# Improper Integral problem

1. Aug 7, 2013

### SirPlus

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:

$\int_{0}^{∞} \frac{dx}{e^{-x} + e^{x}}$

2. Relevant equations

3. The attempt at a solution

Let u = e^x
∴ du = e^x dx

I ended up with:

$\int_{0}^{∞} \frac{u du}{u^{2} + 1}$
I have no idea on how to integrate the above ...

2. Aug 7, 2013

### vanhees71

substitute $v=u^2$.

3. Aug 7, 2013

### tiny-tim

Hi SirPlus!
fine so far
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!