计算定积分∫[4,1]dx/x+√x
问题描述：
计算定积分∫[4,1]dx/x+√x
答
令t = √x,t² = x,2t dt = dxx = 1,t = 1；x = 4,t = 2∫(1→4) dx/(x + √x)= ∫(1→2) 2t/(t² + t) · dt= ∫(1→2) 2/(1 + t) dt= 2[ln(1 + t)]：(1→2)= 2ln(1 + 2) - 2ln(1 + 1)= 2ln(3/2)= ln(9/4)...2ln(1 + 2) - 2ln(1 + 1)这一步是怎么变成= 2ln(3/2)？对数公式lnA - lnB = ln(A/B)