Question: Integral limits

I have a proc as follows:

F:=proc(f,n)
L:=[f];
for j from 1 to n do;
J:=int(1/subs(t=x[j],L[j]),x[j]=2..x[j+1]);
L:=[op(L),J];
end do;
end proc;

I chose to use index variables. However when I try to apply a member of the output list as a function of the outermost limit, I do not get any output when I try to evaluate the function. I suspect maple is having trouble with the variables withing the integral. How can I make this work?

I'd like to have a function that I can evaluate:

g:=F(log(t),3)[3];
f:=unapply(g,x[3]);

f(2.1);

Thanks!

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