Logarithm Tends to Infinity/Proof 2

Theorem
Let $x \in \R$ be a real number such that $x > 0$.

Let $\ln x$ be the natural logarithm of $x$.

Then:


 * $\ln x \to +\infty$ as $x \to +\infty$

Proof
From the definition of the natural logarithm:

The result follows from Integral of Reciprocal is Divergent.