∫_{x=-∞ to ∞} ｆ’(x)ｇ(x)exp(-x^2)dx
= [ｆ(x)ｇ(x)exp(-x^2)][x=-∞ to ∞]−∫_{x=-∞ to ∞} ｆ(x){ｇ(x)exp(-x^2)}’dx
= 0 - ∫_{x=-∞ to ∞} ｆ(x)ｇ’(x)exp(-x^2)dx - ∫_{x=-∞ to ∞} ｆ(x)ｇ(x)(-2x)exp(-x^2)dx
= - ∫_{x=-∞ to ∞} ｆ(x)ｇ’(x)exp(-x^2)dx - 0