Optimal. Leaf size=421 \[ \frac {4 e^{-\frac {a}{b n}} (e f-d g)^2 \sqrt {\pi } (d+e x) \left (c (d+e x)^n\right )^{-1/n} \text {erfi}\left (\frac {\sqrt {a+b \log \left (c (d+e x)^n\right )}}{\sqrt {b} \sqrt {n}}\right )}{3 b^{5/2} e^3 n^{5/2}}+\frac {16 e^{-\frac {2 a}{b n}} g (e f-d g) \sqrt {2 \pi } (d+e x)^2 \left (c (d+e x)^n\right )^{-2/n} \text {erfi}\left (\frac {\sqrt {2} \sqrt {a+b \log \left (c (d+e x)^n\right )}}{\sqrt {b} \sqrt {n}}\right )}{3 b^{5/2} e^3 n^{5/2}}+\frac {4 e^{-\frac {3 a}{b n}} g^2 \sqrt {3 \pi } (d+e x)^3 \left (c (d+e x)^n\right )^{-3/n} \text {erfi}\left (\frac {\sqrt {3} \sqrt {a+b \log \left (c (d+e x)^n\right )}}{\sqrt {b} \sqrt {n}}\right )}{b^{5/2} e^3 n^{5/2}}-\frac {2 (d+e x) (f+g x)^2}{3 b e n \left (a+b \log \left (c (d+e x)^n\right )\right )^{3/2}}+\frac {8 (e f-d g) (d+e x) (f+g x)}{3 b^2 e^2 n^2 \sqrt {a+b \log \left (c (d+e x)^n\right )}}-\frac {4 (d+e x) (f+g x)^2}{b^2 e n^2 \sqrt {a+b \log \left (c (d+e x)^n\right )}} \]
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Rubi [A]
time = 1.01, antiderivative size = 421, normalized size of antiderivative = 1.00, number of steps
used = 41, number of rules used = 8, integrand size = 26, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.308, Rules used = {2447, 2448,
2436, 2337, 2211, 2235, 2437, 2347} \begin {gather*} \frac {16 \sqrt {2 \pi } g e^{-\frac {2 a}{b n}} (d+e x)^2 (e f-d g) \left (c (d+e x)^n\right )^{-2/n} \text {Erfi}\left (\frac {\sqrt {2} \sqrt {a+b \log \left (c (d+e x)^n\right )}}{\sqrt {b} \sqrt {n}}\right )}{3 b^{5/2} e^3 n^{5/2}}+\frac {4 \sqrt {\pi } e^{-\frac {a}{b n}} (d+e x) (e f-d g)^2 \left (c (d+e x)^n\right )^{-1/n} \text {Erfi}\left (\frac {\sqrt {a+b \log \left (c (d+e x)^n\right )}}{\sqrt {b} \sqrt {n}}\right )}{3 b^{5/2} e^3 n^{5/2}}+\frac {4 \sqrt {3 \pi } g^2 e^{-\frac {3 a}{b n}} (d+e x)^3 \left (c (d+e x)^n\right )^{-3/n} \text {Erfi}\left (\frac {\sqrt {3} \sqrt {a+b \log \left (c (d+e x)^n\right )}}{\sqrt {b} \sqrt {n}}\right )}{b^{5/2} e^3 n^{5/2}}+\frac {8 (d+e x) (f+g x) (e f-d g)}{3 b^2 e^2 n^2 \sqrt {a+b \log \left (c (d+e x)^n\right )}}-\frac {4 (d+e x) (f+g x)^2}{b^2 e n^2 \sqrt {a+b \log \left (c (d+e x)^n\right )}}-\frac {2 (d+e x) (f+g x)^2}{3 b e n \left (a+b \log \left (c (d+e x)^n\right )\right )^{3/2}} \end {gather*}
Antiderivative was successfully verified.
