令√(2x+1)=t x=(t^2-1)/2 dx=tdt
∫(x+3)/√(2x+1)dx
=(1/2)*∫(t^2+5)dt
=(1/6)*t^3+(5/2)*t+C
=(1/6)*(2x+1)^(3/2)+(5/2)*√(2x+1)+C