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int(dx)/((1-tanx))=?...

`int(dx)/((1-tanx))=?`

A

`(1)/(2)log|sinx-cosx|+C`

B

`(1)/(2)x+(1)/(2)log|sinx-cosx|+C`

C

`(1)/(2)x-(1)/(2)log|sinx-cosx|+C`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
`I=int(cosx)/((cosx-sinx))dx=int(-cosx)/((sinx-cosx))dx`.
`=((sinx-cosx)-(sinx+cosx))/(2(sinx-cosx))dx=int{(1)/(2)-(1)/(2)*((sinx+cosx))/((sinx-cosx))}dx`
`=(1)/(2)x-(1)/(2)log|sinx-cosx|+C`.
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