Lời giải
\( I = \int_{1}^{2} \left( \frac{1}{\sqrt{x}} + \frac{1}{\sqrt{x+2}} \right) \, dx \)
\(= \left( 2\sqrt{x} + 2\sqrt{x+2} \right) \bigg|_{1}^{2} = \left( 2\sqrt{2} + 4 \right) - \left( 2 + 2\sqrt{3} \right) \)
\(= 2\sqrt{2} + 2 - 2\sqrt{3} \)