Optimal. Leaf size=11 \[ \frac {\text {PolyLog}\left (4,a x^q\right )}{q} \]
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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 = {6724}
\begin {gather*} \frac {\text {Li}_4\left (a x^q\right )}{q} \end {gather*}
Antiderivative was successfully verified.
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Rule 6724
Rubi steps
\begin {align*} \int \frac {\text {Li}_3\left (a x^q\right )}{x} \, dx &=\frac {\text {Li}_4\left (a x^q\right )}{q}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 11, normalized size = 1.00 \begin {gather*} \frac {\text {PolyLog}\left (4,a x^q\right )}{q} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.23, size = 12, normalized size = 1.09
method | result | size |
derivativedivides | \(\frac {\polylog \left (4, a \,x^{q}\right )}{q}\) | \(12\) |
default | \(\frac {\polylog \left (4, a \,x^{q}\right )}{q}\) | \(12\) |
meijerg | \(\frac {\polylog \left (4, a \,x^{q}\right )}{q}\) | \(12\) |
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 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 11, normalized size = 1.00 \begin {gather*} \frac {{\rm polylog}\left (4, a x^{q}\right )}{q} \end {gather*}
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 \begin {gather*} \int \frac {\operatorname {Li}_{3}\left (a x^{q}\right )}{x}\, dx \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 = -0.09 \begin {gather*} \int \frac {\mathrm {polylog}\left (3,a\,x^q\right )}{x} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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