The Most Stunning Solution to an Elegant MIT Integration Bee Problem
Автор: Calculus Diaries
Загружено: 2025-12-24
Просмотров: 447
In this video, we solve the following MIT Integration Bee 2022 Semi-Final problem: The integral from zero to infinity of x(e^(-x)+1)/(e^x-1) dx.
After multiplying the top and bottom by e^(-x), the denominator can be expressed as an infinite sum of n from 0 to infinity of e^(-nx) relying on a geometric series.
The solution to this integral is elegant, relying on the answer to the Basel problem. If you love tricky, but interesting integrals, this integral is for you.
If you enjoy beautiful integrals, contest-style problems, and clever calculus tricks, subscribe to Calculus Diaries for more.
#integralcalculus #integrationbee #integrationtechniques #integration #calculus #maths #integrals #integral
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