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 = {2315} \[ \frac {\text {PolyLog}(2,1-c x)}{c} \]
Antiderivative was successfully verified.
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Rule 2315
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 \[ \frac {\text {Li}_2(1-c x)}{c} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.84, size = 11, normalized size = 0.92 \[ \frac {{\rm Li}_2\left (-c x + 1\right )}{c} \]
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 \[ \int -\frac {\log \left (c x\right )}{c x - 1}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 9, normalized size = 0.75 \[ \frac {\dilog \left (c x \right )}{c} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.54, size = 48, normalized size = 4.00 \[ -\frac {\log \left (c x - 1\right ) \log \left (c x\right )}{c} + \frac {\log \left (c x - 1\right ) \log \relax (x)}{c} - \frac {\log \left (-c x + 1\right ) \log \relax (x) + {\rm Li}_2\left (c x\right )}{c} \]
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 \[ \frac {{\mathrm {Li}}_{\mathrm {2}}\left (c\,x\right )}{c} \]
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 \[ - \int \frac {\log {\left (c x \right )}}{c x - 1}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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