Optimal. Leaf size=9 \[ -\text {Li}_2(1-x) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.01, antiderivative size = 9, normalized size of antiderivative = 1.00, 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 = {2352}
\begin {gather*} -\text {PolyLog}(2,1-x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 2352
Rubi steps
\begin {align*} \int \frac {\log (x)}{-1+x} \, dx &=-\text {Li}_2(1-x)\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.00, size = 9, normalized size = 1.00 \begin {gather*} -\text {Li}_2(1-x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.07, size = 5, normalized size = 0.56
method | result | size |
default | \(-\dilog \left (x \right )\) | \(5\) |
risch | \(-\dilog \left (x \right )\) | \(5\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.30, size = 12, normalized size = 1.33 \begin {gather*} \log \left (x\right ) \log \left (-x + 1\right ) + {\rm Li}_2\left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.40, size = 8, normalized size = 0.89 \begin {gather*} -{\rm Li}_2\left (-x + 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [C] Result contains complex when optimal does not.
time = 0.92, size = 10, normalized size = 1.11 \begin {gather*} - \operatorname {Li}_{2}\left (\left (x - 1\right ) e^{i \pi }\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
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.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.02, size = 4, normalized size = 0.44 \begin {gather*} -{\mathrm {Li}}_{\mathrm {2}}\left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________