My Desk of Integrals has the final situation ##int frac dx x^2+a^2 ## being a 'standard' integral far too, not merely the case wherever ##a=one##. But I think this becoming a Calculus homework dilemma it is predicted of your OP to determine how to do it. Hints got over. Gable https://gabletoppak.com/from-plastic-bottles-to-gabletop-cartons-a-step-toward-solving-the-plastic-pollution-crisis/