\[ \int \frac {2^{\frac {1}{4+e^{3-x}+i \pi +x+\log (5-\log (5))}} e^{2^{\frac {1}{4+e^{3-x}+i \pi +x+\log (5-\log (5))}}} \left (-\log (2)+e^{3-x} \log (2)\right )}{16+e^{6-2 x}+8 x+x^2+e^{3-x} (8+2 x)+\left (8+2 e^{3-x}+2 x\right ) (i \pi +\log (5-\log (5)))+(i \pi +\log (5-\log (5)))^2} \, dx \]
Optimal antiderivative \[ {\mathrm e}^{{\mathrm e}^{\frac {\ln \left (2\right )}{\ln \left (\ln \left (5\right )-5\right )+{\mathrm e}^{2} {\mathrm e}^{1-x}+4+x}}} \]
command
integrate((exp(2)*log(2)*exp(1-x)-log(2))*exp(log(2)/(log(log(5)-5)+exp(2)*exp(1-x)+4+x))*exp(exp(log(2)/(log(log(5)-5)+exp(2)*exp(1-x)+4+x)))/(log(log(5)-5)^2+(2*exp(2)*exp(1-x)+2*x+8)*log(log(5)-5)+exp(2)^2*exp(1-x)^2+(2*x+8)*exp(2)*exp(1-x)+x^2+8*x+16),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ e^{\left (2^{\left (\frac {1}{x + e^{\left (-x + 3\right )} + \log \left (\log \left (5\right ) - 5\right ) + 4}\right )}\right )} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \int \frac {{\left (e^{\left (-x + 3\right )} \log \left (2\right ) - \log \left (2\right )\right )} 2^{\left (\frac {1}{x + e^{\left (-x + 3\right )} + \log \left (\log \left (5\right ) - 5\right ) + 4}\right )} e^{\left (2^{\left (\frac {1}{x + e^{\left (-x + 3\right )} + \log \left (\log \left (5\right ) - 5\right ) + 4}\right )}\right )}}{x^{2} + 2 \, {\left (x + 4\right )} e^{\left (-x + 3\right )} + 2 \, {\left (x + e^{\left (-x + 3\right )} + 4\right )} \log \left (\log \left (5\right ) - 5\right ) + \log \left (\log \left (5\right ) - 5\right )^{2} + 8 \, x + e^{\left (-2 \, x + 6\right )} + 16}\,{d x} \]________________________________________________________________________________________