How do I integrate ln(x)

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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)

Which is:

 x*ln(x)- x + c

Which is our final answer.

Tom M. A Level Further Mathematics  tutor, A Level Maths tutor, GCSE ...

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