Question: Let Jn = x n e x2 /2 dx. (a) Show that J 1 = e x2/2 . (b) Prove that J n = x

Let Jn = ∫xn e−x2/2 dx.
(a) Show that J1 = −e−x2/2.
(b) Prove that Jn = −xn−1e−x2/2 + (n − 1)Jn−2.
(c) Use (a) and (b) to compute J3 and J5.

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