Complex Exponentials to Solve the Laplace Transform of cos(at)

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Typically, solving for the Laplace Transform of the sin(at) and the cos(at) involves two rounds of integration by parts. That isn't fun. The way to make it fun and much simpler is to rephrase the cosine function as a function of complex exponents with Euler's Formula. Then, several properties of the Laplace Transform make the solution short and sweet.
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