Evaluate advanced integral numerically in Cartesian coordinates

Hi

I have previously asked a question regarding how to evaluate a specific integral in MatLAB, see this thread: http://mathworks.com/matlabcentral/answers/43929-evaluate-advanced-integral-numerically#answer_53917

I need to evaluate a similar integral, however this time the numerator has changed a little. In the above thread the part that says sqrt(x^2 + y^2) has now changed to x.

I guess it is too difficult to transform to cylindrical symmetry this time. Can I use any other trick to solve this?

Thanks for any help in advance. I have recieved a lot of feedback from many talented people on this forum, and I would like to tell you all that I appreciate it very much.

Best wishes, Niles.

[Niles Martinsen]

The original integral I am refering to is here: http://www.scribd.com/doc/100400549/mwe

The part that says sqrt(x^2 + y^2) has now changed to x in this case.