Optimal. Leaf size=26 \[ \text{Unintegrable}\left (x \left (a+b \log \left (c x^n\right )\right ) \log \left (d \left (e+f x^m\right )^k\right ),x\right ) \]
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Rubi [A] time = 0.0114566, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ \int x \left (a+b \log \left (c x^n\right )\right ) \log \left (d \left (e+f x^m\right )^k\right ) \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int x \left (a+b \log \left (c x^n\right )\right ) \log \left (d \left (e+f x^m\right )^k\right ) \, dx &=\int x \left (a+b \log \left (c x^n\right )\right ) \log \left (d \left (e+f x^m\right )^k\right ) \, dx\\ \end{align*}
Mathematica [A] time = 0.170561, size = 292, normalized size = 11.23 \[ -\frac{x^2 \left (b e k m (m+2) n \, _3F_2\left (1,\frac{2}{m},\frac{2}{m};1+\frac{2}{m},1+\frac{2}{m};-\frac{f x^m}{e}\right )-8 a e \log \left (d \left (e+f x^m\right )^k\right )-4 a e m \log \left (d \left (e+f x^m\right )^k\right )+4 a f k m x^m \, _2F_1\left (1,\frac{m+2}{m};2+\frac{2}{m};-\frac{f x^m}{e}\right )-8 b e \log \left (c x^n\right ) \log \left (d \left (e+f x^m\right )^k\right )-4 b e m \log \left (c x^n\right ) \log \left (d \left (e+f x^m\right )^k\right )+b e k m (m+2) \left (n-2 \log \left (c x^n\right )\right ) \, _2F_1\left (1,\frac{2}{m};\frac{m+2}{m};-\frac{f x^m}{e}\right )+2 b e k m^2 \log \left (c x^n\right )+4 b e k m \log \left (c x^n\right )+4 b e n \log \left (d \left (e+f x^m\right )^k\right )+2 b e m n \log \left (d \left (e+f x^m\right )^k\right )-2 b e k m^2 n-4 b e k m n\right )}{8 e (m+2)} \]
Warning: Unable to verify antiderivative.
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Maple [A] time = 0.084, size = 0, normalized size = 0. \begin{align*} \int x \left ( a+b\ln \left ( c{x}^{n} \right ) \right ) \ln \left ( d \left ( e+f{x}^{m} \right ) ^{k} \right ) \, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0., size = 0, normalized size = 0. \begin{align*} \frac{1}{4} \,{\left (2 \, b x^{2} \log \left (x^{n}\right ) -{\left (b{\left (n - 2 \, \log \left (c\right )\right )} - 2 \, a\right )} x^{2}\right )} \log \left ({\left (f x^{m} + e\right )}^{k}\right ) + \int -\frac{{\left (2 \,{\left (f k m - 2 \, f \log \left (d\right )\right )} a -{\left (f k m n - 2 \,{\left (f k m - 2 \, f \log \left (d\right )\right )} \log \left (c\right )\right )} b\right )} x x^{m} - 4 \,{\left (b e \log \left (c\right ) \log \left (d\right ) + a e \log \left (d\right )\right )} x + 2 \,{\left ({\left (f k m - 2 \, f \log \left (d\right )\right )} b x x^{m} - 2 \, b e x \log \left (d\right )\right )} \log \left (x^{n}\right )}{4 \,{\left (f x^{m} + e\right )}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left ({\left (b x \log \left (c x^{n}\right ) + a x\right )} \log \left ({\left (f x^{m} + e\right )}^{k} d\right ), x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int{\left (b \log \left (c x^{n}\right ) + a\right )} x \log \left ({\left (f x^{m} + e\right )}^{k} d\right )\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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