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int ("cosec"^(2)x)/((1-cot^(2)x))dx=?...

`int ("cosec"^(2)x)/((1-cot^(2)x))dx=?`

A

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

B

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

C

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

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
Put `cot x=t and -"cosec"^(2)xdx=dt.`
`therefore I=-int(dt)/((1-t^(2)))=-(1)/((2xx1))log |(1+t)/(1-t)|+C=(-1)/(2)log |(1+cotx)/(1-cot x)|+C`
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