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