Optimal. Leaf size=7 \[ \text{PolyLog}(n+1,a x) \]
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Rubi [A] time = 0.0089991, antiderivative size = 7, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111, Rules used = {6589} \[ \text{PolyLog}(n+1,a x) \]
Antiderivative was successfully verified.
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Rule 6589
Rubi steps
\begin{align*} \int \frac{\text{Li}_n(a x)}{x} \, dx &=\text{Li}_{1+n}(a x)\\ \end{align*}
Mathematica [A] time = 0.0011286, size = 7, normalized size = 1. \[ \text{PolyLog}(n+1,a x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.044, size = 8, normalized size = 1.1 \begin{align*}{\it polylog} \left ( 1+n,ax \right ) \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)}{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\right )}{x}, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.528206, size = 5, normalized size = 0.71 \begin{align*} \operatorname{Li}_{n + 1}\left (a x\right ) \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)}{x}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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