My table of Integrals has the final situation ##int frac dx x^two+a^2 ## as being a 'standard' integral far too, not only the case exactly where ##a=one##. But I believe this being a Calculus research challenge it is expected of the OP to determine how to get it done. Hints https://gabletoppak.com/what-makes-gabletop-pak-cartons-a-better-choice-than-plastic-bottles/