\[ \int \frac {e^{-3+\frac {8 e x^2+e^2 \left (4 x^2+e \left (-2 x+4 x^2\right )\right )-8 e^3 \log (\log (x))}{e^3 x}} \left (-8 e^3+\left (8 e x^2+e^2 \left (4 x^2+4 e x^2\right )\right ) \log (x)+8 e^3 \log (x) \log (\log (x))\right )}{x^2 \log (x)} \, dx \]
Optimal antiderivative \[ {\mathrm e}^{8 x \,{\mathrm e}^{-2}+4 x -\frac {8 \ln \left (\ln \left (x \right )\right )}{x}+4 \,{\mathrm e}^{-1} x -2} \]
command
integrate((8*exp(1)*exp(2)*log(x)*log(log(x))+((4*x^2*exp(1)+4*x^2)*exp(2)+8*x^2*exp(1))*log(x)-8*exp(1)*exp(2))*exp((-8*exp(1)*exp(2)*log(log(x))+((4*x^2-2*x)*exp(1)+4*x^2)*exp(2)+8*x^2*exp(1))/x/exp(1)/exp(2))/x^2/exp(1)/exp(2)/log(x),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \text {could not integrate} \]
Giac 1.7.0 via sagemath 9.3 output
\[ e^{\left (4 \, x e^{\left (-1\right )} + 8 \, x e^{\left (-2\right )} + 4 \, x - \frac {8 \, \log \left (\log \left (x\right )\right )}{x} - 2\right )} \]