tell if integral 1/(xlnx) from 0 to 1/e converge or diverge?

Question

anonymous · Answer

you can use a substitution here, let u=lnx, then it's derivative is a equivalent representation of what you have in the function already present.

anonymous · Answer

i would get ln(ln x) but that doesnt tell me if it converge or diverge

lgbasallote · Answer

substitute the limits then...if you get $\infty$ then it diverges...it converges if you get a "real" answer

anonymous · Answer

I see, I get it.

anonymous · Answer

it diverges, since my calc says domain error

lgbasallote · Answer

hmm

anonymous · Answer

just don't write that down on an exam *smiles*.

anonymous · Answer

lol. okay, but it does diverge rt?

anonymous · Answer

rather that the natural log of zero is undefined (which is what your calculator tells you indeed), undefined means that the limit doesn't exist, a bit far fetched in this context since we're dealing with an integral, but yes it diverges.