So I'm trying to understand how to integrate: (dx/(sqrt(-4x - x^2))) without using trig substitution as I'm in a Calc 1 class and we're not supposed to use anything other than u-substitution. I get stuck after completing the square:
indefinite integral of (dx/(sqrt(-4x - x^2)))
indefinite integral of (dx/(sqrt(-(x + 2)^2 + 4)))
Let u = x + 2
indefinite integral of (dx/(sqrt(4 - u^2)))
Perhaps this is an algebra question, but I'm not sure how you get that 4 to be a 1 as it's inside a radical and part of a sum. What do I do from here?
indefinite integral of (dx/(sqrt(-4x - x^2)))
indefinite integral of (dx/(sqrt(-(x + 2)^2 + 4)))
Let u = x + 2
indefinite integral of (dx/(sqrt(4 - u^2)))
Perhaps this is an algebra question, but I'm not sure how you get that 4 to be a 1 as it's inside a radical and part of a sum. What do I do from here?