same reason taking the square root of something is harder then squaring it. Reversing processes is often harder then the original process. Things get even harder for integrating when you move to multiple variables. I've always liked deriving a lot more then integration though recently I've begun liking integration more. Its much more of an art like logical proof or trig identities

Woo, Ultraviolet Voodoo! Oh, mnemonics... Also: Ruler, we learned integration in the second half of AB, but then didn't learn things like integration by parts till BC.  So maybe you're talking about college courses, but AP-wise, integration definitely does NOT necessarily mean you are in BC.  In fact, if you didn't learn to integrate at all, you'd be pretty much screwed on the AP test... =P

Ah yeah, stuff like that : http://cedprog.pagesperso-orange.fr/prepa/math/Chap_13.pdf
(french isn't really important, maths matter here ^^)

Also, I made a program some time ago, that smartly makes integration by parts steps by steps, for the nspire, in basic :
http://tiplanet.org/forum/archives_voir.php?id=4481  (french and english !)

Critor also made one with a GUI and also steps by steps, in Lua, but I can't find it hosted, mayeb it's not ready yet.