\[ \int \frac {75 e^{4+x}}{625 e^2+81 e^{2 x}+450 e^{1+x}} \, dx \]
Optimal antiderivative \[ \frac {{\mathrm e}^{3}}{3+\frac {25 \,{\mathrm e} \,{\mathrm e}^{-x}}{3}} \]
command
integrate(75*exp(1)*exp(3)*exp(x)/(81*exp(x)^2+450*exp(1)*exp(x)+625*exp(1)^2),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ -\frac {25 \, e^{5}}{3 \, {\left (25 \, e^{2} + 9 \, e^{\left (x + 1\right )}\right )}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Exception raised: NotImplementedError} \]________________________________________________________________________________________