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int(dx)/(cosx+sqrt3 sinx)dx is equal to...

`int(dx)/(cosx+sqrt3 sinx)dx` is equal to

A

`(1)/(2)logtan((x)/(2)+(pi)/(12))+C`

B

`(1)/(2)log tan((x)/(2)-(pi)/(12))+C`

C

`log tan((x)/(2)+(pi)/(12))+C`

D

`log tan ((x)/(2)-(pi)/(12))+C`

Text Solution

Verified by Experts

The correct Answer is:
A
`int(dx)/(cosx+sqrt3 sinx)=int(dx)/(2((1)/(2)cosx+(sqrt3)/(2)sinx))`
`=(1)/(2)int sec(x-(pi)/(3))dx`
`=(1)/(2)log tan((x)/(2)-(pi)/(6)+(pi)/(4))+C`
`=(1)/(2)log tan ((x)/(2)+(pi)/(12))+C`
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