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