# Find where an improper integral converges

-∞(dx/x2)

## The Attempt at a Solution

∫(dx/x2) = -1/x

(-1/∞) - (-1/-∞) = 0

However, the answer is that the integral diverges. Why is this the case?

The function $1/x^2$ grows infinitely large as $x \rightarrow 0$, so you have to break this into two improper integrals:
$$\int_{-\infty}^{0} dx/x^2 + \int_{0}^{\infty} dx/x^2$$
You can easily check that both of these integrals diverge to $\infty$.