∫ (ln(x)/(x*(1+ln(x))^2) dx

use u = 1+ln(x) as the substitution du/dx = 1/xdx = x du ∫ (ln(x)/(x*(1+ln(x))^2) dx = ∫ ((u-1)x/ x(u^2)) du = ∫ (u-1)/(u^2) du