Đáp án:

• Đặt \( A = \sqrt{2 + x} \Rightarrow x = t^2 - 2 \Rightarrow dx = 2t \, dt \)

• \( \int \frac{1}{1 + \sqrt{2 + x}} \, dx = \int \frac{2t}{t + 1}\,dt = \int \frac{2(t + 1) - 2}{t + 1} \, dt \)

\( = \int \left( 2 - \frac{2}{t + 1} \right) dt = 2t - 2 \ln |t + 1| + c \)

\( = 2\sqrt{2 + x} - 2 \ln (\sqrt{2 + x} + 1) + c \)