Question

How do you integrate `x^2 e^-x`?

Answer 1

It is

`int x^2*e^-xdx=-e^-x*x^2+int e^-x2xdx=-x^2*e^-x-2x*e^-x+2*int e^-xdx=-e^-x*(x^2+2x+2)+c`

We used integration by parts

`int f'(x)*g(x)dx=f(x)*g(x)-intf(x)*g'(x)dx`