My table of Integrals has the general situation ##int frac dx x^2+a^2 ## being a 'conventional' integral too, not just the case exactly where ##a=1##. But I believe this currently being a Calculus research dilemma it is predicted with the OP to determine how to make it happen. Hints got https://gabletoppak.com/a-revolutionary-step-towards-sustainable-water-bottle-packaging/