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Evaluate: int(sinx)/(sqrt(4cos^2x-1))dx...

Evaluate: `int(sinx)/(sqrt(4cos^2x-1))dx`

A

`-(1)/(2)log |2cosx+sqrt(4cos^(2)x-1)|+C`

B

`-(1)/(3)log |2cosx+sqrt(4cos^(2)x-1)|+C`

C

`-(1)/(6)log |cosx+sqrt(2cos^(2)x-1)|+C`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
Put ` cos x=t and sin x dx =-dt ,` then
`I=-int(dt)/(sqrt(4t^(2)-1))=-(1)/(2)int (dt)/(sqrt(t^(2)-(1)/(4)))=-(1)/(2)log |t+sqrt(t^(2)-(1)/(4))|+C`
`=-(1)/(2)log |2t+sqrt(4t^(2) -1)|+C=-(1)/(2) log|2cos x+sqrt(4 cos^(2)x-1)|+C.`
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