My table of Integrals has the final scenario ##int frac dx x^2+a^2 ## as a 'standard' integral too, not only the situation wherever ##a=1##. But I think this getting a Calculus research difficulty it is predicted in the OP to figure out how to do it. Hints were given over. https://gabletoppak.com/free-water-campaign-advertise-your-brand/