1. The problem statement, all variables and given/known data Assume that u is harmonic everywhere in R^2, and let [tex]v(x,y)=\int_0^y u_x'(x,t)dt - \int_0^x u_y'(s,0)ds[/tex] show that f=u+iv is entire analytic. 2. Relevant equations Maybe Cauchy Riemann: [tex]u_x'=v_y'[/tex] and [tex]u_y'=-v_x'[/tex] 3. The attempt at a solution I have only tried to see what happens if I use the Cauchy Riemann equations, but I get stuck right away. I am not sure how to use the fact that u is harmonic either. Any hints would be very appreciated.