Integration by parts (LIPET Or LIATE)

[Nope]

Homework Statement

Can anyone tell me which one is right (LIPET or LIATE)?
Also, in trig, which one come first? sin,cos or tan?
thx

Homework Equations

The Attempt at a Solution

 

[invisible_man]

i don't get it

 

[Nope]

see this http://en.wikipedia.org/wiki/Integration_by_parts

 

[HallsofIvy]

That site gives "LIATE" but I still have no idea what "LIPET" might be. In any case, it seems to me just silly to "order" functions like that.

\int udv= uv- \int v du

Since you are going to have to go from u to du, u should be a function that you can differentiate. Since you are going to have to go from dv to v, dv should be a function that you can integrate. And, after you have tried that, see it you can integrate \int v du.

 

[rl.bhat]

It is the order in which you have select the first term and the second term in the integration by parts, i.e. in udv, which should be u and which should be dv.
The order is Logarithmic or Inverse, Algebraic, Trigonometric and Exponential.

 

[hgfalling]

Oh, it's like a mnemonic hint on choosing u and dv. Log and inverse functions are hard to integrate but easy to differentiate, so they tend to be u. Exponentials are easy to integrate or differentiate, so they tend to be dv.

Of course you could just say to yourself, "Self! Which of these needs to be u and which dv?" in which case you will probably succeed just as often if you think about it.

 

[rl.bhat]

1.
Can anyone tell me which one is right (LIPET or LIATE)?
Also, in trig, which one come first? sin,cos or tan?
thx
]

Both are correct.
LIPET means Logarithmic, Inverse, Polynomial, Exponential and trigonometric.
LIATE means Logarithmic, Inverse, Algebraic , trigonometric and Exponential.
In the integration by parts , the first two terms usually won't come together. Either one can be taken as u in Intg(u*δv).
Any one of the last two terms can be u, because both are differentiable and integrable.

 

[Char. Limit]

Both are correct.
LIPET means Logarithmic, Inverse, Polynomial, Exponential and trigonometric.
LIATE means Logarithmic, Inverse, Algebraic , trigonometric and Exponential.
In the integration by parts , the first two terms usually won't come together. Either one can be taken as u in Intg(u*δv).
Any one of the last two terms can be u, because both are differentiable and integrable.

QFT that.

Logarthmic Functions are generally the best to derive, especially when paired with polynomials. Exponential and trigonometric functions tend to be bad to derive, as they have an infinite amount of derivatives... that mean something.