What is the antiderivative of F(x) = xcosx?

1 Answer
Apr 27, 2016

intxcosxdx = xsinx+cosx+C

Explanation:

For this problem, we will use the integration by parts formula

intudv = uv-intvdu

along with the following:

  • d/dxx = 1
  • d/dxsinx = cosx
  • intsinxdx = -cosx+C

Let u = x and dv = cosxdx
Then du = dx and v = sinx

Applying the formula, we have

intxcosxdx = xsinx - intsinxdx

=xsinx - (-cosx)+C

=xsinx+cosx+C


Checking our answer, we find that d/dx(xsinx+cosx+C)=xcosx