An Integral problem with x,lnx with progress done [ check it]

[Riazy]

An Integral problem with x,lnx with progress done [please check it]

QUESTION: How and what was changed from the original formula?
Whats up with all the Sqrts above the 5:s
Is this some kind of compensation because the current formula
diverge from the Real formula? How was it done?

Homework Statement

$dx/x(5*(lnx)^2), See a detailed scanned paper below

Homework Equations

You can find everything on the scanned paper below

The Attempt at a Solution

Yes The problem is solved already, but I have questions on why certain things are like they are. See the scanned paper. Thanks

Scanned Solution [PLAIN]http://img146.imageshack.us/img146/3544/kaat001.jpg

 

[slider142]

The formula says that when the denominator is a² + x², the resulting expression uses a. The original expression has $5 + u^2 = (\sqrt{5})^2 + u^2$ in the denominator, so the resulting expression uses $\sqrt{5}$.