My Table of Integrals has the overall situation ##int frac dx x^2+a^2 ## as being a 'regular' integral also, not only the case exactly where ##a=1##. But I do think this remaining a Calculus research challenge it is anticipated on the OP to figure out how to do it. Hints https://gabletoppak.com/glass-bottles-for-beer-soda-and-even-water-found-to-contain-toxic-levels-of-cancer-linked-microplastics-than-plastic-bottles-study-says/