\[ \int \frac {2^{\frac {1}{4+e^{3-x}+i \pi +x+\log (5-\log (5))}} e^{2^{\frac {1}{4+e^{3-x}+i \pi +x+\log (5-\log (5))}}} \left (-\log (2)+e^{3-x} \log (2)\right )}{16+e^{6-2 x}+8 x+x^2+e^{3-x} (8+2 x)+\left (8+2 e^{3-x}+2 x\right ) (i \pi +\log (5-\log (5)))+(i \pi +\log (5-\log (5)))^2} \, dx \]
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
Int[(2^(4 + E^(3 - x) + I*Pi + x + Log[5 - Log[5]])^(-1)*E^2^(4 + E^(3 - x) + I*Pi + x + Log[5 - Log[5]])^(-1)*(-Log[2] + E^(3 - x)*Log[2]))/(16 + E^(6 - 2*x) + 8*x + x^2 + E^(3 - x)*(8 + 2*x) + (8 + 2*E^(3 - x) + 2*x)*(I*Pi + Log[5 - Log[5]]) + (I*Pi + Log[5 - Log[5]])^2),x]
Rubi 4.17.3 under Mathematica 13.3.1 output
\[ e^{2^{\frac {1}{x+e^{3-x}+i \pi +4+\log (5-\log (5))}}} \]
Rubi 4.16.1 under Mathematica 13.3.1 output
\[ \int \frac {2^{\frac {1}{4+e^{3-x}+i \pi +x+\log (5-\log (5))}} e^{2^{\frac {1}{4+e^{3-x}+i \pi +x+\log (5-\log (5))}}} \left (-\log (2)+e^{3-x} \log (2)\right )}{16+e^{6-2 x}+8 x+x^2+e^{3-x} (8+2 x)+\left (8+2 e^{3-x}+2 x\right ) (i \pi +\log (5-\log (5)))+(i \pi +\log (5-\log (5)))^2} \, dx \]________________________________________________________________________________________