My table of Integrals has the general situation ##int frac dx x^2+a^2 ## being a 'typical' integral much too, not just the situation where ##a=1##. But I feel this getting a Calculus research difficulty it is predicted in the OP to determine how to get it done. Hints got earlier https://gabletoppak.com/how-i-integrated-branding-and-design-with-an-indian-paper-bottle-manufacturer/