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Integration by parts

  1. Sep 22, 2010 #1
    We know the formula is [tex]\inline{\int udv=uv-\int vdu}[/tex] but when you say that for example, [tex]dv=e^x dx[/tex], then why when you integrate to get v, you don't include the integration constant?

    For this integral:
    [tex]\int xe^{x}dx[/tex]
    [tex]dv = e^x dx[/tex]
    [tex]v = e^x + C[/tex]?
     
    Last edited: Sep 23, 2010
  2. jcsd
  3. Sep 23, 2010 #2

    CompuChip

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    You can, in this case you would get
    [tex]\int x e^x \, \mathrm dx = (e^x + C) x + \int (e^x + C) \, \mathrm dx = x (e^x + C) - (e^x + C x + C')[/tex]
    If you expand
    [tex]x e^x + C x - (e^x - C x + C') = (x - 1) e^x - C'[/tex]
     
  4. Sep 23, 2010 #3
    oh, haha, I was only paying attention to one side of the equation. Thanks.
     
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