My table of Integrals has the overall case ##int frac dx x^2+a^two ## for a 'common' integral much too, not simply the situation where ##a=1##. But I do think this remaining a Calculus research problem it is predicted on the OP to figure out how to do it. Hints got https://gabletoppak.com/why-gable-top-cartons-are-making-a-splash-in-the-water-industry/