Question:medium

\( \int \frac{x^2 - 1}{(x^4 + 3x^2 + 1)\tan^{-1}\left(x + \frac{1}{x}\right)} \, dx \) is equal to

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If derivative of inner function appears in numerator → try substitution.
Updated On: Apr 23, 2026
  • $\tan^{-1}\left(x + \frac{1}{x}\right) + C$
  • $\cot^{-1}\left(x + \frac{1}{x}\right) + C$
  • $\log\left(x + \frac{1}{x}\right) + C$
  • $\log\left[\tan^{-1}\left(x + \frac{1}{x}\right)\right] + C$
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The Correct Option is D

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