Optimal. Leaf size=5 \[ \text {PolyLog}(4,a x) \]
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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 = {6724}
\begin {gather*} \text {Li}_4(a x) \end {gather*}
Antiderivative was successfully verified.
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Rule 6724
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 \begin {gather*} \text {PolyLog}(4,a x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.13, size = 6, normalized size = 1.20
method | result | size |
derivativedivides | \(\polylog \left (4, a x \right )\) | \(6\) |
default | \(\polylog \left (4, a x \right )\) | \(6\) |
meijerg | \(\polylog \left (4, a x \right )\) | \(6\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.25, size = 5, normalized size = 1.00 \begin {gather*} {\rm Li}_{4}(a x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.19, size = 3, normalized size = 0.60 \begin {gather*} \operatorname {Li}_{4}\left (a x\right ) \end {gather*}
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 \begin {gather*} \text {could not integrate} \end {gather*}
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 \begin {gather*} \int \frac {\mathrm {polylog}\left (3,a\,x\right )}{x} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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