The integral $\int\limits_0^1 {{1 \over {{7^{\left[ {{1 \over x}} \right]}}}}dx} $, where [ . ] denotes the greatest integer function, is equal to

Question

$1 + 6{\log _e}\left( {{6 \over 7}} \right)$

$1 - 6{\log _e}\left( {{6 \over 7}} \right)$

${\log _e}\left( {{7 \over 6}} \right)$

$1 - 7{\log _e}\left( {{6 \over 7}} \right)$

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