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.