\[ \int \frac {-6-24 x+(-1-6 x) \log (2 x)+(24 x+4 \log (x)+(6 x+\log (x)) \log (2 x)+(8+2 \log (2 x)) \log (4+\log (2 x))) \log \left (\frac {8}{6 x+\log (x)+2 \log (4+\log (2 x))}\right )}{24 x+4 \log (x)+(6 x+\log (x)) \log (2 x)+(8+2 \log (2 x)) \log (4+\log (2 x))} \, dx \]
Optimal antiderivative \[ x \ln \! \left (\frac {4}{\frac {\ln \left (x \right )}{2}+3 x +\ln \! \left (\ln \! \left (2 x \right )+4\right )}\right ) \]
command
integrate((((2*ln(2*x)+8)*ln(ln(2*x)+4)+(ln(x)+6*x)*ln(2*x)+4*ln(x)+24*x)*ln(8/(2*ln(ln(2*x)+4)+ln(x)+6*x))+(-6*x-1)*ln(2*x)-24*x-6)/((2*ln(2*x)+8)*ln(ln(2*x)+4)+(ln(x)+6*x)*ln(2*x)+4*ln(x)+24*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
\[ x \log {\left (\frac {8}{6 x + \log {\left (x \right )} + 2 \log {\left (\log {\left (x \right )} + \log {\left (2 \right )} + 4 \right )}} \right )} \]