# Complex integration

The Laplace transform of a function is \\ $C_{n}(s) =\displaystyle \frac{1}{s} \Biggl(\frac{s+2-\sqrt{(s+2)^2-a^2}}{a}\Biggl)^{|n|}$\\ I have to find the function. While doing the complex integration, I understand that s = 0 is a pole. It seems to me that -2 + a and -2 - a are branch points. I don't know how to choose the appropriate cut and solve the integral. I would also like to know if $|n|$ will affect the choice of the branch cuts.\\ Can you please suggest me a way as to solve the problem ?

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