\[ \int \frac {30 x^2-10 x^4+\left (30-10 x^2+9 x^5-6 x^7+x^9-60 x^6 \log (3)\right ) \log (x)+\left (18 x^3-12 x^5+2 x^7-120 x^4 \log (3)\right ) \log ^2(x)+\left (9 x-6 x^3+x^5-60 x^2 \log (3)\right ) \log ^3(x)+\left (\left (-30-50 x^2+40 x^4\right ) \log (x)+20 x^2 \log ^2(x)\right ) \log (\log (x))}{\left (9 x^5-6 x^7+x^9\right ) \log (x)+\left (18 x^3-12 x^5+2 x^7\right ) \log ^2(x)+\left (9 x-6 x^3+x^5\right ) \log ^3(x)} \, dx \]
Optimal antiderivative \[ x -\frac {10 \left (\frac {\ln \left (\ln \left (x \right )\right )}{\ln \left (x \right )+x^{2}}-3 \ln \! \left (3\right )\right )}{x^{2}-3} \]
command
integrate(((20*x**2*ln(x)**2+(40*x**4-50*x**2-30)*ln(x))*ln(ln(x))+(-60*x**2*ln(3)+x**5-6*x**3+9*x)*ln(x)**3+(-120*x**4*ln(3)+2*x**7-12*x**5+18*x**3)*ln(x)**2+(-60*x**6*ln(3)+x**9-6*x**7+9*x**5-10*x**2+30)*ln(x)-10*x**4+30*x**2)/((x**5-6*x**3+9*x)*ln(x)**3+(2*x**7-12*x**5+18*x**3)*ln(x)**2+(x**9-6*x**7+9*x**5)*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
\[ x - \frac {10 \log {\left (\log {\left (x \right )} \right )}}{x^{4} + x^{2} \log {\left (x \right )} - 3 x^{2} - 3 \log {\left (x \right )}} + \frac {30 \log {\left (3 \right )}}{x^{2} - 3} \]