求 ∫ [(x^3)/(x^2-1)^(1/2)]dx,
问题描述：
求 ∫ [(x^3)/(x^2-1)^(1/2)]dx,
答
设u=(x^2-1)^(1/2),则
x^2=u^2+1
dx^2=d(u^2+1)=2udu
∫[(x^3)/(x^2-1)^(1/2)]dx=∫[(x^2)/[2(x^2-1)^(1/2)]]dx^2
=∫[(u^2+1)/(2u)]*2udu
=∫(u^2+1)du
=u^3/3+u
=u(u^2+3)/3
=(x^2-1)^(1/2)(x^2+2)/3