I'm asked to determine if the following integral converges or diverges.
$$\int_{0}^{\infty} \frac{\ln(x)}{x^2+x+1} dx $$.
I know I have to use the comparison test for improper integrals (since there is no elementary anti derivative), but I'm not sure what to use as my comparison.
INTUITIVELY, it seems that the function will converge since the denominator grows very fast, but what can I use for my comparison test here? I need a function that's larger than the integrand in order to determine convergence or divergence of this integral.
Can someone suggest what kind of function I can pick as my comparison?