\[ \int \frac {e^{\frac {-x-e^{2 x} x+\log \left (e^2 x\right )}{-4+x}} \left (-4+5 x+e^{2 x} \left (4 x+8 x^2-2 x^3\right )-x \log \left (e^2 x\right )\right )}{16 x-8 x^2+x^3} \, dx \]
Optimal antiderivative \[ 2+{\mathrm e}^{\frac {\ln \left ({\mathrm e}^{2} x \right )-x \,{\mathrm e}^{2 x}-x}{-4+x}} \]
command
integrate((-x*log(exp(2)*x)+(-2*x^3+8*x^2+4*x)*exp(2*x)+5*x-4)*exp((log(exp(2)*x)-x*exp(2*x)-x)/(x-4))/(x^3-8*x^2+16*x),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
\[ e^{\left (-\frac {x e^{\left (2 \, x\right )}}{x - 4} - \frac {x}{x - 4} + \frac {\log \left (x e^{2}\right )}{x - 4}\right )} \]