Optimal. Leaf size=11 \[ \frac{\text{PolyLog}\left (4,a x^q\right )}{q} \]
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Rubi [A] time = 0.0097364, 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} \[ \frac{\text{PolyLog}\left (4,a x^q\right )}{q} \]
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*}
Mathematica [A] time = 0.0014392, size = 11, normalized size = 1. \[ \frac{\text{PolyLog}\left (4,a x^q\right )}{q} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.041, size = 12, normalized size = 1.1 \begin{align*}{\frac{{\it polylog} \left ( 4,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}{24} \, q^{3} \log \left (x\right )^{4} - \frac{1}{6} \, q^{2} \log \left (-a x^{q} + 1\right ) \log \left (x\right )^{3} + q^{3} \int \frac{\log \left (x\right )^{3}}{6 \,{\left (a x x^{q} - x\right )}}\,{d x} - \frac{1}{2} \, q{\rm Li}_2\left (a x^{q}\right ) \log \left (x\right )^{2} + \log \left (x\right ){\rm Li}_{3}(a x^{q}) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [C] time = 2.72366, size = 209, normalized size = 19. \begin{align*} -\frac{q^{2}{\rm \%iint}\left (a, q, x, -\frac{\log \left (-a x^{q} + 1\right )}{a}, -\log \left (-a x^{q} + 1\right ) \log \left (x\right ), -\frac{q \log \left (-a x^{q} + 1\right )}{x}\right ) \log \left (x\right )^{2} - q^{2}{\rm Li}_2\left (a x^{q}\right ) \log \left (x\right )^{2} - 2 \,{\rm polylog}\left (4, a x^{q}\right )}{2 \, 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}_{3}\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}_{3}(a x^{q})}{x}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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