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int(dx)/((sin^(2)x-4cos^(2)x))=?...

`int(dx)/((sin^(2)x-4cos^(2)x))=?`

A

`(1)/(4)log |(tanx-2)/(tanx+2)|+C`

B

`(1)/(4)log |(tanx+2)/(tanx-2)|+C`

C

`(1)/(4)log |(1-tan x)/(1+tanx)|+C`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
On dividing Nr and Dr by `cos^(2)x`, we get
`I=int(sec^(2)x)/((tan ^(2)x-4))dx=int (dt)/((t^(2)-4)),"where"tan x=t and sec^(2)xdx=dt`
`=int (dt)/({t^(2)-2^(2)})=(1)/((2xx2))log |(t-2)/(t+2)|+c=(1)/(4)log |(tan x-2)/(tanx+2)|+C.`
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