[x(1-x^2)^(3/2)]/3dx在[1,0]的积分怎么求的
问题描述：
[x(1-x^2)^(3/2)]/3dx在[1,0]的积分怎么求的
答
最讨厌积分了
答
具体见图片
答
(1/3)∫[0---->1] x(1-x²)^(3/2)dx
令1-x²=u²,两边微分得：xdx=-udu,u：1--->0,(1-x²)^(3/2)=u³,
=-(1/3)∫[1---->0] u³udu
=(1/3)∫[0---->1] u⁴du
=(1/3)(1/5)u⁵ |[0---->1]
=1/15