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