Optimal. Leaf size=11 \[ \frac {\text {Li}_4\left (a x^q\right )}{q} \]
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Rubi [A] time = 0.01, antiderivative size = 11, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {6589} \[ \frac {\text {PolyLog}\left (4,a x^q\right )}{q} \]
Antiderivative was successfully verified.
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Rule 6589
Rubi steps
\begin {align*} \int \frac {\text {Li}_3\left (a x^q\right )}{x} \, dx &=\frac {\text {Li}_4\left (a x^q\right )}{q}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 11, normalized size = 1.00 \[ \frac {\text {Li}_4\left (a x^q\right )}{q} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.46, size = 11, normalized size = 1.00 \[ \frac {{\rm polylog}\left (4, a x^{q}\right )}{q} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {{\rm Li}_{3}(a x^{q})}{x}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 12, normalized size = 1.09 \[ \frac {\polylog \left (4, a \,x^{q}\right )}{q} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \[ \frac {1}{24} \, q^{3} \log \relax (x)^{4} - \frac {1}{6} \, q^{2} \log \left (-a x^{q} + 1\right ) \log \relax (x)^{3} + q^{3} \int \frac {\log \relax (x)^{3}}{6 \, {\left (a x x^{q} - x\right )}}\,{d x} - \frac {1}{2} \, q {\rm Li}_2\left (a x^{q}\right ) \log \relax (x)^{2} + \log \relax (x) {\rm Li}_{3}(a x^{q}) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.09 \[ \int \frac {\mathrm {polylog}\left (3,a\,x^q\right )}{x} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\operatorname {Li}_{3}\left (a x^{q}\right )}{x}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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