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