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

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(A) Let $I = \int \frac{\sin 2x}{\sin^2 x \cos^2 x} dx$.Using the identity $\sin 2x = 2 \sin x \cos x$,we get:$I = \int \frac{2 \sin x \cos x}{\sin^2

Vedclass · Accepted Answer

$\log |	an^2 x| + c$

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(A) Let $I = \int \frac{\sin 2x}{\sin^2 x \cos^2 x} dx$.Using the identity $\sin 2x = 2 \sin x \cos x$,we get:$I = \int \frac{2 \sin x \cos x}{\sin^2 x \cos^2 x} dx$$I = 2 \int \frac{1}{\sin x \cos x} dx$Multiply numerator and denominator by $2$:$I = 2 \int \frac{2}{2 \sin x \cos x} dx = 4 \int \frac{1}{\sin 2x} dx$$I = 4 \int \operatorname{cosec} 2x dx$Using the formula $\int \operatorname{cosec} u du = \log |	an(u/2)| + c$,we get:$I = 4 	imes \frac{1}{2} \log |	an x| + c = 2 \log |	an x| + c$Using the property $n \log a = \log a^n$,we get:$I = \log |	an^2 x| + c$.

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

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