\[ \int e^{-40+e^{-40+8 x} \left (16 e^5+4 e^{45-8 x}\right )+8 x} \left (e^{40-8 x}+128 e^5 x\right ) \, dx \]
Optimal antiderivative \[ {\mathrm e}^{{\mathrm e}^{5} \left (16 \,{\mathrm e}^{8 x -40}+4\right )} x \]
command
Int[E^(-40 + E^(-40 + 8*x)*(16*E^5 + 4*E^(45 - 8*x)) + 8*x)*(E^(40 - 8*x) + 128*E^5*x),x]
Rubi 4.17.3 under Mathematica 13.3.1 output
\[ \int \exp \left (-40+e^{-40+8 x} \left (16 e^5+4 e^{45-8 x}\right )+8 x\right ) \left (e^{40-8 x}+128 e^5 x\right ) \, dx \]
Rubi 4.16.1 under Mathematica 13.3.1 output
\[ e^{16 e^{8 x-35}+4 e^5} x \]