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Evaluate-x-cos-2-x-dx-




Question Number 40 by user3 last updated on 25/Jan/15
Evaluate   ∫x cos^2 x dx.
Evaluatexcos2xdx.
Answered by user3 last updated on 03/Nov/14
∫x cos^2 x dx =∫x(((1+cos 2x)/2))dx  =(1/2)∫x dx+(1/2)∫x cos 2x dx  =(x^2 /4)+(1/2)∙[x∙∫cos 2x dx−∫{(d/dx)(x)∙∫cos 2x dx}dx]  =(x^2 /4)+(1/2)[((x sin 2x)/2) −∫ ((sin 2x )/2)dx]  =(x^2 /4) + ((x sin 2x)/4) − (1/4)×(((−cos 2x))/2)+C  =(x^2 /4) + ((x sin 2x)/4) + ((cos 2x)/8)+C
xcos2xdx=x(1+cos2x2)dx=12xdx+12xcos2xdx=x24+12[xcos2xdx{ddx(x)cos2xdx}dx]=x24+12[xsin2x2sin2x2dx]=x24+xsin2x414×(cos2x)2+C=x24+xsin2x4+cos2x8+C