Integrating Trigonometric Functions: How to Remember and Use Identities?

[athrun200]

Homework Statement

I have a problem in part b

Homework Equations

The Attempt at a Solution

How to integral the function?

 

[athrun200]

1. Homework Statement
I would like to ask for 18 and20

2. Homework Equations



3. The Attempt at a Solution
Again how to integral the function?

 

[gb7nash]

10a looks fine.

For 10b, take advantage of the following trig identity:

cosh² x = [1 + cosh (2x)]/2

 

[athrun200]

10a looks fine.

For 10b, take advantage of the following trig identity:

cosh² x = [1 + cosh (2x)]/2

Oh no, I know this identity, but there are too many identity and formula so I can't remember it before you tell me. How can I make sure that I remember all of them? Or where can I check these useful identity?

 

[gb7nash]

http://planetmath.org/encyclopedia/HyperbolicIdentities.html

As far as knowing which ones to remember, it would depend on what you're trying to do and what class you're in. For a lot of integral problems, the identities I usually see are sin² + cos² = 1 (and any other pythagorean identities), and half/double angle formulas.

 

[athrun200]

http://planetmath.org/encyclopedia/HyperbolicIdentities.html

As far as knowing which ones to remember, it would depend on what you're trying to do and what class you're in. For a lot of integral problems, the identities I usually see are sin² + cos² = 1 (and any other pythagorean identities), and half/double angle formulas.

Thanks so much.
Shall we move on #2?
I just have some problems.