∫X^3/√(1-x^2)dx,

题目详情

∫X^3/√(1-x^2)dx,

▼优质解答

答案和解析

∫x^3/√(1-x^2)dx
=∫x^2*x/√(1-x^2)dx
=1/2∫x^2/√(1-x^2)dx^2；
令√(1-x^2)=t,
则x^2=1-t^2,dx^2=d(1-t^2)=-2tdt
,则原式可化为
∫(t^2-1)dt
=1/3t^3-t+C
=1/3（1-x^2)^(3/2)-√(1-x^2)+C

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