Question #64963

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Answer 1 · 2017-06-07T08:35:53

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

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:

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