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Evaluate int "cosec"^(4)x dx...

Evaluate `int "cosec"^(4)x dx`

Text Solution

Verified by Experts

The correct Answer is:
`-cot x -(cot^(3)x)/(3)+C`
`I=int "cosec"^(4)x dx=int"cosec"^(2)x " cosec"^(2)x dx`
`="cosec"^(2)x(1+cot^(2)x)dx`
`="cosec"^(2)x dx+int cot^(2)x "cosec"^(2)x dx`
` = -cot x -(cot^(3)x)/(3)+C`
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