Testwiki:Reference desk/Archives/Mathematics/2014 January 12

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January 12

Proof of Integral Expression for Euler's Gamma Constant

How would we prove this integral identity for Euler's γ constant: $\underset{n\to \mathrm{\infty }}{\lim }\underset{\frac{1}{n}}{\overset{n}{\int }}\frac{\frac{1}{2}-\cos x}{x}dx=\gamma$ — 79.118.168.91 (talk) 09:16, 12 January 2014 (UTC)