Finding the Integral of a Rational Function with a Radical in the Denominator

[notSomebody]

Homework Statement

$∫\frac{4dx}{\sqrt{-4x - x^2}}$

Homework Equations

$arcsin(\frac{x}{a}) = \frac{1}{\sqrt{a^2-X^2}}$

Correct Answer: 4sin^-1$\frac{1}{2}$(x + 2) + c

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.

 

[sunjin09]

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