TITLE: Solve: $\int_{2}^{3}\ \left(\sqrt {2x -\sqrt{5\left(4x-5\right)}}+\sqrt {2x +\sqrt{5\left(4x-5\right)}}\right)dx $
QUESTION [5 upvotes]: How to solve following integration?
$$\int_{2}^{3}\ \left(\sqrt {2x -\sqrt{5\left(4x-5\right)}}+\sqrt {2x +\sqrt{5\left(4x-5\right)}}\right)dx $$

REPLY [4 votes]: We pose $u=\sqrt{5(4x-5)}$ and we verify easly that the integral becomes
$$\frac{\sqrt{10}}{50}\int_{\sqrt{15}}^{\sqrt{35}}u^2du.$$
I think you can easily complete the calculation.