x^2/(1-x^2)dx等于多少脑子转不过来了T T,最好有说明谢谢

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x^2/(1-x^2)dx等于多少脑子转不过来了T T,最好有说明谢谢
x^2/(1-x^2)dx等于多少脑子转不过来了T T,最好有说明谢谢

x^2/(1-x^2)dx等于多少脑子转不过来了T T,最好有说明谢谢

∫x²/(1-x²) dx
=∫(x²-1+1)/(1-x²) dx
=∫[-1+1/(1-x²)]dx
=-∫[1+1/(x²-1)]dx
=-∫ dx-∫1/(x²-1)dx
=-∫ dx-½·∫[1/(x-1)-1/(x+1)]dx
=-x-½·(ln|x-1|-ln|x+1|)+C
=-x-½ln|(x-1)/(x+1)|+C

哪个是分母,哪个是分子,这点我搞不清楚