Try and be more precise with your notation. That's squares right? So first look at this thread:

http://www.mathhelpforum.com/math-he...xvariable.html

Then see if you can understand what I'm doing (lazy-style) with the following Mathematica code:

Code:

In[43]:=
u[x_, y_] = Log[x^2 + y^2];
v[x_, y_] = FullSimplify[
Integrate[D[u[x, y], x], y] -
Integrate[D[Integrate[D[u[x, y], x],
y], x] + D[u[x, y], y], x]]
FullSimplify[D[u[x, y], x] -
D[v[x, y], y]]
FullSimplify[D[v[x, y], x] +
D[u[x, y], y]]
Out[44]=
2*ArcTan[y/x]
Out[45]=
0
Out[46]=
0