Integral of $$$\frac{1}{\sin{\left(x \right)} + \cos{\left(x \right)} + 2}$$$

The calculator will find the integral/antiderivative of $$$\frac{1}{\sin{\left(x \right)} + \cos{\left(x \right)} + 2}$$$, with steps shown.

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Find $$$\int \frac{1}{\sin{\left(x \right)} + \cos{\left(x \right)} + 2}\, dx$$$.