int cosec^(3)x dx...

`int cosec^(3)x dx`

Verified by Experts

The correct Answer is:

`I = -1/2 cosec x cot x + 1/2 log|tan (x/2)|+k`

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INTEGRATION BY PARTS
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We can derive different reduction formulas by using integration by parts. If int cosec^(n)x dx=(-cosec^(n-2)x cotx)/(n-1)+A int cosec^(n-2)x dx , then A is equal to-

`(1)/(n-2)`

`(n)/(n-2)`

`(n-1)/(n-2)`

`(n-2)/(n-1)`

`-cot x-(1)/(3) cot^(3) x+c`

`cot x+(1)/(3)cot^(3)x+c`

`tan x+(1)/(3) tan^(3)x+c`

`-cot x+(1)/(3) cot^(3)x+c`

`-cotx + 1/3 cot^(3) x + c`

`cot x + 1/3 cot^(3) x + c`

`cot x - 1/3 cot^(3)x + c`

`-(cotx + 1/3 cot^(3)x) +c`