Optimal. Leaf size=28 \[ \text{Unintegrable}\left (\frac{\left (a+b \log \left (c x^n\right )\right ) \log \left (d \left (e+f x^m\right )^k\right )}{x^3},x\right ) \]
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Rubi [A] time = 0.0193067, 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 = {} \[ \int \frac{\left (a+b \log \left (c x^n\right )\right ) \log \left (d \left (e+f x^m\right )^k\right )}{x^3} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{\left (a+b \log \left (c x^n\right )\right ) \log \left (d \left (e+f x^m\right )^k\right )}{x^3} \, dx &=\int \frac{\left (a+b \log \left (c x^n\right )\right ) \log \left (d \left (e+f x^m\right )^k\right )}{x^3} \, dx\\ \end{align*}
Mathematica [A] time = 0.152721, size = 292, normalized size = 10.43 \[ \frac{b e k (m-2) m n \, _3F_2\left (1,-\frac{2}{m},-\frac{2}{m};1-\frac{2}{m},1-\frac{2}{m};-\frac{f x^m}{e}\right )+8 a e \log \left (d \left (e+f x^m\right )^k\right )-4 a e m \log \left (d \left (e+f x^m\right )^k\right )+4 a f k m x^m \, _2F_1\left (1,\frac{m-2}{m};2-\frac{2}{m};-\frac{f x^m}{e}\right )+8 b e \log \left (c x^n\right ) \log \left (d \left (e+f x^m\right )^k\right )-4 b e m \log \left (c x^n\right ) \log \left (d \left (e+f x^m\right )^k\right )+b e k (m-2) m \left (2 \log \left (c x^n\right )+n\right ) \, _2F_1\left (1,-\frac{2}{m};\frac{m-2}{m};-\frac{f x^m}{e}\right )-2 b e k m^2 \log \left (c x^n\right )+4 b e k m \log \left (c x^n\right )+4 b e n \log \left (d \left (e+f x^m\right )^k\right )-2 b e m n \log \left (d \left (e+f x^m\right )^k\right )-2 b e k m^2 n+4 b e k m n}{8 e (m-2) x^2} \]
Warning: Unable to verify antiderivative.
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Maple [A] time = 0.088, size = 0, normalized size = 0. \begin{align*} \int{\frac{ \left ( a+b\ln \left ( c{x}^{n} \right ) \right ) \ln \left ( d \left ( e+f{x}^{m} \right ) ^{k} \right ) }{{x}^{3}}}\, 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{{\left (b{\left (n + 2 \, \log \left (c\right )\right )} + 2 \, b \log \left (x^{n}\right ) + 2 \, a\right )} \log \left ({\left (f x^{m} + e\right )}^{k}\right )}{4 \, x^{2}} + \int \frac{4 \, b e \log \left (c\right ) \log \left (d\right ) + 4 \, a e \log \left (d\right ) +{\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^{m} + 2 \,{\left ({\left (f k m + 2 \, f \log \left (d\right )\right )} b x^{m} + 2 \, b e \log \left (d\right )\right )} \log \left (x^{n}\right )}{4 \,{\left (f x^{3} x^{m} + e x^{3}\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 (\frac{{\left (b \log \left (c x^{n}\right ) + a\right )} \log \left ({\left (f x^{m} + e\right )}^{k} d\right )}{x^{3}}, 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 \frac{{\left (b \log \left (c x^{n}\right ) + a\right )} \log \left ({\left (f x^{m} + e\right )}^{k} d\right )}{x^{3}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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