$\mathcal{L} \left\{ f(at) \right\} = \dfrac{1}{a} F \left( \dfrac{s}{a} \right)$
$\mathcal{L} \left( \dfrac{\sin 3t}{t} \right) = 3\mathcal{L} \left( \dfrac{\sin 3t}{3t} \right)$, 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