∫e³√xdx

∫e³√xdx

令t=³√x,则x=t³
dx=3t²dt
原式=3∫e^t·t²dt
=3∫t²d(e^t)
=3t²e^t-6∫t·e^tdt
=3t²e^t-6∫td(e^t)
=3t²e^t-6t·e^t+6∫e^tdt
=(3t²-6t+6)·e^t+C
=……