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Question Number 55364 by peter frank last updated on 22/Feb/19

prove that \int_{- \infty}^{\infty} f (x) dx = 1

such that f (x) = \frac{1}{\sqrt{n} β (\frac{n}{2}, \frac{1}{2})} {(1 + \frac{x^{2}}{n})}^{- \frac{1}{2} (1 + n)}

and β (\frac{n}{2}, \frac{1}{2}) = \int_{0}^{\infty} \frac{x^{\frac{n}{2} - 1}}{{(1 + x)}^{\frac{3}{2}}} dx