calculus - $gamma_j(t)=(-1)^j+frac{1}{2}exp(it)$ for $j=1,2$ $int_{gamma_1}f(z) mathrm{d}z + int_{gamma_2}f(z) mathrm{d}z$ on $[0,2pi]$

$f(z)=\frac{1}{z+1}+\frac{1}{z-1}$

$\gamma_j:[0,2\pi]\rightarrow \mathbb{C} \ (j=1,2,3)$

$\gamma_j(t)=(-1)^j+\frac{1}{2}\exp(it)$ for $j=1,2$

$\gamma_3(t)=4\exp(it)$

I need to compute

$\int_{\gamma_1}f(z) \mathrm{d}z + \int_{\gamma_2}f(z) \mathrm{d}z$ and $\int_{\gamma_3}f(z) \mathrm{d}z$.

Are there any better ways to compute these than using

$$\int_{0}^{2\pi}f(\gamma(t))\gamma'(t) \mathrm{d}t$$?