Question

`int (sec^8x)/("cosec" x)  "d"x` = ______.

पर्याय

• `(sec^8x)/8 + "c"`

• `(sec^7x)/7 + "c"`

• `(sec^6x)/6 + "c"`

• `(sec^9x)/9 + "c"`

Answer 1

`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"`