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The integral int(sec^2x)/((secx+tanx)^(9...

The integral `int(sec^2x)/((secx+tanx)^(9/2))dx` equals (for some arbitrary constant `K)dot` `-1/((secx+tanx)^((11)/2)){1/(11)-1/7(secx+tanx)^2}+K` `1/((secx+tanx)^(1/(11))){1/(11)-1/7(secx+tanx)^2}+K` `-1/((secx+tanx)^((11)/2)){1/(11)+1/7(secx+tanx)^2}+K` `1/((secx+tanx)^((11)/2)){1/(11)+1/7(secx+tanx)^2}+K`

A

`(-1)/((sec x + tan x)^(11//2)){(1)/(11)-1/7 (sec x + tan x)^(2)}+K`

B

`(1)/((sec x + tan x)^(11//2)){(1)/(11)-1/7 (sec x + tan x)^(2)}+K`

C

`(-1)/((sec x + tan x)^(11//2)){(1)/(11)+1/7 (sec x + tan x)^(2)}+K`

D

`(1)/((sec x + tan x)^(11//2)){(1)/(11)+1/7 (sec x + tan x)^(2)}+K`

Text Solution

Verified by Experts

The correct Answer is:
C
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The integral int (sec^2x)/(secx+tanx)^(9/2)dx equals to (for some arbitrary constant K ) (A) -1/(secx+tanx)^(11/2){1/11-1/7(secx+tanx)^2}+K (B) 1/(secx+tanx)^(11/2){1/11-1/7(secx+tanx)^2}+K (C) -1/(secx+tanx)^(11/2){1/11+1/7(secx+tanx)^2}+K (D) 1/(secx+tanx)^(11/2){1/11+1/7(secx+tanx)^2}+K

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