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int (cot x)/((cosec x - cot x)) dx = ?...

`int (cot x)/((cosec x - cot x)) dx = ?`

A

`-cosec x - cot x - x + C`

B

`cosec x - cot x - x + C`

C

`-cosec x + cot x -x + C`

D

`cosec x + cot x -x + C`

Text Solution

Verified by Experts

The correct Answer is:
A
`I = int{(cotx)/((cosecx - cot))xx ((cosecx + cotx))/((cosec x + cotx))} dx`
`= int(cosecx cot x + cot^(2)x) dx = int(cosecx cotx +cosec^(2)x - 1) dx`.
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