Integral of Laplace Transform/Examples/Example 1

Examples of Use of Integral of Laplace Transform
Let $\laptrans f$ denote the Laplace transform of the real function $f$.


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

Proof
From Limit of Sine of X over X:


 * $\displaystyle \lim_{x \mathop \to 0} \frac {\sin x} x = 1$

Hence: