I am trying to solve the following integral (eq. $(1)$) containing zero order Bessel function of the second kind but not getting it exactly.
$$P = \int_0^{y}K_0\left(\sqrt{\frac{x}{ab}}\right)\text{d}x \tag{1}$$
where $K_0(.)$ is zero order Bessel function of second kind, $a$ and $b$ are constants.
Any help in this regard will be highly appreciated.
Note: I am getting the answer using Mathematica. But I would like to solve it on my own.