Optimal. Leaf size=16 \[ \log \left (\frac {2 e^{-x} (1-x)}{x}\right ) \]
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Rubi [A]
time = 0.02, antiderivative size = 14, normalized size of antiderivative = 0.88, number of steps
used = 3, number of rules used = 2, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {1607, 907}
\begin {gather*} -x+\log (1-x)-\log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 907
Rule 1607
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {1+x-x^2}{(-1+x) x} \, dx\\ &=\int \left (-1+\frac {1}{-1+x}-\frac {1}{x}\right ) \, dx\\ &=-x+\log (1-x)-\log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 14, normalized size = 0.88 \begin {gather*} -x+\log (1-x)-\log (x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 1.39, size = 13, normalized size = 0.81
method | result | size |
default | \(-x -\ln \left (x \right )+\ln \left (x -1\right )\) | \(13\) |
norman | \(-x -\ln \left (x \right )+\ln \left (x -1\right )\) | \(13\) |
risch | \(-x -\ln \left (x \right )+\ln \left (x -1\right )\) | \(13\) |
meijerg | \(-\ln \left (x \right )-i \pi -x +\ln \left (1-x \right )\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.25, size = 12, normalized size = 0.75 \begin {gather*} -x + \log \left (x - 1\right ) - \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 12, normalized size = 0.75 \begin {gather*} -x + \log \left (x - 1\right ) - \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 8, normalized size = 0.50 \begin {gather*} - x - \log {\left (x \right )} + \log {\left (x - 1 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.42, size = 14, normalized size = 0.88 \begin {gather*} -x + \log \left ({\left | x - 1 \right |}\right ) - \log \left ({\left | x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 7.79, size = 12, normalized size = 0.75 \begin {gather*} -x-2\,\mathrm {atanh}\left (2\,x-1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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