Question

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

• A. $\ln|\tan^{-1}(x+1/x)| + C$
• B. $\tan^{-1}(x+1/x) + C$
• C. $\frac{1}{2} (\tan^{-1}(x+1/x))^2 + C$
• D. $\ln|x^4+3x^2+1| + C$

Hint:

When you see $x^2 \pm 1$ in the numerator and $x^4 + kx^2 + 1$ in the denominator, look for substitutions involving $(x \pm 1/x)$.

Answer 1

The Correct Option is A