Integrate : $\int x\bigg( \large\frac{\sec 2x -1}{\sec 2x+1}\bigg) dx$

Question

$(a)\;x \tan x +\log |\sec x | -\frac{x^2}{2}+c \\(b)\;x \tan x -\log |\sec x | -\frac{x^2}{2}+c \\(c)\; -x \tan x -\log |\sec x | -\frac{x^2}{2}+c \\ (d)\;none $