When integreating by parts, how to choose u and v'?

Hello, I never really understood how to choose the u and the v' when integrating by parts. I know if you choose the wrong one sometimes you end up in a loop.

For the question

Integrate ln x dx

It becomes : Integrate 1 * ln x dx

Now do I set u' as 1 or as ln x? And how do you decide which one is which?

Thank you :)

Re: When integreating by parts, how to choose u and v'?

A general rule for which function to choose as u is given by the mnemonic LIATE:

Integration by parts - Wikipedia, the free encyclopedia

Re: When integreating by parts, how to choose u and v'?

oh thank you , I have been guessing all this time.

1 Attachment(s)

Re: When integreating by parts, how to choose u and v'?

Sorry one more thing.

How come in this question they set u' as the exponential rather than the algebraic Attachment 26135

Re: When integreating by parts, how to choose u and v'?

We are given:

I was taught:

So I would choose:

giving:

It appears in the image you attached, that they are using the reverse of the variables I was taught.

Re: When integreating by parts, how to choose u and v'?

"Guessing" is not a bad method, as long as you **check**! In general, because you want to choose u that can be differentiated, dv that can be integrated, and then check to see if you can integrate .

Re: When integreating by parts, how to choose u and v'?

Re: When integreating by parts, how to choose u and v'?

Thank you all for the help :) I probably should have asked this question a few years ago when we learnt integration by parts but it feels good to finally get it .

Re: When integreating by parts, how to choose u and v'?

I have always just "guessed", or more accurately, set u and dv to what seemed easy to differentiate and integrate. It wasn't until I actually taught Calculus that I learned about the LIATE acronym. One of my students told me about it.

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