Optimal. Leaf size=11 \[ -\frac {1}{2} \text {Li}_2(c x){}^2 \]
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Rubi [A] time = 0.03, antiderivative size = 11, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 2, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {6589, 6601} \[ -\frac {1}{2} \text {PolyLog}(2,c x)^2 \]
Antiderivative was successfully verified.
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Rule 6589
Rule 6601
Rubi steps
\begin {align*} \int \frac {\log (1-c x) \text {Li}_2(c x)}{x} \, dx &=-\frac {1}{2} \text {Li}_2(c x){}^2\\ \end {align*}
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Mathematica [A] time = 0.01, size = 11, normalized size = 1.00 \[ -\frac {1}{2} \text {Li}_2(c x){}^2 \]
Antiderivative was successfully verified.
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fricas [A] time = 1.04, size = 8, normalized size = 0.73 \[ -\frac {1}{2} \, {\rm Li}_2\left (c x\right )^{2} \]
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 \[ \int \frac {{\rm Li}_2\left (c x\right ) \log \left (-c x + 1\right )}{x}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 10, normalized size = 0.91 \[ -\frac {\polylog \left (2, c x \right )^{2}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.29, size = 8, normalized size = 0.73 \[ -\frac {1}{2} \, {\rm Li}_2\left (c x\right )^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.24, size = 9, normalized size = 0.82 \[ -\frac {{\mathrm {polylog}\left (2,c\,x\right )}^2}{2} \]
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 \[ \int \frac {\log {\left (- c x + 1 \right )} \operatorname {Li}_{2}\left (c x\right )}{x}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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