Optimal. Leaf size=11 \[ \frac {\text {Li}_4\left (a x^2\right )}{2} \]
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Rubi [A] time = 0.01, antiderivative size = 11, normalized size of antiderivative = 1.00, 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*}
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Mathematica [A] time = 0.00, size = 11, normalized size = 1.00 \[ \frac {\text {Li}_4\left (a x^2\right )}{2} \]
Antiderivative was successfully verified.
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fricas [F] time = 0.84, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {{\rm polylog}\left (3, a x^{2}\right )}{x}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {{\rm Li}_{3}(a x^{2})}{x}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.13, size = 10, normalized size = 0.91 \[ \frac {\polylog \left (4, a \,x^{2}\right )}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {{\rm Li}_{3}(a x^{2})}{x}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.20, size = 9, normalized size = 0.82 \[ \frac {\mathrm {polylog}\left (4,a\,x^2\right )}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\operatorname {Li}_{3}\left (a x^{2}\right )}{x}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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