Optimal. Leaf size=9 \[ -\text{PolyLog}(2,1-x) \]
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Rubi [A] time = 0.0089794, antiderivative size = 9, normalized size of antiderivative = 1., 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*}
Mathematica [A] time = 0.0015296, size = 9, normalized size = 1. \[ -\text{PolyLog}(2,1-x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 5, normalized size = 0.6 \begin{align*} -{\it dilog} \left ( x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.0358, size = 16, normalized size = 1.78 \begin{align*} \log \left (x\right ) \log \left (-x + 1\right ) +{\rm Li}_2\left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.06785, size = 22, normalized size = 2.44 \begin{align*} -{\rm Li}_2\left (-x + 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [C] time = 1.92516, size = 10, normalized size = 1.11 \begin{align*} - \operatorname{Li}_{2}\left (\left (x - 1\right ) e^{i \pi }\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\log \left (x\right )}{x - 1}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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