\[ \int -\frac {5000 e^{5+625 e^{4 x}+4 x}}{e^{10+1250 e^{4 x}}+2 e^{5+625 e^{4 x}} \log (2)+\log ^2(2)} \, dx \]
Optimal antiderivative \[ \frac {2}{{\mathrm e}^{625 \,{\mathrm e}^{4 x}} {\mathrm e}^{5}+\ln \left (2\right )}-5 \]
command
integrate(-5000*exp(5)*exp(x)^4*exp(625*exp(x)^4)/(exp(5)^2*exp(625*exp(x)^4)^2+2*exp(5)*log(2)*exp(625*exp(x)^4)+log(2)^2),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {2}{e^{\left (625 \, e^{\left (4 \, x\right )} + 5\right )} + \log \left (2\right )} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Exception raised: NotImplementedError} \]________________________________________________________________________________________