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.