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

Question

\[(a)\;e^x \cot x +c \quad (b)\;2e^x \sec^2 x+c \quad (c)\;e^x \cos 2x +c \quad (d)\;e^x \tan x +c \]