Optimal. Leaf size=11 \[ -\frac {1}{2} \text {PolyLog}(2,c x)^2 \]
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Rubi [A]
time = 0.02, 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 = {6724, 6736}
\begin {gather*} -\frac {1}{2} \text {Li}_2(c x){}^2 \end {gather*}
Antiderivative was successfully verified.
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Rule 6724
Rule 6736
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 \begin {gather*} -\frac {1}{2} \text {PolyLog}(2,c x)^2 \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.06, size = 10, normalized size = 0.91
method | result | size |
derivativedivides | \(-\frac {\polylog \left (2, c x \right )^{2}}{2}\) | \(10\) |
default | \(-\frac {\polylog \left (2, c x \right )^{2}}{2}\) | \(10\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.25, size = 8, normalized size = 0.73 \begin {gather*} -\frac {1}{2} \, {\rm Li}_2\left (c x\right )^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 8, normalized size = 0.73 \begin {gather*} -\frac {1}{2} \, {\rm Li}_2\left (c x\right )^{2} \end {gather*}
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 \begin {gather*} \int \frac {\log {\left (- c x + 1 \right )} \operatorname {Li}_{2}\left (c x\right )}{x}\, dx \end {gather*}
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 \begin {gather*} \text {could not integrate} \end {gather*}
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 \begin {gather*} -\frac {{\mathrm {polylog}\left (2,c\,x\right )}^2}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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