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Let I(x) = ∫ + + dx ) 1 x tan x ( ) x tan x sec x ( x 2 2 2 . If I(0) = 0, then I ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ π 4 is equal to-

1. ) 4 ( 4 16 ) 4 ( log 2 2 e + π π + + π
2. ) 4 ( 4 16 ) 4 ( log 2 2 e + π π − + π
3. ) 4 ( 4 32 ) 4 ( log 2 2 e + π π − + π
4. ) 4 ( 4 32 ) 4 ( log 2 2 e + π π + + π

Correct answer: ) 4 ( 4 32 ) 4 ( log 2 2 e + π π − + π

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