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