Optimal. Leaf size=11 \[ \frac{\text{PolyLog}\left (3,a x^q\right )}{q} \]
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Rubi [A] time = 0.0102243, antiderivative size = 11, normalized size of antiderivative = 1., 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} \[ \frac{\text{PolyLog}\left (3,a x^q\right )}{q} \]
Antiderivative was successfully verified.
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Rule 6589
Rubi steps
\begin{align*} \int \frac{\text{Li}_2\left (a x^q\right )}{x} \, dx &=\frac{\text{Li}_3\left (a x^q\right )}{q}\\ \end{align*}
Mathematica [A] time = 0.0017468, size = 11, normalized size = 1. \[ \frac{\text{PolyLog}\left (3,a x^q\right )}{q} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.044, size = 12, normalized size = 1.1 \begin{align*}{\frac{{\it polylog} \left ( 3,a{x}^{q} \right ) }{q}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F] time = 0., size = 0, normalized size = 0. \begin{align*} -\frac{1}{6} \, q^{2} \log \left (x\right )^{3} + \frac{1}{2} \, q \log \left (-a x^{q} + 1\right ) \log \left (x\right )^{2} - q^{2} \int \frac{\log \left (x\right )^{2}}{2 \,{\left (a x x^{q} - x\right )}}\,{d x} +{\rm Li}_2\left (a x^{q}\right ) \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.83852, size = 28, normalized size = 2.55 \begin{align*} \frac{{\rm polylog}\left (3, a x^{q}\right )}{q} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\operatorname{Li}_{2}\left (a x^{q}\right )}{x}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{{\rm Li}_2\left (a x^{q}\right )}{x}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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