\[ \int \frac {32768-8192 x^2+1536 x^3-128 x^4-128 x^5+16 x^6-2 x^7+\frac {e^{25+\log ^2(2)} \left (2048-1536 x+384 x^2-64 x^3\right )}{1024}}{-16384 x^3-4096 x^4+3072 x^5+768 x^6-192 x^7-48 x^8+4 x^9+x^{10}+\frac {e^{50+2 \log ^2(2)} \left (-64 x^3+48 x^4-12 x^5+x^6\right )}{1048576}+\frac {e^{25+\log ^2(2)} \left (-2048 x^3+512 x^4+256 x^5-64 x^6-8 x^7+2 x^8\right )}{1024}} \, dx \]
Optimal antiderivative \[ \frac {\left (\frac {4-x}{x}+\frac {4}{4-x}\right )^{2}}{{\mathrm e}^{\left (\ln \left (2\right )-5\right )^{2}}+\left (4+x \right )^{2}} \]
command
integrate(((-64*x^3+384*x^2-1536*x+2048)*exp(log(2)^2-10*log(2)+25)-2*x^7+16*x^6-128*x^5-128*x^4+1536*x^3-8192*x^2+32768)/((x^6-12*x^5+48*x^4-64*x^3)*exp(log(2)^2-10*log(2)+25)^2+(2*x^8-8*x^7-64*x^6+256*x^5+512*x^4-2048*x^3)*exp(log(2)^2-10*log(2)+25)+x^10+4*x^9-48*x^8-192*x^7+768*x^6+3072*x^5-4096*x^4-16384*x^3),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {384 \, x e^{\left (2 \, \log \left (2\right )^{2} - 20 \, \log \left (2\right ) + 50\right )} + 24576 \, x e^{\left (\log \left (2\right )^{2} - 10 \, \log \left (2\right ) + 25\right )} + 589824 \, x + e^{\left (4 \, \log \left (2\right )^{2} - 40 \, \log \left (2\right ) + 100\right )} + 128 \, e^{\left (3 \, \log \left (2\right )^{2} - 30 \, \log \left (2\right ) + 75\right )} + 8704 \, e^{\left (2 \, \log \left (2\right )^{2} - 20 \, \log \left (2\right ) + 50\right )} + 258048 \, e^{\left (\log \left (2\right )^{2} - 10 \, \log \left (2\right ) + 25\right )} + 4718592}{{\left (x^{2} + 8 \, x + e^{\left (\log \left (2\right )^{2} - 10 \, \log \left (2\right ) + 25\right )} + 16\right )} {\left (e^{\left (4 \, \log \left (2\right )^{2} - 40 \, \log \left (2\right ) + 100\right )} + 160 \, e^{\left (3 \, \log \left (2\right )^{2} - 30 \, \log \left (2\right ) + 75\right )} + 8448 \, e^{\left (2 \, \log \left (2\right )^{2} - 20 \, \log \left (2\right ) + 50\right )} + 163840 \, e^{\left (\log \left (2\right )^{2} - 10 \, \log \left (2\right ) + 25\right )} + 1048576\right )}} - \frac {32 \, {\left (12 \, x^{3} e^{\left (2 \, \log \left (2\right )^{2} - 20 \, \log \left (2\right ) + 50\right )} + 768 \, x^{3} e^{\left (\log \left (2\right )^{2} - 10 \, \log \left (2\right ) + 25\right )} + 18432 \, x^{3} - x^{2} e^{\left (3 \, \log \left (2\right )^{2} - 30 \, \log \left (2\right ) + 75\right )} - 184 \, x^{2} e^{\left (2 \, \log \left (2\right )^{2} - 20 \, \log \left (2\right ) + 50\right )} - 9344 \, x^{2} e^{\left (\log \left (2\right )^{2} - 10 \, \log \left (2\right ) + 25\right )} - 180224 \, x^{2} + 4 \, x e^{\left (3 \, \log \left (2\right )^{2} - 30 \, \log \left (2\right ) + 75\right )} + 640 \, x e^{\left (2 \, \log \left (2\right )^{2} - 20 \, \log \left (2\right ) + 50\right )} + 32768 \, x e^{\left (\log \left (2\right )^{2} - 10 \, \log \left (2\right ) + 25\right )} + 524288 \, x - 8 \, e^{\left (3 \, \log \left (2\right )^{2} - 30 \, \log \left (2\right ) + 75\right )} - 1152 \, e^{\left (2 \, \log \left (2\right )^{2} - 20 \, \log \left (2\right ) + 50\right )} - 49152 \, e^{\left (\log \left (2\right )^{2} - 10 \, \log \left (2\right ) + 25\right )} - 524288\right )}}{{\left (x^{2} - 4 \, x\right )}^{2} {\left (e^{\left (4 \, \log \left (2\right )^{2} - 40 \, \log \left (2\right ) + 100\right )} + 160 \, e^{\left (3 \, \log \left (2\right )^{2} - 30 \, \log \left (2\right ) + 75\right )} + 8448 \, e^{\left (2 \, \log \left (2\right )^{2} - 20 \, \log \left (2\right ) + 50\right )} + 163840 \, e^{\left (\log \left (2\right )^{2} - 10 \, \log \left (2\right ) + 25\right )} + 1048576\right )}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Timed out} \]________________________________________________________________________________________