How do you integrate x^3e^xx3ex?
1 Answer
Apr 18, 2018
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