JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Analyzing +4 | -1

\lim \limits_{{x \rightarrow 0}} \frac{f(x)}{x^2}

exists finitely and

\lim \limits_{{x \rightarrow 0}}\left(1+x+\frac{f(x)}{x}\right)^{1 / x}=e^3

, then

\int f(x) \log _e x d x

is equal to

View answer and explanation

Correct option: A

\frac{2}{3} x^3\left(\log _e x-\frac{1}{3}\right)+c

Option A is correct because after evaluating the limit and integrating, the result matches the given expression

\frac{2}{3} x^3(\log _e x-\frac{1}{3})+c

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