The general rule to evaluate is as follows:
- If m is even and positive, take out, use the identity to convert remaining sec to tan, and substitute
- If n is odd and positive, take out, use the identity to convert remaining tan to sec, and substitute
- If n is odd or even but there is no factor, use the identity and repeat the steps above
- If none of the cases apply, try converting to sine and cosine
Let’s see how it works starting with an example where m is even (click here):
Simply combine the solutions and substitute back .
Here’s another example where n is odd (click here):
One more example where n is odd with no factor of sec(x) (click here):
In the next post we’ll cover trigonometric substitution, stay tuned.