No, there is nothing "really obvious". That is, as you say, an ugly integral and it cannot be done in any simple way.
I've got another integral that I can't solve. =/ I know it looks really ugly but I'm certain it's correct.
If I've missed something really obvious I'd appreciate it if you gave me a hint and not the full solution. Thanks in advance.
Trigonometric substitution seems out the window because of the ln|x| in the denominator.
Doing it by parts doesn't seem to work.
Now looking only at this part of the second term...
etc. So the second integral doesn't look like it can be simplified into anything workable.
So the solution must concern normal u-substitution or some method of integration that I'm not familiar with. I was looking for another method of integration and I read about something called 'Integration by Using Parametric Differentiation', I didn't really understand the article so perhaps that's necessary here?