\[ \int \frac {2 x \log (x)+\left (-216 x^3+216 x^4-72 x^5+8 x^6\right ) \log ^3(x)+(6-2 x+(6-4 x) \log (x)) \log \left (9-6 x+x^2\right )}{\left (-27 x^3+27 x^4-9 x^5+x^6\right ) \log ^3(x)} \, dx \]
Optimal antiderivative \[ \frac {\ln \! \left (\left (-3+x \right )^{2}\right )}{\ln \! \left (x \right )^{2} x^{2} \left (-3+x \right )^{2}}+8 x \]
command
integrate((((6-4*x)*ln(x)+6-2*x)*ln(x**2-6*x+9)+(8*x**6-72*x**5+216*x**4-216*x**3)*ln(x)**3+2*x*ln(x))/(x**6-9*x**5+27*x**4-27*x**3)/ln(x)**3,x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \text {Exception raised: TypeError} \]
Sympy 1.8 under Python 3.8.8 output
\[ 8 x + \frac {\log {\left (x^{2} - 6 x + 9 \right )}}{x^{4} \log {\left (x \right )}^{2} - 6 x^{3} \log {\left (x \right )}^{2} + 9 x^{2} \log {\left (x \right )}^{2}} \]