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int(1)/(sin^(2)x+2sin x cos x +5 cos^(2)...

`int(1)/(sin^(2)x+2sin x cos x +5 cos^(2)x)dx=`

A

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

B

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

C

`(1)/(sqrt(2)) tan^(-1) [ (tan x + 1)/(sqrt(2)) ] + C `

D

`(1)/(2) tan^(-1) [ (tan x + 1)/(2) ] + C `

Text Solution

Verified by Experts

The correct Answer is:
D
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