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This is an integral many people struggle with, but, with a simple trick it becomes a little more straight forward. We will approach this integral using integration by parts.
But what are the parts?
Well, we can write ln(x) as 1*ln(x).
We choose u=ln(x) and dv=1, so du=1/x and v=x
So the integral ln(x) becomes:
x*ln(x) – integral(x/x)
x*ln(x)- x + c
Which is our final answer.see more