# Testing for convergence. (Improper Integral)

How can I test this integral or convergence:

$$\int_1^\infty \frac{2x-1}{\sqrt{x^5 + 2x - 2}} dx$$

I'm trying to find integral of higher function and in result i get divergence, so I cant use this information.

First, $x^5+2x-2>0$ for $x\geq 1$ so we do not need to worry about infinite discontinuity of the integrand within the interval of integration. Next, noting that the numerator is of degree 1 and the denominator of degree $\frac{5}{2}$, we compare the integrand with $x^{-3/2}$ and apply the limit comparison test.