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Rule 2211
Rule 2235
Rule 2337
Rule 2347
Rule 2436
Rule 2437
Rule 2447
Rule 2448
Rubi steps
\begin {align*} \int \frac {(f+g x)^2}{\left (a+b \log \left (c (d+e x)^n\right )\right )^{5/2}} \, dx &=-\frac {2 (d+e x) (f+g x)^2}{3 b e n \left (a+b \log \left (c (d+e x)^n\right )\right )^{3/2}}+\frac {2 \int \frac {(f+g x)^2}{\left (a+b \log \left (c (d+e x)^n\right )\right )^{3/2}} \, dx}{b n}-\frac {(4 (e f-d g)) \int \frac {f+g x}{\left (a+b \log \left (c (d+e x)^n\right )\right )^{3/2}} \, dx}{3 b e n}\\ &=-\frac {2 (d+e x) (f+g x)^2}{3 b e n \left (a+b \log \left (c (d+e x)^n\right )\right )^{3/2}}+\frac {8 (e f-d g) (d+e x) (f+g x)}{3 b^2 e^2 n^2 \sqrt {a+b \log \left (c (d+e x)^n\right )}}-\frac {4 (d+e x) (f+g x)^2}{b^2 e n^2 \sqrt {a+b \log \left (c (d+e x)^n\right )}}+\frac {12 \int \frac {(f+g x)^2}{\sqrt {a+b \log \left (c (d+e x)^n\right )}} \, dx}{b^2 n^2}-\frac {(16 (e f-d g)) \int \frac {f+g x}{\sqrt {a+b \log \left (c (d+e x)^n\right )}} \, dx}{3 b^2 e n^2}-\frac {(8 (e f-d g)) \int \frac {f+g x}{\sqrt {a+b \log \left (c (d+e x)^n\right )}} \, dx}{b^2 e n^2}+\frac {\left (8 (e f-d g)^2\right ) \int \frac {1}{\sqrt {a+b \log \left (c (d+e x)^n\right )}} \, dx}{3 b^2 e^2 n^2}\\ &=-\frac {2 (d+e x) (f+g x)^2}{3 b e n \left (a+b \log \left (c (d+e x)^n\right )\right )^{3/2}}+\frac {8 (e f-d g) (d+e x) (f+g x)}{3 b^2 e^2 n^2 \sqrt {a+b \log \left (c (d+e x)^n\right )}}-\frac {4 (d+e x) (f+g x)^2}{b^2 e n^2 \sqrt {a+b \log \left (c (d+e x)^n\right )}}+\frac {12 \int \left (\frac {(e f-d g)^2}{e^2 \sqrt {a+b \log \left (c (d+e x)^n\right )}}+\frac {2 g (e f-d g) (d+e x)}{e^2 \sqrt {a+b \log \left (c (d+e x)^n\right )}}+\frac {g^2 (d+e x)^2}{e^2 \sqrt {a+b \log \left (c (d+e x)^n\right )}}\right ) \, dx}{b^2 n^2}-\frac {(16 (e f-d g)) \int \left (\frac {e f-d g}{e \sqrt {a+b \log \left (c (d+e x)^n\right )}}+\frac {g (d+e x)}{e \sqrt {a+b \log \left (c (d+e x)^n\right )}}\right ) \, dx}{3 b^2 e n^2}-\frac {(8 (e f-d g)) \int \left (\frac {e f-d g}{e \sqrt {a+b \log \left (c (d+e x)^n\right )}}+\frac {g (d+e x)}{e \sqrt {a+b \log \left (c (d+e x)^n\right )}}\right ) \, dx}{b^2 e n^2}+\frac {\left (8 (e f-d g)^2\right ) \text {Subst}\left (\int \frac {1}{\sqrt {a+b \log \left (c x^n\right )}} \, dx,x,d+e x\right )}{3 b^2 e^3 n^2}\\ &=-\frac {2 (d+e x) (f+g x)^2}{3 b e n \left (a+b \log \left (c (d+e x)^n\right )\right )^{3/2}}+\frac {8 (e f-d g) (d+e x) (f+g x)}{3 b^2 e^2 n^2 \sqrt {a+b \log \left (c (d+e x)^n\right )}}-\frac {4 (d+e x) (f+g