求不定积分dx/（1+3√x）√x 3√x代表的是根号3x

是三次根号x吧?
令t=√x
x=t^3
原式=∫3t^2/(1+t)dt=3∫[t-1+1/(1+t)]dt
=3[t^2/2-t+ln|t+1|]+C
=3(√x^2/2-√x+ln|√x+1|)+C