\[ \int \frac {\left (-16 x+28 x^2-8 x^3\right ) \log (x)+\left (8 x-4 x^2+\left (8 x-28 x^2+12 x^3\right ) \log (x)\right ) \log \left (e^{-2 x} \left (-2 x^2+x^3\right )\right )+\left (-16 x+8 x^2\right ) \log (x) \log \left (e^{-2 x} \left (-2 x^2+x^3\right )\right ) \log \left (\frac {\log \left (e^{-2 x} \left (-2 x^2+x^3\right )\right )}{x \log (x)}\right )}{(-2+x) \log (x) \log \left (e^{-2 x} \left (-2 x^2+x^3\right )\right )} \, dx \]
Optimal antiderivative \[ 4 x^{2} \left (x +\ln \! \left (\frac {\ln \! \left (x^{2} {\mathrm e}^{-2 x} \left (-2+x \right )\right )}{x \ln \! \left (x \right )}\right )\right ) \]
command
integrate(((8*x**2-16*x)*ln(x)*ln((x**3-2*x**2)/exp(x)**2)*ln(ln((x**3-2*x**2)/exp(x)**2)/x/ln(x))+((12*x**3-28*x**2+8*x)*ln(x)-4*x**2+8*x)*ln((x**3-2*x**2)/exp(x)**2)+(-8*x**3+28*x**2-16*x)*ln(x))/(-2+x)/ln(x)/ln((x**3-2*x**2)/exp(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
\[ 4 x^{3} + \left (4 x^{2} - \frac {8}{3}\right ) \log {\left (\frac {\log {\left (\left (x^{3} - 2 x^{2}\right ) e^{- 2 x} \right )}}{x \log {\left (x \right )}} \right )} - \frac {8 \log {\left (x \right )}}{3} - \frac {8 \log {\left (\log {\left (x \right )} \right )}}{3} + \frac {8 \log {\left (\log {\left (\left (x^{3} - 2 x^{2}\right ) e^{- 2 x} \right )} \right )}}{3} \]