D∫sec6xtanx dx = ______. - Mathematics

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MCQ
Fill in the Blanks

`int sec^6 x tan x   "d"x` = ______.

Options

  • `1/6 sec^6x + "c"`

  • `8 sec^8x + "c"`

  • `1/8 sec^8x + "c"`

  • `6 sec^6x + "c"`

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Solution

`int sec^6 x tan x  "d"x` = `1/8 sec^8x + "c"`.

Explanation:

`int sec^6 x tan x  "d"x = int sec^7x sec x tan x  "d"x`

Put sec x = t ⇒ sec x tan x dx = dt

∴ `int sec^8x tanx  "d"x = int"t"^7"dt" = "t"^8/8 + "c"`

= `1/8 sec^8x + "c"`

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