Pyramid 541
Preview $$U_{541}(x, y) = \frac{y^{4} \left(4 x + \frac{\left(- 2 y - \sqrt{1 - 4 y} + 1\right)^{3}}{2 y^{6}}\right)}{\left(- 2 y - \sqrt{1 - 4 y} + 1\right)^{2}}$$
Pyramid 542
Preview $$U_{542}(x, y) = \frac{y^{2} \left(\sqrt{4 x + \frac{\left(- 2 y - \sqrt{1 - 4 y} + 1\right)^{4}}{16 y^{8}}} + \frac{\left(- 2 y - \sqrt{1 - 4 y} + 1\right)^{2}}{4 y^{4}}\right)}{- 2 y - \sqrt{1 - 4 y} + 1}$$
Pyramid 543
Preview $$U_{543}(x, y) = \frac{y^{2} \left(- \sqrt{4 x + \frac{\left(- 2 y - \sqrt{1 - 4 y} + 1\right)^{4}}{16 y^{8}}} + \frac{\left(- 2 y - \sqrt{1 - 4 y} + 1\right)^{2}}{4 y^{4}}\right)}{- 2 y - \sqrt{1 - 4 y} + 1}$$
Pyramid 544
Preview $$U_{544}(x, y) = \frac{4 \sin{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{x}}{2} \right)}}{3} \right)} \sin{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}}{3 \sqrt{x} \sqrt{y}}$$
Pyramid 545
Preview $$U_{545}(x, y) = \frac{- \sqrt{- \frac{32 \sqrt{3} x \sin^{3}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}}{9 y^{\frac{3}{2}}} + \frac{16 \sin^{4}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}}{9 y^{2}}} + \frac{4 \sin^{2}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}}{3 y}}{2 x}$$
Pyramid 546
Preview $$U_{546}(x, y) = - \frac{8 \sqrt{3} \sin^{3}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}}{9 y^{\frac{3}{2}} \left(x - \frac{4 \sin^{2}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}}{3 y}\right)}$$
Pyramid 547
Preview $$U_{547}(x, y) = \frac{y \left(3 x + \frac{8 \sqrt{3} \sin^{3}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}}{3 y^{\frac{3}{2}}}\right)}{4 \sin^{2}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}}$$
Pyramid 548
Preview $$U_{548}(x, y) = \frac{\sqrt{3} \sqrt{y} \left(\sqrt{4 x + \frac{16 \sin^{4}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}}{9 y^{2}}} + \frac{4 \sin^{2}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}}{3 y}\right)}{4 \sin{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}}$$
Pyramid 549
Preview $$U_{549}(x, y) = \frac{\sqrt{3} \sqrt{y} \left(- \sqrt{4 x + \frac{16 \sin^{4}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}}{9 y^{2}}} + \frac{4 \sin^{2}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}}{3 y}\right)}{4 \sin{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}}$$
Pyramid 550
Preview $$U_{550}(x, y) = \frac{y}{2} + \frac{\sqrt{4 x \left(y + 1\right)^{3} + \left(y + 1\right)^{2}}}{2} + \frac{1}{2}$$
Pyramid 551
Preview $$U_{551}(x, y) = x \left(y + 1\right)^{3} + y + 1$$
Pyramid 552
Preview $$U_{552}(x, y) = \frac{- y - 1}{x \left(y + 1\right)^{3} - 1}$$
Pyramid 553
Preview $$U_{553}(x, y) = \frac{1 - \sqrt{- 4 x \left(y + 1\right)^{4} + 1}}{2 x \left(y + 1\right)^{3}}$$
Pyramid 554
Preview $$U_{554}(x, y) = \left(1 - \frac{4 \sin^{2}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{- x}}{2} \right)}}{3} \right)}}{3}\right) \left(y + 1\right)$$
Pyramid 555
Preview $$U_{555}(x, y) = \left(1 - \frac{4 \sin^{2}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{- x}}{2} \right)}}{3} \right)}}{3}\right) \left(y + 1\right)^{2}$$
Pyramid 556
Preview $$U_{556}(x, y) = \frac{\left(y + 1\right)^{2}}{2} + \frac{\sqrt{4 x \left(y + 1\right)^{6} + \left(y + 1\right)^{4}}}{2}$$
Pyramid 557
Preview $$U_{557}(x, y) = x \left(y + 1\right)^{6} + \left(y + 1\right)^{2}$$
Pyramid 558
Preview $$U_{558}(x, y) = - \frac{\left(y + 1\right)^{2}}{x \left(y + 1\right)^{6} - 1}$$
Pyramid 559
Preview $$U_{559}(x, y) = \frac{1 - \sqrt{- 4 x \left(y + 1\right)^{8} + 1}}{2 x \left(y + 1\right)^{6}}$$
Pyramid 560
Preview $$U_{560}(x, y) = \frac{1 - \frac{4 \sin^{2}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{- x}}{2} \right)}}{3} \right)}}{3}}{1 - y}$$
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