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

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

A

`-x+secx-tan+C`

B

`x+cosx-sinx+C`

C

`-log|1-sinx|+C`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
`I=int{(sinx)/((1-sinx))xx((1+sinx))/((1+sinx))}dx=int((sinx+sin^2x)/(cos^(2)x))dx`.
`int{(sinx)/(cos^(2))+(sin^(2)x)/(cos^(2)x)}dxint(secxtanx+tan^(2)x)dx`
`int(secxtanx+sec^(2)x-1)dx=secx+tanx-x+C`.
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