My table of Integrals has the overall case ##int frac dx x^two+a^two ## being a 'normal' integral too, not just the situation exactly where ##a=1##. But I believe this becoming a Calculus research challenge it is anticipated from the OP to figure out how to make it happen. Hints were https://gabletoppak.com/why-gable-top-cartons-are-making-a-splash-in-the-water-industry/