\[ \int \frac {e^8 \left (144 x^2-96 x^3+84 x^4-27 x^6\right )+e^{12} \left (64-96 x+192 x^2-152 x^3+144 x^4-54 x^5+27 x^6\right )}{-135 x^6+e^8 \left (-720 x^2+720 x^3-1260 x^4+540 x^5-405 x^6\right )+e^{12} \left (320-480 x+960 x^2-760 x^3+720 x^4-270 x^5+135 x^6\right )+e^4 \left (540 x^4-270 x^5+405 x^6\right )} \, dx \]
Optimal antiderivative \[ \frac {x}{5 \left (\frac {x \,{\mathrm e}^{-4}}{x +\frac {4}{3 x}-\frac {2}{3}}-1\right )^{2}} \]
command
integrate(((27*x^6-54*x^5+144*x^4-152*x^3+192*x^2-96*x+64)*exp(4)^3+(-27*x^6+84*x^4-96*x^3+144*x^2)*exp(4)^2)/((135*x^6-270*x^5+720*x^4-760*x^3+960*x^2-480*x+320)*exp(4)^3+(-405*x^6+540*x^5-1260*x^4+720*x^3-720*x^2)*exp(4)^2+(405*x^6-270*x^5+540*x^4)*exp(4)-135*x^6),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {x e^{12} - x e^{8}}{5 \, {\left (e^{12} - 3 \, e^{8} + 3 \, e^{4} - 1\right )}} - \frac {4 \, {\left (12 \, x^{3} e^{16} - 33 \, x^{3} e^{12} + 21 \, x^{3} e^{8} + 4 \, x^{2} e^{16} + 12 \, x^{2} e^{12} - 12 \, x^{2} e^{8} + 8 \, x e^{16} - 36 \, x e^{12} + 12 \, x e^{8} + 16 \, e^{16}\right )}}{15 \, {\left (3 \, x^{2} e^{4} - 3 \, x^{2} - 2 \, x e^{4} + 4 \, e^{4}\right )}^{2} {\left (e^{12} - 3 \, e^{8} + 3 \, e^{4} - 1\right )}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Timed out} \]________________________________________________________________________________________