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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!

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    $$\arctan\,u=\frac{\pi}{2}-\arctan\frac1{u}$$ might be useful...2011-10-27

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