(adsbygoogle = window.adsbygoogle || []).push({}); 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

None

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...

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# Homework Help: Show convergence of integral

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