Is this integration probelm right so far?

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The integration problem discussed involves evaluating the improper integral \(\int_{e}^{\infty} \frac{dx}{x \ln x}\), which simplifies to \(\ln|\ln x| + C\) evaluated from \(e\) to infinity. The conclusion reached is that the integral diverges. Participants confirmed the correctness of the steps taken in the evaluation process and clarified that the infinity symbol is represented as \(\infty\).

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\int_{e}^{infinity} \frac{dx}{x \ln x} = \int_{e}^{infinity} \frac{1}{x \ln x} dx = \int_{e}^{infinity} \frac{1}{\ln x} d \ln x = ln|lnx| + Cevaluated from e to infinity

I think I know what I need to do next, I just want to make sure I'm good up to this point. Also, how do you put in an infinity sign, and evaluate sign? Thanks!
 
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Infinity is just \infty. Dunno about the other.

Anyway, it looks correct to me.
 
Looks right. (And divergent:smile:)
 

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