求不定积分∫根号(e^x+1) dx - 知识问答

求不定积分∫根号(e^x+1) dx

2个回答

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

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