# ∫(4dx)/sqrt(-4x - x^2)

by notSomebody
Tags: 𕖲dx or sqrt4x
 P: 5 1. The problem statement, all variables and given/known data $∫\frac{4dx}{\sqrt{-4x - x^2}}$ 2. Relevant equations $arcsin(\frac{x}{a}) = \frac{1}{\sqrt{a^2-X^2}}$ Correct Answer: 4sin-1$\frac{1}{2}$(x + 2) + c 3. The attempt at a solution I am completely lost with this one. I tried pulling a $\sqrt{x}$ out of the bottom. $∫\frac{4dx}{\sqrt{x}\sqrt{-4 - x}}$ u = $\sqrt{x}$ du = $\frac{1}{2}x^{-1/2}dx$ $8∫\frac{du}{\sqrt{-4-u^2}}$ So $a^2 = -4$ $\sqrt{-4}$ is not a real number. I would appreciate any help you could give. Thanks.
 P: 312 try-4x-4x^2=4-(x+2)^2

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