Optimal. Leaf size=10 \[ \text {Li}_2\left (1-\frac {x}{c}\right ) \]
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Rubi [A] time = 0.01, antiderivative size = 10, normalized size of antiderivative = 1.00, 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*}
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Mathematica [A] time = 0.00, size = 11, normalized size = 1.10 \[ \text {Li}_2\left (\frac {c-x}{c}\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.60, size = 9, normalized size = 0.90 \[ {\rm Li}_2\left (-\frac {x}{c} + 1\right ) \]
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 \[ \int \frac {\log \left (\frac {x}{c}\right )}{c - x}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 7, normalized size = 0.70 \[ \dilog \left (\frac {x}{c}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.57, size = 45, normalized size = 4.50 \[ \log \left (c - x\right ) \log \relax (x) - \log \left (c - x\right ) \log \left (\frac {x}{c}\right ) - \log \relax (x) \log \left (-\frac {x}{c} + 1\right ) - {\rm Li}_2\left (\frac {x}{c}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.50, size = 6, normalized size = 0.60 \[ {\mathrm {Li}}_{\mathrm {2}}\left (\frac {x}{c}\right ) \]
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 \[ - \int \frac {\log {\left (\frac {x}{c} \right )}}{- c + x}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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