integral of (1-x)e^(1-x)?

Question

how would i use integration by parts for this?

Answer 1

Int u dv = uv - Int v du
~~
Int (1 - x)e^(1 - x) dx
~
u = 1 - x
du = -dx
dv = e^(1 - x)
v = -e^(1 - x)
~
Int (1 - x)e^(1 - x) dx = -(1 - x)e^(1 - x) - Int e^(1 - x) dx
Int (1 - x)e^(1 - x) dx = (x - 1)e^(1 - x) + e^(1 - x)
Int (1 - x)e^(1 - x) dx = xe^(1 - x)

Answer 2

u = 1-x , e^(1-x)dx = dv

du = -dx , -e^(1-x) = v

v du = e^(1-x) dx

∫(1-x)e^(1-x)dx = -(1-x)e^(1-x) - ∫e^(1-x)dx
= -(1-x)e^(1-x) + e^(1-x) + C = xe^(1-x) + C