`e^(x)((1+sinx)/(1+cosx))`

Explanation

`int((1+sinx)/(1+cosx))e^(x)dx`
`=int((1+2sin.(x)/(2)cos.(x)/(2))/(2cos^(2).(x)/(2)))e^(x)dx`
`=(1)/(2)inte^(x)sec^(2).(x)/(2)dx+inte^(x)tan.(x)/(2)dx`
`=(1)/(2)inte^(x)sec^(2).(x)/(2)dx+tan.(x)/(2)inte^(x)dx-int{(d)/(dx)tan.(x)/(2)inte^(x)dx}dx+C`
`=(1)/(2)inte^(x)sec^(2).(x)/(2)dx+e^(x)tan.(x)/(2)-int(1)/(2)sec^(2).(x)/(2).e^(x)dx+C`
`=e^(x)tan.(x)/(2)+C`