\[ \int \frac {-16 x+4 x^2-4 x^3-4 e^x x^4-9 x^6+\left (16+4 e^x x^3+9 x^5\right ) \log (x)+\left (8 x^3-2 x^4+2 x^5+2 e^x x^6+\left (-8 x^2-2 e^x x^5\right ) \log (x)\right ) \log \left (e^{e^8+e^x} (x-\log (x))\right )}{-9 x^6+9 x^5 \log (x)} \, dx \]
Optimal antiderivative \[ x -\frac {\left (\frac {2}{x^{2}}-\ln \left (\left (x -\ln \left (x \right )\right ) {\mathrm e}^{{\mathrm e}^{x}+{\mathrm e}^{8}}\right )\right ) \left (\frac {2}{3 x^{2}}-\frac {\ln \left (\left (x -\ln \left (x \right )\right ) {\mathrm e}^{{\mathrm e}^{x}+{\mathrm e}^{8}}\right )}{3}\right )}{3} \]
command
integrate((((-2*x**5*exp(x)-8*x**2)*ln(x)+2*x**6*exp(x)+2*x**5-2*x**4+8*x**3)*ln((x-ln(x))*exp(exp(x)+exp(4)**2))+(4*exp(x)*x**3+9*x**5+16)*ln(x)-4*exp(x)*x**4-9*x**6-4*x**3+4*x**2-16*x)/(9*x**5*ln(x)-9*x**6),x)
Sympy 1.10.1 under Python 3.10.4 output
\[ x - \frac {\log {\left (\left (x - \log {\left (x \right )}\right ) e^{e^{x} + e^{8}} \right )}^{2}}{9} + \frac {4 \log {\left (\left (x - \log {\left (x \right )}\right ) e^{e^{x} + e^{8}} \right )}}{9 x^{2}} - \frac {4}{9 x^{4}} \]
Sympy 1.8 under Python 3.8.8 output
\[ \text {Timed out} \]________________________________________________________________________________________