\[ \int \frac {\left (9+e-x^2-18 x^4+8 x^5-7 x^8\right ) (i \pi +\log (3))}{81+e^2-108 x+54 x^2-12 x^3+109 x^4-108 x^5+36 x^6-4 x^7+54 x^8-36 x^9+6 x^{10}+12 x^{12}-4 x^{13}+x^{16}+e \left (18-12 x+2 x^2+12 x^4-4 x^5+2 x^8\right )} \, dx \]
Optimal antiderivative \[ \frac {x \left (\ln \left (3\right )+i \pi \right )}{\left (x^{4}-x +3\right )^{2}+{\mathrm e}} \]
command
integrate((exp(1)-7*x**8+8*x**5-18*x**4-x**2+9)*(ln(3)+I*pi)/(exp(1)**2+(2*x**8-4*x**5+12*x**4+2*x**2-12*x+18)*exp(1)+x**16-4*x**13+12*x**12+6*x**10-36*x**9+54*x**8-4*x**7+36*x**6-108*x**5+109*x**4-12*x**3+54*x**2-108*x+81),x)
Sympy 1.10.1 under Python 3.10.4 output
\[ - \frac {x \left (- \log {\left (3 \right )} - i \pi \right )}{x^{8} - 2 x^{5} + 6 x^{4} + x^{2} - 6 x + e + 9} \]
Sympy 1.8 under Python 3.8.8 output
\[ \text {Timed out} \]________________________________________________________________________________________