Optimal. Leaf size=13 \[ \frac{\text{PolyLog}\left (n+1,a x^q\right )}{q} \]
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Rubi [A] time = 0.0098521, antiderivative size = 13, 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} \[ \frac{\text{PolyLog}\left (n+1,a x^q\right )}{q} \]
Antiderivative was successfully verified.
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Rule 6589
Rubi steps
\begin{align*} \int \frac{\text{Li}_n\left (a x^q\right )}{x} \, dx &=\frac{\text{Li}_{1+n}\left (a x^q\right )}{q}\\ \end{align*}
Mathematica [A] time = 0.0012072, size = 13, normalized size = 1. \[ \frac{\text{PolyLog}\left (n+1,a x^q\right )}{q} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.046, size = 14, normalized size = 1.1 \begin{align*}{\frac{{\it polylog} \left ( 1+n,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*} \int \frac{{\rm Li}_{n}(a x^{q})}{x}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [F] time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{{\rm polylog}\left (n, a x^{q}\right )}{x}, x\right ) \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}_{n}\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}_{n}(a x^{q})}{x}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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