Here we will cover integrals of the form .

The general rule to evaluate is as follows:

- If n is odd, take sin(x) out, use the identity , and substitute
- If m is odd, take cos(x) out, use the identity , and substitute
- If both n and m are odd use either n or m
- If both n and m are even use one of the half angle identities:

Let’s see how it works, starting with an example where m is odd (click here):

From here simply apply the sum rule and substitute back.

Here’s another example where n is odd (click here):

One more example where both n and m are even (click here):

In the next post we will continue with integrals involving powers of tan and sec.

Cheers,

Michal