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If $\int \frac{cosx - sinx}{\sqrt{8 - \sin 2 x}} dx = {asin}^{- 1} (\frac{sinx + cosx}{b}) + c$ ,
Where $c$ is a constant of integration, then the ordered pair $(a, b)$ is equal to:

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$(- 1, 3)$

$(1, 3)$

$(3, 1)$

$(1, - 3)$

answer is C.

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Detailed Solution

$\int \frac{cosx - sinx}{\sqrt{8 - \sin 2 x}} dx =$ $\int \frac{cosx - sinx}{\sqrt{9 - {(sinx + cosx)}^{2}}} dx$

Let $sinx + cosx = t$

$\begin{array}{rcl} \int \frac{dt}{\sqrt{9 - t^{2}}} & = & \sin^{- 1} \frac{t}{3} + c \\ = & \sin^{- 1} (\frac{sinx + cosx}{3}) + c, \\ So a & = & 1, b = 3 . \end{array}$

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