Question

Question #5a569

Answer 1

`int x^3e^xdx = e^x(x^3 -3x^2+6x-6)`

Explanation:

You can calculate the integral by parts iteratively:

`int x^3e^xdx= int x^3 d(e^x) = x^3e^x-int 3x^2e^xdx`

`int x^2e^xdx = x^2e^x-2 int xe^xdx`

`int xe^xdx= xe^x - int e^xdx = e^x(x-1)`

Putting it all together:

`int x^3e^xdx = e^x(x^3 -3x^2+6x-6)`