求不定积分∫[(arctan√x)/(√x(1+x))]dx

来源:学生作业帮助网 编辑:六六作业网 时间:2024/05/20 01:18:52
求不定积分∫[(arctan√x)/(√x(1+x))]dx求不定积分∫[(arctan√x)/(√x(1+x))]dx求不定积分∫[(arctan√x)/(√x(1+x))]dx令y=√x,代入上式

求不定积分∫[(arctan√x)/(√x(1+x))]dx
求不定积分∫[(arctan√x)/(√x(1+x))]dx

求不定积分∫[(arctan√x)/(√x(1+x))]dx
令y=√x,代入上式得:
2∫y[(arctany)/(y(1+y^2))]dy
=2∫[(arctany)/(1+y^2)]dy
=2∫(arctany)d(arctany)=(arctany)^2+c
=(arctan√x)^2+c