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I am trying to find the harmonic conjugate of

$u(x,y) = \dfrac{y}{(x^2 + y^2)}$

I have got $Ux = Vy = \dfrac{-2xy}{(x^2 + y^2)^2}$

And now I need to integrate Vy with respect to y to find V.

However this is a tough integral. In our tutorial our tutor gave some method for doing this by 'switching x with -y'...something along those lines. I didnt get time to take down what he was saying properly.

How am I supposed to get from Vy to V?

3 Answers 3