原式=∫1dt-∫3costdt+∫3cos²tdt-∫cos³tdt
=t-3sint+3/2*∫(1+cos2t)/2d2t-∫(1-sin²t)dsint
=t-3sint+3/2*(2t+sin2t)/2-(sint-sin³t/3) (0,2π)
=5π
原式=∫1dt-∫3costdt+∫3cos²tdt-∫cos³tdt
=t-3sint+3/2*∫(1+cos2t)/2d2t-∫(1-sin²t)dsint
=t-3sint+3/2*(2t+sin2t)/2-(sint-sin³t/3) (0,2π)
=5π