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For what values of M does this integral converge?

  1. Jan 18, 2010 #1
    For what values of M does this integral converge?

    [tex]\int_{-\infty}^{0}\frac{x.e^x}{(1-e^{2x})^M}dx[/tex]


    My pathetic attempt for solution ended here:

    [tex]\frac{2x.e^x}{2.(-1)^M(e^{2x}-1)^M}.x^{M-1}\stackrel{x\rightarrow0}{\longrightarrow}\frac{(-1)^M}{2}[/tex]

    [tex]M-1<1, M<2[/tex]

    Am I going in the right direction? And what to do if [tex]x\rightarrow\infty[/tex]?
     
  2. jcsd
  3. Jan 18, 2010 #2

    tiny-tim

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    Welcome to PF!

    Hi nonaa! Welcome to PF! :smile:

    No, you're misreading the question.

    It means for what values of M is the whole integral finite. :wink:
     
  4. Jan 18, 2010 #3
    Re: Convergence

    Hi, I'm here for almost a day but you people are so nice and helpful :) I'm glad I've found this forum :)

    And how to do this? I've never solved such type of problems before. Would you give me a little hint?
     
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