x)^2}{b^2 e n^2 \sqrt {a+b \log \left (c (d+e x)^n\right )}}+\frac {\left (12 g^2\right ) \int \frac {(d+e x)^2}{\sqrt {a+b \log \left (c (d+e x)^n\right )}} \, dx}{b^2 e^2 n^2}-\frac {(16 g (e f-d g)) \int \frac {d+e x}{\sqrt {a+b \log \left (c (d+e x)^n\right )}} \, dx}{3 b^2 e^2 n^2}-\frac {(8 g (e f-d g)) \int \frac {d+e x}{\sqrt {a+b \log \left (c (d+e x)^n\right )}} \, dx}{b^2 e^2 n^2}+\frac {(24 g (e f-d g)) \int \frac {d+e x}{\sqrt {a+b \log \left (c (d+e x)^n\right )}} \, dx}{b^2 e^2 n^2}-\frac {\left (16 (e f-d g)^2\right ) \int \frac {1}{\sqrt {a+b \log \left (c (d+e x)^n\right )}} \, dx}{3 b^2 e^2 n^2}-\frac {\left (8 (e f-d g)^2\right ) \int \frac {1}{\sqrt {a+b \log \left (c (d+e x)^n\right )}} \, dx}{b^2 e^2 n^2}+\frac {\left (12 (e f-d g)^2\right ) \int \frac {1}{\sqrt {a+b \log \left (c (d+e x)^n\right )}} \, dx}{b^2 e^2 n^2}+\frac {\left (8 (e f-d g)^2 (d+e x) \left (c (d+e x)^n\right )^{-1/n}\right ) \text {Subst}\left (\int \frac {e^{\frac {x}{n}}}{\sqrt {a+b x}} \, dx,x,\log \left (c (d+e x)^n\right )\right )}{3 b^2 e^3 n^3}\\ &=-\frac {2 (d+e x) (f+g x)^2}{3 b e n \left (a+b \log \left (c (d+e x)^n\right )\right )^{3/2}}+\frac {8 (e f-d g) (d+e x) (f+g x)}{3 b^2 e^2 n^2 \sqrt {a+b \log \left (c (d+e x)^n\right )}}-\frac {4 (d+e x) (f+g x)^2}{b^2 e n^2 \sqrt {a+b \log \left (c (d+e x)^n\right )}}+\frac {\left (12 g^2\right ) \text {Subst}\left (\int \frac {x^2}{\sqrt {a+b \log \left (c x^n\right )}} \, dx,x,d+e x\right )}{b^2 e^3 n^2}-\frac {(16 g (e f-d g)) \text {Subst}\left (\int \frac {x}{\sqrt {a+b \log \left (c x^n\right )}} \, dx,x,d+e x\right )}{3 b^2 e^3 n^2}-\frac {(8 g (e f-d g)) \text {Subst}\left (\int \frac {x}{\sqrt {a+b \log \left (c x^n\right )}} \, dx,x,d+e x\right )}{b^2 e^3 n^2}+\frac {(24 g (e f-d g)) \text {Subst}\left (\int \frac {x}{\sqrt {a+b \log \left (c x^n\right )}} \, dx,x,d+e x\right )}{b^2 e^3 n^2}-\frac {\left (16 (e f-d g)^2\right ) \text {Subst}\left (\int \frac {1}{\sqrt {a+b \log \left (c x^n\right )}} \, dx,x,d+e x\right )}{3 b^2 e^3 n^2}-\frac {\left (8 (e f-d g)^2\right ) \text {Subst}\left (\int \frac {1}{\sqrt {a+b \log \left (c x^n\right )}} \, dx,x,d+e x\right )}{b^2 e^3 n^2}+\frac {\left (12 (e f-d g)^2\right ) \text {Subst}\left (\int \frac {1}{\sqrt {a+b \log \left (c x^n\right )}} \, dx,x,d+e x\right )}{b^2 e^3 n^2}+\frac {\left (16 (e f-d g)^2 (d+e x) \left (c (d+e x)^n\right )^{-1/n}\right ) \text {Subst}\left (\int e^{-\frac {a}{b n}+\frac {x^2}{b n}} \, dx,x,\sqrt {a+b \log \left (c (d+e x)^n\right )}\right )}{3 b^3 e^3 