sec x ? d x cos 2 x =

Question

$\int \frac{\sec x d x}{\sqrt{\cos 2 x}} =$

Smart Achievers · Accepted Answer

(1)

Ans. $\sin^{- 1} (\tan x)$

Explanation:

$\int \frac{\sec x d x}{\sqrt{\cos 2 x}} = \int \frac{\sec x}{\sqrt{\cos^{2} x - \sin^{2} x}} d x$

$= \int \frac{\sec^{2} x d x}{\sqrt{1 - \tan^{2} x}}$

$(Multiplying numerator and denominator by \sec x)$

Now put $\tan x = t$

$\Rightarrow$ $\sec^{2} x d x = d t,$

$= \int \frac{d t}{\sqrt{1 - t^{2}}} = \sin^{- 1} t$

$= \sin^{- 1} (\tan x)$

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