∫X^2/1-x^2 dx.

问题描述:

∫X^2/1-x^2 dx.

这个题这样做

∫X^2/(1-x^2 )dx.=(1/2)∫ X/(1-x^2)dx^2=-(1/2) ∫ xd(ln|1-x^2|
=-(1/2)xln|1-x^2|+(1/2) ∫ ln|1-x^2|dx
=-(1/2)xln|1-x^2|+(1/2) ∫ [n|1-x|+ln|1+x|]dx
=-(1/2)xln|1-x^2|+(1/2) (|1-x|)(ln|1-x|-1)+(1/2)(|1+x|)(ln|1+x|-1)+C