\[ \int \frac {e^{\frac {-15+5 x}{\left (39 x-8 x^2-4 x^3+x^4\right ) \log (x)}} \left (-585+315 x+20 x^2-35 x^3+5 x^4+\left (-585+240 x+140 x^2-100 x^3+15 x^4\right ) \log (x)\right )}{\left (1521 x^2-624 x^3-248 x^4+142 x^5-8 x^7+x^8\right ) \log ^2(x)} \, dx \]
Optimal antiderivative \[ \ln \! \left (2\right )-{\mathrm e}^{\frac {5}{\left (3+x \right ) \left (\frac {1}{-3+x}+x -4\right ) x \ln \left (x \right )}} \]
command
integrate(((15*x**4-100*x**3+140*x**2+240*x-585)*ln(x)+5*x**4-35*x**3+20*x**2+315*x-585)*exp((5*x-15)/(x**4-4*x**3-8*x**2+39*x)/ln(x))/(x**8-8*x**7+142*x**5-248*x**4-624*x**3+1521*x**2)/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
\[ - e^{\frac {5 x - 15}{\left (x^{4} - 4 x^{3} - 8 x^{2} + 39 x\right ) \log {\left (x \right )}}} \]