Optimal. Leaf size=16 \[ \frac {1}{2} \left (x^2-\log (1-x)\right ) \]
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Rubi [A]
time = 0.01, antiderivative size = 18, normalized size of antiderivative = 1.12, number of steps
used = 2, number of rules used = 1, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {712}
\begin {gather*} \frac {x^2}{2}-\frac {1}{2} \log (1-x) \end {gather*}
Antiderivative was successfully verified.
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Rule 712
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-\frac {1}{2 (-1+x)}+x\right ) \, dx\\ &=\frac {x^2}{2}-\frac {1}{2} \log (1-x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 17, normalized size = 1.06 \begin {gather*} \frac {1}{2} \left (1+x^2-\log (2-2 x)\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.82, size = 13, normalized size = 0.81
method | result | size |
default | \(\frac {x^{2}}{2}-\frac {\ln \left (x -1\right )}{2}\) | \(13\) |
risch | \(\frac {x^{2}}{2}-\frac {\ln \left (x -1\right )}{2}\) | \(13\) |
norman | \(\frac {x^{2}}{2}-\frac {\ln \left (2 x -2\right )}{2}\) | \(15\) |
meijerg | \(-\frac {\ln \left (1-x \right )}{2}+\frac {x \left (6+3 x \right )}{6}-x\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 12, normalized size = 0.75 \begin {gather*} \frac {1}{2} \, x^{2} - \frac {1}{2} \, \log \left (x - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 12, normalized size = 0.75 \begin {gather*} \frac {1}{2} \, x^{2} - \frac {1}{2} \, \log \left (x - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.02, size = 10, normalized size = 0.62 \begin {gather*} \frac {x^{2}}{2} - \frac {\log {\left (x - 1 \right )}}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 13, normalized size = 0.81 \begin {gather*} \frac {1}{2} \, x^{2} - \frac {1}{2} \, \log \left ({\left | x - 1 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.04, size = 12, normalized size = 0.75 \begin {gather*} \frac {x^2}{2}-\frac {\ln \left (x-1\right )}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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