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The value of int(cos xdx)/((sinx-1)(sinx...

The value of `int(cos xdx)/((sinx-1)(sinx-2))` is equal to

A

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

B

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

C

`log(sinx-2)+C`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
Let `l=int(cosxdx)/((sinx-1)(sinx-2))`
Put `sinx = t rArr cos x dx=dt`
`therefore" "l=int(dt)/((t-1)(t-2))=int((1)/(t-2)-(1)/(t-1))dt`
`=log|t-2|-log|t-1|+C`
`=log|(t-2)/(t-1)|+C=log|(sinx-2)/(sinx-1)|+C`
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