Integrand size = 58, antiderivative size = 721 \[ \int \frac {(a+b x) \left (a b B-a^2 C+b^2 B x+b^2 C x^2\right )}{\sqrt {c+d x} \sqrt {e+f x} \sqrt {g+h x}} \, dx=\frac {2 b^2 (5 b B d f h+2 C (a d f h-2 b (d f g+d e h+c f h))) \sqrt {c+d x} \sqrt {e+f x} \sqrt {g+h x}}{15 d^2 f^2 h^2}+\frac {2 b^2 C (a+b x) \sqrt {c+d x} \sqrt {e+f x} \sqrt {g+h x}}{5 d f h}-\frac {2 b \sqrt {-d e+c f} \left (15 a^2 C d^2 f^2 h^2-10 a b d f h (3 B d f h-C (d f g+d e h+c f h))+b^2 \left (10 B d f h (d f g+d e h+c f h)-C \left (8 c^2 f^2 h^2+7 c d f h (f g+e h)+d^2 \left (8 f^2 g^2+7 e f g h+8 e^2 h^2\right )\right )\right )\right ) \sqrt {\frac {d (e+f x)}{d e-c f}} \sqrt {g+h x} E\left (\arcsin \left (\frac {\sqrt {f} \sqrt {c+d x}}{\sqrt {-d e+c f}}\right )|\frac {(d e-c f) h}{f (d g-c h)}\right )}{15 d^3 f^{5/2} h^3 \sqrt {e+f x} \sqrt {\frac {d (g+h x)}{d g-c h}}}-\frac {2 \sqrt {-d e+c f} \left (15 a^3 C d^2 f^2 h^3-15 a^2 b d^2 f^2 h^2 (C g+B h)+5 a b^2 d f h (6 B d f g h-C (c h (f g-e h)+d g (2 f g+e h)))-b^3 \left (5 B d f h (c h (f g-e h)+d g (2 f g+e h))-C \left (4 c^2 f h^2 (f g-e h)+c d h \left (3 f^2 g^2+e f g h-4 e^2 h^2\right )+d^2 g \left (8 f^2 g^2+3 e f g h+4 e^2 h^2\right )\right )\right )\right ) \sqrt {\frac {d (e+f x)}{d e-c f}} \sqrt {\frac {d (g+h x)}{d g-c h}} \operatorname {EllipticF}\left (\arcsin \left (\frac {\sqrt {f} \sqrt {c+d x}}{\sqrt {-d e+c f}}\right ),\frac {(d e-c f) h}{f (d g-c h)}\right )}{15 d^3 f^{5/2} h^3 \sqrt {e+f x} \sqrt {g+h x}} \]
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Time = 1.20 (sec) , antiderivative size = 720, normalized size of antiderivative = 1.00, number of steps used = 8, number of rules used = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.121, Rules used = {1614, 1629, 164, 115, 114, 122, 121} \[ \int \frac {(a+b x) \left (a b B-a^2 C+b^2 B x+b^2 C x^2\right )}{\sqrt {c+d x} \sqrt {e+f x} \sqrt {g+h x}} \, dx=-\frac {2 b \sqrt {g+h x} \sqrt {c f-d e} \sqrt {\frac {d (e+f x)}{d e-c f}} E\left (\arcsin \left (\frac {\sqrt {f} \sqrt {c+d x}}{\sqrt {c f-d e}}\right )|\frac {(d e-c f) h}{f (d g-c h)}\right ) \left (15 a^2 C d^2 f^2 h^2-10 a b d f h (3 B d f h-C (c f h+d e h+d f g))+b^2 \left (10 B d f h (c f h+d e h+d f g)-C \left (8 c^2 f^2 h^2+7 c d f h (e h+f g)+d^2 \left (8 e^2 h^2+7 e f g h+8 f^2 g^2\right )\right )\right )\right )}{15 d^3 f^{5/2} h^3 \sqrt {e+f x} \sqrt {\frac {d (g+h x)}{d g-c h}}}-\frac {2 \sqrt {c f-d e} \sqrt {\frac {d (e+f x)}{d e-c f}} \sqrt {\frac {d (g+h x)}{d g-c h}} \operatorname {EllipticF}\left (\arcsin \left (\frac {\sqrt {f} \sqrt {c+d x}}{\sqrt {c f-d e}}\right ),\frac {(d e-c f) h}{f (d g-c h)}\right ) \left (15 a^3 C d^2 f^2 h^3-15 a^2 b d^2 f^2 h^2 (B h+C g)+5 a b^2 d f h (6 B d f g h-c C h (f g-e h)-C d g (e h+2 f g))-\left (b^3 \left (5 B