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Improper Integral problem

  1. Aug 7, 2013 #1
    1. The problem statement, all variables and given/known data

    1.Determine the divergence/convergence of the following improper integrals by the evaluation of the limit:

    [itex]\int_{0}^{∞} \frac{dx}{e^{-x} + e^{x}}[/itex]

    2. Relevant equations

    3. The attempt at a solution

    Let u = e^x
    ∴ du = e^x dx

    I ended up with:

    [itex]\int_{0}^{∞} \frac{u du}{u^{2} + 1}[/itex]
    I have no idea on how to integrate the above ...
  2. jcsd
  3. Aug 7, 2013 #2


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    substitute [itex]v=u^2[/itex].
  4. Aug 7, 2013 #3


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    Hi SirPlus! :smile:
    fine so far :wink:
    Sorry, but that's completely wrong (including the limits).

    Start again, and this time write it out carefully step-by-step, with no short-cuts! :smile:
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