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.

Cheers,

Michal