Someone please integrate this!!!?

Question

integrate: (x^2)(e^x)dx

please show the steps....ty

Answer 1

By parts. We know, ∫ u dv = uv - ∫ v du.

Let u = x^2, and dv = e^x dx. Then, du = 2x dx and v = e^x, and we have,

∫ x^2 e^x dx = x^2 e^x - 2 ∫ x e^x dx

Now, repeat this procedure on x e^x dx to give:

∫ x e^x dx = x e^x - ∫ e^x dx = x e^x - e^x

Finally,

∫ x^2 e^x dx = x^2 e^x - 2x e^x + 2e^x = e^x(x^2 - 2x + 2)