Untitled

Plotting the curve of a function with parametric integral using R
n<-3; rho<-0.5;

g<-function(r)
   {
     integrate(
       function(beta)
       {
         1/(cosh(beta)-rho*r)^(n-1)
       }
     ,lower=0,upper=Inf)
   }

curve(g(x),from=0,to=1)

g<-function(r)
    {
      integrate(
        function(beta)
        {
          1/(cosh(beta)-rho*r)^(n-1)
        }
      ,lower=0,upper=Inf)$value   # integrate would return a list otherwise
    }
 gv <- Vectorize(g)
 # Since `g` is not naturally going to handle the vector that `curve` will send
 curve(gv(x),from=0,to=1)