\[ \int \frac {e^{\frac {3-x+3 \log \left (\frac {-20-5 x-2 x^2}{6 x}\right )}{\log \left (\frac {-20-5 x-2 x^2}{6 x}\right )}} \left (60-20 x-6 x^2+2 x^3+\left (-20 x-5 x^2-2 x^3\right ) \log \left (\frac {-20-5 x-2 x^2}{6 x}\right )\right )}{\left (20 x+5 x^2+2 x^3\right ) \log ^2\left (\frac {-20-5 x-2 x^2}{6 x}\right )} \, dx \]
Optimal antiderivative \[ {\mathrm e}^{\frac {3-x}{\ln \left (-\frac {5}{6}-\frac {10}{3 x}-\frac {x}{3}\right )}+3} \]
command
integrate(((-2*x**3-5*x**2-20*x)*ln(1/6*(-2*x**2-5*x-20)/x)+2*x**3-6*x**2-20*x+60)*exp((3*ln(1/6*(-2*x**2-5*x-20)/x)+3-x)/ln(1/6*(-2*x**2-5*x-20)/x))/(2*x**3+5*x**2+20*x)/ln(1/6*(-2*x**2-5*x-20)/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
\[ e^{\frac {- x + 3 \log {\left (\frac {- \frac {x^{2}}{3} - \frac {5 x}{6} - \frac {10}{3}}{x} \right )} + 3}{\log {\left (\frac {- \frac {x^{2}}{3} - \frac {5 x}{6} - \frac {10}{3}}{x} \right )}}} \]