$\frac{x}{x^2+1} \phi(x) < 1 - \Phi(x) < \frac{1}{x} \phi(x)$

$\frac{1}{x^2+1} \phi(x) < 1 - \Phi(x) < \frac{1}{x^2} \phi(x)$

$\frac{x}{x+1} \phi(x) < 1 - \Phi(x) < \frac{1}{x} \phi(x)$

$\frac{x^2}{x^2+1} \phi(x) < 1 - \Phi(x) < x \phi(x)$