x(2x+1)^(1/2)
=（2x+1-1)/2 * (2x+1)^(1/2)
=[(2x+1)^(3/2)-(2x+1)^(1/2)]/2
原式=∫ [(2x+1)^(3/2)-(2x+1)^(1/2)]/2dx
=1/4∫(2x+1)^(3/2)d(2x+1)-1/4∫(2x+1)^(1/2)d(2x+1)
=1/4*1/(5/2) *(2x+1)^(5/2)-1/4*1/(3/2) *(2x+1)^(3/2)+C
=(2x+1)^(5/2)/10-(2x+1)^(3/2)/6+C
x/(x+1)^2=[x+1-1]/(x+1)^2=(x+1)^(-1)-(x+1)^(-2)
原式=∫(x+1)^(-1)-(x+1)^(-2) dx
=ln|x+1|+1/(x+1)