If $\smallint \,\,\frac{{\sqrt x }}{{x + 1}}\,\,dx = A\,\sqrt x + B\,\,{\tan ^{ - 1}}\,\,\sqrt x + c$, then

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1

\int \,\,\frac{{\sqrt x }}{{x + 1}}\,\,dx = A\,\sqrt x + B\,\,{\tan ^{ - 1}}\,\,\sqrt x + c

, then

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Correct option: D

A = 2,\,\,B = - 2

Option D is correct because after performing the substitution and integration, the values of A and B are found to be 2 and -2 respectively.

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