# Contour Integration

#### Nusc

1. The problem statement, all variables and given/known data
Find the poles for the integrals:
$$\int_{c}ds e^{st} \frac{1}{(s + \kappa + \frac{g^{2}}{s+\gamma+\gamma_{n}})}$$

One pole is at $$-(\gamma+\gamma_{n})$$.

Is there another one?

Also
$$\int_{c}ds e^{st} \frac{1}{(s + \kappa + \frac{g^{2}}{s+\gamma+\gamma_{n}})} \frac{1}{s+\gamma+\gamma_{n}}$$
Similiarly, one pole is at $$-(\gamma+\gamma_{n})$$.

Is there another one? I just need to be sure.

Thanks

2. Relevant equations

3. The attempt at a solution

#### Dick

Homework Helper
Poles are the values of the integration variable s where the denominator vanishes, right? I don't think -(gamma+gamma_n) is a pole. In both cases, it looks to me like you are getting a relatively complicated quadratic in s.

#### Nusc

Can you tell me what technique of integration I should use to evaluate this integral?

$$\noindent$$\frac{e^{s t}}{g^2+(s+\text{yn}+\gamma ) (s+\kappa )}$$$$

#### Dick

Homework Helper
The ordinary residue theorem, I think. You can write that as e^(st)/((s-p1)(s-p2)) where p1 and p2 are the poles you get from solving the quadratic equation. It's straightforward in principle, but I don't know a simple way to write the nasty expressions you get from solving the quadratic. Where are you getting these problems??

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