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

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SUMMARY

The integral problem involving the expression \( \frac{dx}{x(5(\ln x)^2)} \) has been addressed, with specific modifications noted in the denominator. The original formula diverges from the real formula, necessitating the introduction of square roots to maintain convergence. The solution indicates that the denominator transforms from \( 5 + u^2 \) to \( (\sqrt{5})^2 + u^2 \), which incorporates \( \sqrt{5} \) in the resulting expression. This adjustment is crucial for understanding the behavior of the integral.

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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
 
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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}.
 

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