My Table of Integrals has the final situation ##int frac dx x^two+a^2 ## as a 'conventional' integral way too, not just the situation in which ##a=one##. But I believe this being a Calculus research issue it is predicted in the OP to determine how to get it done. Hints got https://gabletoppak.com/the-growing-threat-of-marine-pollution-and-how-gabletop-cartons-offer-a-solution/