Why does Int_0toInf (1/x) Diverge whereas Int_0toInf (1/x^2) Converges?

it is hard to visualize a definition of convergence at infinity...in some sense it depends upon the rapidity that the function value approaches 0..1/x not fast enough but 1/x² is fast enough....BUT 1/ [x ln x] is also not fast enough but is certainly faster than 1 / x while 1 / x^(1 + δ) for δ > 0 is fast enough even though its rate is so close to that of 1 /x...that is int of 1/ x^(1+δ) over [1,∞) is finite even if δ = 10 ^-3000