My table of Integrals has the overall situation ##int frac dx x^two+a^two ## for a 'standard' integral also, not simply the case exactly where ##a=1##. But I do think this remaining a Calculus research dilemma it is anticipated in the OP to figure out how to do it. Hints were https://gabletoppak.com/bioplastics-greenwashing-or-genuine-solution-the-truth-behind-the-hype/