My table of Integrals has the final situation ##int frac dx x^2+a^2 ## as a 'typical' integral too, not just the case exactly where ##a=1##. But I feel this currently being a Calculus research dilemma it is anticipated of the OP to determine how to make it happen. Hints were https://gabletoppak.com/chikkamagaluru-dc-to-declare-mullayyanagiri-hill-station-plastic-free-zone-on-world-earth-day/