Optimal. Leaf size=29 \[ -x+\frac {\log ^2\left (\frac {\log (2)}{2 (-3+x) \log (6)}\right )}{9 e^2} \]
________________________________________________________________________________________
Rubi [A] time = 0.08, antiderivative size = 29, normalized size of antiderivative = 1.00, number of steps used = 6, number of rules used = 3, integrand size = 38, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.079, Rules used = {12, 14, 2301} \begin {gather*} \frac {\log ^2\left (-\frac {\log (2)}{(3-x) \log (36)}\right )}{9 e^2}-x \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 14
Rule 2301
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \frac {e^2 (27-9 x)-2 \log \left (\frac {\log (2)}{(-6+2 x) \log (6)}\right )}{-27+9 x} \, dx}{e^2}\\ &=\frac {\operatorname {Subst}\left (\int \frac {-9 e^2 x-2 \log \left (\frac {\log (2)}{2 x \log (6)}\right )}{9 x} \, dx,x,-3+x\right )}{e^2}\\ &=\frac {\operatorname {Subst}\left (\int \frac {-9 e^2 x-2 \log \left (\frac {\log (2)}{2 x \log (6)}\right )}{x} \, dx,x,-3+x\right )}{9 e^2}\\ &=\frac {\operatorname {Subst}\left (\int \left (-9 e^2-\frac {2 \log \left (\frac {\log (2)}{x \log (36)}\right )}{x}\right ) \, dx,x,-3+x\right )}{9 e^2}\\ &=-x-\frac {2 \operatorname {Subst}\left (\int \frac {\log \left (\frac {\log (2)}{x \log (36)}\right )}{x} \, dx,x,-3+x\right )}{9 e^2}\\ &=-x+\frac {\log ^2\left (-\frac {\log (2)}{(3-x) \log (36)}\right )}{9 e^2}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 28, normalized size = 0.97 \begin {gather*} -x+\frac {\log ^2\left (\frac {\log (2)}{(-6+2 x) \log (6)}\right )}{9 e^2} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.61, size = 28, normalized size = 0.97 \begin {gather*} -\frac {1}{9} \, {\left (9 \, x e^{2} - \log \left (\frac {\log \relax (2)}{2 \, {\left (x - 3\right )} \log \relax (6)}\right )^{2}\right )} e^{\left (-2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [B] time = 0.14, size = 145, normalized size = 5.00 \begin {gather*} \frac {{\left (\frac {\log \relax (3) \log \relax (2)^{2} \log \left (\frac {\log \relax (2)}{2 \, {\left (x \log \relax (6) - 3 \, \log \relax (6)\right )}}\right )^{2}}{x \log \relax (6) - 3 \, \log \relax (6)} + \frac {\log \relax (2)^{3} \log \left (\frac {\log \relax (2)}{2 \, {\left (x \log \relax (6) - 3 \, \log \relax (6)\right )}}\right )^{2}}{x \log \relax (6) - 3 \, \log \relax (6)} - 9 \, e^{2} \log \relax (2)^{2}\right )} e^{\left (-2\right )} \log \relax (6)}{9 \, {\left (\frac {\log \relax (3)^{2} \log \relax (2)}{x \log \relax (6) - 3 \, \log \relax (6)} + \frac {2 \, \log \relax (3) \log \relax (2)^{2}}{x \log \relax (6) - 3 \, \log \relax (6)} + \frac {\log \relax (2)^{3}}{x \log \relax (6) - 3 \, \log \relax (6)}\right )} \log \relax (2)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.15, size = 28, normalized size = 0.97
method | result | size |
risch | \(-x +\frac {{\mathrm e}^{-2} \ln \left (\frac {\ln \relax (2)}{2 \left (x -3\right ) \left (\ln \relax (2)+\ln \relax (3)\right )}\right )^{2}}{9}\) | \(28\) |
default | \(\frac {{\mathrm e}^{-2} \left (-9 \left (x -3\right ) {\mathrm e}^{2}+\ln \left (\frac {\ln \relax (2)}{2 \left (x -3\right ) \ln \relax (6)}\right )^{2}\right )}{9}\) | \(33\) |
derivativedivides | \(-\frac {{\mathrm e}^{-2} \left (9 \left (x -3\right ) {\mathrm e}^{2}-\ln \left (\frac {\ln \relax (2)}{2 \left (x -3\right ) \ln \relax (6)}\right )^{2}\right )}{9}\) | \(35\) |
norman | \(\left (-x \,{\mathrm e}+\frac {{\mathrm e}^{-1} \ln \left (\frac {\ln \relax (2)}{\left (2 x -6\right ) \ln \relax (6)}\right )^{2}}{9}\right ) {\mathrm e}^{-1}\) | \(35\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [B] time = 0.44, size = 105, normalized size = 3.62 \begin {gather*} -\frac {1}{9} \, {\left (9 \, {\left (x + 3 \, \log \left (x - 3\right )\right )} e^{2} - {\left (\frac {2 \, \log \left (2 \, x \log \relax (6) - 6 \, \log \relax (6)\right ) \log \left (x - 3\right )}{\log \relax (6)} - \frac {\log \left (x - 3\right )^{2}}{\log \relax (3) + \log \relax (2)}\right )} \log \relax (6) - 27 \, e^{2} \log \left (x - 3\right ) + 2 \, \log \left (2 \, x \log \relax (6) - 6 \, \log \relax (6)\right ) \log \left (x - 3\right ) + 2 \, \log \left (x - 3\right ) \log \left (\frac {\log \relax (2)}{2 \, {\left (x \log \relax (6) - 3 \, \log \relax (6)\right )}}\right )\right )} e^{\left (-2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.62, size = 25, normalized size = 0.86 \begin {gather*} \frac {{\mathrm {e}}^{-2}\,{\ln \left (\frac {\ln \relax (2)}{\ln \relax (6)\,\left (2\,x-6\right )}\right )}^2}{9}-x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.16, size = 20, normalized size = 0.69 \begin {gather*} - x + \frac {\log {\left (\frac {\log {\relax (2 )}}{\left (2 x - 6\right ) \log {\relax (6 )}} \right )}^{2}}{9 e^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________