Optimal. Leaf size=12 \[ \frac {\text {Li}_2(1-c x)}{c} \]
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Rubi [A]
time = 0.01, antiderivative size = 12, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {2352}
\begin {gather*} \frac {\text {PolyLog}(2,1-c x)}{c} \end {gather*}
Antiderivative was successfully verified.
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Rule 2352
Rubi steps
\begin {align*} \int \frac {\log (c x)}{1-c x} \, dx &=\frac {\text {Li}_2(1-c x)}{c}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 12, normalized size = 1.00 \begin {gather*} \frac {\text {Li}_2(1-c x)}{c} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.11, size = 9, normalized size = 0.75
method | result | size |
derivativedivides | \(\frac {\dilog \left (c x \right )}{c}\) | \(9\) |
default | \(\frac {\dilog \left (c x \right )}{c}\) | \(9\) |
risch | \(\frac {\dilog \left (c x \right )}{c}\) | \(9\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 48 vs.
\(2 (11) = 22\).
time = 0.27, size = 48, normalized size = 4.00 \begin {gather*} -\frac {\log \left (c x - 1\right ) \log \left (c x\right )}{c} + \frac {\log \left (c x - 1\right ) \log \left (x\right )}{c} - \frac {\log \left (-c x + 1\right ) \log \left (x\right ) + {\rm Li}_2\left (c x\right )}{c} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.34, size = 11, normalized size = 0.92 \begin {gather*} \frac {{\rm Li}_2\left (-c x + 1\right )}{c} \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 {\log {\left (c x \right )}}{c x - 1}\, 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 [B]
time = 3.46, size = 8, normalized size = 0.67 \begin {gather*} \frac {{\mathrm {Li}}_{\mathrm {2}}\left (c\,x\right )}{c} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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