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## Main Question or Discussion Point

So I've seen this type of integral solved. Specifically, if we have

∫e

What if A has no imaginary part, how would one go about doing such an integral?

∫e

^{-i(Ax2 + Bx)}dx then apparently you can perform this integral in the same way you would a gaussian integral, completing the square etc. I noticed on wikipedia it says doing this is valid when "A" has a positive imaginary part. I can see why that might be important, we would then have an overall decaying magnitude of the integrand, as opposed to purely oscillating.What if A has no imaginary part, how would one go about doing such an integral?