求不定积分∫(1/1+e)的x次方dx
问题描述：
求不定积分∫(1/1+e)的x次方dx
答
∫ [1/(1+e)]^x dx
= [1/(1+e)]^x / ln[1/(1+e)] + C，= 1/(1+e)^x / [-ln(1+e)] + C
= -1/[(1+e)^x * ln(1+e)] + C
若是
∫ 1/(1+e^x) dx
= ∫ [(1+e^x)-e^x]/(1+e^x) dx
= ∫ dx - ∫ e^x/(1+e^x) dx
= x - ∫ d(1+e^x)/(1+e^x)
= x - ln|1+e^x| + C
答
∫1/(1+e^x)dx
=∫1/[e^x(1+e^x)]d(e^x)
=∫[1/e^x-1/(1+e^x)]d(e^x)
=x-ln(1+e^x)+C