Great. I guess the integration wasn't as bad as I thought. Your algebra is a bit off because you wrote down a different u(x,y) than I had.
Using u(x,y)=e^{-y}(x\sin(x)+y\cos(x) I came up with
v(x,y) = e^{-y}(ysin(x)-xcos(x)).
Now my question is how to put this in terms of z only. I think...
Homework Statement
For u(x,y)=e^{-y}(x\sin(x)+y\cos(x)) find a harmonic conjugate v(x,y) and express the analytic function f=u +iv as a function of z alone (where z=x+iy0
Homework Equations
The Cauchy Riemann equations u_x=v_y and u_y=-v_x
and possibly:
sin(x) =...