Optimal. Leaf size=25 \[ \text{Unintegrable}\left (\frac{\log \left (f x^m\right )}{\left (a+b \log \left (c (d+e x)^n\right )\right )^2},x\right ) \]
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Rubi [A] time = 0.0108033, 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 = {} \[ \int \frac{\log \left (f x^m\right )}{\left (a+b \log \left (c (d+e x)^n\right )\right )^2} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{\log \left (f x^m\right )}{\left (a+b \log \left (c (d+e x)^n\right )\right )^2} \, dx &=\int \frac{\log \left (f x^m\right )}{\left (a+b \log \left (c (d+e x)^n\right )\right )^2} \, dx\\ \end{align*}
Mathematica [A] time = 0.462445, size = 0, normalized size = 0. \[ \int \frac{\log \left (f x^m\right )}{\left (a+b \log \left (c (d+e x)^n\right )\right )^2} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 10.89, size = 0, normalized size = 0. \begin{align*} \int{\frac{\ln \left ( f{x}^{m} \right ) }{ \left ( a+b\ln \left ( c \left ( ex+d \right ) ^{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*} -\frac{e x \log \left (f\right ) + d \log \left (f\right ) +{\left (e x + d\right )} \log \left (x^{m}\right )}{b^{2} e n \log \left ({\left (e x + d\right )}^{n}\right ) + b^{2} e n \log \left (c\right ) + a b e n} + \int \frac{e{\left (m + \log \left (f\right )\right )} x + e x \log \left (x^{m}\right ) + d m}{b^{2} e n x \log \left ({\left (e x + d\right )}^{n}\right ) +{\left (b^{2} e n \log \left (c\right ) + a b e n\right )} x}\,{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{\log \left (f x^{m}\right )}{b^{2} \log \left ({\left (e x + d\right )}^{n} c\right )^{2} + 2 \, a b \log \left ({\left (e x + d\right )}^{n} c\right ) + a^{2}}, 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 (f x^{m}\right )}{{\left (b \log \left ({\left (e x + d\right )}^{n} c\right ) + a\right )}^{2}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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