Optimal. Leaf size=30 \[ \text{Unintegrable}\left (\frac{\log \left (d \left (e+f x^m\right )^r\right )}{x \left (a+b \log \left (c x^n\right )\right )^2},x\right ) \]
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Rubi [A] time = 0.0337653, 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 = {} \[ \int \frac{\log \left (d \left (e+f x^m\right )^r\right )}{x \left (a+b \log \left (c x^n\right )\right )^2} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{\log \left (d \left (e+f x^m\right )^r\right )}{x \left (a+b \log \left (c x^n\right )\right )^2} \, dx &=\int \frac{\log \left (d \left (e+f x^m\right )^r\right )}{x \left (a+b \log \left (c x^n\right )\right )^2} \, dx\\ \end{align*}
Mathematica [A] time = 1.77742, size = 0, normalized size = 0. \[ \int \frac{\log \left (d \left (e+f x^m\right )^r\right )}{x \left (a+b \log \left (c x^n\right )\right )^2} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.076, size = 0, normalized size = 0. \begin{align*} \int{\frac{\ln \left ( d \left ( e+f{x}^{m} \right ) ^{r} \right ) }{x \left ( a+b\ln \left ( c{x}^{n} \right ) \right ) ^{2}}}\, 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*} f m r \int \frac{x^{m}}{{\left (b^{2} f n \log \left (c\right ) + a b f n\right )} x x^{m} +{\left (b^{2} e n \log \left (c\right ) + a b e n\right )} x +{\left (b^{2} f n x x^{m} + b^{2} e n x\right )} \log \left (x^{n}\right )}\,{d x} - \frac{\log \left ({\left (f x^{m} + e\right )}^{r}\right ) + \log \left (d\right )}{b^{2} n \log \left (c\right ) + b^{2} n \log \left (x^{n}\right ) + a b n} \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{\log \left ({\left (f x^{m} + e\right )}^{r} d\right )}{b^{2} x \log \left (c x^{n}\right )^{2} + 2 \, a b x \log \left (c x^{n}\right ) + a^{2} x}, 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{\log \left ({\left (f x^{m} + e\right )}^{r} d\right )}{{\left (b \log \left (c x^{n}\right ) + a\right )}^{2} x}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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