 g^2\right)\right)\right)\right)\right)}{15 d^3 f^{5/2} h^3 \sqrt{e+f x} \sqrt{g+h x}}-\frac{2 b \sqrt{g+h x} \sqrt{c f-d e} \sqrt{\frac{d (e+f x)}{d e-c f}} E\left(\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right) \left(15 a^2 C d^2 f^2 h^2-10 a b d f h (3 B d f h-C (c f h+d e h+d f g))+b^2 \left(10 B d f h (c f h+d e h+d f g)-C \left(8 c^2 f^2 h^2+7 c d f h (e h+f g)+d^2 \left(8 e^2 h^2+7 e f g h+8 f^2 g^2\right)\right)\right)\right)}{15 d^3 f^{5/2} h^3 \sqrt{e+f x} \sqrt{\frac{d (g+h x)}{d g-c h}}}+\frac{2 b^2 \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x} (2 C (a d f h-2 b (c f h+d e h+d f g))+5 b B d f h)}{15 d^2 f^2 h^2}+\frac{2 b^2 C (a+b x) \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}}{5 d f h}",1,"(2*b^2*(5*b*B*d*f*h + 2*a*C*d*f*h - 4*b*C*(d*f*g + d*e*h + c*f*h))*Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x])/(15*d^2*f^2*h^2) + (2*b^2*C*(a + b*x)*Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x])/(5*d*f*h) - (2*b*Sqrt[-(d*e) + c*f]*(15*a^2*C*d^2*f^2*h^2 - 10*a*b*d*f*h*(3*B*d*f*h - C*(d*f*g + d*e*h + c*f*h)) + b^2*(10*B*d*f*h*(d*f*g + d*e*h + c*f*h) - C*(8*c^2*f^2*h^2 + 7*c*d*f*h*(f*g + e*h) + d^2*(8*f^2*g^2 + 7*e*f*g*h + 8*e^2*h^2))))*Sqrt[(d*(e + f*x))/(d*e - c*f)]*Sqrt[g + h*x]*EllipticE[ArcSin[(Sqrt[f]*Sqrt[c + d*x])/Sqrt[-(d*e) + c*f]], ((d*e - c*f)*h)/(f*(d*g - c*h))])/(15*d^3*f^(5/2)*h^3*Sqrt[e + f*x]*Sqrt[(d*(g + h*x))/(d*g - c*h)]) - (2*Sqrt[-(d*e) + c*f]*(15*a^3*C*d^2*f^2*h^3 - 15*a^2*b*d^2*f^2*h^2*(C*g + B*h) + 5*a*b^2*d*f*h*(6*B*d*f*g*h - c*C*h*(f*g - e*h) - C*d*g*(2*f*g + e*h)) - b^3*(5*B*d*f*h*(c*h*(f*g - e*h) + d*g*(2*f*g + e*h)) - C*(4*c^2*f*h^2*(f*g - e*h) + c*d*h*(3*f^2*g^2 + e*f*g*h - 4*e^2*h^2) + d^2*g*(8*f^2*g^2 + 3*e*f*g*h + 4*e^2*h^2))))*Sqrt[(d*(e + f*x))/(d*e - c*f)]*Sqrt[(d*(g + h*x))/(d*g - c*h)]*EllipticF[ArcSin[(Sqrt[f]*Sqrt[c + d*x])/Sqrt[-(d*e) + c*f]], ((d*e - c*f)*h)/(f*(d*g - c*h))])/(15*d^3*f^(5/2)*h^3*Sqrt[e + f*x]*Sqrt[g + h*x])","A",8,7,58,0.1207,1,"{1600, 1615, 158, 114, 113, 121, 120}"
17,1,410,0,0.58561,"\int \frac{a b B-a^2 C+b^2 B x+b^2 C x^2}{\sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","Int[(a*b*B - a^2*C + b^2*B*x + b^2*C*x^2)/(Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","\frac{2 \sqrt{c f-d e} \sqrt{\frac{d (e+f x)}{d e-c f}} \sqrt{\frac{d (g+h x)}{d g-c h}} F\left(\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right) \left(-3 a^2 C d f h^2+3 a b B d f h^2+b^2 (-(3 B d f g h-c C h (f g-e h)-C d g (e h+2 f g)))\right)}{3 d^2 f^{3/2} h^2 \sqrt{e+f x} \sqrt{g+h x}}+\frac{2 b^2 \sqrt{g+h x} \sqrt{c f-d e} \sqrt{\frac{d (e+f x)}{d e-c f}} (3 B d f h-2 C (c f h+d e h+d f g)) E\left(\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right)}{3 d^2 f^{3/2} h^2 \sqrt{e+f x} \sqrt{\frac{d (g+h x)}{d g-c h}}}+\frac{2 b^2 C \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}}{3 d f h}","\frac{2 \sqrt{c f-d e} \sqrt{\frac{d (e+f x)}{d e-c f}} \sqrt{\frac{d (g+h x)}{d g-c h}} F\left(\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right) \left(-3 a^2 C d f h^2+3 a b B d f h^2+b^2 (-(3 B d f g h-C (c h (f g-e h)+d g (e h+2 f g))))\right)}{3 d^2 f^{3/2} h^2 \sqrt{e+f x} \sqrt{g+h x}}+\frac{2 b^2 \sqrt{g+h x} \sqrt{c f-d e} \sqrt{\frac{d (e+f x)}{d e-c f}} (3 B d f h-2 C (c f h+d e h+d f g)) E\left(\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right)}{3 d^2 f^{3/2} h^2 \sqrt{e+f x} \sqrt{\frac{d (g+h x)}{d g-c h}}}+\frac{2 b^2 C \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}}{3 d f h}",1,"(2*b^2*C*Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x])/(3*d*f*h) + (2*b^2*Sqrt[-(d*e) + c*f]*(3*B*d*f*h - 2*C*(d*f*g + d*e*h + c*f*h))*Sqrt[(d*(e + f*x))/(d*e - c*f)]*Sqrt[g + h*x]*EllipticE[ArcSin[(Sqrt[f]*Sqrt[c + d*x])/Sqrt[-(d*e) + c*f]], ((d*e - c*f)*h)/(f*(d*g - c*h))])/(3*d^2*f^(3/2)*h^2*Sqrt[e + f*x]*Sqrt[(d*(g + h*x))/(d*g - c*h)]) + (2*Sqrt[-(d*e) + c*f]*(3*a*b*B*d*f*h^2 - 3*a^2*C*d*f*h^2 - b^2*(3*B*d*f*g*h - c*C*h*(f*g - e*h) - C*d*g*(2*f*g + e*h)))*Sqrt[(d*(e + f*x))/(d*e - c*f)]*Sqrt[(d*(g + h*x))/(d*g - c*h)]*EllipticF[ArcSin[(Sqrt[f]*Sqrt[c + d*x])/Sqrt[-(d*e) + c*f]], ((d*e - c*f)*h)/(f*(d*g - c*h))])/(3*d^2*f^(3/2)*h^2*Sqrt[e + f*x]*Sqrt[g + h*x])","A",7,6,53,0.1132,1,"{1615, 158, 114, 113, 121, 120}"
18,1,291,0,0.2786365,"\int \frac{a b B-a^2 C+b^2 B x+b^2 C x^2}{(a+b x) \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","Int[(a*b*B - a^2*C + b^2*B*x + b^2*C*x^2)/((a + b*x)*Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","\frac{2 b C \sqrt{g+h x} \sqrt{c f-d e} \sqrt{\frac{d (e+f x)}{d e-c f}} E\left(\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right)}{d \sqrt{f} h \sqrt{e+f x} \sqrt{\frac{d (g+h x)}{d g-c h}}}-\frac{2 \sqrt{c f-d e} \sqrt{\frac{d (e+f x)}{d e-c f}} \sqrt{\frac{d (g+h x)}{d g-c h}} (a C h-b B h+b C g) F\left(\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right)}{d \sqrt{f} h \sqrt{e+f x} \sqrt{g+h x}}","\frac{2 b C \sqrt{g+h x} \sqrt{c f-d e} \sqrt{\frac{d (e+f x)}{d e-c f}} E\left(\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right)}{d \sqrt{f} h \sqrt{e+f x} \sqrt{\frac{d (g+h x)}{d g-c h}}}-\frac{2 \sqrt{c f-d e} \sqrt{\frac{d (e+f x)}{d e-c f}} \sqrt{\frac{d (g+h x)}{d g-c h}} (a C h-b B h+b C g) F\left(\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right)}{d \sqrt{f} h \sqrt{e+f x} \sqrt{g+h x}}",1,"(2*b*C*Sqrt[-(d*e) + c*f]*Sqrt[(d*(e + f*x))/(d*e - c*f)]*Sqrt[g + h*x]*EllipticE[ArcSin[(Sqrt[f]*Sqrt[c + d*x])/Sqrt[-(d*e) + c*f]], ((d*e - c*f)*h)/(f*(d*g - c*h))])/(d*Sqrt[f]*h*Sqrt[e + f*x]*Sqrt[(d*(g + h*x))/(d*g - c*h)]) - (2*Sqrt[-(d*e) + c*f]*(b*C*g - b*B*h + a*C*h)*Sqrt[(d*(e + f*x))/(d*e - c*f)]*Sqrt[(d*(g + h*x))/(d*g - c*h)]*EllipticF[ArcSin[(Sqrt[f]*Sqrt[c + d*x])/Sqrt[-(d*e) + c*f]], ((d*e - c*f)*h)/(f*(d*g - c*h))])/(d*Sqrt[f]*h*Sqrt[e + f*x]*Sqrt[g + h*x])","A",7,6,60,0.1000,1,"{24, 158, 114, 113, 121, 120}"
19,1,309,0,0.8207397,"\int \frac{a b B-a^2 C+b^2 B x+b^2 C x^2}{(a+b x)^2 \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","Int[(a*b*B - a^2*C + b^2*B*x + b^2*C*x^2)/((a + b*x)^2*Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","\frac{2 C \sqrt{c f-d e} \sqrt{\frac{d (e+f x)}{d e-c f}} \sqrt{\frac{d (g+h x)}{d g-c h}} F\left(\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right)}{d \sqrt{f} \sqrt{e+f x} \sqrt{g+h x}}-\frac{2 (b B-2 a C) \sqrt{c f-d e} \sqrt{\frac{d (e+f x)}{d e-c f}} \sqrt{\frac{d (g+h x)}{d g-c h}} \Pi \left(-\frac{b (d e-c f)}{(b c-a d) f};\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right)}{\sqrt{f} \sqrt{e+f x} \sqrt{g+h x} (b c-a d)}","\frac{2 C \sqrt{c f-d e} \sqrt{\frac{d (e+f x)}{d e-c f}} \sqrt{\frac{d (g+h x)}{d g-c h}} F\left(\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right)}{d \sqrt{f} \sqrt{e+f x} \sqrt{g+h x}}-\frac{2 (b B-2 a C) \sqrt{c f-d e} \sqrt{\frac{d (e+f x)}{d e-c f}} \sqrt{\frac{d (g+h x)}{d g-c h}} \Pi \left(-\frac{b (d e-c f)}{(b c-a d) f};\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right)}{\sqrt{f} \sqrt{e+f x} \sqrt{g+h x} (b c-a d)}",1,"(2*C*Sqrt[-(d*e) + c*f]*Sqrt[(d*(e + f*x))/(d*e - c*f)]*Sqrt[(d*(g + h*x))/(d*g - c*h)]*EllipticF[ArcSin[(Sqrt[f]*Sqrt[c + d*x])/Sqrt[-(d*e) + c*f]], ((d*e - c*f)*h)/(f*(d*g - c*h))])/(d*Sqrt[f]*Sqrt[e + f*x]*Sqrt[g + h*x]) - (2*(b*B - 2*a*C)*Sqrt[-(d*e) + c*f]*Sqrt[(d*(e + f*x))/(d*e - c*f)]*Sqrt[(d*(g + h*x))/(d*g - c*h)]*EllipticPi[-((b*(d*e - c*f))/((b*c - a*d)*f)), ArcSin[(Sqrt[f]*Sqrt[c + d*x])/Sqrt[-(d*e) + c*f]], ((d*e - c*f)*h)/(f*(d*g - c*h))])/((b*c - a*d)*Sqrt[f]*Sqrt[e + f*x]*Sqrt[g + h*x])","A",10,8,60,0.1333,1,"{24, 1607, 169, 538, 537, 12, 121, 120}"
20,1,680,0,1.8150894,"\int \frac{a b B-a^2 C+b^2 B x+b^2 C x^2}{(a+b x)^3 \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","Int[(a*b*B - a^2*C + b^2*B*x + b^2*C*x^2)/((a + b*x)^3*Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","-\frac{\sqrt{c f-d e} \sqrt{\frac{d (e+f x)}{d e-c f}} \sqrt{\frac{d (g+h x)}{d g-c h}} \left(-a^2 b (3 B d f h+2 C (c f h+d e h+d f g))+4 a^3 C d f h+2 a b^2 B (c f h+d e h+d f g)-b^3 (B d e g-c (-B e h-B f g+2 C e g))\right) \Pi \left(-\frac{b (d e-c f)}{(b c-a d) f};\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right)}{\sqrt{f} \sqrt{e+f x} \sqrt{g+h x} (b c-a d)^2 (b e-a f) (b g-a h)}-\frac{b^2 \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x} (b B-2 a C)}{(a+b x) (b c-a d) (b e-a f) (b g-a h)}-\frac{\sqrt{f} (b B-2 a C) \sqrt{c f-d e} \sqrt{\frac{d (e+f x)}{d e-c f}} \sqrt{\frac{d (g+h x)}{d g-c h}} F\left(\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right)}{\sqrt{e+f x} \sqrt{g+h x} (b c-a d) (b e-a f)}+\frac{b \sqrt{f} \sqrt{g+h x} (b B-2 a C) \sqrt{c f-d e} \sqrt{\frac{d (e+f x)}{d e-c f}} E\left(\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right)}{\sqrt{e+f x} (b c-a d) (b e-a f) (b g-a h) \sqrt{\frac{d (g+h x)}{d g-c h}}}","-\frac{\sqrt{c f-d e} \sqrt{\frac{d (e+f x)}{d e-c f}} \sqrt{\frac{d (g+h x)}{d g-c h}} \left(-a^2 b (3 B d f h+2 C (c f h+d e h+d f g))+4 a^3 C d f h+2 a b^2 B (c f h+d e h+d f g)-b^3 (B d e g-c (-B e h-B f g+2 C e g))\right) \Pi \left(-\frac{b (d e-c f)}{(b c-a d) f};\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right)}{\sqrt{f} \sqrt{e+f x} \sqrt{g+h x} (b c-a d)^2 (b e-a f) (b g-a h)}-\frac{b^2 \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x} (b B-2 a