yima1010
幼苗
共回答了16个问题采纳率：87.5% 举报
设√[(x-1)/x]=t
则x=1/(1-t²),dx=2tdt/(1-t²)²
且,当x=1时,t=0
当x=3/2时,t=1/√3
故 原式=∫(0,1/√3)[2t/(1-t²)²]/[t/(1-t²)]dt
=∫(0,1/√3)[2/(1-t²)]dt
=∫(0,1/√3)[1/(1+t)+1/(1-t)]dt
=[ln(1+t)-ln(1-t)]│(0,1/√3)
=ln(1+1/√3)-ln(1-1/√3)
=ln(2+√3).
1年前
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