1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    Science Advisor
    Homework Helper

    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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook