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#