Question

How do you integrate `int xe^(x/2) dx`?

Answer 1

Use integration by parts with `u = x` and `dv = e^(x/2)dx`.

Explanation:

`int xe^(x/2) dx`

Let `u = x` `" "`and `" "` `dv = e^(x/2)dx`

So `du = dx` `" "` and `" "` `v = 2e^(x/2)` `" "`(use substitution `w = x/2`)

`int xe^(x/2) dx = (x)(2e^(x/2)) - int 2e^(x/2) dx`

`= 2xe^(x/2) - 2 int e^(x/2) dx` `" "`(again use substitution `w = x/2`)

`= 2xe^(x/2) - 4e^(x/2) +C`