\[ \int \frac {36 x^3+12 x^4+\left (-36 x^3-9 x^4\right ) \log (x)+\left (-18-9 x-x^2\right ) \log ^2(5) \log ^3(x)+\left (-18 x^3-6 x^4+\left (18 x^3+6 x^4\right ) \log (x)+(9+3 x) \log ^2(5) \log ^3(x)\right ) \log (3+x)}{\left (3 x^2+x^3\right ) \log ^2(5) \log ^3(x)} \, dx \]
Optimal antiderivative \[ \frac {\left (\frac {3 x^{3}}{\ln \left (5\right )^{2} \ln \left (x \right )^{2}}-3-x \right ) \left (\ln \! \left (3+x \right )-2\right )}{x} \]
command
integrate((((3*x+9)*ln(5)**2*ln(x)**3+(6*x**4+18*x**3)*ln(x)-6*x**4-18*x**3)*ln(3+x)+(-x**2-9*x-18)*ln(5)**2*ln(x)**3+(-9*x**4-36*x**3)*ln(x)+12*x**4+36*x**3)/(x**3+3*x**2)/ln(5)**2/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
\[ - \frac {6 x^{2}}{\log {\left (5 \right )}^{2} \log {\left (x \right )}^{2}} - \log {\left (x + 3 \right )} + \frac {\left (3 x^{3} - 3 \log {\left (5 \right )}^{2} \log {\left (x \right )}^{2}\right ) \log {\left (x + 3 \right )}}{x \log {\left (5 \right )}^{2} \log {\left (x \right )}^{2}} + \frac {6}{x} \]