Ononot — If I = \int{0}^{\pi/2} \frac{\sin^n x}{\sin^n x + \cos^n x}

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Integralsmedium

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If $I = \int_{0}^{\pi/2} \frac{\sin^n x}{\sin^n x + \cos^n x} dx$ , what is the value of $I$ regardless of the value of $n > 0$ ?