C)}{(a+b x) (b c-a d) (b e-a f) (b g-a h)}-\frac{\sqrt{f} (b B-2 a C) \sqrt{c f-d e} \sqrt{\frac{d (e+f x)}{d e-c f}} \sqrt{\frac{d (g+h x)}{d g-c h}} F\left(\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right)}{\sqrt{e+f x} \sqrt{g+h x} (b c-a d) (b e-a f)}+\frac{b \sqrt{f} \sqrt{g+h x} (b B-2 a C) \sqrt{c f-d e} \sqrt{\frac{d (e+f x)}{d e-c f}} E\left(\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right)}{\sqrt{e+f x} (b c-a d) (b e-a f) (b g-a h) \sqrt{\frac{d (g+h x)}{d g-c h}}}",1,"-((b^2*(b*B - 2*a*C)*Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x])/((b*c - a*d)*(b*e - a*f)*(b*g - a*h)*(a + b*x))) + (b*(b*B - 2*a*C)*Sqrt[f]*Sqrt[-(d*e) + c*f]*Sqrt[(d*(e + f*x))/(d*e - c*f)]*Sqrt[g + h*x]*EllipticE[ArcSin[(Sqrt[f]*Sqrt[c + d*x])/Sqrt[-(d*e) + c*f]], ((d*e - c*f)*h)/(f*(d*g - c*h))])/((b*c - a*d)*(b*e - a*f)*(b*g - a*h)*Sqrt[e + f*x]*Sqrt[(d*(g + h*x))/(d*g - c*h)]) - ((b*B - 2*a*C)*Sqrt[f]*Sqrt[-(d*e) + c*f]*Sqrt[(d*(e + f*x))/(d*e - c*f)]*Sqrt[(d*(g + h*x))/(d*g - c*h)]*EllipticF[ArcSin[(Sqrt[f]*Sqrt[c + d*x])/Sqrt[-(d*e) + c*f]], ((d*e - c*f)*h)/(f*(d*g - c*h))])/((b*c - a*d)*(b*e - a*f)*Sqrt[e + f*x]*Sqrt[g + h*x]) - (Sqrt[-(d*e) + c*f]*(4*a^3*C*d*f*h + 2*a*b^2*B*(d*f*g + d*e*h + c*f*h) - b^3*(B*d*e*g - c*(2*C*e*g - B*f*g - B*e*h)) - a^2*b*(3*B*d*f*h + 2*C*(d*f*g + d*e*h + c*f*h)))*Sqrt[(d*(e + f*x))/(d*e - c*f)]*Sqrt[(d*(g + h*x))/(d*g - c*h)]*EllipticPi[-((b*(d*e - c*f))/((b*c - a*d)*f)), ArcSin[(Sqrt[f]*Sqrt[c + d*x])/Sqrt[-(d*e) + c*f]], ((d*e - c*f)*h)/(f*(d*g - c*h))])/((b*c - a*d)^2*Sqrt[f]*(b*e - a*f)*(b*g - a*h)*Sqrt[e + f*x]*Sqrt[g + h*x])","A",13,11,60,0.1833,1,"{24, 1599, 1607, 169, 538, 537, 158, 114, 113, 121, 120}"
21,1,976,0,2.7872567,"\int \frac{\sqrt{a+b x} \left(a b B-a^2 C+b^2 B x+b^2 C x^2\right)}{\sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","Int[(Sqrt[a + b*x]*(a*b*B - a^2*C + b^2*B*x + b^2*C*x^2))/(Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","\frac{C \sqrt{a+b x} \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x} b^2}{2 d f h}-\frac{\sqrt{d g-c h} \sqrt{f g-e h} (4 b B d f h+a C d f h-3 b C (d f g+d e h+c f h)) \sqrt{a+b x} \sqrt{-\frac{(d e-c f) (g+h x)}{(f g-e h) (c+d x)}} E\left(\sin ^{-1}\left(\frac{\sqrt{d g-c h} \sqrt{e+f x}}{\sqrt{f g-e h} \sqrt{c+d x}}\right)|\frac{(b c-a d) (f g-e h)}{(b e-a f) (d g-c h)}\right) b}{4 d^2 f^2 h^2 \sqrt{\frac{(d e-c f) (a+b x)}{(b e-a f) (c+d x)}} \sqrt{g+h x}}+\frac{(4 b B d f h+a C d f h-3 b C (d f g+d e h+c f h)) \sqrt{a+b x} \sqrt{e+f x} \sqrt{g+h x} b}{4 d f^2 h^2 \sqrt{c+d x}}-\frac{(b e-a f) \sqrt{b g-a h} (4 b B d f h-a C d f h-b C (c f h+3 d (f g+e h))) \sqrt{\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}} \sqrt{g+h x} F\left(\sin ^{-1}\left(\frac{\sqrt{b g-a h} \sqrt{e+f x}}{\sqrt{f g-e h} \sqrt{a+b x}}\right)|-\frac{(b c-a d) (f g-e h)}{(d e-c f) (b g-a h)}\right)}{4 d f^2 h^2 \sqrt{f g-e h} \sqrt{c+d x} \sqrt{-\frac{(b e-a f) (g+h x)}{(f g-e h) (a+b x)}}}-\frac{\sqrt{c h-d g} \left((a d f h+b (d f g+d e h+c f h)) (4 b B d f h+a C d f h-3 b C (d f g+d e h+c f h))+4 d f h \left(2 C d f h a^2-b (4 B d f h-C (d f g+d e h+c f h)) a+b^2 C (d e g+c f g+c e h)\right)\right) (a+b x) \sqrt{\frac{(b g-a h) (c+d x)}{(d g-c h) (a+b x)}} \sqrt{\frac{(b g-a h) (e+f x)}{(f g-e h) (a+b x)}} \Pi \left(-\frac{b (d g-c h)}{(b c-a d) h};\sin ^{-1}\left(\frac{\sqrt{b c-a d} \sqrt{g+h x}}{\sqrt{c h-d g} \sqrt{a+b x}}\right)|\frac{(b e-a f) (d g-c h)}{(b c-a d) (f g-e h)}\right)}{4 d^2 \sqrt{b c-a d} f^2 h^3 \sqrt{c+d x} \sqrt{e+f x}}","\frac{C \sqrt{a+b x} \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x} b^2}{2 d f h}-\frac{\sqrt{d g-c h} \sqrt{f g-e h} (4 b B d f h+C (a d f h-3 b (d f g+d e h+c f h))) \sqrt{a+b x} \sqrt{-\frac{(d e-c f) (g+h x)}{(f g-e h) (c+d x)}} E\left(\sin ^{-1}\left(\frac{\sqrt{d g-c h} \sqrt{e+f x}}{\sqrt{f g-e h} \sqrt{c+d x}}\right)|\frac{(b c-a d) (f g-e h)}{(b e-a f) (d g-c h)}\right) b}{4 d^2 f^2 h^2 \sqrt{\frac{(d e-c f) (a+b x)}{(b e-a f) (c+d x)}} \sqrt{g+h x}}+\frac{(4 b B d f h+C (a d f h-3 b (d f g+d e h+c f h))) \sqrt{a+b x} \sqrt{e+f x} \sqrt{g+h x} b}{4 d f^2 h^2 \sqrt{c+d x}}+\frac{(b e-a f) \sqrt{b g-a h} (a C d f h-b (4 B d f h-C (3 d f g+3 d e h+c f h))) \sqrt{\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}} \sqrt{g+h x} F\left(\sin ^{-1}\left(\frac{\sqrt{b g-a h} \sqrt{e+f x}}{\sqrt{f g-e h} \sqrt{a+b x}}\right)|-\frac{(b c-a d) (f g-e h)}{(d e-c f) (b g-a h)}\right)}{4 d f^2 h^2 \sqrt{f g-e h} \sqrt{c+d x} \sqrt{-\frac{(b e-a f) (g+h x)}{(f g-e h) (a+b x)}}}-\frac{\sqrt{c h-d g} \left((a d f h+b (d f g+d e h+c f h)) (4 b B d f h+C (a d f h-3 b (d f g+d e h+c f h)))+4 d f h \left(2 C d f h a^2-b (4 B d f h-C (d f g+d e h+c f h)) a+b^2 C (d e g+c f g+c e h)\right)\right) (a+b x) \sqrt{\frac{(b g-a h) (c+d x)}{(d g-c h) (a+b x)}} \sqrt{\frac{(b g-a h) (e+f x)}{(f g-e h) (a+b x)}} \Pi \left(-\frac{b (d g-c h)}{(b c-a d) h};\sin ^{-1}\left(\frac{\sqrt{b c-a d} \sqrt{g+h x}}{\sqrt{c h-d g} \sqrt{a+b x}}\right)|\frac{(b e-a f) (d g-c h)}{(b c-a d) (f g-e h)}\right)}{4 d^2 \sqrt{b c-a d} f^2 h^3 \sqrt{c+d x} \sqrt{e+f x}}",1,"(b*(4*b*B*d*f*h + a*C*d*f*h - 3*b*C*(d*f*g + d*e*h + c*f*h))*Sqrt[a + b*x]*Sqrt[e + f*x]*Sqrt[g + h*x])/(4*d*f^2*h^2*Sqrt[c + d*x]) + (b^2*C*Sqrt[a + b*x]*Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x])/(2*d*f*h) - (b*Sqrt[d*g - c*h]*Sqrt[f*g - e*h]*(4*b*B*d*f*h + a*C*d*f*h - 3*b*C*(d*f*g + d*e*h + c*f*h))*Sqrt[a + b*x]*Sqrt[-(((d*e - c*f)*(g + h*x))/((f*g - e*h)*(c + d*x)))]*EllipticE[ArcSin[(Sqrt[d*g - c*h]*Sqrt[e + f*x])/(Sqrt[f*g - e*h]*Sqrt[c + d*x])], ((b*c - a*d)*(f*g - e*h))/((b*e - a*f)*(d*g - c*h))])/(4*d^2*f^2*h^2*Sqrt[((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x))]*Sqrt[g + h*x]) - ((b*e - a*f)*Sqrt[b*g - a*h]*(4*b*B*d*f*h - a*C*d*f*h - b*C*(c*f*h + 3*d*(f*g + e*h)))*Sqrt[((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))]*Sqrt[g + h*x]*EllipticF[ArcSin[(Sqrt[b*g - a*h]*Sqrt[e + f*x])/(Sqrt[f*g - e*h]*Sqrt[a + b*x])], -(((b*c - a*d)*(f*g - e*h))/((d*e - c*f)*(b*g - a*h)))])/(4*d*f^2*h^2*Sqrt[f*g - e*h]*Sqrt[c + d*x]*Sqrt[-(((b*e - a*f)*(g + h*x))/((f*g - e*h)*(a + b*x)))]) - (Sqrt[-(d*g) + c*h]*((a*d*f*h + b*(d*f*g + d*e*h + c*f*h))*(4*b*B*d*f*h + a*C*d*f*h - 3*b*C*(d*f*g + d*e*h + c*f*h)) + 4*d*f*h*(2*a^2*C*d*f*h + b^2*C*(d*e*g + c*f*g + c*e*h) - a*b*(4*B*d*f*h - C*(d*f*g + d*e*h + c*f*h))))*(a + b*x)*Sqrt[((b*g - a*h)*(c + d*x))/((d*g - c*h)*(a + b*x))]*Sqrt[((b*g - a*h)*(e + f*x))/((f*g - e*h)*(a + b*x))]*EllipticPi[-((b*(d*g - c*h))/((b*c - a*d)*h)), ArcSin[(Sqrt[b*c - a*d]*Sqrt[g + h*x])/(Sqrt[-(d*g) + c*h]*Sqrt[a + b*x])], ((b*e - a*f)*(d*g - c*h))/((b*c - a*d)*(f*g - e*h))])/(4*d^2*Sqrt[b*c - a*d]*f^2*h^3*Sqrt[c + d*x]*Sqrt[e + f*x])","A",9,9,62,0.1452,1,"{1600, 1602, 1598, 170, 419, 165, 537, 176, 424}"
22,1,732,0,0.7115415,"\int \frac{a b B-a^2 C+b^2 B x+b^2 C x^2}{\sqrt{a+b x} \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","Int[(a*b*B - a^2*C + b^2*B*x + b^2*C*x^2)/(Sqrt[a + b*x]*Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","\frac{(a+b x) \sqrt{c h-d g} \sqrt{\frac{(c+d x) (b g-a h)}{(a+b x) (d g-c h)}} \sqrt{\frac{(e+f x) (b g-a h)}{(a+b x) (f g-e h)}} (-a C d f h+2 b B d f h-b C (c f h+d e h+d f g)) \Pi \left(-\frac{b (d g-c h)}{(b c-a d) h};\sin ^{-1}\left(\frac{\sqrt{b c-a d} \sqrt{g+h x}}{\sqrt{c h-d g} \sqrt{a+b x}}\right)|\frac{(b e-a f) (d g-c h)}{(b c-a d) (f g-e h)}\right)}{d f h^2 \sqrt{c+d x} \sqrt{e+f x} \sqrt{b c-a d}}+\frac{b C \sqrt{a+b x} \sqrt{e+f x} \sqrt{g+h x}}{f h \sqrt{c+d x}}-\frac{C \sqrt{g+h x} (b e-a f) \sqrt{b g-a h} \sqrt{\frac{(c+d x) (b e-a f)}{(a+b x) (d e-c f)}} F\left(\sin ^{-1}\left(\frac{\sqrt{b g-a h} \sqrt{e+f x}}{\sqrt{f g-e h} \sqrt{a+b x}}\right)|-\frac{(b c-a d) (f g-e h)}{(d e-c f) (b g-a h)}\right)}{f h \sqrt{c+d x} \sqrt{f g-e h} \sqrt{-\frac{(g+h x) (b e-a f)}{(a+b x) (f g-e h)}}}-\frac{b C \sqrt{a+b x} \sqrt{d g-c h} \sqrt{f g-e h} \sqrt{-\frac{(g+h x) (d e-c f)}{(c+d x) (f g-e h)}} E\left(\sin ^{-1}\left(\frac{\sqrt{d g-c h} \sqrt{e+f x}}{\sqrt{f g-e h} \sqrt{c+d x}}\right)|\frac{(b c-a d) (f g-e h)}{(b e-a f) (d g-c h)}\right)}{d f h \sqrt{g+h x} \sqrt{\frac{(a+b x) (d e-c f)}{(c+d x) (b e-a f)}}}","-\frac{(a+b x) \sqrt{c h-d g} \sqrt{\frac{(c+d x) (b g-a h)}{(a+b x) (d g-c h)}} \sqrt{\frac{(e+f x) (b g-a h)}{(a+b x) (f g-e h)}} (a C d f h-b (2 B d f h-C (c f h+d e h+d f g))) \Pi \left(-\frac{b (d g-c h)}{(b c-a d) h};\sin ^{-1}\left(\frac{\sqrt{b c-a d} \sqrt{g+h x}}{\sqrt{c h-d g} \sqrt{a+b x}}\right)|\frac{(b e-a f) (d g-c h)}{(b c-a d) (f g-e h)}\right)}{d f h^2 \sqrt{c+d x} \sqrt{e+f x} \sqrt{b c-a d}}+\frac{b C \sqrt{a+b x} \sqrt{e+f x} \sqrt{g+h x}}{f h \sqrt{c+d x}}-\frac{C \sqrt{g+h x} (b e-a f) \sqrt{b g-a h} \sqrt{\frac{(c+d x) (b e-a f)}{(a+b x) (d e-c f)}} F\left(\sin ^{-1}\left(\frac{\sqrt{b g-a h} \sqrt{e+f x}}{\sqrt{f g-e h} \sqrt{a+b x}}\right)|-\frac{(b c-a d) (f g-e h)}{(d e-c f) (b g-a h)}\right)}{f h \sqrt{c+d x} \sqrt{f g-e h} \sqrt{-\frac{(g+h x) (b e-a f)}{(a+b x) (f g-e h)}}}-\frac{b C \sqrt{a+b x} \sqrt{d g-c h} \sqrt{f g-e h} \sqrt{-\frac{(g+h x) (d e-c f)}{(c+d x) (f g-e h)}} E\left(\sin ^{-1}\left(\frac{\sqrt{d g-c h} \sqrt{e+f x}}{\sqrt{f g-e h} \sqrt{c+d x}}\right)|\frac{(b c-a d) (f g-e h)}{(b e-a f) (d g-c h)}\right)}{d f h \sqrt{g+h x} \sqrt{\frac{(a+b x) (d e-c f)}{(c+d x) (b e-a f)}}}",1,"(b*C*Sqrt[a + b*x]*Sqrt[e + f*x]*Sqrt[g + h*x])/(f*h*Sqrt[c + d*x]) - (b*C*Sqrt[d*g - c*h]*Sqrt[f*g - e*h]*Sqrt[a + b*x]*Sqrt[-(((d*e - c*f)*(g + h*x))/((f*g - e*h)*(c + d*x)))]*EllipticE[ArcSin[(Sqrt[d*g - c*h]*Sqrt[e + f*x])/(Sqrt[f*g - e*h]*Sqrt[c + d*x])], ((b*c - a*d)*(f*g - e*h))/((b*e - a*f)*(d*g - c*h))])/(d*f*h*Sqrt[((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x))]*Sqrt[g + h*x]) - (C*(b*e - a*f)*Sqrt[b*g - a*h]*Sqrt[((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))]*Sqrt[g + h*x]*EllipticF[ArcSin[(Sqrt[b*g - a*h]*Sqrt[e + f*x])/(Sqrt[f*g - e*h]*Sqrt[a + b*x])], -(((b*c - a*d)*(f*g - e*h))/((d*e - c*f)*(b*g - a*h)))])/(f*h*Sqrt[f*g - e*h]*Sqrt[c + d*x]*Sqrt[-(((b*e - a*f)*(g + h*x))/((f*g - e*h)*(a + b*x)))]) + (Sqrt[-(d*g) + c*h]*(2*b*B*d*f*h - a*C*d*f*h - b*C*(d*f*g + d*e*h + c*f*h))*(a + b*x)*Sqrt[((b*g - a*h)*(c + d*x))/((d*g - c*h)*(a + b*x))]*Sqrt[((b*g - a*h)*(e + f*x))/((f*g - e*h)*(a + b*x))]*EllipticPi[-((b*(d*g - c*h))/((b*c - a*d)*h)), ArcSin[(Sqrt[b*c - a*d]*Sqrt[g + h*x])/(Sqrt[-(d*g) + c*h]*Sqrt[a + b*x])], ((b*e - a*f)*(d*g - c*h))/((b*c - a*d)*(f*g - e*h))])/(d*Sqrt[b*c - a*d]*f*h^2*Sqrt[c + d*x]*Sqrt[e + f*x])","A",8,8,62,0.1290,1,"{1586, 1596, 170, 419, 176, 424, 165, 537}"
