高数问题，第19题，谢谢啦，希望在纸上写了拍上来
展开全部
∫(x²+1)/(x⁴+1)dx
=∫(x²+1)/(x⁴+2x²+1-2x²)dx
=∫(x²+1)/[(x²+1)²-2x²]dx
=∫(x²+1)/[(x²+1-√2x)(x²+1+√2x)]dx
=1/2∫1/(x²+1-√2x)+1/(x²+1+√2x)]dx
=∫1/[(√2x-1)²+1]+1/[(√2x+1)²+1]dx
=1/√2arctan(√2x-1)+1/√2arctan(√2x+1)+C
=∫(x²+1)/(x⁴+2x²+1-2x²)dx
=∫(x²+1)/[(x²+1)²-2x²]dx
=∫(x²+1)/[(x²+1-√2x)(x²+1+√2x)]dx
=1/2∫1/(x²+1-√2x)+1/(x²+1+√2x)]dx
=∫1/[(√2x-1)²+1]+1/[(√2x+1)²+1]dx
=1/√2arctan(√2x-1)+1/√2arctan(√2x+1)+C
更多追问追答
追问
没看懂啊
能在纸上写一下么
本回答由提问者推荐
已赞过
已踩过<
评论
收起
你对这个回答的评价是？
推荐律师服务：
若未解决您的问题，请您详细描述您的问题，通过百度律临进行免费专业咨询
