Why do you use LIATES in integration by parts
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Why do you use LIATES in integration by parts

[From: ] [author: ] [Date: 11-05-02] [Hit: ]
Then you would pick dv as dx and the integration is easy.Done!......
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?

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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!
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