Answer
$$ - 4\cos x + 2\sin x + C$$
Work Step by Step
$$\eqalign{
& \int {\left[ {4\sin x + 2\cos x} \right]} dx \cr
& {\text{sum rule}} \cr
& \int {4\sin x} dx + \int {2\cos x} dx \cr
& = 4\int {\sin x} dx + 2\int {\cos x} dx \cr
& {\text{find antiderivatives}} \cr
& = 4\left( { - \cos x} \right) + 2\left( {\sin x} \right) + C \cr
& = - 4\cos x + 2\sin x + C \cr} $$
