Integral of Reciprocal is Divergent/Unbounded Above/Proof 2

Theorem

$\ds \int_1^n \frac {\d x} x \to +\infty$ as $n \to + \infty$

Proof

From the definition of natural logarithm:

$\ds \ln x = \int_1^x \dfrac 1 t \rd t$

The result follows from Logarithm Tends to Infinity.

$\blacksquare$