\[ \int \frac {e^2 \left (2 x+2 x^2\right )+e \left (52 x+4 x^2\right ) \log (x)+\left (50 x+2 x^2\right ) \log ^2(x)+\left (e (96+48 x)+e^2 \left (2 x+x^2\right )+e \left (4 x+2 x^2\right ) \log (x)+\left (2 x+x^2\right ) \log ^2(x)\right ) \log (2+x)}{e^2 \left (2 x+x^2\right )+e \left (4 x+2 x^2\right ) \log (x)+\left (2 x+x^2\right ) \log ^2(x)} \, dx \]
Optimal antiderivative \[ x -\ln \! \left (2+x \right ) \left (-x -\frac {48 \ln \! \left (x \right )}{{\mathrm e}+\ln \! \left (x \right )}\right ) \]
command
integrate((((x**2+2*x)*ln(x)**2+(2*x**2+4*x)*exp(1)*ln(x)+(x**2+2*x)*exp(1)**2+(48*x+96)*exp(1))*ln(2+x)+(2*x**2+50*x)*ln(x)**2+(4*x**2+52*x)*exp(1)*ln(x)+(2*x**2+2*x)*exp(1)**2)/((x**2+2*x)*ln(x)**2+(2*x**2+4*x)*exp(1)*ln(x)+(x**2+2*x)*exp(1)**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
\[ x + 48 \log {\left (x + 2 \right )} + \frac {\left (x \log {\left (x \right )} + e x - 48 e\right ) \log {\left (x + 2 \right )}}{\log {\left (x \right )} + e} \]