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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: $\lim _{n\to \infty }\int _{\frac {1}{n}}^{n}{\dfrac {{\frac {1}{2}}-\cos x}{x}}\ dx=\gamma$ — 79.118.168.91 (talk) 09:16, 12 January 2014 (UTC)[reply]