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Evaluate int(tan(pi/4 -x))/(cos^(2)x sqr...

Evaluate `int(tan(pi/4 -x))/(cos^(2)x sqrt(tan^(3)x+tan^(2) x+ tan x))dx`.

A

2

B

3

C

6

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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