Optimal. Leaf size=41 \[ -\frac {1}{6} \log (1-x)+\frac {1}{2} \log (2-x)-\frac {1}{2} \log (3-x)+\frac {1}{6} \log (4-x) \]
________________________________________________________________________________________
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 = {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.
[In]
[Out]
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 = 0.01, size = 41, normalized size = 1.00 \[ -\frac {1}{6} \log (1-x)+\frac {1}{2} \log (2-x)-\frac {1}{2} \log (3-x)+\frac {1}{6} \log (4-x) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
IntegrateAlgebraic [A] time = 0.01, size = 25, normalized size = 0.61 \[ \frac {1}{6} \log (x-4)-\frac {1}{6} \log (x-1)-\tanh ^{-1}(5-2 x) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.90, size = 25, normalized size = 0.61 \[ -\frac {1}{6} \, \log \left (x - 1\right ) + \frac {1}{2} \, \log \left (x - 2\right ) - \frac {1}{2} \, \log \left (x - 3\right ) + \frac {1}{6} \, \log \left (x - 4\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.89, size = 29, normalized size = 0.71 \[ -\frac {1}{6} \, \log \left ({\left | x - 1 \right |}\right ) + \frac {1}{2} \, \log \left ({\left | x - 2 \right |}\right ) - \frac {1}{2} \, \log \left ({\left | x - 3 \right |}\right ) + \frac {1}{6} \, \log \left ({\left | x - 4 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.33, size = 26, normalized size = 0.63
method | result | size |
default | \(\frac {\ln \left (-2+x \right )}{2}+\frac {\ln \left (-4+x \right )}{6}-\frac {\ln \left (-3+x \right )}{2}-\frac {\ln \left (-1+x \right )}{6}\) | \(26\) |
norman | \(\frac {\ln \left (-2+x \right )}{2}+\frac {\ln \left (-4+x \right )}{6}-\frac {\ln \left (-3+x \right )}{2}-\frac {\ln \left (-1+x \right )}{6}\) | \(26\) |
risch | \(\frac {\ln \left (-2+x \right )}{2}+\frac {\ln \left (-4+x \right )}{6}-\frac {\ln \left (-3+x \right )}{2}-\frac {\ln \left (-1+x \right )}{6}\) | \(26\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.43, size = 25, normalized size = 0.61 \[ -\frac {1}{6} \, \log \left (x - 1\right ) + \frac {1}{2} \, \log \left (x - 2\right ) - \frac {1}{2} \, \log \left (x - 3\right ) + \frac {1}{6} \, \log \left (x - 4\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.25, size = 15, normalized size = 0.37 \[ \mathrm {atanh}\left (2\,x-5\right )-\frac {\mathrm {atanh}\left (\frac {2\,x}{3}-\frac {5}{3}\right )}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.19, size = 26, normalized size = 0.63 \[ \frac {\log {\left (x - 4 \right )}}{6} - \frac {\log {\left (x - 3 \right )}}{2} + \frac {\log {\left (x - 2 \right )}}{2} - \frac {\log {\left (x - 1 \right )}}{6} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________