Let $q \in (0, 1)$ be a D5407: Positive real number such that
| (i) | $f : [0, \infty) \to [0, \infty)$ is an D4367: Unsigned real function |
| (ii) | \begin{equation} f(x) = q^x \end{equation} |
Then
| (1) | $f$ is an D6103: Improperly Riemann integrable real function on $[0, \infty)$ |
| (2) | \begin{equation} \int^{\infty}_0 q^t \, d t = - \log q \end{equation} |