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(sec^(8)x)/("cosec x")...

`(sec^(8)x)/("cosec x")`

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`"Let"I=int(sec^(8)x)/(cosecx)dx=int(sin x)/(cos^(8)x)dx`
`"Put"cos x=t " "therefore -sinxdx=dt`
`therefore sinx dx=-dt`
`therefore I=int (1)/(t^(8))(-dt)=-int t^(-8)dt`
`=(t^(-7))/(-7)+c=(1)/(7t^(7))+c`
`=(1)/(4cos^(7)x)+c=(1)/(7)sec^(7)x+c`
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