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I'm trying to solve this integral for my complex analysis course however I can't seem to figure out how to get started on it. I think since there's exponentials in the function you want to maybe use a rectangular contour, and rewrite the hyperbolic function in terms of e as well but I'm really unsure.

Any help you guys can give would be great thanks!

$$\int_{-\infty}^{\infty}\frac{e^{x/3}}{\cosh(2x)} dx$$

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