Compute this integral.

I've tried using polar coordinates (it seems the obvious thing to do) but the domain pretty much messed everthing up. since D is the upper right square [0,1]X[0,1].

I got 2 possible boundaries to choose from:

1) 0<=R<=sqrt(2) , 0<=Theta<=sin(1/R)

2) 0<=R<=1/sin(Theta) , 0<=Theta<=pie/2

I couldn't integrate either of them.. your assistance is welcome :-)