>>960
x-1=tと置くとdx=dt
∫x√(x-1)dx=∫(t+1)√tdt=∫(t^(3/2)+t^(1/2))dt=(2/5)t^(5/2)+(2/3)t^(3/2)+C
=(2/5)(x-1)^(5/2)+(2/3)(x-1)^(3/2)+C