int frac{dx}{cos x sqrt{cos 2x}} = | vedclass

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(D) Let $I = \int \frac{dx}{\cos x \sqrt{\cos 2x}}$.Divide the numerator and denominator by $\cos x$ inside the square root or manipulate the expressi

Vedclass · Accepted Answer

$\sin^{-1}(	an x)+c$

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(D) Let $I = \int \frac{dx}{\cos x \sqrt{\cos 2x}}$.Divide the numerator and denominator by $\cos x$ inside the square root or manipulate the expression as follows:$I = \int \frac{dx}{\cos x \sqrt{\cos^2 x - \sin^2 x}} = \int \frac{dx}{\cos x \cdot \cos x \sqrt{1 - 	an^2 x}} = \int \frac{\sec^2 x}{\sqrt{1 - 	an^2 x}} dx$.Let $	an x = t$,then $\sec^2 x \, dx = dt$.Substituting these into the integral,we get:$I = \int \frac{dt}{\sqrt{1 - t^2}} = \sin^{-1}(t) + c$.Replacing $t$ with $	an x$,we get:$I = \sin^{-1}(	an x) + c$.

$\int \frac{dx}{\cos x \sqrt{\cos 2x}} =$

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