Evaluate `int_0^(pi/2)((sin^4x)/(sin^4x+cos^4x))dx`

Explanation

To evaluate the integral

\[ I = \int_0^{\frac{\pi}{2}} \frac{\sin^4 x}{\sin^4 x + \cos^4 x} \, dx, \]

we can use a symmetry property of definite integrals.

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