Answer verifcation: $\int\sin(ax)\cos(ax)\,dx$ where "a" is a constant

Question

I was currently doing a trigonometric substitution, and I noticed my answer is not on Wolfram Alpha Answers. This is the integral which I had to solve:

$$\int\sin(ax)\cos(ax)\,dx \ \mathbf{\ \ \ \ a \ is \ constant}$$

My answer was: $\displaystyle{\frac{1}{a}\frac{\sin^2(ax)}2+C}$

Answer 1

Hint: notice that $$\sin^2(x)+\cos^2(x)=1$$ What's the difference of the $2$ primitive functions?