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This integral might look tricky at first. But here’s the key idea: The numerator is the derivative of the denominator. That means we’re looking at a classic logarithmic pattern: ∫ f '(x) / f(x) dx = ln|f(x)| So with a simple substitution, the answer becomes: ln(e^(-x) 1) from 0 to ∞ = ln(2) A perfect example of recognizing structure over complexity. MIT Integration Bee 2020 Qualifying Exam Problem 2 #mit #math #mathematics #mathchallenge #mathtrick #animation #art #education #science #fyp #minds
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