Step in proof involving Euler-Mascheroni constant

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I was just looking at a proof that shows how the Euler-Mascheroni constant exists and is situated between 0 and 1 . However, I stumbled across a step in the proof that doesn't seem very obvious to me .

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Why is it that Hn>Integral from 1 to n+1 of 1/x dx ? Is it that obvious ?