JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Understanding +4 | -1

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

is equal to

View answer and explanation

Correct option: B

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

Option B is correct because the integral simplifies to a form where the substitution

u = \log_e \frac{{g(x)}}{{f(x)}}

can be used, resulting in

\frac{1}{2}u^2 + C

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