JEE Advance - Mathematics (1985 - No. 34)
Evaluate the following $$\int {\sqrt {{{1 - \sqrt x } \over {1 + \sqrt x }}dx} } $$
$$2\sqrt {1 - x} + {\cos ^{ - 1}}\sqrt x + \sqrt x \sqrt {1 - x} + C$$
$$- 2\sqrt {1 - x} - {\cos ^{ - 1}}\sqrt x + \sqrt x \sqrt {1 - x} + C$$
$$- 2\sqrt {1 - x} + {\sin ^{ - 1}}\sqrt x + \sqrt x \sqrt {1 - x} + C$$
$$ - 2\sqrt {1 - x} + {\cos ^{ - 1}}\sqrt x + \sqrt x \sqrt {1 - x} + C$$
$$ - 2\sqrt {1 + x} + {\cos ^{ - 1}}\sqrt x + \sqrt x \sqrt {1 - x} + C$$