\[ \int \frac {e^{\frac {e^9-x \log \left (\frac {e^{e^2} \log ^2(-4+x)}{x^2}\right )}{\log \left (\frac {e^{e^2} \log ^2(-4+x)}{x^2}\right )}} \left (-2 e^9 x+e^9 (-8+2 x) \log (-4+x)+\left (4 x-x^2\right ) \log (-4+x) \log ^2\left (\frac {e^{e^2} \log ^2(-4+x)}{x^2}\right )\right )}{\left (-4 x+x^2\right ) \log (-4+x) \log ^2\left (\frac {e^{e^2} \log ^2(-4+x)}{x^2}\right )} \, dx \]
Optimal antiderivative \[ {\mathrm e}^{\frac {{\mathrm e}^{9}}{\ln \left (\frac {{\mathrm e}^{{\mathrm e}^{2}} \ln \left (-4+x \right )^{2}}{x^{2}}\right )}-x} \]
command
integrate(((-x^2+4*x)*log(x-4)*log(exp(exp(2))*log(x-4)^2/x^2)^2+(2*x-8)*exp(9)*log(x-4)-2*x*exp(9))*exp((-x*log(exp(exp(2))*log(x-4)^2/x^2)+exp(9))/log(exp(exp(2))*log(x-4)^2/x^2))/(x^2-4*x)/log(x-4)/log(exp(exp(2))*log(x-4)^2/x^2)^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
\[ e^{\left (-x + \frac {e^{9}}{\log \left (\frac {e^{\left (e^{2}\right )} \log \left (x - 4\right )^{2}}{x^{2}}\right )}\right )} \]