\[ \int \frac {e^{-\frac {50 e^{3-x}}{x}} \left (e^{3-x} (7200+7200 x)+e^{\frac {50 e^{3-x}}{x}} \left (18 x^2+18 x^3\right )+e^{\frac {25 e^{3-x}}{x}} \left (-72 x^2+e^{3-x} \left (-1800-3600 x-1800 x^2\right )\right )\right )}{x^2} \, dx \]
Optimal antiderivative \[ 3 \left (1-4 \,{\mathrm e}^{-\frac {25 \,{\mathrm e}^{3-x}}{x}}+x \right ) \left (3-12 \,{\mathrm e}^{-\frac {25 \,{\mathrm e}^{3-x}}{x}}+3 x \right ) \]
command
integrate(((18*x^3+18*x^2)*exp(25*exp(3-x)/x)^2+((-1800*x^2-3600*x-1800)*exp(3-x)-72*x^2)*exp(25*exp(3-x)/x)+(7200*x+7200)*exp(3-x))/x^2/exp(25*exp(3-x)/x)^2,x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \text {could not integrate} \]
Giac 1.7.0 via sagemath 9.3 output
\[ 9 \, {\left (x^{2} e^{\left (-x + 3\right )} + 2 \, x e^{\left (-x + 3\right )} - 8 \, x e^{\left (-\frac {x^{2} - 3 \, x + 25 \, e^{\left (-x + 3\right )}}{x}\right )} + 16 \, e^{\left (-\frac {x^{2} - 3 \, x + 50 \, e^{\left (-x + 3\right )}}{x}\right )} - 8 \, e^{\left (-\frac {x^{2} - 3 \, x + 25 \, e^{\left (-x + 3\right )}}{x}\right )}\right )} e^{\left (x - 3\right )} \]