\[ \int \frac {240 x^2+100 x^3+e^x \left (240 x+100 x^2\right )+\left (-120 x+50 x^2+e^x \left (-20 x-50 x^2\right )\right ) \log (x)+\left (e^x (-120-50 x)-120 x-50 x^2+\left (e^x (-120-50 x)-120 x-50 x^2\right ) \log (x)\right ) \log \left (\frac {144+120 x+25 x^2}{e^x+x}\right )}{\left (12 x^3+5 x^4+e^x \left (12 x^2+5 x^3\right )\right ) \log ^2(x)} \, dx \]
Optimal antiderivative \[ \frac {10 \ln \! \left (\frac {\left (12+5 x \right )^{2}}{x +{\mathrm e}^{x}}\right )-20 x}{x \ln \! \left (x \right )} \]
command
integrate(((((-50*x-120)*exp(x)-50*x**2-120*x)*ln(x)+(-50*x-120)*exp(x)-50*x**2-120*x)*ln((25*x**2+120*x+144)/(exp(x)+x))+((-50*x**2-20*x)*exp(x)+50*x**2-120*x)*ln(x)+(100*x**2+240*x)*exp(x)+100*x**3+240*x**2)/((5*x**3+12*x**2)*exp(x)+5*x**4+12*x**3)/ln(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
\[ - \frac {20}{\log {\left (x \right )}} + \frac {10 \log {\left (\frac {25 x^{2} + 120 x + 144}{x + e^{x}} \right )}}{x \log {\left (x \right )}} \]