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The integral $\begin{align*} \int \frac{dx}{(1+\sqrt x) \sqrt{x - x^2}} \end{align*}$ to :
(where C is a constant of integration.)

$\begin{array}{11}(1)\; -2\sqrt{\frac{1+\sqrt x}{1- \sqrt x}} + C \\(2)\; \; -2\sqrt{\frac{1-\sqrt x}{1+\sqrt x}} + C \\ (3) \; \; -\sqrt{\frac{1-\sqrt x}{1+ \sqrt x}} + C \\ (4)\; \; 2\sqrt{\frac{1+\sqrt x}{1- \sqrt x}} + C \end{array} $

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