求定积分(5,1)根号(x-1)/xdx谢谢

Question

求定积分(5,1)根号(x-1)/x dx
谢谢

Answer 1

令√(x-1)=t
x=t^2+1
dx=2tdt
x=1,t=0,x=5,t=2
∫[0,5] (x-1)/x dx
=∫[0,2] t/(t^2+1) 2tdt
=2∫[0,2] [1-1/(t^2+1) ]dt
=2(t-arctant)[0,2]
=4-2arctan2