Aus Online Mathematik Brückenkurs 2

As the integral stands, it is not so easy to see what the primitive functions are, but if we use the formula for double angles,

\displaystyle \int{2\sin x\cos x}\,dx=\int{\sin 2x}\,dx

we obtain a standard integral where we can write down the primitive functions directly:

\displaystyle \int{\sin 2x}\,dx=-\frac{\cos 2x}{2}+C

where \displaystyle C is an arbitrary constant.