(∫_(-∞)^(+∞)) (E^(c(((x-μ))^2)+b x + a -1)) \[DifferentialD]x

(∫_(-∞)^(+∞)) (E^(c(((x-μ))^2)+b x + a -1))x \[DifferentialD]x

(∫_(-∞)^(+∞)) (E^(c(((x-μ))^2)+b x + a -1))(((x-μ))^2) \[DifferentialD]x

Solve[{(((E^(-1+a-((b^2)/(4 c))+b μ)) (Sqrt[π]))/(Sqrt[-c]))==1,(((E^(-1+a-((b^2)/(4 c))+b μ)) (Sqrt[π]) (b-2 c μ))/(2 (((-c))^(3/2))))==μ,((((b^2)-2 c) (E^(-1+a-((b^2)/(4 c))+b μ)) (Sqrt[π]))/(4 (((-c))^(5/2))))==(σ^2)},{a,b,c}]