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**1. Homework Statement**

The integral I want to solve is

$$ D(x) = \frac{-i}{8\pi^2}\int dr\,d\theta \frac{e^{-irx\cos\theta}}{\sqrt{r^2+m^2}}r^2\sin\theta$$

which I've reduced to

$$ D(x) = \frac{-i}{4\pi x}\int dr \frac{r\sin(rx)}{\sqrt{r^2+m^2}} $$

by integrating over ##\theta##. However, I don't know how to go about solving this bad boy.

**2. Homework Equations**

I'm honestly not sure; maybe residue theorem or Cauchy's integral formula?

**3. The Attempt at a Solution**

I've tried to find a Laurent expansion but to no avail. I've also tried Feynman's trick of differentiating under the integral sign, but it complicates things even more. From the research I've done, it seems that the square root in the denominator indicates a branch cut integral, but I haven't been able to find a source that explains how to do this sufficiently well. Any help would be appreciated, thanks.