∫dx / [x*(x^2-1)^1/2]
=∫dx / [x^2*(1-1/x^2)^1/2]
= -∫d(1/x) / [(1-1/x^2)^1/2]
= -arcsin(1/x) + C
求解一道不定积分的题目：dx / [x*(x^2-1)^1/2]
∫dx / [x*(x^2-1)^1/2]
=∫dx / [x^2*(1-1/x^2)^1/2]
= -∫d(1/x) / [(1-1/x^2)^1/2]
= -arcsin(1/x) + C