$\int \bigg(\large\frac{2 -\sin 2x}{1-\cos 2x}\bigg)$$e^x dx=$

Question

$$\begin {array} {1 1} (1)\;-e^x \cot x +c & \quad (2)\;e^x \cot x +c \\ (3)\;2e^x \cot x +c & \quad (4)\;-2e^{x} \cot x +c \end {array}$$