The value of $\int \frac{\log x}{(x+1)^2} d x$ is

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1

The value of

\int \frac{\log x}{(x+1)^2} d x

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Correct option: A

\frac{-\log x}{x+1}+\log x-\log (x+1)

\frac{-\log x}{x+1}+\log x-\log (x+1)

Option A is correct because the integral of log(x)/(x+1)² dx is found using integration by parts, resulting in -log(x)/(x+1) + log(x) - log(x+1) + c.

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