Evaluate $\int_2^5 \frac{\sqrt{x}}{\sqrt{x} + \sqrt{7 - x}}\,dx$.

Explanation

1. 01

   By $\int_a^b f(x)\,dx = \int_a^b f(a + b - x)\,dx$ with $a + b = 7$, $I = \int_2^5 \frac{\sqrt{7 - x}}{\sqrt{7 - x} + \sqrt{x}}\,dx$.

2. 02

   Adding, $2I = \int_2^5 1\,dx = 3$, so $I = \frac{3}{2}$.