Question

what is the integration of x . e ^(-x) ?

Can you please explain it :)

Thanks

Answer 1

as you know, the derivative of e^u = e^u u'

So, ∫e^u du = e^u

Here, u = -x, so du = -dx

You thus have

∫e^u (-du) = -∫e^u du = -e^u = -e^-x