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