The answer is The Gaussian Integral...Want to know why?

The function in itself is a very ugly function to integrate, but when done across the entire real line, i.e. from minus infinity to infinity, it gives a bizarrely clean answer. It is certainly not obvious at first glance that the area under the curve is the square root of pi. This formula is of extreme importance in statistics, as it represents the normal distribution.
(Source: https://nargaque.com/2011/10/05/10-mind-blowing-mathematical-equations/)

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