Integration of ln x

How to find Integration of ln x ?
We use Integration by parts to find the integration of ln x.
Example 1. Evaluate
Solution
Multiply 1 by ln x to make it product of functions, so that we could use Integration by Parts formula

Here,

Now using Integration by Parts formula

We have,

Answer

Example 2. Evaluate
Solution
NOTE: We always take ln as first function, so

Now here,

Now using Integration by Parts formula

We have,

Answer

Integration by Parts
Integration by Parts of Exponential Functions