Beta Function : Proof

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Prove that

$$\int_{0}^1 \frac{x^{p-1} + x^{q-1}}{(1 + x)^{p+q}} dx = \beta (p,q)$$

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Let $x=\frac{1}{y}$ or $x=\frac{y}{y+1}$ and consider the Euler function.