\[ \int \frac {100 x \log (x)+100 x \log ^2(x)+\left (2 x^4+2 e^x x^4\right ) \log ^4(x)}{625+\left (250 x^2-50 e^x x^2-50 x^3\right ) \log ^2(x)+\left (25 x^4+e^{2 x} x^4-10 x^5+x^6+e^x \left (-10 x^4+2 x^5\right )\right ) \log ^4(x)} \, dx \]
Optimal antiderivative \[ \frac {2}{5+\frac {25}{x^{2} \ln \left (x \right )^{2}}-{\mathrm e}^{x}-x} \]
command
integrate(((2*exp(x)*x^4+2*x^4)*log(x)^4+100*x*log(x)^2+100*x*log(x))/((exp(x)^2*x^4+(2*x^5-10*x^4)*exp(x)+x^6-10*x^5+25*x^4)*log(x)^4+(-50*exp(x)*x^2-50*x^3+250*x^2)*log(x)^2+625),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \text {output too large to display} \]
Giac 1.7.0 via sagemath 9.3 output \[ \text {Timed out} \]_______________________________________________________