Chapter 13 - Review - Review Exercises - Page 1004: 16

$\int xe^{-\frac{x^2}{2}}dx=-e^{-\frac{x^2}{2}}+C$

Substitution: $u=-\frac{x^2}{2}$ $\frac{du}{dx}=-x$ $dx=-\frac{1}{x}du$ $\int xe^{-\frac{x^2}{2}}dx=\int xe^u(-\frac{1}{x}du)=\int-e^udu=-e^u+C=-e^{-\frac{x^2}{2}}+C$