Optimal. Leaf size=26 \[ \text {Int}\left (\frac {\text {Li}_k\left (e x^q\right ) \left (a+b \log \left (c x^n\right )\right )^p}{x},x\right ) \]
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Rubi [A] time = 0.03, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, 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*}
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Mathematica [A] time = 0.05, size = 0, normalized size = 0.00 \[ \int \frac {\left (a+b \log \left (c x^n\right )\right )^p \text {Li}_k\left (e x^q\right )}{x} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.89, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {{\left (b \log \left (c x^{n}\right ) + a\right )}^{p} {\rm polylog}\left (k, e x^{q}\right )}{x}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {{\left (b \log \left (c x^{n}\right ) + a\right )}^{p} {\rm Li}_{k}(e x^{q})}{x}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.07, size = 0, normalized size = 0.00 \[ \int \frac {\left (b \ln \left (c \,x^{n}\right )+a \right )^{p} \polylog \left (k , e \,x^{q}\right )}{x}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {{\left (b \log \left (c x^{n}\right ) + a\right )}^{p} {\rm Li}_{k}(e x^{q})}{x}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [A] time = 0.00, size = -1, normalized size = -0.04 \[ \int \frac {\mathrm {polylog}\left (k,e\,x^q\right )\,{\left (a+b\,\ln \left (c\,x^n\right )\right )}^p}{x} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\left (a + b \log {\left (c x^{n} \right )}\right )^{p} \operatorname {Li}_{k}\left (e x^{q}\right )}{x}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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