For what values of p does the integral ∫(2 to [infinity]) dx / (x(ln x)p) converge, and for which does it diverge? Justify your answer, giving the value of the integral (in terms of p) in the convergent cases.

a) Converges for p < 1, diverges for p ≥ 1, integral value is 1/(p-1)
b) Converges for p > 1, diverges for p ≤ 1, integral value is 1/(1-p)
c) Converges for p ≤ 1, diverges for p > 1, integral value is 1/(p-1)
d) Converges for p ≥ 1, diverges for p < 1, integral value is 1/(1-p)