A Challenging Integration Problem

How would you prove this?

Recently, a high school student passed on this problem to me because his teacher had told him that he had been trying to find a solution to it for a few weeks but had no luck. As many of my regular readers may know, I love tackling problems that are not straightforward, so I was happy to take a look at this particular one.

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Keith McNulty

Expert and Author in Applied Mathematics, Data Science, Statistics. Also writes History, Science, Culture. Find me on Twitter or keithmcnulty.org