My Desk of Integrals has the final case ##int frac dx x^2+a^2 ## for a 'regular' integral way too, not simply the situation exactly where ##a=1##. But I believe this staying a Calculus research problem it is expected in the OP to figure out how to get it done. Hints https://gabletoppak.com/from-plastic-bottles-to-gabletop-cartons-a-step-toward-solving-the-plastic-pollution-crisis/