\[ \int \frac {\left (-20+12 x+(4-2 x) \log \left (e^{8+x}\right )\right ) \log \left (\frac {1}{5} e^{-x} \left (-10 x^2+2 x^2 \log \left (e^{8+x}\right )\right )\right )}{-5 x+x \log \left (e^{8+x}\right )} \, dx \]
Optimal antiderivative \[ \ln \left (\frac {2 \left (\ln \left ({\mathrm e}^{3} {\mathrm e}^{5+x}\right )-5\right ) x^{2} {\mathrm e}^{-x}}{5}\right )^{2} \]
command
integrate(((4-2*x)*log(exp(3)*exp(5+x))+12*x-20)*log(1/5*(2*x^2*log(exp(3)*exp(5+x))-10*x^2)/exp(x))/(x*log(exp(3)*exp(5+x))-5*x),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \log \left (\frac {2}{5} \, x^{3} e^{\left (-x\right )} + \frac {6}{5} \, x^{2} e^{\left (-x\right )}\right )^{2} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \int -\frac {2 \, {\left ({\left (x - 2\right )} \log \left (e^{\left (x + 8\right )}\right ) - 6 \, x + 10\right )} \log \left (\frac {2}{5} \, {\left (x^{2} \log \left (e^{\left (x + 8\right )}\right ) - 5 \, x^{2}\right )} e^{\left (-x\right )}\right )}{x \log \left (e^{\left (x + 8\right )}\right ) - 5 \, x}\,{d x} \]________________________________________________________________________________________