Answer
$$\frac{{{{\sin }^2}ax}}{{2a}} + C$$
Work Step by Step
$$\eqalign{
& \int {\sin ax\cos ax} dx \cr
& {\text{substitute }}u = \sin ax,{\text{ }}du = a\cos axdx \cr
& = \int {\sin ax\cos ax} dx \cr
& = \frac{1}{a}\int u du \cr
& {\text{find the antiderivative by the power rule}} \cr
& = \frac{1}{a}\left( {\frac{{{u^2}}}{2}} \right) + C \cr
& = \frac{{{u^2}}}{{2a}} + C \cr
& {\text{write in terms of }}x,{\text{ replace }}u = \sin ax \cr
& = \frac{{{{\sin }^2}ax}}{{2a}} + C \cr} $$
