Calculate an expression for the int from 1 to e of (ln(x))^k dx in terms of the integral from 1 to e of (ln(x))^k-1 dx.

essentially, I need to integrate by parts to get this equality:

The integral from 1 to e of (ln(x))^k dx= (e-k) times(integral from 1 to e of (ln(x))^k-1 dx.

Then I will take the value of the original integral with k=1 to help me form a table of values for a series of k's.

I get close, but can't get there. Anyone able to help?

## Comments

fractionalderivative, e.g., the 1/2-th derivative of ln(x). Strange and beautiful.