\[ \int \frac {-36 x+36 x^2+\left (3 x-3 x^2\right ) \log (x)+\left (33 x-108 x^2+\left (-3 x+9 x^2\right ) \log (x)\right ) \log (2 x)+(-36 x+3 x \log (x)+(72 x-6 x \log (x)) \log (2 x)) \log \left (\frac {-12+\log (x)}{8 x}\right )}{(-12+\log (x)) \log ^2(2 x)} \, dx \]
Optimal antiderivative \[ \frac {3 x^{2} \left (x -1-\ln \! \left (\frac {\frac {\ln \left (x \right )}{4}-3}{2 x}\right )\right )}{\ln \! \left (2 x \right )} \]
command
integrate((((-6*x*ln(x)+72*x)*ln(2*x)+3*x*ln(x)-36*x)*ln(1/8*(ln(x)-12)/x)+((9*x**2-3*x)*ln(x)-108*x**2+33*x)*ln(2*x)+(-3*x**2+3*x)*ln(x)+36*x**2-36*x)/(ln(x)-12)/ln(2*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
\[ - \frac {3 x^{2} \log {\left (\frac {\frac {\log {\left (x \right )}}{8} - \frac {3}{2}}{x} \right )}}{\log {\left (x \right )} + \log {\left (2 \right )}} + \frac {3 x^{3} - 3 x^{2}}{\log {\left (x \right )} + \log {\left (2 \right )}} \]