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Obtain reduction formula for I(n) =in...

Obtain reduction formula for
`I_(n) =int cosec ^(n) x dx, n` being a positive integer, `nge 2` and deduce the value of `int cosec ^(5) x dx.`

A

`-("cosec"^(3) x cot x)/(4)-(3"cosec"x cot x)/(8)+(3)/(8)log |"cosec" x-cot x|+c`

B

`("cosec"^(3) x cot x)/(4)+(3"cosec"x cot x)/(8)-(3)/(8)log |"cosec" x-cot x|+c`

C

`-("cosec"^(3) x cot x)/(4)-(2"cosec"x cot x)/(8)+ (3)/(8)log |"cosec" x-cot x|+c`

D

`-("cosec"^(3) x cot x)/(4)+(2"cosec"x cot x)/(8)- (3)/(8)log |"cosec" x-cot x|+c`

Text Solution

Verified by Experts

The correct Answer is:
A
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