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int (x+sin x)/(1+cos x) is equal to...

`int (x+sin x)/(1+cos x)` is equal to

A

`x tan (x)/(2)+c`

B

`log (1+cos x)+c`

C

`cot (x)/(2)+c`

D

`log(x+sinx)+c`

Text Solution

Verified by Experts

The correct Answer is:
A
Let `I=int (x+sin x)/(1+cosx)dx`
`=int((x)/(2)sec^(2)""(x)/(2)+tan""(x)/(2))dx`
`=x tan""(x)/(2)-inttan""(x)/(2)dx+inttan""(x)/(2)dx+c`
`=x tan""(x)/(2)+c`
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