\[ \int \frac {(1+9 x) \log (x)+(-22-9 x-\log (x)) \log \left (\frac {1}{2} (22+9 x+\log (x))\right )}{\left (22 x+9 x^2\right ) \log ^2(x)+x \log ^3(x)} \, dx \]
Optimal antiderivative \[ \frac {\ln \! \left (\frac {\ln \left (x \right )}{2}+\frac {9 x}{2}+11\right )}{\ln \! \left (x \right )}+4 \]
command
integrate(((-ln(x)-9*x-22)*ln(1/2*ln(x)+9/2*x+11)+(9*x+1)*ln(x))/(x*ln(x)**3+(9*x**2+22*x)*ln(x)**2),x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \text {Exception raised: TypeError} \]
Sympy 1.8 under Python 3.8.8 output
\[ \frac {\log {\left (\frac {9 x}{2} + \frac {\log {\left (x \right )}}{2} + 11 \right )}}{\log {\left (x \right )}} \]