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For x 2 ≠ n π + 1, n ∈ N (the set of natural numbers), the integral ∫ + dx ) 1 – x ( 2 sin ) 1 – x sin

1. 1 – x ( 2 sin – ) 1 – x sin( 2 x 2 2 2 2 is equal to : (where c is a constant of integration)
2. log e ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ 2 1 – x sec 2 + c
3. log e ) 1 – x ( sec 2 1 2 2 + c
4. 2 1 log e ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ 2 1 – x sec 2 2 + c (4) 2 1 log e |sec(x 2 – 1) | + c

Correct answer: 1 – x ( 2 sin – ) 1 – x sin( 2 x 2 2 2 2 is equal to : (where c is a constant of integration)

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