`intx/(1+cos2x)dx`

Explanation

`int (x)/(1+cos 2x)dx=int (x)/(2cos^(2)x)dx`
`=(1)/(2)int sec^(2)xdx`
`=(1)/(2)[x int sec^(2)xdx-int {(d)/(dx)(x)int sec^(2)xdx}dx]`
`=(1)/(2) [x tanx-int 1.tan x dx]`
`=(1)/(2)[x tan x-log|sec x|]+c`