But The value of $\mu$ are in $(0,1) $, I have set that in Stackexchange post
@Jim Baldwin Thank you so much for your attentionn , it were a wrong typo the integrand is still over sigma from 1 to Infinity , Now it fixed
Just an attempt , I think the constant i have added is work over range (-infinity , infinity)
Did you mean to integrate $\sigma$ from $-\infty$ as $\sigma$ shows up under a square root in your equation? That begs the question as to if this is a legitimate pdf. Also, does this mean you were able to determine the constant of integration in the question you posted at Mathematica StackExchange ?
