Question

`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"`

Answer 1

`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"`