int frac{dx}{cos^2(x) + sin(2x)} = | vedclass

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Question

(C) Let $I = \int \frac{dx}{\cos^2 x + \sin 2x}$.Divide the numerator and denominator by $\cos^2 x$:$I = \int \frac{\sec^2 x dx}{1 + 2 	an x}$.Let $t

Vedclass · Accepted Answer

$\frac{1}{2} \log |1 + 2 	an(x)| + C$

Vedclass · Answer

(C) Let $I = \int \frac{dx}{\cos^2 x + \sin 2x}$.Divide the numerator and denominator by $\cos^2 x$:$I = \int \frac{\sec^2 x dx}{1 + 2 	an x}$.Let $t = 1 + 2 	an x$. Then $dt = 2 \sec^2 x dx$,which implies $\sec^2 x dx = \frac{dt}{2}$.Substituting these into the integral:$I = \int \frac{1}{t} \cdot \frac{dt}{2} = \frac{1}{2} \int \frac{dt}{t} = \frac{1}{2} \log |t| + C$.Substituting back $t = 1 + 2 	an x$:$I = \frac{1}{2} \log |1 + 2 	an x| + C$.Thus,option $C$ is correct.

$\int \frac{dx}{\cos^2(x) + \sin(2x)} = $

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