1. anyone who believes that sqrt(x^2) is |x| is mistaken. As Bill Page says, there are two values. 2. any system that automatically produces |x| can be tricked into committing serious errors. Currently, Maxima apparently does this. Some people consider this a feature. Clearly we have a difference of opinion about sqrt. Mathematica leaves the expression unchanged. 3. I tried Maxima 5.23.2 on the integral and got log(-1) which is nonsense. 4. Mathematica 9 answers ln(2).
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