For an integer n 0, consider the integral I(n) = (upper bound = 1) (lower bound = 0) (ln x)^n dx.

a) Use integration by parts to express I(n) in terms of I(n 1) for n 1

b) Use induction to show that the integral (upper bound = 1) (lower bound = 0) (lnx)^n dx = (1)^nn! for all n 0.