Integration result varying in mathematica 5.2

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SUMMARY

The integration of Log[x] in Mathematica 5.2 yields -x + x Log[x], which contrasts with the expected general solution of x ln(x) + C. This discrepancy also appears when using the DSolve command for differential equations. Users report issues with the output of Integrate[x^2 Log[x], x], where the expected result is -(x^3/9) + ((x^3/3) Log(x)), but instead receive x^2 (-x + x Log[x]). The confusion arises from the handling of constants in the integration process.

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superkan619
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indefinite integral of Log[x] comes out to be
-x + x Log[x]

but, the general solution should be
x ln(x)+C

Such things also occur when using DSolve command to solve differential equations.
Please help!
 
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superkan619 said:
indefinite integral of Log[x] comes out to be
-x + x Log[x]

but, the general solution should be
x ln(x)+C

Such things also occur when using DSolve command to solve differential equations.
Please help!

Why is that the general solution? It's derivative is ln(x)+1, not ln(x).
 
Thank you algebrat. I did some copy/paste job from y answers, but its incorrect...

The problem I actually had is this:
My book says Integrate[xˆ2 Log[x],x] will output -(x3/9)+((x3/3)Log(x))

but I am getting x2 (-x + x Log[x])
Where have the constants gone?
 

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