Question

不定积分 ：∫ xcos^2 xdx

Answer 1

cos^2 x=(cos2x+1)/2

∫ xcos^2 xdx =∫ x(cos2x+1)dx/2+C=(∫xcos2xdx+∫xdx)/2+C=(∫xdsin2x+x^2)/4+C

=(xsin2x-∫sin2xdx+x^2)/4+C=(2xsin2x+cos2x+2x^2)/8+C