You probably know that converges if . So you want to estimate the power of x in the denominator of that fraction, as . The first factor is , the second one is also approximately (because |x–5| will have the same order of magnitude as x, when x is large). Similarly, the third factor is approximately . So the integrand is approximately .

Since –61/60 < –1, you should conclude that the integral converges on the interval , and you prove it by comparing it with .