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The integral int sec^(2//3)x cosec^(4//3...

The integral `int sec^(2//3)x cosec^(4//3)x dx` is equal to :
(Here C is a constant of integration)

A

`3 tan^(-1//3) x +C`

B

`-3 cot^(-1//3)x+C`

C

`- 3/4 tan^((-4//3)) x +C`

D

`-3 tan^(-1//3)x+C`

Text Solution

Verified by Experts

The correct Answer is:
D
`I= int sec^(2//3) x cosec x^(4//3)x dx = int (dx)/(sin^(4//5)x cos^(2//5)x) = int (sec^(2)x dx)/((tan x)^(4//3))`
`rArr I=int (d(tan x))/(tan^(4//3))=((tanx)^(1-4/3))/(1-4/3)+C=-3(tan x)^(-1//3)+C`
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