Answer
$$ - \frac{1}{2}\cos 2y + \frac{1}{3}\sin 3y + C$$
Work Step by Step
$$\eqalign{
& \int {\left( {\sin 2y + \cos 3y} \right)} dy \cr
& {\text{sum Rule}} \cr
& = \int {\sin 2y} dy + \int {\cos 3y} dy \cr
& {\text{use the formula for indefinite integrals of trigonometric functions}} \cr
& \int {\sin ax} dx = - \frac{1}{a}\cos ax + C,{\text{ }}\int {\cos axdx} = \frac{1}{a}sinax + C \cr
& = - \frac{1}{2}\cos 2y + \frac{1}{3}\sin 3y + C \cr
& {\text{check by differentiation}} \cr
& {\text{ = }}\frac{d}{{dx}}\left( { - \frac{1}{2}\cos 2y + \frac{1}{3}\sin 3y + C} \right) \cr
& = - \frac{1}{2}\left( { - 2\sin 2y} \right) + \frac{1}{3}\left( {3\cos 3y} \right) + 0 \cr
& = \sin 2y + \cos 3y \cr} $$
