Hey all I got two convergence problems I am stuck on

1) Determine whether 1/(x((lnx)^2)) from 2 to infinity converges or diverges. I've thought about the integral test and the comparison test but I'm still stuck.

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2) Determine whether (-1)^(n-1)*(n/((n^2)+1)) from 1 to infinity converges or diverges and if it converges what's its limit. I tried direct comparison but that broke down at n=4 so I'm not sure what to do know.

Thanks for any help