∫(4dx)/sqrt(-4x - x^2)

  1. 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.
     
    Last edited: Feb 6, 2012
  2. jcsd
  3. try-4x-4x^2=4-(x+2)^2
     
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