# How do you test the improper integral int x^(-1/3) dx from (-oo, oo) and evaluate if possible?

Nov 25, 2017

It does not converge.

#### Explanation:

For any $n \ge - 1$, ${x}^{n} \ge \frac{1}{x}$ and ${\int}_{0}^{\infty} \frac{1}{x} \mathrm{dx}$ diverges.