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- #1

$$

\int_{\gamma}\frac{dz}{z^2+1} = \int_{\gamma} = \frac{i}{2}\left[\int_{\gamma}\frac{1}{z+i}dz-\int_{\gamma}\frac{1}{z-i}dz\right]

$$

$\gamma(t) = 2e^{it}, \ \ \gamma'(t) = 2ie^{it}$

$$

\int_{\gamma}\frac{2ie^{it}}{2e^{it}+i}dz

$$

Now what can I do from here (just looking at the first integral)?