My table of Integrals has the final situation ##int frac dx x^2+a^two ## as being a 'normal' integral too, not only the case the place ##a=1##. But I think this getting a Calculus research challenge it is anticipated with the OP to determine how to make it happen. Hints were https://gabletoppak.com/beyond-beverages-gable-top-cartons-the-versatile-customized-packaging-solution/