My desk of Integrals has the final scenario ##int frac dx x^two+a^2 ## like a 'common' integral far too, not simply the case in which ##a=1##. But I think this being a Calculus research challenge it is anticipated on the OP to figure out how to do it. Hints got https://gabletoppak.com/quenching-thirst-building-brands-how-free-water-campaigns-on-gable-top-cartons-create-impactful-brand-awareness/