\[ \int \frac {32 x+26 x^2+6 x^4-2 x^5+e^6 \left (2 x+2 x^2\right )+e^3 \left (-16 x-14 x^2-2 x^4\right )}{256+832 x+708 x^2-140 x^3-279 x^4+40 x^5+38 x^6-12 x^7+x^8+e^{12} \left (1+4 x+6 x^2+4 x^3+x^4\right )+e^9 \left (-16-60 x-80 x^2-40 x^3+4 x^5\right )+e^6 \left (96+340 x+398 x^2+124 x^3-60 x^4-24 x^5+6 x^6\right )+e^3 \left (-256-864 x-872 x^2-76 x^3+248 x^4+24 x^5-32 x^6+4 x^7\right )} \, dx \]
Optimal antiderivative \[ \frac {x^{2}}{2 x +\left (1+x \right )^{2} \left ({\mathrm e}^{3}+x -4\right )^{2}} \]
command
integrate(((2*x^2+2*x)*exp(3)^2+(-2*x^4-14*x^2-16*x)*exp(3)-2*x^5+6*x^4+26*x^2+32*x)/((x^4+4*x^3+6*x^2+4*x+1)*exp(3)^4+(4*x^5-40*x^3-80*x^2-60*x-16)*exp(3)^3+(6*x^6-24*x^5-60*x^4+124*x^3+398*x^2+340*x+96)*exp(3)^2+(4*x^7-32*x^6+24*x^5+248*x^4-76*x^3-872*x^2-864*x-256)*exp(3)+x^8-12*x^7+38*x^6+40*x^5-279*x^4-140*x^3+708*x^2+832*x+256),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {x^{2}}{x^{4} + 2 \, x^{3} e^{3} - 6 \, x^{3} + x^{2} e^{6} - 4 \, x^{2} e^{3} + x^{2} + 2 \, x e^{6} - 14 \, x e^{3} + 26 \, x + e^{6} - 8 \, e^{3} + 16} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Timed out} \]________________________________________________________________________________________