27. Evaluate the following definite integrals using integration by parts, and then identify an antiderivative of the integrand (General hint: Once a potential antiderivative is found, this formula can be verified by induction on n:):

(a)

Ð 20 0 xnerx dx for positive integer n, positive real r

(b)

Ð 10 0 xnex2 dx for positive integer odd n ¼ 2m þ 1