Problem 02 | Change of Scale Property of Laplace Transform

$\mathcal{L} \left\{ f(at) \right\} = \dfrac{1}{a} F \left( \dfrac{s}{a} \right)$
 

$\mathcal{L} \left( \dfrac{\sin 3t}{t} \right) = 3\mathcal{L} \left( \dfrac{\sin 3t}{3t} \right)$,   thus,   $a = 3$

$\mathcal{L} \left( \dfrac{\sin 3t}{t} \right) = 3 \left[ \dfrac{1}{3} \arctan \left( \dfrac{1}{s/3} \right) \right]$

$\mathcal{L} \left( \dfrac{\sin 3t}{t} \right) = \arctan \left( \dfrac{3}{s} \right)$           answer