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