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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