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Advanced Integration-Tabular Method

  1. Jan 5, 2013 #1
    "Advanced" Integration-Tabular Method

    When cannot I not use this method?
    If the integral is cyclic is there a way to get around it?
    Any other information would be nice
    Thanks
     
  2. jcsd
  3. Jan 5, 2013 #2

    lurflurf

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    Homework Helper

    Re: "Advanced" Integration-Tabular Method

    Tabular integration is just a systematic way to integrate by parts multiple times. If the original integral reappears (without all other terms having canceled) you can stop and solve for it. A useful case is if p(x)f(x) where f is easy to integrate and p(x) is a polynomial so it will become zero after some number of differentiations.

    Usual examples include

    [tex]\int e^{-s t}\cos(a t) \text{ dt}[/tex]
    [tex]\int (x^2+3x+1)\sin(t) \text{ dt}[/tex]
    [tex]\int t^7 e^{-t} \text{ dt}[/tex]
     
  4. Jan 16, 2013 #3
    Re: "Advanced" Integration-Tabular Method

    Note that you should be careful when the original integral reappears. Try integrating 1/x using integration by parts, with u = 1/x and dv=dx
     
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