Another e integration: xe^ (-x^2)

x times e to the negative x squared

+∞

∫ x · e ^ (-x²) dx = / The substitution: u = - x², x d x = - du / 2

-∞

+∞

= - 1/2 · ∫ e ^ (u) du = - 1/2 · e ^ (-x²) /

- ∞

e^ (-∞) = 1 / e^ (∞)

= - 1/2 · [ 1 / e^ (∞) - 1 / e^ (∞) ] = - 1/2 · (0 - 0) = 0