Integrating a Gaussian wrt its width

Dear All,

I'm interested in integrals of the form:

declare(N,integer) ;
assume(N > 0) ;
assume(N > 1) ;
marginal : 'integrate((1/t-C)^(N-1)*exp(A-B/t^2),t,0,1/C) ;

Inspired by Jeffreys (1961, _Theory of Probability_, Oxford University
Press, p. 139), I thought a nice way forward would be to reduce this
to a finite series of incomplete Gamma functions, using the
substitution

changevar(marginal,u+B/t^2,u,t) ;

but all I get when I issue this changevar command is the error

sign: sign of infinity is undefined.
  -- an error. To debug this try: debugmode(true);


Any ideas, please?

-- 

Thanks,

Dan