Optimal. Leaf size=673 \[ \frac {e \sqrt {a+b x+c x^2}}{(e f-d g)^2 (f+g x)}-\frac {g (b f-2 a g+(2 c f-b g) x) \sqrt {a+b x+c x^2}}{4 (e f-d g) \left (c f^2-b f g+a g^2\right ) (f+g x)^2}-\frac {e (2 c d-b e) \tanh ^{-1}\left (\frac {b+2 c x}{2 \sqrt {c} \sqrt {a+b x+c x^2}}\right )}{2 \sqrt {c} (e f-d g)^3}+\frac {e^2 (2 c f-b g) \tanh ^{-1}\left (\frac {b+2 c x}{2 \sqrt {c} \sqrt {a+b x+c x^2}}\right )}{2 \sqrt {c} g (e f-d g)^3}-\frac {\sqrt {c} e \tanh ^{-1}\left (\frac {b+2 c x}{2 \sqrt {c} \sqrt {a+b x+c x^2}}\right )}{g (e f-d g)^2}+\frac {e \sqrt {c d^2-b d e+a e^2} \tanh ^{-1}\left (\frac {b d-2 a e+(2 c d-b e) x}{2 \sqrt {c d^2-b d e+a e^2} \sqrt {a+b x+c x^2}}\right )}{(e f-d g)^3}+\frac {\left (b^2-4 a c\right ) g \tanh ^{-1}\left (\frac {b f-2 a g+(2 c f-b g) x}{2 \sqrt {c f^2-b f g+a g^2} \sqrt {a+b x+c x^2}}\right )}{8 (e f-d g) \left (c f^2-b f g+a g^2\right )^{3/2}}+\frac {e (2 c f-b g) \tanh ^{-1}\left (\frac {b f-2 a g+(2 c f-b g) x}{2 \sqrt {c f^2-b f g+a g^2} \sqrt {a+b x+c x^2}}\right )}{2 g (e f-d g)^2 \sqrt {c f^2-b f g+a g^2}}-\frac {e^2 \sqrt {c f^2-b f g+a g^2} \tanh ^{-1}\left (\frac {b f-2 a g+(2 c f-b g) x}{2 \sqrt {c f^2-b f g+a g^2} \sqrt {a+b x+c x^2}}\right )}{g (e f-d g)^3} \]
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Rubi [A]
time = 0.56, antiderivative size = 673, normalized size of antiderivative = 1.00, number of steps
used = 23, number of rules used = 8, integrand size = 29, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.276, Rules used = {974, 748, 857,
635, 212, 738, 734, 746} \begin {gather*} \frac {g \left (b^2-4 a c\right ) \tanh ^{-1}\left (\frac {-2 a g+x (2 c f-b g)+b f}{2 \sqrt {a+b x+c x^2} \sqrt {a g^2-b f g+c f^2}}\right )}{8 (e f-d g) \left (a g^2-b f g+c f^2\right )^{3/2}}+\frac {e \sqrt {a e^2-b d e+c d^2} \tanh ^{-1}\left (\frac {-2 a e+x (2 c d-b e)+b d}{2 \sqrt {a+b x+c x^2} \sqrt {a e^2-b d e+c d^2}}\right )}{(e f-d g)^3}-\frac {e^2 \sqrt {a g^2-b f g+c f^2} \tanh ^{-1}\left (\frac {-2 a g+x (2 c f-b g)+b f}{2 \sqrt {a+b x+c x^2} \sqrt {a g^2-b f g+c f^2}}\right )}{g (e f-d g)^3}+\frac {e^2 (2 c f-b g) \tanh ^{-1}\left (\frac {b+2 c x}{2 \sqrt {c} \sqrt {a+b x+c x^2}}\right )}{2 \sqrt {c} g (e f-d g)^3}-\frac {g \sqrt {a+b x+c x^2} (-2 a g+x (2 c f-b g)+b f)}{4 (f+g x)^2 (e f-d g) \left (a g^2-b f g+c f^2\right )}+\frac {e (2 c f-b g) \tanh ^{-1}\left (\frac {-2 a g+x (2 c f-b g)+b f}{2 \sqrt {a+b x+c x^2} \sqrt {a g^2-b f g+c f^2}}\right )}{2 g (e f-d g)^2 \sqrt {a g^2-b f g+c f^2}}+\frac {e \sqrt {a+b x+c x^2}}{(f+g x) (e f-d g)^2}-\frac {\sqrt {c} e \tanh ^{-1}\left (\frac {b+2 c x}{2 \sqrt {c} \sqrt {a+b x+c x^2}}\right )}{g (e f-d g)^2}-\frac {e (2 c d-b e) \tanh ^{-1}\left (\frac {b+2 c x}{2 \sqrt {c} \sqrt {a+b x+c x^2}}\right )}{2 \sqrt {c} (e f-d g)^3} \end {gather*}
Antiderivative was successfully verified.
