\[ \int \frac {-16 e^{4 x}+288 x-576 x^2+e^{e^{5-x}} \left (e^{4 x} \left (-1-9 e^{5-x}\right )+18 x-36 x^2\right )}{144 e^{4 x}+9 e^{e^{5-x}+4 x}} \, dx \]
Optimal antiderivative \[ \ln \left (16+{\mathrm e}^{{\mathrm e}^{5-x}}\right )-\frac {x}{9}-\frac {1}{9}+x^{2} {\mathrm e}^{-4 x} \]
command
integrate((((-9*exp(5-x)-1)*exp(4*x)-36*x^2+18*x)*exp(exp(5-x))-16*exp(4*x)-576*x^2+288*x)/(9*exp(4*x)*exp(exp(5-x))+144*exp(4*x)),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {1}{9} \, {\left (9 \, {\left (x - 5\right )}^{2} e^{\left (-4 \, x + 20\right )} - {\left (x - 5\right )} e^{20} + 90 \, {\left (x - 5\right )} e^{\left (-4 \, x + 20\right )} + 9 \, e^{20} \log \left (e^{\left (e^{\left (-x + 5\right )}\right )} + 16\right ) + 225 \, e^{\left (-4 \, x + 20\right )}\right )} e^{\left (-20\right )} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \int -\frac {576 \, x^{2} + {\left (36 \, x^{2} + {\left (9 \, e^{\left (-x + 5\right )} + 1\right )} e^{\left (4 \, x\right )} - 18 \, x\right )} e^{\left (e^{\left (-x + 5\right )}\right )} - 288 \, x + 16 \, e^{\left (4 \, x\right )}}{9 \, {\left (16 \, e^{\left (4 \, x\right )} + e^{\left (4 \, x + e^{\left (-x + 5\right )}\right )}\right )}}\,{d x} \]________________________________________________________________________________________