I'm glad I'm not doing math anymore.

Mmm, Integlawls. Go CARCARUS! I had actually just got back from calc camp, the irony. We reviewed and took a mock AP test. I GOT A FRIGGING 3. GAAAH. I was 10 points from getting a 4. If only I did better on the free-response...

Anyways, Omcifer is right -- plugged the sucker into the graphing calculator and took the integral, then checked the numeric answer with some main screen arithmetic. But yes, long division is *far* quicker. In either case, you'll need to know Algebra 3-4? ln conversions (which I had to look up because I was a dumbass and took the class in the summer so I could get into pre-calc sophomore year).

Firemage -- if my notes are correct, there is a subtraction sign between csc and cot.

Scotudu --> ln|sinu| + c
Stanudu --> -ln|cosu| + c --> ln|secu| + c
Ssecudu --> ln|secu + tanu| + c
Scscudu --> ln|cscu - cotu| + c

I was told a good way to memorize the last two was to remember the derivatives of them.
For the first, secxtanx
For the second, -cscxcotx

Notice how the derivative of csc has a "-" sign. In the same fashion, the integral of csc will have one, too.

Remember, this is just a means to remember the rule -- it withholds no actual mathematic value.

EDIT:

This is probably a horrible place to ask this question, but does anyone know how to use calc for collision detection in programming? A friend of mine is working on the engine for an rpg we are programming from scratch. While the main screen will be tile-based, the battle screen will be a sidescroller, so there must be collision detection between all sorts of shapes (a circle for a meteor attack, a square for a character (with a circle for the head), etc.).

EDITEDIT:

Wait a sec you had a minus sign in front of the constant. Not having really taken alg 3-4, could that minus sign be put in between csc and cot? In which case, you would have been right.