$$\begin{array}{c}\int (\frac{(2x+1)}{(\sqrt{(4x)}+\sqrt{(2x)})})\\ \int (\frac{(2x+1)}{(\sqrt{(4x)}+\sqrt{(2x)})})\mathrm{.}\frac{(\sqrt{(4x)}-\sqrt{(2x)})}{(\sqrt{(4x)}-\sqrt{(2x)})}\\ \int (\frac{((2x+1)\mathrm{.}(\sqrt{(4x)}-\sqrt{(2x)}))}{({(\sqrt{(4x)})}^2-{(\sqrt{(2x)})}^2)})\\ \int (\frac{(2x\sqrt{(4x)}-2x\sqrt{(2x)}+\sqrt{(4x)}-\sqrt{(2x)})}{(4x-2x)})\\ \int \sqrt{(4x)}-\int (\sqrt{(2x)})+\int (\frac{\sqrt{(4x)}}{(2x)})-\int (\frac{\sqrt{(2x)}}{(2x)})\\ \int 2x^{(\frac{1}{2})}-\int (\sqrt{(2)}{x}^{(\frac{1}{2})})\int (\frac{\sqrt{(x)}}{x})-\int \sqrt{(2x)}{(2x)}^{-1}\\ 2\frac{(x^{(\frac{3}{2})})}{(\frac{3}{2})}+C_1-\sqrt{(2)}\frac{(x^{(\frac{3}{2})})}{(\frac{3}{2})}+C_2+\int x^{(\frac{-1}{2})}-\int {(2x)}^{(\frac{-1}{2})}\\ \frac{4}{3}{x}^{(\frac{3}{2})}+C_1-\frac{(2\sqrt{(2)})}{3}{x}^{(\frac{3}{2})}+C_2+\frac{(x^{(\frac{1}{2})})}{(\frac{1}{2})}+C_3+\frac{({(2x)}^{(\frac{1}{2})})}{(\frac{1}{2})}+C_4\end{array}$$