Question

Hi there,

In integration by parts, is the acronym LIPET (logarithmic, inverse trig, polynomial, exponential, trig) or LIATE (logarithmic, inverse trig, algebraic, trig, exponential)? I've seen both in textbooks, but as you can see one orders trig before exponential and the other reverses it.

I'm asking because I just had a practice problem where I used LIPET, but got it wrong because of my choosing of u and dv (it could have been avoided if I used LIATE). Or should I just forget the acronyms and just pick u and dv accordingly to what I feel is easiest to differentiate/integrate?

Tha

Answer 1

i have always used LIATE
but it is not constant it varies with functions so u have to choose accordingly

Answer 2

I don't really use those to be honest. I just think to myself, "Which function can I differentiate away?" or "Which one is harder to integrate?"

After a while it just becomes sort of obvious, for instance, \[\int\limits x^3e^xdx\] we know that we can differentiate away the x^3 until eventually we're left with e^x. \[\int\limits lnx \ dx\] Here we know we can differentiate lnx fairly easily and integrate 1, so we got that route.

Sure these are some easy little examples, but that's just the reasoning I use. It's usually better than just blindly following rules of LETTERSTUFFNOSENSE which sort of just cuts out all common sense.

Answer 3

Thanks.