\[ \int \frac {7 x^2+(12+4 x) \log ^3(5 x) \log (3+x)+\log ^4(5 x) (-x+(-3-x) \log (3+x))}{147 x^2+49 x^3+\left (-42 x-14 x^2\right ) \log ^4(5 x)+(3+x) \log ^8(5 x)} \, dx \]
Optimal antiderivative \[ \frac {\ln \! \left (3+x \right ) x}{7 x -\ln \! \left (5 x \right )^{4}} \]
command
integrate((((-3-x)*ln(3+x)-x)*ln(5*x)**4+(4*x+12)*ln(3+x)*ln(5*x)**3+7*x**2)/((3+x)*ln(5*x)**8+(-14*x**2-42*x)*ln(5*x)**4+49*x**3+147*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
\[ \frac {x \log {\left (x + 3 \right )}}{7 x - \log {\left (5 x \right )}^{4}} \]