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Question

dx2+sin2x+cos2x equals to

A
12tan1(1+tan x2)
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B
12tan1(1+tan x2)
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C
12tan1(1tan x2)
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D
2tan1(21+tan x)
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Solution

The correct option is A 12tan1(1+tan x2)
dx2+sin2x+cos2x
Put tan x=t
I=12+2t1+t2+1t21+t2.dt1+t2
=1t2+2t+3dt=1(t+1)2+2.dt
=12tan1(t+12)+c
=12tan1(1+tan x2)+c

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