\[ \int \frac {1}{2} e^{8-2 x} \left (64 x-112 x^2+40 x^3-4 x^4+e^{-4+x} \left (16-24 x+4 x^2\right )+3^{2 x} (-1+\log (3))+3^x \left (8-20 x+4 x^2+\left (8 x-2 x^2\right ) \log (3)+e^{-4+x} (-2+2 \log (3))\right )\right ) \, dx \]
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*((ln(3)-1)*exp(x*ln(3))**2+((2*ln(3)-2)*exp(x-4)+(-2*x**2+8*x)*ln(3)+4*x**2-20*x+8)*exp(x*ln(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)
Sympy 1.10.1 under Python 3.10.4 output
\[ x^{4} e^{8} e^{- 2 x} - 8 x^{3} e^{8} e^{- 2 x} - 2 x^{2} e^{4} e^{- x} - x^{2} e^{8} e^{- 2 x} e^{x \log {\left (3 \right )}} + 16 x^{2} e^{8} e^{- 2 x} + 8 x e^{4} e^{- x} + 4 x e^{8} e^{- 2 x} e^{x \log {\left (3 \right )}} + e^{4} e^{- x} e^{x \log {\left (3 \right )}} + \frac {e^{8} e^{- 2 x} e^{2 x \log {\left (3 \right )}}}{4} \]
Sympy 1.8 under Python 3.8.8 output
\[ \text {Timed out} \]________________________________________________________________________________________