One of the best algebra-teaching games I've seen is the "Four 4's" game, where students have to take 4 fours and construct every number from 1-100 using only those fours and algebraic operations:
44/44=1, 4/4+4/4=2, 4-(4/4)^4=3, etc.
This is a great way to get students to explore the power of algebra. It is open ended, requires creativity, and gets students to use a variety of algebraic operations.
Q:Is there anything similar for integration techniques?
By similar, I mean an easily-stated, open-ended task that requires students to be creative and gets them to use a variety of integration techniques.
I've thought of integration bee-type contests, but those aren't open ended.