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The Dirichlet Eta Function Solves This MIT Integral with a Hidden Series
A problem from the 2024 MIT Integration Bee — Semifinal Round 1, Problem 2 — hides a remarkably elegant structure. The key move is to rewrite 1/[1+exp(−x)] as a geometric series, then integrate term by term. This reveals a direct connection to the Dirichlet eta function at s=2, leading to the beautifully simple final answer:1−π^2/12 ...
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