∫x*(cos^2x)dx
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∫x*(cos^2x)dx
![∫x*(cos^2x)dx](/uploads/image/z/18306382-22-2.jpg?t=%E2%88%ABx%2A%28cos%5E2x%29dx)
分步积分吧
∫x*(cos^2x)dx
=1/2∫x*(1+cos2x)dx
=1/4x^2+1/2∫x*cos2xdx
=1/4x^2+1/4∫x*dsin2x
=1/4x^2+1/4x*sin2x-1/4∫sin2xdx
=1/4x^2+1/4x*sin2x+1/8cos2x+C
∫x*(cos^2x)dx
=1/2∫x*(1+cos2x)dx
=1/4x^2+1/2∫x*cos2xdx
=1/4x^2+1/4∫x*dsin2x
=1/4x^2+1/4x*sin2x-1/4∫sin2xdx
=1/4x^2+1/4x*sin2x+1/8cos2x+C