JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1

\int \frac{1}{(x-1)\left(x^2+1\right)} d x=

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Correct option: A

\frac{1}{2} \log (x-1)-\frac{1}{4} \log \left(x^2+1\right)-\frac{1}{2} \tan ^{-1} x+c

Option A,

\frac{1}{2} \log (x-1)-\frac{1}{4} \log (x^2+1)-\frac{1}{2} \tan ^{-1} x+c

, is the correct answer because it results from partial fraction decomposition and integration of the given expression.

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