JEE Main 201610 Apr, Morning shiftMathematicsMediumIntegral Calculus369× since 2002The integral ∫dx(1+x)x−x2\int {{{dx} \over {\left( {1 + \sqrt x } \right)\sqrt {x - {x^2}} }}}∫(1+x)x−x2dx is equal to : (where C is a constant of integration.)AOption A. −21+x1−x+C- 2\sqrt {{{1 + \sqrt x } \over {1 - \sqrt x }}} + C−21−x1+x+CBOption B. −21−x1+x+C- 2\sqrt {{{1 - \sqrt x } \over {1 + \sqrt x }}} + C−21+x1−x+CCOption C. −1−x1+x+C- \sqrt {{{1 - \sqrt x } \over {1 + \sqrt x }}} + C−1+x1−x+CDOption D. 21+x1−x+C2\sqrt {{{1 + \sqrt x } \over {1 - \sqrt x }}} + C21−x1+x+CCheckSkip · show solution
