Laplace Transform by Direct Integration
To get the Laplace transform of the given function $f(t)$, multiply $f(t)$ by $e^{-st}$ and integrate with respect to $t$ from zero to infinity. In symbol,
$\displaystyle \mathcal{L} \left\{f(t)\right\} = \int_0^\infty e^{-st} f(t) \, dt$.
See examples below.
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