d f h (c h (f g-e h)+d g (e h+2 f g))-C \left (4 c^2 f h^2 (f g-e h)+c d h \left (-4 e^2 h^2+e f g h+3 f^2 g^2\right )+d^2 g \left (4 e^2 h^2+3 e f g h+8 f^2 g^2\right )\right )\right )\right )\right )}{15 d^3 f^{5/2} h^3 \sqrt {e+f x} \sqrt {g+h x}}+\frac {2 b^2 \sqrt {c+d x} \sqrt {e+f x} \sqrt {g+h x} (2 a C d f h+5 b B d f h-4 b C (c f h+d e h+d f g))}{15 d^2 f^2 h^2}+\frac {2 b^2 C (a+b x) \sqrt {c+d x} \sqrt {e+f x} \sqrt {g+h x}}{5 d f h} \]
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Rule 114
Rule 115
Rule 121
Rule 122
Rule 164
Rule 1614
Rule 1629
Rubi steps \begin{align*} \text {integral}& = \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 {\int \frac {5 a^2 (b B-a C) d f h-b^2 C (2 b c e g+a (d e g+c f g+c e h))+b (5 a (2 b B-a C) d f h-b C (3 b (d e g+c f g+c e h)+2 a (d f g+d e h+c f h))) x+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)) x^2}{\sqrt {c+d x} \sqrt {e+f x} \sqrt {g+h x}} \, dx}{5 d f h} \\ & = \frac {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}+\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 \int \frac {\frac {1}{2} d \left (15 a^2 b B d^2 f^2 h^2-15 a^3 C d^2 f^2 h^2-5 a b^2 C d f h (d e g+c f g+c e h)-b^3 \left (5 B d f h (d e g+c f g+c e h)-C \left (4 d^2 e g (f g+e h)+4 c^2 f h (f g+e h)+2 c d \left (2 f^2 g^2+3 e f g h+2 e^2 h^2\right )\right )\right )\right )-\frac {1}{2} b d \left (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 \left (10 B d f h (d f g+d e h+c f h)-C \left (8 c^2 f^2 h^2+7 c d f h (f g+e h)+d^2 \left (8 f^2 g^2+7 e f g h+8 e^2 h^2\right )\right )\right )\right ) x}{\sqrt {c+d x} \sqrt {e+f x} \sqrt {g+h x}} \, dx}{15 d^3 f^2 h^2} \\ & = \frac {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}+\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 {\left (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 \left (5 B d f h (c h (f g-e h)+d g (2 f g+e h))-C \left (4 c^2 f h^2 (f g-e h)+c d h \left (3 f^2 g^2+e f g h-4 e^2 h^2\right )+d^2 g \left (8 f^2 g^2+3 e f g h+4 e^2 h^2\right )\right )\right )\right ) \int \frac {1}{\sqrt {c+d x} \sqrt {e+f x} \sqrt {g+h x}} \, dx}{15 d^2 f^2 h^3}-\frac {\left (b \left (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 \left (10 B d f h (d f g+d e h+c f h)-C \left (8 c^2 f^2 h^2+7 c d f h (f g+e h)+d^2 \left (8 f^2 g^2+7 e f g h+8 e^2 h^2\right )\right )\right )\right )\right ) \int \frac {\sqrt {g+h x}}{\sqrt {c+d x} \sqrt {e+f x}} \, dx}{15 d^2 f^2 h^3} \\ & = \frac {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}+\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 {\left (\left (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 \left (5 B d f h (c h (f g-e h)+d g (2 f g+e h))-C \left (4 c^2 f h^2 (f g-e h)+c d h \left (3 f^2 g^2+e f g h-4 e^2 h^2\right )+d^2 g \left (8 f^2 g^2+3 e