Optimal. Leaf size=41 \[ -\frac {1}{6} \log (1-x)+\frac {1}{2} \log (2-x)-\frac {1}{2} \log (3-x)+\frac {1}{6} \log (4-x) \]
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Rubi [A]
time = 0.02, antiderivative size = 41, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 21, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.048, Rules used = {186}
\begin {gather*} -\frac {1}{6} \log (1-x)+\frac {1}{2} \log (2-x)-\frac {1}{2} \log (3-x)+\frac {1}{6} \log (4-x) \end {gather*}
Antiderivative was successfully verified.
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Rule 186
Rubi steps
\begin {align*} \int \frac {1}{(-4+x) (-3+x) (-2+x) (-1+x)} \, dx &=\int \left (\frac {1}{6 (-4+x)}-\frac {1}{2 (-3+x)}+\frac {1}{2 (-2+x)}-\frac {1}{6 (-1+x)}\right ) \, dx\\ &=-\frac {1}{6} \log (1-x)+\frac {1}{2} \log (2-x)-\frac {1}{2} \log (3-x)+\frac {1}{6} \log (4-x)\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 41, normalized size = 1.00 \begin {gather*} -\frac {1}{6} \log (1-x)+\frac {1}{2} \log (2-x)-\frac {1}{2} \log (3-x)+\frac {1}{6} \log (4-x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.08, size = 26, normalized size = 0.63
method | result | size |
default | \(-\frac {\ln \left (-3+x \right )}{2}+\frac {\ln \left (-2+x \right )}{2}-\frac {\ln \left (-1+x \right )}{6}+\frac {\ln \left (x -4\right )}{6}\) | \(26\) |
norman | \(-\frac {\ln \left (-3+x \right )}{2}+\frac {\ln \left (-2+x \right )}{2}-\frac {\ln \left (-1+x \right )}{6}+\frac {\ln \left (x -4\right )}{6}\) | \(26\) |
risch | \(-\frac {\ln \left (-3+x \right )}{2}+\frac {\ln \left (-2+x \right )}{2}-\frac {\ln \left (-1+x \right )}{6}+\frac {\ln \left (x -4\right )}{6}\) | \(26\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 1.29, size = 25, normalized size = 0.61 \begin {gather*} -\frac {1}{6} \, \log \left (x - 1\right ) + \frac {1}{2} \, \log \left (x - 2\right ) - \frac {1}{2} \, \log \left (x - 3\right ) + \frac {1}{6} \, \log \left (x - 4\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.94, size = 25, normalized size = 0.61 \begin {gather*} -\frac {1}{6} \, \log \left (x - 1\right ) + \frac {1}{2} \, \log \left (x - 2\right ) - \frac {1}{2} \, \log \left (x - 3\right ) + \frac {1}{6} \, \log \left (x - 4\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.07, size = 26, normalized size = 0.63 \begin {gather*} \frac {\log {\left (x - 4 \right )}}{6} - \frac {\log {\left (x - 3 \right )}}{2} + \frac {\log {\left (x - 2 \right )}}{2} - \frac {\log {\left (x - 1 \right )}}{6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.54, size = 29, normalized size = 0.71 \begin {gather*} -\frac {1}{6} \, \log \left ({\left | x - 1 \right |}\right ) + \frac {1}{2} \, \log \left ({\left | x - 2 \right |}\right ) - \frac {1}{2} \, \log \left ({\left | x - 3 \right |}\right ) + \frac {1}{6} \, \log \left ({\left | x - 4 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.25, size = 15, normalized size = 0.37 \begin {gather*} \mathrm {atanh}\left (2\,x-5\right )-\frac {\mathrm {atanh}\left (\frac {2\,x}{3}-\frac {5}{3}\right )}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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