计算定积分∫[4,1]dx/x+√x

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计算定积分∫[4,1]dx/x+√x计算定积分∫[4,1]dx/x+√x计算定积分∫[4,1]dx/x+√x令t=√x,t²=x,2tdt=dxx=1,t=1;x=4,t=2∫(1→4)dx

计算定积分∫[4,1]dx/x+√x
计算定积分∫[4,1]dx/x+√x

计算定积分∫[4,1]dx/x+√x
令t = √x,t² = x,2t dt = dx
x = 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)

这个还真不清楚