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Integration with factorials

  1. Jan 14, 2009 #1
    1. The problem statement, all variables and given/known data
    Show that the definite integral from 0 to 1 (ln x)^n dx = n!(-1)^n

    2. Relevant equations

    3. The attempt at a solution
    i tried to integrate by parts and kept going on and on but i dont know how to incorporate the factorial in the answer ...
  2. jcsd
  3. Jan 14, 2009 #2


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    Homework Helper

    When you integrated by parts, what did you get?
  4. Jan 15, 2009 #3

    Gib Z

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    Rather than integrating by parts repeatedly, it may be simpler to try to use induction to show this result. You only need to integrate by parts once if you do that, so it may be easier for you to see your answer.
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