Question

The value of $\int \frac{x^2 - 1}{(x^4 + 3x^2 + 1) \tan^{-1}(x + \frac{1}{x})} dx$ is:

• A. $\log | \tan^{-1}(x + 1/x) | + C$
• B. $\tan^{-1}(x + 1/x) + C$
• C. $\log(x + 1/x) + C$
• D. None of these

Hint:

For integrals with $x^4$ and $x^2$ terms, dividing by $x^2$ often reveals a $x \pm 1/x$ substitution.

Answer 1

The Correct Option is A