f g h+4 e^2 h^2\right )\right )\right )\right ) \sqrt {\frac {d (e+f x)}{d e-c f}}\right ) \int \frac {1}{\sqrt {c+d x} \sqrt {\frac {d e}{d e-c f}+\frac {d f x}{d e-c f}} \sqrt {g+h x}} \, dx}{15 d^2 f^2 h^3 \sqrt {e+f x}}-\frac {\left (b \left (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 \left (10 B d f h (d f g+d e h+c f h)-C \left (8 c^2 f^2 h^2+7 c d f h (f g+e h)+d^2 \left (8 f^2 g^2+7 e f g h+8 e^2 h^2\right )\right )\right )\right ) \sqrt {\frac {d (e+f x)}{d e-c f}} \sqrt {g+h x}\right ) \int \frac {\sqrt {\frac {d g}{d g-c h}+\frac {d h x}{d g-c h}}}{\sqrt {c+d x} \sqrt {\frac {d e}{d e-c f}+\frac {d f x}{d e-c f}}} \, dx}{15 d^2 f^2 h^3 \sqrt {e+f x} \sqrt {\frac {d (g+h x)}{d g-c h}}} \\ & = \frac {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}+\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 b \sqrt {-d e+c f} \left (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 \left (10 B d f h (d f g+d e h+c f h)-C \left (8 c^2 f^2 h^2+7 c d f h (f g+e h)+d^2 \left (8 f^2 g^2+7 e f g h+8 e^2 h^2\right )\right )\right )\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 {-d e+c f}}\right )|\frac {(d e-c f) h}{f (d g-c h)}\right )}{15 d^3 f^{5/2} h^3 \sqrt {e+f x} \sqrt {\frac {d (g+h x)}{d g-c h}}}-\frac {\left (\left (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 \left (5 B d f h (c h (f g-e h)+d g (2 f g+e h))-C \left (4 c^2 f h^2 (f g-e h)+c d h \left (3 f^2 g^2+e f g h-4 e^2 h^2\right )+d^2 g \left (8 f^2 g^2+3 e f g h+4 e^2 h^2\right )\right )\right )\right ) \sqrt {\frac {d (e+f x)}{d e-c f}} \sqrt {\frac {d (g+h x)}{d g-c h}}\right ) \int \frac {1}{\sqrt {c+d x} \sqrt {\frac {d e}{d e-c f}+\frac {d f x}{d e-c f}} \sqrt {\frac {d g}{d g-c h}+\frac {d h x}{d g-c h}}} \, dx}{15 d^2 f^2 h^3 \sqrt {e+f x} \sqrt {g+h x}} \\ & = \frac {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}+\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 b \sqrt {-d e+c f} \left (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 \left (10 B d f h (d f g+d e h+c f h)-C \left (8 c^2 f^2 h^2+7 c d f h (f g+e h)+d^2 \left (8 f^2 g^2+7 e f g h+8 e^2 h^2\right )\right )\right )\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 {-d e+c f}}\right )|\frac {(d e-c f) h}{f (d g-c h)}\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 {-d e+c f} \left (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 \left (5 B d f h (c h (f g-e h)+d g (2 f g+e h))-C \left (4 c^2 f h^2 (f g-e h)+c d h \left (3 f^2 g^2+e f g h-4 e^2 h^2\right )+d^2 g \left (8 f^2 g^2+3 e f g h+4 e^2 h^2\right )\right )\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 {-d e+c f}}\right )|\frac {(d e-c f) h}{f (d g-c h)}\right )}{15 d^3 f^{5/2} h^3 \sqrt {e+f x} \sqrt {g+h x}} \\ \end{align*}
Result contains complex when optimal does not.
