My desk of Integrals has the final circumstance ##int frac dx x^2+a^2 ## to be a 'conventional' integral far too, not merely the situation in which ##a=1##. But I do think this staying a Calculus research dilemma it is anticipated from the OP to determine how to get it done. https://gabletoppak.com/from-plastic-bottles-to-gabletop-cartons-a-step-toward-solving-the-plastic-pollution-crisis/