Can the Definite Integral of (ln x)^n be Expressed Using Factorials?

[razorfever]

Homework Statement

Show that the definite integral from 0 to 1 (ln x)^n dx = n!(-1)^n

Homework Equations

The Attempt at a Solution

i tried to integrate by parts and kept going on and on but i don't know how to incorporate the factorial in the answer ...

 

[rock.freak667]

When you integrated by parts, what did you get?

 

[Gib Z]

Rather than integrating by parts repeatedly, it may be simpler to try to use induction to show this result. You only need to integrate by parts once if you do that, so it may be easier for you to see your answer.