Convergence of $\int_3^{\infty} \frac{1}{(\ln(x))^2(x-\ln(x))}$ Does this integral converge?
$$\int_3^{\infty} \frac{1}{(\ln(x))^2(x-\ln(x))}$$
I've been trying to solve this for the past 2 hours...literally. I know the answer is fairly simple, but I just can't think of it

Hint: Try comparing it to $$\int_{3}^\infty \frac{1}{x(\ln(x))^2} dx.$$
Secondary Hint: $$\frac{1}{x-\ln (x)}\leq \frac{2}{x}.$$
