Since x e x 2 {\displaystyle xe^{x^{2}}} is an odd function, i.e.,
f ( x ) = x e x 2 = − ( − x ) e ( − x ) 2 = − f ( − x ) {\displaystyle f(x)=xe^{x^{2}}=-(-x)e^{(-x)^{2}}=-f(-x)} ,
we have ∫ − 2 2 x e x 2 d x = 0 {\displaystyle \int _{-2}^{2}xe^{x^{2}}dx=0} .
is an odd function, i.e.,
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