23,1,436,0,0.5119773,"\int \frac{a b B-a^2 C+b^2 B x+b^2 C x^2}{(a+b x)^{3/2} \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","Int[(a*b*B - a^2*C + b^2*B*x + b^2*C*x^2)/((a + b*x)^(3/2)*Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","\frac{2 \sqrt{g+h x} (b B-2 a C) \sqrt{\frac{(c+d x) (b e-a f)}{(a+b x) (d e-c f)}} F\left(\sin ^{-1}\left(\frac{\sqrt{b g-a h} \sqrt{e+f x}}{\sqrt{f g-e h} \sqrt{a+b x}}\right)|-\frac{(b c-a d) (f g-e h)}{(d e-c f) (b g-a h)}\right)}{\sqrt{c+d x} \sqrt{b g-a h} \sqrt{f g-e h} \sqrt{-\frac{(g+h x) (b e-a f)}{(a+b x) (f g-e h)}}}+\frac{2 C (a+b x) \sqrt{c h-d g} \sqrt{\frac{(c+d x) (b g-a h)}{(a+b x) (d g-c h)}} \sqrt{\frac{(e+f x) (b g-a h)}{(a+b x) (f g-e h)}} \Pi \left(-\frac{b (d g-c h)}{(b c-a d) h};\sin ^{-1}\left(\frac{\sqrt{b c-a d} \sqrt{g+h x}}{\sqrt{c h-d g} \sqrt{a+b x}}\right)|\frac{(b e-a f) (d g-c h)}{(b c-a d) (f g-e h)}\right)}{h \sqrt{c+d x} \sqrt{e+f x} \sqrt{b c-a d}}","\frac{2 \sqrt{g+h x} (b B-2 a C) \sqrt{\frac{(c+d x) (b e-a f)}{(a+b x) (d e-c f)}} F\left(\sin ^{-1}\left(\frac{\sqrt{b g-a h} \sqrt{e+f x}}{\sqrt{f g-e h} \sqrt{a+b x}}\right)|-\frac{(b c-a d) (f g-e h)}{(d e-c f) (b g-a h)}\right)}{\sqrt{c+d x} \sqrt{b g-a h} \sqrt{f g-e h} \sqrt{-\frac{(g+h x) (b e-a f)}{(a+b x) (f g-e h)}}}+\frac{2 C (a+b x) \sqrt{c h-d g} \sqrt{\frac{(c+d x) (b g-a h)}{(a+b x) (d g-c h)}} \sqrt{\frac{(e+f x) (b g-a h)}{(a+b x) (f g-e h)}} \Pi \left(-\frac{b (d g-c h)}{(b c-a d) h};\sin ^{-1}\left(\frac{\sqrt{b c-a d} \sqrt{g+h x}}{\sqrt{c h-d g} \sqrt{a+b x}}\right)|\frac{(b e-a f) (d g-c h)}{(b c-a d) (f g-e h)}\right)}{h \sqrt{c+d x} \sqrt{e+f x} \sqrt{b c-a d}}",1,"(2*(b*B - 2*a*C)*Sqrt[((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))]*Sqrt[g + h*x]*EllipticF[ArcSin[(Sqrt[b*g - a*h]*Sqrt[e + f*x])/(Sqrt[f*g - e*h]*Sqrt[a + b*x])], -(((b*c - a*d)*(f*g - e*h))/((d*e - c*f)*(b*g - a*h)))])/(Sqrt[b*g - a*h]*Sqrt[f*g - e*h]*Sqrt[c + d*x]*Sqrt[-(((b*e - a*f)*(g + h*x))/((f*g - e*h)*(a + b*x)))]) + (2*C*Sqrt[-(d*g) + c*h]*(a + b*x)*Sqrt[((b*g - a*h)*(c + d*x))/((d*g - c*h)*(a + b*x))]*Sqrt[((b*g - a*h)*(e + f*x))/((f*g - e*h)*(a + b*x))]*EllipticPi[-((b*(d*g - c*h))/((b*c - a*d)*h)), ArcSin[(Sqrt[b*c - a*d]*Sqrt[g + h*x])/(Sqrt[-(d*g) + c*h]*Sqrt[a + b*x])], ((b*e - a*f)*(d*g - c*h))/((b*c - a*d)*(f*g - e*h))])/(Sqrt[b*c - a*d]*h*Sqrt[c + d*x]*Sqrt[e + f*x])","A",6,6,62,0.09677,1,"{24, 1598, 170, 419, 165, 537}"
24,1,616,0,1.1702897,"\int \frac{a b B-a^2 C+b^2 B x+b^2 C x^2}{(a+b x)^{5/2} \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","Int[(a*b*B - a^2*C + b^2*B*x + b^2*C*x^2)/((a + b*x)^(5/2)*Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","-\frac{2 b^2 \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x} (b B-2 a C)}{\sqrt{a+b x} (b c-a d) (b e-a f) (b g-a h)}+\frac{2 b d \sqrt{a+b x} \sqrt{e+f x} \sqrt{g+h x} (b B-2 a C)}{\sqrt{c+d x} (b c-a d) (b e-a f) (b g-a h)}+\frac{2 \sqrt{g+h x} (a C d-b B d+b c C) \sqrt{\frac{(c+d x) (b e-a f)}{(a+b x) (d e-c f)}} F\left(\sin ^{-1}\left(\frac{\sqrt{b g-a h} \sqrt{e+f x}}{\sqrt{f g-e h} \sqrt{a+b x}}\right)|-\frac{(b c-a d) (f g-e h)}{(d e-c f) (b g-a h)}\right)}{\sqrt{c+d x} (b c-a d) \sqrt{b g-a h} \sqrt{f g-e h} \sqrt{-\frac{(g+h x) (b e-a f)}{(a+b x) (f g-e h)}}}-\frac{2 b \sqrt{a+b x} (b B-2 a C) \sqrt{d g-c h} \sqrt{f g-e h} \sqrt{-\frac{(g+h x) (d e-c f)}{(c+d x) (f g-e h)}} E\left(\sin ^{-1}\left(\frac{\sqrt{d g-c h} \sqrt{e+f x}}{\sqrt{f g-e h} \sqrt{c+d x}}\right)|\frac{(b c-a d) (f g-e h)}{(b e-a f) (d g-c h)}\right)}{\sqrt{g+h x} (b c-a d) (b e-a f) (b g-a h) \sqrt{\frac{(a+b x) (d e-c f)}{(c+d x) (b e-a f)}}}","-\frac{2 b^2 \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x} (b B-2 a C)}{\sqrt{a+b x} (b c-a d) (b e-a f) (b g-a h)}+\frac{2 b d \sqrt{a+b x} \sqrt{e+f x} \sqrt{g+h x} (b B-2 a C)}{\sqrt{c+d x} (b c-a d) (b e-a f) (b g-a h)}+\frac{2 \sqrt{g+h x} (a C d-b B d+b c C) \sqrt{\frac{(c+d x) (b e-a f)}{(a+b x) (d e-c f)}} F\left(\sin ^{-1}\left(\frac{\sqrt{b g-a h} \sqrt{e+f x}}{\sqrt{f g-e h} \sqrt{a+b x}}\right)|-\frac{(b c-a d) (f g-e h)}{(d e-c f) (b g-a h)}\right)}{\sqrt{c+d x} (b c-a d) \sqrt{b g-a h} \sqrt{f g-e h} \sqrt{-\frac{(g+h x) (b e-a f)}{(a+b x) (f g-e h)}}}-\frac{2 b \sqrt{a+b x} (b B-2 a C) \sqrt{d g-c h} \sqrt{f g-e h} \sqrt{-\frac{(g+h x) (d e-c f)}{(c+d x) (f g-e h)}} E\left(\sin ^{-1}\left(\frac{\sqrt{d g-c h} \sqrt{e+f x}}{\sqrt{f g-e h} \sqrt{c+d x}}\right)|\frac{(b c-a d) (f g-e h)}{(b e-a f) (d g-c h)}\right)}{\sqrt{g+h x} (b c-a d) (b e-a f) (b g-a h) \sqrt{\frac{(a+b x) (d e-c f)}{(c+d x) (b e-a f)}}}",1,"(2*b*(b*B - 2*a*C)*d*Sqrt[a + b*x]*Sqrt[e + f*x]*Sqrt[g + h*x])/((b*c - a*d)*(b*e - a*f)*(b*g - a*h)*Sqrt[c + d*x]) - (2*b^2*(b*B - 2*a*C)*Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x])/((b*c - a*d)*(b*e - a*f)*(b*g - a*h)*Sqrt[a + b*x]) - (2*b*(b*B - 2*a*C)*Sqrt[d*g - c*h]*Sqrt[f*g - e*h]*Sqrt[a + b*x]*Sqrt[-(((d*e - c*f)*(g + h*x))/((f*g - e*h)*(c + d*x)))]*EllipticE[ArcSin[(Sqrt[d*g - c*h]*Sqrt[e + f*x])/(Sqrt[f*g - e*h]*Sqrt[c + d*x])], ((b*c - a*d)*(f*g - e*h))/((b*e - a*f)*(d*g - c*h))])/((b*c - a*d)*(b*e - a*f)*(b*g - a*h)*Sqrt[((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x))]*Sqrt[g + h*x]) + (2*(b*c*C - b*B*d + a*C*d)*Sqrt[((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))]*Sqrt[g + h*x]*EllipticF[ArcSin[(Sqrt[b*g - a*h]*Sqrt[e + f*x])/(Sqrt[f*g - e*h]*Sqrt[a + b*x])], -(((b*c - a*d)*(f*g - e*h))/((d*e - c*f)*(b*g - a*h)))])/((b*c - a*d)*Sqrt[b*g - a*h]*Sqrt[f*g - e*h]*Sqrt[c + d*x]*Sqrt[-(((b*e - a*f)*(g + h*x))/((f*g - e*h)*(a + b*x)))])","A",8,8,62,0.1290,1,"{24, 1599, 1602, 12, 170, 419, 176, 424}"
25,1,1119,0,4.2988692,"\int \frac{a b B-a^2 C+b^2 B x+b^2 C x^2}{(a+b x)^{7/2} \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","Int[(a*b*B - a^2*C + b^2*B*x + b^2*C*x^2)/((a + b*x)^(7/2)*Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","-\frac{2 \left(9 C d f h a^3-b (6 B d f h+5 C (d f g+d e h+c f h)) a^2+b^2 (C (d e g+c f g+c e h)+4 B (d f g+d e h+c f h)) a+b^3 (3 c C e g-2 B d e g-2 B c (f g+e h))\right) \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x} b^2}{3 (b c-a d)^2 (b e-a f)^2 (b g-a h)^2 \sqrt{a+b x}}-\frac{2 (b B-2 a C) \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x} b^2}{3 (b c-a d) (b e-a f) (b g-a h) (a+b x)^{3/2}}-\frac{2 \sqrt{d g-c h} \sqrt{f g-e h} \left(9 C d f h a^3-b (6 B d f h+5 C (d f g+d e h+c f h)) a^2+b^2 (C (d e g+c f g+c e h)+4 B (d f g+d e h+c f h)) a+b^3 (3 c C e g-2 B d e g-2 B c (f g+e h))\right) \sqrt{a+b x} \sqrt{-\frac{(d e-c f) (g+h x)}{(f g-e h) (c+d x)}} E\left(\sin ^{-1}\left(\frac{\sqrt{d g-c h} \sqrt{e+f x}}{\sqrt{f g-e h} \sqrt{c+d x}}\right)|\frac{(b c-a d) (f g-e h)}{(b e-a f) (d g-c h)}\right) b}{3 (b c-a d)^2 (b e-a f)^2 (b g-a h)^2 \sqrt{\frac{(d e-c f) (a+b x)}{(b e-a f) (c+d x)}} \sqrt{g+h x}}+\frac{2 d \left(9 C d f h a^3-b (6 B d f h+5 C (d f g+d e h+c f h)) a^2+b^2 (C (d e g+c f g+c e h)+4 B (d f g+d e h+c f h)) a+b^3 (3 c C e g-2 B d e g-2 B c (f g+e h))\right) \sqrt{a+b x} \sqrt{e+f x} \sqrt{g+h x} b}{3 (b c-a d)^2 (b e-a f)^2 (b g-a h)^2 \sqrt{c+d x}}-\frac{2 \left(3 C d^2 f h a^3-3 b d (B d f h+C (d f g+d e h-c f h)) a^2+b^2 \left(3 B (f g+e h) d^2+C \left(-2 f h c^2-d f g c-d e h c+d^2 e g\right)\right) a-b^3 \left(-B f h c^2-d (3 C e g-B f g-B e h) c+2 B d^2 e g\right)\right) \sqrt{\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}} \sqrt{g+h x} F\left(\sin ^{-1}\left(\frac{\sqrt{b g-a h} \sqrt{e+f x}}{\sqrt{f g-e h} \sqrt{a+b x}}\right)|-\frac{(b c-a d) (f g-e h)}{(d e-c f) (b g-a h)}\right)}{3 (b c-a d)^2 (b e-a f) (b g-a h)^{3/2} \sqrt{f g-e h} \sqrt{c+d x} \sqrt{-\frac{(b e-a f) (g+h x)}{(f g-e h) (a+b x)}}}","-\frac{2 \left(9 C d f h a^3-b (6 B d f h+5 C (d f g+d e h+c f h)) a^2+b^2 (C (d e g+c f g+c e h)+4 B (d f g+d e h+c f h)) a-b^3 (2 B d e g-c (3 C e g-2 B f g-2 B e h))\right) \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x} b^2}{3 (b c-a d)^2 (b e-a f)^2 (b g-a h)^2 \sqrt{a+b x}}-\frac{2 (b B-2 a