\[ \int \frac {(12+6 x) \log ^2\left (\frac {x}{2+x}\right )+e^{\frac {5 x}{\log \left (\frac {x}{2+x}\right )}} \left (-20+(20+10 x) \log \left (\frac {x}{2+x}\right )\right )}{(2+x) \log ^2\left (\frac {x}{2+x}\right )} \, dx \]
Optimal antiderivative \[ 2 \,{\mathrm e}^{\frac {5 x}{\ln \left (\frac {x}{2+x}\right )}}+6 x \]
command
integrate((((10*x+20)*ln(x/(2+x))-20)*exp(5*x/ln(x/(2+x)))+(6*x+12)*ln(x/(2+x))**2)/(2+x)/ln(x/(2+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
\[ 6 x + 2 e^{\frac {5 x}{\log {\left (\frac {x}{x + 2} \right )}}} \]