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

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SUMMARY

The integral of ln(x)/(1+exp(x)) from 2 to ∞ converges. The discussion clarifies that ln(x) is indeed the natural logarithm function. A comparison test is applied, demonstrating that ln(x)/(1+exp(x)) is bounded above by x/exp(x). Since the integral of x/exp(x) converges, it follows that the original integral also converges.

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