Integral of $\int\frac{\sin x}{\sin x+\cos x}dx$

Hint :

Consider the following system of equations :

$$\begin{cases} J+I = x+c \\ J - I = \ln|\cos x + \sin x | + c\end{cases}$$

See an easy way out for $I$ ?

Tags:

Integration

Trigonometric Integrals

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