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Question
`int (sec^8x)/("cosec" x) "d"x` = ______.
Options
`(sec^8x)/8 + "c"`
`(sec^7x)/7 + "c"`
`(sec^6x)/6 + "c"`
`(sec^9x)/9 + "c"`
MCQ
Fill in the Blanks
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Solution
`int (sec^8x)/("cosec" x) "d"x` = `(sec^7x)/7 + "c"`.
Explanation:
Let I = `int (sec^8x)/("cosec" x) "d"x`
= `int sinx/(cos^8x) "d"x`
= `int tanx* sec^7x "d"x`
= `int sec^6x sec x tan x "d"x`
Put sec x = t
⇒ sec x tan x dx = dt
∴ I = `int "t"^6"dt"`
= `"t"^7/7 + "c"`
= `(sec^7x)/7 + "c"`
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Integrals of Trignometric Functions
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