Question

How do you integrate `int te^-t` by integration by parts method?

Answer 1

`= -e^(-t)(t+1) + C`

Explanation:

For `u, v` functions of `t`,

`int uv'dt = uv - int u'vdt`

`u(t) = t implies u'(t) = 1`

`v'(t) = e^(-t) implies v(t) = -e^(-t)`

`intte^(-t)dt = -te^(-t) + int e^(-t)dt`

`=-te^(-t) - e^(-t) + C = -e^(-t)(t+1) + C`