求∫dx/1+(根号x)

来源:学生作业帮助网 编辑:六六作业网 时间:2024/05/24 20:11:25
求∫dx/1+(根号x)求∫dx/1+(根号x)求∫dx/1+(根号x)解令√x=t则t²=x,dx=2tdt∴∫dx/(1+√x)=∫2tdt/(t+1)=2∫[(t+1)-1]/(t+1

求∫dx/1+(根号x)
求∫dx/1+(根号x)

求∫dx/1+(根号x)

令√x=t
则t²=x,dx=2tdt
∴∫dx/(1+√x)
=∫2tdt/(t+1)
=2∫[(t+1)-1]/(t+1)dt
=2∫1-1/(t+1)dt
=2t-2ln|t+1|+C
=2√x-2ln(√x+1)+C