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Question:
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Integrate the function
$\sqrt{1-4 x-x^2}$
$\sqrt{1-4 x-x^2}$
Solution:
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Verified Answer
$\int \sqrt{1-4 x-x^2} d x=\int \sqrt{(5)^2-(x+2)^2} d x$
$=\frac{x+2}{2} \sqrt{5-(x+2)^2}+\frac{5}{2} \sin ^{-1}\left(\frac{x+2}{\sqrt{5}}\right)+C$
$=\frac{x+2}{2} \sqrt{5-(x+2)^2}+\frac{5}{2} \sin ^{-1}\left(\frac{x+2}{\sqrt{5}}\right)+C$
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