Finding an Analyitic Function given Re(z)

[metgt4]

Homework Statement

Find a function f(z) that is analytic in a suitable part of the Argand diagram for which

Re(z) = sin(2x)/[cosh(2y)-cos(2x)]

The Attempt at a Solution

I've taken the derivative with respect to both x and y and am attempting to integrate them to find an imaginary part of the equation that will satisfy the Cauchy-Reimann relation (du/dx = dv/dy; du/dy = -dv/dx where u is Re(z) and v is Im(z)), but I et to an integral I am not sure how to solve. My work is attached in a scanned document.

Thanks for helping!
Andrew

 

[Dick]

Your expression for du/dy would be a lot easier to integrate dx if it were correct. Can you fix it?