ʃ x cos 2x dx ?

Question

please help me answer the question with the way to solve it thanks!

Answer 1

qn: ∫x.cos(2x) dx

using integretion by parts

let............ u = x.............. du/dx = 1 ................. dv = cos(2x) dx.................. v = 1/2sin2x

 ∫x.cos(2x) dx = 1/2x.sin(2x) - 1/2∫sin(2x) dx

 ∫x.cos(2x) dx =1/2xsin(2x) + 1/4cos(2x) + c

Answer 2

Given ∫xcos(2x) dx

let.. u = x

du/dx = 1

dv/dx = cos(2x)

∫dv = ∫cos(2x) dx

v = 1/2sin(2x)

∫xcos(2x) dx = xsin(2x)/2 - ∫sin(2x)/2 dx

 ∫xcos(2x) dx=xsin(2x)/2 + cos(2x)/4