Answer
$2\sin \sqrt t + C$
Work Step by Step
$$\eqalign{
& \int {\frac{{\cos \sqrt t }}{{\sqrt t }}} dt,{\text{ }}u = \sqrt t \cr
& {\text{Let }}u = \sqrt t \to du = \frac{1}{{2\sqrt t }}dt,{\text{ 2}}du = \frac{1}{{\sqrt t }}dt \cr
& {\text{Applying the substitution}}{\text{, we obtain}} \cr
& \int {\frac{{\cos \sqrt t }}{{\sqrt t }}} dt = \int {\cos u\left( {2du} \right)} \cr
& = 2\int {\cos udu} \cr
& {\text{Integrate }} \cr
& = 2\sin u + C \cr
& {\text{Write in terms of }}t,{\text{ substitute }}u = \sqrt t \cr
& = 2\sin \sqrt t + C \cr} $$
