设t=x^(1/3),x=t^3,dx=3t^2dt,原式=∫e^t*3t^2dt=3(t^2e^t-2∫t*e^tdt)=3[t^2*e^t-2(te^t-∫e^tdt)]=3t^2*e^t-6te^t+6e^t+C=3x^(2/3)e^[x^(1/3)]-6x^(1/3)e^[x^(1/3)]+6e^[x^(1/3)]+C.
