设f(X)的导数=arctan(x-1)^2,f(0)=0,求不定积分（0,1）f(X)dx求详解

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设f(X)的导数=arctan(x-1)^2,f(0)=0,求不定积分（0,1）f(X)dx求详解
设f(X)的导数=arctan(x-1)^2,f(0)=0,求不定积分（0,1）f(X)dx求详解

设f(X)的导数=arctan(x-1)^2,f(0)=0,求不定积分（0,1）f(X)dx求详解
∫（0,1）f(X)dx
= ∫（0,1）f(X)d(x-1)
=(x-1)f(x)|(0,1) - ∫（0,1）(x-1)f‘(X)dx
= - ∫（0,1）(x-1)arctan(x-1)^2dx (u=(x-1)^2
=(1/2) ∫（0,1）arctanudu
=(1/2)(uarctanu|（0,1)-∫（0,1)u^2/(1+u^2)du)
=(1/2)(uarctanu-u+arctanu)|（0,1)
=(1/2)(π/2-1)

宁波富达北方大部分

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