Question 411547
To differentiate {{{x*cos(x)}}}, use the product rule:


{{{(d/dx)x*cos(x) = cos(x) - x*sin(x)}}}.


To integrate {{{int(x*cos(x), dx)}}}, use integration by parts. Let {{{u = x}}}, {{{dv = cos(x)dx}}}. Then, {{{du = dx}}} and {{{v = sin(x)}}}. Hence,


{{{int(x*cos(x), dx) = x*sin(x) - int(sin(x)dx)}}}


{{{int(x*cos(x), dx) = x*sin(x) + cos(x) + C}}} where C is any constant.