来源:学生作业帮 编辑:百度作业网作业帮 分类:数学作业 时间:2024/07/13 15:35:35
不定积分第10题
![](http://img.wesiedu.com/upload/6/d8/6d829e283dd6fdc115c83ed31fa2bef8.jpg)
∫[1/(x^4-1)]dx
=∫{1/[(x^2-1)(x^2+1)]}dx=(1/2)∫[1/(x^2-1)-1/(x^2+1)]dx
=-(1/2)arctanx+(1/2)∫[1/(x-1)(x+1)]dx
=-(1/2)arctanx+(1/4)∫[1/(x-1)-1/(x+1)]dx
=-(1/2)arctanx++(1/4)(ln|x-1|-ln|x+1|)+C