Q59 / 150 · MHT CET 2016 · Mathematics

$\int \frac{1}{\sqrt{8 + 2 x - x^{2}}} d x =$

A
$\frac{1}{3} \sin^{- 1} (\frac{x - 1}{3}) + c$
B
$\sin^{- 1} (\frac{x + 1}{3}) + c$
C
$\frac{1}{3} \sin^{- 1} (\frac{x + 1}{3}) + c$
Correct answer
D
$\sin^{- 1} (\frac{x - 1}{3}) + c$

Solution

Let

I = \int \frac{d x}{\sqrt{8 + 2 x - x^{2}}}

\Rightarrow I = \int \frac{d x}{\sqrt{9 + 2 x - x^{2} - 1}}

\Rightarrow I = \int \frac{d x}{3^{2} - {(x - 1)}^{2}}

∴ I = \sin^{- 1} (\frac{x - 1}{3}) + c

Hence, the correct answer is option: 'D'.

Relevant Questions