Question

Question #64963

Answer 1

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

Explanation:

Using the fact that:

`d(e^x) = e^x`

we can integrate by parts:

`int x^2e^xdx = int x^2 d(e^x) = x^2e^x -int e^x d(x^2) = x^2e^x -2int xe^xdx`

The resulting integral can also be integrated by parts:

`int xe^xdx = int x d(e^x) = xe^x -int e^x dx = xe^x -e^x`

Putting it together:

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