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Problem 11 IMC 2004 Macedonia

Source:

July 26, 2004
integrationlogarithmsinequalitiescalculusIMCcollege contests

Problem Statement

Prove that ∫01∫01dx dy1x+∣log⁡y∣−1≤1. \int^1_0 \int^1_0 \frac { dx \ dy }{ \frac 1x + |\log y| -1 } \leq 1 .
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