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∫(sintcost+cos²t)dt=∫sintcostdt+∫cos²tdt=∫sintdsint+1/2∫(cos2t+1)dt=1/2sin²t+1/4∫cos2td2t+1/2t+C=1/2sin²t+1/4sin2t+1/2t+C解答完毕。