\[ \int \frac {\left (16 x-16 x^2+\left (96 x-48 x^2+\left (-32 x+16 x^2\right ) \log (x)\right ) \log (-3+\log (x))\right ) \log ^3\left (-\frac {x^2 \log (3)}{(-2+2 x) \log (-3+\log (x))}\right )+\left (24 x-24 x^2+\left (-8 x+8 x^2\right ) \log (x)\right ) \log (-3+\log (x)) \log ^4\left (-\frac {x^2 \log (3)}{(-2+2 x) \log (-3+\log (x))}\right )}{(3-3 x+(-1+x) \log (x)) \log (-3+\log (x))} \, dx \]
Optimal antiderivative \[ 4 \ln \! \left (\frac {x^{2} \ln \! \left (3\right )}{2 \left (1-x \right ) \ln \! \left (\ln \! \left (x \right )-3\right )}\right )^{4} x^{2} \]
command
integrate((((8*x**2-8*x)*ln(x)-24*x**2+24*x)*ln(ln(x)-3)*ln(-x**2*ln(3)/(-2+2*x)/ln(ln(x)-3))**4+(((16*x**2-32*x)*ln(x)-48*x**2+96*x)*ln(ln(x)-3)-16*x**2+16*x)*ln(-x**2*ln(3)/(-2+2*x)/ln(ln(x)-3))**3)/((-1+x)*ln(x)-3*x+3)/ln(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
\[ 4 x^{2} \log {\left (- \frac {x^{2} \log {\left (3 \right )}}{\left (2 x - 2\right ) \log {\left (\log {\left (x \right )} - 3 \right )}} \right )}^{4} \]