Problem 03
Find the Laplace transform of $f(t) = \dfrac{\sin^2 t}{t}$.
Solution 03
$f(t) = \dfrac{\sin^2 t}{t}$
$f(t) = \dfrac{\frac{1}{2}(1 - \cos 2t)}{t}$
$f(t) = \dfrac{1}{2} \left[ \dfrac{1}{t} - \dfrac{\cos 2t}{t} \right]$
$\mathcal{L} \left\{ f(t) \right\} = \dfrac{1}{2} \mathcal{L} \left[ \dfrac{1}{t} - \dfrac{\cos 2t}{t} \right]$
$\mathcal{L} \left\{ f(t) \right\} = \dfrac{1}{2} \mathcal{L} \left( \dfrac{1}{t} \right) - \dfrac{1}{2} \left( \dfrac{\cos 2t}{t} \right)$
Since
