\[ \int \frac {-64-768 x^2+256 x^3+x^5+20 x^7-5 x^8+160 x^9-80 x^{10}+650 x^{11}-480 x^{12}+1400 x^{13}-1290 x^{14}+1504 x^{15}-1360 x^{16}+645 x^{17}-160 x^{18}+20 x^{19}-x^{20}+e^8 \left (160 x^9-80 x^{10}+1930 x^{11}-1440 x^{12}+8040 x^{13}-7710 x^{14}+13120 x^{15}-13280 x^{16}+6430 x^{17}-1600 x^{18}+200 x^{19}-10 x^{20}\right )+e^{16} \left (1280 x^{13}-1280 x^{14}+5600 x^{15}-6480 x^{16}+3205 x^{17}-800 x^{18}+100 x^{19}-5 x^{20}\right )+e^{20} \left (-1024 x^{15}+1280 x^{16}-640 x^{17}+160 x^{18}-20 x^{19}+x^{20}\right )+e^4 \left (768 x^2-256 x^3-20 x^7+5 x^8-320 x^9+160 x^{10}-1940 x^{11}+1440 x^{12}-5480 x^{13}+5150 x^{14}-7040 x^{15}+6720 x^{16}-3220 x^{17}+800 x^{18}-100 x^{19}+5 x^{20}\right )+e^{12} \left (-640 x^{11}+480 x^{12}-5240 x^{13}+5130 x^{14}-12160 x^{15}+13120 x^{16}-6420 x^{17}+1600 x^{18}-200 x^{19}+10 x^{20}\right )}{x^5+20 x^7-5 x^8+160 x^9-80 x^{10}+650 x^{11}-480 x^{12}+1400 x^{13}-1290 x^{14}+1504 x^{15}-1360 x^{16}+645 x^{17}-160 x^{18}+20 x^{19}-x^{20}+e^8 \left (160 x^9-80 x^{10}+1930 x^{11}-1440 x^{12}+8040 x^{13}-7710 x^{14}+13120 x^{15}-13280 x^{16}+6430 x^{17}-1600 x^{18}+200 x^{19}-10 x^{20}\right )+e^{16} \left (1280 x^{13}-1280 x^{14}+5600 x^{15}-6480 x^{16}+3205 x^{17}-800 x^{18}+100 x^{19}-5 x^{20}\right )+e^{20} \left (-1024 x^{15}+1280 x^{16}-640 x^{17}+160 x^{18}-20 x^{19}+x^{20}\right )+e^4 \left (-20 x^7+5 x^8-320 x^9+160 x^{10}-1940 x^{11}+1440 x^{12}-5480 x^{13}+5150 x^{14}-7040 x^{15}+6720 x^{16}-3220 x^{17}+800 x^{18}-100 x^{19}+5 x^{20}\right )+e^{12} \left (-640 x^{11}+480 x^{12}-5240 x^{13}+5130 x^{14}-12160 x^{15}+13120 x^{16}-6420 x^{17}+1600 x^{18}-200 x^{19}+10 x^{20}\right )} \, dx \]
Optimal antiderivative \[ \frac {16}{\left (\left (-4+x \right ) \left (x \,{\mathrm e}^{4}-x \right ) x^{2}+x \right )^{4}}+x \]
command
integrate(((x^20-20*x^19+160*x^18-640*x^17+1280*x^16-1024*x^15)*exp(4)^5+(-5*x^20+100*x^19-800*x^18+3205*x^17-6480*x^16+5600*x^15-1280*x^14+1280*x^13)*exp(4)^4+(10*x^20-200*x^19+1600*x^18-6420*x^17+13120*x^16-12160*x^15+5130*x^14-5240*x^13+480*x^12-640*x^11)*exp(4)^3+(-10*x^20+200*x^19-1600*x^18+6430*x^17-13280*x^16+13120*x^15-7710*x^14+8040*x^13-1440*x^12+1930*x^11-80*x^10+160*x^9)*exp(4)^2+(5*x^20-100*x^19+800*x^18-3220*x^17+6720*x^16-7040*x^15+5150*x^14-5480*x^13+1440*x^12-1940*x^11+160*x^10-320*x^9+5*x^8-20*x^7-256*x^3+768*x^2)*exp(4)-x^20+20*x^19-160*x^18+645*x^17-1360*x^16+1504*x^15-1290*x^14+1400*x^13-480*x^12+650*x^11-80*x^10+160*x^9-5*x^8+20*x^7+x^5+256*x^3-768*x^2-64)/((x^20-20*x^19+160*x^18-640*x^17+1280*x^16-1024*x^15)*exp(4)^5+(-5*x^20+100*x^19-800*x^18+3205*x^17-6480*x^16+5600*x^15-1280*x^14+1280*x^13)*exp(4)^4+(10*x^20-200*x^19+1600*x^18-6420*x^17+13120*x^16-12160*x^15+5130*x^14-5240*x^13+480*x^12-640*x^11)*exp(4)^3+(-10*x^20+200*x^19-1600*x^18+6430*x^17-13280*x^16+13120*x^15-7710*x^14+8040*x^13-1440*x^12+1930*x^11-80*x^10+160*x^9)*exp(4)^2+(5*x^20-100*x^19+800*x^18-3220*x^17+6720*x^16-7040*x^15+5150*x^14-5480*x^13+1440*x^12-1940*x^11+160*x^10-320*x^9+5*x^8-20*x^7)*exp(4)-x^20+20*x^19-160*x^18+645*x^17-1360*x^16+1504*x^15-1290*x^14+1400*x^13-480*x^12+650*x^11-80*x^10+160*x^9-5*x^8+20*x^7+x^5),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {x e^{20} - 5 \, x e^{16} + 10 \, x e^{12} - 10 \, x e^{8} + 5 \, x e^{4} - x}{e^{20} - 5 \, e^{16} + 10 \, e^{12} - 10 \, e^{8} + 5 \, e^{4} - 1} + \frac {16}{{\left (x^{4} e^{4} - x^{4} - 4 \, x^{3} e^{4} + 4 \, x^{3} + x\right )}^{4}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Timed out} \]________________________________________________________________________________________