I know it is equal to infinity, and that it diverges. But how do I prove it?
∫[0,1] dx / x = lim[a->0⁺] ∫[a,1] dx / x = lim[a->0⁺] ln(x)|a,1] = lim[a->0⁺] (ln(1) - ln(a)) =
-lim[a->0⁺] ln(a) = -(-∞) = ∞
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∫[0,1] dx / x = lim[a->0⁺] ∫[a,1] dx / x = lim[a->0⁺] ln(x)|a,1] = lim[a->0⁺] (ln(1) - ln(a)) =
-lim[a->0⁺] ln(a) = -(-∞) = ∞