\[ \int \frac {\left (9+e-x^2-18 x^4+8 x^5-7 x^8\right ) (i \pi +\log (3))}{81+e^2-108 x+54 x^2-12 x^3+109 x^4-108 x^5+36 x^6-4 x^7+54 x^8-36 x^9+6 x^{10}+12 x^{12}-4 x^{13}+x^{16}+e \left (18-12 x+2 x^2+12 x^4-4 x^5+2 x^8\right )} \, dx \]
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)*(log(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, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ -\frac {{\left (-i \, \pi - \log \left (3\right )\right )} x}{x^{8} - 2 \, x^{5} + 6 \, x^{4} + x^{2} - 6 \, x + e + 9} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \int -\frac {{\left (i \, \pi + \log \left (3\right )\right )} {\left (7 \, x^{8} - 8 \, x^{5} + 18 \, x^{4} + x^{2} - e - 9\right )}}{x^{16} - 4 \, x^{13} + 12 \, x^{12} + 6 \, x^{10} - 36 \, x^{9} + 54 \, x^{8} - 4 \, x^{7} + 36 \, x^{6} - 108 \, x^{5} + 109 \, x^{4} - 12 \, x^{3} + 54 \, x^{2} + 2 \, {\left (x^{8} - 2 \, x^{5} + 6 \, x^{4} + x^{2} - 6 \, x + 9\right )} e - 108 \, x + e^{2} + 81}\,{d x} \]________________________________________________________________________________________