\[ \int \frac {e^{2+4 e^{e^x}+\frac {e^{2+4 e^{e^x}} (2+2 x)^2}{(3+x)^2}} (2+2 x)^2 \left (4+e^{e^x+x} \left (12+16 x+4 x^2\right )\right )}{(3+x)^2 \left (3+4 x+x^2\right )} \, dx \]
Optimal antiderivative \[ {\mathrm e}^{\frac {4 \left (1+x \right )^{2} {\mathrm e}^{2+4 \,{\mathrm e}^{{\mathrm e}^{x}}}}{\left (3+x \right )^{2}}}-5 \]
command
integrate(((4*x^2+16*x+12)*exp(x)*exp(exp(x))+4)*exp(2*exp(exp(x))+log((2+2*x)/(3+x))+1)^2*exp(exp(2*exp(exp(x))+log((2+2*x)/(3+x))+1)^2)/(x^2+4*x+3),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ e^{\left (\frac {4 \, {\left (x^{2} e^{\left (4 \, e^{\left (e^{x}\right )} + 2\right )} + 2 \, x e^{\left (4 \, e^{\left (e^{x}\right )} + 2\right )} + e^{\left (4 \, e^{\left (e^{x}\right )} + 2\right )}\right )}}{x^{2} + 6 \, x + 9}\right )} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \int \frac {4 \, {\left ({\left (x^{2} + 4 \, x + 3\right )} e^{\left (x + e^{x}\right )} + 1\right )} e^{\left (e^{\left (4 \, e^{\left (e^{x}\right )} + 2 \, \log \left (\frac {2 \, {\left (x + 1\right )}}{x + 3}\right ) + 2\right )} + 4 \, e^{\left (e^{x}\right )} + 2 \, \log \left (\frac {2 \, {\left (x + 1\right )}}{x + 3}\right ) + 2\right )}}{x^{2} + 4 \, x + 3}\,{d x} \]________________________________________________________________________________________