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∫[上限为1,下限为0] (e^x2)(x-x^3)dx
这是我第3次问这条问题啦~请各位大虾不要跳步 不要简写 请一步一步写出结果````我天资愚钝 跳步我是看不明D
人气:236 ℃ 时间:2020-06-19 17:12:25
解答
∫xe^(x^2)dx
=(1/2)∫e^(x^2)dx^2
=(1/2)e^(x^2)
∫x^3e^(x^2)dx
=(1/2)∫x^2e^(x^2)dx^2
=(1/2)∫x^2de^(x^2)
=(1/2)x^2e^(x^2)-(1/2)∫e^(x^2)dx^2
=(1/2)x^2e^(x^2)-(1/2)e^(x^2)
所以原式=∫xe^(x^2)dx-∫x^3e^(x^2)dx
=(1/2)e^(x^2)-(1/2)x^2e^(x^2)+(1/2)e^(x^2)
=e^(x^2)-(1/2)x^2e^(x^2)(0到1)
=(e-e/2)-(1-0)
=e/2-1
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