Question
Find the indefinite integral.
∫xe^-4xdx
∫xe^-4xdx
Answers
Steve
use integration by parts. Let
u = x, du=dx
v = e^-4x dx, v = -1/4 e^-4x
∫ udv = uv - ∫v du
so,
∫(x)(e^-4x dx0 = -1/4 xe^-4x + 1/4 ∫e^-4x dx
= -1/4 xe^-4x - 1/16 e^-4x
= -1/16 e^-4x (4x+1) + C
u = x, du=dx
v = e^-4x dx, v = -1/4 e^-4x
∫ udv = uv - ∫v du
so,
∫(x)(e^-4x dx0 = -1/4 xe^-4x + 1/4 ∫e^-4x dx
= -1/4 xe^-4x - 1/16 e^-4x
= -1/16 e^-4x (4x+1) + C