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The value of int(cos^(3)x)/(sin^(2)x+sin...

The value of `int(cos^(3)x)/(sin^(2)x+sinx)dx` is equal to

A

`log_(e)|sinx|+sinx+C`

B

`log_(e)|sinx|-sinx+C`

C

`-log_(e)|sinx|-sinx+C`

D

`-log_(e)|sinx|+sinx+C`

Text Solution

Verified by Experts

The correct Answer is:
B
`I=int(cos^(3)x)/(sin^(2)x+sinx)dx`
`=int(cosx.(1-sin^(2)x))/(sinx(1+sinx))dx`
Put `sinx=t,` then `cos xdx =dt`
`rArr" "I=int((1-t)(1+t)dt)/(t(1+t))`
`=int((1-t)dt)/(t)`
`=int((1)/(t)-1)dt`
`=log_(e)|t|-t+C`
`=log_(e)|sinx|-sinx+C`
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