My table of Integrals has the final scenario ##int frac dx x^2+a^two ## being a 'normal' integral far too, not just the case the place ##a=one##. But I think this currently being a Calculus research problem it is anticipated with the OP to determine how to do it. Hints were https://gabletoppak.com/single-use-plastic-water-bottles-will-not-be-available-in-himachal-from-june-1-use-glass-bottles-and-dispensers-instead/