Pyramid 501
Preview $$U_{501}(x, y) = \frac{x \left(1 - \sqrt{1 - 4 y}\right)^{2}}{4 y^{2}} + \frac{1 - \sqrt{1 - 4 y}}{2 y}$$
Pyramid 502
Preview $$U_{502}(x, y) = \frac{\sqrt{1 - 4 y} - 1}{y \left(\frac{x \left(1 - \sqrt{1 - 4 y}\right)^{2}}{2 y^{2}} - 2\right)}$$
Pyramid 503
Preview $$U_{503}(x, y) = \frac{y^{2} \left(2 - 2 \sqrt{- \frac{x \left(1 - \sqrt{1 - 4 y}\right)^{3}}{2 y^{3}} + 1}\right)}{x \left(1 - \sqrt{1 - 4 y}\right)^{2}}$$
Pyramid 504
Preview $$U_{504}(x, y) = \frac{\left(y + 1\right)^{2} \left(\sqrt{4 x + 1} + 1\right)}{2}$$
Pyramid 505
Preview $$U_{505}(x, y) = \frac{\sqrt{4 x + 1} + 1}{2 \left(1 - y\right)^{2}}$$
Pyramid 506
Preview $$U_{506}(x, y) = \frac{\left(1 - \sqrt{1 - 4 y}\right) \left(\sqrt{4 x + 1} + 1\right)}{4 y}$$
Pyramid 507
Preview $$U_{507}(x, y) = \frac{\left(\sqrt{4 x + 1} + 1\right) \left(- 2 y - \sqrt{1 - 4 y} + 1\right)}{4 y^{2}}$$
Pyramid 508
Preview $$U_{508}(x, y) = \frac{x \left(- 2 y - \sqrt{1 - 4 y} + 1\right)^{2}}{4 y^{4}} + \frac{- 2 y - \sqrt{1 - 4 y} + 1}{2 y^{2}}$$
Pyramid 509
Preview $$U_{509}(x, y) = \frac{2 y + \sqrt{1 - 4 y} - 1}{y^{2} \left(\frac{x \left(- 2 y - \sqrt{1 - 4 y} + 1\right)^{2}}{2 y^{4}} - 2\right)}$$
Pyramid 510
Preview $$U_{510}(x, y) = \frac{y^{4} \left(2 - 2 \sqrt{- \frac{x \left(- 2 y - \sqrt{1 - 4 y} + 1\right)^{3}}{2 y^{6}} + 1}\right)}{x \left(- 2 y - \sqrt{1 - 4 y} + 1\right)^{2}}$$
Pyramid 511
Preview $$U_{511}(x, y) = \frac{\left(y + 1\right)^{2} - \sqrt{- 4 x \left(y + 1\right)^{3} + \left(y + 1\right)^{4}}}{2 x}$$
Pyramid 512
Preview $$U_{512}(x, y) = - \frac{\left(y + 1\right)^{3}}{x - \left(y + 1\right)^{2}}$$
Pyramid 513
Preview $$U_{513}(x, y) = \frac{x + \left(y + 1\right)^{3}}{\left(y + 1\right)^{2}}$$
Pyramid 514
Preview $$U_{514}(x, y) = \frac{\sqrt{4 x + \left(y + 1\right)^{4}} + \left(y + 1\right)^{2}}{2 y + 2}$$
Pyramid 515
Preview $$U_{515}(x, y) = \frac{- \sqrt{4 x + \left(y + 1\right)^{4}} + \left(y + 1\right)^{2}}{2 y + 2}$$
Pyramid 516
Preview $$U_{516}(x, y) = \frac{2 \sqrt{3} \left(y + 1\right)^{2} \sin{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{x}}{2} \right)}}{3} \right)}}{3 \sqrt{x}}$$
Pyramid 517
Preview $$U_{517}(x, y) = \frac{\left(y + 1\right)^{4} - \sqrt{- 4 x \left(y + 1\right)^{6} + \left(y + 1\right)^{8}}}{2 x}$$
Pyramid 518
Preview $$U_{518}(x, y) = - \frac{\left(y + 1\right)^{6}}{x - \left(y + 1\right)^{4}}$$
Pyramid 519
Preview $$U_{519}(x, y) = \frac{x + \left(y + 1\right)^{6}}{\left(y + 1\right)^{4}}$$
Pyramid 520
Preview $$G_{520}(x, y) = \frac{\sqrt{4 x + \left(y + 1\right)^{8}} + \left(y + 1\right)^{4}}{2 \left(y + 1\right)^{2}}$$
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