f’(x)=arcsin(x-1)^2先求出f(x)=∫arcsin(x-1)^2dx,由于f(0)=0，f(x)=∫(0,x)arcsin(y-1)^2dy然后对f(x)进行积分：∫(0,1)f(x)dx=∫(0,1)dx∫(0,x)arcsin(y-1)^2dy(交换积分顺序）=∫(0,1)dy∫(y,1)arcsin(y-1)^2dx=∫(0,1)(1-y)arcsin(y-1)^2dy=(-1/2)∫(0,1)arcsin(y-1)^2d(y-1)^2
(用公式∫arcsinxdx)=(-1/2)[(y-1)^2arcsin(y-1)^2+√(1-(y-1)^4)] | (0,1)=(-1/2)(...
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