来源：学生作业帮 编辑：作业帮 分类：数学作业 时间：2024/05/10 08:54:57
根号下1+1/(X^2)的积分
∫根号(1+1/x^2)dx
=∫根号(x^2+1)/x dx 令t=根号(x^2+1) x=根号(t^2-1) dx=t/根号(t^2-1) dt
=∫t/根号(t^2-1)*t/根号(t^2-1) dt
=∫t^2/(t^2-1) dt
=∫(t^2-1+1)/(t^2-1) dt
=∫dt+∫dt/(t+1)(t-1)
=t+ln[根号|(t-1)/(t+1)|]+C
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