Integration by parts says

The first question students ask is **What do I make u and what do I make dv**? I used to tell my students to set

*u*equal to the part you’d rather differentiate and

*dv*equal to the part you’d rather integrate. That’s not bad advice, but it begs the question “How do I know what I want to differentiate and what I want to integrate?” Until you have some experience and intuition, that’s hard to answer.

Here’s a good rule of thumb: set *u* to the first term you see on this list:

- logarithm
- inverse trig function
- algebraic function
- trig function
- exponential

This rule doesn’t cover everything — no rule can — but it works remarkably well. I don’t remember just where I found this; I believe it was in an article somewhere. I’m fairly certain I’ve never seen it in a calculus textbook.

**Update**: I found the reference for the rule above. “A Technique for Integration by Parts” by Herbert E. Kasube. American Mathematical Monthly, March 1983, page 210.