My Table of Integrals has the final case ##int frac dx x^2+a^2 ## being a 'normal' integral far too, not only the case exactly where ##a=1##. But I do think this becoming a Calculus homework problem it is anticipated from the OP to determine how to do it. Hints were https://gabletoppak.com/kerala-get-ready-to-say-no-to-plastic-from-october-2/