Question

Primitive of (x+1)e^x​

Answer 1

`\int{(x+1)e^x} dx`

Integrate by parts:
`\int{fg'} = fg - \int{f'g}`, where
`f = x+1`,
`g' = e^x`,
`f' = 1` and
`g = e^x`

`\int{(x + 1)e^x} dx = (x+1)e^x - \int{e^x} dx\\= (x + 1)e^x - e^x + C = xe^x + C`