Time = 28.44 (sec) , antiderivative size = 825, normalized size of antiderivative = 1.14 \[ \int \frac {(a+b x) \left (a b B-a^2 C+b^2 B x+b^2 C x^2\right )}{\sqrt {c+d x} \sqrt {e+f x} \sqrt {g+h x}} \, dx=-\frac {2 \left (b d^2 \sqrt {-c+\frac {d e}{f}} \left (15 a^2 C d^2 f^2 h^2+10 a b d f h (-3 B d f h+C (d f g+d e h+c f h))-b^2 \left (-10 B d f h (d f g+d e h+c f h)+C \left (8 c^2 f^2 h^2+7 c d f h (f g+e h)+d^2 \left (8 f^2 g^2+7 e f g h+8 e^2 h^2\right )\right )\right )\right ) (e+f x) (g+h x)+b^2 d^2 \sqrt {-c+\frac {d e}{f}} f h (c+d x) (e+f x) (g+h x) (-5 b B d f h-5 a C d f h+b C (4 c f h+d (4 f g+4 e h-3 f h x)))+i b (d e-c f) h \left (15 a^2 C d^2 f^2 h^2+10 a b d f h (-3 B d f h+C (d f g+d e h+c f h))-b^2 \left (-10 B d f h (d f g+d e h+c f h)+C \left (8 c^2 f^2 h^2+7 c d f h (f g+e h)+d^2 \left (8 f^2 g^2+7 e f g h+8 e^2 h^2\right )\right )\right )\right ) (c+d x)^{3/2} \sqrt {\frac {d (e+f x)}{f (c+d x)}} \sqrt {\frac {d (g+h x)}{h (c+d x)}} E\left (i \text {arcsinh}\left (\frac {\sqrt {-c+\frac {d e}{f}}}{\sqrt {c+d x}}\right )|\frac {d f g-c f h}{d e h-c f h}\right )+i d h \left (15 a^3 C d^2 f^3 h^2-15 a^2 b d^2 f^2 (C e+B f) h^2-5 a b^2 d f h (-6 B d e f h+c C f (-f g+e h)+C d e (f g+2 e h))+b^3 \left (-5 B d f h (c f (-f g+e h)+d e (f g+2 e h))+C \left (4 c^2 f^2 h (-f g+e h)+c d f \left (-4 f^2 g^2+e f g h+3 e^2 h^2\right )+d^2 e \left (4 f^2 g^2+3 e f g h+8 e^2 h^2\right )\right )\right )\right ) (c+d x)^{3/2} \sqrt {\frac {d (e+f x)}{f (c+d x)}} \sqrt {\frac {d (g+h x)}{h (c+d x)}} \operatorname {EllipticF}\left (i \text {arcsinh}\left (\frac {\sqrt {-c+\frac {d e}{f}}}{\sqrt {c+d x}}\right ),\frac {d f g-c f h}{d e h-c f h}\right )\right )}{15 d^4 \sqrt {-c+\frac {d e}{f}} f^3 h^3 \sqrt {c+d x} \sqrt {e+f x} \sqrt {g+h x}} \]
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Time = 2.50 (sec) , antiderivative size = 880, normalized size of antiderivative = 1.22
method | result | size |
elliptic | \(\frac {\sqrt {\left (d x +c \right ) \left (f x +e \right ) \left (h x +g \right )}\, \left (\frac {2 C \,b^{3} x \sqrt {d f h \,x^{3}+c f h \,x^{2}+d e h \,x^{2}+d f g \,x^{2}+c e h x +c f g x +d e g x +c e g}}{5 d f h}+\frac {2 \left (B \,b^{3}+C \,b^{2} a -\frac {2 C \,b^{3} \left (2 c f h +2 d e h +2 d f g \right )}{5 d f h}\right ) \sqrt {d f h \,x^{3}+c f h \,x^{2}+d e h \,x^{2}+d f g \,x^{2}+c e h x +c f g x +d e g x +c e g}}{3 d f h}+\frac {2 \left (a^{2} b B -C \,a^{3}-\frac {2 C \,b^{3} c e g}{5 d f h}-\frac {2 \left (B \,b^{3}+C \,b^{2} a -\frac {2 C \,b^{3} \left (2 c f h +2 d e h +2 d f g \right )}{5 d f h}\right ) \left (\frac {1}{2} c e h +\frac {1}{2} c f g +\frac {1}{2} d e g \right )}{3 d f h}\right ) \left (\frac {g}{h}-\frac {e}{f}\right ) \sqrt {\frac {x +\frac {g}{h}}{\frac {g}{h}-\frac {e}{f}}}\, \sqrt {\frac {x +\frac {c}{d}}{-\frac {g}{h}+\frac {c}{d}}}\, \sqrt {\frac {x +\frac {e}{f}}{-\frac {g}{h}+\frac {e}{f}}}\, F\left (\sqrt {\frac {x +\frac {g}{h}}{\frac {g}{h}-\frac {e}{f}}}, \sqrt {\frac {-\frac {g}{h}+\frac {e}{f}}{-\frac {g}{h}+\frac {c}{d}}}\right )}{\sqrt {d f h \,x^{3}+c f h \,x^{2}+d e h \,x^{2}+d f g \,x^{2}+c e h x +c f g x +d e g x +c e g}}+\frac {2 \left (2 a \,b^{2} B -C \,a^{2} b -\frac {2 C \,b^{3} \left (\frac {3}{2} c e h +\frac {3}{2} c f g +\frac {3}{2} d e g \right )}{5 d f h}-\frac {2 \left (B \,b^{3}+C \,b^{2} a -\frac {2 C \,b^{3} \left (2 c f h +2 d e h +2 d f g \right )}{5 d f h}\right ) \left (c f h +d e h +d f g \right )}{3 d f h}\right ) \left (\frac {g}{h}-\frac {e}{f}\right ) \sqrt {\frac {x +\frac {g}{h}}{\frac {g}{h}-\frac {e}{f}}}\, \sqrt {\frac {x +\frac {c}{d}}{-\frac {g}{h}+\frac {c}{d}}}\, \sqrt {\frac {x +\frac {e}{f}}{-\frac {g}{h}+\frac {e}{f}}}\, \left (\left (-\frac {g}{h}+\frac {c}{d}\right ) E\left (\sqrt {\frac {x +\frac {g}{h}}{\frac {g}{h}-\frac {e}{f}}}, \sqrt {\frac {-\frac {g}{h}+\frac {e}{f}}{-\frac {g}{h}+\frac {c}{d}}}\right )-\frac {c F\left (\sqrt {\frac {x +\frac {g}{h}}{\frac {g}{h}-\frac {e}{f}}}, \sqrt {\frac {-\frac {g}{h}+\frac {e}{f}}{-\frac {g}{h}+\frac {c}{d}}}\right )}{d}\right )}{\sqrt {d f h \,x^{3}+c f h \,x^{2}+d e h \,x^{2}+d f g \,x^{2}+c e h x +c f g x +d e g x +c e g}}\right )}{\sqrt {d x +c}\, \sqrt {f x +e}\, \sqrt {h x +g}}\) | \(880\) |
default | \(\text {Expression too large to display}\) | \(8421\) |
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Result contains higher order function than in optimal. Order 9 vs. order 4.
Time = 0.16 (sec) , antiderivative size = 1267, normalized size of antiderivative = 1.76 \[ \int \frac {(a+b x) \left (a b B-a^2 C+b^2 B x+b^2 C x^2\right )}{\sqrt {c+d x} \sqrt {e+f x} \sqrt {g+h x}} \, dx=\text {Too large to display} \]
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\[ \int \frac {(a+b x) \left (a b B-a^2 C+b^2 B x+b^2 C x^2\right )}{\sqrt {c+d x} \sqrt {e+f x} \sqrt {g+h x}} \, dx=\int \frac {\left (a + b x\right )^{2} \left (B b - C a + C b x\right )}{\sqrt {c + d x} \sqrt {e + f x} \sqrt {g + h x}}\, dx \]
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\[ \int \frac {(a+b x) \left (a b B-a^2 C+b^2 B x+b^2 C x^2\right )}{\sqrt {c+d x} \sqrt {e+f x} \sqrt {g+h x}} \, dx=\int { \frac {{\left (C b^{2} x^{2} + B b^{2} x - C a^{2} + B a b\right )} {\left (b x + a\right )}}{\sqrt {d x + c} \sqrt {f x + e} \sqrt {h x + g}} \,d x } \]
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\[ \int \frac {(a+b x) \left (a b B-a^2 C+b^2 B x+b^2 C x^2\right )}{\sqrt {c+d x} \sqrt {e+f x} \sqrt {g+h x}} \, dx=\int { \frac {{\left (C b^{2} x^{2} + B b^{2} x - C a^{2} + B a b\right )} {\left (b x + a\right )}}{\sqrt {d x + c} \sqrt {f x + e} \sqrt {h x + g}} \,d x } \]
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Timed out. \[ \int \frac {(a+b x) \left (a b B-a^2 C+b^2 B x+b^2 C x^2\right )}{\sqrt {c+d x} \sqrt {e+f x} \sqrt {g+h x}} \, dx=\text {Hanged} \]
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