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Is it true ?

  1. Mar 11, 2006 #1
    Is the integral (in the interval x=0, x=1) of 1/ (x^x) dx = 1+(1/(2^2)) + (1/ 3^3))+(1/(4^4) ).... ?

    If it is, how would one go about proving it...?
  2. jcsd
  3. Mar 11, 2006 #2
    It is true.

    The jist of the proof isto start by rewriting 1/(x^x) in terms of exponentionals, then rewriting that using the McLuarin series for e^x, then integrating term by term using parts.
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