I'm trying to remember how to do integration by parts and I can't seem to figure out where LIATES comes into play. I know what it stands for but when do you use it? Does it help you pick what to use for u and what to pick for dv? Like you would pick x to be u instead of a trig function?
-
LIATES tells you what you should pick to be "u" - ie. what you should be differentiating. By extension, it also helps you pick "dv" because what isn't u must be dv. The reason the acronym is useful is that using it guarantees that what you're differentiating will be simpler than what you originally. For example, if you have
∫ arctan(x) dx.
By LIATES, you should pick u as arctan(x) (the I in LIATES is inverse trig functions). Differentiating arctan(x) gives 1/(1 + x^2) - which is something that actually makes sense. Then you would pick dv as dx and the integration is easy.
Done!
∫ arctan(x) dx.
By LIATES, you should pick u as arctan(x) (the I in LIATES is inverse trig functions). Differentiating arctan(x) gives 1/(1 + x^2) - which is something that actually makes sense. Then you would pick dv as dx and the integration is easy.
Done!