\[ \int \frac {-108+144 x^3+2 x^6+e^{-1+x} \left (-54+72 x^3+x^6\right )+\left (e^{-1+x} \left (9 x-24 x^4+16 x^7\right )+e^{-1+x} x^7 \log (x)\right ) \log \left (\frac {9-24 x^3+16 x^6+x^6 \log (x)}{x^6}\right )}{9 x-24 x^4+16 x^7+x^7 \log (x)} \, dx \]
Optimal antiderivative \[ \ln \! \left (\ln \! \left (x \right )+\left (4-\frac {3}{x^{3}}\right )^{2}\right ) \left (2+{\mathrm e}^{-1+x}\right ) \]
command
integrate(((x**7*exp(-1+x)*ln(x)+(16*x**7-24*x**4+9*x)*exp(-1+x))*ln((x**6*ln(x)+16*x**6-24*x**3+9)/x**6)+(x**6+72*x**3-54)*exp(-1+x)+2*x**6+144*x**3-108)/(x**7*ln(x)+16*x**7-24*x**4+9*x),x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \text {Timed out} \]
Sympy 1.8 under Python 3.8.8 output
\[ e^{x - 1} \log {\left (\frac {x^{6} \log {\left (x \right )} + 16 x^{6} - 24 x^{3} + 9}{x^{6}} \right )} + 2 \log {\left (\log {\left (x \right )} + \frac {16 x^{6} - 24 x^{3} + 9}{x^{6}} \right )} \]