\[ \int \frac {e^{-2 x} \left (-e^{2 x} x^2+e^{\frac {2 e^{-2 x} \left (-e^4+e^{2 x} (-3+x)\right )}{x}} \left (24 e^{2 x}+e^4 (8+16 x)\right )\right )}{x^2} \, dx \]
Optimal antiderivative \[ 4 \,{\mathrm e}^{\frac {-6+2 x -2 \,{\mathrm e}^{4-2 x}}{x}}+20-x \]
command
integrate(((24*exp(2*x)+(16*x+8)*exp(4))*exp(((-3+x)*exp(2*x)-exp(4))/x/exp(2*x))^2-exp(2*x)*x^2)/exp(2*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
\[ -x + 4 \, e^{\left (\frac {2 \, {\left (x - e^{\left (-2 \, x + 4\right )} - 3\right )}}{x}\right )} \]