1,0,0,700,2.9663525,"\int \frac{(a+b x)^2 (A+B x)}{\sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","IntegrateAlgebraic[((a + b*x)^2*(A + B*x))/(Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","\int \frac{(a+b x)^2 (A+B x)}{\sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","-\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)))-\left(b^2 \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))-\left(b^2 \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,"Could not integrate","F",-1
2,0,0,405,2.5617277,"\int \frac{(a+b x) (A+B x)}{\sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","IntegrateAlgebraic[((a + b*x)*(A + B*x))/(Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","\int \frac{(a+b x) (A+B x)}{\sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","-\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,"Could not integrate","F",-1
3,0,0,284,1.8459056,"\int \frac{A+B x}{\sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","IntegrateAlgebraic[(A + B*x)/(Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","\int \frac{A+B x}{\sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","\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,"Could not integrate","F",-1
4,0,0,313,2.8550634,"\int \frac{A+B x}{(a+b x) \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","IntegrateAlgebraic[(A + B*x)/((a + b*x)*Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","\int \frac{A+B x}{(a+b x) \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","\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,"Could not integrate","F",-1
5,0,0,678,2.9823655,"\int \frac{A+B x}{(a+b x)^2 \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","IntegrateAlgebraic[(A + B*x)/((a + b*x)^2*Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","\int \frac{A+B x}{(a+b x)^2 \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","\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^3 (-B) d f h+3 a^2 A 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,"Could not integrate","F",-1
6,0,0,981,3.3728712,"\int \frac{(a+b x)^{3/2} (A+B x)}{\sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","IntegrateAlgebraic[((a + b*x)^(3/2)*(A + B*x))/(Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","\int \frac{(a+b x)^{3/2} (A+B x)}{\sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","\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,"Could not integrate","F",-1
7,0,0,736,3.0904295,"\int \frac{\sqrt{a+b x} (A+B x)}{\sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","IntegrateAlgebraic[(Sqrt[a + b*x]*(A + B*x))/(Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","\int \frac{\sqrt{a+b x} (A+B x)}{\sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","\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,"Could not integrate","F",-1
8,0,0,442,3.1148193,"\int \frac{A+B x}{\sqrt{a+b x} \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","IntegrateAlgebraic[(A + B*x)/(Sqrt[a + b*x]*Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","\int \frac{A+B x}{\sqrt{a+b x} \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","\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,"Could not integrate","F",-1
9,0,0,606,3.3930925,"\int \frac{A+B x}{(a+b x)^{3/2} \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","IntegrateAlgebraic[(A + B*x)/((a + b*x)^(3/2)*Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","\int \frac{A+B x}{(a+b x)^{3/2} \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","-\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,"Could not integrate","F",-1
10,0,0,1081,3.3923223,"\int \frac{A+B x}{(a+b x)^{5/2} \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","IntegrateAlgebraic[(A + B*x)/((a + b*x)^(5/2)*Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","\int \frac{A+B x}{(a+b x)^{5/2} \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","-\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,"Could not integrate","F",-1
11,0,0,898,3.3461493,"\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","IntegrateAlgebraic[((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]","\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","\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(\left(3 f^2 g^2+e^2 h^2\right) d^2\right)+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,"Could not integrate","F",-1
12,0,0,472,3.0578862,"\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","IntegrateAlgebraic[(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]","\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","-\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,"Could not integrate","F",-1
13,0,0,449,3.1200467,"\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","IntegrateAlgebraic[(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]","\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","\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,"Could not integrate","F",-1
14,0,0,625,3.3615295,"\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","IntegrateAlgebraic[(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]","\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","-\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,"Could not integrate","F",-1
15,0,0,1090,3.3612794,"\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","IntegrateAlgebraic[(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]","\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","-\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,"Could not integrate","F",-1
16,0,0,721,2.9855603,"\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","IntegrateAlgebraic[((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]","\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","-\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 \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^3 C d^2 f^2 h^3-15 a^2 b d^2 f^2 h^2 (B h+C g)+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)))-\left(b^3 \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^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,"Could not integrate","F",-1
17,0,0,410,2.5728831,"\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","IntegrateAlgebraic[(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]","\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","\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-\left(b^2 (3 B d f g h-C (c h (f g-e h)+d g (e h+2 f g)))\right)\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,"Could not integrate","F",-1
