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Evaluate int((cosx)^(n-1))/((sinx)^(n+1)...

Evaluate `int((cosx)^(n-1))/((sinx)^(n+1))dx=`
(A) `-cot^n x/n+c`
(B) `-cot^n x/(n+1)+c`
(C) `cot^n x/n+c`
(D) `cot^n x/(n+1)+c`

A

`(cot^(n)x)/(n)`

B

`(-cot^(n-1)x)/(n-1)`

C

`(-cot^(n)x)/(n)`

D

`(cot^(n-1)x)/(n-1)`

Text Solution

Verified by Experts

The correct Answer is:
C
`int(cos^(n-1)x)/(sin^(n+1)x)dx=int cot^(n-1)x" cosec"^(2)xdx`
`=(-cot^(n)x)/(n)+C`
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