Integrate the following:?

Question

y= -2x*e^x

Answer 1

∫ - 2x e^x dx =

this is a classic by parts integral:

let

e^x dx = dv → e^x = v

- 2x = u → - 2 dx = du

then, integrating, you get:

∫ u dv = u v - ∫ v du →

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

- 2x e^x + 2 ∫ e^x dx =

- 2x e^x + 2e^x + C

in conclusion,

∫ - 2x e^x dx = 2e^x (1 - x) + C

I hope it helps..

Bye!