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Integration by parts (LIPET Or LIATE)

  1. Apr 14, 2010 #1
    1. The problem statement, all variables and given/known data
    Can anyone tell me which one is right (LIPET or LIATE)?
    Also, in trig, which one come first? sin,cos or tan?

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Apr 14, 2010 #2
    i don't get it
  4. Apr 14, 2010 #3
  5. Apr 15, 2010 #4


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    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.

    [tex]\int udv= uv- \int v du[/tex]

    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 [itex]\int v du[/itex].
  6. Apr 15, 2010 #5


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    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.
    Last edited: Apr 15, 2010
  7. Apr 15, 2010 #6
    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.
  8. Apr 15, 2010 #7


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    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.
  9. Apr 15, 2010 #8

    Char. Limit

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    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.
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