Question

What is the antiderivative of `(x-2)sinx`?

Answer 1

`= - (x-2) cos x + sin x + C`

Explanation:

do an IBP

`int (x-2) sin x dx`

`= int (x-2) d/dx (- cos x) dx + C`

`= (x-2) (- cos x) - int d/dx (x-2) (- cos x) dx + C`

`= - (x-2) cos x + int cos x dx + C`

`= - (x-2) cos x + sin x + C`