Optimal. Leaf size=5 \[ \text {Li}_4(a x) \]
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Rubi [A] time = 0.01, antiderivative size = 5, normalized size of antiderivative = 1.00, 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} \[ \text {PolyLog}(4,a x) \]
Antiderivative was successfully verified.
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Rule 6589
Rubi steps
\begin {align*} \int \frac {\text {Li}_3(a x)}{x} \, dx &=\text {Li}_4(a x)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 5, normalized size = 1.00 \[ \text {Li}_4(a x) \]
Antiderivative was successfully verified.
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fricas [F] time = 0.48, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {{\rm polylog}\left (3, a x\right )}{x}, x\right ) \]
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 \[ \int \frac {{\rm Li}_{3}(a x)}{x}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 6, normalized size = 1.20 \[ \polylog \left (4, a x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.32, size = 5, normalized size = 1.00 \[ {\rm Li}_{4}(a x) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.20 \[ \int \frac {\mathrm {polylog}\left (3,a\,x\right )}{x} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.45, size = 3, normalized size = 0.60 \[ \operatorname {Li}_{4}\left (a x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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