Đáp án:

• \( \int \frac{1}{1 + \sin 2x} \, dx = \int \frac{1}{(\cos x + \sin x)^2} \, dx = \int \frac{1}{[\sqrt{2} \cos (x - \frac{\pi}{4})]^2} \, dx \)

\( = \frac{1}{2} \int \frac{1}{\cos^2 (x - \frac{\pi}{4})} \, dx = \frac{1}{2} \tan (x - \frac{\pi}{4}) + C \)