Integrate : $\sqrt { \bigg( \large\frac{1+ \sin 2x}{1+ \cos 2x}\bigg)}$$dx$

Question

$$\begin {array} {1 1} (a)\;\log(\sec x - \tan x)+c \\ (b)\;\{ \log (\sec x )+\tan x + c \\ (c)\;\{\log (\sec x)+x \} /\sqrt 2 +c \\ (d)\;\{ \log \sec x -x\} +c \end {array}$$