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**Skruven** let: $\displaystyle u(x,y) = \sin (x^2-y^2)\cosh (2xy)$

Is there a function $\displaystyle f(x+iy) = u(x,y) + iv(x,y)$ that is analytic in the complex plane.

If so determine all the functions f.

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So i know that if u(x,y) and v(x,y) are harmonic and satisfy the cauchy riemann equations f are analytic.

My standard method for this kind of problems is:

Find $\displaystyle {u}'_{x}$ then with CR(1):$\displaystyle {v}'_{y} = {u}'_{x}$ i integrate so i get v(x,y) = something + g(x).

Then with CR(2): $\displaystyle {u}'_{y} = -{v}'_{x}$ i get g(x).

But with my method it gets really messy! i cant solve the integration, so i wonder if theres another way to do this?

regards