Question

how do you integrate x/e^x ???

Answer 1

by parts

Answer 2

\[\int\limits x e^{-x} dx \]

Answer 3

u = x
du= dx

Answer 4

dv = e^(-x) dx --> v= -e^(-x)

Answer 5

\[= uv - \int\limits (v du) = -xe^{-x} - \int\limits (-e^{-x})(dx) \]

Answer 6

\[= -xe^{-x}-e^{-x} +C = -e^{-x}(1+x) = -\frac{1+x}{e^{x}}\]

Answer 7

+C for the last step, I forgot to carry it over.

Answer 8

thank you :)