# Math Help - evaluating an integral

1. ## evaluating an integral

does anybody know how to evaluate this integral ?

thank you for you help

2. Originally Posted by PeaceSoul
does anybody know how to evaluate this integral ?

thank you for you help
Use the residue theorem! You will have two cases

Case 1:

if $p(b)=0$ then the residue at $b$ is given by

$\displaystyle \text{Res}(f,z=b)=\lim_{z \to b}(z-b)\frac{p(z)}{z-b}=0$

if $p(b)=a$ then the residue at $b$ is given by

$\displaystyle \text{Res}(f,z=b)=\lim_{z \to b}(z-b)\frac{p(z)}{z-b}=p(b)$

so by the residue theorem $\displaystyle \int_c \frac{p(z)}{z-b}dz=2\pi i \text{Res}(f,z=b)=2 \pi i p(b)$

3. thank you SO much