Solving a Stubborn Integral Problem

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SUMMARY

The integral problem discussed involves the expression that yields a result differing by a constant of -2 ln(2) when compared to the output from Wolfram Alpha. The user attempted to solve the integral but encountered a discrepancy regarding the appearance of the extra 2 in the logarithmic result. The discussion highlights the logarithmic identity ln(a · b) = ln(a) + ln(b) as a key concept in understanding the solution. It is noted that Wolfram Alpha or Mathematica employs a different method that naturally incorporates this constant into the logarithmic term.

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Homework Statement


I have to integrate

[PLAIN]http://img69.imageshack.us/img69/4259/integral1.gif

The Attempt at a Solution



This is how I did it

[PLAIN]http://img338.imageshack.us/img338/5508/integral12.gif

wolfram says it is supposed to turnout like this

[PLAIN]http://img690.imageshack.us/img690/1462/integral13.gif

Where does the extra 2 in the log come from?

Thanks
 
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The answers are actually the same, up to a constant -2 ln(2).

With logarithms this is always tricky, because they satisfy
\ln(a \cdot b) = \ln(a) + \ln(b)

Apparently Wolfram Alpha / Mathematica uses some other method to calculate the integral in which the 2 inside the log appear naturally.
 

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