8. 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 di¤erentiation.)

(a)

Ð 10 0 xmex dx for positive integer m (Hint: Implement two or three integration by parts steps and observe the pattern.)

(b)

Ð 20 3 xmex2 dx for positive odd integer m ¼ 2n þ 1 (Hint: Implement two or three integration by parts steps and observe the pattern, using xex2 .)