How do i find the value of p for this integration?

using the integral, find the values of "p" so that the series converges

[tex]\sum[/tex]1/(ln(n)*n^p) (n=2 to ∞)

i had a similar question in which case i had
[tex]\sum[/tex]1/(x*ln^px)

[tex]\int[/tex]dx/(x*ln^px)
and there i simply said t=lnx dt=dx/x

[tex]\int[/tex]dt/t^p

and from there it was really simple, but in the case of this question i have been trying and trying and just cant get it

 

i tried that, but i got stuck, didnt think it was the right way to go, can you help me continue??
for integration n=x

[tex]\int[/tex]dx/(ln(x)*x^p)
t=ln(x)
n=e^t
dt=dx/x

[tex]\int[/tex]dt/(t*e^t(p-1)
now for conveniance i say q=p-1

[tex]\int[/tex]dt/(t*e^tq)

how do i continue this integration?