Does the integral ∫₁⁹ -4/∛(x-9) converge using the comparison test?

[theRukus]

Homework Statement

Does the following interval diverge?
$\int^9_1 \frac{-4}{\sqrt[3]{x-9}}$

Homework Equations

The Attempt at a Solution

Well.. I've used the following function that I think is always less than the above function to prove that the function above DOES NOT diverge (by showing that the function below converges). I'm just wondering if this is an appropriate way of telling that the function above does not diverge...

$\int^9_1 \frac{-4}{x-9}$

 

[Dick]

You don't need a comparison test. You can integrate that function. Just treat it as an improper integral. Integrate from 1 to M and let M approach 9.