1. The problem statement, all variables and given/known data Show that, in a distributional sense, x* Pv(1/x) = 1 2. Relevant equations The function 1/x cannot be integrated locally in the origin. Nevertheless, int(1/x, x=-1..1) =0, and thus convergent. Therefore, one defines the (non-regular) distribution Pv(1/x), as follows: <Pv(1/x), phi(x)> = Pv*int(phi(x)/x, x=-infinity..infinity) which is defined to be equal to: limit( eps->0) ( int( phi(x)/x,x=-infinity..-eps) + int( phi(x)/x, x=eps..infinity) ) 3. The attempt at a solution My problem is that I don't really understand how I can write x*Pv(1/x) as a distribution. My attempt at a solution is as follows:: <x*Pv(1/x), phi(x)> = limit(eps->0) (int( phi(x)/x*x,x=-infinity..-eps) = int( phi(x)/x*x, x=eps..infinity) If this step is allowed, then of course, this integration is equal to : int(phi(x),x=-infinity..infinity) = 1 , because this is a distribution. But surely, it can't be as simple as that!