Optimal. Leaf size=21 \[ e^{\frac {2 (1+i \pi +\log (-3+2 \log (5)))}{x}} \]
________________________________________________________________________________________
Rubi [A] time = 0.08, antiderivative size = 25, normalized size of antiderivative = 1.19, number of steps used = 2, number of rules used = 2, integrand size = 42, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.048, Rules used = {12, 2209} \begin {gather*} e^{\frac {2 (1+i \pi )}{x}} (\log (25)-3)^{2/x} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 2209
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\left ((2 (1+i \pi +\log (-3+\log (25)))) \int \frac {e^{\frac {2 (1+i \pi +\log (-3+2 \log (5)))}{x}}}{x^2} \, dx\right )\\ &=e^{\frac {2 (1+i \pi )}{x}} (-3+\log (25))^{2/x}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [B] time = 0.03, size = 52, normalized size = 2.48 \begin {gather*} -\frac {e^{\frac {2 (1+i \pi +\log (-3+\log (25)))}{x}} (-2 i \pi -2 (1+\log (-3+\log (25))))}{2 (1+i \pi +\log (-3+\log (25)))} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.99, size = 15, normalized size = 0.71 \begin {gather*} e^{\left (\frac {2 \, {\left (\log \left (-2 \, \log \relax (5) + 3\right ) + 1\right )}}{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.35, size = 19, normalized size = 0.90 \begin {gather*} e^{\left (\frac {2 \, \log \left (-2 \, \log \relax (5) + 3\right )}{x} + \frac {2}{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.05, size = 17, normalized size = 0.81
method | result | size |
norman | \({\mathrm e}^{\frac {2 \ln \left (-2 \ln \relax (5)+3\right )+2}{x}}\) | \(17\) |
derivativedivides | \(-\frac {\left (-2 \ln \left (-2 \ln \relax (5)+3\right )-2\right ) {\mathrm e}^{\frac {2 \ln \left (-2 \ln \relax (5)+3\right )+2}{x}}}{2 \left (\ln \left (-2 \ln \relax (5)+3\right )+1\right )}\) | \(41\) |
default | \(-\frac {\left (-2 \ln \left (-2 \ln \relax (5)+3\right )-2\right ) {\mathrm e}^{\frac {2 \ln \left (-2 \ln \relax (5)+3\right )+2}{x}}}{2 \left (\ln \left (-2 \ln \relax (5)+3\right )+1\right )}\) | \(41\) |
risch | \(-\frac {\left (-2 \ln \left (-2 \ln \relax (5)+3\right )-2\right ) \left (-2 \ln \relax (5)+3\right )^{\frac {2}{x}} {\mathrm e}^{\frac {2}{x}}}{2 \left (\ln \left (-2 \ln \relax (5)+3\right )+1\right )}\) | \(43\) |
gosper | error in isolve/isolve: invalid subscript selector\ | N/A |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.35, size = 15, normalized size = 0.71 \begin {gather*} e^{\left (\frac {2 \, {\left (\log \left (-2 \, \log \relax (5) + 3\right ) + 1\right )}}{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.95, size = 19, normalized size = 0.90 \begin {gather*} {\mathrm {e}}^{2/x}\,{\left (3-\ln \left (25\right )\right )}^{2/x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [B] time = 10.96, size = 63, normalized size = 3.00 \begin {gather*} - \frac {\left (-2 - 2 \log {\left (-3 + 2 \log {\relax (5 )} \right )} - 2 i \pi \right ) e^{\frac {2}{x}} e^{\frac {2 \log {\left (-3 + 2 \log {\relax (5 )} \right )}}{x}} e^{\frac {2 i \pi }{x}}}{2 \log {\left (-3 + 2 \log {\relax (5 )} \right )} + 2 + 2 i \pi } \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________