\[ \int \frac {1}{2} e^{8-2 x} \left (64 x-112 x^2+40 x^3-4 x^4+e^{-4+x} \left (16-24 x+4 x^2\right )+3^{2 x} (-1+\log (3))+3^x \left (8-20 x+4 x^2+\left (8 x-2 x^2\right ) \log (3)+e^{-4+x} (-2+2 \log (3))\right )\right ) \, dx \]
Optimal antiderivative \[ \left (1+\left (\frac {{\mathrm e}^{x \ln \left (3\right )}}{2}-x^{2}+4 x \right ) {\mathrm e}^{4-x}\right )^{2} \]
command
integrate(1/2*((log(3)-1)*exp(x*log(3))^2+((2*log(3)-2)*exp(x-4)+(-2*x^2+8*x)*log(3)+4*x^2-20*x+8)*exp(x*log(3))+(4*x^2-24*x+16)*exp(x-4)-4*x^4+40*x^3-112*x^2+64*x)/exp(x-4)^2,x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ -2 \, {\left (x^{2} - 4 \, x\right )} e^{\left (-x + 4\right )} + {\left (x^{4} - 8 \, x^{3} + 16 \, x^{2}\right )} e^{\left (-2 \, x + 8\right )} - \frac {{\left (x^{2} \log \left (3\right )^{3} - 6 \, x^{2} \log \left (3\right )^{2} - 4 \, x \log \left (3\right )^{3} + 12 \, x^{2} \log \left (3\right ) + 24 \, x \log \left (3\right )^{2} - 8 \, x^{2} - 48 \, x \log \left (3\right ) + 32 \, x\right )} e^{\left (x \log \left (3\right ) - 2 \, x + 8\right )}}{\log \left (3\right )^{3} - 6 \, \log \left (3\right )^{2} + 12 \, \log \left (3\right ) - 8} + \frac {1}{4} \, e^{\left (2 \, x \log \left (3\right ) - 2 \, x + 8\right )} + e^{\left (x \log \left (3\right ) - x + 4\right )} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \int -\frac {1}{2} \, {\left (4 \, x^{4} - 40 \, x^{3} - 2 \, {\left (2 \, x^{2} + {\left (\log \left (3\right ) - 1\right )} e^{\left (x - 4\right )} - {\left (x^{2} - 4 \, x\right )} \log \left (3\right ) - 10 \, x + 4\right )} 3^{x} + 112 \, x^{2} - 3^{2 \, x} {\left (\log \left (3\right ) - 1\right )} - 4 \, {\left (x^{2} - 6 \, x + 4\right )} e^{\left (x - 4\right )} - 64 \, x\right )} e^{\left (-2 \, x + 8\right )}\,{d x} \]________________________________________________________________________________________