n^3}\\ &=\frac {8 e^{-\frac {a}{b n}} (e f-d g)^2 \sqrt {\pi } (d+e x) \left (c (d+e x)^n\right )^{-1/n} \text {erfi}\left (\frac {\sqrt {a+b \log \left (c (d+e x)^n\right )}}{\sqrt {b} \sqrt {n}}\right )}{3 b^{5/2} e^3 n^{5/2}}-\frac {2 (d+e x) (f+g x)^2}{3 b e n \left (a+b \log \left (c (d+e x)^n\right )\right )^{3/2}}+\frac {8 (e f-d g) (d+e x) (f+g x)}{3 b^2 e^2 n^2 \sqrt {a+b \log \left (c (d+e x)^n\right )}}-\frac {4 (d+e x) (f+g x)^2}{b^2 e n^2 \sqrt {a+b \log \left (c (d+e x)^n\right )}}+\frac {\left (12 g^2 (d+e x)^3 \left (c (d+e x)^n\right )^{-3/n}\right ) \text {Subst}\left (\int \frac {e^{\frac {3 x}{n}}}{\sqrt {a+b x}} \, dx,x,\log \left (c (d+e x)^n\right )\right )}{b^2 e^3 n^3}-\frac {\left (16 g (e f-d g) (d+e x)^2 \left (c (d+e x)^n\right )^{-2/n}\right ) \text {Subst}\left (\int \frac {e^{\frac {2 x}{n}}}{\sqrt {a+b x}} \, dx,x,\log \left (c (d+e x)^n\right )\right )}{3 b^2 e^3 n^3}-\frac {\left (8 g (e f-d g) (d+e x)^2 \left (c (d+e x)^n\right )^{-2/n}\right ) \text {Subst}\left (\int \frac {e^{\frac {2 x}{n}}}{\sqrt {a+b x}} \, dx,x,\log \left (c (d+e x)^n\right )\right )}{b^2 e^3 n^3}+\frac {\left (24 g (e f-d g) (d+e x)^2 \left (c (d+e x)^n\right )^{-2/n}\right ) \text {Subst}\left (\int \frac {e^{\frac {2 x}{n}}}{\sqrt {a+b x}} \, dx,x,\log \left (c (d+e x)^n\right )\right )}{b^2 e^3 n^3}-\frac {\left (16 (e f-d g)^2 (d+e x) \left (c (d+e x)^n\right )^{-1/n}\right ) \text {Subst}\left (\int \frac {e^{\frac {x}{n}}}{\sqrt {a+b x}} \, dx,x,\log \left (c (d+e x)^n\right )\right )}{3 b^2 e^3 n^3}-\frac {\left (8 (e f-d g)^2 (d+e x) \left (c (d+e x)^n\right )^{-1/n}\right ) \text {Subst}\left (\int \frac {e^{\frac {x}{n}}}{\sqrt {a+b x}} \, dx,x,\log \left (c (d+e x)^n\right )\right )}{b^2 e^3 n^3}+\frac {\left (12 (e f-d g)^2 (d+e x) \left (c (d+e x)^n\right )^{-1/n}\right ) \text {Subst}\left (\int \frac {e^{\frac {x}{n}}}{\sqrt {a+b x}} \, dx,x,\log \left (c (d+e x)^n\right )\right )}{b^2 e^3 n^3}\\ &=\frac {8 e^{-\frac {a}{b n}} (e f-d g)^2 \sqrt {\pi } (d+e x) \left (c (d+e x)^n\right )^{-1/n} \text {erfi}\left (\frac {\sqrt {a+b \log \left (c (d+e x)^n\right )}}{\sqrt {b} \sqrt {n}}\right )}{3 b^{5/2} e^3 n^{5/2}}-\frac {2 (d+e x) (f+g x)^2}{3 b e n \left (a+b \log \left (c (d+e x)^n\right )\right )^{3/2}}+\frac {8 (e f-d g) (d+e x) (f+g x)}{3 b^2 e^2 n^2 \sqrt {a+b \log \left (c (d+e x)^n\right )}}-\frac {4 (d+e x) (f+g x)^2}{b^2 e n^2 \sqrt {a+b \log \left (c (d+e x)^n\right )}}+\frac {\left (24 g^2 (d+e x)^3 \left (c (d+e x)^n\right )^{-3/n}\right ) \text {Subst}\left (\int e^{-\frac {3 a}{b n}+\frac {3 x^2}{b n}} \, dx,x,\sqrt {a+b \log \left (c (d+e x)^n\right )}\right )}{b^3 e^3 n^3}-\frac {\left (32 g (e f-d g) (d+e x)^2 \left (c (d+e x)^n\right )^{-2/n}\right ) \text {Subst}\left (\int e^{-\frac {2 a}{b n}+\frac {2 x^2}{b n}} \, dx,x,\sqrt {a+b \log \left (c (d+e x)^n\right )}\right )}{3 b^3 e^3 n^3}-\frac {\left (16 g (e f-d g) (d+e x)^2 \left (c (d+e x)^n\right )^{-2/n}\right ) \text {Subst}\left (\int e^{-\frac {2 a}{b n}+\frac {2 x^2}{b n}} \, dx,x,\sqrt {a+b \log \left (c (d+e x)^n\right )}\right )}{b^3 e^3 n^3}+\frac {\left (48 g (e f-d g) (d+e x)^2 \left (c (d+e x)^n\right )^{-2/n}\right ) \text {Subst}\left (\int e^{-\frac {2 a}{b n}+\frac {2 x^2}{b n}} \, dx,x,\sqrt {a+b \log \left (c (d+e x)^n\right )}\right )}{b^3 e^3 n^3}-\frac {\left (32 (e f-d g)^2 (d+e x) \left (c (d+e x)^n\right )^{-1/n}\right ) \text {Subst}\left (\int e^{-\frac {a}{b n}+\frac {x^2}{b n}} \, dx,x,\sqrt {a+b \log \left (c (d+e x)^n\right )}\right )}{3 b^3 e^3 n^3}-\frac {\left (16 (e f-d g)^2 (d+e x) \left (c (d+e x)^n\right )^{-1/n}\right ) \text {Subst}\left (\int e^{-\frac {a}{b n}+\frac {x^2}{b n}} \, dx,x,\sqrt {a+b \log \left (c (d+e x)^n\right )}\right )}{b^3 e^3 n^3}+\frac {\left (24 (e f-d g)^2 (d+e x) \left (c (d+e x)^n\right )^{-1/n}\right ) \text {Subst}\left (\int e^{-\frac {a}{b n}+\frac {x^2}{b n}} \, dx,x,\sqrt {a+b \log \left (c (d+e x)^n\right )}\right )}{b^3 e^3 n^3}\\ &=\frac {4 e^{-\frac {a}{b n}} (e f-d g)^2 \sqrt {\pi } (d+e x) \left (c (d+e x)^n\right )^{-1/n} \text {erfi}\left (\frac {\sqrt {a+b \log \left (c (d+e x)^n\right )}}{\sqrt {b} \sqrt {n}}\right )}{3 b^{5/2} e^3 n^{5/2}}+\frac {16 e^{-\frac {2 a}{b n}} g (e f-d g) \sqrt {2 \pi } (d+e x)^2 \left (c (d+e x)^n\right )^{-2/n} \text {erfi}\left (\frac {\sqrt {2} \sqrt {a+b \log \left (c (d+e x)^n\right )}}{\sqrt {b} \sqrt {n}}\right )}{3 b^{5/2} e^3 n^{5/2}}+\frac {4 e^{-\frac {3 a}{b n}} g^2 \sqrt {3 \pi } (d+e x)^3 \left (c (d+e x)^n\right )^{-3/n} \text {erfi}\left (\frac {\sqrt {3} \sqrt {a+b \log \left (c (d+e x)^n\right )}}{\sqrt {b} \sqrt {n}}\right )}{b^{5/2} e^3 n^{5/2}}-\frac {2 (d+e x) (f+g x)^2}{3 b e n \left (a+b \log \left (c (d+e x)^n\right )\right )^{3/2}}+\frac {8 (e f-d g) (d+e x) (f+g x)}{3 b^2 e^2 n^2 \sqrt {a+b \log \left (c (d+e x)^n\right )}}-\frac {4 (d+e x) (f+g x)^2}{b^2 e n^2 \sqrt {a+b \log \left (c (d+e x)^n\right )}}\\ \end {align*}
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Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(1044\) vs. \(2(421)=842\).
