令根号x = t 所以x=t^2 dx=2tdt
∫e^(3根号x)dx
=2∫te^(3t)dt
=(2/3)∫tde^(3t)
用分部积分
=(2/3)[t*e^(3t) - ∫e^(3t)dt] + C
=(2/3)e^(3t)[t - 1/3] + C
然后把t用根号x换回来就可以了