Thread: 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

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

Integration by parts - Wikipedia, the free encyclopedia

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

Sorry one more thing.

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

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.

"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 .

Hello, anees7112!

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

Here's the rule that I was taught:

Let be the "hardest" part you can integrate.


Example: .

We can integrate and we can integrate
. . The harder one is

We have: .

Then: .

. . . . . . .


~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~


Same example: .


Watch what happens if you do it "the other way" . . .

You have: .



The new integral is worse than the original integral!

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 .

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.

- Hollywood