How do I integrate ln(x), using integration by parts?

This is a common question among A-Level Maths students, as integration by parts requires 2 things: 1. Something to integrate ; 2. Something to differentiate. In ln(x), we can immediately see that ln(x) is the 'something' that we differentiate. But what about the 'something' to integrate? Here, we have to put our creative mathematical hats on, and imagine a constant '1' behind the ln(x), so imagine it written as 1 x ln(X). Aha! Now we have the 'something' to integrate, which is the constant '1'. After clarifying this issue, the rest of the solution just requires the implementation of the integration by parts technique, which I'll happily demonstrate in the live session!

MK
Answered by Mustafa K. Maths tutor

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