∫(4dx)/sqrt(-4x - x^2)

notSomebody

1. The problem statement, all variables and given/known data

[itex]∫\frac{4dx}{\sqrt{-4x - x^2}}[/itex]

2. Relevant equations

[itex]arcsin(\frac{x}{a}) = \frac{1}{\sqrt{a^2-X^2}}[/itex]

Correct Answer: 4sin^-1[itex]\frac{1}{2}[/itex](x + 2) + c

3. The attempt at a solution

I am completely lost with this one. I tried pulling a [itex]\sqrt{x}[/itex] out of the bottom.

[itex]∫\frac{4dx}{\sqrt{x}\sqrt{-4 - x}}[/itex]

u = [itex]\sqrt{x}[/itex]
du = [itex]\frac{1}{2}x^{-1/2}dx[/itex]

[itex]8∫\frac{du}{\sqrt{-4-u^2}}[/itex]

So [itex]a^2 = -4[/itex]

[itex]\sqrt{-4}[/itex] is not a real number.

I would appreciate any help you could give. Thanks.

sunjin09

try-4x-4x^2=4-(x+2)^2