∫[1/(e^x)+1]dx要详细步骤

题目

∫[1/(e^x)+1]dx要详细步骤
∫[1/(e^x)+1]dx
X-ln(e^x+1)+C需要详细步骤

答案

积分:dx/(e^x+1)
=积分:(1+e^x-e^x)dx/(e^x+1) (分解)
=积分:1dx-积分:e^xdx/(e^x+1) (把后面的积分内e^x弄到dx中)
=x-积分:d(e^x+1)/(e^x+1)
=x-ln(e^x+1)+C
(c是积分常数)