100.194 Problem number 8257

\[ \int \frac {384+320 e^3+88 e^6+8 e^9-1000 e^{24} x^3+e^8 \left (-1760 x-920 e^3 x-120 e^6 x\right )+e^{16} \left (2400 x^2+600 e^3 x^2\right )}{-64-144 x-108 x^2-27 x^3+e^3 \left (-48-120 x-99 x^2-27 x^3\right )+e^6 \left (-12-33 x-30 x^2-9 x^3\right )+e^9 \left (-1-3 x-3 x^2-x^3\right )+e^{24} \left (125 x^3+375 x^4+375 x^5+125 x^6\right )+e^8 \left (240 x+600 x^2+495 x^3+135 x^4+e^6 \left (15 x+45 x^2+45 x^3+15 x^4\right )+e^3 \left (120 x+330 x^2+300 x^3+90 x^4\right )\right )+e^{16} \left (-300 x^2-825 x^3-750 x^4-225 x^5+e^3 \left (-75 x^2-225 x^3-225 x^4-75 x^5\right )\right )} \, dx \]

Optimal antiderivative \[ \frac {4}{\left (x -\frac {x}{4-5 x \,{\mathrm e}^{8}+{\mathrm e}^{3}}+1\right )^{2}} \]

command

integrate((-1000*x^3*exp(4)^6+(600*x^2*exp(3)+2400*x^2)*exp(4)^4+(-120*x*exp(3)^2-920*x*exp(3)-1760*x)*exp(4)^2+8*exp(3)^3+88*exp(3)^2+320*exp(3)+384)/((125*x^6+375*x^5+375*x^4+125*x^3)*exp(4)^6+((-75*x^5-225*x^4-225*x^3-75*x^2)*exp(3)-225*x^5-750*x^4-825*x^3-300*x^2)*exp(4)^4+((15*x^4+45*x^3+45*x^2+15*x)*exp(3)^2+(90*x^4+300*x^3+330*x^2+120*x)*exp(3)+135*x^4+495*x^3+600*x^2+240*x)*exp(4)^2+(-x^3-3*x^2-3*x-1)*exp(3)^3+(-9*x^3-30*x^2-33*x-12)*exp(3)^2+(-27*x^3-99*x^2-120*x-48)*exp(3)-27*x^3-108*x^2-144*x-64),x, algorithm="giac")

Giac 1.9.0-11 via sagemath 9.6 output

\[ \frac {4 \, {\left (25 \, x^{2} e^{16} - 10 \, x e^{11} - 40 \, x e^{8} + e^{6} + 8 \, e^{3} + 16\right )}}{{\left (5 \, x^{2} e^{8} + 5 \, x e^{8} - x e^{3} - 3 \, x - e^{3} - 4\right )}^{2}} \]

Giac 1.7.0 via sagemath 9.3 output

\[ \text {Timed out} \]________________________________________________________________________________________