My desk of Integrals has the final scenario ##int frac dx x^2+a^2 ## as being a 'normal' integral as well, not just the situation exactly where ##a=one##. But I feel this staying a Calculus research dilemma it is anticipated of the OP to determine how to do it. Hints got https://gabletoppak.com/india-leads-in-generating-plastic-waste-with-10-2-mn-tonnes-a-year-study/