∫(0,3) xf(x-1)dx
题目
∫(0,3) xf(x-1)dx
f(x)=1/x^2 -1
答案
∫(0,3) xf(x-1)dx
=∫[0,2] x/(x-1)^2dx+∫[2,3] x/xdx
前面一项,令x-1=t,dx=dt,x=t+1,x=0,t=-1,x=2,t=1
=∫[-1,1] (t+1)/t^2dt+∫[2,3] x/xdx
=∫[-1,1] (1/t+1/t^2)dt+∫[2,3] x/xdx
第一项没意义?
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