My desk of Integrals has the final case ##int frac dx x^2+a^2 ## like a 'standard' integral as well, not only the case in which ##a=1##. But I believe this currently being a Calculus research challenge it is predicted of your OP to determine how to make it happen. Hints https://gabletoppak.com/travel-green-gabletop-paks-sustainable-shift/