微积分题目:∫上限5下限1 x/√2x-1 dx

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微积分题目:∫上限5下限1x/√2x-1dx微积分题目:∫上限5下限1x/√2x-1dx微积分题目:∫上限5下限1x/√2x-1dx√2x-1=tx=5时,t=3;x=1时,t=1t^2=2x-1x=

微积分题目:∫上限5下限1 x/√2x-1 dx
微积分题目:∫上限5下限1 x/√2x-1 dx

微积分题目:∫上限5下限1 x/√2x-1 dx
√2x-1=t x=5时,t=3 ; x=1时,t=1
t^2=2x-1
x=(t^2+1)/2
dx=dt
代入原式:
=f (1, 3) (t^2+1)/(2t)dt
=f(1,3) (1/2t+1/(2t))dt
=1/4t^2+1/2lnt (1,3)
=(9/4+1/2ln3)-1/4
=2+1/2ln3