Optimal. Leaf size=26 \[ \text{Unintegrable}\left (\frac{(f+g x)^m}{\left (a+b \log \left (c (d+e x)^n\right )\right )^2},x\right ) \]
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Rubi [A] time = 0.0268786, 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 = {} \[ \int \frac{(f+g x)^m}{\left (a+b \log \left (c (d+e x)^n\right )\right )^2} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{(f+g x)^m}{\left (a+b \log \left (c (d+e x)^n\right )\right )^2} \, dx &=\int \frac{(f+g x)^m}{\left (a+b \log \left (c (d+e x)^n\right )\right )^2} \, dx\\ \end{align*}
Mathematica [A] time = 2.64185, size = 0, normalized size = 0. \[ \int \frac{(f+g x)^m}{\left (a+b \log \left (c (d+e x)^n\right )\right )^2} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 6.036, size = 0, normalized size = 0. \begin{align*} \int{\frac{ \left ( gx+f \right ) ^{m}}{ \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{{\left (e x + d\right )}{\left (g x + f\right )}^{m}}{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{{\left (e g{\left (m + 1\right )} x + d g m + e f\right )}{\left (g x + f\right )}^{m}}{b^{2} e f n \log \left (c\right ) + a b e f n +{\left (b^{2} e g n \log \left (c\right ) + a b e g n\right )} x +{\left (b^{2} e g n x + b^{2} e f n\right )} \log \left ({\left (e x + d\right )}^{n}\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 (g x + f\right )}^{m}}{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{{\left (g x + f\right )}^{m}}{{\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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