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Rule 212
Rule 635
Rule 734
Rule 738
Rule 746
Rule 748
Rule 857
Rule 974
Rubi steps
\begin {align*} \int \frac {\sqrt {a+b x+c x^2}}{(d+e x) (f+g x)^3} \, dx &=\int \left (\frac {e^3 \sqrt {a+b x+c x^2}}{(e f-d g)^3 (d+e x)}-\frac {g \sqrt {a+b x+c x^2}}{(e f-d g) (f+g x)^3}-\frac {e g \sqrt {a+b x+c x^2}}{(e f-d g)^2 (f+g x)^2}-\frac {e^2 g \sqrt {a+b x+c x^2}}{(e f-d g)^3 (f+g x)}\right ) \, dx\\ &=\frac {e^3 \int \frac {\sqrt {a+b x+c x^2}}{d+e x} \, dx}{(e f-d g)^3}-\frac {\left (e^2 g\right ) \int \frac {\sqrt {a+b x+c x^2}}{f+g x} \, dx}{(e f-d g)^3}-\frac {(e g) \int \frac {\sqrt {a+b x+c x^2}}{(f+g x)^2} \, dx}{(e f-d g)^2}-\frac {g \int \frac {\sqrt {a+b x+c x^2}}{(f+g x)^3} \, dx}{e f-d g}\\ &=\frac {e \sqrt {a+b x+c x^2}}{(e f-d g)^2 (f+g x)}-\frac {g (b f-2 a g+(2 c f-b g) x) \sqrt {a+b x+c x^2}}{4 (e f-d g) \left (c f^2-b f g+a g^2\right ) (f+g x)^2}-\frac {e^2 \int \frac {b d-2 a e+(2 c d-b e) x}{(d+e x) \sqrt {a+b x+c x^2}} \, dx}{2 (e f-d g)^3}+\frac {e^2 \int \frac {b f-2 a g+(2 c f-b g) x}{(f+g x) \sqrt {a+b x+c x^2}} \, dx}{2 (e f-d g)^3}-\frac {e \int \frac {b+2 c x}{(f+g x) \sqrt {a+b x+c x^2}} \, dx}{2 (e f-d g)^2}+\frac {\left (\left (b^2-4 a c\right ) g\right ) \int \frac {1}{(f+g x) \sqrt {a+b x+c x^2}} \, dx}{8 (e f-d g) \left (c f^2-b f g+a g^2\right )}\\ &=\frac {e \sqrt {a+b x+c x^2}}{(e f-d g)^2 (f+g x)}-\frac {g (b f-2 a g+(2 c f-b g) x) \sqrt {a+b x+c x^2}}{4 (e f-d g) \left (c f^2-b f g+a g^2\right ) (f+g x)^2}-\frac {(e (2 c d-b e)) \int \frac {1}{\sqrt {a+b x+c x^2}} \, dx}{2 (e f-d g)^3}+\frac {\left (e \left (c d^2-b d e+a e^2\right )\right ) \int \frac {1}{(d+e x) \sqrt {a+b x+c x^2}} \, dx}{(e f-d g)^3}+\frac {\left (e^2 (2 c f-b g)\right ) \int \frac {1}{\sqrt {a+b x+c x^2}} \, dx}{2 g (e f-d g)^3}-\frac {(c e) \int \frac {1}{\sqrt {a+b x+c x^2}} \, dx}{g (e f-d g)^2}+\frac {(e (2 c f-b g)) \int \frac {1}{(f+g x) \sqrt {a+b x+c x^2}} \, dx}{2 g (e f-d g)^2}-\frac {\left (\left (b^2-4 a c\right ) g\right ) \text {Subst}\left (\int \frac {1}{4 c f^2-4 b f g+4 a g^2-x^2} \, dx,x,\frac {-b f+2 a g-(2 c f-b g) x}{\sqrt {a+b x+c x^2}}\right )}{4 (e f-d g) \left (c f^2-b f g+a g^2\right )}-\frac {\left (e^2 \left (c f^2-b f g+a g^2\right )\right ) \int \frac {1}{(f+g x) \sqrt {a+b x+c x^2}} \, dx}{g (e f-d g)^3}\\ &=\frac {e \sqrt {a+b x+c x^2}}{(e f-d g)^2 (f+g x)}-\frac {g (b f-2 a g+(2 c f-b g) x) \sqrt {a+b x+c x^2}}{4 (e f-d g) \left (c f^2-b f g+a g^2\right ) (f+g x)^2}+\frac {\left (b^2-4 a c\right ) g \tanh ^{-1}\left (\frac {b f-2 a g+(2 c f-b g) x}{2 \sqrt {c f^2-b f g+a g^2} \sqrt {a+b x+c x^2}}\right )}{8 (e f-d g) \left (c f^2-b f g+a g^2\right )^{3/2}}-\frac {(e (2 c d-b e)) \text {Subst}\left (\int \frac {1}{4 c-x^2} \, dx,x,\frac {b+2 c x}{\sqrt {a+b x+c x^2}}\right )}{(e f-d g)^3}-\frac {\left (2 e \left (c d^2-b d e+a e^2\right )\right ) \text {Subst}\left (\int \frac {1}{4 c d^2-4 b d e+4 a e^2-x^2} \, dx,x,\frac {-b d+2 a e-(2 c d-b e) x}{\sqrt {a+b x+c x^2}}\right )}{(e f-d g)^3}+\frac {\left (e^2 (2 c f-b g)\right ) \text {Subst}\left (\int \frac {1}{4 c-x^2} \, dx,x,\frac {b+2 c x}{\sqrt {a+b x+c x^2}}\right )}{g (e f-d g)^3}-\frac {(2 c e) \text {Subst}\left (\int \frac {1}{4 c-x^2} \, dx,x,\frac {b+2 c x}{\sqrt {a+b x+c x^2}}\right )}{g (e f-d g)^2}-\frac {(e (2 c f-b g)) \text {Subst}\left (\int \frac {1}{4 c f^2-4 b f g+4 a g^2-x^2} \, dx,x,\frac {-b f+2 a g-(2 c f-b g) x}{\sqrt {a+b x+c x^2}}\right )}{g (e f-d g)^2}+\frac {\left (2 e^2 \left (c f^2-b f g+a g^2\right )\right ) \text {Subst}\left (\int \frac {1}{4 c f^2-4 b f g+4 a g^2-x^2} \, dx,x,\frac {-b f+2 a g-(2 c f-b g) x}{\sqrt {a+b x+c x^2}}\right )}{g (e f-d g)^3}\\ &=\frac {e \sqrt {a+b x+c x^2}}{(e f-d g)^2 (f+g x)}-\frac {g (b f-2 a g+(2 c f-b g) x) \sqrt {a+b x+c x^2}}{4 (e f-d g) \left (c f^2-b f g+a g^2\right ) (f+g x)^2}-\frac {e (2 c d-b e) \tanh ^{-1}\left (\frac {b+2 c x}{2 \sqrt {c} \sqrt {a+b x+c x^2}}\right )}{2 \sqrt {c} (e f-d g)^3}+\frac {e^2 (2 c f-b g) \tanh ^{-1}\left (\frac {b+2 c x}{2 \sqrt {c} \sqrt {a+b x+c x^2}}\right )}{2 \sqrt {c} g (e f-d g)^3}-\frac {\sqrt {c} e \tanh ^{-1}\left (\frac {b+2 c x}{2 \sqrt {c} \sqrt {a+b x+c x^2}}\right )}{g (e f-d g)^2}+\frac {e \sqrt {c d^2-b d e+a e^2} \tanh ^{-1}\left (\frac {b d-2 a e+(2 c d-b e) x}{2 \sqrt {c d^2-b d e+a e^2} \sqrt {a+b x+c x^2}}\right )}{(e f-d g)^3}+\frac {\left (b^2-4 a c\right ) g \tanh ^{-1}\left (\frac {b f-2 a g+(2 c f-b g) x}{2 \sqrt {c f^2-b f g+a g^2} \sqrt {a+b x+c x^2}}\right )}{8 (e f-d g) \left (c f^2-b f g+a g^2\right )^{3/2}}+\frac {e (2 c f-b g) \tanh ^{-1}\left (\frac {b f-2 a g+(2 c f-b g) x}{2 \sqrt {c f^2-b f g+a g^2} \sqrt {a+b x+c x^2}}\right )}{2 g (e f-d g)^2 \sqrt {c f^2-b f g+a g^2}}-\frac {e^2 \sqrt {c f^2-b f g+a g^2} \tanh ^{-1}\left (\frac {b f-2 a g+(2 c f-b g) x}{2 \sqrt {c f^2-b f g+a g^2} \sqrt {a+b x+c x^2}}\right )}{g (e f-d g)^3}\\ \end {align*}
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Mathematica [A]
time = 11.03, size = 609, normalized size = 0.90 \begin {gather*} \frac {\frac {8 e (e f-d g) \sqrt {a+x (b+c x)}}{f+g x}+\frac {2 g (e f-d g)^2 (-b f+2 a g-2 c f x+b g x) \sqrt {a+x (b+c x)}}{\left (c f^2+g (-b f+a g)\right ) (f+g x)^2}+\frac {4 e (-2 c d+b e) \tanh ^{-1}\left (\frac {b+2 c x}{2 \sqrt {c} \sqrt {a+x (b+c x)}}\right )}{\sqrt {c}}+8 e \sqrt {c d^2+e (-b d+a e)} \tanh ^{-1}\left (\frac {-2 a e+2 c d x+b (d-e x)}{2 \sqrt {c d^2+e (-b d+a e)} \sqrt {a+x (b+c x)}}\right )+\frac {\left (b^2-4 a c\right ) g (e f-d g)^2 \tanh ^{-1}\left (\frac {-2 a g+2 c f x+b (f-g x)}{2 \sqrt {c f^2+g (-b f+a g)} \sqrt {a+x (b+c x)}}\right )}{\left (c f^2+g (-b f+a g)\right )^{3/2}}-\frac {4 e (e f-d g) \left (2 \sqrt {c} \tanh ^{-1}\left (\frac {b+2 c x}{2 \sqrt {c} \sqrt {a+x (b+c x)}}\right )-\frac {(2 c f-b g) \tanh ^{-1}\left (\frac {-2 a g+2 c f x+b (f-g x)}{2 \sqrt {c f^2+g (-b f+a g)} \sqrt {a+x (b+c x)}}\right )}{\sqrt {c f^2+g (-b f+a g)}}\right )}{g}+\frac {4 e^2 \left ((2 c f-b g) \tanh ^{-1}\left (\frac {b+2 c x}{2 \sqrt {c} \sqrt {a+x (b+c x)}}\right )-2 \sqrt {c} \sqrt {c f^2+g (-b f+a g)} \tanh ^{-1}\left (\frac {-2 a g+2 c f x+b (f-g x)}{2 \sqrt {c f^2+g (-b f+a g)} \sqrt {a+x (b+c x)}}\right )\right )}{\sqrt {c} g}}{8 (e f-d g)^3} \end {gather*}
Antiderivative was successfully verified.
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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(2511\) vs.
\(2(603)=1206\).
time = 0.15, size = 2512, normalized size = 3.73
method | result | size |
default | \(\text {Expression too large to display}\) | \(2512\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [F(-1)] Timed out
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\sqrt {a + b x + c x^{2}}}{\left (d + e x\right ) \left (f + g x\right )^{3}}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 1844 vs.
