Evaluate 􏰍 (ln x)ndx where n is a whole number and x > 0.

Question

Evaluate 􏰍 (ln x)ndx where n is a whole number and x > 0.

show all work please

Answer 1

Your notation is unclear.

If you mean ∫lnⁿx dx, I would suggest that you make the substitution, y=ln x, then dx becomes

e^ydy and your integral becomes ∫yⁿe^y dy for which there is a reduction formula, which starts with integration by parts.