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Question 330006
JEE Mathematics · Medium

Indefinite Integration: Partial fractions MCQ

Solve this quality-checked JEE multiple-choice question, then review the correct answer and explanation.

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Partial fractionsMediumQuestion 330006

Question

∫1/(x²−1) dx using partial fractions gives:
  1. A
    (1/2)ln|(x−1)/(x+1)| + C
    Correct
  2. B
    ln|x²−1| + C
  3. C
    1/(x²−1) + C
  4. D
    (1/2)ln|x+1|/(x−1)| + C

Correct answer

(1/2)ln|(x−1)/(x+1)| + C

Explanation

1/(x²−1) = 1/((x−1)(x+1)) = (1/2)[1/(x−1) − 1/(x+1)]. Integrating: (1/2)[ln|x−1| − ln|x+1|] = (1/2)ln|(x−1)/(x+1)| + C.

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