Do you know for what values of a converges?
I'm given an integral whose bounds are from e to infinity of dx/(x*(lnx)^a) and I have to find for which values of a it converges or diverges. How do you deal with the log in there? the only test I know is a comparison test but it didn't help when I tried it
http://orion.math.iastate.edu/vika/cal3_files/Lec22.pdf
That should help - look at the last page. Essentially, if a>1 the infinite series is convergent. So for a<a1 the infinite series is divergent. The proof is within the link I provided.
The question is a little controverisial... one way to 'attack' the problem is the following: let suppose to define the function as...
(1)
Now integrating by parts (1) You obtain...
(2)
... or equivalently...
(3)
Observing (3) You conclude that...
(4)
... so that may seem obvious that the integral converges for and diverges for ... therefore for someone [a little suprisingly!...] that's not obvious at all and that's a long story ...
Merry Christmas from Italy