Optimal. Leaf size=30 \[ x+\frac {7}{2} \log (1-x)-25 \log (2-x)+\frac {61}{2} \log (3-x) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.06, antiderivative size = 30, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 29, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.034, Rules used = {1612} \[ x+\frac {7}{2} \log (1-x)-25 \log (2-x)+\frac {61}{2} \log (3-x) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 1612
Rubi steps
\begin {align*} \int \frac {1+2 x+3 x^2+x^3}{(-3+x) (-2+x) (-1+x)} \, dx &=\int \left (1+\frac {61}{2 (-3+x)}-\frac {25}{-2+x}+\frac {7}{2 (-1+x)}\right ) \, dx\\ &=x+\frac {7}{2} \log (1-x)-25 \log (2-x)+\frac {61}{2} \log (3-x)\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 24, normalized size = 0.80 \[ x+\frac {61}{2} \log (x-3)-25 \log (x-2)+\frac {7}{2} \log (x-1) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.96, size = 20, normalized size = 0.67 \[ x + \frac {7}{2} \, \log \left (x - 1\right ) - 25 \, \log \left (x - 2\right ) + \frac {61}{2} \, \log \left (x - 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.25, size = 23, normalized size = 0.77 \[ x + \frac {7}{2} \, \log \left ({\left | x - 1 \right |}\right ) - 25 \, \log \left ({\left | x - 2 \right |}\right ) + \frac {61}{2} \, \log \left ({\left | x - 3 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.01, size = 21, normalized size = 0.70 \[ x +\frac {61 \ln \left (x -3\right )}{2}-25 \ln \left (x -2\right )+\frac {7 \ln \left (x -1\right )}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 1.04, size = 20, normalized size = 0.67 \[ x + \frac {7}{2} \, \log \left (x - 1\right ) - 25 \, \log \left (x - 2\right ) + \frac {61}{2} \, \log \left (x - 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 2.13, size = 20, normalized size = 0.67 \[ x+\frac {7\,\ln \left (x-1\right )}{2}-25\,\ln \left (x-2\right )+\frac {61\,\ln \left (x-3\right )}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.15, size = 24, normalized size = 0.80 \[ x + \frac {61 \log {\left (x - 3 \right )}}{2} - 25 \log {\left (x - 2 \right )} + \frac {7 \log {\left (x - 1 \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________