计算瑕积分∫(1,2)x/√(x-1)dx

计算瑕积分∫(1,2)x/√(x-1)dx
计算瑕积分∫(1,2)x/√(x-1)dx

计算瑕积分∫(1,2)x/√(x-1)dx
令√(x-1)=t
则原式=∫(0→1)(t^2+1)/t*2tdt
=∫(0→1)2(t^2+1)dt
=2/3t^3|(0→1)+2t|(0→1)
=2/3+2
=8/3