Question 469480
 


∫{{{x Sin(x) dx}}}


For the integrand {{{x Sin(x) }}}, integrate by parts, ∫{{{f dg}}} = {{{f g}}}- ∫{{{ g df}}}, where


{{{ f = x}}}, 


{{{dg = sin(x) dx}}},


{{{ df = dx}}}, 


{{{g = -cos(x)}}}:


∫ {{{cos(x) dx-x cos(x)}}} 


The ∫ of {{{cos(x)}}} is {{{sin(x)}}}:so,


 ∫{{{x Sin(x) dx= sin(x)-xcos(x)+constant}}}


{{{ graph( 500, 500, -6, 6, -10, 10, sin(x)-x*cos(x))) }}}