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The integral ∫ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ 1 0 x 1 dx 7 1 , where [.] denotes the greatest integer function, is equal to-

1. 1 + 6log e ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ 7 6
2. 1 – 6log e ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ 7 6
3. log e ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ 6 7
4. 1 – 7log e ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ 7 6

Correct answer: 1 + 6log e ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ 7 6

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