Optimal. Leaf size=25 \[ \text{Unintegrable}\left (\frac{\text{PolyLog}\left (k,e x^q\right ) \left (a+b \log \left (c x^n\right )\right )^p}{x},x\right ) \]
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Rubi [A] time = 0.0331453, 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 = {} \[ \int \frac{\left (a+b \log \left (c x^n\right )\right )^p \text{PolyLog}\left (k,e x^q\right )}{x} \, dx \]
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 )^p \text{Li}_k\left (e x^q\right )}{x} \, dx &=\int \frac{\left (a+b \log \left (c x^n\right )\right )^p \text{Li}_k\left (e x^q\right )}{x} \, dx\\ \end{align*}
Mathematica [A] time = 0.0484784, size = 0, normalized size = 0. \[ \int \frac{\left (a+b \log \left (c x^n\right )\right )^p \text{PolyLog}\left (k,e x^q\right )}{x} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.033, size = 0, normalized size = 0. \begin{align*} \int{\frac{ \left ( a+b\ln \left ( c{x}^{n} \right ) \right ) ^{p}{\it polylog} \left ( k,e{x}^{q} \right ) }{x}}\, 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*} \int \frac{{\left (b \log \left (c x^{n}\right ) + a\right )}^{p}{\rm Li}_{k}(e x^{q})}{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{{\left (b \log \left (c x^{n}\right ) + a\right )}^{p}{\rm polylog}\left (k, e x^{q}\right )}{x}, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\left (a + b \log{\left (c x^{n} \right )}\right )^{p} \operatorname{Li}_{k}\left (e x^{q}\right )}{x}\, dx \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 )}^{p}{\rm Li}_{k}(e x^{q})}{x}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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