\[ \int \frac {e^4 (-207360-810 x)+e^9 \left (17694720+138240 x+270 x^2\right )}{81+e^4 \left (-14155776-110592 x-216 x^2\right )+e^{15} \left (-201326592-2359296 x-9216 x^2-12 x^3\right )+e^{20} \left (4294967296+67108864 x+393216 x^2+1024 x^3+x^4\right )+e^8 \left (618475290624+9663676416 x+56623104 x^2+147456 x^3+144 x^4\right )+e^3 \left (e^2 (-27648-108 x)+e^6 \left (2415919104+28311552 x+110592 x^2+144 x^3\right )\right )+e^6 \left (e^4 \left (3538944+27648 x+54 x^2\right )+e^8 \left (-103079215104-1610612736 x-9437184 x^2-24576 x^3-24 x^4\right )\right )} \, dx \]
Optimal antiderivative \[ \frac {5}{\frac {4}{3}-\left (\frac {{\mathrm e}^{3}}{3}-\frac {{\mathrm e}^{-2}}{256+x}\right )^{2}} \]
command
integrate(((270*x^2+138240*x+17694720)*exp(1)^6*exp(3)+(-810*x-207360)*exp(1)^4)/((x^4+1024*x^3+393216*x^2+67108864*x+4294967296)*exp(1)^8*exp(3)^4+(-12*x^3-9216*x^2-2359296*x-201326592)*exp(1)^6*exp(3)^3+((-24*x^4-24576*x^3-9437184*x^2-1610612736*x-103079215104)*exp(1)^8+(54*x^2+27648*x+3538944)*exp(1)^4)*exp(3)^2+((144*x^3+110592*x^2+28311552*x+2415919104)*exp(1)^6+(-108*x-27648)*exp(1)^2)*exp(3)+(144*x^4+147456*x^3+56623104*x^2+9663676416*x+618475290624)*exp(1)^8+(-216*x^2-110592*x-14155776)*exp(1)^4+81),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ -\frac {135 \, {\left (2 \, x e^{5} + 512 \, e^{5} - 3\right )}}{{\left (x^{2} e^{10} - 12 \, x^{2} e^{4} + 512 \, x e^{10} - 6 \, x e^{5} - 6144 \, x e^{4} + 65536 \, e^{10} - 1536 \, e^{5} - 786432 \, e^{4} + 9\right )} {\left (e^{6} - 12\right )}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Timed out} \]________________________________________________________________________________________