Integral of Laplace Transform/Examples

Examples of Use of Integral of Laplace Transform

Let $\laptrans f$ denote the Laplace transform of the real function $f$.

Example $1$

Let $\sin$ denote the real sine function.

Let $\laptrans f$ denote the Laplace transform of a real function $f$.

Then:

$\laptrans {\dfrac {\sin t} t} = \arctan \dfrac 1 s$