\[ \int \frac {e^3 x^2-5 e^8 x^3+e^5 \left (-e^6+10 e^{11} x-25 e^{16} x^2\right )+\left (-e^3 x^2+e^5 \left (-e^6+10 e^{11} x-25 e^{16} x^2\right )\right ) \log (x)}{\left (-e^3 x^3+5 e^8 x^4+e^5 \left (e^6 x-10 e^{11} x^2+25 e^{16} x^3\right )\right ) \log (x)} \, dx \]
Optimal antiderivative \[ \ln \left (\frac {\frac {x}{5 x \,{\mathrm e}^{8}-{\mathrm e}^{3}}+\frac {{\mathrm e}^{5}}{x}}{\ln \left (x \right )}\right ) \]
command
integrate((((-25*x^2*exp(4)^4+10*x*exp(3)*exp(4)^2-exp(3)^2)*exp(5)-x^2*exp(3))*log(x)+(-25*x^2*exp(4)^4+10*x*exp(3)*exp(4)^2-exp(3)^2)*exp(5)-5*x^3*exp(4)^2+x^2*exp(3))/((25*x^3*exp(4)^4-10*x^2*exp(3)*exp(4)^2+x*exp(3)^2)*exp(5)+5*x^4*exp(4)^2-x^3*exp(3))/log(x),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \log \left (x^{2} + 5 \, x e^{13} - e^{8}\right ) - \log \left (5 \, x e^{5} - 1\right ) - \log \left (x\right ) - \log \left (\log \left (x\right )\right ) \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Timed out} \]________________________________________________________________________________________