Question

Find the integral, using techniques from this or the previous chapter.
∫xex dx.

Answer 1

`xe^(x) - e^(x) +C`

Explanation:

we will solve this using integration by parts as the problem is a product of two functions which none of them are constants.

∫udv = uv -∫vdu ..............equ 1

∫
`xe^(x)`

u=x ,

du= 1

dv =
`e^(x)`

v=∫dv=
`e^(x)`

Substituting into equ 1

∫udv =
`xe^(x)` - ∫
`e^(x)dx`

∫udv =
`xe^(x)- e^(x) + C`