Integral of Reciprocal is Divergent/Unbounded Above/Proof 2
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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.
$\blacksquare$