\[ \int \frac {e^{\frac {3+e^{10} \left (-x^2-x^3\right )}{-e^{10} x^2+e^{10} x^2 \log \left (\frac {x}{5 \log (x)}\right )}} \left (3+e^{10} \left (-x^2-x^3\right )+\left (3+e^{10} \left (x^2+2 x^3\right )\right ) \log (x)+\left (-6-e^{10} x^3\right ) \log (x) \log \left (\frac {x}{5 \log (x)}\right )\right )}{e^{10} x^3 \log (x)-2 e^{10} x^3 \log (x) \log \left (\frac {x}{5 \log (x)}\right )+e^{10} x^3 \log (x) \log ^2\left (\frac {x}{5 \log (x)}\right )} \, dx \]
Optimal antiderivative \[ {\mathrm e}^{\frac {\frac {3 \,{\mathrm e}^{-10}}{x^{2}}-x -1}{\ln \left (\frac {x}{5 \ln \left (x \right )}\right )-1}} \]
command
integrate(((-x^3*exp(5)^2-6)*log(x)*log(1/5*x/log(x))+((2*x^3+x^2)*exp(5)^2+3)*log(x)+(-x^3-x^2)*exp(5)^2+3)*exp(((-x^3-x^2)*exp(5)^2+3)/(x^2*exp(5)^2*log(1/5*x/log(x))-x^2*exp(5)^2))/(x^3*exp(5)^2*log(x)*log(1/5*x/log(x))^2-2*x^3*exp(5)^2*log(x)*log(1/5*x/log(x))+x^3*exp(5)^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
\[ e^{\left (-\frac {x^{3} e^{10}}{x^{2} e^{10} \log \left (\frac {x}{5 \, \log \left (x\right )}\right ) - x^{2} e^{10}} - \frac {x^{2} e^{10}}{x^{2} e^{10} \log \left (\frac {x}{5 \, \log \left (x\right )}\right ) - x^{2} e^{10}} + \frac {3}{x^{2} e^{10} \log \left (\frac {x}{5 \, \log \left (x\right )}\right ) - x^{2} e^{10}}\right )} \]