Relation Between Beta and Gamma functions

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PLAGUE
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TL;DR
Proof of Beta Gamma function relation
Screenshot 2024-01-02 173019.png

So, my teacher showed me this proof and unfortunately it is vacation now. I don't understand what just happened in the marked line. Can someone please explain?
 

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The line asserts that [tex] \int_0^\infty e^{-x(1+ y)}x^{m+n-1}\,dx = \frac{\Gamma(m + n)}{(1 + y)^{m + n}}.[/tex] How would you apply the given formulae to arrive at that?
 

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