I think this solution can be used as a prove, but maybe there is an easier way?

And I repeat the question: Why Wikipedia uses incomplete formula?

]]>Starting from here:

Let

Then:

We have a formula #24 in the table of integrals in the textbook:

So:

And here we have first limit is infinity divided by infinity, second limit is infinity and a constant.

Therefore we have an infinity in the final answer...

Did I make any mistakes?]]>

I would have tried the simple numerical method type sub of u = 1 / x in the beginning.

]]>Now I wonder myself where did I got u^6 Thanks.

Now I am not sure what to do next?]]>

According to my calculations it is finite. I suspect I have a mistake, but I cannot find it. Please help:

Surface area is:

Here we have a=1, b=\infty, and f(x)=1/x

Since one of the bounds is infinity, we have an improper integral and have to do it with a limit:

Looking at the description of Gabriel's Horn in Wikipedia, I see that they used for the surface a function:

Why is that? How did they manage to convert into 1?]]>