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 = 0.0204782, antiderivative size = 41, normalized size of antiderivative = 1., 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 = {180} \[ -\frac{1}{6} \log (1-x)+\frac{1}{2} \log (2-x)-\frac{1}{2} \log (3-x)+\frac{1}{6} \log (4-x) \]
Antiderivative was successfully verified.
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Rule 180
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*}
Mathematica [A] time = 0.0073356, size = 41, normalized size = 1. \[ -\frac{1}{6} \log (1-x)+\frac{1}{2} \log (2-x)-\frac{1}{2} \log (3-x)+\frac{1}{6} \log (4-x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.008, size = 26, normalized size = 0.6 \begin{align*} -{\frac{\ln \left ( -1+x \right ) }{6}}-{\frac{\ln \left ( -3+x \right ) }{2}}+{\frac{\ln \left ( -2+x \right ) }{2}}+{\frac{\ln \left ( x-4 \right ) }{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.923479, size = 34, normalized size = 0.83 \begin{align*} -\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{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.20441, size = 92, normalized size = 2.24 \begin{align*} -\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{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.154118, size = 26, normalized size = 0.63 \begin{align*} \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{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.04729, size = 39, normalized size = 0.95 \begin{align*} -\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{align*}
Verification of antiderivative is not currently implemented for this CAS.
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