- #1
rioo
- 6
- 0
Homework Statement
Show that [itex]\int^{\infty}_{-\infty} \frac{e^{kx}}{1+e^{x}}dx[/itex] converges if [itex]0<k<1[/itex]
Homework Equations
None
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...