Can someone show me how to do this one, been stuck on it all day thank you

Question

Integrate (x^2+3x+6)e^4x dx

Answer 1

you need to use integration by parts. That is just the product rule in reverse
d(uv) = u dv + v du
u dv = d(uv) - v du
∫u dv = uv - ∫v du
So, for example,
∫ x^2 e^(4x) dx
Let
u = x^2, dv = e^(4x) dx
du = 2x dx, v = 1/4 e^(4x) dx
∫x^2 e^(4x) dx = 1/4 x^2 e^(4x) - 1/2 ∫x e^(4x) dx
Then do it again to get rid of the x factor.