My table of Integrals has the overall case ##int frac dx x^2+a^two ## to be a 'typical' integral too, not just the case exactly where ##a=one##. But I feel this remaining a Calculus research challenge it is expected in the OP to figure out how to do it. Hints were https://gabletoppak.com/from-plastic-bottles-to-gabletop-cartons-a-step-toward-solving-the-plastic-pollution-crisis/