Question

What is `int xsin(x-pi/2)`?

Answer 1

The answer is `=-xsinx-cosx+C`

Explanation:

The integral is

`I=intxsin(x-pi/2)dx=-intxcosxdx`

Perform the integration by parts

`intuv'=uv-intu'v`

`u=x`, `=>`, `u'=1`

`v'=cosx`, `=>`, `v=sinx`

Therefore,

`I=-xsinx+intsinxdx`

`=-xsinx-cosx+C`