$\int \frac{d x}{\sqrt{5+4 x-x^{2}}}=$

$\int \frac{d x}{\sqrt{5+4 x-x^{2}}}=$
  1. $\sin ^{-1}\left(\frac{x-2}{3}\right)+c$
  2. $\log \left|(x-2)+\sqrt{5+4 x-x^{2}}\right|+c$
  3. $\log \left|(x+2)+\sqrt{5+4 x-x^{2}}\right|+c$
  4. $\sin ^{-1}\left(\frac{x+2}{3}\right)+c$

Solution

$I=\int \frac{d x}{\sqrt{9+\left(-4+4 x-x^{2}\right)}}=\int \frac{d x}{\sqrt{(3)^{2}-(x-2)^{2}}}=\sin ^{-1}\left(\frac{x-2}{3}\right)+c$

Asked in: MHT CET 2020 (12 Oct Shift 1)

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