My Table of Integrals has the final situation ##int frac dx x^two+a^two ## as a 'regular' integral way too, not simply the situation where by ##a=one##. But I feel this being a Calculus research problem it is anticipated with the OP to determine how to do it. Hints were given https://gabletoppak.com/why-gabletop-cartons-outshine-pet-bottles-for-branding-opportunities/