18,0,0,291,1.9780103,"\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","IntegrateAlgebraic[(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]","\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","\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,"Could not integrate","F",-1
19,0,0,309,2.8540968,"\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","IntegrateAlgebraic[(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]","\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","\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,"Could not integrate","F",-1
20,0,0,680,3.0234569,"\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","IntegrateAlgebraic[(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]","\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","-\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(4 a^3 C d f h-a^2 b (3 B d f h+2 C (c f h+d e h+d f g))+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,"Could not integrate","F",-1
21,0,0,980,3.4854146,"\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","IntegrateAlgebraic[(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]","\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","\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,"Could not integrate","F",-1
22,0,0,734,3.4229253,"\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","IntegrateAlgebraic[(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]","\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","-\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,"Could not integrate","F",-1
23,0,0,436,3.7475889,"\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","IntegrateAlgebraic[(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]","\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","\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,"Could not integrate","F",-1
24,0,0,616,3.7604002,"\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","IntegrateAlgebraic[(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]","\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","-\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,"Could not integrate","F",-1
25,0,0,1128,3.7549737,"\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","IntegrateAlgebraic[(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]","\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","-\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,"Could not integrate","F",-1
26,0,0,1097,3.3174196,"\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","IntegrateAlgebraic[((a + b*x)^2*(A + C*x^2))/(Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","\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","\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,"Could not integrate","F",-1
27,0,0,611,2.9027008,"\int \frac{(a+b x) \left(A+C x^2\right)}{\sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","IntegrateAlgebraic[((a + b*x)*(A + C*x^2))/(Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","\int \frac{(a+b x) \left(A+C x^2\right)}{\sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","\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,"Could not integrate","F",-1
28,0,0,368,2.5086109,"\int \frac{A+C x^2}{\sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","IntegrateAlgebraic[(A + C*x^2)/(Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","\int \frac{A+C x^2}{\sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","\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,"Could not integrate","F",-1
29,0,0,465,3.1321013,"\int \frac{A+C x^2}{(a+b x) \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","IntegrateAlgebraic[(A + C*x^2)/((a + b*x)*Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","\int \frac{A+C x^2}{(a+b x) \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","-\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,"Could not integrate","F",-1
30,0,0,738,3.2408818,"\int \frac{A+C x^2}{(a+b x)^2 \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","IntegrateAlgebraic[(A + C*x^2)/((a + b*x)^2*Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","\int \frac{A+C x^2}{(a+b x)^2 \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","-\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{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 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^4 C d f h-2 a^3 b C (c f h+d e h+d f g)-3 a^2 b^2 (A d f h-C (c e h+c f g+d e g))-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)}",1,"Could not integrate","F",-1
31,0,0,1395,3.6740763,"\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","IntegrateAlgebraic[((a + b*x)^(3/2)*(A + C*x^2))/(Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","\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","\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(\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\right)+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,"Could not integrate","F",-1
32,0,0,937,3.3891521,"\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","IntegrateAlgebraic[(Sqrt[a + b*x]*(A + C*x^2))/(Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","\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","-\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,"Could not integrate","F",-1
33,0,0,757,3.4262232,"\int \frac{A+C x^2}{\sqrt{a+b x} \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","IntegrateAlgebraic[(A + C*x^2)/(Sqrt[a + b*x]*Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","\int \frac{A+C x^2}{\sqrt{a+b x} \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","\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,"Could not integrate","F",-1
34,0,0,867,3.6820524,"\int \frac{A+C x^2}{(a+b x)^{3/2} \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","IntegrateAlgebraic[(A + C*x^2)/((a + b*x)^(3/2)*Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","\int \frac{A+C x^2}{(a+b x)^{3/2} \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","-\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,"Could not integrate","F",-1
35,0,0,1070,3.6803799,"\int \frac{A+C x^2}{(a+b x)^{5/2} \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","IntegrateAlgebraic[(A + C*x^2)/((a + b*x)^(5/2)*Sqrt[c + d*x]*Sqrt[e + f*x]*Sqrt[g + h*x]),x]","\int \frac{A+C x^2}{(a+b x)^{5/2} \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx","-\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(\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\right)+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,"Could not integrate","F",-1