Find: ∫_1^4 1/(√(2 x +1)-√(2 x -1)) d x

$$\begin{aligned} & \text { Let } \mathrm{I}=\int_{1}^{4} \frac{1}{\sqrt{2 \mathrm{x}+1}-\sqrt{2 \mathrm{x}-1}} \mathrm{dx} \\ & =\int_{1}^{4} \frac{\sqrt{2 \mathrm{x}+1}+\sqrt{(2 \mathrm{x}-1)}}{2} \mathrm{dx} \\ & =\frac{(2 \mathrm{x}+1)^{3 / 2}}{3 \times 2}+\left.\frac{(2 \mathrm{x}-1)^{3 / 2}}{3 \times 2}\right|_{1} ^{4} \\ & =\left(\frac{27}{6}+\frac{7^{3 / 2}}{6}\right)-\left(\frac{3^{3 / 2}}{6}+\frac{1}{6}\right) \\ & =\frac{26+7^{3 / 2}-3^{3 / 2}}{6} \text { or } \frac{26+7 \sqrt{7}-3 \sqrt{3}}{6} \end{aligned} $$