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-∫01xarctan(x-1)2dx =y(1)-∫01(x-1)arctan(x-1)2d(x-1)-∫01arctan(x-1)2dx =[*]∫01arctan(x-1)2d(x-1)2=[*]∫01arctantdt [*]

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