Optimal. Leaf size=15 \[ \log \left (4 e^x (4-2 x) \log ^2(x)\right ) \]
________________________________________________________________________________________
Rubi [A] time = 0.17, antiderivative size = 13, normalized size of antiderivative = 0.87, number of steps used = 7, number of rules used = 5, integrand size = 29, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.172, Rules used = {1593, 6688, 43, 2302, 29} \begin {gather*} x+\log (2-x)+2 \log (\log (x)) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 29
Rule 43
Rule 1593
Rule 2302
Rule 6688
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-4+2 x+\left (-x+x^2\right ) \log (x)}{(-2+x) x \log (x)} \, dx\\ &=\int \left (\frac {-1+x}{-2+x}+\frac {2}{x \log (x)}\right ) \, dx\\ &=2 \int \frac {1}{x \log (x)} \, dx+\int \frac {-1+x}{-2+x} \, dx\\ &=2 \operatorname {Subst}\left (\int \frac {1}{x} \, dx,x,\log (x)\right )+\int \left (1+\frac {1}{-2+x}\right ) \, dx\\ &=x+\log (2-x)+2 \log (\log (x))\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 11, normalized size = 0.73 \begin {gather*} x+\log (-2+x)+2 \log (\log (x)) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.46, size = 11, normalized size = 0.73 \begin {gather*} x + \log \left (x - 2\right ) + 2 \, \log \left (\log \relax (x)\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.20, size = 11, normalized size = 0.73 \begin {gather*} x + \log \left (x - 2\right ) + 2 \, \log \left (\log \relax (x)\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.17, size = 12, normalized size = 0.80
method | result | size |
default | \(x +\ln \left (x -2\right )+2 \ln \left (\ln \relax (x )\right )\) | \(12\) |
norman | \(x +\ln \left (x -2\right )+2 \ln \left (\ln \relax (x )\right )\) | \(12\) |
risch | \(x +\ln \left (x -2\right )+2 \ln \left (\ln \relax (x )\right )\) | \(12\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.39, size = 11, normalized size = 0.73 \begin {gather*} x + \log \left (x - 2\right ) + 2 \, \log \left (\log \relax (x)\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 3.29, size = 11, normalized size = 0.73 \begin {gather*} x+\ln \left (x-2\right )+2\,\ln \left (\ln \relax (x)\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.11, size = 12, normalized size = 0.80 \begin {gather*} x + \log {\left (x - 2 \right )} + 2 \log {\left (\log {\relax (x )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________