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Integrate the following w.r.t.x x: sec^...

Integrate the following w.r.t.x x: `sec^(n)x. tanx`

Text Solution

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Let `I=int sec^(n)x.tanx dx`
`=int sec^(n-1)x.sec x.tan x dx`
`"Put sec x=t" " "sec x.tan xdx=dt`
`therefore I=int t^(n-1)dx=(t^(n))/(n)+C`
`=(1)/(n)sec^(n)x+c`
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