QuestionEvaluate the integral $\int x e^{-x^{2}} \, dx$.

Studdy Solution
Substitute $u = x^2$ back into the integral to get the final answer.
$$-\frac{1}{2} e^{-x^2} + C$$So, the integral $\int x e^{-x^{2}} d x$ equals $-\frac{1}{2} e^{-x^2} + C$.