Beta Function as Integral of Power of t over Power of t plus 1

Theorem

 * $\displaystyle \Beta \left({x, y}\right) := \int_{\mathop \to 0}^{\mathop \to \infty} \frac {t^{x - 1} } {\left({1 + t}\right)^{x + y} } \ \mathrm d t$

where $\Beta$ denotes the Beta function.