If $\int {{{\sin }^{ - 1}}\left( {\sqrt {\frac{x}{{1 + x}}} } \right)dx\, = \,A(x)\,{{\tan }^{ - 1}}\left( {\sqrt x } \right)\, + \,B\,(x)\, + \,C,\,{\rm{where}}\,C} $ is a constant of integration, then the ordered pair $\left( {A(x),\,B\,(x)} \right)$ can be

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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\int {{{\sin }^{ - 1}}\left( {\sqrt {\frac{x}{{1 + x}}} } \right)dx\, = \,A(x)\,{{\tan }^{ - 1}}\left( {\sqrt x } \right)\, + \,B\,(x)\, + \,C,\,\mathrm{where}\,C}

is a constant of integration, then the ordered pair

\left( {A(x),\,B\,(x)} \right)

can be

View answer and explanation

Correct option: C

\left( {x + 1,\, - \sqrt x } \right)

Option C (

\left( {x + 1,\, - \sqrt x } \right)

) is correct because after evaluating the integral using trigonometric substitution and integration by parts, the result matches the given form with A(x) = x+1 and B(x) = -

\sqrt{x}

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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