Use the Comparison Theorem to determine whether the integral is convergent or divergent.

I can easily see that:

$\displaystyle \frac{1}{x \cos{x}} \leq \frac{1}{x}$ on $\displaystyle 0 to \frac{\pi}{2}$

But I also know that $\displaystyle \int_0^{\frac{\pi}{2}}\frac{1}{x}dx$ is divergent because $\displaystyle \ln{0} = -\infty$

So, that substitution doesn't tell me anything about my original integral. Can anyone suggest another substitution that might help me?

Thanks.