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If int(3tan(x-(pi)/(4)))/(cos^(2)xsqrt(t...

If `int(3tan(x-(pi)/(4)))/(cos^(2)xsqrt(tan^(3)x)+tan^(2)x+tanx)=Ktan^(-1)(sqrt(tanx+1+cotx))+C,` then the value of K is

A

a) 2

B

b) 3

C

c) 6

D

d) 8

Text Solution

Verified by Experts

The correct Answer is:
C
`I=int(3(tanx-1)sec^(2)x)/((tanx+1)sqrt(tan^(2)x+tan^(2)x+tanx))dx`
Put `tan x=t`
`rArr" "I=3int(1-(1)/(t^(2)))/((t+2+(1)/(t))sqrt(t+(1)/(t)+1))dt`
`"Put "t+(1)/(t)+1=z^(2)`
`rArr" "I=3.2 tan^(-1)(sqrt(cosx+tanx+1))+C`
`rArr" "K=6`
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