1. 8.3
Trigonometric
Identities
(Part 2)

2. Objectives
Solve trigonometric integrals involving powers of secant and tangent.

3. (Look at guidelines at the bottom of page 500.)
Evaluating Integrals Involving Secant and Tangent:
(Look at guidelines at the bottom of page 500.)
If power of secant is even and positive:
Save one sec2 factor and convert remaining factors to tan.
Use
If power of tangent is odd and positive:
Save one secxtanx factor and convert remaining factors to sec.
If no sec factors and power of tan is even and positive:
Convert tan2 factor to sec2.
If of form where m is odd and positive, use integration by parts.
If all else fails, convert to sin and cos.

4. Example 4:
tan: power odd and positive (rule #2)

5. Example 5:
tan: power odd and positive (rule #1) Save sec2x and convert sec to tan.

6. Example 6:
No sec, tan is even and positive: rule #3
Convert to tan2 to sec2.

7. Example 7:
Rule #5!

8. Homework
8.3 (page 542)
#25 – 41 odd