My desk of Integrals has the final situation ##int frac dx x^2+a^2 ## like a 'normal' integral too, not just the case where ##a=1##. But I do think this remaining a Calculus research problem it is predicted of the OP to determine how to make it happen. Hints were given https://gabletoppak.com/india-leads-in-generating-plastic-waste-with-10-2-mn-tonnes-a-year-study/