\(2 (618) = 1236\).
time = 6.86, size = 1844, normalized size = 2.74 \begin {gather*} -\frac {{\left (b^{2} d^{2} g^{3} - 4 \, a c d^{2} g^{3} - 8 \, c^{2} d f^{3} e + 12 \, b c d f^{2} g e - 6 \, b^{2} d f g^{2} e + 4 \, a b d g^{3} e + 4 \, b c f^{3} e^{2} - 3 \, b^{2} f^{2} g e^{2} - 12 \, a c f^{2} g e^{2} + 12 \, a b f g^{2} e^{2} - 8 \, a^{2} g^{3} e^{2}\right )} \arctan \left (-\frac {{\left (\sqrt {c} x - \sqrt {c x^{2} + b x + a}\right )} g + \sqrt {c} f}{\sqrt {-c f^{2} + b f g - a g^{2}}}\right )}{4 \, {\left (c d^{3} f^{2} g^{3} - b d^{3} f g^{4} + a d^{3} g^{5} - 3 \, c d^{2} f^{3} g^{2} e + 3 \, b d^{2} f^{2} g^{3} e - 3 \, a d^{2} f g^{4} e + 3 \, c d f^{4} g e^{2} - 3 \, b d f^{3} g^{2} e^{2} + 3 \, a d f^{2} g^{3} e^{2} - c f^{5} e^{3} + b f^{4} g e^{3} - a f^{3} g^{2} e^{3}\right )} \sqrt {-c f^{2} + b f g - a g^{2}}} - \frac {2 \, {\left (c d^{2} e - b d e^{2} + a e^{3}\right )} \arctan \left (-\frac {{\left (\sqrt {c} x - \sqrt {c x^{2} + b x + a}\right )} e + \sqrt {c} d}{\sqrt {-c d^{2} + b d e - a e^{2}}}\right )}{{\left (d^{3} g^{3} - 3 \, d^{2} f g^{2} e + 3 \, d f^{2} g e^{2} - f^{3} e^{3}\right )} \sqrt {-c d^{2} + b d e - a e^{2}}} + \frac {8 \, {\left (\sqrt {c} x - \sqrt {c x^{2} + b x + a}\right )}^{3} c^{2} d f^{2} g^{2} - 8 \, {\left (\sqrt {c} x - \sqrt {c x^{2} + b x + a}\right )}^{3} b c d f g^{3} + {\left (\sqrt {c} x - \sqrt {c x^{2} + b x + a}\right )}^{3} b^{2} d g^{4} + 4 \, {\left (\sqrt {c} x - \sqrt {c x^{2} + b x + a}\right )}^{3} a c d g^{4} - 4 \, {\left (\sqrt {c} x - \sqrt {c x^{2} + b x + a}\right )}^{3} b c f^{2} g^{2} e + 3 \, {\left (\sqrt {c} x - \sqrt {c x^{2} + b x + a}\right )}^{3} b^{2} f g^{3} e + 4 \, {\left (\sqrt {c} x - \sqrt {c x^{2} + b x + a}\right )}^{3} a c f g^{3} e - 4 \, {\left (\sqrt {c} x - \sqrt {c x^{2} + b x + a}\right )}^{3} a b g^{4} e + 8 \, {\left (\sqrt {c} x - \sqrt {c x^{2} + b x + a}\right )}^{2} c^{\frac {5}{2}} d f^{3} g - 5 \, {\left (\sqrt {c} x - \sqrt {c x^{2} + b x + a}\right )}^{2} b^{2} \sqrt {c} d f g^{3} - 4 \, {\left (\sqrt {c} x - \sqrt {c x^{2} + b x + a}\right )}^{2} a c^{\frac {3}{2}} d f g^{3} + 8 \, {\left (\sqrt {c} x - \sqrt {c x^{2} + b x + a}\right )}^{2} a b \sqrt {c} d g^{4} + 8 \, {\left (\sqrt {c} x - \sqrt {c x^{2} + b x + a}\right )}^{2} c^{\frac {5}{2}} f^{4} e - 20 \, {\left (\sqrt {c} x - \sqrt {c x^{2} + b x + a}\right )}^{2} b c^{\frac {3}{2}} f^{3} g e + 9 \, {\left (\sqrt {c} x - \sqrt {c x^{2} + b x + a}\right )}^{2} b^{2} \sqrt {c} f^{2} g^{2} e + 12 \, {\left (\sqrt {c} x - \sqrt {c x^{2} + b x + a}\right )}^{2} a