How do you integrate int xsin(2x) by integration by parts method?

1 Answer
Aug 8, 2016

=1/4sin(2x) - x/2cos(2x) + C

Explanation:

For u(x), v(x)

int uv'dx = uv ' - int u'vdx

u(x) = x implies u'(x) = 1

v'(x) = sin(2x) implies v(x) = -1/2cos(2x)

intxsin(2x)dx = -x/2cos(2x) +1/2intcos(2x)dx

= -x/2cos(2x)+1/4sin(2x)+C