Optimal. Leaf size=22 \[ \text{Unintegrable}\left (\frac{\log \left (c \left (d+e x^n\right )^p\right )}{(f+g x)^2},x\right ) \]
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Rubi [A] time = 0.0122881, 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 = {} \[ \int \frac{\log \left (c \left (d+e x^n\right )^p\right )}{(f+g x)^2} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{\log \left (c \left (d+e x^n\right )^p\right )}{(f+g x)^2} \, dx &=\int \frac{\log \left (c \left (d+e x^n\right )^p\right )}{(f+g x)^2} \, dx\\ \end{align*}
Mathematica [A] time = 0.181424, size = 0, normalized size = 0. \[ \int \frac{\log \left (c \left (d+e x^n\right )^p\right )}{(f+g x)^2} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 2.131, size = 0, normalized size = 0. \begin{align*} \int{\frac{\ln \left ( c \left ( d+e{x}^{n} \right ) ^{p} \right ) }{ \left ( gx+f \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*} -d n p \int \frac{1}{d g^{2} x^{2} + d f g x +{\left (e g^{2} x^{2} + e f g x\right )} x^{n}}\,{d x} - \frac{n p \log \left (g x + f\right )}{f g} - \frac{f \log \left ({\left (e x^{n} + d\right )}^{p}\right ) + f \log \left (c\right ) -{\left (g n p x + f n p\right )} \log \left (x\right )}{f g^{2} x + f^{2} g} \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 (e x^{n} + d\right )}^{p} c\right )}{g^{2} x^{2} + 2 \, f g x + f^{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 ({\left (e x^{n} + d\right )}^{p} c\right )}{{\left (g x + f\right )}^{2}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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