Question #64963

1 Answer
Jun 7, 2017

#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#