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

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