\[ \int \frac {108 x^3+30 x^4+2 x^5+\left (-108 x^3-21 x^4-x^5\right ) \log (x)+\left (27 x^3+3 x^4\right ) \log ^2(x)+\left (\left (432 x^3+105 x^4+7 x^5\right ) \log (x)+\left (-432 x^3-87 x^4-4 x^5\right ) \log ^2(x)+\left (108 x^3+15 x^4\right ) \log ^3(x)\right ) \log (\log (x))}{\left (36+12 x+x^2\right ) \log (x)+(-36-6 x) \log ^2(x)+9 \log ^3(x)} \, dx \]
Optimal antiderivative \[ \frac {x^{4} \left (x +9\right ) \ln \! \left (\ln \! \left (x \right )\right )}{3-\frac {x}{\ln \left (x \right )-2}} \]
command
integrate((((15*x**4+108*x**3)*ln(x)**3+(-4*x**5-87*x**4-432*x**3)*ln(x)**2+(7*x**5+105*x**4+432*x**3)*ln(x))*ln(ln(x))+(3*x**4+27*x**3)*ln(x)**2+(-x**5-21*x**4-108*x**3)*ln(x)+2*x**5+30*x**4+108*x**3)/(9*ln(x)**3+(-6*x-36)*ln(x)**2+(x**2+12*x+36)*ln(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
\[ \frac {\left (- x^{5} \log {\left (x \right )} + 2 x^{5} - 9 x^{4} \log {\left (x \right )} + 18 x^{4}\right ) \log {\left (\log {\left (x \right )} \right )}}{x - 3 \log {\left (x \right )} + 6} \]