time = 2.25, size = 1044, normalized size = 2.48 \begin {gather*} \frac {2 (d+e x) \left (-10 \sqrt {b} d e^{-\frac {2 a}{b n}} g^2 \sqrt {n} \sqrt {\pi } \left (c (d+e x)^n\right )^{-2/n} \left (2 d e^{\frac {a}{b n}} \left (c (d+e x)^n\right )^{\frac {1}{n}} \text {erfi}\left (\frac {\sqrt {a+b \log \left (c (d+e x)^n\right )}}{\sqrt {b} \sqrt {n}}\right )-\sqrt {2} (d+e x) \text {erfi}\left (\frac {\sqrt {2} \sqrt {a+b \log \left (c (d+e x)^n\right )}}{\sqrt {b} \sqrt {n}}\right )\right )+8 \sqrt {b} e e^{-\frac {2 a}{b n}} f g \sqrt {n} \sqrt {\pi } \left (c (d+e x)^n\right )^{-2/n} \left (-2 d e^{\frac {a}{b n}} \left (c (d+e x)^n\right )^{\frac {1}{n}} \text {erfi}\left (\frac {\sqrt {a+b \log \left (c (d+e x)^n\right )}}{\sqrt {b} \sqrt {n}}\right )+\sqrt {2} (d+e x) \text {erfi}\left (\frac {\sqrt {2} \sqrt {a+b \log \left (c (d+e x)^n\right )}}{\sqrt {b} \sqrt {n}}\right )\right )-\frac {6 e^{-\frac {3 a}{b n}} g^2 \sqrt {\pi } \left (c (d+e x)^n\right )^{-3/n} \left (\sqrt {3} (d+e x)^2-3 \sqrt {2} d e^{\frac {a}{b n}} (d+e x) \left (c (d+e x)^n\right )^{\frac {1}{n}}+3 d^2 e^{\frac {2 a}{b n}} \left (c (d+e x)^n\right )^{2/n}-3 d^2 e^{\frac {2 a}{b n}} \left (c (d+e x)^n\right )^{2/n} \text {erf}\left (\sqrt {-\frac {a+b \log \left (c (d+e x)^n\right )}{b n}}\right )+3 \sqrt {2} d e^{\frac {a}{b n}} (d+e x) \left (c (d+e x)^n\right )^{\frac {1}{n}} \text {erf}\left (\sqrt {2} \sqrt {-\frac {a+b \log \left (c (d+e x)^n\right )}{b n}}\right )-\sqrt {3} (d+e x)^2 \text {erf}\left (\sqrt {3} \sqrt {-\frac {a+b \log \left (c (d+e x)^n\right )}{b n}}\right )\right ) \sqrt {a+b \log \left (c (d+e x)^n\right )}}{\sqrt {-\frac {a+b \log \left (c (d+e x)^n\right )}{b n}}}-\frac {2 e^2 e^{-\frac {a}{b n}} f^2 \left (c (d+e x)^n\right )^{-1/n} \Gamma \left (\frac {1}{2},-\frac {a+b \log \left (c (d+e x)^n\right )}{b n}\right ) \sqrt {a+b \log \left (c (d+e x)^n\right )}}{\sqrt {-\frac {a+b \log \left (c (d+e x)^n\right )}{b n}}}-\frac {12 d e e^{-\frac {a}{b n}} f g \left (c (d+e x)^n\right )^{-1/n} \Gamma \left (\frac {1}{2},-\frac {a+b \log \left (c (d+e x)^n\right )}{b n}\right ) \sqrt {a+b \log \left (c (d+e x)^n\right )}}{\sqrt {-\frac {a+b \log \left (c (d+e x)^n\right )}{b n}}}-\frac {4 d^2 e^{-\frac {a}{b n}} g^2 \left (c (d+e x)^n\right )^{-1/n} \Gamma \left (\frac {1}{2},-\frac {a+b \log \left (c (d+e x)^n\right )}{b n}\right ) \sqrt {a+b \log \left (c (d+e x)^n\right )}}{\sqrt {-\frac {a+b \log \left (c (d+e x)^n\right )}{b n}}}-\frac {b e n (f+g x) \left (b e n (f+g x)+2 a (e f+2 d g+3 e g x)+2 b (2 d g+e (f+3 g x)) \log \left (c (d+e x)^n\right )\right )}{\left (a+b \log \left (c (d+e x)^n\right )\right )^{3/2}}\right )}{3 b^3 e^3 n^3} \end {gather*}
Antiderivative was successfully verified.
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Maple [F]
time = 0.15, size = 0, normalized size = 0.00 \[\int \frac {\left (g x +f \right )^{2}}{\left (a +b \ln \left (c \left (e x +d \right )^{n}\right )\right )^{\frac {5}{2}}}\, dx\]
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(-2)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: TypeError} \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 {\left (f + g x\right )^{2}}{\left (a + b \log {\left (c \left (d + e x\right )^{n} \right )}\right )^{\frac {5}{2}}}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \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 {{\left (f+g\,x\right )}^2}{{\left (a+b\,\ln \left (c\,{\left (d+e\,x\right )}^n\right )\right )}^{5/2}} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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[Out]
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