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Question: Answered & Verified by Expert
$$
\int \frac{d x}{\sqrt{5+4 x-x^{2}}}=
$$
MathematicsIndefinite IntegrationMHT CETMHT CET 2020 (12 Oct Shift 1)
Options:
  • A $\sin ^{-1}\left(\frac{x-2}{3}\right)+c$
  • B $\log \left|(x-2)+\sqrt{5+4 x-x^{2}}\right|+c$
  • C $\log \left|(x+2)+\sqrt{5+4 x-x^{2}}\right|+c$
  • D $\sin ^{-1}\left(\frac{x+2}{3}\right)+c$
Solution:
1322 Upvotes Verified Answer
The correct answer is: $\sin ^{-1}\left(\frac{x-2}{3}\right)+c$
$I=\int \frac{d x}{\sqrt{9+\left(-4+4 x-x^{2}\right)}}=\int \frac{d x}{\sqrt{(3)^{2}-(x-2)^{2}}}=\sin ^{-1}\left(\frac{x-2}{3}\right)+c$

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