# Indefinite Integration of ln *x*

How to find the indefinite integration of ln *x*: example and its solution.

## Example

Think ln *x* as (ln *x*)⋅1.

Then use the integration by parts.

Set *u* = ln *x* and *v*' = 1.

Write *u* = ln *x*.

Write *u*' = 1/*x*.

Derivative of ln *x*

Write *v*' = 1 next to *u*' = 1/*x*.

And write *v* = *x* next to *u* = ln *x*.

The integral of, *u**v*', (ln *x*)⋅1 *dx*

is equal to,*u**v*, (ln *x*)⋅*x*

minus the integral of, *u*'*v*, (1/*x*)⋅*x* *dx*.

So ∫ ln *x* *dx* = *x* ln *x* - *x* + *C*.

This is one of the most frequently used formulas.

So it's good to remember it.