设y’=arctan(x一1)2,y(0)=0,求∫01y(x)dx.

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问题 设y’=arctan(x一1)2,y(0)=0,求∫01y(x)dx.

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答案01y(x)dx=xy(x)|01一∫01xaxctan(x一1)2dx =y(1)一f(x一1)arctan(x一1)2d(x一1)一∫01arctan(x一1)2dx [*]

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