Solving the integral of a Modified Bessel function of the second kind I would like to find the answer for the following integral 
$$\int x\ln(x)K_0(x) dx $$
where $K_0(x)$ is the modified Bessel function of the second kind and $\ln(x)$ is the natural-log. Do you have any ideas how to find?
Thanks in advance!

Here's what Mathematica found:

Looks like an integration by parts to me (combined with an identity for modified Bessel functions).
