令√(x-1)=t,那么x=t^2+1
所以原式=∫1/[(t^2+1）×t]d（t^2+1)
=∫2t/[(t^2+1）×t]dt
=∫2/(t^2+1)dt
=2×arctant +C
=2arctan[√(x-1)] +C
方法就是换元.
新春快乐!