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int(a//4)^(3a//4)sqrt(x)/(sqrt(a-x)+sqrt...

`int_(a//4)^(3a//4)sqrt(x)/(sqrt(a-x)+sqrt(x))\ dx=a/4`

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To solve the integral \[ I = \int_{\frac{a}{4}}^{\frac{3a}{4}} \frac{\sqrt{x}}{\sqrt{a-x} + \sqrt{x}} \, dx \] and prove that it is equal to \(\frac{a}{4}\), we will follow these steps: ...
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