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

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

$$\sum$$1/(ln(n)*np) (n=2 to ∞)

$$\sum$$1/(x*lnpx)

$$\int$$dx/(x*lnpx)
and there i simply said t=lnx dt=dx/x

$$\int$$dt/tp

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

Use the same substitution and write:

$$n^p = e^{p \ln n} = e^{pt}$$

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

$$\int$$dx/(ln(x)*xp)
t=ln(x)
n=et
dt=dx/x

$$\int$$dt/(t*et(p-1)
now for conveniance i say q=p-1

$$\int$$dt/(t*etq)

how do i continue this integration?