C) \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x} b^2}{3 (b c-a d) (b e-a f) (b g-a h) (a+b x)^{3/2}}-\frac{2 \sqrt{d g-c h} \sqrt{f g-e h} \left(9 C d f h a^3-b (6 B d f h+5 C (d f g+d e h+c f h)) a^2+b^2 (C (d e g+c f g+c e h)+4 B (d f g+d e h+c f h)) a-b^3 (2 B d e g-c (3 C e g-2 B f g-2 B e h))\right) \sqrt{a+b x} \sqrt{-\frac{(d e-c f) (g+h x)}{(f g-e h) (c+d x)}} E\left(\sin ^{-1}\left(\frac{\sqrt{d g-c h} \sqrt{e+f x}}{\sqrt{f g-e h} \sqrt{c+d x}}\right)|\frac{(b c-a d) (f g-e h)}{(b e-a f) (d g-c h)}\right) b}{3 (b c-a d)^2 (b e-a f)^2 (b g-a h)^2 \sqrt{\frac{(d e-c f) (a+b x)}{(b e-a f) (c+d x)}} \sqrt{g+h x}}+\frac{2 d \left(9 C d f h a^3-b (6 B d f h+5 C (d f g+d e h+c f h)) a^2+b^2 (C (d e g+c f g+c e h)+4 B (d f g+d e h+c f h)) a-b^3 (2 B d e g-c (3 C e g-2 B f g-2 B e h))\right) \sqrt{a+b x} \sqrt{e+f x} \sqrt{g+h x} b}{3 (b c-a d)^2 (b e-a f)^2 (b g-a h)^2 \sqrt{c+d x}}-\frac{2 \left(3 C d^2 f h a^3-3 b d (B d f h+C (d f g+d e h-c f h)) a^2+b^2 \left(3 B (f g+e h) d^2+C \left(-2 f h c^2-d f g c-d e h c+d^2 e g\right)\right) a-b^3 \left(-B f h c^2-d (3 C e g-B f g-B e h) c+2 B d^2 e g\right)\right) \sqrt{\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}} \sqrt{g+h x} F\left(\sin ^{-1}\left(\frac{\sqrt{b g-a h} \sqrt{e+f x}}{\sqrt{f g-e h} \sqrt{a+b x}}\right)|-\frac{(b c-a d) (f g-e h)}{(d e-c f) (b g-a h)}\right)}{3 (b c-a d)^2 (b e-a f) (b g-a h)^{3/2} \sqrt{f g-e h} \sqrt{c+d x} \sqrt{-\frac{(b e-a f) (g+h x)}{(f g-e h) (a+b x)}}}",1,"(2*b*d*(9*a^3*C*d*f*h + b^3*(3*c*C*e*g - 2*B*d*e*g - 2*B*c*(f*g + e*h)) + a*b^2*(C*(d*e*g + c*f*g + c*e*h) + 4*B*(d*f*g + d*e*h + c*f*h)) - a^2*b*(6*B*d*f*h + 5*C*(d*f*g + d*e*h + c*f*h)))*Sqrt[a + b*x]*Sqrt[e + f*x]*Sqrt[g + h*x])/(3*(b*c - a*d)^2*(b*e - a*f)^2*(b*g - a*h)^2*Sqrt[c + d*x]) - (2*b^2*(b*B - 2*a*C)*Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x])/(3*(b*c - a*d)*(b*e - a*f)*(b*g - a*h)*(a + b*x)^(3/2)) - (2*b^2*(9*a^3*C*d*f*h + b^3*(3*c*C*e*g - 2*B*d*e*g - 2*B*c*(f*g + e*h)) + a*b^2*(C*(d*e*g + c*f*g + c*e*h) + 4*B*(d*f*g + d*e*h + c*f*h)) - a^2*b*(6*B*d*f*h + 5*C*(d*f*g + d*e*h + c*f*h)))*Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x])/(3*(b*c - a*d)^2*(b*e - a*f)^2*(b*g - a*h)^2*Sqrt[a + b*x]) - (2*b*Sqrt[d*g - c*h]*Sqrt[f*g - e*h]*(9*a^3*C*d*f*h + b^3*(3*c*C*e*g - 2*B*d*e*g - 2*B*c*(f*g + e*h)) + a*b^2*(C*(d*e*g + c*f*g + c*e*h) + 4*B*(d*f*g + d*e*h + c*f*h)) - a^2*b*(6*B*d*f*h + 5*C*(d*f*g + d*e*h + c*f*h)))*Sqrt[a + b*x]*Sqrt[-(((d*e - c*f)*(g + h*x))/((f*g - e*h)*(c + d*x)))]*EllipticE[ArcSin[(Sqrt[d*g - c*h]*Sqrt[e + f*x])/(Sqrt[f*g - e*h]*Sqrt[c + d*x])], ((b*c - a*d)*(f*g - e*h))/((b*e - a*f)*(d*g - c*h))])/(3*(b*c - a*d)^2*(b*e - a*f)^2*(b*g - a*h)^2*Sqrt[((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x))]*Sqrt[g + h*x]) - (2*(3*a^3*C*d^2*f*h - b^3*(2*B*d^2*e*g - B*c^2*f*h - c*d*(3*C*e*g - B*f*g - B*e*h)) - 3*a^2*b*d*(B*d*f*h + C*(d*f*g + d*e*h - c*f*h)) + a*b^2*(3*B*d^2*(f*g + e*h) + C*(d^2*e*g - c*d*f*g - c*d*e*h - 2*c^2*f*h)))*Sqrt[((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))]*Sqrt[g + h*x]*EllipticF[ArcSin[(Sqrt[b*g - a*h]*Sqrt[e + f*x])/(Sqrt[f*g - e*h]*Sqrt[a + b*x])], -(((b*c - a*d)*(f*g - e*h))/((d*e - c*f)*(b*g - a*h)))])/(3*(b*c - a*d)^2*(b*e - a*f)*(b*g - a*h)^(3/2)*Sqrt[f*g - e*h]*Sqrt[c + d*x]*Sqrt[-(((b*e - a*f)*(g + h*x))/((f*g - e*h)*(a + b*x)))])","A",9,8,62,0.1290,1,"{24, 1599, 1602, 12, 170, 419, 176, 424}"
26,1,1083,0,3.300799,"\int \frac{(a+b x)^2 \left(A+C x^2\right)}{\sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","Int[((a + b*x)^2*(A + C*x^2))/(Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","\frac{2 C \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x} (a+b x)^2}{7 d f h}+\frac{4 C (2 a d f h-3 b (d f g+d e h+c f h)) \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x} (a+b x)}{35 d^2 f^2 h^2}-\frac{4 \sqrt{c f-d e} \left(\left(35 A d^2 f^2 (d f g+d e h+c f h) h^2+2 C \left(2 \left(6 f^3 g^3+5 e f^2 h g^2+5 e^2 f h^2 g+6 e^3 h^3\right) d^3+c f h \left(10 f^2 g^2+9 e f h g+10 e^2 h^2\right) d^2+10 c^2 f^2 h^2 (f g+e h) d+12 c^3 f^3 h^3\right)\right) b^2-7 a d f h \left(15 A d^2 f^2 h^2+C \left(\left(8 f^2 g^2+7 e f h g+8 e^2 h^2\right) d^2+7 c f h (f g+e h) d+8 c^2 f^2 h^2\right)\right) b+35 a^2 C d^2 f^2 h^2 (d f g+d e h+c f h)\right) \sqrt{\frac{d (e+f x)}{d e-c f}} \sqrt{g+h x} E\left(\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right)}{105 d^4 f^{7/2} h^4 \sqrt{e+f x} \sqrt{\frac{d (g+h x)}{d g-c h}}}+\frac{2 \sqrt{c f-d e} \left(\left(35 A d^2 f^2 (c h (f g-e h)+d g (2 f g+e h)) h^2+C \left(g \left(48 f^3 g^3+16 e f^2 h g^2+17 e^2 f h^2 g+24 e^3 h^3\right) d^3+2 c h \left(8 f^3 g^3+e f^2 h g^2+3 e^2 f h^2 g-12 e^3 h^3\right) d^2+c^2 f h^2 \left(17 f^2 g^2+6 e f h g-23 e^2 h^2\right) d+24 c^3 f^2 h^3 (f g-e h)\right)\right) b^2-14 a d f h \left(15 A d^2 f^2 g h^2+C \left(g \left(8 f^2 g^2+3 e f h g+4 e^2 h^2\right) d^2+c h \left(3 f^2 g^2+e f h g-4 e^2 h^2\right) d+4 c^2 f h^2 (f g-e h)\right)\right) b+35 a^2 d^2 f^2 h^2 \left(3 A d f h^2+c C (f g-e h) h+C d g (2 f g+e h)\right)\right) \sqrt{\frac{d (e+f x)}{d e-c f}} \sqrt{\frac{d (g+h x)}{d g-c h}} F\left(\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right)}{105 d^4 f^{7/2} h^4 \sqrt{e+f x} \sqrt{g+h x}}+\frac{2 \left(8 C d f h a^2-38 b C (d f g+d e h+c f h) a+\frac{24 b^2 C (d f g+d e h+c f h)^2}{d f h}+35 A b^2 d f h-25 b^2 C (d e g+c f g+c e h)\right) \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}}{105 d^2 f^2 h^2}","\frac{2 C \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x} (a+b x)^2}{7 d f h}+\frac{4 C (2 a d f h-3 b (d f g+d e h+c f h)) \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x} (a+b x)}{35 d^2 f^2 h^2}-\frac{4 \sqrt{c f-d e} \left(\left(35 A d^2 f^2 (d f g+d e h+c f h) h^2+2 C \left(2 \left(6 f^3 g^3+5 e f^2 h g^2+5 e^2 f h^2 g+6 e^3 h^3\right) d^3+c f h \left(10 f^2 g^2+9 e f h g+10 e^2 h^2\right) d^2+10 c^2 f^2 h^2 (f g+e h) d+12 c^3 f^3 h^3\right)\right) b^2-7 a d f h \left(15 A d^2 f^2 h^2+C \left(\left(8 f^2 g^2+7 e f h g+8 e^2 h^2\right) d^2+7 c f h (f g+e h) d+8 c^2 f^2 h^2\right)\right) b+35 a^2 C d^2 f^2 h^2 (d f g+d e h+c f h)\right) \sqrt{\frac{d (e+f x)}{d e-c f}} \sqrt{g+h x} E\left(\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right)}{105 d^4 f^{7/2} h^4 \sqrt{e+f x} \sqrt{\frac{d (g+h x)}{d g-c h}}}+\frac{2 \sqrt{c f-d e} \left(\left(35 A d^2 f^2 (c h (f g-e h)+d g (2 f g+e h)) h^2+C \left(g \left(48 f^3 g^3+16 e f^2 h g^2+17 e^2 f h^2 g+24 e^3 h^3\right) d^3+2 c h \left(8 f^3 g^3+e f^2 h g^2+3 e^2 f h^2 g-12 e^3 h^3\right) d^2+c^2 f h^2 \left(17 f^2 g^2+6 e f h g-23 e^2 h^2\right) d+24 c^3 f^2 h^3 (f g-e h)\right)\right) b^2-14 a d f h \left(15 A d^2 f^2 g h^2+C \left(g \left(8 f^2 g^2+3 e f h g+4 e^2 h^2\right) d^2+c h \left(3 f^2 g^2+e f h g-4 e^2 h^2\right) d+4 c^2 f h^2 (f g-e h)\right)\right) b+35 a^2 d^2 f^2 h^2 \left(3 A d f h^2+C (c h (f g-e h)+d g (2 f g+e h))\right)\right) \sqrt{\frac{d (e+f x)}{d e-c f}} \sqrt{\frac{d (g+h x)}{d g-c h}} F\left(\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right)}{105 d^4 f^{7/2} h^4 \sqrt{e+f x} \sqrt{g+h x}}+\frac{2 (4 C (2 a d f h-3 b (d f g+d e h+c f h)) (a d f h-2 b (d f g+d e h+c f h))+5 b d f h (7 A b d f h-C (5 b (d e g+c f g+c e h)+2 a (d f g+d e h+c f h)))) \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}}{105 d^3 f^3 h^3}",1,"(2*(35*A*b^2*d*f*h + 8*a^2*C*d*f*h - 25*b^2*C*(d*e*g + c*f*g + c*e*h) - 38*a*b*C*(d*f*g + d*e*h + c*f*h) + (24*b^2*C*(d*f*g + d*e*h + c*f*h)^2)/(d*f*h))*Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x])/(105*d^2*f^2*h^2) + (4*C*(2*a*d*f*h - 3*b*(d*f*g + d*e*h + c*f*h))*(a + b*x)*Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x])/(35*d^2*f^2*h^2) + (2*C*(a + b*x)^2*Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x])/(7*d*f*h) - (4*Sqrt[-(d*e) + c*f]*(35*a^2*C*d^2*f^2*h^2*(d*f*g + d*e*h + c*f*h) - 7*a*b*d*f*h*(15*A*d^2*f^2*h^2 + C*(8*c^2*f^2*h^2 + 7*c*d*f*h*(f*g + e*h) + d^2*(8*f^2*g^2 + 7*e*f*g*h + 8*e^2*h^2))) + b^2*(35*A*d^2*f^2*h^2*(d*f*g + d*e*h + c*f*h) + 2*C*(12*c^3*f^3*h^3 + 10*c^2*d*f^2*h^2*(f*g + e*h) + c*d^2*f*h*(10*f^2*g^2 + 9*e*f*g*h + 10*e^2*h^2) + 2*d^3*(6*f^3*g^3 + 5*e*f^2*g^2*h + 5*e^2*f*g*h^2 + 6*e^3*h^3))))*Sqrt[(d*(e + f*x))/(d*e - c*f)]*Sqrt[g + h*x]*EllipticE[ArcSin[(Sqrt[f]*Sqrt[c + d*x])/Sqrt[-(d*e) + c*f]], ((d*e - c*f)*h)/(f*(d*g - c*h))])/(105*d^4*f^(7/2)*h^4*Sqrt[e + f*x]*Sqrt[(d*(g + h*x))/(d*g - c*h)]) + (2*Sqrt[-(d*e) + c*f]*(35*a^2*d^2*f^2*h^2*(3*A*d*f*h^2 + c*C*h*(f*g - e*h) + C*d*g*(2*f*g + e*h)) - 14*a*b*d*f*h*(15*A*d^2*f^2*g*h^2 + C*(4*c^2*f*h^2*(f*g - e*h) + c*d*h*(3*f^2*g^2 + e*f*g*h - 4*e^2*h^2) + d^2*g*(8*f^2*g^2 + 3*e*f*g*h + 4*e^2*h^2))) + b^2*(35*A*d^2*f^2*h^2*(c*h*(f*g - e*h) + d*g*(2*f*g + e*h)) + C*(24*c^3*f^2*h^3*(f*g - e*h) + c^2*d*f*h^2*(17*f^2*g^2 + 6*e*f*g*h - 23*e^2*h^2) + 2*c*d^2*h*(8*f^3*g^3 + e*f^2*g^2*h + 3*e^2*f*g*h^2 - 12*e^3*h^3) + d^3*g*(48*f^3*g^3 + 16*e*f^2*g^2*h + 17*e^2*f*g*h^2 + 24*e^3*h^3))))*Sqrt[(d*(e + f*x))/(d*e - c*f)]*Sqrt[(d*(g + h*x))/(d*g - c*h)]*EllipticF[ArcSin[(Sqrt[f]*Sqrt[c + d*x])/Sqrt[-(d*e) + c*f]], ((d*e - c*f)*h)/(f*(d*g - c*h))])/(105*d^4*f^(7/2)*h^4*Sqrt[e + f*x]*Sqrt[g + h*x])","A",9,8,42,0.1905,1,"{1601, 1600, 1615, 158, 114, 113, 121, 120}"
