Prove that \( \int_{0}^{\pi / 2} \frac{\sin ^{3} x}{\left(\sin ^{3}...

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Prove that \( \int_{0}^{\pi / 2} \frac{\sin ^{3} x}{\left(\sin ^{3} x+\cos ^{3} x\right)} d x=\frac{\pi}{4} \)
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