求不定积分∫根号(e^x+1) dx 注意 根号内是 e^x+1
问题描述：
求不定积分∫根号(e^x+1) dx
注意 根号内是 e^x+1
答
设t=(e^x+1)^0.5,则x=ln(t^2-1),所以dx=2t/(t^2-1)dt,
原式=∫2t^2/(t^2-1)dt=∫(2+1/(t-1)-1/(t+1))dt
=∫2dt+∫1/(t-1)dt-∫1/(1+t)dt
=2t+ln[(t-1)/(t+1)]+C
答
t=(e^x+1)^0.5
dx=2t/(t^2-1)
∫(e^x+1)^0.5 dx
=∫2t^2/(t^2-1)dt
=∫2 +2/(t^2-1)dt
=2t+ln[(t-1)/(t+1)]+c