\[ \int_{0}^{\pi / 2} \frac{\sin ^{n} x}{\left(\sin ^{n} x+\cos ^{n...

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\[
\int_{0}^{\pi / 2} \frac{\sin ^{n} x}{\left(\sin ^{n} x+\cos ^{n} x\right)} d x=\frac{\pi}{4}
\]
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