I am trying to solve the following integral, which may be thought of as an integral of an exponentially-decaying distance from a point $r$ on the $x$-axis to a circumference of a circle of radius $s$.
$\int_0^{2\pi} \exp\left(-\delta\sqrt{r^2-2\cos(\phi)rs+s^2}\right)\,d\phi$
Does this even have a closed form?