Integrand size = 21, antiderivative size = 41 \[ \int \frac {1}{(-4+x) (-3+x) (-2+x) (-1+x)} \, dx=-\frac {1}{6} \log (1-x)+\frac {1}{2} \log (2-x)-\frac {1}{2} \log (3-x)+\frac {1}{6} \log (4-x) \]
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Time = 0.02 (sec) , antiderivative size = 41, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.048, Rules used = {186} \[ \int \frac {1}{(-4+x) (-3+x) (-2+x) (-1+x)} \, dx=-\frac {1}{6} \log (1-x)+\frac {1}{2} \log (2-x)-\frac {1}{2} \log (3-x)+\frac {1}{6} \log (4-x) \]
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Rule 186
Rubi steps \begin{align*} \text {integral}& = \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*}
Time = 0.01 (sec) , antiderivative size = 41, normalized size of antiderivative = 1.00 \[ \int \frac {1}{(-4+x) (-3+x) (-2+x) (-1+x)} \, dx=-\frac {1}{6} \log (1-x)+\frac {1}{2} \log (2-x)-\frac {1}{2} \log (3-x)+\frac {1}{6} \log (4-x) \]
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Time = 0.26 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.63
method | result | size |
default | \(-\frac {\ln \left (-1+x \right )}{6}-\frac {\ln \left (-3+x \right )}{2}+\frac {\ln \left (x -4\right )}{6}+\frac {\ln \left (-2+x \right )}{2}\) | \(26\) |
norman | \(-\frac {\ln \left (-1+x \right )}{6}-\frac {\ln \left (-3+x \right )}{2}+\frac {\ln \left (x -4\right )}{6}+\frac {\ln \left (-2+x \right )}{2}\) | \(26\) |
risch | \(-\frac {\ln \left (-1+x \right )}{6}-\frac {\ln \left (-3+x \right )}{2}+\frac {\ln \left (x -4\right )}{6}+\frac {\ln \left (-2+x \right )}{2}\) | \(26\) |
parallelrisch | \(-\frac {\ln \left (-1+x \right )}{6}-\frac {\ln \left (-3+x \right )}{2}+\frac {\ln \left (x -4\right )}{6}+\frac {\ln \left (-2+x \right )}{2}\) | \(26\) |
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Time = 0.24 (sec) , antiderivative size = 25, normalized size of antiderivative = 0.61 \[ \int \frac {1}{(-4+x) (-3+x) (-2+x) (-1+x)} \, dx=-\frac {1}{6} \, \log \left (x - 1\right ) + \frac {1}{2} \, \log \left (x - 2\right ) - \frac {1}{2} \, \log \left (x - 3\right ) + \frac {1}{6} \, \log \left (x - 4\right ) \]
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Time = 0.07 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.63 \[ \int \frac {1}{(-4+x) (-3+x) (-2+x) (-1+x)} \, dx=\frac {\log {\left (x - 4 \right )}}{6} - \frac {\log {\left (x - 3 \right )}}{2} + \frac {\log {\left (x - 2 \right )}}{2} - \frac {\log {\left (x - 1 \right )}}{6} \]
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Time = 0.21 (sec) , antiderivative size = 25, normalized size of antiderivative = 0.61 \[ \int \frac {1}{(-4+x) (-3+x) (-2+x) (-1+x)} \, dx=-\frac {1}{6} \, \log \left (x - 1\right ) + \frac {1}{2} \, \log \left (x - 2\right ) - \frac {1}{2} \, \log \left (x - 3\right ) + \frac {1}{6} \, \log \left (x - 4\right ) \]
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Time = 0.27 (sec) , antiderivative size = 29, normalized size of antiderivative = 0.71 \[ \int \frac {1}{(-4+x) (-3+x) (-2+x) (-1+x)} \, dx=-\frac {1}{6} \, \log \left ({\left | x - 1 \right |}\right ) + \frac {1}{2} \, \log \left ({\left | x - 2 \right |}\right ) - \frac {1}{2} \, \log \left ({\left | x - 3 \right |}\right ) + \frac {1}{6} \, \log \left ({\left | x - 4 \right |}\right ) \]
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Time = 0.27 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.37 \[ \int \frac {1}{(-4+x) (-3+x) (-2+x) (-1+x)} \, dx=\mathrm {atanh}\left (2\,x-5\right )-\frac {\mathrm {atanh}\left (\frac {2\,x}{3}-\frac {5}{3}\right )}{3} \]
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