My desk of Integrals has the final situation ##int frac dx x^2+a^two ## as a 'regular' integral far too, not merely the case where ##a=one##. But I believe this remaining a Calculus research challenge it is expected in the OP to determine how to make it happen. Hints were given https://gabletoppak.com/bioplastics-greenwashing-or-genuine-solution-the-truth-behind-the-hype/