Optimal. Leaf size=18 \[ \log \left (\frac {12 e^{-x^2} x}{2-x}\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.02, antiderivative size = 16, normalized size of antiderivative = 0.89, 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 = {1607, 1634}
\begin {gather*} -x^2-\log (2-x)+\log (x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 1607
Rule 1634
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-2+4 x^2-2 x^3}{(-2+x) x} \, dx\\ &=\int \left (\frac {1}{2-x}+\frac {1}{x}-2 x\right ) \, dx\\ &=-x^2-\log (2-x)+\log (x)\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.00, size = 26, normalized size = 1.44 \begin {gather*} -2 \left (\frac {x^2}{2}+\frac {1}{2} \log (2-x)-\frac {\log (x)}{2}\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.32, size = 15, normalized size = 0.83
method | result | size |
default | \(-x^{2}-\ln \left (x -2\right )+\ln \left (x \right )\) | \(15\) |
norman | \(-x^{2}-\ln \left (x -2\right )+\ln \left (x \right )\) | \(15\) |
risch | \(-x^{2}-\ln \left (x -2\right )+\ln \left (x \right )\) | \(15\) |
meijerg | \(-\ln \left (1-\frac {x}{2}\right )+\ln \left (x \right )-\ln \left (2\right )+i \pi -\frac {2 x \left (\frac {3 x}{2}+6\right )}{3}+4 x\) | \(31\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.25, size = 14, normalized size = 0.78 \begin {gather*} -x^{2} - \log \left (x - 2\right ) + \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.35, size = 14, normalized size = 0.78 \begin {gather*} -x^{2} - \log \left (x - 2\right ) + \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.03, size = 10, normalized size = 0.56 \begin {gather*} - x^{2} + \log {\left (x \right )} - \log {\left (x - 2 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.39, size = 16, normalized size = 0.89 \begin {gather*} -x^{2} - \log \left ({\left | x - 2 \right |}\right ) + \log \left ({\left | x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 1.37, size = 12, normalized size = 0.67 \begin {gather*} 2\,\mathrm {atanh}\left (x-1\right )-x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________