Optimal. Leaf size=64 \[ -\frac {\text {Li}_k\left (e x^q\right )}{b n \left (a+b \log \left (c x^n\right )\right )}+\frac {q \text {Int}\left (\frac {\text {Li}_{-1+k}\left (e x^q\right )}{x \left (a+b \log \left (c x^n\right )\right )},x\right )}{b n} \]
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Rubi [A]
time = 0.05, 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 = {}
\begin {gather*} \int \frac {\text {PolyLog}\left (k,e x^q\right )}{x \left (a+b \log \left (c x^n\right )\right )^2} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {\text {Li}_k\left (e x^q\right )}{x \left (a+b \log \left (c x^n\right )\right )^2} \, dx &=-\frac {\text {Li}_k\left (e x^q\right )}{b n \left (a+b \log \left (c x^n\right )\right )}+\frac {q \int \frac {\text {Li}_{-1+k}\left (e x^q\right )}{x \left (a+b \log \left (c x^n\right )\right )} \, dx}{b n}\\ \end {align*}
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Mathematica [A]
time = 0.03, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\text {Li}_k\left (e x^q\right )}{x \left (a+b \log \left (c x^n\right )\right )^2} \, dx \end {gather*}
Verification is not applicable to the result.
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Maple [A]
time = 0.02, size = 0, normalized size = 0.00 \[\int \frac {\polylog \left (k , e \,x^{q}\right )}{x \left (a +b \ln \left (c \,x^{n}\right )\right )^{2}}\, dx\]
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 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
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 \begin {gather*} \int \frac {\operatorname {Li}_{k}\left (e x^{q}\right )}{x \left (a + b \log {\left (c x^{n} \right )}\right )^{2}}\, dx \end {gather*}
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 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [A]
time = 0.00, size = -1, normalized size = -0.02 \begin {gather*} \int \frac {\mathrm {polylog}\left (k,e\,x^q\right )}{x\,{\left (a+b\,\ln \left (c\,x^n\right )\right )}^2} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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