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