\[ \int \frac {e^{1+6 x} \left (30 e^{8-2 x}-20 e^{4-x}\right )}{16+25 e^{8-2 x}-40 e^{4-x}} \, dx \]
Optimal antiderivative \[ \frac {{\mathrm e}^{6 x +1}}{5-4 \,{\mathrm e}^{-4+x}} \]
command
integrate((30*exp(-x+4)^2-20*exp(-x+4))*exp(6*x+1)/(25*exp(-x+4)^2-40*exp(-x+4)+16),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ -\frac {1}{1024} \, {\left (256 \, e^{25} + 320 \, e^{\left (-x + 29\right )} + 400 \, e^{\left (-2 \, x + 33\right )} + 500 \, e^{\left (-3 \, x + 37\right )} + 625 \, e^{\left (-4 \, x + 41\right )}\right )} e^{\left (5 \, x - 20\right )} + \frac {3125 \, e^{25}}{1024 \, {\left (5 \, e^{\left (-x + 4\right )} - 4\right )}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Exception raised: NotImplementedError} \]________________________________________________________________________________________