Solution assignment 10 Integration by parts

In assignment 3 it was asked to calculate the following integral and we applied integration by parts. Is there another way and if so, which?

$\displaystyle\int{\sin^2(x)}dx$

An important formula from trigonometry is:

$\cos(2x)=1-2\sin^2(x)$

Or, written differently:

$\sin^2(x)=\displaystyle\frac{1}{2}(1-\cos(2x))$

This integral can be calculated using standard functions and substitution:

$\displaystyle\int{\sin^2(x)}dx=$

$=\displaystyle\frac{1}{2}\displaystyle\int{(1-\cos(2x))}dx=$

$=\displaystyle\frac{1}{2}(x-\displaystyle\frac{1}{2}\sin(2x))+C$