\[ \int \frac {9-6 e+e^2+(5-2 e) e^x+e^{2 x}}{9-6 e+e^2+(6-2 e) e^x+e^{2 x}} \, dx \]
Optimal antiderivative \[ 4+x +\frac {1}{{\mathrm e}^{x}+3-{\mathrm e}} \]
command
integrate((exp(x)^2+(-2*exp(1)+5)*exp(x)+exp(1)^2-6*exp(1)+9)/(exp(x)^2+(-2*exp(1)+6)*exp(x)+exp(1)^2-6*exp(1)+9),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ x - \frac {1}{e - e^{x} - 3} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Exception raised: NotImplementedError} \]________________________________________________________________________________________