JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Understanding +4 | -1

\int\left(\frac{f(x) g^{\prime}(x)-f^{\prime}(x) g(x)}{f(x) g(x)}\right)(\log (g(x))-\log (f(x))) d x

is equal to:

View answer and explanation

Correct option: C

\frac{1}{2}\left(\log \left(\frac{g(x)}{f(x)}\right)\right)^2+C

Option C (

\frac{{1}}{{2}}\left(\log \left(\frac{{g(x)}}{{f(x)}}\right)\right)^2+C

) is correct because it is the result of integrating the given expression after a suitable substitution.

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