[tex]\int (x^{2}-3x+2)e^{-x}dx = \int x^{2}e^{-x}dx-3\int x.e^{-x}dx+2\int e^{-x}dx=I+H+K[/tex]
K = [tex]2\int e^{-x}dx=-2e^{-x} + C[/tex]
đặt u=x , [tex]dv = e^{-x}[/tex]
=> du = dx , v = [tex]-e^{-x}[/tex]
=> H = [tex]3x.e^{-x}+\frac{3}{2}K=3e^{-x}(x+1)+C[/tex]
đặt [tex]u=x^{2}[/tex], [tex]dv = e^{-x}[/tex]
=> du = 2xdx , v = [tex]-e^{-x}[/tex]
=> I = [tex]-x^{2}.e^{-x}+2\int x.e^{-x}dx = -x^{2}.e^{-x}+\frac{2}{3}H=-e^{-x}(x^{2}+2x+2)+C[/tex]
=> [tex]\int f(x)= e^{-x}(-x^{2}+x-1)+C[/tex]
=> a = -1, b = 1, c = -1
Good luck