of (x-1)/(x^2-2)

So the first step I did was I said that the integral of

(x-1)/(x^2-2) was less than that of (x)/(x^2-2)

So if the integral of the second function converged, then the first did as well. I couldn't figure out the integral of this one though

The integral of

(x-1)/(x^2-2) was greater than that of (x-1)/(x^2)

So if the integral of the second function diverged, then the second did as well

Then I reasoned that the limit as N approaches infinity

of the integral of (x-1)/(x^2) from two to infinity was

-1+lnN-ln0

But the ln of 0 has no value, it doesn't exist so I'm confused as to whether the integral converges or diverges. Welp?