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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

`x"sin"^(2)x/2+c`

C

`log"cos"x/2+c`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
Let `l=int(x+sinx)/(1+cosx)dx`
`=1/2intx sec^(2)x/sdx+int"tan"x/2dx`
`=1/2[x.2"tan"x/2]-int"tan"x/2dx`
`+int"tan"x/2dx+c`
`=x"tan"x/2+c`
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