deletions | additions       diff --git a/untitled.tex b/untitled.tex  index e636caf..29a927c 100644  --- a/untitled.tex  +++ b/untitled.tex 
...
By Theorem 4.23 (Cauchy's Theorem): if f is holomorphic in $\mathbb{C}\setminus\left\{-2\right\}$ and $C[0,3] ~\mathbb{C}\setminus\left\{-2\right\} C[-2,3]$   then   $$\int_{c[0,3]}\frac{dz}{z^2-2z-8}= \int_{c[-2,3]}\frac{dz}{z^2-2z-8} $$  Therefore,$$\int_{c[0,3]}\frac{dz}{z^2-2z-8=\frac{\pi Therefore,$$\int_{c[0,3]}\frac{dz}{z^2-2z-8}=\frac{-\pi  i}{3}$$