Prove that \[ \int_{0}^{\pi / 2} \frac{\cos ^{1 / 4} x}{\left(\sin ...

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Prove that
\[
\int_{0}^{\pi / 2} \frac{\cos ^{1 / 4} x}{\left(\sin ^{1 / 4} x+\cos ^{1 / 4} x\right)} d x=\frac{\pi}{4}
\]
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