求cost×cos(kt)的积分,怎么算求大神解答
答案:1 悬赏:60
解决时间 2021-03-08 06:57
- 提问者网友:星軌
- 2021-03-07 10:55
求cost×cos(kt)的积分,怎么算求大神解答
最佳答案
- 二级知识专家网友:山河有幸埋战骨
- 2021-03-07 11:53
降幂
=(1/8)∫(1+cos2t)³dt
=(1/8)∫(1+3cos2t+3cos²2t+cos³2t)dt
里面的cos²2t还需要降幂
=(1/8)∫(1+3cos2t+(3/2)(1+cos4t)+cos³2t)dt
=(1/8)∫(5/2+3cos2t+(3/2)cos4t)dt+(1/8)∫cos³2tdt
=(1/8)(5t/2+(3/2)sin2t+(3/8)sin4t)+(1/16)∫cos²2td(sin2t)
=(1/8)(5t/2+(3/2)sin2t+(3/8)sin4t)+(1/16)∫[1-sin²2t]d(sin2t)
=(1/8)(5t/2+(3/2)sin2t+(3/8)sin4t)+(1/16)[sin2t-(1/3)sin³2t]
=(1/8)∫(1+cos2t)³dt
=(1/8)∫(1+3cos2t+3cos²2t+cos³2t)dt
里面的cos²2t还需要降幂
=(1/8)∫(1+3cos2t+(3/2)(1+cos4t)+cos³2t)dt
=(1/8)∫(5/2+3cos2t+(3/2)cos4t)dt+(1/8)∫cos³2tdt
=(1/8)(5t/2+(3/2)sin2t+(3/8)sin4t)+(1/16)∫cos²2td(sin2t)
=(1/8)(5t/2+(3/2)sin2t+(3/8)sin4t)+(1/16)∫[1-sin²2t]d(sin2t)
=(1/8)(5t/2+(3/2)sin2t+(3/8)sin4t)+(1/16)[sin2t-(1/3)sin³2t]
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