I'm going to show this:
$$\lim_{x\rightarrow ∞}\,\,\,\int_0^x \! \frac{\arctan{t}}{t} \, \mathrm{d} t = ∞$$
We're working on L.Hopital and integrals... I guess it's very easy. But I struggle... Don't need to solve it for me if you give just give me guidelines. Thank you so much!