`int(cosx)/(1+cosx)dx`

Explanation

`int(cosx)/(1+cosx)dx`
`=int((1+cosx)-1)/(1+cosx)dx`
`=int1dx- int(1)/(1+cosx)dx`
`=int1dx -int(1)/(2cos^(2).(x)/(2))dx`
`=int 1dx -(1)/(2)intsec^(2).(x)/(2)dx`
`=x-(1)/(2)(tan.(x)/(2))/(1//2)+c=x-tan.(x)/(2)+c`