Integrating expression by power reduction formula

Hi everyone! So, I have to integrate the expression:

sin^{2}(x/2) dx

in the book it says that it integrates to become:

1/2 - cosx / 2

In order to get there, the power reduction formula is used, I am just not sure how to use the formula when the initial expression is not sin^{2}x?

Thanks for reading :)

Re: Integrating expression by power reduction formula

The power-reducing formula,

sin^{2} u = (1 - cos 2u)/2,

can be used in cases other than u = x.

Here you need to replace u, in each instance, with x/2.

This results in the relevant formula to your case,

sin^{2} x/2 = (1 - cos 2(x/2))/2 or

sin^{2} x/2 = (1 - cos x)/2.

Hope this helps.

Re: Integrating expression by power reduction formula

Thank you so much for the help! I understand completely now, :)