My Desk of Integrals has the final circumstance ##int frac dx x^two+a^two ## as a 'standard' integral too, not merely the situation the place ##a=1##. But I think this being a Calculus research dilemma it is anticipated from the OP to determine how to make it happen. Hints were given https://gabletoppak.com/why-i-switched-to-water-in-a-sustainable-box/