How do you integrate x^3e^xx3ex?

1 Answer
Apr 18, 2018

int \ x^3e^x \ dx = x^3e^x-3x^2e^x+6xe^x-6e^x+C

Explanation:

Note that:

d/(dx) (x^3e^x) = x^3e^x + 3x^2e^x

d/(dx) (-3x^2e^x) = -3x^2e^x-6xe^x

d/(dx) (6xe^x) = 6xe^x+6e^x

d/(dx) (-6e^x) = -6e^x

So:

d/(dx) (x^3e^x-3x^2e^x+6xe^x-6e^x) = x^3e^x

So:

int \ x^3e^x \ dx = x^3e^x-3x^2e^x+6xe^x-6e^x+C