(1)Find real numbers $\displaystyle a,b,c\text{ such that they minimize the following integration }:$

$\displaystyle \int_0^\infty \left|x^3-a-bx-cx^2\right|^2e^{-x}dx$

(2)Find real numbers $\displaystyle a,b,c\text{ such that they minimize the following integration }:$

$\displaystyle \int_0^\infty \left|x^3-a-bx-cx^2\right|e^{-x}dx$ .

The first problem is easier than the second one. If somebody posts the elaborate correct solution for the second one, I will be very appreciate!