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int(0)^(1)(1)/(sqrt(1+x)-sqrt(x))dx...

`int_(0)^(1)(1)/(sqrt(1+x)-sqrt(x))dx`

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To solve the integral \[ I = \int_{0}^{1} \frac{1}{\sqrt{1+x} - \sqrt{x}} \, dx, \] we will rationalize the denominator. ...
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