Answer
$$2\ln \left| x \right| - 3\cos x + C$$
Work Step by Step
$$\eqalign{
& {\text{Evaluate }}\int {\left[ {\frac{2}{x} + 3\sin x} \right]} dx \cr
& {\text{Sum rule for integration}} \cr
& = \int {\frac{2}{x}} dx + \int {3\sin x} dx \cr
& = 2\int {\frac{1}{x}} dx + 3\int {\sin x} dx \cr
& {\text{Integration basic rules}} \cr
& = 2\ln \left| x \right| + 3\left( { - \cos x} \right) + C \cr
& {\text{simplify}} \cr
& = 2\ln \left| x \right| - 3\cos x + C \cr
& \cr
& {\text{Checking by differentiation}} \cr
& \frac{d}{{dx}}\left[ {2\ln \left| x \right| - 3\cos x + C} \right] \cr
& = 2\left( {\frac{1}{x}} \right) - 3\left( { - \sin x} \right) + 0 \cr
& = \frac{2}{x} + 3\sin x \cr} $$
