Đáp án:

• Xét \( \int \frac{\sin x}{\sin x + \cos x} \, dx = J \)

• \( I + J = \int \frac{\cos x}{\sin x + \cos x} \, dx + \int \frac{\sin x}{\sin x + \cos x} \, dx = x + C \)

• \( I - J = \int \frac{\cos x}{\sin x + \cos x} \, dx - \int \frac{\sin x}{\sin x + \cos x} \, dx = \ln |\sin x + \cos x| + C \)

• \( I = \int \frac{\cos x}{\sin x + \cos x} \, dx = \frac{1}{2} \left( x + \ln |\sin x + \cos x| \right) + C \)