The value of ∫dx4x−3−x2 is equal to

4x−3−x2=−x2−4x+3=−(x−2)2−1=1−(x−2)2So, ∫dx4x−3−x2=∫dx1−(x−2)2=sin−1⁡(x−2)+C

The value of ∫dx4x−3−x2 is equal to

4x−3−x2=−x2−4x+3=−(x−2)2−1=1−(x−2)2So, ∫dx4x−3−x2=∫dx1−(x−2)2=sin−1⁡(x−2)+C

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The value of $\int \frac{d x}{\sqrt{4 x - 3 - x^{2}}}$ is equal to

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$\sin^{- 1} (x - 1) + C$

$\log |(x - 2) + \sqrt{4 x - 3 - x^{2}}|$

$\log |(x - 1) + \sqrt{4 x - 3 - x^{2}}| + C$

$\sin^{- 1} (x - 2) + C$

answer is D.

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Detailed Solution

$\sqrt{4 x - 3 - x^{2}} = \sqrt{- (x^{2} - 4 x + 3)}$

$= \sqrt{- ((x - 2)^{2} - 1)} = \sqrt{1 - (x - 2)^{2}}$

So, $\int \frac{d x}{\sqrt{4 x - 3 - x^{2}}} = \int \frac{d x}{\sqrt{1 - (x - 2)^{2}}} = \sin^{- 1} (x - 2) + C$

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The value of $\int \frac{d x}{\sqrt{4 x - 3 - x^{2}}}$ is equal to