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My desk of Integrals has the final circumstance ##int frac dx x^two+a^2 ## as being a 'normal' integral far too, not merely the situation exactly where ##a=one##. But I feel this becoming a Calculus research problem it is anticipated with the OP to determine how to do it. Hints were https://gabletoppak.com/a-revolutionary-step-towards-sustainable-water-bottle-packaging/

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