∫x/√(x-1) *dx
=∫(x-1 +1)/√(x-1) *dx
=∫[√(x-1) + 1/√(x-1)]*dx
=∫√(x-1) *dx + ∫dx/√(x-1)
=2/3*(x-1)^(3/2) + 2*√(x-1) |x = 1→2
=2/3*[(2-1)^(3/2) - (1-1)^(3/2)] + 2*[√(2-1) -√(1-1)]
=2/3 + 2
=8/3
∫x/√(x-1) *dx
=∫(x-1 +1)/√(x-1) *dx
=∫[√(x-1) + 1/√(x-1)]*dx
=∫√(x-1) *dx + ∫dx/√(x-1)
=2/3*(x-1)^(3/2) + 2*√(x-1) |x = 1→2
=2/3*[(2-1)^(3/2) - (1-1)^(3/2)] + 2*[√(2-1) -√(1-1)]
=2/3 + 2
=8/3