27,1,608,0,1.3571983,"\int \frac{(a+b x) \left(A+C x^2\right)}{\sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","Int[((a + b*x)*(A + C*x^2))/(Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","\frac{2 \sqrt{c f-d e} \sqrt{\frac{d (e+f x)}{d e-c f}} \sqrt{\frac{d (g+h x)}{d g-c h}} F\left(\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right) \left(5 a d f h \left(3 A d f h^2+c C h (f g-e h)+C d g (e h+2 f g)\right)-b \left(15 A d^2 f^2 g h^2+C \left(4 c^2 f h^2 (f g-e h)+c d h \left(-4 e^2 h^2+e f g h+3 f^2 g^2\right)+d^2 g \left(4 e^2 h^2+3 e f g h+8 f^2 g^2\right)\right)\right)\right)}{15 d^3 f^{5/2} h^3 \sqrt{e+f x} \sqrt{g+h x}}+\frac{2 \sqrt{g+h x} \sqrt{c f-d e} \sqrt{\frac{d (e+f x)}{d e-c f}} E\left(\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right) \left(-10 a C d f h (c f h+d e h+d f g)+15 A b d^2 f^2 h^2+b C \left(8 c^2 f^2 h^2+7 c d f h (e h+f g)+d^2 \left(8 e^2 h^2+7 e f g h+8 f^2 g^2\right)\right)\right)}{15 d^3 f^{5/2} h^3 \sqrt{e+f x} \sqrt{\frac{d (g+h x)}{d g-c h}}}+\frac{4 C \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x} (a d f h-2 b (c f h+d e h+d f g))}{15 d^2 f^2 h^2}+\frac{2 C (a+b x) \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}}{5 d f h}","\frac{2 \sqrt{c f-d e} \sqrt{\frac{d (e+f x)}{d e-c f}} \sqrt{\frac{d (g+h x)}{d g-c h}} F\left(\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right) \left(5 a d f h \left(3 A d f h^2+C (c h (f g-e h)+d g (e h+2 f g))\right)-b \left(15 A d^2 f^2 g h^2+C \left(4 c^2 f h^2 (f g-e h)+c d h \left(-4 e^2 h^2+e f g h+3 f^2 g^2\right)+d^2 g \left(4 e^2 h^2+3 e f g h+8 f^2 g^2\right)\right)\right)\right)}{15 d^3 f^{5/2} h^3 \sqrt{e+f x} \sqrt{g+h x}}-\frac{2 \sqrt{g+h x} \sqrt{c f-d e} \sqrt{\frac{d (e+f x)}{d e-c f}} E\left(\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right) \left(10 a C d f h (c f h+d e h+d f g)-b \left(15 A d^2 f^2 h^2+C \left(8 c^2 f^2 h^2+7 c d f h (e h+f g)+d^2 \left(8 e^2 h^2+7 e f g h+8 f^2 g^2\right)\right)\right)\right)}{15 d^3 f^{5/2} h^3 \sqrt{e+f x} \sqrt{\frac{d (g+h x)}{d g-c h}}}+\frac{4 C \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x} (a d f h-2 b (c f h+d e h+d f g))}{15 d^2 f^2 h^2}+\frac{2 C (a+b x) \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}}{5 d f h}",1,"(4*C*(a*d*f*h - 2*b*(d*f*g + d*e*h + c*f*h))*Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x])/(15*d^2*f^2*h^2) + (2*C*(a + b*x)*Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x])/(5*d*f*h) + (2*Sqrt[-(d*e) + c*f]*(15*A*b*d^2*f^2*h^2 - 10*a*C*d*f*h*(d*f*g + d*e*h + c*f*h) + b*C*(8*c^2*f^2*h^2 + 7*c*d*f*h*(f*g + e*h) + d^2*(8*f^2*g^2 + 7*e*f*g*h + 8*e^2*h^2)))*Sqrt[(d*(e + f*x))/(d*e - c*f)]*Sqrt[g + h*x]*EllipticE[ArcSin[(Sqrt[f]*Sqrt[c + d*x])/Sqrt[-(d*e) + c*f]], ((d*e - c*f)*h)/(f*(d*g - c*h))])/(15*d^3*f^(5/2)*h^3*Sqrt[e + f*x]*Sqrt[(d*(g + h*x))/(d*g - c*h)]) + (2*Sqrt[-(d*e) + c*f]*(5*a*d*f*h*(3*A*d*f*h^2 + c*C*h*(f*g - e*h) + C*d*g*(2*f*g + e*h)) - b*(15*A*d^2*f^2*g*h^2 + C*(4*c^2*f*h^2*(f*g - e*h) + c*d*h*(3*f^2*g^2 + e*f*g*h - 4*e^2*h^2) + d^2*g*(8*f^2*g^2 + 3*e*f*g*h + 4*e^2*h^2))))*Sqrt[(d*(e + f*x))/(d*e - c*f)]*Sqrt[(d*(g + h*x))/(d*g - c*h)]*EllipticF[ArcSin[(Sqrt[f]*Sqrt[c + d*x])/Sqrt[-(d*e) + c*f]], ((d*e - c*f)*h)/(f*(d*g - c*h))])/(15*d^3*f^(5/2)*h^3*Sqrt[e + f*x]*Sqrt[g + h*x])","A",8,7,40,0.1750,1,"{1601, 1615, 158, 114, 113, 121, 120}"
28,1,367,0,0.4903377,"\int \frac{A+C x^2}{\sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","Int[(A + C*x^2)/(Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","\frac{2 \sqrt{c f-d e} \sqrt{\frac{d (e+f x)}{d e-c f}} \sqrt{\frac{d (g+h x)}{d g-c h}} \left(3 A d f h^2+c C h (f g-e h)+C d g (e h+2 f g)\right) F\left(\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right)}{3 d^2 f^{3/2} h^2 \sqrt{e+f x} \sqrt{g+h x}}-\frac{4 C \sqrt{g+h x} \sqrt{c f-d e} \sqrt{\frac{d (e+f x)}{d e-c f}} (c f h+d e h+d f g) E\left(\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right)}{3 d^2 f^{3/2} h^2 \sqrt{e+f x} \sqrt{\frac{d (g+h x)}{d g-c h}}}+\frac{2 C \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}}{3 d f h}","\frac{2 \sqrt{c f-d e} \sqrt{\frac{d (e+f x)}{d e-c f}} \sqrt{\frac{d (g+h x)}{d g-c h}} \left(3 A d f h^2+C (c h (f g-e h)+d g (e h+2 f g))\right) F\left(\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right)}{3 d^2 f^{3/2} h^2 \sqrt{e+f x} \sqrt{g+h x}}-\frac{4 C \sqrt{g+h x} \sqrt{c f-d e} \sqrt{\frac{d (e+f x)}{d e-c f}} (c f h+d e h+d f g) E\left(\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right)}{3 d^2 f^{3/2} h^2 \sqrt{e+f x} \sqrt{\frac{d (g+h x)}{d g-c h}}}+\frac{2 C \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}}{3 d f h}",1,"(2*C*Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x])/(3*d*f*h) - (4*C*Sqrt[-(d*e) + c*f]*(d*f*g + d*e*h + c*f*h)*Sqrt[(d*(e + f*x))/(d*e - c*f)]*Sqrt[g + h*x]*EllipticE[ArcSin[(Sqrt[f]*Sqrt[c + d*x])/Sqrt[-(d*e) + c*f]], ((d*e - c*f)*h)/(f*(d*g - c*h))])/(3*d^2*f^(3/2)*h^2*Sqrt[e + f*x]*Sqrt[(d*(g + h*x))/(d*g - c*h)]) + (2*Sqrt[-(d*e) + c*f]*(3*A*d*f*h^2 + c*C*h*(f*g - e*h) + C*d*g*(2*f*g + e*h))*Sqrt[(d*(e + f*x))/(d*e - c*f)]*Sqrt[(d*(g + h*x))/(d*g - c*h)]*EllipticF[ArcSin[(Sqrt[f]*Sqrt[c + d*x])/Sqrt[-(d*e) + c*f]], ((d*e - c*f)*h)/(f*(d*g - c*h))])/(3*d^2*f^(3/2)*h^2*Sqrt[e + f*x]*Sqrt[g + h*x])","A",7,6,35,0.1714,1,"{1615, 158, 114, 113, 121, 120}"
29,1,465,0,0.8055066,"\int \frac{A+C x^2}{(a+b x) \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","Int[(A + C*x^2)/((a + b*x)*Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","-\frac{2 \left(\frac{a^2 C}{b^2}+A\right) \sqrt{c f-d e} \sqrt{\frac{d (e+f x)}{d e-c f}} \sqrt{\frac{d (g+h x)}{d g-c h}} \Pi \left(-\frac{b (d e-c f)}{(b c-a d) f};\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right)}{\sqrt{f} \sqrt{e+f x} \sqrt{g+h x} (b c-a d)}-\frac{2 C (a h+b g) \sqrt{c f-d e} \sqrt{\frac{d (e+f x)}{d e-c f}} \sqrt{\frac{d (g+h x)}{d g-c h}} F\left(\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right)}{b^2 d \sqrt{f} h \sqrt{e+f x} \sqrt{g+h x}}+\frac{2 C \sqrt{g+h x} \sqrt{c f-d e} \sqrt{\frac{d (e+f x)}{d e-c f}} E\left(\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right)}{b d \sqrt{f} h \sqrt{e+f x} \sqrt{\frac{d (g+h x)}{d g-c h}}}","-\frac{2 \left(\frac{a^2 C}{b^2}+A\right) \sqrt{c f-d e} \sqrt{\frac{d (e+f x)}{d e-c f}} \sqrt{\frac{d (g+h x)}{d g-c h}} \Pi \left(-\frac{b (d e-c f)}{(b c-a d) f};\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right)}{\sqrt{f} \sqrt{e+f x} \sqrt{g+h x} (b c-a d)}-\frac{2 C (a h+b g) \sqrt{c f-d e} \sqrt{\frac{d (e+f x)}{d e-c f}} \sqrt{\frac{d (g+h x)}{d g-c h}} F\left(\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right)}{b^2 d \sqrt{f} h \sqrt{e+f x} \sqrt{g+h x}}+\frac{2 C \sqrt{g+h x} \sqrt{c f-d e} \sqrt{\frac{d (e+f x)}{d e-c f}} E\left(\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right)}{b d \sqrt{f} h \sqrt{e+f x} \sqrt{\frac{d (g+h x)}{d g-c h}}}",1,"(2*C*Sqrt[-(d*e) + c*f]*Sqrt[(d*(e + f*x))/(d*e - c*f)]*Sqrt[g + h*x]*EllipticE[ArcSin[(Sqrt[f]*Sqrt[c + d*x])/Sqrt[-(d*e) + c*f]], ((d*e - c*f)*h)/(f*(d*g - c*h))])/(b*d*Sqrt[f]*h*Sqrt[e + f*x]*Sqrt[(d*(g + h*x))/(d*g - c*h)]) - (2*C*Sqrt[-(d*e) + c*f]*(b*g + a*h)*Sqrt[(d*(e + f*x))/(d*e - c*f)]*Sqrt[(d*(g + h*x))/(d*g - c*h)]*EllipticF[ArcSin[(Sqrt[f]*Sqrt[c + d*x])/Sqrt[-(d*e) + c*f]], ((d*e - c*f)*h)/(f*(d*g - c*h))])/(b^2*d*Sqrt[f]*h*Sqrt[e + f*x]*Sqrt[g + h*x]) - (2*(A + (a^2*C)/b^2)*Sqrt[-(d*e) + c*f]*Sqrt[(d*(e + f*x))/(d*e - c*f)]*Sqrt[(d*(g + h*x))/(d*g - c*h)]*EllipticPi[-((b*(d*e - c*f))/((b*c - a*d)*f)), ArcSin[(Sqrt[f]*Sqrt[c + d*x])/Sqrt[-(d*e) + c*f]], ((d*e - c*f)*h)/(f*(d*g - c*h))])/((b*c - a*d)*Sqrt[f]*Sqrt[e + f*x]*Sqrt[g + h*x])","A",11,9,42,0.2143,1,"{1607, 169, 538, 537, 158, 114, 113, 121, 120}"
30,1,738,0,1.9069705,"\int \frac{A+C x^2}{(a+b x)^2 \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","Int[(A + C*x^2)/((a + b*x)^2*Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","-\frac{\sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x} \left(a^2 C+A b^2\right)}{(a+b x) (b c-a d) (b e-a f) (b g-a h)}+\frac{\sqrt{c f-d e} \sqrt{\frac{d (e+f x)}{d e-c f}} \sqrt{\frac{d (g+h x)}{d g-c h}} \left(a^2 C d f-2 a b C (c f+d e)+b^2 (2 c C e-A d f)\right) F\left(\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right)}{b^2 d \sqrt{f} \sqrt{e+f x} \sqrt{g+h x} (b c-a d) (b e-a f)}-\frac{\sqrt{c f-d e} \sqrt{\frac{d (e+f x)}{d e-c f}} \sqrt{\frac{d (g+h x)}{d g-c h}} \left(-3 a^2 b^2 (A d f h-C (c e h+c f g+d e g))-2 a^3 b C (c f h+d e h+d f g)+a^4 C d f h-2 a b^3 (-A c f h-A d e h-A d f g+2 c C e g)-A b^4 (c e h+c f g+d e g)\right) \Pi \left(-\frac{b (d e-c f)}{(b c-a d) f};\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right)}{b^2 \sqrt{f} \sqrt{e+f x} \sqrt{g+h x} (b c-a d)^2 (b e-a f) (b g-a h)}+\frac{\sqrt{f} \sqrt{g+h x} \left(\frac{a^2 C}{b}+A b\right) \sqrt{c f-d e} \sqrt{\frac{d (e+f x)}{d e-c f}} E\left(\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right)}{\sqrt{e+f x} (b c-a d) (b e-a f) (b g-a h) \sqrt{\frac{d (g+h x)}{d g-c h}}}","-\frac{\sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x} \left(a^2 C+A b^2\right)}{(a+b x) (b c-a d) (b e-a f) (b g-a h)}+\frac{\sqrt{c f-d e} \sqrt{\frac{d (e+f x)}{d e-c f}} \sqrt{\frac{d (g+h x)}{d g-c h}} \left(a^2 C d f-2 a b C (c f+d e)+b^2 (2 c C e-A d