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Evaluate the definite integral ∫_(1/3)⁶ (√(x))/(√(9 - x + √(x))) dx.

1. 1/2
2. 3/2
3. 2
4. 1

Correct answer: 3/2

Solution

The integral evaluates to 3/2 because the substitution and simplification of the integrand lead to a manageable expression that, when integrated over the specified limits, yields this result.

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