\[ \int \frac {4-3 x^2-3 x^3+6 x^5-2 x^6+\left (4 x-4 x^3+2 x^4\right ) \log (x)+\left (-x^2+x^5-x^3 \log (x)\right ) \log \left (\frac {1-x^3+x \log (x)}{x}\right )}{\left (4 x+x^2+4 x^3-5 x^4-x^5-4 x^6+x^7+\left (4 x^2+x^3+4 x^4-x^5\right ) \log (x)+\left (x^3-x^6+x^4 \log (x)\right ) \log \left (\frac {1-x^3+x \log (x)}{x}\right )\right ) \log ^2\left (\frac {4+x+4 x^2-x^3+x^2 \log \left (\frac {1-x^3+x \log (x)}{x}\right )}{x}\right )} \, dx \]
Optimal antiderivative \[ \frac {1}{\ln \left (\left (\ln \left (\ln \left (x \right )+\frac {1}{x}-x^{2}\right )-x +4\right ) x +\frac {4+x}{x}\right )} \]
command
integrate(((-x**3*ln(x)+x**5-x**2)*ln((x*ln(x)-x**3+1)/x)+(2*x**4-4*x**3+4*x)*ln(x)-2*x**6+6*x**5-3*x**3-3*x**2+4)/((x**4*ln(x)-x**6+x**3)*ln((x*ln(x)-x**3+1)/x)+(-x**5+4*x**4+x**3+4*x**2)*ln(x)+x**7-4*x**6-x**5-5*x**4+4*x**3+x**2+4*x)/ln((x**2*ln((x*ln(x)-x**3+1)/x)-x**3+4*x**2+x+4)/x)**2,x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \frac {1}{\log {\left (\frac {- x^{3} + x^{2} \log {\left (\frac {- x^{3} + x \log {\left (x \right )} + 1}{x} \right )} + 4 x^{2} + x + 4}{x} \right )}} \]
Sympy 1.8 under Python 3.8.8 output
\[ \text {Timed out} \]________________________________________________________________________________________