# Primitive function

I have a question. Does the function $$z/(z^2+1)$$ have primitive function in a) $$\mathbb{C} \backslash \{-i,i\}$$ b) $$\mathbb{C} \backslash [-i,i]$$

I tried with Cauchy theorem but I did not do it. Thanks in advance.

• Also an open interval is denoted with parentheses, not braces. – Ross Millikan Nov 12 '18 at 21:12
• @RossMillikan, I think the OP means the two-point set $\{-i,i\}$. – lhf Nov 12 '18 at 21:15
• @lhf: probably so, thanks – Ross Millikan Nov 12 '18 at 21:17
• It means without point $-i$ and without point $i$ in point a) – John1357 Nov 12 '18 at 21:18
• Hint: Use residues to calculate the contour integral along a big circle that goes around both poles. – Henning Makholm Nov 12 '18 at 21:20