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Evaluate the integral I = ∫ from 0 to π/2 of ((sin x + cos x)² / √(1 + sin 2x)) dx.

1. 3
2. 1
3. 2
4. 0

Correct answer: 2

Solution

The integral simplifies to a form that can be evaluated using trigonometric identities and symmetry properties of sine and cosine functions, ultimately leading to the result of 2.

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