Use integration by parts to prove the validity of the formula:

Then, use the pythagorean identity for trig functions (i.e., which implies ) to prove the formula:

* Proof. * First, to use integration by parts we define the following functions

Since we then apply integration by parts,

This was the first requested formula. Now, we use the identity to write

In the last line we used the trig identity . This establishes the formula requested

how you got integration of sin^2(x)=