高数,不定积分,
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/24 08:16:58
![高数,不定积分,](/uploads/image/z/1822285-37-5.jpg?t=%E9%AB%98%E6%95%B0%2C%E4%B8%8D%E5%AE%9A%E7%A7%AF%E5%88%86%2C)
高数,不定积分,
高数,不定积分,
高数,不定积分,
要倒过来推:
∫dx/(x^2+1)=x/(x^2+1)-∫xd(1/(x^2+1))
=x/(x^2+1)+2∫x^2dx/(x^2+1)
=x/(x^2+1)+2∫(x^2+1-1)dx/(x^2+1)^2
=x/(x^2+1)+2∫dx/(x^2+1)-2∫dx/(x^2+1)^2
所以∫dx/(x^2+1)^2=x/(2(x^2+1))+1/2*∫dx/(x^2+1)