定积分计算∫2下面1 （2x）/(x+1) dx
问题描述：
定积分计算∫2下面1 （2x）/(x+1) dx
答
∫2下面1(2x)/(x+1)dx
=∫2下面1[2-2/(x+1)]dx
=[2x-2ln(x+1)]|2下面1
=2+2(ln2-ln3)
=2+2ln(2/3)
答
(2x+2-2)/(x+1)=2-2/(x+1) 然后就好做了
答
∫2下面1 （2x）/(x+1) dx
=[1,2]∫[2(x+1)-2]/(x+1)dx
=[1,2]∫2-2/(x+1)dx
=[1,2]2x-2ln(x+1)
=(4-2ln3)-(2-2ln2)
=2+2ln2-2ln3
答
2x/(x+1)
=(2x+2-2)/(x+1)
=2-2/(x+1)
所以原式=2x-2ln(x+1) (1到2)
=(4-2ln3)-(2-2ln2)
=2-2ln(2/3)