Some integration techniques are just "tricks", while some integrals are analytically significant in that they connect different fields of math or they embody higher level concepts.
In the commonly stated form, the Frullani's integral is a definite integral that encompass a nontrivial family of integrand.
With some effort, it can be extended one way or the other. For example, see the answer by fedja in this post, along with other valuable expositions on the derivation of Frullani integral. A certain generalization from the reals to complex can also be made.
How would you introduce the Frullani integral to freshmen calculus students?
How would you re-introduce Frullani integral to junior or senior math majors who presumably care about more than just getting the answers?
The issue with presenting it as a "trick" is that students might learn only the bare minimum (merely the mechanical maneuver). Students at various levels inevitably sometimes wonder if "tricks" are not worth learning at all. How does one carefully make the distinction between tricks and more substantial things (here specifically the Frullani integral).