\[ \int \frac {e^{\frac {e^x}{x^2+x^2 \log \left (\frac {1}{x}\right )}} \left (e^x (90-90 x)+e^x (180-90 x) \log \left (\frac {1}{x}\right )\right )+e^{\frac {2 e^x}{x^2+x^2 \log \left (\frac {1}{x}\right )}} \left (e^x (-50+50 x)+e^x (-100+50 x) \log \left (\frac {1}{x}\right )\right )}{9 x^3+18 x^3 \log \left (\frac {1}{x}\right )+9 x^3 \log ^2\left (\frac {1}{x}\right )} \, dx \]
Optimal antiderivative \[ \left (3-\frac {5 \,{\mathrm e}^{\frac {{\mathrm e}^{x}}{\left (x +x \ln \left (\frac {1}{x}\right )\right ) x}}}{3}\right )^{2} \]
command
integrate((((50*x-100)*exp(x)*log(1/x)+(50*x-50)*exp(x))*exp(exp(x)/(x^2*log(1/x)+x^2))^2+((-90*x+180)*exp(x)*log(1/x)+(-90*x+90)*exp(x))*exp(exp(x)/(x^2*log(1/x)+x^2)))/(9*x^3*log(1/x)^2+18*x^3*log(1/x)+9*x^3),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ -10 \, e^{\left (-\frac {e^{x}}{x^{2} \log \left (x\right ) - x^{2}}\right )} + \frac {25}{9} \, e^{\left (-\frac {2 \, e^{x}}{x^{2} \log \left (x\right ) - x^{2}}\right )} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \int \frac {10 \, {\left (5 \, {\left ({\left (x - 2\right )} e^{x} \log \left (\frac {1}{x}\right ) + {\left (x - 1\right )} e^{x}\right )} e^{\left (\frac {2 \, e^{x}}{x^{2} \log \left (\frac {1}{x}\right ) + x^{2}}\right )} - 9 \, {\left ({\left (x - 2\right )} e^{x} \log \left (\frac {1}{x}\right ) + {\left (x - 1\right )} e^{x}\right )} e^{\left (\frac {e^{x}}{x^{2} \log \left (\frac {1}{x}\right ) + x^{2}}\right )}\right )}}{9 \, {\left (x^{3} \log \left (\frac {1}{x}\right )^{2} + 2 \, x^{3} \log \left (\frac {1}{x}\right ) + x^{3}\right )}}\,{d x} \]________________________________________________________________________________________