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

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

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$	an^2 x$

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(B) Let $I = \int \frac{\sin 2x}{\sin^4 x + \cos^4 x} dx$.Divide numerator and denominator by $\cos^4 x$:$I = \int \frac{2 \sin x \cos x / \cos^4 x}{	an^4 x + 1} dx = \int \frac{2 	an x \sec^2 x}{	an^4 x + 1} dx$.Let $u = 	an^2 x$, then $du = 2 	an x \sec^2 x dx$.$I = \int \frac{du}{u^2 + 1} = 	an^{-1}(u) + c = 	an^{-1}(	an^2 x) + c$.Thus, $f(x) = 	an^{-1}(	an^2 x)$.Therefore, $	an(f(x)) = 	an(	an^{-1}(	an^2 x)) = 	an^2 x$.

If $\int \frac{\sin 2x}{\sin^4 x + \cos^4 x} dx = f(x) + c$ where $c$ is the constant of integration, then the value of $\tan(f(x))$ is

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