# Homework Help: Show convergence of integral

1. Oct 29, 2012

### rioo

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

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 $e^{kx}$ to the bottom and checking limits. The integrand does go to zero at $-\infty \mathrm{and\ } \infty$, but that doesn't guarantee convergence...

2. Oct 29, 2012

### LCKurtz

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.