I was wondering if I could get some pointers on how to at least start on this. In quantum mechanics we are using the WKB approximation, and we end up with a definite integral that looks like this:(adsbygoogle = window.adsbygoogle || []).push({});

∫(1 - a(cosh(x))^{-2})^{1/2}dx = ∫(1/cosh(x)) (1 - a(cosh(x))^{2})^{1/2}dx

where a is a positive constant. I've tried everything I can think of to no avail, the answer on wolfram isnt pretty but it seems like if I can figure out what process to use I could reach it eventually. I asked the professor and he suggested Leibnitz rule, but not sure how differentiation under the integral sign would help here.

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# A Difficult cosh integral using Leibniz rule?

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