∫(x^3+1)(cosx)^2dx=∫(x^3+1)[(1+cos2x)/2]dx=(1/2)∫(x^3+1)dx+(1/2)∫cos2xdx+(1/2)∫x^3cos2xdx=(1/8)x^4+x/2+(1/4)sin2x+(1/4)sin2x*x^3-(1/4)3x^2sin2xdx=(1/8)x^4+x/2+(1/4)sin2x+(1/4)sin2x*x^3+(3/8)cos2x*x^2-(3/4)∫xcos2xdx=(1/8)x^4+x/2+(1/4)sin2x+(1/4)sin2x*x^3+(3/8)cos2x*x^2-(3/8)sin2x*x-(3/16)cos2x+C
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