int(x+sinx)/(1+cosx) dx is equal to...

`int(x+sinx)/(1+cosx) dx` is equal to

A

`x tan.(x)/(2)+C`

B

`log(1+cosx)+C`

C

`cot.(x)/(2)+C`

D

`log(x+sinx)+C`

Text Solution

Verified by Experts

The correct Answer is:

A

Let `l=int(x+sinx)/(1+cosx)dx=int((x)/(2)sec^(2).(x)/(2)+tan.(x)/(2))dx`
`=x tan.(x)/(2)-int tan.(x)/(2)dx+int tan.(x)/(2)dx+C`
`=x tan.(x)/(2)+C`

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