\[ \int \frac {-3 x^2+6 x^3+e^x \left (2 x^2+6 x^3-2 x^4\right )+\left (-6 x^2+e^x \left (-8 x-4 x^2+4 x^3\right )\right ) \log \left (\frac {1}{3} e^{-2 x} \left (-3 x+e^x \left (-4-2 x+2 x^2\right )\right )\right ) \log \left (\log \left (\frac {1}{3} e^{-2 x} \left (-3 x+e^x \left (-4-2 x+2 x^2\right )\right )\right )\right )}{\left (-3 x+e^x \left (-4-2 x+2 x^2\right )\right ) \log \left (\frac {1}{3} e^{-2 x} \left (-3 x+e^x \left (-4-2 x+2 x^2\right )\right )\right )} \, dx \]
Optimal antiderivative \[ x^{2} \ln \! \left (\ln \! \left (\frac {\left (2 x^{2}-4-x \left (3 \,{\mathrm e}^{-x}+2\right )\right ) {\mathrm e}^{-x}}{3}\right )\right ) \]
command
integrate((((4*x**3-4*x**2-8*x)*exp(x)-6*x**2)*ln(1/3*((2*x**2-2*x-4)*exp(x)-3*x)/exp(x)**2)*ln(ln(1/3*((2*x**2-2*x-4)*exp(x)-3*x)/exp(x)**2))+(-2*x**4+6*x**3+2*x**2)*exp(x)+6*x**3-3*x**2)/((2*x**2-2*x-4)*exp(x)-3*x)/ln(1/3*((2*x**2-2*x-4)*exp(x)-3*x)/exp(x)**2),x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \text {Timed out} \]
Sympy 1.8 under Python 3.8.8 output
\[ x^{2} \log {\left (\log {\left (\left (- x + \frac {\left (2 x^{2} - 2 x - 4\right ) e^{x}}{3}\right ) e^{- 2 x} \right )} \right )} \]