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## integral of a real function of a complex variable over complex plane [closed]

how can an integration like: $\int_\mathbb{C}f(|z|^2)dz$ be perfomerd? Function $f(|z|^2)$ is a kind of entropy function, resulted from circular symmetric complex gaussian probability density. The problem is that integrand is real, and can be analytical only in limited numbers of point in plane. I have only seen the result of this integration in a paper, and now have faced a similar one. Thanx for any help.

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 Polar coordinates? Probably more suited for stack exchange. – Igor Rivin Sep 11 at 12:29