Absolute Radiance (all bindings, old nail) while doing an MIT Integration Bee qualifier problem

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Problem is #2 from the 2022 qualifiers. I had not seen this integral before attempting it - this was my 5th or 6th attempt at this challenge and each time I changed the integral I was solving. Possibly the stupidest challenge of all time. Yes I forgot the arctan identity, yes I rederived it on the spot cuz I am an idiot