How do you intergrate ln(x)?

There's a nice trick here you can do, treat the equation as 1*ln(x) then intergrate by parts.

Differentiating ln(x) gives 1/x, while intergrating 1 gives x

So your left with a much easier intergration

x*ln(x)-(Intergral sign)x* 1/x dx

which is simply x*ln(x)-x

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