∫√(1+x) *dx
=∫(1+x)^(1/2) * d(1+x)
=2/3*(1+x)^(3/2) |0 ~ 1
=2/3*[(1+1)^(3/2) - (1+0)^(3/2)]
=2/3*(2√2 - 1)
=4√2/3 - 2/3