求不定积分-f1/(1+e^x)dx

Answer 1

∫1/(1+e^x)dx=∫1/[e^x·(1+e^x)]d(e^x)
=∫[1/e^x - 1/(1+e^x)]d(e^x)
=lne^x - ln(1+e^X)+C
=x - ln(1+e^X)+C