求不定积分∫1/[1+e^x]^(1/2)dx求高手解题要步骤谢谢

Question

求不定积分∫1/[1+e^x]^(1/2)dx求高手解题要步骤谢谢

Answer 1

第一类换元法
令t=[1+e^x]^(1/2),则x=ln(t²-1),dx=2t/(t²-1)dt
原式=∫(1/t)*[2t/(t²-1)]dt
=∫2/(t²-1)dt
=∫[1/(t-1) -1/(t+1)]dt
=ln(t-1) -ln(t+1)+C
=...