\[ \int \frac {e^{-5 x} \left (e^{2 e^{-5 x}} \left (-2 e^{5 x}-10 x\right )-e^{5 x} x^3 \log (4)\right )}{x^3 \log (4)} \, dx \]
Optimal antiderivative \[ -x +\frac {{\mathrm e}^{2 \,{\mathrm e}^{-5 x}}}{2 x^{2} \ln \left (2\right )}-5 \]
command
integrate(1/2*((-2*exp(5*x)-10*x)*exp(2/exp(5*x))-2*x^3*log(2)*exp(5*x))/x^3/log(2)/exp(5*x),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ -\frac {2 \, x^{3} \log \left (2\right ) - e^{\left (2 \, e^{\left (-5 \, x\right )}\right )}}{2 \, x^{2} \log \left (2\right )} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \int -\frac {{\left (x^{3} e^{\left (5 \, x\right )} \log \left (2\right ) + {\left (5 \, x + e^{\left (5 \, x\right )}\right )} e^{\left (2 \, e^{\left (-5 \, x\right )}\right )}\right )} e^{\left (-5 \, x\right )}}{x^{3} \log \left (2\right )}\,{d x} \]________________________________________________________________________________________