\[ \int \frac {e^3 \left (-3+5 x-x^2\right )+e^6 \left (-12+20 x-4 x^2\right ) \log (x)+\left (e^6 \left (-12 x+4 x^2\right )+e^6 (12-4 x) \log \left (3 x-x^2\right )\right ) \log \left (-x+\log \left (3 x-x^2\right )\right )}{30 x^2-10 x^3+\left (-30 x+10 x^2\right ) \log \left (3 x-x^2\right )+\log (x) \left (e^3 \left (240 x^2-80 x^3\right )+e^3 \left (-240 x+80 x^2\right ) \log \left (3 x-x^2\right )\right )+\log ^2(x) \left (e^6 \left (480 x^2-160 x^3\right )+e^6 \left (-480 x+160 x^2\right ) \log \left (3 x-x^2\right )\right )} \, dx \]
Optimal antiderivative \[ \frac {\ln \! \left (\ln \! \left (\left (2-x \right ) x +x \right )-x \right )}{10 \,{\mathrm e}^{-3}+40 \ln \! \left (x \right )} \]
command
integrate((((-4*x+12)*exp(3)**2*ln(-x**2+3*x)+(4*x**2-12*x)*exp(3)**2)*ln(ln(-x**2+3*x)-x)+(-4*x**2+20*x-12)*exp(3)**2*ln(x)+(-x**2+5*x-3)*exp(3))/(((160*x**2-480*x)*exp(3)**2*ln(-x**2+3*x)+(-160*x**3+480*x**2)*exp(3)**2)*ln(x)**2+((80*x**2-240*x)*exp(3)*ln(-x**2+3*x)+(-80*x**3+240*x**2)*exp(3))*ln(x)+(10*x**2-30*x)*ln(-x**2+3*x)-10*x**3+30*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
\[ \frac {e^{3} \log {\left (- x + \log {\left (- x^{2} + 3 x \right )} \right )}}{40 e^{3} \log {\left (x \right )} + 10} \]