My table of Integrals has the overall scenario ##int frac dx x^two+a^two ## as a 'normal' integral way too, not merely the situation where ##a=1##. But I believe this getting a Calculus research challenge it is predicted with the OP to determine how to get it done. Hints were given https://gabletoppak.com/bioplastics-greenwashing-or-genuine-solution-the-truth-behind-the-hype/