>>517
∫x√(x-1)dx
x=t+1
∫(t+1)√tdt
=∫t√tdt+∫√tdt
=∫t^(3/2)dt+∫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