\[ \int \frac {-8-2 x+\left (7+9 x-15 x^2-2 x^3\right ) \log (x)+\left (-x-2 x^2\right ) \log ^2(x)+(1+2 x) \log (x) \log (\log (x))}{\left (64 x+32 x^2+4 x^3\right ) \log (x)+\left (16 x+4 x^2\right ) \log ^2(x)+x \log ^3(x)} \, dx \]
Optimal antiderivative \[ \frac {x -\ln \! \left (\ln \! \left (x \right )\right )+\ln \! \left (x \right )-x^{2}}{8+2 x +\ln \! \left (x \right )} \]
command
integrate(((1+2*x)*ln(x)*ln(ln(x))+(-2*x**2-x)*ln(x)**2+(-2*x**3-15*x**2+9*x+7)*ln(x)-2*x-8)/(x*ln(x)**3+(4*x**2+16*x)*ln(x)**2+(4*x**3+32*x**2+64*x)*ln(x)),x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \text {Exception raised: TypeError} \]
Sympy 1.8 under Python 3.8.8 output
\[ \frac {- x^{2} - x - 8}{2 x + \log {\left (x \right )} + 8} - \frac {\log {\left (\log {\left (x \right )} \right )}}{2 x + \log {\left (x \right )} + 8} \]