求 ∫ [(x^3)/(x^2-1)^(1/2)]dx,

来源：学生作业帮编辑：灵鹊做题网作业帮分类：数学作业时间：2024/04/19 19:02:49

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

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