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Homework Help: Show convergence of integral

  1. Oct 29, 2012 #1
    1. The problem statement, all variables and given/known data
    Show that [itex]\int^{\infty}_{-\infty} \frac{e^{kx}}{1+e^{x}}dx[/itex] converges if [itex]0<k<1[/itex]

    2. Relevant equations

    3. The attempt at a solution
    Well if I can show that the integral is dominated by another that converges then I'm done, but I haven't been able to come up with one. I've tried manipulating the integrand (moving the [itex]e^{kx}[/itex] to the bottom and checking limits. The integrand does go to zero at [itex]-\infty \mathrm{and\ } \infty[/itex], but that doesn't guarantee convergence...
  2. jcsd
  3. Oct 29, 2012 #2


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    Science Advisor
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    Gold Member

    Look at the two cases ##\int_0^\infty## and ##\int_{-\infty}^0## separately and use different overestimates on the different intervals. If you can show they are both finite you are done.
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