I can't figure this one out: Integral from 0 to infinity of xarctanxdx/(1+x^2)^2
I know about lim(T--> Infinity) etc. etc., but I can't figure out the actual integral itself. It appears to be a d/dx arctanx = 1/1+x^2 situation, but I can't seem to get there. I can do it very long and slowly through Integration by parts..
1) u = x^2, du = 2x.
=1/2 (1/(1+u)^2)
and then integrate by parts, but it takes forever and seems wrong.
Any solutions?