JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Analyzing +4 | -1

\int \,\,{\left( {\log \,\,x} \right)^2}dx = x\,\,{\left[ {f\left( x \right)} \right]^2}\,\, + \,\,Ax\,\,\left[ {f\left( x \right) - 1} \right]\,\, + \,\,c

, then

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Correct option: B

f\,\left( x \right) = \log \,\,x,\,\,A = - \,2

Option B (f(x) = log x, A = -2) is correct because integrating by parts twice and comparing with the given form reveals these values for f(x) and A.

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