Question

How do you find the integral of `f(x)=xe^-x` using integration by parts?

Answer 1

`-e^(-x)(x+1)+c`

Explanation:

`int xe^(-x)`
`=x inte^(-x)dx-int [d/(dx)x*inte^(-x)dx]dx`
`=-xe^(-x)-int [1*(-e^(-x))]dx`
`=-xe^(-x)+int [e^(-x)]dx`
`=-xe^(-x)-e^(-x)+c`
`=-e^(-x)(x+1)+c`