The value of the integral $\int\limits_0^1 {{{\sqrt x dx} \over {(1 + x)(1 + 3x)(3 + x)}}} $ is :

Question

${\pi \over 8}\left( {1 - {{\sqrt 3 } \over 2}} \right)$

${\pi \over 4}\left( {1 - {{\sqrt 3 } \over 6}} \right)$

${\pi \over 8}\left( {1 - {{\sqrt 3 } \over 6}} \right)$

${\pi \over 4}\left( {1 - {{\sqrt 3 } \over 2}} \right)$

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