Optimal. Leaf size=10 \[ \text{PolyLog}\left (2,1-\frac{x}{c}\right ) \]
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Rubi [A] time = 0.0105183, antiderivative size = 10, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 14, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.071, Rules used = {2315} \[ \text{PolyLog}\left (2,1-\frac{x}{c}\right ) \]
Antiderivative was successfully verified.
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Rule 2315
Rubi steps
\begin{align*} \int \frac{\log \left (\frac{x}{c}\right )}{c-x} \, dx &=\text{Li}_2\left (1-\frac{x}{c}\right )\\ \end{align*}
Mathematica [A] time = 0.0022178, size = 11, normalized size = 1.1 \[ \text{PolyLog}\left (2,\frac{c-x}{c}\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.039, size = 7, normalized size = 0.7 \begin{align*}{\it dilog} \left ({\frac{x}{c}} \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 1.1079, size = 61, normalized size = 6.1 \begin{align*} \log \left (c - x\right ) \log \left (x\right ) - \log \left (c - x\right ) \log \left (\frac{x}{c}\right ) - \log \left (x\right ) \log \left (-\frac{x}{c} + 1\right ) -{\rm Li}_2\left (\frac{x}{c}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.934072, size = 23, normalized size = 2.3 \begin{align*}{\rm Li}_2\left (-\frac{x}{c} + 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F] time = 0., size = 0, normalized size = 0. \begin{align*} - \int \frac{\log{\left (\frac{x}{c} \right )}}{- c + x}\, dx \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 (\frac{x}{c}\right )}{c - x}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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