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Integration by parts, which to set as v and du/dx?

Does anyone know of any kind of system to choose what to set as v and du/dx when doing integration by parts. Like if you have a trig in it, i think its usually best to set it as the du/dx because its easier to integrate. Same goes for exponential i think. If anyone knows of any kind of order of hierarchy to set what as v and du/dx, id like to know, thanks :smile:
Original post by 4RealBlud
Does anyone know of any kind of system to choose what to set as v and du/dx when doing integration by parts. Like if you have a trig in it, i think its usually best to set it as the du/dx because its easier to integrate. Same goes for exponential i think. If anyone knows of any kind of order of hierarchy to set what as v and du/dx, id like to know, thanks :smile:


It is often the case that you are only able to integrate one of the parts so that is what you choose to be du/dx. If one part is a simple linear function then choose that to be v because differentiation will reduce the power of x.
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Avatar for Gome44
Gome44
10
Original post by 4RealBlud
Does anyone know of any kind of system to choose what to set as v and du/dx when doing integration by parts. Like if you have a trig in it, i think its usually best to set it as the du/dx because its easier to integrate. Same goes for exponential i think. If anyone knows of any kind of order of hierarchy to set what as v and du/dx, id like to know, thanks :smile:


This is the LIATE rule from Wikipedia, and is in order of which part of the integral should be set as u (in most cases)

Logarithmic functions, eg ln(x)
Inverse trig functions, eg arcsin(x)
Algebraic functions, eg x^2
Trig functions, eg tan(x)
Exponential functions, eg e^x
(edited 9 years ago)
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4RealBlud
OP
19
Original post by Gome44
This is the LIATE rule from Wikipedia, and is in order of which part of the integral should be set as u (in most cases)

Logarithmic functions, eg ln(x)
Inverse trig functions, eg arcsin(x)
Algebraic functions, eg x^2
Trig functions, eg tan(x)
Exponential function, eg e^x


This is what i was looking for, thanks a lot! :smile:
Actually there is no need to memorize the LIATE rule; I have never used it once since my days as a student. It is very much about smartly prioritizing what should be integrated (and differentiated) by making sensible deductions.

I wrote this on my site a while back to illustrate my point, which you may wish to refer to.

Hope it helps. Peace.

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