Question

How do you integrate `int xcosx` by integration by parts method?

Answer 1

`int xcosx dx = xsinx + cosx +C`

Explanation:

Integration by parts tell us : `int f(x)g'(x) dx = f(x)g(x) - int f'(x)g(x) dx`

In this example
`f(x) = x` and `g'(x) = cosx -> g(x) = sinx`

Therefore, using integration by parts:
`int xcosx dx = xsinx - int 1 * sinx dx`

`= xsinx + cosx + C`