Optimal. Leaf size=15 \[ -5+x+\log \left (\frac {6 x (-1+2 x)}{e^5}\right ) \]
________________________________________________________________________________________
Rubi [A] time = 0.02, antiderivative size = 10, normalized size of antiderivative = 0.67, number of steps used = 3, number of rules used = 2, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {1593, 893} \begin {gather*} x+\log (1-2 x)+\log (x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 893
Rule 1593
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-1+3 x+2 x^2}{x (-1+2 x)} \, dx\\ &=\int \left (1+\frac {1}{x}+\frac {2}{-1+2 x}\right ) \, dx\\ &=x+\log (1-2 x)+\log (x)\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 10, normalized size = 0.67 \begin {gather*} x+\log (1-2 x)+\log (x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.57, size = 12, normalized size = 0.80 \begin {gather*} x + \log \left (2 \, x^{2} - x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.21, size = 12, normalized size = 0.80 \begin {gather*} x + \log \left ({\left | 2 \, x - 1 \right |}\right ) + \log \left ({\left | x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.07, size = 11, normalized size = 0.73
method | result | size |
default | \(x +\ln \left (2 x -1\right )+\ln \relax (x )\) | \(11\) |
norman | \(x +\ln \left (2 x -1\right )+\ln \relax (x )\) | \(11\) |
risch | \(x +\ln \left (2 x^{2}-x \right )\) | \(13\) |
meijerg | \(\ln \relax (x )+\ln \relax (2)+i \pi +\ln \left (1-2 x \right )+x\) | \(17\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.37, size = 10, normalized size = 0.67 \begin {gather*} x + \log \left (2 \, x - 1\right ) + \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 3.08, size = 10, normalized size = 0.67 \begin {gather*} x+\ln \left (x\,\left (2\,x-1\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.08, size = 8, normalized size = 0.53 \begin {gather*} x + \log {\left (2 x^{2} - x \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________