Laplace transform of the function $$f(t)$$ is given by $$f\left( s \right) = L\left\{ {f\left( t \right)} \right\} = \int\limits_0^\infty {f\left( t \right){e^{ - st}}\,dt.} $$

Laplace transform of the function shown below is given by.

The Laplace transform of $${e^{i5t}}$$ where $$i = \sqrt { - 1} ,$$

Laplace transform of $$\cos \left( {\omega t} \right)$$ is

The Laplace Transform of $$f\left( t \right) = {e^{2t}}\sin \left( {5t} \right)\,u\left( t \right)$$ is