Optimal. Leaf size=14 \[ \frac {e^{\sqrt [5]{e}}}{(-3+\log (x))^2} \]
________________________________________________________________________________________
Rubi [A] time = 0.01, antiderivative size = 16, normalized size of antiderivative = 1.14, number of steps used = 3, number of rules used = 2, integrand size = 33, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.061, Rules used = {12, 32} \begin {gather*} \frac {e^{\sqrt [5]{e}}}{(3-\log (x))^2} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 32
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\left (\left (2 e^{\sqrt [5]{e}}\right ) \int \frac {1}{-27 x+27 x \log (x)-9 x \log ^2(x)+x \log ^3(x)} \, dx\right )\\ &=-\left (\left (2 e^{\sqrt [5]{e}}\right ) \operatorname {Subst}\left (\int \frac {1}{(-3+x)^3} \, dx,x,\log (x)\right )\right )\\ &=\frac {e^{\sqrt [5]{e}}}{(3-\log (x))^2}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 14, normalized size = 1.00 \begin {gather*} \frac {e^{\sqrt [5]{e}}}{(-3+\log (x))^2} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.62, size = 16, normalized size = 1.14 \begin {gather*} \frac {e^{\left (e^{\frac {1}{5}}\right )}}{\log \relax (x)^{2} - 6 \, \log \relax (x) + 9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.19, size = 10, normalized size = 0.71 \begin {gather*} \frac {e^{\left (e^{\frac {1}{5}}\right )}}{{\left (\log \relax (x) - 3\right )}^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.06, size = 11, normalized size = 0.79
method | result | size |
default | \(\frac {{\mathrm e}^{{\mathrm e}^{\frac {1}{5}}}}{\left (\ln \relax (x )-3\right )^{2}}\) | \(11\) |
norman | \(\frac {{\mathrm e}^{{\mathrm e}^{\frac {1}{5}}}}{\left (\ln \relax (x )-3\right )^{2}}\) | \(11\) |
risch | \(\frac {{\mathrm e}^{{\mathrm e}^{\frac {1}{5}}}}{\left (\ln \relax (x )-3\right )^{2}}\) | \(11\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.38, size = 16, normalized size = 1.14 \begin {gather*} \frac {e^{\left (e^{\frac {1}{5}}\right )}}{\log \relax (x)^{2} - 6 \, \log \relax (x) + 9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 3.63, size = 10, normalized size = 0.71 \begin {gather*} \frac {{\mathrm {e}}^{{\mathrm {e}}^{1/5}}}{{\left (\ln \relax (x)-3\right )}^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.10, size = 17, normalized size = 1.21 \begin {gather*} \frac {e^{e^{\frac {1}{5}}}}{\log {\relax (x )}^{2} - 6 \log {\relax (x )} + 9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________