JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1

\int \cot ^{-1}\left(1-x+x^2-x^3+x^4-x^5+\ldots\right) d x(|x| < 1)

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Correct option: A

(x+1) \tan ^{-1}(x+1)-\log \sqrt{1+(x+1)^2}+C

Option A (

(x+1) \tan ^{-1}(x+1)-\log \sqrt{1+(x+1)^2}+C

) is correct because it is the result of integrating the given expression using integration by parts and simplifying the result.

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