\[ \int \frac {65536+256 e^2-98304 x^4+65536 x^6-12288 x^8+e \left (-8192+2048 x^4\right )+e^2 \left (-16384 x+24576 x^3-12288 x^5+2048 x^7+e \left (1024 x-512 x^3\right )\right )}{e^6-24 e^4 x+192 e^2 x^2-512 x^3} \, dx \]
Optimal antiderivative \[ \frac {4 \left (\frac {{\mathrm e}}{4}-\left (-x^{2}+2\right )^{2}\right )^{2}}{\left (x -\frac {{\mathrm e}^{2}}{8}\right )^{2}} \]
command
integrate((((-512*x^3+1024*x)*exp(1)+2048*x^7-12288*x^5+24576*x^3-16384*x)*exp(2)+256*exp(1)^2+(2048*x^4-8192)*exp(1)-12288*x^8+65536*x^6-98304*x^4+65536)/(exp(2)^3-24*x*exp(2)^2+192*x^2*exp(2)-512*x^3),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ 4 \, x^{6} + x^{5} e^{2} + \frac {3}{16} \, x^{4} e^{4} - 32 \, x^{4} + \frac {1}{32} \, x^{3} e^{6} - 8 \, x^{3} e^{2} + \frac {5}{1024} \, x^{2} e^{8} - \frac {3}{2} \, x^{2} e^{4} - 2 \, x^{2} e + 96 \, x^{2} + \frac {3}{4096} \, x e^{10} - \frac {1}{4} \, x e^{6} - \frac {1}{2} \, x e^{3} + 24 \, x e^{2} + \frac {64 \, x e^{14} - 24576 \, x e^{10} - 65536 \, x e^{7} + 3145728 \, x e^{6} + 8388608 \, x e^{3} - 134217728 \, x e^{2} - 7 \, e^{16} + 2560 \, e^{12} + 6144 \, e^{9} - 294912 \, e^{8} - 524288 \, e^{5} + 8388608 \, e^{4} + 1048576 \, e^{2} - 33554432 \, e + 268435456}{65536 \, {\left (8 \, x - e^{2}\right )}^{2}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Timed out} \]________________________________________________________________________________________