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2026 MIT Integration Bee: The Fastest and Cleanest Way to Solve This Improper Integral
This problem comes from the 2026 MIT Integration Bee Quarterfinals, Round 2, Problem 1. Instead of using a long partial-fractions decomposition, apply the standard beta-integral identity:integral from 0 to infinity of x^(a-1)/(1+x^b) is equal to (π/b)* csc(aπ/b ),where a is greater than zero but less than b. For the improper integral of 1/(x ...
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