But thats not an improper integral from what I'm seeing.

An improper integral would have -infinity or +infinity in the boundaries.

Edit: it is improper, because of the denominator being 0 at x=4 - hold on, I'll return.

There's a law for p-series, I remember, about 1/x^2 or 1/x^3 being convergent , but not 1/x because its not fast enough, if that is what you mean.

Edit 2: I graphed it, and here's my answer. Yes, it is divergent. Look at the limits.

Limit as you approach 4 from the negative (left side) is -infinity.

Limit as you approach 4 from the positive (right side) is +infinity.

Does that help?