- #1

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I am just doing this out of curiousity.

## Homework Statement

I want to integrate 1/sqrt(x)exp(ix) dx from minus infinity to infinity.

## Homework Equations

## The Attempt at a Solution

I had a couple of ideas one was to substitute x=u^2

but then you mess up the limits and you get minus imaginary infinity.

The other idea was to use Jordan's Lemma. But as far as I know 1/sqrt(x) doesn't have a residue so it can't be applied.

How do you solve this integral then?

thank you