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