What is your working? It seems sensible to pick u=2x+1 and through algebra x = (u-1)/2. From the sub we know that du = 2 dx or dx = du/2

x/(2x+1)^(1/2) dx = (u-1)/(2u^(1/2)) * du/2 = 1/4 * [(u-1)/u^(1/2)] du

We can simplify that up a bit to give

Those are relatively simple integrals