1. The problem statement, all variables and given/known data The problem is attached in this post. 2. Relevant equations The problem is attached in this post. 3. The attempt at a solution Lim t -> ∞ ∫ dx/xlnx from 1 to t u-substitution: u=lnx du=1/x dx Lim t -> ∞ ∫ 1/u du Lim t -> ∞ ln u Lim t -> ∞ ln(lnx) from 1 to t Lim t -> ∞ ln(lnt) - ln(0) = ∞ - ∞ = 0 (This is incorrect since the answer is that the integral is divergent).