JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Analyzing +4 | -1

\int \,\,\log \,\,\left( {\sqrt {1 - x} \,\, + \,\,\sqrt {1 + x} } \right)dx = x\,\;f\left( x \right) + Ax + B\,\,{\sin ^{ - 1}}x + C

, then

View answer and explanation

Correct option: A

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

Option A (

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

) is correct because after integrating by parts, the function f(x) matches this logarithmic expression.

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