f)\right) F\left(\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right)}{b^2 d \sqrt{f} \sqrt{e+f x} \sqrt{g+h x} (b c-a d) (b e-a f)}-\frac{\sqrt{c f-d e} \sqrt{\frac{d (e+f x)}{d e-c f}} \sqrt{\frac{d (g+h x)}{d g-c h}} \left(-3 a^2 b^2 (A d f h-C (c e h+c f g+d e g))-2 a^3 b C (c f h+d e h+d f g)+a^4 C d f h-2 a b^3 (-A c f h-A d e h-A d f g+2 c C e g)-A b^4 (c e h+c f g+d e g)\right) \Pi \left(-\frac{b (d e-c f)}{(b c-a d) f};\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right)}{b^2 \sqrt{f} \sqrt{e+f x} \sqrt{g+h x} (b c-a d)^2 (b e-a f) (b g-a h)}+\frac{\sqrt{f} \sqrt{g+h x} \left(\frac{a^2 C}{b}+A b\right) \sqrt{c f-d e} \sqrt{\frac{d (e+f x)}{d e-c f}} E\left(\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{c+d x}}{\sqrt{c f-d e}}\right)|\frac{(d e-c f) h}{f (d g-c h)}\right)}{\sqrt{e+f x} (b c-a d) (b e-a f) (b g-a h) \sqrt{\frac{d (g+h x)}{d g-c h}}}",1,"-(((A*b^2 + a^2*C)*Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x])/((b*c - a*d)*(b*e - a*f)*(b*g - a*h)*(a + b*x))) + ((A*b + (a^2*C)/b)*Sqrt[f]*Sqrt[-(d*e) + c*f]*Sqrt[(d*(e + f*x))/(d*e - c*f)]*Sqrt[g + h*x]*EllipticE[ArcSin[(Sqrt[f]*Sqrt[c + d*x])/Sqrt[-(d*e) + c*f]], ((d*e - c*f)*h)/(f*(d*g - c*h))])/((b*c - a*d)*(b*e - a*f)*(b*g - a*h)*Sqrt[e + f*x]*Sqrt[(d*(g + h*x))/(d*g - c*h)]) + (Sqrt[-(d*e) + c*f]*(a^2*C*d*f - 2*a*b*C*(d*e + c*f) + b^2*(2*c*C*e - A*d*f))*Sqrt[(d*(e + f*x))/(d*e - c*f)]*Sqrt[(d*(g + h*x))/(d*g - c*h)]*EllipticF[ArcSin[(Sqrt[f]*Sqrt[c + d*x])/Sqrt[-(d*e) + c*f]], ((d*e - c*f)*h)/(f*(d*g - c*h))])/(b^2*d*(b*c - a*d)*Sqrt[f]*(b*e - a*f)*Sqrt[e + f*x]*Sqrt[g + h*x]) - (Sqrt[-(d*e) + c*f]*(a^4*C*d*f*h - A*b^4*(d*e*g + c*f*g + c*e*h) - 2*a^3*b*C*(d*f*g + d*e*h + c*f*h) - 2*a*b^3*(2*c*C*e*g - A*d*f*g - A*d*e*h - A*c*f*h) - 3*a^2*b^2*(A*d*f*h - C*(d*e*g + c*f*g + c*e*h)))*Sqrt[(d*(e + f*x))/(d*e - c*f)]*Sqrt[(d*(g + h*x))/(d*g - c*h)]*EllipticPi[-((b*(d*e - c*f))/((b*c - a*d)*f)), ArcSin[(Sqrt[f]*Sqrt[c + d*x])/Sqrt[-(d*e) + c*f]], ((d*e - c*f)*h)/(f*(d*g - c*h))])/(b^2*(b*c - a*d)^2*Sqrt[f]*(b*e - a*f)*(b*g - a*h)*Sqrt[e + f*x]*Sqrt[g + h*x])","A",12,10,42,0.2381,1,"{1605, 1607, 169, 538, 537, 158, 114, 113, 121, 120}"
31,1,1376,0,5.742309,"\int \frac{(a+b x)^{3/2} \left(A+C x^2\right)}{\sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","Int[((a + b*x)^(3/2)*(A + C*x^2))/(Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","\frac{C \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x} (a+b x)^{3/2}}{3 d f h}-\frac{\sqrt{c h-d g} \left((a d f h+b (d f g+d e h+c f h)) \left(24 A d^2 f^2 h^2 b^2+15 C (d f g+d e h+c f h)^2 b^2-16 C d f h (d e g+c f g+c e h) b^2-22 a C d f h (d f g+d e h+c f h) b+3 a^2 C d^2 f^2 h^2\right)+4 b d f h \left(C (b (d e g+c f g+c e h)+a (d f g+d e h+c f h)) (3 a d f h-5 b (d f g+d e h+c f h))+2 d f h \left(2 C (d f g+d e h+c f h) a^2-b (12 A d f h-5 C (d e g+c f g+c e h)) a+3 b^2 c C e g\right)\right)\right) \sqrt{\frac{(b g-a h) (c+d x)}{(d g-c h) (a+b x)}} \sqrt{\frac{(b g-a h) (e+f x)}{(f g-e h) (a+b x)}} \Pi \left(-\frac{b (d g-c h)}{(b c-a d) h};\sin ^{-1}\left(\frac{\sqrt{b c-a d} \sqrt{g+h x}}{\sqrt{c h-d g} \sqrt{a+b x}}\right)|\frac{(b e-a f) (d g-c h)}{(b c-a d) (f g-e h)}\right) (a+b x)}{24 b^2 d^3 \sqrt{b c-a d} f^3 h^4 \sqrt{c+d x} \sqrt{e+f x}}-\frac{\sqrt{d g-c h} \sqrt{f g-e h} \left(24 A d^2 f^2 h^2 b^2+15 C (d f g+d e h+c f h)^2 b^2-16 C d f h (d e g+c f g+c e h) b^2-22 a C d f h (d f g+d e h+c f h) b+3 a^2 C d^2 f^2 h^2\right) \sqrt{-\frac{(d e-c f) (g+h x)}{(f g-e h) (c+d x)}} E\left(\sin ^{-1}\left(\frac{\sqrt{d g-c h} \sqrt{e+f x}}{\sqrt{f g-e h} \sqrt{c+d x}}\right)|\frac{(b c-a d) (f g-e h)}{(b e-a f) (d g-c h)}\right) \sqrt{a+b x}}{24 b d^3 f^3 h^3 \sqrt{\frac{(d e-c f) (a+b x)}{(b e-a f) (c+d x)}} \sqrt{g+h x}}+\frac{C (3 a d f h-5 b (d f g+d e h+c f h)) \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x} \sqrt{a+b x}}{12 d^2 f^2 h^2}+\frac{\left(24 A b f h d^2+\frac{3 a^2 C f h d^2}{b}-16 b C (d e g+c f g+c e h) d-22 a C (d f g+d e h+c f h) d+\frac{15 b C (d f g+d e h+c f h)^2}{f h}\right) \sqrt{e+f x} \sqrt{g+h x} \sqrt{a+b x}}{24 d^2 f^2 h^2 \sqrt{c+d x}}+\frac{(b e-a f) \sqrt{b g-a h} \left(-\left(24 A d^2 f^2 h^2+C \left(\left(15 f^2 g^2+14 e f h g+15 e^2 h^2\right) d^2+4 c f h (f g+e h) d+5 c^2 f^2 h^2\right)\right) b^2+6 a C d f h (c f h+2 d (f g+e h)) b+3 a^2 C d^2 f^2 h^2\right) \sqrt{\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}} \sqrt{g+h x} F\left(\sin ^{-1}\left(\frac{\sqrt{b g-a h} \sqrt{e+f x}}{\sqrt{f g-e h} \sqrt{a+b x}}\right)|-\frac{(b c-a d) (f g-e h)}{(d e-c f) (b g-a h)}\right)}{24 b^2 d^2 f^3 h^3 \sqrt{f g-e h} \sqrt{c+d x} \sqrt{-\frac{(b e-a f) (g+h x)}{(f g-e h) (a+b x)}}}","\frac{C \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x} (a+b x)^{3/2}}{3 d f h}-\frac{\sqrt{c h-d g} \left(4 b d f h \left(C (b (d e g+c f g+c e h)+a (d f g+d e h+c f h)) (3 a d f h-5 b (d f g+d e h+c f h))+2 d f h \left(2 C (d f g+d e h+c f h) a^2-b (12 A d f h-5 C (d e g+c f g+c e h)) a+3 b^2 c C e g\right)\right)+(a d f h+b (d f g+d e h+c f h)) (C (3 a d f h-5 b (d f g+d e h+c f h)) (a d f h-3 b (d f g+d e h+c f h))+8 b d f h (3 A b d f h-C (2 b (d e g+c f g+c e h)+a (d f g+d e h+c f h))))\right) \sqrt{\frac{(b g-a h) (c+d x)}{(d g-c h) (a+b x)}} \sqrt{\frac{(b g-a h) (e+f x)}{(f g-e h) (a+b x)}} \Pi \left(-\frac{b (d g-c h)}{(b c-a d) h};\sin ^{-1}\left(\frac{\sqrt{b c-a d} \sqrt{g+h x}}{\sqrt{c h-d g} \sqrt{a+b x}}\right)|\frac{(b e-a f) (d g-c h)}{(b c-a d) (f g-e h)}\right) (a+b x)}{24 b^2 d^3 \sqrt{b c-a d} f^3 h^4 \sqrt{c+d x} \sqrt{e+f x}}-\frac{\sqrt{d g-c h} \sqrt{f g-e h} (C (3 a d f h-5 b (d f g+d e h+c f h)) (a d f h-3 b (d f g+d e h+c f h))+8 b d f h (3 A b d f h-C (2 b (d e g+c f g+c e h)+a (d f g+d e h+c f h)))) \sqrt{-\frac{(d e-c f) (g+h x)}{(f g-e h) (c+d x)}} E\left(\sin ^{-1}\left(\frac{\sqrt{d g-c h} \sqrt{e+f x}}{\sqrt{f g-e h} \sqrt{c+d x}}\right)|\frac{(b c-a d) (f g-e h)}{(b e-a f) (d g-c h)}\right) \sqrt{a+b x}}{24 b d^3 f^3 h^3 \sqrt{\frac{(d e-c f) (a+b x)}{(b e-a f) (c+d x)}} \sqrt{g+h x}}+\frac{C (3 a d f h-5 b (d f g+d e h+c f h)) \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x} \sqrt{a+b x}}{12 d^2 f^2 h^2}+\frac{(C (3 a d f h-5 b (d f g+d e h+c f h)) (a d f h-3 b (d f g+d e h+c f h))+8 b d f h (3 A b d f h-C (2 b (d e g+c f g+c e h)+a (d f g+d e h+c f h)))) \sqrt{e+f x} \sqrt{g+h x} \sqrt{a+b x}}{24 b d^2 f^3 h^3 \sqrt{c+d x}}+\frac{(b e-a f) \sqrt{b g-a h} \left(-\left(24 A d^2 f^2 h^2+C \left(\left(15 f^2 g^2+14 e f h g+15 e^2 h^2\right) d^2+4 c f h (f g+e h) d+5 c^2 f^2 h^2\right)\right) b^2+6 a C d f h (c f h+2 d (f g+e h)) b+3 a^2 C d^2 f^2 h^2\right) \sqrt{\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}} \sqrt{g+h x} F\left(\sin ^{-1}\left(\frac{\sqrt{b g-a h} \sqrt{e+f x}}{\sqrt{f g-e h} \sqrt{a+b x}}\right)|-\frac{(b c-a d) (f g-e h)}{(d e-c f) (b g-a h)}\right)}{24 b^2 d^2 f^3 h^3 \sqrt{f g-e h} \sqrt{c+d x} \sqrt{-\frac{(b e-a f) (g+h x)}{(f g-e h) (a+b x)}}}",1,"((24*A*b*d^2*f*h + (3*a^2*C*d^2*f*h)/b - 16*b*C*d*(d*e*g + c*f*g + c*e*h) - 22*a*C*d*(d*f*g + d*e*h + c*f*h) + (15*b*C*(d*f*g + d*e*h + c*f*h)^2)/(f*h))*Sqrt[a + b*x]*Sqrt[e + f*x]*Sqrt[g + h*x])/(24*d^2*f^2*h^2*Sqrt[c + d*x]) + (C*(3*a*d*f*h - 5*b*(d*f*g + d*e*h + c*f*h))*Sqrt[a + b*x]*Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x])/(12*d^2*f^2*h^2) + (C*(a + b*x)^(3/2)*Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x])/(3*d*f*h) - (Sqrt[d*g - c*h]*Sqrt[f*g - e*h]*(24*A*b^2*d^2*f^2*h^2 + 3*a^2*C*d^2*f^2*h^2 - 16*b^2*C*d*f*h*(d*e*g + c*f*g + c*e*h) - 22*a*b*C*d*f*h*(d*f*g + d*e*h + c*f*h) + 15*b^2*C*(d*f*g + d*e*h + c*f*h)^2)*Sqrt[a + b*x]*Sqrt[-(((d*e - c*f)*(g + h*x))/((f*g - e*h)*(c + d*x)))]*EllipticE[ArcSin[(Sqrt[d*g - c*h]*Sqrt[e + f*x])/(Sqrt[f*g - e*h]*Sqrt[c + d*x])], ((b*c - a*d)*(f*g - e*h))/((b*e - a*f)*(d*g - c*h))])/(24*b*d^3*f^3*h^3*Sqrt[((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x))]*Sqrt[g + h*x]) + ((b*e - a*f)*Sqrt[b*g - a*h]*(3*a^2*C*d^2*f^2*h^2 + 6*a*b*C*d*f*h*(c*f*h + 2*d*(f*g + e*h)) - b^2*(24*A*d^2*f^2*h^2 + C*(5*c^2*f^2*h^2 + 4*c*d*f*h*(f*g + e*h) + d^2*(15*f^2*g^2 + 14*e*f*g*h + 15*e^2*h^2))))*Sqrt[((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))]*Sqrt[g + h*x]*EllipticF[ArcSin[(Sqrt[b*g - a*h]*Sqrt[e + f*x])/(Sqrt[f*g - e*h]*Sqrt[a + b*x])], -(((b*c - a*d)*(f*g - e*h))/((d*e - c*f)*(b*g - a*h)))])/(24*b^2*d^2*f^3*h^3*Sqrt[f*g - e*h]*Sqrt[c + d*x]*Sqrt[-(((b*e - a*f)*(g + h*x))/((f*g - e*h)*(a + b*x)))]) - (Sqrt[-(d*g) + c*h]*((a*d*f*h + b*(d*f*g + d*e*h + c*f*h))*(24*A*b^2*d^2*f^2*h^2 + 3*a^2*C*d^2*f^2*h^2 - 16*b^2*C*d*f*h*(d*e*g + c*f*g + c*e*h) - 22*a*b*C*d*f*h*(d*f*g + d*e*h + c*f*h) + 15*b^2*C*(d*f*g + d*e*h + c*f*h)^2) + 4*b*d*f*h*(C*(b*(d*e*g + c*f*g + c*e*h) + a*(d*f*g + d*e*h + c*f*h))*(3*a*d*f*h - 5*b*(d*f*g + d*e*h + c*f*h)) + 2*d*f*h*(3*b^2*c*C*e*g + 2*a^2*C*(d*f*g + d*e*h + c*f*h) - a*b*(12*A*d*f*h - 5*C*(d*e*g + c*f*g + c*e*h)))))*(a + b*x)*Sqrt[((b*g - a*h)*(c + d*x))/((d*g - c*h)*(a + b*x))]*Sqrt[((b*g - a*h)*(e + f*x))/((f*g - e*h)*(a + b*x))]*EllipticPi[-((b*(d*g - c*h))/((b*c - a*d)*h)), ArcSin[(Sqrt[b*c - a*d]*Sqrt[g + h*x])/(Sqrt[-(d*g) + c*h]*Sqrt[a + b*x])], ((b*e - a*f)*(d*g - c*h))/((b*c - a*d)*(f*g - e*h))])/(24*b^2*d^3*Sqrt[b*c - a*d]*f^3*h^4*Sqrt[c + d*x]*Sqrt[e + f*x])","A",10,10,44,0.2273,1,"{1601, 1600, 1602, 1598, 170, 419, 165, 537, 176, 424}"
