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I tried to solve it in a way but I can't complete in as I don't get any idea how to integrate the Beta kind two integrand within a finite boundary.

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    $\begingroup$ Simply use change of variables. $y=\frac{1}{1+x}\implies x=\frac{1-y}{y}$ and $x>0\implies 0<y<1$. So, $f_Y(y)=f_X(\frac{1-y}{y})\left|\frac{dx}{dy}\right|=\cdots$ $\endgroup$ – StubbornAtom May 25 at 7:56
  • $\begingroup$ Please add the self-study tag. $\endgroup$ – kjetil b halvorsen May 25 at 8:20

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