Why 1/z dont have antiderivative?

[player1_1_1]

Homework Statement

why $$\frac{1}{z}$$ don't have derivative? i know that $$( \log z )'=\frac{1}{z}$$ so why $$\int \frac{1}{z} \mbox{d} z$$ don't exist?

Homework Equations

The Attempt at a Solution

 

[Hurkyl]

The answer lies in all of the details you haven't said -- things like the domain of the functions under consideration and such.

 

[michael.wes]

I just did this on an assignment, so I can answer this question :D

Note that we usually talk about log(z) as being the principal branch; then it is only defined on the cut-plane. It turns out that you cannot define a function such that f'(z)=1/z on the whole complex plane. In other words 1/z does not have a primitive on all of C.