Optimal. Leaf size=9 \[ -\text {Li}_2(1-x) \]
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Rubi [A] time = 0.01, antiderivative size = 9, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 8, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {2315} \[ -\text {PolyLog}(2,1-x) \]
Antiderivative was successfully verified.
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Rule 2315
Rubi steps
\begin {align*} \int \frac {\log (x)}{-1+x} \, dx &=-\text {Li}_2(1-x)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 9, normalized size = 1.00 \[ -\text {Li}_2(1-x) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.42, size = 8, normalized size = 0.89 \[ -{\rm Li}_2\left (-x + 1\right ) \]
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 \[ \int \frac {\log \relax (x)}{x - 1}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 5, normalized size = 0.56 \[ -\dilog \relax (x ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.64, size = 12, normalized size = 1.33 \[ \log \relax (x) \log \left (-x + 1\right ) + {\rm Li}_2\relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 4, normalized size = 0.44 \[ -{\mathrm {Li}}_{\mathrm {2}}\relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [C] time = 1.72, size = 10, normalized size = 1.11 \[ - \operatorname {Li}_{2}\left (\left (x - 1\right ) e^{i \pi }\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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