Does the integral of ln(x)/(1+exp(x)) from 2 to ∞ converge or diverge?

[hoho2666]

determine whether the integral In(x)/(1+exp(x)) from 2 to ∞? converges or diverges?

 

[nicksauce]

What is this function In(x)? Do you mean ln(x)? Assuming so, I think you can do a simple comparison test:

0 < ln(x) / (1+exp(x)) < x / (1+exp(x)) < x / exp(x)

And it's fairly easy to show the integral of x/exp(x) converges.