\[ \int \frac {e^{2 e^{-x}-x} \left (2 e^x-2 x \log \left (\frac {60}{x+4 e^2 x}\right )\right )}{x \log ^3\left (\frac {60}{x+4 e^2 x}\right )} \, dx \]
Optimal antiderivative \[ \frac {{\mathrm e}^{2 \,{\mathrm e}^{-x}}}{\ln \! \left (\frac {3}{\frac {{\mathrm e}^{2} x}{5}+\frac {x}{20}}\right )^{2}} \]
command
int((-2*x*ln(60/(4*x*exp(1)^2+x))+2*exp(x))*exp(1/exp(x))^2/x/exp(x)/ln(60/(4*x*exp(1)^2+x))^3,x)
Maple 2022.1 output
\[\int \frac {\left (-2 x \ln \left (\frac {60}{4 \,{\mathrm e}^{2} x +x}\right )+2 \,{\mathrm e}^{x}\right ) {\mathrm e}^{2 \,{\mathrm e}^{-x}} {\mathrm e}^{-x}}{x \ln \left (\frac {60}{4 \,{\mathrm e}^{2} x +x}\right )^{3}}\, dx\]
Maple 2021.1 output
| method | result | size |
| risch | \(-\frac {4 \,{\mathrm e}^{2 \,{\mathrm e}^{-x}}}{\left (2 i \ln \left (5\right )+2 i \ln \left (3\right )+4 i \ln \left (2\right )-2 i \ln \left (4 \,{\mathrm e}^{2}+1\right )-2 i \ln \left (x \right )\right )^{2}}\) | \(43\) |