Optimal. Leaf size=11 \[ \frac{1}{2} \text{PolyLog}\left (4,a x^2\right ) \]
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Rubi [A] time = 0.0090189, 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} \[ \frac{1}{2} \text{PolyLog}\left (4,a x^2\right ) \]
Antiderivative was successfully verified.
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Rule 6589
Rubi steps
\begin{align*} \int \frac{\text{Li}_3\left (a x^2\right )}{x} \, dx &=\frac{\text{Li}_4\left (a x^2\right )}{2}\\ \end{align*}
Mathematica [A] time = 0.0014221, size = 11, normalized size = 1. \[ \frac{1}{2} \text{PolyLog}\left (4,a x^2\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.154, size = 10, normalized size = 0.9 \begin{align*}{\frac{{\it polylog} \left ( 4,a{x}^{2} \right ) }{2}} \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}_{3}(a x^{2})}{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 (3, a x^{2}\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}_{3}\left (a x^{2}\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^{2})}{x}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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