微积分题目：∫上限5下限1x/√2x-1dx

Question

微积分题目：∫上限5下限1 x/√2x-1 dx

Answer 1

√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