Optimal. Leaf size=22 \[ \frac {5}{1-x}-\log (1-x)+3 \log (x) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.01, antiderivative size = 22, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.062, Rules used = {894} \[ \frac {5}{1-x}-\log (1-x)+3 \log (x) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 894
Rubi steps
\begin {align*} \int \frac {3+2 x^2}{(-1+x)^2 x} \, dx &=\int \left (\frac {1}{1-x}+\frac {5}{(-1+x)^2}+\frac {3}{x}\right ) \, dx\\ &=\frac {5}{1-x}-\log (1-x)+3 \log (x)\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 20, normalized size = 0.91 \[ -\frac {5}{x-1}-\log (1-x)+3 \log (x) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.57, size = 24, normalized size = 1.09 \[ -\frac {{\left (x - 1\right )} \log \left (x - 1\right ) - 3 \, {\left (x - 1\right )} \log \relax (x) + 5}{x - 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.37, size = 28, normalized size = 1.27 \[ -\frac {5}{x - 1} + 2 \, \log \left ({\left | x - 1 \right |}\right ) + 3 \, \log \left ({\left | -\frac {1}{x - 1} - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.01, size = 19, normalized size = 0.86 \[ 3 \ln \relax (x )-\ln \left (x -1\right )-\frac {5}{x -1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 1.09, size = 18, normalized size = 0.82 \[ -\frac {5}{x - 1} - \log \left (x - 1\right ) + 3 \, \log \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.04, size = 18, normalized size = 0.82 \[ 3\,\ln \relax (x)-\ln \left (x-1\right )-\frac {5}{x-1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.11, size = 14, normalized size = 0.64 \[ 3 \log {\relax (x )} - \log {\left (x - 1 \right )} - \frac {5}{x - 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________