My Desk of Integrals has the final case ##int frac dx x^2+a^two ## for a 'typical' integral far too, not simply the case in which ##a=1##. But I do think this remaining a Calculus research dilemma it is anticipated from the OP to figure out how to get it done. https://gabletoppak.com/what-makes-gabletop-pak-cartons-a-better-choice-than-plastic-bottles/