A general rule for which function to choose as u is given by the mnemonic LIATE:
Integration by parts - Wikipedia, the free encyclopedia
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
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!
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