32,1,936,0,2.2834648,"\int \frac{\sqrt{a+b x} \left(A+C x^2\right)}{\sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","Int[(Sqrt[a + b*x]*(A + C*x^2))/(Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","-\frac{\sqrt{d g-c h} \sqrt{f g-e h} (a d f h-3 b (d f g+d e h+c f h)) \sqrt{a+b x} \sqrt{-\frac{(d e-c f) (g+h x)}{(f g-e h) (c+d x)}} E\left(\sin ^{-1}\left(\frac{\sqrt{d g-c h} \sqrt{e+f x}}{\sqrt{f g-e h} \sqrt{c+d x}}\right)|\frac{(b c-a d) (f g-e h)}{(b e-a f) (d g-c h)}\right) C}{4 b d^2 f^2 h^2 \sqrt{\frac{(d e-c f) (a+b x)}{(b e-a f) (c+d x)}} \sqrt{g+h x}}+\frac{(b e-a f) \sqrt{b g-a h} (b c f h+a d f h+3 b d (f g+e h)) \sqrt{\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}} \sqrt{g+h x} F\left(\sin ^{-1}\left(\frac{\sqrt{b g-a h} \sqrt{e+f x}}{\sqrt{f g-e h} \sqrt{a+b x}}\right)|-\frac{(b c-a d) (f g-e h)}{(d e-c f) (b g-a h)}\right) C}{4 b^2 d f^2 h^2 \sqrt{f g-e h} \sqrt{c+d x} \sqrt{-\frac{(b e-a f) (g+h x)}{(f g-e h) (a+b x)}}}+\frac{\sqrt{a+b x} \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x} C}{2 d f h}+\frac{(a d f h-3 b (d f g+d e h+c f h)) \sqrt{a+b x} \sqrt{e+f x} \sqrt{g+h x} C}{4 b d f^2 h^2 \sqrt{c+d x}}-\frac{\sqrt{c h-d g} (C (a d f h-3 b (d f g+d e h+c f h)) (a d f h+b (d f g+d e h+c f h))-4 b d f h (2 A b d f h-C (b (d e g+c f g+c e h)+a (d f g+d e h+c f h)))) (a+b x) \sqrt{\frac{(b g-a h) (c+d x)}{(d g-c h) (a+b x)}} \sqrt{\frac{(b g-a h) (e+f x)}{(f g-e h) (a+b x)}} \Pi \left(-\frac{b (d g-c h)}{(b c-a d) h};\sin ^{-1}\left(\frac{\sqrt{b c-a d} \sqrt{g+h x}}{\sqrt{c h-d g} \sqrt{a+b x}}\right)|\frac{(b e-a f) (d g-c h)}{(b c-a d) (f g-e h)}\right)}{4 b^2 d^2 \sqrt{b c-a d} f^2 h^3 \sqrt{c+d x} \sqrt{e+f x}}","-\frac{\sqrt{d g-c h} \sqrt{f g-e h} (a d f h-3 b (d f g+d e h+c f h)) \sqrt{a+b x} \sqrt{-\frac{(d e-c f) (g+h x)}{(f g-e h) (c+d x)}} E\left(\sin ^{-1}\left(\frac{\sqrt{d g-c h} \sqrt{e+f x}}{\sqrt{f g-e h} \sqrt{c+d x}}\right)|\frac{(b c-a d) (f g-e h)}{(b e-a f) (d g-c h)}\right) C}{4 b d^2 f^2 h^2 \sqrt{\frac{(d e-c f) (a+b x)}{(b e-a f) (c+d x)}} \sqrt{g+h x}}+\frac{(b e-a f) \sqrt{b g-a h} (a d f h+b (c f h+3 d (f g+e h))) \sqrt{\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}} \sqrt{g+h x} F\left(\sin ^{-1}\left(\frac{\sqrt{b g-a h} \sqrt{e+f x}}{\sqrt{f g-e h} \sqrt{a+b x}}\right)|-\frac{(b c-a d) (f g-e h)}{(d e-c f) (b g-a h)}\right) C}{4 b^2 d f^2 h^2 \sqrt{f g-e h} \sqrt{c+d x} \sqrt{-\frac{(b e-a f) (g+h x)}{(f g-e h) (a+b x)}}}+\frac{\sqrt{a+b x} \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x} C}{2 d f h}+\frac{(a d f h-3 b (d f g+d e h+c f h)) \sqrt{a+b x} \sqrt{e+f x} \sqrt{g+h x} C}{4 b d f^2 h^2 \sqrt{c+d x}}-\frac{\sqrt{c h-d g} (C (a d f h-3 b (d f g+d e h+c f h)) (a d f h+b (d f g+d e h+c f h))-4 b d f h (2 A b d f h-C (b (d e g+c f g+c e h)+a (d f g+d e h+c f h)))) (a+b x) \sqrt{\frac{(b g-a h) (c+d x)}{(d g-c h) (a+b x)}} \sqrt{\frac{(b g-a h) (e+f x)}{(f g-e h) (a+b x)}} \Pi \left(-\frac{b (d g-c h)}{(b c-a d) h};\sin ^{-1}\left(\frac{\sqrt{b c-a d} \sqrt{g+h x}}{\sqrt{c h-d g} \sqrt{a+b x}}\right)|\frac{(b e-a f) (d g-c h)}{(b c-a d) (f g-e h)}\right)}{4 b^2 d^2 \sqrt{b c-a d} f^2 h^3 \sqrt{c+d x} \sqrt{e+f x}}",1,"(C*(a*d*f*h - 3*b*(d*f*g + d*e*h + c*f*h))*Sqrt[a + b*x]*Sqrt[e + f*x]*Sqrt[g + h*x])/(4*b*d*f^2*h^2*Sqrt[c + d*x]) + (C*Sqrt[a + b*x]*Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x])/(2*d*f*h) - (C*Sqrt[d*g - c*h]*Sqrt[f*g - e*h]*(a*d*f*h - 3*b*(d*f*g + d*e*h + c*f*h))*Sqrt[a + b*x]*Sqrt[-(((d*e - c*f)*(g + h*x))/((f*g - e*h)*(c + d*x)))]*EllipticE[ArcSin[(Sqrt[d*g - c*h]*Sqrt[e + f*x])/(Sqrt[f*g - e*h]*Sqrt[c + d*x])], ((b*c - a*d)*(f*g - e*h))/((b*e - a*f)*(d*g - c*h))])/(4*b*d^2*f^2*h^2*Sqrt[((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x))]*Sqrt[g + h*x]) + (C*(b*e - a*f)*Sqrt[b*g - a*h]*(b*c*f*h + a*d*f*h + 3*b*d*(f*g + e*h))*Sqrt[((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))]*Sqrt[g + h*x]*EllipticF[ArcSin[(Sqrt[b*g - a*h]*Sqrt[e + f*x])/(Sqrt[f*g - e*h]*Sqrt[a + b*x])], -(((b*c - a*d)*(f*g - e*h))/((d*e - c*f)*(b*g - a*h)))])/(4*b^2*d*f^2*h^2*Sqrt[f*g - e*h]*Sqrt[c + d*x]*Sqrt[-(((b*e - a*f)*(g + h*x))/((f*g - e*h)*(a + b*x)))]) - (Sqrt[-(d*g) + c*h]*(C*(a*d*f*h - 3*b*(d*f*g + d*e*h + c*f*h))*(a*d*f*h + b*(d*f*g + d*e*h + c*f*h)) - 4*b*d*f*h*(2*A*b*d*f*h - C*(b*(d*e*g + c*f*g + c*e*h) + a*(d*f*g + d*e*h + c*f*h))))*(a + b*x)*Sqrt[((b*g - a*h)*(c + d*x))/((d*g - c*h)*(a + b*x))]*Sqrt[((b*g - a*h)*(e + f*x))/((f*g - e*h)*(a + b*x))]*EllipticPi[-((b*(d*g - c*h))/((b*c - a*d)*h)), ArcSin[(Sqrt[b*c - a*d]*Sqrt[g + h*x])/(Sqrt[-(d*g) + c*h]*Sqrt[a + b*x])], ((b*e - a*f)*(d*g - c*h))/((b*c - a*d)*(f*g - e*h))])/(4*b^2*d^2*Sqrt[b*c - a*d]*f^2*h^3*Sqrt[c + d*x]*Sqrt[e + f*x])","A",9,9,44,0.2045,1,"{1601, 1602, 1598, 170, 419, 165, 537, 176, 424}"
33,1,757,0,1.0259762,"\int \frac{A+C x^2}{\sqrt{a+b x} \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","Int[(A + C*x^2)/(Sqrt[a + b*x]*Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","\frac{\sqrt{g+h x} \sqrt{\frac{(c+d x) (b e-a f)}{(a+b x) (d e-c f)}} \left(a^2 C f h+a b C (e h+f g)-b^2 (C e g-2 A f h)\right) F\left(\sin ^{-1}\left(\frac{\sqrt{b g-a h} \sqrt{e+f x}}{\sqrt{f g-e h} \sqrt{a+b x}}\right)|-\frac{(b c-a d) (f g-e h)}{(d e-c f) (b g-a h)}\right)}{b^2 f h \sqrt{c+d x} \sqrt{b g-a h} \sqrt{f g-e h} \sqrt{-\frac{(g+h x) (b e-a f)}{(a+b x) (f g-e h)}}}-\frac{C (a+b x) \sqrt{c h-d g} \sqrt{\frac{(c+d x) (b g-a h)}{(a+b x) (d g-c h)}} \sqrt{\frac{(e+f x) (b g-a h)}{(a+b x) (f g-e h)}} (a d f h+b (c f h+d e h+d f g)) \Pi \left(-\frac{b (d g-c h)}{(b c-a d) h};\sin ^{-1}\left(\frac{\sqrt{b c-a d} \sqrt{g+h x}}{\sqrt{c h-d g} \sqrt{a+b x}}\right)|\frac{(b e-a f) (d g-c h)}{(b c-a d) (f g-e h)}\right)}{b^2 d f h^2 \sqrt{c+d x} \sqrt{e+f x} \sqrt{b c-a d}}+\frac{C \sqrt{a+b x} \sqrt{e+f x} \sqrt{g+h x}}{b f h \sqrt{c+d x}}-\frac{C \sqrt{a+b x} \sqrt{d g-c h} \sqrt{f g-e h} \sqrt{-\frac{(g+h x) (d e-c f)}{(c+d x) (f g-e h)}} E\left(\sin ^{-1}\left(\frac{\sqrt{d g-c h} \sqrt{e+f x}}{\sqrt{f g-e h} \sqrt{c+d x}}\right)|\frac{(b c-a d) (f g-e h)}{(b e-a f) (d g-c h)}\right)}{b d f h \sqrt{g+h x} \sqrt{\frac{(a+b x) (d e-c f)}{(c+d x) (b e-a f)}}}","\frac{\sqrt{g+h x} \sqrt{\frac{(c+d x) (b e-a f)}{(a+b x) (d e-c f)}} \left(a^2 C f h+a b C (e h+f g)-b^2 (C e g-2 A f h)\right) F\left(\sin ^{-1}\left(\frac{\sqrt{b g-a h} \sqrt{e+f x}}{\sqrt{f g-e h} \sqrt{a+b x}}\right)|-\frac{(b c-a d) (f g-e h)}{(d e-c f) (b g-a h)}\right)}{b^2 f h \sqrt{c+d x} \sqrt{b g-a h} \sqrt{f g-e h} \sqrt{-\frac{(g+h x) (b e-a f)}{(a+b x) (f g-e h)}}}-\frac{C (a+b x) \sqrt{c h-d g} \sqrt{\frac{(c+d x) (b g-a h)}{(a+b x) (d g-c h)}} \sqrt{\frac{(e+f x) (b g-a h)}{(a+b x) (f g-e h)}} (a d f h+b (c f h+d e h+d f g)) \Pi \left(-\frac{b (d g-c h)}{(b c-a d) h};\sin ^{-1}\left(\frac{\sqrt{b c-a d} \sqrt{g+h x}}{\sqrt{c h-d g} \sqrt{a+b x}}\right)|\frac{(b e-a f) (d g-c h)}{(b c-a d) (f g-e h)}\right)}{b^2 d f h^2 \sqrt{c+d x} \sqrt{e+f x} \sqrt{b c-a d}}+\frac{C \sqrt{a+b x} \sqrt{e+f x} \sqrt{g+h x}}{b f h \sqrt{c+d x}}-\frac{C \sqrt{a+b x} \sqrt{d g-c h} \sqrt{f g-e h} \sqrt{-\frac{(g+h x) (d e-c f)}{(c+d x) (f g-e h)}} E\left(\sin ^{-1}\left(\frac{\sqrt{d g-c h} \sqrt{e+f x}}{\sqrt{f g-e h} \sqrt{c+d x}}\right)|\frac{(b c-a d) (f g-e h)}{(b e-a f) (d g-c h)}\right)}{b d f h \sqrt{g+h x} \sqrt{\frac{(a+b x) (d e-c f)}{(c+d x) (b e-a f)}}}",1,"(C*Sqrt[a + b*x]*Sqrt[e + f*x]*Sqrt[g + h*x])/(b*f*h*Sqrt[c + d*x]) - (C*Sqrt[d*g - c*h]*Sqrt[f*g - e*h]*Sqrt[a + b*x]*Sqrt[-(((d*e - c*f)*(g + h*x))/((f*g - e*h)*(c + d*x)))]*EllipticE[ArcSin[(Sqrt[d*g - c*h]*Sqrt[e + f*x])/(Sqrt[f*g - e*h]*Sqrt[c + d*x])], ((b*c - a*d)*(f*g - e*h))/((b*e - a*f)*(d*g - c*h))])/(b*d*f*h*Sqrt[((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x))]*Sqrt[g + h*x]) + ((a^2*C*f*h + a*b*C*(f*g + e*h) - b^2*(C*e*g - 2*A*f*h))*Sqrt[((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))]*Sqrt[g + h*x]*EllipticF[ArcSin[(Sqrt[b*g - a*h]*Sqrt[e + f*x])/(Sqrt[f*g - e*h]*Sqrt[a + b*x])], -(((b*c - a*d)*(f*g - e*h))/((d*e - c*f)*(b*g - a*h)))])/(b^2*f*h*Sqrt[b*g - a*h]*Sqrt[f*g - e*h]*Sqrt[c + d*x]*Sqrt[-(((b*e - a*f)*(g + h*x))/((f*g - e*h)*(a + b*x)))]) - (C*Sqrt[-(d*g) + c*h]*(a*d*f*h + b*(d*f*g + d*e*h + c*f*h))*(a + b*x)*Sqrt[((b*g - a*h)*(c + d*x))/((d*g - c*h)*(a + b*x))]*Sqrt[((b*g - a*h)*(e + f*x))/((f*g - e*h)*(a + b*x))]*EllipticPi[-((b*(d*g - c*h))/((b*c - a*d)*h)), ArcSin[(Sqrt[b*c - a*d]*Sqrt[g + h*x])/(Sqrt[-(d*g) + c*h]*Sqrt[a + b*x])], ((b*e - a*f)*(d*g - c*h))/((b*c - a*d)*(f*g - e*h))])/(b^2*d*Sqrt[b*c - a*d]*f*h^2*Sqrt[c + d*x]*Sqrt[e + f*x])","A",8,8,44,0.1818,1,"{1603, 1598, 170, 419, 165, 537, 176, 424}"
