Its true that if you integrate an exponential function from some time t0 to infinity it will converge to a finite value. However, is the same true if it is multiplied by say t, t^2, t^3,t^n. i.e. t*exp(-t) for example. the exp is decaying to zero faaster than t is, so it goes to zero in the limit. But there are functions that decay to zero but their integral is not finite because the rate of decay is not *fast enough*. Would the integral of exp multiplied by any power of t ALWAYs converge to a finite number?