Indefinite Integration of ln x

Indefinite Integration of ln x

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

Example

Find the given indefinite integral. The integral of (ln x) dx

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, uv', (ln x)⋅1 dx
is equal to,
uv, (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.