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How to Integrate logx

Luther Nayhm
Posted 12 years ago
This should be simple, but the solution eludes me.

When I input: Integrate[log(x),x], the output is (logx^2)/2, which is log x. When I Input: Integrate[x*log(x),x], the output is (logx^3)/3, which is also log x.

However, when I input: Intergrate[Integrate[1/x,x]],x], I get the proper answer.

I am using Mathematica 9.0. When I play with the syntax, I just get the Input back.

I am at a loss to understand what is occuring. Any help would be appreciated.
POSTED BY: Luther Nayhm
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Try Log (capital L, argument in brackets [ ] ) 
POSTED BY: Sander Huisman
Bill Simpson
Bill Simpson
Posted 12 years ago
Mathematica is fanatic about correct capitalization and use of () versus [] versus {} and = versus := versus == and there is even an ===. All those are completely different. Make any tiny error in using one of those when another was required and you will incorrect results or error messages you don't know how to interpret or even nothing at all.
In[1]:= Integrate[Log[x], x]

Out[1]= -x + x Log[x]

In[2]:= D[-x + x Log[x], x]

Out[2]= Log[x]
POSTED BY: Bill Simpson
Luther Nayhm
Luther Nayhm
Posted 12 years ago
Argggg. So simple!!! What a dunce.
POSTED BY: Luther Nayhm
Bill Simpson
Bill Simpson
Posted 12 years ago
If you had a toaster, well a toaster built before they incorporated graphical user interfaces and ip addresses and all the rest, that didn't work you would kick it down the stairs and get one that worked. But when it comes to computers people are far more likely to blame failures on themselves.

It is possible at some point in the future little things like this in Mathematica might be recognized and clearly explained with a help message, as opposed to an error message.
POSTED BY: Bill Simpson
Luther Nayhm
Luther Nayhm
Posted 12 years ago
I also meant to say "Thank you."

Unfortunately, such rigidity makes me leary of using Mathematica for complex or nested operations. It is like the olden days of batch processing and looking for syntax errors line by line. 
POSTED BY: Luther Nayhm
By the way, one could also use the free-form linguistics input, where Mathematica (enabled by Wolfram Alpha) actually figures out what was meant:
POSTED BY: Ilian Gachevski
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