I am getting a sign error when evaluating:
$ \int \dfrac {1} {\sqrt{-x^{2} - 4x}}dx$
I completed the square in the denominator leaving me:
$\int \dfrac {1} {\sqrt{-x^{2} - 4x + 4 - 4}}dx$
$\int \dfrac {1} {\sqrt{-(x^{2} + 4x - 4 + 4)}}dx$
$\int \dfrac {1} {\sqrt{-(x+2)^{2} +4}}dx$
I then let $ u = x+2 , du = dx$, and $a = 2.$
$\int \dfrac {du} {\sqrt{-u^{2} + a^{2}}}$
$\arcsin \dfrac {-(x+2)} {2} + C$
However, the correct answer should be $\arcsin \dfrac {x+2} {2} + C$
Where did I go astray?