Answer
$$3\sin x + 4\cos x + C$$
Work Step by Step
$$\eqalign{
& \int {\left( {3\cos x - 4\sin x} \right)} dx \cr
& {\text{use the sum rule for integration}} \cr
& = \int {3\cos x} dx - \int {4\sin x} dx \cr
& {\text{Factor out the constant}} \cr
& = 3\int {\cos x} dx - 4\int {\sin x} dx \cr
& {\text{ using the Basic Trigonometric integrals }}\int {\sin x} dx = - \cos x + C{\text{ and}} \cr
& \int {\cos x} dx = \sin x + C,{\text{ we obtain}} \cr
& = 3\left( {\sin x} \right) - 4\left( { - \cos x} \right) + C \cr
& = 3\sin x + 4\cos x + C \cr} $$
