What I dont understand is how he got from 2 to 3 and from 4 to 5. For three, I had this:
Where c is a place holder for cos 2x.
Check your calculation from step 2 to step 3, since by my reckoning
For the final step Wikipedia is certainly your friend:
List of trigonometric identities - Wikipedia, the free encyclopedia
You can use the half angle, double angle and triple angle identities to make the last two integrations in step 4 manageable.
Wow, I wrote down the problem wrong, I had sine and cosine switched. I copied the above straight from the book, so it's correct. I wrote it wrong in my note book. I swear, I need to postpone calculus until I get down basic reading and writing...