Using the definition determine the Laplace transform of the function f(t) = e ^3t if it exists.

The Laplace transform of a function \( f(t) \) is given by the integral

\[
\mathcal{L} \{ f(t) \} = \int_{0}^{\infty} e^{-st} f(t) \, dt,
\]

where \( s \) is a complex variable, and \( f(t) \) is the given function. In this ______ _______ ________ __________ __________ __________ _________.
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