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Integrate the functions(sin^(-1)sqrt(x)-...

Integrate the functions`(sin^(-1)sqrt(x)-cos^(-1)sqrt(x))/(sin^(-1)sqrt(x)+cos^(-1)sqrt(x)), x in [0,1]`

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To solve the integral \[ I = \int_0^1 \frac{\sin^{-1}(\sqrt{x}) - \cos^{-1}(\sqrt{x})}{\sin^{-1}(\sqrt{x}) + \cos^{-1}(\sqrt{x})} \, dx, \] we can start by using the identity that relates the inverse sine and inverse cosine functions: ...
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