/sci/ - Science & Math

Hi,

I've noticed that I have problems with finding anti-derivatives many times more than I find tolerable, so.. are there any tricks one can use when "thinking in reverse"?
It frustates me that even something as easy as
<span class="math"> \int \cos^2 (\alpha) [/spoiler]
isn't easy enough to solve.

Does anyone see a way to simplify or rather rearrange the sequence <span class="math"> \sqrt {n+1} - \sqrt {n} [/spoiler] so you can calculate a limit for it?
While studying, I've noticed it's mostly a problem of not seeing the rearrangement possibilities, so I'd be grateful for any help. I'm sure it's really not complicated.

Does
<span class="math">\limits_{n \to \infty} (a-b)]
imply
<span class="math">\limits_{n \to \infty} a_n - \limits_{n \to infty} b_n[\math]?

If yes, a short pointer as to why it does would be nice, even though it possibly is trivial.
Many thanks in advance![/spoiler]</spoiler>