c^{\frac {3}{2}} f^{2} g^{2} e - 4 \, {\left (\sqrt {c} x - \sqrt {c x^{2} + b x + a}\right )}^{2} a b \sqrt {c} f g^{3} e - 8 \, {\left (\sqrt {c} x - \sqrt {c x^{2} + b x + a}\right )}^{2} a^{2} \sqrt {c} g^{4} e + 8 \, {\left (\sqrt {c} x - \sqrt {c x^{2} + b x + a}\right )} b c^{2} d f^{3} g - 4 \, {\left (\sqrt {c} x - \sqrt {c x^{2} + b x + a}\right )} b^{2} c d f^{2} g^{2} - 8 \, {\left (\sqrt {c} x - \sqrt {c x^{2} + b x + a}\right )} a c^{2} d f^{2} g^{2} - {\left (\sqrt {c} x - \sqrt {c x^{2} + b x + a}\right )} b^{3} d f g^{3} + 4 \, {\left (\sqrt {c} x - \sqrt {c x^{2} + b x + a}\right )} a b c d f g^{3} + {\left (\sqrt {c} x - \sqrt {c x^{2} + b x + a}\right )} a b^{2} d g^{4} + 4 \, {\left (\sqrt {c} x - \sqrt {c x^{2} + b x + a}\right )} a^{2} c d g^{4} + 8 \, {\left (\sqrt {c} x - \sqrt {c x^{2} + b x + a}\right )} b c^{2} f^{4} e - 16 \, {\left (\sqrt {c} x - \sqrt {c x^{2} + b x + a}\right )} b^{2} c f^{3} g e - 16 \, {\left (\sqrt {c} x - \sqrt {c x^{2} + b x + a}\right )} a c^{2} f^{3} g e + 5 \, {\left (\sqrt {c} x - \sqrt {c x^{2} + b x + a}\right )} b^{3} f^{2} g^{2} e + 40 \, {\left (\sqrt {c} x - \sqrt {c x^{2} + b x + a}\right )} a b c f^{2} g^{2} e - 9 \, {\left (\sqrt {c} x - \sqrt {c x^{2} + b x + a}\right )} a b^{2} f g^{3} e - 28 \, {\left (\sqrt {c} x - \sqrt {c x^{2} + b x + a}\right )} a^{2} c f g^{3} e + 4 \, {\left (\sqrt {c} x - \sqrt {c x^{2} + b x + a}\right )} a^{2} b g^{4} e + 2 \, b^{2} c^{\frac {3}{2}} d f^{3} g - b^{3} \sqrt {c} d f^{2} g^{2} - 4 \, a b c^{\frac {3}{2}} d f^{2} g^{2} + a b^{2} \sqrt {c} d f g^{3} + 4 \, a^{2} c^{\frac {3}{2}} d f g^{3} + 2 \, b^{2} c^{\frac {3}{2}} f^{4} e - 3 \, b^{3} \sqrt {c} f^{3} g e - 8 \, a b c^{\frac {3}{2}} f^{3} g e + 15 \, a b^{2} \sqrt {c} f^{2} g^{2} e + 4 \, a^{2} c^{\frac {3}{2}} f^{2} g^{2} e - 20 \, a^{2} b \sqrt {c} f g^{3} e + 8 \, a^{3} \sqrt {c} g^{4} e}{4 \, {\left (c d^{2} f^{2} g^{3} - b d^{2} f g^{4} + a d^{2} g^{5} - 2 \, c d f^{3} g^{2} e + 2 \, b d f^{2} g^{3} e - 2 \, a d f g^{4} e + c f^{4} g e^{2} - b f^{3} g^{2} e^{2} + a f^{2} g^{3} e^{2}\right )} {\left ({\left (\sqrt {c} x - \sqrt {c x^{2} + b x + a}\right )}^{2} g + 2 \, {\left (\sqrt {c} x - \sqrt {c x^{2} + b x + a}\right )} \sqrt {c} f + b f - a g\right )}^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [F]
time = 0.00, size = -1, normalized size = -0.00 \begin {gather*} \int \frac {\sqrt {c\,x^2+b\,x+a}}{{\left (f+g\,x\right )}^3\,\left (d+e\,x\right )} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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