设t=√x,t^2=x,dx=2tdt,
则∫√x/(1+x)dx
=∫2t^2/(1+t^2)dt
=2∫t^2/(1+t^2)dt
=2(∫1-1/(1+t^2)dt)
=2(t-arctant) +C
=2(√x-arctan√x) +C