The integral $\int {{{dx} \over {\left( {1 + \sqrt x } \right)\sqrt {x - {x^2}} }}} $ is equal to : (where C is a constant of integration.)

Question

The integral $\int {{{dx} \over {\left( {1 + \sqrt x } \right)\sqrt {x - {x^2}} }}} $ is equal to :

(where C is a constant of integration.)

$ - 2\sqrt {{{1 + \sqrt x } \over {1 - \sqrt x }}} + C$

$ - 2\sqrt {{{1 - \sqrt x } \over {1 + \sqrt x }}} + C$

$ - \sqrt {{{1 - \sqrt x } \over {1 + \sqrt x }}} + C$

$2\sqrt {{{1 + \sqrt x } \over {1 - \sqrt x }}} + C$

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