A student has to find the indefinite integral $\displaystyle \int \frac{x^2 - 1}{x^4 + 5x^2 + 1}\,dx, \qquad x > 0.$ The denominator does not factor into real quadratics with rational coefficients, so partial fractions would be slow. There is a faster way. Divide the numerator and the denominator by $x^2$, and look for a new variable whose derivative is exactly the new numerator. Then write the new denominator in terms of that variable; take care with the square of the new variable, because it does not give back $x^2 + \dfrac{1}{x^2}$ on its own. In each option below, $C$ is an arbitrary constant. Which of the following is the integral?