int frac{sin 2x}{sin^4 x + cos^4 x} , dx = | vedclass

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Question

(B) Let $I = \int \frac{\sin 2x}{\sin^4 x + \cos^4 x} \, dx$. Divide the numerator and denominator by $\cos^4 x$: $I = \int \frac{2 \sin x \cos x}{\si

Vedclass · Accepted Answer

$	an^{-1}(	an^2 x) + c$

Vedclass · Answer

(B) Let $I = \int \frac{\sin 2x}{\sin^4 x + \cos^4 x} \, dx$. Divide the numerator and denominator by $\cos^4 x$: $I = \int \frac{2 \sin x \cos x}{\sin^4 x + \cos^4 x} \, dx = \int \frac{2 	an x \sec^2 x}{1 + 	an^4 x} \, dx$. Let $t = 	an^2 x$,then $dt = 2 	an x \sec^2 x \, dx$. Substituting these into the integral,we get: $I = \int \frac{dt}{1 + t^2} = 	an^{-1}(t) + c$. Replacing $t$ with $	an^2 x$,we obtain: $I = 	an^{-1}(	an^2 x) + c$.

$\int \frac{\sin 2x}{\sin^4 x + \cos^4 x} \, dx = $

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