34,1,867,0,1.8130483,"\int \frac{A+C x^2}{(a+b x)^{3/2} \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","Int[(A + C*x^2)/((a + b*x)^(3/2)*Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","-\frac{2 \sqrt{d g-c h} \sqrt{f g-e h} \sqrt{a+b x} \sqrt{-\frac{(d e-c f) (g+h x)}{(f g-e h) (c+d x)}} E\left(\sin ^{-1}\left(\frac{\sqrt{d g-c h} \sqrt{e+f x}}{\sqrt{f g-e h} \sqrt{c+d x}}\right)|\frac{(b c-a d) (f g-e h)}{(b e-a f) (d g-c h)}\right) \left(C a^2+A b^2\right)}{b (b c-a d) (b e-a f) (b g-a h) \sqrt{\frac{(d e-c f) (a+b x)}{(b e-a f) (c+d x)}} \sqrt{g+h x}}-\frac{2 \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x} \left(C a^2+A b^2\right)}{(b c-a d) (b e-a f) (b g-a h) \sqrt{a+b x}}+\frac{2 d \sqrt{a+b x} \sqrt{e+f x} \sqrt{g+h x} \left(C a^2+A b^2\right)}{b (b c-a d) (b e-a f) (b g-a h) \sqrt{c+d x}}-\frac{2 \left(-C d a^2+2 b c C a+A b^2 d\right) \sqrt{\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}} \sqrt{g+h x} F\left(\sin ^{-1}\left(\frac{\sqrt{b g-a h} \sqrt{e+f x}}{\sqrt{f g-e h} \sqrt{a+b x}}\right)|-\frac{(b c-a d) (f g-e h)}{(d e-c f) (b g-a h)}\right)}{b^2 (b c-a d) \sqrt{b g-a h} \sqrt{f g-e h} \sqrt{c+d x} \sqrt{-\frac{(b e-a f) (g+h x)}{(f g-e h) (a+b x)}}}+\frac{2 C \sqrt{c h-d g} (a+b x) \sqrt{\frac{(b g-a h) (c+d x)}{(d g-c h) (a+b x)}} \sqrt{\frac{(b g-a h) (e+f x)}{(f g-e h) (a+b x)}} \Pi \left(-\frac{b (d g-c h)}{(b c-a d) h};\sin ^{-1}\left(\frac{\sqrt{b c-a d} \sqrt{g+h x}}{\sqrt{c h-d g} \sqrt{a+b x}}\right)|\frac{(b e-a f) (d g-c h)}{(b c-a d) (f g-e h)}\right)}{b^2 \sqrt{b c-a d} h \sqrt{c+d x} \sqrt{e+f x}}","-\frac{2 \sqrt{d g-c h} \sqrt{f g-e h} \sqrt{a+b x} \sqrt{-\frac{(d e-c f) (g+h x)}{(f g-e h) (c+d x)}} E\left(\sin ^{-1}\left(\frac{\sqrt{d g-c h} \sqrt{e+f x}}{\sqrt{f g-e h} \sqrt{c+d x}}\right)|\frac{(b c-a d) (f g-e h)}{(b e-a f) (d g-c h)}\right) \left(C a^2+A b^2\right)}{b (b c-a d) (b e-a f) (b g-a h) \sqrt{\frac{(d e-c f) (a+b x)}{(b e-a f) (c+d x)}} \sqrt{g+h x}}-\frac{2 \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x} \left(C a^2+A b^2\right)}{(b c-a d) (b e-a f) (b g-a h) \sqrt{a+b x}}+\frac{2 d \sqrt{a+b x} \sqrt{e+f x} \sqrt{g+h x} \left(C a^2+A b^2\right)}{b (b c-a d) (b e-a f) (b g-a h) \sqrt{c+d x}}-\frac{2 \left(-C d a^2+2 b c C a+A b^2 d\right) \sqrt{\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}} \sqrt{g+h x} F\left(\sin ^{-1}\left(\frac{\sqrt{b g-a h} \sqrt{e+f x}}{\sqrt{f g-e h} \sqrt{a+b x}}\right)|-\frac{(b c-a d) (f g-e h)}{(d e-c f) (b g-a h)}\right)}{b^2 (b c-a d) \sqrt{b g-a h} \sqrt{f g-e h} \sqrt{c+d x} \sqrt{-\frac{(b e-a f) (g+h x)}{(f g-e h) (a+b x)}}}+\frac{2 C \sqrt{c h-d g} (a+b x) \sqrt{\frac{(b g-a h) (c+d x)}{(d g-c h) (a+b x)}} \sqrt{\frac{(b g-a h) (e+f x)}{(f g-e h) (a+b x)}} \Pi \left(-\frac{b (d g-c h)}{(b c-a d) h};\sin ^{-1}\left(\frac{\sqrt{b c-a d} \sqrt{g+h x}}{\sqrt{c h-d g} \sqrt{a+b x}}\right)|\frac{(b e-a f) (d g-c h)}{(b c-a d) (f g-e h)}\right)}{b^2 \sqrt{b c-a d} h \sqrt{c+d x} \sqrt{e+f x}}",1,"(2*(A*b^2 + a^2*C)*d*Sqrt[a + b*x]*Sqrt[e + f*x]*Sqrt[g + h*x])/(b*(b*c - a*d)*(b*e - a*f)*(b*g - a*h)*Sqrt[c + d*x]) - (2*(A*b^2 + a^2*C)*Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x])/((b*c - a*d)*(b*e - a*f)*(b*g - a*h)*Sqrt[a + b*x]) - (2*(A*b^2 + a^2*C)*Sqrt[d*g - c*h]*Sqrt[f*g - e*h]*Sqrt[a + b*x]*Sqrt[-(((d*e - c*f)*(g + h*x))/((f*g - e*h)*(c + d*x)))]*EllipticE[ArcSin[(Sqrt[d*g - c*h]*Sqrt[e + f*x])/(Sqrt[f*g - e*h]*Sqrt[c + d*x])], ((b*c - a*d)*(f*g - e*h))/((b*e - a*f)*(d*g - c*h))])/(b*(b*c - a*d)*(b*e - a*f)*(b*g - a*h)*Sqrt[((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x))]*Sqrt[g + h*x]) - (2*(2*a*b*c*C + A*b^2*d - a^2*C*d)*Sqrt[((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))]*Sqrt[g + h*x]*EllipticF[ArcSin[(Sqrt[b*g - a*h]*Sqrt[e + f*x])/(Sqrt[f*g - e*h]*Sqrt[a + b*x])], -(((b*c - a*d)*(f*g - e*h))/((d*e - c*f)*(b*g - a*h)))])/(b^2*(b*c - a*d)*Sqrt[b*g - a*h]*Sqrt[f*g - e*h]*Sqrt[c + d*x]*Sqrt[-(((b*e - a*f)*(g + h*x))/((f*g - e*h)*(a + b*x)))]) + (2*C*Sqrt[-(d*g) + c*h]*(a + b*x)*Sqrt[((b*g - a*h)*(c + d*x))/((d*g - c*h)*(a + b*x))]*Sqrt[((b*g - a*h)*(e + f*x))/((f*g - e*h)*(a + b*x))]*EllipticPi[-((b*(d*g - c*h))/((b*c - a*d)*h)), ArcSin[(Sqrt[b*c - a*d]*Sqrt[g + h*x])/(Sqrt[-(d*g) + c*h]*Sqrt[a + b*x])], ((b*e - a*f)*(d*g - c*h))/((b*c - a*d)*(f*g - e*h))])/(b^2*Sqrt[b*c - a*d]*h*Sqrt[c + d*x]*Sqrt[e + f*x])","A",9,9,44,0.2045,1,"{1605, 1602, 1598, 170, 419, 165, 537, 176, 424}"
35,1,1070,0,3.4540689,"\int \frac{A+C x^2}{(a+b x)^{5/2} \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","Int[(A + C*x^2)/((a + b*x)^(5/2)*Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","-\frac{2 \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x} \left(C a^2+A b^2\right)}{3 (b c-a d) (b e-a f) (b g-a h) (a+b x)^{3/2}}+\frac{4 \sqrt{d g-c h} \sqrt{f g-e h} \left(C (d f g+d e h+c f h) a^3+b (3 A d f h-2 C (d e g+c f g+c e h)) a^2-b^2 (2 A d (f g+e h)-c (3 C e g-2 A f h)) a+A b^3 (d e g+c f g+c e h)\right) \sqrt{a+b x} \sqrt{-\frac{(d e-c f) (g+h x)}{(f g-e h) (c+d x)}} E\left(\sin ^{-1}\left(\frac{\sqrt{d g-c h} \sqrt{e+f x}}{\sqrt{f g-e h} \sqrt{c+d x}}\right)|\frac{(b c-a d) (f g-e h)}{(b e-a f) (d g-c h)}\right)}{3 (b c-a d)^2 (b e-a f)^2 (b g-a h)^2 \sqrt{\frac{(d e-c f) (a+b x)}{(b e-a f) (c+d x)}} \sqrt{g+h x}}-\frac{2 \left(-\left(3 A d^2 f h-C \left(-2 f h c^2-d f g c-d e h c+d^2 e g\right)\right) a^2+3 b \left(C c^2+A d^2\right) (f g+e h) a-b^2 \left((3 C e g-A f h) c^2+A d (f g+e h) c+2 A d^2 e g\right)\right) \sqrt{\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}} \sqrt{g+h x} F\left(\sin ^{-1}\left(\frac{\sqrt{b g-a h} \sqrt{e+f x}}{\sqrt{f g-e h} \sqrt{a+b x}}\right)|-\frac{(b c-a d) (f g-e h)}{(d e-c f) (b g-a h)}\right)}{3 (b c-a d)^2 (b e-a f) (b g-a h)^{3/2} \sqrt{f g-e h} \sqrt{c+d x} \sqrt{-\frac{(b e-a f) (g+h x)}{(f g-e h) (a+b x)}}}+\frac{4 b \left(C (d f g+d e h+c f h) a^3+b (3 A d f h-2 C (d e g+c f g+c e h)) a^2-b^2 (2 A d (f g+e h)-c (3 C e g-2 A f h)) a+A b^3 (d e g+c f g+c e h)\right) \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}}{3 (b c-a d)^2 (b e-a f)^2 (b g-a h)^2 \sqrt{a+b x}}-\frac{4 d \left(C (d f g+d e h+c f h) a^3+b (3 A d f h-2 C (d e g+c f g+c e h)) a^2-b^2 (2 A d (f g+e h)-c (3 C e g-2 A f h)) a+A b^3 (d e g+c f g+c e h)\right) \sqrt{a+b x} \sqrt{e+f x} \sqrt{g+h x}}{3 (b c-a d)^2 (b e-a f)^2 (b g-a h)^2 \sqrt{c+d x}}","-\frac{2 \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x} \left(C a^2+A b^2\right)}{3 (b c-a d) (b e-a f) (b g-a h) (a+b x)^{3/2}}+\frac{4 \sqrt{d g-c h} \sqrt{f g-e h} \left(C (d f g+d e h+c f h) a^3+b (3 A d f h-2 C (d e g+c f g+c e h)) a^2-b^2 (2 A d (f g+e h)-c (3 C e g-2 A f h)) a+A b^3 (d e g+c f g+c e h)\right) \sqrt{a+b x} \sqrt{-\frac{(d e-c f) (g+h x)}{(f g-e h) (c+d x)}} E\left(\sin ^{-1}\left(\frac{\sqrt{d g-c h} \sqrt{e+f x}}{\sqrt{f g-e h} \sqrt{c+d x}}\right)|\frac{(b c-a d) (f g-e h)}{(b e-a f) (d g-c h)}\right)}{3 (b c-a d)^2 (b e-a f)^2 (b g-a h)^2 \sqrt{\frac{(d e-c f) (a+b x)}{(b e-a f) (c+d x)}} \sqrt{g+h x}}-\frac{2 \left(-\left(3 A d^2 f h-C \left(-2 f h c^2-d f g c-d e h c+d^2 e g\right)\right) a^2+3 b \left(C c^2+A d^2\right) (f g+e h) a-b^2 \left((3 C e g-A f h) c^2+A d (f g+e h) c+2 A d^2 e g\right)\right) \sqrt{\frac{(b e-a f) (c+d x)}{(d e-c f) (a+b x)}} \sqrt{g+h x} F\left(\sin ^{-1}\left(\frac{\sqrt{b g-a h} \sqrt{e+f x}}{\sqrt{f g-e h} \sqrt{a+b x}}\right)|-\frac{(b c-a d) (f g-e h)}{(d e-c f) (b g-a h)}\right)}{3 (b c-a d)^2 (b e-a f) (b g-a h)^{3/2} \sqrt{f g-e h} \sqrt{c+d x} \sqrt{-\frac{(b e-a f) (g+h x)}{(f g-e h) (a+b x)}}}+\frac{4 b \left(C (d f g+d e h+c f h) a^3+b (3 A d f h-2 C (d e g+c f g+c e h)) a^2-b^2 (2 A d (f g+e h)-c (3 C e g-2 A f h)) a+A b^3 (d e g+c f g+c e h)\right) \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}}{3 (b c-a d)^2 (b e-a f)^2 (b g-a h)^2 \sqrt{a+b x}}-\frac{4 d \left(C (d f g+d e h+c f h) a^3+b (3 A d f h-2 C (d e g+c f g+c e h)) a^2-b^2 (2 A d (f g+e h)-c (3 C e g-2 A f h)) a+A b^3 (d e g+c f g+c e h)\right) \sqrt{a+b x} \sqrt{e+f x} \sqrt{g+h x}}{3 (b c-a d)^2 (b e-a f)^2 (b g-a h)^2 \sqrt{c+d x}}",1,"(-4*d*(A*b^3*(d*e*g + c*f*g + c*e*h) + a^3*C*(d*f*g + d*e*h + c*f*h) + a^2*b*(3*A*d*f*h - 2*C*(d*e*g + c*f*g + c*e*h)) - a*b^2*(2*A*d*(f*g + e*h) - c*(3*C*e*g - 2*A*f*h)))*Sqrt[a + b*x]*Sqrt[e + f*x]*Sqrt[g + h*x])/(3*(b*c - a*d)^2*(b*e - a*f)^2*(b*g - a*h)^2*Sqrt[c + d*x]) - (2*(A*b^2 + a^2*C)*Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x])/(3*(b*c - a*d)*(b*e - a*f)*(b*g - a*h)*(a + b*x)^(3/2)) + (4*b*(A*b^3*(d*e*g + c*f*g + c*e*h) + a^3*C*(d*f*g + d*e*h + c*f*h) + a^2*b*(3*A*d*f*h - 2*C*(d*e*g + c*f*g + c*e*h)) - a*b^2*(2*A*d*(f*g + e*h) - c*(3*C*e*g - 2*A*f*h)))*Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x])/(3*(b*c - a*d)^2*(b*e - a*f)^2*(b*g - a*h)^2*Sqrt[a + b*x]) + (4*Sqrt[d*g - c*h]*Sqrt[f*g - e*h]*(A*b^3*(d*e*g + c*f*g + c*e*h) + a^3*C*(d*f*g + d*e*h + c*f*h) + a^2*b*(3*A*d*f*h - 2*C*(d*e*g + c*f*g + c*e*h)) - a*b^2*(2*A*d*(f*g + e*h) - c*(3*C*e*g - 2*A*f*h)))*Sqrt[a + b*x]*Sqrt[-(((d*e - c*f)*(g + h*x))/((f*g - e*h)*(c + d*x)))]*EllipticE[ArcSin[(Sqrt[d*g - c*h]*Sqrt[e + f*x])/(Sqrt[f*g - e*h]*Sqrt[c + d*x])], ((b*c - a*d)*(f*g - e*h))/((b*e - a*f)*(d*g - c*h))])/(3*(b*c - a*d)^2*(b*e - a*f)^2*(b*g - a*h)^2*Sqrt[((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x))]*Sqrt[g + h*x]) - (2*(3*a*b*(c^2*C + A*d^2)*(f*g + e*h) - b^2*(2*A*d^2*e*g + A*c*d*(f*g + e*h) + c^2*(3*C*e*g - A*f*h)) - a^2*(3*A*d^2*f*h - C*(d^2*e*g - c*d*f*g - c*d*e*h - 2*c^2*f*h)))*Sqrt[((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))]*Sqrt[g + h*x]*EllipticF[ArcSin[(Sqrt[b*g - a*h]*Sqrt[e + f*x])/(Sqrt[f*g - e*h]*Sqrt[a + b*x])], -(((b*c - a*d)*(f*g - e*h))/((d*e - c*f)*(b*g - a*h)))])/(3*(b*c - a*d)^2*(b*e - a*f)*(b*g - a*h)^(3/2)*Sqrt[f*g - e*h]*Sqrt[c + d*x]*Sqrt[-(((b*e - a*f)*(g + h*x))/((f*g - e*h)*(a + b*x)))])","A",8,8,44,0.1818,1,"{1605, 1599, 1602, 12, 170, 419, 176, 424}"