\[ \text { Prove that } \int_{0}^{\pi / 2} \frac{\sin ^{5} x}{\left...

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\[
\text { Prove that } \int_{0}^{\pi / 2} \frac{\sin ^{5} x}{\left(\sin ^{5} x+\cos ^{5} x\right)} d x=\frac{\pi}{4}
\]
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