Let $x$ have the probability density:

$$f(x) = \frac{x^{\alpha - 1}(1-x)^{1 - \beta}}{\mathrm{B}(\alpha,\beta)}$$

where $\alpha,\beta$ are two positive parameters and $0 \le x \le 1$ is the domain of $x$. What is the expected value of $1/x$? That is, what is the value of:

$$\langle1/x\rangle = \int_0^1 \frac{f(x)}{x} \mathrm d x$$