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Integration By Parts

  1. Sep 19, 2007 #1

    danago

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    Gold Member

    Hi. When evaluating an integral such as:

    [tex]
    \int {x^4 e^x dx}
    [/tex]

    Is integrating by parts 4 times the best method, or is there a more efficient way?

    Thanks in advance,
    Dan.
     
  2. jcsd
  3. Sep 19, 2007 #2
    I think you are gonna have to do parts 4 times.
     
  4. Sep 19, 2007 #3

    rock.freak667

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    Homework Helper

    Well if the problem was a definite integral for example say:
    [itex]\int_{0}^{1} x^4e^x dx [/itex]

    you could easily make a reduction formula for easy calculations. But that is a different question altogether. As previously stated you would have to integrate by parts at 4 times
     
  5. Sep 19, 2007 #4

    danago

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    Gold Member

    Alright, thanks for the replies guys :smile:
     
  6. Sep 19, 2007 #5
    For an integration of that type you could use the tabular method. THis method can solve that integral in about 30 seconds or less. Tabular method only works for sin, cos, e^cx (c is constant) only.

    [​IMG]
    Following the picture you get:
    [tex]x^{4}e^{x}-4x^{3}e^{x}+12x^{2}e^{x}-24xe^{x}+24e^{x}[/tex]
     
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