∫(x^1/2)sin(x^1/2)dx

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/05/24 14:30:06

∫(x^1/2)sin(x^1/2)dx
二楼写的详细点,三楼做错拉

设x^(1/2)=t
则x=t^2,dx=2tdt
代换得2∫(t^2sint)dt
(分部积分法)
2∫(t^2sint)dt
=2[-t^2cost+∫(2tcost)dt]
=2[-t^2cost+2tsint-∫sintdt]
=2[-t^2cost+2tsint+cost]
再代换得
(x^1/2)sin(x^1/2)dx
=-2xcos√x+4√xsin√x+2cos√x.

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