If the value of the definite integral \( \int_{0}^{1} \frac{\sin ^{...

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If the value of the definite integral \( \int_{0}^{1} \frac{\sin ^{-1} \sqrt{x}}{x^{2}-x+1} d x \) is \( \frac{\pi^{2}}{\sqrt{n}} \)
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W (where \( n \in N \) ), then the value of \( n \) is
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