My desk of Integrals has the overall case ##int frac dx x^two+a^2 ## for a 'normal' integral too, not simply the case where ##a=one##. But I think this getting a Calculus research challenge it is predicted in the OP to figure out how to do it. Hints got above. Photon https://gabletoppak.com/a-revolutionary-step-towards-sustainable-water-bottle-packaging/