My Table of Integrals has the final case ##int frac dx x^2+a^2 ## being a 'typical' integral way too, not just the case wherever ##a=1##. But I believe this remaining a Calculus research trouble it is anticipated of your OP to figure out how to get it done. Hints were https://gabletoppak.com/elevate-your-brand-with-gable-top-paks-white-label-water-packaging/