The article points out that the trick can be applied to integrals to which it doesn't seem applicable, by introducing a new parameter to the integrand which was

The article points out that the trick can be applied to integrals to which it doesn't seem applicable, by introducing a new parameter to the integrand which was not there before. In general, that kind of tactic gives me hope someday mankind might find short, easy solutions to problems that currently seem hopeless (P=NP, Riemann Hypothesis, the 3n+1 problem, etc.) For example, maybe someone will define spaces P(x) and NP(x), depending on a parameter x, with P(1)=P and NP(1)=NP, and then they'll show (in some simple way that makes us all kick ourselves) that P(x)=NP(x) for all x>=sqrt(2) and P(x)<>NP(x) for all x<sqrt(2). "And thus, P<>NP." It makes you realize we really don't have a good sense of distances in the space of mathematical proofs. It's so high-dimensional, a solution that seems light-years away can actually be right under your nose, if you just turn your nose in the correct direction.