Question

How do you integrate `int re^(r/2)` by integration by parts method?

Answer 1

`intre^(r/2)dr=(2r-4)e^(r/2)+C`

Explanation:

Let `u=r` then `u'=1`
and `v'=e^(r/2)` then `v=2e^(r/2)`
`intuv'=uv-intu'v`
so `intre^(r/2)dr=2re^(r/2)-int2e^(r/2)dr`
`=2re^(r/2)-2*2e^(r/2)`
`=2re^(r/2)-4e^(r/2)+C`
`=(2r-4)e^(r/2)+C`