\[ \int \frac {e^5 \left (-432 e x^2-64 e^2 x^6\right )+288 e^6 x^2 \log (2)-48 e^6 x^2 \log ^2(2)}{81-72 e x^4+16 e^2 x^8+\left (-108+48 e x^4\right ) \log (2)+\left (54-8 e x^4\right ) \log ^2(2)-12 \log ^3(2)+\log ^4(2)} \, dx \]
Optimal antiderivative \[ \frac {4 \,{\mathrm e}^{5}}{x -\frac {\left (\ln \left (2\right )-3\right )^{2} {\mathrm e}^{-1}}{4 x^{3}}} \]
command
integrate((-48*x^2*exp(1)*exp(5)*log(2)^2+288*x^2*exp(1)*exp(5)*log(2)+(-64*x^6*exp(1)^2-432*x^2*exp(1))*exp(5))/(log(2)^4-12*log(2)^3+(-8*x^4*exp(1)+54)*log(2)^2+(48*x^4*exp(1)-108)*log(2)+16*x^8*exp(1)^2-72*x^4*exp(1)+81),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {16 \, x^{3} e^{6}}{4 \, x^{4} e - \log \left (2\right )^{2} + 6 \, \log \left (2\right ) - 9} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Timed out} \]________________________________________________________________________________________