My desk of Integrals has the final scenario ##int frac dx x^2+a^2 ## like a 'standard' integral way too, not only the situation in which ##a=one##. But I feel this becoming a Calculus research problem it is predicted on the OP to figure out how to get it done. Hints https://gabletoppak.com/hc-issues-notice-over-plea-to-make-dwarka-plastic-free/