解：令x^(1/6)=t,那么x=t^6，dx=6t^5dt，代入得：∫(x^(1/3)/x(√x+x^(1/3))dx = ∫(t^(2)/t^6(t^3+t^2))6t^5dt=∫(1/(1+t^2))dt=arctant+C =arctanx^(1/6)+C
